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The aim is to characterize finite nilpotent groups that possess exactly five conjugacy classes of non-normal subgroups.

Finite nilpotent groups having exactly five conjugacy classes

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The aim is to characterize finite nilpotent groups that possess exactly five conjugacy classes of non-normal subgroups.
Theoretical analysis of group structures
Classification of nilpotent groups
Investigation of subgroup properties and their conjugacy relations.
Identification of specific properties that determine the structure of finite nilpotent groups with five conjugacy classes.
Demonstration of how these groups differ from others based on their conjugacy class characteristics.

Characterization of finite nilpotent groups with five conjugacy classes of non-normal subgroups, indicating their unique structure.

In this paper, we characterize the finite nilpotent groups having exactly five conjugacy classes of non-normal subgroups.

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Chen et al. (2026) studied this question.

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Characterization of finite nilpotent groups with five conjugacy classes of non-normal subgroups, indicating their unique structure.

In this paper, we characterize the finite nilpotent groups having exactly five conjugacy classes of non-normal subgroups.