Subgroups — C₉×Dic₆₆₅ #37560880

Order 23940.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₇×C₉×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₆₆₅	C₃	1	1	yes	maximal, characteristic
3	C₅×C₇×C₉×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×Dic₁₃₃	—	5	1	no	maximal, Hall
5	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic
6	C₉×Dic₉₅	—	7	1	no	maximal, Hall
7	Dic₆₆₅	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₇×C₉×C₁₉	D₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₁₉	C₃×C₄	1	1	yes	characteristic
10	C₂×C₅×C₉×C₁₉	D₇	1	1	yes	characteristic
11	C₃×Dic₁₃₃	—	5	1	no	—
12	C₂×C₅×C₇×C₁₉	C₂×C₉	1	1	yes	characteristic
13	C₉×Dic₃₅	—	19	1	no	maximal, Hall
14	C₇×C₉×C₁₉	Dic₅	1	1	yes	characteristic, complemented, Hall
15	C₃×Dic₉₅	—	7	1	no	—
16	C₅×C₉×C₁₉	Dic₇	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic
18	C₉×Dic₁₉	—	35	1	no	Hall
19	C₅×C₇×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	C₂×C₅×C₇×C₉	D₁₉	1	1	yes	characteristic
21	C₂×C₃×C₅×C₁₉	C₃×D₇	1	1	yes	characteristic
22	Dic₁₃₃	—	5	1	no	Hall
23	C₃×Dic₃₅	—	19	1	no	—
24	C₃×C₇×C₁₉	C₃×Dic₅	1	1	yes	characteristic
25	Dic₉₅	—	7	1	no	Hall
26	C₂×C₉×C₁₉	D₃₅	1	1	yes	characteristic
27	C₅×C₇×C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₅×C₁₉	C₃×Dic₇	1	1	yes	characteristic
29	C₂×C₇×C₁₉	C₉×D₅	1	1	yes	characteristic
30	C₉×Dic₇	—	95	1	no	Hall
31	C₃×Dic₁₉	—	35	1	no	—
32	C₂×C₃×C₅×C₇	C₃×D₁₉	1	1	yes	characteristic
33	C₂×C₅×C₁₉	C₉×D₇	1	1	yes	characteristic
34	C₉×Dic₅	—	133	1	no	Hall
35	C₉×C₁₉	Dic₃₅	1	1	yes	characteristic, complemented, Hall
36	Dic₃₅	—	19	1	no	Hall
37	C₇×C₁₉	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇×C₉	D₉₅	1	1	yes	characteristic
39	C₂×C₃×C₁₉	C₃×D₃₅	1	1	yes	characteristic
40	C₃×C₅×C₇	C₃×Dic₁₉	1	1	yes	characteristic
41	C₅×C₁₉	C₉×Dic₇	1	1	yes	characteristic, complemented, Hall
42	C₂×C₅×C₉	D₁₃₃	1	1	yes	characteristic
43	C₃×Dic₇	—	95	1	no	—
44	Dic₁₉	—	35	1	no	Hall
45	C₂×C₅×C₇	C₉×D₁₉	1	1	yes	characteristic
46	C₇×C₉	Dic₉₅	1	1	yes	characteristic, complemented, Hall
47	C₃×Dic₅	—	133	1	no	—
48	C₃×C₁₉	C₃×Dic₃₅	1	1	yes	characteristic
49	C₅×C₉	Dic₁₃₃	1	1	yes	characteristic, complemented, Hall
50	C₂×C₃×C₇	C₃×D₉₅	1	1	yes	characteristic
51	C₂×C₁₉	C₉×D₃₅	1	1	yes	characteristic
52	C₄×C₉	—	665	1	no	Hall
53	C₅×C₇	C₉×Dic₁₉	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	C₃×D₁₃₃	1	1	yes	characteristic
55	Dic₇	—	95	1	no	Hall
56	C₃×C₇	C₃×Dic₉₅	1	1	yes	characteristic
57	Dic₅	—	133	1	no	Hall
58	C₁₉	C₉×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₉	D₆₆₅	1	1	yes	characteristic
60	C₃×C₅	C₃×Dic₁₃₃	1	1	yes	characteristic
61	C₂×C₇	C₉×D₉₅	1	1	yes	characteristic
62	C₃×C₄	—	665	1	no	—
63	C₂×C₅	C₉×D₁₃₃	1	1	yes	characteristic
64	C₉	Dic₆₆₅	1	1	yes	characteristic, direct product factor, Sylow
65	C₇	C₉×Dic₉₅	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	C₃×D₆₆₅	1	1	yes	characteristic
67	C₅	C₉×Dic₁₃₃	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	665	1	no	Sylow
69	C₃	C₃×Dic₆₆₅	1	1	yes	characteristic
70	C₂	C₉×D₆₆₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₉	D₆₆₅
commutator, hypocenter	C₅×C₇×C₁₉	C₄×C₉
Frattini	C₂×C₃	C₃×D₆₆₅
Fitting	C₂×C₅×C₇×C₉×C₁₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₅×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×C₉×C₁₉	C₄	semidirect
7. Dic₆₆₅	C₉	direct (N × H)
14. C₇×C₉×C₁₉	Dic₅	semidirect
16. C₅×C₉×C₁₉	Dic₇	semidirect
19. C₅×C₇×C₁₉	C₄×C₉	semidirect
27. C₅×C₇×C₉	Dic₁₉	semidirect
35. C₉×C₁₉	Dic₃₅	semidirect
37. C₇×C₁₉	C₉×Dic₅	semidirect
41. C₅×C₁₉	C₉×Dic₇	semidirect
46. C₇×C₉	Dic₉₅	semidirect
49. C₅×C₉	Dic₁₃₃	semidirect
53. C₅×C₇	C₉×Dic₁₉	semidirect
58. C₁₉	C₉×Dic₃₅	semidirect
64. C₉	Dic₆₆₅	direct (N × H)
65. C₇	C₉×Dic₉₅	semidirect
67. C₅	C₉×Dic₁₃₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×C₇×C₉×C₁₉	2
C₃×Dic₆₆₅	3
C₉×Dic₁₃₃	5
C₉×Dic₉₅	7
C₉×Dic₃₅	19

Subgroups — C9×Dic665 #37560880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×Dic₆₆₅ #37560880