Subgroups — #27548299

Order 13568.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811231	C₂	1	1	yes	maximal, characteristic
2	#20277908	C₂	1	1	yes	maximal, characteristic
3	#20277900	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277894	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277879	C₂	1	1	yes	maximal, characteristic
6	#20277840	C₂	1	1	yes	maximal, characteristic
7	#20277831	C₂	1	1	yes	maximal, characteristic
8	#20277829	C₂	1	1	yes	maximal, characteristic
9	#20277817	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277809	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277806	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277803	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277797	C₂	1	1	yes	maximal, characteristic
14	#20277680	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277609	C₂	1	1	yes	maximal, characteristic
16	#20277568	C₂	1	1	yes	maximal, characteristic
17	#20277519	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277518	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277515	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277514	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277496	C₂	1	1	yes	maximal, characteristic
22	#20277490	C₂	1	1	yes	maximal, characteristic
23	#20277486	C₂	1	1	yes	maximal, characteristic
24	#20277470	C₂	1	1	yes	maximal, characteristic
25	#20277454	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277447	C₂	1	1	yes	maximal, characteristic
27	#20277363	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277265	C₂	1	1	yes	maximal, characteristic
30	#20277191	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2355	C₂	1	1	yes	maximal, characteristic, complemented
32	#16811231	C₄	1	16	yes	complemented
33	C₂×#13133215	C₂²	1	1	yes	characteristic
34	C₂×#13133212	C₂²	1	1	yes	characteristic
35	C₂×#13133212	C₂²	1	1	yes	characteristic
36	C₂×#13133211	C₂²	1	1	yes	characteristic
37	C₂×#13133211	C₂²	1	1	yes	characteristic
38	C₂×#13133209	C₂²	1	1	yes	characteristic
39	C₂×#13133209	C₂²	1	1	yes	characteristic
40	C₂×#13133208	C₂²	1	1	yes	characteristic
41	C₂×#13133207	C₂²	1	1	yes	characteristic
42	C₂×#13133207	C₂²	1	1	yes	characteristic
43	C₂×#13133197	C₂²	1	1	yes	characteristic
44	C₂×#13133193	C₂²	1	1	yes	characteristic
45	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
46	C₂×#13133174	C₂²	1	1	yes	characteristic
47	#16810530	C₂²	1	1	yes	characteristic
48	#16810530	C₂²	1	1	yes	characteristic
49	#16810527	C₂²	1	1	yes	characteristic
50	#16810527	C₂²	1	1	yes	characteristic
51	#16810527	C₂²	1	1	yes	characteristic
52	#16810527	C₂²	1	1	yes	characteristic
53	#16810521	C₂²	1	1	yes	characteristic
54	#16810521	C₂²	1	1	yes	characteristic
55	#16810520	C₂²	1	1	yes	characteristic
56	#16810520	C₂²	1	1	yes	characteristic
57	#16810520	C₂²	1	1	yes	characteristic
58	#16810520	C₂²	1	1	yes	characteristic
59	#16810519	C₂²	1	1	yes	characteristic
60	#16810519	C₂²	1	1	yes	characteristic
61	#16810518	C₂²	1	1	yes	characteristic
62	#16810518	C₂²	1	1	yes	characteristic
63	#16810518	C₂²	1	1	yes	characteristic
64	#16810518	C₂²	1	1	yes	characteristic
65	#16810518	C₂²	1	1	yes	characteristic
66	#16810518	C₂²	1	1	yes	characteristic
67	#16810518	C₂²	1	1	yes	characteristic
68	#16810518	C₂²	1	1	yes	characteristic
69	#16810518	C₂²	1	1	yes	characteristic
70	#16810518	C₂²	1	1	yes	characteristic
71	#16810515	C₂²	1	1	yes	characteristic
72	#16810515	C₂²	1	1	yes	characteristic
73	#16810514	C₂²	1	1	yes	characteristic
74	#16810514	C₂²	1	1	yes	characteristic
75	#16810514	C₂²	1	1	yes	characteristic
76	#16810514	C₂²	1	1	yes	characteristic
77	#16810513	C₂²	1	1	yes	characteristic
78	#16810513	C₂²	1	1	yes	characteristic
79	#16810513	C₂²	1	1	yes	characteristic
80	#16810513	C₂²	1	1	yes	characteristic
81	#16810512	C₂²	1	1	yes	characteristic
82	#16810512	C₂²	1	1	yes	characteristic
83	#16810510	C₂²	1	1	yes	characteristic
84	#16810510	C₂²	1	1	yes	characteristic
85	#16810510	C₂²	1	1	yes	characteristic
86	#16810510	C₂²	1	1	yes	characteristic
87	#16810509	C₂²	1	1	yes	characteristic
88	#16810509	C₂²	1	1	yes	characteristic
89	#16810509	C₂²	1	1	yes	characteristic
90	#16810509	C₂²	1	1	yes	characteristic
91	#16810508	C₂²	1	1	yes	characteristic
92	#16810508	C₂²	1	1	yes	characteristic
93	#16810508	C₂²	1	1	yes	characteristic
94	#16810508	C₂²	1	1	yes	characteristic
95	#16810508	C₂²	1	1	yes	characteristic
96	#16810508	C₂²	1	1	yes	characteristic
97	#16810507	C₂²	1	1	yes	characteristic
98	#16810507	C₂²	1	1	yes	characteristic
99	#16810507	C₂²	1	1	yes	characteristic
100	#16810507	C₂²	1	1	yes	characteristic
101	#16810506	C₂²	1	1	yes	characteristic
102	#16810506	C₂²	1	1	yes	characteristic
103	#16810506	C₂²	1	1	yes	characteristic
104	#16810506	C₂²	1	1	yes	characteristic
105	#16810506	C₂²	1	1	yes	characteristic
106	#16810506	C₂²	1	1	yes	characteristic
107	#16810505	C₂²	1	1	yes	characteristic
108	#16810505	C₂²	1	1	yes	characteristic
109	#16810505	C₂²	1	1	yes	characteristic
110	#16810505	C₂²	1	1	yes	characteristic
111	#16810505	C₂²	1	1	yes	characteristic
112	#16810505	C₂²	1	1	yes	characteristic
113	#16810504	C₂²	1	1	yes	characteristic
114	#16810504	C₂²	1	1	yes	characteristic
115	#16810504	C₂²	1	1	yes	characteristic
116	#16810504	C₂²	1	1	yes	characteristic
117	#16810504	C₂²	1	1	yes	characteristic
118	#16810504	C₂²	1	1	yes	characteristic
119	#16810504	C₂²	1	1	yes	characteristic
120	#16810504	C₂²	1	1	yes	characteristic
121	#16810504	C₂²	1	1	yes	characteristic
122	#16810504	C₂²	1	1	yes	characteristic
123	#16810497	C₂²	1	1	yes	characteristic
124	#16810497	C₂²	1	1	yes	characteristic
125	#16810494	C₂²	1	1	yes	characteristic
126	#16810494	C₂²	1	1	yes	characteristic
127	#16810494	C₂²	1	1	yes	characteristic
128	#16810494	C₂²	1	1	yes	characteristic
129	#16810491	C₂²	1	1	yes	characteristic
130	#16810491	C₂²	1	1	yes	characteristic
131	#16810490	C₂²	1	1	yes	characteristic
132	#16810490	C₂²	1	1	yes	characteristic
133	#16810490	C₂²	1	1	yes	characteristic
134	#16810489	C₂²	1	1	yes	characteristic
135	#16810487	C₂²	1	1	yes	characteristic
136	#16810485	C₂²	1	1	yes	characteristic
137	#16810482	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×#11719919	C₂²	1	1	yes	characteristic
143	C₄×#11719919	C₂²	1	1	yes	characteristic
144	C₄×#11719919	C₂²	1	1	yes	characteristic
145	C₄×#11719919	C₂²	1	1	yes	characteristic
146	C₄×#11719919	C₂²	1	1	yes	characteristic
147	C₄×#11719919	C₂²	1	1	yes	characteristic
148	C₄×#11719919	C₂²	1	1	yes	characteristic
149	C₄×#11719919	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊Dic₅₃	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	#16810474	C₂²	1	1	yes	characteristic
157	#16810474	C₂²	1	1	yes	characteristic
158	#16810474	C₂²	1	1	yes	characteristic
159	#16810474	C₂²	1	1	yes	characteristic
160	C₄×#11719921	C₂²	1	1	yes	characteristic
161	C₄×#11719921	C₂²	1	1	yes	characteristic
162	#16810470	C₂²	1	1	yes	characteristic
163	#16810470	C₂²	1	1	yes	characteristic
164	#16810470	C₂²	1	1	yes	characteristic
165	#16810470	C₂²	1	1	yes	characteristic
166	#16810470	C₂²	1	1	yes	characteristic
167	#16810469	C₂²	1	1	yes	characteristic
168	#16810469	C₂²	1	1	yes	characteristic
169	#16810469	C₂²	1	1	yes	characteristic
170	#16810468	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
173	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#391	C₂²	1	1	yes	characteristic
175	C₅₃×#391	C₂²	1	1	yes	characteristic
176	C₅₃×#387	C₂²	1	1	yes	characteristic
177	C₅₃×#387	C₂²	1	1	yes	characteristic
178	C₅₃×#387	C₂²	1	1	yes	characteristic
179	C₅₃×#387	C₂²	1	1	yes	characteristic
180	C₅₃×#384	C₂²	1	1	yes	characteristic
181	C₅₃×#382	C₂²	1	1	yes	characteristic
182	C₅₃×#382	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
192	#13133215	C₂×C₄	1	8	yes	complemented
193	#13133212	C₂×C₄	1	8	yes	—
194	#13133212	C₂×C₄	1	8	yes	—
195	#13133211	C₂×C₄	1	8	yes	—
196	#13133211	C₂×C₄	1	8	yes	—
197	#13133209	C₂×C₄	1	8	yes	complemented
198	#13133209	C₂×C₄	1	8	yes	complemented
199	#13133208	C₂×C₄	1	8	yes	complemented
200	#13133207	C₂×C₄	1	8	yes	complemented
201	#13133207	C₂×C₄	1	8	yes	complemented
202	#13133197	C₂×C₄	1	8	yes	—
203	#13133193	C₂×C₄	1	8	yes	—
204	C₄×Dic₁₀₆	C₂×C₄	1	8	yes	complemented
205	#13133174	C₂×C₄	1	8	yes	—
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×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₅₃	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×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#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×#11719921	C₂³	1	1	yes	characteristic
247	C₂×#11719921	C₂³	1	1	yes	characteristic
248	C₂×#11719921	C₂³	1	1	yes	characteristic
249	C₂×#11719921	C₂³	1	1	yes	characteristic
250	C₂×#11719921	C₂³	1	1	yes	characteristic
251	C₂×#11719921	C₂³	1	1	yes	characteristic
252	C₂×#11719921	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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	#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	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	C₄×Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
359	C₂×Q₈×C₅₃	—	4	1	no	—
360	C₂×Q₈×C₅₃	—	4	1	no	—
361	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×D₅₃	—	2	2	no	—
393	C₂×C₄×D₅₃	—	4	1	no	—
394	C₂×C₄×D₅₃	—	4	1	no	—
395	C₂×C₄×D₅₃	—	4	1	no	—
396	C₂×C₄×D₅₃	—	4	1	no	—
397	C₂×C₄×D₅₃	—	4	1	no	—
398	C₂×C₄×D₅₃	—	4	1	no	—
399	C₂×C₄×D₅₃	—	4	1	no	—
400	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
401	C₂×Dic₁₀₆	—	4	1	no	—
402	C₂×Dic₁₀₆	—	4	1	no	—
403	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	4	1	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	C₂²×C₄	1	4	yes	—
413	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
414	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
415	C₄²×C₅₃	—	4	1	no	—
416	C₄²×C₅₃	—	4	1	no	—
417	C₄²×C₅₃	—	4	1	no	—
418	C₄²×C₅₃	—	4	1	no	—
419	C₄²×C₅₃	—	4	1	no	—
420	C₄²×C₅₃	—	4	1	no	—
421	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
422	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
423	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
424	#11719921	—	2	2	no	—
425	#11719921	—	4	1	no	—
426	#11719921	—	4	1	no	—
427	#11719921	—	4	1	no	—
428	#11719921	—	4	1	no	—
429	#11719921	—	4	1	no	—
430	#11719921	C₂²×C₄	1	4	yes	—
431	#11719921	C₂²×C₄	1	4	yes	—
432	#11719921	C₂²×C₄	1	4	yes	—
433	#11719921	C₂²×C₄	1	4	yes	—
434	#11719921	C₂²×C₄	1	4	yes	—
435	#11719921	C₂²×C₄	1	4	yes	—
436	C₄⋊Dic₅₃	—	2	2	no	—
437	C₄⋊Dic₅₃	—	4	1	no	—
438	C₄⋊Dic₅₃	—	4	1	no	—
439	C₄⋊Dic₅₃	—	4	1	no	—
440	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
441	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
442	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
443	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
444	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
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	C₂²×C₄	1	4	yes	—
460	#11719919	C₂²×C₄	1	4	yes	—
461	#11719919	C₂²×C₄	1	4	yes	—
462	#11719919	C₂²×C₄	1	4	yes	—
463	#11719919	C₂²×C₄	1	4	yes	—
464	#11719919	C₂²×C₄	1	4	yes	—
465	#11719919	C₂²×C₄	1	4	yes	—
466	#11719919	C₂²×C₄	1	4	yes	—
467	#11719919	C₂²×C₄	1	4	yes	—
468	#11719919	C₂²×C₄	1	4	yes	—
469	#11719919	C₂²×C₄	1	4	yes	—
470	#11719919	C₂²×C₄	1	4	yes	—
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	—	4	1	no	—
481	C₄×Dic₅₃	—	4	1	no	—
482	C₄×Dic₅₃	—	4	1	no	—
483	C₄×Dic₅₃	—	4	1	no	—
484	C₄×Dic₅₃	—	4	1	no	—
485	C₄×Dic₅₃	—	4	1	no	—
486	C₄×Dic₅₃	—	4	1	no	—
487	C₄×Dic₅₃	—	4	1	no	—
488	C₄×Dic₅₃	—	4	1	no	—
489	C₄×Dic₅₃	—	4	1	no	—
490	C₄×Dic₅₃	—	4	1	no	—
491	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
492	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
493	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
494	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
495	C₂²×D₅₃	—	2	1	no	—
496	C₂²×D₅₃	—	2	1	no	—
497	C₂²×D₅₃	—	2	1	no	—
498	C₂²×D₅₃	—	2	1	no	—
499	C₂²×D₅₃	—	2	1	no	—
500	C₂²×D₅₃	—	2	1	no	—
501	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
502	Q₈×C₅₃	—	4	4	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	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
541	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
542	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
543	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
544	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
545	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
546	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
547	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
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	—	2	1	no	—
578	C₂×Dic₅₃	—	2	1	no	—
579	C₂×Dic₅₃	—	2	1	no	—
580	C₂×Dic₅₃	—	2	1	no	—
581	C₂×Dic₅₃	—	2	1	no	—
582	C₂×Dic₅₃	—	2	1	no	—
583	C₂×Dic₅₃	—	2	1	no	—
584	C₂×Dic₅₃	—	2	1	no	—
585	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
586	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
587	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
588	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
589	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
590	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
591	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
592	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
593	C₄×D₅₃	—	4	4	no	—
594	C₄×D₅₃	—	8	2	no	—
595	C₄×D₅₃	—	8	2	no	—
596	Dic₁₀₆	—	4	4	no	—
597	#34445	—	53	1	no	maximal, Sylow
598	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
599	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
600	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
601	C₂²×C₅₃	#585	1	1	yes	characteristic
602	C₂²×C₅₃	#585	1	1	yes	characteristic
603	C₂²×C₅₃	#585	1	1	yes	characteristic
604	C₂²×C₅₃	#585	1	1	yes	characteristic
605	C₂×D₅₃	—	2	2	no	—
606	C₂×D₅₃	—	2	2	no	—
607	C₂×D₅₃	—	2	2	no	—
608	C₂×D₅₃	—	4	1	no	—
609	C₂×D₅₃	—	4	1	no	—
610	C₂×D₅₃	—	4	1	no	—
611	C₂×D₅₃	—	4	1	no	—
612	C₄×C₅₃	—	2	2	no	—
613	C₄×C₅₃	—	2	2	no	—
614	C₄×C₅₃	—	2	2	no	—
615	C₄×C₅₃	—	2	2	no	—
616	C₄×C₅₃	—	2	2	no	—
617	C₄×C₅₃	—	2	2	no	—
618	C₄×C₅₃	—	2	2	no	—
619	C₄×C₅₃	—	2	2	no	—
620	C₄×C₅₃	—	4	1	no	—
621	C₄×C₅₃	—	4	1	no	—
622	C₄×C₅₃	—	4	1	no	—
623	C₄×C₅₃	—	4	1	no	—
624	C₄×C₅₃	—	4	1	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	1	no	—
627	Dic₅₃	—	2	2	no	—
628	Dic₅₃	—	2	2	no	—
629	Dic₅₃	—	2	2	no	—
630	Dic₅₃	—	2	2	no	—
631	Dic₅₃	—	2	2	no	—
632	Dic₅₃	—	2	2	no	—
633	Dic₅₃	—	2	2	no	—
634	Dic₅₃	—	2	2	no	—
635	Dic₅₃	—	4	1	no	—
636	Dic₅₃	—	4	1	no	—
637	Dic₅₃	—	4	1	no	—
638	Dic₅₃	—	4	1	no	—
639	Dic₅₃	—	4	1	no	—
640	Dic₅₃	—	4	1	no	—
641	Dic₅₃	—	4	1	no	—
642	C₂×#541	—	53	1	no	—
643	#2383	—	53	1	no	—
644	#2382	—	53	1	no	—
645	#2381	—	53	1	no	—
646	#2378	—	53	1	no	—
647	#2373	—	53	1	no	—
648	#2373	—	53	1	no	—
649	#2373	—	53	1	no	—
650	#2371	—	53	1	no	—
651	#2370	—	53	1	no	—
652	#2370	—	53	1	no	—
653	#2369	—	53	1	no	—
654	#2368	—	53	1	no	—
655	#2356	—	53	1	no	—
656	#2355	D₅₃	1	1	yes	characteristic, complemented
657	#2347	—	53	1	no	—
658	#2343	—	53	1	no	—
659	#2336	—	53	1	no	—
660	#2336	—	53	1	no	—
661	#2336	—	53	1	no	—
662	#2336	—	53	1	no	—
663	#2334	—	53	1	no	—
664	#2334	—	53	1	no	—
665	#2334	—	53	1	no	—
666	#2332	—	53	1	no	—
667	#2330	—	53	1	no	—
668	#2329	—	53	1	no	—
669	#2320	—	53	1	no	—
670	C₄×#125	—	53	1	no	—
671	C₄×#126	—	53	1	no	—
672	#2295	—	53	1	no	—
673	C₂×C₅₃	#3428	1	1	yes	characteristic
674	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
675	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
676	C₂×C₅₃	#3553	1	1	yes	characteristic
677	C₂×C₅₃	#3555	1	1	yes	characteristic
678	C₂×C₅₃	#3564	1	1	yes	characteristic
679	C₂×C₅₃	#3566	1	1	yes	characteristic
680	D₅₃	—	4	2	no	—
681	#541	—	53	16	no	—
682	C₂×C₄⋊Q₈	—	53	1	no	—
683	C₂×#126	—	53	1	no	—
684	C₂×#126	—	53	1	no	—
685	C₂×#126	—	53	1	no	—
686	C₂×#126	—	53	1	no	—
687	C₂×#125	—	53	1	no	—
688	C₂×#125	—	53	1	no	—
689	C₂×#125	—	53	1	no	—
690	C₂×#125	—	53	1	no	—
691	C₂×#125	—	53	1	no	—
692	C₂×C₂²⋊Q₈	—	53	1	no	—
693	C₂×C₂²⋊Q₈	—	53	1	no	—
694	C₂×C₄×Q₈	—	53	1	no	—
695	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
696	C₂×#117	—	53	1	no	—
697	#391	—	53	1	no	—
698	#391	—	53	1	no	—
699	#391	—	53	1	no	—
700	#391	—	53	1	no	—
701	#391	—	53	1	no	—
702	#391	—	53	1	no	—
703	#391	C₂×D₅₃	1	1	yes	characteristic
704	#391	C₂×D₅₃	1	1	yes	characteristic
705	#389	—	53	1	no	—
706	#389	—	53	1	no	—
707	#389	—	53	1	no	—
708	#389	—	53	1	no	—
709	#389	—	53	1	no	—
710	#389	—	53	1	no	—
711	#389	—	53	1	no	—
712	#389	—	53	1	no	—
713	#389	—	53	1	no	—
714	#389	—	53	1	no	—
715	#389	—	53	1	no	—
716	#389	—	53	1	no	—
717	#389	—	53	1	no	—
718	#389	—	53	1	no	—
719	#389	—	53	1	no	—
720	#389	—	53	1	no	—
721	#389	—	53	1	no	—
722	#389	—	53	1	no	—
723	#388	—	53	1	no	—
724	#388	—	53	1	no	—
725	#388	—	53	1	no	—
726	#388	—	53	1	no	—
727	#388	—	53	1	no	—
728	#388	—	53	1	no	—
729	#388	—	53	1	no	—
730	#388	—	53	1	no	—
731	#388	—	53	1	no	—
732	#388	—	53	1	no	—
733	#388	—	53	1	no	—
734	#388	—	53	1	no	—
735	#387	—	53	1	no	—
736	#387	—	53	1	no	—
737	#387	—	53	1	no	—
738	#387	—	53	1	no	—
739	#387	—	53	1	no	—
740	#387	—	53	1	no	—
741	#387	—	53	1	no	—
742	#387	—	53	1	no	—
743	#387	—	53	1	no	—
744	#387	—	53	1	no	—
745	#387	—	53	1	no	—
746	#387	—	53	1	no	—
747	#387	—	53	1	no	—
748	#387	—	53	1	no	—
749	#387	—	53	1	no	—
750	#387	—	53	1	no	—
751	#387	—	53	1	no	—
752	#387	—	53	1	no	—
753	#387	—	53	1	no	—
754	#387	—	53	1	no	—
755	#387	—	53	1	no	—
756	#387	—	53	1	no	—
757	#387	—	53	1	no	—
758	#387	—	53	1	no	—
759	#387	—	53	1	no	—
760	#387	—	53	1	no	—
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	#387	C₂×D₅₃	1	1	yes	characteristic
778	#387	C₂×D₅₃	1	1	yes	characteristic
779	#385	—	53	1	no	—
780	#385	—	53	1	no	—
781	#385	—	53	1	no	—
782	#385	—	53	1	no	—
783	#385	—	53	1	no	—
784	#385	—	53	1	no	—
785	#384	C₂×D₅₃	1	1	yes	characteristic
786	#383	—	53	1	no	—
787	#383	—	53	1	no	—
788	#383	—	53	1	no	—
789	#383	—	53	1	no	—
790	#383	—	53	1	no	—
791	#382	—	53	1	no	—
792	#382	—	53	1	no	—
793	#382	C₂×D₅₃	1	1	yes	characteristic
794	#382	C₂×D₅₃	1	1	yes	characteristic
795	#381	—	53	1	no	—
796	#380	—	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	—	53	1	no	—
813	C₄×C₄⋊C₄	—	53	1	no	—
814	C₄×C₄⋊C₄	—	53	1	no	—
815	C₄×C₄⋊C₄	—	53	1	no	—
816	C₄×C₄⋊C₄	—	53	1	no	—
817	C₄×C₄⋊C₄	—	53	1	no	—
818	C₄×C₄⋊C₄	—	53	1	no	—
819	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
820	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
821	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
822	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
823	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
824	C₄×C₂²⋊C₄	—	53	1	no	—
825	C₄×C₂²⋊C₄	—	53	1	no	—
826	C₄×C₂²⋊C₄	—	53	1	no	—
827	C₄×C₂²⋊C₄	—	53	1	no	—
828	C₄×C₂²⋊C₄	—	53	1	no	—
829	C₄×C₂²⋊C₄	—	53	1	no	—
830	C₄×C₂²⋊C₄	—	53	1	no	—
831	#376	—	53	1	no	—
832	#376	—	53	1	no	—
833	#376	—	53	1	no	—
834	#376	—	53	1	no	—
835	C₂×#95	—	53	1	no	—
836	C₄³	—	53	1	no	—
837	C₅₃	#34445	1	1	yes	characteristic, complemented, Sylow
838	C₂²×Q₈	—	53	1	no	—
839	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
840	C₂³×C₄	—	53	1	no	—
841	C₂³×C₄	—	53	1	no	—
842	C₂³×C₄	—	53	1	no	—
843	C₄⋊Q₈	—	53	8	no	—
844	#126	—	53	8	no	—
845	#126	—	53	8	no	—
846	#126	—	53	8	no	—
847	#126	—	53	8	no	—
848	#125	—	53	8	no	—
849	#125	—	53	8	no	—
850	#125	—	53	8	no	—
851	#125	—	53	8	no	—
852	#125	—	53	8	no	—
853	C₂²⋊Q₈	—	53	8	no	—
854	C₂²⋊Q₈	—	53	8	no	—
855	C₄×Q₈	—	53	8	no	—
856	C₄×Q₈	C₄×D₅₃	1	8	yes	complemented
857	#117	—	53	8	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	—	53	1	no	—
879	C₂×C₄⋊C₄	—	53	1	no	—
880	C₂×C₄⋊C₄	—	53	1	no	—
881	C₂×C₄⋊C₄	—	53	1	no	—
882	C₂×C₄⋊C₄	—	53	1	no	—
883	C₂×C₄⋊C₄	—	53	1	no	—
884	C₂×C₄⋊C₄	—	53	1	no	—
885	C₂×C₄⋊C₄	—	53	1	no	—
886	C₂×C₄⋊C₄	—	53	1	no	—
887	C₂×C₄⋊C₄	—	53	1	no	—
888	C₂×C₄⋊C₄	—	53	1	no	—
889	C₂×C₄⋊C₄	—	53	1	no	—
890	C₂×C₄⋊C₄	—	53	1	no	—
891	C₂×C₄⋊C₄	—	53	1	no	—
892	C₂×C₄⋊C₄	—	53	1	no	—
893	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
898	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
900	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
904	C₂×C₂²⋊C₄	—	53	1	no	—
905	C₂×C₂²⋊C₄	—	53	1	no	—
906	C₂×C₂²⋊C₄	—	53	1	no	—
907	C₂×C₂²⋊C₄	—	53	1	no	—
908	C₂×C₂²⋊C₄	—	53	1	no	—
909	C₂×C₂²⋊C₄	—	53	1	no	—
910	C₂×C₂²⋊C₄	—	53	1	no	—
911	C₂×C₂²⋊C₄	—	53	1	no	—
912	C₂×C₂²⋊C₄	—	53	1	no	—
913	C₂×C₂²⋊C₄	—	53	1	no	—
914	C₂×C₂²⋊C₄	—	53	1	no	—
915	C₂×C₂²⋊C₄	—	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	—	53	1	no	—
926	C₂×C₄²	—	53	1	no	—
927	C₂×C₄²	—	53	1	no	—
928	C₂×C₄²	—	53	1	no	—
929	C₂×C₄²	—	53	1	no	—
930	C₂×C₄²	—	53	1	no	—
931	C₂×C₄²	—	53	1	no	—
932	C₂×C₄²	—	53	1	no	—
933	C₂×C₄²	—	53	1	no	—
934	C₂×C₄²	—	53	1	no	—
935	C₂×C₄²	—	53	1	no	—
936	C₂×C₄²	—	53	1	no	—
937	C₂×C₄²	—	53	1	no	—
938	C₂×C₄²	—	53	1	no	—
939	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
940	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
941	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
942	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
943	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
944	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
945	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
946	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
947	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
975	#95	—	53	1	no	—
976	#95	—	53	1	no	—
977	#95	—	53	1	no	—
978	#95	—	53	1	no	—
979	#95	—	53	1	no	—
980	#95	—	53	1	no	—
981	#95	—	53	1	no	—
982	#95	—	53	1	no	—
983	#95	—	53	1	no	—
984	#95	—	53	1	no	—
985	#95	—	53	1	no	—
986	#95	—	53	1	no	—
987	#95	—	53	1	no	—
988	#95	—	53	1	no	—
989	#95	—	53	1	no	—
990	#95	—	53	1	no	—
991	#95	—	53	1	no	—
992	#95	—	53	1	no	—
993	#95	—	53	1	no	—
994	#95	C₂²×D₅₃	1	1	yes	characteristic
995	#95	C₂²×D₅₃	1	1	yes	characteristic
996	#95	C₂²×D₅₃	1	1	yes	characteristic
997	#95	C₂²×D₅₃	1	1	yes	characteristic
998	#95	C₂²×D₅₃	1	1	yes	characteristic
999	#95	C₂²×D₅₃	1	1	yes	characteristic
1000	#95	C₂²×D₅₃	1	1	yes	characteristic
1001	#95	C₂²×D₅₃	1	1	yes	characteristic
1002	#95	C₂²×D₅₃	1	1	yes	characteristic
1003	#95	C₂²×D₅₃	1	1	yes	characteristic
1004	#95	C₂²×D₅₃	1	1	yes	characteristic
1005	#95	C₂²×D₅₃	1	1	yes	characteristic
1006	#95	C₂²×D₅₃	1	1	yes	characteristic
1007	#95	C₂²×D₅₃	1	1	yes	characteristic
1008	C₂⁴	—	53	1	no	—
1009	C₂×Q₈	—	4	1	no	—
1010	C₂×Q₈	—	4	1	no	—
1011	C₂×Q₈	—	53	4	no	—
1012	C₂×Q₈	—	212	1	no	—
1013	C₂×Q₈	—	212	1	no	—
1014	C₂×Q₈	C₂×C₄×D₅₃	1	4	yes	—
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	—	53	4	no	—
1024	C₂²×C₄	—	53	1	no	—
1025	C₂²×C₄	—	53	1	no	—
1026	C₂²×C₄	—	53	1	no	—
1027	C₂²×C₄	—	53	1	no	—
1028	C₂²×C₄	—	53	1	no	—
1029	C₂²×C₄	—	53	1	no	—
1030	C₂²×C₄	—	53	1	no	—
1031	C₂²×C₄	—	106	2	no	—
1032	C₂²×C₄	—	212	1	no	—
1033	C₂²×C₄	—	212	1	no	—
1034	C₂²×C₄	—	212	1	no	—
1035	C₂²×C₄	—	212	1	no	—
1036	C₂²×C₄	—	212	1	no	—
1037	C₂²×C₄	—	212	1	no	—
1038	C₂²×C₄	—	212	1	no	—
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	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1047	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1048	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	4	1	no	—
1056	C₄⋊C₄	—	4	1	no	—
1057	C₄⋊C₄	—	4	1	no	—
1058	C₄⋊C₄	—	4	1	no	—
1059	C₄⋊C₄	—	4	1	no	—
1060	C₄⋊C₄	—	4	1	no	—
1061	C₄⋊C₄	—	4	1	no	—
1062	C₄⋊C₄	—	53	4	no	—
1063	C₄⋊C₄	—	53	4	no	—
1064	C₄⋊C₄	—	53	4	no	—
1065	C₄⋊C₄	—	53	4	no	—
1066	C₄⋊C₄	—	53	4	no	—
1067	C₄⋊C₄	—	53	4	no	—
1068	C₄⋊C₄	—	53	4	no	—
1069	C₄⋊C₄	—	53	4	no	—
1070	C₄⋊C₄	—	53	4	no	—
1071	C₄⋊C₄	—	53	4	no	—
1072	C₄⋊C₄	—	53	4	no	—
1073	C₄⋊C₄	—	53	4	no	—
1074	C₄⋊C₄	—	53	4	no	—
1075	C₄⋊C₄	—	53	4	no	—
1076	C₄⋊C₄	—	53	4	no	—
1077	C₄⋊C₄	—	53	4	no	—
1078	C₄⋊C₄	—	53	4	no	—
1079	C₄⋊C₄	—	106	2	no	—
1080	C₄⋊C₄	—	106	2	no	—
1081	C₄⋊C₄	—	106	2	no	—
1082	C₄⋊C₄	—	106	2	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	C₄⋊C₄	—	212	1	no	—
1093	C₄⋊C₄	—	212	1	no	—
1094	C₄⋊C₄	—	212	1	no	—
1095	C₄⋊C₄	—	212	1	no	—
1096	C₄⋊C₄	—	212	1	no	—
1097	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1098	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1099	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1100	C₂²⋊C₄	—	53	4	no	—
1101	C₂²⋊C₄	—	53	4	no	—
1102	C₂²⋊C₄	—	53	4	no	—
1103	C₂²⋊C₄	—	53	4	no	—
1104	C₂²⋊C₄	—	53	4	no	—
1105	C₂²⋊C₄	—	53	4	no	—
1106	C₂²⋊C₄	—	106	2	no	—
1107	C₂²⋊C₄	—	212	1	no	—
1108	C₂²⋊C₄	—	212	1	no	—
1109	C₂²⋊C₄	—	212	1	no	—
1110	C₂²⋊C₄	—	212	1	no	—
1111	C₂²⋊C₄	—	212	1	no	—
1112	C₄²	—	4	1	no	—
1113	C₄²	—	4	1	no	—
1114	C₄²	—	4	1	no	—
1115	C₄²	—	4	1	no	—
1116	C₄²	—	4	1	no	—
1117	C₄²	—	4	1	no	—
1118	C₄²	—	53	4	no	—
1119	C₄²	—	53	4	no	—
1120	C₄²	—	53	4	no	—
1121	C₄²	—	106	2	no	—
1122	C₄²	—	106	2	no	—
1123	C₄²	—	106	2	no	—
1124	C₄²	—	212	1	no	—
1125	C₄²	—	212	1	no	—
1126	C₄²	—	212	1	no	—
1127	C₄²	—	212	1	no	—
1128	C₄²	—	212	1	no	—
1129	C₄²	—	212	1	no	—
1130	C₄²	—	212	1	no	—
1131	C₄²	—	212	1	no	—
1132	C₄²	—	212	1	no	—
1133	C₄²	—	212	1	no	—
1134	C₄²	—	212	1	no	—
1135	C₄²	—	212	1	no	—
1136	C₄²	—	212	1	no	—
1137	C₄²	—	212	1	no	—
1138	C₄²	—	212	1	no	—
1139	C₄²	—	212	1	no	—
1140	C₄²	—	212	1	no	—
1141	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1142	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1143	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1144	C₂³	—	53	2	no	—
1145	C₂³	—	106	1	no	—
1146	C₂³	—	106	1	no	—
1147	C₂³	—	106	1	no	—
1148	C₂³	—	106	1	no	—
1149	C₂³	—	106	1	no	—
1150	C₂³	—	106	1	no	—
1151	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1152	Q₈	—	4	4	no	—
1153	Q₈	—	212	4	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	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	53	2	no	—
1192	C₂×C₄	—	53	2	no	—
1193	C₂×C₄	—	53	2	no	—
1194	C₂×C₄	—	53	2	no	—
1195	C₂×C₄	—	53	2	no	—
1196	C₂×C₄	—	53	2	no	—
1197	C₂×C₄	—	53	2	no	—
1198	C₂×C₄	—	53	2	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	—	106	1	no	—
1227	C₂×C₄	—	106	1	no	—
1228	C₂×C₄	—	106	1	no	—
1229	C₂×C₄	—	106	1	no	—
1230	C₂×C₄	—	106	1	no	—
1231	C₂×C₄	—	106	1	no	—
1232	C₂×C₄	—	106	1	no	—
1233	C₂×C₄	—	106	1	no	—
1234	C₂×C₄	—	106	1	no	—
1235	C₂×C₄	—	106	1	no	—
1236	C₂×C₄	—	424	2	no	—
1237	C₂×C₄	—	424	2	no	—
1238	C₂×C₄	—	212	4	no	—
1239	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1240	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1241	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1242	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1243	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1244	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1245	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1246	C₂×C₄	#13133265	1	2	yes	—
1247	C₂²	—	106	2	no	—
1248	C₂²	—	106	2	no	—
1249	C₂²	—	106	2	no	—
1250	C₂²	—	212	1	no	—
1251	C₂²	—	212	1	no	—
1252	C₂²	—	212	1	no	—
1253	C₂²	—	212	1	no	—
1254	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1255	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1256	C₂²	C₂×#13133265	1	1	yes	characteristic
1257	C₂²	#16811458	1	1	yes	characteristic
1258	C₂²	#16811459	1	1	yes	characteristic
1259	C₂²	#16811459	1	1	yes	characteristic
1260	C₂²	#16811459	1	1	yes	characteristic
1261	C₄	—	2	2	no	—
1262	C₄	—	2	2	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₄	—	2	2	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	106	2	no	—
1277	C₄	—	106	2	no	—
1278	C₄	—	106	2	no	—
1279	C₄	—	106	2	no	—
1280	C₄	—	106	2	no	—
1281	C₄	—	106	2	no	—
1282	C₄	—	106	2	no	—
1283	C₄	—	106	2	no	—
1284	C₄	—	212	1	no	—
1285	C₄	—	212	1	no	—
1286	C₄	—	212	1	no	—
1287	C₄	—	212	1	no	—
1288	C₄	—	212	1	no	—
1289	C₄	—	212	1	no	—
1290	C₄	—	212	1	no	—
1291	C₂	—	212	2	no	—
1292	C₂	#20287916	1	1	yes	characteristic
1293	C₂	#20287926	1	1	yes	characteristic
1294	C₂	C₄×#13133265	1	1	yes	characteristic
1295	C₂	#20289167	1	1	yes	characteristic
1296	C₂	#20289195	1	1	yes	characteristic
1297	C₂	#20289334	1	1	yes	characteristic
1298	C₂	#20289384	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2355	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂³×D₅₃	C₂⁴
hypercenter	#2355	D₅₃
hypocenter	C₅₃	#34445
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2355

Complements

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

N	H ≅ G/N	type
3. #20277900	C₂	semidirect
4. #20277894	C₂	semidirect
9. #20277817	C₂	semidirect
10. #20277809	C₂	semidirect
11. #20277806	C₂	semidirect
12. #20277803	C₂	semidirect
14. #20277680	C₂	semidirect
17. #20277519	C₂	semidirect
18. #20277518	C₂	semidirect
19. #20277515	C₂	semidirect
20. #20277514	C₂	semidirect
25. #20277454	C₂	semidirect
27. #20277363	C₂	semidirect
28. C₄×#13133207	C₂	semidirect
30. #20277191	C₂	semidirect
31. C₅₃×#2355	C₂	semidirect
32. #16811231	C₄	semidirect
192. #13133215	C₂×C₄	semidirect
197. #13133209	C₂×C₄	semidirect
198. #13133209	C₂×C₄	semidirect
199. #13133208	C₂×C₄	semidirect
200. #13133207	C₂×C₄	semidirect
201. #13133207	C₂×C₄	semidirect
204. C₄×Dic₁₀₆	C₂×C₄	semidirect
323. C₄×Q₈×C₅₃	C₂×C₄	semidirect
656. #2355	D₅₃	semidirect
837. C₅₃	#34445	semidirect
856. C₄×Q₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811231	2
#20277908	2
#20277900	2
#20277894	2
#20277879	2
#20277840	2
#20277831	2
#20277829	2
#20277817	2
#20277809	2
#20277806	2
#20277803	2
#20277797	2
#20277680	2
#20277609	2
#20277568	2
#20277519	2
#20277518	2
#20277515	2
#20277514	2
#20277496	2
#20277490	2
#20277486	2
#20277470	2
#20277454	2
#20277447	2
#20277363	2
C₄×#13133207	2
#20277265	2
#20277191	2
C₅₃×#2355	2
#34445	53