Subgroups — C₂×C₃×Dic₂₀ #91622

Order 480.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Dic₁₀	C₂	1	2	yes	maximal
2	C₂×C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic
3	C₃×Dic₂₀	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₂₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×Dic₅	—	2	2	no	—
7	C₃×Dic₁₀	—	2	2	no	—
8	C₃×Dic₁₀	C₂²	1	4	yes	—
9	C₃×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₃×Q₁₆	—	5	1	no	maximal, Hall
11	C₂×Dic₁₀	C₂×C₃	1	2	yes	—
12	C₂×C₅×C₈	C₂×C₃	1	1	yes	characteristic
13	Dic₂₀	C₂×C₃	1	4	yes	direct product factor
14	C₂²×C₃×C₅	D₄	1	1	yes	characteristic
15	C₃×C₄×C₅	D₄	1	1	yes	characteristic
16	C₃×C₄×C₅	C₂³	1	1	yes	characteristic
17	C₃×Dic₅	—	2	4	no	—
18	C₂×C₃×Q₈	—	5	2	no	—
19	C₃×Q₁₆	—	5	4	no	—
20	C₂×C₃×C₈	D₅	1	1	yes	characteristic
21	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
22	C₂×Dic₅	—	2	2	no	—
23	Dic₁₀	—	2	2	no	—
24	Dic₁₀	C₂²×C₃	1	4	yes	—
25	C₅×C₈	C₂²×C₃	1	2	yes	—
26	C₂×Q₁₆	—	5	1	no	Sylow
27	C₂×C₃×C₅	Q₁₆	1	2	yes	complemented
28	C₂×C₃×C₅	C₂×D₄	1	1	yes	characteristic
29	C₃×Q₈	—	5	4	no	—
30	C₃×Q₈	—	10	2	no	—
31	C₂×C₃×C₄	—	10	2	no	—
32	C₂×C₃×C₄	C₂×D₅	1	1	yes	characteristic
33	C₃×C₈	C₂×D₅	1	2	yes	—
34	C₂²×C₅	C₃×D₄	1	1	yes	characteristic
35	C₄×C₅	C₃×D₄	1	1	yes	characteristic
36	C₄×C₅	C₂³×C₃	1	1	yes	characteristic
37	Dic₅	—	2	4	no	—
38	C₂×Q₈	—	5	2	no	—
39	Q₁₆	—	5	4	no	—
40	C₂×C₈	C₃×D₅	1	1	yes	characteristic
41	C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃	D₂₀	1	1	yes	characteristic
43	C₃×C₄	—	10	4	no	—
44	C₃×C₄	D₂₀	1	1	yes	characteristic
45	C₃×C₄	C₂²×D₅	1	1	yes	characteristic
46	C₂×C₅	C₃×Q₁₆	1	2	yes	complemented
47	C₂×C₅	C₂×C₃×D₄	1	1	yes	characteristic
48	Q₈	—	5	4	no	—
49	Q₈	—	10	2	no	—
50	C₂×C₄	—	10	2	no	—
51	C₂×C₄	C₂×C₃×D₅	1	1	yes	characteristic
52	C₈	C₂×C₃×D₅	1	2	yes	—
53	C₂×C₃	Dic₂₀	1	2	yes	direct product factor
54	C₂×C₃	C₂×D₂₀	1	1	yes	characteristic
55	C₅	C₂×C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
56	C₂²	C₃×D₂₀	1	1	yes	characteristic
57	C₄	—	10	4	no	—
58	C₄	C₃×D₂₀	1	1	yes	characteristic
59	C₄	C₂²×C₃×D₅	1	1	yes	characteristic
60	C₃	C₂×Dic₂₀	1	1	yes	characteristic, direct product factor, Sylow
61	C₂	C₃×Dic₂₀	1	2	yes	direct product factor
62	C₂	C₂×C₃×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₂₀
commutator, cosocle	C₄×C₅	C₂³×C₃
Frattini	C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₃×C₈	D₅
hypocenter	C₅	C₂×C₃×Q₁₆
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
3. C₃×Dic₂₀	C₂	direct (N × H)
4. C₂×Dic₂₀	C₃	direct (N × H)
13. Dic₂₀	C₂×C₃	direct (N × H)
27. C₂×C₃×C₅	Q₁₆	semidirect
41. C₃×C₅	C₂×Q₁₆	semidirect
46. C₂×C₅	C₃×Q₁₆	semidirect
53. C₂×C₃	Dic₂₀	direct (N × H)
55. C₅	C₂×C₃×Q₁₆	semidirect
60. C₃	C₂×Dic₂₀	direct (N × H)
61. C₂	C₃×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
C₂×C₃×Dic₁₀	2
C₂×C₃×C₅×C₈	2
C₃×Dic₂₀	2
C₂×Dic₂₀	3
C₂×C₃×Q₁₆	5

Subgroups — C2×C3×Dic20 #91622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×Dic₂₀ #91622