For example, to find the Hall divisors of 60, its prime power factorization is 22 × 3 × 5, so one takes any product of 3, 22 = 4, and 5.
Moreover, any subgroup whose order is a product of primes in π is contained in some Hall π-subgroup.
More precisely, fix a minimal normal subgroup A, which is either a π-group or a π′-group as G is π-separable.
This is a generalization of Burnside's theorem that any group whose order is of the form paqb for primes p and q is solvable, because Sylow's theorem implies that all Hall subgroups exist.
If we have a Sylow system, then the subgroup generated by the groups Sp for p in π is a Hall π-subgroup.