Subgroups — C₃⋊(C₅⋊#64425) #17984388

Order 4410.

88 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	C₃⋊(C₅⋊(C₇⋊D₇))	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅⋊#64425	—	3	1	no	maximal
4	C₃⋊#64425	—	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	2	no	maximal
9	C₅⋊(C₇⋊D₇)	—	3	1	no	Hall
10	C₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×ΓL(1,𝔽₈)	—	7	2	no	—
12	C₃⋊(C₇⋊D₇)	—	5	1	no	—
13	#64425	—	15	1	no	—
14	C₅×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	D₁₀₅	—	7	2	no	—
16	D₁₀₅	—	21	2	no	—
17	C₅⋊AGL(1,𝔽₇)	—	21	2	no	—
18	C₃×C₇²	C₃×D₅	1	1	yes	characteristic, complemented
19	#3862	—	2	1	no	—
20	#3862	D₁₅	1	1	yes	characteristic, complemented
21	C₃⋊AGL(1,𝔽₇)	—	35	2	no	—
22	C₃×C₅×C₇	—	3	2	no	—
23	C₃×C₅×C₇	AGL(1,𝔽₇)	1	2	yes	complemented
24	C₅×ΓL(1,𝔽₈)	—	7	2	no	—
25	C₅×ΓL(1,𝔽₈)	—	14	2	no	—
26	C₇⋊D₇	—	15	1	no	Hall
27	C₃×D₁₅	—	49	1	no	Hall
28	D₃₅	—	21	2	no	—
29	D₃₅	—	63	2	no	—
30	C₃×ΓL(1,𝔽₈)	—	7	2	no	—
31	C₇²	C₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
32	C₃²×C₅	—	49	1	no	Hall
33	D₂₁	—	35	2	no	—
34	D₂₁	—	105	2	no	—
35	AGL(1,𝔽₇)	—	105	2	no	—
36	C₅×C₇	—	3	2	no	—
37	C₅×C₇	C₃⋊AGL(1,𝔽₇)	1	2	yes	complemented
38	D₁₅	—	49	1	no	—
39	C₃×D₅	—	147	1	no	—
40	C₃×C₇	—	3	2	no	—
41	C₃×C₇	C₅⋊AGL(1,𝔽₇)	1	2	yes	complemented
42	ΓL(1,𝔽₈)	—	7	2	no	—
43	ΓL(1,𝔽₈)	—	14	2	no	—
44	C₃×D₃	—	245	1	no	Hall
45	C₃×C₅	—	49	1	no	—
46	C₃×C₅	—	98	1	no	—
47	C₃×C₅	#64425	1	1	yes	characteristic, complemented
48	D₇	—	315	2	no	—
49	D₇	—	105	2	no	—
50	D₅	—	147	1	no	Hall
51	C₃²	—	49	1	no	Sylow
52	C₇	—	3	2	no	—
53	C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	1	2	yes	complemented
54	C₂×C₃	—	735	1	no	—
55	D₃	—	245	1	no	—
56	C₅	C₃⋊#64425	1	1	yes	characteristic, complemented, Sylow
57	C₃	—	49	1	no	—
58	C₃	—	98	1	no	—
59	C₃	C₅⋊#64425	1	1	yes	characteristic, complemented
60	C₂	—	735	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. C₃⋊(C₅⋊(C₇⋊D₇))	C₃	semidirect
5. C₃×C₅×C₇²	C₂×C₃	semidirect
7. C₅×#3862	D₃	semidirect
10. C₃×#3862	D₅	semidirect
14. C₅×C₇²	C₃×D₃	semidirect
18. C₃×C₇²	C₃×D₅	semidirect
20. #3862	D₁₅	semidirect
23. C₃×C₅×C₇	AGL(1,𝔽₇)	semidirect
31. C₇²	C₃×D₁₅	semidirect
37. C₅×C₇	C₃⋊AGL(1,𝔽₇)	semidirect
41. C₃×C₇	C₅⋊AGL(1,𝔽₇)	semidirect
47. C₃×C₅	#64425	semidirect
53. C₇	C₃⋊(C₅⋊AGL(1,𝔽₇))	semidirect
56. C₅	C₃⋊#64425	semidirect
59. C₃	C₅⋊#64425	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
C₃⋊(C₅⋊(C₇⋊D₇))	3
C₅⋊#64425	3
C₃⋊#64425	5
C₃⋊(C₅⋊AGL(1,𝔽₇))	7

Subgroups — C3⋊(C5⋊#64425) #17984388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊#64425) #17984388