Subgroups — #27546804

Order 13568.

2024 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811374	C₂	1	1	yes	maximal, characteristic
2	#20277906	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277905	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277902	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277902	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277899	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277898	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277894	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277893	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277884	C₂	1	1	yes	maximal, characteristic
11	#20277883	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277877	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277876	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277859	C₂	1	1	yes	maximal, characteristic
15	#20277857	C₂	1	1	yes	maximal, characteristic
16	#20277286	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277284	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277274	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277272	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277269	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277269	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277265	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277265	C₂	1	1	yes	maximal, characteristic, complemented
24	#20277256	C₂	1	1	yes	maximal, characteristic
25	#20277253	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂²⋊Q₈×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277249	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277243	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277242	C₂	1	1	yes	maximal, characteristic
30	#20277232	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2378	C₂	1	1	yes	maximal, characteristic, complemented
32	#16811374	C₄	1	16	yes	complemented
33	C₂×#13133216	C₂²	1	1	yes	characteristic
34	C₂×#13133215	C₂²	1	1	yes	characteristic
35	C₂×#13133212	C₂²	1	1	yes	characteristic
36	C₂×#13133212	C₂²	1	1	yes	characteristic
37	C₂×#13133210	C₂²	1	1	yes	characteristic
38	C₂×#13133210	C₂²	1	1	yes	characteristic
39	C₂×#13133208	C₂²	1	1	yes	characteristic
40	C₂×#13133207	C₂²	1	1	yes	characteristic
41	C₂×#13133203	C₂²	1	1	yes	characteristic
42	C₂×#13133200	C₂²	1	1	yes	characteristic
43	C₂×#13133199	C₂²	1	1	yes	characteristic
44	C₂×#13133196	C₂²	1	1	yes	characteristic
45	C₂×#13133195	C₂²	1	1	yes	characteristic
46	C₂×#13133193	C₂²	1	1	yes	characteristic
47	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
48	C₂×#13133182	C₂²	1	1	yes	characteristic
49	C₂×#13133182	C₂²	1	1	yes	characteristic
50	C₂×#13133177	C₂²	1	1	yes	characteristic
51	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
53	#16810530	C₂²	1	1	yes	characteristic
54	#16810529	C₂²	1	1	yes	characteristic
55	#16810528	C₂²	1	1	yes	characteristic
56	#16810527	C₂²	1	1	yes	characteristic
57	#16810527	C₂²	1	1	yes	characteristic
58	#16810527	C₂²	1	1	yes	characteristic
59	#16810527	C₂²	1	1	yes	characteristic
60	#16810523	C₂²	1	1	yes	characteristic
61	#16810522	C₂²	1	1	yes	characteristic
62	#16810521	C₂²	1	1	yes	characteristic
63	#16810521	C₂²	1	1	yes	characteristic
64	#16810521	C₂²	1	1	yes	characteristic
65	#16810520	C₂²	1	1	yes	characteristic
66	#16810520	C₂²	1	1	yes	characteristic
67	#16810520	C₂²	1	1	yes	characteristic
68	#16810520	C₂²	1	1	yes	characteristic
69	#16810520	C₂²	1	1	yes	characteristic
70	#16810520	C₂²	1	1	yes	characteristic
71	#16810519	C₂²	1	1	yes	characteristic
72	#16810518	C₂²	1	1	yes	characteristic
73	#16810518	C₂²	1	1	yes	characteristic
74	#16810518	C₂²	1	1	yes	characteristic
75	#16810517	C₂²	1	1	yes	characteristic
76	#16810517	C₂²	1	1	yes	characteristic
77	#16810517	C₂²	1	1	yes	characteristic
78	#16810515	C₂²	1	1	yes	characteristic
79	#16810515	C₂²	1	1	yes	characteristic
80	#16810514	C₂²	1	1	yes	characteristic
81	#16810514	C₂²	1	1	yes	characteristic
82	#16810514	C₂²	1	1	yes	characteristic
83	#16810513	C₂²	1	1	yes	characteristic
84	#16810513	C₂²	1	1	yes	characteristic
85	#16810513	C₂²	1	1	yes	characteristic
86	#16810512	C₂²	1	1	yes	characteristic
87	#16810512	C₂²	1	1	yes	characteristic
88	#16810511	C₂²	1	1	yes	characteristic
89	#16810511	C₂²	1	1	yes	characteristic
90	#16810511	C₂²	1	1	yes	characteristic
91	#16810510	C₂²	1	1	yes	characteristic
92	#16810510	C₂²	1	1	yes	characteristic
93	#16810510	C₂²	1	1	yes	characteristic
94	#16810510	C₂²	1	1	yes	characteristic
95	#16810510	C₂²	1	1	yes	characteristic
96	#16810509	C₂²	1	1	yes	characteristic
97	#16810509	C₂²	1	1	yes	characteristic
98	#16810508	C₂²	1	1	yes	characteristic
99	#16810508	C₂²	1	1	yes	characteristic
100	#16810508	C₂²	1	1	yes	characteristic
101	#16810508	C₂²	1	1	yes	characteristic
102	#16810508	C₂²	1	1	yes	characteristic
103	#16810507	C₂²	1	1	yes	characteristic
104	#16810507	C₂²	1	1	yes	characteristic
105	#16810507	C₂²	1	1	yes	characteristic
106	#16810507	C₂²	1	1	yes	characteristic
107	#16810507	C₂²	1	1	yes	characteristic
108	#16810506	C₂²	1	1	yes	characteristic
109	#16810506	C₂²	1	1	yes	characteristic
110	#16810506	C₂²	1	1	yes	characteristic
111	#16810505	C₂²	1	1	yes	characteristic
112	#16810505	C₂²	1	1	yes	characteristic
113	#16810505	C₂²	1	1	yes	characteristic
114	#16810505	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	#16810500	C₂²	1	1	yes	characteristic
120	#16810499	C₂²	1	1	yes	characteristic
121	#16810498	C₂²	1	1	yes	characteristic
122	#16810498	C₂²	1	1	yes	characteristic
123	#16810497	C₂²	1	1	yes	characteristic
124	#16810497	C₂²	1	1	yes	characteristic
125	#16810497	C₂²	1	1	yes	characteristic
126	#16810495	C₂²	1	1	yes	characteristic
127	#16810495	C₂²	1	1	yes	characteristic
128	#16810495	C₂²	1	1	yes	characteristic
129	#16810494	C₂²	1	1	yes	characteristic
130	#16810494	C₂²	1	1	yes	characteristic
131	#16810492	C₂²	1	1	yes	characteristic
132	#16810492	C₂²	1	1	yes	characteristic
133	#16810490	C₂²	1	1	yes	characteristic
134	#16810490	C₂²	1	1	yes	characteristic
135	#16810490	C₂²	1	1	yes	characteristic
136	#16810490	C₂²	1	1	yes	characteristic
137	#16810488	C₂²	1	1	yes	characteristic
138	#16810487	C₂²	1	1	yes	characteristic
139	#16810487	C₂²	1	1	yes	characteristic
140	#16810485	C₂²	1	1	yes	characteristic
141	#16810483	C₂²	1	1	yes	characteristic
142	#16810482	C₂²	1	1	yes	characteristic
143	#16810480	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	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
150	C₄⋊C₄×Dic₅₃	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	#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	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
161	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
165	#16810470	C₂²	1	1	yes	characteristic
166	#16810470	C₂²	1	1	yes	characteristic
167	#16810470	C₂²	1	1	yes	characteristic
168	#16810470	C₂²	1	1	yes	characteristic
169	#16810470	C₂²	1	1	yes	characteristic
170	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
173	C₂×C₂²⋊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×#389	C₂²	1	1	yes	characteristic
177	C₅₃×#389	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic
183	C₅₃×#387	C₂²	1	1	yes	characteristic
184	C₅₃×#387	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic
186	C₅₃×#381	C₂²	1	1	yes	characteristic
187	C₅₃×#380	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	#13133216	C₂×C₄	1	8	yes	complemented
197	#13133215	C₂×C₄	1	8	yes	complemented
198	#13133212	C₂×C₄	1	8	yes	complemented
199	#13133212	C₂×C₄	1	8	yes	complemented
200	#13133210	C₂×C₄	1	8	yes	complemented
201	#13133210	C₂×C₄	1	8	yes	complemented
202	#13133208	C₂×C₄	1	8	yes	complemented
203	#13133207	C₂×C₄	1	8	yes	complemented
204	#13133203	C₂×C₄	1	8	yes	—
205	#13133200	C₂×C₄	1	8	yes	—
206	#13133199	C₂×C₄	1	8	yes	—
207	#13133196	C₂×C₄	1	8	yes	complemented
208	#13133195	C₂×C₄	1	8	yes	complemented
209	#13133193	C₂×C₄	1	8	yes	complemented
210	Q₈×Dic₅₃	—	4	2	no	—
211	#13133182	—	4	2	no	—
212	#13133182	—	4	2	no	—
213	#13133177	—	4	2	no	—
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	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×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×#11719921	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₅₃	—	4	2	no	—
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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₄²×D₅₃	—	4	2	no	—
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	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
329	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×Q₈×C₅₃	—	4	1	no	—
367	C₂×Q₈×C₅₃	—	4	1	no	—
368	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
369	C₂²×C₄×C₅₃	—	4	1	no	—
370	C₂²×C₄×C₅₃	—	4	1	no	—
371	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₂²⋊D₅₃	—	4	1	no	—
387	C₂×C₂²⋊D₅₃	—	4	1	no	—
388	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
389	C₂²×Dic₅₃	—	2	2	no	—
390	C₂²×Dic₅₃	—	2	2	no	—
391	C₂²×Dic₅₃	—	2	2	no	—
392	C₂²×Dic₅₃	—	4	1	no	—
393	C₂²×Dic₅₃	—	4	1	no	—
394	C₂²×Dic₅₃	—	4	1	no	—
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₄×D₅₃	—	2	2	no	—
411	C₂×C₄×D₅₃	—	2	2	no	—
412	C₂×C₄×D₅₃	—	2	2	no	—
413	C₂×C₄×D₅₃	—	4	1	no	—
414	C₂×C₄×D₅₃	—	4	1	no	—
415	C₂×C₄×D₅₃	—	4	1	no	—
416	C₂×C₄×D₅₃	—	4	1	no	—
417	C₂×C₄×D₅₃	—	4	1	no	—
418	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
419	C₂×Dic₁₀₆	—	4	1	no	—
420	C₂×Dic₁₀₆	—	4	1	no	—
421	C₂×Dic₁₀₆	—	4	1	no	—
422	C₂×Dic₁₀₆	—	4	1	no	—
423	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
424	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
425	C₄⋊C₄×C₅₃	—	4	1	no	—
426	C₄⋊C₄×C₅₃	—	4	1	no	—
427	C₄⋊C₄×C₅₃	—	4	1	no	—
428	C₄⋊C₄×C₅₃	—	4	1	no	—
429	C₄⋊C₄×C₅₃	—	4	1	no	—
430	C₄⋊C₄×C₅₃	—	4	1	no	—
431	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
432	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
433	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
434	C₂²⋊C₄×C₅₃	—	4	1	no	—
435	C₂²⋊C₄×C₅₃	—	4	1	no	—
436	C₂²⋊C₄×C₅₃	—	4	1	no	—
437	C₂²⋊C₄×C₅₃	—	4	1	no	—
438	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
439	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
440	C₄²×C₅₃	—	4	1	no	—
441	C₄²×C₅₃	—	4	1	no	—
442	C₄²×C₅₃	—	4	1	no	—
443	C₄²×C₅₃	—	4	1	no	—
444	C₂²⋊Dic₅₃	—	4	1	no	—
445	C₂²⋊Dic₅₃	—	4	1	no	—
446	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
447	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
448	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
449	#11719921	—	4	1	no	—
450	#11719921	—	4	1	no	—
451	#11719921	—	4	1	no	—
452	#11719921	—	4	1	no	—
453	#11719921	—	4	1	no	—
454	#11719921	—	4	1	no	—
455	#11719921	C₂²×C₄	1	4	yes	—
456	#11719921	C₂²×C₄	1	4	yes	—
457	#11719921	C₂²×C₄	1	4	yes	—
458	#11719921	C₂²×C₄	1	4	yes	—
459	#11719921	C₂²×C₄	1	4	yes	—
460	C₄⋊Dic₅₃	—	4	1	no	—
461	C₄⋊Dic₅₃	—	4	1	no	—
462	C₄⋊Dic₅₃	—	4	1	no	—
463	C₄⋊Dic₅₃	—	4	1	no	—
464	C₄⋊Dic₅₃	—	4	1	no	—
465	C₄⋊Dic₅₃	—	4	1	no	—
466	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
467	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
468	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
469	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
470	#11719919	—	4	1	no	—
471	#11719919	—	4	1	no	—
472	#11719919	—	4	1	no	—
473	#11719919	—	4	1	no	—
474	#11719919	—	4	1	no	—
475	#11719919	—	4	1	no	—
476	#11719919	—	4	1	no	—
477	#11719919	—	4	1	no	—
478	#11719919	—	4	1	no	—
479	#11719919	—	4	1	no	—
480	#11719919	—	4	1	no	—
481	#11719919	—	4	1	no	—
482	#11719919	—	4	1	no	—
483	#11719919	—	4	1	no	—
484	#11719919	C₂²×C₄	1	4	yes	—
485	#11719919	C₂²×C₄	1	4	yes	—
486	#11719919	C₂²×C₄	1	4	yes	—
487	#11719919	C₂²×C₄	1	4	yes	—
488	#11719919	C₂²×C₄	1	4	yes	—
489	#11719919	C₂²×C₄	1	4	yes	—
490	#11719919	C₂²×C₄	1	4	yes	—
491	#11719919	C₂²×C₄	1	4	yes	—
492	#11719919	C₂²×C₄	1	4	yes	—
493	C₄×Dic₅₃	—	2	2	no	—
494	C₄×Dic₅₃	—	2	2	no	—
495	C₄×Dic₅₃	—	2	2	no	—
496	C₄×Dic₅₃	—	2	2	no	—
497	C₄×Dic₅₃	—	2	2	no	—
498	C₄×Dic₅₃	—	2	2	no	—
499	C₄×Dic₅₃	—	2	2	no	—
500	C₄×Dic₅₃	—	2	2	no	—
501	C₄×Dic₅₃	—	2	2	no	—
502	C₄×Dic₅₃	—	2	2	no	—
503	C₄×Dic₅₃	—	2	2	no	—
504	C₄×Dic₅₃	—	2	2	no	—
505	C₄×Dic₅₃	—	2	2	no	—
506	C₄×Dic₅₃	—	4	1	no	—
507	C₄×Dic₅₃	—	4	1	no	—
508	C₄×Dic₅₃	—	4	1	no	—
509	C₄×Dic₅₃	—	4	1	no	—
510	C₄×Dic₅₃	—	4	1	no	—
511	C₄×Dic₅₃	—	4	1	no	—
512	C₄×Dic₅₃	—	4	1	no	—
513	C₄×Dic₅₃	—	4	1	no	—
514	C₄×Dic₅₃	—	4	1	no	—
515	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
516	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
517	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
518	C₂³×C₅₃	—	2	1	no	—
519	C₂³×C₅₃	—	2	1	no	—
520	C₂³×C₅₃	—	2	1	no	—
521	C₂³×C₅₃	—	2	1	no	—
522	C₂³×C₅₃	—	2	1	no	—
523	C₂³×C₅₃	—	2	1	no	—
524	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
525	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
526	C₂²×D₅₃	—	2	1	no	—
527	C₂²×D₅₃	—	2	1	no	—
528	C₂²×D₅₃	—	2	1	no	—
529	C₂²×D₅₃	—	2	1	no	—
530	C₂²×D₅₃	—	2	1	no	—
531	C₂²×D₅₃	—	2	1	no	—
532	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
533	Q₈×C₅₃	—	4	4	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	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	4	4	no	—
571	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
572	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
573	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
574	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
575	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
576	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
577	C₂²⋊D₅₃	—	4	4	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	—	2	1	no	—
586	C₂×Dic₅₃	—	2	1	no	—
587	C₂×Dic₅₃	—	2	1	no	—
588	C₂×Dic₅₃	—	2	1	no	—
589	C₂×Dic₅₃	—	2	1	no	—
590	C₂×Dic₅₃	—	2	1	no	—
591	C₂×Dic₅₃	—	2	1	no	—
592	C₂×Dic₅₃	—	2	1	no	—
593	C₂×Dic₅₃	—	2	1	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	2	1	no	—
597	C₂×Dic₅₃	—	2	1	no	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	1	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	1	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	4	4	no	—
614	C₂×Dic₅₃	—	4	4	no	—
615	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
616	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
617	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
618	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
619	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
620	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
621	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
622	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
623	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
624	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
625	C₄×D₅₃	—	4	4	no	—
626	C₄×D₅₃	—	4	4	no	—
627	C₄×D₅₃	—	4	4	no	—
628	Dic₁₀₆	—	4	4	no	—
629	Dic₁₀₆	—	4	4	no	—
630	C₄×#563	—	53	1	no	maximal, Sylow
631	C₂²×C₅₃	—	2	2	no	—
632	C₂²×C₅₃	—	2	2	no	—
633	C₂²×C₅₃	—	2	2	no	—
634	C₂²×C₅₃	—	4	1	no	—
635	C₂²×C₅₃	—	4	1	no	—
636	C₂²×C₅₃	—	4	1	no	—
637	C₂²×C₅₃	—	4	1	no	—
638	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
639	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
640	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
641	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
642	C₂²×C₅₃	#585	1	1	yes	characteristic
643	C₂²×C₅₃	#585	1	1	yes	characteristic
644	C₂²×C₅₃	#585	1	1	yes	characteristic
645	C₂×D₅₃	—	2	2	no	—
646	C₂×D₅₃	—	2	2	no	—
647	C₂×D₅₃	—	2	2	no	—
648	C₂×D₅₃	—	4	1	no	—
649	C₂×D₅₃	—	4	1	no	—
650	C₂×D₅₃	—	4	1	no	—
651	C₂×D₅₃	—	4	1	no	—
652	C₄×C₅₃	—	2	2	no	—
653	C₄×C₅₃	—	2	2	no	—
654	C₄×C₅₃	—	2	2	no	—
655	C₄×C₅₃	—	2	2	no	—
656	C₄×C₅₃	—	2	2	no	—
657	C₄×C₅₃	—	2	2	no	—
658	C₄×C₅₃	—	4	1	no	—
659	C₄×C₅₃	—	4	1	no	—
660	C₄×C₅₃	—	4	1	no	—
661	C₄×C₅₃	—	4	1	no	—
662	C₄×C₅₃	—	4	1	no	—
663	C₄×C₅₃	—	4	1	no	—
664	C₄×C₅₃	—	4	1	no	—
665	C₄×C₅₃	—	4	1	no	—
666	Dic₅₃	—	2	2	no	—
667	Dic₅₃	—	2	2	no	—
668	Dic₅₃	—	2	2	no	—
669	Dic₅₃	—	2	2	no	—
670	Dic₅₃	—	2	2	no	—
671	Dic₅₃	—	2	2	no	—
672	Dic₅₃	—	2	2	no	—
673	Dic₅₃	—	4	1	no	—
674	Dic₅₃	—	4	1	no	—
675	Dic₅₃	—	4	1	no	—
676	Dic₅₃	—	4	1	no	—
677	Dic₅₃	—	4	1	no	—
678	Dic₅₃	—	4	1	no	—
679	Dic₅₃	—	4	1	no	—
680	Dic₅₃	#563	1	4	yes	complemented
681	C₂×#563	—	53	1	no	—
682	#2383	—	53	1	no	—
683	#2383	—	53	1	no	—
684	#2383	—	53	1	no	—
685	#2383	—	53	1	no	—
686	#2382	—	53	1	no	—
687	#2382	—	53	1	no	—
688	#2381	—	53	1	no	—
689	#2381	—	53	1	no	—
690	#2379	—	53	1	no	—
691	#2378	—	53	1	no	—
692	#2378	—	53	1	no	—
693	#2378	—	53	1	no	—
694	#2378	D₅₃	1	1	yes	characteristic, complemented
695	#2376	—	53	1	no	—
696	#2376	—	53	1	no	—
697	C₄×C₄⋊Q₈	—	53	1	no	—
698	C₄×C₄⋊Q₈	—	53	1	no	—
699	C₄×#125	—	53	1	no	—
700	C₄×#125	—	53	1	no	—
701	C₄×#126	—	53	1	no	—
702	C₄×#126	—	53	1	no	—
703	C₄×#126	—	53	1	no	—
704	C₄×#126	—	53	1	no	—
705	C₄×#124	—	53	1	no	—
706	C₄×C₂²⋊Q₈	—	53	1	no	—
707	C₄×C₂²⋊Q₈	—	53	1	no	—
708	C₄×C₂²⋊Q₈	—	53	1	no	—
709	C₄×C₂²⋊Q₈	—	53	1	no	—
710	C₄×#123	—	53	1	no	—
711	C₄×#123	—	53	1	no	—
712	C₂×C₅₃	—	4	2	no	—
713	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
715	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
716	C₂×C₅₃	C₂×#563	1	1	yes	characteristic
717	C₂×C₅₃	#3529	1	1	yes	characteristic
718	C₂×C₅₃	#3531	1	1	yes	characteristic
719	C₂×C₅₃	#3531	1	1	yes	characteristic
720	D₅₃	—	4	2	no	—
721	#563	—	53	16	no	—
722	C₂×C₄⋊Q₈	—	53	1	no	—
723	C₂×C₄⋊Q₈	—	53	1	no	—
724	C₂×#126	—	53	1	no	—
725	C₂×#126	—	53	1	no	—
726	C₂×#126	—	53	1	no	—
727	C₂×#126	—	53	1	no	—
728	C₂×#125	—	53	1	no	—
729	C₂×#125	—	53	1	no	—
730	C₂×#124	—	53	1	no	—
731	C₂×#123	—	53	1	no	—
732	C₂×#123	—	53	1	no	—
733	C₂×C₂²⋊Q₈	—	53	1	no	—
734	C₂×C₂²⋊Q₈	—	53	1	no	—
735	C₂×C₂²⋊Q₈	—	53	1	no	—
736	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
737	C₂×C₄×Q₈	—	53	1	no	—
738	C₂×C₄×Q₈	—	53	1	no	—
739	C₂×C₄×Q₈	—	53	1	no	—
740	C₂×C₄×D₄	—	53	1	no	—
741	C₂²×C₄²	—	53	1	no	—
742	C₂²×C₄²	—	53	1	no	—
743	#391	—	53	1	no	—
744	#391	—	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	C₂×D₅₃	1	1	yes	characteristic
751	#391	C₂×D₅₃	1	1	yes	characteristic
752	#390	—	53	1	no	—
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	—	53	1	no	—
761	#389	—	53	1	no	—
762	#389	—	53	1	no	—
763	#389	—	53	1	no	—
764	#389	—	53	1	no	—
765	#389	—	53	1	no	—
766	#389	—	53	1	no	—
767	#389	C₂×D₅₃	1	1	yes	characteristic
768	#389	C₂×D₅₃	1	1	yes	characteristic
769	#388	—	53	1	no	—
770	#388	—	53	1	no	—
771	#388	—	53	1	no	—
772	#388	—	53	1	no	—
773	#388	—	53	1	no	—
774	#388	—	53	1	no	—
775	#388	—	53	1	no	—
776	#388	—	53	1	no	—
777	#388	—	53	1	no	—
778	#388	—	53	1	no	—
779	#388	—	53	1	no	—
780	#388	—	53	1	no	—
781	#388	—	53	1	no	—
782	#388	—	53	1	no	—
783	#388	—	53	1	no	—
784	#388	—	53	1	no	—
785	#388	C₂×D₅₃	1	1	yes	characteristic
786	#388	C₂×D₅₃	1	1	yes	characteristic
787	#388	C₂×D₅₃	1	1	yes	characteristic
788	#388	C₂×D₅₃	1	1	yes	characteristic
789	#387	—	53	1	no	—
790	#387	—	53	1	no	—
791	#387	—	53	1	no	—
792	#387	—	53	1	no	—
793	#387	—	53	1	no	—
794	#387	—	53	1	no	—
795	#387	—	53	1	no	—
796	#387	—	53	1	no	—
797	#387	—	53	1	no	—
798	#387	—	53	1	no	—
799	#387	—	53	1	no	—
800	#387	—	53	1	no	—
801	#387	—	53	1	no	—
802	#387	—	53	1	no	—
803	#387	—	53	1	no	—
804	#387	—	53	1	no	—
805	#387	—	53	1	no	—
806	#387	—	53	1	no	—
807	#387	—	53	1	no	—
808	#387	—	53	1	no	—
809	#387	—	53	1	no	—
810	#387	—	53	1	no	—
811	#387	—	53	1	no	—
812	#387	—	53	1	no	—
813	#387	—	53	1	no	—
814	#387	—	53	1	no	—
815	#387	—	53	1	no	—
816	#387	—	53	1	no	—
817	#387	C₂×D₅₃	1	1	yes	characteristic
818	#387	C₂×D₅₃	1	1	yes	characteristic
819	#387	C₂×D₅₃	1	1	yes	characteristic
820	#387	C₂×D₅₃	1	1	yes	characteristic
821	#386	—	53	1	no	—
822	#386	—	53	1	no	—
823	#385	—	53	1	no	—
824	#385	—	53	1	no	—
825	#385	—	53	1	no	—
826	#385	—	53	1	no	—
827	#385	—	53	1	no	—
828	#385	—	53	1	no	—
829	#385	—	53	1	no	—
830	#385	—	53	1	no	—
831	#385	—	53	1	no	—
832	#385	—	53	1	no	—
833	#384	—	53	1	no	—
834	#384	—	53	1	no	—
835	#383	—	53	1	no	—
836	#383	—	53	1	no	—
837	#383	—	53	1	no	—
838	#383	—	53	1	no	—
839	#382	—	53	1	no	—
840	#382	—	53	1	no	—
841	#382	—	53	1	no	—
842	#381	—	53	1	no	—
843	#381	C₂×D₅₃	1	1	yes	characteristic
844	#380	—	53	1	no	—
845	#380	—	53	1	no	—
846	#380	—	53	1	no	—
847	#380	C₂×D₅₃	1	1	yes	characteristic
848	C₄×C₄⋊C₄	—	53	1	no	—
849	C₄×C₄⋊C₄	—	53	1	no	—
850	C₄×C₄⋊C₄	—	53	1	no	—
851	C₄×C₄⋊C₄	—	53	1	no	—
852	C₄×C₄⋊C₄	—	53	1	no	—
853	C₄×C₄⋊C₄	—	53	1	no	—
854	C₄×C₄⋊C₄	—	53	1	no	—
855	C₄×C₄⋊C₄	—	53	1	no	—
856	C₄×C₄⋊C₄	—	53	1	no	—
857	C₄×C₄⋊C₄	—	53	1	no	—
858	C₄×C₄⋊C₄	—	53	1	no	—
859	C₄×C₄⋊C₄	—	53	1	no	—
860	C₄×C₄⋊C₄	—	53	1	no	—
861	C₄×C₄⋊C₄	—	53	1	no	—
862	C₄×C₄⋊C₄	—	53	1	no	—
863	C₄×C₄⋊C₄	—	53	1	no	—
864	C₄×C₂²⋊C₄	—	53	1	no	—
865	C₄×C₂²⋊C₄	—	53	1	no	—
866	C₄×C₂²⋊C₄	—	53	1	no	—
867	C₄×C₂²⋊C₄	—	53	1	no	—
868	C₄×C₂²⋊C₄	—	53	1	no	—
869	C₄×C₂²⋊C₄	—	53	1	no	—
870	C₄×C₂²⋊C₄	—	53	1	no	—
871	C₄×C₂²⋊C₄	—	53	1	no	—
872	C₄×C₂²⋊C₄	—	53	1	no	—
873	C₄×C₂²⋊C₄	—	53	1	no	—
874	C₄³	—	53	1	no	—
875	C₄³	—	53	1	no	—
876	C₄³	—	53	1	no	—
877	C₅₃	C₄×#563	1	1	yes	characteristic, complemented, Sylow
878	C₂²×Q₈	—	53	1	no	—
879	C₂²×Q₈	—	53	1	no	—
880	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
881	C₂²×D₄	—	53	1	no	—
882	C₂³×C₄	—	53	1	no	—
883	C₂³×C₄	—	53	1	no	—
884	C₂³×C₄	—	53	1	no	—
885	C₂³×C₄	—	53	1	no	—
886	C₂³×C₄	—	53	1	no	—
887	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
888	C₄⋊Q₈	—	53	8	no	—
889	C₄⋊Q₈	—	53	8	no	—
890	#126	—	53	8	no	—
891	#126	—	53	8	no	—
892	#126	—	53	8	no	—
893	#126	—	53	8	no	—
894	#125	—	53	8	no	—
895	#125	—	53	8	no	—
896	#124	—	53	8	no	—
897	#123	—	53	8	no	—
898	#123	—	53	8	no	—
899	C₂²⋊Q₈	—	53	8	no	—
900	C₂²⋊Q₈	—	53	8	no	—
901	C₂²⋊Q₈	—	53	8	no	—
902	C₂²⋊Q₈	C₄×D₅₃	1	8	yes	complemented
903	C₄×Q₈	—	212	2	no	—
904	C₄×Q₈	—	212	2	no	—
905	C₄×Q₈	—	212	2	no	—
906	C₄×D₄	—	212	2	no	—
907	C₂×C₄⋊C₄	—	53	1	no	—
908	C₂×C₄⋊C₄	—	53	1	no	—
909	C₂×C₄⋊C₄	—	53	1	no	—
910	C₂×C₄⋊C₄	—	53	1	no	—
911	C₂×C₄⋊C₄	—	53	1	no	—
912	C₂×C₄⋊C₄	—	53	1	no	—
913	C₂×C₄⋊C₄	—	53	1	no	—
914	C₂×C₄⋊C₄	—	53	1	no	—
915	C₂×C₄⋊C₄	—	53	1	no	—
916	C₂×C₄⋊C₄	—	53	1	no	—
917	C₂×C₄⋊C₄	—	53	1	no	—
918	C₂×C₄⋊C₄	—	53	1	no	—
919	C₂×C₄⋊C₄	—	53	1	no	—
920	C₂×C₄⋊C₄	—	53	1	no	—
921	C₂×C₄⋊C₄	—	53	1	no	—
922	C₂×C₄⋊C₄	—	53	1	no	—
923	C₂×C₄⋊C₄	—	53	1	no	—
924	C₂×C₄⋊C₄	—	53	1	no	—
925	C₂×C₄⋊C₄	—	53	1	no	—
926	C₂×C₄⋊C₄	—	53	1	no	—
927	C₂×C₄⋊C₄	—	53	1	no	—
928	C₂×C₄⋊C₄	—	53	1	no	—
929	C₂×C₄⋊C₄	—	53	1	no	—
930	C₂×C₄⋊C₄	—	53	1	no	—
931	C₂×C₄⋊C₄	—	53	1	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	1	no	—
936	C₂×C₄⋊C₄	—	53	1	no	—
937	C₂×C₄⋊C₄	—	53	1	no	—
938	C₂×C₄⋊C₄	—	53	1	no	—
939	C₂×C₄⋊C₄	—	53	1	no	—
940	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
949	C₂×C₂²⋊C₄	—	53	1	no	—
950	C₂×C₂²⋊C₄	—	53	1	no	—
951	C₂×C₂²⋊C₄	—	53	1	no	—
952	C₂×C₂²⋊C₄	—	53	1	no	—
953	C₂×C₂²⋊C₄	—	53	1	no	—
954	C₂×C₂²⋊C₄	—	53	1	no	—
955	C₂×C₂²⋊C₄	—	53	1	no	—
956	C₂×C₂²⋊C₄	—	53	1	no	—
957	C₂×C₂²⋊C₄	—	53	1	no	—
958	C₂×C₂²⋊C₄	—	53	1	no	—
959	C₂×C₂²⋊C₄	—	53	1	no	—
960	C₂×C₂²⋊C₄	—	53	1	no	—
961	C₂×C₂²⋊C₄	—	53	1	no	—
962	C₂×C₂²⋊C₄	—	53	1	no	—
963	C₂×C₂²⋊C₄	—	53	1	no	—
964	C₂×C₂²⋊C₄	—	53	1	no	—
965	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
966	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
968	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×C₄²	—	53	1	no	—
972	C₂×C₄²	—	53	1	no	—
973	C₂×C₄²	—	53	1	no	—
974	C₂×C₄²	—	53	1	no	—
975	C₂×C₄²	—	53	1	no	—
976	C₂×C₄²	—	53	1	no	—
977	C₂×C₄²	—	53	1	no	—
978	C₂×C₄²	—	53	1	no	—
979	C₂×C₄²	—	53	1	no	—
980	C₂×C₄²	—	53	1	no	—
981	C₂×C₄²	—	53	1	no	—
982	C₂×C₄²	—	53	1	no	—
983	C₂×C₄²	—	53	1	no	—
984	C₂×C₄²	—	53	1	no	—
985	C₂×C₄²	—	53	1	no	—
986	C₂×C₄²	—	53	1	no	—
987	C₂×C₄²	—	53	1	no	—
988	C₂×C₄²	—	53	1	no	—
989	C₂×C₄²	—	53	1	no	—
990	C₂×C₄²	—	53	1	no	—
991	C₂×C₄²	—	53	1	no	—
992	C₂×C₄²	—	53	1	no	—
993	C₂×C₄²	—	53	1	no	—
994	C₂×C₄²	—	53	1	no	—
995	C₂×C₄²	—	53	1	no	—
996	C₂×C₄²	—	212	2	no	—
997	C₂×C₄²	—	212	2	no	—
998	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
999	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1000	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1001	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1002	#95	—	53	1	no	—
1003	#95	—	53	1	no	—
1004	#95	—	53	1	no	—
1005	#95	—	53	1	no	—
1006	#95	—	53	1	no	—
1007	#95	—	53	1	no	—
1008	#95	—	53	1	no	—
1009	#95	—	53	1	no	—
1010	#95	—	53	1	no	—
1011	#95	—	53	1	no	—
1012	#95	—	53	1	no	—
1013	#95	—	53	1	no	—
1014	#95	—	53	1	no	—
1015	#95	—	53	1	no	—
1016	#95	—	53	1	no	—
1017	#95	—	53	1	no	—
1018	#95	—	53	1	no	—
1019	#95	—	53	1	no	—
1020	#95	—	53	1	no	—
1021	#95	—	53	1	no	—
1022	#95	—	53	1	no	—
1023	#95	—	53	1	no	—
1024	#95	—	53	1	no	—
1025	#95	—	53	1	no	—
1026	#95	—	53	1	no	—
1027	#95	—	53	1	no	—
1028	#95	—	53	1	no	—
1029	#95	—	53	1	no	—
1030	#95	—	53	1	no	—
1031	#95	—	53	1	no	—
1032	#95	—	53	1	no	—
1033	#95	—	53	1	no	—
1034	#95	—	53	1	no	—
1035	#95	—	53	1	no	—
1036	#95	—	53	1	no	—
1037	#95	—	53	1	no	—
1038	#95	—	53	1	no	—
1039	#95	—	53	1	no	—
1040	#95	C₂²×D₅₃	1	1	yes	characteristic
1041	#95	C₂²×D₅₃	1	1	yes	characteristic
1042	#95	C₂²×D₅₃	1	1	yes	characteristic
1043	#95	C₂²×D₅₃	1	1	yes	characteristic
1044	#95	C₂²×D₅₃	1	1	yes	characteristic
1045	#95	C₂²×D₅₃	1	1	yes	characteristic
1046	#95	C₂²×D₅₃	1	1	yes	characteristic
1047	#95	C₂²×D₅₃	1	1	yes	characteristic
1048	#95	C₂²×D₅₃	1	1	yes	characteristic
1049	#95	C₂²×D₅₃	1	1	yes	characteristic
1050	#95	C₂²×D₅₃	1	1	yes	characteristic
1051	#95	C₂²×D₅₃	1	1	yes	characteristic
1052	#95	C₂²×D₅₃	1	1	yes	characteristic
1053	#95	C₂²×D₅₃	1	1	yes	characteristic
1054	C₂⁴	—	53	1	no	—
1055	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1056	C₂×Q₈	—	4	1	no	—
1057	C₂×Q₈	—	4	1	no	—
1058	C₂×Q₈	—	53	4	no	—
1059	C₂×Q₈	—	53	4	no	—
1060	C₂×Q₈	—	212	1	no	—
1061	C₂×Q₈	—	212	1	no	—
1062	C₂×Q₈	—	212	1	no	—
1063	C₂×Q₈	—	212	1	no	—
1064	C₂×Q₈	C₂×C₄×D₅₃	1	4	yes	—
1065	C₂×D₄	—	53	4	no	—
1066	C₂×D₄	—	212	1	no	—
1067	C₂×D₄	—	212	1	no	—
1068	C₂²×C₄	—	4	1	no	—
1069	C₂²×C₄	—	4	1	no	—
1070	C₂²×C₄	—	53	1	no	—
1071	C₂²×C₄	—	53	1	no	—
1072	C₂²×C₄	—	53	1	no	—
1073	C₂²×C₄	—	53	1	no	—
1074	C₂²×C₄	—	53	1	no	—
1075	C₂²×C₄	—	53	1	no	—
1076	C₂²×C₄	—	53	1	no	—
1077	C₂²×C₄	—	53	1	no	—
1078	C₂²×C₄	—	53	4	no	—
1079	C₂²×C₄	—	53	1	no	—
1080	C₂²×C₄	—	53	1	no	—
1081	C₂²×C₄	—	53	1	no	—
1082	C₂²×C₄	—	53	1	no	—
1083	C₂²×C₄	—	53	1	no	—
1084	C₂²×C₄	—	53	1	no	—
1085	C₂²×C₄	—	53	1	no	—
1086	C₂²×C₄	—	106	2	no	—
1087	C₂²×C₄	—	106	2	no	—
1088	C₂²×C₄	—	106	2	no	—
1089	C₂²×C₄	—	106	2	no	—
1090	C₂²×C₄	—	106	2	no	—
1091	C₂²×C₄	—	106	2	no	—
1092	C₂²×C₄	—	212	1	no	—
1093	C₂²×C₄	—	212	1	no	—
1094	C₂²×C₄	—	212	1	no	—
1095	C₂²×C₄	—	212	1	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	C₂×C₄×D₅₃	1	4	yes	—
1101	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1102	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1103	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1104	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1105	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1106	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1107	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1108	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1109	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1110	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1112	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1113	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1114	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1115	C₄⋊C₄	—	4	1	no	—
1116	C₄⋊C₄	—	4	1	no	—
1117	C₄⋊C₄	—	4	1	no	—
1118	C₄⋊C₄	—	4	1	no	—
1119	C₄⋊C₄	—	4	1	no	—
1120	C₄⋊C₄	—	4	1	no	—
1121	C₄⋊C₄	—	53	4	no	—
1122	C₄⋊C₄	—	53	4	no	—
1123	C₄⋊C₄	—	53	4	no	—
1124	C₄⋊C₄	—	53	4	no	—
1125	C₄⋊C₄	—	53	4	no	—
1126	C₄⋊C₄	—	53	4	no	—
1127	C₄⋊C₄	—	53	4	no	—
1128	C₄⋊C₄	—	53	4	no	—
1129	C₄⋊C₄	—	53	4	no	—
1130	C₄⋊C₄	—	53	4	no	—
1131	C₄⋊C₄	—	53	4	no	—
1132	C₄⋊C₄	—	53	4	no	—
1133	C₄⋊C₄	—	53	4	no	—
1134	C₄⋊C₄	—	212	1	no	—
1135	C₄⋊C₄	—	212	1	no	—
1136	C₄⋊C₄	—	212	1	no	—
1137	C₄⋊C₄	—	212	1	no	—
1138	C₄⋊C₄	—	212	1	no	—
1139	C₄⋊C₄	—	212	1	no	—
1140	C₄⋊C₄	—	212	1	no	—
1141	C₄⋊C₄	—	212	1	no	—
1142	C₄⋊C₄	—	212	1	no	—
1143	C₄⋊C₄	—	212	1	no	—
1144	C₄⋊C₄	—	212	1	no	—
1145	C₄⋊C₄	—	212	1	no	—
1146	C₄⋊C₄	—	212	1	no	—
1147	C₄⋊C₄	—	212	1	no	—
1148	C₄⋊C₄	—	212	1	no	—
1149	C₄⋊C₄	—	212	1	no	—
1150	C₄⋊C₄	—	212	1	no	—
1151	C₄⋊C₄	—	212	1	no	—
1152	C₄⋊C₄	—	212	1	no	—
1153	C₄⋊C₄	—	212	1	no	—
1154	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1155	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1156	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1157	C₂²⋊C₄	—	4	1	no	—
1158	C₂²⋊C₄	—	4	1	no	—
1159	C₂²⋊C₄	—	4	1	no	—
1160	C₂²⋊C₄	—	4	1	no	—
1161	C₂²⋊C₄	—	53	4	no	—
1162	C₂²⋊C₄	—	53	4	no	—
1163	C₂²⋊C₄	—	53	4	no	—
1164	C₂²⋊C₄	—	53	4	no	—
1165	C₂²⋊C₄	—	53	4	no	—
1166	C₂²⋊C₄	—	53	4	no	—
1167	C₂²⋊C₄	—	53	4	no	—
1168	C₂²⋊C₄	—	53	4	no	—
1169	C₂²⋊C₄	—	212	1	no	—
1170	C₂²⋊C₄	—	212	1	no	—
1171	C₂²⋊C₄	—	212	1	no	—
1172	C₂²⋊C₄	—	212	1	no	—
1173	C₂²⋊C₄	—	212	1	no	—
1174	C₂²⋊C₄	—	212	1	no	—
1175	C₂²⋊C₄	—	212	1	no	—
1176	C₂²⋊C₄	—	212	1	no	—
1177	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1178	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1179	C₄²	—	4	1	no	—
1180	C₄²	—	4	1	no	—
1181	C₄²	—	4	1	no	—
1182	C₄²	—	4	1	no	—
1183	C₄²	—	53	4	no	—
1184	C₄²	—	53	4	no	—
1185	C₄²	—	53	4	no	—
1186	C₄²	—	106	2	no	—
1187	C₄²	—	106	2	no	—
1188	C₄²	—	106	2	no	—
1189	C₄²	—	106	2	no	—
1190	C₄²	—	106	2	no	—
1191	C₄²	—	106	2	no	—
1192	C₄²	—	106	2	no	—
1193	C₄²	—	106	2	no	—
1194	C₄²	—	106	2	no	—
1195	C₄²	—	106	2	no	—
1196	C₄²	—	106	2	no	—
1197	C₄²	—	106	2	no	—
1198	C₄²	—	106	2	no	—
1199	C₄²	—	212	1	no	—
1200	C₄²	—	212	1	no	—
1201	C₄²	—	212	1	no	—
1202	C₄²	—	212	1	no	—
1203	C₄²	—	212	1	no	—
1204	C₄²	—	212	1	no	—
1205	C₄²	—	212	1	no	—
1206	C₄²	—	212	1	no	—
1207	C₄²	—	212	1	no	—
1208	C₂³	—	2	1	no	—
1209	C₂³	—	2	1	no	—
1210	C₂³	—	2	1	no	—
1211	C₂³	—	2	1	no	—
1212	C₂³	—	2	1	no	—
1213	C₂³	—	2	1	no	—
1214	C₂³	—	53	2	no	—
1215	C₂³	—	106	1	no	—
1216	C₂³	—	106	1	no	—
1217	C₂³	—	106	1	no	—
1218	C₂³	—	106	1	no	—
1219	C₂³	—	106	1	no	—
1220	C₂³	—	106	1	no	—
1221	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1222	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1223	Q₈	—	4	4	no	—
1224	Q₈	—	212	4	no	—
1225	Q₈	—	212	4	no	—
1226	D₄	—	212	4	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	4	4	no	—
1264	C₂×C₄	—	53	2	no	—
1265	C₂×C₄	—	53	2	no	—
1266	C₂×C₄	—	53	2	no	—
1267	C₂×C₄	—	53	2	no	—
1268	C₂×C₄	—	53	2	no	—
1269	C₂×C₄	—	53	2	no	—
1270	C₂×C₄	—	53	2	no	—
1271	C₂×C₄	—	53	2	no	—
1272	C₂×C₄	—	53	2	no	—
1273	C₂×C₄	—	53	2	no	—
1274	C₂×C₄	—	106	1	no	—
1275	C₂×C₄	—	106	1	no	—
1276	C₂×C₄	—	106	1	no	—
1277	C₂×C₄	—	106	1	no	—
1278	C₂×C₄	—	106	1	no	—
1279	C₂×C₄	—	106	1	no	—
1280	C₂×C₄	—	106	1	no	—
1281	C₂×C₄	—	106	1	no	—
1282	C₂×C₄	—	106	1	no	—
1283	C₂×C₄	—	106	1	no	—
1284	C₂×C₄	—	106	1	no	—
1285	C₂×C₄	—	106	1	no	—
1286	C₂×C₄	—	106	1	no	—
1287	C₂×C₄	—	106	1	no	—
1288	C₂×C₄	—	106	1	no	—
1289	C₂×C₄	—	106	1	no	—
1290	C₂×C₄	—	106	1	no	—
1291	C₂×C₄	—	106	1	no	—
1292	C₂×C₄	—	106	1	no	—
1293	C₂×C₄	—	106	1	no	—
1294	C₂×C₄	—	106	1	no	—
1295	C₂×C₄	—	106	1	no	—
1296	C₂×C₄	—	106	1	no	—
1297	C₂×C₄	—	106	1	no	—
1298	C₂×C₄	—	106	1	no	—
1299	C₂×C₄	—	106	1	no	—
1300	C₂×C₄	—	106	1	no	—
1301	C₂×C₄	—	106	1	no	—
1302	C₂×C₄	—	106	1	no	—
1303	C₂×C₄	—	106	1	no	—
1304	C₂×C₄	—	106	1	no	—
1305	C₂×C₄	—	106	1	no	—
1306	C₂×C₄	—	106	1	no	—
1307	C₂×C₄	—	106	1	no	—
1308	C₂×C₄	—	106	1	no	—
1309	C₂×C₄	—	212	4	no	—
1310	C₂×C₄	—	212	4	no	—
1311	C₂×C₄	—	212	4	no	—
1312	C₂×C₄	—	212	4	no	—
1313	C₂×C₄	—	212	4	no	—
1314	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1315	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1316	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1317	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1318	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1319	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1320	C₂²	—	2	2	no	—
1321	C₂²	—	2	2	no	—
1322	C₂²	—	2	2	no	—
1323	C₂²	—	4	1	no	—
1324	C₂²	—	4	1	no	—
1325	C₂²	—	4	1	no	—
1326	C₂²	—	4	1	no	—
1327	C₂²	—	106	2	no	—
1328	C₂²	—	106	2	no	—
1329	C₂²	—	106	2	no	—
1330	C₂²	—	212	1	no	—
1331	C₂²	—	212	1	no	—
1332	C₂²	—	212	1	no	—
1333	C₂²	—	212	1	no	—
1334	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1335	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1336	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1337	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1338	C₂²	#16811458	1	1	yes	characteristic
1339	C₂²	#16811458	1	1	yes	characteristic
1340	C₂²	#16811460	1	1	yes	characteristic
1341	C₄	—	2	2	no	—
1342	C₄	—	2	2	no	—
1343	C₄	—	2	2	no	—
1344	C₄	—	2	2	no	—
1345	C₄	—	2	2	no	—
1346	C₄	—	2	2	no	—
1347	C₄	—	4	1	no	—
1348	C₄	—	4	1	no	—
1349	C₄	—	4	1	no	—
1350	C₄	—	4	1	no	—
1351	C₄	—	4	1	no	—
1352	C₄	—	4	1	no	—
1353	C₄	—	4	1	no	—
1354	C₄	—	4	1	no	—
1355	C₄	—	53	4	no	—
1356	C₄	—	106	2	no	—
1357	C₄	—	106	2	no	—
1358	C₄	—	106	2	no	—
1359	C₄	—	106	2	no	—
1360	C₄	—	106	2	no	—
1361	C₄	—	106	2	no	—
1362	C₄	—	106	2	no	—
1363	C₄	—	212	1	no	—
1364	C₄	—	212	1	no	—
1365	C₄	—	212	1	no	—
1366	C₄	—	212	1	no	—
1367	C₄	—	212	1	no	—
1368	C₄	—	212	1	no	—
1369	C₄	—	212	1	no	—
1370	C₂	—	4	2	no	—
1371	C₂	—	212	2	no	—
1372	C₂	#20287919	1	1	yes	characteristic
1373	C₂	#20287924	1	1	yes	characteristic
1374	C₂	#20287926	1	1	yes	characteristic
1375	C₂	#563×D₅₃	1	1	yes	characteristic
1376	C₂	#20288852	1	1	yes	characteristic
1377	C₂	#20288859	1	1	yes	characteristic
1378	C₂	#20288861	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2378	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂²×C₂²⋊D₅₃	C₂³
hypercenter	#2378	D₅₃
hypocenter	C₅₃	C₄×#563
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2378

Complements

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

N	H ≅ G/N	type
2. #20277906	C₂	semidirect
3. #20277905	C₂	semidirect
4. #20277902	C₂	semidirect
5. #20277902	C₂	semidirect
6. #20277899	C₂	semidirect
7. #20277898	C₂	semidirect
8. #20277894	C₂	semidirect
9. #20277893	C₂	semidirect
11. #20277883	C₂	semidirect
12. #20277877	C₂	semidirect
13. #20277876	C₂	semidirect
16. #20277286	C₂	semidirect
17. #20277284	C₂	semidirect
18. #20277274	C₂	semidirect
19. #20277272	C₂	semidirect
20. #20277269	C₂	semidirect
21. #20277269	C₂	semidirect
22. #20277265	C₂	semidirect
23. #20277265	C₂	semidirect
25. #20277253	C₂	semidirect
26. C₂²⋊Q₈×Dic₅₃	C₂	semidirect
27. #20277249	C₂	semidirect
28. #20277243	C₂	semidirect
31. C₅₃×#2378	C₂	semidirect
32. #16811374	C₄	semidirect
196. #13133216	C₂×C₄	semidirect
197. #13133215	C₂×C₄	semidirect
198. #13133212	C₂×C₄	semidirect
199. #13133212	C₂×C₄	semidirect
200. #13133210	C₂×C₄	semidirect
201. #13133210	C₂×C₄	semidirect
202. #13133208	C₂×C₄	semidirect
203. #13133207	C₂×C₄	semidirect
207. #13133196	C₂×C₄	semidirect
208. #13133195	C₂×C₄	semidirect
209. #13133193	C₂×C₄	semidirect
330. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
680. Dic₅₃	#563	semidirect
694. #2378	D₅₃	semidirect
877. C₅₃	C₄×#563	semidirect
902. C₂²⋊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×#16811374	2
#20277906	2
#20277905	2
#20277902	2
#20277899	2
#20277898	2
#20277894	2
#20277893	2
#20277884	2
#20277883	2
#20277877	2
#20277876	2
#20277859	2
#20277857	2
#20277286	2
#20277284	2
#20277274	2
#20277272	2
#20277269	2
#20277265	2
#20277256	2
#20277253	2
C₂²⋊Q₈×Dic₅₃	2
#20277249	2
#20277243	2
#20277242	2
#20277232	2
C₅₃×#2378	2
C₄×#563	53