Subgroups — D₃×C₂₃×D₃₉ #24924567

Order 10764.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×C₃⋊D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₂₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×D₃₉	—	3	1	no	maximal
5	D₃×C₂₃×D₁₃	—	3	1	no	maximal
6	C₃²×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	C₂×C₃×C₁₃×C₂₃	—	3	1	no	—
8	C₂₃×D₃₉	—	3	1	no	—
9	C₂₃×D₃₉	—	3	1	no	—
10	C₂₃×D₃₉	—	6	1	no	—
11	C₂₃×D₃₉	D₃	1	1	yes	characteristic, direct product factor
12	D₃×C₁₃×C₂₃	D₃	1	1	yes	characteristic, complemented
13	C₃×C₂₃×D₁₃	—	3	1	no	—
14	C₂×C₂₃×D₁₃	—	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	D₃²×C₂₃	—	13	1	no	maximal, Hall
19	C₂×C₁₃×C₂₃	—	3	1	no	—
20	C₂₃×D₁₃	—	3	1	no	—
21	C₂₃×D₁₃	—	9	1	no	—
22	D₃×D₃₉	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₃⋊D₃×C₂₃	—	13	1	no	—
24	C₃×D₃×C₂₃	—	13	1	no	—
25	C₃×D₃×C₂₃	D₁₃	1	1	yes	characteristic, complemented
26	C₁₃×C₂₃	D₃²	1	1	yes	characteristic, complemented, Hall
27	C₂×D₃×C₂₃	—	39	1	no	—
28	C₂×D₃×C₂₃	—	39	1	no	—
29	C₃⋊D₃₉	C₂×C₂₃	1	1	yes	characteristic, complemented
30	C₃×D₃₉	C₂×C₂₃	1	1	yes	characteristic, complemented
31	C₃×D₃×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
32	C₃²×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₂×D₃₉	—	3	1	no	—
34	D₃×D₁₃	—	3	1	no	—
35	C₂×C₃×C₂₃	—	3	1	no	—
36	C₂×C₃×C₂₃	—	39	1	no	—
37	D₃×C₂₃	—	13	1	no	—
38	D₃×C₂₃	—	39	1	no	—
39	D₃×C₂₃	—	39	1	no	—
40	D₃×C₂₃	—	78	1	no	—
41	D₃×C₂₃	D₃₉	1	1	yes	characteristic, direct product factor
42	C₃²×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
43	C₂²×C₂₃	—	117	1	no	Hall
44	C₂×C₃×C₁₃	—	3	1	no	—
45	D₃₉	—	3	1	no	—
46	D₃₉	—	3	1	no	—
47	D₃₉	—	6	1	no	—
48	D₃₉	D₃×C₂₃	1	1	yes	characteristic, direct product factor
49	C₃×D₁₃	—	3	1	no	—
50	D₃×C₁₃	D₃×C₂₃	1	1	yes	characteristic, complemented
51	C₃×C₂₃	—	2	1	no	—
52	C₃×C₂₃	D₃×D₁₃	1	1	yes	characteristic, complemented
53	C₃×C₂₃	C₂×D₃₉	1	1	yes	characteristic, complemented
54	C₂×D₁₃	—	9	1	no	Hall
55	C₂×C₂₃	—	3	1	no	—
56	C₂×C₂₃	—	39	1	no	—
57	C₂×C₂₃	—	117	1	no	—
58	C₃×C₁₃	—	2	1	no	—
59	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
60	C₃×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented
61	D₃²	—	13	1	no	Hall
62	C₂×C₁₃	—	3	1	no	—
63	D₁₃	—	3	1	no	—
64	D₁₃	—	9	1	no	—
65	C₂₃	D₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
66	C₃⋊D₃	—	13	1	no	—
67	C₃×D₃	—	13	1	no	—
68	C₃×D₃	C₂₃×D₁₃	1	1	yes	characteristic, complemented
69	C₁₃	D₃²×C₂₃	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₃	—	39	1	no	—
71	C₂×D₃	—	39	1	no	—
72	C₃²	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₃	—	3	1	no	—
74	C₂×C₃	—	39	1	no	—
75	D₃	—	13	1	no	—
76	D₃	—	39	1	no	—
77	D₃	—	39	1	no	—
78	D₃	—	78	1	no	—
79	D₃	C₂₃×D₃₉	1	1	yes	characteristic, direct product factor
80	C₂²	—	117	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×C₂₃×D₁₃	1	1	yes	characteristic, complemented
83	C₃	C₂×C₂₃×D₃₉	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	39	1	no	—
86	C₂	—	117	1	no	—

	subgroup	G/H
center, hypercenter	C₂₃	D₃×D₃₉
commutator, cosocle, hypocenter	C₃²×C₁₃	C₂²×C₂₃
Frattini	C₁	G
Fitting, socle	C₃²×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃²×C₁₃
UCS	C₁ ◁ C₂₃

Complements

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

N	H ≅ G/N	type
1. C₂₃×C₃⋊D₃₉	C₂	semidirect
2. C₃×C₂₃×D₃₉	C₂	semidirect
3. C₃×D₃×C₁₃×C₂₃	C₂	semidirect
6. C₃²×C₁₃×C₂₃	C₂²	semidirect
11. C₂₃×D₃₉	D₃	direct (N × H)
12. D₃×C₁₃×C₂₃	D₃	semidirect
16. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
17. C₃×C₁₃×C₂₃	C₂×D₃	semidirect
22. D₃×D₃₉	C₂₃	direct (N × H)
25. C₃×D₃×C₂₃	D₁₃	semidirect
26. C₁₃×C₂₃	D₃²	semidirect
29. C₃⋊D₃₉	C₂×C₂₃	semidirect
30. C₃×D₃₉	C₂×C₂₃	semidirect
31. C₃×D₃×C₁₃	C₂×C₂₃	semidirect
32. C₃²×C₂₃	C₂×D₁₃	semidirect
41. D₃×C₂₃	D₃₉	direct (N × H)
42. C₃²×C₁₃	C₂²×C₂₃	semidirect
48. D₃₉	D₃×C₂₃	direct (N × H)
50. D₃×C₁₃	D₃×C₂₃	semidirect
52. C₃×C₂₃	D₃×D₁₃	semidirect
53. C₃×C₂₃	C₂×D₃₉	semidirect
59. C₃×C₁₃	C₂×D₃×C₂₃	semidirect
60. C₃×C₁₃	C₂×D₃×C₂₃	semidirect
65. C₂₃	D₃×D₃₉	direct (N × H)
68. C₃×D₃	C₂₃×D₁₃	semidirect
69. C₁₃	D₃²×C₂₃	semidirect
72. C₃²	C₂×C₂₃×D₁₃	semidirect
79. D₃	C₂₃×D₃₉	direct (N × H)
82. C₃	D₃×C₂₃×D₁₃	semidirect
83. C₃	C₂×C₂₃×D₃₉	semidirect

Subgroups — D3×C23×D39 #24924567

Conjugacy classes of subgroups

Complements

Subgroups — D₃×C₂₃×D₃₉ #24924567