Cyclic isomorph-containing subgroup

Definition
A subgroup $$H$$ of a group $$G$$ is termed a cyclic isomorph-containing subgroup if $$H$$ is a cyclic group and $$H$$ is an isomorph-containing subgroup of $$G$$, i.e., every subgroup of $$G$$ isomorphic to $$H$$ is contained in $$H$$.