Abstract: The author considered the influence of the complementability of minimal subgroups and Sylow subgroups on the structure of finite groups. Let F be a formation containing all finite supersolvable groups, and G be a finite group, M>1 be a normal subgroup of G with G/M∈F. The author prove if for any minimal subgroup H of M, H∩F*(G^F) is complemented in G, then G∈F.

Key words: finite groups, complemented subgroups, supersolvable groups, solvable groups