Subgroup whose center is contained in the center of the whole group

Definition
The notion of subgroup whose center is contained in the center of the whole group has the following equivalent definitions:

Extreme examples

 * The trivial subgroup in any group satisfies this property.
 * Every group satisfies this property in itself.

High occurrence examples

 * If the whole group is an abelian group, every subgroup satisfies the property.
 * A centerless group satisfies this property as a subgroup in any bigger group.