Group #27300653 — subgroups

Subgroups — #27300653

Order 13568.

414 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₂×#16810661	C₂	1	1	yes	maximal, characteristic
2	C₂×#16810447	C₂	1	2	yes	maximal, complemented
3	#20276326	C₂	1	1	yes	maximal, characteristic
4	#20272815	C₂	1	2	yes	maximal, complemented
5	C₅₃×#1810	C₂	1	1	yes	maximal, characteristic
6	C₂×#13133176	—	2	1	no	—
7	C₂×#13133157	C₂²	1	2	yes	—
8	#16810661	—	2	4	no	—
9	C₂×#13133151	—	2	1	no	—
10	C₂×#13133149	C₂²	1	2	yes	—
11	#16810447	—	2	4	no	—
12	C₂²⋊#11719908	C₄	1	4	yes	complemented
13	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
14	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
15	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
16	C₅₃×#407	—	2	1	no	—
17	C₅₃×#341	—	2	1	no	—
18	#13133176	—	2	4	no	—
19	#13133176	—	4	2	no	—
20	C₂×C₄⋊Dic₅₃	—	2	2	no	—
21	C₂×C₂²⋊Dic₅₃	—	4	1	no	—
22	C₂×C₄×Dic₅₃	—	4	1	no	—
23	#13133157	—	2	2	no	—
24	#13133157	—	2	2	no	—
25	C₂×#11719908	C₂×C₄	1	4	yes	—
26	#13133151	—	2	4	no	—
27	#13133149	—	2	2	no	—
28	#13133149	D₄	1	4	yes	—
29	C₂³×C₄×C₅₃	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₅₃	—	2	1	no	—
31	C₂×M₁₆×C₅₃	—	2	1	no	—
32	C₂²×C₈×C₅₃	—	2	2	no	—
33	C₂²×C₈×C₅₃	—	2	2	no	—
34	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₅₃	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₅₃	Q₈	1	2	yes	—
37	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
38	#108×C₅₃	—	2	2	no	—
39	#108×C₅₃	—	2	2	no	—
40	C₂²⋊C₈×C₅₃	—	4	2	no	—
41	C₂⁴×C₅₃	SD₁₆	1	1	yes	characteristic
42	C₂²×C₄×C₅₃	—	2	1	no	—
43	C₂²×C₄×C₅₃	—	2	1	no	—
44	C₂²×C₄×C₅₃	—	2	1	no	—
45	C₂²×C₄×C₅₃	—	2	1	no	—
46	C₂²×C₄×C₅₃	C₄⋊C₄	1	2	yes	—
47	C₂²×C₄×C₅₃	SD₁₆	1	1	yes	characteristic
48	C₂²×C₄×C₅₃	SD₁₆	1	2	yes	—
49	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
50	C₂²×Dic₅₃	—	4	2	no	—
51	M₁₆×C₅₃	—	4	1	no	—
52	M₁₆×C₅₃	—	4	1	no	—
53	M₁₆×C₅₃	—	4	1	no	—
54	M₁₆×C₅₃	—	4	1	no	—
55	C₂×C₈×C₅₃	—	2	1	no	—
56	C₂×C₈×C₅₃	—	2	1	no	—
57	C₂×C₈×C₅₃	—	2	4	no	—
58	C₂×C₈×C₅₃	—	2	4	no	—
59	C₂×C₈×C₅₃	—	4	1	no	—
60	C₂×C₈×C₅₃	—	4	1	no	—
61	C₂×C₈×C₅₃	C₄⋊C₄	1	2	yes	—
62	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
64	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
65	C₂×C₈×C₅₃	#41	1	2	yes	—
66	C₂²⋊Dic₅₃	—	4	4	no	—
67	C₄⋊Dic₅₃	—	2	4	no	—
68	C₄⋊Dic₅₃	—	4	2	no	—
69	C₄×Dic₅₃	—	4	4	no	—
70	#11719908	—	2	4	no	—
71	C₂³×C₅₃	—	2	1	no	—
72	C₂³×C₅₃	—	2	1	no	—
73	C₂³×C₅₃	—	4	2	no	—
74	C₂³×C₅₃	#106	1	2	yes	—
75	C₂³×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
76	C₂×C₄×C₅₃	—	2	1	no	—
77	C₂×C₄×C₅₃	—	2	1	no	—
78	C₂×C₄×C₅₃	—	2	2	no	—
79	C₂×C₄×C₅₃	—	2	2	no	—
80	C₂×C₄×C₅₃	—	2	2	no	—
81	C₂×C₄×C₅₃	—	2	2	no	—
82	C₂×C₄×C₅₃	#106	1	2	yes	—
83	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
85	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
86	C₂×C₄×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
87	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
88	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
89	C₂×Dic₅₃	—	4	4	no	—
90	C₂×Dic₅₃	—	8	4	no	—
91	C₈×C₅₃	—	2	2	no	—
92	C₈×C₅₃	—	8	1	no	—
93	C₈×C₅₃	—	8	1	no	—
94	C₈×C₅₃	C₄×D₄	1	2	yes	—
95	C₈×C₅₃	C₂²⋊Q₈	1	2	yes	—
96	#12930	—	53	1	no	maximal, Sylow
97	C₂²×C₅₃	—	2	2	no	—
98	C₂²×C₅₃	—	2	2	no	—
99	C₂²×C₅₃	—	2	4	no	—
100	C₂²×C₅₃	—	4	2	no	—
101	C₂²×C₅₃	—	4	2	no	—
102	C₂²×C₅₃	C₂×#106	1	1	yes	characteristic
103	C₂²×C₅₃	#450	1	1	yes	characteristic
104	C₂²×C₅₃	#483	1	1	yes	characteristic
105	C₄×C₅₃	—	2	2	no	—
106	C₄×C₅₃	#385	1	1	yes	characteristic
107	C₄×C₅₃	#428	1	1	yes	characteristic
108	C₄×C₅₃	#448	1	1	yes	characteristic
109	C₄×C₅₃	#481	1	1	yes	characteristic
110	Dic₅₃	—	8	4	no	—
111	C₂×#427	—	53	1	no	—
112	C₂×#365	—	53	2	no	—
113	#2112	—	53	1	no	—
114	#1810	D₅₃	1	1	yes	characteristic
115	#1383	—	53	2	no	—
116	C₂×C₅₃	—	2	1	no	—
117	C₂×C₅₃	—	2	1	no	—
118	C₂×C₅₃	—	4	2	no	—
119	C₂×C₅₃	#1853	1	1	yes	characteristic
120	C₂×C₅₃	#2155	1	2	yes	—
121	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic
122	C₂×#117	—	106	1	no	—
123	C₂×M₃₂	—	53	2	no	—
124	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
125	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
126	#427	—	106	4	no	—
127	C₂×#107	—	106	1	no	—
128	C₂×#106	—	53	2	no	—
129	#407	—	2	1	no	—
130	#365	—	106	4	no	—
131	C₂²⋊C₁₆	—	53	4	no	—
132	#341	—	2	1	no	—
133	C₅₃	#12930	1	1	yes	characteristic, complemented, Sylow
134	C₂³×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
135	C₂×M₁₆	—	2	1	no	—
136	C₂×M₁₆	—	2	1	no	—
137	C₂²×C₈	—	2	2	no	—
138	C₂²×C₈	—	2	2	no	—
139	C₂²×C₈	Dic₁₀₆	1	2	yes	—
140	C₂²×C₈	C₄×D₅₃	1	2	yes	—
141	C₂²×C₈	C₂²⋊D₅₃	1	1	yes	characteristic
142	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
143	#117	—	106	4	no	—
144	#117	—	212	2	no	—
145	C₂×C₄⋊C₄	—	106	2	no	—
146	C₂×C₂²⋊C₄	—	212	1	no	—
147	C₂×C₄²	—	212	1	no	—
148	M₃₂	—	106	2	no	—
149	M₃₂	—	106	2	no	—
150	C₂×C₁₆	—	53	4	no	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#107	—	106	4	no	—
154	#106	—	53	4	no	—
155	#106	—	106	2	no	—
156	C₂²⋊C₈	—	4	2	no	—
157	C₂⁴	#11719924	1	1	yes	characteristic
158	C₂²×C₄	—	2	1	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	212	2	no	—
163	C₂²×C₄	#11719919	1	2	yes	—
164	C₂²×C₄	#11719923	1	2	yes	—
165	C₂²×C₄	#11719924	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
167	M₁₆	—	4	1	no	—
168	M₁₆	—	4	1	no	—
169	M₁₆	—	4	1	no	—
170	M₁₆	—	4	1	no	—
171	C₂×C₈	—	2	1	no	—
172	C₂×C₈	—	2	1	no	—
173	C₂×C₈	—	2	4	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	4	1	no	—
176	C₂×C₈	—	4	1	no	—
177	C₂×C₈	#11719919	1	2	yes	—
178	C₂×C₈	C₂×Dic₁₀₆	1	1	yes	characteristic
179	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
180	C₂×C₈	D₄×D₅₃	1	2	yes	—
181	C₂×C₈	#11719947	1	2	yes	—
182	C₄⋊C₄	—	106	4	no	—
183	C₄⋊C₄	—	212	2	no	—
184	C₂²⋊C₄	—	212	4	no	—
185	C₄²	—	212	4	no	—
186	C₁₆	—	106	4	no	—
187	C₂³	—	2	1	no	—
188	C₂³	—	2	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	#13133148	1	2	yes	—
191	C₂³	C₂×#11719924	1	1	yes	characteristic
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	424	4	no	—
199	C₂×C₄	—	212	4	no	—
200	C₂×C₄	#13133148	1	2	yes	—
201	C₂×C₄	C₂×#11719919	1	1	yes	characteristic
202	C₂×C₄	#13133185	1	1	yes	characteristic
203	C₂×C₄	#13133198	1	1	yes	characteristic
204	C₂×C₄	C₂×#11719923	1	1	yes	characteristic
205	C₂×C₄	#13133242	1	1	yes	characteristic
206	C₂×C₄	#13133247	1	1	yes	characteristic
207	C₈	—	2	2	no	—
208	C₈	—	8	1	no	—
209	C₈	—	8	1	no	—
210	C₈	#13133177	1	2	yes	—
211	C₈	#13133194	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	2	4	no	—
214	C₂²	—	2	2	no	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	C₂×#13133148	1	1	yes	characteristic
218	C₂²	#16810773	1	1	yes	characteristic
219	C₂²	#16810951	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	424	4	no	—
222	C₄	#16810495	1	1	yes	characteristic
223	C₄	#16810666	1	1	yes	characteristic
224	C₄	#16810761	1	1	yes	characteristic
225	C₄	#16810939	1	1	yes	characteristic
226	C₂	—	2	1	no	—
227	C₂	—	2	1	no	—
228	C₂	—	4	2	no	—
229	C₂	#20274907	1	1	yes	characteristic
230	C₂	#20276489	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16810661

C₂

yes

maximal, characteristic

C₂×#16810447

C₂

yes

maximal, complemented

#20276326

C₂

yes

maximal, characteristic

#20272815

C₂

yes

maximal, complemented

C₅₃×#1810

C₂

yes

maximal, characteristic

C₂×#13133176

—

C₂×#13133157

C₂²

yes

—

#16810661

—

C₂×#13133151

—

C₂×#13133149

C₂²

yes

—

#16810447

—

C₂²⋊#11719908

C₄

yes

complemented

C₂³×C₈×C₅₃

C₂²

yes

characteristic

C₂×#108×C₅₃

C₂²

yes

characteristic

C₂×#108×C₅₃

C₂²

yes

characteristic

C₅₃×#407

—

C₅₃×#341

—

#13133176

—

#13133176

—

C₂×C₄⋊Dic₅₃

—

C₂×C₂²⋊Dic₅₃

—

C₂×C₄×Dic₅₃

—

#13133157

—

#13133157

—

C₂×#11719908

C₂×C₄

yes

—

#13133151

—

#13133149

—

#13133149

D₄

yes

—

C₂³×C₄×C₅₃

D₄

yes

characteristic

C₂×M₁₆×C₅₃

—

C₂×M₁₆×C₅₃

—

C₂²×C₈×C₅₃

—

C₂²×C₈×C₅₃

—

C₂²×C₈×C₅₃

C₂×C₄

yes

—

C₂²×C₈×C₅₃

D₄

yes

characteristic

C₂²×C₈×C₅₃

Q₈

yes

—

C₂²×C₈×C₅₃

C₂³

yes

characteristic

#108×C₅₃

—

#108×C₅₃

—

C₂²⋊C₈×C₅₃

—

C₂⁴×C₅₃

SD₁₆

yes

characteristic

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₄⋊C₄

yes

—

C₂²×C₄×C₅₃

SD₁₆

yes

characteristic

C₂²×C₄×C₅₃

SD₁₆

yes

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×Dic₅₃

—

M₁₆×C₅₃

—

M₁₆×C₅₃

—

M₁₆×C₅₃

—

M₁₆×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

C₄⋊C₄

yes

—

C₂×C₈×C₅₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₅₃

C₂×D₄

yes

—

C₂×C₈×C₅₃

C₂×Q₈

yes

characteristic

C₂×C₈×C₅₃

#41

yes

—

C₂²⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄×Dic₅₃

—

#11719908

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

#106

yes

—

C₂³×C₅₃

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#106

yes

—

C₂×C₄×C₅₃

C₂×C₄⋊C₄

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

C₂×SD₁₆

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

C₄×D₄

yes

—

C₈×C₅₃

C₂²⋊Q₈

yes

—

#12930

—

maximal, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

100

C₂²×C₅₃

—

101

C₂²×C₅₃

—

102

C₂²×C₅₃

C₂×#106

yes

characteristic

103

C₂²×C₅₃

#450

yes

characteristic

104

C₂²×C₅₃

#483

yes

characteristic

105

C₄×C₅₃

—

106

C₄×C₅₃

#385

yes

characteristic

107

C₄×C₅₃

#428

yes

characteristic

108

C₄×C₅₃

#448

yes

characteristic

109

C₄×C₅₃

#481

yes

characteristic

110

Dic₅₃

—

111

C₂×#427

—

112

C₂×#365

—

113

#2112

—

114

#1810

D₅₃

yes

characteristic

115

#1383

—

116

C₂×C₅₃

—

117

C₂×C₅₃

—

118

C₂×C₅₃

—

119

C₂×C₅₃

#1853

yes

characteristic

120

C₂×C₅₃

#2155

yes

—

121

C₂³×C₈

C₂×D₅₃

yes

characteristic

122

C₂×#117

—

106

—

123

C₂×M₃₂

—

124

C₂×#108

C₂×D₅₃

yes

characteristic

125

C₂×#108

C₂×D₅₃

yes

characteristic

126

#427

—

106

—

127

C₂×#107

—

106

—

128

C₂×#106

—

129

#407

—

130

#365

—

106

—

131

C₂²⋊C₁₆

—

132

#341

—

133

C₅₃

#12930

yes

characteristic, complemented, Sylow

134

C₂³×C₄

C₂²⋊D₅₃

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

Dic₁₀₆

yes

—

140

C₂²×C₈

C₄×D₅₃

yes

—

141

C₂²×C₈

C₂²⋊D₅₃

yes

characteristic

142

C₂²×C₈

C₂²×D₅₃

yes

characteristic

143

#117

—

106

—

144

#117

—

212

—

145

C₂×C₄⋊C₄

—

106

—

146

C₂×C₂²⋊C₄

—

212

—

147

C₂×C₄²

—

212

—

148

M₃₂

—

106

—

149

M₃₂

—

106

—

150

C₂×C₁₆

—

151

#108

—

152

#108

—

153

#107

—

106

—

154

#106

—

155

#106

—

106

—

156

C₂²⋊C₈

—

157

C₂⁴

#11719924

yes

characteristic

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

161

C₂²×C₄

—

162

C₂²×C₄

—

212

—

163

C₂²×C₄

#11719919

yes

—

164

C₂²×C₄

#11719923

yes

—

165

C₂²×C₄

#11719924

yes

characteristic

166

C₂²×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

167

M₁₆

—

168

M₁₆

—

169

M₁₆

—

170

M₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

#11719919

yes

—

178

C₂×C₈

C₂×Dic₁₀₆

yes

characteristic

179

C₂×C₈

C₂×C₄×D₅₃

yes

characteristic

180

C₂×C₈

D₄×D₅₃

yes

—

181

C₂×C₈

#11719947

yes

—

182

C₄⋊C₄

—

106

—

183

C₄⋊C₄

—

212

—

184

C₂²⋊C₄

—

212

—

185

C₄²

—

212

—

186

C₁₆

—

106

—

187

C₂³

—

188

C₂³

—

189

C₂³

—

190

C₂³

#13133148

yes

—

191

C₂³

C₂×#11719924

yes

characteristic

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

424

—

199

C₂×C₄

—

212

—

200

C₂×C₄

#13133148

yes

—

201

C₂×C₄

C₂×#11719919

yes

characteristic

202

C₂×C₄

#13133185

yes

characteristic

203

C₂×C₄

#13133198

yes

characteristic

204

C₂×C₄

C₂×#11719923

yes

characteristic

205

C₂×C₄

#13133242

yes

characteristic

206

C₂×C₄

#13133247

yes

characteristic

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

#13133177

yes

—

211

C₈

#13133194

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

C₂×#13133148

yes

characteristic

218

C₂²

#16810773

yes

characteristic

219

C₂²

#16810951

yes

characteristic

220

C₄

—

221

C₄

—

424

—

222

C₄

#16810495

yes

characteristic

223

C₄

#16810666

yes

characteristic

224

C₄

#16810761

yes

characteristic

225

C₄

#16810939

yes

characteristic

226

C₂

—

227

C₂

—

228

C₂

—

229

C₂

#20274907

yes

characteristic

230

C₂

#20276489

yes

—

	subgroup	G/H
center	C₂²	C₂×#13133148
commutator	C₂×C₈×C₅₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₅₃
Fitting	C₅₃×#1810	C₂
socle	C₂²×C₅₃	C₂×#106
prime radical	C₂⁴×C₅₃	SD₁₆
cosocle	C₂²×C₈×C₅₃	C₂³
hypercenter	#1810	D₅₃
hypocenter	C₅₃	#12930
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

subgroup

G/H

center

C₂²

C₂×#13133148

commutator

C₂×C₈×C₅₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₅₃

Fitting

C₅₃×#1810

C₂

socle

C₂²×C₅₃

C₂×#106

prime radical

C₂⁴×C₅₃

SD₁₆

cosocle

C₂²×C₈×C₅₃

C₂³

D₅₃

C₅₃

G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1810

N	H ≅ G/N	type
2. C₂×#16810447	C₂	semidirect
4. #20272815	C₂	semidirect
12. C₂²⋊#11719908	C₄	semidirect
133. C₅₃	#12930	semidirect

H ≅ G/N

type

2. C₂×#16810447

C₂

semidirect

4. #20272815

C₂

semidirect

12. C₂²⋊#11719908

C₄

semidirect

133. C₅₃

#12930

semidirect

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

subgroup	index
C₂×#16810661	2
C₂×#16810447	2
#20276326	2
#20272815	2
C₅₃×#1810	2
#12930	53

subgroup

index

C₅₃×#1810

Subgroups — #27300653

Conjugacy classes of subgroups

Complements

Maximal subgroups