Subgroups — C₂×D₃×C₁₃×C₁₉⋊C₃ #22580331

Order 8892.

88 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	D₃×C₁₃×C₁₉⋊C₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₃×C₁₃×C₁₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₃×C₁₉⋊C₃	—	3	1	no	maximal
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	D₃×C₁₃×C₁₉	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₃×C₁₉⋊C₃	—	2	1	no	—
9	C₂×C₁₃×C₁₉⋊C₃	—	3	2	no	—
10	C₂×C₁₃×C₁₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
11	C₂²×C₁₃×C₁₉	—	3	1	no	Hall
12	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
13	C₁₃×C₁₉⋊C₃	—	2	1	no	—
14	C₁₃×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, direct product factor
15	C₂×D₃×C₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂×C₁₃×C₁₉	—	3	2	no	—
17	C₂×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₃×C₁₃	—	19	1	no	maximal, Hall
19	C₂×C₃×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
20	D₃×C₁₉⋊C₃	C₂×C₁₃	1	2	yes	direct product factor
21	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃²×C₁₃	—	19	1	no	—
23	C₃×D₃×C₁₃	—	19	2	no	—
24	C₂×D₃×C₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
25	C₂²×C₁₉⋊C₃	—	3	1	no	—
26	C₃×C₁₉⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₁₃	—	57	1	no	—
28	C₂×D₃×C₁₃	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
29	C₃²×C₁₃	—	19	1	no	Hall
30	C₂×C₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
31	D₃×C₁₉	C₂×C₃×C₁₃	1	2	yes	complemented
32	C₂×C₁₉⋊C₃	—	2	1	no	—
33	C₂×C₁₉⋊C₃	—	3	2	no	—
34	C₂×C₁₉⋊C₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₁₃	—	19	1	no	—
36	C₂×C₃×C₁₃	—	38	1	no	—
37	C₂×C₃×C₁₃	—	57	2	no	—
38	C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented
39	D₃×C₁₃	C₂×C₁₉⋊C₃	1	2	yes	direct product factor
40	C₂²×C₁₉	—	3	1	no	Hall
41	C₃×C₁₉	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
42	C₁₉⋊C₃	—	2	1	no	—
43	C₁₉⋊C₃	C₂×D₃×C₁₃	1	1	yes	characteristic, direct product factor
44	C₂²×C₁₃	—	3	1	no	Hall
45	C₃×C₁₃	—	19	1	no	—
46	C₃×C₁₃	—	38	1	no	—
47	C₃×C₁₃	C₂²×C₁₉⋊C₃	1	1	yes	characteristic, complemented
48	C₂×C₁₉	—	3	2	no	—
49	C₂×C₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
50	C₂×C₃×D₃	—	19	1	no	Hall
51	C₂×C₁₃	—	3	2	no	—
52	C₂×C₁₃	D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
53	C₁₉	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
54	C₂×C₃²	—	19	1	no	—
55	C₃×D₃	—	19	2	no	—
56	C₁₃	C₂×D₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
57	C₂²×C₃	—	57	1	no	—
58	C₂×D₃	C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
59	C₃²	—	19	1	no	Sylow
60	C₂×C₃	—	19	1	no	—
61	C₂×C₃	—	38	1	no	—
62	C₂×C₃	—	57	2	no	—
63	C₂×C₃	C₂×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
64	D₃	C₂×C₁₃×C₁₉⋊C₃	1	2	yes	direct product factor
65	C₂²	—	3	1	no	Sylow
66	C₃	—	19	1	no	—
67	C₃	—	38	1	no	—
68	C₃	C₂²×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
69	C₂	—	3	2	no	—
70	C₂	D₃×C₁₃×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₃×C₁₉⋊C₃
commutator, hypocenter	C₃×C₁₉	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂×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. D₃×C₁₃×C₁₉⋊C₃	C₂	direct (N × H)
3. C₂×D₃×C₁₃×C₁₉	C₃	semidirect
5. C₃×C₁₃×C₁₉⋊C₃	C₂²	semidirect
6. C₂×C₃×C₁₃×C₁₉	C₂×C₃	semidirect
7. D₃×C₁₃×C₁₉	C₂×C₃	semidirect
10. C₂×C₁₃×C₁₉⋊C₃	D₃	direct (N × H)
12. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
14. C₁₃×C₁₉⋊C₃	C₂×D₃	direct (N × H)
15. C₂×D₃×C₁₉⋊C₃	C₁₃	direct (N × H)
17. C₂×C₁₃×C₁₉	C₃×D₃	semidirect
19. C₂×C₃×C₁₉⋊C₃	C₂×C₁₃	semidirect
20. D₃×C₁₉⋊C₃	C₂×C₁₃	direct (N × H)
21. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
24. C₂×D₃×C₁₉	C₃×C₁₃	semidirect
26. C₃×C₁₉⋊C₃	C₂²×C₁₃	semidirect
28. C₂×D₃×C₁₃	C₁₉⋊C₃	direct (N × H)
30. C₂×C₃×C₁₉	C₂×C₃×C₁₃	semidirect
31. D₃×C₁₉	C₂×C₃×C₁₃	semidirect
34. C₂×C₁₉⋊C₃	D₃×C₁₃	direct (N × H)
38. C₂×C₃×C₁₃	C₂×C₁₉⋊C₃	semidirect
39. D₃×C₁₃	C₂×C₁₉⋊C₃	direct (N × H)
41. C₃×C₁₉	C₂²×C₃×C₁₃	semidirect
43. C₁₉⋊C₃	C₂×D₃×C₁₃	direct (N × H)
47. C₃×C₁₃	C₂²×C₁₉⋊C₃	semidirect
49. C₂×C₁₉	C₃×D₃×C₁₃	semidirect
52. C₂×C₁₃	D₃×C₁₉⋊C₃	direct (N × H)
53. C₁₉	C₂×C₃×D₃×C₁₃	semidirect
56. C₁₃	C₂×D₃×C₁₉⋊C₃	direct (N × H)
58. C₂×D₃	C₁₃×C₁₉⋊C₃	direct (N × H)
63. C₂×C₃	C₂×C₁₃×C₁₉⋊C₃	semidirect
64. D₃	C₂×C₁₃×C₁₉⋊C₃	direct (N × H)
68. C₃	C₂²×C₁₃×C₁₉⋊C₃	semidirect
70. C₂	D₃×C₁₃×C₁₉⋊C₃	direct (N × H)

Subgroups — C2×D3×C13×C19⋊C3 #22580331

Conjugacy classes of subgroups

Complements

Subgroups — C₂×D₃×C₁₃×C₁₉⋊C₃ #22580331