Group #18075530 — subgroups

Subgroups — #18075530

Order 4864.

388 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 93 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	#14572346	C₂	1	1	yes	maximal, characteristic
2	#14562396	C₂	1	2	yes	maximal, complemented
3	#14562269	C₂	1	2	yes	maximal
4	#14561546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597353	C₄	1	2	yes	—
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926621	—	2	2	no	—
9	#11926609	—	2	2	no	—
10	#11926601	C₂²	1	2	yes	—
11	#11926512	C₄	1	2	yes	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926296	—	2	2	no	—
14	#11926294	—	2	2	no	—
15	#11926283	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₂×#64541	C₂×C₄	1	2	yes	—
19	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
21	#10597376	—	2	2	no	—
22	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₁₉⋊C₈	C₂×C₄	1	1	yes	characteristic
24	#10597353	—	4	4	no	—
25	C₂×#64515	—	2	2	no	—
26	C₂×C₈×D₁₉	—	2	2	no	—
27	#10597321	D₄	1	2	yes	—
28	#10597320	Q₈	1	1	yes	characteristic
29	C₄×D₇₆	—	2	2	no	—
30	#10597315	Q₈	1	1	yes	characteristic
31	C₁₉×C₄⋊C₈	—	2	2	no	—
32	C₁₉×C₄⋊C₈	—	2	2	no	—
33	C₁₉×C₂²⋊C₈	—	2	2	no	—
34	C₁₉×#97	—	2	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
36	(C₂×D₁₉)⋊C₈	—	2	4	no	—
37	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
38	#10597260	—	2	2	no	—
39	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
40	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
41	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	#41	1	2	yes	—
43	C₂×C₂²⋊D₁₉	—	2	2	no	—
44	#64541	—	4	2	no	—
45	#64541	—	4	2	no	—
46	C₂×D₇₆	—	2	2	no	—
47	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
48	C₂×C₄×D₁₉	—	2	2	no	—
49	C₂×Dic₃₈	C₄⋊C₄	1	2	yes	—
50	M₁₆×C₁₉	—	4	2	no	—
51	C₂×C₈×C₁₉	—	2	2	no	—
52	C₂×C₈×C₁₉	—	4	2	no	—
53	C₄²×C₁₉	C₂×D₄	1	2	yes	—
54	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
55	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
56	(C₂×D₁₉)⋊C₄	—	2	4	no	—
57	C₄⋊Dic₁₉	—	2	2	no	—
58	C₂×C₁₉⋊C₈	—	2	2	no	—
59	C₂×C₁₉⋊C₈	—	4	1	no	—
60	C₂×C₁₉⋊C₈	—	4	2	no	—
61	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	2	yes	—
62	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₁₉⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
64	#64515	—	4	4	no	—
65	C₈×D₁₉	—	4	4	no	—
66	#8630	—	19	1	no	maximal, Sylow
67	C₂³×C₁₉	#117	1	1	yes	characteristic
68	C₂²×D₁₉	—	2	2	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	4	2	no	—
72	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₉	#121	1	2	yes	—
75	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
76	C₂²⋊D₁₉	—	4	4	no	—
77	C₂×Dic₁₉	—	2	2	no	—
78	D₇₆	—	4	2	no	—
79	D₇₆	—	4	4	no	—
80	C₄×D₁₉	—	4	2	no	—
81	C₄×D₁₉	—	4	2	no	—
82	Dic₃₈	—	4	2	no	—
83	C₈×C₁₉	—	4	2	no	—
84	C₈×C₁₉	—	8	2	no	—
85	C₁₉⋊C₈	—	2	1	no	—
86	C₁₉⋊C₈	—	2	2	no	—
87	C₁₉⋊C₈	—	8	2	no	—
88	C₁₉⋊C₈	#100	1	2	yes	—
89	#2931	—	19	1	no	—
90	#1568	—	19	2	no	—
91	#1536	—	19	2	no	—
92	#1307	—	19	1	no	—
93	#1307	D₁₉	1	1	yes	characteristic, complemented
94	C₂²×C₁₉	—	2	1	no	—
95	C₂²×C₁₉	—	2	2	no	—
96	C₂²×C₁₉	#380	1	1	yes	characteristic
97	C₂×D₁₉	—	4	2	no	—
98	C₂×D₁₉	—	4	4	no	—
99	C₄×C₁₉	—	2	1	no	—
100	C₄×C₁₉	—	2	2	no	—
101	C₄×C₁₉	—	2	2	no	—
102	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
103	C₄×C₁₉	#413	1	1	yes	characteristic
104	Dic₁₉	—	4	2	no	—
105	C₂×#131	—	19	2	no	—
106	#532	—	19	1	no	—
107	#436	—	38	2	no	—
108	C₈×D₄	—	38	2	no	—
109	#432	—	19	2	no	—
110	#432	C₂×D₁₉	1	2	yes	—
111	#423	C₂×D₁₉	1	1	yes	characteristic
112	#408	—	19	2	no	—
113	C₂×C₄×C₈	—	19	1	no	—
114	#335	—	38	2	no	—
115	#334	—	38	2	no	—
116	#329	—	38	4	no	—
117	C₂×C₁₉	—	4	1	no	—
118	C₂×C₁₉	#1800	1	1	yes	characteristic
119	C₂×C₁₉	#1814	1	2	yes	—
120	D₁₉	—	8	2	no	—
121	C₂×#41	—	19	2	no	—
122	#131	—	76	4	no	—
123	C₂×M₁₆	—	38	2	no	—
124	C₂×M₁₆	C₄×D₁₉	1	2	yes	—
125	C₂²×C₈	—	19	1	no	—
126	C₂²×C₈	—	19	1	no	—
127	C₂²×C₈	—	38	2	no	—
128	C₄⋊Q₈	—	19	1	no	—
129	#127	—	19	1	no	—
130	#124	—	19	2	no	—
131	#121	—	38	2	no	—
132	C₄×D₄	—	38	2	no	—
133	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	2	2	no	—
136	C₄⋊C₈	—	38	2	no	—
137	C₂²⋊C₈	—	2	2	no	—
138	C₂²⋊C₈	—	38	4	no	—
139	C₂²⋊C₈	—	38	2	no	—
140	#97	—	2	2	no	—
141	#97	—	38	2	no	—
142	C₄×C₈	—	19	2	no	—
143	C₄×C₈	—	19	2	no	—
144	C₁₉	#8630	1	1	yes	characteristic, complemented, Sylow
145	#41	—	76	2	no	—
146	#41	—	76	2	no	—
147	C₂×Q₈	—	19	2	no	—
148	C₂×D₄	—	19	2	no	—
149	C₂×D₄	—	38	2	no	—
150	C₂×D₄	—	38	2	no	—
151	C₂²×C₄	—	38	2	no	—
152	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
153	C₂²×C₄	#64541	1	2	yes	—
154	M₁₆	—	4	2	no	—
155	M₁₆	—	76	4	no	—
156	C₂×C₈	—	2	2	no	—
157	C₂×C₈	—	4	2	no	—
158	C₂×C₈	—	19	1	no	—
159	C₂×C₈	—	19	2	no	—
160	C₂×C₈	—	19	1	no	—
161	C₂×C₈	—	38	2	no	—
162	C₂×C₈	—	76	4	no	—
163	C₂×C₈	—	76	1	no	—
164	C₂×C₈	—	76	2	no	—
165	C₄⋊C₄	—	38	2	no	—
166	C₂²⋊C₄	—	38	4	no	—
167	C₄²	D₄×D₁₉	1	2	yes	—
168	C₄²	D₄×D₁₉	1	1	yes	characteristic
169	C₄²	Q₈×D₁₉	1	1	yes	characteristic
170	C₂³	—	38	2	no	—
171	C₂³	#10597318	1	1	yes	characteristic
172	Q₈	—	76	2	no	—
173	D₄	—	76	2	no	—
174	D₄	—	76	4	no	—
175	D₄	—	76	4	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	4	2	no	—
179	C₂×C₄	—	38	2	no	—
180	C₂×C₄	—	76	2	no	—
181	C₂×C₄	—	76	2	no	—
182	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
183	C₂×C₄	#10597330	1	2	yes	—
184	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
185	C₂×C₄	#10597342	1	2	yes	—
186	C₈	—	4	2	no	—
187	C₈	—	8	2	no	—
188	C₈	—	19	2	no	—
189	C₈	—	38	1	no	—
190	C₈	—	38	2	no	—
191	C₈	—	152	2	no	—
192	C₂²	—	2	1	no	—
193	C₂²	—	2	2	no	—
194	C₂²	—	76	2	no	—
195	C₂²	—	76	4	no	—
196	C₂²	#11926403	1	1	yes	characteristic
197	C₄	—	2	1	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	2	no	—
200	C₄	—	76	2	no	—
201	C₄	#100×D₁₉	1	1	yes	characteristic
202	C₄	#11926527	1	1	yes	characteristic
203	C₂	—	4	1	no	—
204	C₂	—	152	2	no	—
205	C₂	#14563626	1	1	yes	characteristic
206	C₂	#14563688	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14572346

C₂

yes

maximal, characteristic

#14562396

C₂

yes

maximal, complemented

#14562269

C₂

yes

maximal

#14561546

C₂

yes

maximal, characteristic, complemented

C₁₉×#1307

C₂

yes

maximal, characteristic, complemented

C₂×#10597353

C₄

yes

—

#11927094

C₂²

yes

—

—

C₂²

yes

—

#11926512

C₄

yes

—

C₂×C₄×C₁₉⋊C₈

C₂²

yes

—

—

—

C₁₉×#432

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₂×#64541

C₂×C₄

yes

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

C₂²×C₁₉⋊C₈

C₂×C₄

yes

characteristic

#10597353

—

C₂×#64515

—

C₂×C₈×D₁₉

—

#10597321

D₄

yes

—

#10597320

Q₈

yes

characteristic

C₄×D₇₆

—

#10597315

Q₈

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₂²⋊(C₁₉⋊C₈)

—

(C₂×D₁₉)⋊C₈

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₄×C₁₉⋊C₈

D₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

C₂×C₂²⋊D₁₉

—

#64541

—

#64541

—

C₂×D₇₆

—

C₂×D₇₆

C₄⋊C₄

yes

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

C₄⋊C₄

yes

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×Q₈

yes

characteristic

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

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

#64515

—

C₈×D₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

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

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

D₇₆

—

D₇₆

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

C₈×C₁₉

—

C₈×C₁₉

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

—

C₁₉⋊C₈

#100

yes

—

—

—

—

—

D₁₉

yes

characteristic, complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#380

yes

characteristic

C₂×D₁₉

—

C₂×D₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

C₂×#100

yes

characteristic

103

C₄×C₁₉

#413

yes

characteristic

104

Dic₁₉

—

105

C₂×#131

—

106

#532

—

107

#436

—

108

C₈×D₄

—

109

#432

—

110

#432

C₂×D₁₉

yes

—

111

#423

C₂×D₁₉

yes

characteristic

112

#408

—

113

C₂×C₄×C₈

—

114

#335

—

115

#334

—

116

#329

—

117

C₂×C₁₉

—

118

C₂×C₁₉

#1800

yes

characteristic

119

C₂×C₁₉

#1814

yes

—

120

D₁₉

—

121

C₂×#41

—

122

#131

—

123

C₂×M₁₆

—

124

C₂×M₁₆

C₄×D₁₉

yes

—

125

C₂²×C₈

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₄⋊Q₈

—

129

#127

—

130

#124

—

131

#121

—

132

C₄×D₄

—

133

C₂×C₄²

C₂²×D₁₉

yes

characteristic

134

C₄⋊C₈

—

135

C₄⋊C₈

—

136

C₄⋊C₈

—

137

C₂²⋊C₈

—

138

C₂²⋊C₈

—

139

C₂²⋊C₈

—

140

#97

—

141

#97

—

142

C₄×C₈

—

143

C₄×C₈

—

144

C₁₉

#8630

yes

characteristic, complemented, Sylow

145

#41

—

146

#41

—

147

C₂×Q₈

—

148

C₂×D₄

—

149

C₂×D₄

—

150

C₂×D₄

—

151

C₂²×C₄

—

152

C₂²×C₄

C₂×C₄×D₁₉

yes

characteristic

153

C₂²×C₄

#64541

yes

—

154

M₁₆

—

155

M₁₆

—

156

C₂×C₈

—

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₄⋊C₄

—

166

C₂²⋊C₄

—

167

C₄²

D₄×D₁₉

yes

—

168

C₄²

D₄×D₁₉

yes

characteristic

169

C₄²

Q₈×D₁₉

yes

characteristic

170

C₂³

—

171

C₂³

#10597318

yes

characteristic

172

Q₈

—

173

D₄

—

174

D₄

—

175

D₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

183

C₂×C₄

#10597330

yes

—

184

C₂×C₄

C₄⋊C₄×D₁₉

yes

characteristic

185

C₂×C₄

#10597342

yes

—

186

C₈

—

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

191

C₈

—

152

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

#11926403

yes

characteristic

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

#100×D₁₉

yes

characteristic

202

C₄

#11926527

yes

characteristic

203

C₂

—

204

C₂

—

152

—

205

C₂

#14563626

yes

characteristic

206

C₂

#14563688

yes

—

	subgroup	G/H
center	C₂²	#11926403
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1307	C₂
socle	C₂²×C₁₉	#380
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1307	D₁₉
hypocenter	C₁₉	#8630
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

subgroup

G/H

center

C₂²

#11926403

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1307

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

N	H ≅ G/N	type
2. #14562396	C₂	semidirect
4. #14561546	C₂	semidirect
5. C₁₉×#1307	C₂	semidirect
93. #1307	D₁₉	semidirect
144. C₁₉	#8630	semidirect

H ≅ G/N

type

2. #14562396

C₂

semidirect

4. #14561546

C₂

semidirect

5. C₁₉×#1307

C₂

semidirect

93. #1307

D₁₉

semidirect

144. C₁₉

#8630

semidirect

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

subgroup	index
#14572346	2
#14562396	2
#14562269	2
#14561546	2
C₁₉×#1307	2
#8630	19

subgroup

index

C₁₉×#1307

Subgroups — #18075530

Conjugacy classes of subgroups

Complements

Maximal subgroups