Subgroups — C₂²×C₃×C₄×D₅ #92060

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₄×D₅	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₄×D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₃×D₅	C₄	1	8	yes	direct product factor
8	C₂²×C₃×D₅	C₂²	1	6	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	6	yes	complemented
10	C₂×C₃×Dic₅	C₂²	1	6	yes	complemented
11	C₃×C₄×D₅	C₂²	1	16	yes	direct product factor
12	C₂³×C₃×C₄	—	5	1	no	maximal, Hall
13	C₂³×D₅	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₄×C₅	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂²×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×C₄×D₅	C₂×C₃	1	12	yes	direct product factor
17	C₂²×C₃×C₅	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃×C₅	C₂³	1	3	yes	—
19	C₂×C₃×D₅	C₂×C₄	1	24	yes	direct product factor
20	C₂×C₃×D₅	C₂³	1	4	yes	—
21	C₃×C₄×C₅	C₂³	1	4	yes	complemented
22	C₃×Dic₅	C₂³	1	4	yes	complemented
23	C₂⁴×C₃	—	5	1	no	—
24	C₂²×C₃×C₄	—	5	1	no	—
25	C₂²×C₃×C₄	—	5	12	no	—
26	C₂²×C₃×C₄	D₅	1	1	yes	characteristic, direct product factor
27	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
28	C₂²×D₅	C₃×C₄	1	8	yes	direct product factor
29	C₂²×D₅	C₂²×C₃	1	6	yes	—
30	C₂×C₄×C₅	C₂²×C₃	1	6	yes	complemented
31	C₂×Dic₅	C₂²×C₃	1	6	yes	complemented
32	C₄×D₅	C₂²×C₃	1	16	yes	direct product factor
33	C₂³×C₄	—	5	1	no	Sylow
34	C₂×C₃×C₅	C₂²×C₄	1	6	yes	complemented
35	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
36	C₃×D₅	C₂²×C₄	1	8	yes	direct product factor
37	C₂³×C₃	—	5	8	no	—
38	C₂³×C₃	—	5	6	no	—
39	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
40	C₂×C₃×C₄	—	5	6	no	—
41	C₂×C₃×C₄	—	5	16	no	—
42	C₂×C₃×C₄	C₂×D₅	1	6	yes	direct product factor
43	C₂²×C₅	C₂×C₃×C₄	1	4	yes	complemented
44	C₂²×C₅	C₂³×C₃	1	3	yes	—
45	C₂×D₅	C₂×C₃×C₄	1	24	yes	direct product factor
46	C₂×D₅	C₂³×C₃	1	4	yes	—
47	C₄×C₅	C₂³×C₃	1	4	yes	complemented
48	Dic₅	C₂³×C₃	1	4	yes	complemented
49	C₂⁴	—	5	1	no	—
50	C₂²×C₄	—	5	1	no	—
51	C₂²×C₄	—	5	12	no	—
52	C₂²×C₄	C₃×D₅	1	1	yes	characteristic, direct product factor
53	C₃×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	—	5	24	no	—
55	C₂²×C₃	—	5	4	no	—
56	C₂²×C₃	C₄×D₅	1	4	yes	direct product factor
57	C₂²×C₃	C₂²×D₅	1	3	yes	—
58	C₃×C₄	—	5	4	no	—
59	C₃×C₄	C₂²×D₅	1	4	yes	direct product factor
60	C₂×C₅	C₂²×C₃×C₄	1	6	yes	complemented
61	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
62	D₅	C₂²×C₃×C₄	1	8	yes	direct product factor
63	C₂³	—	5	8	no	—
64	C₂³	—	5	6	no	—
65	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
66	C₂×C₄	—	5	6	no	—
67	C₂×C₄	—	5	16	no	—
68	C₂×C₄	C₂×C₃×D₅	1	6	yes	direct product factor
69	C₂×C₃	—	5	8	no	—
70	C₂×C₃	C₂×C₄×D₅	1	6	yes	direct product factor
71	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
72	C₅	C₂³×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
73	C₂²	—	5	24	no	—
74	C₂²	—	5	4	no	—
75	C₂²	C₃×C₄×D₅	1	4	yes	direct product factor
76	C₂²	C₂²×C₃×D₅	1	3	yes	—
77	C₄	—	5	4	no	—
78	C₄	C₂²×C₃×D₅	1	4	yes	direct product factor
79	C₃	C₂²×C₄×D₅	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	—	5	8	no	—
81	C₂	C₂×C₃×C₄×D₅	1	6	yes	direct product factor
82	C₂	C₂³×C₃×D₅	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄×C₅	C₂	semidirect
3. C₂²×C₃×Dic₅	C₂	semidirect
4. C₂×C₃×C₄×D₅	C₂	direct (N × H)
5. C₂²×C₄×D₅	C₃	direct (N × H)
7. C₂²×C₃×D₅	C₄	direct (N × H)
9. C₂×C₃×C₄×C₅	C₂²	semidirect
10. C₂×C₃×Dic₅	C₂²	semidirect
11. C₃×C₄×D₅	C₂²	direct (N × H)
14. C₂²×C₄×C₅	C₂×C₃	semidirect
15. C₂²×Dic₅	C₂×C₃	semidirect
16. C₂×C₄×D₅	C₂×C₃	direct (N × H)
17. C₂²×C₃×C₅	C₂×C₄	semidirect
19. C₂×C₃×D₅	C₂×C₄	direct (N × H)
21. C₃×C₄×C₅	C₂³	semidirect
22. C₃×Dic₅	C₂³	semidirect
26. C₂²×C₃×C₄	D₅	direct (N × H)
28. C₂²×D₅	C₃×C₄	direct (N × H)
30. C₂×C₄×C₅	C₂²×C₃	semidirect
31. C₂×Dic₅	C₂²×C₃	semidirect
32. C₄×D₅	C₂²×C₃	direct (N × H)
34. C₂×C₃×C₅	C₂²×C₄	semidirect
36. C₃×D₅	C₂²×C₄	direct (N × H)
42. C₂×C₃×C₄	C₂×D₅	direct (N × H)
43. C₂²×C₅	C₂×C₃×C₄	semidirect
45. C₂×D₅	C₂×C₃×C₄	direct (N × H)
47. C₄×C₅	C₂³×C₃	semidirect
48. Dic₅	C₂³×C₃	semidirect
52. C₂²×C₄	C₃×D₅	direct (N × H)
53. C₃×C₅	C₂³×C₄	semidirect
56. C₂²×C₃	C₄×D₅	direct (N × H)
59. C₃×C₄	C₂²×D₅	direct (N × H)
60. C₂×C₅	C₂²×C₃×C₄	semidirect
62. D₅	C₂²×C₃×C₄	direct (N × H)
68. C₂×C₄	C₂×C₃×D₅	direct (N × H)
70. C₂×C₃	C₂×C₄×D₅	direct (N × H)
72. C₅	C₂³×C₃×C₄	semidirect
75. C₂²	C₃×C₄×D₅	direct (N × H)
78. C₄	C₂²×C₃×D₅	direct (N × H)
79. C₃	C₂²×C₄×D₅	direct (N × H)
81. C₂	C₂×C₃×C₄×D₅	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×C₃×D₅	2
C₂²×C₃×C₄×C₅	2
C₂²×C₃×Dic₅	2
C₂×C₃×C₄×D₅	2
C₂²×C₄×D₅	3
C₂³×C₃×C₄	5

Subgroups — C22×C3×C4×D5 #92060

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₄×D₅ #92060