Subgroups — #27591090

Order 13568.

2450 conjugacy classes of subgroups.

The subgroup lattice has 1638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811248	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#123×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20283003	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283001	C₂	1	1	yes	maximal, characteristic, complemented
5	#20281141	C₂	1	1	yes	maximal, characteristic, complemented
6	#20281140	C₂	1	1	yes	maximal, characteristic, complemented
7	#20281137	C₂	1	1	yes	maximal, characteristic, complemented
8	#20281136	C₂	1	1	yes	maximal, characteristic, complemented
9	#20281135	C₂	1	1	yes	maximal, characteristic, complemented
10	#20281132	C₂	1	1	yes	maximal, characteristic, complemented
11	#20281131	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281058	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281057	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281056	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281056	C₂	1	1	yes	maximal, characteristic, complemented
16	#20281053	C₂	1	1	yes	maximal, characteristic, complemented
17	#20281053	C₂	1	1	yes	maximal, characteristic, complemented
18	#20281052	C₂	1	1	yes	maximal, characteristic, complemented
19	#20281051	C₂	1	1	yes	maximal, characteristic, complemented
20	#20280533	C₂	1	1	yes	maximal, characteristic, complemented
21	#20280529	C₂	1	1	yes	maximal, characteristic, complemented
22	#20279871	C₂	1	1	yes	maximal, characteristic, complemented
23	#20279869	C₂	1	1	yes	maximal, characteristic, complemented
24	#20279192	C₂	1	1	yes	maximal, characteristic, complemented
25	#20279188	C₂	1	1	yes	maximal, characteristic, complemented
26	#20278994	C₂	1	1	yes	maximal, characteristic, complemented
27	#20278992	C₂	1	1	yes	maximal, characteristic, complemented
28	#20278041	C₂	1	1	yes	maximal, characteristic
29	#20278037	C₂	1	1	yes	maximal, characteristic
30	#20277309	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2687	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
34	#16811248	—	2	8	no	—
35	C₂×#13133202	C₂²	1	1	yes	characteristic
36	C₂×#13133202	C₂²	1	1	yes	characteristic
37	C₂×#13133202	C₂²	1	1	yes	characteristic
38	C₂×#13133201	C₂²	1	1	yes	characteristic
39	C₂×#13133201	C₂²	1	1	yes	characteristic
40	C₂×#13133200	C₂²	1	1	yes	characteristic
41	C₂×#13133199	C₂²	1	1	yes	characteristic
42	C₂×#13133199	C₂²	1	1	yes	characteristic
43	C₂×#13133199	C₂²	1	1	yes	characteristic
44	C₂×#13133198	C₂²	1	1	yes	characteristic
45	C₂×#13133198	C₂²	1	1	yes	characteristic
46	#123×D₅₃	—	2	8	no	—
47	C₂×#13133197	C₂²	1	1	yes	characteristic
48	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13133197	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
51	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
52	C₂×#13133195	C₂²	1	1	yes	characteristic
53	C₂×#13133195	C₂²	1	1	yes	characteristic
54	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
55	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
56	C₂×#13133195	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
58	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
59	C₂×#13133194	C₂²	1	1	yes	characteristic, complemented
60	C₂×#13133193	C₂²	1	1	yes	characteristic
61	C₂×#13133193	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
64	C₂²×#11719921	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
69	#16810565	C₂²	1	1	yes	characteristic, complemented
70	#16810564	C₂²	1	1	yes	characteristic, complemented
71	#16810561	C₂²	1	1	yes	characteristic, complemented
72	#16810557	C₂²	1	1	yes	characteristic, complemented
73	#16810557	C₂²	1	1	yes	characteristic, complemented
74	#16810557	C₂²	1	1	yes	characteristic, complemented
75	#16810557	C₂²	1	1	yes	characteristic, complemented
76	#16810557	C₂²	1	1	yes	characteristic, complemented
77	#16810557	C₂²	1	1	yes	characteristic, complemented
78	#16810556	C₂²	1	1	yes	characteristic, complemented
79	#16810556	C₂²	1	1	yes	characteristic, complemented
80	#16810555	C₂²	1	1	yes	characteristic, complemented
81	#16810555	C₂²	1	1	yes	characteristic, complemented
82	#16810555	C₂²	1	1	yes	characteristic, complemented
83	#16810554	C₂²	1	1	yes	characteristic, complemented
84	#16810553	C₂²	1	1	yes	characteristic, complemented
85	#16810553	C₂²	1	1	yes	characteristic, complemented
86	#16810552	C₂²	1	1	yes	characteristic, complemented
87	#16810552	C₂²	1	1	yes	characteristic, complemented
88	#16810552	C₂²	1	1	yes	characteristic, complemented
89	#16810551	C₂²	1	1	yes	characteristic, complemented
90	#16810551	C₂²	1	1	yes	characteristic, complemented
91	#16810551	C₂²	1	1	yes	characteristic, complemented
92	#16810550	C₂²	1	1	yes	characteristic, complemented
93	#16810550	C₂²	1	1	yes	characteristic, complemented
94	#16810550	C₂²	1	1	yes	characteristic, complemented
95	#16810548	C₂²	1	1	yes	characteristic, complemented
96	#16810548	C₂²	1	1	yes	characteristic, complemented
97	#16810544	C₂²	1	1	yes	characteristic, complemented
98	#16810544	C₂²	1	1	yes	characteristic, complemented
99	#16810543	C₂²	1	1	yes	characteristic, complemented
100	#16810543	C₂²	1	1	yes	characteristic, complemented
101	#16810541	C₂²	1	1	yes	characteristic
102	#16810541	C₂²	1	1	yes	characteristic
103	#16810539	C₂²	1	1	yes	characteristic
104	#16810539	C₂²	1	1	yes	characteristic
105	#16810539	C₂²	1	1	yes	characteristic
106	#16810538	C₂²	1	1	yes	characteristic
107	#16810537	C₂²	1	1	yes	characteristic
108	#16810536	C₂²	1	1	yes	characteristic, complemented
109	#16810535	C₂²	1	1	yes	characteristic, complemented
110	#16810534	C₂²	1	1	yes	characteristic, complemented
111	#16810530	C₂²	1	1	yes	characteristic, complemented
112	#16810527	C₂²	1	1	yes	characteristic, complemented
113	#16810527	C₂²	1	1	yes	characteristic, complemented
114	#16810517	C₂²	1	1	yes	characteristic, complemented
115	#16810517	C₂²	1	1	yes	characteristic, complemented
116	#16810516	C₂²	1	1	yes	characteristic, complemented
117	#16810515	C₂²	1	1	yes	characteristic, complemented
118	#16810514	C₂²	1	1	yes	characteristic, complemented
119	#16810514	C₂²	1	1	yes	characteristic, complemented
120	#16810513	C₂²	1	1	yes	characteristic, complemented
121	#16810513	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	#16810511	C₂²	1	1	yes	characteristic, complemented
126	#16810511	C₂²	1	1	yes	characteristic, complemented
127	#16810511	C₂²	1	1	yes	characteristic, complemented
128	#16810502	C₂²	1	1	yes	characteristic
129	#16810501	C₂²	1	1	yes	characteristic
130	#16810499	C₂²	1	1	yes	characteristic
131	#16810498	C₂²	1	1	yes	characteristic, complemented
132	#16810498	C₂²	1	1	yes	characteristic, complemented
133	#16810498	C₂²	1	1	yes	characteristic, complemented
134	#16810497	C₂²	1	1	yes	characteristic
135	#16810497	C₂²	1	1	yes	characteristic
136	#16810497	C₂²	1	1	yes	characteristic
137	#16810497	C₂²	1	1	yes	characteristic
138	#16810497	C₂²	1	1	yes	characteristic
139	#16810497	C₂²	1	1	yes	characteristic
140	#16810497	C₂²	1	1	yes	characteristic, complemented
141	#16810497	C₂²	1	1	yes	characteristic, complemented
142	#16810497	C₂²	1	1	yes	characteristic, complemented
143	#16810497	C₂²	1	1	yes	characteristic, complemented
144	#16810496	C₂²	1	1	yes	characteristic, complemented
145	#16810495	C₂²	1	1	yes	characteristic, complemented
146	#16810494	C₂²	1	1	yes	characteristic
147	#16810494	C₂²	1	1	yes	characteristic
148	#16810494	C₂²	1	1	yes	characteristic, complemented
149	#16810494	C₂²	1	1	yes	characteristic, complemented
150	#16810493	C₂²	1	1	yes	characteristic, complemented
151	#16810492	C₂²	1	1	yes	characteristic, complemented
152	#16810492	C₂²	1	1	yes	characteristic, complemented
153	#16810492	C₂²	1	1	yes	characteristic, complemented
154	#16810486	C₂²	1	1	yes	characteristic, complemented
155	#16810485	C₂²	1	1	yes	characteristic
156	#16810485	C₂²	1	1	yes	characteristic
157	#16810485	C₂²	1	1	yes	characteristic
158	#16810485	C₂²	1	1	yes	characteristic
159	#16810485	C₂²	1	1	yes	characteristic, complemented
160	#16810485	C₂²	1	1	yes	characteristic, complemented
161	#16810482	C₂²	1	1	yes	characteristic
162	#16810482	C₂²	1	1	yes	characteristic, complemented
163	#16810481	C₂²	1	1	yes	characteristic, complemented
164	#16810480	C₂²	1	1	yes	characteristic
165	#16810480	C₂²	1	1	yes	characteristic, complemented
166	#16810478	C₂²	1	1	yes	characteristic
167	#16810478	C₂²	1	1	yes	characteristic
168	#16810478	C₂²	1	1	yes	characteristic
169	#16810478	C₂²	1	1	yes	characteristic
170	#16810478	C₂²	1	1	yes	characteristic
171	#16810478	C₂²	1	1	yes	characteristic
172	C₄×#11719921	C₂²	1	1	yes	characteristic
173	#16810470	C₂²	1	1	yes	characteristic
174	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#394	C₂²	1	1	yes	characteristic
181	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#386	C₂²	1	1	yes	characteristic
186	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
189	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
190	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
194	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
195	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
197	C₂×D₄×D₅₃	—	2	4	no	—
198	C₂×D₄×D₅₃	—	4	2	no	—
199	C₂×D₄×D₅₃	—	4	2	no	—
200	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₅₃	—	2	4	no	—
203	C₂²×C₄×D₅₃	—	4	2	no	—
204	C₂²×C₄×D₅₃	—	4	2	no	—
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
214	#13133202	—	2	4	no	—
215	#13133202	—	2	4	no	—
216	#13133202	—	4	2	no	—
217	#13133201	—	2	4	no	—
218	#13133201	—	4	2	no	—
219	#13133200	—	2	4	no	—
220	#13133199	—	2	4	no	—
221	#13133199	—	2	4	no	—
222	#13133199	—	4	2	no	—
223	#13133198	—	2	4	no	—
224	#13133198	—	4	2	no	—
225	#13133197	—	2	4	no	—
226	#13133197	—	2	4	no	—
227	#13133197	—	4	2	no	—
228	#13133196	—	2	4	no	—
229	#13133196	—	4	2	no	—
230	#13133195	—	2	4	no	—
231	#13133195	—	2	4	no	—
232	#13133195	—	2	4	no	—
233	#13133195	—	2	4	no	—
234	#13133195	—	4	2	no	—
235	#13133194	—	2	4	no	—
236	#13133194	—	2	4	no	—
237	#13133194	—	4	2	no	—
238	#13133193	—	2	4	no	—
239	#13133193	—	2	4	no	—
240	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×#11719919	C₂³	1	1	yes	characteristic
253	C₂×#11719919	C₂³	1	1	yes	characteristic
254	C₂×#11719919	C₂³	1	1	yes	characteristic
255	C₂×#11719919	C₂³	1	1	yes	characteristic
256	C₂×#11719919	C₂³	1	1	yes	characteristic
257	C₂×#11719919	C₂³	1	1	yes	characteristic
258	C₂×#11719919	C₂³	1	1	yes	characteristic
259	C₂×#11719919	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	1	yes	characteristic
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×#11719919	C₂³	1	1	yes	characteristic
265	C₂×#11719919	C₂³	1	1	yes	characteristic
266	C₂×#11719919	C₂³	1	1	yes	characteristic
267	C₂×#11719919	C₂³	1	1	yes	characteristic
268	C₂×#11719919	C₂³	1	1	yes	characteristic
269	C₂×#11719919	C₂³	1	1	yes	characteristic
270	C₂×#11719919	C₂³	1	1	yes	characteristic
271	C₂×#11719919	C₂³	1	1	yes	characteristic
272	C₄⋊C₄×D₅₃	—	2	4	no	—
273	C₄⋊C₄×D₅₃	—	2	4	no	—
274	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×#11719921	—	2	4	no	—
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	C₂×#11719921	C₂³	1	1	yes	characteristic
292	C₂×#11719921	C₂³	1	1	yes	characteristic
293	C₂×#11719921	C₂³	1	1	yes	characteristic
294	C₂×#11719921	C₂³	1	1	yes	characteristic
295	C₂×#11719921	C₂³	1	1	yes	characteristic
296	C₂×#11719921	C₂³	1	1	yes	characteristic
297	C₂×#11719921	C₂³	1	1	yes	characteristic
298	C₂×#11719921	C₂³	1	1	yes	characteristic
299	C₂×#11719921	C₂³	1	1	yes	characteristic
300	C₂×#11719921	C₂³	1	1	yes	characteristic
301	C₂×#11719921	C₂³	1	1	yes	characteristic
302	C₂×#11719921	C₂³	1	1	yes	characteristic
303	C₂×#11719921	C₂³	1	1	yes	characteristic
304	C₂×#11719921	C₂³	1	1	yes	characteristic
305	C₂×#11719921	C₂³	1	1	yes	characteristic
306	C₂×#11719921	C₂³	1	1	yes	characteristic
307	C₂×#11719921	C₂³	1	1	yes	characteristic
308	C₂×#11719921	C₂³	1	1	yes	characteristic
309	C₂×#11719921	C₂³	1	1	yes	characteristic
310	C₂×#11719921	C₂³	1	1	yes	characteristic
311	C₂×#11719921	C₂³	1	1	yes	characteristic
312	C₂×#11719921	C₂³	1	1	yes	characteristic
313	C₂²⋊C₄×D₅₃	—	2	4	no	—
314	C₂²⋊C₄×D₅₃	—	2	4	no	—
315	C₂²⋊C₄×D₅₃	—	2	4	no	—
316	C₂²⋊C₄×D₅₃	D₄	1	8	yes	—
317	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄×Dic₅₃	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	#13133124	C₂³	1	1	yes	characteristic
335	#13133124	C₂³	1	1	yes	characteristic
336	#13133124	C₂³	1	1	yes	characteristic
337	#13133124	C₂³	1	1	yes	characteristic
338	#13133124	C₂³	1	1	yes	characteristic
339	#13133124	C₂³	1	1	yes	characteristic
340	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	#13133124	C₂³	1	1	yes	characteristic
347	#13133124	C₂³	1	1	yes	characteristic
348	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
352	#123×C₅₃	—	2	4	no	—
353	C₂²⋊Q₈×C₅₃	—	2	4	no	—
354	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂³×D₅₃	—	2	2	no	—
388	C₂³×D₅₃	—	2	2	no	—
389	C₂³×D₅₃	—	2	2	no	—
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	2	2	no	—
392	C₂³×D₅₃	—	2	2	no	—
393	C₂³×D₅₃	—	2	2	no	—
394	C₂³×D₅₃	—	4	1	no	—
395	C₂³×D₅₃	—	4	1	no	—
396	C₂³×D₅₃	—	4	1	no	—
397	C₂³×D₅₃	—	4	1	no	—
398	C₂³×D₅₃	—	4	1	no	—
399	C₂³×D₅₃	—	4	1	no	—
400	C₂³×D₅₃	C₂×D₄	1	4	yes	—
401	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
402	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
403	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×Q₈×C₅₃	—	2	2	no	—
405	C₂×Q₈×C₅₃	—	4	1	no	—
406	C₂×Q₈×C₅₃	—	4	1	no	—
407	C₂×D₄×C₅₃	—	2	2	no	—
408	C₂×D₄×C₅₃	—	2	2	no	—
409	C₂×D₄×C₅₃	—	4	1	no	—
410	C₂²×C₄×C₅₃	—	2	2	no	—
411	C₂²×C₄×C₅₃	—	2	2	no	—
412	C₂²×C₄×C₅₃	—	2	2	no	—
413	C₂²×C₄×C₅₃	—	4	1	no	—
414	C₂²×C₄×C₅₃	—	4	1	no	—
415	C₂²×C₄×C₅₃	—	4	1	no	—
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂×C₂²⋊D₅₃	—	2	2	no	—
430	C₂×C₂²⋊D₅₃	—	2	2	no	—
431	C₂×C₂²⋊D₅₃	—	2	2	no	—
432	C₂×C₂²⋊D₅₃	—	2	2	no	—
433	C₂×C₂²⋊D₅₃	—	4	1	no	—
434	C₂×C₂²⋊D₅₃	—	4	1	no	—
435	C₂²×Dic₅₃	—	2	2	no	—
436	C₂²×Dic₅₃	—	2	2	no	—
437	C₂²×Dic₅₃	—	2	2	no	—
438	C₂²×Dic₅₃	—	4	1	no	—
439	C₂²×Dic₅₃	—	4	1	no	—
440	C₂²×Dic₅₃	—	4	1	no	—
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	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
452	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
453	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
454	D₄×D₅₃	—	4	16	no	—
455	C₂×D₂₁₂	—	2	2	no	—
456	C₂×D₂₁₂	—	2	2	no	—
457	C₂×D₂₁₂	—	4	1	no	—
458	C₂×C₄×D₅₃	—	2	2	no	—
459	C₂×C₄×D₅₃	—	2	2	no	—
460	C₂×C₄×D₅₃	—	2	2	no	—
461	C₂×C₄×D₅₃	—	2	2	no	—
462	C₂×C₄×D₅₃	—	2	2	no	—
463	C₂×C₄×D₅₃	—	2	2	no	—
464	C₂×C₄×D₅₃	—	2	2	no	—
465	C₂×C₄×D₅₃	—	2	2	no	—
466	C₂×C₄×D₅₃	—	2	2	no	—
467	C₂×C₄×D₅₃	—	2	2	no	—
468	C₂×C₄×D₅₃	—	2	2	no	—
469	C₂×C₄×D₅₃	—	4	1	no	—
470	C₂×C₄×D₅₃	—	4	1	no	—
471	C₂×C₄×D₅₃	—	4	1	no	—
472	C₂×C₄×D₅₃	—	4	1	no	—
473	C₂×C₄×D₅₃	—	4	1	no	—
474	C₂×C₄×D₅₃	—	4	1	no	—
475	C₂×C₄×D₅₃	—	4	1	no	—
476	C₂×C₄×D₅₃	—	4	1	no	—
477	C₂×C₄×D₅₃	—	4	1	no	—
478	C₂×C₄×D₅₃	—	4	1	no	—
479	C₂×C₄×D₅₃	—	4	16	no	—
480	C₂×C₄×D₅₃	—	4	1	no	—
481	C₂×C₄×D₅₃	—	4	1	no	—
482	C₂×C₄×D₅₃	—	4	1	no	—
483	C₂×C₄×D₅₃	—	4	1	no	—
484	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
485	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
486	C₂×Dic₁₀₆	—	2	2	no	—
487	C₂×Dic₁₀₆	—	2	2	no	—
488	C₂×Dic₁₀₆	—	2	2	no	—
489	C₂×Dic₁₀₆	—	4	1	no	—
490	C₂×Dic₁₀₆	—	4	1	no	—
491	C₂×Dic₁₀₆	—	4	1	no	—
492	C₂×Dic₁₀₆	—	4	1	no	—
493	C₂×Dic₁₀₆	—	4	1	no	—
494	C₂×Dic₁₀₆	—	4	1	no	—
495	C₄⋊C₄×C₅₃	—	2	2	no	—
496	C₄⋊C₄×C₅₃	—	2	2	no	—
497	C₄⋊C₄×C₅₃	—	2	2	no	—
498	C₄⋊C₄×C₅₃	—	2	2	no	—
499	C₄⋊C₄×C₅₃	—	2	2	no	—
500	C₄⋊C₄×C₅₃	—	4	1	no	—
501	C₄⋊C₄×C₅₃	—	4	1	no	—
502	C₄⋊C₄×C₅₃	—	4	1	no	—
503	C₂²⋊C₄×C₅₃	—	2	2	no	—
504	C₂²⋊C₄×C₅₃	—	2	2	no	—
505	C₂²⋊C₄×C₅₃	—	2	2	no	—
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	4	1	no	—
508	C₂²⋊C₄×C₅₃	—	4	1	no	—
509	C₂²⋊C₄×C₅₃	—	4	1	no	—
510	C₂²⋊C₄×C₅₃	—	4	1	no	—
511	C₂²⋊C₄×C₅₃	—	4	1	no	—
512	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
513	C₄²×C₅₃	—	4	1	no	—
514	C₂²⋊Dic₅₃	—	2	2	no	—
515	C₂²⋊Dic₅₃	—	2	2	no	—
516	C₂²⋊Dic₅₃	—	2	2	no	—
517	C₂²⋊Dic₅₃	—	2	2	no	—
518	C₂²⋊Dic₅₃	—	2	2	no	—
519	C₂²⋊Dic₅₃	—	2	2	no	—
520	C₂²⋊Dic₅₃	—	4	1	no	—
521	C₂²⋊Dic₅₃	—	4	1	no	—
522	C₂²⋊Dic₅₃	—	4	1	no	—
523	C₂²⋊Dic₅₃	C₂×D₄	1	4	yes	—
524	#11719921	—	2	2	no	—
525	#11719921	—	2	2	no	—
526	#11719921	—	2	2	no	—
527	#11719921	—	2	2	no	—
528	#11719921	—	2	2	no	—
529	#11719921	—	2	2	no	—
530	#11719921	—	2	2	no	—
531	#11719921	—	2	2	no	—
532	#11719921	—	2	2	no	—
533	#11719921	—	2	2	no	—
534	#11719921	—	2	2	no	—
535	#11719921	—	2	2	no	—
536	#11719921	—	2	2	no	—
537	#11719921	—	2	2	no	—
538	#11719921	—	2	2	no	—
539	#11719921	—	2	2	no	—
540	#11719921	—	2	2	no	—
541	#11719921	—	2	2	no	—
542	#11719921	—	4	1	no	—
543	#11719921	—	4	1	no	—
544	#11719921	—	4	1	no	—
545	#11719921	—	4	1	no	—
546	#11719921	—	4	1	no	—
547	#11719921	—	4	1	no	—
548	#11719921	—	4	1	no	—
549	#11719921	—	4	1	no	—
550	#11719921	C₂×D₄	1	4	yes	—
551	#11719921	C₂×D₄	1	4	yes	—
552	C₄⋊Dic₅₃	—	2	2	no	—
553	C₄⋊Dic₅₃	—	2	2	no	—
554	C₄⋊Dic₅₃	—	2	2	no	—
555	C₄⋊Dic₅₃	—	2	2	no	—
556	C₄⋊Dic₅₃	—	2	2	no	—
557	C₄⋊Dic₅₃	—	4	1	no	—
558	C₄⋊Dic₅₃	—	4	1	no	—
559	C₄⋊Dic₅₃	—	4	1	no	—
560	C₄⋊Dic₅₃	—	4	1	no	—
561	C₄⋊Dic₅₃	—	4	1	no	—
562	C₄⋊Dic₅₃	—	4	1	no	—
563	C₄⋊Dic₅₃	—	4	1	no	—
564	#11719919	—	2	2	no	—
565	#11719919	—	2	2	no	—
566	#11719919	—	2	2	no	—
567	#11719919	—	2	2	no	—
568	#11719919	—	2	2	no	—
569	#11719919	—	2	2	no	—
570	#11719919	—	2	2	no	—
571	#11719919	—	2	2	no	—
572	#11719919	—	2	2	no	—
573	#11719919	—	2	2	no	—
574	#11719919	—	4	1	no	—
575	#11719919	—	4	1	no	—
576	#11719919	—	4	1	no	—
577	#11719919	—	4	1	no	—
578	#11719919	—	4	1	no	—
579	#11719919	—	4	1	no	—
580	#11719919	—	4	1	no	—
581	#11719919	—	4	1	no	—
582	#11719919	—	4	1	no	—
583	#11719919	—	4	1	no	—
584	C₄×Dic₅₃	—	4	1	no	—
585	C₄×Dic₅₃	—	4	1	no	—
586	C₄×Dic₅₃	—	4	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	—	2	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	2	1	no	—
598	C₂³×C₅₃	—	2	1	no	—
599	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
600	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
601	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
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	8	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	—	2	1	no	—
613	C₂²×D₅₃	—	2	1	no	—
614	C₂²×D₅₃	—	2	1	no	—
615	C₂²×D₅₃	—	2	1	no	—
616	C₂²×D₅₃	—	2	1	no	—
617	C₂²×D₅₃	—	2	1	no	—
618	C₂²×D₅₃	—	2	1	no	—
619	C₂²×D₅₃	—	2	8	no	—
620	C₂²×D₅₃	—	4	4	no	—
621	C₂²×D₅₃	—	4	4	no	—
622	C₂²×D₅₃	—	4	4	no	—
623	C₂²×D₅₃	—	4	4	no	—
624	C₂²×D₅₃	—	4	4	no	—
625	C₂²×D₅₃	—	4	4	no	—
626	C₂²×D₅₃	—	4	4	no	—
627	C₂²×D₅₃	—	4	4	no	—
628	C₂²×D₅₃	—	8	2	no	—
629	C₂²×D₅₃	—	8	2	no	—
630	C₂²×D₅₃	—	8	2	no	—
631	C₂²×D₅₃	—	8	2	no	—
632	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
633	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
634	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
635	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
636	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
637	Q₈×C₅₃	—	8	2	no	—
638	D₄×C₅₃	—	4	4	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	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	4	4	no	—
677	C₂×C₄×C₅₃	—	8	2	no	—
678	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
679	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
680	C₂²⋊D₅₃	—	4	4	no	—
681	C₂²⋊D₅₃	—	4	4	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	—	2	1	no	—
708	C₂×Dic₅₃	—	2	1	no	—
709	C₂×Dic₅₃	—	2	1	no	—
710	C₂×Dic₅₃	—	2	1	no	—
711	C₂×Dic₅₃	—	2	1	no	—
712	C₂×Dic₅₃	—	2	1	no	—
713	C₂×Dic₅₃	—	2	1	no	—
714	C₂×Dic₅₃	—	2	1	no	—
715	C₂×Dic₅₃	—	2	1	no	—
716	C₂×Dic₅₃	—	2	1	no	—
717	C₂×Dic₅₃	—	2	1	no	—
718	C₂×Dic₅₃	—	2	1	no	—
719	C₂×Dic₅₃	—	4	4	no	—
720	C₂×Dic₅₃	—	8	2	no	—
721	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
722	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
723	D₂₁₂	—	4	4	no	—
724	C₄×D₅₃	—	4	4	no	—
725	C₄×D₅₃	—	4	4	no	—
726	C₄×D₅₃	—	4	4	no	—
727	C₄×D₅₃	—	4	4	no	—
728	C₄×D₅₃	—	4	4	no	—
729	C₄×D₅₃	—	4	4	no	—
730	C₄×D₅₃	—	4	4	no	—
731	C₄×D₅₃	—	8	2	no	—
732	C₄×D₅₃	—	8	2	no	—
733	Dic₁₀₆	—	8	2	no	—
734	Dic₁₀₆	—	8	2	no	—
735	Dic₁₀₆	—	8	2	no	—
736	#36720	—	53	1	no	maximal, Sylow
737	C₂²×C₅₃	—	2	2	no	—
738	C₂²×C₅₃	—	2	2	no	—
739	C₂²×C₅₃	—	2	2	no	—
740	C₂²×C₅₃	—	2	2	no	—
741	C₂²×C₅₃	—	2	2	no	—
742	C₂²×C₅₃	—	2	2	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	—	4	1	no	—
745	C₂²×C₅₃	—	4	1	no	—
746	C₂²×C₅₃	—	4	1	no	—
747	C₂²×C₅₃	—	4	1	no	—
748	C₂²×C₅₃	—	4	1	no	—
749	C₂²×C₅₃	—	4	1	no	—
750	C₂²×C₅₃	—	4	1	no	—
751	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
752	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
753	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
754	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
755	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
756	C₂²×C₅₃	#585	1	1	yes	characteristic
757	C₂²×C₅₃	#585	1	1	yes	characteristic
758	C₂×D₅₃	—	2	2	no	—
759	C₂×D₅₃	—	2	2	no	—
760	C₂×D₅₃	—	2	2	no	—
761	C₂×D₅₃	—	2	2	no	—
762	C₂×D₅₃	—	2	2	no	—
763	C₂×D₅₃	—	2	2	no	—
764	C₂×D₅₃	—	2	2	no	—
765	C₂×D₅₃	—	2	2	no	—
766	C₂×D₅₃	—	2	2	no	—
767	C₂×D₅₃	—	2	2	no	—
768	C₂×D₅₃	—	2	2	no	—
769	C₂×D₅₃	—	2	2	no	—
770	C₂×D₅₃	—	4	16	no	—
771	C₂×D₅₃	—	4	1	no	—
772	C₂×D₅₃	—	4	1	no	—
773	C₂×D₅₃	—	4	1	no	—
774	C₂×D₅₃	—	4	1	no	—
775	C₂×D₅₃	—	4	1	no	—
776	C₂×D₅₃	—	4	1	no	—
777	C₂×D₅₃	—	4	1	no	—
778	C₂×D₅₃	—	4	1	no	—
779	C₂×D₅₃	—	8	8	no	—
780	C₂×D₅₃	#536	1	4	yes	—
781	C₄×C₅₃	—	2	2	no	—
782	C₄×C₅₃	—	2	2	no	—
783	C₄×C₅₃	—	4	1	no	—
784	C₄×C₅₃	—	4	1	no	—
785	C₄×C₅₃	—	4	1	no	—
786	C₄×C₅₃	—	4	1	no	—
787	C₄×C₅₃	—	4	1	no	—
788	C₄×C₅₃	—	4	1	no	—
789	C₄×C₅₃	—	4	1	no	—
790	C₄×C₅₃	—	4	1	no	—
791	C₄×C₅₃	—	4	1	no	—
792	C₄×C₅₃	—	4	1	no	—
793	C₄×C₅₃	—	4	1	no	—
794	Dic₅₃	—	2	2	no	—
795	Dic₅₃	—	2	2	no	—
796	Dic₅₃	—	4	1	no	—
797	Dic₅₃	—	4	1	no	—
798	Dic₅₃	—	4	1	no	—
799	Dic₅₃	—	4	1	no	—
800	Dic₅₃	—	4	1	no	—
801	Dic₅₃	—	4	1	no	—
802	Dic₅₃	—	4	1	no	—
803	Dic₅₃	—	4	1	no	—
804	Dic₅₃	—	4	1	no	—
805	Dic₅₃	—	4	1	no	—
806	Dic₅₃	—	4	1	no	—
807	C₂×#543	—	53	1	no	—
808	C₂²×#123	—	53	1	no	—
809	#2848	—	53	1	no	—
810	#2848	—	53	1	no	—
811	#2687	—	53	1	no	—
812	#2687	—	53	1	no	—
813	#2687	—	53	1	no	—
814	#2687	—	53	1	no	—
815	#2687	—	53	1	no	—
816	#2687	—	53	1	no	—
817	#2687	—	53	1	no	—
818	#2687	D₅₃	1	1	yes	characteristic, complemented
819	#2680	—	53	1	no	—
820	#2680	—	53	1	no	—
821	#2680	—	53	1	no	—
822	#2680	—	53	1	no	—
823	#2680	—	53	1	no	—
824	#2680	—	53	1	no	—
825	#2680	—	53	1	no	—
826	#2680	—	53	1	no	—
827	#2627	—	53	1	no	—
828	#2627	—	53	1	no	—
829	#2561	—	53	1	no	—
830	#2561	—	53	1	no	—
831	#2502	—	53	1	no	—
832	#2502	—	53	1	no	—
833	#2483	—	53	1	no	—
834	#2483	—	53	1	no	—
835	#2405	—	53	1	no	—
836	#2405	—	53	1	no	—
837	#2312	—	53	1	no	—
838	C₂×C₅₃	—	4	2	no	—
839	C₂×C₅₃	—	4	2	no	—
840	C₂×C₅₃	C₂×#536	1	1	yes	characteristic
841	C₂×C₅₃	#3484	1	1	yes	characteristic
842	C₂×C₅₃	#3485	1	1	yes	characteristic
843	C₂×C₅₃	#3535	1	1	yes	characteristic
844	C₂×C₅₃	#3535	1	1	yes	characteristic
845	C₂×C₅₃	#3535	1	1	yes	characteristic
846	C₂×C₅₃	#3535	1	1	yes	characteristic
847	D₅₃	—	2	4	no	—
848	D₅₃	—	4	2	no	—
849	D₅₃	—	4	2	no	—
850	C₂³×D₄	—	53	1	no	—
851	C₂⁴×C₄	—	53	1	no	—
852	#543	—	106	8	no	—
853	C₂×#123	—	53	1	no	—
854	C₂×#123	—	53	1	no	—
855	C₂×#123	—	53	1	no	—
856	C₂×#123	—	53	1	no	—
857	C₂×#123	—	53	1	no	—
858	C₂×#123	—	53	1	no	—
859	C₂×#123	—	53	1	no	—
860	C₂×#123	—	53	1	no	—
861	C₂×#123	—	53	1	no	—
862	C₂×#123	—	53	1	no	—
863	C₂×#123	—	53	1	no	—
864	C₂×#123	—	106	8	no	—
865	C₂×#123	C₂×D₅₃	1	1	yes	characteristic
866	C₂×C₂²⋊Q₈	—	53	1	no	—
867	C₂×C₂²⋊Q₈	—	53	1	no	—
868	C₂×C₂²⋊Q₈	—	53	1	no	—
869	C₂×C₂²⋊Q₈	—	53	1	no	—
870	C₂×C₂²⋊Q₈	—	53	1	no	—
871	C₂×C₂²⋊Q₈	—	53	1	no	—
872	C₂×C₂²⋊Q₈	—	53	1	no	—
873	C₂×C₂²⋊Q₈	—	53	1	no	—
874	C₂×C₂²⋊Q₈	—	53	1	no	—
875	C₂×C₂²⋊Q₈	—	53	1	no	—
876	C₂×C₂²⋊Q₈	—	53	1	no	—
877	C₂×C₂²⋊Q₈	—	53	1	no	—
878	C₂×C₂²⋊Q₈	—	53	1	no	—
879	C₂×C₂²⋊Q₈	—	53	1	no	—
880	C₂×C₂²⋊Q₈	—	53	1	no	—
881	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
882	C₂²×C₄⋊C₄	—	53	1	no	—
883	C₂²×C₄⋊C₄	—	53	1	no	—
884	C₂²×C₂²⋊C₄	—	53	1	no	—
885	C₂²×C₂²⋊C₄	—	53	1	no	—
886	C₂²×C₂²⋊C₄	—	53	1	no	—
887	C₂²×C₂²⋊C₄	—	53	1	no	—
888	C₂²×C₂²⋊C₄	—	53	1	no	—
889	#400	—	53	1	no	—
890	#400	—	53	1	no	—
891	#400	—	53	1	no	—
892	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
893	#398	—	53	1	no	—
894	#398	—	53	1	no	—
895	#398	—	53	1	no	—
896	#398	—	53	1	no	—
897	#398	—	53	1	no	—
898	#398	—	53	1	no	—
899	#398	—	53	1	no	—
900	#398	—	53	1	no	—
901	#398	—	53	1	no	—
902	#398	—	53	1	no	—
903	#398	—	53	1	no	—
904	#398	—	53	1	no	—
905	#398	—	53	1	no	—
906	#398	—	53	1	no	—
907	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
908	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
909	#397	—	53	1	no	—
910	#397	—	53	1	no	—
911	#397	—	53	1	no	—
912	#397	—	53	1	no	—
913	#397	—	53	1	no	—
914	#397	—	53	1	no	—
915	#397	—	53	1	no	—
916	#397	—	53	1	no	—
917	#397	—	53	1	no	—
918	#397	—	53	1	no	—
919	#397	—	53	1	no	—
920	#397	C₂×D₅₃	1	1	yes	characteristic, complemented
921	#395	—	53	1	no	—
922	#395	—	53	1	no	—
923	#395	—	53	1	no	—
924	#395	—	53	1	no	—
925	#394	—	53	1	no	—
926	#394	—	53	1	no	—
927	#394	—	53	1	no	—
928	#394	—	53	1	no	—
929	#394	—	53	1	no	—
930	#394	—	53	1	no	—
931	#394	—	53	1	no	—
932	#394	C₂×D₅₃	1	1	yes	characteristic
933	#393	—	53	1	no	—
934	#393	—	53	1	no	—
935	#393	—	53	1	no	—
936	#393	C₂×D₅₃	1	1	yes	characteristic, complemented
937	#391	—	53	1	no	—
938	#391	—	53	1	no	—
939	#391	—	53	1	no	—
940	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
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	—	53	1	no	—
955	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
956	#388	C₂×D₅₃	1	1	yes	characteristic, complemented
957	#386	—	53	1	no	—
958	#386	—	53	1	no	—
959	#386	—	53	1	no	—
960	#386	C₂×D₅₃	1	1	yes	characteristic
961	#385	—	53	1	no	—
962	#385	—	53	1	no	—
963	#385	—	53	1	no	—
964	#385	—	53	1	no	—
965	#385	—	53	1	no	—
966	#385	—	53	1	no	—
967	#385	—	53	1	no	—
968	#385	—	53	1	no	—
969	#385	—	53	1	no	—
970	#385	—	53	1	no	—
971	#385	—	53	1	no	—
972	#385	—	53	1	no	—
973	#385	—	53	1	no	—
974	#385	—	53	1	no	—
975	#385	—	53	1	no	—
976	#385	—	53	1	no	—
977	#385	—	53	1	no	—
978	#385	—	53	1	no	—
979	#385	—	53	1	no	—
980	#385	C₂×D₅₃	1	1	yes	characteristic, complemented
981	#384	—	53	1	no	—
982	#384	—	53	1	no	—
983	#384	—	53	1	no	—
984	#384	—	53	1	no	—
985	#381	—	53	1	no	—
986	#381	—	53	1	no	—
987	#381	—	53	1	no	—
988	#381	—	53	1	no	—
989	#381	—	53	1	no	—
990	#381	—	53	1	no	—
991	#381	—	53	1	no	—
992	#381	C₂×D₅₃	1	1	yes	characteristic, complemented
993	#380	—	53	1	no	—
994	#380	—	53	1	no	—
995	#380	—	53	1	no	—
996	#380	—	53	1	no	—
997	#380	—	53	1	no	—
998	#380	C₂×D₅₃	1	1	yes	characteristic, complemented
999	#379	—	53	1	no	—
1000	#379	—	53	1	no	—
1001	#379	—	53	1	no	—
1002	#379	—	53	1	no	—
1003	#379	—	53	1	no	—
1004	#379	—	53	1	no	—
1005	C₄×C₂²⋊C₄	—	53	1	no	—
1006	C₄×C₂²⋊C₄	—	53	1	no	—
1007	C₅₃	#36720	1	1	yes	characteristic, complemented, Sylow
1008	C₂⁵	—	53	1	no	—
1009	C₂⁵	—	53	1	no	—
1010	C₂²×Q₈	—	53	1	no	—
1011	C₂²×Q₈	—	53	1	no	—
1012	C₂²×Q₈	—	53	1	no	—
1013	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂²×D₄	—	53	1	no	—
1015	C₂²×D₄	—	53	1	no	—
1016	C₂²×D₄	—	53	1	no	—
1017	C₂²×D₄	—	106	4	no	—
1018	C₂²×D₄	—	212	2	no	—
1019	C₂²×D₄	—	212	2	no	—
1020	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1021	C₂³×C₄	—	53	1	no	—
1022	C₂³×C₄	—	53	1	no	—
1023	C₂³×C₄	—	53	1	no	—
1024	C₂³×C₄	—	53	1	no	—
1025	C₂³×C₄	—	53	1	no	—
1026	C₂³×C₄	—	53	1	no	—
1027	C₂³×C₄	—	53	1	no	—
1028	C₂³×C₄	—	53	1	no	—
1029	C₂³×C₄	—	53	1	no	—
1030	C₂³×C₄	—	53	1	no	—
1031	C₂³×C₄	—	53	1	no	—
1032	C₂³×C₄	—	106	4	no	—
1033	C₂³×C₄	—	212	2	no	—
1034	C₂³×C₄	—	212	2	no	—
1035	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1037	#123	—	2	4	no	—
1038	#123	—	106	4	no	—
1039	#123	—	106	4	no	—
1040	#123	—	106	4	no	—
1041	#123	—	106	4	no	—
1042	#123	—	106	4	no	—
1043	#123	—	106	4	no	—
1044	#123	—	106	4	no	—
1045	#123	—	212	2	no	—
1046	#123	—	212	2	no	—
1047	#123	—	212	2	no	—
1048	#123	—	212	2	no	—
1049	C₂²⋊Q₈	—	2	4	no	—
1050	C₂²⋊Q₈	—	106	4	no	—
1051	C₂²⋊Q₈	—	106	4	no	—
1052	C₂²⋊Q₈	—	106	4	no	—
1053	C₂²⋊Q₈	—	106	4	no	—
1054	C₂²⋊Q₈	—	106	4	no	—
1055	C₂²⋊Q₈	—	106	4	no	—
1056	C₂²⋊Q₈	—	106	4	no	—
1057	C₂²⋊Q₈	—	106	4	no	—
1058	C₂²⋊Q₈	—	106	4	no	—
1059	C₂²⋊Q₈	—	106	4	no	—
1060	C₂²⋊Q₈	—	106	4	no	—
1061	C₂²⋊Q₈	—	212	2	no	—
1062	C₂²⋊Q₈	—	212	2	no	—
1063	C₂²⋊Q₈	—	212	2	no	—
1064	C₂²⋊Q₈	—	212	2	no	—
1065	C₂×C₄⋊C₄	—	53	1	no	—
1066	C₂×C₄⋊C₄	—	53	1	no	—
1067	C₂×C₄⋊C₄	—	53	1	no	—
1068	C₂×C₄⋊C₄	—	53	1	no	—
1069	C₂×C₄⋊C₄	—	53	1	no	—
1070	C₂×C₄⋊C₄	—	53	1	no	—
1071	C₂×C₄⋊C₄	—	53	1	no	—
1072	C₂×C₄⋊C₄	—	53	1	no	—
1073	C₂×C₄⋊C₄	—	53	1	no	—
1074	C₂×C₄⋊C₄	—	53	1	no	—
1075	C₂×C₄⋊C₄	—	53	1	no	—
1076	C₂×C₄⋊C₄	—	53	1	no	—
1077	C₂×C₄⋊C₄	—	53	1	no	—
1078	C₂×C₄⋊C₄	—	53	1	no	—
1079	C₂×C₄⋊C₄	—	53	1	no	—
1080	C₂×C₄⋊C₄	—	53	1	no	—
1081	C₂×C₄⋊C₄	—	53	1	no	—
1082	C₂×C₄⋊C₄	—	53	1	no	—
1083	C₂×C₄⋊C₄	—	53	1	no	—
1084	C₂×C₄⋊C₄	—	53	1	no	—
1085	C₂×C₄⋊C₄	—	53	1	no	—
1086	C₂×C₄⋊C₄	—	53	1	no	—
1087	C₂×C₄⋊C₄	—	53	1	no	—
1088	C₂×C₄⋊C₄	—	53	1	no	—
1089	C₂×C₄⋊C₄	—	53	1	no	—
1090	C₂×C₄⋊C₄	—	53	1	no	—
1091	C₂×C₄⋊C₄	—	53	1	no	—
1092	C₂×C₄⋊C₄	—	53	1	no	—
1093	C₂×C₄⋊C₄	—	53	1	no	—
1094	C₂×C₄⋊C₄	—	53	1	no	—
1095	C₂×C₄⋊C₄	—	53	1	no	—
1096	C₂×C₄⋊C₄	—	53	1	no	—
1097	C₂×C₄⋊C₄	—	106	4	no	—
1098	C₂×C₄⋊C₄	—	106	4	no	—
1099	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1100	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1101	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1102	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1103	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1104	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1105	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1106	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	8	no	—
1111	C₂×C₂²⋊C₄	—	53	1	no	—
1112	C₂×C₂²⋊C₄	—	53	1	no	—
1113	C₂×C₂²⋊C₄	—	53	1	no	—
1114	C₂×C₂²⋊C₄	—	53	1	no	—
1115	C₂×C₂²⋊C₄	—	53	1	no	—
1116	C₂×C₂²⋊C₄	—	53	1	no	—
1117	C₂×C₂²⋊C₄	—	53	1	no	—
1118	C₂×C₂²⋊C₄	—	53	1	no	—
1119	C₂×C₂²⋊C₄	—	53	1	no	—
1120	C₂×C₂²⋊C₄	—	53	1	no	—
1121	C₂×C₂²⋊C₄	—	53	1	no	—
1122	C₂×C₂²⋊C₄	—	53	1	no	—
1123	C₂×C₂²⋊C₄	—	53	1	no	—
1124	C₂×C₂²⋊C₄	—	53	1	no	—
1125	C₂×C₂²⋊C₄	—	53	1	no	—
1126	C₂×C₂²⋊C₄	—	53	1	no	—
1127	C₂×C₂²⋊C₄	—	53	1	no	—
1128	C₂×C₂²⋊C₄	—	53	1	no	—
1129	C₂×C₂²⋊C₄	—	53	1	no	—
1130	C₂×C₂²⋊C₄	—	53	1	no	—
1131	C₂×C₂²⋊C₄	—	53	1	no	—
1132	C₂×C₂²⋊C₄	—	53	1	no	—
1133	C₂×C₂²⋊C₄	—	53	1	no	—
1134	C₂×C₂²⋊C₄	—	53	1	no	—
1135	C₂×C₂²⋊C₄	—	53	1	no	—
1136	C₂×C₂²⋊C₄	—	53	1	no	—
1137	C₂×C₂²⋊C₄	—	53	1	no	—
1138	C₂×C₂²⋊C₄	—	53	1	no	—
1139	C₂×C₂²⋊C₄	—	53	1	no	—
1140	C₂×C₂²⋊C₄	—	53	1	no	—
1141	C₂×C₂²⋊C₄	—	53	1	no	—
1142	C₂×C₂²⋊C₄	—	53	1	no	—
1143	C₂×C₂²⋊C₄	—	53	1	no	—
1144	C₂×C₂²⋊C₄	—	53	1	no	—
1145	C₂×C₂²⋊C₄	—	53	1	no	—
1146	C₂×C₂²⋊C₄	—	106	4	no	—
1147	C₂×C₂²⋊C₄	—	106	4	no	—
1148	C₂×C₂²⋊C₄	—	106	4	no	—
1149	C₂×C₂²⋊C₄	—	106	4	no	—
1150	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1151	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1152	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1153	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1154	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1155	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1156	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1157	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1158	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1159	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1160	C₂×C₄²	—	53	1	no	—
1161	C₂×C₄²	—	53	1	no	—
1162	C₂×C₄²	—	53	1	no	—
1163	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1172	#95	—	53	1	no	—
1173	#95	—	53	1	no	—
1174	#95	—	53	1	no	—
1175	#95	—	53	1	no	—
1176	#95	—	53	1	no	—
1177	#95	—	53	1	no	—
1178	#95	—	53	1	no	—
1179	#95	—	53	1	no	—
1180	#95	—	53	1	no	—
1181	#95	—	53	1	no	—
1182	#95	—	53	1	no	—
1183	#95	—	53	1	no	—
1184	#95	—	53	1	no	—
1185	#95	—	53	1	no	—
1186	#95	—	53	1	no	—
1187	#95	—	53	1	no	—
1188	#95	—	53	1	no	—
1189	#95	—	53	1	no	—
1190	#95	—	53	1	no	—
1191	#95	—	53	1	no	—
1192	#95	C₂²×D₅₃	1	1	yes	characteristic
1193	#95	C₂²×D₅₃	1	1	yes	characteristic
1194	#95	C₂²×D₅₃	1	1	yes	characteristic
1195	#95	C₂²×D₅₃	1	1	yes	characteristic
1196	#95	C₂²×D₅₃	1	1	yes	characteristic
1197	#95	C₂²×D₅₃	1	1	yes	characteristic
1198	#95	C₂²×D₅₃	1	1	yes	characteristic
1199	#95	C₂²×D₅₃	1	1	yes	characteristic
1200	#95	C₂²×D₅₃	1	1	yes	characteristic
1201	#95	C₂²×D₅₃	1	1	yes	characteristic
1202	#95	C₂²×D₅₃	1	1	yes	characteristic
1203	#95	C₂²×D₅₃	1	1	yes	characteristic
1204	C₂⁴	—	53	1	no	—
1205	C₂⁴	—	53	1	no	—
1206	C₂⁴	—	53	1	no	—
1207	C₂⁴	—	53	4	no	—
1208	C₂⁴	—	106	2	no	—
1209	C₂⁴	—	106	2	no	—
1210	C₂⁴	—	106	2	no	—
1211	C₂⁴	—	106	2	no	—
1212	C₂⁴	—	106	2	no	—
1213	C₂⁴	—	106	2	no	—
1214	C₂⁴	—	106	2	no	—
1215	C₂⁴	—	212	1	no	—
1216	C₂⁴	—	212	1	no	—
1217	C₂⁴	—	212	1	no	—
1218	C₂⁴	—	212	1	no	—
1219	C₂⁴	—	212	1	no	—
1220	C₂⁴	—	212	1	no	—
1221	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1222	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1223	C₂×Q₈	—	2	2	no	—
1224	C₂×Q₈	—	4	1	no	—
1225	C₂×Q₈	—	4	1	no	—
1226	C₂×Q₈	—	106	2	no	—
1227	C₂×Q₈	—	106	2	no	—
1228	C₂×Q₈	—	106	2	no	—
1229	C₂×Q₈	—	212	1	no	—
1230	C₂×Q₈	—	212	1	no	—
1231	C₂×Q₈	—	212	1	no	—
1232	C₂×Q₈	—	212	1	no	—
1233	C₂×Q₈	—	212	1	no	—
1234	C₂×Q₈	—	212	1	no	—
1235	C₂×D₄	—	2	2	no	—
1236	C₂×D₄	—	2	2	no	—
1237	C₂×D₄	—	4	1	no	—
1238	C₂×D₄	—	106	2	no	—
1239	C₂×D₄	—	106	2	no	—
1240	C₂×D₄	—	106	2	no	—
1241	C₂×D₄	—	106	2	no	—
1242	C₂×D₄	—	106	2	no	—
1243	C₂×D₄	—	106	2	no	—
1244	C₂×D₄	—	212	1	no	—
1245	C₂×D₄	—	212	1	no	—
1246	C₂×D₄	—	212	1	no	—
1247	C₂×D₄	—	212	16	no	—
1248	C₂²×C₄	—	2	2	no	—
1249	C₂²×C₄	—	2	2	no	—
1250	C₂²×C₄	—	2	2	no	—
1251	C₂²×C₄	—	4	1	no	—
1252	C₂²×C₄	—	4	1	no	—
1253	C₂²×C₄	—	4	1	no	—
1254	C₂²×C₄	—	53	1	no	—
1255	C₂²×C₄	—	53	1	no	—
1256	C₂²×C₄	—	53	4	no	—
1257	C₂²×C₄	—	53	4	no	—
1258	C₂²×C₄	—	53	1	no	—
1259	C₂²×C₄	—	53	1	no	—
1260	C₂²×C₄	—	53	1	no	—
1261	C₂²×C₄	—	53	1	no	—
1262	C₂²×C₄	—	53	1	no	—
1263	C₂²×C₄	—	53	1	no	—
1264	C₂²×C₄	—	53	1	no	—
1265	C₂²×C₄	—	53	1	no	—
1266	C₂²×C₄	—	53	1	no	—
1267	C₂²×C₄	—	53	1	no	—
1268	C₂²×C₄	—	53	1	no	—
1269	C₂²×C₄	—	106	2	no	—
1270	C₂²×C₄	—	106	2	no	—
1271	C₂²×C₄	—	106	2	no	—
1272	C₂²×C₄	—	106	2	no	—
1273	C₂²×C₄	—	106	2	no	—
1274	C₂²×C₄	—	106	2	no	—
1275	C₂²×C₄	—	106	2	no	—
1276	C₂²×C₄	—	106	2	no	—
1277	C₂²×C₄	—	106	2	no	—
1278	C₂²×C₄	—	106	2	no	—
1279	C₂²×C₄	—	106	2	no	—
1280	C₂²×C₄	—	106	2	no	—
1281	C₂²×C₄	—	106	2	no	—
1282	C₂²×C₄	—	106	2	no	—
1283	C₂²×C₄	—	212	1	no	—
1284	C₂²×C₄	—	212	1	no	—
1285	C₂²×C₄	—	212	1	no	—
1286	C₂²×C₄	—	212	1	no	—
1287	C₂²×C₄	—	212	1	no	—
1288	C₂²×C₄	—	212	1	no	—
1289	C₂²×C₄	—	212	1	no	—
1290	C₂²×C₄	—	212	1	no	—
1291	C₂²×C₄	—	212	1	no	—
1292	C₂²×C₄	—	212	1	no	—
1293	C₂²×C₄	—	212	1	no	—
1294	C₂²×C₄	—	212	1	no	—
1295	C₂²×C₄	—	212	1	no	—
1296	C₂²×C₄	—	212	1	no	—
1297	C₂²×C₄	—	212	16	no	—
1298	C₂²×C₄	—	212	1	no	—
1299	C₂²×C₄	—	212	1	no	—
1300	C₂²×C₄	—	212	1	no	—
1301	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1302	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1303	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1304	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1305	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1306	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1307	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1308	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1309	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1310	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1311	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1312	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1313	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1314	C₄⋊C₄	—	2	2	no	—
1315	C₄⋊C₄	—	2	2	no	—
1316	C₄⋊C₄	—	2	2	no	—
1317	C₄⋊C₄	—	2	2	no	—
1318	C₄⋊C₄	—	2	2	no	—
1319	C₄⋊C₄	—	4	1	no	—
1320	C₄⋊C₄	—	4	1	no	—
1321	C₄⋊C₄	—	4	1	no	—
1322	C₄⋊C₄	—	106	2	no	—
1323	C₄⋊C₄	—	106	2	no	—
1324	C₄⋊C₄	—	106	2	no	—
1325	C₄⋊C₄	—	106	2	no	—
1326	C₄⋊C₄	—	106	2	no	—
1327	C₄⋊C₄	—	106	2	no	—
1328	C₄⋊C₄	—	106	2	no	—
1329	C₄⋊C₄	—	106	2	no	—
1330	C₄⋊C₄	—	106	2	no	—
1331	C₄⋊C₄	—	106	2	no	—
1332	C₄⋊C₄	—	106	2	no	—
1333	C₄⋊C₄	—	106	2	no	—
1334	C₄⋊C₄	—	106	2	no	—
1335	C₄⋊C₄	—	106	2	no	—
1336	C₄⋊C₄	—	106	2	no	—
1337	C₄⋊C₄	—	212	1	no	—
1338	C₄⋊C₄	—	212	1	no	—
1339	C₄⋊C₄	—	212	1	no	—
1340	C₄⋊C₄	—	212	1	no	—
1341	C₄⋊C₄	—	212	1	no	—
1342	C₄⋊C₄	—	212	1	no	—
1343	C₄⋊C₄	—	212	1	no	—
1344	C₄⋊C₄	—	212	1	no	—
1345	C₄⋊C₄	—	212	1	no	—
1346	C₄⋊C₄	—	212	1	no	—
1347	C₄⋊C₄	—	212	1	no	—
1348	C₄⋊C₄	—	212	1	no	—
1349	C₄⋊C₄	—	212	1	no	—
1350	C₄⋊C₄	—	212	1	no	—
1351	C₄⋊C₄	—	212	1	no	—
1352	C₄⋊C₄	—	212	1	no	—
1353	C₄⋊C₄	—	212	1	no	—
1354	C₂²⋊C₄	—	2	2	no	—
1355	C₂²⋊C₄	—	2	2	no	—
1356	C₂²⋊C₄	—	2	2	no	—
1357	C₂²⋊C₄	—	2	2	no	—
1358	C₂²⋊C₄	—	4	1	no	—
1359	C₂²⋊C₄	—	4	1	no	—
1360	C₂²⋊C₄	—	4	1	no	—
1361	C₂²⋊C₄	—	4	1	no	—
1362	C₂²⋊C₄	—	4	1	no	—
1363	C₂²⋊C₄	—	53	4	no	—
1364	C₂²⋊C₄	—	53	4	no	—
1365	C₂²⋊C₄	—	53	4	no	—
1366	C₂²⋊C₄	—	106	2	no	—
1367	C₂²⋊C₄	—	106	2	no	—
1368	C₂²⋊C₄	—	106	2	no	—
1369	C₂²⋊C₄	—	106	2	no	—
1370	C₂²⋊C₄	—	106	2	no	—
1371	C₂²⋊C₄	—	106	2	no	—
1372	C₂²⋊C₄	—	106	2	no	—
1373	C₂²⋊C₄	—	106	2	no	—
1374	C₂²⋊C₄	—	106	2	no	—
1375	C₂²⋊C₄	—	106	2	no	—
1376	C₂²⋊C₄	—	106	2	no	—
1377	C₂²⋊C₄	—	106	2	no	—
1378	C₂²⋊C₄	—	106	2	no	—
1379	C₂²⋊C₄	—	106	2	no	—
1380	C₂²⋊C₄	—	106	2	no	—
1381	C₂²⋊C₄	—	106	2	no	—
1382	C₂²⋊C₄	—	106	2	no	—
1383	C₂²⋊C₄	—	106	2	no	—
1384	C₂²⋊C₄	—	106	2	no	—
1385	C₂²⋊C₄	—	106	2	no	—
1386	C₂²⋊C₄	—	106	2	no	—
1387	C₂²⋊C₄	—	106	2	no	—
1388	C₂²⋊C₄	—	106	2	no	—
1389	C₂²⋊C₄	—	106	2	no	—
1390	C₂²⋊C₄	—	212	1	no	—
1391	C₂²⋊C₄	—	212	1	no	—
1392	C₂²⋊C₄	—	212	1	no	—
1393	C₂²⋊C₄	—	212	1	no	—
1394	C₂²⋊C₄	—	212	1	no	—
1395	C₂²⋊C₄	—	212	1	no	—
1396	C₂²⋊C₄	—	212	1	no	—
1397	C₂²⋊C₄	—	212	1	no	—
1398	C₂²⋊C₄	—	212	1	no	—
1399	C₂²⋊C₄	—	212	1	no	—
1400	C₂²⋊C₄	—	212	1	no	—
1401	C₂²⋊C₄	D₄×D₅₃	1	4	yes	—
1402	C₄²	—	4	1	no	—
1403	C₄²	—	212	1	no	—
1404	C₄²	—	212	1	no	—
1405	C₄²	—	212	1	no	—
1406	C₂³	—	2	1	no	—
1407	C₂³	—	2	1	no	—
1408	C₂³	—	2	1	no	—
1409	C₂³	—	2	1	no	—
1410	C₂³	—	2	1	no	—
1411	C₂³	—	2	1	no	—
1412	C₂³	—	2	1	no	—
1413	C₂³	—	2	1	no	—
1414	C₂³	—	2	1	no	—
1415	C₂³	—	2	1	no	—
1416	C₂³	—	2	1	no	—
1417	C₂³	—	2	1	no	—
1418	C₂³	—	53	2	no	—
1419	C₂³	—	53	2	no	—
1420	C₂³	—	53	2	no	—
1421	C₂³	—	53	2	no	—
1422	C₂³	—	53	2	no	—
1423	C₂³	—	106	8	no	—
1424	C₂³	—	106	8	no	—
1425	C₂³	—	106	1	no	—
1426	C₂³	—	106	1	no	—
1427	C₂³	—	106	1	no	—
1428	C₂³	—	106	1	no	—
1429	C₂³	—	106	1	no	—
1430	C₂³	—	106	1	no	—
1431	C₂³	—	106	1	no	—
1432	C₂³	—	106	1	no	—
1433	C₂³	—	106	1	no	—
1434	C₂³	—	106	1	no	—
1435	C₂³	—	106	1	no	—
1436	C₂³	—	106	1	no	—
1437	C₂³	—	106	1	no	—
1438	C₂³	—	106	1	no	—
1439	C₂³	—	106	1	no	—
1440	C₂³	—	106	1	no	—
1441	C₂³	—	424	2	no	—
1442	C₂³	—	424	2	no	—
1443	C₂³	—	424	2	no	—
1444	C₂³	—	424	2	no	—
1445	C₂³	—	212	4	no	—
1446	C₂³	—	212	4	no	—
1447	C₂³	—	212	4	no	—
1448	C₂³	—	212	4	no	—
1449	C₂³	—	212	4	no	—
1450	C₂³	—	212	4	no	—
1451	C₂³	—	212	4	no	—
1452	C₂³	—	212	4	no	—
1453	C₂³	C₂×D₄×D₅₃	1	2	yes	—
1454	C₂³	#13133263	1	2	yes	—
1455	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1456	Q₈	—	8	2	no	—
1457	Q₈	—	424	2	no	—
1458	Q₈	—	424	2	no	—
1459	Q₈	—	424	2	no	—
1460	D₄	—	4	4	no	—
1461	D₄	—	212	4	no	—
1462	D₄	—	212	4	no	—
1463	D₄	—	212	4	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	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	2	1	no	—
1496	C₂×C₄	—	2	1	no	—
1497	C₂×C₄	—	2	1	no	—
1498	C₂×C₄	—	2	1	no	—
1499	C₂×C₄	—	2	1	no	—
1500	C₂×C₄	—	2	1	no	—
1501	C₂×C₄	—	4	4	no	—
1502	C₂×C₄	—	8	2	no	—
1503	C₂×C₄	—	53	2	no	—
1504	C₂×C₄	—	53	2	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	—	106	1	no	—
1527	C₂×C₄	—	106	1	no	—
1528	C₂×C₄	—	106	1	no	—
1529	C₂×C₄	—	106	1	no	—
1530	C₂×C₄	—	106	1	no	—
1531	C₂×C₄	—	106	1	no	—
1532	C₂×C₄	—	106	1	no	—
1533	C₂×C₄	—	106	1	no	—
1534	C₂×C₄	—	106	1	no	—
1535	C₂×C₄	—	106	1	no	—
1536	C₂×C₄	—	106	1	no	—
1537	C₂×C₄	—	106	1	no	—
1538	C₂×C₄	—	106	1	no	—
1539	C₂×C₄	—	106	1	no	—
1540	C₂×C₄	—	106	1	no	—
1541	C₂×C₄	—	106	1	no	—
1542	C₂×C₄	—	424	2	no	—
1543	C₂×C₄	—	424	2	no	—
1544	C₂×C₄	—	424	2	no	—
1545	C₂×C₄	—	212	4	no	—
1546	C₂×C₄	—	212	4	no	—
1547	C₂×C₄	—	212	4	no	—
1548	C₂×C₄	—	212	4	no	—
1549	C₂×C₄	—	212	4	no	—
1550	C₂×C₄	—	212	4	no	—
1551	C₂×C₄	—	212	4	no	—
1552	C₂×C₄	—	212	4	no	—
1553	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1554	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1555	C₂²	—	2	2	no	—
1556	C₂²	—	2	2	no	—
1557	C₂²	—	2	2	no	—
1558	C₂²	—	2	2	no	—
1559	C₂²	—	2	2	no	—
1560	C₂²	—	2	2	no	—
1561	C₂²	—	4	1	no	—
1562	C₂²	—	4	1	no	—
1563	C₂²	—	4	1	no	—
1564	C₂²	—	4	1	no	—
1565	C₂²	—	4	1	no	—
1566	C₂²	—	4	1	no	—
1567	C₂²	—	4	1	no	—
1568	C₂²	—	4	1	no	—
1569	C₂²	—	53	4	no	—
1570	C₂²	—	106	2	no	—
1571	C₂²	—	106	2	no	—
1572	C₂²	—	106	2	no	—
1573	C₂²	—	106	2	no	—
1574	C₂²	—	106	2	no	—
1575	C₂²	—	106	2	no	—
1576	C₂²	—	106	2	no	—
1577	C₂²	—	106	2	no	—
1578	C₂²	—	106	2	no	—
1579	C₂²	—	106	2	no	—
1580	C₂²	—	106	2	no	—
1581	C₂²	—	106	2	no	—
1582	C₂²	—	424	8	no	—
1583	C₂²	—	212	16	no	—
1584	C₂²	—	212	1	no	—
1585	C₂²	—	212	1	no	—
1586	C₂²	—	212	1	no	—
1587	C₂²	—	212	1	no	—
1588	C₂²	—	212	1	no	—
1589	C₂²	—	212	1	no	—
1590	C₂²	—	212	1	no	—
1591	C₂²	—	212	1	no	—
1592	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1593	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1594	C₂²	C₂×#13133263	1	1	yes	characteristic
1595	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1596	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1597	C₂²	#16811458	1	1	yes	characteristic
1598	C₂²	#16811459	1	1	yes	characteristic
1599	C₄	—	2	2	no	—
1600	C₄	—	2	2	no	—
1601	C₄	—	4	1	no	—
1602	C₄	—	4	1	no	—
1603	C₄	—	4	1	no	—
1604	C₄	—	4	1	no	—
1605	C₄	—	4	1	no	—
1606	C₄	—	4	1	no	—
1607	C₄	—	4	1	no	—
1608	C₄	—	4	1	no	—
1609	C₄	—	4	1	no	—
1610	C₄	—	4	1	no	—
1611	C₄	—	4	1	no	—
1612	C₄	—	106	2	no	—
1613	C₄	—	106	2	no	—
1614	C₄	—	212	1	no	—
1615	C₄	—	212	1	no	—
1616	C₄	—	212	1	no	—
1617	C₄	—	212	1	no	—
1618	C₄	—	212	1	no	—
1619	C₄	—	212	1	no	—
1620	C₄	—	212	1	no	—
1621	C₄	—	212	1	no	—
1622	C₄	—	212	1	no	—
1623	C₄	—	212	1	no	—
1624	C₄	—	212	1	no	—
1625	C₂	—	4	2	no	—
1626	C₂	—	4	2	no	—
1627	C₂	—	106	4	no	—
1628	C₂	—	212	2	no	—
1629	C₂	—	212	2	no	—
1630	C₂	#536×D₅₃	1	1	yes	characteristic
1631	C₂	#20288345	1	1	yes	characteristic
1632	C₂	#20288352	1	1	yes	characteristic
1633	C₂	#20288915	1	1	yes	characteristic
1634	C₂	#20288917	1	1	yes	characteristic
1635	C₂	#20288922	1	1	yes	characteristic
1636	C₂	#20288927	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2687	C₂
prime radical	C₂²×D₄×D₅₃	C₂²
hypercenter	#2687	D₅₃
hypocenter	C₅₃	#36720
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2687

Complements

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

N	H ≅ G/N	type
1. C₂×#16811248	C₂	semidirect
3. #20283003	C₂	semidirect
4. #20283001	C₂	semidirect
5. #20281141	C₂	semidirect
6. #20281140	C₂	semidirect
7. #20281137	C₂	semidirect
8. #20281136	C₂	semidirect
9. #20281135	C₂	semidirect
10. #20281132	C₂	semidirect
11. #20281131	C₂	semidirect
12. #20281058	C₂	semidirect
13. #20281057	C₂	semidirect
14. #20281056	C₂	semidirect
15. #20281056	C₂	semidirect
16. #20281053	C₂	semidirect
17. #20281053	C₂	semidirect
18. #20281052	C₂	semidirect
19. #20281051	C₂	semidirect
20. #20280533	C₂	semidirect
21. #20280529	C₂	semidirect
22. #20279871	C₂	semidirect
23. #20279869	C₂	semidirect
24. #20279192	C₂	semidirect
25. #20279188	C₂	semidirect
26. #20278994	C₂	semidirect
27. #20278992	C₂	semidirect
30. #20277309	C₂	semidirect
31. C₅₃×#2687	C₂	semidirect
48. C₂×#13133197	C₂²	semidirect
49. C₂×#13133197	C₂²	semidirect
50. C₂×#13133196	C₂²	semidirect
51. C₂×#13133196	C₂²	semidirect
54. C₂×#13133195	C₂²	semidirect
55. C₂×#13133195	C₂²	semidirect
56. C₂×#13133195	C₂²	semidirect
57. C₂×#13133194	C₂²	semidirect
58. C₂×#13133194	C₂²	semidirect
59. C₂×#13133194	C₂²	semidirect
61. C₂×#13133193	C₂²	semidirect
69. #16810565	C₂²	semidirect
70. #16810564	C₂²	semidirect
71. #16810561	C₂²	semidirect
72. #16810557	C₂²	semidirect
73. #16810557	C₂²	semidirect
74. #16810557	C₂²	semidirect
75. #16810557	C₂²	semidirect
76. #16810557	C₂²	semidirect
77. #16810557	C₂²	semidirect
78. #16810556	C₂²	semidirect
79. #16810556	C₂²	semidirect
80. #16810555	C₂²	semidirect
81. #16810555	C₂²	semidirect
82. #16810555	C₂²	semidirect
83. #16810554	C₂²	semidirect
84. #16810553	C₂²	semidirect
85. #16810553	C₂²	semidirect
86. #16810552	C₂²	semidirect
87. #16810552	C₂²	semidirect
88. #16810552	C₂²	semidirect
89. #16810551	C₂²	semidirect
90. #16810551	C₂²	semidirect
91. #16810551	C₂²	semidirect
92. #16810550	C₂²	semidirect
93. #16810550	C₂²	semidirect
94. #16810550	C₂²	semidirect
95. #16810548	C₂²	semidirect
96. #16810548	C₂²	semidirect
97. #16810544	C₂²	semidirect
98. #16810544	C₂²	semidirect
99. #16810543	C₂²	semidirect
100. #16810543	C₂²	semidirect
108. #16810536	C₂²	semidirect
109. #16810535	C₂²	semidirect
110. #16810534	C₂²	semidirect
111. #16810530	C₂²	semidirect
112. #16810527	C₂²	semidirect
113. #16810527	C₂²	semidirect
114. #16810517	C₂²	semidirect
115. #16810517	C₂²	semidirect
116. #16810516	C₂²	semidirect
117. #16810515	C₂²	semidirect
118. #16810514	C₂²	semidirect
119. #16810514	C₂²	semidirect
120. #16810513	C₂²	semidirect
121. #16810513	C₂²	semidirect
122. #16810512	C₂²	semidirect
123. #16810512	C₂²	semidirect
124. #16810512	C₂²	semidirect
125. #16810511	C₂²	semidirect
126. #16810511	C₂²	semidirect
127. #16810511	C₂²	semidirect
131. #16810498	C₂²	semidirect
132. #16810498	C₂²	semidirect
133. #16810498	C₂²	semidirect
140. #16810497	C₂²	semidirect
141. #16810497	C₂²	semidirect
142. #16810497	C₂²	semidirect
143. #16810497	C₂²	semidirect
144. #16810496	C₂²	semidirect
145. #16810495	C₂²	semidirect
148. #16810494	C₂²	semidirect
149. #16810494	C₂²	semidirect
150. #16810493	C₂²	semidirect
151. #16810492	C₂²	semidirect
152. #16810492	C₂²	semidirect
153. #16810492	C₂²	semidirect
154. #16810486	C₂²	semidirect
159. #16810485	C₂²	semidirect
160. #16810485	C₂²	semidirect
162. #16810482	C₂²	semidirect
163. #16810481	C₂²	semidirect
165. #16810480	C₂²	semidirect
175. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
176. C₅₃×#400	C₂²	semidirect
177. C₅₃×#398	C₂²	semidirect
178. C₅₃×#398	C₂²	semidirect
179. C₅₃×#397	C₂²	semidirect
181. C₅₃×#393	C₂²	semidirect
182. C₅₃×#391	C₂²	semidirect
183. C₅₃×#388	C₂²	semidirect
184. C₅₃×#388	C₂²	semidirect
186. C₅₃×#385	C₂²	semidirect
187. C₅₃×#381	C₂²	semidirect
188. C₅₃×#380	C₂²	semidirect
818. #2687	D₅₃	semidirect
881. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
892. #400	C₂×D₅₃	semidirect
907. #398	C₂×D₅₃	semidirect
908. #398	C₂×D₅₃	semidirect
920. #397	C₂×D₅₃	semidirect
936. #393	C₂×D₅₃	semidirect
940. #391	C₂×D₅₃	semidirect
955. #388	C₂×D₅₃	semidirect
956. #388	C₂×D₅₃	semidirect
980. #385	C₂×D₅₃	semidirect
992. #381	C₂×D₅₃	semidirect
998. #380	C₂×D₅₃	semidirect
1007. C₅₃	#36720	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811248	2
C₂×#123×D₅₃	2
#20283003	2
#20283001	2
#20281141	2
#20281140	2
#20281137	2
#20281136	2
#20281135	2
#20281132	2
#20281131	2
#20281058	2
#20281057	2
#20281056	2
#20281053	2
#20281052	2
#20281051	2
#20280533	2
#20280529	2
#20279871	2
#20279869	2
#20279192	2
#20279188	2
#20278994	2
#20278992	2
#20278041	2
#20278037	2
#20277309	2
C₅₃×#2687	2
#36720	53