Is the external direct product of subgroups a subgroup?

[wakko101]

If A and B are groups, then A x B is a group...does the same hold for subgroups? i.e. if A' is a subgroup of A and B' for B, then is A' x B' a subgroup of A x B?

Cheers,
W. =)

 

[Tinyboss]

Well, does it contain the identity? Is it closed under multiplication (componentwise)? Inverses?