# Order-dominating subgroup

From Groupprops

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]

## Contents

## Definition

### Symbol-free definition

A finite subgroup of a group is termed **order-dominating** if every other subgroup whose order divides its order, is conjugate to a subgroup contained in it.

### Definition with symbols

Let be a group and be a finite subgroup. Then, is termed **order-dominating** in if, for any subgroup such that the order of divides the order of , there exists such that .

## Relation with other properties

### Stronger properties

- Sylow subgroup (in a finite group)
- Hall subgroup in a finite solvable group