Group #27215850 — subgroups

Subgroups — C₅₃×#8338 #27215850

Order 13568.

814 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 174 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×C₅₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#1749	C₂	1	2	yes	maximal
3	C₂×C₅₃×#330	C₂	1	4	yes	maximal, complemented
4	C₅₃×#533	—	2	8	no	—
5	C₂×C₄⋊Q₈×C₅₃	C₄	1	2	yes	—
6	C₂×#125×C₅₃	C₂²	1	2	yes	—
7	C₂×C₂²⋊Q₈×C₅₃	—	2	2	no	—
8	C₂×C₄×Q₈×C₅₃	—	2	2	no	—
9	C₂×#117×C₅₃	C₄	1	2	yes	—
10	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊C₈×C₅₃	—	2	2	no	—
12	C₂×#97×C₅₃	C₂²	1	4	yes	—
13	C₅₃×#336	—	2	2	no	—
14	C₅₃×#330	—	2	8	no	—
15	C₂²×Q₈×C₅₃	—	2	2	no	—
16	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₅₃	D₄	1	2	yes	—
18	C₂²×C₈×C₅₃	—	2	4	no	—
19	C₄⋊Q₈×C₅₃	—	2	8	no	—
20	#125×C₅₃	—	2	4	no	—
21	#125×C₅₃	D₄	1	8	yes	—
22	C₂²⋊Q₈×C₅₃	—	2	16	no	—
23	C₄×Q₈×C₅₃	—	2	16	no	—
24	#117×C₅₃	—	2	8	no	—
25	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
26	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
27	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
28	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
29	C₂×C₄²×C₅₃	—	2	4	no	—
30	C₂×C₄²×C₅₃	—	2	2	no	—
31	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₅₃	D₄	1	2	yes	—
33	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
34	C₂²⋊C₈×C₅₃	—	2	8	no	—
35	#97×C₅₃	—	2	8	no	—
36	C₂⁴×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Q₈×C₅₃	—	2	8	no	—
38	C₂×Q₈×C₅₃	—	4	4	no	—
39	C₂×Q₈×C₅₃	—	4	4	no	—
40	C₂²×C₄×C₅₃	—	2	2	no	—
41	C₂²×C₄×C₅₃	—	2	2	no	—
42	C₂²×C₄×C₅₃	—	2	2	no	—
43	C₂²×C₄×C₅₃	—	2	4	no	—
44	C₂²×C₄×C₅₃	—	2	4	no	—
45	C₂²×C₄×C₅₃	—	2	4	no	—
46	C₂²×C₄×C₅₃	—	4	2	no	—
47	C₂²×C₄×C₅₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
51	C₂×C₈×C₅₃	—	2	8	no	—
52	C₂×C₈×C₅₃	—	4	4	no	—
53	C₂×C₈×C₅₃	—	4	4	no	—
54	C₄⋊C₄×C₅₃	—	2	8	no	—
55	C₄⋊C₄×C₅₃	—	2	4	no	—
56	C₄⋊C₄×C₅₃	—	2	16	no	—
57	C₄⋊C₄×C₅₃	C₂²⋊C₄	1	8	yes	—
58	C₂²⋊C₄×C₅₃	—	2	8	no	—
59	C₄²×C₅₃	—	2	8	no	—
60	C₄²×C₅₃	—	2	2	no	—
61	C₄²×C₅₃	—	2	4	no	—
62	C₄²×C₅₃	C₂×D₄	1	4	yes	—
63	C₂³×C₅₃	—	2	1	no	—
64	C₂³×C₅₃	—	2	1	no	—
65	C₂³×C₅₃	—	2	2	no	—
66	C₂³×C₅₃	—	2	2	no	—
67	C₂³×C₅₃	#101	1	2	yes	—
68	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	Q₈×C₅₃	—	4	16	no	—
70	C₂×C₄×C₅₃	—	2	8	no	—
71	C₂×C₄×C₅₃	—	2	2	no	—
72	C₂×C₄×C₅₃	—	2	1	no	—
73	C₂×C₄×C₅₃	—	2	1	no	—
74	C₂×C₄×C₅₃	—	2	1	no	—
75	C₂×C₄×C₅₃	—	2	1	no	—
76	C₂×C₄×C₅₃	—	2	2	no	—
77	C₂×C₄×C₅₃	—	2	2	no	—
78	C₂×C₄×C₅₃	—	2	2	no	—
79	C₂×C₄×C₅₃	—	2	8	no	—
80	C₂×C₄×C₅₃	—	4	8	no	—
81	C₂×C₄×C₅₃	—	4	4	no	—
82	C₂×C₄×C₅₃	—	4	4	no	—
83	C₂×C₄×C₅₃	#101	1	2	yes	—
84	C₂×C₄×C₅₃	#104	1	4	yes	—
85	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	2	yes	—
86	C₂×C₄×C₅₃	#120	1	4	yes	—
87	C₈×C₅₃	—	4	8	no	—
88	#8338	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₂²×C₅₃	—	2	2	no	—
90	C₂²×C₅₃	—	2	4	no	—
91	C₂²×C₅₃	—	4	1	no	—
92	C₂²×C₅₃	—	4	1	no	—
93	C₂²×C₅₃	—	4	2	no	—
94	C₂²×C₅₃	#379	1	1	yes	characteristic
95	C₂²×C₅₃	C₂×#101	1	1	yes	characteristic
96	C₂²×C₅₃	C₂×#101	1	1	yes	characteristic
97	C₂²×C₅₃	C₂×#104	1	2	yes	—
98	C₂²×C₅₃	#421	1	2	yes	—
99	C₄×C₅₃	—	2	2	no	—
100	C₄×C₅₃	—	2	2	no	—
101	C₄×C₅₃	—	2	4	no	—
102	C₄×C₅₃	—	2	4	no	—
103	C₄×C₅₃	—	4	8	no	—
104	C₂×#533	C₂×C₅₃	1	1	yes	characteristic
105	#1749	C₂×C₅₃	1	2	yes	—
106	C₂×#330	C₂×C₅₃	1	4	yes	complemented
107	C₂×C₅₃	—	4	2	no	—
108	C₂×C₅₃	#1526	1	1	yes	characteristic
109	C₂×C₅₃	#1531	1	2	yes	—
110	C₂×C₅₃	#1537	1	1	yes	characteristic
111	C₂×C₅₃	#1784	1	1	yes	characteristic
112	C₂×C₅₃	#1789	1	2	yes	—
113	#533	—	2	8	no	—
114	C₂×C₄⋊Q₈	C₄×C₅₃	1	2	yes	—
115	C₂×#125	C₂²×C₅₃	1	2	yes	—
116	C₂×C₂²⋊Q₈	—	2	2	no	—
117	C₂×C₄×Q₈	—	2	2	no	—
118	C₂×#117	C₄×C₅₃	1	2	yes	—
119	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
120	C₂×C₂²⋊C₈	—	2	2	no	—
121	C₂×#97	C₂²×C₅₃	1	4	yes	—
122	#336	—	2	2	no	—
123	#330	—	2	8	no	—
124	C₅₃	#8338	1	1	yes	characteristic, direct product factor, Sylow
125	C₂²×Q₈	—	2	2	no	—
126	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
127	C₂³×C₄	D₄×C₅₃	1	2	yes	—
128	C₂²×C₈	—	2	4	no	—
129	C₄⋊Q₈	—	2	8	no	—
130	#125	—	2	4	no	—
131	#125	D₄×C₅₃	1	8	yes	—
132	C₂²⋊Q₈	—	2	16	no	—
133	C₄×Q₈	—	2	16	no	—
134	#117	—	2	8	no	—
135	C₂×C₄⋊C₄	—	2	4	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
138	C₂×C₂²⋊C₄	—	2	2	no	—
139	C₂×C₄²	—	2	2	no	—
140	C₂×C₄²	—	2	4	no	—
141	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
142	C₂×C₄²	D₄×C₅₃	1	2	yes	—
143	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
144	C₂²⋊C₈	—	2	8	no	—
145	#97	—	2	8	no	—
146	C₂⁴	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
147	C₂×Q₈	—	2	8	no	—
148	C₂×Q₈	—	4	4	no	—
149	C₂×Q₈	—	4	4	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	4	no	—
154	C₂²×C₄	—	2	4	no	—
155	C₂²×C₄	—	2	4	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	C₂²⋊C₄×C₅₃	1	1	yes	characteristic
158	C₂²×C₄	C₂²⋊C₄×C₅₃	1	2	yes	—
159	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
160	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
161	C₂×C₈	—	2	8	no	—
162	C₂×C₈	—	4	4	no	—
163	C₂×C₈	—	4	4	no	—
164	C₄⋊C₄	—	2	8	no	—
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	2	16	no	—
167	C₄⋊C₄	C₂²⋊C₄×C₅₃	1	8	yes	—
168	C₂²⋊C₄	—	2	8	no	—
169	C₄²	—	2	8	no	—
170	C₄²	—	2	2	no	—
171	C₄²	—	2	4	no	—
172	C₄²	C₂×D₄×C₅₃	1	4	yes	—
173	C₂³	—	2	1	no	—
174	C₂³	—	2	1	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	2	no	—
177	C₂³	#101×C₅₃	1	2	yes	—
178	C₂³	C₂×C₂²⋊C₄×C₅₃	1	1	yes	characteristic
179	Q₈	—	4	16	no	—
180	C₂×C₄	—	2	8	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	8	no	—
190	C₂×C₄	—	4	8	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	#101×C₅₃	1	2	yes	—
194	C₂×C₄	#104×C₅₃	1	4	yes	—
195	C₂×C₄	C₂×C₂²⋊C₄×C₅₃	1	2	yes	—
196	C₂×C₄	#120×C₅₃	1	4	yes	—
197	C₈	—	4	8	no	—
198	C₂²	—	2	2	no	—
199	C₂²	—	2	4	no	—
200	C₂²	—	4	1	no	—
201	C₂²	—	4	2	no	—
202	C₂²	—	4	1	no	—
203	C₂²	C₅₃×#379	1	1	yes	characteristic
204	C₂²	C₂×#101×C₅₃	1	1	yes	characteristic
205	C₂²	C₂×#101×C₅₃	1	1	yes	characteristic
206	C₂²	C₂×#104×C₅₃	1	2	yes	—
207	C₂²	C₅₃×#421	1	2	yes	—
208	C₄	—	2	2	no	—
209	C₄	—	2	2	no	—
210	C₄	—	2	4	no	—
211	C₄	—	2	4	no	—
212	C₄	—	4	8	no	—
213	C₂	—	4	2	no	—
214	C₂	C₅₃×#1526	1	1	yes	characteristic
215	C₂	C₅₃×#1531	1	2	yes	—
216	C₂	C₅₃×#1537	1	1	yes	characteristic
217	C₂	C₅₃×#1784	1	1	yes	characteristic
218	C₂	C₅₃×#1789	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅₃×#533

C₂

yes

maximal, characteristic

C₅₃×#1749

C₂

yes

maximal

C₂×C₅₃×#330

C₂

yes

maximal, complemented

C₅₃×#533

—

C₂×C₄⋊Q₈×C₅₃

C₄

yes

—

C₂×#125×C₅₃

C₂²

yes

—

C₂×C₂²⋊Q₈×C₅₃

—

C₂×C₄×Q₈×C₅₃

—

C₂×#117×C₅₃

C₄

yes

—

C₂²×C₄²×C₅₃

C₂²

yes

characteristic

C₂×C₂²⋊C₈×C₅₃

—

C₂×#97×C₅₃

C₂²

yes

—

C₅₃×#336

—

C₅₃×#330

—

C₂²×Q₈×C₅₃

—

C₂³×C₄×C₅₃

C₂×C₄

yes

characteristic

C₂³×C₄×C₅₃

D₄

yes

—

C₂²×C₈×C₅₃

—

C₄⋊Q₈×C₅₃

—

#125×C₅₃

—

#125×C₅₃

D₄

yes

—

C₂²⋊Q₈×C₅₃

—

C₄×Q₈×C₅₃

—

#117×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

—

C₂×C₄⋊C₄×C₅₃

C₂×C₄

yes

—

C₂×C₂²⋊C₄×C₅₃

—

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

—

C₂×C₄²×C₅₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₅₃

D₄

yes

—

C₂×C₄²×C₅₃

C₂³

yes

characteristic

C₂²⋊C₈×C₅₃

—

#97×C₅₃

—

C₂⁴×C₅₃

C₂²⋊C₄

yes

characteristic

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂×Q₈×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₅₃

C₂×D₄

yes

—

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

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

—

C₄²×C₅₃

C₂×D₄

yes

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

#101

yes

—

C₂³×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

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

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

—

C₂×C₄×C₅₃

#101

yes

—

C₂×C₄×C₅₃

#104

yes

—

C₂×C₄×C₅₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₅₃

#120

yes

—

C₈×C₅₃

—

#8338

C₅₃

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

C₂²×C₅₃

yes

—

C₂²×C₅₃

#421

yes

—

C₄×C₅₃

—

100

C₄×C₅₃

—

101

C₄×C₅₃

—

102

C₄×C₅₃

—

103

C₄×C₅₃

—

104

C₂×#533

C₂×C₅₃

yes

characteristic

105

#1749

C₂×C₅₃

yes

—

106

C₂×#330

C₂×C₅₃

yes

complemented

107

C₂×C₅₃

—

108

C₂×C₅₃

#1526

yes

characteristic

109

C₂×C₅₃

#1531

yes

—

110

C₂×C₅₃

#1537

yes

characteristic

111

C₂×C₅₃

#1784

yes

characteristic

112

C₂×C₅₃

#1789

yes

—

113

#533

—

114

C₂×C₄⋊Q₈

C₄×C₅₃

yes

—

115

C₂×#125

C₂²×C₅₃

yes

—

116

C₂×C₂²⋊Q₈

—

117

C₂×C₄×Q₈

—

118

C₂×#117

C₄×C₅₃

yes

—

119

C₂²×C₄²

C₂²×C₅₃

yes

characteristic

120

C₂×C₂²⋊C₈

—

121

C₂×#97

C₂²×C₅₃

yes

—

122

#336

—

123

#330

—

124

C₅₃

#8338

yes

characteristic, direct product factor, Sylow

125

C₂²×Q₈

—

126

C₂³×C₄

C₂×C₄×C₅₃

yes

characteristic

127

C₂³×C₄

D₄×C₅₃

yes

—

128

C₂²×C₈

—

129

C₄⋊Q₈

—

130

#125

—

131

#125

D₄×C₅₃

yes

—

132

C₂²⋊Q₈

—

133

C₄×Q₈

—

134

#117

—

135

C₂×C₄⋊C₄

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

C₂×C₄×C₅₃

yes

—

138

C₂×C₂²⋊C₄

—

139

C₂×C₄²

—

140

C₂×C₄²

—

141

C₂×C₄²

C₂×C₄×C₅₃

yes

characteristic

142

C₂×C₄²

D₄×C₅₃

yes

—

143

C₂×C₄²

C₂³×C₅₃

yes

characteristic

144

C₂²⋊C₈

—

145

#97

—

146

C₂⁴

C₂²⋊C₄×C₅₃

yes

characteristic

147

C₂×Q₈

—

148

C₂×Q₈

—

149

C₂×Q₈

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

C₂²⋊C₄×C₅₃

yes

characteristic

158

C₂²×C₄

C₂²⋊C₄×C₅₃

yes

—

159

C₂²×C₄

C₂²×C₄×C₅₃

yes

characteristic

160

C₂²×C₄

C₂×D₄×C₅₃

yes

—

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₄⋊C₄

—

167

C₄⋊C₄

C₂²⋊C₄×C₅₃

yes

—

168

C₂²⋊C₄

—

169

C₄²

—

170

C₄²

—

171

C₄²

—

172

C₄²

C₂×D₄×C₅₃

yes

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

#101×C₅₃

yes

—

178

C₂³

C₂×C₂²⋊C₄×C₅₃

yes

characteristic

179

Q₈

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

#101×C₅₃

yes

—

194

C₂×C₄

#104×C₅₃

yes

—

195

C₂×C₄

C₂×C₂²⋊C₄×C₅₃

yes

—

196

C₂×C₄

#120×C₅₃

yes

—

197

C₈

—

198

C₂²

—

199

C₂²

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

C₅₃×#379

yes

characteristic

204

C₂²

C₂×#101×C₅₃

yes

characteristic

205

C₂²

C₂×#101×C₅₃

yes

characteristic

206

C₂²

C₂×#104×C₅₃

yes

—

207

C₂²

C₅₃×#421

yes

—

208

C₄

—

209

C₄

—

210

C₄

—

211

C₄

—

212

C₄

—

213

C₂

—

214

C₂

C₅₃×#1526

yes

characteristic

215

C₂

C₅₃×#1531

yes

—

216

C₂

C₅₃×#1537

yes

characteristic

217

C₂

C₅₃×#1784

yes

characteristic

218

C₂

C₅₃×#1789

yes

—

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₅₃
Frattini, cosocle	C₂×C₄²	C₂³×C₅₃
prime radical	C₂⁴×C₅₃	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

subgroup

G/H

center, socle

C₂³×C₅₃

C₂×C₂²⋊C₄

commutator

C₂²×C₄

C₂²×C₄×C₅₃

Frattini, cosocle

C₂×C₄²

C₂³×C₅₃

prime radical

C₂⁴×C₅₃

C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂³×C₅₃ ◁ C₂²×C₄²×C₅₃ ◁ G

N	H ≅ G/N	type
3. C₂×C₅₃×#330	C₂	semidirect
88. #8338	C₅₃	direct (N × H)
106. C₂×#330	C₂×C₅₃	semidirect
124. C₅₃	#8338	direct (N × H)

H ≅ G/N

type

3. C₂×C₅₃×#330

C₂

semidirect

88. #8338

C₅₃

direct (N × H)

106. C₂×#330

C₂×C₅₃

semidirect

124. C₅₃

#8338

direct (N × H)

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

subgroup	index
C₂×C₅₃×#533	2
C₅₃×#1749	2
C₂×C₅₃×#330	2
#8338	53

subgroup

index

C₂×C₅₃×#533

C₅₃×#1749

C₂×C₅₃×#330

#8338

Subgroups — C₅₃×#8338 #27215850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C53×#8338 #27215850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#8338 #27215850