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In this paper, we provide some conditions of (super) -solvability and nilpotency of a finite group G based on its number of subgroups Sub (G). Our results generalize the classification of finite groups with less than 20 subgroups by Betz and Nash. We also provide an application of our results in studying comaximal subgroup graph of a group. Finally, we conclude with some open issues.
Das et al. (Sat,) studied this question.