Group #20275860 — subgroups

Subgroups — #20275860

Order 6784.

294 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13133208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13133139	C₂	1	1	yes	maximal, characteristic
3	C₂×#13133137	C₂	1	1	yes	maximal, characteristic
4	#16810524	C₂	1	1	yes	maximal, characteristic
5	#16810385	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810377	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₂₁₂	C₂²	1	1	yes	characteristic
9	C₂²×#88322	C₂²	1	1	yes	characteristic
10	#13133208	—	2	2	no	—
11	#13133208	—	2	2	no	—
12	C₂×C₄⋊Dic₅₃	—	2	1	no	—
13	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
14	C₂×#11719919	—	2	1	no	—
15	C₂×#11719921	—	2	1	no	—
16	C₂×#11719921	—	2	1	no	—
17	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
18	#13133139	—	2	2	no	—
19	#13133137	—	2	2	no	—
20	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
23	C₂³×D₅₃	—	2	1	no	—
24	C₂²×C₄×C₅₃	—	2	1	no	—
25	C₂²×C₄×C₅₃	—	2	1	no	—
26	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
27	C₂²×Dic₅₃	—	2	1	no	—
28	C₂²×Dic₅₃	D₄	1	1	yes	characteristic
29	C₂²×Dic₅₃	D₄	1	1	yes	characteristic
30	C₂×D₂₁₂	—	2	1	no	—
31	C₂×D₂₁₂	—	2	1	no	—
32	C₂×D₂₁₂	—	2	1	no	—
33	C₂×D₂₁₂	—	2	1	no	—
34	C₂×D₂₁₂	—	2	1	no	—
35	C₂×D₂₁₂	Q₈	1	2	yes	—
36	C₂×C₈×C₅₃	—	2	1	no	—
37	C₂×C₈×C₅₃	—	2	1	no	—
38	C₂×C₈×C₅₃	—	2	1	no	—
39	C₄⋊C₄×C₅₃	—	2	1	no	—
40	C₄⋊C₄×C₅₃	—	2	1	no	—
41	C₄⋊C₄×C₅₃	—	2	1	no	—
42	C₄⋊C₄×C₅₃	D₄	1	2	yes	—
43	#11719921	—	4	2	no	—
44	#11719921	—	4	2	no	—
45	C₄⋊Dic₅₃	—	2	4	no	—
46	C₄⋊Dic₅₃	—	2	1	no	—
47	C₄⋊Dic₅₃	D₄	1	2	yes	—
48	#11719919	—	2	4	no	—
49	C₄×Dic₅₃	—	2	1	no	—
50	C₄×Dic₅₃	—	2	1	no	—
51	C₂×#88322	—	2	1	no	—
52	C₂×#88322	—	2	1	no	—
53	C₂×#88322	—	2	1	no	—
54	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
55	C₂²×D₅₃	—	2	2	no	—
56	C₂²×D₅₃	—	4	1	no	—
57	C₂²×D₅₃	—	4	1	no	—
58	C₂²×D₅₃	—	4	1	no	—
59	C₂²×D₅₃	—	4	1	no	—
60	C₂²×D₅₃	—	4	1	no	—
61	C₂²×D₅₃	—	4	1	no	—
62	C₂×C₄×C₅₃	—	2	2	no	—
63	C₂×C₄×C₅₃	—	4	1	no	—
64	C₂×C₄×C₅₃	—	4	1	no	—
65	C₂×C₄×C₅₃	—	4	1	no	—
66	C₂×C₄×C₅₃	—	4	1	no	—
67	C₂×C₄×C₅₃	—	4	1	no	—
68	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
71	C₂×C₄×C₅₃	#41	1	1	yes	characteristic
72	C₂×C₄×C₅₃	#41	1	1	yes	characteristic
73	C₂×C₄×C₅₃	#41	1	1	yes	characteristic
74	C₂×Dic₅₃	—	2	2	no	—
75	C₂×Dic₅₃	—	2	1	no	—
76	C₂×Dic₅₃	—	2	1	no	—
77	C₂×Dic₅₃	—	2	1	no	—
78	C₂×Dic₅₃	—	2	1	no	—
79	C₂×Dic₅₃	—	2	1	no	—
80	C₂×Dic₅₃	—	2	1	no	—
81	C₂×Dic₅₃	—	4	1	no	—
82	C₂×Dic₅₃	—	4	1	no	—
83	D₂₁₂	—	2	2	no	—
84	D₂₁₂	—	2	2	no	—
85	D₂₁₂	—	4	1	no	—
86	D₂₁₂	—	4	1	no	—
87	C₈×C₅₃	—	4	1	no	—
88	#88322	—	4	1	no	—
89	C₂²×C₅₃	#120	1	1	yes	characteristic
90	C₂²×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
91	C₂²×C₅₃	#124	1	1	yes	characteristic
92	C₂²×C₅₃	#135	1	1	yes	characteristic
93	C₂²×C₅₃	#135	1	1	yes	characteristic
94	C₂²×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
95	C₂²×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
96	C₂×D₅₃	—	4	2	no	—
97	C₂×D₅₃	—	4	2	no	—
98	C₂×D₅₃	—	4	2	no	—
99	C₂×D₅₃	—	8	1	no	—
100	C₂×D₅₃	—	8	1	no	—
101	C₂×D₅₃	—	8	1	no	—
102	C₂×D₅₃	—	8	1	no	—
103	C₄×C₅₃	—	4	2	no	—
104	C₄×C₅₃	—	8	1	no	—
105	C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
106	C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
107	C₄×C₅₃	#124	1	1	yes	characteristic
108	C₄×C₅₃	#124	1	1	yes	characteristic
109	Dic₅₃	—	4	1	no	—
110	Dic₅₃	—	4	1	no	—
111	Dic₅₃	—	4	2	no	—
112	#2025	—	53	1	no	maximal, Sylow
113	C₂×C₅₃	#393	1	1	yes	characteristic
114	C₂×C₅₃	#449	1	1	yes	characteristic
115	C₂×C₅₃	#449	1	1	yes	characteristic
116	C₂×C₅₃	#478	1	1	yes	characteristic
117	C₂×C₅₃	#478	1	1	yes	characteristic
118	C₂×C₅₃	#488	1	1	yes	characteristic
119	C₂×C₅₃	#490	1	1	yes	characteristic
120	D₅₃	—	8	2	no	—
121	C₂×#125	—	53	1	no	—
122	C₂×#102	—	53	1	no	—
123	C₂×#102	—	53	1	no	—
124	#390	—	53	1	no	—
125	#340	—	53	1	no	—
126	#340	D₅₃	1	1	yes	characteristic, complemented
127	#336	—	53	1	no	—
128	C₅₃	#2025	1	1	yes	characteristic, complemented, Sylow
129	C₂²×D₄	—	53	1	no	—
130	C₂²×C₈	—	53	1	no	—
131	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
132	#125	—	106	2	no	—
133	#125	—	106	2	no	—
134	C₂×C₄⋊C₄	—	53	1	no	—
135	C₂×C₄⋊C₄	—	106	1	no	—
136	C₂×C₄⋊C₄	—	106	1	no	—
137	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
138	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
139	C₂×C₂²⋊C₄	—	106	1	no	—
140	C₂×C₂²⋊C₄	—	106	1	no	—
141	C₂×C₄²	—	53	1	no	—
142	#102	—	106	2	no	—
143	#102	—	106	2	no	—
144	C₂⁴	—	106	1	no	—
145	C₂×D₄	—	53	2	no	—
146	C₂×D₄	—	106	1	no	—
147	C₂×D₄	—	106	1	no	—
148	C₂×D₄	—	106	1	no	—
149	C₂×D₄	—	106	1	no	—
150	C₂×D₄	—	106	1	no	—
151	C₂²×C₄	—	2	1	no	—
152	C₂²×C₄	—	2	1	no	—
153	C₂²×C₄	—	53	1	no	—
154	C₂²×C₄	—	53	1	no	—
155	C₂²×C₄	—	106	1	no	—
156	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
157	C₂×C₈	—	2	1	no	—
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	106	1	no	—
161	C₂×C₈	—	106	1	no	—
162	C₂×C₈	—	106	1	no	—
163	C₄⋊C₄	—	2	1	no	—
164	C₄⋊C₄	—	2	1	no	—
165	C₄⋊C₄	—	2	1	no	—
166	C₄⋊C₄	—	53	2	no	—
167	C₄⋊C₄	—	106	4	no	—
168	C₄⋊C₄	—	106	4	no	—
169	C₄⋊C₄	—	106	1	no	—
170	C₄⋊C₄	D₂₁₂	1	2	yes	—
171	C₂²⋊C₄	—	212	2	no	—
172	C₂²⋊C₄	—	212	2	no	—
173	C₄²	—	106	1	no	—
174	C₄²	—	106	1	no	—
175	C₂³	—	106	2	no	—
176	C₂³	—	212	1	no	—
177	C₂³	—	212	1	no	—
178	C₂³	—	212	1	no	—
179	C₂³	—	212	1	no	—
180	C₂³	—	212	1	no	—
181	C₂³	—	212	1	no	—
182	C₂³	D₄×D₅₃	1	1	yes	characteristic
183	D₄	—	106	2	no	—
184	D₄	—	106	2	no	—
185	D₄	—	212	1	no	—
186	D₄	—	212	1	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	106	1	no	—
194	C₂×C₄	—	106	1	no	—
195	C₂×C₄	—	106	2	no	—
196	C₂×C₄	—	106	1	no	—
197	C₂×C₄	—	106	1	no	—
198	C₂×C₄	—	106	1	no	—
199	C₂×C₄	—	106	1	no	—
200	C₂×C₄	—	212	1	no	—
201	C₂×C₄	—	212	1	no	—
202	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
203	C₂×C₄	#11719945	1	1	yes	characteristic
204	C₂×C₄	#11719945	1	1	yes	characteristic
205	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
206	C₂×C₄	#11719947	1	1	yes	characteristic
207	C₂×C₄	Q₈×D₅₃	1	1	yes	characteristic
208	C₈	—	4	1	no	—
209	C₈	—	212	1	no	—
210	C₂²	—	424	1	no	—
211	C₂²	—	424	1	no	—
212	C₂²	—	424	1	no	—
213	C₂²	—	424	1	no	—
214	C₂²	—	212	2	no	—
215	C₂²	—	212	2	no	—
216	C₂²	—	212	2	no	—
217	C₂²	#13133187	1	1	yes	characteristic
218	C₂²	#13133195	1	1	yes	characteristic
219	C₂²	#13133203	1	1	yes	characteristic
220	C₂²	#13133238	1	1	yes	characteristic
221	C₂²	#13133240	1	1	yes	characteristic
222	C₂²	#13133241	1	1	yes	characteristic
223	C₂²	#13133244	1	1	yes	characteristic
224	C₄	—	4	2	no	—
225	C₄	—	8	1	no	—
226	C₄	—	212	1	no	—
227	C₄	—	212	1	no	—
228	C₄	—	212	2	no	—
229	C₄	#13133195	1	1	yes	characteristic
230	C₄	#13133197	1	1	yes	characteristic
231	C₄	#13133203	1	1	yes	characteristic
232	C₄	#13133205	1	1	yes	characteristic
233	C₂	—	424	2	no	—
234	C₂	#16810536	1	1	yes	characteristic
235	C₂	#16810769	1	1	yes	characteristic
236	C₂	#16810771	1	1	yes	characteristic
237	C₂	#16810922	1	1	yes	characteristic
238	C₂	#16810926	1	1	yes	characteristic
239	C₂	#16810979	1	1	yes	characteristic
240	C₂	#16810986	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13133208

C₂

yes

maximal, characteristic, complemented

C₂×#13133139

C₂

yes

maximal, characteristic

C₂×#13133137

C₂

yes

maximal, characteristic

#16810524

C₂

yes

maximal, characteristic

#16810385

C₂

yes

maximal, characteristic, complemented

#16810377

C₂

yes

maximal, characteristic, complemented

C₅₃×#340

C₂

yes

maximal, characteristic, complemented

C₂²×D₂₁₂

C₂²

yes

characteristic

C₂²×#88322

C₂²

yes

characteristic

#13133208

—

#13133208

—

C₂×C₄⋊Dic₅₃

—

C₂×C₄⋊Dic₅₃

C₂²

yes

—

—

—

C₂×C₄×Dic₅₃

C₂²

yes

characteristic

#13133139

—

#13133137

—

C₂²×C₈×C₅₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₃

C₂²

yes

characteristic

C₂³×D₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂³

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

D₄

yes

characteristic

C₂²×Dic₅₃

D₄

yes

characteristic

C₂×D₂₁₂

—

C₂×D₂₁₂

—

C₂×D₂₁₂

—

C₂×D₂₁₂

—

C₂×D₂₁₂

—

C₂×D₂₁₂

Q₈

yes

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

D₄

yes

—

#11719921

—

#11719921

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

D₄

yes

—

#11719919

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₂×#88322

—

C₂×#88322

—

C₂×#88322

—

C₂³×C₅₃

C₂×D₄

yes

characteristic

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂²×D₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×Q₈

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

D₂₁₂

—

D₂₁₂

—

D₂₁₂

—

D₂₁₂

—

C₈×C₅₃

—

#88322

—

C₂²×C₅₃

#120

yes

characteristic

C₂²×C₅₃

C₂²⋊Q₈

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

C₂×D₅₃

—

100

C₂×D₅₃

—

101

C₂×D₅₃

—

102

C₂×D₅₃

—

103

C₄×C₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

C₂²⋊Q₈

yes

characteristic

106

C₄×C₅₃

C₂²⋊Q₈

yes

characteristic

107

C₄×C₅₃

#124

yes

characteristic

108

C₄×C₅₃

#124

yes

characteristic

109

Dic₅₃

—

110

Dic₅₃

—

111

Dic₅₃

—

112

#2025

—

maximal, Sylow

113

C₂×C₅₃

#393

yes

characteristic

114

C₂×C₅₃

#449

yes

characteristic

115

C₂×C₅₃

#449

yes

characteristic

116

C₂×C₅₃

#478

yes

characteristic

117

C₂×C₅₃

#478

yes

characteristic

118

C₂×C₅₃

#488

yes

characteristic

119

C₂×C₅₃

#490

yes

characteristic

120

D₅₃

—

121

C₂×#125

—

122

C₂×#102

—

123

C₂×#102

—

124

#390

—

125

#340

—

126

#340

D₅₃

yes

characteristic, complemented

127

#336

—

128

C₅₃

#2025

yes

characteristic, complemented, Sylow

129

C₂²×D₄

—

130

C₂²×C₈

—

131

C₂²×C₈

C₂×D₅₃

yes

characteristic

132

#125

—

106

—

133

#125

—

106

—

134

C₂×C₄⋊C₄

—

135

C₂×C₄⋊C₄

—

106

—

136

C₂×C₄⋊C₄

—

106

—

137

C₂×C₄⋊C₄

C₂×D₅₃

yes

characteristic

138

C₂×C₄⋊C₄

C₂×D₅₃

yes

characteristic

139

C₂×C₂²⋊C₄

—

106

—

140

C₂×C₂²⋊C₄

—

106

—

141

C₂×C₄²

—

142

#102

—

106

—

143

#102

—

106

—

144

C₂⁴

—

106

—

145

C₂×D₄

—

146

C₂×D₄

—

106

—

147

C₂×D₄

—

106

—

148

C₂×D₄

—

106

—

149

C₂×D₄

—

106

—

150

C₂×D₄

—

106

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

106

—

156

C₂²×C₄

C₂²×D₅₃

yes

characteristic

157

C₂×C₈

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

106

—

161

C₂×C₈

—

106

—

162

C₂×C₈

—

106

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

—

106

—

168

C₄⋊C₄

—

106

—

169

C₄⋊C₄

—

106

—

170

C₄⋊C₄

D₂₁₂

yes

—

171

C₂²⋊C₄

—

212

—

172

C₂²⋊C₄

—

212

—

173

C₄²

—

106

—

174

C₄²

—

106

—

175

C₂³

—

106

—

176

C₂³

—

212

—

177

C₂³

—

212

—

178

C₂³

—

212

—

179

C₂³

—

212

—

180

C₂³

—

212

—

181

C₂³

—

212

—

182

C₂³

D₄×D₅₃

yes

characteristic

183

D₄

—

106

—

184

D₄

—

106

—

185

D₄

—

212

—

186

D₄

—

212

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

106

—

194

C₂×C₄

—

106

—

195

C₂×C₄

—

106

—

196

C₂×C₄

—

106

—

197

C₂×C₄

—

106

—

198

C₂×C₄

—

106

—

199

C₂×C₄

—

106

—

200

C₂×C₄

—

212

—

201

C₂×C₄

—

212

—

202

C₂×C₄

C₂×D₂₁₂

yes

characteristic

203

C₂×C₄

#11719945

yes

characteristic

204

C₂×C₄

#11719945

yes

characteristic

205

C₂×C₄

D₄×D₅₃

yes

characteristic

206

C₂×C₄

#11719947

yes

characteristic

207

C₂×C₄

Q₈×D₅₃

yes

characteristic

208

C₈

—

209

C₈

—

212

—

210

C₂²

—

424

—

211

C₂²

—

424

—

212

C₂²

—

424

—

213

C₂²

—

424

—

214

C₂²

—

212

—

215

C₂²

—

212

—

216

C₂²

—

212

—

217

C₂²

#13133187

yes

characteristic

218

C₂²

#13133195

yes

characteristic

219

C₂²

#13133203

yes

characteristic

220

C₂²

#13133238

yes

characteristic

221

C₂²

#13133240

yes

characteristic

222

C₂²

#13133241

yes

characteristic

223

C₂²

#13133244

yes

characteristic

224

C₄

—

225

C₄

—

226

C₄

—

212

—

227

C₄

—

212

—

228

C₄

—

212

—

229

C₄

#13133195

yes

characteristic

230

C₄

#13133197

yes

characteristic

231

C₄

#13133203

yes

characteristic

232

C₄

#13133205

yes

characteristic

233

C₂

—

424

—

234

C₂

#16810536

yes

characteristic

235

C₂

#16810769

yes

characteristic

236

C₂

#16810771

yes

characteristic

237

C₂

#16810922

yes

characteristic

238

C₂

#16810926

yes

characteristic

239

C₂

#16810979

yes

characteristic

240

C₂

#16810986

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₅₃
commutator	C₂²×C₄×C₅₃	C₂³
Frattini	C₂²×C₄	C₂²×D₅₃
Fitting	C₅₃×#340	C₂
socle	C₂³×C₅₃	C₂×D₄
hypercenter	#340	D₅₃
hypocenter	C₅₃	#2025
LCS	G ▷ C₂²×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₅₃

commutator

C₂²×C₄×C₅₃

C₂³

Frattini

C₂²×C₄

C₂²×D₅₃

Fitting

C₅₃×#340

C₂

socle

C₂³×C₅₃

C₂×D₄

D₅₃

C₅₃

G ▷ C₂²×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
1. C₂×#13133208	C₂	semidirect
5. #16810385	C₂	semidirect
6. #16810377	C₂	semidirect
7. C₅₃×#340	C₂	semidirect
126. #340	D₅₃	semidirect
128. C₅₃	#2025	semidirect

H ≅ G/N

type

1. C₂×#13133208

C₂

semidirect

5. #16810385

C₂

semidirect

6. #16810377

C₂

semidirect

7. C₅₃×#340

C₂

semidirect

126. #340

D₅₃

semidirect

128. C₅₃

#2025

semidirect

Subgroups — #20275860

Conjugacy classes of subgroups

Complements