Subgroups — #28292662

Order 13568.

7286 conjugacy classes of subgroups.

The subgroup lattice has 1436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288465	C₂	1	4	yes	maximal, complemented
2	#20288459	C₂	1	4	yes	maximal, complemented
3	#20288448	C₂	1	4	yes	maximal, complemented
4	#20288442	C₂	1	4	yes	maximal, complemented
5	#20288430	C₂	1	4	yes	maximal, complemented
6	#20288420	C₂	1	4	yes	maximal, complemented
7	#20288409	C₂	1	4	yes	maximal, complemented
8	#20288401	C₂	1	4	yes	maximal, complemented
9	#20288271	C₂	1	8	yes	maximal, complemented
10	#20288267	C₂	1	8	yes	maximal, complemented
11	#20288118	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288105	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288103	C₂	1	2	yes	maximal, complemented
14	#20288042	C₂	1	1	yes	maximal, characteristic, complemented
15	#20288012	C₂	1	1	yes	maximal, characteristic, complemented
16	#20288010	C₂	1	1	yes	maximal, characteristic, complemented
17	#20288008	C₂	1	2	yes	maximal, complemented
18	#525×D₅₃	C₂	1	2	yes	maximal, complemented
19	#20287914	C₂	1	2	yes	maximal, complemented
20	C₂×#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#41×D₅₃	C₂²	1	2	yes	—
23	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
24	#16811342	C₂²	1	8	yes	complemented
25	#16811340	C₂²	1	8	yes	complemented
26	#16811337	C₂²	1	8	yes	complemented
27	#16811335	C₂²	1	8	yes	complemented
28	#16811329	C₂²	1	8	yes	complemented
29	#16811327	C₂²	1	8	yes	complemented
30	#16811324	C₂²	1	8	yes	complemented
31	#16811318	C₂²	1	8	yes	complemented
32	#16811318	C₂²	1	8	yes	complemented
33	#16811316	C₂²	1	8	yes	complemented
34	#16811311	C₂²	1	8	yes	complemented
35	#16811310	C₂²	1	8	yes	complemented
36	#16811309	C₂²	1	8	yes	complemented
37	#16811309	C₂²	1	8	yes	complemented
38	#16811309	C₂²	1	8	yes	complemented
39	#16811307	C₂²	1	8	yes	complemented
40	#16811305	C₂²	1	8	yes	complemented
41	#16811305	C₂²	1	8	yes	complemented
42	#16811303	C₂²	1	8	yes	complemented
43	#16811301	C₂²	1	8	yes	complemented
44	#16811301	C₂²	1	8	yes	complemented
45	#16811300	C₂²	1	8	yes	complemented
46	#16811298	C₂²	1	8	yes	complemented
47	#16811298	C₂²	1	8	yes	complemented
48	#16811298	C₂²	1	8	yes	complemented
49	#16811296	C₂²	1	8	yes	complemented
50	#16811275	C₂²	1	8	yes	complemented
51	#16811271	C₂²	1	8	yes	complemented
52	#16811270	C₂²	1	8	yes	complemented
53	#16811266	C₂²	1	8	yes	complemented
54	#16811265	C₂²	1	8	yes	complemented
55	#16811262	C₂²	1	8	yes	complemented
56	#16811253	C₂²	1	4	yes	complemented
57	#16811252	C₂²	1	4	yes	complemented
58	#16811250	C₂²	1	4	yes	complemented
59	#16811248	C₂²	1	4	yes	—
60	#16811246	C₂²	1	4	yes	complemented
61	#16811244	C₂²	1	4	yes	complemented
62	#16811240	C₂²	1	4	yes	complemented
63	#16811235	C₂²	1	2	yes	complemented
64	#16811233	C₂²	1	4	yes	complemented
65	#16811228	C₂²	1	2	yes	complemented
66	#16811226	C₂²	1	4	yes	complemented
67	#16811220	C₂²	1	4	yes	complemented
68	#16811217	C₂²	1	8	yes	complemented
69	#16811211	C₂²	1	4	yes	complemented
70	#16811208	C₂²	1	8	yes	complemented
71	#16811200	C₂²	1	4	yes	complemented
72	#16811198	C₂²	1	2	yes	complemented
73	#16811193	C₂²	1	2	yes	complemented
74	#16811191	C₂²	1	2	yes	complemented
75	#16811186	C₂²	1	2	yes	complemented
76	#16811181	C₂²	1	4	yes	—
77	#16811180	C₂²	1	1	yes	characteristic, complemented
78	#16811178	C₂²	1	2	yes	complemented
79	#16811178	C₂²	1	2	yes	complemented
80	#16811177	C₂²	1	4	yes	complemented
81	#16811177	C₂²	1	8	yes	complemented
82	#16811176	C₂²	1	2	yes	complemented
83	#16811174	C₂²	1	2	yes	complemented
84	#16811173	C₂²	1	1	yes	characteristic, complemented
85	#16811171	C₂²	1	2	yes	complemented
86	#16811170	C₂²	1	4	yes	complemented
87	#16811169	C₂²	1	2	yes	complemented
88	#16811160	C₂²	1	4	yes	complemented
89	#16811160	C₂²	1	4	yes	complemented
90	#16811159	C₂²	1	4	yes	complemented
91	#16811158	C₂²	1	4	yes	complemented
92	#16811155	C₂²	1	8	yes	complemented
93	#16811155	C₂²	1	4	yes	complemented
94	#16811155	C₂²	1	4	yes	complemented
95	#16811154	C₂²	1	4	yes	complemented
96	#16811153	C₂²	1	8	yes	complemented
97	#16811153	C₂²	1	8	yes	complemented
98	#16811152	C₂²	1	4	yes	complemented
99	#16811151	C₂²	1	8	yes	complemented
100	#16811151	C₂²	1	8	yes	complemented
101	#16811136	C₂²	1	4	yes	—
102	#16811136	C₂²	1	4	yes	complemented
103	#16811135	C₂²	1	2	yes	complemented
104	#16811134	C₂²	1	2	yes	complemented
105	#16811133	C₂²	1	4	yes	—
106	#16811133	C₂²	1	4	yes	complemented
107	#16811132	C₂²	1	8	yes	—
108	#16811132	C₂²	1	8	yes	complemented
109	#16811132	C₂²	1	8	yes	complemented
110	#16811131	C₂²	1	4	yes	complemented
111	#16811130	C₂²	1	2	yes	complemented
112	#16811129	C₂²	1	4	yes	complemented
113	#123×D₅₃	C₂²	1	4	yes	—
114	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
115	#121×D₅₃	C₂²	1	4	yes	complemented
116	#120×D₅₃	C₂²	1	4	yes	—
117	#16811105	C₂²	1	4	yes	complemented
118	#16811102	C₂²	1	8	yes	complemented
119	#16811102	C₂²	1	4	yes	complemented
120	#16811099	C₂²	1	4	yes	complemented
121	#16811095	C₂²	1	8	yes	—
122	#16811095	C₂²	1	4	yes	complemented
123	#41×Dic₅₃	C₂²	1	2	yes	complemented
124	C₄×#11719949	C₂²	1	4	yes	complemented
125	C₄×#11719945	C₂²	1	2	yes	complemented
126	C₄×#11719945	C₂²	1	8	yes	complemented
127	C₄×#11719945	C₂²	1	4	yes	complemented
128	#16811091	C₂²	1	2	yes	complemented
129	#16811091	C₂²	1	4	yes	complemented
130	C₄×#11719947	C₂²	1	4	yes	complemented
131	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
132	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
133	C₂×#13133175	C₂²	1	2	yes	—
134	C₂×#13133174	C₂²	1	1	yes	characteristic
135	C₂×#13133174	C₂²	1	1	yes	characteristic
136	C₂×#13133174	C₂²	1	4	yes	complemented
137	C₂×#13133173	C₂²	1	2	yes	complemented
138	#117×D₅₃	C₂²	1	2	yes	—
139	#117×D₅₃	C₂²	1	4	yes	complemented
140	#117×D₅₃	C₂²	1	4	yes	complemented
141	#117×D₅₃	C₂²	1	4	yes	complemented
142	#117×D₅₃	C₂²	1	4	yes	complemented
143	#117×D₅₃	C₂²	1	4	yes	complemented
144	C₂×C₄⋊C₄×D₅₃	C₂²	1	2	yes	complemented
145	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
146	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#542	C₂²	1	4	yes	complemented
149	C₅₃×#541	C₂²	1	2	yes	complemented
150	C₅₃×#540	C₂²	1	2	yes	complemented
151	C₅₃×#539	C₂²	1	4	yes	complemented
152	C₅₃×#538	C₂²	1	4	yes	complemented
153	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#529	C₂²	1	8	yes	complemented
156	C₅₃×#525	C₂²	1	2	yes	complemented
157	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
158	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
159	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
160	C₂×#11719949	C₂³	1	2	yes	—
161	C₂×#11719949	C₂³	1	4	yes	—
162	C₂×#11719945	C₂³	1	4	yes	—
163	C₂×#11719945	C₂³	1	2	yes	—
164	C₂×#11719945	C₂³	1	8	yes	—
165	C₂×#11719947	C₂³	1	4	yes	—
166	C₂×#11719947	C₂³	1	2	yes	—
167	C₂×#11719947	C₂³	1	4	yes	—
168	#41×D₅₃	—	2	16	no	—
169	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
170	C₂×D₄×D₅₃	C₂³	1	4	yes	—
171	C₂×D₄×D₅₃	C₂³	1	2	yes	—
172	C₂×D₄×D₅₃	C₂³	1	8	yes	—
173	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₄×D₅₃	—	2	8	no	—
175	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
178	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
179	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
180	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
182	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
183	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
184	#13133217	C₂³	1	2	yes	complemented
185	#13133217	C₂³	1	1	yes	characteristic, complemented
186	#13133216	C₂³	1	8	yes	complemented
187	#13133216	C₂³	1	4	yes	complemented
188	#13133215	C₂³	1	8	yes	complemented
189	#13133215	C₂³	1	2	yes	complemented
190	#13133214	C₂³	1	1	yes	characteristic, complemented
191	#13133213	C₂³	1	2	yes	complemented
192	#13133212	C₂³	1	8	yes	complemented
193	#13133212	C₂³	1	8	yes	complemented
194	#13133212	C₂³	1	8	yes	complemented
195	#13133212	C₂³	1	8	yes	complemented
196	#13133210	C₂³	1	8	yes	—
197	#13133210	C₂³	1	8	yes	—
198	#13133210	C₂³	1	8	yes	—
199	#13133210	C₂³	1	8	yes	complemented
200	#13133210	C₂³	1	8	yes	complemented
201	#13133210	C₂³	1	8	yes	complemented
202	#13133209	C₂³	1	2	yes	complemented
203	#13133208	C₂³	1	8	yes	complemented
204	#13133208	C₂³	1	4	yes	complemented
205	#13133208	C₂³	1	4	yes	complemented
206	#13133208	C₂³	1	4	yes	complemented
207	#13133207	C₂³	1	8	yes	complemented
208	#13133207	C₂³	1	8	yes	complemented
209	#13133207	C₂³	1	8	yes	complemented
210	#13133207	C₂³	1	8	yes	complemented
211	#13133207	C₂³	1	8	yes	complemented
212	#13133206	C₂³	1	4	yes	complemented
213	#13133206	C₂³	1	2	yes	complemented
214	#13133205	C₂³	1	2	yes	complemented
215	#13133204	C₂³	1	8	yes	—
216	#13133204	C₂³	1	4	yes	complemented
217	#13133204	C₂³	1	2	yes	complemented
218	#13133203	C₂³	1	8	yes	—
219	#13133203	C₂³	1	8	yes	—
220	#13133203	C₂³	1	8	yes	complemented
221	#13133202	C₂³	1	8	yes	—
222	#13133202	C₂³	1	8	yes	—
223	#13133202	C₂³	1	8	yes	—
224	#13133202	C₂³	1	8	yes	—
225	#13133202	C₂³	1	8	yes	complemented
226	#13133201	C₂³	1	4	yes	—
227	#13133201	C₂³	1	8	yes	complemented
228	#13133200	C₂³	1	4	yes	—
229	#13133199	C₂³	1	8	yes	—
230	#13133199	C₂³	1	8	yes	—
231	#13133199	C₂³	1	8	yes	—
232	#13133199	C₂³	1	8	yes	—
233	#13133199	C₂³	1	8	yes	—
234	#13133199	C₂³	1	8	yes	—
235	#13133199	C₂³	1	8	yes	complemented
236	#13133198	C₂³	1	8	yes	—
237	#13133198	C₂³	1	4	yes	—
238	#13133197	C₂³	1	8	yes	—
239	#13133197	C₂³	1	4	yes	—
240	#13133197	C₂³	1	4	yes	—
241	#13133197	C₂³	1	8	yes	complemented
242	#13133196	C₂³	1	4	yes	—
243	#13133196	C₂³	1	4	yes	—
244	#13133195	C₂³	1	8	yes	—
245	#13133195	C₂³	1	8	yes	—
246	#13133195	C₂³	1	8	yes	—
247	#13133195	C₂³	1	8	yes	—
248	#13133195	C₂³	1	8	yes	complemented
249	#13133195	C₂³	1	8	yes	complemented
250	#13133194	C₂³	1	8	yes	—
251	#13133194	C₂³	1	8	yes	—
252	#13133194	C₂³	1	8	yes	complemented
253	#13133194	C₂³	1	8	yes	complemented
254	#13133193	C₂³	1	8	yes	—
255	#13133193	C₂³	1	4	yes	—
256	#13133193	C₂³	1	4	yes	—
257	#13133192	C₂³	1	4	yes	—
258	#13133192	C₂³	1	4	yes	—
259	#13133191	C₂³	1	4	yes	—
260	#13133191	C₂³	1	4	yes	—
261	#13133190	C₂³	1	8	yes	—
262	#13133190	C₂³	1	8	yes	—
263	#13133190	C₂³	1	8	yes	—
264	#13133190	C₂³	1	8	yes	complemented
265	#13133189	C₂³	1	8	yes	—
266	#13133189	C₂³	1	8	yes	—
267	#13133189	C₂³	1	8	yes	—
268	#13133189	C₂³	1	8	yes	complemented
269	#13133188	C₂³	1	8	yes	—
270	#13133188	C₂³	1	4	yes	—
271	#13133188	C₂³	1	4	yes	—
272	#13133187	C₂³	1	8	yes	—
273	#13133187	C₂³	1	8	yes	—
274	#13133187	C₂³	1	4	yes	—
275	#13133186	C₂³	1	4	yes	—
276	#13133185	C₂³	1	8	yes	—
277	#13133185	C₂³	1	8	yes	—
278	#13133185	C₂³	1	4	yes	—
279	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
280	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
281	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
282	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
283	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
284	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
285	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
286	#13133182	C₂³	1	4	yes	complemented
287	#13133182	C₂³	1	8	yes	complemented
288	#13133182	C₂³	1	4	yes	complemented
289	C₄×D₂₁₂	C₂³	1	8	yes	—
290	C₄×D₂₁₂	C₂³	1	8	yes	—
291	C₄×D₂₁₂	C₂³	1	8	yes	—
292	C₄×D₂₁₂	C₂³	1	4	yes	complemented
293	C₄×D₂₁₂	C₂³	1	4	yes	complemented
294	D₄×Dic₅₃	C₂³	1	8	yes	—
295	D₄×Dic₅₃	C₂³	1	8	yes	—
296	D₄×Dic₅₃	C₂³	1	4	yes	complemented
297	D₄×Dic₅₃	C₂³	1	4	yes	complemented
298	#13133179	C₂³	1	8	yes	—
299	#13133179	C₂³	1	8	yes	—
300	#13133179	C₂³	1	8	yes	—
301	#13133179	C₂³	1	4	yes	complemented
302	#13133179	C₂³	1	4	yes	complemented
303	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
304	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
305	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
306	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
307	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
308	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
309	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
310	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
311	#13133177	C₂³	1	8	yes	—
312	#13133177	C₂³	1	8	yes	—
313	#13133177	C₂³	1	8	yes	—
314	#13133177	C₂³	1	8	yes	—
315	#13133177	C₂³	1	8	yes	—
316	#13133177	C₂³	1	8	yes	complemented
317	#13133176	C₂³	1	2	yes	—
318	#13133176	C₂³	1	2	yes	—
319	#13133176	C₂³	1	2	yes	—
320	#13133176	C₂³	1	4	yes	—
321	#13133176	C₂³	1	8	yes	complemented
322	#13133176	C₂³	1	4	yes	complemented
323	#13133175	C₂³	1	4	yes	—
324	#13133175	C₂³	1	4	yes	—
325	#13133175	C₂³	1	4	yes	—
326	#13133175	C₂³	1	8	yes	—
327	#13133175	C₂³	1	4	yes	—
328	#13133175	C₂³	1	4	yes	—
329	#13133175	C₂³	1	4	yes	—
330	#13133175	C₂³	1	4	yes	—
331	#13133175	C₂³	1	8	yes	complemented
332	#13133174	C₂³	1	8	yes	—
333	#13133174	C₂³	1	8	yes	—
334	#13133174	C₂³	1	4	yes	—
335	#13133174	C₂³	1	2	yes	—
336	#13133174	C₂³	1	2	yes	—
337	#13133174	C₂³	1	4	yes	—
338	#13133174	C₂³	1	4	yes	—
339	#13133174	C₂³	1	2	yes	—
340	#13133174	C₂³	1	2	yes	—
341	#13133174	C₂³	1	8	yes	complemented
342	#13133174	C₂³	1	8	yes	complemented
343	#13133174	C₂³	1	4	yes	complemented
344	#13133174	C₂³	1	4	yes	complemented
345	#13133173	C₂³	1	4	yes	—
346	#13133173	C₂³	1	4	yes	—
347	#13133173	C₂³	1	4	yes	—
348	#13133173	C₂³	1	4	yes	—
349	#13133173	C₂³	1	4	yes	—
350	#13133173	C₂³	1	8	yes	complemented
351	#13133173	C₂³	1	8	yes	complemented
352	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
353	C₂×#11719919	C₂³	1	2	yes	—
354	C₂×#11719919	C₂³	1	2	yes	—
355	C₂×#11719919	C₂³	1	8	yes	complemented
356	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
357	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
358	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
359	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
360	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
361	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
362	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
363	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
364	C₂×#11719921	C₂³	1	8	yes	—
365	C₂×#11719921	C₂³	1	2	yes	—
366	C₂×#11719921	C₂³	1	2	yes	—
367	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
368	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
369	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
370	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
371	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
372	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
373	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
374	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
375	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
376	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
377	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
378	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
379	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
380	C₄²×D₅₃	C₂³	1	2	yes	—
381	C₄²×D₅₃	C₂³	1	4	yes	—
382	C₄²×D₅₃	C₂³	1	2	yes	—
383	C₄²×D₅₃	C₂³	1	2	yes	—
384	C₄²×D₅₃	C₂³	1	4	yes	—
385	C₄²×D₅₃	C₂³	1	2	yes	—
386	C₄²×D₅₃	C₂³	1	4	yes	—
387	C₄²×D₅₃	C₂³	1	4	yes	complemented
388	C₄²×D₅₃	C₂³	1	4	yes	complemented
389	C₂×#41×C₅₃	C₂³	1	2	yes	—
390	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
391	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
392	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
393	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
394	#126×C₅₃	C₂³	1	8	yes	—
395	#126×C₅₃	C₂³	1	8	yes	complemented
396	#125×C₅₃	C₂³	1	8	yes	complemented
397	#125×C₅₃	C₂³	1	2	yes	complemented
398	#124×C₅₃	C₂³	1	8	yes	—
399	#124×C₅₃	C₂³	1	2	yes	complemented
400	#123×C₅₃	C₂³	1	8	yes	—
401	#123×C₅₃	C₂³	1	4	yes	—
402	#123×C₅₃	C₂³	1	8	yes	complemented
403	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
404	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
405	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
406	#121×C₅₃	C₂³	1	8	yes	—
407	#121×C₅₃	C₂³	1	4	yes	—
408	#121×C₅₃	C₂³	1	4	yes	—
409	#120×C₅₃	C₂³	1	4	yes	—
410	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
411	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
412	C₄×D₄×C₅₃	C₂³	1	8	yes	—
413	C₄×D₄×C₅₃	C₂³	1	8	yes	—
414	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
415	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
416	#117×C₅₃	C₂³	1	4	yes	—
417	#117×C₅₃	C₂³	1	2	yes	—
418	#117×C₅₃	C₂³	1	2	yes	—
419	#117×C₅₃	C₂³	1	2	yes	—
420	#117×C₅₃	C₂³	1	4	yes	complemented
421	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
422	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
423	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
424	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
425	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
426	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂³×D₅₃	—	2	4	no	—
428	C₂³×D₅₃	—	4	4	no	—
429	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
430	C₂³×D₅₃	C₂⁴	1	4	yes	—
431	C₂³×D₅₃	C₂⁴	1	4	yes	—
432	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
433	#41×C₅₃	—	2	8	no	—
434	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
435	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
436	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
437	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
438	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
439	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
440	C₂²×C₄×C₅₃	—	2	4	no	—
441	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
442	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
444	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
445	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
446	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
447	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
450	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
451	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
452	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
453	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
454	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
455	C₂²×Dic₅₃	—	2	4	no	—
456	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
457	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
458	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
459	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
460	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
461	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
462	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
463	#11719949	—	2	8	no	—
464	#11719949	—	4	8	no	—
465	Q₈×D₅₃	—	2	8	no	—
466	#11719947	—	2	16	no	—
467	#11719947	—	2	8	no	—
468	#11719947	—	4	8	no	—
469	D₄×D₅₃	—	2	16	no	—
470	D₄×D₅₃	—	2	8	no	—
471	D₄×D₅₃	—	4	16	no	—
472	#11719945	—	2	8	no	—
473	#11719945	—	2	16	no	—
474	#11719945	—	4	16	no	—
475	C₂×D₂₁₂	C₂⁴	1	4	yes	—
476	C₂×D₂₁₂	C₂⁴	1	8	yes	—
477	C₂×D₂₁₂	C₂⁴	1	2	yes	—
478	C₂×D₂₁₂	C₂⁴	1	4	yes	—
479	C₂×C₄×D₅₃	—	2	4	no	—
480	C₂×C₄×D₅₃	—	2	4	no	—
481	C₂×C₄×D₅₃	—	2	4	no	—
482	C₂×C₄×D₅₃	—	2	16	no	—
483	C₂×C₄×D₅₃	—	2	16	no	—
484	C₂×C₄×D₅₃	—	2	16	no	—
485	C₂×C₄×D₅₃	—	4	4	no	—
486	C₂×C₄×D₅₃	—	4	4	no	—
487	C₂×C₄×D₅₃	#41	1	8	yes	complemented
488	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
489	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
490	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
491	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
492	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
493	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
494	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
495	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
496	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
497	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
498	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
499	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
500	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
501	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
502	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
503	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
504	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
505	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
506	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
507	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
508	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
509	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
510	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
511	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
512	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
513	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
514	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
515	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
516	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
517	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
518	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
519	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
520	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
521	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
522	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
523	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
524	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
525	C₄²×C₅₃	C₂⁴	1	2	yes	—
526	C₄²×C₅₃	C₂⁴	1	2	yes	—
527	C₄²×C₅₃	C₂⁴	1	2	yes	—
528	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
529	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
530	C₄²×C₅₃	C₂⁴	1	4	yes	—
531	C₄²×C₅₃	C₂⁴	1	8	yes	—
532	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
533	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
534	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
535	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
536	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
537	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
538	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
539	#11719921	C₂⁴	1	4	yes	—
540	#11719921	C₂⁴	1	4	yes	—
541	#11719921	C₂⁴	1	4	yes	—
542	#11719921	C₂⁴	1	8	yes	—
543	#11719921	C₂⁴	1	4	yes	—
544	#11719921	C₂⁴	1	8	yes	—
545	#11719921	C₂⁴	1	8	yes	—
546	#11719921	C₂⁴	1	8	yes	—
547	#11719921	C₂⁴	1	8	yes	—
548	#11719921	C₂⁴	1	8	yes	—
549	#11719921	C₂⁴	1	8	yes	—
550	#11719921	C₂⁴	1	8	yes	—
551	#11719921	C₂⁴	1	8	yes	—
552	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
553	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
554	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
555	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
556	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
557	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
558	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
559	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
560	#11719919	C₂⁴	1	4	yes	—
561	#11719919	C₂⁴	1	4	yes	—
562	#11719919	C₂⁴	1	4	yes	—
563	#11719919	C₂⁴	1	4	yes	—
564	#11719919	C₂⁴	1	8	yes	—
565	#11719919	C₂⁴	1	8	yes	—
566	#11719919	C₂⁴	1	8	yes	—
567	#11719919	C₂⁴	1	8	yes	—
568	#11719919	C₂⁴	1	8	yes	—
569	#11719919	C₂⁴	1	8	yes	—
570	#11719919	C₂⁴	1	8	yes	—
571	#11719919	C₂⁴	1	8	yes	—
572	#11719919	C₂⁴	1	8	yes	—
573	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
574	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
575	C₄×Dic₅₃	C₂⁴	1	2	yes	—
576	C₄×Dic₅₃	C₂⁴	1	4	yes	—
577	C₄×Dic₅₃	C₂⁴	1	2	yes	—
578	C₄×Dic₅₃	C₂⁴	1	4	yes	—
579	C₄×Dic₅₃	C₂⁴	1	2	yes	—
580	C₄×Dic₅₃	C₂⁴	1	2	yes	—
581	C₄×Dic₅₃	C₂⁴	1	2	yes	—
582	C₄×Dic₅₃	C₂⁴	1	2	yes	—
583	C₄×Dic₅₃	C₂⁴	1	2	yes	—
584	C₄×Dic₅₃	C₂⁴	1	4	yes	—
585	C₄×Dic₅₃	C₂⁴	1	8	yes	—
586	C₄×Dic₅₃	C₂⁴	1	8	yes	—
587	C₄×Dic₅₃	C₂⁴	1	8	yes	—
588	C₄×Dic₅₃	C₂⁴	1	8	yes	—
589	C₂³×C₅₃	—	2	2	no	—
590	C₂³×C₅₃	—	4	2	no	—
591	C₂³×C₅₃	C₂⁵	1	4	yes	—
592	C₂³×C₅₃	C₂⁵	1	2	yes	—
593	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
594	C₂²×D₅₃	—	2	2	no	—
595	C₂²×D₅₃	—	2	4	no	—
596	C₂²×D₅₃	—	2	8	no	—
597	C₂²×D₅₃	—	2	8	no	—
598	C₂²×D₅₃	—	2	8	no	—
599	C₂²×D₅₃	—	4	4	no	—
600	C₂²×D₅₃	—	4	2	no	—
601	C₂²×D₅₃	—	4	8	no	—
602	C₂²×D₅₃	—	4	16	no	—
603	C₂²×D₅₃	C₂×#41	1	4	yes	—
604	C₂²×D₅₃	C₂⁵	1	4	yes	—
605	C₂²×D₅₃	C₂⁵	1	2	yes	—
606	C₂²×D₅₃	C₂⁵	1	2	yes	—
607	Q₈×C₅₃	—	2	4	no	—
608	Q₈×C₅₃	—	4	4	no	—
609	D₄×C₅₃	—	2	8	no	—
610	D₄×C₅₃	—	2	4	no	—
611	D₄×C₅₃	—	4	8	no	—
612	D₄×C₅₃	—	4	4	no	—
613	C₂×C₄×C₅₃	—	2	2	no	—
614	C₂×C₄×C₅₃	—	2	4	no	—
615	C₂×C₄×C₅₃	—	2	4	no	—
616	C₂×C₄×C₅₃	—	2	8	no	—
617	C₂×C₄×C₅₃	—	4	2	no	—
618	C₂×C₄×C₅₃	—	4	2	no	—
619	C₂×C₄×C₅₃	—	4	8	no	—
620	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
621	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
622	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
623	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
624	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
625	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
626	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
627	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
628	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
629	C₂²⋊D₅₃	—	2	8	no	—
630	C₂²⋊D₅₃	—	2	8	no	—
631	C₂²⋊D₅₃	—	2	16	no	—
632	C₂²⋊D₅₃	—	2	8	no	—
633	C₂²⋊D₅₃	—	4	8	no	—
634	C₂²⋊D₅₃	—	4	8	no	—
635	C₂×Dic₅₃	—	2	2	no	—
636	C₂×Dic₅₃	—	2	8	no	—
637	C₂×Dic₅₃	—	2	8	no	—
638	C₂×Dic₅₃	—	4	2	no	—
639	C₂×Dic₅₃	—	4	2	no	—
640	C₂×Dic₅₃	—	4	8	no	—
641	C₂×Dic₅₃	C₂×#41	1	4	yes	—
642	C₂×Dic₅₃	C₂⁵	1	4	yes	—
643	C₂×Dic₅₃	C₂⁵	1	4	yes	—
644	C₂×Dic₅₃	C₂⁵	1	8	yes	—
645	C₂×Dic₅₃	C₂⁵	1	2	yes	—
646	C₂×Dic₅₃	C₂⁵	1	2	yes	—
647	C₂×Dic₅₃	C₂⁵	1	2	yes	—
648	C₂×Dic₅₃	C₂⁵	1	2	yes	—
649	D₂₁₂	—	2	8	no	—
650	D₂₁₂	—	2	16	no	—
651	D₂₁₂	—	2	4	no	—
652	D₂₁₂	—	4	4	no	—
653	C₄×D₅₃	—	2	8	no	—
654	C₄×D₅₃	—	2	8	no	—
655	C₄×D₅₃	—	2	8	no	—
656	C₄×D₅₃	—	2	4	no	—
657	C₄×D₅₃	—	2	4	no	—
658	C₄×D₅₃	—	2	4	no	—
659	C₄×D₅₃	—	2	4	no	—
660	C₄×D₅₃	—	2	8	no	—
661	C₄×D₅₃	—	2	8	no	—
662	C₄×D₅₃	—	2	8	no	—
663	C₄×D₅₃	—	4	4	no	—
664	C₄×D₅₃	—	4	2	no	—
665	C₄×D₅₃	—	4	2	no	—
666	C₄×D₅₃	—	4	8	no	—
667	C₄×D₅₃	—	4	8	no	—
668	C₄×D₅₃	—	4	8	no	—
669	C₄×D₅₃	C₂×#41	1	8	yes	—
670	C₄×D₅₃	C₂×#41	1	8	yes	—
671	Dic₁₀₆	—	2	4	no	—
672	Dic₁₀₆	—	2	8	no	—
673	Dic₁₀₆	—	4	8	no	—
674	Dic₁₀₆	—	4	4	no	—
675	#62814	—	53	1	no	maximal, Sylow
676	C₂²×C₅₃	—	2	2	no	—
677	C₂²×C₅₃	—	2	2	no	—
678	C₂²×C₅₃	—	2	4	no	—
679	C₂²×C₅₃	—	2	8	no	—
680	C₂²×C₅₃	—	2	4	no	—
681	C₂²×C₅₃	—	4	4	no	—
682	C₂²×C₅₃	C₂²×#41	1	2	yes	—
683	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
684	C₂×D₅₃	—	2	8	no	—
685	C₂×D₅₃	—	2	2	no	—
686	C₂×D₅₃	—	2	2	no	—
687	C₂×D₅₃	—	2	4	no	—
688	C₂×D₅₃	—	2	4	no	—
689	C₂×D₅₃	—	2	8	no	—
690	C₂×D₅₃	—	4	4	no	—
691	C₂×D₅₃	—	4	16	no	—
692	C₂×D₅₃	—	8	8	no	—
693	C₂×D₅₃	C₂²×#41	1	4	yes	—
694	C₂×D₅₃	#585	1	4	yes	—
695	C₄×C₅₃	—	2	4	no	—
696	C₄×C₅₃	—	2	2	no	—
697	C₄×C₅₃	—	2	2	no	—
698	C₄×C₅₃	—	2	8	no	—
699	C₄×C₅₃	—	2	4	no	—
700	C₄×C₅₃	—	2	2	no	—
701	C₄×C₅₃	C₂²×#41	1	2	yes	—
702	C₄×C₅₃	C₂²×#41	1	2	yes	—
703	Dic₅₃	—	2	4	no	—
704	Dic₅₃	—	2	2	no	—
705	Dic₅₃	—	2	4	no	—
706	Dic₅₃	—	2	8	no	—
707	Dic₅₃	—	2	2	no	—
708	Dic₅₃	—	2	2	no	—
709	Dic₅₃	C₂²×#41	1	4	yes	—
710	#3495	—	53	4	no	—
711	#3495	—	53	4	no	—
712	#3494	—	53	4	no	—
713	#3494	—	53	4	no	—
714	#3493	—	53	4	no	—
715	#3492	—	53	4	no	—
716	#3491	—	53	4	no	—
717	#3490	—	53	4	no	—
718	#3475	—	53	8	no	—
719	#3475	—	53	8	no	—
720	#3458	—	53	1	no	—
721	#3455	—	53	2	no	—
722	#3455	—	53	1	no	—
723	#3455	D₅₃	1	1	yes	characteristic, complemented
724	#3449	—	53	1	no	—
725	#3444	—	53	1	no	—
726	#3444	—	53	1	no	—
727	#3444	—	53	2	no	—
728	C₂×#525	—	53	2	no	—
729	#3428	—	53	2	no	—
730	C₂²×#117	—	53	1	no	—
731	C₂×C₅₃	—	2	2	no	—
732	C₂×C₅₃	—	4	2	no	—
733	C₂×C₅₃	—	4	4	no	—
734	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
735	C₂×C₅₃	C₂×#585	1	2	yes	—
736	D₅₃	—	2	4	no	—
737	D₅₃	—	2	4	no	—
738	D₅₃	—	4	4	no	—
739	C₂²×#41	—	53	2	no	—
740	C₂⁴×C₄	—	53	1	no	—
741	#556	—	53	8	no	—
742	#556	—	53	8	no	—
743	#555	—	53	8	no	—
744	#555	—	53	8	no	—
745	#554	—	53	8	no	—
746	#554	—	53	8	no	—
747	#553	—	53	8	no	—
748	#553	—	53	8	no	—
749	#553	—	53	8	no	—
750	#553	—	53	8	no	—
751	#552	—	53	8	no	—
752	#552	—	53	8	no	—
753	#552	—	53	8	no	—
754	#552	—	53	8	no	—
755	#552	—	53	8	no	—
756	#552	—	53	8	no	—
757	#552	—	53	8	no	—
758	#552	—	53	8	no	—
759	#551	—	53	8	no	—
760	#551	—	53	8	no	—
761	#551	—	53	8	no	—
762	#551	—	53	8	no	—
763	#551	—	53	8	no	—
764	#551	—	53	8	no	—
765	#551	—	53	8	no	—
766	#551	—	53	8	no	—
767	#547	—	53	8	no	—
768	#547	—	53	8	no	—
769	#546	—	53	8	no	—
770	#546	—	53	8	no	—
771	#546	—	53	8	no	—
772	#546	—	53	8	no	—
773	#544	—	53	4	no	—
774	#544	—	53	4	no	—
775	#544	—	53	4	no	—
776	#543	—	53	4	no	—
777	#542	—	53	4	no	—
778	#542	—	53	4	no	—
779	#542	—	53	4	no	—
780	#542	C₂×D₅₃	1	4	yes	complemented
781	#541	—	53	4	no	—
782	#541	—	53	2	no	—
783	#541	C₂×D₅₃	1	2	yes	complemented
784	#540	—	53	4	no	—
785	#540	—	53	2	no	—
786	#540	C₂×D₅₃	1	2	yes	complemented
787	#539	—	53	8	no	—
788	#539	—	53	4	no	—
789	#539	C₂×D₅₃	1	4	yes	complemented
790	#538	—	53	8	no	—
791	#538	—	53	4	no	—
792	#538	C₂×D₅₃	1	4	yes	complemented
793	#537	—	53	4	no	—
794	#536	—	53	2	no	—
795	#536	—	53	2	no	—
796	#535	—	53	2	no	—
797	#535	—	53	2	no	—
798	#534	—	53	4	no	—
799	#533	—	53	2	no	—
800	#533	—	53	2	no	—
801	#533	—	53	4	no	—
802	#533	—	53	8	no	—
803	#533	—	53	2	no	—
804	#533	—	53	1	no	—
805	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
806	#532	—	53	2	no	—
807	#532	—	53	2	no	—
808	#532	—	53	2	no	—
809	#532	—	53	4	no	—
810	#532	—	53	1	no	—
811	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
812	#529	—	53	4	no	—
813	#529	—	53	4	no	—
814	#529	—	53	4	no	—
815	#529	—	53	4	no	—
816	#529	—	53	4	no	—
817	#529	—	53	4	no	—
818	#529	—	53	8	no	—
819	#529	—	53	8	no	—
820	#529	—	53	8	no	—
821	#529	—	53	4	no	—
822	#529	—	53	4	no	—
823	#529	—	53	8	no	—
824	#529	—	53	8	no	—
825	#529	C₂×D₅₃	1	8	yes	complemented
826	#525	—	53	2	no	—
827	#525	—	53	2	no	—
828	#525	—	53	4	no	—
829	#525	—	53	4	no	—
830	#525	—	53	4	no	—
831	#525	—	53	4	no	—
832	#525	—	53	4	no	—
833	#525	—	53	4	no	—
834	#525	—	53	8	no	—
835	#525	—	53	8	no	—
836	#525	—	53	8	no	—
837	#525	—	53	2	no	—
838	#525	C₂×D₅₃	1	2	yes	complemented
839	C₂×#123	—	53	4	no	—
840	C₂×C₂²⋊Q₈	—	53	4	no	—
841	C₂×#121	—	53	4	no	—
842	C₂×#120	—	53	4	no	—
843	#520	—	53	4	no	—
844	#520	—	53	8	no	—
845	#520	—	53	4	no	—
846	#519	—	53	4	no	—
847	#518	—	53	8	no	—
848	#518	—	53	4	no	—
849	C₄×#41	—	53	2	no	—
850	C₄×#41	—	53	4	no	—
851	C₄×#41	—	53	4	no	—
852	C₄×#41	—	53	2	no	—
853	C₄×#41	—	53	4	no	—
854	C₄×#41	—	53	2	no	—
855	C₄×#41	—	53	4	no	—
856	C₄×#41	—	53	8	no	—
857	C₄×#41	C₂×D₅₃	1	2	yes	complemented
858	C₂×C₄×D₄	—	53	8	no	—
859	C₂×#117	—	53	1	no	—
860	C₂×#117	—	53	2	no	—
861	C₂×#117	—	53	4	no	—
862	C₂×#117	—	53	4	no	—
863	C₂×#117	—	53	4	no	—
864	C₂×#117	—	53	4	no	—
865	C₂×#117	—	53	4	no	—
866	C₂×#117	—	53	2	no	—
867	C₂×#117	—	53	2	no	—
868	C₂×#117	—	53	1	no	—
869	C₂×#117	—	53	1	no	—
870	C₂×#117	—	53	4	no	—
871	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
872	C₂²×C₄⋊C₄	—	53	2	no	—
873	C₂²×C₂²⋊C₄	—	53	2	no	—
874	C₂²×C₄²	—	53	1	no	—
875	C₂²×C₄²	—	53	1	no	—
876	C₅₃	#62814	1	1	yes	characteristic, complemented, Sylow
877	C₂⁵	—	53	1	no	—
878	C₂×#41	—	53	2	no	—
879	C₂×#41	—	53	4	no	—
880	C₂×#41	—	53	2	no	—
881	C₂×#41	—	53	4	no	—
882	C₂×#41	—	53	4	no	—
883	C₂×#41	—	53	4	no	—
884	C₂×#41	—	53	2	no	—
885	C₂×#41	—	53	8	no	—
886	C₂×#41	—	106	16	no	—
887	C₂×#41	C₂²×D₅₃	1	2	yes	—
888	C₂²×Q₈	—	53	2	no	—
889	C₂²×D₄	—	53	4	no	—
890	C₂²×D₄	—	53	2	no	—
891	C₂²×D₄	—	53	8	no	—
892	C₂³×C₄	—	53	1	no	—
893	C₂³×C₄	—	53	1	no	—
894	C₂³×C₄	—	53	1	no	—
895	C₂³×C₄	—	53	4	no	—
896	C₂³×C₄	—	53	4	no	—
897	C₂³×C₄	—	53	4	no	—
898	C₂³×C₄	—	53	1	no	—
899	C₂³×C₄	—	53	1	no	—
900	C₂³×C₄	—	53	2	no	—
901	C₂³×C₄	—	53	2	no	—
902	C₂³×C₄	—	106	8	no	—
903	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
904	C₄⋊Q₈	—	53	2	no	—
905	C₄⋊Q₈	—	53	8	no	—
906	C₄⋊Q₈	—	53	4	no	—
907	C₄⋊Q₈	—	53	8	no	—
908	C₄⋊Q₈	—	53	1	no	—
909	C₄⋊Q₈	—	53	2	no	—
910	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
911	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
912	#127	—	53	2	no	—
913	#127	—	53	1	no	—
914	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
915	#126	—	53	8	no	—
916	#126	—	53	8	no	—
917	#126	—	53	8	no	—
918	#126	—	53	8	no	—
919	#126	—	53	8	no	—
920	#126	—	53	8	no	—
921	#126	—	53	8	no	—
922	#126	—	53	8	no	—
923	#126	—	53	8	no	—
924	#126	—	53	8	no	—
925	#126	C₂²×D₅₃	1	8	yes	—
926	#126	C₂²×D₅₃	1	8	yes	complemented
927	#125	—	53	4	no	—
928	#125	—	53	8	no	—
929	#125	—	53	4	no	—
930	#125	—	53	4	no	—
931	#125	—	53	8	no	—
932	#125	—	53	8	no	—
933	#125	—	53	8	no	—
934	#125	—	53	8	no	—
935	#125	—	53	8	no	—
936	#125	—	53	2	no	—
937	#125	C₂²×D₅₃	1	2	yes	complemented
938	#125	C₂²×D₅₃	1	8	yes	complemented
939	#124	—	53	2	no	—
940	#124	—	53	4	no	—
941	#124	—	53	2	no	—
942	#124	—	53	4	no	—
943	#124	—	53	8	no	—
944	#124	—	53	8	no	—
945	#124	—	53	8	no	—
946	#124	—	53	8	no	—
947	#124	—	53	2	no	—
948	#124	C₂²×D₅₃	1	8	yes	—
949	#124	C₂²×D₅₃	1	2	yes	complemented
950	#123	—	53	4	no	—
951	#123	—	53	8	no	—
952	#123	—	53	4	no	—
953	#123	—	53	8	no	—
954	#123	—	53	8	no	—
955	#123	—	53	8	no	—
956	#123	—	53	8	no	—
957	#123	—	53	8	no	—
958	#123	—	53	4	no	—
959	#123	—	53	8	no	—
960	#123	—	53	8	no	—
961	#123	—	53	8	no	—
962	#123	—	53	8	no	—
963	#123	—	53	8	no	—
964	#123	—	53	8	no	—
965	#123	—	53	8	no	—
966	#123	—	53	8	no	—
967	#123	C₂²×D₅₃	1	4	yes	—
968	#123	C₂²×D₅₃	1	8	yes	—
969	#123	C₂²×D₅₃	1	8	yes	complemented
970	C₂²⋊Q₈	—	53	4	no	—
971	C₂²⋊Q₈	—	53	4	no	—
972	C₂²⋊Q₈	—	53	8	no	—
973	C₂²⋊Q₈	—	53	4	no	—
974	C₂²⋊Q₈	—	53	4	no	—
975	C₂²⋊Q₈	—	53	4	no	—
976	C₂²⋊Q₈	—	53	8	no	—
977	C₂²⋊Q₈	—	53	8	no	—
978	C₂²⋊Q₈	—	53	4	no	—
979	C₂²⋊Q₈	—	53	8	no	—
980	C₂²⋊Q₈	—	53	8	no	—
981	C₂²⋊Q₈	—	53	8	no	—
982	C₂²⋊Q₈	—	53	8	no	—
983	C₂²⋊Q₈	—	53	8	no	—
984	C₂²⋊Q₈	—	53	8	no	—
985	C₂²⋊Q₈	—	53	8	no	—
986	C₂²⋊Q₈	—	53	8	no	—
987	C₂²⋊Q₈	—	53	8	no	—
988	C₂²⋊Q₈	—	53	8	no	—
989	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
990	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
991	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
992	#121	—	53	4	no	—
993	#121	—	53	8	no	—
994	#121	—	53	8	no	—
995	#121	—	53	4	no	—
996	#121	—	53	8	no	—
997	#121	—	53	8	no	—
998	#121	—	53	8	no	—
999	#121	—	53	4	no	—
1000	#121	—	53	4	no	—
1001	#121	—	53	4	no	—
1002	#121	—	53	4	no	—
1003	#121	—	53	8	no	—
1004	#121	—	53	8	no	—
1005	#121	—	53	8	no	—
1006	#121	—	53	8	no	—
1007	#121	C₂²×D₅₃	1	4	yes	—
1008	#121	C₂²×D₅₃	1	4	yes	—
1009	#121	C₂²×D₅₃	1	8	yes	—
1010	#120	—	53	4	no	—
1011	#120	—	53	4	no	—
1012	#120	—	53	8	no	—
1013	#120	—	53	8	no	—
1014	#120	—	53	4	no	—
1015	#120	—	53	8	no	—
1016	#120	—	53	8	no	—
1017	#120	C₂²×D₅₃	1	4	yes	—
1018	C₄×Q₈	—	53	4	no	—
1019	C₄×Q₈	—	53	4	no	—
1020	C₄×Q₈	—	53	4	no	—
1021	C₄×Q₈	—	53	8	no	—
1022	C₄×Q₈	—	53	4	no	—
1023	C₄×Q₈	—	53	4	no	—
1024	C₄×Q₈	—	53	8	no	—
1025	C₄×Q₈	—	53	4	no	—
1026	C₄×Q₈	—	53	8	no	—
1027	C₄×Q₈	—	53	8	no	—
1028	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1029	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1030	C₄×D₄	—	53	8	no	—
1031	C₄×D₄	—	53	8	no	—
1032	C₄×D₄	—	53	4	no	—
1033	C₄×D₄	—	53	4	no	—
1034	C₄×D₄	—	53	8	no	—
1035	C₄×D₄	—	53	8	no	—
1036	C₄×D₄	—	53	8	no	—
1037	C₄×D₄	—	53	8	no	—
1038	C₄×D₄	—	53	8	no	—
1039	C₄×D₄	—	53	8	no	—
1040	C₄×D₄	—	53	8	no	—
1041	C₄×D₄	—	53	8	no	—
1042	C₄×D₄	—	53	8	no	—
1043	C₄×D₄	—	53	4	no	—
1044	C₄×D₄	—	53	8	no	—
1045	C₄×D₄	—	53	8	no	—
1046	C₄×D₄	—	53	4	no	—
1047	C₄×D₄	—	53	8	no	—
1048	C₄×D₄	—	53	8	no	—
1049	C₄×D₄	—	53	8	no	—
1050	C₄×D₄	—	53	8	no	—
1051	C₄×D₄	—	53	8	no	—
1052	C₄×D₄	—	53	8	no	—
1053	C₄×D₄	—	53	8	no	—
1054	C₄×D₄	—	53	4	no	—
1055	C₄×D₄	—	53	8	no	—
1056	C₄×D₄	—	53	4	no	—
1057	C₄×D₄	—	53	8	no	—
1058	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1059	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1060	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1061	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1062	#117	—	53	2	no	—
1063	#117	—	53	2	no	—
1064	#117	—	53	4	no	—
1065	#117	—	53	2	no	—
1066	#117	—	53	4	no	—
1067	#117	—	53	8	no	—
1068	#117	—	53	4	no	—
1069	#117	—	53	4	no	—
1070	#117	—	53	4	no	—
1071	#117	—	53	4	no	—
1072	#117	—	53	4	no	—
1073	#117	—	53	8	no	—
1074	#117	—	53	4	no	—
1075	#117	—	53	4	no	—
1076	#117	—	53	8	no	—
1077	#117	—	53	4	no	—
1078	#117	—	53	4	no	—
1079	#117	—	53	4	no	—
1080	#117	—	53	4	no	—
1081	#117	—	53	4	no	—
1082	#117	—	53	8	no	—
1083	#117	—	53	8	no	—
1084	#117	—	53	2	no	—
1085	#117	—	53	2	no	—
1086	#117	—	53	4	no	—
1087	#117	—	53	4	no	—
1088	#117	—	53	4	no	—
1089	#117	—	53	2	no	—
1090	#117	—	53	2	no	—
1091	#117	—	53	4	no	—
1092	#117	—	53	4	no	—
1093	#117	—	53	8	no	—
1094	#117	—	53	8	no	—
1095	#117	—	53	8	no	—
1096	#117	—	53	8	no	—
1097	#117	C₂²×D₅₃	1	4	yes	—
1098	#117	C₂²×D₅₃	1	2	yes	—
1099	#117	C₂²×D₅₃	1	2	yes	—
1100	#117	C₂²×D₅₃	1	2	yes	—
1101	#117	C₂²×D₅₃	1	4	yes	complemented
1102	C₂×C₄⋊C₄	—	53	2	no	—
1103	C₂×C₄⋊C₄	—	53	2	no	—
1104	C₂×C₄⋊C₄	—	53	2	no	—
1105	C₂×C₄⋊C₄	—	53	8	no	—
1106	C₂×C₄⋊C₄	—	53	4	no	—
1107	C₂×C₄⋊C₄	—	53	4	no	—
1108	C₂×C₄⋊C₄	—	53	4	no	—
1109	C₂×C₄⋊C₄	—	53	4	no	—
1110	C₂×C₄⋊C₄	—	53	4	no	—
1111	C₂×C₄⋊C₄	—	53	8	no	—
1112	C₂×C₄⋊C₄	—	53	8	no	—
1113	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	—
1114	C₂×C₂²⋊C₄	—	53	2	no	—
1115	C₂×C₂²⋊C₄	—	53	2	no	—
1116	C₂×C₂²⋊C₄	—	53	2	no	—
1117	C₂×C₂²⋊C₄	—	53	8	no	—
1118	C₂×C₂²⋊C₄	—	53	4	no	—
1119	C₂×C₂²⋊C₄	—	53	4	no	—
1120	C₂×C₂²⋊C₄	—	53	4	no	—
1121	C₂×C₂²⋊C₄	—	53	4	no	—
1122	C₂×C₂²⋊C₄	—	53	4	no	—
1123	C₂×C₂²⋊C₄	—	53	8	no	—
1124	C₂×C₂²⋊C₄	—	53	8	no	—
1125	C₂×C₂²⋊C₄	—	53	8	no	—
1126	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1127	C₂×C₄²	—	53	1	no	—
1128	C₂×C₄²	—	53	2	no	—
1129	C₂×C₄²	—	53	2	no	—
1130	C₂×C₄²	—	53	1	no	—
1131	C₂×C₄²	—	53	4	no	—
1132	C₂×C₄²	—	53	2	no	—
1133	C₂×C₄²	—	53	2	no	—
1134	C₂×C₄²	—	53	4	no	—
1135	C₂×C₄²	—	53	2	no	—
1136	C₂×C₄²	—	53	2	no	—
1137	C₂×C₄²	—	53	4	no	—
1138	C₂×C₄²	—	53	4	no	—
1139	C₂×C₄²	—	53	4	no	—
1140	C₂×C₄²	—	53	4	no	—
1141	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1142	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1143	C₂×C₄²	C₂²×D₅₃	1	4	yes	complemented
1144	C₂⁴	—	53	1	no	—
1145	C₂⁴	—	53	1	no	—
1146	C₂⁴	—	53	4	no	—
1147	C₂⁴	—	53	4	no	—
1148	C₂⁴	—	106	4	no	—
1149	C₂⁴	—	212	4	no	—
1150	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1151	#41	—	2	8	no	—
1152	#41	—	106	16	no	—
1153	#41	—	106	16	no	—
1154	#41	—	106	8	no	—
1155	#41	—	106	8	no	—
1156	#41	—	106	8	no	—
1157	#41	—	212	16	no	—
1158	#41	—	212	8	no	—
1159	#41	—	212	8	no	—
1160	C₂×Q₈	—	53	4	no	—
1161	C₂×Q₈	—	53	2	no	—
1162	C₂×Q₈	—	53	4	no	—
1163	C₂×Q₈	—	53	8	no	—
1164	C₂×Q₈	—	106	8	no	—
1165	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1166	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1167	C₂×D₄	—	53	4	no	—
1168	C₂×D₄	—	53	8	no	—
1169	C₂×D₄	—	53	4	no	—
1170	C₂×D₄	—	53	4	no	—
1171	C₂×D₄	—	53	8	no	—
1172	C₂×D₄	—	53	8	no	—
1173	C₂×D₄	—	53	4	no	—
1174	C₂×D₄	—	53	8	no	—
1175	C₂×D₄	—	53	2	no	—
1176	C₂×D₄	—	53	4	no	—
1177	C₂×D₄	—	106	8	no	—
1178	C₂×D₄	—	106	16	no	—
1179	C₂×D₄	—	212	16	no	—
1180	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1181	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1182	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1183	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1184	C₂²×C₄	—	2	4	no	—
1185	C₂²×C₄	—	53	1	no	—
1186	C₂²×C₄	—	53	8	no	—
1187	C₂²×C₄	—	53	2	no	—
1188	C₂²×C₄	—	53	2	no	—
1189	C₂²×C₄	—	53	1	no	—
1190	C₂²×C₄	—	53	4	no	—
1191	C₂²×C₄	—	53	4	no	—
1192	C₂²×C₄	—	53	2	no	—
1193	C₂²×C₄	—	53	2	no	—
1194	C₂²×C₄	—	53	8	no	—
1195	C₂²×C₄	—	53	2	no	—
1196	C₂²×C₄	—	53	2	no	—
1197	C₂²×C₄	—	53	2	no	—
1198	C₂²×C₄	—	53	4	no	—
1199	C₂²×C₄	—	53	4	no	—
1200	C₂²×C₄	—	53	4	no	—
1201	C₂²×C₄	—	53	4	no	—
1202	C₂²×C₄	—	53	4	no	—
1203	C₂²×C₄	—	53	2	no	—
1204	C₂²×C₄	—	53	4	no	—
1205	C₂²×C₄	—	53	2	no	—
1206	C₂²×C₄	—	53	2	no	—
1207	C₂²×C₄	—	53	4	no	—
1208	C₂²×C₄	—	53	8	no	—
1209	C₂²×C₄	—	53	8	no	—
1210	C₂²×C₄	—	53	8	no	—
1211	C₂²×C₄	—	106	4	no	—
1212	C₂²×C₄	—	106	16	no	—
1213	C₂²×C₄	—	106	16	no	—
1214	C₂²×C₄	—	106	16	no	—
1215	C₂²×C₄	—	106	4	no	—
1216	C₂²×C₄	—	106	4	no	—
1217	C₂²×C₄	—	106	4	no	—
1218	C₂²×C₄	—	212	4	no	—
1219	C₂²×C₄	—	212	4	no	—
1220	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1222	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1223	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1224	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1225	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1226	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1227	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1228	C₄⋊C₄	—	53	4	no	—
1229	C₄⋊C₄	—	53	4	no	—
1230	C₄⋊C₄	—	53	4	no	—
1231	C₄⋊C₄	—	53	8	no	—
1232	C₄⋊C₄	—	53	4	no	—
1233	C₄⋊C₄	—	53	4	no	—
1234	C₄⋊C₄	—	53	4	no	—
1235	C₄⋊C₄	—	53	4	no	—
1236	C₄⋊C₄	—	53	8	no	—
1237	C₄⋊C₄	—	53	8	no	—
1238	C₄⋊C₄	—	53	8	no	—
1239	C₄⋊C₄	—	53	8	no	—
1240	C₄⋊C₄	—	53	8	no	—
1241	C₄⋊C₄	—	53	8	no	—
1242	C₄⋊C₄	—	53	8	no	—
1243	C₄⋊C₄	—	53	8	no	—
1244	C₄⋊C₄	—	53	8	no	—
1245	C₄⋊C₄	—	53	8	no	—
1246	C₄⋊C₄	—	53	4	no	—
1247	C₄⋊C₄	—	53	8	no	—
1248	C₄⋊C₄	—	53	4	no	—
1249	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1250	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1251	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1252	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1253	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1254	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1255	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1256	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1257	C₂²⋊C₄	—	53	4	no	—
1258	C₂²⋊C₄	—	53	4	no	—
1259	C₂²⋊C₄	—	53	4	no	—
1260	C₂²⋊C₄	—	53	8	no	—
1261	C₂²⋊C₄	—	53	8	no	—
1262	C₂²⋊C₄	—	53	8	no	—
1263	C₂²⋊C₄	—	53	8	no	—
1264	C₂²⋊C₄	—	53	4	no	—
1265	C₂²⋊C₄	—	53	4	no	—
1266	C₂²⋊C₄	—	53	4	no	—
1267	C₂²⋊C₄	—	53	8	no	—
1268	C₂²⋊C₄	—	53	4	no	—
1269	C₂²⋊C₄	—	53	8	no	—
1270	C₂²⋊C₄	—	53	8	no	—
1271	C₂²⋊C₄	—	53	8	no	—
1272	C₂²⋊C₄	—	53	8	no	—
1273	C₂²⋊C₄	—	53	8	no	—
1274	C₂²⋊C₄	—	53	8	no	—
1275	C₂²⋊C₄	—	53	8	no	—
1276	C₂²⋊C₄	—	53	8	no	—
1277	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1278	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1279	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1280	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1281	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1282	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1283	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1284	C₄²	—	53	2	no	—
1285	C₄²	—	53	2	no	—
1286	C₄²	—	53	4	no	—
1287	C₄²	—	53	2	no	—
1288	C₄²	—	53	2	no	—
1289	C₄²	—	53	2	no	—
1290	C₄²	—	53	4	no	—
1291	C₄²	—	53	2	no	—
1292	C₄²	—	53	8	no	—
1293	C₄²	—	53	8	no	—
1294	C₄²	—	53	8	no	—
1295	C₄²	—	53	8	no	—
1296	C₄²	—	53	1	no	—
1297	C₄²	—	53	1	no	—
1298	C₄²	—	53	2	no	—
1299	C₄²	—	53	4	no	—
1300	C₄²	C₂³×D₅₃	1	2	yes	—
1301	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1302	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1303	C₄²	C₂³×D₅₃	1	8	yes	—
1304	C₄²	C₂³×D₅₃	1	2	yes	—
1305	C₄²	C₂³×D₅₃	1	2	yes	—
1306	C₄²	C₂³×D₅₃	1	4	yes	—
1307	C₂³	—	2	2	no	—
1308	C₂³	—	4	2	no	—
1309	C₂³	—	53	2	no	—
1310	C₂³	—	53	2	no	—
1311	C₂³	—	53	4	no	—
1312	C₂³	—	53	4	no	—
1313	C₂³	—	106	4	no	—
1314	C₂³	—	106	8	no	—
1315	C₂³	—	106	8	no	—
1316	C₂³	—	106	8	no	—
1317	C₂³	—	106	2	no	—
1318	C₂³	—	212	8	no	—
1319	C₂³	—	212	2	no	—
1320	C₂³	—	212	4	no	—
1321	C₂³	—	212	16	no	—
1322	C₂³	C₂⁴×D₅₃	1	2	yes	—
1323	C₂³	C₂⁴×D₅₃	1	4	yes	—
1324	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1325	Q₈	—	2	4	no	—
1326	Q₈	—	4	4	no	—
1327	Q₈	—	106	8	no	—
1328	Q₈	—	106	4	no	—
1329	Q₈	—	212	4	no	—
1330	Q₈	—	212	8	no	—
1331	D₄	—	2	8	no	—
1332	D₄	—	2	4	no	—
1333	D₄	—	4	8	no	—
1334	D₄	—	4	4	no	—
1335	D₄	—	106	8	no	—
1336	D₄	—	106	16	no	—
1337	D₄	—	106	8	no	—
1338	D₄	—	106	8	no	—
1339	D₄	—	106	16	no	—
1340	D₄	—	106	8	no	—
1341	D₄	—	106	4	no	—
1342	D₄	—	212	4	no	—
1343	D₄	—	212	8	no	—
1344	D₄	—	212	8	no	—
1345	C₂×C₄	—	2	2	no	—
1346	C₂×C₄	—	2	4	no	—
1347	C₂×C₄	—	2	4	no	—
1348	C₂×C₄	—	2	8	no	—
1349	C₂×C₄	—	4	2	no	—
1350	C₂×C₄	—	4	2	no	—
1351	C₂×C₄	—	4	8	no	—
1352	C₂×C₄	—	53	4	no	—
1353	C₂×C₄	—	53	2	no	—
1354	C₂×C₄	—	53	8	no	—
1355	C₂×C₄	—	53	8	no	—
1356	C₂×C₄	—	53	2	no	—
1357	C₂×C₄	—	53	2	no	—
1358	C₂×C₄	—	53	2	no	—
1359	C₂×C₄	—	53	4	no	—
1360	C₂×C₄	—	53	4	no	—
1361	C₂×C₄	—	53	8	no	—
1362	C₂×C₄	—	106	8	no	—
1363	C₂×C₄	—	106	8	no	—
1364	C₂×C₄	—	106	8	no	—
1365	C₂×C₄	—	106	8	no	—
1366	C₂×C₄	—	106	8	no	—
1367	C₂×C₄	—	106	4	no	—
1368	C₂×C₄	—	106	4	no	—
1369	C₂×C₄	—	106	8	no	—
1370	C₂×C₄	—	106	8	no	—
1371	C₂×C₄	—	106	2	no	—
1372	C₂×C₄	—	106	4	no	—
1373	C₂×C₄	—	106	4	no	—
1374	C₂×C₄	—	106	8	no	—
1375	C₂×C₄	—	212	4	no	—
1376	C₂×C₄	—	212	2	no	—
1377	C₂×C₄	—	212	2	no	—
1378	C₂×C₄	—	212	8	no	—
1379	C₂×C₄	—	212	8	no	—
1380	C₂×C₄	—	212	8	no	—
1381	C₂×C₄	—	212	2	no	—
1382	C₂×C₄	—	212	2	no	—
1383	C₂×C₄	—	212	8	no	—
1384	C₂×C₄	#41×D₅₃	1	4	yes	—
1385	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1386	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1387	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1388	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1389	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1390	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1391	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1392	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1393	C₂²	—	2	2	no	—
1394	C₂²	—	2	2	no	—
1395	C₂²	—	2	4	no	—
1396	C₂²	—	2	8	no	—
1397	C₂²	—	2	4	no	—
1398	C₂²	—	4	4	no	—
1399	C₂²	—	53	4	no	—
1400	C₂²	—	53	4	no	—
1401	C₂²	—	106	8	no	—
1402	C₂²	—	106	2	no	—
1403	C₂²	—	106	2	no	—
1404	C₂²	—	106	4	no	—
1405	C₂²	—	106	4	no	—
1406	C₂²	—	106	8	no	—
1407	C₂²	—	424	8	no	—
1408	C₂²	—	212	4	no	—
1409	C₂²	—	212	16	no	—
1410	C₂²	C₂×#41×D₅₃	1	2	yes	—
1411	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1412	C₄	—	2	2	no	—
1413	C₄	—	2	4	no	—
1414	C₄	—	2	4	no	—
1415	C₄	—	2	2	no	—
1416	C₄	—	2	2	no	—
1417	C₄	—	2	8	no	—
1418	C₄	—	53	4	no	—
1419	C₄	—	106	2	no	—
1420	C₄	—	106	4	no	—
1421	C₄	—	106	2	no	—
1422	C₄	—	106	2	no	—
1423	C₄	—	106	4	no	—
1424	C₄	—	106	8	no	—
1425	C₄	C₂×#41×D₅₃	1	2	yes	—
1426	C₄	C₂×#41×D₅₃	1	2	yes	—
1427	C₂	—	2	2	no	—
1428	C₂	—	4	2	no	—
1429	C₂	—	4	4	no	—
1430	C₂	—	106	4	no	—
1431	C₂	—	106	4	no	—
1432	C₂	—	212	4	no	—
1433	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1434	C₂	#585×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂⁴×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Frattini	C₂²	C₂⁵×D₅₃
Fitting	C₅₃×#3455	C₂
hypercenter	#3455	D₅₃
hypocenter	C₅₃	#62814
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #20288465	C₂	semidirect
2. #20288459	C₂	semidirect
3. #20288448	C₂	semidirect
4. #20288442	C₂	semidirect
5. #20288430	C₂	semidirect
6. #20288420	C₂	semidirect
7. #20288409	C₂	semidirect
8. #20288401	C₂	semidirect
9. #20288271	C₂	semidirect
10. #20288267	C₂	semidirect
11. #20288118	C₂	semidirect
12. #20288105	C₂	semidirect
13. #20288103	C₂	semidirect
14. #20288042	C₂	semidirect
15. #20288012	C₂	semidirect
16. #20288010	C₂	semidirect
17. #20288008	C₂	semidirect
18. #525×D₅₃	C₂	semidirect
19. #20287914	C₂	semidirect
20. C₂×#117×D₅₃	C₂	semidirect
21. C₅₃×#3455	C₂	semidirect
24. #16811342	C₂²	semidirect
25. #16811340	C₂²	semidirect
26. #16811337	C₂²	semidirect
27. #16811335	C₂²	semidirect
28. #16811329	C₂²	semidirect
29. #16811327	C₂²	semidirect
30. #16811324	C₂²	semidirect
31. #16811318	C₂²	semidirect
32. #16811318	C₂²	semidirect
33. #16811316	C₂²	semidirect
34. #16811311	C₂²	semidirect
35. #16811310	C₂²	semidirect
36. #16811309	C₂²	semidirect
37. #16811309	C₂²	semidirect
38. #16811309	C₂²	semidirect
39. #16811307	C₂²	semidirect
40. #16811305	C₂²	semidirect
41. #16811305	C₂²	semidirect
42. #16811303	C₂²	semidirect
43. #16811301	C₂²	semidirect
44. #16811301	C₂²	semidirect
45. #16811300	C₂²	semidirect
46. #16811298	C₂²	semidirect
47. #16811298	C₂²	semidirect
48. #16811298	C₂²	semidirect
49. #16811296	C₂²	semidirect
50. #16811275	C₂²	semidirect
51. #16811271	C₂²	semidirect
52. #16811270	C₂²	semidirect
53. #16811266	C₂²	semidirect
54. #16811265	C₂²	semidirect
55. #16811262	C₂²	semidirect
56. #16811253	C₂²	semidirect
57. #16811252	C₂²	semidirect
58. #16811250	C₂²	semidirect
60. #16811246	C₂²	semidirect
61. #16811244	C₂²	semidirect
62. #16811240	C₂²	semidirect
63. #16811235	C₂²	semidirect
64. #16811233	C₂²	semidirect
65. #16811228	C₂²	semidirect
66. #16811226	C₂²	semidirect
67. #16811220	C₂²	semidirect
68. #16811217	C₂²	semidirect
69. #16811211	C₂²	semidirect
70. #16811208	C₂²	semidirect
71. #16811200	C₂²	semidirect
72. #16811198	C₂²	semidirect
73. #16811193	C₂²	semidirect
74. #16811191	C₂²	semidirect
75. #16811186	C₂²	semidirect
77. #16811180	C₂²	semidirect
78. #16811178	C₂²	semidirect
79. #16811178	C₂²	semidirect
80. #16811177	C₂²	semidirect
81. #16811177	C₂²	semidirect
82. #16811176	C₂²	semidirect
83. #16811174	C₂²	semidirect
84. #16811173	C₂²	semidirect
85. #16811171	C₂²	semidirect
86. #16811170	C₂²	semidirect
87. #16811169	C₂²	semidirect
88. #16811160	C₂²	semidirect
89. #16811160	C₂²	semidirect
90. #16811159	C₂²	semidirect
91. #16811158	C₂²	semidirect
92. #16811155	C₂²	semidirect
93. #16811155	C₂²	semidirect
94. #16811155	C₂²	semidirect
95. #16811154	C₂²	semidirect
96. #16811153	C₂²	semidirect
97. #16811153	C₂²	semidirect
98. #16811152	C₂²	semidirect
99. #16811151	C₂²	semidirect
100. #16811151	C₂²	semidirect
102. #16811136	C₂²	semidirect
103. #16811135	C₂²	semidirect
104. #16811134	C₂²	semidirect
106. #16811133	C₂²	semidirect
108. #16811132	C₂²	semidirect
109. #16811132	C₂²	semidirect
110. #16811131	C₂²	semidirect
111. #16811130	C₂²	semidirect
112. #16811129	C₂²	semidirect
114. C₂²⋊Q₈×D₅₃	C₂²	semidirect
115. #121×D₅₃	C₂²	semidirect
117. #16811105	C₂²	semidirect
118. #16811102	C₂²	semidirect
119. #16811102	C₂²	semidirect
120. #16811099	C₂²	semidirect
122. #16811095	C₂²	semidirect
123. #41×Dic₅₃	C₂²	semidirect
124. C₄×#11719949	C₂²	semidirect
125. C₄×#11719945	C₂²	semidirect
126. C₄×#11719945	C₂²	semidirect
127. C₄×#11719945	C₂²	semidirect
128. #16811091	C₂²	semidirect
129. #16811091	C₂²	semidirect
130. C₄×#11719947	C₂²	semidirect
131. C₄×D₄×D₅₃	C₂²	semidirect
132. C₂×#13133176	C₂²	semidirect
136. C₂×#13133174	C₂²	semidirect
137. C₂×#13133173	C₂²	semidirect
139. #117×D₅₃	C₂²	semidirect
140. #117×D₅₃	C₂²	semidirect
141. #117×D₅₃	C₂²	semidirect
142. #117×D₅₃	C₂²	semidirect
143. #117×D₅₃	C₂²	semidirect
144. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
146. C₂×C₄²×D₅₃	C₂²	semidirect
147. C₂×C₄²×D₅₃	C₂²	semidirect
148. C₅₃×#542	C₂²	semidirect
149. C₅₃×#541	C₂²	semidirect
150. C₅₃×#540	C₂²	semidirect
151. C₅₃×#539	C₂²	semidirect
152. C₅₃×#538	C₂²	semidirect
153. C₅₃×#533	C₂²	semidirect
154. C₅₃×#532	C₂²	semidirect
155. C₅₃×#529	C₂²	semidirect
156. C₅₃×#525	C₂²	semidirect
157. C₄×#41×C₅₃	C₂²	semidirect
158. C₂×#117×C₅₃	C₂²	semidirect
184. #13133217	C₂³	semidirect
185. #13133217	C₂³	semidirect
186. #13133216	C₂³	semidirect
187. #13133216	C₂³	semidirect
188. #13133215	C₂³	semidirect
189. #13133215	C₂³	semidirect
190. #13133214	C₂³	semidirect
191. #13133213	C₂³	semidirect
192. #13133212	C₂³	semidirect
193. #13133212	C₂³	semidirect
194. #13133212	C₂³	semidirect
195. #13133212	C₂³	semidirect
199. #13133210	C₂³	semidirect
200. #13133210	C₂³	semidirect
201. #13133210	C₂³	semidirect
202. #13133209	C₂³	semidirect
203. #13133208	C₂³	semidirect
204. #13133208	C₂³	semidirect
205. #13133208	C₂³	semidirect
206. #13133208	C₂³	semidirect
207. #13133207	C₂³	semidirect
208. #13133207	C₂³	semidirect
209. #13133207	C₂³	semidirect
210. #13133207	C₂³	semidirect
211. #13133207	C₂³	semidirect
212. #13133206	C₂³	semidirect
213. #13133206	C₂³	semidirect
214. #13133205	C₂³	semidirect
216. #13133204	C₂³	semidirect
217. #13133204	C₂³	semidirect
220. #13133203	C₂³	semidirect
225. #13133202	C₂³	semidirect
227. #13133201	C₂³	semidirect
235. #13133199	C₂³	semidirect
241. #13133197	C₂³	semidirect
248. #13133195	C₂³	semidirect
249. #13133195	C₂³	semidirect
252. #13133194	C₂³	semidirect
253. #13133194	C₂³	semidirect
264. #13133190	C₂³	semidirect
268. #13133189	C₂³	semidirect
279. Q₈×Dic₅₃	C₂³	semidirect
280. Q₈×Dic₅₃	C₂³	semidirect
281. C₄×Dic₁₀₆	C₂³	semidirect
282. C₄×Dic₁₀₆	C₂³	semidirect
283. C₄×Dic₁₀₆	C₂³	semidirect
284. C₄×Dic₁₀₆	C₂³	semidirect
285. C₄×Dic₁₀₆	C₂³	semidirect
286. #13133182	C₂³	semidirect
287. #13133182	C₂³	semidirect
288. #13133182	C₂³	semidirect
292. C₄×D₂₁₂	C₂³	semidirect
293. C₄×D₂₁₂	C₂³	semidirect
296. D₄×Dic₅₃	C₂³	semidirect
297. D₄×Dic₅₃	C₂³	semidirect
301. #13133179	C₂³	semidirect
302. #13133179	C₂³	semidirect
308. C₄×C₂²⋊D₅₃	C₂³	semidirect
309. C₄×C₂²⋊D₅₃	C₂³	semidirect
310. C₄×C₂²⋊D₅₃	C₂³	semidirect
316. #13133177	C₂³	semidirect
321. #13133176	C₂³	semidirect
322. #13133176	C₂³	semidirect
331. #13133175	C₂³	semidirect
341. #13133174	C₂³	semidirect
342. #13133174	C₂³	semidirect
343. #13133174	C₂³	semidirect
344. #13133174	C₂³	semidirect
350. #13133173	C₂³	semidirect
351. #13133173	C₂³	semidirect
355. C₂×#11719919	C₂³	semidirect
362. C₄⋊C₄×D₅₃	C₂³	semidirect
379. C₂×C₄×Dic₅₃	C₂³	semidirect
387. C₄²×D₅₃	C₂³	semidirect
388. C₄²×D₅₃	C₂³	semidirect
391. C₄⋊Q₈×C₅₃	C₂³	semidirect
392. C₄⋊Q₈×C₅₃	C₂³	semidirect
393. #127×C₅₃	C₂³	semidirect
395. #126×C₅₃	C₂³	semidirect
396. #125×C₅₃	C₂³	semidirect
397. #125×C₅₃	C₂³	semidirect
399. #124×C₅₃	C₂³	semidirect
402. #123×C₅₃	C₂³	semidirect
405. C₂²⋊Q₈×C₅₃	C₂³	semidirect
410. C₄×Q₈×C₅₃	C₂³	semidirect
411. C₄×Q₈×C₅₃	C₂³	semidirect
414. C₄×D₄×C₅₃	C₂³	semidirect
415. C₄×D₄×C₅₃	C₂³	semidirect
420. #117×C₅₃	C₂³	semidirect
425. C₂×C₄²×C₅₃	C₂³	semidirect
487. C₂×C₄×D₅₃	#41	semidirect
723. #3455	D₅₃	semidirect
780. #542	C₂×D₅₃	semidirect
783. #541	C₂×D₅₃	semidirect
786. #540	C₂×D₅₃	semidirect
789. #539	C₂×D₅₃	semidirect
792. #538	C₂×D₅₃	semidirect
805. #533	C₂×D₅₃	semidirect
811. #532	C₂×D₅₃	semidirect
825. #529	C₂×D₅₃	semidirect
838. #525	C₂×D₅₃	semidirect
857. C₄×#41	C₂×D₅₃	semidirect
871. C₂×#117	C₂×D₅₃	semidirect
876. C₅₃	#62814	semidirect
910. C₄⋊Q₈	C₂²×D₅₃	semidirect
911. C₄⋊Q₈	C₂²×D₅₃	semidirect
914. #127	C₂²×D₅₃	semidirect
926. #126	C₂²×D₅₃	semidirect
937. #125	C₂²×D₅₃	semidirect
938. #125	C₂²×D₅₃	semidirect
949. #124	C₂²×D₅₃	semidirect
969. #123	C₂²×D₅₃	semidirect
991. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1028. C₄×Q₈	C₂²×D₅₃	semidirect
1029. C₄×Q₈	C₂²×D₅₃	semidirect
1060. C₄×D₄	C₂²×D₅₃	semidirect
1061. C₄×D₄	C₂²×D₅₃	semidirect
1101. #117	C₂²×D₅₃	semidirect
1143. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288465	2
#20288459	2
#20288448	2
#20288442	2
#20288430	2
#20288420	2
#20288409	2
#20288401	2
#20288271	2
#20288267	2
#20288118	2
#20288105	2
#20288103	2
#20288042	2
#20288012	2
#20288010	2
#20288008	2
#525×D₅₃	2
#20287914	2
C₂×#117×D₅₃	2
C₅₃×#3455	2
#62814	53