  We show that compositions of time-reversal and spatial symmetries, also known
as the magnetic-space-group symmetries, protect topological invariants as well
as surface states that are distinct from those of all preceding topological
states. We obtain, by explicit and exhaustive construction, the topological
classification of electronic band insulators that are magnetically ordered for
each one of the 1421 magnetic space groups in three dimensions. We have also
computed the symmetry-based indicators for each nontrivial class, and, by doing
so, establish the complete mapping from symmetry representations to topological
invariants.
