  We address the existence of vortex solitons supported by azimuthally
modulated lattices and reveal how the global lattice discrete symmetry has
fundamental implications on the possible topological charges of solitons. We
set a general ``charge rule'' using group-theory techniques, which holds for
all lattices belonging to a given symmetry group. Focusing in the case of
Bessel lattices allows us to derive also a overall stability rule for the
allowed vortex solitons.
