# Intermediately normal-to-complemented subgroup

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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

### Symbol-free definition

A subgroup of a group is termed **intermediately normal-to-complemented** if it satisfies the following equivalent conditions:

- It is a complemented normal subgroup inside its normalizer.
- It is a lattice-complemented subgroup inside its normalizer.
- It is a permutably complemented subgroup inside its normalizer.
- It is a complemented normal subgroup inside any intermediate subgroup in which it is a normal subgroup.