Subgroups — C₅₃×#20476 #27227988

Order 13568.

990 conjugacy classes of subgroups.

The subgroup lattice has 322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#432	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₈×C₅₃	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2283	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1770	C₂	1	2	yes	maximal, complemented
5	C₈×C₄⋊C₄×C₅₃	C₂	1	2	yes	maximal, complemented
6	C₅₃×#1752	C₂	1	2	yes	maximal
7	C₈×C₂²⋊C₄×C₅₃	C₂	1	2	yes	maximal
8	C₅₃×#1746	C₂	1	2	yes	maximal, complemented
9	C₅₃×#1726	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
13	C₅₃×#432	C₄	1	8	yes	complemented
14	C₂×C₄⋊C₈×C₅₃	C₂²	1	2	yes	—
15	C₂×C₂²⋊C₈×C₅₃	C₂²	1	2	yes	—
16	C₂×#97×C₅₃	C₂²	1	4	yes	—
17	C₂×#97×C₅₃	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₅₃	C₄	1	8	yes	complemented
19	C₂×C₄×C₈×C₅₃	C₂²	1	4	yes	—
20	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₅₃×#383	C₄	1	2	yes	—
25	C₅₃×#382	C₄	1	2	yes	—
26	C₅₃×#381	C₄	1	2	yes	—
27	C₅₃×#380	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₅₃	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₅₃	C₂²	1	2	yes	—
30	C₅₃×#376	C₂²	1	2	yes	—
31	C₅₃×#336	C₂²	1	4	yes	—
32	C₅₃×#336	C₂²	1	4	yes	—
33	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
36	C₂²×C₈×C₅₃	—	2	4	no	—
37	C₂²×C₈×C₅₃	—	2	4	no	—
38	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₅₃	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₅₃	C₂³	1	4	yes	—
43	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
46	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₅₃	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₅₃	C₂×C₄	1	4	yes	—
49	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₅₃	C₂³	1	4	yes	—
52	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
53	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
55	C₂²⋊C₈×C₅₃	C₂×C₄	1	8	yes	—
56	#97×C₅₃	—	2	8	no	—
57	#97×C₅₃	C₂×C₄	1	8	yes	—
58	C₄×C₈×C₅₃	—	2	8	no	—
59	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
60	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
61	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
62	C₄×C₈×C₅₃	C₂×C₄	1	4	yes	—
63	#95×C₅₃	C₂×C₄	1	4	yes	—
64	#95×C₅₃	C₂×C₄	1	4	yes	—
65	#95×C₅₃	C₂×C₄	1	4	yes	—
66	#95×C₅₃	C₂×C₄	1	4	yes	—
67	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	—	2	4	no	—
69	C₂²×C₄×C₅₃	—	2	4	no	—
70	C₂²×C₄×C₅₃	—	2	2	no	—
71	C₂²×C₄×C₅₃	—	2	2	no	—
72	C₂²×C₄×C₅₃	C₄²	1	4	yes	—
73	C₂²×C₄×C₅₃	C₄²	1	4	yes	—
74	C₂²×C₄×C₅₃	C₂²×C₄	1	8	yes	—
75	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₅₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
83	C₂×C₈×C₅₃	—	2	4	no	—
84	C₂×C₈×C₅₃	—	2	4	no	—
85	C₂×C₈×C₅₃	—	2	2	no	—
86	C₂×C₈×C₅₃	—	2	2	no	—
87	C₂×C₈×C₅₃	—	2	8	no	—
88	C₂×C₈×C₅₃	—	2	8	no	—
89	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
90	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
91	C₂×C₈×C₅₃	C₂²×C₄	1	8	yes	—
92	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₅₃	#41	1	4	yes	—
95	C₂×C₈×C₅₃	#41	1	4	yes	—
96	C₄⋊C₄×C₅₃	—	2	8	no	—
97	C₂²⋊C₄×C₅₃	—	2	8	no	—
98	C₄²×C₅₃	—	2	4	no	—
99	C₄²×C₅₃	—	2	4	no	—
100	C₄²×C₅₃	C₄²	1	4	yes	—
101	C₄²×C₅₃	C₄²	1	4	yes	—
102	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
103	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
104	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
105	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
106	C₂³×C₅₃	—	2	2	no	—
107	C₂³×C₅₃	—	2	2	no	—
108	C₂³×C₅₃	C₂×C₄²	1	2	yes	—
109	C₂³×C₅₃	#131	1	4	yes	—
110	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
111	C₂×C₄×C₅₃	—	2	2	no	—
112	C₂×C₄×C₅₃	—	2	2	no	—
113	C₂×C₄×C₅₃	—	2	2	no	—
114	C₂×C₄×C₅₃	—	2	2	no	—
115	C₂×C₄×C₅₃	—	2	8	no	—
116	C₂×C₄×C₅₃	—	2	2	no	—
117	C₂×C₄×C₅₃	—	2	2	no	—
118	C₂×C₄×C₅₃	—	2	4	no	—
119	C₂×C₄×C₅₃	—	2	8	no	—
120	C₂×C₄×C₅₃	—	2	8	no	—
121	C₂×C₄×C₅₃	—	2	8	no	—
122	C₂×C₄×C₅₃	—	2	8	no	—
123	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
124	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
126	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
127	C₂×C₄×C₅₃	C₂×C₄²	1	2	yes	—
128	C₂×C₄×C₅₃	#131	1	4	yes	—
129	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
132	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
133	C₈×C₅₃	—	2	2	no	—
134	C₈×C₅₃	—	2	2	no	—
135	C₈×C₅₃	—	2	8	no	—
136	C₈×C₅₃	#117	1	4	yes	—
137	C₈×C₅₃	#117	1	4	yes	—
138	#20476	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
139	C₂²×C₅₃	—	2	2	no	—
140	C₂²×C₅₃	—	2	8	no	—
141	C₂²×C₅₃	—	2	2	no	—
142	C₂²×C₅₃	#405	1	4	yes	—
143	C₂²×C₅₃	C₂²×C₄²	1	1	yes	characteristic
144	C₂²×C₅₃	C₄×#41	1	2	yes	—
145	C₂²×C₅₃	C₂×#131	1	2	yes	—
146	C₂²×C₅₃	C₂×#131	1	2	yes	—
147	C₄×C₅₃	—	2	2	no	—
148	C₄×C₅₃	—	2	2	no	—
149	C₄×C₅₃	—	2	2	no	—
150	C₄×C₅₃	—	2	2	no	—
151	C₄×C₅₃	—	4	8	no	—
152	C₄×C₅₃	#405	1	4	yes	—
153	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
154	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
155	C₄×C₅₃	C₄×#41	1	2	yes	—
156	C₂×#432	C₂×C₅₃	1	1	yes	characteristic
157	C₂²×C₄×C₈	C₂×C₅₃	1	1	yes	characteristic
158	#2283	C₂×C₅₃	1	1	yes	characteristic
159	#1770	C₂×C₅₃	1	2	yes	complemented
160	C₈×C₄⋊C₄	C₂×C₅₃	1	2	yes	complemented
161	#1752	C₂×C₅₃	1	2	yes	—
162	C₈×C₂²⋊C₄	C₂×C₅₃	1	2	yes	—
163	#1746	C₂×C₅₃	1	2	yes	complemented
164	#1726	C₂×C₅₃	1	2	yes	complemented
165	C₂×C₅₃	—	2	4	no	—
166	C₂×C₅₃	C₄×#117	1	1	yes	characteristic
167	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
168	C₂×C₅₃	C₂×#405	1	1	yes	characteristic
169	C₂×C₅₃	#2966	1	4	yes	—
170	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
171	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
172	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
173	#432	C₄×C₅₃	1	8	yes	complemented
174	C₂×C₄⋊C₈	C₂²×C₅₃	1	2	yes	—
175	C₂×C₂²⋊C₈	C₂²×C₅₃	1	2	yes	—
176	C₂×#97	C₂²×C₅₃	1	4	yes	—
177	C₂×#97	C₂²×C₅₃	1	2	yes	—
178	C₂×C₄×C₈	C₄×C₅₃	1	8	yes	complemented
179	C₂×C₄×C₈	C₂²×C₅₃	1	4	yes	—
180	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
183	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
184	#383	C₄×C₅₃	1	2	yes	—
185	#382	C₄×C₅₃	1	2	yes	—
186	#381	C₄×C₅₃	1	2	yes	—
187	#380	C₄×C₅₃	1	2	yes	—
188	C₄×C₄⋊C₄	C₂²×C₅₃	1	2	yes	—
189	C₄×C₂²⋊C₄	C₂²×C₅₃	1	2	yes	—
190	#376	C₂²×C₅₃	1	2	yes	—
191	#336	C₂²×C₅₃	1	4	yes	—
192	#336	C₂²×C₅₃	1	4	yes	—
193	C₅₃	#20476	1	1	yes	characteristic, direct product factor, Sylow
194	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
195	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
196	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
197	C₂²×C₈	—	2	4	no	—
198	C₂²×C₈	—	2	4	no	—
199	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	—
200	C₂²×C₈	C₂×C₄×C₅₃	1	4	yes	—
201	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
202	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
203	C₂²×C₈	C₂³×C₅₃	1	4	yes	—
204	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
205	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
206	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
207	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	4	yes	—
208	C₂×C₄²	C₂×C₄×C₅₃	1	4	yes	—
209	C₂×C₄²	C₂×C₄×C₅₃	1	4	yes	—
210	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
211	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
212	C₂×C₄²	C₂³×C₅₃	1	4	yes	—
213	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
214	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
215	C₄⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
216	C₂²⋊C₈	C₂×C₄×C₅₃	1	8	yes	—
217	#97	—	2	8	no	—
218	#97	C₂×C₄×C₅₃	1	8	yes	—
219	C₄×C₈	—	2	8	no	—
220	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	—
221	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	—
222	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	—
223	C₄×C₈	C₂×C₄×C₅₃	1	4	yes	—
224	#95	C₂×C₄×C₅₃	1	4	yes	—
225	#95	C₂×C₄×C₅₃	1	4	yes	—
226	#95	C₂×C₄×C₅₃	1	4	yes	—
227	#95	C₂×C₄×C₅₃	1	4	yes	—
228	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
229	C₂²×C₄	—	2	4	no	—
230	C₂²×C₄	—	2	4	no	—
231	C₂²×C₄	—	2	2	no	—
232	C₂²×C₄	—	2	2	no	—
233	C₂²×C₄	C₄²×C₅₃	1	4	yes	—
234	C₂²×C₄	C₄²×C₅₃	1	4	yes	—
235	C₂²×C₄	C₂²×C₄×C₅₃	1	8	yes	—
236	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
237	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
238	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
239	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
240	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
241	C₂²×C₄	C₂²×C₄×C₅₃	1	2	yes	—
242	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
243	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
244	C₂×C₈	—	2	4	no	—
245	C₂×C₈	—	2	4	no	—
246	C₂×C₈	—	2	2	no	—
247	C₂×C₈	—	2	2	no	—
248	C₂×C₈	—	2	8	no	—
249	C₂×C₈	—	2	8	no	—
250	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
251	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
252	C₂×C₈	C₂²×C₄×C₅₃	1	8	yes	—
253	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
254	C₂×C₈	C₂²×C₄×C₅₃	1	2	yes	—
255	C₂×C₈	#41×C₅₃	1	4	yes	—
256	C₂×C₈	#41×C₅₃	1	4	yes	—
257	C₄⋊C₄	—	2	8	no	—
258	C₂²⋊C₄	—	2	8	no	—
259	C₄²	—	2	4	no	—
260	C₄²	—	2	4	no	—
261	C₄²	C₄²×C₅₃	1	4	yes	—
262	C₄²	C₄²×C₅₃	1	4	yes	—
263	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
264	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
265	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
266	C₄²	C₂²×C₄×C₅₃	1	2	yes	—
267	C₂³	—	2	2	no	—
268	C₂³	—	2	2	no	—
269	C₂³	C₂×C₄²×C₅₃	1	2	yes	—
270	C₂³	#131×C₅₃	1	4	yes	—
271	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
272	C₂×C₄	—	2	2	no	—
273	C₂×C₄	—	2	2	no	—
274	C₂×C₄	—	2	2	no	—
275	C₂×C₄	—	2	2	no	—
276	C₂×C₄	—	2	8	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	4	no	—
280	C₂×C₄	—	2	8	no	—
281	C₂×C₄	—	2	8	no	—
282	C₂×C₄	—	2	8	no	—
283	C₂×C₄	—	2	8	no	—
284	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
285	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
286	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
287	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
288	C₂×C₄	C₂×C₄²×C₅₃	1	2	yes	—
289	C₂×C₄	#131×C₅₃	1	4	yes	—
290	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
291	C₂×C₄	C₂³×C₄×C₅₃	1	1	yes	characteristic
292	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
293	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
294	C₈	—	2	2	no	—
295	C₈	—	2	2	no	—
296	C₈	—	2	8	no	—
297	C₈	#117×C₅₃	1	4	yes	—
298	C₈	#117×C₅₃	1	4	yes	—
299	C₂²	—	2	8	no	—
300	C₂²	—	2	2	no	—
301	C₂²	—	2	2	no	—
302	C₂²	C₅₃×#405	1	4	yes	—
303	C₂²	C₂²×C₄²×C₅₃	1	1	yes	characteristic
304	C₂²	C₄×#41×C₅₃	1	2	yes	—
305	C₂²	C₂×#131×C₅₃	1	2	yes	—
306	C₂²	C₂×#131×C₅₃	1	2	yes	—
307	C₄	—	2	2	no	—
308	C₄	—	2	2	no	—
309	C₄	—	2	2	no	—
310	C₄	—	2	2	no	—
311	C₄	—	4	8	no	—
312	C₄	C₅₃×#405	1	4	yes	—
313	C₄	C₂×#117×C₅₃	1	1	yes	characteristic
314	C₄	C₂×#117×C₅₃	1	1	yes	characteristic
315	C₄	C₄×#41×C₅₃	1	2	yes	—
316	C₂	—	2	4	no	—
317	C₂	C₄×#117×C₅₃	1	1	yes	characteristic
318	C₂	C₂×C₅₃×#405	1	1	yes	characteristic
319	C₂	C₂×C₅₃×#405	1	1	yes	characteristic
320	C₂	C₅₃×#2966	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₅₃	C₂³
commutator	C₂²	C₂²×C₄²×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂⁴×C₅₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₅₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
4. C₅₃×#1770	C₂	semidirect
5. C₈×C₄⋊C₄×C₅₃	C₂	semidirect
8. C₅₃×#1746	C₂	semidirect
9. C₅₃×#1726	C₂	semidirect
13. C₅₃×#432	C₄	semidirect
18. C₂×C₄×C₈×C₅₃	C₄	semidirect
138. #20476	C₅₃	direct (N × H)
159. #1770	C₂×C₅₃	semidirect
160. C₈×C₄⋊C₄	C₂×C₅₃	semidirect
163. #1746	C₂×C₅₃	semidirect
164. #1726	C₂×C₅₃	semidirect
173. #432	C₄×C₅₃	semidirect
178. C₂×C₄×C₈	C₄×C₅₃	semidirect
193. C₅₃	#20476	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#432	2
C₂²×C₄×C₈×C₅₃	2
C₅₃×#2283	2
C₅₃×#1770	2
C₈×C₄⋊C₄×C₅₃	2
C₅₃×#1752	2
C₈×C₂²⋊C₄×C₅₃	2
C₅₃×#1746	2
C₅₃×#1726	2
#20476	53

Subgroups — C53×#20476 #27227988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#20476 #27227988