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Let  G  be a finite group and   ( G ) the set of the numbers of conjugates of noncyclic proper subgroups of  G . We prove that (1) if |  ( G )| ≤ 2, then  G  is solvable, and (2)  G  is a nonsolvable group with |  ( G )| = 3 if and only if  G ≅ PSL (2,5) or  PSL (2,13) or  SL (2,5) or  SL (2,13).

On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups