  The grand-unification gauge group SO(10) contains matter parity as a discrete
subgroup. This symmetry could be at the origin of dark matter stability. The
properties of the dark matter candidates depend on the path along which SO(10)
is broken, in particular through Pati-Salam or left-right symmetric subgroups.
We systematically determine the non-supersymmetric dark matter scenarios that
can be realized along the various paths. We emphasize that the dark matter
candidates may have colored or electrically charged partners at low scale that
belong to the same SO(10) multiplet. These states, which in many cases are
important for co-annihilation, could be observed more easily than the dark
matter particle. We determine the structure of the tree-level and loop-induced
mass splittings between the dark matter candidate and their partners and
discuss the possible phenomenological implications.
