Group #27215699 — subgroups

Subgroups — C₅₃×#8187 #27215699

Order 13568.

428 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 182 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	C₅₃×#2922	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#1476	C₂	1	2	yes	maximal
3	C₅₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈²×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1278	C₂	1	2	yes	maximal, complemented
6	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
7	C₅₃×#433	—	2	2	no	—
8	C₅₃×#431	—	2	2	no	—
9	C₅₃×#431	C₂²	1	2	yes	—
10	C₅₃×#424	C₄	1	2	yes	—
11	C₅₃×#408	C₄	1	2	yes	—
12	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₅₃	C₂²	1	2	yes	—
14	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
15	C₅₃×Q₈⋊C₈	C₄	1	4	yes	—
16	C₅₃×D₄⋊C₈	C₄	1	4	yes	—
17	C₅₃×#322	—	2	2	no	—
18	C₈²×C₅₃	—	2	2	no	—
19	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
20	C₂×M₁₆×C₅₃	C₂×C₄	1	2	yes	—
21	C₂²×C₈×C₅₃	—	2	2	no	—
22	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
23	C₄×Q₈×C₅₃	C₂×C₄	1	2	yes	—
24	C₄×D₄×C₅₃	—	2	2	no	—
25	C₄×D₄×C₅₃	C₂×C₄	1	2	yes	—
26	#117×C₅₃	—	2	1	no	—
27	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₅₃	—	2	1	no	—
29	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₈×C₅₃	—	2	4	no	—
31	C₄⋊C₈×C₅₃	C₂×C₄	1	4	yes	—
32	C₂²⋊C₈×C₅₃	—	2	4	no	—
33	C₂²⋊C₈×C₅₃	—	2	2	no	—
34	#97×C₅₃	—	2	1	no	—
35	C₄×C₈×C₅₃	—	2	2	no	—
36	C₄×C₈×C₅₃	—	2	2	no	—
37	C₄×C₈×C₅₃	—	2	1	no	—
38	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
39	C₄×C₈×C₅₃	D₄	1	2	yes	—
40	C₄×C₈×C₅₃	D₄	1	2	yes	—
41	#41×C₅₃	—	2	4	no	—
42	C₂×Q₈×C₅₃	C₄²	1	1	yes	characteristic
43	C₂×D₄×C₅₃	—	2	1	no	—
44	C₂×D₄×C₅₃	C₄²	1	1	yes	characteristic
45	C₂²×C₄×C₅₃	—	2	1	no	—
46	C₂²×C₄×C₅₃	—	2	2	no	—
47	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₃	#41	1	2	yes	—
49	M₁₆×C₅₃	—	2	4	no	—
50	C₂×C₈×C₅₃	—	2	8	no	—
51	C₂×C₈×C₅₃	—	2	4	no	—
52	C₂×C₈×C₅₃	—	2	4	no	—
53	C₂×C₈×C₅₃	—	2	2	no	—
54	C₂×C₈×C₅₃	—	2	4	no	—
55	C₂×C₈×C₅₃	C₂²⋊C₄	1	4	yes	—
56	C₄⋊C₄×C₅₃	—	2	2	no	—
57	C₄⋊C₄×C₅₃	C₄²	1	2	yes	—
58	C₂²⋊C₄×C₅₃	—	2	1	no	—
59	C₂²⋊C₄×C₅₃	—	2	2	no	—
60	C₄²×C₅₃	—	2	1	no	—
61	C₄²×C₅₃	—	2	2	no	—
62	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
63	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
65	C₂³×C₅₃	—	2	1	no	—
66	C₂³×C₅₃	#117	1	1	yes	characteristic
67	Q₈×C₅₃	—	2	2	no	—
68	D₄×C₅₃	—	2	2	no	—
69	D₄×C₅₃	—	4	2	no	—
70	C₂×C₄×C₅₃	—	2	4	no	—
71	C₂×C₄×C₅₃	—	2	1	no	—
72	C₂×C₄×C₅₃	—	2	2	no	—
73	C₂×C₄×C₅₃	—	4	2	no	—
74	C₂×C₄×C₅₃	—	4	4	no	—
75	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
78	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
79	C₂×C₄×C₅₃	#131	1	4	yes	—
80	C₈×C₅₃	—	2	8	no	—
81	C₈×C₅₃	—	2	4	no	—
82	C₈×C₅₃	—	4	2	no	—
83	C₈×C₅₃	—	4	4	no	—
84	#8187	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
85	C₂²×C₅₃	—	2	2	no	—
86	C₂²×C₅₃	—	4	1	no	—
87	C₂²×C₅₃	—	4	2	no	—
88	C₂²×C₅₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
89	C₂²×C₅₃	#433	1	2	yes	—
90	C₄×C₅₃	—	2	2	no	—
91	C₄×C₅₃	—	4	1	no	—
92	C₄×C₅₃	—	4	2	no	—
93	C₄×C₅₃	#405	1	2	yes	—
94	C₄×C₅₃	#408	1	2	yes	—
95	C₄×C₅₃	#443	1	4	yes	—
96	#2922	C₂×C₅₃	1	1	yes	characteristic
97	#1476	C₂×C₅₃	1	2	yes	—
98	#1452	C₂×C₅₃	1	1	yes	characteristic, complemented
99	C₂×C₈²	C₂×C₅₃	1	1	yes	characteristic, complemented
100	#1278	C₂×C₅₃	1	2	yes	complemented
101	C₂×C₅₃	—	2	2	no	—
102	C₂×C₅₃	—	8	1	no	—
103	C₂×C₅₃	#1750	1	1	yes	characteristic
104	C₂×C₅₃	#1764	1	2	yes	—
105	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
106	#433	—	2	2	no	—
107	#431	—	2	2	no	—
108	#431	C₂²×C₅₃	1	2	yes	—
109	#424	C₄×C₅₃	1	2	yes	—
110	#408	C₄×C₅₃	1	2	yes	—
111	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
112	C₂×C₄×C₈	C₂²×C₅₃	1	2	yes	—
113	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
114	Q₈⋊C₈	C₄×C₅₃	1	4	yes	—
115	D₄⋊C₈	C₄×C₅₃	1	4	yes	—
116	#322	—	2	2	no	—
117	C₈²	—	2	2	no	—
118	C₅₃	#8187	1	1	yes	characteristic, direct product factor, Sylow
119	C₂×#41	C₂×C₄×C₅₃	1	1	yes	characteristic
120	C₂×M₁₆	C₂×C₄×C₅₃	1	2	yes	—
121	C₂²×C₈	—	2	2	no	—
122	C₂²×C₈	C₂×C₄×C₅₃	1	2	yes	—
123	C₄×Q₈	C₂×C₄×C₅₃	1	2	yes	—
124	C₄×D₄	—	2	2	no	—
125	C₄×D₄	C₂×C₄×C₅₃	1	2	yes	—
126	#117	—	2	1	no	—
127	#117	C₂×C₄×C₅₃	1	1	yes	characteristic
128	C₂×C₄²	—	2	1	no	—
129	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
130	C₄⋊C₈	—	2	4	no	—
131	C₄⋊C₈	C₂×C₄×C₅₃	1	4	yes	—
132	C₂²⋊C₈	—	2	2	no	—
133	C₂²⋊C₈	—	2	4	no	—
134	#97	—	2	1	no	—
135	C₄×C₈	—	2	2	no	—
136	C₄×C₈	—	2	2	no	—
137	C₄×C₈	—	2	1	no	—
138	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	—
139	C₄×C₈	D₄×C₅₃	1	2	yes	—
140	C₄×C₈	D₄×C₅₃	1	2	yes	—
141	#41	—	2	4	no	—
142	C₂×Q₈	C₄²×C₅₃	1	1	yes	characteristic
143	C₂×D₄	—	2	1	no	—
144	C₂×D₄	C₄²×C₅₃	1	1	yes	characteristic
145	C₂²×C₄	—	2	1	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
148	C₂²×C₄	#41×C₅₃	1	2	yes	—
149	M₁₆	—	2	4	no	—
150	C₂×C₈	—	2	8	no	—
151	C₂×C₈	—	2	4	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	C₂²⋊C₄×C₅₃	1	4	yes	—
156	C₄⋊C₄	—	2	2	no	—
157	C₄⋊C₄	C₄²×C₅₃	1	2	yes	—
158	C₂²⋊C₄	—	2	1	no	—
159	C₂²⋊C₄	—	2	2	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	2	2	no	—
162	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
163	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
164	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
165	C₂³	—	2	1	no	—
166	C₂³	#117×C₅₃	1	1	yes	characteristic
167	Q₈	—	2	2	no	—
168	D₄	—	2	2	no	—
169	D₄	—	4	2	no	—
170	C₂×C₄	—	2	4	no	—
171	C₂×C₄	—	2	2	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	4	4	no	—
175	C₂×C₄	C₂×C₄²×C₅₃	1	1	yes	characteristic
176	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
177	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
178	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
179	C₂×C₄	#131×C₅₃	1	4	yes	—
180	C₈	—	2	8	no	—
181	C₈	—	2	4	no	—
182	C₈	—	4	2	no	—
183	C₈	—	4	4	no	—
184	C₂²	—	2	2	no	—
185	C₂²	—	4	1	no	—
186	C₂²	—	4	2	no	—
187	C₂²	C₄×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
188	C₂²	C₅₃×#433	1	2	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	4	1	no	—
191	C₄	—	4	2	no	—
192	C₄	C₅₃×#405	1	2	yes	—
193	C₄	C₅₃×#408	1	2	yes	—
194	C₄	C₅₃×#443	1	4	yes	—
195	C₂	—	2	2	no	—
196	C₂	—	8	1	no	—
197	C₂	C₅₃×#1750	1	1	yes	characteristic
198	C₂	C₅₃×#1764	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅₃×#2922

C₂

yes

maximal, characteristic

C₅₃×#1476

C₂

yes

maximal

C₅₃×#1452

C₂

yes

maximal, characteristic, complemented

C₂×C₈²×C₅₃

C₂

yes

maximal, characteristic, complemented

C₅₃×#1278

C₂

yes

maximal, complemented

C₄×#41×C₅₃

C₂²

yes

characteristic

C₅₃×#433

—

C₅₃×#431

—

C₅₃×#431

C₂²

yes

—

C₅₃×#424

C₄

yes

—

C₅₃×#408

C₄

yes

—

C₄×M₁₆×C₅₃

C₂²

yes

characteristic

C₂×C₄×C₈×C₅₃

C₂²

yes

—

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₅₃×Q₈⋊C₈

C₄

yes

—

C₅₃×D₄⋊C₈

C₄

yes

—

C₅₃×#322

—

C₈²×C₅₃

—

C₂×#41×C₅₃

C₂×C₄

yes

characteristic

C₂×M₁₆×C₅₃

C₂×C₄

yes

—

C₂²×C₈×C₅₃

—

C₂²×C₈×C₅₃

C₂×C₄

yes

—

C₄×Q₈×C₅₃

C₂×C₄

yes

—

C₄×D₄×C₅₃

—

C₄×D₄×C₅₃

C₂×C₄

yes

—

#117×C₅₃

—

#117×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

C₄⋊C₈×C₅₃

—

C₄⋊C₈×C₅₃

C₂×C₄

yes

—

C₂²⋊C₈×C₅₃

—

C₂²⋊C₈×C₅₃

—

#97×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

C₂×C₄

yes

—

C₄×C₈×C₅₃

D₄

yes

—

C₄×C₈×C₅₃

D₄

yes

—

#41×C₅₃

—

C₂×Q₈×C₅₃

C₄²

yes

characteristic

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

C₄²

yes

characteristic

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₃

#41

yes

—

M₁₆×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

C₄²

yes

—

C₂²⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂²×C₄

yes

—

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₂³×C₅₃

—

C₂³×C₅₃

#117

yes

characteristic

Q₈×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₄²

yes

characteristic

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

C₄×D₄

yes

—

C₂×C₄×C₅₃

#131

yes

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

#8187

C₅₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

C₄×C₂²⋊C₄

yes

characteristic

C₂²×C₅₃

#433

yes

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

—

C₄×C₅₃

#405

yes

—

C₄×C₅₃

#408

yes

—

C₄×C₅₃

#443

yes

—

#2922

C₂×C₅₃

yes

characteristic

#1476

C₂×C₅₃

yes

—

#1452

C₂×C₅₃

yes

characteristic, complemented

C₂×C₈²

C₂×C₅₃

yes

characteristic, complemented

100

#1278

C₂×C₅₃

yes

complemented

101

C₂×C₅₃

—

102

C₂×C₅₃

—

103

C₂×C₅₃

#1750

yes

characteristic

104

C₂×C₅₃

#1764

yes

—

105

C₄×#41

C₂²×C₅₃

yes

characteristic

106

#433

—

107

#431

—

108

#431

C₂²×C₅₃

yes

—

109

#424

C₄×C₅₃

yes

—

110

#408

C₄×C₅₃

yes

—

111

C₄×M₁₆

C₂²×C₅₃

yes

characteristic

112

C₂×C₄×C₈

C₂²×C₅₃

yes

—

113

C₂×C₄×C₈

C₂²×C₅₃

yes

characteristic

114

Q₈⋊C₈

C₄×C₅₃

yes

—

115

D₄⋊C₈

C₄×C₅₃

yes

—

116

#322

—

117

C₈²

—

118

C₅₃

#8187

yes

characteristic, direct product factor, Sylow

119

C₂×#41

C₂×C₄×C₅₃

yes

characteristic

120

C₂×M₁₆

C₂×C₄×C₅₃

yes

—

121

C₂²×C₈

—

122

C₂²×C₈

C₂×C₄×C₅₃

yes

—

123

C₄×Q₈

C₂×C₄×C₅₃

yes

—

124

C₄×D₄

—

125

C₄×D₄

C₂×C₄×C₅₃

yes

—

126

#117

—

127

#117

C₂×C₄×C₅₃

yes

characteristic

128

C₂×C₄²

—

129

C₂×C₄²

C₂³×C₅₃

yes

characteristic

130

C₄⋊C₈

—

131

C₄⋊C₈

C₂×C₄×C₅₃

yes

—

132

C₂²⋊C₈

—

133

C₂²⋊C₈

—

134

#97

—

135

C₄×C₈

—

136

C₄×C₈

—

137

C₄×C₈

—

138

C₄×C₈

C₂×C₄×C₅₃

yes

—

139

C₄×C₈

D₄×C₅₃

yes

—

140

C₄×C₈

D₄×C₅₃

yes

—

141

#41

—

142

C₂×Q₈

C₄²×C₅₃

yes

characteristic

143

C₂×D₄

—

144

C₂×D₄

C₄²×C₅₃

yes

characteristic

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²×C₄×C₅₃

yes

characteristic

148

C₂²×C₄

#41×C₅₃

yes

—

149

M₁₆

—

150

C₂×C₈

—

151

C₂×C₈

—

152

C₂×C₈

—

153

C₂×C₈

—

154

C₂×C₈

—

155

C₂×C₈

C₂²⋊C₄×C₅₃

yes

—

156

C₄⋊C₄

—

157

C₄⋊C₄

C₄²×C₅₃

yes

—

158

C₂²⋊C₄

—

159

C₂²⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

C₂²×C₄×C₅₃

yes

—

163

C₄²

C₂×D₄×C₅₃

yes

characteristic

164

C₄²

C₂×D₄×C₅₃

yes

characteristic

165

C₂³

—

166

C₂³

#117×C₅₃

yes

characteristic

167

Q₈

—

168

D₄

—

169

D₄

—

170

C₂×C₄

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

C₂×C₄²×C₅₃

yes

characteristic

176

C₂×C₄

C₂×C₂²⋊C₄×C₅₃

yes

characteristic

177

C₂×C₄

C₄×D₄×C₅₃

yes

—

178

C₂×C₄

C₄×D₄×C₅₃

yes

—

179

C₂×C₄

#131×C₅₃

yes

—

180

C₈

—

181

C₈

—

182

C₈

—

183

C₈

—

184

C₂²

—

185

C₂²

—

186

C₂²

—

187

C₂²

C₄×C₂²⋊C₄×C₅₃

yes

characteristic

188

C₂²

C₅₃×#433

yes

—

189

C₄

—

190

C₄

—

191

C₄

—

192

C₄

C₅₃×#405

yes

—

193

C₄

C₅₃×#408

yes

—

194

C₄

C₅₃×#443

yes

—

195

C₂

—

196

C₂

—

197

C₂

C₅₃×#1750

yes

characteristic

198

C₂

C₅₃×#1764

yes

—

	subgroup	G/H
center	C₄²×C₅₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
socle	C₂²×C₅₃	C₄×C₂²⋊C₄
prime radical	C₂×#41×C₅₃	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₅₃ ◁ C₂×C₄×C₈×C₅₃ ◁ G

subgroup

G/H

center

C₄²×C₅₃

C₂×D₄

commutator

C₂×C₄

C₂×C₄²×C₅₃

Frattini, cosocle

C₂×C₄²

C₂³×C₅₃

socle

C₂²×C₅₃

C₄×C₂²⋊C₄

prime radical

C₂×#41×C₅₃

C₂×C₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄²×C₅₃ ◁ C₂×C₄×C₈×C₅₃ ◁ G

N	H ≅ G/N	type
3. C₅₃×#1452	C₂	semidirect
4. C₂×C₈²×C₅₃	C₂	semidirect
5. C₅₃×#1278	C₂	semidirect
84. #8187	C₅₃	direct (N × H)
98. #1452	C₂×C₅₃	semidirect
99. C₂×C₈²	C₂×C₅₃	semidirect
100. #1278	C₂×C₅₃	semidirect
118. C₅₃	#8187	direct (N × H)

H ≅ G/N

type

3. C₅₃×#1452

C₂

semidirect

4. C₂×C₈²×C₅₃

C₂

semidirect

5. C₅₃×#1278

C₂

semidirect

84. #8187

C₅₃

direct (N × H)

98. #1452

C₂×C₅₃

semidirect

99. C₂×C₈²

C₂×C₅₃

semidirect

100. #1278

C₂×C₅₃

semidirect

118. C₅₃

#8187

direct (N × H)

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

subgroup	index
C₅₃×#2922	2
C₅₃×#1476	2
C₅₃×#1452	2
C₂×C₈²×C₅₃	2
C₅₃×#1278	2
#8187	53

subgroup

index

C₅₃×#2922

C₅₃×#1476

C₅₃×#1452

C₂×C₈²×C₅₃

C₅₃×#1278

#8187

Subgroups — C₅₃×#8187 #27215699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C53×#8187 #27215699

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#8187 #27215699