Subgroups — #27549819

Order 13568.

2164 conjugacy classes of subgroups.

The subgroup lattice has 1486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811297	C₂	1	1	yes	maximal, characteristic
2	#20277886	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277860	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277859	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277855	C₂	1	1	yes	maximal, characteristic
6	#20277844	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277838	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277835	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277745	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277743	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277690	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277685	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277601	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277567	C₂	1	1	yes	maximal, characteristic, complemented
15	#20277559	C₂	1	1	yes	maximal, characteristic, complemented
16	#20277508	C₂	1	1	yes	maximal, characteristic, complemented
17	#20277505	C₂	1	1	yes	maximal, characteristic, complemented
18	#20277486	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277483	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277466	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277465	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277426	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277377	C₂	1	1	yes	maximal, characteristic
24	#20277325	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277324	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277312	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277309	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#13133202	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277159	C₂	1	1	yes	maximal, characteristic, complemented
30	#20277157	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2346	C₂	1	1	yes	maximal, characteristic, complemented
32	#16811297	C₄	1	16	yes	complemented
33	C₂×#13133212	C₂²	1	1	yes	characteristic
34	C₂×#13133211	C₂²	1	1	yes	characteristic
35	C₂×#13133205	C₂²	1	1	yes	characteristic
36	C₂×#13133202	C₂²	1	1	yes	characteristic
37	C₂×#13133202	C₂²	1	1	yes	characteristic
38	C₂×#13133200	C₂²	1	1	yes	characteristic
39	C₂×#13133195	C₂²	1	1	yes	characteristic
40	C₂×#13133194	C₂²	1	1	yes	characteristic
41	C₂×#13133187	C₂²	1	1	yes	characteristic
42	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
45	C₂×#13133177	C₂²	1	1	yes	characteristic
46	C₂×#13133174	C₂²	1	1	yes	characteristic
47	C₂×#13133174	C₂²	1	1	yes	characteristic
48	C₂×#13133173	C₂²	1	1	yes	characteristic
49	C₂²×#11719921	C₂²	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
53	#16810529	C₂²	1	1	yes	characteristic, complemented
54	#16810527	C₂²	1	1	yes	characteristic, complemented
55	#16810527	C₂²	1	1	yes	characteristic, complemented
56	#16810525	C₂²	1	1	yes	characteristic
57	#16810524	C₂²	1	1	yes	characteristic
58	#16810524	C₂²	1	1	yes	characteristic
59	#16810523	C₂²	1	1	yes	characteristic
60	#16810523	C₂²	1	1	yes	characteristic
61	#16810520	C₂²	1	1	yes	characteristic, complemented
62	#16810520	C₂²	1	1	yes	characteristic, complemented
63	#16810518	C₂²	1	1	yes	characteristic, complemented
64	#16810518	C₂²	1	1	yes	characteristic, complemented
65	#16810517	C₂²	1	1	yes	characteristic
66	#16810517	C₂²	1	1	yes	characteristic
67	#16810516	C₂²	1	1	yes	characteristic
68	#16810516	C₂²	1	1	yes	characteristic
69	#16810516	C₂²	1	1	yes	characteristic
70	#16810516	C₂²	1	1	yes	characteristic
71	#16810515	C₂²	1	1	yes	characteristic
72	#16810515	C₂²	1	1	yes	characteristic
73	#16810515	C₂²	1	1	yes	characteristic
74	#16810515	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	#16810515	C₂²	1	1	yes	characteristic
80	#16810515	C₂²	1	1	yes	characteristic, complemented
81	#16810515	C₂²	1	1	yes	characteristic, complemented
82	#16810515	C₂²	1	1	yes	characteristic, complemented
83	#16810514	C₂²	1	1	yes	characteristic
84	#16810514	C₂²	1	1	yes	characteristic
85	#16810514	C₂²	1	1	yes	characteristic
86	#16810514	C₂²	1	1	yes	characteristic
87	#16810514	C₂²	1	1	yes	characteristic
88	#16810514	C₂²	1	1	yes	characteristic, complemented
89	#16810513	C₂²	1	1	yes	characteristic
90	#16810513	C₂²	1	1	yes	characteristic
91	#16810513	C₂²	1	1	yes	characteristic
92	#16810513	C₂²	1	1	yes	characteristic
93	#16810513	C₂²	1	1	yes	characteristic
94	#16810513	C₂²	1	1	yes	characteristic
95	#16810513	C₂²	1	1	yes	characteristic, complemented
96	#16810513	C₂²	1	1	yes	characteristic, complemented
97	#16810512	C₂²	1	1	yes	characteristic
98	#16810512	C₂²	1	1	yes	characteristic
99	#16810511	C₂²	1	1	yes	characteristic
100	#16810511	C₂²	1	1	yes	characteristic
101	#16810510	C₂²	1	1	yes	characteristic, complemented
102	#16810510	C₂²	1	1	yes	characteristic, complemented
103	#16810510	C₂²	1	1	yes	characteristic, complemented
104	#16810510	C₂²	1	1	yes	characteristic, complemented
105	#16810509	C₂²	1	1	yes	characteristic, complemented
106	#16810509	C₂²	1	1	yes	characteristic, complemented
107	#16810509	C₂²	1	1	yes	characteristic, complemented
108	#16810509	C₂²	1	1	yes	characteristic, complemented
109	#16810508	C₂²	1	1	yes	characteristic, complemented
110	#16810508	C₂²	1	1	yes	characteristic, complemented
111	#16810507	C₂²	1	1	yes	characteristic, complemented
112	#16810507	C₂²	1	1	yes	characteristic, complemented
113	#16810505	C₂²	1	1	yes	characteristic, complemented
114	#16810505	C₂²	1	1	yes	characteristic, complemented
115	#16810504	C₂²	1	1	yes	characteristic, complemented
116	#16810504	C₂²	1	1	yes	characteristic, complemented
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	#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	#16810497	C₂²	1	1	yes	characteristic
126	#16810497	C₂²	1	1	yes	characteristic, complemented
127	#16810497	C₂²	1	1	yes	characteristic, complemented
128	#16810497	C₂²	1	1	yes	characteristic, complemented
129	#16810494	C₂²	1	1	yes	characteristic
130	#16810494	C₂²	1	1	yes	characteristic
131	#16810494	C₂²	1	1	yes	characteristic, complemented
132	#16810494	C₂²	1	1	yes	characteristic, complemented
133	#16810493	C₂²	1	1	yes	characteristic, complemented
134	#16810489	C₂²	1	1	yes	characteristic, complemented
135	#16810487	C₂²	1	1	yes	characteristic, complemented
136	#16810485	C₂²	1	1	yes	characteristic
137	#16810485	C₂²	1	1	yes	characteristic, complemented
138	#16810484	C₂²	1	1	yes	characteristic
139	#16810483	C₂²	1	1	yes	characteristic
140	#16810483	C₂²	1	1	yes	characteristic
141	#16810482	C₂²	1	1	yes	characteristic
142	#16810480	C₂²	1	1	yes	characteristic
143	#16810480	C₂²	1	1	yes	characteristic
144	#16810478	C₂²	1	1	yes	characteristic
145	#16810478	C₂²	1	1	yes	characteristic
146	#16810478	C₂²	1	1	yes	characteristic
147	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
148	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
149	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
150	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
151	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
152	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
153	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
154	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
155	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
156	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
157	#16810474	C₂²	1	1	yes	characteristic, complemented
158	#16810474	C₂²	1	1	yes	characteristic, complemented
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, complemented
166	C₄×#11719921	C₂²	1	1	yes	characteristic, complemented
167	#16810470	C₂²	1	1	yes	characteristic
168	#16810470	C₂²	1	1	yes	characteristic
169	#16810470	C₂²	1	1	yes	characteristic
170	#16810470	C₂²	1	1	yes	characteristic
171	#16810470	C₂²	1	1	yes	characteristic, complemented
172	#16810468	C₂²	1	1	yes	characteristic, complemented
173	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#388	C₂²	1	1	yes	characteristic
177	C₅₃×#388	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#380	C₂²	1	1	yes	characteristic
183	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
188	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
191	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
192	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
193	C₂³×Dic₅₃	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	#13133212	C₂×C₄	1	8	yes	complemented
202	#13133211	C₂×C₄	1	8	yes	complemented
203	#13133205	C₂×C₄	1	8	yes	—
204	#13133202	C₂×C₄	1	8	yes	—
205	#13133202	C₂×C₄	1	8	yes	complemented
206	#13133200	C₂×C₄	1	8	yes	complemented
207	#13133195	C₂×C₄	1	8	yes	complemented
208	#13133194	C₂×C₄	1	8	yes	complemented
209	#13133187	C₂×C₄	1	8	yes	—
210	C₄×Dic₁₀₆	—	4	2	no	—
211	C₄×D₂₁₂	—	4	2	no	—
212	C₄×D₂₁₂	C₂×C₄	1	8	yes	complemented
213	#13133177	C₂×C₄	1	8	yes	complemented
214	#13133174	—	4	2	no	—
215	#13133174	C₂×C₄	1	8	yes	complemented
216	#13133173	—	4	2	no	—
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×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×#11719921	C₂×C₄	1	8	yes	complemented
245	C₂×#11719921	C₂³	1	1	yes	characteristic
246	C₂×#11719921	C₂³	1	1	yes	characteristic
247	C₂×#11719921	C₂³	1	1	yes	characteristic
248	C₂×#11719921	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×#11719921	C₂³	1	1	yes	characteristic
270	C₂×#11719921	C₂³	1	1	yes	characteristic
271	C₂×#11719921	C₂³	1	1	yes	characteristic
272	C₂×#11719921	C₂³	1	1	yes	characteristic
273	C₂×#11719921	C₂³	1	1	yes	characteristic
274	C₂×#11719921	C₂³	1	1	yes	characteristic
275	C₂×#11719921	C₂³	1	1	yes	characteristic
276	C₂²⋊C₄×D₅₃	—	4	2	no	—
277	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₄²×D₅₃	—	4	2	no	—
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	#117×C₅₃	C₂×C₄	1	8	yes	complemented
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×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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×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	C₂³×D₅₃	—	4	1	no	—
366	C₂³×D₅₃	—	4	1	no	—
367	C₂³×D₅₃	—	4	1	no	—
368	C₂³×D₅₃	—	4	1	no	—
369	C₂³×D₅₃	—	4	1	no	—
370	C₂³×D₅₃	—	4	1	no	—
371	C₂³×D₅₃	C₂²×C₄	1	4	yes	—
372	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
373	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
374	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	—	4	1	no	—
376	C₂²×C₄×C₅₃	—	4	1	no	—
377	C₂²×C₄×C₅₃	C₂²×C₄	1	4	yes	—
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	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×C₂²⋊D₅₃	—	4	1	no	—
393	C₂×C₂²⋊D₅₃	—	4	1	no	—
394	C₂×C₂²⋊D₅₃	C₂²×C₄	1	4	yes	—
395	C₂²×Dic₅₃	—	4	1	no	—
396	C₂²×Dic₅₃	—	4	1	no	—
397	C₂²×Dic₅₃	C₂²×C₄	1	4	yes	—
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	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	C₂×D₂₁₂	—	4	1	no	—
412	C₂×D₂₁₂	—	4	1	no	—
413	C₂×D₂₁₂	—	4	1	no	—
414	C₂×D₂₁₂	—	4	1	no	—
415	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
416	C₂×D₂₁₂	C₂²×C₄	1	4	yes	—
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	—	4	1	no	—
433	C₂×C₄×D₅₃	—	4	1	no	—
434	C₂×C₄×D₅₃	—	4	1	no	—
435	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
436	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
437	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
438	C₂×Dic₁₀₆	—	4	1	no	—
439	C₂×Dic₁₀₆	—	4	1	no	—
440	C₂×Dic₁₀₆	C₂²×C₄	1	4	yes	—
441	C₄⋊C₄×C₅₃	—	4	1	no	—
442	C₄⋊C₄×C₅₃	—	4	1	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₄⋊C₄×C₅₃	—	4	1	no	—
447	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
448	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	4	1	no	—
451	C₂²⋊C₄×C₅₃	—	4	1	no	—
452	C₂²⋊C₄×C₅₃	—	4	1	no	—
453	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
454	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
455	C₄²×C₅₃	—	2	2	no	—
456	C₄²×C₅₃	—	2	2	no	—
457	C₄²×C₅₃	—	4	1	no	—
458	C₄²×C₅₃	—	4	1	no	—
459	C₄²×C₅₃	—	4	1	no	—
460	C₄²×C₅₃	—	4	1	no	—
461	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
462	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
463	C₂²⋊Dic₅₃	—	4	1	no	—
464	C₂²⋊Dic₅₃	—	4	1	no	—
465	C₂²⋊Dic₅₃	—	4	1	no	—
466	C₂²⋊Dic₅₃	—	4	1	no	—
467	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
468	#11719921	—	2	2	no	—
469	#11719921	—	4	1	no	—
470	#11719921	—	4	1	no	—
471	#11719921	—	4	1	no	—
472	#11719921	—	4	1	no	—
473	#11719921	—	4	1	no	—
474	#11719921	—	4	1	no	—
475	#11719921	—	4	1	no	—
476	#11719921	—	4	1	no	—
477	#11719921	—	4	1	no	—
478	#11719921	—	4	1	no	—
479	#11719921	—	4	1	no	—
480	#11719921	—	4	1	no	—
481	#11719921	—	4	1	no	—
482	#11719921	—	4	1	no	—
483	#11719921	—	4	1	no	—
484	#11719921	—	4	1	no	—
485	#11719921	—	4	1	no	—
486	#11719921	—	4	1	no	—
487	#11719921	—	4	1	no	—
488	#11719921	C₂²×C₄	1	4	yes	—
489	#11719921	C₂²×C₄	1	4	yes	—
490	#11719921	C₂²×C₄	1	4	yes	—
491	#11719921	C₂²×C₄	1	4	yes	—
492	#11719921	C₂²×C₄	1	4	yes	—
493	#11719921	C₂²×C₄	1	4	yes	—
494	#11719921	C₂²×C₄	1	4	yes	—
495	#11719921	C₂²×C₄	1	4	yes	—
496	#11719921	C₂²×C₄	1	4	yes	—
497	#11719921	C₂²×C₄	1	4	yes	—
498	#11719921	C₂²×C₄	1	4	yes	—
499	C₄⋊Dic₅₃	—	4	1	no	—
500	C₄⋊Dic₅₃	—	4	1	no	—
501	C₄⋊Dic₅₃	—	4	1	no	—
502	C₄⋊Dic₅₃	—	4	1	no	—
503	C₄⋊Dic₅₃	—	4	1	no	—
504	C₄⋊Dic₅₃	—	4	1	no	—
505	C₄⋊Dic₅₃	—	4	1	no	—
506	C₄⋊Dic₅₃	—	4	1	no	—
507	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
508	#11719919	—	2	2	no	—
509	#11719919	—	2	2	no	—
510	#11719919	—	4	1	no	—
511	#11719919	—	4	1	no	—
512	#11719919	—	4	1	no	—
513	#11719919	—	4	1	no	—
514	#11719919	—	4	1	no	—
515	#11719919	—	4	1	no	—
516	#11719919	C₂²×C₄	1	4	yes	—
517	#11719919	C₂²×C₄	1	4	yes	—
518	#11719919	C₂²×C₄	1	4	yes	—
519	#11719919	C₂²×C₄	1	4	yes	—
520	#11719919	C₂²×C₄	1	4	yes	—
521	C₄×Dic₅₃	—	2	2	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	—	4	1	no	—
527	C₄×Dic₅₃	—	4	1	no	—
528	C₄×Dic₅₃	—	4	1	no	—
529	C₄×Dic₅₃	—	4	1	no	—
530	C₄×Dic₅₃	—	4	1	no	—
531	C₄×Dic₅₃	—	4	1	no	—
532	C₄×Dic₅₃	—	4	1	no	—
533	C₄×Dic₅₃	—	4	1	no	—
534	C₄×Dic₅₃	—	4	1	no	—
535	C₄×Dic₅₃	—	4	1	no	—
536	C₄×Dic₅₃	—	4	1	no	—
537	C₄×Dic₅₃	C₂²×C₄	1	4	yes	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	C₂³×C₄	1	2	yes	—
545	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
546	C₂²×D₅₃	—	2	1	no	—
547	C₂²×D₅₃	—	2	1	no	—
548	C₂²×D₅₃	—	2	1	no	—
549	C₂²×D₅₃	—	2	1	no	—
550	C₂²×D₅₃	—	2	1	no	—
551	C₂²×D₅₃	—	2	1	no	—
552	C₂²×D₅₃	—	2	1	no	—
553	C₂²×D₅₃	—	2	1	no	—
554	C₂²×D₅₃	—	2	1	no	—
555	C₂²×D₅₃	—	2	1	no	—
556	C₂²×D₅₃	—	2	1	no	—
557	C₂²×D₅₃	—	2	1	no	—
558	C₂²×D₅₃	—	2	1	no	—
559	C₂²×D₅₃	—	2	1	no	—
560	C₂²×D₅₃	—	2	1	no	—
561	C₂²×D₅₃	—	2	1	no	—
562	C₂²×D₅₃	—	2	1	no	—
563	C₂²×D₅₃	—	2	1	no	—
564	C₂²×D₅₃	—	4	4	no	—
565	C₂²×D₅₃	—	4	4	no	—
566	C₂²×D₅₃	—	4	4	no	—
567	C₂²×D₅₃	—	8	2	no	—
568	C₂²×D₅₃	—	8	2	no	—
569	C₂²×D₅₃	—	8	2	no	—
570	C₂²×D₅₃	—	8	2	no	—
571	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
572	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
573	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
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	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	4	4	no	—
610	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
611	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
612	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
613	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
614	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
615	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
616	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
617	C₂²⋊D₅₃	—	4	4	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	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	4	4	no	—
653	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
654	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
655	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
656	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
657	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
658	D₂₁₂	—	4	4	no	—
659	D₂₁₂	—	4	4	no	—
660	C₄×D₅₃	—	4	4	no	—
661	C₄×D₅₃	—	4	4	no	—
662	C₄×D₅₃	—	4	4	no	—
663	C₄×D₅₃	—	4	4	no	—
664	C₄×D₅₃	—	4	4	no	—
665	C₄×D₅₃	—	8	2	no	—
666	C₄×D₅₃	—	8	2	no	—
667	Dic₁₀₆	—	4	4	no	—
668	#34508	—	53	1	no	maximal, Sylow
669	C₂²×C₅₃	—	2	2	no	—
670	C₂²×C₅₃	—	2	2	no	—
671	C₂²×C₅₃	—	2	2	no	—
672	C₂²×C₅₃	—	4	1	no	—
673	C₂²×C₅₃	—	4	1	no	—
674	C₂²×C₅₃	—	4	1	no	—
675	C₂²×C₅₃	—	4	1	no	—
676	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
677	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
678	C₂²×C₅₃	#585	1	1	yes	characteristic
679	C₂²×C₅₃	#585	1	1	yes	characteristic
680	C₂²×C₅₃	#585	1	1	yes	characteristic
681	C₂²×C₅₃	#585	1	1	yes	characteristic
682	C₂²×C₅₃	#585	1	1	yes	characteristic
683	C₂×D₅₃	—	2	2	no	—
684	C₂×D₅₃	—	2	2	no	—
685	C₂×D₅₃	—	2	2	no	—
686	C₂×D₅₃	—	2	2	no	—
687	C₂×D₅₃	—	2	2	no	—
688	C₂×D₅₃	—	2	2	no	—
689	C₂×D₅₃	—	2	2	no	—
690	C₂×D₅₃	—	2	2	no	—
691	C₂×D₅₃	—	2	2	no	—
692	C₂×D₅₃	—	4	1	no	—
693	C₂×D₅₃	—	4	1	no	—
694	C₂×D₅₃	—	4	1	no	—
695	C₂×D₅₃	—	4	1	no	—
696	C₂×D₅₃	—	4	1	no	—
697	C₂×D₅₃	—	4	1	no	—
698	C₂×D₅₃	—	4	1	no	—
699	C₂×D₅₃	—	4	1	no	—
700	C₂×D₅₃	—	4	1	no	—
701	C₂×D₅₃	—	4	1	no	—
702	C₂×D₅₃	—	4	1	no	—
703	C₂×D₅₃	—	4	1	no	—
704	C₂×D₅₃	—	8	8	no	—
705	C₄×C₅₃	—	2	2	no	—
706	C₄×C₅₃	—	2	2	no	—
707	C₄×C₅₃	—	2	2	no	—
708	C₄×C₅₃	—	2	2	no	—
709	C₄×C₅₃	—	2	2	no	—
710	C₄×C₅₃	—	2	2	no	—
711	C₄×C₅₃	—	2	2	no	—
712	C₄×C₅₃	—	4	1	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	1	no	—
718	C₄×C₅₃	—	4	1	no	—
719	Dic₅₃	—	2	2	no	—
720	Dic₅₃	—	2	2	no	—
721	Dic₅₃	—	2	2	no	—
722	Dic₅₃	—	2	2	no	—
723	Dic₅₃	—	2	2	no	—
724	Dic₅₃	—	4	1	no	—
725	Dic₅₃	—	4	1	no	—
726	Dic₅₃	—	4	1	no	—
727	Dic₅₃	—	4	1	no	—
728	Dic₅₃	—	4	1	no	—
729	Dic₅₃	—	4	1	no	—
730	Dic₅₃	—	4	1	no	—
731	Dic₅₃	—	4	1	no	—
732	C₂×#551	—	53	1	no	—
733	#2379	—	53	1	no	—
734	#2376	—	53	1	no	—
735	#2376	—	53	1	no	—
736	#2375	—	53	1	no	—
737	#2374	—	53	1	no	—
738	#2373	—	53	1	no	—
739	#2373	—	53	1	no	—
740	#2362	—	53	1	no	—
741	#2362	—	53	1	no	—
742	#2357	—	53	1	no	—
743	#2357	—	53	1	no	—
744	#2346	—	53	1	no	—
745	#2346	D₅₃	1	1	yes	characteristic, complemented
746	#2342	—	53	1	no	—
747	#2342	—	53	1	no	—
748	#2335	—	53	1	no	—
749	#2335	—	53	1	no	—
750	#2334	—	53	1	no	—
751	#2334	—	53	1	no	—
752	#2332	—	53	1	no	—
753	#2332	—	53	1	no	—
754	#2326	—	53	1	no	—
755	#2321	—	53	1	no	—
756	#2314	—	53	1	no	—
757	#2314	—	53	1	no	—
758	#2312	—	53	1	no	—
759	#2312	—	53	1	no	—
760	C₄×#123	—	53	1	no	—
761	#2290	—	53	1	no	—
762	#2290	—	53	1	no	—
763	C₂×C₅₃	—	4	2	no	—
764	C₂×C₅₃	#3428	1	1	yes	characteristic
765	C₂×C₅₃	#3428	1	1	yes	characteristic
766	C₂×C₅₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic
767	C₂×C₅₃	#3533	1	1	yes	characteristic
768	C₂×C₅₃	#3540	1	1	yes	characteristic
769	C₂×C₅₃	#3566	1	1	yes	characteristic
770	C₂×C₅₃	#3566	1	1	yes	characteristic
771	D₅₃	—	4	2	no	—
772	D₅₃	—	4	2	no	—
773	D₅₃	—	4	2	no	—
774	#551	—	53	16	no	—
775	C₂×#126	—	53	1	no	—
776	C₂×#126	—	53	1	no	—
777	C₂×#124	—	53	1	no	—
778	C₂×#123	—	53	1	no	—
779	C₂×#123	—	53	1	no	—
780	C₂×#123	—	53	1	no	—
781	C₂×C₂²⋊Q₈	—	53	1	no	—
782	C₂×C₂²⋊Q₈	—	53	1	no	—
783	C₂×#120	—	53	1	no	—
784	C₂×C₄×Q₈	—	53	1	no	—
785	C₂×C₄×D₄	—	53	1	no	—
786	C₂×C₄×D₄	—	53	1	no	—
787	C₂×C₄×D₄	—	53	1	no	—
788	C₂×#117	—	53	1	no	—
789	C₂×#117	—	53	1	no	—
790	C₂×#117	—	53	1	no	—
791	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
792	C₂²×C₂²⋊C₄	—	53	1	no	—
793	C₂²×C₂²⋊C₄	—	53	1	no	—
794	C₂²×C₂²⋊C₄	—	53	1	no	—
795	C₂²×C₄²	—	53	1	no	—
796	#391	—	53	1	no	—
797	#391	—	53	1	no	—
798	#391	—	53	1	no	—
799	#390	—	53	1	no	—
800	#390	—	53	1	no	—
801	#390	—	53	1	no	—
802	#390	—	53	1	no	—
803	#390	—	53	1	no	—
804	#389	—	53	1	no	—
805	#389	—	53	1	no	—
806	#389	—	53	1	no	—
807	#389	—	53	1	no	—
808	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
809	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
810	#388	—	53	1	no	—
811	#388	—	53	1	no	—
812	#388	—	53	1	no	—
813	#388	—	53	1	no	—
814	#388	—	53	1	no	—
815	#388	—	53	1	no	—
816	#388	—	53	1	no	—
817	#388	—	53	1	no	—
818	#388	—	53	1	no	—
819	#388	—	53	1	no	—
820	#388	—	53	1	no	—
821	#388	—	53	1	no	—
822	#388	—	53	1	no	—
823	#388	—	53	1	no	—
824	#388	—	53	1	no	—
825	#388	—	53	1	no	—
826	#388	—	53	1	no	—
827	#388	—	53	1	no	—
828	#388	—	53	1	no	—
829	#388	—	53	1	no	—
830	#388	—	53	1	no	—
831	#388	—	53	1	no	—
832	#388	—	53	1	no	—
833	#388	—	53	1	no	—
834	#388	—	53	1	no	—
835	#388	—	53	1	no	—
836	#388	—	53	1	no	—
837	#388	—	53	1	no	—
838	#388	—	53	1	no	—
839	#388	—	53	1	no	—
840	#388	—	53	1	no	—
841	#388	—	53	1	no	—
842	#388	—	53	1	no	—
843	#388	—	53	1	no	—
844	#388	—	53	1	no	—
845	#388	—	53	1	no	—
846	#388	C₂×D₅₃	1	1	yes	characteristic
847	#388	C₂×D₅₃	1	1	yes	characteristic
848	#388	C₂×D₅₃	1	1	yes	characteristic
849	#388	C₂×D₅₃	1	1	yes	characteristic
850	#387	—	53	1	no	—
851	#387	—	53	1	no	—
852	#387	—	53	1	no	—
853	#387	—	53	1	no	—
854	#387	—	53	1	no	—
855	#387	—	53	1	no	—
856	#387	—	53	1	no	—
857	#387	—	53	1	no	—
858	#387	—	53	1	no	—
859	#387	—	53	1	no	—
860	#387	—	53	1	no	—
861	#387	—	53	1	no	—
862	#387	—	53	1	no	—
863	#387	—	53	1	no	—
864	#387	—	53	1	no	—
865	#387	—	53	1	no	—
866	#386	—	53	1	no	—
867	#386	—	53	1	no	—
868	#386	—	53	1	no	—
869	#386	—	53	1	no	—
870	#386	—	53	1	no	—
871	#386	—	53	1	no	—
872	#385	—	53	1	no	—
873	#385	—	53	1	no	—
874	#385	—	53	1	no	—
875	#385	—	53	1	no	—
876	#385	—	53	1	no	—
877	#385	—	53	1	no	—
878	#385	—	53	1	no	—
879	#385	—	53	1	no	—
880	#385	—	53	1	no	—
881	#385	—	53	1	no	—
882	#384	—	53	1	no	—
883	#382	—	53	1	no	—
884	#382	—	53	1	no	—
885	#382	C₂×D₅₃	1	1	yes	characteristic, complemented
886	#382	C₂×D₅₃	1	1	yes	characteristic, complemented
887	#381	—	53	1	no	—
888	#381	—	53	1	no	—
889	#381	—	53	1	no	—
890	#380	—	53	1	no	—
891	#380	—	53	1	no	—
892	#380	—	53	1	no	—
893	#380	—	53	1	no	—
894	#380	—	53	1	no	—
895	#380	C₂×D₅₃	1	1	yes	characteristic
896	#379	—	53	1	no	—
897	#379	—	53	1	no	—
898	#379	—	53	1	no	—
899	C₄×C₄⋊C₄	—	53	1	no	—
900	C₄×C₄⋊C₄	—	53	1	no	—
901	C₄×C₄⋊C₄	—	53	1	no	—
902	C₄×C₄⋊C₄	—	53	1	no	—
903	C₄×C₄⋊C₄	—	53	1	no	—
904	C₄×C₄⋊C₄	—	53	1	no	—
905	C₄×C₄⋊C₄	—	53	1	no	—
906	C₄×C₄⋊C₄	—	53	1	no	—
907	C₄×C₄⋊C₄	—	53	1	no	—
908	C₄×C₄⋊C₄	—	53	1	no	—
909	C₄×C₄⋊C₄	—	53	1	no	—
910	C₄×C₄⋊C₄	—	53	1	no	—
911	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
912	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
913	C₄×C₂²⋊C₄	—	53	1	no	—
914	C₄×C₂²⋊C₄	—	53	1	no	—
915	C₄×C₂²⋊C₄	—	53	1	no	—
916	C₄×C₂²⋊C₄	—	53	1	no	—
917	C₄×C₂²⋊C₄	—	53	1	no	—
918	C₄×C₂²⋊C₄	—	53	1	no	—
919	C₄×C₂²⋊C₄	—	53	1	no	—
920	C₄×C₂²⋊C₄	—	53	1	no	—
921	C₄×C₂²⋊C₄	—	53	1	no	—
922	C₄×C₂²⋊C₄	—	53	1	no	—
923	C₄×C₂²⋊C₄	—	53	1	no	—
924	C₄×C₂²⋊C₄	—	53	1	no	—
925	C₄×C₂²⋊C₄	—	53	1	no	—
926	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
927	#376	—	53	1	no	—
928	#376	C₂×D₅₃	1	1	yes	characteristic, complemented
929	#376	C₂×D₅₃	1	1	yes	characteristic, complemented
930	C₅₃	#34508	1	1	yes	characteristic, complemented, Sylow
931	C₂⁵	—	53	1	no	—
932	C₂²×Q₈	—	53	1	no	—
933	C₂²×D₄	—	53	1	no	—
934	C₂²×D₄	—	53	1	no	—
935	C₂²×D₄	—	53	1	no	—
936	C₂³×C₄	—	53	1	no	—
937	C₂³×C₄	—	53	1	no	—
938	C₂³×C₄	—	53	1	no	—
939	C₂³×C₄	—	53	1	no	—
940	C₂³×C₄	—	53	1	no	—
941	C₂³×C₄	—	53	1	no	—
942	C₂³×C₄	—	53	1	no	—
943	C₂³×C₄	—	53	1	no	—
944	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
945	#126	—	53	8	no	—
946	#126	—	53	8	no	—
947	#124	—	53	8	no	—
948	#123	—	53	8	no	—
949	#123	—	53	8	no	—
950	#123	—	53	8	no	—
951	C₂²⋊Q₈	—	53	8	no	—
952	C₂²⋊Q₈	—	53	8	no	—
953	#120	—	53	8	no	—
954	C₄×Q₈	—	212	2	no	—
955	C₄×D₄	—	53	8	no	—
956	C₄×D₄	—	53	8	no	—
957	C₄×D₄	—	212	2	no	—
958	#117	—	53	8	no	—
959	#117	—	212	2	no	—
960	#117	—	212	2	no	—
961	#117	C₄×D₅₃	1	8	yes	complemented
962	C₂×C₄⋊C₄	—	53	1	no	—
963	C₂×C₄⋊C₄	—	53	1	no	—
964	C₂×C₄⋊C₄	—	53	1	no	—
965	C₂×C₄⋊C₄	—	53	1	no	—
966	C₂×C₄⋊C₄	—	53	1	no	—
967	C₂×C₄⋊C₄	—	53	1	no	—
968	C₂×C₄⋊C₄	—	53	1	no	—
969	C₂×C₄⋊C₄	—	53	1	no	—
970	C₂×C₄⋊C₄	—	53	1	no	—
971	C₂×C₄⋊C₄	—	53	1	no	—
972	C₂×C₄⋊C₄	—	53	1	no	—
973	C₂×C₄⋊C₄	—	53	1	no	—
974	C₂×C₄⋊C₄	—	53	1	no	—
975	C₂×C₄⋊C₄	—	53	1	no	—
976	C₂×C₄⋊C₄	—	53	1	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	1	no	—
984	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	—	53	1	no	—
993	C₂×C₂²⋊C₄	—	53	8	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	—	53	1	no	—
998	C₂×C₂²⋊C₄	—	53	1	no	—
999	C₂×C₂²⋊C₄	—	53	1	no	—
1000	C₂×C₂²⋊C₄	—	53	1	no	—
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	1	no	—
1004	C₂×C₂²⋊C₄	—	53	1	no	—
1005	C₂×C₂²⋊C₄	—	53	8	no	—
1006	C₂×C₂²⋊C₄	—	53	1	no	—
1007	C₂×C₂²⋊C₄	—	53	1	no	—
1008	C₂×C₂²⋊C₄	—	53	1	no	—
1009	C₂×C₂²⋊C₄	—	53	1	no	—
1010	C₂×C₂²⋊C₄	—	53	1	no	—
1011	C₂×C₂²⋊C₄	—	53	1	no	—
1012	C₂×C₂²⋊C₄	—	53	1	no	—
1013	C₂×C₂²⋊C₄	—	53	1	no	—
1014	C₂×C₂²⋊C₄	—	53	1	no	—
1015	C₂×C₂²⋊C₄	—	53	1	no	—
1016	C₂×C₂²⋊C₄	—	53	1	no	—
1017	C₂×C₂²⋊C₄	—	53	1	no	—
1018	C₂×C₂²⋊C₄	—	53	1	no	—
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	53	1	no	—
1023	C₂×C₂²⋊C₄	—	53	1	no	—
1024	C₂×C₂²⋊C₄	—	53	1	no	—
1025	C₂×C₂²⋊C₄	—	53	1	no	—
1026	C₂×C₂²⋊C₄	—	53	1	no	—
1027	C₂×C₂²⋊C₄	—	53	1	no	—
1028	C₂×C₂²⋊C₄	—	53	1	no	—
1029	C₂×C₂²⋊C₄	—	53	1	no	—
1030	C₂×C₂²⋊C₄	—	212	2	no	—
1031	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1037	C₂×C₄²	—	53	1	no	—
1038	C₂×C₄²	—	53	1	no	—
1039	C₂×C₄²	—	53	1	no	—
1040	C₂×C₄²	—	53	1	no	—
1041	C₂×C₄²	—	53	1	no	—
1042	C₂×C₄²	—	53	1	no	—
1043	C₂×C₄²	—	53	1	no	—
1044	C₂×C₄²	—	53	1	no	—
1045	C₂×C₄²	—	53	1	no	—
1046	C₂×C₄²	—	53	1	no	—
1047	C₂×C₄²	—	53	1	no	—
1048	C₂×C₄²	—	53	1	no	—
1049	C₂×C₄²	—	53	1	no	—
1050	C₂×C₄²	—	53	1	no	—
1051	C₂×C₄²	—	53	1	no	—
1052	C₂×C₄²	—	53	1	no	—
1053	C₂×C₄²	—	53	1	no	—
1054	C₂×C₄²	—	212	2	no	—
1055	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1056	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1057	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1058	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1059	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1060	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1061	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1062	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	—	53	1	no	—
1072	#95	—	53	1	no	—
1073	#95	—	53	1	no	—
1074	#95	—	53	1	no	—
1075	#95	—	53	1	no	—
1076	#95	—	53	1	no	—
1077	#95	—	53	1	no	—
1078	#95	—	53	1	no	—
1079	#95	—	53	1	no	—
1080	#95	—	53	1	no	—
1081	#95	—	53	1	no	—
1082	#95	—	53	1	no	—
1083	#95	—	53	1	no	—
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	—	53	1	no	—
1095	#95	C₂²×D₅₃	1	1	yes	characteristic
1096	#95	C₂²×D₅₃	1	1	yes	characteristic
1097	#95	C₂²×D₅₃	1	1	yes	characteristic
1098	#95	C₂²×D₅₃	1	1	yes	characteristic
1099	#95	C₂²×D₅₃	1	1	yes	characteristic
1100	#95	C₂²×D₅₃	1	1	yes	characteristic
1101	#95	C₂²×D₅₃	1	1	yes	characteristic
1102	#95	C₂²×D₅₃	1	1	yes	characteristic
1103	#95	C₂²×D₅₃	1	1	yes	characteristic
1104	#95	C₂²×D₅₃	1	1	yes	characteristic
1105	#95	C₂²×D₅₃	1	1	yes	characteristic
1106	#95	C₂²×D₅₃	1	1	yes	characteristic
1107	C₂⁴	—	53	1	no	—
1108	C₂⁴	—	53	1	no	—
1109	C₂⁴	—	53	1	no	—
1110	C₂⁴	—	53	4	no	—
1111	C₂⁴	—	212	1	no	—
1112	C₂⁴	—	212	1	no	—
1113	C₂⁴	—	212	1	no	—
1114	C₂⁴	—	212	1	no	—
1115	C₂⁴	—	212	1	no	—
1116	C₂⁴	—	212	1	no	—
1117	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1118	C₂×Q₈	—	53	4	no	—
1119	C₂×Q₈	—	212	1	no	—
1120	C₂×Q₈	—	212	1	no	—
1121	C₂×D₄	—	53	4	no	—
1122	C₂×D₄	—	53	4	no	—
1123	C₂×D₄	—	53	4	no	—
1124	C₂×D₄	—	212	1	no	—
1125	C₂×D₄	—	212	1	no	—
1126	C₂×D₄	—	212	1	no	—
1127	C₂×D₄	—	212	1	no	—
1128	C₂×D₄	—	212	1	no	—
1129	C₂×D₄	—	212	1	no	—
1130	C₂²×C₄	—	4	1	no	—
1131	C₂²×C₄	—	4	1	no	—
1132	C₂²×C₄	—	53	1	no	—
1133	C₂²×C₄	—	53	1	no	—
1134	C₂²×C₄	—	53	1	no	—
1135	C₂²×C₄	—	53	1	no	—
1136	C₂²×C₄	—	53	1	no	—
1137	C₂²×C₄	—	53	4	no	—
1138	C₂²×C₄	—	53	4	no	—
1139	C₂²×C₄	—	53	4	no	—
1140	C₂²×C₄	—	53	4	no	—
1141	C₂²×C₄	—	53	1	no	—
1142	C₂²×C₄	—	53	1	no	—
1143	C₂²×C₄	—	53	1	no	—
1144	C₂²×C₄	—	53	1	no	—
1145	C₂²×C₄	—	53	1	no	—
1146	C₂²×C₄	—	53	1	no	—
1147	C₂²×C₄	—	53	1	no	—
1148	C₂²×C₄	—	53	1	no	—
1149	C₂²×C₄	—	106	2	no	—
1150	C₂²×C₄	—	106	2	no	—
1151	C₂²×C₄	—	212	1	no	—
1152	C₂²×C₄	—	212	1	no	—
1153	C₂²×C₄	—	212	1	no	—
1154	C₂²×C₄	—	212	1	no	—
1155	C₂²×C₄	—	212	1	no	—
1156	C₂²×C₄	—	212	1	no	—
1157	C₂²×C₄	—	212	1	no	—
1158	C₂²×C₄	—	212	1	no	—
1159	C₂²×C₄	—	212	1	no	—
1160	C₂²×C₄	—	212	1	no	—
1161	C₂²×C₄	—	212	1	no	—
1162	C₂²×C₄	—	212	1	no	—
1163	C₂²×C₄	—	212	1	no	—
1164	C₂²×C₄	—	212	1	no	—
1165	C₂²×C₄	—	212	1	no	—
1166	C₂²×C₄	—	212	1	no	—
1167	C₂²×C₄	—	212	1	no	—
1168	C₂²×C₄	—	212	1	no	—
1169	C₂²×C₄	C₂×C₄×D₅₃	1	4	yes	—
1170	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1171	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1173	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1174	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1175	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1176	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1177	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1178	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1179	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1180	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1181	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1182	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1184	C₄⋊C₄	—	4	1	no	—
1185	C₄⋊C₄	—	4	1	no	—
1186	C₄⋊C₄	—	4	1	no	—
1187	C₄⋊C₄	—	4	1	no	—
1188	C₄⋊C₄	—	4	1	no	—
1189	C₄⋊C₄	—	4	1	no	—
1190	C₄⋊C₄	—	53	4	no	—
1191	C₄⋊C₄	—	53	4	no	—
1192	C₄⋊C₄	—	53	4	no	—
1193	C₄⋊C₄	—	53	4	no	—
1194	C₄⋊C₄	—	53	4	no	—
1195	C₄⋊C₄	—	53	4	no	—
1196	C₄⋊C₄	—	106	2	no	—
1197	C₄⋊C₄	—	106	2	no	—
1198	C₄⋊C₄	—	212	1	no	—
1199	C₄⋊C₄	—	212	1	no	—
1200	C₄⋊C₄	—	212	1	no	—
1201	C₄⋊C₄	—	212	1	no	—
1202	C₄⋊C₄	—	212	1	no	—
1203	C₄⋊C₄	—	212	1	no	—
1204	C₄⋊C₄	—	212	1	no	—
1205	C₄⋊C₄	—	212	1	no	—
1206	C₄⋊C₄	—	212	1	no	—
1207	C₄⋊C₄	—	212	1	no	—
1208	C₄⋊C₄	—	212	1	no	—
1209	C₄⋊C₄	—	212	1	no	—
1210	C₄⋊C₄	—	212	1	no	—
1211	C₄⋊C₄	—	212	1	no	—
1212	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1213	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1214	C₂²⋊C₄	—	2	2	no	—
1215	C₂²⋊C₄	—	4	1	no	—
1216	C₂²⋊C₄	—	4	1	no	—
1217	C₂²⋊C₄	—	4	1	no	—
1218	C₂²⋊C₄	—	53	4	no	—
1219	C₂²⋊C₄	—	53	4	no	—
1220	C₂²⋊C₄	—	53	4	no	—
1221	C₂²⋊C₄	—	53	4	no	—
1222	C₂²⋊C₄	—	53	4	no	—
1223	C₂²⋊C₄	—	53	4	no	—
1224	C₂²⋊C₄	—	53	4	no	—
1225	C₂²⋊C₄	—	53	4	no	—
1226	C₂²⋊C₄	—	53	4	no	—
1227	C₂²⋊C₄	—	53	4	no	—
1228	C₂²⋊C₄	—	53	4	no	—
1229	C₂²⋊C₄	—	53	4	no	—
1230	C₂²⋊C₄	—	106	2	no	—
1231	C₂²⋊C₄	—	212	1	no	—
1232	C₂²⋊C₄	—	212	1	no	—
1233	C₂²⋊C₄	—	212	1	no	—
1234	C₂²⋊C₄	—	212	1	no	—
1235	C₂²⋊C₄	—	212	1	no	—
1236	C₂²⋊C₄	—	212	1	no	—
1237	C₂²⋊C₄	—	212	1	no	—
1238	C₂²⋊C₄	—	212	1	no	—
1239	C₂²⋊C₄	—	212	1	no	—
1240	C₂²⋊C₄	—	212	1	no	—
1241	C₂²⋊C₄	—	212	1	no	—
1242	C₂²⋊C₄	—	212	1	no	—
1243	C₂²⋊C₄	—	212	1	no	—
1244	C₂²⋊C₄	—	212	1	no	—
1245	C₂²⋊C₄	—	212	1	no	—
1246	C₂²⋊C₄	—	212	1	no	—
1247	C₂²⋊C₄	—	212	1	no	—
1248	C₂²⋊C₄	—	212	1	no	—
1249	C₂²⋊C₄	—	212	1	no	—
1250	C₂²⋊C₄	—	212	1	no	—
1251	C₂²⋊C₄	—	212	1	no	—
1252	C₂²⋊C₄	—	212	1	no	—
1253	C₂²⋊C₄	—	212	1	no	—
1254	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1255	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1256	C₄²	—	2	2	no	—
1257	C₄²	—	2	2	no	—
1258	C₄²	—	4	1	no	—
1259	C₄²	—	4	1	no	—
1260	C₄²	—	4	1	no	—
1261	C₄²	—	4	1	no	—
1262	C₄²	—	53	4	no	—
1263	C₄²	—	106	2	no	—
1264	C₄²	—	212	1	no	—
1265	C₄²	—	212	1	no	—
1266	C₄²	—	212	1	no	—
1267	C₄²	—	212	1	no	—
1268	C₄²	—	212	1	no	—
1269	C₄²	—	212	1	no	—
1270	C₄²	—	212	1	no	—
1271	C₄²	—	212	1	no	—
1272	C₄²	—	212	1	no	—
1273	C₄²	—	212	1	no	—
1274	C₄²	—	212	1	no	—
1275	C₄²	—	212	1	no	—
1276	C₄²	—	212	1	no	—
1277	C₄²	—	212	1	no	—
1278	C₄²	—	212	1	no	—
1279	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1280	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1281	C₂³	—	2	1	no	—
1282	C₂³	—	2	1	no	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	53	2	no	—
1288	C₂³	—	53	2	no	—
1289	C₂³	—	53	2	no	—
1290	C₂³	—	106	1	no	—
1291	C₂³	—	106	1	no	—
1292	C₂³	—	106	1	no	—
1293	C₂³	—	106	1	no	—
1294	C₂³	—	106	1	no	—
1295	C₂³	—	106	1	no	—
1296	C₂³	—	106	1	no	—
1297	C₂³	—	106	1	no	—
1298	C₂³	—	106	1	no	—
1299	C₂³	—	106	1	no	—
1300	C₂³	—	106	1	no	—
1301	C₂³	—	106	1	no	—
1302	C₂³	—	106	1	no	—
1303	C₂³	—	106	1	no	—
1304	C₂³	—	106	1	no	—
1305	C₂³	—	106	1	no	—
1306	C₂³	—	106	1	no	—
1307	C₂³	—	106	1	no	—
1308	C₂³	—	424	2	no	—
1309	C₂³	—	424	2	no	—
1310	C₂³	—	424	2	no	—
1311	C₂³	—	424	2	no	—
1312	C₂³	—	212	4	no	—
1313	C₂³	—	212	4	no	—
1314	C₂³	—	212	4	no	—
1315	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1316	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1317	Q₈	—	212	4	no	—
1318	D₄	—	212	4	no	—
1319	D₄	—	212	4	no	—
1320	D₄	—	212	4	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	4	4	no	—
1357	C₂×C₄	—	53	2	no	—
1358	C₂×C₄	—	53	2	no	—
1359	C₂×C₄	—	53	2	no	—
1360	C₂×C₄	—	53	2	no	—
1361	C₂×C₄	—	53	2	no	—
1362	C₂×C₄	—	106	1	no	—
1363	C₂×C₄	—	106	1	no	—
1364	C₂×C₄	—	106	1	no	—
1365	C₂×C₄	—	106	1	no	—
1366	C₂×C₄	—	106	1	no	—
1367	C₂×C₄	—	106	1	no	—
1368	C₂×C₄	—	106	1	no	—
1369	C₂×C₄	—	106	1	no	—
1370	C₂×C₄	—	106	1	no	—
1371	C₂×C₄	—	106	1	no	—
1372	C₂×C₄	—	106	1	no	—
1373	C₂×C₄	—	106	1	no	—
1374	C₂×C₄	—	106	1	no	—
1375	C₂×C₄	—	106	1	no	—
1376	C₂×C₄	—	106	1	no	—
1377	C₂×C₄	—	106	1	no	—
1378	C₂×C₄	—	106	1	no	—
1379	C₂×C₄	—	106	1	no	—
1380	C₂×C₄	—	106	1	no	—
1381	C₂×C₄	—	106	1	no	—
1382	C₂×C₄	—	106	1	no	—
1383	C₂×C₄	—	106	1	no	—
1384	C₂×C₄	—	106	1	no	—
1385	C₂×C₄	—	106	1	no	—
1386	C₂×C₄	—	106	1	no	—
1387	C₂×C₄	—	106	1	no	—
1388	C₂×C₄	—	106	1	no	—
1389	C₂×C₄	—	106	1	no	—
1390	C₂×C₄	—	106	1	no	—
1391	C₂×C₄	—	106	1	no	—
1392	C₂×C₄	—	106	1	no	—
1393	C₂×C₄	—	106	1	no	—
1394	C₂×C₄	—	106	1	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	424	2	no	—
1397	C₂×C₄	—	424	2	no	—
1398	C₂×C₄	—	212	4	no	—
1399	C₂×C₄	—	212	4	no	—
1400	C₂×C₄	—	212	4	no	—
1401	C₂×C₄	—	212	4	no	—
1402	C₂×C₄	—	212	4	no	—
1403	C₂×C₄	—	212	4	no	—
1404	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1405	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1406	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1407	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1408	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1409	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1410	C₂×C₄	#13133263	1	2	yes	—
1411	C₂²	—	2	2	no	—
1412	C₂²	—	2	2	no	—
1413	C₂²	—	2	2	no	—
1414	C₂²	—	4	1	no	—
1415	C₂²	—	4	1	no	—
1416	C₂²	—	4	1	no	—
1417	C₂²	—	4	1	no	—
1418	C₂²	—	106	2	no	—
1419	C₂²	—	106	2	no	—
1420	C₂²	—	106	2	no	—
1421	C₂²	—	106	2	no	—
1422	C₂²	—	106	2	no	—
1423	C₂²	—	106	2	no	—
1424	C₂²	—	106	2	no	—
1425	C₂²	—	106	2	no	—
1426	C₂²	—	106	2	no	—
1427	C₂²	—	424	8	no	—
1428	C₂²	—	212	1	no	—
1429	C₂²	—	212	1	no	—
1430	C₂²	—	212	1	no	—
1431	C₂²	—	212	1	no	—
1432	C₂²	—	212	1	no	—
1433	C₂²	—	212	1	no	—
1434	C₂²	—	212	1	no	—
1435	C₂²	—	212	1	no	—
1436	C₂²	—	212	1	no	—
1437	C₂²	—	212	1	no	—
1438	C₂²	—	212	1	no	—
1439	C₂²	—	212	1	no	—
1440	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1441	C₂²	C₂×#13133263	1	1	yes	characteristic
1442	C₂²	#16811458	1	1	yes	characteristic
1443	C₂²	#16811459	1	1	yes	characteristic
1444	C₂²	#16811459	1	1	yes	characteristic
1445	C₂²	#16811459	1	1	yes	characteristic
1446	C₂²	#16811460	1	1	yes	characteristic
1447	C₄	—	2	2	no	—
1448	C₄	—	2	2	no	—
1449	C₄	—	2	2	no	—
1450	C₄	—	2	2	no	—
1451	C₄	—	2	2	no	—
1452	C₄	—	2	2	no	—
1453	C₄	—	2	2	no	—
1454	C₄	—	4	1	no	—
1455	C₄	—	4	1	no	—
1456	C₄	—	4	1	no	—
1457	C₄	—	4	1	no	—
1458	C₄	—	4	1	no	—
1459	C₄	—	4	1	no	—
1460	C₄	—	4	1	no	—
1461	C₄	—	106	2	no	—
1462	C₄	—	106	2	no	—
1463	C₄	—	106	2	no	—
1464	C₄	—	106	2	no	—
1465	C₄	—	106	2	no	—
1466	C₄	—	212	1	no	—
1467	C₄	—	212	1	no	—
1468	C₄	—	212	1	no	—
1469	C₄	—	212	1	no	—
1470	C₄	—	212	1	no	—
1471	C₄	—	212	1	no	—
1472	C₄	—	212	1	no	—
1473	C₄	—	212	1	no	—
1474	C₂	—	4	2	no	—
1475	C₂	—	212	2	no	—
1476	C₂	—	212	2	no	—
1477	C₂	—	212	2	no	—
1478	C₂	#20287915	1	1	yes	characteristic
1479	C₂	#20287916	1	1	yes	characteristic
1480	C₂	C₄×#13133263	1	1	yes	characteristic
1481	C₂	#20288881	1	1	yes	characteristic
1482	C₂	#20288985	1	1	yes	characteristic
1483	C₂	#20289369	1	1	yes	characteristic
1484	C₂	#20289397	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2346	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂×#13133187	C₂²
hypercenter	#2346	D₅₃
hypocenter	C₅₃	#34508
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2346

Complements

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

N	H ≅ G/N	type
2. #20277886	C₂	semidirect
3. #20277860	C₂	semidirect
4. #20277859	C₂	semidirect
6. #20277844	C₂	semidirect
7. #20277838	C₂	semidirect
8. #20277835	C₂	semidirect
9. #20277745	C₂	semidirect
10. #20277743	C₂	semidirect
11. #20277690	C₂	semidirect
12. #20277685	C₂	semidirect
13. #20277601	C₂	semidirect
14. #20277567	C₂	semidirect
15. #20277559	C₂	semidirect
16. #20277508	C₂	semidirect
17. #20277505	C₂	semidirect
18. #20277486	C₂	semidirect
19. #20277483	C₂	semidirect
20. #20277466	C₂	semidirect
21. #20277465	C₂	semidirect
22. #20277426	C₂	semidirect
24. #20277325	C₂	semidirect
25. #20277324	C₂	semidirect
26. #20277312	C₂	semidirect
27. #20277309	C₂	semidirect
28. C₄×#13133202	C₂	semidirect
29. #20277159	C₂	semidirect
30. #20277157	C₂	semidirect
31. C₅₃×#2346	C₂	semidirect
32. #16811297	C₄	semidirect
42. C₂×C₄×Dic₁₀₆	C₂²	semidirect
52. C₂×C₄²×D₅₃	C₂²	semidirect
53. #16810529	C₂²	semidirect
54. #16810527	C₂²	semidirect
55. #16810527	C₂²	semidirect
61. #16810520	C₂²	semidirect
62. #16810520	C₂²	semidirect
63. #16810518	C₂²	semidirect
64. #16810518	C₂²	semidirect
80. #16810515	C₂²	semidirect
81. #16810515	C₂²	semidirect
82. #16810515	C₂²	semidirect
88. #16810514	C₂²	semidirect
95. #16810513	C₂²	semidirect
96. #16810513	C₂²	semidirect
101. #16810510	C₂²	semidirect
102. #16810510	C₂²	semidirect
103. #16810510	C₂²	semidirect
104. #16810510	C₂²	semidirect
105. #16810509	C₂²	semidirect
106. #16810509	C₂²	semidirect
107. #16810509	C₂²	semidirect
108. #16810509	C₂²	semidirect
109. #16810508	C₂²	semidirect
110. #16810508	C₂²	semidirect
111. #16810507	C₂²	semidirect
112. #16810507	C₂²	semidirect
113. #16810505	C₂²	semidirect
114. #16810505	C₂²	semidirect
115. #16810504	C₂²	semidirect
116. #16810504	C₂²	semidirect
126. #16810497	C₂²	semidirect
127. #16810497	C₂²	semidirect
128. #16810497	C₂²	semidirect
131. #16810494	C₂²	semidirect
132. #16810494	C₂²	semidirect
133. #16810493	C₂²	semidirect
134. #16810489	C₂²	semidirect
135. #16810487	C₂²	semidirect
137. #16810485	C₂²	semidirect
147. C₄⋊C₄×Dic₅₃	C₂²	semidirect
148. C₄⋊C₄×Dic₅₃	C₂²	semidirect
149. C₄⋊C₄×Dic₅₃	C₂²	semidirect
150. C₄⋊C₄×Dic₅₃	C₂²	semidirect
151. C₄×#11719919	C₂²	semidirect
152. C₄×#11719919	C₂²	semidirect
153. C₄×#11719919	C₂²	semidirect
154. C₄×#11719919	C₂²	semidirect
155. C₄×C₄⋊Dic₅₃	C₂²	semidirect
156. C₄×C₄⋊Dic₅₃	C₂²	semidirect
157. #16810474	C₂²	semidirect
158. #16810474	C₂²	semidirect
165. C₄×#11719921	C₂²	semidirect
166. C₄×#11719921	C₂²	semidirect
171. #16810470	C₂²	semidirect
172. #16810468	C₂²	semidirect
174. C₅₃×#389	C₂²	semidirect
175. C₅₃×#389	C₂²	semidirect
180. C₅₃×#382	C₂²	semidirect
181. C₅₃×#382	C₂²	semidirect
183. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
184. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
186. C₅₃×#376	C₂²	semidirect
187. C₅₃×#376	C₂²	semidirect
201. #13133212	C₂×C₄	semidirect
202. #13133211	C₂×C₄	semidirect
205. #13133202	C₂×C₄	semidirect
206. #13133200	C₂×C₄	semidirect
207. #13133195	C₂×C₄	semidirect
208. #13133194	C₂×C₄	semidirect
212. C₄×D₂₁₂	C₂×C₄	semidirect
213. #13133177	C₂×C₄	semidirect
215. #13133174	C₂×C₄	semidirect
244. C₂×#11719921	C₂×C₄	semidirect
277. C₂²⋊C₄×D₅₃	C₂×C₄	semidirect
329. #117×C₅₃	C₂×C₄	semidirect
745. #2346	D₅₃	semidirect
808. #389	C₂×D₅₃	semidirect
809. #389	C₂×D₅₃	semidirect
885. #382	C₂×D₅₃	semidirect
886. #382	C₂×D₅₃	semidirect
911. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
912. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
928. #376	C₂×D₅₃	semidirect
929. #376	C₂×D₅₃	semidirect
930. C₅₃	#34508	semidirect
961. #117	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×#16811297	2
#20277886	2
#20277860	2
#20277859	2
#20277855	2
#20277844	2
#20277838	2
#20277835	2
#20277745	2
#20277743	2
#20277690	2
#20277685	2
#20277601	2
#20277567	2
#20277559	2
#20277508	2
#20277505	2
#20277486	2
#20277483	2
#20277466	2
#20277465	2
#20277426	2
#20277377	2
#20277325	2
#20277324	2
#20277312	2
#20277309	2
C₄×#13133202	2
#20277159	2
#20277157	2
C₅₃×#2346	2
#34508	53