Subgroups — C₄²×C₅×D₃ #91674

Order 480.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×D₃	C₂	1	3	yes	maximal
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×Dic₃	C₂	1	3	yes	maximal, complemented
4	C₂×C₄²×C₅	—	3	1	no	maximal, Hall
5	C₂²×C₅×D₃	C₂²	1	1	yes	characteristic
6	C₂×C₃×C₄×C₅	C₂²	1	3	yes	—
7	C₂×C₅×Dic₃	C₂²	1	3	yes	—
8	C₄×C₅×D₃	C₄	1	12	yes	direct product factor
9	C₄²×D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₄×C₅	—	3	3	no	—
11	C₄²×C₅	—	3	3	no	—
12	C₄²×C₅	D₃	1	1	yes	characteristic, direct product factor
13	C₂²×C₃×C₅	C₂³	1	1	yes	characteristic
14	C₂×C₅×D₃	C₂×C₄	1	6	yes	—
15	C₃×C₄×C₅	C₂×C₄	1	6	yes	complemented
16	C₅×Dic₃	C₂×C₄	1	6	yes	complemented
17	C₂×C₄×D₃	C₂×C₅	1	3	yes	—
18	C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
19	C₄×Dic₃	C₂×C₅	1	3	yes	complemented
20	C₂³×C₅	—	3	1	no	—
21	C₂×C₄×C₅	—	3	3	no	—
22	C₂×C₄×C₅	—	3	12	no	—
23	C₂×C₄×C₅	C₂×D₃	1	3	yes	—
24	C₂×C₄²	—	3	1	no	Sylow
25	C₂×C₃×C₅	C₂²×C₄	1	3	yes	—
26	C₅×D₃	C₄²	1	4	yes	direct product factor
27	C₂²×D₃	C₂²×C₅	1	1	yes	characteristic
28	C₂×C₃×C₄	C₂²×C₅	1	3	yes	—
29	C₂×Dic₃	C₂²×C₅	1	3	yes	—
30	C₄×D₃	C₄×C₅	1	12	yes	direct product factor
31	C₂²×C₅	—	3	6	no	—
32	C₂²×C₅	C₂²×D₃	1	1	yes	characteristic
33	C₄×C₅	—	3	6	no	—
34	C₄×C₅	C₄×D₃	1	6	yes	direct product factor
35	C₂²×C₄	—	3	3	no	—
36	C₄²	—	3	3	no	—
37	C₄²	C₅×D₃	1	1	yes	characteristic, direct product factor
38	C₃×C₅	C₂×C₄²	1	1	yes	characteristic, complemented, Hall
39	C₂²×C₃	C₂³×C₅	1	1	yes	characteristic
40	C₂×D₃	C₂×C₄×C₅	1	6	yes	—
41	C₃×C₄	C₂×C₄×C₅	1	6	yes	complemented
42	Dic₃	C₂×C₄×C₅	1	6	yes	complemented
43	C₂×C₅	—	3	4	no	—
44	C₂×C₅	C₂×C₄×D₃	1	3	yes	—
45	C₂³	—	3	1	no	—
46	C₂×C₄	—	3	3	no	—
47	C₂×C₄	—	3	12	no	—
48	C₂×C₄	C₂×C₅×D₃	1	3	yes	—
49	C₂×C₃	C₂²×C₄×C₅	1	3	yes	—
50	D₃	C₄²×C₅	1	4	yes	direct product factor
51	C₅	C₄²×D₃	1	1	yes	characteristic, direct product factor, Sylow
52	C₂²	—	3	6	no	—
53	C₂²	C₂²×C₅×D₃	1	1	yes	characteristic
54	C₄	—	3	6	no	—
55	C₄	C₄×C₅×D₃	1	6	yes	direct product factor
56	C₃	C₂×C₄²×C₅	1	1	yes	characteristic, complemented, Sylow
57	C₂	—	3	4	no	—
58	C₂	C₂×C₄×C₅×D₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²×C₅	D₃
commutator, hypocenter	C₃	C₂×C₄²×C₅
Frattini	C₂²	C₂²×C₅×D₃
Fitting	C₃×C₄²×C₅	C₂
socle	C₂²×C₃×C₅	C₂³
prime radical	C₂²×C₅×D₃	C₂²
cosocle	C₂²×C₃	C₂³×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₄²×C₅

Complements

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

N	H ≅ G/N	type
2. C₃×C₄²×C₅	C₂	semidirect
3. C₄×C₅×Dic₃	C₂	semidirect
8. C₄×C₅×D₃	C₄	direct (N × H)
9. C₄²×D₃	C₅	direct (N × H)
12. C₄²×C₅	D₃	direct (N × H)
15. C₃×C₄×C₅	C₂×C₄	semidirect
16. C₅×Dic₃	C₂×C₄	semidirect
18. C₃×C₄²	C₂×C₅	semidirect
19. C₄×Dic₃	C₂×C₅	semidirect
26. C₅×D₃	C₄²	direct (N × H)
30. C₄×D₃	C₄×C₅	direct (N × H)
34. C₄×C₅	C₄×D₃	direct (N × H)
37. C₄²	C₅×D₃	direct (N × H)
38. C₃×C₅	C₂×C₄²	semidirect
41. C₃×C₄	C₂×C₄×C₅	semidirect
42. Dic₃	C₂×C₄×C₅	semidirect
50. D₃	C₄²×C₅	direct (N × H)
51. C₅	C₄²×D₃	direct (N × H)
55. C₄	C₄×C₅×D₃	direct (N × H)
56. C₃	C₂×C₄²×C₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×D₃	2
C₃×C₄²×C₅	2
C₄×C₅×Dic₃	2
C₂×C₄²×C₅	3
C₄²×D₃	5

Subgroups — C42×C5×D3 #91674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅×D₃ #91674