Subgroups — C₃×C₃₁×#1043 #22604892

Order 9300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₁×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#1043	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₅²×C₃₁	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×AGL(1,𝔽₅)×C₃₁	—	5	6	no	maximal
5	C₃₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₃×D₅×C₃₁	—	5	6	no	—
7	C₅²×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	AGL(1,𝔽₅)×C₃₁	—	5	6	no	—
9	C₃×C₅×C₃₁	AGL(1,𝔽₅)	1	6	yes	complemented
10	C₃×C₄×C₃₁	—	25	1	no	Hall
11	D₅×C₃₁	—	5	6	no	—
12	C₃×#1043	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₃₁	—	25	1	no	—
14	C₅×C₃₁	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
15	C₃×C₅⋊D₅	C₂×C₃₁	1	1	yes	characteristic
16	C₄×C₃₁	—	25	1	no	Hall
17	#1043	C₃×C₃₁	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₃₁	#1043	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₅²	C₄×C₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃₁	—	25	1	no	—
21	C₃×AGL(1,𝔽₅)	—	5	6	no	—
22	C₅⋊D₅	C₂×C₃×C₃₁	1	1	yes	characteristic
23	C₃₁	C₃×#1043	1	1	yes	characteristic, direct product factor, Sylow
24	C₃×D₅	—	5	6	no	—
25	C₅²	C₃×C₄×C₃₁	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	5	6	no	—
27	C₃×C₅	AGL(1,𝔽₅)×C₃₁	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)×C₃₁	1	6	yes	complemented
32	C₄	—	25	1	no	Sylow
33	C₃	C₃₁×#1043	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₃₁	#1043
commutator, hypocenter	C₅²	C₃×C₄×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₃₁	C₄
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₃₁

Complements

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

N	H ≅ G/N	type
2. C₃₁×#1043	C₃	direct (N × H)
3. C₃×C₅²×C₃₁	C₄	semidirect
7. C₅²×C₃₁	C₃×C₄	semidirect
9. C₃×C₅×C₃₁	AGL(1,𝔽₅)	semidirect
12. C₃×#1043	C₃₁	direct (N × H)
14. C₅×C₃₁	C₃×AGL(1,𝔽₅)	semidirect
17. #1043	C₃×C₃₁	direct (N × H)
18. C₃×C₃₁	#1043	direct (N × H)
19. C₃×C₅²	C₄×C₃₁	semidirect
23. C₃₁	C₃×#1043	direct (N × H)
25. C₅²	C₃×C₄×C₃₁	semidirect
27. C₃×C₅	AGL(1,𝔽₅)×C₃₁	semidirect
31. C₅	C₃×AGL(1,𝔽₅)×C₃₁	semidirect
33. C₃	C₃₁×#1043	direct (N × H)

Subgroups — C3×C31×#1043 #22604892

Conjugacy classes of subgroups

Complements

Subgroups — C₃×C₃₁×#1043 #22604892