Subgroups — C₃×(C₃₁⋊C₃)⋊AGL(1,𝔽₅) #19150113

Order 5580.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₅×C₃₁⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃₁⋊AGL(1,𝔽₅)	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	C₃	1	3	yes	maximal, direct product factor
4	C₃×C₅×C₃₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×(C₃₁⋊C₃)⋊C₄	—	5	1	no	maximal, Hall
6	C₃×D₅×C₃₁	C₂×C₃	1	1	yes	characteristic
7	D₅×C₃₁⋊C₃	C₂×C₃	1	3	yes	—
8	C₃₁⋊AGL(1,𝔽₅)	C₃²	1	1	yes	characteristic, complemented, Hall
9	C₂×C₃×C₃₁⋊C₃	—	5	1	no	—
10	C₃×C₅×C₃₁	C₃×C₄	1	1	yes	characteristic, complemented
11	C₅×C₃₁⋊C₃	C₃×C₄	1	3	yes	complemented
12	C₃×Dic₃₁	—	5	1	no	—
13	(C₃₁⋊C₃)⋊C₄	—	5	3	no	—
14	D₅×C₃₁	C₂×C₃²	1	1	yes	characteristic
15	C₃×C₃₁⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₁	—	5	1	no	—
17	C₂×C₃₁⋊C₃	—	5	3	no	—
18	C₃²×AGL(1,𝔽₅)	—	31	1	no	maximal, Hall
19	C₅×C₃₁	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
20	Dic₃₁	—	5	1	no	Hall
21	C₃×C₃₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
22	C₃₁⋊C₃	C₃×AGL(1,𝔽₅)	1	3	yes	complemented
23	C₃²×D₅	—	31	1	no	—
24	C₂×C₃₁	—	5	1	no	—
25	C₃×AGL(1,𝔽₅)	—	31	3	no	—
26	C₃×AGL(1,𝔽₅)	—	31	1	no	—
27	C₃²×C₅	—	31	1	no	Hall
28	C₃²×C₄	—	155	1	no	Hall
29	C₃₁	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
30	C₃×D₅	—	31	3	no	—
31	C₃×D₅	D₃₁⋊C₃	1	1	yes	characteristic
32	AGL(1,𝔽₅)	—	31	1	no	Hall
33	C₂×C₃²	—	155	1	no	—
34	C₃×C₅	—	31	3	no	—
35	C₃×C₅	(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented
36	C₃×C₄	—	155	1	no	—
37	C₃×C₄	—	155	3	no	—
38	D₅	C₃×D₃₁⋊C₃	1	1	yes	characteristic
39	C₃²	—	31	1	no	Sylow
40	C₂×C₃	—	5	1	no	—
41	C₂×C₃	—	155	3	no	—
42	C₅	C₃×(C₃₁⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
43	C₄	—	155	1	no	Sylow
44	C₃	—	31	3	no	—
45	C₃	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅×C₃₁	C₃²×C₄
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₃₁	C₃×C₄
LCS	G ▷ C₅×C₃₁
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
2. C₃×C₃₁⋊AGL(1,𝔽₅)	C₃	semidirect
3. (C₃₁⋊C₃)⋊AGL(1,𝔽₅)	C₃	direct (N × H)
4. C₃×C₅×C₃₁⋊C₃	C₄	semidirect
8. C₃₁⋊AGL(1,𝔽₅)	C₃²	semidirect
10. C₃×C₅×C₃₁	C₃×C₄	semidirect
11. C₅×C₃₁⋊C₃	C₃×C₄	semidirect
15. C₃×C₃₁⋊C₃	AGL(1,𝔽₅)	semidirect
19. C₅×C₃₁	C₃²×C₄	semidirect
21. C₃×C₃₁	C₃×AGL(1,𝔽₅)	semidirect
22. C₃₁⋊C₃	C₃×AGL(1,𝔽₅)	semidirect
29. C₃₁	C₃²×AGL(1,𝔽₅)	semidirect
35. C₃×C₅	(C₃₁⋊C₃)⋊C₄	semidirect
42. C₅	C₃×(C₃₁⋊C₃)⋊C₄	semidirect
45. C₃	(C₃₁⋊C₃)⋊AGL(1,𝔽₅)	direct (N × H)

Subgroups — C3×(C31⋊C3)⋊AGL(1,𝔽5) #19150113

Conjugacy classes of subgroups

Complements

Subgroups — C₃×(C₃₁⋊C₃)⋊AGL(1,𝔽₅) #19150113