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 $G$

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    $\begingroup$ This doesn't answer your question but the orbits of any normal subgroup form a block system. $\endgroup$ – Derek Holt Aug 9 '18 at 9:04
  • $\begingroup$ Yes. But for the efficient design of specific biomedical experiments, it will be important to know the orbits of all subgroups. Maybe. $\endgroup$ – Slepecky Mamut Aug 9 '18 at 9:22

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