Subgroups — D₃²×C₁₃×C₁₉ #22580365

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃×C₁₉	C₂	1	2	yes	maximal, complemented
3	C₂×D₃×C₁₃×C₁₉	—	3	2	no	maximal
4	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃×C₁₃×C₁₉	—	3	2	no	—
6	D₃×C₁₃×C₁₉	—	3	2	no	—
7	D₃×C₁₃×C₁₉	—	6	1	no	—
8	D₃×C₁₃×C₁₉	D₃	1	2	yes	direct product factor
9	C₂²×C₁₃×C₁₉	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	—	2	1	no	—
11	C₃×C₁₃×C₁₉	C₂×D₃	1	2	yes	complemented
12	D₃²×C₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃×C₁₉	—	3	2	no	—
14	C₂×C₁₃×C₁₉	—	9	1	no	—
15	D₃²×C₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃⋊D₃×C₁₉	C₂×C₁₃	1	1	yes	characteristic, complemented
17	C₃×D₃×C₁₉	C₂×C₁₃	1	2	yes	complemented
18	C₁₃×C₁₉	D₃²	1	1	yes	characteristic, direct product factor, Hall
19	C₁₃×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
20	C₃×D₃×C₁₃	C₂×C₁₉	1	2	yes	complemented
21	C₂×D₃×C₁₉	—	3	2	no	—
22	C₃²×C₁₉	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
23	C₂×D₃×C₁₃	—	3	2	no	—
24	C₃²×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₁₉	—	3	2	no	—
26	D₃×C₁₉	—	3	2	no	—
27	D₃×C₁₉	—	6	1	no	—
28	D₃×C₁₉	D₃×C₁₃	1	2	yes	direct product factor
29	C₂×C₃×C₁₃	—	3	2	no	—
30	D₃×C₁₃	—	3	2	no	—
31	D₃×C₁₃	—	6	1	no	—
32	D₃×C₁₃	D₃×C₁₉	1	2	yes	direct product factor
33	C₂²×C₁₉	—	9	1	no	Hall
34	C₃×C₁₉	—	2	1	no	—
35	C₃×C₁₉	C₂×D₃×C₁₃	1	2	yes	complemented
36	C₂²×C₁₃	—	9	1	no	Hall
37	C₃×C₁₃	—	2	1	no	—
38	C₃×C₁₃	C₂×D₃×C₁₉	1	2	yes	complemented
39	C₂×C₁₉	—	3	2	no	—
40	C₂×C₁₉	—	9	1	no	—
41	D₃²	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₁₃	—	3	2	no	—
43	C₂×C₁₃	—	9	1	no	—
44	C₁₉	D₃²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₃⋊D₃	C₂×C₁₃×C₁₉	1	1	yes	characteristic, complemented
46	C₃×D₃	C₂×C₁₃×C₁₉	1	2	yes	complemented
47	C₁₃	D₃²×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₃	—	3	2	no	—
49	C₃²	C₂²×C₁₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	3	2	no	—
51	D₃	—	3	2	no	—
52	D₃	—	6	1	no	—
53	D₃	D₃×C₁₃×C₁₉	1	2	yes	direct product factor
54	C₂²	—	9	1	no	Sylow
55	C₃	—	2	1	no	—
56	C₃	C₂×D₃×C₁₃×C₁₉	1	2	yes	complemented
57	C₂	—	3	2	no	—
58	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃×C₁₉	D₃²
commutator, hypocenter	C₃²	C₂²×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₃×C₁₉	C₂	semidirect
2. C₃×D₃×C₁₃×C₁₉	C₂	semidirect
4. C₃²×C₁₃×C₁₉	C₂²	semidirect
8. D₃×C₁₃×C₁₉	D₃	direct (N × H)
11. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
12. D₃²×C₁₉	C₁₃	direct (N × H)
15. D₃²×C₁₃	C₁₉	direct (N × H)
16. C₃⋊D₃×C₁₉	C₂×C₁₃	semidirect
17. C₃×D₃×C₁₉	C₂×C₁₃	semidirect
18. C₁₃×C₁₉	D₃²	direct (N × H)
19. C₁₃×C₃⋊D₃	C₂×C₁₉	semidirect
20. C₃×D₃×C₁₃	C₂×C₁₉	semidirect
22. C₃²×C₁₉	C₂²×C₁₃	semidirect
24. C₃²×C₁₃	C₂²×C₁₉	semidirect
28. D₃×C₁₉	D₃×C₁₃	direct (N × H)
32. D₃×C₁₃	D₃×C₁₉	direct (N × H)
35. C₃×C₁₉	C₂×D₃×C₁₃	semidirect
38. C₃×C₁₃	C₂×D₃×C₁₉	semidirect
41. D₃²	C₁₃×C₁₉	direct (N × H)
44. C₁₉	D₃²×C₁₃	direct (N × H)
45. C₃⋊D₃	C₂×C₁₃×C₁₉	semidirect
46. C₃×D₃	C₂×C₁₃×C₁₉	semidirect
47. C₁₃	D₃²×C₁₉	direct (N × H)
49. C₃²	C₂²×C₁₃×C₁₉	semidirect
53. D₃	D₃×C₁₃×C₁₉	direct (N × H)
56. C₃	C₂×D₃×C₁₃×C₁₉	semidirect

Subgroups — D32×C13×C19 #22580365

Conjugacy classes of subgroups

Complements

Subgroups — D₃²×C₁₃×C₁₉ #22580365