Subgroups — C₃×D₁₉×D₃₉ #22580352

Order 8892.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇₄₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₉×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₃×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₉×D₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₃×D₁₃×D₁₉	—	3	1	no	maximal
6	C₃²×C₁₃×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₇₄₁	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₉×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₂₄₇	—	3	1	no	—
10	C₃×C₁₉×D₁₃	—	3	1	no	—
11	C₃×C₁₃×D₁₉	—	2	1	no	—
12	C₃×C₁₃×D₁₉	D₃	1	1	yes	characteristic, complemented
13	C₃×C₁₃×D₁₉	C₂×C₃	1	1	yes	characteristic, complemented
14	D₁₃×D₁₉	—	3	1	no	Hall
15	C₃×C₁₃×C₁₉	—	2	1	no	—
16	C₃×C₁₃×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₃×D₃×D₁₉	—	13	1	no	maximal, Hall
19	D₂₄₇	—	3	1	no	—
20	C₁₃×D₁₉	C₃×D₃	1	1	yes	characteristic, complemented
21	C₁₉×D₁₃	—	3	1	no	—
22	C₂×C₃×D₃₉	—	19	1	no	maximal, Hall
23	C₃×D₅₇	—	13	1	no	—
24	C₃×D₃×C₁₉	—	13	1	no	—
25	C₃²×D₁₉	D₁₃	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×D₃₉	—	19	1	no	—
29	C₃×D₃₉	D₁₉	1	1	yes	characteristic, direct product factor
30	C₂×C₃×D₁₉	—	39	1	no	—
31	D₃×D₁₉	—	13	1	no	—
32	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃₉	—	19	1	no	—
34	C₂×C₃×D₁₃	—	57	1	no	—
35	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₉	—	39	1	no	—
37	D₅₇	—	13	1	no	—
38	C₃×D₁₉	—	2	1	no	—
39	C₃×D₁₉	—	39	1	no	—
40	C₃×D₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
41	C₃×D₁₉	D₃₉	1	1	yes	characteristic, direct product factor
42	D₃×C₁₉	—	13	1	no	—
43	C₂×C₃×C₁₃	—	19	1	no	—
44	C₂×C₃×C₁₃	—	19	1	no	—
45	C₂×C₃×C₁₃	—	38	1	no	—
46	D₃₉	—	19	1	no	—
47	D₃₉	C₃×D₁₉	1	1	yes	characteristic, direct product factor
48	C₃×D₁₃	—	3	1	no	—
49	C₃×D₁₃	—	57	1	no	—
50	C₂×D₁₉	—	39	1	no	Hall
51	C₃×C₁₉	—	2	1	no	—
52	C₃×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×D₃₉	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	57	1	no	Hall
55	C₃×C₁₃	—	2	1	no	—
56	C₃×C₁₃	D₃×D₁₉	1	1	yes	characteristic, complemented
57	C₃×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	39	1	no	—
59	D₁₉	—	39	1	no	—
60	D₁₉	C₃×D₃₉	1	1	yes	characteristic, direct product factor
61	C₂×C₃×D₃	—	247	1	no	Hall
62	C₂×C₁₃	—	19	1	no	—
63	D₁₃	—	3	1	no	—
64	D₁₃	—	57	1	no	—
65	C₁₉	C₂×C₃×D₃₉	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	19	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	—	247	1	no	—
69	C₁₃	C₃×D₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	741	1	no	—
71	C₂×D₃	—	247	1	no	—
72	C₃²	D₁₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	19	1	no	—
74	C₂×C₃	—	19	1	no	—
75	C₂×C₃	—	38	1	no	—
76	C₂×C₃	—	39	1	no	—
77	C₂×C₃	—	741	1	no	—
78	D₃	—	13	1	no	—
79	D₃	—	247	1	no	—
80	C₂²	—	741	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	C₃×D₁₃×D₁₉	1	1	yes	characteristic, complemented
83	C₃	D₁₉×D₃₉	1	1	yes	characteristic, direct product factor
84	C₂	—	19	1	no	—
85	C₂	—	39	1	no	—
86	C₂	—	741	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₉×D₃₉
commutator, hypocenter	C₃×C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₁₉	C₂²
LCS	G ▷ C₃×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₇₄₁	C₂	semidirect
2. C₃×C₁₉×D₃₉	C₂	semidirect
3. C₃²×C₁₃×D₁₉	C₂	semidirect
4. D₁₉×D₃₉	C₃	direct (N × H)
6. C₃²×C₁₃×C₁₉	C₂²	semidirect
7. D₇₄₁	C₂×C₃	semidirect
8. C₁₉×D₃₉	C₂×C₃	semidirect
12. C₃×C₁₃×D₁₉	D₃	semidirect
13. C₃×C₁₃×D₁₉	C₂×C₃	semidirect
16. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
17. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
20. C₁₃×D₁₉	C₃×D₃	semidirect
25. C₃²×D₁₉	D₁₃	semidirect
26. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
29. C₃×D₃₉	D₁₉	direct (N × H)
32. C₃²×C₁₉	C₂×D₁₃	semidirect
35. C₃²×C₁₃	C₂×D₁₉	semidirect
40. C₃×D₁₉	C₃×D₁₃	semidirect
41. C₃×D₁₉	D₃₉	direct (N × H)
47. D₃₉	C₃×D₁₉	direct (N × H)
52. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
53. C₃×C₁₉	C₂×D₃₉	semidirect
56. C₃×C₁₃	D₃×D₁₉	semidirect
57. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
60. D₁₉	C₃×D₃₉	direct (N × H)
65. C₁₉	C₂×C₃×D₃₉	semidirect
69. C₁₃	C₃×D₃×D₁₉	semidirect
72. C₃²	D₁₃×D₁₉	semidirect
82. C₃	C₃×D₁₃×D₁₉	semidirect
83. C₃	D₁₉×D₃₉	direct (N × H)

Subgroups — C3×D19×D39 #22580352

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₉×D₃₉ #22580352