Subgroups — C₃×D₁₃×D₅₇ #22580354

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×C₁₃×D₅₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₅₇	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	C₁₃×D₅₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₃×D₂₄₇	—	3	1	no	—
10	C₃×C₁₉×D₁₃	—	2	1	no	—
11	C₃×C₁₉×D₁₃	D₃	1	1	yes	characteristic, complemented
12	C₃×C₁₉×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
13	C₃×C₁₃×D₁₉	—	3	1	no	—
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	C₂×C₃×D₅₇	—	13	1	no	maximal, Hall
19	D₂₄₇	—	3	1	no	—
20	C₁₃×D₁₉	—	3	1	no	—
21	C₁₉×D₁₃	C₃×D₃	1	1	yes	characteristic, complemented
22	C₃×D₃×D₁₃	—	19	1	no	maximal, Hall
23	C₂×C₃²×C₁₉	—	13	1	no	—
24	C₃×D₅₇	—	13	1	no	—
25	C₃×D₅₇	D₁₃	1	1	yes	characteristic, direct product factor
26	C₁₃×C₁₉	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₃×D₃₉	—	19	1	no	—
28	C₃×D₃×C₁₃	—	19	1	no	—
29	C₃²×D₁₃	D₁₉	1	1	yes	characteristic, complemented
30	C₂×D₅₇	—	13	1	no	—
31	C₂×C₃×D₁₉	—	39	1	no	—
32	C₃²×C₁₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₁₃	—	57	1	no	—
34	D₃×D₁₃	—	19	1	no	—
35	C₃²×C₁₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
36	C₂×C₃×C₁₉	—	13	1	no	—
37	C₂×C₃×C₁₉	—	13	1	no	—
38	C₂×C₃×C₁₉	—	26	1	no	—
39	D₅₇	—	13	1	no	—
40	D₅₇	C₃×D₁₃	1	1	yes	characteristic, direct product factor
41	C₃×D₁₉	—	3	1	no	—
42	C₃×D₁₉	—	39	1	no	—
43	C₂×C₃×C₁₃	—	57	1	no	—
44	D₃₉	—	19	1	no	—
45	C₃×D₁₃	—	2	1	no	—
46	C₃×D₁₃	—	57	1	no	—
47	C₃×D₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
48	C₃×D₁₃	D₅₇	1	1	yes	characteristic, direct product factor
49	D₃×C₁₃	—	19	1	no	—
50	C₂×D₁₉	—	39	1	no	Hall
51	C₃×C₁₉	—	2	1	no	—
52	C₃×C₁₉	D₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₁₉	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	57	1	no	Hall
55	C₃×C₁₃	—	2	1	no	—
56	C₃×C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented
57	C₃×C₁₃	C₂×D₅₇	1	1	yes	characteristic, complemented
58	C₂×C₁₉	—	13	1	no	—
59	D₁₉	—	3	1	no	—
60	D₁₉	—	39	1	no	—
61	C₂×C₃×D₃	—	247	1	no	Hall
62	C₂×C₁₃	—	57	1	no	—
63	D₁₃	—	57	1	no	—
64	D₁₃	C₃×D₅₇	1	1	yes	characteristic, direct product factor
65	C₁₉	C₃×D₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₃²	—	13	1	no	—
67	C₃×D₃	—	19	1	no	—
68	C₃×D₃	—	247	1	no	—
69	C₁₃	C₂×C₃×D₅₇	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	—	13	1	no	—
74	C₂×C₃	—	13	1	no	—
75	C₂×C₃	—	26	1	no	—
76	C₂×C₃	—	57	1	no	—
77	C₂×C₃	—	741	1	no	—
78	D₃	—	19	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	D₁₃×D₅₇	1	1	yes	characteristic, direct product factor
84	C₂	—	13	1	no	—
85	C₂	—	57	1	no	—
86	C₂	—	741	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₅₇
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×C₁₃×D₅₇	C₂	semidirect
3. C₃²×C₁₉×D₁₃	C₂	semidirect
4. D₁₃×D₅₇	C₃	direct (N × H)
6. C₃²×C₁₃×C₁₉	C₂²	semidirect
7. D₇₄₁	C₂×C₃	semidirect
8. C₁₃×D₅₇	C₂×C₃	semidirect
11. C₃×C₁₉×D₁₃	D₃	semidirect
12. C₃×C₁₉×D₁₃	C₂×C₃	semidirect
16. C₃×C₁₃×C₁₉	C₂×D₃	semidirect
17. C₃×C₁₃×C₁₉	C₂²×C₃	semidirect
21. C₁₉×D₁₃	C₃×D₃	semidirect
25. C₃×D₅₇	D₁₃	direct (N × H)
26. C₁₃×C₁₉	C₂×C₃×D₃	semidirect
29. C₃²×D₁₃	D₁₉	semidirect
32. C₃²×C₁₉	C₂×D₁₃	semidirect
35. C₃²×C₁₃	C₂×D₁₉	semidirect
40. D₅₇	C₃×D₁₃	direct (N × H)
47. C₃×D₁₃	C₃×D₁₉	semidirect
48. C₃×D₁₃	D₅₇	direct (N × H)
52. C₃×C₁₉	D₃×D₁₃	semidirect
53. C₃×C₁₉	C₂×C₃×D₁₃	semidirect
56. C₃×C₁₃	C₂×C₃×D₁₉	semidirect
57. C₃×C₁₃	C₂×D₅₇	semidirect
64. D₁₃	C₃×D₅₇	direct (N × H)
65. C₁₉	C₃×D₃×D₁₃	semidirect
69. C₁₃	C₂×C₃×D₅₇	semidirect
72. C₃²	D₁₃×D₁₉	semidirect
82. C₃	C₃×D₁₃×D₁₉	semidirect
83. C₃	D₁₃×D₅₇	direct (N × H)

Subgroups — C3×D13×D57 #22580354

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₃×D₅₇ #22580354