SUBGROUPGRAPH: a computer program for analysis of group–subgroup relations between space groups

Group±subgroup relations between two space groups, G > H, are of essential importance for phase-transition problems: for determination of the relation between the lowand high-symmetry structures, domain structure analysis, displacement-mode analysis, etc. The available subgroup data in the International Tables for Crystallography, Vol. A (1995), are not suf®cient for a detailed treatment of G > H relations. The necessary data will be available in the forthcoming Vol. A1 of the International Tables for Crystallography (2001). The program SUBGROUPGRAPH uses a preliminary CIF version of the Vol. A1 database (Wondratchek et al., 1996). The main aim of SUBGROUPGRAPH is a detailed study of a group±subgroup relation between two space groups, including the construction of chains of maximal subgroups for G > H for a speci®ed/non-speci®ed index i = |G:H| (the so-called G±H graph), the determination of the number of different Hk < G, Hk  H, and their distribution into classes of conjugate subgroups relative to G, etc.