originally published systems and their groups
newly computed systems and their groups
old system 0 [old Group=1,new Group=1] is isomorphic with new system 2 [Group=1] old system 1 [old Group=2,new Group=2] is isomorphic with new system 1 [Group=2] old system 2 [old Group=4,new Group=4] is isomorphic with new system 3 [Group=4]