Subgroups — C₇×D₅×C₁₃×D₁₃ #37556879

Order 23660.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₃×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×D₅×C₁₃²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₃×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₇×C₁₃×D₁₃	—	5	1	no	maximal, Hall
6	D₅×C₁₃×D₁₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₇×C₁₃×D₁₃	—	5	1	no	—
8	C₇×C₁₃×D₁₃	D₅	1	1	yes	characteristic, direct product factor
9	C₂×C₇×C₁₃²	—	5	1	no	—
10	C₂×C₇×D₅×C₁₃	—	13	1	no	maximal
11	C₇×D₅×D₁₃	C₁₃	1	1	yes	maximal, characteristic, direct product factor
12	C₁₃×D₆₅	C₂×C₇	1	1	yes	characteristic, complemented
13	D₅×C₁₃²	C₂×C₇	1	1	yes	characteristic, complemented
14	C₅×C₁₃×D₁₃	C₂×C₇	1	1	yes	characteristic, complemented
15	C₇×C₁₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₅×C₇×C₁₃	—	13	1	no	—
17	C₇×D₆₅	C₂×C₁₃	1	1	yes	characteristic, complemented
18	C₇×D₅×C₁₃	—	2	6	no	—
19	C₇×D₅×C₁₃	—	13	1	no	—
20	C₇×D₅×C₁₃	D₁₃	1	1	yes	characteristic, direct product factor
21	C₇×D₅×C₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
22	C₅×C₇×D₁₃	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₅×C₁₃²	C₂²×C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₁₃×D₁₃	—	5	1	no	Hall
25	C₅×C₇×C₁₃	—	2	6	no	—
26	C₅×C₇×C₁₃	C₂×D₁₃	1	1	yes	characteristic, complemented
27	C₅×C₇×C₁₃	C₂²×C₁₃	1	1	yes	characteristic, complemented
28	C₂²×C₇×C₁₃	—	65	1	no	—
29	C₂×C₇×D₁₃	—	5	1	no	—
30	C₂×C₁₃²	—	5	1	no	—
31	C₁₃×D₁₃	—	5	1	no	—
32	C₁₃×D₁₃	C₇×D₅	1	1	yes	characteristic, direct product factor
33	C₂×D₅×C₁₃	—	13	1	no	—
34	D₅×D₁₃	C₇×C₁₃	1	1	yes	characteristic, direct product factor
35	C₂×C₇×C₁₃	—	5	1	no	—
36	C₂×C₇×C₁₃	—	5	1	no	—
37	C₂×C₇×C₁₃	—	10	6	no	—
38	C₂×C₇×C₁₃	—	13	1	no	—
39	C₂×C₇×C₁₃	—	65	1	no	—
40	C₇×D₁₃	—	5	1	no	—
41	C₇×D₁₃	D₅×C₁₃	1	1	yes	characteristic, direct product factor
42	C₁₃²	C₂×C₇×D₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₇×D₅	—	13	1	no	Hall
44	C₂×C₅×C₁₃	—	13	1	no	—
45	D₆₅	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
46	C₅×D₁₃	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
47	D₅×C₁₃	—	2	6	no	—
48	D₅×C₁₃	—	13	1	no	—
49	D₅×C₁₃	C₇×D₁₃	1	1	yes	characteristic, direct product factor
50	D₅×C₁₃	C₂×C₇×C₁₃	1	1	yes	characteristic, complemented
51	C₇×C₁₃	—	2	6	no	—
52	C₇×C₁₃	D₅×D₁₃	1	1	yes	characteristic, direct product factor
53	C₇×C₁₃	C₂×D₅×C₁₃	1	1	yes	characteristic, complemented
54	C₂×C₅×C₇	—	13	1	no	—
55	C₇×D₅	—	13	1	no	—
56	C₇×D₅	C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
57	C₅×C₁₃	—	2	6	no	—
58	C₅×C₁₃	C₂×C₇×D₁₃	1	1	yes	characteristic, complemented
59	C₅×C₁₃	C₂²×C₇×C₁₃	1	1	yes	characteristic, complemented
60	C₂²×C₁₃	—	65	1	no	—
61	C₂×D₁₃	—	5	1	no	—
62	C₅×C₇	C₂×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Hall
63	C₂²×C₇	—	65	1	no	Hall
64	C₂×C₁₃	—	5	1	no	—
65	C₂×C₁₃	—	5	1	no	—
66	C₂×C₁₃	—	10	6	no	—
67	C₂×C₁₃	—	13	1	no	—
68	C₂×C₁₃	—	65	1	no	—
69	D₁₃	—	5	1	no	—
70	D₁₃	C₇×D₅×C₁₃	1	1	yes	characteristic, direct product factor
71	C₂×D₅	—	13	1	no	Hall
72	C₂×C₇	—	5	1	no	—
73	C₂×C₇	—	13	1	no	—
74	C₂×C₇	—	65	1	no	—
75	C₁₃	—	2	6	no	—
76	C₁₃	C₇×D₅×D₁₃	1	1	yes	characteristic, direct product factor
77	C₁₃	C₂×C₇×D₅×C₁₃	1	1	yes	characteristic, complemented
78	C₂×C₅	—	13	1	no	—
79	D₅	—	13	1	no	—
80	D₅	C₇×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor
81	C₇	D₅×C₁₃×D₁₃	1	1	yes	characteristic, direct product factor, Sylow
82	C₅	C₂×C₇×C₁₃×D₁₃	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	65	1	no	Sylow
84	C₂	—	5	1	no	—
85	C₂	—	13	1	no	—
86	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₁₃	D₅×D₁₃
commutator, cosocle, hypocenter	C₅×C₁₃	C₂²×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₃²	C₂²
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₇×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₃×D₁₃	C₂	semidirect
2. C₇×D₅×C₁₃²	C₂	semidirect
3. C₇×C₁₃×D₆₅	C₂	semidirect
4. C₅×C₇×C₁₃²	C₂²	semidirect
6. D₅×C₁₃×D₁₃	C₇	direct (N × H)
8. C₇×C₁₃×D₁₃	D₅	direct (N × H)
11. C₇×D₅×D₁₃	C₁₃	direct (N × H)
12. C₁₃×D₆₅	C₂×C₇	semidirect
13. D₅×C₁₃²	C₂×C₇	semidirect
14. C₅×C₁₃×D₁₃	C₂×C₇	semidirect
15. C₇×C₁₃²	C₂×D₅	semidirect
17. C₇×D₆₅	C₂×C₁₃	semidirect
20. C₇×D₅×C₁₃	D₁₃	direct (N × H)
21. C₇×D₅×C₁₃	C₂×C₁₃	semidirect
22. C₅×C₇×D₁₃	C₂×C₁₃	semidirect
23. C₅×C₁₃²	C₂²×C₇	semidirect
26. C₅×C₇×C₁₃	C₂×D₁₃	semidirect
27. C₅×C₇×C₁₃	C₂²×C₁₃	semidirect
32. C₁₃×D₁₃	C₇×D₅	direct (N × H)
34. D₅×D₁₃	C₇×C₁₃	direct (N × H)
41. C₇×D₁₃	D₅×C₁₃	direct (N × H)
42. C₁₃²	C₂×C₇×D₅	semidirect
45. D₆₅	C₂×C₇×C₁₃	semidirect
46. C₅×D₁₃	C₂×C₇×C₁₃	semidirect
49. D₅×C₁₃	C₇×D₁₃	direct (N × H)
50. D₅×C₁₃	C₂×C₇×C₁₃	semidirect
52. C₇×C₁₃	D₅×D₁₃	direct (N × H)
53. C₇×C₁₃	C₂×D₅×C₁₃	semidirect
56. C₇×D₅	C₁₃×D₁₃	direct (N × H)
58. C₅×C₁₃	C₂×C₇×D₁₃	semidirect
59. C₅×C₁₃	C₂²×C₇×C₁₃	semidirect
62. C₅×C₇	C₂×C₁₃×D₁₃	semidirect
70. D₁₃	C₇×D₅×C₁₃	direct (N × H)
76. C₁₃	C₇×D₅×D₁₃	direct (N × H)
77. C₁₃	C₂×C₇×D₅×C₁₃	semidirect
80. D₅	C₇×C₁₃×D₁₃	direct (N × H)
81. C₇	D₅×C₁₃×D₁₃	direct (N × H)
82. C₅	C₂×C₇×C₁₃×D₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₇×C₁₃×D₁₃	2
C₇×D₅×C₁₃²	2
C₇×C₁₃×D₆₅	2
C₂×C₇×C₁₃×D₁₃	5
D₅×C₁₃×D₁₃	7
C₂×C₇×D₅×C₁₃	13
C₇×D₅×D₁₃	13

Subgroups — C7×D5×C13×D13 #37556879

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×D₅×C₁₃×D₁₃ #37556879