Group #18083481 — subgroups

Subgroups — #18083481

Order 4864.

512 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 512 conjugacy classes of subgroups — too many to draw. Only its 85 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	#14573753	C₂	1	2	yes	maximal, complemented
2	#14564574	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562246	C₂	1	2	yes	maximal, complemented
4	#14561505	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#3245	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
7	#11926855	—	2	2	no	—
8	#11926836	—	2	2	no	—
9	#11926741	—	2	2	no	—
10	#11926682	—	2	2	no	—
11	#11926644	—	2	4	no	—
12	#11926601	C₂²	1	2	yes	—
13	C₂×#10597260	C₂²	1	1	yes	characteristic
14	#11926298	—	2	2	no	—
15	#11926284	—	2	4	no	—
16	C₁₉×#532	C₂²	1	2	yes	—
17	C₁₉×#474	—	2	2	no	—
18	C₁₉×#466	—	2	2	no	—
19	C₁₉×#459	—	2	2	no	—
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×#41×C₁₉	—	2	2	no	—
22	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
23	C₂×D₈×C₁₉	—	2	2	no	—
24	C₂²×C₈×C₁₉	D₄	1	2	yes	—
25	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
26	C₁₉×#127	D₄	1	2	yes	—
27	C₁₉×#124	—	2	2	no	—
28	C₁₉×#121	—	2	2	no	—
29	C₁₉×#121	—	2	2	no	—
30	C₄×D₄×C₁₉	—	2	2	no	—
31	C₄×D₄×C₁₉	—	2	2	no	—
32	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
33	C₂×#64526	—	2	4	no	—
34	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
35	C₂×Dic₁₉⋊C₄	—	2	1	no	—
36	C₂×C₄×Dic₁₉	—	2	1	no	—
37	C₂²×C₁₉⋊C₈	—	2	1	no	—
38	C₄×Dic₃₈	—	2	2	no	—
39	C₄×Dic₃₈	—	2	2	no	—
40	C₁₉×#107	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×#102	—	2	4	no	—
43	#10597289	—	2	4	no	—
44	C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
45	#10597267	—	2	4	no	—
46	#10597264	—	2	4	no	—
47	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
48	#10597260	—	2	2	no	—
49	#10597260	D₄	1	4	yes	—
50	#41×C₁₉	—	8	4	no	—
51	C₂×Q₈×C₁₉	—	2	2	no	—
52	C₂×D₄×C₁₉	—	2	2	no	—
53	C₂×D₄×C₁₉	—	2	2	no	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	4	2	no	—
56	C₂²×C₄×C₁₉	—	4	2	no	—
57	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
60	C₂²×Dic₁₉	—	2	1	no	—
61	C₂²×Dic₁₉	—	2	1	no	—
62	C₂×Dic₃₈	—	2	2	no	—
63	C₂×Dic₃₈	—	4	2	no	—
64	D₈×C₁₉	—	8	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	4	2	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₂²⋊C₄×C₁₉	—	4	2	no	—
70	C₂²⋊C₄×C₁₉	—	4	2	no	—
71	C₄²×C₁₉	C₂×D₄	1	2	yes	—
72	C₄²×C₁₉	C₂×D₄	1	2	yes	—
73	#64526	—	4	8	no	—
74	C₄⋊Dic₁₉	—	2	2	no	—
75	Dic₁₉⋊C₄	—	4	2	no	—
76	C₄×Dic₁₉	—	4	1	no	—
77	C₄×Dic₁₉	—	4	1	no	—
78	C₂×C₁₉⋊C₈	—	2	2	no	—
79	C₂×C₁₉⋊C₈	—	2	4	no	—
80	C₂×C₁₉⋊C₈	—	4	1	no	—
81	C₂×C₁₉⋊C₈	—	4	1	no	—
82	#10028	—	19	1	no	maximal, Sylow
83	C₂³×C₁₉	—	4	2	no	—
84	C₂³×C₁₉	#121	1	1	yes	characteristic
85	Q₈×C₁₉	—	8	2	no	—
86	D₄×C₁₉	—	4	4	no	—
87	D₄×C₁₉	—	4	2	no	—
88	D₄×C₁₉	—	4	2	no	—
89	D₄×C₁₉	—	8	2	no	—
90	D₄×C₁₉	—	8	4	no	—
91	C₂×C₄×C₁₉	—	2	2	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	8	4	no	—
97	C₂×C₄×C₁₉	#120	1	2	yes	—
98	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
99	C₂×C₄×C₁₉	#121	1	2	yes	—
100	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
101	C₂×Dic₁₉	—	2	2	no	—
102	C₂×Dic₁₉	—	4	1	no	—
103	C₂×Dic₁₉	—	4	1	no	—
104	C₂×Dic₁₉	—	4	1	no	—
105	C₂×Dic₁₉	—	4	2	no	—
106	Dic₃₈	—	2	4	no	—
107	Dic₃₈	—	4	2	no	—
108	C₈×C₁₉	—	4	2	no	—
109	C₁₉⋊C₈	—	4	2	no	—
110	C₁₉⋊C₈	—	4	4	no	—
111	#3245	D₁₉	1	1	yes	characteristic
112	#3112	—	19	2	no	—
113	#1985	—	19	1	no	—
114	#1530	—	19	2	no	—
115	#1290	—	19	1	no	—
116	C₂²×C₁₉	—	2	1	no	—
117	C₂²×C₁₉	—	2	1	no	—
118	C₂²×C₁₉	—	8	2	no	—
119	C₂²×C₁₉	—	8	2	no	—
120	C₂²×C₁₉	—	8	2	no	—
121	C₂²×C₁₉	#392	1	1	yes	characteristic
122	C₂²×C₁₉	#472	1	2	yes	—
123	C₄×C₁₉	—	2	1	no	—
124	C₄×C₁₉	—	2	2	no	—
125	C₄×C₁₉	—	2	2	no	—
126	C₄×C₁₉	—	8	2	no	—
127	C₄×C₁₉	#455	1	1	yes	characteristic
128	C₄×C₁₉	#456	1	1	yes	characteristic
129	Dic₁₉	—	4	2	no	—
130	Dic₁₉	—	8	1	no	—
131	#532	C₂×D₁₉	1	2	yes	—
132	C₂×C₄×Q₈	—	19	1	no	—
133	#480	—	38	2	no	—
134	#477	—	38	2	no	—
135	#474	—	2	2	no	—
136	#466	—	2	2	no	—
137	#460	—	38	2	no	—
138	#459	—	2	2	no	—
139	#448	—	38	2	no	—
140	#440	—	38	4	no	—
141	#432	—	19	2	no	—
142	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
143	C₂×#97	—	19	1	no	—
144	#336	—	38	2	no	—
145	#329	—	38	4	no	—
146	C₂×C₁₉	—	2	2	no	—
147	C₂×C₁₉	—	16	2	no	—
148	C₂×C₁₉	#2007	1	1	yes	characteristic
149	C₂×C₁₉	#2010	1	1	yes	characteristic
150	C₂×C₁₉	#2018	1	1	yes	characteristic
151	C₂×#41	—	2	2	no	—
152	C₂²×Q₈	—	19	1	no	—
153	C₂×SD₁₆	—	38	4	no	—
154	C₂×D₈	—	2	2	no	—
155	C₂²×C₈	—	38	1	no	—
156	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
157	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
158	#127	C₂²⋊D₁₉	1	2	yes	—
159	#124	—	2	2	no	—
160	#121	—	2	2	no	—
161	#121	—	2	2	no	—
162	C₄×Q₈	—	38	2	no	—
163	C₄×Q₈	—	38	2	no	—
164	C₄×D₄	—	2	2	no	—
165	C₄×D₄	—	2	2	no	—
166	C₂×C₄⋊C₄	—	19	1	no	—
167	C₂×C₄⋊C₄	—	38	1	no	—
168	C₂×C₄²	—	38	1	no	—
169	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
170	#107	—	2	2	no	—
171	#107	—	38	4	no	—
172	C₄⋊C₈	—	2	2	no	—
173	C₄⋊C₈	—	38	2	no	—
174	#103	—	38	4	no	—
175	#102	—	2	4	no	—
176	#102	—	38	4	no	—
177	C₂²⋊C₈	—	38	2	no	—
178	#97	—	19	4	no	—
179	#97	—	38	2	no	—
180	C₁₉	#10028	1	1	yes	characteristic, complemented, Sylow
181	#41	—	8	4	no	—
182	C₂×Q₈	—	2	2	no	—
183	C₂×Q₈	—	38	2	no	—
184	C₂×Q₈	—	76	2	no	—
185	C₂×D₄	—	2	2	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	2	2	no	—
188	C₂×D₄	—	4	2	no	—
189	C₂²×C₄	—	4	2	no	—
190	C₂²×C₄	—	38	1	no	—
191	C₂²×C₄	—	38	1	no	—
192	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
193	C₂²×C₄	#64543	1	1	yes	characteristic
194	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
195	SD₁₆	—	76	8	no	—
196	D₈	—	8	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	4	2	no	—
199	C₂×C₈	—	38	2	no	—
200	C₂×C₈	—	38	4	no	—
201	C₂×C₈	—	76	1	no	—
202	C₂×C₈	—	76	1	no	—
203	C₄⋊C₄	—	2	2	no	—
204	C₄⋊C₄	—	2	2	no	—
205	C₄⋊C₄	—	38	2	no	—
206	C₄⋊C₄	—	76	2	no	—
207	C₂²⋊C₄	—	4	2	no	—
208	C₂²⋊C₄	—	4	2	no	—
209	C₄²	—	76	1	no	—
210	C₄²	—	76	1	no	—
211	C₄²	D₄×D₁₉	1	2	yes	—
212	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
213	C₂³	—	4	2	no	—
214	C₂³	#10597384	1	1	yes	characteristic
215	Q₈	—	8	2	no	—
216	Q₈	—	38	4	no	—
217	Q₈	—	76	2	no	—
218	D₄	—	4	4	no	—
219	D₄	—	4	2	no	—
220	D₄	—	4	2	no	—
221	D₄	—	8	2	no	—
222	D₄	—	8	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	8	4	no	—
229	C₂×C₄	—	38	2	no	—
230	C₂×C₄	—	76	1	no	—
231	C₂×C₄	—	76	1	no	—
232	C₂×C₄	—	76	2	no	—
233	C₂×C₄	—	76	1	no	—
234	C₂×C₄	#10597383	1	2	yes	—
235	C₂×C₄	#10597385	1	2	yes	—
236	C₂×C₄	#10597386	1	1	yes	characteristic
237	C₂×C₄	#10597399	1	1	yes	characteristic
238	C₈	—	4	2	no	—
239	C₈	—	76	2	no	—
240	C₈	—	76	4	no	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	8	2	no	—
244	C₂²	—	8	2	no	—
245	C₂²	—	8	2	no	—
246	C₂²	#11926452	1	1	yes	characteristic
247	C₂²	#11926811	1	2	yes	—
248	C₄	—	2	1	no	—
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	8	2	no	—
252	C₄	—	76	2	no	—
253	C₄	—	152	1	no	—
254	C₄	#11926722	1	1	yes	characteristic
255	C₄	#11926727	1	1	yes	characteristic
256	C₂	—	2	2	no	—
257	C₂	—	16	2	no	—
258	C₂	#14564682	1	1	yes	characteristic
259	C₂	#14564699	1	1	yes	characteristic
260	C₂	#14564742	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573753

C₂

yes

maximal, complemented

#14564574

C₂

yes

maximal, characteristic, complemented

#14562246

C₂

yes

maximal, complemented

#14561505

C₂

yes

maximal, characteristic, complemented

C₁₉×#3245

C₂

yes

maximal, characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

—

—

—

C₂²

yes

—

C₂×#10597260

C₂²

yes

characteristic

#11926298

—

#11926284

—

C₁₉×#532

C₂²

yes

—

C₁₉×#474

—

C₁₉×#466

—

C₁₉×#459

—

C₂×C₁₉×C₄⋊C₈

C₂²

yes

characteristic

C₂×#41×C₁₉

—

C₂²×Dic₃₈

D₄

yes

characteristic

C₂×D₈×C₁₉

—

C₂²×C₈×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

D₄

yes

—

C₁₉×#124

—

C₁₉×#121

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64526

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂²×C₁₉⋊C₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×#107

—

C₁₉×C₄⋊C₈

—

C₁₉×#102

—

#10597289

—

C₂²⋊(C₁₉⋊C₈)

—

#10597267

—

#10597264

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

#10597260

D₄

yes

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

D₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

—

#64526

—

C₄⋊Dic₁₉

—

Dic₁₉⋊C₄

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#10028

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#121

yes

characteristic

Q₈×C₁₉

—

D₄×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

#120

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

100

C₂×C₄×C₁₉

#127

yes

characteristic

101

C₂×Dic₁₉

—

102

C₂×Dic₁₉

—

103

C₂×Dic₁₉

—

104

C₂×Dic₁₉

—

105

C₂×Dic₁₉

—

106

Dic₃₈

—

107

Dic₃₈

—

108

C₈×C₁₉

—

109

C₁₉⋊C₈

—

110

C₁₉⋊C₈

—

111

#3245

D₁₉

yes

characteristic

112

#3112

—

113

#1985

—

114

#1530

—

115

#1290

—

116

C₂²×C₁₉

—

117

C₂²×C₁₉

—

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

#392

yes

characteristic

122

C₂²×C₁₉

#472

yes

—

123

C₄×C₁₉

—

124

C₄×C₁₉

—

125

C₄×C₁₉

—

126

C₄×C₁₉

—

127

C₄×C₁₉

#455

yes

characteristic

128

C₄×C₁₉

#456

yes

characteristic

129

Dic₁₉

—

130

Dic₁₉

—

131

#532

C₂×D₁₉

yes

—

132

C₂×C₄×Q₈

—

133

#480

—

134

#477

—

135

#474

—

136

#466

—

137

#460

—

138

#459

—

139

#448

—

140

#440

—

141

#432

—

142

C₂×C₄⋊C₈

C₂×D₁₉

yes

characteristic

143

C₂×#97

—

144

#336

—

145

#329

—

146

C₂×C₁₉

—

147

C₂×C₁₉

—

148

C₂×C₁₉

#2007

yes

characteristic

149

C₂×C₁₉

#2010

yes

characteristic

150

C₂×C₁₉

#2018

yes

characteristic

151

C₂×#41

—

152

C₂²×Q₈

—

153

C₂×SD₁₆

—

154

C₂×D₈

—

155

C₂²×C₈

—

156

C₂²×C₈

C₂²⋊D₁₉

yes

—

157

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

158

#127

C₂²⋊D₁₉

yes

—

159

#124

—

160

#121

—

161

#121

—

162

C₄×Q₈

—

163

C₄×Q₈

—

164

C₄×D₄

—

165

C₄×D₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄²

—

169

C₂×C₄²

C₂²×D₁₉

yes

characteristic

170

#107

—

171

#107

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#103

—

175

#102

—

176

#102

—

177

C₂²⋊C₈

—

178

#97

—

179

#97

—

180

C₁₉

#10028

yes

characteristic, complemented, Sylow

181

#41

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

D₄×D₁₉

yes

characteristic

193

C₂²×C₄

#64543

yes

characteristic

194

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

195

SD₁₆

—

196

D₈

—

197

C₂×C₈

—

198

C₂×C₈

—

199

C₂×C₈

—

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

D₄×D₁₉

yes

—

212

C₄²

C₂×C₂²⋊D₁₉

yes

—

213

C₂³

—

214

C₂³

#10597384

yes

characteristic

215

Q₈

—

216

Q₈

—

217

Q₈

—

218

D₄

—

219

D₄

—

220

D₄

—

221

D₄

—

222

D₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

#10597383

yes

—

235

C₂×C₄

#10597385

yes

—

236

C₂×C₄

#10597386

yes

characteristic

237

C₂×C₄

#10597399

yes

characteristic

238

C₈

—

239

C₈

—

240

C₈

—

241

C₂²

—

242

C₂²

—

243

C₂²

—

244

C₂²

—

245

C₂²

—

246

C₂²

#11926452

yes

characteristic

247

C₂²

#11926811

yes

—

248

C₄

—

249

C₄

—

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

152

—

254

C₄

#11926722

yes

characteristic

255

C₄

#11926727

yes

characteristic

256

C₂

—

257

C₂

—

258

C₂

#14564682

yes

characteristic

259

C₂

#14564699

yes

characteristic

260

C₂

#14564742

yes

characteristic

	subgroup	G/H
center	C₂²	#11926452
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3245	C₂
socle	C₂²×C₁₉	#392
hypercenter	#3245	D₁₉
hypocenter	C₁₉	#10028
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3245

subgroup

G/H

center

C₂²

#11926452

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting, prime radical

C₁₉×#3245

C₂

C₂²×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3245

N	H ≅ G/N	type
1. #14573753	C₂	semidirect
2. #14564574	C₂	semidirect
3. #14562246	C₂	semidirect
4. #14561505	C₂	semidirect
180. C₁₉	#10028	semidirect

H ≅ G/N

type

1. #14573753

C₂

semidirect

2. #14564574

C₂

semidirect

3. #14562246

C₂

semidirect

4. #14561505

C₂

semidirect

180. C₁₉

#10028

semidirect

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

subgroup	index
#14573753	2
#14564574	2
#14562246	2
#14561505	2
C₁₉×#3245	2
#10028	19

subgroup

index

C₁₉×#3245

Subgroups — #18083481

Conjugacy classes of subgroups

Complements

Maximal subgroups