Group #10603887 — subgroups

Subgroups — #10603887

Order 640.

162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 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	#64996	C₂	1	1	yes	maximal, characteristic
2	#64897	C₂	1	1	yes	maximal, characteristic
3	#64895	C₂	1	1	yes	maximal, characteristic
4	#64894	C₂	1	2	yes	maximal
5	#64862	C₂	1	2	yes	maximal
6	#4130	C₂²	1	2	yes	—
7	D₅⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#676	C₂²	1	1	yes	characteristic
9	C₂×#676	C₂²	1	1	yes	characteristic
10	C₄²×D₅	C₂²	1	1	yes	characteristic
11	C₅×#97	C₄	1	1	yes	characteristic, complemented
12	C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
13	C₈×Dic₅	C₄	1	1	yes	characteristic, complemented
14	#3935	C₄	1	1	yes	characteristic, complemented
15	#1841	—	5	1	no	maximal, Sylow
16	C₂×C₄×D₅	—	2	1	no	—
17	C₂×C₄×D₅	C₂³	1	1	yes	characteristic
18	C₂²⋊AGL(1,𝔽₅)	—	2	2	no	—
19	#704	—	2	2	no	—
20	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
21	C₄×AGL(1,𝔽₅)	—	2	2	no	—
22	#700	—	2	2	no	—
23	D₅⋊C₈	—	2	2	no	—
24	C₂×C₅×C₈	C₂×C₄	1	1	yes	characteristic
25	C₂×C₅×C₈	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₅	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₅	—	2	1	no	—
28	C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
29	C₂×#168	C₂×C₄	1	1	yes	characteristic
30	C₂×#168	C₂×C₄	1	1	yes	characteristic
31	#676	—	2	2	no	—
32	#676	—	2	2	no	—
33	C₄×M₁₆	—	5	1	no	—
34	#344	—	5	2	no	—
35	#339	—	5	2	no	—
36	#338	—	5	1	no	—
37	H(3,ℤ/4)	—	5	1	no	—
38	C₂²×D₅	#41	1	1	yes	characteristic
39	C₂×AGL(1,𝔽₅)	—	4	2	no	—
40	C₂×C₄×C₅	—	2	1	no	—
41	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
42	C₂×Dic₅	—	2	1	no	—
43	C₂×Dic₅	#41	1	1	yes	characteristic
44	C₄×D₅	—	4	2	no	—
45	C₄×D₅	#41	1	2	yes	—
46	C₄×D₅	#41	1	2	yes	—
47	#170	—	4	2	no	—
48	C₅×C₈	—	2	1	no	—
49	C₅×C₈	—	2	1	no	—
50	#168	—	2	1	no	—
51	#168	—	2	1	no	—
52	C₂×M₁₆	—	5	1	no	—
53	C₂×M₁₆	—	5	1	no	—
54	C₂×M₁₆	—	5	2	no	—
55	#117	—	5	2	no	—
56	C₂×C₄²	—	5	1	no	—
57	#97	—	5	1	no	—
58	#97	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
59	C₄×C₈	—	5	1	no	—
60	C₄×C₈	—	5	1	no	—
61	C₂²×C₅	#117	1	1	yes	characteristic
62	C₂×D₅	—	4	1	no	—
63	C₂×D₅	#126	1	2	yes	—
64	AGL(1,𝔽₅)	—	8	2	no	—
65	C₄×C₅	—	4	1	no	—
66	C₄×C₅	#117	1	1	yes	characteristic
67	C₄×C₅	#117	1	1	yes	characteristic
68	Dic₅	—	2	2	no	—
69	Dic₅	#126	1	2	yes	—
70	C₂²×C₄	—	5	1	no	—
71	C₂²×C₄	—	10	1	no	—
72	M₁₆	—	10	2	no	—
73	M₁₆	—	10	2	no	—
74	M₁₆	—	10	2	no	—
75	M₁₆	—	10	2	no	—
76	C₂×C₈	—	5	1	no	—
77	C₂×C₈	—	5	1	no	—
78	C₂×C₈	—	10	2	no	—
79	C₂×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
80	C₂×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
81	C₄⋊C₄	—	10	2	no	—
82	C₂²⋊C₄	—	10	2	no	—
83	C₄²	—	5	1	no	—
84	C₄²	—	10	1	no	—
85	C₄²	—	10	2	no	—
86	C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
87	C₂×C₅	—	2	1	no	—
88	C₂×C₅	#383	1	1	yes	characteristic
89	D₅	—	2	2	no	—
90	C₂³	—	5	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	5	1	no	—
93	C₂×C₄	—	5	2	no	—
94	C₂×C₄	—	5	2	no	—
95	C₂×C₄	—	10	1	no	—
96	C₂×C₄	—	20	2	no	—
97	C₂×C₄	—	20	2	no	—
98	C₂×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	2	1	no	—
101	C₈	—	10	1	no	—
102	C₈	—	10	1	no	—
103	C₈	—	20	2	no	—
104	C₅	#1841	1	1	yes	characteristic, complemented, Sylow
105	C₂²	—	5	2	no	—
106	C₂²	—	20	1	no	—
107	C₂²	#4130	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	5	2	no	—
110	C₄	—	10	2	no	—
111	C₄	—	40	2	no	—
112	C₄	#4130	1	1	yes	characteristic
113	C₄	#4130	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	10	2	no	—
116	C₂	#65690	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#64996

C₂

yes

maximal, characteristic

#64897

C₂

yes

maximal, characteristic

#64895

C₂

yes

maximal, characteristic

#64894

C₂

yes

maximal

#64862

C₂

yes

maximal

#4130

C₂²

yes

—

D₅⋊M₁₆

C₂²

yes

—

C₂×#676

C₂²

yes

characteristic

C₂×#676

C₂²

yes

characteristic

C₄²×D₅

C₂²

yes

characteristic

C₅×#97

C₄

yes

characteristic, complemented

C₈×Dic₅

C₄

yes

characteristic, complemented

C₈×Dic₅

C₄

yes

characteristic, complemented

#3935

C₄

yes

characteristic, complemented

#1841

—

maximal, Sylow

C₂×C₄×D₅

—

C₂×C₄×D₅

C₂³

yes

characteristic

C₂²⋊AGL(1,𝔽₅)

—

—

—

—

—

D₅⋊C₈

—

C₂×C₅×C₈

C₂×C₄

yes

characteristic

C₂×C₅×C₈

C₂×C₄

yes

characteristic

C₄²×C₅

C₂×C₄

yes

characteristic

C₄×Dic₅

—

C₄×Dic₅

C₂×C₄

yes

characteristic

C₂×#168

C₂×C₄

yes

characteristic

C₂×#168

C₂×C₄

yes

characteristic

#676

—

#676

—

C₄×M₁₆

—

—

—

—

—

C₂²×D₅

#41

yes

characteristic

C₂×AGL(1,𝔽₅)

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×Dic₅

—

C₂×Dic₅

#41

yes

characteristic

C₄×D₅

—

C₄×D₅

#41

yes

—

C₄×D₅

#41

yes

—

#170

—

C₅×C₈

—

C₅×C₈

—

#168

—

#168

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

#117

—

C₂×C₄²

—

#97

—

#97

AGL(1,𝔽₅)

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

C₂²×C₅

#117

yes

characteristic

C₂×D₅

—

C₂×D₅

#126

yes

—

AGL(1,𝔽₅)

—

C₄×C₅

—

C₄×C₅

yes

C₄×C₅

yes

Dic₅

—

Dic₅

#126

yes

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

C₂×C₅

—

C₂×C₅

#383

yes

characteristic

D₅

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×AGL(1,𝔽₅)

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

—

104

C₅

#1841

yes

characteristic, complemented, Sylow

105

C₂²

—

106

C₂²

—

107

C₂²

#4130

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

#4130

yes

characteristic

113

C₄

#4130

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

#65690

yes

characteristic

	subgroup	G/H
center	C₄	#4130
commutator	C₂×C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×AGL(1,𝔽₅)
Fitting	C₅×#97	C₄
socle	C₂×C₅	#383
prime radical	C₂²×D₅	#41
cosocle	C₂×C₄×D₅	C₂³
hypercenter	#97	AGL(1,𝔽₅)
hypocenter	C₅	#1841
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

subgroup

G/H

center

C₄

#4130

commutator

C₂×C₄×C₅

C₂²×C₄

Frattini

C₂×C₄

C₂²×AGL(1,𝔽₅)

Fitting

C₅×#97

C₄

C₂×C₅

C₂²×D₅

C₂×C₄×D₅

C₂³

C₅

G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

N	H ≅ G/N	type
11. C₅×#97	C₄	semidirect
12. C₈×Dic₅	C₄	semidirect
13. C₈×Dic₅	C₄	semidirect
14. #3935	C₄	semidirect
58. #97	AGL(1,𝔽₅)	semidirect
104. C₅	#1841	semidirect

H ≅ G/N

type

11. C₅×#97

C₄

semidirect

12. C₈×Dic₅

C₄

semidirect

13. C₈×Dic₅

C₄

semidirect

14. #3935

C₄

semidirect

58. #97

AGL(1,𝔽₅)

semidirect

104. C₅

#1841

semidirect

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

subgroup	index
#64996	2
#64897	2
#64895	2
#64894	2
#64862	2
#1841	5

subgroup

index

Subgroups — #10603887

Conjugacy classes of subgroups

Complements

Maximal subgroups