On c-supplemented subgroups of finite groups

Let G be a finite group. A subgroup H of G is said to be c-supplemented in G if there exists a subgroup K of G such that G=HK and H∩K⩽HG, where HG=⋂g∈GHg is the largest normal subgroup of G contained in H. We investigate the structure of G under the assumption that some families of subgroups of G are c-supplemented in G.