Group #20285318 — subgroups

Subgroups — #20285318

Order 6784.

364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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	#16811178	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811152	C₂	1	1	yes	maximal, characteristic
3	#16811032	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810991	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810982	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810878	C₂	1	2	yes	maximal, complemented
7	#16810866	C₂	1	2	yes	maximal
8	Q₁₆×Dic₅₃	C₂	1	2	yes	maximal, complemented
9	SD₁₆×Dic₅₃	C₂	1	2	yes	maximal, complemented
10	#16810575	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#497	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#11719912	C₂²	1	2	yes	—
13	#13133217	C₂²	1	1	yes	characteristic
14	#13133210	—	2	1	no	—
15	#13133209	C₂²	1	1	yes	characteristic
16	#13133208	—	2	1	no	—
17	#13133199	—	2	1	no	—
18	#13133197	—	2	1	no	—
19	#13133193	C₂²	1	2	yes	—
20	#13133193	C₂²	1	1	yes	characteristic
21	#13133188	C₂²	1	1	yes	characteristic
22	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
23	Q₈×Dic₅₃	C₂²	1	2	yes	—
24	#13133182	—	2	1	no	—
25	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
26	#13133177	—	2	1	no	—
27	#13133175	—	2	1	no	—
28	#13133173	—	2	1	no	—
29	C₄²×D₅₃	C₂²	1	1	yes	characteristic
30	#13133151	C₂²	1	2	yes	—
31	#13133149	C₂²	1	2	yes	—
32	#13133141	C₂²	1	2	yes	—
33	#13133141	C₂²	1	2	yes	—
34	#13133141	C₂²	1	2	yes	—
35	#13133138	C₂²	1	2	yes	—
36	#13133128	C₂²	1	1	yes	characteristic
37	C₈×Dic₅₃	C₂²	1	2	yes	—
38	C₂×Q₁₆×C₅₃	C₂²	1	2	yes	—
39	C₂×SD₁₆×C₅₃	C₂²	1	2	yes	—
40	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	#124×C₅₃	C₂²	1	1	yes	characteristic
42	#97×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
44	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
45	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
46	C₂×C₂²⋊D₅₃	—	2	1	no	—
47	C₂²×Dic₅₃	—	2	1	no	—
48	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
49	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
50	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
51	C₂×Dic₁₀₆	—	2	1	no	—
52	Q₁₆×C₅₃	—	2	4	no	—
53	SD₁₆×C₅₃	—	2	4	no	—
54	C₂×C₈×C₅₃	C₂³	1	2	yes	—
55	C₄⋊C₄×C₅₃	—	2	1	no	—
56	C₄⋊C₄×C₅₃	—	2	1	no	—
57	C₂²⋊C₄×C₅₃	—	2	1	no	—
58	C₂²⋊C₄×C₅₃	—	2	1	no	—
59	C₄²×C₅₃	C₂³	1	1	yes	characteristic
60	C₂²⋊Dic₅₃	—	2	1	no	—
61	C₂²⋊Dic₅₃	—	2	1	no	—
62	#11719921	—	2	2	no	—
63	#11719921	—	2	1	no	—
64	C₄⋊Dic₅₃	—	2	1	no	—
65	C₄⋊Dic₅₃	—	2	2	no	—
66	C₄⋊Dic₅₃	—	2	1	no	—
67	C₄⋊Dic₅₃	C₂³	1	2	yes	—
68	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
69	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
70	#11719919	—	2	1	no	—
71	#11719919	—	2	1	no	—
72	#11719919	—	2	1	no	—
73	#11719919	—	2	2	no	—
74	C₄×Dic₅₃	—	2	1	no	—
75	C₄×Dic₅₃	—	2	2	no	—
76	C₄×Dic₅₃	D₄	1	1	yes	characteristic
77	C₄×Dic₅₃	D₄	1	1	yes	characteristic
78	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
79	C₂×#88322	C₂³	1	2	yes	—
80	#11719912	—	2	4	no	—
81	C₂³×C₅₃	—	2	1	no	—
82	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
83	Q₈×C₅₃	—	2	2	no	—
84	Q₈×C₅₃	—	2	2	no	—
85	Q₈×C₅₃	—	2	2	no	—
86	D₄×C₅₃	—	2	2	no	—
87	C₂×C₄×C₅₃	—	2	1	no	—
88	C₂×C₄×C₅₃	—	2	2	no	—
89	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
91	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
92	C₂²⋊D₅₃	—	4	2	no	—
93	C₂×Dic₅₃	—	2	2	no	—
94	C₂×Dic₅₃	—	2	1	no	—
95	C₂×Dic₅₃	—	2	1	no	—
96	C₂×Dic₅₃	—	4	2	no	—
97	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
99	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
100	C₄×D₅₃	—	2	2	no	—
101	C₄×D₅₃	—	2	2	no	—
102	C₄×D₅₃	—	4	1	no	—
103	Dic₁₀₆	—	4	2	no	—
104	C₈×C₅₃	#41	1	4	yes	—
105	#88322	—	2	2	no	—
106	C₂²×C₅₃	—	4	1	no	—
107	C₂²×C₅₃	—	4	1	no	—
108	C₂²×C₅₃	—	4	1	no	—
109	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
110	C₂×D₅₃	—	2	1	no	—
111	C₂×D₅₃	—	2	1	no	—
112	C₂×D₅₃	—	2	1	no	—
113	C₄×C₅₃	—	2	1	no	—
114	C₄×C₅₃	—	2	1	no	—
115	C₄×C₅₃	—	4	1	no	—
116	C₄×C₅₃	—	4	2	no	—
117	C₄×C₅₃	C₂×#41	1	2	yes	—
118	Dic₅₃	—	2	1	no	—
119	Dic₅₃	—	2	1	no	—
120	Dic₅₃	—	4	1	no	—
121	Dic₅₃	—	4	2	no	—
122	Dic₅₃	—	4	1	no	—
123	Dic₅₃	#137	1	2	yes	—
124	#3172	—	53	1	no	maximal, Sylow
125	C₂×C₅₃	—	8	1	no	—
126	C₂×C₅₃	#532	1	1	yes	characteristic
127	C₂×C₅₃	C₂×#137	1	1	yes	characteristic
128	C₂×C₅₃	#575	1	1	yes	characteristic
129	D₅₃	—	4	1	no	—
130	#533	—	53	1	no	—
131	#529	—	53	1	no	—
132	#501	—	53	1	no	—
133	#497	D₅₃	1	1	yes	characteristic, complemented
134	#491	—	53	1	no	—
135	#489	—	53	1	no	—
136	#470	—	53	2	no	—
137	#468	—	53	2	no	—
138	C₄×Q₁₆	—	53	2	no	—
139	C₄×SD₁₆	—	53	2	no	—
140	C₄×M₁₆	—	53	1	no	—
141	C₅₃	#3172	1	1	yes	characteristic, complemented, Sylow
142	C₂×Q₁₆	C₂×D₅₃	1	2	yes	—
143	C₂×SD₁₆	C₂×D₅₃	1	2	yes	—
144	C₂×M₁₆	—	53	2	no	—
145	C₄⋊Q₈	—	53	1	no	—
146	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
147	#126	—	106	1	no	—
148	#125	—	53	1	no	—
149	#125	—	106	1	no	—
150	#124	C₂×D₅₃	1	1	yes	characteristic
151	#123	—	106	1	no	—
152	C₂²⋊Q₈	—	53	1	no	—
153	C₂²⋊Q₈	—	53	2	no	—
154	C₂²⋊Q₈	—	106	1	no	—
155	#121	—	53	1	no	—
156	C₄×Q₈	—	53	1	no	—
157	C₄×Q₈	—	53	2	no	—
158	C₄×Q₈	—	106	1	no	—
159	C₄×D₄	—	53	1	no	—
160	C₄×D₄	—	106	1	no	—
161	#117	—	106	1	no	—
162	#117	—	106	1	no	—
163	C₂×C₄²	—	53	1	no	—
164	#107	—	53	2	no	—
165	#106	—	53	2	no	—
166	#103	—	53	2	no	—
167	#103	—	53	2	no	—
168	#103	—	53	2	no	—
169	#102	—	53	2	no	—
170	#97	—	53	1	no	—
171	#97	C₂×D₅₃	1	1	yes	characteristic
172	C₄×C₈	—	53	2	no	—
173	C₂×Q₈	—	106	1	no	—
174	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
175	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
176	C₂×D₄	—	106	1	no	—
177	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
178	C₂²×C₄	—	53	1	no	—
179	C₂²×C₄	—	53	1	no	—
180	C₂²×C₄	—	53	1	no	—
181	C₂²×C₄	—	106	1	no	—
182	Q₁₆	—	2	4	no	—
183	SD₁₆	—	2	4	no	—
184	M₁₆	—	106	4	no	—
185	C₂×C₈	—	53	2	no	—
186	C₂×C₈	C₂²×D₅₃	1	2	yes	—
187	C₄⋊C₄	—	2	1	no	—
188	C₄⋊C₄	—	2	1	no	—
189	C₄⋊C₄	—	53	2	no	—
190	C₄⋊C₄	—	53	1	no	—
191	C₄⋊C₄	—	53	1	no	—
192	C₄⋊C₄	—	106	1	no	—
193	C₄⋊C₄	—	106	2	no	—
194	C₄⋊C₄	—	106	1	no	—
195	C₄⋊C₄	—	106	2	no	—
196	C₄⋊C₄	—	106	1	no	—
197	C₄⋊C₄	—	106	1	no	—
198	C₄⋊C₄	—	106	1	no	—
199	C₂²⋊C₄	—	2	1	no	—
200	C₂²⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	106	2	no	—
202	C₂²⋊C₄	—	106	1	no	—
203	C₂²⋊C₄	—	106	1	no	—
204	C₂²⋊C₄	—	106	1	no	—
205	C₄²	—	53	1	no	—
206	C₄²	—	53	1	no	—
207	C₄²	—	53	1	no	—
208	C₄²	—	106	1	no	—
209	C₄²	—	106	2	no	—
210	C₄²	C₂²×D₅₃	1	1	yes	characteristic
211	C₂³	—	2	1	no	—
212	C₂³	—	53	1	no	—
213	Q₈	—	2	2	no	—
214	Q₈	—	2	2	no	—
215	Q₈	—	2	2	no	—
216	Q₈	—	212	2	no	—
217	D₄	—	2	2	no	—
218	D₄	—	212	2	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	2	no	—
221	C₂×C₄	—	53	1	no	—
222	C₂×C₄	—	53	1	no	—
223	C₂×C₄	—	53	1	no	—
224	C₂×C₄	—	106	2	no	—
225	C₂×C₄	—	106	2	no	—
226	C₂×C₄	—	106	1	no	—
227	C₂×C₄	—	106	2	no	—
228	C₂×C₄	—	106	1	no	—
229	C₂×C₄	—	212	1	no	—
230	C₂×C₄	—	212	2	no	—
231	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
232	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
233	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
234	C₈	—	106	2	no	—
235	C₈	#11719947	1	4	yes	—
236	C₂²	—	4	1	no	—
237	C₂²	—	4	1	no	—
238	C₂²	—	4	1	no	—
239	C₂²	—	106	1	no	—
240	C₂²	—	106	1	no	—
241	C₂²	—	106	1	no	—
242	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	4	1	no	—
246	C₄	—	4	2	no	—
247	C₄	—	53	2	no	—
248	C₄	—	106	1	no	—
249	C₄	—	106	1	no	—
250	C₄	—	212	1	no	—
251	C₄	—	212	1	no	—
252	C₄	—	212	2	no	—
253	C₄	C₂×#11719947	1	2	yes	—
254	C₂	—	8	1	no	—
255	C₂	—	212	1	no	—
256	C₂	#16811171	1	1	yes	characteristic
257	C₂	#137×D₅₃	1	1	yes	characteristic
258	C₂	#16811422	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16811178

C₂

yes

maximal, characteristic, complemented

#16811152

C₂

yes

maximal, characteristic

#16811032

C₂

yes

maximal, characteristic, complemented

#16810991

C₂

yes

maximal, characteristic, complemented

#16810982

C₂

yes

maximal, characteristic, complemented

#16810878

C₂

yes

maximal, complemented

#16810866

C₂

yes

maximal

Q₁₆×Dic₅₃

C₂

yes

maximal, complemented

SD₁₆×Dic₅₃

C₂

yes

maximal, complemented

#16810575

C₂

yes

maximal, characteristic, complemented

C₅₃×#497

C₂

yes

maximal, characteristic, complemented

C₂×#11719912

C₂²

yes

—

#13133217

C₂²

yes

characteristic

#13133210

—

#13133209

C₂²

yes

—

—

—

C₂²

yes

—

#13133193

C₂²

yes

characteristic

#13133188

C₂²

yes

characteristic

Q₈×Dic₅₃

C₂²

yes

characteristic

Q₈×Dic₅₃

C₂²

yes

—

#13133182

—

D₄×Dic₅₃

C₂²

yes

—

—

—

C₄²×D₅₃

C₂²

yes

characteristic

#13133151

C₂²

yes

—

#13133149

C₂²

yes

—

#13133141

C₂²

yes

—

#13133141

C₂²

yes

—

#13133141

C₂²

yes

—

#13133138

C₂²

yes

—

#13133128

C₂²

yes

characteristic

C₈×Dic₅₃

C₂²

yes

—

C₂×Q₁₆×C₅₃

C₂²

yes

—

C₂×SD₁₆×C₅₃

C₂²

yes

—

C₄⋊Q₈×C₅₃

C₂²

yes

characteristic

#124×C₅₃

C₂²

yes

characteristic

#97×C₅₃

C₂²

yes

characteristic

C₂×Q₈×C₅₃

C₂³

yes

characteristic

C₂×Q₈×C₅₃

C₂³

yes

—

C₂×D₄×C₅₃

C₂³

yes

characteristic

C₂×C₂²⋊D₅₃

—

C₂²×Dic₅₃

—

C₂×C₄×D₅₃

D₄

yes

characteristic

C₂×C₄×D₅₃

D₄

yes

characteristic

C₂×C₄×D₅₃

C₂³

yes

characteristic

C₂×Dic₁₀₆

—

Q₁₆×C₅₃

—

SD₁₆×C₅₃

—

C₂×C₈×C₅₃

C₂³

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₄²×C₅₃

C₂³

yes

characteristic

C₂²⋊Dic₅₃

—

C₂²⋊Dic₅₃

—

#11719921

—

#11719921

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

C₂³

yes

—

C₄⋊Dic₅₃

C₂³

yes

characteristic

C₄⋊Dic₅₃

C₂³

yes

—

—

—

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

D₄

yes

characteristic

C₄×Dic₅₃

D₄

yes

characteristic

C₄×Dic₅₃

C₂³

yes

characteristic

C₂×#88322

C₂³

yes

—

#11719912

—

C₂³×C₅₃

—

C₂²×D₅₃

C₂×D₄

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂⁴

yes

characteristic

C₂²⋊D₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

C₂×D₄

yes

characteristic

C₂×Dic₅₃

C₂×D₄

yes

characteristic

C₂×Dic₅₃

C₂×D₄

yes

characteristic

100

C₄×D₅₃

—

101

C₄×D₅₃

—

102

C₄×D₅₃

—

103

Dic₁₀₆

—

104

C₈×C₅₃

#41

yes

—

105

#88322

—

106

C₂²×C₅₃

—

107

C₂²×C₅₃

—

108

C₂²×C₅₃

—

109

C₂²×C₅₃

C₂²×D₄

yes

characteristic

110

C₂×D₅₃

—

111

C₂×D₅₃

—

112

C₂×D₅₃

—

113

C₄×C₅₃

—

114

C₄×C₅₃

—

115

C₄×C₅₃

—

116

C₄×C₅₃

—

117

C₄×C₅₃

C₂×#41

yes

—

118

Dic₅₃

—

119

Dic₅₃

—

120

Dic₅₃

—

121

Dic₅₃

—

122

Dic₅₃

—

123

Dic₅₃

#137

yes

—

124

#3172

—

maximal, Sylow

125

C₂×C₅₃

—

126

C₂×C₅₃

#532

yes

characteristic

127

C₂×C₅₃

C₂×#137

yes

characteristic

128

C₂×C₅₃

#575

yes

characteristic

129

D₅₃

—

130

#533

—

131

#529

—

132

#501

—

133

#497

D₅₃

yes

characteristic, complemented

134

#491

—

135

#489

—

136

#470

—

137

#468

—

138

C₄×Q₁₆

—

139

C₄×SD₁₆

—

140

C₄×M₁₆

—

141

C₅₃

#3172

yes

characteristic, complemented, Sylow

142

C₂×Q₁₆

C₂×D₅₃

yes

—

143

C₂×SD₁₆

C₂×D₅₃

yes

—

144

C₂×M₁₆

—

145

C₄⋊Q₈

—

146

C₄⋊Q₈

C₂×D₅₃

yes

characteristic

147

#126

—

106

—

148

#125

—

149

#125

—

106

—

150

#124

C₂×D₅₃

yes

characteristic

151

#123

—

106

—

152

C₂²⋊Q₈

—

153

C₂²⋊Q₈

—

154

C₂²⋊Q₈

—

106

—

155

#121

—

156

C₄×Q₈

—

157

C₄×Q₈

—

158

C₄×Q₈

—

106

—

159

C₄×D₄

—

160

C₄×D₄

—

106

—

161

#117

—

106

—

162

#117

—

106

—

163

C₂×C₄²

—

164

#107

—

165

#106

—

166

#103

—

167

#103

—

168

#103

—

169

#102

—

170

#97

—

171

#97

C₂×D₅₃

yes

characteristic

172

C₄×C₈

—

173

C₂×Q₈

—

106

—

174

C₂×Q₈

C₂²×D₅₃

yes

characteristic

175

C₂×Q₈

C₂²×D₅₃

yes

—

176

C₂×D₄

—

106

—

177

C₂×D₄

C₂²×D₅₃

yes

characteristic

178

C₂²×C₄

—

179

C₂²×C₄

—

180

C₂²×C₄

—

181

C₂²×C₄

—

106

—

182

Q₁₆

—

183

SD₁₆

—

184

M₁₆

—

106

—

185

C₂×C₈

—

186

C₂×C₈

C₂²×D₅₃

yes

—

187

C₄⋊C₄

—

188

C₄⋊C₄

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

106

—

193

C₄⋊C₄

—

106

—

194

C₄⋊C₄

—

106

—

195

C₄⋊C₄

—

106

—

196

C₄⋊C₄

—

106

—

197

C₄⋊C₄

—

106

—

198

C₄⋊C₄

—

106

—

199

C₂²⋊C₄

—

200

C₂²⋊C₄

—

201

C₂²⋊C₄

—

106

—

202

C₂²⋊C₄

—

106

—

203

C₂²⋊C₄

—

106

—

204

C₂²⋊C₄

—

106

—

205

C₄²

—

206

C₄²

—

207

C₄²

—

208

C₄²

—

106

—

209

C₄²

—

106

—

210

C₄²

C₂²×D₅₃

yes

characteristic

211

C₂³

—

212

C₂³

—

213

Q₈

—

214

Q₈

—

215

Q₈

—

216

Q₈

—

212

—

217

D₄

—

218

D₄

—

212

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

106

—

225

C₂×C₄

—

106

—

226

C₂×C₄

—

106

—

227

C₂×C₄

—

106

—

228

C₂×C₄

—

106

—

229

C₂×C₄

—

212

—

230

C₂×C₄

—

212

—

231

C₂×C₄

D₄×D₅₃

yes

characteristic

232

C₂×C₄

D₄×D₅₃

yes

characteristic

233

C₂×C₄

C₂³×D₅₃

yes

characteristic

234

C₈

—

106

—

235

C₈

#11719947

yes

—

236

C₂²

—

237

C₂²

—

238

C₂²

—

239

C₂²

—

106

—

240

C₂²

—

106

—

241

C₂²

—

106

—

242

C₂²

C₂×D₄×D₅₃

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

246

C₄

—

247

C₄

—

248

C₄

—

106

—

249

C₄

—

106

—

250

C₄

—

212

—

251

C₄

—

212

—

252

C₄

—

212

—

253

C₄

C₂×#11719947

yes

—

254

C₂

—

255

C₂

—

212

—

256

C₂

#16811171

yes

characteristic

257

C₂

#137×D₅₃

yes

characteristic

258

C₂

#16811422

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#497	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#497	D₅₃
hypocenter	C₅₃	#3172
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #497

subgroup

G/H

center

C₂²

C₂×D₄×D₅₃

commutator

C₂×C₄×C₅₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₅₃

Fitting

C₅₃×#497

C₂

socle

C₂²×C₅₃

C₂²×D₄

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #497

N	H ≅ G/N	type
1. #16811178	C₂	semidirect
3. #16811032	C₂	semidirect
4. #16810991	C₂	semidirect
5. #16810982	C₂	semidirect
6. #16810878	C₂	semidirect
8. Q₁₆×Dic₅₃	C₂	semidirect
9. SD₁₆×Dic₅₃	C₂	semidirect
10. #16810575	C₂	semidirect
11. C₅₃×#497	C₂	semidirect
133. #497	D₅₃	semidirect
141. C₅₃	#3172	semidirect

H ≅ G/N

type

1. #16811178

C₂

semidirect

3. #16811032

C₂

semidirect

4. #16810991

C₂

semidirect

5. #16810982

C₂

semidirect

6. #16810878

C₂

semidirect

8. Q₁₆×Dic₅₃

C₂

semidirect

9. SD₁₆×Dic₅₃

C₂

semidirect

10. #16810575

C₂

semidirect

11. C₅₃×#497

C₂

semidirect

133. #497

D₅₃

semidirect

141. C₅₃

#3172

semidirect

Subgroups — #20285318

Conjugacy classes of subgroups

Complements