(International Tables) Symmetry relations between space groups

International Tables for Crystallography
Volume A1: Symmetry relations between space groups

Second online edition (2011) ISBN: 978-0-470-66079-9 doi: 10.1107/97809553602060000110 | 1 | 2 |

Edited by H. Wondratschek and U. Müller

Contents

Foreword  (p. ix) | html | pdf |
Th. Hahn
Scope of this volume  (p. x) | html | pdf |
Mois I. Aroyo, Ulrich Müller and Hans Wondratschek
Computer production of Parts 2 and 3  (p. xi) | html | pdf |
Preslav Konstantinov, Asen Kirov, Eli B. Kroumova, Mois I. Aroyo and Ulrich Müller
List of symbols and abbreviations used in this volume  (p. xii) | html | pdf |
Mois I. Aroyo, Ulrich Müller and Hans Wondratschek

Space groups and their subgroups
- 1.1. Historical introduction (pp. 2-6) | html | pdf | chapter contents |
  Mois I. Aroyo, Ulrich Müller and Hans Wondratschek
  - 1.1.1. The fundamental laws of crystallography (p. 2) | html | pdf |
  - 1.1.2. Symmetry and crystal-structure determination (pp. 2-3) | html | pdf |
  - 1.1.3. Development of the theory of group–subgroup relations (pp. 3-4) | html | pdf |
  - 1.1.4. Applications of group–subgroup relations (pp. 4-5) | html | pdf |
  - References | html | pdf |
- 1.2. General introduction to the subgroups of space groups (pp. 7-24) | html | pdf | chapter contents |
  Hans Wondratschek
  - 1.2.1. General remarks (p. 7) | html | pdf |
  - 1.2.2. Mappings and matrices (pp. 7-10) | html | pdf |
    - 1.2.2.1. Crystallographic symmetry operations (pp. 7-8) | html | pdf |
    - 1.2.2.2. Coordinate systems and coordinates (p. 8) | html | pdf |
    - 1.2.2.3. The description of mappings (pp. 8-9) | html | pdf |
    - 1.2.2.4. Matrix–column pairs and (n + 1) × (n + 1) matrices (p. 9) | html | pdf |
    - 1.2.2.5. Isometries (p. 9) | html | pdf |
    - 1.2.2.6. Vectors and vector coefficients (p. 10) | html | pdf |
    - 1.2.2.7. Origin shift and change of the basis (p. 10) | html | pdf |
  - 1.2.3. Groups (pp. 10-12) | html | pdf |
    - 1.2.3.1. Some properties of symmetry groups (p. 11) | html | pdf |
    - 1.2.3.2. Group isomorphism and homomorphism (pp. 11-12) | html | pdf |
  - 1.2.4. Subgroups (pp. 12-14) | html | pdf |
    - 1.2.4.1. Definition (p. 12) | html | pdf |
    - 1.2.4.2. Coset decomposition and normal subgroups (pp. 12-13) | html | pdf |
    - 1.2.4.3. Conjugate elements and conjugate subgroups (p. 13) | html | pdf |
    - 1.2.4.4. Factor groups and homomorphism (p. 13) | html | pdf |
    - 1.2.4.5. Normalizers (pp. 13-14) | html | pdf |
  - 1.2.5. Space groups (pp. 14-18) | html | pdf |
    - 1.2.5.1. Space groups and their description (pp. 14-15) | html | pdf |
    - 1.2.5.2. Classifications of space groups (p. 15) | html | pdf |
    - 1.2.5.3. Space groups and space-group types (pp. 15-16) | html | pdf |
    - 1.2.5.4. Point groups and crystal classes (pp. 16-17) | html | pdf |
    - 1.2.5.5. Crystal systems and crystal families (pp. 17-18) | html | pdf |
  - 1.2.6. Types of subgroups of space groups (pp. 18-20) | html | pdf |
    - 1.2.6.1. Introductory remarks (p. 18) | html | pdf |
    - 1.2.6.2. Definitions and examples (pp. 18-19) | html | pdf |
    - 1.2.6.3. The role of normalizers for group–subgroup pairs of space groups (pp. 19-20) | html | pdf |
  - 1.2.7. Application to domain structures (pp. 20-23) | html | pdf |
    - 1.2.7.1. Introductory remarks (p. 20) | html | pdf |
    - 1.2.7.2. Domain states, symmetry states and directional states (pp. 20-22) | html | pdf |
    - 1.2.7.3. Examples (pp. 22-23) | html | pdf |
  - 1.2.8. Lemmata on subgroups of space groups (pp. 23-24) | html | pdf |
    - 1.2.8.1. General lemmata (p. 23) | html | pdf |
    - 1.2.8.2. Lemmata on maximal subgroups (pp. 23-24) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.2.7.1. Group–subgroup relations between the high (HT) and low temperature (LT) forms of gadolinium molybdate (Bärnighausen tree as explained in Section 1.6.3 ) (p. 23) | html | pdf |
  - Tables
    - Table 1.2.3.1. Multiplication table of a group (p. 11) | html | pdf |
- 1.3. Computer checking of the subgroup data (pp. 25-26) | html | pdf | chapter contents |
  Franz Gähler
  - 1.3.1. Introduction (p. 25) | html | pdf |
  - 1.3.2. Basic capabilities of the Cryst package (p. 25) | html | pdf |
  - 1.3.3. Computing maximal subgroups (pp. 25-26) | html | pdf |
  - 1.3.4. Description of the checks (p. 26) | html | pdf |
  - References | html | pdf |
- 1.4. The mathematical background of the subgroup tables (pp. 27-40) | html | pdf | chapter contents |
  Gabriele Nebe
  - 1.4.1. Introduction (p. 27) | html | pdf |
  - 1.4.2. The affine space (pp. 27-29) | html | pdf |
    - 1.4.2.1. Motivation (p. 27) | html | pdf |
    - 1.4.2.2. Vector spaces (pp. 27-28) | html | pdf |
    - 1.4.2.3. The affine space (p. 28) | html | pdf |
    - 1.4.2.4. The affine group (pp. 28-29) | html | pdf |
  - 1.4.3. Groups (pp. 29-33) | html | pdf |
    - 1.4.3.1. Groups (pp. 29-30) | html | pdf |
    - 1.4.3.2. Actions of groups on sets (pp. 30-31) | html | pdf |
    - 1.4.3.3. The Sylow theorems (pp. 31-32) | html | pdf |
    - 1.4.3.4. Isomorphisms (p. 32) | html | pdf |
    - 1.4.3.5. Isomorphism theorems (pp. 32-33) | html | pdf |
    - 1.4.3.6. An example (p. 33) | html | pdf |
  - 1.4.4. Space groups (pp. 33-35) | html | pdf |
    - 1.4.4.1. Definition of space groups (pp. 33-34) | html | pdf |
    - 1.4.4.2. Maximal subgroups of space groups (pp. 34-35) | html | pdf |
  - 1.4.5. Maximal subgroups (pp. 35-37) | html | pdf |
    - 1.4.5.1. Maximal subgroups and primitive $[{\cal G}]$ -sets (pp. 35-36) | html | pdf |
    - 1.4.5.2. Soluble groups (p. 36) | html | pdf |
    - 1.4.5.3. Maximal subgroups of soluble groups (pp. 36-37) | html | pdf |
  - 1.4.6. Quantitative results (pp. 37-38) | html | pdf |
    - 1.4.6.1. General results (p. 37) | html | pdf |
    - 1.4.6.2. Three-dimensional space groups (pp. 37-38) | html | pdf |
  - 1.4.7. Qualitative results (pp. 38-39) | html | pdf |
    - 1.4.7.1. General theory (p. 38) | html | pdf |
    - 1.4.7.2. Three-dimensional space groups (pp. 38-39) | html | pdf |
  - 1.4.8. Minimal supergroups (pp. 39-40) | html | pdf |
  - References | html | pdf |
- 1.5. Remarks on Wyckoff positions (pp. 41-43) | html | pdf | chapter contents |
  Ulrich Müller
  - 1.5.1. Crystallographic orbits and Wyckoff positions (p. 41) | html | pdf |
  - 1.5.2. Derivative structures and phase transitions (pp. 41-42) | html | pdf |
  - 1.5.3. Relations between the positions in group–subgroup relations (pp. 42-43) | html | pdf |
  - References | html | pdf |
- 1.6. Relating crystal structures by group–subgroup relations (pp. 44-56) | html | pdf | chapter contents |
  Ulrich Müller
  - 1.6.1. Introduction (p. 44) | html | pdf |
  - 1.6.2. The symmetry principle in crystal chemistry (p. 44) | html | pdf |
  - 1.6.3. Bärnighausen trees (pp. 44-46) | html | pdf |
  - 1.6.4. The different kinds of symmetry relations among related crystal structures (pp. 46-52) | html | pdf |
    - 1.6.4.1. Translationengleiche maximal subgroups (pp. 46-47) | html | pdf |
    - 1.6.4.2. Klassengleiche maximal subgroups (pp. 47-48) | html | pdf |
    - 1.6.4.3. Isomorphic maximal subgroups (p. 48) | html | pdf |
    - 1.6.4.4. The space groups of two structures having a common supergroup (p. 49) | html | pdf |
    - 1.6.4.5. Can a structure be related to two aristotypes? (pp. 49-50) | html | pdf |
    - 1.6.4.6. Treating voids like atoms (pp. 50-51) | html | pdf |
    - 1.6.4.7. Large families of structures. Prediction of crystal-structure types (pp. 51-52) | html | pdf |
  - 1.6.5. Handling cell transformations (pp. 52-54) | html | pdf |
  - 1.6.6. Comments concerning phase transitions and twin domains (p. 54) | html | pdf |
  - 1.6.7. Exercising care in the use of group–subgroup relations (pp. 54-55) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.6.3.1. Scheme of the formulation of the smallest step of symmetry reduction connecting two related crystal structures (p. 45) | html | pdf |
    - Fig. 1.6.4.10. Bärnighausen tree of hettotypes of the ReO₃ type (p. 52) | html | pdf |
    - Fig. 1.6.4.1. Bärnighausen tree for the family of structures of pyrite (p. 47) | html | pdf |
    - Fig. 1.6.4.2. The structures of AlB₂, ZrBeSi and CaIn₂ (p. 48) | html | pdf |
    - Fig. 1.6.4.3. Both hettotypes of the AlB₂ type have the same space-group type and a doubled c axis, but the space groups are different due to different origin positions relative to the origin of the aristotype (p. 48) | html | pdf |
    - Fig. 1.6.4.4. The group–subgroup relation rutile–trirutile (p. 49) | html | pdf |
    - Fig. 1.6.4.5. The unit cells of β-K₂CO₃ and β-Na₂CO₃ (p. 49) | html | pdf |
    - Fig. 1.6.4.6. Group–subgroup relations among some modifications of the alkali metal carbonates (p. 50) | html | pdf |
    - Fig. 1.6.4.7. The structure of the high-pressure modification Si-XI is related to the structures of both Si-II and Si-V (p. 50) | html | pdf |
    - Fig. 1.6.4.8. The connected coordination octahedra in ReO₃ and FeF₃ (VF₃ type) (p. 50) | html | pdf |
    - Fig. 1.6.4.9. Derivation of the FeF₃ structure either from the ReO₃ type or from the hexagonal closest packing of spheres (p. 51) | html | pdf |
    - Fig. 1.6.5.1. Relative orientations of a cubic to a rhombohedral cell (hexagonal setting) (left) and of a rhombohedral cell (hexagonal setting) to a monoclinic cell (the monoclinic cell has an acute angle β) (p. 53) | html | pdf |
  - Tables
    - Table 1.6.4.1. Crystal data for FeF₃ at different pressures (p. 51) | html | pdf |
- 1.7. The Bilbao Crystallographic Server (pp. 57-69) | html | pdf | chapter contents |
  Mois I. Aroyo, J. Manuel Perez-Mato, Cesar Capillas and Hans Wondratschek
  - 1.7.1. Introduction (p. 57) | html | pdf |
  - 1.7.2. Databases and retrieval tools (pp. 57-58) | html | pdf |
    - 1.7.2.1. Space-group data (pp. 57-58) | html | pdf |
    - 1.7.2.2. Database on maximal subgroups (p. 58) | html | pdf |
      - 1.7.2.2.1. Maximal subgroups of indices 2, 3 and 4 of the space groups (p. 58) | html | pdf |
      - 1.7.2.2.2. Maximal isomorphic subgroups (p. 58) | html | pdf |
  - 1.7.3. Group–subgroup and group–supergroup relations between space groups (pp. 58-66) | html | pdf |
    - 1.7.3.1. Subgroups of space groups (pp. 58-64) | html | pdf |
      - 1.7.3.1.1. The program SUBGROUPGRAPH (pp. 58-61) | html | pdf |
      - 1.7.3.1.2. The program HERMANN (p. 61) | html | pdf |
      - 1.7.3.1.3. The program COSETS (p. 62) | html | pdf |
      - 1.7.3.1.4. The program CELLSUB (pp. 62-63) | html | pdf |
      - 1.7.3.1.5. The program COMMONSUBS (pp. 63-64) | html | pdf |
    - 1.7.3.2. Supergroups of space groups (pp. 64-66) | html | pdf |
      - 1.7.3.2.1. The programs MINSUP and SUPERGROUPS (pp. 64-66) | html | pdf |
      - 1.7.3.2.2. The program CELLSUPER (p. 66) | html | pdf |
      - 1.7.3.2.3. The program COMMONSUPER (p. 66) | html | pdf |
  - 1.7.4. Relations of Wyckoff positions for a group–subgroup pair of space groups (pp. 66-68) | html | pdf |
    - 1.7.4.1. The program WYCKSPLIT (pp. 67-68) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 1.7.3.1. General contracted graph for (No. 92) > (No. 4) as given by the program SUBGROUPGRAPH (p. 60) | html | pdf |
    - Fig. 1.7.3.2. Contracted graph for the pair of space groups (No. 92) > (No. 4), index 4, as given by the program SUBGROUPGRAPH (p. 60) | html | pdf |
    - Fig. 1.7.3.3. Complete graph for $[{P}{4_1 2_1 2}]$ (No. 92) > $[{P}{2_1}]$ (No. 4), index 4, as given by the program SUBGROUPGRAPH (p. 60) | html | pdf |
    - Fig. 1.7.3.4. Group–subgroup graph for (No. 89) > $[{P}{2_1}]$ (No. 4), index 8 (p. 61) | html | pdf |
    - Fig. 1.7.3.5. Space-group diagrams for (a) , No. 16, with specialized cell metrics (see the text) and (b) , No. 89 (p. 65) | html | pdf |
    - Fig. 1.7.4.1. Sequence of calculations of WYCKSPLIT for the splitting of the Wyckoff positions $[{2a}\ {m.mm}\ (0,0,0)]$ and $[{4d}\ {\bar 4..}\ (\textstyle{1\over 2},0,\textstyle{3\over 4})]$ of $[{P}{4_2/mnm}]$ , No. 136, with respect to its subgroup , No. 65, of index 2 (p. 67) | html | pdf |
  - Tables
    - Table 1.7.3.1. Group–subgroup relations for P4₁2₁2 (No. 92) > P2₁ (No. 4), index 4 (p. 59) | html | pdf |
    - Table 1.7.3.2. P422, No. 89, supergroups of P222, No. 16 (a = b = c), index 2, as determined by MINSUP (p. 65) | html | pdf |
    - Table 1.7.4.1. Wyckoff positions of (No. 65) with multiplicities 2 and 8 (p. 67) | html | pdf |

Maximal subgroups of the plane groups and space groups
- 2.1. Guide to the subgroup tables and graphs (pp. 72-96) | html | pdf | chapter contents |
  Hans Wondratschek and Mois I. Aroyo
  - 2.1.1. Contents and arrangement of the subgroup tables (p. 72) | html | pdf |
  - 2.1.2. Structure of the subgroup tables (pp. 72-76) | html | pdf |
    - 2.1.2.1. Headline (p. 72) | html | pdf |
    - 2.1.2.2. Data from IT A (pp. 72-73) | html | pdf |
      - 2.1.2.2.1. Generators selected (p. 72) | html | pdf |
      - 2.1.2.2.2. General position (pp. 72-73) | html | pdf |
    - 2.1.2.3. Specification of the setting (p. 73) | html | pdf |
    - 2.1.2.4. Sequence of the subgroup and supergroup data (p. 73) | html | pdf |
    - 2.1.2.5. Special rules for the setting of the subgroups (pp. 74-76) | html | pdf |
      - 2.1.2.5.1. Monoclinic subgroups (p. 74) | html | pdf |
      - 2.1.2.5.2. Subgroups with two origin choices (pp. 74-75) | html | pdf |
      - 2.1.2.5.3. Space groups with a rhombohedral lattice (pp. 75-76) | html | pdf |
  - 2.1.3. I Maximal translationengleiche subgroups (t-subgroups) (pp. 76-79) | html | pdf |
    - 2.1.3.1. Introduction (p. 76) | html | pdf |
    - 2.1.3.2. A description in close analogy with IT A (pp. 76-77) | html | pdf |
    - 2.1.3.3. Basis transformation and origin shift (pp. 77-79) | html | pdf |
  - 2.1.4. II Maximal klassengleiche subgroups (k-subgroups) (pp. 79-82) | html | pdf |
    - 2.1.4.1. General description (p. 79) | html | pdf |
    - 2.1.4.2. Loss of centring translations (pp. 79-80) | html | pdf |
    - 2.1.4.3. Enlarged unit cell (pp. 80-82) | html | pdf |
      - 2.1.4.3.1. Enlarged unit cell, index 2 (pp. 80-81) | html | pdf |
      - 2.1.4.3.2. Enlarged unit cell, index 3 or 4 (pp. 81-82) | html | pdf |
  - 2.1.5. Series of maximal isomorphic subgroups (pp. 82-84) | html | pdf |
    Y. Billiet
    - 2.1.5.1. General description (p. 82) | html | pdf |
    - 2.1.5.2. Basis transformation (p. 82) | html | pdf |
    - 2.1.5.3. Origin shift (p. 82) | html | pdf |
    - 2.1.5.4. Generators (pp. 82-83) | html | pdf |
    - 2.1.5.5. Special series (pp. 83-84) | html | pdf |
      - 2.1.5.5.1. Monoclinic space groups (p. 83) | html | pdf |
      - 2.1.5.5.2. Trigonal space groups with rhombohedral lattice (p. 83) | html | pdf |
      - 2.1.5.5.3. Space groups with two origin choices (pp. 83-84) | html | pdf |
  - 2.1.6. The data for minimal supergroups (pp. 84-85) | html | pdf |
    - 2.1.6.1. Description of the listed data (p. 84) | html | pdf |
    - 2.1.6.2. I Minimal translationengleiche supergroups (pp. 84-85) | html | pdf |
    - 2.1.6.3. II Minimal non-isomorphic klassengleiche supergroups (p. 85) | html | pdf |
  - 2.1.7. Derivation of the minimal supergroups from the subgroup tables (pp. 86-90) | html | pdf |
    - 2.1.7.1. Determination of the non-isomorphic minimal k-supergroups by inverting the subgroup data (p. 86) | html | pdf |
    - 2.1.7.2. The isomorphic minimal supergroups (pp. 86-87) | html | pdf |
    - 2.1.7.3. Determination of one minimal t-supergroup by inverting the subgroup data (pp. 87-88) | html | pdf |
    - 2.1.7.4. Derivation of further minimal t-supergroups by using normalizers (pp. 88-90) | html | pdf |
    - 2.1.7.5. Derivation of the remaining minimal t-supergroups (p. 90) | html | pdf |
  - 2.1.8. The subgroup graphs (pp. 90-96) | html | pdf |
    - 2.1.8.1. General remarks (pp. 90-91) | html | pdf |
    - 2.1.8.2. Graphs for translationengleiche subgroups (pp. 91-92) | html | pdf |
    - 2.1.8.3. Graphs for klassengleiche subgroups (pp. 92-93) | html | pdf |
    - 2.1.8.4. Graphs for plane groups (p. 93) | html | pdf |
    - 2.1.8.5. Application of the graphs (pp. 93-96) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 2.1.7.1. In the left-hand diagram, there are i conjugate subgroups $[{\cal H}_k \,\lt\, {\cal G}]$ of $[\cal G]$ if [i] is the index of $[\cal H]$ in $[\cal G]$ ; in the right-hand diagram, $[{\cal H}\triangleleft{\cal G}]$ is a normal subgroup of $[\cal G]$ (p. 88) | html | pdf |
    - Fig. 2.1.8.1. Contracted graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to one of those subgroups with index 12 which belong to the space-group type (12) (p. 94) | html | pdf |
    - Fig. 2.1.8.2. Complete graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to one representative belonging to those six (12) subgroups with index 12 whose monoclinic axes are along the $[\langle 110 \rangle]$ directions of $[Fm\overline{3}m]$ (p. 94) | html | pdf |
    - Fig. 2.1.8.3. Complete graph of the group–subgroup chains from $[Fm\overline{3}m]$ (225) to , which is one representative of those three (12) subgroups with index 12 whose monoclinic axes are along the $[\langle 001 \rangle]$ directions of $[Fm\overline{3}m]$ (p. 94) | html | pdf |
    - Fig. 2.1.8.4. Complete graph of the group–subgroup chains from perovskite, $[Pm\overline{3}m]$ , here high-temperature SrTiO₃, to the four subgroups of type I4/mcm with their tetragonal axes in the c direction (p. 96) | html | pdf |
    - Fig. 2.1.8.5. Two different subgroups of P4/mmm, both of type I4/mcm, correspond to two kinds of distortions of the coordination octahedra of the perovskite structure (p. 96) | html | pdf |
- 2.2. Tables of maximal subgroups of the plane groups (pp. 97-114) | html | | chapter contents |
  - Maximal subgroups of plane group 1, p1 (p. 98) | html | pdf |
  - Maximal subgroups of plane group 2, p2 (p. 99) | html | pdf |
  - Maximal subgroups of plane group 3, pm (p. 100) | html | pdf |
  - Maximal subgroups of plane group 4, pg (p. 101) | html | pdf |
  - Maximal subgroups of plane group 5, cm (p. 102) | html | pdf |
  - Maximal subgroups of plane group 6, p2mm (p. 103) | html | pdf |
  - Maximal subgroups of plane group 7, p2mg (p. 104) | html | pdf |
  - Maximal subgroups of plane group 8, p2gg (p. 105) | html | pdf |
  - Maximal subgroups of plane group 9, c2mm (p. 106) | html | pdf |
  - Maximal subgroups of plane group 10, p4 (p. 107) | html | pdf |
  - Maximal subgroups of plane group 11, p4mm (p. 108) | html | pdf |
  - Maximal subgroups of plane group 12, p4gm (p. 109) | html | pdf |
  - Maximal subgroups of plane group 13, p3 (p. 110) | html | pdf |
  - Maximal subgroups of plane group 14, p3m1 (p. 111) | html | pdf |
  - Maximal subgroups of plane group 15, p31m (p. 112) | html | pdf |
  - Maximal subgroups of plane group 16, p6 (p. 113) | html | pdf |
  - Maximal subgroups of plane group 17, p6mm (p. 114) | html | pdf |
- 2.3. Tables of maximal subgroups of the space groups (pp. 115-432) | html | | chapter contents |
  - Maximal subgroups of space group 1, P1 (pp. 116-117) | html | pdf |
  - Maximal subgroups of space group 2, P-1 (pp. 118-119) | html | pdf |
  - Maximal subgroups of space group 3, P2 (pp. 120-122) | html | pdf |
    - Maximal subgroups of space group 3, unique axis b, P2 (pp. 120-121) | html | pdf |
    - Maximal subgroups of space group 3, unique axis c, P2 (pp. 121-122) | html | pdf |
  - Maximal subgroups of space group 4, P2₁ (pp. 123-124) | html | pdf |
    - Maximal subgroups of space group 4, unique axis b, P2₁ (p. 123) | html | pdf |
    - Maximal subgroups of space group 4, unique axis c, P2₁ (p. 124) | html | pdf |
  - Maximal subgroups of space group 5, C2 (pp. 125-127) | html | pdf |
    - Maximal subgroups of space group 5, unique axis b, C2 (pp. 125-126) | html | pdf |
    - Maximal subgroups of space group 5, unique axis c, C2 (pp. 126-127) | html | pdf |
  - Maximal subgroups of space group 6, Pm (pp. 128-130) | html | pdf |
    - Maximal subgroups of space group 6, unique axis b, Pm (pp. 128-129) | html | pdf |
    - Maximal subgroups of space group 6, unique axis c, Pm (pp. 129-130) | html | pdf |
  - Maximal subgroups of space group 7, Pc (pp. 131-132) | html | pdf |
    - Maximal subgroups of space group 7, unique axis b, Pc (p. 131) | html | pdf |
    - Maximal subgroups of space group 7, unique axis c, Pc (p. 132) | html | pdf |
  - Maximal subgroups of space group 8, Cm (pp. 133-134) | html | pdf |
    - Maximal subgroups of space group 8, unique axis b, Cm (p. 133) | html | pdf |
    - Maximal subgroups of space group 8, unique axis c, Cm (p. 134) | html | pdf |
  - Maximal subgroups of space group 9, Cc (pp. 135-136) | html | pdf |
    - Maximal subgroups of space group 9, unique axis b, Cc (p. 135) | html | pdf |
    - Maximal subgroups of space group 9, unique axis c, Cc (p. 136) | html | pdf |
  - Maximal subgroups of space group 10, P2/m (pp. 137-140) | html | pdf |
    - Maximal subgroups of space group 10, unique axis b, P2/m (pp. 137-138) | html | pdf |
    - Maximal subgroups of space group 10, unique axis c, P2/m (pp. 139-140) | html | pdf |
  - Maximal subgroups of space group 11, P2₁/m (pp. 141-143) | html | pdf |
    - Maximal subgroups of space group 11, unique axis b, P2₁/m (pp. 141-142) | html | pdf |
    - Maximal subgroups of space group 11, unique axis c, P2₁/m (pp. 142-143) | html | pdf |
  - Maximal subgroups of space group 12, C2/m (pp. 144-146) | html | pdf |
    - Maximal subgroups of space group 12, unique axis b, C2/m (pp. 144-145) | html | pdf |
    - Maximal subgroups of space group 12, unique axis c, C2/m (pp. 145-146) | html | pdf |
  - Maximal subgroups of space group 13, P2/c (pp. 147-149) | html | pdf |
    - Maximal subgroups of space group 13, unique axis b, P2/c (pp. 147-148) | html | pdf |
    - Maximal subgroups of space group 13, unique axis c, P2/c (pp. 148-149) | html | pdf |
  - Maximal subgroups of space group 14, P2₁/c (pp. 150-152) | html | pdf |
    - Maximal subgroups of space group 14, unique axis b, P2₁/c (pp. 150-151) | html | pdf |
    - Maximal subgroups of space group 14, unique axis c, P2₁/c (pp. 151-152) | html | pdf |
  - Maximal subgroups of space group 15, C2/c (pp. 153-155) | html | pdf |
    - Maximal subgroups of space group 15, unique axis b, C2/c (pp. 153-154) | html | pdf |
    - Maximal subgroups of space group 15, unique axis c, C2/c (pp. 154-155) | html | pdf |
  - Maximal subgroups of space group 16, P222 (pp. 156-157) | html | pdf |
  - Maximal subgroups of space group 17, P222₁ (p. 158) | html | pdf |
  - Maximal subgroups of space group 18, P2₁2₁2 (p. 159) | html | pdf |
  - Maximal subgroups of space group 19, P2₁2₁2₁ (p. 160) | html | pdf |
  - Maximal subgroups of space group 20, C222₁ (p. 161) | html | pdf |
  - Maximal subgroups of space group 21, C222 (pp. 162-163) | html | pdf |
  - Maximal subgroups of space group 22, F222 (pp. 163-164) | html | pdf |
  - Maximal subgroups of space group 23, I222 (p. 165) | html | pdf |
  - Maximal subgroups of space group 24, I2₁2₁2₁ (p. 166) | html | pdf |
  - Maximal subgroups of space group 25, Pmm2 (pp. 167-168) | html | pdf |
  - Maximal subgroups of space group 26, Pmc2₁ (p. 169) | html | pdf |
  - Maximal subgroups of space group 27, Pcc2 (p. 170) | html | pdf |
  - Maximal subgroups of space group 28, Pma2 (p. 171) | html | pdf |
  - Maximal subgroups of space group 29, Pca2₁ (p. 172) | html | pdf |
  - Maximal subgroups of space group 30, Pnc2 (p. 173) | html | pdf |
  - Maximal subgroups of space group 31, Pmn2₁ (p. 174) | html | pdf |
  - Maximal subgroups of space group 32, Pba2 (p. 175) | html | pdf |
  - Maximal subgroups of space group 33, Pna2₁ (p. 176) | html | pdf |
  - Maximal subgroups of space group 34, Pnn2 (p. 177) | html | pdf |
  - Maximal subgroups of space group 35, Cmm2 (p. 178) | html | pdf |
  - Maximal subgroups of space group 36, Cmc2₁ (p. 179) | html | pdf |
  - Maximal subgroups of space group 37, Ccc2 (p. 180) | html | pdf |
  - Maximal subgroups of space group 38, Amm2 (p. 181) | html | pdf |
  - Maximal subgroups of space group 39, Aem2 (p. 182) | html | pdf |
  - Maximal subgroups of space group 40, Ama2 (p. 183) | html | pdf |
  - Maximal subgroups of space group 41, Aea2 (p. 184) | html | pdf |
  - Maximal subgroups of space group 42, Fmm2 (pp. 185-186) | html | pdf |
  - Maximal subgroups of space group 43, Fdd2 (p. 187) | html | pdf |
  - Maximal subgroups of space group 44, Imm2 (p. 188) | html | pdf |
  - Maximal subgroups of space group 45, Iba2 (p. 189) | html | pdf |
  - Maximal subgroups of space group 46, Ima2 (p. 190) | html | pdf |
  - Maximal subgroups of space group 47, Pmmm (pp. 191-192) | html | pdf |
  - Maximal subgroups of space group 48, Pnnn (pp. 193-195) | html | pdf |
    - Maximal subgroups of space group 48, origin choice 1, Pnnn (pp. 193-194) | html | pdf |
    - Maximal subgroups of space group 48, origin choice 2, Pnnn (pp. 194-195) | html | pdf |
  - Maximal subgroups of space group 49, Pccm (pp. 196-197) | html | pdf |
  - Maximal subgroups of space group 50, Pban (pp. 197-200) | html | pdf |
    - Maximal subgroups of space group 50, origin choice 1, Pban (pp. 197-198) | html | pdf |
    - Maximal subgroups of space group 50, origin choice 2, Pban (pp. 199-200) | html | pdf |
  - Maximal subgroups of space group 51, Pmma (pp. 200-201) | html | pdf |
  - Maximal subgroups of space group 52, Pnna (p. 202) | html | pdf |
  - Maximal subgroups of space group 53, Pmna (p. 203) | html | pdf |
  - Maximal subgroups of space group 54, Pcca (p. 204) | html | pdf |
  - Maximal subgroups of space group 55, Pbam (p. 205) | html | pdf |
  - Maximal subgroups of space group 56, Pccn (p. 206) | html | pdf |
  - Maximal subgroups of space group 57, Pbcm (p. 207) | html | pdf |
  - Maximal subgroups of space group 58, Pnnm (p. 208) | html | pdf |
  - Maximal subgroups of space group 59, Pmmn (pp. 209-211) | html | pdf |
    - Maximal subgroups of space group 59, origin choice 1, Pmmn (pp. 209-210) | html | pdf |
    - Maximal subgroups of space group 59, origin choice 2, Pmmn (pp. 210-211) | html | pdf |
  - Maximal subgroups of space group 60, Pbcn (p. 212) | html | pdf |
  - Maximal subgroups of space group 61, Pbca (p. 213) | html | pdf |
  - Maximal subgroups of space group 62, Pnma (p. 214) | html | pdf |
  - Maximal subgroups of space group 63, Cmcm (pp. 215-216) | html | pdf |
  - Maximal subgroups of space group 64, Cmce (pp. 216-217) | html | pdf |
  - Maximal subgroups of space group 65, Cmmm (pp. 218-219) | html | pdf |
  - Maximal subgroups of space group 66, Cccm (pp. 219-220) | html | pdf |
  - Maximal subgroups of space group 67, Cmme (pp. 221-222) | html | pdf |
  - Maximal subgroups of space group 68, Ccce (pp. 223-225) | html | pdf |
    - Maximal subgroups of space group 68, origin choice 1, Ccce (pp. 223-224) | html | pdf |
    - Maximal subgroups of space group 68, origin choice 2, Ccce (pp. 224-225) | html | pdf |
  - Maximal subgroups of space group 69, Fmmm (pp. 226-227) | html | pdf |
  - Maximal subgroups of space group 70, Fddd (pp. 228-230) | html | pdf |
    - Maximal subgroups of space group 70, origin choice 1, Fddd (pp. 228-229) | html | pdf |
    - Maximal subgroups of space group 70, origin choice 2, Fddd (pp. 229-230) | html | pdf |
  - Maximal subgroups of space group 71, Immm (p. 231) | html | pdf |
  - Maximal subgroups of space group 72, Ibam (p. 232) | html | pdf |
  - Maximal subgroups of space group 73, Ibca (pp. 233-234) | html | pdf |
  - Maximal subgroups of space group 74, Imma (pp. 234-235) | html | pdf |
  - Maximal subgroups of space group 75, P4 (p. 236) | html | pdf |
  - Maximal subgroups of space group 76, P4₁ (p. 237) | html | pdf |
  - Maximal subgroups of space group 77, P4₂ (p. 238) | html | pdf |
  - Maximal subgroups of space group 78, P4₃ (p. 239) | html | pdf |
  - Maximal subgroups of space group 79, I4 (p. 240) | html | pdf |
  - Maximal subgroups of space group 80, I4₁ (p. 241) | html | pdf |
  - Maximal subgroups of space group 81, P-4 (p. 242) | html | pdf |
  - Maximal subgroups of space group 82, I-4 (p. 243) | html | pdf |
  - Maximal subgroups of space group 83, P4/m (p. 244) | html | pdf |
  - Maximal subgroups of space group 84, P4₂/m (p. 245) | html | pdf |
  - Maximal subgroups of space group 85, P4/n (pp. 246-247) | html | pdf |
    - Maximal subgroups of space group 85, origin choice 1, P4/n (p. 246) | html | pdf |
    - Maximal subgroups of space group 85, origin choice 2, P4/n (p. 247) | html | pdf |
  - Maximal subgroups of space group 86, P4₂/n (pp. 248-249) | html | pdf |
    - Maximal subgroups of space group 86, origin choice 1, P4₂/n (p. 248) | html | pdf |
    - Maximal subgroups of space group 86, origin choice 2, P4₂/n (p. 249) | html | pdf |
  - Maximal subgroups of space group 87, I4/m (p. 250) | html | pdf |
  - Maximal subgroups of space group 88, I4₁/a (pp. 251-252) | html | pdf |
    - Maximal subgroups of space group 88, origin choice 1, I4₁/a (p. 251) | html | pdf |
    - Maximal subgroups of space group 88, origin choice 2, I4₁/a (p. 252) | html | pdf |
  - Maximal subgroups of space group 89, P422 (p. 253) | html | pdf |
  - Maximal subgroups of space group 90, P42₁2 (p. 254) | html | pdf |
  - Maximal subgroups of space group 91, P4₁22 (p. 255) | html | pdf |
  - Maximal subgroups of space group 92, P4₁2₁2 (p. 256) | html | pdf |
  - Maximal subgroups of space group 93, P4₂22 (p. 257) | html | pdf |
  - Maximal subgroups of space group 94, P4₂2₁2 (p. 258) | html | pdf |
  - Maximal subgroups of space group 95, P4₃22 (p. 259) | html | pdf |
  - Maximal subgroups of space group 96, P4₃2₁2 (p. 260) | html | pdf |
  - Maximal subgroups of space group 97, I422 (p. 261) | html | pdf |
  - Maximal subgroups of space group 98, I4₁22 (p. 262) | html | pdf |
  - Maximal subgroups of space group 99, P4mm (p. 263) | html | pdf |
  - Maximal subgroups of space group 100, P4bm (p. 264) | html | pdf |
  - Maximal subgroups of space group 101, P4₂cm (p. 265) | html | pdf |
  - Maximal subgroups of space group 102, P4₂nm (p. 266) | html | pdf |
  - Maximal subgroups of space group 103, P4cc (p. 267) | html | pdf |
  - Maximal subgroups of space group 104, P4nc (p. 268) | html | pdf |
  - Maximal subgroups of space group 105, P4₂mc (p. 269) | html | pdf |
  - Maximal subgroups of space group 106, P4₂bc (p. 270) | html | pdf |
  - Maximal subgroups of space group 107, I4mm (p. 271) | html | pdf |
  - Maximal subgroups of space group 108, I4cm (p. 272) | html | pdf |
  - Maximal subgroups of space group 109, I4₁md (p. 273) | html | pdf |
  - Maximal subgroups of space group 110, I4₁cd (p. 274) | html | pdf |
  - Maximal subgroups of space group 111, P-42m (p. 275) | html | pdf |
  - Maximal subgroups of space group 112, P-42c (p. 276) | html | pdf |
  - Maximal subgroups of space group 113, P-42₁m (p. 277) | html | pdf |
  - Maximal subgroups of space group 114, P-42₁c (p. 278) | html | pdf |
  - Maximal subgroups of space group 115, P-4m2 (p. 279) | html | pdf |
  - Maximal subgroups of space group 116, P-4c2 (p. 280) | html | pdf |
  - Maximal subgroups of space group 117, P-4b2 (p. 281) | html | pdf |
  - Maximal subgroups of space group 118, P-4n2 (p. 282) | html | pdf |
  - Maximal subgroups of space group 119, I-4m2 (p. 283) | html | pdf |
  - Maximal subgroups of space group 120, I-4c2 (p. 284) | html | pdf |
  - Maximal subgroups of space group 121, I-42m (p. 285) | html | pdf |
  - Maximal subgroups of space group 122, I-42d (p. 286) | html | pdf |
  - Maximal subgroups of space group 123, P4/mmm (pp. 287-288) | html | pdf |
  - Maximal subgroups of space group 124, P4/mcc (p. 289) | html | pdf |
  - Maximal subgroups of space group 125, P4/nbm (pp. 290-291) | html | pdf |
    - Maximal subgroups of space group 125, origin choice 1, P4/nbm (p. 290) | html | pdf |
    - Maximal subgroups of space group 125, origin choice 2, P4/nbm (p. 291) | html | pdf |
  - Maximal subgroups of space group 126, P4/nnc (pp. 292-293) | html | pdf |
    - Maximal subgroups of space group 126, origin choice 1, P4/nnc (p. 292) | html | pdf |
    - Maximal subgroups of space group 126, origin choice 2, P4/nnc (p. 293) | html | pdf |
  - Maximal subgroups of space group 127, P4/mbm (p. 294) | html | pdf |
  - Maximal subgroups of space group 128, P4/mnc (p. 295) | html | pdf |
  - Maximal subgroups of space group 129, P4/nmm (pp. 296-297) | html | pdf |
    - Maximal subgroups of space group 129, origin choice 1, P4/nmm (p. 296) | html | pdf |
    - Maximal subgroups of space group 129, origin choice 2, P4/nmm (p. 297) | html | pdf |
  - Maximal subgroups of space group 130, P4/ncc (pp. 298-299) | html | pdf |
    - Maximal subgroups of space group 130, origin choice 1, P4/ncc (p. 298) | html | pdf |
    - Maximal subgroups of space group 130, origin choice 2, P4/ncc (p. 299) | html | pdf |
  - Maximal subgroups of space group 131, P4₂/mmc (p. 300) | html | pdf |
  - Maximal subgroups of space group 132, P4₂/mcm (p. 301) | html | pdf |
  - Maximal subgroups of space group 133, P4₂/nbc (pp. 302-303) | html | pdf |
    - Maximal subgroups of space group 133, origin choice 1, P4₂/nbc (p. 302) | html | pdf |
    - Maximal subgroups of space group 133, origin choice 2, P4₂/nbc (p. 303) | html | pdf |
  - Maximal subgroups of space group 134, P4₂/nnm (pp. 304-305) | html | pdf |
    - Maximal subgroups of space group 134, origin choice 1, P4₂/nnm (p. 304) | html | pdf |
    - Maximal subgroups of space group 134, origin choice 2, P4₂/nnm (p. 305) | html | pdf |
  - Maximal subgroups of space group 135, P4₂/mbc (p. 306) | html | pdf |
  - Maximal subgroups of space group 136, P4₂/mnm (p. 307) | html | pdf |
  - Maximal subgroups of space group 137, P4₂/nmc (pp. 308-309) | html | pdf |
    - Maximal subgroups of space group 137, origin choice 1, P4₂/nmc (p. 308) | html | pdf |
    - Maximal subgroups of space group 137, origin choice 2, P4₂/nmc (p. 309) | html | pdf |
  - Maximal subgroups of space group 138, P4₂/ncm (pp. 310-311) | html | pdf |
    - Maximal subgroups of space group 138, origin choice 1, P4₂/ncm (p. 310) | html | pdf |
    - Maximal subgroups of space group 138, origin choice 2, P4₂/ncm (p. 311) | html | pdf |
  - Maximal subgroups of space group 139, I4/mmm (p. 312) | html | pdf |
  - Maximal subgroups of space group 140, I4/mcm (p. 313) | html | pdf |
  - Maximal subgroups of space group 141, I4₁/amd (pp. 314-315) | html | pdf |
    - Maximal subgroups of space group 141, origin choice 1, I4₁/amd (p. 314) | html | pdf |
    - Maximal subgroups of space group 141, origin choice 2, I4₁/amd (p. 315) | html | pdf |
  - Maximal subgroups of space group 142, I4₁/acd (pp. 316-317) | html | pdf |
    - Maximal subgroups of space group 142, origin choice 1, I4₁/acd (p. 316) | html | pdf |
    - Maximal subgroups of space group 142, origin choice 2, I4₁/acd (p. 317) | html | pdf |
  - Maximal subgroups of space group 143, P3 (p. 318) | html | pdf |
  - Maximal subgroups of space group 144, P3₁ (p. 319) | html | pdf |
  - Maximal subgroups of space group 145, P3₂ (p. 320) | html | pdf |
  - Maximal subgroups of space group 146, R3 (pp. 321-322) | html | pdf |
    - Maximal subgroups of space group 146, hexagonal axes, R3 (p. 321) | html | pdf |
    - Maximal subgroups of space group 146, rhombohedral axes, R3 (p. 322) | html | pdf |
  - Maximal subgroups of space group 147, P-3 (p. 323) | html | pdf |
  - Maximal subgroups of space group 148, R-3 (pp. 324-325) | html | pdf |
    - Maximal subgroups of space group 148, hexagonal axes, R-3 (p. 324) | html | pdf |
    - Maximal subgroups of space group 148, rhombohedral axes, R-3 (p. 325) | html | pdf |
  - Maximal subgroups of space group 149, P312 (pp. 326-327) | html | pdf |
  - Maximal subgroups of space group 150, P321 (p. 328) | html | pdf |
  - Maximal subgroups of space group 151, P3₁12 (p. 329) | html | pdf |
  - Maximal subgroups of space group 152, P3₁21 (p. 330) | html | pdf |
  - Maximal subgroups of space group 153, P3₂12 (p. 331) | html | pdf |
  - Maximal subgroups of space group 154, P3₂21 (p. 332) | html | pdf |
  - Maximal subgroups of space group 155, R32 (pp. 333-335) | html | pdf |
    - Maximal subgroups of space group 155, hexagonal axes, R32 (p. 333) | html | pdf |
    - Maximal subgroups of space group 155, rhombohedral axes, R32 (pp. 334-335) | html | pdf |
  - Maximal subgroups of space group 156, P3m1 (p. 336) | html | pdf |
  - Maximal subgroups of space group 157, P31m (p. 337) | html | pdf |
  - Maximal subgroups of space group 158, P3c1 (p. 338) | html | pdf |
  - Maximal subgroups of space group 159, P31c (p. 339) | html | pdf |
  - Maximal subgroups of space group 160, R3m (pp. 340-341) | html | pdf |
    - Maximal subgroups of space group 160, hexagonal axes, R3m (p. 340) | html | pdf |
    - Maximal subgroups of space group 160, rhombohedral axes, R3m (p. 341) | html | pdf |
  - Maximal subgroups of space group 161, R3c (pp. 342-343) | html | pdf |
    - Maximal subgroups of space group 161, hexagonal axes, R3c (p. 342) | html | pdf |
    - Maximal subgroups of space group 161, rhombohedral axes, R3c (p. 343) | html | pdf |
  - Maximal subgroups of space group 162, P-31m (pp. 344-345) | html | pdf |
  - Maximal subgroups of space group 163, P-31c (p. 346) | html | pdf |
  - Maximal subgroups of space group 164, P-3m1 (p. 347) | html | pdf |
  - Maximal subgroups of space group 165, P-3c1 (p. 348) | html | pdf |
  - Maximal subgroups of space group 166, R-3m (pp. 349-351) | html | pdf |
    - Maximal subgroups of space group 166, hexagonal axes, R-3m (pp. 349-350) | html | pdf |
    - Maximal subgroups of space group 166, rhombohedral axes, R-3m (pp. 350-351) | html | pdf |
  - Maximal subgroups of space group 167, R-3c (pp. 352-354) | html | pdf |
    - Maximal subgroups of space group 167, hexagonal axes, R-3c (p. 352) | html | pdf |
    - Maximal subgroups of space group 167, rhombohedral axes, R-3c (pp. 353-354) | html | pdf |
  - Maximal subgroups of space group 168, P6 (p. 355) | html | pdf |
  - Maximal subgroups of space group 169, P6₁ (p. 356) | html | pdf |
  - Maximal subgroups of space group 170, P6₅ (p. 357) | html | pdf |
  - Maximal subgroups of space group 171, P6₂ (p. 358) | html | pdf |
  - Maximal subgroups of space group 172, P6₄ (p. 359) | html | pdf |
  - Maximal subgroups of space group 173, P6₃ (p. 360) | html | pdf |
  - Maximal subgroups of space group 174, P-6 (p. 361) | html | pdf |
  - Maximal subgroups of space group 175, P6/m (p. 362) | html | pdf |
  - Maximal subgroups of space group 176, P6₃/m (p. 363) | html | pdf |
  - Maximal subgroups of space group 177, P622 (p. 364) | html | pdf |
  - Maximal subgroups of space group 178, P6₁22 (p. 365) | html | pdf |
  - Maximal subgroups of space group 179, P6₅22 (p. 366) | html | pdf |
  - Maximal subgroups of space group 180, P6₂22 (p. 367) | html | pdf |
  - Maximal subgroups of space group 181, P6₄22 (p. 368) | html | pdf |
  - Maximal subgroups of space group 182, P6₃22 (p. 369) | html | pdf |
  - Maximal subgroups of space group 183, P6mm (p. 370) | html | pdf |
  - Maximal subgroups of space group 184, P6cc (p. 371) | html | pdf |
  - Maximal subgroups of space group 185, P6₃cm (p. 372) | html | pdf |
  - Maximal subgroups of space group 186, P6₃mc (p. 373) | html | pdf |
  - Maximal subgroups of space group 187, P-6m2 (pp. 374-375) | html | pdf |
  - Maximal subgroups of space group 188, P-6c2 (p. 376) | html | pdf |
  - Maximal subgroups of space group 189, P-62m (p. 377) | html | pdf |
  - Maximal subgroups of space group 190, P-62c (p. 378) | html | pdf |
  - Maximal subgroups of space group 191, P6/mmm (pp. 379-380) | html | pdf |
  - Maximal subgroups of space group 192, P6/mcc (p. 381) | html | pdf |
  - Maximal subgroups of space group 193, P6₃/mcm (p. 382) | html | pdf |
  - Maximal subgroups of space group 194, P6₃/mmc (p. 383) | html | pdf |
  - Maximal subgroups of space group 195, P23 (p. 384) | html | pdf |
  - Maximal subgroups of space group 196, F23 (p. 385) | html | pdf |
  - Maximal subgroups of space group 197, I23 (p. 386) | html | pdf |
  - Maximal subgroups of space group 198, P2₁3 (p. 387) | html | pdf |
  - Maximal subgroups of space group 199, I2₁3 (p. 388) | html | pdf |
  - Maximal subgroups of space group 200, Pm-3 (p. 389) | html | pdf |
  - Maximal subgroups of space group 201, Pn-3 (pp. 390-391) | html | pdf |
    - Maximal subgroups of space group 201, origin choice 1, Pn-3 (p. 390) | html | pdf |
    - Maximal subgroups of space group 201, origin choice 2, Pn-3 (p. 391) | html | pdf |
  - Maximal subgroups of space group 202, Fm-3 (pp. 392-393) | html | pdf |
  - Maximal subgroups of space group 203, Fd-3 (pp. 394-395) | html | pdf |
    - Maximal subgroups of space group 203, origin choice 1, Fd-3 (p. 394) | html | pdf |
    - Maximal subgroups of space group 203, origin choice 2, Fd-3 (p. 395) | html | pdf |
  - Maximal subgroups of space group 204, Im-3 (p. 396) | html | pdf |
  - Maximal subgroups of space group 205, Pa-3 (p. 397) | html | pdf |
  - Maximal subgroups of space group 206, Ia-3 (p. 398) | html | pdf |
  - Maximal subgroups of space group 207, P432 (p. 399) | html | pdf |
  - Maximal subgroups of space group 208, P4₂32 (p. 400) | html | pdf |
  - Maximal subgroups of space group 209, F432 (p. 401) | html | pdf |
  - Maximal subgroups of space group 210, F4₁32 (pp. 402-403) | html | pdf |
  - Maximal subgroups of space group 211, I432 (p. 404) | html | pdf |
  - Maximal subgroups of space group 212, P4₃32 (p. 405) | html | pdf |
  - Maximal subgroups of space group 213, P4₁32 (p. 406) | html | pdf |
  - Maximal subgroups of space group 214, I4₁32 (p. 407) | html | pdf |
  - Maximal subgroups of space group 215, P-43m (p. 408) | html | pdf |
  - Maximal subgroups of space group 216, F-43m (p. 409) | html | pdf |
  - Maximal subgroups of space group 217, I-43m (p. 410) | html | pdf |
  - Maximal subgroups of space group 218, P-43n (p. 411) | html | pdf |
  - Maximal subgroups of space group 219, F-43c (p. 412) | html | pdf |
  - Maximal subgroups of space group 220, I-43d (p. 413) | html | pdf |
  - Maximal subgroups of space group 221, Pm-3m (p. 414) | html | pdf |
  - Maximal subgroups of space group 222, Pn-3n (pp. 415-416) | html | pdf |
    - Maximal subgroups of space group 222, origin choice 1, Pn-3n (p. 415) | html | pdf |
    - Maximal subgroups of space group 222, origin choice 2, Pn-3n (p. 416) | html | pdf |
  - Maximal subgroups of space group 223, Pm-3n (p. 417) | html | pdf |
  - Maximal subgroups of space group 224, Pn-3m (pp. 418-420) | html | pdf |
    - Maximal subgroups of space group 224, origin choice 1, Pn-3m (pp. 418-419) | html | pdf |
    - Maximal subgroups of space group 224, origin choice 2, Pn-3m (pp. 419-420) | html | pdf |
  - Maximal subgroups of space group 225, Fm-3m (pp. 421-422) | html | pdf |
  - Maximal subgroups of space group 226, Fm-3c (pp. 423-424) | html | pdf |
  - Maximal subgroups of space group 227, Fd-3m (pp. 425-427) | html | pdf |
    - Maximal subgroups of space group 227, origin choice 1, Fd-3m (pp. 425-426) | html | pdf |
    - Maximal subgroups of space group 227, origin choice 2, Fd-3m (pp. 426-427) | html | pdf |
  - Maximal subgroups of space group 228, Fd-3c (pp. 428-430) | html | pdf |
    - Maximal subgroups of space group 228, origin choice 1, Fd-3c (pp. 428-429) | html | pdf |
    - Maximal subgroups of space group 228, origin choice 2, Fd-3c (pp. 429-430) | html | pdf |
  - Maximal subgroups of space group 229, Im-3m (p. 431) | html | pdf |
  - Maximal subgroups of space group 230, Ia-3d (p. 432) | html | pdf |
- 2.4. Graphs for translationengleiche subgroups (pp. 433-452) | html | pdf | chapter contents |
  Volker Gramlich and Hans Wondratschek
  - 2.4.1. Graphs of the translationengleiche subgroups with a cubic summit (pp. 434-439) | html | pdf |
  - 2.4.2. Graphs of the translationengleiche subgroups with a tetragonal summit (pp. 440-446) | html | pdf |
  - 2.4.3. Graphs of the translationengleiche subgroups with a hexagonal summit (pp. 447-449) | html | pdf |
  - 2.4.4. Graphs of the translationengleiche subgroups with an orthorhombic summit (pp. 450-452) | html | pdf |
  - Figures
    - Fig. 2.4.1.1. Graph of the translationengleiche subgroups of the summit space group $[Pm\overline{3}m]$ and of the included graphs with summits $[{\cal H} \,\lt\,Pm\overline{3}m]$ , see Example 2.1.8.2.3 (p. 434) | html | pdf |
    - Fig. 2.4.1.2. Graph of the translationengleiche subgroups of the summit space group $[Pn\overline{3}n]$ and of the included graphs with summits $[{\cal H} \,\lt\,Pn\overline{3}n]$ , see Example 2.1.8.2.3 (p. 434) | html | pdf |
    - Fig. 2.4.1.3. Graph of the translationengleiche subgroups of the summit space group $[Pm\overline{3}n]$ and of the included graphs with summits $[{\cal H} \,\lt\,Pm\overline{3}n]$ , see Example 2.1.8.2.3 (p. 435) | html | pdf |
    - Fig. 2.4.1.4. Graph of the translationengleiche subgroups of the summit space group $[Pn\overline{3}m]$ and of the included graphs with summits $[{\cal H} \,\lt\,Pn\overline{3}m]$ , see Example 2.1.8.2.3 (p. 435) | html | pdf |
    - Fig. 2.4.1.5. Graph of the translationengleiche subgroups of the summit space group $[Fm\overline{3}m]$ and of the included graphs with summits $[{\cal H} \,\lt\,Fm\overline{3}m]$ , see Example 2.1.8.2.3 (p. 436) | html | pdf |
    - Fig. 2.4.1.6. Graph of the translationengleiche subgroups of the summit space group $[Fm\overline{3}c]$ and of the included graphs with summits $[{\cal H} \,\lt\,Fm\overline{3}c]$ , see Example 2.1.8.2.3 (p. 436) | html | pdf |
    - Fig. 2.4.1.7. Graph of the translationengleiche subgroups of the summit space group $[Fd\overline{3}m]$ and of the included graphs with summits $[{\cal H} \,\lt\,Fd\overline{3}m]$ , see Example 2.1.8.2.3 (p. 437) | html | pdf |
    - Fig. 2.4.1.8. Graph of the translationengleiche subgroups of the summit space group $[Fd\overline{3}c]$ and of the included graphs with summits $[{\cal H} \,\lt\,Fd\overline{3}c]$ , see Example 2.1.8.2.3 (p. 437) | html | pdf |
    - Fig. 2.4.1.9. Graph of the translationengleiche subgroups of the summit space group $[Im\overline{3}m]$ and of the included graphs with summits $[{\cal H} \,\lt\,Im\overline{3}m]$ , see Example 2.1.8.2.3 (p. 438) | html | pdf |
    - Fig. 2.4.1.10. Graph of the translationengleiche subgroups of the summit space group $[Ia\overline{3}d]$ and of the included graphs with summits $[{\cal H} \,\lt\,Ia\overline{3}d]$ , see Example 2.1.8.2.3 (p. 438) | html | pdf |
    - Fig. 2.4.1.11. Graph of the translationengleiche subgroups of the summit space groups , and $[Pa\overline{3}]$ , and of the included graphs with summits $[{\cal H} \,\lt\,P4_132]$ or $[{\cal H} \,\lt\,P4_332]$ or $[{\cal H} \,\lt\,Pa\overline{3}]$ , see Example 2.1.8.2.3 (p. 439) | html | pdf |
    - Fig. 2.4.2.1. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4/mcc]$ , see Example 2.1.8.2.3 (p. 440) | html | pdf |
    - Fig. 2.4.2.2. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4/nbm]$ , see Example 2.1.8.2.3 (p. 440) | html | pdf |
    - Fig. 2.4.2.3. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4/mbm]$ , see Example 2.1.8.2.3 (p. 441) | html | pdf |
    - Fig. 2.4.2.4. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4/mnc]$ , see Example 2.1.8.2.3 (p. 441) | html | pdf |
    - Fig. 2.4.2.5. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4/nmm]$ , see Example 2.1.8.2.3 (p. 442) | html | pdf |
    - Fig. 2.4.2.6. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4/ncc]$ , see Example 2.1.8.2.3 (p. 442) | html | pdf |
    - Fig. 2.4.2.7. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4_2/mcm]$ , see Example 2.1.8.2.3 (p. 443) | html | pdf |
    - Fig. 2.4.2.8. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4_2/nbc]$ , see Example 2.1.8.2.3 (p. 443) | html | pdf |
    - Fig. 2.4.2.9. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4_2/mbc]$ , see Example 2.1.8.2.3 (p. 444) | html | pdf |
    - Fig. 2.4.2.10. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4_2/mnm]$ , see Example 2.1.8.2.3 (p. 444) | html | pdf |
    - Fig. 2.4.2.11. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4_2/nmc]$ , see Example 2.1.8.2.3 (p. 445) | html | pdf |
    - Fig. 2.4.2.12. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P4_2/ncm]$ , see Example 2.1.8.2.3 (p. 445) | html | pdf |
    - Fig. 2.4.2.13. Graph of the translationengleiche subgroups of the summit space groups and and of the included graphs with summits $[{\cal H} \,\lt\,P4_122]$ or $[{\cal H} \,\lt\,P4_322]$ , see Example 2.1.8.2.3 (p. 446) | html | pdf |
    - Fig. 2.4.3.1. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P6/mmm]$ , see Example 2.1.8.2.3 (p. 447) | html | pdf |
    - Fig. 2.4.3.2. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P6/mcc]$ , see Example 2.1.8.2.3 (p. 447) | html | pdf |
    - Fig. 2.4.3.3. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P6_3/mcm]$ , see Example 2.1.8.2.3 (p. 448) | html | pdf |
    - Fig. 2.4.3.4. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,P6_3/mmc]$ , see Example 2.1.8.2.3 (p. 448) | html | pdf |
    - Fig. 2.4.3.5. Graph of the translationengleiche subgroups of the summit space groups , , and , and of the included graphs with summits $[{\cal H} \,\lt\,P6_122]$ or $[{\cal H} \,\lt\,P6_522]$ or $[{\cal H} \,\lt\,P6_222]$ or $[{\cal H} \,\lt\,P6_422]$ , see Example 2.1.8.2.3 (p. 449) | html | pdf |
    - Fig. 2.4.4.1. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pmma]$ , see Example 2.1.8.2.3 (p. 450) | html | pdf |
    - Fig. 2.4.4.2. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pnna]$ , see Example 2.1.8.2.3 (p. 450) | html | pdf |
    - Fig. 2.4.4.3. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pmna]$ , see Example 2.1.8.2.3 (p. 450) | html | pdf |
    - Fig. 2.4.4.4. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pcca]$ , see Example 2.1.8.2.3 (p. 451) | html | pdf |
    - Fig. 2.4.4.5. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pbcm]$ , see Example 2.1.8.2.3 (p. 451) | html | pdf |
    - Fig. 2.4.4.6. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pbcn]$ , see Example 2.1.8.2.3 (p. 451) | html | pdf |
    - Fig. 2.4.4.7. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Pnma]$ , see Example 2.1.8.2.3 (p. 452) | html | pdf |
    - Fig. 2.4.4.8. Graph of the translationengleiche subgroups of the summit space group and of the included graphs with summits $[{\cal H} \,\lt\,Cmce]$ , see Example 2.1.8.2.3 (p. 452) | html | pdf |
- 2.5. Graphs for klassengleiche subgroups (pp. 453-464) | html | pdf | chapter contents |
  Volker Gramlich and Hans Wondratschek
  - 2.5.1. Graphs of the klassengleiche subgroups of monoclinic and orthorhombic space groups (pp. 454-456) | html | pdf |
  - 2.5.2. Graphs of the klassengleiche subgroups of tetragonal space groups (pp. 457-459) | html | pdf |
  - 2.5.3. Graphs of the klassengleiche subgroups of trigonal space groups (p. 460) | html | pdf |
  - 2.5.4. Graphs of the klassengleiche subgroups of hexagonal space groups (p. 461) | html | pdf |
  - 2.5.5. Graphs of the klassengleiche subgroups of cubic space groups (pp. 462-463) | html | pdf |
  - Figures
    - Fig. 2.5.1.1. Graph of the klassengleiche subgroups of the space groups of crystal class 2 (p. 454) | html | pdf |
    - Fig. 2.5.1.2. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 454) | html | pdf |
    - Fig. 2.5.1.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 454) | html | pdf |
    - Fig. 2.5.1.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 454) | html | pdf |
    - Fig. 2.5.1.5. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 455) | html | pdf |
    - Fig. 2.5.1.6. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 456) | html | pdf |
    - Fig. 2.5.2.1. Graph of the klassengleiche subgroups of the space groups of crystal class 4 (p. 457) | html | pdf |
    - Fig. 2.5.2.2. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline4]$ (p. 457) | html | pdf |
    - Fig. 2.5.2.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 457) | html | pdf |
    - Fig. 2.5.2.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 457) | html | pdf |
    - Fig. 2.5.2.5. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 458) | html | pdf |
    - Fig. 2.5.2.6. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline4 2m]$ (p. 458) | html | pdf |
    - Fig. 2.5.2.7. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 459) | html | pdf |
    - Fig. 2.5.3.1. Graph of the klassengleiche subgroups of the space groups of crystal class 3 (p. 460) | html | pdf |
    - Fig. 2.5.3.2. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline3]$ (p. 460) | html | pdf |
    - Fig. 2.5.3.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 460) | html | pdf |
    - Fig. 2.5.3.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 460) | html | pdf |
    - Fig. 2.5.3.5. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline3 m]$ (p. 460) | html | pdf |
    - Fig. 2.5.4.1. Graph of the klassengleiche subgroups of the space groups of crystal class 6 (p. 461) | html | pdf |
    - Fig. 2.5.4.2. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 461) | html | pdf |
    - Fig. 2.5.4.3. Graph of the klassengleiche subgroups of the space groups of crystal class 622 (p. 461) | html | pdf |
    - Fig. 2.5.4.4. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 461) | html | pdf |
    - Fig. 2.5.4.5. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline6 2m]$ (p. 461) | html | pdf |
    - Fig. 2.5.4.6. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 461) | html | pdf |
    - Fig. 2.5.5.1. Graph of the klassengleiche subgroups of the space groups of crystal class 23 (p. 462) | html | pdf |
    - Fig. 2.5.5.2. Graph of the klassengleiche subgroups of the space groups of crystal class $[m\overline3]$ (p. 462) | html | pdf |
    - Fig. 2.5.5.3. Graph of the klassengleiche subgroups of the space groups of crystal class (p. 462) | html | pdf |
    - Fig. 2.5.5.4. Graph of the klassengleiche subgroups of the space groups of crystal class $[\overline4 3m]$ (p. 463) | html | pdf |
    - Fig. 2.5.5.5. Graph of the klassengleiche subgroups of the space groups of crystal class $[m\overline3 m]$ (p. 463) | html | pdf |

Relations between the Wyckoff positions
- 3.1. Guide to the tables (pp. 466-472) | html | pdf | chapter contents |
  Ulrich Müller
  - 3.1.1. Arrangement of the entries (pp. 466-468) | html | pdf |
    - 3.1.1.1. Headline (p. 466) | html | pdf |
    - 3.1.1.2. Specification of the settings (p. 466) | html | pdf |
    - 3.1.1.3. List of Wyckoff positions (p. 466) | html | pdf |
    - 3.1.1.4. Subgroup data (p. 466) | html | pdf |
    - 3.1.1.5. Sequence of the listed subgroups (pp. 466-467) | html | pdf |
    - 3.1.1.6. Information for every subgroup (pp. 467-468) | html | pdf |
      - 3.1.1.6.1. Index (p. 467) | html | pdf |
      - 3.1.1.6.2. Subgroup symbol (p. 467) | html | pdf |
      - 3.1.1.6.3. Basis vectors (p. 467) | html | pdf |
      - 3.1.1.6.4. Coordinates (pp. 467-468) | html | pdf |
      - 3.1.1.6.5. Wyckoff positions (p. 468) | html | pdf |
  - 3.1.2. Cell transformations (p. 468) | html | pdf |
  - 3.1.3. Origin shifts (pp. 468-469) | html | pdf |
  - 3.1.4. Nonconventional settings of orthorhombic space groups (pp. 469-470) | html | pdf |
  - 3.1.5. Conjugate subgroups (pp. 470-471) | html | pdf |
    - 3.1.5.1. Translational conjugation (pp. 470-471) | html | pdf |
    - 3.1.5.2. Orientational conjugation (p. 471) | html | pdf |
  - 3.1.6. Monoclinic and triclinic subgroups (pp. 471-472) | html | pdf |
  - References | html | pdf |
  - Figures
    - Fig. 3.1.6.1. Two paths of group–subgroup relations from P4/m to a subgroup P112/m of index 10 (p. 472) | html | pdf |
- 3.2. Tables of the relations of the Wyckoff positions (pp. 473-760) | html | | chapter contents |
  - Relations of the Wyckoff positions for space group 1, P1 (p. 474) | html | pdf |
  - Relations of the Wyckoff positions for space group 2, P-1 (p. 475) | html | pdf |
  - Relations of the Wyckoff positions for space group 3, P2 (pp. 476-477) | html | pdf |
  - Relations of the Wyckoff positions for space group 4, P2₁ (p. 478) | html | pdf |
  - Relations of the Wyckoff positions for space group 5, C2 (pp. 479-481) | html | pdf |
  - Relations of the Wyckoff positions for space group 6, Pm (pp. 482-483) | html | pdf |
  - Relations of the Wyckoff positions for space group 7, Pc (pp. 484-485) | html | pdf |
  - Relations of the Wyckoff positions for space group 8, Cm (pp. 486-487) | html | pdf |
  - Relations of the Wyckoff positions for space group 9, Cc (pp. 488-489) | html | pdf |
  - Relations of the Wyckoff positions for space group 10, P2/m (pp. 490-493) | html | pdf |
  - Relations of the Wyckoff positions for space group 11, P2₁/m (pp. 494-495) | html | pdf |
  - Relations of the Wyckoff positions for space group 12, C2/m (pp. 496-499) | html | pdf |
  - Relations of the Wyckoff positions for space group 13, P2/c (pp. 500-503) | html | pdf |
  - Relations of the Wyckoff positions for space group 14, P2₁/c (pp. 504-507) | html | pdf |
  - Relations of the Wyckoff positions for space group 15, C2/c (pp. 508-511) | html | pdf |
  - Relations of the Wyckoff positions for space group 16, P222 (pp. 512-513) | html | pdf |
  - Relations of the Wyckoff positions for space group 17, P222₁ (p. 514) | html | pdf |
  - Relations of the Wyckoff positions for space group 18, P2₁2₁2 (p. 515) | html | pdf |
  - Relations of the Wyckoff positions for space group 19, P2₁2₁2₁ (p. 516) | html | pdf |
  - Relations of the Wyckoff positions for space group 20, C222₁ (p. 517) | html | pdf |
  - Relations of the Wyckoff positions for space group 21, C222 (pp. 517-518) | html | pdf |
  - Relations of the Wyckoff positions for space group 22, F222 (p. 519) | html | pdf |
  - Relations of the Wyckoff positions for space group 23, I222 (p. 520) | html | pdf |
  - Relations of the Wyckoff positions for space group 24, I2₁2₁2₁ (p. 521) | html | pdf |
  - Relations of the Wyckoff positions for space group 25, Pmm2 (pp. 522-523) | html | pdf |
  - Relations of the Wyckoff positions for space group 26, Pmc2₁ (p. 524) | html | pdf |
  - Relations of the Wyckoff positions for space group 27, Pcc2 (p. 525) | html | pdf |
  - Relations of the Wyckoff positions for space group 28, Pma2 (p. 526) | html | pdf |
  - Relations of the Wyckoff positions for space group 29, Pca2₁ (p. 527) | html | pdf |
  - Relations of the Wyckoff positions for space group 30, Pnc2 (p. 528) | html | pdf |
  - Relations of the Wyckoff positions for space group 31, Pmn2₁ (p. 529) | html | pdf |
  - Relations of the Wyckoff positions for space group 32, Pba2 (p. 530) | html | pdf |
  - Relations of the Wyckoff positions for space group 33, Pna2₁ (p. 531) | html | pdf |
  - Relations of the Wyckoff positions for space group 34, Pnn2 (p. 532) | html | pdf |
  - Relations of the Wyckoff positions for space group 35, Cmm2 (p. 533) | html | pdf |
  - Relations of the Wyckoff positions for space group 36, Cmc2₁ (p. 534) | html | pdf |
  - Relations of the Wyckoff positions for space group 37, Ccc2 (p. 535) | html | pdf |
  - Relations of the Wyckoff positions for space group 38, Amm2 (p. 536) | html | pdf |
  - Relations of the Wyckoff positions for space group 39, Aem2 (p. 537) | html | pdf |
  - Relations of the Wyckoff positions for space group 40, Ama2 (p. 538) | html | pdf |
  - Relations of the Wyckoff positions for space group 41, Aea2 (p. 539) | html | pdf |
  - Relations of the Wyckoff positions for space group 42, Fmm2 (p. 540) | html | pdf |
  - Relations of the Wyckoff positions for space group 43, Fdd2 (p. 541) | html | pdf |
  - Relations of the Wyckoff positions for space group 44, Imm2 (p. 542) | html | pdf |
  - Relations of the Wyckoff positions for space group 45, Iba2 (p. 543) | html | pdf |
  - Relations of the Wyckoff positions for space group 46, Ima2 (p. 544) | html | pdf |
  - Relations of the Wyckoff positions for space group 47, Pmmm (pp. 545-549) | html | pdf |
  - Relations of the Wyckoff positions for space group 48, Pnnn (pp. 550-551) | html | pdf |
  - Relations of the Wyckoff positions for space group 49, Pccm (pp. 551-553) | html | pdf |
  - Relations of the Wyckoff positions for space group 50, Pban (pp. 554-555) | html | pdf |
  - Relations of the Wyckoff positions for space group 51, Pmma (pp. 556-557) | html | pdf |
  - Relations of the Wyckoff positions for space group 52, Pnna (p. 558) | html | pdf |
  - Relations of the Wyckoff positions for space group 53, Pmna (p. 559) | html | pdf |
  - Relations of the Wyckoff positions for space group 54, Pcca (p. 560) | html | pdf |
  - Relations of the Wyckoff positions for space group 55, Pbam (p. 561) | html | pdf |
  - Relations of the Wyckoff positions for space group 56, Pccn (p. 562) | html | pdf |
  - Relations of the Wyckoff positions for space group 57, Pbcm (p. 563) | html | pdf |
  - Relations of the Wyckoff positions for space group 58, Pnnm (p. 564) | html | pdf |
  - Relations of the Wyckoff positions for space group 59, Pmmn (p. 565) | html | pdf |
  - Relations of the Wyckoff positions for space group 60, Pbcn (p. 566) | html | pdf |
  - Relations of the Wyckoff positions for space group 61, Pbca (p. 567) | html | pdf |
  - Relations of the Wyckoff positions for space group 62, Pnma (p. 568) | html | pdf |
  - Relations of the Wyckoff positions for space group 63, Cmcm (pp. 568-569) | html | pdf |
  - Relations of the Wyckoff positions for space group 64, Cmce (p. 570) | html | pdf |
  - Relations of the Wyckoff positions for space group 65, Cmmm (pp. 571-573) | html | pdf |
  - Relations of the Wyckoff positions for space group 66, Cccm (pp. 574-575) | html | pdf |
  - Relations of the Wyckoff positions for space group 67, Cmme (pp. 576-578) | html | pdf |
  - Relations of the Wyckoff positions for space group 68, Ccce (pp. 578-579) | html | pdf |
  - Relations of the Wyckoff positions for space group 69, Fmmm (pp. 580-581) | html | pdf |
  - Relations of the Wyckoff positions for space group 70, Fddd (p. 582) | html | pdf |
  - Relations of the Wyckoff positions for space group 71, Immm (pp. 583-584) | html | pdf |
  - Relations of the Wyckoff positions for space group 72, Ibam (p. 585) | html | pdf |
  - Relations of the Wyckoff positions for space group 73, Ibca (p. 586) | html | pdf |
  - Relations of the Wyckoff positions for space group 74, Imma (p. 587) | html | pdf |
  - Relations of the Wyckoff positions for space group 75, P4 (p. 588) | html | pdf |
  - Relations of the Wyckoff positions for space group 76, P4₁ (p. 589) | html | pdf |
  - Relations of the Wyckoff positions for space group 77, P4₂ (p. 590) | html | pdf |
  - Relations of the Wyckoff positions for space group 78, P4₃ (p. 589) | html | pdf |
  - Relations of the Wyckoff positions for space group 79, I4 (p. 591) | html | pdf |
  - Relations of the Wyckoff positions for space group 80, I4₁ (p. 592) | html | pdf |
  - Relations of the Wyckoff positions for space group 81, P-4 (p. 593) | html | pdf |
  - Relations of the Wyckoff positions for space group 82, I-4 (p. 594) | html | pdf |
  - Relations of the Wyckoff positions for space group 83, P4/m (pp. 595-596) | html | pdf |
  - Relations of the Wyckoff positions for space group 84, P4₂/m (p. 597) | html | pdf |
  - Relations of the Wyckoff positions for space group 85, P4/n (p. 598) | html | pdf |
  - Relations of the Wyckoff positions for space group 86, P4₂/n (p. 599) | html | pdf |
  - Relations of the Wyckoff positions for space group 87, I4/m (p. 600) | html | pdf |
  - Relations of the Wyckoff positions for space group 88, I4₁/a (p. 601) | html | pdf |
  - Relations of the Wyckoff positions for space group 89, P422 (pp. 602-603) | html | pdf |
  - Relations of the Wyckoff positions for space group 90, P42₁2 (p. 604) | html | pdf |
  - Relations of the Wyckoff positions for space group 91, P4₁22 (p. 605) | html | pdf |
  - Relations of the Wyckoff positions for space group 92, P4₁2₁2 (p. 606) | html | pdf |
  - Relations of the Wyckoff positions for space group 93, P4₂22 (pp. 606-607) | html | pdf |
  - Relations of the Wyckoff positions for space group 94, P4₂2₁2 (p. 608) | html | pdf |
  - Relations of the Wyckoff positions for space group 95, P4₃22 (p. 609) | html | pdf |
  - Relations of the Wyckoff positions for space group 96, P4₃2₁2 (p. 610) | html | pdf |
  - Relations of the Wyckoff positions for space group 97, I422 (p. 611) | html | pdf |
  - Relations of the Wyckoff positions for space group 98, I4₁22 (p. 612) | html | pdf |
  - Relations of the Wyckoff positions for space group 99, P4mm (p. 613) | html | pdf |
  - Relations of the Wyckoff positions for space group 100, P4bm (p. 614) | html | pdf |
  - Relations of the Wyckoff positions for space group 101, P4₂cm (p. 615) | html | pdf |
  - Relations of the Wyckoff positions for space group 102, P4₂nm (p. 616) | html | pdf |
  - Relations of the Wyckoff positions for space group 103, P4cc (p. 617) | html | pdf |
  - Relations of the Wyckoff positions for space group 104, P4nc (p. 618) | html | pdf |
  - Relations of the Wyckoff positions for space group 105, P4₂mc (p. 619) | html | pdf |
  - Relations of the Wyckoff positions for space group 106, P4₂bc (p. 620) | html | pdf |
  - Relations of the Wyckoff positions for space group 107, I4mm (p. 621) | html | pdf |
  - Relations of the Wyckoff positions for space group 108, I4cm (p. 622) | html | pdf |
  - Relations of the Wyckoff positions for space group 109, I4₁md (p. 623) | html | pdf |
  - Relations of the Wyckoff positions for space group 110, I4₁cd (p. 624) | html | pdf |
  - Relations of the Wyckoff positions for space group 111, P-42m (pp. 624-625) | html | pdf |
  - Relations of the Wyckoff positions for space group 112, P-42c (p. 626) | html | pdf |
  - Relations of the Wyckoff positions for space group 113, P-42₁m (p. 627) | html | pdf |
  - Relations of the Wyckoff positions for space group 114, P-42₁c (p. 628) | html | pdf |
  - Relations of the Wyckoff positions for space group 115, P-4m2 (pp. 628-629) | html | pdf |
  - Relations of the Wyckoff positions for space group 116, P-4c2 (p. 630) | html | pdf |
  - Relations of the Wyckoff positions for space group 117, P-4b2 (p. 631) | html | pdf |
  - Relations of the Wyckoff positions for space group 118, P-4n2 (p. 632) | html | pdf |
  - Relations of the Wyckoff positions for space group 119, I-4m2 (p. 633) | html | pdf |
  - Relations of the Wyckoff positions for space group 120, I-4c2 (p. 634) | html | pdf |
  - Relations of the Wyckoff positions for space group 121, I-42m (p. 635) | html | pdf |
  - Relations of the Wyckoff positions for space group 122, I-42d (p. 636) | html | pdf |
  - Relations of the Wyckoff positions for space group 123, P4/mmm (pp. 637-639) | html | pdf |
  - Relations of the Wyckoff positions for space group 124, P4/mcc (pp. 640-641) | html | pdf |
  - Relations of the Wyckoff positions for space group 125, P4/nbm (pp. 642-643) | html | pdf |
  - Relations of the Wyckoff positions for space group 126, P4/nnc (p. 644) | html | pdf |
  - Relations of the Wyckoff positions for space group 127, P4/mbm (p. 645) | html | pdf |
  - Relations of the Wyckoff positions for space group 128, P4/mnc (p. 646) | html | pdf |
  - Relations of the Wyckoff positions for space group 129, P4/nmm (p. 647) | html | pdf |
  - Relations of the Wyckoff positions for space group 130, P4/ncc (p. 648) | html | pdf |
  - Relations of the Wyckoff positions for space group 131, P4₂/mmc (pp. 649-650) | html | pdf |
  - Relations of the Wyckoff positions for space group 132, P4₂/mcm (pp. 651-652) | html | pdf |
  - Relations of the Wyckoff positions for space group 133, P4₂/nbc (p. 653) | html | pdf |
  - Relations of the Wyckoff positions for space group 134, P4₂/nnm (pp. 654-655) | html | pdf |
  - Relations of the Wyckoff positions for space group 135, P4₂/mbc (p. 656) | html | pdf |
  - Relations of the Wyckoff positions for space group 136, P4₂/mnm (p. 657) | html | pdf |
  - Relations of the Wyckoff positions for space group 137, P4₂/nmc (p. 658) | html | pdf |
  - Relations of the Wyckoff positions for space group 138, P4₂/ncm (p. 659) | html | pdf |
  - Relations of the Wyckoff positions for space group 139, I4/mmm (pp. 660-661) | html | pdf |
  - Relations of the Wyckoff positions for space group 140, I4/mcm (pp. 662-663) | html | pdf |
  - Relations of the Wyckoff positions for space group 141, I4₁/amd (p. 664) | html | pdf |
  - Relations of the Wyckoff positions for space group 142, I4₁/acd (p. 665) | html | pdf |
  - Relations of the Wyckoff positions for space group 143, P3 (p. 666) | html | pdf |
  - Relations of the Wyckoff positions for space group 144, P3₁ (p. 667) | html | pdf |
  - Relations of the Wyckoff positions for space group 145, P3₂ (p. 667) | html | pdf |
  - Relations of the Wyckoff positions for space group 146, R3 (p. 668) | html | pdf |
  - Relations of the Wyckoff positions for space group 147, P-3 (p. 669) | html | pdf |
  - Relations of the Wyckoff positions for space group 148, R-3 (p. 670) | html | pdf |
  - Relations of the Wyckoff positions for space group 149, P312 (pp. 670-671) | html | pdf |
  - Relations of the Wyckoff positions for space group 150, P321 (p. 672) | html | pdf |
  - Relations of the Wyckoff positions for space group 151, P3₁12 (p. 673) | html | pdf |
  - Relations of the Wyckoff positions for space group 152, P3₁21 (p. 674) | html | pdf |
  - Relations of the Wyckoff positions for space group 153, P3₂12 (p. 675) | html | pdf |
  - Relations of the Wyckoff positions for space group 154, P3₂21 (p. 676) | html | pdf |
  - Relations of the Wyckoff positions for space group 155, R32 (p. 677) | html | pdf |
  - Relations of the Wyckoff positions for space group 156, P3m1 (p. 678) | html | pdf |
  - Relations of the Wyckoff positions for space group 157, P31m (p. 679) | html | pdf |
  - Relations of the Wyckoff positions for space group 158, P3c1 (p. 680) | html | pdf |
  - Relations of the Wyckoff positions for space group 159, P31c (p. 681) | html | pdf |
  - Relations of the Wyckoff positions for space group 160, R3m (p. 682) | html | pdf |
  - Relations of the Wyckoff positions for space group 161, R3c (p. 683) | html | pdf |
  - Relations of the Wyckoff positions for space group 162, P-31m (p. 684) | html | pdf |
  - Relations of the Wyckoff positions for space group 163, P-31c (p. 685) | html | pdf |
  - Relations of the Wyckoff positions for space group 164, P-3m1 (p. 686) | html | pdf |
  - Relations of the Wyckoff positions for space group 165, P-3c1 (p. 687) | html | pdf |
  - Relations of the Wyckoff positions for space group 166, R-3m (p. 688) | html | pdf |
  - Relations of the Wyckoff positions for space group 167, R-3c (p. 689) | html | pdf |
  - Relations of the Wyckoff positions for space group 168, P6 (p. 690) | html | pdf |
  - Relations of the Wyckoff positions for space group 169, P6₁ (p. 691) | html | pdf |
  - Relations of the Wyckoff positions for space group 170, P6₅ (p. 691) | html | pdf |
  - Relations of the Wyckoff positions for space group 171, P6₂ (p. 692) | html | pdf |
  - Relations of the Wyckoff positions for space group 172, P6₄ (p. 692) | html | pdf |
  - Relations of the Wyckoff positions for space group 173, P6₃ (p. 693) | html | pdf |
  - Relations of the Wyckoff positions for space group 174, P-6 (p. 694) | html | pdf |
  - Relations of the Wyckoff positions for space group 175, P6/m (p. 695) | html | pdf |
  - Relations of the Wyckoff positions for space group 176, P6₃/m (p. 696) | html | pdf |
  - Relations of the Wyckoff positions for space group 177, P622 (p. 697) | html | pdf |
  - Relations of the Wyckoff positions for space group 178, P6₁22 (p. 698) | html | pdf |
  - Relations of the Wyckoff positions for space group 179, P6₅22 (p. 699) | html | pdf |
  - Relations of the Wyckoff positions for space group 180, P6₂22 (p. 700) | html | pdf |
  - Relations of the Wyckoff positions for space group 181, P6₄22 (p. 701) | html | pdf |
  - Relations of the Wyckoff positions for space group 182, P6₃22 (p. 702) | html | pdf |
  - Relations of the Wyckoff positions for space group 183, P6mm (p. 703) | html | pdf |
  - Relations of the Wyckoff positions for space group 184, P6cc (p. 704) | html | pdf |
  - Relations of the Wyckoff positions for space group 185, P6₃cm (p. 705) | html | pdf |
  - Relations of the Wyckoff positions for space group 186, P6₃mc (p. 706) | html | pdf |
  - Relations of the Wyckoff positions for space group 187, P-6m2 (pp. 706-707) | html | pdf |
  - Relations of the Wyckoff positions for space group 188, P-6c2 (p. 708) | html | pdf |
  - Relations of the Wyckoff positions for space group 189, P-62m (p. 709) | html | pdf |
  - Relations of the Wyckoff positions for space group 190, P-62c (p. 710) | html | pdf |
  - Relations of the Wyckoff positions for space group 191, P6/mmm (pp. 711-712) | html | pdf |
  - Relations of the Wyckoff positions for space group 192, P6/mcc (p. 713) | html | pdf |
  - Relations of the Wyckoff positions for space group 193, P6₃/mcm (p. 714) | html | pdf |
  - Relations of the Wyckoff positions for space group 194, P6₃/mmc (p. 715) | html | pdf |
  - Relations of the Wyckoff positions for space group 195, P23 (pp. 716-717) | html | pdf |
  - Relations of the Wyckoff positions for space group 196, F23 (p. 718) | html | pdf |
  - Relations of the Wyckoff positions for space group 197, I23 (p. 719) | html | pdf |
  - Relations of the Wyckoff positions for space group 198, P2₁3 (p. 720) | html | pdf |
  - Relations of the Wyckoff positions for space group 199, I2₁3 (p. 721) | html | pdf |
  - Relations of the Wyckoff positions for space group 200, Pm-3 (pp. 722-723) | html | pdf |
  - Relations of the Wyckoff positions for space group 201, Pn-3 (p. 724) | html | pdf |
  - Relations of the Wyckoff positions for space group 202, Fm-3 (p. 725) | html | pdf |
  - Relations of the Wyckoff positions for space group 203, Fd-3 (p. 726) | html | pdf |
  - Relations of the Wyckoff positions for space group 204, Im-3 (p. 727) | html | pdf |
  - Relations of the Wyckoff positions for space group 205, Pa-3 (p. 728) | html | pdf |
  - Relations of the Wyckoff positions for space group 206, Ia-3 (p. 729) | html | pdf |
  - Relations of the Wyckoff positions for space group 207, P432 (p. 730) | html | pdf |
  - Relations of the Wyckoff positions for space group 208, P4₂32 (pp. 731-732) | html | pdf |
  - Relations of the Wyckoff positions for space group 209, F432 (p. 733) | html | pdf |
  - Relations of the Wyckoff positions for space group 210, F4₁32 (p. 734) | html | pdf |
  - Relations of the Wyckoff positions for space group 211, I432 (p. 735) | html | pdf |
  - Relations of the Wyckoff positions for space group 212, P4₃32 (p. 736) | html | pdf |
  - Relations of the Wyckoff positions for space group 213, P4₁32 (p. 737) | html | pdf |
  - Relations of the Wyckoff positions for space group 214, I4₁32 (p. 738) | html | pdf |
  - Relations of the Wyckoff positions for space group 215, P-43m (pp. 739-740) | html | pdf |
  - Relations of the Wyckoff positions for space group 216, F-43m (p. 741) | html | pdf |
  - Relations of the Wyckoff positions for space group 217, I-43m (p. 742) | html | pdf |
  - Relations of the Wyckoff positions for space group 218, P-43n (p. 743) | html | pdf |
  - Relations of the Wyckoff positions for space group 219, F-43c (p. 744) | html | pdf |
  - Relations of the Wyckoff positions for space group 220, I-43d (p. 745) | html | pdf |
  - Relations of the Wyckoff positions for space group 221, Pm-3m (pp. 746-747) | html | pdf |
  - Relations of the Wyckoff positions for space group 222, Pn-3n (p. 748) | html | pdf |
  - Relations of the Wyckoff positions for space group 223, Pm-3n (pp. 749-750) | html | pdf |
  - Relations of the Wyckoff positions for space group 224, Pn-3m (pp. 750-751) | html | pdf |
  - Relations of the Wyckoff positions for space group 225, Fm-3m (pp. 752-753) | html | pdf |
  - Relations of the Wyckoff positions for space group 226, Fm-3c (pp. 753-754) | html | pdf |
  - Relations of the Wyckoff positions for space group 227, Fd-3m (pp. 755-756) | html | pdf |
  - Relations of the Wyckoff positions for space group 228, Fd-3c (pp. 756-757) | html | pdf |
  - Relations of the Wyckoff positions for space group 229, Im-3m (pp. 758-759) | html | pdf |
  - Relations of the Wyckoff positions for space group 230, Ia-3d (p. 760) | html | pdf |

Appendix. Differences in the presentation of Parts 2 and 3 (pp. 761-762) | html | pdf |
Ulrich Müller and Hans Wondratschek