Group #27302325 — subgroups

Subgroups — #27302325

Order 13568.

590 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 167 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×#16810424	C₂	1	4	yes	maximal, complemented
2	C₂×#16810399	C₂	1	1	yes	maximal, characteristic, complemented
3	#20274879	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅₃×#493	C₂	1	1	yes	maximal, characteristic
5	C₂²×#11719908	C₂²	1	2	yes	—
6	C₂×#13133151	C₂²	1	2	yes	—
7	C₂×#13133149	—	2	1	no	—
8	#16810489	—	2	1	no	—
9	#16810424	—	2	8	no	—
10	#16810399	—	2	2	no	—
11	C₂²×D₈×C₅₃	—	2	1	no	—
12	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
13	C₂×#127×C₅₃	—	2	1	no	—
14	C₅₃×#493	—	2	2	no	—
15	C₅₃×#493	C₄	1	4	yes	complemented
16	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₅₃	—	2	2	no	—
18	C₂×#11719908	—	2	2	no	—
19	C₂×#11719908	—	2	2	no	—
20	C₂×#11719908	D₄	1	4	yes	complemented
21	#13133151	—	2	4	no	—
22	#13133149	—	4	2	no	—
23	#13133124	—	4	2	no	—
24	C₂²×D₄×C₅₃	—	2	2	no	—
25	C₂²×D₄×C₅₃	—	4	2	no	—
26	C₂×D₈×C₅₃	—	2	4	no	—
27	C₂×D₈×C₅₃	—	2	2	no	—
28	C₂×D₈×C₅₃	—	2	4	no	—
29	C₂×D₈×C₅₃	—	2	4	no	—
30	C₂×D₈×C₅₃	—	4	2	no	—
31	C₂×D₈×C₅₃	—	4	2	no	—
32	C₂×D₈×C₅₃	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
35	#127×C₅₃	—	2	4	no	—
36	#127×C₅₃	—	4	2	no	—
37	C₂×C₄²×C₅₃	D₄	1	1	yes	characteristic
38	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₅₃	D₄	1	2	yes	—
40	C₂⁴×C₅₃	—	4	2	no	—
41	C₂×D₄×C₅₃	—	2	4	no	—
42	C₂×D₄×C₅₃	—	4	8	no	—
43	C₂×D₄×C₅₃	—	4	2	no	—
44	C₂×D₄×C₅₃	—	4	2	no	—
45	C₂×D₄×C₅₃	—	4	2	no	—
46	C₂×D₄×C₅₃	—	4	2	no	—
47	C₂×D₄×C₅₃	—	4	2	no	—
48	C₂×D₄×C₅₃	—	8	8	no	—
49	C₂²×C₄×C₅₃	D₈	1	2	yes	—
50	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₅₃	—	4	2	no	—
52	D₈×C₅₃	—	2	8	no	—
53	D₈×C₅₃	—	4	8	no	—
54	D₈×C₅₃	—	4	4	no	—
55	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
56	C₂×C₈×C₅₃	D₈	1	2	yes	—
57	C₂×C₈×C₅₃	SD₁₆	1	2	yes	—
58	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
60	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₈×C₅₃	#41	1	2	yes	—
62	C₄²×C₅₃	C₂²⋊C₄	1	2	yes	—
63	C₄²×C₅₃	SD₁₆	1	2	yes	—
64	C₄⋊Dic₅₃	—	4	2	no	—
65	C₄⋊Dic₅₃	—	4	2	no	—
66	#11719908	—	2	4	no	—
67	C₂³×C₅₃	—	4	4	no	—
68	C₂³×C₅₃	—	8	2	no	—
69	C₂³×C₅₃	—	8	2	no	—
70	C₂³×C₅₃	—	8	8	no	—
71	C₂³×C₅₃	C₂×D₈	1	1	yes	characteristic
72	D₄×C₅₃	—	4	4	no	—
73	D₄×C₅₃	—	4	4	no	—
74	D₄×C₅₃	—	8	16	no	—
75	D₄×C₅₃	—	8	2	no	—
76	D₄×C₅₃	—	8	2	no	—
77	C₂×C₄×C₅₃	—	2	4	no	—
78	C₂×C₄×C₅₃	#102	1	4	yes	—
79	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
81	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
82	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
84	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×Dic₅₃	—	8	2	no	—
86	C₂×Dic₅₃	—	8	4	no	—
87	C₈×C₅₃	#102	1	4	yes	—
88	C₈×C₅₃	C₄×D₄	1	2	yes	—
89	C₈×C₅₃	#121	1	2	yes	—
90	#13206	—	53	1	no	maximal, Sylow
91	C₂²×C₅₃	—	8	8	no	—
92	C₂²×C₅₃	—	8	4	no	—
93	C₂²×C₅₃	—	16	4	no	—
94	C₂²×C₅₃	—	16	4	no	—
95	C₂²×C₅₃	C₂×#102	1	1	yes	characteristic
96	C₂²×C₅₃	#486	1	1	yes	characteristic
97	C₂²×C₅₃	#493	1	1	yes	characteristic
98	C₂²×C₅₃	#509	1	4	yes	—
99	C₄×C₅₃	—	2	4	no	—
100	C₄×C₅₃	#390	1	1	yes	characteristic
101	C₄×C₅₃	C₂×#102	1	1	yes	characteristic
102	C₄×C₅₃	#486	1	1	yes	characteristic
103	C₄×C₅₃	#492	1	1	yes	characteristic
104	Dic₅₃	—	16	2	no	—
105	C₂×#493	D₅₃	1	1	yes	characteristic
106	C₂×#357	—	53	4	no	—
107	C₂×#346	—	53	1	no	—
108	#1846	—	53	1	no	—
109	C₂×C₅₃	—	16	4	no	—
110	C₂×C₅₃	#1957	1	1	yes	characteristic
111	C₂×C₅₃	#2140	1	2	yes	—
112	C₂×C₅₃	#2244	1	2	yes	—
113	C₂×C₅₃	#2250	1	2	yes	—
114	C₂²×D₈	—	2	1	no	—
115	C₂²×D₈	C₂×D₅₃	1	2	yes	—
116	C₂×#127	—	2	1	no	—
117	C₂²×C₁₆	—	53	2	no	—
118	#493	—	2	2	no	—
119	#493	Dic₅₃	1	4	yes	complemented
120	C₂×#107	—	53	2	no	—
121	C₂×#106	—	106	1	no	—
122	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
123	#382	—	106	1	no	—
124	#357	—	106	8	no	—
125	#346	—	106	2	no	—
126	C₅₃	#13206	1	1	yes	characteristic, complemented, Sylow
127	C₂²×D₄	—	2	2	no	—
128	C₂²×D₄	—	4	2	no	—
129	C₂×D₈	—	2	4	no	—
130	C₂×D₈	—	2	4	no	—
131	C₂×D₈	—	2	2	no	—
132	C₂×D₈	—	2	4	no	—
133	C₂×D₈	—	4	2	no	—
134	C₂×D₈	—	4	2	no	—
135	C₂×D₈	C₂×Dic₅₃	1	4	yes	—
136	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
137	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
138	#127	—	2	4	no	—
139	#127	—	4	2	no	—
140	C₂×C₄⋊C₄	—	106	2	no	—
141	C₂×C₄²	C₂²⋊D₅₃	1	1	yes	characteristic
142	C₂×C₁₆	—	53	4	no	—
143	C₂×C₁₆	—	106	2	no	—
144	C₂×C₁₆	—	106	2	no	—
145	#107	—	106	4	no	—
146	#106	—	212	2	no	—
147	C₄×C₈	C₂×Dic₅₃	1	2	yes	—
148	C₄×C₈	C₂²⋊D₅₃	1	2	yes	—
149	#95	—	212	2	no	—
150	C₂⁴	—	4	2	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	—	4	8	no	—
153	C₂×D₄	—	4	2	no	—
154	C₂×D₄	—	4	2	no	—
155	C₂×D₄	—	4	2	no	—
156	C₂×D₄	—	4	2	no	—
157	C₂×D₄	—	4	2	no	—
158	C₂×D₄	—	8	8	no	—
159	C₂²×C₄	—	212	2	no	—
160	C₂²×C₄	#11719922	1	2	yes	—
161	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
162	D₈	—	2	8	no	—
163	D₈	—	4	8	no	—
164	D₈	—	4	4	no	—
165	C₂×C₈	#11719922	1	2	yes	—
166	C₂×C₈	#11719923	1	2	yes	—
167	C₂×C₈	C₂²⋊Dic₅₃	1	2	yes	—
168	C₂×C₈	D₄×D₅₃	1	2	yes	—
169	C₂×C₈	#11719947	1	2	yes	—
170	C₂×C₈	C₂²×Dic₅₃	1	1	yes	characteristic
171	C₂×C₈	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
172	C₄⋊C₄	—	212	2	no	—
173	C₄⋊C₄	—	212	2	no	—
174	C₄²	#11719923	1	2	yes	—
175	C₄²	C₂²⋊Dic₅₃	1	2	yes	—
176	C₁₆	—	106	4	no	—
177	C₂³	—	4	4	no	—
178	C₂³	—	8	8	no	—
179	C₂³	—	8	2	no	—
180	C₂³	—	8	2	no	—
181	C₂³	C₂×#11719922	1	1	yes	characteristic
182	D₄	—	4	4	no	—
183	D₄	—	4	4	no	—
184	D₄	—	8	16	no	—
185	D₄	—	8	2	no	—
186	D₄	—	8	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	424	4	no	—
189	C₂×C₄	—	424	2	no	—
190	C₂×C₄	#13133138	1	4	yes	—
191	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
192	C₂×C₄	#13133204	1	1	yes	characteristic
193	C₂×C₄	#13133213	1	1	yes	characteristic
194	C₂×C₄	C₂×#11719922	1	1	yes	characteristic
195	C₂×C₄	C₂×#11719923	1	1	yes	characteristic
196	C₂×C₄	C₂×#11719923	1	1	yes	characteristic
197	C₈	#13133138	1	4	yes	—
198	C₈	D₄×Dic₅₃	1	2	yes	—
199	C₈	#13133188	1	2	yes	—
200	C₂²	—	8	4	no	—
201	C₂²	—	8	8	no	—
202	C₂²	—	16	4	no	—
203	C₂²	—	16	4	no	—
204	C₂²	C₂×#13133138	1	1	yes	characteristic
205	C₂²	#16810969	1	1	yes	characteristic
206	C₂²	#16810999	1	1	yes	characteristic
207	C₂²	#16811059	1	4	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	848	2	no	—
210	C₄	#16810526	1	1	yes	characteristic
211	C₄	C₂×#13133138	1	1	yes	characteristic
212	C₄	#16810969	1	1	yes	characteristic
213	C₄	#16810995	1	1	yes	characteristic
214	C₂	—	16	4	no	—
215	C₂	#20275522	1	1	yes	characteristic
216	C₂	#20276431	1	2	yes	—
217	C₂	#20276956	1	2	yes	—
218	C₂	#20276979	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16810424

C₂

yes

maximal, complemented

C₂×#16810399

C₂

yes

maximal, characteristic, complemented

#20274879

C₂

yes

maximal, characteristic, complemented

C₂×C₅₃×#493

C₂

yes

maximal, characteristic

C₂²×#11719908

C₂²

yes

—

C₂×#13133151

C₂²

yes

—

—

—

—

—

C₂²×D₈×C₅₃

—

C₂²×D₈×C₅₃

C₂²

yes

—

C₂×#127×C₅₃

—

C₅₃×#493

—

C₅₃×#493

C₄

yes

complemented

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×C₄⋊Dic₅₃

—

C₂×#11719908

—

C₂×#11719908

—

C₂×#11719908

D₄

yes

—

—

—

C₂²×D₄×C₅₃

—

C₂²×D₄×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

—

C₂×D₈×C₅₃

C₂×C₄

yes

—

C₂²×C₈×C₅₃

D₄

yes

characteristic

C₂²×C₈×C₅₃

C₂³

yes

characteristic

#127×C₅₃

—

#127×C₅₃

—

C₂×C₄²×C₅₃

D₄

yes

characteristic

C₄×C₈×C₅₃

C₂×C₄

yes

—

C₄×C₈×C₅₃

D₄

yes

—

C₂⁴×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂²×C₄×C₅₃

D₈

yes

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×Dic₅₃

—

D₈×C₅₃

—

D₈×C₅₃

—

D₈×C₅₃

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₂×C₈×C₅₃

D₈

yes

—

C₂×C₈×C₅₃

SD₁₆

yes

—

C₂×C₈×C₅₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂×D₄

yes

—

C₂×C₈×C₅₃

C₂×D₄

yes

characteristic

C₂×C₈×C₅₃

#41

yes

—

C₄²×C₅₃

C₂²⋊C₄

yes

—

C₄²×C₅₃

SD₁₆

yes

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

#11719908

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

C₂×D₈

yes

characteristic

D₄×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#102

yes

—

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

C₂×D₈

yes

characteristic

C₂×C₄×C₅₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₃

C₂×SD₁₆

yes

characteristic

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₈×C₅₃

#102

yes

—

C₈×C₅₃

C₄×D₄

yes

—

C₈×C₅₃

#121

yes

—

#13206

—

maximal, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

—

C₄×C₅₃

—

100

C₄×C₅₃

#390

yes

characteristic

101

C₄×C₅₃

C₂×#102

yes

characteristic

102

C₄×C₅₃

#486

yes

characteristic

103

C₄×C₅₃

#492

yes

characteristic

104

Dic₅₃

—

105

C₂×#493

D₅₃

yes

characteristic

106

C₂×#357

—

107

C₂×#346

—

108

#1846

—

109

C₂×C₅₃

—

110

C₂×C₅₃

#1957

yes

characteristic

111

C₂×C₅₃

#2140

yes

—

112

C₂×C₅₃

#2244

yes

—

113

C₂×C₅₃

#2250

yes

—

114

C₂²×D₈

—

115

C₂²×D₈

C₂×D₅₃

yes

—

116

C₂×#127

—

117

C₂²×C₁₆

—

118

#493

—

119

#493

Dic₅₃

yes

complemented

120

C₂×#107

—

121

C₂×#106

—

106

—

122

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

123

#382

—

106

—

124

#357

—

106

—

125

#346

—

106

—

126

C₅₃

#13206

yes

characteristic, complemented, Sylow

127

C₂²×D₄

—

128

C₂²×D₄

—

129

C₂×D₈

—

130

C₂×D₈

—

131

C₂×D₈

—

132

C₂×D₈

—

133

C₂×D₈

—

134

C₂×D₈

—

135

C₂×D₈

C₂×Dic₅₃

yes

—

136

C₂²×C₈

C₂²⋊D₅₃

yes

characteristic

137

C₂²×C₈

C₂²×D₅₃

yes

characteristic

138

#127

—

139

#127

—

140

C₂×C₄⋊C₄

—

106

—

141

C₂×C₄²

C₂²⋊D₅₃

yes

characteristic

142

C₂×C₁₆

—

143

C₂×C₁₆

—

106

—

144

C₂×C₁₆

—

106

—

145

#107

—

106

—

146

#106

—

212

—

147

C₄×C₈

C₂×Dic₅₃

yes

—

148

C₄×C₈

C₂²⋊D₅₃

yes

—

149

#95

—

212

—

150

C₂⁴

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂²×C₄

—

212

—

160

C₂²×C₄

#11719922

yes

—

161

C₂²×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

162

D₈

—

163

D₈

—

164

D₈

—

165

C₂×C₈

#11719922

yes

—

166

C₂×C₈

#11719923

yes

—

167

C₂×C₈

C₂²⋊Dic₅₃

yes

—

168

C₂×C₈

D₄×D₅₃

yes

—

169

C₂×C₈

#11719947

yes

—

170

C₂×C₈

C₂²×Dic₅₃

yes

characteristic

171

C₂×C₈

C₂×C₂²⋊D₅₃

yes

characteristic

172

C₄⋊C₄

—

212

—

173

C₄⋊C₄

—

212

—

174

C₄²

#11719923

yes

—

175

C₄²

C₂²⋊Dic₅₃

yes

—

176

C₁₆

—

106

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

C₂×#11719922

yes

characteristic

182

D₄

—

183

D₄

—

184

D₄

—

185

D₄

—

186

D₄

—

187

C₂×C₄

—

188

C₂×C₄

—

424

—

189

C₂×C₄

—

424

—

190

C₂×C₄

#13133138

yes

—

191

C₂×C₄

C₂×C₂²⋊Dic₅₃

yes

characteristic

192

C₂×C₄

#13133204

yes

characteristic

193

C₂×C₄

#13133213

yes

characteristic

194

C₂×C₄

C₂×#11719922

yes

characteristic

195

C₂×C₄

C₂×#11719923

yes

characteristic

196

C₂×C₄

C₂×#11719923

yes

characteristic

197

C₈

#13133138

yes

—

198

C₈

D₄×Dic₅₃

yes

—

199

C₈

#13133188

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

C₂×#13133138

yes

characteristic

205

C₂²

#16810969

yes

characteristic

206

C₂²

#16810999

yes

characteristic

207

C₂²

#16811059

yes

—

208

C₄

—

209

C₄

—

848

—

210

C₄

#16810526

yes

characteristic

211

C₄

C₂×#13133138

yes

characteristic

212

C₄

#16810969

yes

characteristic

213

C₄

#16810995

yes

characteristic

214

C₂

—

215

C₂

#20275522

yes

characteristic

216

C₂

#20276431

yes

—

217

C₂

#20276956

yes

—

218

C₂

#20276979

yes

—

	subgroup	G/H
center	C₂³	C₂×#11719922
commutator	C₂×C₈×C₅₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₃
Fitting, prime radical	C₂×C₅₃×#493	C₂
socle	C₂³×C₅₃	C₂×D₈
cosocle	C₂²×C₈×C₅₃	C₂³
hypercenter	C₂×#493	D₅₃
hypocenter	C₅₃	#13206
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂³

C₂×#11719922

commutator

C₂×C₈×C₅₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₃

Fitting, prime radical

C₂×C₅₃×#493

C₂

socle

C₂³×C₅₃

C₂×D₈

cosocle

C₂²×C₈×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

N	H ≅ G/N	type
1. C₂×#16810424	C₂	semidirect
2. C₂×#16810399	C₂	semidirect
3. #20274879	C₂	semidirect
15. C₅₃×#493	C₄	semidirect
20. C₂×#11719908	D₄	semidirect
119. #493	Dic₅₃	semidirect
126. C₅₃	#13206	semidirect

H ≅ G/N

type

1. C₂×#16810424

C₂

semidirect

2. C₂×#16810399

C₂

semidirect

3. #20274879

C₂

semidirect

15. C₅₃×#493

C₄

semidirect

20. C₂×#11719908

D₄

semidirect

119. #493

Dic₅₃

semidirect

126. C₅₃

#13206

semidirect

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

subgroup	index
C₂×#16810424	2
C₂×#16810399	2
#20274879	2
C₂×C₅₃×#493	2
#13206	53

subgroup

index

C₂×C₅₃×#493

Subgroups — #27302325

Conjugacy classes of subgroups

Complements

Maximal subgroups