We therefore thank the VolkswagenStiftung (Grant no. 93764 ) and the Royal Society (Grant code URF\R\180015) again for their financial support of this earlier work. For financial support during the more recent advances, we thank the DFG (Grant no. WA 3089/9-1) and again the Royal Society (Grant codes RGF\EA\181005 and URF\R\180015 ).

Partition backtrack is the current generic state of the art algorithm to search for subgroups of a given permutation group. We describe an improvement of partition backtrack for set stabilizers and intersections of subgroups by using orbital graphs. With extensive experiments we demonstrate that our methods improve performance of partition backtrack – in some cases by several orders of magnitude.