Subgroups — C₂²×D₆₀ #92091

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₁₅	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₆₀	C₂	1	12	yes	maximal, direct product factor
4	C₂²×D₂₀	—	3	1	no	maximal, Hall
5	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
6	C₂²×D₁₅	—	2	8	no	—
7	C₂²×D₁₅	C₂²	1	12	yes	complemented
8	C₂×C₃×C₄×C₅	C₂²	1	6	yes	complemented
9	D₆₀	C₂²	1	16	yes	direct product factor
10	C₂²×D₁₂	—	5	1	no	maximal, Hall
11	C₂³×D₅	—	3	2	no	—
12	C₂²×C₄×C₅	D₃	1	1	yes	characteristic, complemented
13	C₂×D₂₀	—	3	12	no	—
14	C₂²×C₃×C₅	D₄	1	4	yes	complemented
15	C₂²×C₃×C₅	C₂³	1	3	yes	—
16	C₂×D₁₅	—	2	24	no	—
17	C₂×D₁₅	C₂³	1	8	yes	complemented
18	C₃×C₄×C₅	C₂³	1	4	yes	complemented
19	C₂³×D₃	—	5	2	no	—
20	C₂²×C₃×C₄	D₅	1	1	yes	characteristic, complemented
21	C₂×D₁₂	—	5	12	no	—
22	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
23	C₂²×D₅	—	3	12	no	—
24	C₂²×D₅	—	6	8	no	—
25	C₂×C₄×C₅	C₂×D₃	1	6	yes	complemented
26	D₂₀	—	3	16	no	—
27	C₂²×D₄	—	15	1	no	Sylow
28	C₂×C₃×C₅	C₂×D₄	1	6	yes	complemented
29	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
30	D₁₅	—	2	8	no	—
31	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
32	C₂²×D₃	—	5	12	no	—
33	C₂²×D₃	—	10	8	no	—
34	C₂×C₃×C₄	C₂×D₅	1	6	yes	complemented
35	D₁₂	—	5	16	no	—
36	C₂²×C₅	D₁₂	1	4	yes	complemented
37	C₂²×C₅	C₂²×D₃	1	3	yes	—
38	C₂×D₅	—	3	8	no	—
39	C₂×D₅	—	6	24	no	—
40	C₄×C₅	C₂²×D₃	1	4	yes	complemented
41	C₂⁴	—	15	2	no	—
42	C₂×D₄	—	15	12	no	—
43	C₂²×C₄	D₁₅	1	1	yes	characteristic, complemented
44	C₃×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
45	C₂²×C₃	D₂₀	1	4	yes	complemented
46	C₂²×C₃	C₂²×D₅	1	3	yes	—
47	C₂×D₃	—	5	8	no	—
48	C₂×D₃	—	10	24	no	—
49	C₃×C₄	C₂²×D₅	1	4	yes	complemented
50	C₂×C₅	C₂×D₁₂	1	6	yes	complemented
51	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
52	D₅	—	6	8	no	—
53	C₂³	—	15	12	no	—
54	C₂³	—	30	8	no	—
55	C₂³	C₂×D₁₅	1	1	yes	characteristic
56	D₄	—	15	16	no	—
57	C₂×C₄	C₂×D₁₅	1	6	yes	complemented
58	C₂×C₃	C₂×D₂₀	1	6	yes	complemented
59	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
60	D₃	—	10	8	no	—
61	C₅	C₂²×D₁₂	1	1	yes	characteristic, complemented, Sylow
62	C₂²	—	15	8	no	—
63	C₂²	—	30	24	no	—
64	C₂²	D₆₀	1	4	yes	direct product factor
65	C₂²	C₂²×D₁₅	1	3	yes	—
66	C₄	C₂²×D₁₅	1	4	yes	complemented
67	C₃	C₂²×D₂₀	1	1	yes	characteristic, complemented, Sylow
68	C₂	—	30	8	no	—
69	C₂	C₂×D₆₀	1	6	yes	direct product factor
70	C₂	C₂³×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₁₅
commutator, cosocle	C₂×C₃×C₅	C₂⁴
Frattini	C₂	C₂³×D₁₅
Fitting	C₂²×C₃×C₄×C₅	C₂
socle	C₂³×C₃×C₅	C₂²
hypercenter	C₂²×C₄	D₁₅
hypocenter	C₃×C₅	C₂²×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂³×D₁₅	C₂	semidirect
2. C₂²×C₃×C₄×C₅	C₂	semidirect
3. C₂×D₆₀	C₂	direct (N × H)
7. C₂²×D₁₅	C₂²	semidirect
8. C₂×C₃×C₄×C₅	C₂²	semidirect
9. D₆₀	C₂²	direct (N × H)
12. C₂²×C₄×C₅	D₃	semidirect
14. C₂²×C₃×C₅	D₄	semidirect
17. C₂×D₁₅	C₂³	semidirect
18. C₃×C₄×C₅	C₂³	semidirect
20. C₂²×C₃×C₄	D₅	semidirect
25. C₂×C₄×C₅	C₂×D₃	semidirect
28. C₂×C₃×C₅	C₂×D₄	semidirect
34. C₂×C₃×C₄	C₂×D₅	semidirect
36. C₂²×C₅	D₁₂	semidirect
40. C₄×C₅	C₂²×D₃	semidirect
43. C₂²×C₄	D₁₅	semidirect
44. C₃×C₅	C₂²×D₄	semidirect
45. C₂²×C₃	D₂₀	semidirect
49. C₃×C₄	C₂²×D₅	semidirect
50. C₂×C₅	C₂×D₁₂	semidirect
57. C₂×C₄	C₂×D₁₅	semidirect
58. C₂×C₃	C₂×D₂₀	semidirect
61. C₅	C₂²×D₁₂	semidirect
64. C₂²	D₆₀	direct (N × H)
66. C₄	C₂²×D₁₅	semidirect
67. C₃	C₂²×D₂₀	semidirect
69. C₂	C₂×D₆₀	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×D₁₅	2
C₂²×C₃×C₄×C₅	2
C₂×D₆₀	2
C₂²×D₂₀	3
C₂²×D₁₂	5

Subgroups — C22×D60 #92091

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₆₀ #92091