Normal subgroup whose automorphism group is abelian

Statement
A subgroup $$H$$ of a group $$G$$ is termed an normal subgroup whose automorphism group is abelian of $$G$$ if it satisfies both these conditions:


 * $$H$$ is a normal subgroup of $$G$$.
 * $$H$$ is a group whose automorphism group is abelian: the automorphism group $$\operatorname{Aut}(H)$$ is an abelian group.