# Normal-subhomomorph-containing 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 normal subgroup of a group is termed a **normal-subhomomorph-containing subgroup** if, for any subgroup of and any homomorphism of groups such that is a normal subgroup of , is contained in .