Subgroups — C₉×C₇⋊#10596817 #49141259

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	C₃	1	1	yes	maximal, characteristic
3	C₅×C₇×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉×C₇⋊#1181	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇×D₂₉	C₂×C₃	1	1	yes	characteristic
6	C₉×#10596817	—	7	1	no	maximal, Hall
7	C₇⋊#10596817	C₉	1	1	yes	characteristic, direct product factor, Hall
8	C₇×C₉×D₂₉	D₅	1	1	yes	characteristic
9	C₃×C₅×C₇×C₂₉	C₃×C₄	1	1	yes	characteristic
10	C₅×C₉×D₂₉	D₇	1	1	yes	characteristic
11	C₃×C₇⋊#1181	—	5	1	no	—
12	C₅×C₇×D₂₉	C₂×C₉	1	1	yes	characteristic
13	C₇×C₉×C₂₉	Dic₅	1	1	yes	characteristic, complemented, Hall
14	C₃×#10596817	—	7	1	no	—
15	C₅×C₉×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₉×Dic₃₅	—	29	1	no	maximal, Hall
17	C₃×C₇×D₂₉	C₃×D₅	1	1	yes	characteristic
18	C₉×#1181	—	35	1	no	Hall
19	C₅×C₇×C₂₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₅×D₂₉	C₃×D₇	1	1	yes	characteristic
21	C₇⋊#1181	—	5	1	no	Hall
22	C₂×C₅×C₇×C₉	—	29	1	no	—
23	C₃×C₇×C₂₉	C₃×Dic₅	1	1	yes	characteristic
24	#10596817	—	7	1	no	Hall
25	C₉×D₂₉	D₃₅	1	1	yes	characteristic
26	C₃×C₅×C₂₉	C₃×Dic₇	1	1	yes	characteristic
27	C₃×Dic₃₅	—	29	1	no	—
28	C₇×D₂₉	C₉×D₅	1	1	yes	characteristic
29	C₃×#1181	—	35	1	no	—
30	C₅×C₇×C₉	#1181	1	1	yes	characteristic, complemented, Hall
31	C₅×D₂₉	C₉×D₇	1	1	yes	characteristic
32	C₉×C₂₉	Dic₃₅	1	1	yes	characteristic, complemented, Hall
33	C₉×Dic₇	—	145	1	no	Hall
34	C₂×C₃×C₅×C₇	—	29	1	no	—
35	C₇×C₂₉	C₉×Dic₅	1	1	yes	characteristic, complemented, Hall
36	C₉×Dic₅	—	203	1	no	Hall
37	C₃×D₂₉	C₃×D₃₅	1	1	yes	characteristic
38	C₅×C₂₉	C₉×Dic₇	1	1	yes	characteristic, complemented, Hall
39	Dic₃₅	—	29	1	no	Hall
40	C₂×C₇×C₉	—	29	1	no	—
41	#1181	—	35	1	no	Hall
42	C₃×C₅×C₇	C₃×#1181	1	1	yes	characteristic
43	C₂×C₅×C₉	—	29	1	no	—
44	C₃×C₂₉	C₃×Dic₃₅	1	1	yes	characteristic
45	C₃×Dic₇	—	145	1	no	—
46	C₂×C₅×C₇	—	29	1	no	—
47	C₇×C₉	#10596817	1	1	yes	characteristic, complemented, Hall
48	C₃×Dic₅	—	203	1	no	—
49	D₂₉	C₉×D₃₅	1	1	yes	characteristic
50	C₅×C₉	C₇⋊#1181	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	—	29	1	no	—
52	C₄×C₉	—	1015	1	no	Hall
53	C₅×C₇	C₉×#1181	1	1	yes	characteristic, complemented, Hall
54	C₂×C₃×C₅	—	29	1	no	—
55	C₂₉	C₉×Dic₃₅	1	1	yes	characteristic, complemented, Sylow
56	Dic₇	—	145	1	no	Hall
57	C₃×C₇	C₃×#10596817	1	1	yes	characteristic
58	Dic₅	—	203	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	C₃×C₄	—	1015	1	no	—
63	C₂×C₅	—	29	1	no	—
64	C₉	C₇⋊#10596817	1	1	yes	characteristic, direct product factor, Sylow
65	C₇	C₉×#10596817	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	29	1	no	—
67	C₅	C₉×C₇⋊#1181	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	1015	1	no	Sylow
69	C₃	C₃×C₇⋊#10596817	1	1	yes	characteristic
70	C₂	—	29	1	no	—

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

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×C₉×C₂₉	C₄	semidirect
7. C₇⋊#10596817	C₉	direct (N × H)
13. C₇×C₉×C₂₉	Dic₅	semidirect
15. C₅×C₉×C₂₉	Dic₇	semidirect
19. C₅×C₇×C₂₉	C₄×C₉	semidirect
30. C₅×C₇×C₉	#1181	semidirect
32. C₉×C₂₉	Dic₃₅	semidirect
35. C₇×C₂₉	C₉×Dic₅	semidirect
38. C₅×C₂₉	C₉×Dic₇	semidirect
47. C₇×C₉	#10596817	semidirect
50. C₅×C₉	C₇⋊#1181	semidirect
53. C₅×C₇	C₉×#1181	semidirect
55. C₂₉	C₉×Dic₃₅	semidirect
64. C₉	C₇⋊#10596817	direct (N × H)
65. C₇	C₉×#10596817	semidirect
67. C₅	C₉×C₇⋊#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
C₉×C₇⋊#1181	5
C₉×#10596817	7
C₉×Dic₃₅	29

Subgroups — C9×C7⋊#10596817 #49141259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×C₇⋊#10596817 #49141259