Subgroups — #28293133

Order 13568.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288789	C₂	1	4	yes	maximal, complemented
2	#20288787	C₂	1	4	yes	maximal, complemented
3	#20288749	C₂	1	4	yes	maximal, complemented
4	#20288745	C₂	1	4	yes	maximal, complemented
5	#20288678	C₂	1	4	yes	maximal, complemented
6	#20288674	C₂	1	4	yes	maximal, complemented
7	#20288661	C₂	1	4	yes	maximal, complemented
8	#20288659	C₂	1	4	yes	maximal, complemented
9	#20288569	C₂	1	1	yes	maximal, characteristic, complemented
10	#20288564	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288547	C₂	1	4	yes	maximal, complemented
12	#20288516	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288477	C₂	1	1	yes	maximal, characteristic, complemented
14	#20288432	C₂	1	2	yes	maximal, complemented
15	#20288401	C₂	1	4	yes	maximal, complemented
16	#20288348	C₂	1	2	yes	maximal, complemented
17	#20288131	C₂	1	2	yes	maximal, complemented
18	#20288123	C₂	1	4	yes	maximal, complemented
19	#20288105	C₂	1	1	yes	maximal, characteristic, complemented
20	#538×D₅₃	C₂	1	4	yes	maximal, complemented
21	C₄×#13133263	C₂	1	2	yes	maximal, complemented
22	C₂×#16811097	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133263	C₂²	1	2	yes	—
25	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
26	#16811358	C₂²	1	4	yes	complemented
27	#16811355	C₂²	1	4	yes	complemented
28	#16811347	C₂²	1	2	yes	complemented
29	#16811346	C₂²	1	2	yes	complemented
30	#16811344	C₂²	1	4	yes	complemented
31	#16811343	C₂²	1	4	yes	complemented
32	#16811339	C₂²	1	2	yes	complemented
33	#16811338	C₂²	1	4	yes	complemented
34	#16811338	C₂²	1	2	yes	complemented
35	#16811337	C₂²	1	4	yes	complemented
36	#16811334	C₂²	1	2	yes	complemented
37	#16811333	C₂²	1	4	yes	complemented
38	#16811333	C₂²	1	2	yes	complemented
39	#16811329	C₂²	1	4	yes	complemented
40	#16811326	C₂²	1	8	yes	complemented
41	#16811326	C₂²	1	4	yes	complemented
42	#16811324	C₂²	1	8	yes	complemented
43	#16811320	C₂²	1	4	yes	complemented
44	#16811319	C₂²	1	4	yes	complemented
45	#16811319	C₂²	1	4	yes	complemented
46	#16811318	C₂²	1	8	yes	complemented
47	#16811313	C₂²	1	4	yes	complemented
48	#16811307	C₂²	1	4	yes	complemented
49	#16811305	C₂²	1	8	yes	complemented
50	#16811303	C₂²	1	8	yes	complemented
51	#16811301	C₂²	1	8	yes	complemented
52	#16811300	C₂²	1	8	yes	complemented
53	#16811298	C₂²	1	8	yes	complemented
54	#16811298	C₂²	1	8	yes	complemented
55	#16811298	C₂²	1	8	yes	complemented
56	#16811295	C₂²	1	2	yes	complemented
57	#16811293	C₂²	1	2	yes	complemented
58	Q₈×D₂₁₂	C₂²	1	2	yes	complemented
59	#16811288	C₂²	1	2	yes	complemented
60	#16811283	C₂²	1	8	yes	complemented
61	#16811278	C₂²	1	2	yes	complemented
62	#16811277	C₂²	1	2	yes	complemented
63	#16811276	C₂²	1	2	yes	complemented
64	#16811276	C₂²	1	2	yes	complemented
65	#16811270	C₂²	1	8	yes	complemented
66	#16811269	C₂²	1	4	yes	complemented
67	#16811269	C₂²	1	4	yes	complemented
68	#16811269	C₂²	1	4	yes	complemented
69	#16811266	C₂²	1	8	yes	complemented
70	#16811266	C₂²	1	4	yes	complemented
71	#16811265	C₂²	1	8	yes	complemented
72	#16811265	C₂²	1	8	yes	complemented
73	#16811264	C₂²	1	4	yes	complemented
74	#16811264	C₂²	1	4	yes	complemented
75	#16811262	C₂²	1	8	yes	complemented
76	D₄×D₂₁₂	C₂²	1	4	yes	complemented
77	D₄×D₂₁₂	C₂²	1	4	yes	complemented
78	D₄×D₂₁₂	C₂²	1	2	yes	complemented
79	#16811258	C₂²	1	2	yes	complemented
80	#16811257	C₂²	1	4	yes	complemented
81	#16811257	C₂²	1	4	yes	complemented
82	#16811251	C₂²	1	2	yes	complemented
83	#16811248	C₂²	1	4	yes	complemented
84	#16811245	C₂²	1	4	yes	complemented
85	#16811244	C₂²	1	2	yes	complemented
86	#16811244	C₂²	1	2	yes	complemented
87	#16811244	C₂²	1	4	yes	complemented
88	#16811235	C₂²	1	2	yes	complemented
89	#16811228	C₂²	1	2	yes	complemented
90	#16811228	C₂²	1	4	yes	complemented
91	#16811224	C₂²	1	4	yes	complemented
92	#16811221	C₂²	1	8	yes	complemented
93	#16811220	C₂²	1	2	yes	complemented
94	#16811220	C₂²	1	2	yes	complemented
95	#16811219	C₂²	1	8	yes	complemented
96	#16811213	C₂²	1	4	yes	complemented
97	#16811212	C₂²	1	8	yes	complemented
98	#16811212	C₂²	1	8	yes	complemented
99	#16811211	C₂²	1	2	yes	complemented
100	#16811211	C₂²	1	2	yes	complemented
101	#16811210	C₂²	1	4	yes	complemented
102	#16811209	C₂²	1	8	yes	complemented
103	#16811209	C₂²	1	8	yes	complemented
104	#16811208	C₂²	1	8	yes	complemented
105	#16811207	C₂²	1	8	yes	complemented
106	#16811206	C₂²	1	8	yes	complemented
107	#16811205	C₂²	1	8	yes	complemented
108	#16811201	C₂²	1	2	yes	complemented
109	#16811192	C₂²	1	2	yes	complemented
110	#16811187	C₂²	1	2	yes	complemented
111	#16811184	C₂²	1	8	yes	complemented
112	#16811181	C₂²	1	4	yes	complemented
113	#16811180	C₂²	1	1	yes	characteristic, complemented
114	#16811173	C₂²	1	1	yes	characteristic, complemented
115	#16811173	C₂²	1	4	yes	complemented
116	#16811170	C₂²	1	4	yes	complemented
117	#16811160	C₂²	1	4	yes	complemented
118	#16811158	C₂²	1	8	yes	complemented
119	#16811157	C₂²	1	4	yes	complemented
120	#16811156	C₂²	1	8	yes	complemented
121	#16811151	C₂²	1	4	yes	complemented
122	#16811151	C₂²	1	4	yes	complemented
123	#16811150	C₂²	1	8	yes	complemented
124	#126×D₅₃	C₂²	1	8	yes	complemented
125	#124×D₅₃	C₂²	1	8	yes	complemented
126	#16811136	C₂²	1	4	yes	complemented
127	#16811136	C₂²	1	8	yes	complemented
128	#16811134	C₂²	1	2	yes	complemented
129	#16811133	C₂²	1	4	yes	complemented
130	#16811132	C₂²	1	8	yes	complemented
131	#16811131	C₂²	1	8	yes	complemented
132	#123×D₅₃	C₂²	1	8	yes	complemented
133	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
134	#121×D₅₃	C₂²	1	8	yes	complemented
135	#121×D₅₃	C₂²	1	4	yes	complemented
136	#120×D₅₃	C₂²	1	8	yes	complemented
137	#16811106	C₂²	1	2	yes	complemented
138	#16811105	C₂²	1	4	yes	complemented
139	#16811103	C₂²	1	2	yes	complemented
140	#16811103	C₂²	1	4	yes	complemented
141	#16811097	C₂²	1	2	yes	—
142	#16811097	C₂²	1	4	yes	complemented
143	#16811097	C₂²	1	4	yes	complemented
144	#16811097	C₂²	1	4	yes	complemented
145	#16811097	C₂²	1	4	yes	complemented
146	#16811097	C₂²	1	4	yes	complemented
147	#16811095	C₂²	1	8	yes	complemented
148	#16811095	C₂²	1	4	yes	complemented
149	C₄×#11719949	C₂²	1	4	yes	complemented
150	C₄×#11719945	C₂²	1	2	yes	complemented
151	C₄×#11719945	C₂²	1	4	yes	complemented
152	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
153	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
154	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
155	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
156	C₂×C₄×D₂₁₂	C₂²	1	4	yes	complemented
157	C₂×#13133179	C₂²	1	2	yes	complemented
158	C₂×#13133179	C₂²	1	2	yes	complemented
159	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
160	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
161	C₂×#13133176	C₂²	1	1	yes	characteristic, complemented
162	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
163	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
164	C₅₃×#542	C₂²	1	2	yes	complemented
165	C₅₃×#542	C₂²	1	2	yes	complemented
166	C₅₃×#541	C₂²	1	2	yes	complemented
167	C₅₃×#540	C₂²	1	2	yes	complemented
168	C₅₃×#539	C₂²	1	2	yes	complemented
169	C₅₃×#539	C₂²	1	2	yes	complemented
170	C₅₃×#538	C₂²	1	2	yes	complemented
171	C₅₃×#538	C₂²	1	2	yes	complemented
172	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#529	C₂²	1	4	yes	complemented
175	C₅₃×#529	C₂²	1	4	yes	complemented
176	C₅₃×#525	C₂²	1	2	yes	complemented
177	C₄×#41×C₅₃	C₂²	1	2	yes	complemented
178	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₂⁴×D₅₃	C₂³	1	2	yes	—
180	#13133263	—	2	16	no	—
181	C₂×#11719949	C₂³	1	4	yes	—
182	C₂×#11719949	C₂³	1	4	yes	complemented
183	C₂×#11719945	C₂³	1	4	yes	—
184	C₂×#11719945	C₂³	1	2	yes	—
185	C₂×#11719945	C₂³	1	8	yes	complemented
186	C₂×#11719947	C₂³	1	4	yes	complemented
187	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
188	C₂²×D₂₁₂	—	2	8	no	—
189	C₂²×D₂₁₂	C₂³	1	4	yes	—
190	C₂²×D₂₁₂	C₂³	1	4	yes	—
191	C₂²×D₂₁₂	C₂³	1	4	yes	—
192	C₂²×D₂₁₂	C₂³	1	2	yes	—
193	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
194	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
195	C₂×D₄×D₅₃	C₂³	1	4	yes	—
196	C₂×D₄×D₅₃	C₂³	1	8	yes	—
197	C₂×D₄×D₅₃	C₂³	1	8	yes	—
198	C₂×D₄×D₅₃	C₂³	1	8	yes	—
199	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
200	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
201	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
202	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
203	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
204	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
205	#13133217	C₂³	1	1	yes	characteristic, complemented
206	#13133217	C₂³	1	1	yes	characteristic, complemented
207	#13133217	C₂³	1	1	yes	characteristic, complemented
208	#13133217	C₂³	1	4	yes	complemented
209	#13133216	C₂³	1	4	yes	complemented
210	#13133214	C₂³	1	4	yes	—
211	#13133214	C₂³	1	1	yes	characteristic, complemented
212	#13133213	C₂³	1	4	yes	—
213	#13133212	C₂³	1	4	yes	complemented
214	#13133212	C₂³	1	8	yes	complemented
215	#13133212	C₂³	1	8	yes	complemented
216	#13133212	C₂³	1	8	yes	complemented
217	#13133212	C₂³	1	8	yes	complemented
218	#13133212	C₂³	1	4	yes	complemented
219	#13133211	C₂³	1	8	yes	complemented
220	#13133210	C₂³	1	8	yes	—
221	#13133210	C₂³	1	8	yes	—
222	#13133210	C₂³	1	4	yes	—
223	#13133210	C₂³	1	4	yes	—
224	#13133210	C₂³	1	8	yes	complemented
225	#13133209	C₂³	1	4	yes	complemented
226	#13133209	C₂³	1	2	yes	complemented
227	#13133208	C₂³	1	4	yes	complemented
228	#13133207	C₂³	1	4	yes	complemented
229	#13133207	C₂³	1	8	yes	complemented
230	#13133207	C₂³	1	4	yes	complemented
231	#13133206	C₂³	1	4	yes	—
232	#13133206	C₂³	1	8	yes	complemented
233	#13133205	C₂³	1	4	yes	—
234	#13133205	C₂³	1	2	yes	complemented
235	#13133205	C₂³	1	8	yes	complemented
236	#13133204	C₂³	1	8	yes	—
237	#13133203	C₂³	1	8	yes	—
238	#13133203	C₂³	1	4	yes	—
239	#13133203	C₂³	1	4	yes	—
240	#13133203	C₂³	1	8	yes	complemented
241	#13133203	C₂³	1	8	yes	complemented
242	#13133203	C₂³	1	8	yes	complemented
243	#13133202	C₂³	1	8	yes	—
244	#13133202	C₂³	1	8	yes	—
245	#13133202	C₂³	1	4	yes	complemented
246	#13133202	C₂³	1	8	yes	complemented
247	#13133202	C₂³	1	8	yes	complemented
248	#13133202	C₂³	1	8	yes	complemented
249	#13133202	C₂³	1	8	yes	complemented
250	#13133202	C₂³	1	8	yes	complemented
251	#13133202	C₂³	1	4	yes	complemented
252	#13133201	C₂³	1	8	yes	complemented
253	#13133200	C₂³	1	4	yes	—
254	#13133200	C₂³	1	8	yes	complemented
255	#13133199	C₂³	1	8	yes	—
256	#13133199	C₂³	1	4	yes	—
257	#13133199	C₂³	1	4	yes	—
258	#13133199	C₂³	1	8	yes	complemented
259	#13133199	C₂³	1	8	yes	complemented
260	#13133199	C₂³	1	8	yes	complemented
261	#13133198	C₂³	1	8	yes	—
262	#13133197	C₂³	1	8	yes	complemented
263	#13133197	C₂³	1	4	yes	complemented
264	#13133197	C₂³	1	4	yes	complemented
265	#13133196	C₂³	1	2	yes	—
266	#13133196	C₂³	1	2	yes	—
267	#13133196	C₂³	1	2	yes	—
268	#13133196	C₂³	1	2	yes	—
269	#13133196	C₂³	1	4	yes	complemented
270	#13133195	C₂³	1	8	yes	complemented
271	#13133195	C₂³	1	8	yes	complemented
272	#13133195	C₂³	1	4	yes	complemented
273	#13133195	C₂³	1	8	yes	complemented
274	#13133195	C₂³	1	8	yes	complemented
275	#13133195	C₂³	1	4	yes	complemented
276	#13133194	C₂³	1	8	yes	—
277	#13133193	C₂³	1	4	yes	complemented
278	#13133193	C₂³	1	8	yes	complemented
279	#13133193	C₂³	1	4	yes	complemented
280	#13133193	C₂³	1	4	yes	complemented
281	#13133192	C₂³	1	4	yes	—
282	#13133192	C₂³	1	8	yes	—
283	#13133192	C₂³	1	8	yes	—
284	#13133192	C₂³	1	4	yes	—
285	#13133192	C₂³	1	4	yes	complemented
286	#13133192	C₂³	1	8	yes	complemented
287	#13133192	C₂³	1	4	yes	complemented
288	#13133191	C₂³	1	4	yes	—
289	#13133191	C₂³	1	4	yes	—
290	#13133191	C₂³	1	2	yes	—
291	#13133191	C₂³	1	2	yes	—
292	#13133191	C₂³	1	2	yes	—
293	#13133191	C₂³	1	2	yes	—
294	#13133191	C₂³	1	4	yes	complemented
295	#13133191	C₂³	1	8	yes	complemented
296	#13133190	C₂³	1	4	yes	—
297	#13133190	C₂³	1	8	yes	—
298	#13133190	C₂³	1	8	yes	—
299	#13133190	C₂³	1	4	yes	—
300	#13133190	C₂³	1	8	yes	complemented
301	#13133190	C₂³	1	8	yes	complemented
302	#13133190	C₂³	1	8	yes	complemented
303	#13133189	C₂³	1	8	yes	—
304	#13133189	C₂³	1	8	yes	—
305	#13133189	C₂³	1	8	yes	complemented
306	#13133188	C₂³	1	8	yes	—
307	#13133188	C₂³	1	4	yes	complemented
308	#13133188	C₂³	1	4	yes	complemented
309	#13133188	C₂³	1	4	yes	complemented
310	#13133187	C₂³	1	8	yes	—
311	#13133187	C₂³	1	8	yes	—
312	#13133187	C₂³	1	8	yes	—
313	#13133187	C₂³	1	8	yes	—
314	#13133187	C₂³	1	8	yes	—
315	#13133187	C₂³	1	8	yes	complemented
316	#13133186	C₂³	1	4	yes	—
317	#13133185	C₂³	1	8	yes	—
318	#13133185	C₂³	1	8	yes	—
319	#13133185	C₂³	1	8	yes	—
320	#13133185	C₂³	1	8	yes	complemented
321	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
322	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
323	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
324	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
325	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
326	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
327	#13133182	C₂³	1	8	yes	complemented
328	C₄×D₂₁₂	C₂³	1	2	yes	—
329	C₄×D₂₁₂	C₂³	1	2	yes	—
330	C₄×D₂₁₂	C₂³	1	4	yes	—
331	C₄×D₂₁₂	C₂³	1	4	yes	—
332	C₄×D₂₁₂	C₂³	1	2	yes	—
333	C₄×D₂₁₂	C₂³	1	2	yes	—
334	C₄×D₂₁₂	C₂³	1	2	yes	—
335	C₄×D₂₁₂	C₂³	1	2	yes	—
336	C₄×D₂₁₂	C₂³	1	2	yes	—
337	C₄×D₂₁₂	C₂³	1	2	yes	—
338	C₄×D₂₁₂	C₂³	1	4	yes	—
339	C₄×D₂₁₂	C₂³	1	4	yes	—
340	C₄×D₂₁₂	C₂³	1	4	yes	—
341	C₄×D₂₁₂	C₂³	1	4	yes	—
342	C₄×D₂₁₂	C₂³	1	2	yes	complemented
343	C₄×D₂₁₂	C₂³	1	8	yes	complemented
344	C₄×D₂₁₂	C₂³	1	8	yes	complemented
345	C₄×D₂₁₂	C₂³	1	2	yes	complemented
346	C₄×D₂₁₂	C₂³	1	4	yes	complemented
347	C₄×D₂₁₂	C₂³	1	8	yes	complemented
348	C₄×D₂₁₂	C₂³	1	2	yes	complemented
349	C₄×D₂₁₂	C₂³	1	2	yes	complemented
350	D₄×Dic₅₃	C₂³	1	8	yes	—
351	D₄×Dic₅₃	C₂³	1	4	yes	complemented
352	#13133179	C₂³	1	4	yes	—
353	#13133179	C₂³	1	4	yes	—
354	#13133179	C₂³	1	8	yes	—
355	#13133179	C₂³	1	8	yes	—
356	#13133179	C₂³	1	8	yes	—
357	#13133179	C₂³	1	8	yes	—
358	#13133179	C₂³	1	8	yes	complemented
359	#13133179	C₂³	1	8	yes	complemented
360	#13133179	C₂³	1	8	yes	complemented
361	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
362	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
363	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
364	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
365	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
366	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
367	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
368	#13133177	C₂³	1	8	yes	—
369	#13133177	C₂³	1	8	yes	complemented
370	#13133177	C₂³	1	8	yes	complemented
371	#13133177	C₂³	1	8	yes	complemented
372	#13133177	C₂³	1	8	yes	complemented
373	#13133176	C₂³	1	4	yes	—
374	#13133176	C₂³	1	4	yes	—
375	#13133176	C₂³	1	2	yes	—
376	#13133176	C₂³	1	4	yes	complemented
377	#13133175	C₂³	1	4	yes	complemented
378	#13133175	C₂³	1	8	yes	complemented
379	#13133175	C₂³	1	8	yes	complemented
380	#13133175	C₂³	1	4	yes	complemented
381	#13133175	C₂³	1	4	yes	complemented
382	#13133174	C₂³	1	8	yes	complemented
383	#13133174	C₂³	1	8	yes	complemented
384	#13133174	C₂³	1	4	yes	complemented
385	#13133173	C₂³	1	8	yes	complemented
386	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
387	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
388	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
389	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
390	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
391	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
392	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
393	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
394	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
395	C₂×#11719921	C₂³	1	2	yes	—
396	C₂×#11719921	C₂³	1	2	yes	—
397	C₂×#11719921	C₂³	1	2	yes	—
398	C₂×#11719921	C₂³	1	2	yes	—
399	C₂×#11719921	C₂³	1	8	yes	complemented
400	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
401	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
402	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
403	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
404	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
405	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
406	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
407	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
408	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
409	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
410	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
411	C₄²×D₅₃	C₂³	1	8	yes	complemented
412	C₄²×D₅₃	C₂³	1	4	yes	complemented
413	C₂×#41×C₅₃	C₂³	1	2	yes	—
414	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
415	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
416	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
417	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
418	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
419	#126×C₅₃	C₂³	1	4	yes	—
420	#126×C₅₃	C₂³	1	4	yes	—
421	#126×C₅₃	C₂³	1	4	yes	complemented
422	#126×C₅₃	C₂³	1	4	yes	complemented
423	#125×C₅₃	C₂³	1	4	yes	complemented
424	#125×C₅₃	C₂³	1	4	yes	complemented
425	#125×C₅₃	C₂³	1	2	yes	complemented
426	#124×C₅₃	C₂³	1	4	yes	—
427	#124×C₅₃	C₂³	1	4	yes	—
428	#124×C₅₃	C₂³	1	2	yes	complemented
429	#123×C₅₃	C₂³	1	4	yes	—
430	#123×C₅₃	C₂³	1	4	yes	—
431	#123×C₅₃	C₂³	1	4	yes	—
432	#123×C₅₃	C₂³	1	4	yes	complemented
433	#123×C₅₃	C₂³	1	4	yes	complemented
434	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
435	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
436	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
437	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
438	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
439	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
440	#121×C₅₃	C₂³	1	4	yes	—
441	#121×C₅₃	C₂³	1	2	yes	—
442	#121×C₅₃	C₂³	1	2	yes	—
443	#121×C₅₃	C₂³	1	4	yes	—
444	#121×C₅₃	C₂³	1	2	yes	—
445	#121×C₅₃	C₂³	1	2	yes	—
446	#120×C₅₃	C₂³	1	4	yes	—
447	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
448	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
449	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
450	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
451	C₄×D₄×C₅₃	C₂³	1	4	yes	—
452	C₄×D₄×C₅₃	C₂³	1	4	yes	—
453	C₄×D₄×C₅₃	C₂³	1	4	yes	—
454	C₄×D₄×C₅₃	C₂³	1	4	yes	—
455	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
456	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
457	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
458	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
459	#117×C₅₃	C₂³	1	2	yes	—
460	#117×C₅₃	C₂³	1	2	yes	—
461	#117×C₅₃	C₂³	1	2	yes	—
462	#117×C₅₃	C₂³	1	2	yes	—
463	#117×C₅₃	C₂³	1	2	yes	—
464	#117×C₅₃	C₂³	1	4	yes	complemented
465	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
466	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
467	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
468	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
469	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
470	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
471	C₂×C₄²×C₅₃	C₂³	1	4	yes	complemented
472	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
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	8	yes	—
478	C₂³×D₅₃	C₂⁴	1	2	yes	—
479	C₂³×D₅₃	C₂⁴	1	2	yes	—
480	#41×C₅₃	—	2	8	no	—
481	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
482	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
483	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
484	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
485	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
486	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
487	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
488	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
489	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
490	C₂²×C₄×C₅₃	—	2	4	no	—
491	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
492	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
493	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
494	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
495	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
497	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
498	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
500	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
501	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
502	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
503	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
504	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
505	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
506	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
507	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
508	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
509	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
510	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
511	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
512	#11719949	—	2	16	no	—
513	#11719949	—	8	4	no	—
514	Q₈×D₅₃	—	8	4	no	—
515	#11719947	—	8	4	no	—
516	D₄×D₅₃	—	2	32	no	—
517	D₄×D₅₃	—	2	16	no	—
518	D₄×D₅₃	—	8	8	no	—
519	D₄×D₅₃	—	8	8	no	—
520	D₄×D₅₃	—	8	4	no	—
521	#11719945	—	2	8	no	—
522	#11719945	—	2	16	no	—
523	#11719945	—	8	8	no	—
524	C₂×D₂₁₂	—	2	8	no	—
525	C₂×D₂₁₂	—	2	4	no	—
526	C₂×D₂₁₂	—	2	16	no	—
527	C₂×D₂₁₂	—	2	16	no	—
528	C₂×D₂₁₂	—	2	16	no	—
529	C₂×D₂₁₂	#41	1	8	yes	complemented
530	C₂×D₂₁₂	C₂⁴	1	8	yes	—
531	C₂×D₂₁₂	C₂⁴	1	8	yes	—
532	C₂×D₂₁₂	C₂⁴	1	2	yes	—
533	C₂×D₂₁₂	C₂⁴	1	2	yes	—
534	C₂×D₂₁₂	C₂⁴	1	2	yes	—
535	C₂×D₂₁₂	C₂⁴	1	8	yes	—
536	C₂×D₂₁₂	C₂⁴	1	8	yes	—
537	C₂×D₂₁₂	C₂⁴	1	2	yes	—
538	C₂×D₂₁₂	C₂⁴	1	2	yes	—
539	C₂×D₂₁₂	C₂⁴	1	2	yes	—
540	C₂×D₂₁₂	C₂⁴	1	2	yes	—
541	C₂×C₄×D₅₃	—	8	2	no	—
542	C₂×C₄×D₅₃	—	8	2	no	—
543	C₂×C₄×D₅₃	—	8	2	no	—
544	C₂×C₄×D₅₃	—	8	2	no	—
545	C₂×C₄×D₅₃	—	8	8	no	—
546	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
547	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
548	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
549	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
550	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
551	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
552	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
553	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
554	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
555	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
556	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
557	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
558	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
559	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
560	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
561	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
562	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
563	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
564	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
565	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
566	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
567	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
568	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
569	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
570	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
571	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
572	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
573	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
574	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
575	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
576	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
577	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
578	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
579	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
580	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
581	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
582	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
583	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
584	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
585	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
586	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
587	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
588	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
589	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
590	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
591	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
592	C₄²×C₅₃	C₂⁴	1	2	yes	—
593	C₄²×C₅₃	C₂⁴	1	2	yes	—
594	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₄²×C₅₃	C₂⁴	1	4	yes	—
599	C₄²×C₅₃	C₂⁴	1	4	yes	—
600	C₄²×C₅₃	C₂⁴	1	4	yes	—
601	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
602	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
603	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
604	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
605	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
606	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
607	#11719921	C₂⁴	1	8	yes	—
608	#11719921	C₂⁴	1	4	yes	—
609	#11719921	C₂⁴	1	4	yes	—
610	#11719921	C₂⁴	1	4	yes	—
611	#11719921	C₂⁴	1	8	yes	—
612	#11719921	C₂⁴	1	4	yes	—
613	#11719921	C₂⁴	1	8	yes	—
614	#11719921	C₂⁴	1	8	yes	—
615	#11719921	C₂⁴	1	8	yes	—
616	#11719921	C₂⁴	1	8	yes	—
617	#11719921	C₂⁴	1	8	yes	—
618	#11719921	C₂⁴	1	8	yes	—
619	#11719921	C₂⁴	1	4	yes	—
620	#11719921	C₂⁴	1	4	yes	—
621	#11719921	C₂⁴	1	8	yes	—
622	#11719921	C₂⁴	1	8	yes	—
623	#11719921	C₂⁴	1	4	yes	—
624	#11719921	C₂⁴	1	4	yes	—
625	#11719921	C₂⁴	1	4	yes	—
626	#11719921	C₂⁴	1	4	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	8	yes	—
631	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
632	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
633	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
634	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
635	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
636	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
637	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
638	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
639	#11719919	C₂⁴	1	8	yes	—
640	#11719919	C₂⁴	1	4	yes	—
641	#11719919	C₂⁴	1	4	yes	—
642	#11719919	C₂⁴	1	8	yes	—
643	#11719919	C₂⁴	1	8	yes	—
644	#11719919	C₂⁴	1	8	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	8	yes	—
651	C₄×Dic₅₃	C₂⁴	1	4	yes	—
652	C₄×Dic₅₃	C₂⁴	1	8	yes	—
653	C₄×Dic₅₃	C₂⁴	1	4	yes	—
654	C₄×Dic₅₃	C₂⁴	1	8	yes	—
655	C₂³×C₅₃	—	2	2	no	—
656	C₂³×C₅₃	—	4	1	no	—
657	C₂³×C₅₃	—	4	1	no	—
658	C₂³×C₅₃	C₂⁵	1	4	yes	—
659	C₂³×C₅₃	C₂⁵	1	2	yes	—
660	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
661	C₂²×D₅₃	—	2	4	no	—
662	C₂²×D₅₃	—	2	16	no	—
663	C₂²×D₅₃	—	2	16	no	—
664	C₂²×D₅₃	—	4	2	no	—
665	C₂²×D₅₃	—	4	2	no	—
666	C₂²×D₅₃	—	4	2	no	—
667	C₂²×D₅₃	—	4	2	no	—
668	C₂²×D₅₃	—	4	8	no	—
669	C₂²×D₅₃	—	4	8	no	—
670	C₂²×D₅₃	—	4	8	no	—
671	C₂²×D₅₃	—	4	8	no	—
672	C₂²×D₅₃	—	8	16	no	—
673	C₂²×D₅₃	C₂×#41	1	8	yes	—
674	C₂²×D₅₃	C₂⁵	1	4	yes	—
675	C₂²×D₅₃	C₂⁵	1	4	yes	—
676	C₂²×D₅₃	C₂⁵	1	4	yes	—
677	Q₈×C₅₃	—	2	4	no	—
678	Q₈×C₅₃	—	4	2	no	—
679	Q₈×C₅₃	—	4	2	no	—
680	D₄×C₅₃	—	2	8	no	—
681	D₄×C₅₃	—	2	4	no	—
682	D₄×C₅₃	—	4	4	no	—
683	D₄×C₅₃	—	4	2	no	—
684	D₄×C₅₃	—	4	4	no	—
685	D₄×C₅₃	—	4	2	no	—
686	C₂×C₄×C₅₃	—	2	2	no	—
687	C₂×C₄×C₅₃	—	2	4	no	—
688	C₂×C₄×C₅₃	—	2	4	no	—
689	C₂×C₄×C₅₃	—	2	8	no	—
690	C₂×C₄×C₅₃	—	4	1	no	—
691	C₂×C₄×C₅₃	—	4	1	no	—
692	C₂×C₄×C₅₃	—	4	1	no	—
693	C₂×C₄×C₅₃	—	4	1	no	—
694	C₂×C₄×C₅₃	—	4	4	no	—
695	C₂×C₄×C₅₃	—	4	4	no	—
696	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
697	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
698	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
699	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
700	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
701	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
702	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
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	2	yes	—
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	16	no	—
711	C₂²⋊D₅₃	—	4	8	no	—
712	C₂²⋊D₅₃	—	4	8	no	—
713	C₂²⋊D₅₃	—	4	4	no	—
714	C₂²⋊D₅₃	—	4	4	no	—
715	C₂²⋊D₅₃	—	4	8	no	—
716	C₂×Dic₅₃	—	4	2	no	—
717	C₂×Dic₅₃	—	4	2	no	—
718	C₂×Dic₅₃	—	4	8	no	—
719	C₂×Dic₅₃	C₂⁵	1	4	yes	—
720	C₂×Dic₅₃	C₂⁵	1	4	yes	—
721	C₂×Dic₅₃	C₂⁵	1	4	yes	—
722	C₂×Dic₅₃	C₂⁵	1	4	yes	—
723	C₂×Dic₅₃	C₂⁵	1	4	yes	—
724	D₂₁₂	—	2	16	no	—
725	D₂₁₂	—	2	16	no	—
726	D₂₁₂	—	2	4	no	—
727	D₂₁₂	—	2	4	no	—
728	D₂₁₂	—	2	4	no	—
729	D₂₁₂	—	4	8	no	—
730	D₂₁₂	—	4	2	no	—
731	D₂₁₂	—	4	8	no	—
732	D₂₁₂	—	4	2	no	—
733	D₂₁₂	C₂×#41	1	8	yes	—
734	D₂₁₂	C₂×#41	1	8	yes	—
735	C₄×D₅₃	—	2	16	no	—
736	C₄×D₅₃	—	2	8	no	—
737	C₄×D₅₃	—	4	4	no	—
738	C₄×D₅₃	—	4	8	no	—
739	C₄×D₅₃	—	4	8	no	—
740	C₄×D₅₃	—	4	4	no	—
741	C₄×D₅₃	—	4	8	no	—
742	C₄×D₅₃	—	4	4	no	—
743	C₄×D₅₃	—	4	4	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	Dic₁₀₆	—	2	4	no	—
749	Dic₁₀₆	—	4	8	no	—
750	Dic₁₀₆	—	4	2	no	—
751	Dic₁₀₆	—	4	2	no	—
752	#62846	—	53	1	no	maximal, Sylow
753	C₂²×C₅₃	—	2	1	no	—
754	C₂²×C₅₃	—	2	1	no	—
755	C₂²×C₅₃	—	2	4	no	—
756	C₂²×C₅₃	—	2	2	no	—
757	C₂²×C₅₃	—	2	4	no	—
758	C₂²×C₅₃	—	2	4	no	—
759	C₂²×C₅₃	—	2	2	no	—
760	C₂²×C₅₃	—	2	2	no	—
761	C₂²×C₅₃	—	4	4	no	—
762	C₂²×C₅₃	C₂²×#41	1	2	yes	—
763	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
764	C₂×D₅₃	—	2	4	no	—
765	C₂×D₅₃	—	2	4	no	—
766	C₂×D₅₃	—	2	4	no	—
767	C₂×D₅₃	—	2	4	no	—
768	C₂×D₅₃	—	2	4	no	—
769	C₂×D₅₃	—	2	4	no	—
770	C₂×D₅₃	—	2	4	no	—
771	C₂×D₅₃	—	2	4	no	—
772	C₂×D₅₃	—	4	8	no	—
773	C₂×D₅₃	—	4	8	no	—
774	C₂×D₅₃	—	8	16	no	—
775	C₂×D₅₃	—	8	16	no	—
776	C₂×D₅₃	C₂²×#41	1	8	yes	—
777	C₄×C₅₃	—	2	4	no	—
778	C₄×C₅₃	—	2	2	no	—
779	C₄×C₅₃	—	2	1	no	—
780	C₄×C₅₃	—	2	1	no	—
781	C₄×C₅₃	—	2	4	no	—
782	C₄×C₅₃	—	2	2	no	—
783	C₄×C₅₃	—	2	2	no	—
784	C₄×C₅₃	—	2	1	no	—
785	C₄×C₅₃	—	2	4	no	—
786	C₄×C₅₃	—	2	1	no	—
787	C₄×C₅₃	C₂²×#41	1	2	yes	—
788	C₄×C₅₃	C₂²×#41	1	2	yes	—
789	Dic₅₃	—	2	4	no	—
790	Dic₅₃	—	2	4	no	—
791	Dic₅₃	—	2	4	no	—
792	Dic₅₃	—	2	4	no	—
793	Dic₅₃	—	2	4	no	—
794	#3521	—	53	4	no	—
795	#3521	—	53	4	no	—
796	#3519	—	53	4	no	—
797	#3519	—	53	4	no	—
798	#3514	—	53	4	no	—
799	#3514	—	53	4	no	—
800	#3513	—	53	4	no	—
801	#3513	—	53	4	no	—
802	#3506	—	53	1	no	—
803	#3506	—	53	1	no	—
804	#3505	—	53	4	no	—
805	#3501	—	53	1	no	—
806	#3496	—	53	1	no	—
807	#3493	—	53	2	no	—
808	#3490	—	53	4	no	—
809	#3484	—	53	2	no	—
810	#3460	—	53	2	no	—
811	#3459	—	53	4	no	—
812	#3455	—	53	1	no	—
813	#3455	D₅₃	1	1	yes	characteristic, complemented
814	C₂×#538	—	53	4	no	—
815	C₄×H(5,𝔽₂)	—	53	2	no	—
816	C₂×#518	—	53	1	no	—
817	C₂×C₅₃	—	2	2	no	—
818	C₂×C₅₃	—	4	2	no	—
819	C₂×C₅₃	—	4	4	no	—
820	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
821	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
822	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
823	D₅₃	—	2	8	no	—
824	D₅₃	—	4	4	no	—
825	D₅₃	—	4	4	no	—
826	C₂×H(5,𝔽₂)	—	53	2	no	—
827	C₂³×D₄	—	53	1	no	—
828	#559	—	53	4	no	—
829	#559	—	53	4	no	—
830	#556	—	53	2	no	—
831	#556	—	53	4	no	—
832	#556	—	53	2	no	—
833	#556	—	53	4	no	—
834	#555	—	53	2	no	—
835	#555	—	53	4	no	—
836	#555	—	53	4	no	—
837	#555	—	53	2	no	—
838	#554	—	53	2	no	—
839	#554	—	53	4	no	—
840	#554	—	53	2	no	—
841	#554	—	53	4	no	—
842	#553	—	53	8	no	—
843	#553	—	53	8	no	—
844	#553	—	53	4	no	—
845	#553	—	53	8	no	—
846	#553	—	53	4	no	—
847	#553	—	53	4	no	—
848	#553	—	53	4	no	—
849	#552	—	53	8	no	—
850	#552	—	53	4	no	—
851	#552	—	53	4	no	—
852	#551	—	53	8	no	—
853	#551	—	53	8	no	—
854	#551	—	53	8	no	—
855	#551	—	53	8	no	—
856	#551	—	53	8	no	—
857	#551	—	53	8	no	—
858	#550	—	53	2	no	—
859	#550	—	53	2	no	—
860	D₄×Q₈	—	53	2	no	—
861	D₄×Q₈	—	53	2	no	—
862	#548	—	53	8	no	—
863	#547	—	53	2	no	—
864	#547	—	53	2	no	—
865	#547	—	53	2	no	—
866	#547	—	53	2	no	—
867	#546	—	53	8	no	—
868	#546	—	53	4	no	—
869	#546	—	53	8	no	—
870	#546	—	53	8	no	—
871	#546	—	53	4	no	—
872	#546	—	53	4	no	—
873	#546	—	53	8	no	—
874	#546	—	53	8	no	—
875	#546	—	53	4	no	—
876	#546	—	53	4	no	—
877	#546	—	53	4	no	—
878	D₄²	—	53	2	no	—
879	D₄²	—	53	4	no	—
880	D₄²	—	53	4	no	—
881	D₄²	—	53	4	no	—
882	D₄²	—	53	4	no	—
883	D₄²	—	53	2	no	—
884	#544	—	53	2	no	—
885	#543	—	53	4	no	—
886	#542	—	53	4	no	—
887	#542	—	53	2	no	—
888	#542	—	53	2	no	—
889	#542	—	53	4	no	—
890	#542	C₂×D₅₃	1	2	yes	complemented
891	#542	C₂×D₅₃	1	2	yes	complemented
892	#541	—	53	2	no	—
893	#541	C₂×D₅₃	1	2	yes	complemented
894	#540	—	53	4	no	—
895	#540	—	53	2	no	—
896	#540	—	53	4	no	—
897	#540	C₂×D₅₃	1	2	yes	complemented
898	#539	—	53	8	no	—
899	#539	—	53	8	no	—
900	#539	—	53	2	no	—
901	#539	—	53	2	no	—
902	#539	C₂×D₅₃	1	2	yes	complemented
903	#539	C₂×D₅₃	1	2	yes	complemented
904	#538	—	53	8	no	—
905	#538	—	53	8	no	—
906	#538	—	53	8	no	—
907	#538	—	53	8	no	—
908	#538	—	53	8	no	—
909	#538	—	53	4	no	—
910	#538	—	53	4	no	—
911	#538	—	53	8	no	—
912	#538	—	53	8	no	—
913	#538	—	53	8	no	—
914	#538	—	53	2	no	—
915	#538	—	53	2	no	—
916	#538	C₂×D₅₃	1	2	yes	complemented
917	#538	C₂×D₅₃	1	2	yes	complemented
918	#537	—	53	2	no	—
919	#535	—	53	2	no	—
920	#535	—	53	2	no	—
921	#534	—	53	8	no	—
922	#534	—	53	4	no	—
923	#533	—	53	1	no	—
924	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
925	#532	—	53	4	no	—
926	#532	—	53	1	no	—
927	#532	—	53	4	no	—
928	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
929	#529	—	53	8	no	—
930	#529	—	53	8	no	—
931	#529	—	53	8	no	—
932	#529	—	53	4	no	—
933	#529	—	53	4	no	—
934	#529	—	53	4	no	—
935	#529	—	53	4	no	—
936	#529	C₂×D₅₃	1	4	yes	complemented
937	#529	C₂×D₅₃	1	4	yes	complemented
938	C₂×#126	—	53	8	no	—
939	C₂×#124	—	53	8	no	—
940	#525	—	53	2	no	—
941	#525	—	53	8	no	—
942	#525	—	53	4	no	—
943	#525	—	53	8	no	—
944	#525	—	53	4	no	—
945	#525	—	53	8	no	—
946	#525	C₂×D₅₃	1	2	yes	complemented
947	C₂×#123	—	53	8	no	—
948	C₂×C₂²⋊Q₈	—	53	4	no	—
949	C₂×#121	—	53	4	no	—
950	C₂×#121	—	53	8	no	—
951	C₂×#120	—	53	8	no	—
952	#520	—	53	2	no	—
953	#520	—	53	4	no	—
954	#520	—	53	2	no	—
955	#520	—	53	4	no	—
956	#518	—	53	8	no	—
957	#518	—	53	4	no	—
958	#518	—	53	2	no	—
959	#518	—	53	4	no	—
960	#518	—	53	4	no	—
961	#518	—	53	4	no	—
962	#518	—	53	4	no	—
963	#518	—	53	4	no	—
964	C₄×#41	—	53	4	no	—
965	C₄×#41	—	53	2	no	—
966	C₄×#41	—	53	4	no	—
967	C₄×#41	C₂×D₅₃	1	2	yes	complemented
968	C₂×C₄×D₄	—	53	8	no	—
969	C₂×C₄×D₄	—	53	4	no	—
970	C₂×C₄×D₄	—	53	2	no	—
971	C₂×C₄×D₄	—	53	2	no	—
972	C₂×C₄×D₄	—	53	1	no	—
973	C₂×C₄×D₄	—	53	1	no	—
974	C₂×C₄×D₄	—	53	1	no	—
975	C₂×C₄×D₄	—	53	1	no	—
976	C₂×C₄×D₄	—	53	4	no	—
977	C₂×#117	—	53	1	no	—
978	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
979	C₂²×C₂²⋊C₄	—	53	2	no	—
980	C₂²×C₂²⋊C₄	—	53	2	no	—
981	C₅₃	#62846	1	1	yes	characteristic, complemented, Sylow
982	C₂⁵	—	53	2	no	—
983	H(5,𝔽₂)	—	106	16	no	—
984	C₂×#41	—	53	4	no	—
985	C₂×#41	—	53	4	no	—
986	C₂×#41	—	53	4	no	—
987	C₂×#41	—	53	2	no	—
988	C₂×#41	—	53	4	no	—
989	C₂×#41	—	53	8	no	—
990	C₂×#41	C₂²×D₅₃	1	2	yes	—
991	C₂²×Q₈	—	53	4	no	—
992	C₂²×D₄	—	53	8	no	—
993	C₂²×D₄	—	53	4	no	—
994	C₂²×D₄	—	53	8	no	—
995	C₂²×D₄	—	53	8	no	—
996	C₂²×D₄	—	53	4	no	—
997	C₂²×D₄	—	53	1	no	—
998	C₂²×D₄	—	53	2	no	—
999	C₂²×D₄	—	53	1	no	—
1000	C₂²×D₄	—	53	4	no	—
1001	C₂²×D₄	—	53	4	no	—
1002	C₂²×D₄	—	53	4	no	—
1003	C₂²×D₄	—	106	8	no	—
1004	C₂³×C₄	—	53	2	no	—
1005	C₂³×C₄	—	53	2	no	—
1006	C₂³×C₄	—	53	2	no	—
1007	C₂³×C₄	—	53	2	no	—
1008	C₂³×C₄	—	53	8	no	—
1009	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
1010	C₄⋊Q₈	—	53	4	no	—
1011	C₄⋊Q₈	—	53	1	no	—
1012	C₄⋊Q₈	—	53	4	no	—
1013	C₄⋊Q₈	—	53	1	no	—
1014	C₄⋊Q₈	—	53	1	no	—
1015	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1016	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1017	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1018	#127	—	53	4	no	—
1019	#127	—	53	4	no	—
1020	#127	—	53	1	no	—
1021	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
1022	#126	—	53	8	no	—
1023	#126	—	53	8	no	—
1024	#126	—	53	8	no	—
1025	#126	—	53	4	no	—
1026	#126	—	53	8	no	—
1027	#126	—	53	4	no	—
1028	#126	—	53	4	no	—
1029	#126	—	53	8	no	—
1030	#126	—	53	8	no	—
1031	#126	—	53	8	no	—
1032	#126	—	53	4	no	—
1033	#126	—	53	8	no	—
1034	#126	C₂²×D₅₃	1	4	yes	—
1035	#126	C₂²×D₅₃	1	4	yes	—
1036	#126	C₂²×D₅₃	1	4	yes	complemented
1037	#126	C₂²×D₅₃	1	4	yes	complemented
1038	#125	—	53	4	no	—
1039	#125	—	53	8	no	—
1040	#125	—	53	4	no	—
1041	#125	—	53	4	no	—
1042	#125	—	53	4	no	—
1043	#125	—	53	2	no	—
1044	#125	C₂²×D₅₃	1	4	yes	complemented
1045	#125	C₂²×D₅₃	1	4	yes	complemented
1046	#125	C₂²×D₅₃	1	2	yes	complemented
1047	#124	—	53	8	no	—
1048	#124	—	53	4	no	—
1049	#124	—	53	8	no	—
1050	#124	—	53	4	no	—
1051	#124	—	53	8	no	—
1052	#124	—	53	8	no	—
1053	#124	—	53	8	no	—
1054	#124	—	53	8	no	—
1055	#124	—	53	4	no	—
1056	#124	—	53	8	no	—
1057	#124	—	53	4	no	—
1058	#124	—	53	2	no	—
1059	#124	C₂²×D₅₃	1	4	yes	—
1060	#124	C₂²×D₅₃	1	4	yes	—
1061	#124	C₂²×D₅₃	1	2	yes	complemented
1062	#123	—	53	8	no	—
1063	#123	—	53	8	no	—
1064	#123	—	53	4	no	—
1065	#123	—	53	8	no	—
1066	#123	—	53	8	no	—
1067	#123	—	53	4	no	—
1068	#123	—	53	8	no	—
1069	#123	—	53	8	no	—
1070	#123	—	53	8	no	—
1071	#123	—	53	8	no	—
1072	#123	—	53	8	no	—
1073	#123	—	53	4	no	—
1074	#123	—	53	4	no	—
1075	#123	—	53	8	no	—
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	C₂²×D₅₃	1	4	yes	—
1082	#123	C₂²×D₅₃	1	4	yes	—
1083	#123	C₂²×D₅₃	1	4	yes	—
1084	#123	C₂²×D₅₃	1	4	yes	complemented
1085	#123	C₂²×D₅₃	1	4	yes	complemented
1086	C₂²⋊Q₈	—	53	4	no	—
1087	C₂²⋊Q₈	—	53	4	no	—
1088	C₂²⋊Q₈	—	53	8	no	—
1089	C₂²⋊Q₈	—	53	4	no	—
1090	C₂²⋊Q₈	—	53	2	no	—
1091	C₂²⋊Q₈	—	53	2	no	—
1092	C₂²⋊Q₈	—	53	2	no	—
1093	C₂²⋊Q₈	—	53	2	no	—
1094	C₂²⋊Q₈	—	53	4	no	—
1095	C₂²⋊Q₈	—	53	8	no	—
1096	C₂²⋊Q₈	—	53	4	no	—
1097	C₂²⋊Q₈	—	53	4	no	—
1098	C₂²⋊Q₈	—	53	4	no	—
1099	C₂²⋊Q₈	—	53	8	no	—
1100	C₂²⋊Q₈	—	53	8	no	—
1101	C₂²⋊Q₈	—	53	8	no	—
1102	C₂²⋊Q₈	—	53	8	no	—
1103	C₂²⋊Q₈	—	53	4	no	—
1104	C₂²⋊Q₈	—	53	8	no	—
1105	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
1106	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
1107	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
1108	C₂²⋊Q₈	C₂²×D₅₃	1	2	yes	—
1109	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1110	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1111	#121	—	53	8	no	—
1112	#121	—	53	4	no	—
1113	#121	—	53	8	no	—
1114	#121	—	53	8	no	—
1115	#121	—	53	8	no	—
1116	#121	—	53	4	no	—
1117	#121	—	53	4	no	—
1118	#121	—	53	2	no	—
1119	#121	—	53	8	no	—
1120	#121	—	53	2	no	—
1121	#121	—	53	2	no	—
1122	#121	—	53	2	no	—
1123	#121	—	53	4	no	—
1124	#121	—	53	4	no	—
1125	#121	—	53	4	no	—
1126	#121	—	53	4	no	—
1127	#121	—	53	8	no	—
1128	#121	—	53	8	no	—
1129	#121	—	53	4	no	—
1130	#121	—	53	8	no	—
1131	#121	—	53	4	no	—
1132	#121	—	53	4	no	—
1133	#121	—	53	4	no	—
1134	#121	—	53	8	no	—
1135	#121	—	53	8	no	—
1136	#121	—	53	8	no	—
1137	#121	—	53	8	no	—
1138	#121	—	53	8	no	—
1139	#121	—	53	4	no	—
1140	#121	C₂²×D₅₃	1	4	yes	—
1141	#121	C₂²×D₅₃	1	2	yes	—
1142	#121	C₂²×D₅₃	1	2	yes	—
1143	#121	C₂²×D₅₃	1	2	yes	—
1144	#121	C₂²×D₅₃	1	2	yes	—
1145	#121	C₂²×D₅₃	1	4	yes	—
1146	#120	—	53	4	no	—
1147	#120	—	53	8	no	—
1148	#120	—	53	8	no	—
1149	#120	—	53	8	no	—
1150	#120	—	53	8	no	—
1151	#120	—	53	8	no	—
1152	#120	—	53	8	no	—
1153	#120	—	53	8	no	—
1154	#120	—	53	8	no	—
1155	#120	—	53	8	no	—
1156	#120	—	53	8	no	—
1157	#120	C₂²×D₅₃	1	4	yes	—
1158	C₄×Q₈	—	53	4	no	—
1159	C₄×Q₈	—	53	8	no	—
1160	C₄×Q₈	—	53	2	no	—
1161	C₄×Q₈	—	53	2	no	—
1162	C₄×Q₈	—	53	4	no	—
1163	C₄×Q₈	—	53	2	no	—
1164	C₄×Q₈	—	53	2	no	—
1165	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1166	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1167	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1168	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1169	C₄×D₄	—	53	8	no	—
1170	C₄×D₄	—	53	4	no	—
1171	C₄×D₄	—	53	4	no	—
1172	C₄×D₄	—	53	8	no	—
1173	C₄×D₄	—	53	4	no	—
1174	C₄×D₄	—	53	8	no	—
1175	C₄×D₄	—	53	4	no	—
1176	C₄×D₄	—	53	4	no	—
1177	C₄×D₄	—	53	8	no	—
1178	C₄×D₄	—	53	8	no	—
1179	C₄×D₄	—	53	8	no	—
1180	C₄×D₄	—	53	8	no	—
1181	C₄×D₄	—	53	8	no	—
1182	C₄×D₄	—	53	8	no	—
1183	C₄×D₄	—	53	4	no	—
1184	C₄×D₄	—	53	4	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	8	no	—
1191	C₄×D₄	—	53	8	no	—
1192	C₄×D₄	—	53	4	no	—
1193	C₄×D₄	—	53	4	no	—
1194	C₄×D₄	—	53	8	no	—
1195	C₄×D₄	—	53	2	no	—
1196	C₄×D₄	—	53	4	no	—
1197	C₄×D₄	—	53	4	no	—
1198	C₄×D₄	—	53	2	no	—
1199	C₄×D₄	—	53	2	no	—
1200	C₄×D₄	—	53	2	no	—
1201	C₄×D₄	—	53	2	no	—
1202	C₄×D₄	—	53	2	no	—
1203	C₄×D₄	—	53	2	no	—
1204	C₄×D₄	—	53	2	no	—
1205	C₄×D₄	—	53	2	no	—
1206	C₄×D₄	—	53	4	no	—
1207	C₄×D₄	—	53	8	no	—
1208	C₄×D₄	—	53	4	no	—
1209	C₄×D₄	—	53	2	no	—
1210	C₄×D₄	—	53	4	no	—
1211	C₄×D₄	—	53	8	no	—
1212	C₄×D₄	—	53	2	no	—
1213	C₄×D₄	—	53	2	no	—
1214	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1215	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1216	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1217	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1218	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1219	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1220	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1221	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1222	#117	—	53	4	no	—
1223	#117	—	53	4	no	—
1224	#117	—	53	2	no	—
1225	#117	—	53	4	no	—
1226	#117	—	53	8	no	—
1227	#117	—	53	4	no	—
1228	#117	—	53	4	no	—
1229	#117	—	53	4	no	—
1230	#117	—	53	8	no	—
1231	#117	—	53	8	no	—
1232	#117	—	53	4	no	—
1233	#117	—	53	8	no	—
1234	#117	—	53	8	no	—
1235	#117	C₂²×D₅₃	1	2	yes	—
1236	#117	C₂²×D₅₃	1	2	yes	—
1237	#117	C₂²×D₅₃	1	2	yes	—
1238	#117	C₂²×D₅₃	1	2	yes	—
1239	#117	C₂²×D₅₃	1	2	yes	—
1240	#117	C₂²×D₅₃	1	4	yes	complemented
1241	C₂×C₄⋊C₄	—	53	1	no	—
1242	C₂×C₄⋊C₄	—	53	1	no	—
1243	C₂×C₄⋊C₄	—	53	4	no	—
1244	C₂×C₄⋊C₄	—	53	8	no	—
1245	C₂×C₄⋊C₄	—	53	4	no	—
1246	C₂×C₄⋊C₄	—	53	8	no	—
1247	C₂×C₄⋊C₄	—	53	4	no	—
1248	C₂×C₄⋊C₄	—	53	4	no	—
1249	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1250	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1251	C₂×C₂²⋊C₄	—	53	2	no	—
1252	C₂×C₂²⋊C₄	—	53	2	no	—
1253	C₂×C₂²⋊C₄	—	53	2	no	—
1254	C₂×C₂²⋊C₄	—	53	2	no	—
1255	C₂×C₂²⋊C₄	—	53	2	no	—
1256	C₂×C₂²⋊C₄	—	53	8	no	—
1257	C₂×C₂²⋊C₄	—	53	8	no	—
1258	C₂×C₂²⋊C₄	—	53	8	no	—
1259	C₂×C₂²⋊C₄	—	53	8	no	—
1260	C₂×C₂²⋊C₄	—	53	8	no	—
1261	C₂×C₂²⋊C₄	—	53	8	no	—
1262	C₂×C₂²⋊C₄	—	53	8	no	—
1263	C₂×C₂²⋊C₄	—	53	8	no	—
1264	C₂×C₂²⋊C₄	—	53	8	no	—
1265	C₂×C₂²⋊C₄	—	53	8	no	—
1266	C₂×C₂²⋊C₄	—	53	8	no	—
1267	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1268	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1269	C₂×C₄²	—	53	2	no	—
1270	C₂×C₄²	—	53	8	no	—
1271	C₂×C₄²	—	53	4	no	—
1272	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1273	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1274	C₂×C₄²	C₂²×D₅₃	1	4	yes	complemented
1275	C₂⁴	—	53	2	no	—
1276	C₂⁴	—	53	8	no	—
1277	C₂⁴	—	53	8	no	—
1278	C₂⁴	—	53	2	no	—
1279	C₂⁴	—	106	8	no	—
1280	C₂⁴	—	424	2	no	—
1281	C₂⁴	—	424	2	no	—
1282	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1283	#41	—	2	8	no	—
1284	#41	—	106	16	no	—
1285	#41	—	106	16	no	—
1286	#41	—	106	8	no	—
1287	#41	—	424	8	no	—
1288	#41	—	424	4	no	—
1289	#41	—	424	4	no	—
1290	C₂×Q₈	—	53	2	no	—
1291	C₂×Q₈	—	53	2	no	—
1292	C₂×Q₈	—	53	2	no	—
1293	C₂×Q₈	—	53	8	no	—
1294	C₂×Q₈	—	424	4	no	—
1295	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1296	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1297	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1298	C₂×D₄	—	53	8	no	—
1299	C₂×D₄	—	53	4	no	—
1300	C₂×D₄	—	53	4	no	—
1301	C₂×D₄	—	53	8	no	—
1302	C₂×D₄	—	53	4	no	—
1303	C₂×D₄	—	53	8	no	—
1304	C₂×D₄	—	53	8	no	—
1305	C₂×D₄	—	53	8	no	—
1306	C₂×D₄	—	53	2	no	—
1307	C₂×D₄	—	53	2	no	—
1308	C₂×D₄	—	53	8	no	—
1309	C₂×D₄	—	53	8	no	—
1310	C₂×D₄	—	53	2	no	—
1311	C₂×D₄	—	53	2	no	—
1312	C₂×D₄	—	53	2	no	—
1313	C₂×D₄	—	53	2	no	—
1314	C₂×D₄	—	53	8	no	—
1315	C₂×D₄	—	53	8	no	—
1316	C₂×D₄	—	53	2	no	—
1317	C₂×D₄	—	106	16	no	—
1318	C₂×D₄	—	106	16	no	—
1319	C₂×D₄	—	106	16	no	—
1320	C₂×D₄	—	106	8	no	—
1321	C₂×D₄	—	106	16	no	—
1322	C₂×D₄	—	106	32	no	—
1323	C₂×D₄	—	106	4	no	—
1324	C₂×D₄	—	424	4	no	—
1325	C₂×D₄	—	424	8	no	—
1326	C₂×D₄	—	424	8	no	—
1327	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1328	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1329	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1330	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1331	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1332	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1333	C₂²×C₄	—	2	4	no	—
1334	C₂²×C₄	—	53	2	no	—
1335	C₂²×C₄	—	53	2	no	—
1336	C₂²×C₄	—	53	8	no	—
1337	C₂²×C₄	—	53	8	no	—
1338	C₂²×C₄	—	53	4	no	—
1339	C₂²×C₄	—	53	8	no	—
1340	C₂²×C₄	—	53	8	no	—
1341	C₂²×C₄	—	53	4	no	—
1342	C₂²×C₄	—	53	4	no	—
1343	C₂²×C₄	—	53	4	no	—
1344	C₂²×C₄	—	53	4	no	—
1345	C₂²×C₄	—	53	8	no	—
1346	C₂²×C₄	—	53	4	no	—
1347	C₂²×C₄	—	53	4	no	—
1348	C₂²×C₄	—	53	8	no	—
1349	C₂²×C₄	—	53	8	no	—
1350	C₂²×C₄	—	424	2	no	—
1351	C₂²×C₄	—	424	8	no	—
1352	C₂²×C₄	—	424	2	no	—
1353	C₂²×C₄	—	424	2	no	—
1354	C₂²×C₄	—	424	2	no	—
1355	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1356	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1357	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1358	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1359	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1360	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1361	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1362	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1363	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1364	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1365	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1366	C₄⋊C₄	—	53	2	no	—
1367	C₄⋊C₄	—	53	2	no	—
1368	C₄⋊C₄	—	53	2	no	—
1369	C₄⋊C₄	—	53	8	no	—
1370	C₄⋊C₄	—	53	4	no	—
1371	C₄⋊C₄	—	53	8	no	—
1372	C₄⋊C₄	—	53	2	no	—
1373	C₄⋊C₄	—	53	4	no	—
1374	C₄⋊C₄	—	53	2	no	—
1375	C₄⋊C₄	—	53	2	no	—
1376	C₄⋊C₄	—	53	2	no	—
1377	C₄⋊C₄	—	53	8	no	—
1378	C₄⋊C₄	—	53	8	no	—
1379	C₄⋊C₄	—	53	8	no	—
1380	C₄⋊C₄	—	53	8	no	—
1381	C₄⋊C₄	—	53	2	no	—
1382	C₄⋊C₄	—	53	4	no	—
1383	C₄⋊C₄	—	53	4	no	—
1384	C₄⋊C₄	—	53	2	no	—
1385	C₄⋊C₄	—	53	2	no	—
1386	C₄⋊C₄	—	53	4	no	—
1387	C₄⋊C₄	—	53	4	no	—
1388	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1389	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1390	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1391	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1392	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1393	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1394	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1395	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1396	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1397	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1398	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1399	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1400	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1401	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1402	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1403	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1404	C₂²⋊C₄	—	53	8	no	—
1405	C₂²⋊C₄	—	53	4	no	—
1406	C₂²⋊C₄	—	53	8	no	—
1407	C₂²⋊C₄	—	53	4	no	—
1408	C₂²⋊C₄	—	53	4	no	—
1409	C₂²⋊C₄	—	53	8	no	—
1410	C₂²⋊C₄	—	53	8	no	—
1411	C₂²⋊C₄	—	53	4	no	—
1412	C₂²⋊C₄	—	53	4	no	—
1413	C₂²⋊C₄	—	53	4	no	—
1414	C₂²⋊C₄	—	53	8	no	—
1415	C₂²⋊C₄	—	53	4	no	—
1416	C₂²⋊C₄	—	53	8	no	—
1417	C₂²⋊C₄	—	53	8	no	—
1418	C₂²⋊C₄	—	53	4	no	—
1419	C₂²⋊C₄	—	53	8	no	—
1420	C₂²⋊C₄	—	53	4	no	—
1421	C₂²⋊C₄	—	53	4	no	—
1422	C₂²⋊C₄	—	53	8	no	—
1423	C₂²⋊C₄	—	53	8	no	—
1424	C₂²⋊C₄	—	53	8	no	—
1425	C₂²⋊C₄	—	53	8	no	—
1426	C₂²⋊C₄	—	53	8	no	—
1427	C₂²⋊C₄	—	53	4	no	—
1428	C₂²⋊C₄	—	53	4	no	—
1429	C₂²⋊C₄	—	53	4	no	—
1430	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1431	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1432	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1433	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1434	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1435	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1436	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1437	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1438	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1439	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1440	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1441	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1442	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1443	C₄²	—	53	4	no	—
1444	C₄²	—	53	8	no	—
1445	C₄²	—	53	4	no	—
1446	C₄²	—	53	8	no	—
1447	C₄²	—	53	8	no	—
1448	C₄²	—	53	4	no	—
1449	C₄²	C₂³×D₅₃	1	2	yes	—
1450	C₄²	C₂³×D₅₃	1	4	yes	—
1451	C₄²	C₂³×D₅₃	1	2	yes	—
1452	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1453	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1454	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1455	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1456	C₄²	C₂³×D₅₃	1	4	yes	—
1457	C₄²	C₂³×D₅₃	1	4	yes	—
1458	C₂³	—	2	2	no	—
1459	C₂³	—	4	1	no	—
1460	C₂³	—	4	1	no	—
1461	C₂³	—	53	4	no	—
1462	C₂³	—	53	8	no	—
1463	C₂³	—	53	4	no	—
1464	C₂³	—	53	4	no	—
1465	C₂³	—	106	16	no	—
1466	C₂³	—	106	16	no	—
1467	C₂³	—	106	4	no	—
1468	C₂³	—	424	16	no	—
1469	C₂³	—	212	8	no	—
1470	C₂³	—	212	8	no	—
1471	C₂³	—	212	8	no	—
1472	C₂³	—	212	8	no	—
1473	C₂³	—	212	2	no	—
1474	C₂³	—	212	2	no	—
1475	C₂³	—	212	2	no	—
1476	C₂³	—	212	2	no	—
1477	C₂³	C₂⁴×D₅₃	1	2	yes	—
1478	C₂³	C₂⁴×D₅₃	1	4	yes	—
1479	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1480	Q₈	—	2	4	no	—
1481	Q₈	—	4	2	no	—
1482	Q₈	—	4	2	no	—
1483	Q₈	—	106	4	no	—
1484	Q₈	—	212	2	no	—
1485	Q₈	—	212	8	no	—
1486	Q₈	—	212	2	no	—
1487	D₄	—	2	8	no	—
1488	D₄	—	2	4	no	—
1489	D₄	—	4	2	no	—
1490	D₄	—	4	4	no	—
1491	D₄	—	4	4	no	—
1492	D₄	—	4	2	no	—
1493	D₄	—	53	8	no	—
1494	D₄	—	53	8	no	—
1495	D₄	—	106	16	no	—
1496	D₄	—	106	16	no	—
1497	D₄	—	106	16	no	—
1498	D₄	—	106	8	no	—
1499	D₄	—	106	4	no	—
1500	D₄	—	106	4	no	—
1501	D₄	—	106	4	no	—
1502	D₄	—	212	2	no	—
1503	D₄	—	212	8	no	—
1504	D₄	—	212	8	no	—
1505	D₄	—	212	2	no	—
1506	D₄	—	212	4	no	—
1507	D₄	—	212	4	no	—
1508	D₄	—	212	8	no	—
1509	D₄	—	212	8	no	—
1510	D₄	—	212	8	no	—
1511	C₂×C₄	—	2	2	no	—
1512	C₂×C₄	—	2	4	no	—
1513	C₂×C₄	—	2	4	no	—
1514	C₂×C₄	—	2	8	no	—
1515	C₂×C₄	—	4	1	no	—
1516	C₂×C₄	—	4	1	no	—
1517	C₂×C₄	—	4	4	no	—
1518	C₂×C₄	—	4	1	no	—
1519	C₂×C₄	—	4	1	no	—
1520	C₂×C₄	—	4	4	no	—
1521	C₂×C₄	—	53	4	no	—
1522	C₂×C₄	—	53	4	no	—
1523	C₂×C₄	—	53	4	no	—
1524	C₂×C₄	—	53	4	no	—
1525	C₂×C₄	—	53	4	no	—
1526	C₂×C₄	—	106	16	no	—
1527	C₂×C₄	—	106	8	no	—
1528	C₂×C₄	—	212	8	no	—
1529	C₂×C₄	—	212	4	no	—
1530	C₂×C₄	—	212	4	no	—
1531	C₂×C₄	—	212	8	no	—
1532	C₂×C₄	—	212	4	no	—
1533	C₂×C₄	—	212	8	no	—
1534	C₂×C₄	—	212	4	no	—
1535	C₂×C₄	—	212	8	no	—
1536	C₂×C₄	—	212	4	no	—
1537	C₂×C₄	—	212	8	no	—
1538	C₂×C₄	—	212	4	no	—
1539	C₂×C₄	—	212	2	no	—
1540	C₂×C₄	—	212	2	no	—
1541	C₂×C₄	—	212	8	no	—
1542	C₂×C₄	#41×D₅₃	1	4	yes	—
1543	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1544	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1545	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1546	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1547	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1548	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1549	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1550	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1551	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1552	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1553	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1554	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1555	C₂²	—	2	1	no	—
1556	C₂²	—	2	1	no	—
1557	C₂²	—	2	2	no	—
1558	C₂²	—	2	4	no	—
1559	C₂²	—	2	4	no	—
1560	C₂²	—	2	4	no	—
1561	C₂²	—	2	2	no	—
1562	C₂²	—	2	2	no	—
1563	C₂²	—	4	4	no	—
1564	C₂²	—	53	8	no	—
1565	C₂²	—	106	4	no	—
1566	C₂²	—	106	4	no	—
1567	C₂²	—	106	4	no	—
1568	C₂²	—	106	4	no	—
1569	C₂²	—	106	4	no	—
1570	C₂²	—	106	4	no	—
1571	C₂²	—	106	4	no	—
1572	C₂²	—	106	4	no	—
1573	C₂²	—	424	16	no	—
1574	C₂²	—	424	16	no	—
1575	C₂²	—	212	8	no	—
1576	C₂²	—	212	8	no	—
1577	C₂²	C₂×#41×D₅₃	1	2	yes	—
1578	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1579	C₄	—	2	2	no	—
1580	C₄	—	2	4	no	—
1581	C₄	—	2	2	no	—
1582	C₄	—	2	2	no	—
1583	C₄	—	2	1	no	—
1584	C₄	—	2	1	no	—
1585	C₄	—	2	4	no	—
1586	C₄	—	2	1	no	—
1587	C₄	—	2	1	no	—
1588	C₄	—	2	4	no	—
1589	C₄	—	106	4	no	—
1590	C₄	—	106	4	no	—
1591	C₄	—	106	4	no	—
1592	C₄	—	106	4	no	—
1593	C₄	—	106	4	no	—
1594	C₄	C₂×#41×D₅₃	1	2	yes	—
1595	C₄	C₂×#41×D₅₃	1	2	yes	—
1596	C₂	—	2	2	no	—
1597	C₂	—	4	2	no	—
1598	C₂	—	4	4	no	—
1599	C₂	—	106	8	no	—
1600	C₂	—	212	4	no	—
1601	C₂	—	212	4	no	—
1602	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1603	C₂	#20289526	1	1	yes	characteristic
1604	C₂	#20289526	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3455	C₂
hypercenter	#3455	D₅₃
hypocenter	C₅₃	#62846
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #20288789	C₂	semidirect
2. #20288787	C₂	semidirect
3. #20288749	C₂	semidirect
4. #20288745	C₂	semidirect
5. #20288678	C₂	semidirect
6. #20288674	C₂	semidirect
7. #20288661	C₂	semidirect
8. #20288659	C₂	semidirect
9. #20288569	C₂	semidirect
10. #20288564	C₂	semidirect
11. #20288547	C₂	semidirect
12. #20288516	C₂	semidirect
13. #20288477	C₂	semidirect
14. #20288432	C₂	semidirect
15. #20288401	C₂	semidirect
16. #20288348	C₂	semidirect
17. #20288131	C₂	semidirect
18. #20288123	C₂	semidirect
19. #20288105	C₂	semidirect
20. #538×D₅₃	C₂	semidirect
21. C₄×#13133263	C₂	semidirect
22. C₂×#16811097	C₂	semidirect
23. C₅₃×#3455	C₂	semidirect
26. #16811358	C₂²	semidirect
27. #16811355	C₂²	semidirect
28. #16811347	C₂²	semidirect
29. #16811346	C₂²	semidirect
30. #16811344	C₂²	semidirect
31. #16811343	C₂²	semidirect
32. #16811339	C₂²	semidirect
33. #16811338	C₂²	semidirect
34. #16811338	C₂²	semidirect
35. #16811337	C₂²	semidirect
36. #16811334	C₂²	semidirect
37. #16811333	C₂²	semidirect
38. #16811333	C₂²	semidirect
39. #16811329	C₂²	semidirect
40. #16811326	C₂²	semidirect
41. #16811326	C₂²	semidirect
42. #16811324	C₂²	semidirect
43. #16811320	C₂²	semidirect
44. #16811319	C₂²	semidirect
45. #16811319	C₂²	semidirect
46. #16811318	C₂²	semidirect
47. #16811313	C₂²	semidirect
48. #16811307	C₂²	semidirect
49. #16811305	C₂²	semidirect
50. #16811303	C₂²	semidirect
51. #16811301	C₂²	semidirect
52. #16811300	C₂²	semidirect
53. #16811298	C₂²	semidirect
54. #16811298	C₂²	semidirect
55. #16811298	C₂²	semidirect
56. #16811295	C₂²	semidirect
57. #16811293	C₂²	semidirect
58. Q₈×D₂₁₂	C₂²	semidirect
59. #16811288	C₂²	semidirect
60. #16811283	C₂²	semidirect
61. #16811278	C₂²	semidirect
62. #16811277	C₂²	semidirect
63. #16811276	C₂²	semidirect
64. #16811276	C₂²	semidirect
65. #16811270	C₂²	semidirect
66. #16811269	C₂²	semidirect
67. #16811269	C₂²	semidirect
68. #16811269	C₂²	semidirect
69. #16811266	C₂²	semidirect
70. #16811266	C₂²	semidirect
71. #16811265	C₂²	semidirect
72. #16811265	C₂²	semidirect
73. #16811264	C₂²	semidirect
74. #16811264	C₂²	semidirect
75. #16811262	C₂²	semidirect
76. D₄×D₂₁₂	C₂²	semidirect
77. D₄×D₂₁₂	C₂²	semidirect
78. D₄×D₂₁₂	C₂²	semidirect
79. #16811258	C₂²	semidirect
80. #16811257	C₂²	semidirect
81. #16811257	C₂²	semidirect
82. #16811251	C₂²	semidirect
83. #16811248	C₂²	semidirect
84. #16811245	C₂²	semidirect
85. #16811244	C₂²	semidirect
86. #16811244	C₂²	semidirect
87. #16811244	C₂²	semidirect
88. #16811235	C₂²	semidirect
89. #16811228	C₂²	semidirect
90. #16811228	C₂²	semidirect
91. #16811224	C₂²	semidirect
92. #16811221	C₂²	semidirect
93. #16811220	C₂²	semidirect
94. #16811220	C₂²	semidirect
95. #16811219	C₂²	semidirect
96. #16811213	C₂²	semidirect
97. #16811212	C₂²	semidirect
98. #16811212	C₂²	semidirect
99. #16811211	C₂²	semidirect
100. #16811211	C₂²	semidirect
101. #16811210	C₂²	semidirect
102. #16811209	C₂²	semidirect
103. #16811209	C₂²	semidirect
104. #16811208	C₂²	semidirect
105. #16811207	C₂²	semidirect
106. #16811206	C₂²	semidirect
107. #16811205	C₂²	semidirect
108. #16811201	C₂²	semidirect
109. #16811192	C₂²	semidirect
110. #16811187	C₂²	semidirect
111. #16811184	C₂²	semidirect
112. #16811181	C₂²	semidirect
113. #16811180	C₂²	semidirect
114. #16811173	C₂²	semidirect
115. #16811173	C₂²	semidirect
116. #16811170	C₂²	semidirect
117. #16811160	C₂²	semidirect
118. #16811158	C₂²	semidirect
119. #16811157	C₂²	semidirect
120. #16811156	C₂²	semidirect
121. #16811151	C₂²	semidirect
122. #16811151	C₂²	semidirect
123. #16811150	C₂²	semidirect
124. #126×D₅₃	C₂²	semidirect
125. #124×D₅₃	C₂²	semidirect
126. #16811136	C₂²	semidirect
127. #16811136	C₂²	semidirect
128. #16811134	C₂²	semidirect
129. #16811133	C₂²	semidirect
130. #16811132	C₂²	semidirect
131. #16811131	C₂²	semidirect
132. #123×D₅₃	C₂²	semidirect
133. C₂²⋊Q₈×D₅₃	C₂²	semidirect
134. #121×D₅₃	C₂²	semidirect
135. #121×D₅₃	C₂²	semidirect
136. #120×D₅₃	C₂²	semidirect
137. #16811106	C₂²	semidirect
138. #16811105	C₂²	semidirect
139. #16811103	C₂²	semidirect
140. #16811103	C₂²	semidirect
142. #16811097	C₂²	semidirect
143. #16811097	C₂²	semidirect
144. #16811097	C₂²	semidirect
145. #16811097	C₂²	semidirect
146. #16811097	C₂²	semidirect
147. #16811095	C₂²	semidirect
148. #16811095	C₂²	semidirect
149. C₄×#11719949	C₂²	semidirect
150. C₄×#11719945	C₂²	semidirect
151. C₄×#11719945	C₂²	semidirect
154. C₂×C₄×D₂₁₂	C₂²	semidirect
155. C₂×C₄×D₂₁₂	C₂²	semidirect
156. C₂×C₄×D₂₁₂	C₂²	semidirect
157. C₂×#13133179	C₂²	semidirect
158. C₂×#13133179	C₂²	semidirect
159. C₄×D₄×D₅₃	C₂²	semidirect
160. C₄×D₄×D₅₃	C₂²	semidirect
161. C₂×#13133176	C₂²	semidirect
162. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
163. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
164. C₅₃×#542	C₂²	semidirect
165. C₅₃×#542	C₂²	semidirect
166. C₅₃×#541	C₂²	semidirect
167. C₅₃×#540	C₂²	semidirect
168. C₅₃×#539	C₂²	semidirect
169. C₅₃×#539	C₂²	semidirect
170. C₅₃×#538	C₂²	semidirect
171. C₅₃×#538	C₂²	semidirect
172. C₅₃×#533	C₂²	semidirect
173. C₅₃×#532	C₂²	semidirect
174. C₅₃×#529	C₂²	semidirect
175. C₅₃×#529	C₂²	semidirect
176. C₅₃×#525	C₂²	semidirect
177. C₄×#41×C₅₃	C₂²	semidirect
178. C₂×#117×C₅₃	C₂²	semidirect
182. C₂×#11719949	C₂³	semidirect
185. C₂×#11719945	C₂³	semidirect
186. C₂×#11719947	C₂³	semidirect
187. C₂×Q₈×D₅₃	C₂³	semidirect
199. C₂×D₄×D₅₃	C₂³	semidirect
204. C₂²×C₄×D₅₃	C₂³	semidirect
205. #13133217	C₂³	semidirect
206. #13133217	C₂³	semidirect
207. #13133217	C₂³	semidirect
208. #13133217	C₂³	semidirect
209. #13133216	C₂³	semidirect
211. #13133214	C₂³	semidirect
213. #13133212	C₂³	semidirect
214. #13133212	C₂³	semidirect
215. #13133212	C₂³	semidirect
216. #13133212	C₂³	semidirect
217. #13133212	C₂³	semidirect
218. #13133212	C₂³	semidirect
219. #13133211	C₂³	semidirect
224. #13133210	C₂³	semidirect
225. #13133209	C₂³	semidirect
226. #13133209	C₂³	semidirect
227. #13133208	C₂³	semidirect
228. #13133207	C₂³	semidirect
229. #13133207	C₂³	semidirect
230. #13133207	C₂³	semidirect
232. #13133206	C₂³	semidirect
234. #13133205	C₂³	semidirect
235. #13133205	C₂³	semidirect
240. #13133203	C₂³	semidirect
241. #13133203	C₂³	semidirect
242. #13133203	C₂³	semidirect
245. #13133202	C₂³	semidirect
246. #13133202	C₂³	semidirect
247. #13133202	C₂³	semidirect
248. #13133202	C₂³	semidirect
249. #13133202	C₂³	semidirect
250. #13133202	C₂³	semidirect
251. #13133202	C₂³	semidirect
252. #13133201	C₂³	semidirect
254. #13133200	C₂³	semidirect
258. #13133199	C₂³	semidirect
259. #13133199	C₂³	semidirect
260. #13133199	C₂³	semidirect
262. #13133197	C₂³	semidirect
263. #13133197	C₂³	semidirect
264. #13133197	C₂³	semidirect
269. #13133196	C₂³	semidirect
270. #13133195	C₂³	semidirect
271. #13133195	C₂³	semidirect
272. #13133195	C₂³	semidirect
273. #13133195	C₂³	semidirect
274. #13133195	C₂³	semidirect
275. #13133195	C₂³	semidirect
277. #13133193	C₂³	semidirect
278. #13133193	C₂³	semidirect
279. #13133193	C₂³	semidirect
280. #13133193	C₂³	semidirect
285. #13133192	C₂³	semidirect
286. #13133192	C₂³	semidirect
287. #13133192	C₂³	semidirect
294. #13133191	C₂³	semidirect
295. #13133191	C₂³	semidirect
300. #13133190	C₂³	semidirect
301. #13133190	C₂³	semidirect
302. #13133190	C₂³	semidirect
305. #13133189	C₂³	semidirect
307. #13133188	C₂³	semidirect
308. #13133188	C₂³	semidirect
309. #13133188	C₂³	semidirect
315. #13133187	C₂³	semidirect
320. #13133185	C₂³	semidirect
321. Q₈×Dic₅₃	C₂³	semidirect
322. C₄×Dic₁₀₆	C₂³	semidirect
323. C₄×Dic₁₀₆	C₂³	semidirect
324. C₄×Dic₁₀₆	C₂³	semidirect
325. C₄×Dic₁₀₆	C₂³	semidirect
326. C₄×Dic₁₀₆	C₂³	semidirect
327. #13133182	C₂³	semidirect
342. C₄×D₂₁₂	C₂³	semidirect
343. C₄×D₂₁₂	C₂³	semidirect
344. C₄×D₂₁₂	C₂³	semidirect
345. C₄×D₂₁₂	C₂³	semidirect
346. C₄×D₂₁₂	C₂³	semidirect
347. C₄×D₂₁₂	C₂³	semidirect
348. C₄×D₂₁₂	C₂³	semidirect
349. C₄×D₂₁₂	C₂³	semidirect
351. D₄×Dic₅₃	C₂³	semidirect
358. #13133179	C₂³	semidirect
359. #13133179	C₂³	semidirect
360. #13133179	C₂³	semidirect
365. C₄×C₂²⋊D₅₃	C₂³	semidirect
366. C₄×C₂²⋊D₅₃	C₂³	semidirect
367. C₄×C₂²⋊D₅₃	C₂³	semidirect
369. #13133177	C₂³	semidirect
370. #13133177	C₂³	semidirect
371. #13133177	C₂³	semidirect
372. #13133177	C₂³	semidirect
376. #13133176	C₂³	semidirect
377. #13133175	C₂³	semidirect
378. #13133175	C₂³	semidirect
379. #13133175	C₂³	semidirect
380. #13133175	C₂³	semidirect
381. #13133175	C₂³	semidirect
382. #13133174	C₂³	semidirect
383. #13133174	C₂³	semidirect
384. #13133174	C₂³	semidirect
385. #13133173	C₂³	semidirect
388. C₂×C₄⋊Dic₅₃	C₂³	semidirect
389. C₄⋊C₄×D₅₃	C₂³	semidirect
390. C₄⋊C₄×D₅₃	C₂³	semidirect
391. C₄⋊C₄×D₅₃	C₂³	semidirect
392. C₄⋊C₄×D₅₃	C₂³	semidirect
393. C₄⋊C₄×D₅₃	C₂³	semidirect
399. C₂×#11719921	C₂³	semidirect
407. C₂²⋊C₄×D₅₃	C₂³	semidirect
408. C₂²⋊C₄×D₅₃	C₂³	semidirect
409. C₂²⋊C₄×D₅₃	C₂³	semidirect
411. C₄²×D₅₃	C₂³	semidirect
412. C₄²×D₅₃	C₂³	semidirect
415. C₄⋊Q₈×C₅₃	C₂³	semidirect
416. C₄⋊Q₈×C₅₃	C₂³	semidirect
417. C₄⋊Q₈×C₅₃	C₂³	semidirect
418. #127×C₅₃	C₂³	semidirect
421. #126×C₅₃	C₂³	semidirect
422. #126×C₅₃	C₂³	semidirect
423. #125×C₅₃	C₂³	semidirect
424. #125×C₅₃	C₂³	semidirect
425. #125×C₅₃	C₂³	semidirect
428. #124×C₅₃	C₂³	semidirect
432. #123×C₅₃	C₂³	semidirect
433. #123×C₅₃	C₂³	semidirect
438. C₂²⋊Q₈×C₅₃	C₂³	semidirect
439. C₂²⋊Q₈×C₅₃	C₂³	semidirect
447. C₄×Q₈×C₅₃	C₂³	semidirect
448. C₄×Q₈×C₅₃	C₂³	semidirect
449. C₄×Q₈×C₅₃	C₂³	semidirect
450. C₄×Q₈×C₅₃	C₂³	semidirect
455. C₄×D₄×C₅₃	C₂³	semidirect
456. C₄×D₄×C₅₃	C₂³	semidirect
457. C₄×D₄×C₅₃	C₂³	semidirect
458. C₄×D₄×C₅₃	C₂³	semidirect
464. #117×C₅₃	C₂³	semidirect
471. C₂×C₄²×C₅₃	C₂³	semidirect
529. C₂×D₂₁₂	#41	semidirect
813. #3455	D₅₃	semidirect
890. #542	C₂×D₅₃	semidirect
891. #542	C₂×D₅₃	semidirect
893. #541	C₂×D₅₃	semidirect
897. #540	C₂×D₅₃	semidirect
902. #539	C₂×D₅₃	semidirect
903. #539	C₂×D₅₃	semidirect
916. #538	C₂×D₅₃	semidirect
917. #538	C₂×D₅₃	semidirect
924. #533	C₂×D₅₃	semidirect
928. #532	C₂×D₅₃	semidirect
936. #529	C₂×D₅₃	semidirect
937. #529	C₂×D₅₃	semidirect
946. #525	C₂×D₅₃	semidirect
967. C₄×#41	C₂×D₅₃	semidirect
978. C₂×#117	C₂×D₅₃	semidirect
981. C₅₃	#62846	semidirect
1015. C₄⋊Q₈	C₂²×D₅₃	semidirect
1016. C₄⋊Q₈	C₂²×D₅₃	semidirect
1017. C₄⋊Q₈	C₂²×D₅₃	semidirect
1021. #127	C₂²×D₅₃	semidirect
1036. #126	C₂²×D₅₃	semidirect
1037. #126	C₂²×D₅₃	semidirect
1044. #125	C₂²×D₅₃	semidirect
1045. #125	C₂²×D₅₃	semidirect
1046. #125	C₂²×D₅₃	semidirect
1061. #124	C₂²×D₅₃	semidirect
1084. #123	C₂²×D₅₃	semidirect
1085. #123	C₂²×D₅₃	semidirect
1109. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1110. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1165. C₄×Q₈	C₂²×D₅₃	semidirect
1166. C₄×Q₈	C₂²×D₅₃	semidirect
1167. C₄×Q₈	C₂²×D₅₃	semidirect
1168. C₄×Q₈	C₂²×D₅₃	semidirect
1218. C₄×D₄	C₂²×D₅₃	semidirect
1219. C₄×D₄	C₂²×D₅₃	semidirect
1220. C₄×D₄	C₂²×D₅₃	semidirect
1221. C₄×D₄	C₂²×D₅₃	semidirect
1240. #117	C₂²×D₅₃	semidirect
1274. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20288789	2
#20288787	2
#20288749	2
#20288745	2
#20288678	2
#20288674	2
#20288661	2
#20288659	2
#20288569	2
#20288564	2
#20288547	2
#20288516	2
#20288477	2
#20288432	2
#20288401	2
#20288348	2
#20288131	2
#20288123	2
#20288105	2
#538×D₅₃	2
C₄×#13133263	2
C₂×#16811097	2
C₅₃×#3455	2
#62846	53