Group #18039780 — subgroups

Subgroups — C₁₉×#33821 #18039780

Order 4864.

484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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×#3170	C₂	1	2	yes	maximal
2	C₁₉×#2225	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2219	C₂	1	4	yes	maximal
4	C₁₉×#2209	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2150	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#533	—	2	2	no	—
7	C₂×C₁₉×Q₃₂	C₂²	1	4	yes	—
8	C₂×C₁₉×M₃₂	C₂²	1	2	yes	—
9	C₁₉×#500	C₂²	1	2	yes	—
10	C₁₉×#494	C₂²	1	2	yes	—
11	C₁₉×#487	—	2	2	no	—
12	C₁₉×#467	—	2	2	no	—
13	C₁₉×#467	C₂²	1	4	yes	—
14	C₄×Q₁₆×C₁₉	—	2	2	no	—
15	C₄×Q₁₆×C₁₉	C₂²	1	4	yes	—
16	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
17	C₁₉×#367	C₂²	1	4	yes	—
18	C₁₉×C₄⋊C₁₆	C₂²	1	4	yes	—
19	C₁₉×#358	C₂²	1	8	yes	—
20	C₂×Q₁₆×C₁₉	—	2	2	no	—
21	C₂×Q₁₆×C₁₉	C₂³	1	4	yes	—
22	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
24	C₁₉×C₄⋊Q₈	—	2	2	no	—
25	C₁₉×C₄⋊Q₈	—	2	2	no	—
26	C₁₉×#125	—	4	2	no	—
27	C₁₉×C₂²⋊Q₈	—	2	4	no	—
28	C₁₉×C₂²⋊Q₈	—	4	2	no	—
29	C₄×Q₈×C₁₉	—	2	4	no	—
30	C₄×Q₈×C₁₉	—	4	2	no	—
31	C₁₉×#117	—	4	2	no	—
32	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
33	C₁₉×Q₃₂	—	4	4	no	—
34	C₁₉×M₃₂	—	4	2	no	—
35	C₂×C₁₆×C₁₉	C₂³	1	4	yes	—
36	C₁₉×#107	—	2	2	no	—
37	C₁₉×#107	C₂³	1	4	yes	—
38	C₁₉×#103	—	2	4	no	—
39	C₁₉×#103	—	2	4	no	—
40	C₄×C₈×C₁₉	D₄	1	2	yes	—
41	C₄×C₈×C₁₉	C₂³	1	2	yes	—
42	C₂×Q₈×C₁₉	—	2	4	no	—
43	C₂×Q₈×C₁₉	—	4	2	no	—
44	C₂²×C₄×C₁₉	D₈	1	2	yes	—
45	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
46	Q₁₆×C₁₉	—	2	4	no	—
47	Q₁₆×C₁₉	—	2	4	no	—
48	Q₁₆×C₁₉	—	4	4	no	—
49	C₂×C₈×C₁₉	—	2	1	no	—
50	C₂×C₈×C₁₉	—	2	1	no	—
51	C₂×C₈×C₁₉	—	4	1	no	—
52	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
53	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
55	C₄⋊C₄×C₁₉	—	2	4	no	—
56	C₄⋊C₄×C₁₉	—	4	2	no	—
57	C₄⋊C₄×C₁₉	—	4	2	no	—
58	C₄⋊C₄×C₁₉	—	4	4	no	—
59	C₄⋊C₄×C₁₉	—	4	4	no	—
60	C₄⋊C₄×C₁₉	—	4	2	no	—
61	C₂²⋊C₄×C₁₉	—	4	4	no	—
62	C₄²×C₁₉	—	4	4	no	—
63	C₄²×C₁₉	D₈	1	1	yes	characteristic
64	C₄²×C₁₉	D₈	1	1	yes	characteristic
65	C₄²×C₁₉	C₂×D₄	1	2	yes	—
66	C₁₆×C₁₉	—	2	4	no	—
67	#33821	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
68	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
69	Q₈×C₁₉	—	4	4	no	—
70	Q₈×C₁₉	—	4	4	no	—
71	Q₈×C₁₉	—	8	4	no	—
72	C₂×C₄×C₁₉	—	2	1	no	—
73	C₂×C₄×C₁₉	—	2	1	no	—
74	C₂×C₄×C₁₉	—	2	4	no	—
75	C₂×C₄×C₁₉	—	4	4	no	—
76	C₂×C₄×C₁₉	—	4	4	no	—
77	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
78	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
79	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
80	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
81	C₈×C₁₉	—	2	1	no	—
82	C₈×C₁₉	—	2	2	no	—
83	C₈×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
84	C₈×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
85	#3170	C₂×C₁₉	1	2	yes	—
86	#2225	C₂×C₁₉	1	4	yes	complemented
87	#2219	C₂×C₁₉	1	4	yes	—
88	#2209	C₂×C₁₉	1	4	yes	complemented
89	#2150	C₂×C₁₉	1	1	yes	characteristic
90	C₂²×C₁₉	—	2	2	no	—
91	C₂²×C₁₉	—	2	1	no	—
92	C₂²×C₁₉	C₂²×D₈	1	1	yes	characteristic
93	C₄×C₁₉	—	2	2	no	—
94	C₄×C₁₉	—	2	1	no	—
95	C₄×C₁₉	—	8	4	no	—
96	C₄×C₁₉	—	8	4	no	—
97	C₄×C₁₉	#510	1	4	yes	—
98	C₄×C₁₉	#537	1	1	yes	characteristic
99	C₄×C₁₉	#575	1	1	yes	characteristic
100	#533	—	2	2	no	—
101	C₂×Q₃₂	C₂²×C₁₉	1	4	yes	—
102	C₂×M₃₂	C₂²×C₁₉	1	2	yes	—
103	#500	C₂²×C₁₉	1	2	yes	—
104	#494	C₂²×C₁₉	1	2	yes	—
105	#487	—	2	2	no	—
106	#467	—	2	2	no	—
107	#467	C₂²×C₁₉	1	4	yes	—
108	C₄×Q₁₆	—	2	2	no	—
109	C₄×Q₁₆	C₂²×C₁₉	1	4	yes	—
110	C₂×C₄×C₈	C₂²×C₁₉	1	1	yes	characteristic
111	#367	C₂²×C₁₉	1	4	yes	—
112	C₄⋊C₁₆	C₂²×C₁₉	1	4	yes	—
113	#358	C₂²×C₁₉	1	8	yes	—
114	C₂×C₁₉	—	4	1	no	—
115	C₂×C₁₉	#3245	1	1	yes	characteristic
116	C₂×C₁₉	C₂×#510	1	2	yes	—
117	C₂×Q₁₆	—	2	2	no	—
118	C₂×Q₁₆	C₂³×C₁₉	1	4	yes	—
119	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
120	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
121	C₄⋊Q₈	—	2	2	no	—
122	C₄⋊Q₈	—	2	2	no	—
123	#125	—	4	2	no	—
124	C₂²⋊Q₈	—	2	4	no	—
125	C₂²⋊Q₈	—	4	2	no	—
126	C₄×Q₈	—	2	4	no	—
127	C₄×Q₈	—	4	2	no	—
128	#117	—	4	2	no	—
129	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
130	Q₃₂	—	4	4	no	—
131	M₃₂	—	4	2	no	—
132	C₂×C₁₆	C₂³×C₁₉	1	4	yes	—
133	#107	—	2	2	no	—
134	#107	C₂³×C₁₉	1	4	yes	—
135	#103	—	2	4	no	—
136	#103	—	2	4	no	—
137	C₄×C₈	D₄×C₁₉	1	2	yes	—
138	C₄×C₈	C₂³×C₁₉	1	2	yes	—
139	C₁₉	#33821	1	1	yes	characteristic, direct product factor, Sylow
140	C₂×Q₈	—	2	4	no	—
141	C₂×Q₈	—	4	2	no	—
142	C₂²×C₄	D₈×C₁₉	1	2	yes	—
143	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
144	Q₁₆	—	2	4	no	—
145	Q₁₆	—	2	4	no	—
146	Q₁₆	—	4	4	no	—
147	C₂×C₈	—	2	1	no	—
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	4	1	no	—
150	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
151	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
152	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	4	no	—
157	C₄⋊C₄	—	4	4	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₂²⋊C₄	—	4	4	no	—
160	C₄²	—	4	4	no	—
161	C₄²	D₈×C₁₉	1	1	yes	characteristic
162	C₄²	D₈×C₁₉	1	1	yes	characteristic
163	C₄²	C₂×D₄×C₁₉	1	2	yes	—
164	C₁₆	—	2	4	no	—
165	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
166	Q₈	—	4	4	no	—
167	Q₈	—	4	4	no	—
168	Q₈	—	8	4	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	4	4	no	—
173	C₂×C₄	—	4	4	no	—
174	C₂×C₄	C₂×D₈×C₁₉	1	1	yes	characteristic
175	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
176	C₂×C₄	C₂×D₈×C₁₉	1	2	yes	—
177	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
178	C₈	—	2	1	no	—
179	C₈	—	2	2	no	—
180	C₈	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
181	C₈	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
182	C₂²	—	2	1	no	—
183	C₂²	—	2	2	no	—
184	C₂²	C₂²×D₈×C₁₉	1	1	yes	characteristic
185	C₄	—	2	1	no	—
186	C₄	—	2	2	no	—
187	C₄	—	8	4	no	—
188	C₄	—	8	4	no	—
189	C₄	C₁₉×#510	1	4	yes	—
190	C₄	C₁₉×#537	1	1	yes	characteristic
191	C₄	C₁₉×#575	1	1	yes	characteristic
192	C₂	—	4	1	no	—
193	C₂	C₁₉×#3245	1	1	yes	characteristic
194	C₂	C₂×C₁₉×#510	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₉×#3170

C₂

yes

maximal

C₁₉×#2225

C₂

yes

maximal, complemented

C₁₉×#2219

C₂

yes

maximal

C₁₉×#2209

C₂

yes

maximal, complemented

C₁₉×#2150

C₂

yes

maximal, characteristic

C₁₉×#533

—

C₂×C₁₉×Q₃₂

C₂²

yes

—

C₂×C₁₉×M₃₂

C₂²

yes

—

C₁₉×#500

C₂²

yes

—

C₁₉×#494

C₂²

yes

—

C₁₉×#487

—

C₁₉×#467

—

C₁₉×#467

C₂²

yes

—

C₄×Q₁₆×C₁₉

—

C₄×Q₁₆×C₁₉

C₂²

yes

—

C₂×C₄×C₈×C₁₉

C₂²

yes

characteristic

C₁₉×#367

C₂²

yes

—

C₁₉×C₄⋊C₁₆

C₂²

yes

—

C₁₉×#358

C₂²

yes

—

C₂×Q₁₆×C₁₉

—

C₂×Q₁₆×C₁₉

C₂³

yes

—

C₂²×C₈×C₁₉

D₄

yes

characteristic

C₂²×C₈×C₁₉

C₂³

yes

characteristic

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×#125

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₁₉×#117

—

C₂×C₄²×C₁₉

D₄

yes

characteristic

C₁₉×Q₃₂

—

C₁₉×M₃₂

—

C₂×C₁₆×C₁₉

C₂³

yes

—

C₁₉×#107

—

C₁₉×#107

C₂³

yes

—

C₁₉×#103

—

C₁₉×#103

—

C₄×C₈×C₁₉

D₄

yes

—

C₄×C₈×C₁₉

C₂³

yes

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂²×C₄×C₁₉

D₈

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

Q₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

C₂×D₄

yes

—

C₂×C₈×C₁₉

C₂×D₄

yes

characteristic

C₂×C₈×C₁₉

C₂⁴

yes

characteristic

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

D₈

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₁₆×C₁₉

—

#33821

C₁₉

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₁₉

C₂×D₈

yes

characteristic

Q₈×C₁₉

—

Q₈×C₁₉

—

Q₈×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

C₂×D₈

yes

characteristic

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂×D₈

yes

—

C₂×C₄×C₁₉

C₂²×D₄

yes

characteristic

C₈×C₁₉

—

C₈×C₁₉

—

C₈×C₁₉

H(5,𝔽₂)

yes

characteristic

C₈×C₁₉

2₋¹⁺⁴

yes

characteristic

#3170

C₂×C₁₉

yes

—

#2225

C₂×C₁₉

yes

complemented

#2219

C₂×C₁₉

yes

—

#2209

C₂×C₁₉

yes

complemented

#2150

C₂×C₁₉

yes

characteristic

C₂²×C₁₉

—

C₂²×C₁₉

—

C₂²×C₁₉

C₂²×D₈

yes

characteristic

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#510

yes

—

C₄×C₁₉

yes

C₄×C₁₉

yes

100

—

101

C₂×Q₃₂

C₂²×C₁₉

yes

—

102

C₂×M₃₂

C₂²×C₁₉

yes

—

103

#500

C₂²×C₁₉

yes

—

104

#494

C₂²×C₁₉

yes

—

105

#487

—

106

#467

—

107

#467

C₂²×C₁₉

yes

—

108

C₄×Q₁₆

—

109

C₄×Q₁₆

C₂²×C₁₉

yes

—

110

C₂×C₄×C₈

C₂²×C₁₉

yes

characteristic

111

#367

C₂²×C₁₉

yes

—

112

C₄⋊C₁₆

C₂²×C₁₉

yes

—

113

#358

C₂²×C₁₉

yes

—

114

C₂×C₁₉

—

115

C₂×C₁₉

#3245

yes

characteristic

116

C₂×C₁₉

C₂×#510

yes

—

117

C₂×Q₁₆

—

118

C₂×Q₁₆

C₂³×C₁₉

yes

—

119

C₂²×C₈

D₄×C₁₉

yes

characteristic

120

C₂²×C₈

C₂³×C₁₉

yes

characteristic

121

C₄⋊Q₈

—

122

C₄⋊Q₈

—

123

#125

—

124

C₂²⋊Q₈

—

125

C₂²⋊Q₈

—

126

C₄×Q₈

—

127

C₄×Q₈

—

128

#117

—

129

C₂×C₄²

D₄×C₁₉

yes

characteristic

130

Q₃₂

—

131

M₃₂

—

132

C₂×C₁₆

C₂³×C₁₉

yes

—

133

#107

—

134

#107

C₂³×C₁₉

yes

—

135

#103

—

136

#103

—

137

C₄×C₈

D₄×C₁₉

yes

—

138

C₄×C₈

C₂³×C₁₉

yes

—

139

C₁₉

#33821

yes

characteristic, direct product factor, Sylow

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂²×C₄

D₈×C₁₉

yes

—

143

C₂²×C₄

C₂×D₄×C₁₉

yes

characteristic

144

Q₁₆

—

145

Q₁₆

—

146

Q₁₆

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

C₂×D₄×C₁₉

yes

characteristic

151

C₂×C₈

C₂×D₄×C₁₉

yes

—

152

C₂×C₈

C₂⁴×C₁₉

yes

characteristic

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

D₈×C₁₉

yes

characteristic

162

C₄²

D₈×C₁₉

yes

characteristic

163

C₄²

C₂×D₄×C₁₉

yes

—

164

C₁₆

—

165

C₂³

C₂×D₈×C₁₉

yes

characteristic

166

Q₈

—

167

Q₈

—

168

Q₈

—

169

C₂×C₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

C₂×D₈×C₁₉

yes

characteristic

175

C₂×C₄

C₂×D₈×C₁₉

yes

—

176

C₂×C₄

C₂×D₈×C₁₉

yes

—

177

C₂×C₄

C₂²×D₄×C₁₉

yes

characteristic

178

C₈

—

179

C₈

—

180

C₈

C₁₉×H(5,𝔽₂)

yes

characteristic

181

C₈

C₁₉×2₋¹⁺⁴

yes

characteristic

182

C₂²

—

183

C₂²

—

184

C₂²

C₂²×D₈×C₁₉

yes

characteristic

185

C₄

—

186

C₄

—

187

C₄

—

188

C₄

—

189

C₄

C₁₉×#510

yes

—

190

C₄

C₁₉×#537

yes

characteristic

191

C₄

C₁₉×#575

yes

characteristic

192

C₂

—

193

C₂

C₁₉×#3245

yes

characteristic

194

C₂

C₂×C₁₉×#510

yes

—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₉
prime radical	C₂³×C₁₉	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₉

C₂²×D₈

commutator, Frattini, cosocle

C₂×C₈

C₂⁴×C₁₉

prime radical

C₂³×C₁₉

C₂×D₈

LCS

G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ C₂×C₄×C₈×C₁₉ ◁ G

N	H ≅ G/N	type
2. C₁₉×#2225	C₂	semidirect
4. C₁₉×#2209	C₂	semidirect
67. #33821	C₁₉	direct (N × H)
86. #2225	C₂×C₁₉	semidirect
88. #2209	C₂×C₁₉	semidirect
139. C₁₉	#33821	direct (N × H)

H ≅ G/N

type

2. C₁₉×#2225

C₂

semidirect

4. C₁₉×#2209

C₂

semidirect

67. #33821

C₁₉

direct (N × H)

86. #2225

C₂×C₁₉

semidirect

88. #2209

C₂×C₁₉

semidirect

139. C₁₉

#33821

direct (N × H)

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

subgroup	index
C₁₉×#3170	2
C₁₉×#2225	2
C₁₉×#2219	2
C₁₉×#2209	2
C₁₉×#2150	2
#33821	19

subgroup

index

C₁₉×#3170

C₁₉×#2225

C₁₉×#2219

C₁₉×#2209

C₁₉×#2150

#33821

Subgroups — C₁₉×#33821 #18039780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C19×#33821 #18039780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#33821 #18039780