Group #18015380 — subgroups

Subgroups — C₁₉×#9421 #18015380

Order 4864.

488 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 488 conjugacy classes of subgroups — too many to draw. Only its 118 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×#3152	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2980	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1556	C₂	1	2	yes	maximal, complemented
4	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1291	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₉×#137	—	2	2	no	—
7	C₁₉×#532	C₂²	1	1	yes	characteristic
8	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
9	C₁₉×#497	—	2	2	no	—
10	C₁₉×#494	C₄	1	2	yes	—
11	C₁₉×#492	C₄	1	2	yes	—
12	C₁₉×#435	—	2	4	no	—
13	C₁₉×#432	C₂²	1	2	yes	—
14	C₁₉×#432	C₂²	1	2	yes	—
15	C₁₉×#408	—	2	2	no	—
16	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#332	—	2	4	no	—
18	C₁₉×#329	—	2	2	no	—
19	C₂×#41×C₁₉	D₄	1	2	yes	—
20	C₂²×Q₈×C₁₉	—	2	1	no	—
21	C₁₉×#137	—	4	4	no	—
22	C₁₉×#137	—	4	4	no	—
23	C₂×Q₁₆×C₁₉	—	2	4	no	—
24	C₂×SD₁₆×C₁₉	—	2	4	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	2	no	—
27	C₂²×C₈×C₁₉	—	2	2	no	—
28	C₁₉×C₄⋊Q₈	—	2	2	no	—
29	C₁₉×C₄⋊Q₈	—	2	1	no	—
30	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	—
31	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
32	C₁₉×#127	C₂×C₄	1	1	yes	characteristic
33	C₁₉×#124	D₄	1	2	yes	—
34	C₁₉×#121	—	2	2	no	—
35	C₄×D₄×C₁₉	—	2	2	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₁₉×C₄⋊C₈	—	2	2	no	—
39	C₁₉×C₄⋊C₈	D₄	1	4	yes	—
40	C₁₉×C₂²⋊C₈	—	2	4	no	—
41	C₁₉×C₂²⋊C₈	—	2	2	no	—
42	C₁₉×C₂²⋊C₈	—	2	2	no	—
43	C₁₉×#97	—	2	1	no	—
44	C₁₉×#97	—	2	2	no	—
45	C₁₉×#97	—	2	2	no	—
46	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	—
47	#41×C₁₉	—	4	2	no	—
48	#41×C₁₉	—	4	2	no	—
49	C₂×Q₈×C₁₉	—	2	2	no	—
50	C₂×Q₈×C₁₉	—	4	2	no	—
51	C₂×Q₈×C₁₉	—	4	2	no	—
52	C₂×Q₈×C₁₉	—	4	1	no	—
53	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
54	C₂×D₄×C₁₉	—	2	2	no	—
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₉	—	2	2	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₉	#41	1	2	yes	—
61	Q₁₆×C₁₉	—	4	8	no	—
62	SD₁₆×C₁₉	—	4	8	no	—
63	M₁₆×C₁₉	—	2	4	no	—
64	M₁₆×C₁₉	—	8	2	no	—
65	C₂×C₈×C₁₉	—	2	2	no	—
66	C₂×C₈×C₁₉	—	2	4	no	—
67	C₂×C₈×C₁₉	—	4	2	no	—
68	C₂×C₈×C₁₉	—	8	2	no	—
69	C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₄⋊C₄×C₁₉	—	4	2	no	—
72	C₂²⋊C₄×C₁₉	—	2	4	no	—
73	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₉	C₂×D₄	1	2	yes	—
76	#9421	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
77	C₂³×C₁₉	—	2	2	no	—
78	C₂³×C₁₉	#123	1	1	yes	characteristic
79	Q₈×C₁₉	—	4	2	no	—
80	Q₈×C₁₉	—	4	4	no	—
81	Q₈×C₁₉	—	8	2	no	—
82	D₄×C₁₉	—	4	2	no	—
83	D₄×C₁₉	—	8	2	no	—
84	D₄×C₁₉	—	8	2	no	—
85	C₂×C₄×C₁₉	—	2	2	no	—
86	C₂×C₄×C₁₉	—	2	2	no	—
87	C₂×C₄×C₁₉	—	4	2	no	—
88	C₂×C₄×C₁₉	—	4	2	no	—
89	C₂×C₄×C₁₉	—	4	2	no	—
90	C₂×C₄×C₁₉	—	4	2	no	—
91	C₂×C₄×C₁₉	—	8	1	no	—
92	C₂×C₄×C₁₉	—	8	1	no	—
93	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
96	C₂×C₄×C₁₉	#121	1	2	yes	—
97	C₈×C₁₉	—	2	4	no	—
98	C₈×C₁₉	—	4	4	no	—
99	C₈×C₁₉	—	8	2	no	—
100	#3152	C₂×C₁₉	1	1	yes	characteristic
101	#2980	C₂×C₁₉	1	1	yes	characteristic
102	#1556	C₂×C₁₉	1	2	yes	complemented
103	#1536	C₂×C₁₉	1	1	yes	characteristic
104	#1291	C₂×C₁₉	1	2	yes	complemented
105	C₂²×C₁₉	—	2	1	no	—
106	C₂²×C₁₉	—	2	2	no	—
107	C₂²×C₁₉	—	4	2	no	—
108	C₂²×C₁₉	—	4	4	no	—
109	C₂²×C₁₉	#386	1	1	yes	characteristic
110	C₄×C₁₉	—	2	1	no	—
111	C₄×C₁₉	—	2	2	no	—
112	C₄×C₁₉	—	2	2	no	—
113	C₄×C₁₉	—	4	2	no	—
114	C₄×C₁₉	—	8	2	no	—
115	C₄×C₁₉	#453	1	2	yes	—
116	C₂×#137	—	2	2	no	—
117	#532	C₂²×C₁₉	1	1	yes	characteristic
118	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
119	#497	—	2	2	no	—
120	#494	C₄×C₁₉	1	2	yes	—
121	#492	C₄×C₁₉	1	2	yes	—
122	#435	—	2	4	no	—
123	#432	C₂²×C₁₉	1	2	yes	—
124	#432	C₂²×C₁₉	1	2	yes	—
125	#408	—	2	2	no	—
126	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
127	#332	—	2	4	no	—
128	#329	—	2	2	no	—
129	C₂×C₁₉	—	4	1	no	—
130	C₂×C₁₉	—	8	2	no	—
131	C₂×C₁₉	#1887	1	1	yes	characteristic
132	C₂×C₁₉	#1902	1	2	yes	—
133	C₂×#41	D₄×C₁₉	1	2	yes	—
134	C₂²×Q₈	—	2	1	no	—
135	#137	—	4	4	no	—
136	#137	—	4	4	no	—
137	C₂×Q₁₆	—	2	4	no	—
138	C₂×SD₁₆	—	2	4	no	—
139	C₂×M₁₆	—	2	1	no	—
140	C₂×M₁₆	—	2	2	no	—
141	C₂²×C₈	—	2	2	no	—
142	C₄⋊Q₈	—	2	2	no	—
143	C₄⋊Q₈	—	2	1	no	—
144	C₄⋊Q₈	C₂×C₄×C₁₉	1	2	yes	—
145	C₄⋊Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
146	#127	C₂×C₄×C₁₉	1	1	yes	characteristic
147	#124	D₄×C₁₉	1	2	yes	—
148	#121	—	2	2	no	—
149	C₄×D₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	D₄×C₁₉	1	4	yes	—
154	C₂²⋊C₈	—	2	4	no	—
155	C₂²⋊C₈	—	2	2	no	—
156	C₂²⋊C₈	—	2	2	no	—
157	#97	—	2	1	no	—
158	#97	—	2	2	no	—
159	#97	—	2	2	no	—
160	C₄×C₈	C₂×C₄×C₁₉	1	2	yes	—
161	C₁₉	#9421	1	1	yes	characteristic, direct product factor, Sylow
162	#41	—	4	2	no	—
163	#41	—	4	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×Q₈	—	4	2	no	—
166	C₂×Q₈	—	4	2	no	—
167	C₂×Q₈	—	4	1	no	—
168	C₂×Q₈	C₂²⋊C₄×C₁₉	1	2	yes	—
169	C₂×D₄	—	2	2	no	—
170	C₂×D₄	—	2	2	no	—
171	C₂×D₄	C₂²⋊C₄×C₁₉	1	2	yes	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	4	1	no	—
174	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
175	C₂²×C₄	#41×C₁₉	1	2	yes	—
176	Q₁₆	—	4	8	no	—
177	SD₁₆	—	4	8	no	—
178	M₁₆	—	2	4	no	—
179	M₁₆	—	8	2	no	—
180	C₂×C₈	—	2	2	no	—
181	C₂×C₈	—	2	4	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	8	2	no	—
184	C₄⋊C₄	—	2	2	no	—
185	C₄⋊C₄	—	2	4	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₂²⋊C₄	—	2	4	no	—
188	C₄²	C₂²×C₄×C₁₉	1	1	yes	characteristic
189	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
190	C₄²	C₂×D₄×C₁₉	1	2	yes	—
191	C₂³	—	2	2	no	—
192	C₂³	C₁₉×#123	1	1	yes	characteristic
193	Q₈	—	4	2	no	—
194	Q₈	—	4	4	no	—
195	Q₈	—	8	2	no	—
196	D₄	—	4	2	no	—
197	D₄	—	8	2	no	—
198	D₄	—	8	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	2	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	8	1	no	—
206	C₂×C₄	—	8	1	no	—
207	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
208	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
209	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
210	C₂×C₄	C₁₉×#121	1	2	yes	—
211	C₈	—	2	4	no	—
212	C₈	—	4	4	no	—
213	C₈	—	8	2	no	—
214	C₂²	—	2	1	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	—	4	4	no	—
218	C₂²	C₁₉×#386	1	1	yes	characteristic
219	C₄	—	2	1	no	—
220	C₄	—	2	2	no	—
221	C₄	—	2	2	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	2	no	—
224	C₄	C₁₉×#453	1	2	yes	—
225	C₂	—	4	1	no	—
226	C₂	—	8	2	no	—
227	C₂	C₁₉×#1887	1	1	yes	characteristic
228	C₂	C₁₉×#1902	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3152

C₂

yes

maximal, characteristic

C₁₉×#2980

C₂

yes

maximal, characteristic

C₁₉×#1556

C₂

yes

maximal, complemented

C₁₉×#1536

C₂

yes

maximal, characteristic

C₁₉×#1291

C₂

yes

maximal, complemented

C₂×C₁₉×#137

—

C₁₉×#532

C₂²

yes

characteristic

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#497

—

C₁₉×#494

C₄

yes

—

C₁₉×#492

C₄

yes

—

C₁₉×#435

—

C₁₉×#432

C₂²

yes

—

C₁₉×#432

C₂²

yes

—

C₁₉×#408

—

C₄×M₁₆×C₁₉

C₂²

yes

characteristic

C₁₉×#332

—

C₁₉×#329

—

C₂×#41×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

—

C₁₉×#137

—

C₁₉×#137

—

C₂×Q₁₆×C₁₉

—

C₂×SD₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

—

C₁₉×C₄⋊Q₈

C₂×C₄

yes

characteristic

C₁₉×#127

C₂×C₄

yes

characteristic

C₁₉×#124

D₄

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#97

—

C₁₉×#97

—

C₄×C₈×C₁₉

C₂×C₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

#41

yes

—

Q₁₆×C₁₉

—

SD₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

#9421

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

#123

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×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

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₄×D₄

yes

—

C₂×C₄×C₁₉

#120

yes

characteristic

C₂×C₄×C₁₉

#121

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

100

#3152

C₂×C₁₉

yes

characteristic

101

#2980

C₂×C₁₉

yes

characteristic

102

#1556

C₂×C₁₉

yes

complemented

103

#1536

C₂×C₁₉

yes

characteristic

104

#1291

C₂×C₁₉

yes

complemented

105

C₂²×C₁₉

—

106

C₂²×C₁₉

—

107

C₂²×C₁₉

—

108

C₂²×C₁₉

—

109

C₂²×C₁₉

#386

yes

characteristic

110

C₄×C₁₉

—

111

C₄×C₁₉

—

112

C₄×C₁₉

—

113

C₄×C₁₉

—

114

C₄×C₁₉

—

115

C₄×C₁₉

#453

yes

—

116

C₂×#137

—

117

#532

C₂²×C₁₉

yes

characteristic

118

C₂×C₄⋊Q₈

C₂²×C₁₉

yes

characteristic

119

#497

—

120

#494

C₄×C₁₉

yes

—

121

#492

C₄×C₁₉

yes

—

122

#435

—

123

#432

C₂²×C₁₉

yes

—

124

#432

C₂²×C₁₉

yes

—

125

#408

—

126

C₄×M₁₆

C₂²×C₁₉

yes

characteristic

127

#332

—

128

#329

—

129

C₂×C₁₉

—

130

C₂×C₁₉

—

131

C₂×C₁₉

#1887

yes

characteristic

132

C₂×C₁₉

#1902

yes

—

133

C₂×#41

D₄×C₁₉

yes

—

134

C₂²×Q₈

—

135

#137

—

136

#137

—

137

C₂×Q₁₆

—

138

C₂×SD₁₆

—

139

C₂×M₁₆

—

140

C₂×M₁₆

—

141

C₂²×C₈

—

142

C₄⋊Q₈

—

143

C₄⋊Q₈

—

144

C₄⋊Q₈

C₂×C₄×C₁₉

yes

—

145

C₄⋊Q₈

C₂×C₄×C₁₉

yes

characteristic

146

#127

C₂×C₄×C₁₉

yes

characteristic

147

#124

D₄×C₁₉

yes

—

148

#121

—

149

C₄×D₄

—

150

C₂×C₄⋊C₄

—

151

C₂×C₄²

C₂³×C₁₉

yes

characteristic

152

C₄⋊C₈

—

153

C₄⋊C₈

D₄×C₁₉

yes

—

154

C₂²⋊C₈

—

155

C₂²⋊C₈

—

156

C₂²⋊C₈

—

157

#97

—

158

#97

—

159

#97

—

160

C₄×C₈

C₂×C₄×C₁₉

yes

—

161

C₁₉

#9421

yes

characteristic, direct product factor, Sylow

162

#41

—

163

#41

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂×Q₈

—

168

C₂×Q₈

C₂²⋊C₄×C₁₉

yes

—

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

C₂²⋊C₄×C₁₉

yes

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

175

C₂²×C₄

#41×C₁₉

yes

—

176

Q₁₆

—

177

SD₁₆

—

178

M₁₆

—

179

M₁₆

—

180

C₂×C₈

—

181

C₂×C₈

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₂²⋊C₄

—

188

C₄²

C₂²×C₄×C₁₉

yes

characteristic

189

C₄²

C₂×D₄×C₁₉

yes

characteristic

190

C₄²

C₂×D₄×C₁₉

yes

—

191

C₂³

—

192

C₂³

C₁₉×#123

yes

characteristic

193

Q₈

—

194

Q₈

—

195

Q₈

—

196

D₄

—

197

D₄

—

198

D₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

208

C₂×C₄

C₄×D₄×C₁₉

yes

—

209

C₂×C₄

C₁₉×#120

yes

characteristic

210

C₂×C₄

C₁₉×#121

yes

—

211

C₈

—

212

C₈

—

213

C₈

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

C₁₉×#386

yes

characteristic

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₄

—

224

C₄

C₁₉×#453

yes

—

225

C₂

—

226

C₂

—

227

C₂

C₁₉×#1887

yes

characteristic

228

C₂

C₁₉×#1902

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#386
commutator	C₄²	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₁₉×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#386

commutator

C₄²

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₁₉×#532

C₂²

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1556	C₂	semidirect
5. C₁₉×#1291	C₂	semidirect
76. #9421	C₁₉	direct (N × H)
102. #1556	C₂×C₁₉	semidirect
104. #1291	C₂×C₁₉	semidirect
161. C₁₉	#9421	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1556

C₂

semidirect

5. C₁₉×#1291

C₂

semidirect

76. #9421

C₁₉

direct (N × H)

102. #1556

C₂×C₁₉

semidirect

104. #1291

C₂×C₁₉

semidirect

161. C₁₉

#9421

direct (N × H)

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

subgroup	index
C₁₉×#3152	2
C₁₉×#2980	2
C₁₉×#1556	2
C₁₉×#1536	2
C₁₉×#1291	2
#9421	19

subgroup

index

C₁₉×#3152

C₁₉×#2980

C₁₉×#1556

C₁₉×#1536

C₁₉×#1291

#9421

Subgroups — C₁₉×#9421 #18015380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#9421 #18015380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#9421 #18015380