Subgroups — C₂²×C₃×Dic₁₀ #92059

Order 480.

312 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×Dic₅	C₂	1	2	yes	maximal
3	C₂×C₃×Dic₁₀	C₂	1	12	yes	maximal, direct product factor
4	C₂²×Dic₁₀	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	6	yes	—
7	C₂×C₃×Dic₅	C₂²	1	12	yes	—
8	C₃×Dic₁₀	C₂²	1	16	yes	direct product factor
9	C₂²×C₃×Q₈	—	5	1	no	maximal, Hall
10	C₂²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
11	C₂²×Dic₅	C₂×C₃	1	2	yes	—
12	C₂×Dic₁₀	C₂×C₃	1	12	yes	direct product factor
13	C₂²×C₃×C₅	Q₈	1	4	yes	complemented
14	C₂²×C₃×C₅	C₂³	1	3	yes	—
15	C₃×C₄×C₅	C₂³	1	4	yes	—
16	C₃×Dic₅	C₂³	1	8	yes	—
17	C₂×C₃×Q₈	—	5	12	no	—
18	C₂²×C₃×C₄	—	5	2	no	—
19	C₂²×C₃×C₄	D₅	1	1	yes	characteristic
20	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
21	C₂×C₄×C₅	C₂²×C₃	1	6	yes	—
22	C₂×Dic₅	C₂²×C₃	1	12	yes	—
23	Dic₁₀	C₂²×C₃	1	16	yes	direct product factor
24	C₂²×Q₈	—	5	1	no	Sylow
25	C₂×C₃×C₅	C₂×Q₈	1	6	yes	complemented
26	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
27	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
28	C₃×Q₈	—	5	16	no	—
29	C₂×C₃×C₄	—	5	12	no	—
30	C₂×C₃×C₄	C₂×D₅	1	6	yes	—
31	C₂²×C₅	C₃×Q₈	1	4	yes	complemented
32	C₂²×C₅	C₂³×C₃	1	3	yes	—
33	C₄×C₅	C₂³×C₃	1	4	yes	—
34	Dic₅	C₂³×C₃	1	8	yes	—
35	C₂×Q₈	—	5	12	no	—
36	C₂²×C₄	—	5	2	no	—
37	C₂²×C₄	C₃×D₅	1	1	yes	characteristic
38	C₃×C₅	C₂²×Q₈	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃	Dic₁₀	1	4	yes	direct product factor
40	C₂²×C₃	C₂²×D₅	1	3	yes	—
41	C₃×C₄	—	5	8	no	—
42	C₃×C₄	C₂²×D₅	1	4	yes	—
43	C₂×C₅	C₂×C₃×Q₈	1	6	yes	complemented
44	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
45	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
46	Q₈	—	5	16	no	—
47	C₂×C₄	—	5	12	no	—
48	C₂×C₄	C₂×C₃×D₅	1	6	yes	—
49	C₂×C₃	C₂×Dic₁₀	1	6	yes	direct product factor
50	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
51	C₅	C₂²×C₃×Q₈	1	1	yes	characteristic, complemented, Sylow
52	C₂²	C₃×Dic₁₀	1	4	yes	direct product factor
53	C₂²	C₂²×C₃×D₅	1	3	yes	—
54	C₄	—	5	8	no	—
55	C₄	C₂²×C₃×D₅	1	4	yes	—
56	C₃	C₂²×Dic₁₀	1	1	yes	characteristic, direct product factor, Sylow
57	C₂	C₂×C₃×Dic₁₀	1	6	yes	direct product factor
58	C₂	C₂³×C₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₃
Frattini	C₂	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₄×C₅	C₂
socle, prime radical	C₂³×C₃×C₅	C₂²
hypercenter	C₂²×C₃×C₄	D₅
hypocenter	C₅	C₂²×C₃×Q₈
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂²×C₃×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₃×Dic₁₀	C₂	direct (N × H)
4. C₂²×Dic₁₀	C₃	direct (N × H)
8. C₃×Dic₁₀	C₂²	direct (N × H)
12. C₂×Dic₁₀	C₂×C₃	direct (N × H)
13. C₂²×C₃×C₅	Q₈	semidirect
23. Dic₁₀	C₂²×C₃	direct (N × H)
25. C₂×C₃×C₅	C₂×Q₈	semidirect
31. C₂²×C₅	C₃×Q₈	semidirect
38. C₃×C₅	C₂²×Q₈	semidirect
39. C₂²×C₃	Dic₁₀	direct (N × H)
43. C₂×C₅	C₂×C₃×Q₈	semidirect
49. C₂×C₃	C₂×Dic₁₀	direct (N × H)
51. C₅	C₂²×C₃×Q₈	semidirect
52. C₂²	C₃×Dic₁₀	direct (N × H)
56. C₃	C₂²×Dic₁₀	direct (N × H)
57. C₂	C₂×C₃×Dic₁₀	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×C₃×C₄×C₅	2
C₂²×C₃×Dic₅	2
C₂×C₃×Dic₁₀	2
C₂²×Dic₁₀	3
C₂²×C₃×Q₈	5

Subgroups — C22×C3×Dic10 #92059

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×Dic₁₀ #92059