Lattice-isomorph-free subgroup

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Definition

A subgroup $H$ of a group $G$ is termed lattice-isomorph-free in $G$ if there is no other subgroup of $G$ whose lattice of subgroups is isomorphic to the lattice of subgroups of $H$.

Relation with other properties

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
Isomorph-free subgroup
Characteristic subgroup