Direct product-closed subgroup property

Definition with symbols
A subgroup property $$p$$ is termed direct product-closed if, given a nonempty indexing set $$I$$, and a collection of group-subgroup pairs $$H_i \le G_i$$ for $$i \in I$$, such that each $$H_i$$ satisfies $$p$$ as a subgroup of $$G_i$$, then the direct product of the $$H_i$$s satisfies $$p$$ via its natural embedding in the direct product of $$G_i$$s.