Abstract: A subgroup H of a finite group G is said to be c-normal in G if there exists a normal subgroup K of G such that G=HK and H∩ K≤HG=CoreG(H),where HG=∩x∈G Hx is the largest normal subgroup of G,contained in H.In this paper,the author gives some conditions of a solvable group by using c-normality of subgroups.

Key words: maximal group, c-normal subgroup, CI-section, solvable group