Subgroup of finite group

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