Group #11936256 — subgroups

Subgroups — C₅×#13536 #11936256

Order 1280.

318 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 114 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×#365	C₂	1	2	yes	maximal
2	C₂×C₅×#362	C₂	1	2	yes	maximal
3	C₅×#1971	C₂	1	1	yes	maximal, characteristic
4	C₅×#1849	C₂	1	1	yes	maximal, characteristic
5	C₅×#1377	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₅×M₃₂	C₂²	1	2	yes	—
8	C₂×C₅×#108	—	2	1	no	—
9	C₂×C₅×#108	C₂²	1	2	yes	—
10	C₂×C₅×#106	C₂²	1	1	yes	characteristic
11	C₅×#423	—	2	1	no	—
12	C₂×C₅×#103	—	2	1	no	—
13	C₂×C₅×#97	C₂²	1	1	yes	characteristic
14	C₅×#391	—	2	1	no	—
15	C₅×#365	—	2	4	no	—
16	C₅×#362	—	2	4	no	—
17	#13536	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×Q₈	—	2	1	no	—
19	C₂×C₅×Q₁₆	—	2	2	no	—
20	C₂×C₅×Q₁₆	—	2	2	no	—
21	C₂×C₅×Q₁₆	—	2	1	no	—
22	C₂×C₅×Q₁₆	Q₈	1	2	yes	—
23	C₂×C₅×M₁₆	—	2	2	no	—
24	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
25	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₄	—	2	1	no	—
27	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
28	C₅×M₃₂	—	2	2	no	—
29	C₅×M₃₂	D₄	1	4	yes	—
30	C₂×C₅×C₁₆	—	2	2	no	—
31	C₅×#108	—	2	2	no	—
32	C₅×#108	—	2	2	no	—
33	C₅×#108	—	4	2	no	—
34	C₅×#106	—	2	2	no	—
35	C₅×C₄⋊C₈	—	4	2	no	—
36	C₅×#103	—	4	2	no	—
37	C₅×#97	—	2	2	no	—
38	C₅×#95	—	4	2	no	—
39	C₂×#365	C₂×C₅	1	2	yes	—
40	C₂×#362	C₂×C₅	1	2	yes	—
41	#1971	C₂×C₅	1	1	yes	characteristic
42	#1849	C₂×C₅	1	1	yes	characteristic
43	#1377	C₂×C₅	1	1	yes	characteristic
44	C₂×C₅×Q₈	—	2	2	no	—
45	C₂×C₅×Q₈	—	4	1	no	—
46	C₂×C₅×Q₈	—	4	1	no	—
47	C₂×C₅×Q₈	—	4	1	no	—
48	C₂×C₅×Q₈	—	4	1	no	—
49	C₂×C₅×Q₈	—	4	1	no	—
50	C₂²×C₄×C₅	—	4	1	no	—
51	C₂²×C₄×C₅	—	4	1	no	—
52	C₂²×C₄×C₅	SD₁₆	1	2	yes	—
53	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
54	C₅×Q₁₆	—	2	4	no	—
55	C₅×Q₁₆	—	4	2	no	—
56	C₅×M₁₆	—	4	2	no	—
57	C₅×M₁₆	—	4	2	no	—
58	C₂×C₅×C₈	—	2	1	no	—
59	C₂×C₅×C₈	—	2	1	no	—
60	C₂×C₅×C₈	—	4	2	no	—
61	C₂×C₅×C₈	SD₁₆	1	2	yes	—
62	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
63	C₂×C₅×C₈	C₂×Q₈	1	1	yes	characteristic
64	C₂×C₅×C₈	#41	1	2	yes	—
65	C₂×C₅×C₈	#41	1	1	yes	characteristic
66	C₅×C₄⋊C₄	—	4	1	no	—
67	C₅×C₄⋊C₄	—	4	1	no	—
68	C₄²×C₅	—	2	1	no	—
69	C₄²×C₅	—	2	1	no	—
70	C₅×C₁₆	—	2	4	no	—
71	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
72	C₂×M₃₂	C₂²×C₅	1	2	yes	—
73	C₂×#108	—	2	1	no	—
74	C₂×#108	C₂²×C₅	1	2	yes	—
75	C₂×#106	C₂²×C₅	1	1	yes	characteristic
76	#423	—	2	1	no	—
77	C₂×#103	—	2	1	no	—
78	C₂×#97	C₂²×C₅	1	1	yes	characteristic
79	#391	—	2	1	no	—
80	#365	—	2	4	no	—
81	#362	—	2	4	no	—
82	C₂³×C₅	C₂×SD₁₆	1	1	yes	characteristic
83	C₅×Q₈	—	4	2	no	—
84	C₅×Q₈	—	4	2	no	—
85	C₅×Q₈	—	8	1	no	—
86	C₅×Q₈	—	8	1	no	—
87	C₂×C₄×C₅	—	2	2	no	—
88	C₂×C₄×C₅	—	4	2	no	—
89	C₂×C₄×C₅	—	4	2	no	—
90	C₂×C₄×C₅	—	8	1	no	—
91	C₂×C₄×C₅	—	8	1	no	—
92	C₂×C₄×C₅	—	8	2	no	—
93	C₂×C₄×C₅	—	8	1	no	—
94	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
95	C₂×C₄×C₅	#123	1	1	yes	characteristic
96	C₂×C₄×C₅	#127	1	1	yes	characteristic
97	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
98	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
99	C₂×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
100	C₅×C₈	—	2	2	no	—
101	C₅×C₈	—	8	2	no	—
102	C₅×C₈	C₂²⋊Q₈	1	2	yes	—
103	C₅×C₈	#123	1	2	yes	—
104	C₂²×Q₈	—	2	1	no	—
105	C₂×Q₁₆	—	2	2	no	—
106	C₂×Q₁₆	—	2	2	no	—
107	C₂×Q₁₆	—	2	1	no	—
108	C₂×Q₁₆	C₅×Q₈	1	2	yes	—
109	C₂×M₁₆	—	2	2	no	—
110	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
111	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
112	C₂×C₄⋊C₄	—	2	1	no	—
113	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
114	M₃₂	—	2	2	no	—
115	M₃₂	C₅×D₄	1	4	yes	—
116	C₂×C₁₆	—	2	2	no	—
117	#108	—	2	2	no	—
118	#108	—	2	2	no	—
119	#108	—	4	2	no	—
120	#106	—	2	2	no	—
121	C₄⋊C₈	—	4	2	no	—
122	#103	—	4	2	no	—
123	#97	—	2	2	no	—
124	#95	—	4	2	no	—
125	C₂²×C₅	—	2	2	no	—
126	C₂²×C₅	#476	1	1	yes	characteristic
127	C₂²×C₅	#481	1	1	yes	characteristic
128	C₂²×C₅	#492	1	1	yes	characteristic
129	C₄×C₅	—	4	2	no	—
130	C₄×C₅	—	8	2	no	—
131	C₄×C₅	—	16	1	no	—
132	C₄×C₅	#399	1	1	yes	characteristic
133	C₄×C₅	#476	1	1	yes	characteristic
134	C₄×C₅	#481	1	1	yes	characteristic
135	C₄×C₅	#496	1	1	yes	characteristic
136	C₂×Q₈	—	2	2	no	—
137	C₂×Q₈	—	4	1	no	—
138	C₂×Q₈	—	4	1	no	—
139	C₂×Q₈	—	4	1	no	—
140	C₂×Q₈	—	4	1	no	—
141	C₂×Q₈	—	4	1	no	—
142	C₂²×C₄	—	4	1	no	—
143	C₂²×C₄	—	4	1	no	—
144	C₂²×C₄	C₅×SD₁₆	1	2	yes	—
145	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
146	Q₁₆	—	2	4	no	—
147	Q₁₆	—	4	2	no	—
148	M₁₆	—	4	2	no	—
149	M₁₆	—	4	2	no	—
150	C₂×C₈	—	2	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	4	2	no	—
153	C₂×C₈	C₅×SD₁₆	1	2	yes	—
154	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
155	C₂×C₈	C₂×C₅×Q₈	1	1	yes	characteristic
156	C₂×C₈	C₅×#41	1	2	yes	—
157	C₂×C₈	C₅×#41	1	1	yes	characteristic
158	C₄⋊C₄	—	4	1	no	—
159	C₄⋊C₄	—	4	1	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	2	1	no	—
162	C₁₆	—	2	4	no	—
163	C₂×C₅	—	2	1	no	—
164	C₂×C₅	—	2	1	no	—
165	C₂×C₅	#2094	1	1	yes	characteristic
166	C₂×C₅	#2239	1	2	yes	—
167	C₂³	C₂×C₅×SD₁₆	1	1	yes	characteristic
168	Q₈	—	4	2	no	—
169	Q₈	—	4	2	no	—
170	Q₈	—	8	1	no	—
171	Q₈	—	8	1	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	2	no	—
175	C₂×C₄	—	8	1	no	—
176	C₂×C₄	—	8	1	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	1	no	—
179	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
180	C₂×C₄	C₅×#123	1	1	yes	characteristic
181	C₂×C₄	C₅×#127	1	1	yes	characteristic
182	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
183	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×C₄	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₈	—	2	2	no	—
186	C₈	—	8	2	no	—
187	C₈	C₅×C₂²⋊Q₈	1	2	yes	—
188	C₈	C₅×#123	1	2	yes	—
189	C₅	#13536	1	1	yes	characteristic, direct product factor, Sylow
190	C₂²	—	2	2	no	—
191	C₂²	C₅×#476	1	1	yes	characteristic
192	C₂²	C₅×#481	1	1	yes	characteristic
193	C₂²	C₅×#492	1	1	yes	characteristic
194	C₄	—	4	2	no	—
195	C₄	—	8	2	no	—
196	C₄	—	16	1	no	—
197	C₄	C₅×#399	1	1	yes	characteristic
198	C₄	C₅×#476	1	1	yes	characteristic
199	C₄	C₅×#481	1	1	yes	characteristic
200	C₄	C₅×#496	1	1	yes	characteristic
201	C₂	—	2	1	no	—
202	C₂	—	2	1	no	—
203	C₂	C₅×#2094	1	1	yes	characteristic
204	C₂	C₅×#2239	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×#365

C₂

yes

maximal

C₂×C₅×#362

C₂

yes

maximal

C₅×#1971

C₂

yes

maximal, characteristic

C₅×#1849

C₂

yes

maximal, characteristic

C₅×#1377

C₂

yes

maximal, characteristic

C₂²×C₅×Q₁₆

C₂²

yes

characteristic

C₂×C₅×M₃₂

C₂²

yes

—

C₂×C₅×#108

—

C₂×C₅×#108

C₂²

yes

—

C₂×C₅×#106

C₂²

yes

characteristic

C₅×#423

—

C₂×C₅×#103

—

C₂×C₅×#97

C₂²

yes

—

—

—

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

—

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

—

C₂×C₅×Q₁₆

Q₈

yes

—

C₂×C₅×M₁₆

—

C₂²×C₅×C₈

D₄

yes

characteristic

C₂²×C₅×C₈

C₂³

yes

characteristic

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

D₄

yes

characteristic

C₅×M₃₂

—

C₅×M₃₂

D₄

yes

—

C₂×C₅×C₁₆

—

—

—

—

—

C₅×C₄⋊C₈

—

C₅×#103

—

C₅×#97

—

C₅×#95

—

C₂×#365

C₂×C₅

yes

—

C₂×#362

C₂×C₅

yes

—

#1971

C₂×C₅

yes

characteristic

#1849

C₂×C₅

yes

characteristic

#1377

C₂×C₅

yes

characteristic

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

SD₁₆

yes

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₅×Q₁₆

—

C₅×Q₁₆

—

C₅×M₁₆

—

C₅×M₁₆

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

SD₁₆

yes

—

C₂×C₅×C₈

C₂×D₄

yes

—

C₂×C₅×C₈

C₂×Q₈

yes

characteristic

C₂×C₅×C₈

#41

yes

—

C₂×C₅×C₈

#41

yes

characteristic

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₅×C₁₆

—

C₂²×Q₁₆

C₂²×C₅

yes

characteristic

C₂×M₃₂

C₂²×C₅

yes

—

C₂×#108

—

C₂×#108

C₂²×C₅

yes

—

C₂×#106

C₂²×C₅

yes

characteristic

#423

—

C₂×#103

—

C₂×#97

C₂²×C₅

yes

—

—

—

C₂³×C₅

C₂×SD₁₆

yes

characteristic

C₅×Q₈

—

C₅×Q₈

—

C₅×Q₈

—

C₅×Q₈

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

C₂×SD₁₆

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

100

C₅×C₈

—

101

C₅×C₈

—

102

C₅×C₈

C₂²⋊Q₈

yes

—

103

C₅×C₈

#123

yes

—

104

C₂²×Q₈

—

105

C₂×Q₁₆

—

106

C₂×Q₁₆

—

107

C₂×Q₁₆

—

108

C₂×Q₁₆

C₅×Q₈

yes

—

109

C₂×M₁₆

—

110

C₂²×C₈

C₅×D₄

yes

characteristic

111

C₂²×C₈

C₂³×C₅

yes

characteristic

112

C₂×C₄⋊C₄

—

113

C₂×C₄²

C₅×D₄

yes

characteristic

114

M₃₂

—

115

M₃₂

C₅×D₄

yes

—

116

C₂×C₁₆

—

117

#108

—

118

#108

—

119

#108

—

120

#106

—

121

C₄⋊C₈

—

122

#103

—

123

#97

—

124

#95

—

125

C₂²×C₅

—

126

C₂²×C₅

#476

yes

characteristic

127

C₂²×C₅

#481

yes

characteristic

128

C₂²×C₅

#492

yes

characteristic

129

C₄×C₅

—

130

C₄×C₅

—

131

C₄×C₅

—

132

C₄×C₅

#399

yes

characteristic

133

C₄×C₅

#476

yes

characteristic

134

C₄×C₅

#481

yes

characteristic

135

C₄×C₅

#496

yes

characteristic

136

C₂×Q₈

—

137

C₂×Q₈

—

138

C₂×Q₈

—

139

C₂×Q₈

—

140

C₂×Q₈

—

141

C₂×Q₈

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₅×SD₁₆

yes

—

145

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

146

Q₁₆

—

147

Q₁₆

—

148

M₁₆

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

C₅×SD₁₆

yes

—

154

C₂×C₈

C₂×C₅×D₄

yes

—

155

C₂×C₈

C₂×C₅×Q₈

yes

characteristic

156

C₂×C₈

C₅×#41

yes

—

157

C₂×C₈

C₅×#41

yes

characteristic

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₁₆

—

163

C₂×C₅

—

164

C₂×C₅

—

165

C₂×C₅

#2094

yes

characteristic

166

C₂×C₅

#2239

yes

—

167

C₂³

C₂×C₅×SD₁₆

yes

characteristic

168

Q₈

—

169

Q₈

—

170

Q₈

—

171

Q₈

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

C₅×C₂²⋊Q₈

yes

characteristic

180

C₂×C₄

C₅×#123

yes

characteristic

181

C₂×C₄

C₅×#127

yes

characteristic

182

C₂×C₄

C₂×C₅×SD₁₆

yes

characteristic

183

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

characteristic

184

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

characteristic

185

C₈

—

186

C₈

—

187

C₈

C₅×C₂²⋊Q₈

yes

—

188

C₈

C₅×#123

yes

—

189

C₅

#13536

yes

characteristic, direct product factor, Sylow

190

C₂²

—

191

C₂²

C₅×#476

yes

characteristic

192

C₂²

C₅×#481

yes

characteristic

193

C₂²

C₅×#492

yes

characteristic

194

C₄

—

195

C₄

—

196

C₄

—

197

C₄

C₅×#399

yes

characteristic

198

C₄

C₅×#476

yes

characteristic

199

C₄

C₅×#481

yes

characteristic

200

C₄

C₅×#496

yes

characteristic

201

C₂

—

202

C₂

—

203

C₂

C₅×#2094

yes

characteristic

204

C₂

C₅×#2239

yes

—

	subgroup	G/H
center, socle	C₂²×C₅	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅
prime radical	C₂³×C₅	C₂×SD₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#481

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₅

prime radical

C₂³×C₅

C₂×SD₁₆

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

N	H ≅ G/N	type
17. #13536	C₅	direct (N × H)
189. C₅	#13536	direct (N × H)

H ≅ G/N

type

17. #13536

C₅

direct (N × H)

189. C₅

#13536

direct (N × H)

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

subgroup	index
C₂×C₅×#365	2
C₂×C₅×#362	2
C₅×#1971	2
C₅×#1849	2
C₅×#1377	2
#13536	5

subgroup

index

C₂×C₅×#365

C₂×C₅×#362

Subgroups — C₅×#13536 #11936256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#13536 #11936256

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#13536 #11936256