  One of the main obstacles that prevents practical applications of
antiferromagnets is the difficulty of manipulating the magnetic order
parameter. Recently, following the theoretical prediction [J. \v{Z}elezn\'y et
al., PRL 113, 157201 (2014)], the electrical switching of magnetic moments in
an antiferromagnet has been demonstrated [P. Wadley et al., Science 351, 587
(2016)]. The switching is due to the so-called spin-orbit torque, which has
been extensively studied in ferromagnets. In this phenomena a non-equilibrium
spin-polarization exchange coupled to the ordered local moments is induced by
current, hence exerting a torque on the order parameter. Here we give a general
systematic analysis of the symmetry of the spin-orbit torque in locally and
globally non-centrosymmetric crystals. We study when the symmetry allows for a
nonzero torque, when is the torque effective, and its dependence on the applied
current direction and orientation of magnetic moments. For comparison, we
consider both antiferromagnetic and ferromagnetic orders. In two representative
model crystals we perform microscopic calculations of the spin-orbit torque to
illustrate its symmetry properties and to highlight conditions under which the
spin-orbit torque can be efficient for manipulating antiferromagnetic moments.
