Subgroups — D₃×C₇×C₂₃×D₁₃ #38737418

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₂₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₃×C₇×C₁₃×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×C₂₃×D₁₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×C₂₃×D₁₃	—	3	1	no	—
7	C₇×C₂₃×D₁₃	D₃	1	1	yes	characteristic, direct product factor
8	C₂×C₇×C₁₃×C₂₃	—	3	1	no	—
9	D₃×C₂₃×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₃×C₇×C₂₃	—	13	1	no	maximal, Hall
12	C₂₃×D₃₉	C₂×C₇	1	1	yes	characteristic, complemented
13	D₃×C₁₃×C₂₃	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×C₂₃×D₁₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₂×C₂₃×D₁₃	—	3	1	no	Hall
16	D₃×C₇×D₁₃	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₇×C₂₃	—	13	1	no	—
18	D₃×C₇×C₂₃	—	13	1	no	—
19	D₃×C₇×C₂₃	D₁₃	1	1	yes	characteristic, direct product factor
20	C₃×C₁₃×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂²×C₇×C₂₃	—	39	1	no	Hall
22	C₂×C₁₃×C₂₃	—	3	1	no	—
23	C₂₃×D₁₃	—	3	1	no	—
24	C₂₃×D₁₃	D₃×C₇	1	1	yes	characteristic, direct product factor
25	C₇×D₃₉	C₂×C₂₃	1	1	yes	characteristic, complemented
26	D₃×C₇×C₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
27	C₃×C₇×D₁₃	C₂×C₂₃	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇×D₁₃	—	3	1	no	Hall
30	C₂×C₇×C₂₃	—	3	1	no	—
31	C₂×C₇×C₂₃	—	13	1	no	—
32	C₂×C₇×C₂₃	—	39	1	no	—
33	C₁₃×C₂₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃×C₂₃	—	13	1	no	Hall
35	C₃×C₇×C₁₃	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₁₃	—	3	1	no	—
37	C₇×D₁₃	—	3	1	no	—
38	C₇×D₁₃	D₃×C₂₃	1	1	yes	characteristic, direct product factor
39	C₇×C₂₃	D₃×D₁₃	1	1	yes	characteristic, direct product factor, Hall
40	D₃×D₁₃	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
41	C₂×C₃×C₂₃	—	13	1	no	—
42	D₃×C₂₃	—	13	1	no	—
43	D₃×C₂₃	C₇×D₁₃	1	1	yes	characteristic, direct product factor
44	C₂²×C₂₃	—	39	1	no	Hall
45	C₇×C₁₃	C₂×D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂×D₃×C₇	—	13	1	no	Hall
47	D₃₉	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
48	C₃×D₁₃	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
49	D₃×C₁₃	C₂×C₇×C₂₃	1	1	yes	characteristic, complemented
50	C₃×C₂₃	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	3	1	no	Hall
52	C₂×C₂₃	—	3	1	no	—
53	C₂×C₂₃	—	13	1	no	—
54	C₂×C₂₃	—	39	1	no	—
55	C₂×C₃×C₇	—	13	1	no	—
56	D₃×C₇	—	13	1	no	—
57	D₃×C₇	C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
58	C₃×C₁₃	C₂²×C₇×C₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₇	—	39	1	no	Hall
60	C₂×C₁₃	—	3	1	no	—
61	D₁₃	—	3	1	no	—
62	D₁₃	D₃×C₇×C₂₃	1	1	yes	characteristic, direct product factor
63	C₂₃	D₃×C₇×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
64	C₃×C₇	C₂×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	3	1	no	—
66	C₂×C₇	—	13	1	no	—
67	C₂×C₇	—	39	1	no	—
68	C₁₃	C₂×D₃×C₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	13	1	no	Hall
70	C₇	D₃×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	13	1	no	—
72	D₃	—	13	1	no	—
73	D₃	C₇×C₂₃×D₁₃	1	1	yes	characteristic, direct product factor
74	C₂²	—	39	1	no	Sylow
75	C₃	C₂×C₇×C₂₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	3	1	no	—
77	C₂	—	13	1	no	—
78	C₂	—	39	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₂₃	D₃×D₁₃
commutator, cosocle, hypocenter	C₃×C₁₃	C₂²×C₇×C₂₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ C₇×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₇×C₂₃×D₃₉	C₂	semidirect
2. D₃×C₇×C₁₃×C₂₃	C₂	semidirect
3. C₃×C₇×C₂₃×D₁₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
7. C₇×C₂₃×D₁₃	D₃	direct (N × H)
9. D₃×C₂₃×D₁₃	C₇	direct (N × H)
10. C₇×C₁₃×C₂₃	C₂×D₃	semidirect
12. C₂₃×D₃₉	C₂×C₇	semidirect
13. D₃×C₁₃×C₂₃	C₂×C₇	semidirect
14. C₃×C₂₃×D₁₃	C₂×C₇	semidirect
16. D₃×C₇×D₁₃	C₂₃	direct (N × H)
19. D₃×C₇×C₂₃	D₁₃	direct (N × H)
20. C₃×C₁₃×C₂₃	C₂²×C₇	semidirect
24. C₂₃×D₁₃	D₃×C₇	direct (N × H)
25. C₇×D₃₉	C₂×C₂₃	semidirect
26. D₃×C₇×C₁₃	C₂×C₂₃	semidirect
27. C₃×C₇×D₁₃	C₂×C₂₃	semidirect
28. C₃×C₇×C₂₃	C₂×D₁₃	semidirect
33. C₁₃×C₂₃	C₂×D₃×C₇	semidirect
35. C₃×C₇×C₁₃	C₂²×C₂₃	semidirect
38. C₇×D₁₃	D₃×C₂₃	direct (N × H)
39. C₇×C₂₃	D₃×D₁₃	direct (N × H)
40. D₃×D₁₃	C₇×C₂₃	direct (N × H)
43. D₃×C₂₃	C₇×D₁₃	direct (N × H)
45. C₇×C₁₃	C₂×D₃×C₂₃	semidirect
47. D₃₉	C₂×C₇×C₂₃	semidirect
48. C₃×D₁₃	C₂×C₇×C₂₃	semidirect
49. D₃×C₁₃	C₂×C₇×C₂₃	semidirect
50. C₃×C₂₃	C₂×C₇×D₁₃	semidirect
57. D₃×C₇	C₂₃×D₁₃	direct (N × H)
58. C₃×C₁₃	C₂²×C₇×C₂₃	semidirect
62. D₁₃	D₃×C₇×C₂₃	direct (N × H)
63. C₂₃	D₃×C₇×D₁₃	direct (N × H)
64. C₃×C₇	C₂×C₂₃×D₁₃	semidirect
68. C₁₃	C₂×D₃×C₇×C₂₃	semidirect
70. C₇	D₃×C₂₃×D₁₃	direct (N × H)
73. D₃	C₇×C₂₃×D₁₃	direct (N × H)
75. C₃	C₂×C₇×C₂₃×D₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×C₂₃×D₃₉	2
D₃×C₇×C₁₃×C₂₃	2
C₃×C₇×C₂₃×D₁₃	2
C₂×C₇×C₂₃×D₁₃	3
D₃×C₂₃×D₁₃	7
C₂×D₃×C₇×C₂₃	13
D₃×C₇×D₁₃	23

Subgroups — D3×C7×C23×D13 #38737418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₇×C₂₃×D₁₃ #38737418