Subgroups — #28265586

Order 13568.

2000 conjugacy classes of subgroups.

The subgroup lattice has 1776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288322	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288320	C₂	1	1	yes	maximal, characteristic, complemented
3	#20287722	C₂	1	1	yes	maximal, characteristic, complemented
4	#20287577	C₂	1	1	yes	maximal, characteristic, complemented
5	#20287376	C₂	1	1	yes	maximal, characteristic, complemented
6	#20287372	C₂	1	1	yes	maximal, characteristic, complemented
7	#20287111	C₂	1	1	yes	maximal, characteristic, complemented
8	#20287110	C₂	1	1	yes	maximal, characteristic, complemented
9	#20287102	C₂	1	1	yes	maximal, characteristic, complemented
10	#20286567	C₂	1	1	yes	maximal, characteristic, complemented
11	#20286566	C₂	1	1	yes	maximal, characteristic, complemented
12	#20286560	C₂	1	1	yes	maximal, characteristic, complemented
13	#20286535	C₂	1	1	yes	maximal, characteristic, complemented
14	#20286534	C₂	1	1	yes	maximal, characteristic, complemented
15	#20286398	C₂	1	1	yes	maximal, characteristic, complemented
16	#20286396	C₂	1	1	yes	maximal, characteristic, complemented
17	#20286385	C₂	1	1	yes	maximal, characteristic, complemented
18	#20285289	C₂	1	1	yes	maximal, characteristic, complemented
19	#20285284	C₂	1	1	yes	maximal, characteristic, complemented
20	#20285278	C₂	1	1	yes	maximal, characteristic, complemented
21	#20284770	C₂	1	1	yes	maximal, characteristic, complemented
22	#20284768	C₂	1	1	yes	maximal, characteristic, complemented
23	#20284767	C₂	1	1	yes	maximal, characteristic, complemented
24	#20284765	C₂	1	1	yes	maximal, characteristic, complemented
25	#20284761	C₂	1	1	yes	maximal, characteristic, complemented
26	#20284757	C₂	1	1	yes	maximal, characteristic, complemented
27	C₈×#11719947	C₂	1	1	yes	maximal, characteristic, complemented
28	#20283483	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#16810703	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133237	C₂²	1	1	yes	characteristic
33	C₂²×#11719922	C₂²	1	1	yes	characteristic
34	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
35	#16811356	C₂²	1	1	yes	characteristic, complemented
36	#16811355	C₂²	1	1	yes	characteristic, complemented
37	#16811332	C₂²	1	1	yes	characteristic, complemented
38	#16811331	C₂²	1	1	yes	characteristic
39	#16811329	C₂²	1	1	yes	characteristic, complemented
40	#16811328	C₂²	1	1	yes	characteristic
41	#16811320	C₂²	1	1	yes	characteristic, complemented
42	#16811319	C₂²	1	1	yes	characteristic, complemented
43	#16811318	—	2	1	no	—
44	#16811317	C₂²	1	1	yes	characteristic, complemented
45	#16811316	—	2	1	no	—
46	#16811302	—	2	1	no	—
47	#16811299	—	2	1	no	—
48	#16811298	—	2	1	no	—
49	#16811296	—	2	1	no	—
50	#16811270	C₂²	1	1	yes	characteristic, complemented
51	#16811269	C₂²	1	1	yes	characteristic, complemented
52	#16811262	—	2	1	no	—
53	#16811261	C₂²	1	1	yes	characteristic, complemented
54	#16811260	—	2	1	no	—
55	#16811257	C₂²	1	1	yes	characteristic
56	D₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
57	#16811168	C₂²	1	1	yes	characteristic, complemented
58	#16811168	C₂²	1	1	yes	characteristic, complemented
59	#16811159	C₂²	1	1	yes	characteristic, complemented
60	#16811158	C₂²	1	1	yes	characteristic, complemented
61	#16811156	—	2	1	no	—
62	#16811154	C₂²	1	1	yes	characteristic, complemented
63	#16811152	C₂²	1	1	yes	characteristic, complemented
64	#16811150	—	2	1	no	—
65	#16811133	—	2	1	no	—
66	#16811133	—	2	1	no	—
67	#16811131	—	2	1	no	—
68	#16811129	—	2	1	no	—
69	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
70	#16811091	C₂²	1	1	yes	characteristic, complemented
71	C₄×#11719947	C₂²	1	1	yes	characteristic
72	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
73	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
74	C₂×#13133177	—	2	1	no	—
75	C₄×D₄×D₅₃	—	2	1	no	—
76	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
77	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
78	#16811027	C₂²	1	1	yes	characteristic, complemented
79	#16811023	C₂²	1	1	yes	characteristic, complemented
80	#16811022	C₂²	1	1	yes	characteristic, complemented
81	#16811005	C₂²	1	1	yes	characteristic, complemented
82	#16811004	C₂²	1	1	yes	characteristic, complemented
83	#16810998	C₂²	1	1	yes	characteristic
84	#16810979	C₂²	1	1	yes	characteristic, complemented
85	#16810978	C₂²	1	1	yes	characteristic, complemented
86	#16810976	C₂²	1	1	yes	characteristic, complemented
87	#16810968	C₂²	1	1	yes	characteristic, complemented
88	#16810968	C₂²	1	1	yes	characteristic, complemented
89	#16810960	C₂²	1	1	yes	characteristic, complemented
90	#16810959	C₂²	1	1	yes	characteristic, complemented
91	#16810957	C₂²	1	1	yes	characteristic, complemented
92	#16810948	C₂²	1	1	yes	characteristic, complemented
93	#16810947	C₂²	1	1	yes	characteristic, complemented
94	#16810944	C₂²	1	1	yes	characteristic, complemented
95	#16810943	C₂²	1	1	yes	characteristic, complemented
96	#16810941	C₂²	1	1	yes	characteristic, complemented
97	#16810940	C₂²	1	1	yes	characteristic, complemented
98	#16810939	C₂²	1	1	yes	characteristic, complemented
99	#16810926	C₂²	1	1	yes	characteristic, complemented
100	#16810926	C₂²	1	1	yes	characteristic, complemented
101	#16810924	C₂²	1	1	yes	characteristic, complemented
102	#16810923	C₂²	1	1	yes	characteristic, complemented
103	#16810921	C₂²	1	1	yes	characteristic, complemented
104	#16810921	C₂²	1	1	yes	characteristic, complemented
105	#16810920	C₂²	1	1	yes	characteristic, complemented
106	#16810917	C₂²	1	1	yes	characteristic, complemented
107	#16810916	C₂²	1	1	yes	characteristic, complemented
108	#16810912	C₂²	1	1	yes	characteristic, complemented
109	#16810911	C₂²	1	1	yes	characteristic, complemented
110	#16810863	C₂²	1	1	yes	characteristic, complemented
111	#16810862	C₂²	1	1	yes	characteristic, complemented
112	#16810859	C₂²	1	1	yes	characteristic, complemented
113	#16810858	C₂²	1	1	yes	characteristic
114	#16810857	C₂²	1	1	yes	characteristic
115	#16810857	C₂²	1	1	yes	characteristic, complemented
116	#16810857	C₂²	1	1	yes	characteristic, complemented
117	#16810855	C₂²	1	1	yes	characteristic, complemented
118	#16810852	C₂²	1	1	yes	characteristic, complemented
119	#16810851	C₂²	1	1	yes	characteristic, complemented
120	#16810841	C₂²	1	1	yes	characteristic, complemented
121	#16810841	C₂²	1	1	yes	characteristic, complemented
122	#16810839	C₂²	1	1	yes	characteristic, complemented
123	#16810838	C₂²	1	1	yes	characteristic, complemented
124	#16810836	C₂²	1	1	yes	characteristic, complemented
125	#16810836	C₂²	1	1	yes	characteristic, complemented
126	#16810835	C₂²	1	1	yes	characteristic, complemented
127	#16810822	C₂²	1	1	yes	characteristic, complemented
128	#16810821	C₂²	1	1	yes	characteristic, complemented
129	#16810817	C₂²	1	1	yes	characteristic
130	#16810816	C₂²	1	1	yes	characteristic
131	#16810775	C₂²	1	1	yes	characteristic, complemented
132	#16810774	C₂²	1	1	yes	characteristic, complemented
133	#16810773	C₂²	1	1	yes	characteristic, complemented
134	#16810772	C₂²	1	1	yes	characteristic, complemented
135	#16810770	C₂²	1	1	yes	characteristic, complemented
136	#16810768	C₂²	1	1	yes	characteristic, complemented
137	#16810766	C₂²	1	1	yes	characteristic, complemented
138	#16810759	C₂²	1	1	yes	characteristic
139	#16810758	C₂²	1	1	yes	characteristic
140	#16810755	C₂²	1	1	yes	characteristic
141	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
142	#16810747	C₂²	1	1	yes	characteristic, complemented
143	#16810715	C₂²	1	1	yes	characteristic, complemented
144	#16810715	C₂²	1	1	yes	characteristic, complemented
145	#16810714	C₂²	1	1	yes	characteristic, complemented
146	#16810714	C₂²	1	1	yes	characteristic, complemented
147	#16810714	C₂²	1	1	yes	characteristic, complemented
148	SD₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
149	#16810710	C₂²	1	1	yes	characteristic, complemented
150	#16810708	C₂²	1	1	yes	characteristic, complemented
151	#16810708	C₂²	1	1	yes	characteristic, complemented
152	#16810708	C₂²	1	1	yes	characteristic, complemented
153	C₄×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
154	D₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
155	D₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
156	#16810705	C₂²	1	1	yes	characteristic, complemented
157	#16810705	C₂²	1	1	yes	characteristic, complemented
158	C₄×#11719922	C₂²	1	1	yes	characteristic
159	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
160	#16810703	C₂²	1	1	yes	characteristic
161	#16810703	C₂²	1	1	yes	characteristic
162	#16810703	C₂²	1	1	yes	characteristic
163	#16810703	C₂²	1	1	yes	characteristic, complemented
164	#16810703	C₂²	1	1	yes	characteristic, complemented
165	#16810703	C₂²	1	1	yes	characteristic, complemented
166	#16810703	C₂²	1	1	yes	characteristic, complemented
167	#16810703	C₂²	1	1	yes	characteristic, complemented
168	#16810703	C₂²	1	1	yes	characteristic, complemented
169	#16810703	C₂²	1	1	yes	characteristic, complemented
170	D₄×#88322	C₂²	1	1	yes	characteristic, complemented
171	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
172	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
173	#16810686	C₂²	1	1	yes	characteristic
174	#16810686	C₂²	1	1	yes	characteristic, complemented
175	#16810675	C₂²	1	1	yes	characteristic, complemented
176	#16810673	C₂²	1	1	yes	characteristic, complemented
177	#16810673	C₂²	1	1	yes	characteristic, complemented
178	#16810659	C₂²	1	1	yes	characteristic, complemented
179	C₂×#13133150	C₂²	1	1	yes	characteristic, complemented
180	#107×D₅₃	C₂²	1	1	yes	characteristic, complemented
181	#16810620	C₂²	1	1	yes	characteristic, complemented
182	C₂×#13133139	C₂²	1	1	yes	characteristic, complemented
183	#102×D₅₃	C₂²	1	1	yes	characteristic, complemented
184	#102×D₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#447	C₂²	1	1	yes	characteristic
199	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
200	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#11719945	C₂³	1	1	yes	characteristic
204	C₂×#11719947	—	2	1	no	—
205	C₂×#11719947	—	2	1	no	—
206	C₂×#11719947	D₄	1	1	yes	characteristic
207	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
208	C₂²×C₂²⋊D₅₃	—	2	1	no	—
209	C₂×D₄×D₅₃	—	2	1	no	—
210	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂³×Dic₅₃	—	2	1	no	—
213	C₂²×C₄×D₅₃	—	2	1	no	—
214	C₂²×C₄×D₅₃	—	2	1	no	—
215	C₂²×C₄×D₅₃	—	2	1	no	—
216	#13133237	—	2	4	no	—
217	C₂×#11719925	C₂³	1	1	yes	characteristic
218	C₂×#11719913	C₂³	1	1	yes	characteristic
219	C₂×#11719923	C₂³	1	1	yes	characteristic
220	C₂×#11719923	C₂³	1	1	yes	characteristic
221	C₂×#11719924	C₂³	1	1	yes	characteristic
222	C₂×#11719924	C₂³	1	1	yes	characteristic
223	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
224	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
225	C₂×#11719922	—	2	4	no	—
226	C₂×#11719922	C₂³	1	1	yes	characteristic
227	C₂×#11719922	C₂³	1	1	yes	characteristic
228	C₂×#11719922	C₂³	1	1	yes	characteristic
229	C₂×#11719922	C₂³	1	1	yes	characteristic
230	C₂×#11719922	C₂³	1	1	yes	characteristic
231	D₈×D₅₃	—	2	4	no	—
232	C₂²×#88322	C₂³	1	1	yes	characteristic
233	C₂²×#88322	C₂³	1	1	yes	characteristic
234	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
236	#13133216	C₂³	1	1	yes	characteristic
237	#13133216	C₂³	1	1	yes	characteristic
238	#13133213	C₂³	1	1	yes	characteristic
239	#13133213	C₂³	1	1	yes	characteristic
240	#13133212	—	2	1	no	—
241	#13133212	—	2	1	no	—
242	#13133212	—	2	1	no	—
243	#13133211	—	2	1	no	—
244	#13133210	—	2	1	no	—
245	#13133210	—	2	1	no	—
246	#13133210	—	2	1	no	—
247	#13133209	C₂³	1	1	yes	characteristic
248	#13133208	C₂³	1	1	yes	characteristic
249	#13133208	C₂³	1	1	yes	characteristic
250	#13133207	—	2	1	no	—
251	#13133207	—	2	1	no	—
252	#13133206	C₂³	1	1	yes	characteristic
253	#13133205	C₂³	1	1	yes	characteristic
254	#13133204	C₂³	1	1	yes	characteristic
255	#13133203	—	2	1	no	—
256	#13133203	—	2	1	no	—
257	#13133203	—	2	1	no	—
258	#13133203	—	2	1	no	—
259	#13133202	—	2	1	no	—
260	#13133202	—	2	1	no	—
261	#13133201	—	2	1	no	—
262	#13133201	—	2	1	no	—
263	#13133200	—	2	1	no	—
264	#13133200	—	2	1	no	—
265	#13133199	—	2	1	no	—
266	#13133199	—	2	1	no	—
267	#13133199	—	2	1	no	—
268	#13133199	—	2	1	no	—
269	#13133199	—	2	1	no	—
270	#13133199	—	2	1	no	—
271	#13133198	—	2	1	no	—
272	#13133198	—	2	1	no	—
273	#13133197	—	2	1	no	—
274	#13133197	—	2	1	no	—
275	#13133197	C₂³	1	1	yes	characteristic
276	#13133196	—	2	1	no	—
277	#13133196	—	2	1	no	—
278	#13133196	C₂³	1	1	yes	characteristic
279	#13133195	—	2	1	no	—
280	#13133195	—	2	1	no	—
281	#13133195	—	2	1	no	—
282	#13133194	—	2	1	no	—
283	#13133194	—	2	1	no	—
284	#13133194	—	2	1	no	—
285	#13133193	C₂³	1	1	yes	characteristic
286	#13133192	C₂³	1	1	yes	characteristic
287	#13133191	C₂³	1	1	yes	characteristic
288	#13133191	C₂³	1	1	yes	characteristic
289	#13133191	C₂³	1	1	yes	characteristic
290	#13133190	—	2	1	no	—
291	#13133190	—	2	1	no	—
292	#13133190	—	2	1	no	—
293	#13133189	—	2	1	no	—
294	#13133189	—	2	1	no	—
295	#13133189	—	2	1	no	—
296	#13133189	—	2	1	no	—
297	#13133189	—	2	1	no	—
298	#13133188	—	2	1	no	—
299	#13133188	—	2	1	no	—
300	#13133188	C₂³	1	1	yes	characteristic
301	#13133187	—	2	1	no	—
302	#13133186	—	2	1	no	—
303	#13133185	—	2	1	no	—
304	#13133185	—	2	1	no	—
305	#13133185	—	2	1	no	—
306	#13133185	—	2	1	no	—
307	#13133185	—	2	1	no	—
308	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic
309	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
311	#13133182	D₄	1	1	yes	characteristic
312	#13133182	C₂³	1	1	yes	characteristic
313	#13133182	C₂³	1	1	yes	characteristic
314	C₄×D₂₁₂	—	2	1	no	—
315	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
316	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
317	D₄×Dic₅₃	—	2	1	no	—
318	D₄×Dic₅₃	—	2	1	no	—
319	D₄×Dic₅₃	—	2	1	no	—
320	D₄×Dic₅₃	—	2	1	no	—
321	D₄×Dic₅₃	—	2	1	no	—
322	D₄×Dic₅₃	D₄	1	1	yes	characteristic
323	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
324	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
325	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
326	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
327	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
328	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
329	#13133179	—	2	1	no	—
330	#13133179	—	2	1	no	—
331	#13133179	—	2	1	no	—
332	#13133179	C₂³	1	1	yes	characteristic
333	#13133179	C₂³	1	1	yes	characteristic
334	#13133179	C₂³	1	1	yes	characteristic
335	#13133179	C₂³	1	1	yes	characteristic
336	#13133179	C₂³	1	1	yes	characteristic
337	#13133179	C₂³	1	1	yes	characteristic
338	C₄×C₂²⋊D₅₃	—	2	1	no	—
339	C₄×C₂²⋊D₅₃	—	2	1	no	—
340	C₄×C₂²⋊D₅₃	—	2	1	no	—
341	C₄×C₂²⋊D₅₃	—	2	1	no	—
342	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
343	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
344	#13133177	—	2	1	no	—
345	#13133177	—	2	1	no	—
346	#13133177	—	2	1	no	—
347	#13133177	—	2	1	no	—
348	#13133177	—	2	1	no	—
349	#13133177	—	2	1	no	—
350	#13133177	—	2	1	no	—
351	#13133177	—	2	1	no	—
352	#13133177	—	2	1	no	—
353	#13133177	—	2	1	no	—
354	#13133177	—	2	1	no	—
355	#13133177	—	2	1	no	—
356	#13133177	D₄	1	1	yes	characteristic
357	#13133177	D₄	1	1	yes	characteristic
358	#13133176	—	2	1	no	—
359	#13133176	C₂³	1	1	yes	characteristic
360	#13133175	—	2	1	no	—
361	#13133175	—	2	1	no	—
362	#13133175	D₄	1	1	yes	characteristic
363	#13133174	—	2	1	no	—
364	#13133173	—	2	1	no	—
365	#13133173	—	2	1	no	—
366	#13133173	D₄	1	1	yes	characteristic
367	#13133173	D₄	1	1	yes	characteristic
368	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
369	C₂×#11719919	—	2	1	no	—
370	C₄⋊C₄×D₅₃	—	2	1	no	—
371	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
372	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
373	C₂×C₂²⋊Dic₅₃	—	2	1	no	—
374	C₂×#11719921	—	2	1	no	—
375	C₂×#11719921	—	2	1	no	—
376	C₂²⋊C₄×D₅₃	—	2	1	no	—
377	C₂²⋊C₄×D₅₃	—	2	1	no	—
378	C₂²⋊C₄×D₅₃	—	2	1	no	—
379	C₂²⋊C₄×D₅₃	—	2	1	no	—
380	C₂×C₄×Dic₅₃	—	2	1	no	—
381	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
382	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
383	C₄²×D₅₃	—	2	1	no	—
384	C₄²×D₅₃	C₂³	1	1	yes	characteristic
385	#13133151	C₂³	1	1	yes	characteristic
386	#13133151	C₂³	1	1	yes	characteristic
387	#13133150	C₂³	1	1	yes	characteristic
388	#13133150	C₂³	1	1	yes	characteristic
389	#13133150	C₂³	1	1	yes	characteristic
390	#13133150	C₂³	1	1	yes	characteristic
391	#13133150	C₂³	1	1	yes	characteristic
392	#13133150	C₂³	1	1	yes	characteristic
393	#13133149	C₂³	1	1	yes	characteristic
394	#13133148	C₂³	1	1	yes	characteristic
395	#13133148	C₂³	1	1	yes	characteristic
396	#13133148	C₂³	1	1	yes	characteristic
397	#13133148	C₂³	1	1	yes	characteristic
398	C₄⋊#88322	C₂³	1	1	yes	characteristic
399	#13133146	C₂³	1	1	yes	characteristic
400	#13133146	C₂³	1	1	yes	characteristic
401	#13133146	C₂³	1	1	yes	characteristic
402	#13133146	C₂³	1	1	yes	characteristic
403	#13133142	C₂³	1	1	yes	characteristic
404	#13133142	C₂³	1	1	yes	characteristic
405	#13133142	C₂³	1	1	yes	characteristic
406	#13133141	C₂³	1	1	yes	characteristic
407	#13133140	C₂³	1	1	yes	characteristic
408	#13133139	C₂³	1	1	yes	characteristic
409	#13133139	C₂³	1	1	yes	characteristic
410	#13133139	C₂³	1	1	yes	characteristic
411	#13133139	C₂³	1	1	yes	characteristic
412	#13133139	C₂³	1	1	yes	characteristic
413	#13133139	C₂³	1	1	yes	characteristic
414	#13133139	C₂³	1	1	yes	characteristic
415	#13133138	C₂³	1	1	yes	characteristic
416	#13133138	C₂³	1	1	yes	characteristic
417	#13133138	C₂³	1	1	yes	characteristic
418	#13133138	C₂³	1	1	yes	characteristic
419	#13133138	C₂³	1	1	yes	characteristic
420	#13133137	C₂³	1	1	yes	characteristic
421	#13133137	C₂³	1	1	yes	characteristic
422	#13133137	C₂³	1	1	yes	characteristic
423	#13133137	C₂³	1	1	yes	characteristic
424	#13133137	C₂³	1	1	yes	characteristic
425	C₂²⋊#88322	C₂³	1	1	yes	characteristic
426	C₂²⋊#88322	C₂³	1	1	yes	characteristic
427	#13133129	C₂³	1	1	yes	characteristic
428	#13133129	C₂³	1	1	yes	characteristic
429	C₄×#88322	C₂³	1	1	yes	characteristic
430	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
431	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
432	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
433	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
434	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
435	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
436	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
437	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
438	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
439	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
440	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
441	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
442	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
443	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
444	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
445	#126×C₅₃	—	2	1	no	—
446	#125×C₅₃	C₂³	1	1	yes	characteristic
447	#124×C₅₃	C₂³	1	1	yes	characteristic
448	#123×C₅₃	—	2	1	no	—
449	#123×C₅₃	—	2	1	no	—
450	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
451	#121×C₅₃	—	2	1	no	—
452	#121×C₅₃	—	2	1	no	—
453	#121×C₅₃	C₂³	1	1	yes	characteristic
454	#121×C₅₃	C₂³	1	1	yes	characteristic
455	#121×C₅₃	C₂³	1	1	yes	characteristic
456	#120×C₅₃	—	2	1	no	—
457	C₄×D₄×C₅₃	—	2	1	no	—
458	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
459	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
460	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
461	#117×C₅₃	C₂³	1	1	yes	characteristic
462	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
463	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
464	#107×C₅₃	C₂³	1	1	yes	characteristic
465	#107×C₅₃	C₂³	1	1	yes	characteristic
466	#106×C₅₃	C₂³	1	1	yes	characteristic
467	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
468	#103×C₅₃	C₂³	1	1	yes	characteristic
469	#103×C₅₃	C₂³	1	1	yes	characteristic
470	#103×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	#102×C₅₃	C₂³	1	1	yes	characteristic
473	#102×C₅₃	C₂³	1	1	yes	characteristic
474	#102×C₅₃	C₂³	1	1	yes	characteristic
475	#102×C₅₃	C₂³	1	1	yes	characteristic
476	#102×C₅₃	C₂³	1	1	yes	characteristic
477	#102×C₅₃	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂⁴×C₅₃	—	2	1	no	—
482	C₂³×D₅₃	—	2	1	no	—
483	C₂³×D₅₃	—	2	1	no	—
484	C₂³×D₅₃	—	2	1	no	—
485	#41×C₅₃	—	2	2	no	—
486	#41×C₅₃	—	4	1	no	—
487	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
488	C₂×D₄×C₅₃	—	2	2	no	—
489	C₂×D₄×C₅₃	—	2	1	no	—
490	C₂×D₄×C₅₃	—	2	1	no	—
491	C₂×D₄×C₅₃	—	2	1	no	—
492	C₂×D₄×C₅₃	—	2	1	no	—
493	C₂×D₄×C₅₃	—	2	1	no	—
494	C₂×D₄×C₅₃	—	4	1	no	—
495	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
496	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
497	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
498	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₅₃	—	2	1	no	—
500	C₂²×C₄×C₅₃	—	2	1	no	—
501	C₂²×C₄×C₅₃	—	2	1	no	—
502	C₂²×C₄×C₅₃	—	2	1	no	—
503	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
504	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₂×C₂²⋊D₅₃	—	2	1	no	—
506	C₂×C₂²⋊D₅₃	—	2	1	no	—
507	C₂×C₂²⋊D₅₃	—	2	1	no	—
508	C₂×C₂²⋊D₅₃	—	2	1	no	—
509	C₂×C₂²⋊D₅₃	—	2	1	no	—
510	C₂×C₂²⋊D₅₃	—	2	1	no	—
511	C₂×C₂²⋊D₅₃	—	2	1	no	—
512	C₂×C₂²⋊D₅₃	—	2	1	no	—
513	C₂×C₂²⋊D₅₃	—	2	1	no	—
514	C₂×C₂²⋊D₅₃	—	2	1	no	—
515	C₂×C₂²⋊D₅₃	—	2	1	no	—
516	C₂×C₂²⋊D₅₃	—	4	4	no	—
517	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
519	C₂²×Dic₅₃	—	2	1	no	—
520	C₂²×Dic₅₃	—	2	1	no	—
521	C₂²×Dic₅₃	—	2	1	no	—
522	C₂²×Dic₅₃	—	2	1	no	—
523	C₂²×Dic₅₃	—	2	1	no	—
524	C₂²×Dic₅₃	—	2	1	no	—
525	C₂²×Dic₅₃	—	2	1	no	—
526	C₂²×Dic₅₃	—	8	2	no	—
527	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
528	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
529	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
530	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
531	#11719947	—	2	4	no	—
532	#11719947	—	8	2	no	—
533	#11719947	—	8	2	no	—
534	D₄×D₅₃	—	2	2	no	—
535	D₄×D₅₃	—	2	2	no	—
536	D₄×D₅₃	—	4	1	no	—
537	D₄×D₅₃	—	4	1	no	—
538	D₄×D₅₃	—	4	4	no	—
539	#11719945	—	2	2	no	—
540	#11719945	—	4	1	no	—
541	C₂×D₂₁₂	—	2	2	no	—
542	C₂×D₂₁₂	—	2	1	no	—
543	C₂×D₂₁₂	—	2	1	no	—
544	C₂×D₂₁₂	—	4	1	no	—
545	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
546	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
547	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
548	C₂×C₄×D₅₃	—	2	1	no	—
549	C₂×C₄×D₅₃	—	2	1	no	—
550	C₂×C₄×D₅₃	—	2	1	no	—
551	C₂×C₄×D₅₃	—	2	1	no	—
552	C₂×C₄×D₅₃	—	2	1	no	—
553	C₂×C₄×D₅₃	—	2	1	no	—
554	C₂×C₄×D₅₃	—	2	1	no	—
555	C₂×C₄×D₅₃	—	2	1	no	—
556	C₂×C₄×D₅₃	—	2	1	no	—
557	C₂×C₄×D₅₃	—	2	1	no	—
558	C₂×C₄×D₅₃	—	2	1	no	—
559	C₂×C₄×D₅₃	—	8	2	no	—
560	C₂×C₄×D₅₃	—	8	2	no	—
561	C₂×C₄×D₅₃	—	8	2	no	—
562	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
563	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
564	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
565	C₂×Dic₁₀₆	—	2	1	no	—
566	C₂×Dic₁₀₆	—	2	1	no	—
567	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
568	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
569	SD₁₆×C₅₃	—	4	1	no	—
570	D₈×C₅₃	—	2	2	no	—
571	D₈×C₅₃	—	4	1	no	—
572	C₂×C₈×C₅₃	—	4	1	no	—
573	C₂×C₈×C₅₃	—	4	1	no	—
574	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
576	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
577	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
578	C₄⋊C₄×C₅₃	—	2	1	no	—
579	C₄⋊C₄×C₅₃	—	2	1	no	—
580	C₄⋊C₄×C₅₃	—	2	1	no	—
581	C₄⋊C₄×C₅₃	—	2	1	no	—
582	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
583	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
584	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
586	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
587	C₂²⋊C₄×C₅₃	—	2	1	no	—
588	C₂²⋊C₄×C₅₃	—	2	1	no	—
589	C₂²⋊C₄×C₅₃	—	2	1	no	—
590	C₂²⋊C₄×C₅₃	—	2	1	no	—
591	C₂²⋊C₄×C₅₃	—	2	1	no	—
592	C₂²⋊C₄×C₅₃	—	2	1	no	—
593	C₂²⋊C₄×C₅₃	—	2	1	no	—
594	C₂²⋊C₄×C₅₃	—	2	1	no	—
595	C₂²⋊C₄×C₅₃	—	2	1	no	—
596	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
597	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
598	C₄²×C₅₃	—	2	1	no	—
599	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₂²⋊Dic₅₃	—	2	1	no	—
601	C₂²⋊Dic₅₃	—	2	1	no	—
602	C₂²⋊Dic₅₃	—	2	1	no	—
603	C₂²⋊Dic₅₃	—	2	1	no	—
604	C₂²⋊Dic₅₃	—	2	1	no	—
605	C₂²⋊Dic₅₃	—	2	1	no	—
606	C₂²⋊Dic₅₃	—	2	1	no	—
607	C₂²⋊Dic₅₃	—	2	1	no	—
608	C₂²⋊Dic₅₃	—	2	1	no	—
609	C₂²⋊Dic₅₃	—	2	1	no	—
610	C₂²⋊Dic₅₃	—	2	1	no	—
611	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
612	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
613	#11719925	—	2	2	no	—
614	#11719924	—	2	2	no	—
615	#11719924	—	4	1	no	—
616	#11719923	—	2	2	no	—
617	#11719923	—	4	1	no	—
618	#11719922	—	2	2	no	—
619	#11719922	—	2	2	no	—
620	#11719922	—	2	2	no	—
621	#11719922	—	2	2	no	—
622	#11719922	#41	1	4	yes	complemented
623	#11719921	—	2	1	no	—
624	#11719921	—	2	1	no	—
625	#11719921	—	2	1	no	—
626	#11719921	—	2	1	no	—
627	#11719921	—	2	1	no	—
628	#11719921	—	2	1	no	—
629	#11719921	—	2	1	no	—
630	#11719921	—	2	1	no	—
631	#11719921	—	2	1	no	—
632	#11719921	—	2	1	no	—
633	#11719921	—	2	1	no	—
634	#11719921	—	2	1	no	—
635	#11719921	—	2	1	no	—
636	#11719921	—	2	1	no	—
637	#11719921	—	2	1	no	—
638	#11719921	—	2	1	no	—
639	#11719921	—	2	1	no	—
640	#11719921	—	2	1	no	—
641	#11719921	C₂×D₄	1	1	yes	characteristic
642	#11719921	C₂×D₄	1	1	yes	characteristic
643	C₄⋊Dic₅₃	—	2	1	no	—
644	C₄⋊Dic₅₃	—	2	1	no	—
645	C₄⋊Dic₅₃	—	2	1	no	—
646	C₄⋊Dic₅₃	—	2	1	no	—
647	C₄⋊Dic₅₃	—	2	1	no	—
648	C₄⋊Dic₅₃	—	2	1	no	—
649	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
650	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
651	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
652	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
653	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
654	#11719919	—	2	1	no	—
655	#11719919	—	2	1	no	—
656	#11719919	—	2	1	no	—
657	#11719919	—	2	1	no	—
658	#11719919	—	2	1	no	—
659	#11719919	—	2	1	no	—
660	#11719919	—	2	1	no	—
661	#11719919	—	2	1	no	—
662	#11719919	—	2	1	no	—
663	#11719919	—	2	1	no	—
664	#11719919	—	2	1	no	—
665	#11719919	—	2	1	no	—
666	#11719919	C₂×D₄	1	1	yes	characteristic
667	#11719919	C₂×D₄	1	1	yes	characteristic
668	#11719919	C₂×D₄	1	1	yes	characteristic
669	#11719919	C₂×D₄	1	1	yes	characteristic
670	C₄×Dic₅₃	—	2	1	no	—
671	C₄×Dic₅₃	—	2	1	no	—
672	C₄×Dic₅₃	—	2	1	no	—
673	C₄×Dic₅₃	—	2	1	no	—
674	C₄×Dic₅₃	—	2	1	no	—
675	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
676	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
677	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
678	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
679	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
680	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
681	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
682	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
683	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
684	C₂×#88322	—	2	2	no	—
685	C₂×#88322	—	2	2	no	—
686	C₂×#88322	C₂⁴	1	1	yes	characteristic
687	C₂×#88322	C₂⁴	1	1	yes	characteristic
688	C₂×#88322	C₂⁴	1	1	yes	characteristic
689	C₂×#88322	C₂⁴	1	1	yes	characteristic
690	D₄₂₄	—	2	2	no	—
691	D₄₂₄	—	4	1	no	—
692	#11719913	—	4	1	no	—
693	C₈×D₅₃	—	2	2	no	—
694	C₈×D₅₃	—	4	1	no	—
695	C₂³×C₅₃	—	2	1	no	—
696	C₂³×C₅₃	—	2	1	no	—
697	C₂³×C₅₃	—	2	1	no	—
698	C₂³×C₅₃	—	4	2	no	—
699	C₂³×C₅₃	—	4	2	no	—
700	C₂³×C₅₃	—	8	1	no	—
701	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
702	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
703	C₂²×D₅₃	—	2	1	no	—
704	C₂²×D₅₃	—	2	1	no	—
705	C₂²×D₅₃	—	2	1	no	—
706	C₂²×D₅₃	—	4	2	no	—
707	C₂²×D₅₃	—	4	2	no	—
708	C₂²×D₅₃	—	4	2	no	—
709	C₂²×D₅₃	—	4	2	no	—
710	C₂²×D₅₃	—	4	2	no	—
711	C₂²×D₅₃	—	4	2	no	—
712	C₂²×D₅₃	—	8	1	no	—
713	C₂²×D₅₃	—	8	1	no	—
714	C₂²×D₅₃	—	8	1	no	—
715	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
716	Q₈×C₅₃	—	2	1	no	—
717	Q₈×C₅₃	—	2	1	no	—
718	D₄×C₅₃	—	2	2	no	—
719	D₄×C₅₃	—	2	1	no	—
720	D₄×C₅₃	—	2	1	no	—
721	D₄×C₅₃	—	2	1	no	—
722	D₄×C₅₃	—	2	1	no	—
723	D₄×C₅₃	—	2	1	no	—
724	D₄×C₅₃	—	4	2	no	—
725	D₄×C₅₃	—	4	2	no	—
726	D₄×C₅₃	—	4	2	no	—
727	D₄×C₅₃	—	8	1	no	—
728	D₄×C₅₃	—	8	1	no	—
729	D₄×C₅₃	C₂×#41	1	2	yes	—
730	C₂×C₄×C₅₃	—	2	1	no	—
731	C₂×C₄×C₅₃	—	2	1	no	—
732	C₂×C₄×C₅₃	—	2	1	no	—
733	C₂×C₄×C₅₃	—	2	1	no	—
734	C₂×C₄×C₅₃	—	2	1	no	—
735	C₂×C₄×C₅₃	—	2	1	no	—
736	C₂×C₄×C₅₃	—	2	1	no	—
737	C₂×C₄×C₅₃	—	2	1	no	—
738	C₂×C₄×C₅₃	—	2	1	no	—
739	C₂×C₄×C₅₃	—	4	2	no	—
740	C₂×C₄×C₅₃	—	8	1	no	—
741	C₂×C₄×C₅₃	—	8	1	no	—
742	C₂×C₄×C₅₃	—	8	1	no	—
743	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
748	C₂²⋊D₅₃	—	2	2	no	—
749	C₂²⋊D₅₃	—	4	2	no	—
750	C₂²⋊D₅₃	—	4	2	no	—
751	C₂²⋊D₅₃	—	4	2	no	—
752	C₂²⋊D₅₃	—	4	2	no	—
753	C₂²⋊D₅₃	—	4	2	no	—
754	C₂²⋊D₅₃	—	4	2	no	—
755	C₂²⋊D₅₃	—	4	2	no	—
756	C₂²⋊D₅₃	—	8	1	no	—
757	C₂²⋊D₅₃	—	8	1	no	—
758	C₂²⋊D₅₃	—	8	1	no	—
759	C₂²⋊D₅₃	—	8	1	no	—
760	C₂²⋊D₅₃	#135	1	4	yes	complemented
761	C₂×Dic₅₃	—	2	2	no	—
762	C₂×Dic₅₃	—	2	2	no	—
763	C₂×Dic₅₃	—	2	2	no	—
764	C₂×Dic₅₃	—	2	2	no	—
765	C₂×Dic₅₃	—	2	1	no	—
766	C₂×Dic₅₃	—	2	1	no	—
767	C₂×Dic₅₃	—	2	1	no	—
768	C₂×Dic₅₃	—	2	1	no	—
769	C₂×Dic₅₃	—	2	1	no	—
770	C₂×Dic₅₃	—	4	2	no	—
771	C₂×Dic₅₃	—	4	2	no	—
772	C₂×Dic₅₃	—	4	2	no	—
773	C₂×Dic₅₃	—	4	2	no	—
774	C₂×Dic₅₃	—	8	1	no	—
775	C₂×Dic₅₃	—	8	1	no	—
776	C₂×Dic₅₃	—	8	1	no	—
777	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
778	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
779	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
780	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
781	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
782	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
783	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
784	D₂₁₂	—	2	1	no	—
785	D₂₁₂	—	2	1	no	—
786	D₂₁₂	—	2	1	no	—
787	D₂₁₂	—	2	1	no	—
788	D₂₁₂	—	2	1	no	—
789	D₂₁₂	—	4	2	no	—
790	D₂₁₂	—	4	2	no	—
791	D₂₁₂	C₂×#41	1	2	yes	—
792	C₄×D₅₃	—	2	2	no	—
793	C₄×D₅₃	—	2	1	no	—
794	C₄×D₅₃	—	2	1	no	—
795	C₄×D₅₃	—	2	2	no	—
796	C₄×D₅₃	—	4	2	no	—
797	C₄×D₅₃	—	4	2	no	—
798	C₄×D₅₃	—	4	2	no	—
799	C₄×D₅₃	—	4	2	no	—
800	C₄×D₅₃	—	4	2	no	—
801	C₄×D₅₃	—	8	1	no	—
802	C₄×D₅₃	—	8	1	no	—
803	C₄×D₅₃	—	8	1	no	—
804	C₄×D₅₃	—	8	1	no	—
805	C₄×D₅₃	—	8	1	no	—
806	C₄×D₅₃	—	8	1	no	—
807	Dic₁₀₆	—	2	2	no	—
808	Dic₁₀₆	—	2	1	no	—
809	Dic₁₀₆	—	2	1	no	—
810	Dic₁₀₆	—	8	1	no	—
811	Dic₁₀₆	—	8	1	no	—
812	C₈×C₅₃	—	2	1	no	—
813	C₈×C₅₃	—	2	1	no	—
814	C₈×C₅₃	—	2	1	no	—
815	C₈×C₅₃	—	2	1	no	—
816	#88322	—	2	1	no	—
817	#88322	—	2	1	no	—
818	#88322	—	2	1	no	—
819	#88322	C₂×#41	1	2	yes	—
820	#61431	—	53	1	no	maximal, Sylow
821	C₂²×C₅₃	—	2	1	no	—
822	C₂²×C₅₃	—	2	1	no	—
823	C₂²×C₅₃	—	2	1	no	—
824	C₂²×C₅₃	—	2	2	no	—
825	C₂²×C₅₃	—	2	1	no	—
826	C₂²×C₅₃	—	2	1	no	—
827	C₂²×C₅₃	—	4	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	—	4	1	no	—
832	C₂²×C₅₃	—	4	1	no	—
833	C₂²×C₅₃	—	4	1	no	—
834	C₂²×C₅₃	—	4	1	no	—
835	C₂²×C₅₃	—	8	4	no	—
836	C₂²×C₅₃	C₂×#135	1	2	yes	—
837	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
838	C₂×D₅₃	—	2	1	no	—
839	C₂×D₅₃	—	2	1	no	—
840	C₂×D₅₃	—	2	2	no	—
841	C₂×D₅₃	—	4	1	no	—
842	C₂×D₅₃	—	4	1	no	—
843	C₂×D₅₃	—	4	1	no	—
844	C₂×D₅₃	—	4	1	no	—
845	C₂×D₅₃	—	4	1	no	—
846	C₂×D₅₃	—	4	1	no	—
847	C₂×D₅₃	—	4	1	no	—
848	C₂×D₅₃	—	4	1	no	—
849	C₂×D₅₃	—	8	4	no	—
850	C₂×D₅₃	—	8	4	no	—
851	C₂×D₅₃	—	8	4	no	—
852	C₂×D₅₃	C₂×#135	1	2	yes	—
853	C₄×C₅₃	—	2	1	no	—
854	C₄×C₅₃	—	2	1	no	—
855	C₄×C₅₃	—	2	1	no	—
856	C₄×C₅₃	—	2	1	no	—
857	C₄×C₅₃	—	4	1	no	—
858	C₄×C₅₃	—	4	1	no	—
859	C₄×C₅₃	—	4	1	no	—
860	C₄×C₅₃	—	4	1	no	—
861	C₄×C₅₃	—	4	1	no	—
862	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
863	C₄×C₅₃	#585	1	1	yes	characteristic
864	Dic₅₃	—	2	1	no	—
865	Dic₅₃	—	2	1	no	—
866	Dic₅₃	—	2	1	no	—
867	Dic₅₃	—	2	1	no	—
868	Dic₅₃	—	2	1	no	—
869	Dic₅₃	—	4	1	no	—
870	Dic₅₃	—	4	1	no	—
871	Dic₅₃	—	4	1	no	—
872	Dic₅₃	—	4	1	no	—
873	Dic₅₃	—	4	1	no	—
874	Dic₅₃	C₂×#135	1	2	yes	—
875	Dic₅₃	#576	1	2	yes	—
876	#3481	—	53	1	no	—
877	#3481	—	53	1	no	—
878	#3396	—	53	1	no	—
879	#3380	—	53	1	no	—
880	#3361	—	53	1	no	—
881	#3361	—	53	1	no	—
882	#3339	—	53	1	no	—
883	#3339	—	53	1	no	—
884	#3338	—	53	1	no	—
885	#3297	—	53	1	no	—
886	#3297	—	53	1	no	—
887	#3297	—	53	1	no	—
888	#3297	D₅₃	1	1	yes	characteristic, complemented
889	#3295	—	53	1	no	—
890	#3295	—	53	1	no	—
891	#3280	—	53	1	no	—
892	#3280	—	53	1	no	—
893	D₄×D₈	—	53	1	no	—
894	#3169	—	53	1	no	—
895	#3168	—	53	1	no	—
896	#3168	—	53	1	no	—
897	#3106	—	53	1	no	—
898	#3106	—	53	1	no	—
899	#3105	—	53	1	no	—
900	#3105	—	53	1	no	—
901	#3105	—	53	1	no	—
902	#3105	—	53	1	no	—
903	C₈×#41	—	53	1	no	—
904	C₄×#135	—	53	1	no	—
905	C₂×C₄×D₈	—	53	1	no	—
906	C₂×C₄×D₈	—	53	1	no	—
907	C₂×C₅₃	—	2	2	no	—
908	C₂×C₅₃	—	4	2	no	—
909	C₂×C₅₃	—	4	1	no	—
910	C₂×C₅₃	—	8	1	no	—
911	C₂×C₅₃	—	8	1	no	—
912	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
913	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
914	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
915	D₅₃	—	2	2	no	—
916	D₅₃	—	4	2	no	—
917	D₅₃	—	8	1	no	—
918	D₅₃	—	8	1	no	—
919	C₂×#135	—	53	1	no	—
920	C₂²×D₈	—	53	1	no	—
921	C₂²×D₈	—	53	1	no	—
922	#559	—	53	1	no	—
923	#559	—	53	1	no	—
924	#554	—	53	1	no	—
925	#554	—	53	1	no	—
926	#554	—	53	1	no	—
927	#554	—	53	1	no	—
928	#553	—	53	1	no	—
929	#553	—	53	1	no	—
930	#553	—	53	1	no	—
931	#553	—	106	1	no	—
932	#553	—	106	1	no	—
933	#553	C₂×D₅₃	1	1	yes	characteristic, complemented
934	#551	—	106	1	no	—
935	#551	—	106	1	no	—
936	#551	—	106	1	no	—
937	#551	—	106	1	no	—
938	#546	—	53	1	no	—
939	#546	—	53	1	no	—
940	#546	—	53	1	no	—
941	#546	—	106	1	no	—
942	#546	—	106	1	no	—
943	#546	C₂×D₅₃	1	1	yes	characteristic, complemented
944	D₄²	—	53	1	no	—
945	D₄²	—	53	1	no	—
946	#532	—	53	1	no	—
947	#532	—	53	1	no	—
948	#529	—	53	1	no	—
949	#529	—	53	1	no	—
950	#529	—	53	1	no	—
951	#529	—	53	1	no	—
952	#529	—	106	1	no	—
953	#529	—	106	1	no	—
954	#525	—	106	1	no	—
955	#525	—	106	1	no	—
956	#525	—	106	1	no	—
957	#525	—	106	1	no	—
958	C₄×#41	—	53	1	no	—
959	C₄×#41	—	53	1	no	—
960	C₄×#41	—	53	1	no	—
961	C₂×C₄×D₄	—	53	1	no	—
962	C₂×C₄×D₄	—	53	1	no	—
963	C₂×C₄×D₄	—	53	1	no	—
964	C₂×C₄×D₄	—	53	1	no	—
965	C₂×C₄×D₄	—	106	1	no	—
966	C₂×C₄×D₄	—	106	1	no	—
967	#500	—	53	1	no	—
968	#499	—	53	1	no	—
969	#499	—	53	1	no	—
970	#495	—	53	1	no	—
971	#495	—	53	1	no	—
972	#493	—	53	1	no	—
973	#488	—	53	1	no	—
974	#488	—	53	1	no	—
975	#488	—	53	1	no	—
976	#488	C₂×D₅₃	1	1	yes	characteristic, complemented
977	#486	—	53	1	no	—
978	#486	—	53	1	no	—
979	#484	—	53	1	no	—
980	#484	—	53	1	no	—
981	#484	—	53	1	no	—
982	#484	C₂×D₅₃	1	1	yes	characteristic, complemented
983	#482	—	53	1	no	—
984	#482	—	53	1	no	—
985	#482	—	53	1	no	—
986	#482	C₂×D₅₃	1	1	yes	characteristic, complemented
987	#481	—	53	1	no	—
988	#481	—	53	1	no	—
989	#481	—	53	1	no	—
990	#481	—	53	1	no	—
991	#478	—	53	1	no	—
992	#478	—	53	1	no	—
993	#478	—	53	1	no	—
994	#478	—	53	1	no	—
995	#478	—	53	1	no	—
996	#478	—	53	1	no	—
997	#478	—	53	1	no	—
998	#478	C₂×D₅₃	1	1	yes	characteristic, complemented
999	#477	—	53	1	no	—
1000	#477	—	53	1	no	—
1001	#476	—	53	1	no	—
1002	#476	—	53	1	no	—
1003	#467	—	53	1	no	—
1004	#467	—	53	1	no	—
1005	#466	—	53	1	no	—
1006	#466	—	53	1	no	—
1007	#466	—	53	1	no	—
1008	#466	—	53	1	no	—
1009	#466	—	53	1	no	—
1010	#466	C₂×D₅₃	1	1	yes	characteristic, complemented
1011	#465	—	53	1	no	—
1012	#465	—	53	1	no	—
1013	#465	—	53	1	no	—
1014	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
1015	#463	—	53	1	no	—
1016	#463	—	53	1	no	—
1017	#463	—	53	1	no	—
1018	#463	—	53	1	no	—
1019	#463	—	53	1	no	—
1020	#463	—	53	1	no	—
1021	#463	—	53	1	no	—
1022	#463	C₂×D₅₃	1	1	yes	characteristic, complemented
1023	#460	—	53	1	no	—
1024	#460	—	53	1	no	—
1025	#459	—	53	1	no	—
1026	#459	—	53	1	no	—
1027	#450	—	53	1	no	—
1028	#450	—	53	1	no	—
1029	#450	—	53	1	no	—
1030	#450	—	53	1	no	—
1031	#449	—	53	1	no	—
1032	#449	—	53	1	no	—
1033	#449	—	53	1	no	—
1034	#449	C₂×D₅₃	1	1	yes	characteristic, complemented
1035	#447	—	53	1	no	—
1036	#447	—	53	1	no	—
1037	#447	—	53	1	no	—
1038	#447	C₂×D₅₃	1	1	yes	characteristic
1039	C₈×Q₈	—	53	1	no	—
1040	C₈×Q₈	—	53	1	no	—
1041	C₄×Q₁₆	—	53	1	no	—
1042	C₄×Q₁₆	—	53	1	no	—
1043	C₄×SD₁₆	—	53	1	no	—
1044	C₄×SD₁₆	—	53	1	no	—
1045	C₄×SD₁₆	—	53	1	no	—
1046	C₄×SD₁₆	—	53	1	no	—
1047	C₄×SD₁₆	—	53	1	no	—
1048	C₄×SD₁₆	—	53	1	no	—
1049	C₄×SD₁₆	—	53	1	no	—
1050	C₄×SD₁₆	—	53	1	no	—
1051	C₄×D₈	—	53	1	no	—
1052	C₄×D₈	—	53	1	no	—
1053	C₄×D₈	—	53	1	no	—
1054	C₄×D₈	—	53	1	no	—
1055	C₄×D₈	—	53	1	no	—
1056	C₄×D₈	—	53	1	no	—
1057	C₄×D₈	—	53	1	no	—
1058	C₄×D₈	—	53	1	no	—
1059	C₄×D₈	—	53	1	no	—
1060	C₄×D₈	—	53	1	no	—
1061	C₄×D₈	—	53	1	no	—
1062	C₄×D₈	—	53	1	no	—
1063	C₄×D₈	—	53	1	no	—
1064	C₄×D₈	—	53	1	no	—
1065	C₄×D₈	—	53	1	no	—
1066	C₄×D₈	—	53	1	no	—
1067	C₄×D₈	—	53	1	no	—
1068	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1069	C₈×D₄	—	53	1	no	—
1070	C₈×D₄	—	53	1	no	—
1071	C₈×D₄	—	53	1	no	—
1072	C₈×D₄	—	53	1	no	—
1073	C₈×D₄	—	53	1	no	—
1074	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
1075	#431	—	53	1	no	—
1076	#431	—	53	1	no	—
1077	#431	—	53	1	no	—
1078	#427	—	53	1	no	—
1079	C₂×#107	—	53	1	no	—
1080	C₂×#107	—	53	1	no	—
1081	#416	—	53	1	no	—
1082	#416	C₂×D₅₃	1	1	yes	characteristic, complemented
1083	C₂×#102	—	53	1	no	—
1084	C₂×#102	—	53	1	no	—
1085	C₂×#102	—	53	1	no	—
1086	C₂×#102	C₂×D₅₃	1	1	yes	characteristic, complemented
1087	C₂×C₄×C₈	—	53	1	no	—
1088	C₂×C₄×C₈	—	53	1	no	—
1089	C₂×C₄×C₈	—	53	1	no	—
1090	C₅₃	#61431	1	1	yes	characteristic, complemented, Sylow
1091	C₂×#41	—	53	1	no	—
1092	C₂×#41	—	53	1	no	—
1093	C₂×#41	—	106	1	no	—
1094	C₂×#41	—	106	1	no	—
1095	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1096	C₂²×D₄	—	53	1	no	—
1097	C₂²×D₄	—	53	1	no	—
1098	C₂²×D₄	—	53	1	no	—
1099	C₂²×D₄	—	106	1	no	—
1100	C₂²×D₄	—	106	1	no	—
1101	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1102	C₂³×C₄	—	106	1	no	—
1103	C₂³×C₄	—	106	1	no	—
1104	C₂³×C₄	—	106	1	no	—
1105	C₂³×C₄	—	106	1	no	—
1106	#135	—	106	4	no	—
1107	C₂×Q₁₆	—	53	1	no	—
1108	C₂×SD₁₆	—	53	1	no	—
1109	C₂×SD₁₆	—	53	1	no	—
1110	C₂×SD₁₆	—	53	1	no	—
1111	C₂×SD₁₆	—	53	1	no	—
1112	C₂×SD₁₆	—	53	1	no	—
1113	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1114	C₂×D₈	—	53	1	no	—
1115	C₂×D₈	—	53	1	no	—
1116	C₂×D₈	—	53	1	no	—
1117	C₂×D₈	—	53	1	no	—
1118	C₂×D₈	—	53	1	no	—
1119	C₂×D₈	—	53	1	no	—
1120	C₂×D₈	—	53	1	no	—
1121	C₂×D₈	—	106	4	no	—
1122	C₂×D₈	—	106	4	no	—
1123	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1124	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1125	C₂²×C₈	—	53	1	no	—
1126	C₂²×C₈	—	53	1	no	—
1127	C₂²×C₈	—	53	1	no	—
1128	C₂²×C₈	—	53	1	no	—
1129	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1130	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1131	C₄⋊Q₈	—	53	1	no	—
1132	C₄⋊Q₈	—	53	1	no	—
1133	#127	—	53	1	no	—
1134	#127	—	53	1	no	—
1135	#126	—	2	1	no	—
1136	#126	—	106	1	no	—
1137	#126	—	106	1	no	—
1138	#126	—	106	1	no	—
1139	#126	—	106	1	no	—
1140	#126	—	106	1	no	—
1141	#126	—	106	1	no	—
1142	#126	—	106	1	no	—
1143	#125	—	53	1	no	—
1144	#125	—	53	1	no	—
1145	#125	—	53	1	no	—
1146	#125	—	106	1	no	—
1147	#125	—	106	1	no	—
1148	#125	C₂²×D₅₃	1	1	yes	characteristic
1149	#124	—	53	1	no	—
1150	#124	—	53	1	no	—
1151	#124	—	53	1	no	—
1152	#124	—	106	1	no	—
1153	#124	—	106	1	no	—
1154	#124	—	106	1	no	—
1155	#124	—	106	1	no	—
1156	#124	C₂²×D₅₃	1	1	yes	characteristic
1157	#123	—	2	1	no	—
1158	#123	—	2	1	no	—
1159	#123	—	106	1	no	—
1160	#123	—	106	1	no	—
1161	#123	—	106	1	no	—
1162	#123	—	106	1	no	—
1163	#123	—	106	1	no	—
1164	#123	—	106	1	no	—
1165	#123	—	106	1	no	—
1166	#123	—	106	1	no	—
1167	#123	—	106	1	no	—
1168	#123	—	106	1	no	—
1169	#123	—	106	1	no	—
1170	#123	—	106	1	no	—
1171	#123	—	106	1	no	—
1172	#123	—	106	1	no	—
1173	C₂²⋊Q₈	—	53	1	no	—
1174	C₂²⋊Q₈	—	53	1	no	—
1175	C₂²⋊Q₈	—	53	1	no	—
1176	C₂²⋊Q₈	—	106	1	no	—
1177	C₂²⋊Q₈	—	106	1	no	—
1178	C₂²⋊Q₈	—	106	1	no	—
1179	C₂²⋊Q₈	—	106	1	no	—
1180	C₂²⋊Q₈	—	106	1	no	—
1181	C₂²⋊Q₈	—	106	1	no	—
1182	C₂²⋊Q₈	—	106	1	no	—
1183	C₂²⋊Q₈	—	106	1	no	—
1184	C₂²⋊Q₈	—	106	1	no	—
1185	C₂²⋊Q₈	—	106	1	no	—
1186	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
1187	#121	—	2	1	no	—
1188	#121	—	2	1	no	—
1189	#121	—	53	1	no	—
1190	#121	—	53	1	no	—
1191	#121	—	53	1	no	—
1192	#121	—	53	1	no	—
1193	#121	—	53	1	no	—
1194	#121	—	106	1	no	—
1195	#121	—	106	1	no	—
1196	#121	—	106	1	no	—
1197	#121	—	106	1	no	—
1198	#121	—	106	1	no	—
1199	#121	—	106	1	no	—
1200	#121	—	106	1	no	—
1201	#121	—	106	1	no	—
1202	#121	—	106	1	no	—
1203	#121	—	106	1	no	—
1204	#121	C₂²×D₅₃	1	1	yes	characteristic
1205	#121	C₂²×D₅₃	1	1	yes	characteristic
1206	#121	C₂²×D₅₃	1	1	yes	characteristic
1207	#120	—	2	1	no	—
1208	#120	—	106	1	no	—
1209	#120	—	106	1	no	—
1210	#120	—	106	1	no	—
1211	#120	—	106	1	no	—
1212	#120	—	106	1	no	—
1213	#120	—	106	1	no	—
1214	#120	—	106	1	no	—
1215	C₄×Q₈	—	53	1	no	—
1216	C₄×Q₈	—	53	1	no	—
1217	C₄×Q₈	—	53	1	no	—
1218	C₄×Q₈	—	53	1	no	—
1219	C₄×Q₈	—	53	1	no	—
1220	C₄×Q₈	—	53	1	no	—
1221	C₄×D₄	—	2	1	no	—
1222	C₄×D₄	—	53	1	no	—
1223	C₄×D₄	—	53	1	no	—
1224	C₄×D₄	—	53	1	no	—
1225	C₄×D₄	—	53	1	no	—
1226	C₄×D₄	—	53	1	no	—
1227	C₄×D₄	—	53	1	no	—
1228	C₄×D₄	—	53	1	no	—
1229	C₄×D₄	—	53	1	no	—
1230	C₄×D₄	—	53	1	no	—
1231	C₄×D₄	—	53	1	no	—
1232	C₄×D₄	—	53	1	no	—
1233	C₄×D₄	—	53	1	no	—
1234	C₄×D₄	—	53	1	no	—
1235	C₄×D₄	—	53	1	no	—
1236	C₄×D₄	—	53	1	no	—
1237	C₄×D₄	—	53	1	no	—
1238	C₄×D₄	—	53	1	no	—
1239	C₄×D₄	—	53	1	no	—
1240	C₄×D₄	—	53	1	no	—
1241	C₄×D₄	—	106	1	no	—
1242	C₄×D₄	—	106	1	no	—
1243	C₄×D₄	—	106	1	no	—
1244	C₄×D₄	—	106	1	no	—
1245	C₄×D₄	—	106	1	no	—
1246	C₄×D₄	—	106	1	no	—
1247	C₄×D₄	—	106	1	no	—
1248	C₄×D₄	—	106	1	no	—
1249	C₄×D₄	—	106	1	no	—
1250	C₄×D₄	—	106	1	no	—
1251	C₄×D₄	—	106	1	no	—
1252	C₄×D₄	—	106	1	no	—
1253	C₄×D₄	—	106	1	no	—
1254	C₄×D₄	—	106	1	no	—
1255	C₄×D₄	—	106	1	no	—
1256	C₄×D₄	—	106	1	no	—
1257	C₄×D₄	—	106	1	no	—
1258	C₄×D₄	—	106	1	no	—
1259	C₄×D₄	—	106	1	no	—
1260	C₄×D₄	—	106	1	no	—
1261	C₄×D₄	—	106	1	no	—
1262	C₄×D₄	—	106	1	no	—
1263	C₄×D₄	—	106	1	no	—
1264	C₄×D₄	—	106	1	no	—
1265	C₄×D₄	—	106	1	no	—
1266	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1267	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1268	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1269	#117	—	53	1	no	—
1270	#117	—	53	1	no	—
1271	#117	—	53	1	no	—
1272	#117	—	53	1	no	—
1273	#117	—	106	1	no	—
1274	#117	—	106	1	no	—
1275	#117	—	106	1	no	—
1276	#117	—	106	1	no	—
1277	#117	—	106	1	no	—
1278	#117	—	106	1	no	—
1279	#117	C₂²×D₅₃	1	1	yes	characteristic
1280	C₂×C₄⋊C₄	—	53	1	no	—
1281	C₂×C₄⋊C₄	—	53	1	no	—
1282	C₂×C₄⋊C₄	—	53	1	no	—
1283	C₂×C₄⋊C₄	—	106	1	no	—
1284	C₂×C₄⋊C₄	—	106	1	no	—
1285	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1286	C₂×C₂²⋊C₄	—	2	1	no	—
1287	C₂×C₂²⋊C₄	—	106	1	no	—
1288	C₂×C₂²⋊C₄	—	106	1	no	—
1289	C₂×C₂²⋊C₄	—	106	1	no	—
1290	C₂×C₂²⋊C₄	—	106	1	no	—
1291	C₂×C₂²⋊C₄	—	106	1	no	—
1292	C₂×C₂²⋊C₄	—	106	1	no	—
1293	C₂×C₂²⋊C₄	—	106	1	no	—
1294	C₂×C₄²	—	53	1	no	—
1295	C₂×C₄²	—	53	1	no	—
1296	C₂×C₄²	—	53	1	no	—
1297	C₂×C₄²	—	106	1	no	—
1298	C₂×C₄²	—	106	1	no	—
1299	#107	—	53	1	no	—
1300	#107	—	53	1	no	—
1301	#107	—	53	1	no	—
1302	#107	—	53	1	no	—
1303	#107	—	53	1	no	—
1304	#107	—	53	1	no	—
1305	#107	—	53	1	no	—
1306	#107	—	53	1	no	—
1307	#107	C₂²×D₅₃	1	1	yes	characteristic
1308	#107	C₂²×D₅₃	1	1	yes	characteristic
1309	#106	—	53	1	no	—
1310	#106	—	53	1	no	—
1311	#106	—	53	1	no	—
1312	#106	—	53	1	no	—
1313	#106	—	53	1	no	—
1314	#106	C₂²×D₅₃	1	1	yes	characteristic
1315	C₄⋊C₈	—	53	1	no	—
1316	C₄⋊C₈	—	53	1	no	—
1317	C₄⋊C₈	—	53	1	no	—
1318	C₄⋊C₈	—	53	1	no	—
1319	C₄⋊C₈	—	53	1	no	—
1320	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1321	#103	—	53	1	no	—
1322	#103	—	53	1	no	—
1323	#103	—	53	1	no	—
1324	#103	—	53	1	no	—
1325	#103	—	53	1	no	—
1326	#103	C₂²×D₅₃	1	1	yes	characteristic
1327	#103	C₂²×D₅₃	1	1	yes	characteristic
1328	#103	C₂²×D₅₃	1	1	yes	characteristic
1329	#102	—	53	1	no	—
1330	#102	—	53	1	no	—
1331	#102	—	53	1	no	—
1332	#102	—	53	1	no	—
1333	#102	—	53	1	no	—
1334	#102	—	53	1	no	—
1335	#102	—	53	1	no	—
1336	#102	—	53	1	no	—
1337	#102	—	53	1	no	—
1338	#102	—	53	1	no	—
1339	#102	—	53	1	no	—
1340	#102	—	53	1	no	—
1341	#102	—	53	1	no	—
1342	#102	—	53	1	no	—
1343	#102	—	53	1	no	—
1344	#102	—	53	1	no	—
1345	#102	—	53	1	no	—
1346	#102	C₂²×D₅₃	1	1	yes	characteristic
1347	#102	C₂²×D₅₃	1	1	yes	characteristic
1348	#102	C₂²×D₅₃	1	1	yes	characteristic
1349	#102	C₂²×D₅₃	1	1	yes	characteristic
1350	#102	C₂²×D₅₃	1	1	yes	characteristic
1351	#102	C₂²×D₅₃	1	1	yes	characteristic
1352	#102	C₂²×D₅₃	1	1	yes	characteristic
1353	C₂²⋊C₈	—	53	1	no	—
1354	C₂²⋊C₈	—	53	1	no	—
1355	C₂²⋊C₈	—	53	1	no	—
1356	C₂²⋊C₈	—	53	1	no	—
1357	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1358	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1359	C₄×C₈	—	53	1	no	—
1360	C₄×C₈	—	53	1	no	—
1361	C₄×C₈	—	53	1	no	—
1362	C₄×C₈	—	53	1	no	—
1363	C₄×C₈	—	53	1	no	—
1364	C₄×C₈	—	53	1	no	—
1365	C₄×C₈	—	53	1	no	—
1366	C₄×C₈	—	53	1	no	—
1367	C₄×C₈	—	53	1	no	—
1368	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1369	C₂⁴	—	2	1	no	—
1370	C₂⁴	—	106	1	no	—
1371	C₂⁴	—	106	1	no	—
1372	C₂⁴	—	106	1	no	—
1373	#41	—	2	2	no	—
1374	#41	—	4	1	no	—
1375	#41	—	106	2	no	—
1376	#41	—	106	4	no	—
1377	#41	—	424	2	no	—
1378	#41	—	424	2	no	—
1379	#41	—	212	1	no	—
1380	C₂×Q₈	—	53	1	no	—
1381	C₂×Q₈	—	53	1	no	—
1382	C₂×Q₈	—	106	1	no	—
1383	C₂×Q₈	—	106	1	no	—
1384	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1385	C₂×D₄	—	2	2	no	—
1386	C₂×D₄	—	2	1	no	—
1387	C₂×D₄	—	2	1	no	—
1388	C₂×D₄	—	2	1	no	—
1389	C₂×D₄	—	2	1	no	—
1390	C₂×D₄	—	2	1	no	—
1391	C₂×D₄	—	4	1	no	—
1392	C₂×D₄	—	53	1	no	—
1393	C₂×D₄	—	53	1	no	—
1394	C₂×D₄	—	53	1	no	—
1395	C₂×D₄	—	53	1	no	—
1396	C₂×D₄	—	53	1	no	—
1397	C₂×D₄	—	106	2	no	—
1398	C₂×D₄	—	106	1	no	—
1399	C₂×D₄	—	106	1	no	—
1400	C₂×D₄	—	106	1	no	—
1401	C₂×D₄	—	106	1	no	—
1402	C₂×D₄	—	106	1	no	—
1403	C₂×D₄	—	106	1	no	—
1404	C₂×D₄	—	106	1	no	—
1405	C₂×D₄	—	106	2	no	—
1406	C₂×D₄	—	106	2	no	—
1407	C₂×D₄	—	106	1	no	—
1408	C₂×D₄	—	106	1	no	—
1409	C₂×D₄	—	106	1	no	—
1410	C₂×D₄	—	106	1	no	—
1411	C₂×D₄	—	106	1	no	—
1412	C₂×D₄	—	106	1	no	—
1413	C₂×D₄	—	212	1	no	—
1414	C₂×D₄	—	212	1	no	—
1415	C₂×D₄	—	212	1	no	—
1416	C₂×D₄	—	212	4	no	—
1417	C₂×D₄	—	212	4	no	—
1418	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
1419	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1420	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1421	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1422	C₂²×C₄	—	2	1	no	—
1423	C₂²×C₄	—	2	1	no	—
1424	C₂²×C₄	—	2	1	no	—
1425	C₂²×C₄	—	2	1	no	—
1426	C₂²×C₄	—	53	1	no	—
1427	C₂²×C₄	—	53	1	no	—
1428	C₂²×C₄	—	53	1	no	—
1429	C₂²×C₄	—	53	1	no	—
1430	C₂²×C₄	—	53	1	no	—
1431	C₂²×C₄	—	53	1	no	—
1432	C₂²×C₄	—	53	1	no	—
1433	C₂²×C₄	—	106	1	no	—
1434	C₂²×C₄	—	106	1	no	—
1435	C₂²×C₄	—	106	1	no	—
1436	C₂²×C₄	—	106	1	no	—
1437	C₂²×C₄	—	106	1	no	—
1438	C₂²×C₄	—	106	1	no	—
1439	C₂²×C₄	—	106	1	no	—
1440	C₂²×C₄	—	106	1	no	—
1441	C₂²×C₄	—	106	1	no	—
1442	C₂²×C₄	—	106	1	no	—
1443	C₂²×C₄	—	106	1	no	—
1444	C₂²×C₄	—	106	1	no	—
1445	C₂²×C₄	—	106	1	no	—
1446	C₂²×C₄	—	106	1	no	—
1447	C₂²×C₄	—	106	1	no	—
1448	C₂²×C₄	—	106	1	no	—
1449	C₂²×C₄	—	106	1	no	—
1450	C₂²×C₄	—	106	1	no	—
1451	C₂²×C₄	—	424	2	no	—
1452	C₂²×C₄	—	424	2	no	—
1453	C₂²×C₄	—	424	2	no	—
1454	C₂²×C₄	—	424	2	no	—
1455	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1456	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1457	Q₁₆	—	106	2	no	—
1458	SD₁₆	—	4	1	no	—
1459	SD₁₆	—	106	2	no	—
1460	SD₁₆	—	106	2	no	—
1461	SD₁₆	—	212	1	no	—
1462	SD₁₆	—	212	1	no	—
1463	SD₁₆	—	212	1	no	—
1464	D₈	—	2	2	no	—
1465	D₈	—	4	1	no	—
1466	D₈	—	53	4	no	—
1467	D₈	—	106	2	no	—
1468	D₈	—	106	2	no	—
1469	D₈	—	106	2	no	—
1470	D₈	—	106	2	no	—
1471	D₈	—	106	2	no	—
1472	D₈	—	212	1	no	—
1473	C₂×C₈	—	4	1	no	—
1474	C₂×C₈	—	4	1	no	—
1475	C₂×C₈	—	53	1	no	—
1476	C₂×C₈	—	53	1	no	—
1477	C₂×C₈	—	53	1	no	—
1478	C₂×C₈	—	53	1	no	—
1479	C₂×C₈	—	106	2	no	—
1480	C₂×C₈	—	106	2	no	—
1481	C₂×C₈	—	106	2	no	—
1482	C₂×C₈	—	212	1	no	—
1483	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1484	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1485	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1486	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	53	1	no	—
1492	C₄⋊C₄	—	53	1	no	—
1493	C₄⋊C₄	—	53	1	no	—
1494	C₄⋊C₄	—	53	1	no	—
1495	C₄⋊C₄	—	53	1	no	—
1496	C₄⋊C₄	—	53	1	no	—
1497	C₄⋊C₄	—	53	1	no	—
1498	C₄⋊C₄	—	53	1	no	—
1499	C₄⋊C₄	—	53	1	no	—
1500	C₄⋊C₄	—	106	1	no	—
1501	C₄⋊C₄	—	106	1	no	—
1502	C₄⋊C₄	—	106	1	no	—
1503	C₄⋊C₄	—	106	1	no	—
1504	C₄⋊C₄	—	106	1	no	—
1505	C₄⋊C₄	—	106	1	no	—
1506	C₄⋊C₄	—	106	1	no	—
1507	C₄⋊C₄	—	106	1	no	—
1508	C₄⋊C₄	—	106	1	no	—
1509	C₄⋊C₄	—	106	1	no	—
1510	C₄⋊C₄	—	106	1	no	—
1511	C₄⋊C₄	—	106	1	no	—
1512	C₄⋊C₄	—	106	1	no	—
1513	C₄⋊C₄	—	106	1	no	—
1514	C₄⋊C₄	—	106	1	no	—
1515	C₄⋊C₄	—	106	1	no	—
1516	C₄⋊C₄	—	106	1	no	—
1517	C₄⋊C₄	—	106	1	no	—
1518	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1519	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1520	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1521	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1522	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	53	1	no	—
1533	C₂²⋊C₄	—	53	1	no	—
1534	C₂²⋊C₄	—	53	1	no	—
1535	C₂²⋊C₄	—	53	1	no	—
1536	C₂²⋊C₄	—	106	1	no	—
1537	C₂²⋊C₄	—	106	1	no	—
1538	C₂²⋊C₄	—	106	1	no	—
1539	C₂²⋊C₄	—	106	1	no	—
1540	C₂²⋊C₄	—	106	1	no	—
1541	C₂²⋊C₄	—	106	1	no	—
1542	C₂²⋊C₄	—	106	1	no	—
1543	C₂²⋊C₄	—	106	1	no	—
1544	C₂²⋊C₄	—	106	1	no	—
1545	C₂²⋊C₄	—	106	1	no	—
1546	C₂²⋊C₄	—	106	1	no	—
1547	C₂²⋊C₄	—	106	1	no	—
1548	C₂²⋊C₄	—	106	1	no	—
1549	C₂²⋊C₄	—	106	1	no	—
1550	C₂²⋊C₄	—	106	1	no	—
1551	C₂²⋊C₄	—	106	1	no	—
1552	C₂²⋊C₄	—	106	1	no	—
1553	C₂²⋊C₄	—	106	1	no	—
1554	C₂²⋊C₄	—	106	1	no	—
1555	C₂²⋊C₄	—	106	1	no	—
1556	C₂²⋊C₄	—	106	1	no	—
1557	C₂²⋊C₄	—	106	1	no	—
1558	C₂²⋊C₄	—	106	1	no	—
1559	C₂²⋊C₄	—	106	1	no	—
1560	C₂²⋊C₄	—	106	1	no	—
1561	C₂²⋊C₄	—	106	1	no	—
1562	C₂²⋊C₄	—	106	1	no	—
1563	C₂²⋊C₄	—	106	1	no	—
1564	C₂²⋊C₄	—	106	1	no	—
1565	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1566	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1567	C₄²	—	2	1	no	—
1568	C₄²	—	53	1	no	—
1569	C₄²	—	53	1	no	—
1570	C₄²	—	53	1	no	—
1571	C₄²	—	53	1	no	—
1572	C₄²	—	53	1	no	—
1573	C₄²	—	53	1	no	—
1574	C₄²	—	53	1	no	—
1575	C₄²	—	53	1	no	—
1576	C₄²	—	53	1	no	—
1577	C₄²	—	106	1	no	—
1578	C₄²	—	106	1	no	—
1579	C₄²	—	106	1	no	—
1580	C₄²	—	106	1	no	—
1581	C₄²	—	106	1	no	—
1582	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1583	C₂³	—	2	1	no	—
1584	C₂³	—	2	1	no	—
1585	C₂³	—	2	1	no	—
1586	C₂³	—	4	2	no	—
1587	C₂³	—	4	2	no	—
1588	C₂³	—	8	1	no	—
1589	C₂³	—	53	1	no	—
1590	C₂³	—	106	1	no	—
1591	C₂³	—	106	1	no	—
1592	C₂³	—	106	1	no	—
1593	C₂³	—	424	1	no	—
1594	C₂³	—	424	1	no	—
1595	C₂³	—	424	1	no	—
1596	C₂³	—	212	2	no	—
1597	C₂³	—	212	2	no	—
1598	C₂³	—	212	2	no	—
1599	C₂³	—	212	2	no	—
1600	C₂³	—	212	2	no	—
1601	C₂³	—	212	2	no	—
1602	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1603	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1604	Q₈	—	2	1	no	—
1605	Q₈	—	2	1	no	—
1606	Q₈	—	106	2	no	—
1607	Q₈	—	106	1	no	—
1608	Q₈	—	106	1	no	—
1609	Q₈	—	424	1	no	—
1610	Q₈	—	424	1	no	—
1611	D₄	—	2	2	no	—
1612	D₄	—	2	1	no	—
1613	D₄	—	2	1	no	—
1614	D₄	—	2	1	no	—
1615	D₄	—	2	1	no	—
1616	D₄	—	2	1	no	—
1617	D₄	—	4	2	no	—
1618	D₄	—	4	2	no	—
1619	D₄	—	4	2	no	—
1620	D₄	—	8	1	no	—
1621	D₄	—	8	1	no	—
1622	D₄	—	53	4	no	—
1623	D₄	—	53	2	no	—
1624	D₄	—	106	2	no	—
1625	D₄	—	106	1	no	—
1626	D₄	—	106	1	no	—
1627	D₄	—	106	1	no	—
1628	D₄	—	106	1	no	—
1629	D₄	—	106	1	no	—
1630	D₄	—	424	1	no	—
1631	D₄	—	424	1	no	—
1632	D₄	—	424	1	no	—
1633	D₄	—	424	1	no	—
1634	D₄	—	212	2	no	—
1635	D₄	—	212	2	no	—
1636	D₄	—	212	2	no	—
1637	D₄	—	212	2	no	—
1638	D₄	—	212	2	no	—
1639	D₄	—	212	2	no	—
1640	D₄	—	212	2	no	—
1641	D₄	—	212	2	no	—
1642	D₄	—	212	2	no	—
1643	D₄	#41×D₅₃	1	2	yes	—
1644	C₂×C₄	—	2	1	no	—
1645	C₂×C₄	—	2	1	no	—
1646	C₂×C₄	—	2	1	no	—
1647	C₂×C₄	—	2	1	no	—
1648	C₂×C₄	—	2	1	no	—
1649	C₂×C₄	—	2	1	no	—
1650	C₂×C₄	—	2	1	no	—
1651	C₂×C₄	—	2	1	no	—
1652	C₂×C₄	—	2	1	no	—
1653	C₂×C₄	—	4	2	no	—
1654	C₂×C₄	—	8	1	no	—
1655	C₂×C₄	—	8	1	no	—
1656	C₂×C₄	—	8	1	no	—
1657	C₂×C₄	—	53	1	no	—
1658	C₂×C₄	—	53	1	no	—
1659	C₂×C₄	—	53	1	no	—
1660	C₂×C₄	—	53	1	no	—
1661	C₂×C₄	—	53	1	no	—
1662	C₂×C₄	—	53	1	no	—
1663	C₂×C₄	—	53	1	no	—
1664	C₂×C₄	—	106	2	no	—
1665	C₂×C₄	—	106	2	no	—
1666	C₂×C₄	—	106	2	no	—
1667	C₂×C₄	—	106	2	no	—
1668	C₂×C₄	—	106	2	no	—
1669	C₂×C₄	—	106	2	no	—
1670	C₂×C₄	—	106	1	no	—
1671	C₂×C₄	—	106	1	no	—
1672	C₂×C₄	—	106	1	no	—
1673	C₂×C₄	—	106	1	no	—
1674	C₂×C₄	—	106	1	no	—
1675	C₂×C₄	—	106	1	no	—
1676	C₂×C₄	—	106	1	no	—
1677	C₂×C₄	—	424	1	no	—
1678	C₂×C₄	—	424	1	no	—
1679	C₂×C₄	—	424	1	no	—
1680	C₂×C₄	—	424	1	no	—
1681	C₂×C₄	—	424	1	no	—
1682	C₂×C₄	—	424	1	no	—
1683	C₂×C₄	—	424	1	no	—
1684	C₂×C₄	—	424	1	no	—
1685	C₂×C₄	—	424	1	no	—
1686	C₂×C₄	—	212	2	no	—
1687	C₂×C₄	—	212	2	no	—
1688	C₂×C₄	—	212	2	no	—
1689	C₂×C₄	—	212	2	no	—
1690	C₂×C₄	—	212	2	no	—
1691	C₂×C₄	—	212	2	no	—
1692	C₂×C₄	—	212	2	no	—
1693	C₂×C₄	—	212	2	no	—
1694	C₂×C₄	—	212	2	no	—
1695	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1696	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1697	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1698	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1699	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1700	C₈	—	2	1	no	—
1701	C₈	—	2	1	no	—
1702	C₈	—	2	1	no	—
1703	C₈	—	2	1	no	—
1704	C₈	—	53	2	no	—
1705	C₈	—	106	1	no	—
1706	C₈	—	106	1	no	—
1707	C₈	—	106	1	no	—
1708	C₂²	—	2	1	no	—
1709	C₂²	—	2	1	no	—
1710	C₂²	—	2	1	no	—
1711	C₂²	—	2	1	no	—
1712	C₂²	—	2	1	no	—
1713	C₂²	—	2	2	no	—
1714	C₂²	—	4	1	no	—
1715	C₂²	—	4	1	no	—
1716	C₂²	—	4	1	no	—
1717	C₂²	—	4	1	no	—
1718	C₂²	—	4	1	no	—
1719	C₂²	—	4	1	no	—
1720	C₂²	—	4	1	no	—
1721	C₂²	—	4	1	no	—
1722	C₂²	—	8	4	no	—
1723	C₂²	—	53	2	no	—
1724	C₂²	—	106	1	no	—
1725	C₂²	—	106	1	no	—
1726	C₂²	—	106	2	no	—
1727	C₂²	—	424	4	no	—
1728	C₂²	—	424	4	no	—
1729	C₂²	—	424	4	no	—
1730	C₂²	—	212	1	no	—
1731	C₂²	—	212	1	no	—
1732	C₂²	—	212	1	no	—
1733	C₂²	—	212	1	no	—
1734	C₂²	—	212	1	no	—
1735	C₂²	—	212	1	no	—
1736	C₂²	—	212	1	no	—
1737	C₂²	—	212	1	no	—
1738	C₂²	#135×D₅₃	1	2	yes	—
1739	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1740	C₄	—	2	1	no	—
1741	C₄	—	2	1	no	—
1742	C₄	—	2	1	no	—
1743	C₄	—	2	1	no	—
1744	C₄	—	4	1	no	—
1745	C₄	—	4	1	no	—
1746	C₄	—	4	1	no	—
1747	C₄	—	4	1	no	—
1748	C₄	—	4	1	no	—
1749	C₄	—	53	2	no	—
1750	C₄	—	53	2	no	—
1751	C₄	—	106	1	no	—
1752	C₄	—	106	1	no	—
1753	C₄	—	106	1	no	—
1754	C₄	—	106	1	no	—
1755	C₄	—	106	1	no	—
1756	C₄	—	212	1	no	—
1757	C₄	—	212	1	no	—
1758	C₄	—	212	1	no	—
1759	C₄	—	212	1	no	—
1760	C₄	—	212	1	no	—
1761	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1762	C₄	#16811458	1	1	yes	characteristic
1763	C₂	—	2	2	no	—
1764	C₂	—	4	1	no	—
1765	C₂	—	4	2	no	—
1766	C₂	—	8	1	no	—
1767	C₂	—	8	1	no	—
1768	C₂	—	106	2	no	—
1769	C₂	—	424	1	no	—
1770	C₂	—	424	1	no	—
1771	C₂	—	212	2	no	—
1772	C₂	#20288199	1	1	yes	characteristic
1773	C₂	C₂×#135×D₅₃	1	1	yes	characteristic
1774	C₂	#576×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3297	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3297	D₅₃
hypocenter	C₅₃	#61431
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3297

Complements

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

N	H ≅ G/N	type
1. #20288322	C₂	semidirect
2. #20288320	C₂	semidirect
3. #20287722	C₂	semidirect
4. #20287577	C₂	semidirect
5. #20287376	C₂	semidirect
6. #20287372	C₂	semidirect
7. #20287111	C₂	semidirect
8. #20287110	C₂	semidirect
9. #20287102	C₂	semidirect
10. #20286567	C₂	semidirect
11. #20286566	C₂	semidirect
12. #20286560	C₂	semidirect
13. #20286535	C₂	semidirect
14. #20286534	C₂	semidirect
15. #20286398	C₂	semidirect
16. #20286396	C₂	semidirect
17. #20286385	C₂	semidirect
18. #20285289	C₂	semidirect
19. #20285284	C₂	semidirect
20. #20285278	C₂	semidirect
21. #20284770	C₂	semidirect
22. #20284768	C₂	semidirect
23. #20284767	C₂	semidirect
24. #20284765	C₂	semidirect
25. #20284761	C₂	semidirect
26. #20284757	C₂	semidirect
27. C₈×#11719947	C₂	semidirect
28. #20283483	C₂	semidirect
29. C₂×#16810703	C₂	semidirect
30. C₄×D₈×D₅₃	C₂	semidirect
31. C₅₃×#3297	C₂	semidirect
35. #16811356	C₂²	semidirect
36. #16811355	C₂²	semidirect
37. #16811332	C₂²	semidirect
39. #16811329	C₂²	semidirect
41. #16811320	C₂²	semidirect
42. #16811319	C₂²	semidirect
44. #16811317	C₂²	semidirect
50. #16811270	C₂²	semidirect
51. #16811269	C₂²	semidirect
53. #16811261	C₂²	semidirect
57. #16811168	C₂²	semidirect
58. #16811168	C₂²	semidirect
59. #16811159	C₂²	semidirect
60. #16811158	C₂²	semidirect
62. #16811154	C₂²	semidirect
63. #16811152	C₂²	semidirect
69. #41×Dic₅₃	C₂²	semidirect
70. #16811091	C₂²	semidirect
72. C₂×D₄×Dic₅₃	C₂²	semidirect
73. C₂×#13133179	C₂²	semidirect
76. C₄×D₄×D₅₃	C₂²	semidirect
77. C₄×D₄×D₅₃	C₂²	semidirect
78. #16811027	C₂²	semidirect
79. #16811023	C₂²	semidirect
80. #16811022	C₂²	semidirect
81. #16811005	C₂²	semidirect
82. #16811004	C₂²	semidirect
84. #16810979	C₂²	semidirect
85. #16810978	C₂²	semidirect
86. #16810976	C₂²	semidirect
87. #16810968	C₂²	semidirect
88. #16810968	C₂²	semidirect
89. #16810960	C₂²	semidirect
90. #16810959	C₂²	semidirect
91. #16810957	C₂²	semidirect
92. #16810948	C₂²	semidirect
93. #16810947	C₂²	semidirect
94. #16810944	C₂²	semidirect
95. #16810943	C₂²	semidirect
96. #16810941	C₂²	semidirect
97. #16810940	C₂²	semidirect
98. #16810939	C₂²	semidirect
99. #16810926	C₂²	semidirect
100. #16810926	C₂²	semidirect
101. #16810924	C₂²	semidirect
102. #16810923	C₂²	semidirect
103. #16810921	C₂²	semidirect
104. #16810921	C₂²	semidirect
105. #16810920	C₂²	semidirect
106. #16810917	C₂²	semidirect
107. #16810916	C₂²	semidirect
108. #16810912	C₂²	semidirect
109. #16810911	C₂²	semidirect
110. #16810863	C₂²	semidirect
111. #16810862	C₂²	semidirect
112. #16810859	C₂²	semidirect
115. #16810857	C₂²	semidirect
116. #16810857	C₂²	semidirect
117. #16810855	C₂²	semidirect
118. #16810852	C₂²	semidirect
119. #16810851	C₂²	semidirect
120. #16810841	C₂²	semidirect
121. #16810841	C₂²	semidirect
122. #16810839	C₂²	semidirect
123. #16810838	C₂²	semidirect
124. #16810836	C₂²	semidirect
125. #16810836	C₂²	semidirect
126. #16810835	C₂²	semidirect
127. #16810822	C₂²	semidirect
128. #16810821	C₂²	semidirect
131. #16810775	C₂²	semidirect
132. #16810774	C₂²	semidirect
133. #16810773	C₂²	semidirect
134. #16810772	C₂²	semidirect
135. #16810770	C₂²	semidirect
136. #16810768	C₂²	semidirect
137. #16810766	C₂²	semidirect
141. C₈×Dic₁₀₆	C₂²	semidirect
142. #16810747	C₂²	semidirect
143. #16810715	C₂²	semidirect
144. #16810715	C₂²	semidirect
145. #16810714	C₂²	semidirect
146. #16810714	C₂²	semidirect
147. #16810714	C₂²	semidirect
148. SD₁₆×Dic₅₃	C₂²	semidirect
149. #16810710	C₂²	semidirect
150. #16810708	C₂²	semidirect
151. #16810708	C₂²	semidirect
152. #16810708	C₂²	semidirect
153. C₄×D₄₂₄	C₂²	semidirect
154. D₈×Dic₅₃	C₂²	semidirect
155. D₈×Dic₅₃	C₂²	semidirect
156. #16810705	C₂²	semidirect
157. #16810705	C₂²	semidirect
159. C₄×#11719922	C₂²	semidirect
163. #16810703	C₂²	semidirect
164. #16810703	C₂²	semidirect
165. #16810703	C₂²	semidirect
166. #16810703	C₂²	semidirect
167. #16810703	C₂²	semidirect
168. #16810703	C₂²	semidirect
169. #16810703	C₂²	semidirect
170. D₄×#88322	C₂²	semidirect
172. C₈×C₂²⋊D₅₃	C₂²	semidirect
174. #16810686	C₂²	semidirect
175. #16810675	C₂²	semidirect
176. #16810673	C₂²	semidirect
177. #16810673	C₂²	semidirect
178. #16810659	C₂²	semidirect
179. C₂×#13133150	C₂²	semidirect
180. #107×D₅₃	C₂²	semidirect
181. #16810620	C₂²	semidirect
182. C₂×#13133139	C₂²	semidirect
183. #102×D₅₃	C₂²	semidirect
184. #102×D₅₃	C₂²	semidirect
185. C₂×C₈×Dic₅₃	C₂²	semidirect
186. C₂×C₈×Dic₅₃	C₂²	semidirect
187. C₄×C₈×D₅₃	C₂²	semidirect
188. C₅₃×#553	C₂²	semidirect
189. C₅₃×#546	C₂²	semidirect
190. C₅₃×#488	C₂²	semidirect
191. C₅₃×#484	C₂²	semidirect
192. C₅₃×#482	C₂²	semidirect
193. C₅₃×#478	C₂²	semidirect
194. C₅₃×#466	C₂²	semidirect
195. C₅₃×#465	C₂²	semidirect
196. C₅₃×#463	C₂²	semidirect
197. C₅₃×#449	C₂²	semidirect
199. C₄×D₈×C₅₃	C₂²	semidirect
200. C₈×D₄×C₅₃	C₂²	semidirect
201. C₅₃×#416	C₂²	semidirect
202. C₂×#102×C₅₃	C₂²	semidirect
622. #11719922	#41	semidirect
760. C₂²⋊D₅₃	#135	semidirect
888. #3297	D₅₃	semidirect
933. #553	C₂×D₅₃	semidirect
943. #546	C₂×D₅₃	semidirect
976. #488	C₂×D₅₃	semidirect
982. #484	C₂×D₅₃	semidirect
986. #482	C₂×D₅₃	semidirect
998. #478	C₂×D₅₃	semidirect
1010. #466	C₂×D₅₃	semidirect
1014. #465	C₂×D₅₃	semidirect
1022. #463	C₂×D₅₃	semidirect
1034. #449	C₂×D₅₃	semidirect
1068. C₄×D₈	C₂×D₅₃	semidirect
1074. C₈×D₄	C₂×D₅₃	semidirect
1082. #416	C₂×D₅₃	semidirect
1086. C₂×#102	C₂×D₅₃	semidirect
1090. C₅₃	#61431	semidirect

Maximal subgroups

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

subgroup	index
#20288322	2
#20288320	2
#20287722	2
#20287577	2
#20287376	2
#20287372	2
#20287111	2
#20287110	2
#20287102	2
#20286567	2
#20286566	2
#20286560	2
#20286535	2
#20286534	2
#20286398	2
#20286396	2
#20286385	2
#20285289	2
#20285284	2
#20285278	2
#20284770	2
#20284768	2
#20284767	2
#20284765	2
#20284761	2
#20284757	2
C₈×#11719947	2
#20283483	2
C₂×#16810703	2
C₄×D₈×D₅₃	2
C₅₃×#3297	2
#61431	53