Subgroups — C₇⋊(C₉⋊#10596816) #49141280

Order 36540.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#10596816)	—	3	1	no	maximal
3	C₅×C₇×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₈₂₇	—	5	1	no	maximal, Hall
5	C₃×C₇×D₅×C₂₉	D₃	1	1	yes	characteristic
6	C₉⋊#10596816	—	7	1	no	maximal, Hall
7	C₇⋊#10596816	—	9	1	no	Hall
8	C₂×C₇×C₉×C₂₉	—	5	1	no	—
9	C₃×C₅×C₇×C₂₉	Dic₃	1	1	yes	characteristic
10	C₉×D₅×C₂₉	D₇	1	1	yes	characteristic
11	Dic₆₀₉	—	15	1	no	—
12	C₇×D₅×C₂₉	D₉	1	1	yes	characteristic
13	C₇×C₉×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
14	C₃⋊#10596816	—	21	1	no	—
15	C₅×C₉×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
16	C₇⋊(C₉⋊AGL(1,𝔽₅))	—	29	1	no	maximal, Hall
17	C₂×C₃×C₇×C₂₉	—	5	1	no	—
18	Dic₂₆₁	—	35	1	no	Hall
19	C₅×C₇×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
20	C₃×D₅×C₂₉	D₂₁	1	1	yes	characteristic
21	Dic₂₀₃	—	45	1	no	Hall
22	C₇×C₉×D₅	D₂₉	1	1	yes	characteristic
23	C₃×C₇×C₂₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
24	#10596816	—	63	1	no	Hall
25	C₂×C₉×C₂₉	—	5	1	no	—
26	C₃×C₅×C₂₉	Dic₂₁	1	1	yes	characteristic
27	C₃⋊(C₇⋊AGL(1,𝔽₅))	—	87	1	no	—
28	C₂×C₇×C₂₉	—	5	1	no	—
29	Dic₈₇	—	105	1	no	—
30	C₅×C₇×C₉	Dic₂₉	1	1	yes	characteristic, complemented, Hall
31	D₅×C₂₉	D₆₃	1	1	yes	characteristic
32	C₉×C₂₉	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
33	Dic₆₃	—	145	1	no	Hall
34	C₃×C₇×D₅	D₈₇	1	1	yes	characteristic
35	C₇×C₂₉	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
36	C₉⋊AGL(1,𝔽₅)	—	203	1	no	Hall
37	C₂×C₃×C₂₉	—	5	1	no	—
38	C₅×C₂₉	Dic₆₃	1	1	yes	characteristic, complemented, Hall
39	C₇⋊AGL(1,𝔽₅)	—	261	1	no	Hall
40	C₂×C₇×C₉	—	5	1	no	—
41	Dic₂₉	—	315	1	no	Hall
42	C₃×C₅×C₇	Dic₈₇	1	1	yes	characteristic
43	C₉×D₅	D₂₀₃	1	1	yes	characteristic
44	C₃×C₂₉	C₃⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic
45	Dic₂₁	—	435	1	no	—
46	C₇×D₅	D₂₆₁	1	1	yes	characteristic
47	C₇×C₉	#10596816	1	1	yes	characteristic, complemented, Hall
48	ΓL(1,𝔽₁₆)	—	609	1	no	—
49	C₂×C₂₉	—	5	1	no	—
50	C₅×C₉	Dic₂₀₃	1	1	yes	characteristic, complemented, Hall
51	C₂×C₃×C₇	—	5	1	no	—
52	Dic₉	—	1015	1	no	Hall
53	C₅×C₇	Dic₂₆₁	1	1	yes	characteristic, complemented, Hall
54	C₃×D₅	D₆₀₉	1	1	yes	characteristic
55	C₂₉	C₇⋊(C₉⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
56	Dic₇	—	1305	1	no	Hall
57	C₃×C₇	C₃⋊#10596816	1	1	yes	characteristic
58	AGL(1,𝔽₅)	—	1827	1	no	Hall
59	C₂×C₉	—	5	1	no	—
60	C₃×C₅	Dic₆₀₉	1	1	yes	characteristic
61	C₂×C₇	—	5	1	no	—
62	Dic₃	—	3045	1	no	—
63	D₅	D₁₈₂₇	1	1	yes	characteristic
64	C₉	C₇⋊#10596816	1	1	yes	characteristic, complemented, Sylow
65	C₇	C₉⋊#10596816	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	5	1	no	—
67	C₅	Dic₁₈₂₇	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	9135	1	no	Sylow
69	C₃	C₃⋊(C₇⋊#10596816)	1	1	yes	characteristic
70	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₇×C₉×C₂₉	C₄
Frattini	C₃	C₃⋊(C₇⋊#10596816)
socle	C₃×C₅×C₇×C₂₉	Dic₃
prime radical	C₃×C₇×D₅×C₂₉	D₃
cosocle	C₇×C₉×D₅×C₂₉	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	AGL(1,𝔽₅)	semidirect
15. C₅×C₉×C₂₉	Dic₇	semidirect
19. C₅×C₇×C₂₉	Dic₉	semidirect
30. C₅×C₇×C₉	Dic₂₉	semidirect
32. C₉×C₂₉	C₇⋊AGL(1,𝔽₅)	semidirect
35. C₇×C₂₉	C₉⋊AGL(1,𝔽₅)	semidirect
38. C₅×C₂₉	Dic₆₃	semidirect
47. C₇×C₉	#10596816	semidirect
50. C₅×C₉	Dic₂₀₃	semidirect
53. C₅×C₇	Dic₂₆₁	semidirect
55. C₂₉	C₇⋊(C₉⋊AGL(1,𝔽₅))	semidirect
64. C₉	C₇⋊#10596816	semidirect
65. C₇	C₉⋊#10596816	semidirect
67. C₅	Dic₁₈₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₉×D₅×C₂₉	2
C₃⋊(C₇⋊#10596816)	3
Dic₁₈₂₇	5
C₉⋊#10596816	7
C₇⋊(C₉⋊AGL(1,𝔽₅))	29

Subgroups — C7⋊(C9⋊#10596816) #49141280

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊(C₉⋊#10596816) #49141280