Group #14574872 — subgroups

Subgroups — #14574872

Order 2432.

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

normal subgroups only

This group has 328 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	#11927099	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927073	C₂	1	1	yes	maximal, characteristic
3	#11926953	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926950	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926903	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926884	C₂	1	2	yes	maximal, complemented
7	#11926867	C₂	1	2	yes	maximal
8	#11926849	C₂	1	2	yes	maximal, complemented
9	#11926842	C₂	1	2	yes	maximal, complemented
10	#11926599	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₉×#124	C₂²	1	1	yes	characteristic
14	#10597392	—	2	1	no	—
15	#10597392	C₂²	1	1	yes	characteristic
16	Q₈×Dic₁₉	—	2	1	no	—
17	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic
18	#10597384	C₂²	1	1	yes	characteristic
19	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
20	#10597343	—	2	1	no	—
21	#10597338	C₂²	1	2	yes	—
22	#10597336	C₂²	1	2	yes	—
23	#10597333	—	2	1	no	—
24	#10597329	—	2	1	no	—
25	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
26	#10597325	—	2	1	no	—
27	#10597323	—	2	1	no	—
28	C₄²×D₁₉	C₂²	1	1	yes	characteristic
29	#10597316	C₂²	1	1	yes	characteristic
30	#10597315	C₂²	1	1	yes	characteristic
31	C₁₉×#103	C₂²	1	2	yes	—
32	C₁₉×#102	C₂²	1	2	yes	—
33	C₁₉×#97	C₂²	1	1	yes	characteristic
34	#10597292	C₂²	1	2	yes	—
35	#10597289	C₂²	1	2	yes	—
36	(C₂×D₁₉)⋊C₈	C₂²	1	2	yes	—
37	#10597275	C₂²	1	2	yes	—
38	#10597274	C₂²	1	2	yes	—
39	Dic₁₉⋊C₈	C₂²	1	2	yes	—
40	#10597265	C₂²	1	2	yes	—
41	#10597264	C₂²	1	2	yes	—
42	#10597260	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₁₉	—	2	1	no	—
44	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
45	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊D₁₉	—	2	1	no	—
47	C₂²×Dic₁₉	—	2	1	no	—
48	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
51	C₂×Dic₃₈	—	2	1	no	—
52	C₂×C₈×C₁₉	C₂³	1	2	yes	—
53	C₄⋊C₄×C₁₉	—	2	1	no	—
54	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
55	C₂²⋊C₄×C₁₉	—	2	1	no	—
56	C₂²⋊C₄×C₁₉	—	2	1	no	—
57	C₄²×C₁₉	C₂³	1	1	yes	characteristic
58	C₂²⋊Dic₁₉	—	2	1	no	—
59	C₂²⋊Dic₁₉	—	2	1	no	—
60	(C₂×D₁₉)⋊C₄	—	2	2	no	—
61	(C₂×D₁₉)⋊C₄	—	2	1	no	—
62	C₄⋊Dic₁₉	—	2	1	no	—
63	C₄⋊Dic₁₉	—	2	2	no	—
64	C₄⋊Dic₁₉	—	2	1	no	—
65	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
67	C₄⋊Dic₁₉	C₂³	1	2	yes	—
68	Dic₁₉⋊C₄	—	2	1	no	—
69	Dic₁₉⋊C₄	—	2	1	no	—
70	Dic₁₉⋊C₄	—	2	2	no	—
71	Dic₁₉⋊C₄	—	2	1	no	—
72	C₄×Dic₁₉	—	2	2	no	—
73	C₄×Dic₁₉	—	2	1	no	—
74	C₄×Dic₁₉	D₄	1	1	yes	characteristic
75	C₄×Dic₁₉	D₄	1	1	yes	characteristic
76	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
77	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
78	C₂³×C₁₉	—	2	1	no	—
79	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
80	Q₈×C₁₉	—	2	2	no	—
81	Q₈×C₁₉	—	4	2	no	—
82	D₄×C₁₉	—	2	2	no	—
83	C₂×C₄×C₁₉	—	2	1	no	—
84	C₂×C₄×C₁₉	—	2	2	no	—
85	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
88	C₂²⋊D₁₉	—	4	2	no	—
89	C₂×Dic₁₉	—	2	1	no	—
90	C₂×Dic₁₉	—	2	2	no	—
91	C₂×Dic₁₉	—	2	1	no	—
92	C₂×Dic₁₉	—	4	2	no	—
93	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
96	C₄×D₁₉	—	2	2	no	—
97	C₄×D₁₉	—	4	1	no	—
98	C₄×D₁₉	—	4	1	no	—
99	Dic₃₈	—	4	2	no	—
100	C₈×C₁₉	—	2	2	no	—
101	C₁₉⋊C₈	—	2	2	no	—
102	#3240	—	19	1	no	maximal, Sylow
103	C₂²×C₁₉	—	4	1	no	—
104	C₂²×C₁₉	—	4	1	no	—
105	C₂²×C₁₉	—	4	1	no	—
106	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
107	C₂×D₁₉	—	2	1	no	—
108	C₂×D₁₉	—	2	1	no	—
109	C₂×D₁₉	—	2	1	no	—
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	2	1	no	—
112	C₄×C₁₉	—	4	1	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
115	Dic₁₉	—	2	1	no	—
116	Dic₁₉	—	2	1	no	—
117	Dic₁₉	—	2	1	no	—
118	Dic₁₉	—	4	2	no	—
119	Dic₁₉	—	4	1	no	—
120	Dic₁₉	—	4	1	no	—
121	#533	—	19	1	no	—
122	#529	—	19	1	no	—
123	#501	—	19	1	no	—
124	#501	—	19	1	no	—
125	#489	—	19	1	no	—
126	#489	D₁₉	1	1	yes	characteristic, complemented
127	#485	—	19	2	no	—
128	#482	—	19	2	no	—
129	#479	—	19	2	no	—
130	#478	—	19	2	no	—
131	#432	—	19	1	no	—
132	C₂×C₁₉	—	8	1	no	—
133	C₂×C₁₉	#536	1	1	yes	characteristic
134	C₂×C₁₉	#575	1	1	yes	characteristic
135	C₂×C₁₉	#575	1	1	yes	characteristic
136	D₁₉	—	4	1	no	—
137	C₄⋊Q₈	—	19	1	no	—
138	C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
139	#126	—	38	1	no	—
140	#125	—	19	2	no	—
141	#125	—	19	1	no	—
142	#124	C₂×D₁₉	1	1	yes	characteristic
143	#123	—	38	1	no	—
144	C₂²⋊Q₈	—	19	1	no	—
145	C₂²⋊Q₈	—	38	1	no	—
146	C₂²⋊Q₈	—	38	1	no	—
147	#121	—	19	1	no	—
148	C₄×Q₈	—	19	1	no	—
149	C₄×Q₈	—	38	1	no	—
150	C₄×Q₈	—	38	1	no	—
151	C₄×D₄	—	19	1	no	—
152	C₄×D₄	—	38	1	no	—
153	#117	—	19	2	no	—
154	#117	—	38	1	no	—
155	C₂×C₄²	—	19	1	no	—
156	#107	—	19	2	no	—
157	#107	—	19	2	no	—
158	#106	—	19	2	no	—
159	#106	—	19	2	no	—
160	C₄⋊C₈	—	19	2	no	—
161	#103	—	19	2	no	—
162	#103	C₂×D₁₉	1	2	yes	—
163	#102	—	19	2	no	—
164	#102	C₂×D₁₉	1	2	yes	—
165	C₂²⋊C₈	—	19	2	no	—
166	#97	—	19	1	no	—
167	#97	C₂×D₁₉	1	1	yes	characteristic
168	C₁₉	#3240	1	1	yes	characteristic, complemented, Sylow
169	C₂×Q₈	—	2	1	no	—
170	C₂×Q₈	—	38	1	no	—
171	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
172	C₂×D₄	—	38	1	no	—
173	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
174	C₂²×C₄	—	19	1	no	—
175	C₂²×C₄	—	19	1	no	—
176	C₂²×C₄	—	19	1	no	—
177	C₂²×C₄	—	38	1	no	—
178	C₂×C₈	—	19	2	no	—
179	C₂×C₈	C₂²×D₁₉	1	2	yes	—
180	C₄⋊C₄	—	2	1	no	—
181	C₄⋊C₄	—	19	2	no	—
182	C₄⋊C₄	—	19	1	no	—
183	C₄⋊C₄	—	19	1	no	—
184	C₄⋊C₄	—	38	1	no	—
185	C₄⋊C₄	—	38	2	no	—
186	C₄⋊C₄	—	38	1	no	—
187	C₄⋊C₄	—	38	2	no	—
188	C₄⋊C₄	—	38	1	no	—
189	C₄⋊C₄	—	38	1	no	—
190	C₄⋊C₄	—	38	1	no	—
191	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
192	C₂²⋊C₄	—	2	1	no	—
193	C₂²⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	38	2	no	—
195	C₂²⋊C₄	—	38	1	no	—
196	C₂²⋊C₄	—	38	1	no	—
197	C₂²⋊C₄	—	38	1	no	—
198	C₄²	—	19	1	no	—
199	C₄²	—	19	1	no	—
200	C₄²	—	19	1	no	—
201	C₄²	—	38	2	no	—
202	C₄²	—	38	1	no	—
203	C₄²	C₂²×D₁₉	1	1	yes	characteristic
204	C₂³	—	2	1	no	—
205	C₂³	—	19	1	no	—
206	Q₈	—	2	2	no	—
207	Q₈	—	4	2	no	—
208	Q₈	—	76	2	no	—
209	D₄	—	2	2	no	—
210	D₄	—	76	2	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	19	1	no	—
214	C₂×C₄	—	19	1	no	—
215	C₂×C₄	—	19	1	no	—
216	C₂×C₄	—	38	2	no	—
217	C₂×C₄	—	38	1	no	—
218	C₂×C₄	—	38	2	no	—
219	C₂×C₄	—	38	1	no	—
220	C₂×C₄	—	76	1	no	—
221	C₂×C₄	—	76	1	no	—
222	C₂×C₄	—	76	2	no	—
223	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
224	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
225	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
226	C₈	—	2	2	no	—
227	C₈	—	38	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	—	4	1	no	—
231	C₂²	—	38	1	no	—
232	C₂²	—	38	1	no	—
233	C₂²	—	38	1	no	—
234	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
235	C₄	—	2	1	no	—
236	C₄	—	2	1	no	—
237	C₄	—	4	2	no	—
238	C₄	—	4	1	no	—
239	C₄	—	38	1	no	—
240	C₄	—	38	1	no	—
241	C₄	—	38	1	no	—
242	C₄	—	76	1	no	—
243	C₄	—	76	1	no	—
244	C₄	—	76	2	no	—
245	C₄	#10597436	1	2	yes	—
246	C₂	—	8	1	no	—
247	C₂	—	76	1	no	—
248	C₂	#11927114	1	1	yes	characteristic
249	C₂	#11927340	1	1	yes	characteristic
250	C₂	#11927343	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11927099

C₂

yes

maximal, characteristic, complemented

#11927073

C₂

yes

maximal, characteristic

#11926953

C₂

yes

maximal, characteristic, complemented

#11926950

C₂

yes

maximal, characteristic, complemented

#11926903

C₂

yes

maximal, characteristic, complemented

#11926884

C₂

yes

maximal, complemented

#11926867

C₂

yes

maximal

#11926849

C₂

yes

maximal, complemented

#11926842

C₂

yes

maximal, complemented

#11926599

C₂

yes

maximal, characteristic, complemented

C₁₉×#489

C₂

yes

maximal, characteristic, complemented

C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#124

C₂²

yes

characteristic

#10597392

—

#10597392

C₂²

yes

characteristic

Q₈×Dic₁₉

—

Q₈×Dic₁₉

C₂²

yes

characteristic

#10597384

C₂²

yes

characteristic

D₄×Dic₁₉

C₂²

yes

characteristic

#10597343

—

#10597338

C₂²

yes

—

#10597336

C₂²

yes

—

#10597333

—

#10597329

—

(C₂²⋊D₁₉)⋊C₄

—

#10597325

—

#10597323

—

C₄²×D₁₉

C₂²

yes

characteristic

#10597316

C₂²

yes

characteristic

#10597315

C₂²

yes

characteristic

C₁₉×#103

C₂²

yes

—

C₁₉×#102

C₂²

yes

—

C₁₉×#97

C₂²

yes

characteristic

#10597292

C₂²

yes

—

#10597289

C₂²

yes

—

(C₂×D₁₉)⋊C₈

C₂²

yes

—

#10597275

C₂²

yes

—

#10597274

C₂²

yes

—

Dic₁₉⋊C₈

C₂²

yes

—

#10597265

C₂²

yes

—

#10597264

C₂²

yes

—

#10597260

C₂²

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂³

yes

characteristic

C₂×D₄×C₁₉

C₂³

yes

characteristic

C₂×C₂²⋊D₁₉

—

C₂²×Dic₁₉

—

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

D₄

yes

characteristic

C₂×C₄×D₁₉

C₂³

yes

characteristic

C₂×Dic₃₈

—

C₂×C₈×C₁₉

C₂³

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂³

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂³

yes

characteristic

C₂²⋊Dic₁₉

—

C₂²⋊Dic₁₉

—

(C₂×D₁₉)⋊C₄

—

(C₂×D₁₉)⋊C₄

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

characteristic

C₄⋊Dic₁₉

C₂³

yes

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

D₄

yes

characteristic

C₄×Dic₁₉

C₂³

yes

characteristic

C₂×C₁₉⋊C₈

C₂³

yes

—

C₂³×C₁₉

—

C₂²×D₁₉

C₂×D₄

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂×C₄×C₁₉

C₂⁴

yes

characteristic

C₂²⋊D₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

—

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₂×Dic₁₉

C₂×D₄

yes

characteristic

C₄×D₁₉

—

C₄×D₁₉

—

C₄×D₁₉

—

Dic₃₈

—

100

C₈×C₁₉

—

101

C₁₉⋊C₈

—

102

#3240

—

maximal, Sylow

103

C₂²×C₁₉

—

104

C₂²×C₁₉

—

105

C₂²×C₁₉

—

106

C₂²×C₁₉

C₂²×D₄

yes

characteristic

107

C₂×D₁₉

—

108

C₂×D₁₉

—

109

C₂×D₁₉

—

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

2₋¹⁺⁴

yes

—

115

Dic₁₉

—

116

Dic₁₉

—

117

Dic₁₉

—

118

Dic₁₉

—

119

Dic₁₉

—

120

Dic₁₉

—

121

#533

—

122

#529

—

123

#501

—

124

#501

—

125

#489

—

126

#489

D₁₉

yes

characteristic, complemented

127

#485

—

128

#482

—

129

#479

—

130

#478

—

131

#432

—

132

C₂×C₁₉

—

133

C₂×C₁₉

#536

yes

characteristic

134

C₂×C₁₉

#575

yes

characteristic

135

C₂×C₁₉

#575

yes

characteristic

136

D₁₉

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

C₂×D₁₉

yes

characteristic

139

#126

—

140

#125

—

141

#125

—

142

#124

C₂×D₁₉

yes

characteristic

143

#123

—

144

C₂²⋊Q₈

—

145

C₂²⋊Q₈

—

146

C₂²⋊Q₈

—

147

#121

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

C₄×Q₈

—

151

C₄×D₄

—

152

C₄×D₄

—

153

#117

—

154

#117

—

155

C₂×C₄²

—

156

#107

—

157

#107

—

158

#106

—

159

#106

—

160

C₄⋊C₈

—

161

#103

—

162

#103

C₂×D₁₉

yes

—

163

#102

—

164

#102

C₂×D₁₉

yes

—

165

C₂²⋊C₈

—

166

#97

—

167

#97

C₂×D₁₉

yes

characteristic

168

C₁₉

#3240

yes

characteristic, complemented, Sylow

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂×Q₈

C₂²×D₁₉

yes

characteristic

172

C₂×D₄

—

173

C₂×D₄

C₂²×D₁₉

yes

characteristic

174

C₂²×C₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

C₂²×C₄

—

178

C₂×C₈

—

179

C₂×C₈

C₂²×D₁₉

yes

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

C₂²×D₁₉

yes

—

192

C₂²⋊C₄

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₂²⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

—

202

C₄²

—

203

C₄²

C₂²×D₁₉

yes

characteristic

204

C₂³

—

205

C₂³

—

206

Q₈

—

207

Q₈

—

208

Q₈

—

209

D₄

—

210

D₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

D₄×D₁₉

yes

characteristic

224

C₂×C₄

D₄×D₁₉

yes

characteristic

225

C₂×C₄

C₂³×D₁₉

yes

characteristic

226

C₈

—

227

C₈

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

234

C₂²

C₂×D₄×D₁₉

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

—

242

C₄

—

243

C₄

—

244

C₄

—

245

C₄

#10597436

yes

—

246

C₂

—

247

C₂

—

248

C₂

#11927114

yes

characteristic

249

C₂

#11927340

yes

characteristic

250

C₂

#11927343

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#489	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	#10597384	C₂²
hypercenter	#489	D₁₉
hypocenter	C₁₉	#3240
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #489

subgroup

G/H

center

C₂²

C₂×D₄×D₁₉

commutator, cosocle

C₂×C₄×C₁₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₉

Fitting

C₁₉×#489

C₂

socle

C₂²×C₁₉

C₂²×D₄

C₂²

D₁₉

C₁₉

G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #489

N	H ≅ G/N	type
1. #11927099	C₂	semidirect
3. #11926953	C₂	semidirect
4. #11926950	C₂	semidirect
5. #11926903	C₂	semidirect
6. #11926884	C₂	semidirect
8. #11926849	C₂	semidirect
9. #11926842	C₂	semidirect
10. #11926599	C₂	semidirect
11. C₁₉×#489	C₂	semidirect
126. #489	D₁₉	semidirect
168. C₁₉	#3240	semidirect

H ≅ G/N

type

1. #11927099

C₂

semidirect

3. #11926953

C₂

semidirect

4. #11926950

C₂

semidirect

5. #11926903

C₂

semidirect

6. #11926884

C₂

semidirect

8. #11926849

C₂

semidirect

9. #11926842

C₂

semidirect

10. #11926599

C₂

semidirect

11. C₁₉×#489

C₂

semidirect

126. #489

D₁₉

semidirect

168. C₁₉

#3240

semidirect

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

subgroup	index
#11927099	2
#11927073	2
#11926953	2
#11926950	2
#11926903	2
#11926884	2
#11926867	2
#11926849	2
#11926842	2
#11926599	2
C₁₉×#489	2
#3240	19

subgroup

index

C₁₉×#489

Subgroups — #14574872

Conjugacy classes of subgroups

Complements

Maximal subgroups