Subgroups — C₇×D₁₃×D₆₉ #38737419

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×C₁₃×D₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₇×C₂₃×D₁₃	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	D₃	1	1	yes	characteristic, complemented
8	C₇×C₁₃×D₂₃	—	3	1	no	—
9	D₁₃×D₆₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₇×C₁₃×C₂₃	C₂×D₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₇×D₆₉	—	13	1	no	maximal, Hall
12	D₈₉₇	C₂×C₇	1	1	yes	characteristic, complemented
13	C₁₃×D₆₉	C₂×C₇	1	1	yes	characteristic, complemented
14	C₃×C₂₃×D₁₃	C₂×C₇	1	1	yes	characteristic, complemented
15	D₁₃×D₂₃	—	3	1	no	Hall
16	D₃×C₇×D₁₃	—	23	1	no	maximal, Hall
17	C₂×C₃×C₇×C₂₃	—	13	1	no	—
18	C₇×D₆₉	—	13	1	no	—
19	C₇×D₆₉	D₁₃	1	1	yes	characteristic, direct product factor
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	—	3	1	no	—
24	C₂₃×D₁₃	D₃×C₇	1	1	yes	characteristic, complemented
25	C₇×D₃₉	—	23	1	no	—
26	D₃×C₇×C₁₃	—	23	1	no	—
27	C₃×C₇×D₁₃	D₂₃	1	1	yes	characteristic, complemented
28	C₃×C₇×C₂₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
29	C₂×C₇×D₁₃	—	69	1	no	Hall
30	C₂×C₇×C₂₃	—	13	1	no	—
31	C₇×D₂₃	—	3	1	no	—
32	C₇×D₂₃	—	39	1	no	—
33	C₁₃×C₂₃	C₂×D₃×C₇	1	1	yes	characteristic, complemented, Hall
34	C₂×D₆₉	—	13	1	no	Hall
35	C₃×C₇×C₁₃	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
36	C₂×C₇×C₁₃	—	69	1	no	—
37	C₇×D₁₃	—	69	1	no	—
38	C₇×D₁₃	D₆₉	1	1	yes	characteristic, direct product factor
39	C₇×C₂₃	D₃×D₁₃	1	1	yes	characteristic, complemented, Hall
40	D₃×D₁₃	—	23	1	no	Hall
41	C₂×C₃×C₂₃	—	13	1	no	—
42	D₆₉	—	13	1	no	—
43	D₆₉	C₇×D₁₃	1	1	yes	characteristic, direct product factor
44	C₂×D₂₃	—	39	1	no	Hall
45	C₇×C₁₃	C₂×D₆₉	1	1	yes	characteristic, complemented, Hall
46	C₂×D₃×C₇	—	299	1	no	Hall
47	D₃₉	—	23	1	no	—
48	C₃×D₁₃	C₇×D₂₃	1	1	yes	characteristic, complemented
49	D₃×C₁₃	—	23	1	no	—
50	C₃×C₂₃	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented, Hall
51	C₂×D₁₃	—	69	1	no	Hall
52	C₂×C₂₃	—	13	1	no	—
53	D₂₃	—	3	1	no	—
54	D₂₃	—	39	1	no	—
55	C₂×C₃×C₇	—	13	1	no	—
56	D₃×C₇	—	23	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	—	69	1	no	—
61	D₁₃	—	69	1	no	—
62	D₁₃	C₇×D₆₉	1	1	yes	characteristic, direct product factor
63	C₂₃	D₃×C₇×D₁₃	1	1	yes	characteristic, complemented, Sylow
64	C₃×C₇	D₁₃×D₂₃	1	1	yes	characteristic, complemented, Hall
65	C₂×C₇	—	13	1	no	—
66	C₂×C₇	—	69	1	no	—
67	C₂×C₇	—	897	1	no	—
68	C₁₃	C₂×C₇×D₆₉	1	1	yes	characteristic, complemented, Sylow
69	C₂×D₃	—	299	1	no	Hall
70	C₇	D₁₃×D₆₉	1	1	yes	characteristic, direct product factor, Sylow
71	C₂×C₃	—	13	1	no	—
72	D₃	—	23	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	—	13	1	no	—
77	C₂	—	69	1	no	—
78	C₂	—	897	1	no	—

	subgroup	G/H
center, hypercenter	C₇	D₁₃×D₆₉
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×C₁₃×D₆₉	C₂	semidirect
3. C₃×C₇×C₂₃×D₁₃	C₂	semidirect
5. C₃×C₇×C₁₃×C₂₃	C₂²	semidirect
7. C₇×C₂₃×D₁₃	D₃	semidirect
9. D₁₃×D₆₉	C₇	direct (N × H)
10. C₇×C₁₃×C₂₃	C₂×D₃	semidirect
12. D₈₉₇	C₂×C₇	semidirect
13. C₁₃×D₆₉	C₂×C₇	semidirect
14. C₃×C₂₃×D₁₃	C₂×C₇	semidirect
19. C₇×D₆₉	D₁₃	direct (N × H)
20. C₃×C₁₃×C₂₃	C₂²×C₇	semidirect
24. C₂₃×D₁₃	D₃×C₇	semidirect
27. C₃×C₇×D₁₃	D₂₃	semidirect
28. C₃×C₇×C₂₃	C₂×D₁₃	semidirect
33. C₁₃×C₂₃	C₂×D₃×C₇	semidirect
35. C₃×C₇×C₁₃	C₂×D₂₃	semidirect
38. C₇×D₁₃	D₆₉	direct (N × H)
39. C₇×C₂₃	D₃×D₁₃	semidirect
43. D₆₉	C₇×D₁₃	direct (N × H)
45. C₇×C₁₃	C₂×D₆₉	semidirect
48. C₃×D₁₃	C₇×D₂₃	semidirect
50. C₃×C₂₃	C₂×C₇×D₁₃	semidirect
58. C₃×C₁₃	C₂×C₇×D₂₃	semidirect
62. D₁₃	C₇×D₆₉	direct (N × H)
63. C₂₃	D₃×C₇×D₁₃	semidirect
64. C₃×C₇	D₁₃×D₂₃	semidirect
68. C₁₃	C₂×C₇×D₆₉	semidirect
70. C₇	D₁₃×D₆₉	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×C₁₃×D₆₉	2
C₃×C₇×C₂₃×D₁₃	2
C₇×D₁₃×D₂₃	3
D₁₃×D₆₉	7
C₂×C₇×D₆₉	13
D₃×C₇×D₁₃	23

Subgroups — C7×D13×D69 #38737419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₁₃×D₆₉ #38737419