International Tables for Crystallography (2006). Vol. A1. ch. 1.2, pp. 6-23   | 1 | 2 |
https://doi.org/10.1107/97809553602060000538

Chapter 1.2. General introduction to the subgroups of space groups

Chapter index

Abelian group 1.2.3.1
abstract group 1.2.3.2
affine group 1.2.6.3
affine mapping 1.2.2.1
affine normalizer 1.2.6.3
affine space-group type 1.2.5.3, 1.2.5.3, 1.2.5.3
associative law 1.2.3.1
augmented matrix 1.2.2.4
axis of a rotation 1.2.2.1
axis of a rotoinversion 1.2.2.1
axis of a screw rotation 1.2.2.1
basis 1.2.2.2
conventional 1.2.2.2, 1.2.5.1
crystallographic 1.2.2.2
lattice 1.2.2.2
primitive 1.2.2.2
basis vector 1.2.5.1
Bravais flock 1.2.5.2
Bravais lattice 1.2.5.4
Bravais system 1.2.5.4
Bravais type 1.2.5.4
Cayley table 1.2.3.2
centred lattice 1.2.5.1
centre of a rotoinversion 1.2.2.1
centre of inversion 1.2.2.1
centre of symmetry 1.2.2.1
closure 1.2.3.1
column part 1.2.2.3
commutative group 1.2.3.1
composition, law of 1.2.3.1
composition series 1.2.5.1
conjugacy class 1.2.4.3, 1.2.4.3, 1.2.4.3
conjugate elements 1.2.4.3
conjugate subgroups 1.2.4.3
continuum approach to phase transitions 1.2.7.3
continuum description 1.2.7.2
conventional basis 1.2.2.2, 1.2.5.1
conventional coordinate system 1.2.5.1
coordinates 1.2.2.2
coordinate system 1.2.2.2
conventional 1.2.5.1
transformation of 1.2.2.7
coset decomposition 1.2.4.2
coset length 1.2.4.2
coset representatives 1.2.4.2
cosets, left and right 1.2.4.2, 1.2.4.2
crystal, macroscopic 1.2.2.1
crystal class 1.2.5.4
geometric 1.2.5.2
holohedral 1.2.5.4
of space groups 1.2.5.4
crystal family 1.2.5.2, 1.2.5.5
crystallographic basis 1.2.2.2
crystallographic point group 1.2.5.4
crystallographic space-group type 1.2.5.3
crystallographic symmetry operation 1.2.2.1, 1.2.3
crystal pattern 1.2.2.1, 1.2.7.2
crystal system 1.2.5.2, 1.2.5.5
cyclic group 1.2.3.1
daughter phase 1.2.7.1
Deckoperation 1.2.2.1
decomposition of a group into cosets 1.2.4.2
deformed phase 1.2.7.1
detwinning 1.2.7.2
domain boundary 1.2.7.1
domain region 1.2.7.2
domains 1.2.7.1, 1.2.7.2
ferroelectric 1.2.7.2
domain state 1.2.7.2
secondary 1.2.7.2
domain structure 1.2.7.1
translational 1.2.7.3
domain wall 1.2.7.1
enantiomorphic space groups 1.2.5.3, 1.2.6.2
enantiomorphic space-group types 1.2.5.3
Euclidean group 1.2.6.3
Euclidean normalizer 1.2.6.3
specialized 1.2.6.3
typical 1.2.6.3
factor group 1.2.4.4
ferroelastic phase transitions 1.2.7.2
ferroelectric domains 1.2.7.2
fixed point 1.2.2.1, 1.2.2.1
general subgroup 1.2.6.2
generators 1.2.3.1
geometric crystal class 1.2.5.2
glide plane 1.2.2.1
glide reflection 1.2.2.1
glide vector 1.2.2.1
graphs of group–subgroup relations
for translationengleiche subgroups 1.2.5.4
group postulates 1.2.3.1
groups 1.2.3
Abelian 1.2.3.1
abstract 1.2.3.2
affine 1.2.6.3
commutative 1.2.3.1
cyclic 1.2.3.1
Euclidean 1.2.6.3
factor 1.2.4.4
homomorphic 1.2.3.2
isomorphic 1.2.3.2, 1.2.3.2
orthogonal 1.2.6.3
plane 1.2.5.1
translation 1.2.2.2, 1.2.5.1, 1.2.6.3
group–subgroup relations between space groups 1.2.6.1
group table 1.2.3.2
handedness 1.2.2.1
Hermann, theorem of 1.2.8.1, 1.2.8.1
Hermann's group 1.2.7.3
holohedral crystal class 1.2.5.4
holohedry 1.2.5.4, 1.2.5.4
homomorphic groups 1.2.3.2
homomorphic image 1.2.3.2, 1.2.4.4
homomorphic mapping 1.2.3.2
homomorphism 1.2.3.2, 1.2.3.2, 1.2.4.4
kernel of 1.2.4.4
identity mapping (operation) 1.2.2.1
image, homomorphic 1.2.3.2, 1.2.4.4
image point 1.2.2.1
index of a subgroup 1.2.4.2, 1.2.8.2
invariant subgroup 1.2.4.2
inverse operation 1.2.2.1, 1.2.3.1
inversion 1.2.2.1, 1.2.5.1
inversion centre 1.2.2.1
isometry 1.2.2.1, 1.2.2.5
isomorphic groups 1.2.3.2, 1.2.3.2
isomorphic subgroups 1.2.6.2, 1.2.8.2, 1.2.8.2
isomorphism 1.2.3.2
isomorphism class 1.2.3.2
isomorphism type 1.2.3.2
kernel
of a homomorphism 1.2.4.4
klassengleiche (k-) subgroups 1.2.6.2
Lagrange, theorem of 1.2.4.2
lattice basis 1.2.2.2
lattice
Bravais 1.2.5.4
centred 1.2.5.1
primitive 1.2.5.1
vector 1.2.2.2, 1.2.5.1
lattice parameters 1.2.2.5
lattice system 1.2.5.4
lattice type 1.2.5.4
lattice vector 1.2.2.2, 1.2.5.1
law, associative 1.2.3.1
law of composition 1.2.3.1
left coset 1.2.4.2
length of a coset 1.2.4.2
linear part 1.2.2.3
macroscopic crystal 1.2.2.1
macroscopic description 1.2.7.2
mapping
affine 1.2.2.1
homomorphic 1.2.3.2
identity 1.2.2.1
orthogonal 1.2.2.6
reversible 1.2.2.1
matrix
augmented 1.2.2.4
metric 1.2.2.5
matrix–column pair 1.2.2.3
matrix part 1.2.2.3
maximal subgroups 1.2.4.1, 1.2.8.2
metric matrix 1.2.2.5
microscopic description 1.2.7.2
minimal supergroups 1.2.4.1
mirror plane 1.2.2.1
motion 1.2.2.1
rigid 1.2.2.1
multiplication table 1.2.3.2
neutral element 1.2.3.1
N-fold rotation 1.2.2.1
N-fold rotoinversion 1.2.2.1
non-ferroelastic phase transitions 1.2.7.2
non-isomorphic subgroups 1.2.6.2, 1.2.8.2
normalizers 1.2.4.5
affine 1.2.6.3
Euclidean 1.2.6.3
normal subgroups 1.2.4.2, 1.2.4.3
order of a group 1.2.3.1
order of an element 1.2.3.1
orientation state 1.2.7.3
origin choice 1.2.5.1, 1.2.5.1
origin shift 1.2.2.7
orthogonal group 1.2.6.3
orthogonal mapping 1.2.2.6
parent-clamping approximation (PCA) 1.2.7.1
parent phase 1.2.7.1
periodicity 1.2.2.1
phase transitions
continuum approach to 1.2.7.3
ferroelastic 1.2.7.2
non-ferroelastic 1.2.7.2
plane group 1.2.5.1
point, fixed 1.2.2.1
point group, crystallographic 1.2.5.4, 1.2.5.4
point-group type 1.2.5.4
primitive basis 1.2.2.2
primitive lattice 1.2.5.1
product of group elements 1.2.3.1
product of sets of group elements 1.2.4.4
proper subgroups 1.2.4.1
reflection 1.2.2.1
reflection plane 1.2.2.1
region of a domain 1.2.7.2
representatives, coset 1.2.4.2
reversible mapping 1.2.2.1
right coset 1.2.4.2
rigid motion 1.2.2.1
rotation 1.2.2.1
N-fold 1.2.2.1
rotation axis 1.2.2.1
rotoinversion 1.2.2.1
N-fold 1.2.2.1
rotoinversion axis 1.2.2.1
screw axis 1.2.2.1
screw rotation 1.2.2.1
screw vector 1.2.2.1
secondary domain state 1.2.7.2
Seitz symbol 1.2.2.3
set of generators 1.2.3.1
single-domain state 1.2.7.2
single-domain structure 1.2.7.2
site-symmetry group 1.2.5.4
space groups 1.2.5.1, 1.2.5.3
enantiomorphic 1.2.5.3, 1.2.6.2
symmorphic 1.2.5.3
space-group types 1.2.5.3
affine 1.2.5.3, 1.2.5.3, 1.2.5.3
crystallographic 1.2.5.3
enantiomorphic 1.2.5.3
symmorphic 1.2.5.3
spontaneous deformation 1.2.7.1
spontaneous strain 1.2.7.1
state
domain 1.2.7.2
orientation 1.2.7.3
symmetry 1.2.7.2
subgroups 1.2.4.1
conjugate 1.2.4.3
general 1.2.6.2
invariant 1.2.4.2
isomorphic 1.2.6.2, 1.2.8.2, 1.2.8.2
klassengleiche 1.2.6.2
maximal 1.2.4.1, 1.2.8.2
non-isomorphic 1.2.6.2, 1.2.8.2
normal 1.2.4.2, 1.2.4.3
of space groups 1.2.6
proper 1.2.4.1
translationengleiche 1.2.6.2, 1.2.8.2
trivial 1.2.4.3
supergroups 1.2.4.1
minimal 1.2.4.1
symbols
Seitz 1.2.2.3
symmetry
centre of 1.2.2.1
symmetry element 1.2.3.1
symmetry operation 1.2.2.1
crystallographic 1.2.2.1, 1.2.3
symmetry state 1.2.7.2
symmorphic space groups 1.2.5.3
symmorphic space-group types 1.2.5.3
theorems
Hermann's theorem 1.2.8.1, 1.2.8.1
Lagrange's theorem 1.2.4.2
transformation of coordinate system 1.2.2.7
translation 1.2.2.1, 1.2.5.1
translational domain structure 1.2.7.3
translationengleiche (t-) subgroups 1.2.6.2, 1.2.8.2
translation group 1.2.2.2, 1.2.5.1, 1.2.6.3
translation part 1.2.2.3
translation twins 1.2.7.3
translation vector 1.2.2.2
trivial subgroup 1.2.4.3
twins 1.2.7.1, 1.2.7.2, 1.2.7.3
unit element 1.2.3.1
vector 1.2.2.6
basis 1.2.5.1
lattice 1.2.2.2, 1.2.5.1
translation 1.2.2.2
vector lattice 1.2.2.2, 1.2.5.1