Originally Posted by

**alunw** In the first place you need to specify that N1,N2,etc is the collection of ALL normal subgroups of G that are subgroups of H because if not I can certainly pick specific collections that will disprove your claim. Also you need to decide whether H is a proper subgroup of G, and whether the word "proper" should be inserted before "subgroups of H" when limiting the collection. Presumably it is not given that H itself is a normal subgroup of G.

Then you might have a conjecture which it would take me some time to come up with a counter-example for, and if it took a really long time, I might start to believe it could be true, but, since my knowledge of group theory is more practical than theoretical I would probably have a lot of trouble proving it.

What grounds do you have for believing your claim? If it is a known theorem then please provide a reference.