Subgroups — C₅₃×#24897 #27232409

Order 13568.

1204 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#447	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2420	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2076	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#1934	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#1923	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#1879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#1786	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
18	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
19	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₂²⋊C₄×C₅₃	—	2	1	no	—
24	C₅₃×#447	—	2	4	no	—
25	C₄×D₈×C₅₃	—	2	4	no	—
26	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
31	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
32	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#397	—	2	1	no	—
41	C₅₃×#394	—	2	1	no	—
42	C₅₃×#390	C₂²	1	1	yes	characteristic
43	C₅₃×#390	C₂²	1	1	yes	characteristic
44	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#386	—	2	1	no	—
47	C₅₃×#386	—	2	1	no	—
48	C₅₃×#386	—	2	1	no	—
49	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#381	—	2	1	no	—
51	C₅₃×#380	C₂²	1	1	yes	characteristic
52	C₅₃×#380	C₂²	1	1	yes	characteristic
53	C₅₃×#379	—	2	1	no	—
54	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#340	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#336	C₂²	1	1	yes	characteristic, complemented
61	C₂⁵×C₅₃	—	2	1	no	—
62	C₂²×D₄×C₅₃	—	2	2	no	—
63	C₂²×D₄×C₅₃	—	2	2	no	—
64	C₂²×D₄×C₅₃	—	2	2	no	—
65	C₂²×D₄×C₅₃	—	2	2	no	—
66	C₂²×D₄×C₅₃	—	2	1	no	—
67	C₂²×D₄×C₅₃	—	2	1	no	—
68	C₂²×D₄×C₅₃	—	4	1	no	—
69	C₂²×D₄×C₅₃	—	4	1	no	—
70	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
71	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₅₃	—	2	1	no	—
74	C₂³×C₄×C₅₃	—	2	1	no	—
75	C₂³×C₄×C₅₃	—	2	1	no	—
76	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
77	C₂×D₈×C₅₃	—	2	2	no	—
78	C₂×D₈×C₅₃	—	2	2	no	—
79	C₂×D₈×C₅₃	—	2	2	no	—
80	C₂×D₈×C₅₃	—	2	2	no	—
81	C₂×D₈×C₅₃	—	4	1	no	—
82	C₂×D₈×C₅₃	D₄	1	4	yes	—
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	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
87	#121×C₅₃	—	2	2	no	—
88	#121×C₅₃	—	4	1	no	—
89	C₄×D₄×C₅₃	—	2	2	no	—
90	C₄×D₄×C₅₃	—	2	2	no	—
91	C₄×D₄×C₅₃	—	2	2	no	—
92	C₄×D₄×C₅₃	—	4	1	no	—
93	C₄×D₄×C₅₃	—	4	1	no	—
94	C₄×D₄×C₅₃	—	4	1	no	—
95	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
106	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
111	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
112	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
113	C₂×C₂²⋊C₄×C₅₃	—	4	4	no	—
114	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
118	#107×C₅₃	—	2	2	no	—
119	#106×C₅₃	—	4	1	no	—
120	C₄⋊C₈×C₅₃	—	4	1	no	—
121	#102×C₅₃	—	2	2	no	—
122	#102×C₅₃	—	2	2	no	—
123	#102×C₅₃	—	2	2	no	—
124	#102×C₅₃	—	2	2	no	—
125	#102×C₅₃	—	2	2	no	—
126	#102×C₅₃	—	2	2	no	—
127	#102×C₅₃	—	4	1	no	—
128	#102×C₅₃	—	4	1	no	—
129	C₂²⋊C₈×C₅₃	—	2	2	no	—
130	C₂²⋊C₈×C₅₃	—	4	1	no	—
131	C₄×C₈×C₅₃	—	2	2	no	—
132	#95×C₅₃	—	2	1	no	—
133	#95×C₅₃	—	2	1	no	—
134	#95×C₅₃	—	2	1	no	—
135	#95×C₅₃	—	2	1	no	—
136	#95×C₅₃	—	2	1	no	—
137	#95×C₅₃	D₄	1	1	yes	characteristic
138	#95×C₅₃	D₄	1	1	yes	characteristic
139	C₂⁴×C₅₃	—	2	1	no	—
140	C₂⁴×C₅₃	—	2	4	no	—
141	C₂⁴×C₅₃	—	2	1	no	—
142	C₂⁴×C₅₃	—	2	1	no	—
143	C₂⁴×C₅₃	—	4	2	no	—
144	C₂⁴×C₅₃	—	4	2	no	—
145	C₂⁴×C₅₃	—	4	2	no	—
146	C₂⁴×C₅₃	—	4	2	no	—
147	C₂⁴×C₅₃	—	8	1	no	—
148	C₂⁴×C₅₃	—	8	1	no	—
149	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₅₃	—	2	4	no	—
151	C₂×D₄×C₅₃	—	2	1	no	—
152	C₂×D₄×C₅₃	—	2	1	no	—
153	C₂×D₄×C₅₃	—	2	1	no	—
154	C₂×D₄×C₅₃	—	2	1	no	—
155	C₂×D₄×C₅₃	—	2	1	no	—
156	C₂×D₄×C₅₃	—	2	1	no	—
157	C₂×D₄×C₅₃	—	2	1	no	—
158	C₂×D₄×C₅₃	—	2	1	no	—
159	C₂×D₄×C₅₃	—	2	1	no	—
160	C₂×D₄×C₅₃	—	2	1	no	—
161	C₂×D₄×C₅₃	—	2	1	no	—
162	C₂×D₄×C₅₃	—	2	1	no	—
163	C₂×D₄×C₅₃	—	2	1	no	—
164	C₂×D₄×C₅₃	—	4	2	no	—
165	C₂×D₄×C₅₃	—	4	2	no	—
166	C₂×D₄×C₅₃	—	4	4	no	—
167	C₂×D₄×C₅₃	—	4	4	no	—
168	C₂×D₄×C₅₃	—	4	4	no	—
169	C₂×D₄×C₅₃	—	4	4	no	—
170	C₂×D₄×C₅₃	—	4	2	no	—
171	C₂×D₄×C₅₃	—	4	2	no	—
172	C₂×D₄×C₅₃	—	8	1	no	—
173	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
174	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
175	C₂×D₄×C₅₃	#41	1	2	yes	—
176	C₂×D₄×C₅₃	#41	1	2	yes	—
177	C₂×D₄×C₅₃	#41	1	2	yes	—
178	C₂²×C₄×C₅₃	—	2	1	no	—
179	C₂²×C₄×C₅₃	—	2	1	no	—
180	C₂²×C₄×C₅₃	—	2	1	no	—
181	C₂²×C₄×C₅₃	—	2	1	no	—
182	C₂²×C₄×C₅₃	—	2	1	no	—
183	C₂²×C₄×C₅₃	—	2	1	no	—
184	C₂²×C₄×C₅₃	—	2	1	no	—
185	C₂²×C₄×C₅₃	—	2	1	no	—
186	C₂²×C₄×C₅₃	—	2	1	no	—
187	C₂²×C₄×C₅₃	—	2	1	no	—
188	C₂²×C₄×C₅₃	—	2	1	no	—
189	C₂²×C₄×C₅₃	—	4	2	no	—
190	C₂²×C₄×C₅₃	—	4	2	no	—
191	C₂²×C₄×C₅₃	—	4	2	no	—
192	C₂²×C₄×C₅₃	—	4	2	no	—
193	C₂²×C₄×C₅₃	—	4	2	no	—
194	C₂²×C₄×C₅₃	—	4	2	no	—
195	C₂²×C₄×C₅₃	—	8	1	no	—
196	C₂²×C₄×C₅₃	—	8	1	no	—
197	C₂²×C₄×C₅₃	—	8	1	no	—
198	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
201	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
202	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
203	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
204	D₈×C₅₃	—	2	8	no	—
205	D₈×C₅₃	—	4	4	no	—
206	C₂×C₈×C₅₃	—	2	1	no	—
207	C₂×C₈×C₅₃	—	2	1	no	—
208	C₂×C₈×C₅₃	—	2	1	no	—
209	C₂×C₈×C₅₃	—	2	1	no	—
210	C₂×C₈×C₅₃	—	2	1	no	—
211	C₂×C₈×C₅₃	—	2	1	no	—
212	C₂×C₈×C₅₃	—	2	1	no	—
213	C₂×C₈×C₅₃	—	2	1	no	—
214	C₂×C₈×C₅₃	—	2	1	no	—
215	C₂×C₈×C₅₃	—	2	1	no	—
216	C₂×C₈×C₅₃	—	2	1	no	—
217	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
218	C₄⋊C₄×C₅₃	—	2	1	no	—
219	C₄⋊C₄×C₅₃	—	2	1	no	—
220	C₄⋊C₄×C₅₃	—	2	1	no	—
221	C₄⋊C₄×C₅₃	—	2	1	no	—
222	C₄⋊C₄×C₅₃	—	2	1	no	—
223	C₄⋊C₄×C₅₃	—	2	1	no	—
224	C₄⋊C₄×C₅₃	—	2	1	no	—
225	C₄⋊C₄×C₅₃	—	2	1	no	—
226	C₄⋊C₄×C₅₃	—	2	1	no	—
227	C₄⋊C₄×C₅₃	—	2	1	no	—
228	C₄⋊C₄×C₅₃	—	8	1	no	—
229	C₂²⋊C₄×C₅₃	—	2	2	no	—
230	C₂²⋊C₄×C₅₃	—	2	2	no	—
231	C₂²⋊C₄×C₅₃	—	4	2	no	—
232	C₂²⋊C₄×C₅₃	—	4	2	no	—
233	C₂²⋊C₄×C₅₃	—	4	2	no	—
234	C₂²⋊C₄×C₅₃	—	4	2	no	—
235	C₂²⋊C₄×C₅₃	—	4	2	no	—
236	C₂²⋊C₄×C₅₃	—	4	2	no	—
237	C₂²⋊C₄×C₅₃	—	4	2	no	—
238	C₂²⋊C₄×C₅₃	—	8	1	no	—
239	C₂²⋊C₄×C₅₃	—	8	1	no	—
240	C₂²⋊C₄×C₅₃	—	8	1	no	—
241	C₂²⋊C₄×C₅₃	—	8	1	no	—
242	C₂²⋊C₄×C₅₃	—	8	1	no	—
243	C₄²×C₅₃	—	2	1	no	—
244	C₄²×C₅₃	—	2	1	no	—
245	C₄²×C₅₃	—	2	1	no	—
246	C₄²×C₅₃	—	2	1	no	—
247	C₂³×C₅₃	—	2	1	no	—
248	C₂³×C₅₃	—	2	2	no	—
249	C₂³×C₅₃	—	2	1	no	—
250	C₂³×C₅₃	—	2	2	no	—
251	C₂³×C₅₃	—	2	1	no	—
252	C₂³×C₅₃	—	2	2	no	—
253	C₂³×C₅₃	—	2	1	no	—
254	C₂³×C₅₃	—	2	1	no	—
255	C₂³×C₅₃	—	2	1	no	—
256	C₂³×C₅₃	—	2	2	no	—
257	C₂³×C₅₃	—	2	2	no	—
258	C₂³×C₅₃	—	4	8	no	—
259	C₂³×C₅₃	—	4	8	no	—
260	C₂³×C₅₃	—	4	1	no	—
261	C₂³×C₅₃	—	4	1	no	—
262	C₂³×C₅₃	—	4	1	no	—
263	C₂³×C₅₃	—	4	1	no	—
264	C₂³×C₅₃	—	4	1	no	—
265	C₂³×C₅₃	—	4	1	no	—
266	C₂³×C₅₃	—	4	1	no	—
267	C₂³×C₅₃	—	4	1	no	—
268	C₂³×C₅₃	—	4	1	no	—
269	C₂³×C₅₃	—	4	1	no	—
270	C₂³×C₅₃	—	4	1	no	—
271	C₂³×C₅₃	—	4	1	no	—
272	C₂³×C₅₃	—	4	1	no	—
273	C₂³×C₅₃	—	4	1	no	—
274	C₂³×C₅₃	—	4	1	no	—
275	C₂³×C₅₃	—	4	1	no	—
276	C₂³×C₅₃	—	8	4	no	—
277	C₂³×C₅₃	—	8	4	no	—
278	C₂³×C₅₃	—	8	4	no	—
279	C₂³×C₅₃	—	8	4	no	—
280	C₂³×C₅₃	—	8	4	no	—
281	C₂³×C₅₃	#135	1	2	yes	—
282	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
283	D₄×C₅₃	—	2	2	no	—
284	D₄×C₅₃	—	2	2	no	—
285	D₄×C₅₃	—	2	2	no	—
286	D₄×C₅₃	—	2	2	no	—
287	D₄×C₅₃	—	2	2	no	—
288	D₄×C₅₃	—	2	2	no	—
289	D₄×C₅₃	—	2	2	no	—
290	D₄×C₅₃	—	4	8	no	—
291	D₄×C₅₃	—	4	1	no	—
292	D₄×C₅₃	—	4	1	no	—
293	D₄×C₅₃	—	4	1	no	—
294	D₄×C₅₃	—	4	1	no	—
295	D₄×C₅₃	—	8	4	no	—
296	D₄×C₅₃	#123	1	4	yes	—
297	C₂×C₄×C₅₃	—	2	1	no	—
298	C₂×C₄×C₅₃	—	2	1	no	—
299	C₂×C₄×C₅₃	—	2	1	no	—
300	C₂×C₄×C₅₃	—	2	1	no	—
301	C₂×C₄×C₅₃	—	2	1	no	—
302	C₂×C₄×C₅₃	—	2	1	no	—
303	C₂×C₄×C₅₃	—	2	1	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	1	no	—
307	C₂×C₄×C₅₃	—	2	1	no	—
308	C₂×C₄×C₅₃	—	2	1	no	—
309	C₂×C₄×C₅₃	—	2	1	no	—
310	C₂×C₄×C₅₃	—	2	1	no	—
311	C₂×C₄×C₅₃	—	4	1	no	—
312	C₂×C₄×C₅₃	—	4	1	no	—
313	C₂×C₄×C₅₃	—	4	1	no	—
314	C₂×C₄×C₅₃	—	4	1	no	—
315	C₂×C₄×C₅₃	—	4	1	no	—
316	C₂×C₄×C₅₃	—	4	1	no	—
317	C₂×C₄×C₅₃	—	4	1	no	—
318	C₂×C₄×C₅₃	—	4	1	no	—
319	C₂×C₄×C₅₃	—	4	1	no	—
320	C₂×C₄×C₅₃	—	4	1	no	—
321	C₂×C₄×C₅₃	—	4	1	no	—
322	C₂×C₄×C₅₃	—	4	1	no	—
323	C₂×C₄×C₅₃	—	4	1	no	—
324	C₂×C₄×C₅₃	—	4	1	no	—
325	C₂×C₄×C₅₃	—	4	1	no	—
326	C₂×C₄×C₅₃	—	4	1	no	—
327	C₂×C₄×C₅₃	—	4	1	no	—
328	C₂×C₄×C₅₃	—	4	1	no	—
329	C₂×C₄×C₅₃	—	4	1	no	—
330	C₂×C₄×C₅₃	—	8	4	no	—
331	C₂×C₄×C₅₃	—	8	4	no	—
332	C₂×C₄×C₅₃	—	8	4	no	—
333	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	2	yes	—
334	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
336	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
337	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
338	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
340	C₈×C₅₃	—	2	2	no	—
341	C₈×C₅₃	—	4	1	no	—
342	C₈×C₅₃	—	4	1	no	—
343	C₈×C₅₃	—	4	1	no	—
344	#24897	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂²×C₅₃	—	2	2	no	—
346	C₂²×C₅₃	—	2	4	no	—
347	C₂²×C₅₃	—	2	2	no	—
348	C₂²×C₅₃	—	2	2	no	—
349	C₂²×C₅₃	—	4	2	no	—
350	C₂²×C₅₃	—	4	1	no	—
351	C₂²×C₅₃	—	4	2	no	—
352	C₂²×C₅₃	—	4	1	no	—
353	C₂²×C₅₃	—	4	2	no	—
354	C₂²×C₅₃	—	4	1	no	—
355	C₂²×C₅₃	—	4	2	no	—
356	C₂²×C₅₃	—	4	2	no	—
357	C₂²×C₅₃	—	4	2	no	—
358	C₂²×C₅₃	—	4	1	no	—
359	C₂²×C₅₃	—	4	2	no	—
360	C₂²×C₅₃	—	4	2	no	—
361	C₂²×C₅₃	—	4	2	no	—
362	C₂²×C₅₃	—	4	2	no	—
363	C₂²×C₅₃	—	4	2	no	—
364	C₂²×C₅₃	—	4	2	no	—
365	C₂²×C₅₃	—	8	16	no	—
366	C₂²×C₅₃	—	8	1	no	—
367	C₂²×C₅₃	—	8	1	no	—
368	C₂²×C₅₃	—	8	1	no	—
369	C₂²×C₅₃	—	8	1	no	—
370	C₂²×C₅₃	—	8	1	no	—
371	C₂²×C₅₃	—	8	1	no	—
372	C₂²×C₅₃	—	8	1	no	—
373	C₂²×C₅₃	—	8	1	no	—
374	C₂²×C₅₃	#525	1	1	yes	characteristic
375	C₂²×C₅₃	D₄²	1	1	yes	characteristic
376	C₂²×C₅₃	#546	1	1	yes	characteristic
377	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
378	C₂²×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
379	C₂²×C₅₃	#576	1	1	yes	characteristic
380	C₂²×C₅₃	#576	1	1	yes	characteristic
381	C₄×C₅₃	—	2	2	no	—
382	C₄×C₅₃	—	4	1	no	—
383	C₄×C₅₃	—	4	1	no	—
384	C₄×C₅₃	—	4	1	no	—
385	C₄×C₅₃	—	4	1	no	—
386	C₄×C₅₃	—	8	1	no	—
387	C₄×C₅₃	—	8	1	no	—
388	C₄×C₅₃	—	8	1	no	—
389	C₄×C₅₃	—	8	1	no	—
390	C₄×C₅₃	—	8	1	no	—
391	C₄×C₅₃	C₂×#123	1	1	yes	characteristic
392	C₄×C₅₃	#538	1	1	yes	characteristic
393	C₄×C₅₃	#546	1	1	yes	characteristic
394	C₄×C₅₃	#551	1	1	yes	characteristic
395	C₂×#447	C₂×C₅₃	1	1	yes	characteristic
396	C₂×C₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
397	#2420	C₂×C₅₃	1	1	yes	characteristic, complemented
398	D₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
399	#2092	C₂×C₅₃	1	1	yes	characteristic, complemented
400	#2076	C₂×C₅₃	1	1	yes	characteristic, complemented
401	#2054	C₂×C₅₃	1	1	yes	characteristic, complemented
402	#2034	C₂×C₅₃	1	1	yes	characteristic, complemented
403	#1934	C₂×C₅₃	1	1	yes	characteristic, complemented
404	#1923	C₂×C₅₃	1	1	yes	characteristic, complemented
405	#1879	C₂×C₅₃	1	1	yes	characteristic, complemented
406	#1879	C₂×C₅₃	1	1	yes	characteristic, complemented
407	#1864	C₂×C₅₃	1	1	yes	characteristic, complemented
408	#1804	C₂×C₅₃	1	1	yes	characteristic, complemented
409	#1786	C₂×C₅₃	1	1	yes	characteristic, complemented
410	C₂×C₅₃	—	4	2	no	—
411	C₂×C₅₃	—	4	4	no	—
412	C₂×C₅₃	—	8	2	no	—
413	C₂×C₅₃	—	8	2	no	—
414	C₂×C₅₃	#2418	1	1	yes	characteristic
415	C₂×C₅₃	#3105	1	1	yes	characteristic
416	C₂×C₅₃	#3122	1	1	yes	characteristic
417	C₂×C₅₃	#3264	1	1	yes	characteristic
418	C₂×C₅₃	#3280	1	1	yes	characteristic
419	C₂×C₅₃	#3297	1	1	yes	characteristic
420	C₂×C₅₃	#3325	1	1	yes	characteristic
421	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
422	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
423	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
424	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
425	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
428	C₂²×C₂²⋊C₄	—	2	1	no	—
429	#447	—	2	4	no	—
430	C₄×D₈	—	2	4	no	—
431	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
432	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
433	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
434	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
437	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
438	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
441	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
442	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
443	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
444	C₂×C₄×C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
445	#397	—	2	1	no	—
446	#394	—	2	1	no	—
447	#390	C₂²×C₅₃	1	1	yes	characteristic
448	#390	C₂²×C₅₃	1	1	yes	characteristic
449	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
450	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
451	#386	—	2	1	no	—
452	#386	—	2	1	no	—
453	#386	—	2	1	no	—
454	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
455	#381	—	2	1	no	—
456	#380	C₂²×C₅₃	1	1	yes	characteristic
457	#380	C₂²×C₅₃	1	1	yes	characteristic
458	#379	—	2	1	no	—
459	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
460	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
461	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
462	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
463	#340	C₂²×C₅₃	1	1	yes	characteristic, complemented
464	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
465	#336	C₂²×C₅₃	1	1	yes	characteristic, complemented
466	C₅₃	#24897	1	1	yes	characteristic, direct product factor, Sylow
467	C₂⁵	—	2	1	no	—
468	C₂²×D₄	—	2	2	no	—
469	C₂²×D₄	—	2	2	no	—
470	C₂²×D₄	—	2	2	no	—
471	C₂²×D₄	—	2	2	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	—	4	1	no	—
475	C₂²×D₄	—	4	1	no	—
476	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
477	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
478	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	—	2	1	no	—
481	C₂³×C₄	—	2	1	no	—
482	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
483	C₂×D₈	—	2	2	no	—
484	C₂×D₈	—	2	2	no	—
485	C₂×D₈	—	2	2	no	—
486	C₂×D₈	—	2	2	no	—
487	C₂×D₈	—	4	1	no	—
488	C₂×D₈	D₄×C₅₃	1	4	yes	—
489	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
490	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
491	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
492	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
493	#121	—	2	2	no	—
494	#121	—	4	1	no	—
495	C₄×D₄	—	2	2	no	—
496	C₄×D₄	—	2	2	no	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	—	4	1	no	—
499	C₄×D₄	—	4	1	no	—
500	C₄×D₄	—	4	1	no	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
503	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
504	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
505	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
506	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
507	C₂×C₂²⋊C₄	—	2	1	no	—
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	1	no	—
510	C₂×C₂²⋊C₄	—	2	1	no	—
511	C₂×C₂²⋊C₄	—	2	1	no	—
512	C₂×C₂²⋊C₄	—	2	1	no	—
513	C₂×C₂²⋊C₄	—	2	1	no	—
514	C₂×C₂²⋊C₄	—	2	1	no	—
515	C₂×C₂²⋊C₄	—	2	1	no	—
516	C₂×C₂²⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	4	4	no	—
520	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
521	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
522	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
523	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
524	#107	—	2	2	no	—
525	#106	—	4	1	no	—
526	C₄⋊C₈	—	4	1	no	—
527	#102	—	2	2	no	—
528	#102	—	2	2	no	—
529	#102	—	2	2	no	—
530	#102	—	2	2	no	—
531	#102	—	2	2	no	—
532	#102	—	2	2	no	—
533	#102	—	4	1	no	—
534	#102	—	4	1	no	—
535	C₂²⋊C₈	—	2	2	no	—
536	C₂²⋊C₈	—	4	1	no	—
537	C₄×C₈	—	2	2	no	—
538	#95	—	2	1	no	—
539	#95	—	2	1	no	—
540	#95	—	2	1	no	—
541	#95	—	2	1	no	—
542	#95	—	2	1	no	—
543	#95	D₄×C₅₃	1	1	yes	characteristic
544	#95	D₄×C₅₃	1	1	yes	characteristic
545	C₂⁴	—	2	1	no	—
546	C₂⁴	—	2	4	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	—	2	1	no	—
549	C₂⁴	—	4	2	no	—
550	C₂⁴	—	4	2	no	—
551	C₂⁴	—	4	2	no	—
552	C₂⁴	—	4	2	no	—
553	C₂⁴	—	8	1	no	—
554	C₂⁴	—	8	1	no	—
555	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
556	C₂×D₄	—	2	4	no	—
557	C₂×D₄	—	2	1	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	2	1	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	4	2	no	—
571	C₂×D₄	—	4	2	no	—
572	C₂×D₄	—	4	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	4	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	8	1	no	—
579	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
580	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
581	C₂×D₄	#41×C₅₃	1	2	yes	—
582	C₂×D₄	#41×C₅₃	1	2	yes	—
583	C₂×D₄	#41×C₅₃	1	2	yes	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	1	no	—
594	C₂²×C₄	—	2	1	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	2	no	—
597	C₂²×C₄	—	4	2	no	—
598	C₂²×C₄	—	4	2	no	—
599	C₂²×C₄	—	4	2	no	—
600	C₂²×C₄	—	4	2	no	—
601	C₂²×C₄	—	8	1	no	—
602	C₂²×C₄	—	8	1	no	—
603	C₂²×C₄	—	8	1	no	—
604	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
608	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
610	D₈	—	2	8	no	—
611	D₈	—	4	4	no	—
612	C₂×C₈	—	2	1	no	—
613	C₂×C₈	—	2	1	no	—
614	C₂×C₈	—	2	1	no	—
615	C₂×C₈	—	2	1	no	—
616	C₂×C₈	—	2	1	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	C₂×D₄×C₅₃	1	2	yes	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	—	2	1	no	—
630	C₄⋊C₄	—	2	1	no	—
631	C₄⋊C₄	—	2	1	no	—
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	8	1	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	4	2	no	—
638	C₂²⋊C₄	—	4	2	no	—
639	C₂²⋊C₄	—	4	2	no	—
640	C₂²⋊C₄	—	4	2	no	—
641	C₂²⋊C₄	—	4	2	no	—
642	C₂²⋊C₄	—	4	2	no	—
643	C₂²⋊C₄	—	4	2	no	—
644	C₂²⋊C₄	—	8	1	no	—
645	C₂²⋊C₄	—	8	1	no	—
646	C₂²⋊C₄	—	8	1	no	—
647	C₂²⋊C₄	—	8	1	no	—
648	C₂²⋊C₄	—	8	1	no	—
649	C₄²	—	2	1	no	—
650	C₄²	—	2	1	no	—
651	C₄²	—	2	1	no	—
652	C₄²	—	2	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	1	no	—
659	C₂³	—	2	1	no	—
660	C₂³	—	2	1	no	—
661	C₂³	—	2	1	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	8	no	—
665	C₂³	—	4	8	no	—
666	C₂³	—	4	1	no	—
667	C₂³	—	4	1	no	—
668	C₂³	—	4	1	no	—
669	C₂³	—	4	1	no	—
670	C₂³	—	4	1	no	—
671	C₂³	—	4	1	no	—
672	C₂³	—	4	1	no	—
673	C₂³	—	4	1	no	—
674	C₂³	—	4	1	no	—
675	C₂³	—	4	1	no	—
676	C₂³	—	4	1	no	—
677	C₂³	—	4	1	no	—
678	C₂³	—	4	1	no	—
679	C₂³	—	4	1	no	—
680	C₂³	—	4	1	no	—
681	C₂³	—	4	1	no	—
682	C₂³	—	8	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	4	no	—
685	C₂³	—	8	4	no	—
686	C₂³	—	8	4	no	—
687	C₂³	#135×C₅₃	1	2	yes	—
688	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
689	D₄	—	2	2	no	—
690	D₄	—	2	2	no	—
691	D₄	—	2	2	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	4	8	no	—
697	D₄	—	4	1	no	—
698	D₄	—	4	1	no	—
699	D₄	—	4	1	no	—
700	D₄	—	4	1	no	—
701	D₄	—	8	4	no	—
702	D₄	#123×C₅₃	1	4	yes	—
703	C₂×C₄	—	2	1	no	—
704	C₂×C₄	—	2	1	no	—
705	C₂×C₄	—	2	1	no	—
706	C₂×C₄	—	2	1	no	—
707	C₂×C₄	—	2	1	no	—
708	C₂×C₄	—	2	1	no	—
709	C₂×C₄	—	2	1	no	—
710	C₂×C₄	—	2	1	no	—
711	C₂×C₄	—	2	1	no	—
712	C₂×C₄	—	2	1	no	—
713	C₂×C₄	—	2	1	no	—
714	C₂×C₄	—	2	1	no	—
715	C₂×C₄	—	2	1	no	—
716	C₂×C₄	—	2	1	no	—
717	C₂×C₄	—	4	1	no	—
718	C₂×C₄	—	4	1	no	—
719	C₂×C₄	—	4	1	no	—
720	C₂×C₄	—	4	1	no	—
721	C₂×C₄	—	4	1	no	—
722	C₂×C₄	—	4	1	no	—
723	C₂×C₄	—	4	1	no	—
724	C₂×C₄	—	4	1	no	—
725	C₂×C₄	—	4	1	no	—
726	C₂×C₄	—	4	1	no	—
727	C₂×C₄	—	4	1	no	—
728	C₂×C₄	—	4	1	no	—
729	C₂×C₄	—	4	1	no	—
730	C₂×C₄	—	4	1	no	—
731	C₂×C₄	—	4	1	no	—
732	C₂×C₄	—	4	1	no	—
733	C₂×C₄	—	4	1	no	—
734	C₂×C₄	—	4	1	no	—
735	C₂×C₄	—	4	1	no	—
736	C₂×C₄	—	8	4	no	—
737	C₂×C₄	—	8	4	no	—
738	C₂×C₄	—	8	4	no	—
739	C₂×C₄	AGL(1,ℤ/8)×C₅₃	1	2	yes	—
740	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
741	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
742	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
743	C₂×C₄	C₂×#41×C₅₃	1	1	yes	characteristic
744	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
745	C₂×C₄	H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
746	C₈	—	2	2	no	—
747	C₈	—	4	1	no	—
748	C₈	—	4	1	no	—
749	C₈	—	4	1	no	—
750	C₂²	—	2	2	no	—
751	C₂²	—	2	2	no	—
752	C₂²	—	2	2	no	—
753	C₂²	—	2	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	2	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	2	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	2	no	—
765	C₂²	—	4	2	no	—
766	C₂²	—	4	2	no	—
767	C₂²	—	4	2	no	—
768	C₂²	—	4	2	no	—
769	C₂²	—	4	2	no	—
770	C₂²	—	8	16	no	—
771	C₂²	—	8	1	no	—
772	C₂²	—	8	1	no	—
773	C₂²	—	8	1	no	—
774	C₂²	—	8	1	no	—
775	C₂²	—	8	1	no	—
776	C₂²	—	8	1	no	—
777	C₂²	—	8	1	no	—
778	C₂²	—	8	1	no	—
779	C₂²	C₅₃×#525	1	1	yes	characteristic
780	C₂²	D₄²×C₅₃	1	1	yes	characteristic
781	C₂²	C₅₃×#546	1	1	yes	characteristic
782	C₂²	C₂×#135×C₅₃	1	1	yes	characteristic
783	C₂²	C₂×AGL(1,ℤ/8)×C₅₃	1	1	yes	characteristic
784	C₂²	C₅₃×#576	1	1	yes	characteristic
785	C₂²	C₅₃×#576	1	1	yes	characteristic
786	C₄	—	2	2	no	—
787	C₄	—	4	1	no	—
788	C₄	—	4	1	no	—
789	C₄	—	4	1	no	—
790	C₄	—	4	1	no	—
791	C₄	—	8	1	no	—
792	C₄	—	8	1	no	—
793	C₄	—	8	1	no	—
794	C₄	—	8	1	no	—
795	C₄	—	8	1	no	—
796	C₄	C₂×#123×C₅₃	1	1	yes	characteristic
797	C₄	C₅₃×#538	1	1	yes	characteristic
798	C₄	C₅₃×#546	1	1	yes	characteristic
799	C₄	C₅₃×#551	1	1	yes	characteristic
800	C₂	—	4	2	no	—
801	C₂	—	4	4	no	—
802	C₂	—	8	2	no	—
803	C₂	—	8	2	no	—
804	C₂	C₅₃×#2418	1	1	yes	characteristic
805	C₂	C₅₃×#3105	1	1	yes	characteristic
806	C₂	C₅₃×#3122	1	1	yes	characteristic
807	C₂	C₅₃×#3264	1	1	yes	characteristic
808	C₂	C₅₃×#3280	1	1	yes	characteristic
809	C₂	C₅₃×#3297	1	1	yes	characteristic
810	C₂	C₅₃×#3325	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₃
prime radical	C₂×C₅₃×#447	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₄×C₂²⋊C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₈×C₅₃	C₂	semidirect
3. C₅₃×#2420	C₂	semidirect
4. D₄×C₂²⋊C₄×C₅₃	C₂	semidirect
5. C₅₃×#2092	C₂	semidirect
6. C₅₃×#2076	C₂	semidirect
7. C₅₃×#2054	C₂	semidirect
8. C₅₃×#2034	C₂	semidirect
9. C₅₃×#1934	C₂	semidirect
10. C₅₃×#1923	C₂	semidirect
11. C₅₃×#1879	C₂	semidirect
12. C₅₃×#1879	C₂	semidirect
13. C₅₃×#1864	C₂	semidirect
14. C₅₃×#1804	C₂	semidirect
15. C₅₃×#1786	C₂	semidirect
22. C₂×C₄×D₄×C₅₃	C₂²	semidirect
26. C₂×#107×C₅₃	C₂²	semidirect
27. C₂×#106×C₅₃	C₂²	semidirect
28. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
35. C₂×#102×C₅₃	C₂²	semidirect
36. C₂×#102×C₅₃	C₂²	semidirect
39. C₂×C₄×C₈×C₅₃	C₂²	semidirect
44. C₅₃×#390	C₂²	semidirect
45. C₅₃×#389	C₂²	semidirect
49. C₅₃×#382	C₂²	semidirect
55. C₅₃×#340	C₂²	semidirect
56. C₅₃×#340	C₂²	semidirect
57. C₅₃×#340	C₂²	semidirect
58. C₅₃×#340	C₂²	semidirect
59. C₅₃×#336	C₂²	semidirect
60. C₅₃×#336	C₂²	semidirect
344. #24897	C₅₃	direct (N × H)
396. C₂×C₄×D₈	C₂×C₅₃	semidirect
397. #2420	C₂×C₅₃	semidirect
398. D₄×C₂²⋊C₄	C₂×C₅₃	semidirect
399. #2092	C₂×C₅₃	semidirect
400. #2076	C₂×C₅₃	semidirect
401. #2054	C₂×C₅₃	semidirect
402. #2034	C₂×C₅₃	semidirect
403. #1934	C₂×C₅₃	semidirect
404. #1923	C₂×C₅₃	semidirect
405. #1879	C₂×C₅₃	semidirect
406. #1879	C₂×C₅₃	semidirect
407. #1864	C₂×C₅₃	semidirect
408. #1804	C₂×C₅₃	semidirect
409. #1786	C₂×C₅₃	semidirect
427. C₂×C₄×D₄	C₂²×C₅₃	semidirect
431. C₂×#107	C₂²×C₅₃	semidirect
432. C₂×#106	C₂²×C₅₃	semidirect
433. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
440. C₂×#102	C₂²×C₅₃	semidirect
441. C₂×#102	C₂²×C₅₃	semidirect
444. C₂×C₄×C₈	C₂²×C₅₃	semidirect
449. #390	C₂²×C₅₃	semidirect
450. #389	C₂²×C₅₃	semidirect
454. #382	C₂²×C₅₃	semidirect
460. #340	C₂²×C₅₃	semidirect
461. #340	C₂²×C₅₃	semidirect
462. #340	C₂²×C₅₃	semidirect
463. #340	C₂²×C₅₃	semidirect
464. #336	C₂²×C₅₃	semidirect
465. #336	C₂²×C₅₃	semidirect
466. C₅₃	#24897	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×#447	2
C₂×C₄×D₈×C₅₃	2
C₅₃×#2420	2
D₄×C₂²⋊C₄×C₅₃	2
C₅₃×#2092	2
C₅₃×#2076	2
C₅₃×#2054	2
C₅₃×#2034	2
C₅₃×#1934	2
C₅₃×#1923	2
C₅₃×#1879	2
C₅₃×#1864	2
C₅₃×#1804	2
C₅₃×#1786	2
#24897	53

Subgroups — C53×#24897 #27232409

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#24897 #27232409