# Category:Index of Subgroups

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This category contains results about **Index of Subgroups**.

Definitions specific to this category can be found in Definitions/Index of Subgroups.

Let $G$ be a group.

Let $H$ be a subgroup of $G$.

The **index of $H$ (in $G$)**, denoted $\index G H$, is the cardinality of the left (or right) coset space $G / H$.

### Finite Index

If $G / H$ is a finite set, then $\index G H$ is **finite**, and $H$ is **of finite index** in $G$.

### Infinite Index

If $G / H$ is an infinite set, then $\index G H$ is **infinite**, and $H$ is **of infinite index** in $G$.

## Subcategories

This category has the following 3 subcategories, out of 3 total.

## Pages in category "Index of Subgroups"

The following 8 pages are in this category, out of 8 total.