  The properties of electrons in magnetically ordered crystals are of interest
both from the viewpoint of realizing novel topological phases, such as magnetic
Weyl semimetals, and from the applications perspective of creating
energy-efficient memories. A systematic study of symmetry and topology in
magnetic materials has been challenging given that there are 1651 magnetic
space groups (MSGs). Here, by using an efficient representation of allowed band
structures, we obtain a systematic description of several basic properties of
free electrons in all MSGs in three dimensions as well as in the 528 magnetic
layer groups relevant to two dimensional magnetic materials. We compute
constraints on electron fillings and band connectivity compatible with
insulating behavior. Also, by contrasting with atomic insulators, we identify
band topology entailed by the symmetry transformation of bands, as determined
by the MSG alone. We give an application of our results to identifying
topological semimetals arising in periodic arrangements of hedgehog-like
magnetic textures.
