Group #20275033 — subgroups

Subgroups — #20275033

Order 6784.

456 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 129 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	C₂²×C₄⋊Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13133138	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊#88322	C₂	1	1	yes	maximal, characteristic, complemented
4	#16810385	C₂	1	2	yes	maximal, complemented
5	C₂×#121×C₅₃	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₅₃	—	2	1	no	—
7	C₂²×#88322	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₅₃	—	2	4	no	—
9	C₂×C₄⋊Dic₅₃	—	2	1	no	—
10	C₂×C₄⋊Dic₅₃	C₂²	1	2	yes	—
11	#13133138	—	2	4	no	—
12	C₂²⋊#88322	—	2	2	no	—
13	C₂²×D₄×C₅₃	—	2	1	no	—
14	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
15	C₂³×C₄×C₅₃	C₂²	1	1	yes	characteristic
16	#121×C₅₃	—	2	2	no	—
17	#121×C₅₃	C₄	1	4	yes	complemented
18	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
20	C₂⁴×C₅₃	—	2	1	no	—
21	C₂⁴×C₅₃	D₄	1	1	yes	characteristic
22	C₂×D₄×C₅₃	—	2	4	no	—
23	C₂×D₄×C₅₃	—	2	2	no	—
24	C₂×D₄×C₅₃	—	2	1	no	—
25	C₂×D₄×C₅₃	—	2	2	no	—
26	C₂×D₄×C₅₃	—	4	2	no	—
27	C₂×D₄×C₅₃	—	4	2	no	—
28	C₂×D₄×C₅₃	C₂×C₄	1	2	yes	complemented
29	C₂²×C₄×C₅₃	—	2	2	no	—
30	C₂²×C₄×C₅₃	—	2	2	no	—
31	C₂²×C₄×C₅₃	—	2	1	no	—
32	C₂²×C₄×C₅₃	C₂×C₄	1	2	yes	—
33	C₂²×C₄×C₅₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×C₅₃	D₄	1	2	yes	—
35	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
36	C₂²×Dic₅₃	—	2	4	no	—
37	C₂²×Dic₅₃	—	2	2	no	—
38	C₂²×Dic₅₃	—	4	2	no	—
39	C₂²×Dic₅₃	—	4	2	no	—
40	C₄⋊C₄×C₅₃	—	2	1	no	—
41	C₄⋊C₄×C₅₃	C₂×C₄	1	2	yes	complemented
42	C₂²⋊C₄×C₅₃	—	2	4	no	—
43	C₄⋊Dic₅₃	—	2	4	no	—
44	C₄⋊Dic₅₃	—	2	2	no	—
45	C₄⋊Dic₅₃	D₄	1	4	yes	complemented
46	C₂×#88322	—	2	2	no	—
47	C₂×#88322	—	2	2	no	—
48	C₂×#88322	—	2	2	no	—
49	C₂³×C₅₃	—	2	1	no	—
50	C₂³×C₅₃	—	2	1	no	—
51	C₂³×C₅₃	—	2	1	no	—
52	C₂³×C₅₃	—	2	1	no	—
53	C₂³×C₅₃	—	2	2	no	—
54	C₂³×C₅₃	—	4	1	no	—
55	C₂³×C₅₃	—	4	1	no	—
56	C₂³×C₅₃	—	4	1	no	—
57	C₂³×C₅₃	—	4	1	no	—
58	C₂³×C₅₃	—	4	1	no	—
59	C₂³×C₅₃	—	4	1	no	—
60	C₂³×C₅₃	C₂²⋊C₄	1	2	yes	—
61	C₂³×C₅₃	D₈	1	2	yes	—
62	C₂³×C₅₃	SD₁₆	1	2	yes	—
63	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
64	D₄×C₅₃	—	2	4	no	—
65	D₄×C₅₃	—	4	8	no	—
66	D₄×C₅₃	—	4	2	no	—
67	C₂×C₄×C₅₃	—	2	1	no	—
68	C₂×C₄×C₅₃	—	2	1	no	—
69	C₂×C₄×C₅₃	—	2	4	no	—
70	C₂×C₄×C₅₃	—	2	4	no	—
71	C₂×C₄×C₅₃	—	2	2	no	—
72	C₂×C₄×C₅₃	—	4	1	no	—
73	C₂×C₄×C₅₃	—	4	1	no	—
74	C₂×C₄×C₅₃	C₂²⋊C₄	1	2	yes	—
75	C₂×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₄×C₅₃	C₂×D₄	1	2	yes	—
77	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₅₃	#41	1	2	yes	—
79	C₂×Dic₅₃	—	2	4	no	—
80	C₂×Dic₅₃	—	4	8	no	—
81	C₂×Dic₅₃	—	4	2	no	—
82	C₂×Dic₅₃	—	4	2	no	—
83	#88322	—	4	2	no	—
84	C₂²×C₅₃	—	2	2	no	—
85	C₂²×C₅₃	—	2	2	no	—
86	C₂²×C₅₃	—	2	2	no	—
87	C₂²×C₅₃	—	2	2	no	—
88	C₂²×C₅₃	—	2	2	no	—
89	C₂²×C₅₃	—	2	2	no	—
90	C₂²×C₅₃	—	4	2	no	—
91	C₂²×C₅₃	—	4	2	no	—
92	C₂²×C₅₃	—	4	2	no	—
93	C₂²×C₅₃	—	8	1	no	—
94	C₂²×C₅₃	—	8	1	no	—
95	C₂²×C₅₃	—	8	1	no	—
96	C₂²×C₅₃	—	8	1	no	—
97	C₂²×C₅₃	#102	1	4	yes	complemented
98	C₂²×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂²×C₅₃	#120	1	1	yes	characteristic
100	C₂²×C₅₃	#123	1	1	yes	characteristic
101	C₂²×C₅₃	C₂×D₈	1	1	yes	characteristic
102	C₂²×C₅₃	C₂×SD₁₆	1	1	yes	characteristic
103	C₂²×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂²×C₅₃	#137	1	1	yes	characteristic
105	C₄×C₅₃	—	2	2	no	—
106	C₄×C₅₃	—	4	2	no	—
107	C₄×C₅₃	C₄×D₄	1	2	yes	—
108	C₄×C₅₃	#121	1	2	yes	—
109	Dic₅₃	—	4	4	no	—
110	#1874	—	53	1	no	maximal, Sylow
111	C₂×C₅₃	—	2	4	no	—
112	C₂×C₅₃	—	8	2	no	—
113	C₂×C₅₃	#386	1	1	yes	characteristic
114	C₂×C₅₃	C₂×#102	1	1	yes	characteristic
115	C₂×C₅₃	#417	1	1	yes	characteristic
116	C₂×C₅₃	#447	1	1	yes	characteristic
117	C₂×C₅₃	#448	1	1	yes	characteristic
118	C₂×C₅₃	#480	1	1	yes	characteristic
119	C₂×C₅₃	#481	1	1	yes	characteristic
120	C₂×#121	D₅₃	1	1	yes	characteristic
121	C₂²×C₄⋊C₄	—	53	1	no	—
122	C₂×#102	—	53	2	no	—
123	C₂×C₂²⋊C₈	—	53	1	no	—
124	#340	—	53	2	no	—
125	C₅₃	#1874	1	1	yes	characteristic, complemented, Sylow
126	C₂²×D₄	—	2	1	no	—
127	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
128	C₂³×C₄	—	106	1	no	—
129	C₂³×C₄	C₂×D₅₃	1	1	yes	characteristic
130	C₂²×C₈	—	53	2	no	—
131	#121	—	2	2	no	—
132	#121	Dic₅₃	1	4	yes	complemented
133	C₂×C₄⋊C₄	—	53	2	no	—
134	C₂×C₄⋊C₄	—	106	4	no	—
135	C₂×C₄⋊C₄	—	106	1	no	—
136	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
137	C₂×C₂²⋊C₄	—	2	1	no	—
138	#102	—	106	4	no	—
139	C₂²⋊C₈	—	106	2	no	—
140	C₂⁴	—	2	1	no	—
141	C₂⁴	C₂²⋊D₅₃	1	1	yes	characteristic
142	C₂×D₄	—	2	4	no	—
143	C₂×D₄	—	2	2	no	—
144	C₂×D₄	—	2	2	no	—
145	C₂×D₄	—	2	1	no	—
146	C₂×D₄	—	4	2	no	—
147	C₂×D₄	—	4	2	no	—
148	C₂×D₄	C₂×Dic₅₃	1	2	yes	complemented
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	2	2	no	—
151	C₂²×C₄	—	2	1	no	—
152	C₂²×C₄	—	106	4	no	—
153	C₂²×C₄	—	106	2	no	—
154	C₂²×C₄	—	212	2	no	—
155	C₂²×C₄	—	212	2	no	—
156	C₂²×C₄	C₂×Dic₅₃	1	2	yes	—
157	C₂²×C₄	C₂²⋊D₅₃	1	2	yes	—
158	C₂²×C₄	C₂²⋊D₅₃	1	1	yes	characteristic
159	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
160	C₂×C₈	—	106	2	no	—
161	C₂×C₈	—	106	2	no	—
162	C₂×C₈	—	106	2	no	—
163	C₄⋊C₄	—	2	1	no	—
164	C₄⋊C₄	—	53	4	no	—
165	C₄⋊C₄	—	106	4	no	—
166	C₄⋊C₄	—	106	2	no	—
167	C₄⋊C₄	C₂×Dic₅₃	1	2	yes	complemented
168	C₂²⋊C₄	—	2	4	no	—
169	C₂³	—	2	1	no	—
170	C₂³	—	2	1	no	—
171	C₂³	—	2	1	no	—
172	C₂³	—	2	1	no	—
173	C₂³	—	2	2	no	—
174	C₂³	—	4	1	no	—
175	C₂³	—	4	1	no	—
176	C₂³	—	4	1	no	—
177	C₂³	—	4	1	no	—
178	C₂³	—	4	1	no	—
179	C₂³	—	4	1	no	—
180	C₂³	#11719922	1	2	yes	—
181	C₂³	#11719923	1	2	yes	—
182	C₂³	C₂²⋊Dic₅₃	1	2	yes	—
183	C₂³	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
184	D₄	—	2	4	no	—
185	D₄	—	4	8	no	—
186	D₄	—	4	2	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	4	no	—
190	C₂×C₄	—	2	4	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	106	4	no	—
195	C₂×C₄	—	212	8	no	—
196	C₂×C₄	—	212	2	no	—
197	C₂×C₄	—	212	2	no	—
198	C₂×C₄	C₂²⋊Dic₅₃	1	2	yes	—
199	C₂×C₄	D₄×D₅₃	1	2	yes	—
200	C₂×C₄	#11719947	1	2	yes	—
201	C₂×C₄	C₂²×Dic₅₃	1	1	yes	characteristic
202	C₂×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
203	C₈	—	212	2	no	—
204	C₂²	—	2	2	no	—
205	C₂²	—	2	2	no	—
206	C₂²	—	2	2	no	—
207	C₂²	—	2	2	no	—
208	C₂²	—	2	2	no	—
209	C₂²	—	2	2	no	—
210	C₂²	—	4	2	no	—
211	C₂²	—	4	2	no	—
212	C₂²	—	4	2	no	—
213	C₂²	—	8	1	no	—
214	C₂²	—	8	1	no	—
215	C₂²	—	8	1	no	—
216	C₂²	—	8	1	no	—
217	C₂²	#13133138	1	4	yes	complemented
218	C₂²	C₂×C₂²⋊Dic₅₃	1	1	yes	characteristic
219	C₂²	#13133185	1	1	yes	characteristic
220	C₂²	#13133198	1	1	yes	characteristic
221	C₂²	C₂×#11719922	1	1	yes	characteristic
222	C₂²	C₂×#11719923	1	1	yes	characteristic
223	C₂²	#13133242	1	1	yes	characteristic
224	C₂²	#13133247	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	4	2	no	—
227	C₄	—	212	4	no	—
228	C₄	D₄×Dic₅₃	1	2	yes	—
229	C₄	#13133189	1	2	yes	—
230	C₂	—	2	4	no	—
231	C₂	—	8	2	no	—
232	C₂	#16810503	1	1	yes	characteristic
233	C₂	C₂×#13133138	1	1	yes	characteristic
234	C₂	#16810624	1	1	yes	characteristic
235	C₂	#16810756	1	1	yes	characteristic
236	C₂	#16810761	1	1	yes	characteristic
237	C₂	#16810934	1	1	yes	characteristic
238	C₂	#16810939	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₅₃

C₂

yes

maximal, characteristic, complemented

C₂×#13133138

C₂

yes

maximal, complemented

C₂×C₂²⋊#88322

C₂

yes

maximal, characteristic, complemented

#16810385

C₂

yes

maximal, complemented

C₂×#121×C₅₃

C₂

yes

maximal, characteristic

C₂³×Dic₅₃

—

C₂²×#88322

C₂²

yes

—

C₂×C₄⋊Dic₅₃

—

C₂×C₄⋊Dic₅₃

—

C₂×C₄⋊Dic₅₃

C₂²

yes

—

#13133138

—

C₂²⋊#88322

—

C₂²×D₄×C₅₃

—

C₂²×D₄×C₅₃

C₂²

yes

characteristic

C₂³×C₄×C₅₃

C₂²

yes

characteristic

#121×C₅₃

—

#121×C₅₃

C₄

yes

complemented

C₂×C₄⋊C₄×C₅₃

C₂²

yes

characteristic

C₂×C₂²⋊C₄×C₅₃

—

C₂⁴×C₅₃

—

C₂⁴×C₅₃

D₄

yes

characteristic

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

—

C₂×D₄×C₅₃

C₂×C₄

yes

complemented

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

—

C₂²×C₄×C₅₃

C₂×C₄

yes

—

C₂²×C₄×C₅₃

D₄

yes

characteristic

C₂²×C₄×C₅₃

D₄

yes

—

C₂²×C₄×C₅₃

C₂³

yes

characteristic

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₂²×Dic₅₃

—

C₄⋊C₄×C₅₃

—

C₄⋊C₄×C₅₃

C₂×C₄

yes

complemented

C₂²⋊C₄×C₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

—

C₄⋊Dic₅₃

D₄

yes

—

—

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

—

C₂³×C₅₃

C₂²⋊C₄

yes

—

C₂³×C₅₃

D₈

yes

—

C₂³×C₅₃

SD₁₆

yes

—

C₂³×C₅₃

C₂×D₄

yes

characteristic

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×C₄×C₅₃

C₂²⋊C₄

yes

—

C₂×C₄×C₅₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₅₃

C₂×D₄

yes

—

C₂×C₄×C₅₃

C₂×D₄

yes

characteristic

C₂×C₄×C₅₃

#41

yes

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

C₂×Dic₅₃

—

#88322

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

—

C₂²×C₅₃

#102

yes

complemented

C₂²×C₅₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₅₃

#120

yes

characteristic

100

C₂²×C₅₃

#123

yes

characteristic

101

C₂²×C₅₃

C₂×D₈

yes

characteristic

102

C₂²×C₅₃

C₂×SD₁₆

yes

characteristic

103

C₂²×C₅₃

AGL(1,ℤ/8)

yes

characteristic

104

C₂²×C₅₃

#137

yes

characteristic

105

C₄×C₅₃

—

106

C₄×C₅₃

—

107

C₄×C₅₃

C₄×D₄

yes

—

108

C₄×C₅₃

#121

yes

—

109

Dic₅₃

—

110

#1874

—

maximal, Sylow

111

C₂×C₅₃

—

112

C₂×C₅₃

—

113

C₂×C₅₃

#386

yes

characteristic

114

C₂×C₅₃

C₂×#102

yes

characteristic

115

C₂×C₅₃

#417

yes

characteristic

116

C₂×C₅₃

#447

yes

characteristic

117

C₂×C₅₃

#448

yes

characteristic

118

C₂×C₅₃

#480

yes

characteristic

119

C₂×C₅₃

#481

yes

characteristic

120

C₂×#121

D₅₃

yes

characteristic

121

C₂²×C₄⋊C₄

—

122

C₂×#102

—

123

C₂×C₂²⋊C₈

—

124

#340

—

125

C₅₃

#1874

yes

characteristic, complemented, Sylow

126

C₂²×D₄

—

127

C₂²×D₄

C₂×D₅₃

yes

characteristic

128

C₂³×C₄

—

106

—

129

C₂³×C₄

C₂×D₅₃

yes

characteristic

130

C₂²×C₈

—

131

#121

—

132

#121

Dic₅₃

yes

complemented

133

C₂×C₄⋊C₄

—

134

C₂×C₄⋊C₄

—

106

—

135

C₂×C₄⋊C₄

—

106

—

136

C₂×C₄⋊C₄

C₂×D₅₃

yes

characteristic

137

C₂×C₂²⋊C₄

—

138

#102

—

106

—

139

C₂²⋊C₈

—

106

—

140

C₂⁴

—

141

C₂⁴

C₂²⋊D₅₃

yes

characteristic

142

C₂×D₄

—

143

C₂×D₄

—

144

C₂×D₄

—

145

C₂×D₄

—

146

C₂×D₄

—

147

C₂×D₄

—

148

C₂×D₄

C₂×Dic₅₃

yes

complemented

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

152

C₂²×C₄

—

106

—

153

C₂²×C₄

—

106

—

154

C₂²×C₄

—

212

—

155

C₂²×C₄

—

212

—

156

C₂²×C₄

C₂×Dic₅₃

yes

—

157

C₂²×C₄

C₂²⋊D₅₃

yes

—

158

C₂²×C₄

C₂²⋊D₅₃

yes

characteristic

159

C₂²×C₄

C₂²×D₅₃

yes

characteristic

160

C₂×C₈

—

106

—

161

C₂×C₈

—

106

—

162

C₂×C₈

—

106

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

106

—

166

C₄⋊C₄

—

106

—

167

C₄⋊C₄

C₂×Dic₅₃

yes

complemented

168

C₂²⋊C₄

—

169

C₂³

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

174

C₂³

—

175

C₂³

—

176

C₂³

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

#11719922

yes

—

181

C₂³

#11719923

yes

—

182

C₂³

C₂²⋊Dic₅₃

yes

—

183

C₂³

C₂×C₂²⋊D₅₃

yes

characteristic

184

D₄

—

185

D₄

—

186

D₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

106

—

195

C₂×C₄

—

212

—

196

C₂×C₄

—

212

—

197

C₂×C₄

—

212

—

198

C₂×C₄

C₂²⋊Dic₅₃

yes

—

199

C₂×C₄

D₄×D₅₃

yes

—

200

C₂×C₄

#11719947

yes

—

201

C₂×C₄

C₂²×Dic₅₃

yes

characteristic

202

C₂×C₄

C₂×C₂²⋊D₅₃

yes

characteristic

203

C₈

—

212

—

204

C₂²

—

205

C₂²

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

—

216

C₂²

—

217

C₂²

#13133138

yes

complemented

218

C₂²

C₂×C₂²⋊Dic₅₃

yes

characteristic

219

C₂²

#13133185

yes

characteristic

220

C₂²

#13133198

yes

characteristic

221

C₂²

C₂×#11719922

yes

characteristic

222

C₂²

C₂×#11719923

yes

characteristic

223

C₂²

#13133242

yes

characteristic

224

C₂²

#13133247

yes

characteristic

225

C₄

—

226

C₄

—

227

C₄

—

212

—

228

C₄

D₄×Dic₅₃

yes

—

229

C₄

#13133189

yes

—

230

C₂

—

231

C₂

—

232

C₂

#16810503

yes

characteristic

233

C₂

C₂×#13133138

yes

characteristic

234

C₂

#16810624

yes

characteristic

235

C₂

#16810756

yes

characteristic

236

C₂

#16810761

yes

characteristic

237

C₂

#16810934

yes

characteristic

238

C₂

#16810939

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₅₃
commutator	C₂×C₄×C₅₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₅₃
Fitting	C₂×#121×C₅₃	C₂
socle	C₂³×C₅₃	C₂×D₄
hypercenter	C₂×#121	D₅₃
hypocenter	C₅₃	#1874
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#121

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₅₃

commutator

C₂×C₄×C₅₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₅₃

Fitting

C₂×#121×C₅₃

C₂

socle

C₂³×C₅₃

C₂×D₄

D₅₃

C₅₃

G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#121

N	H ≅ G/N	type
1. C₂²×C₄⋊Dic₅₃	C₂	semidirect
2. C₂×#13133138	C₂	semidirect
3. C₂×C₂²⋊#88322	C₂	semidirect
4. #16810385	C₂	semidirect
17. #121×C₅₃	C₄	semidirect
28. C₂×D₄×C₅₃	C₂×C₄	semidirect
41. C₄⋊C₄×C₅₃	C₂×C₄	semidirect
45. C₄⋊Dic₅₃	D₄	semidirect
97. C₂²×C₅₃	#102	semidirect
125. C₅₃	#1874	semidirect
132. #121	Dic₅₃	semidirect
148. C₂×D₄	C₂×Dic₅₃	semidirect
167. C₄⋊C₄	C₂×Dic₅₃	semidirect
217. C₂²	#13133138	semidirect

H ≅ G/N

type

1. C₂²×C₄⋊Dic₅₃

C₂

semidirect

2. C₂×#13133138

C₂

semidirect

3. C₂×C₂²⋊#88322

C₂

semidirect

4. #16810385

C₂

semidirect

17. #121×C₅₃

C₄

semidirect

28. C₂×D₄×C₅₃

C₂×C₄

semidirect

41. C₄⋊C₄×C₅₃

C₂×C₄

semidirect

45. C₄⋊Dic₅₃

D₄

semidirect

97. C₂²×C₅₃

#102

semidirect

125. C₅₃

#1874

semidirect

132. #121

Dic₅₃

semidirect

148. C₂×D₄

C₂×Dic₅₃

semidirect

167. C₄⋊C₄

C₂×Dic₅₃

semidirect

217. C₂²

#13133138

semidirect

Subgroups — #20275033

Conjugacy classes of subgroups

Complements