Abstract
As an extension of Shi and Zhang's 2011 article [4], we prove that any finite group having at most 23 non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5), and any finite group having at most three conjugacy classes of non-normal non-nilpotent proper subgroups is solvable except for G ≅ A 5 or SL(2, 5).
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