Subgroups — C₃×D₃×C₂₃×D₁₃ #24924552

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₂₃×D₁₃	—	3	1	no	maximal
5	D₃×C₂₃×D₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃×C₂₃	—	3	1	no	—
8	C₂₃×D₃₉	C₂×C₃	1	1	yes	characteristic, complemented
9	D₃×C₁₃×C₂₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×C₂₃×D₁₃	—	2	1	no	—
11	C₃×C₂₃×D₁₃	—	3	1	no	—
12	C₃×C₂₃×D₁₃	D₃	1	1	yes	characteristic, direct product factor
13	C₃×C₂₃×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
14	C₂×C₂₃×D₁₃	—	3	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	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×C₃×D₃×C₂₃	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₂₃	—	3	1	no	—
20	C₂₃×D₁₃	—	3	1	no	—
21	C₂₃×D₁₃	C₃×D₃	1	1	yes	characteristic, direct product factor
22	C₃×D₃×D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂×C₃²×C₂₃	—	13	1	no	—
24	C₃×D₃×C₂₃	—	13	1	no	—
25	C₃×D₃×C₂₃	D₁₃	1	1	yes	characteristic, direct product factor
26	C₁₃×C₂₃	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₂₃	—	39	1	no	—
28	C₂×D₃×C₂₃	—	13	1	no	—
29	C₃×D₃₉	C₂×C₂₃	1	1	yes	characteristic, complemented
30	C₃×D₃×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
31	C₃²×D₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
32	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₁₃	—	3	1	no	—
34	D₃×D₁₃	C₃×C₂₃	1	1	yes	characteristic, direct product factor
35	C₂×C₃×C₂₃	—	3	1	no	—
36	C₂×C₃×C₂₃	—	13	1	no	—
37	C₂×C₃×C₂₃	—	13	1	no	—
38	C₂×C₃×C₂₃	—	26	1	no	—
39	C₂×C₃×C₂₃	—	39	1	no	—
40	D₃×C₂₃	—	13	1	no	—
41	D₃×C₂₃	C₃×D₁₃	1	1	yes	characteristic, direct product factor
42	C₃²×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₂₃	—	39	1	no	Hall
44	C₂×C₃×C₁₃	—	3	1	no	—
45	D₃₉	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
46	C₃×D₁₃	—	2	1	no	—
47	C₃×D₁₃	—	3	1	no	—
48	C₃×D₁₃	D₃×C₂₃	1	1	yes	characteristic, direct product factor
49	C₃×D₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
50	D₃×C₁₃	C₂×C₃×C₂₃	1	1	yes	characteristic, complemented
51	C₃×C₂₃	—	2	1	no	—
52	C₃×C₂₃	D₃×D₁₃	1	1	yes	characteristic, direct product factor
53	C₃×C₂₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	3	1	no	Hall
55	C₂×C₂₃	—	3	1	no	—
56	C₂×C₂₃	—	13	1	no	—
57	C₂×C₂₃	—	39	1	no	—
58	C₃×C₁₃	—	2	1	no	—
59	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
60	C₃×C₁₃	C₂²×C₃×C₂₃	1	1	yes	characteristic, complemented
61	C₂×C₃×D₃	—	13	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	D₁₃	—	3	1	no	—
64	D₁₃	C₃×D₃×C₂₃	1	1	yes	characteristic, direct product factor
65	C₂₃	C₃×D₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
66	C₂×C₃²	—	13	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
69	C₁₃	C₂×C₃×D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²×C₃	—	39	1	no	—
71	C₂×D₃	—	13	1	no	—
72	C₃²	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	13	1	no	—
75	C₂×C₃	—	13	1	no	—
76	C₂×C₃	—	26	1	no	—
77	C₂×C₃	—	39	1	no	—
78	D₃	—	13	1	no	—
79	D₃	C₃×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
80	C₂²	—	39	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
83	C₃	C₂×C₃×C₂₃×D₁₃	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	13	1	no	—
86	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₃×C₂₃	D₃×D₁₃
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₃×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₃×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₃×D₃₉	C₂	semidirect
2. C₃×D₃×C₁₃×C₂₃	C₂	semidirect
3. C₃²×C₂₃×D₁₃	C₂	semidirect
5. D₃×C₂₃×D₁₃	C₃	direct (N × H)
6. C₃²×C₁₃×C₂₃	C₂²	semidirect
8. C₂₃×D₃₉	C₂×C₃	semidirect
9. D₃×C₁₃×C₂₃	C₂×C₃	semidirect
12. C₃×C₂₃×D₁₃	D₃	direct (N × H)
13. C₃×C₂₃×D₁₃	C₂×C₃	semidirect
16. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₂₃	C₂²×C₃	semidirect
21. C₂₃×D₁₃	C₃×D₃	direct (N × H)
22. C₃×D₃×D₁₃	C₂₃	direct (N × H)
25. C₃×D₃×C₂₃	D₁₃	direct (N × H)
26. C₁₃×C₂₃	C₂×C₃×D₃	semidirect
29. C₃×D₃₉	C₂×C₂₃	semidirect
30. C₃×D₃×C₁₃	C₂×C₂₃	semidirect
31. C₃²×D₁₃	C₂×C₂₃	semidirect
32. C₃²×C₂₃	C₂×D₁₃	semidirect
34. D₃×D₁₃	C₃×C₂₃	direct (N × H)
41. D₃×C₂₃	C₃×D₁₃	direct (N × H)
42. C₃²×C₁₃	C₂²×C₂₃	semidirect
45. D₃₉	C₂×C₃×C₂₃	semidirect
48. C₃×D₁₃	D₃×C₂₃	direct (N × H)
49. C₃×D₁₃	C₂×C₃×C₂₃	semidirect
50. D₃×C₁₃	C₂×C₃×C₂₃	semidirect
52. C₃×C₂₃	D₃×D₁₃	direct (N × H)
53. C₃×C₂₃	C₂×C₃×D₁₃	semidirect
59. C₃×C₁₃	C₂×D₃×C₂₃	semidirect
60. C₃×C₁₃	C₂²×C₃×C₂₃	semidirect
64. D₁₃	C₃×D₃×C₂₃	direct (N × H)
65. C₂₃	C₃×D₃×D₁₃	direct (N × H)
68. C₃×D₃	C₂₃×D₁₃	direct (N × H)
69. C₁₃	C₂×C₃×D₃×C₂₃	semidirect
72. C₃²	C₂×C₂₃×D₁₃	semidirect
79. D₃	C₃×C₂₃×D₁₃	direct (N × H)
82. C₃	D₃×C₂₃×D₁₃	direct (N × H)
83. C₃	C₂×C₃×C₂₃×D₁₃	semidirect

Subgroups — C3×D3×C23×D13 #24924552

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₃×C₂₃×D₁₃ #24924552