Subgroups — C₃⋊D₃×C₁₉×D₁₃ #22580361

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊D₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₉×D₁₃	—	3	4	no	maximal
5	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₁₉×D₃₉	—	3	4	no	—
7	D₃×C₁₃×C₁₉	—	3	4	no	—
8	C₃×C₁₉×D₁₃	D₃	1	4	yes	complemented
9	C₂×C₁₉×D₁₃	—	9	1	no	Hall
10	C₃×C₁₃×C₁₉	C₂×D₃	1	4	yes	complemented
11	C₂×C₃⋊D₃×C₁₉	—	13	1	no	maximal, Hall
12	C₂×C₁₃×C₁₉	—	9	1	no	—
13	C₁₉×D₁₃	—	9	1	no	—
14	C₁₉×D₁₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃⋊D₃×D₁₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₃²×C₁₉	—	13	1	no	—
17	C₃⋊D₃×C₁₉	—	13	1	no	—
18	C₃⋊D₃×C₁₉	D₁₃	1	1	yes	characteristic, direct product factor
19	C₁₃×C₁₉	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
20	C₃⋊D₃₉	C₂×C₁₉	1	1	yes	characteristic, complemented
21	C₁₃×C₃⋊D₃	C₂×C₁₉	1	1	yes	characteristic, complemented
22	C₃²×D₁₃	C₂×C₁₉	1	1	yes	characteristic, complemented
23	C₂×D₃×C₁₉	—	39	4	no	—
24	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
25	D₃×D₁₃	—	3	4	no	—
26	C₃²×C₁₃	C₂²×C₁₉	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₉	—	13	4	no	—
28	D₃×C₁₉	—	3	4	no	—
29	D₃×C₁₉	—	39	4	no	—
30	D₃₉	—	3	4	no	—
31	C₃×D₁₃	D₃×C₁₉	1	4	yes	complemented
32	D₃×C₁₃	—	3	4	no	—
33	C₂²×C₁₉	—	117	1	no	Hall
34	C₃×C₁₉	D₃×D₁₃	1	4	yes	complemented
35	C₂×D₁₃	—	9	1	no	Hall
36	C₃×C₁₃	C₂×D₃×C₁₉	1	4	yes	complemented
37	C₂×C₁₉	—	9	1	no	—
38	C₂×C₁₉	—	13	1	no	—
39	C₂×C₁₉	—	117	1	no	—
40	C₂×C₃⋊D₃	—	13	1	no	Hall
41	C₂×C₁₃	—	9	1	no	—
42	D₁₃	—	9	1	no	—
43	D₁₃	C₃⋊D₃×C₁₉	1	1	yes	characteristic, direct product factor
44	C₁₉	C₃⋊D₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
45	C₂×C₃²	—	13	1	no	—
46	C₃⋊D₃	—	13	1	no	—
47	C₃⋊D₃	C₁₉×D₁₃	1	1	yes	characteristic, direct product factor
48	C₁₃	C₂×C₃⋊D₃×C₁₉	1	1	yes	characteristic, complemented, Sylow
49	C₂×D₃	—	39	4	no	—
50	C₃²	C₂×C₁₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
51	C₂×C₃	—	13	4	no	—
52	D₃	—	3	4	no	—
53	D₃	—	39	4	no	—
54	C₂²	—	117	1	no	Sylow
55	C₃	D₃×C₁₉×D₁₃	1	4	yes	complemented
56	C₂	—	9	1	no	—
57	C₂	—	13	1	no	—
58	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	C₃⋊D₃×D₁₃
commutator, hypocenter	C₃²×C₁₃	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
1. C₁₉×C₃⋊D₃₉	C₂	semidirect
2. C₁₃×C₃⋊D₃×C₁₉	C₂	semidirect
3. C₃²×C₁₉×D₁₃	C₂	semidirect
5. C₃²×C₁₃×C₁₉	C₂²	semidirect
8. C₃×C₁₉×D₁₃	D₃	semidirect
10. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
14. C₁₉×D₁₃	C₃⋊D₃	direct (N × H)
15. C₃⋊D₃×D₁₃	C₁₉	direct (N × H)
18. C₃⋊D₃×C₁₉	D₁₃	direct (N × H)
19. C₁₃×C₁₉	C₂×C₃⋊D₃	semidirect
20. C₃⋊D₃₉	C₂×C₁₉	semidirect
21. C₁₃×C₃⋊D₃	C₂×C₁₉	semidirect
22. C₃²×D₁₃	C₂×C₁₉	semidirect
24. C₃²×C₁₉	C₂×D₁₃	semidirect
26. C₃²×C₁₃	C₂²×C₁₉	semidirect
31. C₃×D₁₃	D₃×C₁₉	semidirect
34. C₃×C₁₉	D₃×D₁₃	semidirect
36. C₃×C₁₃	C₂×D₃×C₁₉	semidirect
43. D₁₃	C₃⋊D₃×C₁₉	direct (N × H)
44. C₁₉	C₃⋊D₃×D₁₃	direct (N × H)
47. C₃⋊D₃	C₁₉×D₁₃	direct (N × H)
48. C₁₃	C₂×C₃⋊D₃×C₁₉	semidirect
50. C₃²	C₂×C₁₉×D₁₃	semidirect
55. C₃	D₃×C₁₉×D₁₃	semidirect

Subgroups — C3⋊D3×C19×D13 #22580361

Conjugacy classes of subgroups

Complements

Subgroups — C₃⋊D₃×C₁₉×D₁₃ #22580361