Let $G$ be a group and $H$ be a subgroup. $H$ is normal, written $H \unlhd G$, if it is closed under conjugation, i.e. for any $g \in G$ and for all $a \in H$,
\[\conj_g a \in H.\]
All subgroups of an abelian group are normal.
Let $G$ be a group and $H$ be a subgroup. $H$ is normal, written $H \unlhd G$, if it is closed under conjugation, i.e. for any $g \in G$ and for all $a \in H$,
\[\conj_g a \in H.\]
All subgroups of an abelian group are normal.