Sublattice enumeration. IV. Equivalence classes of plane sublattices by parent Patterson symmetry and colour lattice group type

The Dirichlet generating functions for the number of sublattices fixed under each symmetry operation of the parent Patterson group may be combined to count the number of crystallographically nonequivalent sublattices, in total, by sublattice point group and by colour lattice group type. The combinatorial formulae used imply the existence of various congruences among the corresponding arithmetic functions.