Finite p-group with cyclic maximal subgroup

Definition
A finite $$p$$-group with cyclic maximal subgroup is a finite $$p$$-group (i.e., a group of prime power order where the underlying prime is $$p$$) if it contains a cyclic subgroup of index $$p$$. If the group has order $$p^n$$, the cyclic subgroup has order $$p^{n-1}$$.