Subgroups — C₃×C₅×C₈₃⋊AGL(1,𝔽₅) #38735255

Order 24900.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₅×C₈₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈₃⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₈₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₈₃⋊AGL(1,𝔽₅)	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×Dic₈₃	—	5	1	no	maximal
6	C₅×D₅×C₈₃	C₂×C₃	1	1	yes	characteristic
7	C₃×D₅×C₈₃	C₂×C₅	1	1	yes	characteristic
8	C₂×C₃×C₅×C₈₃	—	5	1	no	—
9	C₅²×C₈₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
10	C₈₃⋊AGL(1,𝔽₅)	C₃×C₅	1	1	yes	characteristic, direct product factor
11	C₅×Dic₈₃	—	5	1	no	—
12	C₃×C₅×C₈₃	—	4	1	no	—
13	C₃×C₅×C₈₃	C₄×C₅	1	1	yes	characteristic, complemented
14	C₃×C₅×C₈₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	C₃×Dic₈₃	—	5	1	no	Hall
16	C₂×C₅×C₈₃	—	5	1	no	—
17	D₅×C₈₃	C₂×C₃×C₅	1	1	yes	characteristic
18	C₂×C₃×C₈₃	—	5	1	no	—
19	C₅×C₈₃	—	4	1	no	—
20	C₅×C₈₃	C₃×C₄×C₅	1	1	yes	characteristic, complemented
21	C₅×C₈₃	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
22	Dic₈₃	—	5	1	no	Hall
23	C₃×C₅×AGL(1,𝔽₅)	—	83	1	no	maximal, Hall
24	C₃×C₈₃	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
25	C₂×C₈₃	—	5	1	no	—
26	C₃×C₅×D₅	D₈₃	1	1	yes	characteristic
27	C₅×AGL(1,𝔽₅)	—	83	1	no	Hall
28	C₈₃	C₃×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
29	C₃×C₅²	Dic₈₃	1	1	yes	characteristic, complemented, Hall
30	C₃×AGL(1,𝔽₅)	—	83	1	no	—
31	C₃×C₄×C₅	—	415	1	no	—
32	C₅×D₅	C₃×D₈₃	1	1	yes	characteristic
33	C₂×C₃×C₅	—	5	1	no	—
34	C₃×D₅	C₅×D₈₃	1	1	yes	characteristic
35	C₅²	C₃×Dic₈₃	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	83	1	no	—
37	C₄×C₅	—	415	1	no	—
38	C₃×C₅	—	4	1	no	—
39	C₃×C₅	C₅×Dic₈₃	1	1	yes	characteristic, complemented
40	C₃×C₅	C₈₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
41	C₃×C₄	—	415	1	no	Hall
42	C₂×C₅	—	5	1	no	—
43	D₅	C₃×C₅×D₈₃	1	1	yes	characteristic
44	C₂×C₃	—	5	1	no	—
45	C₅	—	4	1	no	—
46	C₅	C₃×C₅×Dic₈₃	1	1	yes	characteristic, complemented
47	C₅	C₃×C₈₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
48	C₄	—	415	1	no	Sylow
49	C₃	C₅×C₈₃⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
50	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₅	C₈₃⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₈₃	C₃×C₄×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₈₃	C₄
prime radical	C₃×C₅×D₅×C₈₃	C₂
cosocle	D₅×C₈₃	C₂×C₃×C₅
LCS	G ▷ C₅×C₈₃
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₅×C₈₃⋊AGL(1,𝔽₅)	C₃	direct (N × H)
3. C₃×C₅²×C₈₃	C₄	semidirect
4. C₃×C₈₃⋊AGL(1,𝔽₅)	C₅	direct (N × H)
9. C₅²×C₈₃	C₃×C₄	semidirect
10. C₈₃⋊AGL(1,𝔽₅)	C₃×C₅	direct (N × H)
13. C₃×C₅×C₈₃	C₄×C₅	semidirect
14. C₃×C₅×C₈₃	AGL(1,𝔽₅)	semidirect
20. C₅×C₈₃	C₃×C₄×C₅	semidirect
21. C₅×C₈₃	C₃×AGL(1,𝔽₅)	semidirect
24. C₃×C₈₃	C₅×AGL(1,𝔽₅)	semidirect
28. C₈₃	C₃×C₅×AGL(1,𝔽₅)	semidirect
29. C₃×C₅²	Dic₈₃	semidirect
35. C₅²	C₃×Dic₈₃	semidirect
39. C₃×C₅	C₅×Dic₈₃	semidirect
40. C₃×C₅	C₈₃⋊AGL(1,𝔽₅)	direct (N × H)
46. C₅	C₃×C₅×Dic₈₃	semidirect
47. C₅	C₃×C₈₃⋊AGL(1,𝔽₅)	direct (N × H)
49. C₃	C₅×C₈₃⋊AGL(1,𝔽₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×D₅×C₈₃	2
C₅×C₈₃⋊AGL(1,𝔽₅)	3
C₃×C₈₃⋊AGL(1,𝔽₅)	5
C₃×C₅×Dic₈₃	5
C₃×C₅×AGL(1,𝔽₅)	83

Subgroups — C3×C5×C83⋊AGL(1,𝔽5) #38735255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₈₃⋊AGL(1,𝔽₅) #38735255