Subgroups — C₁₃⋊C₉×D₈₅ #34091037

Order 19890.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₃×D₈₅	C₃	1	1	yes	maximal, characteristic
3	D₁₇×C₁₃⋊C₉	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃×D₈₅	C₉	1	1	yes	characteristic, complemented, Hall
6	C₁₇×C₁₃⋊C₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₉×D₈₅	—	13	1	no	maximal, Hall
8	C₃×C₁₃×D₁₇	—	5	1	no	—
9	D₅×C₁₃⋊C₉	—	17	1	no	maximal, Hall
10	C₅×C₁₃×C₁₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
11	C₅×C₉×C₁₇	—	13	1	no	Hall
12	C₃×C₁₃×C₁₇	C₃×D₅	1	1	yes	characteristic
13	C₅×C₁₃⋊C₉	D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×D₈₅	C₁₃⋊C₃	1	1	yes	characteristic
15	C₁₃×D₁₇	—	5	1	no	Hall
16	C₃×D₅×C₁₃	—	17	1	no	—
17	C₉×D₁₇	—	65	1	no	Hall
18	C₃×C₅×C₁₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
19	C₂×C₁₃⋊C₉	—	85	1	no	Hall
20	C₁₃×C₁₇	C₉×D₅	1	1	yes	characteristic, complemented, Hall
21	C₃×C₅×C₁₃	C₃×D₁₇	1	1	yes	characteristic
22	D₈₅	C₁₃⋊C₉	1	1	yes	characteristic, direct product factor, Hall
23	C₉×C₁₇	—	13	1	no	Hall
24	D₅×C₁₃	—	17	1	no	Hall
25	C₁₃⋊C₉	D₈₅	1	1	yes	characteristic, direct product factor, Hall
26	C₃×D₁₇	—	5	1	no	—
27	C₉×D₅	—	221	1	no	Hall
28	C₅×C₁₇	C₂×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Hall
29	C₂×C₃×C₁₃	—	85	1	no	—
30	C₅×C₁₃	C₉×D₁₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₇	D₅×C₁₃⋊C₃	1	1	yes	characteristic
32	C₅×C₉	—	13	1	no	Hall
33	C₃×C₁₃	C₃×D₈₅	1	1	yes	characteristic
34	D₁₇	—	5	1	no	Hall
35	C₃×D₅	—	17	1	no	—
36	C₂×C₁₃	—	85	1	no	Hall
37	C₂×C₉	—	1105	1	no	Hall
38	C₁₇	D₅×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	D₁₇×C₁₃⋊C₃	1	1	yes	characteristic
40	C₁₃	C₉×D₈₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	17	1	no	Hall
42	C₉	—	13	1	no	Sylow
43	C₂×C₃	—	85	1	no	—
44	C₅	D₁₇×C₁₃⋊C₉	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₁₃⋊C₃×D₈₅	1	1	yes	characteristic
46	C₂	—	85	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₃⋊C₃×D₈₅
commutator, hypocenter	C₅×C₁₃×C₁₇	C₂×C₉
Fitting, socle, cosocle	C₃×C₅×C₁₃×C₁₇	C₂×C₃
prime radical	C₃×C₁₃×D₈₅	C₃
LCS	G ▷ C₅×C₁₃×C₁₇
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₇×C₁₃⋊C₉	C₂	semidirect
5. C₁₃×D₈₅	C₉	semidirect
6. C₁₇×C₁₃⋊C₉	D₅	semidirect
10. C₅×C₁₃×C₁₇	C₂×C₉	semidirect
13. C₅×C₁₃⋊C₉	D₁₇	semidirect
20. C₁₃×C₁₇	C₉×D₅	semidirect
22. D₈₅	C₁₃⋊C₉	direct (N × H)
25. C₁₃⋊C₉	D₈₅	direct (N × H)
28. C₅×C₁₇	C₂×C₁₃⋊C₉	semidirect
30. C₅×C₁₃	C₉×D₁₇	semidirect
38. C₁₇	D₅×C₁₃⋊C₉	semidirect
40. C₁₃	C₉×D₈₅	semidirect
44. C₅	D₁₇×C₁₃⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₇×C₁₃⋊C₉	2
C₃×C₁₃×D₈₅	3
D₁₇×C₁₃⋊C₉	5
C₉×D₈₅	13
D₅×C₁₃⋊C₉	17

Subgroups — C13⋊C9×D85 #34091037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₉×D₈₅ #34091037