Question: How to find subgroup of Sz?

i find that Suzuki group is very large, 

and finding subrgoup is still not solved 

and when find subgroup of suzuki group that is very slow

i would like to find two subgroup which are not isomorphric and then

prove a normaliser that make them isomorphric

with(GroupTheory):
G := SuzukiGroup();
IsFinite(G);
gorder := GroupOrder(G);
ifactor(gorder);
spg := SylowSubgroup(2, G);
IsAbelian(spg);
Elements(spg);
lprint(%);
H := Subgroup(Elements(G), spg);
N := Normaliser(G, spg);
#N := Normaliser(spg, G);
Elements(N);
lprint(%);
Elements(G);
H2 := Subgroup({[[5,2],[3,4]]}, G);
H2 := Subgroup(Elements(G), G);
elements2 := convert(Elements(G), 'list');
generators := map(ListTools:-Search, [Perm([[1,2,3]])], elements2);
H2 := Subgroup([52], G);
SubgroupMembership(H2, G);
H2 := Subgroup([3], G);
elist := Elements(H2);
AreConjugate(elist[2], elist[3], N); #N*elist[1]*N^(-1) = elist[2]
for ii from 1 to nops(elist) do
for jj from ii+1 to nops(elist) do
if AreIsomorphic(Group(elist[ii]),Group(elist[jj])) = false then
print("noniso");
print(ii);
print(jj);
end if:
od:
od:
AreConjugate(elist[8], elist[22], N); #N*elist[1]*N^(-1) = elist[2]

Please Wait...