On nonnormal nonabelian subgroups of finite groups

‎In this paper we prove that a finite group G having at most three‎ ‎conjugacy classes of nonnormal nonabelian proper subgroups is‎ ‎always solvable except for Gcong{rm{A_5}}‎, ‎which extends Theorem 3.3‎ ‎in [Some sufficient conditions on the number of‎ ‎nonabelian subgroups of a finite group to be solvable‎, ‎Acta Math‎. ‎Sinica (English Series) 27 (2011) 891896.]‎. ‎Moreover‎, ‎we show that a‎ ‎finite group G with at most three same order classes of nonnormal‎ ‎nonabelian proper subgroups is always solvable except for Gcong‎{A_5}.