Group #13106466 — subgroups

Subgroups — C₂×#11717059 #13106466

Order 1600.

760 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 760 conjugacy classes of subgroups — too many to draw. Only its 136 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×#87904	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#87877	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#688	C₂	1	2	yes	maximal, complemented
4	#11717059	C₂	1	8	yes	maximal, direct product factor
5	C₂×#87771	C₂	1	2	yes	maximal, complemented
6	C₂×#87769	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₅²	—	2	1	no	—
8	C₂×C₅²×Q₈	C₂²	1	1	yes	characteristic, complemented
9	#87904	—	2	2	no	—
10	#87904	C₂²	1	4	yes	complemented
11	C₂×C₄⋊(C₅⋊D₅)	—	2	1	no	—
12	C₂×C₄⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₄×C₅⋊D₅	—	2	1	no	—
14	C₂×C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×D₂₀	C₂²	1	2	yes	—
16	C₂×#6037	—	2	1	no	—
17	#87877	—	2	2	no	—
18	#87877	C₂²	1	4	yes	complemented
19	C₅×#688	C₂²	1	8	yes	complemented
20	C₂×C₅×#168	C₂²	1	2	yes	complemented
21	#87771	C₂²	1	8	yes	complemented
22	#87769	C₂²	1	4	yes	complemented
23	C₂×#4060	—	5	2	no	maximal
24	C₂²×C₅⋊D₅	—	2	1	no	—
25	C₂²×C₅⋊D₅	D₄	1	1	yes	characteristic
26	C₂²×C₅×D₅	—	2	2	no	—
27	C₂×D₅²	—	2	4	no	—
28	C₂×D₅²	—	4	4	no	—
29	C₅²×Q₈	—	2	1	no	—
30	C₅²×Q₈	C₂³	1	2	yes	complemented
31	C₂×C₄×C₅²	—	2	1	no	—
32	C₂×C₄×C₅²	C₂³	1	1	yes	characteristic
33	C₂×#1039	D₄	1	1	yes	characteristic
34	C₄⋊(C₅⋊D₅)	—	2	4	no	—
35	C₄⋊(C₅⋊D₅)	—	2	1	no	—
36	C₄⋊(C₅⋊D₅)	C₂³	1	2	yes	complemented
37	C₄×C₅⋊D₅	—	2	4	no	—
38	C₄×C₅⋊D₅	D₄	1	2	yes	—
39	C₄×C₅⋊D₅	C₂³	1	2	yes	—
40	C₅×D₂₀	—	2	2	no	—
41	C₅×D₂₀	C₂³	1	4	yes	—
42	#6037	—	2	4	no	—
43	C₅×#168	C₂³	1	4	yes	complemented
44	C₂×#713	—	5	2	no	—
45	C₂×#713	—	10	2	no	—
46	C₂×D₄×D₅	—	5	2	no	—
47	C₂×C₅×SD₁₆	—	5	2	no	—
48	C₂×#688	D₅	1	2	yes	complemented
49	C₂×#686	—	5	2	no	—
50	#4060	—	5	16	no	—
51	C₂×D₄₀	—	5	2	no	—
52	C₂×#676	—	5	2	no	—
53	C₂²×C₅²	C₂×D₄	1	1	yes	characteristic
54	C₂×C₅⋊D₅	—	2	2	no	—
55	C₂×C₅⋊D₅	—	2	2	no	—
56	C₂×C₅⋊D₅	—	4	2	no	—
57	C₂×C₅⋊D₅	C₂×D₄	1	2	yes	—
58	C₂×C₅×D₅	—	2	4	no	—
59	C₂×C₅×D₅	—	4	4	no	—
60	D₅²	—	4	8	no	—
61	C₄×C₅²	—	2	2	no	—
62	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
63	C₄×C₅²	C₂⁴	1	1	yes	characteristic
64	#1039	C₂×D₄	1	2	yes	—
65	C₂³×D₅	—	10	2	no	—
66	C₂×C₅×Q₈	—	2	2	no	—
67	C₂×C₅×Q₈	C₂×D₅	1	2	yes	complemented
68	C₂×C₅×D₄	—	5	2	no	—
69	C₂×C₂²⋊D₅	—	10	2	no	—
70	#713	—	5	8	no	—
71	#713	—	10	8	no	—
72	#713	—	10	4	no	—
73	#713	—	10	8	no	—
74	D₄×D₅	—	5	8	no	—
75	D₄×D₅	—	10	4	no	—
76	C₂×D₂₀	—	5	2	no	—
77	C₂×D₂₀	—	10	2	no	—
78	C₂×D₂₀	—	10	2	no	—
79	C₂×D₂₀	—	10	4	no	—
80	C₂×D₂₀	C₂×D₅	1	2	yes	—
81	C₂×C₄×D₅	—	5	2	no	—
82	C₂×C₄×D₅	—	10	2	no	—
83	C₂×C₄×D₅	—	10	2	no	—
84	C₂×C₄×D₅	—	10	4	no	—
85	C₅×SD₁₆	—	5	8	no	—
86	C₂×C₅×C₈	—	5	2	no	—
87	#688	C₂×D₅	1	8	yes	complemented
88	#686	—	5	8	no	—
89	C₂×#168	C₂×D₅	1	2	yes	complemented
90	D₄₀	—	5	8	no	—
91	#676	—	5	8	no	—
92	C₂×AGL(1,ℤ/8)	—	25	1	no	Sylow
93	C₂×C₅²	AGL(1,ℤ/8)	1	2	yes	complemented
94	C₂×C₅²	C₂²×D₄	1	1	yes	characteristic
95	C₅⋊D₅	—	2	2	no	—
96	C₅⋊D₅	—	4	2	no	—
97	C₅×D₅	—	4	4	no	—
98	C₂³×C₅	—	10	2	no	—
99	C₂²×D₅	—	2	2	no	—
100	C₂²×D₅	—	5	2	no	—
101	C₂²×D₅	—	10	2	no	—
102	C₂²×D₅	—	10	8	no	—
103	C₂²×D₅	—	10	4	no	—
104	C₂²×D₅	—	10	2	no	—
105	C₂²×D₅	—	20	8	no	—
106	C₅×Q₈	—	2	4	no	—
107	C₅×Q₈	—	2	2	no	—
108	C₅×Q₈	—	2	4	no	—
109	C₅×Q₈	C₂²×D₅	1	4	yes	complemented
110	C₅×D₄	—	5	4	no	—
111	C₅×D₄	—	10	2	no	—
112	C₂×C₄×C₅	—	2	4	no	—
113	C₂×C₄×C₅	—	2	2	no	—
114	C₂×C₄×C₅	—	2	2	no	—
115	C₂×C₄×C₅	C₂²×D₅	1	2	yes	—
116	C₂²⋊D₅	—	10	8	no	—
117	C₂×Dic₅	—	5	2	no	—
118	C₂×Dic₅	—	10	2	no	—
119	D₂₀	—	2	2	no	—
120	D₂₀	—	5	4	no	—
121	D₂₀	—	10	4	no	—
122	D₂₀	—	10	8	no	—
123	D₂₀	—	10	16	no	—
124	D₂₀	—	10	4	no	—
125	D₂₀	—	10	2	no	—
126	D₂₀	C₂²×D₅	1	4	yes	—
127	C₄×D₅	—	5	4	no	—
128	C₄×D₅	—	5	4	no	—
129	C₄×D₅	—	10	4	no	—
130	C₄×D₅	—	10	4	no	—
131	C₄×D₅	—	10	8	no	—
132	C₄×D₅	—	10	16	no	—
133	C₅×C₈	—	5	4	no	—
134	#168	C₂²×D₅	1	4	yes	complemented
135	C₂×#41	—	25	1	no	—
136	C₂²×D₄	—	25	1	no	—
137	AGL(1,ℤ/8)	—	25	8	no	—
138	C₂×SD₁₆	—	5	2	no	—
139	C₂×D₈	—	25	2	no	—
140	C₂×M₁₆	—	25	1	no	—
141	C₅²	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
142	C₂²×C₅	—	2	2	no	—
143	C₂²×C₅	—	10	4	no	—
144	C₂²×C₅	—	20	4	no	—
145	C₂²×C₅	D₄×D₅	1	2	yes	—
146	C₂×D₅	—	2	4	no	—
147	C₂×D₅	—	4	4	no	—
148	C₂×D₅	—	5	4	no	—
149	C₂×D₅	—	10	4	no	—
150	C₂×D₅	—	10	4	no	—
151	C₂×D₅	—	10	8	no	—
152	C₂×D₅	—	10	4	no	—
153	C₂×D₅	—	20	4	no	—
154	C₂×D₅	—	20	16	no	—
155	C₂×D₅	—	20	8	no	—
156	C₂×D₅	—	20	4	no	—
157	C₄×C₅	—	2	8	no	—
158	C₄×C₅	—	2	4	no	—
159	C₄×C₅	—	2	2	no	—
160	C₄×C₅	—	2	2	no	—
161	C₄×C₅	D₄×D₅	1	2	yes	—
162	C₄×C₅	C₂³×D₅	1	2	yes	—
163	Dic₅	—	5	4	no	—
164	Dic₅	—	10	4	no	—
165	C₂⁴	—	50	1	no	—
166	#41	—	25	4	no	—
167	#41	—	50	2	no	—
168	C₂×Q₈	D₅²	1	1	yes	characteristic, complemented
169	C₂×D₄	—	5	2	no	—
170	C₂×D₄	—	25	4	no	—
171	C₂×D₄	—	25	1	no	—
172	C₂×D₄	—	50	1	no	—
173	C₂×D₄	—	50	2	no	—
174	C₂×D₄	—	50	1	no	—
175	C₂²×C₄	—	25	1	no	—
176	C₂²×C₄	—	50	1	no	—
177	SD₁₆	—	5	8	no	—
178	D₈	—	25	8	no	—
179	M₁₆	—	25	4	no	—
180	C₂×C₈	—	5	2	no	—
181	C₂×C₅	—	2	2	no	—
182	C₂×C₅	—	2	4	no	—
183	C₂×C₅	—	20	4	no	—
184	C₂×C₅	#4060	1	4	yes	complemented
185	C₂×C₅	C₂×D₄×D₅	1	2	yes	—
186	D₅	—	4	4	no	—
187	D₅	—	10	4	no	—
188	D₅	—	20	4	no	—
189	D₅	—	20	8	no	—
190	D₅	—	20	4	no	—
191	C₂³	—	10	2	no	—
192	C₂³	—	25	1	no	—
193	C₂³	—	50	4	no	—
194	C₂³	—	50	1	no	—
195	C₂³	—	100	4	no	—
196	Q₈	—	2	1	no	—
197	Q₈	C₂×D₅²	1	2	yes	complemented
198	D₄	—	5	4	no	—
199	D₄	—	10	2	no	—
200	D₄	—	25	2	no	—
201	D₄	—	50	4	no	—
202	D₄	—	50	4	no	—
203	D₄	—	50	1	no	—
204	C₂×C₄	—	2	1	no	—
205	C₂×C₄	—	25	1	no	—
206	C₂×C₄	—	25	2	no	—
207	C₂×C₄	—	25	2	no	—
208	C₂×C₄	—	50	4	no	—
209	C₂×C₄	C₂×D₅²	1	1	yes	characteristic
210	C₈	—	5	4	no	—
211	C₅	—	2	2	no	—
212	C₅	C₂×#4060	1	2	yes	complemented
213	C₂²	—	10	4	no	—
214	C₂²	—	20	4	no	—
215	C₂²	—	25	2	no	—
216	C₂²	—	50	2	no	—
217	C₂²	—	50	2	no	—
218	C₂²	—	100	8	no	—
219	C₂²	—	100	2	no	—
220	C₂²	#87886	1	1	yes	characteristic
221	C₄	—	2	2	no	—
222	C₄	—	25	2	no	—
223	C₄	#87886	1	1	yes	characteristic
224	C₄	C₂²×D₅²	1	1	yes	characteristic
225	C₂	—	20	4	no	—
226	C₂	—	50	2	no	—
227	C₂	—	100	2	no	—
228	C₂	#11717059	1	2	yes	direct product factor
229	C₂	C₂×#87886	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#87904

C₂

yes

maximal, characteristic, complemented

C₂×#87877

C₂

yes

maximal, characteristic, complemented

C₂×C₅×#688

C₂

yes

maximal, complemented

#11717059

C₂

yes

maximal, direct product factor

C₂×#87771

C₂

yes

maximal, complemented

C₂×#87769

C₂

yes

maximal, characteristic, complemented

C₂²×D₅²

—

C₂×C₅²×Q₈

C₂²

yes

characteristic, complemented

#87904

—

#87904

C₂²

yes

complemented

C₂×C₄⋊(C₅⋊D₅)

—

C₂×C₄⋊(C₅⋊D₅)

C₂²

yes

characteristic, complemented

C₂×C₄×C₅⋊D₅

—

C₂×C₄×C₅⋊D₅

C₂²

yes

characteristic

C₂×C₅×D₂₀

C₂²

yes

—

C₂×#6037

—

#87877

—

#87877

C₂²

yes

complemented

C₅×#688

C₂²

yes

complemented

C₂×C₅×#168

C₂²

yes

complemented

#87771

C₂²

yes

complemented

#87769

C₂²

yes

complemented

C₂×#4060

—

maximal

C₂²×C₅⋊D₅

—

C₂²×C₅⋊D₅

D₄

yes

characteristic

C₂²×C₅×D₅

—

C₂×D₅²

—

C₂×D₅²

—

C₅²×Q₈

—

C₅²×Q₈

C₂³

yes

complemented

C₂×C₄×C₅²

—

C₂×C₄×C₅²

C₂³

yes

characteristic

C₂×#1039

D₄

yes

characteristic

C₄⋊(C₅⋊D₅)

—

C₄⋊(C₅⋊D₅)

—

C₄⋊(C₅⋊D₅)

C₂³

yes

complemented

C₄×C₅⋊D₅

—

C₄×C₅⋊D₅

D₄

yes

—

C₄×C₅⋊D₅

C₂³

yes

—

C₅×D₂₀

—

C₅×D₂₀

C₂³

yes

—

#6037

—

C₅×#168

C₂³

yes

complemented

C₂×#713

—

C₂×#713

—

C₂×D₄×D₅

—

C₂×C₅×SD₁₆

—

C₂×#688

D₅

yes

complemented

C₂×#686

—

#4060

—

C₂×D₄₀

—

C₂×#676

—

C₂²×C₅²

C₂×D₄

yes

characteristic

C₂×C₅⋊D₅

—

C₂×C₅⋊D₅

—

C₂×C₅⋊D₅

—

C₂×C₅⋊D₅

C₂×D₄

yes

—

C₂×C₅×D₅

—

C₂×C₅×D₅

—

D₅²

—

C₄×C₅²

—

C₄×C₅²

C₂×D₄

yes

characteristic

C₄×C₅²

C₂⁴

yes

characteristic

#1039

C₂×D₄

yes

—

C₂³×D₅

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

C₂×D₅

yes

complemented

C₂×C₅×D₄

—

C₂×C₂²⋊D₅

—

—

—

—

—

D₄×D₅

—

D₄×D₅

—

C₂×D₂₀

—

C₂×D₂₀

—

C₂×D₂₀

—

C₂×D₂₀

—

C₂×D₂₀

C₂×D₅

yes

—

C₂×C₄×D₅

—

C₂×C₄×D₅

—

C₂×C₄×D₅

—

C₂×C₄×D₅

—

C₅×SD₁₆

—

C₂×C₅×C₈

—

#688

C₂×D₅

yes

complemented

#686

—

C₂×#168

C₂×D₅

yes

complemented

D₄₀

—

—

—

C₂×C₅²

yes

C₂×C₅²

C₂²×D₄

yes

characteristic

C₅⋊D₅

—

C₅⋊D₅

—

C₅×D₅

—

C₂³×C₅

—

C₂²×D₅

—

100

C₂²×D₅

—

101

C₂²×D₅

—

102

C₂²×D₅

—

103

C₂²×D₅

—

104

C₂²×D₅

—

105

C₂²×D₅

—

106

C₅×Q₈

—

107

C₅×Q₈

—

108

C₅×Q₈

—

109

C₅×Q₈

C₂²×D₅

yes

complemented

110

C₅×D₄

—

111

C₅×D₄

—

112

C₂×C₄×C₅

—

113

C₂×C₄×C₅

—

114

C₂×C₄×C₅

—

115

C₂×C₄×C₅

C₂²×D₅

yes

—

116

C₂²⋊D₅

—

117

C₂×Dic₅

—

118

C₂×Dic₅

—

119

D₂₀

—

120

D₂₀

—

121

D₂₀

—

122

D₂₀

—

123

D₂₀

—

124

D₂₀

—

125

D₂₀

—

126

D₂₀

C₂²×D₅

yes

—

127

C₄×D₅

—

128

C₄×D₅

—

129

C₄×D₅

—

130

C₄×D₅

—

131

C₄×D₅

—

132

C₄×D₅

—

133

C₅×C₈

—

134

#168

C₂²×D₅

yes

complemented

135

C₂×#41

—

136

C₂²×D₄

—

137

AGL(1,ℤ/8)

—

138

C₂×SD₁₆

—

139

C₂×D₈

—

140

C₂×M₁₆

—

141

C₅²

C₂×AGL(1,ℤ/8)

yes

characteristic, complemented, Sylow

142

C₂²×C₅

—

143

C₂²×C₅

—

144

C₂²×C₅

—

145

C₂²×C₅

D₄×D₅

yes

—

146

C₂×D₅

—

147

C₂×D₅

—

148

C₂×D₅

—

149

C₂×D₅

—

150

C₂×D₅

—

151

C₂×D₅

—

152

C₂×D₅

—

153

C₂×D₅

—

154

C₂×D₅

—

155

C₂×D₅

—

156

C₂×D₅

—

157

C₄×C₅

—

158

C₄×C₅

—

159

C₄×C₅

—

160

C₄×C₅

—

161

C₄×C₅

D₄×D₅

yes

—

162

C₄×C₅

C₂³×D₅

yes

—

163

Dic₅

—

164

Dic₅

—

165

C₂⁴

—

166

#41

—

167

#41

—

168

C₂×Q₈

D₅²

yes

characteristic, complemented

169

C₂×D₄

—

170

C₂×D₄

—

171

C₂×D₄

—

172

C₂×D₄

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂²×C₄

—

176

C₂²×C₄

—

177

SD₁₆

—

178

D₈

—

179

M₁₆

—

180

C₂×C₈

—

181

C₂×C₅

—

182

C₂×C₅

—

183

C₂×C₅

—

184

C₂×C₅

#4060

yes

complemented

185

C₂×C₅

C₂×D₄×D₅

yes

—

186

D₅

—

187

D₅

—

188

D₅

—

189

D₅

—

190

D₅

—

191

C₂³

—

192

C₂³

—

193

C₂³

—

194

C₂³

—

195

C₂³

—

100

—

196

Q₈

—

197

Q₈

C₂×D₅²

yes

complemented

198

D₄

—

199

D₄

—

200

D₄

—

201

D₄

—

202

D₄

—

203

D₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

C₂×D₅²

yes

characteristic

210

C₈

—

211

C₅

—

212

C₅

C₂×#4060

yes

complemented

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

100

—

219

C₂²

—

100

—

220

C₂²

#87886

yes

characteristic

221

C₄

—

222

C₄

—

223

C₄

#87886

yes

characteristic

224

C₄

C₂²×D₅²

yes

characteristic

225

C₂

—

226

C₂

—

227

C₂

—

100

—

228

C₂

#11717059

yes

direct product factor

229

C₂

C₂×#87886

yes

characteristic

	subgroup	G/H
center	C₂²	#87886
commutator, cosocle	C₄×C₅²	C₂⁴
Frattini	C₄	C₂²×D₅²
Fitting	C₂×C₅²×Q₈	C₂²
socle	C₂²×C₅²	C₂×D₄
hypercenter	C₂×Q₈	D₅²
hypocenter	C₅²	C₂×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

subgroup

G/H

center

C₂²

#87886

commutator, cosocle

C₄×C₅²

C₂⁴

Frattini

C₄

C₂²×D₅²

Fitting

C₂×C₅²×Q₈

C₂²

socle

C₂²×C₅²

C₂×D₄

hypercenter

C₂×Q₈

D₅²

hypocenter

C₅²

C₂×AGL(1,ℤ/8)

LCS

G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

N	H ≅ G/N	type
1. C₂×#87904	C₂	semidirect
2. C₂×#87877	C₂	semidirect
3. C₂×C₅×#688	C₂	semidirect
4. #11717059	C₂	direct (N × H)
5. C₂×#87771	C₂	semidirect
6. C₂×#87769	C₂	semidirect
8. C₂×C₅²×Q₈	C₂²	semidirect
10. #87904	C₂²	semidirect
12. C₂×C₄⋊(C₅⋊D₅)	C₂²	semidirect
18. #87877	C₂²	semidirect
19. C₅×#688	C₂²	semidirect
20. C₂×C₅×#168	C₂²	semidirect
21. #87771	C₂²	semidirect
22. #87769	C₂²	semidirect
30. C₅²×Q₈	C₂³	semidirect
36. C₄⋊(C₅⋊D₅)	C₂³	semidirect
43. C₅×#168	C₂³	semidirect
48. C₂×#688	D₅	semidirect
67. C₂×C₅×Q₈	C₂×D₅	semidirect
87. #688	C₂×D₅	semidirect
89. C₂×#168	C₂×D₅	semidirect
93. C₂×C₅²	AGL(1,ℤ/8)	semidirect
109. C₅×Q₈	C₂²×D₅	semidirect
134. #168	C₂²×D₅	semidirect
141. C₅²	C₂×AGL(1,ℤ/8)	semidirect
168. C₂×Q₈	D₅²	semidirect
184. C₂×C₅	#4060	semidirect
197. Q₈	C₂×D₅²	semidirect
212. C₅	C₂×#4060	semidirect
228. C₂	#11717059	direct (N × H)

H ≅ G/N

type

1. C₂×#87904

C₂

semidirect

2. C₂×#87877

C₂

semidirect

3. C₂×C₅×#688

C₂

semidirect

4. #11717059

C₂

direct (N × H)

5. C₂×#87771

C₂

semidirect

6. C₂×#87769

C₂

semidirect

8. C₂×C₅²×Q₈

C₂²

semidirect

10. #87904

C₂²

semidirect

12. C₂×C₄⋊(C₅⋊D₅)

C₂²

semidirect

18. #87877

C₂²

semidirect

19. C₅×#688

C₂²

semidirect

20. C₂×C₅×#168

C₂²

semidirect

21. #87771

C₂²

semidirect

22. #87769

C₂²

semidirect

30. C₅²×Q₈

C₂³

semidirect

36. C₄⋊(C₅⋊D₅)

C₂³

semidirect

43. C₅×#168

C₂³

semidirect

48. C₂×#688

D₅

semidirect

67. C₂×C₅×Q₈

C₂×D₅

semidirect

87. #688

C₂×D₅

semidirect

89. C₂×#168

C₂×D₅

semidirect

93. C₂×C₅²

AGL(1,ℤ/8)

semidirect

109. C₅×Q₈

C₂²×D₅

semidirect

134. #168

C₂²×D₅

semidirect

141. C₅²

C₂×AGL(1,ℤ/8)

semidirect

168. C₂×Q₈

D₅²

semidirect

184. C₂×C₅

#4060

semidirect

197. Q₈

C₂×D₅²

semidirect

212. C₅

C₂×#4060

semidirect

228. C₂

#11717059

direct (N × H)

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

subgroup	index
C₂×#87904	2
C₂×#87877	2
C₂×C₅×#688	2
#11717059	2
C₂×#87771	2
C₂×#87769	2
C₂×#4060	5

subgroup

index

C₂×C₅×#688

Subgroups — C₂×#11717059 #13106466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11717059 #13106466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11717059 #13106466