Subgroups — C₂²×C₄×C₅×D₃ #92075

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×D₃	C₂	1	12	yes	maximal, direct product factor
5	C₂³×C₄×C₅	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₅×D₃	C₄	1	8	yes	direct product factor
8	C₂²×C₅×D₃	C₂²	1	6	yes	—
9	C₂×C₃×C₄×C₅	C₂²	1	6	yes	complemented
10	C₂×C₅×Dic₃	C₂²	1	6	yes	complemented
11	C₄×C₅×D₃	C₂²	1	16	yes	direct product factor
12	C₂²×C₄×D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₅	—	3	1	no	—
14	C₂²×C₄×C₅	—	3	1	no	—
15	C₂²×C₄×C₅	—	3	12	no	—
16	C₂²×C₄×C₅	D₃	1	1	yes	characteristic, direct product factor
17	C₂²×C₃×C₅	C₂×C₄	1	4	yes	complemented
18	C₂²×C₃×C₅	C₂³	1	3	yes	—
19	C₂×C₅×D₃	C₂×C₄	1	24	yes	direct product factor
20	C₂×C₅×D₃	C₂³	1	4	yes	—
21	C₃×C₄×C₅	C₂³	1	4	yes	complemented
22	C₅×Dic₃	C₂³	1	4	yes	complemented
23	C₂³×D₃	C₂×C₅	1	1	yes	characteristic
24	C₂²×C₃×C₄	C₂×C₅	1	1	yes	characteristic, complemented
25	C₂²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
26	C₂×C₄×D₃	C₂×C₅	1	12	yes	direct product factor
27	C₂³×C₅	—	3	8	no	—
28	C₂³×C₅	—	3	6	no	—
29	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
30	C₂×C₄×C₅	—	3	6	no	—
31	C₂×C₄×C₅	—	3	16	no	—
32	C₂×C₄×C₅	C₂×D₃	1	6	yes	direct product factor
33	C₂³×C₄	—	3	1	no	Sylow
34	C₂×C₃×C₅	C₂²×C₄	1	6	yes	complemented
35	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
36	C₅×D₃	C₂²×C₄	1	8	yes	direct product factor
37	C₂³×C₃	C₂²×C₅	1	1	yes	characteristic
38	C₂²×D₃	C₄×C₅	1	8	yes	direct product factor
39	C₂²×D₃	C₂²×C₅	1	6	yes	—
40	C₂×C₃×C₄	C₂²×C₅	1	6	yes	complemented
41	C₂×Dic₃	C₂²×C₅	1	6	yes	complemented
42	C₄×D₃	C₂²×C₅	1	16	yes	direct product factor
43	C₂²×C₅	—	3	24	no	—
44	C₂²×C₅	—	3	4	no	—
45	C₂²×C₅	C₄×D₃	1	4	yes	direct product factor
46	C₂²×C₅	C₂²×D₃	1	3	yes	—
47	C₄×C₅	—	3	4	no	—
48	C₄×C₅	C₂²×D₃	1	4	yes	direct product factor
49	C₂⁴	—	3	1	no	—
50	C₂²×C₄	—	3	1	no	—
51	C₂²×C₄	—	3	12	no	—
52	C₂²×C₄	C₅×D₃	1	1	yes	characteristic, direct product factor
53	C₃×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	C₂×C₄×C₅	1	4	yes	complemented
55	C₂²×C₃	C₂³×C₅	1	3	yes	—
56	C₂×D₃	C₂×C₄×C₅	1	24	yes	direct product factor
57	C₂×D₃	C₂³×C₅	1	4	yes	—
58	C₃×C₄	C₂³×C₅	1	4	yes	complemented
59	Dic₃	C₂³×C₅	1	4	yes	complemented
60	C₂×C₅	—	3	8	no	—
61	C₂×C₅	C₂×C₄×D₃	1	6	yes	direct product factor
62	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
63	C₂³	—	3	8	no	—
64	C₂³	—	3	6	no	—
65	C₂³	C₂×C₅×D₃	1	1	yes	characteristic
66	C₂×C₄	—	3	6	no	—
67	C₂×C₄	—	3	16	no	—
68	C₂×C₄	C₂×C₅×D₃	1	6	yes	direct product factor
69	C₂×C₃	C₂²×C₄×C₅	1	6	yes	complemented
70	C₂×C₃	C₂⁴×C₅	1	1	yes	characteristic
71	D₃	C₂²×C₄×C₅	1	8	yes	direct product factor
72	C₅	C₂²×C₄×D₃	1	1	yes	characteristic, direct product factor, Sylow
73	C₂²	—	3	24	no	—
74	C₂²	—	3	4	no	—
75	C₂²	C₄×C₅×D₃	1	4	yes	direct product factor
76	C₂²	C₂²×C₅×D₃	1	3	yes	—
77	C₄	—	3	4	no	—
78	C₄	C₂²×C₅×D₃	1	4	yes	direct product factor
79	C₃	C₂³×C₄×C₅	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	3	8	no	—
81	C₂	C₂×C₄×C₅×D₃	1	6	yes	direct product factor
82	C₂	C₂³×C₅×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₄×C₅	D₃
commutator, hypocenter	C₃	C₂³×C₄×C₅
Frattini	C₂	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₄×C₅	C₂
socle	C₂³×C₃×C₅	C₂²
prime radical	C₂³×C₅×D₃	C₂
cosocle	C₂×C₃	C₂⁴×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅

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×C₅×Dic₃	C₂	semidirect
4. C₂×C₄×C₅×D₃	C₂	direct (N × H)
7. C₂²×C₅×D₃	C₄	direct (N × H)
9. C₂×C₃×C₄×C₅	C₂²	semidirect
10. C₂×C₅×Dic₃	C₂²	semidirect
11. C₄×C₅×D₃	C₂²	direct (N × H)
12. C₂²×C₄×D₃	C₅	direct (N × H)
16. C₂²×C₄×C₅	D₃	direct (N × H)
17. C₂²×C₃×C₅	C₂×C₄	semidirect
19. C₂×C₅×D₃	C₂×C₄	direct (N × H)
21. C₃×C₄×C₅	C₂³	semidirect
22. C₅×Dic₃	C₂³	semidirect
24. C₂²×C₃×C₄	C₂×C₅	semidirect
25. C₂²×Dic₃	C₂×C₅	semidirect
26. C₂×C₄×D₃	C₂×C₅	direct (N × H)
32. C₂×C₄×C₅	C₂×D₃	direct (N × H)
34. C₂×C₃×C₅	C₂²×C₄	semidirect
36. C₅×D₃	C₂²×C₄	direct (N × H)
38. C₂²×D₃	C₄×C₅	direct (N × H)
40. C₂×C₃×C₄	C₂²×C₅	semidirect
41. C₂×Dic₃	C₂²×C₅	semidirect
42. C₄×D₃	C₂²×C₅	direct (N × H)
45. C₂²×C₅	C₄×D₃	direct (N × H)
48. C₄×C₅	C₂²×D₃	direct (N × H)
52. C₂²×C₄	C₅×D₃	direct (N × H)
53. C₃×C₅	C₂³×C₄	semidirect
54. C₂²×C₃	C₂×C₄×C₅	semidirect
56. C₂×D₃	C₂×C₄×C₅	direct (N × H)
58. C₃×C₄	C₂³×C₅	semidirect
59. Dic₃	C₂³×C₅	semidirect
61. C₂×C₅	C₂×C₄×D₃	direct (N × H)
68. C₂×C₄	C₂×C₅×D₃	direct (N × H)
69. C₂×C₃	C₂²×C₄×C₅	semidirect
71. D₃	C₂²×C₄×C₅	direct (N × H)
72. C₅	C₂²×C₄×D₃	direct (N × H)
75. C₂²	C₄×C₅×D₃	direct (N × H)
78. C₄	C₂²×C₅×D₃	direct (N × H)
79. C₃	C₂³×C₄×C₅	semidirect
81. C₂	C₂×C₄×C₅×D₃	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×C₅×D₃	2
C₂²×C₃×C₄×C₅	2
C₂²×C₅×Dic₃	2
C₂×C₄×C₅×D₃	2
C₂³×C₄×C₅	3
C₂²×C₄×D₃	5

Subgroups — C22×C4×C5×D3 #92075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₅×D₃ #92075