Subgroups — C₃×C₈₃×#1044 #38735264

Order 24900.

64 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	C₈₃×#1044	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₈₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×AGL(1,𝔽₅)×C₈₃	—	5	2	no	maximal
5	C₅⋊D₅×C₈₃	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₈₃	—	5	2	no	—
7	C₃×D₅×C₈₃	—	10	2	no	—
8	C₅²×C₈₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
9	AGL(1,𝔽₅)×C₈₃	—	5	2	no	—
10	C₃×C₅×C₈₃	—	2	2	no	—
11	C₃×C₅×C₈₃	AGL(1,𝔽₅)	1	2	yes	complemented
12	C₃×C₄×C₈₃	—	25	1	no	Hall
13	D₅×C₈₃	—	5	2	no	—
14	D₅×C₈₃	—	10	2	no	—
15	C₂×C₃×C₈₃	—	25	1	no	—
16	C₅×C₈₃	—	2	2	no	—
17	C₅×C₈₃	C₃×AGL(1,𝔽₅)	1	2	yes	complemented
18	C₄×C₈₃	—	25	1	no	Hall
19	C₃×#1044	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₃×C₈₃	#1044	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₈₃	—	25	1	no	—
22	C₃×C₅⋊D₅	C₂×C₈₃	1	1	yes	characteristic
23	#1044	C₃×C₈₃	1	1	yes	characteristic, direct product factor, Hall
24	C₈₃	C₃×#1044	1	1	yes	characteristic, direct product factor, Sylow
25	C₃×C₅²	C₄×C₈₃	1	1	yes	characteristic, complemented, Hall
26	C₃×AGL(1,𝔽₅)	—	5	2	no	—
27	C₅⋊D₅	C₂×C₃×C₈₃	1	1	yes	characteristic
28	C₃×D₅	—	5	2	no	—
29	C₃×D₅	—	10	2	no	—
30	C₅²	C₃×C₄×C₈₃	1	1	yes	characteristic, complemented, Sylow
31	AGL(1,𝔽₅)	—	5	2	no	—
32	C₃×C₅	—	2	2	no	—
33	C₃×C₅	AGL(1,𝔽₅)×C₈₃	1	2	yes	complemented
34	C₃×C₄	—	25	1	no	Hall
35	D₅	—	5	2	no	—
36	D₅	—	10	2	no	—
37	C₂×C₃	—	25	1	no	—
38	C₅	—	2	2	no	—
39	C₅	C₃×AGL(1,𝔽₅)×C₈₃	1	2	yes	complemented
40	C₄	—	25	1	no	Sylow
41	C₃	C₈₃×#1044	1	1	yes	characteristic, direct product factor, Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₈₃	#1044
commutator, hypocenter	C₅²	C₃×C₄×C₈₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₈₃	C₄
prime radical	C₃×C₅⋊D₅×C₈₃	C₂
cosocle	C₅⋊D₅	C₂×C₃×C₈₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₈₃

Complements

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

N	H ≅ G/N	type
2. C₈₃×#1044	C₃	direct (N × H)
3. C₃×C₅²×C₈₃	C₄	semidirect
8. C₅²×C₈₃	C₃×C₄	semidirect
11. C₃×C₅×C₈₃	AGL(1,𝔽₅)	semidirect
17. C₅×C₈₃	C₃×AGL(1,𝔽₅)	semidirect
19. C₃×#1044	C₈₃	direct (N × H)
20. C₃×C₈₃	#1044	direct (N × H)
23. #1044	C₃×C₈₃	direct (N × H)
24. C₈₃	C₃×#1044	direct (N × H)
25. C₃×C₅²	C₄×C₈₃	semidirect
30. C₅²	C₃×C₄×C₈₃	semidirect
33. C₃×C₅	AGL(1,𝔽₅)×C₈₃	semidirect
39. C₅	C₃×AGL(1,𝔽₅)×C₈₃	semidirect
41. C₃	C₈₃×#1044	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
C₈₃×#1044	3
C₃×AGL(1,𝔽₅)×C₈₃	5
C₃×#1044	83

Subgroups — C3×C83×#1044 #38735264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈₃×#1044 #38735264