Group #20275057 — subgroups

Subgroups — #20275057

Order 6784.

338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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	C₂²×Dic₂₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#13133182	C₂	1	1	yes	maximal, characteristic
3	C₂×#13133140	C₂	1	1	yes	maximal, characteristic
4	C₂×#13133140	C₂	1	1	yes	maximal, characteristic
5	#16810528	C₂	1	1	yes	maximal, characteristic
6	#16810377	C₂	1	1	yes	maximal, characteristic
7	C₅₃×#340	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic
10	C₂×Dic₂₁₂	—	2	2	no	—
11	C₂×Dic₂₁₂	—	2	2	no	—
12	C₂×Dic₂₁₂	C₄	1	4	yes	complemented
13	C₂²×#88322	C₂²	1	1	yes	characteristic
14	#13133182	—	2	2	no	—
15	#13133182	—	2	2	no	—
16	C₂×#11719919	—	2	1	no	—
17	C₂×C₄×Dic₅₃	—	2	1	no	—
18	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
19	#13133140	—	2	2	no	—
20	#13133140	—	2	2	no	—
21	#13133124	—	2	1	no	—
22	#13133124	—	2	1	no	—
23	C₂²×C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄×C₅₃	—	2	1	no	—
27	C₂²×C₄×C₅₃	—	2	1	no	—
28	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
29	C₂²×Dic₅₃	—	2	1	no	—
30	C₂²×Dic₅₃	—	2	1	no	—
31	C₂²×Dic₅₃	D₄	1	1	yes	characteristic
32	C₂²×Dic₅₃	D₄	1	1	yes	characteristic
33	C₂×Dic₁₀₆	—	2	1	no	—
34	C₂×Dic₁₀₆	—	2	1	no	—
35	C₂×Dic₁₀₆	—	2	1	no	—
36	C₂×Dic₁₀₆	—	2	1	no	—
37	C₂×Dic₁₀₆	—	2	1	no	—
38	C₂×Dic₁₀₆	—	2	1	no	—
39	C₂×Dic₁₀₆	—	2	1	no	—
40	C₂×Dic₁₀₆	—	2	1	no	—
41	C₂×Dic₁₀₆	C₂×C₄	1	2	yes	—
42	C₂×Dic₁₀₆	C₂×C₄	1	2	yes	—
43	C₂×Dic₁₀₆	D₄	1	2	yes	—
44	C₂×Dic₁₀₆	D₄	1	2	yes	—
45	C₂×C₈×C₅₃	—	2	1	no	—
46	C₂×C₈×C₅₃	—	2	1	no	—
47	C₂×C₈×C₅₃	C₂×C₄	1	2	yes	—
48	C₄⋊C₄×C₅₃	—	2	1	no	—
49	C₄⋊C₄×C₅₃	—	2	1	no	—
50	C₄⋊C₄×C₅₃	—	2	1	no	—
51	C₄⋊C₄×C₅₃	D₄	1	2	yes	—
52	#11719919	—	2	4	no	—
53	C₄×Dic₅₃	—	2	4	no	—
54	C₄×Dic₅₃	—	2	1	no	—
55	C₄×Dic₅₃	—	2	1	no	—
56	C₂×#88322	—	2	1	no	—
57	C₂×#88322	—	2	1	no	—
58	C₂×#88322	—	2	1	no	—
59	Dic₂₁₂	—	2	8	no	—
60	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₅₃	—	2	2	no	—
62	C₂×C₄×C₅₃	—	4	1	no	—
63	C₂×C₄×C₅₃	—	4	1	no	—
64	C₂×C₄×C₅₃	—	4	1	no	—
65	C₂×C₄×C₅₃	—	4	1	no	—
66	C₂×C₄×C₅₃	—	4	1	no	—
67	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₅₃	#41	1	1	yes	characteristic
72	C₂×C₄×C₅₃	#41	1	1	yes	characteristic
73	C₂×Dic₅₃	—	2	2	no	—
74	C₂×Dic₅₃	—	2	2	no	—
75	C₂×Dic₅₃	—	2	1	no	—
76	C₂×Dic₅₃	—	2	2	no	—
77	C₂×Dic₅₃	—	2	1	no	—
78	C₂×Dic₅₃	—	2	2	no	—
79	C₂×Dic₅₃	—	2	1	no	—
80	C₂×Dic₅₃	—	2	1	no	—
81	C₂×Dic₅₃	—	2	1	no	—
82	C₂×Dic₅₃	—	4	1	no	—
83	C₂×Dic₅₃	—	4	1	no	—
84	C₂×Dic₅₃	Q₁₆	1	2	yes	complemented
85	Dic₁₀₆	—	2	2	no	—
86	Dic₁₀₆	—	2	2	no	—
87	Dic₁₀₆	—	2	2	no	—
88	Dic₁₀₆	—	2	2	no	—
89	Dic₁₀₆	—	2	2	no	—
90	Dic₁₀₆	—	4	1	no	—
91	Dic₁₀₆	—	4	1	no	—
92	Dic₁₀₆	C₂²⋊C₄	1	4	yes	—
93	C₈×C₅₃	—	2	2	no	—
94	#88322	—	4	1	no	—
95	C₂²×C₅₃	C₄×D₄	1	1	yes	characteristic
96	C₂²×C₅₃	#120	1	1	yes	characteristic
97	C₂²×C₅₃	#121	1	1	yes	characteristic
98	C₂²×C₅₃	C₂×Q₁₆	1	1	yes	characteristic
99	C₂²×C₅₃	#135	1	1	yes	characteristic
100	C₂²×C₅₃	#137	1	1	yes	characteristic
101	C₂²×C₅₃	#137	1	1	yes	characteristic
102	C₄×C₅₃	—	4	2	no	—
103	C₄×C₅₃	—	8	1	no	—
104	C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
106	C₄×C₅₃	#121	1	1	yes	characteristic
107	C₄×C₅₃	#123	1	1	yes	characteristic
108	Dic₅₃	—	2	4	no	—
109	Dic₅₃	—	2	2	no	—
110	Dic₅₃	—	4	2	no	—
111	Dic₅₃	—	4	1	no	—
112	#1878	—	53	1	no	maximal, Sylow
113	C₂×C₅₃	#386	1	1	yes	characteristic
114	C₂×C₅₃	C₄×Q₁₆	1	1	yes	characteristic
115	C₂×C₅₃	#441	1	1	yes	characteristic
116	C₂×C₅₃	#451	1	1	yes	characteristic
117	C₂×C₅₃	#452	1	1	yes	characteristic
118	C₂×C₅₃	#462	1	1	yes	characteristic
119	C₂×C₅₃	#464	1	1	yes	characteristic
120	C₂²×Q₁₆	—	53	1	no	—
121	C₂×C₄×Q₈	—	53	1	no	—
122	C₂×#103	—	53	1	no	—
123	C₂×#103	—	53	1	no	—
124	#391	—	53	1	no	—
125	#340	D₅₃	1	1	yes	characteristic
126	#336	—	53	1	no	—
127	C₅₃	#1878	1	1	yes	characteristic, complemented, Sylow
128	C₂²×Q₈	—	53	1	no	—
129	C₂²×Q₈	—	53	1	no	—
130	C₂×Q₁₆	—	53	4	no	—
131	C₂×Q₁₆	—	106	2	no	—
132	C₂×Q₁₆	—	106	2	no	—
133	C₂²×C₈	—	53	1	no	—
134	C₂²×C₈	C₂×D₅₃	1	1	yes	characteristic
135	C₄×Q₈	—	106	2	no	—
136	C₄×Q₈	—	106	2	no	—
137	C₂×C₄⋊C₄	—	106	1	no	—
138	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
139	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
140	C₂×C₄²	—	53	1	no	—
141	C₂×C₄²	—	106	1	no	—
142	#103	—	106	2	no	—
143	#103	—	106	2	no	—
144	#95	—	106	1	no	—
145	#95	—	106	1	no	—
146	C₂×Q₈	—	53	2	no	—
147	C₂×Q₈	—	53	2	no	—
148	C₂×Q₈	—	53	2	no	—
149	C₂×Q₈	—	53	2	no	—
150	C₂×Q₈	—	106	1	no	—
151	C₂×Q₈	—	106	1	no	—
152	C₂×Q₈	—	106	1	no	—
153	C₂×Q₈	—	106	1	no	—
154	C₂×Q₈	—	106	1	no	—
155	C₂×Q₈	—	106	1	no	—
156	C₂×Q₈	—	106	1	no	—
157	C₂×Q₈	—	106	1	no	—
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	53	1	no	—
161	C₂²×C₄	—	53	1	no	—
162	C₂²×C₄	—	106	1	no	—
163	C₂²×C₄	—	106	1	no	—
164	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
165	Q₁₆	—	106	8	no	—
166	C₂×C₈	—	2	1	no	—
167	C₂×C₈	—	2	1	no	—
168	C₂×C₈	—	106	1	no	—
169	C₂×C₈	—	106	1	no	—
170	C₂×C₈	—	106	1	no	—
171	C₂×C₈	C₄×D₅₃	1	2	yes	—
172	C₄⋊C₄	—	2	1	no	—
173	C₄⋊C₄	—	2	1	no	—
174	C₄⋊C₄	—	2	1	no	—
175	C₄⋊C₄	—	106	4	no	—
176	C₄⋊C₄	D₂₁₂	1	2	yes	—
177	C₄²	—	106	4	no	—
178	C₄²	—	106	1	no	—
179	C₄²	—	106	1	no	—
180	C₂³	D₄×D₅₃	1	1	yes	characteristic
181	Q₈	—	53	4	no	—
182	Q₈	—	106	2	no	—
183	Q₈	—	106	2	no	—
184	Q₈	—	106	2	no	—
185	Q₈	—	106	2	no	—
186	Q₈	—	106	2	no	—
187	Q₈	—	212	1	no	—
188	Q₈	—	212	1	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	53	2	no	—
196	C₂×C₄	—	106	2	no	—
197	C₂×C₄	—	106	1	no	—
198	C₂×C₄	—	106	2	no	—
199	C₂×C₄	—	106	2	no	—
200	C₂×C₄	—	106	1	no	—
201	C₂×C₄	—	106	2	no	—
202	C₂×C₄	—	106	1	no	—
203	C₂×C₄	—	106	1	no	—
204	C₂×C₄	—	106	1	no	—
205	C₂×C₄	—	212	1	no	—
206	C₂×C₄	—	212	1	no	—
207	C₂×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
208	C₂×C₄	C₂×D₂₁₂	1	1	yes	characteristic
209	C₂×C₄	#11719945	1	1	yes	characteristic
210	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
211	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
212	C₂×C₄	#11719949	1	1	yes	characteristic
213	C₈	—	2	2	no	—
214	C₈	—	212	1	no	—
215	C₂²	#13133179	1	1	yes	characteristic
216	C₂²	#13133187	1	1	yes	characteristic
217	C₂²	#13133190	1	1	yes	characteristic
218	C₂²	Q₁₆×D₅₃	1	1	yes	characteristic
219	C₂²	#13133236	1	1	yes	characteristic
220	C₂²	#13133246	1	1	yes	characteristic
221	C₂²	#13133246	1	1	yes	characteristic
222	C₄	—	4	2	no	—
223	C₄	—	8	1	no	—
224	C₄	—	106	4	no	—
225	C₄	—	106	2	no	—
226	C₄	—	212	2	no	—
227	C₄	—	212	1	no	—
228	C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
229	C₄	C₄×D₂₁₂	1	1	yes	characteristic
230	C₄	#13133192	1	1	yes	characteristic
231	C₄	#13133202	1	1	yes	characteristic
232	C₂	#16810501	1	1	yes	characteristic
233	C₂	#16810717	1	1	yes	characteristic
234	C₂	#16810729	1	1	yes	characteristic
235	C₂	#16810780	1	1	yes	characteristic
236	C₂	#16810786	1	1	yes	characteristic
237	C₂	#16810832	1	1	yes	characteristic
238	C₂	#16810844	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₁₂

C₂

yes

maximal, characteristic

C₂×#13133182

C₂

yes

maximal, characteristic

C₂×#13133140

C₂

yes

maximal, characteristic

C₂×#13133140

C₂

yes

maximal, characteristic

#16810528

C₂

yes

maximal, characteristic

#16810377

C₂

yes

maximal, characteristic

C₅₃×#340

C₂

yes

maximal, characteristic

C₂²×Dic₁₀₆

C₂²

yes

characteristic

C₂²×Dic₁₀₆

C₂²

yes

characteristic

C₂×Dic₂₁₂

—

C₂×Dic₂₁₂

—

C₂×Dic₂₁₂

C₄

yes

complemented

C₂²×#88322

C₂²

yes

—

—

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

C₂²

yes

—

—

—

—

C₂²×C₈×C₅₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₅₃

C₂²

yes

characteristic

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂³

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

D₄

yes

characteristic

C₂²×Dic₅₃

D₄

yes

characteristic

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

—

C₂×Dic₁₀₆

C₂×C₄

yes

—

C₂×Dic₁₀₆

C₂×C₄

yes

—

C₂×Dic₁₀₆

D₄

yes

—

C₂×Dic₁₀₆

D₄

yes

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂×C₄

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

D₄

yes

—

#11719919

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₂×#88322

—

C₂×#88322

—

C₂×#88322

—

Dic₂₁₂

—

C₂³×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

Q₁₆

yes

complemented

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

—

Dic₁₀₆

C₂²⋊C₄

yes

—

C₈×C₅₃

—

#88322

—

C₂²×C₅₃

C₄×D₄

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

C₂×Q₁₆

yes

characteristic

C₂²×C₅₃

#135

yes

characteristic

100

C₂²×C₅₃

#137

yes

characteristic

101

C₂²×C₅₃

#137

yes

characteristic

102

C₄×C₅₃

—

103

C₄×C₅₃

—

104

C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

105

C₄×C₅₃

C₄×D₄

yes

characteristic

106

C₄×C₅₃

#121

yes

characteristic

107

C₄×C₅₃

#123

yes

characteristic

108

Dic₅₃

—

109

Dic₅₃

—

110

Dic₅₃

—

111

Dic₅₃

—

112

#1878

—

maximal, Sylow

113

C₂×C₅₃

#386

yes

characteristic

114

C₂×C₅₃

C₄×Q₁₆

yes

characteristic

115

C₂×C₅₃

#441

yes

characteristic

116

C₂×C₅₃

#451

yes

characteristic

117

C₂×C₅₃

#452

yes

characteristic

118

C₂×C₅₃

#462

yes

characteristic

119

C₂×C₅₃

#464

yes

characteristic

120

C₂²×Q₁₆

—

121

C₂×C₄×Q₈

—

122

C₂×#103

—

123

C₂×#103

—

124

#391

—

125

#340

D₅₃

yes

characteristic

126

#336

—

127

C₅₃

#1878

yes

characteristic, complemented, Sylow

128

C₂²×Q₈

—

129

C₂²×Q₈

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

106

—

132

C₂×Q₁₆

—

106

—

133

C₂²×C₈

—

134

C₂²×C₈

C₂×D₅₃

yes

characteristic

135

C₄×Q₈

—

106

—

136

C₄×Q₈

—

106

—

137

C₂×C₄⋊C₄

—

106

—

138

C₂×C₄⋊C₄

C₂×D₅₃

yes

characteristic

139

C₂×C₄⋊C₄

C₂×D₅₃

yes

characteristic

140

C₂×C₄²

—

141

C₂×C₄²

—

106

—

142

#103

—

106

—

143

#103

—

106

—

144

#95

—

106

—

145

#95

—

106

—

146

C₂×Q₈

—

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂×Q₈

—

106

—

151

C₂×Q₈

—

106

—

152

C₂×Q₈

—

106

—

153

C₂×Q₈

—

106

—

154

C₂×Q₈

—

106

—

155

C₂×Q₈

—

106

—

156

C₂×Q₈

—

106

—

157

C₂×Q₈

—

106

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

106

—

163

C₂²×C₄

—

106

—

164

C₂²×C₄

C₂²×D₅₃

yes

characteristic

165

Q₁₆

—

106

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

106

—

169

C₂×C₈

—

106

—

170

C₂×C₈

—

106

—

171

C₂×C₈

C₄×D₅₃

yes

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

106

—

176

C₄⋊C₄

D₂₁₂

yes

—

177

C₄²

—

106

—

178

C₄²

—

106

—

179

C₄²

—

106

—

180

C₂³

D₄×D₅₃

yes

characteristic

181

Q₈

—

182

Q₈

—

106

—

183

Q₈

—

106

—

184

Q₈

—

106

—

185

Q₈

—

106

—

186

Q₈

—

106

—

187

Q₈

—

212

—

188

Q₈

—

212

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

106

—

197

C₂×C₄

—

106

—

198

C₂×C₄

—

106

—

199

C₂×C₄

—

106

—

200

C₂×C₄

—

106

—

201

C₂×C₄

—

106

—

202

C₂×C₄

—

106

—

203

C₂×C₄

—

106

—

204

C₂×C₄

—

106

—

205

C₂×C₄

—

212

—

206

C₂×C₄

—

212

—

207

C₂×C₄

C₂×C₄×D₅₃

yes

characteristic

208

C₂×C₄

C₂×D₂₁₂

yes

characteristic

209

C₂×C₄

#11719945

yes

characteristic

210

C₂×C₄

D₄×D₅₃

yes

characteristic

211

C₂×C₄

D₄×D₅₃

yes

characteristic

212

C₂×C₄

#11719949

yes

characteristic

213

C₈

—

214

C₈

—

212

—

215

C₂²

#13133179

yes

characteristic

216

C₂²

#13133187

yes

characteristic

217

C₂²

#13133190

yes

characteristic

218

C₂²

Q₁₆×D₅₃

yes

characteristic

219

C₂²

#13133236

yes

characteristic

220

C₂²

#13133246

yes

characteristic

221

C₂²

#13133246

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

106

—

225

C₄

—

106

—

226

C₄

—

212

—

227

C₄

—

212

—

228

C₄

C₂²⋊C₄×D₅₃

yes

characteristic

229

C₄

C₄×D₂₁₂

yes

characteristic

230

C₄

#13133192

yes

characteristic

231

C₄

#13133202

yes

characteristic

232

C₂

#16810501

yes

characteristic

233

C₂

#16810717

yes

characteristic

234

C₂

#16810729

yes

characteristic

235

C₂

#16810780

yes

characteristic

236

C₂

#16810786

yes

characteristic

237

C₂

#16810832

yes

characteristic

238

C₂

#16810844

yes

characteristic

	subgroup	G/H
center	C₂³	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₃
Fitting	C₅₃×#340	C₂
socle	C₂³×C₅₃	C₂×D₄
hypercenter	#340	D₅₃
hypocenter	C₅₃	#1878
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₅₃

commutator

C₂×C₄×C₅₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₃

Fitting

C₅₃×#340

C₂

socle

C₂³×C₅₃

C₂×D₄

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
12. C₂×Dic₂₁₂	C₄	semidirect
84. C₂×Dic₅₃	Q₁₆	semidirect
127. C₅₃	#1878	semidirect

H ≅ G/N

type

12. C₂×Dic₂₁₂

C₄

semidirect

84. C₂×Dic₅₃

Q₁₆

semidirect

127. C₅₃

#1878

semidirect

Subgroups — #20275057

Conjugacy classes of subgroups

Complements