Group #13103836 — subgroups

Subgroups — D₅⋊(D₅⋊C₁₆) #13103836

Order 1600.

224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₅²	C₂	1	1	yes	maximal, characteristic
2	#11716882	C₂	1	1	yes	maximal, characteristic, complemented
3	#11716857	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅⋊#674	C₂	1	4	yes	maximal, complemented
5	C₄×D₅²	C₄	1	1	yes	characteristic
6	C₈×C₅⋊D₅	C₂²	1	1	yes	characteristic
7	C₅×C₈×D₅	C₄	1	2	yes	—
8	#87767	C₄	1	1	yes	characteristic
9	D₅×#168	C₂²	1	2	yes	—
10	#87765	C₂²	1	2	yes	complemented
11	#87764	C₂²	1	2	yes	complemented
12	C₂×D₅⋊C₁₆	—	5	2	no	maximal
13	C₂×D₅²	C₈	1	1	yes	characteristic
14	C₄×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
15	C₄×C₅×D₅	C₂×C₄	1	2	yes	—
16	#6036	C₈	1	1	yes	characteristic
17	D₅×Dic₅	C₈	1	2	yes	—
18	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
19	#6029	C₂³	1	1	yes	characteristic
20	C₅×#168	C₂×C₄	1	2	yes	—
21	C₂×C₈×D₅	—	5	2	no	—
22	C₂×#674	—	5	4	no	—
23	D₅⋊C₁₆	—	5	2	no	—
24	D₅⋊C₁₆	—	5	4	no	—
25	D₅⋊C₁₆	—	5	2	no	—
26	D₅⋊C₁₆	—	10	2	no	—
27	C₂×C₅⋊D₅	C₂×C₈	1	1	yes	characteristic
28	C₂×C₅×D₅	C₂×C₈	1	2	yes	—
29	D₅²	C₁₆	1	4	yes	complemented
30	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
31	#1039	C₂×C₈	1	1	yes	characteristic
32	C₅×Dic₅	C₂×C₈	1	2	yes	—
33	C₂×C₄×D₅	—	5	2	no	—
34	C₂×C₅×C₈	—	5	2	no	—
35	C₂×#168	—	5	2	no	—
36	C₈×D₅	—	5	2	no	—
37	C₈×D₅	—	5	2	no	—
38	C₈×D₅	—	5	2	no	—
39	C₈×D₅	—	10	2	no	—
40	C₈×D₅	AGL(1,𝔽₅)	1	2	yes	—
41	#674	—	5	4	no	—
42	#674	—	5	4	no	—
43	#674	—	10	4	no	—
44	C₂²×C₁₆	—	25	1	no	Sylow
45	C₂×C₅²	C₂²×C₈	1	1	yes	characteristic
46	C₅⋊D₅	C₂×C₁₆	1	2	yes	complemented
47	C₅×D₅	C₂×C₁₆	1	4	yes	complemented
48	C₂²×D₅	—	5	2	no	—
49	C₂×C₄×C₅	—	5	2	no	—
50	C₂×Dic₅	—	5	2	no	—
51	C₄×D₅	—	5	2	no	—
52	C₄×D₅	—	5	2	no	—
53	C₄×D₅	—	5	2	no	—
54	C₄×D₅	—	10	2	no	—
55	C₄×D₅	C₂×AGL(1,𝔽₅)	1	2	yes	—
56	C₅×C₈	—	2	2	no	—
57	C₅×C₈	—	5	2	no	—
58	C₅×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
59	#168	—	5	2	no	—
60	#168	—	10	2	no	—
61	#168	C₂×AGL(1,𝔽₅)	1	2	yes	—
62	C₂²×C₈	—	25	1	no	—
63	C₂×C₁₆	—	25	1	no	—
64	C₂×C₁₆	—	25	1	no	—
65	C₂×C₁₆	—	25	4	no	—
66	C₅²	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₅	—	5	2	no	—
68	C₂×D₅	—	5	2	no	—
69	C₂×D₅	—	5	8	no	—
70	C₂×D₅	—	10	2	no	—
71	C₂×D₅	D₅⋊C₈	1	2	yes	—
72	C₄×C₅	—	2	2	no	—
73	C₄×C₅	—	5	2	no	—
74	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
75	Dic₅	—	5	2	no	—
76	Dic₅	—	10	2	no	—
77	Dic₅	D₅⋊C₈	1	2	yes	—
78	C₂²×C₄	—	25	1	no	—
79	C₂×C₈	—	5	2	no	—
80	C₂×C₈	—	25	1	no	—
81	C₂×C₈	—	25	2	no	—
82	C₂×C₈	—	25	1	no	—
83	C₁₆	—	25	2	no	—
84	C₁₆	—	25	2	no	—
85	C₂×C₅	—	2	2	no	—
86	C₂×C₅	—	5	4	no	—
87	C₂×C₅	C₂×D₅⋊C₈	1	2	yes	—
88	D₅	—	5	4	no	—
89	D₅	—	10	4	no	—
90	D₅	D₅⋊C₁₆	1	4	yes	complemented
91	C₂³	—	25	1	no	—
92	C₂×C₄	—	5	2	no	—
93	C₂×C₄	—	25	1	no	—
94	C₂×C₄	—	25	2	no	—
95	C₂×C₄	—	25	1	no	—
96	C₈	—	5	2	no	—
97	C₈	—	25	1	no	—
98	C₈	D₅⋊AGL(1,𝔽₅)	1	1	yes	characteristic
99	C₅	—	2	2	no	—
100	C₅	C₂×D₅⋊C₁₆	1	2	yes	complemented
101	C₂²	—	5	2	no	—
102	C₂²	—	25	4	no	—
103	C₂²	—	25	1	no	—
104	C₄	—	5	2	no	—
105	C₄	—	25	1	no	—
106	C₄	C₂×D₅⋊AGL(1,𝔽₅)	1	1	yes	characteristic
107	C₂	—	5	4	no	—
108	C₂	—	25	2	no	—
109	C₂	D₅⋊(D₅⋊C₈)	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈×D₅²

C₂

yes

maximal, characteristic

#11716882

C₂

yes

maximal, characteristic, complemented

#11716857

C₂

yes

maximal, characteristic, complemented

D₅⋊#674

C₂

yes

maximal, complemented

C₄×D₅²

C₄

yes

characteristic

C₈×C₅⋊D₅

C₂²

yes

characteristic

C₅×C₈×D₅

C₄

yes

—

#87767

C₄

yes

characteristic

D₅×#168

C₂²

yes

—

#87765

C₂²

yes

complemented

#87764

C₂²

yes

complemented

C₂×D₅⋊C₁₆

—

maximal

C₂×D₅²

C₈

yes

characteristic

C₄×C₅⋊D₅

C₂×C₄

yes

characteristic

C₄×C₅×D₅

C₂×C₄

yes

—

#6036

C₈

yes

characteristic

D₅×Dic₅

C₈

yes

—

C₅²×C₈

C₂×C₄

yes

characteristic

#6029

C₂³

yes

characteristic

C₅×#168

C₂×C₄

yes

—

C₂×C₈×D₅

—

C₂×#674

—

D₅⋊C₁₆

—

D₅⋊C₁₆

—

D₅⋊C₁₆

—

D₅⋊C₁₆

—

C₂×C₅⋊D₅

C₂×C₈

yes

characteristic

C₂×C₅×D₅

C₂×C₈

yes

—

D₅²

C₁₆

yes

complemented

C₄×C₅²

C₂²×C₄

yes

characteristic

#1039

C₂×C₈

yes

characteristic

C₅×Dic₅

C₂×C₈

yes

—

C₂×C₄×D₅

—

C₂×C₅×C₈

—

C₂×#168

—

C₈×D₅

—

C₈×D₅

—

C₈×D₅

—

C₈×D₅

—

C₈×D₅

AGL(1,𝔽₅)

yes

—

#674

—

#674

—

#674

—

C₂²×C₁₆

—

Sylow

C₂×C₅²

C₂²×C₈

yes

characteristic

C₅⋊D₅

C₂×C₁₆

yes

complemented

C₅×D₅

C₂×C₁₆

yes

complemented

C₂²×D₅

—

C₂×C₄×C₅

—

C₂×Dic₅

—

C₄×D₅

—

C₄×D₅

—

C₄×D₅

—

C₄×D₅

—

C₄×D₅

C₂×AGL(1,𝔽₅)

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

C₂×AGL(1,𝔽₅)

yes

—

—

—

yes

—

C₂²×C₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₅²

C₂²×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₅

—

C₂×D₅

—

C₂×D₅

—

C₂×D₅

—

C₂×D₅

D₅⋊C₈

yes

—

C₄×C₅

—

C₄×C₅

—

C₄×C₅

C₂²×AGL(1,𝔽₅)

yes

—

Dic₅

—

Dic₅

—

Dic₅

D₅⋊C₈

yes

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₁₆

—

C₁₆

—

C₂×C₅

—

C₂×C₅

—

C₂×C₅

C₂×D₅⋊C₈

yes

—

D₅

—

D₅

—

D₅

D₅⋊C₁₆

yes

complemented

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₈

—

C₈

—

C₈

D₅⋊AGL(1,𝔽₅)

yes

characteristic

C₅

—

100

C₅

C₂×D₅⋊C₁₆

yes

complemented

101

C₂²

—

102

C₂²

—

103

C₂²

—

104

C₄

—

105

C₄

—

106

C₄

C₂×D₅⋊AGL(1,𝔽₅)

yes

characteristic

107

C₂

—

108

C₂

—

109

C₂

D₅⋊(D₅⋊C₈)

yes

characteristic

	subgroup	G/H
center, hypercenter	C₈	D₅⋊AGL(1,𝔽₅)
commutator, hypocenter	C₅²	C₂²×C₁₆
Frattini	C₄	C₂×D₅⋊AGL(1,𝔽₅)
Fitting	C₅²×C₈	C₂×C₄
socle	C₂×C₅²	C₂²×C₈
prime radical	C₂×D₅²	C₈
cosocle	#6029	C₂³
LCS	G ▷ C₅²
UCS	C₁ ◁ C₈

subgroup

G/H

center, hypercenter

C₈

D₅⋊AGL(1,𝔽₅)

commutator, hypocenter

C₅²

C₂²×C₁₆

Frattini

C₄

C₂×D₅⋊AGL(1,𝔽₅)

Fitting

C₅²×C₈

C₂×C₄

socle

C₂×C₅²

C₂²×C₈

prime radical

C₂×D₅²

C₈

C₂³

G ▷ C₅²

C₁ ◁ C₈

N	H ≅ G/N	type
2. #11716882	C₂	semidirect
3. #11716857	C₂	semidirect
4. D₅⋊#674	C₂	semidirect
10. #87765	C₂²	semidirect
11. #87764	C₂²	semidirect
29. D₅²	C₁₆	semidirect
46. C₅⋊D₅	C₂×C₁₆	semidirect
47. C₅×D₅	C₂×C₁₆	semidirect
66. C₅²	C₂²×C₁₆	semidirect
90. D₅	D₅⋊C₁₆	semidirect
100. C₅	C₂×D₅⋊C₁₆	semidirect

H ≅ G/N

type

2. #11716882

C₂

semidirect

3. #11716857

C₂

semidirect

4. D₅⋊#674

C₂

semidirect

10. #87765

C₂²

semidirect

11. #87764

C₂²

semidirect

29. D₅²

C₁₆

semidirect

46. C₅⋊D₅

C₂×C₁₆

semidirect

47. C₅×D₅

C₂×C₁₆

semidirect

66. C₅²

C₂²×C₁₆

semidirect

90. D₅

D₅⋊C₁₆

semidirect

100. C₅

C₂×D₅⋊C₁₆

semidirect

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

subgroup	index
C₈×D₅²	2
#11716882	2
#11716857	2
D₅⋊#674	2
C₂×D₅⋊C₁₆	5

subgroup

index

C₈×D₅²

#11716882

#11716857

D₅⋊#674

C₂×D₅⋊C₁₆

Subgroups — D₅⋊(D₅⋊C₁₆) #13103836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D5⋊(D5⋊C16) #13103836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅⋊(D₅⋊C₁₆) #13103836