Subgroups — C₅₉×C₆₁⋊C₉ #44569263

Order 32391.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₉×C₆₁	C₃	1	1	yes	maximal, characteristic
2	C₅₉×C₆₁	C₉	1	1	yes	characteristic, complemented, Hall
3	C₆₁⋊C₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₉×C₅₉	—	61	1	no	maximal, Hall
5	C₃×C₆₁	C₃×C₅₉	1	1	yes	characteristic
6	C₃×C₅₉	C₆₁⋊C₃	1	1	yes	characteristic
7	C₆₁	C₉×C₅₉	1	1	yes	characteristic, complemented, Sylow
8	C₅₉	C₆₁⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	—	61	1	no	Sylow
10	C₃	C₅₉×C₆₁⋊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.