Group #27277959 — subgroups

Subgroups — #27277959

Order 13568.

410 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 143 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	#20275652	C₂	1	1	yes	maximal, characteristic
2	C₄×#13133136	C₂	1	1	yes	maximal, characteristic
3	#20273468	C₂	1	2	yes	maximal
4	#20272551	C₂	1	2	yes	maximal
5	C₅₃×#2982	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
7	C₂×#13133136	C₄	1	1	yes	characteristic
8	C₂×#13133136	C₄	1	1	yes	characteristic
9	C₄×#11719917	C₂²	1	2	yes	—
10	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
11	#16810392	C₄	1	2	yes	—
12	#16810378	—	2	2	no	—
13	#16810375	—	2	2	no	—
14	#16810373	—	2	2	no	—
15	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
16	C₈×Q₈×C₅₃	—	2	2	no	—
17	C₈×Q₈×C₅₃	—	2	2	no	—
18	C₅₃×#431	—	2	2	no	—
19	C₅₃×#431	C₂²	1	2	yes	—
20	C₂×#11719917	C₂×C₄	1	2	yes	—
21	C₂×#11719917	C₂×C₄	1	2	yes	—
22	C₂²×#88322	—	2	1	no	—
23	C₂²×#88322	—	2	1	no	—
24	C₄⋊#88322	—	2	2	no	—
25	#13133136	—	2	2	no	—
26	#13133136	C₈	1	4	yes	complemented
27	#13133128	—	2	2	no	—
28	C₄×#88322	—	2	2	no	—
29	C₄×#88322	—	2	2	no	—
30	C₂²×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Q₈×C₅₃	—	2	2	no	—
32	C₄×Q₈×C₅₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₅₃	Q₈	1	2	yes	—
35	C₂×C₄²×C₅₃	D₄	1	2	yes	—
36	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₅₃	—	2	2	no	—
38	C₄⋊C₈×C₅₃	—	2	2	no	—
39	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
40	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
41	C₂²⋊C₈×C₅₃	—	2	2	no	—
42	C₄×C₈×C₅₃	—	2	4	no	—
43	C₄×C₈×C₅₃	—	2	2	no	—
44	C₂×Q₈×C₅₃	—	2	2	no	—
45	C₂×Q₈×C₅₃	—	2	2	no	—
46	C₂×Q₈×C₅₃	C₂×C₈	1	2	yes	—
47	C₂×Q₈×C₅₃	M₁₆	1	2	yes	—
48	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
49	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
50	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
52	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
53	C₂×C₈×C₅₃	—	2	2	no	—
54	C₂×C₈×C₅₃	—	2	2	no	—
55	C₄⋊C₄×C₅₃	—	2	2	no	—
56	C₄⋊C₄×C₅₃	—	2	4	no	—
57	C₄²×C₅₃	—	2	2	no	—
58	C₄²×C₅₃	—	2	2	no	—
59	C₄²×C₅₃	C₂×D₄	1	2	yes	—
60	C₄²×C₅₃	#41	1	2	yes	—
61	#11719917	—	2	2	no	—
62	#11719917	—	2	2	no	—
63	#11719917	—	2	2	no	—
64	#11719917	C₂×C₈	1	4	yes	—
65	C₂×#88322	—	2	2	no	—
66	C₂×#88322	—	2	2	no	—
67	C₂×#88322	—	2	2	no	—
68	C₂×#88322	—	4	1	no	—
69	C₂×#88322	—	4	1	no	—
70	C₂×#88322	—	4	2	no	—
71	C₂×#88322	—	4	1	no	—
72	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
73	Q₈×C₅₃	—	2	4	no	—
74	Q₈×C₅₃	—	2	4	no	—
75	C₂×C₄×C₅₃	—	2	2	no	—
76	C₂×C₄×C₅₃	—	2	2	no	—
77	C₂×C₄×C₅₃	—	2	1	no	—
78	C₂×C₄×C₅₃	—	2	1	no	—
79	C₂×C₄×C₅₃	—	2	2	no	—
80	C₂×C₄×C₅₃	—	4	1	no	—
81	C₂×C₄×C₅₃	—	4	2	no	—
82	C₂×C₄×C₅₃	C₄⋊C₈	1	4	yes	—
83	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
85	C₂×C₄×C₅₃	C₂²⋊Q₈	1	2	yes	—
86	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
87	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
88	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
89	C₂×C₄×C₅₃	#131	1	2	yes	—
90	C₈×C₅₃	—	4	2	no	—
91	C₈×C₅₃	—	4	2	no	—
92	#88322	—	2	4	no	—
93	#88322	—	4	2	no	—
94	#88322	—	4	2	no	—
95	#88322	—	8	1	no	—
96	#8836	—	53	1	no	maximal, Sylow
97	C₂²×C₅₃	—	2	1	no	—
98	C₂²×C₅₃	—	2	1	no	—
99	C₂²×C₅₃	#385	1	1	yes	characteristic
100	C₂²×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
101	C₂²×C₅₃	#424	1	1	yes	characteristic
102	C₄×C₅₃	—	2	4	no	—
103	C₄×C₅₃	—	2	1	no	—
104	C₄×C₅₃	—	2	2	no	—
105	C₄×C₅₃	—	4	2	no	—
106	C₄×C₅₃	C₈×D₄	1	2	yes	—
107	C₄×C₅₃	#435	1	2	yes	—
108	C₄×C₅₃	#454	1	1	yes	characteristic
109	C₄×C₅₃	#456	1	1	yes	characteristic
110	#2982	D₅₃	1	1	yes	characteristic
111	#1984	—	53	1	no	—
112	C₄×#101	—	53	1	no	—
113	#1565	—	53	2	no	—
114	#1278	—	53	2	no	—
115	C₂×C₅₃	—	2	1	no	—
116	C₂×C₅₃	—	2	1	no	—
117	C₂×C₅₃	#1850	1	1	yes	characteristic
118	C₂×C₅₃	#1857	1	1	yes	characteristic
119	C₂×C₅₃	#1858	1	1	yes	characteristic
120	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
121	C₈×Q₈	—	2	2	no	—
122	C₈×Q₈	—	2	2	no	—
123	#431	—	2	2	no	—
124	#431	C₂×D₅₃	1	2	yes	—
125	C₂×C₄⋊C₈	—	53	1	no	—
126	C₂×#101	—	53	1	no	—
127	C₂×#101	—	53	1	no	—
128	C₄×M₁₆	—	53	2	no	—
129	C₂×C₄×C₈	—	53	1	no	—
130	#343	—	53	2	no	—
131	#336	—	106	2	no	—
132	#335	—	106	2	no	—
133	#334	—	106	2	no	—
134	C₅₃	#8836	1	1	yes	characteristic, complemented, Sylow
135	C₂²×Q₈	C₄×D₅₃	1	1	yes	characteristic
136	C₂×M₁₆	—	53	2	no	—
137	C₂×M₁₆	—	53	2	no	—
138	C₂²×C₈	—	106	1	no	—
139	C₂²×C₈	—	106	1	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₄×Q₈	—	2	2	no	—
142	C₂×C₄⋊C₄	Dic₁₀₆	1	2	yes	—
143	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
144	C₂×C₄²	C₂²⋊D₅₃	1	2	yes	—
145	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	2	2	no	—
148	C₄⋊C₈	—	106	2	no	—
149	C₄⋊C₈	C₂²⋊D₅₃	1	2	yes	—
150	C₄⋊C₈	C₂²⋊D₅₃	1	2	yes	—
151	#101	—	53	4	no	—
152	#101	—	106	2	no	—
153	C₂²⋊C₈	—	2	2	no	—
154	#97	—	106	2	no	—
155	C₄×C₈	—	2	4	no	—
156	C₄×C₈	—	2	2	no	—
157	C₄×C₈	—	106	2	no	—
158	C₄×C₈	—	106	2	no	—
159	C₂×Q₈	—	2	2	no	—
160	C₂×Q₈	—	2	2	no	—
161	C₂×Q₈	C₈×D₅₃	1	2	yes	—
162	C₂×Q₈	#11719912	1	2	yes	—
163	C₂²×C₄	#11719919	1	2	yes	—
164	C₂²×C₄	#11719919	1	2	yes	—
165	C₂²×C₄	C₂×Dic₁₀₆	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
167	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
168	M₁₆	—	53	4	no	—
169	M₁₆	—	106	2	no	—
170	M₁₆	—	106	2	no	—
171	M₁₆	—	106	2	no	—
172	C₂×C₈	—	2	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	106	2	no	—
175	C₂×C₈	—	106	2	no	—
176	C₂×C₈	—	106	2	no	—
177	C₂×C₈	—	212	2	no	—
178	C₂×C₈	—	212	1	no	—
179	C₂×C₈	—	212	1	no	—
180	C₂×C₈	—	212	1	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄²	—	2	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	#11719945	1	2	yes	—
186	C₄²	C₂×C₂²⋊D₅₃	1	2	yes	—
187	C₂³	C₂×#11719919	1	1	yes	characteristic
188	Q₈	—	2	4	no	—
189	Q₈	—	2	4	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	#13133146	1	4	yes	—
198	C₂×C₄	C₄×C₂²⋊D₅₃	1	2	yes	—
199	C₂×C₄	#13133186	1	1	yes	characteristic
200	C₂×C₄	#13133196	1	2	yes	—
201	C₂×C₄	#13133200	1	1	yes	characteristic
202	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
203	C₂×C₄	C₂×#11719912	1	1	yes	characteristic
204	C₂×C₄	#13133223	1	2	yes	—
205	C₈	—	4	2	no	—
206	C₈	—	4	2	no	—
207	C₈	—	106	4	no	—
208	C₈	—	424	1	no	—
209	C₈	—	212	2	no	—
210	C₈	—	212	2	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	#16810496	1	1	yes	characteristic
214	C₂²	C₂×#13133146	1	1	yes	characteristic
215	C₂²	#16810649	1	1	yes	characteristic
216	C₄	—	2	4	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	2	no	—
220	C₄	C₈×C₂²⋊D₅₃	1	2	yes	—
221	C₄	#16810694	1	2	yes	—
222	C₄	#16810796	1	1	yes	characteristic
223	C₄	#16810806	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	#20274893	1	1	yes	characteristic
227	C₂	#20274930	1	1	yes	characteristic
228	C₂	#20274935	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20275652

C₂

yes

maximal, characteristic

C₄×#13133136

C₂

yes

maximal, characteristic

#20273468

C₂

yes

maximal

#20272551

C₂

yes

maximal

C₅₃×#2982

C₂

yes

maximal, characteristic

C₂×C₄⋊#88322

C₂²

yes

characteristic

C₂×#13133136

C₄

yes

characteristic

C₂×#13133136

C₄

yes

characteristic

C₄×#11719917

C₂²

yes

—

C₂×C₄×#88322

C₂²

yes

characteristic

#16810392

C₄

yes

—

#16810378

—

#16810375

—

#16810373

—

C₂×C₄×Q₈×C₅₃

C₂²

yes

characteristic

C₈×Q₈×C₅₃

—

C₈×Q₈×C₅₃

—

C₅₃×#431

—

C₅₃×#431

C₂²

yes

—

C₂×#11719917

C₂×C₄

yes

—

C₂×#11719917

C₂×C₄

yes

—

C₂²×#88322

—

C₂²×#88322

—

C₄⋊#88322

—

#13133136

—

#13133136

C₈

yes

—

—

—

C₂²×Q₈×C₅₃

C₂×C₄

yes

characteristic

C₄×Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

C₂×C₄⋊C₄×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₅₃

Q₈

yes

—

C₂×C₄²×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

C₄⋊C₈×C₅₃

—

C₄⋊C₈×C₅₃

—

C₄⋊C₈×C₅₃

D₄

yes

—

C₄⋊C₈×C₅₃

D₄

yes

—

C₂²⋊C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

C₂×C₈

yes

—

C₂×Q₈×C₅₃

M₁₆

yes

—

C₂²×C₄×C₅₃

C₄⋊C₄

yes

—

C₂²×C₄×C₅₃

C₄⋊C₄

yes

—

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂×D₄

yes

—

C₄²×C₅₃

#41

yes

—

—

—

—

C₂×C₈

yes

—

—

—

—

—

—

—

—

C₂³×C₅₃

C₂×C₄⋊C₄

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₄⋊C₈

yes

—

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

#120

yes

characteristic

C₂×C₄×C₅₃

C₂²⋊Q₈

yes

—

C₂×C₄×C₅₃

#123

yes

characteristic

C₂×C₄×C₅₃

C₂²×C₈

yes

characteristic

C₂×C₄×C₅₃

C₂×M₁₆

yes

characteristic

C₂×C₄×C₅₃

#131

yes

—

C₈×C₅₃

—

C₈×C₅₃

—

—

—

—

—

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

#385

yes

characteristic

100

C₂²×C₅₃

C₂×C₄⋊C₈

yes

characteristic

101

C₂²×C₅₃

#424

yes

characteristic

102

C₄×C₅₃

—

103

C₄×C₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

—

106

C₄×C₅₃

C₈×D₄

yes

—

107

C₄×C₅₃

#435

yes

—

108

C₄×C₅₃

#454

yes

characteristic

109

C₄×C₅₃

#456

yes

characteristic

110

#2982

D₅₃

yes

characteristic

111

#1984

—

112

C₄×#101

—

113

#1565

—

114

#1278

—

115

C₂×C₅₃

—

116

C₂×C₅₃

—

117

C₂×C₅₃

#1850

yes

characteristic

118

C₂×C₅₃

#1857

yes

characteristic

119

C₂×C₅₃

#1858

yes

characteristic

120

C₂×C₄×Q₈

C₂×D₅₃

yes

characteristic

121

C₈×Q₈

—

122

C₈×Q₈

—

123

#431

—

124

#431

C₂×D₅₃

yes

—

125

C₂×C₄⋊C₈

—

126

C₂×#101

—

127

C₂×#101

—

128

C₄×M₁₆

—

129

C₂×C₄×C₈

—

130

#343

—

131

#336

—

106

—

132

#335

—

106

—

133

#334

—

106

—

134

C₅₃

#8836

yes

characteristic, complemented, Sylow

135

C₂²×Q₈

C₄×D₅₃

yes

characteristic

136

C₂×M₁₆

—

137

C₂×M₁₆

—

138

C₂²×C₈

—

106

—

139

C₂²×C₈

—

106

—

140

C₄×Q₈

—

141

C₄×Q₈

—

142

C₂×C₄⋊C₄

Dic₁₀₆

yes

—

143

C₂×C₄⋊C₄

C₄×D₅₃

yes

characteristic

144

C₂×C₄²

C₂²⋊D₅₃

yes

—

145

C₂×C₄²

C₂²×D₅₃

yes

characteristic

146

C₄⋊C₈

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

106

—

149

C₄⋊C₈

C₂²⋊D₅₃

yes

—

150

C₄⋊C₈

C₂²⋊D₅₃

yes

—

151

#101

—

152

#101

—

106

—

153

C₂²⋊C₈

—

154

#97

—

106

—

155

C₄×C₈

—

156

C₄×C₈

—

157

C₄×C₈

—

106

—

158

C₄×C₈

—

106

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

C₈×D₅₃

yes

—

162

C₂×Q₈

#11719912

yes

—

163

C₂²×C₄

#11719919

yes

—

164

C₂²×C₄

#11719919

yes

—

165

C₂²×C₄

C₂×Dic₁₀₆

yes

characteristic

166

C₂²×C₄

C₂×C₄×D₅₃

yes

characteristic

167

C₂²×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

168

M₁₆

—

169

M₁₆

—

106

—

170

M₁₆

—

106

—

171

M₁₆

—

106

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

106

—

175

C₂×C₈

—

106

—

176

C₂×C₈

—

106

—

177

C₂×C₈

—

212

—

178

C₂×C₈

—

212

—

179

C₂×C₈

—

212

—

180

C₂×C₈

—

212

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄²

—

184

C₄²

—

185

C₄²

#11719945

yes

—

186

C₄²

C₂×C₂²⋊D₅₃

yes

—

187

C₂³

C₂×#11719919

yes

characteristic

188

Q₈

—

189

Q₈

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

#13133146

yes

—

198

C₂×C₄

C₄×C₂²⋊D₅₃

yes

—

199

C₂×C₄

#13133186

yes

characteristic

200

C₂×C₄

#13133196

yes

—

201

C₂×C₄

#13133200

yes

characteristic

202

C₂×C₄

C₂×C₈×D₅₃

yes

characteristic

203

C₂×C₄

C₂×#11719912

yes

characteristic

204

C₂×C₄

#13133223

yes

—

205

C₈

—

206

C₈

—

207

C₈

—

106

—

208

C₈

—

424

—

209

C₈

—

212

—

210

C₈

—

212

—

211

C₂²

—

212

C₂²

—

213

C₂²

#16810496

yes

characteristic

214

C₂²

C₂×#13133146

yes

characteristic

215

C₂²

#16810649

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₈×C₂²⋊D₅₃

yes

—

221

C₄

#16810694

yes

—

222

C₄

#16810796

yes

characteristic

223

C₄

#16810806

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

#20274893

yes

characteristic

227

C₂

#20274930

yes

characteristic

228

C₂

#20274935

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13133186
commutator	C₂×C₄×C₅₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#2982	C₂
socle	C₂²×C₅₃	#385
prime radical	C₂³×C₅₃	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#2982	D₅₃
hypocenter	C₅₃	#8836
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2982

subgroup

G/H

center

C₂×C₄

#13133186

commutator

C₂×C₄×C₅₃

C₂²×C₈

Frattini

C₂×C₄²

C₂²×D₅₃

Fitting

C₅₃×#2982

C₂

socle

C₂²×C₅₃

#385

prime radical

C₂³×C₅₃

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2982

N	H ≅ G/N	type
26. #13133136	C₈	semidirect
134. C₅₃	#8836	semidirect

H ≅ G/N

type

26. #13133136

C₈

semidirect

134. C₅₃

#8836

semidirect

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

subgroup	index
#20275652	2
C₄×#13133136	2
#20273468	2
#20272551	2
C₅₃×#2982	2
#8836	53

subgroup

index

C₅₃×#2982

Subgroups — #27277959

Conjugacy classes of subgroups

Complements

Maximal subgroups