Subgroups — C₅×D₁₁×#3861 #30633539

Order 16170.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×#3861	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇²×D₁₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	D₁₁×#3861	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇²×C₁₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₅×ΓL(1,𝔽₈)×D₁₁	—	7	8	no	maximal
6	C₁₁×#3861	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₅×#3861	—	11	1	no	maximal, Hall
8	C₅×C₁₁×ΓL(1,𝔽₈)	—	7	8	no	—
9	C₇²×D₁₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₅×C₇×D₁₁	ΓL(1,𝔽₈)	1	8	yes	complemented
11	C₅×#3861	D₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₇²×C₁₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₇²	—	11	1	no	Hall
14	ΓL(1,𝔽₈)×D₁₁	—	7	8	no	—
15	C₅×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	1	8	yes	complemented
16	C₃×C₅×D₁₁	—	49	1	no	Hall
17	C₂×#3861	—	11	1	no	Hall
18	C₅×C₇²	C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
19	C₁₁×ΓL(1,𝔽₈)	—	7	8	no	—
20	C₂×C₅×ΓL(1,𝔽₈)	—	77	8	no	—
21	C₃×C₅×C₁₁	—	49	1	no	Hall
22	C₇×D₁₁	C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
23	#3861	C₅×D₁₁	1	1	yes	characteristic, direct product factor, Hall
24	C₅×D₁₁	#3861	1	1	yes	characteristic, direct product factor, Hall
25	C₅×ΓL(1,𝔽₈)	—	7	8	no	—
26	C₂×C₇²	—	11	1	no	Hall
27	C₇×C₁₁	C₂×C₅×ΓL(1,𝔽₈)	1	8	yes	complemented
28	C₂×C₅×C₇	—	11	8	no	—
29	C₃×D₁₁	—	49	1	no	Hall
30	C₅×C₁₁	C₂×#3861	1	1	yes	characteristic, complemented, Hall
31	C₇²	C₃×C₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
32	C₂×ΓL(1,𝔽₈)	—	77	8	no	—
33	C₅×C₇	ΓL(1,𝔽₈)×D₁₁	1	8	yes	complemented
34	C₃×C₁₁	—	49	1	no	Hall
35	C₂×C₃×C₅	—	539	1	no	Hall
36	D₁₁	C₅×#3861	1	1	yes	characteristic, direct product factor, Hall
37	ΓL(1,𝔽₈)	—	7	8	no	—
38	C₃×C₅	—	49	1	no	Hall
39	C₂×C₇	—	11	8	no	—
40	C₁₁	C₂×C₅×#3861	1	1	yes	characteristic, complemented, Sylow
41	C₂×C₅	—	11	1	no	Hall
42	C₇	C₅×ΓL(1,𝔽₈)×D₁₁	1	8	yes	complemented
43	C₂×C₃	—	539	1	no	Hall
44	C₅	D₁₁×#3861	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	49	1	no	Sylow
46	C₂	—	11	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₁×#3861
commutator, cosocle, hypocenter	C₇²×C₁₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₁	C₂×C₃
LCS	G ▷ C₇²×C₁₁
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₁×#3861	C₂	semidirect
2. C₅×C₇²×D₁₁	C₃	semidirect
3. D₁₁×#3861	C₅	direct (N × H)
4. C₅×C₇²×C₁₁	C₂×C₃	semidirect
6. C₁₁×#3861	C₂×C₅	semidirect
9. C₇²×D₁₁	C₃×C₅	semidirect
10. C₅×C₇×D₁₁	ΓL(1,𝔽₈)	semidirect
11. C₅×#3861	D₁₁	direct (N × H)
12. C₇²×C₁₁	C₂×C₃×C₅	semidirect
15. C₅×C₇×C₁₁	C₂×ΓL(1,𝔽₈)	semidirect
18. C₅×C₇²	C₃×D₁₁	semidirect
22. C₇×D₁₁	C₅×ΓL(1,𝔽₈)	semidirect
23. #3861	C₅×D₁₁	direct (N × H)
24. C₅×D₁₁	#3861	direct (N × H)
27. C₇×C₁₁	C₂×C₅×ΓL(1,𝔽₈)	semidirect
30. C₅×C₁₁	C₂×#3861	semidirect
31. C₇²	C₃×C₅×D₁₁	semidirect
33. C₅×C₇	ΓL(1,𝔽₈)×D₁₁	semidirect
36. D₁₁	C₅×#3861	direct (N × H)
40. C₁₁	C₂×C₅×#3861	semidirect
42. C₇	C₅×ΓL(1,𝔽₈)×D₁₁	semidirect
44. C₅	D₁₁×#3861	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₁₁×#3861	2
C₅×C₇²×D₁₁	3
D₁₁×#3861	5
C₅×ΓL(1,𝔽₈)×D₁₁	7
C₂×C₅×#3861	11

Subgroups — C5×D11×#3861 #30633539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₁×#3861 #30633539