Group #27216582 — subgroups

Subgroups — C₅₃×#9070 #27216582

Order 13568.

426 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 126 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×#3131	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2986	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#1526	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#1484	C₂	1	2	yes	maximal
5	C₅₃×#1278	C₂	1	2	yes	maximal, complemented
6	C₅₃×#533	C₂²	1	1	yes	characteristic
7	C₅₃×#532	C₂²	1	1	yes	characteristic
8	C₅₃×#488	—	2	2	no	—
9	C₅₃×#487	C₄	1	2	yes	—
10	C₅₃×#486	C₄	1	2	yes	—
11	C₅₃×#446	—	2	2	no	—
12	C₈×Q₈×C₅₃	—	2	2	no	—
13	C₅₃×#433	—	2	2	no	—
14	C₅₃×#431	C₂²	1	2	yes	—
15	C₅₃×#416	—	2	2	no	—
16	C₄×M₁₆×C₅₃	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₅₃×#330	—	2	2	no	—
19	C₅₃×D₄⋊C₈	—	2	2	no	—
20	C₅₃×D₄⋊C₈	—	2	2	no	—
21	C₂×#41×C₅₃	—	2	1	no	—
22	C₂×M₁₆×C₅₃	—	2	2	no	—
23	C₂²×C₈×C₅₃	—	2	1	no	—
24	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
25	C₄⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
26	#127×C₅₃	C₂×C₄	1	1	yes	characteristic
27	#125×C₅₃	D₄	1	2	yes	—
28	#124×C₅₃	—	2	1	no	—
29	C₂²⋊Q₈×C₅₃	—	2	2	no	—
30	#121×C₅₃	—	2	2	no	—
31	C₄×Q₈×C₅₃	—	2	2	no	—
32	C₄×D₄×C₅₃	—	2	2	no	—
33	#117×C₅₃	D₄	1	2	yes	—
34	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
35	C₄⋊C₈×C₅₃	—	2	4	no	—
36	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
37	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
38	#103×C₅₃	—	2	4	no	—
39	#102×C₅₃	—	2	4	no	—
40	C₂²⋊C₈×C₅₃	—	2	2	no	—
41	#97×C₅₃	—	2	2	no	—
42	#97×C₅₃	—	2	2	no	—
43	C₄×C₈×C₅₃	—	2	2	no	—
44	C₄×C₈×C₅₃	—	2	1	no	—
45	C₄×C₈×C₅₃	—	2	2	no	—
46	C₄×C₈×C₅₃	—	2	2	no	—
47	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
48	#41×C₅₃	—	4	4	no	—
49	C₂×Q₈×C₅₃	—	2	2	no	—
50	C₂×Q₈×C₅₃	—	2	1	no	—
51	C₂×D₄×C₅₃	—	2	1	no	—
52	C₂×D₄×C₅₃	—	2	2	no	—
53	C₂×D₄×C₅₃	—	4	1	no	—
54	C₂²×C₄×C₅₃	—	4	1	no	—
55	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₅₃	#41	1	2	yes	—
57	M₁₆×C₅₃	—	2	4	no	—
58	M₁₆×C₅₃	—	4	2	no	—
59	C₂×C₈×C₅₃	—	2	2	no	—
60	C₂×C₈×C₅₃	—	2	2	no	—
61	C₂×C₈×C₅₃	—	2	2	no	—
62	C₂×C₈×C₅₃	—	4	2	no	—
63	C₂×C₈×C₅₃	—	4	2	no	—
64	C₄⋊C₄×C₅₃	—	2	2	no	—
65	C₄⋊C₄×C₅₃	—	2	4	no	—
66	C₄⋊C₄×C₅₃	—	2	2	no	—
67	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	4	yes	—
68	C₂²⋊C₄×C₅₃	—	2	2	no	—
69	C₂²⋊C₄×C₅₃	—	4	2	no	—
70	C₄²×C₅₃	—	2	2	no	—
71	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
72	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₅₃	C₂×D₄	1	2	yes	—
74	C₂³×C₅₃	—	4	1	no	—
75	C₂³×C₅₃	#123	1	1	yes	characteristic
76	Q₈×C₅₃	—	4	2	no	—
77	Q₈×C₅₃	—	4	2	no	—
78	Q₈×C₅₃	—	4	2	no	—
79	D₄×C₅₃	—	4	2	no	—
80	D₄×C₅₃	—	4	2	no	—
81	D₄×C₅₃	—	4	2	no	—
82	D₄×C₅₃	—	8	2	no	—
83	C₂×C₄×C₅₃	—	2	2	no	—
84	C₂×C₄×C₅₃	—	2	2	no	—
85	C₂×C₄×C₅₃	—	2	2	no	—
86	C₂×C₄×C₅₃	—	2	4	no	—
87	C₂×C₄×C₅₃	—	4	1	no	—
88	C₂×C₄×C₅₃	—	8	2	no	—
89	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
90	C₂×C₄×C₅₃	C₄×D₄	1	2	yes	—
91	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
92	C₂×C₄×C₅₃	#121	1	2	yes	—
93	C₈×C₅₃	—	4	2	no	—
94	C₈×C₅₃	—	4	4	no	—
95	C₈×C₅₃	—	4	2	no	—
96	C₈×C₅₃	—	4	2	no	—
97	#9070	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂²×C₅₃	—	2	2	no	—
99	C₂²×C₅₃	—	2	1	no	—
100	C₂²×C₅₃	—	8	2	no	—
101	C₂²×C₅₃	—	8	1	no	—
102	C₂²×C₅₃	#386	1	1	yes	characteristic
103	C₄×C₅₃	—	2	2	no	—
104	C₄×C₅₃	—	2	1	no	—
105	C₄×C₅₃	—	4	4	no	—
106	C₄×C₅₃	—	8	1	no	—
107	C₄×C₅₃	#443	1	2	yes	—
108	C₄×C₅₃	#444	1	2	yes	—
109	C₄×C₅₃	#454	1	2	yes	—
110	#3131	C₂×C₅₃	1	1	yes	characteristic
111	#2986	C₂×C₅₃	1	1	yes	characteristic, complemented
112	#1526	C₂×C₅₃	1	1	yes	characteristic, complemented
113	#1484	C₂×C₅₃	1	2	yes	—
114	#1278	C₂×C₅₃	1	2	yes	complemented
115	C₂×C₅₃	—	4	1	no	—
116	C₂×C₅₃	—	16	1	no	—
117	C₂×C₅₃	#1876	1	2	yes	—
118	C₂×C₅₃	#1888	1	1	yes	characteristic
119	#533	C₂²×C₅₃	1	1	yes	characteristic
120	#532	C₂²×C₅₃	1	1	yes	characteristic
121	#488	—	2	2	no	—
122	#487	C₄×C₅₃	1	2	yes	—
123	#486	C₄×C₅₃	1	2	yes	—
124	#446	—	2	2	no	—
125	C₈×Q₈	—	2	2	no	—
126	#433	—	2	2	no	—
127	#431	C₂²×C₅₃	1	2	yes	—
128	#416	—	2	2	no	—
129	C₄×M₁₆	C₂²×C₅₃	1	2	yes	—
130	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
131	#330	—	2	2	no	—
132	D₄⋊C₈	—	2	2	no	—
133	D₄⋊C₈	—	2	2	no	—
134	C₅₃	#9070	1	1	yes	characteristic, direct product factor, Sylow
135	C₂×#41	—	2	1	no	—
136	C₂×M₁₆	—	2	2	no	—
137	C₂²×C₈	—	2	1	no	—
138	C₄⋊Q₈	C₂×C₄×C₅₃	1	1	yes	characteristic
139	C₄⋊Q₈	C₂×C₄×C₅₃	1	2	yes	—
140	#127	C₂×C₄×C₅₃	1	1	yes	characteristic
141	#125	D₄×C₅₃	1	2	yes	—
142	#124	—	2	1	no	—
143	C₂²⋊Q₈	—	2	2	no	—
144	#121	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×D₄	—	2	2	no	—
147	#117	D₄×C₅₃	1	2	yes	—
148	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
149	C₄⋊C₈	—	2	4	no	—
150	C₄⋊C₈	D₄×C₅₃	1	2	yes	—
151	C₄⋊C₈	D₄×C₅₃	1	2	yes	—
152	#103	—	2	4	no	—
153	#102	—	2	4	no	—
154	C₂²⋊C₈	—	2	2	no	—
155	#97	—	2	2	no	—
156	#97	—	2	2	no	—
157	C₄×C₈	—	2	2	no	—
158	C₄×C₈	—	2	1	no	—
159	C₄×C₈	—	2	2	no	—
160	C₄×C₈	—	2	2	no	—
161	C₄×C₈	C₂×C₄×C₅₃	1	2	yes	—
162	#41	—	4	4	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	1	no	—
165	C₂×D₄	—	2	1	no	—
166	C₂×D₄	—	2	2	no	—
167	C₂×D₄	—	4	1	no	—
168	C₂²×C₄	—	4	1	no	—
169	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
170	C₂²×C₄	#41×C₅₃	1	2	yes	—
171	M₁₆	—	2	4	no	—
172	M₁₆	—	4	2	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	4	2	no	—
178	C₄⋊C₄	—	2	2	no	—
179	C₄⋊C₄	—	2	4	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	4	yes	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	4	2	no	—
184	C₄²	—	2	2	no	—
185	C₄²	C₂²×C₄×C₅₃	1	1	yes	characteristic
186	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
187	C₄²	C₂×D₄×C₅₃	1	2	yes	—
188	C₂³	—	4	1	no	—
189	C₂³	#123×C₅₃	1	1	yes	characteristic
190	Q₈	—	4	2	no	—
191	Q₈	—	4	2	no	—
192	Q₈	—	4	2	no	—
193	D₄	—	4	2	no	—
194	D₄	—	4	2	no	—
195	D₄	—	4	2	no	—
196	D₄	—	8	2	no	—
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	2	no	—
200	C₂×C₄	—	2	4	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	8	2	no	—
203	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
204	C₂×C₄	C₄×D₄×C₅₃	1	2	yes	—
205	C₂×C₄	#120×C₅₃	1	1	yes	characteristic
206	C₂×C₄	#121×C₅₃	1	2	yes	—
207	C₈	—	4	2	no	—
208	C₈	—	4	4	no	—
209	C₈	—	4	2	no	—
210	C₈	—	4	2	no	—
211	C₂²	—	2	2	no	—
212	C₂²	—	2	1	no	—
213	C₂²	—	8	2	no	—
214	C₂²	—	8	1	no	—
215	C₂²	C₅₃×#386	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	4	no	—
219	C₄	—	8	1	no	—
220	C₄	C₅₃×#443	1	2	yes	—
221	C₄	C₅₃×#444	1	2	yes	—
222	C₄	C₅₃×#454	1	2	yes	—
223	C₂	—	4	1	no	—
224	C₂	—	16	1	no	—
225	C₂	C₅₃×#1876	1	2	yes	—
226	C₂	C₅₃×#1888	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅₃×#3131

C₂

yes

maximal, characteristic

C₅₃×#2986

C₂

yes

maximal, characteristic, complemented

C₅₃×#1526

C₂

yes

maximal, characteristic, complemented

C₅₃×#1484

C₂

yes

maximal

C₅₃×#1278

C₂

yes

maximal, complemented

C₅₃×#533

C₂²

yes

characteristic

C₅₃×#532

C₂²

yes

characteristic

C₅₃×#488

—

C₅₃×#487

C₄

yes

—

C₅₃×#486

C₄

yes

—

C₅₃×#446

—

C₈×Q₈×C₅₃

—

C₅₃×#433

—

C₅₃×#431

C₂²

yes

—

C₅₃×#416

—

C₄×M₁₆×C₅₃

C₂²

yes

—

C₂×C₄×C₈×C₅₃

C₂²

yes

characteristic

C₅₃×#330

—

C₅₃×D₄⋊C₈

—

C₅₃×D₄⋊C₈

—

C₂×#41×C₅₃

—

C₂×M₁₆×C₅₃

—

C₂²×C₈×C₅₃

—

C₄⋊Q₈×C₅₃

C₂×C₄

yes

characteristic

C₄⋊Q₈×C₅₃

C₂×C₄

yes

—

#127×C₅₃

C₂×C₄

yes

characteristic

#125×C₅₃

D₄

yes

—

#124×C₅₃

—

C₂²⋊Q₈×C₅₃

—

#121×C₅₃

—

C₄×Q₈×C₅₃

—

C₄×D₄×C₅₃

—

#117×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

C₄⋊C₈×C₅₃

—

C₄⋊C₈×C₅₃

D₄

yes

—

C₄⋊C₈×C₅₃

D₄

yes

—

#103×C₅₃

—

#102×C₅₃

—

C₂²⋊C₈×C₅₃

—

#97×C₅₃

—

#97×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

—

C₄×C₈×C₅₃

C₂×C₄

yes

—

#41×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₅₃

#41

yes

—

M₁₆×C₅₃

—

M₁₆×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₅₃

—

C₂²⋊C₄×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂²×C₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

—

C₂³×C₅₃

—

C₂³×C₅₃

#123

yes

characteristic

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

D₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×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

—

C₂×C₄×C₅₃

#120

yes

characteristic

C₂×C₄×C₅₃

#121

yes

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

C₈×C₅₃

—

#9070

C₅₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

100

C₂²×C₅₃

—

101

C₂²×C₅₃

—

102

C₂²×C₅₃

#386

yes

characteristic

103

C₄×C₅₃

—

104

C₄×C₅₃

—

105

C₄×C₅₃

—

106

C₄×C₅₃

—

107

C₄×C₅₃

#443

yes

—

108

C₄×C₅₃

#444

yes

—

109

C₄×C₅₃

#454

yes

—

110

#3131

C₂×C₅₃

yes

characteristic

111

#2986

C₂×C₅₃

yes

characteristic, complemented

112

#1526

C₂×C₅₃

yes

characteristic, complemented

113

#1484

C₂×C₅₃

yes

—

114

#1278

C₂×C₅₃

yes

complemented

115

C₂×C₅₃

—

116

C₂×C₅₃

—

117

C₂×C₅₃

#1876

yes

—

118

C₂×C₅₃

#1888

yes

characteristic

119

#533

C₂²×C₅₃

yes

characteristic

120

#532

C₂²×C₅₃

yes

characteristic

121

#488

—

122

#487

C₄×C₅₃

yes

—

123

#486

C₄×C₅₃

yes

—

124

#446

—

125

C₈×Q₈

—

126

#433

—

127

#431

C₂²×C₅₃

yes

—

128

#416

—

129

C₄×M₁₆

C₂²×C₅₃

yes

—

130

C₂×C₄×C₈

C₂²×C₅₃

yes

characteristic

131

#330

—

132

D₄⋊C₈

—

133

D₄⋊C₈

—

134

C₅₃

#9070

yes

characteristic, direct product factor, Sylow

135

C₂×#41

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

138

C₄⋊Q₈

C₂×C₄×C₅₃

yes

characteristic

139

C₄⋊Q₈

C₂×C₄×C₅₃

yes

—

140

#127

C₂×C₄×C₅₃

yes

characteristic

141

#125

D₄×C₅₃

yes

—

142

#124

—

143

C₂²⋊Q₈

—

144

#121

—

145

C₄×Q₈

—

146

C₄×D₄

—

147

#117

D₄×C₅₃

yes

—

148

C₂×C₄²

C₂³×C₅₃

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

D₄×C₅₃

yes

—

151

C₄⋊C₈

D₄×C₅₃

yes

—

152

#103

—

153

#102

—

154

C₂²⋊C₈

—

155

#97

—

156

#97

—

157

C₄×C₈

—

158

C₄×C₈

—

159

C₄×C₈

—

160

C₄×C₈

—

161

C₄×C₈

C₂×C₄×C₅₃

yes

—

162

#41

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂²×C₄

—

169

C₂²×C₄

C₂×D₄×C₅₃

yes

characteristic

170

C₂²×C₄

#41×C₅₃

yes

—

171

M₁₆

—

172

M₁₆

—

173

C₂×C₈

—

174

C₂×C₈

—

175

C₂×C₈

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄⋊C₄

C₂²⋊C₄×C₅₃

yes

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₄²

—

185

C₄²

C₂²×C₄×C₅₃

yes

characteristic

186

C₄²

C₂×D₄×C₅₃

yes

characteristic

187

C₄²

C₂×D₄×C₅₃

yes

—

188

C₂³

—

189

C₂³

#123×C₅₃

yes

characteristic

190

Q₈

—

191

Q₈

—

192

Q₈

—

193

D₄

—

194

D₄

—

195

D₄

—

196

D₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

C₂×C₂²⋊C₄×C₅₃

yes

characteristic

204

C₂×C₄

C₄×D₄×C₅₃

yes

—

205

C₂×C₄

#120×C₅₃

yes

characteristic

206

C₂×C₄

#121×C₅₃

yes

—

207

C₈

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₅₃×#386

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

C₅₃×#443

yes

—

221

C₄

C₅₃×#444

yes

—

222

C₄

C₅₃×#454

yes

—

223

C₂

—

224

C₂

—

225

C₂

C₅₃×#1876

yes

—

226

C₂

C₅₃×#1888

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	#120
commutator	C₄²	C₂²×C₄×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
socle	C₂²×C₅₃	#386
prime radical	C₅₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

subgroup

G/H

center

C₂×C₄×C₅₃

#120

commutator

C₄²

C₂²×C₄×C₅₃

Frattini, cosocle

C₂×C₄²

C₂³×C₅₃

socle

C₂²×C₅₃

#386

prime radical

C₅₃×#532

C₂²

LCS

G ▷ C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

N	H ≅ G/N	type
2. C₅₃×#2986	C₂	semidirect
3. C₅₃×#1526	C₂	semidirect
5. C₅₃×#1278	C₂	semidirect
97. #9070	C₅₃	direct (N × H)
111. #2986	C₂×C₅₃	semidirect
112. #1526	C₂×C₅₃	semidirect
114. #1278	C₂×C₅₃	semidirect
134. C₅₃	#9070	direct (N × H)

H ≅ G/N

type

2. C₅₃×#2986

C₂

semidirect

3. C₅₃×#1526

C₂

semidirect

5. C₅₃×#1278

C₂

semidirect

97. #9070

C₅₃

direct (N × H)

111. #2986

C₂×C₅₃

semidirect

112. #1526

C₂×C₅₃

semidirect

114. #1278

C₂×C₅₃

semidirect

134. C₅₃

#9070

direct (N × H)

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

subgroup	index
C₅₃×#3131	2
C₅₃×#2986	2
C₅₃×#1526	2
C₅₃×#1484	2
C₅₃×#1278	2
#9070	53

subgroup

index

C₅₃×#3131

C₅₃×#2986

C₅₃×#1526

C₅₃×#1484

C₅₃×#1278

#9070

Subgroups — C₅₃×#9070 #27216582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C53×#9070 #27216582

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#9070 #27216582