Group #15774488 — subgroups

Subgroups — #15774488

Order 3328.

270 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 115 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	#13116590	C₂	1	2	yes	maximal
2	C₈²×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13112906	C₂	1	1	yes	maximal, characteristic, complemented
4	#13112905	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88038	—	2	2	no	—
7	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
8	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
9	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×C₄⋊C₁₆	C₂²	1	2	yes	—
11	C₈²×C₁₃	C₂²	1	1	yes	characteristic
12	#11718093	—	2	2	no	—
13	C₄⋊#6090	C₂²	1	2	yes	—
14	C₈×#1055	C₄	1	1	yes	characteristic
15	C₈×#1055	C₄	1	1	yes	characteristic
16	C₈×#1055	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₁₃	—	2	1	no	—
18	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
19	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
20	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
21	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
22	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₃×C₁₆	—	2	2	no	—
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
27	C₈×Dic₁₃	—	2	1	no	—
28	C₈×Dic₁₃	C₈	1	1	yes	characteristic
29	C₈×Dic₁₃	C₈	1	1	yes	characteristic
30	C₈×Dic₁₃	D₄	1	1	yes	characteristic
31	C₈×Dic₁₃	Q₈	1	1	yes	characteristic
32	C₂×#6090	—	2	2	no	—
33	C₄×#1055	C₂×C₄	1	1	yes	characteristic
34	C₄×#1055	C₂×C₄	1	1	yes	characteristic
35	C₄×#1055	C₂×C₄	1	1	yes	characteristic
36	#88038	—	4	4	no	—
37	#12004	—	13	1	no	maximal, Sylow
38	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
40	C₂×C₄×D₁₃	M₁₆	1	1	yes	characteristic
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
44	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
46	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
48	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
49	C₄×Dic₁₃	M₁₆	1	1	yes	characteristic
50	C₂×#1055	—	2	1	no	—
51	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
52	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
53	C₂×#1055	C₂×C₈	1	1	yes	characteristic
54	C₂×#1055	C₂×C₈	1	1	yes	characteristic
55	C₈×D₁₃	—	2	4	no	—
56	C₈×D₁₃	—	2	2	no	—
57	C₈×D₁₃	—	2	2	no	—
58	C₈×D₁₃	—	2	2	no	—
59	C₈×D₁₃	D₈	1	2	yes	—
60	C₈×D₁₃	Q₁₆	1	2	yes	—
61	C₁₃×C₁₆	—	4	2	no	—
62	#6090	—	4	2	no	—
63	#2150	—	13	2	no	—
64	C₂×C₈²	—	13	1	no	—
65	#1370	—	13	2	no	—
66	#1370	—	13	1	no	—
67	#1370	D₁₃	1	1	yes	characteristic, complemented
68	C₂²×D₁₃	C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
72	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
73	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
74	C₂×Dic₁₃	C₄⋊C₈	1	1	yes	characteristic
75	C₄×D₁₃	—	2	1	no	—
76	C₄×D₁₃	—	2	1	no	—
77	C₄×D₁₃	—	2	2	no	—
78	C₄×D₁₃	#107	1	2	yes	—
79	C₄×D₁₃	#108	1	2	yes	—
80	C₈×C₁₃	—	2	2	no	—
81	C₈×C₁₃	—	2	1	no	—
82	C₈×C₁₃	—	2	1	no	—
83	C₈×C₁₃	M₃₂	1	2	yes	complemented
84	C₈×C₁₃	C₂×D₈	1	1	yes	characteristic
85	C₈×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
86	#1055	—	2	2	no	—
87	#1055	—	2	1	no	—
88	#1055	—	2	1	no	—
89	#1055	#107	1	2	yes	—
90	#1055	M₃₂	1	2	yes	complemented
91	C₂×M₃₂	—	26	2	no	—
92	C₂×C₄×C₈	—	13	1	no	—
93	C₂×C₄×C₈	—	13	1	no	—
94	C₂×C₄×C₈	—	13	1	no	—
95	C₄⋊C₁₆	—	13	2	no	—
96	C₄⋊C₁₆	—	26	2	no	—
97	C₄⋊C₁₆	C₂×D₁₃	1	2	yes	—
98	C₈²	—	13	1	no	—
99	C₈²	—	13	1	no	—
100	C₈²	—	13	1	no	—
101	C₈²	C₂×D₁₃	1	1	yes	characteristic
102	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
103	C₂×D₁₃	—	2	1	no	—
104	C₂×D₁₃	—	2	1	no	—
105	C₂×D₁₃	#335	1	2	yes	—
106	C₄×C₁₃	—	2	1	no	—
107	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
108	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
109	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
110	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
111	Dic₁₃	—	2	1	no	—
112	Dic₁₃	#335	1	2	yes	—
113	Dic₁₃	#364	1	2	yes	—
114	C₂²×C₈	—	13	1	no	—
115	C₂²×C₈	—	13	1	no	—
116	C₂²×C₈	—	13	1	no	—
117	C₂²×C₈	—	13	1	no	—
118	C₂²×C₈	—	26	1	no	—
119	C₂×C₄²	—	13	1	no	—
120	M₃₂	—	52	4	no	—
121	C₂×C₁₆	—	2	2	no	—
122	C₂×C₁₆	—	26	2	no	—
123	C₄×C₈	—	13	1	no	—
124	C₄×C₈	—	13	1	no	—
125	C₄×C₈	—	13	1	no	—
126	C₄×C₈	—	13	1	no	—
127	C₄×C₈	—	13	1	no	—
128	C₄×C₈	—	13	1	no	—
129	C₄×C₈	—	13	1	no	—
130	C₄×C₈	—	26	1	no	—
131	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
132	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
133	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
134	C₂×C₁₃	C₂×#335	1	1	yes	characteristic
135	C₂×C₁₃	#2150	1	1	yes	characteristic
136	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
137	D₁₃	—	2	2	no	—
138	C₂²×C₄	—	13	1	no	—
139	C₂²×C₄	—	13	1	no	—
140	C₂²×C₄	—	13	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	13	1	no	—
143	C₂×C₈	—	13	1	no	—
144	C₂×C₈	—	13	2	no	—
145	C₂×C₈	—	13	2	no	—
146	C₂×C₈	—	13	1	no	—
147	C₂×C₈	—	13	1	no	—
148	C₂×C₈	—	26	2	no	—
149	C₂×C₈	—	26	2	no	—
150	C₂×C₈	—	26	4	no	—
151	C₂×C₈	—	26	1	no	—
152	C₂×C₈	—	26	2	no	—
153	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
154	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
155	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
156	C₂×C₈	Q₈×D₁₃	1	1	yes	characteristic
157	C₄²	—	13	1	no	—
158	C₄²	—	13	1	no	—
159	C₄²	—	13	1	no	—
160	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
161	C₁₆	—	4	2	no	—
162	C₁₆	—	52	2	no	—
163	C₁₃	#12004	1	1	yes	characteristic, complemented, Sylow
164	C₂³	—	13	1	no	—
165	C₂×C₄	—	13	1	no	—
166	C₂×C₄	—	13	1	no	—
167	C₂×C₄	—	13	2	no	—
168	C₂×C₄	—	13	2	no	—
169	C₂×C₄	—	13	1	no	—
170	C₂×C₄	—	26	2	no	—
171	C₂×C₄	—	26	1	no	—
172	C₂×C₄	—	26	1	no	—
173	C₂×C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
174	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
175	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	2	1	no	—
178	C₈	—	2	1	no	—
179	C₈	—	13	2	no	—
180	C₈	—	13	2	no	—
181	C₈	—	26	2	no	—
182	C₈	—	26	1	no	—
183	C₈	—	26	1	no	—
184	C₈	#88038	1	2	yes	complemented
185	C₈	D₈×D₁₃	1	1	yes	characteristic
186	C₈	Q₁₆×D₁₃	1	1	yes	characteristic
187	C₂²	—	13	2	no	—
188	C₂²	—	26	1	no	—
189	C₂²	—	26	1	no	—
190	C₂²	D₁₃×C₄⋊C₈	1	1	yes	characteristic
191	C₄	—	2	1	no	—
192	C₄	—	13	2	no	—
193	C₄	—	13	2	no	—
194	C₄	—	26	1	no	—
195	C₄	D₁₃×#107	1	1	yes	characteristic
196	C₄	D₁₃×#108	1	1	yes	characteristic
197	C₄	C₂×#88038	1	1	yes	characteristic
198	C₄	D₁₃×M₃₂	1	1	yes	characteristic
199	C₂	—	26	2	no	—
200	C₂	D₁₃×#335	1	1	yes	characteristic
201	C₂	#13116590	1	1	yes	characteristic
202	C₂	D₁₃×#364	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13116590

C₂

yes

maximal

C₈²×D₁₃

C₂

yes

maximal, characteristic

#13112906

C₂

yes

maximal, characteristic, complemented

#13112905

C₂

yes

maximal, complemented

C₁₃×#1370

C₂

yes

maximal, characteristic, complemented

C₂×#88038

—

C₄×C₈×D₁₃

C₄

yes

characteristic

C₄×C₈×D₁₃

C₄

yes

characteristic

C₄×C₈×D₁₃

C₂²

yes

characteristic

C₁₃×C₄⋊C₁₆

C₂²

yes

—

C₈²×C₁₃

C₂²

yes

characteristic

#11718093

—

C₄⋊#6090

C₂²

yes

—

C₈×#1055

C₄

yes

characteristic

C₈×#1055

C₄

yes

characteristic

C₈×#1055

C₂²

yes

characteristic

C₂×C₈×D₁₃

—

C₂×C₈×D₁₃

C₈

yes

characteristic

C₂×C₈×D₁₃

C₈

yes

characteristic

C₂×C₈×D₁₃

D₄

yes

characteristic

C₂×C₈×D₁₃

Q₈

yes

characteristic

C₄²×D₁₃

C₂×C₄

yes

characteristic

C₂×C₁₃×C₁₆

—

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂×C₄

yes

characteristic

C₄×C₈×C₁₃

C₂³

yes

characteristic

C₈×Dic₁₃

—

C₈×Dic₁₃

C₈

yes

characteristic

C₈×Dic₁₃

C₈

yes

characteristic

C₈×Dic₁₃

D₄

yes

characteristic

C₈×Dic₁₃

Q₈

yes

characteristic

C₂×#6090

—

C₄×#1055

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

characteristic

C₄×#1055

C₂×C₄

yes

—

—

C₂×C₄×D₁₃

C₄⋊C₄

yes

characteristic

C₂×C₄×D₁₃

C₂×C₈

yes

characteristic

C₂×C₄×D₁₃

M₁₆

yes

characteristic

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂×C₈

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

C₂²×C₄

yes

characteristic

C₄×Dic₁₃

C₄⋊C₄

yes

characteristic

C₄×Dic₁₃

C₂×C₈

yes

characteristic

C₄×Dic₁₃

M₁₆

yes

characteristic

C₂×#1055

—

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

C₄⋊C₄

yes

characteristic

C₂×#1055

C₂×C₈

yes

characteristic

C₂×#1055

C₂×C₈

yes

characteristic

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

—

C₈×D₁₃

D₈

yes

—

C₈×D₁₃

Q₁₆

yes

—

C₁₃×C₁₆

—

#6090

—

#2150

—

C₂×C₈²

—

#1370

—

#1370

—

#1370

D₁₃

yes

characteristic, complemented

C₂²×D₁₃

C₄⋊C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₃

C₂×M₁₆

yes

characteristic

C₂×Dic₁₃

C₄⋊C₈

yes

characteristic

C₂×Dic₁₃

C₄⋊C₈

yes

characteristic

C₂×Dic₁₃

C₄⋊C₈

yes

characteristic

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

—

C₄×D₁₃

#107

yes

—

C₄×D₁₃

#108

yes

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

—

C₈×C₁₃

M₃₂

yes

complemented

C₈×C₁₃

C₂×D₈

yes

characteristic

C₈×C₁₃

C₂×Q₁₆

yes

—

—

—

yes

—

#1055

M₃₂

yes

complemented

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄⋊C₁₆

C₂×D₁₃

yes

—

C₈²

—

C₈²

—

100

C₈²

—

101

C₈²

C₂×D₁₃

yes

characteristic

102

C₂²×C₁₃

C₂×C₄⋊C₈

yes

characteristic

103

C₂×D₁₃

—

104

C₂×D₁₃

—

105

C₂×D₁₃

#335

yes

—

106

C₄×C₁₃

—

107

C₄×C₁₃

C₂×#107

yes

characteristic

108

C₄×C₁₃

C₂×#108

yes

characteristic

109

C₄×C₁₃

C₂×M₃₂

yes

characteristic

110

C₄×C₁₃

C₂×M₃₂

yes

characteristic

111

Dic₁₃

—

112

Dic₁₃

#335

yes

—

113

Dic₁₃

#364

yes

—

114

C₂²×C₈

—

115

C₂²×C₈

—

116

C₂²×C₈

—

117

C₂²×C₈

—

118

C₂²×C₈

—

119

C₂×C₄²

—

120

M₃₂

—

121

C₂×C₁₆

—

122

C₂×C₁₆

—

123

C₄×C₈

—

124

C₄×C₈

—

125

C₄×C₈

—

126

C₄×C₈

—

127

C₄×C₈

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₄×C₈

C₄×D₁₃

yes

characteristic

132

C₄×C₈

C₄×D₁₃

yes

characteristic

133

C₄×C₈

C₂²×D₁₃

yes

characteristic

134

C₂×C₁₃

C₂×#335

yes

characteristic

135

C₂×C₁₃

#2150

yes

characteristic

136

C₂×C₁₃

C₂×#364

yes

characteristic

137

D₁₃

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

C₈×D₁₃

yes

characteristic

154

C₂×C₈

C₈×D₁₃

yes

characteristic

155

C₂×C₈

D₄×D₁₃

yes

characteristic

156

C₂×C₈

Q₈×D₁₃

yes

characteristic

157

C₄²

—

158

C₄²

—

159

C₄²

—

160

C₄²

C₂×C₄×D₁₃

yes

characteristic

161

C₁₆

—

162

C₁₆

—

163

C₁₃

#12004

yes

characteristic, complemented, Sylow

164

C₂³

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

C₄⋊C₄×D₁₃

yes

characteristic

174

C₂×C₄

C₂×C₈×D₁₃

yes

characteristic

175

C₂×C₄

M₁₆×D₁₃

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

—

184

C₈

#88038

yes

complemented

185

C₈

D₈×D₁₃

yes

characteristic

186

C₈

Q₁₆×D₁₃

yes

characteristic

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

D₁₃×C₄⋊C₈

yes

characteristic

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

195

C₄

D₁₃×#107

yes

characteristic

196

C₄

D₁₃×#108

yes

characteristic

197

C₄

C₂×#88038

yes

characteristic

198

C₄

D₁₃×M₃₂

yes

characteristic

199

C₂

—

200

C₂

D₁₃×#335

yes

characteristic

201

C₂

#13116590

yes

characteristic

202

C₂

D₁₃×#364

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₁₃
commutator	C₂×C₄×C₁₃	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₁₃×#1370	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₈
prime radical	C₂²×D₁₃	C₄⋊C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	#1370	D₁₃
hypocenter	C₁₃	#12004
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₁₃

commutator

C₂×C₄×C₁₃

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₁₃

Fitting

C₁₃×#1370

C₂

socle

C₂²×C₁₃

C₂×C₄⋊C₈

prime radical

C₂²×D₁₃

C₄⋊C₈

cosocle

C₄×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
3. #13112906	C₂	semidirect
4. #13112905	C₂	semidirect
5. C₁₃×#1370	C₂	semidirect
67. #1370	D₁₃	semidirect
83. C₈×C₁₃	M₃₂	semidirect
90. #1055	M₃₂	semidirect
163. C₁₃	#12004	semidirect
184. C₈	#88038	semidirect

H ≅ G/N

type

3. #13112906

C₂

semidirect

4. #13112905

C₂

semidirect

5. C₁₃×#1370

C₂

semidirect

67. #1370

D₁₃

semidirect

83. C₈×C₁₃

M₃₂

semidirect

90. #1055

M₃₂

semidirect

163. C₁₃

#12004

semidirect

184. C₈

#88038

semidirect

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

subgroup	index
#13116590	2
C₈²×D₁₃	2
#13112906	2
#13112905	2
C₁₃×#1370	2
#12004	13

subgroup

index

C₈²×D₁₃

C₁₃×#1370

Subgroups — #15774488

Conjugacy classes of subgroups

Complements

Maximal subgroups