Subgroups — C₇⋊(C₉⋊#10596817) #49141283

Order 36540.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₉×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#10596817)	—	3	1	no	maximal
3	C₅×C₇×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇⋊(C₉⋊#1181)	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇×D₂₉	D₃	1	1	yes	characteristic
6	C₉⋊#10596817	—	7	1	no	maximal, Hall
7	C₇⋊#10596817	—	9	1	no	Hall
8	C₇×C₉×D₂₉	D₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₂₉	Dic₃	1	1	yes	characteristic
10	C₅×C₉×D₂₉	D₇	1	1	yes	characteristic
11	C₃⋊(C₇⋊#1181)	—	15	1	no	—
12	C₅×C₇×D₂₉	D₉	1	1	yes	characteristic
13	C₇×C₉×C₂₉	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₃⋊#10596817	—	21	1	no	—
15	C₅×C₉×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
16	Dic₃₁₅	—	29	1	no	maximal, Hall
17	C₃×C₇×D₂₉	D₁₅	1	1	yes	characteristic
18	C₉⋊#1181	—	35	1	no	Hall
19	C₅×C₇×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅×D₂₉	D₂₁	1	1	yes	characteristic
21	C₇⋊#1181	—	45	1	no	Hall
22	C₂×C₅×C₇×C₉	—	29	1	no	—
23	C₃×C₇×C₂₉	Dic₁₅	1	1	yes	characteristic
24	#10596817	—	63	1	no	Hall
25	C₉×D₂₉	D₃₅	1	1	yes	characteristic
26	C₃×C₅×C₂₉	Dic₂₁	1	1	yes	characteristic
27	Dic₁₀₅	—	87	1	no	—
28	C₇×D₂₉	D₄₅	1	1	yes	characteristic
29	C₃⋊#1181	—	105	1	no	—
30	C₅×C₇×C₉	#1181	1	1	yes	characteristic, complemented, Hall
31	C₅×D₂₉	D₆₃	1	1	yes	characteristic
32	C₉×C₂₉	Dic₃₅	1	1	yes	characteristic, complemented, Hall
33	Dic₆₃	—	145	1	no	Hall
34	C₂×C₃×C₅×C₇	—	29	1	no	—
35	C₇×C₂₉	Dic₄₅	1	1	yes	characteristic, complemented, Hall
36	Dic₄₅	—	203	1	no	Hall
37	C₃×D₂₉	D₁₀₅	1	1	yes	characteristic
38	C₅×C₂₉	Dic₆₃	1	1	yes	characteristic, complemented, Hall
39	Dic₃₅	—	261	1	no	Hall
40	C₂×C₇×C₉	—	29	1	no	—
41	#1181	—	315	1	no	Hall
42	C₃×C₅×C₇	C₃⋊#1181	1	1	yes	characteristic
43	C₂×C₅×C₉	—	29	1	no	—
44	C₃×C₂₉	Dic₁₀₅	1	1	yes	characteristic
45	Dic₂₁	—	435	1	no	—
46	C₂×C₅×C₇	—	29	1	no	—
47	C₇×C₉	#10596817	1	1	yes	characteristic, complemented, Hall
48	Dic₁₅	—	609	1	no	—
49	D₂₉	D₃₁₅	1	1	yes	characteristic
50	C₅×C₉	C₇⋊#1181	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	—	29	1	no	—
52	Dic₉	—	1015	1	no	Hall
53	C₅×C₇	C₉⋊#1181	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	29	1	no	—
55	C₂₉	Dic₃₁₅	1	1	yes	characteristic, complemented, Sylow
56	Dic₇	—	1305	1	no	Hall
57	C₃×C₇	C₃⋊#10596817	1	1	yes	characteristic
58	Dic₅	—	1827	1	no	Hall
59	C₂×C₉	—	29	1	no	—
60	C₃×C₅	C₃⋊(C₇⋊#1181)	1	1	yes	characteristic
61	C₂×C₇	—	29	1	no	—
62	Dic₃	—	3045	1	no	—
63	C₂×C₅	—	29	1	no	—
64	C₉	C₇⋊#10596817	1	1	yes	characteristic, complemented, Sylow
65	C₇	C₉⋊#10596817	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	29	1	no	—
67	C₅	C₇⋊(C₉⋊#1181)	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	9135	1	no	Sylow
69	C₃	C₃⋊(C₇⋊#10596817)	1	1	yes	characteristic
70	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₇×C₉×C₂₉	C₄
Frattini	C₃	C₃⋊(C₇⋊#10596817)
socle	C₃×C₅×C₇×C₂₉	Dic₃
prime radical	C₃×C₅×C₇×D₂₉	D₃
cosocle	C₅×C₇×C₉×D₂₉	C₂
LCS	G ▷ C₅×C₇×C₉×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×C₉×C₂₉	C₄	semidirect
13. C₇×C₉×C₂₉	Dic₅	semidirect
15. C₅×C₉×C₂₉	Dic₇	semidirect
19. C₅×C₇×C₂₉	Dic₉	semidirect
30. C₅×C₇×C₉	#1181	semidirect
32. C₉×C₂₉	Dic₃₅	semidirect
35. C₇×C₂₉	Dic₄₅	semidirect
38. C₅×C₂₉	Dic₆₃	semidirect
47. C₇×C₉	#10596817	semidirect
50. C₅×C₉	C₇⋊#1181	semidirect
53. C₅×C₇	C₉⋊#1181	semidirect
55. C₂₉	Dic₃₁₅	semidirect
64. C₉	C₇⋊#10596817	semidirect
65. C₇	C₉⋊#10596817	semidirect
67. C₅	C₇⋊(C₉⋊#1181)	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₉×D₂₉	2
C₃⋊(C₇⋊#10596817)	3
C₇⋊(C₉⋊#1181)	5
C₉⋊#10596817	7
Dic₃₁₅	29

Subgroups — C7⋊(C9⋊#10596817) #49141283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊(C₉⋊#10596817) #49141283