TITLE: Normal subgroups of $S_4$
QUESTION [32 upvotes]: Can anyone tell me how to find all normal subgroups of the symmetric group $S_4$?
In particular are $H=\{e,(1 2)(3 4)\}$ and $K=\{e,(1 2)(3 4), (1 3)(2 4),(1 4)(2 3)\}$ normal subgroups?

REPLY [3 votes]: As suggested by Babak Sorouh, the answer can be found easily using GAP using the SONATA library.  Here's the code:
G:=SymmetricGroup(4);
S:=Filtered(Subgroups(G),H->IsNormal(G,H));
for H in S do
  Print(StructureDescription(H),"\n");
od;

So as to not spoil Arturo Magidin's answer, here's the output if I replace G:=SymmetricGroup(4); with G:=DihedralGroup(32); (the dihedral group of order $32$)
1
C2
C4
C8
D16
D16
C16
D32