Title Some results on the minimum index of subgroups of a finite group Type Presentation Keywords Index of a subgroup, Maximal subgroup, Cayley’s theorem Abstract In this paper, we study a numerical invariant of finite groups. For a finite group G, set mi(G)=min{[G : H] : H < G}. We prove that mi(G) is a prime number if G is a solvable group. Also we prove that mi(G) is not equal to 4 for any group G Researchers hamidreza dorbidi (First researcher)