Subgroups — C₄×C₅×C₃⋊C₈ #91045

Order 480.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₃⋊C₈	C₂	1	2	yes	maximal
3	C₄×C₅×C₈	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₅	C₄	1	2	yes	—
5	C₂×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₅×C₃⋊C₈	C₄	1	4	yes	direct product factor
7	C₄×C₃⋊C₈	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₈	—	3	2	no	—
9	C₄²×C₅	D₃	1	1	yes	characteristic
10	C₂²×C₃×C₅	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₅	C₈	1	4	yes	complemented
12	C₃×C₄×C₅	C₂×C₄	1	2	yes	—
13	C₃×C₄²	C₂×C₅	1	1	yes	characteristic
14	C₂×C₃⋊C₈	C₂×C₅	1	2	yes	—
15	C₂×C₄×C₅	Dic₃	1	2	yes	—
16	C₂×C₄×C₅	C₂×D₃	1	1	yes	characteristic
17	C₅×C₈	—	3	4	no	—
18	C₄×C₈	—	3	1	no	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×Dic₃	1	1	yes	characteristic
25	C₄×C₅	C₃⋊C₈	1	4	yes	direct product factor
26	C₄×C₅	C₄×D₃	1	2	yes	—
27	C₂×C₈	—	3	2	no	—
28	C₄²	C₅×D₃	1	1	yes	characteristic
29	C₃×C₅	C₄×C₈	1	1	yes	characteristic, complemented, Hall
30	C₂²×C₃	C₂×C₄×C₅	1	1	yes	characteristic
31	C₃×C₄	C₅×C₈	1	4	yes	complemented
32	C₃×C₄	C₂×C₄×C₅	1	2	yes	—
33	C₂×C₅	C₂×C₃⋊C₈	1	2	yes	—
34	C₂×C₅	C₄×Dic₃	1	1	yes	characteristic
35	C₂×C₄	C₅×Dic₃	1	2	yes	—
36	C₂×C₄	C₂×C₅×D₃	1	1	yes	characteristic
37	C₈	—	3	4	no	—
38	C₂×C₃	C₄²×C₅	1	1	yes	characteristic
39	C₂×C₃	C₂×C₅×C₈	1	2	yes	—
40	C₅	C₄×C₃⋊C₈	1	1	yes	characteristic, direct product factor, Sylow
41	C₂²	C₂×C₅×Dic₃	1	1	yes	characteristic
42	C₄	C₅×C₃⋊C₈	1	4	yes	direct product factor
43	C₄	C₄×C₅×D₃	1	2	yes	—
44	C₃	C₄×C₅×C₈	1	1	yes	characteristic, complemented, Sylow
45	C₂	C₂×C₅×C₃⋊C₈	1	2	yes	—
46	C₂	C₄×C₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄²×C₅	D₃
commutator, hypocenter	C₃	C₄×C₅×C₈
Frattini	C₂×C₄	C₂×C₅×D₃
Fitting	C₃×C₄²×C₅	C₂
socle, prime radical	C₂²×C₃×C₅	C₂×C₄
cosocle	C₂×C₃×C₄	C₂²×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₄²×C₅

Complements

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

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

Maximal subgroups

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

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

Subgroups — C4×C5×C3⋊C8 #91045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×C₃⋊C₈ #91045