Finite groups having at most 27 non-normal proper subgroups of non-prime-power order

Abstract

We prove that any finite group having at most 27 nonnormal proper subgroups of non-prime-power order is solvable except for G ∼ = A 5 , the alternating group of degree 5. 2010 Mathematics Subject Classification. 20D10. Key words and phrases. Finite group, solvable group, subgroup of non-prime-power order.