Subgroups — #28249379

Order 13568.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288306	C₂	1	1	yes	maximal, characteristic
2	#20283884	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283880	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283879	C₂	1	1	yes	maximal, characteristic, complemented
5	#20283869	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283868	C₂	1	1	yes	maximal, characteristic, complemented
7	#20283862	C₂	1	1	yes	maximal, characteristic, complemented
8	#20283861	C₂	1	1	yes	maximal, characteristic, complemented
9	#20283855	C₂	1	1	yes	maximal, characteristic, complemented
10	#20283854	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283853	C₂	1	1	yes	maximal, characteristic, complemented
12	#20283852	C₂	1	1	yes	maximal, characteristic, complemented
13	#20283842	C₂	1	1	yes	maximal, characteristic, complemented
14	#20283835	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283829	C₂	1	1	yes	maximal, characteristic, complemented
16	#20283827	C₂	1	1	yes	maximal, characteristic, complemented
17	#20283667	C₂	1	1	yes	maximal, characteristic, complemented
18	#446×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#20283460	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283456	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283456	C₂	1	1	yes	maximal, characteristic, complemented
22	#20283429	C₂	1	1	yes	maximal, characteristic, complemented
23	#20283429	C₂	1	1	yes	maximal, characteristic, complemented
24	#20283424	C₂	1	1	yes	maximal, characteristic, complemented
25	#20283363	C₂	1	1	yes	maximal, characteristic, complemented
26	#20283361	C₂	1	1	yes	maximal, characteristic, complemented
27	#20283356	C₂	1	1	yes	maximal, characteristic, complemented
28	#20283284	C₂	1	1	yes	maximal, characteristic, complemented
29	#20283282	C₂	1	1	yes	maximal, characteristic, complemented
30	#20283282	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133225	C₂²	1	1	yes	characteristic
33	C₂×#13133225	C₂²	1	1	yes	characteristic
34	C₂×#13133225	C₂²	1	1	yes	characteristic
35	C₂×#13133225	C₂²	1	1	yes	characteristic
36	C₂×#13133223	C₂²	1	1	yes	characteristic
37	C₂×#13133223	C₂²	1	1	yes	characteristic
38	#16811357	C₄	1	1	yes	characteristic
39	#16811357	C₄	1	1	yes	characteristic
40	#16811355	C₄	1	1	yes	characteristic
41	#16811350	C₄	1	1	yes	characteristic
42	#16811344	C₄	1	1	yes	characteristic
43	#16811340	C₄	1	1	yes	characteristic
44	#16811340	C₄	1	1	yes	characteristic
45	#16811326	C₄	1	1	yes	characteristic
46	#16811324	C₄	1	1	yes	characteristic
47	#16811324	C₄	1	1	yes	characteristic
48	#16811320	C₄	1	1	yes	characteristic
49	#16811318	C₄	1	1	yes	characteristic
50	#16811318	C₄	1	1	yes	characteristic
51	#16811291	C₄	1	1	yes	characteristic
52	#16811283	C₄	1	1	yes	characteristic
53	#16811281	C₄	1	1	yes	characteristic
54	#16811170	C₂²	1	1	yes	characteristic
55	#16811170	C₂²	1	1	yes	characteristic
56	#16811170	C₂²	1	1	yes	characteristic
57	#16811160	C₂²	1	1	yes	characteristic
58	#16811153	C₂²	1	1	yes	characteristic
59	#16811153	C₂²	1	1	yes	characteristic
60	#16811151	C₂²	1	1	yes	characteristic
61	#16811151	C₂²	1	1	yes	characteristic
62	C₄×#11719945	C₂²	1	1	yes	characteristic
63	C₄×#11719945	C₂²	1	1	yes	characteristic
64	#16811091	C₂²	1	1	yes	characteristic
65	#16811091	C₂²	1	1	yes	characteristic
66	C₄×#11719947	C₂²	1	1	yes	characteristic
67	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
68	#16810754	C₂²	1	1	yes	characteristic
69	#16810754	C₂²	1	1	yes	characteristic
70	#16810753	C₂²	1	1	yes	characteristic
71	#16810752	C₂²	1	1	yes	characteristic
72	#16810752	C₂²	1	1	yes	characteristic
73	#16810752	C₂²	1	1	yes	characteristic
74	#16810752	C₂²	1	1	yes	characteristic
75	#16810751	C₂²	1	1	yes	characteristic
76	#16810751	C₂²	1	1	yes	characteristic
77	#16810751	C₂²	1	1	yes	characteristic
78	#16810751	C₂²	1	1	yes	characteristic
79	#16810750	C₂²	1	1	yes	characteristic
80	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
81	#16810747	C₂²	1	1	yes	characteristic
82	#16810702	C₂²	1	1	yes	characteristic
83	#16810700	C₂²	1	1	yes	characteristic
84	#16810699	C₂²	1	1	yes	characteristic
85	#16810699	C₂²	1	1	yes	characteristic
86	#16810699	C₂²	1	1	yes	characteristic
87	#16810699	C₂²	1	1	yes	characteristic
88	#16810698	C₂²	1	1	yes	characteristic
89	#16810698	C₂²	1	1	yes	characteristic
90	#16810697	C₂²	1	1	yes	characteristic
91	#16810697	C₂²	1	1	yes	characteristic
92	#16810696	C₂²	1	1	yes	characteristic
93	#16810696	C₂²	1	1	yes	characteristic
94	#16810696	C₂²	1	1	yes	characteristic
95	#16810696	C₂²	1	1	yes	characteristic
96	#16810695	C₂²	1	1	yes	characteristic
97	#16810695	C₂²	1	1	yes	characteristic
98	#16810695	C₂²	1	1	yes	characteristic
99	#16810695	C₂²	1	1	yes	characteristic
100	#16810694	C₂²	1	1	yes	characteristic
101	#16810694	C₂²	1	1	yes	characteristic
102	#16810693	C₂²	1	1	yes	characteristic
103	#16810693	C₂²	1	1	yes	characteristic
104	#16810693	C₂²	1	1	yes	characteristic
105	#16810693	C₂²	1	1	yes	characteristic
106	#16810692	C₂²	1	1	yes	characteristic
107	#16810692	C₂²	1	1	yes	characteristic
108	#16810692	C₂²	1	1	yes	characteristic
109	#16810692	C₂²	1	1	yes	characteristic
110	#16810691	C₂²	1	1	yes	characteristic
111	#16810691	C₂²	1	1	yes	characteristic
112	#16810691	C₂²	1	1	yes	characteristic
113	#16810691	C₂²	1	1	yes	characteristic
114	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
115	D₄×#88322	C₂²	1	1	yes	characteristic
116	D₄×#88322	C₂²	1	1	yes	characteristic
117	#16810688	C₂²	1	1	yes	characteristic
118	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
119	C₈×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
120	#16810686	C₂²	1	1	yes	characteristic
121	#16810686	C₂²	1	1	yes	characteristic
122	#16810686	C₂²	1	1	yes	characteristic
123	#16810686	C₂²	1	1	yes	characteristic
124	#16810685	C₂²	1	1	yes	characteristic
125	#16810685	C₂²	1	1	yes	characteristic
126	#16810684	C₂²	1	1	yes	characteristic
127	#16810684	C₂²	1	1	yes	characteristic
128	#16810683	C₂²	1	1	yes	characteristic
129	#16810683	C₂²	1	1	yes	characteristic
130	#16810682	C₂²	1	1	yes	characteristic
131	#16810682	C₂²	1	1	yes	characteristic
132	#16810681	C₂²	1	1	yes	characteristic
133	#16810681	C₂²	1	1	yes	characteristic
134	#16810680	C₂²	1	1	yes	characteristic
135	#16810679	C₂²	1	1	yes	characteristic
136	#16810679	C₂²	1	1	yes	characteristic
137	#16810678	C₂²	1	1	yes	characteristic
138	#16810678	C₂²	1	1	yes	characteristic
139	#16810677	C₂²	1	1	yes	characteristic
140	#16810677	C₂²	1	1	yes	characteristic
141	#16810675	C₂²	1	1	yes	characteristic
142	#16810675	C₂²	1	1	yes	characteristic
143	#16810673	C₂²	1	1	yes	characteristic
144	#16810673	C₂²	1	1	yes	characteristic
145	#16810651	C₂²	1	1	yes	characteristic
146	#16810651	C₂²	1	1	yes	characteristic
147	#16810650	C₂²	1	1	yes	characteristic
148	#16810650	C₂²	1	1	yes	characteristic
149	#16810648	C₂²	1	1	yes	characteristic
150	#16810648	C₂²	1	1	yes	characteristic
151	#16810648	C₂²	1	1	yes	characteristic
152	#16810648	C₂²	1	1	yes	characteristic
153	#16810648	C₂²	1	1	yes	characteristic
154	#16810648	C₂²	1	1	yes	characteristic
155	#16810648	C₂²	1	1	yes	characteristic
156	#16810648	C₂²	1	1	yes	characteristic
157	#16810648	C₂²	1	1	yes	characteristic
158	#16810648	C₂²	1	1	yes	characteristic
159	#16810646	C₂²	1	1	yes	characteristic
160	#16810646	C₂²	1	1	yes	characteristic
161	#16810645	C₂²	1	1	yes	characteristic
162	#16810645	C₂²	1	1	yes	characteristic
163	#16810645	C₂²	1	1	yes	characteristic
164	#16810645	C₂²	1	1	yes	characteristic
165	#16810645	C₂²	1	1	yes	characteristic
166	#16810645	C₂²	1	1	yes	characteristic
167	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
168	C₂×#13133146	C₂²	1	1	yes	characteristic
169	C₂×#13133146	C₂²	1	1	yes	characteristic
170	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
171	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
172	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
173	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
174	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
175	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
176	#16810588	C₂²	1	1	yes	characteristic
177	#16810588	C₂²	1	1	yes	characteristic
178	#16810588	C₂²	1	1	yes	characteristic
179	#16810588	C₂²	1	1	yes	characteristic
180	#16810588	C₂²	1	1	yes	characteristic
181	#16810588	C₂²	1	1	yes	characteristic
182	#16810575	C₂²	1	1	yes	characteristic
183	#16810575	C₂²	1	1	yes	characteristic
184	C₄×#11719912	C₂²	1	1	yes	characteristic
185	#97×D₅₃	C₂²	1	1	yes	characteristic
186	#97×D₅₃	C₂²	1	1	yes	characteristic
187	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
188	C₅₃×#529	C₂²	1	1	yes	characteristic
189	C₅₃×#446	C₂²	1	1	yes	characteristic
190	C₅₃×#446	C₂²	1	1	yes	characteristic
191	C₅₃×#436	C₂²	1	1	yes	characteristic
192	C₅₃×#436	C₂²	1	1	yes	characteristic
193	C₅₃×#435	C₂²	1	1	yes	characteristic
194	C₅₃×#435	C₂²	1	1	yes	characteristic
195	C₅₃×#435	C₂²	1	1	yes	characteristic
196	C₅₃×#435	C₂²	1	1	yes	characteristic
197	C₅₃×#433	C₂²	1	1	yes	characteristic
198	C₅₃×#433	C₂²	1	1	yes	characteristic
199	C₅₃×#432	C₂²	1	1	yes	characteristic
200	C₅₃×#424	C₂²	1	1	yes	characteristic
201	C₅₃×#424	C₂²	1	1	yes	characteristic
202	C₅₃×#423	C₂²	1	1	yes	characteristic
203	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
204	C₂×#11719945	C₂³	1	1	yes	characteristic
205	C₂×#11719945	C₂³	1	1	yes	characteristic
206	C₂×#11719945	C₂³	1	1	yes	characteristic
207	C₂×#11719947	C₂×C₄	1	1	yes	characteristic
208	C₂×Q₈×D₅₃	C₂×C₄	1	1	yes	characteristic
209	#13133225	—	4	2	no	—
210	#13133225	—	4	2	no	—
211	#13133225	—	4	2	no	—
212	#13133225	—	4	2	no	—
213	#13133223	—	4	2	no	—
214	#13133223	—	4	2	no	—
215	C₂×#11719917	C₂³	1	1	yes	characteristic
216	C₂×#11719917	C₂³	1	1	yes	characteristic
217	C₂×#11719912	C₂³	1	1	yes	characteristic
218	C₂×#11719912	C₂³	1	1	yes	characteristic
219	C₂×#11719912	C₂³	1	1	yes	characteristic
220	C₂×#11719912	C₂³	1	1	yes	characteristic
221	C₂×#11719912	C₂³	1	1	yes	characteristic
222	C₂×#11719912	C₂³	1	1	yes	characteristic
223	C₂×#11719912	C₂³	1	1	yes	characteristic
224	C₂×#11719912	C₂³	1	1	yes	characteristic
225	C₂×#11719912	C₂³	1	1	yes	characteristic
226	C₂×#11719912	C₂³	1	1	yes	characteristic
227	C₂²×#88322	C₂³	1	1	yes	characteristic
228	C₂²×#88322	C₂³	1	1	yes	characteristic
229	C₂²×#88322	C₂³	1	1	yes	characteristic
230	C₂²×#88322	C₂³	1	1	yes	characteristic
231	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
241	#13133216	C₂×C₄	1	1	yes	characteristic
242	#13133216	C₂×C₄	1	1	yes	characteristic
243	#13133216	C₂×C₄	1	1	yes	characteristic
244	#13133213	C₂×C₄	1	1	yes	characteristic
245	#13133213	C₂×C₄	1	1	yes	characteristic
246	#13133213	C₂×C₄	1	1	yes	characteristic
247	#13133212	C₂×C₄	1	1	yes	characteristic
248	#13133212	C₂×C₄	1	1	yes	characteristic
249	#13133212	C₂×C₄	1	1	yes	characteristic
250	#13133212	C₂×C₄	1	1	yes	characteristic
251	#13133212	C₂×C₄	1	1	yes	characteristic
252	#13133212	C₂×C₄	1	1	yes	characteristic
253	#13133210	C₂×C₄	1	1	yes	characteristic
254	#13133210	C₂×C₄	1	1	yes	characteristic
255	#13133210	C₂×C₄	1	1	yes	characteristic
256	#13133210	C₂×C₄	1	1	yes	characteristic
257	#13133208	C₂×C₄	1	1	yes	characteristic
258	#13133207	C₂×C₄	1	1	yes	characteristic
259	#13133207	C₂×C₄	1	1	yes	characteristic
260	#13133207	C₂×C₄	1	1	yes	characteristic
261	#13133207	C₂×C₄	1	1	yes	characteristic
262	#13133206	C₂×C₄	1	1	yes	characteristic
263	#13133203	C₂×C₄	1	1	yes	characteristic
264	#13133203	C₂×C₄	1	1	yes	characteristic
265	#13133203	C₂×C₄	1	1	yes	characteristic
266	#13133203	C₂×C₄	1	1	yes	characteristic
267	#13133203	C₂×C₄	1	1	yes	characteristic
268	#13133203	C₂×C₄	1	1	yes	characteristic
269	#13133203	C₂×C₄	1	1	yes	characteristic
270	#13133203	C₂×C₄	1	1	yes	characteristic
271	#13133203	C₂×C₄	1	1	yes	characteristic
272	#13133203	C₂×C₄	1	1	yes	characteristic
273	#13133202	C₂×C₄	1	1	yes	characteristic
274	#13133202	C₂×C₄	1	1	yes	characteristic
275	#13133202	C₂×C₄	1	1	yes	characteristic
276	#13133202	C₂×C₄	1	1	yes	characteristic
277	#13133201	C₂×C₄	1	1	yes	characteristic
278	#13133201	C₂×C₄	1	1	yes	characteristic
279	#13133199	C₂×C₄	1	1	yes	characteristic
280	#13133199	C₂×C₄	1	1	yes	characteristic
281	#13133198	C₂×C₄	1	1	yes	characteristic
282	#13133198	C₂×C₄	1	1	yes	characteristic
283	#13133195	C₂×C₄	1	1	yes	characteristic
284	#13133195	C₂×C₄	1	1	yes	characteristic
285	#13133194	C₂×C₄	1	1	yes	characteristic
286	#13133194	C₂×C₄	1	1	yes	characteristic
287	#13133193	C₂×C₄	1	1	yes	characteristic
288	#13133192	C₂×C₄	1	1	yes	characteristic
289	#13133192	C₂×C₄	1	1	yes	characteristic
290	#13133192	C₂×C₄	1	1	yes	characteristic
291	#13133192	C₂×C₄	1	1	yes	characteristic
292	#13133190	C₂×C₄	1	1	yes	characteristic
293	#13133190	C₂×C₄	1	1	yes	characteristic
294	#13133190	C₂×C₄	1	1	yes	characteristic
295	#13133190	C₂×C₄	1	1	yes	characteristic
296	#13133190	C₂×C₄	1	1	yes	characteristic
297	#13133190	C₂×C₄	1	1	yes	characteristic
298	#13133190	C₂×C₄	1	1	yes	characteristic
299	#13133190	C₂×C₄	1	1	yes	characteristic
300	#13133189	C₂×C₄	1	1	yes	characteristic
301	#13133189	C₂×C₄	1	1	yes	characteristic
302	#13133188	C₂×C₄	1	1	yes	characteristic
303	#13133188	C₂×C₄	1	1	yes	characteristic
304	#13133188	C₂×C₄	1	1	yes	characteristic
305	Q₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
306	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
307	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
308	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
309	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
310	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
311	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
312	#13133182	C₂×C₄	1	1	yes	characteristic
313	#13133182	C₂×C₄	1	1	yes	characteristic
314	#13133182	C₂×C₄	1	1	yes	characteristic
315	#13133182	C₂×C₄	1	1	yes	characteristic
316	#13133182	C₂×C₄	1	1	yes	characteristic
317	#13133182	C₂×C₄	1	1	yes	characteristic
318	#13133182	C₂×C₄	1	1	yes	characteristic
319	#13133182	C₂×C₄	1	1	yes	characteristic
320	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
321	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
322	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
323	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
324	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
325	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
326	D₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
327	#13133179	C₂×C₄	1	1	yes	characteristic
328	#13133179	C₂×C₄	1	1	yes	characteristic
329	#13133179	C₂×C₄	1	1	yes	characteristic
330	#13133179	C₂×C₄	1	1	yes	characteristic
331	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
332	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
333	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
334	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
335	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
336	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
337	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
338	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
339	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
340	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
341	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
342	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
343	#13133177	C₂×C₄	1	1	yes	characteristic
344	#13133177	C₂×C₄	1	1	yes	characteristic
345	#13133177	C₂×C₄	1	1	yes	characteristic
346	#13133177	C₂×C₄	1	1	yes	characteristic
347	#13133177	C₂×C₄	1	1	yes	characteristic
348	#13133177	C₂×C₄	1	1	yes	characteristic
349	#13133177	C₂×C₄	1	1	yes	characteristic
350	#13133177	C₂×C₄	1	1	yes	characteristic
351	#13133177	C₂×C₄	1	1	yes	characteristic
352	#13133177	C₂×C₄	1	1	yes	characteristic
353	#13133176	C₂×C₄	1	1	yes	characteristic
354	#13133176	C₂³	1	1	yes	characteristic
355	#13133175	C₂×C₄	1	1	yes	characteristic
356	#13133174	C₂×C₄	1	1	yes	characteristic
357	#13133174	C₂×C₄	1	1	yes	characteristic
358	#13133174	C₂³	1	1	yes	characteristic
359	#13133174	C₂³	1	1	yes	characteristic
360	#13133174	C₂³	1	1	yes	characteristic
361	#13133174	C₂³	1	1	yes	characteristic
362	#13133173	C₂×C₄	1	1	yes	characteristic
363	#13133173	C₂×C₄	1	1	yes	characteristic
364	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
365	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
366	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
367	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
369	C₄²×D₅₃	C₂³	1	1	yes	characteristic
370	C₄²×D₅₃	C₂³	1	1	yes	characteristic
371	C₄²×D₅₃	C₂³	1	1	yes	characteristic
372	C₄²×D₅₃	C₂³	1	1	yes	characteristic
373	C₄²×D₅₃	C₂³	1	1	yes	characteristic
374	C₄²×D₅₃	C₂³	1	1	yes	characteristic
375	C₄⋊#88322	C₂³	1	1	yes	characteristic
376	C₄⋊#88322	C₂³	1	1	yes	characteristic
377	C₄⋊#88322	C₂³	1	1	yes	characteristic
378	C₄⋊#88322	C₂³	1	1	yes	characteristic
379	C₄⋊#88322	C₂³	1	1	yes	characteristic
380	C₄⋊#88322	C₂³	1	1	yes	characteristic
381	C₄⋊#88322	C₂³	1	1	yes	characteristic
382	C₄⋊#88322	C₂³	1	1	yes	characteristic
383	C₄⋊#88322	C₂³	1	1	yes	characteristic
384	C₄⋊#88322	C₂³	1	1	yes	characteristic
385	#13133146	C₂³	1	1	yes	characteristic
386	#13133146	C₂³	1	1	yes	characteristic
387	#13133146	C₂³	1	1	yes	characteristic
388	#13133146	C₂³	1	1	yes	characteristic
389	#13133146	C₂³	1	1	yes	characteristic
390	#13133146	C₂³	1	1	yes	characteristic
391	#13133146	C₂³	1	1	yes	characteristic
392	#13133146	C₂³	1	1	yes	characteristic
393	#13133146	C₂³	1	1	yes	characteristic
394	#13133146	C₂³	1	1	yes	characteristic
395	#13133146	C₂³	1	1	yes	characteristic
396	#13133146	C₂³	1	1	yes	characteristic
397	#13133146	C₂³	1	1	yes	characteristic
398	#13133146	C₂³	1	1	yes	characteristic
399	#13133146	C₂³	1	1	yes	characteristic
400	#13133146	C₂³	1	1	yes	characteristic
401	#13133146	C₂³	1	1	yes	characteristic
402	#13133146	C₂³	1	1	yes	characteristic
403	#13133146	C₂³	1	1	yes	characteristic
404	#13133146	C₂³	1	1	yes	characteristic
405	C₂²⋊#88322	C₂³	1	1	yes	characteristic
406	C₂²⋊#88322	C₂³	1	1	yes	characteristic
407	C₂²⋊#88322	C₂³	1	1	yes	characteristic
408	C₂²⋊#88322	C₂³	1	1	yes	characteristic
409	C₂²⋊#88322	C₂³	1	1	yes	characteristic
410	C₂²⋊#88322	C₂³	1	1	yes	characteristic
411	#13133129	C₂³	1	1	yes	characteristic
412	#13133129	C₂³	1	1	yes	characteristic
413	#13133129	C₂³	1	1	yes	characteristic
414	#13133129	C₂³	1	1	yes	characteristic
415	#13133129	C₂³	1	1	yes	characteristic
416	#13133129	C₂³	1	1	yes	characteristic
417	#13133129	C₂³	1	1	yes	characteristic
418	#13133129	C₂³	1	1	yes	characteristic
419	#13133129	C₂³	1	1	yes	characteristic
420	#13133129	C₂³	1	1	yes	characteristic
421	#13133129	C₂³	1	1	yes	characteristic
422	#13133129	C₂³	1	1	yes	characteristic
423	#13133128	C₂³	1	1	yes	characteristic
424	#13133128	C₂³	1	1	yes	characteristic
425	#13133128	C₂³	1	1	yes	characteristic
426	#13133128	C₂³	1	1	yes	characteristic
427	#13133127	C₂³	1	1	yes	characteristic
428	#13133127	C₂³	1	1	yes	characteristic
429	#13133127	C₂³	1	1	yes	characteristic
430	#13133127	C₂³	1	1	yes	characteristic
431	#13133127	C₂³	1	1	yes	characteristic
432	#13133127	C₂³	1	1	yes	characteristic
433	C₄×#88322	C₂³	1	1	yes	characteristic
434	C₄×#88322	C₂³	1	1	yes	characteristic
435	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
436	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
437	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
438	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
439	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
440	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
441	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
442	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
443	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
444	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
445	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
446	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
447	#126×C₅₃	C₂×C₄	1	1	yes	characteristic
448	#126×C₅₃	C₂×C₄	1	1	yes	characteristic
449	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
450	#124×C₅₃	C₂×C₄	1	1	yes	characteristic
451	#123×C₅₃	C₂×C₄	1	1	yes	characteristic
452	#123×C₅₃	C₂×C₄	1	1	yes	characteristic
453	C₂²⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
454	#121×C₅₃	C₂×C₄	1	1	yes	characteristic
455	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
456	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
457	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
458	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
459	#117×C₅₃	C₂³	1	1	yes	characteristic
460	#117×C₅₃	C₂³	1	1	yes	characteristic
461	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
462	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
463	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
464	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
465	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
466	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
467	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
468	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
469	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
470	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
471	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	#97×C₅₃	C₂³	1	1	yes	characteristic
479	#97×C₅₃	C₂³	1	1	yes	characteristic
480	#97×C₅₃	C₂³	1	1	yes	characteristic
481	#97×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
485	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
486	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
487	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
488	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
489	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
490	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
491	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
492	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
493	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
494	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
495	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
496	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
497	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
498	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
499	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
500	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
501	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
502	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
503	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
504	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
505	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
506	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
507	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
508	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
509	Q₈×D₅₃	—	4	2	no	—
510	#11719947	—	4	2	no	—
511	#11719945	—	2	2	no	—
512	#11719945	—	2	2	no	—
513	#11719945	—	2	2	no	—
514	#11719945	—	2	2	no	—
515	#11719945	—	2	2	no	—
516	#11719945	—	2	2	no	—
517	#11719945	—	4	2	no	—
518	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
519	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
520	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
521	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
522	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
523	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
524	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
525	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
526	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
527	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
528	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
529	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
530	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
531	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
532	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
533	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
534	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
535	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
536	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
539	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
540	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
541	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
542	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
543	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
544	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
545	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
546	M₁₆×C₅₃	—	4	1	no	—
547	M₁₆×C₅₃	—	4	1	no	—
548	M₁₆×C₅₃	—	4	1	no	—
549	M₁₆×C₅₃	—	4	1	no	—
550	C₂×C₈×C₅₃	—	4	1	no	—
551	C₂×C₈×C₅₃	—	4	1	no	—
552	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
553	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
554	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
555	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
556	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
558	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
561	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
562	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
563	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
564	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
565	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
566	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
567	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
568	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
569	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
570	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
571	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
572	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
573	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
574	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
575	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
576	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
577	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
578	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
579	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
580	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
581	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
582	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
583	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
584	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
586	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
587	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
588	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
589	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
590	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
591	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
592	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
593	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
594	#11719921	C₂²×C₄	1	1	yes	characteristic
595	#11719921	C₂²×C₄	1	1	yes	characteristic
596	#11719921	C₂²×C₄	1	1	yes	characteristic
597	#11719921	C₂²×C₄	1	1	yes	characteristic
598	#11719921	C₂²×C₄	1	1	yes	characteristic
599	#11719921	C₂²×C₄	1	1	yes	characteristic
600	#11719921	C₂²×C₄	1	1	yes	characteristic
601	#11719921	C₂²×C₄	1	1	yes	characteristic
602	#11719921	C₂²×C₄	1	1	yes	characteristic
603	#11719921	C₂²×C₄	1	1	yes	characteristic
604	#11719921	C₂²×C₄	1	1	yes	characteristic
605	#11719921	C₂²×C₄	1	1	yes	characteristic
606	#11719921	C₂²×C₄	1	1	yes	characteristic
607	#11719921	C₂²×C₄	1	1	yes	characteristic
608	#11719921	C₂²×C₄	1	1	yes	characteristic
609	#11719921	C₂²×C₄	1	1	yes	characteristic
610	#11719921	C₂²×C₄	1	1	yes	characteristic
611	#11719921	C₂²×C₄	1	1	yes	characteristic
612	#11719921	C₂²×C₄	1	1	yes	characteristic
613	#11719921	C₂²×C₄	1	1	yes	characteristic
614	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
615	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
616	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
617	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
618	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
619	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
620	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
621	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
622	#11719919	C₂²×C₄	1	1	yes	characteristic
623	#11719919	C₂²×C₄	1	1	yes	characteristic
624	#11719919	C₂²×C₄	1	1	yes	characteristic
625	#11719919	C₂²×C₄	1	1	yes	characteristic
626	#11719919	C₂²×C₄	1	1	yes	characteristic
627	#11719919	C₂²×C₄	1	1	yes	characteristic
628	#11719919	C₂²×C₄	1	1	yes	characteristic
629	#11719919	C₂²×C₄	1	1	yes	characteristic
630	#11719919	C₂²×C₄	1	1	yes	characteristic
631	#11719919	C₂²×C₄	1	1	yes	characteristic
632	#11719919	C₂²×C₄	1	1	yes	characteristic
633	#11719919	C₂²×C₄	1	1	yes	characteristic
634	#11719919	C₂²×C₄	1	1	yes	characteristic
635	#11719919	C₂²×C₄	1	1	yes	characteristic
636	#11719919	C₂²×C₄	1	1	yes	characteristic
637	#11719919	C₂²×C₄	1	1	yes	characteristic
638	#11719919	C₂²×C₄	1	1	yes	characteristic
639	#11719919	C₂²×C₄	1	1	yes	characteristic
640	#11719919	C₂²×C₄	1	1	yes	characteristic
641	#11719919	C₂²×C₄	1	1	yes	characteristic
642	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
643	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
644	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
645	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
646	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
647	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
648	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
649	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
650	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
651	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
652	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
653	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
654	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
655	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
656	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
657	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
658	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
659	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
660	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
661	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
662	#11719917	—	4	1	no	—
663	#11719917	—	4	1	no	—
664	C₂×#88322	—	4	1	no	—
665	C₂×#88322	—	4	1	no	—
666	C₂×#88322	—	4	1	no	—
667	C₂×#88322	—	4	1	no	—
668	C₂×#88322	C₂⁴	1	1	yes	characteristic
669	C₂×#88322	C₂⁴	1	1	yes	characteristic
670	C₂×#88322	C₂⁴	1	1	yes	characteristic
671	C₂×#88322	C₂⁴	1	1	yes	characteristic
672	C₂×#88322	C₂⁴	1	1	yes	characteristic
673	C₂×#88322	C₂⁴	1	1	yes	characteristic
674	C₂×#88322	C₂⁴	1	1	yes	characteristic
675	C₂×#88322	C₂⁴	1	1	yes	characteristic
676	#11719912	—	2	2	no	—
677	#11719912	—	2	2	no	—
678	#11719912	—	2	2	no	—
679	#11719912	—	2	2	no	—
680	#11719912	—	4	1	no	—
681	#11719912	—	4	1	no	—
682	#11719912	—	4	1	no	—
683	#11719912	—	4	1	no	—
684	#11719912	—	4	1	no	—
685	#11719912	—	4	1	no	—
686	C₈×D₅₃	—	2	2	no	—
687	C₈×D₅₃	—	2	2	no	—
688	C₈×D₅₃	—	2	2	no	—
689	C₈×D₅₃	—	2	2	no	—
690	C₈×D₅₃	—	4	1	no	—
691	C₈×D₅₃	—	4	1	no	—
692	C₈×D₅₃	—	4	1	no	—
693	C₈×D₅₃	—	4	1	no	—
694	C₈×D₅₃	—	4	1	no	—
695	C₈×D₅₃	—	4	1	no	—
696	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
697	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
698	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
699	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
700	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
701	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
702	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
703	Q₈×C₅₃	—	4	1	no	—
704	D₄×C₅₃	—	4	1	no	—
705	D₄×C₅₃	—	4	1	no	—
706	D₄×C₅₃	—	4	1	no	—
707	C₂×C₄×C₅₃	—	2	1	no	—
708	C₂×C₄×C₅₃	—	2	1	no	—
709	C₂×C₄×C₅₃	—	2	1	no	—
710	C₂×C₄×C₅₃	—	2	1	no	—
711	C₂×C₄×C₅₃	—	2	1	no	—
712	C₂×C₄×C₅₃	—	2	1	no	—
713	C₂×C₄×C₅₃	—	4	1	no	—
714	C₂×C₄×C₅₃	—	4	1	no	—
715	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
716	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
717	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
718	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
719	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
720	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
721	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
722	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
723	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
724	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
725	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
726	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
727	C₂²⋊D₅₃	—	2	2	no	—
728	C₂²⋊D₅₃	—	2	2	no	—
729	C₂²⋊D₅₃	—	2	2	no	—
730	C₂²⋊D₅₃	—	2	2	no	—
731	C₂²⋊D₅₃	—	2	2	no	—
732	C₂²⋊D₅₃	—	2	2	no	—
733	C₂²⋊D₅₃	—	2	2	no	—
734	C₂²⋊D₅₃	—	2	2	no	—
735	C₂²⋊D₅₃	—	4	1	no	—
736	C₂²⋊D₅₃	—	4	1	no	—
737	C₂²⋊D₅₃	—	4	1	no	—
738	C₂²⋊D₅₃	—	4	1	no	—
739	C₂×Dic₅₃	—	2	2	no	—
740	C₂×Dic₅₃	—	4	1	no	—
741	C₂×Dic₅₃	—	4	1	no	—
742	C₂×Dic₅₃	—	4	1	no	—
743	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
744	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
745	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
746	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
747	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
748	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
749	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
750	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
751	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
752	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
753	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
754	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
755	D₂₁₂	—	2	2	no	—
756	D₂₁₂	—	2	2	no	—
757	D₂₁₂	—	2	2	no	—
758	D₂₁₂	—	4	1	no	—
759	D₂₁₂	—	4	1	no	—
760	D₂₁₂	—	4	1	no	—
761	C₄×D₅₃	—	2	1	no	—
762	C₄×D₅₃	—	2	1	no	—
763	C₄×D₅₃	—	2	1	no	—
764	C₄×D₅₃	—	2	1	no	—
765	C₄×D₅₃	—	2	1	no	—
766	C₄×D₅₃	—	2	1	no	—
767	C₄×D₅₃	—	2	2	no	—
768	C₄×D₅₃	—	2	2	no	—
769	C₄×D₅₃	—	4	1	no	—
770	C₄×D₅₃	—	4	1	no	—
771	C₄×D₅₃	—	4	1	no	—
772	C₄×D₅₃	—	4	1	no	—
773	C₄×D₅₃	—	4	1	no	—
774	C₄×D₅₃	—	4	1	no	—
775	C₄×D₅₃	—	4	1	no	—
776	C₄×D₅₃	—	4	1	no	—
777	C₄×D₅₃	—	4	1	no	—
778	C₄×D₅₃	—	4	1	no	—
779	C₄×D₅₃	H(5,𝔽₂)	1	2	yes	—
780	C₄×D₅₃	2₋¹⁺⁴	1	2	yes	—
781	Dic₁₀₆	—	2	2	no	—
782	Dic₁₀₆	—	2	2	no	—
783	Dic₁₀₆	—	2	2	no	—
784	Dic₁₀₆	—	2	2	no	—
785	Dic₁₀₆	—	2	2	no	—
786	Dic₁₀₆	—	4	1	no	—
787	C₈×C₅₃	—	2	1	no	—
788	C₈×C₅₃	—	2	1	no	—
789	C₈×C₅₃	—	2	1	no	—
790	C₈×C₅₃	—	2	1	no	—
791	C₈×C₅₃	—	2	1	no	—
792	C₈×C₅₃	—	2	1	no	—
793	C₈×C₅₃	—	2	1	no	—
794	C₈×C₅₃	—	2	1	no	—
795	#88322	—	2	1	no	—
796	#88322	—	2	1	no	—
797	#88322	—	2	1	no	—
798	#88322	—	2	1	no	—
799	#88322	—	2	1	no	—
800	#88322	—	2	1	no	—
801	#88322	—	2	1	no	—
802	#88322	—	2	1	no	—
803	#60275	—	53	1	no	maximal, Sylow
804	C₂²×C₅₃	—	2	1	no	—
805	C₂²×C₅₃	—	2	1	no	—
806	C₂²×C₅₃	—	2	1	no	—
807	C₂²×C₅₃	—	2	1	no	—
808	C₂²×C₅₃	—	2	1	no	—
809	C₂²×C₅₃	—	2	1	no	—
810	C₂²×C₅₃	—	2	1	no	—
811	C₂²×C₅₃	—	2	1	no	—
812	C₂²×C₅₃	—	2	1	no	—
813	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
814	C₂×D₅₃	—	2	1	no	—
815	C₂×D₅₃	—	2	1	no	—
816	C₂×D₅₃	—	2	1	no	—
817	C₂×D₅₃	—	2	1	no	—
818	C₂×D₅₃	—	2	1	no	—
819	C₂×D₅₃	—	2	1	no	—
820	C₂×D₅₃	—	2	1	no	—
821	C₂×D₅₃	—	2	1	no	—
822	C₂×D₅₃	—	2	1	no	—
823	C₂×D₅₃	—	2	1	no	—
824	C₂×D₅₃	—	2	1	no	—
825	C₂×D₅₃	#520	1	2	yes	—
826	C₄×C₅₃	—	2	1	no	—
827	C₄×C₅₃	—	2	1	no	—
828	C₄×C₅₃	—	2	1	no	—
829	C₄×C₅₃	—	2	1	no	—
830	C₄×C₅₃	—	2	1	no	—
831	C₄×C₅₃	—	2	1	no	—
832	C₄×C₅₃	—	2	1	no	—
833	C₄×C₅₃	—	2	1	no	—
834	C₄×C₅₃	—	2	1	no	—
835	C₄×C₅₃	—	2	1	no	—
836	C₄×C₅₃	—	2	1	no	—
837	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
838	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
839	Dic₅₃	—	2	1	no	—
840	Dic₅₃	—	2	1	no	—
841	Dic₅₃	—	2	1	no	—
842	Dic₅₃	—	2	1	no	—
843	Dic₅₃	—	2	1	no	—
844	Dic₅₃	—	2	1	no	—
845	Dic₅₃	—	2	1	no	—
846	Dic₅₃	—	2	1	no	—
847	Dic₅₃	—	2	1	no	—
848	Dic₅₃	—	2	1	no	—
849	Dic₅₃	#520	1	2	yes	—
850	Dic₅₃	#568	1	2	yes	—
851	#3480	—	53	1	no	—
852	#2995	—	53	1	no	—
853	#2995	—	53	1	no	—
854	#2995	—	53	1	no	—
855	#2995	D₅₃	1	1	yes	characteristic, complemented
856	#2994	—	53	1	no	—
857	#2994	—	53	1	no	—
858	#2993	—	53	1	no	—
859	#2993	—	53	1	no	—
860	#2992	—	53	1	no	—
861	#2992	—	53	1	no	—
862	#2992	—	53	1	no	—
863	#2992	—	53	1	no	—
864	#2990	—	53	1	no	—
865	#2990	—	53	1	no	—
866	#2989	—	53	1	no	—
867	#2989	—	53	1	no	—
868	Q₈×M₁₆	—	53	1	no	—
869	C₂×#446	—	53	1	no	—
870	#2935	—	53	1	no	—
871	#2935	—	53	1	no	—
872	#2935	—	53	1	no	—
873	#2932	—	53	1	no	—
874	#2932	—	53	1	no	—
875	#2931	—	53	1	no	—
876	#2923	—	53	1	no	—
877	#2923	—	53	1	no	—
878	#2922	—	53	1	no	—
879	#2906	—	53	1	no	—
880	#2906	—	53	1	no	—
881	#2906	—	53	1	no	—
882	C₂×C₅₃	—	4	1	no	—
883	C₂×C₅₃	—	4	1	no	—
884	C₂×C₅₃	—	4	1	no	—
885	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
886	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
887	C₂×C₅₃	#3573	1	1	yes	characteristic
888	D₅₃	—	2	2	no	—
889	D₅₃	—	4	1	no	—
890	D₅₃	—	4	1	no	—
891	D₅₃	—	4	1	no	—
892	C₂×#131	—	53	1	no	—
893	C₂×#131	—	53	1	no	—
894	C₂×#131	—	53	1	no	—
895	C₂×#131	—	53	1	no	—
896	C₂×#131	—	53	1	no	—
897	C₂×#131	—	53	1	no	—
898	#559	—	53	1	no	—
899	#559	—	53	1	no	—
900	#559	—	53	1	no	—
901	#557	—	53	1	no	—
902	#556	—	53	1	no	—
903	#556	—	53	1	no	—
904	#556	—	53	1	no	—
905	#553	—	53	1	no	—
906	#553	—	53	1	no	—
907	#553	—	53	1	no	—
908	#553	—	53	1	no	—
909	#553	—	53	1	no	—
910	#553	—	53	1	no	—
911	#550	—	53	1	no	—
912	#548	—	53	1	no	—
913	#548	—	53	1	no	—
914	#532	—	53	1	no	—
915	#532	—	53	1	no	—
916	#532	—	53	1	no	—
917	#529	—	53	1	no	—
918	#529	—	53	1	no	—
919	#529	—	53	1	no	—
920	#529	—	53	1	no	—
921	#529	—	53	1	no	—
922	#529	C₂×D₅₃	1	1	yes	characteristic
923	C₄×#41	—	53	1	no	—
924	C₄×#41	—	53	1	no	—
925	C₄×#41	—	53	1	no	—
926	C₄×#41	—	53	1	no	—
927	C₄×#41	—	53	1	no	—
928	C₂×C₄×Q₈	—	53	1	no	—
929	#446	—	53	1	no	—
930	#446	—	53	1	no	—
931	#446	—	53	1	no	—
932	#446	—	53	1	no	—
933	#446	—	53	1	no	—
934	#446	—	53	1	no	—
935	#446	—	53	1	no	—
936	#446	—	53	1	no	—
937	#446	—	53	1	no	—
938	#446	—	53	1	no	—
939	#446	—	53	1	no	—
940	#446	—	53	1	no	—
941	#446	C₂×D₅₃	1	1	yes	characteristic
942	#446	C₂×D₅₃	1	1	yes	characteristic
943	C₈×Q₈	—	53	1	no	—
944	C₈×Q₈	—	53	1	no	—
945	#436	—	53	1	no	—
946	#436	—	53	1	no	—
947	#436	—	53	1	no	—
948	#436	—	53	1	no	—
949	#436	—	53	1	no	—
950	#436	—	53	1	no	—
951	#436	—	53	1	no	—
952	#436	—	53	1	no	—
953	#436	C₂×D₅₃	1	1	yes	characteristic
954	#436	C₂×D₅₃	1	1	yes	characteristic
955	#435	—	53	1	no	—
956	#435	—	53	1	no	—
957	#435	—	53	1	no	—
958	#435	—	53	1	no	—
959	#435	—	53	1	no	—
960	#435	—	53	1	no	—
961	#435	—	53	1	no	—
962	#435	—	53	1	no	—
963	#435	—	53	1	no	—
964	#435	—	53	1	no	—
965	#435	—	53	1	no	—
966	#435	—	53	1	no	—
967	#435	—	53	1	no	—
968	#435	—	53	1	no	—
969	#435	—	53	1	no	—
970	#435	—	53	1	no	—
971	#435	—	53	1	no	—
972	#435	—	53	1	no	—
973	#435	—	53	1	no	—
974	#435	—	53	1	no	—
975	#435	—	53	1	no	—
976	#435	—	53	1	no	—
977	#435	—	53	1	no	—
978	#435	—	53	1	no	—
979	#435	C₂×D₅₃	1	1	yes	characteristic
980	#435	C₂×D₅₃	1	1	yes	characteristic
981	#435	C₂×D₅₃	1	1	yes	characteristic
982	#435	C₂×D₅₃	1	1	yes	characteristic
983	C₈×D₄	—	53	1	no	—
984	C₈×D₄	—	53	1	no	—
985	C₈×D₄	—	53	1	no	—
986	C₈×D₄	—	53	1	no	—
987	C₈×D₄	—	53	1	no	—
988	C₈×D₄	—	53	1	no	—
989	C₈×D₄	—	53	1	no	—
990	C₈×D₄	—	53	1	no	—
991	C₈×D₄	—	53	1	no	—
992	C₈×D₄	—	53	1	no	—
993	#433	—	53	1	no	—
994	#433	—	53	1	no	—
995	#433	—	53	1	no	—
996	#433	—	53	1	no	—
997	#433	—	53	1	no	—
998	#433	—	53	1	no	—
999	#433	—	53	1	no	—
1000	#433	—	53	1	no	—
1001	#433	—	53	1	no	—
1002	#433	—	53	1	no	—
1003	#433	C₂×D₅₃	1	1	yes	characteristic
1004	#433	C₂×D₅₃	1	1	yes	characteristic
1005	#432	—	53	1	no	—
1006	#432	—	53	1	no	—
1007	#432	—	53	1	no	—
1008	#432	—	53	1	no	—
1009	#432	—	53	1	no	—
1010	#432	—	53	1	no	—
1011	#432	—	53	1	no	—
1012	#432	C₂×D₅₃	1	1	yes	characteristic
1013	#431	—	53	1	no	—
1014	#431	—	53	1	no	—
1015	#431	—	53	1	no	—
1016	#431	—	53	1	no	—
1017	#424	—	53	1	no	—
1018	#424	—	53	1	no	—
1019	#424	—	53	1	no	—
1020	#424	—	53	1	no	—
1021	#424	—	53	1	no	—
1022	#424	—	53	1	no	—
1023	#424	—	53	1	no	—
1024	#424	—	53	1	no	—
1025	#424	—	53	1	no	—
1026	#424	—	53	1	no	—
1027	#424	—	53	1	no	—
1028	#424	—	53	1	no	—
1029	#424	—	53	1	no	—
1030	#424	—	53	1	no	—
1031	#424	C₂×D₅₃	1	1	yes	characteristic
1032	#424	C₂×D₅₃	1	1	yes	characteristic
1033	#423	—	53	1	no	—
1034	#423	—	53	1	no	—
1035	#423	—	53	1	no	—
1036	#423	—	53	1	no	—
1037	#423	—	53	1	no	—
1038	#423	—	53	1	no	—
1039	#423	—	53	1	no	—
1040	#423	—	53	1	no	—
1041	#423	C₂×D₅₃	1	1	yes	characteristic
1042	C₂×C₄⋊C₈	—	53	1	no	—
1043	C₂×C₄⋊C₈	—	53	1	no	—
1044	C₂×C₄⋊C₈	—	53	1	no	—
1045	C₂×C₄⋊C₈	—	53	1	no	—
1046	C₂×C₄⋊C₈	—	53	1	no	—
1047	C₂×C₄⋊C₈	—	53	1	no	—
1048	C₂×C₄⋊C₈	—	53	1	no	—
1049	C₂×C₄⋊C₈	—	53	1	no	—
1050	C₂×C₄⋊C₈	—	53	1	no	—
1051	#408	—	53	1	no	—
1052	#408	—	53	1	no	—
1053	#408	—	53	1	no	—
1054	#408	—	53	1	no	—
1055	#408	—	53	1	no	—
1056	#408	—	53	1	no	—
1057	C₄×M₁₆	—	53	1	no	—
1058	C₄×M₁₆	—	53	1	no	—
1059	C₄×M₁₆	—	53	1	no	—
1060	C₂×#97	—	53	1	no	—
1061	C₂×#97	—	53	1	no	—
1062	C₂×C₄×C₈	—	53	1	no	—
1063	C₅₃	#60275	1	1	yes	characteristic, complemented, Sylow
1064	C₂×#41	—	53	1	no	—
1065	C₂×#41	—	53	1	no	—
1066	C₂×#41	—	53	1	no	—
1067	C₂×#41	—	53	1	no	—
1068	C₂×#41	—	53	1	no	—
1069	C₂²×Q₈	—	53	1	no	—
1070	#131	—	212	2	no	—
1071	#131	—	212	2	no	—
1072	#131	—	212	2	no	—
1073	#131	—	212	2	no	—
1074	#131	—	212	2	no	—
1075	#131	—	212	2	no	—
1076	C₂×M₁₆	—	53	1	no	—
1077	C₂×M₁₆	—	53	1	no	—
1078	C₂×M₁₆	—	53	1	no	—
1079	C₂×M₁₆	—	53	1	no	—
1080	C₂×M₁₆	—	53	1	no	—
1081	C₂×M₁₆	—	53	1	no	—
1082	C₂×M₁₆	—	53	1	no	—
1083	C₂×M₁₆	—	53	1	no	—
1084	C₂×M₁₆	—	53	1	no	—
1085	C₂×M₁₆	—	53	1	no	—
1086	C₂×M₁₆	—	53	1	no	—
1087	C₂×M₁₆	—	53	1	no	—
1088	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1089	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1090	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1091	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1092	C₂²×C₈	—	53	1	no	—
1093	C₂²×C₈	—	53	1	no	—
1094	C₂²×C₈	—	53	1	no	—
1095	C₂²×C₈	—	53	1	no	—
1096	C₂²×C₈	—	53	1	no	—
1097	C₂²×C₈	—	53	1	no	—
1098	C₂²×C₈	—	53	1	no	—
1099	C₂²×C₈	—	53	1	no	—
1100	C₂²×C₈	—	53	1	no	—
1101	C₂²×C₈	—	53	1	no	—
1102	C₂²×C₈	—	53	1	no	—
1103	C₂²×C₈	—	53	1	no	—
1104	C₂²×C₈	—	53	1	no	—
1105	C₂²×C₈	—	53	1	no	—
1106	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1107	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1108	C₄⋊Q₈	—	53	1	no	—
1109	C₄⋊Q₈	—	53	1	no	—
1110	C₄⋊Q₈	—	53	1	no	—
1111	#127	—	53	1	no	—
1112	#127	—	53	1	no	—
1113	#127	—	53	1	no	—
1114	#126	—	53	1	no	—
1115	#126	—	53	1	no	—
1116	#126	—	53	1	no	—
1117	#126	—	53	1	no	—
1118	#126	—	53	1	no	—
1119	#126	—	53	1	no	—
1120	#126	—	53	1	no	—
1121	#126	—	53	1	no	—
1122	#126	—	53	1	no	—
1123	#126	—	53	1	no	—
1124	#126	C₄×D₅₃	1	1	yes	characteristic
1125	#126	C₄×D₅₃	1	1	yes	characteristic
1126	#125	—	53	1	no	—
1127	#125	—	53	1	no	—
1128	#125	—	53	1	no	—
1129	#125	—	53	1	no	—
1130	#125	—	53	1	no	—
1131	#125	C₄×D₅₃	1	1	yes	characteristic
1132	#124	—	53	1	no	—
1133	#124	—	53	1	no	—
1134	#124	—	53	1	no	—
1135	#124	—	53	1	no	—
1136	#124	—	53	1	no	—
1137	#124	—	53	1	no	—
1138	#124	—	53	1	no	—
1139	#124	—	53	1	no	—
1140	#124	—	53	1	no	—
1141	#124	—	53	1	no	—
1142	#124	—	53	1	no	—
1143	#124	C₄×D₅₃	1	1	yes	characteristic
1144	#123	—	53	1	no	—
1145	#123	—	53	1	no	—
1146	#123	—	53	1	no	—
1147	#123	—	53	1	no	—
1148	#123	—	53	1	no	—
1149	#123	—	53	1	no	—
1150	#123	—	53	1	no	—
1151	#123	—	53	1	no	—
1152	#123	—	53	1	no	—
1153	#123	—	53	1	no	—
1154	#123	C₄×D₅₃	1	1	yes	characteristic
1155	#123	C₄×D₅₃	1	1	yes	characteristic
1156	C₂²⋊Q₈	—	53	1	no	—
1157	C₂²⋊Q₈	—	53	1	no	—
1158	C₂²⋊Q₈	—	53	1	no	—
1159	C₂²⋊Q₈	—	53	1	no	—
1160	C₂²⋊Q₈	—	53	1	no	—
1161	C₂²⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
1162	#121	—	53	1	no	—
1163	#121	—	53	1	no	—
1164	#121	—	53	1	no	—
1165	#121	—	53	1	no	—
1166	#121	—	53	1	no	—
1167	#121	—	53	1	no	—
1168	#121	—	53	1	no	—
1169	#121	—	53	1	no	—
1170	#121	—	53	1	no	—
1171	#121	—	53	1	no	—
1172	#121	—	53	1	no	—
1173	#121	—	53	1	no	—
1174	#121	—	53	1	no	—
1175	#121	—	53	1	no	—
1176	#121	—	53	1	no	—
1177	#121	—	53	1	no	—
1178	#121	—	53	1	no	—
1179	#121	C₄×D₅₃	1	1	yes	characteristic
1180	C₄×Q₈	—	53	1	no	—
1181	C₄×Q₈	—	53	1	no	—
1182	C₄×Q₈	—	53	1	no	—
1183	C₄×Q₈	—	53	1	no	—
1184	C₄×Q₈	—	53	1	no	—
1185	C₄×Q₈	—	53	1	no	—
1186	C₄×Q₈	—	53	1	no	—
1187	C₄×Q₈	—	53	1	no	—
1188	C₄×Q₈	—	53	1	no	—
1189	C₄×Q₈	—	53	1	no	—
1190	C₄×Q₈	—	53	1	no	—
1191	C₄×Q₈	—	53	1	no	—
1192	C₄×Q₈	—	53	1	no	—
1193	C₄×Q₈	—	53	1	no	—
1194	C₄×Q₈	—	53	1	no	—
1195	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1196	C₄×D₄	—	53	1	no	—
1197	C₄×D₄	—	53	1	no	—
1198	C₄×D₄	—	53	1	no	—
1199	C₄×D₄	—	53	1	no	—
1200	C₄×D₄	—	53	1	no	—
1201	C₄×D₄	—	53	1	no	—
1202	C₄×D₄	—	53	1	no	—
1203	C₄×D₄	—	53	1	no	—
1204	C₄×D₄	—	53	1	no	—
1205	C₄×D₄	—	53	1	no	—
1206	C₄×D₄	—	53	1	no	—
1207	C₄×D₄	—	53	1	no	—
1208	C₄×D₄	—	53	1	no	—
1209	C₄×D₄	—	53	1	no	—
1210	C₄×D₄	—	53	1	no	—
1211	C₄×D₄	—	53	1	no	—
1212	C₄×D₄	—	53	1	no	—
1213	C₄×D₄	—	53	1	no	—
1214	C₄×D₄	—	53	1	no	—
1215	C₄×D₄	—	53	1	no	—
1216	C₄×D₄	—	53	1	no	—
1217	C₄×D₄	—	53	1	no	—
1218	C₄×D₄	—	53	1	no	—
1219	C₄×D₄	—	53	1	no	—
1220	C₄×D₄	—	53	1	no	—
1221	C₄×D₄	—	53	1	no	—
1222	C₄×D₄	—	53	1	no	—
1223	C₄×D₄	—	53	1	no	—
1224	C₄×D₄	—	53	1	no	—
1225	C₄×D₄	—	53	1	no	—
1226	C₄×D₄	—	53	1	no	—
1227	C₄×D₄	—	53	1	no	—
1228	C₄×D₄	—	53	1	no	—
1229	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1230	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1231	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1232	#117	—	53	1	no	—
1233	#117	—	53	1	no	—
1234	#117	—	53	1	no	—
1235	#117	—	53	1	no	—
1236	#117	—	53	1	no	—
1237	#117	—	53	1	no	—
1238	#117	—	53	1	no	—
1239	#117	—	53	1	no	—
1240	#117	—	53	1	no	—
1241	#117	—	53	1	no	—
1242	#117	—	53	1	no	—
1243	#117	C₂²×D₅₃	1	1	yes	characteristic
1244	#117	C₂²×D₅₃	1	1	yes	characteristic
1245	C₂×C₄⋊C₄	—	53	1	no	—
1246	C₂×C₄⋊C₄	—	53	1	no	—
1247	C₂×C₄⋊C₄	—	53	1	no	—
1248	C₂×C₄²	—	53	1	no	—
1249	C₂×C₄²	—	53	1	no	—
1250	C₂×C₄²	—	53	1	no	—
1251	C₂×C₄²	—	53	1	no	—
1252	C₂×C₄²	—	53	1	no	—
1253	C₂×C₄²	—	53	1	no	—
1254	C₂×C₄²	—	53	1	no	—
1255	C₂×C₄²	—	53	1	no	—
1256	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1257	C₄⋊C₈	—	53	1	no	—
1258	C₄⋊C₈	—	53	1	no	—
1259	C₄⋊C₈	—	53	1	no	—
1260	C₄⋊C₈	—	53	1	no	—
1261	C₄⋊C₈	—	53	1	no	—
1262	C₄⋊C₈	—	53	1	no	—
1263	C₄⋊C₈	—	53	1	no	—
1264	C₄⋊C₈	—	53	1	no	—
1265	C₄⋊C₈	—	53	1	no	—
1266	C₄⋊C₈	—	53	1	no	—
1267	C₄⋊C₈	—	53	1	no	—
1268	C₄⋊C₈	—	53	1	no	—
1269	C₄⋊C₈	—	53	1	no	—
1270	C₄⋊C₈	—	53	1	no	—
1271	C₄⋊C₈	—	53	1	no	—
1272	C₄⋊C₈	—	53	1	no	—
1273	C₄⋊C₈	—	53	1	no	—
1274	C₄⋊C₈	—	53	1	no	—
1275	C₄⋊C₈	—	53	1	no	—
1276	C₄⋊C₈	—	53	1	no	—
1277	C₄⋊C₈	—	53	1	no	—
1278	C₄⋊C₈	—	53	1	no	—
1279	C₄⋊C₈	—	53	1	no	—
1280	C₄⋊C₈	—	53	1	no	—
1281	C₄⋊C₈	—	53	1	no	—
1282	C₄⋊C₈	—	53	1	no	—
1283	C₄⋊C₈	—	53	1	no	—
1284	C₄⋊C₈	—	53	1	no	—
1285	C₄⋊C₈	—	53	1	no	—
1286	C₄⋊C₈	—	53	1	no	—
1287	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1288	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1289	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1290	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1291	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1292	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1293	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1294	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1295	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1296	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1297	C₂²⋊C₈	—	53	1	no	—
1298	C₂²⋊C₈	—	53	1	no	—
1299	C₂²⋊C₈	—	53	1	no	—
1300	C₂²⋊C₈	—	53	1	no	—
1301	C₂²⋊C₈	—	53	1	no	—
1302	C₂²⋊C₈	—	53	1	no	—
1303	C₂²⋊C₈	—	53	1	no	—
1304	C₂²⋊C₈	—	53	1	no	—
1305	C₂²⋊C₈	—	53	1	no	—
1306	C₂²⋊C₈	—	53	1	no	—
1307	C₂²⋊C₈	—	53	1	no	—
1308	C₂²⋊C₈	—	53	1	no	—
1309	C₂²⋊C₈	—	53	1	no	—
1310	C₂²⋊C₈	—	53	1	no	—
1311	C₂²⋊C₈	—	53	1	no	—
1312	C₂²⋊C₈	—	53	1	no	—
1313	C₂²⋊C₈	—	53	1	no	—
1314	C₂²⋊C₈	—	53	1	no	—
1315	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1316	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1317	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1318	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1319	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1320	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1321	#97	—	53	1	no	—
1322	#97	—	53	1	no	—
1323	#97	—	53	1	no	—
1324	#97	—	53	1	no	—
1325	#97	—	53	1	no	—
1326	#97	—	53	1	no	—
1327	#97	—	53	1	no	—
1328	#97	—	53	1	no	—
1329	#97	—	53	1	no	—
1330	#97	—	53	1	no	—
1331	#97	C₂²×D₅₃	1	1	yes	characteristic
1332	#97	C₂²×D₅₃	1	1	yes	characteristic
1333	#97	C₂²×D₅₃	1	1	yes	characteristic
1334	#97	C₂²×D₅₃	1	1	yes	characteristic
1335	C₄×C₈	—	53	1	no	—
1336	C₄×C₈	—	53	1	no	—
1337	C₄×C₈	—	53	1	no	—
1338	C₄×C₈	—	53	1	no	—
1339	C₄×C₈	—	53	1	no	—
1340	C₄×C₈	—	53	1	no	—
1341	C₄×C₈	—	53	1	no	—
1342	C₄×C₈	—	53	1	no	—
1343	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1344	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1345	#41	—	106	2	no	—
1346	#41	—	106	2	no	—
1347	#41	—	106	2	no	—
1348	#41	—	106	2	no	—
1349	#41	—	106	2	no	—
1350	#41	—	106	2	no	—
1351	#41	—	212	2	no	—
1352	#41	—	212	2	no	—
1353	C₂×Q₈	—	53	1	no	—
1354	C₂×Q₈	—	53	1	no	—
1355	C₂×Q₈	—	53	1	no	—
1356	C₂×Q₈	—	53	1	no	—
1357	C₂×Q₈	—	53	1	no	—
1358	C₂×Q₈	—	53	1	no	—
1359	C₂×Q₈	—	212	2	no	—
1360	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
1361	C₂×D₄	—	53	1	no	—
1362	C₂×D₄	—	53	1	no	—
1363	C₂×D₄	—	53	1	no	—
1364	C₂×D₄	—	53	1	no	—
1365	C₂×D₄	—	53	1	no	—
1366	C₂×D₄	—	53	1	no	—
1367	C₂×D₄	—	53	1	no	—
1368	C₂×D₄	—	53	1	no	—
1369	C₂×D₄	—	53	1	no	—
1370	C₂×D₄	—	53	1	no	—
1371	C₂×D₄	—	53	1	no	—
1372	C₂×D₄	—	53	1	no	—
1373	C₂×D₄	—	53	1	no	—
1374	C₂×D₄	—	53	1	no	—
1375	C₂×D₄	—	53	1	no	—
1376	C₂×D₄	—	53	1	no	—
1377	C₂×D₄	—	53	1	no	—
1378	C₂×D₄	—	53	1	no	—
1379	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1380	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1381	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1382	C₂²×C₄	—	53	1	no	—
1383	C₂²×C₄	—	53	1	no	—
1384	C₂²×C₄	—	53	1	no	—
1385	C₂²×C₄	—	53	1	no	—
1386	C₂²×C₄	—	53	1	no	—
1387	C₂²×C₄	—	53	1	no	—
1388	C₂²×C₄	—	53	1	no	—
1389	C₂²×C₄	—	53	1	no	—
1390	C₂²×C₄	—	53	1	no	—
1391	C₂²×C₄	—	53	1	no	—
1392	C₂²×C₄	—	53	1	no	—
1393	C₂²×C₄	—	53	1	no	—
1394	C₂²×C₄	—	53	1	no	—
1395	C₂²×C₄	—	53	1	no	—
1396	C₂²×C₄	—	53	1	no	—
1397	C₂²×C₄	—	53	1	no	—
1398	C₂²×C₄	—	53	1	no	—
1399	C₂²×C₄	—	53	1	no	—
1400	C₂²×C₄	—	53	1	no	—
1401	C₂²×C₄	—	53	1	no	—
1402	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1403	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1404	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1405	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1406	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1407	M₁₆	—	4	1	no	—
1408	M₁₆	—	4	1	no	—
1409	M₁₆	—	4	1	no	—
1410	M₁₆	—	4	1	no	—
1411	M₁₆	—	106	2	no	—
1412	M₁₆	—	106	2	no	—
1413	M₁₆	—	106	2	no	—
1414	M₁₆	—	106	2	no	—
1415	M₁₆	—	212	1	no	—
1416	M₁₆	—	212	1	no	—
1417	M₁₆	—	212	1	no	—
1418	M₁₆	—	212	1	no	—
1419	M₁₆	—	212	1	no	—
1420	M₁₆	—	212	1	no	—
1421	M₁₆	—	212	1	no	—
1422	M₁₆	—	212	1	no	—
1423	C₂×C₈	—	4	1	no	—
1424	C₂×C₈	—	4	1	no	—
1425	C₂×C₈	—	53	1	no	—
1426	C₂×C₈	—	53	1	no	—
1427	C₂×C₈	—	53	1	no	—
1428	C₂×C₈	—	53	1	no	—
1429	C₂×C₈	—	53	1	no	—
1430	C₂×C₈	—	53	1	no	—
1431	C₂×C₈	—	53	1	no	—
1432	C₂×C₈	—	53	1	no	—
1433	C₂×C₈	—	106	2	no	—
1434	C₂×C₈	—	106	2	no	—
1435	C₂×C₈	—	106	2	no	—
1436	C₂×C₈	—	106	2	no	—
1437	C₂×C₈	—	212	1	no	—
1438	C₂×C₈	—	212	1	no	—
1439	C₂×C₈	—	212	1	no	—
1440	C₂×C₈	—	212	1	no	—
1441	C₂×C₈	—	212	1	no	—
1442	C₂×C₈	—	212	1	no	—
1443	C₂×C₈	—	212	1	no	—
1444	C₂×C₈	—	212	1	no	—
1445	C₂×C₈	—	212	1	no	—
1446	C₂×C₈	—	212	1	no	—
1447	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1448	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1449	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1450	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1451	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1452	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1453	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1454	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1455	C₄⋊C₄	—	53	1	no	—
1456	C₄⋊C₄	—	53	1	no	—
1457	C₄⋊C₄	—	53	1	no	—
1458	C₄⋊C₄	—	53	1	no	—
1459	C₄⋊C₄	—	53	1	no	—
1460	C₄⋊C₄	—	53	1	no	—
1461	C₄⋊C₄	—	53	1	no	—
1462	C₄⋊C₄	—	53	1	no	—
1463	C₄⋊C₄	—	53	1	no	—
1464	C₄⋊C₄	—	53	1	no	—
1465	C₄⋊C₄	—	53	1	no	—
1466	C₄⋊C₄	—	53	1	no	—
1467	C₄⋊C₄	—	53	1	no	—
1468	C₄⋊C₄	—	53	1	no	—
1469	C₄⋊C₄	—	53	1	no	—
1470	C₄⋊C₄	—	53	1	no	—
1471	C₄⋊C₄	—	53	1	no	—
1472	C₄⋊C₄	—	53	1	no	—
1473	C₄⋊C₄	—	53	1	no	—
1474	C₄⋊C₄	—	53	1	no	—
1475	C₄⋊C₄	—	53	1	no	—
1476	C₄⋊C₄	—	53	1	no	—
1477	C₄⋊C₄	—	53	1	no	—
1478	C₄⋊C₄	—	53	1	no	—
1479	C₄⋊C₄	—	53	1	no	—
1480	C₄⋊C₄	—	53	1	no	—
1481	C₄⋊C₄	—	53	1	no	—
1482	C₄⋊C₄	—	53	1	no	—
1483	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1484	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1485	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1486	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1487	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1488	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1489	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1490	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1491	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1492	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1493	C₂²⋊C₄	—	53	1	no	—
1494	C₂²⋊C₄	—	53	1	no	—
1495	C₂²⋊C₄	—	53	1	no	—
1496	C₂²⋊C₄	—	53	1	no	—
1497	C₂²⋊C₄	—	53	1	no	—
1498	C₂²⋊C₄	—	53	1	no	—
1499	C₂²⋊C₄	—	53	1	no	—
1500	C₂²⋊C₄	—	53	1	no	—
1501	C₂²⋊C₄	—	53	1	no	—
1502	C₂²⋊C₄	—	53	1	no	—
1503	C₂²⋊C₄	—	53	1	no	—
1504	C₂²⋊C₄	—	53	1	no	—
1505	C₂²⋊C₄	—	53	1	no	—
1506	C₂²⋊C₄	—	53	1	no	—
1507	C₂²⋊C₄	—	53	1	no	—
1508	C₂²⋊C₄	—	53	1	no	—
1509	C₂²⋊C₄	—	53	1	no	—
1510	C₂²⋊C₄	—	53	1	no	—
1511	C₂²⋊C₄	—	53	1	no	—
1512	C₂²⋊C₄	—	53	1	no	—
1513	C₂²⋊C₄	—	53	1	no	—
1514	C₂²⋊C₄	—	53	1	no	—
1515	C₂²⋊C₄	—	53	1	no	—
1516	C₂²⋊C₄	—	53	1	no	—
1517	C₂²⋊C₄	—	53	1	no	—
1518	C₂²⋊C₄	—	53	1	no	—
1519	C₂²⋊C₄	—	53	1	no	—
1520	C₂²⋊C₄	—	53	1	no	—
1521	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1522	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1523	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1524	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1525	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1526	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1527	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1528	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1529	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1530	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1531	C₄²	—	53	1	no	—
1532	C₄²	—	53	1	no	—
1533	C₄²	—	53	1	no	—
1534	C₄²	—	53	1	no	—
1535	C₄²	—	53	1	no	—
1536	C₄²	—	53	1	no	—
1537	C₄²	—	53	1	no	—
1538	C₄²	—	53	1	no	—
1539	C₄²	—	53	1	no	—
1540	C₄²	—	53	1	no	—
1541	C₄²	—	53	1	no	—
1542	C₄²	—	53	1	no	—
1543	C₄²	—	53	1	no	—
1544	C₄²	—	53	1	no	—
1545	C₄²	—	53	1	no	—
1546	C₄²	—	53	1	no	—
1547	C₄²	—	53	1	no	—
1548	C₄²	—	53	1	no	—
1549	C₄²	—	53	1	no	—
1550	C₄²	—	53	1	no	—
1551	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1552	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1553	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1554	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1555	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1556	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1557	C₂³	—	53	1	no	—
1558	C₂³	—	53	1	no	—
1559	C₂³	—	53	1	no	—
1560	C₂³	—	53	1	no	—
1561	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1562	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1563	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1564	Q₈	—	4	1	no	—
1565	Q₈	—	106	2	no	—
1566	Q₈	—	106	2	no	—
1567	Q₈	—	106	2	no	—
1568	Q₈	—	106	2	no	—
1569	Q₈	—	106	2	no	—
1570	Q₈	—	212	1	no	—
1571	D₄	—	4	1	no	—
1572	D₄	—	4	1	no	—
1573	D₄	—	4	1	no	—
1574	D₄	—	106	2	no	—
1575	D₄	—	106	2	no	—
1576	D₄	—	106	2	no	—
1577	D₄	—	106	2	no	—
1578	D₄	—	106	2	no	—
1579	D₄	—	106	2	no	—
1580	D₄	—	106	2	no	—
1581	D₄	—	106	2	no	—
1582	D₄	—	106	2	no	—
1583	D₄	—	106	2	no	—
1584	D₄	—	106	2	no	—
1585	D₄	—	212	1	no	—
1586	D₄	—	212	1	no	—
1587	D₄	—	212	1	no	—
1588	D₄	—	212	1	no	—
1589	D₄	—	212	1	no	—
1590	D₄	—	212	1	no	—
1591	D₄	—	212	1	no	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	4	1	no	—
1599	C₂×C₄	—	4	1	no	—
1600	C₂×C₄	—	53	1	no	—
1601	C₂×C₄	—	53	1	no	—
1602	C₂×C₄	—	53	2	no	—
1603	C₂×C₄	—	53	2	no	—
1604	C₂×C₄	—	53	1	no	—
1605	C₂×C₄	—	53	1	no	—
1606	C₂×C₄	—	53	1	no	—
1607	C₂×C₄	—	53	1	no	—
1608	C₂×C₄	—	53	1	no	—
1609	C₂×C₄	—	53	1	no	—
1610	C₂×C₄	—	53	1	no	—
1611	C₂×C₄	—	53	1	no	—
1612	C₂×C₄	—	53	1	no	—
1613	C₂×C₄	—	53	1	no	—
1614	C₂×C₄	—	106	2	no	—
1615	C₂×C₄	—	106	2	no	—
1616	C₂×C₄	—	106	2	no	—
1617	C₂×C₄	—	106	1	no	—
1618	C₂×C₄	—	106	1	no	—
1619	C₂×C₄	—	106	1	no	—
1620	C₂×C₄	—	106	1	no	—
1621	C₂×C₄	—	106	1	no	—
1622	C₂×C₄	—	106	1	no	—
1623	C₂×C₄	—	212	1	no	—
1624	C₂×C₄	—	212	1	no	—
1625	C₂×C₄	—	212	1	no	—
1626	C₂×C₄	—	212	1	no	—
1627	C₂×C₄	—	212	1	no	—
1628	C₂×C₄	—	212	1	no	—
1629	C₂×C₄	—	212	1	no	—
1630	C₂×C₄	—	212	1	no	—
1631	C₂×C₄	—	212	1	no	—
1632	C₂×C₄	—	212	1	no	—
1633	C₂×C₄	—	212	1	no	—
1634	C₂×C₄	—	212	1	no	—
1635	C₂×C₄	—	212	1	no	—
1636	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1637	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1638	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1639	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1640	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1641	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1642	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1643	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1644	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1645	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1646	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1647	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1648	C₈	—	2	1	no	—
1649	C₈	—	2	1	no	—
1650	C₈	—	2	1	no	—
1651	C₈	—	2	1	no	—
1652	C₈	—	2	1	no	—
1653	C₈	—	2	1	no	—
1654	C₈	—	2	1	no	—
1655	C₈	—	2	1	no	—
1656	C₈	—	106	1	no	—
1657	C₈	—	106	1	no	—
1658	C₈	—	106	1	no	—
1659	C₈	—	106	1	no	—
1660	C₈	—	106	1	no	—
1661	C₈	—	106	1	no	—
1662	C₈	—	106	1	no	—
1663	C₈	—	106	1	no	—
1664	C₂²	—	2	1	no	—
1665	C₂²	—	2	1	no	—
1666	C₂²	—	2	1	no	—
1667	C₂²	—	2	1	no	—
1668	C₂²	—	2	1	no	—
1669	C₂²	—	2	1	no	—
1670	C₂²	—	2	1	no	—
1671	C₂²	—	2	1	no	—
1672	C₂²	—	2	1	no	—
1673	C₂²	—	53	2	no	—
1674	C₂²	—	106	1	no	—
1675	C₂²	—	106	1	no	—
1676	C₂²	—	106	1	no	—
1677	C₂²	—	106	1	no	—
1678	C₂²	—	106	1	no	—
1679	C₂²	—	106	1	no	—
1680	C₂²	—	106	1	no	—
1681	C₂²	—	106	1	no	—
1682	C₂²	—	106	1	no	—
1683	C₂²	—	106	1	no	—
1684	C₂²	—	106	1	no	—
1685	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1686	C₄	—	2	1	no	—
1687	C₄	—	2	1	no	—
1688	C₄	—	2	1	no	—
1689	C₄	—	2	1	no	—
1690	C₄	—	2	1	no	—
1691	C₄	—	2	1	no	—
1692	C₄	—	2	1	no	—
1693	C₄	—	2	1	no	—
1694	C₄	—	2	1	no	—
1695	C₄	—	2	1	no	—
1696	C₄	—	2	1	no	—
1697	C₄	—	53	2	no	—
1698	C₄	—	53	2	no	—
1699	C₄	—	106	1	no	—
1700	C₄	—	106	1	no	—
1701	C₄	—	106	1	no	—
1702	C₄	—	106	1	no	—
1703	C₄	—	106	1	no	—
1704	C₄	—	106	1	no	—
1705	C₄	—	106	1	no	—
1706	C₄	—	106	1	no	—
1707	C₄	—	106	1	no	—
1708	C₄	—	106	1	no	—
1709	C₄	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1710	C₄	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1711	C₂	—	4	1	no	—
1712	C₂	—	4	1	no	—
1713	C₂	—	4	1	no	—
1714	C₂	—	106	2	no	—
1715	C₂	—	212	1	no	—
1716	C₂	—	212	1	no	—
1717	C₂	—	212	1	no	—
1718	C₂	#520×D₅₃	1	1	yes	characteristic
1719	C₂	#568×D₅₃	1	1	yes	characteristic
1720	C₂	#20289428	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2995	C₂
prime radical	#20288306	C₂
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2995	D₅₃
hypocenter	C₅₃	#60275
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #2995

Complements

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

N	H ≅ G/N	type
2. #20283884	C₂	semidirect
3. #20283880	C₂	semidirect
4. #20283879	C₂	semidirect
5. #20283869	C₂	semidirect
6. #20283868	C₂	semidirect
7. #20283862	C₂	semidirect
8. #20283861	C₂	semidirect
9. #20283855	C₂	semidirect
10. #20283854	C₂	semidirect
11. #20283853	C₂	semidirect
12. #20283852	C₂	semidirect
13. #20283842	C₂	semidirect
14. #20283835	C₂	semidirect
15. #20283829	C₂	semidirect
16. #20283827	C₂	semidirect
17. #20283667	C₂	semidirect
18. #446×D₅₃	C₂	semidirect
19. #20283460	C₂	semidirect
20. #20283456	C₂	semidirect
21. #20283456	C₂	semidirect
22. #20283429	C₂	semidirect
23. #20283429	C₂	semidirect
24. #20283424	C₂	semidirect
25. #20283363	C₂	semidirect
26. #20283361	C₂	semidirect
27. #20283356	C₂	semidirect
28. #20283284	C₂	semidirect
29. #20283282	C₂	semidirect
30. #20283282	C₂	semidirect
31. C₅₃×#2995	C₂	semidirect
855. #2995	D₅₃	semidirect
1063. C₅₃	#60275	semidirect

Maximal subgroups

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

subgroup	index
#20288306	2
#20283884	2
#20283880	2
#20283879	2
#20283869	2
#20283868	2
#20283862	2
#20283861	2
#20283855	2
#20283854	2
#20283853	2
#20283852	2
#20283842	2
#20283835	2
#20283829	2
#20283827	2
#20283667	2
#446×D₅₃	2
#20283460	2
#20283456	2
#20283429	2
#20283424	2
#20283363	2
#20283361	2
#20283356	2
#20283284	2
#20283282	2
C₅₃×#2995	2
#60275	53