Subgroups — C₅×C₇⋊(C₉⋊#1181) #49141267

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	C₅×C₃⋊(C₇⋊#1181)	—	3	1	no	maximal
3	C₅×C₇×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇⋊(C₉⋊#1181)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇×D₂₉	D₃	1	1	yes	characteristic
6	C₅×C₉⋊#1181	—	7	1	no	maximal, Hall
7	C₅×C₇⋊#1181	—	9	1	no	Hall
8	C₇×C₉×D₂₉	C₂×C₅	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)	—	3	1	no	—
12	C₅×C₇×D₂₉	D₉	1	1	yes	characteristic
13	C₇×C₉×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented, Hall
14	C₅×C₃⋊#1181	—	21	1	no	—
15	C₅×C₉×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₅×Dic₆₃	—	29	1	no	maximal, Hall
17	C₃×C₇×D₂₉	C₅×D₃	1	1	yes	characteristic
18	C₉⋊#1181	—	7	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	—	9	1	no	Hall
22	C₂×C₅×C₇×C₉	—	29	1	no	—
23	C₃×C₇×C₂₉	C₅×Dic₃	1	1	yes	characteristic
24	C₅×#1181	—	63	1	no	Hall
25	C₉×D₂₉	C₅×D₇	1	1	yes	characteristic
26	C₃×C₅×C₂₉	Dic₂₁	1	1	yes	characteristic
27	C₅×Dic₂₁	—	87	1	no	—
28	C₇×D₂₉	C₅×D₉	1	1	yes	characteristic
29	C₃⋊#1181	—	21	1	no	—
30	C₅×C₇×C₉	#1181	1	1	yes	characteristic, complemented, Hall
31	C₅×D₂₉	D₆₃	1	1	yes	characteristic
32	C₉×C₂₉	C₅×Dic₇	1	1	yes	characteristic, complemented, Hall
33	Dic₆₃	—	29	1	no	Hall
34	C₂×C₃×C₅×C₇	—	29	1	no	—
35	C₇×C₂₉	C₅×Dic₉	1	1	yes	characteristic, complemented, Hall
36	C₅×Dic₉	—	203	1	no	Hall
37	C₃×D₂₉	C₅×D₂₁	1	1	yes	characteristic
38	C₅×C₂₉	Dic₆₃	1	1	yes	characteristic, complemented, Hall
39	C₅×Dic₇	—	261	1	no	Hall
40	C₂×C₇×C₉	—	29	1	no	—
41	#1181	—	63	1	no	Hall
42	C₃×C₅×C₇	C₃⋊#1181	1	1	yes	characteristic
43	C₂×C₅×C₉	—	29	1	no	—
44	C₃×C₂₉	C₅×Dic₂₁	1	1	yes	characteristic
45	Dic₂₁	—	87	1	no	—
46	C₂×C₅×C₇	—	29	1	no	—
47	C₇×C₉	C₅×#1181	1	1	yes	characteristic, complemented, Hall
48	C₅×Dic₃	—	609	1	no	—
49	D₂₉	C₅×D₆₃	1	1	yes	characteristic
50	C₅×C₉	C₇⋊#1181	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	—	29	1	no	—
52	Dic₉	—	203	1	no	Hall
53	C₅×C₇	C₉⋊#1181	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	29	1	no	—
55	C₂₉	C₅×Dic₆₃	1	1	yes	characteristic, complemented, Sylow
56	Dic₇	—	261	1	no	Hall
57	C₃×C₇	C₅×C₃⋊#1181	1	1	yes	characteristic
58	C₄×C₅	—	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	—	609	1	no	—
63	C₂×C₅	—	29	1	no	—
64	C₉	C₅×C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
65	C₇	C₅×C₉⋊#1181	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	29	1	no	—
67	C₅	C₇⋊(C₉⋊#1181)	1	1	yes	characteristic, direct product factor, Sylow
68	C₄	—	1827	1	no	Sylow
69	C₃	C₅×C₃⋊(C₇⋊#1181)	1	1	yes	characteristic
70	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₇⋊(C₉⋊#1181)
commutator, hypocenter	C₇×C₉×C₂₉	C₄×C₅
Frattini	C₃	C₅×C₃⋊(C₇⋊#1181)
Fitting	C₅×C₇×C₉×C₂₉	C₄
socle	C₃×C₅×C₇×C₂₉	Dic₃
prime radical	C₃×C₅×C₇×D₂₉	D₃
cosocle	C₇×C₉×D₂₉	C₂×C₅
LCS	G ▷ C₇×C₉×C₂₉
UCS	C₁ ◁ C₅

Complements

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

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

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
C₅×C₃⋊(C₇⋊#1181)	3
C₇⋊(C₉⋊#1181)	5
C₅×C₉⋊#1181	7
C₅×Dic₆₃	29

Subgroups — C5×C7⋊(C9⋊#1181) #49141267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₇⋊(C₉⋊#1181) #49141267