Subgroups — C₂×C₃×C₁₃×D₁₉⋊C₃ #22580318

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₁₉⋊C₃	C₃	1	3	yes	maximal, direct product factor
5	C₃×C₁₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
7	C₃×C₁₃×D₁₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	1	3	yes	complemented
9	C₁₃×D₁₉⋊C₃	C₂×C₃	1	6	yes	direct product factor
10	C₂×C₁₃×D₁₉	C₃²	1	1	yes	characteristic, complemented, Hall
11	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
12	C₁₃×C₁₉⋊C₃	C₂²×C₃	1	3	yes	complemented
13	C₂×C₃×D₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂×C₁₃×C₁₉	C₂×C₃²	1	1	yes	characteristic, complemented
15	C₁₃×D₁₉	C₂×C₃²	1	2	yes	complemented
16	C₂²×C₃²×C₁₃	—	19	1	no	maximal, Hall
17	C₂×C₃×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₃×D₁₉⋊C₃	C₂×C₁₃	1	2	yes	direct product factor
19	C₁₃×C₁₉	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃²×C₁₃	—	19	2	no	—
21	C₂×C₃²×C₁₃	—	19	1	no	—
22	C₂×C₃×D₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
23	C₂×D₁₉⋊C₃	C₃×C₁₃	1	3	yes	direct product factor
24	C₃×C₁₉⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃×C₁₃	—	19	3	no	—
26	C₂²×C₃×C₁₃	—	19	1	no	—
27	C₃²×C₁₃	—	19	1	no	Hall
28	C₂×C₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
29	C₃×D₁₉	C₂×C₃×C₁₃	1	2	yes	complemented
30	C₂×C₁₉⋊C₃	C₂×C₃×C₁₃	1	3	yes	complemented
31	D₁₉⋊C₃	C₂×C₃×C₁₃	1	6	yes	direct product factor
32	C₂×C₃×C₁₃	—	19	6	no	—
33	C₂×C₃×C₁₃	—	19	2	no	—
34	C₂×C₃×C₁₃	—	19	3	no	—
35	C₂×C₃×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
36	C₂×D₁₉	C₃²×C₁₃	1	1	yes	characteristic, complemented, Hall
37	C₃×C₁₉	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
38	C₁₉⋊C₃	C₂²×C₃×C₁₃	1	3	yes	complemented
39	C₂²×C₁₃	—	19	1	no	Hall
40	C₃×C₁₃	—	19	3	no	—
41	C₃×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
42	C₂×C₁₉	C₂×C₃²×C₁₃	1	1	yes	characteristic, complemented
43	D₁₉	C₂×C₃²×C₁₃	1	2	yes	complemented
44	C₂²×C₃²	—	19	1	no	Hall
45	C₂×C₁₃	—	19	2	no	—
46	C₂×C₁₃	C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
47	C₁₉	C₂²×C₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
48	C₂×C₃²	—	19	2	no	—
49	C₂×C₃²	—	19	1	no	—
50	C₁₃	C₂×C₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
51	C₂²×C₃	—	19	3	no	—
52	C₂²×C₃	—	19	1	no	—
53	C₃²	—	19	1	no	Sylow
54	C₂×C₃	—	19	6	no	—
55	C₂×C₃	—	19	2	no	—
56	C₂×C₃	—	19	3	no	—
57	C₂×C₃	C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂²	—	19	1	no	Sylow
59	C₃	—	19	3	no	—
60	C₃	C₂×C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
61	C₂	—	19	2	no	—
62	C₂	C₃×C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₃²×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₃×C₁₉⋊C₃	C₂	semidirect
2. C₃×C₁₃×D₁₉⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₁₃×D₁₉	C₃	semidirect
4. C₂×C₁₃×D₁₉⋊C₃	C₃	direct (N × H)
5. C₃×C₁₃×C₁₉⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₃×C₁₃×D₁₉	C₂×C₃	semidirect
8. C₂×C₁₃×C₁₉⋊C₃	C₂×C₃	semidirect
9. C₁₃×D₁₉⋊C₃	C₂×C₃	direct (N × H)
10. C₂×C₁₃×D₁₉	C₃²	semidirect
11. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
12. C₁₃×C₁₉⋊C₃	C₂²×C₃	semidirect
13. C₂×C₃×D₁₉⋊C₃	C₁₃	direct (N × H)
14. C₂×C₁₃×C₁₉	C₂×C₃²	semidirect
15. C₁₃×D₁₉	C₂×C₃²	semidirect
17. C₂×C₃×C₁₉⋊C₃	C₂×C₁₃	semidirect
18. C₃×D₁₉⋊C₃	C₂×C₁₃	direct (N × H)
19. C₁₃×C₁₉	C₂²×C₃²	semidirect
22. C₂×C₃×D₁₉	C₃×C₁₃	semidirect
23. C₂×D₁₉⋊C₃	C₃×C₁₃	direct (N × H)
24. C₃×C₁₉⋊C₃	C₂²×C₁₃	semidirect
28. C₂×C₃×C₁₉	C₂×C₃×C₁₃	semidirect
29. C₃×D₁₉	C₂×C₃×C₁₃	semidirect
30. C₂×C₁₉⋊C₃	C₂×C₃×C₁₃	semidirect
31. D₁₉⋊C₃	C₂×C₃×C₁₃	direct (N × H)
35. C₂×C₃×C₁₃	D₁₉⋊C₃	direct (N × H)
36. C₂×D₁₉	C₃²×C₁₃	semidirect
37. C₃×C₁₉	C₂²×C₃×C₁₃	semidirect
38. C₁₉⋊C₃	C₂²×C₃×C₁₃	semidirect
41. C₃×C₁₃	C₂×D₁₉⋊C₃	direct (N × H)
42. C₂×C₁₉	C₂×C₃²×C₁₃	semidirect
43. D₁₉	C₂×C₃²×C₁₃	semidirect
46. C₂×C₁₃	C₃×D₁₉⋊C₃	direct (N × H)
47. C₁₉	C₂²×C₃²×C₁₃	semidirect
50. C₁₃	C₂×C₃×D₁₉⋊C₃	direct (N × H)
57. C₂×C₃	C₁₃×D₁₉⋊C₃	direct (N × H)
60. C₃	C₂×C₁₃×D₁₉⋊C₃	direct (N × H)
62. C₂	C₃×C₁₃×D₁₉⋊C₃	direct (N × H)

Subgroups — C2×C3×C13×D19⋊C3 #22580318

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₃×D₁₉⋊C₃ #22580318