Subgroups — C₂×C₃×C₁₃×D₆₉ #24924589

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₆₉
commutator, cosocle, hypocenter	C₃×C₂₃	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃×C₂₃	C₂
LCS	G ▷ C₃×C₂₃
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×D₆₉	C₂	direct (N × H)
2. C₂×C₃²×C₁₃×C₂₃	C₂	semidirect
3. C₂×C₁₃×D₆₉	C₃	direct (N × H)
5. C₃²×C₁₃×C₂₃	C₂²	semidirect
7. C₂×C₃×C₁₃×C₂₃	D₃	semidirect
8. C₂×C₃×C₁₃×C₂₃	C₂×C₃	semidirect
9. C₁₃×D₆₉	C₂×C₃	direct (N × H)
13. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
14. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
15. C₂×C₃×D₆₉	C₁₃	direct (N × H)
16. C₂×C₁₃×C₂₃	C₃×D₃	semidirect
19. C₂×C₃²×C₂₃	C₂×C₁₃	semidirect
20. C₃×D₆₉	C₂×C₁₃	direct (N × H)
21. C₁₃×C₂₃	C₂×C₃×D₃	semidirect
22. C₂×D₆₉	C₃×C₁₃	direct (N × H)
24. C₂×C₃²×C₁₃	D₂₃	semidirect
26. C₃²×C₂₃	C₂²×C₁₃	semidirect
30. C₂×C₃×C₂₃	D₃×C₁₃	semidirect
31. C₂×C₃×C₂₃	C₂×C₃×C₁₃	semidirect
32. D₆₉	C₂×C₃×C₁₃	direct (N × H)
34. C₃²×C₁₃	C₂×D₂₃	semidirect
38. C₂×C₃×C₁₃	C₃×D₂₃	semidirect
39. C₂×C₃×C₁₃	D₆₉	direct (N × H)
42. C₃×C₂₃	C₂×D₃×C₁₃	semidirect
43. C₃×C₂₃	C₂²×C₃×C₁₃	semidirect
45. C₂×C₂₃	C₃×D₃×C₁₃	semidirect
48. C₃×C₁₃	C₂×C₃×D₂₃	semidirect
49. C₃×C₁₃	C₂×D₆₉	direct (N × H)
52. C₂×C₁₃	C₃×D₆₉	direct (N × H)
53. C₂₃	C₂×C₃×D₃×C₁₃	semidirect
54. C₂×C₃²	C₁₃×D₂₃	semidirect
56. C₁₃	C₂×C₃×D₆₉	direct (N × H)
59. C₃²	C₂×C₁₃×D₂₃	semidirect
62. C₂×C₃	C₃×C₁₃×D₂₃	semidirect
63. C₂×C₃	C₁₃×D₆₉	direct (N × H)
67. C₃	C₂×C₃×C₁₃×D₂₃	semidirect
68. C₃	C₂×C₁₃×D₆₉	direct (N × H)
70. C₂	C₃×C₁₃×D₆₉	direct (N × H)

Subgroups — C2×C3×C13×D69 #24924589

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₃×C₁₃×D₆₉ #24924589