Examples
- Any Sylow subgroup of a group is a Hall subgroup.
- If G = A5, the only simple group of order 60, then 15 and 20 are Hall divisors of the order of G, but G has no subgroups of these orders.
- The simple group of order 168 has two different conjugacy classes of Hall subgroups of order 24 (though they are conjugate under an outer automorphism of G).
- The simple group of order 660 has two Hall subgroups of order 12 that are not isomorphic.
Read more about this topic: Hall Subgroup
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