Group #18017450 — subgroups

Subgroups — C₁₉×#11491 #18017450

Order 4864.

356 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2931	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2163	C₂	1	2	yes	maximal, complemented
3	C₁₉×#1315	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₉×#131	C₄	1	2	yes	—
5	C₁₉×#532	C₄	1	1	yes	characteristic
6	C₁₉×#436	—	2	2	no	—
7	C₈×D₄×C₁₉	—	2	2	no	—
8	C₁₉×#423	C₄	1	1	yes	characteristic
9	C₁₉×#408	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
11	C₁₉×C₄⋊C₁₆	—	2	2	no	—
12	C₁₉×C₂²⋊C₁₆	C₂²	1	4	yes	—
13	C₁₉×#346	—	2	2	no	—
14	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
15	C₁₉×#131	—	4	4	no	—
16	C₂×M₁₆×C₁₉	—	2	2	no	—
17	C₂×M₁₆×C₁₉	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₉	—	2	2	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
21	C₁₉×C₄⋊Q₈	C₈	1	1	yes	characteristic
22	C₁₉×#127	C₈	1	1	yes	characteristic
23	C₁₉×#124	C₈	1	2	yes	—
24	C₁₉×#121	—	2	2	no	—
25	C₄×D₄×C₁₉	—	2	2	no	—
26	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
27	C₂×C₁₆×C₁₉	—	2	4	no	—
28	C₁₉×C₄⋊C₈	—	2	2	no	—
29	C₁₉×C₂²⋊C₈	—	2	4	no	—
30	C₄×C₈×C₁₉	D₄	1	2	yes	—
31	C₄×C₈×C₁₉	D₄	1	2	yes	—
32	#41×C₁₉	—	4	2	no	—
33	#41×C₁₉	—	4	2	no	—
34	C₂×Q₈×C₁₉	C₂×C₈	1	2	yes	—
35	C₂×D₄×C₁₉	—	2	2	no	—
36	C₂×D₄×C₁₉	—	2	2	no	—
37	C₂×D₄×C₁₉	C₂×C₈	1	2	yes	—
38	C₂²×C₄×C₁₉	—	2	2	no	—
39	C₂²×C₄×C₁₉	M₁₆	1	2	yes	—
40	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
41	M₁₆×C₁₉	—	4	4	no	—
42	M₁₆×C₁₉	—	4	2	no	—
43	C₂×C₈×C₁₉	—	2	2	no	—
44	C₂×C₈×C₁₉	—	2	2	no	—
45	C₂×C₈×C₁₉	—	4	1	no	—
46	C₂×C₈×C₁₉	—	4	4	no	—
47	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
50	C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂²⋊C₄×C₁₉	—	2	4	no	—
52	C₄²×C₁₉	C₂²⋊C₄	1	2	yes	—
53	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
54	C₄²×C₁₉	C₂×C₈	1	1	yes	characteristic
55	C₁₆×C₁₉	—	4	4	no	—
56	#11491	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
57	C₂³×C₁₉	—	2	2	no	—
58	C₂³×C₁₉	C₂×M₁₆	1	1	yes	characteristic
59	Q₈×C₁₉	—	4	2	no	—
60	D₄×C₁₉	—	4	2	no	—
61	D₄×C₁₉	—	4	4	no	—
62	D₄×C₁₉	—	4	4	no	—
63	C₂×C₄×C₁₉	—	2	1	no	—
64	C₂×C₄×C₁₉	—	2	1	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
70	C₂×C₄×C₁₉	C₂²⋊C₈	1	2	yes	—
71	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₉	C₂²×C₈	1	1	yes	characteristic
73	C₈×C₁₉	—	2	2	no	—
74	C₈×C₁₉	—	2	1	no	—
75	C₈×C₁₉	—	4	2	no	—
76	C₈×C₁₉	#100	1	2	yes	—
77	#2931	C₂×C₁₉	1	1	yes	characteristic
78	#2163	C₂×C₁₉	1	2	yes	complemented
79	#1315	C₂×C₁₉	1	4	yes	complemented
80	C₂²×C₁₉	—	2	2	no	—
81	C₂²×C₁₉	—	2	1	no	—
82	C₂²×C₁₉	—	4	4	no	—
83	C₂²×C₁₉	—	4	2	no	—
84	C₂²×C₁₉	C₂×C₂²⋊C₈	1	1	yes	characteristic
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	1	no	—
88	C₄×C₁₉	—	4	2	no	—
89	C₄×C₁₉	#410	1	1	yes	characteristic
90	C₄×C₁₉	C₂×#100	1	1	yes	characteristic
91	C₂×#131	C₄×C₁₉	1	2	yes	—
92	#532	C₄×C₁₉	1	1	yes	characteristic
93	#436	—	2	2	no	—
94	C₈×D₄	—	2	2	no	—
95	#423	C₄×C₁₉	1	1	yes	characteristic
96	#408	C₂²×C₁₉	1	2	yes	—
97	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
98	C₄⋊C₁₆	—	2	2	no	—
99	C₂²⋊C₁₆	C₂²×C₁₉	1	4	yes	—
100	#346	—	2	2	no	—
101	C₂×C₁₉	—	4	1	no	—
102	C₂×C₁₉	—	8	2	no	—
103	C₂×C₁₉	#1460	1	1	yes	characteristic
104	C₂×C₁₉	#2117	1	2	yes	—
105	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
106	#131	—	4	4	no	—
107	C₂×M₁₆	—	2	2	no	—
108	C₂×M₁₆	C₂×C₄×C₁₉	1	2	yes	—
109	C₂²×C₈	—	2	2	no	—
110	C₂²×C₈	C₂×C₄×C₁₉	1	1	yes	characteristic
111	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
112	C₄⋊Q₈	C₈×C₁₉	1	1	yes	characteristic
113	#127	C₈×C₁₉	1	1	yes	characteristic
114	#124	C₈×C₁₉	1	2	yes	—
115	#121	—	2	2	no	—
116	C₄×D₄	—	2	2	no	—
117	C₂×C₄²	C₂×C₄×C₁₉	1	1	yes	characteristic
118	C₂×C₁₆	—	2	4	no	—
119	C₄⋊C₈	—	2	2	no	—
120	C₂²⋊C₈	—	2	4	no	—
121	C₄×C₈	D₄×C₁₉	1	2	yes	—
122	C₄×C₈	D₄×C₁₉	1	2	yes	—
123	C₁₉	#11491	1	1	yes	characteristic, direct product factor, Sylow
124	#41	—	4	2	no	—
125	#41	—	4	2	no	—
126	C₂×Q₈	C₂×C₈×C₁₉	1	2	yes	—
127	C₂×D₄	—	2	2	no	—
128	C₂×D₄	—	2	2	no	—
129	C₂×D₄	C₂×C₈×C₁₉	1	2	yes	—
130	C₂²×C₄	—	2	2	no	—
131	C₂²×C₄	M₁₆×C₁₉	1	2	yes	—
132	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
133	M₁₆	—	4	4	no	—
134	M₁₆	—	4	2	no	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	4	1	no	—
138	C₂×C₈	—	4	4	no	—
139	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
140	C₂×C₈	C₂²⋊C₄×C₁₉	1	1	yes	characteristic
141	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
142	C₄⋊C₄	—	2	2	no	—
143	C₂²⋊C₄	—	2	4	no	—
144	C₄²	C₂²⋊C₄×C₁₉	1	2	yes	—
145	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
146	C₄²	C₂×C₈×C₁₉	1	1	yes	characteristic
147	C₁₆	—	4	4	no	—
148	C₂³	—	2	2	no	—
149	C₂³	C₂×M₁₆×C₁₉	1	1	yes	characteristic
150	Q₈	—	4	2	no	—
151	D₄	—	4	2	no	—
152	D₄	—	4	4	no	—
153	D₄	—	4	4	no	—
154	C₂×C₄	—	2	1	no	—
155	C₂×C₄	—	2	1	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	4	2	no	—
158	C₂×C₄	—	4	2	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
161	C₂×C₄	C₁₉×C₂²⋊C₈	1	2	yes	—
162	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
163	C₂×C₄	C₂²×C₈×C₁₉	1	1	yes	characteristic
164	C₈	—	2	2	no	—
165	C₈	—	2	1	no	—
166	C₈	—	4	2	no	—
167	C₈	C₁₉×#100	1	2	yes	—
168	C₂²	—	2	1	no	—
169	C₂²	—	2	2	no	—
170	C₂²	—	4	2	no	—
171	C₂²	—	4	4	no	—
172	C₂²	C₂×C₁₉×C₂²⋊C₈	1	1	yes	characteristic
173	C₄	—	2	1	no	—
174	C₄	—	2	2	no	—
175	C₄	—	2	2	no	—
176	C₄	—	4	2	no	—
177	C₄	C₁₉×#410	1	1	yes	characteristic
178	C₄	C₂×C₁₉×#100	1	1	yes	characteristic
179	C₂	—	4	1	no	—
180	C₂	—	8	2	no	—
181	C₂	C₁₉×#1460	1	1	yes	characteristic
182	C₂	C₁₉×#2117	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#2931

C₂

yes

maximal, characteristic

C₁₉×#2163

C₂

yes

maximal, complemented

C₁₉×#1315

C₂

yes

maximal, complemented

C₂×C₁₉×#131

C₄

yes

—

C₁₉×#532

C₄

yes

characteristic

C₁₉×#436

—

C₈×D₄×C₁₉

—

C₁₉×#423

C₄

yes

characteristic

C₁₉×#408

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×C₄⋊C₁₆

—

C₁₉×C₂²⋊C₁₆

C₂²

yes

—

C₁₉×#346

—

C₂×#41×C₁₉

C₂×C₄

yes

—

C₁₉×#131

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

C₈

yes

characteristic

C₁₉×#127

C₈

yes

characteristic

C₁₉×#124

C₈

yes

—

C₁₉×#121

—

C₄×D₄×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₉

—

C₁₉×C₄⋊C₈

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

D₄

yes

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

C₂×C₈

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂×C₈

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

M₁₆

yes

—

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

C₂²⋊C₄

yes

—

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₄²×C₁₉

C₂×C₈

yes

characteristic

C₁₆×C₁₉

—

#11491

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

C₂×M₁₆

yes

characteristic

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

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₂²⋊C₈

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

C₂²×C₈

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#100

yes

—

#2931

C₂×C₁₉

yes

characteristic

#2163

C₂×C₁₉

yes

complemented

#1315

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

#532

C₄×C₁₉

yes

characteristic

#436

—

C₈×D₄

—

#423

C₄×C₁₉

yes

characteristic

#408

C₂²×C₁₉

yes

—

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

C₄⋊C₁₆

—

C₂²⋊C₁₆

C₂²×C₁₉

yes

—

100

#346

—

101

C₂×C₁₉

—

102

C₂×C₁₉

—

103

C₂×C₁₉

#1460

yes

characteristic

104

C₂×C₁₉

#2117

yes

—

105

C₂×#41

C₂×C₄×C₁₉

yes

—

106

#131

—

107

C₂×M₁₆

—

108

C₂×M₁₆

C₂×C₄×C₁₉

yes

—

109

C₂²×C₈

—

110

C₂²×C₈

C₂×C₄×C₁₉

yes

characteristic

111

C₂²×C₈

C₂³×C₁₉

yes

characteristic

112

C₄⋊Q₈

C₈×C₁₉

yes

characteristic

113

#127

C₈×C₁₉

yes

characteristic

114

#124

C₈×C₁₉

yes

—

115

#121

—

116

C₄×D₄

—

117

C₂×C₄²

C₂×C₄×C₁₉

yes

characteristic

118

C₂×C₁₆

—

119

C₄⋊C₈

—

120

C₂²⋊C₈

—

121

C₄×C₈

D₄×C₁₉

yes

—

122

C₄×C₈

D₄×C₁₉

yes

—

123

C₁₉

#11491

yes

characteristic, direct product factor, Sylow

124

#41

—

125

#41

—

126

C₂×Q₈

C₂×C₈×C₁₉

yes

—

127

C₂×D₄

—

128

C₂×D₄

—

129

C₂×D₄

C₂×C₈×C₁₉

yes

—

130

C₂²×C₄

—

131

C₂²×C₄

M₁₆×C₁₉

yes

—

132

C₂²×C₄

C₂²×C₄×C₁₉

yes

characteristic

133

M₁₆

—

134

M₁₆

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

140

C₂×C₈

C₂²⋊C₄×C₁₉

yes

characteristic

141

C₂×C₈

C₂×D₄×C₁₉

yes

—

142

C₄⋊C₄

—

143

C₂²⋊C₄

—

144

C₄²

C₂²⋊C₄×C₁₉

yes

—

145

C₄²

C₂×C₈×C₁₉

yes

characteristic

146

C₄²

C₂×C₈×C₁₉

yes

characteristic

147

C₁₆

—

148

C₂³

—

149

C₂³

C₂×M₁₆×C₁₉

yes

characteristic

150

Q₈

—

151

D₄

—

152

D₄

—

153

D₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

C₁₉×C₂²⋊C₈

yes

—

161

C₂×C₄

C₁₉×C₂²⋊C₈

yes

—

162

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

163

C₂×C₄

C₂²×C₈×C₁₉

yes

characteristic

164

C₈

—

165

C₈

—

166

C₈

—

167

C₈

C₁₉×#100

yes

—

168

C₂²

—

169

C₂²

—

170

C₂²

—

171

C₂²

—

172

C₂²

C₂×C₁₉×C₂²⋊C₈

yes

characteristic

173

C₄

—

174

C₄

—

175

C₄

—

176

C₄

—

177

C₄

C₁₉×#410

yes

characteristic

178

C₄

C₂×C₁₉×#100

yes

characteristic

179

C₂

—

180

C₂

—

181

C₂

C₁₉×#1460

yes

characteristic

182

C₂

C₁₉×#2117

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₈×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
socle	C₂²×C₁₉	C₂×C₂²⋊C₈
prime radical	C₁₉×#532	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

commutator

C₂×C₄

C₂²×C₈×C₁₉

Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

socle

C₂²×C₁₉

C₂×C₂²⋊C₈

prime radical

C₁₉×#532

C₄

LCS

G ▷ C₂×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2163	C₂	semidirect
3. C₁₉×#1315	C₂	semidirect
56. #11491	C₁₉	direct (N × H)
78. #2163	C₂×C₁₉	semidirect
79. #1315	C₂×C₁₉	semidirect
123. C₁₉	#11491	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2163

C₂

semidirect

3. C₁₉×#1315

C₂

semidirect

56. #11491

C₁₉

direct (N × H)

78. #2163

C₂×C₁₉

semidirect

79. #1315

C₂×C₁₉

semidirect

123. C₁₉

#11491

direct (N × H)

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

subgroup	index
C₁₉×#2931	2
C₁₉×#2163	2
C₁₉×#1315	2
#11491	19

subgroup

index

C₁₉×#2931

C₁₉×#2163

C₁₉×#1315

#11491

Subgroups — C₁₉×#11491 #18017450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11491 #18017450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11491 #18017450