Group #27283993 — subgroups

Subgroups — #27283993

Order 13568.

422 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 131 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	#20275693	C₂	1	2	yes	maximal
2	#20274460	C₂	1	1	yes	maximal, characteristic
3	#20273474	C₂	1	1	yes	maximal, characteristic
4	#20273170	C₂	1	2	yes	maximal
5	C₅₃×#3170	C₂	1	1	yes	maximal, characteristic
6	#16810647	C₂²	1	2	yes	—
7	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
8	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
9	#16810382	—	2	4	no	—
10	#16810377	—	2	2	no	—
11	#16810376	—	2	2	no	—
12	Q₈⋊#88322	—	2	4	no	—
13	C₅₃×#533	C₂²	1	2	yes	—
14	C₅₃×#500	C₄	1	1	yes	characteristic, complemented
15	C₅₃×#494	C₄	1	1	yes	characteristic, complemented
16	C₅₃×#487	C₄	1	2	yes	complemented
17	C₅₃×#467	—	2	2	no	—
18	C₄×Q₁₆×C₅₃	—	2	2	no	—
19	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×#11719917	—	2	2	no	—
21	C₂²×#88322	—	2	1	no	—
22	C₂×C₄×Dic₅₃	—	2	1	no	—
23	C₂×C₄×Dic₅₃	—	2	1	no	—
24	C₂×C₄×Dic₅₃	D₄	1	2	yes	—
25	C₄⋊#88322	—	2	2	no	—
26	C₄⋊#88322	—	2	2	no	—
27	C₄×#88322	—	2	1	no	—
28	C₄×#88322	D₄	1	2	yes	—
29	C₂×Q₁₆×C₅₃	—	2	2	no	—
30	C₂²×C₈×C₅₃	D₄	1	2	yes	—
31	C₄⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
32	C₄⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
33	#125×C₅₃	—	2	2	no	—
34	C₂²⋊Q₈×C₅₃	—	2	2	no	—
35	C₂²⋊Q₈×C₅₃	—	2	2	no	—
36	C₄×Q₈×C₅₃	—	2	2	no	—
37	C₄×Q₈×C₅₃	—	2	2	no	—
38	#117×C₅₃	—	2	2	no	—
39	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
40	#107×C₅₃	—	2	2	no	—
41	#103×C₅₃	—	2	4	no	—
42	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₅₃	D₄	1	2	yes	—
45	C₂×Q₈×C₅₃	—	2	2	no	—
46	C₂×Q₈×C₅₃	—	2	2	no	—
47	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
49	C₂²×C₄×C₅₃	#41	1	1	yes	characteristic
50	C₂²×Dic₅₃	—	2	2	no	—
51	Q₁₆×C₅₃	—	4	4	no	—
52	C₂×C₈×C₅₃	—	4	2	no	—
53	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
54	C₂×C₈×C₅₃	C₂²⋊C₄	1	2	yes	—
55	C₄⋊C₄×C₅₃	—	2	2	no	—
56	C₄⋊C₄×C₅₃	—	2	2	no	—
57	C₄⋊C₄×C₅₃	—	2	2	no	—
58	C₄⋊C₄×C₅₃	—	2	2	no	—
59	C₄⋊C₄×C₅₃	—	4	2	no	—
60	C₄⋊C₄×C₅₃	—	4	2	no	—
61	C₂²⋊C₄×C₅₃	—	4	2	no	—
62	C₄²×C₅₃	—	4	2	no	—
63	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
66	C₄²×C₅₃	#41	1	1	yes	characteristic
67	C₄×Dic₅₃	—	2	2	no	—
68	C₄×Dic₅₃	—	4	2	no	—
69	C₄×Dic₅₃	—	4	2	no	—
70	C₄×Dic₅₃	Q₁₆	1	4	yes	complemented
71	#11719917	—	4	4	no	—
72	C₂×#88322	—	2	2	no	—
73	C₂×#88322	—	4	2	no	—
74	C₂×#88322	—	4	2	no	—
75	C₂³×C₅₃	#121	1	1	yes	characteristic
76	Q₈×C₅₃	—	4	4	no	—
77	Q₈×C₅₃	—	4	4	no	—
78	C₂×C₄×C₅₃	—	2	2	no	—
79	C₂×C₄×C₅₃	—	2	2	no	—
80	C₂×C₄×C₅₃	—	4	2	no	—
81	C₂×C₄×C₅₃	—	4	2	no	—
82	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
84	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
86	C₂×C₄×C₅₃	#124	1	1	yes	characteristic
87	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
88	C₂×C₄×C₅₃	C₂×Q₁₆	1	2	yes	—
89	C₂×C₄×C₅₃	#135	1	2	yes	—
90	C₂×Dic₅₃	—	2	4	no	—
91	C₂×Dic₅₃	—	4	2	no	—
92	C₂×Dic₅₃	—	4	2	no	—
93	C₈×C₅₃	—	2	2	no	—
94	C₈×C₅₃	—	2	2	no	—
95	#88322	—	4	2	no	—
96	#88322	—	8	2	no	—
97	#9848	—	53	1	no	maximal, Sylow
98	C₂²×C₅₃	—	2	1	no	—
99	C₂²×C₅₃	—	2	1	no	—
100	C₂²×C₅₃	#390	1	1	yes	characteristic
101	C₂²×C₅₃	#467	1	2	yes	—
102	C₄×C₅₃	—	2	1	no	—
103	C₄×C₅₃	—	2	1	no	—
104	C₄×C₅₃	—	8	2	no	—
105	C₄×C₅₃	—	8	2	no	—
106	C₄×C₅₃	#421	1	2	yes	—
107	C₄×C₅₃	C₄×Q₁₆	1	2	yes	—
108	C₄×C₅₃	#444	1	2	yes	—
109	C₄×C₅₃	#494	1	1	yes	characteristic
110	C₄×C₅₃	#495	1	1	yes	characteristic
111	Dic₅₃	—	4	4	no	—
112	#3170	D₅₃	1	1	yes	characteristic
113	#1994	—	53	2	no	—
114	#1744	—	53	1	no	—
115	#1567	—	53	1	no	—
116	#1493	—	53	2	no	—
117	C₂×C₅₃	—	2	2	no	—
118	C₂×C₅₃	#1963	1	1	yes	characteristic
119	C₂×C₅₃	#1969	1	1	yes	characteristic
120	C₂×C₅₃	#1975	1	1	yes	characteristic
121	#533	C₂×D₅₃	1	2	yes	—
122	#500	Dic₅₃	1	1	yes	characteristic, complemented
123	#494	Dic₅₃	1	1	yes	characteristic, complemented
124	#487	Dic₅₃	1	2	yes	complemented
125	#467	—	2	2	no	—
126	C₄×Q₁₆	—	2	2	no	—
127	#423	—	53	2	no	—
128	C₂×C₄×C₈	—	53	1	no	—
129	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
130	C₄³	—	53	1	no	—
131	#339	—	106	4	no	—
132	#336	—	106	2	no	—
133	#335	—	106	2	no	—
134	Q₈⋊C₈	—	106	4	no	—
135	C₅₃	#9848	1	1	yes	characteristic, complemented, Sylow
136	C₂×Q₁₆	—	2	2	no	—
137	C₂×M₁₆	—	106	2	no	—
138	C₂²×C₈	—	106	1	no	—
139	C₂²×C₈	C₂²⋊D₅₃	1	2	yes	—
140	C₄⋊Q₈	C₂×Dic₅₃	1	2	yes	—
141	C₄⋊Q₈	C₂×Dic₅₃	1	2	yes	—
142	#125	—	2	2	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	#117	—	2	2	no	—
148	C₂×C₄²	—	53	2	no	—
149	C₂×C₄²	—	106	1	no	—
150	C₂×C₄²	—	106	1	no	—
151	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
152	#107	—	2	2	no	—
153	C₄⋊C₈	—	106	2	no	—
154	C₄⋊C₈	—	106	2	no	—
155	#103	—	2	4	no	—
156	C₄×C₈	—	53	2	no	—
157	C₄×C₈	—	106	1	no	—
158	C₄×C₈	C₂×Dic₅₃	1	1	yes	characteristic
159	C₄×C₈	C₂×Dic₅₃	1	1	yes	characteristic
160	C₄×C₈	C₂²⋊D₅₃	1	2	yes	—
161	C₂×Q₈	—	2	2	no	—
162	C₂×Q₈	—	2	2	no	—
163	C₂²×C₄	—	106	2	no	—
164	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
165	C₂²×C₄	#11719947	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
167	Q₁₆	—	4	4	no	—
168	M₁₆	—	212	4	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	106	2	no	—
171	C₂×C₈	—	212	2	no	—
172	C₂×C₈	—	212	2	no	—
173	C₂×C₈	C₂²⋊Dic₅₃	1	2	yes	—
174	C₂×C₈	C₂²⋊Dic₅₃	1	2	yes	—
175	C₄⋊C₄	—	2	2	no	—
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	4	2	no	—
180	C₄⋊C₄	—	4	2	no	—
181	C₂²⋊C₄	—	4	2	no	—
182	C₄²	—	4	2	no	—
183	C₄²	—	53	4	no	—
184	C₄²	—	106	2	no	—
185	C₄²	—	212	2	no	—
186	C₄²	—	212	2	no	—
187	C₄²	D₄×D₅₃	1	1	yes	characteristic
188	C₄²	#11719947	1	1	yes	characteristic
189	C₄²	C₂²×Dic₅₃	1	1	yes	characteristic
190	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
191	C₂³	#13133188	1	1	yes	characteristic
192	Q₈	—	4	4	no	—
193	Q₈	—	4	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	4	2	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	106	4	no	—
199	C₂×C₄	—	212	2	no	—
200	C₂×C₄	—	212	2	no	—
201	C₂×C₄	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
202	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
203	C₂×C₄	D₄×Dic₅₃	1	1	yes	characteristic
204	C₂×C₄	#13133188	1	1	yes	characteristic
205	C₂×C₄	#13133204	1	1	yes	characteristic
206	C₂×C₄	#13133213	1	1	yes	characteristic
207	C₂×C₄	Q₁₆×D₅₃	1	2	yes	—
208	C₂×C₄	#13133240	1	2	yes	—
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	424	2	no	—
212	C₈	—	212	2	no	—
213	C₂²	—	2	1	no	—
214	C₂²	—	2	1	no	—
215	C₂²	#16810526	1	1	yes	characteristic
216	C₂²	#16810861	1	2	yes	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	8	2	no	—
220	C₄	—	8	2	no	—
221	C₄	—	212	4	no	—
222	C₄	#16810640	1	2	yes	—
223	C₄	Q₁₆×Dic₅₃	1	2	yes	—
224	C₄	#16810745	1	2	yes	—
225	C₄	#16811001	1	1	yes	characteristic
226	C₄	#16811008	1	1	yes	characteristic
227	C₂	—	2	2	no	—
228	C₂	#20275548	1	1	yes	characteristic
229	C₂	#20275577	1	1	yes	characteristic
230	C₂	#20275609	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20275693

C₂

yes

maximal

#20274460

C₂

yes

maximal, characteristic

#20273474

C₂

yes

maximal, characteristic

#20273170

C₂

yes

maximal

C₅₃×#3170

C₂

yes

maximal, characteristic

#16810647

C₂²

yes

—

C₂×C₄×#88322

C₂²

yes

characteristic

C₄²×Dic₅₃

C₂²

yes

—

—

—

—

C₅₃×#533

C₂²

yes

—

C₅₃×#500

C₄

yes

characteristic, complemented

C₅₃×#494

C₄

yes

characteristic, complemented

C₅₃×#487

C₄

yes

complemented

C₅₃×#467

—

C₄×Q₁₆×C₅₃

—

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₂×#11719917

—

C₂²×#88322

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

—

C₂×C₄×Dic₅₃

D₄

yes

—

—

—

—

D₄

yes

—

C₂×Q₁₆×C₅₃

—

C₂²×C₈×C₅₃

D₄

yes

—

C₄⋊Q₈×C₅₃

C₂×C₄

yes

—

C₄⋊Q₈×C₅₃

C₂×C₄

yes

—

#125×C₅₃

—

C₂²⋊Q₈×C₅₃

—

C₂²⋊Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

#117×C₅₃

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

#107×C₅₃

—

#103×C₅₃

—

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

C₂×C₄

yes

characteristic

C₄×C₈×C₅₃

D₄

yes

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

#41

yes

characteristic

C₂²×Dic₅₃

—

Q₁₆×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₂×C₈×C₅₃

C₂²⋊C₄

yes

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

#41

yes

characteristic

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

—

C₄×Dic₅₃

Q₁₆

yes

—

—

—

—

C₂³×C₅₃

#121

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

characteristic

C₂×C₄×C₅₃

C₄×D₄

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

C₂×Q₁₆

yes

—

C₂×C₄×C₅₃

#135

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

—

—

—

C₂²×C₅₃

—

C₂²×C₅₃

—

100

C₂²×C₅₃

#390

yes

characteristic

101

C₂²×C₅₃

#467

yes

—

102

C₄×C₅₃

—

103

C₄×C₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

—

106

C₄×C₅₃

#421

yes

—

107

C₄×C₅₃

C₄×Q₁₆

yes

—

108

C₄×C₅₃

#444

yes

—

109

C₄×C₅₃

#494

yes

characteristic

110

C₄×C₅₃

#495

yes

characteristic

111

Dic₅₃

—

112

#3170

D₅₃

yes

characteristic

113

#1994

—

114

#1744

—

115

#1567

—

116

#1493

—

117

C₂×C₅₃

—

118

C₂×C₅₃

#1963

yes

characteristic

119

C₂×C₅₃

#1969

yes

characteristic

120

C₂×C₅₃

#1975

yes

characteristic

121

#533

C₂×D₅₃

yes

—

122

#500

Dic₅₃

yes

characteristic, complemented

123

#494

Dic₅₃

yes

characteristic, complemented

124

#487

Dic₅₃

yes

complemented

125

#467

—

126

C₄×Q₁₆

—

127

#423

—

128

C₂×C₄×C₈

—

129

C₂×C₄×C₈

C₂×D₅₃

yes

characteristic

130

C₄³

—

131

#339

—

106

—

132

#336

—

106

—

133

#335

—

106

—

134

Q₈⋊C₈

—

106

—

135

C₅₃

#9848

yes

characteristic, complemented, Sylow

136

C₂×Q₁₆

—

137

C₂×M₁₆

—

106

—

138

C₂²×C₈

—

106

—

139

C₂²×C₈

C₂²⋊D₅₃

yes

—

140

C₄⋊Q₈

C₂×Dic₅₃

yes

—

141

C₄⋊Q₈

C₂×Dic₅₃

yes

—

142

#125

—

143

C₂²⋊Q₈

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

#117

—

148

C₂×C₄²

—

149

C₂×C₄²

—

106

—

150

C₂×C₄²

—

106

—

151

C₂×C₄²

C₂²×D₅₃

yes

characteristic

152

#107

—

153

C₄⋊C₈

—

106

—

154

C₄⋊C₈

—

106

—

155

#103

—

156

C₄×C₈

—

157

C₄×C₈

—

106

—

158

C₄×C₈

C₂×Dic₅₃

yes

characteristic

159

C₄×C₈

C₂×Dic₅₃

yes

characteristic

160

C₄×C₈

C₂²⋊D₅₃

yes

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

106

—

164

C₂²×C₄

D₄×D₅₃

yes

characteristic

165

C₂²×C₄

#11719947

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

167

Q₁₆

—

168

M₁₆

—

212

—

169

C₂×C₈

—

170

C₂×C₈

—

106

—

171

C₂×C₈

—

212

—

172

C₂×C₈

—

212

—

173

C₂×C₈

C₂²⋊Dic₅₃

yes

—

174

C₂×C₈

C₂²⋊Dic₅₃

yes

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

177

C₄⋊C₄

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₂²⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₄²

—

106

—

185

C₄²

—

212

—

186

C₄²

—

212

—

187

C₄²

D₄×D₅₃

yes

characteristic

188

C₄²

#11719947

yes

characteristic

189

C₄²

C₂²×Dic₅₃

yes

characteristic

190

C₄²

C₂×C₂²⋊D₅₃

yes

characteristic

191

C₂³

#13133188

yes

characteristic

192

Q₈

—

193

Q₈

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

106

—

199

C₂×C₄

—

212

—

200

C₂×C₄

—

212

—

201

C₂×C₄

C₂×C₂²⋊Dic₅₃

yes

characteristic

202

C₂×C₄

D₄×Dic₅₃

yes

characteristic

203

C₂×C₄

D₄×Dic₅₃

yes

characteristic

204

C₂×C₄

#13133188

yes

characteristic

205

C₂×C₄

#13133204

yes

characteristic

206

C₂×C₄

#13133213

yes

characteristic

207

C₂×C₄

Q₁₆×D₅₃

yes

—

208

C₂×C₄

#13133240

yes

—

209

C₈

—

210

C₈

—

211

C₈

—

424

—

212

C₈

—

212

—

213

C₂²

—

214

C₂²

—

215

C₂²

#16810526

yes

characteristic

216

C₂²

#16810861

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

212

—

222

C₄

#16810640

yes

—

223

C₄

Q₁₆×Dic₅₃

yes

—

224

C₄

#16810745

yes

—

225

C₄

#16811001

yes

characteristic

226

C₄

#16811008

yes

characteristic

227

C₂

—

228

C₂

#20275548

yes

characteristic

229

C₂

#20275577

yes

characteristic

230

C₂

#20275609

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13133213
commutator	C₄²×C₅₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#3170	C₂
socle	C₂²×C₅₃	#390
prime radical	C₂³×C₅₃	#121
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#3170	D₅₃
hypocenter	C₅₃	#9848
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

subgroup

G/H

center

C₂×C₄

#13133213

commutator

C₄²×C₅₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₅₃

Fitting

C₅₃×#3170

C₂

C₂²×C₅₃

C₂³×C₅₃

C₂×C₄²×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

N	H ≅ G/N	type
14. C₅₃×#500	C₄	semidirect
15. C₅₃×#494	C₄	semidirect
16. C₅₃×#487	C₄	semidirect
70. C₄×Dic₅₃	Q₁₆	semidirect
122. #500	Dic₅₃	semidirect
123. #494	Dic₅₃	semidirect
124. #487	Dic₅₃	semidirect
135. C₅₃	#9848	semidirect

H ≅ G/N

type

14. C₅₃×#500

C₄

semidirect

15. C₅₃×#494

C₄

semidirect

16. C₅₃×#487

C₄

semidirect

70. C₄×Dic₅₃

Q₁₆

semidirect

122. #500

Dic₅₃

semidirect

123. #494

Dic₅₃

semidirect

124. #487

Dic₅₃

semidirect

135. C₅₃

#9848

semidirect

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

subgroup	index
#20275693	2
#20274460	2
#20273474	2
#20273170	2
C₅₃×#3170	2
#9848	53

subgroup

index

C₅₃×#3170

Subgroups — #27283993

Conjugacy classes of subgroups

Complements

Maximal subgroups