Group #18075941 — subgroups

Subgroups — #18075941

Order 4864.

554 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14563397	C₂	1	2	yes	maximal
2	#14561516	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₉×#382	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×#10597260	C₂²	1	4	yes	—
6	#11926299	—	2	2	no	—
7	C₂²×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
8	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
9	C₁₉×#382	—	2	2	no	—
10	C₁₉×#382	C₄	1	2	yes	—
11	C₁₉×#382	C₂²	1	2	yes	—
12	C₂×C₁₉×#95	—	2	2	no	—
13	C₂³×C₄×C₁₉	—	2	2	no	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄⋊C₄×C₁₉	—	4	4	no	—
18	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₁₉	—	2	4	no	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	D₄	1	2	yes	—
22	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	—	2	4	no	—
24	C₁₉×#95	—	2	4	no	—
25	C₁₉×#95	—	2	4	no	—
26	C₂²⋊(C₁₉⋊C₈)	—	2	8	no	—
27	#10597260	—	2	8	no	—
28	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²×C₄×C₁₉	—	2	2	no	—
30	C₂²×C₄×C₁₉	—	2	2	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	4	no	—
33	C₂²×C₄×C₁₉	—	2	4	no	—
34	C₂²×C₄×C₁₉	—	2	4	no	—
35	C₂²×C₄×C₁₉	—	4	2	no	—
36	C₂²×C₄×C₁₉	—	4	4	no	—
37	C₂²×C₄×C₁₉	—	4	4	no	—
38	C₂²×C₄×C₁₉	—	4	4	no	—
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
43	C₄⋊C₄×C₁₉	—	4	4	no	—
44	C₄⋊C₄×C₁₉	—	4	4	no	—
45	C₄²×C₁₉	—	2	2	no	—
46	C₄²×C₁₉	—	2	4	no	—
47	C₄²×C₁₉	#41	1	4	yes	—
48	C₂×C₁₉⋊C₈	—	2	8	no	—
49	C₂×C₁₉⋊C₈	—	4	4	no	—
50	C₂×C₁₉⋊C₈	—	4	4	no	—
51	#8719	—	19	1	no	maximal, Sylow
52	C₂³×C₁₉	—	2	1	no	—
53	C₂³×C₁₉	—	2	1	no	—
54	C₂³×C₁₉	—	2	2	no	—
55	C₂³×C₁₉	#101	1	2	yes	—
56	C₂³×C₁₉	#104	1	4	yes	—
57	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₉	—	2	8	no	—
59	C₂×C₄×C₁₉	—	2	1	no	—
60	C₂×C₄×C₁₉	—	2	1	no	—
61	C₂×C₄×C₁₉	—	2	1	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	2	no	—
67	C₂×C₄×C₁₉	—	2	2	no	—
68	C₂×C₄×C₁₉	—	4	8	no	—
69	C₂×C₄×C₁₉	—	4	4	no	—
70	C₂×C₄×C₁₉	—	4	4	no	—
71	C₂×C₄×C₁₉	—	4	4	no	—
72	C₂×C₄×C₁₉	—	8	8	no	—
73	C₂×C₄×C₁₉	#100	1	2	yes	—
74	C₂×C₄×C₁₉	#117	1	2	yes	—
75	C₂×C₄×C₁₉	#123	1	4	yes	—
76	C₁₉⋊C₈	—	4	8	no	—
77	C₂×#382	D₁₉	1	1	yes	characteristic
78	#1749	—	19	2	no	—
79	#1295	—	19	4	no	—
80	C₂²×C₁₉	—	2	2	no	—
81	C₂²×C₁₉	—	2	4	no	—
82	C₂²×C₁₉	—	2	4	no	—
83	C₂²×C₁₉	—	2	2	no	—
84	C₂²×C₁₉	#330	1	4	yes	—
85	C₂²×C₁₉	#381	1	1	yes	characteristic
86	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
87	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
88	C₂²×C₁₉	C₂×#104	1	2	yes	—
89	C₂²×C₁₉	#421	1	2	yes	—
90	C₄×C₁₉	—	2	2	no	—
91	C₄×C₁₉	—	2	2	no	—
92	C₄×C₁₉	—	2	4	no	—
93	C₄×C₁₉	—	4	2	no	—
94	C₄×C₁₉	—	8	4	no	—
95	C₂²×C₄⋊C₄	Dic₁₉	1	2	yes	—
96	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
97	C₂×C₂²⋊C₈	—	38	2	no	—
98	C₂×#97	—	19	4	no	—
99	#382	—	2	2	no	—
100	#382	Dic₁₉	1	2	yes	—
101	#382	C₂×D₁₉	1	2	yes	—
102	C₂×#95	—	2	2	no	—
103	#336	—	38	2	no	—
104	C₂×C₁₉	—	2	4	no	—
105	C₂×C₁₉	C₂×#330	1	1	yes	characteristic
106	C₂×C₁₉	#1527	1	2	yes	—
107	C₂×C₁₉	#1534	1	1	yes	characteristic
108	C₂×C₁₉	#1821	1	1	yes	characteristic
109	C₂×C₁₉	#1826	1	2	yes	—
110	C₂³×C₄	—	2	2	no	—
111	C₂³×C₄	C₂×Dic₁₉	1	1	yes	characteristic
112	C₂³×C₄	C₂²⋊D₁₉	1	2	yes	—
113	C₂²×C₈	—	38	4	no	—
114	C₂×C₄⋊C₄	—	2	2	no	—
115	C₂×C₄⋊C₄	—	4	4	no	—
116	C₂×C₄⋊C₄	C₂×Dic₁₉	1	4	yes	—
117	C₂×C₄²	—	2	4	no	—
118	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
119	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
120	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
121	C₂²⋊C₈	—	38	8	no	—
122	#97	—	38	8	no	—
123	#95	—	2	4	no	—
124	#95	—	2	4	no	—
125	C₁₉	#8719	1	1	yes	characteristic, complemented, Sylow
126	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
127	C₂²×C₄	—	2	2	no	—
128	C₂²×C₄	—	2	2	no	—
129	C₂²×C₄	—	2	2	no	—
130	C₂²×C₄	—	2	4	no	—
131	C₂²×C₄	—	2	4	no	—
132	C₂²×C₄	—	2	4	no	—
133	C₂²×C₄	—	4	2	no	—
134	C₂²×C₄	—	4	4	no	—
135	C₂²×C₄	—	4	4	no	—
136	C₂²×C₄	—	4	4	no	—
137	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
138	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
139	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
140	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
141	C₂×C₈	—	38	8	no	—
142	C₂×C₈	—	76	4	no	—
143	C₂×C₈	—	76	4	no	—
144	C₄⋊C₄	—	4	4	no	—
145	C₄⋊C₄	—	4	4	no	—
146	C₄²	—	2	2	no	—
147	C₄²	—	2	4	no	—
148	C₄²	#64541	1	4	yes	—
149	C₂³	—	2	2	no	—
150	C₂³	—	2	1	no	—
151	C₂³	—	2	1	no	—
152	C₂³	#10597293	1	2	yes	—
153	C₂³	#10597294	1	4	yes	—
154	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
155	C₂×C₄	—	2	8	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	4	8	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	—	4	4	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	8	8	no	—
170	C₂×C₄	#10597290	1	2	yes	—
171	C₂×C₄	#10597372	1	2	yes	—
172	C₂×C₄	#10597375	1	4	yes	—
173	C₈	—	76	8	no	—
174	C₂²	—	2	2	no	—
175	C₂²	—	2	4	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	2	2	no	—
178	C₂²	#11926286	1	4	yes	—
179	C₂²	#11926407	1	1	yes	characteristic
180	C₂²	C₂×#10597290	1	1	yes	characteristic
181	C₂²	C₂×#10597293	1	1	yes	characteristic
182	C₂²	C₂×#10597294	1	2	yes	—
183	C₂²	#11926561	1	2	yes	—
184	C₄	—	2	2	no	—
185	C₄	—	2	2	no	—
186	C₄	—	2	4	no	—
187	C₄	—	4	2	no	—
188	C₄	—	8	4	no	—
189	C₂	—	2	4	no	—
190	C₂	C₂×#11926286	1	1	yes	characteristic
191	C₂	#14562233	1	2	yes	—
192	C₂	#14562262	1	1	yes	characteristic
193	C₂	#14563715	1	1	yes	characteristic
194	C₂	#14563734	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14563397

C₂

yes

maximal

#14561516

C₂

yes

maximal, complemented

C₂×C₁₉×#382

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×#10597260

C₂²

yes

—

#11926299

—

C₂²×C₄⋊C₄×C₁₉

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₁₉×#382

—

C₁₉×#382

C₄

yes

—

C₁₉×#382

C₂²

yes

—

C₂×C₁₉×#95

—

C₂³×C₄×C₁₉

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#8719

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#101

yes

—

C₂³×C₁₉

#104

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₁₉⋊C₈

—

C₂×#382

D₁₉

yes

characteristic

#1749

—

#1295

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#330

yes

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#421

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₂²×C₄⋊C₄

Dic₁₉

yes

—

C₂²×C₄²

C₂×D₁₉

yes

characteristic

C₂×C₂²⋊C₈

—

C₂×#97

—

#382

—

100

#382

Dic₁₉

yes

—

101

#382

C₂×D₁₉

yes

—

102

C₂×#95

—

103

#336

—

104

C₂×C₁₉

—

105

C₂×C₁₉

C₂×#330

yes

characteristic

106

C₂×C₁₉

#1527

yes

—

107

C₂×C₁₉

#1534

yes

characteristic

108

C₂×C₁₉

#1821

yes

characteristic

109

C₂×C₁₉

#1826

yes

—

110

C₂³×C₄

—

111

C₂³×C₄

C₂×Dic₁₉

yes

characteristic

112

C₂³×C₄

C₂²⋊D₁₉

yes

—

113

C₂²×C₈

—

114

C₂×C₄⋊C₄

—

115

C₂×C₄⋊C₄

—

116

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

117

C₂×C₄²

—

118

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

119

C₂×C₄²

C₂²⋊D₁₉

yes

—

120

C₂×C₄²

C₂²×D₁₉

yes

characteristic

121

C₂²⋊C₈

—

122

#97

—

123

#95

—

124

#95

—

125

C₁₉

#8719

yes

characteristic, complemented, Sylow

126

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

127

C₂²×C₄

—

128

C₂²×C₄

—

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

—

136

C₂²×C₄

—

137

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

138

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

139

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

140

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄²

—

147

C₄²

—

148

C₄²

#64541

yes

—

149

C₂³

—

150

C₂³

—

151

C₂³

—

152

C₂³

#10597293

yes

—

153

C₂³

#10597294

yes

—

154

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

#10597290

yes

—

171

C₂×C₄

#10597372

yes

—

172

C₂×C₄

#10597375

yes

—

173

C₈

—

174

C₂²

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

#11926286

yes

—

179

C₂²

#11926407

yes

characteristic

180

C₂²

C₂×#10597290

yes

characteristic

181

C₂²

C₂×#10597293

yes

characteristic

182

C₂²

C₂×#10597294

yes

—

183

C₂²

#11926561

yes

—

184

C₄

—

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₂

—

190

C₂

C₂×#11926286

yes

characteristic

191

C₂

#14562233

yes

—

192

C₂

#14562262

yes

characteristic

193

C₂

#14563715

yes

characteristic

194

C₂

#14563734

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#382	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#382	D₁₉
hypocenter	C₁₉	#8719
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#382

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₂×C₁₉×#382

C₂

socle

C₂³×C₁₉

C₂×C₂²⋊C₄

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#382

N	H ≅ G/N	type
2. #14561516	C₂	semidirect
125. C₁₉	#8719	semidirect

H ≅ G/N

type

2. #14561516

C₂

semidirect

125. C₁₉

#8719

semidirect

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

subgroup	index
#14563397	2
#14561516	2
C₂×C₁₉×#382	2
#8719	19

subgroup

index

#14563397

#14561516

C₂×C₁₉×#382

#8719

Subgroups — #18075941

Conjugacy classes of subgroups

Complements

Maximal subgroups