Group #18014680 — subgroups

Subgroups — C₁₉×#8721 #18014680

Order 4864.

526 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 526 conjugacy classes of subgroups — too many to draw. Only its 142 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×#2285	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1749	C₂	1	2	yes	maximal
3	C₁₉×#1295	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#117	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₉×C₂²⋊C₈	—	2	2	no	—
7	C₂×C₁₉×#97	C₂²	1	4	yes	—
8	C₁₉×#384	C₄	1	1	yes	characteristic
9	C₁₉×#384	C₄	1	1	yes	characteristic
10	C₁₉×#382	C₂²	1	2	yes	—
11	C₁₉×#380	—	2	2	no	—
12	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
13	C₁₉×#336	—	2	2	no	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	D₄	1	2	yes	—
16	C₂²×C₈×C₁₉	—	2	4	no	—
17	C₁₉×#117	—	4	4	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
21	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
22	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
23	C₂×C₄²×C₁₉	—	2	4	no	—
24	C₂×C₄²×C₁₉	—	2	2	no	—
25	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	D₄	1	2	yes	—
27	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
28	C₁₉×C₂²⋊C₈	—	2	8	no	—
29	C₁₉×#97	—	2	8	no	—
30	C₁₉×#95	—	2	4	no	—
31	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	—	2	2	no	—
34	C₂²×C₄×C₁₉	—	2	2	no	—
35	C₂²×C₄×C₁₉	—	2	4	no	—
36	C₂²×C₄×C₁₉	—	2	4	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	4	2	no	—
40	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
42	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
44	C₂×C₈×C₁₉	—	2	8	no	—
45	C₂×C₈×C₁₉	—	4	4	no	—
46	C₂×C₈×C₁₉	—	4	4	no	—
47	C₄⋊C₄×C₁₉	—	4	2	no	—
48	C₄⋊C₄×C₁₉	—	4	2	no	—
49	C₄⋊C₄×C₁₉	—	4	4	no	—
50	C₄⋊C₄×C₁₉	—	4	4	no	—
51	C₂²⋊C₄×C₁₉	—	4	4	no	—
52	C₄²×C₁₉	—	2	2	no	—
53	C₄²×C₁₉	—	2	4	no	—
54	C₄²×C₁₉	—	4	4	no	—
55	C₄²×C₁₉	#41	1	4	yes	—
56	#8721	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂³×C₁₉	—	2	1	no	—
58	C₂³×C₁₉	—	2	1	no	—
59	C₂³×C₁₉	—	2	2	no	—
60	C₂³×C₁₉	—	2	2	no	—
61	C₂³×C₁₉	#101	1	2	yes	—
62	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₄×C₁₉	—	2	8	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	1	no	—
67	C₂×C₄×C₁₉	—	2	1	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	2	no	—
70	C₂×C₄×C₁₉	—	2	2	no	—
71	C₂×C₄×C₁₉	—	2	2	no	—
72	C₂×C₄×C₁₉	—	4	8	no	—
73	C₂×C₄×C₁₉	—	4	2	no	—
74	C₂×C₄×C₁₉	—	4	2	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	#100	1	2	yes	—
78	C₂×C₄×C₁₉	#104	1	4	yes	—
79	C₂×C₄×C₁₉	#117	1	2	yes	—
80	C₂×C₄×C₁₉	#123	1	4	yes	—
81	C₈×C₁₉	—	4	8	no	—
82	#2285	C₂×C₁₉	1	1	yes	characteristic
83	#1749	C₂×C₁₉	1	2	yes	—
84	#1295	C₂×C₁₉	1	4	yes	complemented
85	C₂²×C₁₉	—	2	2	no	—
86	C₂²×C₁₉	—	2	4	no	—
87	C₂²×C₁₉	—	4	1	no	—
88	C₂²×C₁₉	—	4	2	no	—
89	C₂²×C₁₉	—	4	1	no	—
90	C₂²×C₁₉	#381	1	1	yes	characteristic
91	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
92	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
93	C₂²×C₁₉	C₂×#104	1	2	yes	—
94	C₂²×C₁₉	#421	1	2	yes	—
95	C₄×C₁₉	—	2	2	no	—
96	C₄×C₁₉	—	2	2	no	—
97	C₄×C₁₉	—	2	4	no	—
98	C₄×C₁₉	—	2	4	no	—
99	C₄×C₁₉	—	8	2	no	—
100	C₄×C₁₉	—	8	2	no	—
101	C₂×#117	C₄×C₁₉	1	2	yes	—
102	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
103	C₂×C₂²⋊C₈	—	2	2	no	—
104	C₂×#97	C₂²×C₁₉	1	4	yes	—
105	#384	C₄×C₁₉	1	1	yes	characteristic
106	#384	C₄×C₁₉	1	1	yes	characteristic
107	#382	C₂²×C₁₉	1	2	yes	—
108	#380	—	2	2	no	—
109	C₄×C₄⋊C₄	—	2	2	no	—
110	#336	—	2	2	no	—
111	C₂×C₁₉	—	4	2	no	—
112	C₂×C₁₉	#1525	1	1	yes	characteristic
113	C₂×C₁₉	#1531	1	2	yes	—
114	C₂×C₁₉	#1536	1	1	yes	characteristic
115	C₂×C₁₉	#1821	1	1	yes	characteristic
116	C₂×C₁₉	#1826	1	2	yes	—
117	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
118	C₂³×C₄	D₄×C₁₉	1	2	yes	—
119	C₂²×C₈	—	2	4	no	—
120	#117	—	4	4	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	2	2	no	—
123	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
124	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
125	C₂×C₂²⋊C₄	—	2	2	no	—
126	C₂×C₄²	—	2	4	no	—
127	C₂×C₄²	—	2	2	no	—
128	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
129	C₂×C₄²	D₄×C₁₉	1	2	yes	—
130	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
131	C₂²⋊C₈	—	2	8	no	—
132	#97	—	2	8	no	—
133	#95	—	2	4	no	—
134	C₁₉	#8721	1	1	yes	characteristic, direct product factor, Sylow
135	C₂⁴	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	4	2	no	—
144	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
145	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
146	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
147	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
148	C₂×C₈	—	2	8	no	—
149	C₂×C₈	—	4	4	no	—
150	C₂×C₈	—	4	4	no	—
151	C₄⋊C₄	—	4	2	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄⋊C₄	—	4	4	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₂²⋊C₄	—	4	4	no	—
156	C₄²	—	2	2	no	—
157	C₄²	—	2	4	no	—
158	C₄²	—	4	4	no	—
159	C₄²	#41×C₁₉	1	4	yes	—
160	C₂³	—	2	1	no	—
161	C₂³	—	2	1	no	—
162	C₂³	—	2	2	no	—
163	C₂³	—	2	2	no	—
164	C₂³	C₁₉×#101	1	2	yes	—
165	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
166	C₂×C₄	—	2	8	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	4	8	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	4	2	no	—
178	C₂×C₄	—	4	4	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	C₁₉×#100	1	2	yes	—
181	C₂×C₄	C₁₉×#104	1	4	yes	—
182	C₂×C₄	C₁₉×#117	1	2	yes	—
183	C₂×C₄	C₁₉×#123	1	4	yes	—
184	C₈	—	4	8	no	—
185	C₂²	—	2	4	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	4	1	no	—
188	C₂²	—	4	1	no	—
189	C₂²	—	4	2	no	—
190	C₂²	C₁₉×#381	1	1	yes	characteristic
191	C₂²	C₂×C₁₉×#100	1	1	yes	characteristic
192	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
193	C₂²	C₂×C₁₉×#104	1	2	yes	—
194	C₂²	C₁₉×#421	1	2	yes	—
195	C₄	—	2	2	no	—
196	C₄	—	2	2	no	—
197	C₄	—	2	4	no	—
198	C₄	—	2	4	no	—
199	C₄	—	8	2	no	—
200	C₄	—	8	2	no	—
201	C₂	—	4	2	no	—
202	C₂	C₁₉×#1525	1	1	yes	characteristic
203	C₂	C₁₉×#1531	1	2	yes	—
204	C₂	C₁₉×#1536	1	1	yes	characteristic
205	C₂	C₁₉×#1821	1	1	yes	characteristic
206	C₂	C₁₉×#1826	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2285

C₂

yes

maximal, characteristic

C₁₉×#1749

C₂

yes

maximal

C₁₉×#1295

C₂

yes

maximal, complemented

C₂×C₁₉×#117

C₄

yes

—

C₂²×C₄²×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×C₂²⋊C₈

—

C₂×C₁₉×#97

C₂²

yes

—

C₁₉×#384

C₄

yes

characteristic

C₁₉×#384

C₄

yes

characteristic

C₁₉×#382

C₂²

yes

—

C₁₉×#380

—

C₄×C₄⋊C₄×C₁₉

—

C₁₉×#336

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

#41

yes

—

#8721

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#101

yes

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#100

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

#117

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₈×C₁₉

—

#2285

C₂×C₁₉

yes

characteristic

#1749

C₂×C₁₉

yes

—

#1295

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

#421

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₂×#117

C₄×C₁₉

yes

—

102

C₂²×C₄²

C₂²×C₁₉

yes

characteristic

103

C₂×C₂²⋊C₈

—

104

C₂×#97

C₂²×C₁₉

yes

—

105

#384

C₄×C₁₉

yes

characteristic

106

#384

C₄×C₁₉

yes

characteristic

107

#382

C₂²×C₁₉

yes

—

108

#380

—

109

C₄×C₄⋊C₄

—

110

#336

—

111

C₂×C₁₉

—

112

C₂×C₁₉

#1525

yes

characteristic

113

C₂×C₁₉

#1531

yes

—

114

C₂×C₁₉

#1536

yes

characteristic

115

C₂×C₁₉

#1821

yes

characteristic

116

C₂×C₁₉

#1826

yes

—

117

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

118

C₂³×C₄

D₄×C₁₉

yes

—

119

C₂²×C₈

—

120

#117

—

121

C₂×C₄⋊C₄

—

122

C₂×C₄⋊C₄

—

123

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

124

C₂×C₄⋊C₄

C₂×C₄×C₁₉

yes

—

125

C₂×C₂²⋊C₄

—

126

C₂×C₄²

—

127

C₂×C₄²

—

128

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

129

C₂×C₄²

D₄×C₁₉

yes

—

130

C₂×C₄²

C₂³×C₁₉

yes

characteristic

131

C₂²⋊C₈

—

132

#97

—

133

#95

—

134

C₁₉

#8721

yes

characteristic, direct product factor, Sylow

135

C₂⁴

C₂²⋊C₄×C₁₉

yes

characteristic

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

145

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

146

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

147

C₂²×C₄

C₂×D₄×C₁₉

yes

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₂²⋊C₄

—

156

C₄²

—

157

C₄²

—

158

C₄²

—

159

C₄²

#41×C₁₉

yes

—

160

C₂³

—

161

C₂³

—

162

C₂³

—

163

C₂³

—

164

C₂³

C₁₉×#101

yes

—

165

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

C₁₉×#100

yes

—

181

C₂×C₄

C₁₉×#104

yes

—

182

C₂×C₄

C₁₉×#117

yes

—

183

C₂×C₄

C₁₉×#123

yes

—

184

C₈

—

185

C₂²

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

C₁₉×#381

yes

characteristic

191

C₂²

C₂×C₁₉×#100

yes

characteristic

192

C₂²

C₂×C₁₉×#101

yes

characteristic

193

C₂²

C₂×C₁₉×#104

yes

—

194

C₂²

C₁₉×#421

yes

—

195

C₄

—

196

C₄

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₂

—

202

C₂

C₁₉×#1525

yes

characteristic

203

C₂

C₁₉×#1531

yes

—

204

C₂

C₁₉×#1536

yes

characteristic

205

C₂

C₁₉×#1821

yes

characteristic

206

C₂

C₁₉×#1826

yes

—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂³×C₁₉

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

N	H ≅ G/N	type
3. C₁₉×#1295	C₂	semidirect
56. #8721	C₁₉	direct (N × H)
84. #1295	C₂×C₁₉	semidirect
134. C₁₉	#8721	direct (N × H)

H ≅ G/N

type

3. C₁₉×#1295

C₂

semidirect

56. #8721

C₁₉

direct (N × H)

84. #1295

C₂×C₁₉

semidirect

134. C₁₉

#8721

direct (N × H)

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

subgroup	index
C₁₉×#2285	2
C₁₉×#1749	2
C₁₉×#1295	2
#8721	19

subgroup

index

C₁₉×#2285

C₁₉×#1749

C₁₉×#1295

#8721

Subgroups — C₁₉×#8721 #18014680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#8721 #18014680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#8721 #18014680