Subgroups — #27557442

Order 13568.

1840 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283106	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283105	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283035	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283033	C₂	1	1	yes	maximal, characteristic, complemented
5	#20280786	C₂	1	1	yes	maximal, characteristic, complemented
6	#20280783	C₂	1	1	yes	maximal, characteristic, complemented
7	#20280726	C₂	1	1	yes	maximal, characteristic, complemented
8	#20280723	C₂	1	1	yes	maximal, characteristic, complemented
9	#20280266	C₂	1	1	yes	maximal, characteristic, complemented
10	#20280245	C₂	1	1	yes	maximal, characteristic, complemented
11	#20280238	C₂	1	1	yes	maximal, characteristic, complemented
12	#20279937	C₂	1	1	yes	maximal, characteristic, complemented
13	#20279894	C₂	1	1	yes	maximal, characteristic, complemented
14	#20279871	C₂	1	1	yes	maximal, characteristic, complemented
15	#20279609	C₂	1	1	yes	maximal, characteristic
16	#20279479	C₂	1	1	yes	maximal, characteristic, complemented
17	#20279348	C₂	1	1	yes	maximal, characteristic, complemented
18	#20279095	C₂	1	1	yes	maximal, characteristic, complemented
19	#20278964	C₂	1	1	yes	maximal, characteristic, complemented
20	#20278803	C₂	1	1	yes	maximal, characteristic, complemented
21	#20278636	C₂	1	1	yes	maximal, characteristic, complemented
22	#20278193	C₂	1	1	yes	maximal, characteristic, complemented
23	#20278178	C₂	1	1	yes	maximal, characteristic
24	#20277379	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277368	C₂	1	1	yes	maximal, characteristic
26	#20277314	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277309	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
29	#388×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#13133179	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2594	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133212	C₂²	1	1	yes	characteristic
33	C₂×#13133202	C₂²	1	1	yes	characteristic
34	C₂×#13133199	C₂²	1	1	yes	characteristic
35	C₂×#13133195	C₂²	1	1	yes	characteristic
36	C₂×#13133187	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
39	C₂×#13133179	C₂²	1	1	yes	characteristic
40	C₂×#13133179	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
47	#16810565	C₂²	1	1	yes	characteristic, complemented
48	#16810565	C₂²	1	1	yes	characteristic, complemented
49	#16810564	C₂²	1	1	yes	characteristic, complemented
50	#16810564	C₂²	1	1	yes	characteristic, complemented
51	#16810563	C₂²	1	1	yes	characteristic, complemented
52	#16810561	C₂²	1	1	yes	characteristic, complemented
53	#16810561	C₂²	1	1	yes	characteristic, complemented
54	#16810558	C₂²	1	1	yes	characteristic
55	#16810558	C₂²	1	1	yes	characteristic, complemented
56	#16810557	C₂²	1	1	yes	characteristic, complemented
57	#16810554	C₂²	1	1	yes	characteristic, complemented
58	#16810552	C₂²	1	1	yes	characteristic
59	#16810552	C₂²	1	1	yes	characteristic
60	#16810551	C₂²	1	1	yes	characteristic
61	#16810550	C₂²	1	1	yes	characteristic, complemented
62	#16810549	C₂²	1	1	yes	characteristic
63	#16810549	C₂²	1	1	yes	characteristic, complemented
64	#16810548	C₂²	1	1	yes	characteristic
65	#16810546	C₂²	1	1	yes	characteristic
66	#16810545	C₂²	1	1	yes	characteristic
67	#16810544	C₂²	1	1	yes	characteristic, complemented
68	#16810541	C₂²	1	1	yes	characteristic
69	#16810541	C₂²	1	1	yes	characteristic
70	#16810538	C₂²	1	1	yes	characteristic
71	#16810538	C₂²	1	1	yes	characteristic
72	#16810536	C₂²	1	1	yes	characteristic
73	#16810536	C₂²	1	1	yes	characteristic, complemented
74	#16810535	C₂²	1	1	yes	characteristic
75	#16810527	C₂²	1	1	yes	characteristic, complemented
76	#16810525	C₂²	1	1	yes	characteristic
77	#16810523	C₂²	1	1	yes	characteristic
78	#16810518	C₂²	1	1	yes	characteristic, complemented
79	#16810518	C₂²	1	1	yes	characteristic, complemented
80	#16810517	C₂²	1	1	yes	characteristic
81	#16810517	C₂²	1	1	yes	characteristic
82	#16810517	C₂²	1	1	yes	characteristic
83	#16810517	C₂²	1	1	yes	characteristic
84	#16810516	C₂²	1	1	yes	characteristic
85	#16810516	C₂²	1	1	yes	characteristic
86	#16810516	C₂²	1	1	yes	characteristic
87	#16810515	C₂²	1	1	yes	characteristic
88	#16810515	C₂²	1	1	yes	characteristic
89	#16810515	C₂²	1	1	yes	characteristic
90	#16810514	C₂²	1	1	yes	characteristic
91	#16810514	C₂²	1	1	yes	characteristic
92	#16810514	C₂²	1	1	yes	characteristic
93	#16810514	C₂²	1	1	yes	characteristic
94	#16810514	C₂²	1	1	yes	characteristic, complemented
95	#16810513	C₂²	1	1	yes	characteristic
96	#16810513	C₂²	1	1	yes	characteristic
97	#16810513	C₂²	1	1	yes	characteristic
98	#16810513	C₂²	1	1	yes	characteristic
99	#16810513	C₂²	1	1	yes	characteristic
100	#16810513	C₂²	1	1	yes	characteristic, complemented
101	#16810512	C₂²	1	1	yes	characteristic
102	#16810512	C₂²	1	1	yes	characteristic
103	#16810512	C₂²	1	1	yes	characteristic
104	#16810511	C₂²	1	1	yes	characteristic
105	#16810511	C₂²	1	1	yes	characteristic
106	#16810511	C₂²	1	1	yes	characteristic
107	#16810511	C₂²	1	1	yes	characteristic
108	#16810510	C₂²	1	1	yes	characteristic, complemented
109	#16810510	C₂²	1	1	yes	characteristic, complemented
110	#16810510	C₂²	1	1	yes	characteristic, complemented
111	#16810510	C₂²	1	1	yes	characteristic, complemented
112	#16810509	C₂²	1	1	yes	characteristic, complemented
113	#16810509	C₂²	1	1	yes	characteristic, complemented
114	#16810509	C₂²	1	1	yes	characteristic, complemented
115	#16810508	C₂²	1	1	yes	characteristic, complemented
116	#16810508	C₂²	1	1	yes	characteristic, complemented
117	#16810508	C₂²	1	1	yes	characteristic, complemented
118	#16810507	C₂²	1	1	yes	characteristic, complemented
119	#16810507	C₂²	1	1	yes	characteristic, complemented
120	#16810507	C₂²	1	1	yes	characteristic, complemented
121	#16810506	C₂²	1	1	yes	characteristic, complemented
122	#16810506	C₂²	1	1	yes	characteristic, complemented
123	#16810505	C₂²	1	1	yes	characteristic, complemented
124	#16810505	C₂²	1	1	yes	characteristic, complemented
125	#16810505	C₂²	1	1	yes	characteristic, complemented
126	#16810504	C₂²	1	1	yes	characteristic, complemented
127	#16810504	C₂²	1	1	yes	characteristic, complemented
128	#16810501	C₂²	1	1	yes	characteristic
129	#16810501	C₂²	1	1	yes	characteristic
130	#16810501	C₂²	1	1	yes	characteristic
131	#16810501	C₂²	1	1	yes	characteristic
132	#16810501	C₂²	1	1	yes	characteristic
133	#16810499	C₂²	1	1	yes	characteristic
134	#16810499	C₂²	1	1	yes	characteristic
135	#16810497	C₂²	1	1	yes	characteristic
136	#16810497	C₂²	1	1	yes	characteristic
137	#16810497	C₂²	1	1	yes	characteristic, complemented
138	#16810497	C₂²	1	1	yes	characteristic, complemented
139	#16810494	C₂²	1	1	yes	characteristic
140	#16810494	C₂²	1	1	yes	characteristic
141	#16810494	C₂²	1	1	yes	characteristic, complemented
142	#16810494	C₂²	1	1	yes	characteristic, complemented
143	#16810494	C₂²	1	1	yes	characteristic, complemented
144	#16810490	C₂²	1	1	yes	characteristic, complemented
145	#16810485	C₂²	1	1	yes	characteristic
146	#16810485	C₂²	1	1	yes	characteristic
147	#16810485	C₂²	1	1	yes	characteristic
148	#16810485	C₂²	1	1	yes	characteristic, complemented
149	#16810482	C₂²	1	1	yes	characteristic
150	#16810482	C₂²	1	1	yes	characteristic
151	#16810482	C₂²	1	1	yes	characteristic
152	#16810480	C₂²	1	1	yes	characteristic
153	#16810480	C₂²	1	1	yes	characteristic
154	#16810478	C₂²	1	1	yes	characteristic
155	#16810478	C₂²	1	1	yes	characteristic
156	#16810478	C₂²	1	1	yes	characteristic
157	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
158	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
159	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
160	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
161	C₄×#11719921	C₂²	1	1	yes	characteristic
162	C₄×#11719921	C₂²	1	1	yes	characteristic
163	C₄×#11719921	C₂²	1	1	yes	characteristic
164	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
165	#16810470	C₂²	1	1	yes	characteristic
166	#16810470	C₂²	1	1	yes	characteristic
167	#16810470	C₂²	1	1	yes	characteristic, complemented
168	#16810470	C₂²	1	1	yes	characteristic, complemented
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#401	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#397	C₂²	1	1	yes	characteristic
175	C₅₃×#396	C₂²	1	1	yes	characteristic
176	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#388	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, complemented
183	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
190	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
191	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₅₃	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	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	#13133212	—	4	2	no	—
202	#13133202	—	2	4	no	—
203	#13133199	—	4	2	no	—
204	#13133195	—	2	4	no	—
205	#13133187	—	2	4	no	—
206	C₄×Dic₁₀₆	—	4	2	no	—
207	C₄×D₂₁₂	—	2	4	no	—
208	#13133179	—	2	4	no	—
209	#13133179	—	2	4	no	—
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×C₄⋊Dic₅₃	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	C₄⋊C₄×D₅₃	—	2	4	no	—
232	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₂²⋊Dic₅₃	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×#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×#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×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×D₅₃	—	2	4	no	—
268	C₂²⋊C₄×D₅₃	—	2	4	no	—
269	C₂²⋊C₄×D₅₃	—	4	2	no	—
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	C₄²×D₅₃	—	4	2	no	—
283	C₄²×D₅₃	—	4	2	no	—
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	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×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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×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	#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	#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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂³×D₅₃	—	2	2	no	—
359	C₂³×D₅₃	—	2	2	no	—
360	C₂³×D₅₃	—	2	2	no	—
361	C₂³×D₅₃	—	4	1	no	—
362	C₂³×D₅₃	—	4	1	no	—
363	C₂³×D₅₃	—	4	1	no	—
364	C₂³×D₅₃	—	4	1	no	—
365	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
366	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
367	C₂³×D₅₃	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×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	C₂×C₂²⋊D₅₃	—	2	2	no	—
383	C₂×C₂²⋊D₅₃	—	4	1	no	—
384	C₂×C₂²⋊D₅₃	—	4	1	no	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₂₁₂	—	2	2	no	—
399	C₂×D₂₁₂	—	2	2	no	—
400	C₂×D₂₁₂	—	2	2	no	—
401	C₂×D₂₁₂	—	4	1	no	—
402	C₂×D₂₁₂	—	4	1	no	—
403	C₂×D₂₁₂	#41	1	4	yes	—
404	C₂×C₄×D₅₃	—	2	2	no	—
405	C₂×C₄×D₅₃	—	2	2	no	—
406	C₂×C₄×D₅₃	—	2	2	no	—
407	C₂×C₄×D₅₃	—	2	2	no	—
408	C₂×C₄×D₅₃	—	2	2	no	—
409	C₂×C₄×D₅₃	—	2	2	no	—
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	—	2	2	no	—
414	C₂×C₄×D₅₃	—	2	2	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	—	4	1	no	—
419	C₂×C₄×D₅₃	—	4	1	no	—
420	C₂×C₄×D₅₃	—	4	1	no	—
421	C₂×C₄×D₅₃	—	4	1	no	—
422	C₂×C₄×D₅₃	—	4	1	no	—
423	C₂×C₄×D₅₃	—	4	1	no	—
424	C₂×C₄×D₅₃	—	4	1	no	—
425	C₂×C₄×D₅₃	—	4	1	no	—
426	C₂×C₄×D₅₃	—	4	1	no	—
427	C₂×C₄×D₅₃	—	4	1	no	—
428	C₂×C₄×D₅₃	—	4	1	no	—
429	C₂×C₄×D₅₃	#41	1	4	yes	—
430	C₂×C₄×D₅₃	#41	1	4	yes	—
431	C₂×Dic₁₀₆	—	2	2	no	—
432	C₂×Dic₁₀₆	—	4	1	no	—
433	C₂×Dic₁₀₆	—	4	1	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	4	1	no	—
440	C₄⋊C₄×C₅₃	—	4	1	no	—
441	C₄⋊C₄×C₅₃	—	4	1	no	—
442	C₄⋊C₄×C₅₃	—	4	1	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	4	1	no	—
447	C₂²⋊C₄×C₅₃	—	4	1	no	—
448	C₂²⋊C₄×C₅₃	—	4	1	no	—
449	C₂²⋊C₄×C₅₃	—	4	1	no	—
450	C₄²×C₅₃	—	2	2	no	—
451	C₄²×C₅₃	—	4	1	no	—
452	C₄²×C₅₃	—	4	1	no	—
453	C₄²×C₅₃	—	4	1	no	—
454	C₄²×C₅₃	—	4	1	no	—
455	C₂²⋊Dic₅₃	—	2	2	no	—
456	C₂²⋊Dic₅₃	—	2	2	no	—
457	C₂²⋊Dic₅₃	—	2	2	no	—
458	C₂²⋊Dic₅₃	—	4	1	no	—
459	C₂²⋊Dic₅₃	—	4	1	no	—
460	C₂²⋊Dic₅₃	—	4	1	no	—
461	#11719921	—	2	2	no	—
462	#11719921	—	2	2	no	—
463	#11719921	—	2	2	no	—
464	#11719921	—	2	2	no	—
465	#11719921	—	2	2	no	—
466	#11719921	—	2	2	no	—
467	#11719921	—	2	2	no	—
468	#11719921	—	2	2	no	—
469	#11719921	—	2	2	no	—
470	#11719921	—	2	2	no	—
471	#11719921	—	2	2	no	—
472	#11719921	—	2	2	no	—
473	#11719921	—	2	2	no	—
474	#11719921	—	2	2	no	—
475	#11719921	—	2	2	no	—
476	#11719921	—	2	2	no	—
477	#11719921	—	2	2	no	—
478	#11719921	—	2	2	no	—
479	#11719921	—	4	1	no	—
480	#11719921	—	4	1	no	—
481	#11719921	—	4	1	no	—
482	#11719921	—	4	1	no	—
483	#11719921	—	4	1	no	—
484	#11719921	—	4	1	no	—
485	#11719921	—	4	1	no	—
486	#11719921	—	4	1	no	—
487	#11719921	—	4	1	no	—
488	#11719921	—	4	1	no	—
489	#11719921	—	4	1	no	—
490	C₄⋊Dic₅₃	—	2	2	no	—
491	C₄⋊Dic₅₃	—	2	2	no	—
492	C₄⋊Dic₅₃	—	2	2	no	—
493	C₄⋊Dic₅₃	—	4	1	no	—
494	C₄⋊Dic₅₃	—	4	1	no	—
495	C₄⋊Dic₅₃	—	4	1	no	—
496	#11719919	—	2	2	no	—
497	#11719919	—	2	2	no	—
498	#11719919	—	2	2	no	—
499	#11719919	—	2	2	no	—
500	#11719919	—	2	2	no	—
501	#11719919	—	2	2	no	—
502	#11719919	—	4	1	no	—
503	#11719919	—	4	1	no	—
504	#11719919	—	4	1	no	—
505	#11719919	—	4	1	no	—
506	#11719919	—	4	1	no	—
507	#11719919	—	4	1	no	—
508	#11719919	—	4	1	no	—
509	#11719919	—	4	1	no	—
510	#11719919	—	4	1	no	—
511	C₄×Dic₅₃	—	2	2	no	—
512	C₄×Dic₅₃	—	2	2	no	—
513	C₄×Dic₅₃	—	2	2	no	—
514	C₄×Dic₅₃	—	2	2	no	—
515	C₄×Dic₅₃	—	2	2	no	—
516	C₄×Dic₅₃	—	4	1	no	—
517	C₄×Dic₅₃	—	4	1	no	—
518	C₄×Dic₅₃	—	4	1	no	—
519	C₄×Dic₅₃	—	4	1	no	—
520	C₄×Dic₅₃	—	4	1	no	—
521	C₄×Dic₅₃	—	4	1	no	—
522	C₄×Dic₅₃	—	4	1	no	—
523	C₂³×C₅₃	—	2	1	no	—
524	C₂³×C₅₃	—	2	1	no	—
525	C₂³×C₅₃	—	2	1	no	—
526	C₂³×C₅₃	—	2	1	no	—
527	C₂³×C₅₃	—	2	1	no	—
528	C₂³×C₅₃	—	2	1	no	—
529	C₂³×C₅₃	—	2	1	no	—
530	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
531	C₂²×D₅₃	—	2	1	no	—
532	C₂²×D₅₃	—	2	1	no	—
533	C₂²×D₅₃	—	2	1	no	—
534	C₂²×D₅₃	—	2	1	no	—
535	C₂²×D₅₃	—	2	1	no	—
536	C₂²×D₅₃	—	2	1	no	—
537	C₂²×D₅₃	—	2	1	no	—
538	C₂²×D₅₃	—	2	1	no	—
539	C₂²×D₅₃	—	2	1	no	—
540	C₂²×D₅₃	—	2	1	no	—
541	C₂²×D₅₃	—	2	1	no	—
542	C₂²×D₅₃	—	2	1	no	—
543	C₂²×D₅₃	—	2	1	no	—
544	C₂²×D₅₃	—	2	1	no	—
545	C₂²×D₅₃	—	2	1	no	—
546	C₂²×D₅₃	—	2	1	no	—
547	C₂²×D₅₃	—	2	1	no	—
548	C₂²×D₅₃	—	4	4	no	—
549	C₂²×D₅₃	—	4	4	no	—
550	C₂²×D₅₃	—	4	4	no	—
551	C₂²×D₅₃	—	8	2	no	—
552	C₂²×D₅₃	—	8	2	no	—
553	C₂²×D₅₃	—	8	2	no	—
554	C₂²×D₅₃	—	8	2	no	—
555	C₂²×D₅₃	C₂×#41	1	2	yes	—
556	C₂²×D₅₃	C₂×#41	1	2	yes	—
557	C₂²×D₅₃	C₂×#41	1	2	yes	—
558	C₂²×D₅₃	C₂×#41	1	2	yes	—
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	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
599	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
600	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
601	C₂²⋊D₅₃	—	8	2	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	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	C₂×#41	1	2	yes	—
639	C₂×Dic₅₃	C₂×#41	1	2	yes	—
640	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
641	D₂₁₂	—	2	8	no	—
642	D₂₁₂	—	8	2	no	—
643	C₄×D₅₃	—	4	4	no	—
644	C₄×D₅₃	—	4	4	no	—
645	C₄×D₅₃	—	4	4	no	—
646	C₄×D₅₃	—	4	4	no	—
647	C₄×D₅₃	—	4	4	no	—
648	C₄×D₅₃	—	4	4	no	—
649	C₄×D₅₃	—	4	4	no	—
650	C₄×D₅₃	—	8	2	no	—
651	C₄×D₅₃	—	8	2	no	—
652	Dic₁₀₆	—	4	4	no	—
653	#35027	—	53	1	no	maximal, Sylow
654	C₂²×C₅₃	—	4	1	no	—
655	C₂²×C₅₃	—	4	1	no	—
656	C₂²×C₅₃	—	4	1	no	—
657	C₂²×C₅₃	—	4	1	no	—
658	C₂²×C₅₃	—	4	1	no	—
659	C₂²×C₅₃	—	4	1	no	—
660	C₂²×C₅₃	—	4	1	no	—
661	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
662	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
663	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
664	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
665	C₂²×C₅₃	#585	1	1	yes	characteristic
666	C₂²×C₅₃	#585	1	1	yes	characteristic
667	C₂²×C₅₃	#585	1	1	yes	characteristic
668	C₂×D₅₃	—	2	2	no	—
669	C₂×D₅₃	—	2	2	no	—
670	C₂×D₅₃	—	2	2	no	—
671	C₂×D₅₃	—	2	2	no	—
672	C₂×D₅₃	—	2	2	no	—
673	C₂×D₅₃	—	2	2	no	—
674	C₂×D₅₃	—	2	2	no	—
675	C₂×D₅₃	—	2	2	no	—
676	C₂×D₅₃	—	2	2	no	—
677	C₂×D₅₃	—	4	1	no	—
678	C₂×D₅₃	—	4	1	no	—
679	C₂×D₅₃	—	4	1	no	—
680	C₂×D₅₃	—	4	1	no	—
681	C₂×D₅₃	—	4	1	no	—
682	C₂×D₅₃	—	4	1	no	—
683	C₂×D₅₃	—	4	1	no	—
684	C₂×D₅₃	—	4	1	no	—
685	C₂×D₅₃	—	4	1	no	—
686	C₂×D₅₃	—	4	1	no	—
687	C₂×D₅₃	—	4	1	no	—
688	C₂×D₅₃	—	8	8	no	—
689	C₂×D₅₃	#529	1	4	yes	—
690	C₄×C₅₃	—	2	2	no	—
691	C₄×C₅₃	—	2	2	no	—
692	C₄×C₅₃	—	2	2	no	—
693	C₄×C₅₃	—	4	1	no	—
694	C₄×C₅₃	—	4	1	no	—
695	C₄×C₅₃	—	4	1	no	—
696	C₄×C₅₃	—	4	1	no	—
697	C₄×C₅₃	—	4	1	no	—
698	C₄×C₅₃	—	4	1	no	—
699	C₄×C₅₃	—	4	1	no	—
700	C₄×C₅₃	—	4	1	no	—
701	C₄×C₅₃	—	4	1	no	—
702	C₄×C₅₃	—	4	1	no	—
703	C₄×C₅₃	—	4	1	no	—
704	Dic₅₃	—	2	2	no	—
705	Dic₅₃	—	2	2	no	—
706	Dic₅₃	—	2	2	no	—
707	Dic₅₃	—	4	1	no	—
708	Dic₅₃	—	4	1	no	—
709	Dic₅₃	—	4	1	no	—
710	Dic₅₃	—	4	1	no	—
711	Dic₅₃	—	4	1	no	—
712	Dic₅₃	—	4	1	no	—
713	Dic₅₃	—	4	1	no	—
714	Dic₅₃	—	4	1	no	—
715	Dic₅₃	—	4	1	no	—
716	Dic₅₃	—	4	1	no	—
717	#2866	—	53	1	no	—
718	#2865	—	53	1	no	—
719	#2853	—	53	1	no	—
720	#2852	—	53	1	no	—
721	#2654	—	53	1	no	—
722	#2653	—	53	1	no	—
723	#2650	—	53	1	no	—
724	#2649	—	53	1	no	—
725	#2597	—	53	1	no	—
726	#2596	—	53	1	no	—
727	#2595	—	53	1	no	—
728	#2594	D₅₃	1	1	yes	characteristic, complemented
729	#2569	—	53	1	no	—
730	#2564	—	53	1	no	—
731	#2561	—	53	1	no	—
732	#2534	—	53	1	no	—
733	#2525	—	53	1	no	—
734	#2516	—	53	1	no	—
735	#2493	—	53	1	no	—
736	#2480	—	53	1	no	—
737	#2469	—	53	1	no	—
738	#2458	—	53	1	no	—
739	#2419	—	53	1	no	—
740	#2418	—	53	1	no	—
741	#2322	—	53	1	no	—
742	#2321	—	53	1	no	—
743	#2313	—	53	1	no	—
744	#2312	—	53	1	no	—
745	C₄×C₂²⋊Q₈	—	53	1	no	—
746	C₂×#388	—	53	1	no	—
747	C₄²×D₄	—	53	1	no	—
748	C₂×C₅₃	—	8	1	no	—
749	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
750	C₂×C₅₃	#3455	1	1	yes	characteristic
751	C₂×C₅₃	#3459	1	1	yes	characteristic
752	C₂×C₅₃	#3505	1	1	yes	characteristic
753	C₂×C₅₃	#3510	1	1	yes	characteristic
754	C₂×C₅₃	#3513	1	1	yes	characteristic
755	C₂×C₅₃	#3521	1	1	yes	characteristic
756	D₅₃	—	2	4	no	—
757	D₅₃	—	4	2	no	—
758	D₅₃	—	8	1	no	—
759	C₂×#126	—	53	1	no	—
760	C₂×#123	—	53	1	no	—
761	C₂×#123	—	53	1	no	—
762	C₂×C₂²⋊Q₈	—	53	1	no	—
763	C₂×#120	—	53	1	no	—
764	C₂×C₄×Q₈	—	53	1	no	—
765	C₂×C₄×D₄	—	53	1	no	—
766	C₂×C₄×D₄	—	53	1	no	—
767	C₂×C₄×D₄	—	53	1	no	—
768	C₂²×C₄⋊C₄	—	53	1	no	—
769	C₂²×C₂²⋊C₄	—	53	1	no	—
770	C₂²×C₂²⋊C₄	—	53	1	no	—
771	C₂²×C₂²⋊C₄	—	53	1	no	—
772	C₂²×C₄²	—	53	1	no	—
773	C₂²×C₄²	—	53	1	no	—
774	#401	C₂×D₅₃	1	1	yes	characteristic, complemented
775	#400	—	53	1	no	—
776	#400	—	53	1	no	—
777	#400	—	53	1	no	—
778	#400	—	53	1	no	—
779	#400	—	53	1	no	—
780	#400	—	53	1	no	—
781	#400	—	53	1	no	—
782	#399	—	53	1	no	—
783	#399	—	53	1	no	—
784	#398	—	53	1	no	—
785	#398	—	53	1	no	—
786	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
787	#397	—	53	1	no	—
788	#397	—	53	1	no	—
789	#397	—	53	1	no	—
790	#397	—	53	1	no	—
791	#397	—	53	1	no	—
792	#397	—	53	1	no	—
793	#397	—	53	1	no	—
794	#397	C₂×D₅₃	1	1	yes	characteristic
795	#396	—	53	1	no	—
796	#396	—	53	1	no	—
797	#396	C₂×D₅₃	1	1	yes	characteristic
798	#395	—	53	1	no	—
799	#394	—	53	1	no	—
800	#394	—	53	1	no	—
801	#394	—	53	1	no	—
802	#394	—	53	1	no	—
803	#393	—	53	1	no	—
804	#393	—	53	1	no	—
805	#393	—	53	1	no	—
806	#391	—	53	1	no	—
807	#390	—	53	1	no	—
808	#390	—	53	1	no	—
809	#389	—	53	1	no	—
810	#389	—	53	1	no	—
811	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
812	#388	—	53	1	no	—
813	#388	—	53	1	no	—
814	#388	—	53	1	no	—
815	#388	—	53	1	no	—
816	#388	—	53	1	no	—
817	#388	—	53	1	no	—
818	#388	—	53	1	no	—
819	#388	—	53	1	no	—
820	#388	—	53	1	no	—
821	#388	—	53	1	no	—
822	#388	—	53	1	no	—
823	#388	—	53	1	no	—
824	#388	—	53	1	no	—
825	#388	—	53	1	no	—
826	#388	—	53	1	no	—
827	#388	—	53	1	no	—
828	#388	—	53	1	no	—
829	#388	—	53	1	no	—
830	#388	—	53	1	no	—
831	#388	—	53	1	no	—
832	#388	—	53	1	no	—
833	#388	—	53	1	no	—
834	#388	—	53	1	no	—
835	#388	—	53	1	no	—
836	#388	—	53	1	no	—
837	#388	—	53	1	no	—
838	#388	—	53	1	no	—
839	#388	—	53	1	no	—
840	#388	C₂×D₅₃	1	1	yes	characteristic
841	#388	C₂×D₅₃	1	1	yes	characteristic
842	#388	C₂×D₅₃	1	1	yes	characteristic
843	#388	C₂×D₅₃	1	1	yes	characteristic
844	#388	C₂×D₅₃	1	1	yes	characteristic
845	#387	—	53	1	no	—
846	#387	—	53	1	no	—
847	#387	—	53	1	no	—
848	#387	—	53	1	no	—
849	#387	—	53	1	no	—
850	#387	—	53	1	no	—
851	#387	—	53	1	no	—
852	#387	—	53	1	no	—
853	#387	—	53	1	no	—
854	#387	—	53	1	no	—
855	#387	—	53	1	no	—
856	#387	—	53	1	no	—
857	#387	—	53	1	no	—
858	#387	—	53	1	no	—
859	#387	—	53	1	no	—
860	#387	—	53	1	no	—
861	#387	—	53	1	no	—
862	#387	—	53	1	no	—
863	#387	—	53	1	no	—
864	#387	—	53	1	no	—
865	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
866	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
867	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
868	#386	—	53	1	no	—
869	#386	—	53	1	no	—
870	#386	—	53	1	no	—
871	#386	—	53	1	no	—
872	#386	—	53	1	no	—
873	#386	—	53	1	no	—
874	#386	—	53	1	no	—
875	#385	—	53	1	no	—
876	#385	—	53	1	no	—
877	#385	—	53	1	no	—
878	#385	—	53	1	no	—
879	#385	—	53	1	no	—
880	#385	—	53	1	no	—
881	#385	—	53	1	no	—
882	#385	—	53	1	no	—
883	#385	—	53	1	no	—
884	#383	—	53	1	no	—
885	#381	—	53	1	no	—
886	#381	—	53	1	no	—
887	#381	—	53	1	no	—
888	#381	—	53	1	no	—
889	#380	—	53	1	no	—
890	#380	—	53	1	no	—
891	#380	—	53	1	no	—
892	#380	—	53	1	no	—
893	#380	—	53	1	no	—
894	#379	—	53	1	no	—
895	#379	—	53	1	no	—
896	#379	—	53	1	no	—
897	C₄×C₄⋊C₄	—	53	1	no	—
898	C₄×C₄⋊C₄	—	53	1	no	—
899	C₄×C₄⋊C₄	—	53	1	no	—
900	C₄×C₄⋊C₄	—	53	1	no	—
901	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
902	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
903	C₄×C₂²⋊C₄	—	53	1	no	—
904	C₄×C₂²⋊C₄	—	53	1	no	—
905	C₄×C₂²⋊C₄	—	53	1	no	—
906	C₄×C₂²⋊C₄	—	53	1	no	—
907	C₄×C₂²⋊C₄	—	53	1	no	—
908	C₄×C₂²⋊C₄	—	53	1	no	—
909	C₄×C₂²⋊C₄	—	53	1	no	—
910	C₄×C₂²⋊C₄	—	53	1	no	—
911	C₂×#95	—	53	1	no	—
912	C₂×#95	—	53	1	no	—
913	C₄³	—	53	1	no	—
914	C₅₃	#35027	1	1	yes	characteristic, complemented, Sylow
915	C₂⁵	—	53	1	no	—
916	C₂²×Q₈	—	53	1	no	—
917	C₂²×D₄	—	53	1	no	—
918	C₂²×D₄	—	53	1	no	—
919	C₂²×D₄	—	53	1	no	—
920	C₂³×C₄	—	53	1	no	—
921	C₂³×C₄	—	53	1	no	—
922	C₂³×C₄	—	53	1	no	—
923	C₂³×C₄	—	53	1	no	—
924	C₂³×C₄	—	53	1	no	—
925	C₂³×C₄	—	53	1	no	—
926	C₂³×C₄	—	53	1	no	—
927	C₂³×C₄	—	53	1	no	—
928	C₂³×C₄	—	53	1	no	—
929	#126	—	212	2	no	—
930	#123	—	106	4	no	—
931	#123	—	212	2	no	—
932	C₂²⋊Q₈	—	106	4	no	—
933	#120	—	106	4	no	—
934	C₄×Q₈	—	212	2	no	—
935	C₄×D₄	—	106	4	no	—
936	C₄×D₄	—	106	4	no	—
937	C₄×D₄	—	106	4	no	—
938	C₂×C₄⋊C₄	—	53	1	no	—
939	C₂×C₄⋊C₄	—	53	1	no	—
940	C₂×C₄⋊C₄	—	53	1	no	—
941	C₂×C₄⋊C₄	—	53	1	no	—
942	C₂×C₄⋊C₄	—	53	1	no	—
943	C₂×C₄⋊C₄	—	53	1	no	—
944	C₂×C₄⋊C₄	—	53	1	no	—
945	C₂×C₄⋊C₄	—	53	1	no	—
946	C₂×C₄⋊C₄	—	53	1	no	—
947	C₂×C₄⋊C₄	—	53	1	no	—
948	C₂×C₄⋊C₄	—	53	1	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	1	no	—
951	C₂×C₄⋊C₄	—	53	1	no	—
952	C₂×C₄⋊C₄	—	53	1	no	—
953	C₂×C₄⋊C₄	—	53	1	no	—
954	C₂×C₄⋊C₄	—	53	1	no	—
955	C₂×C₄⋊C₄	—	53	1	no	—
956	C₂×C₄⋊C₄	—	53	1	no	—
957	C₂×C₄⋊C₄	—	53	1	no	—
958	C₂×C₄⋊C₄	—	53	1	no	—
959	C₂×C₄⋊C₄	—	106	4	no	—
960	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	—	53	1	no	—
970	C₂×C₂²⋊C₄	—	53	1	no	—
971	C₂×C₂²⋊C₄	—	53	1	no	—
972	C₂×C₂²⋊C₄	—	53	1	no	—
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	no	—
975	C₂×C₂²⋊C₄	—	53	1	no	—
976	C₂×C₂²⋊C₄	—	53	1	no	—
977	C₂×C₂²⋊C₄	—	53	1	no	—
978	C₂×C₂²⋊C₄	—	53	1	no	—
979	C₂×C₂²⋊C₄	—	53	1	no	—
980	C₂×C₂²⋊C₄	—	53	1	no	—
981	C₂×C₂²⋊C₄	—	53	1	no	—
982	C₂×C₂²⋊C₄	—	53	1	no	—
983	C₂×C₂²⋊C₄	—	53	1	no	—
984	C₂×C₂²⋊C₄	—	53	1	no	—
985	C₂×C₂²⋊C₄	—	53	1	no	—
986	C₂×C₂²⋊C₄	—	53	1	no	—
987	C₂×C₂²⋊C₄	—	53	1	no	—
988	C₂×C₂²⋊C₄	—	53	1	no	—
989	C₂×C₂²⋊C₄	—	53	1	no	—
990	C₂×C₂²⋊C₄	—	53	1	no	—
991	C₂×C₂²⋊C₄	—	53	1	no	—
992	C₂×C₂²⋊C₄	—	53	1	no	—
993	C₂×C₂²⋊C₄	—	53	1	no	—
994	C₂×C₂²⋊C₄	—	53	1	no	—
995	C₂×C₂²⋊C₄	—	53	1	no	—
996	C₂×C₂²⋊C₄	—	53	1	no	—
997	C₂×C₂²⋊C₄	—	53	1	no	—
998	C₂×C₂²⋊C₄	—	53	1	no	—
999	C₂×C₂²⋊C₄	—	53	1	no	—
1000	C₂×C₂²⋊C₄	—	53	1	no	—
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	1	no	—
1004	C₂×C₂²⋊C₄	—	106	4	no	—
1005	C₂×C₂²⋊C₄	—	106	4	no	—
1006	C₂×C₂²⋊C₄	—	212	2	no	—
1007	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂×C₄²	—	53	1	no	—
1015	C₂×C₄²	—	53	1	no	—
1016	C₂×C₄²	—	53	1	no	—
1017	C₂×C₄²	—	53	1	no	—
1018	C₂×C₄²	—	53	1	no	—
1019	C₂×C₄²	—	53	1	no	—
1020	C₂×C₄²	—	53	1	no	—
1021	C₂×C₄²	—	53	1	no	—
1022	C₂×C₄²	—	53	1	no	—
1023	C₂×C₄²	—	53	1	no	—
1024	C₂×C₄²	—	53	1	no	—
1025	C₂×C₄²	—	53	1	no	—
1026	C₂×C₄²	—	212	2	no	—
1027	C₂×C₄²	—	212	2	no	—
1028	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1029	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1030	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1041	#95	—	53	1	no	—
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	C₂²×D₅₃	1	1	yes	characteristic
1072	#95	C₂²×D₅₃	1	1	yes	characteristic
1073	#95	C₂²×D₅₃	1	1	yes	characteristic
1074	#95	C₂²×D₅₃	1	1	yes	characteristic
1075	#95	C₂²×D₅₃	1	1	yes	characteristic
1076	#95	C₂²×D₅₃	1	1	yes	characteristic
1077	#95	C₂²×D₅₃	1	1	yes	characteristic
1078	#95	C₂²×D₅₃	1	1	yes	characteristic
1079	#95	C₂²×D₅₃	1	1	yes	characteristic
1080	#95	C₂²×D₅₃	1	1	yes	characteristic
1081	#95	C₂²×D₅₃	1	1	yes	characteristic
1082	#95	C₂²×D₅₃	1	1	yes	characteristic
1083	#95	C₂²×D₅₃	1	1	yes	characteristic
1084	#95	C₂²×D₅₃	1	1	yes	characteristic
1085	C₂⁴	—	53	1	no	—
1086	C₂⁴	—	53	1	no	—
1087	C₂⁴	—	53	1	no	—
1088	C₂⁴	—	106	2	no	—
1089	C₂⁴	—	106	2	no	—
1090	C₂⁴	—	106	2	no	—
1091	C₂⁴	—	212	1	no	—
1092	C₂⁴	—	212	1	no	—
1093	C₂⁴	—	212	1	no	—
1094	C₂⁴	—	212	1	no	—
1095	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1096	C₂×Q₈	—	106	2	no	—
1097	C₂×Q₈	—	212	1	no	—
1098	C₂×Q₈	—	212	1	no	—
1099	C₂×D₄	—	53	4	no	—
1100	C₂×D₄	—	106	2	no	—
1101	C₂×D₄	—	106	2	no	—
1102	C₂×D₄	—	106	2	no	—
1103	C₂×D₄	—	106	2	no	—
1104	C₂×D₄	—	212	1	no	—
1105	C₂×D₄	—	212	1	no	—
1106	C₂×D₄	—	212	1	no	—
1107	C₂×D₄	—	212	1	no	—
1108	C₂²×C₄	—	53	1	no	—
1109	C₂²×C₄	—	53	1	no	—
1110	C₂²×C₄	—	53	1	no	—
1111	C₂²×C₄	—	53	4	no	—
1112	C₂²×C₄	—	53	4	no	—
1113	C₂²×C₄	—	53	1	no	—
1114	C₂²×C₄	—	53	1	no	—
1115	C₂²×C₄	—	53	1	no	—
1116	C₂²×C₄	—	53	1	no	—
1117	C₂²×C₄	—	53	1	no	—
1118	C₂²×C₄	—	53	1	no	—
1119	C₂²×C₄	—	53	1	no	—
1120	C₂²×C₄	—	53	1	no	—
1121	C₂²×C₄	—	53	1	no	—
1122	C₂²×C₄	—	53	1	no	—
1123	C₂²×C₄	—	106	2	no	—
1124	C₂²×C₄	—	106	2	no	—
1125	C₂²×C₄	—	106	2	no	—
1126	C₂²×C₄	—	106	2	no	—
1127	C₂²×C₄	—	106	2	no	—
1128	C₂²×C₄	—	106	2	no	—
1129	C₂²×C₄	—	106	2	no	—
1130	C₂²×C₄	—	106	2	no	—
1131	C₂²×C₄	—	106	2	no	—
1132	C₂²×C₄	—	106	2	no	—
1133	C₂²×C₄	—	106	2	no	—
1134	C₂²×C₄	—	212	1	no	—
1135	C₂²×C₄	—	212	1	no	—
1136	C₂²×C₄	—	212	1	no	—
1137	C₂²×C₄	—	212	1	no	—
1138	C₂²×C₄	—	212	1	no	—
1139	C₂²×C₄	—	212	1	no	—
1140	C₂²×C₄	—	212	1	no	—
1141	C₂²×C₄	—	212	1	no	—
1142	C₂²×C₄	—	212	1	no	—
1143	C₂²×C₄	—	212	1	no	—
1144	C₂²×C₄	—	212	1	no	—
1145	C₂²×C₄	—	212	1	no	—
1146	C₂²×C₄	—	212	1	no	—
1147	C₂²×C₄	—	212	1	no	—
1148	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1151	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1152	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1153	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1154	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1155	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1156	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1157	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1158	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1159	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1161	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1162	C₄⋊C₄	—	2	2	no	—
1163	C₄⋊C₄	—	2	2	no	—
1164	C₄⋊C₄	—	2	2	no	—
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	2	no	—
1167	C₄⋊C₄	—	4	1	no	—
1168	C₄⋊C₄	—	4	1	no	—
1169	C₄⋊C₄	—	4	1	no	—
1170	C₄⋊C₄	—	4	1	no	—
1171	C₄⋊C₄	—	106	2	no	—
1172	C₄⋊C₄	—	106	2	no	—
1173	C₄⋊C₄	—	106	2	no	—
1174	C₄⋊C₄	—	106	2	no	—
1175	C₄⋊C₄	—	106	2	no	—
1176	C₄⋊C₄	—	106	2	no	—
1177	C₄⋊C₄	—	106	2	no	—
1178	C₄⋊C₄	—	106	2	no	—
1179	C₄⋊C₄	—	106	2	no	—
1180	C₄⋊C₄	—	212	1	no	—
1181	C₄⋊C₄	—	212	1	no	—
1182	C₄⋊C₄	—	212	1	no	—
1183	C₄⋊C₄	—	212	1	no	—
1184	C₄⋊C₄	—	212	1	no	—
1185	C₄⋊C₄	—	212	1	no	—
1186	C₄⋊C₄	—	212	1	no	—
1187	C₄⋊C₄	—	212	1	no	—
1188	C₄⋊C₄	—	212	1	no	—
1189	C₄⋊C₄	—	212	1	no	—
1190	C₄⋊C₄	—	212	1	no	—
1191	C₄⋊C₄	—	212	1	no	—
1192	C₂²⋊C₄	—	2	2	no	—
1193	C₂²⋊C₄	—	2	2	no	—
1194	C₂²⋊C₄	—	2	2	no	—
1195	C₂²⋊C₄	—	4	1	no	—
1196	C₂²⋊C₄	—	4	1	no	—
1197	C₂²⋊C₄	—	4	1	no	—
1198	C₂²⋊C₄	—	4	1	no	—
1199	C₂²⋊C₄	—	106	2	no	—
1200	C₂²⋊C₄	—	106	2	no	—
1201	C₂²⋊C₄	—	106	2	no	—
1202	C₂²⋊C₄	—	106	2	no	—
1203	C₂²⋊C₄	—	106	2	no	—
1204	C₂²⋊C₄	—	106	2	no	—
1205	C₂²⋊C₄	—	106	2	no	—
1206	C₂²⋊C₄	—	106	2	no	—
1207	C₂²⋊C₄	—	106	2	no	—
1208	C₂²⋊C₄	—	106	2	no	—
1209	C₂²⋊C₄	—	106	2	no	—
1210	C₂²⋊C₄	—	106	2	no	—
1211	C₂²⋊C₄	—	106	2	no	—
1212	C₂²⋊C₄	—	106	2	no	—
1213	C₂²⋊C₄	—	106	2	no	—
1214	C₂²⋊C₄	—	106	2	no	—
1215	C₂²⋊C₄	—	106	2	no	—
1216	C₂²⋊C₄	—	106	2	no	—
1217	C₂²⋊C₄	—	106	2	no	—
1218	C₂²⋊C₄	—	106	2	no	—
1219	C₂²⋊C₄	—	106	2	no	—
1220	C₂²⋊C₄	—	212	1	no	—
1221	C₂²⋊C₄	—	212	1	no	—
1222	C₂²⋊C₄	—	212	1	no	—
1223	C₂²⋊C₄	—	212	1	no	—
1224	C₂²⋊C₄	—	212	1	no	—
1225	C₂²⋊C₄	—	212	1	no	—
1226	C₂²⋊C₄	—	212	1	no	—
1227	C₂²⋊C₄	—	212	1	no	—
1228	C₂²⋊C₄	—	212	1	no	—
1229	C₂²⋊C₄	—	212	1	no	—
1230	C₂²⋊C₄	—	212	1	no	—
1231	C₂²⋊C₄	—	212	1	no	—
1232	C₂²⋊C₄	—	212	1	no	—
1233	C₂²⋊C₄	—	212	1	no	—
1234	C₄²	—	2	2	no	—
1235	C₄²	—	4	1	no	—
1236	C₄²	—	4	1	no	—
1237	C₄²	—	4	1	no	—
1238	C₄²	—	4	1	no	—
1239	C₄²	—	106	2	no	—
1240	C₄²	—	106	2	no	—
1241	C₄²	—	106	2	no	—
1242	C₄²	—	106	2	no	—
1243	C₄²	—	106	2	no	—
1244	C₄²	—	212	1	no	—
1245	C₄²	—	212	1	no	—
1246	C₄²	—	212	1	no	—
1247	C₄²	—	212	1	no	—
1248	C₄²	—	212	1	no	—
1249	C₄²	—	212	1	no	—
1250	C₄²	—	212	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	53	2	no	—
1259	C₂³	—	53	2	no	—
1260	C₂³	—	53	2	no	—
1261	C₂³	—	53	2	no	—
1262	C₂³	—	106	1	no	—
1263	C₂³	—	106	1	no	—
1264	C₂³	—	106	1	no	—
1265	C₂³	—	106	1	no	—
1266	C₂³	—	106	1	no	—
1267	C₂³	—	106	1	no	—
1268	C₂³	—	106	1	no	—
1269	C₂³	—	106	1	no	—
1270	C₂³	—	106	1	no	—
1271	C₂³	—	106	1	no	—
1272	C₂³	—	106	1	no	—
1273	C₂³	—	106	1	no	—
1274	C₂³	—	106	1	no	—
1275	C₂³	—	106	1	no	—
1276	C₂³	—	106	1	no	—
1277	C₂³	—	106	1	no	—
1278	C₂³	—	106	1	no	—
1279	C₂³	—	424	2	no	—
1280	C₂³	—	424	2	no	—
1281	C₂³	—	424	2	no	—
1282	C₂³	—	424	2	no	—
1283	C₂³	—	212	4	no	—
1284	C₂³	—	212	4	no	—
1285	C₂³	—	212	4	no	—
1286	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1287	Q₈	—	212	4	no	—
1288	D₄	—	106	8	no	—
1289	D₄	—	424	2	no	—
1290	D₄	—	424	2	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	53	2	no	—
1331	C₂×C₄	—	53	2	no	—
1332	C₂×C₄	—	53	2	no	—
1333	C₂×C₄	—	106	1	no	—
1334	C₂×C₄	—	106	1	no	—
1335	C₂×C₄	—	106	1	no	—
1336	C₂×C₄	—	106	1	no	—
1337	C₂×C₄	—	106	1	no	—
1338	C₂×C₄	—	106	1	no	—
1339	C₂×C₄	—	106	1	no	—
1340	C₂×C₄	—	106	1	no	—
1341	C₂×C₄	—	106	1	no	—
1342	C₂×C₄	—	106	1	no	—
1343	C₂×C₄	—	106	1	no	—
1344	C₂×C₄	—	106	1	no	—
1345	C₂×C₄	—	106	1	no	—
1346	C₂×C₄	—	106	1	no	—
1347	C₂×C₄	—	106	1	no	—
1348	C₂×C₄	—	106	1	no	—
1349	C₂×C₄	—	106	1	no	—
1350	C₂×C₄	—	106	1	no	—
1351	C₂×C₄	—	106	1	no	—
1352	C₂×C₄	—	106	1	no	—
1353	C₂×C₄	—	106	1	no	—
1354	C₂×C₄	—	106	1	no	—
1355	C₂×C₄	—	106	1	no	—
1356	C₂×C₄	—	106	1	no	—
1357	C₂×C₄	—	106	1	no	—
1358	C₂×C₄	—	106	1	no	—
1359	C₂×C₄	—	106	1	no	—
1360	C₂×C₄	—	106	1	no	—
1361	C₂×C₄	—	106	1	no	—
1362	C₂×C₄	—	106	1	no	—
1363	C₂×C₄	—	106	1	no	—
1364	C₂×C₄	—	106	1	no	—
1365	C₂×C₄	—	106	1	no	—
1366	C₂×C₄	—	106	1	no	—
1367	C₂×C₄	—	106	1	no	—
1368	C₂×C₄	—	106	1	no	—
1369	C₂×C₄	—	424	2	no	—
1370	C₂×C₄	—	424	2	no	—
1371	C₂×C₄	—	212	4	no	—
1372	C₂×C₄	—	212	4	no	—
1373	C₂×C₄	—	212	4	no	—
1374	C₂×C₄	—	212	4	no	—
1375	C₂×C₄	—	212	4	no	—
1376	C₂×C₄	—	212	4	no	—
1377	C₂×C₄	—	212	4	no	—
1378	C₂×C₄	#41×D₅₃	1	2	yes	—
1379	C₂×C₄	#41×D₅₃	1	2	yes	—
1380	C₂×C₄	#41×D₅₃	1	2	yes	—
1381	C₂²	—	4	1	no	—
1382	C₂²	—	4	1	no	—
1383	C₂²	—	4	1	no	—
1384	C₂²	—	4	1	no	—
1385	C₂²	—	4	1	no	—
1386	C₂²	—	4	1	no	—
1387	C₂²	—	4	1	no	—
1388	C₂²	—	53	4	no	—
1389	C₂²	—	106	2	no	—
1390	C₂²	—	106	2	no	—
1391	C₂²	—	106	2	no	—
1392	C₂²	—	106	2	no	—
1393	C₂²	—	106	2	no	—
1394	C₂²	—	106	2	no	—
1395	C₂²	—	106	2	no	—
1396	C₂²	—	106	2	no	—
1397	C₂²	—	106	2	no	—
1398	C₂²	—	424	8	no	—
1399	C₂²	—	212	1	no	—
1400	C₂²	—	212	1	no	—
1401	C₂²	—	212	1	no	—
1402	C₂²	—	212	1	no	—
1403	C₂²	—	212	1	no	—
1404	C₂²	—	212	1	no	—
1405	C₂²	—	212	1	no	—
1406	C₂²	—	212	1	no	—
1407	C₂²	—	212	1	no	—
1408	C₂²	—	212	1	no	—
1409	C₂²	—	212	1	no	—
1410	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1411	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1412	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1413	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1414	C₂²	#16811459	1	1	yes	characteristic
1415	C₂²	#16811459	1	1	yes	characteristic
1416	C₂²	#16811460	1	1	yes	characteristic
1417	C₄	—	2	2	no	—
1418	C₄	—	2	2	no	—
1419	C₄	—	2	2	no	—
1420	C₄	—	4	1	no	—
1421	C₄	—	4	1	no	—
1422	C₄	—	4	1	no	—
1423	C₄	—	4	1	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	1	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	4	1	no	—
1429	C₄	—	4	1	no	—
1430	C₄	—	4	1	no	—
1431	C₄	—	106	2	no	—
1432	C₄	—	106	2	no	—
1433	C₄	—	106	2	no	—
1434	C₄	—	212	1	no	—
1435	C₄	—	212	1	no	—
1436	C₄	—	212	1	no	—
1437	C₄	—	212	1	no	—
1438	C₄	—	212	1	no	—
1439	C₄	—	212	1	no	—
1440	C₄	—	212	1	no	—
1441	C₄	—	212	1	no	—
1442	C₄	—	212	1	no	—
1443	C₄	—	212	1	no	—
1444	C₂	—	8	1	no	—
1445	C₂	—	106	4	no	—
1446	C₂	—	424	1	no	—
1447	C₂	—	212	2	no	—
1448	C₂	#529×D₅₃	1	1	yes	characteristic
1449	C₂	#20288098	1	1	yes	characteristic
1450	C₂	#20288123	1	1	yes	characteristic
1451	C₂	#20288548	1	1	yes	characteristic
1452	C₂	#20288605	1	1	yes	characteristic
1453	C₂	#20288662	1	1	yes	characteristic
1454	C₂	#20288782	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2594	C₂
prime radical	C₂×#13133187	C₂²
hypercenter	#2594	D₅₃
hypocenter	C₅₃	#35027
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2594

Complements

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

N	H ≅ G/N	type
1. #20283106	C₂	semidirect
2. #20283105	C₂	semidirect
3. #20283035	C₂	semidirect
4. #20283033	C₂	semidirect
5. #20280786	C₂	semidirect
6. #20280783	C₂	semidirect
7. #20280726	C₂	semidirect
8. #20280723	C₂	semidirect
9. #20280266	C₂	semidirect
10. #20280245	C₂	semidirect
11. #20280238	C₂	semidirect
12. #20279937	C₂	semidirect
13. #20279894	C₂	semidirect
14. #20279871	C₂	semidirect
16. #20279479	C₂	semidirect
17. #20279348	C₂	semidirect
18. #20279095	C₂	semidirect
19. #20278964	C₂	semidirect
20. #20278803	C₂	semidirect
21. #20278636	C₂	semidirect
22. #20278193	C₂	semidirect
24. #20277379	C₂	semidirect
26. #20277314	C₂	semidirect
27. #20277309	C₂	semidirect
28. C₄×#13133195	C₂	semidirect
29. #388×D₅₃	C₂	semidirect
30. C₄×#13133179	C₂	semidirect
31. C₅₃×#2594	C₂	semidirect
37. C₂×C₄×Dic₁₀₆	C₂²	semidirect
46. C₂×C₄²×D₅₃	C₂²	semidirect
47. #16810565	C₂²	semidirect
48. #16810565	C₂²	semidirect
49. #16810564	C₂²	semidirect
50. #16810564	C₂²	semidirect
51. #16810563	C₂²	semidirect
52. #16810561	C₂²	semidirect
53. #16810561	C₂²	semidirect
55. #16810558	C₂²	semidirect
56. #16810557	C₂²	semidirect
57. #16810554	C₂²	semidirect
61. #16810550	C₂²	semidirect
63. #16810549	C₂²	semidirect
67. #16810544	C₂²	semidirect
73. #16810536	C₂²	semidirect
75. #16810527	C₂²	semidirect
78. #16810518	C₂²	semidirect
79. #16810518	C₂²	semidirect
94. #16810514	C₂²	semidirect
100. #16810513	C₂²	semidirect
108. #16810510	C₂²	semidirect
109. #16810510	C₂²	semidirect
110. #16810510	C₂²	semidirect
111. #16810510	C₂²	semidirect
112. #16810509	C₂²	semidirect
113. #16810509	C₂²	semidirect
114. #16810509	C₂²	semidirect
115. #16810508	C₂²	semidirect
116. #16810508	C₂²	semidirect
117. #16810508	C₂²	semidirect
118. #16810507	C₂²	semidirect
119. #16810507	C₂²	semidirect
120. #16810507	C₂²	semidirect
121. #16810506	C₂²	semidirect
122. #16810506	C₂²	semidirect
123. #16810505	C₂²	semidirect
124. #16810505	C₂²	semidirect
125. #16810505	C₂²	semidirect
126. #16810504	C₂²	semidirect
127. #16810504	C₂²	semidirect
137. #16810497	C₂²	semidirect
138. #16810497	C₂²	semidirect
141. #16810494	C₂²	semidirect
142. #16810494	C₂²	semidirect
143. #16810494	C₂²	semidirect
144. #16810490	C₂²	semidirect
148. #16810485	C₂²	semidirect
157. C₄⋊C₄×Dic₅₃	C₂²	semidirect
158. C₄⋊C₄×Dic₅₃	C₂²	semidirect
159. C₄×#11719919	C₂²	semidirect
160. C₄×#11719919	C₂²	semidirect
164. C₄×#11719921	C₂²	semidirect
167. #16810470	C₂²	semidirect
168. #16810470	C₂²	semidirect
171. C₄²×Dic₅₃	C₂²	semidirect
172. C₅₃×#401	C₂²	semidirect
173. C₅₃×#398	C₂²	semidirect
176. C₅₃×#389	C₂²	semidirect
182. C₅₃×#387	C₂²	semidirect
183. C₅₃×#387	C₂²	semidirect
184. C₅₃×#387	C₂²	semidirect
185. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
728. #2594	D₅₃	semidirect
774. #401	C₂×D₅₃	semidirect
786. #398	C₂×D₅₃	semidirect
811. #389	C₂×D₅₃	semidirect
865. #387	C₂×D₅₃	semidirect
866. #387	C₂×D₅₃	semidirect
867. #387	C₂×D₅₃	semidirect
901. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
902. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
914. C₅₃	#35027	semidirect

Maximal subgroups

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

subgroup	index
#20283106	2
#20283105	2
#20283035	2
#20283033	2
#20280786	2
#20280783	2
#20280726	2
#20280723	2
#20280266	2
#20280245	2
#20280238	2
#20279937	2
#20279894	2
#20279871	2
#20279609	2
#20279479	2
#20279348	2
#20279095	2
#20278964	2
#20278803	2
#20278636	2
#20278193	2
#20278178	2
#20277379	2
#20277368	2
#20277314	2
#20277309	2
C₄×#13133195	2
#388×D₅₃	2
C₄×#13133179	2
C₅₃×#2594	2
#35027	53