Group #11933405 — subgroups

Subgroups — C₅×#10685 #11933405

Order 1280.

442 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 178 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	C₅×#1990	C₂	1	2	yes	maximal
2	C₅×#1956	C₂	1	1	yes	maximal, characteristic
3	C₅×#1844	C₂	1	2	yes	maximal
4	C₅×#1844	C₂	1	1	yes	maximal, characteristic
5	C₅×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₅×#106	—	2	4	no	—
8	C₂×C₅×#106	—	2	2	no	—
9	C₂×C₅×#103	—	2	2	no	—
10	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
12	C₅×#384	C₂²	1	1	yes	characteristic
13	C₅×#384	C₂²	1	2	yes	—
14	C₅×#340	—	2	4	no	—
15	#10685	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂²×C₅×Q₈	—	2	1	no	—
17	C₂²×C₅×C₈	D₄	1	4	yes	—
18	C₂²×C₅×C₈	D₄	1	2	yes	—
19	C₅×C₄⋊Q₈	—	2	2	no	—
20	C₅×C₄⋊Q₈	—	2	1	no	—
21	C₅×C₄⋊Q₈	Q₈	1	2	yes	—
22	C₂×C₅×C₄⋊C₄	—	2	2	no	—
23	C₂×C₅×C₄⋊C₄	—	2	2	no	—
24	C₂×C₅×C₄⋊C₄	—	2	1	no	—
25	C₂×C₅×C₄⋊C₄	—	2	2	no	—
26	C₂×C₅×C₄⋊C₄	—	2	2	no	—
27	C₂×C₅×C₄⋊C₄	—	2	2	no	—
28	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
29	C₅×#106	—	4	4	no	—
30	C₅×#106	—	4	8	no	—
31	C₅×#103	—	4	4	no	—
32	C₄×C₅×C₈	—	2	2	no	—
33	C₄×C₅×C₈	—	2	2	no	—
34	C₄×C₅×C₈	—	2	2	no	—
35	#1990	C₂×C₅	1	2	yes	—
36	#1956	C₂×C₅	1	1	yes	characteristic
37	#1844	C₂×C₅	1	2	yes	—
38	#1844	C₂×C₅	1	1	yes	characteristic
39	#1273	C₂×C₅	1	1	yes	characteristic
40	C₂×C₅×Q₈	—	2	2	no	—
41	C₂×C₅×Q₈	—	4	1	no	—
42	C₂×C₅×Q₈	—	4	2	no	—
43	C₂×C₅×Q₈	—	4	2	no	—
44	C₂²×C₄×C₅	—	4	1	no	—
45	C₂²×C₄×C₅	—	4	1	no	—
46	C₂²×C₄×C₅	—	4	2	no	—
47	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	2	4	no	—
51	C₂×C₅×C₈	—	2	2	no	—
52	C₂×C₅×C₈	—	2	4	no	—
53	C₂×C₅×C₈	SD₁₆	1	4	yes	—
54	C₂×C₅×C₈	SD₁₆	1	8	yes	—
55	C₅×C₄⋊C₄	—	2	4	no	—
56	C₅×C₄⋊C₄	—	4	2	no	—
57	C₅×C₄⋊C₄	—	4	2	no	—
58	C₅×C₄⋊C₄	—	4	4	no	—
59	C₅×C₄⋊C₄	—	4	4	no	—
60	C₅×C₄⋊C₄	—	4	4	no	—
61	C₅×C₄⋊C₄	—	4	4	no	—
62	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
63	C₄²×C₅	#41	1	2	yes	—
64	C₄²×C₅	#41	1	1	yes	characteristic
65	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
66	C₂×#106	—	2	2	no	—
67	C₂×#106	—	2	4	no	—
68	C₂×#103	—	2	2	no	—
69	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
70	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
71	#384	C₂²×C₅	1	1	yes	characteristic
72	#384	C₂²×C₅	1	2	yes	—
73	#340	—	2	4	no	—
74	C₂³×C₅	#127	1	1	yes	characteristic
75	C₅×Q₈	—	4	4	no	—
76	C₅×Q₈	—	8	2	no	—
77	C₂×C₄×C₅	—	4	2	no	—
78	C₂×C₄×C₅	—	8	1	no	—
79	C₂×C₄×C₅	—	8	1	no	—
80	C₂×C₄×C₅	—	8	1	no	—
81	C₂×C₄×C₅	—	8	2	no	—
82	C₂×C₄×C₅	—	8	2	no	—
83	C₂×C₄×C₅	—	8	2	no	—
84	C₂×C₄×C₅	—	8	2	no	—
85	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×C₅	#123	1	1	yes	characteristic
88	C₂×C₄×C₅	#123	1	2	yes	—
89	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
90	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
91	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
92	C₂×C₄×C₅	#137	1	4	yes	—
93	C₅×C₈	—	2	4	no	—
94	C₅×C₈	—	2	8	no	—
95	C₂²×Q₈	—	2	1	no	—
96	C₂²×C₈	C₅×D₄	1	4	yes	—
97	C₂²×C₈	C₅×D₄	1	2	yes	—
98	C₄⋊Q₈	—	2	2	no	—
99	C₄⋊Q₈	—	2	1	no	—
100	C₄⋊Q₈	C₅×Q₈	1	2	yes	—
101	C₂×C₄⋊C₄	—	2	2	no	—
102	C₂×C₄⋊C₄	—	2	2	no	—
103	C₂×C₄⋊C₄	—	2	1	no	—
104	C₂×C₄⋊C₄	—	2	2	no	—
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	—	2	2	no	—
107	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
108	#106	—	4	4	no	—
109	#106	—	4	8	no	—
110	#103	—	4	4	no	—
111	C₄×C₈	—	2	2	no	—
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	—	2	2	no	—
114	C₂²×C₅	#399	1	1	yes	characteristic
115	C₂²×C₅	#492	1	1	yes	characteristic
116	C₂²×C₅	#492	1	2	yes	—
117	C₂²×C₅	#496	1	1	yes	characteristic
118	C₂²×C₅	#497	1	2	yes	—
119	C₄×C₅	—	8	2	no	—
120	C₄×C₅	—	16	1	no	—
121	C₄×C₅	—	16	2	no	—
122	C₄×C₅	#475	1	4	yes	—
123	C₄×C₅	#476	1	2	yes	—
124	C₄×C₅	#481	1	2	yes	—
125	C₄×C₅	#483	1	4	yes	—
126	C₂×Q₈	—	2	2	no	—
127	C₂×Q₈	—	4	1	no	—
128	C₂×Q₈	—	4	2	no	—
129	C₂×Q₈	—	4	2	no	—
130	C₂²×C₄	—	4	1	no	—
131	C₂²×C₄	—	4	1	no	—
132	C₂²×C₄	—	4	2	no	—
133	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
134	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	2	2	no	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	C₅×SD₁₆	1	4	yes	—
140	C₂×C₈	C₅×SD₁₆	1	8	yes	—
141	C₄⋊C₄	—	2	4	no	—
142	C₄⋊C₄	—	4	2	no	—
143	C₄⋊C₄	—	4	2	no	—
144	C₄⋊C₄	—	4	4	no	—
145	C₄⋊C₄	—	4	4	no	—
146	C₄⋊C₄	—	4	4	no	—
147	C₄⋊C₄	—	4	4	no	—
148	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
149	C₄²	C₅×#41	1	2	yes	—
150	C₄²	C₅×#41	1	1	yes	characteristic
151	C₂×C₅	#1705	1	1	yes	characteristic
152	C₂×C₅	#1714	1	2	yes	—
153	C₂×C₅	#1716	1	1	yes	characteristic
154	C₂×C₅	#2094	1	1	yes	characteristic
155	C₂×C₅	#2096	1	2	yes	—
156	C₂³	C₅×#127	1	1	yes	characteristic
157	Q₈	—	4	4	no	—
158	Q₈	—	8	2	no	—
159	C₂×C₄	—	4	2	no	—
160	C₂×C₄	—	8	1	no	—
161	C₂×C₄	—	8	1	no	—
162	C₂×C₄	—	8	1	no	—
163	C₂×C₄	—	8	2	no	—
164	C₂×C₄	—	8	2	no	—
165	C₂×C₄	—	8	2	no	—
166	C₂×C₄	—	8	2	no	—
167	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄	C₅×#123	1	1	yes	characteristic
170	C₂×C₄	C₅×#123	1	2	yes	—
171	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
172	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
173	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄	C₅×#137	1	4	yes	—
175	C₈	—	2	4	no	—
176	C₈	—	2	8	no	—
177	C₅	#10685	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²	C₅×#399	1	1	yes	characteristic
179	C₂²	C₅×#492	1	1	yes	characteristic
180	C₂²	C₅×#492	1	2	yes	—
181	C₂²	C₅×#496	1	1	yes	characteristic
182	C₂²	C₅×#497	1	2	yes	—
183	C₄	—	8	2	no	—
184	C₄	—	16	1	no	—
185	C₄	—	16	2	no	—
186	C₄	C₅×#475	1	4	yes	—
187	C₄	C₅×#476	1	2	yes	—
188	C₄	C₅×#481	1	2	yes	—
189	C₄	C₅×#483	1	4	yes	—
190	C₂	C₅×#1705	1	1	yes	characteristic
191	C₂	C₅×#1714	1	2	yes	—
192	C₂	C₅×#1716	1	1	yes	characteristic
193	C₂	C₅×#2094	1	1	yes	characteristic
194	C₂	C₅×#2096	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#1990

C₂

yes

maximal

C₅×#1956

C₂

yes

maximal, characteristic

C₅×#1844

C₂

yes

maximal

C₅×#1844

C₂

yes

maximal, characteristic

C₅×#1273

C₂

yes

maximal, characteristic

C₂×C₅×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₅×#106

—

C₂×C₅×#106

—

C₂×C₅×#103

—

C₂×C₄×C₅×C₈

C₂²

yes

characteristic

C₂×C₄×C₅×C₈

C₂²

yes

—

C₅×#384

C₂²

yes

characteristic

C₅×#384

C₂²

yes

—

C₅×#340

—

#10685

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×Q₈

—

C₂²×C₅×C₈

D₄

yes

—

C₂²×C₅×C₈

D₄

yes

—

C₅×C₄⋊Q₈

—

C₅×C₄⋊Q₈

—

C₅×C₄⋊Q₈

Q₈

yes

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₄²×C₅

C₂³

yes

—

—

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

C₄×C₅×C₈

—

#1990

C₂×C₅

yes

—

#1956

C₂×C₅

yes

characteristic

#1844

C₂×C₅

yes

—

#1844

C₂×C₅

yes

characteristic

#1273

C₂×C₅

yes

characteristic

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂×C₅×Q₈

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

SD₁₆

yes

—

C₂×C₅×C₈

SD₁₆

yes

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₄²×C₅

C₂×Q₈

yes

characteristic

C₄²×C₅

#41

yes

—

C₄²×C₅

#41

yes

characteristic

C₂×C₄⋊Q₈

C₂²×C₅

yes

—

—

—

C₂×C₄×C₈

C₂²×C₅

yes

characteristic

C₂×C₄×C₈

C₂²×C₅

yes

—

#384

C₂²×C₅

yes

characteristic

#384

C₂²×C₅

yes

—

#340

—

C₂³×C₅

#127

yes

characteristic

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

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

C₂×SD₁₆

yes

—

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₅

#137

yes

—

C₅×C₈

—

C₅×C₈

—

C₂²×Q₈

—

C₂²×C₈

C₅×D₄

yes

—

C₂²×C₈

C₅×D₄

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

100

C₄⋊Q₈

C₅×Q₈

yes

—

101

C₂×C₄⋊C₄

—

102

C₂×C₄⋊C₄

—

103

C₂×C₄⋊C₄

—

104

C₂×C₄⋊C₄

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄²

C₂³×C₅

yes

characteristic

108

#106

—

109

#106

—

110

#103

—

111

C₄×C₈

—

112

C₄×C₈

—

113

C₄×C₈

—

114

C₂²×C₅

#399

yes

characteristic

115

C₂²×C₅

#492

yes

characteristic

116

C₂²×C₅

#492

yes

—

117

C₂²×C₅

#496

yes

characteristic

118

C₂²×C₅

#497

yes

—

119

C₄×C₅

—

120

C₄×C₅

—

121

C₄×C₅

—

122

C₄×C₅

#475

yes

—

123

C₄×C₅

#476

yes

—

124

C₄×C₅

#481

yes

—

125

C₄×C₅

#483

yes

—

126

C₂×Q₈

—

127

C₂×Q₈

—

128

C₂×Q₈

—

129

C₂×Q₈

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

134

C₂²×C₄

C₂×C₅×D₄

yes

—

135

C₂×C₈

—

136

C₂×C₈

—

137

C₂×C₈

—

138

C₂×C₈

—

139

C₂×C₈

C₅×SD₁₆

yes

—

140

C₂×C₈

C₅×SD₁₆

yes

—

141

C₄⋊C₄

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄⋊C₄

—

145

C₄⋊C₄

—

146

C₄⋊C₄

—

147

C₄⋊C₄

—

148

C₄²

C₂×C₅×Q₈

yes

characteristic

149

C₄²

C₅×#41

yes

—

150

C₄²

C₅×#41

yes

characteristic

151

C₂×C₅

#1705

yes

characteristic

152

C₂×C₅

#1714

yes

—

153

C₂×C₅

#1716

yes

characteristic

154

C₂×C₅

#2094

yes

characteristic

155

C₂×C₅

#2096

yes

—

156

C₂³

C₅×#127

yes

characteristic

157

Q₈

—

158

Q₈

—

159

C₂×C₄

—

160

C₂×C₄

—

161

C₂×C₄

—

162

C₂×C₄

—

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

168

C₂×C₄

C₅×C₂²⋊Q₈

yes

characteristic

169

C₂×C₄

C₅×#123

yes

characteristic

170

C₂×C₄

C₅×#123

yes

—

171

C₂×C₄

C₂×C₅×SD₁₆

yes

—

172

C₂×C₄

C₂×C₅×SD₁₆

yes

—

173

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

174

C₂×C₄

C₅×#137

yes

—

175

C₈

—

176

C₈

—

177

C₅

#10685

yes

characteristic, direct product factor, Sylow

178

C₂²

C₅×#399

yes

characteristic

179

C₂²

C₅×#492

yes

characteristic

180

C₂²

C₅×#492

yes

—

181

C₂²

C₅×#496

yes

characteristic

182

C₂²

C₅×#497

yes

—

183

C₄

—

184

C₄

—

185

C₄

—

186

C₄

C₅×#475

yes

—

187

C₄

C₅×#476

yes

—

188

C₄

C₅×#481

yes

—

189

C₄

C₅×#483

yes

—

190

C₂

C₅×#1705

yes

characteristic

191

C₂

C₅×#1714

yes

—

192

C₂

C₅×#1716

yes

characteristic

193

C₂

C₅×#2094

yes

characteristic

194

C₂

C₅×#2096

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₅

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅

LCS

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
15. #10685	C₅	direct (N × H)
177. C₅	#10685	direct (N × H)

H ≅ G/N

type

15. #10685

C₅

direct (N × H)

177. C₅

#10685

direct (N × H)

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

subgroup	index
C₅×#1990	2
C₅×#1956	2
C₅×#1844	2
C₅×#1273	2
#10685	5

subgroup

index

Subgroups — C₅×#10685 #11933405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#10685 #11933405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10685 #11933405