Subperiodic groups isomorphic to factor groups of reducible space groups

A relationship exists between factor groups of space groups and subperiodic groups. This relationship, an isomorphism between factor groups of reducible space groups and subperiodic groups, can be used in the derivation of higher-dimensional space groups, of lattices of space groups, and of irreducible representations of space groups. Tables of the layer and rod subperiodic groups isomorphic to factor groups of reducible space groups are explicitly given. The manifestation of this relationship, in terms of the symmetry diagrams of space groups and subperiodic groups, is also discussed.