Subgroups — C₃×C₈₃×#1043 #38735262

Order 24900.

96 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×#1043	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	6	no	maximal
5	C₅⋊D₅×C₈₃	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₈₃	—	5	6	no	—
7	C₅²×C₈₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₈₃	—	5	6	no	—
9	C₃×C₅×C₈₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₃×C₄×C₈₃	—	25	1	no	Hall
11	D₅×C₈₃	—	5	6	no	—
12	C₂×C₃×C₈₃	—	25	1	no	—
13	C₅×C₈₃	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
14	C₄×C₈₃	—	25	1	no	Hall
15	C₃×#1043	C₈₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₈₃	#1043	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₈₃	—	25	1	no	—
18	C₃×C₅⋊D₅	C₂×C₈₃	1	1	yes	characteristic
19	#1043	C₃×C₈₃	1	1	yes	characteristic, direct product factor, Hall
20	C₈₃	C₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₅²	C₄×C₈₃	1	1	yes	characteristic, complemented, Hall
22	C₃×AGL(1,𝔽₅)	—	5	6	no	—
23	C₅⋊D₅	C₂×C₃×C₈₃	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₃×C₄×C₈₃	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₈₃	1	6	yes	complemented
28	C₃×C₄	—	25	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃×AGL(1,𝔽₅)×C₈₃	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	C₈₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₈₃	#1043
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×#1043	C₃	direct (N × H)
3. C₃×C₅²×C₈₃	C₄	semidirect
7. C₅²×C₈₃	C₃×C₄	semidirect
9. C₃×C₅×C₈₃	AGL(1,𝔽₅)	semidirect
13. C₅×C₈₃	C₃×AGL(1,𝔽₅)	semidirect
15. C₃×#1043	C₈₃	direct (N × H)
16. C₃×C₈₃	#1043	direct (N × H)
19. #1043	C₃×C₈₃	direct (N × H)
20. C₈₃	C₃×#1043	direct (N × H)
21. C₃×C₅²	C₄×C₈₃	semidirect
25. C₅²	C₃×C₄×C₈₃	semidirect
27. C₃×C₅	AGL(1,𝔽₅)×C₈₃	semidirect
31. C₅	C₃×AGL(1,𝔽₅)×C₈₃	semidirect
33. C₃	C₈₃×#1043	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×#1043	3
C₃×AGL(1,𝔽₅)×C₈₃	5
C₃×#1043	83

Subgroups — C3×C83×#1043 #38735262

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈₃×#1043 #38735262