Subgroups — C₃×C₄×C₅×C₈ #91123

Order 480.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₈	C₂	1	2	yes	maximal
2	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₈	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₄×C₅	C₄	1	2	yes	—
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₃×C₅×C₈	C₄	1	4	yes	direct product factor
7	C₃×C₄×C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈	C₂×C₃	1	2	yes	—
9	C₄²×C₅	C₂×C₃	1	1	yes	characteristic
10	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₅	C₈	1	4	yes	direct product factor
12	C₃×C₄×C₅	C₂×C₄	1	2	yes	—
13	C₂×C₃×C₈	C₂×C₅	1	2	yes	—
14	C₃×C₄²	C₂×C₅	1	1	yes	characteristic
15	C₂×C₄×C₅	C₃×C₄	1	2	yes	—
16	C₂×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
17	C₅×C₈	C₃×C₄	1	4	yes	direct product factor
18	C₄×C₈	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₃×C₅	C₄²	1	1	yes	characteristic
20	C₂×C₃×C₅	C₂×C₈	1	2	yes	—
21	C₂×C₃×C₄	C₄×C₅	1	2	yes	—
22	C₂×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
23	C₃×C₈	C₄×C₅	1	4	yes	direct product factor
24	C₂²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
25	C₄×C₅	C₃×C₈	1	4	yes	direct product factor
26	C₄×C₅	C₂×C₃×C₄	1	2	yes	—
27	C₂×C₈	C₂×C₃×C₅	1	2	yes	—
28	C₄²	C₂×C₃×C₅	1	1	yes	characteristic
29	C₃×C₅	C₄×C₈	1	1	yes	characteristic, direct product factor, Hall
30	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
31	C₃×C₄	C₅×C₈	1	4	yes	direct product factor
32	C₃×C₄	C₂×C₄×C₅	1	2	yes	—
33	C₂×C₅	C₃×C₄²	1	1	yes	characteristic
34	C₂×C₅	C₂×C₃×C₈	1	2	yes	—
35	C₂×C₄	C₃×C₄×C₅	1	2	yes	—
36	C₂×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
37	C₈	C₃×C₄×C₅	1	4	yes	direct product factor
38	C₂×C₃	C₄²×C₅	1	1	yes	characteristic
39	C₂×C₃	C₂×C₅×C₈	1	2	yes	—
40	C₅	C₃×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₂×C₃×C₄×C₅	1	1	yes	characteristic
42	C₄	C₃×C₅×C₈	1	4	yes	direct product factor
43	C₄	C₂×C₃×C₄×C₅	1	2	yes	—
44	C₃	C₄×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
45	C₂	C₃×C₄²×C₅	1	1	yes	characteristic
46	C₂	C₂×C₃×C₅×C₈	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂²×C₃×C₅
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₅×C₈	C₃	direct (N × H)
6. C₃×C₅×C₈	C₄	direct (N × H)
7. C₃×C₄×C₈	C₅	direct (N × H)
11. C₃×C₄×C₅	C₈	direct (N × H)
17. C₅×C₈	C₃×C₄	direct (N × H)
18. C₄×C₈	C₃×C₅	direct (N × H)
23. C₃×C₈	C₄×C₅	direct (N × H)
25. C₄×C₅	C₃×C₈	direct (N × H)
29. C₃×C₅	C₄×C₈	direct (N × H)
31. C₃×C₄	C₅×C₈	direct (N × H)
37. C₈	C₃×C₄×C₅	direct (N × H)
40. C₅	C₃×C₄×C₈	direct (N × H)
42. C₄	C₃×C₅×C₈	direct (N × H)
44. C₃	C₄×C₅×C₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₈	2
C₃×C₄²×C₅	2
C₄×C₅×C₈	3
C₃×C₄×C₈	5

Subgroups — C3×C4×C5×C8 #91123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×C₈ #91123