Group #27217529 — subgroups

Subgroups — C₅₃×#10017 #27217529

Order 13568.

528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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×#3104	C₂	1	2	yes	maximal
2	C₅₃×#2399	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#1995	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1487	C₂	1	2	yes	maximal
5	C₅₃×#1274	C₂	1	1	yes	maximal, characteristic
6	C₅₃×#533	C₂²	1	1	yes	characteristic
7	C₂×C₄×Q₈×C₅₃	C₂²	1	2	yes	—
8	C₅₃×#484	—	2	2	no	—
9	C₅₃×#477	—	2	2	no	—
10	C₅₃×#462	—	2	2	no	—
11	C₅₃×#451	—	2	2	no	—
12	C₄×Q₁₆×C₅₃	—	2	4	no	—
13	C₅₃×#431	C₂²	1	2	yes	—
14	C₅₃×#423	C₂²	1	1	yes	characteristic
15	C₅₃×#398	—	2	2	no	—
16	C₅₃×#395	—	2	2	no	—
17	C₄×C₄⋊C₄×C₅₃	—	2	2	no	—
18	C₅₃×#376	C₂²	1	1	yes	characteristic
19	C₅₃×#339	—	2	2	no	—
20	C₅₃×Q₈⋊C₈	—	2	4	no	—
21	C₂²×Q₈×C₅₃	D₄	1	2	yes	—
22	C₂×Q₁₆×C₅₃	—	2	4	no	—
23	C₂×M₁₆×C₅₃	—	2	1	no	—
24	C₄⋊Q₈×C₅₃	D₄	1	2	yes	—
25	#125×C₅₃	—	2	1	no	—
26	C₂²⋊Q₈×C₅₃	—	2	2	no	—
27	C₄×Q₈×C₅₃	—	2	2	no	—
28	C₄×Q₈×C₅₃	—	2	2	no	—
29	C₄×Q₈×C₅₃	—	2	2	no	—
30	C₄×Q₈×C₅₃	—	2	2	no	—
31	C₄×Q₈×C₅₃	—	2	2	no	—
32	#117×C₅₃	—	2	1	no	—
33	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
34	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
35	C₂×C₄⋊C₄×C₅₃	D₄	1	2	yes	—
36	C₂×C₄²×C₅₃	—	2	2	no	—
37	C₂×C₄²×C₅₃	D₄	1	2	yes	—
38	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
39	#107×C₅₃	—	2	4	no	—
40	C₄⋊C₈×C₅₃	—	2	2	no	—
41	C₄⋊C₈×C₅₃	—	2	2	no	—
42	#103×C₅₃	—	2	4	no	—
43	#103×C₅₃	—	2	4	no	—
44	C₂²⋊C₈×C₅₃	—	2	2	no	—
45	C₄×C₈×C₅₃	D₄	1	4	yes	—
46	#95×C₅₃	—	2	2	no	—
47	#95×C₅₃	—	2	2	no	—
48	#95×C₅₃	—	2	2	no	—
49	C₂×Q₈×C₅₃	—	2	2	no	—
50	C₂×Q₈×C₅₃	—	2	2	no	—
51	C₂×Q₈×C₅₃	—	2	2	no	—
52	C₂×Q₈×C₅₃	—	4	4	no	—
53	C₂²×C₄×C₅₃	—	2	2	no	—
54	C₂²×C₄×C₅₃	—	2	2	no	—
55	C₂²×C₄×C₅₃	—	2	2	no	—
56	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
57	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
58	Q₁₆×C₅₃	—	4	8	no	—
59	M₁₆×C₅₃	—	4	2	no	—
60	C₂×C₈×C₅₃	—	2	4	no	—
61	C₂×C₈×C₅₃	—	4	1	no	—
62	C₄⋊C₄×C₅₃	—	2	2	no	—
63	C₄⋊C₄×C₅₃	—	2	2	no	—
64	C₄⋊C₄×C₅₃	—	2	2	no	—
65	C₄⋊C₄×C₅₃	—	2	2	no	—
66	C₄⋊C₄×C₅₃	—	4	8	no	—
67	C₄⋊C₄×C₅₃	—	4	2	no	—
68	C₄⋊C₄×C₅₃	—	4	2	no	—
69	C₄⋊C₄×C₅₃	—	4	2	no	—
70	C₂²⋊C₄×C₅₃	—	4	1	no	—
71	C₄²×C₅₃	—	2	2	no	—
72	C₄²×C₅₃	—	4	2	no	—
73	C₄²×C₅₃	—	4	2	no	—
74	C₄²×C₅₃	—	4	1	no	—
75	C₄²×C₅₃	Q₁₆	1	4	yes	complemented
76	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₅₃	C₂×D₄	1	2	yes	—
78	C₄²×C₅₃	#41	1	1	yes	characteristic
79	C₂³×C₅₃	#120	1	1	yes	characteristic
80	Q₈×C₅₃	—	2	4	no	—
81	Q₈×C₅₃	—	2	4	no	—
82	Q₈×C₅₃	—	4	2	no	—
83	Q₈×C₅₃	—	4	2	no	—
84	Q₈×C₅₃	—	4	4	no	—
85	C₂×C₄×C₅₃	—	2	4	no	—
86	C₂×C₄×C₅₃	—	2	4	no	—
87	C₂×C₄×C₅₃	—	4	2	no	—
88	C₂×C₄×C₅₃	—	4	2	no	—
89	C₂×C₄×C₅₃	—	4	4	no	—
90	C₂×C₄×C₅₃	—	4	2	no	—
91	C₂×C₄×C₅₃	—	4	4	no	—
92	C₂×C₄×C₅₃	—	4	2	no	—
93	C₂×C₄×C₅₃	—	4	2	no	—
94	C₂×C₄×C₅₃	#120	1	2	yes	—
95	C₂×C₄×C₅₃	#121	1	2	yes	—
96	C₂×C₄×C₅₃	#121	1	1	yes	characteristic
97	C₂×C₄×C₅₃	#127	1	1	yes	characteristic
98	C₂×C₄×C₅₃	C₂×Q₁₆	1	2	yes	—
99	C₂×C₄×C₅₃	#137	1	2	yes	—
100	C₈×C₅₃	—	4	4	no	—
101	C₈×C₅₃	—	8	1	no	—
102	#10017	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
103	C₂²×C₅₃	—	2	2	no	—
104	C₂²×C₅₃	#392	1	1	yes	characteristic
105	C₂²×C₅₃	#451	1	2	yes	—
106	C₄×C₅₃	—	2	2	no	—
107	C₄×C₅₃	—	2	2	no	—
108	C₄×C₅₃	—	4	4	no	—
109	C₄×C₅₃	—	4	4	no	—
110	C₄×C₅₃	—	8	2	no	—
111	C₄×C₅₃	—	8	2	no	—
112	C₄×C₅₃	#462	1	2	yes	—
113	C₄×C₅₃	#494	1	1	yes	characteristic
114	C₄×C₅₃	#497	1	1	yes	characteristic
115	#3104	C₂×C₅₃	1	2	yes	—
116	#2399	C₂×C₅₃	1	1	yes	characteristic
117	#1995	C₂×C₅₃	1	1	yes	characteristic
118	#1487	C₂×C₅₃	1	2	yes	—
119	#1274	C₂×C₅₃	1	1	yes	characteristic
120	C₂×C₅₃	—	2	2	no	—
121	C₂×C₅₃	#2010	1	2	yes	—
122	C₂×C₅₃	#2016	1	1	yes	characteristic
123	#533	C₂²×C₅₃	1	1	yes	characteristic
124	C₂×C₄×Q₈	C₂²×C₅₃	1	2	yes	—
125	#484	—	2	2	no	—
126	#477	—	2	2	no	—
127	#462	—	2	2	no	—
128	#451	—	2	2	no	—
129	C₄×Q₁₆	—	2	4	no	—
130	#431	C₂²×C₅₃	1	2	yes	—
131	#423	C₂²×C₅₃	1	1	yes	characteristic
132	#398	—	2	2	no	—
133	#395	—	2	2	no	—
134	C₄×C₄⋊C₄	—	2	2	no	—
135	#376	C₂²×C₅₃	1	1	yes	characteristic
136	#339	—	2	2	no	—
137	Q₈⋊C₈	—	2	4	no	—
138	C₅₃	#10017	1	1	yes	characteristic, direct product factor, Sylow
139	C₂²×Q₈	D₄×C₅₃	1	2	yes	—
140	C₂×Q₁₆	—	2	4	no	—
141	C₂×M₁₆	—	2	1	no	—
142	C₄⋊Q₈	D₄×C₅₃	1	2	yes	—
143	#125	—	2	1	no	—
144	C₂²⋊Q₈	—	2	2	no	—
145	C₄×Q₈	—	2	2	no	—
146	C₄×Q₈	—	2	2	no	—
147	C₄×Q₈	—	2	2	no	—
148	C₄×Q₈	—	2	2	no	—
149	C₄×Q₈	—	2	2	no	—
150	#117	—	2	1	no	—
151	C₂×C₄⋊C₄	—	2	4	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	D₄×C₅₃	1	2	yes	—
154	C₂×C₄²	—	2	2	no	—
155	C₂×C₄²	D₄×C₅₃	1	2	yes	—
156	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
157	#107	—	2	4	no	—
158	C₄⋊C₈	—	2	2	no	—
159	C₄⋊C₈	—	2	2	no	—
160	#103	—	2	4	no	—
161	#103	—	2	4	no	—
162	C₂²⋊C₈	—	2	2	no	—
163	C₄×C₈	D₄×C₅₃	1	4	yes	—
164	#95	—	2	2	no	—
165	#95	—	2	2	no	—
166	#95	—	2	2	no	—
167	C₂×Q₈	—	2	2	no	—
168	C₂×Q₈	—	2	2	no	—
169	C₂×Q₈	—	2	2	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂²×C₄	—	2	2	no	—
172	C₂²×C₄	—	2	2	no	—
173	C₂²×C₄	—	2	2	no	—
174	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
175	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
176	Q₁₆	—	4	8	no	—
177	M₁₆	—	4	2	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	4	1	no	—
180	C₄⋊C₄	—	2	2	no	—
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	2	no	—
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	4	8	no	—
185	C₄⋊C₄	—	4	2	no	—
186	C₄⋊C₄	—	4	2	no	—
187	C₄⋊C₄	—	4	2	no	—
188	C₂²⋊C₄	—	4	1	no	—
189	C₄²	—	2	2	no	—
190	C₄²	—	4	2	no	—
191	C₄²	—	4	2	no	—
192	C₄²	—	4	1	no	—
193	C₄²	Q₁₆×C₅₃	1	4	yes	complemented
194	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
195	C₄²	C₂×D₄×C₅₃	1	2	yes	—
196	C₄²	#41×C₅₃	1	1	yes	characteristic
197	C₂³	#120×C₅₃	1	1	yes	characteristic
198	Q₈	—	2	4	no	—
199	Q₈	—	2	4	no	—
200	Q₈	—	4	2	no	—
201	Q₈	—	4	2	no	—
202	Q₈	—	4	4	no	—
203	C₂×C₄	—	2	4	no	—
204	C₂×C₄	—	2	4	no	—
205	C₂×C₄	—	4	2	no	—
206	C₂×C₄	—	4	4	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	2	no	—
209	C₂×C₄	—	4	4	no	—
210	C₂×C₄	—	4	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	#120×C₅₃	1	2	yes	—
213	C₂×C₄	#121×C₅₃	1	2	yes	—
214	C₂×C₄	#121×C₅₃	1	1	yes	characteristic
215	C₂×C₄	#127×C₅₃	1	1	yes	characteristic
216	C₂×C₄	C₂×Q₁₆×C₅₃	1	2	yes	—
217	C₂×C₄	#137×C₅₃	1	2	yes	—
218	C₈	—	4	4	no	—
219	C₈	—	8	1	no	—
220	C₂²	—	2	2	no	—
221	C₂²	C₅₃×#392	1	1	yes	characteristic
222	C₂²	C₅₃×#451	1	2	yes	—
223	C₄	—	2	2	no	—
224	C₄	—	2	2	no	—
225	C₄	—	4	4	no	—
226	C₄	—	4	4	no	—
227	C₄	—	8	2	no	—
228	C₄	—	8	2	no	—
229	C₄	C₅₃×#462	1	2	yes	—
230	C₄	C₅₃×#494	1	1	yes	characteristic
231	C₄	C₅₃×#497	1	1	yes	characteristic
232	C₂	—	2	2	no	—
233	C₂	C₅₃×#2010	1	2	yes	—
234	C₂	C₅₃×#2016	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₅₃×#3104

C₂

yes

maximal

C₅₃×#2399

C₂

yes

maximal, characteristic

C₅₃×#1995

C₂

yes

maximal, characteristic

C₅₃×#1487

C₂

yes

maximal

C₅₃×#1274

C₂

yes

maximal, characteristic

C₅₃×#533

C₂²

yes

characteristic

C₂×C₄×Q₈×C₅₃

C₂²

yes

—

C₅₃×#484

—

C₅₃×#477

—

C₅₃×#462

—

C₅₃×#451

—

C₄×Q₁₆×C₅₃

—

C₅₃×#431

C₂²

yes

—

C₅₃×#423

C₂²

yes

characteristic

C₅₃×#398

—

C₅₃×#395

—

C₄×C₄⋊C₄×C₅₃

—

C₅₃×#376

C₂²

yes

characteristic

C₅₃×#339

—

C₅₃×Q₈⋊C₈

—

C₂²×Q₈×C₅₃

D₄

yes

—

C₂×Q₁₆×C₅₃

—

C₂×M₁₆×C₅₃

—

C₄⋊Q₈×C₅₃

D₄

yes

—

#125×C₅₃

—

C₂²⋊Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

#117×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

#107×C₅₃

—

C₄⋊C₈×C₅₃

—

C₄⋊C₈×C₅₃

—

#103×C₅₃

—

#103×C₅₃

—

C₂²⋊C₈×C₅₃

—

C₄×C₈×C₅₃

D₄

yes

—

#95×C₅₃

—

#95×C₅₃

—

#95×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×D₄

yes

—

C₂²×C₄×C₅₃

C₂×D₄

yes

characteristic

Q₁₆×C₅₃

—

M₁₆×C₅₃

—

C₂×C₈×C₅₃

—

C₂×C₈×C₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

—

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

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

Q₁₆

yes

complemented

C₄²×C₅₃

C₂×D₄

yes

characteristic

C₄²×C₅₃

C₂×D₄

yes

—

C₄²×C₅₃

yes

C₂³×C₅₃

yes

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

Q₈×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#120

yes

—

C₂×C₄×C₅₃

#121

yes

—

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

yes

C₂×C₄×C₅₃

C₂×Q₁₆

yes

—

C₂×C₄×C₅₃

#137

yes

—

100

C₈×C₅₃

—

101

C₈×C₅₃

—

102

#10017

C₅₃

yes

maximal, characteristic, direct product factor, Sylow

103

C₂²×C₅₃

—

104

C₂²×C₅₃

#392

yes

characteristic

105

C₂²×C₅₃

#451

yes

—

106

C₄×C₅₃

—

107

C₄×C₅₃

—

108

C₄×C₅₃

—

109

C₄×C₅₃

—

110

C₄×C₅₃

—

111

C₄×C₅₃

—

112

C₄×C₅₃

#462

yes

—

113

C₄×C₅₃

#494

yes

characteristic

114

C₄×C₅₃

#497

yes

characteristic

115

#3104

C₂×C₅₃

yes

—

116

#2399

C₂×C₅₃

yes

characteristic

117

#1995

C₂×C₅₃

yes

characteristic

118

#1487

C₂×C₅₃

yes

—

119

#1274

C₂×C₅₃

yes

characteristic

120

C₂×C₅₃

—

121

C₂×C₅₃

#2010

yes

—

122

C₂×C₅₃

#2016

yes

characteristic

123

#533

C₂²×C₅₃

yes

characteristic

124

C₂×C₄×Q₈

C₂²×C₅₃

yes

—

125

#484

—

126

#477

—

127

#462

—

128

#451

—

129

C₄×Q₁₆

—

130

#431

C₂²×C₅₃

yes

—

131

#423

C₂²×C₅₃

yes

characteristic

132

#398

—

133

#395

—

134

C₄×C₄⋊C₄

—

135

#376

C₂²×C₅₃

yes

characteristic

136

#339

—

137

Q₈⋊C₈

—

138

C₅₃

#10017

yes

characteristic, direct product factor, Sylow

139

C₂²×Q₈

D₄×C₅₃

yes

—

140

C₂×Q₁₆

—

141

C₂×M₁₆

—

142

C₄⋊Q₈

D₄×C₅₃

yes

—

143

#125

—

144

C₂²⋊Q₈

—

145

C₄×Q₈

—

146

C₄×Q₈

—

147

C₄×Q₈

—

148

C₄×Q₈

—

149

C₄×Q₈

—

150

#117

—

151

C₂×C₄⋊C₄

—

152

C₂×C₄⋊C₄

—

153

C₂×C₄⋊C₄

D₄×C₅₃

yes

—

154

C₂×C₄²

—

155

C₂×C₄²

D₄×C₅₃

yes

—

156

C₂×C₄²

C₂³×C₅₃

yes

characteristic

157

#107

—

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

161

#103

—

162

C₂²⋊C₈

—

163

C₄×C₈

D₄×C₅₃

yes

—

164

#95

—

165

#95

—

166

#95

—

167

C₂×Q₈

—

168

C₂×Q₈

—

169

C₂×Q₈

—

170

C₂×Q₈

—

171

C₂²×C₄

—

172

C₂²×C₄

—

173

C₂²×C₄

—

174

C₂²×C₄

C₂×D₄×C₅₃

yes

—

175

C₂²×C₄

C₂×D₄×C₅₃

yes

characteristic

176

Q₁₆

—

177

M₁₆

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄⋊C₄

—

186

C₄⋊C₄

—

187

C₄⋊C₄

—

188

C₂²⋊C₄

—

189

C₄²

—

190

C₄²

—

191

C₄²

—

192

C₄²

—

193

C₄²

Q₁₆×C₅₃

yes

complemented

194

C₄²

C₂×D₄×C₅₃

yes

characteristic

195

C₄²

C₂×D₄×C₅₃

yes

—

196

C₄²

#41×C₅₃

yes

characteristic

197

C₂³

#120×C₅₃

yes

characteristic

198

Q₈

—

199

Q₈

—

200

Q₈

—

201

Q₈

—

202

Q₈

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

#120×C₅₃

yes

—

213

C₂×C₄

#121×C₅₃

yes

—

214

C₂×C₄

#121×C₅₃

yes

characteristic

215

C₂×C₄

#127×C₅₃

yes

characteristic

216

C₂×C₄

C₂×Q₁₆×C₅₃

yes

—

217

C₂×C₄

#137×C₅₃

yes

—

218

C₈

—

219

C₈

—

220

C₂²

—

221

C₂²

C₅₃×#392

yes

characteristic

222

C₂²

C₅₃×#451

yes

—

223

C₄

—

224

C₄

—

225

C₄

—

226

C₄

—

227

C₄

—

228

C₄

—

229

C₄

C₅₃×#462

yes

—

230

C₄

C₅₃×#494

yes

characteristic

231

C₄

C₅₃×#497

yes

characteristic

232

C₂

—

233

C₂

C₅₃×#2010

yes

—

234

C₂

C₅₃×#2016

yes

characteristic

	subgroup	G/H
center	C₂×C₄×C₅₃	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
socle	C₂²×C₅₃	#392
prime radical	C₂³×C₅₃	#120
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

subgroup

G/H

center

C₂×C₄×C₅₃

#127

commutator, Frattini, cosocle

C₂×C₄²

C₂³×C₅₃

C₂²×C₅₃

C₂³×C₅₃

G ▷ C₂×C₄² ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂×C₄×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

N	H ≅ G/N	type
75. C₄²×C₅₃	Q₁₆	semidirect
102. #10017	C₅₃	direct (N × H)
138. C₅₃	#10017	direct (N × H)
193. C₄²	Q₁₆×C₅₃	semidirect

H ≅ G/N

type

75. C₄²×C₅₃

Q₁₆

semidirect

102. #10017

C₅₃

direct (N × H)

138. C₅₃

#10017

direct (N × H)

193. C₄²

Q₁₆×C₅₃

semidirect

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

subgroup	index
C₅₃×#3104	2
C₅₃×#2399	2
C₅₃×#1995	2
C₅₃×#1487	2
C₅₃×#1274	2
#10017	53

subgroup

index

C₅₃×#3104

C₅₃×#2399

C₅₃×#1995

C₅₃×#1487

C₅₃×#1274

#10017

Subgroups — C₅₃×#10017 #27217529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C53×#10017 #27217529

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#10017 #27217529