Subgroups — C₁₁×C₃⋊(C₄₇⋊AGL(1,𝔽₅)) #44526657

Order 31020.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₁₁×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₁₁×C₄₇⋊AGL(1,𝔽₅)	—	3	1	no	maximal, Hall
3	C₃×C₅×C₁₁×C₄₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×Dic₁₄₁	—	5	1	no	maximal, Hall
5	D₅×C₁₁×C₄₇	D₃	1	1	yes	characteristic
6	C₂×C₃×C₁₁×C₄₇	—	5	1	no	—
7	C₃⋊(C₄₇⋊AGL(1,𝔽₅))	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₁×C₄₇	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₁₁×Dic₄₇	—	15	1	no	Hall
10	C₃×C₁₁×C₄₇	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
11	C₃×D₅×C₄₇	C₂×C₁₁	1	1	yes	characteristic
12	C₂×C₁₁×C₄₇	—	5	1	no	—
13	C₄₇⋊AGL(1,𝔽₅)	—	3	1	no	Hall
14	C₃×C₅×C₄₇	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
15	C₁₁×ΓL(1,𝔽₁₆)	—	47	1	no	maximal, Hall
16	Dic₁₄₁	—	5	1	no	Hall
17	C₁₁×C₄₇	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
18	D₅×C₄₇	D₃×C₁₁	1	1	yes	characteristic
19	C₃×D₅×C₁₁	D₄₇	1	1	yes	characteristic
20	C₂×C₃×C₄₇	—	5	1	no	—
21	C₅×C₄₇	C₁₁×Dic₃	1	1	yes	characteristic, complemented, Hall
22	C₁₁×AGL(1,𝔽₅)	—	141	1	no	Hall
23	Dic₄₇	—	15	1	no	Hall
24	C₃×C₅×C₁₁	Dic₄₇	1	1	yes	characteristic, complemented, Hall
25	C₃×C₄₇	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
26	C₁₁×Dic₃	—	235	1	no	Hall
27	D₅×C₁₁	D₁₄₁	1	1	yes	characteristic
28	C₂×C₄₇	—	5	1	no	—
29	C₂×C₃×C₁₁	—	5	1	no	—
30	ΓL(1,𝔽₁₆)	—	47	1	no	Hall
31	C₅×C₁₁	Dic₁₄₁	1	1	yes	characteristic, complemented, Hall
32	C₄₇	C₁₁×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Sylow
33	C₄×C₁₁	—	705	1	no	Hall
34	C₃×C₁₁	C₄₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
35	C₃×D₅	C₁₁×D₄₇	1	1	yes	characteristic
36	C₂×C₁₁	—	5	1	no	—
37	AGL(1,𝔽₅)	—	141	1	no	Hall
38	C₃×C₅	C₁₁×Dic₄₇	1	1	yes	characteristic, complemented, Hall
39	Dic₃	—	235	1	no	Hall
40	C₁₁	C₃⋊(C₄₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic, direct product factor, Sylow
41	D₅	C₁₁×D₁₄₁	1	1	yes	characteristic
42	C₂×C₃	—	5	1	no	—
43	C₅	C₁₁×Dic₁₄₁	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	705	1	no	Sylow
45	C₃	C₁₁×C₄₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁	C₃⋊(C₄₇⋊AGL(1,𝔽₅))
commutator, hypocenter	C₃×C₅×C₄₇	C₄×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₄₇	C₄
prime radical	C₃×D₅×C₁₁×C₄₇	C₂
cosocle	C₃×D₅×C₄₇	C₂×C₁₁
LCS	G ▷ C₃×C₅×C₄₇
UCS	C₁ ◁ C₁₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₁₁×C₄₇	C₄	semidirect
7. C₃⋊(C₄₇⋊AGL(1,𝔽₅))	C₁₁	direct (N × H)
8. C₅×C₁₁×C₄₇	Dic₃	semidirect
10. C₃×C₁₁×C₄₇	AGL(1,𝔽₅)	semidirect
14. C₃×C₅×C₄₇	C₄×C₁₁	semidirect
17. C₁₁×C₄₇	ΓL(1,𝔽₁₆)	semidirect
21. C₅×C₄₇	C₁₁×Dic₃	semidirect
24. C₃×C₅×C₁₁	Dic₄₇	semidirect
25. C₃×C₄₇	C₁₁×AGL(1,𝔽₅)	semidirect
31. C₅×C₁₁	Dic₁₄₁	semidirect
32. C₄₇	C₁₁×ΓL(1,𝔽₁₆)	semidirect
34. C₃×C₁₁	C₄₇⋊AGL(1,𝔽₅)	semidirect
38. C₃×C₅	C₁₁×Dic₄₇	semidirect
40. C₁₁	C₃⋊(C₄₇⋊AGL(1,𝔽₅))	direct (N × H)
43. C₅	C₁₁×Dic₁₄₁	semidirect
45. C₃	C₁₁×C₄₇⋊AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₃×D₅×C₁₁×C₄₇	2
C₁₁×C₄₇⋊AGL(1,𝔽₅)	3
C₁₁×Dic₁₄₁	5
C₃⋊(C₄₇⋊AGL(1,𝔽₅))	11
C₁₁×ΓL(1,𝔽₁₆)	47

Subgroups — C11×C3⋊(C47⋊AGL(1,𝔽5)) #44526657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₃⋊(C₄₇⋊AGL(1,𝔽₅)) #44526657