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Group-subgroup and group-supergroup relations between space groups
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3, pp. 58-66 [ doi:10.1107/97809553602060000796 ]
... . Given the space-group types and and an index [i], both programs determine all different subgroups of with the given ... their conjugation relations with elements of . Input to SUBGROUPGRAPH: (i) As input, the program needs the specification of the space ... Output of SUBGROUPGRAPH: The output is illustrated by Example 1.7.3.1.1. (i) Group-subgroup pairs with non-specified indices. When the ...

The program CELLSUPER
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.2.2, p. 66 [ doi:10.1107/97809553602060000796 ]
... to the low-symmetry group . The output data include: (i) The space-group types of the supergroups of with the corresponding indices [i], [iP] and [iL]. The supergroups are classified into t ... different supergroups of of the space-group type and index [i]. Each supergroup is specified by the corresponding transformation ...

The programs MINSUP and SUPERGROUPS
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.2.1, pp. 64-66 [ doi:10.1107/97809553602060000796 ]
... all supergroups of a given space-group type and index [i] of a space group can be done by inverting the data for the subgroups of of index [i]. In the following we outline the basic arguments of ... space group and be one of its subgroups of index [i]. Then all subgroups of of the same index [ ...

Supergroups of space groups
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.2, pp. 64-66 [ doi:10.1107/97809553602060000796 ]
... that are isomorphic to and are of the same index [i]. In the literature there are few papers treating the supergroups of space groups in detail (Koch, 1984; Wondratschek & Aroyo, 2001). In IT A one finds only listings of ... programs that solve this problem for a given finite index [i] (Ivantchev et al., 2002): (i) MINSUP, which gives all ...

The program COMMONSUBS
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.1.5, pp. 63-64 [ doi:10.1107/97809553602060000796 ]
... the point-group index and the lattice index , such that , m = 1, 2. The point-group indices are finite, ; the lattice ... the program COMMONSUBS calculates the common subgroups in several steps: (i) A dedicated module of the program CELLSUB (cf. Section 1.7.3.1.4 ... space-group types of the common subgroups of and with , m = 1, 2. (iii) The program COMMONSUBS selects and lists ...

The program CELLSUB
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.1.4, pp. 62-63 [ doi:10.1107/97809553602060000796 ]
... space group for a given maximal index in two steps: (i) It determines all possible space-group types which form group ... For each pair of space-group types and their index [i] satisfying the above condition, CELLSUB finds all possible subgroups specified ... maximal subgroups, imposing the additional condition . Input to CELLSUB: (i) The space group . It can be specified either ...

The program COSETS
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.1.3, p. 62 [ doi:10.1107/97809553602060000796 ]
The program COSETS 1.7.3.1.3. The program COSETS The coset decomposition of a group with respect to a subgroup is a basic step in many problems that involve group-subgroup relations between space groups, e.g. the distribution of subgroups into conjugacy classes (cf. Section 1.2.6.3 ) or the determination of supergroups of space ...

The program HERMANN
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.1.2, p. 61 [ doi:10.1107/97809553602060000796 ]
... a group-subgroup pair , with a general subgroup of index [i]. The existence and the uniqueness of Hermann's group ... possibility of factorizing the group-subgroup chain and its index [i] into two subchains of smaller indices with . The first ... lattices.) The program HERMANN calculates all subgroups of of index [i] and distributes them into conjugacy classes with respect to ...

The program SUBGROUPGRAPH
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.1.1, pp. 58-61 [ doi:10.1107/97809553602060000796 ]
... their conjugation relations with elements of . Input to SUBGROUPGRAPH: (i) As input, the program needs the specification of the space ... Output of SUBGROUPGRAPH: The output is illustrated by Example 1.7.3.1.1. (i) Group-subgroup pairs with non-specified indices. When the index ... corresponds to a maximal subgroup pair of the indicated index [i]. Isomorphic subgroups (of indices 2 and 3) are ...

Subgroups of space groups
Aroyo, M. I., Perez-Mato, J. M., Capillas, C. and Wondratschek, H.  International Tables for Crystallography (2011). Vol. A1, Section 1.7.3.1, pp. 58-64 [ doi:10.1107/97809553602060000796 ]
... . Given the space-group types and and an index [i], both programs determine all different subgroups of with the given ... their conjugation relations with elements of . Input to SUBGROUPGRAPH: (i) As input, the program needs the specification of the space ... Output of SUBGROUPGRAPH: The output is illustrated by Example 1.7.3.1.1. (i) Group-subgroup pairs with non-specified indices. When the ...

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