Subgroups — C₅×C₃⋊#64418 #17984384

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	C₅×C₇×D₂₁	—	3	1	no	maximal
3	C₅×#64418	—	3	3	no	maximal
4	C₃⋊#64418	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₇²	D₃	1	1	yes	characteristic, complemented
6	C₅×#3862	D₃	1	3	yes	complemented
7	C₅×C₇×D₇	—	9	1	no	Hall
8	C₃×#3862	C₂×C₅	1	1	yes	characteristic, complemented, Hall
9	C₃×C₅×ΓL(1,𝔽₈)	—	14	1	no	—
10	C₇×D₂₁	—	3	1	no	—
11	#64418	—	3	3	no	—
12	C₅×C₇²	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
13	C₅×D₂₁	—	3	1	no	—
14	C₅×D₃×C₇	—	21	1	no	—
15	C₃×C₇²	C₅×D₃	1	1	yes	characteristic, complemented
16	#3862	C₅×D₃	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	—	9	1	no	Hall
22	C₅×C₃⋊D₃	—	49	1	no	maximal, Hall
23	C₂×C₅×C₇	—	63	1	no	—
24	C₅×D₇	—	9	1	no	—
25	C₃×ΓL(1,𝔽₈)	—	14	1	no	—
26	C₇²	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
27	C₃²×C₅	—	49	1	no	Hall
28	D₂₁	—	3	1	no	—
29	D₃×C₇	—	21	1	no	—
30	C₅×C₇	—	2	1	no	—
31	C₅×C₇	—	3	1	no	—
32	C₅×C₇	—	3	1	no	—
33	C₅×D₃	—	21	1	no	—
34	C₅×D₃	—	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	—	49	1	no	Hall
40	C₃×C₅	—	49	3	no	—
41	C₃×C₅	#64418	1	1	yes	characteristic, complemented
42	C₂×C₇	—	63	1	no	—
43	D₇	—	9	1	no	—
44	C₂×C₅	—	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	—	21	1	no	—
50	D₃	—	147	3	no	—
51	C₅	C₃⋊#64418	1	1	yes	characteristic, direct product factor, Sylow
52	C₃	—	49	3	no	—
53	C₃	C₅×#64418	1	1	yes	characteristic, complemented
54	C₂	—	63	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₃⋊#64418
commutator, cosocle, hypocenter	C₃×#3862	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²	D₃
LCS	G ▷ C₃×#3862
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#3862	C₂	semidirect
4. C₃⋊#64418	C₅	direct (N × H)
5. C₃×C₅×C₇²	D₃	semidirect
6. C₅×#3862	D₃	semidirect
8. C₃×#3862	C₂×C₅	semidirect
12. C₅×C₇²	C₃⋊D₃	semidirect
15. C₃×C₇²	C₅×D₃	semidirect
16. #3862	C₅×D₃	semidirect
26. C₇²	C₅×C₃⋊D₃	semidirect
41. C₃×C₅	#64418	semidirect
51. C₅	C₃⋊#64418	direct (N × H)
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
C₅×C₇×D₂₁	3
C₅×#64418	3
C₃⋊#64418	5
C₅×C₃⋊D₃	49

Subgroups — C5×C3⋊#64418 #17984384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₃⋊#64418 #17984384