Subgroups — C₂×Dic₂₂₀ #13183204

Order 1760.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₁₀	C₂	1	2	yes	maximal
2	C₂×C₅×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
3	Dic₂₂₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₅×C₁₁	C₂²	1	1	yes	characteristic
5	C₂×Dic₅₅	—	2	2	no	—
6	Dic₁₁₀	—	2	2	no	—
7	Dic₁₁₀	C₂²	1	4	yes	—
8	C₅×C₈×C₁₁	C₂²	1	2	yes	—
9	C₂×Dic₄₄	—	5	1	no	maximal, Hall
10	C₂²×C₅×C₁₁	D₄	1	1	yes	characteristic
11	C₄×C₅×C₁₁	D₄	1	1	yes	characteristic
12	C₄×C₅×C₁₁	C₂³	1	1	yes	characteristic
13	Dic₅₅	—	2	4	no	—
14	C₂×Dic₂₂	—	5	2	no	—
15	C₂×C₈×C₁₁	D₅	1	1	yes	characteristic
16	Dic₄₄	—	5	4	no	—
17	C₂×Dic₂₀	—	11	1	no	maximal, Hall
18	C₂×C₅×C₁₁	Q₁₆	1	2	yes	complemented
19	C₂×C₅×C₁₁	C₂×D₄	1	1	yes	characteristic
20	C₂×C₄×C₁₁	C₂×D₅	1	1	yes	characteristic
21	C₂×Dic₁₁	—	10	2	no	—
22	Dic₂₂	—	5	4	no	—
23	Dic₂₂	—	10	2	no	—
24	C₈×C₁₁	C₂×D₅	1	2	yes	—
25	C₂×Dic₁₀	—	11	2	no	—
26	C₂×C₅×C₈	D₁₁	1	1	yes	characteristic
27	Dic₂₀	—	11	4	no	—
28	C₅×C₁₁	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₁₁	D₂₀	1	1	yes	characteristic
30	C₄×C₁₁	D₂₀	1	1	yes	characteristic
31	C₄×C₁₁	C₂²×D₅	1	1	yes	characteristic
32	Dic₁₁	—	10	4	no	—
33	C₂×C₄×C₅	C₂×D₁₁	1	1	yes	characteristic
34	C₂×Dic₅	—	22	2	no	—
35	Dic₁₀	—	11	4	no	—
36	Dic₁₀	—	22	2	no	—
37	C₅×C₈	C₂×D₁₁	1	2	yes	—
38	C₂×Q₁₆	—	55	1	no	Sylow
39	C₂×C₁₁	Dic₂₀	1	2	yes	complemented
40	C₂×C₁₁	C₂×D₂₀	1	1	yes	characteristic
41	C₂²×C₅	D₄₄	1	1	yes	characteristic
42	C₄×C₅	D₄₄	1	1	yes	characteristic
43	C₄×C₅	C₂²×D₁₁	1	1	yes	characteristic
44	Dic₅	—	22	4	no	—
45	C₂×Q₈	—	55	2	no	—
46	Q₁₆	—	55	4	no	—
47	C₂×C₈	D₅₅	1	1	yes	characteristic
48	C₁₁	C₂×Dic₂₀	1	1	yes	characteristic, complemented, Sylow
49	C₂×C₅	Dic₄₄	1	2	yes	complemented
50	C₂×C₅	C₂×D₄₄	1	1	yes	characteristic
51	Q₈	—	55	4	no	—
52	Q₈	—	110	2	no	—
53	C₂×C₄	—	110	2	no	—
54	C₂×C₄	C₂×D₅₅	1	1	yes	characteristic
55	C₈	C₂×D₅₅	1	2	yes	—
56	C₅	C₂×Dic₄₄	1	1	yes	characteristic, complemented, Sylow
57	C₂²	D₂₂₀	1	1	yes	characteristic
58	C₄	—	110	4	no	—
59	C₄	D₂₂₀	1	1	yes	characteristic
60	C₄	C₂²×D₅₅	1	1	yes	characteristic
61	C₂	Dic₂₂₀	1	2	yes	direct product factor
62	C₂	C₂×D₂₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₂₂₀
commutator, cosocle	C₄×C₅×C₁₁	C₂³
Frattini	C₄	C₂²×D₅₅
Fitting	C₂×C₅×C₈×C₁₁	C₂
socle, prime radical	C₂²×C₅×C₁₁	D₄
hypercenter	C₂×C₈	D₅₅
hypocenter	C₅×C₁₁	C₂×Q₁₆
LCS	G ▷ C₄×C₅×C₁₁ ▷ C₂×C₅×C₁₁ ▷ C₅×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
3. Dic₂₂₀	C₂	direct (N × H)
18. C₂×C₅×C₁₁	Q₁₆	semidirect
28. C₅×C₁₁	C₂×Q₁₆	semidirect
39. C₂×C₁₁	Dic₂₀	semidirect
48. C₁₁	C₂×Dic₂₀	semidirect
49. C₂×C₅	Dic₄₄	semidirect
56. C₅	C₂×Dic₄₄	semidirect
61. C₂	Dic₂₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₁₁₀	2
C₂×C₅×C₈×C₁₁	2
Dic₂₂₀	2
C₂×Dic₄₄	5
C₂×Dic₂₀	11

Subgroups — C2×Dic220 #13183204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₂₂₀ #13183204