Subgroups — C₅₃×#22699 #27230211

Order 13568.

904 conjugacy classes of subgroups.

The subgroup lattice has 696 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅₃×#435	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic
4	C₅₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1850	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1832	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1729	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1728	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
23	C₅₃×#436	—	2	4	no	—
24	C₅₃×#435	—	2	4	no	—
25	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₅₃×#388	C₄	1	1	yes	characteristic
40	C₅₃×#388	C₄	1	1	yes	characteristic
41	C₅₃×#387	C₄	1	1	yes	characteristic
42	C₅₃×#387	C₄	1	1	yes	characteristic
43	C₅₃×#386	C₄	1	1	yes	characteristic
44	C₅₃×#386	C₄	1	1	yes	characteristic
45	C₅₃×#385	C₄	1	1	yes	characteristic
46	C₅₃×#385	C₄	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₅₃×#376	C₂²	1	1	yes	characteristic
51	C₅₃×#336	C₂²	1	1	yes	characteristic
52	C₅₃×#336	C₂²	1	1	yes	characteristic
53	C₅₃×#336	C₂²	1	1	yes	characteristic
54	C₅₃×#336	C₂²	1	1	yes	characteristic
55	C₅₃×#336	C₂²	1	1	yes	characteristic
56	C₅₃×#336	C₂²	1	1	yes	characteristic
57	C₅₃×#336	C₂²	1	1	yes	characteristic
58	C₅₃×#336	C₂²	1	1	yes	characteristic
59	C₅₃×#336	C₂²	1	1	yes	characteristic
60	C₅₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
66	C₂×M₁₆×C₅₃	—	2	2	no	—
67	C₂×M₁₆×C₅₃	—	2	2	no	—
68	C₂×M₁₆×C₅₃	—	2	2	no	—
69	C₂×M₁₆×C₅₃	—	2	2	no	—
70	C₂×M₁₆×C₅₃	—	2	2	no	—
71	C₂×M₁₆×C₅₃	—	2	2	no	—
72	C₂×M₁₆×C₅₃	—	4	1	no	—
73	C₂×M₁₆×C₅₃	—	4	1	no	—
74	C₂×M₁₆×C₅₃	—	4	1	no	—
75	C₂²×C₈×C₅₃	—	2	2	no	—
76	C₂²×C₈×C₅₃	—	2	2	no	—
77	C₂²×C₈×C₅₃	—	4	1	no	—
78	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₅₃	D₄	1	4	yes	—
87	C₄×D₄×C₅₃	Q₈	1	4	yes	—
88	#117×C₅₃	—	4	1	no	—
89	#117×C₅₃	—	4	1	no	—
90	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
95	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₅₃	—	4	1	no	—
104	C₂×C₄²×C₅₃	—	4	1	no	—
105	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₅₃	—	2	2	no	—
113	C₄⋊C₈×C₅₃	—	2	2	no	—
114	C₄⋊C₈×C₅₃	—	2	2	no	—
115	C₄⋊C₈×C₅₃	—	2	2	no	—
116	C₄⋊C₈×C₅₃	—	4	1	no	—
117	C₄⋊C₈×C₅₃	—	4	1	no	—
118	C₄⋊C₈×C₅₃	—	4	1	no	—
119	C₄⋊C₈×C₅₃	—	4	1	no	—
120	C₂²⋊C₈×C₅₃	—	2	2	no	—
121	C₂²⋊C₈×C₅₃	—	2	2	no	—
122	C₂²⋊C₈×C₅₃	—	2	2	no	—
123	C₂²⋊C₈×C₅₃	—	2	2	no	—
124	#97×C₅₃	—	2	2	no	—
125	C₄×C₈×C₅₃	—	2	2	no	—
126	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
127	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
128	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
129	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
130	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
131	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
132	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
133	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
134	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
135	#95×C₅₃	C₂×C₄	1	1	yes	characteristic
136	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
137	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×D₄×C₅₃	—	4	1	no	—
139	C₂×D₄×C₅₃	—	4	1	no	—
140	C₂×D₄×C₅₃	C₄⋊C₄	1	4	yes	—
141	C₂²×C₄×C₅₃	—	2	1	no	—
142	C₂²×C₄×C₅₃	—	2	1	no	—
143	C₂²×C₄×C₅₃	—	2	1	no	—
144	C₂²×C₄×C₅₃	—	2	1	no	—
145	C₂²×C₄×C₅₃	—	2	1	no	—
146	C₂²×C₄×C₅₃	—	2	1	no	—
147	C₂²×C₄×C₅₃	—	2	1	no	—
148	C₂²×C₄×C₅₃	—	2	1	no	—
149	C₂²×C₄×C₅₃	—	2	2	no	—
150	C₂²×C₄×C₅₃	—	4	1	no	—
151	C₂²×C₄×C₅₃	—	4	1	no	—
152	C₂²×C₄×C₅₃	—	4	1	no	—
153	C₂²×C₄×C₅₃	—	4	1	no	—
154	C₂²×C₄×C₅₃	—	4	1	no	—
155	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
170	C₂²×C₄×C₅₃	C₂×Q₈	1	2	yes	—
171	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
172	M₁₆×C₅₃	—	4	4	no	—
173	M₁₆×C₅₃	—	4	4	no	—
174	M₁₆×C₅₃	—	4	4	no	—
175	C₂×C₈×C₅₃	—	2	1	no	—
176	C₂×C₈×C₅₃	—	2	1	no	—
177	C₂×C₈×C₅₃	—	2	1	no	—
178	C₂×C₈×C₅₃	—	2	1	no	—
179	C₂×C₈×C₅₃	—	2	1	no	—
180	C₂×C₈×C₅₃	—	2	1	no	—
181	C₂×C₈×C₅₃	—	2	1	no	—
182	C₂×C₈×C₅₃	—	2	1	no	—
183	C₂×C₈×C₅₃	—	2	1	no	—
184	C₂×C₈×C₅₃	—	2	1	no	—
185	C₂×C₈×C₅₃	—	2	1	no	—
186	C₂×C₈×C₅₃	—	2	1	no	—
187	C₂×C₈×C₅₃	—	2	1	no	—
188	C₂×C₈×C₅₃	—	2	1	no	—
189	C₂×C₈×C₅₃	—	2	1	no	—
190	C₂×C₈×C₅₃	—	2	1	no	—
191	C₂×C₈×C₅₃	—	2	1	no	—
192	C₂×C₈×C₅₃	—	2	1	no	—
193	C₂×C₈×C₅₃	—	2	1	no	—
194	C₂×C₈×C₅₃	—	2	1	no	—
195	C₂×C₈×C₅₃	—	2	1	no	—
196	C₂×C₈×C₅₃	—	2	1	no	—
197	C₂×C₈×C₅₃	—	4	4	no	—
198	C₂×C₈×C₅₃	#41	1	2	yes	—
199	C₂×C₈×C₅₃	#41	1	2	yes	—
200	C₄⋊C₄×C₅₃	—	2	2	no	—
201	C₄⋊C₄×C₅₃	—	4	1	no	—
202	C₄⋊C₄×C₅₃	—	4	1	no	—
203	C₄⋊C₄×C₅₃	—	4	1	no	—
204	C₄⋊C₄×C₅₃	C₄⋊C₄	1	4	yes	—
205	C₂²⋊C₄×C₅₃	—	2	2	no	—
206	C₂²⋊C₄×C₅₃	—	4	1	no	—
207	C₂²⋊C₄×C₅₃	—	4	1	no	—
208	C₂²⋊C₄×C₅₃	—	4	1	no	—
209	C₂²⋊C₄×C₅₃	—	4	1	no	—
210	C₂²⋊C₄×C₅₃	—	4	1	no	—
211	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	4	yes	—
212	C₂²⋊C₄×C₅₃	C₄⋊C₄	1	4	yes	—
213	C₄²×C₅₃	—	2	1	no	—
214	C₄²×C₅₃	—	2	1	no	—
215	C₄²×C₅₃	—	2	1	no	—
216	C₄²×C₅₃	—	2	1	no	—
217	C₄²×C₅₃	—	2	1	no	—
218	C₄²×C₅₃	—	2	1	no	—
219	C₄²×C₅₃	—	2	1	no	—
220	C₄²×C₅₃	—	2	1	no	—
221	C₄²×C₅₃	—	4	1	no	—
222	C₄²×C₅₃	—	4	1	no	—
223	C₄²×C₅₃	C₂×D₄	1	2	yes	—
224	C₄²×C₅₃	C₂×Q₈	1	2	yes	—
225	C₂³×C₅₃	—	2	1	no	—
226	C₂³×C₅₃	—	2	1	no	—
227	C₂³×C₅₃	—	2	1	no	—
228	C₂³×C₅₃	—	2	1	no	—
229	C₂³×C₅₃	—	2	1	no	—
230	C₂³×C₅₃	—	2	1	no	—
231	C₂³×C₅₃	—	2	1	no	—
232	C₂³×C₅₃	—	2	1	no	—
233	C₂³×C₅₃	—	2	1	no	—
234	C₂³×C₅₃	—	2	1	no	—
235	C₂³×C₅₃	—	2	1	no	—
236	C₂³×C₅₃	—	2	1	no	—
237	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
238	C₂³×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
239	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
240	D₄×C₅₃	—	4	4	no	—
241	C₂×C₄×C₅₃	—	2	1	no	—
242	C₂×C₄×C₅₃	—	2	1	no	—
243	C₂×C₄×C₅₃	—	2	1	no	—
244	C₂×C₄×C₅₃	—	2	1	no	—
245	C₂×C₄×C₅₃	—	2	1	no	—
246	C₂×C₄×C₅₃	—	2	1	no	—
247	C₂×C₄×C₅₃	—	2	1	no	—
248	C₂×C₄×C₅₃	—	2	1	no	—
249	C₂×C₄×C₅₃	—	2	1	no	—
250	C₂×C₄×C₅₃	—	2	1	no	—
251	C₂×C₄×C₅₃	—	2	2	no	—
252	C₂×C₄×C₅₃	—	2	2	no	—
253	C₂×C₄×C₅₃	—	2	2	no	—
254	C₂×C₄×C₅₃	—	2	2	no	—
255	C₂×C₄×C₅₃	—	2	2	no	—
256	C₂×C₄×C₅₃	—	2	2	no	—
257	C₂×C₄×C₅₃	—	2	2	no	—
258	C₂×C₄×C₅₃	—	2	2	no	—
259	C₂×C₄×C₅₃	—	2	1	no	—
260	C₂×C₄×C₅₃	—	2	1	no	—
261	C₂×C₄×C₅₃	—	2	1	no	—
262	C₂×C₄×C₅₃	—	2	1	no	—
263	C₂×C₄×C₅₃	—	2	1	no	—
264	C₂×C₄×C₅₃	—	2	1	no	—
265	C₂×C₄×C₅₃	—	2	1	no	—
266	C₂×C₄×C₅₃	—	2	1	no	—
267	C₂×C₄×C₅₃	—	2	1	no	—
268	C₂×C₄×C₅₃	—	2	1	no	—
269	C₂×C₄×C₅₃	—	2	1	no	—
270	C₂×C₄×C₅₃	—	2	1	no	—
271	C₂×C₄×C₅₃	—	2	1	no	—
272	C₂×C₄×C₅₃	—	2	1	no	—
273	C₂×C₄×C₅₃	—	2	1	no	—
274	C₂×C₄×C₅₃	—	2	1	no	—
275	C₂×C₄×C₅₃	—	2	1	no	—
276	C₂×C₄×C₅₃	—	2	1	no	—
277	C₂×C₄×C₅₃	—	2	1	no	—
278	C₂×C₄×C₅₃	—	2	1	no	—
279	C₂×C₄×C₅₃	—	2	1	no	—
280	C₂×C₄×C₅₃	—	4	4	no	—
281	C₂×C₄×C₅₃	—	4	4	no	—
282	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
283	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
284	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
285	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	2	yes	—
286	C₂×C₄×C₅₃	#131	1	2	yes	—
287	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
289	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
292	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
293	C₈×C₅₃	—	2	2	no	—
294	C₈×C₅₃	—	2	2	no	—
295	C₈×C₅₃	—	4	1	no	—
296	C₈×C₅₃	—	4	1	no	—
297	C₈×C₅₃	—	4	1	no	—
298	C₈×C₅₃	—	4	1	no	—
299	C₈×C₅₃	—	4	1	no	—
300	C₈×C₅₃	—	4	1	no	—
301	#22699	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂²×C₅₃	—	2	2	no	—
303	C₂²×C₅₃	—	2	2	no	—
304	C₂²×C₅₃	—	2	2	no	—
305	C₂²×C₅₃	—	2	2	no	—
306	C₂²×C₅₃	—	2	2	no	—
307	C₂²×C₅₃	—	2	2	no	—
308	C₂²×C₅₃	—	4	1	no	—
309	C₂²×C₅₃	—	4	1	no	—
310	C₂²×C₅₃	—	4	1	no	—
311	C₂²×C₅₃	—	4	1	no	—
312	C₂²×C₅₃	—	4	1	no	—
313	C₂²×C₅₃	—	4	1	no	—
314	C₂²×C₅₃	—	4	1	no	—
315	C₂²×C₅₃	—	4	1	no	—
316	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
317	C₂²×C₅₃	C₄×#41	1	1	yes	characteristic
318	C₂²×C₅₃	#518	1	1	yes	characteristic
319	C₂²×C₅₃	C₂×#131	1	1	yes	characteristic
320	C₂²×C₅₃	#568	1	1	yes	characteristic
321	C₂²×C₅₃	#568	1	1	yes	characteristic
322	C₂²×C₅₃	#568	1	1	yes	characteristic
323	C₄×C₅₃	—	2	2	no	—
324	C₄×C₅₃	—	2	2	no	—
325	C₄×C₅₃	—	2	2	no	—
326	C₄×C₅₃	—	2	2	no	—
327	C₄×C₅₃	—	2	2	no	—
328	C₄×C₅₃	—	4	1	no	—
329	C₄×C₅₃	—	4	1	no	—
330	C₄×C₅₃	—	4	1	no	—
331	C₄×C₅₃	—	4	1	no	—
332	C₄×C₅₃	—	4	1	no	—
333	C₄×C₅₃	—	4	1	no	—
334	C₄×C₅₃	—	4	1	no	—
335	C₄×C₅₃	#546	1	1	yes	characteristic
336	C₄×C₅₃	#546	1	1	yes	characteristic
337	C₄×C₅₃	#554	1	1	yes	characteristic
338	C₄×C₅₃	#554	1	1	yes	characteristic
339	C₂×#436	C₂×C₅₃	1	1	yes	characteristic
340	C₂×#435	C₂×C₅₃	1	1	yes	characteristic
341	#2290	C₂×C₅₃	1	1	yes	characteristic
342	#1940	C₂×C₅₃	1	1	yes	characteristic, complemented
343	#1939	C₂×C₅₃	1	1	yes	characteristic, complemented
344	#1851	C₂×C₅₃	1	1	yes	characteristic, complemented
345	#1851	C₂×C₅₃	1	1	yes	characteristic, complemented
346	#1851	C₂×C₅₃	1	1	yes	characteristic, complemented
347	#1850	C₂×C₅₃	1	1	yes	characteristic, complemented
348	#1832	C₂×C₅₃	1	1	yes	characteristic, complemented
349	#1798	C₂×C₅₃	1	1	yes	characteristic, complemented
350	#1797	C₂×C₅₃	1	1	yes	characteristic, complemented
351	#1768	C₂×C₅₃	1	1	yes	characteristic, complemented
352	#1729	C₂×C₅₃	1	1	yes	characteristic, complemented
353	#1728	C₂×C₅₃	1	1	yes	characteristic, complemented
354	C₂×C₅₃	—	4	2	no	—
355	C₂×C₅₃	—	4	2	no	—
356	C₂×C₅₃	#2349	1	1	yes	characteristic
357	C₂×C₅₃	#2905	1	1	yes	characteristic
358	C₂×C₅₃	#2906	1	1	yes	characteristic
359	C₂×C₅₃	#2967	1	1	yes	characteristic
360	C₂×C₅₃	#2969	1	1	yes	characteristic
361	C₂×C₅₃	#2976	1	1	yes	characteristic
362	C₂×C₅₃	#2978	1	1	yes	characteristic
363	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
364	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
365	C₂²×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
366	C₂³×C₈	C₂²×C₅₃	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
368	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
369	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
370	#436	—	2	4	no	—
371	#435	—	2	4	no	—
372	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
373	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
374	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
375	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
376	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
377	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
378	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
379	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
380	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
381	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
383	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
384	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic
385	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic
386	#388	C₄×C₅₃	1	1	yes	characteristic
387	#388	C₄×C₅₃	1	1	yes	characteristic
388	#387	C₄×C₅₃	1	1	yes	characteristic
389	#387	C₄×C₅₃	1	1	yes	characteristic
390	#386	C₄×C₅₃	1	1	yes	characteristic
391	#386	C₄×C₅₃	1	1	yes	characteristic
392	#385	C₄×C₅₃	1	1	yes	characteristic
393	#385	C₄×C₅₃	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
396	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
397	#376	C₂²×C₅₃	1	1	yes	characteristic
398	#336	C₂²×C₅₃	1	1	yes	characteristic
399	#336	C₂²×C₅₃	1	1	yes	characteristic
400	#336	C₂²×C₅₃	1	1	yes	characteristic
401	#336	C₂²×C₅₃	1	1	yes	characteristic
402	#336	C₂²×C₅₃	1	1	yes	characteristic
403	#336	C₂²×C₅₃	1	1	yes	characteristic
404	#336	C₂²×C₅₃	1	1	yes	characteristic
405	#336	C₂²×C₅₃	1	1	yes	characteristic
406	#336	C₂²×C₅₃	1	1	yes	characteristic
407	#336	C₂²×C₅₃	1	1	yes	characteristic
408	C₅₃	#22699	1	1	yes	characteristic, direct product factor, Sylow
409	C₂²×D₄	C₂×C₄×C₅₃	1	1	yes	characteristic
410	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
411	C₂³×C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
412	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
413	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	—	2	2	no	—
416	C₂×M₁₆	—	2	2	no	—
417	C₂×M₁₆	—	2	2	no	—
418	C₂×M₁₆	—	2	2	no	—
419	C₂×M₁₆	—	2	2	no	—
420	C₂×M₁₆	—	4	1	no	—
421	C₂×M₁₆	—	4	1	no	—
422	C₂×M₁₆	—	4	1	no	—
423	C₂²×C₈	—	2	2	no	—
424	C₂²×C₈	—	2	2	no	—
425	C₂²×C₈	—	4	1	no	—
426	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
427	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
428	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
429	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
430	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
434	C₄×D₄	D₄×C₅₃	1	4	yes	—
435	C₄×D₄	Q₈×C₅₃	1	4	yes	—
436	#117	—	4	1	no	—
437	#117	—	4	1	no	—
438	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
439	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
446	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
447	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
448	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
450	C₂×C₂²⋊C₄	C₂×C₄×C₅₃	1	1	yes	characteristic
451	C₂×C₄²	—	4	1	no	—
452	C₂×C₄²	—	4	1	no	—
453	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
454	C₂×C₄²	C₂×C₄×C₅₃	1	1	yes	characteristic
455	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
456	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
457	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
458	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
459	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
460	C₄⋊C₈	—	2	2	no	—
461	C₄⋊C₈	—	2	2	no	—
462	C₄⋊C₈	—	2	2	no	—
463	C₄⋊C₈	—	2	2	no	—
464	C₄⋊C₈	—	4	1	no	—
465	C₄⋊C₈	—	4	1	no	—
466	C₄⋊C₈	—	4	1	no	—
467	C₄⋊C₈	—	4	1	no	—
468	C₂²⋊C₈	—	2	2	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	C₂²⋊C₈	—	2	2	no	—
471	C₂²⋊C₈	—	2	2	no	—
472	#97	—	2	2	no	—
473	C₄×C₈	—	2	2	no	—
474	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
475	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
476	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
477	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
478	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
479	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
480	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
481	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
482	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
483	#95	C₂×C₄×C₅₃	1	1	yes	characteristic
484	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
485	C₂⁴	C₂²×C₄×C₅₃	1	1	yes	characteristic
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	C₄⋊C₄×C₅₃	1	4	yes	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	4	1	no	—
499	C₂²×C₄	—	4	1	no	—
500	C₂²×C₄	—	4	1	no	—
501	C₂²×C₄	—	4	1	no	—
502	C₂²×C₄	—	4	1	no	—
503	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
504	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
505	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
506	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
507	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
508	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
509	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
511	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
513	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
514	C₂²×C₄	C₂²×C₄×C₅₃	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
516	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
517	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
518	C₂²×C₄	C₂×Q₈×C₅₃	1	2	yes	—
519	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
520	M₁₆	—	4	4	no	—
521	M₁₆	—	4	4	no	—
522	M₁₆	—	4	4	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	4	4	no	—
546	C₂×C₈	#41×C₅₃	1	2	yes	—
547	C₂×C₈	#41×C₅₃	1	2	yes	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₄⋊C₄	—	4	1	no	—
552	C₄⋊C₄	C₄⋊C₄×C₅₃	1	4	yes	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	4	1	no	—
555	C₂²⋊C₄	—	4	1	no	—
556	C₂²⋊C₄	—	4	1	no	—
557	C₂²⋊C₄	—	4	1	no	—
558	C₂²⋊C₄	—	4	1	no	—
559	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	4	yes	—
560	C₂²⋊C₄	C₄⋊C₄×C₅₃	1	4	yes	—
561	C₄²	—	2	1	no	—
562	C₄²	—	2	1	no	—
563	C₄²	—	2	1	no	—
564	C₄²	—	2	1	no	—
565	C₄²	—	2	1	no	—
566	C₄²	—	2	1	no	—
567	C₄²	—	2	1	no	—
568	C₄²	—	2	1	no	—
569	C₄²	—	4	1	no	—
570	C₄²	—	4	1	no	—
571	C₄²	C₂×D₄×C₅₃	1	2	yes	—
572	C₄²	C₂×Q₈×C₅₃	1	2	yes	—
573	C₂³	—	2	1	no	—
574	C₂³	—	2	1	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	2	1	no	—
579	C₂³	—	2	1	no	—
580	C₂³	—	2	1	no	—
581	C₂³	—	2	1	no	—
582	C₂³	—	2	1	no	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
586	C₂³	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
587	C₂³	C₂³×C₄×C₅₃	1	1	yes	characteristic
588	D₄	—	4	4	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	4	4	no	—
629	C₂×C₄	—	4	4	no	—
630	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
631	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
632	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
633	C₂×C₄	C₂×C₄⋊C₄×C₅₃	1	2	yes	—
634	C₂×C₄	#131×C₅₃	1	2	yes	—
635	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
636	C₂×C₄	C₂²×Q₈×C₅₃	1	1	yes	characteristic
637	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
638	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
639	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
640	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
641	C₈	—	2	2	no	—
642	C₈	—	2	2	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₈	—	4	1	no	—
646	C₈	—	4	1	no	—
647	C₈	—	4	1	no	—
648	C₈	—	4	1	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	2	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	C₂²×C₄⋊C₄×C₅₃	1	1	yes	characteristic
664	C₂²	C₄×#41×C₅₃	1	1	yes	characteristic
665	C₂²	C₅₃×#518	1	1	yes	characteristic
666	C₂²	C₂×#131×C₅₃	1	1	yes	characteristic
667	C₂²	C₅₃×#568	1	1	yes	characteristic
668	C₂²	C₅₃×#568	1	1	yes	characteristic
669	C₂²	C₅₃×#568	1	1	yes	characteristic
670	C₄	—	2	2	no	—
671	C₄	—	2	2	no	—
672	C₄	—	2	2	no	—
673	C₄	—	2	2	no	—
674	C₄	—	2	2	no	—
675	C₄	—	4	1	no	—
676	C₄	—	4	1	no	—
677	C₄	—	4	1	no	—
678	C₄	—	4	1	no	—
679	C₄	—	4	1	no	—
680	C₄	—	4	1	no	—
681	C₄	—	4	1	no	—
682	C₄	C₅₃×#546	1	1	yes	characteristic
683	C₄	C₅₃×#546	1	1	yes	characteristic
684	C₄	C₅₃×#554	1	1	yes	characteristic
685	C₄	C₅₃×#554	1	1	yes	characteristic
686	C₂	—	4	2	no	—
687	C₂	—	4	2	no	—
688	C₂	C₅₃×#2349	1	1	yes	characteristic
689	C₂	C₅₃×#2905	1	1	yes	characteristic
690	C₂	C₅₃×#2906	1	1	yes	characteristic
691	C₂	C₅₃×#2967	1	1	yes	characteristic
692	C₂	C₅₃×#2969	1	1	yes	characteristic
693	C₂	C₅₃×#2976	1	1	yes	characteristic
694	C₂	C₅₃×#2978	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₅₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
socle	C₂³×C₅₃	C₂³×C₄
prime radical	C₂²×D₄×C₅₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅₃×#1940	C₂	semidirect
5. C₅₃×#1939	C₂	semidirect
6. C₅₃×#1851	C₂	semidirect
7. C₅₃×#1851	C₂	semidirect
8. C₅₃×#1851	C₂	semidirect
9. C₅₃×#1850	C₂	semidirect
10. C₅₃×#1832	C₂	semidirect
11. C₅₃×#1798	C₂	semidirect
12. C₅₃×#1797	C₂	semidirect
13. C₅₃×#1768	C₂	semidirect
14. C₅₃×#1729	C₂	semidirect
15. C₅₃×#1728	C₂	semidirect
301. #22699	C₅₃	direct (N × H)
342. #1940	C₂×C₅₃	semidirect
343. #1939	C₂×C₅₃	semidirect
344. #1851	C₂×C₅₃	semidirect
345. #1851	C₂×C₅₃	semidirect
346. #1851	C₂×C₅₃	semidirect
347. #1850	C₂×C₅₃	semidirect
348. #1832	C₂×C₅₃	semidirect
349. #1798	C₂×C₅₃	semidirect
350. #1797	C₂×C₅₃	semidirect
351. #1768	C₂×C₅₃	semidirect
352. #1729	C₂×C₅₃	semidirect
353. #1728	C₂×C₅₃	semidirect
408. C₅₃	#22699	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×#436	2
C₂×C₅₃×#435	2
C₅₃×#2290	2
C₅₃×#1940	2
C₅₃×#1939	2
C₅₃×#1851	2
C₅₃×#1850	2
C₅₃×#1832	2
C₅₃×#1798	2
C₅₃×#1797	2
C₅₃×#1768	2
C₅₃×#1729	2
C₅₃×#1728	2
#22699	53

Subgroups — C53×#22699 #27230211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#22699 #27230211