Group #18016176 — subgroups

Subgroups — C₁₉×#10217 #18016176

Order 4864.

430 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₁₉×#3255	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3237	C₂	1	2	yes	maximal
3	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1506	C₂	1	2	yes	maximal
5	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#533	C₂²	1	1	yes	characteristic
7	C₁₉×#533	C₂²	1	2	yes	—
8	C₁₉×#501	—	2	2	no	—
9	C₁₉×#491	—	2	2	no	—
10	C₁₉×#485	—	2	4	no	—
11	C₁₉×#477	—	2	2	no	—
12	C₁₉×#475	—	2	2	no	—
13	C₁₉×#475	—	2	2	no	—
14	C₁₉×#470	—	2	2	no	—
15	C₁₉×#462	—	2	2	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₁₉×#376	C₂²	1	1	yes	characteristic
19	C₁₉×#339	—	2	2	no	—
20	C₁₉×#328	—	2	4	no	—
21	C₂×Q₁₆×C₁₉	—	2	2	no	—
22	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
23	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
24	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₁₉×#125	—	2	2	no	—
27	C₁₉×#125	—	2	1	no	—
28	C₁₉×C₂²⋊Q₈	—	2	2	no	—
29	C₁₉×C₂²⋊Q₈	—	2	2	no	—
30	C₁₉×C₂²⋊Q₈	—	2	2	no	—
31	C₄×Q₈×C₁₉	—	2	2	no	—
32	C₄×Q₈×C₁₉	—	2	2	no	—
33	C₄×Q₈×C₁₉	—	2	2	no	—
34	C₁₉×#117	—	2	2	no	—
35	C₁₉×#117	—	2	1	no	—
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₁₉×#107	—	2	4	no	—
39	C₁₉×#106	—	2	2	no	—
40	C₁₉×#106	—	2	4	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×#103	—	2	4	no	—
44	C₁₉×#103	—	2	4	no	—
45	C₁₉×#103	—	2	4	no	—
46	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
47	C₁₉×#97	—	2	2	no	—
48	C₁₉×#95	—	2	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	2	2	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂²×C₄×C₁₉	—	4	1	no	—
53	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
55	Q₁₆×C₁₉	—	8	2	no	—
56	M₁₆×C₁₉	—	4	2	no	—
57	C₂×C₈×C₁₉	—	2	2	no	—
58	C₂×C₈×C₁₉	—	2	4	no	—
59	C₄⋊C₄×C₁₉	—	2	2	no	—
60	C₄⋊C₄×C₁₉	—	2	2	no	—
61	C₄⋊C₄×C₁₉	—	2	2	no	—
62	C₄⋊C₄×C₁₉	—	2	2	no	—
63	C₄⋊C₄×C₁₉	—	2	2	no	—
64	C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₄⋊C₄×C₁₉	—	4	2	no	—
66	C₄⋊C₄×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	4	2	no	—
68	C₂²⋊C₄×C₁₉	—	4	2	no	—
69	C₂²⋊C₄×C₁₉	—	4	1	no	—
70	C₄²×C₁₉	—	2	2	no	—
71	C₄²×C₁₉	—	4	1	no	—
72	C₄²×C₁₉	—	4	1	no	—
73	C₄²×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	C₂×D₄	1	2	yes	—
75	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₉	#41	1	1	yes	characteristic
77	#10217	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
78	C₂³×C₁₉	#127	1	1	yes	characteristic
79	Q₈×C₁₉	—	4	4	no	—
80	Q₈×C₁₉	—	4	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	Q₈×C₁₉	—	8	2	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	1	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	—	4	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	8	2	no	—
91	C₂×C₄×C₁₉	#120	1	2	yes	—
92	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
93	C₂×C₄×C₁₉	#121	1	2	yes	—
94	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
95	C₈×C₁₉	—	4	4	no	—
96	C₈×C₁₉	—	4	2	no	—
97	#3255	C₂×C₁₉	1	1	yes	characteristic
98	#3237	C₂×C₁₉	1	2	yes	—
99	#1995	C₂×C₁₉	1	1	yes	characteristic
100	#1506	C₂×C₁₉	1	2	yes	—
101	#1307	C₂×C₁₉	1	1	yes	characteristic
102	C₂²×C₁₉	—	2	1	no	—
103	C₂²×C₁₉	—	2	2	no	—
104	C₂²×C₁₉	#392	1	1	yes	characteristic
105	C₄×C₁₉	—	2	1	no	—
106	C₄×C₁₉	—	2	2	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	8	2	no	—
109	C₄×C₁₉	—	8	2	no	—
110	C₄×C₁₉	—	8	2	no	—
111	C₄×C₁₉	—	8	2	no	—
112	C₄×C₁₉	#455	1	1	yes	characteristic
113	C₄×C₁₉	#456	1	1	yes	characteristic
114	#533	C₂²×C₁₉	1	1	yes	characteristic
115	#533	C₂²×C₁₉	1	2	yes	—
116	#501	—	2	2	no	—
117	#491	—	2	2	no	—
118	#485	—	2	4	no	—
119	#477	—	2	2	no	—
120	#475	—	2	2	no	—
121	#475	—	2	2	no	—
122	#470	—	2	2	no	—
123	#462	—	2	2	no	—
124	#432	C₂²×C₁₉	1	2	yes	—
125	#423	C₂²×C₁₉	1	1	yes	characteristic
126	#376	C₂²×C₁₉	1	1	yes	characteristic
127	#339	—	2	2	no	—
128	#328	—	2	4	no	—
129	C₂×C₁₉	—	4	1	no	—
130	C₂×C₁₉	#2007	1	1	yes	characteristic
131	C₂×C₁₉	#2009	1	2	yes	—
132	C₂×Q₁₆	—	2	2	no	—
133	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
134	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
135	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
136	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
137	#125	—	2	2	no	—
138	#125	—	2	1	no	—
139	C₂²⋊Q₈	—	2	2	no	—
140	C₂²⋊Q₈	—	2	2	no	—
141	C₂²⋊Q₈	—	2	2	no	—
142	C₄×Q₈	—	2	2	no	—
143	C₄×Q₈	—	2	2	no	—
144	C₄×Q₈	—	2	2	no	—
145	#117	—	2	1	no	—
146	#117	—	2	2	no	—
147	C₂×C₄²	—	2	1	no	—
148	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
149	#107	—	2	4	no	—
150	#106	—	2	2	no	—
151	#106	—	2	4	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	#103	—	2	4	no	—
155	#103	—	2	4	no	—
156	#103	—	2	4	no	—
157	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
158	#97	—	2	2	no	—
159	#95	—	2	2	no	—
160	C₁₉	#10217	1	1	yes	characteristic, direct product factor, Sylow
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂²×C₄	—	4	1	no	—
165	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
166	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
167	Q₁₆	—	8	2	no	—
168	M₁₆	—	4	2	no	—
169	C₂×C₈	—	2	4	no	—
170	C₂×C₈	—	2	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	2	2	no	—
173	C₄⋊C₄	—	2	2	no	—
174	C₄⋊C₄	—	2	2	no	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	4	2	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₂²⋊C₄	—	4	1	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	—	4	1	no	—
184	C₄²	—	4	1	no	—
185	C₄²	—	4	2	no	—
186	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
187	C₄²	C₂×D₄×C₁₉	1	2	yes	—
188	C₄²	#41×C₁₉	1	1	yes	characteristic
189	C₂³	C₁₉×#127	1	1	yes	characteristic
190	Q₈	—	4	4	no	—
191	Q₈	—	4	2	no	—
192	Q₈	—	4	2	no	—
193	Q₈	—	8	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	8	2	no	—
202	C₂×C₄	C₁₉×#120	1	2	yes	—
203	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
204	C₂×C₄	C₁₉×#121	1	2	yes	—
205	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
206	C₈	—	4	4	no	—
207	C₈	—	4	2	no	—
208	C₂²	—	2	1	no	—
209	C₂²	—	2	2	no	—
210	C₂²	C₁₉×#392	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	2	2	no	—
213	C₄	—	2	2	no	—
214	C₄	—	8	2	no	—
215	C₄	—	8	2	no	—
216	C₄	—	8	2	no	—
217	C₄	—	8	2	no	—
218	C₄	C₁₉×#455	1	1	yes	characteristic
219	C₄	C₁₉×#456	1	1	yes	characteristic
220	C₂	—	4	1	no	—
221	C₂	C₁₉×#2007	1	1	yes	characteristic
222	C₂	C₁₉×#2009	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3255

C₂

yes

maximal, characteristic

C₁₉×#3237

C₂

yes

maximal

C₁₉×#1995

C₂

yes

maximal, characteristic

C₁₉×#1506

C₂

yes

maximal

C₁₉×#1307

C₂

yes

maximal, characteristic

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#533

C₂²

yes

—

C₁₉×#501

—

C₁₉×#491

—

C₁₉×#485

—

C₁₉×#477

—

C₁₉×#475

—

C₁₉×#475

—

C₁₉×#470

—

C₁₉×#462

—

C₁₉×#432

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#339

—

C₁₉×#328

—

C₂×Q₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×#106

—

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×#103

—

C₁₉×C₂²⋊C₈

D₄

yes

—

C₁₉×#97

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

Q₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#121

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

#3255

C₂×C₁₉

yes

characteristic

#3237

C₂×C₁₉

yes

—

#1995

C₂×C₁₉

yes

characteristic

100

#1506

C₂×C₁₉

yes

—

101

#1307

C₂×C₁₉

yes

characteristic

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

#392

yes

characteristic

105

C₄×C₁₉

—

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

#455

yes

characteristic

113

C₄×C₁₉

#456

yes

characteristic

114

#533

C₂²×C₁₉

yes

characteristic

115

#533

C₂²×C₁₉

yes

—

116

#501

—

117

#491

—

118

#485

—

119

#477

—

120

#475

—

121

#475

—

122

#470

—

123

#462

—

124

#432

C₂²×C₁₉

yes

—

125

#423

C₂²×C₁₉

yes

characteristic

126

#376

C₂²×C₁₉

yes

characteristic

127

#339

—

128

#328

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#2007

yes

characteristic

131

C₂×C₁₉

#2009

yes

—

132

C₂×Q₁₆

—

133

C₂×M₁₆

D₄×C₁₉

yes

—

134

C₄⋊Q₈

D₄×C₁₉

yes

—

135

C₄⋊Q₈

D₄×C₁₉

yes

—

136

C₄⋊Q₈

D₄×C₁₉

yes

—

137

#125

—

138

#125

—

139

C₂²⋊Q₈

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

142

C₄×Q₈

—

143

C₄×Q₈

—

144

C₄×Q₈

—

145

#117

—

146

#117

—

147

C₂×C₄²

—

148

C₂×C₄²

C₂³×C₁₉

yes

characteristic

149

#107

—

150

#106

—

151

#106

—

152

C₄⋊C₈

—

153

C₄⋊C₈

—

154

#103

—

155

#103

—

156

#103

—

157

C₂²⋊C₈

D₄×C₁₉

yes

—

158

#97

—

159

#95

—

160

C₁₉

#10217

yes

characteristic, direct product factor, Sylow

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂²×C₄

—

165

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

166

C₂²×C₄

C₂×D₄×C₁₉

yes

—

167

Q₁₆

—

168

M₁₆

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₂²⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

186

C₄²

C₂×D₄×C₁₉

yes

characteristic

187

C₄²

C₂×D₄×C₁₉

yes

—

188

C₄²

#41×C₁₉

yes

characteristic

189

C₂³

C₁₉×#127

yes

characteristic

190

Q₈

—

191

Q₈

—

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

C₁₉×#120

yes

—

203

C₂×C₄

C₁₉×#120

yes

characteristic

204

C₂×C₄

C₁₉×#121

yes

—

205

C₂×C₄

C₁₉×#121

yes

characteristic

206

C₈

—

207

C₈

—

208

C₂²

—

209

C₂²

—

210

C₂²

C₁₉×#392

yes

characteristic

211

C₄

—

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

C₁₉×#455

yes

characteristic

219

C₄

C₁₉×#456

yes

characteristic

220

C₂

—

221

C₂

C₁₉×#2007

yes

characteristic

222

C₂

C₁₉×#2009

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#127
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂³×C₁₉

#127

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
77. #10217	C₁₉	direct (N × H)
160. C₁₉	#10217	direct (N × H)

H ≅ G/N

type

77. #10217

C₁₉

direct (N × H)

160. C₁₉

#10217

direct (N × H)

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

subgroup	index
C₁₉×#3255	2
C₁₉×#3237	2
C₁₉×#1995	2
C₁₉×#1506	2
C₁₉×#1307	2
#10217	19

subgroup

index

C₁₉×#3255

C₁₉×#3237

C₁₉×#1995

C₁₉×#1506

C₁₉×#1307

#10217

Subgroups — C₁₉×#10217 #18016176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10217 #18016176

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10217 #18016176