Group #11931340 — subgroups

Subgroups — C₅×#8620 #11931340

Order 1280.

450 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 142 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×D₄	C₂	1	1	yes	maximal, characteristic
2	C₅×#1568	C₂	1	2	yes	maximal, complemented
3	C₅×#1466	C₂	1	2	yes	maximal
4	C₅×#1290	C₂	1	2	yes	maximal, complemented
5	C₂³×C₅×C₈	C₄	1	2	yes	—
6	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
7	C₅×C₈×D₄	—	2	2	no	—
8	C₅×C₈×D₄	—	2	2	no	—
9	C₅×#432	C₂²	1	4	yes	—
10	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₂²⋊C₈	C₄	1	2	yes	—
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₅×#335	—	2	2	no	—
14	C₅×#334	—	2	2	no	—
15	C₅×#323	—	2	4	no	—
16	#8620	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂²×C₅×D₄	Q₈	1	1	yes	characteristic
18	C₂³×C₄×C₅	C₂×C₄	1	2	yes	—
19	C₂²×C₅×C₈	—	2	2	no	—
20	C₂²×C₅×C₈	—	2	2	no	—
21	C₂²×C₅×C₈	—	4	4	no	—
22	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
24	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
25	C₄×C₅×D₄	—	2	2	no	—
26	C₄×C₅×D₄	—	2	2	no	—
27	C₂×C₅×C₄⋊C₄	Q₈	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
29	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
30	C₅×C₄⋊C₈	—	2	2	no	—
31	C₅×C₄⋊C₈	—	2	4	no	—
32	C₅×C₂²⋊C₈	—	2	4	no	—
33	C₅×C₂²⋊C₈	—	2	4	no	—
34	C₅×#97	—	2	4	no	—
35	C₄×C₅×C₈	D₄	1	2	yes	—
36	C₄×C₅×C₈	D₄	1	2	yes	—
37	C₂×C₈×D₄	C₂×C₅	1	1	yes	characteristic
38	#1568	C₂×C₅	1	2	yes	complemented
39	#1466	C₂×C₅	1	2	yes	—
40	#1290	C₂×C₅	1	2	yes	complemented
41	C₂⁴×C₅	C₄⋊C₄	1	2	yes	—
42	C₂×C₅×D₄	—	2	4	no	—
43	C₂×C₅×D₄	—	2	2	no	—
44	C₂²×C₄×C₅	—	2	2	no	—
45	C₂²×C₄×C₅	—	2	2	no	—
46	C₂²×C₄×C₅	—	4	2	no	—
47	C₂²×C₄×C₅	—	4	2	no	—
48	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
51	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₅×C₈	—	2	2	no	—
53	C₂×C₅×C₈	—	2	2	no	—
54	C₂×C₅×C₈	—	4	1	no	—
55	C₂×C₅×C₈	—	4	4	no	—
56	C₂×C₅×C₈	—	4	4	no	—
57	C₂×C₅×C₈	—	4	2	no	—
58	C₂×C₅×C₈	—	4	4	no	—
59	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
61	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
62	C₅×C₄⋊C₄	—	2	2	no	—
63	C₅×C₂²⋊C₄	—	2	4	no	—
64	C₄²×C₅	C₂×D₄	1	2	yes	—
65	C₄²×C₅	#41	1	2	yes	—
66	C₂³×C₈	C₄×C₅	1	2	yes	—
67	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
68	C₈×D₄	—	2	2	no	—
69	C₈×D₄	—	2	2	no	—
70	#432	C₂²×C₅	1	4	yes	—
71	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
72	C₂×C₂²⋊C₈	C₄×C₅	1	2	yes	—
73	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
74	#335	—	2	2	no	—
75	#334	—	2	2	no	—
76	#323	—	2	4	no	—
77	C₂³×C₅	—	2	2	no	—
78	C₂³×C₅	—	2	2	no	—
79	C₂³×C₅	—	4	2	no	—
80	C₂³×C₅	—	4	2	no	—
81	C₂³×C₅	#108	1	4	yes	—
82	C₂³×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₅×D₄	—	2	8	no	—
84	C₂×C₄×C₅	—	2	2	no	—
85	C₂×C₄×C₅	—	2	1	no	—
86	C₂×C₄×C₅	—	2	1	no	—
87	C₂×C₄×C₅	—	2	2	no	—
88	C₂×C₄×C₅	—	4	1	no	—
89	C₂×C₄×C₅	—	4	4	no	—
90	C₂×C₄×C₅	—	4	2	no	—
91	C₂×C₄×C₅	—	4	2	no	—
92	C₂×C₄×C₅	—	4	2	no	—
93	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₅	#117	1	1	yes	characteristic
95	C₂×C₄×C₅	#121	1	2	yes	—
96	C₂×C₄×C₅	C₂²⋊Q₈	1	2	yes	—
97	C₅×C₈	—	2	1	no	—
98	C₅×C₈	—	2	2	no	—
99	C₅×C₈	—	4	2	no	—
100	C₅×C₈	—	8	4	no	—
101	C₅×C₈	#100	1	2	yes	—
102	C₂²×D₄	C₅×Q₈	1	1	yes	characteristic
103	C₂³×C₄	C₂×C₄×C₅	1	2	yes	—
104	C₂²×C₈	—	2	2	no	—
105	C₂²×C₈	—	2	2	no	—
106	C₂²×C₈	—	4	4	no	—
107	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
108	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
109	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
110	C₄×D₄	—	2	2	no	—
111	C₄×D₄	—	2	2	no	—
112	C₂×C₄⋊C₄	C₅×Q₈	1	1	yes	characteristic
113	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
114	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
115	C₄⋊C₈	—	2	2	no	—
116	C₄⋊C₈	—	2	4	no	—
117	C₂²⋊C₈	—	2	4	no	—
118	C₂²⋊C₈	—	2	4	no	—
119	#97	—	2	4	no	—
120	C₄×C₈	C₅×D₄	1	2	yes	—
121	C₄×C₈	C₅×D₄	1	2	yes	—
122	C₂²×C₅	—	2	1	no	—
123	C₂²×C₅	—	2	1	no	—
124	C₂²×C₅	—	2	4	no	—
125	C₂²×C₅	—	4	4	no	—
126	C₂²×C₅	—	4	4	no	—
127	C₂²×C₅	—	4	2	no	—
128	C₂²×C₅	—	4	2	no	—
129	C₂²×C₅	#380	1	1	yes	characteristic
130	C₂²×C₅	C₂×#108	1	2	yes	—
131	C₄×C₅	—	2	1	no	—
132	C₄×C₅	—	2	2	no	—
133	C₄×C₅	—	2	2	no	—
134	C₄×C₅	—	4	2	no	—
135	C₄×C₅	C₂×#100	1	1	yes	characteristic
136	C₄×C₅	#413	1	1	yes	characteristic
137	C₂⁴	C₅×C₄⋊C₄	1	2	yes	—
138	C₂×D₄	—	2	4	no	—
139	C₂×D₄	—	2	2	no	—
140	C₂²×C₄	—	2	2	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	4	2	no	—
143	C₂²×C₄	—	4	2	no	—
144	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
145	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
146	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
147	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
148	C₂×C₈	—	2	2	no	—
149	C₂×C₈	—	2	2	no	—
150	C₂×C₈	—	4	1	no	—
151	C₂×C₈	—	4	4	no	—
152	C₂×C₈	—	4	4	no	—
153	C₂×C₈	—	4	2	no	—
154	C₂×C₈	—	4	4	no	—
155	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
156	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
157	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
158	C₄⋊C₄	—	2	2	no	—
159	C₂²⋊C₄	—	2	4	no	—
160	C₄²	C₂×C₅×D₄	1	2	yes	—
161	C₄²	C₅×#41	1	2	yes	—
162	C₂×C₅	—	2	2	no	—
163	C₂×C₅	—	4	4	no	—
164	C₂×C₅	#1800	1	1	yes	characteristic
165	C₂×C₅	#1810	1	1	yes	characteristic
166	C₂×C₅	#1812	1	1	yes	characteristic
167	C₂³	—	2	2	no	—
168	C₂³	—	2	2	no	—
169	C₂³	—	4	2	no	—
170	C₂³	—	4	2	no	—
171	C₂³	C₅×#108	1	4	yes	—
172	C₂³	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
173	D₄	—	2	8	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	4	1	no	—
179	C₂×C₄	—	4	4	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄	C₅×#117	1	1	yes	characteristic
185	C₂×C₄	C₅×#121	1	2	yes	—
186	C₂×C₄	C₅×C₂²⋊Q₈	1	2	yes	—
187	C₈	—	2	1	no	—
188	C₈	—	2	2	no	—
189	C₈	—	4	2	no	—
190	C₈	—	8	4	no	—
191	C₈	C₅×#100	1	2	yes	—
192	C₅	#8620	1	1	yes	characteristic, direct product factor, Sylow
193	C₂²	—	2	1	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	2	4	no	—
196	C₂²	—	4	4	no	—
197	C₂²	—	4	4	no	—
198	C₂²	—	4	2	no	—
199	C₂²	—	4	2	no	—
200	C₂²	C₅×#380	1	1	yes	characteristic
201	C₂²	C₂×C₅×#108	1	2	yes	—
202	C₄	—	2	1	no	—
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	4	2	no	—
206	C₄	C₂×C₅×#100	1	1	yes	characteristic
207	C₄	C₅×#413	1	1	yes	characteristic
208	C₂	—	2	2	no	—
209	C₂	—	4	4	no	—
210	C₂	C₅×#1800	1	1	yes	characteristic
211	C₂	C₅×#1810	1	1	yes	characteristic
212	C₂	C₅×#1812	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅×C₈×D₄

C₂

yes

maximal, characteristic

C₅×#1568

C₂

yes

maximal, complemented

C₅×#1466

C₂

yes

maximal

C₅×#1290

C₂

yes

maximal, complemented

C₂³×C₅×C₈

C₄

yes

—

C₂×C₄×C₅×D₄

C₂²

yes

characteristic

C₅×C₈×D₄

—

C₅×C₈×D₄

—

C₅×#432

C₂²

yes

—

C₂×C₅×C₄⋊C₈

C₂²

yes

characteristic

C₂×C₅×C₂²⋊C₈

C₄

yes

—

C₂×C₄×C₅×C₈

C₂²

yes

—

—

—

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅×D₄

Q₈

yes

characteristic

C₂³×C₄×C₅

C₂×C₄

yes

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

—

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₂²×C₅×C₈

C₂×C₄

yes

—

C₂²×C₅×C₈

C₂×C₄

yes

characteristic

C₄×C₅×D₄

—

C₄×C₅×D₄

—

C₂×C₅×C₄⋊C₄

Q₈

yes

characteristic

C₂×C₅×C₂²⋊C₄

D₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#97

—

C₄×C₅×C₈

D₄

yes

—

C₄×C₅×C₈

D₄

yes

—

C₂×C₈×D₄

C₂×C₅

yes

characteristic

#1568

C₂×C₅

yes

complemented

#1466

C₂×C₅

yes

—

#1290

C₂×C₅

yes

complemented

C₂⁴×C₅

C₄⋊C₄

yes

—

C₂×C₅×D₄

—

C₂×C₅×D₄

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₄⋊C₄

yes

—

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

characteristic

C₂²×C₄×C₅

C₂×Q₈

yes

characteristic

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₂×C₅×C₈

C₂²⋊C₄

yes

—

C₂×C₅×C₈

C₂²⋊C₄

yes

characteristic

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

C₂×D₄

yes

—

C₄²×C₅

#41

yes

—

C₂³×C₈

C₄×C₅

yes

—

C₂×C₄×D₄

C₂²×C₅

yes

characteristic

C₈×D₄

—

C₈×D₄

—

#432

C₂²×C₅

yes

—

C₂×C₄⋊C₈

C₂²×C₅

yes

characteristic

C₂×C₂²⋊C₈

C₄×C₅

yes

—

C₂×C₄×C₈

C₂²×C₅

yes

—

—

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#108

yes

—

C₂³×C₅

C₂×C₄⋊C₄

yes

characteristic

C₅×D₄

—

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

—

C₂×C₄×C₅

C₂×C₂²⋊C₄

yes

C₂×C₄×C₅

yes

C₂×C₄×C₅

yes

—

C₂×C₄×C₅

C₂²⋊Q₈

yes

—

C₅×C₈

—

C₅×C₈

—

C₅×C₈

—

100

C₅×C₈

—

101

C₅×C₈

#100

yes

—

102

C₂²×D₄

C₅×Q₈

yes

characteristic

103

C₂³×C₄

C₂×C₄×C₅

yes

—

104

C₂²×C₈

—

105

C₂²×C₈

—

106

C₂²×C₈

—

107

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

108

C₂²×C₈

C₂×C₄×C₅

yes

—

109

C₂²×C₈

C₂×C₄×C₅

yes

characteristic

110

C₄×D₄

—

111

C₄×D₄

—

112

C₂×C₄⋊C₄

C₅×Q₈

yes

characteristic

113

C₂×C₂²⋊C₄

C₅×D₄

yes

—

114

C₂×C₄²

C₂³×C₅

yes

characteristic

115

C₄⋊C₈

—

116

C₄⋊C₈

—

117

C₂²⋊C₈

—

118

C₂²⋊C₈

—

119

#97

—

120

C₄×C₈

C₅×D₄

yes

—

121

C₄×C₈

C₅×D₄

yes

—

122

C₂²×C₅

—

123

C₂²×C₅

—

124

C₂²×C₅

—

125

C₂²×C₅

—

126

C₂²×C₅

—

127

C₂²×C₅

—

128

C₂²×C₅

—

129

C₂²×C₅

#380

yes

characteristic

130

C₂²×C₅

C₂×#108

yes

—

131

C₄×C₅

—

132

C₄×C₅

—

133

C₄×C₅

—

134

C₄×C₅

—

135

C₄×C₅

C₂×#100

yes

characteristic

136

C₄×C₅

#413

yes

characteristic

137

C₂⁴

C₅×C₄⋊C₄

yes

—

138

C₂×D₄

—

139

C₂×D₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

C₅×C₄⋊C₄

yes

—

145

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

146

C₂²×C₄

C₂×C₅×D₄

yes

characteristic

147

C₂²×C₄

C₂×C₅×Q₈

yes

characteristic

148

C₂×C₈

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

C₅×C₂²⋊C₄

yes

—

156

C₂×C₈

C₅×C₂²⋊C₄

yes

characteristic

157

C₂×C₈

C₅×C₂²⋊C₄

yes

characteristic

158

C₄⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

C₂×C₅×D₄

yes

—

161

C₄²

C₅×#41

yes

—

162

C₂×C₅

—

163

C₂×C₅

—

164

C₂×C₅

#1800

yes

characteristic

165

C₂×C₅

#1810

yes

characteristic

166

C₂×C₅

#1812

yes

characteristic

167

C₂³

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

C₅×#108

yes

—

172

C₂³

C₂×C₅×C₄⋊C₄

yes

characteristic

173

D₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

C₂×C₅×C₂²⋊C₄

yes

characteristic

184

C₂×C₄

C₅×#117

yes

characteristic

185

C₂×C₄

C₅×#121

yes

—

186

C₂×C₄

C₅×C₂²⋊Q₈

yes

—

187

C₈

—

188

C₈

—

189

C₈

—

190

C₈

—

191

C₈

C₅×#100

yes

—

192

C₅

#8620

yes

characteristic, direct product factor, Sylow

193

C₂²

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

C₅×#380

yes

characteristic

201

C₂²

C₂×C₅×#108

yes

—

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

—

206

C₄

C₂×C₅×#100

yes

characteristic

207

C₄

C₅×#413

yes

characteristic

208

C₂

—

209

C₂

—

210

C₂

C₅×#1800

yes

characteristic

211

C₂

C₅×#1810

yes

characteristic

212

C₂

C₅×#1812

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#380
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂²×C₅×D₄	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂²×C₅

#380

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂²×C₅×D₄

Q₈

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

N	H ≅ G/N	type
2. C₅×#1568	C₂	semidirect
4. C₅×#1290	C₂	semidirect
16. #8620	C₅	direct (N × H)
38. #1568	C₂×C₅	semidirect
40. #1290	C₂×C₅	semidirect
192. C₅	#8620	direct (N × H)

H ≅ G/N

type

2. C₅×#1568

C₂

semidirect

4. C₅×#1290

C₂

semidirect

16. #8620

C₅

direct (N × H)

38. #1568

C₂×C₅

semidirect

40. #1290

C₂×C₅

semidirect

192. C₅

#8620

direct (N × H)

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

subgroup	index
C₂×C₅×C₈×D₄	2
C₅×#1568	2
C₅×#1466	2
C₅×#1290	2
#8620	5

subgroup

index

C₂×C₅×C₈×D₄

Subgroups — C₅×#8620 #11931340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8620 #11931340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8620 #11931340