Subgroups — C₄×D₅⋊C₈ #65675

Order 320.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅⋊C₈	C₂	1	2	yes	maximal
2	C₄²×D₅	C₂	1	1	yes	maximal, characteristic
3	C₄×#170	C₂	1	4	yes	maximal, complemented
4	C₂×C₄×D₅	C₄	1	2	yes	—
5	C₂×C₄×D₅	C₂²	1	1	yes	characteristic
6	C₂×#170	C₂²	1	4	yes	—
7	D₅⋊C₈	C₄	1	8	yes	direct product factor
8	C₄²×C₅	C₄	1	1	yes	characteristic
9	C₄×Dic₅	C₄	1	1	yes	characteristic
10	C₄×Dic₅	C₂²	1	2	yes	—
11	C₂×C₄×C₈	—	5	1	no	maximal, Sylow
12	C₂²×D₅	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
15	C₂×Dic₅	C₂×C₄	1	2	yes	—
16	C₂×Dic₅	C₂³	1	1	yes	characteristic
17	C₄×D₅	C₈	1	8	yes	complemented
18	C₄×D₅	C₂×C₄	1	4	yes	—
19	#170	C₂×C₄	1	8	yes	complemented
20	C₂²×C₈	—	5	2	no	—
21	C₂×C₄²	—	5	1	no	—
22	C₄×C₈	—	5	4	no	—
23	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₅	C₄²	1	2	yes	—
25	C₂×D₅	C₂×C₈	1	4	yes	—
26	C₄×C₅	C₄²	1	2	yes	—
27	C₄×C₅	C₂×C₈	1	4	yes	complemented
28	Dic₅	C₂×C₈	1	4	yes	complemented
29	Dic₅	C₂²×C₄	1	2	yes	—
30	C₂²×C₄	—	5	1	no	—
31	C₂²×C₄	—	5	2	no	—
32	C₂×C₈	—	5	4	no	—
33	C₂×C₈	—	5	8	no	—
34	C₄²	—	5	2	no	—
35	C₄²	—	5	1	no	—
36	C₄²	AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₅	C₂²×C₈	1	2	yes	—
39	D₅	C₄×C₈	1	4	yes	complemented
40	C₂³	—	5	1	no	—
41	C₂×C₄	—	5	1	no	—
42	C₂×C₄	—	5	2	no	—
43	C₂×C₄	—	5	8	no	—
44	C₂×C₄	—	5	4	no	—
45	C₂×C₄	C₂×AGL(1,𝔽₅)	1	2	yes	—
46	C₂×C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
47	C₈	—	5	8	no	—
48	C₅	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
49	C₂²	—	5	4	no	—
50	C₂²	—	5	2	no	—
51	C₂²	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
52	C₄	—	5	4	no	—
53	C₄	—	5	2	no	—
54	C₄	D₅⋊C₈	1	4	yes	direct product factor
55	C₄	C₄×AGL(1,𝔽₅)	1	2	yes	—
56	C₂	—	5	4	no	—
57	C₂	C₂×D₅⋊C₈	1	2	yes	—
58	C₂	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄²	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₂×C₄×C₈
Frattini	C₂²	C₂²×AGL(1,𝔽₅)
Fitting	C₄²×C₅	C₄
socle	C₂²×C₅	C₂²×C₄
prime radical	C₂²×D₅	C₂×C₄
cosocle	C₂×Dic₅	C₂³
LCS	G ▷ C₅
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
3. C₄×#170	C₂	semidirect
7. D₅⋊C₈	C₄	direct (N × H)
17. C₄×D₅	C₈	semidirect
19. #170	C₂×C₄	semidirect
27. C₄×C₅	C₂×C₈	semidirect
28. Dic₅	C₂×C₈	semidirect
39. D₅	C₄×C₈	semidirect
48. C₅	C₂×C₄×C₈	semidirect
54. C₄	D₅⋊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×D₅⋊C₈	2
C₄²×D₅	2
C₄×#170	2
C₂×C₄×C₈	5

Subgroups — C4×D5⋊C8 #65675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₅⋊C₈ #65675