Subgroups — D₅×D₁₆ #65199

Order 320.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×D₈	C₂	1	2	yes	maximal, complemented
2	C₅×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#3958	C₂	1	2	yes	maximal, complemented
4	D₈₀	C₂	1	1	yes	maximal, characteristic, complemented
5	D₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×D₅	—	2	2	no	—
7	C₅×D₈	C₂²	1	2	yes	complemented
8	#686	—	2	2	no	—
9	D₄₀	C₂²	1	2	yes	complemented
10	C₈×D₅	C₂²	1	1	yes	characteristic
11	C₅×C₁₆	C₂²	1	1	yes	characteristic, complemented
12	#672	C₂²	1	1	yes	characteristic, complemented
13	C₂×D₁₆	—	5	1	no	maximal, Sylow
14	C₂²×D₅	—	4	2	no	—
15	C₅×D₄	—	2	2	no	—
16	C₂²⋊D₅	—	4	2	no	—
17	D₂₀	—	2	2	no	—
18	C₄×D₅	D₄	1	1	yes	characteristic
19	C₅×C₈	C₂³	1	1	yes	characteristic
20	#168	D₄	1	1	yes	characteristic
21	C₂×D₈	—	5	2	no	—
22	D₁₆	—	5	2	no	—
23	D₁₆	—	5	1	no	—
24	D₁₆	D₅	1	1	yes	characteristic, direct product factor
25	C₂×C₁₆	—	5	1	no	—
26	C₂²×C₅	—	4	2	no	—
27	C₂×D₅	—	4	2	no	—
28	C₂×D₅	—	8	4	no	—
29	C₂×D₅	D₈	1	1	yes	characteristic
30	C₄×C₅	C₂×D₄	1	1	yes	characteristic
31	Dic₅	D₈	1	1	yes	characteristic
32	C₂×D₄	—	10	2	no	—
33	D₈	—	5	2	no	—
34	D₈	—	10	2	no	—
35	D₈	C₂×D₅	1	2	yes	complemented
36	C₂×C₈	—	5	1	no	—
37	C₁₆	—	5	1	no	—
38	C₁₆	C₂×D₅	1	1	yes	characteristic, complemented
39	C₂×C₅	—	8	2	no	—
40	C₂×C₅	C₂×D₈	1	1	yes	characteristic
41	D₅	—	8	2	no	—
42	D₅	D₁₆	1	2	yes	direct product factor
43	C₂³	—	20	2	no	—
44	D₄	—	2	2	no	—
45	D₄	—	10	2	no	—
46	D₄	—	20	2	no	—
47	C₂×C₄	—	5	1	no	—
48	C₈	—	5	1	no	—
49	C₈	C₂²×D₅	1	1	yes	characteristic
50	C₅	C₂×D₁₆	1	1	yes	characteristic, complemented, Sylow
51	C₂²	—	4	2	no	—
52	C₂²	—	5	1	no	—
53	C₂²	—	20	2	no	—
54	C₂²	—	40	4	no	—
55	C₄	—	5	1	no	—
56	C₄	D₄×D₅	1	1	yes	characteristic
57	C₂	—	5	2	no	—
58	C₂	—	8	2	no	—
59	C₂	—	40	2	no	—
60	C₂	D₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₅×D₈
commutator, cosocle	C₅×C₈	C₂³
Frattini	C₈	C₂²×D₅
Fitting	C₅×D₁₆	C₂
socle	C₂×C₅	C₂×D₈
hypercenter	D₁₆	D₅
hypocenter	C₅	C₂×D₁₆
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. D₅×D₈	C₂	semidirect
2. C₅×D₁₆	C₂	semidirect
3. #3958	C₂	semidirect
4. D₈₀	C₂	semidirect
5. D₅×C₁₆	C₂	semidirect
7. C₅×D₈	C₂²	semidirect
9. D₄₀	C₂²	semidirect
11. C₅×C₁₆	C₂²	semidirect
12. #672	C₂²	semidirect
24. D₁₆	D₅	direct (N × H)
35. D₈	C₂×D₅	semidirect
38. C₁₆	C₂×D₅	semidirect
42. D₅	D₁₆	direct (N × H)
50. C₅	C₂×D₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₅×D₈	2
C₅×D₁₆	2
#3958	2
D₈₀	2
D₅×C₁₆	2
C₂×D₁₆	5

Subgroups — D5×D16 #65199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₆ #65199