Subgroups — C₅×C₈×A₄ #91583

Order 480.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×A₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×C₈	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₅×A₄	C₄	1	1	yes	characteristic
4	C₃×C₅×C₈	—	4	1	no	maximal
5	C₈×A₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₄×C₅	C₂×C₃	1	1	yes	characteristic
7	C₂×C₅×C₈	—	3	1	no	—
8	C₂×C₅×C₈	—	3	1	no	—
9	C₅×A₄	C₈	1	1	yes	characteristic, direct product factor
10	C₃×C₄×C₅	—	4	1	no	—
11	C₄×A₄	C₂×C₅	1	1	yes	characteristic
12	C₂³×C₅	C₃×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅	—	3	1	no	—
14	C₂×C₄×C₅	—	3	1	no	—
15	C₅×C₈	—	3	1	no	—
16	C₅×C₈	A₄	1	1	yes	characteristic, direct product factor
17	C₂²×C₈	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₃×C₅	—	4	1	no	—
19	C₂×A₄	C₄×C₅	1	1	yes	characteristic
20	C₃×C₈	—	4	1	no	—
21	C₂²×C₅	—	3	1	no	—
22	C₂²×C₅	—	3	1	no	—
23	C₂²×C₅	C₃×C₈	1	1	yes	characteristic, complemented
24	C₄×C₅	—	3	1	no	—
25	C₄×C₅	C₂×A₄	1	1	yes	characteristic
26	C₂²×C₄	C₂×C₃×C₅	1	1	yes	characteristic
27	C₂×C₈	—	3	1	no	—
28	C₂×C₈	—	3	1	no	—
29	C₃×C₅	—	4	1	no	Hall
30	A₄	C₅×C₈	1	1	yes	characteristic, direct product factor
31	C₃×C₄	—	4	1	no	—
32	C₂×C₅	—	3	1	no	—
33	C₂×C₅	—	3	1	no	—
34	C₂×C₅	C₄×A₄	1	1	yes	characteristic
35	C₂³	C₃×C₄×C₅	1	1	yes	characteristic
36	C₂×C₄	—	3	1	no	—
37	C₂×C₄	—	3	1	no	—
38	C₈	—	3	1	no	—
39	C₈	C₅×A₄	1	1	yes	characteristic, direct product factor
40	C₂×C₃	—	4	1	no	—
41	C₅	C₈×A₄	1	1	yes	characteristic, direct product factor, Sylow
42	C₂²	—	3	1	no	—
43	C₂²	—	3	1	no	—
44	C₂²	C₃×C₅×C₈	1	1	yes	characteristic, complemented
45	C₄	—	3	1	no	—
46	C₄	C₂×C₅×A₄	1	1	yes	characteristic
47	C₃	—	4	1	no	Sylow
48	C₂	—	3	1	no	—
49	C₂	—	3	1	no	—
50	C₂	C₄×C₅×A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₅×C₈	A₄
commutator, hypocenter	C₂²	C₃×C₅×C₈
Frattini	C₄	C₂×C₅×A₄
Fitting	C₂²×C₅×C₈	C₃
socle	C₂³×C₅	C₃×C₄
prime radical	C₂×C₅×A₄	C₄
cosocle	C₂²×C₄	C₂×C₃×C₅
LCS	G ▷ C₂²
UCS	C₁ ◁ C₅×C₈

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×C₈	C₃	semidirect
5. C₈×A₄	C₅	direct (N × H)
9. C₅×A₄	C₈	direct (N × H)
16. C₅×C₈	A₄	direct (N × H)
17. C₂²×C₈	C₃×C₅	semidirect
23. C₂²×C₅	C₃×C₈	semidirect
30. A₄	C₅×C₈	direct (N × H)
39. C₈	C₅×A₄	direct (N × H)
41. C₅	C₈×A₄	direct (N × H)
44. C₂²	C₃×C₅×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×A₄	2
C₂²×C₅×C₈	3
C₃×C₅×C₈	4
C₈×A₄	5

Subgroups — C5×C8×A4 #91583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈×A₄ #91583