Subgroups — C₁₁×C₂₃×C₇⋊AGL(1,𝔽₅) #47978445

Order 35420.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₅×C₁₁×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₇×C₁₁×C₂₃	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₁×C₂₃×Dic₇	—	5	1	no	maximal, Hall
4	C₁₁×AGL(1,𝔽₅)×C₂₃	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₁×C₂₃	—	5	1	no	—
6	C₂₃×C₇⋊AGL(1,𝔽₅)	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅×C₁₁×C₂₃	D₇	1	1	yes	characteristic
8	C₇×C₁₁×C₂₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅×C₂₃	C₂×C₁₁	1	1	yes	characteristic
10	C₁₁×C₇⋊AGL(1,𝔽₅)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₂₃	Dic₇	1	1	yes	characteristic, complemented, Hall
12	C₄×C₁₁×C₂₃	—	35	1	no	Hall
13	C₅×C₇×C₂₃	C₄×C₁₁	1	1	yes	characteristic, complemented, Hall
14	C₇×D₅×C₁₁	C₂×C₂₃	1	1	yes	characteristic
15	C₂₃×Dic₇	—	5	1	no	Hall
16	C₂×C₁₁×C₂₃	—	5	1	no	—
17	AGL(1,𝔽₅)×C₂₃	—	7	1	no	Hall
18	C₅×C₇×C₁₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₃	—	5	1	no	—
20	C₁₁×Dic₇	—	5	1	no	Hall
21	C₁₁×C₂₃	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
22	D₅×C₂₃	C₁₁×D₇	1	1	yes	characteristic
23	C₁₁×AGL(1,𝔽₅)	—	7	1	no	Hall
24	C₇×C₂₃	C₁₁×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
25	C₂×C₇×C₁₁	—	5	1	no	—
26	C₇⋊AGL(1,𝔽₅)	C₁₁×C₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₂₃	C₁₁×Dic₇	1	1	yes	characteristic, complemented, Hall
28	D₅×C₁₁	D₇×C₂₃	1	1	yes	characteristic
29	C₄×C₂₃	—	35	1	no	Hall
30	C₇×C₁₁	AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Hall
31	C₇×D₅	C₂×C₁₁×C₂₃	1	1	yes	characteristic
32	C₅×C₁₁	C₂₃×Dic₇	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	—	5	1	no	—
34	C₄×C₁₁	—	35	1	no	Hall
35	C₅×C₇	C₄×C₁₁×C₂₃	1	1	yes	characteristic, complemented, Hall
36	Dic₇	—	5	1	no	Hall
37	C₂₃	C₁₁×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	—	5	1	no	—
39	AGL(1,𝔽₅)	—	7	1	no	Hall
40	C₂×C₇	—	5	1	no	—
41	C₁₁	C₂₃×C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
42	D₅	C₁₁×D₇×C₂₃	1	1	yes	characteristic
43	C₇	C₁₁×AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Sylow
44	C₅	C₁₁×C₂₃×Dic₇	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	35	1	no	Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₁₁×C₂₃	C₇⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₇	C₄×C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₁×C₂₃	C₄
prime radical	C₇×D₅×C₁₁×C₂₃	C₂
cosocle	C₇×D₅	C₂×C₁₁×C₂₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₁₁×C₂₃

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₁×C₂₃	C₄	semidirect
6. C₂₃×C₇⋊AGL(1,𝔽₅)	C₁₁	direct (N × H)
8. C₇×C₁₁×C₂₃	AGL(1,𝔽₅)	semidirect
10. C₁₁×C₇⋊AGL(1,𝔽₅)	C₂₃	direct (N × H)
11. C₅×C₁₁×C₂₃	Dic₇	semidirect
13. C₅×C₇×C₂₃	C₄×C₁₁	semidirect
18. C₅×C₇×C₁₁	C₄×C₂₃	semidirect
21. C₁₁×C₂₃	C₇⋊AGL(1,𝔽₅)	direct (N × H)
24. C₇×C₂₃	C₁₁×AGL(1,𝔽₅)	semidirect
26. C₇⋊AGL(1,𝔽₅)	C₁₁×C₂₃	direct (N × H)
27. C₅×C₂₃	C₁₁×Dic₇	semidirect
30. C₇×C₁₁	AGL(1,𝔽₅)×C₂₃	semidirect
32. C₅×C₁₁	C₂₃×Dic₇	semidirect
35. C₅×C₇	C₄×C₁₁×C₂₃	semidirect
37. C₂₃	C₁₁×C₇⋊AGL(1,𝔽₅)	direct (N × H)
41. C₁₁	C₂₃×C₇⋊AGL(1,𝔽₅)	direct (N × H)
43. C₇	C₁₁×AGL(1,𝔽₅)×C₂₃	semidirect
44. C₅	C₁₁×C₂₃×Dic₇	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₅×C₁₁×C₂₃	2
C₁₁×C₂₃×Dic₇	5
C₁₁×AGL(1,𝔽₅)×C₂₃	7
C₂₃×C₇⋊AGL(1,𝔽₅)	11
C₁₁×C₇⋊AGL(1,𝔽₅)	23

Subgroups — C11×C23×C7⋊AGL(1,𝔽5) #47978445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×C₂₃×C₇⋊AGL(1,𝔽₅) #47978445