Group #27283990 — subgroups

Subgroups — #27283990

Order 13568.

422 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 123 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	#20285301	C₂	1	1	yes	maximal, characteristic
2	#20275691	C₂	1	2	yes	maximal
3	#20274460	C₂	1	1	yes	maximal, characteristic
4	#20273169	C₂	1	2	yes	maximal
5	C₅₃×#1567	C₂	1	1	yes	maximal, characteristic
6	#16811180	C₂²	1	2	yes	—
7	#16811028	C₄	1	1	yes	characteristic, complemented
8	#16811003	C₄	1	1	yes	characteristic, complemented
9	#16810974	C₄	1	2	yes	complemented
10	#16810864	—	2	2	no	—
11	C₄×Dic₂₁₂	—	2	2	no	—
12	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
13	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
14	#16810384	—	2	4	no	—
15	#16810377	—	2	2	no	—
16	#16810353	—	2	4	no	—
17	C₅₃×#423	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₅₃×#335	—	2	2	no	—
20	C₂×Dic₂₁₂	—	2	2	no	—
21	C₂²×#88322	—	2	1	no	—
22	#13133217	C₂×C₄	1	2	yes	—
23	#13133217	C₂×C₄	1	2	yes	—
24	#13133209	—	2	2	no	—
25	#13133196	—	2	2	no	—
26	#13133196	—	2	2	no	—
27	C₄×Dic₁₀₆	—	2	2	no	—
28	C₄×Dic₁₀₆	—	2	2	no	—
29	#13133176	—	2	2	no	—
30	C₂×C₄×Dic₅₃	—	2	1	no	—
31	C₂×C₄×Dic₅₃	—	2	1	no	—
32	C₂×C₄×Dic₅₃	D₄	1	2	yes	—
33	#13133151	—	2	2	no	—
34	#13133142	—	2	4	no	—
35	C₄×#88322	—	2	1	no	—
36	C₄×#88322	D₄	1	2	yes	—
37	C₂×M₁₆×C₅₃	—	2	2	no	—
38	C₂²×C₈×C₅₃	D₄	1	2	yes	—
39	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
40	C₄⋊C₈×C₅₃	—	2	2	no	—
41	C₄⋊C₈×C₅₃	—	2	2	no	—
42	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₅₃	D₄	1	2	yes	—
45	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
46	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
47	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
48	C₂²×Dic₅₃	—	2	2	no	—
49	C₂×Dic₁₀₆	—	2	2	no	—
50	C₂×Dic₁₀₆	—	2	2	no	—
51	M₁₆×C₅₃	—	4	4	no	—
52	C₂×C₈×C₅₃	—	4	2	no	—
53	C₂×C₈×C₅₃	—	4	2	no	—
54	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
56	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
57	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
59	C₄²×C₅₃	#41	1	1	yes	characteristic
60	C₂²⋊Dic₅₃	—	4	2	no	—
61	C₄⋊Dic₅₃	—	2	2	no	—
62	C₄⋊Dic₅₃	—	2	2	no	—
63	C₄⋊Dic₅₃	—	2	2	no	—
64	C₄⋊Dic₅₃	—	2	2	no	—
65	#11719919	—	4	2	no	—
66	#11719919	—	4	2	no	—
67	C₄×Dic₅₃	—	2	2	no	—
68	C₄×Dic₅₃	—	4	2	no	—
69	C₄×Dic₅₃	—	4	2	no	—
70	C₄×Dic₅₃	—	4	2	no	—
71	C₄×Dic₅₃	Q₁₆	1	4	yes	complemented
72	C₂×#88322	—	2	2	no	—
73	C₂×#88322	—	4	2	no	—
74	Dic₂₁₂	—	4	4	no	—
75	C₂³×C₅₃	#121	1	1	yes	characteristic
76	C₂×C₄×C₅₃	—	2	2	no	—
77	C₂×C₄×C₅₃	—	2	2	no	—
78	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
80	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
81	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
82	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
83	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
84	C₂×C₄×C₅₃	C₂×Q₁₆	1	2	yes	—
85	C₂×C₄×C₅₃	#135	1	2	yes	—
86	C₂×Dic₅₃	—	2	4	no	—
87	C₂×Dic₅₃	—	4	2	no	—
88	C₂×Dic₅₃	—	4	2	no	—
89	C₂×Dic₅₃	—	4	2	no	—
90	C₂×Dic₅₃	—	4	2	no	—
91	Dic₁₀₆	—	4	4	no	—
92	Dic₁₀₆	—	4	4	no	—
93	C₈×C₅₃	—	2	2	no	—
94	C₈×C₅₃	—	2	2	no	—
95	C₈×C₅₃	—	8	2	no	—
96	#88322	—	4	2	no	—
97	#9848	—	53	1	no	maximal, Sylow
98	C₂²×C₅₃	—	2	1	no	—
99	C₂²×C₅₃	—	2	1	no	—
100	C₂²×C₅₃	#390	1	1	yes	characteristic
101	C₂²×C₅₃	#467	1	2	yes	—
102	C₄×C₅₃	—	2	1	no	—
103	C₄×C₅₃	—	2	1	no	—
104	C₄×C₅₃	#421	1	2	yes	—
105	C₄×C₅₃	C₄×Q₁₆	1	2	yes	—
106	C₄×C₅₃	#444	1	2	yes	—
107	C₄×C₅₃	#494	1	1	yes	characteristic
108	C₄×C₅₃	#495	1	1	yes	characteristic
109	Dic₅₃	—	4	4	no	—
110	Dic₅₃	—	8	2	no	—
111	Dic₅₃	—	8	2	no	—
112	#3170	—	53	1	no	—
113	#1994	—	53	2	no	—
114	#1744	—	53	1	no	—
115	#1567	D₅₃	1	1	yes	characteristic
116	#1493	—	53	2	no	—
117	C₂×C₅₃	—	2	2	no	—
118	C₂×C₅₃	#1963	1	1	yes	characteristic
119	C₂×C₅₃	#1969	1	1	yes	characteristic
120	C₂×C₅₃	#1975	1	1	yes	characteristic
121	#533	—	53	2	no	—
122	#500	—	53	1	no	—
123	#494	—	53	1	no	—
124	#487	—	53	2	no	—
125	#467	—	106	2	no	—
126	C₄×Q₁₆	—	106	2	no	—
127	#423	C₂×D₅₃	1	2	yes	—
128	C₂×C₄×C₈	—	53	1	no	—
129	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
130	C₄³	—	53	1	no	—
131	#339	—	106	4	no	—
132	#336	—	106	2	no	—
133	#335	—	2	2	no	—
134	Q₈⋊C₈	—	106	4	no	—
135	C₅₃	#9848	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	106	2	no	—
137	C₂×M₁₆	—	2	2	no	—
138	C₂²×C₈	—	106	1	no	—
139	C₂²×C₈	D₂₁₂	1	2	yes	—
140	C₄⋊Q₈	—	53	2	no	—
141	C₄⋊Q₈	—	53	2	no	—
142	#125	—	106	2	no	—
143	C₂²⋊Q₈	—	106	2	no	—
144	C₂²⋊Q₈	—	106	2	no	—
145	C₄×Q₈	—	106	2	no	—
146	C₄×Q₈	—	106	2	no	—
147	#117	—	106	2	no	—
148	C₂×C₄²	—	53	2	no	—
149	C₂×C₄²	—	106	1	no	—
150	C₂×C₄²	—	106	1	no	—
151	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
152	#107	—	106	2	no	—
153	C₄⋊C₈	—	2	2	no	—
154	C₄⋊C₈	—	2	2	no	—
155	#103	—	106	4	no	—
156	C₄×C₈	—	53	2	no	—
157	C₄×C₈	—	106	1	no	—
158	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
159	C₄×C₈	C₄×D₅₃	1	1	yes	characteristic
160	C₄×C₈	C₂²⋊D₅₃	1	2	yes	—
161	C₂×Q₈	—	106	2	no	—
162	C₂×Q₈	—	106	2	no	—
163	C₂²×C₄	—	106	2	no	—
164	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
165	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
166	C₂²×C₄	#11719949	1	1	yes	characteristic
167	Q₁₆	—	212	4	no	—
168	M₁₆	—	4	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₂×C₈	—	106	2	no	—
172	C₂×C₈	—	212	2	no	—
173	C₂×C₈	#11719921	1	2	yes	—
174	C₂×C₈	#11719921	1	2	yes	—
175	C₄⋊C₄	—	106	2	no	—
176	C₄⋊C₄	—	106	2	no	—
177	C₄⋊C₄	—	106	2	no	—
178	C₄⋊C₄	—	106	2	no	—
179	C₄⋊C₄	—	212	2	no	—
180	C₄⋊C₄	—	212	2	no	—
181	C₂²⋊C₄	—	212	2	no	—
182	C₄²	—	53	4	no	—
183	C₄²	—	106	2	no	—
184	C₄²	—	212	2	no	—
185	C₄²	—	212	2	no	—
186	C₄²	—	212	2	no	—
187	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
188	C₄²	D₄×D₅₃	1	1	yes	characteristic
189	C₄²	#11719949	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
191	C₂³	#13133192	1	1	yes	characteristic
192	Q₈	—	212	4	no	—
193	Q₈	—	212	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	106	4	no	—
197	C₂×C₄	—	212	2	no	—
198	C₂×C₄	—	212	2	no	—
199	C₂×C₄	—	212	2	no	—
200	C₂×C₄	—	212	2	no	—
201	C₂×C₄	C₂×#11719921	1	1	yes	characteristic
202	C₂×C₄	#13133179	1	1	yes	characteristic
203	C₂×C₄	#13133179	1	1	yes	characteristic
204	C₂×C₄	#13133192	1	1	yes	characteristic
205	C₂×C₄	#13133206	1	1	yes	characteristic
206	C₂×C₄	#13133213	1	1	yes	characteristic
207	C₂×C₄	Q₁₆×D₅₃	1	2	yes	—
208	C₂×C₄	#13133236	1	2	yes	—
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	8	2	no	—
212	C₈	—	212	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#16810524	1	1	yes	characteristic
216	C₂²	#16810865	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	424	2	no	—
220	C₄	—	424	2	no	—
221	C₄	—	212	4	no	—
222	C₄	#16810639	1	2	yes	—
223	C₄	#16810717	1	2	yes	—
224	C₄	#16810744	1	2	yes	—
225	C₄	#16811001	1	1	yes	characteristic
226	C₄	#16811006	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#20275546	1	1	yes	characteristic
229	C₂	#20275574	1	1	yes	characteristic
230	C₂	#20275606	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20285301

C₂

yes

maximal, characteristic

#20275691

C₂

yes

maximal

#20274460

C₂

yes

maximal, characteristic

#20273169

C₂

yes

maximal

C₅₃×#1567

C₂

yes

maximal, characteristic

#16811180

C₂²

yes

—

#16811028

C₄

yes

characteristic, complemented

#16811003

C₄

yes

characteristic, complemented

#16810974

C₄

yes

complemented

#16810864

—

C₄×Dic₂₁₂

—

C₂×C₄×#88322

C₂²

yes

characteristic

C₄²×Dic₅₃

C₂²

yes

—

—

—

C₅₃×#423

C₂²

yes

—

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₅₃×#335

—

C₂×Dic₂₁₂

—

C₂²×#88322

—

#13133217

C₂×C₄

yes

—

#13133217

C₂×C₄

yes

—

#13133209

—

#13133196

—

#13133196

—

C₄×Dic₁₀₆

—

C₄×Dic₁₀₆

—

#13133176

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

D₄

yes

—

—

—

—

D₄

yes

—

C₂×M₁₆×C₅₃

—

C₂²×C₈×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

C₄⋊C₈×C₅₃

—

C₄⋊C₈×C₅₃

—

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

D₄

yes

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

#41

yes

characteristic

C₂²×Dic₅₃

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

M₁₆×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

#41

yes

characteristic

C₂²⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

#11719919

—

#11719919

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

Q₁₆

yes

complemented

C₂×#88322

—

C₂×#88322

—

Dic₂₁₂

—

C₂³×C₅₃

#121

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

C₂×Q₁₆

yes

—

C₂×C₄×C₅₃

#135

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

Dic₁₀₆

—

Dic₁₀₆

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

#88322

—

#9848

—

maximal, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

100

C₂²×C₅₃

#390

yes

characteristic

101

C₂²×C₅₃

#467

yes

—

102

C₄×C₅₃

—

103

C₄×C₅₃

—

104

C₄×C₅₃

#421

yes

—

105

C₄×C₅₃

C₄×Q₁₆

yes

—

106

C₄×C₅₃

#444

yes

—

107

C₄×C₅₃

#494

yes

characteristic

108

C₄×C₅₃

#495

yes

characteristic

109

Dic₅₃

—

110

Dic₅₃

—

111

Dic₅₃

—

112

#3170

—

113

#1994

—

114

#1744

—

115

#1567

D₅₃

yes

characteristic

116

#1493

—

117

C₂×C₅₃

—

118

C₂×C₅₃

#1963

yes

characteristic

119

C₂×C₅₃

#1969

yes

characteristic

120

C₂×C₅₃

#1975

yes

characteristic

121

#533

—

122

#500

—

123

#494

—

124

#487

—

125

#467

—

106

—

126

C₄×Q₁₆

—

106

—

127

#423

C₂×D₅₃

yes

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

130

C₄³

—

131

#339

—

106

—

132

#336

—

106

—

133

#335

—

134

Q₈⋊C₈

—

106

—

135

C₅₃

#9848

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

106

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

106

—

139

C₂²×C₈

D₂₁₂

yes

—

140

C₄⋊Q₈

—

141

C₄⋊Q₈

—

142

#125

—

106

—

143

C₂²⋊Q₈

—

106

—

144

C₂²⋊Q₈

—

106

—

145

C₄×Q₈

—

106

—

146

C₄×Q₈

—

106

—

147

#117

—

106

—

148

C₂×C₄²

—

149

C₂×C₄²

—

106

—

150

C₂×C₄²

—

106

—

151

C₂×C₄²

C₂²×D₅₃

yes

characteristic

152

#107

—

106

—

153

C₄⋊C₈

—

154

C₄⋊C₈

—

155

#103

—

106

—

156

C₄×C₈

—

157

C₄×C₈

—

106

—

158

C₄×C₈

C₄×D₅₃

yes

characteristic

159

C₄×C₈

C₄×D₅₃

yes

characteristic

160

C₄×C₈

C₂²⋊D₅₃

yes

—

161

C₂×Q₈

—

106

—

162

C₂×Q₈

—

106

—

163

C₂²×C₄

—

106

—

164

C₂²×C₄

C₂×D₂₁₂

yes

characteristic

165

C₂²×C₄

D₄×D₅₃

yes

characteristic

166

C₂²×C₄

#11719949

yes

characteristic

167

Q₁₆

—

212

—

168

M₁₆

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

106

—

172

C₂×C₈

—

212

—

173

C₂×C₈

#11719921

yes

—

174

C₂×C₈

#11719921

yes

—

175

C₄⋊C₄

—

106

—

176

C₄⋊C₄

—

106

—

177

C₄⋊C₄

—

106

—

178

C₄⋊C₄

—

106

—

179

C₄⋊C₄

—

212

—

180

C₄⋊C₄

—

212

—

181

C₂²⋊C₄

—

212

—

182

C₄²

—

183

C₄²

—

106

—

184

C₄²

—

212

—

185

C₄²

—

212

—

186

C₄²

—

212

—

187

C₄²

C₂×C₄×D₅₃

yes

characteristic

188

C₄²

D₄×D₅₃

yes

characteristic

189

C₄²

#11719949

yes

characteristic

190

C₄²

C₂×C₂²⋊D₅₃

yes

characteristic

191

C₂³

#13133192

yes

characteristic

192

Q₈

—

212

—

193

Q₈

—

212

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

106

—

197

C₂×C₄

—

212

—

198

C₂×C₄

—

212

—

199

C₂×C₄

—

212

—

200

C₂×C₄

—

212

—

201

C₂×C₄

C₂×#11719921

yes

characteristic

202

C₂×C₄

#13133179

yes

characteristic

203

C₂×C₄

#13133179

yes

characteristic

204

C₂×C₄

#13133192

yes

characteristic

205

C₂×C₄

#13133206

yes

characteristic

206

C₂×C₄

#13133213

yes

characteristic

207

C₂×C₄

Q₁₆×D₅₃

yes

—

208

C₂×C₄

#13133236

yes

—

209

C₈

—

210

C₈

—

211

C₈

—

212

C₈

—

212

—

213

C₂²

—

214

C₂²

—

215

C₂²

#16810524

yes

characteristic

216

C₂²

#16810865

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

424

—

220

C₄

—

424

—

221

C₄

—

212

—

222

C₄

#16810639

yes

—

223

C₄

#16810717

yes

—

224

C₄

#16810744

yes

—

225

C₄

#16811001

yes

characteristic

226

C₄

#16811006

yes

characteristic

227

C₂

—

228

C₂

#20275546

yes

characteristic

229

C₂

#20275574

yes

characteristic

230

C₂

#20275606

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13133213
commutator	C₄²×C₅₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1567	C₂
socle	C₂²×C₅₃	#390
prime radical	C₂³×C₅₃	#121
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1567	D₅₃
hypocenter	C₅₃	#9848
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

subgroup

G/H

center

C₂×C₄

#13133213

commutator

C₄²×C₅₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₃

Fitting

C₅₃×#1567

C₂

C₂²×C₅₃

C₂³×C₅₃

C₂×C₄²×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1567

N	H ≅ G/N	type
7. #16811028	C₄	semidirect
8. #16811003	C₄	semidirect
9. #16810974	C₄	semidirect
71. C₄×Dic₅₃	Q₁₆	semidirect
135. C₅₃	#9848	semidirect

H ≅ G/N

type

7. #16811028

C₄

semidirect

8. #16811003

C₄

semidirect

9. #16810974

C₄

semidirect

71. C₄×Dic₅₃

Q₁₆

semidirect

135. C₅₃

#9848

semidirect

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

subgroup	index
#20285301	2
#20275691	2
#20274460	2
#20273169	2
C₅₃×#1567	2
#9848	53

subgroup

index

C₅₃×#1567

Subgroups — #27283990

Conjugacy classes of subgroups

Complements

Maximal subgroups