Group #11931448 — subgroups

Subgroups — C₅×#8728 #11931448

Order 1280.

514 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 166 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×#2285	C₂	1	1	yes	maximal, characteristic
2	C₅×#1797	C₂	1	2	yes	maximal
3	C₅×#1296	C₂	1	2	yes	maximal, complemented
4	C₅×#1296	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#117	C₄	1	2	yes	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
8	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
9	C₅×#384	C₂²	1	1	yes	characteristic
10	C₅×#384	C₂²	1	1	yes	characteristic
11	C₅×#382	C₄	1	2	yes	—
12	C₅×#380	—	2	2	no	—
13	C₄×C₅×C₄⋊C₄	—	2	2	no	—
14	C₅×#336	—	2	2	no	—
15	#8728	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₅	D₄	1	2	yes	—
18	C₂²×C₅×C₈	—	2	4	no	—
19	C₅×#117	—	4	4	no	—
20	C₂×C₅×C₄⋊C₄	—	2	2	no	—
21	C₂×C₅×C₄⋊C₄	—	2	2	no	—
22	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
23	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
24	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
25	C₂×C₄²×C₅	—	2	4	no	—
26	C₂×C₄²×C₅	—	2	2	no	—
27	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₅	D₄	1	2	yes	—
29	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
30	C₅×C₄⋊C₈	—	2	8	no	—
31	C₅×C₂²⋊C₈	—	4	4	no	—
32	C₅×#95	—	2	4	no	—
33	#2285	C₂×C₅	1	1	yes	characteristic
34	#1797	C₂×C₅	1	2	yes	—
35	#1296	C₂×C₅	1	2	yes	complemented
36	#1296	C₂×C₅	1	2	yes	complemented
37	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₅	—	2	2	no	—
39	C₂²×C₄×C₅	—	2	2	no	—
40	C₂²×C₄×C₅	—	2	2	no	—
41	C₂²×C₄×C₅	—	2	4	no	—
42	C₂²×C₄×C₅	—	2	4	no	—
43	C₂²×C₄×C₅	—	2	2	no	—
44	C₂²×C₄×C₅	—	2	2	no	—
45	C₂²×C₄×C₅	—	2	2	no	—
46	C₂²×C₄×C₅	—	2	2	no	—
47	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
51	C₂×C₅×C₈	—	4	4	no	—
52	C₂×C₅×C₈	—	4	4	no	—
53	C₂×C₅×C₈	—	4	4	no	—
54	C₅×C₄⋊C₄	—	4	2	no	—
55	C₅×C₄⋊C₄	—	4	2	no	—
56	C₅×C₄⋊C₄	—	4	4	no	—
57	C₅×C₄⋊C₄	—	4	2	no	—
58	C₅×C₄⋊C₄	—	4	2	no	—
59	C₅×C₂²⋊C₄	—	4	4	no	—
60	C₄²×C₅	—	2	2	no	—
61	C₄²×C₅	—	2	4	no	—
62	C₄²×C₅	—	4	4	no	—
63	C₄²×C₅	#41	1	4	yes	—
64	C₂×#117	C₄×C₅	1	2	yes	—
65	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
66	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
67	C₂×C₂²⋊C₈	—	2	2	no	—
68	#384	C₂²×C₅	1	1	yes	characteristic
69	#384	C₂²×C₅	1	1	yes	characteristic
70	#382	C₄×C₅	1	2	yes	—
71	#380	—	2	2	no	—
72	C₄×C₄⋊C₄	—	2	2	no	—
73	#336	—	2	2	no	—
74	C₂³×C₅	—	2	1	no	—
75	C₂³×C₅	—	2	1	no	—
76	C₂³×C₅	—	2	2	no	—
77	C₂³×C₅	—	2	2	no	—
78	C₂³×C₅	#101	1	2	yes	—
79	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₅	—	2	8	no	—
81	C₂×C₄×C₅	—	2	1	no	—
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	1	no	—
84	C₂×C₄×C₅	—	2	1	no	—
85	C₂×C₄×C₅	—	2	2	no	—
86	C₂×C₄×C₅	—	2	2	no	—
87	C₂×C₄×C₅	—	2	2	no	—
88	C₂×C₄×C₅	—	4	4	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	4	no	—
93	C₂×C₄×C₅	—	4	4	no	—
94	C₂×C₄×C₅	#100	1	2	yes	—
95	C₂×C₄×C₅	#117	1	2	yes	—
96	C₂×C₄×C₅	#123	1	4	yes	—
97	C₂×C₄×C₅	#135	1	4	yes	—
98	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
99	C₂×C₄×C₅	#137	1	2	yes	—
100	C₅×C₈	—	8	4	no	—
101	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
102	C₂³×C₄	C₅×D₄	1	2	yes	—
103	C₂²×C₈	—	2	4	no	—
104	#117	—	4	4	no	—
105	C₂×C₄⋊C₄	—	2	2	no	—
106	C₂×C₄⋊C₄	—	2	2	no	—
107	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
108	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
109	C₂×C₂²⋊C₄	—	2	2	no	—
110	C₂×C₄²	—	2	4	no	—
111	C₂×C₄²	—	2	2	no	—
112	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
113	C₂×C₄²	C₅×D₄	1	2	yes	—
114	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
115	C₄⋊C₈	—	2	8	no	—
116	C₂²⋊C₈	—	4	4	no	—
117	#95	—	2	4	no	—
118	C₂²×C₅	—	2	4	no	—
119	C₂²×C₅	—	2	2	no	—
120	C₂²×C₅	—	4	1	no	—
121	C₂²×C₅	—	4	1	no	—
122	C₂²×C₅	—	4	2	no	—
123	C₂²×C₅	#381	1	1	yes	characteristic
124	C₂²×C₅	C₂×#100	1	1	yes	characteristic
125	C₂²×C₅	C₂×#101	1	1	yes	characteristic
126	C₂²×C₅	#416	1	2	yes	—
127	C₂²×C₅	#417	1	2	yes	—
128	C₄×C₅	—	2	2	no	—
129	C₄×C₅	—	2	2	no	—
130	C₄×C₅	—	4	2	no	—
131	C₄×C₅	—	8	2	no	—
132	C₄×C₅	—	8	2	no	—
133	C₄×C₅	#482	1	4	yes	—
134	C₄×C₅	#485	1	4	yes	—
135	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×C₄	—	2	2	no	—
137	C₂²×C₄	—	2	2	no	—
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	4	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	—	2	2	no	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	—	2	2	no	—
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
146	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
148	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
149	C₂×C₈	—	4	4	no	—
150	C₂×C₈	—	4	4	no	—
151	C₂×C₈	—	4	4	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₂²⋊C₄	—	4	4	no	—
158	C₄²	—	2	2	no	—
159	C₄²	—	2	4	no	—
160	C₄²	—	4	4	no	—
161	C₄²	C₅×#41	1	4	yes	—
162	C₂×C₅	—	4	2	no	—
163	C₂×C₅	#1543	1	1	yes	characteristic
164	C₂×C₅	#1552	1	2	yes	—
165	C₂×C₅	#1560	1	1	yes	characteristic
166	C₂×C₅	#1821	1	1	yes	characteristic
167	C₂×C₅	#1825	1	2	yes	—
168	C₂³	—	2	1	no	—
169	C₂³	—	2	1	no	—
170	C₂³	—	2	2	no	—
171	C₂³	—	2	2	no	—
172	C₂³	C₅×#101	1	2	yes	—
173	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄	—	2	8	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	4	4	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	2	no	—
186	C₂×C₄	—	4	4	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	C₅×#100	1	2	yes	—
189	C₂×C₄	C₅×#117	1	2	yes	—
190	C₂×C₄	C₅×#123	1	4	yes	—
191	C₂×C₄	C₅×#135	1	4	yes	—
192	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
193	C₂×C₄	C₅×#137	1	2	yes	—
194	C₈	—	8	4	no	—
195	C₅	#8728	1	1	yes	characteristic, direct product factor, Sylow
196	C₂²	—	2	4	no	—
197	C₂²	—	2	2	no	—
198	C₂²	—	4	1	no	—
199	C₂²	—	4	1	no	—
200	C₂²	—	4	2	no	—
201	C₂²	C₅×#381	1	1	yes	characteristic
202	C₂²	C₂×C₅×#100	1	1	yes	characteristic
203	C₂²	C₂×C₅×#101	1	1	yes	characteristic
204	C₂²	C₅×#416	1	2	yes	—
205	C₂²	C₅×#417	1	2	yes	—
206	C₄	—	2	2	no	—
207	C₄	—	2	2	no	—
208	C₄	—	4	2	no	—
209	C₄	—	8	2	no	—
210	C₄	—	8	2	no	—
211	C₄	C₅×#482	1	4	yes	—
212	C₄	C₅×#485	1	4	yes	—
213	C₂	—	4	2	no	—
214	C₂	C₅×#1543	1	1	yes	characteristic
215	C₂	C₅×#1552	1	2	yes	—
216	C₂	C₅×#1560	1	1	yes	characteristic
217	C₂	C₅×#1821	1	1	yes	characteristic
218	C₂	C₅×#1825	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅×#2285

C₂

yes

maximal, characteristic

C₅×#1797

C₂

yes

maximal

C₅×#1296

C₂

yes

maximal, complemented

C₅×#1296

C₂

yes

maximal, complemented

C₂×C₅×#117

C₄

yes

—

C₂²×C₄²×C₅

C₂²

yes

characteristic

C₂×C₅×C₄⋊C₈

C₂²

yes

—

C₂×C₅×C₂²⋊C₈

—

C₅×#384

C₂²

yes

characteristic

C₅×#384

C₂²

yes

characteristic

C₅×#382

C₄

yes

—

C₅×#380

—

C₄×C₅×C₄⋊C₄

—

C₅×#336

—

#8728

C₅

yes

maximal, characteristic, direct product factor, Sylow

C₂³×C₄×C₅

C₂×C₄

yes

characteristic

C₂³×C₄×C₅

D₄

yes

—

C₂²×C₅×C₈

—

C₅×#117

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

—

C₂×C₅×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₅×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₅×C₂²⋊C₄

—

C₂×C₄²×C₅

—

C₂×C₄²×C₅

—

C₂×C₄²×C₅

C₂×C₄

yes

characteristic

C₂×C₄²×C₅

D₄

yes

—

C₂×C₄²×C₅

C₂³

yes

characteristic

C₅×C₄⋊C₈

—

C₅×C₂²⋊C₈

—

C₅×#95

—

#2285

C₂×C₅

yes

characteristic

#1797

C₂×C₅

yes

—

#1296

C₂×C₅

yes

complemented

#1296

C₂×C₅

yes

complemented

C₂⁴×C₅

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

—

C₂²×C₄×C₅

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅

C₂×D₄

yes

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₂×C₅×C₈

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₄⋊C₄

—

C₅×C₂²⋊C₄

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

—

C₄²×C₅

#41

yes

—

C₂×#117

C₄×C₅

yes

—

C₂²×C₄²

C₂²×C₅

yes

characteristic

C₂×C₄⋊C₈

C₂²×C₅

yes

—

C₂×C₂²⋊C₈

—

#384

C₂²×C₅

yes

characteristic

#384

C₂²×C₅

yes

characteristic

#382

C₄×C₅

yes

—

#380

—

C₄×C₄⋊C₄

—

#336

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

—

C₂³×C₅

#101

yes

—

C₂³×C₅

C₂×C₂²⋊C₄

yes

characteristic

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×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

—

C₂×C₄×C₅

#100

yes

—

C₂×C₄×C₅

#117

yes

—

C₂×C₄×C₅

#123

yes

—

C₂×C₄×C₅

#135

yes

—

C₂×C₄×C₅

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₅

#137

yes

—

100

C₅×C₈

—

101

C₂³×C₄

C₂×C₄×C₅

yes

characteristic

102

C₂³×C₄

C₅×D₄

yes

—

103

C₂²×C₈

—

104

#117

—

105

C₂×C₄⋊C₄

—

106

C₂×C₄⋊C₄

—

107

C₂×C₄⋊C₄

C₂×C₄×C₅

yes

—

108

C₂×C₄⋊C₄

C₂×C₄×C₅

yes

—

109

C₂×C₂²⋊C₄

—

110

C₂×C₄²

—

111

C₂×C₄²

—

112

C₂×C₄²

C₂×C₄×C₅

yes

characteristic

113

C₂×C₄²

C₅×D₄

yes

—

114

C₂×C₄²

C₂³×C₅

yes

characteristic

115

C₄⋊C₈

—

116

C₂²⋊C₈

—

117

#95

—

118

C₂²×C₅

—

119

C₂²×C₅

—

120

C₂²×C₅

—

121

C₂²×C₅

—

122

C₂²×C₅

—

123

C₂²×C₅

#381

yes

characteristic

124

C₂²×C₅

C₂×#100

yes

characteristic

125

C₂²×C₅

C₂×#101

yes

characteristic

126

C₂²×C₅

#416

yes

—

127

C₂²×C₅

#417

yes

—

128

C₄×C₅

—

129

C₄×C₅

—

130

C₄×C₅

—

131

C₄×C₅

—

132

C₄×C₅

—

133

C₄×C₅

#482

yes

—

134

C₄×C₅

#485

yes

—

135

C₂⁴

C₅×C₂²⋊C₄

yes

characteristic

136

C₂²×C₄

—

137

C₂²×C₄

—

138

C₂²×C₄

—

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂²×C₄

—

143

C₂²×C₄

—

144

C₂²×C₄

—

145

C₂²×C₄

C₅×C₂²⋊C₄

yes

—

146

C₂²×C₄

C₅×C₂²⋊C₄

yes

characteristic

147

C₂²×C₄

C₂²×C₄×C₅

yes

characteristic

148

C₂²×C₄

C₂×C₅×D₄

yes

—

149

C₂×C₈

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₄⋊C₄

—

153

C₄⋊C₄

—

154

C₄⋊C₄

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₂²⋊C₄

—

158

C₄²

—

159

C₄²

—

160

C₄²

—

161

C₄²

C₅×#41

yes

—

162

C₂×C₅

—

163

C₂×C₅

#1543

yes

characteristic

164

C₂×C₅

#1552

yes

—

165

C₂×C₅

#1560

yes

characteristic

166

C₂×C₅

#1821

yes

characteristic

167

C₂×C₅

#1825

yes

—

168

C₂³

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

C₅×#101

yes

—

173

C₂³

C₂×C₅×C₂²⋊C₄

yes

characteristic

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

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

C₅×#100

yes

—

189

C₂×C₄

C₅×#117

yes

—

190

C₂×C₄

C₅×#123

yes

—

191

C₂×C₄

C₅×#135

yes

—

192

C₂×C₄

C₅×AGL(1,ℤ/8)

yes

—

193

C₂×C₄

C₅×#137

yes

—

194

C₈

—

195

C₅

#8728

yes

characteristic, direct product factor, Sylow

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

C₅×#381

yes

characteristic

202

C₂²

C₂×C₅×#100

yes

characteristic

203

C₂²

C₂×C₅×#101

yes

characteristic

204

C₂²

C₅×#416

yes

—

205

C₂²

C₅×#417

yes

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

C₅×#482

yes

—

212

C₄

C₅×#485

yes

—

213

C₂

—

214

C₂

C₅×#1543

yes

characteristic

215

C₂

C₅×#1552

yes

—

216

C₂

C₅×#1560

yes

characteristic

217

C₂

C₅×#1821

yes

characteristic

218

C₂

C₅×#1825

yes

—

	subgroup	G/H
center, socle	C₂³×C₅	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
prime radical	C₂⁴×C₅	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

subgroup

G/H

center, socle

C₂³×C₅

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₅

Frattini, cosocle

C₂×C₄²

C₂³×C₅

prime radical

C₂⁴×C₅

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

N	H ≅ G/N	type
3. C₅×#1296	C₂	semidirect
4. C₅×#1296	C₂	semidirect
15. #8728	C₅	direct (N × H)
35. #1296	C₂×C₅	semidirect
36. #1296	C₂×C₅	semidirect
195. C₅	#8728	direct (N × H)

H ≅ G/N

type

3. C₅×#1296

C₂

semidirect

4. C₅×#1296

C₂

semidirect

15. #8728

C₅

direct (N × H)

35. #1296

C₂×C₅

semidirect

36. #1296

C₂×C₅

semidirect

195. C₅

#8728

direct (N × H)

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

subgroup	index
C₅×#2285	2
C₅×#1797	2
C₅×#1296	2
#8728	5

subgroup

index

Subgroups — C₅×#8728 #11931448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C5×#8728 #11931448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8728 #11931448