Is there an established name for the system of all orbit of all subgroups of transitive permutation group $G$? Or, at least, was this or equivalent concept examined in a some book/article?
For instance, the cyclic group $ G=C_{6} $ has an unique orbit $ \{0,1,2,3,4,5\} $, but $G$ contain also subgroups with orbits $\{0\},\{1\},\{2\},\{3\},\{4\},\{5\}$ and $ \{0,2,4\},\{1,3,5\} $
In general, this does not the same as a set of blocks $G$