Abstract: A subgroup H of a finite group G is said to be weakly c-normal in G;if there exists a subnormal subgroup K of G such that G=HK and H∩K≤HG=CoreG(H),where HG=∩x∈GHx is the　largest normal subgroup of G,contained in H.Some conditions of a solvable group are given by using weakly　c-normality of subgroups.

Key words: maximal group, weakly c-normal subgroup, solvable group