Group #13025637 — subgroups

Subgroups — #13025637

Order 1280.

358 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 168 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	C₂×#64859	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#674	C₂	1	1	yes	maximal, characteristic
3	#10600597	C₂	1	1	yes	maximal, characteristic
4	#10598777	C₂	1	4	yes	maximal
5	C₂²×#674	C₂²	1	2	yes	—
6	C₂²×#674	C₂²	1	2	yes	—
7	C₂×C₅×#97	C₄	1	1	yes	characteristic
8	C₂×#3947	C₄	1	2	yes	—
9	C₂×C₈×Dic₅	C₂²	1	2	yes	—
10	#65221	C₄	1	1	yes	characteristic
11	C₂×C₄×#168	C₂²	1	1	yes	characteristic
12	#64859	C₄	1	4	yes	complemented
13	C₄×#674	C₄	1	4	yes	complemented
14	#12592	—	5	1	no	maximal, Sylow
15	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×Dic₅	C₂×C₄	1	2	yes	—
18	C₂²×#168	C₂×C₄	1	1	yes	characteristic
19	C₂²×#168	C₂³	1	1	yes	characteristic
20	C₂×#674	—	2	4	no	—
21	C₂×#674	—	2	4	no	—
22	C₂×#674	C₂×C₄	1	4	yes	—
23	C₂×#674	C₂×C₄	1	4	yes	—
24	C₅×#97	C₈	1	4	yes	—
25	#3963	C₈	1	4	yes	—
26	#3947	—	2	4	no	—
27	C₈×Dic₅	—	2	4	no	—
28	C₄×#168	C₂×C₄	1	2	yes	—
29	C₄×#168	C₂×C₄	1	2	yes	—
30	C₂×#346	—	5	1	no	—
31	C₂×C₄×C₁₆	—	5	1	no	—
32	#1726	—	5	1	no	—
33	#1374	—	5	4	no	—
34	C₂²×C₄×C₅	C₂×C₈	1	2	yes	—
35	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₂²×Dic₅	C₂×C₈	1	4	yes	—
37	C₂×C₅×C₈	—	2	2	no	—
38	C₂×C₅×C₈	—	2	2	no	—
39	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
40	C₄²×C₅	C₄²	1	2	yes	—
41	C₄²×C₅	C₂×C₈	1	2	yes	—
42	C₄×Dic₅	—	2	2	no	—
43	C₄×Dic₅	—	2	2	no	—
44	C₂×#168	C₄²	1	2	yes	—
45	C₂×#168	M₁₆	1	4	yes	—
46	C₂×#168	C₂²×C₄	1	1	yes	characteristic
47	C₂×#168	C₂²×C₄	1	1	yes	characteristic
48	C₂×#168	#41	1	4	yes	—
49	#674	—	2	4	no	—
50	#674	—	2	4	no	—
51	C₂²×C₁₆	—	5	2	no	—
52	C₂²×C₁₆	—	5	2	no	—
53	C₂×#97	—	5	2	no	—
54	C₂×#97	AGL(1,𝔽₅)	1	1	yes	characteristic
55	C₂×C₄×C₈	—	5	1	no	—
56	C₂×C₄×C₈	—	5	2	no	—
57	#376	—	5	1	no	—
58	#346	—	5	4	no	—
59	C₄×C₁₆	—	5	4	no	—
60	C₂³×C₅	C₂²×C₈	1	1	yes	characteristic
61	C₂×C₄×C₅	—	2	4	no	—
62	C₂×C₄×C₅	C₄×C₈	1	4	yes	—
63	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₅	#117	1	2	yes	—
65	C₂×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
66	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
67	C₂×Dic₅	—	2	4	no	—
68	C₂×Dic₅	—	2	8	no	—
69	C₅×C₈	—	2	4	no	—
70	#168	#97	1	4	yes	—
71	#168	#117	1	2	yes	—
72	#168	#117	1	2	yes	—
73	C₂²×C₈	—	5	1	no	—
74	C₂²×C₈	—	5	1	no	—
75	C₂²×C₈	C₂×AGL(1,𝔽₅)	1	2	yes	—
76	C₂×C₄²	—	5	2	no	—
77	C₂×C₄²	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
78	C₂×C₁₆	—	5	4	no	—
79	C₂×C₁₆	—	5	4	no	—
80	C₂×C₁₆	—	10	4	no	—
81	C₂×C₁₆	—	10	4	no	—
82	#97	—	10	4	no	—
83	#97	#170	1	4	yes	—
84	C₄×C₈	—	5	2	no	—
85	C₄×C₈	—	5	2	no	—
86	C₄×C₈	—	10	4	no	—
87	#95	—	5	4	no	—
88	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
89	C₂²×C₅	#431	1	2	yes	—
90	C₂²×C₅	#504	1	4	yes	—
91	C₄×C₅	—	2	4	no	—
92	C₄×C₅	#376	1	1	yes	characteristic
93	C₄×C₅	C₂×#97	1	1	yes	characteristic
94	C₄×C₅	#431	1	2	yes	—
95	Dic₅	—	4	4	no	—
96	C₂²×C₄	—	5	4	no	—
97	C₂²×C₄	D₅⋊C₈	1	2	yes	—
98	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	—	2	2	no	—
101	C₂×C₈	—	5	4	no	—
102	C₂×C₈	—	5	1	no	—
103	C₂×C₈	—	5	1	no	—
104	C₂×C₈	—	5	2	no	—
105	C₂×C₈	—	5	4	no	—
106	C₂×C₈	C₂×#170	1	4	yes	—
107	C₄²	—	10	2	no	—
108	C₄²	—	10	2	no	—
109	C₄²	C₄×AGL(1,𝔽₅)	1	2	yes	—
110	C₄²	C₂×#170	1	2	yes	—
111	C₁₆	—	10	4	no	—
112	C₁₆	—	10	4	no	—
113	C₂×C₅	#1744	1	1	yes	characteristic
114	C₂×C₅	#2108	1	2	yes	—
115	C₂×C₅	#2164	1	4	yes	—
116	C₂³	C₂×D₅⋊C₈	1	1	yes	characteristic
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	10	4	no	—
119	C₂×C₄	—	10	8	no	—
120	C₂×C₄	C₄×#170	1	4	yes	—
121	C₂×C₄	D₅⋊M₁₆	1	2	yes	—
122	C₂×C₄	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
123	C₂×C₄	#4130	1	2	yes	—
124	C₂×C₄	C₂²×#170	1	1	yes	characteristic
125	C₈	—	2	4	no	—
126	C₈	—	5	4	no	—
127	C₈	—	5	2	no	—
128	C₈	—	5	2	no	—
129	C₅	#12592	1	1	yes	characteristic, complemented, Sylow
130	C₂²	#65678	1	2	yes	—
131	C₂²	#65725	1	4	yes	—
132	C₂²	C₂×C₄×#170	1	1	yes	characteristic
133	C₄	—	2	4	no	—
134	C₄	—	20	4	no	—
135	C₄	#65676	1	1	yes	characteristic
136	C₄	#65686	1	1	yes	characteristic
137	C₄	#65748	1	2	yes	—
138	C₂	#10603870	1	4	yes	—
139	C₂	#10604173	1	1	yes	characteristic
140	C₂	#10604741	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#64859

C₂

yes

maximal, characteristic

C₂×C₄×#674

C₂

yes

maximal, characteristic

#10600597

C₂

yes

maximal, characteristic

#10598777

C₂

yes

maximal

C₂²×#674

C₂²

yes

—

C₂²×#674

C₂²

yes

—

C₂×C₅×#97

C₄

yes

characteristic

C₂×#3947

C₄

yes

—

C₂×C₈×Dic₅

C₂²

yes

—

#65221

C₄

yes

characteristic

C₂×C₄×#168

C₂²

yes

characteristic

#64859

C₄

yes

complemented

C₄×#674

C₄

yes

complemented

#12592

—

maximal, Sylow

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₄×Dic₅

C₂×C₄

yes

—

C₂²×#168

C₂×C₄

yes

characteristic

C₂²×#168

C₂³

yes

—

—

C₂×C₄

yes

—

C₂×#674

C₂×C₄

yes

—

C₅×#97

C₈

yes

—

#3963

C₈

yes

—

#3947

—

C₈×Dic₅

—

C₄×#168

C₂×C₄

yes

—

C₄×#168

C₂×C₄

yes

—

C₂×#346

—

C₂×C₄×C₁₆

—

#1726

—

#1374

—

C₂²×C₄×C₅

C₂×C₈

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×Dic₅

C₂×C₈

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂×C₈

yes

—

C₄²×C₅

C₄²

yes

—

C₄²×C₅

C₂×C₈

yes

—

C₄×Dic₅

—

C₄×Dic₅

—

C₂×#168

C₄²

yes

—

C₂×#168

M₁₆

yes

—

C₂×#168

C₂²×C₄

yes

characteristic

C₂×#168

C₂²×C₄

yes

characteristic

C₂×#168

#41

yes

—

#674

—

#674

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×#97

—

C₂×#97

AGL(1,𝔽₅)

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

#346

—

C₄×C₁₆

—

C₂³×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

—

C₂×C₄×C₅

C₄×C₈

yes

—

C₂×C₄×C₅

C₂×C₄²

yes

characteristic

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

C₂²×C₈

yes

characteristic

C₂×C₄×C₅

C₂×M₁₆

yes

—

C₂×Dic₅

—

C₂×Dic₅

—

C₅×C₈

—

#168

#97

yes

—

#168

#117

yes

—

#168

#117

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

C₂×AGL(1,𝔽₅)

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×AGL(1,𝔽₅)

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

#170

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

#95

—

C₂²×C₅

C₂×C₄×C₈

yes

characteristic

C₂²×C₅

#431

yes

—

C₂²×C₅

#504

yes

—

C₄×C₅

—

C₄×C₅

#376

yes

characteristic

C₄×C₅

C₂×#97

yes

characteristic

C₄×C₅

#431

yes

—

Dic₅

—

C₂²×C₄

—

C₂²×C₄

D₅⋊C₈

yes

—

C₂²×C₄

C₂²×AGL(1,𝔽₅)

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

C₂×#170

yes

—

107

C₄²

—

108

C₄²

—

109

C₄²

C₄×AGL(1,𝔽₅)

yes

—

110

C₄²

C₂×#170

yes

—

111

C₁₆

—

112

C₁₆

—

113

C₂×C₅

#1744

yes

characteristic

114

C₂×C₅

#2108

yes

—

115

C₂×C₅

#2164

yes

—

116

C₂³

C₂×D₅⋊C₈

yes

characteristic

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

C₄×#170

yes

—

121

C₂×C₄

D₅⋊M₁₆

yes

—

122

C₂×C₄

C₂×C₄×AGL(1,𝔽₅)

yes

characteristic

123

C₂×C₄

#4130

yes

—

124

C₂×C₄

C₂²×#170

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₅

#12592

yes

characteristic, complemented, Sylow

130

C₂²

#65678

yes

—

131

C₂²

#65725

yes

—

132

C₂²

C₂×C₄×#170

yes

characteristic

133

C₄

—

134

C₄

—

135

C₄

#65676

yes

characteristic

136

C₄

#65686

yes

characteristic

137

C₄

#65748

yes

—

138

C₂

#10603870

yes

—

139

C₂

#10604173

yes

characteristic

140

C₂

#10604741

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×AGL(1,𝔽₅)
commutator	C₂²×C₅	C₂×C₄×C₈
Fitting	C₂×C₅×#97	C₄
socle, prime radical	C₂³×C₅	C₂²×C₈
cosocle	C₂²×#168	C₂³
hypercenter	C₂×#97	AGL(1,𝔽₅)
hypocenter	C₅	#12592
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×AGL(1,𝔽₅)

commutator

C₂²×C₅

C₂×C₄×C₈

Fitting

C₂×C₅×#97

C₄

socle, prime radical

C₂³×C₅

C₂²×C₈

cosocle

C₂²×#168

C₂³

C₂×#97

C₅

G ▷ C₂²×C₅ ▷ C₅

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
12. #64859	C₄	semidirect
13. C₄×#674	C₄	semidirect
129. C₅	#12592	semidirect

H ≅ G/N

type

12. #64859

C₄

semidirect

13. C₄×#674

C₄

semidirect

129. C₅

#12592

semidirect

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

subgroup	index
C₂×#64859	2
C₂×C₄×#674	2
#10600597	2
#10598777	2
#12592	5

subgroup

index

C₂×C₄×#674

Subgroups — #13025637

Conjugacy classes of subgroups

Complements

Maximal subgroups