Subgroups — #27554456

Order 13568.

1944 conjugacy classes of subgroups.

The subgroup lattice has 1398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20280174	C₂	1	1	yes	maximal, characteristic, complemented
2	#20280167	C₂	1	1	yes	maximal, characteristic, complemented
3	#20280146	C₂	1	1	yes	maximal, characteristic, complemented
4	#20280139	C₂	1	1	yes	maximal, characteristic, complemented
5	#20280120	C₂	1	1	yes	maximal, characteristic, complemented
6	#20280107	C₂	1	1	yes	maximal, characteristic, complemented
7	#20280089	C₂	1	1	yes	maximal, characteristic, complemented
8	#20280063	C₂	1	1	yes	maximal, characteristic
9	#20279992	C₂	1	1	yes	maximal, characteristic, complemented
10	#20279898	C₂	1	1	yes	maximal, characteristic
11	#20279794	C₂	1	1	yes	maximal, characteristic, complemented
12	#20279722	C₂	1	1	yes	maximal, characteristic, complemented
13	#20279219	C₂	1	1	yes	maximal, characteristic, complemented
14	#20278851	C₂	1	1	yes	maximal, characteristic, complemented
15	#20278542	C₂	1	1	yes	maximal, characteristic
16	#20278519	C₂	1	1	yes	maximal, characteristic
17	#20278009	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277991	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277991	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13133208	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13133197	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13133197	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277195	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277187	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277159	C₂	1	1	yes	maximal, characteristic
28	#20277156	C₂	1	1	yes	maximal, characteristic
29	C₄×#13133179	C₂	1	1	yes	maximal, characteristic
30	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2402	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133208	C₂²	1	1	yes	characteristic
33	C₂×#13133197	C₂²	1	1	yes	characteristic
34	C₂×#13133197	C₂²	1	1	yes	characteristic
35	C₂×#13133195	C₂²	1	1	yes	characteristic
36	C₂×#13133195	C₂²	1	1	yes	characteristic
37	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
38	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
39	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
41	C₂×#13133179	C₂²	1	1	yes	characteristic
42	C₂×#13133179	C₂²	1	1	yes	characteristic
43	C₂×#13133174	C₂²	1	1	yes	characteristic
44	C₂×#13133174	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
51	#16810564	C₂²	1	1	yes	characteristic
52	#16810564	C₂²	1	1	yes	characteristic
53	#16810558	C₂²	1	1	yes	characteristic
54	#16810558	C₂²	1	1	yes	characteristic
55	#16810557	C₂²	1	1	yes	characteristic
56	#16810557	C₂²	1	1	yes	characteristic
57	#16810557	C₂²	1	1	yes	characteristic
58	#16810557	C₂²	1	1	yes	characteristic
59	#16810556	C₂²	1	1	yes	characteristic
60	#16810556	C₂²	1	1	yes	characteristic
61	#16810554	C₂²	1	1	yes	characteristic
62	#16810554	C₂²	1	1	yes	characteristic
63	#16810547	C₂²	1	1	yes	characteristic
64	#16810547	C₂²	1	1	yes	characteristic
65	#16810545	C₂²	1	1	yes	characteristic
66	#16810545	C₂²	1	1	yes	characteristic
67	#16810544	C₂²	1	1	yes	characteristic
68	#16810544	C₂²	1	1	yes	characteristic
69	#16810543	C₂²	1	1	yes	characteristic
70	#16810543	C₂²	1	1	yes	characteristic
71	#16810543	C₂²	1	1	yes	characteristic
72	#16810543	C₂²	1	1	yes	characteristic
73	#16810536	C₂²	1	1	yes	characteristic
74	#16810536	C₂²	1	1	yes	characteristic
75	#16810528	C₂²	1	1	yes	characteristic
76	#16810528	C₂²	1	1	yes	characteristic
77	#16810527	C₂²	1	1	yes	characteristic
78	#16810527	C₂²	1	1	yes	characteristic
79	#16810527	C₂²	1	1	yes	characteristic
80	#16810527	C₂²	1	1	yes	characteristic
81	#16810522	C₂²	1	1	yes	characteristic
82	#16810522	C₂²	1	1	yes	characteristic
83	#16810522	C₂²	1	1	yes	characteristic
84	#16810520	C₂²	1	1	yes	characteristic
85	#16810520	C₂²	1	1	yes	characteristic
86	#16810520	C₂²	1	1	yes	characteristic
87	#16810520	C₂²	1	1	yes	characteristic
88	#16810519	C₂²	1	1	yes	characteristic
89	#16810518	C₂²	1	1	yes	characteristic
90	#16810518	C₂²	1	1	yes	characteristic
91	#16810518	C₂²	1	1	yes	characteristic
92	#16810518	C₂²	1	1	yes	characteristic
93	#16810515	C₂²	1	1	yes	characteristic
94	#16810515	C₂²	1	1	yes	characteristic
95	#16810513	C₂²	1	1	yes	characteristic
96	#16810513	C₂²	1	1	yes	characteristic
97	#16810510	C₂²	1	1	yes	characteristic
98	#16810510	C₂²	1	1	yes	characteristic
99	#16810510	C₂²	1	1	yes	characteristic
100	#16810510	C₂²	1	1	yes	characteristic
101	#16810509	C₂²	1	1	yes	characteristic
102	#16810509	C₂²	1	1	yes	characteristic
103	#16810508	C₂²	1	1	yes	characteristic
104	#16810508	C₂²	1	1	yes	characteristic
105	#16810508	C₂²	1	1	yes	characteristic
106	#16810508	C₂²	1	1	yes	characteristic
107	#16810508	C₂²	1	1	yes	characteristic
108	#16810508	C₂²	1	1	yes	characteristic
109	#16810506	C₂²	1	1	yes	characteristic
110	#16810506	C₂²	1	1	yes	characteristic
111	#16810506	C₂²	1	1	yes	characteristic
112	#16810506	C₂²	1	1	yes	characteristic
113	#16810506	C₂²	1	1	yes	characteristic
114	#16810506	C₂²	1	1	yes	characteristic
115	#16810505	C₂²	1	1	yes	characteristic
116	#16810505	C₂²	1	1	yes	characteristic
117	#16810501	C₂²	1	1	yes	characteristic
118	#16810501	C₂²	1	1	yes	characteristic
119	#16810501	C₂²	1	1	yes	characteristic
120	#16810501	C₂²	1	1	yes	characteristic
121	#16810497	C₂²	1	1	yes	characteristic
122	#16810497	C₂²	1	1	yes	characteristic
123	#16810497	C₂²	1	1	yes	characteristic
124	#16810497	C₂²	1	1	yes	characteristic
125	#16810497	C₂²	1	1	yes	characteristic
126	#16810497	C₂²	1	1	yes	characteristic
127	#16810497	C₂²	1	1	yes	characteristic
128	#16810497	C₂²	1	1	yes	characteristic
129	#16810497	C₂²	1	1	yes	characteristic
130	#16810497	C₂²	1	1	yes	characteristic
131	#16810494	C₂²	1	1	yes	characteristic
132	#16810494	C₂²	1	1	yes	characteristic
133	#16810494	C₂²	1	1	yes	characteristic
134	#16810494	C₂²	1	1	yes	characteristic
135	#16810494	C₂²	1	1	yes	characteristic
136	#16810494	C₂²	1	1	yes	characteristic
137	#16810488	C₂²	1	1	yes	characteristic
138	#16810482	C₂²	1	1	yes	characteristic
139	#16810482	C₂²	1	1	yes	characteristic
140	#16810480	C₂²	1	1	yes	characteristic
141	#16810480	C₂²	1	1	yes	characteristic
142	C₄⋊C₄×Dic₅₃	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×#11719919	C₂²	1	1	yes	characteristic
147	C₄×#11719919	C₂²	1	1	yes	characteristic
148	C₄×#11719919	C₂²	1	1	yes	characteristic
149	C₄×#11719919	C₂²	1	1	yes	characteristic
150	C₄×#11719919	C₂²	1	1	yes	characteristic
151	C₄×#11719919	C₂²	1	1	yes	characteristic
152	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
153	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
154	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
156	#16810474	C₂²	1	1	yes	characteristic
157	#16810474	C₂²	1	1	yes	characteristic
158	C₄×#11719921	C₂²	1	1	yes	characteristic
159	C₄×#11719921	C₂²	1	1	yes	characteristic
160	C₄×#11719921	C₂²	1	1	yes	characteristic
161	C₄×#11719921	C₂²	1	1	yes	characteristic
162	C₄×#11719921	C₂²	1	1	yes	characteristic
163	C₄×#11719921	C₂²	1	1	yes	characteristic
164	#16810470	C₂²	1	1	yes	characteristic
165	#16810470	C₂²	1	1	yes	characteristic
166	#16810470	C₂²	1	1	yes	characteristic
167	#16810470	C₂²	1	1	yes	characteristic
168	#16810469	C₂²	1	1	yes	characteristic
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₅₃×#400	C₂²	1	1	yes	characteristic
173	C₅₃×#400	C₂²	1	1	yes	characteristic
174	C₅₃×#400	C₂²	1	1	yes	characteristic
175	C₅₃×#400	C₂²	1	1	yes	characteristic
176	C₅₃×#398	C₂²	1	1	yes	characteristic
177	C₅₃×#398	C₂²	1	1	yes	characteristic
178	C₅₃×#398	C₂²	1	1	yes	characteristic
179	C₅₃×#398	C₂²	1	1	yes	characteristic
180	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₅₃×#376	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	#13133208	—	2	4	no	—
202	#13133197	—	2	4	no	—
203	#13133197	—	2	4	no	—
204	#13133195	—	2	4	no	—
205	#13133195	—	2	4	no	—
206	C₄×Dic₁₀₆	—	2	4	no	—
207	C₄×Dic₁₀₆	—	4	2	no	—
208	C₄×Dic₁₀₆	—	4	2	no	—
209	C₄×D₂₁₂	Q₈	1	8	yes	complemented
210	#13133179	—	2	4	no	—
211	#13133179	—	2	4	no	—
212	#13133174	—	2	4	no	—
213	#13133174	—	4	2	no	—
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×#11719919	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×D₅₃	—	2	4	no	—
249	C₄⋊C₄×D₅₃	—	2	4	no	—
250	C₂×#11719921	C₂³	1	1	yes	characteristic
251	C₂×#11719921	C₂³	1	1	yes	characteristic
252	C₂×#11719921	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₄²×D₅₃	—	2	4	no	—
287	C₄²×D₅₃	—	4	2	no	—
288	C₄²×D₅₃	—	4	2	no	—
289	C₄²×D₅₃	—	4	2	no	—
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×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×C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
362	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×D₂₁₂	—	2	2	no	—
393	C₂×D₂₁₂	—	2	2	no	—
394	C₂×D₂₁₂	C₂×Q₈	1	4	yes	—
395	C₂×C₄×D₅₃	—	2	2	no	—
396	C₂×C₄×D₅₃	—	2	2	no	—
397	C₂×C₄×D₅₃	—	2	2	no	—
398	C₂×C₄×D₅₃	—	2	2	no	—
399	C₂×C₄×D₅₃	—	2	2	no	—
400	C₂×C₄×D₅₃	—	2	2	no	—
401	C₂×C₄×D₅₃	—	2	2	no	—
402	C₂×C₄×D₅₃	—	2	2	no	—
403	C₂×C₄×D₅₃	—	2	2	no	—
404	C₂×C₄×D₅₃	—	2	2	no	—
405	C₂×C₄×D₅₃	—	2	2	no	—
406	C₂×C₄×D₅₃	—	2	2	no	—
407	C₂×C₄×D₅₃	—	2	2	no	—
408	C₂×C₄×D₅₃	—	2	2	no	—
409	C₂×C₄×D₅₃	—	2	2	no	—
410	C₂×C₄×D₅₃	—	2	2	no	—
411	C₂×C₄×D₅₃	—	2	2	no	—
412	C₂×C₄×D₅₃	—	4	1	no	—
413	C₂×C₄×D₅₃	—	4	1	no	—
414	C₂×C₄×D₅₃	—	4	1	no	—
415	C₂×C₄×D₅₃	—	4	1	no	—
416	C₂×C₄×D₅₃	—	4	1	no	—
417	C₂×C₄×D₅₃	—	4	1	no	—
418	C₂×C₄×D₅₃	—	4	1	no	—
419	C₂×C₄×D₅₃	—	4	1	no	—
420	C₂×C₄×D₅₃	—	4	1	no	—
421	C₂×C₄×D₅₃	—	4	1	no	—
422	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
423	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
424	C₂×C₄×D₅₃	#41	1	4	yes	—
425	C₂×Dic₁₀₆	—	2	2	no	—
426	C₂×Dic₁₀₆	—	2	2	no	—
427	C₂×Dic₁₀₆	—	2	2	no	—
428	C₂×Dic₁₀₆	—	2	2	no	—
429	C₂×Dic₁₀₆	—	2	2	no	—
430	C₂×Dic₁₀₆	—	4	1	no	—
431	C₂×Dic₁₀₆	—	4	1	no	—
432	C₂×Dic₁₀₆	—	4	1	no	—
433	C₂×Dic₁₀₆	—	4	1	no	—
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	—	2	2	no	—
448	C₄²×C₅₃	—	2	2	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	2	no	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	C₂×Q₈	1	4	yes	—
453	#11719921	—	2	2	no	—
454	#11719921	—	2	2	no	—
455	#11719921	—	2	2	no	—
456	#11719921	—	2	2	no	—
457	#11719921	—	2	2	no	—
458	#11719921	—	2	2	no	—
459	#11719921	—	2	2	no	—
460	#11719921	—	2	2	no	—
461	#11719921	—	2	2	no	—
462	#11719921	—	2	2	no	—
463	#11719921	—	2	2	no	—
464	#11719921	—	4	1	no	—
465	#11719921	—	4	1	no	—
466	#11719921	—	4	1	no	—
467	#11719921	—	4	1	no	—
468	#11719921	C₂×Q₈	1	4	yes	—
469	#11719921	C₂×Q₈	1	4	yes	—
470	#11719921	#41	1	4	yes	—
471	C₄⋊Dic₅₃	—	2	2	no	—
472	C₄⋊Dic₅₃	—	2	2	no	—
473	C₄⋊Dic₅₃	—	2	2	no	—
474	C₄⋊Dic₅₃	—	2	2	no	—
475	C₄⋊Dic₅₃	—	2	2	no	—
476	C₄⋊Dic₅₃	—	2	2	no	—
477	C₄⋊Dic₅₃	—	2	2	no	—
478	C₄⋊Dic₅₃	—	4	1	no	—
479	C₄⋊Dic₅₃	—	4	1	no	—
480	C₄⋊Dic₅₃	—	4	1	no	—
481	C₄⋊Dic₅₃	C₂×Q₈	1	4	yes	—
482	C₄⋊Dic₅₃	#41	1	4	yes	—
483	#11719919	—	2	2	no	—
484	#11719919	—	2	2	no	—
485	#11719919	—	2	2	no	—
486	#11719919	—	2	2	no	—
487	#11719919	—	2	2	no	—
488	#11719919	—	2	2	no	—
489	#11719919	—	2	2	no	—
490	#11719919	—	2	2	no	—
491	#11719919	—	2	2	no	—
492	#11719919	—	2	2	no	—
493	#11719919	—	2	2	no	—
494	#11719919	—	2	2	no	—
495	#11719919	—	2	2	no	—
496	#11719919	—	2	2	no	—
497	#11719919	—	4	1	no	—
498	#11719919	—	4	1	no	—
499	#11719919	—	4	1	no	—
500	#11719919	—	4	1	no	—
501	#11719919	—	4	1	no	—
502	#11719919	—	4	1	no	—
503	#11719919	—	4	1	no	—
504	#11719919	—	4	1	no	—
505	C₄×Dic₅₃	—	2	2	no	—
506	C₄×Dic₅₃	—	2	2	no	—
507	C₄×Dic₅₃	—	2	2	no	—
508	C₄×Dic₅₃	—	2	2	no	—
509	C₄×Dic₅₃	—	2	2	no	—
510	C₄×Dic₅₃	—	2	2	no	—
511	C₄×Dic₅₃	—	2	2	no	—
512	C₄×Dic₅₃	—	2	2	no	—
513	C₄×Dic₅₃	—	2	2	no	—
514	C₄×Dic₅₃	—	2	2	no	—
515	C₄×Dic₅₃	—	4	1	no	—
516	C₄×Dic₅₃	—	4	1	no	—
517	C₄×Dic₅₃	—	4	1	no	—
518	C₄×Dic₅₃	—	4	1	no	—
519	C₄×Dic₅₃	—	4	1	no	—
520	C₄×Dic₅₃	—	4	1	no	—
521	C₄×Dic₅₃	—	4	1	no	—
522	C₄×Dic₅₃	#41	1	4	yes	—
523	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
524	C₂²×D₅₃	—	2	1	no	—
525	C₂²×D₅₃	—	2	1	no	—
526	C₂²×D₅₃	—	2	1	no	—
527	C₂²×D₅₃	—	2	1	no	—
528	C₂²×D₅₃	—	2	1	no	—
529	C₂²×D₅₃	—	2	1	no	—
530	C₂²×D₅₃	—	2	1	no	—
531	C₂²×D₅₃	—	2	1	no	—
532	C₂²×D₅₃	—	2	1	no	—
533	C₂²×D₅₃	—	2	1	no	—
534	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
535	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
536	C₂²×D₅₃	C₂×#41	1	2	yes	—
537	C₂²×D₅₃	C₂×#41	1	2	yes	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
576	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
577	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
578	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
579	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
580	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
581	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
582	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
583	C₂×Dic₅₃	—	2	1	no	—
584	C₂×Dic₅₃	—	2	1	no	—
585	C₂×Dic₅₃	—	2	1	no	—
586	C₂×Dic₅₃	—	2	1	no	—
587	C₂×Dic₅₃	—	2	1	no	—
588	C₂×Dic₅₃	—	2	1	no	—
589	C₂×Dic₅₃	—	2	1	no	—
590	C₂×Dic₅₃	—	2	1	no	—
591	C₂×Dic₅₃	—	2	1	no	—
592	C₂×Dic₅₃	—	2	1	no	—
593	C₂×Dic₅₃	—	2	1	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	2	1	no	—
597	C₂×Dic₅₃	—	2	1	no	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	1	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	1	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
618	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
619	C₂×Dic₅₃	C₂×#41	1	2	yes	—
620	C₂×Dic₅₃	C₂×#41	1	2	yes	—
621	C₂×Dic₅₃	C₂×#41	1	2	yes	—
622	C₂×Dic₅₃	C₂×#41	1	2	yes	—
623	C₂×Dic₅₃	C₂×#41	1	2	yes	—
624	C₂×Dic₅₃	C₂×#41	1	2	yes	—
625	D₂₁₂	—	2	8	no	—
626	C₄×D₅₃	—	2	8	no	—
627	C₄×D₅₃	—	2	8	no	—
628	C₄×D₅₃	—	2	8	no	—
629	C₄×D₅₃	—	4	4	no	—
630	C₄×D₅₃	—	4	4	no	—
631	C₄×D₅₃	—	4	4	no	—
632	C₄×D₅₃	—	4	4	no	—
633	C₄×D₅₃	—	4	4	no	—
634	C₄×D₅₃	—	4	4	no	—
635	C₄×D₅₃	—	4	4	no	—
636	Dic₁₀₆	—	4	4	no	—
637	Dic₁₀₆	—	4	4	no	—
638	Dic₁₀₆	—	4	4	no	—
639	#34840	—	53	1	no	maximal, Sylow
640	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
641	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
642	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
643	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
644	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
645	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
646	C₂²×C₅₃	#585	1	1	yes	characteristic
647	C₂×D₅₃	—	2	2	no	—
648	C₂×D₅₃	—	2	2	no	—
649	C₂×D₅₃	—	2	2	no	—
650	C₂×D₅₃	—	2	2	no	—
651	C₂×D₅₃	—	2	2	no	—
652	C₂×D₅₃	—	2	2	no	—
653	C₂×D₅₃	—	2	2	no	—
654	C₂×D₅₃	—	2	2	no	—
655	C₂×D₅₃	—	2	2	no	—
656	C₂×D₅₃	—	4	1	no	—
657	C₂×D₅₃	—	4	1	no	—
658	C₂×D₅₃	—	4	1	no	—
659	C₂×D₅₃	—	4	1	no	—
660	C₂×D₅₃	#533	1	4	yes	—
661	C₄×C₅₃	—	2	2	no	—
662	C₄×C₅₃	—	2	2	no	—
663	C₄×C₅₃	—	2	2	no	—
664	C₄×C₅₃	—	2	2	no	—
665	C₄×C₅₃	—	2	2	no	—
666	C₄×C₅₃	—	4	1	no	—
667	C₄×C₅₃	—	4	1	no	—
668	C₄×C₅₃	—	4	1	no	—
669	C₄×C₅₃	—	4	1	no	—
670	C₄×C₅₃	—	4	1	no	—
671	C₄×C₅₃	—	4	1	no	—
672	C₄×C₅₃	—	4	1	no	—
673	C₄×C₅₃	—	4	1	no	—
674	C₄×C₅₃	—	4	1	no	—
675	C₄×C₅₃	#554	1	4	yes	—
676	Dic₅₃	—	2	2	no	—
677	Dic₅₃	—	2	2	no	—
678	Dic₅₃	—	2	2	no	—
679	Dic₅₃	—	2	2	no	—
680	Dic₅₃	—	2	2	no	—
681	Dic₅₃	—	2	2	no	—
682	Dic₅₃	—	2	2	no	—
683	Dic₅₃	—	2	2	no	—
684	Dic₅₃	—	4	1	no	—
685	Dic₅₃	—	4	1	no	—
686	Dic₅₃	—	4	1	no	—
687	Dic₅₃	—	4	1	no	—
688	Dic₅₃	—	4	1	no	—
689	Dic₅₃	—	4	1	no	—
690	#2590	—	53	1	no	—
691	#2589	—	53	1	no	—
692	#2588	—	53	1	no	—
693	#2587	—	53	1	no	—
694	#2586	—	53	1	no	—
695	#2585	—	53	1	no	—
696	#2583	—	53	1	no	—
697	#2579	—	53	1	no	—
698	#2574	—	53	1	no	—
699	#2564	—	53	1	no	—
700	#2556	—	53	1	no	—
701	#2549	—	53	1	no	—
702	#2505	—	53	1	no	—
703	#2473	—	53	1	no	—
704	#2450	—	53	1	no	—
705	#2449	—	53	1	no	—
706	#2402	D₅₃	1	1	yes	characteristic, complemented
707	#2399	—	53	1	no	—
708	#2396	—	53	1	no	—
709	#2396	—	53	1	no	—
710	C₄×#125	—	53	1	no	—
711	C₄×C₂²⋊Q₈	—	53	1	no	—
712	C₄×C₂²⋊Q₈	—	53	1	no	—
713	C₄×C₂²⋊Q₈	—	53	1	no	—
714	C₄×C₂²⋊Q₈	—	53	1	no	—
715	#2296	—	53	1	no	—
716	#2295	—	53	1	no	—
717	#2290	—	53	1	no	—
718	#2290	—	53	1	no	—
719	C₄²×D₄	—	53	1	no	—
720	C₂×C₄×C₄⋊C₄	—	53	1	no	—
721	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
722	C₂×C₅₃	#3444	1	1	yes	characteristic
723	C₂×C₅₃	#3459	1	1	yes	characteristic
724	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
725	C₂×C₅₃	#3475	1	1	yes	characteristic
726	C₂×C₅₃	Q₈×#41	1	1	yes	characteristic
727	C₂×C₅₃	#3481	1	1	yes	characteristic
728	D₅₃	—	2	4	no	—
729	D₅₃	—	4	2	no	—
730	C₂×#125	—	53	1	no	—
731	C₂×C₂²⋊Q₈	—	53	1	no	—
732	C₂×C₂²⋊Q₈	—	53	1	no	—
733	C₂×C₂²⋊Q₈	—	53	1	no	—
734	C₂×C₂²⋊Q₈	—	53	1	no	—
735	C₂×C₄×Q₈	—	53	1	no	—
736	C₂×C₄×Q₈	—	53	1	no	—
737	C₂×C₄×Q₈	—	53	1	no	—
738	C₂×C₄×D₄	—	53	1	no	—
739	C₂×C₄×D₄	—	53	1	no	—
740	C₂×C₄×D₄	—	53	1	no	—
741	C₂×#117	—	53	1	no	—
742	C₂×#117	—	53	1	no	—
743	C₂²×C₄⋊C₄	—	53	1	no	—
744	C₂²×C₄⋊C₄	—	53	1	no	—
745	C₂²×C₄²	—	53	1	no	—
746	C₂²×C₄²	—	53	1	no	—
747	C₂²×C₄²	—	53	1	no	—
748	C₂²×C₄²	—	53	1	no	—
749	#400	—	53	1	no	—
750	#400	—	53	1	no	—
751	#400	C₂×D₅₃	1	1	yes	characteristic
752	#400	C₂×D₅₃	1	1	yes	characteristic
753	#400	C₂×D₅₃	1	1	yes	characteristic
754	#400	C₂×D₅₃	1	1	yes	characteristic
755	#399	—	53	1	no	—
756	#399	—	53	1	no	—
757	#398	—	53	1	no	—
758	#398	—	53	1	no	—
759	#398	—	53	1	no	—
760	#398	—	53	1	no	—
761	#398	—	53	1	no	—
762	#398	—	53	1	no	—
763	#398	—	53	1	no	—
764	#398	—	53	1	no	—
765	#398	C₂×D₅₃	1	1	yes	characteristic
766	#398	C₂×D₅₃	1	1	yes	characteristic
767	#398	C₂×D₅₃	1	1	yes	characteristic
768	#398	C₂×D₅₃	1	1	yes	characteristic
769	#396	—	53	1	no	—
770	#396	—	53	1	no	—
771	#396	—	53	1	no	—
772	#396	—	53	1	no	—
773	#395	—	53	1	no	—
774	#395	—	53	1	no	—
775	#395	—	53	1	no	—
776	#395	—	53	1	no	—
777	#395	—	53	1	no	—
778	#395	—	53	1	no	—
779	#393	—	53	1	no	—
780	#393	—	53	1	no	—
781	#391	—	53	1	no	—
782	#391	—	53	1	no	—
783	#391	—	53	1	no	—
784	#391	—	53	1	no	—
785	#391	—	53	1	no	—
786	#391	—	53	1	no	—
787	#389	—	53	1	no	—
788	#389	—	53	1	no	—
789	#389	—	53	1	no	—
790	#389	—	53	1	no	—
791	#389	—	53	1	no	—
792	#389	—	53	1	no	—
793	#389	—	53	1	no	—
794	#389	—	53	1	no	—
795	#389	—	53	1	no	—
796	#389	—	53	1	no	—
797	#389	—	53	1	no	—
798	#389	—	53	1	no	—
799	#388	—	53	1	no	—
800	#388	—	53	1	no	—
801	#388	—	53	1	no	—
802	#388	—	53	1	no	—
803	#387	—	53	1	no	—
804	#387	—	53	1	no	—
805	#387	—	53	1	no	—
806	#387	—	53	1	no	—
807	#387	—	53	1	no	—
808	#387	—	53	1	no	—
809	#387	—	53	1	no	—
810	#387	—	53	1	no	—
811	#387	—	53	1	no	—
812	#387	—	53	1	no	—
813	#387	—	53	1	no	—
814	#387	—	53	1	no	—
815	#387	—	53	1	no	—
816	#387	—	53	1	no	—
817	#387	—	53	1	no	—
818	#387	—	53	1	no	—
819	#387	—	53	1	no	—
820	#387	—	53	1	no	—
821	#387	—	53	1	no	—
822	#387	—	53	1	no	—
823	#386	—	53	1	no	—
824	#386	—	53	1	no	—
825	#386	—	53	1	no	—
826	#386	—	53	1	no	—
827	#385	—	53	1	no	—
828	#385	—	53	1	no	—
829	#385	—	53	1	no	—
830	#385	—	53	1	no	—
831	#385	—	53	1	no	—
832	#385	—	53	1	no	—
833	#385	—	53	1	no	—
834	#385	—	53	1	no	—
835	#385	—	53	1	no	—
836	#385	—	53	1	no	—
837	#385	—	53	1	no	—
838	#385	—	53	1	no	—
839	#385	—	53	1	no	—
840	#385	—	53	1	no	—
841	#385	—	53	1	no	—
842	#385	—	53	1	no	—
843	#382	—	53	1	no	—
844	#380	—	53	1	no	—
845	#380	—	53	1	no	—
846	#380	—	53	1	no	—
847	#380	—	53	1	no	—
848	C₄×C₄⋊C₄	—	53	1	no	—
849	C₄×C₄⋊C₄	—	53	1	no	—
850	C₄×C₄⋊C₄	—	53	1	no	—
851	C₄×C₄⋊C₄	—	53	1	no	—
852	C₄×C₄⋊C₄	—	53	1	no	—
853	C₄×C₄⋊C₄	—	53	1	no	—
854	C₄×C₄⋊C₄	—	53	1	no	—
855	C₄×C₄⋊C₄	—	53	1	no	—
856	C₄×C₄⋊C₄	—	53	1	no	—
857	C₄×C₄⋊C₄	—	53	1	no	—
858	C₄×C₄⋊C₄	—	53	1	no	—
859	C₄×C₄⋊C₄	—	53	1	no	—
860	C₄×C₄⋊C₄	—	53	1	no	—
861	C₄×C₄⋊C₄	—	53	1	no	—
862	C₄×C₄⋊C₄	—	53	1	no	—
863	C₄×C₄⋊C₄	—	53	1	no	—
864	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
865	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
866	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
867	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
868	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
869	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
870	C₄×C₂²⋊C₄	—	53	1	no	—
871	C₄×C₂²⋊C₄	—	53	1	no	—
872	C₄×C₂²⋊C₄	—	53	1	no	—
873	C₄×C₂²⋊C₄	—	53	1	no	—
874	C₄×C₂²⋊C₄	—	53	1	no	—
875	C₄×C₂²⋊C₄	—	53	1	no	—
876	C₄×C₂²⋊C₄	—	53	1	no	—
877	C₄×C₂²⋊C₄	—	53	1	no	—
878	C₄×C₂²⋊C₄	—	53	1	no	—
879	C₄×C₂²⋊C₄	—	53	1	no	—
880	#376	—	53	1	no	—
881	#376	C₂×D₅₃	1	1	yes	characteristic
882	C₂×#95	—	53	1	no	—
883	C₂×#95	—	53	1	no	—
884	C₄³	—	53	1	no	—
885	C₅₃	#34840	1	1	yes	characteristic, complemented, Sylow
886	C₂²×Q₈	—	53	1	no	—
887	C₂²×Q₈	—	53	1	no	—
888	C₂²×Q₈	—	53	1	no	—
889	C₂²×D₄	—	53	1	no	—
890	C₂³×C₄	—	53	1	no	—
891	C₂³×C₄	—	53	1	no	—
892	C₂³×C₄	—	53	1	no	—
893	C₂³×C₄	—	53	1	no	—
894	C₂³×C₄	—	53	1	no	—
895	C₂³×C₄	—	53	1	no	—
896	C₂³×C₄	—	53	1	no	—
897	C₂³×C₄	—	53	1	no	—
898	C₂³×C₄	—	53	1	no	—
899	C₂³×C₄	—	53	1	no	—
900	#125	—	106	4	no	—
901	C₂²⋊Q₈	—	106	4	no	—
902	C₂²⋊Q₈	—	106	4	no	—
903	C₂²⋊Q₈	—	106	4	no	—
904	C₂²⋊Q₈	—	106	4	no	—
905	C₄×Q₈	—	106	4	no	—
906	C₄×Q₈	—	212	2	no	—
907	C₄×Q₈	—	212	2	no	—
908	C₄×D₄	—	53	8	no	—
909	C₄×D₄	—	106	4	no	—
910	C₄×D₄	—	106	4	no	—
911	#117	—	106	4	no	—
912	#117	—	212	2	no	—
913	C₂×C₄⋊C₄	—	53	1	no	—
914	C₂×C₄⋊C₄	—	53	1	no	—
915	C₂×C₄⋊C₄	—	53	1	no	—
916	C₂×C₄⋊C₄	—	53	1	no	—
917	C₂×C₄⋊C₄	—	53	1	no	—
918	C₂×C₄⋊C₄	—	53	1	no	—
919	C₂×C₄⋊C₄	—	53	1	no	—
920	C₂×C₄⋊C₄	—	53	1	no	—
921	C₂×C₄⋊C₄	—	53	1	no	—
922	C₂×C₄⋊C₄	—	53	1	no	—
923	C₂×C₄⋊C₄	—	53	1	no	—
924	C₂×C₄⋊C₄	—	53	1	no	—
925	C₂×C₄⋊C₄	—	53	1	no	—
926	C₂×C₄⋊C₄	—	53	1	no	—
927	C₂×C₄⋊C₄	—	53	1	no	—
928	C₂×C₄⋊C₄	—	53	1	no	—
929	C₂×C₄⋊C₄	—	53	1	no	—
930	C₂×C₄⋊C₄	—	53	1	no	—
931	C₂×C₄⋊C₄	—	53	1	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	1	no	—
936	C₂×C₄⋊C₄	—	53	1	no	—
937	C₂×C₄⋊C₄	—	53	1	no	—
938	C₂×C₄⋊C₄	—	53	1	no	—
939	C₂×C₄⋊C₄	—	53	1	no	—
940	C₂×C₄⋊C₄	—	53	1	no	—
941	C₂×C₄⋊C₄	—	53	1	no	—
942	C₂×C₄⋊C₄	—	53	1	no	—
943	C₂×C₄⋊C₄	—	53	1	no	—
944	C₂×C₄⋊C₄	—	53	1	no	—
945	C₂×C₄⋊C₄	—	53	1	no	—
946	C₂×C₄⋊C₄	—	53	1	no	—
947	C₂×C₄⋊C₄	—	106	4	no	—
948	C₂×C₄⋊C₄	—	106	4	no	—
949	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
961	C₂×C₂²⋊C₄	—	53	1	no	—
962	C₂×C₂²⋊C₄	—	53	1	no	—
963	C₂×C₂²⋊C₄	—	53	1	no	—
964	C₂×C₂²⋊C₄	—	53	1	no	—
965	C₂×C₂²⋊C₄	—	53	1	no	—
966	C₂×C₂²⋊C₄	—	53	1	no	—
967	C₂×C₂²⋊C₄	—	53	1	no	—
968	C₂×C₂²⋊C₄	—	53	1	no	—
969	C₂×C₂²⋊C₄	—	53	1	no	—
970	C₂×C₂²⋊C₄	—	53	1	no	—
971	C₂×C₂²⋊C₄	—	53	1	no	—
972	C₂×C₂²⋊C₄	—	53	1	no	—
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	no	—
975	C₂×C₂²⋊C₄	—	53	1	no	—
976	C₂×C₂²⋊C₄	—	53	1	no	—
977	C₂×C₂²⋊C₄	—	53	1	no	—
978	C₂×C₂²⋊C₄	—	53	1	no	—
979	C₂×C₄²	—	53	1	no	—
980	C₂×C₄²	—	53	1	no	—
981	C₂×C₄²	—	53	1	no	—
982	C₂×C₄²	—	53	1	no	—
983	C₂×C₄²	—	53	1	no	—
984	C₂×C₄²	—	53	1	no	—
985	C₂×C₄²	—	53	1	no	—
986	C₂×C₄²	—	53	1	no	—
987	C₂×C₄²	—	53	1	no	—
988	C₂×C₄²	—	53	1	no	—
989	C₂×C₄²	—	53	1	no	—
990	C₂×C₄²	—	53	1	no	—
991	C₂×C₄²	—	53	1	no	—
992	C₂×C₄²	—	53	1	no	—
993	C₂×C₄²	—	53	1	no	—
994	C₂×C₄²	—	53	1	no	—
995	C₂×C₄²	—	53	1	no	—
996	C₂×C₄²	—	53	1	no	—
997	C₂×C₄²	—	106	4	no	—
998	C₂×C₄²	—	212	2	no	—
999	C₂×C₄²	—	212	2	no	—
1000	C₂×C₄²	—	212	2	no	—
1001	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1002	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1003	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1004	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1005	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1006	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1007	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1008	#95	—	53	1	no	—
1009	#95	—	53	1	no	—
1010	#95	—	53	1	no	—
1011	#95	—	53	1	no	—
1012	#95	—	53	1	no	—
1013	#95	—	53	1	no	—
1014	#95	—	53	1	no	—
1015	#95	—	53	1	no	—
1016	#95	—	53	1	no	—
1017	#95	—	53	1	no	—
1018	#95	—	53	1	no	—
1019	#95	—	53	1	no	—
1020	#95	—	53	1	no	—
1021	#95	—	53	1	no	—
1022	#95	—	53	1	no	—
1023	#95	—	53	1	no	—
1024	#95	—	53	1	no	—
1025	#95	—	53	1	no	—
1026	#95	—	53	1	no	—
1027	#95	—	53	1	no	—
1028	#95	—	53	1	no	—
1029	#95	—	53	1	no	—
1030	#95	—	53	1	no	—
1031	#95	—	53	1	no	—
1032	#95	—	53	1	no	—
1033	#95	—	53	1	no	—
1034	#95	—	53	1	no	—
1035	#95	—	53	1	no	—
1036	#95	—	53	1	no	—
1037	#95	—	53	1	no	—
1038	#95	—	53	1	no	—
1039	#95	—	53	1	no	—
1040	#95	—	53	1	no	—
1041	#95	—	53	1	no	—
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	C₂²×D₅₃	1	1	yes	characteristic
1045	#95	C₂²×D₅₃	1	1	yes	characteristic
1046	#95	C₂²×D₅₃	1	1	yes	characteristic
1047	#95	C₂²×D₅₃	1	1	yes	characteristic
1048	#95	C₂²×D₅₃	1	1	yes	characteristic
1049	#95	C₂²×D₅₃	1	1	yes	characteristic
1050	#95	C₂²×D₅₃	1	1	yes	characteristic
1051	#95	C₂²×D₅₃	1	1	yes	characteristic
1052	#95	C₂²×D₅₃	1	1	yes	characteristic
1053	#95	C₂²×D₅₃	1	1	yes	characteristic
1054	#95	C₂²×D₅₃	1	1	yes	characteristic
1055	#95	C₂²×D₅₃	1	1	yes	characteristic
1056	#95	C₂²×D₅₃	1	1	yes	characteristic
1057	#95	C₂²×D₅₃	1	1	yes	characteristic
1058	#95	C₂²×D₅₃	1	1	yes	characteristic
1059	#95	C₂²×D₅₃	1	1	yes	characteristic
1060	C₂⁴	—	53	1	no	—
1061	C₂⁴	—	53	1	no	—
1062	C₂×Q₈	—	106	2	no	—
1063	C₂×Q₈	—	106	2	no	—
1064	C₂×Q₈	—	106	2	no	—
1065	C₂×Q₈	—	106	2	no	—
1066	C₂×Q₈	—	106	2	no	—
1067	C₂×Q₈	—	212	1	no	—
1068	C₂×Q₈	—	212	1	no	—
1069	C₂×Q₈	—	212	1	no	—
1070	C₂×Q₈	—	212	1	no	—
1071	C₂×D₄	—	53	4	no	—
1072	C₂×D₄	—	106	2	no	—
1073	C₂×D₄	—	106	2	no	—
1074	C₂²×C₄	—	53	1	no	—
1075	C₂²×C₄	—	53	1	no	—
1076	C₂²×C₄	—	53	1	no	—
1077	C₂²×C₄	—	53	1	no	—
1078	C₂²×C₄	—	53	1	no	—
1079	C₂²×C₄	—	53	1	no	—
1080	C₂²×C₄	—	53	1	no	—
1081	C₂²×C₄	—	53	1	no	—
1082	C₂²×C₄	—	53	4	no	—
1083	C₂²×C₄	—	53	4	no	—
1084	C₂²×C₄	—	53	4	no	—
1085	C₂²×C₄	—	53	1	no	—
1086	C₂²×C₄	—	53	1	no	—
1087	C₂²×C₄	—	53	1	no	—
1088	C₂²×C₄	—	53	1	no	—
1089	C₂²×C₄	—	53	1	no	—
1090	C₂²×C₄	—	53	1	no	—
1091	C₂²×C₄	—	106	2	no	—
1092	C₂²×C₄	—	106	2	no	—
1093	C₂²×C₄	—	106	2	no	—
1094	C₂²×C₄	—	106	2	no	—
1095	C₂²×C₄	—	106	2	no	—
1096	C₂²×C₄	—	106	2	no	—
1097	C₂²×C₄	—	106	2	no	—
1098	C₂²×C₄	—	106	2	no	—
1099	C₂²×C₄	—	106	2	no	—
1100	C₂²×C₄	—	106	2	no	—
1101	C₂²×C₄	—	106	2	no	—
1102	C₂²×C₄	—	106	2	no	—
1103	C₂²×C₄	—	106	2	no	—
1104	C₂²×C₄	—	106	2	no	—
1105	C₂²×C₄	—	106	2	no	—
1106	C₂²×C₄	—	106	2	no	—
1107	C₂²×C₄	—	106	2	no	—
1108	C₂²×C₄	—	212	1	no	—
1109	C₂²×C₄	—	212	1	no	—
1110	C₂²×C₄	—	212	1	no	—
1111	C₂²×C₄	—	212	1	no	—
1112	C₂²×C₄	—	212	1	no	—
1113	C₂²×C₄	—	212	1	no	—
1114	C₂²×C₄	—	212	1	no	—
1115	C₂²×C₄	—	212	1	no	—
1116	C₂²×C₄	—	212	1	no	—
1117	C₂²×C₄	—	212	1	no	—
1118	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1119	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1120	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1123	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1129	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1133	C₄⋊C₄	—	2	2	no	—
1134	C₄⋊C₄	—	2	2	no	—
1135	C₄⋊C₄	—	2	2	no	—
1136	C₄⋊C₄	—	2	2	no	—
1137	C₄⋊C₄	—	2	2	no	—
1138	C₄⋊C₄	—	2	2	no	—
1139	C₄⋊C₄	—	2	2	no	—
1140	C₄⋊C₄	—	2	2	no	—
1141	C₄⋊C₄	—	2	2	no	—
1142	C₄⋊C₄	—	4	1	no	—
1143	C₄⋊C₄	—	4	1	no	—
1144	C₄⋊C₄	—	4	1	no	—
1145	C₄⋊C₄	—	53	4	no	—
1146	C₄⋊C₄	—	53	4	no	—
1147	C₄⋊C₄	—	106	2	no	—
1148	C₄⋊C₄	—	106	2	no	—
1149	C₄⋊C₄	—	106	2	no	—
1150	C₄⋊C₄	—	106	2	no	—
1151	C₄⋊C₄	—	106	2	no	—
1152	C₄⋊C₄	—	106	2	no	—
1153	C₄⋊C₄	—	106	2	no	—
1154	C₄⋊C₄	—	106	2	no	—
1155	C₄⋊C₄	—	106	2	no	—
1156	C₄⋊C₄	—	106	2	no	—
1157	C₄⋊C₄	—	106	2	no	—
1158	C₄⋊C₄	—	106	2	no	—
1159	C₄⋊C₄	—	106	2	no	—
1160	C₄⋊C₄	—	106	2	no	—
1161	C₄⋊C₄	—	106	2	no	—
1162	C₄⋊C₄	—	106	2	no	—
1163	C₄⋊C₄	—	106	2	no	—
1164	C₄⋊C₄	—	106	2	no	—
1165	C₄⋊C₄	—	106	2	no	—
1166	C₄⋊C₄	—	106	2	no	—
1167	C₄⋊C₄	—	106	2	no	—
1168	C₄⋊C₄	—	212	1	no	—
1169	C₄⋊C₄	—	212	1	no	—
1170	C₄⋊C₄	—	212	1	no	—
1171	C₄⋊C₄	—	212	1	no	—
1172	C₄⋊C₄	—	212	1	no	—
1173	C₄⋊C₄	—	212	1	no	—
1174	C₄⋊C₄	—	212	1	no	—
1175	C₄⋊C₄	—	212	1	no	—
1176	C₄⋊C₄	—	212	1	no	—
1177	C₄⋊C₄	—	212	1	no	—
1178	C₄⋊C₄	—	212	1	no	—
1179	C₂²⋊C₄	—	53	4	no	—
1180	C₂²⋊C₄	—	53	4	no	—
1181	C₂²⋊C₄	—	53	4	no	—
1182	C₂²⋊C₄	—	106	2	no	—
1183	C₂²⋊C₄	—	106	2	no	—
1184	C₂²⋊C₄	—	106	2	no	—
1185	C₂²⋊C₄	—	106	2	no	—
1186	C₂²⋊C₄	—	106	2	no	—
1187	C₂²⋊C₄	—	106	2	no	—
1188	C₂²⋊C₄	—	106	2	no	—
1189	C₂²⋊C₄	—	106	2	no	—
1190	C₂²⋊C₄	—	106	2	no	—
1191	C₂²⋊C₄	—	106	2	no	—
1192	C₂²⋊C₄	—	106	2	no	—
1193	C₂²⋊C₄	—	212	1	no	—
1194	C₂²⋊C₄	—	212	1	no	—
1195	C₂²⋊C₄	—	212	1	no	—
1196	C₂²⋊C₄	—	212	1	no	—
1197	C₄²	—	2	2	no	—
1198	C₄²	—	2	2	no	—
1199	C₄²	—	2	2	no	—
1200	C₄²	—	2	2	no	—
1201	C₄²	—	2	2	no	—
1202	C₄²	—	2	2	no	—
1203	C₄²	—	53	4	no	—
1204	C₄²	—	106	2	no	—
1205	C₄²	—	106	2	no	—
1206	C₄²	—	106	2	no	—
1207	C₄²	—	106	2	no	—
1208	C₄²	—	106	2	no	—
1209	C₄²	—	106	2	no	—
1210	C₄²	—	106	2	no	—
1211	C₄²	—	106	2	no	—
1212	C₄²	—	106	2	no	—
1213	C₄²	—	106	2	no	—
1214	C₄²	—	212	1	no	—
1215	C₄²	—	212	1	no	—
1216	C₄²	—	212	1	no	—
1217	C₄²	—	212	1	no	—
1218	C₄²	—	212	1	no	—
1219	C₄²	—	212	1	no	—
1220	C₄²	—	212	1	no	—
1221	C₄²	Q₈×D₅₃	1	4	yes	—
1222	C₂³	—	53	2	no	—
1223	C₂³	—	53	2	no	—
1224	C₂³	—	53	2	no	—
1225	C₂³	—	53	2	no	—
1226	C₂³	—	106	1	no	—
1227	C₂³	—	106	1	no	—
1228	C₂³	—	106	1	no	—
1229	C₂³	—	106	1	no	—
1230	C₂³	—	106	1	no	—
1231	C₂³	—	106	1	no	—
1232	C₂³	—	106	1	no	—
1233	C₂³	—	106	1	no	—
1234	C₂³	—	106	1	no	—
1235	C₂³	—	106	1	no	—
1236	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1237	Q₈	—	212	4	no	—
1238	Q₈	—	212	4	no	—
1239	Q₈	—	212	4	no	—
1240	D₄	—	106	8	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	2	1	no	—
1252	C₂×C₄	—	2	1	no	—
1253	C₂×C₄	—	2	1	no	—
1254	C₂×C₄	—	2	1	no	—
1255	C₂×C₄	—	2	1	no	—
1256	C₂×C₄	—	2	1	no	—
1257	C₂×C₄	—	2	1	no	—
1258	C₂×C₄	—	2	1	no	—
1259	C₂×C₄	—	2	1	no	—
1260	C₂×C₄	—	2	1	no	—
1261	C₂×C₄	—	2	1	no	—
1262	C₂×C₄	—	2	1	no	—
1263	C₂×C₄	—	2	1	no	—
1264	C₂×C₄	—	2	1	no	—
1265	C₂×C₄	—	2	1	no	—
1266	C₂×C₄	—	2	1	no	—
1267	C₂×C₄	—	2	1	no	—
1268	C₂×C₄	—	2	1	no	—
1269	C₂×C₄	—	2	1	no	—
1270	C₂×C₄	—	2	1	no	—
1271	C₂×C₄	—	2	1	no	—
1272	C₂×C₄	—	2	1	no	—
1273	C₂×C₄	—	2	1	no	—
1274	C₂×C₄	—	2	1	no	—
1275	C₂×C₄	—	2	1	no	—
1276	C₂×C₄	—	2	1	no	—
1277	C₂×C₄	—	2	1	no	—
1278	C₂×C₄	—	53	2	no	—
1279	C₂×C₄	—	53	2	no	—
1280	C₂×C₄	—	53	2	no	—
1281	C₂×C₄	—	53	2	no	—
1282	C₂×C₄	—	53	2	no	—
1283	C₂×C₄	—	53	2	no	—
1284	C₂×C₄	—	53	2	no	—
1285	C₂×C₄	—	53	2	no	—
1286	C₂×C₄	—	106	8	no	—
1287	C₂×C₄	—	106	1	no	—
1288	C₂×C₄	—	106	1	no	—
1289	C₂×C₄	—	106	1	no	—
1290	C₂×C₄	—	106	1	no	—
1291	C₂×C₄	—	106	1	no	—
1292	C₂×C₄	—	106	1	no	—
1293	C₂×C₄	—	106	1	no	—
1294	C₂×C₄	—	106	1	no	—
1295	C₂×C₄	—	106	1	no	—
1296	C₂×C₄	—	106	1	no	—
1297	C₂×C₄	—	106	1	no	—
1298	C₂×C₄	—	106	1	no	—
1299	C₂×C₄	—	106	1	no	—
1300	C₂×C₄	—	106	1	no	—
1301	C₂×C₄	—	106	1	no	—
1302	C₂×C₄	—	106	1	no	—
1303	C₂×C₄	—	106	8	no	—
1304	C₂×C₄	—	106	8	no	—
1305	C₂×C₄	—	106	1	no	—
1306	C₂×C₄	—	106	1	no	—
1307	C₂×C₄	—	106	1	no	—
1308	C₂×C₄	—	106	1	no	—
1309	C₂×C₄	—	106	1	no	—
1310	C₂×C₄	—	106	1	no	—
1311	C₂×C₄	—	106	1	no	—
1312	C₂×C₄	—	106	1	no	—
1313	C₂×C₄	—	106	1	no	—
1314	C₂×C₄	—	106	1	no	—
1315	C₂×C₄	—	106	1	no	—
1316	C₂×C₄	—	106	1	no	—
1317	C₂×C₄	—	106	1	no	—
1318	C₂×C₄	—	106	1	no	—
1319	C₂×C₄	—	106	1	no	—
1320	C₂×C₄	—	106	1	no	—
1321	C₂×C₄	—	106	1	no	—
1322	C₂×C₄	—	106	1	no	—
1323	C₂×C₄	—	212	4	no	—
1324	C₂×C₄	—	212	4	no	—
1325	C₂×C₄	—	212	4	no	—
1326	C₂×C₄	—	212	4	no	—
1327	C₂×C₄	—	212	4	no	—
1328	C₂×C₄	—	212	4	no	—
1329	C₂×C₄	—	212	4	no	—
1330	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1331	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1332	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1333	C₂×C₄	#41×D₅₃	1	2	yes	—
1334	C₂×C₄	#41×D₅₃	1	2	yes	—
1335	C₂×C₄	#41×D₅₃	1	2	yes	—
1336	C₂×C₄	#41×D₅₃	1	2	yes	—
1337	C₂×C₄	#13133263	1	2	yes	—
1338	C₂²	—	53	4	no	—
1339	C₂²	—	106	2	no	—
1340	C₂²	—	106	2	no	—
1341	C₂²	—	106	2	no	—
1342	C₂²	—	106	2	no	—
1343	C₂²	—	106	2	no	—
1344	C₂²	—	106	2	no	—
1345	C₂²	—	106	2	no	—
1346	C₂²	—	106	2	no	—
1347	C₂²	—	106	2	no	—
1348	C₂²	—	212	1	no	—
1349	C₂²	—	212	1	no	—
1350	C₂²	—	212	1	no	—
1351	C₂²	—	212	1	no	—
1352	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1353	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1354	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1355	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1356	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1357	C₂²	C₂×#13133263	1	1	yes	characteristic
1358	C₂²	#16811459	1	1	yes	characteristic
1359	C₄	—	2	2	no	—
1360	C₄	—	2	2	no	—
1361	C₄	—	2	2	no	—
1362	C₄	—	2	2	no	—
1363	C₄	—	2	2	no	—
1364	C₄	—	4	1	no	—
1365	C₄	—	4	1	no	—
1366	C₄	—	4	1	no	—
1367	C₄	—	4	1	no	—
1368	C₄	—	4	1	no	—
1369	C₄	—	4	1	no	—
1370	C₄	—	4	1	no	—
1371	C₄	—	4	1	no	—
1372	C₄	—	4	1	no	—
1373	C₄	—	106	2	no	—
1374	C₄	—	106	2	no	—
1375	C₄	—	106	2	no	—
1376	C₄	—	106	2	no	—
1377	C₄	—	106	2	no	—
1378	C₄	—	106	2	no	—
1379	C₄	—	106	2	no	—
1380	C₄	—	106	2	no	—
1381	C₄	—	212	1	no	—
1382	C₄	—	212	1	no	—
1383	C₄	—	212	1	no	—
1384	C₄	—	212	1	no	—
1385	C₄	—	212	1	no	—
1386	C₄	—	212	1	no	—
1387	C₄	#16811329	1	4	yes	—
1388	C₂	—	106	4	no	—
1389	C₂	—	212	2	no	—
1390	C₂	#533×D₅₃	1	1	yes	characteristic
1391	C₂	#20288009	1	1	yes	characteristic
1392	C₂	#20288125	1	1	yes	characteristic
1393	C₂	C₂×#16811329	1	1	yes	characteristic
1394	C₂	#20288271	1	1	yes	characteristic
1395	C₂	#20288293	1	1	yes	characteristic
1396	C₂	#20288321	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Frattini	C₂³	C₂⁴×D₅₃
Fitting	C₅₃×#2402	C₂
prime radical	C₂²×D₂₁₂	C₂³
hypercenter	#2402	D₅₃
hypocenter	C₅₃	#34840
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ #2402

Complements

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

N	H ≅ G/N	type
1. #20280174	C₂	semidirect
2. #20280167	C₂	semidirect
3. #20280146	C₂	semidirect
4. #20280139	C₂	semidirect
5. #20280120	C₂	semidirect
6. #20280107	C₂	semidirect
7. #20280089	C₂	semidirect
9. #20279992	C₂	semidirect
11. #20279794	C₂	semidirect
12. #20279722	C₂	semidirect
13. #20279219	C₂	semidirect
14. #20278851	C₂	semidirect
17. #20278009	C₂	semidirect
18. #20277991	C₂	semidirect
19. #20277991	C₂	semidirect
20. C₄×#13133208	C₂	semidirect
21. C₄×#13133197	C₂	semidirect
22. C₄×#13133197	C₂	semidirect
23. C₄×#13133195	C₂	semidirect
24. C₄×#13133195	C₂	semidirect
25. #20277195	C₂	semidirect
26. #20277187	C₂	semidirect
30. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2402	C₂	semidirect
209. C₄×D₂₁₂	Q₈	semidirect
706. #2402	D₅₃	semidirect
885. C₅₃	#34840	semidirect

Maximal subgroups

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

subgroup	index
#20280174	2
#20280167	2
#20280146	2
#20280139	2
#20280120	2
#20280107	2
#20280089	2
#20280063	2
#20279992	2
#20279898	2
#20279794	2
#20279722	2
#20279219	2
#20278851	2
#20278542	2
#20278519	2
#20278009	2
#20277991	2
C₄×#13133208	2
C₄×#13133197	2
C₄×#13133195	2
#20277195	2
#20277187	2
#20277159	2
#20277156	2
C₄×#13133179	2
C₄×C₄⋊C₄×D₅₃	2
C₅₃×#2402	2
#34840	53