I am trying to do the following in GAP:
$G$ is a given group of order $2^{19}$ and $H$ is a subgroup (but not normal) of $G$ of order $2^{15}$. My aim is to find a representative, say $A$, for each of the conjugacy classes of subgroups of $G$ such that $A\not \subseteq H$.
I tried the following in GAP:
Filtered(List(ConjugacyClassesSubgroups(G),y->Representative(y)),x-> not IsSubset(H,x));
But since the group $G$ is very large, this is practically consuming all memory and taking infinite time.
Is there any other way I can use in GAP to overcome the situation? Any help will be greatly appreciated.
Pasteable descriptions of the groups are given below:
G:=PcGroupCode(8131228045254952190140857101752853639830107614464014650851209692873866777500298856184821519032105153814704456451033872646102911\ 4739105578388317100628340028962041397792456162362856790287035433614614445724770154742066261363277062070491534257341845886065760\ 9680893404023629145887435702630822420577559446012280802787875613789812926252815799729640075785252102776099420886867267522205122\ 48, 2^19);
H:= PcGroupCode(63259843161787529259663104123028807771949615600420226627717675945661695659171\ 01261938932942099569279276682015405496285786548265341726439956203516708900070\ 21155088492850709644054534706704466392622607233970153096962475626323, 2^15);
Thanks