Group #18075555 — subgroups

Subgroups — #18075555

Order 4864.

404 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 109 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	#14572347	C₂	1	1	yes	maximal, characteristic
2	#14562390	C₂	1	2	yes	maximal, complemented
3	#14562370	C₂	1	1	yes	maximal, characteristic
4	C₁₉⋊#1309	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1560	C₂	1	1	yes	maximal, characteristic
6	C₂×#10597394	C₄	1	2	yes	—
7	#11926622	—	2	2	no	—
8	D₄×C₁₉⋊C₈	—	2	2	no	—
9	#11926568	C₂²	1	2	yes	—
10	#11926568	C₂²	1	1	yes	characteristic
11	#11926511	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926294	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926293	—	2	1	no	—
16	#11926288	—	2	1	no	—
17	C₁₉×#532	C₂²	1	1	yes	characteristic
18	C₁₉×#423	C₂²	1	2	yes	—
19	C₁₉×#333	—	2	1	no	—
20	C₁₉×#331	—	2	1	no	—
21	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×M₁₆×C₁₉	—	2	2	no	—
23	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
24	C₁₉×#127	D₄	1	1	yes	characteristic
25	C₁₉×#124	Q₈	1	2	yes	—
26	C₁₉×#121	—	2	2	no	—
27	C₄×D₄×C₁₉	—	2	2	no	—
28	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
29	#10597394	—	4	4	no	—
30	C₂×#64520	—	2	2	no	—
31	C₂×#64520	—	2	2	no	—
32	C₂×#64520	C₂×C₄	1	2	yes	—
33	C₂²×C₁₉⋊C₈	—	2	2	no	—
34	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₄⋊C₈	—	2	2	no	—
38	C₂²⋊(C₁₉⋊C₈)	—	2	4	no	—
39	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
42	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
43	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
44	#41×C₁₉	—	4	2	no	—
45	#41×C₁₉	—	4	2	no	—
46	C₂×Q₈×C₁₉	C₄⋊C₄	1	2	yes	—
47	C₂×D₄×C₁₉	—	2	2	no	—
48	C₂×D₄×C₁₉	—	2	2	no	—
49	C₂×D₄×C₁₉	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₉	—	2	2	no	—
51	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₉	#41	1	2	yes	—
53	M₁₆×C₁₉	—	8	2	no	—
54	C₂×C₈×C₁₉	—	4	2	no	—
55	C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	C₂×D₄	1	2	yes	—
58	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
60	#64520	—	4	4	no	—
61	#64520	—	4	2	no	—
62	#64520	—	8	2	no	—
63	C₂×C₁₉⋊C₈	—	2	2	no	—
64	C₂×C₁₉⋊C₈	—	2	2	no	—
65	C₂×C₁₉⋊C₈	—	4	1	no	—
66	C₂×C₁₉⋊C₈	—	4	4	no	—
67	C₂×C₁₉⋊C₈	—	4	2	no	—
68	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
69	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
71	#8636	—	19	1	no	maximal, Sylow
72	C₂³×C₁₉	—	2	2	no	—
73	C₂³×C₁₉	#117	1	1	yes	characteristic
74	Q₈×C₁₉	—	4	2	no	—
75	D₄×C₁₉	—	4	2	no	—
76	D₄×C₁₉	—	4	4	no	—
77	D₄×C₁₉	—	4	2	no	—
78	D₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	2	1	no	—
80	C₂×C₄×C₁₉	—	2	1	no	—
81	C₂×C₄×C₁₉	—	2	2	no	—
82	C₂×C₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	2	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	—	4	2	no	—
86	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×C₁₉	#121	1	2	yes	—
89	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
90	C₈×C₁₉	—	8	2	no	—
91	C₁₉⋊C₈	—	2	1	no	—
92	C₁₉⋊C₈	—	2	2	no	—
93	C₁₉⋊C₈	—	4	2	no	—
94	C₁₉⋊C₈	—	8	2	no	—
95	C₁₉⋊C₈	#100	1	2	yes	—
96	#2931	—	19	1	no	—
97	#1566	—	19	2	no	—
98	#1560	—	19	1	no	—
99	#1560	D₁₉	1	1	yes	characteristic
100	#1309	—	19	2	no	—
101	C₂²×C₁₉	—	2	1	no	—
102	C₂²×C₁₉	—	2	2	no	—
103	C₂²×C₁₉	—	4	2	no	—
104	C₂²×C₁₉	—	4	4	no	—
105	C₂²×C₁₉	#380	1	1	yes	characteristic
106	C₄×C₁₉	—	2	1	no	—
107	C₄×C₁₉	—	2	2	no	—
108	C₄×C₁₉	—	4	2	no	—
109	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
110	C₄×C₁₉	#413	1	1	yes	characteristic
111	C₄×C₁₉	#471	1	2	yes	—
112	C₄×C₁₉	#471	1	2	yes	—
113	C₂×#131	—	19	2	no	—
114	#532	C₂×D₁₉	1	1	yes	characteristic
115	#436	—	38	2	no	—
116	C₈×D₄	—	38	2	no	—
117	#423	—	19	1	no	—
118	#423	—	19	2	no	—
119	#423	C₂×D₁₉	1	2	yes	—
120	#408	—	19	2	no	—
121	C₂×C₄×C₈	—	19	1	no	—
122	#334	—	38	2	no	—
123	#334	—	38	2	no	—
124	#333	—	2	1	no	—
125	#333	—	38	1	no	—
126	#331	—	2	1	no	—
127	#331	—	38	1	no	—
128	C₂×C₁₉	—	4	1	no	—
129	C₂×C₁₉	—	8	2	no	—
130	C₂×C₁₉	#1800	1	1	yes	characteristic
131	C₂×C₁₉	#1815	1	2	yes	—
132	C₂×#41	C₄×D₁₉	1	2	yes	—
133	#131	—	76	4	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂×M₁₆	—	19	2	no	—
136	C₂×M₁₆	—	38	2	no	—
137	C₂×M₁₆	—	38	2	no	—
138	C₂²×C₈	—	19	1	no	—
139	C₂²×C₈	—	19	1	no	—
140	C₂²×C₈	—	38	2	no	—
141	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
142	#127	C₂²⋊D₁₉	1	1	yes	characteristic
143	#124	Dic₃₈	1	2	yes	—
144	#121	—	2	2	no	—
145	C₄×D₄	—	2	2	no	—
146	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	C₄⋊C₈	—	38	2	no	—
150	C₄⋊C₈	—	38	2	no	—
151	C₄⋊C₈	—	38	2	no	—
152	C₂²⋊C₈	—	38	4	no	—
153	C₄×C₈	—	19	2	no	—
154	C₄×C₈	—	19	2	no	—
155	C₁₉	#8636	1	1	yes	characteristic, complemented, Sylow
156	#41	—	4	2	no	—
157	#41	—	4	2	no	—
158	C₂×Q₈	Dic₁₉⋊C₄	1	2	yes	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	—	2	2	no	—
161	C₂×D₄	Dic₁₉⋊C₄	1	2	yes	—
162	C₂²×C₄	—	2	2	no	—
163	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
164	C₂²×C₄	#64543	1	2	yes	—
165	M₁₆	—	8	2	no	—
166	M₁₆	—	76	4	no	—
167	M₁₆	—	76	2	no	—
168	M₁₆	—	152	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	19	1	no	—
171	C₂×C₈	—	19	2	no	—
172	C₂×C₈	—	19	1	no	—
173	C₂×C₈	—	38	2	no	—
174	C₂×C₈	—	38	2	no	—
175	C₂×C₈	—	76	4	no	—
176	C₂×C₈	—	76	1	no	—
177	C₂×C₈	—	76	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₂²⋊C₄	—	2	4	no	—
180	C₄²	C₂×Dic₃₈	1	1	yes	characteristic
181	C₄²	D₄×D₁₉	1	2	yes	—
182	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
183	C₂³	—	2	2	no	—
184	C₂³	#10597323	1	1	yes	characteristic
185	Q₈	—	4	2	no	—
186	D₄	—	4	2	no	—
187	D₄	—	4	4	no	—
188	D₄	—	4	2	no	—
189	D₄	—	4	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	#10597324	1	2	yes	—
198	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
199	C₂×C₄	C₂×Dic₁₉⋊C₄	1	1	yes	characteristic
200	C₂×C₄	#10597385	1	2	yes	—
201	C₈	—	8	2	no	—
202	C₈	—	19	2	no	—
203	C₈	—	38	1	no	—
204	C₈	—	38	2	no	—
205	C₈	—	76	2	no	—
206	C₈	—	152	2	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	4	2	no	—
210	C₂²	—	4	4	no	—
211	C₂²	#11926402	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	2	no	—
214	C₄	—	4	2	no	—
215	C₄	#100×D₁₉	1	1	yes	characteristic
216	C₄	#11926525	1	1	yes	characteristic
217	C₄	#11926805	1	2	yes	—
218	C₄	#11926809	1	2	yes	—
219	C₂	—	4	1	no	—
220	C₂	—	8	2	no	—
221	C₂	#14563625	1	1	yes	characteristic
222	C₂	#14563692	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572347

C₂

yes

maximal, characteristic

#14562390

C₂

yes

maximal, complemented

#14562370

C₂

yes

maximal, characteristic

C₁₉⋊#1309

C₂

yes

maximal, complemented

C₁₉×#1560

C₂

yes

maximal, characteristic

C₂×#10597394

C₄

yes

—

#11926622

—

D₄×C₁₉⋊C₈

—

#11926568

C₂²

yes

—

#11926568

C₂²

yes

characteristic

#11926511

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

—

C₁₉×#532

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

—

C₁₉×#333

—

C₁₉×#331

—

C₂×#41×C₁₉

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×#127

D₄

yes

characteristic

C₁₉×#124

Q₈

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

—

—

—

C₂×C₄

yes

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₂²⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₄⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₄⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

—

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

C₂×C₁₉⋊C₈

C₂²⋊C₄

yes

characteristic

#8636

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#117

yes

characteristic

Q₈×C₁₉

—

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×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

C₂²⋊Q₈

yes

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#100

yes

—

—

—

—

D₁₉

yes

characteristic

100

#1309

—

101

C₂²×C₁₉

—

102

C₂²×C₁₉

—

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

#380

yes

characteristic

106

C₄×C₁₉

—

107

C₄×C₁₉

—

108

C₄×C₁₉

—

109

C₄×C₁₉

C₂×#100

yes

characteristic

110

C₄×C₁₉

#413

yes

characteristic

111

C₄×C₁₉

#471

yes

—

112

C₄×C₁₉

#471

yes

—

113

C₂×#131

—

114

#532

C₂×D₁₉

yes

characteristic

115

#436

—

116

C₈×D₄

—

117

#423

—

118

#423

—

119

#423

C₂×D₁₉

yes

—

120

#408

—

121

C₂×C₄×C₈

—

122

#334

—

123

#334

—

124

#333

—

125

#333

—

126

#331

—

127

#331

—

128

C₂×C₁₉

—

129

C₂×C₁₉

—

130

C₂×C₁₉

#1800

yes

characteristic

131

C₂×C₁₉

#1815

yes

—

132

C₂×#41

C₄×D₁₉

yes

—

133

#131

—

134

C₂×M₁₆

—

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

139

C₂²×C₈

—

140

C₂²×C₈

—

141

C₄⋊Q₈

C₂²⋊D₁₉

yes

characteristic

142

#127

C₂²⋊D₁₉

yes

characteristic

143

#124

Dic₃₈

yes

—

144

#121

—

145

C₄×D₄

—

146

C₂×C₄²

C₂²×D₁₉

yes

characteristic

147

C₄⋊C₈

—

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

C₄⋊C₈

—

152

C₂²⋊C₈

—

153

C₄×C₈

—

154

C₄×C₈

—

155

C₁₉

#8636

yes

characteristic, complemented, Sylow

156

#41

—

157

#41

—

158

C₂×Q₈

Dic₁₉⋊C₄

yes

—

159

C₂×D₄

—

160

C₂×D₄

—

161

C₂×D₄

Dic₁₉⋊C₄

yes

—

162

C₂²×C₄

—

163

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

164

C₂²×C₄

#64543

yes

—

165

M₁₆

—

166

M₁₆

—

167

M₁₆

—

168

M₁₆

—

152

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₂²⋊C₄

—

180

C₄²

C₂×Dic₃₈

yes

characteristic

181

C₄²

D₄×D₁₉

yes

—

182

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

183

C₂³

—

184

C₂³

#10597323

yes

characteristic

185

Q₈

—

186

D₄

—

187

D₄

—

188

D₄

—

189

D₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

#10597324

yes

—

198

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

199

C₂×C₄

C₂×Dic₁₉⋊C₄

yes

characteristic

200

C₂×C₄

#10597385

yes

—

201

C₈

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₈

—

152

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

#11926402

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

#100×D₁₉

yes

characteristic

216

C₄

#11926525

yes

characteristic

217

C₄

#11926805

yes

—

218

C₄

#11926809

yes

—

219

C₂

—

220

C₂

—

221

C₂

#14563625

yes

characteristic

222

C₂

#14563692

yes

—

	subgroup	G/H
center	C₂²	#11926402
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1560	C₂
socle	C₂²×C₁₉	#380
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1560	D₁₉
hypocenter	C₁₉	#8636
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1560

subgroup

G/H

center

C₂²

#11926402

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1560

C₂

socle

C₂²×C₁₉

#380

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1560

N	H ≅ G/N	type
2. #14562390	C₂	semidirect
4. C₁₉⋊#1309	C₂	semidirect
155. C₁₉	#8636	semidirect

H ≅ G/N

type

2. #14562390

C₂

semidirect

4. C₁₉⋊#1309

C₂

semidirect

155. C₁₉

#8636

semidirect

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

subgroup	index
#14572347	2
#14562390	2
#14562370	2
C₁₉⋊#1309	2
C₁₉×#1560	2
#8636	19

subgroup

index

#14572347

#14562390

#14562370

C₁₉⋊#1309

C₁₉×#1560

#8636

Subgroups — #18075555

Conjugacy classes of subgroups

Complements

Maximal subgroups