Subgroups — C₃²×AGL(1,𝔽₅)×C₃₇ #20269121

Order 6660.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₅×C₃₇	C₂	1	1	yes	maximal, characteristic
2	C₃×AGL(1,𝔽₅)×C₃₇	C₃	1	4	yes	maximal, direct product factor
3	C₃²×C₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃²×C₄×C₃₇	—	5	1	no	maximal, Hall
5	C₃×D₅×C₃₇	C₂×C₃	1	4	yes	—
6	AGL(1,𝔽₅)×C₃₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃²×C₃₇	—	5	1	no	—
8	C₃×C₅×C₃₇	C₃×C₄	1	4	yes	complemented
9	C₃×C₄×C₃₇	—	5	4	no	—
10	D₅×C₃₇	C₂×C₃²	1	1	yes	characteristic
11	C₃²×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃×C₃₇	—	5	4	no	—
13	C₅×C₃₇	C₃²×C₄	1	1	yes	characteristic, complemented, Hall
14	C₃²×AGL(1,𝔽₅)	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₄×C₃₇	—	5	1	no	Hall
16	C₃×C₃₇	C₃×AGL(1,𝔽₅)	1	4	yes	direct product factor
17	C₃²×D₅	C₂×C₃₇	1	1	yes	characteristic
18	C₂×C₃₇	—	5	1	no	—
19	C₃×AGL(1,𝔽₅)	C₃×C₃₇	1	4	yes	direct product factor
20	C₃²×C₅	C₄×C₃₇	1	1	yes	characteristic, complemented, Hall
21	C₃₇	C₃²×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
22	C₃²×C₄	—	5	1	no	Hall
23	C₃×D₅	C₂×C₃×C₃₇	1	4	yes	—
24	AGL(1,𝔽₅)	C₃²×C₃₇	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₃²	—	5	1	no	—
26	C₃×C₅	C₃×C₄×C₃₇	1	4	yes	complemented
27	C₃×C₄	—	5	4	no	—
28	D₅	C₂×C₃²×C₃₇	1	1	yes	characteristic
29	C₃²	AGL(1,𝔽₅)×C₃₇	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	—	5	4	no	—
31	C₅	C₃²×C₄×C₃₇	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	5	1	no	Sylow
33	C₃	C₃×AGL(1,𝔽₅)×C₃₇	1	4	yes	direct product factor
34	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₃²×C₃₇	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₃²×C₄×C₃₇
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₇	C₄
LCS	G ▷ C₅
UCS	C₁ ◁ C₃²×C₃₇

Complements

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

N	H ≅ G/N	type
2. C₃×AGL(1,𝔽₅)×C₃₇	C₃	direct (N × H)
3. C₃²×C₅×C₃₇	C₄	semidirect
6. AGL(1,𝔽₅)×C₃₇	C₃²	direct (N × H)
8. C₃×C₅×C₃₇	C₃×C₄	semidirect
11. C₃²×C₃₇	AGL(1,𝔽₅)	direct (N × H)
13. C₅×C₃₇	C₃²×C₄	semidirect
14. C₃²×AGL(1,𝔽₅)	C₃₇	direct (N × H)
16. C₃×C₃₇	C₃×AGL(1,𝔽₅)	direct (N × H)
19. C₃×AGL(1,𝔽₅)	C₃×C₃₇	direct (N × H)
20. C₃²×C₅	C₄×C₃₇	semidirect
21. C₃₇	C₃²×AGL(1,𝔽₅)	direct (N × H)
24. AGL(1,𝔽₅)	C₃²×C₃₇	direct (N × H)
26. C₃×C₅	C₃×C₄×C₃₇	semidirect
29. C₃²	AGL(1,𝔽₅)×C₃₇	direct (N × H)
31. C₅	C₃²×C₄×C₃₇	semidirect
33. C₃	C₃×AGL(1,𝔽₅)×C₃₇	direct (N × H)

Subgroups — C32×AGL(1,𝔽5)×C37 #20269121

Conjugacy classes of subgroups

Complements

Subgroups — C₃²×AGL(1,𝔽₅)×C₃₇ #20269121