Subgroups — C₅×D₃×#3861 #17984381

Order 4410.

180 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	C₅×D₃×C₇²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#3861	—	3	1	no	maximal
4	D₃×#3861	C₅	1	1	yes	maximal, characteristic, direct product factor, 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, direct product factor
8	C₅×D₃×ΓL(1,𝔽₈)	—	7	8	no	maximal
9	C₂×C₅×C₇²	—	3	1	no	Hall
10	C₃×#3861	C₂×C₅	1	1	yes	characteristic, complemented, Hall
11	C₃×C₅×ΓL(1,𝔽₈)	—	7	8	no	—
12	D₃×C₇²	C₃×C₅	1	1	yes	characteristic, complemented
13	C₂×#3861	—	3	1	no	—
14	C₅×C₇²	C₃×D₃	1	1	yes	characteristic, complemented, Hall
15	C₅×D₃×C₇	ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₂×C₅×ΓL(1,𝔽₈)	—	21	8	no	—
17	C₃×C₇²	C₂×C₃×C₅	1	1	yes	characteristic, complemented
18	#3861	—	2	1	no	—
19	#3861	C₅×D₃	1	1	yes	characteristic, direct product factor
20	D₃×ΓL(1,𝔽₈)	—	7	8	no	—
21	C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
22	C₅×ΓL(1,𝔽₈)	—	7	8	no	—
23	C₅×ΓL(1,𝔽₈)	—	14	8	no	—
24	C₂×C₇²	—	3	1	no	Hall
25	C₃×C₅×D₃	—	49	1	no	Hall
26	C₂×C₅×C₇	—	3	8	no	—
27	C₃×ΓL(1,𝔽₈)	—	7	8	no	—
28	C₇²	C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
29	C₃²×C₅	—	49	1	no	Hall
30	D₃×C₇	C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
31	C₂×ΓL(1,𝔽₈)	—	21	8	no	—
32	C₅×C₇	D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
33	C₂×C₃×C₅	—	147	1	no	—
34	C₅×D₃	#3861	1	1	yes	characteristic, direct product factor
35	C₃×C₇	C₂×C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
36	ΓL(1,𝔽₈)	—	7	8	no	—
37	ΓL(1,𝔽₈)	—	14	8	no	—
38	C₃×D₃	—	49	1	no	Hall
39	C₃×C₅	—	49	1	no	—
40	C₃×C₅	—	98	1	no	—
41	C₃×C₅	C₂×#3861	1	1	yes	characteristic, complemented
42	C₂×C₇	—	3	8	no	—
43	C₂×C₅	—	3	1	no	Hall
44	C₃²	—	49	1	no	Sylow
45	C₇	C₅×D₃×ΓL(1,𝔽₈)	1	8	yes	complemented
46	C₂×C₃	—	147	1	no	—
47	D₃	C₅×#3861	1	1	yes	characteristic, direct product factor
48	C₅	D₃×#3861	1	1	yes	characteristic, direct product factor, Sylow
49	C₃	—	49	1	no	—
50	C₃	—	98	1	no	—
51	C₃	C₂×C₅×#3861	1	1	yes	characteristic, complemented
52	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₃×#3861
commutator, cosocle, hypocenter	C₃×C₇²	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²	C₂×C₃
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#3861	C₂	semidirect
2. C₅×D₃×C₇²	C₃	semidirect
4. D₃×#3861	C₅	direct (N × H)
5. C₃×C₅×C₇²	C₂×C₃	semidirect
7. C₅×#3861	D₃	direct (N × H)
10. C₃×#3861	C₂×C₅	semidirect
12. D₃×C₇²	C₃×C₅	semidirect
14. C₅×C₇²	C₃×D₃	semidirect
15. C₅×D₃×C₇	ΓL(1,𝔽₈)	semidirect
17. C₃×C₇²	C₂×C₃×C₅	semidirect
19. #3861	C₅×D₃	direct (N × H)
21. C₃×C₅×C₇	C₂×ΓL(1,𝔽₈)	semidirect
28. C₇²	C₃×C₅×D₃	semidirect
30. D₃×C₇	C₅×ΓL(1,𝔽₈)	semidirect
32. C₅×C₇	D₃×ΓL(1,𝔽₈)	semidirect
34. C₅×D₃	#3861	direct (N × H)
35. C₃×C₇	C₂×C₅×ΓL(1,𝔽₈)	semidirect
41. C₃×C₅	C₂×#3861	semidirect
45. C₇	C₅×D₃×ΓL(1,𝔽₈)	semidirect
47. D₃	C₅×#3861	direct (N × H)
48. C₅	D₃×#3861	direct (N × H)
51. C₃	C₂×C₅×#3861	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
C₅×D₃×C₇²	3
C₂×C₅×#3861	3
D₃×#3861	5
C₅×D₃×ΓL(1,𝔽₈)	7

Subgroups — C5×D3×#3861 #17984381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×#3861 #17984381