# Order-dominated 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 finite group is termed **order-dominated** in if, given any finite subgroup of such that the order of divides the order of , there exists such that .

## Relation with other properties

### Stronger properties

- Sylow subgroup:
`For full proof, refer: Sylow implies order-dominated`

### Weaker properties

- Order-conjugate subgroup
- Isomorph-conjugate subgroup
- Prehomomorph-dominated subgroup (when the whole group is finite)