Subgroups — C₃⋊(C₅⋊#64423) #17984389

Order 4410.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×D₁₀₅	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#64423	—	3	1	no	maximal
4	C₃⋊#64423	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇²	C₂×C₃	1	1	yes	characteristic, complemented
6	C₅×#3861	—	2	1	no	—
7	C₅×#3861	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×#3861	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	C₃×C₅×ΓL(1,𝔽₈)	—	14	3	no	—
15	C₇×D₂₁	—	5	1	no	—
16	#64423	—	15	1	no	—
17	C₅×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
18	D₁₀₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
19	C₇×D₁₅	—	7	1	no	—
20	C₅⋊AGL(1,𝔽₇)	—	21	1	no	—
21	D₅×ΓL(1,𝔽₈)	—	21	1	no	—
22	C₃×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
23	#3861	—	2	1	no	—
24	#3861	D₁₅	1	1	yes	characteristic, complemented
25	C₃⋊AGL(1,𝔽₇)	—	35	1	no	—
26	D₃×ΓL(1,𝔽₈)	—	35	1	no	—
27	C₃×C₅×C₇	—	2	3	no	—
28	C₃×C₅×C₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
29	C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
30	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
31	C₅×ΓL(1,𝔽₈)	—	7	1	no	—
32	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
33	C₅×ΓL(1,𝔽₈)	—	14	6	no	—
34	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
35	C₅×ΓL(1,𝔽₈)	—	14	1	no	—
36	C₇×D₇	—	15	1	no	Hall
37	C₃×D₁₅	—	49	1	no	Hall
38	D₃₅	—	3	1	no	—
39	C₇×D₅	—	21	1	no	—
40	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
41	C₃×ΓL(1,𝔽₈)	—	7	1	no	—
42	C₃×ΓL(1,𝔽₈)	—	14	3	no	—
43	C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
44	C₃²×C₅	—	49	1	no	Hall
45	D₂₁	—	5	1	no	—
46	D₃×C₇	—	35	1	no	—
47	C₂×ΓL(1,𝔽₈)	—	105	1	no	—
48	AGL(1,𝔽₇)	—	105	1	no	—
49	C₅×C₇	—	2	3	no	—
50	C₅×C₇	D₃×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
51	C₅×C₇	C₃⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
52	D₁₅	—	7	1	no	—
53	C₃×D₅	—	147	1	no	—
54	C₃×C₇	—	2	3	no	—
55	C₃×C₇	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
56	C₃×C₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
57	ΓL(1,𝔽₈)	—	7	1	no	—
58	ΓL(1,𝔽₈)	—	7	1	no	—
59	ΓL(1,𝔽₈)	—	14	3	no	—
60	ΓL(1,𝔽₈)	—	14	6	no	—
61	ΓL(1,𝔽₈)	—	14	1	no	—
62	ΓL(1,𝔽₈)	—	14	1	no	—
63	C₃×D₃	—	245	1	no	Hall
64	C₃×C₅	—	49	1	no	—
65	C₃×C₅	—	98	1	no	—
66	C₃×C₅	#64423	1	1	yes	characteristic, complemented
67	C₂×C₇	—	105	1	no	—
68	D₇	—	15	1	no	—
69	D₅	—	21	1	no	Hall
70	C₃²	—	49	1	no	Sylow
71	C₇	—	2	3	no	—
72	C₇	ΓL(1,𝔽₈)×D₁₅	1	1	yes	characteristic, complemented
73	C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented
74	C₂×C₃	—	735	1	no	—
75	D₃	—	35	1	no	—
76	C₅	C₃⋊#64423	1	1	yes	characteristic, complemented, Sylow
77	C₃	—	49	1	no	—
78	C₃	—	98	1	no	—
79	C₃	C₅⋊#64423	1	1	yes	characteristic, complemented
80	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×#3861	C₂	semidirect
2. C₇×D₁₀₅	C₃	semidirect
5. C₃×C₅×C₇²	C₂×C₃	semidirect
7. C₅×#3861	D₃	semidirect
11. C₃×#3861	D₅	semidirect
17. C₅×C₇²	C₃×D₃	semidirect
18. D₁₀₅	ΓL(1,𝔽₈)	semidirect
22. C₃×C₇²	C₃×D₅	semidirect
24. #3861	D₁₅	semidirect
28. C₃×C₅×C₇	AGL(1,𝔽₇)	semidirect
29. C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	semidirect
43. C₇²	C₃×D₁₅	semidirect
50. C₅×C₇	D₃×ΓL(1,𝔽₈)	semidirect
51. C₅×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
55. C₃×C₇	D₅×ΓL(1,𝔽₈)	semidirect
56. C₃×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
66. C₃×C₅	#64423	semidirect
72. C₇	ΓL(1,𝔽₈)×D₁₅	semidirect
73. C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
76. C₅	C₃⋊#64423	semidirect
79. C₃	C₅⋊#64423	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#3861	2
C₇×D₁₀₅	3
C₅⋊#64423	3
C₃⋊#64423	5
C₃⋊(C₅⋊AGL(1,𝔽₇))	7
ΓL(1,𝔽₈)×D₁₅	7

Subgroups — C3⋊(C5⋊#64423) #17984389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊#64423) #17984389