Subgroups — Dic₁₉₈₀ #72212357

Order 7920.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₉₉₀	C₂	1	2	yes	maximal
2	Dic₆₆₀	—	3	1	no	maximal
3	C₅×C₈×C₉×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₉×C₁₁	C₂²	1	1	yes	characteristic
5	Dic₄₉₅	—	2	2	no	—
6	Dic₃₉₆	—	5	1	no	maximal, Hall
7	Dic₃₃₀	—	3	2	no	—
8	C₃×C₅×C₈×C₁₁	D₃	1	1	yes	characteristic
9	C₂×C₅×C₉×C₁₁	D₄	1	1	yes	characteristic
10	Dic₂₂₀	—	9	1	no	Hall
11	Dic₁₉₈	—	5	2	no	—
12	C₈×C₉×C₁₁	D₅	1	1	yes	characteristic
13	Dic₁₈₀	—	11	1	no	maximal, Hall
14	C₃×C₄×C₅×C₁₁	C₂×D₃	1	1	yes	characteristic
15	Dic₁₆₅	—	6	2	no	—
16	Dic₁₃₂	—	15	1	no	—
17	C₅×C₉×C₁₁	Q₁₆	1	1	yes	characteristic, complemented, Hall
18	Dic₁₁₀	—	9	2	no	—
19	C₅×C₈×C₁₁	D₉	1	1	yes	characteristic
20	C₄×C₉×C₁₁	C₂×D₅	1	1	yes	characteristic
21	Dic₉₉	—	10	2	no	—
22	Dic₉₀	—	11	2	no	—
23	C₅×C₈×C₉	D₁₁	1	1	yes	characteristic
24	C₂×C₃×C₅×C₁₁	D₁₂	1	1	yes	characteristic
25	Dic₆₆	—	15	2	no	—
26	C₃×C₈×C₁₁	D₁₅	1	1	yes	characteristic
27	Dic₆₀	—	33	1	no	—
28	C₄×C₅×C₁₁	C₂×D₉	1	1	yes	characteristic
29	Dic₅₅	—	18	2	no	—
30	C₂×C₉×C₁₁	D₂₀	1	1	yes	characteristic
31	C₄×C₅×C₉	C₂×D₁₁	1	1	yes	characteristic
32	Dic₄₅	—	22	2	no	—
33	Dic₄₄	—	45	1	no	Hall
34	C₃×C₅×C₁₁	Dic₁₂	1	1	yes	characteristic
35	Dic₃₆	—	55	1	no	Hall
36	C₃×C₄×C₁₁	C₂×D₁₅	1	1	yes	characteristic
37	Dic₃₃	—	30	2	no	—
38	Dic₃₀	—	33	2	no	—
39	C₃×C₅×C₈	D₃₃	1	1	yes	characteristic
40	C₂×C₅×C₁₁	D₃₆	1	1	yes	characteristic
41	C₉×C₁₁	Dic₂₀	1	1	yes	characteristic, complemented, Hall
42	C₂×C₅×C₉	D₄₄	1	1	yes	characteristic
43	Dic₂₂	—	45	2	no	—
44	C₈×C₁₁	D₄₅	1	1	yes	characteristic
45	Dic₂₀	—	99	1	no	Hall
46	Dic₁₈	—	55	2	no	—
47	C₈×C₉	D₅₅	1	1	yes	characteristic
48	C₂×C₃×C₁₁	D₆₀	1	1	yes	characteristic
49	C₃×C₄×C₅	C₂×D₃₃	1	1	yes	characteristic
50	Dic₁₅	—	66	2	no	—
51	C₅×C₁₁	Dic₃₆	1	1	yes	characteristic, complemented, Hall
52	Dic₁₂	—	165	1	no	—
53	C₅×C₉	Dic₄₄	1	1	yes	characteristic, complemented, Hall
54	C₄×C₁₁	C₂×D₄₅	1	1	yes	characteristic
55	Dic₁₁	—	90	2	no	—
56	Dic₁₀	—	99	2	no	—
57	C₅×C₈	D₉₉	1	1	yes	characteristic
58	C₄×C₉	C₂×D₅₅	1	1	yes	characteristic
59	Dic₉	—	110	2	no	—
60	C₃×C₁₁	Dic₆₀	1	1	yes	characteristic
61	C₂×C₃×C₅	D₁₃₂	1	1	yes	characteristic
62	Dic₆	—	165	2	no	—
63	C₃×C₈	D₁₆₅	1	1	yes	characteristic
64	C₂×C₁₁	D₁₈₀	1	1	yes	characteristic
65	C₄×C₅	C₂×D₉₉	1	1	yes	characteristic
66	Dic₅	—	198	2	no	—
67	C₂×C₉	D₂₂₀	1	1	yes	characteristic
68	Q₁₆	—	495	1	no	Sylow
69	C₃×C₅	Dic₁₃₂	1	1	yes	characteristic
70	C₃×C₄	C₂×D₁₆₅	1	1	yes	characteristic
71	Dic₃	—	330	2	no	—
72	C₁₁	Dic₁₈₀	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₅	D₃₉₆	1	1	yes	characteristic
74	C₉	Dic₂₂₀	1	1	yes	characteristic, complemented, Sylow
75	Q₈	—	495	2	no	—
76	C₈	D₄₉₅	1	1	yes	characteristic
77	C₂×C₃	D₆₆₀	1	1	yes	characteristic
78	C₅	Dic₃₉₆	1	1	yes	characteristic, complemented, Sylow
79	C₄	—	990	2	no	—
80	C₄	C₂×D₄₉₅	1	1	yes	characteristic
81	C₃	Dic₆₆₀	1	1	yes	characteristic
82	C₂	D₁₉₈₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₁₉₈₀
commutator, cosocle	C₄×C₅×C₉×C₁₁	C₂²
Frattini	C₃×C₄	C₂×D₁₆₅
Fitting	C₅×C₈×C₉×C₁₁	C₂
socle, prime radical	C₂×C₃×C₅×C₁₁	D₁₂
hypercenter	C₈	D₄₉₅
hypocenter	C₅×C₉×C₁₁	Q₁₆
LCS	G ▷ C₄×C₅×C₉×C₁₁ ▷ C₂×C₅×C₉×C₁₁ ▷ C₅×C₉×C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
17. C₅×C₉×C₁₁	Q₁₆	semidirect
41. C₉×C₁₁	Dic₂₀	semidirect
51. C₅×C₁₁	Dic₃₆	semidirect
53. C₅×C₉	Dic₄₄	semidirect
72. C₁₁	Dic₁₈₀	semidirect
74. C₉	Dic₂₂₀	semidirect
78. C₅	Dic₃₉₆	semidirect

Maximal subgroups

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

subgroup	index
Dic₉₉₀	2
Dic₆₆₀	3
C₅×C₈×C₉×C₁₁	2
Dic₃₉₆	5
Dic₁₈₀	11

Subgroups — Dic1980 #72212357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₉₈₀ #72212357