Subgroups — #27545002

Order 13568.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#126×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20277841	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277840	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277837	C₂	1	1	yes	maximal, characteristic, complemented
5	#20277836	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277833	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277832	C₂	1	1	yes	maximal, characteristic, complemented
8	#20277829	C₂	1	1	yes	maximal, characteristic, complemented
9	#20277828	C₂	1	1	yes	maximal, characteristic, complemented
10	#20277589	C₂	1	1	yes	maximal, characteristic, complemented
11	#20277588	C₂	1	1	yes	maximal, characteristic, complemented
12	#20277581	C₂	1	1	yes	maximal, characteristic, complemented
13	#20277580	C₂	1	1	yes	maximal, characteristic, complemented
14	#20277563	C₂	1	1	yes	maximal, characteristic
15	#20277559	C₂	1	1	yes	maximal, characteristic
16	#20277558	C₂	1	1	yes	maximal, characteristic
17	#20277558	C₂	1	1	yes	maximal, characteristic
18	#20277496	C₂	1	1	yes	maximal, characteristic, complemented
19	#20277492	C₂	1	1	yes	maximal, characteristic, complemented
20	#20277488	C₂	1	1	yes	maximal, characteristic, complemented
21	#20277484	C₂	1	1	yes	maximal, characteristic, complemented
22	#20277314	C₂	1	1	yes	maximal, characteristic, complemented
23	#20277309	C₂	1	1	yes	maximal, characteristic
24	#126×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#13133211	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277263	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277112	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277069	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277067	C₂	1	1	yes	maximal, characteristic
30	C₄×#13133174	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#126×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133212	C₂²	1	1	yes	characteristic
33	C₂×#13133212	C₂²	1	1	yes	characteristic
34	C₂×#13133212	C₂²	1	1	yes	characteristic
35	C₂×#13133211	C₂²	1	1	yes	characteristic
36	C₂×#13133210	C₂²	1	1	yes	characteristic
37	C₂×#13133210	C₂²	1	1	yes	characteristic
38	C₂×#13133210	C₂²	1	1	yes	characteristic
39	#126×D₅₃	C₄	1	16	yes	complemented
40	C₂×#13133175	C₂²	1	1	yes	characteristic
41	C₂×#13133174	C₂²	1	1	yes	characteristic
42	C₂×#13133174	C₂²	1	1	yes	characteristic
43	C₂×#13133174	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂²×#11719921	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₂²⋊C₄×D₅₃	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
53	#16810521	C₂²	1	1	yes	characteristic, complemented
54	#16810521	C₂²	1	1	yes	characteristic, complemented
55	#16810520	C₂²	1	1	yes	characteristic, complemented
56	#16810520	C₂²	1	1	yes	characteristic, complemented
57	#16810519	C₂²	1	1	yes	characteristic, complemented
58	#16810519	C₂²	1	1	yes	characteristic, complemented
59	#16810518	C₂²	1	1	yes	characteristic, complemented
60	#16810518	C₂²	1	1	yes	characteristic, complemented
61	#16810517	C₂²	1	1	yes	characteristic
62	#16810517	C₂²	1	1	yes	characteristic
63	#16810517	C₂²	1	1	yes	characteristic
64	#16810516	C₂²	1	1	yes	characteristic
65	#16810516	C₂²	1	1	yes	characteristic
66	#16810516	C₂²	1	1	yes	characteristic
67	#16810515	C₂²	1	1	yes	characteristic
68	#16810514	C₂²	1	1	yes	characteristic
69	#16810514	C₂²	1	1	yes	characteristic
70	#16810514	C₂²	1	1	yes	characteristic
71	#16810514	C₂²	1	1	yes	characteristic
72	#16810514	C₂²	1	1	yes	characteristic
73	#16810513	C₂²	1	1	yes	characteristic
74	#16810512	C₂²	1	1	yes	characteristic
75	#16810512	C₂²	1	1	yes	characteristic
76	#16810512	C₂²	1	1	yes	characteristic
77	#16810512	C₂²	1	1	yes	characteristic
78	#16810512	C₂²	1	1	yes	characteristic
79	#16810511	C₂²	1	1	yes	characteristic
80	#16810511	C₂²	1	1	yes	characteristic
81	#16810511	C₂²	1	1	yes	characteristic
82	#16810510	C₂²	1	1	yes	characteristic, complemented
83	#16810509	C₂²	1	1	yes	characteristic, complemented
84	#16810509	C₂²	1	1	yes	characteristic, complemented
85	#16810509	C₂²	1	1	yes	characteristic, complemented
86	#16810508	C₂²	1	1	yes	characteristic, complemented
87	#16810508	C₂²	1	1	yes	characteristic, complemented
88	#16810508	C₂²	1	1	yes	characteristic, complemented
89	#16810507	C₂²	1	1	yes	characteristic, complemented
90	#16810507	C₂²	1	1	yes	characteristic, complemented
91	#16810507	C₂²	1	1	yes	characteristic, complemented
92	#16810507	C₂²	1	1	yes	characteristic, complemented
93	#16810507	C₂²	1	1	yes	characteristic, complemented
94	#16810506	C₂²	1	1	yes	characteristic, complemented
95	#16810506	C₂²	1	1	yes	characteristic, complemented
96	#16810506	C₂²	1	1	yes	characteristic, complemented
97	#16810505	C₂²	1	1	yes	characteristic, complemented
98	#16810505	C₂²	1	1	yes	characteristic, complemented
99	#16810505	C₂²	1	1	yes	characteristic, complemented
100	#16810505	C₂²	1	1	yes	characteristic, complemented
101	#16810505	C₂²	1	1	yes	characteristic, complemented
102	#16810504	C₂²	1	1	yes	characteristic, complemented
103	#16810497	C₂²	1	1	yes	characteristic
104	#16810497	C₂²	1	1	yes	characteristic
105	#16810496	C₂²	1	1	yes	characteristic
106	#16810496	C₂²	1	1	yes	characteristic
107	#16810495	C₂²	1	1	yes	characteristic
108	#16810495	C₂²	1	1	yes	characteristic
109	#16810494	C₂²	1	1	yes	characteristic
110	#16810494	C₂²	1	1	yes	characteristic
111	#16810491	C₂²	1	1	yes	characteristic, complemented
112	#16810487	C₂²	1	1	yes	characteristic, complemented
113	#16810487	C₂²	1	1	yes	characteristic, complemented
114	#16810485	C₂²	1	1	yes	characteristic
115	#16810485	C₂²	1	1	yes	characteristic
116	#16810485	C₂²	1	1	yes	characteristic
117	#16810485	C₂²	1	1	yes	characteristic
118	#16810482	C₂²	1	1	yes	characteristic
119	#16810482	C₂²	1	1	yes	characteristic
120	#16810482	C₂²	1	1	yes	characteristic
121	#16810482	C₂²	1	1	yes	characteristic
122	#16810480	C₂²	1	1	yes	characteristic
123	#16810480	C₂²	1	1	yes	characteristic
124	#16810478	C₂²	1	1	yes	characteristic
125	#16810478	C₂²	1	1	yes	characteristic
126	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
131	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
132	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
133	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
134	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
135	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
136	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
137	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
138	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
139	#16810474	C₂²	1	1	yes	characteristic, complemented
140	#16810474	C₂²	1	1	yes	characteristic, complemented
141	#16810474	C₂²	1	1	yes	characteristic, complemented
142	#16810474	C₂²	1	1	yes	characteristic, complemented
143	#16810474	C₂²	1	1	yes	characteristic, complemented
144	#16810474	C₂²	1	1	yes	characteristic, complemented
145	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
146	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
147	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
148	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄×#11719921	C₂²	1	1	yes	characteristic
150	C₄×#11719921	C₂²	1	1	yes	characteristic
151	C₄×#11719921	C₂²	1	1	yes	characteristic
152	C₄×#11719921	C₂²	1	1	yes	characteristic
153	C₄×#11719921	C₂²	1	1	yes	characteristic
154	C₄×#11719921	C₂²	1	1	yes	characteristic
155	C₄×#11719921	C₂²	1	1	yes	characteristic
156	C₄×#11719921	C₂²	1	1	yes	characteristic
157	C₄×#11719921	C₂²	1	1	yes	characteristic
158	C₄×#11719921	C₂²	1	1	yes	characteristic
159	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
160	#16810470	C₂²	1	1	yes	characteristic
161	#16810470	C₂²	1	1	yes	characteristic
162	#16810470	C₂²	1	1	yes	characteristic
163	#16810470	C₂²	1	1	yes	characteristic
164	#16810470	C₂²	1	1	yes	characteristic
165	#16810470	C₂²	1	1	yes	characteristic
166	#16810470	C₂²	1	1	yes	characteristic
167	#16810470	C₂²	1	1	yes	characteristic
168	#16810469	C₂²	1	1	yes	characteristic, complemented
169	#16810469	C₂²	1	1	yes	characteristic, complemented
170	#16810468	C₂²	1	1	yes	characteristic, complemented
171	#16810468	C₂²	1	1	yes	characteristic, complemented
172	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
174	C₅₃×#388	C₂²	1	1	yes	characteristic
175	C₅₃×#388	C₂²	1	1	yes	characteristic
176	C₅₃×#388	C₂²	1	1	yes	characteristic
177	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
181	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₄³×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
189	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	#13133212	C₂×C₄	1	8	yes	complemented
199	#13133212	C₂×C₄	1	8	yes	complemented
200	#13133212	C₂×C₄	1	8	yes	complemented
201	#13133211	C₂×C₄	1	8	yes	complemented
202	#13133210	C₂×C₄	1	8	yes	complemented
203	#13133210	C₂×C₄	1	8	yes	complemented
204	#13133210	C₂×C₄	1	8	yes	complemented
205	#13133175	—	2	4	no	—
206	#13133174	—	2	4	no	—
207	#13133174	—	2	4	no	—
208	#13133174	—	2	4	no	—
209	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×#11719919	C₂³	1	1	yes	characteristic
216	C₂×#11719919	C₂³	1	1	yes	characteristic
217	C₂×#11719919	C₂³	1	1	yes	characteristic
218	C₂×#11719919	C₂³	1	1	yes	characteristic
219	C₂×#11719919	C₂³	1	1	yes	characteristic
220	C₂×#11719919	C₂³	1	1	yes	characteristic
221	C₂×#11719919	C₂³	1	1	yes	characteristic
222	C₂×#11719919	C₂³	1	1	yes	characteristic
223	C₂×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
236	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
237	C₄⋊C₄×D₅₃	C₂×C₄	1	8	yes	complemented
238	C₂×C₂²⋊Dic₅₃	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	—	2	4	no	—
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	C₂²⋊C₄×D₅₃	—	2	4	no	—
266	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
267	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
268	C₂²⋊C₄×D₅₃	C₂×C₄	1	8	yes	—
269	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
288	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	C₄²×D₅₃	C₂×C₄	1	8	yes	complemented
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
329	#126×C₅₃	C₂×C₄	1	8	yes	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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂³×D₅₃	—	2	2	no	—
366	C₂³×D₅₃	—	2	2	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	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	4	1	no	—
376	C₂²×C₄×C₅₃	—	4	1	no	—
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	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×Dic₅₃	—	2	2	no	—
392	C₂²×Dic₅₃	—	4	1	no	—
393	C₂²×Dic₅₃	—	4	1	no	—
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	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	C₂×C₄×D₅₃	—	2	2	no	—
409	C₂×C₄×D₅₃	—	2	2	no	—
410	C₂×C₄×D₅₃	—	2	2	no	—
411	C₂×C₄×D₅₃	—	2	2	no	—
412	C₂×C₄×D₅₃	—	2	2	no	—
413	C₂×C₄×D₅₃	—	2	2	no	—
414	C₂×C₄×D₅₃	—	4	1	no	—
415	C₂×C₄×D₅₃	—	4	1	no	—
416	C₂×C₄×D₅₃	—	4	1	no	—
417	C₂×C₄×D₅₃	—	4	1	no	—
418	C₂×C₄×D₅₃	—	4	1	no	—
419	C₂×C₄×D₅₃	—	4	1	no	—
420	C₂×C₄×D₅₃	—	4	1	no	—
421	C₂×C₄×D₅₃	—	4	1	no	—
422	C₂×C₄×D₅₃	—	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	C₂²×C₄	1	4	yes	—
427	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
428	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
429	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
430	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
431	C₂×C₄×D₅₃	C₂²×C₄	1	4	yes	—
432	C₄⋊C₄×C₅₃	—	2	2	no	—
433	C₄⋊C₄×C₅₃	—	4	1	no	—
434	C₄⋊C₄×C₅₃	—	4	1	no	—
435	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
436	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
437	C₄⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
438	C₂²⋊C₄×C₅₃	—	2	2	no	—
439	C₂²⋊C₄×C₅₃	—	4	1	no	—
440	C₂²⋊C₄×C₅₃	—	4	1	no	—
441	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
442	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
443	C₂²⋊C₄×C₅₃	C₂²×C₄	1	4	yes	—
444	C₄²×C₅₃	—	2	2	no	—
445	C₄²×C₅₃	—	2	2	no	—
446	C₄²×C₅₃	—	2	2	no	—
447	C₄²×C₅₃	—	4	1	no	—
448	C₄²×C₅₃	—	4	1	no	—
449	C₄²×C₅₃	—	4	1	no	—
450	C₄²×C₅₃	—	4	1	no	—
451	C₄²×C₅₃	—	4	1	no	—
452	C₄²×C₅₃	—	4	1	no	—
453	C₄²×C₅₃	C₂²×C₄	1	4	yes	—
454	C₂²⋊Dic₅₃	—	2	2	no	—
455	C₂²⋊Dic₅₃	—	4	1	no	—
456	C₂²⋊Dic₅₃	—	4	1	no	—
457	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
458	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
459	C₂²⋊Dic₅₃	C₂²×C₄	1	4	yes	—
460	#11719921	—	2	2	no	—
461	#11719921	—	2	2	no	—
462	#11719921	—	2	2	no	—
463	#11719921	—	2	2	no	—
464	#11719921	—	2	2	no	—
465	#11719921	—	2	2	no	—
466	#11719921	—	2	2	no	—
467	#11719921	—	2	2	no	—
468	#11719921	—	4	1	no	—
469	#11719921	—	4	1	no	—
470	#11719921	—	4	1	no	—
471	#11719921	—	4	1	no	—
472	#11719921	C₂²×C₄	1	4	yes	—
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	#41	1	4	yes	—
479	#11719921	#41	1	4	yes	—
480	C₄⋊Dic₅₃	—	2	2	no	—
481	C₄⋊Dic₅₃	—	4	1	no	—
482	C₄⋊Dic₅₃	—	4	1	no	—
483	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
484	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
485	C₄⋊Dic₅₃	C₂²×C₄	1	4	yes	—
486	#11719919	—	2	2	no	—
487	#11719919	—	2	2	no	—
488	#11719919	—	2	2	no	—
489	#11719919	—	2	2	no	—
490	#11719919	—	2	2	no	—
491	#11719919	—	2	2	no	—
492	#11719919	—	4	1	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	C₂²×C₄	1	4	yes	—
501	#11719919	C₂²×C₄	1	4	yes	—
502	#11719919	C₂²×C₄	1	4	yes	—
503	#11719919	C₂²×C₄	1	4	yes	—
504	#11719919	C₂²×C₄	1	4	yes	—
505	#11719919	C₂²×C₄	1	4	yes	—
506	C₄×Dic₅₃	—	2	2	no	—
507	C₄×Dic₅₃	—	2	2	no	—
508	C₄×Dic₅₃	—	2	2	no	—
509	C₄×Dic₅₃	—	2	2	no	—
510	C₄×Dic₅₃	—	2	2	no	—
511	C₄×Dic₅₃	—	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	C₂²×C₄	1	4	yes	—
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	8	no	—
547	C₂²×D₅₃	—	4	4	no	—
548	C₂²×D₅₃	—	4	4	no	—
549	C₂²×D₅₃	—	8	2	no	—
550	C₂²×D₅₃	—	8	2	no	—
551	C₂²×D₅₃	—	8	2	no	—
552	C₂²×D₅₃	—	8	2	no	—
553	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
554	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
555	C₂²×D₅₃	C₂×#41	1	2	yes	—
556	C₂²×D₅₃	C₂×#41	1	2	yes	—
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	—	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	—	8	2	no	—
592	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
593	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
594	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
595	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
596	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
597	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
598	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
599	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
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	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	8	2	no	—
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	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
641	C₂×Dic₅₃	C₂×#41	1	2	yes	—
642	C₂×Dic₅₃	C₂×#41	1	2	yes	—
643	C₄×D₅₃	—	2	8	no	—
644	C₄×D₅₃	—	2	8	no	—
645	C₄×D₅₃	—	4	4	no	—
646	C₄×D₅₃	—	4	4	no	—
647	C₄×D₅₃	—	4	4	no	—
648	C₄×D₅₃	—	4	4	no	—
649	C₄×D₅₃	—	8	2	no	—
650	C₄×D₅₃	—	8	2	no	—
651	#34247	—	53	1	no	maximal, Sylow
652	C₂²×C₅₃	—	2	2	no	—
653	C₂²×C₅₃	—	2	2	no	—
654	C₂²×C₅₃	—	2	2	no	—
655	C₂²×C₅₃	—	4	1	no	—
656	C₂²×C₅₃	—	4	1	no	—
657	C₂²×C₅₃	—	4	1	no	—
658	C₂²×C₅₃	—	4	1	no	—
659	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
660	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
661	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
662	C₂²×C₅₃	#585	1	1	yes	characteristic
663	C₂²×C₅₃	#585	1	1	yes	characteristic
664	C₂²×C₅₃	#585	1	1	yes	characteristic
665	C₂²×C₅₃	#585	1	1	yes	characteristic
666	C₂×D₅₃	—	2	2	no	—
667	C₂×D₅₃	—	2	2	no	—
668	C₂×D₅₃	—	2	2	no	—
669	C₂×D₅₃	—	2	2	no	—
670	C₂×D₅₃	—	2	2	no	—
671	C₂×D₅₃	—	2	2	no	—
672	C₂×D₅₃	—	2	2	no	—
673	C₂×D₅₃	—	2	2	no	—
674	C₂×D₅₃	—	2	2	no	—
675	C₂×D₅₃	—	4	1	no	—
676	C₂×D₅₃	—	4	1	no	—
677	C₂×D₅₃	—	4	1	no	—
678	C₂×D₅₃	—	4	1	no	—
679	C₂×D₅₃	—	8	8	no	—
680	C₂×D₅₃	C₄×#41	1	4	yes	—
681	C₄×C₅₃	—	2	2	no	—
682	C₄×C₅₃	—	2	2	no	—
683	C₄×C₅₃	—	2	2	no	—
684	C₄×C₅₃	—	2	2	no	—
685	C₄×C₅₃	—	2	2	no	—
686	C₄×C₅₃	—	2	2	no	—
687	C₄×C₅₃	—	2	2	no	—
688	C₄×C₅₃	—	2	2	no	—
689	C₄×C₅₃	—	4	1	no	—
690	C₄×C₅₃	—	4	1	no	—
691	C₄×C₅₃	—	4	1	no	—
692	C₄×C₅₃	—	4	1	no	—
693	C₄×C₅₃	—	4	1	no	—
694	C₄×C₅₃	—	4	1	no	—
695	Dic₅₃	—	2	2	no	—
696	Dic₅₃	—	2	2	no	—
697	Dic₅₃	—	2	2	no	—
698	Dic₅₃	—	2	2	no	—
699	Dic₅₃	—	2	2	no	—
700	Dic₅₃	—	2	2	no	—
701	Dic₅₃	—	2	2	no	—
702	Dic₅₃	—	2	2	no	—
703	Dic₅₃	—	4	1	no	—
704	Dic₅₃	—	4	1	no	—
705	Dic₅₃	—	4	1	no	—
706	Dic₅₃	—	4	1	no	—
707	Dic₅₃	—	4	1	no	—
708	Dic₅₃	—	4	1	no	—
709	C₂²×#126	—	53	1	no	—
710	#2373	—	53	1	no	—
711	#2373	—	53	1	no	—
712	#2373	—	53	1	no	—
713	#2373	—	53	1	no	—
714	#2373	—	53	1	no	—
715	#2373	—	53	1	no	—
716	#2373	—	53	1	no	—
717	#2373	—	53	1	no	—
718	#2345	—	53	1	no	—
719	#2345	—	53	1	no	—
720	#2344	—	53	1	no	—
721	#2344	—	53	1	no	—
722	#2342	—	53	1	no	—
723	#2342	—	53	1	no	—
724	#2342	—	53	1	no	—
725	#2342	—	53	1	no	—
726	#2334	—	53	1	no	—
727	#2334	—	53	1	no	—
728	#2334	—	53	1	no	—
729	#2334	—	53	1	no	—
730	#2313	—	53	1	no	—
731	#2312	—	53	1	no	—
732	C₄×#126	—	53	1	no	—
733	C₄×#126	—	53	1	no	—
734	C₄×#126	—	53	1	no	—
735	C₄×#126	D₅₃	1	1	yes	characteristic, complemented
736	#2283	—	53	1	no	—
737	#2274	—	53	1	no	—
738	#2273	—	53	1	no	—
739	C₄×#117	—	53	1	no	—
740	C₂×C₅₃	—	4	2	no	—
741	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
742	C₂×C₅₃	#3428	1	1	yes	characteristic
743	C₂×C₅₃	#3428	1	1	yes	characteristic
744	C₂×C₅₃	#3521	1	1	yes	characteristic
745	C₂×C₅₃	#3521	1	1	yes	characteristic
746	C₂×C₅₃	#3521	1	1	yes	characteristic
747	C₂×C₅₃	#3521	1	1	yes	characteristic
748	D₅₃	—	2	4	no	—
749	D₅₃	—	4	2	no	—
750	C₂×#126	—	53	16	no	—
751	C₂×#126	—	53	1	no	—
752	C₂×#126	—	53	1	no	—
753	C₂×#126	—	53	1	no	—
754	C₂×#126	—	53	1	no	—
755	C₂×#126	—	53	1	no	—
756	C₂×#126	—	53	1	no	—
757	C₂×#126	—	53	1	no	—
758	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
759	C₂×#117	—	53	1	no	—
760	C₂×#117	—	53	1	no	—
761	C₂×#117	—	53	1	no	—
762	C₂×#117	—	53	1	no	—
763	C₂²×C₄⋊C₄	—	53	1	no	—
764	C₂²×C₄⋊C₄	—	53	1	no	—
765	C₂²×C₄⋊C₄	—	53	1	no	—
766	C₂²×C₂²⋊C₄	—	53	1	no	—
767	C₂²×C₂²⋊C₄	—	53	1	no	—
768	C₂²×C₂²⋊C₄	—	53	1	no	—
769	C₂²×C₂²⋊C₄	—	53	1	no	—
770	C₂²×C₂²⋊C₄	—	53	1	no	—
771	C₂²×C₄²	—	53	1	no	—
772	#389	—	53	1	no	—
773	#389	—	53	1	no	—
774	#389	—	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	#388	—	53	1	no	—
781	#388	—	53	1	no	—
782	#388	—	53	1	no	—
783	#388	—	53	1	no	—
784	#388	—	53	1	no	—
785	#388	—	53	1	no	—
786	#388	—	53	1	no	—
787	#388	—	53	1	no	—
788	#388	—	53	1	no	—
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	C₂×D₅₃	1	1	yes	characteristic
802	#388	C₂×D₅₃	1	1	yes	characteristic
803	#388	C₂×D₅₃	1	1	yes	characteristic
804	#387	—	53	1	no	—
805	#387	—	53	1	no	—
806	#387	—	53	1	no	—
807	#387	—	53	1	no	—
808	#387	—	53	1	no	—
809	#387	—	53	1	no	—
810	#387	—	53	1	no	—
811	#387	—	53	1	no	—
812	#387	—	53	1	no	—
813	#387	—	53	1	no	—
814	#387	—	53	1	no	—
815	#387	—	53	1	no	—
816	#387	—	53	1	no	—
817	#387	—	53	1	no	—
818	#387	—	53	1	no	—
819	#387	—	53	1	no	—
820	#387	—	53	1	no	—
821	#387	—	53	1	no	—
822	#387	—	53	1	no	—
823	#387	—	53	1	no	—
824	#387	—	53	1	no	—
825	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
826	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
827	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
828	#385	—	53	1	no	—
829	#385	—	53	1	no	—
830	#385	—	53	1	no	—
831	#385	—	53	1	no	—
832	#385	—	53	1	no	—
833	#385	—	53	1	no	—
834	#385	—	53	1	no	—
835	#385	—	53	1	no	—
836	#383	—	53	1	no	—
837	#383	C₂×D₅₃	1	1	yes	characteristic, complemented
838	#382	—	53	1	no	—
839	#382	—	53	1	no	—
840	#381	—	53	1	no	—
841	#381	—	53	1	no	—
842	#381	—	53	1	no	—
843	#381	—	53	1	no	—
844	#380	—	53	1	no	—
845	#380	—	53	1	no	—
846	#380	—	53	1	no	—
847	#380	—	53	1	no	—
848	#380	—	53	1	no	—
849	#380	—	53	1	no	—
850	#379	—	53	1	no	—
851	#379	—	53	1	no	—
852	C₄×C₄⋊C₄	—	53	1	no	—
853	C₄×C₄⋊C₄	—	53	1	no	—
854	C₄×C₄⋊C₄	—	53	1	no	—
855	C₄×C₄⋊C₄	—	53	1	no	—
856	C₄×C₄⋊C₄	—	53	1	no	—
857	C₄×C₄⋊C₄	—	53	1	no	—
858	C₄×C₄⋊C₄	—	53	1	no	—
859	C₄×C₄⋊C₄	—	53	1	no	—
860	C₄×C₄⋊C₄	—	53	1	no	—
861	C₄×C₄⋊C₄	—	53	1	no	—
862	C₄×C₄⋊C₄	—	53	1	no	—
863	C₄×C₄⋊C₄	—	53	1	no	—
864	C₄×C₄⋊C₄	—	53	1	no	—
865	C₄×C₄⋊C₄	—	53	1	no	—
866	C₄×C₄⋊C₄	—	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	C₂×D₅₃	1	1	yes	characteristic, complemented
872	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
873	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
874	C₄×C₂²⋊C₄	—	53	1	no	—
875	C₄×C₂²⋊C₄	—	53	1	no	—
876	C₄×C₂²⋊C₄	—	53	1	no	—
877	C₄×C₂²⋊C₄	—	53	1	no	—
878	C₄×C₂²⋊C₄	—	53	1	no	—
879	C₄×C₂²⋊C₄	—	53	1	no	—
880	C₄×C₂²⋊C₄	—	53	1	no	—
881	C₄×C₂²⋊C₄	—	53	1	no	—
882	C₄×C₂²⋊C₄	—	53	1	no	—
883	C₄×C₂²⋊C₄	—	53	1	no	—
884	C₄×C₂²⋊C₄	—	53	1	no	—
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	C₂×D₅₃	1	1	yes	characteristic
898	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
899	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
900	#376	—	53	1	no	—
901	#376	—	53	1	no	—
902	#376	—	53	1	no	—
903	#376	—	53	1	no	—
904	C₄³	—	53	1	no	—
905	C₄³	C₂×D₅₃	1	1	yes	characteristic, complemented
906	C₅₃	#34247	1	1	yes	characteristic, complemented, Sylow
907	C₂⁵	—	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	—	53	1	no	—
915	C₂³×C₄	—	53	1	no	—
916	C₂³×C₄	—	53	1	no	—
917	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
918	#126	—	53	8	no	—
919	#126	—	53	8	no	—
920	#126	—	53	8	no	—
921	#126	—	53	8	no	—
922	#126	—	53	8	no	—
923	#126	—	53	8	no	—
924	#126	—	53	8	no	—
925	#126	C₄×D₅₃	1	8	yes	complemented
926	#117	—	106	4	no	—
927	#117	—	106	4	no	—
928	#117	—	106	4	no	—
929	#117	—	106	4	no	—
930	C₂×C₄⋊C₄	—	53	1	no	—
931	C₂×C₄⋊C₄	—	53	1	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	1	no	—
936	C₂×C₄⋊C₄	—	53	1	no	—
937	C₂×C₄⋊C₄	—	53	1	no	—
938	C₂×C₄⋊C₄	—	53	1	no	—
939	C₂×C₄⋊C₄	—	53	8	no	—
940	C₂×C₄⋊C₄	—	53	8	no	—
941	C₂×C₄⋊C₄	—	53	8	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	C₂²×D₅₃	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
965	C₂×C₂²⋊C₄	—	53	1	no	—
966	C₂×C₂²⋊C₄	—	53	1	no	—
967	C₂×C₂²⋊C₄	—	53	1	no	—
968	C₂×C₂²⋊C₄	—	53	1	no	—
969	C₂×C₂²⋊C₄	—	53	1	no	—
970	C₂×C₂²⋊C₄	—	53	1	no	—
971	C₂×C₂²⋊C₄	—	53	1	no	—
972	C₂×C₂²⋊C₄	—	53	1	no	—
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	no	—
975	C₂×C₂²⋊C₄	—	53	1	no	—
976	C₂×C₂²⋊C₄	—	53	8	no	—
977	C₂×C₂²⋊C₄	—	53	8	no	—
978	C₂×C₂²⋊C₄	—	53	8	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	—	106	4	no	—
995	C₂×C₂²⋊C₄	—	106	4	no	—
996	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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×C₄²	—	53	1	no	—
1003	C₂×C₄²	—	53	1	no	—
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	8	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	—	53	1	no	—
1022	C₂×C₄²	—	53	1	no	—
1023	C₂×C₄²	—	53	1	no	—
1024	C₂×C₄²	—	53	1	no	—
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	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
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	#95	C₂²×D₅₃	1	1	yes	characteristic
1079	#95	C₂²×D₅₃	1	1	yes	characteristic
1080	#95	C₂²×D₅₃	1	1	yes	characteristic
1081	#95	C₂²×D₅₃	1	1	yes	characteristic
1082	#95	C₂²×D₅₃	1	1	yes	characteristic
1083	C₂⁴	—	53	1	no	—
1084	C₂⁴	—	53	1	no	—
1085	C₂⁴	—	53	4	no	—
1086	C₂⁴	—	106	2	no	—
1087	C₂⁴	—	106	2	no	—
1088	C₂⁴	—	212	1	no	—
1089	C₂⁴	—	212	1	no	—
1090	C₂⁴	—	212	1	no	—
1091	C₂⁴	—	212	1	no	—
1092	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1093	C₂²×C₄	—	2	2	no	—
1094	C₂²×C₄	—	4	1	no	—
1095	C₂²×C₄	—	4	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	1	no	—
1102	C₂²×C₄	—	53	1	no	—
1103	C₂²×C₄	—	53	1	no	—
1104	C₂²×C₄	—	53	4	no	—
1105	C₂²×C₄	—	53	4	no	—
1106	C₂²×C₄	—	53	4	no	—
1107	C₂²×C₄	—	53	4	no	—
1108	C₂²×C₄	—	53	4	no	—
1109	C₂²×C₄	—	53	4	no	—
1110	C₂²×C₄	—	53	1	no	—
1111	C₂²×C₄	—	53	1	no	—
1112	C₂²×C₄	—	53	1	no	—
1113	C₂²×C₄	—	53	1	no	—
1114	C₂²×C₄	—	53	1	no	—
1115	C₂²×C₄	—	53	1	no	—
1116	C₂²×C₄	—	106	2	no	—
1117	C₂²×C₄	—	106	2	no	—
1118	C₂²×C₄	—	106	2	no	—
1119	C₂²×C₄	—	106	2	no	—
1120	C₂²×C₄	—	106	2	no	—
1121	C₂²×C₄	—	106	2	no	—
1122	C₂²×C₄	—	106	2	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	—	212	1	no	—
1134	C₂²×C₄	—	212	1	no	—
1135	C₂²×C₄	—	212	1	no	—
1136	C₂²×C₄	—	212	1	no	—
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	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
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	—	106	2	no	—
1164	C₄⋊C₄	—	106	2	no	—
1165	C₄⋊C₄	—	106	2	no	—
1166	C₄⋊C₄	—	106	2	no	—
1167	C₄⋊C₄	—	106	2	no	—
1168	C₄⋊C₄	—	106	2	no	—
1169	C₄⋊C₄	—	106	2	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	C₂×C₄×D₅₃	1	4	yes	—
1181	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1182	C₄⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1183	C₂²⋊C₄	—	2	2	no	—
1184	C₂²⋊C₄	—	4	1	no	—
1185	C₂²⋊C₄	—	4	1	no	—
1186	C₂²⋊C₄	—	53	4	no	—
1187	C₂²⋊C₄	—	53	4	no	—
1188	C₂²⋊C₄	—	53	4	no	—
1189	C₂²⋊C₄	—	53	4	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	—	106	2	no	—
1198	C₂²⋊C₄	—	106	2	no	—
1199	C₂²⋊C₄	—	106	2	no	—
1200	C₂²⋊C₄	—	106	2	no	—
1201	C₂²⋊C₄	—	106	2	no	—
1202	C₂²⋊C₄	—	106	2	no	—
1203	C₂²⋊C₄	—	106	2	no	—
1204	C₂²⋊C₄	—	106	2	no	—
1205	C₂²⋊C₄	—	106	2	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	C₂×C₄×D₅₃	1	4	yes	—
1213	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1214	C₂²⋊C₄	C₂×C₄×D₅₃	1	4	yes	—
1215	C₄²	—	2	2	no	—
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	—	53	4	no	—
1227	C₄²	—	106	2	no	—
1228	C₄²	—	106	2	no	—
1229	C₄²	—	106	2	no	—
1230	C₄²	—	106	2	no	—
1231	C₄²	—	106	2	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	C₄²	—	212	1	no	—
1243	C₄²	—	212	1	no	—
1244	C₄²	—	212	1	no	—
1245	C₄²	—	212	1	no	—
1246	C₄²	C₂×C₄×D₅₃	1	4	yes	—
1247	C₂³	—	2	1	no	—
1248	C₂³	—	2	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	53	2	no	—
1254	C₂³	—	53	2	no	—
1255	C₂³	—	53	2	no	—
1256	C₂³	—	53	2	no	—
1257	C₂³	—	106	8	no	—
1258	C₂³	—	106	1	no	—
1259	C₂³	—	106	1	no	—
1260	C₂³	—	106	1	no	—
1261	C₂³	—	106	1	no	—
1262	C₂³	—	106	1	no	—
1263	C₂³	—	106	1	no	—
1264	C₂³	—	106	1	no	—
1265	C₂³	—	106	1	no	—
1266	C₂³	—	106	1	no	—
1267	C₂³	—	106	1	no	—
1268	C₂³	—	424	2	no	—
1269	C₂³	—	424	2	no	—
1270	C₂³	—	424	2	no	—
1271	C₂³	—	424	2	no	—
1272	C₂³	—	212	4	no	—
1273	C₂³	—	212	4	no	—
1274	C₂³	C₂²×C₄×D₅₃	1	2	yes	—
1275	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	8	2	no	—
1311	C₂×C₄	—	53	2	no	—
1312	C₂×C₄	—	53	2	no	—
1313	C₂×C₄	—	53	2	no	—
1314	C₂×C₄	—	53	2	no	—
1315	C₂×C₄	—	53	2	no	—
1316	C₂×C₄	—	53	2	no	—
1317	C₂×C₄	—	53	2	no	—
1318	C₂×C₄	—	53	2	no	—
1319	C₂×C₄	—	106	8	no	—
1320	C₂×C₄	—	106	8	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	—	106	1	no	—
1346	C₂×C₄	—	106	1	no	—
1347	C₂×C₄	—	106	1	no	—
1348	C₂×C₄	—	106	1	no	—
1349	C₂×C₄	—	106	1	no	—
1350	C₂×C₄	—	106	1	no	—
1351	C₂×C₄	—	106	1	no	—
1352	C₂×C₄	—	106	1	no	—
1353	C₂×C₄	—	106	1	no	—
1354	C₂×C₄	—	106	1	no	—
1355	C₂×C₄	—	424	2	no	—
1356	C₂×C₄	—	424	2	no	—
1357	C₂×C₄	—	424	2	no	—
1358	C₂×C₄	—	212	4	no	—
1359	C₂×C₄	—	212	4	no	—
1360	C₂×C₄	—	212	4	no	—
1361	C₂×C₄	—	212	4	no	—
1362	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1363	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1364	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1365	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1366	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1367	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1368	C₂×C₄	#41×D₅₃	1	2	yes	—
1369	C₂×C₄	#41×D₅₃	1	2	yes	—
1370	C₂²	—	2	2	no	—
1371	C₂²	—	2	2	no	—
1372	C₂²	—	2	2	no	—
1373	C₂²	—	4	1	no	—
1374	C₂²	—	4	1	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	53	4	no	—
1378	C₂²	—	106	2	no	—
1379	C₂²	—	106	2	no	—
1380	C₂²	—	106	2	no	—
1381	C₂²	—	106	2	no	—
1382	C₂²	—	106	2	no	—
1383	C₂²	—	106	2	no	—
1384	C₂²	—	106	2	no	—
1385	C₂²	—	106	2	no	—
1386	C₂²	—	106	2	no	—
1387	C₂²	—	424	8	no	—
1388	C₂²	—	212	1	no	—
1389	C₂²	—	212	1	no	—
1390	C₂²	—	212	1	no	—
1391	C₂²	—	212	1	no	—
1392	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1393	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1394	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1395	C₂²	#16811459	1	1	yes	characteristic
1396	C₂²	#16811459	1	1	yes	characteristic
1397	C₂²	#16811459	1	1	yes	characteristic
1398	C₂²	#16811459	1	1	yes	characteristic
1399	C₄	—	2	2	no	—
1400	C₄	—	2	2	no	—
1401	C₄	—	2	2	no	—
1402	C₄	—	2	2	no	—
1403	C₄	—	2	2	no	—
1404	C₄	—	2	2	no	—
1405	C₄	—	2	2	no	—
1406	C₄	—	2	2	no	—
1407	C₄	—	4	1	no	—
1408	C₄	—	4	1	no	—
1409	C₄	—	4	1	no	—
1410	C₄	—	4	1	no	—
1411	C₄	—	4	1	no	—
1412	C₄	—	4	1	no	—
1413	C₄	—	106	2	no	—
1414	C₄	—	106	2	no	—
1415	C₄	—	106	2	no	—
1416	C₄	—	106	2	no	—
1417	C₄	—	106	2	no	—
1418	C₄	—	106	2	no	—
1419	C₄	—	106	2	no	—
1420	C₄	—	106	2	no	—
1421	C₄	—	212	1	no	—
1422	C₄	—	212	1	no	—
1423	C₄	—	212	1	no	—
1424	C₄	—	212	1	no	—
1425	C₄	—	212	1	no	—
1426	C₄	—	212	1	no	—
1427	C₂	—	4	2	no	—
1428	C₂	—	106	4	no	—
1429	C₂	—	212	2	no	—
1430	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1431	C₂	#20287914	1	1	yes	characteristic
1432	C₂	#20287914	1	1	yes	characteristic
1433	C₂	#20288769	1	1	yes	characteristic
1434	C₂	#20288775	1	1	yes	characteristic
1435	C₂	#20288777	1	1	yes	characteristic
1436	C₂	#20288787	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₄×#126×C₅₃	C₂
socle, cosocle	C₂³×C₅₃	C₂⁵
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	C₄×#126	D₅₃
hypocenter	C₅₃	#34247
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ C₄×#126

Complements

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

N	H ≅ G/N	type
2. #20277841	C₂	semidirect
3. #20277840	C₂	semidirect
4. #20277837	C₂	semidirect
5. #20277836	C₂	semidirect
6. #20277833	C₂	semidirect
7. #20277832	C₂	semidirect
8. #20277829	C₂	semidirect
9. #20277828	C₂	semidirect
10. #20277589	C₂	semidirect
11. #20277588	C₂	semidirect
12. #20277581	C₂	semidirect
13. #20277580	C₂	semidirect
18. #20277496	C₂	semidirect
19. #20277492	C₂	semidirect
20. #20277488	C₂	semidirect
21. #20277484	C₂	semidirect
22. #20277314	C₂	semidirect
24. #126×Dic₅₃	C₂	semidirect
25. C₄×#13133211	C₂	semidirect
26. #20277263	C₂	semidirect
27. #20277112	C₂	semidirect
28. #20277069	C₂	semidirect
30. C₄×#13133174	C₂	semidirect
31. C₄×#126×C₅₃	C₂	semidirect
39. #126×D₅₃	C₄	semidirect
53. #16810521	C₂²	semidirect
54. #16810521	C₂²	semidirect
55. #16810520	C₂²	semidirect
56. #16810520	C₂²	semidirect
57. #16810519	C₂²	semidirect
58. #16810519	C₂²	semidirect
59. #16810518	C₂²	semidirect
60. #16810518	C₂²	semidirect
82. #16810510	C₂²	semidirect
83. #16810509	C₂²	semidirect
84. #16810509	C₂²	semidirect
85. #16810509	C₂²	semidirect
86. #16810508	C₂²	semidirect
87. #16810508	C₂²	semidirect
88. #16810508	C₂²	semidirect
89. #16810507	C₂²	semidirect
90. #16810507	C₂²	semidirect
91. #16810507	C₂²	semidirect
92. #16810507	C₂²	semidirect
93. #16810507	C₂²	semidirect
94. #16810506	C₂²	semidirect
95. #16810506	C₂²	semidirect
96. #16810506	C₂²	semidirect
97. #16810505	C₂²	semidirect
98. #16810505	C₂²	semidirect
99. #16810505	C₂²	semidirect
100. #16810505	C₂²	semidirect
101. #16810505	C₂²	semidirect
102. #16810504	C₂²	semidirect
111. #16810491	C₂²	semidirect
112. #16810487	C₂²	semidirect
113. #16810487	C₂²	semidirect
126. C₄⋊C₄×Dic₅₃	C₂²	semidirect
127. C₄⋊C₄×Dic₅₃	C₂²	semidirect
128. C₄⋊C₄×Dic₅₃	C₂²	semidirect
129. C₄⋊C₄×Dic₅₃	C₂²	semidirect
130. C₄×#11719919	C₂²	semidirect
131. C₄×#11719919	C₂²	semidirect
132. C₄×#11719919	C₂²	semidirect
133. C₄×#11719919	C₂²	semidirect
134. C₄×#11719919	C₂²	semidirect
135. C₄×#11719919	C₂²	semidirect
136. C₄×#11719919	C₂²	semidirect
137. C₄×#11719919	C₂²	semidirect
138. C₄×C₄⋊Dic₅₃	C₂²	semidirect
139. #16810474	C₂²	semidirect
140. #16810474	C₂²	semidirect
141. #16810474	C₂²	semidirect
142. #16810474	C₂²	semidirect
143. #16810474	C₂²	semidirect
144. #16810474	C₂²	semidirect
168. #16810469	C₂²	semidirect
169. #16810469	C₂²	semidirect
170. #16810468	C₂²	semidirect
171. #16810468	C₂²	semidirect
172. C₄²×Dic₅₃	C₂²	semidirect
177. C₅₃×#387	C₂²	semidirect
178. C₅₃×#387	C₂²	semidirect
179. C₅₃×#387	C₂²	semidirect
180. C₅₃×#383	C₂²	semidirect
181. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
183. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
187. C₄³×C₅₃	C₂²	semidirect
198. #13133212	C₂×C₄	semidirect
199. #13133212	C₂×C₄	semidirect
200. #13133212	C₂×C₄	semidirect
201. #13133211	C₂×C₄	semidirect
202. #13133210	C₂×C₄	semidirect
203. #13133210	C₂×C₄	semidirect
204. #13133210	C₂×C₄	semidirect
235. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
236. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
237. C₄⋊C₄×D₅₃	C₂×C₄	semidirect
291. C₄²×D₅₃	C₂×C₄	semidirect
329. #126×C₅₃	C₂×C₄	semidirect
735. C₄×#126	D₅₃	semidirect
825. #387	C₂×D₅₃	semidirect
826. #387	C₂×D₅₃	semidirect
827. #387	C₂×D₅₃	semidirect
837. #383	C₂×D₅₃	semidirect
871. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
872. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
873. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
905. C₄³	C₂×D₅₃	semidirect
906. C₅₃	#34247	semidirect
925. #126	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×#126×D₅₃	2
#20277841	2
#20277840	2
#20277837	2
#20277836	2
#20277833	2
#20277832	2
#20277829	2
#20277828	2
#20277589	2
#20277588	2
#20277581	2
#20277580	2
#20277563	2
#20277559	2
#20277558	2
#20277496	2
#20277492	2
#20277488	2
#20277484	2
#20277314	2
#20277309	2
#126×Dic₅₃	2
C₄×#13133211	2
#20277263	2
#20277112	2
#20277069	2
#20277067	2
C₄×#13133174	2
C₄×#126×C₅₃	2
#34247	53