Subgroups — D₅₉×D₆₄ #28509730

Order 15104.

142 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₂×D₅₉	C₂	1	2	yes	maximal, complemented
2	D₃₇₇₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#21422308	C₂	1	2	yes	maximal, complemented
4	C₆₄×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₉×D₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₆×D₅₉	—	2	2	no	—
7	D₁₈₈₈	C₂²	1	2	yes	complemented
8	#16837237	—	2	2	no	—
9	C₃₂×D₅₉	C₂²	1	1	yes	characteristic
10	C₅₉⋊C₆₄	C₂²	1	1	yes	characteristic, complemented
11	C₅₉×D₃₂	C₂²	1	2	yes	complemented
12	C₅₉×C₆₄	C₂²	1	1	yes	characteristic, complemented
13	D₈×D₅₉	—	4	2	no	—
14	D₉₄₄	—	2	2	no	—
15	#14273668	—	4	2	no	—
16	C₁₆×D₅₉	D₄	1	1	yes	characteristic
17	C₅₉⋊C₃₂	D₄	1	1	yes	characteristic
18	D₁₆×C₅₉	—	2	2	no	—
19	C₃₂×C₅₉	C₂³	1	1	yes	characteristic
20	D₄×D₅₉	—	8	2	no	—
21	D₈×C₅₉	—	4	2	no	—
22	#11745669	—	8	2	no	—
23	D₄₇₂	—	4	2	no	—
24	C₈×D₅₉	D₈	1	1	yes	characteristic
25	C₁₆×C₅₉	C₂×D₄	1	1	yes	characteristic
26	C₅₉⋊C₁₆	D₈	1	1	yes	characteristic
27	C₂²×D₅₉	—	16	2	no	—
28	D₄×C₅₉	—	8	2	no	—
29	C₂²⋊D₅₉	—	16	2	no	—
30	D₂₃₆	—	8	2	no	—
31	C₄×D₅₉	D₁₆	1	1	yes	characteristic
32	C₈×C₅₉	C₂×D₈	1	1	yes	characteristic
33	C₅₉⋊C₈	D₁₆	1	1	yes	characteristic
34	C₂×D₆₄	—	59	1	no	maximal, Sylow
35	C₂²×C₅₉	—	16	2	no	—
36	C₂×D₅₉	—	16	2	no	—
37	C₂×D₅₉	—	32	4	no	—
38	C₂×D₅₉	D₃₂	1	1	yes	characteristic
39	C₄×C₅₉	C₂×D₁₆	1	1	yes	characteristic
40	Dic₅₉	D₃₂	1	1	yes	characteristic
41	C₂×D₃₂	—	59	2	no	—
42	D₆₄	—	59	2	no	—
43	D₆₄	—	59	1	no	—
44	D₆₄	D₅₉	1	1	yes	characteristic, direct product factor
45	C₂×C₆₄	—	59	1	no	—
46	C₂×C₅₉	—	32	2	no	—
47	C₂×C₅₉	C₂×D₃₂	1	1	yes	characteristic
48	D₅₉	—	32	2	no	—
49	D₅₉	D₆₄	1	2	yes	direct product factor
50	C₂×D₁₆	—	118	2	no	—
51	D₃₂	—	59	2	no	—
52	D₃₂	—	118	2	no	—
53	D₃₂	C₂×D₅₉	1	2	yes	complemented
54	C₂×C₃₂	—	59	1	no	—
55	C₆₄	—	59	1	no	—
56	C₆₄	C₂×D₅₉	1	1	yes	characteristic, complemented
57	C₅₉	C₂×D₆₄	1	1	yes	characteristic, complemented, Sylow
58	C₂×D₈	—	236	2	no	—
59	D₁₆	—	2	2	no	—
60	D₁₆	—	118	2	no	—
61	D₁₆	—	236	2	no	—
62	C₂×C₁₆	—	59	1	no	—
63	C₃₂	—	59	1	no	—
64	C₃₂	C₂²×D₅₉	1	1	yes	characteristic
65	C₂×D₄	—	472	2	no	—
66	D₈	—	4	2	no	—
67	D₈	—	472	2	no	—
68	D₈	—	236	2	no	—
69	C₂×C₈	—	59	1	no	—
70	C₁₆	—	59	1	no	—
71	C₁₆	D₄×D₅₉	1	1	yes	characteristic
72	C₂³	—	944	2	no	—
73	D₄	—	8	2	no	—
74	D₄	—	944	2	no	—
75	D₄	—	472	2	no	—
76	C₂×C₄	—	59	1	no	—
77	C₈	—	59	1	no	—
78	C₈	D₈×D₅₉	1	1	yes	characteristic
79	C₂²	—	16	2	no	—
80	C₂²	—	59	1	no	—
81	C₂²	—	1888	4	no	—
82	C₂²	—	944	2	no	—
83	C₄	—	59	1	no	—
84	C₄	D₁₆×D₅₉	1	1	yes	characteristic
85	C₂	—	32	2	no	—
86	C₂	—	59	2	no	—
87	C₂	—	1888	2	no	—
88	C₂	D₃₂×D₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₃₂×D₅₉
commutator, cosocle	C₃₂×C₅₉	C₂³
Frattini	C₃₂	C₂²×D₅₉
Fitting	C₅₉×D₆₄	C₂
socle	C₂×C₅₉	C₂×D₃₂
hypercenter	D₆₄	D₅₉
hypocenter	C₅₉	C₂×D₆₄
LCS	G ▷ C₃₂×C₅₉ ▷ C₁₆×C₅₉ ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ C₃₂ ◁ D₆₄

Complements

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

N	H ≅ G/N	type
1. D₃₂×D₅₉	C₂	semidirect
2. D₃₇₇₆	C₂	semidirect
3. #21422308	C₂	semidirect
4. C₆₄×D₅₉	C₂	semidirect
5. C₅₉×D₆₄	C₂	semidirect
7. D₁₈₈₈	C₂²	semidirect
10. C₅₉⋊C₆₄	C₂²	semidirect
11. C₅₉×D₃₂	C₂²	semidirect
12. C₅₉×C₆₄	C₂²	semidirect
44. D₆₄	D₅₉	direct (N × H)
49. D₅₉	D₆₄	direct (N × H)
53. D₃₂	C₂×D₅₉	semidirect
56. C₆₄	C₂×D₅₉	semidirect
57. C₅₉	C₂×D₆₄	semidirect

Maximal subgroups

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

subgroup	index
D₃₂×D₅₉	2
D₃₇₇₆	2
#21422308	2
C₆₄×D₅₉	2
C₅₉×D₆₄	2
C₂×D₆₄	59

Subgroups — D59×D64 #28509730

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×D₆₄ #28509730