Group #14298905 — subgroups

Subgroups — #14298905

Order 1920.

376 conjugacy classes of subgroups; only the 148 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 148 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×C₅×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
2	#11748440	C₂	1	2	yes	maximal
3	#11746373	C₂	1	1	yes	maximal, characteristic
4	C₃×#64772	C₂	1	1	yes	maximal, characteristic
5	#11745983	C₂	1	2	yes	maximal
6	#10600584	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
8	C₂×#6710	C₂²	1	2	yes	—
9	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
10	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×#681	C₂²	1	2	yes	—
12	C₅×C₈×Dic₃	C₄	1	2	yes	—
13	C₅×C₈×Dic₃	C₄	1	2	yes	—
14	Dic₃⋊#168	—	2	4	no	—
15	#68928	—	5	1	no	maximal, Hall
16	C₂×C₄×C₅×C₈	—	3	1	no	—
17	#65213	—	3	2	no	—
18	#64772	—	3	2	no	—
19	#64772	—	3	1	no	—
20	#64772	D₃	1	1	yes	characteristic
21	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂²×C₅×Dic₃	Q₈	1	2	yes	—
23	C₂×C₃×C₅×C₈	—	2	2	no	—
24	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
25	#6710	—	2	2	no	—
26	#6710	—	2	2	no	—
27	C₂×C₃⋊#168	—	2	2	no	—
28	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
29	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
30	C₄×C₅×Dic₃	D₄	1	2	yes	—
31	C₂×C₅×C₃⋊C₈	—	2	2	no	—
32	C₂×C₅×C₃⋊C₈	C₂×C₄	1	2	yes	—
33	C₃×#681	—	2	2	no	—
34	C₃×#681	—	2	2	no	—
35	C₂×C₃×#168	—	2	2	no	—
36	#5118	—	5	2	no	—
37	C₂×C₈×Dic₃	D₅	1	1	yes	characteristic
38	C₃×#341	—	5	1	no	—
39	#4558	—	5	2	no	—
40	#4552	—	5	1	no	—
41	C₂²×C₅×C₈	—	3	1	no	—
42	C₂²×C₅×C₈	C₂×D₃	1	1	yes	characteristic
43	C₂×C₄²×C₅	—	3	1	no	—
44	C₂×#681	—	3	2	no	—
45	C₂×#681	C₂×D₃	1	2	yes	—
46	C₄×C₅×C₈	—	3	2	no	—
47	C₄×C₅×C₈	—	3	2	no	—
48	C₄⋊#168	—	6	4	no	—
49	#1837	—	15	1	no	Sylow
50	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂×C₃×C₄×C₅	#41	1	2	yes	—
54	C₂×C₃×C₄×C₅	#41	1	2	yes	—
55	C₂×C₅×Dic₃	—	2	4	no	—
56	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
57	C₂×C₅×Dic₃	C₄⋊C₄	1	2	yes	—
58	C₃×C₅×C₈	—	2	2	no	—
59	C₃⋊#168	—	4	2	no	—
60	C₃×#168	—	4	2	no	—
61	C₅×C₃⋊C₈	—	2	2	no	—
62	C₂×C₃×M₁₆	—	5	2	no	—
63	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
64	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
65	C₂×#208	—	5	2	no	—
66	C₂²×C₃⋊C₈	C₂×D₅	1	1	yes	characteristic
67	Dic₃⋊C₈	—	10	4	no	—
68	C₈×Dic₃	Dic₅	1	2	yes	—
69	C₈×Dic₃	Dic₅	1	2	yes	—
70	C₂²×C₄×C₅	—	3	2	no	—
71	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
72	C₂×C₅×C₈	—	2	2	no	—
73	C₂×C₅×C₈	—	3	2	no	—
74	C₂×C₅×C₈	—	6	2	no	—
75	C₂×C₅×C₈	C₄×D₃	1	2	yes	—
76	C₄²×C₅	—	3	1	no	—
77	C₄²×C₅	—	3	1	no	—
78	C₄²×C₅	—	3	2	no	—
79	#681	—	2	2	no	—
80	#681	—	2	2	no	—
81	#681	—	6	2	no	—
82	#681	—	6	2	no	—
83	C₂×#168	—	2	2	no	—
84	C₂×#168	—	6	2	no	—
85	#423	—	15	2	no	—
86	C₂×C₄×C₈	—	3	1	no	—
87	#341	—	5	1	no	—
88	#341	—	15	2	no	—
89	#341	—	15	1	no	—
90	C₂²×C₃×C₅	—	2	2	no	—
91	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₃×C₅	#125	1	2	yes	—
93	C₃×C₄×C₅	#117	1	1	yes	characteristic
94	C₃×C₄×C₅	#117	1	1	yes	characteristic
95	C₃×C₄×C₅	#124	1	2	yes	—
96	C₅×Dic₃	—	2	2	no	—
97	C₅×Dic₃	#108	1	4	yes	—
98	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
99	C₂²×Dic₃	Dic₁₀	1	2	yes	—
100	C₃×M₁₆	—	10	2	no	—
101	C₃×M₁₆	—	10	2	no	—
102	C₂×C₃×C₈	—	2	2	no	—
103	C₂×C₃×C₈	—	10	2	no	—
104	C₂×C₃×C₈	C₂×Dic₅	1	2	yes	—
105	C₄×Dic₃	D₂₀	1	2	yes	—
106	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
107	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
108	#208	—	10	2	no	—
109	#208	—	10	2	no	—
110	C₂×C₃⋊C₈	—	2	2	no	—
111	C₂×C₃⋊C₈	—	10	2	no	—
112	C₂×C₃⋊C₈	C₂×Dic₅	1	2	yes	—
113	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
114	C₂×C₄×C₅	—	3	2	no	—
115	C₂×C₄×C₅	—	3	2	no	—
116	C₂×C₄×C₅	—	6	4	no	—
117	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
118	C₂×C₄×C₅	#235	1	2	yes	—
119	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
120	C₂×C₄×C₅	#237	1	2	yes	—
121	C₅×C₈	—	2	2	no	—
122	C₅×C₈	—	6	2	no	—
123	#168	—	4	2	no	—
124	#168	—	12	2	no	—
125	C₂×M₁₆	—	5	2	no	—
126	C₂×M₁₆	—	15	2	no	—
127	C₂²×C₈	—	3	1	no	—
128	C₂²×C₈	D₃×D₅	1	1	yes	characteristic
129	C₂×C₄²	—	3	1	no	—
130	C₄⋊C₈	—	30	4	no	—
131	C₄×C₈	—	3	2	no	—
132	C₄×C₈	—	3	2	no	—
133	C₂×C₃×C₅	—	2	2	no	—
134	C₂×C₃×C₅	#382	1	1	yes	characteristic
135	C₂×C₃×C₅	C₂×#108	1	2	yes	—
136	C₂³×C₃	C₂×Dic₁₀	1	1	yes	characteristic
137	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
138	C₂×C₃×C₄	#709	1	2	yes	—
139	C₂×C₃×C₄	#709	1	2	yes	—
140	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
141	C₂×Dic₃	—	2	4	no	—
142	C₂×Dic₃	C₄⋊Dic₅	1	2	yes	—
143	C₂×Dic₃	C₄⋊Dic₅	1	2	yes	—
144	C₃×C₈	—	2	2	no	—
145	C₃×C₈	—	20	2	no	—
146	C₃⋊C₈	—	2	2	no	—
147	C₃⋊C₈	—	20	2	no	—
148	C₂²×C₅	—	2	2	no	—
149	C₂²×C₅	#889	1	2	yes	—
150	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
151	C₄×C₅	—	3	4	no	—
152	C₄×C₅	—	6	2	no	—
153	C₄×C₅	#872	1	1	yes	characteristic
154	C₄×C₅	#877	1	1	yes	characteristic
155	C₄×C₅	#885	1	2	yes	—
156	C₂²×C₄	—	3	2	no	—
157	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
158	M₁₆	—	10	2	no	—
159	M₁₆	—	10	2	no	—
160	M₁₆	—	30	2	no	—
161	M₁₆	—	30	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	3	2	no	—
164	C₂×C₈	—	6	2	no	—
165	C₂×C₈	—	10	2	no	—
166	C₂×C₈	—	30	2	no	—
167	C₂×C₈	D₃×Dic₅	1	2	yes	—
168	C₄²	—	3	2	no	—
169	C₄²	—	3	1	no	—
170	C₄²	—	3	1	no	—
171	C₃×C₅	#1837	1	1	yes	characteristic, complemented, Hall
172	C₂²×C₃	—	2	2	no	—
173	C₂²×C₃	#4016	1	2	yes	—
174	C₂²×C₃	C₂×C₄⋊Dic₅	1	1	yes	characteristic
175	C₃×C₄	#4021	1	2	yes	—
176	C₃×C₄	#4072	1	1	yes	characteristic
177	C₃×C₄	#4072	1	1	yes	characteristic
178	Dic₃	—	2	2	no	—
179	Dic₃	#3951	1	4	yes	—
180	C₂×C₅	—	2	2	no	—
181	C₂×C₅	#4650	1	1	yes	characteristic
182	C₂×C₅	D₃×#108	1	2	yes	—
183	C₂³	D₃×Dic₁₀	1	1	yes	characteristic
184	C₂×C₄	—	3	2	no	—
185	C₂×C₄	—	3	2	no	—
186	C₂×C₄	—	6	4	no	—
187	C₂×C₄	#6771	1	2	yes	—
188	C₂×C₄	D₃×D₂₀	1	1	yes	characteristic
189	C₂×C₄	#6779	1	2	yes	—
190	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
191	C₈	—	2	2	no	—
192	C₈	—	6	2	no	—
193	C₈	—	20	2	no	—
194	C₈	—	60	2	no	—
195	C₂×C₃	—	2	2	no	—
196	C₂×C₃	#65225	1	1	yes	characteristic
197	C₂×C₃	C₂×#3951	1	2	yes	—
198	C₅	#68928	1	1	yes	characteristic, complemented, Sylow
199	C₂²	—	2	2	no	—
200	C₂²	#91379	1	2	yes	—
201	C₂²	D₃×C₄⋊Dic₅	1	1	yes	characteristic
202	C₄	—	3	4	no	—
203	C₄	—	6	2	no	—
204	C₄	#91353	1	2	yes	—
205	C₄	#91371	1	1	yes	characteristic
206	C₄	#91529	1	1	yes	characteristic
207	C₃	#10600584	1	1	yes	characteristic, complemented, Sylow
208	C₂	—	2	2	no	—
209	C₂	D₃×#3951	1	2	yes	—
210	C₂	#11748600	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₈×Dic₃

C₂

yes

maximal, characteristic

#11748440

C₂

yes

maximal

#11746373

C₂

yes

maximal, characteristic

C₃×#64772

C₂

yes

maximal, characteristic

#11745983

C₂

yes

maximal

#10600584

—

maximal, Hall

C₂²×C₃×C₅×C₈

C₂²

yes

characteristic

C₂×#6710

C₂²

yes

—

C₂×C₄×C₅×Dic₃

C₂²

yes

characteristic

C₂²×C₅×C₃⋊C₈

C₂²

yes

characteristic

C₂×C₃×#681

C₂²

yes

—

C₅×C₈×Dic₃

C₄

yes

—

C₅×C₈×Dic₃

C₄

yes

—

Dic₃⋊#168

—

#68928

—

maximal, Hall

C₂×C₄×C₅×C₈

—

—

—

—

D₃

yes

characteristic

C₂²×C₃×C₄×C₅

C₂³

yes

characteristic

C₂²×C₅×Dic₃

Q₈

yes

—

C₂×C₃×C₅×C₈

—

C₂×C₃×C₅×C₈

C₂×C₄

yes

—

#6710

—

#6710

—

C₂×C₃⋊#168

—

C₄×C₅×Dic₃

C₂×C₄

yes

characteristic

C₄×C₅×Dic₃

C₂×C₄

yes

characteristic

C₄×C₅×Dic₃

D₄

yes

—

C₂×C₅×C₃⋊C₈

—

C₂×C₅×C₃⋊C₈

C₂×C₄

yes

—

C₃×#681

—

C₃×#681

—

C₂×C₃×#168

—

#5118

—

C₂×C₈×Dic₃

D₅

yes

—

—

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

C₂×D₃

yes

characteristic

C₂×C₄²×C₅

—

C₂×#681

—

C₂×#681

C₂×D₃

yes

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

C₄⋊#168

—

#1837

—

Sylow

C₂³×C₃×C₅

C₂×Q₈

yes

characteristic

C₂×C₃×C₄×C₅

C₂²×C₄

yes

characteristic

C₂×C₃×C₄×C₅

C₂×D₄

yes

characteristic

C₂×C₃×C₄×C₅

#41

yes

—

C₂×C₃×C₄×C₅

#41

yes

—

C₂×C₅×Dic₃

—

C₂×C₅×Dic₃

C₄⋊C₄

yes

—

C₂×C₅×Dic₃

C₄⋊C₄

yes

—

C₃×C₅×C₈

—

C₃⋊#168

—

C₃×#168

—

C₅×C₃⋊C₈

—

C₂×C₃×M₁₆

—

C₂²×C₃×C₈

C₂×D₅

yes

characteristic

C₂×C₄×Dic₃

C₂×D₅

yes

characteristic

C₂×#208

—

C₂²×C₃⋊C₈

C₂×D₅

yes

characteristic

Dic₃⋊C₈

—

C₈×Dic₃

Dic₅

yes

—

C₈×Dic₃

Dic₅

yes

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²×D₃

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₄×D₃

yes

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

—

—

—

—

—

—

—

—

C₂×C₄×C₈

—

#341

—

#341

—

#341

—

C₂²×C₃×C₅

—

C₂²×C₃×C₅

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₃×C₅

#125

yes

—

C₃×C₄×C₅

yes

C₃×C₄×C₅

yes

C₃×C₄×C₅

yes

—

C₅×Dic₃

—

C₅×Dic₃

#108

yes

—

C₂²×C₃×C₄

C₂²×D₅

yes

characteristic

C₂²×Dic₃

Dic₁₀

yes

—

100

C₃×M₁₆

—

101

C₃×M₁₆

—

102

C₂×C₃×C₈

—

103

C₂×C₃×C₈

—

104

C₂×C₃×C₈

C₂×Dic₅

yes

—

105

C₄×Dic₃

D₂₀

yes

—

106

C₄×Dic₃

C₂×Dic₅

yes

characteristic

107

C₄×Dic₃

C₂×Dic₅

yes

characteristic

108

#208

—

109

#208

—

110

C₂×C₃⋊C₈

—

111

C₂×C₃⋊C₈

—

112

C₂×C₃⋊C₈

C₂×Dic₅

yes

—

113

C₂³×C₅

D₃×Q₈

yes

characteristic

114

C₂×C₄×C₅

—

115

C₂×C₄×C₅

—

116

C₂×C₄×C₅

—

117

C₂×C₄×C₅

C₂×C₄×D₃

yes

characteristic

118

C₂×C₄×C₅

#235

yes

—

119

C₂×C₄×C₅

D₃×D₄

yes

characteristic

120

C₂×C₄×C₅

#237

yes

—

121

C₅×C₈

—

122

C₅×C₈

—

123

#168

—

124

#168

—

125

C₂×M₁₆

—

126

C₂×M₁₆

—

127

C₂²×C₈

—

128

C₂²×C₈

D₃×D₅

yes

characteristic

129

C₂×C₄²

—

130

C₄⋊C₈

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₂×C₃×C₅

—

134

C₂×C₃×C₅

#382

yes

characteristic

135

C₂×C₃×C₅

C₂×#108

yes

—

136

C₂³×C₃

C₂×Dic₁₀

yes

characteristic

137

C₂×C₃×C₄

C₂×D₂₀

yes

characteristic

138

C₂×C₃×C₄

#709

yes

—

139

C₂×C₃×C₄

#709

yes

—

140

C₂×C₃×C₄

C₂²×Dic₅

yes

characteristic

141

C₂×Dic₃

—

142

C₂×Dic₃

C₄⋊Dic₅

yes

—

143

C₂×Dic₃

C₄⋊Dic₅

yes

—

144

C₃×C₈

—

145

C₃×C₈

—

146

C₃⋊C₈

—

147

C₃⋊C₈

—

148

C₂²×C₅

—

149

C₂²×C₅

#889

yes

—

150

C₂²×C₅

D₃×C₄⋊C₄

yes

characteristic

151

C₄×C₅

—

152

C₄×C₅

—

153

C₄×C₅

#872

yes

characteristic

154

C₄×C₅

#877

yes

characteristic

155

C₄×C₅

#885

yes

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂×D₃×D₅

yes

characteristic

158

M₁₆

—

159

M₁₆

—

160

M₁₆

—

161

M₁₆

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

D₃×Dic₅

yes

—

168

C₄²

—

169

C₄²

—

170

C₄²

—

171

C₃×C₅

#1837

yes

characteristic, complemented, Hall

172

C₂²×C₃

—

173

C₂²×C₃

#4016

yes

—

174

C₂²×C₃

C₂×C₄⋊Dic₅

yes

characteristic

175

C₃×C₄

#4021

yes

—

176

C₃×C₄

#4072

yes

characteristic

177

C₃×C₄

#4072

yes

characteristic

178

Dic₃

—

179

Dic₃

#3951

yes

—

180

C₂×C₅

—

181

C₂×C₅

#4650

yes

characteristic

182

C₂×C₅

D₃×#108

yes

—

183

C₂³

D₃×Dic₁₀

yes

characteristic

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

#6771

yes

—

188

C₂×C₄

D₃×D₂₀

yes

characteristic

189

C₂×C₄

#6779

yes

—

190

C₂×C₄

C₂×D₃×Dic₅

yes

characteristic

191

C₈

—

192

C₈

—

193

C₈

—

194

C₈

—

195

C₂×C₃

—

196

C₂×C₃

#65225

yes

characteristic

197

C₂×C₃

C₂×#3951

yes

—

198

C₅

#68928

yes

characteristic, complemented, Sylow

199

C₂²

—

200

C₂²

#91379

yes

—

201

C₂²

D₃×C₄⋊Dic₅

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

#91353

yes

—

205

C₄

#91371

yes

characteristic

206

C₄

#91529

yes

characteristic

207

C₃

#10600584

yes

characteristic, complemented, Sylow

208

C₂

—

209

C₂

D₃×#3951

yes

—

210

C₂

#11748600

yes

characteristic

	subgroup	G/H
center	C₂×C₄	D₃×D₂₀
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃×D₅
Fitting	C₂²×C₃×C₅×C₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂³×C₃×C₅	C₂×Q₈
cosocle	C₂²×C₃×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₃×D₅
hypocenter	C₃×C₅	#1837
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂×C₄

D₃×D₂₀

commutator

C₂×C₃×C₄×C₅

C₂²×C₄

Frattini

C₂²×C₄

C₂×D₃×D₅

Fitting

C₂²×C₃×C₅×C₈

C₂²

socle

C₂²×C₃×C₅

C₂×C₄⋊C₄

prime radical

C₂³×C₃×C₅

C₂×Q₈

cosocle

C₂²×C₃×C₄×C₅

C₂³

hypercenter

C₂²×C₈

D₃×D₅

hypocenter

C₃×C₅

#1837

LCS

G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
171. C₃×C₅	#1837	semidirect
198. C₅	#68928	semidirect
207. C₃	#10600584	semidirect

H ≅ G/N

type

171. C₃×C₅

#1837

semidirect

198. C₅

#68928

semidirect

207. C₃

#10600584

semidirect

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

subgroup	index
C₂×C₅×C₈×Dic₃	2
#11748440	2
#11746373	2
C₃×#64772	2
#11745983	2
#10600584	3
#68928	5

subgroup

index

C₂×C₅×C₈×Dic₃

Subgroups — #14298905

Conjugacy classes of subgroups

Complements

Maximal subgroups