Group #18070803 — subgroups

Subgroups — #18070803

Order 4864.

436 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 135 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	#14563488	C₂	1	2	yes	maximal
2	#14561458	C₂	1	4	yes	maximal
3	C₄×C₁₉×#125	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
5	C₂×#10597260	—	2	2	no	—
6	#11926299	C₂²	1	4	yes	—
7	C₂×C₁₉×#125	C₄	1	1	yes	characteristic
8	C₁₉×#389	C₂²	1	2	yes	—
9	C₁₉×#387	—	2	2	no	—
10	C₁₉×#382	C₄	1	1	yes	characteristic
11	C₄×C₄⋊C₄×C₁₉	—	2	2	no	—
12	C₄×C₄⋊C₄×C₁₉	C₄	1	2	yes	—
13	C₄³×C₁₉	C₂²	1	1	yes	characteristic
14	C₁₉×#125	—	2	4	no	—
15	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
16	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
17	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
18	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
19	C₂×C₄²×C₁₉	—	2	2	no	—
20	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₉	D₄	1	2	yes	—
23	C₂×C₄²×C₁₉	D₄	1	2	yes	—
24	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	—	2	4	no	—
26	C₁₉×#95	—	2	2	no	—
27	C₁₉×#95	—	2	2	no	—
28	C₁₉×#95	—	2	2	no	—
29	C₄⋊(C₁₉⋊C₈)	—	2	8	no	—
30	#10597260	—	4	4	no	—
31	C₂²×C₄×C₁₉	—	2	2	no	—
32	C₂²×C₄×C₁₉	—	2	2	no	—
33	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
34	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
38	C₄⋊C₄×C₁₉	—	2	8	no	—
39	C₄⋊C₄×C₁₉	—	2	2	no	—
40	C₄⋊C₄×C₁₉	—	4	2	no	—
41	C₄⋊C₄×C₁₉	—	4	2	no	—
42	C₄⋊C₄×C₁₉	—	4	2	no	—
43	C₄⋊C₄×C₁₉	M₁₆	1	4	yes	—
44	C₄²×C₁₉	—	2	2	no	—
45	C₄²×C₁₉	—	2	4	no	—
46	C₄²×C₁₉	—	2	2	no	—
47	C₄²×C₁₉	—	2	2	no	—
48	C₄²×C₁₉	—	2	2	no	—
49	C₄²×C₁₉	—	4	1	no	—
50	C₄²×C₁₉	—	4	4	no	—
51	C₂×C₁₉⋊C₈	—	2	8	no	—
52	C₂×C₁₉⋊C₈	—	4	4	no	—
53	C₂×C₁₉⋊C₈	—	4	4	no	—
54	#7636	—	19	1	no	maximal, Sylow
55	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₉	—	2	2	no	—
57	C₂×C₄×C₁₉	—	2	1	no	—
58	C₂×C₄×C₁₉	—	2	1	no	—
59	C₂×C₄×C₁₉	—	2	2	no	—
60	C₂×C₄×C₁₉	—	2	2	no	—
61	C₂×C₄×C₁₉	—	2	4	no	—
62	C₂×C₄×C₁₉	—	2	1	no	—
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	—	4	2	no	—
67	C₂×C₄×C₁₉	—	4	2	no	—
68	C₂×C₄×C₁₉	—	4	2	no	—
69	C₂×C₄×C₁₉	—	4	2	no	—
70	C₂×C₄×C₁₉	—	4	2	no	—
71	C₂×C₄×C₁₉	#101	1	2	yes	—
72	C₂×C₄×C₁₉	#104	1	4	yes	—
73	C₂×C₄×C₁₉	C₂×M₁₆	1	2	yes	—
74	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
75	C₂×C₄×C₁₉	#137	1	2	yes	—
76	C₁₉⋊C₈	—	4	8	no	—
77	C₄×#125	D₁₉	1	1	yes	characteristic
78	#1767	—	19	2	no	—
79	#1271	—	19	4	no	—
80	C₂²×C₁₉	#407	1	1	yes	characteristic
81	C₂²×C₁₉	#410	1	1	yes	characteristic
82	C₂²×C₁₉	C₂×#101	1	1	yes	characteristic
83	C₂²×C₁₉	#417	1	2	yes	—
84	C₂²×C₁₉	C₂×#104	1	2	yes	—
85	C₄×C₁₉	—	2	2	no	—
86	C₄×C₁₉	—	2	2	no	—
87	C₄×C₁₉	—	2	2	no	—
88	C₄×C₁₉	—	4	1	no	—
89	C₄×C₁₉	—	4	2	no	—
90	C₄×C₁₉	—	4	4	no	—
91	C₄×C₁₉	—	8	2	no	—
92	C₄×C₁₉	#330	1	4	yes	—
93	C₂×#125	Dic₁₉	1	1	yes	characteristic
94	C₂×C₄⋊C₈	—	38	2	no	—
95	C₂×#97	—	38	2	no	—
96	#389	C₂×D₁₉	1	2	yes	—
97	#387	—	2	2	no	—
98	#382	Dic₁₉	1	1	yes	characteristic
99	C₄×C₄⋊C₄	—	2	2	no	—
100	C₄×C₄⋊C₄	Dic₁₉	1	2	yes	—
101	C₄³	C₂×D₁₉	1	1	yes	characteristic
102	#336	—	19	4	no	—
103	C₂×C₁₉	#1467	1	1	yes	characteristic
104	C₂×C₁₉	#1489	1	2	yes	—
105	C₂×C₁₉	#1509	1	2	yes	—
106	C₂×C₁₉	C₂×#330	1	1	yes	characteristic
107	C₂×C₁₉	#1561	1	1	yes	characteristic
108	C₂²×C₈	—	38	4	no	—
109	#125	—	2	4	no	—
110	C₂×C₄⋊C₄	—	2	2	no	—
111	C₂×C₄⋊C₄	—	2	2	no	—
112	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
113	C₂×C₄⋊C₄	C₂×Dic₁₉	1	2	yes	—
114	C₂×C₄²	—	2	2	no	—
115	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
116	C₂×C₄²	C₂×Dic₁₉	1	1	yes	characteristic
117	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
118	C₂×C₄²	C₂²⋊D₁₉	1	2	yes	—
119	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
120	C₄⋊C₈	—	38	8	no	—
121	#97	—	76	4	no	—
122	#95	—	2	2	no	—
123	#95	—	2	2	no	—
124	#95	—	2	2	no	—
125	C₁₉	#7636	1	1	yes	characteristic, complemented, Sylow
126	C₂²×C₄	—	2	2	no	—
127	C₂²×C₄	—	2	2	no	—
128	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
129	C₂²×C₄	C₂²⋊Dic₁₉	1	2	yes	—
130	C₂²×C₄	C₂²⋊Dic₁₉	1	1	yes	characteristic
131	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
132	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
133	C₂×C₈	—	38	8	no	—
134	C₂×C₈	—	76	4	no	—
135	C₂×C₈	—	76	4	no	—
136	C₄⋊C₄	—	2	8	no	—
137	C₄⋊C₄	—	2	2	no	—
138	C₄⋊C₄	—	4	2	no	—
139	C₄⋊C₄	—	4	2	no	—
140	C₄⋊C₄	—	4	2	no	—
141	C₄⋊C₄	#64520	1	4	yes	—
142	C₄²	—	2	2	no	—
143	C₄²	—	2	2	no	—
144	C₄²	—	2	2	no	—
145	C₄²	—	2	4	no	—
146	C₄²	—	2	2	no	—
147	C₄²	—	4	1	no	—
148	C₄²	—	4	4	no	—
149	C₂³	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	1	no	—
154	C₂×C₄	—	2	2	no	—
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	—	2	1	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	—	4	2	no	—
162	C₂×C₄	—	4	2	no	—
163	C₂×C₄	—	4	2	no	—
164	C₂×C₄	—	4	2	no	—
165	C₂×C₄	#10597293	1	2	yes	—
166	C₂×C₄	#10597294	1	4	yes	—
167	C₂×C₄	C₂×#64520	1	2	yes	—
168	C₂×C₄	#10597395	1	2	yes	—
169	C₂×C₄	#10597397	1	2	yes	—
170	C₈	—	76	8	no	—
171	C₂²	#11926508	1	1	yes	characteristic
172	C₂²	#11926518	1	1	yes	characteristic
173	C₂²	C₂×#10597293	1	1	yes	characteristic
174	C₂²	#11926545	1	2	yes	—
175	C₂²	C₂×#10597294	1	2	yes	—
176	C₄	—	2	2	no	—
177	C₄	—	2	2	no	—
178	C₄	—	2	2	no	—
179	C₄	—	4	2	no	—
180	C₄	—	4	4	no	—
181	C₄	—	4	1	no	—
182	C₄	—	8	2	no	—
183	C₄	#11926286	1	4	yes	—
184	C₂	#14561979	1	1	yes	characteristic
185	C₂	#14562074	1	2	yes	—
186	C₂	#14562160	1	2	yes	—
187	C₂	C₂×#11926286	1	1	yes	characteristic
188	C₂	#14562373	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563488

C₂

yes

maximal

#14561458

C₂

yes

maximal

C₄×C₁₉×#125

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₁₉⋊C₈)

—

C₂×#10597260

—

#11926299

C₂²

yes

—

C₂×C₁₉×#125

C₄

yes

characteristic

C₁₉×#389

C₂²

yes

—

C₁₉×#387

—

C₁₉×#382

C₄

yes

characteristic

C₄×C₄⋊C₄×C₁₉

—

C₄×C₄⋊C₄×C₁₉

C₄

yes

—

C₄³×C₁₉

C₂²

yes

characteristic

C₁₉×#125

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

C₂×C₄

yes

characteristic

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂²×C₁₉⋊C₈

—

C₁₉×#95

—

C₁₉×#95

—

C₁₉×#95

—

C₄⋊(C₁₉⋊C₈)

—

#10597260

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

M₁₆

yes

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7636

—

maximal, Sylow

C₂³×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

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

#101

yes

—

C₂×C₄×C₁₉

#104

yes

—

C₂×C₄×C₁₉

C₂×M₁₆

yes

—

C₂×C₄×C₁₉

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₁₉

#137

yes

—

C₁₉⋊C₈

—

C₄×#125

D₁₉

yes

characteristic

#1767

—

#1271

—

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

C₂²×C₁₉

yes

—

C₂²×C₁₉

C₂×#104

yes

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

—

C₄×C₁₉

#330

yes

—

C₂×#125

Dic₁₉

yes

characteristic

C₂×C₄⋊C₈

—

C₂×#97

—

#389

C₂×D₁₉

yes

—

#387

—

#382

Dic₁₉

yes

characteristic

C₄×C₄⋊C₄

—

100

C₄×C₄⋊C₄

Dic₁₉

yes

—

101

C₄³

C₂×D₁₉

yes

characteristic

102

#336

—

103

C₂×C₁₉

#1467

yes

characteristic

104

C₂×C₁₉

#1489

yes

—

105

C₂×C₁₉

#1509

yes

—

106

C₂×C₁₉

C₂×#330

yes

characteristic

107

C₂×C₁₉

#1561

yes

characteristic

108

C₂²×C₈

—

109

#125

—

110

C₂×C₄⋊C₄

—

111

C₂×C₄⋊C₄

—

112

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

113

C₂×C₄⋊C₄

C₂×Dic₁₉

yes

—

114

C₂×C₄²

—

115

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

116

C₂×C₄²

C₂×Dic₁₉

yes

characteristic

117

C₂×C₄²

C₂²⋊D₁₉

yes

—

118

C₂×C₄²

C₂²⋊D₁₉

yes

—

119

C₂×C₄²

C₂²×D₁₉

yes

characteristic

120

C₄⋊C₈

—

121

#97

—

122

#95

—

123

#95

—

124

#95

—

125

C₁₉

#7636

yes

characteristic, complemented, Sylow

126

C₂²×C₄

—

127

C₂²×C₄

—

128

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

129

C₂²×C₄

C₂²⋊Dic₁₉

yes

—

130

C₂²×C₄

C₂²⋊Dic₁₉

yes

characteristic

131

C₂²×C₄

C₂²×Dic₁₉

yes

characteristic

132

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

133

C₂×C₈

—

134

C₂×C₈

—

135

C₂×C₈

—

136

C₄⋊C₄

—

137

C₄⋊C₄

—

138

C₄⋊C₄

—

139

C₄⋊C₄

—

140

C₄⋊C₄

—

141

C₄⋊C₄

#64520

yes

—

142

C₄²

—

143

C₄²

—

144

C₄²

—

145

C₄²

—

146

C₄²

—

147

C₄²

—

148

C₄²

—

149

C₂³

C₂×C₂²⋊Dic₁₉

yes

characteristic

150

C₂×C₄

—

151

C₂×C₄

—

152

C₂×C₄

—

153

C₂×C₄

—

154

C₂×C₄

—

155

C₂×C₄

—

156

C₂×C₄

—

157

C₂×C₄

—

158

C₂×C₄

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

#10597293

yes

—

166

C₂×C₄

#10597294

yes

—

167

C₂×C₄

C₂×#64520

yes

—

168

C₂×C₄

#10597395

yes

—

169

C₂×C₄

#10597397

yes

—

170

C₈

—

171

C₂²

#11926508

yes

characteristic

172

C₂²

#11926518

yes

characteristic

173

C₂²

C₂×#10597293

yes

characteristic

174

C₂²

#11926545

yes

—

175

C₂²

C₂×#10597294

yes

—

176

C₄

—

177

C₄

—

178

C₄

—

179

C₄

—

180

C₄

—

181

C₄

—

182

C₄

—

183

C₄

#11926286

yes

—

184

C₂

#14561979

yes

characteristic

185

C₂

#14562074

yes

—

186

C₂

#14562160

yes

—

187

C₂

C₂×#11926286

yes

characteristic

188

C₂

#14562373

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₄×C₁₉×#125	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×#125	D₁₉
hypocenter	C₁₉	#7636
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#125

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₉

commutator

C₂²×C₄×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₄×C₁₉×#125

C₂

socle, prime radical

C₂³×C₁₉

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#125

N	H ≅ G/N	type
125. C₁₉	#7636	semidirect

H ≅ G/N

type

125. C₁₉

#7636

semidirect

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

subgroup	index
#14563488	2
#14561458	2
C₄×C₁₉×#125	2
#7636	19

subgroup

index

#14563488

#14561458

C₄×C₁₉×#125

#7636

Subgroups — #18070803

Conjugacy classes of subgroups

Complements

Maximal subgroups