Subgroups — D₅⋊M₁₆ #4127

Order 160.

68 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	#704	C₂	1	2	yes	maximal, complemented
3	#700	C₂	1	2	yes	maximal, complemented
4	D₅⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₂²×D₅	C₄	1	1	yes	characteristic
6	C₂×C₄×C₅	C₄	1	1	yes	characteristic
7	C₂×Dic₅	C₂²	1	1	yes	characteristic
8	C₄×D₅	C₄	1	1	yes	characteristic
9	C₄×D₅	C₄	1	1	yes	characteristic
10	C₄×D₅	C₂²	1	1	yes	characteristic
11	C₄×D₅	C₂²	1	1	yes	characteristic
12	#170	C₂²	1	4	yes	complemented
13	C₂×M₁₆	—	5	1	no	maximal, Sylow
14	C₂²×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×D₅	—	2	2	no	—
16	C₂×D₅	C₂×C₄	1	1	yes	characteristic
17	C₂×D₅	C₂×C₄	1	1	yes	characteristic
18	C₄×C₅	C₂×C₄	1	1	yes	characteristic
19	C₄×C₅	C₂×C₄	1	1	yes	characteristic
20	Dic₅	C₂×C₄	1	1	yes	characteristic
21	Dic₅	C₂³	1	1	yes	characteristic
22	C₂²×C₄	—	5	1	no	—
23	M₁₆	—	5	2	no	—
24	M₁₆	—	5	2	no	—
25	C₂×C₈	—	5	2	no	—
26	C₂×C₅	—	2	1	no	—
27	C₂×C₅	C₂²×C₄	1	1	yes	characteristic
28	D₅	—	2	1	no	—
29	D₅	M₁₆	1	2	yes	complemented
30	C₂³	—	5	1	no	—
31	C₂×C₄	—	5	1	no	—
32	C₂×C₄	—	5	1	no	—
33	C₂×C₄	—	5	1	no	—
34	C₂×C₄	—	5	1	no	—
35	C₂×C₄	—	5	1	no	—
36	C₂×C₄	AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₈	—	5	4	no	—
38	C₅	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂²	—	5	1	no	—
40	C₂²	—	5	1	no	—
41	C₂²	—	10	2	no	—
42	C₂²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
43	C₄	—	5	1	no	—
44	C₄	—	5	1	no	—
45	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
46	C₄	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
47	C₂	—	2	1	no	—
48	C₂	—	5	2	no	—
49	C₂	—	10	1	no	—
50	C₂	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×AGL(1,𝔽₅)
commutator, socle	C₂×C₅	C₂²×C₄
Frattini	C₂	C₂²×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅	C₄
prime radical	C₂²×D₅	C₄
cosocle	Dic₅	C₂³
hypercenter	C₂×C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₂×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #704	C₂	semidirect
3. #700	C₂	semidirect
4. D₅⋊C₈	C₂	semidirect
12. #170	C₂²	semidirect
29. D₅	M₁₆	semidirect
38. C₅	C₂×M₁₆	semidirect

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
#704	2
#700	2
D₅⋊C₈	2
C₂×M₁₆	5

Subgroups — D5⋊M16 #4127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊M₁₆ #4127