Group #18018831 — subgroups

Subgroups — C₁₉×#12872 #18018831

Order 4864.

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

normal subgroups only

This group has 398 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	C₂×C₁₉×#427	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2112	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1387	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₉×#117	—	2	1	no	—
7	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
8	C₂×C₁₉×#108	C₂²	1	2	yes	—
9	C₁₉×#427	—	2	2	no	—
10	C₁₉×#427	C₄	1	4	yes	—
11	C₂×C₁₉×#107	C₂²	1	2	yes	—
12	C₂×C₁₉×#106	—	2	1	no	—
13	C₁₉×#407	—	2	1	no	—
14	C₁₉×C₂²⋊C₁₆	—	2	2	no	—
15	C₁₉×#341	—	2	1	no	—
16	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
17	C₂×M₁₆×C₁₉	—	2	2	no	—
18	C₂²×C₈×C₁₉	—	2	4	no	—
19	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₉	D₄	1	2	yes	—
22	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
23	C₁₉×#117	—	2	4	no	—
24	C₁₉×#117	—	4	2	no	—
25	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	4	1	no	—
27	C₂×C₄²×C₁₉	—	4	1	no	—
28	C₁₉×M₃₂	—	2	4	no	—
29	C₂×C₁₆×C₁₉	—	2	2	no	—
30	C₁₉×#108	—	2	4	no	—
31	C₁₉×#107	—	2	2	no	—
32	C₁₉×#107	C₂×C₄	1	4	yes	—
33	C₁₉×#106	—	2	4	no	—
34	C₁₉×C₂²⋊C₈	—	4	2	no	—
35	C₂⁴×C₁₉	SD₁₆	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	—	2	2	no	—
37	C₂²×C₄×C₁₉	—	2	2	no	—
38	C₂²×C₄×C₁₉	—	4	2	no	—
39	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₉	D₈	1	2	yes	—
41	C₂²×C₄×C₁₉	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
43	M₁₆×C₁₉	—	4	2	no	—
44	M₁₆×C₁₉	—	4	2	no	—
45	C₂×C₈×C₁₉	—	2	2	no	—
46	C₂×C₈×C₁₉	—	2	4	no	—
47	C₂×C₈×C₁₉	—	2	4	no	—
48	C₂×C₈×C₁₉	—	4	2	no	—
49	C₂×C₈×C₁₉	C₂²⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₉	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₉	#41	1	4	yes	—
53	C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₄⋊C₄×C₁₉	—	4	2	no	—
55	C₂²⋊C₄×C₁₉	—	4	4	no	—
56	C₄²×C₁₉	—	4	4	no	—
57	C₁₆×C₁₉	—	4	2	no	—
58	#12872	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂³×C₁₉	—	2	2	no	—
60	C₂³×C₁₉	—	4	2	no	—
61	C₂³×C₁₉	#102	1	2	yes	—
62	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
63	C₂×C₄×C₁₉	—	2	2	no	—
64	C₂×C₄×C₁₉	—	2	2	no	—
65	C₂×C₄×C₁₉	—	2	2	no	—
66	C₂×C₄×C₁₉	—	2	4	no	—
67	C₂×C₄×C₁₉	—	4	4	no	—
68	C₂×C₄×C₁₉	—	8	4	no	—
69	C₂×C₄×C₁₉	#102	1	2	yes	—
70	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₉	#123	1	2	yes	—
72	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₁₉	#137	1	2	yes	—
74	C₈×C₁₉	—	2	2	no	—
75	C₈×C₁₉	—	8	2	no	—
76	C₈×C₁₉	#117	1	2	yes	—
77	C₈×C₁₉	#123	1	2	yes	—
78	C₂×#427	C₂×C₁₉	1	1	yes	characteristic
79	#2112	C₂×C₁₉	1	1	yes	characteristic
80	#1810	C₂×C₁₉	1	1	yes	characteristic
81	#1387	C₂×C₁₉	1	4	yes	complemented
82	C₂²×C₁₉	—	2	2	no	—
83	C₂²×C₁₉	—	2	2	no	—
84	C₂²×C₁₉	—	2	4	no	—
85	C₂²×C₁₉	—	4	4	no	—
86	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
87	C₂²×C₁₉	#483	1	2	yes	—
88	C₄×C₁₉	—	2	2	no	—
89	C₄×C₁₉	—	8	4	no	—
90	C₄×C₁₉	#381	1	1	yes	characteristic
91	C₄×C₁₉	#419	1	1	yes	characteristic
92	C₄×C₁₉	#480	1	2	yes	—
93	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
94	C₂×#117	—	2	1	no	—
95	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
96	C₂×#108	C₂²×C₁₉	1	2	yes	—
97	#427	—	2	2	no	—
98	#427	C₄×C₁₉	1	4	yes	—
99	C₂×#107	C₂²×C₁₉	1	2	yes	—
100	C₂×#106	—	2	1	no	—
101	#407	—	2	1	no	—
102	C₂²⋊C₁₆	—	2	2	no	—
103	#341	—	2	1	no	—
104	C₂×C₁₉	—	2	2	no	—
105	C₂×C₁₉	—	4	2	no	—
106	C₂×C₁₉	#1823	1	1	yes	characteristic
107	C₂×C₁₉	#2148	1	2	yes	—
108	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
109	C₂×M₁₆	—	2	2	no	—
110	C₂²×C₈	—	2	4	no	—
111	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
112	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
113	C₂²×C₈	D₄×C₁₉	1	2	yes	—
114	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
115	#117	—	2	4	no	—
116	#117	—	4	2	no	—
117	C₂×C₄⋊C₄	—	2	2	no	—
118	C₂×C₂²⋊C₄	—	4	1	no	—
119	C₂×C₄²	—	4	1	no	—
120	M₃₂	—	2	4	no	—
121	C₂×C₁₆	—	2	2	no	—
122	#108	—	2	4	no	—
123	#107	—	2	2	no	—
124	#107	C₂×C₄×C₁₉	1	4	yes	—
125	#106	—	2	4	no	—
126	C₂²⋊C₈	—	4	2	no	—
127	C₁₉	#12872	1	1	yes	characteristic, direct product factor, Sylow
128	C₂⁴	SD₁₆×C₁₉	1	1	yes	characteristic
129	C₂²×C₄	—	2	2	no	—
130	C₂²×C₄	—	2	2	no	—
131	C₂²×C₄	—	4	2	no	—
132	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
133	C₂²×C₄	D₈×C₁₉	1	2	yes	—
134	C₂²×C₄	SD₁₆×C₁₉	1	1	yes	characteristic
135	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
136	M₁₆	—	4	2	no	—
137	M₁₆	—	4	2	no	—
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	4	2	no	—
142	C₂×C₈	C₂²⋊C₄×C₁₉	1	2	yes	—
143	C₂×C₈	C₂²×C₄×C₁₉	1	1	yes	characteristic
144	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
145	C₂×C₈	#41×C₁₉	1	4	yes	—
146	C₄⋊C₄	—	2	4	no	—
147	C₄⋊C₄	—	4	2	no	—
148	C₂²⋊C₄	—	4	4	no	—
149	C₄²	—	4	4	no	—
150	C₁₆	—	4	2	no	—
151	C₂³	—	2	2	no	—
152	C₂³	—	4	2	no	—
153	C₂³	C₁₉×#102	1	2	yes	—
154	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	4	4	no	—
160	C₂×C₄	—	8	4	no	—
161	C₂×C₄	C₁₉×#102	1	2	yes	—
162	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
163	C₂×C₄	C₁₉×#123	1	2	yes	—
164	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
165	C₂×C₄	C₁₉×#137	1	2	yes	—
166	C₈	—	2	2	no	—
167	C₈	—	8	2	no	—
168	C₈	C₁₉×#117	1	2	yes	—
169	C₈	C₁₉×#123	1	2	yes	—
170	C₂²	—	2	2	no	—
171	C₂²	—	2	4	no	—
172	C₂²	—	2	2	no	—
173	C₂²	—	4	4	no	—
174	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
175	C₂²	C₁₉×#483	1	2	yes	—
176	C₄	—	2	2	no	—
177	C₄	—	8	4	no	—
178	C₄	C₁₉×#381	1	1	yes	characteristic
179	C₄	C₁₉×#419	1	1	yes	characteristic
180	C₄	C₁₉×#480	1	2	yes	—
181	C₂	—	2	2	no	—
182	C₂	—	4	2	no	—
183	C₂	C₁₉×#1823	1	1	yes	characteristic
184	C₂	C₁₉×#2148	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₁₉×#427

C₂

yes

maximal, characteristic

C₁₉×#2112

C₂

yes

maximal, characteristic

C₁₉×#1810

C₂

yes

maximal, characteristic

C₁₉×#1387

C₂

yes

maximal, complemented

C₂³×C₈×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#117

—

C₂×C₁₉×M₃₂

C₂²

yes

—

C₂×C₁₉×#108

C₂²

yes

—

C₁₉×#427

—

C₁₉×#427

C₄

yes

—

C₂×C₁₉×#107

C₂²

yes

—

C₂×C₁₉×#106

—

C₁₉×#407

—

C₁₉×C₂²⋊C₁₆

—

C₁₉×#341

—

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂²×C₈×C₁₉

—

C₂²×C₈×C₁₉

C₂×C₄

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

D₄

yes

—

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×#117

—

C₁₉×#117

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

—

C₁₉×#108

—

C₁₉×#107

—

C₁₉×#107

C₂×C₄

yes

—

C₁₉×#106

—

C₁₉×C₂²⋊C₈

—

C₂⁴×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

SD₁₆

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂²⋊C₄

yes

—

C₂×C₈×C₁₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

#41

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₁₆×C₁₉

—

#12872

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#102

yes

—

C₂³×C₁₉

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

#102

yes

—

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₉

#123

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

#137

yes

—

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

#117

yes

—

C₈×C₁₉

#123

yes

—

C₂×#427

C₂×C₁₉

yes

characteristic

#2112

C₂×C₁₉

yes

characteristic

#1810

C₂×C₁₉

yes

characteristic

#1387

C₂×C₁₉

yes

complemented

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂×#102

yes

characteristic

C₂²×C₁₉

#483

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

yes

C₄×C₁₉

yes

C₄×C₁₉

yes

—

C₂³×C₈

C₂²×C₁₉

yes

characteristic

C₂×#117

—

C₂×M₃₂

C₂²×C₁₉

yes

—

C₂×#108

C₂²×C₁₉

yes

—

#427

—

#427

C₄×C₁₉

yes

—

C₂×#107

C₂²×C₁₉

yes

—

100

C₂×#106

—

101

#407

—

102

C₂²⋊C₁₆

—

103

#341

—

104

C₂×C₁₉

—

105

C₂×C₁₉

—

106

C₂×C₁₉

#1823

yes

characteristic

107

C₂×C₁₉

#2148

yes

—

108

C₂³×C₄

D₄×C₁₉

yes

characteristic

109

C₂×M₁₆

—

110

C₂²×C₈

—

111

C₂²×C₈

C₂×C₄×C₁₉

yes

—

112

C₂²×C₈

D₄×C₁₉

yes

characteristic

113

C₂²×C₈

D₄×C₁₉

yes

—

114

C₂²×C₈

C₂³×C₁₉

yes

characteristic

115

#117

—

116

#117

—

117

C₂×C₄⋊C₄

—

118

C₂×C₂²⋊C₄

—

119

C₂×C₄²

—

120

M₃₂

—

121

C₂×C₁₆

—

122

#108

—

123

#107

—

124

#107

C₂×C₄×C₁₉

yes

—

125

#106

—

126

C₂²⋊C₈

—

127

C₁₉

#12872

yes

characteristic, direct product factor, Sylow

128

C₂⁴

SD₁₆×C₁₉

yes

characteristic

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

C₂²⋊C₄×C₁₉

yes

—

133

C₂²×C₄

D₈×C₁₉

yes

—

134

C₂²×C₄

SD₁₆×C₁₉

yes

characteristic

135

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

136

M₁₆

—

137

M₁₆

—

138

C₂×C₈

—

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

C₂²⋊C₄×C₁₉

yes

—

143

C₂×C₈

C₂²×C₄×C₁₉

yes

characteristic

144

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

145

C₂×C₈

#41×C₁₉

yes

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₂²⋊C₄

—

149

C₄²

—

150

C₁₆

—

151

C₂³

—

152

C₂³

—

153

C₂³

C₁₉×#102

yes

—

154

C₂³

C₂×SD₁₆×C₁₉

yes

characteristic

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

C₁₉×#102

yes

—

162

C₂×C₄

C₂×C₂²⋊C₄×C₁₉

yes

characteristic

163

C₂×C₄

C₁₉×#123

yes

—

164

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

165

C₂×C₄

C₁₉×#137

yes

—

166

C₈

—

167

C₈

—

168

C₈

C₁₉×#117

yes

—

169

C₈

C₁₉×#123

yes

—

170

C₂²

—

171

C₂²

—

172

C₂²

—

173

C₂²

—

174

C₂²

C₂×C₁₉×#102

yes

characteristic

175

C₂²

C₁₉×#483

yes

—

176

C₄

—

177

C₄

—

178

C₄

C₁₉×#381

yes

characteristic

179

C₄

C₁₉×#419

yes

characteristic

180

C₄

C₁₉×#480

yes

—

181

C₂

—

182

C₂

—

183

C₂

C₁₉×#1823

yes

characteristic

184

C₂

C₁₉×#2148

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₉
Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂⁴×C₁₉	SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂×#102

commutator

C₂×C₈

C₂²×C₄×C₁₉

Frattini, cosocle

C₂²×C₈

C₂³×C₁₉

prime radical

C₂⁴×C₁₉

SD₁₆

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ C₂³×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
4. C₁₉×#1387	C₂	semidirect
58. #12872	C₁₉	direct (N × H)
81. #1387	C₂×C₁₉	semidirect
127. C₁₉	#12872	direct (N × H)

H ≅ G/N

type

4. C₁₉×#1387

C₂

semidirect

58. #12872

C₁₉

direct (N × H)

81. #1387

C₂×C₁₉

semidirect

127. C₁₉

#12872

direct (N × H)

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

subgroup	index
C₂×C₁₉×#427	2
C₁₉×#2112	2
C₁₉×#1810	2
C₁₉×#1387	2
#12872	19

subgroup

index

C₂×C₁₉×#427

C₁₉×#2112

C₁₉×#1810

C₁₉×#1387

#12872

Subgroups — C₁₉×#12872 #18018831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#12872 #18018831

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#12872 #18018831