Group #18016254 — subgroups

Subgroups — C₁₉×#10295 #18016254

Order 4864.

504 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 130 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×#3230	C₂	1	2	yes	maximal
2	C₁₉×#2862	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1994	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1549	C₂	1	2	yes	maximal
5	C₁₉×#1276	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#533	C₂²	1	1	yes	characteristic
7	C₂×C₁₉×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₁₉×#500	—	2	2	no	—
9	C₁₉×#487	—	2	2	no	—
10	C₁₉×#484	—	2	4	no	—
11	C₁₉×#477	—	2	4	no	—
12	C₁₉×#431	C₂²	1	2	yes	—
13	C₁₉×#423	C₂²	1	1	yes	characteristic
14	C₁₉×#391	—	2	4	no	—
15	C₁₉×#382	—	2	2	no	—
16	C₄³×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#339	—	2	2	no	—
18	C₁₉×#332	—	2	4	no	—
19	C₂²×Q₈×C₁₉	—	2	2	no	—
20	C₂×M₁₆×C₁₉	—	2	1	no	—
21	C₁₉×C₄⋊Q₈	—	2	2	no	—
22	C₁₉×C₄⋊Q₈	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	—	2	2	no	—
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₁₉×#125	—	2	1	no	—
27	C₁₉×C₂²⋊Q₈	—	2	2	no	—
28	C₄×Q₈×C₁₉	—	2	2	no	—
29	C₁₉×#117	—	2	1	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
32	C₂×C₄²×C₁₉	—	2	2	no	—
33	C₂×C₄²×C₁₉	D₄	1	2	yes	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₁₉×#107	—	2	8	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
38	C₁₉×#103	—	2	8	no	—
39	C₁₉×C₂²⋊C₈	—	2	2	no	—
40	C₄×C₈×C₁₉	—	2	2	no	—
41	C₁₉×#95	—	2	8	no	—
42	C₂×Q₈×C₁₉	—	2	2	no	—
43	C₂×Q₈×C₁₉	—	4	8	no	—
44	C₂×Q₈×C₁₉	—	4	2	no	—
45	C₂×Q₈×C₁₉	—	4	2	no	—
46	C₂²×C₄×C₁₉	—	2	2	no	—
47	C₂²×C₄×C₁₉	—	2	4	no	—
48	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
50	M₁₆×C₁₉	—	4	2	no	—
51	C₂×C₈×C₁₉	—	2	4	no	—
52	C₂×C₈×C₁₉	—	4	1	no	—
53	C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₄⋊C₄×C₁₉	—	2	2	no	—
55	C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	—	4	2	no	—
59	C₄⋊C₄×C₁₉	—	4	2	no	—
60	C₂²⋊C₄×C₁₉	—	4	1	no	—
61	C₄²×C₁₉	—	2	2	no	—
62	C₄²×C₁₉	—	4	4	no	—
63	C₄²×C₁₉	—	4	1	no	—
64	C₄²×C₁₉	Q₁₆	1	4	yes	—
65	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₁₉	C₂×D₄	1	2	yes	—
67	C₄²×C₁₉	#41	1	1	yes	characteristic
68	#10295	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₉	#120	1	1	yes	characteristic
70	Q₈×C₁₉	—	4	4	no	—
71	Q₈×C₁₉	—	8	4	no	—
72	Q₈×C₁₉	—	8	4	no	—
73	C₂×C₄×C₁₉	—	2	4	no	—
74	C₂×C₄×C₁₉	—	2	4	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	8	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	4	no	—
79	C₂×C₄×C₁₉	#120	1	2	yes	—
80	C₂×C₄×C₁₉	#121	1	2	yes	—
81	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
82	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
83	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
84	C₂×C₄×C₁₉	#137	1	2	yes	—
85	C₈×C₁₉	—	4	4	no	—
86	C₈×C₁₉	—	8	1	no	—
87	#3230	C₂×C₁₉	1	2	yes	—
88	#2862	C₂×C₁₉	1	1	yes	characteristic
89	#1994	C₂×C₁₉	1	1	yes	characteristic
90	#1549	C₂×C₁₉	1	2	yes	—
91	#1276	C₂×C₁₉	1	1	yes	characteristic
92	C₂²×C₁₉	—	2	2	no	—
93	C₂²×C₁₉	#392	1	1	yes	characteristic
94	C₂²×C₁₉	#451	1	2	yes	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	4	4	no	—
97	C₄×C₁₉	—	8	4	no	—
98	C₄×C₁₉	—	8	2	no	—
99	C₄×C₁₉	#454	1	4	yes	—
100	C₄×C₁₉	#462	1	2	yes	—
101	C₄×C₁₉	#494	1	1	yes	characteristic
102	C₄×C₁₉	#497	1	1	yes	characteristic
103	#533	C₂²×C₁₉	1	1	yes	characteristic
104	C₂×C₄⋊Q₈	C₂²×C₁₉	1	2	yes	—
105	#500	—	2	2	no	—
106	#487	—	2	2	no	—
107	#484	—	2	4	no	—
108	#477	—	2	4	no	—
109	#431	C₂²×C₁₉	1	2	yes	—
110	#423	C₂²×C₁₉	1	1	yes	characteristic
111	#391	—	2	4	no	—
112	#382	—	2	2	no	—
113	C₄³	C₂²×C₁₉	1	1	yes	characteristic
114	#339	—	2	2	no	—
115	#332	—	2	4	no	—
116	C₂×C₁₉	—	2	2	no	—
117	C₂×C₁₉	#2003	1	2	yes	—
118	C₂×C₁₉	#2016	1	1	yes	characteristic
119	C₂²×Q₈	—	2	2	no	—
120	C₂×M₁₆	—	2	1	no	—
121	C₄⋊Q₈	—	2	2	no	—
122	C₄⋊Q₈	—	2	2	no	—
123	C₄⋊Q₈	—	2	2	no	—
124	C₄⋊Q₈	—	2	2	no	—
125	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
126	#125	—	2	1	no	—
127	C₂²⋊Q₈	—	2	2	no	—
128	C₄×Q₈	—	2	2	no	—
129	#117	—	2	1	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
132	C₂×C₄²	—	2	2	no	—
133	C₂×C₄²	D₄×C₁₉	1	2	yes	—
134	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
135	#107	—	2	8	no	—
136	C₄⋊C₈	—	2	2	no	—
137	C₄⋊C₈	D₄×C₁₉	1	4	yes	—
138	#103	—	2	8	no	—
139	C₂²⋊C₈	—	2	2	no	—
140	C₄×C₈	—	2	2	no	—
141	#95	—	2	8	no	—
142	C₁₉	#10295	1	1	yes	characteristic, direct product factor, Sylow
143	C₂×Q₈	—	2	2	no	—
144	C₂×Q₈	—	4	8	no	—
145	C₂×Q₈	—	4	2	no	—
146	C₂×Q₈	—	4	2	no	—
147	C₂²×C₄	—	2	2	no	—
148	C₂²×C₄	—	2	4	no	—
149	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
150	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
151	M₁₆	—	4	2	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	4	1	no	—
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	—	2	2	no	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	2	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	4	2	no	—
160	C₄⋊C₄	—	4	2	no	—
161	C₂²⋊C₄	—	4	1	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	4	4	no	—
164	C₄²	—	4	1	no	—
165	C₄²	Q₁₆×C₁₉	1	4	yes	—
166	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
167	C₄²	C₂×D₄×C₁₉	1	2	yes	—
168	C₄²	#41×C₁₉	1	1	yes	characteristic
169	C₂³	C₁₉×#120	1	1	yes	characteristic
170	Q₈	—	4	4	no	—
171	Q₈	—	8	4	no	—
172	Q₈	—	8	4	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	4	4	no	—
176	C₂×C₄	—	4	8	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	C₁₉×#120	1	2	yes	—
180	C₂×C₄	C₁₉×#121	1	2	yes	—
181	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
182	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
183	C₂×C₄	C₂×Q₁₆×C₁₉	1	2	yes	—
184	C₂×C₄	C₁₉×#137	1	2	yes	—
185	C₈	—	4	4	no	—
186	C₈	—	8	1	no	—
187	C₂²	—	2	2	no	—
188	C₂²	C₁₉×#392	1	1	yes	characteristic
189	C₂²	C₁₉×#451	1	2	yes	—
190	C₄	—	2	2	no	—
191	C₄	—	4	4	no	—
192	C₄	—	8	4	no	—
193	C₄	—	8	2	no	—
194	C₄	C₁₉×#454	1	4	yes	—
195	C₄	C₁₉×#462	1	2	yes	—
196	C₄	C₁₉×#494	1	1	yes	characteristic
197	C₄	C₁₉×#497	1	1	yes	characteristic
198	C₂	—	2	2	no	—
199	C₂	C₁₉×#2003	1	2	yes	—
200	C₂	C₁₉×#2016	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3230

C₂

yes

maximal

C₁₉×#2862

C₂

yes

maximal, characteristic

C₁₉×#1994

C₂

yes

maximal, characteristic

C₁₉×#1549

C₂

yes

maximal

C₁₉×#1276

C₂

yes

maximal, characteristic

C₁₉×#533

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

—

C₁₉×#500

—

C₁₉×#487

—

C₁₉×#484

—

C₁₉×#477

—

C₁₉×#431

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#391

—

C₁₉×#382

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#339

—

C₁₉×#332

—

C₂²×Q₈×C₁₉

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×#103

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

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

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

Q₁₆

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

#41

yes

characteristic

#10295

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

#120

yes

characteristic

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

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

#3230

C₂×C₁₉

yes

—

#2862

C₂×C₁₉

yes

characteristic

#1994

C₂×C₁₉

yes

characteristic

#1549

C₂×C₁₉

yes

—

#1276

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

#392

yes

characteristic

C₂²×C₁₉

#451

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#454

yes

—

100

C₄×C₁₉

#462

yes

—

101

C₄×C₁₉

#494

yes

characteristic

102

C₄×C₁₉

#497

yes

characteristic

103

#533

C₂²×C₁₉

yes

characteristic

104

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

—

105

#500

—

106

#487

—

107

#484

—

108

#477

—

109

#431

C₂²×C₁₉

yes

—

110

#423

C₂²×C₁₉

yes

characteristic

111

#391

—

112

#382

—

113

C₄³

C₂²×C₁₉

yes

characteristic

114

#339

—

115

#332

—

116

C₂×C₁₉

—

117

C₂×C₁₉

#2003

yes

—

118

C₂×C₁₉

#2016

yes

characteristic

119

C₂²×Q₈

—

120

C₂×M₁₆

—

121

C₄⋊Q₈

—

122

C₄⋊Q₈

—

123

C₄⋊Q₈

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

D₄×C₁₉

yes

—

126

#125

—

127

C₂²⋊Q₈

—

128

C₄×Q₈

—

129

#117

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

132

C₂×C₄²

—

133

C₂×C₄²

D₄×C₁₉

yes

—

134

C₂×C₄²

C₂³×C₁₉

yes

characteristic

135

#107

—

136

C₄⋊C₈

—

137

C₄⋊C₈

D₄×C₁₉

yes

—

138

#103

—

139

C₂²⋊C₈

—

140

C₄×C₈

—

141

#95

—

142

C₁₉

#10295

yes

characteristic, direct product factor, Sylow

143

C₂×Q₈

—

144

C₂×Q₈

—

145

C₂×Q₈

—

146

C₂×Q₈

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

C₂×D₄×C₁₉

yes

—

150

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

151

M₁₆

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄⋊C₄

—

161

C₂²⋊C₄

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₄²

Q₁₆×C₁₉

yes

—

166

C₄²

C₂×D₄×C₁₉

yes

characteristic

167

C₄²

C₂×D₄×C₁₉

yes

—

168

C₄²

#41×C₁₉

yes

characteristic

169

C₂³

C₁₉×#120

yes

characteristic

170

Q₈

—

171

Q₈

—

172

Q₈

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

C₁₉×#120

yes

—

180

C₂×C₄

C₁₉×#121

yes

—

181

C₂×C₄

C₁₉×#121

yes

characteristic

182

C₂×C₄

C₁₉×#127

yes

characteristic

183

C₂×C₄

C₂×Q₁₆×C₁₉

yes

—

184

C₂×C₄

C₁₉×#137

yes

—

185

C₈

—

186

C₈

—

187

C₂²

—

188

C₂²

C₁₉×#392

yes

characteristic

189

C₂²

C₁₉×#451

yes

—

190

C₄

—

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

C₁₉×#454

yes

—

195

C₄

C₁₉×#462

yes

—

196

C₄

C₁₉×#494

yes

characteristic

197

C₄

C₁₉×#497

yes

characteristic

198

C₂

—

199

C₂

C₁₉×#2003

yes

—

200

C₂

C₁₉×#2016

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂³×C₁₉	#120
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

#120

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
68. #10295	C₁₉	direct (N × H)
142. C₁₉	#10295	direct (N × H)

H ≅ G/N

type

68. #10295

C₁₉

direct (N × H)

142. C₁₉

#10295

direct (N × H)

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

subgroup	index
C₁₉×#3230	2
C₁₉×#2862	2
C₁₉×#1994	2
C₁₉×#1549	2
C₁₉×#1276	2
#10295	19

subgroup

index

C₁₉×#3230

C₁₉×#2862

C₁₉×#1994

C₁₉×#1549

C₁₉×#1276

#10295

Subgroups — C₁₉×#10295 #18016254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10295 #18016254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10295 #18016254