# Isomorph-characteristic subgroup

From Groupprops

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

A subgroup of a group is termed an **isomorph-characteristic subgroup** if every subgroup of the group isomorphic to it is a characteristic subgroup of the whole group.