Subgroups — C₄×#16811230 #27543229

Order 13568.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811230	C₂	1	1	yes	maximal, characteristic
2	#20277520	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277518	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277517	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277516	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277497	C₂	1	1	yes	maximal, characteristic
7	#20277494	C₂	1	1	yes	maximal, characteristic
8	#20277488	C₂	1	1	yes	maximal, characteristic
9	#20277487	C₂	1	1	yes	maximal, characteristic
10	#20277451	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277430	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277394	C₂	1	1	yes	maximal, characteristic
13	#20277390	C₂	1	1	yes	maximal, characteristic
14	#20277365	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277364	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277319	C₂	1	1	yes	maximal, characteristic
17	C₄×#13133216	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×#13133209	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13133208	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#13133210	C₂	1	1	yes	maximal, characteristic
24	C₄×#13133210	C₂	1	1	yes	maximal, characteristic
25	C₄×#13133210	C₂	1	1	yes	maximal, characteristic
26	C₄×#13133194	C₂	1	1	yes	maximal, characteristic
27	C₄×#13133194	C₂	1	1	yes	maximal, characteristic
28	C₄²×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#13133182	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#13133173	C₂	1	1	yes	maximal, characteristic
31	C₄×#126×C₅₃	C₂	1	1	yes	maximal, characteristic
32	#16811230	C₄	1	16	yes	direct product factor
33	C₂×#13133216	C₂²	1	1	yes	characteristic
34	C₂×#13133210	C₂²	1	1	yes	characteristic
35	C₂×#13133210	C₂²	1	1	yes	characteristic
36	C₂×#13133210	C₂²	1	1	yes	characteristic
37	C₂×#13133209	C₂²	1	1	yes	characteristic
38	C₂×#13133208	C₂²	1	1	yes	characteristic
39	C₂×#13133207	C₂²	1	1	yes	characteristic
40	C₂×#13133207	C₂²	1	1	yes	characteristic
41	C₂×#13133207	C₂²	1	1	yes	characteristic
42	C₂×#13133194	C₂²	1	1	yes	characteristic
43	C₂×#13133194	C₂²	1	1	yes	characteristic
44	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
45	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
46	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
47	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
48	C₂×#13133182	C₂²	1	1	yes	characteristic
49	C₂×#13133182	C₂²	1	1	yes	characteristic
50	C₂×#13133173	C₂²	1	1	yes	characteristic
51	C₂×#13133173	C₂²	1	1	yes	characteristic
52	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
53	#16810527	C₂²	1	1	yes	characteristic
54	#16810527	C₂²	1	1	yes	characteristic
55	#16810527	C₂²	1	1	yes	characteristic
56	#16810527	C₂²	1	1	yes	characteristic
57	#16810522	C₂²	1	1	yes	characteristic
58	#16810522	C₂²	1	1	yes	characteristic
59	#16810521	C₂²	1	1	yes	characteristic
60	#16810521	C₂²	1	1	yes	characteristic
61	#16810520	C₂²	1	1	yes	characteristic
62	#16810520	C₂²	1	1	yes	characteristic
63	#16810520	C₂²	1	1	yes	characteristic
64	#16810520	C₂²	1	1	yes	characteristic
65	#16810520	C₂²	1	1	yes	characteristic
66	#16810520	C₂²	1	1	yes	characteristic
67	#16810520	C₂²	1	1	yes	characteristic
68	#16810519	C₂²	1	1	yes	characteristic
69	#16810519	C₂²	1	1	yes	characteristic
70	#16810518	C₂²	1	1	yes	characteristic
71	#16810518	C₂²	1	1	yes	characteristic
72	#16810518	C₂²	1	1	yes	characteristic
73	#16810517	C₂²	1	1	yes	characteristic
74	#16810517	C₂²	1	1	yes	characteristic
75	#16810517	C₂²	1	1	yes	characteristic
76	#16810516	C₂²	1	1	yes	characteristic
77	#16810516	C₂²	1	1	yes	characteristic
78	#16810516	C₂²	1	1	yes	characteristic
79	#16810511	C₂²	1	1	yes	characteristic
80	#16810511	C₂²	1	1	yes	characteristic
81	#16810511	C₂²	1	1	yes	characteristic
82	#16810510	C₂²	1	1	yes	characteristic
83	#16810510	C₂²	1	1	yes	characteristic
84	#16810510	C₂²	1	1	yes	characteristic
85	#16810510	C₂²	1	1	yes	characteristic
86	#16810510	C₂²	1	1	yes	characteristic
87	#16810510	C₂²	1	1	yes	characteristic
88	#16810510	C₂²	1	1	yes	characteristic
89	#16810509	C₂²	1	1	yes	characteristic
90	#16810509	C₂²	1	1	yes	characteristic
91	#16810509	C₂²	1	1	yes	characteristic
92	#16810508	C₂²	1	1	yes	characteristic
93	#16810508	C₂²	1	1	yes	characteristic
94	#16810508	C₂²	1	1	yes	characteristic
95	#16810508	C₂²	1	1	yes	characteristic
96	#16810508	C₂²	1	1	yes	characteristic
97	#16810508	C₂²	1	1	yes	characteristic
98	#16810507	C₂²	1	1	yes	characteristic
99	#16810507	C₂²	1	1	yes	characteristic
100	#16810507	C₂²	1	1	yes	characteristic
101	#16810507	C₂²	1	1	yes	characteristic
102	#16810506	C₂²	1	1	yes	characteristic
103	#16810506	C₂²	1	1	yes	characteristic
104	#16810506	C₂²	1	1	yes	characteristic
105	#16810506	C₂²	1	1	yes	characteristic
106	#16810505	C₂²	1	1	yes	characteristic
107	#16810505	C₂²	1	1	yes	characteristic
108	#16810505	C₂²	1	1	yes	characteristic
109	#16810505	C₂²	1	1	yes	characteristic
110	#16810505	C₂²	1	1	yes	characteristic
111	#16810505	C₂²	1	1	yes	characteristic
112	#16810504	C₂²	1	1	yes	characteristic
113	#16810504	C₂²	1	1	yes	characteristic
114	#16810504	C₂²	1	1	yes	characteristic
115	#16810498	C₂²	1	1	yes	characteristic
116	#16810498	C₂²	1	1	yes	characteristic
117	#16810495	C₂²	1	1	yes	characteristic
118	#16810495	C₂²	1	1	yes	characteristic
119	#16810492	C₂²	1	1	yes	characteristic
120	#16810490	C₂²	1	1	yes	characteristic
121	#16810490	C₂²	1	1	yes	characteristic
122	#16810490	C₂²	1	1	yes	characteristic
123	#16810489	C₂²	1	1	yes	characteristic
124	#16810488	C₂²	1	1	yes	characteristic
125	#16810487	C₂²	1	1	yes	characteristic
126	#16810487	C₂²	1	1	yes	characteristic
127	#16810487	C₂²	1	1	yes	characteristic
128	#16810481	C₂²	1	1	yes	characteristic
129	#16810481	C₂²	1	1	yes	characteristic
130	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
131	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
132	C₄×#11719919	C₂²	1	1	yes	characteristic
133	C₄×#11719919	C₂²	1	1	yes	characteristic
134	C₄×#11719919	C₂²	1	1	yes	characteristic
135	C₄×#11719919	C₂²	1	1	yes	characteristic
136	C₄×#11719919	C₂²	1	1	yes	characteristic
137	C₄×#11719919	C₂²	1	1	yes	characteristic
138	C₄×#11719919	C₂²	1	1	yes	characteristic
139	C₄×#11719919	C₂²	1	1	yes	characteristic
140	C₄×#11719919	C₂²	1	1	yes	characteristic
141	C₄×#11719919	C₂²	1	1	yes	characteristic
142	C₄×#11719919	C₂²	1	1	yes	characteristic
143	C₄×#11719919	C₂²	1	1	yes	characteristic
144	C₄×#11719919	C₂²	1	1	yes	characteristic
145	C₄×#11719919	C₂²	1	1	yes	characteristic
146	C₄×#11719919	C₂²	1	1	yes	characteristic
147	C₄×#11719919	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
150	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
151	C₄×C₄⋊Dic₅₃	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	#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	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
162	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
163	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
164	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
165	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
166	#16810468	C₂²	1	1	yes	characteristic
167	#16810468	C₂²	1	1	yes	characteristic
168	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
169	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
170	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
171	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic
173	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#388	C₂²	1	1	yes	characteristic
175	C₅₃×#388	C₂²	1	1	yes	characteristic
176	C₅₃×#388	C₂²	1	1	yes	characteristic
177	C₅₃×#387	C₂²	1	1	yes	characteristic
178	C₅₃×#387	C₂²	1	1	yes	characteristic
179	C₅₃×#387	C₂²	1	1	yes	characteristic
180	C₅₃×#383	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×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₄³×C₅₃	C₂²	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	#13133216	C₂×C₄	1	8	yes	complemented
193	#13133210	C₂×C₄	1	8	yes	—
194	#13133210	C₂×C₄	1	8	yes	—
195	#13133210	C₂×C₄	1	8	yes	—
196	#13133209	C₂×C₄	1	8	yes	complemented
197	#13133208	C₂×C₄	1	8	yes	complemented
198	#13133207	C₂×C₄	1	8	yes	complemented
199	#13133207	C₂×C₄	1	8	yes	complemented
200	#13133207	C₂×C₄	1	8	yes	complemented
201	#13133194	C₂×C₄	1	8	yes	—
202	#13133194	C₂×C₄	1	8	yes	—
203	C₄×Dic₁₀₆	—	2	4	no	—
204	C₄×Dic₁₀₆	—	2	4	no	—
205	C₄×Dic₁₀₆	—	2	4	no	—
206	C₄×Dic₁₀₆	C₂×C₄	1	8	yes	complemented
207	#13133182	—	2	4	no	—
208	#13133182	C₂×C₄	1	8	yes	complemented
209	#13133173	—	2	4	no	—
210	#13133173	C₂×C₄	1	8	yes	—
211	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂×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×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	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	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×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₅₃	—	2	4	no	—
258	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
329	#126×C₅₃	C₂×C₄	1	8	yes	—
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	2	2	no	—
368	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₅₃	—	2	2	no	—
383	C₂²×Dic₅₃	—	2	2	no	—
384	C₂²×Dic₅₃	—	2	2	no	—
385	C₂²×Dic₅₃	—	4	1	no	—
386	C₂²×Dic₅₃	—	4	1	no	—
387	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
388	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₁₀₆	—	2	2	no	—
405	C₂×Dic₁₀₆	—	2	2	no	—
406	C₂×Dic₁₀₆	—	2	2	no	—
407	C₂×Dic₁₀₆	—	2	2	no	—
408	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
409	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
410	C₄⋊C₄×C₅₃	—	2	2	no	—
411	C₄⋊C₄×C₅₃	—	4	1	no	—
412	C₄⋊C₄×C₅₃	—	4	1	no	—
413	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
414	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
415	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	4	1	no	—
418	C₂²⋊C₄×C₅₃	—	4	1	no	—
419	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
420	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
421	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
422	C₄²×C₅₃	—	2	2	no	—
423	C₄²×C₅₃	—	2	2	no	—
424	C₄²×C₅₃	—	2	2	no	—
425	C₄²×C₅₃	—	2	2	no	—
426	C₄²×C₅₃	—	2	2	no	—
427	C₄²×C₅₃	—	2	2	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	4	1	no	—
430	C₄²×C₅₃	—	4	1	no	—
431	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
432	C₂²⋊Dic₅₃	—	2	2	no	—
433	C₂²⋊Dic₅₃	—	4	1	no	—
434	C₂²⋊Dic₅₃	—	4	1	no	—
435	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
436	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
437	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
438	C₄⋊Dic₅₃	—	2	2	no	—
439	C₄⋊Dic₅₃	—	2	2	no	—
440	C₄⋊Dic₅₃	—	2	2	no	—
441	C₄⋊Dic₅₃	—	4	1	no	—
442	C₄⋊Dic₅₃	—	4	1	no	—
443	C₄⋊Dic₅₃	—	4	1	no	—
444	C₄⋊Dic₅₃	—	4	1	no	—
445	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
446	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
447	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
448	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
449	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
450	#11719919	—	2	2	no	—
451	#11719919	—	2	2	no	—
452	#11719919	—	2	2	no	—
453	#11719919	—	2	2	no	—
454	#11719919	—	2	2	no	—
455	#11719919	—	2	2	no	—
456	#11719919	—	2	2	no	—
457	#11719919	—	2	2	no	—
458	#11719919	—	2	2	no	—
459	#11719919	—	2	2	no	—
460	#11719919	—	4	1	no	—
461	#11719919	—	4	1	no	—
462	#11719919	—	4	1	no	—
463	#11719919	—	4	1	no	—
464	#11719919	—	4	1	no	—
465	#11719919	—	4	1	no	—
466	#11719919	C₂²×C₄	1	4	yes	—
467	#11719919	C₂²×C₄	1	4	yes	—
468	#11719919	C₂²×C₄	1	4	yes	—
469	#11719919	C₂²×C₄	1	4	yes	—
470	#11719919	C₂²×C₄	1	4	yes	—
471	#11719919	C₂²×C₄	1	4	yes	—
472	#11719919	C₂²×C₄	1	4	yes	—
473	#11719919	C₂²×C₄	1	4	yes	—
474	#11719919	C₂²×C₄	1	4	yes	—
475	#11719919	C₂²×C₄	1	4	yes	—
476	#11719919	C₂²×C₄	1	4	yes	—
477	#11719919	C₂²×C₄	1	4	yes	—
478	C₄×Dic₅₃	—	2	2	no	—
479	C₄×Dic₅₃	—	2	2	no	—
480	C₄×Dic₅₃	—	2	2	no	—
481	C₄×Dic₅₃	—	2	2	no	—
482	C₄×Dic₅₃	—	2	2	no	—
483	C₄×Dic₅₃	—	2	2	no	—
484	C₄×Dic₅₃	—	2	2	no	—
485	C₄×Dic₅₃	—	2	2	no	—
486	C₄×Dic₅₃	—	2	2	no	—
487	C₄×Dic₅₃	—	2	2	no	—
488	C₄×Dic₅₃	—	2	2	no	—
489	C₄×Dic₅₃	—	2	2	no	—
490	C₄×Dic₅₃	—	2	2	no	—
491	C₄×Dic₅₃	—	4	1	no	—
492	C₄×Dic₅₃	—	4	1	no	—
493	C₄×Dic₅₃	—	4	1	no	—
494	C₄×Dic₅₃	—	4	1	no	—
495	C₄×Dic₅₃	—	4	1	no	—
496	C₄×Dic₅₃	—	4	1	no	—
497	C₄×Dic₅₃	—	4	1	no	—
498	C₄×Dic₅₃	—	4	1	no	—
499	C₄×Dic₅₃	—	4	1	no	—
500	C₄×Dic₅₃	—	4	1	no	—
501	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
502	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
503	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
504	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
505	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
506	C₄×Dic₅₃	#41	1	4	yes	—
507	C₄×Dic₅₃	#41	1	4	yes	—
508	C₂³×C₅₃	—	2	1	no	—
509	C₂³×C₅₃	—	2	1	no	—
510	C₂³×C₅₃	—	2	1	no	—
511	C₂³×C₅₃	—	2	1	no	—
512	C₂³×C₅₃	—	2	1	no	—
513	C₂³×C₅₃	—	2	1	no	—
514	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
515	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	2	1	no	—
519	C₂×C₄×C₅₃	—	2	1	no	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	1	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	4	4	no	—
549	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
550	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
551	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
552	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
553	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
554	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
555	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
556	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
557	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
558	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
559	C₂×Dic₅₃	—	2	1	no	—
560	C₂×Dic₅₃	—	2	1	no	—
561	C₂×Dic₅₃	—	2	1	no	—
562	C₂×Dic₅₃	—	2	1	no	—
563	C₂×Dic₅₃	—	2	1	no	—
564	C₂×Dic₅₃	—	2	1	no	—
565	C₂×Dic₅₃	—	2	1	no	—
566	C₂×Dic₅₃	—	2	1	no	—
567	C₂×Dic₅₃	—	2	1	no	—
568	C₂×Dic₅₃	—	2	1	no	—
569	C₂×Dic₅₃	—	2	1	no	—
570	C₂×Dic₅₃	—	2	1	no	—
571	C₂×Dic₅₃	—	2	1	no	—
572	C₂×Dic₅₃	—	2	1	no	—
573	C₂×Dic₅₃	—	2	1	no	—
574	C₂×Dic₅₃	—	2	1	no	—
575	C₂×Dic₅₃	—	2	1	no	—
576	C₂×Dic₅₃	—	2	1	no	—
577	C₂×Dic₅₃	—	2	8	no	—
578	C₂×Dic₅₃	—	2	1	no	—
579	C₂×Dic₅₃	—	2	1	no	—
580	C₂×Dic₅₃	—	2	1	no	—
581	C₂×Dic₅₃	—	2	1	no	—
582	C₂×Dic₅₃	—	2	1	no	—
583	C₂×Dic₅₃	—	2	1	no	—
584	C₂×Dic₅₃	—	2	1	no	—
585	C₂×Dic₅₃	—	2	1	no	—
586	C₂×Dic₅₃	—	2	1	no	—
587	C₂×Dic₅₃	—	2	1	no	—
588	C₂×Dic₅₃	—	2	1	no	—
589	C₂×Dic₅₃	—	2	1	no	—
590	C₂×Dic₅₃	—	2	1	no	—
591	C₂×Dic₅₃	—	2	1	no	—
592	C₂×Dic₅₃	—	2	1	no	—
593	C₂×Dic₅₃	—	2	1	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	4	4	no	—
597	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
598	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
599	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
600	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
601	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
602	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
603	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
604	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
605	C₂×Dic₅₃	C₂×#41	1	2	yes	—
606	C₂×Dic₅₃	C₂×#41	1	2	yes	—
607	C₂×Dic₅₃	C₂×#41	1	2	yes	—
608	C₂×Dic₅₃	C₂×#41	1	2	yes	—
609	Dic₁₀₆	—	2	8	no	—
610	Dic₁₀₆	—	2	8	no	—
611	C₄×#541	—	53	1	no	maximal, Sylow
612	C₂²×C₅₃	—	2	2	no	—
613	C₂²×C₅₃	—	2	2	no	—
614	C₂²×C₅₃	—	2	2	no	—
615	C₂²×C₅₃	—	4	1	no	—
616	C₂²×C₅₃	—	4	1	no	—
617	C₂²×C₅₃	—	4	1	no	—
618	C₂²×C₅₃	—	4	1	no	—
619	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
620	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
621	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
622	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
623	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
624	C₂²×C₅₃	#585	1	1	yes	characteristic
625	C₂²×C₅₃	#585	1	1	yes	characteristic
626	C₄×C₅₃	—	2	2	no	—
627	C₄×C₅₃	—	2	2	no	—
628	C₄×C₅₃	—	2	2	no	—
629	C₄×C₅₃	—	2	2	no	—
630	C₄×C₅₃	—	2	2	no	—
631	C₄×C₅₃	—	2	2	no	—
632	C₄×C₅₃	—	2	2	no	—
633	C₄×C₅₃	—	4	1	no	—
634	C₄×C₅₃	—	4	1	no	—
635	C₄×C₅₃	—	4	1	no	—
636	C₄×C₅₃	—	4	1	no	—
637	C₄×C₅₃	—	4	1	no	—
638	C₄×C₅₃	—	4	1	no	—
639	C₄×C₅₃	#541	1	4	yes	complemented
640	Dic₅₃	—	2	2	no	—
641	Dic₅₃	—	2	2	no	—
642	Dic₅₃	—	2	2	no	—
643	Dic₅₃	—	2	2	no	—
644	Dic₅₃	—	2	2	no	—
645	Dic₅₃	—	2	2	no	—
646	Dic₅₃	—	2	2	no	—
647	Dic₅₃	—	2	2	no	—
648	Dic₅₃	—	2	2	no	—
649	Dic₅₃	—	4	1	no	—
650	Dic₅₃	—	4	1	no	—
651	Dic₅₃	—	4	1	no	—
652	Dic₅₃	—	4	1	no	—
653	Dic₅₃	—	4	1	no	—
654	Dic₅₃	—	4	1	no	—
655	Dic₅₃	C₄×#41	1	4	yes	—
656	C₂×#541	—	53	1	no	—
657	#2336	—	53	1	no	—
658	#2336	—	53	1	no	—
659	#2336	—	53	1	no	—
660	#2336	—	53	1	no	—
661	#2334	—	53	1	no	—
662	#2334	—	53	1	no	—
663	#2334	—	53	1	no	—
664	#2334	—	53	1	no	—
665	#2330	—	53	1	no	—
666	#2327	—	53	1	no	—
667	#2323	—	53	1	no	—
668	#2323	—	53	1	no	—
669	#2320	—	53	1	no	—
670	#2320	—	53	1	no	—
671	#2314	—	53	1	no	—
672	C₄×C₄⋊Q₈	—	53	1	no	—
673	C₄×#125	—	53	1	no	—
674	C₄×#125	—	53	1	no	—
675	C₄×#125	—	53	1	no	—
676	C₄×#125	—	53	1	no	—
677	C₄×#125	—	53	1	no	—
678	C₄×#126	—	53	1	no	—
679	C₄×#126	—	53	1	no	—
680	C₄×#126	—	53	1	no	—
681	C₄×#126	D₅₃	1	1	yes	characteristic
682	C₄×C₂²⋊Q₈	—	53	1	no	—
683	C₄×C₂²⋊Q₈	—	53	1	no	—
684	C₄²×Q₈	—	53	1	no	—
685	C₄²×Q₈	—	53	1	no	—
686	C₄×#117	—	53	1	no	—
687	C₂×C₅₃	—	4	2	no	—
688	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
689	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
690	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
691	C₂×C₅₃	C₂×#541	1	1	yes	characteristic
692	C₂×C₅₃	#3455	1	1	yes	characteristic
693	C₂×C₅₃	#3461	1	1	yes	characteristic
694	C₂×C₅₃	#3461	1	1	yes	characteristic
695	#541	—	53	16	no	—
696	C₂×C₄⋊Q₈	—	53	1	no	—
697	C₂×#126	—	53	1	no	—
698	C₂×#126	—	53	1	no	—
699	C₂×#126	—	53	1	no	—
700	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
701	C₂×#125	—	53	1	no	—
702	C₂×#125	—	53	1	no	—
703	C₂×#125	—	53	1	no	—
704	C₂×#125	—	53	1	no	—
705	C₂×#125	—	53	1	no	—
706	C₂×C₂²⋊Q₈	—	53	1	no	—
707	C₂×C₂²⋊Q₈	—	53	1	no	—
708	C₂×C₄×Q₈	—	53	1	no	—
709	C₂×C₄×Q₈	—	53	1	no	—
710	C₂×C₄×Q₈	—	53	1	no	—
711	C₂×C₄×Q₈	—	53	1	no	—
712	C₂×C₄×Q₈	—	53	1	no	—
713	C₂×C₄×Q₈	—	53	1	no	—
714	C₂×#117	—	53	1	no	—
715	C₂×#117	—	53	1	no	—
716	C₂²×C₄²	—	53	1	no	—
717	#391	—	53	1	no	—
718	#391	—	53	1	no	—
719	#391	—	53	1	no	—
720	#391	—	53	1	no	—
721	#389	—	53	1	no	—
722	#389	—	53	1	no	—
723	#389	—	53	1	no	—
724	#389	—	53	1	no	—
725	#389	—	53	1	no	—
726	#389	—	53	1	no	—
727	#389	—	53	1	no	—
728	#389	—	53	1	no	—
729	#389	—	53	1	no	—
730	#389	—	53	1	no	—
731	#389	—	53	1	no	—
732	#389	—	53	1	no	—
733	#389	—	53	1	no	—
734	#389	—	53	1	no	—
735	#389	—	53	1	no	—
736	#389	—	53	1	no	—
737	#388	—	53	1	no	—
738	#388	—	53	1	no	—
739	#388	—	53	1	no	—
740	#388	—	53	1	no	—
741	#388	—	53	1	no	—
742	#388	—	53	1	no	—
743	#388	—	53	1	no	—
744	#388	—	53	1	no	—
745	#388	—	53	1	no	—
746	#388	C₂×D₅₃	1	1	yes	characteristic
747	#388	C₂×D₅₃	1	1	yes	characteristic
748	#388	C₂×D₅₃	1	1	yes	characteristic
749	#387	—	53	1	no	—
750	#387	—	53	1	no	—
751	#387	—	53	1	no	—
752	#387	—	53	1	no	—
753	#387	—	53	1	no	—
754	#387	—	53	1	no	—
755	#387	—	53	1	no	—
756	#387	—	53	1	no	—
757	#387	—	53	1	no	—
758	#387	—	53	1	no	—
759	#387	—	53	1	no	—
760	#387	—	53	1	no	—
761	#387	—	53	1	no	—
762	#387	—	53	1	no	—
763	#387	—	53	1	no	—
764	#387	—	53	1	no	—
765	#387	—	53	1	no	—
766	#387	—	53	1	no	—
767	#387	—	53	1	no	—
768	#387	—	53	1	no	—
769	#387	—	53	1	no	—
770	#387	—	53	1	no	—
771	#387	—	53	1	no	—
772	#387	—	53	1	no	—
773	#387	—	53	1	no	—
774	#387	—	53	1	no	—
775	#387	—	53	1	no	—
776	#387	—	53	1	no	—
777	#387	—	53	1	no	—
778	#387	—	53	1	no	—
779	#387	—	53	1	no	—
780	#387	—	53	1	no	—
781	#387	—	53	1	no	—
782	#387	C₂×D₅₃	1	1	yes	characteristic
783	#387	C₂×D₅₃	1	1	yes	characteristic
784	#387	C₂×D₅₃	1	1	yes	characteristic
785	#385	—	53	1	no	—
786	#385	—	53	1	no	—
787	#385	—	53	1	no	—
788	#385	—	53	1	no	—
789	#384	—	53	1	no	—
790	#383	—	53	1	no	—
791	#383	—	53	1	no	—
792	#383	—	53	1	no	—
793	#383	C₂×D₅₃	1	1	yes	characteristic
794	#382	—	53	1	no	—
795	#382	—	53	1	no	—
796	#382	—	53	1	no	—
797	#382	—	53	1	no	—
798	#382	—	53	1	no	—
799	#380	—	53	1	no	—
800	#380	—	53	1	no	—
801	C₄×C₄⋊C₄	—	53	1	no	—
802	C₄×C₄⋊C₄	—	53	1	no	—
803	C₄×C₄⋊C₄	—	53	1	no	—
804	C₄×C₄⋊C₄	—	53	1	no	—
805	C₄×C₄⋊C₄	—	53	1	no	—
806	C₄×C₄⋊C₄	—	53	1	no	—
807	C₄×C₄⋊C₄	—	53	1	no	—
808	C₄×C₄⋊C₄	—	53	1	no	—
809	C₄×C₄⋊C₄	—	53	1	no	—
810	C₄×C₄⋊C₄	—	53	1	no	—
811	C₄×C₄⋊C₄	—	53	1	no	—
812	C₄×C₄⋊C₄	—	53	1	no	—
813	C₄×C₄⋊C₄	—	53	1	no	—
814	C₄×C₄⋊C₄	—	53	1	no	—
815	C₄×C₄⋊C₄	—	53	1	no	—
816	C₄×C₄⋊C₄	—	53	1	no	—
817	C₄×C₄⋊C₄	—	53	1	no	—
818	C₄×C₄⋊C₄	—	53	1	no	—
819	C₄×C₄⋊C₄	—	53	1	no	—
820	C₄×C₄⋊C₄	—	53	1	no	—
821	C₄×C₄⋊C₄	—	53	1	no	—
822	C₄×C₄⋊C₄	—	53	1	no	—
823	C₄×C₄⋊C₄	—	53	1	no	—
824	C₄×C₄⋊C₄	—	53	1	no	—
825	C₄×C₄⋊C₄	—	53	1	no	—
826	C₄×C₄⋊C₄	—	53	1	no	—
827	C₄×C₄⋊C₄	—	53	1	no	—
828	C₄×C₄⋊C₄	—	53	1	no	—
829	C₄×C₄⋊C₄	—	53	1	no	—
830	C₄×C₄⋊C₄	—	53	1	no	—
831	C₄×C₄⋊C₄	—	53	1	no	—
832	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
833	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
834	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
835	C₄×C₂²⋊C₄	—	53	1	no	—
836	C₄×C₂²⋊C₄	—	53	1	no	—
837	C₄×C₂²⋊C₄	—	53	1	no	—
838	C₄×C₂²⋊C₄	—	53	1	no	—
839	C₄×C₂²⋊C₄	—	53	1	no	—
840	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
841	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
842	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
843	#376	—	53	1	no	—
844	#376	—	53	1	no	—
845	C₄³	—	53	1	no	—
846	C₄³	—	53	1	no	—
847	C₄³	—	53	1	no	—
848	C₄³	—	53	1	no	—
849	C₄³	—	53	1	no	—
850	C₄³	C₂×D₅₃	1	1	yes	characteristic
851	C₅₃	C₄×#541	1	1	yes	characteristic, complemented, Sylow
852	C₂²×Q₈	—	53	1	no	—
853	C₂²×Q₈	—	53	1	no	—
854	C₂³×C₄	—	53	1	no	—
855	C₂³×C₄	—	53	1	no	—
856	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
857	C₄⋊Q₈	—	53	8	no	—
858	#126	—	53	8	no	—
859	#126	—	53	8	no	—
860	#126	—	53	8	no	—
861	#126	C₄×D₅₃	1	8	yes	—
862	#125	—	53	8	no	—
863	#125	—	53	8	no	—
864	#125	—	53	8	no	—
865	#125	—	53	8	no	—
866	#125	—	53	8	no	—
867	C₂²⋊Q₈	—	53	8	no	—
868	C₂²⋊Q₈	—	53	8	no	—
869	C₄×Q₈	—	53	8	no	—
870	C₄×Q₈	—	53	8	no	—
871	C₄×Q₈	—	106	4	no	—
872	C₄×Q₈	—	106	4	no	—
873	C₄×Q₈	—	106	4	no	—
874	C₄×Q₈	—	106	4	no	—
875	#117	—	53	8	no	—
876	#117	—	106	4	no	—
877	C₂×C₄⋊C₄	—	53	1	no	—
878	C₂×C₄⋊C₄	—	53	1	no	—
879	C₂×C₄⋊C₄	—	53	1	no	—
880	C₂×C₄⋊C₄	—	53	1	no	—
881	C₂×C₄⋊C₄	—	53	1	no	—
882	C₂×C₄⋊C₄	—	53	1	no	—
883	C₂×C₄⋊C₄	—	53	1	no	—
884	C₂×C₄⋊C₄	—	53	1	no	—
885	C₂×C₄⋊C₄	—	53	1	no	—
886	C₂×C₄⋊C₄	—	53	1	no	—
887	C₂×C₄⋊C₄	—	53	1	no	—
888	C₂×C₄⋊C₄	—	53	1	no	—
889	C₂×C₄⋊C₄	—	53	1	no	—
890	C₂×C₄⋊C₄	—	53	1	no	—
891	C₂×C₄⋊C₄	—	53	1	no	—
892	C₂×C₄⋊C₄	—	53	1	no	—
893	C₂×C₄⋊C₄	—	53	1	no	—
894	C₂×C₄⋊C₄	—	53	1	no	—
895	C₂×C₄⋊C₄	—	53	1	no	—
896	C₂×C₄⋊C₄	—	53	1	no	—
897	C₂×C₄⋊C₄	—	53	1	no	—
898	C₂×C₄⋊C₄	—	53	1	no	—
899	C₂×C₄⋊C₄	—	53	1	no	—
900	C₂×C₄⋊C₄	—	53	1	no	—
901	C₂×C₄⋊C₄	—	53	1	no	—
902	C₂×C₄⋊C₄	—	53	1	no	—
903	C₂×C₄⋊C₄	—	53	1	no	—
904	C₂×C₄⋊C₄	—	53	1	no	—
905	C₂×C₄⋊C₄	—	53	1	no	—
906	C₂×C₄⋊C₄	—	53	1	no	—
907	C₂×C₄⋊C₄	—	53	1	no	—
908	C₂×C₄⋊C₄	—	53	1	no	—
909	C₂×C₄⋊C₄	—	53	1	no	—
910	C₂×C₄⋊C₄	—	53	1	no	—
911	C₂×C₄⋊C₄	—	53	1	no	—
912	C₂×C₄⋊C₄	—	53	1	no	—
913	C₂×C₄⋊C₄	—	53	1	no	—
914	C₂×C₄⋊C₄	—	53	1	no	—
915	C₂×C₄⋊C₄	—	53	1	no	—
916	C₂×C₄⋊C₄	—	53	1	no	—
917	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
919	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
920	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
921	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
922	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
923	C₂×C₂²⋊C₄	—	53	1	no	—
924	C₂×C₂²⋊C₄	—	53	1	no	—
925	C₂×C₂²⋊C₄	—	53	1	no	—
926	C₂×C₂²⋊C₄	—	53	1	no	—
927	C₂×C₂²⋊C₄	—	53	1	no	—
928	C₂×C₂²⋊C₄	—	53	1	no	—
929	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
930	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
931	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
932	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
933	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
934	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
935	C₂×C₄²	—	53	1	no	—
936	C₂×C₄²	—	53	1	no	—
937	C₂×C₄²	—	53	1	no	—
938	C₂×C₄²	—	53	1	no	—
939	C₂×C₄²	—	53	1	no	—
940	C₂×C₄²	—	53	1	no	—
941	C₂×C₄²	—	53	1	no	—
942	C₂×C₄²	—	53	1	no	—
943	C₂×C₄²	—	53	1	no	—
944	C₂×C₄²	—	53	1	no	—
945	C₂×C₄²	—	53	1	no	—
946	C₂×C₄²	—	53	1	no	—
947	C₂×C₄²	—	53	1	no	—
948	C₂×C₄²	—	53	1	no	—
949	C₂×C₄²	—	53	1	no	—
950	C₂×C₄²	—	53	1	no	—
951	C₂×C₄²	—	53	1	no	—
952	C₂×C₄²	—	53	1	no	—
953	C₂×C₄²	—	53	1	no	—
954	C₂×C₄²	—	53	1	no	—
955	C₂×C₄²	—	53	1	no	—
956	C₂×C₄²	—	53	1	no	—
957	C₂×C₄²	—	53	1	no	—
958	C₂×C₄²	—	53	1	no	—
959	C₂×C₄²	—	53	1	no	—
960	C₂×C₄²	—	53	1	no	—
961	C₂×C₄²	—	53	1	no	—
962	C₂×C₄²	—	53	1	no	—
963	C₂×C₄²	—	53	1	no	—
964	C₂×C₄²	—	53	1	no	—
965	C₂×C₄²	—	106	4	no	—
966	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
968	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
972	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
973	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
974	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
975	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
976	#95	—	53	1	no	—
977	#95	—	53	1	no	—
978	#95	—	53	1	no	—
979	#95	—	53	1	no	—
980	#95	—	53	1	no	—
981	#95	—	53	1	no	—
982	#95	—	53	1	no	—
983	#95	—	53	1	no	—
984	#95	—	53	1	no	—
985	#95	—	53	1	no	—
986	#95	—	53	1	no	—
987	#95	—	53	1	no	—
988	#95	—	53	1	no	—
989	#95	—	53	1	no	—
990	#95	—	53	1	no	—
991	#95	—	53	1	no	—
992	#95	—	53	1	no	—
993	#95	—	53	1	no	—
994	#95	—	53	1	no	—
995	#95	—	53	1	no	—
996	#95	—	53	1	no	—
997	#95	—	53	1	no	—
998	#95	—	53	1	no	—
999	#95	—	53	1	no	—
1000	#95	—	53	1	no	—
1001	#95	—	53	1	no	—
1002	#95	—	53	1	no	—
1003	#95	—	53	1	no	—
1004	#95	—	53	1	no	—
1005	#95	—	53	1	no	—
1006	#95	—	53	1	no	—
1007	#95	—	53	1	no	—
1008	#95	—	53	1	no	—
1009	#95	—	53	1	no	—
1010	#95	—	53	1	no	—
1011	#95	—	53	1	no	—
1012	#95	—	53	1	no	—
1013	#95	—	53	1	no	—
1014	#95	—	53	1	no	—
1015	#95	—	53	1	no	—
1016	#95	C₂²×D₅₃	1	1	yes	characteristic
1017	#95	C₂²×D₅₃	1	1	yes	characteristic
1018	#95	C₂²×D₅₃	1	1	yes	characteristic
1019	#95	C₂²×D₅₃	1	1	yes	characteristic
1020	#95	C₂²×D₅₃	1	1	yes	characteristic
1021	#95	C₂²×D₅₃	1	1	yes	characteristic
1022	#95	C₂²×D₅₃	1	1	yes	characteristic
1023	#95	C₂²×D₅₃	1	1	yes	characteristic
1024	#95	C₂²×D₅₃	1	1	yes	characteristic
1025	#95	C₂²×D₅₃	1	1	yes	characteristic
1026	#95	C₂²×D₅₃	1	1	yes	characteristic
1027	#95	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1029	C₂×Q₈	—	53	4	no	—
1030	C₂×Q₈	—	53	4	no	—
1031	C₂×Q₈	—	106	2	no	—
1032	C₂×Q₈	—	106	2	no	—
1033	C₂×Q₈	—	106	2	no	—
1034	C₂×Q₈	—	106	2	no	—
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	53	1	no	—
1039	C₂²×C₄	—	53	4	no	—
1040	C₂²×C₄	—	53	1	no	—
1041	C₂²×C₄	—	53	1	no	—
1042	C₂²×C₄	—	53	1	no	—
1043	C₂²×C₄	—	53	1	no	—
1044	C₂²×C₄	—	53	1	no	—
1045	C₂²×C₄	—	53	1	no	—
1046	C₂²×C₄	—	53	1	no	—
1047	C₂²×C₄	—	53	1	no	—
1048	C₂²×C₄	—	53	1	no	—
1049	C₂²×C₄	—	53	1	no	—
1050	C₂²×C₄	—	53	1	no	—
1051	C₂²×C₄	—	53	1	no	—
1052	C₂²×C₄	—	53	1	no	—
1053	C₂²×C₄	—	53	1	no	—
1054	C₂²×C₄	—	53	1	no	—
1055	C₂²×C₄	—	106	2	no	—
1056	C₂²×C₄	—	106	2	no	—
1057	C₂²×C₄	—	106	2	no	—
1058	C₂²×C₄	—	212	1	no	—
1059	C₂²×C₄	—	212	1	no	—
1060	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1062	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1063	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1065	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1066	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1067	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1068	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1069	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1070	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1071	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1072	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1073	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	4	1	no	—
1076	C₄⋊C₄	—	4	1	no	—
1077	C₄⋊C₄	—	53	4	no	—
1078	C₄⋊C₄	—	53	4	no	—
1079	C₄⋊C₄	—	53	4	no	—
1080	C₄⋊C₄	—	53	4	no	—
1081	C₄⋊C₄	—	53	4	no	—
1082	C₄⋊C₄	—	53	4	no	—
1083	C₄⋊C₄	—	53	4	no	—
1084	C₄⋊C₄	—	53	4	no	—
1085	C₄⋊C₄	—	53	4	no	—
1086	C₄⋊C₄	—	53	4	no	—
1087	C₄⋊C₄	—	53	4	no	—
1088	C₄⋊C₄	—	53	4	no	—
1089	C₄⋊C₄	—	53	4	no	—
1090	C₄⋊C₄	—	53	4	no	—
1091	C₄⋊C₄	—	53	4	no	—
1092	C₄⋊C₄	—	53	4	no	—
1093	C₄⋊C₄	—	53	4	no	—
1094	C₄⋊C₄	—	106	2	no	—
1095	C₄⋊C₄	—	106	2	no	—
1096	C₄⋊C₄	—	106	2	no	—
1097	C₄⋊C₄	—	106	2	no	—
1098	C₄⋊C₄	—	106	2	no	—
1099	C₄⋊C₄	—	106	2	no	—
1100	C₄⋊C₄	—	106	2	no	—
1101	C₄⋊C₄	—	106	2	no	—
1102	C₄⋊C₄	—	106	2	no	—
1103	C₄⋊C₄	—	106	2	no	—
1104	C₄⋊C₄	—	106	2	no	—
1105	C₄⋊C₄	—	106	2	no	—
1106	C₄⋊C₄	—	106	2	no	—
1107	C₄⋊C₄	—	212	1	no	—
1108	C₄⋊C₄	—	212	1	no	—
1109	C₄⋊C₄	—	212	1	no	—
1110	C₄⋊C₄	—	212	1	no	—
1111	C₄⋊C₄	—	212	1	no	—
1112	C₄⋊C₄	—	212	1	no	—
1113	C₄⋊C₄	—	212	1	no	—
1114	C₄⋊C₄	—	212	1	no	—
1115	C₄⋊C₄	—	212	1	no	—
1116	C₄⋊C₄	—	212	1	no	—
1117	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1118	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1119	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	4	1	no	—
1122	C₂²⋊C₄	—	4	1	no	—
1123	C₂²⋊C₄	—	53	4	no	—
1124	C₂²⋊C₄	—	53	4	no	—
1125	C₂²⋊C₄	—	53	4	no	—
1126	C₂²⋊C₄	—	106	2	no	—
1127	C₂²⋊C₄	—	212	1	no	—
1128	C₂²⋊C₄	—	212	1	no	—
1129	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1130	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1131	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1132	C₄²	—	2	2	no	—
1133	C₄²	—	2	2	no	—
1134	C₄²	—	2	2	no	—
1135	C₄²	—	2	2	no	—
1136	C₄²	—	2	2	no	—
1137	C₄²	—	2	2	no	—
1138	C₄²	—	2	2	no	—
1139	C₄²	—	4	1	no	—
1140	C₄²	—	4	1	no	—
1141	C₄²	—	53	4	no	—
1142	C₄²	—	53	4	no	—
1143	C₄²	—	53	4	no	—
1144	C₄²	—	53	4	no	—
1145	C₄²	—	53	4	no	—
1146	C₄²	—	53	4	no	—
1147	C₄²	—	53	4	no	—
1148	C₄²	—	106	2	no	—
1149	C₄²	—	106	2	no	—
1150	C₄²	—	106	2	no	—
1151	C₄²	—	106	2	no	—
1152	C₄²	—	106	2	no	—
1153	C₄²	—	106	2	no	—
1154	C₄²	—	106	2	no	—
1155	C₄²	—	106	2	no	—
1156	C₄²	—	106	2	no	—
1157	C₄²	—	106	2	no	—
1158	C₄²	—	106	2	no	—
1159	C₄²	—	106	2	no	—
1160	C₄²	—	106	2	no	—
1161	C₄²	—	212	1	no	—
1162	C₄²	—	212	1	no	—
1163	C₄²	—	212	1	no	—
1164	C₄²	—	212	1	no	—
1165	C₄²	—	212	1	no	—
1166	C₄²	—	212	1	no	—
1167	C₄²	—	212	1	no	—
1168	C₄²	—	212	1	no	—
1169	C₄²	—	212	1	no	—
1170	C₄²	—	212	1	no	—
1171	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1172	C₂³	—	2	1	no	—
1173	C₂³	—	2	1	no	—
1174	C₂³	—	2	1	no	—
1175	C₂³	—	2	1	no	—
1176	C₂³	—	2	1	no	—
1177	C₂³	—	2	1	no	—
1178	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1179	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1180	Q₈	—	106	8	no	—
1181	Q₈	—	106	8	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	4	4	no	—
1215	C₂×C₄	—	53	2	no	—
1216	C₂×C₄	—	53	2	no	—
1217	C₂×C₄	—	53	2	no	—
1218	C₂×C₄	—	53	2	no	—
1219	C₂×C₄	—	53	2	no	—
1220	C₂×C₄	—	53	2	no	—
1221	C₂×C₄	—	53	2	no	—
1222	C₂×C₄	—	53	2	no	—
1223	C₂×C₄	—	53	2	no	—
1224	C₂×C₄	—	53	2	no	—
1225	C₂×C₄	—	53	2	no	—
1226	C₂×C₄	—	53	2	no	—
1227	C₂×C₄	—	106	8	no	—
1228	C₂×C₄	—	106	1	no	—
1229	C₂×C₄	—	106	1	no	—
1230	C₂×C₄	—	106	1	no	—
1231	C₂×C₄	—	106	1	no	—
1232	C₂×C₄	—	106	1	no	—
1233	C₂×C₄	—	106	1	no	—
1234	C₂×C₄	—	106	1	no	—
1235	C₂×C₄	—	106	1	no	—
1236	C₂×C₄	—	106	1	no	—
1237	C₂×C₄	—	106	1	no	—
1238	C₂×C₄	—	106	1	no	—
1239	C₂×C₄	—	106	1	no	—
1240	C₂×C₄	—	106	1	no	—
1241	C₂×C₄	—	106	1	no	—
1242	C₂×C₄	—	106	1	no	—
1243	C₂×C₄	—	106	1	no	—
1244	C₂×C₄	—	106	1	no	—
1245	C₂×C₄	—	106	1	no	—
1246	C₂×C₄	—	106	1	no	—
1247	C₂×C₄	—	106	1	no	—
1248	C₂×C₄	—	106	1	no	—
1249	C₂×C₄	—	106	1	no	—
1250	C₂×C₄	—	106	1	no	—
1251	C₂×C₄	—	106	1	no	—
1252	C₂×C₄	—	106	1	no	—
1253	C₂×C₄	—	106	1	no	—
1254	C₂×C₄	—	106	1	no	—
1255	C₂×C₄	—	106	1	no	—
1256	C₂×C₄	—	106	1	no	—
1257	C₂×C₄	—	106	1	no	—
1258	C₂×C₄	—	106	1	no	—
1259	C₂×C₄	—	106	1	no	—
1260	C₂×C₄	—	106	1	no	—
1261	C₂×C₄	—	106	1	no	—
1262	C₂×C₄	—	106	1	no	—
1263	C₂×C₄	—	106	1	no	—
1264	C₂×C₄	—	212	4	no	—
1265	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1266	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1267	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1268	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1269	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1270	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1271	C₂×C₄	#41×D₅₃	1	2	yes	—
1272	C₂×C₄	#41×D₅₃	1	2	yes	—
1273	C₂×C₄	#13133264	1	2	yes	—
1274	C₂×C₄	#13133264	1	2	yes	—
1275	C₂²	—	2	2	no	—
1276	C₂²	—	2	2	no	—
1277	C₂²	—	2	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	1	no	—
1281	C₂²	—	4	1	no	—
1282	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1283	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1284	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1285	C₂²	C₂×#13133264	1	1	yes	characteristic
1286	C₂²	C₂×#13133264	1	1	yes	characteristic
1287	C₂²	#16811459	1	1	yes	characteristic
1288	C₂²	#16811459	1	1	yes	characteristic
1289	C₄	—	2	2	no	—
1290	C₄	—	2	2	no	—
1291	C₄	—	2	2	no	—
1292	C₄	—	2	2	no	—
1293	C₄	—	2	2	no	—
1294	C₄	—	2	2	no	—
1295	C₄	—	2	2	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	1	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	53	4	no	—
1303	C₄	—	106	2	no	—
1304	C₄	—	106	2	no	—
1305	C₄	—	106	2	no	—
1306	C₄	—	106	2	no	—
1307	C₄	—	106	2	no	—
1308	C₄	—	106	2	no	—
1309	C₄	—	106	2	no	—
1310	C₄	—	106	2	no	—
1311	C₄	—	106	2	no	—
1312	C₄	—	212	1	no	—
1313	C₄	—	212	1	no	—
1314	C₄	—	212	1	no	—
1315	C₄	—	212	1	no	—
1316	C₄	—	212	1	no	—
1317	C₄	—	212	1	no	—
1318	C₄	#16811230	1	4	yes	direct product factor
1319	C₂	—	4	2	no	—
1320	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1321	C₂	C₄×#13133264	1	1	yes	characteristic
1322	C₂	C₄×#13133264	1	1	yes	characteristic
1323	C₂	C₂×#16811230	1	1	yes	characteristic
1324	C₂	#20288098	1	1	yes	characteristic
1325	C₂	#20288140	1	1	yes	characteristic
1326	C₂	#20288144	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂³×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₅₃
Fitting	C₄×#126×C₅₃	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂⁴×C₅₃	C₂⁴
hypercenter	C₄×#126	D₅₃
hypocenter	C₅₃	C₄×#541
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×#126

Complements

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

N	H ≅ G/N	type
2. #20277520	C₂	semidirect
3. #20277518	C₂	semidirect
4. #20277517	C₂	semidirect
5. #20277516	C₂	semidirect
10. #20277451	C₂	semidirect
11. #20277430	C₂	semidirect
14. #20277365	C₂	semidirect
15. #20277364	C₂	semidirect
17. C₄×#13133216	C₂	semidirect
18. C₄×#13133209	C₂	semidirect
19. C₄×#13133208	C₂	semidirect
20. C₄×#13133207	C₂	semidirect
21. C₄×#13133207	C₂	semidirect
22. C₄×#13133207	C₂	semidirect
28. C₄²×Dic₁₀₆	C₂	semidirect
29. C₄×#13133182	C₂	semidirect
32. #16811230	C₄	direct (N × H)
192. #13133216	C₂×C₄	semidirect
196. #13133209	C₂×C₄	semidirect
197. #13133208	C₂×C₄	semidirect
198. #13133207	C₂×C₄	semidirect
199. #13133207	C₂×C₄	semidirect
200. #13133207	C₂×C₄	semidirect
206. C₄×Dic₁₀₆	C₂×C₄	semidirect
208. #13133182	C₂×C₄	semidirect
639. C₄×C₅₃	#541	semidirect
851. C₅₃	C₄×#541	semidirect
1318. C₄	#16811230	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16811230	2
#20277520	2
#20277518	2
#20277517	2
#20277516	2
#20277497	2
#20277494	2
#20277488	2
#20277487	2
#20277451	2
#20277430	2
#20277394	2
#20277390	2
#20277365	2
#20277364	2
#20277319	2
C₄×#13133216	2
C₄×#13133209	2
C₄×#13133208	2
C₄×#13133207	2
C₄×#13133210	2
C₄×#13133194	2
C₄²×Dic₁₀₆	2
C₄×#13133182	2
C₄×#13133173	2
C₄×#126×C₅₃	2
C₄×#541	53

Subgroups — C4×#16811230 #27543229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16811230 #27543229