# Subgroup of prime index

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 subgroup is said to be **of prime index** in a group if its index in the whole group is a prime number.

### Definition with symbols

A subgroup of a group is said to be **of prime index** if is a prime number.