Group #18016172 — subgroups

Subgroups — C₁₉×#10213 #18016172

Order 4864.

498 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 98 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	C₁₉×#3253	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3216	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1995	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1505	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1307	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#533	C₂²	1	1	yes	characteristic
7	C₁₉×#532	C₂²	1	2	yes	—
8	C₁₉×#497	—	2	2	no	—
9	C₁₉×#489	—	2	2	no	—
10	C₁₉×#476	—	2	2	no	—
11	C₁₉×#469	—	2	2	no	—
12	C₁₉×#462	—	2	2	no	—
13	C₁₉×#460	—	2	2	no	—
14	C₁₉×#459	—	2	2	no	—
15	C₁₉×#452	—	2	4	no	—
16	C₁₉×#432	C₂²	1	2	yes	—
17	C₁₉×#423	C₂²	1	1	yes	characteristic
18	C₁₉×#376	C₂²	1	1	yes	characteristic
19	C₁₉×#339	—	2	2	no	—
20	C₁₉×#327	—	2	4	no	—
21	C₂×#41×C₁₉	—	2	2	no	—
22	C₂×Q₁₆×C₁₉	—	2	4	no	—
23	C₂×SD₁₆×C₁₉	—	2	4	no	—
24	C₂×D₈×C₁₉	—	2	2	no	—
25	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
26	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
27	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
28	C₁₉×#127	D₄	1	2	yes	—
29	C₁₉×#125	—	2	1	no	—
30	C₁₉×#124	—	2	2	no	—
31	C₁₉×C₂²⋊Q₈	—	2	2	no	—
32	C₁₉×#121	—	2	2	no	—
33	C₁₉×#121	—	2	2	no	—
34	C₄×Q₈×C₁₉	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₄×D₄×C₁₉	—	2	2	no	—
37	C₁₉×#117	—	2	1	no	—
38	C₂×C₄²×C₁₉	—	2	1	no	—
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	C₁₉×#106	—	2	2	no	—
41	C₁₉×C₄⋊C₈	—	2	2	no	—
42	C₁₉×C₄⋊C₈	—	2	2	no	—
43	C₁₉×#103	—	2	4	no	—
44	C₁₉×#102	—	2	4	no	—
45	C₁₉×#102	—	2	4	no	—
46	C₁₉×C₂²⋊C₈	D₄	1	4	yes	—
47	C₁₉×#97	—	2	2	no	—
48	C₁₉×#95	—	2	2	no	—
49	#41×C₁₉	—	8	4	no	—
50	C₂×Q₈×C₁₉	—	2	2	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	1	no	—
57	C₂²×C₄×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
60	Q₁₆×C₁₉	—	8	4	no	—
61	SD₁₆×C₁₉	—	8	4	no	—
62	D₈×C₁₉	—	8	2	no	—
63	M₁₆×C₁₉	—	4	2	no	—
64	C₂×C₈×C₁₉	—	2	2	no	—
65	C₂×C₈×C₁₉	—	2	4	no	—
66	C₄⋊C₄×C₁₉	—	2	2	no	—
67	C₄⋊C₄×C₁₉	—	2	2	no	—
68	C₄⋊C₄×C₁₉	—	2	2	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	4	2	no	—
71	C₂²⋊C₄×C₁₉	—	4	1	no	—
72	C₂²⋊C₄×C₁₉	—	4	2	no	—
73	C₂²⋊C₄×C₁₉	—	4	2	no	—
74	C₄²×C₁₉	—	2	2	no	—
75	C₄²×C₁₉	—	4	1	no	—
76	C₄²×C₁₉	—	4	1	no	—
77	C₄²×C₁₉	C₂×D₄	1	2	yes	—
78	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₉	#41	1	1	yes	characteristic
80	#10213	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
81	C₂³×C₁₉	—	4	2	no	—
82	C₂³×C₁₉	#127	1	1	yes	characteristic
83	Q₈×C₁₉	—	4	2	no	—
84	Q₈×C₁₉	—	4	2	no	—
85	Q₈×C₁₉	—	4	4	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	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	4	2	no	—
94	C₂×C₄×C₁₉	—	4	2	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	4	2	no	—
97	C₂×C₄×C₁₉	—	8	4	no	—
98	C₂×C₄×C₁₉	—	8	2	no	—
99	C₂×C₄×C₁₉	#120	1	2	yes	—
100	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
101	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#121	1	2	yes	—
103	C₈×C₁₉	—	4	4	no	—
104	C₈×C₁₉	—	4	2	no	—
105	#3253	C₂×C₁₉	1	1	yes	characteristic
106	#3216	C₂×C₁₉	1	2	yes	complemented
107	#1995	C₂×C₁₉	1	1	yes	characteristic, complemented
108	#1505	C₂×C₁₉	1	2	yes	complemented
109	#1307	C₂×C₁₉	1	1	yes	characteristic, complemented
110	C₂²×C₁₉	—	2	1	no	—
111	C₂²×C₁₉	—	2	2	no	—
112	C₂²×C₁₉	—	8	2	no	—
113	C₂²×C₁₉	—	8	2	no	—
114	C₂²×C₁₉	—	8	2	no	—
115	C₂²×C₁₉	#392	1	1	yes	characteristic
116	C₄×C₁₉	—	2	1	no	—
117	C₄×C₁₉	—	2	2	no	—
118	C₄×C₁₉	—	2	2	no	—
119	C₄×C₁₉	—	8	2	no	—
120	C₄×C₁₉	—	8	2	no	—
121	C₄×C₁₉	—	8	2	no	—
122	C₄×C₁₉	#455	1	1	yes	characteristic
123	C₄×C₁₉	#456	1	1	yes	characteristic
124	#533	C₂²×C₁₉	1	1	yes	characteristic
125	#532	C₂²×C₁₉	1	2	yes	—
126	#497	—	2	2	no	—
127	#489	—	2	2	no	—
128	#476	—	2	2	no	—
129	#469	—	2	2	no	—
130	#462	—	2	2	no	—
131	#460	—	2	2	no	—
132	#459	—	2	2	no	—
133	#452	—	2	4	no	—
134	#432	C₂²×C₁₉	1	2	yes	—
135	#423	C₂²×C₁₉	1	1	yes	characteristic
136	#376	C₂²×C₁₉	1	1	yes	characteristic
137	#339	—	2	2	no	—
138	#327	—	2	4	no	—
139	C₂×C₁₉	—	4	1	no	—
140	C₂×C₁₉	—	16	2	no	—
141	C₂×C₁₉	#2007	1	1	yes	characteristic
142	C₂×C₁₉	#2008	1	2	yes	—
143	C₂×#41	—	2	2	no	—
144	C₂×Q₁₆	—	2	4	no	—
145	C₂×SD₁₆	—	2	4	no	—
146	C₂×D₈	—	2	2	no	—
147	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
148	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
149	C₄⋊Q₈	D₄×C₁₉	1	2	yes	—
150	#127	D₄×C₁₉	1	2	yes	—
151	#125	—	2	1	no	—
152	#124	—	2	2	no	—
153	C₂²⋊Q₈	—	2	2	no	—
154	#121	—	2	2	no	—
155	#121	—	2	2	no	—
156	C₄×Q₈	—	2	2	no	—
157	C₄×D₄	—	2	2	no	—
158	C₄×D₄	—	2	2	no	—
159	#117	—	2	1	no	—
160	C₂×C₄²	—	2	1	no	—
161	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
162	#106	—	2	2	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	#103	—	2	4	no	—
166	#102	—	2	4	no	—
167	#102	—	2	4	no	—
168	C₂²⋊C₈	D₄×C₁₉	1	4	yes	—
169	#97	—	2	2	no	—
170	#95	—	2	2	no	—
171	C₁₉	#10213	1	1	yes	characteristic, direct product factor, Sylow
172	#41	—	8	4	no	—
173	C₂×Q₈	—	2	2	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	—	2	2	no	—
177	C₂×D₄	—	2	2	no	—
178	C₂×D₄	—	4	2	no	—
179	C₂²×C₄	—	4	1	no	—
180	C₂²×C₄	—	4	2	no	—
181	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
183	Q₁₆	—	8	4	no	—
184	SD₁₆	—	8	4	no	—
185	D₈	—	8	2	no	—
186	M₁₆	—	4	2	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	2	2	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₂²⋊C₄	—	4	1	no	—
195	C₂²⋊C₄	—	4	2	no	—
196	C₂²⋊C₄	—	4	2	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	4	1	no	—
199	C₄²	—	4	1	no	—
200	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
201	C₄²	C₂×D₄×C₁₉	1	2	yes	—
202	C₄²	#41×C₁₉	1	1	yes	characteristic
203	C₂³	—	4	2	no	—
204	C₂³	C₁₉×#127	1	1	yes	characteristic
205	Q₈	—	4	2	no	—
206	Q₈	—	4	2	no	—
207	Q₈	—	4	4	no	—
208	D₄	—	4	4	no	—
209	D₄	—	4	2	no	—
210	D₄	—	4	2	no	—
211	D₄	—	8	2	no	—
212	D₄	—	8	4	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	8	4	no	—
220	C₂×C₄	—	8	2	no	—
221	C₂×C₄	C₁₉×#120	1	2	yes	—
222	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
223	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
224	C₂×C₄	C₁₉×#121	1	2	yes	—
225	C₈	—	4	4	no	—
226	C₈	—	4	2	no	—
227	C₂²	—	2	1	no	—
228	C₂²	—	2	2	no	—
229	C₂²	—	8	2	no	—
230	C₂²	—	8	2	no	—
231	C₂²	—	8	2	no	—
232	C₂²	C₁₉×#392	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	2	no	—
235	C₄	—	2	2	no	—
236	C₄	—	8	2	no	—
237	C₄	—	8	2	no	—
238	C₄	—	8	2	no	—
239	C₄	C₁₉×#455	1	1	yes	characteristic
240	C₄	C₁₉×#456	1	1	yes	characteristic
241	C₂	—	4	1	no	—
242	C₂	—	16	2	no	—
243	C₂	C₁₉×#2007	1	1	yes	characteristic
244	C₂	C₁₉×#2008	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3253

C₂

yes

maximal, characteristic

C₁₉×#3216

C₂

yes

maximal, complemented

C₁₉×#1995

C₂

yes

maximal, characteristic, complemented

C₁₉×#1505

C₂

yes

maximal, complemented

C₁₉×#1307

C₂

yes

maximal, characteristic, complemented

C₁₉×#533

C₂²

yes

characteristic

C₁₉×#532

C₂²

yes

—

C₁₉×#497

—

C₁₉×#489

—

C₁₉×#476

—

C₁₉×#469

—

C₁₉×#462

—

C₁₉×#460

—

C₁₉×#459

—

C₁₉×#452

—

C₁₉×#432

C₂²

yes

—

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#376

C₂²

yes

characteristic

C₁₉×#339

—

C₁₉×#327

—

C₂×#41×C₁₉

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×D₈×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

D₄

yes

—

C₁₉×#125

—

C₁₉×#124

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×#106

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×#103

—

C₁₉×#102

—

C₁₉×#102

—

C₁₉×C₂²⋊C₈

D₄

yes

—

C₁₉×#97

—

C₁₉×#95

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

D₈×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#127

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

100

C₂×C₄×C₁₉

#120

yes

characteristic

101

C₂×C₄×C₁₉

#121

yes

characteristic

102

C₂×C₄×C₁₉

#121

yes

—

103

C₈×C₁₉

—

104

C₈×C₁₉

—

105

#3253

C₂×C₁₉

yes

characteristic

106

#3216

C₂×C₁₉

yes

complemented

107

#1995

C₂×C₁₉

yes

characteristic, complemented

108

#1505

C₂×C₁₉

yes

complemented

109

#1307

C₂×C₁₉

yes

characteristic, complemented

110

C₂²×C₁₉

—

111

C₂²×C₁₉

—

112

C₂²×C₁₉

—

113

C₂²×C₁₉

—

114

C₂²×C₁₉

—

115

C₂²×C₁₉

#392

yes

characteristic

116

C₄×C₁₉

—

117

C₄×C₁₉

—

118

C₄×C₁₉

—

119

C₄×C₁₉

—

120

C₄×C₁₉

—

121

C₄×C₁₉

—

122

C₄×C₁₉

#455

yes

characteristic

123

C₄×C₁₉

#456

yes

characteristic

124

#533

C₂²×C₁₉

yes

characteristic

125

#532

C₂²×C₁₉

yes

—

126

#497

—

127

#489

—

128

#476

—

129

#469

—

130

#462

—

131

#460

—

132

#459

—

133

#452

—

134

#432

C₂²×C₁₉

yes

—

135

#423

C₂²×C₁₉

yes

characteristic

136

#376

C₂²×C₁₉

yes

characteristic

137

#339

—

138

#327

—

139

C₂×C₁₉

—

140

C₂×C₁₉

—

141

C₂×C₁₉

#2007

yes

characteristic

142

C₂×C₁₉

#2008

yes

—

143

C₂×#41

—

144

C₂×Q₁₆

—

145

C₂×SD₁₆

—

146

C₂×D₈

—

147

C₂×M₁₆

D₄×C₁₉

yes

—

148

C₄⋊Q₈

D₄×C₁₉

yes

—

149

C₄⋊Q₈

D₄×C₁₉

yes

—

150

#127

D₄×C₁₉

yes

—

151

#125

—

152

#124

—

153

C₂²⋊Q₈

—

154

#121

—

155

#121

—

156

C₄×Q₈

—

157

C₄×D₄

—

158

C₄×D₄

—

159

#117

—

160

C₂×C₄²

—

161

C₂×C₄²

C₂³×C₁₉

yes

characteristic

162

#106

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

#103

—

166

#102

—

167

#102

—

168

C₂²⋊C₈

D₄×C₁₉

yes

—

169

#97

—

170

#95

—

171

C₁₉

#10213

yes

characteristic, direct product factor, Sylow

172

#41

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×D₄

—

176

C₂×D₄

—

177

C₂×D₄

—

178

C₂×D₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

182

C₂²×C₄

C₂×D₄×C₁₉

yes

—

183

Q₁₆

—

184

SD₁₆

—

185

D₈

—

186

M₁₆

—

187

C₂×C₈

—

188

C₂×C₈

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₂²⋊C₄

—

195

C₂²⋊C₄

—

196

C₂²⋊C₄

—

197

C₄²

—

198

C₄²

—

199

C₄²

—

200

C₄²

C₂×D₄×C₁₉

yes

characteristic

201

C₄²

C₂×D₄×C₁₉

yes

—

202

C₄²

#41×C₁₉

yes

characteristic

203

C₂³

—

204

C₂³

C₁₉×#127

yes

characteristic

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

D₄

—

209

D₄

—

210

D₄

—

211

D₄

—

212

D₄

—

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

C₁₉×#120

yes

—

222

C₂×C₄

C₁₉×#120

yes

characteristic

223

C₂×C₄

C₁₉×#121

yes

characteristic

224

C₂×C₄

C₁₉×#121

yes

—

225

C₈

—

226

C₈

—

227

C₂²

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

C₁₉×#392

yes

characteristic

233

C₄

—

234

C₄

—

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

C₁₉×#455

yes

characteristic

240

C₄

C₁₉×#456

yes

characteristic

241

C₂

—

242

C₂

—

243

C₂

C₁₉×#2007

yes

characteristic

244

C₂

C₁₉×#2008

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#3253	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#392

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₁₉×#3253

C₂

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#3216	C₂	semidirect
3. C₁₉×#1995	C₂	semidirect
4. C₁₉×#1505	C₂	semidirect
5. C₁₉×#1307	C₂	semidirect
80. #10213	C₁₉	direct (N × H)
106. #3216	C₂×C₁₉	semidirect
107. #1995	C₂×C₁₉	semidirect
108. #1505	C₂×C₁₉	semidirect
109. #1307	C₂×C₁₉	semidirect
171. C₁₉	#10213	direct (N × H)

H ≅ G/N

type

2. C₁₉×#3216

C₂

semidirect

3. C₁₉×#1995

C₂

semidirect

4. C₁₉×#1505

C₂

semidirect

5. C₁₉×#1307

C₂

semidirect

80. #10213

C₁₉

direct (N × H)

106. #3216

C₂×C₁₉

semidirect

107. #1995

C₂×C₁₉

semidirect

108. #1505

C₂×C₁₉

semidirect

109. #1307

C₂×C₁₉

semidirect

171. C₁₉

#10213

direct (N × H)

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

subgroup	index
C₁₉×#3253	2
C₁₉×#3216	2
C₁₉×#1995	2
C₁₉×#1505	2
C₁₉×#1307	2
#10213	19

subgroup

index

C₁₉×#3253

C₁₉×#3216

C₁₉×#1995

C₁₉×#1505

C₁₉×#1307

#10213

Subgroups — C₁₉×#10213 #18016172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#10213 #18016172

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#10213 #18016172