Subgroups — C₅₃×C₆₇⋊C₉ #44544178

Order 31959.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₃×C₆₇	C₃	1	1	yes	maximal, characteristic
2	C₅₃×C₆₇	C₉	1	1	yes	characteristic, complemented, Hall
3	C₆₇⋊C₉	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉×C₅₃	—	67	1	no	maximal, Hall
5	C₃×C₆₇	C₃×C₅₃	1	1	yes	characteristic
6	C₃×C₅₃	C₆₇⋊C₃	1	1	yes	characteristic
7	C₆₇	C₉×C₅₃	1	1	yes	characteristic, complemented, Sylow
8	C₅₃	C₆₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	—	67	1	no	Sylow
10	C₃	C₅₃×C₆₇⋊C₃	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.