Subgroups — C₃⋊(C₅⋊#64422) #17984390

Order 4410.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₀₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#64422	—	3	1	no	maximal
4	C₃⋊#64422	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×#3862	—	2	1	no	—
7	C₅×#3862	D₃	1	1	yes	characteristic, complemented
8	C₃⋊(C₅⋊AGL(1,𝔽₇))	—	7	1	no	maximal
9	ΓL(1,𝔽₈)×D₁₅	—	7	1	no	maximal
10	C₇×D₃₅	—	3	1	no	Hall
11	C₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
12	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
13	C₃×C₅×ΓL(1,𝔽₈)	—	7	1	no	—
14	C₇×D₂₁	—	5	1	no	—
15	#64422	—	15	1	no	—
16	C₅×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
17	D₁₀₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
18	C₇×D₁₅	—	7	1	no	—
19	C₅⋊AGL(1,𝔽₇)	—	21	1	no	—
20	D₅×ΓL(1,𝔽₈)	—	21	1	no	—
21	C₃×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
22	#3862	—	2	1	no	—
23	#3862	D₁₅	1	1	yes	characteristic, complemented
24	C₃⋊AGL(1,𝔽₇)	—	35	1	no	—
25	D₃×ΓL(1,𝔽₈)	—	35	1	no	—
26	C₃×C₅×C₇	—	6	1	no	—
27	C₃×C₅×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
28	C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
29	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
30	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
31	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
32	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
33	C₇×D₇	—	15	1	no	Hall
34	C₃×D₁₅	—	49	1	no	Hall
35	D₃₅	—	3	1	no	—
36	C₇×D₅	—	21	1	no	—
37	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
38	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
39	C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
40	C₃²×C₅	—	49	1	no	Hall
41	D₂₁	—	5	1	no	—
42	D₃×C₇	—	35	1	no	—
43	C₂×ΓL(1,𝔽₈)	—	105	1	no	—
44	AGL(1,𝔽₇)	—	105	1	no	—
45	C₅×C₇	—	6	1	no	—
46	C₅×C₇	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
47	C₅×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
48	D₁₅	—	7	1	no	—
49	C₃×D₅	—	147	1	no	—
50	C₃×C₇	—	6	1	no	—
51	C₃×C₇	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
52	C₃×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
53	ΓL(1,𝔽₈)	—	7	1	no	—
54	ΓL(1,𝔽₈)	—	7	1	no	—
55	ΓL(1,𝔽₈)	—	14	1	no	—
56	ΓL(1,𝔽₈)	—	14	1	no	—
57	C₃×D₃	—	245	1	no	Hall
58	C₃×C₅	—	49	1	no	—
59	C₃×C₅	—	98	1	no	—
60	C₃×C₅	#64422	1	1	yes	characteristic, complemented
61	C₂×C₇	—	105	1	no	—
62	D₇	—	15	1	no	—
63	D₅	—	21	1	no	Hall
64	C₃²	—	49	1	no	Sylow
65	C₇	—	6	1	no	—
66	C₇	ΓL(1,𝔽₈)×D₁₅	1	1	yes	characteristic, complemented
67	C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
68	C₂×C₃	—	735	1	no	—
69	D₃	—	35	1	no	—
70	C₅	C₃⋊#64422	1	1	yes	characteristic, complemented, Sylow
71	C₃	—	49	1	no	—
72	C₃	—	98	1	no	—
73	C₃	C₅⋊#64422	1	1	yes	characteristic, complemented
74	C₂	—	105	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₇²	C₂×C₃
LCS	G ▷ C₃×C₅×C₇²
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#3862	C₂	semidirect
2. C₇×D₁₀₅	C₃	semidirect
5. C₃×C₅×C₇²	C₂×C₃	semidirect
7. C₅×#3862	D₃	semidirect
11. C₃×#3862	D₅	semidirect
16. C₅×C₇²	C₃×D₃	semidirect
17. D₁₀₅	ΓL(1,𝔽₈)	semidirect
21. C₃×C₇²	C₃×D₅	semidirect
23. #3862	D₁₅	semidirect
27. C₃×C₅×C₇	AGL(1,𝔽₇)	semidirect
28. C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	semidirect
39. C₇²	C₃×D₁₅	semidirect
46. C₅×C₇	D₃×ΓL(1,𝔽₈)	semidirect
47. C₅×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
51. C₃×C₇	D₅×ΓL(1,𝔽₈)	semidirect
52. C₃×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
60. C₃×C₅	#64422	semidirect
66. C₇	ΓL(1,𝔽₈)×D₁₅	semidirect
67. C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
70. C₅	C₃⋊#64422	semidirect
73. C₃	C₅⋊#64422	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#3862	2
C₇×D₁₀₅	3
C₅⋊#64422	3
C₃⋊#64422	5
C₃⋊(C₅⋊AGL(1,𝔽₇))	7
ΓL(1,𝔽₈)×D₁₅	7

Subgroups — C3⋊(C5⋊#64422) #17984390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊#64422) #17984390