Subgroups — C₉×D₂₃×C₅₉ #37567660

Order 24426.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₂₃×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₂₃×C₅₉	C₃	1	1	yes	maximal, characteristic
3	C₃×C₂₃×C₅₉	C₂×C₃	1	1	yes	characteristic
4	D₂₃×C₅₉	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₂₃×C₅₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
6	C₂×C₉×C₅₉	—	23	1	no	maximal, Hall
7	C₉×C₅₉	D₂₃	1	1	yes	characteristic, direct product factor, Hall
8	C₉×D₂₃	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₅₉	—	23	1	no	—
10	C₉×C₂₃	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅₉	C₃×D₂₃	1	1	yes	characteristic
12	C₃×D₂₃	C₃×C₅₉	1	1	yes	characteristic
13	C₂×C₅₉	—	23	1	no	Hall
14	C₃×C₂₃	C₂×C₃×C₅₉	1	1	yes	characteristic
15	C₅₉	C₉×D₂₃	1	1	yes	characteristic, direct product factor, Sylow
16	D₂₃	C₉×C₅₉	1	1	yes	characteristic, direct product factor, Hall
17	C₂₃	C₂×C₉×C₅₉	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₉	—	23	1	no	Hall
19	C₉	D₂₃×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	23	1	no	—
21	C₃	C₃×D₂₃×C₅₉	1	1	yes	characteristic
22	C₂	—	23	1	no	Sylow

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.