  In (1+1)D topological phases, unpaired Majorana zero modes (MZMs) can arise
only if the internal symmetry group $G_f$ of the ground state splits as $G_f =
G_b \times \mathbb{Z}_2^f$, where $\mathbb{Z}_2^f$ is generated by fermion
parity, $(-1)^F$. In contrast, (2+1)D topological superconductors (TSC) can
host unpaired MZMs at defects even when $G_f$ is not of the form $G_b \times
\mathbb{Z}_2^f$. In this paper we study how $G_f$ together with the chiral
central charge $c_-$ strongly constrain the existence of unpaired MZMs and the
quantum numbers of symmetry defects. Our results utilize a recent algebraic
characterization of (2+1)D invertible fermionic topological states, which
provides a non-perturbative approach based on topological quantum field theory,
beyond free fermions. We study physically relevant groups such as
$\mathrm{U}(1)^f\rtimes H,\mathrm{SU}(2)^f \times H, \mathrm{U}(2)^f\rtimes H
$, generic Abelian groups, as well as more general compact Lie groups,
antiunitary symmetries and crystalline symmetries. We present an algebraic
formula for the fermionic crystalline equivalence principle, which gives an
equivalence between states with crystalline and internal symmetries. In light
of our theory, we discuss several previously proposed realizations of unpaired
MZMs in TSC materials such as Sr$_2$RuO$_4$, transition metal dichalcogenides
and iron superconductors, in which crystalline symmetries are often important;
in some cases we present additional predictions for the properties of these
models.
