Normal subgroups of a non-albelian group

[futurebird]

I have the table for a non-albelian group. I know the subgroups of this group. I need to know which subgroups are normal. How can I tell?

 

[latentcorpse]

http://mathworld.wolfram.com/NormalSubgroup.html

 

[futurebird]

So you need to check every single entry?

 

[latentcorpse]

Well some of these groups will be infinite so that's impossible but for finite groups I guess it would work but would be a tad tedious. We're looking for a more generic proof.

Consider the following,
Let $H \subset G$. The group $G$ is abelian and therefore has commutivity of elements by design i.e.
$ah=ha$
However, this holds $\forall h \in H$ and $\forall a \in G$
$\Rightarrow aH=Ha \Rightarrow a^{-1}aH=a^{-1}Ha$
$a^{-1}Ha=H$

 

[futurebird]

But my group isn't abelian.

 

[latentcorpse]

haha i am being silly...let me reconsider

 

[latentcorpse]

could u post the question?

 

[futurebird]

It's for a take-home final so I'm trying to ask for help on the concepts without doing that. I'll post it after I turn it in.