When N\sub M is an inclusion of factors with finite index and a group G acts on N\sub M, we compare the standard invariants of N\sub M and the crossed product inclusion N\rtimes G\sub M\rtimes G. The cases when G is a discrete group and when G is a locally compact abelian group are separately considered. Applying to a common crossed product decomposition, we obtain comparison results between the type II and type III standard invariants of an inclusion of type III factors.