  We report a diversity of stable gap solitons in a spin-orbit coupled
Bose-Einstein condensate subject to a spatially periodic Zeeman field. It is
shown that the solitons, can be classified by the main physical symmetries they
obey, i.e. symmetries with respect to parity (P), time (T), and internal degree
of freedom, i.e. spin, (C) inversions. The conventional gap and gap-stripe
solitons are obtained in lattices with different parameters. It is shown that
solitons of the same type but obeying different symmetries can exist in the
same lattice at different spatial locations. PT and CPT symmetric solitons have
anti-ferromagnetic structure and are characterized respectively by nonzero and
zero total magnetizations.
