Subgroups — #27551490

Order 13568.

1570 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20280916	C₂	1	1	yes	maximal, characteristic
2	#20280915	C₂	1	1	yes	maximal, characteristic
3	#20280914	C₂	1	1	yes	maximal, characteristic
4	#20280913	C₂	1	1	yes	maximal, characteristic
5	#20280899	C₂	1	1	yes	maximal, characteristic, complemented
6	#20280898	C₂	1	1	yes	maximal, characteristic, complemented
7	#20280897	C₂	1	1	yes	maximal, characteristic, complemented
8	#20280896	C₂	1	1	yes	maximal, characteristic, complemented
9	#20280895	C₂	1	1	yes	maximal, characteristic, complemented
10	#20280894	C₂	1	1	yes	maximal, characteristic, complemented
11	#20280893	C₂	1	1	yes	maximal, characteristic, complemented
12	#20280892	C₂	1	1	yes	maximal, characteristic
13	#20280891	C₂	1	1	yes	maximal, characteristic
14	#20280890	C₂	1	1	yes	maximal, characteristic
15	#20280889	C₂	1	1	yes	maximal, characteristic
16	#20278021	C₂	1	1	yes	maximal, characteristic, complemented
17	#20278019	C₂	1	1	yes	maximal, characteristic, complemented
18	#20278007	C₂	1	1	yes	maximal, characteristic, complemented
19	#20278005	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277992	C₂	1	1	yes	maximal, characteristic
21	#20277992	C₂	1	1	yes	maximal, characteristic
22	#20277988	C₂	1	1	yes	maximal, characteristic
23	#20277986	C₂	1	1	yes	maximal, characteristic
24	#20277190	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277188	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277188	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277186	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277112	C₂	1	1	yes	maximal, characteristic
29	#20277108	C₂	1	1	yes	maximal, characteristic
30	C₄×#13133175	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2666	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133182	C₂²	1	1	yes	characteristic
34	C₂×#13133182	C₂²	1	1	yes	characteristic
35	C₂×#13133182	C₂²	1	1	yes	characteristic
36	C₂×#13133175	C₂²	1	1	yes	characteristic
37	C₂×#13133175	C₂²	1	1	yes	characteristic
38	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
39	#16810565	C₂²	1	1	yes	characteristic
40	#16810565	C₂²	1	1	yes	characteristic
41	#16810565	C₂²	1	1	yes	characteristic
42	#16810565	C₂²	1	1	yes	characteristic
43	#16810564	C₂²	1	1	yes	characteristic
44	#16810564	C₂²	1	1	yes	characteristic
45	#16810563	C₂²	1	1	yes	characteristic
46	#16810562	C₂²	1	1	yes	characteristic
47	#16810562	C₂²	1	1	yes	characteristic
48	#16810561	C₂²	1	1	yes	characteristic
49	#16810560	C₂²	1	1	yes	characteristic
50	#16810558	C₂²	1	1	yes	characteristic
51	#16810558	C₂²	1	1	yes	characteristic
52	#16810558	C₂²	1	1	yes	characteristic
53	#16810557	C₂²	1	1	yes	characteristic
54	#16810557	C₂²	1	1	yes	characteristic
55	#16810557	C₂²	1	1	yes	characteristic
56	#16810557	C₂²	1	1	yes	characteristic
57	#16810557	C₂²	1	1	yes	characteristic
58	#16810557	C₂²	1	1	yes	characteristic
59	#16810556	C₂²	1	1	yes	characteristic
60	#16810556	C₂²	1	1	yes	characteristic
61	#16810556	C₂²	1	1	yes	characteristic
62	#16810556	C₂²	1	1	yes	characteristic
63	#16810556	C₂²	1	1	yes	characteristic
64	#16810556	C₂²	1	1	yes	characteristic
65	#16810555	C₂²	1	1	yes	characteristic
66	#16810555	C₂²	1	1	yes	characteristic
67	#16810555	C₂²	1	1	yes	characteristic
68	#16810555	C₂²	1	1	yes	characteristic
69	#16810554	C₂²	1	1	yes	characteristic
70	#16810554	C₂²	1	1	yes	characteristic
71	#16810553	C₂²	1	1	yes	characteristic
72	#16810553	C₂²	1	1	yes	characteristic
73	#16810547	C₂²	1	1	yes	characteristic
74	#16810547	C₂²	1	1	yes	characteristic
75	#16810545	C₂²	1	1	yes	characteristic
76	#16810545	C₂²	1	1	yes	characteristic
77	#16810545	C₂²	1	1	yes	characteristic
78	#16810545	C₂²	1	1	yes	characteristic
79	#16810545	C₂²	1	1	yes	characteristic
80	#16810545	C₂²	1	1	yes	characteristic
81	#16810544	C₂²	1	1	yes	characteristic
82	#16810544	C₂²	1	1	yes	characteristic
83	#16810544	C₂²	1	1	yes	characteristic
84	#16810544	C₂²	1	1	yes	characteristic
85	#16810544	C₂²	1	1	yes	characteristic
86	#16810543	C₂²	1	1	yes	characteristic
87	#16810543	C₂²	1	1	yes	characteristic
88	#16810543	C₂²	1	1	yes	characteristic
89	#16810543	C₂²	1	1	yes	characteristic
90	#16810542	C₂²	1	1	yes	characteristic
91	#16810536	C₂²	1	1	yes	characteristic
92	#16810536	C₂²	1	1	yes	characteristic
93	#16810536	C₂²	1	1	yes	characteristic
94	#16810534	C₂²	1	1	yes	characteristic
95	#16810530	C₂²	1	1	yes	characteristic
96	#16810529	C₂²	1	1	yes	characteristic
97	#16810528	C₂²	1	1	yes	characteristic
98	#16810527	C₂²	1	1	yes	characteristic
99	#16810527	C₂²	1	1	yes	characteristic
100	#16810527	C₂²	1	1	yes	characteristic
101	#16810527	C₂²	1	1	yes	characteristic
102	#16810522	C₂²	1	1	yes	characteristic
103	#16810521	C₂²	1	1	yes	characteristic
104	#16810520	C₂²	1	1	yes	characteristic
105	#16810520	C₂²	1	1	yes	characteristic
106	#16810519	C₂²	1	1	yes	characteristic
107	#16810518	C₂²	1	1	yes	characteristic
108	#16810518	C₂²	1	1	yes	characteristic
109	#16810510	C₂²	1	1	yes	characteristic
110	#16810510	C₂²	1	1	yes	characteristic
111	#16810509	C₂²	1	1	yes	characteristic
112	#16810509	C₂²	1	1	yes	characteristic
113	#16810508	C₂²	1	1	yes	characteristic
114	#16810508	C₂²	1	1	yes	characteristic
115	#16810507	C₂²	1	1	yes	characteristic
116	#16810507	C₂²	1	1	yes	characteristic
117	#16810506	C₂²	1	1	yes	characteristic
118	#16810506	C₂²	1	1	yes	characteristic
119	#16810505	C₂²	1	1	yes	characteristic
120	#16810505	C₂²	1	1	yes	characteristic
121	#16810504	C₂²	1	1	yes	characteristic
122	#16810504	C₂²	1	1	yes	characteristic
123	#16810491	C₂²	1	1	yes	characteristic
124	#16810490	C₂²	1	1	yes	characteristic
125	#16810490	C₂²	1	1	yes	characteristic
126	#16810489	C₂²	1	1	yes	characteristic
127	#16810487	C₂²	1	1	yes	characteristic
128	#16810487	C₂²	1	1	yes	characteristic
129	#16810485	C₂²	1	1	yes	characteristic
130	#16810485	C₂²	1	1	yes	characteristic
131	#16810485	C₂²	1	1	yes	characteristic
132	#16810485	C₂²	1	1	yes	characteristic
133	#16810482	C₂²	1	1	yes	characteristic
134	#16810482	C₂²	1	1	yes	characteristic
135	#16810480	C₂²	1	1	yes	characteristic
136	#16810480	C₂²	1	1	yes	characteristic
137	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
138	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
139	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
140	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
141	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
142	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
143	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
147	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
148	#16810474	C₂²	1	1	yes	characteristic
149	#16810474	C₂²	1	1	yes	characteristic
150	#16810474	C₂²	1	1	yes	characteristic
151	#16810474	C₂²	1	1	yes	characteristic
152	#16810474	C₂²	1	1	yes	characteristic
153	#16810474	C₂²	1	1	yes	characteristic
154	#16810474	C₂²	1	1	yes	characteristic
155	#16810474	C₂²	1	1	yes	characteristic
156	C₄×#11719921	C₂²	1	1	yes	characteristic
157	C₄×#11719921	C₂²	1	1	yes	characteristic
158	#16810470	C₂²	1	1	yes	characteristic
159	#16810470	C₂²	1	1	yes	characteristic
160	#16810470	C₂²	1	1	yes	characteristic
161	#16810470	C₂²	1	1	yes	characteristic
162	#16810470	C₂²	1	1	yes	characteristic
163	#16810470	C₂²	1	1	yes	characteristic
164	#16810468	C₂²	1	1	yes	characteristic
165	#16810468	C₂²	1	1	yes	characteristic
166	#16810468	C₂²	1	1	yes	characteristic
167	#16810468	C₂²	1	1	yes	characteristic
168	#16810468	C₂²	1	1	yes	characteristic
169	#16810468	C₂²	1	1	yes	characteristic
170	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₅₃×#400	C₂²	1	1	yes	characteristic
173	C₅₃×#400	C₂²	1	1	yes	characteristic
174	C₅₃×#398	C₂²	1	1	yes	characteristic
175	C₅₃×#398	C₂²	1	1	yes	characteristic
176	C₅₃×#398	C₂²	1	1	yes	characteristic
177	C₅₃×#398	C₂²	1	1	yes	characteristic
178	C₅₃×#395	C₂²	1	1	yes	characteristic
179	C₅₃×#395	C₂²	1	1	yes	characteristic
180	C₅₃×#391	C₂²	1	1	yes	characteristic
181	C₅₃×#389	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic
183	C₅₃×#387	C₂²	1	1	yes	characteristic
184	C₅₃×#383	C₂²	1	1	yes	characteristic
185	C₅₃×#382	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
193	Q₈×Dic₅₃	—	2	4	no	—
194	#13133182	—	2	4	no	—
195	#13133182	—	2	4	no	—
196	#13133182	—	2	4	no	—
197	#13133175	—	2	4	no	—
198	#13133175	—	2	4	no	—
199	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂×#11719919	C₂³	1	1	yes	characteristic
213	C₂×#11719919	C₂³	1	1	yes	characteristic
214	C₂×#11719919	C₂³	1	1	yes	characteristic
215	C₂×#11719919	C₂³	1	1	yes	characteristic
216	C₂×#11719919	C₂³	1	1	yes	characteristic
217	C₂×#11719919	C₂³	1	1	yes	characteristic
218	C₂×#11719919	C₂³	1	1	yes	characteristic
219	C₂×#11719919	C₂³	1	1	yes	characteristic
220	C₂×#11719919	C₂³	1	1	yes	characteristic
221	C₂×#11719919	C₂³	1	1	yes	characteristic
222	C₂×#11719919	C₂³	1	1	yes	characteristic
223	C₂×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719921	C₂³	1	1	yes	characteristic
235	C₂×#11719921	C₂³	1	1	yes	characteristic
236	C₂×#11719921	C₂³	1	1	yes	characteristic
237	C₂×#11719921	C₂³	1	1	yes	characteristic
238	C₂×#11719921	C₂³	1	1	yes	characteristic
239	C₂×#11719921	C₂³	1	1	yes	characteristic
240	C₂×#11719921	C₂³	1	1	yes	characteristic
241	C₂×#11719921	C₂³	1	1	yes	characteristic
242	C₂×#11719921	C₂³	1	1	yes	characteristic
243	C₂×#11719921	C₂³	1	1	yes	characteristic
244	C₂×#11719921	C₂³	1	1	yes	characteristic
245	C₂×#11719921	C₂³	1	1	yes	characteristic
246	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
267	C₄²×D₅₃	Q₈	1	8	yes	complemented
268	#13133124	C₂³	1	1	yes	characteristic
269	#13133124	C₂³	1	1	yes	characteristic
270	#13133124	C₂³	1	1	yes	characteristic
271	#13133124	C₂³	1	1	yes	characteristic
272	#13133124	C₂³	1	1	yes	characteristic
273	#13133124	C₂³	1	1	yes	characteristic
274	#13133124	C₂³	1	1	yes	characteristic
275	#13133124	C₂³	1	1	yes	characteristic
276	#13133124	C₂³	1	1	yes	characteristic
277	#13133124	C₂³	1	1	yes	characteristic
278	#13133124	C₂³	1	1	yes	characteristic
279	#13133124	C₂³	1	1	yes	characteristic
280	#13133124	C₂³	1	1	yes	characteristic
281	#13133124	C₂³	1	1	yes	characteristic
282	#13133124	C₂³	1	1	yes	characteristic
283	#13133124	C₂³	1	1	yes	characteristic
284	#13133124	C₂³	1	1	yes	characteristic
285	#13133124	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
350	C₂×Q₈×C₅₃	—	2	2	no	—
351	C₂×Q₈×C₅₃	—	4	1	no	—
352	C₂×Q₈×C₅₃	—	4	1	no	—
353	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×D₅₃	—	2	2	no	—
384	C₂×C₄×D₅₃	—	2	2	no	—
385	C₂×C₄×D₅₃	—	4	1	no	—
386	C₂×C₄×D₅₃	—	4	1	no	—
387	C₂×C₄×D₅₃	—	4	1	no	—
388	C₂×C₄×D₅₃	—	4	1	no	—
389	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
390	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
391	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
392	C₂×Dic₁₀₆	—	2	2	no	—
393	C₂×Dic₁₀₆	—	2	2	no	—
394	C₂×Dic₁₀₆	—	2	2	no	—
395	C₂×Dic₁₀₆	—	4	1	no	—
396	C₂×Dic₁₀₆	—	4	1	no	—
397	C₂×Dic₁₀₆	—	4	1	no	—
398	C₂×Dic₁₀₆	—	4	1	no	—
399	C₂×Dic₁₀₆	—	4	1	no	—
400	C₂×Dic₁₀₆	—	4	1	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	4	1	no	—
407	C₄⋊C₄×C₅₃	—	4	1	no	—
408	C₄⋊C₄×C₅₃	—	4	1	no	—
409	C₄⋊C₄×C₅₃	—	4	1	no	—
410	C₄⋊C₄×C₅₃	—	4	1	no	—
411	C₄⋊C₄×C₅₃	—	4	1	no	—
412	C₄⋊C₄×C₅₃	—	4	1	no	—
413	C₄⋊C₄×C₅₃	—	4	1	no	—
414	C₄²×C₅₃	—	4	1	no	—
415	C₄²×C₅₃	—	4	1	no	—
416	C₄²×C₅₃	C₂×Q₈	1	4	yes	—
417	#11719921	—	2	2	no	—
418	#11719921	—	2	2	no	—
419	#11719921	—	2	2	no	—
420	#11719921	—	2	2	no	—
421	#11719921	—	4	1	no	—
422	#11719921	—	4	1	no	—
423	#11719921	—	4	1	no	—
424	#11719921	—	4	1	no	—
425	#11719921	—	4	1	no	—
426	#11719921	—	4	1	no	—
427	#11719921	—	4	1	no	—
428	#11719921	—	4	1	no	—
429	C₄⋊Dic₅₃	—	2	2	no	—
430	C₄⋊Dic₅₃	—	2	2	no	—
431	C₄⋊Dic₅₃	—	2	2	no	—
432	C₄⋊Dic₅₃	—	2	2	no	—
433	C₄⋊Dic₅₃	—	2	2	no	—
434	C₄⋊Dic₅₃	—	4	1	no	—
435	C₄⋊Dic₅₃	—	4	1	no	—
436	C₄⋊Dic₅₃	—	4	1	no	—
437	C₄⋊Dic₅₃	—	4	1	no	—
438	C₄⋊Dic₅₃	—	4	1	no	—
439	C₄⋊Dic₅₃	—	4	1	no	—
440	C₄⋊Dic₅₃	—	4	1	no	—
441	C₄⋊Dic₅₃	—	4	1	no	—
442	#11719919	—	2	2	no	—
443	#11719919	—	2	2	no	—
444	#11719919	—	2	2	no	—
445	#11719919	—	2	2	no	—
446	#11719919	—	2	2	no	—
447	#11719919	—	2	2	no	—
448	#11719919	—	4	1	no	—
449	#11719919	—	4	1	no	—
450	#11719919	—	4	1	no	—
451	#11719919	—	4	1	no	—
452	#11719919	—	4	1	no	—
453	#11719919	—	4	1	no	—
454	#11719919	—	4	1	no	—
455	#11719919	—	4	1	no	—
456	#11719919	—	4	1	no	—
457	#11719919	—	4	1	no	—
458	#11719919	—	4	1	no	—
459	#11719919	—	4	1	no	—
460	#11719919	—	4	1	no	—
461	#11719919	—	4	1	no	—
462	#11719919	—	4	1	no	—
463	#11719919	—	4	1	no	—
464	C₄×Dic₅₃	—	2	2	no	—
465	C₄×Dic₅₃	—	2	2	no	—
466	C₄×Dic₅₃	—	2	2	no	—
467	C₄×Dic₅₃	—	2	2	no	—
468	C₄×Dic₅₃	—	2	2	no	—
469	C₄×Dic₅₃	—	2	2	no	—
470	C₄×Dic₅₃	—	2	2	no	—
471	C₄×Dic₅₃	—	2	2	no	—
472	C₄×Dic₅₃	—	2	2	no	—
473	C₄×Dic₅₃	—	2	2	no	—
474	C₄×Dic₅₃	—	4	1	no	—
475	C₄×Dic₅₃	—	4	1	no	—
476	C₄×Dic₅₃	—	4	1	no	—
477	C₄×Dic₅₃	—	4	1	no	—
478	C₄×Dic₅₃	—	4	1	no	—
479	C₄×Dic₅₃	—	4	1	no	—
480	C₄×Dic₅₃	C₂×Q₈	1	4	yes	—
481	C₄×Dic₅₃	C₂×Q₈	1	4	yes	—
482	C₄×Dic₅₃	C₂×Q₈	1	4	yes	—
483	C₄×Dic₅₃	#41	1	4	yes	—
484	C₄×Dic₅₃	#41	1	4	yes	—
485	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
486	C₂²×D₅₃	—	2	1	no	—
487	C₂²×D₅₃	—	2	1	no	—
488	C₂²×D₅₃	—	2	1	no	—
489	C₂²×D₅₃	—	2	1	no	—
490	C₂²×D₅₃	—	2	1	no	—
491	C₂²×D₅₃	—	2	1	no	—
492	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
493	Q₈×C₅₃	—	4	4	no	—
494	C₂×C₄×C₅₃	—	2	1	no	—
495	C₂×C₄×C₅₃	—	2	1	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	1	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	2	1	no	—
519	C₂×C₄×C₅₃	—	2	1	no	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	1	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
535	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
536	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
537	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
538	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
539	C₂×Dic₅₃	—	2	1	no	—
540	C₂×Dic₅₃	—	2	1	no	—
541	C₂×Dic₅₃	—	2	1	no	—
542	C₂×Dic₅₃	—	2	1	no	—
543	C₂×Dic₅₃	—	2	1	no	—
544	C₂×Dic₅₃	—	2	1	no	—
545	C₂×Dic₅₃	—	2	1	no	—
546	C₂×Dic₅₃	—	2	1	no	—
547	C₂×Dic₅₃	—	2	1	no	—
548	C₂×Dic₅₃	—	2	1	no	—
549	C₂×Dic₅₃	—	2	1	no	—
550	C₂×Dic₅₃	—	2	1	no	—
551	C₂×Dic₅₃	—	2	1	no	—
552	C₂×Dic₅₃	—	2	1	no	—
553	C₂×Dic₅₃	—	2	1	no	—
554	C₂×Dic₅₃	—	2	1	no	—
555	C₂×Dic₅₃	—	2	1	no	—
556	C₂×Dic₅₃	—	2	1	no	—
557	C₂×Dic₅₃	—	2	1	no	—
558	C₂×Dic₅₃	—	2	1	no	—
559	C₂×Dic₅₃	—	2	1	no	—
560	C₂×Dic₅₃	—	2	1	no	—
561	C₂×Dic₅₃	—	2	1	no	—
562	C₂×Dic₅₃	—	2	1	no	—
563	C₂×Dic₅₃	—	2	1	no	—
564	C₂×Dic₅₃	—	2	1	no	—
565	C₂×Dic₅₃	—	2	1	no	—
566	C₂×Dic₅₃	—	2	1	no	—
567	C₂×Dic₅₃	—	2	1	no	—
568	C₂×Dic₅₃	—	2	1	no	—
569	C₂×Dic₅₃	—	2	1	no	—
570	C₂×Dic₅₃	—	2	1	no	—
571	C₂×Dic₅₃	—	2	1	no	—
572	C₂×Dic₅₃	—	2	1	no	—
573	C₂×Dic₅₃	—	2	1	no	—
574	C₂×Dic₅₃	—	2	1	no	—
575	C₂×Dic₅₃	—	2	1	no	—
576	C₂×Dic₅₃	—	2	1	no	—
577	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
578	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
579	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
580	C₂×Dic₅₃	C₂×#41	1	2	yes	—
581	C₂×Dic₅₃	C₂×#41	1	2	yes	—
582	C₂×Dic₅₃	C₂×#41	1	2	yes	—
583	C₂×Dic₅₃	C₂×#41	1	2	yes	—
584	C₄×D₅₃	—	2	8	no	—
585	C₄×D₅₃	—	4	4	no	—
586	C₄×D₅₃	—	4	4	no	—
587	Dic₁₀₆	—	4	4	no	—
588	Dic₁₀₆	—	4	4	no	—
589	Dic₁₀₆	—	4	4	no	—
590	#34644	—	53	1	no	maximal, Sylow
591	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
592	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
593	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
594	C₂²×C₅₃	#585	1	1	yes	characteristic
595	C₂²×C₅₃	#585	1	1	yes	characteristic
596	C₂²×C₅₃	#585	1	1	yes	characteristic
597	C₂²×C₅₃	#585	1	1	yes	characteristic
598	C₂×D₅₃	—	2	2	no	—
599	C₂×D₅₃	—	2	2	no	—
600	C₂×D₅₃	—	2	2	no	—
601	C₂×D₅₃	—	4	1	no	—
602	C₂×D₅₃	—	4	1	no	—
603	C₂×D₅₃	—	4	1	no	—
604	C₂×D₅₃	—	4	1	no	—
605	C₄×C₅₃	—	2	2	no	—
606	C₄×C₅₃	—	2	2	no	—
607	C₄×C₅₃	—	2	2	no	—
608	C₄×C₅₃	—	2	2	no	—
609	C₄×C₅₃	—	2	2	no	—
610	C₄×C₅₃	—	4	1	no	—
611	C₄×C₅₃	—	4	1	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	—	4	1	no	—
614	C₄×C₅₃	—	4	1	no	—
615	C₄×C₅₃	—	4	1	no	—
616	C₄×C₅₃	—	4	1	no	—
617	C₄×C₅₃	—	4	1	no	—
618	C₄×C₅₃	—	4	1	no	—
619	C₄×C₅₃	—	4	1	no	—
620	Dic₅₃	—	2	2	no	—
621	Dic₅₃	—	2	2	no	—
622	Dic₅₃	—	2	2	no	—
623	Dic₅₃	—	2	2	no	—
624	Dic₅₃	—	4	1	no	—
625	Dic₅₃	—	4	1	no	—
626	Dic₅₃	—	4	1	no	—
627	Dic₅₃	—	4	1	no	—
628	Dic₅₃	—	4	1	no	—
629	Dic₅₃	—	4	1	no	—
630	Dic₅₃	—	4	1	no	—
631	Dic₅₃	—	4	1	no	—
632	Dic₅₃	—	4	1	no	—
633	Dic₅₃	—	4	1	no	—
634	Dic₅₃	#533	1	4	yes	—
635	#2667	—	53	1	no	—
636	#2667	—	53	1	no	—
637	#2667	—	53	1	no	—
638	#2667	—	53	1	no	—
639	#2666	—	53	1	no	—
640	#2666	—	53	1	no	—
641	#2666	—	53	1	no	—
642	#2666	—	53	1	no	—
643	#2666	—	53	1	no	—
644	#2666	—	53	1	no	—
645	#2666	—	53	1	no	—
646	#2666	D₅₃	1	1	yes	characteristic, complemented
647	#2665	—	53	1	no	—
648	#2665	—	53	1	no	—
649	#2665	—	53	1	no	—
650	#2665	—	53	1	no	—
651	#2402	—	53	1	no	—
652	#2402	—	53	1	no	—
653	#2399	—	53	1	no	—
654	#2399	—	53	1	no	—
655	#2396	—	53	1	no	—
656	#2396	—	53	1	no	—
657	#2396	—	53	1	no	—
658	#2396	—	53	1	no	—
659	#2295	—	53	1	no	—
660	#2295	—	53	1	no	—
661	#2295	—	53	1	no	—
662	#2295	—	53	1	no	—
663	#2283	—	53	1	no	—
664	#2283	—	53	1	no	—
665	C₄×#117	—	53	1	no	—
666	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
667	C₂×C₅₃	#3455	1	1	yes	characteristic
668	C₂×C₅₃	#3455	1	1	yes	characteristic
669	C₂×C₅₃	#3455	1	1	yes	characteristic
670	C₂×C₅₃	#3455	1	1	yes	characteristic
671	C₂×C₅₃	#3458	1	1	yes	characteristic
672	C₂×C₅₃	#3458	1	1	yes	characteristic
673	D₅₃	—	4	2	no	—
674	C₂×C₄×Q₈	—	53	1	no	—
675	C₂×C₄×Q₈	—	53	1	no	—
676	C₂×C₄×Q₈	—	53	1	no	—
677	C₂×C₄×Q₈	—	53	1	no	—
678	C₂×#117	—	53	1	no	—
679	C₂×#117	—	53	1	no	—
680	C₂²×C₄²	—	53	1	no	—
681	#400	—	53	1	no	—
682	#400	—	53	1	no	—
683	#400	—	53	1	no	—
684	#400	—	53	1	no	—
685	#400	—	53	1	no	—
686	#400	—	53	1	no	—
687	#400	—	53	1	no	—
688	#400	—	53	1	no	—
689	#400	—	53	1	no	—
690	#400	—	53	1	no	—
691	#400	C₂×D₅₃	1	1	yes	characteristic
692	#400	C₂×D₅₃	1	1	yes	characteristic
693	#399	—	53	1	no	—
694	#399	—	53	1	no	—
695	#399	—	53	1	no	—
696	#399	—	53	1	no	—
697	#398	—	53	1	no	—
698	#398	—	53	1	no	—
699	#398	—	53	1	no	—
700	#398	—	53	1	no	—
701	#398	—	53	1	no	—
702	#398	—	53	1	no	—
703	#398	—	53	1	no	—
704	#398	—	53	1	no	—
705	#398	—	53	1	no	—
706	#398	—	53	1	no	—
707	#398	—	53	1	no	—
708	#398	—	53	1	no	—
709	#398	—	53	1	no	—
710	#398	—	53	1	no	—
711	#398	—	53	1	no	—
712	#398	—	53	1	no	—
713	#398	—	53	1	no	—
714	#398	—	53	1	no	—
715	#398	—	53	1	no	—
716	#398	—	53	1	no	—
717	#398	C₂×D₅₃	1	1	yes	characteristic
718	#398	C₂×D₅₃	1	1	yes	characteristic
719	#398	C₂×D₅₃	1	1	yes	characteristic
720	#398	C₂×D₅₃	1	1	yes	characteristic
721	#396	—	53	1	no	—
722	#396	—	53	1	no	—
723	#396	—	53	1	no	—
724	#396	—	53	1	no	—
725	#396	—	53	1	no	—
726	#396	—	53	1	no	—
727	#396	—	53	1	no	—
728	#396	—	53	1	no	—
729	#395	—	53	1	no	—
730	#395	—	53	1	no	—
731	#395	—	53	1	no	—
732	#395	—	53	1	no	—
733	#395	—	53	1	no	—
734	#395	—	53	1	no	—
735	#395	—	53	1	no	—
736	#395	—	53	1	no	—
737	#395	—	53	1	no	—
738	#395	—	53	1	no	—
739	#395	C₂×D₅₃	1	1	yes	characteristic
740	#395	C₂×D₅₃	1	1	yes	characteristic
741	#393	—	53	1	no	—
742	#393	—	53	1	no	—
743	#393	—	53	1	no	—
744	#393	—	53	1	no	—
745	#391	—	53	1	no	—
746	#391	—	53	1	no	—
747	#391	—	53	1	no	—
748	#391	—	53	1	no	—
749	#391	—	53	1	no	—
750	#391	—	53	1	no	—
751	#391	—	53	1	no	—
752	#391	C₂×D₅₃	1	1	yes	characteristic
753	#389	—	53	1	no	—
754	#389	—	53	1	no	—
755	#389	—	53	1	no	—
756	#389	—	53	1	no	—
757	#389	—	53	1	no	—
758	#389	—	53	1	no	—
759	#389	—	53	1	no	—
760	#389	C₂×D₅₃	1	1	yes	characteristic
761	#387	—	53	1	no	—
762	#387	—	53	1	no	—
763	#387	—	53	1	no	—
764	#387	—	53	1	no	—
765	#387	—	53	1	no	—
766	#387	—	53	1	no	—
767	#387	—	53	1	no	—
768	#387	—	53	1	no	—
769	#387	—	53	1	no	—
770	#387	—	53	1	no	—
771	#387	—	53	1	no	—
772	#387	—	53	1	no	—
773	#387	—	53	1	no	—
774	#387	—	53	1	no	—
775	#387	C₂×D₅₃	1	1	yes	characteristic
776	#387	C₂×D₅₃	1	1	yes	characteristic
777	#383	—	53	1	no	—
778	#383	—	53	1	no	—
779	#383	—	53	1	no	—
780	#383	C₂×D₅₃	1	1	yes	characteristic
781	#382	—	53	1	no	—
782	#382	—	53	1	no	—
783	#382	—	53	1	no	—
784	#382	C₂×D₅₃	1	1	yes	characteristic
785	#381	—	53	1	no	—
786	#381	—	53	1	no	—
787	#381	—	53	1	no	—
788	#381	—	53	1	no	—
789	#380	—	53	1	no	—
790	#380	—	53	1	no	—
791	#380	—	53	1	no	—
792	#380	—	53	1	no	—
793	C₄×C₄⋊C₄	—	53	1	no	—
794	C₄×C₄⋊C₄	—	53	1	no	—
795	C₄×C₄⋊C₄	—	53	1	no	—
796	C₄×C₄⋊C₄	—	53	1	no	—
797	C₄×C₄⋊C₄	—	53	1	no	—
798	C₄×C₄⋊C₄	—	53	1	no	—
799	C₄×C₄⋊C₄	—	53	1	no	—
800	C₄×C₄⋊C₄	—	53	1	no	—
801	C₄×C₄⋊C₄	—	53	1	no	—
802	C₄×C₄⋊C₄	—	53	1	no	—
803	C₄×C₄⋊C₄	—	53	1	no	—
804	C₄×C₄⋊C₄	—	53	1	no	—
805	C₄×C₄⋊C₄	—	53	1	no	—
806	C₄×C₄⋊C₄	—	53	1	no	—
807	C₄×C₄⋊C₄	—	53	1	no	—
808	C₄×C₄⋊C₄	—	53	1	no	—
809	C₄×C₄⋊C₄	—	53	1	no	—
810	C₄×C₄⋊C₄	—	53	1	no	—
811	C₄×C₄⋊C₄	—	53	1	no	—
812	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
813	C₄×C₂²⋊C₄	—	53	1	no	—
814	C₄×C₂²⋊C₄	—	53	1	no	—
815	C₄×C₂²⋊C₄	—	53	1	no	—
816	C₄×C₂²⋊C₄	—	53	1	no	—
817	C₄×C₂²⋊C₄	—	53	1	no	—
818	C₄×C₂²⋊C₄	—	53	1	no	—
819	C₄×C₂²⋊C₄	—	53	1	no	—
820	C₄×C₂²⋊C₄	—	53	1	no	—
821	#376	—	53	1	no	—
822	#376	—	53	1	no	—
823	#376	—	53	1	no	—
824	#376	—	53	1	no	—
825	#376	—	53	1	no	—
826	#376	—	53	1	no	—
827	C₄³	—	53	1	no	—
828	C₄³	—	53	1	no	—
829	C₅₃	#34644	1	1	yes	characteristic, complemented, Sylow
830	C₂²×Q₈	—	53	1	no	—
831	C₂²×Q₈	—	53	1	no	—
832	C₂²×Q₈	—	53	1	no	—
833	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
834	C₂³×C₄	—	53	1	no	—
835	C₂³×C₄	—	53	1	no	—
836	C₂³×C₄	—	53	1	no	—
837	C₄×Q₈	—	106	4	no	—
838	C₄×Q₈	—	106	4	no	—
839	C₄×Q₈	—	106	4	no	—
840	C₄×Q₈	—	106	4	no	—
841	#117	—	106	4	no	—
842	#117	—	106	4	no	—
843	C₂×C₄⋊C₄	—	53	1	no	—
844	C₂×C₄⋊C₄	—	53	1	no	—
845	C₂×C₄⋊C₄	—	53	1	no	—
846	C₂×C₄⋊C₄	—	53	1	no	—
847	C₂×C₄⋊C₄	—	53	1	no	—
848	C₂×C₄⋊C₄	—	53	1	no	—
849	C₂×C₄⋊C₄	—	53	1	no	—
850	C₂×C₄⋊C₄	—	53	1	no	—
851	C₂×C₄⋊C₄	—	53	1	no	—
852	C₂×C₄⋊C₄	—	53	1	no	—
853	C₂×C₄⋊C₄	—	53	1	no	—
854	C₂×C₄⋊C₄	—	53	1	no	—
855	C₂×C₄⋊C₄	—	53	1	no	—
856	C₂×C₄⋊C₄	—	53	1	no	—
857	C₂×C₄⋊C₄	—	53	1	no	—
858	C₂×C₄⋊C₄	—	53	1	no	—
859	C₂×C₄⋊C₄	—	53	1	no	—
860	C₂×C₄⋊C₄	—	53	1	no	—
861	C₂×C₄⋊C₄	—	53	1	no	—
862	C₂×C₄⋊C₄	—	53	1	no	—
863	C₂×C₄⋊C₄	—	53	1	no	—
864	C₂×C₄⋊C₄	—	53	1	no	—
865	C₂×C₄⋊C₄	—	53	1	no	—
866	C₂×C₄⋊C₄	—	53	1	no	—
867	C₂×C₄⋊C₄	—	53	1	no	—
868	C₂×C₄⋊C₄	—	53	1	no	—
869	C₂×C₄⋊C₄	—	53	1	no	—
870	C₂×C₄⋊C₄	—	53	1	no	—
871	C₂×C₄⋊C₄	—	53	1	no	—
872	C₂×C₄⋊C₄	—	53	1	no	—
873	C₂×C₄⋊C₄	—	53	1	no	—
874	C₂×C₄⋊C₄	—	53	1	no	—
875	C₂×C₄⋊C₄	—	53	1	no	—
876	C₂×C₄⋊C₄	—	53	1	no	—
877	C₂×C₄⋊C₄	—	53	1	no	—
878	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
891	C₂×C₂²⋊C₄	—	53	1	no	—
892	C₂×C₂²⋊C₄	—	53	1	no	—
893	C₂×C₂²⋊C₄	—	53	1	no	—
894	C₂×C₂²⋊C₄	—	53	1	no	—
895	C₂×C₂²⋊C₄	—	53	1	no	—
896	C₂×C₂²⋊C₄	—	53	1	no	—
897	C₂×C₂²⋊C₄	—	53	1	no	—
898	C₂×C₂²⋊C₄	—	53	1	no	—
899	C₂×C₂²⋊C₄	—	53	1	no	—
900	C₂×C₂²⋊C₄	—	53	1	no	—
901	C₂×C₂²⋊C₄	—	53	1	no	—
902	C₂×C₂²⋊C₄	—	53	1	no	—
903	C₂×C₄²	—	53	1	no	—
904	C₂×C₄²	—	53	1	no	—
905	C₂×C₄²	—	53	1	no	—
906	C₂×C₄²	—	53	1	no	—
907	C₂×C₄²	—	53	1	no	—
908	C₂×C₄²	—	53	8	no	—
909	C₂×C₄²	—	53	1	no	—
910	C₂×C₄²	—	53	1	no	—
911	C₂×C₄²	—	53	1	no	—
912	C₂×C₄²	—	53	1	no	—
913	C₂×C₄²	—	53	1	no	—
914	C₂×C₄²	—	53	1	no	—
915	C₂×C₄²	—	53	1	no	—
916	C₂×C₄²	—	53	1	no	—
917	C₂×C₄²	—	53	1	no	—
918	C₂×C₄²	—	53	1	no	—
919	C₂×C₄²	—	53	1	no	—
920	C₂×C₄²	—	53	1	no	—
921	C₂×C₄²	—	53	1	no	—
922	C₂×C₄²	—	53	1	no	—
923	C₂×C₄²	—	53	1	no	—
924	C₂×C₄²	—	53	1	no	—
925	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
926	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
927	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
928	#95	—	53	1	no	—
929	#95	—	53	1	no	—
930	#95	—	53	1	no	—
931	#95	—	53	1	no	—
932	#95	—	53	1	no	—
933	#95	—	53	1	no	—
934	#95	—	53	1	no	—
935	#95	—	53	1	no	—
936	#95	—	53	1	no	—
937	#95	—	53	1	no	—
938	#95	—	53	1	no	—
939	#95	—	53	1	no	—
940	#95	—	53	1	no	—
941	#95	—	53	1	no	—
942	#95	—	53	1	no	—
943	#95	—	53	1	no	—
944	#95	—	53	1	no	—
945	#95	—	53	1	no	—
946	#95	—	53	1	no	—
947	#95	—	53	1	no	—
948	#95	—	53	1	no	—
949	#95	—	53	1	no	—
950	#95	—	53	1	no	—
951	#95	—	53	1	no	—
952	#95	—	53	1	no	—
953	#95	—	53	1	no	—
954	#95	—	53	1	no	—
955	#95	—	53	1	no	—
956	#95	—	53	1	no	—
957	#95	—	53	1	no	—
958	#95	—	53	1	no	—
959	#95	—	53	1	no	—
960	#95	—	53	1	no	—
961	#95	—	53	1	no	—
962	#95	—	53	1	no	—
963	#95	—	53	1	no	—
964	#95	—	53	1	no	—
965	#95	—	53	1	no	—
966	#95	—	53	1	no	—
967	#95	—	53	1	no	—
968	#95	—	53	1	no	—
969	#95	—	53	1	no	—
970	#95	—	53	1	no	—
971	#95	—	53	1	no	—
972	#95	—	53	1	no	—
973	#95	—	53	1	no	—
974	#95	C₂²×D₅₃	1	1	yes	characteristic
975	#95	C₂²×D₅₃	1	1	yes	characteristic
976	#95	C₂²×D₅₃	1	1	yes	characteristic
977	#95	C₂²×D₅₃	1	1	yes	characteristic
978	#95	C₂²×D₅₃	1	1	yes	characteristic
979	#95	C₂²×D₅₃	1	1	yes	characteristic
980	#95	C₂²×D₅₃	1	1	yes	characteristic
981	#95	C₂²×D₅₃	1	1	yes	characteristic
982	#95	C₂²×D₅₃	1	1	yes	characteristic
983	#95	C₂²×D₅₃	1	1	yes	characteristic
984	#95	C₂²×D₅₃	1	1	yes	characteristic
985	#95	C₂²×D₅₃	1	1	yes	characteristic
986	#95	C₂²×D₅₃	1	1	yes	characteristic
987	#95	C₂²×D₅₃	1	1	yes	characteristic
988	#95	C₂²×D₅₃	1	1	yes	characteristic
989	#95	C₂²×D₅₃	1	1	yes	characteristic
990	#95	C₂²×D₅₃	1	1	yes	characteristic
991	#95	C₂²×D₅₃	1	1	yes	characteristic
992	C₂⁴	—	53	1	no	—
993	C₂×Q₈	—	2	2	no	—
994	C₂×Q₈	—	4	1	no	—
995	C₂×Q₈	—	4	1	no	—
996	C₂×Q₈	—	106	2	no	—
997	C₂×Q₈	—	106	2	no	—
998	C₂×Q₈	—	106	2	no	—
999	C₂×Q₈	—	212	1	no	—
1000	C₂×Q₈	—	212	1	no	—
1001	C₂×Q₈	—	212	1	no	—
1002	C₂×Q₈	—	212	1	no	—
1003	C₂×Q₈	—	212	1	no	—
1004	C₂×Q₈	—	212	1	no	—
1005	C₂²×C₄	—	53	1	no	—
1006	C₂²×C₄	—	53	1	no	—
1007	C₂²×C₄	—	53	1	no	—
1008	C₂²×C₄	—	53	1	no	—
1009	C₂²×C₄	—	53	1	no	—
1010	C₂²×C₄	—	53	4	no	—
1011	C₂²×C₄	—	53	4	no	—
1012	C₂²×C₄	—	53	4	no	—
1013	C₂²×C₄	—	53	1	no	—
1014	C₂²×C₄	—	53	1	no	—
1015	C₂²×C₄	—	53	1	no	—
1016	C₂²×C₄	—	53	1	no	—
1017	C₂²×C₄	—	53	1	no	—
1018	C₂²×C₄	—	53	1	no	—
1019	C₂²×C₄	—	53	1	no	—
1020	C₂²×C₄	—	53	1	no	—
1021	C₂²×C₄	—	53	1	no	—
1022	C₂²×C₄	—	53	1	no	—
1023	C₂²×C₄	—	106	2	no	—
1024	C₂²×C₄	—	106	2	no	—
1025	C₂²×C₄	—	212	1	no	—
1026	C₂²×C₄	—	212	1	no	—
1027	C₂²×C₄	—	212	1	no	—
1028	C₂²×C₄	—	212	1	no	—
1029	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1030	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1031	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1032	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1033	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1034	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1035	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1036	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1037	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1038	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1039	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1040	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1041	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1042	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1043	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	—	2	2	no	—
1047	C₄⋊C₄	—	2	2	no	—
1048	C₄⋊C₄	—	2	2	no	—
1049	C₄⋊C₄	—	4	1	no	—
1050	C₄⋊C₄	—	4	1	no	—
1051	C₄⋊C₄	—	4	1	no	—
1052	C₄⋊C₄	—	4	1	no	—
1053	C₄⋊C₄	—	4	1	no	—
1054	C₄⋊C₄	—	4	1	no	—
1055	C₄⋊C₄	—	4	1	no	—
1056	C₄⋊C₄	—	4	1	no	—
1057	C₄⋊C₄	—	106	2	no	—
1058	C₄⋊C₄	—	106	2	no	—
1059	C₄⋊C₄	—	106	2	no	—
1060	C₄⋊C₄	—	106	2	no	—
1061	C₄⋊C₄	—	106	2	no	—
1062	C₄⋊C₄	—	106	2	no	—
1063	C₄⋊C₄	—	106	2	no	—
1064	C₄⋊C₄	—	106	2	no	—
1065	C₄⋊C₄	—	106	2	no	—
1066	C₄⋊C₄	—	106	2	no	—
1067	C₄⋊C₄	—	106	2	no	—
1068	C₄⋊C₄	—	212	1	no	—
1069	C₄⋊C₄	—	212	1	no	—
1070	C₄⋊C₄	—	212	1	no	—
1071	C₄⋊C₄	—	212	1	no	—
1072	C₄⋊C₄	—	212	1	no	—
1073	C₄⋊C₄	—	212	1	no	—
1074	C₄⋊C₄	—	212	1	no	—
1075	C₄⋊C₄	—	212	1	no	—
1076	C₄⋊C₄	—	212	1	no	—
1077	C₄⋊C₄	—	212	1	no	—
1078	C₄⋊C₄	—	212	1	no	—
1079	C₄⋊C₄	—	212	1	no	—
1080	C₄⋊C₄	—	212	1	no	—
1081	C₄⋊C₄	—	212	1	no	—
1082	C₄⋊C₄	—	212	1	no	—
1083	C₄⋊C₄	—	212	1	no	—
1084	C₄⋊C₄	—	212	1	no	—
1085	C₄⋊C₄	—	212	1	no	—
1086	C₄⋊C₄	—	212	1	no	—
1087	C₄⋊C₄	—	212	1	no	—
1088	C₄⋊C₄	—	212	1	no	—
1089	C₄⋊C₄	—	212	1	no	—
1090	C₄⋊C₄	—	212	1	no	—
1091	C₄⋊C₄	—	212	1	no	—
1092	C₂²⋊C₄	—	106	2	no	—
1093	C₂²⋊C₄	—	106	2	no	—
1094	C₂²⋊C₄	—	106	2	no	—
1095	C₂²⋊C₄	—	106	2	no	—
1096	C₂²⋊C₄	—	212	1	no	—
1097	C₂²⋊C₄	—	212	1	no	—
1098	C₂²⋊C₄	—	212	1	no	—
1099	C₂²⋊C₄	—	212	1	no	—
1100	C₂²⋊C₄	—	212	1	no	—
1101	C₂²⋊C₄	—	212	1	no	—
1102	C₂²⋊C₄	—	212	1	no	—
1103	C₂²⋊C₄	—	212	1	no	—
1104	C₄²	—	4	1	no	—
1105	C₄²	—	4	1	no	—
1106	C₄²	—	53	4	no	—
1107	C₄²	—	53	4	no	—
1108	C₄²	—	53	4	no	—
1109	C₄²	—	53	4	no	—
1110	C₄²	—	53	4	no	—
1111	C₄²	—	106	2	no	—
1112	C₄²	—	106	2	no	—
1113	C₄²	—	106	2	no	—
1114	C₄²	—	106	2	no	—
1115	C₄²	—	106	2	no	—
1116	C₄²	—	106	2	no	—
1117	C₄²	—	106	2	no	—
1118	C₄²	—	106	2	no	—
1119	C₄²	—	106	2	no	—
1120	C₄²	—	106	2	no	—
1121	C₄²	—	212	1	no	—
1122	C₄²	—	212	1	no	—
1123	C₄²	—	212	1	no	—
1124	C₄²	—	212	1	no	—
1125	C₄²	—	212	1	no	—
1126	C₄²	—	212	1	no	—
1127	C₄²	Q₈×D₅₃	1	4	yes	—
1128	C₂³	—	53	2	no	—
1129	C₂³	—	106	1	no	—
1130	C₂³	—	106	1	no	—
1131	C₂³	—	106	1	no	—
1132	C₂³	—	106	1	no	—
1133	C₂³	—	106	1	no	—
1134	C₂³	—	106	1	no	—
1135	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1136	Q₈	—	4	4	no	—
1137	Q₈	—	212	4	no	—
1138	Q₈	—	212	4	no	—
1139	Q₈	—	212	4	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	2	1	no	—
1150	C₂×C₄	—	2	1	no	—
1151	C₂×C₄	—	2	1	no	—
1152	C₂×C₄	—	2	1	no	—
1153	C₂×C₄	—	2	1	no	—
1154	C₂×C₄	—	2	1	no	—
1155	C₂×C₄	—	2	1	no	—
1156	C₂×C₄	—	2	1	no	—
1157	C₂×C₄	—	2	1	no	—
1158	C₂×C₄	—	2	1	no	—
1159	C₂×C₄	—	2	1	no	—
1160	C₂×C₄	—	2	1	no	—
1161	C₂×C₄	—	2	1	no	—
1162	C₂×C₄	—	2	1	no	—
1163	C₂×C₄	—	2	1	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	1	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	53	2	no	—
1181	C₂×C₄	—	53	2	no	—
1182	C₂×C₄	—	53	2	no	—
1183	C₂×C₄	—	53	2	no	—
1184	C₂×C₄	—	53	2	no	—
1185	C₂×C₄	—	53	2	no	—
1186	C₂×C₄	—	53	2	no	—
1187	C₂×C₄	—	106	8	no	—
1188	C₂×C₄	—	106	1	no	—
1189	C₂×C₄	—	106	1	no	—
1190	C₂×C₄	—	106	1	no	—
1191	C₂×C₄	—	106	1	no	—
1192	C₂×C₄	—	106	1	no	—
1193	C₂×C₄	—	106	1	no	—
1194	C₂×C₄	—	106	1	no	—
1195	C₂×C₄	—	106	1	no	—
1196	C₂×C₄	—	106	1	no	—
1197	C₂×C₄	—	106	1	no	—
1198	C₂×C₄	—	106	1	no	—
1199	C₂×C₄	—	106	1	no	—
1200	C₂×C₄	—	106	1	no	—
1201	C₂×C₄	—	106	1	no	—
1202	C₂×C₄	—	106	1	no	—
1203	C₂×C₄	—	106	1	no	—
1204	C₂×C₄	—	106	1	no	—
1205	C₂×C₄	—	106	1	no	—
1206	C₂×C₄	—	106	1	no	—
1207	C₂×C₄	—	106	1	no	—
1208	C₂×C₄	—	106	1	no	—
1209	C₂×C₄	—	106	1	no	—
1210	C₂×C₄	—	106	1	no	—
1211	C₂×C₄	—	106	1	no	—
1212	C₂×C₄	—	106	1	no	—
1213	C₂×C₄	—	106	1	no	—
1214	C₂×C₄	—	106	1	no	—
1215	C₂×C₄	—	106	1	no	—
1216	C₂×C₄	—	106	1	no	—
1217	C₂×C₄	—	106	1	no	—
1218	C₂×C₄	—	106	1	no	—
1219	C₂×C₄	—	106	1	no	—
1220	C₂×C₄	—	106	1	no	—
1221	C₂×C₄	—	106	1	no	—
1222	C₂×C₄	—	106	1	no	—
1223	C₂×C₄	—	106	1	no	—
1224	C₂×C₄	—	106	1	no	—
1225	C₂×C₄	—	106	1	no	—
1226	C₂×C₄	—	212	4	no	—
1227	C₂×C₄	—	212	4	no	—
1228	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1229	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1230	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1231	C₂×C₄	#41×D₅₃	1	2	yes	—
1232	C₂×C₄	#41×D₅₃	1	2	yes	—
1233	C₂²	—	106	2	no	—
1234	C₂²	—	106	2	no	—
1235	C₂²	—	106	2	no	—
1236	C₂²	—	212	1	no	—
1237	C₂²	—	212	1	no	—
1238	C₂²	—	212	1	no	—
1239	C₂²	—	212	1	no	—
1240	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1241	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1242	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1243	C₂²	#16811458	1	1	yes	characteristic
1244	C₂²	#16811458	1	1	yes	characteristic
1245	C₂²	#16811460	1	1	yes	characteristic
1246	C₂²	#16811460	1	1	yes	characteristic
1247	C₄	—	2	2	no	—
1248	C₄	—	2	2	no	—
1249	C₄	—	2	2	no	—
1250	C₄	—	2	2	no	—
1251	C₄	—	2	2	no	—
1252	C₄	—	4	1	no	—
1253	C₄	—	4	1	no	—
1254	C₄	—	4	1	no	—
1255	C₄	—	4	1	no	—
1256	C₄	—	4	1	no	—
1257	C₄	—	4	1	no	—
1258	C₄	—	4	1	no	—
1259	C₄	—	4	1	no	—
1260	C₄	—	4	1	no	—
1261	C₄	—	4	1	no	—
1262	C₄	—	53	4	no	—
1263	C₄	—	106	2	no	—
1264	C₄	—	106	2	no	—
1265	C₄	—	106	2	no	—
1266	C₄	—	106	2	no	—
1267	C₄	—	212	1	no	—
1268	C₄	—	212	1	no	—
1269	C₄	—	212	1	no	—
1270	C₄	—	212	1	no	—
1271	C₄	—	212	1	no	—
1272	C₄	—	212	1	no	—
1273	C₄	—	212	1	no	—
1274	C₄	—	212	1	no	—
1275	C₄	—	212	1	no	—
1276	C₄	—	212	1	no	—
1277	C₂	—	212	2	no	—
1278	C₂	#533×D₅₃	1	1	yes	characteristic
1279	C₂	#20288097	1	1	yes	characteristic
1280	C₂	#20288101	1	1	yes	characteristic
1281	C₂	#20288102	1	1	yes	characteristic
1282	C₂	#20288106	1	1	yes	characteristic
1283	C₂	#20288119	1	1	yes	characteristic
1284	C₂	#20288119	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2666	C₂
prime radical	C₂³×D₅₃	C₂⁴
hypercenter	#2666	D₅₃
hypocenter	C₅₃	#34644
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2666

Complements

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

N	H ≅ G/N	type
5. #20280899	C₂	semidirect
6. #20280898	C₂	semidirect
7. #20280897	C₂	semidirect
8. #20280896	C₂	semidirect
9. #20280895	C₂	semidirect
10. #20280894	C₂	semidirect
11. #20280893	C₂	semidirect
16. #20278021	C₂	semidirect
17. #20278019	C₂	semidirect
18. #20278007	C₂	semidirect
19. #20278005	C₂	semidirect
24. #20277190	C₂	semidirect
25. #20277188	C₂	semidirect
26. #20277188	C₂	semidirect
27. #20277186	C₂	semidirect
31. C₅₃×#2666	C₂	semidirect
267. C₄²×D₅₃	Q₈	semidirect
646. #2666	D₅₃	semidirect
829. C₅₃	#34644	semidirect

Maximal subgroups

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

subgroup	index
#20280916	2
#20280915	2
#20280914	2
#20280913	2
#20280899	2
#20280898	2
#20280897	2
#20280896	2
#20280895	2
#20280894	2
#20280893	2
#20280892	2
#20280891	2
#20280890	2
#20280889	2
#20278021	2
#20278019	2
#20278007	2
#20278005	2
#20277992	2
#20277988	2
#20277986	2
#20277190	2
#20277188	2
#20277186	2
#20277112	2
#20277108	2
C₄×#13133175	2
C₅₃×#2666	2
#34644	53