Subgroups — C₂×C₃⋊D₃×ΓL(1,𝔽₃₂) #19150128

Order 5580.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊D₃×ΓL(1,𝔽₃₂)	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×ΓL(1,𝔽₃₂)	—	3	4	no	maximal
4	C₃²×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₃×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₃×ΓL(1,𝔽₃₂)	D₃	1	4	yes	complemented
7	D₃×ΓL(1,𝔽₃₂)	—	3	8	no	—
8	C₂²×ΓL(1,𝔽₃₂)	—	9	1	no	Hall
9	C₂×C₃²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃⋊D₃×C₃₁	C₂×C₅	1	2	yes	complemented
11	C₃×ΓL(1,𝔽₃₂)	C₂×D₃	1	4	yes	complemented
12	C₂×D₃×C₃₁	—	3	4	no	—
13	C₂×ΓL(1,𝔽₃₂)	—	9	2	no	—
14	C₂×ΓL(1,𝔽₃₂)	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃²×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₃×C₃₁	C₅×D₃	1	4	yes	complemented
17	D₃×C₃₁	—	3	8	no	—
18	C₂×C₅×C₃⋊D₃	—	31	1	no	maximal, Hall
19	ΓL(1,𝔽₃₂)	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂²×C₃₁	—	9	1	no	Hall
21	C₃×C₃₁	C₂×C₅×D₃	1	4	yes	complemented
22	C₂×C₃²×C₅	—	31	1	no	—
23	C₅×C₃⋊D₃	—	31	2	no	—
24	C₂×C₃₁	—	9	2	no	—
25	C₂×C₃₁	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
26	C₂×C₅×D₃	—	93	4	no	—
27	C₃²×C₅	—	31	1	no	Hall
28	C₂×C₃⋊D₃	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
29	C₃₁	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃×C₅	—	31	4	no	—
31	C₅×D₃	—	93	8	no	—
32	C₂²×C₅	—	279	1	no	Hall
33	C₂×C₃²	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented
34	C₃⋊D₃	C₂×ΓL(1,𝔽₃₂)	1	2	yes	direct product factor
35	C₃×C₅	—	31	4	no	—
36	C₂×D₃	—	3	4	no	—
37	C₂×C₅	—	279	2	no	—
38	C₂×C₅	—	31	1	no	—
39	C₃²	C₂²×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, complemented, Sylow
40	C₂×C₃	D₃×ΓL(1,𝔽₃₂)	1	4	yes	complemented
41	D₃	—	3	8	no	—
42	C₅	—	31	1	no	Sylow
43	C₂²	—	9	1	no	Sylow
44	C₃	C₂×D₃×ΓL(1,𝔽₃₂)	1	4	yes	complemented
45	C₂	—	9	2	no	—
46	C₂	C₃⋊D₃×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊D₃×ΓL(1,𝔽₃₂)
commutator, hypocenter	C₃²×C₃₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₃₁	C₂×C₅
LCS	G ▷ C₃²×C₃₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃²×ΓL(1,𝔽₃₂)	C₂	semidirect
2. C₃⋊D₃×ΓL(1,𝔽₃₂)	C₂	direct (N × H)
4. C₃²×ΓL(1,𝔽₃₂)	C₂²	semidirect
5. C₂×C₃⋊D₃×C₃₁	C₅	semidirect
6. C₂×C₃×ΓL(1,𝔽₃₂)	D₃	semidirect
9. C₂×C₃²×C₃₁	C₂×C₅	semidirect
10. C₃⋊D₃×C₃₁	C₂×C₅	semidirect
11. C₃×ΓL(1,𝔽₃₂)	C₂×D₃	semidirect
14. C₂×ΓL(1,𝔽₃₂)	C₃⋊D₃	direct (N × H)
15. C₃²×C₃₁	C₂²×C₅	semidirect
16. C₂×C₃×C₃₁	C₅×D₃	semidirect
19. ΓL(1,𝔽₃₂)	C₂×C₃⋊D₃	direct (N × H)
21. C₃×C₃₁	C₂×C₅×D₃	semidirect
25. C₂×C₃₁	C₅×C₃⋊D₃	semidirect
28. C₂×C₃⋊D₃	ΓL(1,𝔽₃₂)	direct (N × H)
29. C₃₁	C₂×C₅×C₃⋊D₃	semidirect
33. C₂×C₃²	C₂×ΓL(1,𝔽₃₂)	semidirect
34. C₃⋊D₃	C₂×ΓL(1,𝔽₃₂)	direct (N × H)
39. C₃²	C₂²×ΓL(1,𝔽₃₂)	semidirect
40. C₂×C₃	D₃×ΓL(1,𝔽₃₂)	semidirect
44. C₃	C₂×D₃×ΓL(1,𝔽₃₂)	semidirect
46. C₂	C₃⋊D₃×ΓL(1,𝔽₃₂)	direct (N × H)

Subgroups — C2×C3⋊D3×ΓL(1,𝔽32) #19150128

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃⋊D₃×ΓL(1,𝔽₃₂) #19150128