Subgroups — D₃×C₁₃×D₁₉⋊C₃ #22580271

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃×C₁₃×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×C₃⋊(D₁₉⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₁₃×D₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₁₃×D₁₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×D₁₉⋊C₃	—	3	1	no	maximal
6	C₃×C₁₃×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₁₃×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
8	D₃×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₂×C₁₃×C₁₉⋊C₃	—	3	1	no	—
11	C₁₃×D₁₉⋊C₃	—	2	1	no	—
12	C₁₃×D₁₉⋊C₃	—	3	1	no	—
13	C₁₃×D₁₉⋊C₃	D₃	1	1	yes	characteristic, direct product factor
14	C₂×C₁₃×D₁₉	—	3	1	no	Hall
15	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₁₃×C₁₉⋊C₃	—	2	1	no	—
17	C₁₃×C₁₉⋊C₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₁₉⋊C₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₃×C₁₉	—	3	1	no	—
20	C₁₃×D₁₉	—	3	1	no	—
21	C₁₃×D₁₉	C₃×D₃	1	1	yes	characteristic, complemented
22	C₂×C₃×D₃×C₁₃	—	19	1	no	maximal, Hall
23	C₃⋊(D₁₉⋊C₃)	C₂×C₁₃	1	1	yes	characteristic, complemented
24	D₃×C₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₃×D₁₉⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃²×C₁₃	—	19	1	no	—
28	C₃×D₃×C₁₃	—	19	1	no	—
29	C₃×D₃×C₁₃	—	19	1	no	—
30	D₃×D₁₉	C₃×C₁₃	1	1	yes	characteristic, complemented
31	C₂×D₁₉⋊C₃	—	3	1	no	—
32	C₃×C₁₉⋊C₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃×C₁₃	—	57	1	no	—
34	C₂×D₃×C₁₃	—	19	1	no	—
35	C₃²×C₁₃	—	19	1	no	Hall
36	D₅₇	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
37	C₃×D₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
38	D₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
39	C₂×C₁₉⋊C₃	—	3	1	no	—
40	D₁₉⋊C₃	—	2	1	no	—
41	D₁₉⋊C₃	—	3	1	no	—
42	D₁₉⋊C₃	D₃×C₁₃	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₁₃	—	19	1	no	—
44	C₂×C₃×C₁₃	—	19	1	no	—
45	C₂×C₃×C₁₃	—	38	1	no	—
46	C₂×C₃×C₁₃	—	57	1	no	—
47	C₂×C₃×C₁₃	—	57	1	no	—
48	D₃×C₁₃	—	19	1	no	—
49	D₃×C₁₃	D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
50	C₂×D₁₉	—	3	1	no	Hall
51	C₃×C₁₉	C₂²×C₃×C₁₃	1	1	yes	characteristic, complemented
52	C₁₉⋊C₃	—	2	1	no	—
53	C₁₉⋊C₃	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
54	C₂²×C₁₃	—	57	1	no	Hall
55	C₃×C₁₃	—	19	1	no	—
56	C₃×C₁₃	—	38	1	no	—
57	C₃×C₁₃	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	3	1	no	—
59	D₁₉	—	3	1	no	—
60	D₁₉	C₃×D₃×C₁₃	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃	—	19	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	C₂×C₁₃	—	19	1	no	—
64	C₂×C₁₃	—	57	1	no	—
65	C₁₉	C₂×C₃×D₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	19	1	no	—
67	C₃×D₃	—	19	1	no	—
68	C₃×D₃	—	19	1	no	—
69	C₁₃	D₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²×C₃	—	57	1	no	—
71	C₂×D₃	—	19	1	no	—
72	C₃²	—	19	1	no	Sylow
73	C₂×C₃	—	19	1	no	—
74	C₂×C₃	—	19	1	no	—
75	C₂×C₃	—	38	1	no	—
76	C₂×C₃	—	57	1	no	—
77	C₂×C₃	—	57	1	no	—
78	D₃	—	19	1	no	—
79	D₃	C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	57	1	no	Sylow
81	C₃	—	19	1	no	—
82	C₃	—	38	1	no	—
83	C₃	C₂×C₁₃×D₁₉⋊C₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	19	1	no	—
86	C₂	—	57	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₁₉⋊C₃
commutator, hypocenter	C₃×C₁₉	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₁₉	C₂²×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. D₃×C₁₃×C₁₉⋊C₃	C₂	semidirect
2. C₁₃×C₃⋊(D₁₉⋊C₃)	C₂	semidirect
3. C₃×C₁₃×D₁₉⋊C₃	C₂	semidirect
4. D₃×C₁₃×D₁₉	C₃	semidirect
6. C₃×C₁₃×C₁₉⋊C₃	C₂²	semidirect
7. C₁₃×D₅₇	C₂×C₃	semidirect
8. D₃×C₁₃×C₁₉	C₂×C₃	semidirect
9. C₃×C₁₃×D₁₉	C₂×C₃	semidirect
13. C₁₃×D₁₉⋊C₃	D₃	direct (N × H)
15. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
17. C₁₃×C₁₉⋊C₃	C₂×D₃	semidirect
18. D₃×D₁₉⋊C₃	C₁₃	direct (N × H)
21. C₁₃×D₁₉	C₃×D₃	semidirect
23. C₃⋊(D₁₉⋊C₃)	C₂×C₁₃	semidirect
24. D₃×C₁₉⋊C₃	C₂×C₁₃	semidirect
25. C₃×D₁₉⋊C₃	C₂×C₁₃	semidirect
26. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
30. D₃×D₁₉	C₃×C₁₃	semidirect
32. C₃×C₁₉⋊C₃	C₂²×C₁₃	semidirect
36. D₅₇	C₂×C₃×C₁₃	semidirect
37. C₃×D₁₉	C₂×C₃×C₁₃	semidirect
38. D₃×C₁₉	C₂×C₃×C₁₃	semidirect
42. D₁₉⋊C₃	D₃×C₁₃	direct (N × H)
49. D₃×C₁₃	D₁₉⋊C₃	direct (N × H)
51. C₃×C₁₉	C₂²×C₃×C₁₃	semidirect
53. C₁₉⋊C₃	C₂×D₃×C₁₃	semidirect
57. C₃×C₁₃	C₂×D₁₉⋊C₃	semidirect
60. D₁₉	C₃×D₃×C₁₃	semidirect
65. C₁₉	C₂×C₃×D₃×C₁₃	semidirect
69. C₁₃	D₃×D₁₉⋊C₃	direct (N × H)
79. D₃	C₁₃×D₁₉⋊C₃	direct (N × H)
83. C₃	C₂×C₁₃×D₁₉⋊C₃	semidirect

Subgroups — D3×C13×D19⋊C3 #22580271

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₃×D₁₉⋊C₃ #22580271