Subgroups — C₉×D₁₇₀₅ #44501654

Order 30690.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₉×C₁₁×C₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×D₁₇₀₅	C₃	1	1	yes	maximal, characteristic
3	C₉×D₃₄₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₁×C₃₁	C₂×C₃	1	1	yes	characteristic
5	D₁₇₀₅	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₉×C₁₁×C₃₁	D₅	1	1	yes	characteristic, complemented, Hall
7	C₉×D₁₅₅	—	11	1	no	maximal, Hall
8	C₃×D₃₄₁	—	5	1	no	—
9	C₅×C₁₁×C₃₁	C₂×C₉	1	1	yes	characteristic, complemented, Hall
10	C₅×C₉×C₃₁	D₁₁	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₁×C₃₁	C₃×D₅	1	1	yes	characteristic
12	C₉×D₅₅	—	31	1	no	maximal, Hall
13	C₃×D₁₅₅	—	11	1	no	—
14	D₃₄₁	—	5	1	no	Hall
15	C₉×D₃₁	—	55	1	no	Hall
16	C₅×C₉×C₁₁	D₃₁	1	1	yes	characteristic, complemented, Hall
17	C₃×C₅×C₃₁	C₃×D₁₁	1	1	yes	characteristic
18	C₁₁×C₃₁	C₉×D₅	1	1	yes	characteristic, complemented, Hall
19	C₃×D₅₅	—	31	1	no	—
20	D₁₅₅	—	11	1	no	Hall
21	C₉×C₃₁	D₅₅	1	1	yes	characteristic, complemented, Hall
22	C₉×D₁₁	—	155	1	no	Hall
23	C₃×D₃₁	—	55	1	no	—
24	C₃×C₅×C₁₁	C₃×D₃₁	1	1	yes	characteristic
25	C₅×C₃₁	C₉×D₁₁	1	1	yes	characteristic, complemented, Hall
26	D₅₅	—	31	1	no	Hall
27	C₉×C₁₁	D₁₅₅	1	1	yes	characteristic, complemented, Hall
28	C₃×C₃₁	C₃×D₅₅	1	1	yes	characteristic
29	C₉×D₅	—	341	1	no	Hall
30	C₃×D₁₁	—	155	1	no	—
31	D₃₁	—	55	1	no	Hall
32	C₅×C₁₁	C₉×D₃₁	1	1	yes	characteristic, complemented, Hall
33	C₅×C₉	D₃₄₁	1	1	yes	characteristic, complemented, Hall
34	C₃×C₁₁	C₃×D₁₅₅	1	1	yes	characteristic
35	C₃₁	C₉×D₅₅	1	1	yes	characteristic, complemented, Sylow
36	C₃×D₅	—	341	1	no	—
37	D₁₁	—	155	1	no	Hall
38	C₂×C₉	—	1705	1	no	Hall
39	C₃×C₅	C₃×D₃₄₁	1	1	yes	characteristic
40	C₁₁	C₉×D₁₅₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	341	1	no	Hall
42	C₉	D₁₇₀₅	1	1	yes	characteristic, direct product factor, Sylow
43	C₂×C₃	—	1705	1	no	—
44	C₅	C₉×D₃₄₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	C₃×D₁₇₀₅	1	1	yes	characteristic
46	C₂	—	1705	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₉	D₁₇₀₅
commutator, hypocenter	C₅×C₁₁×C₃₁	C₂×C₉
Frattini	C₃	C₃×D₁₇₀₅
Fitting	C₅×C₉×C₁₁×C₃₁	C₂
socle, cosocle	C₃×C₅×C₁₁×C₃₁	C₂×C₃
prime radical	C₃×D₁₇₀₅	C₃
LCS	G ▷ C₅×C₁₁×C₃₁
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₅×C₉×C₁₁×C₃₁	C₂	semidirect
5. D₁₇₀₅	C₉	direct (N × H)
6. C₉×C₁₁×C₃₁	D₅	semidirect
9. C₅×C₁₁×C₃₁	C₂×C₉	semidirect
10. C₅×C₉×C₃₁	D₁₁	semidirect
16. C₅×C₉×C₁₁	D₃₁	semidirect
18. C₁₁×C₃₁	C₉×D₅	semidirect
21. C₉×C₃₁	D₅₅	semidirect
25. C₅×C₃₁	C₉×D₁₁	semidirect
27. C₉×C₁₁	D₁₅₅	semidirect
32. C₅×C₁₁	C₉×D₃₁	semidirect
33. C₅×C₉	D₃₄₁	semidirect
35. C₃₁	C₉×D₅₅	semidirect
40. C₁₁	C₉×D₁₅₅	semidirect
42. C₉	D₁₇₀₅	direct (N × H)
44. C₅	C₉×D₃₄₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₉×C₁₁×C₃₁	2
C₃×D₁₇₀₅	3
C₉×D₃₄₁	5
C₉×D₁₅₅	11
C₉×D₅₅	31

Subgroups — C9×D1705 #44501654

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×D₁₇₀₅ #44501654