# Order-normal 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 finite subgroup of a group is termed an **order-normal subgroup** if every subgroup of having the same order as is a normal subgroup of .

## Relation with other properties

### Stronger properties

- Order-unique subgroup
- Normal Hall subgroup
- Normal Sylow subgroup
- Maximal subgroup of group of prime power order
- Maximal subgroup of finite nilpotent group