Group #18017130 — subgroups

Subgroups — C₁₉×#11171 #18017130

Order 4864.

802 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 802 conjugacy classes of subgroups — too many to draw. Only its 222 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	C₂²×C₁₉×#101	C₂	1	2	yes	maximal
2	C₁₉×#2310	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#344	C₂	1	4	yes	maximal
4	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
5	C₂²×M₁₆×C₁₉	C₂²	1	4	yes	—
6	C₂×C₁₉×#117	C₂²	1	2	yes	—
7	C₂×C₁₉×#101	—	2	4	no	—
8	C₂×C₁₉×#101	—	2	8	no	—
9	C₁₉×#391	—	2	4	no	—
10	C₁₉×#381	C₄	1	4	yes	—
11	C₁₉×#344	—	2	8	no	—
12	C₂²×Q₈×C₁₉	—	2	4	no	—
13	C₂²×Q₈×C₁₉	—	2	4	no	—
14	C₂²×Q₈×C₁₉	—	2	4	no	—
15	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
16	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
17	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	—	2	4	no	—
19	C₂×M₁₆×C₁₉	—	2	4	no	—
20	C₂×M₁₆×C₁₉	—	2	4	no	—
21	C₂×M₁₆×C₁₉	—	2	4	no	—
22	C₂×M₁₆×C₁₉	—	2	4	no	—
23	C₂×M₁₆×C₁₉	D₄	1	8	yes	—
24	C₂²×C₈×C₁₉	—	2	4	no	—
25	C₁₉×#117	—	2	4	no	—
26	C₁₉×#117	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
28	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₉	—	2	2	no	—
30	C₁₉×#101	—	2	16	no	—
31	C₁₉×#95	—	2	8	no	—
32	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
33	C₂×Q₈×C₁₉	—	2	4	no	—
34	C₂×Q₈×C₁₉	—	2	8	no	—
35	C₂×Q₈×C₁₉	—	2	8	no	—
36	C₂×Q₈×C₁₉	—	2	4	no	—
37	C₂×Q₈×C₁₉	—	4	4	no	—
38	C₂×Q₈×C₁₉	—	4	4	no	—
39	C₂×Q₈×C₁₉	—	4	4	no	—
40	C₂×Q₈×C₁₉	—	4	4	no	—
41	C₂²×C₄×C₁₉	—	2	4	no	—
42	C₂²×C₄×C₁₉	—	2	8	no	—
43	C₂²×C₄×C₁₉	—	2	4	no	—
44	C₂²×C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
45	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
46	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
47	C₂²×C₄×C₁₉	#41	1	4	yes	—
48	C₂²×C₄×C₁₉	#41	1	4	yes	—
49	M₁₆×C₁₉	—	2	8	no	—
50	M₁₆×C₁₉	—	2	8	no	—
51	M₁₆×C₁₉	—	4	4	no	—
52	M₁₆×C₁₉	—	4	4	no	—
53	C₂×C₈×C₁₉	—	2	8	no	—
54	C₂×C₈×C₁₉	—	4	4	no	—
55	C₂×C₈×C₁₉	—	4	4	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₂²⋊C₄×C₁₉	—	2	8	no	—
59	C₄²×C₁₉	—	4	4	no	—
60	#11171	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
61	C₂³×C₁₉	—	4	2	no	—
62	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	C₂³×C₁₉	#117	1	2	yes	—
64	C₂³×C₁₉	C₄×D₄	1	4	yes	—
65	Q₈×C₁₉	—	4	8	no	—
66	Q₈×C₁₉	—	4	8	no	—
67	C₂×C₄×C₁₉	—	2	4	no	—
68	C₂×C₄×C₁₉	—	2	8	no	—
69	C₂×C₄×C₁₉	—	4	8	no	—
70	C₂×C₄×C₁₉	—	4	8	no	—
71	C₂×C₄×C₁₉	—	4	4	no	—
72	C₂×C₄×C₁₉	#120	1	2	yes	—
73	C₂×C₄×C₁₉	#121	1	4	yes	—
74	C₂×C₄×C₁₉	#121	1	4	yes	—
75	C₂×C₄×C₁₉	#123	1	4	yes	—
76	C₂×C₄×C₁₉	#123	1	4	yes	—
77	C₂×C₄×C₁₉	#123	1	2	yes	—
78	C₂×C₄×C₁₉	#124	1	4	yes	—
79	C₂×C₄×C₁₉	#126	1	4	yes	—
80	C₈×C₁₉	—	4	8	no	—
81	C₂²×#101	C₂×C₁₉	1	2	yes	—
82	#2310	C₂×C₁₉	1	1	yes	characteristic
83	C₂×#344	C₂×C₁₉	1	4	yes	—
84	C₂²×C₁₉	—	2	2	no	—
85	C₂²×C₁₉	—	2	4	no	—
86	C₂²×C₁₉	—	4	4	no	—
87	C₂²×C₁₉	#381	1	1	yes	characteristic
88	C₂²×C₁₉	#386	1	2	yes	—
89	C₂²×C₁₉	#388	1	4	yes	—
90	C₄×C₁₉	—	4	4	no	—
91	C₄×C₁₉	—	8	4	no	—
92	C₄×C₁₉	#394	1	4	yes	—
93	C₄×C₁₉	#397	1	4	yes	—
94	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
95	C₂²×M₁₆	C₂²×C₁₉	1	4	yes	—
96	C₂×#117	C₂²×C₁₉	1	2	yes	—
97	C₂×#101	—	2	4	no	—
98	C₂×#101	—	2	8	no	—
99	#391	—	2	4	no	—
100	#381	C₄×C₁₉	1	4	yes	—
101	#344	—	2	8	no	—
102	C₂×C₁₉	—	2	2	no	—
103	C₂×C₁₉	—	2	4	no	—
104	C₂×C₁₉	#1440	1	1	yes	characteristic
105	C₂×C₁₉	#1830	1	2	yes	—
106	C₂²×Q₈	—	2	4	no	—
107	C₂²×Q₈	—	2	4	no	—
108	C₂²×Q₈	—	2	4	no	—
109	C₂²×Q₈	D₄×C₁₉	1	4	yes	—
110	C₂³×C₄	C₂×C₄×C₁₉	1	2	yes	—
111	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
112	C₂×M₁₆	—	2	4	no	—
113	C₂×M₁₆	—	2	4	no	—
114	C₂×M₁₆	—	2	4	no	—
115	C₂×M₁₆	—	2	4	no	—
116	C₂×M₁₆	—	2	4	no	—
117	C₂×M₁₆	D₄×C₁₉	1	8	yes	—
118	C₂²×C₈	—	2	4	no	—
119	#117	—	2	4	no	—
120	#117	—	2	4	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	4	yes	—
123	C₂×C₄²	—	2	2	no	—
124	#101	—	2	16	no	—
125	#95	—	2	8	no	—
126	C₁₉	#11171	1	1	yes	characteristic, direct product factor, Sylow
127	C₂⁴	C₂²×C₄×C₁₉	1	1	yes	characteristic
128	C₂×Q₈	—	2	4	no	—
129	C₂×Q₈	—	2	8	no	—
130	C₂×Q₈	—	2	8	no	—
131	C₂×Q₈	—	2	4	no	—
132	C₂×Q₈	—	4	4	no	—
133	C₂×Q₈	—	4	4	no	—
134	C₂×Q₈	—	4	4	no	—
135	C₂×Q₈	—	4	4	no	—
136	C₂²×C₄	—	2	4	no	—
137	C₂²×C₄	—	2	8	no	—
138	C₂²×C₄	—	2	4	no	—
139	C₂²×C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
140	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
141	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
142	C₂²×C₄	#41×C₁₉	1	4	yes	—
143	C₂²×C₄	#41×C₁₉	1	4	yes	—
144	M₁₆	—	2	8	no	—
145	M₁₆	—	2	8	no	—
146	M₁₆	—	4	4	no	—
147	M₁₆	—	4	4	no	—
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	C₂²⋊C₄	—	2	8	no	—
154	C₄²	—	4	4	no	—
155	C₂³	—	4	2	no	—
156	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
157	C₂³	C₁₉×#117	1	2	yes	—
158	C₂³	C₄×D₄×C₁₉	1	4	yes	—
159	Q₈	—	4	8	no	—
160	Q₈	—	4	8	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	2	8	no	—
163	C₂×C₄	—	4	8	no	—
164	C₂×C₄	—	4	8	no	—
165	C₂×C₄	—	4	4	no	—
166	C₂×C₄	C₁₉×#120	1	2	yes	—
167	C₂×C₄	C₁₉×#121	1	4	yes	—
168	C₂×C₄	C₁₉×#121	1	4	yes	—
169	C₂×C₄	C₁₉×#123	1	4	yes	—
170	C₂×C₄	C₁₉×#123	1	4	yes	—
171	C₂×C₄	C₁₉×#123	1	2	yes	—
172	C₂×C₄	C₁₉×#124	1	4	yes	—
173	C₂×C₄	C₁₉×#126	1	4	yes	—
174	C₈	—	4	8	no	—
175	C₂²	—	2	2	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	4	4	no	—
178	C₂²	C₁₉×#381	1	1	yes	characteristic
179	C₂²	C₁₉×#386	1	2	yes	—
180	C₂²	C₁₉×#388	1	4	yes	—
181	C₄	—	4	4	no	—
182	C₄	—	8	4	no	—
183	C₄	C₁₉×#394	1	4	yes	—
184	C₄	C₁₉×#397	1	4	yes	—
185	C₂	—	2	2	no	—
186	C₂	—	2	4	no	—
187	C₂	C₁₉×#1440	1	1	yes	characteristic
188	C₂	C₁₉×#1830	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₉×#101

C₂

yes

maximal

C₁₉×#2310

C₂

yes

maximal, characteristic

C₂×C₁₉×#344

C₂

yes

maximal

C₂³×Q₈×C₁₉

C₂²

yes

characteristic

C₂²×M₁₆×C₁₉

C₂²

yes

—

C₂×C₁₉×#117

C₂²

yes

—

C₂×C₁₉×#101

—

C₂×C₁₉×#101

—

C₁₉×#391

—

C₁₉×#381

C₄

yes

—

C₁₉×#344

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂³×C₄×C₁₉

C₂×C₄

yes

—

C₂³×C₄×C₁₉

C₂³

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

—

C₂×M₁₆×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

—

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₁₉×#101

—

C₁₉×#95

—

C₂⁴×C₁₉

C₂²×C₄

yes

characteristic

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

#41

yes

—

C₂²×C₄×C₁₉

#41

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

#11171

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂³×C₁₉

#117

yes

—

C₂³×C₁₉

C₄×D₄

yes

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#120

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#121

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

#124

yes

—

C₂×C₄×C₁₉

#126

yes

—

C₈×C₁₉

—

C₂²×#101

C₂×C₁₉

yes

—

#2310

C₂×C₁₉

yes

characteristic

C₂×#344

C₂×C₁₉

yes

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

#381

yes

characteristic

C₂²×C₁₉

#386

yes

—

C₂²×C₁₉

#388

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#394

yes

—

C₄×C₁₉

#397

yes

—

C₂³×Q₈

C₂²×C₁₉

yes

characteristic

C₂²×M₁₆

C₂²×C₁₉

yes

—

C₂×#117

C₂²×C₁₉

yes

—

C₂×#101

—

C₂×#101

—

#391

—

100

#381

C₄×C₁₉

yes

—

101

#344

—

102

C₂×C₁₉

—

103

C₂×C₁₉

—

104

C₂×C₁₉

#1440

yes

characteristic

105

C₂×C₁₉

#1830

yes

—

106

C₂²×Q₈

—

107

C₂²×Q₈

—

108

C₂²×Q₈

—

109

C₂²×Q₈

D₄×C₁₉

yes

—

110

C₂³×C₄

C₂×C₄×C₁₉

yes

—

111

C₂³×C₄

C₂³×C₁₉

yes

characteristic

112

C₂×M₁₆

—

113

C₂×M₁₆

—

114

C₂×M₁₆

—

115

C₂×M₁₆

—

116

C₂×M₁₆

—

117

C₂×M₁₆

D₄×C₁₉

yes

—

118

C₂²×C₈

—

119

#117

—

120

#117

—

121

C₂×C₄⋊C₄

—

122

C₂×C₂²⋊C₄

C₂×C₄×C₁₉

yes

—

123

C₂×C₄²

—

124

#101

—

125

#95

—

126

C₁₉

#11171

yes

characteristic, direct product factor, Sylow

127

C₂⁴

C₂²×C₄×C₁₉

yes

characteristic

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂×Q₈

—

131

C₂×Q₈

—

132

C₂×Q₈

—

133

C₂×Q₈

—

134

C₂×Q₈

—

135

C₂×Q₈

—

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

140

C₂²×C₄

C₂×D₄×C₁₉

yes

—

141

C₂²×C₄

C₂×D₄×C₁₉

yes

—

142

C₂²×C₄

#41×C₁₉

yes

—

143

C₂²×C₄

#41×C₁₉

yes

—

144

M₁₆

—

145

M₁₆

—

146

M₁₆

—

147

M₁₆

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₄⋊C₄

—

152

C₄⋊C₄

—

153

C₂²⋊C₄

—

154

C₄²

—

155

C₂³

—

156

C₂³

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

157

C₂³

C₁₉×#117

yes

—

158

C₂³

C₄×D₄×C₁₉

yes

—

159

Q₈

—

160

Q₈

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

C₁₉×#120

yes

—

167

C₂×C₄

C₁₉×#121

yes

—

168

C₂×C₄

C₁₉×#121

yes

—

169

C₂×C₄

C₁₉×#123

yes

—

170

C₂×C₄

C₁₉×#123

yes

—

171

C₂×C₄

C₁₉×#123

yes

—

172

C₂×C₄

C₁₉×#124

yes

—

173

C₂×C₄

C₁₉×#126

yes

—

174

C₈

—

175

C₂²

—

176

C₂²

—

177

C₂²

—

178

C₂²

C₁₉×#381

yes

characteristic

179

C₂²

C₁₉×#386

yes

—

180

C₂²

C₁₉×#388

yes

—

181

C₄

—

182

C₄

—

183

C₄

C₁₉×#394

yes

—

184

C₄

C₁₉×#397

yes

—

185

C₂

—

186

C₂

—

187

C₂

C₁₉×#1440

yes

characteristic

188

C₂

C₁₉×#1830

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	#381
commutator	C₂⁴	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

#381

commutator

C₂⁴

C₂²×C₄×C₁₉

Frattini, cosocle

C₂³×C₄

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

C₂²×C₄

LCS

G ▷ C₂⁴ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

N	H ≅ G/N	type
60. #11171	C₁₉	direct (N × H)
126. C₁₉	#11171	direct (N × H)

H ≅ G/N

type

60. #11171

C₁₉

direct (N × H)

126. C₁₉

#11171

direct (N × H)

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

subgroup	index
C₂²×C₁₉×#101	2
C₁₉×#2310	2
C₂×C₁₉×#344	2
#11171	19

subgroup

index

C₂²×C₁₉×#101

C₁₉×#2310

C₂×C₁₉×#344

#11171

Subgroups — C₁₉×#11171 #18017130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#11171 #18017130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11171 #18017130