Group #18080076 — subgroups

Subgroups — #18080076

Order 4864.

534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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	#14574009	C₂	1	1	yes	maximal, characteristic
2	#14562349	C₂	1	1	yes	maximal, characteristic
3	#14562185	C₂	1	2	yes	maximal, complemented
4	#14561499	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2380	C₂	1	1	yes	maximal, characteristic
6	#11927101	C₂²	1	1	yes	characteristic
7	#11926908	—	2	2	no	—
8	#11926890	C₄	1	4	yes	complemented
9	#11926601	C₂²	1	2	yes	—
10	#11926549	—	2	2	no	—
11	C₄×#64520	C₂²	1	1	yes	characteristic
12	#11926288	—	2	2	no	—
13	#11926280	—	2	4	no	—
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₁₉×#386	—	2	4	no	—
16	C₁₉×#386	—	2	2	no	—
17	C₁₉×#383	C₂²	1	2	yes	—
18	C₂²×D₄×C₁₉	—	2	2	no	—
19	C₂²×D₄×C₁₉	D₄	1	2	yes	—
20	C₂³×C₄×C₁₉	—	2	2	no	—
21	C₁₉×#127	—	2	2	no	—
22	C₁₉×#127	C₂×C₄	1	2	yes	—
23	C₁₉×#127	D₄	1	2	yes	—
24	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
27	#10597372	—	2	1	no	—
28	#10597370	—	2	2	no	—
29	C₂×#64520	—	2	1	no	—
30	#10597316	—	2	1	no	—
31	#10597315	C₂×C₄	1	2	yes	complemented
32	C₄×Dic₃₈	—	2	2	no	—
33	C₁₉×#95	—	2	2	no	—
34	C₁₉×#95	—	2	2	no	—
35	C₁₉×#95	D₄	1	4	yes	—
36	#10597289	—	2	8	no	—
37	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
39	#10597260	—	2	1	no	—
40	#10597260	—	2	2	no	—
41	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	complemented
42	C₂⁴×C₁₉	—	2	2	no	—
43	C₂×D₄×C₁₉	—	2	4	no	—
44	C₂×D₄×C₁₉	—	2	4	no	—
45	C₂×D₄×C₁₉	—	2	2	no	—
46	C₂×D₄×C₁₉	—	4	2	no	—
47	C₂×D₄×C₁₉	—	4	2	no	—
48	C₂×D₄×C₁₉	—	8	2	no	—
49	C₂×D₄×C₁₉	—	8	2	no	—
50	C₂×D₄×C₁₉	C₂²⋊C₄	1	4	yes	—
51	C₂²×C₄×C₁₉	—	2	4	no	—
52	C₂²×C₄×C₁₉	—	8	4	no	—
53	C₂²×C₄×C₁₉	—	8	2	no	—
54	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
56	C₂×Dic₃₈	—	2	2	no	—
57	C₂²⋊C₄×C₁₉	—	8	4	no	—
58	C₂²⋊C₄×C₁₉	—	8	2	no	—
59	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
60	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
61	C₄²×C₁₉	#41	1	2	yes	—
62	C₂²⋊Dic₁₉	—	4	1	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	C₄⋊Dic₁₉	—	2	2	no	—
65	Dic₁₉⋊C₄	—	4	2	no	—
66	C₄×Dic₁₉	—	4	1	no	—
67	#64520	—	4	2	no	—
68	C₂×C₁₉⋊C₈	—	2	2	no	—
69	C₂×C₁₉⋊C₈	—	4	2	no	—
70	#9425	—	19	1	no	maximal, Sylow
71	C₂³×C₁₉	—	2	4	no	—
72	C₂³×C₁₉	—	4	4	no	—
73	C₂³×C₁₉	—	4	4	no	—
74	C₂³×C₁₉	—	4	2	no	—
75	C₂³×C₁₉	—	4	2	no	—
76	C₂³×C₁₉	#120	1	1	yes	characteristic
77	D₄×C₁₉	—	4	4	no	—
78	D₄×C₁₉	—	8	2	no	—
79	D₄×C₁₉	—	8	4	no	—
80	D₄×C₁₉	—	8	4	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	8	no	—
84	C₂×C₄×C₁₉	—	4	4	no	—
85	C₂×C₄×C₁₉	—	8	8	no	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₁₉	#121	1	2	yes	—
89	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
90	C₂×Dic₁₉	—	4	2	no	—
91	Dic₃₈	—	8	2	no	—
92	C₁₉⋊C₈	—	4	2	no	—
93	C₁₉⋊C₈	—	8	2	no	—
94	#3138	—	19	1	no	—
95	#2380	D₁₉	1	1	yes	characteristic
96	#1555	—	19	1	no	—
97	#1515	—	19	2	no	—
98	#1288	—	19	2	no	—
99	C₂²×C₁₉	—	2	2	no	—
100	C₂²×C₁₉	—	4	4	no	—
101	C₂²×C₁₉	—	4	8	no	—
102	C₂²×C₁₉	—	8	2	no	—
103	C₂²×C₁₉	—	8	2	no	—
104	C₂²×C₁₉	—	8	4	no	—
105	C₂²×C₁₉	#386	1	1	yes	characteristic
106	C₂²×C₁₉	#455	1	2	yes	—
107	C₄×C₁₉	—	2	1	no	—
108	C₄×C₁₉	—	2	1	no	—
109	C₄×C₁₉	—	2	2	no	—
110	C₄×C₁₉	—	2	2	no	—
111	C₄×C₁₉	—	8	4	no	—
112	Dic₁₉	—	8	2	no	—
113	#533	—	19	1	no	—
114	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
115	#490	—	38	2	no	—
116	#486	—	19	4	no	—
117	#432	—	19	2	no	—
118	#418	—	38	2	no	—
119	C₄×M₁₆	—	19	1	no	—
120	#386	—	2	2	no	—
121	#386	—	2	4	no	—
122	#383	C₂×D₁₉	1	2	yes	—
123	#331	—	38	2	no	—
124	#328	—	38	4	no	—
125	C₂×C₁₉	—	2	2	no	—
126	C₂×C₁₉	—	8	4	no	—
127	C₂×C₁₉	#1885	1	1	yes	characteristic
128	C₂×C₁₉	#1904	1	2	yes	—
129	C₂²×D₄	—	2	2	no	—
130	C₂²×D₄	C₂²⋊D₁₉	1	2	yes	—
131	C₂³×C₄	—	2	2	no	—
132	C₂×M₁₆	—	38	1	no	—
133	C₄⋊Q₈	—	19	2	no	—
134	#127	—	2	2	no	—
135	#127	C₄×D₁₉	1	2	yes	—
136	#127	D₇₆	1	2	yes	—
137	#125	—	38	1	no	—
138	C₂²⋊Q₈	—	38	2	no	—
139	C₄×Q₈	—	38	2	no	—
140	#117	—	38	1	no	—
141	C₂×C₂²⋊C₄	—	2	4	no	—
142	C₂×C₂²⋊C₄	—	2	2	no	—
143	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
144	C₄⋊C₈	—	38	2	no	—
145	#102	—	38	8	no	—
146	C₂²⋊C₈	—	38	2	no	—
147	#97	—	38	1	no	—
148	#97	—	38	2	no	—
149	C₄×C₈	—	19	2	no	—
150	#95	—	2	2	no	—
151	#95	—	2	2	no	—
152	#95	C₂²⋊D₁₉	1	4	yes	—
153	C₁₉	#9425	1	1	yes	characteristic, complemented, Sylow
154	C₂⁴	—	2	2	no	—
155	C₂×Q₈	—	38	2	no	—
156	C₂×D₄	—	2	4	no	—
157	C₂×D₄	—	2	4	no	—
158	C₂×D₄	—	2	2	no	—
159	C₂×D₄	—	4	2	no	—
160	C₂×D₄	—	4	2	no	—
161	C₂×D₄	—	8	2	no	—
162	C₂×D₄	—	8	2	no	—
163	C₂×D₄	(C₂×D₁₉)⋊C₄	1	4	yes	—
164	C₂²×C₄	—	2	4	no	—
165	C₂²×C₄	—	8	4	no	—
166	C₂²×C₄	—	8	2	no	—
167	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
168	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
169	M₁₆	—	76	2	no	—
170	C₂×C₈	—	38	2	no	—
171	C₂×C₈	—	76	2	no	—
172	C₄⋊C₄	—	38	2	no	—
173	C₄⋊C₄	—	38	2	no	—
174	C₄⋊C₄	—	76	2	no	—
175	C₂²⋊C₄	—	8	4	no	—
176	C₂²⋊C₄	—	8	2	no	—
177	C₂²⋊C₄	—	76	1	no	—
178	C₄²	—	76	1	no	—
179	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
180	C₄²	C₂×D₇₆	1	1	yes	characteristic
181	C₄²	#64541	1	2	yes	—
182	C₂³	—	2	4	no	—
183	C₂³	—	4	4	no	—
184	C₂³	—	4	4	no	—
185	C₂³	—	4	2	no	—
186	C₂³	—	4	2	no	—
187	C₂³	#10597399	1	1	yes	characteristic
188	Q₈	—	152	2	no	—
189	D₄	—	4	4	no	—
190	D₄	—	8	2	no	—
191	D₄	—	8	4	no	—
192	D₄	—	8	4	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	8	no	—
196	C₂×C₄	—	4	4	no	—
197	C₂×C₄	—	8	8	no	—
198	C₂×C₄	—	76	2	no	—
199	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
200	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
201	C₂×C₄	#10597375	1	1	yes	characteristic
202	C₂×C₄	#10597376	1	2	yes	—
203	C₈	—	76	2	no	—
204	C₈	—	152	2	no	—
205	C₂²	—	2	2	no	—
206	C₂²	—	4	8	no	—
207	C₂²	—	4	4	no	—
208	C₂²	—	8	2	no	—
209	C₂²	—	8	2	no	—
210	C₂²	—	8	4	no	—
211	C₂²	#11926423	1	1	yes	characteristic
212	C₂²	#11926722	1	2	yes	—
213	C₄	—	2	2	no	—
214	C₄	—	2	2	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	8	4	no	—
218	C₄	—	152	2	no	—
219	C₂	—	2	2	no	—
220	C₂	—	8	4	no	—
221	C₂	#14564023	1	1	yes	characteristic
222	C₂	#14564122	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14574009

C₂

yes

maximal, characteristic

#14562349

C₂

yes

maximal, characteristic

#14562185

C₂

yes

maximal, complemented

#14561499

C₂

yes

maximal, complemented

C₁₉×#2380

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

#11926908

—

#11926890

C₄

yes

complemented

#11926601

C₂²

yes

—

#11926549

—

C₄×#64520

C₂²

yes

characteristic

#11926288

—

#11926280

—

C₂×C₁₉×#127

C₂²

yes

characteristic

C₁₉×#386

—

C₁₉×#386

—

C₁₉×#383

C₂²

yes

—

C₂²×D₄×C₁₉

—

C₂²×D₄×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

—

C₁₉×#127

—

C₁₉×#127

C₂×C₄

yes

—

C₁₉×#127

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

—

C₂×C₄

yes

complemented

C₄×Dic₃₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

D₄

yes

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

—

C₄×C₁₉⋊C₈

C₂×C₄

yes

complemented

C₂⁴×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×Dic₃₈

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

#64520

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#9425

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#120

yes

characteristic

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

characteristic

C₂×Dic₁₉

—

Dic₃₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

#3138

—

#2380

D₁₉

yes

—

—

—

C₂²×C₁₉

—

100

C₂²×C₁₉

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#386

yes

characteristic

106

C₂²×C₁₉

#455

yes

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

Dic₁₉

—

113

#533

—

114

C₂×#127

C₂×D₁₉

yes

characteristic

115

#490

—

116

#486

—

117

#432

—

118

#418

—

119

C₄×M₁₆

—

120

#386

—

121

#386

—

122

#383

C₂×D₁₉

yes

—

123

#331

—

124

#328

—

125

C₂×C₁₉

—

126

C₂×C₁₉

—

127

C₂×C₁₉

#1885

yes

characteristic

128

C₂×C₁₉

#1904

yes

—

129

C₂²×D₄

—

130

C₂²×D₄

C₂²⋊D₁₉

yes

—

131

C₂³×C₄

—

132

C₂×M₁₆

—

133

C₄⋊Q₈

—

134

#127

—

135

#127

C₄×D₁₉

yes

—

136

#127

D₇₆

yes

—

137

#125

—

138

C₂²⋊Q₈

—

139

C₄×Q₈

—

140

#117

—

141

C₂×C₂²⋊C₄

—

142

C₂×C₂²⋊C₄

—

143

C₂×C₄²

C₂²×D₁₉

yes

characteristic

144

C₄⋊C₈

—

145

#102

—

146

C₂²⋊C₈

—

147

#97

—

148

#97

—

149

C₄×C₈

—

150

#95

—

151

#95

—

152

#95

C₂²⋊D₁₉

yes

—

153

C₁₉

#9425

yes

characteristic, complemented, Sylow

154

C₂⁴

—

155

C₂×Q₈

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

—

162

C₂×D₄

—

163

C₂×D₄

(C₂×D₁₉)⋊C₄

yes

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

—

167

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

168

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

169

M₁₆

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₂²⋊C₄

—

176

C₂²⋊C₄

—

177

C₂²⋊C₄

—

178

C₄²

—

179

C₄²

C₂×C₄×D₁₉

yes

characteristic

180

C₄²

C₂×D₇₆

yes

characteristic

181

C₄²

#64541

yes

—

182

C₂³

—

183

C₂³

—

184

C₂³

—

185

C₂³

—

186

C₂³

—

187

C₂³

#10597399

yes

characteristic

188

Q₈

—

152

—

189

D₄

—

190

D₄

—

191

D₄

—

192

D₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

200

C₂×C₄

C₄×C₂²⋊D₁₉

yes

—

201

C₂×C₄

#10597375

yes

characteristic

202

C₂×C₄

#10597376

yes

—

203

C₈

—

204

C₈

—

152

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

#11926423

yes

characteristic

212

C₂²

#11926722

yes

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

152

—

219

C₂

—

220

C₂

—

221

C₂

#14564023

yes

characteristic

222

C₂

#14564122

yes

—

	subgroup	G/H
center	C₂²	#11926423
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2380	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂×C₁₉×#127	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#2380	D₁₉
hypocenter	C₁₉	#9425
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2380

subgroup

G/H

center

C₂²

#11926423

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#2380

C₂

socle

C₂²×C₁₉

#386

prime radical

C₂×C₁₉×#127

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2380

N	H ≅ G/N	type
3. #14562185	C₂	semidirect
4. #14561499	C₂	semidirect
8. #11926890	C₄	semidirect
31. #10597315	C₂×C₄	semidirect
41. C₄×C₁₉⋊C₈	C₂×C₄	semidirect
153. C₁₉	#9425	semidirect

H ≅ G/N

type

3. #14562185

C₂

semidirect

4. #14561499

C₂

semidirect

8. #11926890

C₄

semidirect

31. #10597315

C₂×C₄

semidirect

41. C₄×C₁₉⋊C₈

C₂×C₄

semidirect

153. C₁₉

#9425

semidirect

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

subgroup	index
#14574009	2
#14562349	2
#14562185	2
#14561499	2
C₁₉×#2380	2
#9425	19

subgroup

index

C₁₉×#2380

Subgroups — #18080076

Conjugacy classes of subgroups

Complements

Maximal subgroups