Subgroups — C₂×C₈×D₅ #4045

Order 160.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#168	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₅	C₂	1	4	yes	maximal, direct product factor
5	C₂²×D₅	C₄	1	1	yes	characteristic
6	C₂×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂×Dic₅	C₄	1	1	yes	characteristic
8	C₄×D₅	C₄	1	2	yes	—
9	C₄×D₅	C₂²	1	2	yes	—
10	C₅×C₈	C₂²	1	2	yes	complemented
11	#168	C₂²	1	2	yes	complemented
12	C₂²×C₈	—	5	1	no	maximal, Sylow
13	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂×D₅	C₈	1	4	yes	direct product factor
15	C₂×D₅	C₂×C₄	1	2	yes	—
16	C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₄×C₅	C₂³	1	1	yes	characteristic
18	Dic₅	C₂×C₄	1	2	yes	—
19	C₂²×C₄	—	5	1	no	—
20	C₂×C₈	—	5	1	no	—
21	C₂×C₈	—	5	4	no	—
22	C₂×C₈	D₅	1	1	yes	characteristic, direct product factor
23	C₂×C₅	C₂×C₈	1	2	yes	complemented
24	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
25	D₅	C₂×C₈	1	4	yes	direct product factor
26	C₂³	—	5	1	no	—
27	C₂×C₄	—	5	1	no	—
28	C₂×C₄	—	5	2	no	—
29	C₂×C₄	—	5	2	no	—
30	C₂×C₄	C₂×D₅	1	1	yes	characteristic
31	C₈	—	5	2	no	—
32	C₈	C₂×D₅	1	2	yes	direct product factor
33	C₅	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	5	4	no	—
35	C₂²	—	5	2	no	—
36	C₂²	C₄×D₅	1	1	yes	characteristic
37	C₄	—	5	2	no	—
38	C₄	C₄×D₅	1	1	yes	characteristic
39	C₄	C₂²×D₅	1	1	yes	characteristic
40	C₂	—	5	4	no	—
41	C₂	C₈×D₅	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	D₅
commutator, hypocenter	C₅	C₂²×C₈
Frattini	C₄	C₂²×D₅
Fitting	C₂×C₅×C₈	C₂
socle	C₂²×C₅	C₂×C₄
prime radical	C₂²×D₅	C₄
cosocle	C₄×C₅	C₂³
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×C₈	C₂	semidirect
3. C₂×#168	C₂	semidirect
4. C₈×D₅	C₂	direct (N × H)
10. C₅×C₈	C₂²	semidirect
11. #168	C₂²	semidirect
14. C₂×D₅	C₈	direct (N × H)
22. C₂×C₈	D₅	direct (N × H)
23. C₂×C₅	C₂×C₈	semidirect
25. D₅	C₂×C₈	direct (N × H)
32. C₈	C₂×D₅	direct (N × H)
33. C₅	C₂²×C₈	semidirect
41. C₂	C₈×D₅	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×C₄×D₅	2
C₂×C₅×C₈	2
C₂×#168	2
C₈×D₅	2
C₂²×C₈	5

Subgroups — C2×C8×D5 #4045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×D₅ #4045