Subgroups — C₇×C₂₃×C₁₁⋊AGL(1,𝔽₅) #47978443

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	C₇×C₂₃×Dic₁₁	—	5	1	no	maximal, Hall
4	C₂₃×C₁₁⋊AGL(1,𝔽₅)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₇×C₁₁×C₂₃	—	5	1	no	—
6	C₇×AGL(1,𝔽₅)×C₂₃	—	11	1	no	maximal, Hall
7	D₅×C₁₁×C₂₃	C₂×C₇	1	1	yes	characteristic
8	C₇×C₁₁×C₂₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
9	C₇×D₅×C₂₃	D₁₁	1	1	yes	characteristic
10	C₇×C₁₁⋊AGL(1,𝔽₅)	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₅×C₁₁×C₂₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₂₃×Dic₁₁	—	5	1	no	Hall
13	C₅×C₇×C₂₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
14	C₇×D₅×C₁₁	C₂×C₂₃	1	1	yes	characteristic
15	C₄×C₇×C₂₃	—	55	1	no	Hall
16	C₂×C₁₁×C₂₃	—	5	1	no	—
17	AGL(1,𝔽₅)×C₂₃	—	11	1	no	Hall
18	C₅×C₇×C₁₁	C₄×C₂₃	1	1	yes	characteristic, complemented, Hall
19	C₂×C₇×C₂₃	—	5	1	no	—
20	C₇×Dic₁₁	—	5	1	no	Hall
21	C₁₁×C₂₃	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
22	D₅×C₂₃	C₇×D₁₁	1	1	yes	characteristic
23	C₁₁⋊AGL(1,𝔽₅)	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₇×C₂₃	C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇×C₁₁	—	5	1	no	—
26	C₇×AGL(1,𝔽₅)	—	11	1	no	Hall
27	C₅×C₂₃	C₇×Dic₁₁	1	1	yes	characteristic, complemented, Hall
28	D₅×C₁₁	C₂×C₇×C₂₃	1	1	yes	characteristic
29	C₄×C₂₃	—	55	1	no	Hall
30	C₇×C₁₁	AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Hall
31	C₇×D₅	D₁₁×C₂₃	1	1	yes	characteristic
32	C₅×C₁₁	C₄×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₂₃	—	5	1	no	—
34	Dic₁₁	—	5	1	no	Hall
35	C₅×C₇	C₂₃×Dic₁₁	1	1	yes	characteristic, complemented, Hall
36	C₄×C₇	—	55	1	no	Hall
37	C₂₃	C₇×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
38	C₂×C₁₁	—	5	1	no	—
39	AGL(1,𝔽₅)	—	11	1	no	Hall
40	C₂×C₇	—	5	1	no	—
41	C₁₁	C₇×AGL(1,𝔽₅)×C₂₃	1	1	yes	characteristic, complemented, Sylow
42	D₅	C₇×D₁₁×C₂₃	1	1	yes	characteristic
43	C₇	C₂₃×C₁₁⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
44	C₅	C₇×C₂₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
45	C₄	—	55	1	no	Sylow
46	C₂	—	5	1	no	—

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

Complements

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

N	H ≅ G/N	type
2. C₅×C₇×C₁₁×C₂₃	C₄	semidirect
4. C₂₃×C₁₁⋊AGL(1,𝔽₅)	C₇	direct (N × H)
8. C₇×C₁₁×C₂₃	AGL(1,𝔽₅)	semidirect
10. C₇×C₁₁⋊AGL(1,𝔽₅)	C₂₃	direct (N × H)
11. C₅×C₁₁×C₂₃	C₄×C₇	semidirect
13. C₅×C₇×C₂₃	Dic₁₁	semidirect
18. C₅×C₇×C₁₁	C₄×C₂₃	semidirect
21. C₁₁×C₂₃	C₇×AGL(1,𝔽₅)	semidirect
23. C₁₁⋊AGL(1,𝔽₅)	C₇×C₂₃	direct (N × H)
24. C₇×C₂₃	C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
27. C₅×C₂₃	C₇×Dic₁₁	semidirect
30. C₇×C₁₁	AGL(1,𝔽₅)×C₂₃	semidirect
32. C₅×C₁₁	C₄×C₇×C₂₃	semidirect
35. C₅×C₇	C₂₃×Dic₁₁	semidirect
37. C₂₃	C₇×C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
41. C₁₁	C₇×AGL(1,𝔽₅)×C₂₃	semidirect
43. C₇	C₂₃×C₁₁⋊AGL(1,𝔽₅)	direct (N × H)
44. C₅	C₇×C₂₃×Dic₁₁	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
C₇×C₂₃×Dic₁₁	5
C₂₃×C₁₁⋊AGL(1,𝔽₅)	7
C₇×AGL(1,𝔽₅)×C₂₃	11
C₇×C₁₁⋊AGL(1,𝔽₅)	23

Subgroups — C7×C23×C11⋊AGL(1,𝔽5) #47978443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×C₂₃×C₁₁⋊AGL(1,𝔽₅) #47978443