Subgroups — D₅₃×#2596 #27554637

Order 13568.

2074 conjugacy classes of subgroups.

The subgroup lattice has 1444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20280258	C₂	1	1	yes	maximal, characteristic, complemented
2	#20280257	C₂	1	1	yes	maximal, characteristic, complemented
3	#20280256	C₂	1	1	yes	maximal, characteristic, complemented
4	#20280255	C₂	1	1	yes	maximal, characteristic, complemented
5	#20280254	C₂	1	1	yes	maximal, characteristic, complemented
6	#20280253	C₂	1	1	yes	maximal, characteristic, complemented
7	#20280252	C₂	1	1	yes	maximal, characteristic, complemented
8	#20280251	C₂	1	1	yes	maximal, characteristic, complemented
9	#20280250	C₂	1	1	yes	maximal, characteristic, complemented
10	#20280249	C₂	1	1	yes	maximal, characteristic, complemented
11	#20280248	C₂	1	1	yes	maximal, characteristic, complemented
12	#20280247	C₂	1	1	yes	maximal, characteristic, complemented
13	#20280246	C₂	1	1	yes	maximal, characteristic, complemented
14	#20280245	C₂	1	1	yes	maximal, characteristic, complemented
15	#20280244	C₂	1	1	yes	maximal, characteristic, complemented
16	#400×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#400×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#399×D₅₃	C₂	1	1	yes	maximal, characteristic
19	#397×D₅₃	C₂	1	1	yes	maximal, characteristic
20	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
22	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
23	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
24	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
25	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
26	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2596	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
53	#16810565	C₂²	1	1	yes	characteristic, complemented
54	#16810565	C₂²	1	1	yes	characteristic, complemented
55	#16810565	C₂²	1	1	yes	characteristic, complemented
56	#16810565	C₂²	1	1	yes	characteristic, complemented
57	#16810564	C₂²	1	1	yes	characteristic, complemented
58	#16810564	C₂²	1	1	yes	characteristic, complemented
59	#16810564	C₂²	1	1	yes	characteristic, complemented
60	#16810564	C₂²	1	1	yes	characteristic, complemented
61	#16810563	C₂²	1	1	yes	characteristic, complemented
62	#16810563	C₂²	1	1	yes	characteristic, complemented
63	#16810562	C₂²	1	1	yes	characteristic, complemented
64	#16810562	C₂²	1	1	yes	characteristic, complemented
65	#16810561	C₂²	1	1	yes	characteristic, complemented
66	#16810561	C₂²	1	1	yes	characteristic, complemented
67	#16810560	C₂²	1	1	yes	characteristic
68	#16810559	C₂²	1	1	yes	characteristic
69	#16810559	C₂²	1	1	yes	characteristic
70	#16810559	C₂²	1	1	yes	characteristic
71	#16810558	C₂²	1	1	yes	characteristic
72	#16810558	C₂²	1	1	yes	characteristic
73	#16810558	C₂²	1	1	yes	characteristic
74	#16810552	C₂²	1	1	yes	characteristic
75	#16810552	C₂²	1	1	yes	characteristic
76	#16810551	C₂²	1	1	yes	characteristic
77	#16810551	C₂²	1	1	yes	characteristic
78	#16810550	C₂²	1	1	yes	characteristic
79	#16810549	C₂²	1	1	yes	characteristic
80	#16810548	C₂²	1	1	yes	characteristic
81	#16810522	C₂²	1	1	yes	characteristic, complemented
82	#16810521	C₂²	1	1	yes	characteristic, complemented
83	#16810520	C₂²	1	1	yes	characteristic, complemented
84	#16810520	C₂²	1	1	yes	characteristic, complemented
85	#16810519	C₂²	1	1	yes	characteristic, complemented
86	#16810518	C₂²	1	1	yes	characteristic, complemented
87	#16810518	C₂²	1	1	yes	characteristic, complemented
88	#16810517	C₂²	1	1	yes	characteristic
89	#16810517	C₂²	1	1	yes	characteristic
90	#16810517	C₂²	1	1	yes	characteristic
91	#16810517	C₂²	1	1	yes	characteristic
92	#16810517	C₂²	1	1	yes	characteristic
93	#16810516	C₂²	1	1	yes	characteristic
94	#16810516	C₂²	1	1	yes	characteristic
95	#16810516	C₂²	1	1	yes	characteristic
96	#16810516	C₂²	1	1	yes	characteristic
97	#16810516	C₂²	1	1	yes	characteristic
98	#16810515	C₂²	1	1	yes	characteristic
99	#16810515	C₂²	1	1	yes	characteristic
100	#16810515	C₂²	1	1	yes	characteristic
101	#16810515	C₂²	1	1	yes	characteristic
102	#16810515	C₂²	1	1	yes	characteristic
103	#16810514	C₂²	1	1	yes	characteristic
104	#16810514	C₂²	1	1	yes	characteristic
105	#16810514	C₂²	1	1	yes	characteristic
106	#16810514	C₂²	1	1	yes	characteristic
107	#16810514	C₂²	1	1	yes	characteristic
108	#16810513	C₂²	1	1	yes	characteristic
109	#16810513	C₂²	1	1	yes	characteristic
110	#16810513	C₂²	1	1	yes	characteristic
111	#16810513	C₂²	1	1	yes	characteristic
112	#16810513	C₂²	1	1	yes	characteristic
113	#16810512	C₂²	1	1	yes	characteristic
114	#16810512	C₂²	1	1	yes	characteristic
115	#16810512	C₂²	1	1	yes	characteristic
116	#16810512	C₂²	1	1	yes	characteristic
117	#16810512	C₂²	1	1	yes	characteristic
118	#16810511	C₂²	1	1	yes	characteristic
119	#16810511	C₂²	1	1	yes	characteristic
120	#16810511	C₂²	1	1	yes	characteristic
121	#16810511	C₂²	1	1	yes	characteristic
122	#16810511	C₂²	1	1	yes	characteristic
123	#16810510	C₂²	1	1	yes	characteristic, complemented
124	#16810510	C₂²	1	1	yes	characteristic, complemented
125	#16810510	C₂²	1	1	yes	characteristic, complemented
126	#16810509	C₂²	1	1	yes	characteristic, complemented
127	#16810509	C₂²	1	1	yes	characteristic, complemented
128	#16810509	C₂²	1	1	yes	characteristic, complemented
129	#16810508	C₂²	1	1	yes	characteristic, complemented
130	#16810508	C₂²	1	1	yes	characteristic, complemented
131	#16810508	C₂²	1	1	yes	characteristic, complemented
132	#16810507	C₂²	1	1	yes	characteristic, complemented
133	#16810507	C₂²	1	1	yes	characteristic, complemented
134	#16810507	C₂²	1	1	yes	characteristic, complemented
135	#16810506	C₂²	1	1	yes	characteristic, complemented
136	#16810506	C₂²	1	1	yes	characteristic, complemented
137	#16810506	C₂²	1	1	yes	characteristic, complemented
138	#16810505	C₂²	1	1	yes	characteristic, complemented
139	#16810505	C₂²	1	1	yes	characteristic, complemented
140	#16810505	C₂²	1	1	yes	characteristic, complemented
141	#16810504	C₂²	1	1	yes	characteristic, complemented
142	#16810504	C₂²	1	1	yes	characteristic, complemented
143	#16810504	C₂²	1	1	yes	characteristic, complemented
144	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
147	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
148	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
149	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
150	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
151	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
152	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
153	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
154	#16810474	C₂²	1	1	yes	characteristic, complemented
155	#16810474	C₂²	1	1	yes	characteristic, complemented
156	#16810474	C₂²	1	1	yes	characteristic, complemented
157	#16810474	C₂²	1	1	yes	characteristic, complemented
158	#95×D₅₃	C₂²	1	1	yes	characteristic
159	#95×D₅₃	C₂²	1	1	yes	characteristic
160	#95×D₅₃	C₂²	1	1	yes	characteristic
161	#95×D₅₃	C₂²	1	1	yes	characteristic
162	#95×D₅₃	C₂²	1	1	yes	characteristic
163	#95×D₅₃	C₂²	1	1	yes	characteristic
164	#95×D₅₃	C₂²	1	1	yes	characteristic
165	#95×D₅₃	C₂²	1	1	yes	characteristic
166	#95×D₅₃	C₂²	1	1	yes	characteristic
167	#95×D₅₃	C₂²	1	1	yes	characteristic
168	#95×D₅₃	C₂²	1	1	yes	characteristic
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#399	C₂²	1	1	yes	characteristic
175	C₅₃×#397	C₂²	1	1	yes	characteristic
176	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#388	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
188	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂×#11719919	C₂³	1	1	yes	characteristic
212	C₂×#11719919	C₂³	1	1	yes	characteristic
213	C₂×#11719919	C₂³	1	1	yes	characteristic
214	C₂×#11719919	C₂³	1	1	yes	characteristic
215	C₂×#11719919	C₂³	1	1	yes	characteristic
216	C₂×#11719919	C₂³	1	1	yes	characteristic
217	C₂×#11719919	C₂³	1	1	yes	characteristic
218	C₂×#11719919	C₂³	1	1	yes	characteristic
219	C₂×#11719919	C₂³	1	1	yes	characteristic
220	C₂×#11719919	C₂³	1	1	yes	characteristic
221	C₂×#11719919	C₂³	1	1	yes	characteristic
222	C₂×#11719919	C₂³	1	1	yes	characteristic
223	C₂×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₄⋊C₄×D₅₃	—	2	4	no	—
230	C₄⋊C₄×D₅₃	—	2	4	no	—
231	C₄⋊C₄×D₅₃	—	2	4	no	—
232	C₄⋊C₄×D₅₃	—	2	4	no	—
233	C₄⋊C₄×D₅₃	—	2	4	no	—
234	C₄⋊C₄×D₅₃	—	2	4	no	—
235	C₄⋊C₄×D₅₃	—	2	4	no	—
236	C₄⋊C₄×D₅₃	—	2	4	no	—
237	C₄⋊C₄×D₅₃	—	4	2	no	—
238	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂×#11719921	C₂³	1	1	yes	characteristic
246	C₂×#11719921	C₂³	1	1	yes	characteristic
247	C₂×#11719921	C₂³	1	1	yes	characteristic
248	C₂×#11719921	C₂³	1	1	yes	characteristic
249	C₂×#11719921	C₂³	1	1	yes	characteristic
250	C₂×#11719921	C₂³	1	1	yes	characteristic
251	C₂×#11719921	C₂³	1	1	yes	characteristic
252	C₂×#11719921	C₂³	1	1	yes	characteristic
253	C₂×#11719921	C₂³	1	1	yes	characteristic
254	C₂×#11719921	C₂³	1	1	yes	characteristic
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂²⋊C₄×D₅₃	—	2	4	no	—
260	C₂²⋊C₄×D₅₃	—	2	4	no	—
261	C₂²⋊C₄×D₅₃	—	2	4	no	—
262	C₂²⋊C₄×D₅₃	—	2	4	no	—
263	C₂²⋊C₄×D₅₃	—	2	4	no	—
264	C₂²⋊C₄×D₅₃	—	4	2	no	—
265	C₂²⋊C₄×D₅₃	—	4	2	no	—
266	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₄²×D₅₃	—	2	4	no	—
282	C₄²×D₅₃	—	2	4	no	—
283	C₄²×D₅₃	—	4	2	no	—
284	C₄²×D₅₃	—	4	2	no	—
285	C₄²×D₅₃	—	4	2	no	—
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂³×D₅₃	—	2	2	no	—
365	C₂³×D₅₃	—	2	2	no	—
366	C₂³×D₅₃	—	2	2	no	—
367	C₂³×D₅₃	—	2	2	no	—
368	C₂³×D₅₃	—	2	2	no	—
369	C₂³×D₅₃	—	2	2	no	—
370	C₂³×D₅₃	—	2	2	no	—
371	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
372	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×D₅₃	—	2	2	no	—
402	C₂×C₄×D₅₃	—	2	2	no	—
403	C₂×C₄×D₅₃	—	2	2	no	—
404	C₂×C₄×D₅₃	—	2	2	no	—
405	C₂×C₄×D₅₃	—	2	2	no	—
406	C₂×C₄×D₅₃	—	2	2	no	—
407	C₂×C₄×D₅₃	—	2	2	no	—
408	C₂×C₄×D₅₃	—	2	2	no	—
409	C₂×C₄×D₅₃	—	2	2	no	—
410	C₂×C₄×D₅₃	—	2	2	no	—
411	C₂×C₄×D₅₃	—	2	2	no	—
412	C₂×C₄×D₅₃	—	2	2	no	—
413	C₂×C₄×D₅₃	—	2	2	no	—
414	C₂×C₄×D₅₃	—	2	2	no	—
415	C₂×C₄×D₅₃	—	2	2	no	—
416	C₂×C₄×D₅₃	—	2	2	no	—
417	C₂×C₄×D₅₃	—	2	2	no	—
418	C₂×C₄×D₅₃	—	2	2	no	—
419	C₂×C₄×D₅₃	—	2	2	no	—
420	C₂×C₄×D₅₃	—	2	2	no	—
421	C₂×C₄×D₅₃	—	2	2	no	—
422	C₂×C₄×D₅₃	—	2	2	no	—
423	C₂×C₄×D₅₃	—	2	2	no	—
424	C₂×C₄×D₅₃	—	2	2	no	—
425	C₂×C₄×D₅₃	—	2	2	no	—
426	C₂×C₄×D₅₃	—	2	2	no	—
427	C₂×C₄×D₅₃	—	2	2	no	—
428	C₂×C₄×D₅₃	—	2	2	no	—
429	C₂×C₄×D₅₃	—	2	2	no	—
430	C₂×C₄×D₅₃	—	2	2	no	—
431	C₂×C₄×D₅₃	—	2	2	no	—
432	C₂×C₄×D₅₃	—	2	2	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	2	2	no	—
437	C₂×C₄×D₅₃	—	2	2	no	—
438	C₂×C₄×D₅₃	#41	1	4	yes	—
439	C₂×C₄×D₅₃	#41	1	4	yes	—
440	C₂×C₄×D₅₃	#41	1	4	yes	—
441	C₂×C₄×D₅₃	#41	1	4	yes	—
442	C₂×C₄×D₅₃	#41	1	4	yes	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	—	2	2	no	—
447	C₄⋊C₄×C₅₃	—	2	2	no	—
448	C₄⋊C₄×C₅₃	—	2	2	no	—
449	C₄⋊C₄×C₅₃	—	2	2	no	—
450	C₄⋊C₄×C₅₃	—	2	2	no	—
451	C₄⋊C₄×C₅₃	—	4	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	2	no	—
456	C₂²⋊C₄×C₅₃	—	2	2	no	—
457	C₂²⋊C₄×C₅₃	—	4	1	no	—
458	C₂²⋊C₄×C₅₃	—	4	1	no	—
459	C₄²×C₅₃	—	2	2	no	—
460	C₄²×C₅₃	—	2	2	no	—
461	C₄²×C₅₃	—	4	1	no	—
462	C₄²×C₅₃	—	4	1	no	—
463	C₄²×C₅₃	—	4	1	no	—
464	C₂²⋊Dic₅₃	—	2	2	no	—
465	C₂²⋊Dic₅₃	—	2	2	no	—
466	C₂²⋊Dic₅₃	—	2	2	no	—
467	C₂²⋊Dic₅₃	—	2	2	no	—
468	C₂²⋊Dic₅₃	—	2	2	no	—
469	C₂²⋊Dic₅₃	—	4	1	no	—
470	C₂²⋊Dic₅₃	—	4	1	no	—
471	#11719921	—	2	2	no	—
472	#11719921	—	2	2	no	—
473	#11719921	—	2	2	no	—
474	#11719921	—	2	2	no	—
475	#11719921	—	2	2	no	—
476	#11719921	—	2	2	no	—
477	#11719921	—	2	2	no	—
478	#11719921	—	2	2	no	—
479	#11719921	—	2	2	no	—
480	#11719921	—	2	2	no	—
481	#11719921	—	4	1	no	—
482	#11719921	—	4	1	no	—
483	#11719921	—	4	1	no	—
484	#11719921	—	4	1	no	—
485	C₄⋊Dic₅₃	—	2	2	no	—
486	C₄⋊Dic₅₃	—	2	2	no	—
487	C₄⋊Dic₅₃	—	2	2	no	—
488	C₄⋊Dic₅₃	—	2	2	no	—
489	C₄⋊Dic₅₃	—	2	2	no	—
490	C₄⋊Dic₅₃	—	2	2	no	—
491	C₄⋊Dic₅₃	—	2	2	no	—
492	C₄⋊Dic₅₃	—	2	2	no	—
493	C₄⋊Dic₅₃	—	4	1	no	—
494	#11719919	—	2	2	no	—
495	#11719919	—	2	2	no	—
496	#11719919	—	2	2	no	—
497	#11719919	—	2	2	no	—
498	#11719919	—	2	2	no	—
499	#11719919	—	2	2	no	—
500	#11719919	—	2	2	no	—
501	#11719919	—	2	2	no	—
502	#11719919	—	2	2	no	—
503	#11719919	—	2	2	no	—
504	#11719919	—	2	2	no	—
505	#11719919	—	2	2	no	—
506	#11719919	—	2	2	no	—
507	#11719919	—	2	2	no	—
508	#11719919	—	2	2	no	—
509	#11719919	—	2	2	no	—
510	#11719919	—	4	1	no	—
511	#11719919	—	4	1	no	—
512	C₄×Dic₅₃	—	2	2	no	—
513	C₄×Dic₅₃	—	2	2	no	—
514	C₄×Dic₅₃	—	2	2	no	—
515	C₄×Dic₅₃	—	2	2	no	—
516	C₄×Dic₅₃	—	2	2	no	—
517	C₄×Dic₅₃	—	2	2	no	—
518	C₄×Dic₅₃	—	4	1	no	—
519	C₄×Dic₅₃	—	4	1	no	—
520	C₄×Dic₅₃	—	4	1	no	—
521	C₄×Dic₅₃	—	4	1	no	—
522	C₄×Dic₅₃	—	4	1	no	—
523	C₄×Dic₅₃	—	4	1	no	—
524	C₄×Dic₅₃	—	4	1	no	—
525	C₄×Dic₅₃	—	4	1	no	—
526	C₄×Dic₅₃	—	4	1	no	—
527	C₂³×C₅₃	—	2	1	no	—
528	C₂³×C₅₃	—	2	1	no	—
529	C₂³×C₅₃	—	2	1	no	—
530	C₂³×C₅₃	—	2	1	no	—
531	C₂³×C₅₃	—	2	1	no	—
532	C₂³×C₅₃	—	2	1	no	—
533	C₂³×C₅₃	—	2	1	no	—
534	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
535	C₂²×D₅₃	—	2	1	no	—
536	C₂²×D₅₃	—	2	1	no	—
537	C₂²×D₅₃	—	2	1	no	—
538	C₂²×D₅₃	—	2	1	no	—
539	C₂²×D₅₃	—	2	1	no	—
540	C₂²×D₅₃	—	2	1	no	—
541	C₂²×D₅₃	—	2	1	no	—
542	C₂²×D₅₃	—	4	4	no	—
543	C₂²×D₅₃	—	4	4	no	—
544	C₂²×D₅₃	—	4	4	no	—
545	C₂²×D₅₃	—	4	4	no	—
546	C₂²×D₅₃	—	4	4	no	—
547	C₂²×D₅₃	—	4	4	no	—
548	C₂²×D₅₃	—	4	4	no	—
549	C₂²×D₅₃	C₂×#41	1	2	yes	—
550	C₂²×D₅₃	C₂×#41	1	2	yes	—
551	C₂²×D₅₃	C₂×#41	1	2	yes	—
552	C₂²×D₅₃	C₂×#41	1	2	yes	—
553	C₂²×D₅₃	C₂×#41	1	2	yes	—
554	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
555	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
594	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
595	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
596	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
597	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	1	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	1	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	C₂×#41	1	2	yes	—
636	C₂×Dic₅₃	C₂×#41	1	2	yes	—
637	C₂×Dic₅₃	C₂×#41	1	2	yes	—
638	C₂×Dic₅₃	C₂×#41	1	2	yes	—
639	C₂×Dic₅₃	C₂×#41	1	2	yes	—
640	C₄×D₅₃	—	2	8	no	—
641	C₄×D₅₃	—	2	8	no	—
642	C₄×D₅₃	—	2	8	no	—
643	C₄×D₅₃	—	2	8	no	—
644	C₄×D₅₃	—	2	8	no	—
645	C₄×D₅₃	—	4	4	no	—
646	C₄×D₅₃	—	4	4	no	—
647	C₄×D₅₃	—	4	4	no	—
648	C₄×D₅₃	—	4	4	no	—
649	C₄×D₅₃	—	4	4	no	—
650	C₄×D₅₃	—	4	4	no	—
651	C₄×D₅₃	—	4	4	no	—
652	C₄×D₅₃	—	4	4	no	—
653	C₄×D₅₃	—	4	4	no	—
654	C₂×#2596	—	53	1	no	maximal, Sylow
655	C₂²×C₅₃	—	4	1	no	—
656	C₂²×C₅₃	—	4	1	no	—
657	C₂²×C₅₃	—	4	1	no	—
658	C₂²×C₅₃	—	4	1	no	—
659	C₂²×C₅₃	—	4	1	no	—
660	C₂²×C₅₃	—	4	1	no	—
661	C₂²×C₅₃	—	4	1	no	—
662	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
663	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
664	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
665	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
666	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
667	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
668	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
669	C₂×D₅₃	—	4	1	no	—
670	C₂×D₅₃	—	4	1	no	—
671	C₂×D₅₃	—	4	1	no	—
672	C₂×D₅₃	—	4	1	no	—
673	C₂×D₅₃	—	4	1	no	—
674	C₂×D₅₃	—	4	1	no	—
675	C₂×D₅₃	—	4	1	no	—
676	C₂×D₅₃	—	8	8	no	—
677	C₂×D₅₃	#529	1	4	yes	—
678	C₂×D₅₃	#529	1	4	yes	—
679	C₂×D₅₃	#539	1	4	yes	—
680	C₂×D₅₃	#552	1	4	yes	—
681	C₂×D₅₃	#553	1	4	yes	—
682	C₂×D₅₃	#556	1	4	yes	—
683	C₂×D₅₃	#559	1	4	yes	—
684	C₄×C₅₃	—	2	2	no	—
685	C₄×C₅₃	—	2	2	no	—
686	C₄×C₅₃	—	2	2	no	—
687	C₄×C₅₃	—	2	2	no	—
688	C₄×C₅₃	—	2	2	no	—
689	C₄×C₅₃	—	4	1	no	—
690	C₄×C₅₃	—	4	1	no	—
691	C₄×C₅₃	—	4	1	no	—
692	C₄×C₅₃	—	4	1	no	—
693	C₄×C₅₃	—	4	1	no	—
694	C₄×C₅₃	—	4	1	no	—
695	C₄×C₅₃	—	4	1	no	—
696	C₄×C₅₃	—	4	1	no	—
697	C₄×C₅₃	—	4	1	no	—
698	Dic₅₃	—	2	2	no	—
699	Dic₅₃	—	2	2	no	—
700	Dic₅₃	—	2	2	no	—
701	Dic₅₃	—	2	2	no	—
702	Dic₅₃	—	2	2	no	—
703	Dic₅₃	—	4	1	no	—
704	Dic₅₃	—	4	1	no	—
705	Dic₅₃	—	4	1	no	—
706	Dic₅₃	—	4	1	no	—
707	Dic₅₃	—	4	1	no	—
708	Dic₅₃	—	4	1	no	—
709	Dic₅₃	—	4	1	no	—
710	Dic₅₃	—	4	1	no	—
711	Dic₅₃	—	4	1	no	—
712	#2596	—	53	1	no	—
713	#2596	—	53	1	no	—
714	#2596	—	53	1	no	—
715	#2596	—	53	1	no	—
716	#2596	—	53	1	no	—
717	#2596	—	53	1	no	—
718	#2596	—	53	1	no	—
719	#2596	—	53	1	no	—
720	#2596	—	53	1	no	—
721	#2596	—	53	1	no	—
722	#2596	—	53	1	no	—
723	#2596	—	53	1	no	—
724	#2596	—	53	1	no	—
725	#2596	—	53	1	no	—
726	#2596	—	53	1	no	—
727	#2596	D₅₃	1	1	yes	characteristic, direct product factor
728	C₂×#400	—	53	1	no	—
729	C₂×#400	—	53	1	no	—
730	C₂×#399	—	53	1	no	—
731	C₂×#397	—	53	1	no	—
732	C₂×#389	—	53	1	no	—
733	C₂×#388	—	53	1	no	—
734	C₂×#388	—	53	1	no	—
735	C₂×#388	—	53	1	no	—
736	C₂×#388	—	53	1	no	—
737	C₂×#388	—	53	1	no	—
738	C₂×#387	—	53	1	no	—
739	C₂×#387	—	53	1	no	—
740	C₂×#387	—	53	1	no	—
741	C₂×C₄×C₄⋊C₄	—	53	1	no	—
742	C₂×C₄×C₄⋊C₄	—	53	1	no	—
743	C₂×C₅₃	—	8	1	no	—
744	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
745	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
746	C₂×C₅₃	C₂×#539	1	1	yes	characteristic
747	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
748	C₂×C₅₃	C₂×#553	1	1	yes	characteristic
749	C₂×C₅₃	C₂×#556	1	1	yes	characteristic
750	C₂×C₅₃	C₂×#559	1	1	yes	characteristic
751	D₅₃	—	8	1	no	—
752	D₅₃	#2596	1	8	yes	direct product factor
753	C₂²×C₄⋊C₄	—	53	1	no	—
754	C₂²×C₄⋊C₄	—	53	1	no	—
755	C₂²×C₄⋊C₄	—	53	1	no	—
756	C₂²×C₄⋊C₄	—	53	1	no	—
757	C₂²×C₄⋊C₄	—	53	1	no	—
758	C₂²×C₄⋊C₄	—	53	1	no	—
759	C₂²×C₄⋊C₄	—	53	1	no	—
760	C₂²×C₄⋊C₄	—	53	1	no	—
761	C₂²×C₄⋊C₄	—	53	1	no	—
762	C₂²×C₂²⋊C₄	—	53	1	no	—
763	C₂²×C₂²⋊C₄	—	53	1	no	—
764	C₂²×C₂²⋊C₄	—	53	1	no	—
765	C₂²×C₂²⋊C₄	—	53	1	no	—
766	C₂²×C₂²⋊C₄	—	53	1	no	—
767	C₂²×C₂²⋊C₄	—	53	1	no	—
768	C₂²×C₂²⋊C₄	—	53	1	no	—
769	C₂²×C₄²	—	53	1	no	—
770	C₂²×C₄²	—	53	1	no	—
771	C₂²×C₄²	—	53	1	no	—
772	C₂²×C₄²	—	53	1	no	—
773	C₂²×C₄²	—	53	1	no	—
774	#400	—	53	1	no	—
775	#400	—	53	1	no	—
776	#400	—	53	1	no	—
777	#400	—	53	1	no	—
778	#400	—	53	1	no	—
779	#400	—	53	1	no	—
780	#400	—	53	1	no	—
781	#400	—	53	1	no	—
782	#400	—	53	1	no	—
783	#400	—	53	1	no	—
784	#400	—	53	1	no	—
785	#400	—	53	1	no	—
786	#400	—	53	1	no	—
787	#400	—	53	1	no	—
788	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
789	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
790	#399	—	53	1	no	—
791	#399	—	53	1	no	—
792	#399	—	53	1	no	—
793	#399	—	53	1	no	—
794	#399	—	53	1	no	—
795	#399	—	53	1	no	—
796	#399	—	53	1	no	—
797	#399	C₂×D₅₃	1	1	yes	characteristic
798	#397	—	53	1	no	—
799	#397	—	53	1	no	—
800	#397	—	53	1	no	—
801	#397	—	53	1	no	—
802	#397	—	53	1	no	—
803	#397	—	53	1	no	—
804	#397	—	53	1	no	—
805	#397	C₂×D₅₃	1	1	yes	characteristic
806	#389	—	53	1	no	—
807	#389	—	53	1	no	—
808	#389	—	53	1	no	—
809	#389	—	53	1	no	—
810	#389	—	53	1	no	—
811	#389	—	53	1	no	—
812	#389	—	53	1	no	—
813	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
814	#388	—	53	1	no	—
815	#388	—	53	1	no	—
816	#388	—	53	1	no	—
817	#388	—	53	1	no	—
818	#388	—	53	1	no	—
819	#388	—	53	1	no	—
820	#388	—	53	1	no	—
821	#388	—	53	1	no	—
822	#388	—	53	1	no	—
823	#388	—	53	1	no	—
824	#388	—	53	1	no	—
825	#388	—	53	1	no	—
826	#388	—	53	1	no	—
827	#388	—	53	1	no	—
828	#388	—	53	1	no	—
829	#388	—	53	1	no	—
830	#388	—	53	1	no	—
831	#388	—	53	1	no	—
832	#388	—	53	1	no	—
833	#388	—	53	1	no	—
834	#388	—	53	1	no	—
835	#388	—	53	1	no	—
836	#388	—	53	1	no	—
837	#388	—	53	1	no	—
838	#388	—	53	1	no	—
839	#388	—	53	1	no	—
840	#388	—	53	1	no	—
841	#388	—	53	1	no	—
842	#388	—	53	1	no	—
843	#388	—	53	1	no	—
844	#388	—	53	1	no	—
845	#388	—	53	1	no	—
846	#388	—	53	1	no	—
847	#388	—	53	1	no	—
848	#388	—	53	1	no	—
849	#388	C₂×D₅₃	1	1	yes	characteristic
850	#388	C₂×D₅₃	1	1	yes	characteristic
851	#388	C₂×D₅₃	1	1	yes	characteristic
852	#388	C₂×D₅₃	1	1	yes	characteristic
853	#388	C₂×D₅₃	1	1	yes	characteristic
854	#387	—	53	1	no	—
855	#387	—	53	1	no	—
856	#387	—	53	1	no	—
857	#387	—	53	1	no	—
858	#387	—	53	1	no	—
859	#387	—	53	1	no	—
860	#387	—	53	1	no	—
861	#387	—	53	1	no	—
862	#387	—	53	1	no	—
863	#387	—	53	1	no	—
864	#387	—	53	1	no	—
865	#387	—	53	1	no	—
866	#387	—	53	1	no	—
867	#387	—	53	1	no	—
868	#387	—	53	1	no	—
869	#387	—	53	1	no	—
870	#387	—	53	1	no	—
871	#387	—	53	1	no	—
872	#387	—	53	1	no	—
873	#387	—	53	1	no	—
874	#387	—	53	1	no	—
875	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
876	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
877	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
878	C₄×C₄⋊C₄	—	53	1	no	—
879	C₄×C₄⋊C₄	—	53	1	no	—
880	C₄×C₄⋊C₄	—	53	1	no	—
881	C₄×C₄⋊C₄	—	53	1	no	—
882	C₄×C₄⋊C₄	—	53	1	no	—
883	C₄×C₄⋊C₄	—	53	1	no	—
884	C₄×C₄⋊C₄	—	53	1	no	—
885	C₄×C₄⋊C₄	—	53	1	no	—
886	C₄×C₄⋊C₄	—	53	1	no	—
887	C₄×C₄⋊C₄	—	53	1	no	—
888	C₄×C₄⋊C₄	—	53	1	no	—
889	C₄×C₄⋊C₄	—	53	1	no	—
890	C₄×C₄⋊C₄	—	53	1	no	—
891	C₄×C₄⋊C₄	—	53	1	no	—
892	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
893	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
894	C₂×#95	—	53	1	no	—
895	C₂×#95	—	53	1	no	—
896	C₂×#95	—	53	1	no	—
897	C₂×#95	—	53	1	no	—
898	C₂×#95	—	53	1	no	—
899	C₂×#95	—	53	1	no	—
900	C₂×#95	—	53	1	no	—
901	C₂×#95	—	53	1	no	—
902	C₂×#95	—	53	1	no	—
903	C₂×#95	—	53	1	no	—
904	C₂×#95	—	53	1	no	—
905	C₂×#95	—	53	1	no	—
906	C₂×#95	—	53	1	no	—
907	C₂×#95	—	53	1	no	—
908	C₅₃	C₂×#2596	1	1	yes	characteristic, complemented, Sylow
909	C₂⁵	—	53	1	no	—
910	C₂³×C₄	—	53	1	no	—
911	C₂³×C₄	—	53	1	no	—
912	C₂³×C₄	—	53	1	no	—
913	C₂³×C₄	—	53	1	no	—
914	C₂³×C₄	—	53	1	no	—
915	C₂³×C₄	—	53	1	no	—
916	C₂³×C₄	—	53	1	no	—
917	C₂³×C₄	—	53	1	no	—
918	C₂³×C₄	—	53	1	no	—
919	C₂³×C₄	—	53	1	no	—
920	C₂³×C₄	—	53	1	no	—
921	C₂³×C₄	—	53	1	no	—
922	C₂³×C₄	—	53	1	no	—
923	C₂³×C₄	—	53	1	no	—
924	C₂×C₄⋊C₄	—	53	1	no	—
925	C₂×C₄⋊C₄	—	53	1	no	—
926	C₂×C₄⋊C₄	—	53	1	no	—
927	C₂×C₄⋊C₄	—	53	1	no	—
928	C₂×C₄⋊C₄	—	53	1	no	—
929	C₂×C₄⋊C₄	—	53	1	no	—
930	C₂×C₄⋊C₄	—	53	1	no	—
931	C₂×C₄⋊C₄	—	53	1	no	—
932	C₂×C₄⋊C₄	—	53	1	no	—
933	C₂×C₄⋊C₄	—	53	1	no	—
934	C₂×C₄⋊C₄	—	53	1	no	—
935	C₂×C₄⋊C₄	—	53	1	no	—
936	C₂×C₄⋊C₄	—	53	1	no	—
937	C₂×C₄⋊C₄	—	53	1	no	—
938	C₂×C₄⋊C₄	—	53	1	no	—
939	C₂×C₄⋊C₄	—	53	1	no	—
940	C₂×C₄⋊C₄	—	53	1	no	—
941	C₂×C₄⋊C₄	—	53	1	no	—
942	C₂×C₄⋊C₄	—	53	1	no	—
943	C₂×C₄⋊C₄	—	53	1	no	—
944	C₂×C₄⋊C₄	—	53	1	no	—
945	C₂×C₄⋊C₄	—	53	1	no	—
946	C₂×C₄⋊C₄	—	53	1	no	—
947	C₂×C₄⋊C₄	—	53	1	no	—
948	C₂×C₄⋊C₄	—	53	1	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	1	no	—
951	C₂×C₄⋊C₄	—	106	4	no	—
952	C₂×C₄⋊C₄	—	106	4	no	—
953	C₂×C₄⋊C₄	—	106	4	no	—
954	C₂×C₄⋊C₄	—	106	4	no	—
955	C₂×C₄⋊C₄	—	106	4	no	—
956	C₂×C₄⋊C₄	—	106	4	no	—
957	C₂×C₄⋊C₄	—	106	4	no	—
958	C₂×C₄⋊C₄	—	106	4	no	—
959	C₂×C₄⋊C₄	—	212	2	no	—
960	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	—	53	1	no	—
970	C₂×C₂²⋊C₄	—	53	1	no	—
971	C₂×C₂²⋊C₄	—	53	1	no	—
972	C₂×C₂²⋊C₄	—	53	1	no	—
973	C₂×C₂²⋊C₄	—	53	1	no	—
974	C₂×C₂²⋊C₄	—	53	1	no	—
975	C₂×C₂²⋊C₄	—	53	1	no	—
976	C₂×C₂²⋊C₄	—	53	1	no	—
977	C₂×C₂²⋊C₄	—	53	1	no	—
978	C₂×C₂²⋊C₄	—	53	1	no	—
979	C₂×C₂²⋊C₄	—	53	1	no	—
980	C₂×C₂²⋊C₄	—	53	1	no	—
981	C₂×C₂²⋊C₄	—	53	1	no	—
982	C₂×C₂²⋊C₄	—	53	1	no	—
983	C₂×C₂²⋊C₄	—	53	1	no	—
984	C₂×C₂²⋊C₄	—	53	1	no	—
985	C₂×C₂²⋊C₄	—	53	1	no	—
986	C₂×C₂²⋊C₄	—	53	1	no	—
987	C₂×C₂²⋊C₄	—	53	1	no	—
988	C₂×C₂²⋊C₄	—	53	1	no	—
989	C₂×C₂²⋊C₄	—	53	1	no	—
990	C₂×C₂²⋊C₄	—	106	4	no	—
991	C₂×C₂²⋊C₄	—	106	4	no	—
992	C₂×C₂²⋊C₄	—	106	4	no	—
993	C₂×C₂²⋊C₄	—	106	4	no	—
994	C₂×C₂²⋊C₄	—	106	4	no	—
995	C₂×C₂²⋊C₄	—	212	2	no	—
996	C₂×C₂²⋊C₄	—	212	2	no	—
997	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	1	no	—
1006	C₂×C₄²	—	53	1	no	—
1007	C₂×C₄²	—	53	1	no	—
1008	C₂×C₄²	—	53	1	no	—
1009	C₂×C₄²	—	53	1	no	—
1010	C₂×C₄²	—	53	1	no	—
1011	C₂×C₄²	—	53	1	no	—
1012	C₂×C₄²	—	53	1	no	—
1013	C₂×C₄²	—	53	1	no	—
1014	C₂×C₄²	—	53	1	no	—
1015	C₂×C₄²	—	53	1	no	—
1016	C₂×C₄²	—	53	1	no	—
1017	C₂×C₄²	—	53	1	no	—
1018	C₂×C₄²	—	53	1	no	—
1019	C₂×C₄²	—	106	4	no	—
1020	C₂×C₄²	—	106	4	no	—
1021	C₂×C₄²	—	212	2	no	—
1022	C₂×C₄²	—	212	2	no	—
1023	C₂×C₄²	—	212	2	no	—
1024	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1029	#95	—	53	1	no	—
1030	#95	—	53	1	no	—
1031	#95	—	53	1	no	—
1032	#95	—	53	1	no	—
1033	#95	—	53	1	no	—
1034	#95	—	53	1	no	—
1035	#95	—	53	1	no	—
1036	#95	—	53	1	no	—
1037	#95	—	53	1	no	—
1038	#95	—	53	1	no	—
1039	#95	—	53	1	no	—
1040	#95	—	53	1	no	—
1041	#95	—	53	1	no	—
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	C₂²×D₅₃	1	1	yes	characteristic
1072	#95	C₂²×D₅₃	1	1	yes	characteristic
1073	#95	C₂²×D₅₃	1	1	yes	characteristic
1074	#95	C₂²×D₅₃	1	1	yes	characteristic
1075	#95	C₂²×D₅₃	1	1	yes	characteristic
1076	#95	C₂²×D₅₃	1	1	yes	characteristic
1077	#95	C₂²×D₅₃	1	1	yes	characteristic
1078	#95	C₂²×D₅₃	1	1	yes	characteristic
1079	#95	C₂²×D₅₃	1	1	yes	characteristic
1080	#95	C₂²×D₅₃	1	1	yes	characteristic
1081	#95	C₂²×D₅₃	1	1	yes	characteristic
1082	#95	C₂²×D₅₃	1	1	yes	characteristic
1083	#95	C₂²×D₅₃	1	1	yes	characteristic
1084	#95	C₂²×D₅₃	1	1	yes	characteristic
1085	C₂⁴	—	53	1	no	—
1086	C₂⁴	—	53	1	no	—
1087	C₂⁴	—	106	2	no	—
1088	C₂⁴	—	106	2	no	—
1089	C₂⁴	—	106	2	no	—
1090	C₂⁴	—	106	2	no	—
1091	C₂⁴	—	106	2	no	—
1092	C₂⁴	—	106	2	no	—
1093	C₂⁴	—	106	2	no	—
1094	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1095	C₂²×C₄	—	53	1	no	—
1096	C₂²×C₄	—	53	1	no	—
1097	C₂²×C₄	—	53	1	no	—
1098	C₂²×C₄	—	53	1	no	—
1099	C₂²×C₄	—	53	1	no	—
1100	C₂²×C₄	—	53	4	no	—
1101	C₂²×C₄	—	53	4	no	—
1102	C₂²×C₄	—	53	4	no	—
1103	C₂²×C₄	—	53	4	no	—
1104	C₂²×C₄	—	53	4	no	—
1105	C₂²×C₄	—	53	1	no	—
1106	C₂²×C₄	—	53	1	no	—
1107	C₂²×C₄	—	53	1	no	—
1108	C₂²×C₄	—	53	1	no	—
1109	C₂²×C₄	—	53	1	no	—
1110	C₂²×C₄	—	53	1	no	—
1111	C₂²×C₄	—	53	1	no	—
1112	C₂²×C₄	—	53	1	no	—
1113	C₂²×C₄	—	53	1	no	—
1114	C₂²×C₄	—	106	2	no	—
1115	C₂²×C₄	—	106	2	no	—
1116	C₂²×C₄	—	106	2	no	—
1117	C₂²×C₄	—	106	2	no	—
1118	C₂²×C₄	—	106	2	no	—
1119	C₂²×C₄	—	106	2	no	—
1120	C₂²×C₄	—	106	2	no	—
1121	C₂²×C₄	—	106	2	no	—
1122	C₂²×C₄	—	106	2	no	—
1123	C₂²×C₄	—	106	2	no	—
1124	C₂²×C₄	—	106	2	no	—
1125	C₂²×C₄	—	106	2	no	—
1126	C₂²×C₄	—	106	2	no	—
1127	C₂²×C₄	—	106	2	no	—
1128	C₂²×C₄	—	106	2	no	—
1129	C₂²×C₄	—	106	2	no	—
1130	C₂²×C₄	—	106	2	no	—
1131	C₂²×C₄	—	106	2	no	—
1132	C₂²×C₄	—	106	2	no	—
1133	C₂²×C₄	—	106	2	no	—
1134	C₂²×C₄	—	106	2	no	—
1135	C₂²×C₄	—	106	2	no	—
1136	C₂²×C₄	—	106	2	no	—
1137	C₂²×C₄	—	106	2	no	—
1138	C₂²×C₄	—	106	2	no	—
1139	C₂²×C₄	—	106	2	no	—
1140	C₂²×C₄	—	106	2	no	—
1141	C₂²×C₄	—	106	2	no	—
1142	C₂²×C₄	—	106	2	no	—
1143	C₂²×C₄	—	106	2	no	—
1144	C₂²×C₄	—	106	2	no	—
1145	C₂²×C₄	—	106	2	no	—
1146	C₂²×C₄	—	106	2	no	—
1147	C₂²×C₄	—	106	2	no	—
1148	C₂²×C₄	—	106	2	no	—
1149	C₂²×C₄	—	106	2	no	—
1150	C₂²×C₄	—	106	2	no	—
1151	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1152	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1153	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1154	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1155	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1156	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1157	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1158	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1159	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1161	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1162	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1163	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1164	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	2	no	—
1167	C₄⋊C₄	—	2	2	no	—
1168	C₄⋊C₄	—	2	2	no	—
1169	C₄⋊C₄	—	2	2	no	—
1170	C₄⋊C₄	—	2	2	no	—
1171	C₄⋊C₄	—	2	2	no	—
1172	C₄⋊C₄	—	2	2	no	—
1173	C₄⋊C₄	—	4	1	no	—
1174	C₄⋊C₄	—	106	2	no	—
1175	C₄⋊C₄	—	106	2	no	—
1176	C₄⋊C₄	—	106	2	no	—
1177	C₄⋊C₄	—	106	2	no	—
1178	C₄⋊C₄	—	106	2	no	—
1179	C₄⋊C₄	—	106	2	no	—
1180	C₄⋊C₄	—	106	2	no	—
1181	C₄⋊C₄	—	106	2	no	—
1182	C₄⋊C₄	—	106	2	no	—
1183	C₄⋊C₄	—	106	2	no	—
1184	C₄⋊C₄	—	106	2	no	—
1185	C₄⋊C₄	—	106	2	no	—
1186	C₄⋊C₄	—	106	2	no	—
1187	C₄⋊C₄	—	106	2	no	—
1188	C₄⋊C₄	—	106	2	no	—
1189	C₄⋊C₄	—	106	2	no	—
1190	C₄⋊C₄	—	106	2	no	—
1191	C₄⋊C₄	—	106	2	no	—
1192	C₄⋊C₄	—	106	2	no	—
1193	C₄⋊C₄	—	106	2	no	—
1194	C₄⋊C₄	—	106	2	no	—
1195	C₄⋊C₄	—	106	2	no	—
1196	C₄⋊C₄	—	106	2	no	—
1197	C₄⋊C₄	—	106	2	no	—
1198	C₄⋊C₄	—	212	1	no	—
1199	C₄⋊C₄	—	212	1	no	—
1200	C₄⋊C₄	—	212	1	no	—
1201	C₂²⋊C₄	—	2	2	no	—
1202	C₂²⋊C₄	—	2	2	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	2	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	4	1	no	—
1207	C₂²⋊C₄	—	4	1	no	—
1208	C₂²⋊C₄	—	106	2	no	—
1209	C₂²⋊C₄	—	106	2	no	—
1210	C₂²⋊C₄	—	106	2	no	—
1211	C₂²⋊C₄	—	106	2	no	—
1212	C₂²⋊C₄	—	106	2	no	—
1213	C₂²⋊C₄	—	106	2	no	—
1214	C₂²⋊C₄	—	106	2	no	—
1215	C₂²⋊C₄	—	106	2	no	—
1216	C₂²⋊C₄	—	106	2	no	—
1217	C₂²⋊C₄	—	106	2	no	—
1218	C₂²⋊C₄	—	106	2	no	—
1219	C₂²⋊C₄	—	106	2	no	—
1220	C₂²⋊C₄	—	106	2	no	—
1221	C₂²⋊C₄	—	106	2	no	—
1222	C₂²⋊C₄	—	106	2	no	—
1223	C₂²⋊C₄	—	212	1	no	—
1224	C₂²⋊C₄	—	212	1	no	—
1225	C₂²⋊C₄	—	212	1	no	—
1226	C₂²⋊C₄	—	212	1	no	—
1227	C₂²⋊C₄	—	212	1	no	—
1228	C₂²⋊C₄	—	212	1	no	—
1229	C₄²	—	2	2	no	—
1230	C₄²	—	2	2	no	—
1231	C₄²	—	4	1	no	—
1232	C₄²	—	4	1	no	—
1233	C₄²	—	4	1	no	—
1234	C₄²	—	106	2	no	—
1235	C₄²	—	106	2	no	—
1236	C₄²	—	106	2	no	—
1237	C₄²	—	106	2	no	—
1238	C₄²	—	106	2	no	—
1239	C₄²	—	106	2	no	—
1240	C₄²	—	212	1	no	—
1241	C₄²	—	212	1	no	—
1242	C₄²	—	212	1	no	—
1243	C₄²	—	212	1	no	—
1244	C₄²	—	212	1	no	—
1245	C₄²	—	212	1	no	—
1246	C₄²	—	212	1	no	—
1247	C₄²	—	212	1	no	—
1248	C₄²	—	212	1	no	—
1249	C₂³	—	2	1	no	—
1250	C₂³	—	2	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	53	2	no	—
1257	C₂³	—	53	2	no	—
1258	C₂³	—	53	2	no	—
1259	C₂³	—	53	2	no	—
1260	C₂³	—	53	2	no	—
1261	C₂³	—	53	2	no	—
1262	C₂³	—	53	2	no	—
1263	C₂³	—	106	1	no	—
1264	C₂³	—	106	1	no	—
1265	C₂³	—	106	1	no	—
1266	C₂³	—	106	1	no	—
1267	C₂³	—	106	1	no	—
1268	C₂³	—	106	1	no	—
1269	C₂³	—	106	1	no	—
1270	C₂³	—	212	4	no	—
1271	C₂³	—	212	4	no	—
1272	C₂³	—	212	4	no	—
1273	C₂³	—	212	4	no	—
1274	C₂³	—	212	4	no	—
1275	C₂³	—	212	4	no	—
1276	C₂³	—	212	4	no	—
1277	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1278	C₂×C₄	—	2	1	no	—
1279	C₂×C₄	—	2	1	no	—
1280	C₂×C₄	—	2	1	no	—
1281	C₂×C₄	—	2	1	no	—
1282	C₂×C₄	—	2	1	no	—
1283	C₂×C₄	—	2	1	no	—
1284	C₂×C₄	—	2	1	no	—
1285	C₂×C₄	—	2	1	no	—
1286	C₂×C₄	—	2	1	no	—
1287	C₂×C₄	—	2	1	no	—
1288	C₂×C₄	—	2	1	no	—
1289	C₂×C₄	—	2	1	no	—
1290	C₂×C₄	—	2	1	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	53	2	no	—
1316	C₂×C₄	—	53	2	no	—
1317	C₂×C₄	—	53	2	no	—
1318	C₂×C₄	—	53	2	no	—
1319	C₂×C₄	—	53	2	no	—
1320	C₂×C₄	—	106	8	no	—
1321	C₂×C₄	—	106	8	no	—
1322	C₂×C₄	—	106	8	no	—
1323	C₂×C₄	—	106	8	no	—
1324	C₂×C₄	—	106	8	no	—
1325	C₂×C₄	—	106	1	no	—
1326	C₂×C₄	—	106	1	no	—
1327	C₂×C₄	—	106	1	no	—
1328	C₂×C₄	—	106	1	no	—
1329	C₂×C₄	—	106	1	no	—
1330	C₂×C₄	—	106	1	no	—
1331	C₂×C₄	—	106	1	no	—
1332	C₂×C₄	—	106	1	no	—
1333	C₂×C₄	—	106	1	no	—
1334	C₂×C₄	—	106	1	no	—
1335	C₂×C₄	—	106	1	no	—
1336	C₂×C₄	—	106	1	no	—
1337	C₂×C₄	—	106	1	no	—
1338	C₂×C₄	—	106	1	no	—
1339	C₂×C₄	—	106	1	no	—
1340	C₂×C₄	—	106	1	no	—
1341	C₂×C₄	—	106	1	no	—
1342	C₂×C₄	—	106	1	no	—
1343	C₂×C₄	—	106	1	no	—
1344	C₂×C₄	—	106	1	no	—
1345	C₂×C₄	—	106	1	no	—
1346	C₂×C₄	—	106	1	no	—
1347	C₂×C₄	—	106	1	no	—
1348	C₂×C₄	—	106	1	no	—
1349	C₂×C₄	—	106	1	no	—
1350	C₂×C₄	—	106	1	no	—
1351	C₂×C₄	—	106	1	no	—
1352	C₂×C₄	—	106	1	no	—
1353	C₂×C₄	—	106	1	no	—
1354	C₂×C₄	—	106	1	no	—
1355	C₂×C₄	—	106	1	no	—
1356	C₂×C₄	—	106	1	no	—
1357	C₂×C₄	—	106	1	no	—
1358	C₂×C₄	—	106	1	no	—
1359	C₂×C₄	—	106	1	no	—
1360	C₂×C₄	—	106	1	no	—
1361	C₂×C₄	—	106	1	no	—
1362	C₂×C₄	—	212	4	no	—
1363	C₂×C₄	—	212	4	no	—
1364	C₂×C₄	—	212	4	no	—
1365	C₂×C₄	—	212	4	no	—
1366	C₂×C₄	—	212	4	no	—
1367	C₂×C₄	—	212	4	no	—
1368	C₂×C₄	—	212	4	no	—
1369	C₂×C₄	—	212	4	no	—
1370	C₂×C₄	—	212	4	no	—
1371	C₂×C₄	#41×D₅₃	1	2	yes	—
1372	C₂×C₄	#41×D₅₃	1	2	yes	—
1373	C₂×C₄	#41×D₅₃	1	2	yes	—
1374	C₂×C₄	#41×D₅₃	1	2	yes	—
1375	C₂×C₄	#41×D₅₃	1	2	yes	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	1	no	—
1378	C₂²	—	4	1	no	—
1379	C₂²	—	4	1	no	—
1380	C₂²	—	4	1	no	—
1381	C₂²	—	4	1	no	—
1382	C₂²	—	4	1	no	—
1383	C₂²	—	53	4	no	—
1384	C₂²	—	53	4	no	—
1385	C₂²	—	53	4	no	—
1386	C₂²	—	53	4	no	—
1387	C₂²	—	53	4	no	—
1388	C₂²	—	53	4	no	—
1389	C₂²	—	53	4	no	—
1390	C₂²	—	424	8	no	—
1391	C₂²	—	212	1	no	—
1392	C₂²	—	212	1	no	—
1393	C₂²	—	212	1	no	—
1394	C₂²	—	212	1	no	—
1395	C₂²	—	212	1	no	—
1396	C₂²	—	212	1	no	—
1397	C₂²	—	212	1	no	—
1398	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1399	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1400	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1401	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1402	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1403	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1404	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1405	C₄	—	2	2	no	—
1406	C₄	—	2	2	no	—
1407	C₄	—	2	2	no	—
1408	C₄	—	2	2	no	—
1409	C₄	—	2	2	no	—
1410	C₄	—	4	1	no	—
1411	C₄	—	4	1	no	—
1412	C₄	—	4	1	no	—
1413	C₄	—	4	1	no	—
1414	C₄	—	4	1	no	—
1415	C₄	—	4	1	no	—
1416	C₄	—	4	1	no	—
1417	C₄	—	4	1	no	—
1418	C₄	—	4	1	no	—
1419	C₄	—	106	2	no	—
1420	C₄	—	106	2	no	—
1421	C₄	—	106	2	no	—
1422	C₄	—	106	2	no	—
1423	C₄	—	106	2	no	—
1424	C₄	—	212	1	no	—
1425	C₄	—	212	1	no	—
1426	C₄	—	212	1	no	—
1427	C₄	—	212	1	no	—
1428	C₄	—	212	1	no	—
1429	C₄	—	212	1	no	—
1430	C₄	—	212	1	no	—
1431	C₄	—	212	1	no	—
1432	C₄	—	212	1	no	—
1433	C₂	—	8	1	no	—
1434	C₂	—	53	8	no	—
1435	C₂	—	424	1	no	—
1436	C₂	#529×D₅₃	1	1	yes	characteristic
1437	C₂	#529×D₅₃	1	1	yes	characteristic
1438	C₂	#539×D₅₃	1	1	yes	characteristic
1439	C₂	#552×D₅₃	1	1	yes	characteristic
1440	C₂	#553×D₅₃	1	1	yes	characteristic
1441	C₂	#556×D₅₃	1	1	yes	characteristic
1442	C₂	#559×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2596	C₂
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2596	D₅₃
hypocenter	C₅₃	C₂×#2596
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2596

Complements

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

N	H ≅ G/N	type
1. #20280258	C₂	semidirect
2. #20280257	C₂	semidirect
3. #20280256	C₂	semidirect
4. #20280255	C₂	semidirect
5. #20280254	C₂	semidirect
6. #20280253	C₂	semidirect
7. #20280252	C₂	semidirect
8. #20280251	C₂	semidirect
9. #20280250	C₂	semidirect
10. #20280249	C₂	semidirect
11. #20280248	C₂	semidirect
12. #20280247	C₂	semidirect
13. #20280246	C₂	semidirect
14. #20280245	C₂	semidirect
15. #20280244	C₂	semidirect
16. #400×D₅₃	C₂	semidirect
17. #400×D₅₃	C₂	semidirect
20. #389×D₅₃	C₂	semidirect
26. #387×D₅₃	C₂	semidirect
27. #387×D₅₃	C₂	semidirect
28. #387×D₅₃	C₂	semidirect
29. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
30. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2596	C₂	semidirect
53. #16810565	C₂²	semidirect
54. #16810565	C₂²	semidirect
55. #16810565	C₂²	semidirect
56. #16810565	C₂²	semidirect
57. #16810564	C₂²	semidirect
58. #16810564	C₂²	semidirect
59. #16810564	C₂²	semidirect
60. #16810564	C₂²	semidirect
61. #16810563	C₂²	semidirect
62. #16810563	C₂²	semidirect
63. #16810562	C₂²	semidirect
64. #16810562	C₂²	semidirect
65. #16810561	C₂²	semidirect
66. #16810561	C₂²	semidirect
81. #16810522	C₂²	semidirect
82. #16810521	C₂²	semidirect
83. #16810520	C₂²	semidirect
84. #16810520	C₂²	semidirect
85. #16810519	C₂²	semidirect
86. #16810518	C₂²	semidirect
87. #16810518	C₂²	semidirect
123. #16810510	C₂²	semidirect
124. #16810510	C₂²	semidirect
125. #16810510	C₂²	semidirect
126. #16810509	C₂²	semidirect
127. #16810509	C₂²	semidirect
128. #16810509	C₂²	semidirect
129. #16810508	C₂²	semidirect
130. #16810508	C₂²	semidirect
131. #16810508	C₂²	semidirect
132. #16810507	C₂²	semidirect
133. #16810507	C₂²	semidirect
134. #16810507	C₂²	semidirect
135. #16810506	C₂²	semidirect
136. #16810506	C₂²	semidirect
137. #16810506	C₂²	semidirect
138. #16810505	C₂²	semidirect
139. #16810505	C₂²	semidirect
140. #16810505	C₂²	semidirect
141. #16810504	C₂²	semidirect
142. #16810504	C₂²	semidirect
143. #16810504	C₂²	semidirect
144. C₄⋊C₄×Dic₅₃	C₂²	semidirect
145. C₄⋊C₄×Dic₅₃	C₂²	semidirect
146. C₄⋊C₄×Dic₅₃	C₂²	semidirect
147. C₄⋊C₄×Dic₅₃	C₂²	semidirect
148. C₄×#11719919	C₂²	semidirect
149. C₄×#11719919	C₂²	semidirect
150. C₄×#11719919	C₂²	semidirect
151. C₄×#11719919	C₂²	semidirect
152. C₄×C₄⋊Dic₅₃	C₂²	semidirect
153. C₄×C₄⋊Dic₅₃	C₂²	semidirect
154. #16810474	C₂²	semidirect
155. #16810474	C₂²	semidirect
156. #16810474	C₂²	semidirect
157. #16810474	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
173. C₅₃×#400	C₂²	semidirect
176. C₅₃×#389	C₂²	semidirect
182. C₅₃×#387	C₂²	semidirect
183. C₅₃×#387	C₂²	semidirect
184. C₅₃×#387	C₂²	semidirect
185. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
727. #2596	D₅₃	direct (N × H)
752. D₅₃	#2596	direct (N × H)
788. #400	C₂×D₅₃	semidirect
789. #400	C₂×D₅₃	semidirect
813. #389	C₂×D₅₃	semidirect
875. #387	C₂×D₅₃	semidirect
876. #387	C₂×D₅₃	semidirect
877. #387	C₂×D₅₃	semidirect
892. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
893. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
908. C₅₃	C₂×#2596	semidirect

Maximal subgroups

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

subgroup	index
#20280258	2
#20280257	2
#20280256	2
#20280255	2
#20280254	2
#20280253	2
#20280252	2
#20280251	2
#20280250	2
#20280249	2
#20280248	2
#20280247	2
#20280246	2
#20280245	2
#20280244	2
#400×D₅₃	2
#399×D₅₃	2
#397×D₅₃	2
#389×D₅₃	2
#388×D₅₃	2
#387×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₅₃×#2596	2
C₂×#2596	53

Subgroups — D53×#2596 #27554637

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2596 #27554637