We observe that an n-dimensional crystallographic group G has periodic cohomology in degrees greater than n if it contains a torsion free finite index normal subgroup S (sic) G whose quotient G/S has periodic cohomology. We then consider a different type of periodicity. Namely, we provide hypotheses on a crystallographic group G that imply isomorphisms H-i(G/gamma T-c, F) congruent to H-i(G/gamma Tc+d,F) for F the field of p elements and gamma T-c a term in the relative lower central series of the translation subgroup T <= G. The latter periodicity provides a means of calculating the mod-p homology of certain infinite families of finite p-groups using a finite (machine) computation. (C) 2015 Published by Elsevier Inc.