  We provide a simplified characterization of entanglement in physical systems
which are symmetric under the action of subgroups of the symmetric group acting
on the party labels. Sets of entanglements are inherently equal, lying in the
same orbit under the group action, which we demonstrate for cyclic, dihedral,
and polyhedral groups. We then introduce new, generalized relationships for the
maxima of those entanglement by exploiting the normalizer and normal subgroups
of the physical symmetry group.
