Subgroups — #27555885

Order 13568.

2308 conjugacy classes of subgroups.

The subgroup lattice has 1474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811179	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16811175	C₂	1	1	yes	maximal, characteristic, complemented
3	#20279801	C₂	1	1	yes	maximal, characteristic, complemented
4	#20279799	C₂	1	1	yes	maximal, characteristic, complemented
5	#20279793	C₂	1	1	yes	maximal, characteristic, complemented
6	#20279740	C₂	1	1	yes	maximal, characteristic, complemented
7	#20279699	C₂	1	1	yes	maximal, characteristic, complemented
8	#20279663	C₂	1	1	yes	maximal, characteristic
9	#20279632	C₂	1	1	yes	maximal, characteristic
10	#20279230	C₂	1	1	yes	maximal, characteristic, complemented
11	#20279228	C₂	1	1	yes	maximal, characteristic, complemented
12	#20279088	C₂	1	1	yes	maximal, characteristic, complemented
13	#20279086	C₂	1	1	yes	maximal, characteristic, complemented
14	#20278564	C₂	1	1	yes	maximal, characteristic
15	#20278562	C₂	1	1	yes	maximal, characteristic
16	#20278313	C₂	1	1	yes	maximal, characteristic, complemented
17	#20278311	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277992	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277990	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277986	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277984	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277286	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277286	C₂	1	1	yes	maximal, characteristic, complemented
24	#20277284	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277249	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277247	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277175	C₂	1	1	yes	maximal, characteristic
28	#20277175	C₂	1	1	yes	maximal, characteristic
29	C₄×#13133182	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#13133177	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2556	C₂	1	1	yes	maximal, characteristic, complemented
32	#16811179	—	2	8	no	—
33	#16811175	—	2	8	no	—
34	C₂×#13133216	C₂²	1	1	yes	characteristic
35	C₂×#13133216	C₂²	1	1	yes	characteristic
36	C₂×#13133216	C₂²	1	1	yes	characteristic
37	C₂×#13133216	C₂²	1	1	yes	characteristic
38	C₂×#13133216	C₂²	1	1	yes	characteristic
39	C₂×#13133215	C₂²	1	1	yes	characteristic
40	C₂×#13133215	C₂²	1	1	yes	characteristic
41	C₂×#13133209	C₂²	1	1	yes	characteristic
42	C₂×#13133207	C₂²	1	1	yes	characteristic
43	C₂×#13133207	C₂²	1	1	yes	characteristic
44	C₂×#13133196	C₂²	1	1	yes	characteristic
45	C₂×#13133195	C₂²	1	1	yes	characteristic
46	C₂×#13133195	C₂²	1	1	yes	characteristic
47	C₂×#13133195	C₂²	1	1	yes	characteristic
48	C₂×#13133195	C₂²	1	1	yes	characteristic
49	C₂×#13133195	C₂²	1	1	yes	characteristic
50	C₂×#13133194	C₂²	1	1	yes	characteristic
51	C₂×#13133194	C₂²	1	1	yes	characteristic
52	C₂×#13133194	C₂²	1	1	yes	characteristic
53	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
55	C₂×#13133182	C₂²	1	1	yes	characteristic
56	C₂×#13133182	C₂²	1	1	yes	characteristic
57	C₂×#13133182	C₂²	1	1	yes	characteristic
58	C₂×#13133182	C₂²	1	1	yes	characteristic
59	C₂×#13133182	C₂²	1	1	yes	characteristic
60	C₂×#13133182	C₂²	1	1	yes	characteristic
61	C₂×#13133182	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
63	C₂×#13133177	C₂²	1	1	yes	characteristic
64	C₂×#13133177	C₂²	1	1	yes	characteristic
65	C₂×#13133175	C₂²	1	1	yes	characteristic
66	C₂×#13133175	C₂²	1	1	yes	characteristic
67	C₂×#13133173	C₂²	1	1	yes	characteristic
68	C₂×#13133173	C₂²	1	1	yes	characteristic
69	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
70	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
71	#16810565	C₂²	1	1	yes	characteristic
72	#16810564	C₂²	1	1	yes	characteristic
73	#16810562	C₂²	1	1	yes	characteristic
74	#16810561	C₂²	1	1	yes	characteristic
75	#16810560	C₂²	1	1	yes	characteristic
76	#16810559	C₂²	1	1	yes	characteristic
77	#16810558	C₂²	1	1	yes	characteristic
78	#16810556	C₂²	1	1	yes	characteristic
79	#16810556	C₂²	1	1	yes	characteristic
80	#16810555	C₂²	1	1	yes	characteristic
81	#16810555	C₂²	1	1	yes	characteristic
82	#16810554	C₂²	1	1	yes	characteristic
83	#16810554	C₂²	1	1	yes	characteristic
84	#16810553	C₂²	1	1	yes	characteristic
85	#16810546	C₂²	1	1	yes	characteristic
86	#16810546	C₂²	1	1	yes	characteristic
87	#16810546	C₂²	1	1	yes	characteristic
88	#16810545	C₂²	1	1	yes	characteristic
89	#16810545	C₂²	1	1	yes	characteristic
90	#16810545	C₂²	1	1	yes	characteristic
91	#16810545	C₂²	1	1	yes	characteristic
92	#16810544	C₂²	1	1	yes	characteristic
93	#16810544	C₂²	1	1	yes	characteristic
94	#16810543	C₂²	1	1	yes	characteristic
95	#16810536	C₂²	1	1	yes	characteristic
96	#16810535	C₂²	1	1	yes	characteristic
97	#16810535	C₂²	1	1	yes	characteristic
98	#16810534	C₂²	1	1	yes	characteristic
99	#16810529	C₂²	1	1	yes	characteristic
100	#16810527	C₂²	1	1	yes	characteristic
101	#16810527	C₂²	1	1	yes	characteristic
102	#16810527	C₂²	1	1	yes	characteristic
103	#16810527	C₂²	1	1	yes	characteristic
104	#16810527	C₂²	1	1	yes	characteristic
105	#16810527	C₂²	1	1	yes	characteristic
106	#16810523	C₂²	1	1	yes	characteristic
107	#16810523	C₂²	1	1	yes	characteristic
108	#16810523	C₂²	1	1	yes	characteristic
109	#16810523	C₂²	1	1	yes	characteristic
110	#16810521	C₂²	1	1	yes	characteristic
111	#16810521	C₂²	1	1	yes	characteristic
112	#16810520	C₂²	1	1	yes	characteristic
113	#16810520	C₂²	1	1	yes	characteristic
114	#16810520	C₂²	1	1	yes	characteristic
115	#16810520	C₂²	1	1	yes	characteristic
116	#16810520	C₂²	1	1	yes	characteristic
117	#16810520	C₂²	1	1	yes	characteristic
118	#16810520	C₂²	1	1	yes	characteristic
119	#16810518	C₂²	1	1	yes	characteristic
120	#16810518	C₂²	1	1	yes	characteristic
121	#16810518	C₂²	1	1	yes	characteristic
122	#16810518	C₂²	1	1	yes	characteristic
123	#16810518	C₂²	1	1	yes	characteristic
124	#16810518	C₂²	1	1	yes	characteristic
125	#16810518	C₂²	1	1	yes	characteristic
126	#16810516	C₂²	1	1	yes	characteristic
127	#16810516	C₂²	1	1	yes	characteristic
128	#16810514	C₂²	1	1	yes	characteristic
129	#16810514	C₂²	1	1	yes	characteristic
130	#16810512	C₂²	1	1	yes	characteristic
131	#16810512	C₂²	1	1	yes	characteristic
132	#16810508	C₂²	1	1	yes	characteristic
133	#16810507	C₂²	1	1	yes	characteristic
134	#16810504	C₂²	1	1	yes	characteristic
135	#16810497	C₂²	1	1	yes	characteristic
136	#16810496	C₂²	1	1	yes	characteristic
137	#16810494	C₂²	1	1	yes	characteristic
138	#16810492	C₂²	1	1	yes	characteristic
139	#16810492	C₂²	1	1	yes	characteristic
140	#16810492	C₂²	1	1	yes	characteristic
141	#16810482	C₂²	1	1	yes	characteristic
142	#16810481	C₂²	1	1	yes	characteristic
143	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
145	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
146	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
148	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄×#11719919	C₂²	1	1	yes	characteristic
150	C₄×#11719919	C₂²	1	1	yes	characteristic
151	C₄×#11719919	C₂²	1	1	yes	characteristic
152	#16810474	C₂²	1	1	yes	characteristic
153	#16810474	C₂²	1	1	yes	characteristic
154	#16810474	C₂²	1	1	yes	characteristic
155	#16810474	C₂²	1	1	yes	characteristic
156	#16810474	C₂²	1	1	yes	characteristic
157	#16810474	C₂²	1	1	yes	characteristic
158	#16810474	C₂²	1	1	yes	characteristic
159	#16810474	C₂²	1	1	yes	characteristic
160	#16810474	C₂²	1	1	yes	characteristic
161	#16810474	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
163	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
164	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
166	C₄×#11719921	C₂²	1	1	yes	characteristic
167	#16810470	C₂²	1	1	yes	characteristic
168	#16810470	C₂²	1	1	yes	characteristic
169	#16810470	C₂²	1	1	yes	characteristic
170	#16810470	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
173	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
174	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
176	C₅₃×#399	C₂²	1	1	yes	characteristic
177	C₅₃×#398	C₂²	1	1	yes	characteristic
178	C₅₃×#396	C₂²	1	1	yes	characteristic
179	C₅₃×#395	C₂²	1	1	yes	characteristic
180	C₅₃×#391	C₂²	1	1	yes	characteristic
181	C₅₃×#389	C₂²	1	1	yes	characteristic
182	C₅₃×#389	C₂²	1	1	yes	characteristic
183	C₅₃×#388	C₂²	1	1	yes	characteristic
184	C₅₃×#388	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic
186	C₅₃×#385	C₂²	1	1	yes	characteristic
187	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
194	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
195	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂³×Dic₅₃	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	#13133216	—	2	4	no	—
202	#13133216	—	2	4	no	—
203	#13133216	—	2	4	no	—
204	#13133216	—	2	4	no	—
205	#13133216	—	2	4	no	—
206	#13133215	—	2	4	no	—
207	#13133215	—	2	4	no	—
208	#13133209	—	2	4	no	—
209	#13133207	—	2	4	no	—
210	#13133207	—	2	4	no	—
211	#13133196	—	2	4	no	—
212	#13133195	—	2	4	no	—
213	#13133195	—	2	4	no	—
214	#13133195	—	2	4	no	—
215	#13133195	—	2	4	no	—
216	#13133195	—	2	4	no	—
217	#13133194	—	2	4	no	—
218	#13133194	—	2	4	no	—
219	#13133194	—	2	4	no	—
220	Q₈×Dic₅₃	—	2	4	no	—
221	C₄×Dic₁₀₆	—	2	4	no	—
222	#13133182	—	2	4	no	—
223	#13133182	—	2	4	no	—
224	#13133182	—	2	4	no	—
225	#13133182	—	2	4	no	—
226	#13133182	—	2	4	no	—
227	#13133182	—	2	4	no	—
228	#13133182	D₄	1	8	yes	complemented
229	C₄×C₂²⋊D₅₃	—	2	4	no	—
230	#13133177	—	2	4	no	—
231	#13133177	Q₈	1	8	yes	complemented
232	#13133175	—	2	4	no	—
233	#13133175	—	2	4	no	—
234	#13133173	—	2	4	no	—
235	#13133173	—	2	4	no	—
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×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊Dic₅₃	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	C₂×#11719919	C₂³	1	1	yes	characteristic
259	C₂×#11719919	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	1	yes	characteristic
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×#11719919	C₂³	1	1	yes	characteristic
265	C₂×#11719919	C₂³	1	1	yes	characteristic
266	C₂×#11719919	C₂³	1	1	yes	characteristic
267	C₂×#11719919	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	1	yes	characteristic
269	C₂×#11719919	C₂³	1	1	yes	characteristic
270	C₂×#11719919	C₂³	1	1	yes	characteristic
271	C₂×#11719919	C₂³	1	1	yes	characteristic
272	C₂×#11719919	C₂³	1	1	yes	characteristic
273	C₂×#11719919	C₂³	1	1	yes	characteristic
274	C₂×#11719919	C₂³	1	1	yes	characteristic
275	C₂×#11719919	C₂³	1	1	yes	characteristic
276	C₂×#11719919	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊Dic₅₃	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×C₄×Dic₅₃	—	2	4	no	—
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
319	C₄²×D₅₃	—	2	4	no	—
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	#13133124	C₂³	1	1	yes	characteristic
335	#13133124	C₂³	1	1	yes	characteristic
336	#13133124	C₂³	1	1	yes	characteristic
337	#13133124	C₂³	1	1	yes	characteristic
338	#13133124	C₂³	1	1	yes	characteristic
339	#13133124	C₂³	1	1	yes	characteristic
340	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
347	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
348	#125×C₅₃	—	2	4	no	—
349	C₂²⋊Q₈×C₅₃	—	2	4	no	—
350	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×Q₈×C₅₃	—	2	2	no	—
386	C₂×Q₈×C₅₃	—	2	2	no	—
387	C₂×Q₈×C₅₃	—	4	1	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	4	1	no	—
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	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₂²⋊D₅₃	—	2	2	no	—
406	C₂×C₂²⋊D₅₃	—	2	2	no	—
407	C₂×C₂²⋊D₅₃	C₂×Q₈	1	4	yes	—
408	C₂²×Dic₅₃	—	2	2	no	—
409	C₂²×Dic₅₃	—	2	2	no	—
410	C₂²×Dic₅₃	—	2	2	no	—
411	C₂²×Dic₅₃	—	2	2	no	—
412	C₂²×Dic₅₃	—	2	2	no	—
413	C₂²×Dic₅₃	C₂×Q₈	1	4	yes	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂×C₄×D₅₃	—	2	2	no	—
430	C₂×C₄×D₅₃	—	2	2	no	—
431	C₂×C₄×D₅₃	—	2	2	no	—
432	C₂×C₄×D₅₃	—	2	2	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	4	1	no	—
437	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
438	C₂×Dic₁₀₆	—	2	2	no	—
439	C₂×Dic₁₀₆	—	2	2	no	—
440	C₂×Dic₁₀₆	—	2	2	no	—
441	C₂×Dic₁₀₆	—	2	2	no	—
442	C₂×Dic₁₀₆	—	2	2	no	—
443	C₂×Dic₁₀₆	—	2	2	no	—
444	C₂×Dic₁₀₆	—	2	2	no	—
445	C₂×Dic₁₀₆	—	2	2	no	—
446	C₂×Dic₁₀₆	—	2	2	no	—
447	C₂×Dic₁₀₆	—	2	2	no	—
448	C₂×Dic₁₀₆	—	2	2	no	—
449	C₂×Dic₁₀₆	—	2	2	no	—
450	C₂×Dic₁₀₆	—	2	2	no	—
451	C₂×Dic₁₀₆	—	2	2	no	—
452	C₂×Dic₁₀₆	—	4	1	no	—
453	C₂×Dic₁₀₆	—	4	1	no	—
454	C₂×Dic₁₀₆	—	4	1	no	—
455	C₂×Dic₁₀₆	C₂×D₄	1	4	yes	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	2	no	—
458	C₄⋊C₄×C₅₃	—	2	2	no	—
459	C₄⋊C₄×C₅₃	—	2	2	no	—
460	C₄⋊C₄×C₅₃	—	2	2	no	—
461	C₄⋊C₄×C₅₃	—	2	2	no	—
462	C₄⋊C₄×C₅₃	—	2	2	no	—
463	C₄⋊C₄×C₅₃	—	2	2	no	—
464	C₄⋊C₄×C₅₃	—	2	2	no	—
465	C₄⋊C₄×C₅₃	—	2	2	no	—
466	C₄⋊C₄×C₅₃	—	2	2	no	—
467	C₄⋊C₄×C₅₃	—	4	1	no	—
468	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	4	1	no	—
474	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
475	C₄²×C₅₃	—	2	2	no	—
476	C₄²×C₅₃	—	2	2	no	—
477	C₄²×C₅₃	—	4	1	no	—
478	C₄²×C₅₃	—	4	1	no	—
479	C₂²⋊Dic₅₃	—	2	2	no	—
480	C₂²⋊Dic₅₃	—	2	2	no	—
481	C₂²⋊Dic₅₃	—	2	2	no	—
482	C₂²⋊Dic₅₃	—	2	2	no	—
483	C₂²⋊Dic₅₃	—	4	1	no	—
484	#11719921	—	2	2	no	—
485	#11719921	—	2	2	no	—
486	#11719921	—	2	2	no	—
487	#11719921	—	2	2	no	—
488	#11719921	—	2	2	no	—
489	#11719921	—	2	2	no	—
490	#11719921	—	2	2	no	—
491	#11719921	—	2	2	no	—
492	#11719921	—	4	1	no	—
493	#11719921	—	4	1	no	—
494	#11719921	C₂×Q₈	1	4	yes	—
495	C₄⋊Dic₅₃	—	2	2	no	—
496	C₄⋊Dic₅₃	—	2	2	no	—
497	C₄⋊Dic₅₃	—	2	2	no	—
498	C₄⋊Dic₅₃	—	2	2	no	—
499	C₄⋊Dic₅₃	—	2	2	no	—
500	C₄⋊Dic₅₃	—	2	2	no	—
501	C₄⋊Dic₅₃	—	2	2	no	—
502	C₄⋊Dic₅₃	—	2	2	no	—
503	C₄⋊Dic₅₃	—	2	2	no	—
504	C₄⋊Dic₅₃	—	4	1	no	—
505	#11719919	—	2	2	no	—
506	#11719919	—	2	2	no	—
507	#11719919	—	2	2	no	—
508	#11719919	—	2	2	no	—
509	#11719919	—	2	2	no	—
510	#11719919	—	2	2	no	—
511	#11719919	—	2	2	no	—
512	#11719919	—	2	2	no	—
513	#11719919	—	2	2	no	—
514	#11719919	—	2	2	no	—
515	#11719919	—	2	2	no	—
516	#11719919	—	2	2	no	—
517	#11719919	—	2	2	no	—
518	#11719919	—	2	2	no	—
519	#11719919	—	2	2	no	—
520	#11719919	—	2	2	no	—
521	#11719919	—	2	2	no	—
522	#11719919	—	2	2	no	—
523	#11719919	—	2	2	no	—
524	#11719919	—	2	2	no	—
525	#11719919	—	2	2	no	—
526	#11719919	—	2	2	no	—
527	#11719919	—	2	2	no	—
528	#11719919	—	2	2	no	—
529	#11719919	—	2	2	no	—
530	#11719919	—	2	2	no	—
531	#11719919	C₂×D₄	1	4	yes	—
532	#11719919	C₂×D₄	1	4	yes	—
533	#11719919	C₂×Q₈	1	4	yes	—
534	#11719919	#41	1	4	yes	—
535	#11719919	#41	1	4	yes	—
536	C₄×Dic₅₃	—	2	2	no	—
537	C₄×Dic₅₃	—	2	2	no	—
538	C₄×Dic₅₃	—	2	2	no	—
539	C₄×Dic₅₃	—	2	2	no	—
540	C₄×Dic₅₃	—	2	2	no	—
541	C₄×Dic₅₃	—	2	2	no	—
542	C₄×Dic₅₃	—	2	2	no	—
543	C₄×Dic₅₃	—	2	2	no	—
544	C₄×Dic₅₃	—	2	2	no	—
545	C₄×Dic₅₃	—	2	2	no	—
546	C₄×Dic₅₃	—	2	2	no	—
547	C₄×Dic₅₃	—	2	2	no	—
548	C₄×Dic₅₃	—	2	2	no	—
549	C₄×Dic₅₃	—	2	2	no	—
550	C₄×Dic₅₃	—	2	2	no	—
551	C₄×Dic₅₃	—	2	2	no	—
552	C₄×Dic₅₃	—	2	2	no	—
553	C₄×Dic₅₃	—	2	2	no	—
554	C₄×Dic₅₃	—	2	2	no	—
555	C₄×Dic₅₃	—	4	1	no	—
556	C₄×Dic₅₃	C₂×D₄	1	4	yes	—
557	C₄×Dic₅₃	C₂×D₄	1	4	yes	—
558	C₄×Dic₅₃	C₂×D₄	1	4	yes	—
559	C₄×Dic₅₃	C₂×Q₈	1	4	yes	—
560	C₄×Dic₅₃	#41	1	4	yes	—
561	C₂³×C₅₃	—	2	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	C₂²×Q₈	1	2	yes	—
568	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
569	C₂²×D₅₃	—	2	1	no	—
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	1	no	—
575	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
576	Q₈×C₅₃	—	4	4	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	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
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	—	4	4	no	—
612	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
613	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
614	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
615	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
616	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
617	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
618	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
619	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
620	C₂²⋊D₅₃	—	2	8	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	8	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	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	4	4	no	—
654	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
655	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
656	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
657	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
658	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
659	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
660	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
661	C₂×Dic₅₃	C₂×#41	1	2	yes	—
662	C₂×Dic₅₃	C₂×#41	1	2	yes	—
663	C₂×Dic₅₃	C₂×#41	1	2	yes	—
664	C₂×Dic₅₃	C₂×#41	1	2	yes	—
665	C₂×Dic₅₃	C₂×#41	1	2	yes	—
666	C₂×Dic₅₃	C₂×#41	1	2	yes	—
667	C₂×Dic₅₃	2₋¹⁺⁴	1	2	yes	—
668	C₄×D₅₃	—	2	8	no	—
669	C₄×D₅₃	—	4	4	no	—
670	C₄×D₅₃	—	4	4	no	—
671	Dic₁₀₆	—	2	8	no	—
672	Dic₁₀₆	—	4	4	no	—
673	Dic₁₀₆	—	4	4	no	—
674	Dic₁₀₆	—	4	4	no	—
675	Dic₁₀₆	—	4	4	no	—
676	Dic₁₀₆	—	4	4	no	—
677	#34929	—	53	1	no	maximal, Sylow
678	C₂²×C₅₃	—	2	2	no	—
679	C₂²×C₅₃	—	2	2	no	—
680	C₂²×C₅₃	—	2	2	no	—
681	C₂²×C₅₃	—	4	1	no	—
682	C₂²×C₅₃	—	4	1	no	—
683	C₂²×C₅₃	—	4	1	no	—
684	C₂²×C₅₃	—	4	1	no	—
685	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
686	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
687	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
688	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
689	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
690	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂²×C₅₃	#585	1	1	yes	characteristic
692	C₂×D₅₃	—	2	2	no	—
693	C₂×D₅₃	—	2	2	no	—
694	C₂×D₅₃	—	2	2	no	—
695	C₂×D₅₃	—	4	1	no	—
696	C₂×D₅₃	—	4	1	no	—
697	C₂×D₅₃	—	4	1	no	—
698	C₂×D₅₃	—	4	1	no	—
699	C₄×C₅₃	—	2	2	no	—
700	C₄×C₅₃	—	2	2	no	—
701	C₄×C₅₃	—	2	2	no	—
702	C₄×C₅₃	—	2	2	no	—
703	C₄×C₅₃	—	2	2	no	—
704	C₄×C₅₃	—	2	2	no	—
705	C₄×C₅₃	—	2	2	no	—
706	C₄×C₅₃	—	2	2	no	—
707	C₄×C₅₃	—	4	1	no	—
708	C₄×C₅₃	—	4	1	no	—
709	C₄×C₅₃	—	4	1	no	—
710	C₄×C₅₃	—	4	1	no	—
711	C₄×C₅₃	—	4	1	no	—
712	C₄×C₅₃	—	4	1	no	—
713	Dic₅₃	—	2	2	no	—
714	Dic₅₃	—	2	2	no	—
715	Dic₅₃	—	2	2	no	—
716	Dic₅₃	—	2	2	no	—
717	Dic₅₃	—	2	2	no	—
718	Dic₅₃	—	4	1	no	—
719	Dic₅₃	—	4	1	no	—
720	Dic₅₃	—	4	1	no	—
721	Dic₅₃	—	4	1	no	—
722	Dic₅₃	—	4	1	no	—
723	Dic₅₃	—	4	1	no	—
724	Dic₅₃	—	4	1	no	—
725	Dic₅₃	#532	1	4	yes	—
726	Dic₅₃	#533	1	4	yes	complemented
727	Dic₅₃	D₄×Q₈	1	4	yes	—
728	C₂×#533	—	53	1	no	—
729	C₂×#533	—	53	1	no	—
730	#2556	—	53	1	no	—
731	#2556	—	53	1	no	—
732	#2556	—	53	1	no	—
733	#2556	D₅₃	1	1	yes	characteristic, complemented
734	#2551	—	53	1	no	—
735	#2546	—	53	1	no	—
736	#2542	—	53	1	no	—
737	#2538	—	53	1	no	—
738	#2506	—	53	1	no	—
739	#2506	—	53	1	no	—
740	#2492	—	53	1	no	—
741	#2492	—	53	1	no	—
742	#2452	—	53	1	no	—
743	#2452	—	53	1	no	—
744	#2429	—	53	1	no	—
745	#2429	—	53	1	no	—
746	#2396	—	53	1	no	—
747	#2396	—	53	1	no	—
748	#2396	—	53	1	no	—
749	#2396	—	53	1	no	—
750	C₄×C₄⋊Q₈	—	53	1	no	—
751	C₄×C₄⋊Q₈	—	53	1	no	—
752	C₄×C₄⋊Q₈	—	53	1	no	—
753	C₄×C₂²⋊Q₈	—	53	1	no	—
754	C₄×C₂²⋊Q₈	—	53	1	no	—
755	#2293	—	53	1	no	—
756	#2293	—	53	1	no	—
757	C₄²×Q₈	—	53	1	no	—
758	C₄²×D₄	—	53	1	no	—
759	C₂×C₅₃	—	4	2	no	—
760	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
761	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
762	C₂×C₅₃	#3461	1	1	yes	characteristic
763	C₂×C₅₃	C₂×D₄×Q₈	1	1	yes	characteristic
764	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
765	C₂×C₅₃	Q₈×#41	1	1	yes	characteristic
766	C₂×C₅₃	#3482	1	1	yes	characteristic
767	D₅₃	—	4	2	no	—
768	#533	—	106	8	no	—
769	#533	—	106	8	no	—
770	C₂×C₄⋊Q₈	—	53	1	no	—
771	C₂×C₄⋊Q₈	—	53	1	no	—
772	C₂×C₄⋊Q₈	—	53	1	no	—
773	C₂×C₄⋊Q₈	—	53	1	no	—
774	C₂×C₄⋊Q₈	—	53	1	no	—
775	C₂×C₄⋊Q₈	—	53	1	no	—
776	C₂×C₄⋊Q₈	—	53	1	no	—
777	C₂×#125	—	53	1	no	—
778	C₂×#125	—	53	1	no	—
779	C₂×#125	—	53	1	no	—
780	C₂×#125	C₂×D₅₃	1	1	yes	characteristic
781	C₂×C₂²⋊Q₈	—	53	1	no	—
782	C₂×C₂²⋊Q₈	—	53	1	no	—
783	C₂×C₂²⋊Q₈	—	53	1	no	—
784	C₂×C₂²⋊Q₈	—	53	1	no	—
785	C₂×C₂²⋊Q₈	—	53	1	no	—
786	C₂×C₂²⋊Q₈	—	53	1	no	—
787	C₂×C₂²⋊Q₈	—	53	1	no	—
788	C₂×C₂²⋊Q₈	—	53	1	no	—
789	C₂×C₂²⋊Q₈	—	53	1	no	—
790	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
791	C₂×C₄×Q₈	—	53	1	no	—
792	C₂×C₄×Q₈	—	53	1	no	—
793	C₂×C₄×Q₈	—	53	1	no	—
794	C₂×C₄×Q₈	—	53	1	no	—
795	C₂×C₄×Q₈	—	53	1	no	—
796	C₂×C₄×Q₈	—	53	1	no	—
797	C₂×C₄×Q₈	—	53	1	no	—
798	C₂×C₄×Q₈	—	53	1	no	—
799	C₂×C₄×Q₈	—	53	1	no	—
800	C₂×C₄×D₄	—	53	1	no	—
801	C₂×C₄×D₄	—	53	1	no	—
802	C₂×C₄×D₄	—	53	1	no	—
803	C₂×#117	—	53	1	no	—
804	C₂×#117	—	53	1	no	—
805	C₂×#117	—	53	1	no	—
806	C₂×#117	—	53	1	no	—
807	C₂²×C₄²	—	53	1	no	—
808	C₂²×C₄²	—	53	1	no	—
809	#400	—	53	1	no	—
810	#400	—	53	1	no	—
811	#400	—	53	1	no	—
812	#400	—	53	1	no	—
813	#399	—	53	1	no	—
814	#399	—	53	1	no	—
815	#399	—	53	1	no	—
816	#399	C₂×D₅₃	1	1	yes	characteristic
817	#398	—	53	1	no	—
818	#398	—	53	1	no	—
819	#398	—	53	1	no	—
820	#398	—	53	1	no	—
821	#398	—	53	1	no	—
822	#398	—	53	1	no	—
823	#398	—	53	1	no	—
824	#398	C₂×D₅₃	1	1	yes	characteristic
825	#396	—	53	1	no	—
826	#396	—	53	1	no	—
827	#396	—	53	1	no	—
828	#396	—	53	1	no	—
829	#396	—	53	1	no	—
830	#396	—	53	1	no	—
831	#396	—	53	1	no	—
832	#396	C₂×D₅₃	1	1	yes	characteristic
833	#395	—	53	1	no	—
834	#395	—	53	1	no	—
835	#395	—	53	1	no	—
836	#395	C₂×D₅₃	1	1	yes	characteristic
837	#393	—	53	1	no	—
838	#393	—	53	1	no	—
839	#393	—	53	1	no	—
840	#393	—	53	1	no	—
841	#391	—	53	1	no	—
842	#391	—	53	1	no	—
843	#391	—	53	1	no	—
844	#391	—	53	1	no	—
845	#391	—	53	1	no	—
846	#391	—	53	1	no	—
847	#391	—	53	1	no	—
848	#391	C₂×D₅₃	1	1	yes	characteristic
849	#390	—	53	1	no	—
850	#390	—	53	1	no	—
851	#390	—	53	1	no	—
852	#390	—	53	1	no	—
853	#389	—	53	1	no	—
854	#389	—	53	1	no	—
855	#389	—	53	1	no	—
856	#389	—	53	1	no	—
857	#389	—	53	1	no	—
858	#389	—	53	1	no	—
859	#389	—	53	1	no	—
860	#389	—	53	1	no	—
861	#389	—	53	1	no	—
862	#389	—	53	1	no	—
863	#389	—	53	1	no	—
864	#389	—	53	1	no	—
865	#389	—	53	1	no	—
866	#389	—	53	1	no	—
867	#389	—	53	1	no	—
868	#389	—	53	1	no	—
869	#389	C₂×D₅₃	1	1	yes	characteristic
870	#389	C₂×D₅₃	1	1	yes	characteristic
871	#388	—	53	1	no	—
872	#388	—	53	1	no	—
873	#388	—	53	1	no	—
874	#388	—	53	1	no	—
875	#388	—	53	1	no	—
876	#388	—	53	1	no	—
877	#388	C₂×D₅₃	1	1	yes	characteristic
878	#388	C₂×D₅₃	1	1	yes	characteristic
879	#387	—	53	1	no	—
880	#387	—	53	1	no	—
881	#387	—	53	1	no	—
882	#387	C₂×D₅₃	1	1	yes	characteristic
883	#385	—	53	1	no	—
884	#385	—	53	1	no	—
885	#385	—	53	1	no	—
886	#385	C₂×D₅₃	1	1	yes	characteristic
887	#384	—	53	1	no	—
888	#384	—	53	1	no	—
889	#384	—	53	1	no	—
890	#380	—	53	1	no	—
891	#380	—	53	1	no	—
892	C₄×C₄⋊C₄	—	53	1	no	—
893	C₄×C₄⋊C₄	—	53	1	no	—
894	C₄×C₄⋊C₄	—	53	1	no	—
895	C₄×C₄⋊C₄	—	53	1	no	—
896	C₄×C₄⋊C₄	—	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	—	53	1	no	—
902	C₄×C₄⋊C₄	—	53	1	no	—
903	C₄×C₄⋊C₄	—	53	1	no	—
904	C₄×C₄⋊C₄	—	53	1	no	—
905	C₄×C₄⋊C₄	—	53	1	no	—
906	C₄×C₄⋊C₄	—	53	1	no	—
907	C₄×C₄⋊C₄	—	53	1	no	—
908	C₄×C₄⋊C₄	—	53	1	no	—
909	C₄×C₄⋊C₄	—	53	1	no	—
910	C₄×C₄⋊C₄	—	53	1	no	—
911	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
912	C₄×C₂²⋊C₄	—	53	1	no	—
913	C₄×C₂²⋊C₄	—	53	1	no	—
914	C₄×C₂²⋊C₄	—	53	1	no	—
915	C₄×C₂²⋊C₄	—	53	1	no	—
916	C₄×C₂²⋊C₄	—	53	1	no	—
917	C₄×C₂²⋊C₄	—	53	1	no	—
918	C₄×C₂²⋊C₄	—	53	1	no	—
919	C₄×C₂²⋊C₄	—	53	1	no	—
920	C₄×C₂²⋊C₄	—	53	1	no	—
921	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
922	C₄³	—	53	1	no	—
923	C₄³	—	53	1	no	—
924	C₄³	—	53	1	no	—
925	C₅₃	#34929	1	1	yes	characteristic, complemented, Sylow
926	C₂²×Q₈	—	53	1	no	—
927	C₂²×Q₈	—	53	1	no	—
928	C₂²×Q₈	—	53	1	no	—
929	C₂²×Q₈	—	53	1	no	—
930	C₂²×Q₈	—	53	1	no	—
931	C₂²×Q₈	—	53	1	no	—
932	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
933	C₂²×D₄	—	53	1	no	—
934	C₂³×C₄	—	53	1	no	—
935	C₂³×C₄	—	53	1	no	—
936	C₂³×C₄	—	53	1	no	—
937	C₂³×C₄	—	53	1	no	—
938	C₂³×C₄	—	53	1	no	—
939	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
940	C₄⋊Q₈	—	106	4	no	—
941	C₄⋊Q₈	—	106	4	no	—
942	C₄⋊Q₈	—	106	4	no	—
943	C₄⋊Q₈	—	106	4	no	—
944	C₄⋊Q₈	—	106	4	no	—
945	C₄⋊Q₈	—	106	4	no	—
946	C₄⋊Q₈	—	106	4	no	—
947	#125	—	2	4	no	—
948	#125	—	106	4	no	—
949	#125	—	106	4	no	—
950	#125	—	106	4	no	—
951	C₂²⋊Q₈	—	2	4	no	—
952	C₂²⋊Q₈	—	106	4	no	—
953	C₂²⋊Q₈	—	106	4	no	—
954	C₂²⋊Q₈	—	106	4	no	—
955	C₂²⋊Q₈	—	106	4	no	—
956	C₂²⋊Q₈	—	106	4	no	—
957	C₂²⋊Q₈	—	106	4	no	—
958	C₂²⋊Q₈	—	106	4	no	—
959	C₂²⋊Q₈	—	106	4	no	—
960	C₂²⋊Q₈	—	106	4	no	—
961	C₄×Q₈	—	53	8	no	—
962	C₄×Q₈	—	106	4	no	—
963	C₄×Q₈	—	106	4	no	—
964	C₄×Q₈	—	106	4	no	—
965	C₄×Q₈	—	106	4	no	—
966	C₄×Q₈	—	106	4	no	—
967	C₄×Q₈	—	106	4	no	—
968	C₄×Q₈	—	106	4	no	—
969	C₄×Q₈	—	106	4	no	—
970	C₄×D₄	—	53	8	no	—
971	C₄×D₄	—	106	4	no	—
972	C₄×D₄	—	106	4	no	—
973	#117	—	106	4	no	—
974	#117	—	106	4	no	—
975	#117	—	106	4	no	—
976	#117	—	106	4	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	1	no	—
984	C₂×C₄⋊C₄	—	53	1	no	—
985	C₂×C₄⋊C₄	—	53	1	no	—
986	C₂×C₄⋊C₄	—	53	1	no	—
987	C₂×C₄⋊C₄	—	53	1	no	—
988	C₂×C₄⋊C₄	—	53	1	no	—
989	C₂×C₄⋊C₄	—	53	1	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	—	53	1	no	—
992	C₂×C₄⋊C₄	—	53	1	no	—
993	C₂×C₄⋊C₄	—	53	1	no	—
994	C₂×C₄⋊C₄	—	53	1	no	—
995	C₂×C₄⋊C₄	—	53	1	no	—
996	C₂×C₄⋊C₄	—	53	1	no	—
997	C₂×C₄⋊C₄	—	53	1	no	—
998	C₂×C₄⋊C₄	—	53	1	no	—
999	C₂×C₄⋊C₄	—	53	1	no	—
1000	C₂×C₄⋊C₄	—	53	1	no	—
1001	C₂×C₄⋊C₄	—	53	1	no	—
1002	C₂×C₄⋊C₄	—	53	1	no	—
1003	C₂×C₄⋊C₄	—	53	1	no	—
1004	C₂×C₄⋊C₄	—	53	1	no	—
1005	C₂×C₄⋊C₄	—	53	1	no	—
1006	C₂×C₄⋊C₄	—	53	1	no	—
1007	C₂×C₄⋊C₄	—	53	1	no	—
1008	C₂×C₄⋊C₄	—	53	1	no	—
1009	C₂×C₄⋊C₄	—	53	1	no	—
1010	C₂×C₄⋊C₄	—	53	1	no	—
1011	C₂×C₄⋊C₄	—	53	1	no	—
1012	C₂×C₄⋊C₄	—	53	1	no	—
1013	C₂×C₄⋊C₄	—	53	1	no	—
1014	C₂×C₄⋊C₄	—	53	1	no	—
1015	C₂×C₄⋊C₄	—	53	1	no	—
1016	C₂×C₄⋊C₄	—	53	1	no	—
1017	C₂×C₄⋊C₄	—	53	1	no	—
1018	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1022	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1023	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1024	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1029	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1030	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	—	53	1	no	—
1032	C₂×C₂²⋊C₄	—	53	1	no	—
1033	C₂×C₂²⋊C₄	—	53	1	no	—
1034	C₂×C₂²⋊C₄	—	53	1	no	—
1035	C₂×C₂²⋊C₄	—	53	1	no	—
1036	C₂×C₂²⋊C₄	—	53	1	no	—
1037	C₂×C₂²⋊C₄	—	53	1	no	—
1038	C₂×C₂²⋊C₄	—	53	1	no	—
1039	C₂×C₂²⋊C₄	—	53	1	no	—
1040	C₂×C₂²⋊C₄	—	53	1	no	—
1041	C₂×C₂²⋊C₄	—	53	1	no	—
1042	C₂×C₂²⋊C₄	—	53	1	no	—
1043	C₂×C₂²⋊C₄	—	53	1	no	—
1044	C₂×C₂²⋊C₄	—	53	1	no	—
1045	C₂×C₂²⋊C₄	—	53	1	no	—
1046	C₂×C₂²⋊C₄	—	53	1	no	—
1047	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1053	C₂×C₄²	—	53	1	no	—
1054	C₂×C₄²	—	53	1	no	—
1055	C₂×C₄²	—	53	1	no	—
1056	C₂×C₄²	—	53	1	no	—
1057	C₂×C₄²	—	53	1	no	—
1058	C₂×C₄²	—	53	1	no	—
1059	C₂×C₄²	—	53	1	no	—
1060	C₂×C₄²	—	53	1	no	—
1061	C₂×C₄²	—	53	1	no	—
1062	C₂×C₄²	—	53	1	no	—
1063	C₂×C₄²	—	53	1	no	—
1064	C₂×C₄²	—	53	1	no	—
1065	C₂×C₄²	—	53	1	no	—
1066	C₂×C₄²	—	53	1	no	—
1067	C₂×C₄²	—	53	1	no	—
1068	C₂×C₄²	—	53	1	no	—
1069	C₂×C₄²	—	53	1	no	—
1070	C₂×C₄²	—	53	1	no	—
1071	C₂×C₄²	—	53	1	no	—
1072	C₂×C₄²	—	53	1	no	—
1073	C₂×C₄²	—	53	1	no	—
1074	C₂×C₄²	—	53	1	no	—
1075	C₂×C₄²	—	53	1	no	—
1076	C₂×C₄²	—	53	1	no	—
1077	C₂×C₄²	—	53	1	no	—
1078	C₂×C₄²	—	106	4	no	—
1079	C₂×C₄²	—	106	4	no	—
1080	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1081	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1082	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1083	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	—	53	1	no	—
1095	#95	—	53	1	no	—
1096	#95	—	53	1	no	—
1097	#95	—	53	1	no	—
1098	#95	—	53	1	no	—
1099	#95	—	53	1	no	—
1100	#95	—	53	1	no	—
1101	#95	—	53	1	no	—
1102	#95	—	53	1	no	—
1103	#95	—	53	1	no	—
1104	#95	—	53	1	no	—
1105	#95	—	53	1	no	—
1106	#95	—	53	1	no	—
1107	#95	—	53	1	no	—
1108	#95	—	53	1	no	—
1109	#95	—	53	1	no	—
1110	#95	C₂²×D₅₃	1	1	yes	characteristic
1111	#95	C₂²×D₅₃	1	1	yes	characteristic
1112	#95	C₂²×D₅₃	1	1	yes	characteristic
1113	#95	C₂²×D₅₃	1	1	yes	characteristic
1114	#95	C₂²×D₅₃	1	1	yes	characteristic
1115	#95	C₂²×D₅₃	1	1	yes	characteristic
1116	#95	C₂²×D₅₃	1	1	yes	characteristic
1117	#95	C₂²×D₅₃	1	1	yes	characteristic
1118	#95	C₂²×D₅₃	1	1	yes	characteristic
1119	#95	C₂²×D₅₃	1	1	yes	characteristic
1120	C₂⁴	—	53	1	no	—
1121	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1122	C₂×Q₈	—	2	2	no	—
1123	C₂×Q₈	—	2	2	no	—
1124	C₂×Q₈	—	4	1	no	—
1125	C₂×Q₈	—	53	4	no	—
1126	C₂×Q₈	—	106	2	no	—
1127	C₂×Q₈	—	106	2	no	—
1128	C₂×Q₈	—	106	2	no	—
1129	C₂×Q₈	—	106	2	no	—
1130	C₂×Q₈	—	106	2	no	—
1131	C₂×Q₈	—	106	2	no	—
1132	C₂×Q₈	—	106	2	no	—
1133	C₂×Q₈	—	106	2	no	—
1134	C₂×Q₈	—	106	2	no	—
1135	C₂×Q₈	—	106	2	no	—
1136	C₂×Q₈	—	106	2	no	—
1137	C₂×Q₈	—	106	2	no	—
1138	C₂×Q₈	—	106	2	no	—
1139	C₂×Q₈	—	106	2	no	—
1140	C₂×Q₈	—	212	1	no	—
1141	C₂×Q₈	—	212	1	no	—
1142	C₂×Q₈	—	212	1	no	—
1143	C₂×D₄	—	53	4	no	—
1144	C₂×D₄	—	106	2	no	—
1145	C₂×D₄	—	106	2	no	—
1146	C₂²×C₄	—	2	2	no	—
1147	C₂²×C₄	—	2	2	no	—
1148	C₂²×C₄	—	4	1	no	—
1149	C₂²×C₄	—	53	1	no	—
1150	C₂²×C₄	—	53	1	no	—
1151	C₂²×C₄	—	53	1	no	—
1152	C₂²×C₄	—	53	4	no	—
1153	C₂²×C₄	—	53	1	no	—
1154	C₂²×C₄	—	53	1	no	—
1155	C₂²×C₄	—	53	1	no	—
1156	C₂²×C₄	—	53	1	no	—
1157	C₂²×C₄	—	53	1	no	—
1158	C₂²×C₄	—	53	4	no	—
1159	C₂²×C₄	—	53	1	no	—
1160	C₂²×C₄	—	53	1	no	—
1161	C₂²×C₄	—	53	1	no	—
1162	C₂²×C₄	—	53	1	no	—
1163	C₂²×C₄	—	53	1	no	—
1164	C₂²×C₄	—	53	1	no	—
1165	C₂²×C₄	—	53	1	no	—
1166	C₂²×C₄	—	106	2	no	—
1167	C₂²×C₄	—	106	2	no	—
1168	C₂²×C₄	—	106	2	no	—
1169	C₂²×C₄	—	106	2	no	—
1170	C₂²×C₄	—	106	2	no	—
1171	C₂²×C₄	—	106	2	no	—
1172	C₂²×C₄	—	106	2	no	—
1173	C₂²×C₄	—	106	2	no	—
1174	C₂²×C₄	—	106	2	no	—
1175	C₂²×C₄	—	106	2	no	—
1176	C₂²×C₄	—	106	2	no	—
1177	C₂²×C₄	—	106	2	no	—
1178	C₂²×C₄	—	212	1	no	—
1179	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1180	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1184	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1185	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1186	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1187	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1188	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1189	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1191	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1192	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1193	C₄⋊C₄	—	2	2	no	—
1194	C₄⋊C₄	—	2	2	no	—
1195	C₄⋊C₄	—	2	2	no	—
1196	C₄⋊C₄	—	2	2	no	—
1197	C₄⋊C₄	—	2	2	no	—
1198	C₄⋊C₄	—	2	2	no	—
1199	C₄⋊C₄	—	2	2	no	—
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	2	no	—
1203	C₄⋊C₄	—	2	2	no	—
1204	C₄⋊C₄	—	4	1	no	—
1205	C₄⋊C₄	—	53	4	no	—
1206	C₄⋊C₄	—	53	4	no	—
1207	C₄⋊C₄	—	53	4	no	—
1208	C₄⋊C₄	—	53	4	no	—
1209	C₄⋊C₄	—	53	4	no	—
1210	C₄⋊C₄	—	106	2	no	—
1211	C₄⋊C₄	—	106	2	no	—
1212	C₄⋊C₄	—	106	2	no	—
1213	C₄⋊C₄	—	106	2	no	—
1214	C₄⋊C₄	—	106	2	no	—
1215	C₄⋊C₄	—	106	2	no	—
1216	C₄⋊C₄	—	106	2	no	—
1217	C₄⋊C₄	—	106	2	no	—
1218	C₄⋊C₄	—	106	2	no	—
1219	C₄⋊C₄	—	106	2	no	—
1220	C₄⋊C₄	—	106	2	no	—
1221	C₄⋊C₄	—	106	2	no	—
1222	C₄⋊C₄	—	106	2	no	—
1223	C₄⋊C₄	—	106	2	no	—
1224	C₄⋊C₄	—	106	2	no	—
1225	C₄⋊C₄	—	106	2	no	—
1226	C₄⋊C₄	—	106	2	no	—
1227	C₄⋊C₄	—	106	2	no	—
1228	C₄⋊C₄	—	106	2	no	—
1229	C₄⋊C₄	—	106	2	no	—
1230	C₄⋊C₄	—	106	2	no	—
1231	C₄⋊C₄	—	106	2	no	—
1232	C₄⋊C₄	—	106	2	no	—
1233	C₄⋊C₄	—	106	2	no	—
1234	C₄⋊C₄	—	106	2	no	—
1235	C₄⋊C₄	—	106	2	no	—
1236	C₄⋊C₄	—	106	2	no	—
1237	C₄⋊C₄	—	106	2	no	—
1238	C₄⋊C₄	—	106	2	no	—
1239	C₄⋊C₄	—	106	2	no	—
1240	C₄⋊C₄	—	106	2	no	—
1241	C₄⋊C₄	—	106	2	no	—
1242	C₄⋊C₄	—	106	2	no	—
1243	C₄⋊C₄	—	106	2	no	—
1244	C₄⋊C₄	—	106	2	no	—
1245	C₄⋊C₄	—	212	1	no	—
1246	C₄⋊C₄	D₄×D₅₃	1	4	yes	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	2	2	no	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	2	2	no	—
1251	C₂²⋊C₄	—	4	1	no	—
1252	C₂²⋊C₄	—	53	4	no	—
1253	C₂²⋊C₄	—	106	2	no	—
1254	C₂²⋊C₄	—	106	2	no	—
1255	C₂²⋊C₄	—	106	2	no	—
1256	C₂²⋊C₄	—	106	2	no	—
1257	C₂²⋊C₄	—	106	2	no	—
1258	C₂²⋊C₄	—	106	2	no	—
1259	C₂²⋊C₄	—	106	2	no	—
1260	C₂²⋊C₄	—	106	2	no	—
1261	C₂²⋊C₄	—	106	2	no	—
1262	C₂²⋊C₄	—	106	2	no	—
1263	C₂²⋊C₄	—	106	2	no	—
1264	C₂²⋊C₄	—	106	2	no	—
1265	C₂²⋊C₄	—	212	1	no	—
1266	C₂²⋊C₄	—	212	1	no	—
1267	C₂²⋊C₄	—	212	1	no	—
1268	C₂²⋊C₄	Q₈×D₅₃	1	4	yes	—
1269	C₄²	—	2	2	no	—
1270	C₄²	—	2	2	no	—
1271	C₄²	—	4	1	no	—
1272	C₄²	—	4	1	no	—
1273	C₄²	—	53	4	no	—
1274	C₄²	—	53	4	no	—
1275	C₄²	—	53	4	no	—
1276	C₄²	—	53	4	no	—
1277	C₄²	—	53	4	no	—
1278	C₄²	—	106	2	no	—
1279	C₄²	—	106	2	no	—
1280	C₄²	—	106	2	no	—
1281	C₄²	—	106	2	no	—
1282	C₄²	—	106	2	no	—
1283	C₄²	—	106	2	no	—
1284	C₄²	—	106	2	no	—
1285	C₄²	—	106	2	no	—
1286	C₄²	—	106	2	no	—
1287	C₄²	—	106	2	no	—
1288	C₄²	—	106	2	no	—
1289	C₄²	—	106	2	no	—
1290	C₄²	—	106	2	no	—
1291	C₄²	—	106	2	no	—
1292	C₄²	—	106	2	no	—
1293	C₄²	—	106	2	no	—
1294	C₄²	—	106	2	no	—
1295	C₄²	—	106	2	no	—
1296	C₄²	—	106	2	no	—
1297	C₄²	—	212	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	2	1	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	53	2	no	—
1305	C₂³	—	106	1	no	—
1306	C₂³	—	106	1	no	—
1307	C₂³	—	106	1	no	—
1308	C₂³	—	106	1	no	—
1309	C₂³	—	106	1	no	—
1310	C₂³	—	106	1	no	—
1311	C₂³	C₂×Q₈×D₅₃	1	2	yes	—
1312	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1313	Q₈	—	4	4	no	—
1314	Q₈	—	106	8	no	—
1315	Q₈	—	212	4	no	—
1316	Q₈	—	212	4	no	—
1317	Q₈	—	212	4	no	—
1318	Q₈	—	212	4	no	—
1319	Q₈	—	212	4	no	—
1320	D₄	—	106	8	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	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	4	4	no	—
1356	C₂×C₄	—	53	2	no	—
1357	C₂×C₄	—	53	2	no	—
1358	C₂×C₄	—	53	2	no	—
1359	C₂×C₄	—	53	2	no	—
1360	C₂×C₄	—	53	2	no	—
1361	C₂×C₄	—	53	2	no	—
1362	C₂×C₄	—	53	2	no	—
1363	C₂×C₄	—	53	2	no	—
1364	C₂×C₄	—	53	2	no	—
1365	C₂×C₄	—	53	2	no	—
1366	C₂×C₄	—	53	2	no	—
1367	C₂×C₄	—	53	2	no	—
1368	C₂×C₄	—	53	2	no	—
1369	C₂×C₄	—	53	2	no	—
1370	C₂×C₄	—	106	8	no	—
1371	C₂×C₄	—	106	8	no	—
1372	C₂×C₄	—	106	1	no	—
1373	C₂×C₄	—	106	1	no	—
1374	C₂×C₄	—	106	1	no	—
1375	C₂×C₄	—	106	1	no	—
1376	C₂×C₄	—	106	1	no	—
1377	C₂×C₄	—	106	1	no	—
1378	C₂×C₄	—	106	1	no	—
1379	C₂×C₄	—	106	1	no	—
1380	C₂×C₄	—	106	1	no	—
1381	C₂×C₄	—	106	1	no	—
1382	C₂×C₄	—	106	1	no	—
1383	C₂×C₄	—	106	1	no	—
1384	C₂×C₄	—	106	1	no	—
1385	C₂×C₄	—	106	1	no	—
1386	C₂×C₄	—	106	1	no	—
1387	C₂×C₄	—	106	1	no	—
1388	C₂×C₄	—	106	1	no	—
1389	C₂×C₄	—	106	1	no	—
1390	C₂×C₄	—	106	1	no	—
1391	C₂×C₄	—	106	1	no	—
1392	C₂×C₄	—	106	1	no	—
1393	C₂×C₄	—	106	1	no	—
1394	C₂×C₄	—	106	1	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	106	1	no	—
1397	C₂×C₄	—	106	1	no	—
1398	C₂×C₄	—	106	1	no	—
1399	C₂×C₄	—	106	1	no	—
1400	C₂×C₄	—	106	1	no	—
1401	C₂×C₄	—	106	1	no	—
1402	C₂×C₄	—	106	1	no	—
1403	C₂×C₄	—	212	4	no	—
1404	C₂×C₄	—	212	4	no	—
1405	C₂×C₄	—	212	4	no	—
1406	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1407	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1408	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1409	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1410	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1411	C₂×C₄	#41×D₅₃	1	2	yes	—
1412	C₂×C₄	#41×D₅₃	1	2	yes	—
1413	C₂×C₄	#41×D₅₃	1	2	yes	—
1414	C₂²	—	2	2	no	—
1415	C₂²	—	2	2	no	—
1416	C₂²	—	2	2	no	—
1417	C₂²	—	4	1	no	—
1418	C₂²	—	4	1	no	—
1419	C₂²	—	4	1	no	—
1420	C₂²	—	4	1	no	—
1421	C₂²	—	106	2	no	—
1422	C₂²	—	106	2	no	—
1423	C₂²	—	106	2	no	—
1424	C₂²	—	212	1	no	—
1425	C₂²	—	212	1	no	—
1426	C₂²	—	212	1	no	—
1427	C₂²	—	212	1	no	—
1428	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1429	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1430	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1431	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1432	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1433	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1434	C₂²	#16811458	1	1	yes	characteristic
1435	C₄	—	2	2	no	—
1436	C₄	—	2	2	no	—
1437	C₄	—	2	2	no	—
1438	C₄	—	2	2	no	—
1439	C₄	—	2	2	no	—
1440	C₄	—	2	2	no	—
1441	C₄	—	2	2	no	—
1442	C₄	—	2	2	no	—
1443	C₄	—	4	1	no	—
1444	C₄	—	4	1	no	—
1445	C₄	—	4	1	no	—
1446	C₄	—	4	1	no	—
1447	C₄	—	4	1	no	—
1448	C₄	—	4	1	no	—
1449	C₄	—	53	4	no	—
1450	C₄	—	53	4	no	—
1451	C₄	—	53	4	no	—
1452	C₄	—	106	2	no	—
1453	C₄	—	106	2	no	—
1454	C₄	—	106	2	no	—
1455	C₄	—	106	2	no	—
1456	C₄	—	106	2	no	—
1457	C₄	—	212	1	no	—
1458	C₄	—	212	1	no	—
1459	C₄	—	212	1	no	—
1460	C₄	—	212	1	no	—
1461	C₄	—	212	1	no	—
1462	C₄	—	212	1	no	—
1463	C₄	—	212	1	no	—
1464	C₂	—	4	2	no	—
1465	C₂	—	212	2	no	—
1466	C₂	#532×D₅₃	1	1	yes	characteristic
1467	C₂	#533×D₅₃	1	1	yes	characteristic
1468	C₂	#20288145	1	1	yes	characteristic
1469	C₂	D₄×Q₈×D₅₃	1	1	yes	characteristic
1470	C₂	#20288199	1	1	yes	characteristic
1471	C₂	#20288294	1	1	yes	characteristic
1472	C₂	#20288329	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2556	C₂
prime radical	C₂²×C₂²⋊D₅₃	C₂³
hypercenter	#2556	D₅₃
hypocenter	C₅₃	#34929
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2556

Complements

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

N	H ≅ G/N	type
1. C₂×#16811179	C₂	semidirect
2. C₂×#16811175	C₂	semidirect
3. #20279801	C₂	semidirect
4. #20279799	C₂	semidirect
5. #20279793	C₂	semidirect
6. #20279740	C₂	semidirect
7. #20279699	C₂	semidirect
10. #20279230	C₂	semidirect
11. #20279228	C₂	semidirect
12. #20279088	C₂	semidirect
13. #20279086	C₂	semidirect
16. #20278313	C₂	semidirect
17. #20278311	C₂	semidirect
18. #20277992	C₂	semidirect
19. #20277990	C₂	semidirect
20. #20277986	C₂	semidirect
21. #20277984	C₂	semidirect
22. #20277286	C₂	semidirect
23. #20277286	C₂	semidirect
24. #20277284	C₂	semidirect
25. #20277249	C₂	semidirect
26. #20277247	C₂	semidirect
29. C₄×#13133182	C₂	semidirect
31. C₅₃×#2556	C₂	semidirect
228. #13133182	D₄	semidirect
231. #13133177	Q₈	semidirect
726. Dic₅₃	#533	semidirect
733. #2556	D₅₃	semidirect
925. C₅₃	#34929	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811179	2
C₂×#16811175	2
#20279801	2
#20279799	2
#20279793	2
#20279740	2
#20279699	2
#20279663	2
#20279632	2
#20279230	2
#20279228	2
#20279088	2
#20279086	2
#20278564	2
#20278562	2
#20278313	2
#20278311	2
#20277992	2
#20277990	2
#20277986	2
#20277984	2
#20277286	2
#20277284	2
#20277249	2
#20277247	2
#20277175	2
C₄×#13133182	2
C₄×#13133177	2
C₅₃×#2556	2
#34929	53