Coset

If $H$ is a subgroup of $G$ and $g$ lies in $G$, then

• $gH$ is a left coset
• $Hg$ is a right coset

Each coset is a translated copy of the subgroup.

In finite groups, cosets partition the whole group and each coset has the same size as $H$.

One-line intuition

A coset is what you get by shifting a subgroup through the group.