Subgroups — #28293226

Order 13568.

7370 conjugacy classes of subgroups.

The subgroup lattice has 1620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288608	C₂	1	4	yes	maximal, complemented
2	#20288605	C₂	1	4	yes	maximal, complemented
3	#20288588	C₂	1	4	yes	maximal, complemented
4	#20288585	C₂	1	4	yes	maximal, complemented
5	#20288569	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288567	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288566	C₂	1	2	yes	maximal, complemented
8	#20288564	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288560	C₂	1	2	yes	maximal, complemented
10	#20288449	C₂	1	4	yes	maximal, complemented
11	#20288446	C₂	1	4	yes	maximal, complemented
12	#20288443	C₂	1	4	yes	maximal, complemented
13	#20288439	C₂	1	4	yes	maximal, complemented
14	#20288401	C₂	1	4	yes	maximal, complemented
15	#20288398	C₂	1	4	yes	maximal, complemented
16	#20288134	C₂	1	4	yes	maximal, complemented
17	#20288133	C₂	1	4	yes	maximal, complemented
18	#20288118	C₂	1	1	yes	maximal, characteristic, complemented
19	#20288042	C₂	1	1	yes	maximal, characteristic, complemented
20	#535×D₅₃	C₂	1	2	yes	maximal, complemented
21	#20287915	C₂	1	2	yes	maximal, complemented
22	C₂×#16811095	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×D₅₃	C₂²	1	2	yes	—
25	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
26	#16811359	C₂²	1	4	yes	complemented
27	#16811358	C₂²	1	4	yes	complemented
28	#16811358	C₂²	1	4	yes	complemented
29	#16811356	C₂²	1	4	yes	complemented
30	#16811356	C₂²	1	4	yes	complemented
31	#16811355	C₂²	1	4	yes	complemented
32	#16811355	C₂²	1	4	yes	complemented
33	#16811347	C₂²	1	2	yes	complemented
34	#16811346	C₂²	1	2	yes	complemented
35	#16811345	C₂²	1	4	yes	complemented
36	#16811343	C₂²	1	2	yes	complemented
37	#16811342	C₂²	1	4	yes	complemented
38	#16811339	C₂²	1	2	yes	complemented
39	#16811338	C₂²	1	2	yes	complemented
40	#16811338	C₂²	1	2	yes	complemented
41	#16811337	C₂²	1	4	yes	complemented
42	#16811336	C₂²	1	4	yes	complemented
43	#16811326	C₂²	1	4	yes	complemented
44	#16811325	C₂²	1	4	yes	complemented
45	#16811323	C₂²	1	4	yes	complemented
46	#16811321	C₂²	1	4	yes	complemented
47	#16811320	C₂²	1	4	yes	complemented
48	#16811319	C₂²	1	4	yes	complemented
49	#16811317	C₂²	1	4	yes	complemented
50	#16811303	C₂²	1	8	yes	complemented
51	#16811302	C₂²	1	8	yes	complemented
52	#16811301	C₂²	1	8	yes	complemented
53	#16811300	C₂²	1	8	yes	complemented
54	#16811298	C₂²	1	8	yes	complemented
55	#16811298	C₂²	1	8	yes	complemented
56	#16811297	C₂²	1	8	yes	complemented
57	#16811296	C₂²	1	8	yes	complemented
58	#16811295	C₂²	1	2	yes	complemented
59	#16811294	C₂²	1	2	yes	complemented
60	#16811294	C₂²	1	4	yes	complemented
61	#16811293	C₂²	1	4	yes	complemented
62	#16811293	C₂²	1	2	yes	complemented
63	#16811278	C₂²	1	2	yes	complemented
64	#16811277	C₂²	1	2	yes	complemented
65	#16811276	C₂²	1	2	yes	complemented
66	#16811274	C₂²	1	4	yes	complemented
67	#16811273	C₂²	1	4	yes	complemented
68	#16811270	C₂²	1	8	yes	complemented
69	#16811268	C₂²	1	8	yes	complemented
70	#16811266	C₂²	1	8	yes	complemented
71	#16811265	C₂²	1	8	yes	complemented
72	#16811265	C₂²	1	8	yes	complemented
73	#16811262	C₂²	1	8	yes	complemented
74	#16811262	C₂²	1	8	yes	complemented
75	#16811261	C₂²	1	8	yes	complemented
76	#16811253	C₂²	1	2	yes	complemented
77	#16811253	C₂²	1	2	yes	complemented
78	#16811252	C₂²	1	2	yes	complemented
79	#16811252	C₂²	1	2	yes	complemented
80	#16811250	C₂²	1	2	yes	complemented
81	#16811250	C₂²	1	2	yes	complemented
82	#16811248	C₂²	1	2	yes	—
83	#16811248	C₂²	1	2	yes	—
84	#16811243	C₂²	1	8	yes	complemented
85	#16811241	C₂²	1	8	yes	complemented
86	#16811239	C₂²	1	8	yes	complemented
87	#16811237	C₂²	1	8	yes	complemented
88	#16811225	C₂²	1	8	yes	complemented
89	#16811225	C₂²	1	8	yes	complemented
90	#16811223	C₂²	1	8	yes	complemented
91	#16811223	C₂²	1	8	yes	complemented
92	#16811213	C₂²	1	4	yes	complemented
93	#16811211	C₂²	1	4	yes	complemented
94	#16811210	C₂²	1	4	yes	complemented
95	#16811208	C₂²	1	8	yes	complemented
96	#16811206	C₂²	1	8	yes	complemented
97	#16811200	C₂²	1	2	yes	complemented
98	#16811200	C₂²	1	2	yes	complemented
99	#16811198	C₂²	1	2	yes	complemented
100	#16811193	C₂²	1	2	yes	complemented
101	#16811192	C₂²	1	2	yes	complemented
102	#16811191	C₂²	1	4	yes	—
103	#16811191	C₂²	1	2	yes	complemented
104	#16811190	C₂²	1	2	yes	complemented
105	#16811189	C₂²	1	4	yes	—
106	#16811189	C₂²	1	4	yes	—
107	#16811188	C₂²	1	8	yes	complemented
108	#16811187	C₂²	1	2	yes	complemented
109	#16811186	C₂²	1	4	yes	—
110	#16811186	C₂²	1	2	yes	complemented
111	#16811181	C₂²	1	2	yes	—
112	#16811181	C₂²	1	2	yes	—
113	#16811180	C₂²	1	1	yes	characteristic, complemented
114	#16811177	C₂²	1	4	yes	complemented
115	#16811177	C₂²	1	4	yes	complemented
116	#16811176	C₂²	1	2	yes	complemented
117	#16811173	C₂²	1	1	yes	characteristic, complemented
118	#16811172	C₂²	1	8	yes	complemented
119	#16811170	C₂²	1	8	yes	complemented
120	#16811169	C₂²	1	2	yes	complemented
121	#16811169	C₂²	1	8	yes	complemented
122	#16811168	C₂²	1	8	yes	complemented
123	#127×D₅₃	C₂²	1	4	yes	complemented
124	#16811156	C₂²	1	8	yes	complemented
125	#16811153	C₂²	1	8	yes	complemented
126	#16811151	C₂²	1	8	yes	complemented
127	#16811150	C₂²	1	8	yes	complemented
128	#124×D₅₃	C₂²	1	4	yes	complemented
129	#16811136	C₂²	1	4	yes	complemented
130	#16811134	C₂²	1	4	yes	complemented
131	#16811133	C₂²	1	4	yes	complemented
132	#16811132	C₂²	1	8	yes	complemented
133	#16811132	C₂²	1	4	yes	complemented
134	#16811132	C₂²	1	4	yes	complemented
135	#16811129	C₂²	1	8	yes	complemented
136	#121×D₅₃	C₂²	1	4	yes	complemented
137	#121×D₅₃	C₂²	1	4	yes	complemented
138	#120×D₅₃	C₂²	1	8	yes	—
139	#16811106	C₂²	1	2	yes	complemented
140	#16811104	C₂²	1	2	yes	complemented
141	#16811104	C₂²	1	4	yes	complemented
142	#16811103	C₂²	1	2	yes	complemented
143	#16811103	C₂²	1	4	yes	complemented
144	#16811099	C₂²	1	4	yes	complemented
145	#16811095	C₂²	1	8	yes	—
146	#16811095	C₂²	1	4	yes	complemented
147	#16811095	C₂²	1	4	yes	complemented
148	#16811095	C₂²	1	4	yes	complemented
149	#16811095	C₂²	1	4	yes	complemented
150	#16811095	C₂²	1	4	yes	complemented
151	C₄×#11719949	C₂²	1	4	yes	complemented
152	C₄×#11719947	C₂²	1	8	yes	complemented
153	C₄×#11719947	C₂²	1	4	yes	complemented
154	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
155	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
156	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
157	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
158	C₂×#13133177	C₂²	1	2	yes	complemented
159	C₂×#13133175	C₂²	1	1	yes	characteristic
160	C₂×#13133175	C₂²	1	4	yes	complemented
161	C₂×#13133174	C₂²	1	1	yes	characteristic
162	#117×D₅₃	C₂²	1	2	yes	—
163	#117×D₅₃	C₂²	1	4	yes	complemented
164	C₂²×#11719921	C₂²	1	2	yes	—
165	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	—
166	C₅₃×#559	C₂²	1	4	yes	complemented
167	C₅₃×#556	C₂²	1	2	yes	complemented
168	C₅₃×#555	C₂²	1	2	yes	complemented
169	C₅₃×#553	C₂²	1	4	yes	complemented
170	C₅₃×#550	C₂²	1	2	yes	complemented
171	C₅₃×#547	C₂²	1	2	yes	complemented
172	C₅₃×#538	C₂²	1	4	yes	complemented
173	C₅₃×#535	C₂²	1	2	yes	complemented
174	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#525	C₂²	1	4	yes	complemented
177	C₅₃×#520	C₂²	1	2	yes	complemented
178	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂⁴×D₅₃	C₂³	1	2	yes	—
180	C₂×#11719949	C₂³	1	2	yes	—
181	C₂×#11719949	C₂³	1	4	yes	complemented
182	C₂×#11719945	C₂³	1	4	yes	—
183	C₂×#11719945	C₂³	1	2	yes	—
184	C₂×#11719945	C₂³	1	4	yes	complemented
185	C₂×#11719945	C₂³	1	8	yes	complemented
186	C₂×#11719947	C₂³	1	2	yes	—
187	C₂×#11719947	C₂³	1	4	yes	—
188	C₂×#11719947	C₂³	1	8	yes	complemented
189	C₂×#11719947	C₂³	1	4	yes	complemented
190	#41×D₅₃	—	2	16	no	—
191	C₂×Q₈×D₅₃	C₂³	1	2	yes	—
192	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
193	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
194	C₂×D₄×D₅₃	—	2	8	no	—
195	C₂×D₄×D₅₃	C₂³	1	4	yes	—
196	C₂×D₄×D₅₃	C₂³	1	4	yes	—
197	C₂×D₄×D₅₃	C₂³	1	4	yes	—
198	C₂×D₄×D₅₃	C₂³	1	2	yes	—
199	C₂×D₄×D₅₃	C₂³	1	8	yes	—
200	C₂×D₄×D₅₃	C₂³	1	8	yes	—
201	C₂³×Dic₅₃	C₂³	1	2	yes	—
202	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
203	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
204	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	#13133217	C₂³	1	1	yes	characteristic, complemented
207	#13133217	C₂³	1	1	yes	characteristic, complemented
208	#13133217	C₂³	1	1	yes	characteristic, complemented
209	#13133216	C₂³	1	2	yes	complemented
210	#13133216	C₂³	1	2	yes	complemented
211	#13133216	C₂³	1	4	yes	complemented
212	#13133216	C₂³	1	4	yes	complemented
213	#13133215	C₂³	1	2	yes	complemented
214	#13133215	C₂³	1	4	yes	complemented
215	#13133215	C₂³	1	4	yes	complemented
216	#13133214	C₂³	1	4	yes	—
217	#13133214	C₂³	1	1	yes	characteristic, complemented
218	#13133213	C₂³	1	4	yes	—
219	#13133213	C₂³	1	4	yes	—
220	#13133213	C₂³	1	8	yes	—
221	#13133213	C₂³	1	8	yes	—
222	#13133213	C₂³	1	2	yes	complemented
223	#13133212	C₂³	1	8	yes	complemented
224	#13133212	C₂³	1	8	yes	complemented
225	#13133212	C₂³	1	8	yes	complemented
226	#13133211	C₂³	1	8	yes	complemented
227	#13133210	C₂³	1	8	yes	complemented
228	#13133210	C₂³	1	8	yes	complemented
229	#13133210	C₂³	1	8	yes	complemented
230	#13133209	C₂³	1	2	yes	complemented
231	#13133208	C₂³	1	2	yes	complemented
232	#13133208	C₂³	1	2	yes	complemented
233	#13133207	C₂³	1	4	yes	complemented
234	#13133207	C₂³	1	4	yes	complemented
235	#13133207	C₂³	1	4	yes	complemented
236	#13133207	C₂³	1	4	yes	complemented
237	#13133206	C₂³	1	4	yes	—
238	#13133206	C₂³	1	8	yes	complemented
239	#13133206	C₂³	1	2	yes	complemented
240	#13133205	C₂³	1	4	yes	—
241	#13133205	C₂³	1	8	yes	complemented
242	#13133205	C₂³	1	2	yes	complemented
243	#13133204	C₂³	1	4	yes	—
244	#13133204	C₂³	1	8	yes	complemented
245	#13133204	C₂³	1	2	yes	complemented
246	#13133203	C₂³	1	8	yes	—
247	#13133203	C₂³	1	8	yes	—
248	#13133203	C₂³	1	8	yes	complemented
249	#13133203	C₂³	1	8	yes	complemented
250	#13133203	C₂³	1	8	yes	complemented
251	#13133203	C₂³	1	8	yes	complemented
252	#13133202	C₂³	1	4	yes	—
253	#13133202	C₂³	1	4	yes	—
254	#13133202	C₂³	1	8	yes	complemented
255	#13133202	C₂³	1	8	yes	complemented
256	#13133202	C₂³	1	8	yes	complemented
257	#13133202	C₂³	1	8	yes	complemented
258	#13133201	C₂³	1	8	yes	complemented
259	#13133201	C₂³	1	8	yes	complemented
260	#13133200	C₂³	1	8	yes	complemented
261	#13133200	C₂³	1	8	yes	complemented
262	#13133199	C₂³	1	4	yes	—
263	#13133199	C₂³	1	4	yes	—
264	#13133199	C₂³	1	8	yes	complemented
265	#13133199	C₂³	1	8	yes	complemented
266	#13133199	C₂³	1	8	yes	complemented
267	#13133199	C₂³	1	8	yes	complemented
268	#13133198	C₂³	1	8	yes	complemented
269	#13133198	C₂³	1	8	yes	complemented
270	#13133197	C₂³	1	4	yes	—
271	#13133197	C₂³	1	4	yes	—
272	#13133197	C₂³	1	4	yes	complemented
273	#13133196	C₂³	1	2	yes	—
274	#13133196	C₂³	1	2	yes	—
275	#13133196	C₂³	1	4	yes	complemented
276	#13133195	C₂³	1	4	yes	—
277	#13133195	C₂³	1	4	yes	—
278	#13133195	C₂³	1	4	yes	—
279	#13133195	C₂³	1	4	yes	—
280	#13133195	C₂³	1	8	yes	complemented
281	#13133195	C₂³	1	4	yes	complemented
282	#13133195	C₂³	1	4	yes	complemented
283	#13133194	C₂³	1	4	yes	—
284	#13133194	C₂³	1	4	yes	—
285	#13133194	C₂³	1	8	yes	complemented
286	#13133194	C₂³	1	4	yes	complemented
287	#13133194	C₂³	1	4	yes	complemented
288	#13133193	C₂³	1	4	yes	—
289	#13133193	C₂³	1	4	yes	—
290	#13133193	C₂³	1	4	yes	complemented
291	#13133192	C₂³	1	4	yes	—
292	#13133192	C₂³	1	4	yes	—
293	#13133192	C₂³	1	4	yes	complemented
294	#13133192	C₂³	1	8	yes	complemented
295	#13133191	C₂³	1	4	yes	—
296	#13133191	C₂³	1	4	yes	—
297	#13133191	C₂³	1	2	yes	—
298	#13133191	C₂³	1	2	yes	—
299	#13133191	C₂³	1	4	yes	complemented
300	#13133191	C₂³	1	8	yes	complemented
301	#13133190	C₂³	1	8	yes	—
302	#13133190	C₂³	1	8	yes	—
303	#13133190	C₂³	1	8	yes	complemented
304	#13133190	C₂³	1	8	yes	complemented
305	#13133190	C₂³	1	8	yes	complemented
306	#13133190	C₂³	1	4	yes	complemented
307	#13133190	C₂³	1	4	yes	complemented
308	#13133189	C₂³	1	8	yes	—
309	#13133189	C₂³	1	8	yes	—
310	#13133189	C₂³	1	4	yes	—
311	#13133189	C₂³	1	4	yes	—
312	#13133189	C₂³	1	8	yes	complemented
313	#13133189	C₂³	1	8	yes	complemented
314	#13133189	C₂³	1	8	yes	complemented
315	#13133189	C₂³	1	4	yes	complemented
316	#13133189	C₂³	1	4	yes	complemented
317	#13133188	C₂³	1	4	yes	—
318	#13133188	C₂³	1	4	yes	—
319	#13133188	C₂³	1	8	yes	complemented
320	#13133188	C₂³	1	4	yes	complemented
321	#13133187	C₂³	1	4	yes	—
322	#13133187	C₂³	1	4	yes	—
323	#13133187	C₂³	1	8	yes	—
324	#13133187	C₂³	1	8	yes	—
325	#13133187	C₂³	1	8	yes	—
326	#13133186	C₂³	1	8	yes	—
327	#13133185	C₂³	1	4	yes	—
328	#13133185	C₂³	1	8	yes	—
329	#13133185	C₂³	1	8	yes	—
330	#13133185	C₂³	1	8	yes	—
331	#13133185	C₂³	1	4	yes	—
332	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
333	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
334	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
335	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
336	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
337	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
338	C₄×Dic₁₀₆	C₂³	1	8	yes	complemented
339	#13133182	C₂³	1	4	yes	complemented
340	#13133182	C₂³	1	8	yes	complemented
341	C₄×D₂₁₂	C₂³	1	8	yes	—
342	C₄×D₂₁₂	C₂³	1	2	yes	—
343	C₄×D₂₁₂	C₂³	1	2	yes	—
344	C₄×D₂₁₂	C₂³	1	2	yes	—
345	C₄×D₂₁₂	C₂³	1	2	yes	—
346	C₄×D₂₁₂	C₂³	1	8	yes	complemented
347	C₄×D₂₁₂	C₂³	1	2	yes	complemented
348	C₄×D₂₁₂	C₂³	1	2	yes	complemented
349	C₄×D₂₁₂	C₂³	1	4	yes	complemented
350	D₄×Dic₅₃	C₂³	1	4	yes	—
351	D₄×Dic₅₃	C₂³	1	4	yes	—
352	D₄×Dic₅₃	C₂³	1	8	yes	—
353	D₄×Dic₅₃	C₂³	1	4	yes	complemented
354	D₄×Dic₅₃	C₂³	1	8	yes	complemented
355	#13133179	C₂³	1	8	yes	—
356	#13133179	C₂³	1	4	yes	—
357	#13133179	C₂³	1	4	yes	—
358	#13133179	C₂³	1	8	yes	complemented
359	#13133179	C₂³	1	4	yes	complemented
360	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
361	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
362	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
363	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
364	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
365	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
366	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
367	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
368	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
369	#13133177	C₂³	1	8	yes	—
370	#13133177	C₂³	1	8	yes	—
371	#13133177	C₂³	1	8	yes	—
372	#13133177	C₂³	1	8	yes	—
373	#13133177	C₂³	1	8	yes	complemented
374	#13133177	C₂³	1	8	yes	complemented
375	#13133177	C₂³	1	8	yes	complemented
376	#13133176	C₂³	1	2	yes	—
377	#13133176	C₂³	1	4	yes	complemented
378	#13133176	C₂³	1	4	yes	complemented
379	#13133175	C₂³	1	8	yes	—
380	#13133175	C₂³	1	2	yes	—
381	#13133175	C₂³	1	2	yes	—
382	#13133175	C₂³	1	4	yes	—
383	#13133175	C₂³	1	4	yes	—
384	#13133175	C₂³	1	4	yes	complemented
385	#13133175	C₂³	1	4	yes	complemented
386	#13133175	C₂³	1	4	yes	complemented
387	#13133175	C₂³	1	4	yes	complemented
388	#13133175	C₂³	1	8	yes	complemented
389	#13133174	C₂³	1	8	yes	—
390	#13133174	C₂³	1	4	yes	—
391	#13133174	C₂³	1	2	yes	—
392	#13133174	C₂³	1	2	yes	—
393	#13133174	C₂³	1	2	yes	—
394	#13133174	C₂³	1	2	yes	—
395	#13133174	C₂³	1	8	yes	complemented
396	#13133173	C₂³	1	4	yes	—
397	#13133173	C₂³	1	8	yes	complemented
398	#13133173	C₂³	1	8	yes	complemented
399	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
401	C₂×#11719919	C₂³	1	1	yes	characteristic
402	C₂×#11719919	C₂³	1	1	yes	characteristic
403	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
404	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
405	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
406	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
407	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
408	C₂×#11719921	C₂³	1	8	yes	—
409	C₂×#11719921	C₂³	1	8	yes	—
410	C₂×#11719921	C₂³	1	8	yes	—
411	C₂×#11719921	C₂³	1	1	yes	characteristic
412	C₂×#11719921	C₂³	1	2	yes	—
413	C₂×#11719921	C₂³	1	1	yes	characteristic
414	C₂×#11719921	C₂³	1	2	yes	—
415	C₂×#11719921	C₂³	1	2	yes	—
416	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
417	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
418	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
419	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
420	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
421	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
422	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
423	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
424	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
425	C₄²×D₅₃	C₂³	1	4	yes	—
426	C₄²×D₅₃	C₂³	1	8	yes	complemented
427	C₂×#41×C₅₃	C₂³	1	2	yes	—
428	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
429	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
430	C₂³×C₄×C₅₃	C₂³	1	2	yes	—
431	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
432	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
433	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
434	#127×C₅₃	C₂³	1	4	yes	—
435	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
436	#126×C₅₃	C₂³	1	8	yes	complemented
437	#125×C₅₃	C₂³	1	2	yes	complemented
438	#124×C₅₃	C₂³	1	4	yes	—
439	#124×C₅₃	C₂³	1	8	yes	complemented
440	#124×C₅₃	C₂³	1	2	yes	complemented
441	#123×C₅₃	C₂³	1	8	yes	complemented
442	#123×C₅₃	C₂³	1	8	yes	complemented
443	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
444	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
445	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
446	#121×C₅₃	C₂³	1	4	yes	—
447	#121×C₅₃	C₂³	1	2	yes	—
448	#121×C₅₃	C₂³	1	2	yes	—
449	#121×C₅₃	C₂³	1	4	yes	—
450	#121×C₅₃	C₂³	1	8	yes	complemented
451	#121×C₅₃	C₂³	1	4	yes	complemented
452	#120×C₅₃	C₂³	1	8	yes	—
453	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
454	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
455	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
456	C₄×D₄×C₅₃	C₂³	1	2	yes	—
457	C₄×D₄×C₅₃	C₂³	1	2	yes	—
458	C₄×D₄×C₅₃	C₂³	1	2	yes	—
459	C₄×D₄×C₅₃	C₂³	1	2	yes	—
460	C₄×D₄×C₅₃	C₂³	1	8	yes	—
461	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
462	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
463	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
464	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
465	#117×C₅₃	C₂³	1	2	yes	—
466	#117×C₅₃	C₂³	1	4	yes	complemented
467	#117×C₅₃	C₂³	1	4	yes	complemented
468	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
469	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
470	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
471	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
472	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
473	C₂³×D₅₃	—	2	8	no	—
474	C₂³×D₅₃	—	8	2	no	—
475	C₂³×D₅₃	—	8	2	no	—
476	C₂³×D₅₃	C₂⁴	1	8	yes	—
477	C₂³×D₅₃	C₂⁴	1	4	yes	—
478	C₂³×D₅₃	C₂⁴	1	2	yes	—
479	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
480	#41×C₅₃	—	2	8	no	—
481	#41×C₅₃	—	8	4	no	—
482	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
483	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
484	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
485	C₂×D₄×C₅₃	—	2	4	no	—
486	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
487	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
488	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
489	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
490	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
491	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
492	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
493	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
494	C₂²×C₄×C₅₃	—	8	2	no	—
495	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
496	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
499	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
500	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
501	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
502	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
503	C₂×C₂²⋊D₅₃	—	2	8	no	—
504	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
505	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
506	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
507	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
508	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
509	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
510	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
511	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
512	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
513	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
514	C₂²×Dic₅₃	—	8	2	no	—
515	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
516	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
517	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
518	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
519	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
520	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
521	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
522	#11719949	—	2	8	no	—
523	#11719949	—	8	4	no	—
524	Q₈×D₅₃	—	2	8	no	—
525	#11719947	—	2	16	no	—
526	#11719947	—	2	8	no	—
527	#11719947	—	8	4	no	—
528	#11719947	—	8	8	no	—
529	D₄×D₅₃	—	2	16	no	—
530	D₄×D₅₃	—	2	16	no	—
531	D₄×D₅₃	—	2	16	no	—
532	D₄×D₅₃	—	2	8	no	—
533	D₄×D₅₃	—	8	8	no	—
534	D₄×D₅₃	—	8	8	no	—
535	#11719945	—	2	8	no	—
536	#11719945	—	2	16	no	—
537	#11719945	—	8	8	no	—
538	#11719945	—	8	4	no	—
539	C₂×D₂₁₂	—	2	4	no	—
540	C₂×D₂₁₂	C₂⁴	1	4	yes	—
541	C₂×D₂₁₂	C₂⁴	1	2	yes	—
542	C₂×D₂₁₂	C₂⁴	1	2	yes	—
543	C₂×D₂₁₂	C₂⁴	1	2	yes	—
544	C₂×D₂₁₂	C₂⁴	1	8	yes	—
545	C₂×D₂₁₂	C₂⁴	1	8	yes	—
546	C₂×D₂₁₂	C₂⁴	1	2	yes	—
547	C₂×D₂₁₂	C₂⁴	1	2	yes	—
548	C₂×C₄×D₅₃	—	2	16	no	—
549	C₂×C₄×D₅₃	—	8	2	no	—
550	C₂×C₄×D₅₃	—	8	2	no	—
551	C₂×C₄×D₅₃	#41	1	8	yes	complemented
552	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
553	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
554	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
555	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
556	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
557	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
558	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
559	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
560	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
561	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
562	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
563	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
564	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
565	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
566	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
567	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
568	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
569	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
570	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
571	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
572	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
573	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
574	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
575	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
576	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
577	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
578	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
579	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
580	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
581	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
582	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
583	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
584	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
585	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
586	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
587	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
588	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
589	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
590	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
591	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
592	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
593	C₄²×C₅₃	C₂⁴	1	4	yes	—
594	C₄²×C₅₃	C₂⁴	1	8	yes	—
595	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
596	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
597	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
598	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
599	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
600	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
601	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
602	#11719921	C₂⁴	1	2	yes	—
603	#11719921	C₂⁴	1	2	yes	—
604	#11719921	C₂⁴	1	8	yes	—
605	#11719921	C₂⁴	1	4	yes	—
606	#11719921	C₂⁴	1	4	yes	—
607	#11719921	C₂⁴	1	8	yes	—
608	#11719921	C₂⁴	1	8	yes	—
609	#11719921	C₂⁴	1	8	yes	—
610	#11719921	C₂⁴	1	8	yes	—
611	#11719921	C₂⁴	1	2	yes	—
612	#11719921	C₂⁴	1	2	yes	—
613	#11719921	C₂⁴	1	8	yes	—
614	#11719921	C₂⁴	1	4	yes	—
615	#11719921	C₂⁴	1	4	yes	—
616	#11719921	C₂⁴	1	8	yes	—
617	#11719921	C₂⁴	1	8	yes	—
618	#11719921	C₂⁴	1	4	yes	—
619	#11719921	C₂⁴	1	4	yes	—
620	#11719921	C₂⁴	1	4	yes	—
621	#11719921	C₂⁴	1	4	yes	—
622	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
623	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
624	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
625	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
626	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
627	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
628	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
629	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
630	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
631	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
632	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
633	#11719919	C₂⁴	1	4	yes	—
634	#11719919	C₂⁴	1	4	yes	—
635	#11719919	C₂⁴	1	8	yes	—
636	#11719919	C₂⁴	1	8	yes	—
637	#11719919	C₂⁴	1	2	yes	—
638	#11719919	C₂⁴	1	2	yes	—
639	#11719919	C₂⁴	1	2	yes	—
640	#11719919	C₂⁴	1	2	yes	—
641	#11719919	C₂⁴	1	4	yes	—
642	#11719919	C₂⁴	1	4	yes	—
643	#11719919	C₂⁴	1	4	yes	—
644	#11719919	C₂⁴	1	4	yes	—
645	#11719919	C₂⁴	1	4	yes	—
646	#11719919	C₂⁴	1	4	yes	—
647	#11719919	C₂⁴	1	4	yes	—
648	#11719919	C₂⁴	1	4	yes	—
649	C₄×Dic₅₃	C₂⁴	1	4	yes	—
650	C₄×Dic₅₃	C₂⁴	1	4	yes	—
651	C₄×Dic₅₃	C₂⁴	1	4	yes	—
652	C₄×Dic₅₃	C₂⁴	1	8	yes	—
653	C₄×Dic₅₃	C₂⁴	1	8	yes	—
654	C₄×Dic₅₃	C₂⁴	1	2	yes	—
655	C₄×Dic₅₃	C₂⁴	1	2	yes	—
656	C₄×Dic₅₃	C₂⁴	1	8	yes	—
657	C₄×Dic₅₃	C₂⁴	1	8	yes	—
658	C₂³×C₅₃	—	2	4	no	—
659	C₂³×C₅₃	—	4	2	no	—
660	C₂³×C₅₃	—	4	2	no	—
661	C₂³×C₅₃	C₂⁵	1	4	yes	—
662	C₂³×C₅₃	C₂⁵	1	4	yes	—
663	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
664	C₂²×D₅₃	—	2	4	no	—
665	C₂²×D₅₃	—	2	8	no	—
666	C₂²×D₅₃	—	2	16	no	—
667	C₂²×D₅₃	—	4	2	no	—
668	C₂²×D₅₃	—	4	2	no	—
669	C₂²×D₅₃	—	4	1	no	—
670	C₂²×D₅₃	—	4	1	no	—
671	C₂²×D₅₃	—	4	4	no	—
672	C₂²×D₅₃	—	4	4	no	—
673	C₂²×D₅₃	—	4	8	no	—
674	C₂²×D₅₃	—	4	8	no	—
675	C₂²×D₅₃	—	8	16	no	—
676	C₂²×D₅₃	C₂×#41	1	4	yes	—
677	C₂²×D₅₃	C₂⁵	1	4	yes	—
678	C₂²×D₅₃	C₂⁵	1	4	yes	—
679	C₂²×D₅₃	C₂⁵	1	2	yes	—
680	Q₈×C₅₃	—	2	4	no	—
681	Q₈×C₅₃	—	4	2	no	—
682	Q₈×C₅₃	—	4	2	no	—
683	D₄×C₅₃	—	2	8	no	—
684	D₄×C₅₃	—	2	4	no	—
685	D₄×C₅₃	—	2	4	no	—
686	D₄×C₅₃	—	2	4	no	—
687	D₄×C₅₃	—	4	8	no	—
688	D₄×C₅₃	—	4	8	no	—
689	D₄×C₅₃	—	4	2	no	—
690	D₄×C₅₃	—	4	2	no	—
691	C₂×C₄×C₅₃	—	2	8	no	—
692	C₂×C₄×C₅₃	—	4	1	no	—
693	C₂×C₄×C₅₃	—	4	2	no	—
694	C₂×C₄×C₅₃	—	4	4	no	—
695	C₂×C₄×C₅₃	—	4	8	no	—
696	C₂×C₄×C₅₃	—	4	1	no	—
697	C₂×C₄×C₅₃	—	4	4	no	—
698	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
699	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
700	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
701	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
702	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
703	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
704	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
705	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
706	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
707	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
708	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
709	C₂²⋊D₅₃	—	2	8	no	—
710	C₂²⋊D₅₃	—	2	8	no	—
711	C₂²⋊D₅₃	—	2	8	no	—
712	C₂²⋊D₅₃	—	2	16	no	—
713	C₂²⋊D₅₃	—	4	4	no	—
714	C₂²⋊D₅₃	—	4	8	no	—
715	C₂²⋊D₅₃	—	4	8	no	—
716	C₂²⋊D₅₃	—	4	8	no	—
717	C₂²⋊D₅₃	—	4	8	no	—
718	C₂²⋊D₅₃	—	4	4	no	—
719	C₂×Dic₅₃	—	2	8	no	—
720	C₂×Dic₅₃	—	4	1	no	—
721	C₂×Dic₅₃	—	4	2	no	—
722	C₂×Dic₅₃	—	4	8	no	—
723	C₂×Dic₅₃	—	4	8	no	—
724	C₂×Dic₅₃	—	4	1	no	—
725	C₂×Dic₅₃	C₂×#41	1	4	yes	—
726	C₂×Dic₅₃	C₂⁵	1	2	yes	—
727	C₂×Dic₅₃	C₂⁵	1	4	yes	—
728	C₂×Dic₅₃	C₂⁵	1	4	yes	—
729	C₂×Dic₅₃	C₂⁵	1	4	yes	—
730	C₂×Dic₅₃	C₂⁵	1	2	yes	—
731	C₂×Dic₅₃	C₂⁵	1	4	yes	—
732	C₂×Dic₅₃	C₂⁵	1	2	yes	—
733	D₂₁₂	—	2	8	no	—
734	D₂₁₂	—	2	4	no	—
735	D₂₁₂	—	2	4	no	—
736	D₂₁₂	—	2	4	no	—
737	D₂₁₂	—	4	2	no	—
738	D₂₁₂	—	4	8	no	—
739	D₂₁₂	—	4	8	no	—
740	D₂₁₂	—	4	2	no	—
741	C₄×D₅₃	—	2	8	no	—
742	C₄×D₅₃	—	2	8	no	—
743	C₄×D₅₃	—	2	8	no	—
744	C₄×D₅₃	—	4	8	no	—
745	C₄×D₅₃	—	4	4	no	—
746	C₄×D₅₃	—	4	4	no	—
747	C₄×D₅₃	—	4	8	no	—
748	C₄×D₅₃	—	4	4	no	—
749	C₄×D₅₃	—	4	4	no	—
750	C₄×D₅₃	—	4	8	no	—
751	C₄×D₅₃	C₂×#41	1	8	yes	—
752	C₄×D₅₃	C₂×#41	1	8	yes	—
753	Dic₁₀₆	—	2	4	no	—
754	Dic₁₀₆	—	2	8	no	—
755	Dic₁₀₆	—	4	4	no	—
756	Dic₁₀₆	—	4	2	no	—
757	Dic₁₀₆	—	4	2	no	—
758	Dic₁₀₆	—	4	4	no	—
759	#62855	—	53	1	no	maximal, Sylow
760	C₂²×C₅₃	—	2	1	no	—
761	C₂²×C₅₃	—	2	1	no	—
762	C₂²×C₅₃	—	2	4	no	—
763	C₂²×C₅₃	—	2	4	no	—
764	C₂²×C₅₃	—	2	4	no	—
765	C₂²×C₅₃	—	2	4	no	—
766	C₂²×C₅₃	—	2	4	no	—
767	C₂²×C₅₃	—	2	4	no	—
768	C₂²×C₅₃	—	4	8	no	—
769	C₂²×C₅₃	C₂²×#41	1	2	yes	—
770	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
771	C₂×D₅₃	—	2	2	no	—
772	C₂×D₅₃	—	2	2	no	—
773	C₂×D₅₃	—	2	4	no	—
774	C₂×D₅₃	—	2	4	no	—
775	C₂×D₅₃	—	2	4	no	—
776	C₂×D₅₃	—	2	4	no	—
777	C₂×D₅₃	—	2	4	no	—
778	C₂×D₅₃	—	2	4	no	—
779	C₂×D₅₃	—	4	4	no	—
780	C₂×D₅₃	—	4	8	no	—
781	C₂×D₅₃	—	8	8	no	—
782	C₂×D₅₃	—	8	16	no	—
783	C₂×D₅₃	C₂²×#41	1	4	yes	—
784	C₄×C₅₃	—	2	4	no	—
785	C₄×C₅₃	—	2	1	no	—
786	C₄×C₅₃	—	2	1	no	—
787	C₄×C₅₃	—	2	4	no	—
788	C₄×C₅₃	—	2	4	no	—
789	C₄×C₅₃	—	2	1	no	—
790	C₄×C₅₃	—	2	4	no	—
791	C₄×C₅₃	—	2	1	no	—
792	C₄×C₅₃	C₂²×#41	1	2	yes	—
793	C₄×C₅₃	C₂²×#41	1	2	yes	—
794	Dic₅₃	—	2	4	no	—
795	Dic₅₃	—	2	2	no	—
796	Dic₅₃	—	2	4	no	—
797	Dic₅₃	—	2	4	no	—
798	Dic₅₃	—	2	2	no	—
799	Dic₅₃	—	2	4	no	—
800	Dic₅₃	C₂²×#41	1	4	yes	—
801	#3510	—	53	4	no	—
802	#3510	—	53	4	no	—
803	#3508	—	53	4	no	—
804	#3508	—	53	4	no	—
805	#3506	—	53	2	no	—
806	#3506	—	53	1	no	—
807	#3506	—	53	1	no	—
808	#3506	—	53	2	no	—
809	#3506	—	53	1	no	—
810	#3506	D₅₃	1	1	yes	characteristic, complemented
811	#3494	—	53	4	no	—
812	#3494	—	53	4	no	—
813	#3494	—	53	4	no	—
814	#3494	—	53	4	no	—
815	#3490	—	53	4	no	—
816	#3490	—	53	4	no	—
817	#3460	—	53	4	no	—
818	#3460	—	53	4	no	—
819	#3458	—	53	1	no	—
820	#3449	—	53	1	no	—
821	C₂×#535	—	53	2	no	—
822	#3428	—	53	2	no	—
823	C₂×#518	—	53	1	no	—
824	C₂×C₅₃	—	2	2	no	—
825	C₂×C₅₃	—	4	4	no	—
826	C₂×C₅₃	—	4	4	no	—
827	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
828	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
829	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
830	D₅₃	—	2	4	no	—
831	D₅₃	—	4	4	no	—
832	D₅₃	—	4	4	no	—
833	C₂²×#41	—	53	2	no	—
834	C₂³×D₄	—	53	1	no	—
835	#559	—	53	4	no	—
836	#559	—	53	4	no	—
837	#559	—	53	4	no	—
838	#559	—	53	4	no	—
839	#559	—	53	4	no	—
840	#559	—	53	4	no	—
841	#559	—	53	4	no	—
842	#559	C₂×D₅₃	1	4	yes	complemented
843	#556	—	53	2	no	—
844	#556	—	53	4	no	—
845	#556	—	53	4	no	—
846	#556	—	53	2	no	—
847	#556	—	53	2	no	—
848	#556	C₂×D₅₃	1	2	yes	complemented
849	#555	—	53	2	no	—
850	#555	—	53	4	no	—
851	#555	—	53	2	no	—
852	#555	—	53	2	no	—
853	#555	—	53	4	no	—
854	#555	C₂×D₅₃	1	2	yes	complemented
855	#553	—	53	4	no	—
856	#553	—	53	4	no	—
857	#553	—	53	4	no	—
858	#553	—	53	4	no	—
859	#553	—	53	4	no	—
860	#553	—	53	4	no	—
861	#553	—	53	4	no	—
862	#553	C₂×D₅₃	1	4	yes	complemented
863	#551	—	53	8	no	—
864	#551	—	53	8	no	—
865	#551	—	53	8	no	—
866	#551	—	53	8	no	—
867	#551	—	53	8	no	—
868	#551	—	53	8	no	—
869	#551	—	53	8	no	—
870	#551	—	53	8	no	—
871	#550	—	53	4	no	—
872	#550	—	53	2	no	—
873	#550	—	53	2	no	—
874	#550	—	53	2	no	—
875	#550	—	53	4	no	—
876	#550	C₂×D₅₃	1	2	yes	complemented
877	#547	—	53	2	no	—
878	#547	—	53	4	no	—
879	#547	—	53	2	no	—
880	#547	—	53	2	no	—
881	#547	—	53	4	no	—
882	#547	C₂×D₅₃	1	2	yes	complemented
883	#546	—	53	8	no	—
884	#546	—	53	8	no	—
885	#546	—	53	8	no	—
886	#546	—	53	8	no	—
887	#546	—	53	8	no	—
888	#546	—	53	8	no	—
889	#546	—	53	8	no	—
890	#546	—	53	8	no	—
891	#544	—	53	2	no	—
892	#544	—	53	2	no	—
893	#544	—	53	2	no	—
894	#544	—	53	2	no	—
895	#544	—	53	2	no	—
896	#544	—	53	2	no	—
897	#543	—	53	2	no	—
898	#543	—	53	2	no	—
899	#542	—	53	8	no	—
900	#542	—	53	8	no	—
901	#542	—	53	8	no	—
902	#542	—	53	8	no	—
903	#540	—	53	8	no	—
904	#540	—	53	8	no	—
905	#540	—	53	8	no	—
906	#540	—	53	8	no	—
907	#538	—	53	4	no	—
908	#538	—	53	4	no	—
909	#538	—	53	8	no	—
910	#538	—	53	8	no	—
911	#538	—	53	4	no	—
912	#538	C₂×D₅₃	1	4	yes	complemented
913	#537	—	53	2	no	—
914	#537	—	53	2	no	—
915	#536	—	53	2	no	—
916	#536	—	53	2	no	—
917	#535	—	53	2	no	—
918	#535	—	53	2	no	—
919	#535	—	53	4	no	—
920	#535	—	53	2	no	—
921	#535	—	53	4	no	—
922	#535	—	53	2	no	—
923	#535	—	53	4	no	—
924	#535	—	53	4	no	—
925	#535	—	53	8	no	—
926	#535	—	53	2	no	—
927	#535	C₂×D₅₃	1	2	yes	complemented
928	#534	—	53	2	no	—
929	#534	—	53	2	no	—
930	#533	—	53	4	no	—
931	#533	—	53	4	no	—
932	#533	—	53	2	no	—
933	#533	—	53	1	no	—
934	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
935	#532	—	53	2	no	—
936	#532	—	53	8	no	—
937	#532	—	53	8	no	—
938	#532	—	53	8	no	—
939	#532	—	53	8	no	—
940	#532	—	53	1	no	—
941	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
942	C₂×#127	—	53	4	no	—
943	#529	—	53	8	no	—
944	#529	—	53	8	no	—
945	#529	—	53	8	no	—
946	#529	—	53	8	no	—
947	C₂×#124	—	53	4	no	—
948	#525	—	53	4	no	—
949	#525	—	53	4	no	—
950	#525	—	53	4	no	—
951	#525	—	53	8	no	—
952	#525	—	53	8	no	—
953	#525	—	53	4	no	—
954	#525	—	53	4	no	—
955	#525	C₂×D₅₃	1	4	yes	complemented
956	C₂×#121	—	53	4	no	—
957	C₂×#121	—	53	4	no	—
958	C₂×#120	—	53	8	no	—
959	#520	—	53	2	no	—
960	#520	—	53	2	no	—
961	#520	—	53	4	no	—
962	#520	—	53	2	no	—
963	#520	—	53	4	no	—
964	#520	C₂×D₅₃	1	2	yes	complemented
965	#519	—	53	4	no	—
966	#518	—	53	8	no	—
967	#518	—	53	4	no	—
968	#518	—	53	4	no	—
969	#518	—	53	4	no	—
970	#518	—	53	4	no	—
971	#518	—	53	4	no	—
972	C₄×#41	—	53	4	no	—
973	C₄×#41	—	53	8	no	—
974	C₄×#41	—	53	4	no	—
975	C₂×C₄×D₄	—	53	1	no	—
976	C₂×C₄×D₄	—	53	2	no	—
977	C₂×C₄×D₄	—	53	1	no	—
978	C₂×C₄×D₄	—	53	2	no	—
979	C₂×C₄×D₄	—	53	1	no	—
980	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
981	C₂×#117	—	53	2	no	—
982	C₂×#117	—	53	4	no	—
983	C₂×#117	—	53	1	no	—
984	C₂×#117	—	53	4	no	—
985	C₂×#117	—	53	1	no	—
986	C₂²×C₂²⋊C₄	—	53	2	no	—
987	C₂²×C₂²⋊C₄	—	53	2	no	—
988	C₅₃	#62855	1	1	yes	characteristic, complemented, Sylow
989	C₂⁵	—	53	2	no	—
990	C₂×#41	—	53	2	no	—
991	C₂×#41	—	53	4	no	—
992	C₂×#41	—	53	2	no	—
993	C₂×#41	—	53	4	no	—
994	C₂×#41	—	53	4	no	—
995	C₂×#41	—	53	8	no	—
996	C₂×#41	—	53	4	no	—
997	C₂×#41	—	53	2	no	—
998	C₂×#41	—	53	4	no	—
999	C₂×#41	—	53	8	no	—
1000	C₂×#41	—	106	16	no	—
1001	C₂×#41	C₂²×D₅₃	1	2	yes	—
1002	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
1003	C₂²×Q₈	—	53	2	no	—
1004	C₂²×D₄	—	53	2	no	—
1005	C₂²×D₄	—	53	4	no	—
1006	C₂²×D₄	—	53	4	no	—
1007	C₂²×D₄	—	53	4	no	—
1008	C₂²×D₄	—	53	2	no	—
1009	C₂²×D₄	—	53	8	no	—
1010	C₂²×D₄	—	53	8	no	—
1011	C₂²×D₄	—	53	1	no	—
1012	C₂²×D₄	—	106	8	no	—
1013	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂³×C₄	—	53	1	no	—
1015	C₂³×C₄	—	53	2	no	—
1016	C₂³×C₄	—	53	4	no	—
1017	C₂³×C₄	—	53	2	no	—
1018	C₂³×C₄	—	53	2	no	—
1019	C₂³×C₄	C₂²×D₅₃	1	2	yes	—
1020	C₄⋊Q₈	—	53	4	no	—
1021	C₄⋊Q₈	—	53	4	no	—
1022	C₄⋊Q₈	—	53	2	no	—
1023	C₄⋊Q₈	—	53	4	no	—
1024	C₄⋊Q₈	—	53	4	no	—
1025	C₄⋊Q₈	—	53	2	no	—
1026	C₄⋊Q₈	—	53	2	no	—
1027	C₄⋊Q₈	—	53	1	no	—
1028	C₄⋊Q₈	—	53	1	no	—
1029	C₄⋊Q₈	—	53	1	no	—
1030	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1031	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1032	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1033	#127	—	53	8	no	—
1034	#127	—	53	8	no	—
1035	#127	—	53	4	no	—
1036	#127	—	53	4	no	—
1037	#127	—	53	2	no	—
1038	#127	—	53	4	no	—
1039	#127	—	53	1	no	—
1040	#127	C₂²×D₅₃	1	4	yes	—
1041	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
1042	#126	—	53	8	no	—
1043	#126	—	53	8	no	—
1044	#126	—	53	8	no	—
1045	#126	—	53	8	no	—
1046	#126	—	53	8	no	—
1047	#126	—	53	8	no	—
1048	#126	—	53	8	no	—
1049	#126	C₂²×D₅₃	1	8	yes	complemented
1050	#125	—	53	4	no	—
1051	#125	—	53	4	no	—
1052	#125	—	53	4	no	—
1053	#125	—	53	4	no	—
1054	#125	—	53	2	no	—
1055	#125	—	53	2	no	—
1056	#125	—	53	2	no	—
1057	#125	C₂²×D₅₃	1	2	yes	complemented
1058	#124	—	53	4	no	—
1059	#124	—	53	2	no	—
1060	#124	—	53	8	no	—
1061	#124	—	53	4	no	—
1062	#124	—	53	2	no	—
1063	#124	—	53	8	no	—
1064	#124	—	53	8	no	—
1065	#124	—	53	8	no	—
1066	#124	—	53	8	no	—
1067	#124	—	53	8	no	—
1068	#124	—	53	8	no	—
1069	#124	—	53	8	no	—
1070	#124	—	53	4	no	—
1071	#124	—	53	2	no	—
1072	#124	—	53	8	no	—
1073	#124	C₂²×D₅₃	1	4	yes	—
1074	#124	C₂²×D₅₃	1	8	yes	complemented
1075	#124	C₂²×D₅₃	1	2	yes	complemented
1076	#123	—	53	8	no	—
1077	#123	—	53	8	no	—
1078	#123	—	53	8	no	—
1079	#123	—	53	8	no	—
1080	#123	—	53	4	no	—
1081	#123	—	53	4	no	—
1082	#123	—	53	8	no	—
1083	#123	—	53	8	no	—
1084	#123	—	53	8	no	—
1085	#123	—	53	8	no	—
1086	#123	—	53	4	no	—
1087	#123	—	53	4	no	—
1088	#123	—	53	8	no	—
1089	#123	—	53	8	no	—
1090	#123	—	53	8	no	—
1091	#123	—	53	8	no	—
1092	#123	—	53	8	no	—
1093	#123	—	53	8	no	—
1094	#123	C₂²×D₅₃	1	8	yes	complemented
1095	#123	C₂²×D₅₃	1	8	yes	complemented
1096	C₂²⋊Q₈	—	53	4	no	—
1097	C₂²⋊Q₈	—	53	4	no	—
1098	C₂²⋊Q₈	—	53	4	no	—
1099	C₂²⋊Q₈	—	53	2	no	—
1100	C₂²⋊Q₈	—	53	2	no	—
1101	C₂²⋊Q₈	—	53	4	no	—
1102	C₂²⋊Q₈	—	53	4	no	—
1103	C₂²⋊Q₈	—	53	4	no	—
1104	C₂²⋊Q₈	—	53	8	no	—
1105	C₂²⋊Q₈	—	53	4	no	—
1106	C₂²⋊Q₈	—	53	4	no	—
1107	C₂²⋊Q₈	—	53	4	no	—
1108	C₂²⋊Q₈	—	53	4	no	—
1109	C₂²⋊Q₈	—	53	4	no	—
1110	C₂²⋊Q₈	—	53	4	no	—
1111	C₂²⋊Q₈	—	53	4	no	—
1112	C₂²⋊Q₈	—	53	4	no	—
1113	C₂²⋊Q₈	—	53	4	no	—
1114	C₂²⋊Q₈	—	53	4	no	—
1115	C₂²⋊Q₈	—	53	4	no	—
1116	C₂²⋊Q₈	—	53	8	no	—
1117	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
1118	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
1119	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1120	#121	—	53	8	no	—
1121	#121	—	53	8	no	—
1122	#121	—	53	4	no	—
1123	#121	—	53	4	no	—
1124	#121	—	53	4	no	—
1125	#121	—	53	4	no	—
1126	#121	—	53	4	no	—
1127	#121	—	53	4	no	—
1128	#121	—	53	4	no	—
1129	#121	—	53	8	no	—
1130	#121	—	53	8	no	—
1131	#121	—	53	8	no	—
1132	#121	—	53	8	no	—
1133	#121	—	53	4	no	—
1134	#121	—	53	4	no	—
1135	#121	—	53	2	no	—
1136	#121	—	53	2	no	—
1137	#121	—	53	4	no	—
1138	#121	—	53	8	no	—
1139	#121	—	53	4	no	—
1140	#121	—	53	4	no	—
1141	#121	—	53	4	no	—
1142	#121	—	53	8	no	—
1143	#121	—	53	8	no	—
1144	#121	—	53	8	no	—
1145	#121	—	53	4	no	—
1146	#121	—	53	4	no	—
1147	#121	—	53	8	no	—
1148	#121	—	53	8	no	—
1149	#121	—	53	8	no	—
1150	#121	C₂²×D₅₃	1	4	yes	—
1151	#121	C₂²×D₅₃	1	4	yes	—
1152	#121	C₂²×D₅₃	1	2	yes	—
1153	#121	C₂²×D₅₃	1	2	yes	—
1154	#121	C₂²×D₅₃	1	4	yes	complemented
1155	#121	C₂²×D₅₃	1	8	yes	complemented
1156	#120	—	53	8	no	—
1157	#120	—	53	8	no	—
1158	#120	—	53	8	no	—
1159	#120	—	53	8	no	—
1160	#120	—	53	4	no	—
1161	#120	—	53	4	no	—
1162	#120	—	53	8	no	—
1163	#120	—	53	8	no	—
1164	#120	—	53	8	no	—
1165	#120	—	53	4	no	—
1166	#120	—	53	4	no	—
1167	#120	C₂²×D₅₃	1	8	yes	—
1168	C₄×Q₈	—	53	4	no	—
1169	C₄×Q₈	—	53	8	no	—
1170	C₄×Q₈	—	53	4	no	—
1171	C₄×Q₈	—	53	8	no	—
1172	C₄×Q₈	—	53	4	no	—
1173	C₄×Q₈	—	53	4	no	—
1174	C₄×Q₈	—	53	4	no	—
1175	C₄×Q₈	—	53	2	no	—
1176	C₄×Q₈	—	53	2	no	—
1177	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1178	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1179	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1180	C₄×D₄	—	53	4	no	—
1181	C₄×D₄	—	53	4	no	—
1182	C₄×D₄	—	53	8	no	—
1183	C₄×D₄	—	53	4	no	—
1184	C₄×D₄	—	53	8	no	—
1185	C₄×D₄	—	53	8	no	—
1186	C₄×D₄	—	53	8	no	—
1187	C₄×D₄	—	53	8	no	—
1188	C₄×D₄	—	53	8	no	—
1189	C₄×D₄	—	53	8	no	—
1190	C₄×D₄	—	53	4	no	—
1191	C₄×D₄	—	53	4	no	—
1192	C₄×D₄	—	53	8	no	—
1193	C₄×D₄	—	53	8	no	—
1194	C₄×D₄	—	53	4	no	—
1195	C₄×D₄	—	53	4	no	—
1196	C₄×D₄	—	53	8	no	—
1197	C₄×D₄	—	53	4	no	—
1198	C₄×D₄	—	53	8	no	—
1199	C₄×D₄	—	53	8	no	—
1200	C₄×D₄	—	53	8	no	—
1201	C₄×D₄	—	53	8	no	—
1202	C₄×D₄	—	53	8	no	—
1203	C₄×D₄	—	53	8	no	—
1204	C₄×D₄	—	53	8	no	—
1205	C₄×D₄	—	53	8	no	—
1206	C₄×D₄	—	53	2	no	—
1207	C₄×D₄	—	53	2	no	—
1208	C₄×D₄	—	53	2	no	—
1209	C₄×D₄	—	53	2	no	—
1210	C₄×D₄	—	53	8	no	—
1211	C₄×D₄	—	53	4	no	—
1212	C₄×D₄	—	53	2	no	—
1213	C₄×D₄	—	53	2	no	—
1214	C₄×D₄	—	53	8	no	—
1215	C₄×D₄	C₂²×D₅₃	1	2	yes	—
1216	C₄×D₄	C₂²×D₅₃	1	2	yes	—
1217	C₄×D₄	C₂²×D₅₃	1	2	yes	—
1218	C₄×D₄	C₂²×D₅₃	1	2	yes	—
1219	C₄×D₄	C₂²×D₅₃	1	8	yes	—
1220	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1221	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1222	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1223	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1224	#117	—	53	2	no	—
1225	#117	—	53	4	no	—
1226	#117	—	53	4	no	—
1227	#117	—	53	4	no	—
1228	#117	—	53	2	no	—
1229	#117	—	53	2	no	—
1230	#117	—	53	4	no	—
1231	#117	—	53	8	no	—
1232	#117	—	53	8	no	—
1233	#117	—	53	4	no	—
1234	#117	—	53	4	no	—
1235	#117	—	53	4	no	—
1236	#117	—	53	4	no	—
1237	#117	—	53	4	no	—
1238	#117	—	53	8	no	—
1239	#117	—	53	8	no	—
1240	#117	—	53	2	no	—
1241	#117	—	53	2	no	—
1242	#117	—	53	2	no	—
1243	#117	—	53	2	no	—
1244	#117	—	53	4	no	—
1245	#117	—	53	8	no	—
1246	#117	—	53	8	no	—
1247	#117	C₂²×D₅₃	1	2	yes	—
1248	#117	C₂²×D₅₃	1	4	yes	complemented
1249	#117	C₂²×D₅₃	1	4	yes	complemented
1250	C₂×C₄⋊C₄	—	53	1	no	—
1251	C₂×C₄⋊C₄	—	53	1	no	—
1252	C₂×C₄⋊C₄	—	53	1	no	—
1253	C₂×C₄⋊C₄	—	53	4	no	—
1254	C₂×C₄⋊C₄	—	53	2	no	—
1255	C₂×C₄⋊C₄	—	53	2	no	—
1256	C₂×C₄⋊C₄	—	53	4	no	—
1257	C₂×C₄⋊C₄	—	53	4	no	—
1258	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1259	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1260	C₂×C₂²⋊C₄	—	53	2	no	—
1261	C₂×C₂²⋊C₄	—	53	2	no	—
1262	C₂×C₂²⋊C₄	—	53	1	no	—
1263	C₂×C₂²⋊C₄	—	53	1	no	—
1264	C₂×C₂²⋊C₄	—	53	2	no	—
1265	C₂×C₂²⋊C₄	—	53	2	no	—
1266	C₂×C₂²⋊C₄	—	53	8	no	—
1267	C₂×C₂²⋊C₄	—	53	8	no	—
1268	C₂×C₂²⋊C₄	—	53	8	no	—
1269	C₂×C₂²⋊C₄	—	53	8	no	—
1270	C₂×C₂²⋊C₄	—	53	8	no	—
1271	C₂×C₂²⋊C₄	—	53	4	no	—
1272	C₂×C₂²⋊C₄	—	53	8	no	—
1273	C₂×C₂²⋊C₄	—	53	8	no	—
1274	C₂×C₂²⋊C₄	—	53	8	no	—
1275	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1276	C₂×C₄²	—	53	2	no	—
1277	C₂×C₄²	—	53	1	no	—
1278	C₂×C₄²	—	53	8	no	—
1279	C₂×C₄²	—	53	4	no	—
1280	C₂×C₄²	—	53	8	no	—
1281	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1282	C₂⁴	—	53	1	no	—
1283	C₂⁴	—	53	8	no	—
1284	C₂⁴	—	53	4	no	—
1285	C₂⁴	—	53	2	no	—
1286	C₂⁴	—	106	8	no	—
1287	C₂⁴	—	424	2	no	—
1288	C₂⁴	—	424	2	no	—
1289	C₂⁴	C₂³×D₅₃	1	2	yes	—
1290	#41	—	2	8	no	—
1291	#41	—	8	4	no	—
1292	#41	—	106	16	no	—
1293	#41	—	106	16	no	—
1294	#41	—	106	8	no	—
1295	#41	—	106	8	no	—
1296	#41	—	106	8	no	—
1297	#41	—	424	4	no	—
1298	#41	—	424	8	no	—
1299	#41	—	424	4	no	—
1300	#41	—	424	8	no	—
1301	#41	—	424	4	no	—
1302	C₂×Q₈	—	53	4	no	—
1303	C₂×Q₈	—	53	2	no	—
1304	C₂×Q₈	—	53	2	no	—
1305	C₂×Q₈	—	53	2	no	—
1306	C₂×Q₈	—	53	4	no	—
1307	C₂×Q₈	—	53	4	no	—
1308	C₂×Q₈	—	106	8	no	—
1309	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1310	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1311	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1312	C₂×D₄	—	2	4	no	—
1313	C₂×D₄	—	53	4	no	—
1314	C₂×D₄	—	53	4	no	—
1315	C₂×D₄	—	53	8	no	—
1316	C₂×D₄	—	53	4	no	—
1317	C₂×D₄	—	53	4	no	—
1318	C₂×D₄	—	53	4	no	—
1319	C₂×D₄	—	53	8	no	—
1320	C₂×D₄	—	53	8	no	—
1321	C₂×D₄	—	53	8	no	—
1322	C₂×D₄	—	53	8	no	—
1323	C₂×D₄	—	53	4	no	—
1324	C₂×D₄	—	53	2	no	—
1325	C₂×D₄	—	53	2	no	—
1326	C₂×D₄	—	53	2	no	—
1327	C₂×D₄	—	53	2	no	—
1328	C₂×D₄	—	53	2	no	—
1329	C₂×D₄	—	53	8	no	—
1330	C₂×D₄	—	53	8	no	—
1331	C₂×D₄	—	106	16	no	—
1332	C₂×D₄	—	106	16	no	—
1333	C₂×D₄	—	106	8	no	—
1334	C₂×D₄	—	106	8	no	—
1335	C₂×D₄	—	106	16	no	—
1336	C₂×D₄	—	106	4	no	—
1337	C₂×D₄	—	424	8	no	—
1338	C₂×D₄	—	424	8	no	—
1339	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1340	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1341	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1342	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1343	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1344	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1345	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1346	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1347	C₂²×C₄	—	8	2	no	—
1348	C₂²×C₄	—	53	1	no	—
1349	C₂²×C₄	—	53	8	no	—
1350	C₂²×C₄	—	53	2	no	—
1351	C₂²×C₄	—	53	2	no	—
1352	C₂²×C₄	—	53	4	no	—
1353	C₂²×C₄	—	53	2	no	—
1354	C₂²×C₄	—	53	1	no	—
1355	C₂²×C₄	—	53	1	no	—
1356	C₂²×C₄	—	53	8	no	—
1357	C₂²×C₄	—	53	8	no	—
1358	C₂²×C₄	—	53	4	no	—
1359	C₂²×C₄	—	53	4	no	—
1360	C₂²×C₄	—	53	4	no	—
1361	C₂²×C₄	—	53	4	no	—
1362	C₂²×C₄	—	53	4	no	—
1363	C₂²×C₄	—	53	8	no	—
1364	C₂²×C₄	—	53	8	no	—
1365	C₂²×C₄	—	53	4	no	—
1366	C₂²×C₄	—	53	4	no	—
1367	C₂²×C₄	—	53	8	no	—
1368	C₂²×C₄	—	106	16	no	—
1369	C₂²×C₄	—	424	2	no	—
1370	C₂²×C₄	—	424	2	no	—
1371	C₂²×C₄	—	424	2	no	—
1372	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1373	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1374	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1375	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1376	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1377	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1378	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1379	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1380	C₄⋊C₄	—	53	2	no	—
1381	C₄⋊C₄	—	53	2	no	—
1382	C₄⋊C₄	—	53	2	no	—
1383	C₄⋊C₄	—	53	2	no	—
1384	C₄⋊C₄	—	53	2	no	—
1385	C₄⋊C₄	—	53	2	no	—
1386	C₄⋊C₄	—	53	2	no	—
1387	C₄⋊C₄	—	53	2	no	—
1388	C₄⋊C₄	—	53	4	no	—
1389	C₄⋊C₄	—	53	4	no	—
1390	C₄⋊C₄	—	53	8	no	—
1391	C₄⋊C₄	—	53	8	no	—
1392	C₄⋊C₄	—	53	8	no	—
1393	C₄⋊C₄	—	53	4	no	—
1394	C₄⋊C₄	—	53	4	no	—
1395	C₄⋊C₄	—	53	2	no	—
1396	C₄⋊C₄	—	53	2	no	—
1397	C₄⋊C₄	—	53	4	no	—
1398	C₄⋊C₄	—	53	4	no	—
1399	C₄⋊C₄	—	53	2	no	—
1400	C₄⋊C₄	—	53	2	no	—
1401	C₄⋊C₄	—	53	4	no	—
1402	C₄⋊C₄	—	53	4	no	—
1403	C₄⋊C₄	—	53	4	no	—
1404	C₄⋊C₄	—	53	4	no	—
1405	C₄⋊C₄	—	53	4	no	—
1406	C₄⋊C₄	—	53	4	no	—
1407	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1408	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1409	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1410	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1411	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1412	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1413	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1414	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1415	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1416	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1417	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1418	C₂²⋊C₄	—	53	8	no	—
1419	C₂²⋊C₄	—	53	4	no	—
1420	C₂²⋊C₄	—	53	8	no	—
1421	C₂²⋊C₄	—	53	8	no	—
1422	C₂²⋊C₄	—	53	8	no	—
1423	C₂²⋊C₄	—	53	4	no	—
1424	C₂²⋊C₄	—	53	4	no	—
1425	C₂²⋊C₄	—	53	8	no	—
1426	C₂²⋊C₄	—	53	2	no	—
1427	C₂²⋊C₄	—	53	2	no	—
1428	C₂²⋊C₄	—	53	2	no	—
1429	C₂²⋊C₄	—	53	2	no	—
1430	C₂²⋊C₄	—	53	4	no	—
1431	C₂²⋊C₄	—	53	4	no	—
1432	C₂²⋊C₄	—	53	4	no	—
1433	C₂²⋊C₄	—	53	4	no	—
1434	C₂²⋊C₄	—	53	8	no	—
1435	C₂²⋊C₄	—	53	8	no	—
1436	C₂²⋊C₄	—	53	8	no	—
1437	C₂²⋊C₄	—	53	8	no	—
1438	C₂²⋊C₄	—	53	8	no	—
1439	C₂²⋊C₄	—	53	8	no	—
1440	C₂²⋊C₄	—	53	8	no	—
1441	C₂²⋊C₄	—	53	4	no	—
1442	C₂²⋊C₄	—	53	4	no	—
1443	C₂²⋊C₄	—	53	4	no	—
1444	C₂²⋊C₄	—	53	4	no	—
1445	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1446	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1447	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1448	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1449	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1450	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1451	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1452	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1453	C₄²	—	53	8	no	—
1454	C₄²	—	53	4	no	—
1455	C₄²	—	53	4	no	—
1456	C₄²	—	53	8	no	—
1457	C₄²	—	53	8	no	—
1458	C₄²	—	53	8	no	—
1459	C₄²	—	53	2	no	—
1460	C₄²	—	53	2	no	—
1461	C₄²	—	53	4	no	—
1462	C₄²	C₂³×D₅₃	1	8	yes	—
1463	C₄²	C₂³×D₅₃	1	4	yes	—
1464	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1465	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1466	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1467	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1468	C₂³	—	2	4	no	—
1469	C₂³	—	4	2	no	—
1470	C₂³	—	4	2	no	—
1471	C₂³	—	53	2	no	—
1472	C₂³	—	53	4	no	—
1473	C₂³	—	53	4	no	—
1474	C₂³	—	53	4	no	—
1475	C₂³	—	106	8	no	—
1476	C₂³	—	106	16	no	—
1477	C₂³	—	106	4	no	—
1478	C₂³	—	424	16	no	—
1479	C₂³	—	212	4	no	—
1480	C₂³	—	212	4	no	—
1481	C₂³	—	212	8	no	—
1482	C₂³	—	212	8	no	—
1483	C₂³	—	212	2	no	—
1484	C₂³	—	212	2	no	—
1485	C₂³	—	212	1	no	—
1486	C₂³	—	212	1	no	—
1487	C₂³	C₂⁴×D₅₃	1	4	yes	—
1488	C₂³	C₂⁴×D₅₃	1	4	yes	—
1489	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1490	Q₈	—	2	4	no	—
1491	Q₈	—	4	2	no	—
1492	Q₈	—	4	2	no	—
1493	Q₈	—	106	8	no	—
1494	Q₈	—	106	4	no	—
1495	Q₈	—	212	2	no	—
1496	Q₈	—	212	4	no	—
1497	Q₈	—	212	2	no	—
1498	Q₈	—	212	4	no	—
1499	D₄	—	2	8	no	—
1500	D₄	—	2	4	no	—
1501	D₄	—	2	4	no	—
1502	D₄	—	2	4	no	—
1503	D₄	—	4	8	no	—
1504	D₄	—	4	8	no	—
1505	D₄	—	4	2	no	—
1506	D₄	—	4	2	no	—
1507	D₄	—	106	8	no	—
1508	D₄	—	106	16	no	—
1509	D₄	—	106	8	no	—
1510	D₄	—	106	8	no	—
1511	D₄	—	106	8	no	—
1512	D₄	—	106	4	no	—
1513	D₄	—	106	4	no	—
1514	D₄	—	106	4	no	—
1515	D₄	—	212	8	no	—
1516	D₄	—	212	8	no	—
1517	D₄	—	212	2	no	—
1518	D₄	—	212	2	no	—
1519	D₄	—	212	8	no	—
1520	D₄	—	212	8	no	—
1521	D₄	—	212	8	no	—
1522	D₄	—	212	8	no	—
1523	D₄	—	212	4	no	—
1524	D₄	—	212	4	no	—
1525	C₂×C₄	—	2	8	no	—
1526	C₂×C₄	—	4	1	no	—
1527	C₂×C₄	—	4	2	no	—
1528	C₂×C₄	—	4	4	no	—
1529	C₂×C₄	—	4	4	no	—
1530	C₂×C₄	—	4	1	no	—
1531	C₂×C₄	—	4	8	no	—
1532	C₂×C₄	—	53	4	no	—
1533	C₂×C₄	—	53	2	no	—
1534	C₂×C₄	—	53	8	no	—
1535	C₂×C₄	—	53	8	no	—
1536	C₂×C₄	—	53	4	no	—
1537	C₂×C₄	—	53	4	no	—
1538	C₂×C₄	—	53	4	no	—
1539	C₂×C₄	—	53	4	no	—
1540	C₂×C₄	—	53	2	no	—
1541	C₂×C₄	—	53	2	no	—
1542	C₂×C₄	—	106	8	no	—
1543	C₂×C₄	—	106	8	no	—
1544	C₂×C₄	—	106	8	no	—
1545	C₂×C₄	—	106	8	no	—
1546	C₂×C₄	—	212	8	no	—
1547	C₂×C₄	—	212	4	no	—
1548	C₂×C₄	—	212	4	no	—
1549	C₂×C₄	—	212	4	no	—
1550	C₂×C₄	—	212	4	no	—
1551	C₂×C₄	—	212	8	no	—
1552	C₂×C₄	—	212	8	no	—
1553	C₂×C₄	—	212	1	no	—
1554	C₂×C₄	—	212	2	no	—
1555	C₂×C₄	—	212	1	no	—
1556	C₂×C₄	—	212	8	no	—
1557	C₂×C₄	—	212	8	no	—
1558	C₂×C₄	#41×D₅₃	1	4	yes	—
1559	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1560	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1561	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1562	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1563	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1564	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1565	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1566	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1567	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1568	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1569	C₂²	—	2	1	no	—
1570	C₂²	—	2	1	no	—
1571	C₂²	—	2	4	no	—
1572	C₂²	—	2	4	no	—
1573	C₂²	—	2	4	no	—
1574	C₂²	—	2	4	no	—
1575	C₂²	—	2	4	no	—
1576	C₂²	—	2	4	no	—
1577	C₂²	—	4	8	no	—
1578	C₂²	—	53	4	no	—
1579	C₂²	—	106	2	no	—
1580	C₂²	—	106	2	no	—
1581	C₂²	—	106	4	no	—
1582	C₂²	—	106	4	no	—
1583	C₂²	—	106	4	no	—
1584	C₂²	—	106	4	no	—
1585	C₂²	—	106	4	no	—
1586	C₂²	—	106	4	no	—
1587	C₂²	—	424	16	no	—
1588	C₂²	—	424	8	no	—
1589	C₂²	—	212	4	no	—
1590	C₂²	—	212	8	no	—
1591	C₂²	C₂×#41×D₅₃	1	2	yes	—
1592	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1593	C₄	—	2	4	no	—
1594	C₄	—	2	4	no	—
1595	C₄	—	2	1	no	—
1596	C₄	—	2	1	no	—
1597	C₄	—	2	4	no	—
1598	C₄	—	2	1	no	—
1599	C₄	—	2	1	no	—
1600	C₄	—	2	4	no	—
1601	C₄	—	53	4	no	—
1602	C₄	—	106	4	no	—
1603	C₄	—	106	2	no	—
1604	C₄	—	106	4	no	—
1605	C₄	—	106	4	no	—
1606	C₄	—	106	2	no	—
1607	C₄	—	106	4	no	—
1608	C₄	C₂×#41×D₅₃	1	2	yes	—
1609	C₄	C₂×#41×D₅₃	1	2	yes	—
1610	C₂	—	2	2	no	—
1611	C₂	—	4	4	no	—
1612	C₂	—	4	4	no	—
1613	C₂	—	106	4	no	—
1614	C₂	—	212	4	no	—
1615	C₂	—	212	4	no	—
1616	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1617	C₂	#20289525	1	1	yes	characteristic
1618	C₂	#20289526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3506	C₂
hypercenter	#3506	D₅₃
hypocenter	C₅₃	#62855
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3506

Complements

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

N	H ≅ G/N	type
1. #20288608	C₂	semidirect
2. #20288605	C₂	semidirect
3. #20288588	C₂	semidirect
4. #20288585	C₂	semidirect
5. #20288569	C₂	semidirect
6. #20288567	C₂	semidirect
7. #20288566	C₂	semidirect
8. #20288564	C₂	semidirect
9. #20288560	C₂	semidirect
10. #20288449	C₂	semidirect
11. #20288446	C₂	semidirect
12. #20288443	C₂	semidirect
13. #20288439	C₂	semidirect
14. #20288401	C₂	semidirect
15. #20288398	C₂	semidirect
16. #20288134	C₂	semidirect
17. #20288133	C₂	semidirect
18. #20288118	C₂	semidirect
19. #20288042	C₂	semidirect
20. #535×D₅₃	C₂	semidirect
21. #20287915	C₂	semidirect
22. C₂×#16811095	C₂	semidirect
23. C₅₃×#3506	C₂	semidirect
26. #16811359	C₂²	semidirect
27. #16811358	C₂²	semidirect
28. #16811358	C₂²	semidirect
29. #16811356	C₂²	semidirect
30. #16811356	C₂²	semidirect
31. #16811355	C₂²	semidirect
32. #16811355	C₂²	semidirect
33. #16811347	C₂²	semidirect
34. #16811346	C₂²	semidirect
35. #16811345	C₂²	semidirect
36. #16811343	C₂²	semidirect
37. #16811342	C₂²	semidirect
38. #16811339	C₂²	semidirect
39. #16811338	C₂²	semidirect
40. #16811338	C₂²	semidirect
41. #16811337	C₂²	semidirect
42. #16811336	C₂²	semidirect
43. #16811326	C₂²	semidirect
44. #16811325	C₂²	semidirect
45. #16811323	C₂²	semidirect
46. #16811321	C₂²	semidirect
47. #16811320	C₂²	semidirect
48. #16811319	C₂²	semidirect
49. #16811317	C₂²	semidirect
50. #16811303	C₂²	semidirect
51. #16811302	C₂²	semidirect
52. #16811301	C₂²	semidirect
53. #16811300	C₂²	semidirect
54. #16811298	C₂²	semidirect
55. #16811298	C₂²	semidirect
56. #16811297	C₂²	semidirect
57. #16811296	C₂²	semidirect
58. #16811295	C₂²	semidirect
59. #16811294	C₂²	semidirect
60. #16811294	C₂²	semidirect
61. #16811293	C₂²	semidirect
62. #16811293	C₂²	semidirect
63. #16811278	C₂²	semidirect
64. #16811277	C₂²	semidirect
65. #16811276	C₂²	semidirect
66. #16811274	C₂²	semidirect
67. #16811273	C₂²	semidirect
68. #16811270	C₂²	semidirect
69. #16811268	C₂²	semidirect
70. #16811266	C₂²	semidirect
71. #16811265	C₂²	semidirect
72. #16811265	C₂²	semidirect
73. #16811262	C₂²	semidirect
74. #16811262	C₂²	semidirect
75. #16811261	C₂²	semidirect
76. #16811253	C₂²	semidirect
77. #16811253	C₂²	semidirect
78. #16811252	C₂²	semidirect
79. #16811252	C₂²	semidirect
80. #16811250	C₂²	semidirect
81. #16811250	C₂²	semidirect
84. #16811243	C₂²	semidirect
85. #16811241	C₂²	semidirect
86. #16811239	C₂²	semidirect
87. #16811237	C₂²	semidirect
88. #16811225	C₂²	semidirect
89. #16811225	C₂²	semidirect
90. #16811223	C₂²	semidirect
91. #16811223	C₂²	semidirect
92. #16811213	C₂²	semidirect
93. #16811211	C₂²	semidirect
94. #16811210	C₂²	semidirect
95. #16811208	C₂²	semidirect
96. #16811206	C₂²	semidirect
97. #16811200	C₂²	semidirect
98. #16811200	C₂²	semidirect
99. #16811198	C₂²	semidirect
100. #16811193	C₂²	semidirect
101. #16811192	C₂²	semidirect
103. #16811191	C₂²	semidirect
104. #16811190	C₂²	semidirect
107. #16811188	C₂²	semidirect
108. #16811187	C₂²	semidirect
110. #16811186	C₂²	semidirect
113. #16811180	C₂²	semidirect
114. #16811177	C₂²	semidirect
115. #16811177	C₂²	semidirect
116. #16811176	C₂²	semidirect
117. #16811173	C₂²	semidirect
118. #16811172	C₂²	semidirect
119. #16811170	C₂²	semidirect
120. #16811169	C₂²	semidirect
121. #16811169	C₂²	semidirect
122. #16811168	C₂²	semidirect
123. #127×D₅₃	C₂²	semidirect
124. #16811156	C₂²	semidirect
125. #16811153	C₂²	semidirect
126. #16811151	C₂²	semidirect
127. #16811150	C₂²	semidirect
128. #124×D₅₃	C₂²	semidirect
129. #16811136	C₂²	semidirect
130. #16811134	C₂²	semidirect
131. #16811133	C₂²	semidirect
132. #16811132	C₂²	semidirect
133. #16811132	C₂²	semidirect
134. #16811132	C₂²	semidirect
135. #16811129	C₂²	semidirect
136. #121×D₅₃	C₂²	semidirect
137. #121×D₅₃	C₂²	semidirect
139. #16811106	C₂²	semidirect
140. #16811104	C₂²	semidirect
141. #16811104	C₂²	semidirect
142. #16811103	C₂²	semidirect
143. #16811103	C₂²	semidirect
144. #16811099	C₂²	semidirect
146. #16811095	C₂²	semidirect
147. #16811095	C₂²	semidirect
148. #16811095	C₂²	semidirect
149. #16811095	C₂²	semidirect
150. #16811095	C₂²	semidirect
151. C₄×#11719949	C₂²	semidirect
152. C₄×#11719947	C₂²	semidirect
153. C₄×#11719947	C₂²	semidirect
154. C₂×C₄×D₂₁₂	C₂²	semidirect
155. C₂×D₄×Dic₅₃	C₂²	semidirect
156. C₂×#13133179	C₂²	semidirect
157. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
158. C₂×#13133177	C₂²	semidirect
160. C₂×#13133175	C₂²	semidirect
163. #117×D₅₃	C₂²	semidirect
166. C₅₃×#559	C₂²	semidirect
167. C₅₃×#556	C₂²	semidirect
168. C₅₃×#555	C₂²	semidirect
169. C₅₃×#553	C₂²	semidirect
170. C₅₃×#550	C₂²	semidirect
171. C₅₃×#547	C₂²	semidirect
172. C₅₃×#538	C₂²	semidirect
173. C₅₃×#535	C₂²	semidirect
174. C₅₃×#533	C₂²	semidirect
175. C₅₃×#532	C₂²	semidirect
176. C₅₃×#525	C₂²	semidirect
177. C₅₃×#520	C₂²	semidirect
178. C₂×C₄×D₄×C₅₃	C₂²	semidirect
181. C₂×#11719949	C₂³	semidirect
184. C₂×#11719945	C₂³	semidirect
185. C₂×#11719945	C₂³	semidirect
188. C₂×#11719947	C₂³	semidirect
189. C₂×#11719947	C₂³	semidirect
206. #13133217	C₂³	semidirect
207. #13133217	C₂³	semidirect
208. #13133217	C₂³	semidirect
209. #13133216	C₂³	semidirect
210. #13133216	C₂³	semidirect
211. #13133216	C₂³	semidirect
212. #13133216	C₂³	semidirect
213. #13133215	C₂³	semidirect
214. #13133215	C₂³	semidirect
215. #13133215	C₂³	semidirect
217. #13133214	C₂³	semidirect
222. #13133213	C₂³	semidirect
223. #13133212	C₂³	semidirect
224. #13133212	C₂³	semidirect
225. #13133212	C₂³	semidirect
226. #13133211	C₂³	semidirect
227. #13133210	C₂³	semidirect
228. #13133210	C₂³	semidirect
229. #13133210	C₂³	semidirect
230. #13133209	C₂³	semidirect
231. #13133208	C₂³	semidirect
232. #13133208	C₂³	semidirect
233. #13133207	C₂³	semidirect
234. #13133207	C₂³	semidirect
235. #13133207	C₂³	semidirect
236. #13133207	C₂³	semidirect
238. #13133206	C₂³	semidirect
239. #13133206	C₂³	semidirect
241. #13133205	C₂³	semidirect
242. #13133205	C₂³	semidirect
244. #13133204	C₂³	semidirect
245. #13133204	C₂³	semidirect
248. #13133203	C₂³	semidirect
249. #13133203	C₂³	semidirect
250. #13133203	C₂³	semidirect
251. #13133203	C₂³	semidirect
254. #13133202	C₂³	semidirect
255. #13133202	C₂³	semidirect
256. #13133202	C₂³	semidirect
257. #13133202	C₂³	semidirect
258. #13133201	C₂³	semidirect
259. #13133201	C₂³	semidirect
260. #13133200	C₂³	semidirect
261. #13133200	C₂³	semidirect
264. #13133199	C₂³	semidirect
265. #13133199	C₂³	semidirect
266. #13133199	C₂³	semidirect
267. #13133199	C₂³	semidirect
268. #13133198	C₂³	semidirect
269. #13133198	C₂³	semidirect
272. #13133197	C₂³	semidirect
275. #13133196	C₂³	semidirect
280. #13133195	C₂³	semidirect
281. #13133195	C₂³	semidirect
282. #13133195	C₂³	semidirect
285. #13133194	C₂³	semidirect
286. #13133194	C₂³	semidirect
287. #13133194	C₂³	semidirect
290. #13133193	C₂³	semidirect
293. #13133192	C₂³	semidirect
294. #13133192	C₂³	semidirect
299. #13133191	C₂³	semidirect
300. #13133191	C₂³	semidirect
303. #13133190	C₂³	semidirect
304. #13133190	C₂³	semidirect
305. #13133190	C₂³	semidirect
306. #13133190	C₂³	semidirect
307. #13133190	C₂³	semidirect
312. #13133189	C₂³	semidirect
313. #13133189	C₂³	semidirect
314. #13133189	C₂³	semidirect
315. #13133189	C₂³	semidirect
316. #13133189	C₂³	semidirect
319. #13133188	C₂³	semidirect
320. #13133188	C₂³	semidirect
332. Q₈×Dic₅₃	C₂³	semidirect
333. C₄×Dic₁₀₆	C₂³	semidirect
334. C₄×Dic₁₀₆	C₂³	semidirect
335. C₄×Dic₁₀₆	C₂³	semidirect
336. C₄×Dic₁₀₆	C₂³	semidirect
337. C₄×Dic₁₀₆	C₂³	semidirect
338. C₄×Dic₁₀₆	C₂³	semidirect
339. #13133182	C₂³	semidirect
340. #13133182	C₂³	semidirect
346. C₄×D₂₁₂	C₂³	semidirect
347. C₄×D₂₁₂	C₂³	semidirect
348. C₄×D₂₁₂	C₂³	semidirect
349. C₄×D₂₁₂	C₂³	semidirect
353. D₄×Dic₅₃	C₂³	semidirect
354. D₄×Dic₅₃	C₂³	semidirect
358. #13133179	C₂³	semidirect
359. #13133179	C₂³	semidirect
364. C₄×C₂²⋊D₅₃	C₂³	semidirect
365. C₄×C₂²⋊D₅₃	C₂³	semidirect
366. C₄×C₂²⋊D₅₃	C₂³	semidirect
367. C₄×C₂²⋊D₅₃	C₂³	semidirect
368. C₄×C₂²⋊D₅₃	C₂³	semidirect
373. #13133177	C₂³	semidirect
374. #13133177	C₂³	semidirect
375. #13133177	C₂³	semidirect
377. #13133176	C₂³	semidirect
378. #13133176	C₂³	semidirect
384. #13133175	C₂³	semidirect
385. #13133175	C₂³	semidirect
386. #13133175	C₂³	semidirect
387. #13133175	C₂³	semidirect
388. #13133175	C₂³	semidirect
395. #13133174	C₂³	semidirect
397. #13133173	C₂³	semidirect
398. #13133173	C₂³	semidirect
400. C₂×C₄⋊Dic₅₃	C₂³	semidirect
405. C₄⋊C₄×D₅₃	C₂³	semidirect
406. C₄⋊C₄×D₅₃	C₂³	semidirect
424. C₂×C₄×Dic₅₃	C₂³	semidirect
426. C₄²×D₅₃	C₂³	semidirect
428. C₂×#41×C₅₃	C₂³	semidirect
431. C₄⋊Q₈×C₅₃	C₂³	semidirect
432. C₄⋊Q₈×C₅₃	C₂³	semidirect
433. C₄⋊Q₈×C₅₃	C₂³	semidirect
435. #127×C₅₃	C₂³	semidirect
436. #126×C₅₃	C₂³	semidirect
437. #125×C₅₃	C₂³	semidirect
439. #124×C₅₃	C₂³	semidirect
440. #124×C₅₃	C₂³	semidirect
441. #123×C₅₃	C₂³	semidirect
442. #123×C₅₃	C₂³	semidirect
445. C₂²⋊Q₈×C₅₃	C₂³	semidirect
450. #121×C₅₃	C₂³	semidirect
451. #121×C₅₃	C₂³	semidirect
453. C₄×Q₈×C₅₃	C₂³	semidirect
454. C₄×Q₈×C₅₃	C₂³	semidirect
455. C₄×Q₈×C₅₃	C₂³	semidirect
461. C₄×D₄×C₅₃	C₂³	semidirect
462. C₄×D₄×C₅₃	C₂³	semidirect
463. C₄×D₄×C₅₃	C₂³	semidirect
464. C₄×D₄×C₅₃	C₂³	semidirect
466. #117×C₅₃	C₂³	semidirect
467. #117×C₅₃	C₂³	semidirect
469. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
551. C₂×C₄×D₅₃	#41	semidirect
810. #3506	D₅₃	semidirect
842. #559	C₂×D₅₃	semidirect
848. #556	C₂×D₅₃	semidirect
854. #555	C₂×D₅₃	semidirect
862. #553	C₂×D₅₃	semidirect
876. #550	C₂×D₅₃	semidirect
882. #547	C₂×D₅₃	semidirect
912. #538	C₂×D₅₃	semidirect
927. #535	C₂×D₅₃	semidirect
934. #533	C₂×D₅₃	semidirect
941. #532	C₂×D₅₃	semidirect
955. #525	C₂×D₅₃	semidirect
964. #520	C₂×D₅₃	semidirect
980. C₂×C₄×D₄	C₂×D₅₃	semidirect
988. C₅₃	#62855	semidirect
1002. C₂×#41	C₂²×D₅₃	semidirect
1030. C₄⋊Q₈	C₂²×D₅₃	semidirect
1031. C₄⋊Q₈	C₂²×D₅₃	semidirect
1032. C₄⋊Q₈	C₂²×D₅₃	semidirect
1041. #127	C₂²×D₅₃	semidirect
1049. #126	C₂²×D₅₃	semidirect
1057. #125	C₂²×D₅₃	semidirect
1074. #124	C₂²×D₅₃	semidirect
1075. #124	C₂²×D₅₃	semidirect
1094. #123	C₂²×D₅₃	semidirect
1095. #123	C₂²×D₅₃	semidirect
1119. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1154. #121	C₂²×D₅₃	semidirect
1155. #121	C₂²×D₅₃	semidirect
1177. C₄×Q₈	C₂²×D₅₃	semidirect
1178. C₄×Q₈	C₂²×D₅₃	semidirect
1179. C₄×Q₈	C₂²×D₅₃	semidirect
1220. C₄×D₄	C₂²×D₅₃	semidirect
1221. C₄×D₄	C₂²×D₅₃	semidirect
1222. C₄×D₄	C₂²×D₅₃	semidirect
1223. C₄×D₄	C₂²×D₅₃	semidirect
1248. #117	C₂²×D₅₃	semidirect
1249. #117	C₂²×D₅₃	semidirect
1259. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288608	2
#20288605	2
#20288588	2
#20288585	2
#20288569	2
#20288567	2
#20288566	2
#20288564	2
#20288560	2
#20288449	2
#20288446	2
#20288443	2
#20288439	2
#20288401	2
#20288398	2
#20288134	2
#20288133	2
#20288118	2
#20288042	2
#535×D₅₃	2
#20287915	2
C₂×#16811095	2
C₅₃×#3506	2
#62855	53