Subgroups — #27554573

Order 13568.

2160 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20280055	C₂	1	1	yes	maximal, characteristic, complemented
2	#20280032	C₂	1	1	yes	maximal, characteristic, complemented
3	#20280023	C₂	1	1	yes	maximal, characteristic, complemented
4	#20280000	C₂	1	1	yes	maximal, characteristic, complemented
5	#20279991	C₂	1	1	yes	maximal, characteristic, complemented
6	#20279974	C₂	1	1	yes	maximal, characteristic, complemented
7	#20279935	C₂	1	1	yes	maximal, characteristic, complemented
8	#20279892	C₂	1	1	yes	maximal, characteristic, complemented
9	#20279869	C₂	1	1	yes	maximal, characteristic, complemented
10	#20279760	C₂	1	1	yes	maximal, characteristic, complemented
11	#20279600	C₂	1	1	yes	maximal, characteristic
12	#20279097	C₂	1	1	yes	maximal, characteristic, complemented
13	#20278965	C₂	1	1	yes	maximal, characteristic, complemented
14	#20278189	C₂	1	1	yes	maximal, characteristic, complemented
15	#20278176	C₂	1	1	yes	maximal, characteristic
16	#20278014	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277997	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277982	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277971	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277263	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277253	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277242	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277232	C₂	1	1	yes	maximal, characteristic, complemented
24	#20277220	C₂	1	1	yes	maximal, characteristic
25	#20277209	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277155	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277112	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277095	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#13133177	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2572	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133211	C₂²	1	1	yes	characteristic
34	C₂×#13133200	C₂²	1	1	yes	characteristic
35	C₂×#13133199	C₂²	1	1	yes	characteristic
36	C₂×#13133193	C₂²	1	1	yes	characteristic
37	C₂×#13133185	C₂²	1	1	yes	characteristic
38	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
41	C₂×#13133177	C₂²	1	1	yes	characteristic
42	C₂×#13133177	C₂²	1	1	yes	characteristic
43	C₂×#13133177	C₂²	1	1	yes	characteristic
44	C₂×#13133173	C₂²	1	1	yes	characteristic
45	C₂×#13133173	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
48	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
51	C₅₃⋊#401	C₂²	1	1	yes	characteristic, complemented
52	#16810565	C₂²	1	1	yes	characteristic, complemented
53	#16810565	C₂²	1	1	yes	characteristic, complemented
54	#16810565	C₂²	1	1	yes	characteristic, complemented
55	#16810565	C₂²	1	1	yes	characteristic, complemented
56	#16810563	C₂²	1	1	yes	characteristic, complemented
57	#16810563	C₂²	1	1	yes	characteristic, complemented
58	#16810559	C₂²	1	1	yes	characteristic
59	#16810559	C₂²	1	1	yes	characteristic, complemented
60	#16810557	C₂²	1	1	yes	characteristic, complemented
61	#16810557	C₂²	1	1	yes	characteristic, complemented
62	#16810556	C₂²	1	1	yes	characteristic, complemented
63	#16810552	C₂²	1	1	yes	characteristic
64	#16810551	C₂²	1	1	yes	characteristic
65	#16810551	C₂²	1	1	yes	characteristic, complemented
66	#16810550	C₂²	1	1	yes	characteristic
67	#16810550	C₂²	1	1	yes	characteristic
68	#16810549	C₂²	1	1	yes	characteristic
69	#16810548	C₂²	1	1	yes	characteristic
70	#16810548	C₂²	1	1	yes	characteristic, complemented
71	#16810546	C₂²	1	1	yes	characteristic
72	#16810546	C₂²	1	1	yes	characteristic
73	#16810545	C₂²	1	1	yes	characteristic
74	#16810542	C₂²	1	1	yes	characteristic, complemented
75	#16810539	C₂²	1	1	yes	characteristic
76	#16810539	C₂²	1	1	yes	characteristic
77	#16810537	C₂²	1	1	yes	characteristic
78	#16810534	C₂²	1	1	yes	characteristic
79	#16810521	C₂²	1	1	yes	characteristic, complemented
80	#16810517	C₂²	1	1	yes	characteristic
81	#16810517	C₂²	1	1	yes	characteristic
82	#16810516	C₂²	1	1	yes	characteristic
83	#16810512	C₂²	1	1	yes	characteristic
84	#16810512	C₂²	1	1	yes	characteristic
85	#16810512	C₂²	1	1	yes	characteristic
86	#16810512	C₂²	1	1	yes	characteristic
87	#16810512	C₂²	1	1	yes	characteristic
88	#16810511	C₂²	1	1	yes	characteristic
89	#16810511	C₂²	1	1	yes	characteristic
90	#16810511	C₂²	1	1	yes	characteristic, complemented
91	#16810510	C₂²	1	1	yes	characteristic, complemented
92	#16810510	C₂²	1	1	yes	characteristic, complemented
93	#16810510	C₂²	1	1	yes	characteristic, complemented
94	#16810508	C₂²	1	1	yes	characteristic, complemented
95	#16810508	C₂²	1	1	yes	characteristic, complemented
96	#16810507	C₂²	1	1	yes	characteristic, complemented
97	#16810507	C₂²	1	1	yes	characteristic, complemented
98	#16810506	C₂²	1	1	yes	characteristic, complemented
99	#16810505	C₂²	1	1	yes	characteristic, complemented
100	#16810505	C₂²	1	1	yes	characteristic, complemented
101	#16810505	C₂²	1	1	yes	characteristic, complemented
102	#16810505	C₂²	1	1	yes	characteristic, complemented
103	#16810505	C₂²	1	1	yes	characteristic, complemented
104	#16810505	C₂²	1	1	yes	characteristic, complemented
105	#16810504	C₂²	1	1	yes	characteristic, complemented
106	#16810503	C₂²	1	1	yes	characteristic
107	#16810500	C₂²	1	1	yes	characteristic
108	#16810499	C₂²	1	1	yes	characteristic
109	#16810499	C₂²	1	1	yes	characteristic
110	#16810499	C₂²	1	1	yes	characteristic
111	#16810497	C₂²	1	1	yes	characteristic
112	#16810497	C₂²	1	1	yes	characteristic
113	#16810497	C₂²	1	1	yes	characteristic
114	#16810497	C₂²	1	1	yes	characteristic
115	#16810496	C₂²	1	1	yes	characteristic
116	#16810496	C₂²	1	1	yes	characteristic, complemented
117	#16810495	C₂²	1	1	yes	characteristic, complemented
118	#16810495	C₂²	1	1	yes	characteristic, complemented
119	#16810494	C₂²	1	1	yes	characteristic
120	#16810491	C₂²	1	1	yes	characteristic, complemented
121	#16810487	C₂²	1	1	yes	characteristic, complemented
122	#16810487	C₂²	1	1	yes	characteristic, complemented
123	#16810486	C₂²	1	1	yes	characteristic
124	#16810485	C₂²	1	1	yes	characteristic
125	#16810485	C₂²	1	1	yes	characteristic
126	#16810485	C₂²	1	1	yes	characteristic
127	#16810482	C₂²	1	1	yes	characteristic
128	#16810482	C₂²	1	1	yes	characteristic
129	#16810482	C₂²	1	1	yes	characteristic
130	#16810482	C₂²	1	1	yes	characteristic
131	#16810482	C₂²	1	1	yes	characteristic
132	#16810482	C₂²	1	1	yes	characteristic
133	#16810480	C₂²	1	1	yes	characteristic
134	#16810478	C₂²	1	1	yes	characteristic
135	#16810478	C₂²	1	1	yes	characteristic
136	#16810478	C₂²	1	1	yes	characteristic
137	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
138	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
140	#16810474	C₂²	1	1	yes	characteristic, complemented
141	#16810474	C₂²	1	1	yes	characteristic, complemented
142	#16810474	C₂²	1	1	yes	characteristic, complemented
143	#16810474	C₂²	1	1	yes	characteristic, complemented
144	#16810474	C₂²	1	1	yes	characteristic, complemented
145	#16810474	C₂²	1	1	yes	characteristic, complemented
146	#16810474	C₂²	1	1	yes	characteristic, complemented
147	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
148	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
149	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
150	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
152	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
153	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
154	C₄×#11719921	C₂²	1	1	yes	characteristic
155	C₄×#11719921	C₂²	1	1	yes	characteristic
156	C₄×#11719921	C₂²	1	1	yes	characteristic
157	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
158	#16810470	C₂²	1	1	yes	characteristic
159	#16810470	C₂²	1	1	yes	characteristic
160	#16810470	C₂²	1	1	yes	characteristic
161	#16810470	C₂²	1	1	yes	characteristic
162	#16810470	C₂²	1	1	yes	characteristic
163	#16810470	C₂²	1	1	yes	characteristic
164	#16810470	C₂²	1	1	yes	characteristic
165	#16810470	C₂²	1	1	yes	characteristic
166	#16810470	C₂²	1	1	yes	characteristic
167	#16810468	C₂²	1	1	yes	characteristic, complemented
168	#16810468	C₂²	1	1	yes	characteristic, complemented
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#394	C₂²	1	1	yes	characteristic
174	C₅₃×#393	C₂²	1	1	yes	characteristic
175	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#388	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#386	C₂²	1	1	yes	characteristic
180	C₅₃×#386	C₂²	1	1	yes	characteristic
181	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#381	C₂²	1	1	yes	characteristic
184	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
188	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
189	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
190	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₅₃	—	2	4	no	—
194	C₂²×C₄×D₅₃	—	2	4	no	—
195	C₂²×C₄×D₅₃	—	4	2	no	—
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	#13133211	—	2	4	no	—
205	#13133200	—	2	4	no	—
206	#13133199	—	2	4	no	—
207	#13133193	—	2	4	no	—
208	#13133185	—	2	4	no	—
209	Q₈×Dic₅₃	—	4	2	no	—
210	D₄×Dic₅₃	—	2	4	no	—
211	C₄×C₂²⋊D₅₃	—	2	4	no	—
212	#13133177	—	2	4	no	—
213	#13133177	—	2	4	no	—
214	#13133177	—	4	2	no	—
215	#13133173	—	2	4	no	—
216	#13133173	—	4	2	no	—
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×#11719921	C₂³	1	1	yes	characteristic
252	C₂×#11719921	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×#11719921	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×D₅₃	—	2	4	no	—
270	C₂²⋊C₄×D₅₃	—	2	4	no	—
271	C₂×C₄×Dic₅₃	—	4	2	no	—
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
290	C₄²×D₅₃	—	2	4	no	—
291	C₄²×D₅₃	—	4	2	no	—
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
329	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂³×D₅₃	—	2	2	no	—
366	C₂³×D₅₃	—	2	2	no	—
367	C₂³×D₅₃	—	2	2	no	—
368	C₂³×D₅₃	—	2	2	no	—
369	C₂³×D₅₃	—	2	2	no	—
370	C₂³×D₅₃	—	4	1	no	—
371	C₂³×D₅₃	—	4	1	no	—
372	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
373	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×Q₈×C₅₃	—	2	2	no	—
375	C₂×Q₈×C₅₃	—	4	1	no	—
376	C₂×Q₈×C₅₃	—	4	1	no	—
377	C₂×D₄×C₅₃	—	2	2	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	4	1	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	4	1	no	—
385	C₂²×C₄×C₅₃	—	4	1	no	—
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₂²⋊D₅₃	—	2	2	no	—
400	C₂×C₂²⋊D₅₃	—	2	2	no	—
401	C₂×C₂²⋊D₅₃	—	2	2	no	—
402	C₂×C₂²⋊D₅₃	—	2	2	no	—
403	C₂×C₂²⋊D₅₃	—	4	1	no	—
404	C₂×C₂²⋊D₅₃	#41	1	4	yes	—
405	C₂²×Dic₅₃	—	2	2	no	—
406	C₂²×Dic₅₃	—	2	2	no	—
407	C₂²×Dic₅₃	—	2	2	no	—
408	C₂²×Dic₅₃	—	2	2	no	—
409	C₂²×Dic₅₃	—	2	2	no	—
410	C₂²×Dic₅₃	—	2	2	no	—
411	C₂²×Dic₅₃	—	4	1	no	—
412	C₂²×Dic₅₃	—	4	1	no	—
413	C₂²×Dic₅₃	#41	1	4	yes	—
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₄×D₅₃	—	2	2	no	—
429	C₂×C₄×D₅₃	—	2	2	no	—
430	C₂×C₄×D₅₃	—	2	2	no	—
431	C₂×C₄×D₅₃	—	2	2	no	—
432	C₂×C₄×D₅₃	—	2	2	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	2	2	no	—
437	C₂×C₄×D₅₃	—	2	2	no	—
438	C₂×C₄×D₅₃	—	2	2	no	—
439	C₂×C₄×D₅₃	—	2	2	no	—
440	C₂×C₄×D₅₃	—	2	2	no	—
441	C₂×C₄×D₅₃	—	2	2	no	—
442	C₂×C₄×D₅₃	—	2	2	no	—
443	C₂×C₄×D₅₃	—	2	2	no	—
444	C₂×C₄×D₅₃	—	4	16	no	—
445	C₂×C₄×D₅₃	—	4	1	no	—
446	C₂×C₄×D₅₃	—	4	1	no	—
447	C₂×C₄×D₅₃	—	4	1	no	—
448	C₂×C₄×D₅₃	—	4	1	no	—
449	C₂×C₄×D₅₃	—	4	1	no	—
450	C₂×C₄×D₅₃	—	4	1	no	—
451	C₂×C₄×D₅₃	#41	1	4	yes	—
452	C₂×C₄×D₅₃	#41	1	4	yes	—
453	C₄⋊C₄×C₅₃	—	4	1	no	—
454	C₄⋊C₄×C₅₃	—	4	1	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	4	1	no	—
462	C₂²⋊C₄×C₅₃	—	4	1	no	—
463	C₂²⋊C₄×C₅₃	—	4	1	no	—
464	C₂²⋊C₄×C₅₃	—	4	1	no	—
465	C₄²×C₅₃	—	2	2	no	—
466	C₄²×C₅₃	—	2	2	no	—
467	C₄²×C₅₃	—	4	1	no	—
468	C₂²⋊Dic₅₃	—	2	2	no	—
469	C₂²⋊Dic₅₃	—	2	2	no	—
470	C₂²⋊Dic₅₃	—	2	2	no	—
471	C₂²⋊Dic₅₃	—	2	2	no	—
472	C₂²⋊Dic₅₃	—	2	2	no	—
473	C₂²⋊Dic₅₃	—	2	2	no	—
474	C₂²⋊Dic₅₃	—	2	2	no	—
475	C₂²⋊Dic₅₃	—	2	2	no	—
476	C₂²⋊Dic₅₃	—	2	2	no	—
477	C₂²⋊Dic₅₃	—	4	1	no	—
478	#11719921	—	2	2	no	—
479	#11719921	—	2	2	no	—
480	#11719921	—	2	2	no	—
481	#11719921	—	2	2	no	—
482	#11719921	—	2	2	no	—
483	#11719921	—	2	2	no	—
484	#11719921	—	2	2	no	—
485	#11719921	—	2	2	no	—
486	#11719921	—	2	2	no	—
487	#11719921	—	2	2	no	—
488	#11719921	—	2	2	no	—
489	#11719921	—	2	2	no	—
490	#11719921	—	2	2	no	—
491	#11719921	—	2	2	no	—
492	#11719921	—	4	1	no	—
493	#11719921	—	4	1	no	—
494	#11719921	—	4	1	no	—
495	#11719921	#41	1	4	yes	—
496	C₄⋊Dic₅₃	—	2	2	no	—
497	C₄⋊Dic₅₃	—	2	2	no	—
498	C₄⋊Dic₅₃	—	2	2	no	—
499	C₄⋊Dic₅₃	—	4	1	no	—
500	C₄⋊Dic₅₃	—	4	1	no	—
501	C₄⋊Dic₅₃	—	4	1	no	—
502	#11719919	—	2	2	no	—
503	#11719919	—	2	2	no	—
504	#11719919	—	2	2	no	—
505	#11719919	—	2	2	no	—
506	#11719919	—	2	2	no	—
507	#11719919	—	2	2	no	—
508	#11719919	—	2	2	no	—
509	#11719919	—	2	2	no	—
510	#11719919	—	2	2	no	—
511	#11719919	—	2	2	no	—
512	#11719919	—	2	2	no	—
513	#11719919	—	2	2	no	—
514	#11719919	—	2	2	no	—
515	#11719919	—	4	1	no	—
516	#11719919	—	4	1	no	—
517	#11719919	—	4	1	no	—
518	#11719919	—	4	1	no	—
519	#11719919	—	4	1	no	—
520	C₄×Dic₅₃	—	2	2	no	—
521	C₄×Dic₅₃	—	2	2	no	—
522	C₄×Dic₅₃	—	2	2	no	—
523	C₄×Dic₅₃	—	2	2	no	—
524	C₄×Dic₅₃	—	2	2	no	—
525	C₄×Dic₅₃	—	2	2	no	—
526	C₄×Dic₅₃	—	2	2	no	—
527	C₄×Dic₅₃	—	2	2	no	—
528	C₄×Dic₅₃	—	2	2	no	—
529	C₄×Dic₅₃	—	2	2	no	—
530	C₄×Dic₅₃	—	2	2	no	—
531	C₄×Dic₅₃	—	2	2	no	—
532	C₄×Dic₅₃	—	2	2	no	—
533	C₄×Dic₅₃	—	2	2	no	—
534	C₄×Dic₅₃	—	4	1	no	—
535	C₄×Dic₅₃	—	4	1	no	—
536	C₄×Dic₅₃	—	4	1	no	—
537	C₄×Dic₅₃	—	4	1	no	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	1	no	—
547	C₂³×C₅₃	—	2	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	C₂×#41	1	2	yes	—
551	C₂³×C₅₃	C₂×#41	1	2	yes	—
552	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
553	C₂²×D₅₃	—	2	1	no	—
554	C₂²×D₅₃	—	2	1	no	—
555	C₂²×D₅₃	—	2	1	no	—
556	C₂²×D₅₃	—	2	1	no	—
557	C₂²×D₅₃	—	2	8	no	—
558	C₂²×D₅₃	—	2	1	no	—
559	C₂²×D₅₃	—	2	1	no	—
560	C₂²×D₅₃	—	2	1	no	—
561	C₂²×D₅₃	—	2	1	no	—
562	C₂²×D₅₃	—	2	1	no	—
563	C₂²×D₅₃	—	2	1	no	—
564	C₂²×D₅₃	—	4	4	no	—
565	C₂²×D₅₃	—	4	4	no	—
566	C₂²×D₅₃	—	4	4	no	—
567	C₂²×D₅₃	—	4	4	no	—
568	C₂²×D₅₃	—	4	4	no	—
569	C₂²×D₅₃	—	4	4	no	—
570	C₂²×D₅₃	C₂×#41	1	2	yes	—
571	C₂²×D₅₃	C₂×#41	1	2	yes	—
572	C₂²×D₅₃	C₂×#41	1	2	yes	—
573	C₂²×D₅₃	C₂×#41	1	2	yes	—
574	Q₈×C₅₃	—	4	4	no	—
575	D₄×C₅₃	—	4	4	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	4	4	no	—
613	C₂×C₄×C₅₃	—	4	4	no	—
614	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
615	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
616	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
617	C₂²⋊D₅₃	—	2	8	no	—
618	C₂²⋊D₅₃	—	4	4	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	8	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	2	1	no	—
654	C₂×Dic₅₃	—	2	1	no	—
655	C₂×Dic₅₃	—	4	4	no	—
656	C₂×Dic₅₃	—	4	4	no	—
657	C₂×Dic₅₃	C₂×#41	1	2	yes	—
658	C₂×Dic₅₃	C₂×#41	1	2	yes	—
659	C₂×Dic₅₃	C₂×#41	1	2	yes	—
660	C₂×Dic₅₃	C₂×#41	1	2	yes	—
661	C₂×Dic₅₃	C₂×#41	1	2	yes	—
662	C₂×Dic₅₃	C₂×#41	1	2	yes	—
663	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
664	C₄×D₅₃	—	2	8	no	—
665	C₄×D₅₃	—	4	4	no	—
666	C₄×D₅₃	—	4	4	no	—
667	C₄×D₅₃	—	4	4	no	—
668	C₄×D₅₃	—	4	4	no	—
669	C₄×D₅₃	—	4	4	no	—
670	C₄×D₅₃	—	4	4	no	—
671	C₄×D₅₃	—	4	4	no	—
672	#34849	—	53	1	no	maximal, Sylow
673	C₂²×C₅₃	—	2	2	no	—
674	C₂²×C₅₃	—	2	2	no	—
675	C₂²×C₅₃	—	2	2	no	—
676	C₂²×C₅₃	—	2	2	no	—
677	C₂²×C₅₃	—	2	2	no	—
678	C₂²×C₅₃	—	2	2	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	4	1	no	—
682	C₂²×C₅₃	—	4	1	no	—
683	C₂²×C₅₃	—	4	1	no	—
684	C₂²×C₅₃	—	4	1	no	—
685	C₂²×C₅₃	—	4	1	no	—
686	C₂²×C₅₃	—	4	1	no	—
687	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
688	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
689	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
690	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
691	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
692	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
693	C₂²×C₅₃	#585	1	1	yes	characteristic
694	C₂×D₅₃	—	2	2	no	—
695	C₂×D₅₃	—	2	2	no	—
696	C₂×D₅₃	—	2	2	no	—
697	C₂×D₅₃	—	2	2	no	—
698	C₂×D₅₃	—	2	2	no	—
699	C₂×D₅₃	—	2	2	no	—
700	C₂×D₅₃	—	2	2	no	—
701	C₂×D₅₃	—	2	2	no	—
702	C₂×D₅₃	—	2	2	no	—
703	C₂×D₅₃	—	4	16	no	—
704	C₂×D₅₃	—	4	1	no	—
705	C₂×D₅₃	—	4	1	no	—
706	C₂×D₅₃	—	4	1	no	—
707	C₂×D₅₃	—	4	1	no	—
708	C₂×D₅₃	#529	1	4	yes	—
709	C₄×C₅₃	—	2	2	no	—
710	C₄×C₅₃	—	2	2	no	—
711	C₄×C₅₃	—	2	2	no	—
712	C₄×C₅₃	—	4	1	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	1	no	—
718	C₄×C₅₃	—	4	1	no	—
719	C₄×C₅₃	—	4	1	no	—
720	C₄×C₅₃	—	4	1	no	—
721	C₄×C₅₃	—	4	1	no	—
722	Dic₅₃	—	2	2	no	—
723	Dic₅₃	—	2	2	no	—
724	Dic₅₃	—	2	2	no	—
725	Dic₅₃	—	2	2	no	—
726	Dic₅₃	—	4	1	no	—
727	Dic₅₃	—	4	1	no	—
728	Dic₅₃	—	4	1	no	—
729	Dic₅₃	—	4	1	no	—
730	Dic₅₃	—	4	1	no	—
731	Dic₅₃	—	4	1	no	—
732	Dic₅₃	—	4	1	no	—
733	Dic₅₃	—	4	1	no	—
734	Dic₅₃	—	4	1	no	—
735	Dic₅₃	#551	1	4	yes	—
736	#2578	—	53	1	no	—
737	#2577	—	53	1	no	—
738	#2576	—	53	1	no	—
739	#2575	—	53	1	no	—
740	#2574	—	53	1	no	—
741	#2573	—	53	1	no	—
742	#2572	D₅₃	1	1	yes	characteristic, complemented
743	#2569	—	53	1	no	—
744	#2564	—	53	1	no	—
745	#2561	—	53	1	no	—
746	#2553	—	53	1	no	—
747	#2534	—	53	1	no	—
748	#2493	—	53	1	no	—
749	#2480	—	53	1	no	—
750	#2419	—	53	1	no	—
751	#2418	—	53	1	no	—
752	#2401	—	53	1	no	—
753	#2398	—	53	1	no	—
754	#2396	—	53	1	no	—
755	#2395	—	53	1	no	—
756	C₄×#126	—	53	1	no	—
757	C₄×C₂²⋊Q₈	—	53	1	no	—
758	C₄×#123	—	53	1	no	—
759	C₄×#123	—	53	1	no	—
760	C₄×#120	—	53	1	no	—
761	#2298	—	53	1	no	—
762	#2290	—	53	1	no	—
763	#2283	—	53	1	no	—
764	#2280	—	53	1	no	—
765	C₄²×D₄	—	53	1	no	—
766	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
767	C₂×C₅₃	—	4	2	no	—
768	C₂×C₅₃	—	4	2	no	—
769	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
770	C₂×C₅₃	#3444	1	1	yes	characteristic
771	C₂×C₅₃	#3459	1	1	yes	characteristic
772	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
773	C₂×C₅₃	#3475	1	1	yes	characteristic
774	C₂×C₅₃	#3475	1	1	yes	characteristic
775	C₂×C₅₃	#3481	1	1	yes	characteristic
776	D₅₃	—	2	4	no	—
777	D₅₃	—	4	2	no	—
778	C₂⁴×C₄	—	53	1	no	—
779	C₂×#126	—	53	1	no	—
780	C₂×#123	—	53	1	no	—
781	C₂×#123	—	53	1	no	—
782	C₂×C₂²⋊Q₈	—	53	1	no	—
783	C₂×#120	—	53	1	no	—
784	C₂×C₄×Q₈	—	53	1	no	—
785	C₂×C₄×D₄	—	53	1	no	—
786	C₂×C₄×D₄	—	53	1	no	—
787	C₂×C₄×D₄	—	53	1	no	—
788	C₂×C₄×D₄	—	53	1	no	—
789	C₂×C₄×D₄	—	53	1	no	—
790	C₂×#117	—	53	1	no	—
791	C₂×#117	—	53	1	no	—
792	C₂²×C₂²⋊C₄	—	53	1	no	—
793	C₂²×C₂²⋊C₄	—	53	1	no	—
794	C₂²×C₄²	—	53	1	no	—
795	C₂²×C₄²	—	53	1	no	—
796	C₂²×C₄²	—	53	1	no	—
797	#401	—	53	1	no	—
798	#400	—	53	1	no	—
799	#400	—	53	1	no	—
800	#400	—	53	1	no	—
801	#400	—	53	1	no	—
802	#400	—	53	1	no	—
803	#400	—	53	1	no	—
804	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
805	#399	—	53	1	no	—
806	#399	—	53	1	no	—
807	#398	—	53	1	no	—
808	#398	—	53	1	no	—
809	#398	—	53	1	no	—
810	#397	—	53	1	no	—
811	#397	—	53	1	no	—
812	#397	—	53	1	no	—
813	#397	—	53	1	no	—
814	#397	—	53	1	no	—
815	#397	—	53	1	no	—
816	#397	—	53	1	no	—
817	#397	—	53	1	no	—
818	#396	—	53	1	no	—
819	#396	—	53	1	no	—
820	#396	—	53	1	no	—
821	#395	—	53	1	no	—
822	#394	—	53	1	no	—
823	#394	—	53	1	no	—
824	#394	—	53	1	no	—
825	#394	C₂×D₅₃	1	1	yes	characteristic
826	#393	—	53	1	no	—
827	#393	C₂×D₅₃	1	1	yes	characteristic
828	#393	C₂×D₅₃	1	1	yes	characteristic, complemented
829	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
830	#389	—	53	1	no	—
831	#388	—	53	1	no	—
832	#388	—	53	1	no	—
833	#388	—	53	1	no	—
834	#388	—	53	1	no	—
835	#388	—	53	1	no	—
836	#388	—	53	1	no	—
837	#388	—	53	1	no	—
838	#388	—	53	1	no	—
839	#388	—	53	1	no	—
840	#388	—	53	1	no	—
841	#388	—	53	1	no	—
842	#388	C₂×D₅₃	1	1	yes	characteristic
843	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
844	#387	—	53	1	no	—
845	#387	—	53	1	no	—
846	#387	—	53	1	no	—
847	#387	—	53	1	no	—
848	#387	—	53	1	no	—
849	#387	—	53	1	no	—
850	#387	—	53	1	no	—
851	#387	—	53	1	no	—
852	#387	—	53	1	no	—
853	#387	—	53	1	no	—
854	#387	—	53	1	no	—
855	#387	—	53	1	no	—
856	#387	—	53	1	no	—
857	#387	—	53	1	no	—
858	#387	—	53	1	no	—
859	#386	—	53	1	no	—
860	#386	—	53	1	no	—
861	#386	—	53	1	no	—
862	#386	—	53	1	no	—
863	#386	—	53	1	no	—
864	#386	C₂×D₅₃	1	1	yes	characteristic
865	#386	C₂×D₅₃	1	1	yes	characteristic
866	#385	—	53	1	no	—
867	#385	—	53	1	no	—
868	#385	—	53	1	no	—
869	#385	—	53	1	no	—
870	#385	—	53	1	no	—
871	#385	—	53	1	no	—
872	#385	—	53	1	no	—
873	#385	—	53	1	no	—
874	#385	—	53	1	no	—
875	#383	—	53	1	no	—
876	#383	C₂×D₅₃	1	1	yes	characteristic, complemented
877	#383	C₂×D₅₃	1	1	yes	characteristic, complemented
878	#382	—	53	1	no	—
879	#382	—	53	1	no	—
880	#381	—	53	1	no	—
881	#381	—	53	1	no	—
882	#381	—	53	1	no	—
883	#381	—	53	1	no	—
884	#381	C₂×D₅₃	1	1	yes	characteristic
885	#381	C₂×D₅₃	1	1	yes	characteristic, complemented
886	#380	—	53	1	no	—
887	#380	—	53	1	no	—
888	#380	—	53	1	no	—
889	#380	—	53	1	no	—
890	#380	—	53	1	no	—
891	#380	—	53	1	no	—
892	#380	—	53	1	no	—
893	#379	—	53	1	no	—
894	#379	—	53	1	no	—
895	#379	—	53	1	no	—
896	C₄×C₄⋊C₄	—	53	1	no	—
897	C₄×C₄⋊C₄	—	53	1	no	—
898	C₄×C₄⋊C₄	—	53	1	no	—
899	C₄×C₄⋊C₄	—	53	1	no	—
900	C₄×C₄⋊C₄	—	53	1	no	—
901	C₄×C₄⋊C₄	—	53	1	no	—
902	C₄×C₄⋊C₄	—	53	1	no	—
903	C₄×C₄⋊C₄	—	53	1	no	—
904	C₄×C₄⋊C₄	—	53	1	no	—
905	C₄×C₄⋊C₄	—	53	1	no	—
906	C₄×C₂²⋊C₄	—	53	1	no	—
907	C₄×C₂²⋊C₄	—	53	1	no	—
908	C₄×C₂²⋊C₄	—	53	1	no	—
909	C₄×C₂²⋊C₄	—	53	1	no	—
910	C₄×C₂²⋊C₄	—	53	1	no	—
911	C₄×C₂²⋊C₄	—	53	1	no	—
912	C₄×C₂²⋊C₄	—	53	1	no	—
913	C₄×C₂²⋊C₄	—	53	1	no	—
914	C₄×C₂²⋊C₄	—	53	1	no	—
915	C₄×C₂²⋊C₄	—	53	1	no	—
916	C₄×C₂²⋊C₄	—	53	1	no	—
917	C₄×C₂²⋊C₄	—	53	1	no	—
918	C₄×C₂²⋊C₄	—	53	1	no	—
919	C₄×C₂²⋊C₄	—	53	1	no	—
920	C₄×C₂²⋊C₄	—	53	1	no	—
921	C₄×C₂²⋊C₄	—	53	1	no	—
922	C₄×C₂²⋊C₄	—	53	1	no	—
923	C₄×C₂²⋊C₄	—	53	1	no	—
924	C₄×C₂²⋊C₄	—	53	1	no	—
925	C₄×C₂²⋊C₄	—	53	1	no	—
926	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
927	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
928	#376	—	53	1	no	—
929	#376	—	53	1	no	—
930	C₂×#95	—	53	1	no	—
931	C₂×#95	—	53	1	no	—
932	C₄³	—	53	1	no	—
933	C₅₃	#34849	1	1	yes	characteristic, complemented, Sylow
934	C₂⁵	—	53	1	no	—
935	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
936	C₂²×D₄	—	53	1	no	—
937	C₂²×D₄	—	53	1	no	—
938	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
939	C₂³×C₄	—	53	1	no	—
940	C₂³×C₄	—	53	1	no	—
941	C₂³×C₄	—	53	1	no	—
942	C₂³×C₄	—	53	1	no	—
943	C₂³×C₄	—	53	1	no	—
944	C₂³×C₄	—	53	1	no	—
945	C₂³×C₄	—	53	1	no	—
946	C₂³×C₄	—	53	1	no	—
947	C₂³×C₄	—	53	1	no	—
948	C₂³×C₄	—	53	1	no	—
949	C₂³×C₄	—	53	1	no	—
950	C₂³×C₄	—	106	4	no	—
951	C₂³×C₄	—	106	4	no	—
952	C₂³×C₄	—	212	2	no	—
953	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
954	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
955	#126	—	106	4	no	—
956	#123	—	106	4	no	—
957	#123	—	106	4	no	—
958	C₂²⋊Q₈	—	106	4	no	—
959	#120	—	106	4	no	—
960	C₄×Q₈	—	212	2	no	—
961	C₄×D₄	—	106	4	no	—
962	C₄×D₄	—	106	4	no	—
963	C₄×D₄	—	106	4	no	—
964	C₄×D₄	—	106	4	no	—
965	C₄×D₄	—	212	2	no	—
966	#117	—	106	4	no	—
967	#117	—	212	2	no	—
968	C₂×C₄⋊C₄	—	53	1	no	—
969	C₂×C₄⋊C₄	—	53	1	no	—
970	C₂×C₄⋊C₄	—	53	1	no	—
971	C₂×C₄⋊C₄	—	53	1	no	—
972	C₂×C₄⋊C₄	—	53	1	no	—
973	C₂×C₄⋊C₄	—	53	1	no	—
974	C₂×C₄⋊C₄	—	53	1	no	—
975	C₂×C₄⋊C₄	—	53	1	no	—
976	C₂×C₄⋊C₄	—	53	1	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	1	no	—
984	C₂×C₄⋊C₄	—	53	1	no	—
985	C₂×C₄⋊C₄	—	53	1	no	—
986	C₂×C₄⋊C₄	—	53	1	no	—
987	C₂×C₄⋊C₄	—	53	1	no	—
988	C₂×C₄⋊C₄	—	53	1	no	—
989	C₂×C₄⋊C₄	—	53	1	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	—	53	1	no	—
992	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	—	53	1	no	—
995	C₂×C₂²⋊C₄	—	53	1	no	—
996	C₂×C₂²⋊C₄	—	53	1	no	—
997	C₂×C₂²⋊C₄	—	53	1	no	—
998	C₂×C₂²⋊C₄	—	53	1	no	—
999	C₂×C₂²⋊C₄	—	53	1	no	—
1000	C₂×C₂²⋊C₄	—	53	1	no	—
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	1	no	—
1004	C₂×C₂²⋊C₄	—	53	1	no	—
1005	C₂×C₂²⋊C₄	—	53	1	no	—
1006	C₂×C₂²⋊C₄	—	53	1	no	—
1007	C₂×C₂²⋊C₄	—	53	1	no	—
1008	C₂×C₂²⋊C₄	—	53	1	no	—
1009	C₂×C₂²⋊C₄	—	53	1	no	—
1010	C₂×C₂²⋊C₄	—	53	1	no	—
1011	C₂×C₂²⋊C₄	—	53	1	no	—
1012	C₂×C₂²⋊C₄	—	53	1	no	—
1013	C₂×C₂²⋊C₄	—	53	1	no	—
1014	C₂×C₂²⋊C₄	—	53	1	no	—
1015	C₂×C₂²⋊C₄	—	53	1	no	—
1016	C₂×C₂²⋊C₄	—	53	1	no	—
1017	C₂×C₂²⋊C₄	—	53	1	no	—
1018	C₂×C₂²⋊C₄	—	53	1	no	—
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	106	4	no	—
1023	C₂×C₂²⋊C₄	—	106	4	no	—
1024	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₄²	—	53	1	no	—
1035	C₂×C₄²	—	53	1	no	—
1036	C₂×C₄²	—	53	1	no	—
1037	C₂×C₄²	—	53	1	no	—
1038	C₂×C₄²	—	53	1	no	—
1039	C₂×C₄²	—	53	1	no	—
1040	C₂×C₄²	—	53	1	no	—
1041	C₂×C₄²	—	53	1	no	—
1042	C₂×C₄²	—	53	1	no	—
1043	C₂×C₄²	—	53	1	no	—
1044	C₂×C₄²	—	53	1	no	—
1045	C₂×C₄²	—	53	1	no	—
1046	C₂×C₄²	—	53	1	no	—
1047	C₂×C₄²	—	53	1	no	—
1048	C₂×C₄²	—	53	1	no	—
1049	C₂×C₄²	—	53	1	no	—
1050	C₂×C₄²	—	53	1	no	—
1051	C₂×C₄²	—	53	1	no	—
1052	C₂×C₄²	—	106	4	no	—
1053	C₂×C₄²	—	212	2	no	—
1054	C₂×C₄²	—	212	2	no	—
1055	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1056	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1057	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	—	53	1	no	—
1072	#95	—	53	1	no	—
1073	#95	—	53	1	no	—
1074	#95	—	53	1	no	—
1075	#95	—	53	1	no	—
1076	#95	—	53	1	no	—
1077	#95	—	53	1	no	—
1078	#95	—	53	1	no	—
1079	#95	—	53	1	no	—
1080	#95	—	53	1	no	—
1081	#95	—	53	1	no	—
1082	#95	—	53	1	no	—
1083	#95	—	53	1	no	—
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	C₂²×D₅₃	1	1	yes	characteristic
1095	#95	C₂²×D₅₃	1	1	yes	characteristic
1096	#95	C₂²×D₅₃	1	1	yes	characteristic
1097	#95	C₂²×D₅₃	1	1	yes	characteristic
1098	#95	C₂²×D₅₃	1	1	yes	characteristic
1099	#95	C₂²×D₅₃	1	1	yes	characteristic
1100	#95	C₂²×D₅₃	1	1	yes	characteristic
1101	#95	C₂²×D₅₃	1	1	yes	characteristic
1102	#95	C₂²×D₅₃	1	1	yes	characteristic
1103	#95	C₂²×D₅₃	1	1	yes	characteristic
1104	#95	C₂²×D₅₃	1	1	yes	characteristic
1105	#95	C₂²×D₅₃	1	1	yes	characteristic
1106	#95	C₂²×D₅₃	1	1	yes	characteristic
1107	#95	C₂²×D₅₃	1	1	yes	characteristic
1108	#95	C₂²×D₅₃	1	1	yes	characteristic
1109	#95	C₂²×D₅₃	1	1	yes	characteristic
1110	C₂⁴	—	53	1	no	—
1111	C₂⁴	—	53	1	no	—
1112	C₂⁴	—	106	2	no	—
1113	C₂⁴	—	106	2	no	—
1114	C₂⁴	—	106	2	no	—
1115	C₂⁴	—	106	2	no	—
1116	C₂⁴	—	106	2	no	—
1117	C₂⁴	—	212	1	no	—
1118	C₂⁴	—	212	1	no	—
1119	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1120	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1121	C₂×Q₈	—	2	2	no	—
1122	C₂×Q₈	—	4	1	no	—
1123	C₂×Q₈	—	4	1	no	—
1124	C₂×D₄	—	2	2	no	—
1125	C₂×D₄	—	2	2	no	—
1126	C₂×D₄	—	4	1	no	—
1127	C₂×D₄	—	53	4	no	—
1128	C₂×D₄	—	106	2	no	—
1129	C₂×D₄	—	106	2	no	—
1130	C₂×D₄	—	106	2	no	—
1131	C₂×D₄	—	106	2	no	—
1132	C₂×D₄	—	212	1	no	—
1133	C₂²×C₄	—	2	2	no	—
1134	C₂²×C₄	—	2	2	no	—
1135	C₂²×C₄	—	2	2	no	—
1136	C₂²×C₄	—	2	2	no	—
1137	C₂²×C₄	—	4	1	no	—
1138	C₂²×C₄	—	4	1	no	—
1139	C₂²×C₄	—	53	1	no	—
1140	C₂²×C₄	—	53	4	no	—
1141	C₂²×C₄	—	53	1	no	—
1142	C₂²×C₄	—	53	1	no	—
1143	C₂²×C₄	—	53	1	no	—
1144	C₂²×C₄	—	53	1	no	—
1145	C₂²×C₄	—	53	4	no	—
1146	C₂²×C₄	—	53	4	no	—
1147	C₂²×C₄	—	53	1	no	—
1148	C₂²×C₄	—	53	1	no	—
1149	C₂²×C₄	—	53	1	no	—
1150	C₂²×C₄	—	53	1	no	—
1151	C₂²×C₄	—	53	1	no	—
1152	C₂²×C₄	—	53	1	no	—
1153	C₂²×C₄	—	53	1	no	—
1154	C₂²×C₄	—	53	1	no	—
1155	C₂²×C₄	—	53	1	no	—
1156	C₂²×C₄	—	106	2	no	—
1157	C₂²×C₄	—	106	2	no	—
1158	C₂²×C₄	—	106	2	no	—
1159	C₂²×C₄	—	106	2	no	—
1160	C₂²×C₄	—	106	2	no	—
1161	C₂²×C₄	—	106	2	no	—
1162	C₂²×C₄	—	106	2	no	—
1163	C₂²×C₄	—	106	2	no	—
1164	C₂²×C₄	—	106	2	no	—
1165	C₂²×C₄	—	106	2	no	—
1166	C₂²×C₄	—	106	2	no	—
1167	C₂²×C₄	—	106	2	no	—
1168	C₂²×C₄	—	106	2	no	—
1169	C₂²×C₄	—	106	2	no	—
1170	C₂²×C₄	—	106	2	no	—
1171	C₂²×C₄	—	106	2	no	—
1172	C₂²×C₄	—	106	2	no	—
1173	C₂²×C₄	—	106	2	no	—
1174	C₂²×C₄	—	106	2	no	—
1175	C₂²×C₄	—	106	2	no	—
1176	C₂²×C₄	—	106	2	no	—
1177	C₂²×C₄	—	106	2	no	—
1178	C₂²×C₄	—	212	1	no	—
1179	C₂²×C₄	—	212	1	no	—
1180	C₂²×C₄	—	212	1	no	—
1181	C₂²×C₄	—	212	1	no	—
1182	C₂²×C₄	—	212	1	no	—
1183	C₂²×C₄	—	212	1	no	—
1184	C₂²×C₄	—	212	16	no	—
1185	C₂²×C₄	—	212	1	no	—
1186	C₂²×C₄	—	212	1	no	—
1187	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1188	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1189	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1191	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1192	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1193	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1195	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1196	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1200	C₄⋊C₄	—	4	1	no	—
1201	C₄⋊C₄	—	4	1	no	—
1202	C₄⋊C₄	—	106	2	no	—
1203	C₄⋊C₄	—	106	2	no	—
1204	C₄⋊C₄	—	106	2	no	—
1205	C₄⋊C₄	—	106	2	no	—
1206	C₄⋊C₄	—	106	2	no	—
1207	C₄⋊C₄	—	106	2	no	—
1208	C₄⋊C₄	—	106	2	no	—
1209	C₄⋊C₄	—	106	2	no	—
1210	C₄⋊C₄	—	106	2	no	—
1211	C₄⋊C₄	—	106	2	no	—
1212	C₄⋊C₄	—	106	2	no	—
1213	C₄⋊C₄	—	106	2	no	—
1214	C₄⋊C₄	—	106	2	no	—
1215	C₄⋊C₄	—	106	2	no	—
1216	C₄⋊C₄	—	106	2	no	—
1217	C₄⋊C₄	—	106	2	no	—
1218	C₄⋊C₄	—	212	1	no	—
1219	C₄⋊C₄	—	212	1	no	—
1220	C₄⋊C₄	—	212	1	no	—
1221	C₄⋊C₄	—	212	1	no	—
1222	C₄⋊C₄	—	212	1	no	—
1223	C₄⋊C₄	—	212	1	no	—
1224	C₄⋊C₄	—	212	1	no	—
1225	C₄⋊C₄	—	212	1	no	—
1226	C₂²⋊C₄	—	2	2	no	—
1227	C₂²⋊C₄	—	2	2	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	2	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₂²⋊C₄	—	4	1	no	—
1235	C₂²⋊C₄	—	4	1	no	—
1236	C₂²⋊C₄	—	53	4	no	—
1237	C₂²⋊C₄	—	106	2	no	—
1238	C₂²⋊C₄	—	106	2	no	—
1239	C₂²⋊C₄	—	106	2	no	—
1240	C₂²⋊C₄	—	106	2	no	—
1241	C₂²⋊C₄	—	106	2	no	—
1242	C₂²⋊C₄	—	106	2	no	—
1243	C₂²⋊C₄	—	106	2	no	—
1244	C₂²⋊C₄	—	106	2	no	—
1245	C₂²⋊C₄	—	106	2	no	—
1246	C₂²⋊C₄	—	106	2	no	—
1247	C₂²⋊C₄	—	106	2	no	—
1248	C₂²⋊C₄	—	106	2	no	—
1249	C₂²⋊C₄	—	106	2	no	—
1250	C₂²⋊C₄	—	106	2	no	—
1251	C₂²⋊C₄	—	106	2	no	—
1252	C₂²⋊C₄	—	106	2	no	—
1253	C₂²⋊C₄	—	106	2	no	—
1254	C₂²⋊C₄	—	106	2	no	—
1255	C₂²⋊C₄	—	106	2	no	—
1256	C₂²⋊C₄	—	106	2	no	—
1257	C₂²⋊C₄	—	106	2	no	—
1258	C₂²⋊C₄	—	106	2	no	—
1259	C₂²⋊C₄	—	106	2	no	—
1260	C₂²⋊C₄	—	212	1	no	—
1261	C₂²⋊C₄	—	212	1	no	—
1262	C₂²⋊C₄	—	212	1	no	—
1263	C₂²⋊C₄	—	212	1	no	—
1264	C₄²	—	2	2	no	—
1265	C₄²	—	2	2	no	—
1266	C₄²	—	4	1	no	—
1267	C₄²	—	106	2	no	—
1268	C₄²	—	106	2	no	—
1269	C₄²	—	106	2	no	—
1270	C₄²	—	106	2	no	—
1271	C₄²	—	106	2	no	—
1272	C₄²	—	106	2	no	—
1273	C₄²	—	106	2	no	—
1274	C₄²	—	106	2	no	—
1275	C₄²	—	106	2	no	—
1276	C₄²	—	106	2	no	—
1277	C₄²	—	106	2	no	—
1278	C₄²	—	106	2	no	—
1279	C₄²	—	106	2	no	—
1280	C₄²	—	106	2	no	—
1281	C₄²	—	212	1	no	—
1282	C₄²	—	212	1	no	—
1283	C₄²	—	212	1	no	—
1284	C₄²	—	212	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	53	2	no	—
1298	C₂³	—	53	2	no	—
1299	C₂³	—	53	2	no	—
1300	C₂³	—	53	2	no	—
1301	C₂³	—	106	8	no	—
1302	C₂³	—	106	1	no	—
1303	C₂³	—	106	1	no	—
1304	C₂³	—	106	1	no	—
1305	C₂³	—	106	1	no	—
1306	C₂³	—	106	1	no	—
1307	C₂³	—	106	1	no	—
1308	C₂³	—	106	1	no	—
1309	C₂³	—	106	1	no	—
1310	C₂³	—	106	1	no	—
1311	C₂³	—	106	1	no	—
1312	C₂³	—	212	4	no	—
1313	C₂³	—	212	4	no	—
1314	C₂³	—	212	4	no	—
1315	C₂³	—	212	4	no	—
1316	C₂³	—	212	4	no	—
1317	C₂³	—	212	4	no	—
1318	C₂³	#41×D₅₃	1	2	yes	—
1319	C₂³	#41×D₅₃	1	2	yes	—
1320	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1321	Q₈	—	4	4	no	—
1322	D₄	—	4	4	no	—
1323	D₄	—	106	8	no	—
1324	D₄	—	212	4	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	4	4	no	—
1362	C₂×C₄	—	4	4	no	—
1363	C₂×C₄	—	53	2	no	—
1364	C₂×C₄	—	53	2	no	—
1365	C₂×C₄	—	53	2	no	—
1366	C₂×C₄	—	53	2	no	—
1367	C₂×C₄	—	53	2	no	—
1368	C₂×C₄	—	53	2	no	—
1369	C₂×C₄	—	53	2	no	—
1370	C₂×C₄	—	106	8	no	—
1371	C₂×C₄	—	106	8	no	—
1372	C₂×C₄	—	106	1	no	—
1373	C₂×C₄	—	106	1	no	—
1374	C₂×C₄	—	106	1	no	—
1375	C₂×C₄	—	106	1	no	—
1376	C₂×C₄	—	106	1	no	—
1377	C₂×C₄	—	106	1	no	—
1378	C₂×C₄	—	106	1	no	—
1379	C₂×C₄	—	106	1	no	—
1380	C₂×C₄	—	106	1	no	—
1381	C₂×C₄	—	106	1	no	—
1382	C₂×C₄	—	106	1	no	—
1383	C₂×C₄	—	106	1	no	—
1384	C₂×C₄	—	106	1	no	—
1385	C₂×C₄	—	106	1	no	—
1386	C₂×C₄	—	106	1	no	—
1387	C₂×C₄	—	106	1	no	—
1388	C₂×C₄	—	106	1	no	—
1389	C₂×C₄	—	106	1	no	—
1390	C₂×C₄	—	106	1	no	—
1391	C₂×C₄	—	106	1	no	—
1392	C₂×C₄	—	106	1	no	—
1393	C₂×C₄	—	106	1	no	—
1394	C₂×C₄	—	106	1	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	106	1	no	—
1397	C₂×C₄	—	106	1	no	—
1398	C₂×C₄	—	106	1	no	—
1399	C₂×C₄	—	106	1	no	—
1400	C₂×C₄	—	106	1	no	—
1401	C₂×C₄	—	106	1	no	—
1402	C₂×C₄	—	106	1	no	—
1403	C₂×C₄	—	106	1	no	—
1404	C₂×C₄	—	106	1	no	—
1405	C₂×C₄	—	106	1	no	—
1406	C₂×C₄	—	106	1	no	—
1407	C₂×C₄	—	212	4	no	—
1408	C₂×C₄	—	212	4	no	—
1409	C₂×C₄	—	212	4	no	—
1410	C₂×C₄	—	212	4	no	—
1411	C₂×C₄	—	212	4	no	—
1412	C₂×C₄	—	212	4	no	—
1413	C₂×C₄	—	212	4	no	—
1414	C₂×C₄	—	212	4	no	—
1415	C₂×C₄	—	212	4	no	—
1416	C₂×C₄	#41×D₅₃	1	2	yes	—
1417	C₂×C₄	#41×D₅₃	1	2	yes	—
1418	C₂×C₄	#41×D₅₃	1	2	yes	—
1419	C₂²	—	2	2	no	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	2	2	no	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	2	2	no	—
1425	C₂²	—	4	1	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	4	1	no	—
1428	C₂²	—	4	1	no	—
1429	C₂²	—	4	1	no	—
1430	C₂²	—	4	1	no	—
1431	C₂²	—	4	1	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	53	4	no	—
1434	C₂²	—	106	2	no	—
1435	C₂²	—	106	2	no	—
1436	C₂²	—	106	2	no	—
1437	C₂²	—	106	2	no	—
1438	C₂²	—	106	2	no	—
1439	C₂²	—	106	2	no	—
1440	C₂²	—	106	2	no	—
1441	C₂²	—	106	2	no	—
1442	C₂²	—	106	2	no	—
1443	C₂²	—	212	16	no	—
1444	C₂²	—	212	1	no	—
1445	C₂²	—	212	1	no	—
1446	C₂²	—	212	1	no	—
1447	C₂²	—	212	1	no	—
1448	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1449	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1450	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1451	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1452	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1453	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1454	C₂²	#16811458	1	1	yes	characteristic
1455	C₄	—	2	2	no	—
1456	C₄	—	2	2	no	—
1457	C₄	—	2	2	no	—
1458	C₄	—	4	1	no	—
1459	C₄	—	4	1	no	—
1460	C₄	—	4	1	no	—
1461	C₄	—	4	1	no	—
1462	C₄	—	4	1	no	—
1463	C₄	—	4	1	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	4	1	no	—
1468	C₄	—	53	4	no	—
1469	C₄	—	106	2	no	—
1470	C₄	—	106	2	no	—
1471	C₄	—	106	2	no	—
1472	C₄	—	106	2	no	—
1473	C₄	—	212	1	no	—
1474	C₄	—	212	1	no	—
1475	C₄	—	212	1	no	—
1476	C₄	—	212	1	no	—
1477	C₄	—	212	1	no	—
1478	C₄	—	212	1	no	—
1479	C₄	—	212	1	no	—
1480	C₄	—	212	1	no	—
1481	C₄	—	212	1	no	—
1482	C₂	—	4	2	no	—
1483	C₂	—	4	2	no	—
1484	C₂	—	106	4	no	—
1485	C₂	—	212	2	no	—
1486	C₂	#529×D₅₃	1	1	yes	characteristic
1487	C₂	#20288009	1	1	yes	characteristic
1488	C₂	#20288126	1	1	yes	characteristic
1489	C₂	#551×D₅₃	1	1	yes	characteristic
1490	C₂	#20288270	1	1	yes	characteristic
1491	C₂	#20288272	1	1	yes	characteristic
1492	C₂	#20288318	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2572	C₂
prime radical	C₂×#13133185	C₂²
hypercenter	#2572	D₅₃
hypocenter	C₅₃	#34849
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2572

Complements

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

N	H ≅ G/N	type
1. #20280055	C₂	semidirect
2. #20280032	C₂	semidirect
3. #20280023	C₂	semidirect
4. #20280000	C₂	semidirect
5. #20279991	C₂	semidirect
6. #20279974	C₂	semidirect
7. #20279935	C₂	semidirect
8. #20279892	C₂	semidirect
9. #20279869	C₂	semidirect
10. #20279760	C₂	semidirect
12. #20279097	C₂	semidirect
13. #20278965	C₂	semidirect
14. #20278189	C₂	semidirect
16. #20278014	C₂	semidirect
17. #20277997	C₂	semidirect
18. #20277982	C₂	semidirect
19. #20277971	C₂	semidirect
20. #20277263	C₂	semidirect
21. #20277253	C₂	semidirect
22. #20277242	C₂	semidirect
23. #20277232	C₂	semidirect
25. #20277209	C₂	semidirect
26. #20277155	C₂	semidirect
27. #20277112	C₂	semidirect
28. #20277095	C₂	semidirect
29. C₄×#13133177	C₂	semidirect
30. C₄×C₂²⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2572	C₂	semidirect
38. C₂×Q₈×Dic₅₃	C₂²	semidirect
48. C₂²×C₄×Dic₅₃	C₂²	semidirect
51. C₅₃⋊#401	C₂²	semidirect
52. #16810565	C₂²	semidirect
53. #16810565	C₂²	semidirect
54. #16810565	C₂²	semidirect
55. #16810565	C₂²	semidirect
56. #16810563	C₂²	semidirect
57. #16810563	C₂²	semidirect
59. #16810559	C₂²	semidirect
60. #16810557	C₂²	semidirect
61. #16810557	C₂²	semidirect
62. #16810556	C₂²	semidirect
65. #16810551	C₂²	semidirect
70. #16810548	C₂²	semidirect
74. #16810542	C₂²	semidirect
79. #16810521	C₂²	semidirect
90. #16810511	C₂²	semidirect
91. #16810510	C₂²	semidirect
92. #16810510	C₂²	semidirect
93. #16810510	C₂²	semidirect
94. #16810508	C₂²	semidirect
95. #16810508	C₂²	semidirect
96. #16810507	C₂²	semidirect
97. #16810507	C₂²	semidirect
98. #16810506	C₂²	semidirect
99. #16810505	C₂²	semidirect
100. #16810505	C₂²	semidirect
101. #16810505	C₂²	semidirect
102. #16810505	C₂²	semidirect
103. #16810505	C₂²	semidirect
104. #16810505	C₂²	semidirect
105. #16810504	C₂²	semidirect
116. #16810496	C₂²	semidirect
117. #16810495	C₂²	semidirect
118. #16810495	C₂²	semidirect
120. #16810491	C₂²	semidirect
121. #16810487	C₂²	semidirect
122. #16810487	C₂²	semidirect
137. C₄⋊C₄×Dic₅₃	C₂²	semidirect
138. C₄⋊C₄×Dic₅₃	C₂²	semidirect
139. C₄×#11719919	C₂²	semidirect
140. #16810474	C₂²	semidirect
141. #16810474	C₂²	semidirect
142. #16810474	C₂²	semidirect
143. #16810474	C₂²	semidirect
144. #16810474	C₂²	semidirect
145. #16810474	C₂²	semidirect
146. #16810474	C₂²	semidirect
150. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
151. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
152. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
153. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
167. #16810468	C₂²	semidirect
168. #16810468	C₂²	semidirect
171. C₄²×Dic₅₃	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
175. C₅₃×#393	C₂²	semidirect
176. C₅₃×#391	C₂²	semidirect
178. C₅₃×#388	C₂²	semidirect
181. C₅₃×#383	C₂²	semidirect
182. C₅₃×#383	C₂²	semidirect
184. C₅₃×#381	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
742. #2572	D₅₃	semidirect
804. #400	C₂×D₅₃	semidirect
828. #393	C₂×D₅₃	semidirect
829. #391	C₂×D₅₃	semidirect
843. #388	C₂×D₅₃	semidirect
876. #383	C₂×D₅₃	semidirect
877. #383	C₂×D₅₃	semidirect
885. #381	C₂×D₅₃	semidirect
927. C₄×C₂²⋊C₄	C₂×D₅₃	semidirect
933. C₅₃	#34849	semidirect

Maximal subgroups

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

subgroup	index
#20280055	2
#20280032	2
#20280023	2
#20280000	2
#20279991	2
#20279974	2
#20279935	2
#20279892	2
#20279869	2
#20279760	2
#20279600	2
#20279097	2
#20278965	2
#20278189	2
#20278176	2
#20278014	2
#20277997	2
#20277982	2
#20277971	2
#20277263	2
#20277253	2
#20277242	2
#20277232	2
#20277220	2
#20277209	2
#20277155	2
#20277112	2
#20277095	2
C₄×#13133177	2
C₄×C₂²⋊C₄×D₅₃	2
C₅₃×#2572	2
#34849	53