Subgroups — #28261313

Order 13568.

2286 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288421	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288348	C₂	1	1	yes	maximal, characteristic, complemented
3	#20286862	C₂	1	2	yes	maximal, complemented
4	#20286802	C₂	1	2	yes	maximal, complemented
5	#20286742	C₂	1	2	yes	maximal, complemented
6	#20286682	C₂	1	2	yes	maximal, complemented
7	#20286571	C₂	1	2	yes	maximal, complemented
8	#20286556	C₂	1	2	yes	maximal, complemented
9	#20286534	C₂	1	2	yes	maximal, complemented
10	#20286523	C₂	1	2	yes	maximal, complemented
11	#20285073	C₂	1	1	yes	maximal, characteristic, complemented
12	#20284676	C₂	1	1	yes	maximal, characteristic, complemented
13	#20284635	C₂	1	1	yes	maximal, characteristic, complemented
14	#20284549	C₂	1	1	yes	maximal, characteristic, complemented
15	#20284398	C₂	1	1	yes	maximal, characteristic, complemented
16	#20284252	C₂	1	1	yes	maximal, characteristic, complemented
17	#20284015	C₂	1	1	yes	maximal, characteristic, complemented
18	#20283941	C₂	1	1	yes	maximal, characteristic, complemented
19	#20283550	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283409	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283237	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂²×#13133139	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3050	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133263	C₂²	1	1	yes	characteristic
25	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
26	C₂×#13133242	C₂²	1	1	yes	characteristic
27	C₂×#13133242	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13133223	C₂²	1	1	yes	characteristic, complemented
29	#16811331	C₂²	1	2	yes	complemented
30	#16811330	—	2	1	no	—
31	#16811325	C₂²	1	2	yes	complemented
32	#16811319	—	2	1	no	—
33	#16811315	C₂²	1	2	yes	complemented
34	#16811313	—	2	1	no	—
35	#16811277	—	2	1	no	—
36	#16811273	C₂²	1	2	yes	complemented
37	#16811269	—	2	1	no	—
38	#16811269	—	2	1	no	—
39	#16811264	C₂²	1	2	yes	—
40	#16811264	C₂²	1	2	yes	—
41	D₄×D₂₁₂	—	2	1	no	—
42	D₄×D₂₁₂	—	2	1	no	—
43	#16811257	C₂²	1	2	yes	—
44	#16811257	C₂²	1	2	yes	—
45	#16811251	C₂²	1	1	yes	characteristic, complemented
46	#16811217	—	2	2	no	—
47	#16811201	C₂²	1	1	yes	characteristic, complemented
48	#16811192	C₂²	1	1	yes	characteristic
49	#16811187	C₂²	1	1	yes	characteristic
50	#16811184	—	2	2	no	—
51	#16811134	C₂²	1	1	yes	characteristic
52	#16811129	—	2	2	no	—
53	#120×D₅₃	—	2	2	no	—
54	#16811106	C₂²	1	1	yes	characteristic, complemented
55	#16811103	C₂²	1	1	yes	characteristic, complemented
56	#16811097	C₂²	1	1	yes	characteristic
57	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
58	#16810986	C₂²	1	2	yes	complemented
59	#16810984	C₂²	1	2	yes	complemented
60	#16810979	C₂²	1	2	yes	complemented
61	#16810968	C₂²	1	2	yes	complemented
62	#16810956	C₂²	1	2	yes	complemented
63	#16810951	C₂²	1	2	yes	complemented
64	#16810950	C₂²	1	2	yes	complemented
65	#16810949	C₂²	1	2	yes	complemented
66	#16810943	C₂²	1	2	yes	complemented
67	#16810939	C₂²	1	2	yes	complemented
68	#16810938	C₂²	1	2	yes	complemented
69	#16810934	C₂²	1	2	yes	complemented
70	#16810926	C₂²	1	2	yes	complemented
71	#16810922	C₂²	1	2	yes	complemented
72	#16810912	C₂²	1	2	yes	complemented
73	#16810902	C₂²	1	2	yes	complemented
74	#16810875	C₂²	1	2	yes	complemented
75	#16810872	C₂²	1	2	yes	complemented
76	#16810858	C₂²	1	2	yes	complemented
77	#16810855	C₂²	1	2	yes	complemented
78	#16810847	C₂²	1	2	yes	complemented
79	#16810840	C₂²	1	2	yes	complemented
80	#16810821	C₂²	1	2	yes	complemented
81	#16810816	C₂²	1	2	yes	complemented
82	#16810784	C₂²	1	2	yes	complemented
83	#16810773	C₂²	1	2	yes	complemented
84	#16810773	C₂²	1	2	yes	complemented
85	#16810772	C₂²	1	2	yes	complemented
86	#16810767	C₂²	1	2	yes	complemented
87	#16810756	C₂²	1	2	yes	complemented
88	#16810756	C₂²	1	2	yes	complemented
89	#16810755	C₂²	1	2	yes	complemented
90	#16810732	C₂²	1	2	yes	complemented
91	#16810726	C₂²	1	2	yes	complemented
92	#16810708	C₂²	1	2	yes	complemented
93	#16810703	C₂²	1	2	yes	complemented
94	#16810694	C₂²	1	2	yes	complemented
95	#16810694	C₂²	1	2	yes	complemented
96	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
97	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
98	#16810666	C₂²	1	1	yes	characteristic, complemented
99	#16810666	C₂²	1	1	yes	characteristic, complemented
100	#16810649	C₂²	1	1	yes	characteristic, complemented
101	#16810627	C₂²	1	1	yes	characteristic
102	#16810627	C₂²	1	1	yes	characteristic, complemented
103	#16810626	C₂²	1	2	yes	complemented
104	#16810624	C₂²	1	1	yes	characteristic, complemented
105	#16810624	C₂²	1	1	yes	characteristic, complemented
106	#16810623	C₂²	1	2	yes	complemented
107	#16810618	C₂²	1	2	yes	complemented
108	C₂×#13133139	C₂²	1	1	yes	characteristic
109	C₂×#13133139	C₂²	1	1	yes	characteristic
110	C₂×#13133139	C₂²	1	1	yes	characteristic, complemented
111	C₂×#13133139	C₂²	1	2	yes	complemented
112	C₂×#13133139	C₂²	1	2	yes	complemented
113	C₂×#13133139	C₂²	1	2	yes	complemented
114	C₂×#13133139	C₂²	1	2	yes	complemented
115	C₂×#13133139	C₂²	1	1	yes	characteristic, complemented
116	#102×D₅₃	C₂²	1	2	yes	complemented
117	#16810589	C₂²	1	1	yes	characteristic, complemented
118	#16810587	C₂²	1	1	yes	characteristic, complemented
119	#16810578	C₂²	1	1	yes	characteristic, complemented
120	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₂³×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#525	C₂²	1	1	yes	characteristic
123	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
135	C₂⁴×D₅₃	—	2	1	no	—
136	#13133263	—	2	4	no	—
137	#13133263	—	4	2	no	—
138	C₂×#11719949	C₂³	1	2	yes	—
139	C₂×#11719945	—	2	1	no	—
140	C₂×#11719945	C₂³	1	1	yes	characteristic
141	C₂×#11719947	—	2	2	no	—
142	C₂²×D₂₁₂	—	2	4	no	—
143	C₂²×D₂₁₂	—	2	1	no	—
144	C₂²×D₂₁₂	—	2	1	no	—
145	C₂²×D₂₁₂	—	2	1	no	—
146	C₂²×D₂₁₂	—	2	1	no	—
147	C₂²×D₂₁₂	—	4	2	no	—
148	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
149	C₂²×D₂₁₂	C₂³	1	2	yes	—
150	C₂²×D₂₁₂	C₂³	1	2	yes	—
151	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
152	C₂×D₄×D₅₃	—	2	2	no	—
153	C₂×D₄×D₅₃	—	2	2	no	—
154	C₂×D₄×D₅₃	—	2	2	no	—
155	C₂×D₄×D₅₃	C₂³	1	2	yes	—
156	C₂³×Dic₅₃	—	2	1	no	—
157	#13133242	—	2	4	no	—
158	#13133242	—	4	2	no	—
159	C₂×#11719924	C₂³	1	2	yes	—
160	C₂×#11719924	C₂³	1	2	yes	—
161	C₂×#11719922	C₂³	1	2	yes	—
162	C₂×#11719922	C₂³	1	2	yes	—
163	#13133223	—	4	2	no	—
164	C₂×#11719917	C₂³	1	1	yes	characteristic
165	C₂×#11719917	C₂³	1	1	yes	characteristic
166	C₂×#11719912	C₂³	1	2	yes	complemented
167	C₂×C₈×D₅₃	C₂³	1	2	yes	complemented
168	#13133217	—	2	1	no	—
169	#13133216	C₂³	1	2	yes	complemented
170	#13133214	—	2	1	no	—
171	#13133213	C₂³	1	2	yes	—
172	#13133212	—	2	2	no	—
173	#13133210	—	2	2	no	—
174	#13133209	—	2	1	no	—
175	#13133208	—	2	2	no	—
176	#13133208	C₂³	1	2	yes	complemented
177	#13133207	—	2	2	no	—
178	#13133206	C₂³	1	2	yes	—
179	#13133205	—	2	1	no	—
180	#13133202	—	2	2	no	—
181	#13133202	—	2	2	no	—
182	#13133201	—	2	2	no	—
183	#13133201	—	2	2	no	—
184	#13133200	D₄	1	2	yes	—
185	#13133199	—	2	2	no	—
186	#13133198	—	2	2	no	—
187	#13133197	—	2	2	no	—
188	#13133196	—	2	1	no	—
189	#13133196	D₄	1	1	yes	characteristic
190	#13133196	D₄	1	1	yes	characteristic
191	#13133194	—	2	2	no	—
192	#13133194	—	2	2	no	—
193	#13133194	—	2	2	no	—
194	#13133193	C₂³	1	2	yes	complemented
195	#13133192	—	2	2	no	—
196	#13133192	—	2	2	no	—
197	#13133192	C₂³	1	2	yes	—
198	#13133192	C₂³	1	2	yes	—
199	#13133191	—	2	1	no	—
200	#13133191	—	2	1	no	—
201	#13133191	—	2	1	no	—
202	#13133191	D₄	1	1	yes	characteristic
203	#13133191	D₄	1	1	yes	characteristic
204	#13133190	—	2	2	no	—
205	#13133190	—	2	2	no	—
206	#13133189	—	2	2	no	—
207	#13133189	—	2	2	no	—
208	#13133188	C₂³	1	2	yes	complemented
209	#13133187	—	2	2	no	—
210	#13133187	—	2	2	no	—
211	#13133187	—	2	2	no	—
212	#13133187	—	2	2	no	—
213	#13133187	—	2	2	no	—
214	#13133186	D₄	1	2	yes	—
215	#13133185	—	2	2	no	—
216	#13133185	—	2	2	no	—
217	#13133185	—	2	2	no	—
218	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
219	C₄×Dic₁₀₆	—	2	1	no	—
220	C₄×D₂₁₂	—	2	1	no	—
221	C₄×D₂₁₂	—	2	1	no	—
222	C₄×D₂₁₂	—	2	1	no	—
223	D₄×Dic₅₃	—	2	2	no	—
224	D₄×Dic₅₃	—	2	2	no	—
225	D₄×Dic₅₃	C₂³	1	2	yes	complemented
226	#13133179	C₂³	1	2	yes	—
227	#13133179	C₂³	1	2	yes	—
228	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
229	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
230	#13133177	—	2	2	no	—
231	#13133177	—	2	2	no	—
232	#13133176	—	2	1	no	—
233	#13133176	C₂³	1	1	yes	characteristic
234	#13133175	C₂³	1	2	yes	complemented
235	#13133173	—	2	2	no	—
236	C₂×C₄⋊Dic₅₃	—	2	1	no	—
237	C₂×C₄⋊Dic₅₃	—	2	1	no	—
238	C₂×C₄⋊Dic₅₃	—	2	1	no	—
239	C₂×C₄⋊Dic₅₃	—	2	1	no	—
240	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
241	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
242	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×D₅₃	C₂³	1	2	yes	complemented
245	C₂²⋊C₄×D₅₃	—	2	2	no	—
246	C₂²⋊C₄×D₅₃	—	2	2	no	—
247	C₂²⋊C₄×D₅₃	—	2	2	no	—
248	#13133150	C₂³	1	2	yes	complemented
249	#13133150	C₂³	1	2	yes	complemented
250	#13133148	C₂³	1	2	yes	complemented
251	#13133148	C₂³	1	2	yes	complemented
252	#13133146	C₂³	1	2	yes	complemented
253	#13133146	C₂³	1	2	yes	complemented
254	#13133141	C₂³	1	2	yes	complemented
255	#13133141	C₂³	1	2	yes	complemented
256	#13133139	C₂³	1	2	yes	—
257	#13133139	C₂³	1	2	yes	—
258	#13133139	C₂³	1	2	yes	—
259	#13133139	C₂³	1	2	yes	—
260	#13133139	C₂³	1	2	yes	—
261	#13133139	C₂³	1	2	yes	—
262	#13133139	C₂³	1	2	yes	—
263	#13133139	C₂³	1	2	yes	—
264	#13133138	C₂³	1	2	yes	complemented
265	#13133138	C₂³	1	2	yes	complemented
266	#13133137	C₂³	1	2	yes	—
267	#13133137	C₂³	1	2	yes	—
268	#13133137	C₂³	1	2	yes	—
269	#13133137	C₂³	1	2	yes	—
270	C₂²⋊#88322	C₂³	1	2	yes	—
271	C₂²⋊#88322	C₂³	1	2	yes	—
272	#13133129	C₂³	1	2	yes	complemented
273	#13133129	C₂³	1	2	yes	complemented
274	#13133127	C₂³	1	2	yes	complemented
275	C₈×Dic₅₃	C₂³	1	2	yes	complemented
276	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
278	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
279	#135×C₅₃	—	4	2	no	—
280	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
281	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
282	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
283	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
284	C₂²×C₈×C₅₃	—	4	2	no	—
285	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
291	#123×C₅₃	—	2	1	no	—
292	#123×C₅₃	—	2	1	no	—
293	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
296	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
297	#121×C₅₃	C₂³	1	1	yes	characteristic
298	#121×C₅₃	C₂³	1	1	yes	characteristic
299	#121×C₅₃	C₂³	1	1	yes	characteristic
300	#121×C₅₃	C₂³	1	1	yes	characteristic
301	#120×C₅₃	—	2	1	no	—
302	#120×C₅₃	—	2	1	no	—
303	C₄×D₄×C₅₃	—	2	1	no	—
304	C₄×D₄×C₅₃	—	2	1	no	—
305	C₄×D₄×C₅₃	—	2	1	no	—
306	C₄×D₄×C₅₃	—	2	1	no	—
307	#117×C₅₃	C₂³	1	1	yes	characteristic
308	#117×C₅₃	C₂³	1	1	yes	characteristic
309	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
310	#107×C₅₃	C₂³	1	1	yes	characteristic, complemented
311	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
312	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
313	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
314	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
315	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
316	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
317	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
318	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
319	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
320	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
321	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
322	C₂³×D₅₃	—	2	1	no	—
323	C₂³×D₅₃	—	2	2	no	—
324	C₂³×D₅₃	—	2	2	no	—
325	C₂³×D₅₃	—	2	1	no	—
326	C₂³×D₅₃	—	2	2	no	—
327	C₂³×D₅₃	—	4	4	no	—
328	C₂³×D₅₃	—	8	2	no	—
329	C₂³×D₅₃	—	8	2	no	—
330	#41×C₅₃	—	2	2	no	—
331	#41×C₅₃	—	2	2	no	—
332	#41×C₅₃	—	2	2	no	—
333	#41×C₅₃	—	2	2	no	—
334	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	1	no	—
338	C₂×D₄×C₅₃	—	2	1	no	—
339	C₂×D₄×C₅₃	—	2	1	no	—
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂²×C₄×C₅₃	—	2	2	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	1	no	—
347	C₂²×C₄×C₅₃	—	2	1	no	—
348	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
349	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₂²⋊D₅₃	—	2	2	no	—
355	C₂×C₂²⋊D₅₃	—	2	2	no	—
356	C₂×C₂²⋊D₅₃	—	2	2	no	—
357	C₂×C₂²⋊D₅₃	—	2	2	no	—
358	C₂×C₂²⋊D₅₃	C₂×D₄	1	2	yes	—
359	C₂×C₂²⋊D₅₃	C₂×D₄	1	2	yes	—
360	C₂×C₂²⋊D₅₃	C₂×D₄	1	2	yes	—
361	C₂²×Dic₅₃	—	2	2	no	—
362	C₂²×Dic₅₃	—	2	1	no	—
363	C₂²×Dic₅₃	—	2	2	no	—
364	C₂²×Dic₅₃	—	2	1	no	—
365	C₂²×Dic₅₃	—	2	2	no	—
366	C₂²×Dic₅₃	—	8	2	no	—
367	#11719949	—	2	4	no	—
368	#11719949	—	4	2	no	—
369	#11719947	—	8	4	no	—
370	D₄×D₅₃	—	2	4	no	—
371	D₄×D₅₃	—	4	2	no	—
372	D₄×D₅₃	—	4	8	no	—
373	D₄×D₅₃	—	8	4	no	—
374	D₄×D₅₃	—	8	4	no	—
375	#11719945	—	2	2	no	—
376	#11719945	—	2	2	no	—
377	#11719945	—	4	4	no	—
378	C₂×D₂₁₂	—	2	1	no	—
379	C₂×D₂₁₂	—	2	2	no	—
380	C₂×D₂₁₂	—	2	2	no	—
381	C₂×D₂₁₂	—	2	2	no	—
382	C₂×D₂₁₂	—	2	4	no	—
383	C₂×D₂₁₂	—	2	4	no	—
384	C₂×D₂₁₂	—	2	2	no	—
385	C₂×D₂₁₂	—	2	2	no	—
386	C₂×D₂₁₂	—	2	2	no	—
387	C₂×D₂₁₂	—	2	1	no	—
388	C₂×D₂₁₂	—	2	2	no	—
389	C₂×D₂₁₂	—	2	2	no	—
390	C₂×D₂₁₂	—	4	2	no	—
391	C₂×D₂₁₂	—	4	2	no	—
392	C₂×D₂₁₂	—	4	4	no	—
393	C₂×D₂₁₂	—	4	4	no	—
394	C₂×D₂₁₂	—	4	4	no	—
395	C₂×D₂₁₂	—	4	4	no	—
396	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
397	C₂×D₂₁₂	#41	1	4	yes	complemented
398	C₂×D₂₁₂	C₂⁴	1	2	yes	—
399	C₂×D₂₁₂	C₂⁴	1	2	yes	—
400	C₂×C₄×D₅₃	—	2	2	no	—
401	C₂×C₄×D₅₃	—	2	2	no	—
402	C₂×C₄×D₅₃	—	2	2	no	—
403	C₂×C₄×D₅₃	—	2	2	no	—
404	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
405	C₂×Dic₁₀₆	—	2	2	no	—
406	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
407	Q₁₆×C₅₃	—	4	1	no	—
408	SD₁₆×C₅₃	—	4	1	no	—
409	SD₁₆×C₅₃	—	4	1	no	—
410	D₈×C₅₃	—	4	1	no	—
411	C₂×C₈×C₅₃	—	2	2	no	—
412	C₂×C₈×C₅₃	—	2	2	no	—
413	C₂×C₈×C₅₃	—	4	1	no	—
414	C₂×C₈×C₅₃	—	4	1	no	—
415	C₂×C₈×C₅₃	—	4	1	no	—
416	C₂×C₈×C₅₃	—	4	1	no	—
417	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₄⋊C₄×C₅₃	—	2	1	no	—
425	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	—	2	1	no	—
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	—	2	1	no	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	1	no	—
436	C₂²⋊C₄×C₅₃	—	2	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	1	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₄²×C₅₃	—	2	1	no	—
440	C₄²×C₅₃	—	2	1	no	—
441	C₂²⋊Dic₅₃	—	2	2	no	—
442	C₂²⋊Dic₅₃	—	2	2	no	—
443	C₂²⋊Dic₅₃	C₂×D₄	1	2	yes	—
444	C₂²⋊Dic₅₃	C₂×D₄	1	2	yes	—
445	C₂²⋊Dic₅₃	C₂×D₄	1	2	yes	—
446	#11719924	—	2	4	no	—
447	#11719924	—	4	2	no	—
448	#11719922	—	2	4	no	—
449	#11719922	—	4	2	no	—
450	#11719921	—	2	2	no	—
451	#11719921	—	2	2	no	—
452	#11719921	—	2	2	no	—
453	#11719921	—	2	2	no	—
454	#11719921	—	2	2	no	—
455	#11719921	—	2	2	no	—
456	#11719921	—	2	2	no	—
457	#11719921	—	2	2	no	—
458	#11719921	C₂×D₄	1	2	yes	—
459	#11719921	C₂×D₄	1	2	yes	—
460	C₄⋊Dic₅₃	—	2	1	no	—
461	C₄⋊Dic₅₃	—	2	1	no	—
462	C₄⋊Dic₅₃	—	2	2	no	—
463	C₄⋊Dic₅₃	—	2	2	no	—
464	C₄⋊Dic₅₃	—	2	2	no	—
465	C₄⋊Dic₅₃	—	2	2	no	—
466	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
467	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
468	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
469	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
470	#11719919	—	2	2	no	—
471	#11719919	—	2	2	no	—
472	#11719919	—	2	2	no	—
473	#11719919	—	2	2	no	—
474	#11719919	C₂×D₄	1	2	yes	—
475	#11719919	C₂×D₄	1	2	yes	—
476	C₄×Dic₅₃	—	2	2	no	—
477	C₄×Dic₅₃	—	2	2	no	—
478	C₄×Dic₅₃	C₂⁴	1	2	yes	—
479	#11719917	—	2	2	no	—
480	#11719917	—	2	2	no	—
481	C₂×#88322	C₂⁴	1	2	yes	—
482	C₂×#88322	C₂⁴	1	2	yes	—
483	#11719912	—	4	2	no	—
484	C₈×D₅₃	—	4	2	no	—
485	C₂³×C₅₃	—	2	2	no	—
486	C₂³×C₅₃	—	2	2	no	—
487	C₂³×C₅₃	—	2	2	no	—
488	C₂³×C₅₃	—	2	1	no	—
489	C₂³×C₅₃	—	2	1	no	—
490	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
491	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
493	C₂²×D₅₃	—	2	2	no	—
494	C₂²×D₅₃	—	2	4	no	—
495	C₂²×D₅₃	—	2	2	no	—
496	C₂²×D₅₃	—	4	4	no	—
497	C₂²×D₅₃	—	4	4	no	—
498	C₂²×D₅₃	—	4	4	no	—
499	C₂²×D₅₃	—	4	2	no	—
500	C₂²×D₅₃	—	4	4	no	—
501	C₂²×D₅₃	—	4	4	no	—
502	C₂²×D₅₃	—	8	2	no	—
503	C₂²×D₅₃	—	8	2	no	—
504	C₂²×D₅₃	—	8	1	no	—
505	C₂²×D₅₃	—	8	2	no	—
506	C₂²×D₅₃	—	8	1	no	—
507	C₂²×D₅₃	—	8	2	no	—
508	C₂²×D₅₃	—	8	1	no	—
509	C₂²×D₅₃	—	8	1	no	—
510	C₂²×D₅₃	—	8	16	no	—
511	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
512	Q₈×C₅₃	—	2	1	no	—
513	Q₈×C₅₃	—	2	1	no	—
514	Q₈×C₅₃	—	2	1	no	—
515	Q₈×C₅₃	—	2	1	no	—
516	D₄×C₅₃	—	2	1	no	—
517	D₄×C₅₃	—	2	1	no	—
518	D₄×C₅₃	—	2	1	no	—
519	D₄×C₅₃	—	2	1	no	—
520	D₄×C₅₃	—	4	2	no	—
521	D₄×C₅₃	—	4	2	no	—
522	D₄×C₅₃	—	4	2	no	—
523	D₄×C₅₃	—	4	2	no	—
524	D₄×C₅₃	—	4	2	no	—
525	D₄×C₅₃	—	4	2	no	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	2	no	—
528	C₂×C₄×C₅₃	—	2	2	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	4	2	no	—
540	C₂×C₄×C₅₃	—	4	2	no	—
541	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
545	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
546	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
547	C₂²⋊D₅₃	—	2	4	no	—
548	C₂²⋊D₅₃	—	2	4	no	—
549	C₂²⋊D₅₃	—	2	4	no	—
550	C₂²⋊D₅₃	—	4	4	no	—
551	C₂²⋊D₅₃	—	8	2	no	—
552	C₂²⋊D₅₃	—	8	2	no	—
553	C₂²⋊D₅₃	—	8	2	no	—
554	C₂×Dic₅₃	—	2	2	no	—
555	C₂×Dic₅₃	—	2	2	no	—
556	C₂×Dic₅₃	—	4	4	no	—
557	C₂×Dic₅₃	—	8	2	no	—
558	C₂×Dic₅₃	—	8	1	no	—
559	C₂×Dic₅₃	—	8	2	no	—
560	C₂×Dic₅₃	—	8	1	no	—
561	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
562	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
563	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
564	D₂₁₂	—	2	4	no	—
565	D₂₁₂	—	2	2	no	—
566	D₂₁₂	—	2	2	no	—
567	D₂₁₂	—	2	2	no	—
568	D₂₁₂	—	2	2	no	—
569	D₂₁₂	—	4	4	no	—
570	D₂₁₂	—	4	4	no	—
571	D₂₁₂	—	4	4	no	—
572	D₂₁₂	—	4	2	no	—
573	D₂₁₂	—	8	2	no	—
574	D₂₁₂	—	8	2	no	—
575	D₂₁₂	C₂×#41	1	4	yes	—
576	C₄×D₅₃	—	2	2	no	—
577	C₄×D₅₃	—	2	2	no	—
578	C₄×D₅₃	—	4	4	no	—
579	C₄×D₅₃	—	8	2	no	—
580	C₄×D₅₃	—	8	2	no	—
581	C₄×D₅₃	—	8	2	no	—
582	Dic₁₀₆	—	2	2	no	—
583	Dic₁₀₆	—	8	2	no	—
584	C₈×C₅₃	—	2	1	no	—
585	C₈×C₅₃	—	2	1	no	—
586	C₈×C₅₃	—	2	1	no	—
587	C₈×C₅₃	—	2	1	no	—
588	#88322	—	2	2	no	—
589	#88322	—	2	2	no	—
590	#61167	—	53	1	no	maximal, Sylow
591	C₂²×C₅₃	—	2	8	no	—
592	C₂²×C₅₃	—	2	1	no	—
593	C₂²×C₅₃	—	2	1	no	—
594	C₂²×C₅₃	—	2	1	no	—
595	C₂²×C₅₃	—	2	1	no	—
596	C₂²×C₅₃	—	2	1	no	—
597	C₂²×C₅₃	—	2	1	no	—
598	C₂²×C₅₃	—	4	1	no	—
599	C₂²×C₅₃	—	4	1	no	—
600	C₂²×C₅₃	—	4	1	no	—
601	C₂²×C₅₃	—	4	1	no	—
602	C₂²×C₅₃	—	4	1	no	—
603	C₂²×C₅₃	—	4	1	no	—
604	C₂²×C₅₃	#546	1	2	yes	—
605	C₂²×C₅₃	#576	1	2	yes	—
606	C₂²×C₅₃	#577	1	2	yes	—
607	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
608	C₂×D₅₃	—	2	2	no	—
609	C₂×D₅₃	—	2	4	no	—
610	C₂×D₅₃	—	2	2	no	—
611	C₂×D₅₃	—	2	2	no	—
612	C₂×D₅₃	—	4	2	no	—
613	C₂×D₅₃	—	4	2	no	—
614	C₂×D₅₃	—	4	2	no	—
615	C₂×D₅₃	—	4	2	no	—
616	C₂×D₅₃	—	4	2	no	—
617	C₂×D₅₃	—	8	4	no	—
618	C₂×D₅₃	—	8	8	no	—
619	C₂×D₅₃	—	8	8	no	—
620	C₂×D₅₃	—	8	4	no	—
621	C₂×D₅₃	—	16	4	no	—
622	C₄×C₅₃	—	2	1	no	—
623	C₄×C₅₃	—	2	1	no	—
624	C₄×C₅₃	—	4	1	no	—
625	C₄×C₅₃	—	4	1	no	—
626	C₄×C₅₃	—	4	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	1	no	—
630	C₄×C₅₃	#546	1	2	yes	—
631	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
632	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
633	Dic₅₃	—	2	2	no	—
634	Dic₅₃	—	2	2	no	—
635	Dic₅₃	—	2	2	no	—
636	Dic₅₃	—	4	2	no	—
637	Dic₅₃	—	4	2	no	—
638	#3492	—	53	1	no	—
639	#3484	—	53	1	no	—
640	#3318	—	53	2	no	—
641	#3314	—	53	2	no	—
642	#3310	—	53	2	no	—
643	#3306	—	53	2	no	—
644	#3297	—	53	2	no	—
645	#3296	—	53	2	no	—
646	#3295	—	53	2	no	—
647	#3294	—	53	2	no	—
648	#3136	—	53	1	no	—
649	#3096	—	53	1	no	—
650	#3092	—	53	1	no	—
651	#3081	—	53	1	no	—
652	#3062	—	53	1	no	—
653	#3050	D₅₃	1	1	yes	characteristic, complemented
654	#3045	—	53	1	no	—
655	#3012	—	53	1	no	—
656	#3003	—	53	1	no	—
657	#2946	—	53	1	no	—
658	#2929	—	53	1	no	—
659	#2897	—	53	1	no	—
660	C₂²×#102	—	53	1	no	—
661	C₂×C₅₃	—	2	2	no	—
662	C₂×C₅₃	—	2	2	no	—
663	C₂×C₅₃	—	2	2	no	—
664	C₂×C₅₃	—	8	1	no	—
665	C₂×C₅₃	—	8	1	no	—
666	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
667	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
668	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
669	D₅₃	—	4	2	no	—
670	D₅₃	—	4	4	no	—
671	D₅₃	—	8	2	no	—
672	C₂×H(5,𝔽₂)	—	53	1	no	—
673	C₂³×D₄	—	53	1	no	—
674	C₂×AGL(1,ℤ/8)	—	53	1	no	—
675	C₂×AGL(1,ℤ/8)	—	53	1	no	—
676	C₂×#135	C₂×D₅₃	1	1	yes	characteristic, complemented
677	C₂×#131	—	53	1	no	—
678	C₂³×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
679	#554	—	53	2	no	—
680	#554	—	106	1	no	—
681	#553	—	53	2	no	—
682	#553	—	106	1	no	—
683	#552	—	53	2	no	—
684	#552	—	106	1	no	—
685	#547	—	53	2	no	—
686	#547	—	106	1	no	—
687	#546	—	53	2	no	—
688	#546	—	53	2	no	—
689	#546	—	106	1	no	—
690	#546	—	106	1	no	—
691	D₄²	—	53	2	no	—
692	D₄²	—	53	2	no	—
693	D₄²	—	106	1	no	—
694	D₄²	—	106	1	no	—
695	#544	—	53	1	no	—
696	#539	—	106	2	no	—
697	#537	—	53	1	no	—
698	#535	—	53	1	no	—
699	#535	—	53	1	no	—
700	#534	—	106	2	no	—
701	#525	—	53	1	no	—
702	#525	—	106	2	no	—
703	#525	C₂×D₅₃	1	1	yes	characteristic
704	#525	C₂×D₅₃	1	1	yes	characteristic, complemented
705	C₂×#120	—	106	2	no	—
706	#520	—	53	1	no	—
707	#520	—	53	1	no	—
708	#518	—	53	1	no	—
709	C₂²×C₄⋊C₄	—	53	1	no	—
710	#490	—	53	2	no	—
711	#489	—	53	2	no	—
712	#488	—	53	2	no	—
713	#486	—	53	2	no	—
714	#484	—	53	2	no	—
715	#483	—	53	2	no	—
716	#482	—	53	2	no	—
717	#482	—	53	2	no	—
718	#481	—	53	2	no	—
719	#481	—	53	2	no	—
720	#480	—	53	2	no	—
721	#480	—	53	2	no	—
722	#478	—	53	2	no	—
723	#478	—	53	2	no	—
724	#476	—	53	2	no	—
725	#474	—	53	2	no	—
726	#469	—	53	2	no	—
727	#468	—	53	2	no	—
728	#467	C₂×D₅₃	1	1	yes	characteristic, complemented
729	#467	C₂×D₅₃	1	1	yes	characteristic, complemented
730	#466	—	53	2	no	—
731	#466	C₂×D₅₃	1	1	yes	characteristic, complemented
732	#466	C₂×D₅₃	1	1	yes	characteristic, complemented
733	#465	—	53	2	no	—
734	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
735	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
736	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
737	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
738	#464	—	53	2	no	—
739	#463	—	53	2	no	—
740	#460	—	53	2	no	—
741	#459	—	53	2	no	—
742	#452	—	53	2	no	—
743	#450	—	53	2	no	—
744	#450	—	53	2	no	—
745	#450	—	53	2	no	—
746	#449	—	53	2	no	—
747	#447	—	53	2	no	—
748	#447	—	53	2	no	—
749	#447	—	53	2	no	—
750	#442	—	53	2	no	—
751	#440	—	53	2	no	—
752	C₄×SD₁₆	—	53	2	no	—
753	C₄×D₈	—	53	2	no	—
754	#435	—	53	2	no	—
755	#435	—	53	2	no	—
756	C₈×D₄	—	53	2	no	—
757	C₈×D₄	—	53	2	no	—
758	#428	—	53	1	no	—
759	#428	—	53	1	no	—
760	#427	C₂×D₅₃	1	1	yes	characteristic, complemented
761	#424	—	53	1	no	—
762	#418	—	53	1	no	—
763	#418	—	53	1	no	—
764	#418	—	53	2	no	—
765	#417	—	53	1	no	—
766	#417	—	53	1	no	—
767	#417	—	53	2	no	—
768	#416	—	53	2	no	—
769	#416	C₂×D₅₃	1	1	yes	characteristic, complemented
770	#416	C₂×D₅₃	1	1	yes	characteristic, complemented
771	C₂×#102	—	53	1	no	—
772	C₂×#102	—	53	1	no	—
773	C₂×#102	—	53	1	no	—
774	C₂×#102	—	53	1	no	—
775	C₂×#102	—	53	2	no	—
776	C₂×#102	—	53	2	no	—
777	C₂×#102	—	53	2	no	—
778	C₂×#102	—	53	2	no	—
779	C₂×#102	—	53	2	no	—
780	#408	—	53	1	no	—
781	#407	—	53	1	no	—
782	#405	—	53	1	no	—
783	C₅₃	#61167	1	1	yes	characteristic, complemented, Sylow
784	C₂⁵	—	106	1	no	—
785	H(5,𝔽₂)	—	106	4	no	—
786	H(5,𝔽₂)	—	212	2	no	—
787	C₂×#41	—	53	1	no	—
788	C₂×#41	—	53	2	no	—
789	C₂×#41	—	106	1	no	—
790	C₂×#41	—	106	2	no	—
791	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
792	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
793	C₂²×D₄	—	53	2	no	—
794	C₂²×D₄	—	53	1	no	—
795	C₂²×D₄	—	53	1	no	—
796	C₂²×D₄	—	53	2	no	—
797	C₂²×D₄	—	53	2	no	—
798	C₂²×D₄	—	106	4	no	—
799	C₂²×D₄	—	106	1	no	—
800	C₂²×D₄	—	106	2	no	—
801	C₂²×D₄	—	106	2	no	—
802	C₂²×D₄	—	106	2	no	—
803	C₂²×D₄	—	106	1	no	—
804	C₂²×D₄	—	106	1	no	—
805	C₂²×D₄	—	106	1	no	—
806	C₂²×D₄	—	212	2	no	—
807	C₂³×C₄	—	106	1	no	—
808	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
809	AGL(1,ℤ/8)	—	106	4	no	—
810	AGL(1,ℤ/8)	—	212	2	no	—
811	#135	—	4	2	no	—
812	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
813	C₂×SD₁₆	—	53	2	no	—
814	C₂×SD₁₆	—	53	2	no	—
815	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
816	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
817	C₂×D₈	—	53	2	no	—
818	C₂×D₈	—	53	2	no	—
819	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
820	#131	—	212	2	no	—
821	C₂×M₁₆	—	53	1	no	—
822	C₂×M₁₆	—	53	1	no	—
823	C₂×M₁₆	—	53	2	no	—
824	C₂²×C₈	—	4	2	no	—
825	C₂²×C₈	—	53	2	no	—
826	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
827	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
828	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
829	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
830	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
831	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
832	C₄⋊Q₈	—	53	2	no	—
833	C₄⋊Q₈	—	106	1	no	—
834	#127	—	53	2	no	—
835	#127	—	106	1	no	—
836	#126	—	106	2	no	—
837	#126	—	106	2	no	—
838	#125	—	53	2	no	—
839	#125	—	106	1	no	—
840	#125	—	106	2	no	—
841	#125	—	106	2	no	—
842	#124	—	53	2	no	—
843	#124	—	106	1	no	—
844	#123	—	2	1	no	—
845	#123	—	2	1	no	—
846	#123	—	53	2	no	—
847	#123	—	106	2	no	—
848	#123	—	106	2	no	—
849	#123	—	106	2	no	—
850	#123	—	106	2	no	—
851	#123	—	106	2	no	—
852	#123	—	106	2	no	—
853	C₂²⋊Q₈	—	53	1	no	—
854	C₂²⋊Q₈	—	53	1	no	—
855	C₂²⋊Q₈	—	53	2	no	—
856	C₂²⋊Q₈	—	106	2	no	—
857	C₂²⋊Q₈	—	106	2	no	—
858	C₂²⋊Q₈	—	106	2	no	—
859	C₂²⋊Q₈	—	106	2	no	—
860	C₂²⋊Q₈	—	106	1	no	—
861	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
862	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
863	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
864	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
865	#121	—	53	1	no	—
866	#121	—	53	1	no	—
867	#121	—	53	2	no	—
868	#121	—	53	2	no	—
869	#121	—	53	2	no	—
870	#121	—	106	2	no	—
871	#121	—	106	2	no	—
872	#121	—	106	2	no	—
873	#121	—	106	2	no	—
874	#121	—	106	1	no	—
875	#121	—	106	1	no	—
876	#121	—	106	1	no	—
877	#121	—	106	2	no	—
878	#121	—	106	2	no	—
879	#121	C₂²×D₅₃	1	1	yes	characteristic
880	#121	C₂²×D₅₃	1	1	yes	characteristic
881	#121	C₂²×D₅₃	1	1	yes	characteristic
882	#121	C₂²×D₅₃	1	1	yes	characteristic
883	#120	—	2	1	no	—
884	#120	—	2	1	no	—
885	#120	—	53	2	no	—
886	#120	—	106	2	no	—
887	#120	—	106	2	no	—
888	#120	—	106	2	no	—
889	#120	—	106	2	no	—
890	#120	—	106	2	no	—
891	#120	—	106	2	no	—
892	#120	—	106	2	no	—
893	#120	—	106	2	no	—
894	C₄×Q₈	—	53	2	no	—
895	C₄×Q₈	—	106	1	no	—
896	C₄×D₄	—	2	1	no	—
897	C₄×D₄	—	2	1	no	—
898	C₄×D₄	—	2	1	no	—
899	C₄×D₄	—	2	1	no	—
900	C₄×D₄	—	53	2	no	—
901	C₄×D₄	—	53	2	no	—
902	C₄×D₄	—	53	2	no	—
903	C₄×D₄	—	53	2	no	—
904	C₄×D₄	—	53	2	no	—
905	C₄×D₄	—	106	1	no	—
906	C₄×D₄	—	106	1	no	—
907	C₄×D₄	—	106	1	no	—
908	C₄×D₄	—	106	2	no	—
909	C₄×D₄	—	106	2	no	—
910	C₄×D₄	—	106	2	no	—
911	C₄×D₄	—	106	2	no	—
912	#117	—	53	1	no	—
913	#117	—	53	2	no	—
914	#117	—	106	2	no	—
915	#117	—	106	1	no	—
916	#117	C₂²×D₅₃	1	1	yes	characteristic
917	#117	C₂²×D₅₃	1	1	yes	characteristic
918	C₂×C₄⋊C₄	—	53	1	no	—
919	C₂×C₄⋊C₄	—	53	1	no	—
920	C₂×C₄⋊C₄	—	53	2	no	—
921	C₂×C₄⋊C₄	—	53	2	no	—
922	C₂×C₄⋊C₄	—	53	2	no	—
923	C₂×C₄⋊C₄	—	106	1	no	—
924	C₂×C₄⋊C₄	—	106	1	no	—
925	C₂×C₄⋊C₄	—	106	1	no	—
926	C₂×C₄⋊C₄	—	106	1	no	—
927	C₂×C₂²⋊C₄	—	106	2	no	—
928	C₂×C₂²⋊C₄	—	106	2	no	—
929	C₂×C₂²⋊C₄	—	106	2	no	—
930	#107	—	53	2	no	—
931	#107	—	53	2	no	—
932	#107	C₂²×D₅₃	1	1	yes	characteristic, complemented
933	#107	C₂²×D₅₃	1	1	yes	characteristic, complemented
934	#106	—	53	2	no	—
935	#106	—	53	2	no	—
936	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
937	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
938	C₄⋊C₈	—	53	2	no	—
939	C₄⋊C₈	—	53	2	no	—
940	#103	—	53	2	no	—
941	#103	—	53	2	no	—
942	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
943	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
944	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
945	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
946	#102	—	53	2	no	—
947	#102	—	53	2	no	—
948	#102	—	53	2	no	—
949	#102	—	53	2	no	—
950	#102	—	53	2	no	—
951	#102	—	53	2	no	—
952	#102	—	53	2	no	—
953	#102	—	53	2	no	—
954	#102	—	53	2	no	—
955	#102	—	53	2	no	—
956	#102	—	53	2	no	—
957	#102	—	53	2	no	—
958	#102	—	53	2	no	—
959	#102	—	53	2	no	—
960	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
961	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
962	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
963	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
964	C₂²⋊C₈	—	53	2	no	—
965	C₂²⋊C₈	—	53	2	no	—
966	C₂²⋊C₈	—	53	2	no	—
967	C₂²⋊C₈	—	53	2	no	—
968	#97	—	53	2	no	—
969	C₄×C₈	—	53	2	no	—
970	C₂⁴	—	106	2	no	—
971	C₂⁴	—	106	1	no	—
972	C₂⁴	—	106	1	no	—
973	C₂⁴	—	106	2	no	—
974	C₂⁴	—	106	2	no	—
975	C₂⁴	—	424	2	no	—
976	C₂⁴	—	424	2	no	—
977	C₂⁴	—	212	4	no	—
978	C₂⁴	D₄×D₅₃	1	1	yes	characteristic
979	#41	—	2	2	no	—
980	#41	—	2	2	no	—
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	106	2	no	—
984	#41	—	106	2	no	—
985	#41	—	106	4	no	—
986	#41	—	424	4	no	—
987	#41	—	212	4	no	—
988	#41	—	212	2	no	—
989	C₂×Q₈	—	53	1	no	—
990	C₂×Q₈	—	106	2	no	—
991	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
992	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	1	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	53	2	no	—
1000	C₂×D₄	—	53	2	no	—
1001	C₂×D₄	—	53	2	no	—
1002	C₂×D₄	—	53	1	no	—
1003	C₂×D₄	—	53	4	no	—
1004	C₂×D₄	—	53	2	no	—
1005	C₂×D₄	—	53	2	no	—
1006	C₂×D₄	—	106	4	no	—
1007	C₂×D₄	—	106	4	no	—
1008	C₂×D₄	—	106	2	no	—
1009	C₂×D₄	—	106	2	no	—
1010	C₂×D₄	—	106	2	no	—
1011	C₂×D₄	—	106	2	no	—
1012	C₂×D₄	—	106	2	no	—
1013	C₂×D₄	—	106	2	no	—
1014	C₂×D₄	—	106	4	no	—
1015	C₂×D₄	—	106	2	no	—
1016	C₂×D₄	—	106	1	no	—
1017	C₂×D₄	—	106	2	no	—
1018	C₂×D₄	—	106	2	no	—
1019	C₂×D₄	—	106	1	no	—
1020	C₂×D₄	—	106	2	no	—
1021	C₂×D₄	—	106	2	no	—
1022	C₂×D₄	—	106	2	no	—
1023	C₂×D₄	—	424	4	no	—
1024	C₂×D₄	—	424	4	no	—
1025	C₂×D₄	—	212	2	no	—
1026	C₂×D₄	—	212	2	no	—
1027	C₂×D₄	—	212	4	no	—
1028	C₂×D₄	—	212	4	no	—
1029	C₂×D₄	—	212	4	no	—
1030	C₂×D₄	—	212	4	no	—
1031	C₂×D₄	—	212	2	no	—
1032	C₂×D₄	—	212	8	no	—
1033	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1034	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1035	C₂²×C₄	—	2	2	no	—
1036	C₂²×C₄	—	2	2	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	53	2	no	—
1040	C₂²×C₄	—	106	2	no	—
1041	C₂²×C₄	—	106	2	no	—
1042	C₂²×C₄	—	106	2	no	—
1043	C₂²×C₄	—	106	2	no	—
1044	C₂²×C₄	—	106	2	no	—
1045	C₂²×C₄	—	106	1	no	—
1046	C₂²×C₄	—	106	2	no	—
1047	C₂²×C₄	—	106	1	no	—
1048	C₂²×C₄	—	106	2	no	—
1049	C₂²×C₄	—	424	2	no	—
1050	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
1051	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
1052	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1054	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1055	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1056	Q₁₆	—	4	1	no	—
1057	SD₁₆	—	4	1	no	—
1058	SD₁₆	—	4	1	no	—
1059	SD₁₆	—	106	4	no	—
1060	SD₁₆	—	212	2	no	—
1061	D₈	—	4	1	no	—
1062	D₈	—	106	4	no	—
1063	D₈	—	212	2	no	—
1064	M₁₆	—	106	2	no	—
1065	M₁₆	—	106	2	no	—
1066	M₁₆	—	212	2	no	—
1067	C₂×C₈	—	2	2	no	—
1068	C₂×C₈	—	2	2	no	—
1069	C₂×C₈	—	4	1	no	—
1070	C₂×C₈	—	4	1	no	—
1071	C₂×C₈	—	4	1	no	—
1072	C₂×C₈	—	4	1	no	—
1073	C₂×C₈	—	53	2	no	—
1074	C₂×C₈	—	53	2	no	—
1075	C₂×C₈	—	212	2	no	—
1076	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1077	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1078	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1079	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	53	1	no	—
1085	C₄⋊C₄	—	53	1	no	—
1086	C₄⋊C₄	—	53	2	no	—
1087	C₄⋊C₄	—	53	2	no	—
1088	C₄⋊C₄	—	53	2	no	—
1089	C₄⋊C₄	—	53	2	no	—
1090	C₄⋊C₄	—	106	2	no	—
1091	C₄⋊C₄	—	106	2	no	—
1092	C₄⋊C₄	—	106	2	no	—
1093	C₄⋊C₄	—	106	2	no	—
1094	C₄⋊C₄	—	106	2	no	—
1095	C₄⋊C₄	—	106	2	no	—
1096	C₄⋊C₄	—	106	1	no	—
1097	C₄⋊C₄	—	106	1	no	—
1098	C₄⋊C₄	—	106	2	no	—
1099	C₄⋊C₄	—	106	2	no	—
1100	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1101	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1102	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1103	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1104	C₂²⋊C₄	—	2	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	53	2	no	—
1115	C₂²⋊C₄	—	53	2	no	—
1116	C₂²⋊C₄	—	53	2	no	—
1117	C₂²⋊C₄	—	53	2	no	—
1118	C₂²⋊C₄	—	53	2	no	—
1119	C₂²⋊C₄	—	106	2	no	—
1120	C₂²⋊C₄	—	106	2	no	—
1121	C₂²⋊C₄	—	106	2	no	—
1122	C₂²⋊C₄	—	106	2	no	—
1123	C₂²⋊C₄	—	106	2	no	—
1124	C₂²⋊C₄	—	106	2	no	—
1125	C₂²⋊C₄	—	106	2	no	—
1126	C₂²⋊C₄	—	106	2	no	—
1127	C₂²⋊C₄	—	106	2	no	—
1128	C₂²⋊C₄	—	106	2	no	—
1129	C₄²	—	2	1	no	—
1130	C₄²	—	2	1	no	—
1131	C₄²	—	53	2	no	—
1132	C₄²	—	106	2	no	—
1133	C₄²	—	106	2	no	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	2	no	—
1137	C₂³	—	2	1	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	53	2	no	—
1140	C₂³	—	106	4	no	—
1141	C₂³	—	106	2	no	—
1142	C₂³	—	106	2	no	—
1143	C₂³	—	424	16	no	—
1144	C₂³	—	424	1	no	—
1145	C₂³	—	424	2	no	—
1146	C₂³	—	424	1	no	—
1147	C₂³	—	424	1	no	—
1148	C₂³	—	424	2	no	—
1149	C₂³	—	424	1	no	—
1150	C₂³	—	424	2	no	—
1151	C₂³	—	424	2	no	—
1152	C₂³	—	212	4	no	—
1153	C₂³	—	212	4	no	—
1154	C₂³	—	212	4	no	—
1155	C₂³	—	212	4	no	—
1156	C₂³	—	212	4	no	—
1157	C₂³	—	212	2	no	—
1158	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1159	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1160	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1161	Q₈	—	2	1	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	106	2	no	—
1166	Q₈	—	424	2	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	2	no	—
1172	D₄	—	4	2	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	53	4	no	—
1178	D₄	—	106	4	no	—
1179	D₄	—	106	4	no	—
1180	D₄	—	106	4	no	—
1181	D₄	—	106	2	no	—
1182	D₄	—	106	2	no	—
1183	D₄	—	106	2	no	—
1184	D₄	—	106	4	no	—
1185	D₄	—	106	2	no	—
1186	D₄	—	424	2	no	—
1187	D₄	—	424	2	no	—
1188	D₄	—	424	2	no	—
1189	D₄	—	424	2	no	—
1190	D₄	—	424	2	no	—
1191	D₄	—	212	4	no	—
1192	D₄	—	212	4	no	—
1193	D₄	—	212	4	no	—
1194	D₄	—	212	4	no	—
1195	D₄	—	212	2	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	4	2	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	53	2	no	—
1212	C₂×C₄	—	53	2	no	—
1213	C₂×C₄	—	53	2	no	—
1214	C₂×C₄	—	106	2	no	—
1215	C₂×C₄	—	106	2	no	—
1216	C₂×C₄	—	106	2	no	—
1217	C₂×C₄	—	106	2	no	—
1218	C₂×C₄	—	424	2	no	—
1219	C₂×C₄	—	424	2	no	—
1220	C₂×C₄	—	424	2	no	—
1221	C₂×C₄	—	424	2	no	—
1222	C₂×C₄	—	424	1	no	—
1223	C₂×C₄	—	424	2	no	—
1224	C₂×C₄	—	424	1	no	—
1225	C₂×C₄	—	212	4	no	—
1226	C₂×C₄	—	212	4	no	—
1227	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1228	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1229	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1230	C₂×C₄	#41×D₅₃	1	2	yes	—
1231	C₂×C₄	#13133262	1	2	yes	—
1232	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1233	C₈	—	2	1	no	—
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	106	2	no	—
1238	C₈	—	106	2	no	—
1239	C₂²	—	2	8	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	848	4	no	—
1253	C₂²	—	106	2	no	—
1254	C₂²	—	106	4	no	—
1255	C₂²	—	106	2	no	—
1256	C₂²	—	106	2	no	—
1257	C₂²	—	424	4	no	—
1258	C₂²	—	424	8	no	—
1259	C₂²	—	424	8	no	—
1260	C₂²	—	424	4	no	—
1261	C₂²	—	212	2	no	—
1262	C₂²	—	212	2	no	—
1263	C₂²	—	212	2	no	—
1264	C₂²	—	212	2	no	—
1265	C₂²	—	212	2	no	—
1266	C₂²	#16811262	1	2	yes	—
1267	C₂²	#16811425	1	2	yes	—
1268	C₂²	#16811430	1	2	yes	—
1269	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	106	2	no	—
1279	C₄	—	106	2	no	—
1280	C₄	—	106	2	no	—
1281	C₄	—	212	2	no	—
1282	C₄	—	212	2	no	—
1283	C₄	#16811262	1	2	yes	—
1284	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1285	C₄	C₂×#13133262	1	1	yes	characteristic
1286	C₂	—	2	2	no	—
1287	C₂	—	2	2	no	—
1288	C₂	—	2	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	—	8	1	no	—
1291	C₂	—	424	2	no	—
1292	C₂	—	212	2	no	—
1293	C₂	—	212	4	no	—
1294	C₂	C₂×#16811262	1	1	yes	characteristic
1295	C₂	C₂×#16811425	1	1	yes	characteristic
1296	C₂	C₂×#16811430	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3050	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3050	D₅₃
hypocenter	C₅₃	#61167
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3050

Complements

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

N	H ≅ G/N	type
1. #20288421	C₂	semidirect
2. #20288348	C₂	semidirect
3. #20286862	C₂	semidirect
4. #20286802	C₂	semidirect
5. #20286742	C₂	semidirect
6. #20286682	C₂	semidirect
7. #20286571	C₂	semidirect
8. #20286556	C₂	semidirect
9. #20286534	C₂	semidirect
10. #20286523	C₂	semidirect
11. #20285073	C₂	semidirect
12. #20284676	C₂	semidirect
13. #20284635	C₂	semidirect
14. #20284549	C₂	semidirect
15. #20284398	C₂	semidirect
16. #20284252	C₂	semidirect
17. #20284015	C₂	semidirect
18. #20283941	C₂	semidirect
19. #20283550	C₂	semidirect
20. #20283409	C₂	semidirect
21. #20283237	C₂	semidirect
22. C₂²×#13133139	C₂	semidirect
23. C₅₃×#3050	C₂	semidirect
27. C₂×#13133242	C₂²	semidirect
28. C₂×#13133223	C₂²	semidirect
29. #16811331	C₂²	semidirect
31. #16811325	C₂²	semidirect
33. #16811315	C₂²	semidirect
36. #16811273	C₂²	semidirect
45. #16811251	C₂²	semidirect
47. #16811201	C₂²	semidirect
54. #16811106	C₂²	semidirect
55. #16811103	C₂²	semidirect
57. C₂²×C₄⋊Dic₅₃	C₂²	semidirect
58. #16810986	C₂²	semidirect
59. #16810984	C₂²	semidirect
60. #16810979	C₂²	semidirect
61. #16810968	C₂²	semidirect
62. #16810956	C₂²	semidirect
63. #16810951	C₂²	semidirect
64. #16810950	C₂²	semidirect
65. #16810949	C₂²	semidirect
66. #16810943	C₂²	semidirect
67. #16810939	C₂²	semidirect
68. #16810938	C₂²	semidirect
69. #16810934	C₂²	semidirect
70. #16810926	C₂²	semidirect
71. #16810922	C₂²	semidirect
72. #16810912	C₂²	semidirect
73. #16810902	C₂²	semidirect
74. #16810875	C₂²	semidirect
75. #16810872	C₂²	semidirect
76. #16810858	C₂²	semidirect
77. #16810855	C₂²	semidirect
78. #16810847	C₂²	semidirect
79. #16810840	C₂²	semidirect
80. #16810821	C₂²	semidirect
81. #16810816	C₂²	semidirect
82. #16810784	C₂²	semidirect
83. #16810773	C₂²	semidirect
84. #16810773	C₂²	semidirect
85. #16810772	C₂²	semidirect
86. #16810767	C₂²	semidirect
87. #16810756	C₂²	semidirect
88. #16810756	C₂²	semidirect
89. #16810755	C₂²	semidirect
90. #16810732	C₂²	semidirect
91. #16810726	C₂²	semidirect
92. #16810708	C₂²	semidirect
93. #16810703	C₂²	semidirect
94. #16810694	C₂²	semidirect
95. #16810694	C₂²	semidirect
96. C₈×C₂²⋊D₅₃	C₂²	semidirect
97. C₈×C₂²⋊D₅₃	C₂²	semidirect
98. #16810666	C₂²	semidirect
99. #16810666	C₂²	semidirect
100. #16810649	C₂²	semidirect
102. #16810627	C₂²	semidirect
103. #16810626	C₂²	semidirect
104. #16810624	C₂²	semidirect
105. #16810624	C₂²	semidirect
106. #16810623	C₂²	semidirect
107. #16810618	C₂²	semidirect
110. C₂×#13133139	C₂²	semidirect
111. C₂×#13133139	C₂²	semidirect
112. C₂×#13133139	C₂²	semidirect
113. C₂×#13133139	C₂²	semidirect
114. C₂×#13133139	C₂²	semidirect
115. C₂×#13133139	C₂²	semidirect
116. #102×D₅₃	C₂²	semidirect
117. #16810589	C₂²	semidirect
118. #16810587	C₂²	semidirect
119. #16810578	C₂²	semidirect
120. C₂×#135×C₅₃	C₂²	semidirect
121. C₂³×C₈×C₅₃	C₂²	semidirect
123. C₅₃×#525	C₂²	semidirect
124. C₅₃×#467	C₂²	semidirect
125. C₅₃×#467	C₂²	semidirect
126. C₅₃×#466	C₂²	semidirect
127. C₅₃×#466	C₂²	semidirect
128. C₅₃×#465	C₂²	semidirect
129. C₅₃×#465	C₂²	semidirect
130. C₅₃×#465	C₂²	semidirect
131. C₅₃×#465	C₂²	semidirect
132. C₅₃×#427	C₂²	semidirect
133. C₅₃×#416	C₂²	semidirect
134. C₅₃×#416	C₂²	semidirect
166. C₂×#11719912	C₂³	semidirect
167. C₂×C₈×D₅₃	C₂³	semidirect
169. #13133216	C₂³	semidirect
176. #13133208	C₂³	semidirect
194. #13133193	C₂³	semidirect
208. #13133188	C₂³	semidirect
218. Q₈×Dic₅₃	C₂³	semidirect
225. D₄×Dic₅₃	C₂³	semidirect
234. #13133175	C₂³	semidirect
244. C₄⋊C₄×D₅₃	C₂³	semidirect
248. #13133150	C₂³	semidirect
249. #13133150	C₂³	semidirect
250. #13133148	C₂³	semidirect
251. #13133148	C₂³	semidirect
252. #13133146	C₂³	semidirect
253. #13133146	C₂³	semidirect
254. #13133141	C₂³	semidirect
255. #13133141	C₂³	semidirect
264. #13133138	C₂³	semidirect
265. #13133138	C₂³	semidirect
272. #13133129	C₂³	semidirect
273. #13133129	C₂³	semidirect
274. #13133127	C₂³	semidirect
275. C₈×Dic₅₃	C₂³	semidirect
280. C₂×Q₁₆×C₅₃	C₂³	semidirect
281. C₂×SD₁₆×C₅₃	C₂³	semidirect
282. C₂×SD₁₆×C₅₃	C₂³	semidirect
283. C₂×D₈×C₅₃	C₂³	semidirect
309. #107×C₅₃	C₂³	semidirect
310. #107×C₅₃	C₂³	semidirect
311. #106×C₅₃	C₂³	semidirect
312. #106×C₅₃	C₂³	semidirect
313. #103×C₅₃	C₂³	semidirect
314. #103×C₅₃	C₂³	semidirect
315. #103×C₅₃	C₂³	semidirect
316. #103×C₅₃	C₂³	semidirect
317. #102×C₅₃	C₂³	semidirect
318. #102×C₅₃	C₂³	semidirect
319. #102×C₅₃	C₂³	semidirect
320. #102×C₅₃	C₂³	semidirect
397. C₂×D₂₁₂	#41	semidirect
653. #3050	D₅₃	semidirect
676. C₂×#135	C₂×D₅₃	semidirect
678. C₂³×C₈	C₂×D₅₃	semidirect
704. #525	C₂×D₅₃	semidirect
728. #467	C₂×D₅₃	semidirect
729. #467	C₂×D₅₃	semidirect
731. #466	C₂×D₅₃	semidirect
732. #466	C₂×D₅₃	semidirect
734. #465	C₂×D₅₃	semidirect
735. #465	C₂×D₅₃	semidirect
736. #465	C₂×D₅₃	semidirect
737. #465	C₂×D₅₃	semidirect
760. #427	C₂×D₅₃	semidirect
769. #416	C₂×D₅₃	semidirect
770. #416	C₂×D₅₃	semidirect
783. C₅₃	#61167	semidirect
812. C₂×Q₁₆	C₂²×D₅₃	semidirect
815. C₂×SD₁₆	C₂²×D₅₃	semidirect
816. C₂×SD₁₆	C₂²×D₅₃	semidirect
819. C₂×D₈	C₂²×D₅₃	semidirect
932. #107	C₂²×D₅₃	semidirect
933. #107	C₂²×D₅₃	semidirect
936. #106	C₂²×D₅₃	semidirect
937. #106	C₂²×D₅₃	semidirect
942. #103	C₂²×D₅₃	semidirect
943. #103	C₂²×D₅₃	semidirect
944. #103	C₂²×D₅₃	semidirect
945. #103	C₂²×D₅₃	semidirect
960. #102	C₂²×D₅₃	semidirect
961. #102	C₂²×D₅₃	semidirect
962. #102	C₂²×D₅₃	semidirect
963. #102	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288421	2
#20288348	2
#20286862	2
#20286802	2
#20286742	2
#20286682	2
#20286571	2
#20286556	2
#20286534	2
#20286523	2
#20285073	2
#20284676	2
#20284635	2
#20284549	2
#20284398	2
#20284252	2
#20284015	2
#20283941	2
#20283550	2
#20283409	2
#20283237	2
C₂²×#13133139	2
C₅₃×#3050	2
#61167	53