Dear Avital and dear gap-forum,
no, I mean to look for the subgroups, of G x H, whose projections onto G
and H are in the known lists of the self-normalized subgroups (such
subgroups don't need to be subdirect products). This may be
computationally easier that looking for all the subgroups and then testing
whether a subgroup is self-normalized. Of course, you will need some
accuracy in preparing a Gap program to do that.
Greetings,
Marco

Dear Marco,

Thank you. I didn't think of that. If I understand correctly, then it is
enough to find the subdirect products of all M and N such that M is
self-normalized in G and N is self-normalized in H.

Still, I do not see how that could give me a more efficient way of
calculating the set of self-normalized subgroups of G x H. I could not find
a way to calculate the set of subdirect products of two groups.

Thanks,
Avital.