Subgroups — C₂×C₃×C₁₉×D₁₃⋊C₃ #22580319

Order 8892.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₂²×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₃×C₁₉×D₁₃⋊C₃	C₂	direct (N × H)
3. C₂×C₃×C₁₉×D₁₃	C₃	semidirect
4. C₂×C₁₉×D₁₃⋊C₃	C₃	direct (N × H)
5. C₃×C₁₉×C₁₃⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. C₃×C₁₉×D₁₃	C₂×C₃	semidirect
8. C₂×C₁₉×C₁₃⋊C₃	C₂×C₃	semidirect
9. C₁₉×D₁₃⋊C₃	C₂×C₃	direct (N × H)
10. C₂×C₁₉×D₁₃	C₃²	semidirect
11. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
12. C₁₉×C₁₃⋊C₃	C₂²×C₃	semidirect
14. C₂×C₁₃×C₁₉	C₂×C₃²	semidirect
15. C₁₉×D₁₃	C₂×C₃²	semidirect
16. C₂×C₃×D₁₃⋊C₃	C₁₉	direct (N × H)
19. C₁₃×C₁₉	C₂²×C₃²	semidirect
20. C₂×C₃×C₁₃⋊C₃	C₂×C₁₉	semidirect
21. C₃×D₁₃⋊C₃	C₂×C₁₉	direct (N × H)
25. C₂×C₃×D₁₃	C₃×C₁₉	semidirect
26. C₂×D₁₃⋊C₃	C₃×C₁₉	direct (N × H)
27. C₃×C₁₃⋊C₃	C₂²×C₁₉	semidirect
31. C₂×C₃×C₁₉	D₁₃⋊C₃	direct (N × H)
32. C₂×C₃×C₁₃	C₂×C₃×C₁₉	semidirect
33. C₃×D₁₃	C₂×C₃×C₁₉	semidirect
34. C₂×C₁₃⋊C₃	C₂×C₃×C₁₉	semidirect
35. D₁₃⋊C₃	C₂×C₃×C₁₉	direct (N × H)
38. C₃×C₁₉	C₂×D₁₃⋊C₃	direct (N × H)
39. C₂×D₁₃	C₃²×C₁₉	semidirect
40. C₃×C₁₃	C₂²×C₃×C₁₉	semidirect
41. C₁₃⋊C₃	C₂²×C₃×C₁₉	semidirect
43. C₂×C₁₉	C₃×D₁₃⋊C₃	direct (N × H)
45. C₂×C₁₃	C₂×C₃²×C₁₉	semidirect
46. D₁₃	C₂×C₃²×C₁₉	semidirect
47. C₁₉	C₂×C₃×D₁₃⋊C₃	direct (N × H)
50. C₁₃	C₂²×C₃²×C₁₉	semidirect
57. C₂×C₃	C₁₉×D₁₃⋊C₃	direct (N × H)
60. C₃	C₂×C₁₉×D₁₃⋊C₃	direct (N × H)
62. C₂	C₃×C₁₉×D₁₃⋊C₃	direct (N × H)

Subgroups — C2×C3×C19×D13⋊C3 #22580319

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₉×D₁₃⋊C₃ #22580319