Subgroups — #27591275

Order 13568.

2034 conjugacy classes of subgroups.

The subgroup lattice has 1574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283001	C₂	1	1	yes	maximal, characteristic, complemented
2	#20282998	C₂	1	1	yes	maximal, characteristic
3	#20281910	C₂	1	1	yes	maximal, characteristic, complemented
4	#20281843	C₂	1	1	yes	maximal, characteristic, complemented
5	#20281839	C₂	1	1	yes	maximal, characteristic, complemented
6	#20281837	C₂	1	1	yes	maximal, characteristic, complemented
7	#20281825	C₂	1	1	yes	maximal, characteristic, complemented
8	#20281549	C₂	1	1	yes	maximal, characteristic, complemented
9	#20281549	C₂	1	1	yes	maximal, characteristic, complemented
10	#20281344	C₂	1	1	yes	maximal, characteristic, complemented
11	#20281340	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281213	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281209	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281203	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281199	C₂	1	1	yes	maximal, characteristic, complemented
16	#20280969	C₂	1	1	yes	maximal, characteristic, complemented
17	#20280967	C₂	1	1	yes	maximal, characteristic, complemented
18	#20280830	C₂	1	1	yes	maximal, characteristic, complemented
19	#20280647	C₂	1	1	yes	maximal, characteristic, complemented
20	#20278980	C₂	1	1	yes	maximal, characteristic, complemented
21	#20278979	C₂	1	1	yes	maximal, characteristic, complemented
22	#20278839	C₂	1	1	yes	maximal, characteristic, complemented
23	#20278834	C₂	1	1	yes	maximal, characteristic, complemented
24	#20278529	C₂	1	1	yes	maximal, characteristic, complemented
25	#20278519	C₂	1	1	yes	maximal, characteristic, complemented
26	#20278182	C₂	1	1	yes	maximal, characteristic, complemented
27	#20278178	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277442	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277414	C₂	1	1	yes	maximal, characteristic, complemented
30	#380×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2747	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133212	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13133211	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133203	C₂²	1	1	yes	characteristic
36	C₂×#13133203	C₂²	1	1	yes	characteristic
37	C₂×#13133199	C₂²	1	1	yes	characteristic
38	C₂×#13133199	C₂²	1	1	yes	characteristic
39	C₂×#13133197	C₂²	1	1	yes	characteristic
40	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13133195	C₂²	1	1	yes	characteristic
42	C₂×#13133195	C₂²	1	1	yes	characteristic
43	C₂×#13133195	C₂²	1	1	yes	characteristic
44	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13133194	C₂²	1	1	yes	characteristic
46	C₂×#13133192	C₂²	1	1	yes	characteristic
47	C₂×#13133192	C₂²	1	1	yes	characteristic
48	C₂×#13133191	C₂²	1	1	yes	characteristic
49	C₂×#13133187	C₂²	1	1	yes	characteristic
50	C₂×#13133187	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
52	C₂×#13133179	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	#16810565	C₂²	1	1	yes	characteristic, complemented
58	#16810565	C₂²	1	1	yes	characteristic, complemented
59	#16810564	C₂²	1	1	yes	characteristic, complemented
60	#16810561	C₂²	1	1	yes	characteristic, complemented
61	#16810560	C₂²	1	1	yes	characteristic
62	#16810560	C₂²	1	1	yes	characteristic, complemented
63	#16810558	C₂²	1	1	yes	characteristic
64	#16810558	C₂²	1	1	yes	characteristic, complemented
65	#16810556	C₂²	1	1	yes	characteristic, complemented
66	#16810556	C₂²	1	1	yes	characteristic, complemented
67	#16810555	C₂²	1	1	yes	characteristic, complemented
68	#16810554	C₂²	1	1	yes	characteristic, complemented
69	#16810552	C₂²	1	1	yes	characteristic, complemented
70	#16810552	C₂²	1	1	yes	characteristic, complemented
71	#16810552	C₂²	1	1	yes	characteristic, complemented
72	#16810552	C₂²	1	1	yes	characteristic, complemented
73	#16810548	C₂²	1	1	yes	characteristic
74	#16810548	C₂²	1	1	yes	characteristic
75	#16810547	C₂²	1	1	yes	characteristic, complemented
76	#16810545	C₂²	1	1	yes	characteristic, complemented
77	#16810545	C₂²	1	1	yes	characteristic, complemented
78	#16810545	C₂²	1	1	yes	characteristic, complemented
79	#16810544	C₂²	1	1	yes	characteristic, complemented
80	#16810544	C₂²	1	1	yes	characteristic, complemented
81	#16810544	C₂²	1	1	yes	characteristic, complemented
82	#16810544	C₂²	1	1	yes	characteristic, complemented
83	#16810543	C₂²	1	1	yes	characteristic, complemented
84	#16810543	C₂²	1	1	yes	characteristic, complemented
85	#16810541	C₂²	1	1	yes	characteristic
86	#16810541	C₂²	1	1	yes	characteristic
87	#16810541	C₂²	1	1	yes	characteristic, complemented
88	#16810540	C₂²	1	1	yes	characteristic
89	#16810540	C₂²	1	1	yes	characteristic
90	#16810540	C₂²	1	1	yes	characteristic, complemented
91	#16810539	C₂²	1	1	yes	characteristic
92	#16810539	C₂²	1	1	yes	characteristic
93	#16810538	C₂²	1	1	yes	characteristic
94	#16810538	C₂²	1	1	yes	characteristic
95	#16810536	C₂²	1	1	yes	characteristic
96	#16810536	C₂²	1	1	yes	characteristic
97	#16810536	C₂²	1	1	yes	characteristic, complemented
98	#16810536	C₂²	1	1	yes	characteristic, complemented
99	#16810529	C₂²	1	1	yes	characteristic, complemented
100	#16810527	C₂²	1	1	yes	characteristic, complemented
101	#16810525	C₂²	1	1	yes	characteristic
102	#16810524	C₂²	1	1	yes	characteristic
103	#16810522	C₂²	1	1	yes	characteristic, complemented
104	#16810521	C₂²	1	1	yes	characteristic, complemented
105	#16810520	C₂²	1	1	yes	characteristic, complemented
106	#16810520	C₂²	1	1	yes	characteristic, complemented
107	#16810517	C₂²	1	1	yes	characteristic
108	#16810515	C₂²	1	1	yes	characteristic
109	#16810515	C₂²	1	1	yes	characteristic
110	#16810515	C₂²	1	1	yes	characteristic, complemented
111	#16810514	C₂²	1	1	yes	characteristic
112	#16810514	C₂²	1	1	yes	characteristic, complemented
113	#16810513	C₂²	1	1	yes	characteristic, complemented
114	#16810512	C₂²	1	1	yes	characteristic
115	#16810512	C₂²	1	1	yes	characteristic, complemented
116	#16810511	C₂²	1	1	yes	characteristic
117	#16810510	C₂²	1	1	yes	characteristic, complemented
118	#16810510	C₂²	1	1	yes	characteristic, complemented
119	#16810510	C₂²	1	1	yes	characteristic, complemented
120	#16810509	C₂²	1	1	yes	characteristic, complemented
121	#16810506	C₂²	1	1	yes	characteristic, complemented
122	#16810505	C₂²	1	1	yes	characteristic, complemented
123	#16810505	C₂²	1	1	yes	characteristic, complemented
124	#16810504	C₂²	1	1	yes	characteristic, complemented
125	#16810501	C₂²	1	1	yes	characteristic
126	#16810501	C₂²	1	1	yes	characteristic
127	#16810501	C₂²	1	1	yes	characteristic
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	#16810501	C₂²	1	1	yes	characteristic
134	#16810501	C₂²	1	1	yes	characteristic
135	#16810501	C₂²	1	1	yes	characteristic
136	#16810501	C₂²	1	1	yes	characteristic
137	#16810501	C₂²	1	1	yes	characteristic, complemented
138	#16810501	C₂²	1	1	yes	characteristic, complemented
139	#16810500	C₂²	1	1	yes	characteristic
140	#16810500	C₂²	1	1	yes	characteristic
141	#16810497	C₂²	1	1	yes	characteristic
142	#16810497	C₂²	1	1	yes	characteristic
143	#16810497	C₂²	1	1	yes	characteristic
144	#16810497	C₂²	1	1	yes	characteristic
145	#16810497	C₂²	1	1	yes	characteristic, complemented
146	#16810497	C₂²	1	1	yes	characteristic, complemented
147	#16810496	C₂²	1	1	yes	characteristic
148	#16810494	C₂²	1	1	yes	characteristic
149	#16810494	C₂²	1	1	yes	characteristic
150	#16810494	C₂²	1	1	yes	characteristic, complemented
151	#16810494	C₂²	1	1	yes	characteristic, complemented
152	#16810483	C₂²	1	1	yes	characteristic
153	#16810482	C₂²	1	1	yes	characteristic
154	#16810482	C₂²	1	1	yes	characteristic
155	#16810482	C₂²	1	1	yes	characteristic
156	#16810482	C₂²	1	1	yes	characteristic
157	#16810482	C₂²	1	1	yes	characteristic
158	#16810481	C₂²	1	1	yes	characteristic
159	#16810481	C₂²	1	1	yes	characteristic
160	#16810481	C₂²	1	1	yes	characteristic
161	#16810480	C₂²	1	1	yes	characteristic
162	#16810480	C₂²	1	1	yes	characteristic
163	#16810480	C₂²	1	1	yes	characteristic
164	#16810480	C₂²	1	1	yes	characteristic
165	#16810480	C₂²	1	1	yes	characteristic
166	#16810478	C₂²	1	1	yes	characteristic
167	#16810478	C₂²	1	1	yes	characteristic
168	C₄×#11719921	C₂²	1	1	yes	characteristic
169	#16810470	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#397	C₂²	1	1	yes	characteristic
177	C₅₃×#397	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#385	C₂²	1	1	yes	characteristic
185	C₅₃×#380	C₂²	1	1	yes	characteristic
186	C₅₃×#380	C₂²	1	1	yes	characteristic
187	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
192	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
193	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
194	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
195	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
196	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
198	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	—	2	4	no	—
200	C₂²×C₄×D₅₃	—	4	2	no	—
201	C₂²×C₄×D₅₃	—	4	2	no	—
202	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	#13133212	—	4	2	no	—
213	#13133211	—	4	2	no	—
214	#13133203	—	4	2	no	—
215	#13133203	—	4	2	no	—
216	#13133199	—	4	2	no	—
217	#13133199	—	4	2	no	—
218	#13133197	—	4	2	no	—
219	#13133197	—	4	2	no	—
220	#13133195	—	2	4	no	—
221	#13133195	—	4	2	no	—
222	#13133195	—	4	2	no	—
223	#13133195	—	4	2	no	—
224	#13133194	—	4	2	no	—
225	#13133192	—	2	4	no	—
226	#13133192	—	4	2	no	—
227	#13133191	—	4	2	no	—
228	#13133187	—	4	2	no	—
229	#13133187	—	4	2	no	—
230	C₄×D₂₁₂	—	4	2	no	—
231	#13133179	—	4	2	no	—
232	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊Dic₅₃	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×#11719919	C₂³	1	1	yes	characteristic
248	C₂×#11719919	C₂³	1	1	yes	characteristic
249	C₂×#11719919	C₂³	1	1	yes	characteristic
250	C₂×#11719919	C₂³	1	1	yes	characteristic
251	C₂×#11719919	C₂³	1	1	yes	characteristic
252	C₂×#11719919	C₂³	1	1	yes	characteristic
253	C₂×#11719919	C₂³	1	1	yes	characteristic
254	C₂×#11719919	C₂³	1	1	yes	characteristic
255	C₂×#11719919	C₂³	1	1	yes	characteristic
256	C₂×#11719919	C₂³	1	1	yes	characteristic
257	C₂×#11719919	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×D₅₃	—	4	2	no	—
259	C₄⋊C₄×D₅₃	—	4	2	no	—
260	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊Dic₅₃	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	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×#11719921	C₂³	1	1	yes	characteristic
269	C₂×#11719921	C₂³	1	1	yes	characteristic
270	C₂×#11719921	C₂³	1	1	yes	characteristic
271	C₂×#11719921	C₂³	1	1	yes	characteristic
272	C₂×#11719921	C₂³	1	1	yes	characteristic
273	C₂×#11719921	C₂³	1	1	yes	characteristic
274	C₂×#11719921	C₂³	1	1	yes	characteristic
275	C₂×#11719921	C₂³	1	1	yes	characteristic
276	C₂×#11719921	C₂³	1	1	yes	characteristic
277	C₂×#11719921	C₂³	1	1	yes	characteristic
278	C₂×#11719921	C₂³	1	1	yes	characteristic
279	C₂×#11719921	C₂³	1	1	yes	characteristic
280	C₂×#11719921	C₂³	1	1	yes	characteristic
281	C₂×#11719921	C₂³	1	1	yes	characteristic
282	C₂×#11719921	C₂³	1	1	yes	characteristic
283	C₂×#11719921	C₂³	1	1	yes	characteristic
284	C₂×#11719921	C₂³	1	1	yes	characteristic
285	C₂×#11719921	C₂³	1	1	yes	characteristic
286	C₂×#11719921	C₂³	1	1	yes	characteristic
287	C₂×#11719921	C₂³	1	1	yes	characteristic
288	C₂×#11719921	C₂³	1	1	yes	characteristic
289	C₂×#11719921	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	1	yes	characteristic
291	C₂×#11719921	C₂³	1	1	yes	characteristic
292	C₂×#11719921	C₂³	1	1	yes	characteristic
293	C₂×#11719921	C₂³	1	1	yes	characteristic
294	C₂×#11719921	C₂³	1	1	yes	characteristic
295	C₂×#11719921	C₂³	1	1	yes	characteristic
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	1	yes	characteristic
298	C₂×#11719921	C₂³	1	1	yes	characteristic
299	C₂×#11719921	C₂³	1	1	yes	characteristic
300	C₂²⋊C₄×D₅₃	—	4	2	no	—
301	C₂²⋊C₄×D₅₃	—	4	2	no	—
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₅₃	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	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	#13133124	C₂³	1	1	yes	characteristic
333	#13133124	C₂³	1	1	yes	characteristic
334	C₂³×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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂³×D₅₃	—	2	2	no	—
371	C₂³×D₅₃	—	2	2	no	—
372	C₂³×D₅₃	—	2	2	no	—
373	C₂³×D₅₃	—	2	2	no	—
374	C₂³×D₅₃	—	2	2	no	—
375	C₂³×D₅₃	—	4	1	no	—
376	C₂³×D₅₃	—	4	1	no	—
377	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
378	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
379	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
380	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	4	1	no	—
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₂²⋊D₅₃	—	2	2	no	—
399	C₂×C₂²⋊D₅₃	—	2	2	no	—
400	C₂×C₂²⋊D₅₃	—	4	1	no	—
401	C₂×C₂²⋊D₅₃	—	4	1	no	—
402	C₂×C₂²⋊D₅₃	—	4	1	no	—
403	C₂×C₂²⋊D₅₃	—	4	1	no	—
404	C₂²×Dic₅₃	—	2	2	no	—
405	C₂²×Dic₅₃	—	2	2	no	—
406	C₂²×Dic₅₃	—	4	1	no	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×D₂₁₂	—	2	2	no	—
420	C₂×D₂₁₂	—	2	2	no	—
421	C₂×D₂₁₂	—	2	2	no	—
422	C₂×D₂₁₂	—	2	2	no	—
423	C₂×D₂₁₂	—	2	2	no	—
424	C₂×D₂₁₂	—	2	2	no	—
425	C₂×D₂₁₂	—	2	2	no	—
426	C₂×D₂₁₂	—	2	2	no	—
427	C₂×D₂₁₂	—	2	2	no	—
428	C₂×D₂₁₂	—	4	1	no	—
429	C₂×D₂₁₂	—	4	1	no	—
430	C₂×D₂₁₂	—	4	1	no	—
431	C₂×D₂₁₂	—	4	1	no	—
432	C₂×D₂₁₂	—	4	1	no	—
433	C₂×D₂₁₂	—	4	1	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	2	2	no	—
437	C₂×C₄×D₅₃	—	2	2	no	—
438	C₂×C₄×D₅₃	—	2	2	no	—
439	C₂×C₄×D₅₃	—	2	2	no	—
440	C₂×C₄×D₅₃	—	2	2	no	—
441	C₂×C₄×D₅₃	—	2	2	no	—
442	C₂×C₄×D₅₃	—	2	2	no	—
443	C₂×C₄×D₅₃	—	2	2	no	—
444	C₂×C₄×D₅₃	—	2	2	no	—
445	C₂×C₄×D₅₃	—	4	16	no	—
446	C₂×C₄×D₅₃	—	4	1	no	—
447	C₂×C₄×D₅₃	—	4	1	no	—
448	C₂×C₄×D₅₃	—	4	1	no	—
449	C₂×C₄×D₅₃	—	4	1	no	—
450	C₂×C₄×D₅₃	—	4	1	no	—
451	C₂×C₄×D₅₃	—	4	1	no	—
452	C₂×C₄×D₅₃	—	4	1	no	—
453	C₂×C₄×D₅₃	—	4	1	no	—
454	C₂×C₄×D₅₃	—	4	1	no	—
455	C₂×C₄×D₅₃	—	4	1	no	—
456	C₂×C₄×D₅₃	—	4	1	no	—
457	C₂×C₄×D₅₃	—	4	1	no	—
458	C₂×C₄×D₅₃	—	4	1	no	—
459	C₂×C₄×D₅₃	—	4	1	no	—
460	C₂×C₄×D₅₃	—	4	1	no	—
461	C₂×C₄×D₅₃	—	4	1	no	—
462	C₂×C₄×D₅₃	—	4	1	no	—
463	C₂×C₄×D₅₃	—	4	1	no	—
464	C₂×C₄×D₅₃	#41	1	4	yes	—
465	C₂×Dic₁₀₆	—	2	2	no	—
466	C₂×Dic₁₀₆	—	4	1	no	—
467	C₂×Dic₁₀₆	—	4	1	no	—
468	C₂×Dic₁₀₆	—	4	1	no	—
469	C₂×Dic₁₀₆	—	4	1	no	—
470	C₂×Dic₁₀₆	—	4	1	no	—
471	C₂×Dic₁₀₆	—	4	1	no	—
472	C₂×Dic₁₀₆	—	4	1	no	—
473	C₂×Dic₁₀₆	—	4	1	no	—
474	C₄⋊C₄×C₅₃	—	2	2	no	—
475	C₄⋊C₄×C₅₃	—	2	2	no	—
476	C₄⋊C₄×C₅₃	—	2	2	no	—
477	C₄⋊C₄×C₅₃	—	2	2	no	—
478	C₄⋊C₄×C₅₃	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	4	1	no	—
480	C₄⋊C₄×C₅₃	—	4	1	no	—
481	C₄⋊C₄×C₅₃	—	4	1	no	—
482	C₄⋊C₄×C₅₃	—	4	1	no	—
483	C₄⋊C₄×C₅₃	—	4	1	no	—
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	2	no	—
487	C₂²⋊C₄×C₅₃	—	4	1	no	—
488	C₂²⋊C₄×C₅₃	—	4	1	no	—
489	C₂²⋊C₄×C₅₃	—	4	1	no	—
490	C₄²×C₅₃	—	4	1	no	—
491	C₄²×C₅₃	—	4	1	no	—
492	C₂²⋊Dic₅₃	—	2	2	no	—
493	C₂²⋊Dic₅₃	—	2	2	no	—
494	C₂²⋊Dic₅₃	—	2	2	no	—
495	C₂²⋊Dic₅₃	—	4	1	no	—
496	#11719921	—	2	2	no	—
497	#11719921	—	2	2	no	—
498	#11719921	—	2	2	no	—
499	#11719921	—	2	2	no	—
500	#11719921	—	2	2	no	—
501	#11719921	—	2	2	no	—
502	#11719921	—	2	2	no	—
503	#11719921	—	2	2	no	—
504	#11719921	—	2	2	no	—
505	#11719921	—	2	2	no	—
506	#11719921	—	2	2	no	—
507	#11719921	—	2	2	no	—
508	#11719921	—	2	2	no	—
509	#11719921	—	2	2	no	—
510	#11719921	—	4	1	no	—
511	#11719921	—	4	1	no	—
512	#11719921	—	4	1	no	—
513	#11719921	—	4	1	no	—
514	#11719921	—	4	1	no	—
515	#11719921	—	4	1	no	—
516	#11719921	—	4	1	no	—
517	#11719921	—	4	1	no	—
518	#11719921	—	4	1	no	—
519	#11719921	—	4	1	no	—
520	#11719921	—	4	1	no	—
521	#11719921	—	4	1	no	—
522	#11719921	—	4	1	no	—
523	#11719921	—	4	1	no	—
524	#11719921	—	4	1	no	—
525	#11719921	—	4	1	no	—
526	#11719921	—	4	1	no	—
527	#11719921	—	4	1	no	—
528	#11719921	—	4	1	no	—
529	#11719921	—	4	1	no	—
530	#11719921	—	4	1	no	—
531	#11719921	—	4	1	no	—
532	C₄⋊Dic₅₃	—	2	2	no	—
533	C₄⋊Dic₅₃	—	2	2	no	—
534	C₄⋊Dic₅₃	—	4	1	no	—
535	C₄⋊Dic₅₃	—	4	1	no	—
536	C₄⋊Dic₅₃	—	4	1	no	—
537	C₄⋊Dic₅₃	—	4	1	no	—
538	C₄⋊Dic₅₃	—	4	1	no	—
539	C₄⋊Dic₅₃	—	4	1	no	—
540	C₄⋊Dic₅₃	—	4	1	no	—
541	C₄⋊Dic₅₃	—	4	1	no	—
542	#11719919	—	2	2	no	—
543	#11719919	—	2	2	no	—
544	#11719919	—	2	2	no	—
545	#11719919	—	2	2	no	—
546	#11719919	—	2	2	no	—
547	#11719919	—	2	2	no	—
548	#11719919	—	4	1	no	—
549	#11719919	—	4	1	no	—
550	#11719919	—	4	1	no	—
551	#11719919	—	4	1	no	—
552	#11719919	—	4	1	no	—
553	#11719919	—	4	1	no	—
554	#11719919	—	4	1	no	—
555	#11719919	—	4	1	no	—
556	#11719919	—	4	1	no	—
557	#11719919	—	4	1	no	—
558	C₄×Dic₅₃	—	4	1	no	—
559	C₄×Dic₅₃	—	4	1	no	—
560	C₄×Dic₅₃	—	4	1	no	—
561	C₄×Dic₅₃	—	4	1	no	—
562	C₂³×C₅₃	—	2	1	no	—
563	C₂³×C₅₃	—	2	1	no	—
564	C₂³×C₅₃	—	2	1	no	—
565	C₂³×C₅₃	—	2	1	no	—
566	C₂³×C₅₃	—	2	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
569	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
570	C₂²×D₅₃	—	2	1	no	—
571	C₂²×D₅₃	—	2	1	no	—
572	C₂²×D₅₃	—	2	1	no	—
573	C₂²×D₅₃	—	2	1	no	—
574	C₂²×D₅₃	—	2	8	no	—
575	C₂²×D₅₃	—	2	1	no	—
576	C₂²×D₅₃	—	2	1	no	—
577	C₂²×D₅₃	—	2	1	no	—
578	C₂²×D₅₃	—	2	1	no	—
579	C₂²×D₅₃	—	2	1	no	—
580	C₂²×D₅₃	—	2	1	no	—
581	C₂²×D₅₃	—	2	1	no	—
582	C₂²×D₅₃	—	2	1	no	—
583	C₂²×D₅₃	—	2	1	no	—
584	C₂²×D₅₃	—	2	1	no	—
585	C₂²×D₅₃	—	2	1	no	—
586	C₂²×D₅₃	—	2	1	no	—
587	C₂²×D₅₃	—	2	1	no	—
588	C₂²×D₅₃	—	2	1	no	—
589	C₂²×D₅₃	—	2	1	no	—
590	C₂²×D₅₃	—	2	1	no	—
591	C₂²×D₅₃	—	2	1	no	—
592	C₂²×D₅₃	—	2	1	no	—
593	C₂²×D₅₃	—	2	1	no	—
594	C₂²×D₅₃	—	2	1	no	—
595	C₂²×D₅₃	—	4	4	no	—
596	C₂²×D₅₃	—	4	4	no	—
597	C₂²×D₅₃	—	4	4	no	—
598	C₂²×D₅₃	—	4	4	no	—
599	C₂²×D₅₃	—	4	4	no	—
600	C₂²×D₅₃	—	4	4	no	—
601	C₂²×D₅₃	C₂×#41	1	2	yes	—
602	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
603	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
604	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	4	4	no	—
646	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
647	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
648	C₂²⋊D₅₃	—	8	2	no	—
649	C₂²⋊D₅₃	—	8	2	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	2	1	no	—
654	C₂×Dic₅₃	—	2	1	no	—
655	C₂×Dic₅₃	—	2	1	no	—
656	C₂×Dic₅₃	—	2	1	no	—
657	C₂×Dic₅₃	—	2	1	no	—
658	C₂×Dic₅₃	—	2	1	no	—
659	C₂×Dic₅₃	—	2	1	no	—
660	C₂×Dic₅₃	—	2	1	no	—
661	C₂×Dic₅₃	—	2	1	no	—
662	C₂×Dic₅₃	—	2	1	no	—
663	C₂×Dic₅₃	—	2	1	no	—
664	C₂×Dic₅₃	—	2	1	no	—
665	C₂×Dic₅₃	—	2	1	no	—
666	C₂×Dic₅₃	—	2	1	no	—
667	C₂×Dic₅₃	—	2	1	no	—
668	C₂×Dic₅₃	—	2	1	no	—
669	C₂×Dic₅₃	—	2	1	no	—
670	C₂×Dic₅₃	—	2	1	no	—
671	C₂×Dic₅₃	—	2	1	no	—
672	C₂×Dic₅₃	—	2	1	no	—
673	C₂×Dic₅₃	—	2	1	no	—
674	C₂×Dic₅₃	—	2	1	no	—
675	C₂×Dic₅₃	—	2	1	no	—
676	C₂×Dic₅₃	—	2	1	no	—
677	C₂×Dic₅₃	—	2	1	no	—
678	C₂×Dic₅₃	—	2	1	no	—
679	C₂×Dic₅₃	—	2	1	no	—
680	C₂×Dic₅₃	—	2	1	no	—
681	C₂×Dic₅₃	—	2	1	no	—
682	C₂×Dic₅₃	—	2	1	no	—
683	C₂×Dic₅₃	—	2	1	no	—
684	C₂×Dic₅₃	—	4	4	no	—
685	C₂×Dic₅₃	C₂×#41	1	2	yes	—
686	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
687	D₂₁₂	—	4	4	no	—
688	D₂₁₂	—	4	4	no	—
689	D₂₁₂	—	8	2	no	—
690	D₂₁₂	—	8	2	no	—
691	D₂₁₂	—	8	2	no	—
692	C₄×D₅₃	—	2	8	no	—
693	C₄×D₅₃	—	4	4	no	—
694	C₄×D₅₃	—	4	4	no	—
695	C₄×D₅₃	—	4	4	no	—
696	C₄×D₅₃	—	8	2	no	—
697	C₄×D₅₃	—	8	2	no	—
698	C₄×D₅₃	—	8	2	no	—
699	C₄×D₅₃	—	8	2	no	—
700	C₄×D₅₃	—	8	2	no	—
701	C₄×D₅₃	—	8	2	no	—
702	Dic₁₀₆	—	8	2	no	—
703	Dic₁₀₆	—	8	2	no	—
704	Dic₁₀₆	—	8	2	no	—
705	#36729	—	53	1	no	maximal, Sylow
706	C₂²×C₅₃	—	2	2	no	—
707	C₂²×C₅₃	—	2	2	no	—
708	C₂²×C₅₃	—	2	2	no	—
709	C₂²×C₅₃	—	4	1	no	—
710	C₂²×C₅₃	—	4	1	no	—
711	C₂²×C₅₃	—	4	1	no	—
712	C₂²×C₅₃	—	4	1	no	—
713	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
714	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
715	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
716	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
717	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
718	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
719	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
720	C₂×D₅₃	—	2	2	no	—
721	C₂×D₅₃	—	2	2	no	—
722	C₂×D₅₃	—	2	2	no	—
723	C₂×D₅₃	—	2	2	no	—
724	C₂×D₅₃	—	2	2	no	—
725	C₂×D₅₃	—	2	2	no	—
726	C₂×D₅₃	—	2	2	no	—
727	C₂×D₅₃	—	2	2	no	—
728	C₂×D₅₃	—	2	2	no	—
729	C₂×D₅₃	—	4	16	no	—
730	C₂×D₅₃	—	4	1	no	—
731	C₂×D₅₃	—	4	1	no	—
732	C₂×D₅₃	—	4	1	no	—
733	C₂×D₅₃	—	4	1	no	—
734	C₂×D₅₃	—	4	1	no	—
735	C₂×D₅₃	—	4	1	no	—
736	C₂×D₅₃	—	4	1	no	—
737	C₂×D₅₃	—	4	1	no	—
738	C₂×D₅₃	—	4	1	no	—
739	C₂×D₅₃	—	4	1	no	—
740	C₂×D₅₃	—	4	1	no	—
741	C₂×D₅₃	—	4	1	no	—
742	C₂×D₅₃	—	4	1	no	—
743	C₂×D₅₃	—	4	1	no	—
744	C₂×D₅₃	—	4	1	no	—
745	C₂×D₅₃	—	4	1	no	—
746	C₂×D₅₃	—	4	1	no	—
747	C₂×D₅₃	—	4	1	no	—
748	C₂×D₅₃	#542	1	4	yes	—
749	C₄×C₅₃	—	2	2	no	—
750	C₄×C₅₃	—	2	2	no	—
751	C₄×C₅₃	—	4	1	no	—
752	C₄×C₅₃	—	4	1	no	—
753	C₄×C₅₃	—	4	1	no	—
754	C₄×C₅₃	—	4	1	no	—
755	C₄×C₅₃	—	4	1	no	—
756	C₄×C₅₃	—	4	1	no	—
757	C₄×C₅₃	—	4	1	no	—
758	C₄×C₅₃	—	4	1	no	—
759	C₄×C₅₃	—	4	1	no	—
760	C₄×C₅₃	—	4	1	no	—
761	C₄×C₅₃	—	4	1	no	—
762	C₄×C₅₃	—	4	1	no	—
763	Dic₅₃	—	2	2	no	—
764	Dic₅₃	—	2	2	no	—
765	Dic₅₃	—	4	1	no	—
766	Dic₅₃	—	4	1	no	—
767	Dic₅₃	—	4	1	no	—
768	Dic₅₃	—	4	1	no	—
769	Dic₅₃	—	4	1	no	—
770	Dic₅₃	—	4	1	no	—
771	Dic₅₃	—	4	1	no	—
772	Dic₅₃	—	4	1	no	—
773	Dic₅₃	—	4	1	no	—
774	Dic₅₃	—	4	1	no	—
775	#2848	—	53	1	no	—
776	#2847	—	53	1	no	—
777	#2747	—	53	1	no	—
778	#2747	D₅₃	1	1	yes	characteristic, complemented
779	#2742	—	53	1	no	—
780	#2742	—	53	1	no	—
781	#2741	—	53	1	no	—
782	#2741	—	53	1	no	—
783	#2717	—	53	1	no	—
784	#2717	—	53	1	no	—
785	#2702	—	53	1	no	—
786	#2702	—	53	1	no	—
787	#2692	—	53	1	no	—
788	#2692	—	53	1	no	—
789	#2691	—	53	1	no	—
790	#2691	—	53	1	no	—
791	#2672	—	53	1	no	—
792	#2672	—	53	1	no	—
793	#2659	—	53	1	no	—
794	#2639	—	53	1	no	—
795	#2481	—	53	1	no	—
796	#2481	—	53	1	no	—
797	#2472	—	53	1	no	—
798	#2472	—	53	1	no	—
799	#2449	—	53	1	no	—
800	#2449	—	53	1	no	—
801	#2418	—	53	1	no	—
802	#2418	—	53	1	no	—
803	#2329	—	53	1	no	—
804	#2325	—	53	1	no	—
805	C₂×#380	—	53	1	no	—
806	C₂×C₅₃	—	4	2	no	—
807	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
808	C₂×C₅₃	#3490	1	1	yes	characteristic
809	C₂×C₅₃	#3492	1	1	yes	characteristic
810	C₂×C₅₃	#3536	1	1	yes	characteristic
811	C₂×C₅₃	#3536	1	1	yes	characteristic
812	C₂×C₅₃	#3537	1	1	yes	characteristic
813	C₂×C₅₃	#3538	1	1	yes	characteristic
814	D₅₃	—	2	4	no	—
815	D₅₃	—	4	2	no	—
816	D₅₃	—	8	1	no	—
817	D₅₃	—	8	1	no	—
818	C₂⁴×C₄	—	53	1	no	—
819	C₂×#126	—	53	1	no	—
820	C₂×#126	—	53	1	no	—
821	C₂×#124	—	53	1	no	—
822	C₂×#124	—	53	1	no	—
823	C₂×#123	—	53	1	no	—
824	C₂×#123	—	53	1	no	—
825	C₂×C₂²⋊Q₈	—	53	1	no	—
826	C₂×C₂²⋊Q₈	—	53	1	no	—
827	C₂×C₂²⋊Q₈	—	53	1	no	—
828	C₂×C₂²⋊Q₈	—	53	1	no	—
829	C₂×C₂²⋊Q₈	—	53	1	no	—
830	C₂×C₂²⋊Q₈	—	53	1	no	—
831	C₂×C₂²⋊Q₈	—	53	1	no	—
832	C₂×#121	—	53	1	no	—
833	C₂×#121	—	53	1	no	—
834	C₂×#121	—	53	1	no	—
835	C₂×#120	—	53	1	no	—
836	C₂×#120	—	53	1	no	—
837	C₂×C₄×D₄	—	53	1	no	—
838	C₂×C₄×D₄	—	53	1	no	—
839	C₂²×C₄⋊C₄	—	53	1	no	—
840	C₂²×C₄⋊C₄	—	53	1	no	—
841	C₂²×C₂²⋊C₄	—	53	1	no	—
842	C₂²×C₂²⋊C₄	—	53	1	no	—
843	#400	—	53	1	no	—
844	#400	—	53	1	no	—
845	#400	—	53	1	no	—
846	#400	—	53	1	no	—
847	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
848	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
849	#399	—	53	1	no	—
850	#399	—	53	1	no	—
851	#399	—	53	1	no	—
852	#399	—	53	1	no	—
853	#398	—	53	1	no	—
854	#398	—	53	1	no	—
855	#398	—	53	1	no	—
856	#398	—	53	1	no	—
857	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
858	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
859	#397	—	53	1	no	—
860	#397	—	53	1	no	—
861	#397	—	53	1	no	—
862	#397	—	53	1	no	—
863	#397	—	53	1	no	—
864	#397	—	53	1	no	—
865	#397	C₂×D₅₃	1	1	yes	characteristic
866	#397	C₂×D₅₃	1	1	yes	characteristic
867	#396	—	53	1	no	—
868	#396	—	53	1	no	—
869	#396	—	53	1	no	—
870	#396	—	53	1	no	—
871	#395	—	53	1	no	—
872	#395	—	53	1	no	—
873	#395	—	53	1	no	—
874	#395	—	53	1	no	—
875	#395	—	53	1	no	—
876	#395	—	53	1	no	—
877	#394	—	53	1	no	—
878	#394	—	53	1	no	—
879	#394	—	53	1	no	—
880	#394	—	53	1	no	—
881	#394	—	53	1	no	—
882	#394	—	53	1	no	—
883	#394	—	53	1	no	—
884	#394	—	53	1	no	—
885	#394	—	53	1	no	—
886	#394	—	53	1	no	—
887	#393	—	53	1	no	—
888	#393	—	53	1	no	—
889	#393	—	53	1	no	—
890	#393	—	53	1	no	—
891	#391	—	53	1	no	—
892	#391	—	53	1	no	—
893	#390	—	53	1	no	—
894	#390	—	53	1	no	—
895	#389	—	53	1	no	—
896	#389	—	53	1	no	—
897	#389	—	53	1	no	—
898	#389	—	53	1	no	—
899	#388	—	53	1	no	—
900	#388	—	53	1	no	—
901	#388	—	53	1	no	—
902	#388	—	53	1	no	—
903	#388	—	53	1	no	—
904	#388	—	53	1	no	—
905	#388	—	53	1	no	—
906	#388	—	53	1	no	—
907	#388	—	53	1	no	—
908	#388	—	53	1	no	—
909	#388	C₂×D₅₃	1	1	yes	characteristic
910	#388	C₂×D₅₃	1	1	yes	characteristic
911	#387	—	53	1	no	—
912	#387	—	53	1	no	—
913	#387	—	53	1	no	—
914	#387	—	53	1	no	—
915	#387	—	53	1	no	—
916	#387	—	53	1	no	—
917	#387	—	53	1	no	—
918	#387	—	53	1	no	—
919	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
920	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
921	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
922	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
923	#386	—	53	1	no	—
924	#386	—	53	1	no	—
925	#386	—	53	1	no	—
926	#386	—	53	1	no	—
927	#386	—	53	1	no	—
928	#386	—	53	1	no	—
929	#386	—	53	1	no	—
930	#386	—	53	1	no	—
931	#386	—	53	1	no	—
932	#386	—	53	1	no	—
933	#386	—	53	1	no	—
934	#386	—	53	1	no	—
935	#386	—	53	1	no	—
936	#386	—	53	1	no	—
937	#386	—	53	1	no	—
938	#386	—	53	1	no	—
939	#385	—	53	1	no	—
940	#385	—	53	1	no	—
941	#385	—	53	1	no	—
942	#385	—	53	1	no	—
943	#385	—	53	1	no	—
944	#385	—	53	1	no	—
945	#385	—	53	1	no	—
946	#385	—	53	1	no	—
947	#385	—	53	1	no	—
948	#385	—	53	1	no	—
949	#385	—	53	1	no	—
950	#385	C₂×D₅₃	1	1	yes	characteristic
951	#380	—	53	1	no	—
952	#380	—	53	1	no	—
953	#380	—	53	1	no	—
954	#380	—	53	1	no	—
955	#380	—	53	1	no	—
956	#380	—	53	1	no	—
957	#380	—	53	1	no	—
958	#380	—	53	1	no	—
959	#380	—	53	1	no	—
960	#380	—	53	1	no	—
961	#380	—	53	1	no	—
962	#380	—	53	1	no	—
963	#380	—	53	1	no	—
964	#380	—	53	1	no	—
965	#380	C₂×D₅₃	1	1	yes	characteristic
966	#380	C₂×D₅₃	1	1	yes	characteristic
967	#379	—	53	1	no	—
968	#379	—	53	1	no	—
969	C₄×C₂²⋊C₄	—	53	1	no	—
970	C₄×C₂²⋊C₄	—	53	1	no	—
971	C₂×#95	—	53	1	no	—
972	C₂×#95	—	53	1	no	—
973	C₅₃	#36729	1	1	yes	characteristic, complemented, Sylow
974	C₂⁵	—	53	1	no	—
975	C₂²×Q₈	—	53	1	no	—
976	C₂²×Q₈	—	53	1	no	—
977	C₂²×Q₈	—	53	1	no	—
978	C₂²×D₄	—	53	1	no	—
979	C₂²×D₄	—	53	1	no	—
980	C₂²×D₄	—	53	1	no	—
981	C₂²×D₄	—	53	1	no	—
982	C₂²×D₄	—	53	1	no	—
983	C₂²×D₄	—	53	1	no	—
984	C₂²×D₄	—	53	1	no	—
985	C₂³×C₄	—	53	1	no	—
986	C₂³×C₄	—	53	1	no	—
987	C₂³×C₄	—	53	1	no	—
988	C₂³×C₄	—	53	1	no	—
989	C₂³×C₄	—	53	1	no	—
990	C₂³×C₄	—	53	1	no	—
991	C₂³×C₄	—	53	1	no	—
992	C₂³×C₄	—	53	1	no	—
993	C₂³×C₄	—	53	1	no	—
994	C₂³×C₄	—	53	1	no	—
995	C₂³×C₄	—	53	1	no	—
996	C₂³×C₄	—	106	4	no	—
997	C₂³×C₄	—	212	2	no	—
998	C₂³×C₄	—	212	2	no	—
999	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1000	#126	—	212	2	no	—
1001	#126	—	212	2	no	—
1002	#124	—	212	2	no	—
1003	#124	—	212	2	no	—
1004	#123	—	212	2	no	—
1005	#123	—	212	2	no	—
1006	C₂²⋊Q₈	—	106	4	no	—
1007	C₂²⋊Q₈	—	212	2	no	—
1008	C₂²⋊Q₈	—	212	2	no	—
1009	C₂²⋊Q₈	—	212	2	no	—
1010	C₂²⋊Q₈	—	212	2	no	—
1011	C₂²⋊Q₈	—	212	2	no	—
1012	C₂²⋊Q₈	—	212	2	no	—
1013	#121	—	106	4	no	—
1014	#121	—	212	2	no	—
1015	#121	—	212	2	no	—
1016	#120	—	212	2	no	—
1017	#120	—	212	2	no	—
1018	C₄×D₄	—	212	2	no	—
1019	C₄×D₄	—	212	2	no	—
1020	C₂×C₄⋊C₄	—	53	1	no	—
1021	C₂×C₄⋊C₄	—	53	1	no	—
1022	C₂×C₄⋊C₄	—	53	1	no	—
1023	C₂×C₄⋊C₄	—	53	1	no	—
1024	C₂×C₄⋊C₄	—	53	1	no	—
1025	C₂×C₄⋊C₄	—	53	1	no	—
1026	C₂×C₄⋊C₄	—	53	1	no	—
1027	C₂×C₄⋊C₄	—	53	1	no	—
1028	C₂×C₄⋊C₄	—	53	1	no	—
1029	C₂×C₄⋊C₄	—	53	1	no	—
1030	C₂×C₄⋊C₄	—	53	1	no	—
1031	C₂×C₄⋊C₄	—	53	1	no	—
1032	C₂×C₄⋊C₄	—	53	1	no	—
1033	C₂×C₄⋊C₄	—	53	1	no	—
1034	C₂×C₄⋊C₄	—	53	1	no	—
1035	C₂×C₄⋊C₄	—	53	1	no	—
1036	C₂×C₄⋊C₄	—	53	1	no	—
1037	C₂×C₄⋊C₄	—	53	1	no	—
1038	C₂×C₄⋊C₄	—	53	1	no	—
1039	C₂×C₄⋊C₄	—	53	1	no	—
1040	C₂×C₄⋊C₄	—	53	1	no	—
1041	C₂×C₄⋊C₄	—	53	1	no	—
1042	C₂×C₄⋊C₄	—	53	1	no	—
1043	C₂×C₄⋊C₄	—	53	1	no	—
1044	C₂×C₄⋊C₄	—	53	1	no	—
1045	C₂×C₄⋊C₄	—	53	1	no	—
1046	C₂×C₄⋊C₄	—	212	2	no	—
1047	C₂×C₄⋊C₄	—	212	2	no	—
1048	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	—	53	1	no	—
1059	C₂×C₂²⋊C₄	—	53	1	no	—
1060	C₂×C₂²⋊C₄	—	53	1	no	—
1061	C₂×C₂²⋊C₄	—	53	1	no	—
1062	C₂×C₂²⋊C₄	—	53	1	no	—
1063	C₂×C₂²⋊C₄	—	53	1	no	—
1064	C₂×C₂²⋊C₄	—	53	1	no	—
1065	C₂×C₂²⋊C₄	—	53	1	no	—
1066	C₂×C₂²⋊C₄	—	53	1	no	—
1067	C₂×C₂²⋊C₄	—	53	1	no	—
1068	C₂×C₂²⋊C₄	—	53	1	no	—
1069	C₂×C₂²⋊C₄	—	53	1	no	—
1070	C₂×C₂²⋊C₄	—	53	1	no	—
1071	C₂×C₂²⋊C₄	—	53	1	no	—
1072	C₂×C₂²⋊C₄	—	53	1	no	—
1073	C₂×C₂²⋊C₄	—	53	1	no	—
1074	C₂×C₂²⋊C₄	—	53	1	no	—
1075	C₂×C₂²⋊C₄	—	53	1	no	—
1076	C₂×C₂²⋊C₄	—	53	1	no	—
1077	C₂×C₂²⋊C₄	—	53	1	no	—
1078	C₂×C₂²⋊C₄	—	53	1	no	—
1079	C₂×C₂²⋊C₄	—	53	1	no	—
1080	C₂×C₂²⋊C₄	—	53	1	no	—
1081	C₂×C₂²⋊C₄	—	53	1	no	—
1082	C₂×C₂²⋊C₄	—	53	1	no	—
1083	C₂×C₂²⋊C₄	—	53	1	no	—
1084	C₂×C₂²⋊C₄	—	53	1	no	—
1085	C₂×C₂²⋊C₄	—	53	1	no	—
1086	C₂×C₂²⋊C₄	—	53	1	no	—
1087	C₂×C₂²⋊C₄	—	53	1	no	—
1088	C₂×C₂²⋊C₄	—	53	1	no	—
1089	C₂×C₂²⋊C₄	—	53	1	no	—
1090	C₂×C₂²⋊C₄	—	53	1	no	—
1091	C₂×C₂²⋊C₄	—	53	1	no	—
1092	C₂×C₂²⋊C₄	—	53	1	no	—
1093	C₂×C₂²⋊C₄	—	53	1	no	—
1094	C₂×C₂²⋊C₄	—	53	1	no	—
1095	C₂×C₂²⋊C₄	—	53	1	no	—
1096	C₂×C₂²⋊C₄	—	53	1	no	—
1097	C₂×C₂²⋊C₄	—	53	1	no	—
1098	C₂×C₂²⋊C₄	—	212	2	no	—
1099	C₂×C₂²⋊C₄	—	212	2	no	—
1100	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1104	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1105	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1106	C₂×C₄²	—	53	1	no	—
1107	C₂×C₄²	—	53	1	no	—
1108	C₂×C₄²	—	53	1	no	—
1109	C₂×C₄²	—	53	1	no	—
1110	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1111	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1112	#95	—	53	1	no	—
1113	#95	—	53	1	no	—
1114	#95	—	53	1	no	—
1115	#95	—	53	1	no	—
1116	#95	—	53	1	no	—
1117	#95	—	53	1	no	—
1118	#95	—	53	1	no	—
1119	#95	—	53	1	no	—
1120	#95	—	53	1	no	—
1121	#95	—	53	1	no	—
1122	#95	—	53	1	no	—
1123	#95	—	53	1	no	—
1124	#95	—	53	1	no	—
1125	#95	—	53	1	no	—
1126	#95	—	53	1	no	—
1127	#95	—	53	1	no	—
1128	#95	—	53	1	no	—
1129	#95	—	53	1	no	—
1130	#95	—	53	1	no	—
1131	#95	—	53	1	no	—
1132	#95	—	53	1	no	—
1133	#95	—	53	1	no	—
1134	#95	—	53	1	no	—
1135	#95	—	53	1	no	—
1136	#95	—	53	1	no	—
1137	#95	—	53	1	no	—
1138	#95	—	53	1	no	—
1139	#95	—	53	1	no	—
1140	#95	C₂²×D₅₃	1	1	yes	characteristic
1141	#95	C₂²×D₅₃	1	1	yes	characteristic
1142	#95	C₂²×D₅₃	1	1	yes	characteristic
1143	#95	C₂²×D₅₃	1	1	yes	characteristic
1144	#95	C₂²×D₅₃	1	1	yes	characteristic
1145	#95	C₂²×D₅₃	1	1	yes	characteristic
1146	#95	C₂²×D₅₃	1	1	yes	characteristic
1147	#95	C₂²×D₅₃	1	1	yes	characteristic
1148	#95	C₂²×D₅₃	1	1	yes	characteristic
1149	#95	C₂²×D₅₃	1	1	yes	characteristic
1150	#95	C₂²×D₅₃	1	1	yes	characteristic
1151	#95	C₂²×D₅₃	1	1	yes	characteristic
1152	#95	C₂²×D₅₃	1	1	yes	characteristic
1153	#95	C₂²×D₅₃	1	1	yes	characteristic
1154	#95	C₂²×D₅₃	1	1	yes	characteristic
1155	#95	C₂²×D₅₃	1	1	yes	characteristic
1156	C₂⁴	—	53	1	no	—
1157	C₂⁴	—	53	1	no	—
1158	C₂⁴	—	53	1	no	—
1159	C₂⁴	—	53	1	no	—
1160	C₂⁴	—	106	2	no	—
1161	C₂⁴	—	106	2	no	—
1162	C₂⁴	—	106	2	no	—
1163	C₂⁴	—	106	2	no	—
1164	C₂⁴	—	106	2	no	—
1165	C₂⁴	—	212	1	no	—
1166	C₂⁴	—	212	1	no	—
1167	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1168	C₂×Q₈	—	106	2	no	—
1169	C₂×Q₈	—	212	1	no	—
1170	C₂×Q₈	—	212	1	no	—
1171	C₂×Q₈	—	212	1	no	—
1172	C₂×Q₈	—	212	1	no	—
1173	C₂×Q₈	—	212	1	no	—
1174	C₂×Q₈	—	212	1	no	—
1175	C₂×Q₈	—	212	1	no	—
1176	C₂×Q₈	—	212	1	no	—
1177	C₂×D₄	—	106	2	no	—
1178	C₂×D₄	—	106	2	no	—
1179	C₂×D₄	—	106	2	no	—
1180	C₂×D₄	—	106	2	no	—
1181	C₂×D₄	—	106	2	no	—
1182	C₂×D₄	—	106	2	no	—
1183	C₂×D₄	—	106	2	no	—
1184	C₂×D₄	—	106	2	no	—
1185	C₂×D₄	—	106	2	no	—
1186	C₂×D₄	—	106	2	no	—
1187	C₂×D₄	—	106	2	no	—
1188	C₂×D₄	—	212	1	no	—
1189	C₂×D₄	—	212	1	no	—
1190	C₂×D₄	—	212	1	no	—
1191	C₂×D₄	—	212	1	no	—
1192	C₂×D₄	—	212	1	no	—
1193	C₂×D₄	—	212	1	no	—
1194	C₂×D₄	—	212	1	no	—
1195	C₂×D₄	—	212	1	no	—
1196	C₂×D₄	—	212	1	no	—
1197	C₂×D₄	—	212	1	no	—
1198	C₂²×C₄	—	2	2	no	—
1199	C₂²×C₄	—	2	2	no	—
1200	C₂²×C₄	—	4	1	no	—
1201	C₂²×C₄	—	53	1	no	—
1202	C₂²×C₄	—	53	1	no	—
1203	C₂²×C₄	—	53	4	no	—
1204	C₂²×C₄	—	53	1	no	—
1205	C₂²×C₄	—	53	1	no	—
1206	C₂²×C₄	—	53	1	no	—
1207	C₂²×C₄	—	53	1	no	—
1208	C₂²×C₄	—	53	1	no	—
1209	C₂²×C₄	—	53	1	no	—
1210	C₂²×C₄	—	53	1	no	—
1211	C₂²×C₄	—	53	1	no	—
1212	C₂²×C₄	—	53	1	no	—
1213	C₂²×C₄	—	53	1	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	—	106	2	no	—
1221	C₂²×C₄	—	106	2	no	—
1222	C₂²×C₄	—	106	2	no	—
1223	C₂²×C₄	—	106	2	no	—
1224	C₂²×C₄	—	106	2	no	—
1225	C₂²×C₄	—	106	2	no	—
1226	C₂²×C₄	—	106	2	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	C₂²×C₄	—	212	1	no	—
1235	C₂²×C₄	—	212	1	no	—
1236	C₂²×C₄	—	212	1	no	—
1237	C₂²×C₄	—	212	1	no	—
1238	C₂²×C₄	—	212	1	no	—
1239	C₂²×C₄	—	212	1	no	—
1240	C₂²×C₄	—	212	1	no	—
1241	C₂²×C₄	—	212	1	no	—
1242	C₂²×C₄	—	212	1	no	—
1243	C₂²×C₄	—	212	1	no	—
1244	C₂²×C₄	—	212	1	no	—
1245	C₂²×C₄	—	212	16	no	—
1246	C₂²×C₄	—	212	1	no	—
1247	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1248	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1249	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1250	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1251	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1252	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1253	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1254	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1255	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1256	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1257	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1258	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1259	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1260	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1261	C₄⋊C₄	—	2	2	no	—
1262	C₄⋊C₄	—	2	2	no	—
1263	C₄⋊C₄	—	2	2	no	—
1264	C₄⋊C₄	—	2	2	no	—
1265	C₄⋊C₄	—	4	1	no	—
1266	C₄⋊C₄	—	4	1	no	—
1267	C₄⋊C₄	—	4	1	no	—
1268	C₄⋊C₄	—	4	1	no	—
1269	C₄⋊C₄	—	4	1	no	—
1270	C₄⋊C₄	—	4	1	no	—
1271	C₄⋊C₄	—	106	2	no	—
1272	C₄⋊C₄	—	106	2	no	—
1273	C₄⋊C₄	—	106	2	no	—
1274	C₄⋊C₄	—	106	2	no	—
1275	C₄⋊C₄	—	106	2	no	—
1276	C₄⋊C₄	—	106	2	no	—
1277	C₄⋊C₄	—	106	2	no	—
1278	C₄⋊C₄	—	106	2	no	—
1279	C₄⋊C₄	—	212	1	no	—
1280	C₄⋊C₄	—	212	1	no	—
1281	C₄⋊C₄	—	212	1	no	—
1282	C₄⋊C₄	—	212	1	no	—
1283	C₄⋊C₄	—	212	1	no	—
1284	C₄⋊C₄	—	212	1	no	—
1285	C₄⋊C₄	—	212	1	no	—
1286	C₄⋊C₄	—	212	1	no	—
1287	C₄⋊C₄	—	212	1	no	—
1288	C₄⋊C₄	—	212	1	no	—
1289	C₄⋊C₄	—	212	1	no	—
1290	C₄⋊C₄	—	212	1	no	—
1291	C₄⋊C₄	—	212	1	no	—
1292	C₄⋊C₄	—	212	1	no	—
1293	C₄⋊C₄	—	212	1	no	—
1294	C₄⋊C₄	—	212	1	no	—
1295	C₄⋊C₄	—	212	1	no	—
1296	C₄⋊C₄	—	212	1	no	—
1297	C₂²⋊C₄	—	2	2	no	—
1298	C₂²⋊C₄	—	2	2	no	—
1299	C₂²⋊C₄	—	2	2	no	—
1300	C₂²⋊C₄	—	4	1	no	—
1301	C₂²⋊C₄	—	4	1	no	—
1302	C₂²⋊C₄	—	4	1	no	—
1303	C₂²⋊C₄	—	106	2	no	—
1304	C₂²⋊C₄	—	106	2	no	—
1305	C₂²⋊C₄	—	106	2	no	—
1306	C₂²⋊C₄	—	106	2	no	—
1307	C₂²⋊C₄	—	106	2	no	—
1308	C₂²⋊C₄	—	106	2	no	—
1309	C₂²⋊C₄	—	106	2	no	—
1310	C₂²⋊C₄	—	106	2	no	—
1311	C₂²⋊C₄	—	106	2	no	—
1312	C₂²⋊C₄	—	106	2	no	—
1313	C₂²⋊C₄	—	106	2	no	—
1314	C₂²⋊C₄	—	106	2	no	—
1315	C₂²⋊C₄	—	106	2	no	—
1316	C₂²⋊C₄	—	106	2	no	—
1317	C₂²⋊C₄	—	106	2	no	—
1318	C₂²⋊C₄	—	106	2	no	—
1319	C₂²⋊C₄	—	106	2	no	—
1320	C₂²⋊C₄	—	212	1	no	—
1321	C₂²⋊C₄	—	212	1	no	—
1322	C₂²⋊C₄	—	212	1	no	—
1323	C₂²⋊C₄	—	212	1	no	—
1324	C₂²⋊C₄	—	212	1	no	—
1325	C₂²⋊C₄	—	212	1	no	—
1326	C₂²⋊C₄	—	212	1	no	—
1327	C₂²⋊C₄	—	212	1	no	—
1328	C₂²⋊C₄	—	212	1	no	—
1329	C₂²⋊C₄	—	212	1	no	—
1330	C₂²⋊C₄	—	212	1	no	—
1331	C₂²⋊C₄	—	212	1	no	—
1332	C₂²⋊C₄	—	212	1	no	—
1333	C₂²⋊C₄	—	212	1	no	—
1334	C₂²⋊C₄	—	212	1	no	—
1335	C₂²⋊C₄	—	212	1	no	—
1336	C₂²⋊C₄	—	212	1	no	—
1337	C₂²⋊C₄	—	212	1	no	—
1338	C₂²⋊C₄	—	212	1	no	—
1339	C₂²⋊C₄	—	212	1	no	—
1340	C₂²⋊C₄	—	212	1	no	—
1341	C₂²⋊C₄	—	212	1	no	—
1342	C₂²⋊C₄	—	212	1	no	—
1343	C₄²	—	4	1	no	—
1344	C₄²	—	4	1	no	—
1345	C₄²	—	212	1	no	—
1346	C₄²	—	212	1	no	—
1347	C₄²	—	212	1	no	—
1348	C₄²	—	212	1	no	—
1349	C₂³	—	2	1	no	—
1350	C₂³	—	2	1	no	—
1351	C₂³	—	2	1	no	—
1352	C₂³	—	2	1	no	—
1353	C₂³	—	2	1	no	—
1354	C₂³	—	2	1	no	—
1355	C₂³	—	53	2	no	—
1356	C₂³	—	53	2	no	—
1357	C₂³	—	53	2	no	—
1358	C₂³	—	53	2	no	—
1359	C₂³	—	106	8	no	—
1360	C₂³	—	106	1	no	—
1361	C₂³	—	106	1	no	—
1362	C₂³	—	106	1	no	—
1363	C₂³	—	106	1	no	—
1364	C₂³	—	106	1	no	—
1365	C₂³	—	106	1	no	—
1366	C₂³	—	106	1	no	—
1367	C₂³	—	106	1	no	—
1368	C₂³	—	106	1	no	—
1369	C₂³	—	106	1	no	—
1370	C₂³	—	106	1	no	—
1371	C₂³	—	106	1	no	—
1372	C₂³	—	106	1	no	—
1373	C₂³	—	106	1	no	—
1374	C₂³	—	106	1	no	—
1375	C₂³	—	106	1	no	—
1376	C₂³	—	106	1	no	—
1377	C₂³	—	106	1	no	—
1378	C₂³	—	106	1	no	—
1379	C₂³	—	106	1	no	—
1380	C₂³	—	106	1	no	—
1381	C₂³	—	106	1	no	—
1382	C₂³	—	106	1	no	—
1383	C₂³	—	106	1	no	—
1384	C₂³	—	212	4	no	—
1385	C₂³	—	212	4	no	—
1386	C₂³	—	212	4	no	—
1387	C₂³	—	212	4	no	—
1388	C₂³	—	212	4	no	—
1389	C₂³	—	212	4	no	—
1390	C₂³	#13133263	1	2	yes	—
1391	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1392	Q₈	—	424	2	no	—
1393	Q₈	—	424	2	no	—
1394	Q₈	—	424	2	no	—
1395	D₄	—	424	2	no	—
1396	D₄	—	424	2	no	—
1397	D₄	—	424	2	no	—
1398	D₄	—	424	2	no	—
1399	D₄	—	424	2	no	—
1400	D₄	—	212	4	no	—
1401	D₄	—	212	4	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	4	4	no	—
1443	C₂×C₄	—	53	2	no	—
1444	C₂×C₄	—	53	2	no	—
1445	C₂×C₄	—	106	8	no	—
1446	C₂×C₄	—	106	1	no	—
1447	C₂×C₄	—	106	1	no	—
1448	C₂×C₄	—	106	1	no	—
1449	C₂×C₄	—	106	1	no	—
1450	C₂×C₄	—	106	1	no	—
1451	C₂×C₄	—	106	1	no	—
1452	C₂×C₄	—	106	1	no	—
1453	C₂×C₄	—	106	1	no	—
1454	C₂×C₄	—	106	1	no	—
1455	C₂×C₄	—	106	1	no	—
1456	C₂×C₄	—	106	1	no	—
1457	C₂×C₄	—	106	1	no	—
1458	C₂×C₄	—	106	1	no	—
1459	C₂×C₄	—	106	1	no	—
1460	C₂×C₄	—	106	1	no	—
1461	C₂×C₄	—	106	1	no	—
1462	C₂×C₄	—	106	1	no	—
1463	C₂×C₄	—	106	1	no	—
1464	C₂×C₄	—	106	1	no	—
1465	C₂×C₄	—	106	1	no	—
1466	C₂×C₄	—	106	1	no	—
1467	C₂×C₄	—	106	1	no	—
1468	C₂×C₄	—	106	1	no	—
1469	C₂×C₄	—	106	1	no	—
1470	C₂×C₄	—	106	1	no	—
1471	C₂×C₄	—	106	1	no	—
1472	C₂×C₄	—	106	1	no	—
1473	C₂×C₄	—	106	1	no	—
1474	C₂×C₄	—	106	1	no	—
1475	C₂×C₄	—	106	1	no	—
1476	C₂×C₄	—	106	1	no	—
1477	C₂×C₄	—	106	1	no	—
1478	C₂×C₄	—	106	1	no	—
1479	C₂×C₄	—	106	1	no	—
1480	C₂×C₄	—	424	2	no	—
1481	C₂×C₄	—	424	2	no	—
1482	C₂×C₄	—	424	2	no	—
1483	C₂×C₄	—	424	2	no	—
1484	C₂×C₄	—	424	2	no	—
1485	C₂×C₄	—	424	2	no	—
1486	C₂×C₄	—	212	4	no	—
1487	C₂×C₄	—	212	4	no	—
1488	C₂×C₄	—	212	4	no	—
1489	C₂×C₄	—	212	4	no	—
1490	C₂×C₄	#41×D₅₃	1	2	yes	—
1491	C₂×C₄	#13133263	1	2	yes	—
1492	C₂²	—	2	2	no	—
1493	C₂²	—	2	2	no	—
1494	C₂²	—	2	2	no	—
1495	C₂²	—	4	1	no	—
1496	C₂²	—	4	1	no	—
1497	C₂²	—	4	1	no	—
1498	C₂²	—	4	1	no	—
1499	C₂²	—	53	4	no	—
1500	C₂²	—	106	2	no	—
1501	C₂²	—	106	2	no	—
1502	C₂²	—	106	2	no	—
1503	C₂²	—	106	2	no	—
1504	C₂²	—	106	2	no	—
1505	C₂²	—	106	2	no	—
1506	C₂²	—	106	2	no	—
1507	C₂²	—	106	2	no	—
1508	C₂²	—	106	2	no	—
1509	C₂²	—	212	16	no	—
1510	C₂²	—	212	1	no	—
1511	C₂²	—	212	1	no	—
1512	C₂²	—	212	1	no	—
1513	C₂²	—	212	1	no	—
1514	C₂²	—	212	1	no	—
1515	C₂²	—	212	1	no	—
1516	C₂²	—	212	1	no	—
1517	C₂²	—	212	1	no	—
1518	C₂²	—	212	1	no	—
1519	C₂²	—	212	1	no	—
1520	C₂²	—	212	1	no	—
1521	C₂²	—	212	1	no	—
1522	C₂²	—	212	1	no	—
1523	C₂²	—	212	1	no	—
1524	C₂²	—	212	1	no	—
1525	C₂²	—	212	1	no	—
1526	C₂²	—	212	1	no	—
1527	C₂²	—	212	1	no	—
1528	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1529	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1530	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1531	C₂²	C₂×#13133263	1	1	yes	characteristic
1532	C₂²	C₂×#13133263	1	1	yes	characteristic
1533	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1534	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1535	C₄	—	2	2	no	—
1536	C₄	—	2	2	no	—
1537	C₄	—	4	1	no	—
1538	C₄	—	4	1	no	—
1539	C₄	—	4	1	no	—
1540	C₄	—	4	1	no	—
1541	C₄	—	4	1	no	—
1542	C₄	—	4	1	no	—
1543	C₄	—	4	1	no	—
1544	C₄	—	4	1	no	—
1545	C₄	—	4	1	no	—
1546	C₄	—	4	1	no	—
1547	C₄	—	4	1	no	—
1548	C₄	—	4	1	no	—
1549	C₄	—	106	2	no	—
1550	C₄	—	106	2	no	—
1551	C₄	—	212	1	no	—
1552	C₄	—	212	1	no	—
1553	C₄	—	212	1	no	—
1554	C₄	—	212	1	no	—
1555	C₄	—	212	1	no	—
1556	C₄	—	212	1	no	—
1557	C₄	—	212	1	no	—
1558	C₄	—	212	1	no	—
1559	C₄	—	212	1	no	—
1560	C₄	—	212	1	no	—
1561	C₂	—	4	2	no	—
1562	C₂	—	106	4	no	—
1563	C₂	—	424	1	no	—
1564	C₂	—	424	1	no	—
1565	C₂	—	212	2	no	—
1566	C₂	#542×D₅₃	1	1	yes	characteristic
1567	C₂	#20288399	1	1	yes	characteristic
1568	C₂	#20288415	1	1	yes	characteristic
1569	C₂	#20288934	1	1	yes	characteristic
1570	C₂	#20288939	1	1	yes	characteristic
1571	C₂	#20288951	1	1	yes	characteristic
1572	C₂	#20288963	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2747	C₂
prime radical	#20282998	C₂
hypercenter	#2747	D₅₃
hypocenter	C₅₃	#36729
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2747

Complements

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

N	H ≅ G/N	type
1. #20283001	C₂	semidirect
3. #20281910	C₂	semidirect
4. #20281843	C₂	semidirect
5. #20281839	C₂	semidirect
6. #20281837	C₂	semidirect
7. #20281825	C₂	semidirect
8. #20281549	C₂	semidirect
9. #20281549	C₂	semidirect
10. #20281344	C₂	semidirect
11. #20281340	C₂	semidirect
12. #20281213	C₂	semidirect
13. #20281209	C₂	semidirect
14. #20281203	C₂	semidirect
15. #20281199	C₂	semidirect
16. #20280969	C₂	semidirect
17. #20280967	C₂	semidirect
18. #20280830	C₂	semidirect
19. #20280647	C₂	semidirect
20. #20278980	C₂	semidirect
21. #20278979	C₂	semidirect
22. #20278839	C₂	semidirect
23. #20278834	C₂	semidirect
24. #20278529	C₂	semidirect
25. #20278519	C₂	semidirect
26. #20278182	C₂	semidirect
27. #20278178	C₂	semidirect
28. #20277442	C₂	semidirect
29. #20277414	C₂	semidirect
30. #380×D₅₃	C₂	semidirect
31. C₅₃×#2747	C₂	semidirect
33. C₂×#13133212	C₂²	semidirect
34. C₂×#13133211	C₂²	semidirect
40. C₂×#13133197	C₂²	semidirect
44. C₂×#13133195	C₂²	semidirect
57. #16810565	C₂²	semidirect
58. #16810565	C₂²	semidirect
59. #16810564	C₂²	semidirect
60. #16810561	C₂²	semidirect
62. #16810560	C₂²	semidirect
64. #16810558	C₂²	semidirect
65. #16810556	C₂²	semidirect
66. #16810556	C₂²	semidirect
67. #16810555	C₂²	semidirect
68. #16810554	C₂²	semidirect
69. #16810552	C₂²	semidirect
70. #16810552	C₂²	semidirect
71. #16810552	C₂²	semidirect
72. #16810552	C₂²	semidirect
75. #16810547	C₂²	semidirect
76. #16810545	C₂²	semidirect
77. #16810545	C₂²	semidirect
78. #16810545	C₂²	semidirect
79. #16810544	C₂²	semidirect
80. #16810544	C₂²	semidirect
81. #16810544	C₂²	semidirect
82. #16810544	C₂²	semidirect
83. #16810543	C₂²	semidirect
84. #16810543	C₂²	semidirect
87. #16810541	C₂²	semidirect
90. #16810540	C₂²	semidirect
97. #16810536	C₂²	semidirect
98. #16810536	C₂²	semidirect
99. #16810529	C₂²	semidirect
100. #16810527	C₂²	semidirect
103. #16810522	C₂²	semidirect
104. #16810521	C₂²	semidirect
105. #16810520	C₂²	semidirect
106. #16810520	C₂²	semidirect
110. #16810515	C₂²	semidirect
112. #16810514	C₂²	semidirect
113. #16810513	C₂²	semidirect
115. #16810512	C₂²	semidirect
117. #16810510	C₂²	semidirect
118. #16810510	C₂²	semidirect
119. #16810510	C₂²	semidirect
120. #16810509	C₂²	semidirect
121. #16810506	C₂²	semidirect
122. #16810505	C₂²	semidirect
123. #16810505	C₂²	semidirect
124. #16810504	C₂²	semidirect
137. #16810501	C₂²	semidirect
138. #16810501	C₂²	semidirect
145. #16810497	C₂²	semidirect
146. #16810497	C₂²	semidirect
150. #16810494	C₂²	semidirect
151. #16810494	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
173. C₅₃×#400	C₂²	semidirect
174. C₅₃×#398	C₂²	semidirect
175. C₅₃×#398	C₂²	semidirect
180. C₅₃×#387	C₂²	semidirect
181. C₅₃×#387	C₂²	semidirect
182. C₅₃×#387	C₂²	semidirect
183. C₅₃×#387	C₂²	semidirect
778. #2747	D₅₃	semidirect
847. #400	C₂×D₅₃	semidirect
848. #400	C₂×D₅₃	semidirect
857. #398	C₂×D₅₃	semidirect
858. #398	C₂×D₅₃	semidirect
919. #387	C₂×D₅₃	semidirect
920. #387	C₂×D₅₃	semidirect
921. #387	C₂×D₅₃	semidirect
922. #387	C₂×D₅₃	semidirect
973. C₅₃	#36729	semidirect

Maximal subgroups

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

subgroup	index
#20283001	2
#20282998	2
#20281910	2
#20281843	2
#20281839	2
#20281837	2
#20281825	2
#20281549	2
#20281344	2
#20281340	2
#20281213	2
#20281209	2
#20281203	2
#20281199	2
#20280969	2
#20280967	2
#20280830	2
#20280647	2
#20278980	2
#20278979	2
#20278839	2
#20278834	2
#20278529	2
#20278519	2
#20278182	2
#20278178	2
#20277442	2
#20277414	2
#380×D₅₃	2
C₅₃×#2747	2
#36729	53