Subgroups — C₇×D₂₃×D₃₉ #38737417

Order 25116.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×D₈₉₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₂₃×D₃₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₁₃×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×D₁₃×D₂₃	—	3	1	no	maximal, Hall
5	C₃×C₇×C₁₃×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₇×D₂₉₉	—	3	1	no	—
7	C₇×C₂₃×D₁₃	—	3	1	no	—
8	C₇×C₁₃×D₂₃	D₃	1	1	yes	characteristic, complemented
9	D₂₃×D₃₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃×C₇×D₂₃	—	13	1	no	maximal, Hall
12	D₈₉₇	C₂×C₇	1	1	yes	characteristic, complemented
13	C₂₃×D₃₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×C₁₃×D₂₃	C₂×C₇	1	1	yes	characteristic, complemented
15	D₁₃×D₂₃	—	3	1	no	Hall
16	C₂×C₇×D₃₉	—	23	1	no	maximal, Hall
17	C₇×D₆₉	—	13	1	no	—
18	D₃×C₇×C₂₃	—	13	1	no	—
19	C₃×C₇×D₂₃	D₁₃	1	1	yes	characteristic, complemented
20	C₃×C₁₃×C₂₃	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
21	C₂×C₇×D₂₃	—	39	1	no	Hall
22	D₂₉₉	—	3	1	no	—
23	C₁₃×D₂₃	D₃×C₇	1	1	yes	characteristic, complemented
24	C₂₃×D₁₃	—	3	1	no	—
25	C₂×C₃×C₇×C₁₃	—	23	1	no	—
26	C₇×D₃₉	—	23	1	no	—
27	C₇×D₃₉	D₂₃	1	1	yes	characteristic, direct product factor
28	C₃×C₇×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇×D₁₃	—	69	1	no	Hall
30	C₂×C₇×C₂₃	—	39	1	no	—
31	C₇×D₂₃	—	39	1	no	—
32	C₇×D₂₃	D₃₉	1	1	yes	characteristic, direct product factor
33	C₁₃×C₂₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
34	D₃×D₂₃	—	13	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₁₃	—	23	1	no	—
37	C₇×D₁₃	—	3	1	no	—
38	C₇×D₁₃	—	69	1	no	—
39	C₇×C₂₃	C₂×D₃₉	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃₉	—	23	1	no	Hall
41	D₆₉	—	13	1	no	—
42	C₃×D₂₃	C₇×D₁₃	1	1	yes	characteristic, complemented
43	D₃×C₂₃	—	13	1	no	—
44	C₂×D₂₃	—	39	1	no	Hall
45	C₇×C₁₃	D₃×D₂₃	1	1	yes	characteristic, complemented, Hall
46	C₂×D₃×C₇	—	299	1	no	Hall
47	C₂×C₃×C₁₃	—	23	1	no	—
48	D₃₉	—	23	1	no	—
49	D₃₉	C₇×D₂₃	1	1	yes	characteristic, direct product factor
50	C₃×C₂₃	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	69	1	no	Hall
52	C₂×C₂₃	—	39	1	no	—
53	D₂₃	—	39	1	no	—
54	D₂₃	C₇×D₃₉	1	1	yes	characteristic, direct product factor
55	C₂×C₃×C₇	—	23	1	no	—
56	D₃×C₇	—	13	1	no	—
57	D₃×C₇	—	299	1	no	—
58	C₃×C₁₃	C₂×C₇×D₂₃	1	1	yes	characteristic, complemented, Hall
59	C₂²×C₇	—	897	1	no	Hall
60	C₂×C₁₃	—	23	1	no	—
61	D₁₃	—	3	1	no	—
62	D₁₃	—	69	1	no	—
63	C₂₃	C₂×C₇×D₃₉	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	D₁₃×D₂₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	23	1	no	—
66	C₂×C₇	—	39	1	no	—
67	C₂×C₇	—	897	1	no	—
68	C₁₃	D₃×C₇×D₂₃	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	299	1	no	Hall
70	C₇	D₂₃×D₃₉	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	23	1	no	—
72	D₃	—	13	1	no	—
73	D₃	—	299	1	no	—
74	C₂²	—	897	1	no	Sylow
75	C₃	C₇×D₁₃×D₂₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	23	1	no	—
77	C₂	—	39	1	no	—
78	C₂	—	897	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₂₃×D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃×C₂₃	C₂²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₂₃	C₂²
LCS	G ▷ C₃×C₁₃×C₂₃
UCS	C₁ ◁ C₇

Complements

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

N	H ≅ G/N	type
1. C₇×D₈₉₇	C₂	semidirect
2. C₇×C₂₃×D₃₉	C₂	semidirect
3. C₃×C₇×C₁₃×D₂₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
8. C₇×C₁₃×D₂₃	D₃	semidirect
9. D₂₃×D₃₉	C₇	direct (N × H)
10. C₇×C₁₃×C₂₃	C₂×D₃	semidirect
12. D₈₉₇	C₂×C₇	semidirect
13. C₂₃×D₃₉	C₂×C₇	semidirect
14. C₃×C₁₃×D₂₃	C₂×C₇	semidirect
19. C₃×C₇×D₂₃	D₁₃	semidirect
20. C₃×C₁₃×C₂₃	C₂²×C₇	semidirect
23. C₁₃×D₂₃	D₃×C₇	semidirect
27. C₇×D₃₉	D₂₃	direct (N × H)
28. C₃×C₇×C₂₃	C₂×D₁₃	semidirect
32. C₇×D₂₃	D₃₉	direct (N × H)
33. C₁₃×C₂₃	C₂×D₃×C₇	semidirect
35. C₃×C₇×C₁₃	C₂×D₂₃	semidirect
39. C₇×C₂₃	C₂×D₃₉	semidirect
42. C₃×D₂₃	C₇×D₁₃	semidirect
45. C₇×C₁₃	D₃×D₂₃	semidirect
49. D₃₉	C₇×D₂₃	direct (N × H)
50. C₃×C₂₃	C₂×C₇×D₁₃	semidirect
54. D₂₃	C₇×D₃₉	direct (N × H)
58. C₃×C₁₃	C₂×C₇×D₂₃	semidirect
63. C₂₃	C₂×C₇×D₃₉	semidirect
64. C₃×C₇	D₁₃×D₂₃	semidirect
68. C₁₃	D₃×C₇×D₂₃	semidirect
70. C₇	D₂₃×D₃₉	direct (N × H)
75. C₃	C₇×D₁₃×D₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₇×D₈₉₇	2
C₇×C₂₃×D₃₉	2
C₃×C₇×C₁₃×D₂₃	2
C₇×D₁₃×D₂₃	3
D₂₃×D₃₉	7
D₃×C₇×D₂₃	13
C₂×C₇×D₃₉	23

Subgroups — C7×D23×D39 #38737417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₂₃×D₃₉ #38737417