Subgroups — #27548402

Order 13568.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811222	C₂	1	1	yes	maximal, characteristic
2	#20277898	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277881	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277876	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277861	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277845	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277838	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277829	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277819	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277813	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277807	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277716	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277685	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277643	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277593	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277585	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277504	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277499	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277498	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277498	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277484	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277483	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277480	C₂	1	1	yes	maximal, characteristic
24	#20277470	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277408	C₂	1	1	yes	maximal, characteristic
26	#20277388	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277356	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#13133193	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#13133202	C₂	1	1	yes	maximal, characteristic, complemented
30	#20277157	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2362	C₂	1	1	yes	maximal, characteristic, complemented
32	#16811222	C₄	1	16	yes	complemented
33	C₂×#13133212	C₂²	1	1	yes	characteristic
34	C₂×#13133212	C₂²	1	1	yes	characteristic
35	C₂×#13133208	C₂²	1	1	yes	characteristic
36	C₂×#13133208	C₂²	1	1	yes	characteristic
37	C₂×#13133202	C₂²	1	1	yes	characteristic
38	C₂×#13133202	C₂²	1	1	yes	characteristic
39	C₂×#13133201	C₂²	1	1	yes	characteristic
40	C₂×#13133201	C₂²	1	1	yes	characteristic
41	C₂×#13133193	C₂²	1	1	yes	characteristic
42	C₂×#13133193	C₂²	1	1	yes	characteristic
43	C₂×#13133191	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
45	C₂×#13133177	C₂²	1	1	yes	characteristic
46	C₂×#13133177	C₂²	1	1	yes	characteristic
47	C₂×#13133173	C₂²	1	1	yes	characteristic
48	C₂²×#11719919	C₂²	1	1	yes	characteristic
49	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
51	#16810530	C₂²	1	1	yes	characteristic
52	#16810530	C₂²	1	1	yes	characteristic
53	#16810525	C₂²	1	1	yes	characteristic
54	#16810523	C₂²	1	1	yes	characteristic
55	#16810523	C₂²	1	1	yes	characteristic
56	#16810523	C₂²	1	1	yes	characteristic
57	#16810523	C₂²	1	1	yes	characteristic
58	#16810522	C₂²	1	1	yes	characteristic
59	#16810522	C₂²	1	1	yes	characteristic
60	#16810521	C₂²	1	1	yes	characteristic
61	#16810521	C₂²	1	1	yes	characteristic
62	#16810521	C₂²	1	1	yes	characteristic
63	#16810521	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	#16810519	C₂²	1	1	yes	characteristic
68	#16810518	C₂²	1	1	yes	characteristic
69	#16810518	C₂²	1	1	yes	characteristic
70	#16810518	C₂²	1	1	yes	characteristic
71	#16810516	C₂²	1	1	yes	characteristic
72	#16810516	C₂²	1	1	yes	characteristic
73	#16810516	C₂²	1	1	yes	characteristic
74	#16810516	C₂²	1	1	yes	characteristic
75	#16810515	C₂²	1	1	yes	characteristic
76	#16810515	C₂²	1	1	yes	characteristic
77	#16810515	C₂²	1	1	yes	characteristic
78	#16810515	C₂²	1	1	yes	characteristic
79	#16810514	C₂²	1	1	yes	characteristic
80	#16810514	C₂²	1	1	yes	characteristic
81	#16810514	C₂²	1	1	yes	characteristic
82	#16810514	C₂²	1	1	yes	characteristic
83	#16810513	C₂²	1	1	yes	characteristic
84	#16810513	C₂²	1	1	yes	characteristic
85	#16810513	C₂²	1	1	yes	characteristic
86	#16810513	C₂²	1	1	yes	characteristic
87	#16810512	C₂²	1	1	yes	characteristic
88	#16810512	C₂²	1	1	yes	characteristic
89	#16810512	C₂²	1	1	yes	characteristic
90	#16810512	C₂²	1	1	yes	characteristic
91	#16810510	C₂²	1	1	yes	characteristic
92	#16810510	C₂²	1	1	yes	characteristic
93	#16810510	C₂²	1	1	yes	characteristic
94	#16810509	C₂²	1	1	yes	characteristic
95	#16810509	C₂²	1	1	yes	characteristic
96	#16810509	C₂²	1	1	yes	characteristic
97	#16810509	C₂²	1	1	yes	characteristic
98	#16810508	C₂²	1	1	yes	characteristic
99	#16810508	C₂²	1	1	yes	characteristic
100	#16810508	C₂²	1	1	yes	characteristic
101	#16810508	C₂²	1	1	yes	characteristic
102	#16810507	C₂²	1	1	yes	characteristic
103	#16810507	C₂²	1	1	yes	characteristic
104	#16810507	C₂²	1	1	yes	characteristic
105	#16810507	C₂²	1	1	yes	characteristic
106	#16810507	C₂²	1	1	yes	characteristic
107	#16810506	C₂²	1	1	yes	characteristic
108	#16810506	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	#16810505	C₂²	1	1	yes	characteristic
114	#16810504	C₂²	1	1	yes	characteristic
115	#16810504	C₂²	1	1	yes	characteristic
116	#16810504	C₂²	1	1	yes	characteristic
117	#16810501	C₂²	1	1	yes	characteristic
118	#16810501	C₂²	1	1	yes	characteristic
119	#16810499	C₂²	1	1	yes	characteristic
120	#16810499	C₂²	1	1	yes	characteristic
121	#16810499	C₂²	1	1	yes	characteristic
122	#16810499	C₂²	1	1	yes	characteristic
123	#16810497	C₂²	1	1	yes	characteristic
124	#16810497	C₂²	1	1	yes	characteristic
125	#16810494	C₂²	1	1	yes	characteristic
126	#16810494	C₂²	1	1	yes	characteristic
127	#16810494	C₂²	1	1	yes	characteristic
128	#16810494	C₂²	1	1	yes	characteristic
129	#16810494	C₂²	1	1	yes	characteristic
130	#16810494	C₂²	1	1	yes	characteristic
131	#16810487	C₂²	1	1	yes	characteristic
132	#16810487	C₂²	1	1	yes	characteristic
133	#16810486	C₂²	1	1	yes	characteristic
134	#16810485	C₂²	1	1	yes	characteristic
135	#16810485	C₂²	1	1	yes	characteristic
136	#16810484	C₂²	1	1	yes	characteristic
137	#16810483	C₂²	1	1	yes	characteristic
138	#16810482	C₂²	1	1	yes	characteristic
139	#16810481	C₂²	1	1	yes	characteristic
140	#16810481	C₂²	1	1	yes	characteristic
141	#16810481	C₂²	1	1	yes	characteristic
142	#16810480	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×#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×#11719919	C₂²	1	1	yes	characteristic
153	C₄×#11719919	C₂²	1	1	yes	characteristic
154	C₄×#11719919	C₂²	1	1	yes	characteristic
155	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
156	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
157	#16810474	C₂²	1	1	yes	characteristic
158	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
159	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
160	C₂²⋊C₄×Dic₅₃	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	C₄×#11719921	C₂²	1	1	yes	characteristic
165	C₄×#11719921	C₂²	1	1	yes	characteristic
166	C₄×#11719921	C₂²	1	1	yes	characteristic
167	C₄×#11719921	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	#16810468	C₂²	1	1	yes	characteristic
172	#16810468	C₂²	1	1	yes	characteristic
173	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
174	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
176	C₅₃×#391	C₂²	1	1	yes	characteristic
177	C₅₃×#389	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic
183	C₅₃×#387	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	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
188	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
189	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
192	C₂³×Dic₅₃	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	#13133212	C₂×C₄	1	8	yes	complemented
200	#13133212	C₂×C₄	1	8	yes	complemented
201	#13133208	C₂×C₄	1	8	yes	complemented
202	#13133208	C₂×C₄	1	8	yes	complemented
203	#13133202	C₂×C₄	1	8	yes	—
204	#13133202	C₂×C₄	1	8	yes	—
205	#13133201	C₂×C₄	1	8	yes	complemented
206	#13133201	C₂×C₄	1	8	yes	complemented
207	#13133193	C₂×C₄	1	8	yes	complemented
208	#13133193	C₂×C₄	1	8	yes	complemented
209	#13133191	C₂×C₄	1	8	yes	—
210	C₄×D₂₁₂	—	4	2	no	—
211	#13133177	C₂×C₄	1	8	yes	complemented
212	#13133177	C₂×C₄	1	8	yes	complemented
213	#13133173	—	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×#11719919	C₂×C₄	1	8	yes	complemented
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	C₄⋊C₄×D₅₃	—	4	2	no	—
245	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×#11719921	C₂³	1	1	yes	characteristic
250	C₂×#11719921	C₂³	1	1	yes	characteristic
251	C₂×#11719921	C₂³	1	1	yes	characteristic
252	C₂×#11719921	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂×#11719921	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	C₄²×D₅₃	—	4	2	no	—
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	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
327	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂²⋊Q₈×C₅₃	C₂×C₄	1	8	yes	complemented
329	C₄×Q₈×C₅₃	—	4	2	no	—
330	#117×C₅₃	—	4	2	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄²×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	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
366	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×Q₈×C₅₃	—	4	1	no	—
368	C₂×Q₈×C₅₃	—	4	1	no	—
369	C₂×Q₈×C₅₃	C₂²×C₄	1	4	yes	—
370	C₂²×C₄×C₅₃	—	4	1	no	—
371	C₂²×C₄×C₅₃	—	4	1	no	—
372	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₂²⋊D₅₃	—	4	1	no	—
388	C₂×C₂²⋊D₅₃	—	4	1	no	—
389	C₂×C₂²⋊D₅₃	—	4	1	no	—
390	C₂×C₂²⋊D₅₃	—	4	1	no	—
391	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
392	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
393	C₂²×Dic₅₃	—	4	1	no	—
394	C₂²×Dic₅₃	—	4	1	no	—
395	C₂²×Dic₅₃	—	4	1	no	—
396	C₂²×Dic₅₃	—	4	1	no	—
397	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
398	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×D₂₁₂	—	4	1	no	—
414	C₂×D₂₁₂	—	4	1	no	—
415	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
416	C₂×C₄×D₅₃	—	2	2	no	—
417	C₂×C₄×D₅₃	—	2	2	no	—
418	C₂×C₄×D₅₃	—	2	2	no	—
419	C₂×C₄×D₅₃	—	4	1	no	—
420	C₂×C₄×D₅₃	—	4	1	no	—
421	C₂×C₄×D₅₃	—	4	1	no	—
422	C₂×C₄×D₅₃	—	4	1	no	—
423	C₂×C₄×D₅₃	—	4	1	no	—
424	C₂×C₄×D₅₃	—	4	1	no	—
425	C₂×C₄×D₅₃	—	4	1	no	—
426	C₂×C₄×D₅₃	—	4	1	no	—
427	C₂×C₄×D₅₃	—	4	1	no	—
428	C₂×C₄×D₅₃	—	4	1	no	—
429	C₂×C₄×D₅₃	—	4	1	no	—
430	C₂×C₄×D₅₃	—	4	1	no	—
431	C₂×C₄×D₅₃	—	4	1	no	—
432	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
433	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
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	—	4	1	no	—
439	C₄⋊C₄×C₅₃	—	4	1	no	—
440	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
441	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
442	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	4	1	no	—
446	C₂²⋊C₄×C₅₃	—	4	1	no	—
447	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
448	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	2	no	—
451	C₄²×C₅₃	—	4	1	no	—
452	C₄²×C₅₃	—	4	1	no	—
453	C₄²×C₅₃	—	4	1	no	—
454	C₄²×C₅₃	—	4	1	no	—
455	C₄²×C₅₃	—	4	1	no	—
456	C₄²×C₅₃	—	4	1	no	—
457	C₂²⋊Dic₅₃	—	4	1	no	—
458	C₂²⋊Dic₅₃	—	4	1	no	—
459	C₂²⋊Dic₅₃	—	4	1	no	—
460	C₂²⋊Dic₅₃	—	4	1	no	—
461	#11719921	—	2	2	no	—
462	#11719921	—	4	1	no	—
463	#11719921	—	4	1	no	—
464	#11719921	—	4	1	no	—
465	#11719921	—	4	1	no	—
466	#11719921	—	4	1	no	—
467	#11719921	—	4	1	no	—
468	#11719921	—	4	1	no	—
469	#11719921	—	4	1	no	—
470	#11719921	—	4	1	no	—
471	#11719921	—	4	1	no	—
472	#11719921	—	4	1	no	—
473	#11719921	C₂²×C₄	1	4	yes	—
474	#11719921	C₂²×C₄	1	4	yes	—
475	#11719921	C₂²×C₄	1	4	yes	—
476	#11719921	C₂²×C₄	1	4	yes	—
477	#11719921	C₂²×C₄	1	4	yes	—
478	#11719921	C₂²×C₄	1	4	yes	—
479	#11719921	C₂²×C₄	1	4	yes	—
480	#11719921	C₂²×C₄	1	4	yes	—
481	C₄⋊Dic₅₃	—	4	1	no	—
482	C₄⋊Dic₅₃	—	4	1	no	—
483	C₄⋊Dic₅₃	—	4	1	no	—
484	C₄⋊Dic₅₃	—	4	1	no	—
485	C₄⋊Dic₅₃	—	4	1	no	—
486	C₄⋊Dic₅₃	—	4	1	no	—
487	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
488	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
489	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
490	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
491	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
492	#11719919	—	2	2	no	—
493	#11719919	—	4	1	no	—
494	#11719919	—	4	1	no	—
495	#11719919	—	4	1	no	—
496	#11719919	—	4	1	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	C₂²×C₄	1	4	yes	—
505	#11719919	C₂²×C₄	1	4	yes	—
506	#11719919	C₂²×C₄	1	4	yes	—
507	#11719919	C₂²×C₄	1	4	yes	—
508	#11719919	C₂²×C₄	1	4	yes	—
509	#11719919	C₂²×C₄	1	4	yes	—
510	C₄×Dic₅₃	—	2	2	no	—
511	C₄×Dic₅₃	—	4	1	no	—
512	C₄×Dic₅₃	—	4	1	no	—
513	C₄×Dic₅₃	—	4	1	no	—
514	C₄×Dic₅₃	—	4	1	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	—	4	1	no	—
523	C₄×Dic₅₃	—	4	1	no	—
524	C₄×Dic₅₃	—	4	1	no	—
525	C₄×Dic₅₃	—	4	1	no	—
526	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
527	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
528	C₂³×C₅₃	—	2	1	no	—
529	C₂³×C₅₃	—	2	1	no	—
530	C₂³×C₅₃	—	2	1	no	—
531	C₂³×C₅₃	—	2	1	no	—
532	C₂³×C₅₃	—	2	1	no	—
533	C₂³×C₅₃	—	2	1	no	—
534	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
535	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
536	C₂²×D₅₃	—	2	1	no	—
537	C₂²×D₅₃	—	2	1	no	—
538	C₂²×D₅₃	—	2	1	no	—
539	C₂²×D₅₃	—	2	1	no	—
540	C₂²×D₅₃	—	2	1	no	—
541	C₂²×D₅₃	—	2	1	no	—
542	C₂²×D₅₃	—	2	1	no	—
543	C₂²×D₅₃	—	2	1	no	—
544	C₂²×D₅₃	—	2	1	no	—
545	C₂²×D₅₃	—	2	1	no	—
546	C₂²×D₅₃	—	2	1	no	—
547	C₂²×D₅₃	—	2	1	no	—
548	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
549	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
550	Q₈×C₅₃	—	4	4	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	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	4	4	no	—
586	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
587	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
588	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
589	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
590	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
591	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
592	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
593	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
594	C₂²⋊D₅₃	—	4	4	no	—
595	C₂²⋊D₅₃	—	4	4	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	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	4	4	no	—
633	C₂×Dic₅₃	—	4	4	no	—
634	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
635	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
636	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
637	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
638	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
639	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
640	D₂₁₂	—	4	4	no	—
641	C₄×D₅₃	—	4	4	no	—
642	C₄×D₅₃	—	4	4	no	—
643	C₄×D₅₃	—	4	4	no	—
644	C₄×D₅₃	—	4	4	no	—
645	C₄×D₅₃	—	8	2	no	—
646	C₄×D₅₃	—	8	2	no	—
647	#34449	—	53	1	no	maximal, Sylow
648	C₂²×C₅₃	—	2	2	no	—
649	C₂²×C₅₃	—	2	2	no	—
650	C₂²×C₅₃	—	2	2	no	—
651	C₂²×C₅₃	—	4	1	no	—
652	C₂²×C₅₃	—	4	1	no	—
653	C₂²×C₅₃	—	4	1	no	—
654	C₂²×C₅₃	—	4	1	no	—
655	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
656	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
657	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
658	C₂²×C₅₃	#585	1	1	yes	characteristic
659	C₂²×C₅₃	#585	1	1	yes	characteristic
660	C₂²×C₅₃	#585	1	1	yes	characteristic
661	C₂²×C₅₃	#585	1	1	yes	characteristic
662	C₂×D₅₃	—	2	2	no	—
663	C₂×D₅₃	—	2	2	no	—
664	C₂×D₅₃	—	2	2	no	—
665	C₂×D₅₃	—	2	2	no	—
666	C₂×D₅₃	—	2	2	no	—
667	C₂×D₅₃	—	2	2	no	—
668	C₂×D₅₃	—	4	1	no	—
669	C₂×D₅₃	—	4	1	no	—
670	C₂×D₅₃	—	4	1	no	—
671	C₂×D₅₃	—	4	1	no	—
672	C₂×D₅₃	—	4	1	no	—
673	C₂×D₅₃	—	4	1	no	—
674	C₂×D₅₃	—	4	1	no	—
675	C₂×D₅₃	—	4	1	no	—
676	C₄×C₅₃	—	2	2	no	—
677	C₄×C₅₃	—	2	2	no	—
678	C₄×C₅₃	—	2	2	no	—
679	C₄×C₅₃	—	2	2	no	—
680	C₄×C₅₃	—	2	2	no	—
681	C₄×C₅₃	—	2	2	no	—
682	C₄×C₅₃	—	2	2	no	—
683	C₄×C₅₃	—	2	2	no	—
684	C₄×C₅₃	—	4	1	no	—
685	C₄×C₅₃	—	4	1	no	—
686	C₄×C₅₃	—	4	1	no	—
687	C₄×C₅₃	—	4	1	no	—
688	C₄×C₅₃	—	4	1	no	—
689	C₄×C₅₃	—	4	1	no	—
690	Dic₅₃	—	2	2	no	—
691	Dic₅₃	—	2	2	no	—
692	Dic₅₃	—	2	2	no	—
693	Dic₅₃	—	2	2	no	—
694	Dic₅₃	—	2	2	no	—
695	Dic₅₃	—	2	2	no	—
696	Dic₅₃	—	4	1	no	—
697	Dic₅₃	—	4	1	no	—
698	Dic₅₃	—	4	1	no	—
699	Dic₅₃	—	4	1	no	—
700	Dic₅₃	—	4	1	no	—
701	Dic₅₃	—	4	1	no	—
702	Dic₅₃	—	4	1	no	—
703	Dic₅₃	—	4	1	no	—
704	C₂×#539	—	53	1	no	—
705	#2382	—	53	1	no	—
706	#2378	—	53	1	no	—
707	#2378	—	53	1	no	—
708	#2376	—	53	1	no	—
709	#2374	—	53	1	no	—
710	#2373	—	53	1	no	—
711	#2373	—	53	1	no	—
712	#2371	—	53	1	no	—
713	#2370	—	53	1	no	—
714	#2370	—	53	1	no	—
715	#2362	D₅₃	1	1	yes	characteristic, complemented
716	#2360	—	53	1	no	—
717	#2357	—	53	1	no	—
718	#2352	—	53	1	no	—
719	#2345	—	53	1	no	—
720	#2344	—	53	1	no	—
721	#2335	—	53	1	no	—
722	#2335	—	53	1	no	—
723	#2335	—	53	1	no	—
724	#2335	—	53	1	no	—
725	#2334	—	53	1	no	—
726	#2334	—	53	1	no	—
727	#2333	—	53	1	no	—
728	#2332	—	53	1	no	—
729	#2324	—	53	1	no	—
730	#2322	—	53	1	no	—
731	#2319	—	53	1	no	—
732	C₄×C₂²⋊Q₈	—	53	1	no	—
733	C₄×#123	—	53	1	no	—
734	#2290	—	53	1	no	—
735	C₂×C₅₃	—	4	2	no	—
736	C₂×C₅₃	#3428	1	1	yes	characteristic
737	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
738	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
739	C₂×C₅₃	#3533	1	1	yes	characteristic
740	C₂×C₅₃	#3541	1	1	yes	characteristic
741	C₂×C₅₃	#3557	1	1	yes	characteristic
742	C₂×C₅₃	#3567	1	1	yes	characteristic
743	D₅₃	—	4	2	no	—
744	D₅₃	—	4	2	no	—
745	#539	—	53	16	no	—
746	C₂×#126	—	53	1	no	—
747	C₂×#126	—	53	1	no	—
748	C₂×#125	—	53	1	no	—
749	C₂×#125	—	53	1	no	—
750	C₂×#123	—	53	1	no	—
751	C₂×#123	—	53	1	no	—
752	C₂×#123	—	53	1	no	—
753	C₂×#123	—	53	1	no	—
754	C₂×C₂²⋊Q₈	—	53	1	no	—
755	C₂×C₂²⋊Q₈	—	53	1	no	—
756	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
757	C₂×#121	—	53	1	no	—
758	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
759	C₂×C₄×D₄	—	53	1	no	—
760	C₂×C₄×D₄	—	53	1	no	—
761	C₂×C₄×D₄	—	53	1	no	—
762	C₂×#117	—	53	1	no	—
763	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
764	C₂²×C₄⋊C₄	—	53	1	no	—
765	C₂²×C₄⋊C₄	—	53	1	no	—
766	C₂²×C₄²	—	53	1	no	—
767	#391	—	53	1	no	—
768	#391	—	53	1	no	—
769	#391	C₂×D₅₃	1	1	yes	characteristic
770	#390	—	53	1	no	—
771	#390	—	53	1	no	—
772	#390	—	53	1	no	—
773	#390	—	53	1	no	—
774	#390	—	53	1	no	—
775	#389	—	53	1	no	—
776	#389	—	53	1	no	—
777	#389	—	53	1	no	—
778	#389	—	53	1	no	—
779	#389	—	53	1	no	—
780	#389	—	53	1	no	—
781	#389	—	53	1	no	—
782	#389	—	53	1	no	—
783	#389	—	53	1	no	—
784	#389	—	53	1	no	—
785	#389	—	53	1	no	—
786	#389	—	53	1	no	—
787	#389	—	53	1	no	—
788	#389	C₂×D₅₃	1	1	yes	characteristic
789	#388	—	53	1	no	—
790	#388	—	53	1	no	—
791	#388	—	53	1	no	—
792	#388	—	53	1	no	—
793	#388	—	53	1	no	—
794	#388	—	53	1	no	—
795	#388	—	53	1	no	—
796	#388	—	53	1	no	—
797	#388	—	53	1	no	—
798	#388	—	53	1	no	—
799	#388	—	53	1	no	—
800	#388	—	53	1	no	—
801	#388	—	53	1	no	—
802	#388	—	53	1	no	—
803	#388	—	53	1	no	—
804	#388	—	53	1	no	—
805	#388	—	53	1	no	—
806	#388	—	53	1	no	—
807	#388	—	53	1	no	—
808	#388	—	53	1	no	—
809	#388	C₂×D₅₃	1	1	yes	characteristic
810	#388	C₂×D₅₃	1	1	yes	characteristic
811	#388	C₂×D₅₃	1	1	yes	characteristic
812	#388	C₂×D₅₃	1	1	yes	characteristic
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	#387	—	53	1	no	—
824	#387	—	53	1	no	—
825	#387	—	53	1	no	—
826	#387	—	53	1	no	—
827	#387	—	53	1	no	—
828	#387	—	53	1	no	—
829	#387	—	53	1	no	—
830	#387	—	53	1	no	—
831	#387	—	53	1	no	—
832	#387	—	53	1	no	—
833	#387	—	53	1	no	—
834	#387	—	53	1	no	—
835	#387	—	53	1	no	—
836	#387	—	53	1	no	—
837	#387	—	53	1	no	—
838	#387	—	53	1	no	—
839	#387	C₂×D₅₃	1	1	yes	characteristic
840	#387	C₂×D₅₃	1	1	yes	characteristic
841	#386	—	53	1	no	—
842	#386	—	53	1	no	—
843	#386	—	53	1	no	—
844	#386	—	53	1	no	—
845	#386	—	53	1	no	—
846	#386	—	53	1	no	—
847	#385	—	53	1	no	—
848	#385	—	53	1	no	—
849	#385	—	53	1	no	—
850	#385	—	53	1	no	—
851	#385	—	53	1	no	—
852	#385	—	53	1	no	—
853	#385	—	53	1	no	—
854	#385	—	53	1	no	—
855	#382	—	53	1	no	—
856	#382	—	53	1	no	—
857	#381	—	53	1	no	—
858	#381	—	53	1	no	—
859	#381	—	53	1	no	—
860	#381	—	53	1	no	—
861	#380	—	53	1	no	—
862	#380	—	53	1	no	—
863	#380	—	53	1	no	—
864	#380	—	53	1	no	—
865	#380	—	53	1	no	—
866	#380	—	53	1	no	—
867	C₄×C₄⋊C₄	—	53	1	no	—
868	C₄×C₄⋊C₄	—	53	1	no	—
869	C₄×C₄⋊C₄	—	53	1	no	—
870	C₄×C₄⋊C₄	—	53	1	no	—
871	C₄×C₄⋊C₄	—	53	1	no	—
872	C₄×C₄⋊C₄	—	53	1	no	—
873	C₄×C₄⋊C₄	—	53	1	no	—
874	C₄×C₄⋊C₄	—	53	1	no	—
875	C₄×C₄⋊C₄	—	53	1	no	—
876	C₄×C₄⋊C₄	—	53	1	no	—
877	C₄×C₄⋊C₄	—	53	1	no	—
878	C₄×C₄⋊C₄	—	53	1	no	—
879	C₄×C₄⋊C₄	—	53	1	no	—
880	C₄×C₄⋊C₄	—	53	1	no	—
881	C₄×C₄⋊C₄	—	53	1	no	—
882	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
883	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
884	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
885	C₄×C₂²⋊C₄	—	53	1	no	—
886	C₄×C₂²⋊C₄	—	53	1	no	—
887	C₄×C₂²⋊C₄	—	53	1	no	—
888	C₄×C₂²⋊C₄	—	53	1	no	—
889	C₄×C₂²⋊C₄	—	53	1	no	—
890	C₄×C₂²⋊C₄	—	53	1	no	—
891	C₄×C₂²⋊C₄	—	53	1	no	—
892	C₄×C₂²⋊C₄	—	53	1	no	—
893	C₄×C₂²⋊C₄	—	53	1	no	—
894	C₄×C₂²⋊C₄	—	53	1	no	—
895	C₄×C₂²⋊C₄	—	53	1	no	—
896	C₄×C₂²⋊C₄	—	53	1	no	—
897	C₄×C₂²⋊C₄	—	53	1	no	—
898	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
899	#376	—	53	1	no	—
900	#376	—	53	1	no	—
901	C₅₃	#34449	1	1	yes	characteristic, complemented, Sylow
902	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
903	C₂²×D₄	—	53	1	no	—
904	C₂²×D₄	—	53	1	no	—
905	C₂²×D₄	—	53	1	no	—
906	C₂³×C₄	—	53	1	no	—
907	C₂³×C₄	—	53	1	no	—
908	C₂³×C₄	—	53	1	no	—
909	C₂³×C₄	—	53	1	no	—
910	C₂³×C₄	—	53	1	no	—
911	C₂³×C₄	—	53	1	no	—
912	C₂³×C₄	—	53	1	no	—
913	C₂³×C₄	—	53	1	no	—
914	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
915	#126	—	53	8	no	—
916	#126	—	53	8	no	—
917	#125	—	53	8	no	—
918	#125	—	53	8	no	—
919	#123	—	53	8	no	—
920	#123	—	53	8	no	—
921	#123	—	53	8	no	—
922	#123	—	53	8	no	—
923	C₂²⋊Q₈	—	53	8	no	—
924	C₂²⋊Q₈	—	53	8	no	—
925	C₂²⋊Q₈	C₄×D₅₃	1	8	yes	complemented
926	#121	—	53	8	no	—
927	C₄×Q₈	—	4	2	no	—
928	C₄×D₄	—	53	8	no	—
929	C₄×D₄	—	53	8	no	—
930	C₄×D₄	—	212	2	no	—
931	#117	—	4	2	no	—
932	#117	—	212	2	no	—
933	C₂×C₄⋊C₄	—	53	8	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	—	53	1	no	—
948	C₂×C₄⋊C₄	—	53	1	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	1	no	—
951	C₂×C₄⋊C₄	—	53	1	no	—
952	C₂×C₄⋊C₄	—	53	1	no	—
953	C₂×C₄⋊C₄	—	53	1	no	—
954	C₂×C₄⋊C₄	—	53	1	no	—
955	C₂×C₄⋊C₄	—	53	1	no	—
956	C₂×C₄⋊C₄	—	53	1	no	—
957	C₂×C₄⋊C₄	—	53	1	no	—
958	C₂×C₄⋊C₄	—	53	1	no	—
959	C₂×C₄⋊C₄	—	53	1	no	—
960	C₂×C₄⋊C₄	—	53	1	no	—
961	C₂×C₄⋊C₄	—	53	1	no	—
962	C₂×C₄⋊C₄	—	53	1	no	—
963	C₂×C₄⋊C₄	—	212	2	no	—
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	no	—
975	C₂×C₂²⋊C₄	—	53	1	no	—
976	C₂×C₂²⋊C₄	—	53	1	no	—
977	C₂×C₂²⋊C₄	—	53	1	no	—
978	C₂×C₂²⋊C₄	—	53	1	no	—
979	C₂×C₂²⋊C₄	—	53	1	no	—
980	C₂×C₂²⋊C₄	—	53	1	no	—
981	C₂×C₂²⋊C₄	—	53	1	no	—
982	C₂×C₂²⋊C₄	—	53	1	no	—
983	C₂×C₂²⋊C₄	—	53	1	no	—
984	C₂×C₂²⋊C₄	—	53	1	no	—
985	C₂×C₂²⋊C₄	—	53	1	no	—
986	C₂×C₂²⋊C₄	—	53	1	no	—
987	C₂×C₂²⋊C₄	—	53	1	no	—
988	C₂×C₂²⋊C₄	—	53	1	no	—
989	C₂×C₂²⋊C₄	—	53	1	no	—
990	C₂×C₂²⋊C₄	—	53	1	no	—
991	C₂×C₂²⋊C₄	—	53	1	no	—
992	C₂×C₂²⋊C₄	—	53	1	no	—
993	C₂×C₂²⋊C₄	—	53	1	no	—
994	C₂×C₂²⋊C₄	—	53	1	no	—
995	C₂×C₂²⋊C₄	—	53	1	no	—
996	C₂×C₂²⋊C₄	—	53	1	no	—
997	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1003	C₂×C₄²	—	53	1	no	—
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	1	no	—
1006	C₂×C₄²	—	53	1	no	—
1007	C₂×C₄²	—	53	1	no	—
1008	C₂×C₄²	—	53	1	no	—
1009	C₂×C₄²	—	53	1	no	—
1010	C₂×C₄²	—	53	1	no	—
1011	C₂×C₄²	—	53	1	no	—
1012	C₂×C₄²	—	53	1	no	—
1013	C₂×C₄²	—	53	1	no	—
1014	C₂×C₄²	—	53	1	no	—
1015	C₂×C₄²	—	53	1	no	—
1016	C₂×C₄²	—	53	1	no	—
1017	C₂×C₄²	—	53	1	no	—
1018	C₂×C₄²	—	53	1	no	—
1019	C₂×C₄²	—	53	1	no	—
1020	C₂×C₄²	—	53	1	no	—
1021	C₂×C₄²	—	212	2	no	—
1022	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1023	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1024	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1029	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	C₂²×D₅₃	1	1	yes	characteristic
1069	#95	C₂²×D₅₃	1	1	yes	characteristic
1070	#95	C₂²×D₅₃	1	1	yes	characteristic
1071	#95	C₂²×D₅₃	1	1	yes	characteristic
1072	#95	C₂²×D₅₃	1	1	yes	characteristic
1073	#95	C₂²×D₅₃	1	1	yes	characteristic
1074	#95	C₂²×D₅₃	1	1	yes	characteristic
1075	#95	C₂²×D₅₃	1	1	yes	characteristic
1076	#95	C₂²×D₅₃	1	1	yes	characteristic
1077	#95	C₂²×D₅₃	1	1	yes	characteristic
1078	C₂⁴	—	53	1	no	—
1079	C₂⁴	—	53	1	no	—
1080	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1081	C₂×Q₈	—	4	1	no	—
1082	C₂×Q₈	—	4	1	no	—
1083	C₂×Q₈	C₂×C₄×D₅₃	1	4	yes	—
1084	C₂×D₄	—	53	4	no	—
1085	C₂×D₄	—	53	4	no	—
1086	C₂×D₄	—	53	4	no	—
1087	C₂×D₄	—	212	1	no	—
1088	C₂×D₄	—	212	1	no	—
1089	C₂×D₄	—	212	1	no	—
1090	C₂×D₄	—	212	1	no	—
1091	C₂×D₄	—	212	1	no	—
1092	C₂×D₄	—	212	1	no	—
1093	C₂²×C₄	—	4	1	no	—
1094	C₂²×C₄	—	4	1	no	—
1095	C₂²×C₄	—	53	1	no	—
1096	C₂²×C₄	—	53	1	no	—
1097	C₂²×C₄	—	53	1	no	—
1098	C₂²×C₄	—	53	1	no	—
1099	C₂²×C₄	—	53	1	no	—
1100	C₂²×C₄	—	53	1	no	—
1101	C₂²×C₄	—	53	4	no	—
1102	C₂²×C₄	—	53	4	no	—
1103	C₂²×C₄	—	53	4	no	—
1104	C₂²×C₄	—	53	4	no	—
1105	C₂²×C₄	—	53	1	no	—
1106	C₂²×C₄	—	53	1	no	—
1107	C₂²×C₄	—	53	1	no	—
1108	C₂²×C₄	—	53	1	no	—
1109	C₂²×C₄	—	53	1	no	—
1110	C₂²×C₄	—	53	1	no	—
1111	C₂²×C₄	—	53	1	no	—
1112	C₂²×C₄	—	53	1	no	—
1113	C₂²×C₄	—	106	2	no	—
1114	C₂²×C₄	—	106	2	no	—
1115	C₂²×C₄	—	106	2	no	—
1116	C₂²×C₄	—	212	1	no	—
1117	C₂²×C₄	—	212	1	no	—
1118	C₂²×C₄	—	212	1	no	—
1119	C₂²×C₄	—	212	1	no	—
1120	C₂²×C₄	—	212	1	no	—
1121	C₂²×C₄	—	212	1	no	—
1122	C₂²×C₄	—	212	1	no	—
1123	C₂²×C₄	—	212	1	no	—
1124	C₂²×C₄	—	212	1	no	—
1125	C₂²×C₄	—	212	1	no	—
1126	C₂²×C₄	—	212	1	no	—
1127	C₂²×C₄	—	212	1	no	—
1128	C₂²×C₄	—	212	1	no	—
1129	C₂²×C₄	—	212	1	no	—
1130	C₂²×C₄	—	212	1	no	—
1131	C₂²×C₄	—	212	1	no	—
1132	C₂²×C₄	—	212	1	no	—
1133	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
1134	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1135	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1136	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1137	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1138	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1140	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1143	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1148	C₄⋊C₄	—	2	2	no	—
1149	C₄⋊C₄	—	2	2	no	—
1150	C₄⋊C₄	—	2	2	no	—
1151	C₄⋊C₄	—	2	2	no	—
1152	C₄⋊C₄	—	4	1	no	—
1153	C₄⋊C₄	—	4	1	no	—
1154	C₄⋊C₄	—	53	4	no	—
1155	C₄⋊C₄	—	53	4	no	—
1156	C₄⋊C₄	—	53	4	no	—
1157	C₄⋊C₄	—	53	4	no	—
1158	C₄⋊C₄	—	53	4	no	—
1159	C₄⋊C₄	—	53	4	no	—
1160	C₄⋊C₄	—	53	4	no	—
1161	C₄⋊C₄	—	53	4	no	—
1162	C₄⋊C₄	—	53	4	no	—
1163	C₄⋊C₄	—	53	4	no	—
1164	C₄⋊C₄	—	53	4	no	—
1165	C₄⋊C₄	—	106	2	no	—
1166	C₄⋊C₄	—	212	1	no	—
1167	C₄⋊C₄	—	212	1	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	C₄⋊C₄	—	212	1	no	—
1180	C₄⋊C₄	—	212	1	no	—
1181	C₄⋊C₄	—	212	1	no	—
1182	C₄⋊C₄	—	212	1	no	—
1183	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1184	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1185	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1186	C₂²⋊C₄	—	2	2	no	—
1187	C₂²⋊C₄	—	2	2	no	—
1188	C₂²⋊C₄	—	4	1	no	—
1189	C₂²⋊C₄	—	4	1	no	—
1190	C₂²⋊C₄	—	53	4	no	—
1191	C₂²⋊C₄	—	53	4	no	—
1192	C₂²⋊C₄	—	53	4	no	—
1193	C₂²⋊C₄	—	53	4	no	—
1194	C₂²⋊C₄	—	53	4	no	—
1195	C₂²⋊C₄	—	53	4	no	—
1196	C₂²⋊C₄	—	53	4	no	—
1197	C₂²⋊C₄	—	53	4	no	—
1198	C₂²⋊C₄	—	106	2	no	—
1199	C₂²⋊C₄	—	212	1	no	—
1200	C₂²⋊C₄	—	212	1	no	—
1201	C₂²⋊C₄	—	212	1	no	—
1202	C₂²⋊C₄	—	212	1	no	—
1203	C₂²⋊C₄	—	212	1	no	—
1204	C₂²⋊C₄	—	212	1	no	—
1205	C₂²⋊C₄	—	212	1	no	—
1206	C₂²⋊C₄	—	212	1	no	—
1207	C₂²⋊C₄	—	212	1	no	—
1208	C₂²⋊C₄	—	212	1	no	—
1209	C₂²⋊C₄	—	212	1	no	—
1210	C₂²⋊C₄	—	212	1	no	—
1211	C₂²⋊C₄	—	212	1	no	—
1212	C₂²⋊C₄	—	212	1	no	—
1213	C₂²⋊C₄	—	212	1	no	—
1214	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1215	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1216	C₄²	—	2	2	no	—
1217	C₄²	—	2	2	no	—
1218	C₄²	—	4	1	no	—
1219	C₄²	—	4	1	no	—
1220	C₄²	—	4	1	no	—
1221	C₄²	—	4	1	no	—
1222	C₄²	—	4	1	no	—
1223	C₄²	—	4	1	no	—
1224	C₄²	—	53	4	no	—
1225	C₄²	—	53	4	no	—
1226	C₄²	—	106	2	no	—
1227	C₄²	—	212	1	no	—
1228	C₄²	—	212	1	no	—
1229	C₄²	—	212	1	no	—
1230	C₄²	—	212	1	no	—
1231	C₄²	—	212	1	no	—
1232	C₄²	—	212	1	no	—
1233	C₄²	—	212	1	no	—
1234	C₄²	—	212	1	no	—
1235	C₄²	—	212	1	no	—
1236	C₄²	—	212	1	no	—
1237	C₄²	—	212	1	no	—
1238	C₄²	—	212	1	no	—
1239	C₄²	—	212	1	no	—
1240	C₄²	—	212	1	no	—
1241	C₄²	—	212	1	no	—
1242	C₂³	—	2	1	no	—
1243	C₂³	—	2	1	no	—
1244	C₂³	—	2	1	no	—
1245	C₂³	—	2	1	no	—
1246	C₂³	—	2	1	no	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	53	2	no	—
1249	C₂³	—	53	2	no	—
1250	C₂³	—	106	1	no	—
1251	C₂³	—	106	1	no	—
1252	C₂³	—	106	1	no	—
1253	C₂³	—	106	1	no	—
1254	C₂³	—	106	1	no	—
1255	C₂³	—	106	1	no	—
1256	C₂³	—	106	1	no	—
1257	C₂³	—	106	1	no	—
1258	C₂³	—	106	1	no	—
1259	C₂³	—	106	1	no	—
1260	C₂³	—	106	1	no	—
1261	C₂³	—	106	1	no	—
1262	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1263	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1264	Q₈	—	4	4	no	—
1265	D₄	—	212	4	no	—
1266	D₄	—	212	4	no	—
1267	D₄	—	212	4	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	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	4	4	no	—
1303	C₂×C₄	—	53	2	no	—
1304	C₂×C₄	—	53	2	no	—
1305	C₂×C₄	—	53	2	no	—
1306	C₂×C₄	—	53	2	no	—
1307	C₂×C₄	—	53	2	no	—
1308	C₂×C₄	—	53	2	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	—	106	1	no	—
1324	C₂×C₄	—	106	1	no	—
1325	C₂×C₄	—	106	1	no	—
1326	C₂×C₄	—	106	1	no	—
1327	C₂×C₄	—	106	1	no	—
1328	C₂×C₄	—	106	1	no	—
1329	C₂×C₄	—	106	1	no	—
1330	C₂×C₄	—	106	1	no	—
1331	C₂×C₄	—	106	1	no	—
1332	C₂×C₄	—	106	1	no	—
1333	C₂×C₄	—	106	1	no	—
1334	C₂×C₄	—	106	1	no	—
1335	C₂×C₄	—	106	1	no	—
1336	C₂×C₄	—	106	1	no	—
1337	C₂×C₄	—	106	1	no	—
1338	C₂×C₄	—	106	1	no	—
1339	C₂×C₄	—	106	1	no	—
1340	C₂×C₄	—	106	1	no	—
1341	C₂×C₄	—	106	1	no	—
1342	C₂×C₄	—	106	1	no	—
1343	C₂×C₄	—	106	1	no	—
1344	C₂×C₄	—	106	1	no	—
1345	C₂×C₄	—	424	2	no	—
1346	C₂×C₄	—	424	2	no	—
1347	C₂×C₄	—	212	4	no	—
1348	C₂×C₄	—	212	4	no	—
1349	C₂×C₄	—	212	4	no	—
1350	C₂×C₄	—	212	4	no	—
1351	C₂×C₄	—	212	4	no	—
1352	C₂×C₄	—	212	4	no	—
1353	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1354	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1355	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1356	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1357	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1358	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1359	C₂×C₄	#13133262	1	2	yes	—
1360	C₂×C₄	#13133264	1	2	yes	—
1361	C₂²	—	2	2	no	—
1362	C₂²	—	2	2	no	—
1363	C₂²	—	2	2	no	—
1364	C₂²	—	4	1	no	—
1365	C₂²	—	4	1	no	—
1366	C₂²	—	4	1	no	—
1367	C₂²	—	4	1	no	—
1368	C₂²	—	106	2	no	—
1369	C₂²	—	106	2	no	—
1370	C₂²	—	106	2	no	—
1371	C₂²	—	106	2	no	—
1372	C₂²	—	106	2	no	—
1373	C₂²	—	106	2	no	—
1374	C₂²	—	212	1	no	—
1375	C₂²	—	212	1	no	—
1376	C₂²	—	212	1	no	—
1377	C₂²	—	212	1	no	—
1378	C₂²	—	212	1	no	—
1379	C₂²	—	212	1	no	—
1380	C₂²	—	212	1	no	—
1381	C₂²	—	212	1	no	—
1382	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1383	C₂²	C₂×#13133262	1	1	yes	characteristic
1384	C₂²	C₂×#13133264	1	1	yes	characteristic
1385	C₂²	#16811459	1	1	yes	characteristic
1386	C₂²	#16811459	1	1	yes	characteristic
1387	C₂²	#16811460	1	1	yes	characteristic
1388	C₂²	#16811460	1	1	yes	characteristic
1389	C₄	—	2	2	no	—
1390	C₄	—	2	2	no	—
1391	C₄	—	2	2	no	—
1392	C₄	—	2	2	no	—
1393	C₄	—	2	2	no	—
1394	C₄	—	2	2	no	—
1395	C₄	—	2	2	no	—
1396	C₄	—	2	2	no	—
1397	C₄	—	4	1	no	—
1398	C₄	—	4	1	no	—
1399	C₄	—	4	1	no	—
1400	C₄	—	4	1	no	—
1401	C₄	—	4	1	no	—
1402	C₄	—	4	1	no	—
1403	C₄	—	106	2	no	—
1404	C₄	—	106	2	no	—
1405	C₄	—	106	2	no	—
1406	C₄	—	106	2	no	—
1407	C₄	—	106	2	no	—
1408	C₄	—	106	2	no	—
1409	C₄	—	212	1	no	—
1410	C₄	—	212	1	no	—
1411	C₄	—	212	1	no	—
1412	C₄	—	212	1	no	—
1413	C₄	—	212	1	no	—
1414	C₄	—	212	1	no	—
1415	C₄	—	212	1	no	—
1416	C₄	—	212	1	no	—
1417	C₂	—	4	2	no	—
1418	C₂	—	212	2	no	—
1419	C₂	—	212	2	no	—
1420	C₂	#20287917	1	1	yes	characteristic
1421	C₂	C₄×#13133262	1	1	yes	characteristic
1422	C₂	C₄×#13133264	1	1	yes	characteristic
1423	C₂	#20288885	1	1	yes	characteristic
1424	C₂	#20288994	1	1	yes	characteristic
1425	C₂	#20289218	1	1	yes	characteristic
1426	C₂	#20289404	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2362	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂×#13133191	C₂²
hypercenter	#2362	D₅₃
hypocenter	C₅₃	#34449
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2362

Complements

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

N	H ≅ G/N	type
2. #20277898	C₂	semidirect
3. #20277881	C₂	semidirect
4. #20277876	C₂	semidirect
5. #20277861	C₂	semidirect
6. #20277845	C₂	semidirect
7. #20277838	C₂	semidirect
8. #20277829	C₂	semidirect
9. #20277819	C₂	semidirect
10. #20277813	C₂	semidirect
11. #20277807	C₂	semidirect
12. #20277716	C₂	semidirect
13. #20277685	C₂	semidirect
14. #20277643	C₂	semidirect
15. #20277593	C₂	semidirect
16. #20277585	C₂	semidirect
17. #20277504	C₂	semidirect
18. #20277499	C₂	semidirect
19. #20277498	C₂	semidirect
20. #20277498	C₂	semidirect
21. #20277484	C₂	semidirect
22. #20277483	C₂	semidirect
24. #20277470	C₂	semidirect
26. #20277388	C₂	semidirect
27. #20277356	C₂	semidirect
28. C₄×#13133193	C₂	semidirect
29. C₄×#13133202	C₂	semidirect
30. #20277157	C₂	semidirect
31. C₅₃×#2362	C₂	semidirect
32. #16811222	C₄	semidirect
199. #13133212	C₂×C₄	semidirect
200. #13133212	C₂×C₄	semidirect
201. #13133208	C₂×C₄	semidirect
202. #13133208	C₂×C₄	semidirect
205. #13133201	C₂×C₄	semidirect
206. #13133201	C₂×C₄	semidirect
207. #13133193	C₂×C₄	semidirect
208. #13133193	C₂×C₄	semidirect
211. #13133177	C₂×C₄	semidirect
212. #13133177	C₂×C₄	semidirect
225. C₂×#11719919	C₂×C₄	semidirect
328. C₂²⋊Q₈×C₅₃	C₂×C₄	semidirect
715. #2362	D₅₃	semidirect
901. C₅₃	#34449	semidirect
925. C₂²⋊Q₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811222	2
#20277898	2
#20277881	2
#20277876	2
#20277861	2
#20277845	2
#20277838	2
#20277829	2
#20277819	2
#20277813	2
#20277807	2
#20277716	2
#20277685	2
#20277643	2
#20277593	2
#20277585	2
#20277504	2
#20277499	2
#20277498	2
#20277484	2
#20277483	2
#20277480	2
#20277470	2
#20277408	2
#20277388	2
#20277356	2
C₄×#13133193	2
C₄×#13133202	2
#20277157	2
C₅₃×#2362	2
#34449	53