Group #18017477 — subgroups

Subgroups — C₁₉×#11518 #18017477

Order 4864.

446 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 446 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2296	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#1464	C₂	1	2	yes	maximal
3	C₁₉×#1326	C₂	1	4	yes	maximal
4	C₂×C₁₉×#117	C₄	1	1	yes	characteristic
5	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₁₉	C₄	1	1	yes	characteristic
7	C₁₉×#432	—	2	2	no	—
8	C₁₉×#389	—	2	2	no	—
9	C₁₉×#385	C₄	1	2	yes	—
10	C₁₉×#385	C₂²	1	2	yes	—
11	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
12	C₁₉×#324	—	2	2	no	—
13	C₁₉×#323	C₂²	1	4	yes	—
14	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
16	C₁₉×#117	—	2	4	no	—
17	C₁₉×#117	—	4	2	no	—
18	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
19	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
20	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
21	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
22	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
23	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
25	C₂×C₄²×C₁₉	—	2	1	no	—
26	C₂×C₄²×C₁₉	—	2	1	no	—
27	C₂×C₄²×C₁₉	—	2	1	no	—
28	C₂×C₄²×C₁₉	—	4	2	no	—
29	C₂×C₄²×C₁₉	D₄	1	2	yes	—
30	C₁₉×C₄⋊C₈	—	4	2	no	—
31	C₁₉×C₂²⋊C₈	—	2	4	no	—
32	C₁₉×#97	—	4	2	no	—
33	C₁₉×#95	—	2	2	no	—
34	C₁₉×#95	—	2	2	no	—
35	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	—	2	2	no	—
40	C₂²×C₄×C₁₉	—	2	2	no	—
41	C₂²×C₄×C₁₉	—	4	4	no	—
42	C₂²×C₄×C₁₉	—	4	2	no	—
43	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂×C₈×C₁₉	—	4	4	no	—
48	C₄⋊C₄×C₁₉	—	2	4	no	—
49	C₄⋊C₄×C₁₉	—	4	2	no	—
50	C₄⋊C₄×C₁₉	—	4	4	no	—
51	C₄⋊C₄×C₁₉	—	4	4	no	—
52	C₂²⋊C₄×C₁₉	—	2	2	no	—
53	C₂²⋊C₄×C₁₉	—	4	1	no	—
54	C₂²⋊C₄×C₁₉	—	4	1	no	—
55	C₂²⋊C₄×C₁₉	M₁₆	1	4	yes	—
56	C₄²×C₁₉	—	2	4	no	—
57	C₄²×C₁₉	—	2	2	no	—
58	C₄²×C₁₉	—	2	2	no	—
59	C₄²×C₁₉	—	4	2	no	—
60	C₄²×C₁₉	—	4	2	no	—
61	#11518	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂³×C₁₉	—	2	1	no	—
63	C₂³×C₁₉	—	2	1	no	—
64	C₂³×C₁₉	—	4	2	no	—
65	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂³×C₁₉	C₂×M₁₆	1	2	yes	—
67	C₂×C₄×C₁₉	—	2	8	no	—
68	C₂×C₄×C₁₉	—	2	1	no	—
69	C₂×C₄×C₁₉	—	2	1	no	—
70	C₂×C₄×C₁₉	—	2	1	no	—
71	C₂×C₄×C₁₉	—	2	1	no	—
72	C₂×C₄×C₁₉	—	2	4	no	—
73	C₂×C₄×C₁₉	—	2	4	no	—
74	C₂×C₄×C₁₉	—	2	2	no	—
75	C₂×C₄×C₁₉	—	2	2	no	—
76	C₂×C₄×C₁₉	—	4	2	no	—
77	C₂×C₄×C₁₉	—	4	2	no	—
78	C₂×C₄×C₁₉	—	4	2	no	—
79	C₂×C₄×C₁₉	—	4	4	no	—
80	C₂×C₄×C₁₉	—	4	2	no	—
81	C₂×C₄×C₁₉	—	4	2	no	—
82	C₂×C₄×C₁₉	—	4	2	no	—
83	C₂×C₄×C₁₉	—	4	4	no	—
84	C₂×C₄×C₁₉	#99	1	2	yes	—
85	C₂×C₄×C₁₉	#101	1	2	yes	—
86	C₈×C₁₉	—	8	4	no	—
87	#2296	C₂×C₁₉	1	1	yes	characteristic
88	#1464	C₂×C₁₉	1	2	yes	—
89	#1326	C₂×C₁₉	1	4	yes	—
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	—	2	2	no	—
92	C₂²×C₁₉	—	4	2	no	—
93	C₂²×C₁₉	—	4	2	no	—
94	C₂²×C₁₉	—	4	2	no	—
95	C₂²×C₁₉	#407	1	1	yes	characteristic
96	C₂²×C₁₉	C₂×#99	1	1	yes	characteristic
97	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
98	C₄×C₁₉	—	2	2	no	—
99	C₄×C₁₉	—	2	2	no	—
100	C₄×C₁₉	—	4	4	no	—
101	C₄×C₁₉	—	4	2	no	—
102	C₄×C₁₉	—	4	2	no	—
103	C₄×C₁₉	—	4	4	no	—
104	C₂×#117	C₄×C₁₉	1	1	yes	characteristic
105	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
106	C₂²×C₄²	C₄×C₁₉	1	1	yes	characteristic
107	#432	—	2	2	no	—
108	#389	—	2	2	no	—
109	#385	C₄×C₁₉	1	2	yes	—
110	#385	C₂²×C₁₉	1	2	yes	—
111	C₄×C₄⋊C₄	—	2	2	no	—
112	#324	—	2	2	no	—
113	#323	C₂²×C₁₉	1	4	yes	—
114	C₂×C₁₉	—	2	1	no	—
115	C₂×C₁₉	—	2	1	no	—
116	C₂×C₁₉	—	4	2	no	—
117	C₂×C₁₉	#1463	1	1	yes	characteristic
118	C₂×C₁₉	#2120	1	2	yes	—
119	C₂³×C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
120	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
121	#117	—	2	4	no	—
122	#117	—	4	2	no	—
123	C₂×C₄⋊C₄	—	2	1	no	—
124	C₂×C₄⋊C₄	—	2	2	no	—
125	C₂×C₄⋊C₄	—	2	2	no	—
126	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
127	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
128	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	1	yes	characteristic
129	C₂×C₂²⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
130	C₂×C₄²	—	2	1	no	—
131	C₂×C₄²	—	2	1	no	—
132	C₂×C₄²	—	2	1	no	—
133	C₂×C₄²	—	4	2	no	—
134	C₂×C₄²	D₄×C₁₉	1	2	yes	—
135	C₄⋊C₈	—	4	2	no	—
136	C₂²⋊C₈	—	2	4	no	—
137	#97	—	4	2	no	—
138	#95	—	2	2	no	—
139	#95	—	2	2	no	—
140	C₁₉	#11518	1	1	yes	characteristic, direct product factor, Sylow
141	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	—	4	4	no	—
148	C₂²×C₄	—	4	2	no	—
149	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
150	C₂²×C₄	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
151	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
152	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
153	C₂×C₈	—	4	4	no	—
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	4	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₂²⋊C₄	—	2	2	no	—
159	C₂²⋊C₄	—	4	1	no	—
160	C₂²⋊C₄	—	4	1	no	—
161	C₂²⋊C₄	M₁₆×C₁₉	1	4	yes	—
162	C₄²	—	2	4	no	—
163	C₄²	—	2	2	no	—
164	C₄²	—	2	2	no	—
165	C₄²	—	4	2	no	—
166	C₄²	—	4	2	no	—
167	C₂³	—	2	1	no	—
168	C₂³	—	2	1	no	—
169	C₂³	—	4	2	no	—
170	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
171	C₂³	C₂×M₁₆×C₁₉	1	2	yes	—
172	C₂×C₄	—	2	8	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	4	no	—
189	C₂×C₄	C₁₉×#99	1	2	yes	—
190	C₂×C₄	C₁₉×#101	1	2	yes	—
191	C₈	—	8	4	no	—
192	C₂²	—	2	2	no	—
193	C₂²	—	2	2	no	—
194	C₂²	—	4	2	no	—
195	C₂²	—	4	2	no	—
196	C₂²	—	4	2	no	—
197	C₂²	C₁₉×#407	1	1	yes	characteristic
198	C₂²	C₂×C₁₉×#99	1	1	yes	characteristic
199	C₂²	C₂×C₁₉×#101	1	1	yes	characteristic
200	C₄	—	2	2	no	—
201	C₄	—	2	2	no	—
202	C₄	—	4	4	no	—
203	C₄	—	4	2	no	—
204	C₄	—	4	4	no	—
205	C₄	—	4	2	no	—
206	C₂	—	2	1	no	—
207	C₂	—	2	1	no	—
208	C₂	—	4	2	no	—
209	C₂	C₁₉×#1463	1	1	yes	characteristic
210	C₂	C₁₉×#2120	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2296

C₂

yes

maximal, characteristic

C₁₉×#1464

C₂

yes

maximal

C₁₉×#1326

C₂

yes

maximal

C₂×C₁₉×#117

C₄

yes

characteristic

C₂×C₁₉×#117

C₂²

yes

characteristic

C₂²×C₄²×C₁₉

C₄

yes

characteristic

C₁₉×#432

—

C₁₉×#389

—

C₁₉×#385

C₄

yes

—

C₁₉×#385

C₂²

yes

—

C₄×C₄⋊C₄×C₁₉

—

C₁₉×#324

—

C₁₉×#323

C₂²

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

D₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

C₂³

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₁₉×#97

—

C₁₉×#95

—

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

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

#11518

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

C₂×M₁₆

yes

—

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

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#99

yes

—

C₂×C₄×C₁₉

#101

yes

—

C₈×C₁₉

—

#2296

C₂×C₁₉

yes

characteristic

#1464

C₂×C₁₉

yes

—

#1326

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#407

yes

characteristic

C₂²×C₁₉

C₂×#99

yes

characteristic

C₂²×C₁₉

C₂×#101

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

100

C₄×C₁₉

—

101

C₄×C₁₉

—

102

C₄×C₁₉

—

103

C₄×C₁₉

—

104

C₂×#117

C₄×C₁₉

yes

characteristic

105

C₂×#117

C₂²×C₁₉

yes

characteristic

106

C₂²×C₄²

C₄×C₁₉

yes

characteristic

107

#432

—

108

#389

—

109

#385

C₄×C₁₉

yes

—

110

#385

C₂²×C₁₉

yes

—

111

C₄×C₄⋊C₄

—

112

#324

—

113

#323

C₂²×C₁₉

yes

—

114

C₂×C₁₉

—

115

C₂×C₁₉

—

116

C₂×C₁₉

—

117

C₂×C₁₉

#1463

yes

characteristic

118

C₂×C₁₉

#2120

yes

—

119

C₂³×C₄

C₂×C₄×C₁₉

yes

characteristic

120

C₂³×C₄

C₂×C₄×C₁₉

yes

—

121

#117

—

122

#117

—

123

C₂×C₄⋊C₄

—

124

C₂×C₄⋊C₄

—

125

C₂×C₄⋊C₄

—

126

C₂×C₄⋊C₄

D₄×C₁₉

yes

—

127

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

—

128

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

characteristic

129

C₂×C₂²⋊C₄

C₂³×C₁₉

yes

characteristic

130

C₂×C₄²

—

131

C₂×C₄²

—

132

C₂×C₄²

—

133

C₂×C₄²

—

134

C₂×C₄²

D₄×C₁₉

yes

—

135

C₄⋊C₈

—

136

C₂²⋊C₈

—

137

#97

—

138

#95

—

139

#95

—

140

C₁₉

#11518

yes

characteristic, direct product factor, Sylow

141

C₂⁴

C₂²×C₄×C₁₉

yes

characteristic

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

—

148

C₂²×C₄

—

149

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

150

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

characteristic

151

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

152

C₂²×C₄

C₂×D₄×C₁₉

yes

—

153

C₂×C₈

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₂²⋊C₄

—

159

C₂²⋊C₄

—

160

C₂²⋊C₄

—

161

C₂²⋊C₄

M₁₆×C₁₉

yes

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₄²

—

166

C₄²

—

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

171

C₂³

C₂×M₁₆×C₁₉

yes

—

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

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

C₁₉×#99

yes

—

190

C₂×C₄

C₁₉×#101

yes

—

191

C₈

—

192

C₂²

—

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

C₁₉×#407

yes

characteristic

198

C₂²

C₂×C₁₉×#99

yes

characteristic

199

C₂²

C₂×C₁₉×#101

yes

characteristic

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₂

—

207

C₂

—

208

C₂

—

209

C₂

C₁₉×#1463

yes

characteristic

210

C₂

C₁₉×#2120

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#99

commutator

C₂⁴

C₂²×C₄×C₁₉

Frattini, cosocle

C₂×C₂²⋊C₄

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

N	H ≅ G/N	type
61. #11518	C₁₉	direct (N × H)
140. C₁₉	#11518	direct (N × H)

H ≅ G/N

type

61. #11518

C₁₉

direct (N × H)

140. C₁₉

#11518

direct (N × H)

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

subgroup	index
C₁₉×#2296	2
C₁₉×#1464	2
C₁₉×#1326	2
#11518	19

subgroup

index

C₁₉×#2296

C₁₉×#1464

C₁₉×#1326

#11518

Subgroups — C₁₉×#11518 #18017477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11518 #18017477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11518 #18017477