Complement of a normal subgroup
= Complement of a normal subgroup
{title2=$G=NH,\quad N\cap H=1$}
= Group complement
{synonym}
A group complement to a <normal subgroup> $N\triangleleft G$ is a <subgroup> $H$ with $G=NH$ and $N\cap H=1$. Projection identifies $H$ with $G/N$, and conjugation gives $G=N\rtimes H$. This is a <subgroup> notion, not the set-theoretic complement of $N$.