Subgroups — D₆₅×D₉₁ #37556899

Order 23660.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃×D₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×C₁₃×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅⋊(C₇⋊(C₁₃⋊D₁₃))	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₇×C₁₃²	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₃×D₉₁	—	5	1	no	maximal, Hall
6	D₁₃×D₆₅	—	7	1	no	maximal, Hall
7	C₇⋊(C₁₃⋊D₁₃)	—	5	1	no	—
8	C₁₃×D₉₁	D₅	1	1	yes	characteristic, complemented
9	C₇×C₁₃×D₁₃	—	5	1	no	—
10	D₅×D₉₁	—	13	1	no	maximal
11	D₇×D₆₅	—	13	1	no	maximal
12	C₅⋊(C₁₃⋊D₁₃)	—	7	1	no	—
13	C₁₃×D₆₅	D₇	1	1	yes	characteristic, complemented
14	C₅×C₁₃×D₁₃	—	7	1	no	—
15	C₇×C₁₃²	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	D₄₅₅	—	13	1	no	—
17	D₄₅₅	—	13	1	no	—
18	D₄₅₅	—	26	6	no	—
19	C₇×D₆₅	D₁₃	1	1	yes	characteristic, complemented
20	C₇×D₅×C₁₃	—	13	1	no	—
21	C₅×D₉₁	D₁₃	1	1	yes	characteristic, complemented
22	C₅×C₁₃×D₇	—	13	1	no	—
23	C₅×C₁₃²	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	D₁₃²	—	35	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	C₂×D₁₃	1	1	yes	characteristic, complemented
28	C₂×D₉₁	—	65	1	no	—
29	D₇×D₁₃	—	65	1	no	—
30	C₁₃⋊D₁₃	—	35	1	no	—
31	C₁₃×D₁₃	—	5	1	no	—
32	C₁₃×D₁₃	—	7	1	no	—
33	C₂×D₆₅	—	91	1	no	—
34	D₅×D₁₃	—	91	1	no	—
35	C₂×C₇×C₁₃	—	65	1	no	—
36	D₉₁	—	65	1	no	—
37	D₉₁	—	65	1	no	—
38	D₉₁	—	130	6	no	—
39	D₉₁	D₆₅	1	1	yes	characteristic, direct product factor
40	C₇×D₁₃	—	5	1	no	—
41	C₁₃×D₇	—	13	1	no	—
42	C₁₃²	D₅×D₇	1	1	yes	characteristic, complemented, Sylow
43	D₅×D₇	—	169	1	no	Hall
44	C₂×C₅×C₁₃	—	91	1	no	—
45	D₆₅	—	91	1	no	—
46	D₆₅	—	91	1	no	—
47	D₆₅	—	182	6	no	—
48	D₆₅	D₉₁	1	1	yes	characteristic, direct product factor
49	C₅×D₁₃	—	7	1	no	—
50	D₅×C₁₃	—	13	1	no	—
51	C₇×C₁₃	—	2	6	no	—
52	C₇×C₁₃	D₅×D₁₃	1	1	yes	characteristic, complemented
53	C₇×C₁₃	C₂×D₆₅	1	1	yes	characteristic, complemented
54	D₃₅	—	169	1	no	—
55	C₅×D₇	—	13	1	no	—
56	C₇×D₅	—	13	1	no	—
57	C₅×C₁₃	—	2	6	no	—
58	C₅×C₁₃	D₇×D₁₃	1	1	yes	characteristic, complemented
59	C₅×C₁₃	C₂×D₉₁	1	1	yes	characteristic, complemented
60	C₂×D₁₃	—	455	1	no	—
61	C₂×D₁₃	—	455	1	no	—
62	C₅×C₇	D₁₃²	1	1	yes	characteristic, complemented, Hall
63	C₂×D₇	—	845	1	no	Hall
64	C₂×C₁₃	—	65	1	no	—
65	C₂×C₁₃	—	91	1	no	—
66	D₁₃	—	5	1	no	—
67	D₁₃	—	7	1	no	—
68	D₁₃	—	910	6	no	—
69	D₁₃	—	455	1	no	—
70	D₁₃	—	455	1	no	—
71	C₂×D₅	—	1183	1	no	Hall
72	C₂×C₇	—	65	1	no	—
73	D₇	—	13	1	no	—
74	D₇	—	845	1	no	—
75	C₁₃	—	2	6	no	—
76	C₁₃	D₇×D₆₅	1	1	yes	characteristic, complemented
77	C₁₃	D₅×D₉₁	1	1	yes	characteristic, complemented
78	C₂×C₅	—	91	1	no	—
79	D₅	—	13	1	no	—
80	D₅	—	1183	1	no	—
81	C₇	D₁₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
82	C₅	D₁₃×D₉₁	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	5915	1	no	Sylow
84	C₂	—	5915	1	no	—
85	C₂	—	65	1	no	—
86	C₂	—	91	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₅×C₁₃×D₉₁	C₂	semidirect
2. C₇×C₁₃×D₆₅	C₂	semidirect
3. C₅⋊(C₇⋊(C₁₃⋊D₁₃))	C₂	semidirect
4. C₅×C₇×C₁₃²	C₂²	semidirect
8. C₁₃×D₉₁	D₅	semidirect
13. C₁₃×D₆₅	D₇	semidirect
15. C₇×C₁₃²	C₂×D₅	semidirect
19. C₇×D₆₅	D₁₃	semidirect
21. C₅×D₉₁	D₁₃	semidirect
23. C₅×C₁₃²	C₂×D₇	semidirect
26. C₅×C₇×C₁₃	C₂×D₁₃	semidirect
27. C₅×C₇×C₁₃	C₂×D₁₃	semidirect
39. D₉₁	D₆₅	direct (N × H)
42. C₁₃²	D₅×D₇	semidirect
48. D₆₅	D₉₁	direct (N × H)
52. C₇×C₁₃	D₅×D₁₃	semidirect
53. C₇×C₁₃	C₂×D₆₅	semidirect
58. C₅×C₁₃	D₇×D₁₃	semidirect
59. C₅×C₁₃	C₂×D₉₁	semidirect
62. C₅×C₇	D₁₃²	semidirect
76. C₁₃	D₇×D₆₅	semidirect
77. C₁₃	D₅×D₉₁	semidirect
81. C₇	D₁₃×D₆₅	semidirect
82. C₅	D₁₃×D₉₁	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₁₃×D₉₁	2
C₇×C₁₃×D₆₅	2
C₅⋊(C₇⋊(C₁₃⋊D₁₃))	2
D₁₃×D₉₁	5
D₁₃×D₆₅	7
D₅×D₉₁	13
D₇×D₆₅	13

Subgroups — D65×D91 #37556899

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₅×D₉₁ #37556899