Subgroups — D₃×C₁₃×D₆₉ #24924565

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃⋊D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×D₆₉	—	3	1	no	maximal
5	D₃×C₁₃×D₂₃	—	3	1	no	maximal
6	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃×C₂₃	—	3	1	no	—
8	C₁₃×D₆₉	—	3	1	no	—
9	C₁₃×D₆₉	—	3	1	no	—
10	C₁₃×D₆₉	—	6	1	no	—
11	C₁₃×D₆₉	D₃	1	1	yes	characteristic, direct product factor
12	D₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic, complemented
13	C₃×C₁₃×D₂₃	—	3	1	no	—
14	C₂×C₁₃×D₂₃	—	9	1	no	Hall
15	C₃×C₁₃×C₂₃	—	2	1	no	—
16	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented
18	D₃×D₆₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₃×C₂₃	—	3	1	no	—
20	C₁₃×D₂₃	—	3	1	no	—
21	C₁₃×D₂₃	—	9	1	no	—
22	D₃²×C₁₃	—	23	1	no	maximal, Hall
23	C₃⋊D₆₉	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₃×D₆₉	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₃×D₃×C₂₃	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₁₃×C₂₃	D₃²	1	1	yes	characteristic, complemented, Hall
27	C₂×D₆₉	—	3	1	no	—
28	D₃×D₂₃	—	3	1	no	—
29	C₁₃×C₃⋊D₃	—	23	1	no	—
30	C₃×D₃×C₁₃	—	23	1	no	—
31	C₃×D₃×C₁₃	D₂₃	1	1	yes	characteristic, complemented
32	C₃²×C₂₃	C₂²×C₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃×C₁₃	—	69	1	no	—
34	C₂×D₃×C₁₃	—	69	1	no	—
35	C₂×C₃×C₂₃	—	3	1	no	—
36	D₆₉	—	3	1	no	—
37	D₆₉	—	3	1	no	—
38	D₆₉	—	6	1	no	—
39	D₆₉	D₃×C₁₃	1	1	yes	characteristic, direct product factor
40	C₃×D₂₃	—	3	1	no	—
41	D₃×C₂₃	D₃×C₁₃	1	1	yes	characteristic, complemented
42	C₃²×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂×D₂₃	—	9	1	no	Hall
44	C₂×C₃×C₁₃	—	3	1	no	—
45	C₂×C₃×C₁₃	—	69	1	no	—
46	D₃×C₁₃	—	23	1	no	—
47	D₃×C₁₃	—	69	1	no	—
48	D₃×C₁₃	—	69	1	no	—
49	D₃×C₁₃	—	138	1	no	—
50	D₃×C₁₃	D₆₉	1	1	yes	characteristic, direct product factor
51	C₃×C₂₃	—	2	1	no	—
52	C₃×C₂₃	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
53	C₃×C₂₃	C₂×D₃×C₁₃	1	1	yes	characteristic, complemented
54	C₂²×C₁₃	—	207	1	no	Hall
55	C₂×C₂₃	—	3	1	no	—
56	D₂₃	—	3	1	no	—
57	D₂₃	—	9	1	no	—
58	C₃×C₁₃	—	2	1	no	—
59	C₃×C₁₃	D₃×D₂₃	1	1	yes	characteristic, complemented
60	C₃×C₁₃	C₂×D₆₉	1	1	yes	characteristic, complemented
61	D₃²	—	23	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	C₂×C₁₃	—	69	1	no	—
64	C₂×C₁₃	—	207	1	no	—
65	C₂₃	D₃²×C₁₃	1	1	yes	characteristic, complemented, Sylow
66	C₃⋊D₃	—	23	1	no	—
67	C₃×D₃	—	23	1	no	—
68	C₃×D₃	C₁₃×D₂₃	1	1	yes	characteristic, complemented
69	C₁₃	D₃×D₆₉	1	1	yes	characteristic, direct product factor, Sylow
70	C₂×D₃	—	69	1	no	—
71	C₂×D₃	—	69	1	no	—
72	C₃²	C₂×C₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	69	1	no	—
75	D₃	—	23	1	no	—
76	D₃	—	69	1	no	—
77	D₃	—	69	1	no	—
78	D₃	—	138	1	no	—
79	D₃	C₁₃×D₆₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	207	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₁₃×D₂₃	1	1	yes	characteristic, complemented
83	C₃	C₂×C₁₃×D₆₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	69	1	no	—
86	C₂	—	207	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	D₃×D₆₉
commutator, cosocle, hypocenter	C₃²×C₂₃	C₂²×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃²×C₂₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₃⋊D₆₉	C₂	semidirect
2. C₃×C₁₃×D₆₉	C₂	semidirect
3. C₃×D₃×C₁₃×C₂₃	C₂	semidirect
6. C₃²×C₁₃×C₂₃	C₂²	semidirect
11. C₁₃×D₆₉	D₃	direct (N × H)
12. D₃×C₁₃×C₂₃	D₃	semidirect
16. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
18. D₃×D₆₉	C₁₃	direct (N × H)
23. C₃⋊D₆₉	C₂×C₁₃	semidirect
24. C₃×D₆₉	C₂×C₁₃	semidirect
25. C₃×D₃×C₂₃	C₂×C₁₃	semidirect
26. C₁₃×C₂₃	D₃²	semidirect
31. C₃×D₃×C₁₃	D₂₃	semidirect
32. C₃²×C₂₃	C₂²×C₁₃	semidirect
39. D₆₉	D₃×C₁₃	direct (N × H)
41. D₃×C₂₃	D₃×C₁₃	semidirect
42. C₃²×C₁₃	C₂×D₂₃	semidirect
50. D₃×C₁₃	D₆₉	direct (N × H)
52. C₃×C₂₃	C₂×D₃×C₁₃	semidirect
53. C₃×C₂₃	C₂×D₃×C₁₃	semidirect
59. C₃×C₁₃	D₃×D₂₃	semidirect
60. C₃×C₁₃	C₂×D₆₉	semidirect
65. C₂₃	D₃²×C₁₃	semidirect
68. C₃×D₃	C₁₃×D₂₃	semidirect
69. C₁₃	D₃×D₆₉	direct (N × H)
72. C₃²	C₂×C₁₃×D₂₃	semidirect
79. D₃	C₁₃×D₆₉	direct (N × H)
82. C₃	D₃×C₁₃×D₂₃	semidirect
83. C₃	C₂×C₁₃×D₆₉	semidirect

Subgroups — D3×C13×D69 #24924565

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₁₃×D₆₉ #24924565