Group #18081927 — subgroups

Subgroups — #18081927

Order 4864.

408 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14573958	C₂	1	1	yes	maximal, characteristic
2	#14563799	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562200	C₂	1	2	yes	maximal, complemented
4	#14562196	C₂	1	2	yes	maximal
5	C₁₉×#1452	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927101	C₂²	1	1	yes	characteristic
7	#11927094	C₂²	1	1	yes	characteristic
8	#11926899	—	2	2	no	—
9	#11926895	C₄	1	2	yes	complemented
10	#11926891	C₄	1	2	yes	complemented
11	C₂×#10597275	—	2	1	no	—
12	C₂×#10597274	—	2	1	no	—
13	#11926541	—	2	1	no	—
14	#11926541	—	2	1	no	—
15	#11926410	C₂²	1	2	yes	—
16	#11926282	—	2	4	no	—
17	#11926279	—	2	4	no	—
18	C₁₉×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#322	—	2	2	no	—
21	C₂×#64541	—	2	1	no	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	#10597376	—	2	2	no	—
26	#10597372	—	2	1	no	—
27	C₂×C₄⋊Dic₁₉	—	2	2	no	—
28	#10597370	—	2	2	no	—
29	#10597321	—	2	1	no	—
30	#10597320	C₂×C₄	1	1	yes	characteristic
31	C₄×D₇₆	—	2	2	no	—
32	#10597316	—	2	1	no	—
33	#10597315	C₂×C₄	1	1	yes	characteristic
34	#10597315	C₂×C₄	1	2	yes	—
35	C₄×Dic₃₈	—	2	2	no	—
36	C₁₉×C₄⋊C₈	—	2	2	no	—
37	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
38	C₄×C₈×C₁₉	—	2	2	no	—
39	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₁₉⋊#95	—	2	2	no	—
42	C₁₉⋊#95	—	2	2	no	—
43	#10597278	—	2	2	no	—
44	#10597278	—	2	2	no	—
45	#10597275	—	4	2	no	—
46	#10597274	—	4	2	no	—
47	#10597273	—	2	2	no	—
48	#10597273	—	2	2	no	—
49	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
50	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
51	C₂×C₂²⋊D₁₉	—	4	1	no	—
52	C₂²×Dic₁₉	—	4	2	no	—
53	#64541	—	4	1	no	—
54	#64541	—	4	1	no	—
55	#64541	—	4	1	no	—
56	#64541	—	4	1	no	—
57	C₂×D₇₆	—	2	1	no	—
58	C₂×D₇₆	—	2	2	no	—
59	C₂×C₄×D₁₉	—	4	1	no	—
60	C₂×Dic₃₈	—	2	1	no	—
61	C₂×Dic₃₈	—	2	2	no	—
62	C₂×C₈×C₁₉	—	2	1	no	—
63	C₂×C₈×C₁₉	—	2	1	no	—
64	C₂×C₈×C₁₉	—	2	1	no	—
65	C₂×C₈×C₁₉	—	2	1	no	—
66	C₂×C₈×C₁₉	—	2	4	no	—
67	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
70	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₁₉	#41	1	2	yes	—
72	C₂²⋊Dic₁₉	—	4	1	no	—
73	(C₂×D₁₉)⋊C₄	—	4	2	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	C₄⋊Dic₁₉	—	2	2	no	—
76	C₄⋊Dic₁₉	—	2	2	no	—
77	C₄⋊Dic₁₉	—	4	2	no	—
78	C₄⋊Dic₁₉	—	4	2	no	—
79	Dic₁₉⋊C₄	—	4	2	no	—
80	C₄×Dic₁₉	—	4	1	no	—
81	#9758	—	19	1	no	maximal, Sylow
82	C₂³×C₁₉	#127	1	1	yes	characteristic
83	C₂²×D₁₉	—	4	1	no	—
84	C₂×C₄×C₁₉	—	4	2	no	—
85	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
87	C₂×C₄×C₁₉	#121	1	2	yes	—
88	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
89	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
91	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
92	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
93	C₂²⋊D₁₉	—	8	1	no	—
94	C₂²⋊D₁₉	—	8	1	no	—
95	C₂×Dic₁₉	—	4	2	no	—
96	C₂×Dic₁₉	—	4	1	no	—
97	C₂×Dic₁₉	—	8	4	no	—
98	C₂×Dic₁₉	—	8	2	no	—
99	D₇₆	—	4	1	no	—
100	D₇₆	—	4	1	no	—
101	D₇₆	—	8	2	no	—
102	C₄×D₁₉	—	8	1	no	—
103	C₄×D₁₉	—	8	1	no	—
104	Dic₃₈	—	4	1	no	—
105	Dic₃₈	—	4	1	no	—
106	Dic₃₈	—	8	2	no	—
107	C₈×C₁₉	—	2	2	no	—
108	C₈×C₁₉	—	2	2	no	—
109	C₈×C₁₉	—	4	4	no	—
110	#3131	—	19	1	no	—
111	#1846	—	19	1	no	—
112	#1518	—	19	2	no	—
113	#1517	—	19	2	no	—
114	#1452	D₁₉	1	1	yes	characteristic, complemented
115	C₂²×C₁₉	—	2	2	no	—
116	C₂²×C₁₉	#390	1	1	yes	characteristic
117	C₂²×C₁₉	#496	1	1	yes	characteristic
118	C₂²×C₁₉	#497	1	1	yes	characteristic
119	C₂×D₁₉	—	8	1	no	—
120	C₂×D₁₉	—	8	2	no	—
121	C₄×C₁₉	—	2	2	no	—
122	C₄×C₁₉	—	2	2	no	—
123	C₄×C₁₉	#417	1	1	yes	characteristic
124	C₄×C₁₉	#417	1	1	yes	characteristic
125	C₄×C₁₉	#489	1	1	yes	characteristic
126	C₄×C₁₉	#489	1	1	yes	characteristic
127	Dic₁₉	—	8	1	no	—
128	Dic₁₉	—	8	2	no	—
129	Dic₁₉	—	16	2	no	—
130	#533	—	19	1	no	—
131	#532	—	19	1	no	—
132	#488	—	38	2	no	—
133	#487	—	19	2	no	—
134	#486	—	19	2	no	—
135	#431	C₂×D₁₉	1	2	yes	—
136	C₂×#107	—	38	1	no	—
137	C₂×#106	—	38	1	no	—
138	#416	—	38	1	no	—
139	#416	—	38	1	no	—
140	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
141	#382	—	19	2	no	—
142	#328	—	38	4	no	—
143	#327	—	38	4	no	—
144	#322	—	2	2	no	—
145	C₂×C₁₉	—	2	1	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	#1959	1	1	yes	characteristic
148	C₂×C₁₉	#1976	1	2	yes	—
149	D₁₉	—	16	1	no	—
150	C₂×#41	—	38	1	no	—
151	C₂²×C₈	D₇₆	1	1	yes	characteristic
152	C₂²×C₈	D₇₆	1	1	yes	characteristic
153	C₄⋊Q₈	—	19	1	no	—
154	C₄⋊Q₈	—	19	2	no	—
155	#127	—	19	1	no	—
156	#125	—	38	1	no	—
157	#124	—	38	1	no	—
158	C₂²⋊Q₈	—	38	2	no	—
159	#121	—	38	2	no	—
160	C₄×Q₈	—	38	2	no	—
161	C₄×D₄	—	38	2	no	—
162	#117	—	38	1	no	—
163	C₂×C₄⋊C₄	—	38	2	no	—
164	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
165	#107	—	76	2	no	—
166	#106	—	76	2	no	—
167	C₄⋊C₈	—	2	2	no	—
168	#103	—	38	2	no	—
169	#103	—	38	2	no	—
170	#102	—	38	2	no	—
171	#102	—	38	2	no	—
172	C₂²⋊C₈	D₇₆	1	4	yes	—
173	C₄×C₈	—	2	2	no	—
174	C₄×C₈	C₄×D₁₉	1	2	yes	—
175	C₄×C₈	C₂²⋊D₁₉	1	2	yes	—
176	#95	—	38	2	no	—
177	#95	—	38	2	no	—
178	C₁₉	#9758	1	1	yes	characteristic, complemented, Sylow
179	#41	—	76	1	no	—
180	#41	—	76	1	no	—
181	#41	—	76	1	no	—
182	#41	—	76	1	no	—
183	C₂×Q₈	—	38	2	no	—
184	C₂×Q₈	—	38	1	no	—
185	C₂×D₄	—	38	2	no	—
186	C₂×D₄	—	38	1	no	—
187	C₂×D₄	—	76	1	no	—
188	C₂²×C₄	—	76	1	no	—
189	C₂²×C₄	—	76	2	no	—
190	C₂²×C₄	C₂×D₇₆	1	2	yes	—
191	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	2	1	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	4	no	—
197	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
198	C₂×C₈	(C₂×D₁₉)⋊C₄	1	2	yes	—
199	C₄⋊C₄	—	38	2	no	—
200	C₄⋊C₄	—	38	2	no	—
201	C₄⋊C₄	—	38	2	no	—
202	C₄⋊C₄	—	76	2	no	—
203	C₄⋊C₄	—	76	2	no	—
204	C₄⋊C₄	—	76	2	no	—
205	C₂²⋊C₄	—	76	1	no	—
206	C₂²⋊C₄	—	76	2	no	—
207	C₄²	—	76	1	no	—
208	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
209	C₄²	#64541	1	2	yes	—
210	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
211	C₂³	—	76	1	no	—
212	C₂³	#10597320	1	1	yes	characteristic
213	Q₈	—	76	1	no	—
214	Q₈	—	76	1	no	—
215	Q₈	—	152	2	no	—
216	D₄	—	76	1	no	—
217	D₄	—	76	1	no	—
218	D₄	—	152	2	no	—
219	D₄	—	152	1	no	—
220	D₄	—	152	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	76	2	no	—
223	C₂×C₄	—	76	1	no	—
224	C₂×C₄	—	152	4	no	—
225	C₂×C₄	—	152	2	no	—
226	C₂×C₄	—	152	1	no	—
227	C₂×C₄	—	152	1	no	—
228	C₂×C₄	C₄×D₇₆	1	2	yes	—
229	C₂×C₄	#10597321	1	1	yes	characteristic
230	C₂×C₄	#10597354	1	1	yes	characteristic
231	C₂×C₄	#10597354	1	1	yes	characteristic
232	C₂×C₄	#10597355	1	1	yes	characteristic
233	C₂×C₄	#10597355	1	1	yes	characteristic
234	C₂×C₄	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
235	C₂×C₄	#10597376	1	2	yes	—
236	C₈	—	2	2	no	—
237	C₈	—	2	2	no	—
238	C₈	—	4	4	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	152	1	no	—
241	C₂²	—	152	2	no	—
242	C₂²	#11926446	1	1	yes	characteristic
243	C₂²	#11926933	1	1	yes	characteristic
244	C₂²	#11926938	1	1	yes	characteristic
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	304	2	no	—
248	C₄	—	152	1	no	—
249	C₄	—	152	2	no	—
250	C₄	#11926546	1	1	yes	characteristic
251	C₄	#11926546	1	1	yes	characteristic
252	C₄	#11926904	1	1	yes	characteristic
253	C₄	#11926904	1	1	yes	characteristic
254	C₂	—	2	1	no	—
255	C₂	—	2	1	no	—
256	C₂	—	304	1	no	—
257	C₂	#14564451	1	1	yes	characteristic
258	C₂	#14564533	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14573958

C₂

yes

maximal, characteristic

#14563799

C₂

yes

maximal, characteristic, complemented

#14562200

C₂

yes

maximal, complemented

#14562196

C₂

yes

maximal

C₁₉×#1452

C₂

yes

maximal, characteristic, complemented

#11927101

C₂²

yes

characteristic

#11927094

C₂²

yes

characteristic

#11926899

—

#11926895

C₄

yes

complemented

#11926891

C₄

yes

—

—

—

—

C₂²

yes

—

#11926282

—

#11926279

—

C₁₉×#431

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#322

—

C₂×#64541

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597376

—

#10597372

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597321

—

#10597320

C₂×C₄

yes

characteristic

C₄×D₇₆

—

#10597316

—

#10597315

C₂×C₄

yes

characteristic

#10597315

C₂×C₄

yes

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

D₄

yes

—

C₄×C₈×C₁₉

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

C₁₉⋊#95

—

C₁₉⋊#95

—

—

—

—

—

—

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

—

—

—

—

C₂×D₇₆

—

C₂×D₇₆

—

C₂×C₄×D₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

—

C₂³×C₁₉

yes

C₂²×D₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂×C₄×C₁₉

yes

C₂²⋊D₁₉

—

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

D₇₆

—

100

D₇₆

—

101

D₇₆

—

102

C₄×D₁₉

—

103

C₄×D₁₉

—

104

Dic₃₈

—

105

Dic₃₈

—

106

Dic₃₈

—

107

C₈×C₁₉

—

108

C₈×C₁₉

—

109

C₈×C₁₉

—

110

#3131

—

111

#1846

—

112

#1518

—

113

#1517

—

114

#1452

D₁₉

yes

characteristic, complemented

115

C₂²×C₁₉

—

116

C₂²×C₁₉

#390

yes

characteristic

117

C₂²×C₁₉

#496

yes

characteristic

118

C₂²×C₁₉

#497

yes

characteristic

119

C₂×D₁₉

—

120

C₂×D₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

—

123

C₄×C₁₉

#417

yes

characteristic

124

C₄×C₁₉

#417

yes

characteristic

125

C₄×C₁₉

#489

yes

characteristic

126

C₄×C₁₉

#489

yes

characteristic

127

Dic₁₉

—

128

Dic₁₉

—

129

Dic₁₉

—

130

#533

—

131

#532

—

132

#488

—

133

#487

—

134

#486

—

135

#431

C₂×D₁₉

yes

—

136

C₂×#107

—

137

C₂×#106

—

138

#416

—

139

#416

—

140

C₂×C₄×C₈

C₂×D₁₉

yes

characteristic

141

#382

—

142

#328

—

143

#327

—

144

#322

—

145

C₂×C₁₉

—

146

C₂×C₁₉

—

147

C₂×C₁₉

#1959

yes

characteristic

148

C₂×C₁₉

#1976

yes

—

149

D₁₉

—

150

C₂×#41

—

151

C₂²×C₈

D₇₆

yes

characteristic

152

C₂²×C₈

D₇₆

yes

characteristic

153

C₄⋊Q₈

—

154

C₄⋊Q₈

—

155

#127

—

156

#125

—

157

#124

—

158

C₂²⋊Q₈

—

159

#121

—

160

C₄×Q₈

—

161

C₄×D₄

—

162

#117

—

163

C₂×C₄⋊C₄

—

164

C₂×C₄²

C₂²×D₁₉

yes

characteristic

165

#107

—

166

#106

—

167

C₄⋊C₈

—

168

#103

—

169

#103

—

170

#102

—

171

#102

—

172

C₂²⋊C₈

D₇₆

yes

—

173

C₄×C₈

—

174

C₄×C₈

C₄×D₁₉

yes

—

175

C₄×C₈

C₂²⋊D₁₉

yes

—

176

#95

—

177

#95

—

178

C₁₉

#9758

yes

characteristic, complemented, Sylow

179

#41

—

180

#41

—

181

#41

—

182

#41

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

C₂×D₇₆

yes

—

191

C₂²×C₄

C₂×D₇₆

yes

characteristic

192

C₂×C₈

—

193

C₂×C₈

—

194

C₂×C₈

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

198

C₂×C₈

(C₂×D₁₉)⋊C₄

yes

—

199

C₄⋊C₄

—

200

C₄⋊C₄

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₂²⋊C₄

—

206

C₂²⋊C₄

—

207

C₄²

—

208

C₄²

C₂×C₄×D₁₉

yes

characteristic

209

C₄²

#64541

yes

—

210

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

211

C₂³

—

212

C₂³

#10597320

yes

characteristic

213

Q₈

—

214

Q₈

—

215

Q₈

—

152

—

216

D₄

—

217

D₄

—

218

D₄

—

152

—

219

D₄

—

152

—

220

D₄

—

152

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

152

—

225

C₂×C₄

—

152

—

226

C₂×C₄

—

152

—

227

C₂×C₄

—

152

—

228

C₂×C₄

C₄×D₇₆

yes

—

229

C₂×C₄

#10597321

yes

characteristic

230

C₂×C₄

#10597354

yes

characteristic

231

C₂×C₄

#10597354

yes

characteristic

232

C₂×C₄

#10597355

yes

characteristic

233

C₂×C₄

#10597355

yes

characteristic

234

C₂×C₄

C₂×(C₂×D₁₉)⋊C₄

yes

characteristic

235

C₂×C₄

#10597376

yes

—

236

C₈

—

237

C₈

—

238

C₈

—

239

C₂²

—

240

C₂²

—

152

—

241

C₂²

—

152

—

242

C₂²

#11926446

yes

characteristic

243

C₂²

#11926933

yes

characteristic

244

C₂²

#11926938

yes

characteristic

245

C₄

—

246

C₄

—

247

C₄

—

304

—

248

C₄

—

152

—

249

C₄

—

152

—

250

C₄

#11926546

yes

characteristic

251

C₄

#11926546

yes

characteristic

252

C₄

#11926904

yes

characteristic

253

C₄

#11926904

yes

characteristic

254

C₂

—

255

C₂

—

256

C₂

—

304

—

257

C₂

#14564451

yes

characteristic

258

C₂

#14564533

yes

—

	subgroup	G/H
center	C₂²	#11926446
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1452	C₂
socle	C₂²×C₁₉	#390
prime radical	#11927094	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1452	D₁₉
hypocenter	C₁₉	#9758
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

subgroup

G/H

center

C₂²

#11926446

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1452

C₂

C₂²×C₁₉

C₂²

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1452

N	H ≅ G/N	type
2. #14563799	C₂	semidirect
3. #14562200	C₂	semidirect
5. C₁₉×#1452	C₂	semidirect
9. #11926895	C₄	semidirect
10. #11926891	C₄	semidirect
114. #1452	D₁₉	semidirect
178. C₁₉	#9758	semidirect

H ≅ G/N

type

2. #14563799

C₂

semidirect

3. #14562200

C₂

semidirect

5. C₁₉×#1452

C₂

semidirect

9. #11926895

C₄

semidirect

10. #11926891

C₄

semidirect

114. #1452

D₁₉

semidirect

178. C₁₉

#9758

semidirect

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

subgroup	index
#14573958	2
#14563799	2
#14562200	2
#14562196	2
C₁₉×#1452	2
#9758	19

subgroup

index

C₁₉×#1452

Subgroups — #18081927

Conjugacy classes of subgroups

Complements

Maximal subgroups