Subgroups — C₂²×Dic₂₀ #66076

Order 320.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₁₀	C₂	1	2	yes	maximal
2	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₂₀	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
5	C₂²×Dic₅	—	2	2	no	—
6	C₂×Dic₁₀	—	2	6	no	—
7	C₂×Dic₁₀	C₂²	1	12	yes	—
8	C₂×C₅×C₈	C₂²	1	6	yes	—
9	Dic₂₀	C₂²	1	16	yes	direct product factor
10	C₂²×Q₁₆	—	5	1	no	maximal, Sylow
11	C₂³×C₅	D₄	1	1	yes	characteristic
12	C₂×C₄×C₅	D₄	1	3	yes	—
13	C₂×C₄×C₅	C₂³	1	3	yes	—
14	C₂×Dic₅	—	2	12	no	—
15	Dic₁₀	—	2	12	no	—
16	Dic₁₀	C₂³	1	8	yes	—
17	C₅×C₈	C₂³	1	4	yes	—
18	C₂²×Q₈	—	5	2	no	—
19	C₂×Q₁₆	—	5	12	no	—
20	C₂²×C₈	D₅	1	1	yes	characteristic
21	C₂²×C₅	Q₁₆	1	4	yes	complemented
22	C₂²×C₅	C₂×D₄	1	3	yes	—
23	C₄×C₅	C₂×D₄	1	3	yes	—
24	C₄×C₅	C₂⁴	1	1	yes	characteristic
25	Dic₅	—	2	8	no	—
26	C₂×Q₈	—	5	12	no	—
27	C₂×Q₈	—	10	6	no	—
28	C₂²×C₄	—	10	2	no	—
29	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
30	Q₁₆	—	5	16	no	—
31	C₂×C₈	C₂×D₅	1	6	yes	—
32	C₂×C₅	C₂×Q₁₆	1	6	yes	complemented
33	C₂×C₅	C₂²×D₄	1	1	yes	characteristic
34	C₂³	D₂₀	1	1	yes	characteristic
35	Q₈	—	5	8	no	—
36	Q₈	—	10	12	no	—
37	C₂×C₄	—	10	12	no	—
38	C₂×C₄	D₂₀	1	3	yes	—
39	C₂×C₄	C₂²×D₅	1	3	yes	—
40	C₈	C₂²×D₅	1	4	yes	—
41	C₅	C₂²×Q₁₆	1	1	yes	characteristic, complemented, Sylow
42	C₂²	Dic₂₀	1	4	yes	direct product factor
43	C₂²	C₂×D₂₀	1	3	yes	—
44	C₄	—	10	8	no	—
45	C₄	C₂×D₂₀	1	3	yes	—
46	C₄	C₂³×D₅	1	1	yes	characteristic
47	C₂	C₂×Dic₂₀	1	6	yes	direct product factor
48	C₂	C₂²×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₂₀
commutator, cosocle	C₄×C₅	C₂⁴
Frattini	C₄	C₂³×D₅
Fitting	C₂²×C₅×C₈	C₂
socle, prime radical	C₂³×C₅	D₄
hypercenter	C₂²×C₈	D₅
hypocenter	C₅	C₂²×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. C₂×Dic₂₀	C₂	direct (N × H)
9. Dic₂₀	C₂²	direct (N × H)
21. C₂²×C₅	Q₁₆	semidirect
32. C₂×C₅	C₂×Q₁₆	semidirect
41. C₅	C₂²×Q₁₆	semidirect
42. C₂²	Dic₂₀	direct (N × H)
47. C₂	C₂×Dic₂₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₁₀	2
C₂²×C₅×C₈	2
C₂×Dic₂₀	2
C₂²×Q₁₆	5

Subgroups — C22×Dic20 #66076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×Dic₂₀ #66076