Subgroups — C₅×D₃×C₈ #6688

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₈	C₂	semidirect
3. C₅×C₃⋊C₈	C₂	semidirect
8. D₃×C₈	C₅	direct (N × H)
11. C₅×C₈	D₃	direct (N × H)
13. C₅×D₃	C₈	direct (N × H)
15. C₃×C₈	C₂×C₅	semidirect
16. C₃⋊C₈	C₂×C₅	semidirect
21. C₃×C₅	C₂×C₈	semidirect
29. C₈	C₅×D₃	direct (N × H)
31. D₃	C₅×C₈	direct (N × H)
32. C₅	D₃×C₈	direct (N × H)
36. C₃	C₂×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×D₃	2
C₃×C₅×C₈	2
C₅×C₃⋊C₈	2
C₂×C₅×C₈	3
D₃×C₈	5

Subgroups — C5×D3×C8 #6688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₈ #6688