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

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 defining ingredient::maximal subgroup is an defining ingredient::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.

Stronger properties

 * Weaker than::Cyclic group of prime power order

Weaker properties

 * Stronger than::Group of prime power order in which every maximal subgroup is characteristic
 * Stronger than::Group in which every maximal subgroup is characteristic

Opposite properties

 * Group of prime power order in which all maximal subgroups are isomorphic
 * Group of prime power order in which all maximal subgroups are automorphic