Subgroups — #28292748

Order 13568.

7382 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288924	C₂	1	4	yes	maximal, complemented
2	#20288918	C₂	1	4	yes	maximal, complemented
3	#20288905	C₂	1	4	yes	maximal, complemented
4	#20288899	C₂	1	4	yes	maximal, complemented
5	#20288879	C₂	1	8	yes	maximal, complemented
6	#20288655	C₂	1	8	yes	maximal, complemented
7	#20288641	C₂	1	8	yes	maximal, complemented
8	#20288416	C₂	1	4	yes	maximal, complemented
9	#20288413	C₂	1	2	yes	maximal, complemented
10	#20288411	C₂	1	2	yes	maximal, complemented
11	#20288402	C₂	1	2	yes	maximal, complemented
12	#20288398	C₂	1	4	yes	maximal, complemented
13	#20288359	C₂	1	2	yes	maximal, complemented
14	#20288353	C₂	1	2	yes	maximal, complemented
15	#20288344	C₂	1	2	yes	maximal, complemented
16	C₂×#16811134	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#13133200	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#13133262	C₂²	1	2	yes	complemented
20	C₂²×#11719945	C₂²	1	1	yes	characteristic, complemented
21	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
22	#16811374	C₂²	1	8	yes	complemented
23	#16811369	C₂²	1	8	yes	complemented
24	#16811368	C₂²	1	8	yes	complemented
25	#16811361	C₂²	1	8	yes	complemented
26	#16811356	C₂²	1	8	yes	complemented
27	#16811332	C₂²	1	8	yes	complemented
28	#16811327	C₂²	1	8	yes	complemented
29	#16811323	C₂²	1	8	yes	complemented
30	#16811322	C₂²	1	8	yes	complemented
31	#16811322	C₂²	1	8	yes	complemented
32	#16811316	C₂²	1	8	yes	complemented
33	#16811310	C₂²	1	8	yes	complemented
34	#16811308	C₂²	1	8	yes	complemented
35	#16811306	C₂²	1	8	yes	complemented
36	#16811306	C₂²	1	8	yes	complemented
37	#16811304	C₂²	1	8	yes	complemented
38	#16811302	C₂²	1	8	yes	complemented
39	#16811302	C₂²	1	8	yes	complemented
40	#16811300	C₂²	1	8	yes	complemented
41	#16811299	C₂²	1	8	yes	complemented
42	#16811299	C₂²	1	8	yes	complemented
43	#16811297	C₂²	1	8	yes	complemented
44	#16811297	C₂²	1	8	yes	complemented
45	#16811296	C₂²	1	8	yes	complemented
46	#16811274	C₂²	1	8	yes	complemented
47	#16811272	C₂²	1	8	yes	complemented
48	#16811272	C₂²	1	8	yes	complemented
49	#16811271	C₂²	1	8	yes	complemented
50	#16811268	C₂²	1	8	yes	complemented
51	#16811267	C₂²	1	8	yes	complemented
52	#16811265	C₂²	1	8	yes	complemented
53	#16811263	C₂²	1	8	yes	complemented
54	#16811263	C₂²	1	8	yes	complemented
55	#16811262	C₂²	1	8	yes	complemented
56	#16811261	C₂²	1	8	yes	complemented
57	#16811261	C₂²	1	8	yes	complemented
58	#16811260	C₂²	1	8	yes	complemented
59	#16811260	C₂²	1	8	yes	complemented
60	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
61	#16811255	C₂²	1	8	yes	complemented
62	#16811252	C₂²	1	4	yes	complemented
63	#16811249	C₂²	1	2	yes	complemented
64	#16811248	C₂²	1	4	yes	complemented
65	#16811243	C₂²	1	8	yes	complemented
66	#16811238	C₂²	1	8	yes	complemented
67	#16811224	C₂²	1	8	yes	complemented
68	#16811223	C₂²	1	8	yes	complemented
69	#16811222	C₂²	1	4	yes	complemented
70	#16811220	C₂²	1	8	yes	complemented
71	#16811219	C₂²	1	8	yes	complemented
72	#16811218	C₂²	1	4	yes	complemented
73	#16811217	C₂²	1	8	yes	complemented
74	#16811215	C₂²	1	8	yes	complemented
75	#16811215	C₂²	1	8	yes	complemented
76	#16811213	C₂²	1	4	yes	complemented
77	#16811210	C₂²	1	4	yes	complemented
78	#16811208	C₂²	1	8	yes	complemented
79	#16811206	C₂²	1	8	yes	complemented
80	#16811206	C₂²	1	8	yes	complemented
81	#16811205	C₂²	1	8	yes	complemented
82	#16811200	C₂²	1	4	yes	complemented
83	#16811197	C₂²	1	4	yes	complemented
84	#16811195	C₂²	1	4	yes	complemented
85	#16811188	C₂²	1	4	yes	complemented
86	#16811185	C₂²	1	2	yes	—
87	#16811184	C₂²	1	4	yes	complemented
88	#16811183	C₂²	1	4	yes	complemented
89	#16811182	C₂²	1	2	yes	—
90	#16811182	C₂²	1	2	yes	complemented
91	#16811182	C₂²	1	4	yes	complemented
92	#16811181	C₂²	1	4	yes	complemented
93	#16811157	C₂²	1	8	yes	complemented
94	#16811150	C₂²	1	8	yes	complemented
95	#16811134	C₂²	1	4	yes	complemented
96	#16811134	C₂²	1	4	yes	complemented
97	#16811134	C₂²	1	4	yes	complemented
98	#16811134	C₂²	1	4	yes	complemented
99	#16811134	C₂²	1	4	yes	complemented
100	#16811131	C₂²	1	4	yes	complemented
101	#16811129	C₂²	1	4	yes	complemented
102	#16811129	C₂²	1	8	yes	complemented
103	C₂×#13133200	C₂²	1	2	yes	complemented
104	C₂×#13133200	C₂²	1	2	yes	complemented
105	C₂×#13133200	C₂²	1	4	yes	complemented
106	C₂×#13133200	C₂²	1	4	yes	complemented
107	C₂×#13133200	C₂²	1	4	yes	complemented
108	C₂×#13133200	C₂²	1	4	yes	complemented
109	C₂×#13133200	C₂²	1	4	yes	complemented
110	C₂×#13133200	C₂²	1	2	yes	complemented
111	C₂×#13133200	C₂²	1	4	yes	complemented
112	#123×D₅₃	C₂²	1	4	yes	complemented
113	C₂×#13133196	C₂²	1	2	yes	complemented
114	C₂×#13133191	C₂²	1	2	yes	complemented
115	C₂×#13133186	C₂²	1	2	yes	complemented
116	#120×D₅₃	C₂²	1	4	yes	complemented
117	#16811102	C₂²	1	8	yes	complemented
118	#16811098	C₂²	1	2	yes	complemented
119	#16811096	C₂²	1	2	yes	complemented
120	#16811096	C₂²	1	2	yes	complemented
121	#16811095	C₂²	1	8	yes	complemented
122	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
123	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
124	C₂²×#11719919	C₂²	1	2	yes	complemented
125	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂²×#11719921	C₂²	1	2	yes	complemented
127	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#525	C₂²	1	4	yes	complemented
130	C₅₃×#525	C₂²	1	4	yes	complemented
131	C₅₃×#525	C₂²	1	4	yes	complemented
132	C₅₃×#525	C₂²	1	4	yes	complemented
133	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
134	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
136	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
137	C₂×C₄×D₄×C₅₃	C₂²	1	4	yes	complemented
138	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
140	#13133262	—	4	8	no	—
141	C₂×#11719945	—	4	4	no	—
142	C₂×#11719945	C₂³	1	4	yes	—
143	C₂×#11719945	C₂³	1	4	yes	—
144	C₂×#11719945	C₂³	1	4	yes	complemented
145	C₂×#11719947	C₂³	1	8	yes	—
146	C₂×#11719947	C₂³	1	4	yes	—
147	C₂×#11719947	C₂³	1	4	yes	—
148	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
149	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
150	C₂²×C₂²⋊D₅₃	—	4	4	no	—
151	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
152	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
154	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
155	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
157	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
158	C₂×D₄×D₅₃	C₂³	1	4	yes	—
159	C₂×D₄×D₅₃	C₂³	1	8	yes	—
160	C₂×D₄×D₅₃	C₂³	1	4	yes	—
161	C₂³×Dic₅₃	C₂³	1	2	yes	—
162	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
163	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
164	#13133216	C₂³	1	8	yes	complemented
165	#13133215	C₂³	1	8	yes	complemented
166	#13133213	C₂³	1	8	yes	—
167	#13133212	C₂³	1	8	yes	complemented
168	#13133212	C₂³	1	8	yes	complemented
169	#13133212	C₂³	1	8	yes	complemented
170	#13133212	C₂³	1	8	yes	complemented
171	#13133211	C₂³	1	8	yes	complemented
172	#13133211	C₂³	1	8	yes	complemented
173	#13133210	C₂³	1	8	yes	complemented
174	#13133210	C₂³	1	8	yes	complemented
175	#13133210	C₂³	1	8	yes	complemented
176	#13133210	C₂³	1	8	yes	complemented
177	#13133209	C₂³	1	8	yes	complemented
178	#13133208	C₂³	1	8	yes	complemented
179	#13133207	C₂³	1	8	yes	complemented
180	#13133207	C₂³	1	8	yes	complemented
181	#13133207	C₂³	1	8	yes	complemented
182	#13133207	C₂³	1	8	yes	complemented
183	#13133206	C₂³	1	8	yes	complemented
184	#13133205	C₂³	1	8	yes	complemented
185	#13133204	C₂³	1	8	yes	complemented
186	#13133203	C₂³	1	8	yes	—
187	#13133203	C₂³	1	8	yes	complemented
188	#13133203	C₂³	1	8	yes	complemented
189	#13133203	C₂³	1	8	yes	complemented
190	#13133202	C₂³	1	8	yes	complemented
191	#13133202	C₂³	1	8	yes	complemented
192	#13133202	C₂³	1	8	yes	complemented
193	#13133202	C₂³	1	8	yes	complemented
194	#13133201	C₂³	1	8	yes	—
195	#13133201	C₂³	1	4	yes	—
196	#13133201	C₂³	1	4	yes	—
197	#13133201	C₂³	1	8	yes	complemented
198	#13133200	C₂³	1	8	yes	—
199	#13133200	C₂³	1	8	yes	—
200	#13133200	C₂³	1	8	yes	—
201	#13133200	C₂³	1	8	yes	—
202	#13133200	C₂³	1	4	yes	—
203	#13133200	C₂³	1	8	yes	—
204	#13133200	C₂³	1	4	yes	—
205	#13133200	C₂³	1	4	yes	—
206	#13133200	C₂³	1	4	yes	—
207	#13133200	C₂³	1	4	yes	—
208	#13133200	C₂³	1	8	yes	—
209	#13133200	C₂³	1	8	yes	—
210	#13133200	C₂³	1	8	yes	complemented
211	#13133200	C₂³	1	8	yes	complemented
212	#13133200	C₂³	1	4	yes	complemented
213	#13133200	C₂³	1	4	yes	complemented
214	#13133200	C₂³	1	4	yes	complemented
215	#13133199	C₂³	1	8	yes	—
216	#13133199	C₂³	1	8	yes	complemented
217	#13133199	C₂³	1	8	yes	complemented
218	#13133199	C₂³	1	8	yes	complemented
219	#13133198	C₂³	1	8	yes	—
220	#13133198	C₂³	1	4	yes	—
221	#13133198	C₂³	1	8	yes	complemented
222	#13133198	C₂³	1	4	yes	complemented
223	#13133198	C₂³	1	8	yes	complemented
224	#13133197	C₂³	1	8	yes	complemented
225	#13133196	C₂³	1	4	yes	—
226	#13133196	C₂³	1	4	yes	—
227	#13133196	C₂³	1	8	yes	complemented
228	#13133196	C₂³	1	8	yes	complemented
229	#13133196	C₂³	1	4	yes	complemented
230	#13133196	C₂³	1	4	yes	complemented
231	#13133195	C₂³	1	8	yes	complemented
232	#13133195	C₂³	1	8	yes	complemented
233	#13133195	C₂³	1	8	yes	complemented
234	#13133195	C₂³	1	8	yes	complemented
235	#13133194	C₂³	1	8	yes	—
236	#13133194	C₂³	1	8	yes	—
237	#13133194	C₂³	1	8	yes	—
238	#13133194	C₂³	1	8	yes	complemented
239	#13133194	C₂³	1	8	yes	complemented
240	#13133194	C₂³	1	8	yes	complemented
241	#13133193	C₂³	1	8	yes	complemented
242	#13133193	C₂³	1	8	yes	complemented
243	#13133192	C₂³	1	8	yes	complemented
244	#13133191	C₂³	1	4	yes	—
245	#13133191	C₂³	1	8	yes	—
246	#13133191	C₂³	1	4	yes	—
247	#13133191	C₂³	1	8	yes	complemented
248	#13133191	C₂³	1	4	yes	complemented
249	#13133191	C₂³	1	4	yes	complemented
250	#13133190	C₂³	1	8	yes	—
251	#13133190	C₂³	1	8	yes	—
252	#13133190	C₂³	1	8	yes	complemented
253	#13133190	C₂³	1	8	yes	complemented
254	#13133189	C₂³	1	8	yes	—
255	#13133189	C₂³	1	8	yes	—
256	#13133189	C₂³	1	8	yes	—
257	#13133189	C₂³	1	8	yes	—
258	#13133189	C₂³	1	8	yes	—
259	#13133189	C₂³	1	8	yes	complemented
260	#13133189	C₂³	1	8	yes	complemented
261	#13133189	C₂³	1	8	yes	complemented
262	#13133188	C₂³	1	8	yes	—
263	#13133188	C₂³	1	8	yes	complemented
264	#13133187	C₂³	1	4	yes	—
265	#13133187	C₂³	1	8	yes	—
266	#13133187	C₂³	1	4	yes	—
267	#13133187	C₂³	1	8	yes	complemented
268	#13133186	C₂³	1	8	yes	—
269	#13133186	C₂³	1	4	yes	—
270	#13133186	C₂³	1	4	yes	—
271	#13133186	C₂³	1	4	yes	—
272	#13133186	C₂³	1	4	yes	complemented
273	#13133185	C₂³	1	4	yes	—
274	#13133185	C₂³	1	8	yes	—
275	#13133185	C₂³	1	8	yes	—
276	#13133185	C₂³	1	8	yes	complemented
277	#13133185	C₂³	1	4	yes	complemented
278	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
279	#13133182	C₂³	1	8	yes	complemented
280	C₄×D₂₁₂	C₂³	1	8	yes	complemented
281	D₄×Dic₅₃	C₂³	1	8	yes	—
282	D₄×Dic₅₃	C₂³	1	8	yes	—
283	D₄×Dic₅₃	C₂³	1	8	yes	—
284	D₄×Dic₅₃	C₂³	1	8	yes	complemented
285	#13133179	C₂³	1	8	yes	complemented
286	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
287	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
288	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
289	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
290	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
291	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
292	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
293	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
294	#13133177	C₂³	1	8	yes	—
295	#13133177	C₂³	1	8	yes	—
296	#13133177	C₂³	1	8	yes	—
297	#13133177	C₂³	1	8	yes	—
298	#13133177	C₂³	1	8	yes	complemented
299	#13133177	C₂³	1	8	yes	complemented
300	#13133176	C₂³	1	4	yes	—
301	#13133176	C₂³	1	4	yes	complemented
302	#13133176	C₂³	1	4	yes	complemented
303	#13133175	C₂³	1	8	yes	complemented
304	#13133174	C₂³	1	8	yes	complemented
305	#13133174	C₂³	1	8	yes	complemented
306	#13133173	C₂³	1	8	yes	—
307	#13133173	C₂³	1	4	yes	—
308	#13133173	C₂³	1	8	yes	complemented
309	#13133173	C₂³	1	4	yes	complemented
310	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	complemented
311	C₂×#11719919	C₂³	1	4	yes	—
312	C₂×#11719919	C₂³	1	4	yes	—
313	C₂×#11719919	C₂³	1	4	yes	—
314	C₂×#11719919	C₂³	1	4	yes	—
315	C₂×#11719919	C₂³	1	4	yes	—
316	C₂×#11719919	C₂³	1	4	yes	—
317	C₂×#11719919	C₂³	1	4	yes	complemented
318	C₂×#11719919	C₂³	1	8	yes	complemented
319	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
320	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
321	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
322	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
323	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
324	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
325	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
326	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
327	C₂×#11719921	C₂³	1	4	yes	—
328	C₂×#11719921	C₂³	1	4	yes	—
329	C₂×#11719921	C₂³	1	4	yes	—
330	C₂×#11719921	C₂³	1	4	yes	—
331	C₂×#11719921	C₂³	1	4	yes	—
332	C₂×#11719921	C₂³	1	4	yes	—
333	C₂×#11719921	C₂³	1	8	yes	complemented
334	C₂×#11719921	C₂³	1	4	yes	complemented
335	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
336	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
337	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
338	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	complemented
339	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
340	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×#41×C₅₃	—	4	4	no	—
342	C₂×#41×C₅₃	C₂³	1	4	yes	—
343	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
344	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
345	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
346	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
347	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
348	C₂³×C₄×C₅₃	—	4	4	no	—
349	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
352	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
353	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
354	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
355	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
356	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
357	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
358	#123×C₅₃	C₂³	1	8	yes	—
359	#123×C₅₃	C₂³	1	4	yes	complemented
360	#123×C₅₃	C₂³	1	4	yes	complemented
361	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
362	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
363	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
364	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
365	#121×C₅₃	C₂³	1	4	yes	—
366	#121×C₅₃	C₂³	1	4	yes	—
367	#121×C₅₃	C₂³	1	4	yes	complemented
368	#121×C₅₃	C₂³	1	4	yes	complemented
369	#120×C₅₃	C₂³	1	8	yes	—
370	#120×C₅₃	C₂³	1	4	yes	—
371	#120×C₅₃	C₂³	1	4	yes	—
372	C₄×D₄×C₅₃	C₂³	1	8	yes	—
373	C₄×D₄×C₅₃	C₂³	1	8	yes	—
374	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
375	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
376	#117×C₅₃	C₂³	1	4	yes	—
377	#117×C₅₃	C₂³	1	4	yes	complemented
378	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
379	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
380	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
381	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
382	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
383	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
384	C₂⁴×C₅₃	—	2	4	no	—
385	C₂⁴×C₅₃	—	4	4	no	—
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
388	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
389	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
390	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂³×D₅₃	—	4	2	no	—
393	C₂³×D₅₃	—	4	4	no	—
394	C₂³×D₅₃	C₂⁴	1	2	yes	—
395	C₂³×D₅₃	C₂⁴	1	4	yes	—
396	C₂³×D₅₃	C₂⁴	1	2	yes	—
397	C₂³×D₅₃	C₂⁴	1	4	yes	—
398	#41×C₅₃	—	4	8	no	—
399	#41×C₅₃	—	4	8	no	—
400	C₂×Q₈×C₅₃	—	4	2	no	—
401	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
402	C₂×D₄×C₅₃	—	2	8	no	—
403	C₂×D₄×C₅₃	—	4	2	no	—
404	C₂×D₄×C₅₃	—	4	8	no	—
405	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
406	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
407	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
408	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
409	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
410	C₂²×C₄×C₅₃	—	2	4	no	—
411	C₂²×C₄×C₅₃	—	2	4	no	—
412	C₂²×C₄×C₅₃	—	4	4	no	—
413	C₂²×C₄×C₅₃	—	4	4	no	—
414	C₂²×C₄×C₅₃	—	4	4	no	—
415	C₂²×C₄×C₅₃	—	4	4	no	—
416	C₂²×C₄×C₅₃	—	4	4	no	—
417	C₂²×C₄×C₅₃	—	4	4	no	—
418	C₂²×C₄×C₅₃	—	4	4	no	—
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
421	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
424	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
425	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
426	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
429	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
430	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
431	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
432	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
433	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
434	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
435	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
436	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
437	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
438	C₂×C₂²⋊D₅₃	—	2	8	no	—
439	C₂×C₂²⋊D₅₃	—	2	8	no	—
440	C₂×C₂²⋊D₅₃	—	4	4	no	—
441	C₂×C₂²⋊D₅₃	—	4	8	no	—
442	C₂×C₂²⋊D₅₃	—	4	8	no	—
443	C₂×C₂²⋊D₅₃	—	4	8	no	—
444	C₂×C₂²⋊D₅₃	—	4	8	no	—
445	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
446	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
447	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
448	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
449	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
450	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
451	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
452	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
453	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
454	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
455	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
456	C₂²×Dic₅₃	—	4	4	no	—
457	C₂²×Dic₅₃	—	4	2	no	—
458	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
459	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
460	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
461	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
462	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
463	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
464	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
465	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
466	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
467	#11719947	—	4	16	no	—
468	#11719947	—	4	8	no	—
469	#11719947	—	4	8	no	—
470	D₄×D₅₃	—	4	16	no	—
471	D₄×D₅₃	—	4	8	no	—
472	D₄×D₅₃	—	4	8	no	—
473	#11719945	—	4	8	no	—
474	#11719945	—	4	8	no	—
475	#11719945	—	4	8	no	—
476	C₂×D₂₁₂	—	4	2	no	—
477	C₂×D₂₁₂	C₂⁴	1	8	yes	—
478	C₂×D₂₁₂	C₂⁴	1	4	yes	—
479	C₂×D₂₁₂	C₂⁴	1	4	yes	—
480	C₂×C₄×D₅₃	—	4	4	no	—
481	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
482	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
483	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
484	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
485	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
486	C₂×Dic₁₀₆	—	4	2	no	—
487	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
488	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
489	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
490	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
491	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
492	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
493	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
494	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
495	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
497	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
498	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
499	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
500	C₄²×C₅₃	C₂⁴	1	8	yes	—
501	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
503	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
504	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
505	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
506	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
507	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
508	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
509	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
510	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
511	#11719921	C₂⁴	1	8	yes	—
512	#11719921	C₂⁴	1	8	yes	—
513	#11719921	C₂⁴	1	8	yes	—
514	#11719921	C₂⁴	1	8	yes	—
515	#11719921	C₂⁴	1	8	yes	—
516	#11719921	C₂⁴	1	8	yes	—
517	#11719921	C₂⁴	1	8	yes	—
518	#11719921	C₂⁴	1	8	yes	—
519	#11719921	C₂⁴	1	8	yes	—
520	#11719921	C₂⁴	1	8	yes	—
521	#11719921	C₂⁴	1	8	yes	—
522	#11719921	C₂⁴	1	8	yes	—
523	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
524	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
525	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
526	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
527	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
528	#11719919	C₂⁴	1	8	yes	—
529	#11719919	C₂⁴	1	8	yes	—
530	#11719919	C₂⁴	1	8	yes	—
531	#11719919	C₂⁴	1	8	yes	—
532	#11719919	C₂⁴	1	8	yes	—
533	#11719919	C₂⁴	1	8	yes	—
534	#11719919	C₂⁴	1	8	yes	—
535	#11719919	C₂⁴	1	8	yes	—
536	#11719919	C₂⁴	1	8	yes	—
537	#11719919	C₂⁴	1	8	yes	—
538	#11719919	C₂⁴	1	8	yes	—
539	#11719919	C₂⁴	1	8	yes	—
540	C₄×Dic₅₃	C₂⁴	1	8	yes	—
541	C₄×Dic₅₃	C₂⁴	1	8	yes	—
542	C₄×Dic₅₃	C₂⁴	1	8	yes	—
543	C₄×Dic₅₃	C₂⁴	1	8	yes	—
544	C₂³×C₅₃	—	2	2	no	—
545	C₂³×C₅₃	—	2	4	no	—
546	C₂³×C₅₃	—	2	4	no	—
547	C₂³×C₅₃	—	2	4	no	—
548	C₂³×C₅₃	—	2	2	no	—
549	C₂³×C₅₃	—	2	4	no	—
550	C₂³×C₅₃	—	2	4	no	—
551	C₂³×C₅₃	—	2	4	no	—
552	C₂³×C₅₃	—	4	2	no	—
553	C₂³×C₅₃	—	4	2	no	—
554	C₂³×C₅₃	—	4	2	no	—
555	C₂³×C₅₃	—	4	2	no	—
556	C₂³×C₅₃	—	4	4	no	—
557	C₂³×C₅₃	—	4	16	no	—
558	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
559	C₂³×C₅₃	C₂⁵	1	4	yes	—
560	C₂³×C₅₃	C₂⁵	1	2	yes	—
561	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
562	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
563	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
564	C₂³×C₅₃	C₂⁵	1	2	yes	—
565	C₂²×D₅₃	—	2	4	no	—
566	C₂²×D₅₃	—	2	4	no	—
567	C₂²×D₅₃	—	2	8	no	—
568	C₂²×D₅₃	—	4	4	no	—
569	C₂²×D₅₃	—	4	4	no	—
570	C₂²×D₅₃	—	4	4	no	—
571	C₂²×D₅₃	—	4	4	no	—
572	C₂²×D₅₃	—	4	4	no	—
573	C₂²×D₅₃	—	4	8	no	—
574	C₂²×D₅₃	—	8	8	no	—
575	C₂²×D₅₃	C₂⁵	1	4	yes	—
576	C₂²×D₅₃	C₂⁵	1	4	yes	—
577	Q₈×C₅₃	—	4	4	no	—
578	D₄×C₅₃	—	2	8	no	—
579	D₄×C₅₃	—	2	8	no	—
580	D₄×C₅₃	—	2	16	no	—
581	D₄×C₅₃	—	4	8	no	—
582	D₄×C₅₃	—	4	4	no	—
583	C₂×C₄×C₅₃	—	2	2	no	—
584	C₂×C₄×C₅₃	—	2	2	no	—
585	C₂×C₄×C₅₃	—	2	4	no	—
586	C₂×C₄×C₅₃	—	2	4	no	—
587	C₂×C₄×C₅₃	—	2	4	no	—
588	C₂×C₄×C₅₃	—	2	2	no	—
589	C₂×C₄×C₅₃	—	2	2	no	—
590	C₂×C₄×C₅₃	—	2	4	no	—
591	C₂×C₄×C₅₃	—	2	4	no	—
592	C₂×C₄×C₅₃	—	4	2	no	—
593	C₂×C₄×C₅₃	—	4	2	no	—
594	C₂×C₄×C₅₃	—	4	2	no	—
595	C₂×C₄×C₅₃	—	4	2	no	—
596	C₂×C₄×C₅₃	—	4	2	no	—
597	C₂×C₄×C₅₃	—	4	2	no	—
598	C₂×C₄×C₅₃	—	4	2	no	—
599	C₂×C₄×C₅₃	—	4	2	no	—
600	C₂×C₄×C₅₃	—	4	8	no	—
601	C₂×C₄×C₅₃	—	4	4	no	—
602	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
603	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
604	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
605	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
606	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
607	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
608	C₂²⋊D₅₃	—	2	8	no	—
609	C₂²⋊D₅₃	—	2	8	no	—
610	C₂²⋊D₅₃	—	2	8	no	—
611	C₂²⋊D₅₃	—	2	8	no	—
612	C₂²⋊D₅₃	—	2	16	no	—
613	C₂²⋊D₅₃	—	4	4	no	—
614	C₂²⋊D₅₃	—	4	4	no	—
615	C₂²⋊D₅₃	—	4	8	no	—
616	C₂²⋊D₅₃	—	4	8	no	—
617	C₂²⋊D₅₃	—	4	8	no	—
618	C₂²⋊D₅₃	—	4	8	no	—
619	C₂×Dic₅₃	—	2	4	no	—
620	C₂×Dic₅₃	—	2	4	no	—
621	C₂×Dic₅₃	—	2	8	no	—
622	C₂×Dic₅₃	—	4	4	no	—
623	C₂×Dic₅₃	—	4	8	no	—
624	C₂×Dic₅₃	—	4	4	no	—
625	C₂×Dic₅₃	—	4	4	no	—
626	C₂×Dic₅₃	—	4	4	no	—
627	C₂×Dic₅₃	—	4	4	no	—
628	C₂×Dic₅₃	C₂⁵	1	4	yes	—
629	C₂×Dic₅₃	C₂⁵	1	4	yes	—
630	C₂×Dic₅₃	C₂⁵	1	8	yes	—
631	C₂×Dic₅₃	C₂⁵	1	8	yes	—
632	D₂₁₂	—	4	4	no	—
633	D₂₁₂	—	4	4	no	—
634	D₂₁₂	—	4	8	no	—
635	C₄×D₅₃	—	4	8	no	—
636	C₄×D₅₃	—	4	4	no	—
637	C₄×D₅₃	—	4	4	no	—
638	C₄×D₅₃	—	4	8	no	—
639	C₄×D₅₃	—	4	8	no	—
640	Dic₁₀₆	—	4	4	no	—
641	Dic₁₀₆	—	4	4	no	—
642	Dic₁₀₆	—	4	8	no	—
643	#62820	—	53	1	no	maximal, Sylow
644	C₂²×C₅₃	—	2	8	no	—
645	C₂²×C₅₃	—	2	2	no	—
646	C₂²×C₅₃	—	2	2	no	—
647	C₂²×C₅₃	—	2	2	no	—
648	C₂²×C₅₃	—	2	2	no	—
649	C₂²×C₅₃	—	2	2	no	—
650	C₂²×C₅₃	—	2	4	no	—
651	C₂²×C₅₃	—	2	2	no	—
652	C₂²×C₅₃	—	2	8	no	—
653	C₂²×C₅₃	—	2	2	no	—
654	C₂²×C₅₃	—	2	2	no	—
655	C₂²×C₅₃	—	4	4	no	—
656	C₂²×C₅₃	—	4	8	no	—
657	C₂²×C₅₃	—	4	8	no	—
658	C₂²×C₅₃	—	4	4	no	—
659	C₂²×C₅₃	—	8	4	no	—
660	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
661	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
662	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
663	C₂²×C₅₃	#585	1	4	yes	—
664	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
665	C₂×D₅₃	—	2	4	no	—
666	C₂×D₅₃	—	2	4	no	—
667	C₂×D₅₃	—	2	8	no	—
668	C₂×D₅₃	—	2	8	no	—
669	C₂×D₅₃	—	8	4	no	—
670	C₂×D₅₃	—	8	4	no	—
671	C₂×D₅₃	—	8	8	no	—
672	C₂×D₅₃	—	16	4	no	—
673	C₄×C₅₃	—	2	2	no	—
674	C₄×C₅₃	—	2	4	no	—
675	C₄×C₅₃	—	2	2	no	—
676	C₄×C₅₃	—	2	2	no	—
677	C₄×C₅₃	—	2	2	no	—
678	C₄×C₅₃	—	2	8	no	—
679	Dic₅₃	—	2	4	no	—
680	Dic₅₃	—	2	4	no	—
681	Dic₅₃	—	2	8	no	—
682	Dic₅₃	—	2	8	no	—
683	#3535	—	53	4	no	—
684	#3535	—	53	4	no	—
685	#3534	—	53	4	no	—
686	#3534	—	53	4	no	—
687	#3533	—	53	8	no	—
688	#3513	—	53	8	no	—
689	#3513	—	53	8	no	—
690	#3492	—	53	4	no	—
691	#3491	—	53	2	no	—
692	#3491	—	53	2	no	—
693	#3490	—	53	4	no	—
694	#3490	—	53	2	no	—
695	#3485	—	53	2	no	—
696	#3485	—	53	2	no	—
697	#3484	—	53	2	no	—
698	C₂×#525	—	53	1	no	—
699	C₂×#525	D₅₃	1	1	yes	characteristic, complemented
700	C₂²×#123	—	53	1	no	—
701	C₂×C₅₃	—	2	2	no	—
702	C₂×C₅₃	—	2	4	no	—
703	C₂×C₅₃	—	2	2	no	—
704	C₂×C₅₃	—	2	2	no	—
705	C₂×C₅₃	—	4	4	no	—
706	C₂×C₅₃	—	4	2	no	—
707	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂×C₅₃	C₂×#585	1	2	yes	—
709	D₅₃	—	4	4	no	—
710	D₅₃	—	4	4	no	—
711	C₂×H(5,𝔽₂)	—	53	2	no	—
712	C₂²×#41	—	53	1	no	—
713	C₂²×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
714	C₂³×D₄	—	53	1	no	—
715	C₂⁴×C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
716	#563	—	53	8	no	—
717	#562	—	53	8	no	—
718	#562	—	53	8	no	—
719	#560	—	53	8	no	—
720	#559	—	53	8	no	—
721	#554	—	53	8	no	—
722	#554	—	53	8	no	—
723	#553	—	53	8	no	—
724	#553	—	53	8	no	—
725	#553	—	53	8	no	—
726	#553	—	53	8	no	—
727	#552	—	53	8	no	—
728	#552	—	53	8	no	—
729	#552	—	53	8	no	—
730	#552	—	53	8	no	—
731	#551	—	53	8	no	—
732	#551	—	53	8	no	—
733	#551	—	53	8	no	—
734	#551	—	53	8	no	—
735	#551	—	53	8	no	—
736	#551	—	53	8	no	—
737	#551	—	53	8	no	—
738	#551	—	53	8	no	—
739	#551	—	53	8	no	—
740	#547	—	53	8	no	—
741	#547	—	53	8	no	—
742	#547	—	53	8	no	—
743	#547	—	53	8	no	—
744	#546	—	53	8	no	—
745	#546	—	53	8	no	—
746	#546	—	53	8	no	—
747	#546	—	53	8	no	—
748	#546	—	53	8	no	—
749	#546	—	53	8	no	—
750	#546	—	53	8	no	—
751	#546	—	53	8	no	—
752	#546	—	53	8	no	—
753	#546	—	53	8	no	—
754	D₄²	—	53	8	no	—
755	D₄²	—	53	8	no	—
756	#544	—	53	4	no	—
757	#543	—	53	4	no	—
758	#543	—	53	2	no	—
759	#542	—	53	8	no	—
760	#542	—	53	8	no	—
761	#540	—	53	8	no	—
762	#540	—	53	8	no	—
763	#539	—	53	8	no	—
764	#539	—	53	4	no	—
765	#539	—	53	8	no	—
766	#539	—	53	4	no	—
767	#539	—	53	8	no	—
768	#539	—	53	8	no	—
769	#539	—	53	8	no	—
770	#538	—	53	4	no	—
771	#538	—	53	4	no	—
772	#538	—	53	8	no	—
773	#538	—	53	8	no	—
774	#538	—	53	8	no	—
775	#538	—	53	8	no	—
776	#537	—	53	4	no	—
777	#536	—	53	4	no	—
778	#536	—	53	4	no	—
779	#535	—	53	4	no	—
780	#534	—	53	2	no	—
781	#534	—	53	2	no	—
782	#534	—	53	4	no	—
783	#534	—	53	4	no	—
784	#534	—	53	4	no	—
785	#534	—	53	4	no	—
786	#534	—	53	2	no	—
787	#529	—	53	8	no	—
788	#529	—	53	8	no	—
789	#525	—	53	4	no	—
790	#525	—	53	4	no	—
791	#525	—	53	4	no	—
792	#525	—	53	4	no	—
793	#525	—	53	4	no	—
794	#525	—	53	4	no	—
795	#525	—	53	4	no	—
796	#525	—	53	8	no	—
797	#525	C₂×D₅₃	1	4	yes	complemented
798	#525	C₂×D₅₃	1	4	yes	complemented
799	#525	C₂×D₅₃	1	4	yes	complemented
800	#525	C₂×D₅₃	1	4	yes	complemented
801	C₂×#123	—	53	2	no	—
802	C₂×#123	—	53	2	no	—
803	C₂×#123	—	53	4	no	—
804	C₂×#123	—	53	4	no	—
805	C₂×#123	—	53	4	no	—
806	C₂×#123	—	53	4	no	—
807	C₂×#123	—	53	4	no	—
808	C₂×#123	—	53	2	no	—
809	C₂×#123	—	53	4	no	—
810	C₂×#123	—	53	4	no	—
811	C₂×#123	C₂×D₅₃	1	2	yes	complemented
812	C₂×C₂²⋊Q₈	—	53	2	no	—
813	C₂×C₂²⋊Q₈	C₂×D₅₃	1	2	yes	complemented
814	C₂×#121	—	53	2	no	—
815	C₂×#121	C₂×D₅₃	1	2	yes	complemented
816	C₂×#120	—	53	2	no	—
817	C₂×#120	—	53	4	no	—
818	C₂×#120	C₂×D₅₃	1	2	yes	complemented
819	#520	—	53	8	no	—
820	#518	—	53	2	no	—
821	#518	—	53	8	no	—
822	#518	—	53	2	no	—
823	#518	—	53	2	no	—
824	C₂×C₄×D₄	—	53	4	no	—
825	C₂×C₄×D₄	C₂×D₅₃	1	4	yes	complemented
826	C₂×#117	—	53	1	no	—
827	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
828	C₂²×C₄⋊C₄	—	53	2	no	—
829	C₂²×C₂²⋊C₄	—	53	1	no	—
830	C₂²×C₂²⋊C₄	—	53	2	no	—
831	C₅₃	#62820	1	1	yes	characteristic, complemented, Sylow
832	C₂⁵	—	53	1	no	—
833	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
834	H(5,𝔽₂)	—	212	8	no	—
835	C₂×#41	—	4	4	no	—
836	C₂×#41	—	53	8	no	—
837	C₂×#41	—	53	4	no	—
838	C₂×#41	—	53	4	no	—
839	C₂×#41	—	53	4	no	—
840	C₂×#41	—	53	4	no	—
841	C₂×#41	—	53	4	no	—
842	C₂×#41	—	212	4	no	—
843	C₂×#41	C₂²×D₅₃	1	4	yes	—
844	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
845	C₂²×Q₈	—	53	1	no	—
846	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
847	C₂²×D₄	—	53	2	no	—
848	C₂²×D₄	—	53	2	no	—
849	C₂²×D₄	—	53	4	no	—
850	C₂²×D₄	—	53	2	no	—
851	C₂²×D₄	—	53	4	no	—
852	C₂²×D₄	—	53	4	no	—
853	C₂²×D₄	—	53	4	no	—
854	C₂²×D₄	—	53	8	no	—
855	C₂²×D₄	—	53	4	no	—
856	C₂²×D₄	—	53	4	no	—
857	C₂²×D₄	—	53	1	no	—
858	C₂²×D₄	—	212	4	no	—
859	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
860	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
861	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
862	C₂³×C₄	—	4	4	no	—
863	C₂³×C₄	—	53	2	no	—
864	C₂³×C₄	—	53	1	no	—
865	C₂³×C₄	—	53	2	no	—
866	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
867	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
868	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
869	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
870	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
871	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
872	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
873	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
874	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
875	C₄⋊Q₈	—	53	8	no	—
876	C₄⋊Q₈	—	53	8	no	—
877	#127	—	53	8	no	—
878	#126	—	53	8	no	—
879	#126	—	53	8	no	—
880	#126	—	53	8	no	—
881	#126	—	53	8	no	—
882	#126	—	53	8	no	—
883	#126	—	53	8	no	—
884	#126	—	53	8	no	—
885	#126	—	53	8	no	—
886	#126	—	53	8	no	—
887	#126	—	53	8	no	—
888	#125	—	53	8	no	—
889	#125	—	53	8	no	—
890	#125	—	53	8	no	—
891	#125	—	53	8	no	—
892	#125	—	53	8	no	—
893	#125	—	53	8	no	—
894	#124	—	53	8	no	—
895	#124	—	53	8	no	—
896	#124	—	53	8	no	—
897	#124	—	53	8	no	—
898	#124	—	53	8	no	—
899	#124	—	53	8	no	—
900	#124	—	53	8	no	—
901	#123	—	53	4	no	—
902	#123	—	53	4	no	—
903	#123	—	53	8	no	—
904	#123	—	53	8	no	—
905	#123	—	53	8	no	—
906	#123	—	53	4	no	—
907	#123	—	53	4	no	—
908	#123	—	53	4	no	—
909	#123	—	53	4	no	—
910	#123	—	53	8	no	—
911	#123	—	53	8	no	—
912	#123	—	53	8	no	—
913	#123	—	53	8	no	—
914	#123	—	53	8	no	—
915	#123	—	53	8	no	—
916	#123	—	53	4	no	—
917	#123	—	53	4	no	—
918	#123	—	53	8	no	—
919	#123	—	53	4	no	—
920	#123	—	53	4	no	—
921	#123	—	53	8	no	—
922	#123	—	53	8	no	—
923	#123	—	53	8	no	—
924	#123	—	53	8	no	—
925	#123	—	53	8	no	—
926	#123	—	53	8	no	—
927	#123	—	53	4	no	—
928	#123	—	53	8	no	—
929	#123	—	53	4	no	—
930	#123	—	53	8	no	—
931	#123	—	53	8	no	—
932	#123	—	53	8	no	—
933	#123	—	53	8	no	—
934	#123	—	53	8	no	—
935	#123	C₂²×D₅₃	1	8	yes	—
936	#123	C₂²×D₅₃	1	4	yes	complemented
937	#123	C₂²×D₅₃	1	4	yes	complemented
938	C₂²⋊Q₈	—	53	8	no	—
939	C₂²⋊Q₈	—	53	8	no	—
940	C₂²⋊Q₈	—	53	4	no	—
941	C₂²⋊Q₈	—	53	4	no	—
942	C₂²⋊Q₈	—	53	4	no	—
943	C₂²⋊Q₈	—	53	4	no	—
944	C₂²⋊Q₈	—	53	8	no	—
945	C₂²⋊Q₈	—	53	8	no	—
946	C₂²⋊Q₈	—	53	8	no	—
947	C₂²⋊Q₈	—	53	8	no	—
948	C₂²⋊Q₈	—	53	8	no	—
949	C₂²⋊Q₈	—	53	8	no	—
950	C₂²⋊Q₈	—	53	8	no	—
951	C₂²⋊Q₈	—	53	8	no	—
952	C₂²⋊Q₈	—	53	8	no	—
953	C₂²⋊Q₈	—	53	8	no	—
954	C₂²⋊Q₈	—	53	8	no	—
955	C₂²⋊Q₈	—	53	8	no	—
956	C₂²⋊Q₈	—	53	8	no	—
957	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
958	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
959	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
960	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
961	#121	—	53	8	no	—
962	#121	—	53	8	no	—
963	#121	—	53	8	no	—
964	#121	—	53	8	no	—
965	#121	—	53	8	no	—
966	#121	—	53	8	no	—
967	#121	—	53	8	no	—
968	#121	—	53	8	no	—
969	#121	—	53	8	no	—
970	#121	—	53	8	no	—
971	#121	—	53	4	no	—
972	#121	—	53	4	no	—
973	#121	—	53	4	no	—
974	#121	—	53	4	no	—
975	#121	—	53	8	no	—
976	#121	—	53	8	no	—
977	#121	—	53	8	no	—
978	#121	—	53	8	no	—
979	#121	—	53	8	no	—
980	#121	—	53	8	no	—
981	#121	—	53	8	no	—
982	#121	C₂²×D₅₃	1	4	yes	—
983	#121	C₂²×D₅₃	1	4	yes	—
984	#121	C₂²×D₅₃	1	4	yes	complemented
985	#121	C₂²×D₅₃	1	4	yes	complemented
986	#120	—	53	4	no	—
987	#120	—	53	4	no	—
988	#120	—	53	8	no	—
989	#120	—	53	4	no	—
990	#120	—	53	4	no	—
991	#120	—	53	4	no	—
992	#120	—	53	8	no	—
993	#120	—	53	4	no	—
994	#120	—	53	8	no	—
995	#120	—	53	8	no	—
996	#120	—	53	4	no	—
997	#120	—	53	8	no	—
998	#120	—	53	4	no	—
999	#120	—	53	8	no	—
1000	#120	C₂²×D₅₃	1	4	yes	—
1001	#120	C₂²×D₅₃	1	4	yes	—
1002	#120	C₂²×D₅₃	1	8	yes	—
1003	C₄×Q₈	—	53	8	no	—
1004	C₄×Q₈	—	53	8	no	—
1005	C₄×D₄	—	53	8	no	—
1006	C₄×D₄	—	53	8	no	—
1007	C₄×D₄	—	53	8	no	—
1008	C₄×D₄	—	53	8	no	—
1009	C₄×D₄	—	53	8	no	—
1010	C₄×D₄	—	53	8	no	—
1011	C₄×D₄	—	53	8	no	—
1012	C₄×D₄	—	53	8	no	—
1013	C₄×D₄	—	53	8	no	—
1014	C₄×D₄	—	53	8	no	—
1015	C₄×D₄	—	53	8	no	—
1016	C₄×D₄	—	53	8	no	—
1017	C₄×D₄	—	53	8	no	—
1018	C₄×D₄	—	53	8	no	—
1019	C₄×D₄	—	53	8	no	—
1020	C₄×D₄	—	53	8	no	—
1021	C₄×D₄	—	53	8	no	—
1022	C₄×D₄	—	53	8	no	—
1023	C₄×D₄	—	53	8	no	—
1024	C₄×D₄	—	53	8	no	—
1025	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1026	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1027	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1028	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1029	#117	—	53	4	no	—
1030	#117	—	53	4	no	—
1031	#117	—	53	4	no	—
1032	#117	—	53	8	no	—
1033	#117	—	53	4	no	—
1034	#117	—	53	4	no	—
1035	#117	—	53	8	no	—
1036	#117	—	53	8	no	—
1037	#117	—	53	8	no	—
1038	#117	—	53	8	no	—
1039	#117	C₂²×D₅₃	1	4	yes	—
1040	#117	C₂²×D₅₃	1	4	yes	complemented
1041	C₂×C₄⋊C₄	—	53	4	no	—
1042	C₂×C₄⋊C₄	—	53	4	no	—
1043	C₂×C₄⋊C₄	—	53	4	no	—
1044	C₂×C₄⋊C₄	—	53	4	no	—
1045	C₂×C₄⋊C₄	—	53	4	no	—
1046	C₂×C₄⋊C₄	—	53	4	no	—
1047	C₂×C₄⋊C₄	—	53	2	no	—
1048	C₂×C₄⋊C₄	—	53	4	no	—
1049	C₂×C₄⋊C₄	—	53	8	no	—
1050	C₂×C₄⋊C₄	—	53	8	no	—
1051	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1052	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1053	C₂×C₂²⋊C₄	—	53	2	no	—
1054	C₂×C₂²⋊C₄	—	53	2	no	—
1055	C₂×C₂²⋊C₄	—	53	4	no	—
1056	C₂×C₂²⋊C₄	—	53	4	no	—
1057	C₂×C₂²⋊C₄	—	53	2	no	—
1058	C₂×C₂²⋊C₄	—	53	4	no	—
1059	C₂×C₂²⋊C₄	—	53	4	no	—
1060	C₂×C₂²⋊C₄	—	53	4	no	—
1061	C₂×C₂²⋊C₄	—	53	4	no	—
1062	C₂×C₂²⋊C₄	—	53	4	no	—
1063	C₂×C₂²⋊C₄	—	53	4	no	—
1064	C₂×C₂²⋊C₄	—	53	4	no	—
1065	C₂×C₂²⋊C₄	—	53	4	no	—
1066	C₂×C₂²⋊C₄	—	53	4	no	—
1067	C₂×C₂²⋊C₄	—	53	8	no	—
1068	C₂×C₂²⋊C₄	—	53	4	no	—
1069	C₂×C₂²⋊C₄	—	53	8	no	—
1070	C₂×C₂²⋊C₄	—	53	4	no	—
1071	C₂×C₂²⋊C₄	—	53	8	no	—
1072	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1073	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1074	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1075	C₂×C₄²	—	53	2	no	—
1076	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1077	C₂⁴	—	2	4	no	—
1078	C₂⁴	—	4	4	no	—
1079	C₂⁴	—	53	2	no	—
1080	C₂⁴	—	53	4	no	—
1081	C₂⁴	—	53	2	no	—
1082	C₂⁴	—	53	4	no	—
1083	C₂⁴	—	212	2	no	—
1084	C₂⁴	—	212	4	no	—
1085	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1086	C₂⁴	C₂³×D₅₃	1	2	yes	—
1087	C₂⁴	C₂³×D₅₃	1	2	yes	—
1088	C₂⁴	C₂³×D₅₃	1	2	yes	—
1089	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1090	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1091	#41	—	4	8	no	—
1092	#41	—	4	8	no	—
1093	#41	—	212	8	no	—
1094	#41	—	212	8	no	—
1095	#41	—	212	8	no	—
1096	#41	—	212	16	no	—
1097	#41	—	212	8	no	—
1098	#41	—	212	8	no	—
1099	C₂×Q₈	—	4	2	no	—
1100	C₂×Q₈	—	53	8	no	—
1101	C₂×Q₈	—	53	4	no	—
1102	C₂×Q₈	—	53	4	no	—
1103	C₂×Q₈	—	212	2	no	—
1104	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1105	C₂×D₄	—	2	8	no	—
1106	C₂×D₄	—	4	2	no	—
1107	C₂×D₄	—	4	8	no	—
1108	C₂×D₄	—	53	8	no	—
1109	C₂×D₄	—	53	4	no	—
1110	C₂×D₄	—	53	4	no	—
1111	C₂×D₄	—	53	4	no	—
1112	C₂×D₄	—	53	4	no	—
1113	C₂×D₄	—	53	8	no	—
1114	C₂×D₄	—	53	8	no	—
1115	C₂×D₄	—	53	8	no	—
1116	C₂×D₄	—	53	4	no	—
1117	C₂×D₄	—	53	8	no	—
1118	C₂×D₄	—	53	4	no	—
1119	C₂×D₄	—	53	8	no	—
1120	C₂×D₄	—	53	4	no	—
1121	C₂×D₄	—	53	4	no	—
1122	C₂×D₄	—	106	8	no	—
1123	C₂×D₄	—	106	8	no	—
1124	C₂×D₄	—	212	2	no	—
1125	C₂×D₄	—	212	4	no	—
1126	C₂×D₄	—	212	16	no	—
1127	C₂×D₄	—	212	8	no	—
1128	C₂×D₄	—	212	8	no	—
1129	C₂×D₄	—	212	8	no	—
1130	C₂×D₄	—	212	8	no	—
1131	C₂×D₄	—	212	8	no	—
1132	C₂×D₄	—	212	8	no	—
1133	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1134	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1135	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1136	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1137	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1138	C₂²×C₄	—	2	4	no	—
1139	C₂²×C₄	—	2	4	no	—
1140	C₂²×C₄	—	4	4	no	—
1141	C₂²×C₄	—	4	4	no	—
1142	C₂²×C₄	—	4	4	no	—
1143	C₂²×C₄	—	4	4	no	—
1144	C₂²×C₄	—	4	4	no	—
1145	C₂²×C₄	—	4	4	no	—
1146	C₂²×C₄	—	4	4	no	—
1147	C₂²×C₄	—	53	4	no	—
1148	C₂²×C₄	—	53	2	no	—
1149	C₂²×C₄	—	53	2	no	—
1150	C₂²×C₄	—	53	4	no	—
1151	C₂²×C₄	—	53	4	no	—
1152	C₂²×C₄	—	53	4	no	—
1153	C₂²×C₄	—	53	8	no	—
1154	C₂²×C₄	—	53	4	no	—
1155	C₂²×C₄	—	53	4	no	—
1156	C₂²×C₄	—	53	8	no	—
1157	C₂²×C₄	—	53	8	no	—
1158	C₂²×C₄	—	53	4	no	—
1159	C₂²×C₄	—	53	8	no	—
1160	C₂²×C₄	—	53	4	no	—
1161	C₂²×C₄	—	212	4	no	—
1162	C₂²×C₄	—	212	4	no	—
1163	C₂²×C₄	—	212	2	no	—
1164	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1165	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1166	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1167	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1168	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1169	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1170	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1171	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1173	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1174	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1175	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1176	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1177	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1178	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1179	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1180	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1181	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1182	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1183	C₄⋊C₄	—	53	8	no	—
1184	C₄⋊C₄	—	53	8	no	—
1185	C₄⋊C₄	—	53	8	no	—
1186	C₄⋊C₄	—	53	8	no	—
1187	C₄⋊C₄	—	53	8	no	—
1188	C₄⋊C₄	—	53	8	no	—
1189	C₄⋊C₄	—	53	4	no	—
1190	C₄⋊C₄	—	53	4	no	—
1191	C₄⋊C₄	—	53	8	no	—
1192	C₄⋊C₄	—	53	8	no	—
1193	C₄⋊C₄	—	53	8	no	—
1194	C₄⋊C₄	—	53	8	no	—
1195	C₄⋊C₄	—	53	8	no	—
1196	C₄⋊C₄	—	53	8	no	—
1197	C₄⋊C₄	—	53	8	no	—
1198	C₄⋊C₄	—	53	8	no	—
1199	C₄⋊C₄	—	53	8	no	—
1200	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1201	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1202	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1203	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1204	C₂²⋊C₄	—	53	4	no	—
1205	C₂²⋊C₄	—	53	4	no	—
1206	C₂²⋊C₄	—	53	8	no	—
1207	C₂²⋊C₄	—	53	4	no	—
1208	C₂²⋊C₄	—	53	4	no	—
1209	C₂²⋊C₄	—	53	8	no	—
1210	C₂²⋊C₄	—	53	8	no	—
1211	C₂²⋊C₄	—	53	8	no	—
1212	C₂²⋊C₄	—	53	8	no	—
1213	C₂²⋊C₄	—	53	8	no	—
1214	C₂²⋊C₄	—	53	8	no	—
1215	C₂²⋊C₄	—	53	8	no	—
1216	C₂²⋊C₄	—	53	8	no	—
1217	C₂²⋊C₄	—	53	8	no	—
1218	C₂²⋊C₄	—	53	8	no	—
1219	C₂²⋊C₄	—	53	8	no	—
1220	C₂²⋊C₄	—	53	8	no	—
1221	C₂²⋊C₄	—	53	8	no	—
1222	C₂²⋊C₄	—	53	8	no	—
1223	C₂²⋊C₄	—	53	8	no	—
1224	C₂²⋊C₄	—	53	8	no	—
1225	C₂²⋊C₄	—	53	8	no	—
1226	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1227	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1228	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1229	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1230	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1231	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1232	C₄²	—	53	8	no	—
1233	C₄²	—	53	8	no	—
1234	C₄²	—	53	8	no	—
1235	C₄²	—	53	8	no	—
1236	C₄²	C₂³×D₅₃	1	8	yes	—
1237	C₂³	—	2	2	no	—
1238	C₂³	—	2	4	no	—
1239	C₂³	—	2	4	no	—
1240	C₂³	—	2	4	no	—
1241	C₂³	—	2	2	no	—
1242	C₂³	—	2	4	no	—
1243	C₂³	—	2	4	no	—
1244	C₂³	—	2	4	no	—
1245	C₂³	—	4	2	no	—
1246	C₂³	—	4	2	no	—
1247	C₂³	—	4	2	no	—
1248	C₂³	—	4	2	no	—
1249	C₂³	—	4	4	no	—
1250	C₂³	—	4	16	no	—
1251	C₂³	—	53	4	no	—
1252	C₂³	—	53	4	no	—
1253	C₂³	—	106	4	no	—
1254	C₂³	—	106	4	no	—
1255	C₂³	—	106	8	no	—
1256	C₂³	—	424	8	no	—
1257	C₂³	—	212	4	no	—
1258	C₂³	—	212	8	no	—
1259	C₂³	—	212	4	no	—
1260	C₂³	—	212	4	no	—
1261	C₂³	—	212	4	no	—
1262	C₂³	—	212	4	no	—
1263	C₂³	#13133262	1	4	yes	—
1264	C₂³	C₂⁴×D₅₃	1	2	yes	—
1265	C₂³	C₂⁴×D₅₃	1	4	yes	—
1266	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1267	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1268	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1269	C₂³	C₂⁴×D₅₃	1	2	yes	—
1270	Q₈	—	4	4	no	—
1271	Q₈	—	212	4	no	—
1272	Q₈	—	212	8	no	—
1273	Q₈	—	212	4	no	—
1274	D₄	—	2	8	no	—
1275	D₄	—	2	8	no	—
1276	D₄	—	2	16	no	—
1277	D₄	—	4	8	no	—
1278	D₄	—	4	4	no	—
1279	D₄	—	106	8	no	—
1280	D₄	—	106	8	no	—
1281	D₄	—	106	8	no	—
1282	D₄	—	106	8	no	—
1283	D₄	—	106	16	no	—
1284	D₄	—	212	8	no	—
1285	D₄	—	212	4	no	—
1286	D₄	—	212	4	no	—
1287	D₄	—	212	8	no	—
1288	D₄	—	212	8	no	—
1289	D₄	—	212	8	no	—
1290	D₄	—	212	4	no	—
1291	D₄	—	212	4	no	—
1292	D₄	—	212	8	no	—
1293	C₂×C₄	—	2	2	no	—
1294	C₂×C₄	—	2	2	no	—
1295	C₂×C₄	—	2	2	no	—
1296	C₂×C₄	—	2	2	no	—
1297	C₂×C₄	—	2	4	no	—
1298	C₂×C₄	—	2	4	no	—
1299	C₂×C₄	—	2	4	no	—
1300	C₂×C₄	—	2	4	no	—
1301	C₂×C₄	—	2	4	no	—
1302	C₂×C₄	—	4	2	no	—
1303	C₂×C₄	—	4	2	no	—
1304	C₂×C₄	—	4	2	no	—
1305	C₂×C₄	—	4	2	no	—
1306	C₂×C₄	—	4	2	no	—
1307	C₂×C₄	—	4	2	no	—
1308	C₂×C₄	—	4	2	no	—
1309	C₂×C₄	—	4	2	no	—
1310	C₂×C₄	—	4	8	no	—
1311	C₂×C₄	—	4	4	no	—
1312	C₂×C₄	—	53	8	no	—
1313	C₂×C₄	—	53	8	no	—
1314	C₂×C₄	—	53	4	no	—
1315	C₂×C₄	—	53	4	no	—
1316	C₂×C₄	—	106	4	no	—
1317	C₂×C₄	—	106	4	no	—
1318	C₂×C₄	—	106	8	no	—
1319	C₂×C₄	—	212	8	no	—
1320	C₂×C₄	—	212	8	no	—
1321	C₂×C₄	—	212	4	no	—
1322	C₂×C₄	—	212	4	no	—
1323	C₂×C₄	—	212	8	no	—
1324	C₂×C₄	—	212	4	no	—
1325	C₂×C₄	—	212	4	no	—
1326	C₂×C₄	—	212	4	no	—
1327	C₂×C₄	—	212	4	no	—
1328	C₂×C₄	—	212	4	no	—
1329	C₂×C₄	—	212	8	no	—
1330	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1331	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1332	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1333	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1334	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1335	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1336	C₂²	—	2	8	no	—
1337	C₂²	—	2	2	no	—
1338	C₂²	—	2	2	no	—
1339	C₂²	—	2	2	no	—
1340	C₂²	—	2	2	no	—
1341	C₂²	—	2	2	no	—
1342	C₂²	—	2	2	no	—
1343	C₂²	—	2	4	no	—
1344	C₂²	—	2	8	no	—
1345	C₂²	—	2	2	no	—
1346	C₂²	—	2	2	no	—
1347	C₂²	—	4	4	no	—
1348	C₂²	—	4	8	no	—
1349	C₂²	—	4	8	no	—
1350	C₂²	—	4	4	no	—
1351	C₂²	—	8	4	no	—
1352	C₂²	—	848	4	no	—
1353	C₂²	—	106	4	no	—
1354	C₂²	—	106	4	no	—
1355	C₂²	—	106	8	no	—
1356	C₂²	—	106	8	no	—
1357	C₂²	—	424	4	no	—
1358	C₂²	—	424	8	no	—
1359	C₂²	—	424	4	no	—
1360	C₂²	C₂×#13133262	1	2	yes	—
1361	C₂²	C₂×#13133262	1	2	yes	—
1362	C₂²	C₂×#13133262	1	2	yes	—
1363	C₂²	#16811459	1	4	yes	—
1364	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1365	C₄	—	2	2	no	—
1366	C₄	—	2	2	no	—
1367	C₄	—	2	2	no	—
1368	C₄	—	2	2	no	—
1369	C₄	—	2	4	no	—
1370	C₄	—	2	8	no	—
1371	C₄	—	106	4	no	—
1372	C₄	—	106	4	no	—
1373	C₄	—	106	8	no	—
1374	C₄	—	106	8	no	—
1375	C₂	—	2	2	no	—
1376	C₂	—	2	4	no	—
1377	C₂	—	2	2	no	—
1378	C₂	—	2	2	no	—
1379	C₂	—	4	2	no	—
1380	C₂	—	4	4	no	—
1381	C₂	—	212	4	no	—
1382	C₂	—	212	4	no	—
1383	C₂	C₂²×#13133262	1	1	yes	characteristic
1384	C₂	C₂×#16811459	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#525	C₂
hypercenter	C₂×#525	D₅₃
hypocenter	C₅₃	#62820
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #20288924	C₂	semidirect
2. #20288918	C₂	semidirect
3. #20288905	C₂	semidirect
4. #20288899	C₂	semidirect
5. #20288879	C₂	semidirect
6. #20288655	C₂	semidirect
7. #20288641	C₂	semidirect
8. #20288416	C₂	semidirect
9. #20288413	C₂	semidirect
10. #20288411	C₂	semidirect
11. #20288402	C₂	semidirect
12. #20288398	C₂	semidirect
13. #20288359	C₂	semidirect
14. #20288353	C₂	semidirect
15. #20288344	C₂	semidirect
16. C₂×#16811134	C₂	semidirect
17. C₂²×#13133200	C₂	semidirect
18. C₂×C₅₃×#525	C₂	semidirect
19. C₂×#13133262	C₂²	semidirect
20. C₂²×#11719945	C₂²	semidirect
22. #16811374	C₂²	semidirect
23. #16811369	C₂²	semidirect
24. #16811368	C₂²	semidirect
25. #16811361	C₂²	semidirect
26. #16811356	C₂²	semidirect
27. #16811332	C₂²	semidirect
28. #16811327	C₂²	semidirect
29. #16811323	C₂²	semidirect
30. #16811322	C₂²	semidirect
31. #16811322	C₂²	semidirect
32. #16811316	C₂²	semidirect
33. #16811310	C₂²	semidirect
34. #16811308	C₂²	semidirect
35. #16811306	C₂²	semidirect
36. #16811306	C₂²	semidirect
37. #16811304	C₂²	semidirect
38. #16811302	C₂²	semidirect
39. #16811302	C₂²	semidirect
40. #16811300	C₂²	semidirect
41. #16811299	C₂²	semidirect
42. #16811299	C₂²	semidirect
43. #16811297	C₂²	semidirect
44. #16811297	C₂²	semidirect
45. #16811296	C₂²	semidirect
46. #16811274	C₂²	semidirect
47. #16811272	C₂²	semidirect
48. #16811272	C₂²	semidirect
49. #16811271	C₂²	semidirect
50. #16811268	C₂²	semidirect
51. #16811267	C₂²	semidirect
52. #16811265	C₂²	semidirect
53. #16811263	C₂²	semidirect
54. #16811263	C₂²	semidirect
55. #16811262	C₂²	semidirect
56. #16811261	C₂²	semidirect
57. #16811261	C₂²	semidirect
58. #16811260	C₂²	semidirect
59. #16811260	C₂²	semidirect
60. D₄×C₂²⋊D₅₃	C₂²	semidirect
61. #16811255	C₂²	semidirect
62. #16811252	C₂²	semidirect
63. #16811249	C₂²	semidirect
64. #16811248	C₂²	semidirect
65. #16811243	C₂²	semidirect
66. #16811238	C₂²	semidirect
67. #16811224	C₂²	semidirect
68. #16811223	C₂²	semidirect
69. #16811222	C₂²	semidirect
70. #16811220	C₂²	semidirect
71. #16811219	C₂²	semidirect
72. #16811218	C₂²	semidirect
73. #16811217	C₂²	semidirect
74. #16811215	C₂²	semidirect
75. #16811215	C₂²	semidirect
76. #16811213	C₂²	semidirect
77. #16811210	C₂²	semidirect
78. #16811208	C₂²	semidirect
79. #16811206	C₂²	semidirect
80. #16811206	C₂²	semidirect
81. #16811205	C₂²	semidirect
82. #16811200	C₂²	semidirect
83. #16811197	C₂²	semidirect
84. #16811195	C₂²	semidirect
85. #16811188	C₂²	semidirect
87. #16811184	C₂²	semidirect
88. #16811183	C₂²	semidirect
90. #16811182	C₂²	semidirect
91. #16811182	C₂²	semidirect
92. #16811181	C₂²	semidirect
93. #16811157	C₂²	semidirect
94. #16811150	C₂²	semidirect
95. #16811134	C₂²	semidirect
96. #16811134	C₂²	semidirect
97. #16811134	C₂²	semidirect
98. #16811134	C₂²	semidirect
99. #16811134	C₂²	semidirect
100. #16811131	C₂²	semidirect
101. #16811129	C₂²	semidirect
102. #16811129	C₂²	semidirect
103. C₂×#13133200	C₂²	semidirect
104. C₂×#13133200	C₂²	semidirect
105. C₂×#13133200	C₂²	semidirect
106. C₂×#13133200	C₂²	semidirect
107. C₂×#13133200	C₂²	semidirect
108. C₂×#13133200	C₂²	semidirect
109. C₂×#13133200	C₂²	semidirect
110. C₂×#13133200	C₂²	semidirect
111. C₂×#13133200	C₂²	semidirect
112. #123×D₅₃	C₂²	semidirect
113. C₂×#13133196	C₂²	semidirect
114. C₂×#13133191	C₂²	semidirect
115. C₂×#13133186	C₂²	semidirect
116. #120×D₅₃	C₂²	semidirect
117. #16811102	C₂²	semidirect
118. #16811098	C₂²	semidirect
119. #16811096	C₂²	semidirect
120. #16811096	C₂²	semidirect
121. #16811095	C₂²	semidirect
122. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
123. C₂×#13133176	C₂²	semidirect
124. C₂²×#11719919	C₂²	semidirect
125. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
126. C₂²×#11719921	C₂²	semidirect
127. C₂²×#41×C₅₃	C₂²	semidirect
128. C₂⁴×C₄×C₅₃	C₂²	semidirect
129. C₅₃×#525	C₂²	semidirect
130. C₅₃×#525	C₂²	semidirect
131. C₅₃×#525	C₂²	semidirect
132. C₅₃×#525	C₂²	semidirect
133. C₂×#123×C₅₃	C₂²	semidirect
134. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
135. C₂×#121×C₅₃	C₂²	semidirect
136. C₂×#120×C₅₃	C₂²	semidirect
137. C₂×C₄×D₄×C₅₃	C₂²	semidirect
138. C₂×#117×C₅₃	C₂²	semidirect
144. C₂×#11719945	C₂³	semidirect
148. C₂²×Dic₁₀₆	C₂³	semidirect
149. C₂²×D₂₁₂	C₂³	semidirect
163. C₂²×C₄×D₅₃	C₂³	semidirect
164. #13133216	C₂³	semidirect
165. #13133215	C₂³	semidirect
167. #13133212	C₂³	semidirect
168. #13133212	C₂³	semidirect
169. #13133212	C₂³	semidirect
170. #13133212	C₂³	semidirect
171. #13133211	C₂³	semidirect
172. #13133211	C₂³	semidirect
173. #13133210	C₂³	semidirect
174. #13133210	C₂³	semidirect
175. #13133210	C₂³	semidirect
176. #13133210	C₂³	semidirect
177. #13133209	C₂³	semidirect
178. #13133208	C₂³	semidirect
179. #13133207	C₂³	semidirect
180. #13133207	C₂³	semidirect
181. #13133207	C₂³	semidirect
182. #13133207	C₂³	semidirect
183. #13133206	C₂³	semidirect
184. #13133205	C₂³	semidirect
185. #13133204	C₂³	semidirect
187. #13133203	C₂³	semidirect
188. #13133203	C₂³	semidirect
189. #13133203	C₂³	semidirect
190. #13133202	C₂³	semidirect
191. #13133202	C₂³	semidirect
192. #13133202	C₂³	semidirect
193. #13133202	C₂³	semidirect
197. #13133201	C₂³	semidirect
210. #13133200	C₂³	semidirect
211. #13133200	C₂³	semidirect
212. #13133200	C₂³	semidirect
213. #13133200	C₂³	semidirect
214. #13133200	C₂³	semidirect
216. #13133199	C₂³	semidirect
217. #13133199	C₂³	semidirect
218. #13133199	C₂³	semidirect
221. #13133198	C₂³	semidirect
222. #13133198	C₂³	semidirect
223. #13133198	C₂³	semidirect
224. #13133197	C₂³	semidirect
227. #13133196	C₂³	semidirect
228. #13133196	C₂³	semidirect
229. #13133196	C₂³	semidirect
230. #13133196	C₂³	semidirect
231. #13133195	C₂³	semidirect
232. #13133195	C₂³	semidirect
233. #13133195	C₂³	semidirect
234. #13133195	C₂³	semidirect
238. #13133194	C₂³	semidirect
239. #13133194	C₂³	semidirect
240. #13133194	C₂³	semidirect
241. #13133193	C₂³	semidirect
242. #13133193	C₂³	semidirect
243. #13133192	C₂³	semidirect
247. #13133191	C₂³	semidirect
248. #13133191	C₂³	semidirect
249. #13133191	C₂³	semidirect
252. #13133190	C₂³	semidirect
253. #13133190	C₂³	semidirect
259. #13133189	C₂³	semidirect
260. #13133189	C₂³	semidirect
261. #13133189	C₂³	semidirect
263. #13133188	C₂³	semidirect
267. #13133187	C₂³	semidirect
272. #13133186	C₂³	semidirect
276. #13133185	C₂³	semidirect
277. #13133185	C₂³	semidirect
278. C₄×Dic₁₀₆	C₂³	semidirect
279. #13133182	C₂³	semidirect
280. C₄×D₂₁₂	C₂³	semidirect
284. D₄×Dic₅₃	C₂³	semidirect
285. #13133179	C₂³	semidirect
289. C₄×C₂²⋊D₅₃	C₂³	semidirect
290. C₄×C₂²⋊D₅₃	C₂³	semidirect
291. C₄×C₂²⋊D₅₃	C₂³	semidirect
292. C₄×C₂²⋊D₅₃	C₂³	semidirect
293. C₄×C₂²⋊D₅₃	C₂³	semidirect
298. #13133177	C₂³	semidirect
299. #13133177	C₂³	semidirect
301. #13133176	C₂³	semidirect
302. #13133176	C₂³	semidirect
303. #13133175	C₂³	semidirect
304. #13133174	C₂³	semidirect
305. #13133174	C₂³	semidirect
308. #13133173	C₂³	semidirect
309. #13133173	C₂³	semidirect
310. C₂×C₄⋊Dic₅₃	C₂³	semidirect
317. C₂×#11719919	C₂³	semidirect
318. C₂×#11719919	C₂³	semidirect
319. C₄⋊C₄×D₅₃	C₂³	semidirect
326. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
333. C₂×#11719921	C₂³	semidirect
334. C₂×#11719921	C₂³	semidirect
337. C₂²⋊C₄×D₅₃	C₂³	semidirect
338. C₂²⋊C₄×D₅₃	C₂³	semidirect
339. C₂×C₄×Dic₅₃	C₂³	semidirect
343. C₂×#41×C₅₃	C₂³	semidirect
344. C₂²×Q₈×C₅₃	C₂³	semidirect
347. C₂²×D₄×C₅₃	C₂³	semidirect
357. C₂³×C₄×C₅₃	C₂³	semidirect
359. #123×C₅₃	C₂³	semidirect
360. #123×C₅₃	C₂³	semidirect
363. C₂²⋊Q₈×C₅₃	C₂³	semidirect
364. C₂²⋊Q₈×C₅₃	C₂³	semidirect
367. #121×C₅₃	C₂³	semidirect
368. #121×C₅₃	C₂³	semidirect
374. C₄×D₄×C₅₃	C₂³	semidirect
375. C₄×D₄×C₅₃	C₂³	semidirect
377. #117×C₅₃	C₂³	semidirect
378. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
379. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
382. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
383. C₂×C₄²×C₅₃	C₂³	semidirect
699. C₂×#525	D₅₃	semidirect
713. C₂²×#41	C₂×D₅₃	semidirect
715. C₂⁴×C₄	C₂×D₅₃	semidirect
797. #525	C₂×D₅₃	semidirect
798. #525	C₂×D₅₃	semidirect
799. #525	C₂×D₅₃	semidirect
800. #525	C₂×D₅₃	semidirect
811. C₂×#123	C₂×D₅₃	semidirect
813. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
815. C₂×#121	C₂×D₅₃	semidirect
818. C₂×#120	C₂×D₅₃	semidirect
825. C₂×C₄×D₄	C₂×D₅₃	semidirect
827. C₂×#117	C₂×D₅₃	semidirect
831. C₅₃	#62820	semidirect
844. C₂×#41	C₂²×D₅₃	semidirect
846. C₂²×Q₈	C₂²×D₅₃	semidirect
861. C₂²×D₄	C₂²×D₅₃	semidirect
874. C₂³×C₄	C₂²×D₅₃	semidirect
936. #123	C₂²×D₅₃	semidirect
937. #123	C₂²×D₅₃	semidirect
959. C₂²⋊Q₈	C₂²×D₅₃	semidirect
960. C₂²⋊Q₈	C₂²×D₅₃	semidirect
984. #121	C₂²×D₅₃	semidirect
985. #121	C₂²×D₅₃	semidirect
1027. C₄×D₄	C₂²×D₅₃	semidirect
1028. C₄×D₄	C₂²×D₅₃	semidirect
1040. #117	C₂²×D₅₃	semidirect
1051. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1052. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1074. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1076. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288924	2
#20288918	2
#20288905	2
#20288899	2
#20288879	2
#20288655	2
#20288641	2
#20288416	2
#20288413	2
#20288411	2
#20288402	2
#20288398	2
#20288359	2
#20288353	2
#20288344	2
C₂×#16811134	2
C₂²×#13133200	2
C₂×C₅₃×#525	2
#62820	53