Subgroups — C₃×C₈₉×#1043 #40998949

Order 26700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#1043	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₈₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×AGL(1,𝔽₅)×C₈₉	—	5	6	no	maximal
5	C₅⋊D₅×C₈₉	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₈₉	—	5	6	no	—
7	C₅²×C₈₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₈₉	—	5	6	no	—
9	C₃×C₅×C₈₉	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₃×C₄×C₈₉	—	25	1	no	Hall
11	D₅×C₈₉	—	5	6	no	—
12	C₂×C₃×C₈₉	—	25	1	no	—
13	C₅×C₈₉	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
14	C₄×C₈₉	—	25	1	no	Hall
15	C₃×#1043	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₈₉	#1043	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₈₉	—	25	1	no	—
18	C₃×C₅⋊D₅	C₂×C₈₉	1	1	yes	characteristic
19	#1043	C₃×C₈₉	1	1	yes	characteristic, direct product factor, Hall
20	C₈₉	C₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
21	C₃×C₅²	C₄×C₈₉	1	1	yes	characteristic, complemented, Hall
22	C₃×AGL(1,𝔽₅)	—	5	6	no	—
23	C₅⋊D₅	C₂×C₃×C₈₉	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₃×C₄×C₈₉	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₈₉	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)×C₈₉	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	C₈₉×#1043	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₈₉	#1043
commutator, hypocenter	C₅²	C₃×C₄×C₈₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₈₉	C₄
prime radical	C₃×C₅⋊D₅×C₈₉	C₂
cosocle	C₅⋊D₅	C₂×C₃×C₈₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₈₉

Complements

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

N	H ≅ G/N	type
2. C₈₉×#1043	C₃	direct (N × H)
3. C₃×C₅²×C₈₉	C₄	semidirect
7. C₅²×C₈₉	C₃×C₄	semidirect
9. C₃×C₅×C₈₉	AGL(1,𝔽₅)	semidirect
13. C₅×C₈₉	C₃×AGL(1,𝔽₅)	semidirect
15. C₃×#1043	C₈₉	direct (N × H)
16. C₃×C₈₉	#1043	direct (N × H)
19. #1043	C₃×C₈₉	direct (N × H)
20. C₈₉	C₃×#1043	direct (N × H)
21. C₃×C₅²	C₄×C₈₉	semidirect
25. C₅²	C₃×C₄×C₈₉	semidirect
27. C₃×C₅	AGL(1,𝔽₅)×C₈₉	semidirect
31. C₅	C₃×AGL(1,𝔽₅)×C₈₉	semidirect
33. C₃	C₈₉×#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×C₈₉	2
C₈₉×#1043	3
C₃×AGL(1,𝔽₅)×C₈₉	5
C₃×#1043	89

Subgroups — C3×C89×#1043 #40998949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₈₉×#1043 #40998949