# Category:Examples of Use of Lagrange's Theorem (Group Theory)

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This category contains examples of Lagrange's Theorem (Group Theory).

Let $G$ be a finite group.

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

Then:

- $\order H$ divides $\order G$

where $\order G$ and $\order H$ are the order of $G$ and $H$ respectively.

In fact:

- $\index G H = \dfrac {\order G} {\order H}$

where $\index G H$ is the index of $H$ in $G$.

When $G$ is an infinite group, we can still interpret this theorem sensibly:

- A subgroup of finite index in an infinite group is itself an infinite group.

- A finite subgroup of an infinite group has infinite index.

## Pages in category "Examples of Use of Lagrange's Theorem (Group Theory)"

The following 4 pages are in this category, out of 4 total.

### L

- Lagrange's Theorem (Group Theory)/Examples
- Lagrange's Theorem (Group Theory)/Examples/Intersection of Subgroups of Order 25 and 36
- Lagrange's Theorem (Group Theory)/Examples/Order of Group with Subgroups of Order 25 and 36
- Lagrange's Theorem (Group Theory)/Examples/Order of Union of Subgroups of Order 16