//First, we check 5S4.

R:=IntegerRing(5);
GL5:=GeneralLinearGroup(2,R);
H:=sub<GL5|[0,3,3,4],[2,0,0,2],[3,0,4,4]>;
SubH:=Subgroups(H: IndexEqual:=6);
S2:=SubH[2]`subgroup;
ClassS2:=Class(GL5,S2);
ClassS2;

//Next, we check 13S4.

R:=IntegerRing(13);
GL13:=GeneralLinearGroup(2,R);
H:=sub<GL13|[3,0,12,9], [2,0,0,2],[9,5,0,6]>;
SubH:=Subgroups(H: IndexEqual:=6);
S4:=SubH[4]`subgroup;
ClassS4:=Class(GL13,S4);
ClassS4;