# Subgroup of finite group

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property imposed on theambient group: finite group

View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

## Definition

A **subgroup of finite group** is a subgroup inside a finite group.

## Relation with other properties

### Weaker properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

Finite subgroup | subgroup that is finite, i.e., its order is a finite number | |||

Subgroup of finite index | subgroup whose index is a finite number |