For a finite group G, a subgroup H is called c-normal in G if there is a normal subgroup K such that G=HK and H∩K≤HG, the largest normal subgroup of G contained in H. c-normality was replaced by c-π-quasinormality or c-sub-normality. The following were showed equivalent. First, there is a solvable maximal subgroup M such that M is c-π-quasi-normal in G.Second, every maximal subgroup with composite index of G is c-π-quasi-normal in G. Third, every maximal subgroup of G is c-subnormal in G. Fourth, G is solvable.