Subgroups — C₂²×D₃×Dic₅ #92039

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×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₃×Dic₅	C₂	1	12	yes	maximal, direct product factor
5	C₂³×Dic₅	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂²×C₅×D₃	C₄	1	8	yes	complemented
8	C₂²×C₅×D₃	C₂²	1	6	yes	—
9	C₂×Dic₁₅	C₂²	1	6	yes	complemented
10	C₂×C₃×Dic₅	C₂²	1	6	yes	complemented
11	D₃×Dic₅	C₂²	1	16	yes	direct product factor
12	C₂²×C₄×D₃	—	5	1	no	maximal, Hall
13	C₂⁴×C₅	—	3	1	no	—
14	C₂²×Dic₅	—	3	1	no	—
15	C₂²×Dic₅	—	3	12	no	—
16	C₂²×Dic₅	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	complemented
20	C₂×C₅×D₃	C₂³	1	4	yes	—
21	Dic₁₅	C₂³	1	4	yes	complemented
22	C₃×Dic₅	C₂³	1	4	yes	complemented
23	C₂³×D₃	D₅	1	1	yes	characteristic
24	C₂²×C₃×C₄	—	5	1	no	—
25	C₂²×Dic₃	—	5	1	no	—
26	C₂×C₄×D₃	—	5	12	no	—
27	C₂³×C₅	—	3	8	no	—
28	C₂³×C₅	—	3	6	no	—
29	C₂³×C₅	C₂×D₃	1	1	yes	characteristic
30	C₂×Dic₅	—	3	6	no	—
31	C₂×Dic₅	—	3	16	no	—
32	C₂×Dic₅	C₂×D₃	1	6	yes	direct product factor
33	C₂³×C₄	—	15	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	complemented
37	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
38	C₂²×D₃	Dic₅	1	8	yes	direct product factor
39	C₂²×D₃	C₂×D₅	1	6	yes	—
40	C₂×C₃×C₄	—	5	6	no	—
41	C₂×Dic₃	—	5	6	no	—
42	C₄×D₃	—	5	16	no	—
43	C₂²×C₅	—	3	24	no	—
44	C₂²×C₅	—	3	4	no	—
45	C₂²×C₅	C₄×D₃	1	4	yes	complemented
46	C₂²×C₅	C₂²×D₃	1	3	yes	—
47	Dic₅	—	3	4	no	—
48	Dic₅	C₂²×D₃	1	4	yes	direct product factor
49	C₂⁴	—	3	1	no	—
50	C₂²×C₄	—	5	1	no	—
51	C₂²×C₄	—	15	12	no	—
52	C₂²×C₄	—	15	1	no	—
53	C₃×C₅	C₂³×C₄	1	1	yes	characteristic, complemented, Hall
54	C₂²×C₃	C₂×Dic₅	1	4	yes	complemented
55	C₂²×C₃	C₂²×D₅	1	3	yes	—
56	C₂×D₃	C₂×Dic₅	1	24	yes	direct product factor
57	C₂×D₃	C₂²×D₅	1	4	yes	—
58	C₃×C₄	—	5	4	no	—
59	Dic₃	—	5	4	no	—
60	C₂×C₅	—	3	8	no	—
61	C₂×C₅	C₂×C₄×D₃	1	6	yes	complemented
62	C₂×C₅	C₂³×D₃	1	1	yes	characteristic
63	C₂³	—	3	8	no	—
64	C₂³	—	3	6	no	—
65	C₂³	D₃×D₅	1	1	yes	characteristic
66	C₂×C₄	—	5	6	no	—
67	C₂×C₄	—	15	16	no	—
68	C₂×C₄	—	15	6	no	—
69	C₂×C₃	C₂²×Dic₅	1	6	yes	complemented
70	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
71	D₃	C₂²×Dic₅	1	8	yes	direct product factor
72	C₅	C₂²×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
73	C₂²	—	3	24	no	—
74	C₂²	—	3	4	no	—
75	C₂²	D₃×Dic₅	1	4	yes	direct product factor
76	C₂²	C₂×D₃×D₅	1	3	yes	—
77	C₄	—	5	4	no	—
78	C₄	—	15	4	no	—
79	C₃	C₂³×Dic₅	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	3	8	no	—
81	C₂	C₂×D₃×Dic₅	1	6	yes	direct product factor
82	C₂	C₂²×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂³×C₄
Frattini	C₂	C₂²×D₃×D₅
Fitting, socle	C₂³×C₃×C₅	C₂²
prime radical	C₂³×C₅×D₃	C₂
cosocle	C₂×C₃×C₅	C₂⁴
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₁₅	C₂	semidirect
3. C₂²×C₃×Dic₅	C₂	semidirect
4. C₂×D₃×Dic₅	C₂	direct (N × H)
7. C₂²×C₅×D₃	C₄	semidirect
9. C₂×Dic₁₅	C₂²	semidirect
10. C₂×C₃×Dic₅	C₂²	semidirect
11. D₃×Dic₅	C₂²	direct (N × H)
16. C₂²×Dic₅	D₃	direct (N × H)
17. C₂²×C₃×C₅	C₂×C₄	semidirect
19. C₂×C₅×D₃	C₂×C₄	semidirect
21. Dic₁₅	C₂³	semidirect
22. C₃×Dic₅	C₂³	semidirect
32. C₂×Dic₅	C₂×D₃	direct (N × H)
34. C₂×C₃×C₅	C₂²×C₄	semidirect
36. C₅×D₃	C₂²×C₄	semidirect
38. C₂²×D₃	Dic₅	direct (N × H)
45. C₂²×C₅	C₄×D₃	semidirect
48. Dic₅	C₂²×D₃	direct (N × H)
53. C₃×C₅	C₂³×C₄	semidirect
54. C₂²×C₃	C₂×Dic₅	semidirect
56. C₂×D₃	C₂×Dic₅	direct (N × H)
61. C₂×C₅	C₂×C₄×D₃	semidirect
69. C₂×C₃	C₂²×Dic₅	semidirect
71. D₃	C₂²×Dic₅	direct (N × H)
72. C₅	C₂²×C₄×D₃	semidirect
75. C₂²	D₃×Dic₅	direct (N × H)
79. C₃	C₂³×Dic₅	semidirect
81. C₂	C₂×D₃×Dic₅	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×Dic₁₅	2
C₂²×C₃×Dic₅	2
C₂×D₃×Dic₅	2
C₂³×Dic₅	3
C₂²×C₄×D₃	5

Subgroups — C22×D3×Dic5 #92039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×D₃×Dic₅ #92039