Subgroups — C₉×C₂₉×C₈₉ #37551187

Order 23229.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₈₉	C₃	1	1	yes	maximal, characteristic
2	C₂₉×C₈₉	C₉	1	1	yes	characteristic, direct product factor, Hall
3	C₉×C₈₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₈₉	C₃×C₂₉	1	1	yes	characteristic
5	C₉×C₂₉	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₈₉	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
7	C₃×C₂₉	C₃×C₈₉	1	1	yes	characteristic
8	C₂₉	C₉×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₉	C₂₉×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₃×C₂₉×C₈₉	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.