(International Tables) Symmetry relations between space groups

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

First online edition (2006) ISBN: 978-1-4020-2355-2 eISBN: 978-1-4020-5413-6 doi: 10.1107/97809553602060000101

Edited by H. Wondratschek and U. Müller

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

Part 1. Space groups and their subgroups
- 1.1. Historical introduction (pp. 2-5) | 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. 6-23) | html | pdf | chapter contents |
  Hans Wondratschek
  - 1.2.1. General remarks (p. 6) | html | pdf |
  - 1.2.2. Mappings and matrices (pp. 6-9) | html | pdf |
  - 1.2.3. Groups (pp. 9-10) | html | pdf |
  - 1.2.4. Subgroups (pp. 11-12) | html | pdf |
  - 1.2.5. Space groups (pp. 13-16) | html | pdf |
  - 1.2.6. Types of subgroups of space groups (pp. 16-18) | html | pdf |
  - 1.2.7. Application to domain structures (pp. 18-22) | html | pdf |
  - 1.2.8. Lemmata on subgroups of space groups (pp. 22-23) | html | pdf |
  - References | html | pdf |
- 1.3. Remarks on Wyckoff positions (pp. 24-26) | html | pdf | chapter contents |
  Ulrich Müller
  - 1.3.1. Introduction (p. 24) | html | pdf |
  - 1.3.2. Crystallographic orbits and Wyckoff positions (pp. 24-25) | html | pdf |
  - 1.3.3. Derivative structures and phase transitions (p. 25) | html | pdf |
  - 1.3.4. Relations between the positions in group–subgroup relations (pp. 25-26) | html | pdf |
  - References | html | pdf |
- 1.4. Computer checking of the subgroup data (pp. 27-28) | html | pdf | chapter contents |
  Franz Gähler
  - 1.4.1. Introduction (p. 27) | html | pdf |
  - 1.4.2. Basic capabilities of the Cryst package (p. 27) | html | pdf |
  - 1.4.3. Computing maximal subgroups (p. 27) | html | pdf |
  - 1.4.4. Description of the checks (p. 28) | html | pdf |
  - References | html | pdf |
- 1.5. The mathematical background of the subgroup tables (pp. 29-40) | html | pdf | chapter contents |
  Gabriele Nebe
  - 1.5.1. Introduction (p. 29) | html | pdf |
  - 1.5.2. The affine space (pp. 29-31) | html | pdf |
  - 1.5.3. Groups (pp. 31-34) | html | pdf |
  - 1.5.4. Space groups (pp. 34-36) | html | pdf |
  - 1.5.5. Maximal subgroups (pp. 36-38) | html | pdf |
  - 1.5.6. Quantitative results (pp. 38-39) | html | pdf |
  - 1.5.7. Qualitative results (pp. 39-40) | html | pdf |
  - References | html | pdf |

Part 2. Maximal subgroups of the plane groups and space groups
- 2.1. Guide to the subgroup tables and graphs (pp. 42-58) | html | pdf | chapter contents |
  Hans Wondratschek and Mois I. Aroyo
  - 2.1.1. Contents and arrangement of the subgroup tables (p. 42) | html | pdf |
  - 2.1.2. Structure of the subgroup tables (pp. 42-45) | html | pdf |
  - 2.1.3. I Maximal translationengleiche subgroups ( t -subgroups) (pp. 45-48) | html | pdf |
  - 2.1.4. II Maximal klassengleiche subgroups ( k -subgroups) (pp. 48-51) | html | pdf |
  - 2.1.5. Series of maximal isomorphic subgroups (pp. 51-53) | html | pdf |
    Y. Billiet
  - 2.1.6. Minimal supergroups (pp. 53-54) | html | pdf |
  - 2.1.7. The subgroup graphs (pp. 54-58) | html | pdf |
  - References | html | pdf |
- 2.2. Tables of maximal subgroups of the plane groups (pp. 59-76) | html | | chapter contents |
  - Maximal subgroups of plane group 1 (p. 60) | html | pdf |
  - Maximal subgroups of plane group 2 (p. 61) | html | pdf |
  - Maximal subgroups of plane group 3 (p. 62) | html | pdf |
  - Maximal subgroups of plane group 4 (p. 63) | html | pdf |
  - Maximal subgroups of plane group 5 (p. 64) | html | pdf |
  - Maximal subgroups of plane group 6 (p. 65) | html | pdf |
  - Maximal subgroups of plane group 7 (p. 66) | html | pdf |
  - Maximal subgroups of plane group 8 (p. 67) | html | pdf |
  - Maximal subgroups of plane group 9 (p. 68) | html | pdf |
  - Maximal subgroups of plane group 10 (p. 69) | html | pdf |
  - Maximal subgroups of plane group 11 (p. 70) | html | pdf |
  - Maximal subgroups of plane group 12 (p. 71) | html | pdf |
  - Maximal subgroups of plane group 13 (p. 72) | html | pdf |
  - Maximal subgroups of plane group 14 (p. 73) | html | pdf |
  - Maximal subgroups of plane group 15 (p. 74) | html | pdf |
  - Maximal subgroups of plane group 16 (p. 75) | html | pdf |
  - Maximal subgroups of plane group 17 (p. 76) | html | pdf |
- 2.3. Tables of maximal subgroups of the space groups (pp. 77-394) | html | | chapter contents |
  - Maximal subgroups of space group 1 (pp. 78-79) | html | pdf |
  - Maximal subgroups of space group 2 (pp. 80-81) | html | pdf |
  - Maximal subgroups of space group 3 (pp. 82-84) | html | pdf |
  - Maximal subgroups of space group 4 (pp. 85-86) | html | pdf |
  - Maximal subgroups of space group 5 (pp. 87-89) | html | pdf |
  - Maximal subgroups of space group 6 (pp. 90-92) | html | pdf |
  - Maximal subgroups of space group 7 (pp. 93-94) | html | pdf |
  - Maximal subgroups of space group 8 (pp. 95-96) | html | pdf |
  - Maximal subgroups of space group 9 (pp. 97-98) | html | pdf |
  - Maximal subgroups of space group 10 (pp. 99-102) | html | pdf |
  - Maximal subgroups of space group 11 (pp. 103-105) | html | pdf |
  - Maximal subgroups of space group 12 (pp. 106-108) | html | pdf |
  - Maximal subgroups of space group 13 (pp. 109-111) | html | pdf |
  - Maximal subgroups of space group 14 (pp. 112-114) | html | pdf |
  - Maximal subgroups of space group 15 (pp. 115-117) | html | pdf |
  - Maximal subgroups of space group 16 (pp. 118-119) | html | pdf |
  - Maximal subgroups of space group 17 (p. 120) | html | pdf |
  - Maximal subgroups of space group 18 (p. 121) | html | pdf |
  - Maximal subgroups of space group 19 (p. 122) | html | pdf |
  - Maximal subgroups of space group 20 (p. 123) | html | pdf |
  - Maximal subgroups of space group 21 (pp. 124-125) | html | pdf |
  - Maximal subgroups of space group 22 (pp. 125-126) | html | pdf |
  - Maximal subgroups of space group 23 (p. 127) | html | pdf |
  - Maximal subgroups of space group 24 (p. 128) | html | pdf |
  - Maximal subgroups of space group 25 (pp. 129-130) | html | pdf |
  - Maximal subgroups of space group 26 (p. 131) | html | pdf |
  - Maximal subgroups of space group 27 (p. 132) | html | pdf |
  - Maximal subgroups of space group 28 (p. 133) | html | pdf |
  - Maximal subgroups of space group 29 (p. 134) | html | pdf |
  - Maximal subgroups of space group 30 (p. 135) | html | pdf |
  - Maximal subgroups of space group 31 (p. 136) | html | pdf |
  - Maximal subgroups of space group 32 (p. 137) | html | pdf |
  - Maximal subgroups of space group 33 (p. 138) | html | pdf |
  - Maximal subgroups of space group 34 (p. 139) | html | pdf |
  - Maximal subgroups of space group 35 (p. 140) | html | pdf |
  - Maximal subgroups of space group 36 (p. 141) | html | pdf |
  - Maximal subgroups of space group 37 (p. 142) | html | pdf |
  - Maximal subgroups of space group 38 (p. 143) | html | pdf |
  - Maximal subgroups of space group 39 (p. 144) | html | pdf |
  - Maximal subgroups of space group 40 (p. 145) | html | pdf |
  - Maximal subgroups of space group 41 (p. 146) | html | pdf |
  - Maximal subgroups of space group 42 (pp. 147-148) | html | pdf |
  - Maximal subgroups of space group 43 (p. 149) | html | pdf |
  - Maximal subgroups of space group 44 (p. 150) | html | pdf |
  - Maximal subgroups of space group 45 (p. 151) | html | pdf |
  - Maximal subgroups of space group 46 (p. 152) | html | pdf |
  - Maximal subgroups of space group 47 (pp. 153-154) | html | pdf |
  - Maximal subgroups of space group 48 (pp. 155-157) | html | pdf |
  - Maximal subgroups of space group 49 (pp. 158-159) | html | pdf |
  - Maximal subgroups of space group 50 (pp. 159-162) | html | pdf |
  - Maximal subgroups of space group 51 (pp. 162-163) | html | pdf |
  - Maximal subgroups of space group 52 (p. 164) | html | pdf |
  - Maximal subgroups of space group 53 (p. 165) | html | pdf |
  - Maximal subgroups of space group 54 (p. 166) | html | pdf |
  - Maximal subgroups of space group 55 (p. 167) | html | pdf |
  - Maximal subgroups of space group 56 (p. 168) | html | pdf |
  - Maximal subgroups of space group 57 (p. 169) | html | pdf |
  - Maximal subgroups of space group 58 (p. 170) | html | pdf |
  - Maximal subgroups of space group 59 (pp. 171-173) | html | pdf |
  - Maximal subgroups of space group 60 (p. 174) | html | pdf |
  - Maximal subgroups of space group 61 (p. 175) | html | pdf |
  - Maximal subgroups of space group 62 (p. 176) | html | pdf |
  - Maximal subgroups of space group 63 (pp. 177-178) | html | pdf |
  - Maximal subgroups of space group 64 (pp. 178-179) | html | pdf |
  - Maximal subgroups of space group 65 (pp. 180-181) | html | pdf |
  - Maximal subgroups of space group 66 (pp. 181-182) | html | pdf |
  - Maximal subgroups of space group 67 (pp. 183-184) | html | pdf |
  - Maximal subgroups of space group 68 (pp. 185-187) | html | pdf |
  - Maximal subgroups of space group 69 (pp. 188-189) | html | pdf |
  - Maximal subgroups of space group 70 (pp. 190-192) | html | pdf |
  - Maximal subgroups of space group 71 (p. 193) | html | pdf |
  - Maximal subgroups of space group 72 (p. 194) | html | pdf |
  - Maximal subgroups of space group 73 (pp. 195-196) | html | pdf |
  - Maximal subgroups of space group 74 (pp. 196-197) | html | pdf |
  - Maximal subgroups of space group 75 (p. 198) | html | pdf |
  - Maximal subgroups of space group 76 (p. 199) | html | pdf |
  - Maximal subgroups of space group 77 (p. 200) | html | pdf |
  - Maximal subgroups of space group 78 (p. 201) | html | pdf |
  - Maximal subgroups of space group 79 (p. 202) | html | pdf |
  - Maximal subgroups of space group 80 (p. 203) | html | pdf |
  - Maximal subgroups of space group 81 (p. 204) | html | pdf |
  - Maximal subgroups of space group 82 (p. 205) | html | pdf |
  - Maximal subgroups of space group 83 (p. 206) | html | pdf |
  - Maximal subgroups of space group 84 (p. 207) | html | pdf |
  - Maximal subgroups of space group 85 (pp. 208-209) | html | pdf |
  - Maximal subgroups of space group 86 (pp. 210-211) | html | pdf |
  - Maximal subgroups of space group 87 (p. 212) | html | pdf |
  - Maximal subgroups of space group 88 (pp. 213-214) | html | pdf |
  - Maximal subgroups of space group 89 (p. 215) | html | pdf |
  - Maximal subgroups of space group 90 (p. 216) | html | pdf |
  - Maximal subgroups of space group 91 (p. 217) | html | pdf |
  - Maximal subgroups of space group 92 (p. 218) | html | pdf |
  - Maximal subgroups of space group 93 (p. 219) | html | pdf |
  - Maximal subgroups of space group 94 (p. 220) | html | pdf |
  - Maximal subgroups of space group 95 (p. 221) | html | pdf |
  - Maximal subgroups of space group 96 (p. 222) | html | pdf |
  - Maximal subgroups of space group 97 (p. 223) | html | pdf |
  - Maximal subgroups of space group 98 (p. 224) | html | pdf |
  - Maximal subgroups of space group 99 (p. 225) | html | pdf |
  - Maximal subgroups of space group 100 (p. 226) | html | pdf |
  - Maximal subgroups of space group 101 (p. 227) | html | pdf |
  - Maximal subgroups of space group 102 (p. 228) | html | pdf |
  - Maximal subgroups of space group 103 (p. 229) | html | pdf |
  - Maximal subgroups of space group 104 (p. 230) | html | pdf |
  - Maximal subgroups of space group 105 (p. 231) | html | pdf |
  - Maximal subgroups of space group 106 (p. 232) | html | pdf |
  - Maximal subgroups of space group 107 (p. 233) | html | pdf |
  - Maximal subgroups of space group 108 (p. 234) | html | pdf |
  - Maximal subgroups of space group 109 (p. 235) | html | pdf |
  - Maximal subgroups of space group 110 (p. 236) | html | pdf |
  - Maximal subgroups of space group 111 (p. 237) | html | pdf |
  - Maximal subgroups of space group 112 (p. 238) | html | pdf |
  - Maximal subgroups of space group 113 (p. 239) | html | pdf |
  - Maximal subgroups of space group 114 (p. 240) | html | pdf |
  - Maximal subgroups of space group 115 (p. 241) | html | pdf |
  - Maximal subgroups of space group 116 (p. 242) | html | pdf |
  - Maximal subgroups of space group 117 (p. 243) | html | pdf |
  - Maximal subgroups of space group 118 (p. 244) | html | pdf |
  - Maximal subgroups of space group 119 (p. 245) | html | pdf |
  - Maximal subgroups of space group 120 (p. 246) | html | pdf |
  - Maximal subgroups of space group 121 (p. 247) | html | pdf |
  - Maximal subgroups of space group 122 (p. 248) | html | pdf |
  - Maximal subgroups of space group 123 (pp. 249-250) | html | pdf |
  - Maximal subgroups of space group 124 (p. 251) | html | pdf |
  - Maximal subgroups of space group 125 (pp. 252-253) | html | pdf |
  - Maximal subgroups of space group 126 (pp. 254-255) | html | pdf |
  - Maximal subgroups of space group 127 (p. 256) | html | pdf |
  - Maximal subgroups of space group 128 (p. 257) | html | pdf |
  - Maximal subgroups of space group 129 (pp. 258-259) | html | pdf |
  - Maximal subgroups of space group 130 (pp. 260-261) | html | pdf |
  - Maximal subgroups of space group 131 (p. 262) | html | pdf |
  - Maximal subgroups of space group 132 (p. 263) | html | pdf |
  - Maximal subgroups of space group 133 (pp. 264-265) | html | pdf |
  - Maximal subgroups of space group 134 (pp. 266-267) | html | pdf |
  - Maximal subgroups of space group 135 (p. 268) | html | pdf |
  - Maximal subgroups of space group 136 (p. 269) | html | pdf |
  - Maximal subgroups of space group 137 (pp. 270-271) | html | pdf |
  - Maximal subgroups of space group 138 (pp. 272-273) | html | pdf |
  - Maximal subgroups of space group 139 (p. 274) | html | pdf |
  - Maximal subgroups of space group 140 (p. 275) | html | pdf |
  - Maximal subgroups of space group 141 (pp. 276-277) | html | pdf |
  - Maximal subgroups of space group 142 (pp. 278-279) | html | pdf |
  - Maximal subgroups of space group 143 (p. 280) | html | pdf |
  - Maximal subgroups of space group 144 (p. 281) | html | pdf |
  - Maximal subgroups of space group 145 (p. 282) | html | pdf |
  - Maximal subgroups of space group 146 (pp. 283-284) | html | pdf |
  - Maximal subgroups of space group 147 (p. 285) | html | pdf |
  - Maximal subgroups of space group 148 (pp. 286-287) | html | pdf |
  - Maximal subgroups of space group 149 (pp. 288-289) | html | pdf |
  - Maximal subgroups of space group 150 (p. 290) | html | pdf |
  - Maximal subgroups of space group 151 (p. 291) | html | pdf |
  - Maximal subgroups of space group 152 (p. 292) | html | pdf |
  - Maximal subgroups of space group 153 (p. 293) | html | pdf |
  - Maximal subgroups of space group 154 (p. 294) | html | pdf |
  - Maximal subgroups of space group 155 (pp. 295-297) | html | pdf |
  - Maximal subgroups of space group 156 (p. 298) | html | pdf |
  - Maximal subgroups of space group 157 (p. 299) | html | pdf |
  - Maximal subgroups of space group 158 (p. 300) | html | pdf |
  - Maximal subgroups of space group 159 (p. 301) | html | pdf |
  - Maximal subgroups of space group 160 (pp. 302-303) | html | pdf |
  - Maximal subgroups of space group 161 (pp. 304-305) | html | pdf |
  - Maximal subgroups of space group 162 (pp. 306-307) | html | pdf |
  - Maximal subgroups of space group 163 (p. 308) | html | pdf |
  - Maximal subgroups of space group 164 (p. 309) | html | pdf |
  - Maximal subgroups of space group 165 (p. 310) | html | pdf |
  - Maximal subgroups of space group 166 (pp. 311-313) | html | pdf |
  - Maximal subgroups of space group 167 (pp. 314-316) | html | pdf |
  - Maximal subgroups of space group 168 (p. 317) | html | pdf |
  - Maximal subgroups of space group 169 (p. 318) | html | pdf |
  - Maximal subgroups of space group 170 (p. 319) | html | pdf |
  - Maximal subgroups of space group 171 (p. 320) | html | pdf |
  - Maximal subgroups of space group 172 (p. 321) | html | pdf |
  - Maximal subgroups of space group 173 (p. 322) | html | pdf |
  - Maximal subgroups of space group 174 (p. 323) | html | pdf |
  - Maximal subgroups of space group 175 (p. 324) | html | pdf |
  - Maximal subgroups of space group 176 (p. 325) | html | pdf |
  - Maximal subgroups of space group 177 (p. 326) | html | pdf |
  - Maximal subgroups of space group 178 (p. 327) | html | pdf |
  - Maximal subgroups of space group 179 (p. 328) | html | pdf |
  - Maximal subgroups of space group 180 (p. 329) | html |

International Tables for CrystallographyVolume A1: Symmetry relations between space groups

Edited by H. Wondratschek and U. Müller

Contents

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