ENHANCE: Small improvements to descending subgroup iterator

lib/grplatt.gi

@@ -3429,6 +3429,14 @@ local d,ind,i,ma,ab,a,p,b,c,e,n;
       elif IsPrimeInt(ind) then return d;fi;
     fi;
   fi;
+  if Size(G)>1 and SIZE_OBJ(G.1)*Length(GeneratorsOfGroup(G))>10000 then
+    a:=SmallGeneratingSet(G);
+    if Length(a)<Length(GeneratorsOfGroup(G))-1 then
+      b:=Size(G);
+      G:=Group(a);
+      SetSize(G,b);
+    fi;
+  fi;
   return G;
 end);
 
@@ -3451,7 +3459,7 @@ local divs,limit,mode,l,process,done,bound,maxer,prime;
   maxer:=function(sub)
   local m,a,b,len,sz,i,j,k,r,tb;
     #Print("call maxer for ",Size(sub)," |l|=",Length(l)," |process|=",Length(process),"\n");
-    if bound>1 and 2^(Length(AbelianInvariants(sub))-3)>bound then
+    if bound>1 and prime^(Length(AbelianInvariants(sub))-3)>bound then
       i:=0;
       repeat
         m:=BoundedIndexAbelianized(G,sub,bound*prime^i);
@@ -3460,7 +3468,19 @@ local divs,limit,mode,l,process,done,bound,maxer,prime;
       if Size(m)^2<Size(sub) then
         m:=MaximalSubgroupClassReps(sub:cheap:=false);
       else
-        m:=[m];
+        # add maxes not containing derived
+        if IsSolvableGroup(sub) then
+          i:=IsomorphismPcGroup(sub);
+          a:=DerivedSubgroup(Image(i));
+          a:=Filtered(MaximalSubgroupClassReps(Image(i)),
+            x->not IsSubset(x,a));
+          a:=List(a,x->PreImage(i,x));
+        else
+          a:=DerivedSubgroup(sub);
+          a:=Filtered(MaximalSubgroupClassReps(sub),
+            x->not IsSubset(x,a));
+        fi;
+        m:=Concatenation([m],a);
       fi;
     else
       m:=MaximalSubgroupClassReps(sub:cheap:=false);