Group #15767967 — subgroups

Subgroups — #15767967

Order 3328.

526 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 153 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	#13115642	C₂	1	1	yes	maximal, characteristic
2	#13115641	C₂	1	2	yes	maximal
3	#13114995	C₂	1	2	yes	maximal, complemented
4	#13112663	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88128	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#107	—	2	2	no	—
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#384	C₂²	1	2	yes	—
10	C₂×#88061	—	2	2	no	—
11	C₂×#88049	—	2	4	no	—
12	C₂×#88047	—	2	4	no	—
13	#11718596	C₂²	1	1	yes	characteristic
14	C₂×C₄×#1055	C₂²	1	2	yes	—
15	C₂²×D₅₂	—	2	1	no	—
16	C₂²×D₅₂	—	2	2	no	—
17	C₂²×C₈×C₁₃	D₄	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
21	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₃	—	2	1	no	—
23	C₂×C₄⋊Dic₁₃	—	2	2	no	—
24	C₂²×#1055	D₄	1	4	yes	—
25	#88128	—	2	2	no	—
26	#88128	—	2	1	no	—
27	#88128	Q₈	1	2	yes	—
28	C₁₃×#107	—	4	4	no	—
29	C₄×C₈×C₁₃	—	2	2	no	—
30	#88061	—	4	4	no	—
31	#88049	—	4	8	no	—
32	#88047	—	4	8	no	—
33	C₄×#1055	—	2	2	no	—
34	C₄×#1055	—	2	2	no	—
35	#10673	—	13	1	no	maximal, Sylow
36	C₂³×D₁₃	—	4	1	no	—
37	C₂²×C₄×C₁₃	—	4	2	no	—
38	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
40	C₂²×Dic₁₃	—	4	1	no	—
41	C₂×D₅₂	—	2	4	no	—
42	C₂×D₅₂	—	2	2	no	—
43	C₂×D₅₂	—	4	4	no	—
44	C₂×D₅₂	—	4	2	no	—
45	C₂×D₅₂	—	4	4	no	—
46	C₂×D₅₂	—	4	2	no	—
47	C₂×D₅₂	—	4	2	no	—
48	C₂×D₅₂	—	4	1	no	—
49	C₂×C₈×C₁₃	—	2	2	no	—
50	C₂×C₈×C₁₃	—	2	2	no	—
51	C₂×C₈×C₁₃	D₈	1	4	yes	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₄⋊C₄	—	4	4	no	—
54	C₁₃×C₄⋊C₄	—	4	4	no	—
55	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₄²×C₁₃	#41	1	2	yes	—
57	C₄²×C₁₃	#41	1	1	yes	characteristic
58	C₄⋊Dic₁₃	—	4	4	no	—
59	C₄⋊Dic₁₃	—	4	2	no	—
60	C₂×#1055	—	2	4	no	—
61	C₂×#1055	—	2	4	no	—
62	C₂×#1055	D₈	1	8	yes	—
63	#1957	—	13	1	no	—
64	#1957	—	13	2	no	—
65	#1845	—	13	2	no	—
66	#1845	D₁₃	1	1	yes	characteristic, complemented
67	#1273	—	13	1	no	—
68	C₂³×C₁₃	#127	1	1	yes	characteristic
69	C₂²×D₁₃	—	4	2	no	—
70	C₂²×D₁₃	—	8	1	no	—
71	C₂²×D₁₃	—	8	2	no	—
72	C₂²×D₁₃	—	8	1	no	—
73	C₂²×D₁₃	—	8	2	no	—
74	C₂×C₄×C₁₃	—	8	2	no	—
75	C₂×C₄×C₁₃	—	8	2	no	—
76	C₂×C₄×C₁₃	—	8	2	no	—
77	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#123	1	2	yes	—
80	C₂×C₄×C₁₃	#123	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×D₈	1	4	yes	—
82	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
83	C₂×C₄×C₁₃	#137	1	4	yes	—
84	C₂×C₄×C₁₃	#137	1	2	yes	—
85	C₂×Dic₁₃	—	8	1	no	—
86	C₂×Dic₁₃	—	8	2	no	—
87	D₅₂	—	4	4	no	—
88	D₅₂	—	4	8	no	—
89	D₅₂	—	8	4	no	—
90	D₅₂	—	8	2	no	—
91	C₈×C₁₃	—	2	4	no	—
92	#1055	—	2	8	no	—
93	C₂×#127	—	13	1	no	—
94	C₂×#107	—	2	2	no	—
95	C₂×#107	—	26	4	no	—
96	C₂×#102	—	26	4	no	—
97	C₂×#102	—	26	2	no	—
98	C₂×C₄×C₈	—	13	2	no	—
99	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
100	#384	—	13	1	no	—
101	#384	C₂×D₁₃	1	2	yes	—
102	C₂²×C₁₃	#399	1	1	yes	characteristic
103	C₂²×C₁₃	#493	1	1	yes	characteristic
104	C₂²×C₁₃	#493	1	2	yes	—
105	C₂²×C₁₃	#497	1	1	yes	characteristic
106	C₂²×C₁₃	#497	1	2	yes	—
107	C₂×D₁₃	—	8	4	no	—
108	C₂×D₁₃	—	8	2	no	—
109	C₂×D₁₃	—	16	1	no	—
110	C₂×D₁₃	—	16	2	no	—
111	C₂×D₁₃	—	16	1	no	—
112	C₄×C₁₃	—	16	2	no	—
113	C₄×C₁₃	#474	1	2	yes	—
114	C₄×C₁₃	#474	1	4	yes	—
115	C₄×C₁₃	#480	1	4	yes	—
116	C₄×C₁₃	#480	1	2	yes	—
117	Dic₁₃	—	16	1	no	—
118	C₂²×D₄	—	26	2	no	—
119	C₂²×D₄	—	26	1	no	—
120	C₂²×C₈	—	13	4	no	—
121	C₂²×C₈	C₂²⋊D₁₃	1	2	yes	—
122	#127	—	13	2	no	—
123	#127	—	26	2	no	—
124	#127	—	26	1	no	—
125	C₂×C₄⋊C₄	—	2	2	no	—
126	C₂×C₄⋊C₄	—	2	2	no	—
127	C₂×C₄⋊C₄	—	2	2	no	—
128	C₂×C₄⋊C₄	—	26	2	no	—
129	C₂×C₄⋊C₄	—	26	1	no	—
130	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
131	#107	—	4	4	no	—
132	#107	—	52	8	no	—
133	#102	—	52	8	no	—
134	#102	—	52	4	no	—
135	C₄×C₈	—	2	2	no	—
136	C₄×C₈	—	26	2	no	—
137	C₄×C₈	—	26	2	no	—
138	C₂×C₁₃	#1712	1	1	yes	characteristic
139	C₂×C₁₃	#1722	1	2	yes	—
140	C₂×C₁₃	#1722	1	1	yes	characteristic
141	C₂×C₁₃	#2093	1	2	yes	—
142	C₂×C₁₃	#2093	1	1	yes	characteristic
143	D₁₃	—	16	2	no	—
144	C₂⁴	—	52	1	no	—
145	C₂×D₄	—	26	4	no	—
146	C₂×D₄	—	26	2	no	—
147	C₂×D₄	—	52	2	no	—
148	C₂×D₄	—	52	4	no	—
149	C₂×D₄	—	52	4	no	—
150	C₂×D₄	—	52	1	no	—
151	C₂×D₄	—	52	2	no	—
152	C₂×D₄	—	52	2	no	—
153	C₂²×C₄	—	4	2	no	—
154	C₂²×C₄	—	52	1	no	—
155	C₂²×C₄	D₄×D₁₃	1	2	yes	—
156	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
157	C₂×C₈	—	2	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	13	8	no	—
160	C₂×C₈	—	26	4	no	—
161	C₂×C₈	—	26	4	no	—
162	C₂×C₈	#6104	1	4	yes	—
163	C₄⋊C₄	—	4	4	no	—
164	C₄⋊C₄	—	4	4	no	—
165	C₄⋊C₄	—	4	4	no	—
166	C₄⋊C₄	—	52	4	no	—
167	C₄⋊C₄	—	52	2	no	—
168	C₄²	#6127	1	2	yes	—
169	C₄²	Q₈×D₁₃	1	1	yes	characteristic
170	C₄²	#6131	1	1	yes	characteristic
171	C₁₃	#10673	1	1	yes	characteristic, complemented, Sylow
172	C₂³	—	52	2	no	—
173	C₂³	—	104	1	no	—
174	C₂³	—	104	1	no	—
175	C₂³	—	104	2	no	—
176	C₂³	—	104	2	no	—
177	C₂³	#88194	1	1	yes	characteristic
178	D₄	—	52	4	no	—
179	D₄	—	52	8	no	—
180	D₄	—	104	4	no	—
181	D₄	—	104	2	no	—
182	C₂×C₄	—	8	2	no	—
183	C₂×C₄	—	8	2	no	—
184	C₂×C₄	—	8	2	no	—
185	C₂×C₄	—	104	1	no	—
186	C₂×C₄	—	104	2	no	—
187	C₂×C₄	#88148	1	2	yes	—
188	C₂×C₄	#88150	1	2	yes	—
189	C₂×C₄	D₈×D₁₃	1	4	yes	—
190	C₂×C₄	#88172	1	4	yes	—
191	C₂×C₄	#88183	1	1	yes	characteristic
192	C₂×C₄	C₂×#6104	1	2	yes	—
193	C₂×C₄	#88196	1	2	yes	—
194	C₂×C₄	#88200	1	1	yes	characteristic
195	C₈	—	2	4	no	—
196	C₈	—	26	8	no	—
197	C₂²	—	104	4	no	—
198	C₂²	—	104	2	no	—
199	C₂²	—	208	1	no	—
200	C₂²	—	208	2	no	—
201	C₂²	—	208	1	no	—
202	C₂²	#11718653	1	1	yes	characteristic
203	C₂²	#11718734	1	1	yes	characteristic
204	C₂²	#11718747	1	1	yes	characteristic
205	C₂²	#11718812	1	2	yes	—
206	C₂²	#11718851	1	2	yes	—
207	C₄	—	16	2	no	—
208	C₄	—	208	1	no	—
209	C₄	#11718543	1	4	yes	—
210	C₄	#11718551	1	4	yes	—
211	C₄	#11718628	1	2	yes	—
212	C₄	#11718748	1	2	yes	—
213	C₂	—	208	2	no	—
214	C₂	#13114450	1	1	yes	characteristic
215	C₂	#13114506	1	2	yes	—
216	C₂	#13114508	1	1	yes	characteristic
217	C₂	#13116361	1	2	yes	—
218	C₂	#13116365	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13115642

C₂

yes

maximal, characteristic

#13115641

C₂

yes

maximal

#13114995

C₂

yes

maximal, complemented

#13112663

C₂

yes

maximal, characteristic, complemented

C₁₃×#1845

C₂

yes

maximal, characteristic, complemented

C₂×#88128

C₂²

yes

characteristic

C₂×C₁₃×#107

—

C₂×C₄×C₈×C₁₃

C₂²

yes

characteristic

C₁₃×#384

C₂²

yes

—

—

—

—

C₂²

yes

characteristic

C₂×C₄×#1055

C₂²

yes

—

C₂²×D₅₂

—

C₂²×D₅₂

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

C₂²×#1055

D₄

yes

—

#88128

—

#88128

—

#88128

Q₈

yes

—

C₁₃×#107

—

C₄×C₈×C₁₃

—

—

—

—

—

—

—

C₂³×D₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂×D₄

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×D₅₂

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

D₈

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₄²×C₁₃

C₂×Q₈

yes

characteristic

C₄²×C₁₃

#41

yes

—

C₄²×C₁₃

#41

yes

characteristic

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₂×#1055

—

C₂×#1055

—

C₂×#1055

D₈

yes

—

—

—

—

D₁₃

yes

characteristic, complemented

#1273

—

C₂³×C₁₃

#127

yes

characteristic

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂²×D₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₃

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₁₃

#123

yes

—

C₂×C₄×C₁₃

#123

yes

characteristic

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

C₂×D₈

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×C₄×C₁₃

#137

yes

—

C₂×Dic₁₃

—

C₂×Dic₁₃

—

D₅₂

—

D₅₂

—

D₅₂

—

D₅₂

—

C₈×C₁₃

—

—

—

—

—

—

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₁₃

yes

characteristic

100

#384

—

101

#384

C₂×D₁₃

yes

—

102

C₂²×C₁₃

#399

yes

characteristic

103

C₂²×C₁₃

#493

yes

characteristic

104

C₂²×C₁₃

#493

yes

—

105

C₂²×C₁₃

#497

yes

characteristic

106

C₂²×C₁₃

#497

yes

—

107

C₂×D₁₃

—

108

C₂×D₁₃

—

109

C₂×D₁₃

—

110

C₂×D₁₃

—

111

C₂×D₁₃

—

112

C₄×C₁₃

—

113

C₄×C₁₃

#474

yes

—

114

C₄×C₁₃

#474

yes

—

115

C₄×C₁₃

#480

yes

—

116

C₄×C₁₃

#480

yes

—

117

Dic₁₃

—

118

C₂²×D₄

—

119

C₂²×D₄

—

120

C₂²×C₈

—

121

C₂²×C₈

C₂²⋊D₁₃

yes

—

122

#127

—

123

#127

—

124

#127

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

—

127

C₂×C₄⋊C₄

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄²

C₂²×D₁₃

yes

characteristic

131

#107

—

132

#107

—

133

#102

—

134

#102

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₂×C₁₃

#1712

yes

characteristic

139

C₂×C₁₃

#1722

yes

—

140

C₂×C₁₃

#1722

yes

characteristic

141

C₂×C₁₃

#2093

yes

—

142

C₂×C₁₃

#2093

yes

characteristic

143

D₁₃

—

144

C₂⁴

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

D₄×D₁₃

yes

—

156

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

#6104

yes

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

168

C₄²

#6127

yes

—

169

C₄²

Q₈×D₁₃

yes

characteristic

170

C₄²

#6131

yes

characteristic

171

C₁₃

#10673

yes

characteristic, complemented, Sylow

172

C₂³

—

173

C₂³

—

104

—

174

C₂³

—

104

—

175

C₂³

—

104

—

176

C₂³

—

104

—

177

C₂³

#88194

yes

characteristic

178

D₄

—

179

D₄

—

180

D₄

—

104

—

181

D₄

—

104

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

104

—

186

C₂×C₄

—

104

—

187

C₂×C₄

#88148

yes

—

188

C₂×C₄

#88150

yes

—

189

C₂×C₄

D₈×D₁₃

yes

—

190

C₂×C₄

#88172

yes

—

191

C₂×C₄

#88183

yes

characteristic

192

C₂×C₄

C₂×#6104

yes

—

193

C₂×C₄

#88196

yes

—

194

C₂×C₄

#88200

yes

characteristic

195

C₈

—

196

C₈

—

197

C₂²

—

104

—

198

C₂²

—

104

—

199

C₂²

—

208

—

200

C₂²

—

208

—

201

C₂²

—

208

—

202

C₂²

#11718653

yes

characteristic

203

C₂²

#11718734

yes

characteristic

204

C₂²

#11718747

yes

characteristic

205

C₂²

#11718812

yes

—

206

C₂²

#11718851

yes

—

207

C₄

—

208

C₄

—

208

—

209

C₄

#11718543

yes

—

210

C₄

#11718551

yes

—

211

C₄

#11718628

yes

—

212

C₄

#11718748

yes

—

213

C₂

—

208

—

214

C₂

#13114450

yes

characteristic

215

C₂

#13114506

yes

—

216

C₂

#13114508

yes

characteristic

217

C₂

#13116361

yes

—

218

C₂

#13116365

yes

characteristic

	subgroup	G/H
center	C₂³	#88194
commutator, cosocle	C₂×C₄²×C₁₃	C₂³
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#1845	C₂
socle	C₂³×C₁₃	#127
prime radical	C₂×#88128	C₂²
hypercenter	#1845	D₁₃
hypocenter	C₁₃	#10673
LCS	G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

subgroup

G/H

center

C₂³

#88194

commutator, cosocle

C₂×C₄²×C₁₃

C₂³

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#1845

C₂

C₂³×C₁₃

C₂²

D₁₃

C₁₃

G ▷ C₂×C₄²×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1845

N	H ≅ G/N	type
3. #13114995	C₂	semidirect
4. #13112663	C₂	semidirect
5. C₁₃×#1845	C₂	semidirect
66. #1845	D₁₃	semidirect
171. C₁₃	#10673	semidirect

H ≅ G/N

type

3. #13114995

C₂

semidirect

4. #13112663

C₂

semidirect

5. C₁₃×#1845

C₂

semidirect

66. #1845

D₁₃

semidirect

171. C₁₃

#10673

semidirect

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

subgroup	index
#13115642	2
#13115641	2
#13114995	2
#13112663	2
C₁₃×#1845	2
#10673	13

subgroup

index

C₁₃×#1845

Subgroups — #15767967

Conjugacy classes of subgroups

Complements

Maximal subgroups