Subgroups — #27557379

Order 13568.

2176 conjugacy classes of subgroups.

The subgroup lattice has 1624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283084	C₂	1	1	yes	maximal, characteristic, complemented
2	#20283081	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283043	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283012	C₂	1	1	yes	maximal, characteristic, complemented
5	#20280754	C₂	1	1	yes	maximal, characteristic, complemented
6	#20280752	C₂	1	1	yes	maximal, characteristic, complemented
7	#20280697	C₂	1	1	yes	maximal, characteristic, complemented
8	#20280212	C₂	1	1	yes	maximal, characteristic, complemented
9	#20280207	C₂	1	1	yes	maximal, characteristic, complemented
10	#20279776	C₂	1	1	yes	maximal, characteristic, complemented
11	#20279768	C₂	1	1	yes	maximal, characteristic, complemented
12	#20279305	C₂	1	1	yes	maximal, characteristic, complemented
13	#20279060	C₂	1	1	yes	maximal, characteristic, complemented
14	#20278962	C₂	1	1	yes	maximal, characteristic, complemented
15	#20278954	C₂	1	1	yes	maximal, characteristic, complemented
16	#20278506	C₂	1	1	yes	maximal, characteristic, complemented
17	#20278432	C₂	1	1	yes	maximal, characteristic, complemented
18	#20278361	C₂	1	1	yes	maximal, characteristic, complemented
19	#20278274	C₂	1	1	yes	maximal, characteristic, complemented
20	#20278172	C₂	1	1	yes	maximal, characteristic, complemented
21	#20278170	C₂	1	1	yes	maximal, characteristic, complemented
22	#20278159	C₂	1	1	yes	maximal, characteristic, complemented
23	#20278064	C₂	1	1	yes	maximal, characteristic
24	#20277371	C₂	1	1	yes	maximal, characteristic, complemented
25	#20277371	C₂	1	1	yes	maximal, characteristic, complemented
26	#20277309	C₂	1	1	yes	maximal, characteristic, complemented
27	#20277309	C₂	1	1	yes	maximal, characteristic, complemented
28	#20277249	C₂	1	1	yes	maximal, characteristic, complemented
29	#390×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#13133177	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2648	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133212	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13133210	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133207	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13133203	C₂²	1	1	yes	characteristic
37	C₂×#13133203	C₂²	1	1	yes	characteristic
38	C₂×#13133201	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133198	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133195	C₂²	1	1	yes	characteristic
41	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13133189	C₂²	1	1	yes	characteristic
43	C₂×#13133189	C₂²	1	1	yes	characteristic
44	C₂×#13133185	C₂²	1	1	yes	characteristic
45	C₂×#13133185	C₂²	1	1	yes	characteristic
46	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
48	C₂×#13133177	C₂²	1	1	yes	characteristic
49	C₂×#13133177	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
57	#16810565	C₂²	1	1	yes	characteristic, complemented
58	#16810559	C₂²	1	1	yes	characteristic, complemented
59	#16810558	C₂²	1	1	yes	characteristic, complemented
60	#16810556	C₂²	1	1	yes	characteristic, complemented
61	#16810556	C₂²	1	1	yes	characteristic, complemented
62	#16810555	C₂²	1	1	yes	characteristic, complemented
63	#16810553	C₂²	1	1	yes	characteristic, complemented
64	#16810552	C₂²	1	1	yes	characteristic, complemented
65	#16810552	C₂²	1	1	yes	characteristic, complemented
66	#16810552	C₂²	1	1	yes	characteristic, complemented
67	#16810551	C₂²	1	1	yes	characteristic, complemented
68	#16810551	C₂²	1	1	yes	characteristic, complemented
69	#16810550	C₂²	1	1	yes	characteristic, complemented
70	#16810546	C₂²	1	1	yes	characteristic, complemented
71	#16810546	C₂²	1	1	yes	characteristic, complemented
72	#16810545	C₂²	1	1	yes	characteristic, complemented
73	#16810541	C₂²	1	1	yes	characteristic
74	#16810541	C₂²	1	1	yes	characteristic
75	#16810540	C₂²	1	1	yes	characteristic
76	#16810538	C₂²	1	1	yes	characteristic, complemented
77	#16810538	C₂²	1	1	yes	characteristic, complemented
78	#16810537	C₂²	1	1	yes	characteristic
79	#16810537	C₂²	1	1	yes	characteristic
80	#16810532	C₂²	1	1	yes	characteristic
81	#16810527	C₂²	1	1	yes	characteristic, complemented
82	#16810527	C₂²	1	1	yes	characteristic, complemented
83	#16810526	C₂²	1	1	yes	characteristic
84	#16810526	C₂²	1	1	yes	characteristic, complemented
85	#16810526	C₂²	1	1	yes	characteristic, complemented
86	#16810525	C₂²	1	1	yes	characteristic
87	#16810524	C₂²	1	1	yes	characteristic
88	#16810523	C₂²	1	1	yes	characteristic
89	#16810523	C₂²	1	1	yes	characteristic
90	#16810523	C₂²	1	1	yes	characteristic
91	#16810523	C₂²	1	1	yes	characteristic
92	#16810523	C₂²	1	1	yes	characteristic
93	#16810523	C₂²	1	1	yes	characteristic
94	#16810523	C₂²	1	1	yes	characteristic
95	#16810523	C₂²	1	1	yes	characteristic
96	#16810523	C₂²	1	1	yes	characteristic, complemented
97	#16810523	C₂²	1	1	yes	characteristic, complemented
98	#16810520	C₂²	1	1	yes	characteristic, complemented
99	#16810520	C₂²	1	1	yes	characteristic, complemented
100	#16810520	C₂²	1	1	yes	characteristic, complemented
101	#16810518	C₂²	1	1	yes	characteristic, complemented
102	#16810517	C₂²	1	1	yes	characteristic, complemented
103	#16810517	C₂²	1	1	yes	characteristic, complemented
104	#16810517	C₂²	1	1	yes	characteristic, complemented
105	#16810516	C₂²	1	1	yes	characteristic, complemented
106	#16810516	C₂²	1	1	yes	characteristic, complemented
107	#16810516	C₂²	1	1	yes	characteristic, complemented
108	#16810516	C₂²	1	1	yes	characteristic, complemented
109	#16810516	C₂²	1	1	yes	characteristic, complemented
110	#16810515	C₂²	1	1	yes	characteristic, complemented
111	#16810515	C₂²	1	1	yes	characteristic, complemented
112	#16810515	C₂²	1	1	yes	characteristic, complemented
113	#16810515	C₂²	1	1	yes	characteristic, complemented
114	#16810515	C₂²	1	1	yes	characteristic, complemented
115	#16810514	C₂²	1	1	yes	characteristic, complemented
116	#16810514	C₂²	1	1	yes	characteristic, complemented
117	#16810513	C₂²	1	1	yes	characteristic, complemented
118	#16810513	C₂²	1	1	yes	characteristic, complemented
119	#16810513	C₂²	1	1	yes	characteristic, complemented
120	#16810512	C₂²	1	1	yes	characteristic, complemented
121	#16810512	C₂²	1	1	yes	characteristic, complemented
122	#16810512	C₂²	1	1	yes	characteristic, complemented
123	#16810512	C₂²	1	1	yes	characteristic, complemented
124	#16810512	C₂²	1	1	yes	characteristic, complemented
125	#16810512	C₂²	1	1	yes	characteristic, complemented
126	#16810512	C₂²	1	1	yes	characteristic, complemented
127	#16810511	C₂²	1	1	yes	characteristic, complemented
128	#16810511	C₂²	1	1	yes	characteristic, complemented
129	#16810511	C₂²	1	1	yes	characteristic, complemented
130	#16810511	C₂²	1	1	yes	characteristic, complemented
131	#16810511	C₂²	1	1	yes	characteristic, complemented
132	#16810511	C₂²	1	1	yes	characteristic, complemented
133	#16810511	C₂²	1	1	yes	characteristic, complemented
134	#16810507	C₂²	1	1	yes	characteristic, complemented
135	#16810503	C₂²	1	1	yes	characteristic, complemented
136	#16810502	C₂²	1	1	yes	characteristic, complemented
137	#16810502	C₂²	1	1	yes	characteristic, complemented
138	#16810500	C₂²	1	1	yes	characteristic, complemented
139	#16810499	C₂²	1	1	yes	characteristic
140	#16810499	C₂²	1	1	yes	characteristic
141	#16810497	C₂²	1	1	yes	characteristic
142	#16810497	C₂²	1	1	yes	characteristic
143	#16810497	C₂²	1	1	yes	characteristic
144	#16810494	C₂²	1	1	yes	characteristic
145	#16810487	C₂²	1	1	yes	characteristic, complemented
146	#16810482	C₂²	1	1	yes	characteristic
147	#16810482	C₂²	1	1	yes	characteristic
148	#16810482	C₂²	1	1	yes	characteristic
149	#16810481	C₂²	1	1	yes	characteristic, complemented
150	#16810480	C₂²	1	1	yes	characteristic
151	#16810480	C₂²	1	1	yes	characteristic
152	#16810478	C₂²	1	1	yes	characteristic
153	#16810478	C₂²	1	1	yes	characteristic
154	#16810478	C₂²	1	1	yes	characteristic
155	#16810478	C₂²	1	1	yes	characteristic
156	#16810478	C₂²	1	1	yes	characteristic
157	#16810478	C₂²	1	1	yes	characteristic
158	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
159	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
160	#16810474	C₂²	1	1	yes	characteristic, complemented
161	#16810474	C₂²	1	1	yes	characteristic, complemented
162	#16810474	C₂²	1	1	yes	characteristic, complemented
163	#16810474	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₄×#11719921	C₂²	1	1	yes	characteristic
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	C₄²×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#394	C₂²	1	1	yes	characteristic
177	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#392	C₂²	1	1	yes	characteristic
180	C₅₃×#390	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
196	C₂×D₄×D₅₃	—	2	4	no	—
197	C₂×D₄×D₅₃	—	4	2	no	—
198	C₂×D₄×D₅₃	—	4	2	no	—
199	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	#13133212	—	4	2	no	—
207	#13133210	—	4	2	no	—
208	#13133207	—	4	2	no	—
209	#13133203	—	4	2	no	—
210	#13133203	—	4	2	no	—
211	#13133201	—	4	2	no	—
212	#13133198	—	4	2	no	—
213	#13133195	—	2	4	no	—
214	#13133194	—	4	2	no	—
215	#13133189	—	4	2	no	—
216	#13133189	—	4	2	no	—
217	#13133185	—	2	4	no	—
218	#13133185	—	2	4	no	—
219	#13133182	—	4	2	no	—
220	C₄×C₂²⋊D₅₃	—	2	4	no	—
221	#13133177	—	2	4	no	—
222	#13133177	—	2	4	no	—
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×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	C₂³	1	1	yes	characteristic
234	C₂×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×D₅₃	—	4	2	no	—
247	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊Dic₅₃	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	C₂×#11719921	C₂³	1	1	yes	characteristic
277	C₂×#11719921	C₂³	1	1	yes	characteristic
278	C₂×#11719921	C₂³	1	1	yes	characteristic
279	C₂×#11719921	C₂³	1	1	yes	characteristic
280	C₂×#11719921	C₂³	1	1	yes	characteristic
281	C₂×#11719921	C₂³	1	1	yes	characteristic
282	C₂×#11719921	C₂³	1	1	yes	characteristic
283	C₂×#11719921	C₂³	1	1	yes	characteristic
284	C₂×#11719921	C₂³	1	1	yes	characteristic
285	C₂×#11719921	C₂³	1	1	yes	characteristic
286	C₂×#11719921	C₂³	1	1	yes	characteristic
287	C₂×#11719921	C₂³	1	1	yes	characteristic
288	C₂×#11719921	C₂³	1	1	yes	characteristic
289	C₂×#11719921	C₂³	1	1	yes	characteristic
290	C₂×#11719921	C₂³	1	1	yes	characteristic
291	C₂²⋊C₄×D₅₃	—	2	4	no	—
292	C₂²⋊C₄×D₅₃	—	2	4	no	—
293	C₂²⋊C₄×D₅₃	—	4	2	no	—
294	C₂²⋊C₄×D₅₃	—	4	2	no	—
295	C₂×C₄×Dic₅₃	—	4	2	no	—
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
311	C₄²×D₅₃	—	4	2	no	—
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	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	#13133124	C₂³	1	1	yes	characteristic
333	#13133124	C₂³	1	1	yes	characteristic
334	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂³×D₅₃	—	2	2	no	—
373	C₂³×D₅₃	—	2	2	no	—
374	C₂³×D₅₃	—	2	2	no	—
375	C₂³×D₅₃	—	2	2	no	—
376	C₂³×D₅₃	—	2	2	no	—
377	C₂³×D₅₃	—	2	2	no	—
378	C₂³×D₅₃	—	4	1	no	—
379	C₂³×D₅₃	—	4	1	no	—
380	C₂³×D₅₃	—	4	1	no	—
381	C₂³×D₅₃	—	4	1	no	—
382	C₂³×D₅₃	—	4	1	no	—
383	C₂³×D₅₃	—	4	1	no	—
384	C₂³×D₅₃	—	4	1	no	—
385	C₂³×D₅₃	—	4	1	no	—
386	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
387	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
388	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×D₄×C₅₃	—	2	2	no	—
390	C₂×D₄×C₅₃	—	2	2	no	—
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	4	1	no	—
393	C₂×D₄×C₅₃	—	4	1	no	—
394	C₂×D₄×C₅₃	—	4	1	no	—
395	C₂×D₄×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	4	1	no	—
397	C₂×D₄×C₅₃	—	4	1	no	—
398	C₂²×C₄×C₅₃	—	2	2	no	—
399	C₂²×C₄×C₅₃	—	4	1	no	—
400	C₂²×C₄×C₅₃	—	4	1	no	—
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₂²⋊D₅₃	—	2	2	no	—
414	C₂×C₂²⋊D₅₃	—	2	2	no	—
415	C₂×C₂²⋊D₅₃	—	2	2	no	—
416	C₂×C₂²⋊D₅₃	—	2	2	no	—
417	C₂×C₂²⋊D₅₃	—	2	2	no	—
418	C₂×C₂²⋊D₅₃	—	2	2	no	—
419	C₂×C₂²⋊D₅₃	—	2	2	no	—
420	C₂×C₂²⋊D₅₃	—	2	2	no	—
421	C₂×C₂²⋊D₅₃	—	2	2	no	—
422	C₂×C₂²⋊D₅₃	—	2	2	no	—
423	C₂×C₂²⋊D₅₃	—	4	1	no	—
424	C₂×C₂²⋊D₅₃	—	4	1	no	—
425	C₂×C₂²⋊D₅₃	—	4	1	no	—
426	C₂×C₂²⋊D₅₃	—	4	1	no	—
427	C₂×C₂²⋊D₅₃	#41	1	4	yes	—
428	C₂²×Dic₅₃	—	2	2	no	—
429	C₂²×Dic₅₃	—	2	2	no	—
430	C₂²×Dic₅₃	—	2	2	no	—
431	C₂²×Dic₅₃	—	2	2	no	—
432	C₂²×Dic₅₃	—	2	2	no	—
433	C₂²×Dic₅₃	—	4	1	no	—
434	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
447	D₄×D₅₃	—	4	16	no	—
448	C₂×D₂₁₂	—	2	2	no	—
449	C₂×D₂₁₂	—	4	1	no	—
450	C₂×D₂₁₂	—	4	1	no	—
451	C₂×C₄×D₅₃	—	2	2	no	—
452	C₂×C₄×D₅₃	—	2	2	no	—
453	C₂×C₄×D₅₃	—	2	2	no	—
454	C₂×C₄×D₅₃	—	2	2	no	—
455	C₂×C₄×D₅₃	—	2	2	no	—
456	C₂×C₄×D₅₃	—	2	2	no	—
457	C₂×C₄×D₅₃	—	4	1	no	—
458	C₂×C₄×D₅₃	—	4	1	no	—
459	C₂×C₄×D₅₃	—	4	1	no	—
460	C₂×C₄×D₅₃	—	4	1	no	—
461	C₂×C₄×D₅₃	—	4	1	no	—
462	C₂×C₄×D₅₃	—	4	1	no	—
463	C₂×C₄×D₅₃	—	4	1	no	—
464	C₂×C₄×D₅₃	#41	1	4	yes	—
465	C₂×C₄×D₅₃	#41	1	4	yes	—
466	C₂×Dic₁₀₆	—	2	2	no	—
467	C₂×Dic₁₀₆	—	2	2	no	—
468	C₂×Dic₁₀₆	—	2	2	no	—
469	C₄⋊C₄×C₅₃	—	2	2	no	—
470	C₄⋊C₄×C₅₃	—	4	1	no	—
471	C₄⋊C₄×C₅₃	—	4	1	no	—
472	C₄⋊C₄×C₅₃	—	4	1	no	—
473	C₄⋊C₄×C₅₃	—	4	1	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	4	1	no	—
479	C₂²⋊C₄×C₅₃	—	4	1	no	—
480	C₂²⋊C₄×C₅₃	—	4	1	no	—
481	C₂²⋊C₄×C₅₃	—	4	1	no	—
482	C₂²⋊C₄×C₅₃	—	4	1	no	—
483	C₂²⋊C₄×C₅₃	—	4	1	no	—
484	C₂²⋊C₄×C₅₃	—	4	1	no	—
485	C₂²⋊C₄×C₅₃	—	4	1	no	—
486	C₂²⋊C₄×C₅₃	—	4	1	no	—
487	C₂²⋊C₄×C₅₃	—	4	1	no	—
488	C₄²×C₅₃	—	4	1	no	—
489	C₄²×C₅₃	—	4	1	no	—
490	C₂²⋊Dic₅₃	—	2	2	no	—
491	C₂²⋊Dic₅₃	—	2	2	no	—
492	C₂²⋊Dic₅₃	—	2	2	no	—
493	C₂²⋊Dic₅₃	—	2	2	no	—
494	C₂²⋊Dic₅₃	—	2	2	no	—
495	C₂²⋊Dic₅₃	—	2	2	no	—
496	C₂²⋊Dic₅₃	—	2	2	no	—
497	C₂²⋊Dic₅₃	—	4	1	no	—
498	C₂²⋊Dic₅₃	—	4	1	no	—
499	C₂²⋊Dic₅₃	—	4	1	no	—
500	C₂²⋊Dic₅₃	—	4	1	no	—
501	C₂²⋊Dic₅₃	—	4	1	no	—
502	C₂²⋊Dic₅₃	—	4	1	no	—
503	C₂²⋊Dic₅₃	—	4	1	no	—
504	C₂²⋊Dic₅₃	—	4	1	no	—
505	#11719921	—	2	2	no	—
506	#11719921	—	2	2	no	—
507	#11719921	—	2	2	no	—
508	#11719921	—	2	2	no	—
509	#11719921	—	2	2	no	—
510	#11719921	—	2	2	no	—
511	#11719921	—	2	2	no	—
512	#11719921	—	2	2	no	—
513	#11719921	—	2	2	no	—
514	#11719921	—	2	2	no	—
515	#11719921	—	2	2	no	—
516	#11719921	—	2	2	no	—
517	#11719921	—	2	2	no	—
518	#11719921	—	2	2	no	—
519	#11719921	—	2	2	no	—
520	#11719921	—	4	1	no	—
521	#11719921	—	4	1	no	—
522	#11719921	—	4	1	no	—
523	#11719921	—	4	1	no	—
524	#11719921	—	4	1	no	—
525	#11719921	—	4	1	no	—
526	#11719921	—	4	1	no	—
527	#11719921	—	4	1	no	—
528	#11719921	—	4	1	no	—
529	#11719921	—	4	1	no	—
530	#11719921	—	4	1	no	—
531	#11719921	—	4	1	no	—
532	#11719921	—	4	1	no	—
533	#11719921	—	4	1	no	—
534	C₄⋊Dic₅₃	—	2	2	no	—
535	C₄⋊Dic₅₃	—	4	1	no	—
536	C₄⋊Dic₅₃	—	4	1	no	—
537	C₄⋊Dic₅₃	—	4	1	no	—
538	C₄⋊Dic₅₃	—	4	1	no	—
539	C₄⋊Dic₅₃	—	4	1	no	—
540	#11719919	—	2	2	no	—
541	#11719919	—	2	2	no	—
542	#11719919	—	2	2	no	—
543	#11719919	—	2	2	no	—
544	#11719919	—	2	2	no	—
545	#11719919	—	2	2	no	—
546	#11719919	—	2	2	no	—
547	#11719919	—	2	2	no	—
548	#11719919	—	2	2	no	—
549	#11719919	—	2	2	no	—
550	#11719919	—	4	1	no	—
551	#11719919	—	4	1	no	—
552	#11719919	—	4	1	no	—
553	#11719919	—	4	1	no	—
554	#11719919	—	4	1	no	—
555	#11719919	—	4	1	no	—
556	#11719919	—	4	1	no	—
557	C₄×Dic₅₃	—	2	2	no	—
558	C₄×Dic₅₃	—	2	2	no	—
559	C₄×Dic₅₃	—	2	2	no	—
560	C₄×Dic₅₃	—	2	2	no	—
561	C₄×Dic₅₃	—	2	2	no	—
562	C₄×Dic₅₃	—	2	2	no	—
563	C₄×Dic₅₃	—	2	2	no	—
564	C₄×Dic₅₃	—	2	2	no	—
565	C₄×Dic₅₃	—	4	1	no	—
566	C₄×Dic₅₃	—	4	1	no	—
567	C₄×Dic₅₃	—	4	1	no	—
568	C₄×Dic₅₃	—	4	1	no	—
569	C₄×Dic₅₃	—	4	1	no	—
570	C₄×Dic₅₃	—	4	1	no	—
571	C₄×Dic₅₃	—	4	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	—	2	1	no	—
574	C₂³×C₅₃	—	2	1	no	—
575	C₂³×C₅₃	—	2	1	no	—
576	C₂³×C₅₃	—	2	1	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	2	1	no	—
581	C₂³×C₅₃	—	2	1	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	C₂×#41	1	2	yes	—
593	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
594	C₂²×D₅₃	—	2	1	no	—
595	C₂²×D₅₃	—	2	1	no	—
596	C₂²×D₅₃	—	2	1	no	—
597	C₂²×D₅₃	—	2	1	no	—
598	C₂²×D₅₃	—	2	1	no	—
599	C₂²×D₅₃	—	2	1	no	—
600	C₂²×D₅₃	—	2	1	no	—
601	C₂²×D₅₃	—	2	1	no	—
602	C₂²×D₅₃	—	2	1	no	—
603	C₂²×D₅₃	—	2	1	no	—
604	C₂²×D₅₃	—	2	1	no	—
605	C₂²×D₅₃	—	2	1	no	—
606	C₂²×D₅₃	—	2	1	no	—
607	C₂²×D₅₃	—	2	1	no	—
608	C₂²×D₅₃	—	2	1	no	—
609	C₂²×D₅₃	—	2	1	no	—
610	C₂²×D₅₃	—	2	1	no	—
611	C₂²×D₅₃	—	2	1	no	—
612	C₂²×D₅₃	—	4	4	no	—
613	C₂²×D₅₃	—	4	4	no	—
614	C₂²×D₅₃	—	4	4	no	—
615	C₂²×D₅₃	—	4	4	no	—
616	C₂²×D₅₃	—	4	4	no	—
617	C₂²×D₅₃	—	4	4	no	—
618	C₂²×D₅₃	—	8	2	no	—
619	C₂²×D₅₃	—	8	2	no	—
620	C₂²×D₅₃	—	8	2	no	—
621	C₂²×D₅₃	—	8	2	no	—
622	C₂²×D₅₃	—	8	2	no	—
623	C₂²×D₅₃	—	8	2	no	—
624	C₂²×D₅₃	—	8	2	no	—
625	C₂²×D₅₃	—	8	2	no	—
626	C₂²×D₅₃	C₂×#41	1	2	yes	—
627	C₂²×D₅₃	C₂×#41	1	2	yes	—
628	C₂²×D₅₃	C₂×#41	1	2	yes	—
629	D₄×C₅₃	—	4	4	no	—
630	D₄×C₅₃	—	8	2	no	—
631	D₄×C₅₃	—	8	2	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	4	4	no	—
667	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
668	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
669	C₂²⋊D₅₃	—	2	8	no	—
670	C₂²⋊D₅₃	—	4	4	no	—
671	C₂²⋊D₅₃	—	4	4	no	—
672	C₂²⋊D₅₃	—	8	2	no	—
673	C₂²⋊D₅₃	—	8	2	no	—
674	C₂×Dic₅₃	—	2	1	no	—
675	C₂×Dic₅₃	—	2	1	no	—
676	C₂×Dic₅₃	—	2	1	no	—
677	C₂×Dic₅₃	—	2	1	no	—
678	C₂×Dic₅₃	—	2	1	no	—
679	C₂×Dic₅₃	—	2	1	no	—
680	C₂×Dic₅₃	—	2	1	no	—
681	C₂×Dic₅₃	—	2	1	no	—
682	C₂×Dic₅₃	—	2	1	no	—
683	C₂×Dic₅₃	—	2	1	no	—
684	C₂×Dic₅₃	—	2	1	no	—
685	C₂×Dic₅₃	—	2	1	no	—
686	C₂×Dic₅₃	—	2	1	no	—
687	C₂×Dic₅₃	—	2	1	no	—
688	C₂×Dic₅₃	—	2	1	no	—
689	C₂×Dic₅₃	—	2	1	no	—
690	C₂×Dic₅₃	—	2	1	no	—
691	C₂×Dic₅₃	—	2	1	no	—
692	C₂×Dic₅₃	—	2	1	no	—
693	C₂×Dic₅₃	—	2	1	no	—
694	C₂×Dic₅₃	—	2	1	no	—
695	C₂×Dic₅₃	—	2	1	no	—
696	C₂×Dic₅₃	—	2	1	no	—
697	C₂×Dic₅₃	—	2	1	no	—
698	C₂×Dic₅₃	—	2	1	no	—
699	C₂×Dic₅₃	—	2	1	no	—
700	C₂×Dic₅₃	—	2	1	no	—
701	C₂×Dic₅₃	—	2	1	no	—
702	C₂×Dic₅₃	—	2	1	no	—
703	C₂×Dic₅₃	—	2	1	no	—
704	C₂×Dic₅₃	—	2	1	no	—
705	C₂×Dic₅₃	—	2	1	no	—
706	C₂×Dic₅₃	—	2	1	no	—
707	C₂×Dic₅₃	—	4	4	no	—
708	C₂×Dic₅₃	—	4	4	no	—
709	C₂×Dic₅₃	C₂×#41	1	2	yes	—
710	C₂×Dic₅₃	C₂×#41	1	2	yes	—
711	C₂×Dic₅₃	C₂×#41	1	2	yes	—
712	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
713	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
714	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
715	D₂₁₂	—	4	4	no	—
716	C₄×D₅₃	—	2	8	no	—
717	C₄×D₅₃	—	4	4	no	—
718	C₄×D₅₃	—	4	4	no	—
719	C₄×D₅₃	—	8	2	no	—
720	C₄×D₅₃	—	8	2	no	—
721	Dic₁₀₆	—	4	4	no	—
722	#35025	—	53	1	no	maximal, Sylow
723	C₂²×C₅₃	—	2	2	no	—
724	C₂²×C₅₃	—	2	2	no	—
725	C₂²×C₅₃	—	2	2	no	—
726	C₂²×C₅₃	—	4	1	no	—
727	C₂²×C₅₃	—	4	1	no	—
728	C₂²×C₅₃	—	4	1	no	—
729	C₂²×C₅₃	—	4	1	no	—
730	C₂²×C₅₃	—	4	1	no	—
731	C₂²×C₅₃	—	4	1	no	—
732	C₂²×C₅₃	—	4	1	no	—
733	C₂²×C₅₃	—	4	1	no	—
734	C₂²×C₅₃	—	4	1	no	—
735	C₂²×C₅₃	—	4	1	no	—
736	C₂²×C₅₃	—	4	1	no	—
737	C₂²×C₅₃	—	4	1	no	—
738	C₂²×C₅₃	—	4	1	no	—
739	C₂²×C₅₃	—	4	1	no	—
740	C₂²×C₅₃	—	4	1	no	—
741	C₂²×C₅₃	—	4	1	no	—
742	C₂²×C₅₃	—	4	1	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
745	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
746	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
747	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
748	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
749	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
750	C₂²×C₅₃	#585	1	1	yes	characteristic
751	C₂×D₅₃	—	2	2	no	—
752	C₂×D₅₃	—	2	2	no	—
753	C₂×D₅₃	—	2	2	no	—
754	C₂×D₅₃	—	2	2	no	—
755	C₂×D₅₃	—	2	2	no	—
756	C₂×D₅₃	—	2	2	no	—
757	C₂×D₅₃	—	4	1	no	—
758	C₂×D₅₃	—	4	1	no	—
759	C₂×D₅₃	—	4	1	no	—
760	C₂×D₅₃	—	4	1	no	—
761	C₂×D₅₃	—	4	1	no	—
762	C₂×D₅₃	—	4	1	no	—
763	C₂×D₅₃	—	4	1	no	—
764	C₂×D₅₃	—	4	1	no	—
765	C₂×D₅₃	—	4	1	no	—
766	C₂×D₅₃	—	4	1	no	—
767	C₂×D₅₃	—	4	1	no	—
768	C₂×D₅₃	—	4	1	no	—
769	C₂×D₅₃	—	4	1	no	—
770	C₂×D₅₃	—	4	1	no	—
771	C₂×D₅₃	—	8	8	no	—
772	C₂×D₅₃	—	8	8	no	—
773	C₂×D₅₃	#529	1	4	yes	—
774	C₄×C₅₃	—	2	2	no	—
775	C₄×C₅₃	—	2	2	no	—
776	C₄×C₅₃	—	4	1	no	—
777	C₄×C₅₃	—	4	1	no	—
778	C₄×C₅₃	—	4	1	no	—
779	C₄×C₅₃	—	4	1	no	—
780	C₄×C₅₃	—	4	1	no	—
781	C₄×C₅₃	—	4	1	no	—
782	C₄×C₅₃	—	4	1	no	—
783	C₄×C₅₃	—	4	1	no	—
784	C₄×C₅₃	—	4	1	no	—
785	C₄×C₅₃	—	4	1	no	—
786	Dic₅₃	—	2	2	no	—
787	Dic₅₃	—	2	2	no	—
788	Dic₅₃	—	2	2	no	—
789	Dic₅₃	—	4	1	no	—
790	Dic₅₃	—	4	1	no	—
791	Dic₅₃	—	4	1	no	—
792	Dic₅₃	—	4	1	no	—
793	Dic₅₃	—	4	1	no	—
794	Dic₅₃	—	4	1	no	—
795	Dic₅₃	—	4	1	no	—
796	Dic₅₃	—	4	1	no	—
797	Dic₅₃	—	4	1	no	—
798	Dic₅₃	#538	1	4	yes	—
799	#2861	—	53	1	no	—
800	#2860	—	53	1	no	—
801	#2854	—	53	1	no	—
802	#2850	—	53	1	no	—
803	#2651	—	53	1	no	—
804	#2651	—	53	1	no	—
805	#2648	—	53	1	no	—
806	#2648	D₅₃	1	1	yes	characteristic, complemented
807	#2593	—	53	1	no	—
808	#2593	—	53	1	no	—
809	#2554	—	53	1	no	—
810	#2554	—	53	1	no	—
811	#2513	—	53	1	no	—
812	#2490	—	53	1	no	—
813	#2480	—	53	1	no	—
814	#2480	—	53	1	no	—
815	#2448	—	53	1	no	—
816	#2442	—	53	1	no	—
817	#2435	—	53	1	no	—
818	#2426	—	53	1	no	—
819	#2418	—	53	1	no	—
820	#2418	—	53	1	no	—
821	#2417	—	53	1	no	—
822	#2408	—	53	1	no	—
823	#2321	—	53	1	no	—
824	#2321	—	53	1	no	—
825	#2312	—	53	1	no	—
826	#2312	—	53	1	no	—
827	C₄×C₂²⋊Q₈	—	53	1	no	—
828	C₂×#390	—	53	1	no	—
829	C₄²×D₄	—	53	1	no	—
830	C₂×C₅₃	—	4	2	no	—
831	C₂×C₅₃	—	8	1	no	—
832	C₂×C₅₃	—	8	1	no	—
833	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
834	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
835	C₂×C₅₃	#3460	1	1	yes	characteristic
836	C₂×C₅₃	#3505	1	1	yes	characteristic
837	C₂×C₅₃	#3508	1	1	yes	characteristic
838	C₂×C₅₃	#3514	1	1	yes	characteristic
839	C₂×C₅₃	#3519	1	1	yes	characteristic
840	D₅₃	—	2	4	no	—
841	D₅₃	—	8	1	no	—
842	D₅₃	—	8	1	no	—
843	C₂³×D₄	—	53	1	no	—
844	C₂×#126	—	53	1	no	—
845	C₂×#126	—	53	1	no	—
846	C₂×#125	—	53	1	no	—
847	C₂×#124	—	53	1	no	—
848	C₂×#124	—	53	1	no	—
849	C₂×#123	—	53	1	no	—
850	C₂×#123	—	53	1	no	—
851	C₂×C₂²⋊Q₈	—	53	1	no	—
852	C₂×C₂²⋊Q₈	—	53	1	no	—
853	C₂×#121	—	53	1	no	—
854	C₂×#121	—	53	1	no	—
855	C₂×#120	—	53	1	no	—
856	C₂×#120	—	53	1	no	—
857	C₂×C₄×Q₈	—	53	1	no	—
858	C₂×C₄×D₄	—	53	1	no	—
859	C₂×C₄×D₄	—	53	1	no	—
860	C₂×C₄×D₄	—	53	1	no	—
861	C₂²×C₄⋊C₄	—	53	1	no	—
862	C₂²×C₂²⋊C₄	—	53	1	no	—
863	C₂²×C₂²⋊C₄	—	53	1	no	—
864	C₂²×C₂²⋊C₄	—	53	1	no	—
865	C₂²×C₂²⋊C₄	—	53	1	no	—
866	C₂²×C₄²	—	53	1	no	—
867	C₂²×C₄²	—	53	1	no	—
868	#400	—	53	1	no	—
869	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
870	#399	—	53	1	no	—
871	#399	—	53	1	no	—
872	#398	—	53	1	no	—
873	#398	—	53	1	no	—
874	#398	—	53	1	no	—
875	#398	—	53	1	no	—
876	#397	—	53	1	no	—
877	#397	—	53	1	no	—
878	#397	—	53	1	no	—
879	#397	—	53	1	no	—
880	#397	—	53	1	no	—
881	#397	—	53	1	no	—
882	#397	C₂×D₅₃	1	1	yes	characteristic, complemented
883	#397	C₂×D₅₃	1	1	yes	characteristic, complemented
884	#396	—	53	1	no	—
885	#396	—	53	1	no	—
886	#396	—	53	1	no	—
887	#396	C₂×D₅₃	1	1	yes	characteristic, complemented
888	#394	—	53	1	no	—
889	#394	—	53	1	no	—
890	#394	—	53	1	no	—
891	#394	—	53	1	no	—
892	#394	—	53	1	no	—
893	#394	—	53	1	no	—
894	#394	—	53	1	no	—
895	#394	C₂×D₅₃	1	1	yes	characteristic
896	#394	C₂×D₅₃	1	1	yes	characteristic, complemented
897	#394	C₂×D₅₃	1	1	yes	characteristic, complemented
898	#392	—	53	1	no	—
899	#392	C₂×D₅₃	1	1	yes	characteristic
900	#391	—	53	1	no	—
901	#391	—	53	1	no	—
902	#390	—	53	1	no	—
903	#390	—	53	1	no	—
904	#390	—	53	1	no	—
905	#390	—	53	1	no	—
906	#390	—	53	1	no	—
907	#390	—	53	1	no	—
908	#390	—	53	1	no	—
909	#390	—	53	1	no	—
910	#390	—	53	1	no	—
911	#390	—	53	1	no	—
912	#390	—	53	1	no	—
913	#390	—	53	1	no	—
914	#390	—	53	1	no	—
915	#390	—	53	1	no	—
916	#390	—	53	1	no	—
917	#390	C₂×D₅₃	1	1	yes	characteristic
918	#389	—	53	1	no	—
919	#389	—	53	1	no	—
920	#389	—	53	1	no	—
921	#389	—	53	1	no	—
922	#388	—	53	1	no	—
923	#388	—	53	1	no	—
924	#388	—	53	1	no	—
925	#388	—	53	1	no	—
926	#388	—	53	1	no	—
927	#388	—	53	1	no	—
928	#388	—	53	1	no	—
929	#388	—	53	1	no	—
930	#388	—	53	1	no	—
931	#388	—	53	1	no	—
932	#388	—	53	1	no	—
933	#388	—	53	1	no	—
934	#388	—	53	1	no	—
935	#388	—	53	1	no	—
936	#388	—	53	1	no	—
937	#388	—	53	1	no	—
938	#388	—	53	1	no	—
939	#388	—	53	1	no	—
940	#388	—	53	1	no	—
941	#388	—	53	1	no	—
942	#388	—	53	1	no	—
943	#388	—	53	1	no	—
944	#388	—	53	1	no	—
945	#388	—	53	1	no	—
946	#388	—	53	1	no	—
947	#388	—	53	1	no	—
948	#388	—	53	1	no	—
949	#388	—	53	1	no	—
950	#388	—	53	1	no	—
951	#388	—	53	1	no	—
952	#388	—	53	1	no	—
953	#388	—	53	1	no	—
954	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
955	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
956	#387	—	53	1	no	—
957	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
958	#386	—	53	1	no	—
959	#386	—	53	1	no	—
960	#386	—	53	1	no	—
961	#386	—	53	1	no	—
962	#386	—	53	1	no	—
963	#386	—	53	1	no	—
964	#386	C₂×D₅₃	1	1	yes	characteristic, complemented
965	#386	C₂×D₅₃	1	1	yes	characteristic, complemented
966	#385	—	53	1	no	—
967	#385	—	53	1	no	—
968	#385	—	53	1	no	—
969	#385	—	53	1	no	—
970	#382	—	53	1	no	—
971	#380	—	53	1	no	—
972	#380	—	53	1	no	—
973	#380	—	53	1	no	—
974	#380	—	53	1	no	—
975	#380	—	53	1	no	—
976	#380	—	53	1	no	—
977	#379	—	53	1	no	—
978	#379	—	53	1	no	—
979	#379	—	53	1	no	—
980	#379	—	53	1	no	—
981	#379	—	53	1	no	—
982	#379	—	53	1	no	—
983	C₄×C₄⋊C₄	—	53	1	no	—
984	C₄×C₄⋊C₄	—	53	1	no	—
985	C₄×C₄⋊C₄	—	53	1	no	—
986	C₄×C₄⋊C₄	—	53	1	no	—
987	C₄×C₄⋊C₄	—	53	1	no	—
988	C₄×C₄⋊C₄	—	53	1	no	—
989	C₄×C₂²⋊C₄	—	53	1	no	—
990	C₄×C₂²⋊C₄	—	53	1	no	—
991	C₄×C₂²⋊C₄	—	53	1	no	—
992	C₄×C₂²⋊C₄	—	53	1	no	—
993	C₄×C₂²⋊C₄	—	53	1	no	—
994	C₄×C₂²⋊C₄	—	53	1	no	—
995	C₄×C₂²⋊C₄	—	53	1	no	—
996	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
997	C₄³	—	53	1	no	—
998	C₅₃	#35025	1	1	yes	characteristic, complemented, Sylow
999	C₂⁵	—	53	1	no	—
1000	C₂⁵	—	53	1	no	—
1001	C₂²×Q₈	—	53	1	no	—
1002	C₂²×D₄	—	53	1	no	—
1003	C₂²×D₄	—	53	1	no	—
1004	C₂²×D₄	—	53	1	no	—
1005	C₂²×D₄	—	53	1	no	—
1006	C₂²×D₄	—	53	1	no	—
1007	C₂²×D₄	—	53	1	no	—
1008	C₂²×D₄	—	106	4	no	—
1009	C₂²×D₄	—	212	2	no	—
1010	C₂²×D₄	—	212	2	no	—
1011	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1012	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1013	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂³×C₄	—	53	1	no	—
1015	C₂³×C₄	—	53	1	no	—
1016	C₂³×C₄	—	53	1	no	—
1017	C₂³×C₄	—	53	1	no	—
1018	C₂³×C₄	—	53	1	no	—
1019	C₂³×C₄	—	53	1	no	—
1020	C₂³×C₄	—	53	1	no	—
1021	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1022	#126	—	212	2	no	—
1023	#126	—	212	2	no	—
1024	#125	—	212	2	no	—
1025	#124	—	212	2	no	—
1026	#124	—	212	2	no	—
1027	#123	—	212	2	no	—
1028	#123	—	212	2	no	—
1029	C₂²⋊Q₈	—	106	4	no	—
1030	C₂²⋊Q₈	—	212	2	no	—
1031	#121	—	212	2	no	—
1032	#121	—	212	2	no	—
1033	#120	—	106	4	no	—
1034	#120	—	106	4	no	—
1035	C₄×Q₈	—	212	2	no	—
1036	C₄×D₄	—	106	4	no	—
1037	C₄×D₄	—	106	4	no	—
1038	C₄×D₄	—	106	4	no	—
1039	C₂×C₄⋊C₄	—	53	1	no	—
1040	C₂×C₄⋊C₄	—	53	1	no	—
1041	C₂×C₄⋊C₄	—	53	1	no	—
1042	C₂×C₄⋊C₄	—	53	1	no	—
1043	C₂×C₄⋊C₄	—	53	1	no	—
1044	C₂×C₄⋊C₄	—	53	1	no	—
1045	C₂×C₄⋊C₄	—	53	1	no	—
1046	C₂×C₄⋊C₄	—	53	1	no	—
1047	C₂×C₄⋊C₄	—	53	1	no	—
1048	C₂×C₄⋊C₄	—	53	1	no	—
1049	C₂×C₄⋊C₄	—	53	1	no	—
1050	C₂×C₄⋊C₄	—	53	1	no	—
1051	C₂×C₄⋊C₄	—	53	1	no	—
1052	C₂×C₄⋊C₄	—	53	1	no	—
1053	C₂×C₄⋊C₄	—	53	1	no	—
1054	C₂×C₄⋊C₄	—	53	1	no	—
1055	C₂×C₄⋊C₄	—	53	1	no	—
1056	C₂×C₄⋊C₄	—	53	1	no	—
1057	C₂×C₄⋊C₄	—	53	1	no	—
1058	C₂×C₄⋊C₄	—	53	1	no	—
1059	C₂×C₄⋊C₄	—	53	1	no	—
1060	C₂×C₄⋊C₄	—	53	1	no	—
1061	C₂×C₄⋊C₄	—	53	1	no	—
1062	C₂×C₄⋊C₄	—	212	2	no	—
1063	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1064	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1065	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1066	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1067	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	—	53	1	no	—
1069	C₂×C₂²⋊C₄	—	53	1	no	—
1070	C₂×C₂²⋊C₄	—	53	1	no	—
1071	C₂×C₂²⋊C₄	—	53	1	no	—
1072	C₂×C₂²⋊C₄	—	53	1	no	—
1073	C₂×C₂²⋊C₄	—	53	1	no	—
1074	C₂×C₂²⋊C₄	—	53	1	no	—
1075	C₂×C₂²⋊C₄	—	53	1	no	—
1076	C₂×C₂²⋊C₄	—	53	1	no	—
1077	C₂×C₂²⋊C₄	—	53	1	no	—
1078	C₂×C₂²⋊C₄	—	53	1	no	—
1079	C₂×C₂²⋊C₄	—	53	1	no	—
1080	C₂×C₂²⋊C₄	—	53	1	no	—
1081	C₂×C₂²⋊C₄	—	53	1	no	—
1082	C₂×C₂²⋊C₄	—	53	1	no	—
1083	C₂×C₂²⋊C₄	—	53	1	no	—
1084	C₂×C₂²⋊C₄	—	53	1	no	—
1085	C₂×C₂²⋊C₄	—	53	1	no	—
1086	C₂×C₂²⋊C₄	—	53	1	no	—
1087	C₂×C₂²⋊C₄	—	53	1	no	—
1088	C₂×C₂²⋊C₄	—	53	1	no	—
1089	C₂×C₂²⋊C₄	—	53	1	no	—
1090	C₂×C₂²⋊C₄	—	53	1	no	—
1091	C₂×C₂²⋊C₄	—	53	1	no	—
1092	C₂×C₂²⋊C₄	—	53	1	no	—
1093	C₂×C₂²⋊C₄	—	53	1	no	—
1094	C₂×C₂²⋊C₄	—	53	1	no	—
1095	C₂×C₂²⋊C₄	—	53	1	no	—
1096	C₂×C₂²⋊C₄	—	53	1	no	—
1097	C₂×C₂²⋊C₄	—	53	1	no	—
1098	C₂×C₂²⋊C₄	—	53	1	no	—
1099	C₂×C₂²⋊C₄	—	53	1	no	—
1100	C₂×C₂²⋊C₄	—	53	1	no	—
1101	C₂×C₂²⋊C₄	—	53	1	no	—
1102	C₂×C₂²⋊C₄	—	53	1	no	—
1103	C₂×C₂²⋊C₄	—	53	1	no	—
1104	C₂×C₂²⋊C₄	—	53	1	no	—
1105	C₂×C₂²⋊C₄	—	53	1	no	—
1106	C₂×C₂²⋊C₄	—	53	1	no	—
1107	C₂×C₂²⋊C₄	—	53	1	no	—
1108	C₂×C₂²⋊C₄	—	53	1	no	—
1109	C₂×C₂²⋊C₄	—	53	1	no	—
1110	C₂×C₂²⋊C₄	—	53	1	no	—
1111	C₂×C₂²⋊C₄	—	53	1	no	—
1112	C₂×C₂²⋊C₄	—	106	4	no	—
1113	C₂×C₂²⋊C₄	—	106	4	no	—
1114	C₂×C₂²⋊C₄	—	212	2	no	—
1115	C₂×C₂²⋊C₄	—	212	2	no	—
1116	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1119	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1122	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1123	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1124	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1125	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1126	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1127	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1128	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1129	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1130	C₂×C₄²	—	53	1	no	—
1131	C₂×C₄²	—	53	1	no	—
1132	C₂×C₄²	—	53	1	no	—
1133	C₂×C₄²	—	53	1	no	—
1134	C₂×C₄²	—	53	1	no	—
1135	C₂×C₄²	—	53	1	no	—
1136	C₂×C₄²	—	53	1	no	—
1137	C₂×C₄²	—	53	1	no	—
1138	C₂×C₄²	—	53	1	no	—
1139	C₂×C₄²	—	53	1	no	—
1140	C₂×C₄²	—	53	1	no	—
1141	C₂×C₄²	—	53	1	no	—
1142	C₂×C₄²	—	53	1	no	—
1143	C₂×C₄²	—	53	1	no	—
1144	C₂×C₄²	—	53	1	no	—
1145	C₂×C₄²	—	212	2	no	—
1146	C₂×C₄²	—	212	2	no	—
1147	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1148	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1149	#95	—	53	1	no	—
1150	#95	—	53	1	no	—
1151	#95	—	53	1	no	—
1152	#95	—	53	1	no	—
1153	#95	—	53	1	no	—
1154	#95	—	53	1	no	—
1155	#95	—	53	1	no	—
1156	#95	—	53	1	no	—
1157	#95	—	53	1	no	—
1158	#95	—	53	1	no	—
1159	#95	—	53	1	no	—
1160	#95	—	53	1	no	—
1161	#95	—	53	1	no	—
1162	#95	—	53	1	no	—
1163	#95	—	53	1	no	—
1164	#95	—	53	1	no	—
1165	#95	—	53	1	no	—
1166	#95	—	53	1	no	—
1167	#95	—	53	1	no	—
1168	#95	—	53	1	no	—
1169	#95	—	53	1	no	—
1170	#95	—	53	1	no	—
1171	#95	C₂²×D₅₃	1	1	yes	characteristic
1172	#95	C₂²×D₅₃	1	1	yes	characteristic
1173	#95	C₂²×D₅₃	1	1	yes	characteristic
1174	#95	C₂²×D₅₃	1	1	yes	characteristic
1175	#95	C₂²×D₅₃	1	1	yes	characteristic
1176	#95	C₂²×D₅₃	1	1	yes	characteristic
1177	#95	C₂²×D₅₃	1	1	yes	characteristic
1178	#95	C₂²×D₅₃	1	1	yes	characteristic
1179	#95	C₂²×D₅₃	1	1	yes	characteristic
1180	#95	C₂²×D₅₃	1	1	yes	characteristic
1181	C₂⁴	—	53	1	no	—
1182	C₂⁴	—	53	1	no	—
1183	C₂⁴	—	53	1	no	—
1184	C₂⁴	—	106	2	no	—
1185	C₂⁴	—	106	2	no	—
1186	C₂⁴	—	106	2	no	—
1187	C₂⁴	—	106	2	no	—
1188	C₂⁴	—	106	2	no	—
1189	C₂⁴	—	106	2	no	—
1190	C₂⁴	—	212	1	no	—
1191	C₂⁴	—	212	1	no	—
1192	C₂⁴	—	212	1	no	—
1193	C₂⁴	—	212	1	no	—
1194	C₂⁴	—	212	1	no	—
1195	C₂⁴	—	212	1	no	—
1196	C₂⁴	—	212	1	no	—
1197	C₂⁴	—	212	1	no	—
1198	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1199	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1200	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1201	C₂×Q₈	—	106	2	no	—
1202	C₂×Q₈	—	106	2	no	—
1203	C₂×Q₈	—	106	2	no	—
1204	C₂×D₄	—	2	2	no	—
1205	C₂×D₄	—	2	2	no	—
1206	C₂×D₄	—	2	2	no	—
1207	C₂×D₄	—	4	1	no	—
1208	C₂×D₄	—	4	1	no	—
1209	C₂×D₄	—	4	1	no	—
1210	C₂×D₄	—	4	1	no	—
1211	C₂×D₄	—	4	1	no	—
1212	C₂×D₄	—	4	1	no	—
1213	C₂×D₄	—	53	4	no	—
1214	C₂×D₄	—	106	2	no	—
1215	C₂×D₄	—	106	2	no	—
1216	C₂×D₄	—	106	2	no	—
1217	C₂×D₄	—	106	2	no	—
1218	C₂×D₄	—	106	2	no	—
1219	C₂×D₄	—	106	2	no	—
1220	C₂×D₄	—	106	2	no	—
1221	C₂×D₄	—	106	2	no	—
1222	C₂×D₄	—	106	2	no	—
1223	C₂×D₄	—	106	2	no	—
1224	C₂×D₄	—	106	2	no	—
1225	C₂×D₄	—	212	1	no	—
1226	C₂×D₄	—	212	1	no	—
1227	C₂×D₄	—	212	16	no	—
1228	C₂×D₄	—	212	1	no	—
1229	C₂×D₄	—	212	1	no	—
1230	C₂×D₄	—	212	1	no	—
1231	C₂×D₄	—	212	1	no	—
1232	C₂²×C₄	—	2	2	no	—
1233	C₂²×C₄	—	4	1	no	—
1234	C₂²×C₄	—	4	1	no	—
1235	C₂²×C₄	—	53	1	no	—
1236	C₂²×C₄	—	53	1	no	—
1237	C₂²×C₄	—	53	1	no	—
1238	C₂²×C₄	—	53	1	no	—
1239	C₂²×C₄	—	53	4	no	—
1240	C₂²×C₄	—	53	4	no	—
1241	C₂²×C₄	—	53	1	no	—
1242	C₂²×C₄	—	53	1	no	—
1243	C₂²×C₄	—	53	1	no	—
1244	C₂²×C₄	—	53	1	no	—
1245	C₂²×C₄	—	53	1	no	—
1246	C₂²×C₄	—	53	1	no	—
1247	C₂²×C₄	—	53	1	no	—
1248	C₂²×C₄	—	53	1	no	—
1249	C₂²×C₄	—	53	1	no	—
1250	C₂²×C₄	—	106	2	no	—
1251	C₂²×C₄	—	106	2	no	—
1252	C₂²×C₄	—	106	2	no	—
1253	C₂²×C₄	—	106	2	no	—
1254	C₂²×C₄	—	106	2	no	—
1255	C₂²×C₄	—	106	2	no	—
1256	C₂²×C₄	—	106	2	no	—
1257	C₂²×C₄	—	106	2	no	—
1258	C₂²×C₄	—	106	2	no	—
1259	C₂²×C₄	—	106	2	no	—
1260	C₂²×C₄	—	106	2	no	—
1261	C₂²×C₄	—	212	1	no	—
1262	C₂²×C₄	—	212	1	no	—
1263	C₂²×C₄	—	212	1	no	—
1264	C₂²×C₄	—	212	1	no	—
1265	C₂²×C₄	—	212	1	no	—
1266	C₂²×C₄	—	212	1	no	—
1267	C₂²×C₄	—	212	1	no	—
1268	C₂²×C₄	—	212	1	no	—
1269	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1270	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1271	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1272	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1273	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1274	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1275	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1276	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1277	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1278	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1279	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1280	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1281	C₄⋊C₄	—	2	2	no	—
1282	C₄⋊C₄	—	4	1	no	—
1283	C₄⋊C₄	—	4	1	no	—
1284	C₄⋊C₄	—	4	1	no	—
1285	C₄⋊C₄	—	4	1	no	—
1286	C₄⋊C₄	—	106	2	no	—
1287	C₄⋊C₄	—	106	2	no	—
1288	C₄⋊C₄	—	106	2	no	—
1289	C₄⋊C₄	—	106	2	no	—
1290	C₄⋊C₄	—	106	2	no	—
1291	C₄⋊C₄	—	106	2	no	—
1292	C₄⋊C₄	—	106	2	no	—
1293	C₄⋊C₄	—	106	2	no	—
1294	C₄⋊C₄	—	106	2	no	—
1295	C₄⋊C₄	—	106	2	no	—
1296	C₄⋊C₄	—	106	2	no	—
1297	C₄⋊C₄	—	212	1	no	—
1298	C₄⋊C₄	—	212	1	no	—
1299	C₄⋊C₄	—	212	1	no	—
1300	C₄⋊C₄	—	212	1	no	—
1301	C₄⋊C₄	—	212	1	no	—
1302	C₄⋊C₄	—	212	1	no	—
1303	C₄⋊C₄	—	212	1	no	—
1304	C₄⋊C₄	—	212	1	no	—
1305	C₄⋊C₄	—	212	1	no	—
1306	C₄⋊C₄	—	212	1	no	—
1307	C₄⋊C₄	—	212	1	no	—
1308	C₄⋊C₄	—	212	1	no	—
1309	C₂²⋊C₄	—	2	2	no	—
1310	C₂²⋊C₄	—	2	2	no	—
1311	C₂²⋊C₄	—	2	2	no	—
1312	C₂²⋊C₄	—	2	2	no	—
1313	C₂²⋊C₄	—	4	1	no	—
1314	C₂²⋊C₄	—	4	1	no	—
1315	C₂²⋊C₄	—	4	1	no	—
1316	C₂²⋊C₄	—	4	1	no	—
1317	C₂²⋊C₄	—	4	1	no	—
1318	C₂²⋊C₄	—	4	1	no	—
1319	C₂²⋊C₄	—	4	1	no	—
1320	C₂²⋊C₄	—	4	1	no	—
1321	C₂²⋊C₄	—	4	1	no	—
1322	C₂²⋊C₄	—	4	1	no	—
1323	C₂²⋊C₄	—	106	2	no	—
1324	C₂²⋊C₄	—	106	2	no	—
1325	C₂²⋊C₄	—	106	2	no	—
1326	C₂²⋊C₄	—	106	2	no	—
1327	C₂²⋊C₄	—	106	2	no	—
1328	C₂²⋊C₄	—	106	2	no	—
1329	C₂²⋊C₄	—	106	2	no	—
1330	C₂²⋊C₄	—	106	2	no	—
1331	C₂²⋊C₄	—	106	2	no	—
1332	C₂²⋊C₄	—	106	2	no	—
1333	C₂²⋊C₄	—	106	2	no	—
1334	C₂²⋊C₄	—	106	2	no	—
1335	C₂²⋊C₄	—	106	2	no	—
1336	C₂²⋊C₄	—	106	2	no	—
1337	C₂²⋊C₄	—	106	2	no	—
1338	C₂²⋊C₄	—	106	2	no	—
1339	C₂²⋊C₄	—	106	2	no	—
1340	C₂²⋊C₄	—	106	2	no	—
1341	C₂²⋊C₄	—	106	2	no	—
1342	C₂²⋊C₄	—	106	2	no	—
1343	C₂²⋊C₄	—	106	2	no	—
1344	C₂²⋊C₄	—	106	2	no	—
1345	C₂²⋊C₄	—	212	1	no	—
1346	C₂²⋊C₄	—	212	1	no	—
1347	C₂²⋊C₄	—	212	1	no	—
1348	C₂²⋊C₄	—	212	1	no	—
1349	C₂²⋊C₄	—	212	1	no	—
1350	C₂²⋊C₄	—	212	1	no	—
1351	C₂²⋊C₄	—	212	1	no	—
1352	C₂²⋊C₄	—	212	1	no	—
1353	C₂²⋊C₄	—	212	1	no	—
1354	C₂²⋊C₄	—	212	1	no	—
1355	C₂²⋊C₄	—	212	1	no	—
1356	C₂²⋊C₄	—	212	1	no	—
1357	C₂²⋊C₄	—	212	1	no	—
1358	C₂²⋊C₄	—	212	1	no	—
1359	C₂²⋊C₄	—	212	1	no	—
1360	C₂²⋊C₄	—	212	1	no	—
1361	C₂²⋊C₄	—	212	1	no	—
1362	C₂²⋊C₄	—	212	1	no	—
1363	C₂²⋊C₄	—	212	1	no	—
1364	C₂²⋊C₄	—	212	1	no	—
1365	C₂²⋊C₄	—	212	1	no	—
1366	C₂²⋊C₄	—	212	1	no	—
1367	C₄²	—	4	1	no	—
1368	C₄²	—	4	1	no	—
1369	C₄²	—	106	2	no	—
1370	C₄²	—	106	2	no	—
1371	C₄²	—	106	2	no	—
1372	C₄²	—	106	2	no	—
1373	C₄²	—	106	2	no	—
1374	C₄²	—	106	2	no	—
1375	C₄²	—	106	2	no	—
1376	C₄²	—	106	2	no	—
1377	C₄²	—	212	1	no	—
1378	C₄²	—	212	1	no	—
1379	C₄²	—	212	1	no	—
1380	C₄²	—	212	1	no	—
1381	C₄²	—	212	1	no	—
1382	C₄²	—	212	1	no	—
1383	C₄²	—	212	1	no	—
1384	C₂³	—	2	1	no	—
1385	C₂³	—	2	1	no	—
1386	C₂³	—	2	1	no	—
1387	C₂³	—	2	1	no	—
1388	C₂³	—	2	1	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	2	1	no	—
1393	C₂³	—	2	1	no	—
1394	C₂³	—	2	1	no	—
1395	C₂³	—	2	1	no	—
1396	C₂³	—	2	1	no	—
1397	C₂³	—	2	1	no	—
1398	C₂³	—	2	1	no	—
1399	C₂³	—	2	1	no	—
1400	C₂³	—	2	1	no	—
1401	C₂³	—	2	1	no	—
1402	C₂³	—	2	1	no	—
1403	C₂³	—	2	1	no	—
1404	C₂³	—	53	2	no	—
1405	C₂³	—	53	2	no	—
1406	C₂³	—	53	2	no	—
1407	C₂³	—	106	1	no	—
1408	C₂³	—	106	1	no	—
1409	C₂³	—	106	1	no	—
1410	C₂³	—	106	1	no	—
1411	C₂³	—	106	1	no	—
1412	C₂³	—	106	1	no	—
1413	C₂³	—	106	1	no	—
1414	C₂³	—	106	1	no	—
1415	C₂³	—	106	1	no	—
1416	C₂³	—	106	1	no	—
1417	C₂³	—	106	1	no	—
1418	C₂³	—	106	1	no	—
1419	C₂³	—	106	1	no	—
1420	C₂³	—	106	1	no	—
1421	C₂³	—	106	1	no	—
1422	C₂³	—	106	1	no	—
1423	C₂³	—	106	1	no	—
1424	C₂³	—	106	1	no	—
1425	C₂³	—	424	2	no	—
1426	C₂³	—	424	2	no	—
1427	C₂³	—	424	2	no	—
1428	C₂³	—	424	2	no	—
1429	C₂³	—	424	2	no	—
1430	C₂³	—	424	2	no	—
1431	C₂³	—	424	2	no	—
1432	C₂³	—	424	2	no	—
1433	C₂³	—	212	4	no	—
1434	C₂³	—	212	4	no	—
1435	C₂³	—	212	4	no	—
1436	C₂³	—	212	4	no	—
1437	C₂³	—	212	4	no	—
1438	C₂³	—	212	4	no	—
1439	C₂³	#41×D₅₃	1	2	yes	—
1440	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1441	Q₈	—	212	4	no	—
1442	D₄	—	4	4	no	—
1443	D₄	—	8	2	no	—
1444	D₄	—	8	2	no	—
1445	D₄	—	106	8	no	—
1446	D₄	—	424	2	no	—
1447	D₄	—	424	2	no	—
1448	D₄	—	212	4	no	—
1449	D₄	—	212	4	no	—
1450	D₄	—	212	4	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	1	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	1	no	—
1462	C₂×C₄	—	2	1	no	—
1463	C₂×C₄	—	2	1	no	—
1464	C₂×C₄	—	2	1	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	4	4	no	—
1486	C₂×C₄	—	53	2	no	—
1487	C₂×C₄	—	53	2	no	—
1488	C₂×C₄	—	53	2	no	—
1489	C₂×C₄	—	53	2	no	—
1490	C₂×C₄	—	53	2	no	—
1491	C₂×C₄	—	53	2	no	—
1492	C₂×C₄	—	106	8	no	—
1493	C₂×C₄	—	106	1	no	—
1494	C₂×C₄	—	106	1	no	—
1495	C₂×C₄	—	106	1	no	—
1496	C₂×C₄	—	106	1	no	—
1497	C₂×C₄	—	106	1	no	—
1498	C₂×C₄	—	106	1	no	—
1499	C₂×C₄	—	106	1	no	—
1500	C₂×C₄	—	106	1	no	—
1501	C₂×C₄	—	106	1	no	—
1502	C₂×C₄	—	106	1	no	—
1503	C₂×C₄	—	106	1	no	—
1504	C₂×C₄	—	106	1	no	—
1505	C₂×C₄	—	106	1	no	—
1506	C₂×C₄	—	106	1	no	—
1507	C₂×C₄	—	106	1	no	—
1508	C₂×C₄	—	106	1	no	—
1509	C₂×C₄	—	106	1	no	—
1510	C₂×C₄	—	106	1	no	—
1511	C₂×C₄	—	106	1	no	—
1512	C₂×C₄	—	106	1	no	—
1513	C₂×C₄	—	106	1	no	—
1514	C₂×C₄	—	106	1	no	—
1515	C₂×C₄	—	106	1	no	—
1516	C₂×C₄	—	106	1	no	—
1517	C₂×C₄	—	106	1	no	—
1518	C₂×C₄	—	106	1	no	—
1519	C₂×C₄	—	106	1	no	—
1520	C₂×C₄	—	106	1	no	—
1521	C₂×C₄	—	106	1	no	—
1522	C₂×C₄	—	106	1	no	—
1523	C₂×C₄	—	106	1	no	—
1524	C₂×C₄	—	106	1	no	—
1525	C₂×C₄	—	106	1	no	—
1526	C₂×C₄	—	424	2	no	—
1527	C₂×C₄	—	424	2	no	—
1528	C₂×C₄	—	212	4	no	—
1529	C₂×C₄	—	212	4	no	—
1530	C₂×C₄	—	212	4	no	—
1531	C₂×C₄	—	212	4	no	—
1532	C₂×C₄	#41×D₅₃	1	2	yes	—
1533	C₂×C₄	#41×D₅₃	1	2	yes	—
1534	C₂²	—	2	2	no	—
1535	C₂²	—	2	2	no	—
1536	C₂²	—	2	2	no	—
1537	C₂²	—	4	1	no	—
1538	C₂²	—	4	1	no	—
1539	C₂²	—	4	1	no	—
1540	C₂²	—	4	1	no	—
1541	C₂²	—	4	1	no	—
1542	C₂²	—	4	1	no	—
1543	C₂²	—	4	1	no	—
1544	C₂²	—	4	1	no	—
1545	C₂²	—	4	1	no	—
1546	C₂²	—	4	1	no	—
1547	C₂²	—	4	1	no	—
1548	C₂²	—	4	1	no	—
1549	C₂²	—	4	1	no	—
1550	C₂²	—	4	1	no	—
1551	C₂²	—	4	1	no	—
1552	C₂²	—	4	1	no	—
1553	C₂²	—	4	1	no	—
1554	C₂²	—	4	1	no	—
1555	C₂²	—	53	4	no	—
1556	C₂²	—	106	2	no	—
1557	C₂²	—	106	2	no	—
1558	C₂²	—	106	2	no	—
1559	C₂²	—	106	2	no	—
1560	C₂²	—	106	2	no	—
1561	C₂²	—	106	2	no	—
1562	C₂²	—	424	8	no	—
1563	C₂²	—	424	8	no	—
1564	C₂²	—	212	1	no	—
1565	C₂²	—	212	1	no	—
1566	C₂²	—	212	1	no	—
1567	C₂²	—	212	1	no	—
1568	C₂²	—	212	1	no	—
1569	C₂²	—	212	1	no	—
1570	C₂²	—	212	1	no	—
1571	C₂²	—	212	1	no	—
1572	C₂²	—	212	1	no	—
1573	C₂²	—	212	1	no	—
1574	C₂²	—	212	1	no	—
1575	C₂²	—	212	1	no	—
1576	C₂²	—	212	1	no	—
1577	C₂²	—	212	1	no	—
1578	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1579	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1580	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1581	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1582	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1583	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1584	C₂²	#16811458	1	1	yes	characteristic
1585	C₄	—	2	2	no	—
1586	C₄	—	2	2	no	—
1587	C₄	—	4	1	no	—
1588	C₄	—	4	1	no	—
1589	C₄	—	4	1	no	—
1590	C₄	—	4	1	no	—
1591	C₄	—	4	1	no	—
1592	C₄	—	4	1	no	—
1593	C₄	—	4	1	no	—
1594	C₄	—	4	1	no	—
1595	C₄	—	4	1	no	—
1596	C₄	—	4	1	no	—
1597	C₄	—	53	4	no	—
1598	C₄	—	106	2	no	—
1599	C₄	—	106	2	no	—
1600	C₄	—	106	2	no	—
1601	C₄	—	212	1	no	—
1602	C₄	—	212	1	no	—
1603	C₄	—	212	1	no	—
1604	C₄	—	212	1	no	—
1605	C₄	—	212	1	no	—
1606	C₄	—	212	1	no	—
1607	C₄	—	212	1	no	—
1608	C₄	—	212	1	no	—
1609	C₄	—	212	1	no	—
1610	C₂	—	4	2	no	—
1611	C₂	—	8	1	no	—
1612	C₂	—	8	1	no	—
1613	C₂	—	106	4	no	—
1614	C₂	—	424	1	no	—
1615	C₂	—	424	1	no	—
1616	C₂	#529×D₅₃	1	1	yes	characteristic
1617	C₂	#538×D₅₃	1	1	yes	characteristic
1618	C₂	#20288130	1	1	yes	characteristic
1619	C₂	#20288553	1	1	yes	characteristic
1620	C₂	#20288587	1	1	yes	characteristic
1621	C₂	#20288668	1	1	yes	characteristic
1622	C₂	#20288739	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2648	C₂
prime radical	#20278064	C₂
hypercenter	#2648	D₅₃
hypocenter	C₅₃	#35025
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2648

Complements

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

N	H ≅ G/N	type
1. #20283084	C₂	semidirect
2. #20283081	C₂	semidirect
3. #20283043	C₂	semidirect
4. #20283012	C₂	semidirect
5. #20280754	C₂	semidirect
6. #20280752	C₂	semidirect
7. #20280697	C₂	semidirect
8. #20280212	C₂	semidirect
9. #20280207	C₂	semidirect
10. #20279776	C₂	semidirect
11. #20279768	C₂	semidirect
12. #20279305	C₂	semidirect
13. #20279060	C₂	semidirect
14. #20278962	C₂	semidirect
15. #20278954	C₂	semidirect
16. #20278506	C₂	semidirect
17. #20278432	C₂	semidirect
18. #20278361	C₂	semidirect
19. #20278274	C₂	semidirect
20. #20278172	C₂	semidirect
21. #20278170	C₂	semidirect
22. #20278159	C₂	semidirect
24. #20277371	C₂	semidirect
25. #20277371	C₂	semidirect
26. #20277309	C₂	semidirect
27. #20277309	C₂	semidirect
28. #20277249	C₂	semidirect
29. #390×D₅₃	C₂	semidirect
30. C₄×#13133177	C₂	semidirect
31. C₅₃×#2648	C₂	semidirect
33. C₂×#13133212	C₂²	semidirect
34. C₂×#13133210	C₂²	semidirect
35. C₂×#13133207	C₂²	semidirect
38. C₂×#13133201	C₂²	semidirect
39. C₂×#13133198	C₂²	semidirect
41. C₂×#13133194	C₂²	semidirect
46. C₂×#13133182	C₂²	semidirect
55. C₂²×C₄×Dic₅₃	C₂²	semidirect
57. #16810565	C₂²	semidirect
58. #16810559	C₂²	semidirect
59. #16810558	C₂²	semidirect
60. #16810556	C₂²	semidirect
61. #16810556	C₂²	semidirect
62. #16810555	C₂²	semidirect
63. #16810553	C₂²	semidirect
64. #16810552	C₂²	semidirect
65. #16810552	C₂²	semidirect
66. #16810552	C₂²	semidirect
67. #16810551	C₂²	semidirect
68. #16810551	C₂²	semidirect
69. #16810550	C₂²	semidirect
70. #16810546	C₂²	semidirect
71. #16810546	C₂²	semidirect
72. #16810545	C₂²	semidirect
76. #16810538	C₂²	semidirect
77. #16810538	C₂²	semidirect
81. #16810527	C₂²	semidirect
82. #16810527	C₂²	semidirect
84. #16810526	C₂²	semidirect
85. #16810526	C₂²	semidirect
96. #16810523	C₂²	semidirect
97. #16810523	C₂²	semidirect
98. #16810520	C₂²	semidirect
99. #16810520	C₂²	semidirect
100. #16810520	C₂²	semidirect
101. #16810518	C₂²	semidirect
102. #16810517	C₂²	semidirect
103. #16810517	C₂²	semidirect
104. #16810517	C₂²	semidirect
105. #16810516	C₂²	semidirect
106. #16810516	C₂²	semidirect
107. #16810516	C₂²	semidirect
108. #16810516	C₂²	semidirect
109. #16810516	C₂²	semidirect
110. #16810515	C₂²	semidirect
111. #16810515	C₂²	semidirect
112. #16810515	C₂²	semidirect
113. #16810515	C₂²	semidirect
114. #16810515	C₂²	semidirect
115. #16810514	C₂²	semidirect
116. #16810514	C₂²	semidirect
117. #16810513	C₂²	semidirect
118. #16810513	C₂²	semidirect
119. #16810513	C₂²	semidirect
120. #16810512	C₂²	semidirect
121. #16810512	C₂²	semidirect
122. #16810512	C₂²	semidirect
123. #16810512	C₂²	semidirect
124. #16810512	C₂²	semidirect
125. #16810512	C₂²	semidirect
126. #16810512	C₂²	semidirect
127. #16810511	C₂²	semidirect
128. #16810511	C₂²	semidirect
129. #16810511	C₂²	semidirect
130. #16810511	C₂²	semidirect
131. #16810511	C₂²	semidirect
132. #16810511	C₂²	semidirect
133. #16810511	C₂²	semidirect
134. #16810507	C₂²	semidirect
135. #16810503	C₂²	semidirect
136. #16810502	C₂²	semidirect
137. #16810502	C₂²	semidirect
138. #16810500	C₂²	semidirect
145. #16810487	C₂²	semidirect
149. #16810481	C₂²	semidirect
158. C₄⋊C₄×Dic₅₃	C₂²	semidirect
159. C₄×#11719919	C₂²	semidirect
160. #16810474	C₂²	semidirect
161. #16810474	C₂²	semidirect
162. #16810474	C₂²	semidirect
163. #16810474	C₂²	semidirect
164. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
165. C₂²⋊C₄×Dic₅₃	C₂²	semidirect
171. C₄²×Dic₅₃	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
173. C₅₃×#397	C₂²	semidirect
174. C₅₃×#397	C₂²	semidirect
175. C₅₃×#396	C₂²	semidirect
177. C₅₃×#394	C₂²	semidirect
178. C₅₃×#394	C₂²	semidirect
181. C₅₃×#388	C₂²	semidirect
182. C₅₃×#388	C₂²	semidirect
183. C₅₃×#387	C₂²	semidirect
184. C₅₃×#386	C₂²	semidirect
185. C₅₃×#386	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
806. #2648	D₅₃	semidirect
869. #400	C₂×D₅₃	semidirect
882. #397	C₂×D₅₃	semidirect
883. #397	C₂×D₅₃	semidirect
887. #396	C₂×D₅₃	semidirect
896. #394	C₂×D₅₃	semidirect
897. #394	C₂×D₅₃	semidirect
954. #388	C₂×D₅₃	semidirect
955. #388	C₂×D₅₃	semidirect
957. #387	C₂×D₅₃	semidirect
964. #386	C₂×D₅₃	semidirect
965. #386	C₂×D₅₃	semidirect
996. C₄×C₂²⋊C₄	C₂×D₅₃	semidirect
998. C₅₃	#35025	semidirect

Maximal subgroups

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

subgroup	index
#20283084	2
#20283081	2
#20283043	2
#20283012	2
#20280754	2
#20280752	2
#20280697	2
#20280212	2
#20280207	2
#20279776	2
#20279768	2
#20279305	2
#20279060	2
#20278962	2
#20278954	2
#20278506	2
#20278432	2
#20278361	2
#20278274	2
#20278172	2
#20278170	2
#20278159	2
#20278064	2
#20277371	2
#20277309	2
#20277249	2
#390×D₅₃	2
C₄×#13133177	2
C₅₃×#2648	2
#35025	53