Subgroup-closed group property

Symbol-free definition
A group property is said to be subgroup-closed or S-closed if any subgroup of a group having the property also has the property.

Definition with symbols
A group property $$p$$ is said to be subgroup-closed or S-closed if whenever $$G$$ satisfies property $$p$$ and $$H$$ is a subgroup of $$G$$, $$H$$ must also satisfy property $$p$$.

Stronger metaproperties

 * SQ-closed group property
 * Quasivarietal group property
 * Varietal group property

Weaker metaproperties

 * Normal subgroup-closed group property