Subgroups — C₇⋊(C₉⋊#63121) #30655137

Order 16380.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₉×D₆₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(C₇⋊#63121)	—	3	1	no	maximal
3	C₅×C₇×C₉×C₁₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇⋊(C₉⋊#261)	—	5	1	no	maximal, Hall
5	C₃×C₇×D₆₅	D₃	1	1	yes	characteristic
6	C₉⋊#63121	—	7	1	no	maximal, Hall
7	C₇⋊#63121	—	9	1	no	Hall
8	C₇×C₉×D₁₃	—	5	1	no	—
9	C₃×C₅×C₇×C₁₃	Dic₃	1	1	yes	characteristic
10	C₇⋊(C₉⋊AGL(1,𝔽₅))	—	13	1	no	maximal, Hall
11	C₉×D₆₅	D₇	1	1	yes	characteristic
12	C₃⋊(C₇⋊#261)	—	15	1	no	—
13	C₇×D₆₅	D₉	1	1	yes	characteristic
14	C₇×C₉×C₁₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
15	C₃⋊#63121	—	21	1	no	—
16	C₇×C₉×D₅	—	13	1	no	—
17	C₅×C₉×C₁₃	Dic₇	1	1	yes	characteristic, complemented, Hall
18	C₃×C₇×D₁₃	—	5	1	no	—
19	C₉⋊#261	—	35	1	no	Hall
20	C₅×C₇×C₁₃	Dic₉	1	1	yes	characteristic, complemented, Hall
21	C₃⋊(C₇⋊AGL(1,𝔽₅))	—	39	1	no	—
22	C₃×D₆₅	D₂₁	1	1	yes	characteristic
23	C₇⋊#261	—	45	1	no	Hall
24	C₅×C₇×C₉	#261	1	1	yes	characteristic, complemented, Hall
25	C₃×C₇×C₁₃	ΓL(1,𝔽₁₆)	1	1	yes	characteristic
26	#63121	—	63	1	no	Hall
27	Dic₆₃	—	65	1	no	Hall
28	C₉×D₁₃	—	5	1	no	—
29	C₃×C₇×D₅	—	13	1	no	—
30	C₃×C₅×C₁₃	Dic₂₁	1	1	yes	characteristic
31	C₇×D₁₃	—	5	1	no	—
32	C₉⋊AGL(1,𝔽₅)	—	91	1	no	Hall
33	C₃⋊#261	—	105	1	no	—
34	C₇⋊AGL(1,𝔽₅)	—	117	1	no	Hall
35	D₆₅	D₆₃	1	1	yes	characteristic
36	C₂×C₇×C₉	—	65	1	no	—
37	C₉×C₁₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
38	C₃×C₅×C₇	C₃⋊#261	1	1	yes	characteristic
39	C₇×C₁₃	C₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
40	C₉×D₅	—	13	1	no	—
41	Dic₂₁	—	195	1	no	—
42	C₃×D₁₃	—	5	1	no	—
43	C₇×D₅	—	13	1	no	—
44	C₅×C₁₃	Dic₆₃	1	1	yes	characteristic, complemented, Hall
45	C₇×C₉	#63121	1	1	yes	characteristic, complemented, Hall
46	ΓL(1,𝔽₁₆)	—	273	1	no	—
47	#261	—	315	1	no	Hall
48	C₅×C₉	C₇⋊#261	1	1	yes	characteristic, complemented, Hall
49	C₂×C₃×C₇	—	65	1	no	—
50	C₃×C₁₃	C₃⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic
51	Dic₉	—	455	1	no	Hall
52	C₅×C₇	C₉⋊#261	1	1	yes	characteristic, complemented, Hall
53	C₃×D₅	—	13	1	no	—
54	Dic₇	—	585	1	no	Hall
55	D₁₃	—	5	1	no	—
56	C₃×C₇	C₃⋊#63121	1	1	yes	characteristic
57	AGL(1,𝔽₅)	—	819	1	no	Hall
58	C₂×C₉	—	65	1	no	—
59	C₃×C₅	C₃⋊(C₇⋊#261)	1	1	yes	characteristic
60	C₂×C₇	—	65	1	no	—
61	C₁₃	C₇⋊(C₉⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
62	Dic₃	—	1365	1	no	—
63	D₅	—	13	1	no	—
64	C₉	C₇⋊#63121	1	1	yes	characteristic, complemented, Sylow
65	C₇	C₉⋊#63121	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃	—	65	1	no	—
67	C₅	C₇⋊(C₉⋊#261)	1	1	yes	characteristic, complemented, Sylow
68	C₄	—	4095	1	no	Sylow
69	C₃	C₃⋊(C₇⋊#63121)	1	1	yes	characteristic
70	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅×C₇×C₉×C₁₃	C₄
Frattini	C₃	C₃⋊(C₇⋊#63121)
socle	C₃×C₅×C₇×C₁₃	Dic₃
prime radical	C₃×C₇×D₆₅	D₃
cosocle	C₇×C₉×D₆₅	C₂
LCS	G ▷ C₅×C₇×C₉×C₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₅×C₇×C₉×C₁₃	C₄	semidirect
14. C₇×C₉×C₁₃	AGL(1,𝔽₅)	semidirect
17. C₅×C₉×C₁₃	Dic₇	semidirect
20. C₅×C₇×C₁₃	Dic₉	semidirect
24. C₅×C₇×C₉	#261	semidirect
37. C₉×C₁₃	C₇⋊AGL(1,𝔽₅)	semidirect
39. C₇×C₁₃	C₉⋊AGL(1,𝔽₅)	semidirect
44. C₅×C₁₃	Dic₆₃	semidirect
45. C₇×C₉	#63121	semidirect
48. C₅×C₉	C₇⋊#261	semidirect
52. C₅×C₇	C₉⋊#261	semidirect
61. C₁₃	C₇⋊(C₉⋊AGL(1,𝔽₅))	semidirect
64. C₉	C₇⋊#63121	semidirect
65. C₇	C₉⋊#63121	semidirect
67. C₅	C₇⋊(C₉⋊#261)	semidirect

Maximal subgroups

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

subgroup	index
C₇×C₉×D₆₅	2
C₃⋊(C₇⋊#63121)	3
C₇⋊(C₉⋊#261)	5
C₉⋊#63121	7
C₇⋊(C₉⋊AGL(1,𝔽₅))	13

Subgroups — C7⋊(C9⋊#63121) #30655137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇⋊(C₉⋊#63121) #30655137