Subgroups — C₉×D₁₁₅₇ #35209694

Order 20826.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₁₃×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₁₅₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₁₃×C₈₉	C₂×C₃	1	1	yes	characteristic
4	D₁₁₅₇	C₉	1	1	yes	characteristic, direct product factor, Hall
5	C₉×D₈₉	—	13	1	no	maximal, Hall
6	C₁₃×C₈₉	C₂×C₉	1	1	yes	characteristic, complemented, Hall
7	C₉×C₈₉	D₁₃	1	1	yes	characteristic, complemented, Hall
8	C₃×D₈₉	—	13	1	no	—
9	C₃×C₈₉	C₃×D₁₃	1	1	yes	characteristic
10	C₉×D₁₃	—	89	1	no	maximal, Hall
11	D₈₉	—	13	1	no	Hall
12	C₉×C₁₃	D₈₉	1	1	yes	characteristic, complemented, Hall
13	C₈₉	C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×D₁₃	—	89	1	no	—
15	C₃×C₁₃	C₃×D₈₉	1	1	yes	characteristic
16	D₁₃	—	89	1	no	Hall
17	C₂×C₉	—	1157	1	no	Hall
18	C₁₃	C₉×D₈₉	1	1	yes	characteristic, complemented, Sylow
19	C₉	D₁₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	—	1157	1	no	—
21	C₃	C₃×D₁₁₅₇	1	1	yes	characteristic
22	C₂	—	1157	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.