# Quotient-isomorph-free 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 **quotient-isomorph-free** if is normal in , and there is no *other* normal subgroup of such that is isomorphic to .

## Relation with other properties

### Stronger properties

- Quotient-subisomorph-containing subgroup when the quotient is a Hopfian group.