Group of prime power order in which every maximal subgroup is isomorph-free

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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Definition

A group of prime power order in which every maximal subgroup is isomorph-free is a group of prime power order in which every maximal subgroup is an isomorph-free subgroup.

Examples

• Any cyclic group of prime power order satisfies this property. In fact, a cyclic group of prime power order $p^k$ has a unique maximal subgroup, which has order $p^{k-1}$ and equals the first agemo subgroup, i.e., the set of $p^{th}$ powers.
• Among the non-cyclic groups of prime power order, the smallest example of one in which every maximal subgroup is isomorph-free is the semidihedral group of order sixteen (also see subgroup structure of semidihedral group:SD16. This is a group of order $16$ having three maximal subgroups of order $8$: a cyclic group, dihedral group and quaternion group.