Subgroups — C₂×C₃×C₃⋊(D₃₁⋊C₅) #19150125

Order 5580.

88 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×C₃⋊(D₃₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊(D₃₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₃₁⋊C₅	—	3	1	no	maximal
5	C₃²×ΓL(1,𝔽₃₂)	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₉₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₂×C₃×ΓL(1,𝔽₃₂)	—	2	1	no	—
8	C₂×C₃×ΓL(1,𝔽₃₂)	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃⋊(D₃₁⋊C₅)	C₂×C₃	1	2	yes	direct product factor
11	C₃×D₃₁⋊C₅	—	3	2	no	—
12	C₂×D₃₁⋊C₅	—	3	1	no	Hall
13	C₂×C₃²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented
14	C₃×D₉₃	C₂×C₅	1	2	yes	complemented
15	C₃×ΓL(1,𝔽₃₂)	—	2	1	no	—
16	C₃×ΓL(1,𝔽₃₂)	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×ΓL(1,𝔽₃₂)	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×D₉₃	C₃×C₅	1	1	yes	characteristic, complemented
19	C₂×C₃×D₃₁	—	3	1	no	—
20	C₂×ΓL(1,𝔽₃₂)	C₃×D₃	1	1	yes	characteristic, complemented
21	D₃₁⋊C₅	—	3	2	no	—
22	C₃²×C₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₃₁	—	2	1	no	—
24	C₂×C₃×C₃₁	C₅×D₃	1	1	yes	characteristic, complemented
25	C₂×C₃×C₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	D₉₃	C₂×C₃×C₅	1	2	yes	complemented
27	C₃×D₃₁	—	3	2	no	—
28	C₂×C₃×C₅×D₃	—	31	1	no	maximal, Hall
29	ΓL(1,𝔽₃₂)	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
30	C₂×D₃₁	—	3	1	no	Hall
31	C₃×C₃₁	—	2	1	no	—
32	C₃×C₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
33	C₃×C₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
34	C₂×C₃²×C₅	—	31	1	no	—
35	C₃×C₅×D₃	—	31	2	no	—
36	C₂×C₃₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented
37	D₃₁	—	3	2	no	—
38	C₂²×C₃×C₅	—	93	1	no	—
39	C₂×C₅×D₃	—	31	1	no	—
40	C₃²×C₅	—	31	1	no	Hall
41	C₂×C₃×D₃	—	31	1	no	Hall
42	C₃₁	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃×C₅	—	31	1	no	—
44	C₂×C₃×C₅	—	31	1	no	—
45	C₂×C₃×C₅	—	62	1	no	—
46	C₂×C₃×C₅	—	93	2	no	—
47	C₅×D₃	—	31	2	no	—
48	C₂²×C₅	—	93	1	no	Hall
49	C₂×C₃²	D₃₁⋊C₅	1	1	yes	characteristic, complemented
50	C₃×D₃	—	31	2	no	—
51	C₃×C₅	—	31	1	no	—
52	C₃×C₅	—	31	1	no	—
53	C₃×C₅	—	62	1	no	—
54	C₂²×C₃	—	93	1	no	—
55	C₂×D₃	—	31	1	no	—
56	C₂×C₅	—	31	1	no	—
57	C₂×C₅	—	93	2	no	—
58	C₃²	C₂×D₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	93	2	no	—
61	C₂×C₃	C₃×D₃₁⋊C₅	1	1	yes	characteristic, complemented
62	C₂×C₃	C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
63	D₃	—	31	2	no	—
64	C₅	—	31	1	no	Sylow
65	C₂²	—	93	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₃₁⋊C₅	1	1	yes	characteristic, complemented
68	C₃	C₂×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
69	C₂	—	93	2	no	—
70	C₂	C₃×C₃⋊(D₃₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(D₃₁⋊C₅)
commutator, hypocenter	C₃×C₃₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₃₁	C₂×C₅
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ C₂×C₃

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×C₃⋊(D₃₁⋊C₅)	C₂	direct (N × H)
3. C₂×C₃⋊(D₃₁⋊C₅)	C₃	direct (N × H)
5. C₃²×ΓL(1,𝔽₃₂)	C₂²	semidirect
6. C₂×C₃×D₉₃	C₅	semidirect
8. C₂×C₃×ΓL(1,𝔽₃₂)	D₃	semidirect
9. C₂×C₃×ΓL(1,𝔽₃₂)	C₂×C₃	semidirect
10. C₃⋊(D₃₁⋊C₅)	C₂×C₃	direct (N × H)
13. C₂×C₃²×C₃₁	C₂×C₅	semidirect
14. C₃×D₉₃	C₂×C₅	semidirect
16. C₃×ΓL(1,𝔽₃₂)	C₂×D₃	semidirect
17. C₃×ΓL(1,𝔽₃₂)	C₂²×C₃	semidirect
18. C₂×D₉₃	C₃×C₅	semidirect
20. C₂×ΓL(1,𝔽₃₂)	C₃×D₃	semidirect
22. C₃²×C₃₁	C₂²×C₅	semidirect
24. C₂×C₃×C₃₁	C₅×D₃	semidirect
25. C₂×C₃×C₃₁	C₂×C₃×C₅	semidirect
26. D₉₃	C₂×C₃×C₅	semidirect
29. ΓL(1,𝔽₃₂)	C₂×C₃×D₃	semidirect
32. C₃×C₃₁	C₂×C₅×D₃	semidirect
33. C₃×C₃₁	C₂²×C₃×C₅	semidirect
36. C₂×C₃₁	C₃×C₅×D₃	semidirect
42. C₃₁	C₂×C₃×C₅×D₃	semidirect
49. C₂×C₃²	D₃₁⋊C₅	semidirect
58. C₃²	C₂×D₃₁⋊C₅	semidirect
61. C₂×C₃	C₃×D₃₁⋊C₅	semidirect
62. C₂×C₃	C₃⋊(D₃₁⋊C₅)	direct (N × H)
67. C₃	C₂×C₃×D₃₁⋊C₅	semidirect
68. C₃	C₂×C₃⋊(D₃₁⋊C₅)	direct (N × H)
70. C₂	C₃×C₃⋊(D₃₁⋊C₅)	direct (N × H)

Subgroups — C2×C3×C3⋊(D31⋊C5) #19150125

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₃⋊(D₃₁⋊C₅) #19150125