# Isomorph-normal characteristic subgroup

From Groupprops

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: isomorph-normal subgroup and characteristic subgroup

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## Definition

A subgroup of a group is termed an **isomorph-normal characteristic subgroup** if it satisfies the following two conditions:

- It is characteristic in the whole group.
- It is isomorph-normal in the whole group: every subgroup of the group that is isomorphic to it is normal in the whole group.