/* maximal subgroup list production */

ListMaximals := function (G, ParentName, L)
  X := []; Names := []; Orders := []; Index := [];
    for i in [1..#L] do
      if assigned L[i]`Parent and L[i]`Parent eq ParentName and #L[i]`generators gt 0 then 
         F := Parent (L[i]`generators[1]);
         a := F.1; b := F.2;
         f := hom <F -> G | [G.1, G.2]>;
         images := [f (w): w in L[i]`generators];
         X[#X + 1] := sub <G | images>;
         Names[#Names + 1] := L[i]`Name;
         Orders[#Orders + 1] := L[i]`Order;
         Index[#Index + 1] := L[i]`Index;
      end if;
   end for;
   return X, Names, Orders, Index;
end function;