ENHANCE: Use TOM data also for subgroups of almost simple.

Also avoid pc isom in NormalizerParemtSA if the task is pathetic anyhow.

lib/gpprmsya.gi

@@ -1365,7 +1365,7 @@ syll, act, typ, sel, bas, wdom, comp, lperm, other, away, i, j,b0,opg,bp;
   if not issym then 
     pg:=AlternatingSubgroup(pg);
   fi;
-  if IsSolvableGroup(pg) then
+  if (Size(pg)/Size(u))>10000 and IsSolvableGroup(pg) then
     perm:=IsomorphismPcGroup(pg);
     pg:=PreImage(perm,Normalizer(Image(perm,pg),Image(perm,u)));
   fi;

lib/grplatt.gi

@@ -2806,6 +2806,23 @@ InstallGlobalFunction("SubgroupsTrivialFitting",function(G)
   local s,a,n,fac,iso,types,t,p,i,map,go,gold,nf,tom,sub,len;
 
   n:=DirectFactorsFittingFreeSocle(G);
+
+  # is it almost simple and stored?
+  if Length(n)=1 then
+    tom:=TomDataAlmostSimpleRecognition(G);
+    if tom<>fail and
+	ValueOption(NO_PRECOMPUTED_DATA_OPTION)<>true then
+      Info(InfoPerformance,2,"Using Table of Marks Library");
+      go:=ImagesSource(tom[1]);
+      tom:=tom[2];
+      Info(InfoLattice,1, "Fetching subgroups of simple ",
+	  Identifier(tom)," from table of marks");
+      len:=LengthsTom(tom);
+      sub:=List([1..Length(len)],x->RepresentativeTom(tom,x));
+      return sub;
+    fi;
+  fi;
+
   s:=Socle(G);
 
   a:=TrivialSubgroup(G);