Subgroups — C₃⋊(C₅⋊#64418) #17984395

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	—	3	1	no	maximal
3	C₅⋊#64418	—	3	3	no	maximal
4	C₃⋊#64418	—	5	1	no	maximal, Hall
5	C₃×C₅×C₇²	D₃	1	1	yes	characteristic, complemented
6	C₅×#3862	D₃	1	3	yes	complemented
7	C₇×D₃₅	—	9	1	no	Hall
8	C₃×#3862	D₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
10	C₇×D₂₁	—	15	1	no	—
11	#64418	—	15	3	no	—
12	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
13	D₁₀₅	—	3	1	no	—
14	C₇×D₁₅	—	21	1	no	—
15	C₃×C₇²	D₁₅	1	1	yes	characteristic, complemented
16	#3862	D₁₅	1	3	yes	complemented
17	C₃×C₅×C₇	—	2	1	no	—
18	C₃×C₅×C₇	—	3	1	no	—
19	C₃×C₅×C₇	—	3	1	no	—
20	C₅×ΓL(1,𝔽₈)	—	14	3	no	—
21	C₇×D₇	—	45	1	no	Hall
22	C₃⋊D₁₅	—	49	1	no	maximal, Hall
23	D₃₅	—	9	1	no	—
24	C₇×D₅	—	63	1	no	—
25	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
26	C₇²	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Sylow
27	C₃²×C₅	—	49	1	no	Hall
28	D₂₁	—	15	1	no	—
29	D₃×C₇	—	105	1	no	—
30	C₅×C₇	—	2	1	no	—
31	C₅×C₇	—	3	1	no	—
32	C₅×C₇	—	3	1	no	—
33	D₁₅	—	21	1	no	—
34	D₁₅	—	147	3	no	—
35	C₃×C₇	—	2	1	no	—
36	C₃×C₇	—	3	1	no	—
37	C₃×C₇	—	3	1	no	—
38	ΓL(1,𝔽₈)	—	14	3	no	—
39	C₃⋊D₃	—	245	1	no	Hall
40	C₃×C₅	—	49	3	no	—
41	C₃×C₅	#64418	1	1	yes	characteristic, complemented
42	C₂×C₇	—	315	1	no	—
43	D₇	—	45	1	no	—
44	D₅	—	63	1	no	Hall
45	C₃²	—	49	1	no	Sylow
46	C₇	—	2	1	no	—
47	C₇	—	3	1	no	—
48	C₇	—	3	1	no	—
49	D₃	—	105	1	no	—
50	D₃	—	735	3	no	—
51	C₅	C₃⋊#64418	1	1	yes	characteristic, complemented, Sylow
52	C₃	—	49	3	no	—
53	C₃	C₅⋊#64418	1	1	yes	characteristic, complemented
54	C₂	—	315	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃×C₅×#3862	C₂
Fitting, socle	C₃×C₅×C₇²	D₃
LCS	G ▷ C₃×C₅×#3862
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#3862	C₂	semidirect
5. C₃×C₅×C₇²	D₃	semidirect
6. C₅×#3862	D₃	semidirect
8. C₃×#3862	D₅	semidirect
12. C₅×C₇²	C₃⋊D₃	semidirect
15. C₃×C₇²	D₁₅	semidirect
16. #3862	D₁₅	semidirect
26. C₇²	C₃⋊D₁₅	semidirect
41. C₃×C₅	#64418	semidirect
51. C₅	C₃⋊#64418	semidirect
53. C₃	C₅⋊#64418	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⋊#64418	3
C₃⋊#64418	5
C₃⋊D₁₅	49

Subgroups — C3⋊(C5⋊#64418) #17984395

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₅⋊#64418) #17984395