Subgroups — #28292806

Order 13568.

7330 conjugacy classes of subgroups.

The subgroup lattice has 1728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289278	C₂	1	4	yes	maximal, complemented
2	#20289276	C₂	1	4	yes	maximal, complemented
3	#20289233	C₂	1	4	yes	maximal, complemented
4	#20289224	C₂	1	4	yes	maximal, complemented
5	#20289062	C₂	1	8	yes	maximal, complemented
6	#20288673	C₂	1	4	yes	maximal, complemented
7	#20288671	C₂	1	4	yes	maximal, complemented
8	#20288670	C₂	1	4	yes	maximal, complemented
9	#20288669	C₂	1	4	yes	maximal, complemented
10	#20288614	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288611	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288610	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288609	C₂	1	1	yes	maximal, characteristic, complemented
14	#20288509	C₂	1	1	yes	maximal, characteristic, complemented
15	#20288503	C₂	1	1	yes	maximal, characteristic, complemented
16	#20288502	C₂	1	1	yes	maximal, characteristic, complemented
17	#20288397	C₂	1	8	yes	maximal, complemented
18	#20288364	C₂	1	1	yes	maximal, characteristic, complemented
19	#20288363	C₂	1	1	yes	maximal, characteristic, complemented
20	#20288349	C₂	1	1	yes	maximal, characteristic, complemented
21	#20288346	C₂	1	1	yes	maximal, characteristic, complemented
22	#20288010	C₂	1	1	yes	maximal, characteristic, complemented
23	#20288008	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#124×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3500	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#13133264	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
28	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
29	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
30	#16811374	C₂²	1	8	yes	complemented
31	#16811370	C₂²	1	8	yes	complemented
32	#16811368	C₂²	1	8	yes	complemented
33	#16811366	C₂²	1	8	yes	complemented
34	#16811359	C₂²	1	4	yes	complemented
35	#16811356	C₂²	1	4	yes	complemented
36	#16811355	C₂²	1	4	yes	complemented
37	#16811355	C₂²	1	4	yes	complemented
38	#16811347	C₂²	1	4	yes	complemented
39	#16811345	C₂²	1	4	yes	complemented
40	#16811342	C₂²	1	4	yes	complemented
41	#16811342	C₂²	1	4	yes	complemented
42	#16811337	C₂²	1	8	yes	complemented
43	#16811335	C₂²	1	8	yes	complemented
44	#16811304	C₂²	1	8	yes	complemented
45	#16811303	C₂²	1	8	yes	complemented
46	#16811302	C₂²	1	8	yes	complemented
47	#16811302	C₂²	1	8	yes	complemented
48	#16811302	C₂²	1	8	yes	complemented
49	#16811301	C₂²	1	8	yes	complemented
50	#16811300	C₂²	1	8	yes	complemented
51	#16811299	C₂²	1	8	yes	complemented
52	#16811299	C₂²	1	8	yes	complemented
53	#16811296	C₂²	1	8	yes	complemented
54	#16811288	C₂²	1	4	yes	complemented
55	Q₈×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
56	Q₈×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
57	#16811286	C₂²	1	4	yes	complemented
58	#16811284	C₂²	1	4	yes	complemented
59	#16811283	C₂²	1	4	yes	complemented
60	#16811282	C₂²	1	4	yes	complemented
61	#16811281	C₂²	1	4	yes	complemented
62	#16811280	C₂²	1	4	yes	complemented
63	#16811280	C₂²	1	4	yes	complemented
64	#16811280	C₂²	1	4	yes	complemented
65	#16811270	C₂²	1	4	yes	complemented
66	#16811270	C₂²	1	8	yes	complemented
67	#16811269	C₂²	1	4	yes	complemented
68	#16811267	C₂²	1	8	yes	complemented
69	#16811267	C₂²	1	4	yes	complemented
70	#16811266	C₂²	1	4	yes	complemented
71	#16811263	C₂²	1	8	yes	complemented
72	#16811262	C₂²	1	8	yes	complemented
73	#16811262	C₂²	1	8	yes	complemented
74	#16811261	C₂²	1	4	yes	complemented
75	#16811261	C₂²	1	4	yes	complemented
76	#16811261	C₂²	1	8	yes	complemented
77	#16811261	C₂²	1	4	yes	complemented
78	#16811260	C₂²	1	8	yes	complemented
79	#16811258	C₂²	1	4	yes	complemented
80	#16811257	C₂²	1	4	yes	complemented
81	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
82	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
83	#16811248	C₂²	1	8	yes	complemented
84	#16811246	C₂²	1	4	yes	complemented
85	#16811244	C₂²	1	4	yes	complemented
86	#16811243	C₂²	1	8	yes	complemented
87	#16811242	C₂²	1	4	yes	complemented
88	#16811241	C₂²	1	8	yes	complemented
89	#16811240	C₂²	1	4	yes	complemented
90	#16811238	C₂²	1	8	yes	complemented
91	#16811237	C₂²	1	8	yes	complemented
92	#16811211	C₂²	1	8	yes	complemented
93	#16811210	C₂²	1	8	yes	complemented
94	#16811209	C₂²	1	8	yes	complemented
95	#16811208	C₂²	1	8	yes	complemented
96	#16811207	C₂²	1	8	yes	complemented
97	#16811205	C₂²	1	8	yes	complemented
98	#16811205	C₂²	1	8	yes	complemented
99	#16811205	C₂²	1	8	yes	complemented
100	#16811198	C₂²	1	2	yes	complemented
101	#16811197	C₂²	1	1	yes	characteristic, complemented
102	#16811197	C₂²	1	2	yes	complemented
103	#16811195	C₂²	1	4	yes	complemented
104	#16811194	C₂²	1	4	yes	complemented
105	#16811194	C₂²	1	1	yes	characteristic, complemented
106	#16811194	C₂²	1	1	yes	characteristic, complemented
107	#16811194	C₂²	1	2	yes	complemented
108	#16811190	C₂²	1	1	yes	characteristic
109	#16811190	C₂²	1	2	yes	complemented
110	#16811187	C₂²	1	1	yes	characteristic
111	#16811187	C₂²	1	1	yes	characteristic
112	#16811187	C₂²	1	2	yes	complemented
113	#16811186	C₂²	1	2	yes	complemented
114	#16811183	C₂²	1	4	yes	complemented
115	#16811183	C₂²	1	8	yes	complemented
116	#16811182	C₂²	1	4	yes	complemented
117	#16811180	C₂²	1	1	yes	characteristic, complemented
118	#16811178	C₂²	1	2	yes	complemented
119	#16811177	C₂²	1	2	yes	complemented
120	#16811176	C₂²	1	1	yes	characteristic, complemented
121	#16811172	C₂²	1	2	yes	complemented
122	#16811171	C₂²	1	2	yes	complemented
123	#16811170	C₂²	1	2	yes	complemented
124	#16811169	C₂²	1	1	yes	characteristic, complemented
125	#16811169	C₂²	1	2	yes	complemented
126	#16811169	C₂²	1	2	yes	complemented
127	#16811160	C₂²	1	2	yes	complemented
128	#16811159	C₂²	1	4	yes	complemented
129	#16811157	C₂²	1	4	yes	complemented
130	#16811155	C₂²	1	2	yes	complemented
131	#16811155	C₂²	1	4	yes	complemented
132	#16811154	C₂²	1	4	yes	complemented
133	#16811154	C₂²	1	4	yes	complemented
134	#16811153	C₂²	1	4	yes	complemented
135	#16811152	C₂²	1	4	yes	complemented
136	#16811152	C₂²	1	2	yes	complemented
137	#16811152	C₂²	1	2	yes	complemented
138	#16811151	C₂²	1	4	yes	complemented
139	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
140	C₂×#13133206	C₂²	1	2	yes	complemented
141	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
142	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
143	C₂×#13133204	C₂²	1	2	yes	complemented
144	C₂×#13133203	C₂²	1	4	yes	complemented
145	#124×D₅₃	C₂²	1	4	yes	complemented
146	#124×D₅₃	C₂²	1	4	yes	complemented
147	#124×D₅₃	C₂²	1	4	yes	complemented
148	#124×D₅₃	C₂²	1	4	yes	complemented
149	#124×D₅₃	C₂²	1	2	yes	complemented
150	#16811135	C₂²	1	1	yes	characteristic, complemented
151	#16811133	C₂²	1	4	yes	complemented
152	#16811132	C₂²	1	4	yes	complemented
153	#16811131	C₂²	1	4	yes	complemented
154	#16811130	C₂²	1	1	yes	characteristic, complemented
155	#16811130	C₂²	1	1	yes	characteristic, complemented
156	#16811130	C₂²	1	1	yes	characteristic, complemented
157	#16811130	C₂²	1	4	yes	complemented
158	C₂×#13133185	C₂²	1	4	yes	complemented
159	#120×D₅₃	C₂²	1	4	yes	complemented
160	#16811101	C₂²	1	1	yes	characteristic, complemented
161	#16811100	C₂²	1	1	yes	characteristic, complemented
162	#16811098	C₂²	1	1	yes	characteristic, complemented
163	#16811097	C₂²	1	1	yes	characteristic, complemented
164	#16811096	C₂²	1	8	yes	complemented
165	#16811095	C₂²	1	8	yes	complemented
166	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
167	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
169	C₄×#11719945	C₂²	1	4	yes	complemented
170	C₄×#11719947	C₂²	1	4	yes	complemented
171	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
172	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#548	C₂²	1	4	yes	complemented
176	C₅₃×#546	C₂²	1	8	yes	complemented
177	C₅₃×#546	C₂²	1	4	yes	complemented
178	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#536	C₂²	1	2	yes	complemented
180	C₅₃×#535	C₂²	1	1	yes	characteristic
181	C₅₃×#535	C₂²	1	2	yes	complemented
182	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#532	C₂²	1	2	yes	complemented
184	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
186	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	2	yes	—
188	#13133264	—	4	4	no	—
189	#13133263	—	4	4	no	—
190	C₂×#11719949	C₂³	1	2	yes	—
191	C₂×#11719945	C₂³	1	1	yes	characteristic
192	C₂×#11719945	C₂³	1	2	yes	—
193	C₂×#11719945	C₂³	1	4	yes	—
194	C₂×#11719945	C₂³	1	2	yes	complemented
195	C₂×#11719947	C₂³	1	4	yes	—
196	C₂×#11719947	C₂³	1	4	yes	—
197	C₂×#11719947	C₂³	1	2	yes	complemented
198	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
199	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
200	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
201	C₂×Q₈×D₅₃	—	4	4	no	—
202	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
203	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
204	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
205	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
206	C₂²×D₂₁₂	C₂³	1	2	yes	—
207	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
208	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
209	C₂×D₄×D₅₃	—	4	4	no	—
210	C₂×D₄×D₅₃	C₂³	1	4	yes	—
211	C₂×D₄×D₅₃	C₂³	1	8	yes	—
212	C₂×D₄×D₅₃	C₂³	1	4	yes	—
213	C₂×D₄×D₅₃	C₂³	1	4	yes	—
214	C₂×D₄×D₅₃	C₂³	1	2	yes	—
215	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
217	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
218	#13133217	C₂³	1	2	yes	complemented
219	#13133216	C₂³	1	8	yes	complemented
220	#13133216	C₂³	1	2	yes	complemented
221	#13133215	C₂³	1	2	yes	complemented
222	#13133215	C₂³	1	8	yes	complemented
223	#13133215	C₂³	1	2	yes	complemented
224	#13133215	C₂³	1	2	yes	complemented
225	#13133215	C₂³	1	1	yes	characteristic, complemented
226	#13133213	C₂³	1	2	yes	—
227	#13133213	C₂³	1	2	yes	—
228	#13133213	C₂³	1	2	yes	—
229	#13133213	C₂³	1	1	yes	characteristic, complemented
230	#13133212	C₂³	1	8	yes	complemented
231	#13133212	C₂³	1	8	yes	complemented
232	#13133212	C₂³	1	8	yes	complemented
233	#13133212	C₂³	1	4	yes	complemented
234	#13133211	C₂³	1	8	yes	complemented
235	#13133210	C₂³	1	8	yes	complemented
236	#13133210	C₂³	1	8	yes	complemented
237	#13133210	C₂³	1	8	yes	complemented
238	#13133210	C₂³	1	8	yes	complemented
239	#13133210	C₂³	1	4	yes	complemented
240	#13133210	C₂³	1	4	yes	complemented
241	#13133210	C₂³	1	4	yes	complemented
242	#13133209	C₂³	1	2	yes	complemented
243	#13133208	C₂³	1	4	yes	complemented
244	#13133208	C₂³	1	2	yes	complemented
245	#13133207	C₂³	1	4	yes	complemented
246	#13133206	C₂³	1	4	yes	—
247	#13133206	C₂³	1	2	yes	—
248	#13133206	C₂³	1	2	yes	—
249	#13133206	C₂³	1	2	yes	—
250	#13133206	C₂³	1	2	yes	—
251	#13133206	C₂³	1	2	yes	complemented
252	#13133206	C₂³	1	8	yes	complemented
253	#13133206	C₂³	1	1	yes	characteristic, complemented
254	#13133205	C₂³	1	4	yes	—
255	#13133205	C₂³	1	2	yes	—
256	#13133205	C₂³	1	2	yes	—
257	#13133204	C₂³	1	4	yes	—
258	#13133204	C₂³	1	2	yes	—
259	#13133204	C₂³	1	2	yes	—
260	#13133204	C₂³	1	2	yes	—
261	#13133204	C₂³	1	8	yes	complemented
262	#13133204	C₂³	1	8	yes	complemented
263	#13133204	C₂³	1	8	yes	complemented
264	#13133204	C₂³	1	2	yes	complemented
265	#13133204	C₂³	1	2	yes	complemented
266	#13133204	C₂³	1	4	yes	complemented
267	#13133204	C₂³	1	1	yes	characteristic, complemented
268	#13133203	C₂³	1	8	yes	—
269	#13133203	C₂³	1	8	yes	—
270	#13133203	C₂³	1	8	yes	—
271	#13133203	C₂³	1	8	yes	—
272	#13133203	C₂³	1	8	yes	complemented
273	#13133203	C₂³	1	8	yes	complemented
274	#13133203	C₂³	1	8	yes	complemented
275	#13133203	C₂³	1	8	yes	complemented
276	#13133203	C₂³	1	8	yes	complemented
277	#13133203	C₂³	1	4	yes	complemented
278	#13133202	C₂³	1	4	yes	—
279	#13133202	C₂³	1	8	yes	complemented
280	#13133201	C₂³	1	2	yes	—
281	#13133201	C₂³	1	8	yes	complemented
282	#13133201	C₂³	1	8	yes	complemented
283	#13133200	C₂³	1	4	yes	—
284	#13133200	C₂³	1	8	yes	—
285	#13133200	C₂³	1	8	yes	complemented
286	#13133200	C₂³	1	8	yes	complemented
287	#13133199	C₂³	1	8	yes	—
288	#13133199	C₂³	1	4	yes	—
289	#13133199	C₂³	1	4	yes	—
290	#13133199	C₂³	1	4	yes	—
291	#13133199	C₂³	1	8	yes	complemented
292	#13133199	C₂³	1	8	yes	complemented
293	#13133199	C₂³	1	8	yes	complemented
294	#13133198	C₂³	1	4	yes	—
295	#13133198	C₂³	1	4	yes	—
296	#13133198	C₂³	1	2	yes	—
297	#13133198	C₂³	1	2	yes	—
298	#13133198	C₂³	1	2	yes	—
299	#13133198	C₂³	1	8	yes	complemented
300	#13133198	C₂³	1	8	yes	complemented
301	#13133198	C₂³	1	8	yes	complemented
302	#13133197	C₂³	1	2	yes	—
303	#13133197	C₂³	1	4	yes	—
304	#13133197	C₂³	1	8	yes	complemented
305	#13133196	C₂³	1	4	yes	—
306	#13133196	C₂³	1	4	yes	complemented
307	#13133196	C₂³	1	8	yes	complemented
308	#13133196	C₂³	1	4	yes	complemented
309	#13133196	C₂³	1	8	yes	complemented
310	#13133196	C₂³	1	8	yes	complemented
311	#13133195	C₂³	1	8	yes	—
312	#13133195	C₂³	1	4	yes	—
313	#13133195	C₂³	1	8	yes	complemented
314	#13133195	C₂³	1	8	yes	complemented
315	#13133195	C₂³	1	8	yes	complemented
316	#13133194	C₂³	1	4	yes	—
317	#13133194	C₂³	1	8	yes	complemented
318	#13133194	C₂³	1	8	yes	complemented
319	#13133194	C₂³	1	8	yes	complemented
320	#13133193	C₂³	1	2	yes	—
321	#13133193	C₂³	1	8	yes	—
322	#13133193	C₂³	1	2	yes	—
323	#13133193	C₂³	1	2	yes	—
324	#13133193	C₂³	1	4	yes	complemented
325	#13133193	C₂³	1	8	yes	complemented
326	#13133192	C₂³	1	2	yes	—
327	#13133191	C₂³	1	4	yes	—
328	#13133191	C₂³	1	4	yes	—
329	#13133191	C₂³	1	8	yes	complemented
330	#13133190	C₂³	1	8	yes	—
331	#13133190	C₂³	1	8	yes	—
332	#13133190	C₂³	1	4	yes	—
333	#13133190	C₂³	1	8	yes	complemented
334	#13133189	C₂³	1	4	yes	—
335	#13133189	C₂³	1	8	yes	—
336	#13133189	C₂³	1	8	yes	—
337	#13133189	C₂³	1	8	yes	complemented
338	#13133189	C₂³	1	8	yes	complemented
339	#13133189	C₂³	1	8	yes	complemented
340	#13133188	C₂³	1	4	yes	—
341	#13133188	C₂³	1	8	yes	—
342	#13133188	C₂³	1	8	yes	—
343	#13133188	C₂³	1	2	yes	—
344	#13133188	C₂³	1	2	yes	—
345	#13133188	C₂³	1	2	yes	—
346	#13133188	C₂³	1	4	yes	—
347	#13133188	C₂³	1	8	yes	complemented
348	#13133187	C₂³	1	8	yes	—
349	#13133187	C₂³	1	2	yes	—
350	#13133186	C₂³	1	4	yes	—
351	#13133186	C₂³	1	8	yes	—
352	#13133186	C₂³	1	8	yes	complemented
353	#13133185	C₂³	1	8	yes	—
354	#13133185	C₂³	1	8	yes	—
355	#13133185	C₂³	1	4	yes	—
356	#13133185	C₂³	1	4	yes	—
357	#13133185	C₂³	1	8	yes	—
358	#13133185	C₂³	1	8	yes	—
359	#13133185	C₂³	1	2	yes	—
360	#13133185	C₂³	1	2	yes	—
361	#13133185	C₂³	1	2	yes	—
362	#13133185	C₂³	1	8	yes	complemented
363	#13133185	C₂³	1	8	yes	complemented
364	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
365	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
366	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
367	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
368	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
369	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
370	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
371	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
372	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
373	#13133182	C₂³	1	4	yes	complemented
374	#13133182	C₂³	1	4	yes	complemented
375	C₄×D₂₁₂	C₂³	1	4	yes	—
376	C₄×D₂₁₂	C₂³	1	4	yes	—
377	C₄×D₂₁₂	C₂³	1	4	yes	—
378	C₄×D₂₁₂	C₂³	1	2	yes	complemented
379	D₄×Dic₅₃	C₂³	1	4	yes	—
380	D₄×Dic₅₃	C₂³	1	4	yes	—
381	D₄×Dic₅₃	C₂³	1	4	yes	—
382	D₄×Dic₅₃	C₂³	1	4	yes	—
383	D₄×Dic₅₃	C₂³	1	2	yes	complemented
384	D₄×Dic₅₃	C₂³	1	8	yes	complemented
385	D₄×Dic₅₃	C₂³	1	4	yes	complemented
386	D₄×Dic₅₃	C₂³	1	2	yes	complemented
387	#13133179	C₂³	1	8	yes	—
388	#13133179	C₂³	1	4	yes	—
389	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
390	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
391	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
392	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
393	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
394	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
395	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
396	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
397	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
398	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
399	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
400	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
401	#13133177	C₂³	1	8	yes	—
402	#13133177	C₂³	1	4	yes	—
403	#13133177	C₂³	1	4	yes	—
404	#13133177	C₂³	1	8	yes	complemented
405	#13133177	C₂³	1	8	yes	complemented
406	#13133177	C₂³	1	8	yes	complemented
407	#13133176	C₂³	1	4	yes	—
408	#13133176	C₂³	1	1	yes	characteristic
409	#13133176	C₂³	1	1	yes	characteristic
410	#13133176	C₂³	1	1	yes	characteristic
411	#13133176	C₂³	1	4	yes	complemented
412	#13133176	C₂³	1	2	yes	complemented
413	#13133176	C₂³	1	2	yes	complemented
414	#13133175	C₂³	1	4	yes	—
415	#13133175	C₂³	1	8	yes	complemented
416	#13133174	C₂³	1	4	yes	—
417	#13133174	C₂³	1	4	yes	complemented
418	#13133174	C₂³	1	8	yes	complemented
419	#13133174	C₂³	1	2	yes	complemented
420	#13133173	C₂³	1	4	yes	—
421	#13133173	C₂³	1	4	yes	complemented
422	#13133173	C₂³	1	8	yes	complemented
423	#13133173	C₂³	1	8	yes	complemented
424	#13133173	C₂³	1	4	yes	complemented
425	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
426	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
427	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
428	C₂×#11719921	C₂³	1	4	yes	—
429	C₂×#11719921	C₂³	1	8	yes	—
430	C₂×#11719921	C₂³	1	4	yes	—
431	C₂×#11719921	C₂³	1	8	yes	complemented
432	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
433	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
434	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
435	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
436	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
437	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
438	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
439	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
440	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
441	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
442	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
443	C₄²×D₅₃	C₂³	1	2	yes	—
444	C₄²×D₅₃	C₂³	1	2	yes	—
445	C₄²×D₅₃	C₂³	1	2	yes	—
446	C₄²×D₅₃	C₂³	1	2	yes	—
447	C₄²×D₅₃	C₂³	1	2	yes	complemented
448	2₋¹⁺⁴×C₅₃	—	4	4	no	—
449	H(5,𝔽₂)×C₅₃	—	4	4	no	—
450	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
451	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
452	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
453	C₂×#41×C₅₃	C₂³	1	2	yes	—
454	C₂×#41×C₅₃	C₂³	1	4	yes	—
455	C₂×#41×C₅₃	C₂³	1	2	yes	—
456	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
457	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
458	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
459	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
460	C₂²×Q₈×C₅₃	C₂³	1	2	yes	complemented
461	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
462	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
463	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
464	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
465	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
466	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
467	#127×C₅₃	C₂³	1	2	yes	—
468	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
469	#124×C₅₃	C₂³	1	2	yes	—
470	#124×C₅₃	C₂³	1	2	yes	—
471	#124×C₅₃	C₂³	1	2	yes	—
472	#124×C₅₃	C₂³	1	4	yes	—
473	#124×C₅₃	C₂³	1	2	yes	complemented
474	#124×C₅₃	C₂³	1	8	yes	complemented
475	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
476	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
477	#123×C₅₃	C₂³	1	4	yes	—
478	#123×C₅₃	C₂³	1	8	yes	complemented
479	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
480	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
481	#121×C₅₃	C₂³	1	4	yes	—
482	#121×C₅₃	C₂³	1	4	yes	—
483	#121×C₅₃	C₂³	1	8	yes	complemented
484	#121×C₅₃	C₂³	1	8	yes	complemented
485	#120×C₅₃	C₂³	1	4	yes	—
486	#120×C₅₃	C₂³	1	8	yes	complemented
487	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
488	C₄×D₄×C₅₃	C₂³	1	4	yes	—
489	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
490	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
491	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
492	#117×C₅₃	C₂³	1	1	yes	characteristic
493	#117×C₅₃	C₂³	1	2	yes	complemented
494	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
495	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
496	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
497	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
498	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
499	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
500	C₂³×D₅₃	—	4	8	no	—
501	C₂³×D₅₃	—	4	4	no	—
502	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
503	C₂³×D₅₃	C₂⁴	1	8	yes	—
504	C₂³×D₅₃	C₂⁴	1	2	yes	—
505	C₂³×D₅₃	C₂⁴	1	4	yes	—
506	#41×C₅₃	—	2	4	no	—
507	#41×C₅₃	—	2	4	no	—
508	#41×C₅₃	—	2	4	no	—
509	#41×C₅₃	—	4	8	no	—
510	#41×C₅₃	—	4	4	no	—
511	#41×C₅₃	—	4	4	no	—
512	#41×C₅₃	—	4	4	no	—
513	#41×C₅₃	—	4	4	no	—
514	C₂×Q₈×C₅₃	—	2	4	no	—
515	C₂×Q₈×C₅₃	—	4	4	no	—
516	C₂×Q₈×C₅₃	—	4	4	no	—
517	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
518	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
519	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
520	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
522	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
523	C₂×D₄×C₅₃	—	2	4	no	—
524	C₂×D₄×C₅₃	—	4	4	no	—
525	C₂×D₄×C₅₃	—	4	4	no	—
526	C₂×D₄×C₅₃	—	4	8	no	—
527	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
528	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
529	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
530	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
531	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
532	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
533	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
536	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
537	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
538	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
539	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
540	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
541	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
542	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
543	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
544	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
545	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
546	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
547	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
548	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
549	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
550	C₂×C₂²⋊D₅₃	—	4	4	no	—
551	C₂×C₂²⋊D₅₃	—	4	16	no	—
552	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
553	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
554	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
555	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
556	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
557	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
558	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
559	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
560	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
561	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
562	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
563	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
564	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
565	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
566	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
567	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
568	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
569	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
570	#11719949	—	4	4	no	—
571	Q₈×D₅₃	—	4	8	no	—
572	Q₈×D₅₃	—	4	8	no	—
573	Q₈×D₅₃	—	4	4	no	—
574	#11719947	—	4	4	no	—
575	#11719947	—	4	8	no	—
576	#11719947	—	4	8	no	—
577	D₄×D₅₃	—	4	8	no	—
578	D₄×D₅₃	—	4	8	no	—
579	D₄×D₅₃	—	4	4	no	—
580	D₄×D₅₃	—	4	16	no	—
581	D₄×D₅₃	—	4	8	no	—
582	#11719945	—	2	4	no	—
583	#11719945	—	4	4	no	—
584	#11719945	—	4	4	no	—
585	#11719945	—	4	8	no	—
586	C₂×D₂₁₂	—	2	4	no	—
587	C₂×D₂₁₂	—	4	4	no	—
588	C₂×D₂₁₂	C₂⁴	1	4	yes	—
589	C₂×D₂₁₂	C₂⁴	1	2	yes	—
590	C₂×D₂₁₂	C₂⁴	1	2	yes	—
591	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
592	C₂×D₂₁₂	C₂⁴	1	4	yes	—
593	C₂×C₄×D₅₃	—	2	4	no	—
594	C₂×C₄×D₅₃	—	4	4	no	—
595	C₂×C₄×D₅₃	—	4	4	no	—
596	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
597	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
598	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
599	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
600	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
601	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
602	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
603	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
604	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
605	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
606	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
607	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
608	C₂×Dic₁₀₆	—	2	4	no	—
609	C₂×Dic₁₀₆	—	4	4	no	—
610	C₂×Dic₁₀₆	—	4	4	no	—
611	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
612	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
613	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
614	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
615	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
616	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
617	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
618	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
619	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
620	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
621	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
622	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
623	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
624	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
625	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
626	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
627	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
628	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
629	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
630	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
631	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
632	C₄²×C₅₃	C₂⁴	1	2	yes	—
633	C₄²×C₅₃	C₂⁴	1	2	yes	—
634	C₄²×C₅₃	C₂⁴	1	4	yes	—
635	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
636	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
637	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
638	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
639	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
640	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
641	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
642	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
643	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
644	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
645	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
646	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
647	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
648	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
649	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
650	#11719921	C₂⁴	1	8	yes	—
651	#11719921	C₂⁴	1	8	yes	—
652	#11719921	C₂⁴	1	8	yes	—
653	#11719921	C₂⁴	1	8	yes	—
654	#11719921	C₂⁴	1	4	yes	—
655	#11719921	C₂⁴	1	4	yes	—
656	#11719921	C₂⁴	1	8	yes	—
657	#11719921	C₂⁴	1	8	yes	—
658	#11719921	C₂⁴	1	4	yes	—
659	#11719921	C₂⁴	1	4	yes	—
660	#11719921	C₂⁴	1	8	yes	—
661	#11719921	C₂⁴	1	4	yes	—
662	#11719921	C₂⁴	1	8	yes	—
663	#11719921	C₂⁴	1	4	yes	—
664	#11719921	C₂⁴	1	4	yes	—
665	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
666	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
667	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
668	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
669	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
670	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
671	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
672	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
673	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
674	#11719919	C₂⁴	1	8	yes	—
675	#11719919	C₂⁴	1	4	yes	—
676	#11719919	C₂⁴	1	4	yes	—
677	#11719919	C₂⁴	1	4	yes	—
678	#11719919	C₂⁴	1	8	yes	—
679	#11719919	C₂⁴	1	8	yes	—
680	#11719919	C₂⁴	1	4	yes	—
681	#11719919	C₂⁴	1	4	yes	—
682	#11719919	C₂⁴	1	4	yes	—
683	#11719919	C₂⁴	1	4	yes	—
684	#11719919	C₂⁴	1	8	yes	—
685	#11719919	C₂⁴	1	4	yes	—
686	#11719919	C₂⁴	1	4	yes	—
687	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
688	C₄×Dic₅₃	C₂⁴	1	2	yes	—
689	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
690	C₄×Dic₅₃	C₂⁴	1	2	yes	—
691	C₄×Dic₅₃	C₂⁴	1	2	yes	—
692	C₄×Dic₅₃	C₂⁴	1	2	yes	—
693	C₄×Dic₅₃	C₂⁴	1	2	yes	—
694	C₄×Dic₅₃	C₂⁴	1	4	yes	—
695	C₄×Dic₅₃	C₂⁴	1	2	yes	—
696	C₄×Dic₅₃	C₂⁴	1	4	yes	—
697	C₄×Dic₅₃	C₂⁴	1	4	yes	—
698	C₄×Dic₅₃	C₂⁴	1	2	yes	—
699	C₄×Dic₅₃	C₂⁴	1	2	yes	—
700	C₄×Dic₅₃	C₂⁴	1	8	yes	—
701	C₄×Dic₅₃	C₂⁴	1	8	yes	—
702	C₂³×C₅₃	—	2	4	no	—
703	C₂³×C₅₃	—	4	4	no	—
704	C₂³×C₅₃	—	4	8	no	—
705	C₂³×C₅₃	—	4	4	no	—
706	C₂³×C₅₃	C₂⁵	1	2	yes	—
707	C₂³×C₅₃	C₂⁵	1	2	yes	—
708	C₂³×C₅₃	C₂⁵	1	4	yes	—
709	C₂³×C₅₃	C₂⁵	1	2	yes	—
710	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
711	C₂²×D₅₃	—	2	2	no	—
712	C₂²×D₅₃	—	2	4	no	—
713	C₂²×D₅₃	—	2	4	no	—
714	C₂²×D₅₃	—	2	16	no	—
715	C₂²×D₅₃	—	4	8	no	—
716	C₂²×D₅₃	—	4	8	no	—
717	C₂²×D₅₃	—	4	4	no	—
718	C₂²×D₅₃	—	4	4	no	—
719	C₂²×D₅₃	—	4	8	no	—
720	C₂²×D₅₃	—	8	16	no	—
721	C₂²×D₅₃	C₂⁵	1	2	yes	—
722	C₂²×D₅₃	C₂⁵	1	4	yes	—
723	C₂²×D₅₃	C₂⁵	1	2	yes	—
724	Q₈×C₅₃	—	2	4	no	—
725	Q₈×C₅₃	—	2	4	no	—
726	Q₈×C₅₃	—	2	2	no	—
727	Q₈×C₅₃	—	2	2	no	—
728	Q₈×C₅₃	—	2	2	no	—
729	Q₈×C₅₃	—	4	4	no	—
730	D₄×C₅₃	—	2	4	no	—
731	D₄×C₅₃	—	2	4	no	—
732	D₄×C₅₃	—	2	4	no	—
733	D₄×C₅₃	—	2	4	no	—
734	D₄×C₅₃	—	2	4	no	—
735	D₄×C₅₃	—	2	2	no	—
736	D₄×C₅₃	—	2	2	no	—
737	D₄×C₅₃	—	2	2	no	—
738	D₄×C₅₃	—	4	8	no	—
739	D₄×C₅₃	—	4	4	no	—
740	D₄×C₅₃	—	4	4	no	—
741	D₄×C₅₃	—	4	4	no	—
742	D₄×C₅₃	—	4	4	no	—
743	C₂×C₄×C₅₃	—	2	4	no	—
744	C₂×C₄×C₅₃	—	2	4	no	—
745	C₂×C₄×C₅₃	—	2	4	no	—
746	C₂×C₄×C₅₃	—	2	4	no	—
747	C₂×C₄×C₅₃	—	4	2	no	—
748	C₂×C₄×C₅₃	—	4	4	no	—
749	C₂×C₄×C₅₃	—	4	4	no	—
750	C₂×C₄×C₅₃	—	4	4	no	—
751	C₂×C₄×C₅₃	—	4	4	no	—
752	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
753	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
754	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
755	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
756	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
757	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
758	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
759	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
760	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
761	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
762	C₂²⋊D₅₃	—	2	4	no	—
763	C₂²⋊D₅₃	—	2	8	no	—
764	C₂²⋊D₅₃	—	2	8	no	—
765	C₂²⋊D₅₃	—	2	8	no	—
766	C₂²⋊D₅₃	—	4	4	no	—
767	C₂²⋊D₅₃	—	4	4	no	—
768	C₂²⋊D₅₃	—	4	4	no	—
769	C₂²⋊D₅₃	—	4	8	no	—
770	C₂²⋊D₅₃	—	4	8	no	—
771	C₂²⋊D₅₃	—	4	8	no	—
772	C₂²⋊D₅₃	—	4	8	no	—
773	C₂×Dic₅₃	—	2	4	no	—
774	C₂×Dic₅₃	—	2	2	no	—
775	C₂×Dic₅₃	—	4	4	no	—
776	C₂×Dic₅₃	—	4	2	no	—
777	C₂×Dic₅₃	—	4	4	no	—
778	C₂×Dic₅₃	—	4	4	no	—
779	C₂×Dic₅₃	—	4	8	no	—
780	C₂×Dic₅₃	C₂⁵	1	4	yes	—
781	C₂×Dic₅₃	C₂⁵	1	2	yes	—
782	C₂×Dic₅₃	C₂⁵	1	2	yes	—
783	C₂×Dic₅₃	C₂⁵	1	2	yes	—
784	C₂×Dic₅₃	C₂⁵	1	4	yes	—
785	C₂×Dic₅₃	C₂⁵	1	4	yes	—
786	C₂×Dic₅₃	C₂⁵	1	4	yes	—
787	C₂×Dic₅₃	C₂⁵	1	2	yes	—
788	D₂₁₂	—	2	8	no	—
789	D₂₁₂	—	2	4	no	—
790	D₂₁₂	—	2	4	no	—
791	D₂₁₂	—	2	2	no	—
792	D₂₁₂	—	4	4	no	—
793	C₄×D₅₃	—	2	4	no	—
794	C₄×D₅₃	—	2	4	no	—
795	C₄×D₅₃	—	2	4	no	—
796	C₄×D₅₃	—	2	4	no	—
797	C₄×D₅₃	—	2	4	no	—
798	C₄×D₅₃	—	4	2	no	—
799	C₄×D₅₃	—	4	2	no	—
800	C₄×D₅₃	—	4	8	no	—
801	C₄×D₅₃	—	4	4	no	—
802	C₄×D₅₃	—	4	4	no	—
803	C₄×D₅₃	—	4	4	no	—
804	C₄×D₅₃	—	4	8	no	—
805	Dic₁₀₆	—	2	4	no	—
806	Dic₁₀₆	—	2	4	no	—
807	Dic₁₀₆	—	2	2	no	—
808	Dic₁₀₆	—	4	4	no	—
809	Dic₁₀₆	—	4	8	no	—
810	Dic₁₀₆	—	4	4	no	—
811	Dic₁₀₆	—	4	4	no	—
812	#62824	—	53	1	no	maximal, Sylow
813	C₂²×C₅₃	—	2	2	no	—
814	C₂²×C₅₃	—	2	2	no	—
815	C₂²×C₅₃	—	2	2	no	—
816	C₂²×C₅₃	—	2	4	no	—
817	C₂²×C₅₃	—	2	2	no	—
818	C₂²×C₅₃	—	2	4	no	—
819	C₂²×C₅₃	—	2	4	no	—
820	C₂²×C₅₃	—	2	8	no	—
821	C₂²×C₅₃	—	2	4	no	—
822	C₂²×C₅₃	—	8	4	no	—
823	C₂²×C₅₃	—	16	4	no	—
824	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
825	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
826	C₂×D₅₃	—	2	8	no	—
827	C₂×D₅₃	—	2	2	no	—
828	C₂×D₅₃	—	2	2	no	—
829	C₂×D₅₃	—	2	2	no	—
830	C₂×D₅₃	—	2	4	no	—
831	C₂×D₅₃	—	2	4	no	—
832	C₂×D₅₃	—	2	8	no	—
833	C₂×D₅₃	—	8	16	no	—
834	C₂×D₅₃	—	8	4	no	—
835	C₂×D₅₃	—	16	4	no	—
836	C₂×D₅₃	#585	1	4	yes	—
837	C₄×C₅₃	—	2	2	no	—
838	C₄×C₅₃	—	2	4	no	—
839	C₄×C₅₃	—	2	2	no	—
840	C₄×C₅₃	—	2	2	no	—
841	C₄×C₅₃	—	2	2	no	—
842	C₄×C₅₃	—	2	4	no	—
843	C₄×C₅₃	—	2	2	no	—
844	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
845	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
846	Dic₅₃	—	2	4	no	—
847	Dic₅₃	—	2	2	no	—
848	Dic₅₃	—	2	2	no	—
849	Dic₅₃	—	2	2	no	—
850	Dic₅₃	—	2	4	no	—
851	Dic₅₃	—	2	4	no	—
852	Dic₅₃	—	2	4	no	—
853	Dic₅₃	—	2	2	no	—
854	#3561	—	53	4	no	—
855	#3561	—	53	4	no	—
856	#3558	—	53	4	no	—
857	#3558	—	53	4	no	—
858	#3545	—	53	8	no	—
859	#3514	—	53	4	no	—
860	#3514	—	53	4	no	—
861	#3514	—	53	4	no	—
862	#3514	—	53	4	no	—
863	#3510	—	53	1	no	—
864	#3510	—	53	1	no	—
865	#3510	—	53	1	no	—
866	#3510	—	53	1	no	—
867	#3500	—	53	1	no	—
868	#3500	—	53	1	no	—
869	#3500	—	53	1	no	—
870	#3500	D₅₃	1	1	yes	characteristic, complemented
871	#3490	—	53	8	no	—
872	#3486	—	53	1	no	—
873	#3486	—	53	1	no	—
874	#3484	—	53	1	no	—
875	#3484	—	53	1	no	—
876	#3444	—	53	1	no	—
877	#3444	—	53	1	no	—
878	C₂²×#124	—	53	1	no	—
879	C₂×C₅₃	—	2	2	no	—
880	C₂×C₅₃	—	4	4	no	—
881	C₂×C₅₃	—	4	2	no	—
882	C₂×C₅₃	—	4	2	no	—
883	C₂×C₅₃	—	4	2	no	—
884	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
885	C₂×C₅₃	C₂×#585	1	2	yes	—
886	D₅₃	—	2	4	no	—
887	D₅₃	—	4	4	no	—
888	D₅₃	—	4	2	no	—
889	C₂×2₋¹⁺⁴	—	53	1	no	—
890	C₂×2₋¹⁺⁴	C₂×D₅₃	1	1	yes	characteristic, complemented
891	C₂×H(5,𝔽₂)	—	53	1	no	—
892	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
893	C₂³×Q₈	—	53	1	no	—
894	C₂³×D₄	—	53	1	no	—
895	#563	—	53	8	no	—
896	#562	—	53	8	no	—
897	#562	—	53	8	no	—
898	H(3,𝔽₄)	—	53	8	no	—
899	#559	—	53	4	no	—
900	#559	—	53	4	no	—
901	#559	—	53	4	no	—
902	#559	—	53	4	no	—
903	#556	—	53	4	no	—
904	#556	—	53	4	no	—
905	#556	—	53	4	no	—
906	#556	—	53	4	no	—
907	#555	—	53	8	no	—
908	#555	—	53	8	no	—
909	#551	—	53	8	no	—
910	#551	—	53	8	no	—
911	#551	—	53	8	no	—
912	#551	—	53	8	no	—
913	#551	—	53	8	no	—
914	#551	—	53	8	no	—
915	#551	—	53	8	no	—
916	#551	—	53	8	no	—
917	#551	—	53	8	no	—
918	#551	—	53	8	no	—
919	D₄×Q₈	—	53	4	no	—
920	D₄×Q₈	—	53	4	no	—
921	D₄×Q₈	—	53	4	no	—
922	D₄×Q₈	—	53	4	no	—
923	#548	—	53	4	no	—
924	#548	—	53	4	no	—
925	#548	—	53	4	no	—
926	#548	—	53	4	no	—
927	#548	—	53	4	no	—
928	#548	—	53	4	no	—
929	#548	—	53	4	no	—
930	#548	C₂×D₅₃	1	4	yes	complemented
931	#546	—	53	4	no	—
932	#546	—	53	4	no	—
933	#546	—	53	8	no	—
934	#546	—	53	4	no	—
935	#546	—	53	8	no	—
936	#546	—	53	4	no	—
937	#546	—	53	4	no	—
938	#546	—	53	4	no	—
939	#546	—	53	8	no	—
940	#546	—	53	8	no	—
941	#546	—	53	8	no	—
942	#546	—	53	8	no	—
943	#546	—	53	4	no	—
944	#546	—	53	8	no	—
945	#546	C₂×D₅₃	1	8	yes	complemented
946	#546	C₂×D₅₃	1	4	yes	complemented
947	D₄²	—	53	4	no	—
948	D₄²	—	53	4	no	—
949	D₄²	—	53	4	no	—
950	D₄²	—	53	4	no	—
951	#543	—	53	8	no	—
952	#542	—	53	4	no	—
953	#542	—	53	8	no	—
954	#542	—	53	8	no	—
955	#542	—	53	4	no	—
956	#542	—	53	8	no	—
957	#542	—	53	4	no	—
958	#542	—	53	8	no	—
959	#542	—	53	4	no	—
960	#538	—	53	8	no	—
961	#538	—	53	8	no	—
962	#538	—	53	8	no	—
963	#538	—	53	8	no	—
964	#538	—	53	8	no	—
965	#538	—	53	8	no	—
966	#538	—	53	8	no	—
967	#538	—	53	8	no	—
968	#536	—	53	1	no	—
969	#536	—	53	1	no	—
970	#536	—	53	4	no	—
971	#536	—	53	2	no	—
972	#536	—	53	1	no	—
973	#536	—	53	2	no	—
974	#536	—	53	2	no	—
975	#536	—	53	4	no	—
976	#536	C₂×D₅₃	1	1	yes	characteristic, complemented
977	#536	C₂×D₅₃	1	2	yes	complemented
978	#535	—	53	1	no	—
979	#535	—	53	1	no	—
980	#535	—	53	2	no	—
981	#535	—	53	1	no	—
982	#535	—	53	2	no	—
983	#535	—	53	2	no	—
984	#535	C₂×D₅₃	1	1	yes	characteristic
985	#535	C₂×D₅₃	1	2	yes	complemented
986	#534	—	53	4	no	—
987	#534	—	53	4	no	—
988	#534	—	53	8	no	—
989	#533	—	53	2	no	—
990	#533	—	53	2	no	—
991	#533	—	53	1	no	—
992	#533	—	53	1	no	—
993	#532	—	53	1	no	—
994	#532	—	53	2	no	—
995	#532	—	53	2	no	—
996	#532	—	53	2	no	—
997	#532	—	53	2	no	—
998	#532	—	53	2	no	—
999	#532	C₂×D₅₃	1	1	yes	characteristic, complemented
1000	#532	C₂×D₅₃	1	2	yes	complemented
1001	#529	—	53	4	no	—
1002	#529	—	53	2	no	—
1003	#529	—	53	2	no	—
1004	#529	—	53	4	no	—
1005	#529	—	53	4	no	—
1006	#529	—	53	4	no	—
1007	#529	—	53	2	no	—
1008	#529	—	53	4	no	—
1009	#529	—	53	2	no	—
1010	#529	—	53	4	no	—
1011	#529	—	53	4	no	—
1012	#529	—	53	4	no	—
1013	C₂×#124	—	53	1	no	—
1014	C₂×#124	—	53	2	no	—
1015	C₂×#124	—	53	1	no	—
1016	C₂×#124	—	53	2	no	—
1017	C₂×#124	—	53	4	no	—
1018	C₂×#124	—	53	4	no	—
1019	C₂×#124	—	53	4	no	—
1020	C₂×#124	—	53	4	no	—
1021	C₂×#124	—	53	2	no	—
1022	C₂×#124	—	53	4	no	—
1023	C₂×#124	—	53	1	no	—
1024	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
1025	C₂×#124	C₂×D₅₃	1	2	yes	complemented
1026	#525	—	53	1	no	—
1027	#525	—	53	1	no	—
1028	#525	—	53	1	no	—
1029	#525	—	53	4	no	—
1030	#525	—	53	4	no	—
1031	#525	—	53	4	no	—
1032	#525	—	53	4	no	—
1033	#525	—	53	1	no	—
1034	C₂×#120	—	53	4	no	—
1035	C₂×#120	—	53	4	no	—
1036	#519	—	53	1	no	—
1037	#519	—	53	1	no	—
1038	#518	—	53	1	no	—
1039	#518	—	53	8	no	—
1040	#518	—	53	1	no	—
1041	#518	—	53	8	no	—
1042	C₄×#41	—	53	1	no	—
1043	C₄×#41	—	53	1	no	—
1044	C₄×#41	—	53	4	no	—
1045	C₄×#41	—	53	1	no	—
1046	C₄×#41	—	53	4	no	—
1047	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
1048	C₂²×C₂²⋊C₄	—	53	4	no	—
1049	C₂²×C₄²	—	53	1	no	—
1050	C₅₃	#62824	1	1	yes	characteristic, complemented, Sylow
1051	C₂⁵	—	53	2	no	—
1052	2₋¹⁺⁴	—	4	4	no	—
1053	2₋¹⁺⁴	—	212	4	no	—
1054	H(5,𝔽₂)	—	4	4	no	—
1055	H(5,𝔽₂)	—	212	4	no	—
1056	C₂×#41	—	53	2	no	—
1057	C₂×#41	—	53	4	no	—
1058	C₂×#41	—	53	4	no	—
1059	C₂×#41	—	53	2	no	—
1060	C₂×#41	—	53	1	no	—
1061	C₂×#41	—	53	4	no	—
1062	C₂×#41	—	53	2	no	—
1063	C₂×#41	—	53	2	no	—
1064	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1065	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1066	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1067	C₂×#41	C₂²×D₅₃	1	4	yes	—
1068	C₂×#41	C₂²×D₅₃	1	2	yes	—
1069	C₂×#41	C₂²×D₅₃	1	2	yes	—
1070	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
1071	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
1072	C₂²×Q₈	—	53	4	no	—
1073	C₂²×Q₈	—	53	4	no	—
1074	C₂²×Q₈	—	53	2	no	—
1075	C₂²×Q₈	—	53	1	no	—
1076	C₂²×Q₈	—	53	2	no	—
1077	C₂²×Q₈	—	53	2	no	—
1078	C₂²×Q₈	—	212	4	no	—
1079	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1080	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
1081	C₂²×Q₈	C₂²×D₅₃	1	2	yes	complemented
1082	C₂²×D₄	—	53	8	no	—
1083	C₂²×D₄	—	53	2	no	—
1084	C₂²×D₄	—	53	8	no	—
1085	C₂²×D₄	—	53	4	no	—
1086	C₂²×D₄	—	53	4	no	—
1087	C₂²×D₄	—	53	4	no	—
1088	C₂²×D₄	—	53	2	no	—
1089	C₂²×D₄	—	53	1	no	—
1090	C₂²×D₄	—	53	2	no	—
1091	C₂²×D₄	—	212	4	no	—
1092	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1093	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
1094	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
1095	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
1096	C₂³×C₄	—	53	1	no	—
1097	C₂³×C₄	—	53	2	no	—
1098	C₂³×C₄	—	53	2	no	—
1099	C₄⋊Q₈	—	53	1	no	—
1100	C₄⋊Q₈	—	53	2	no	—
1101	C₄⋊Q₈	—	53	2	no	—
1102	C₄⋊Q₈	—	53	2	no	—
1103	C₄⋊Q₈	—	53	8	no	—
1104	C₄⋊Q₈	—	53	2	no	—
1105	C₄⋊Q₈	—	53	8	no	—
1106	C₄⋊Q₈	—	53	2	no	—
1107	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1108	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1109	#127	—	53	1	no	—
1110	#127	—	53	2	no	—
1111	#127	—	53	2	no	—
1112	#127	—	53	2	no	—
1113	#127	C₂²×D₅₃	1	2	yes	—
1114	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
1115	#126	—	53	4	no	—
1116	#126	—	53	8	no	—
1117	#126	—	53	8	no	—
1118	#126	—	53	8	no	—
1119	#126	—	53	4	no	—
1120	#126	—	53	4	no	—
1121	#126	—	53	4	no	—
1122	#126	—	53	8	no	—
1123	#126	—	53	8	no	—
1124	#126	—	53	8	no	—
1125	#126	—	53	8	no	—
1126	#126	—	53	8	no	—
1127	#125	—	53	2	no	—
1128	#125	—	53	4	no	—
1129	#125	—	53	4	no	—
1130	#125	—	53	2	no	—
1131	#124	—	53	2	no	—
1132	#124	—	53	2	no	—
1133	#124	—	53	4	no	—
1134	#124	—	53	1	no	—
1135	#124	—	53	2	no	—
1136	#124	—	53	2	no	—
1137	#124	—	53	2	no	—
1138	#124	—	53	8	no	—
1139	#124	—	53	2	no	—
1140	#124	—	53	2	no	—
1141	#124	—	53	4	no	—
1142	#124	—	53	1	no	—
1143	#124	—	53	2	no	—
1144	#124	—	53	2	no	—
1145	#124	—	53	2	no	—
1146	#124	—	53	8	no	—
1147	#124	—	53	4	no	—
1148	#124	—	53	8	no	—
1149	#124	—	53	8	no	—
1150	#124	—	53	8	no	—
1151	#124	—	53	8	no	—
1152	#124	—	53	8	no	—
1153	#124	—	53	8	no	—
1154	#124	—	53	8	no	—
1155	#124	—	53	4	no	—
1156	#124	—	53	8	no	—
1157	#124	—	53	8	no	—
1158	#124	—	53	8	no	—
1159	#124	—	53	8	no	—
1160	#124	—	53	2	no	—
1161	#124	—	53	2	no	—
1162	#124	—	53	4	no	—
1163	#124	C₂²×D₅₃	1	2	yes	—
1164	#124	C₂²×D₅₃	1	2	yes	—
1165	#124	C₂²×D₅₃	1	4	yes	—
1166	#124	C₂²×D₅₃	1	2	yes	—
1167	#124	C₂²×D₅₃	1	1	yes	characteristic, complemented
1168	#124	C₂²×D₅₃	1	1	yes	characteristic, complemented
1169	#124	C₂²×D₅₃	1	2	yes	complemented
1170	#124	C₂²×D₅₃	1	8	yes	complemented
1171	#123	—	53	2	no	—
1172	#123	—	53	2	no	—
1173	#123	—	53	2	no	—
1174	#123	—	53	4	no	—
1175	#123	—	53	4	no	—
1176	#123	—	53	8	no	—
1177	#123	—	53	8	no	—
1178	#123	—	53	8	no	—
1179	#123	—	53	4	no	—
1180	#123	—	53	8	no	—
1181	#123	—	53	8	no	—
1182	#123	—	53	8	no	—
1183	#123	—	53	4	no	—
1184	#123	—	53	8	no	—
1185	#123	—	53	2	no	—
1186	#123	—	53	4	no	—
1187	#123	—	53	4	no	—
1188	#123	—	53	4	no	—
1189	#123	—	53	8	no	—
1190	#123	—	53	8	no	—
1191	#123	—	53	8	no	—
1192	#123	—	53	8	no	—
1193	#123	—	53	8	no	—
1194	#123	—	53	8	no	—
1195	#123	C₂²×D₅₃	1	4	yes	—
1196	#123	C₂²×D₅₃	1	8	yes	complemented
1197	C₂²⋊Q₈	—	53	2	no	—
1198	C₂²⋊Q₈	—	53	2	no	—
1199	C₂²⋊Q₈	—	53	2	no	—
1200	C₂²⋊Q₈	—	53	8	no	—
1201	C₂²⋊Q₈	—	53	4	no	—
1202	C₂²⋊Q₈	—	53	8	no	—
1203	C₂²⋊Q₈	—	53	4	no	—
1204	C₂²⋊Q₈	—	53	4	no	—
1205	C₂²⋊Q₈	—	53	4	no	—
1206	C₂²⋊Q₈	—	53	8	no	—
1207	C₂²⋊Q₈	—	53	8	no	—
1208	C₂²⋊Q₈	—	53	8	no	—
1209	C₂²⋊Q₈	—	53	4	no	—
1210	C₂²⋊Q₈	—	53	4	no	—
1211	C₂²⋊Q₈	—	53	2	no	—
1212	C₂²⋊Q₈	—	53	8	no	—
1213	C₂²⋊Q₈	—	53	8	no	—
1214	C₂²⋊Q₈	—	53	8	no	—
1215	C₂²⋊Q₈	—	53	8	no	—
1216	C₂²⋊Q₈	—	53	8	no	—
1217	C₂²⋊Q₈	—	53	4	no	—
1218	C₂²⋊Q₈	—	53	8	no	—
1219	C₂²⋊Q₈	—	53	8	no	—
1220	C₂²⋊Q₈	—	53	8	no	—
1221	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1222	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1223	#121	—	53	4	no	—
1224	#121	—	53	2	no	—
1225	#121	—	53	2	no	—
1226	#121	—	53	2	no	—
1227	#121	—	53	4	no	—
1228	#121	—	53	8	no	—
1229	#121	—	53	4	no	—
1230	#121	—	53	8	no	—
1231	#121	—	53	8	no	—
1232	#121	—	53	8	no	—
1233	#121	—	53	8	no	—
1234	#121	—	53	8	no	—
1235	#121	—	53	8	no	—
1236	#121	—	53	8	no	—
1237	#121	—	53	4	no	—
1238	#121	—	53	4	no	—
1239	#121	—	53	8	no	—
1240	#121	—	53	2	no	—
1241	#121	—	53	4	no	—
1242	#121	—	53	8	no	—
1243	#121	—	53	8	no	—
1244	#121	—	53	8	no	—
1245	#121	C₂²×D₅₃	1	4	yes	—
1246	#121	C₂²×D₅₃	1	4	yes	—
1247	#121	C₂²×D₅₃	1	8	yes	complemented
1248	#121	C₂²×D₅₃	1	8	yes	complemented
1249	#120	—	53	4	no	—
1250	#120	—	53	8	no	—
1251	#120	—	53	8	no	—
1252	#120	—	53	2	no	—
1253	#120	—	53	2	no	—
1254	#120	—	53	2	no	—
1255	#120	—	53	4	no	—
1256	#120	—	53	4	no	—
1257	#120	—	53	8	no	—
1258	#120	—	53	8	no	—
1259	#120	—	53	8	no	—
1260	#120	—	53	8	no	—
1261	#120	—	53	8	no	—
1262	#120	—	53	8	no	—
1263	#120	—	53	2	no	—
1264	#120	—	53	8	no	—
1265	#120	C₂²×D₅₃	1	4	yes	—
1266	#120	C₂²×D₅₃	1	8	yes	complemented
1267	C₄×Q₈	—	53	2	no	—
1268	C₄×Q₈	—	53	2	no	—
1269	C₄×Q₈	—	53	4	no	—
1270	C₄×Q₈	—	53	4	no	—
1271	C₄×Q₈	—	53	4	no	—
1272	C₄×Q₈	—	53	4	no	—
1273	C₄×Q₈	—	53	4	no	—
1274	C₄×Q₈	—	53	2	no	—
1275	C₄×Q₈	—	53	4	no	—
1276	C₄×Q₈	—	53	4	no	—
1277	C₄×Q₈	—	53	4	no	—
1278	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1279	C₄×D₄	—	53	4	no	—
1280	C₄×D₄	—	53	4	no	—
1281	C₄×D₄	—	53	4	no	—
1282	C₄×D₄	—	53	2	no	—
1283	C₄×D₄	—	53	2	no	—
1284	C₄×D₄	—	53	8	no	—
1285	C₄×D₄	—	53	4	no	—
1286	C₄×D₄	—	53	4	no	—
1287	C₄×D₄	—	53	4	no	—
1288	C₄×D₄	—	53	4	no	—
1289	C₄×D₄	—	53	4	no	—
1290	C₄×D₄	—	53	4	no	—
1291	C₄×D₄	—	53	4	no	—
1292	C₄×D₄	—	53	4	no	—
1293	C₄×D₄	—	53	4	no	—
1294	C₄×D₄	—	53	8	no	—
1295	C₄×D₄	—	53	8	no	—
1296	C₄×D₄	—	53	8	no	—
1297	C₄×D₄	—	53	8	no	—
1298	C₄×D₄	—	53	8	no	—
1299	C₄×D₄	—	53	8	no	—
1300	C₄×D₄	—	53	4	no	—
1301	C₄×D₄	—	53	4	no	—
1302	C₄×D₄	—	53	4	no	—
1303	C₄×D₄	—	53	8	no	—
1304	C₄×D₄	—	53	8	no	—
1305	C₄×D₄	—	53	8	no	—
1306	C₄×D₄	—	53	8	no	—
1307	C₄×D₄	—	53	4	no	—
1308	C₄×D₄	—	53	4	no	—
1309	C₄×D₄	—	53	2	no	—
1310	C₄×D₄	—	53	4	no	—
1311	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1312	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1313	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1314	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1315	#117	—	53	1	no	—
1316	#117	—	53	1	no	—
1317	#117	—	53	1	no	—
1318	#117	—	53	2	no	—
1319	#117	—	53	2	no	—
1320	#117	—	53	4	no	—
1321	#117	—	53	4	no	—
1322	#117	—	53	4	no	—
1323	#117	—	53	8	no	—
1324	#117	—	53	4	no	—
1325	#117	—	53	4	no	—
1326	#117	—	53	8	no	—
1327	#117	—	53	8	no	—
1328	#117	—	53	4	no	—
1329	#117	—	53	4	no	—
1330	#117	—	53	2	no	—
1331	#117	—	53	4	no	—
1332	#117	—	53	8	no	—
1333	#117	C₂²×D₅₃	1	1	yes	characteristic
1334	#117	C₂²×D₅₃	1	2	yes	complemented
1335	C₂×C₂²⋊C₄	—	53	4	no	—
1336	C₂×C₂²⋊C₄	—	53	4	no	—
1337	C₂×C₂²⋊C₄	—	53	8	no	—
1338	C₂×C₂²⋊C₄	—	53	4	no	—
1339	C₂×C₂²⋊C₄	—	53	4	no	—
1340	C₂×C₂²⋊C₄	—	53	8	no	—
1341	C₂×C₂²⋊C₄	—	53	8	no	—
1342	C₂×C₂²⋊C₄	—	53	8	no	—
1343	C₂×C₂²⋊C₄	—	53	8	no	—
1344	C₂×C₂²⋊C₄	—	53	8	no	—
1345	C₂×C₂²⋊C₄	—	53	8	no	—
1346	C₂×C₂²⋊C₄	—	53	4	no	—
1347	C₂×C₂²⋊C₄	—	53	8	no	—
1348	C₂×C₂²⋊C₄	—	53	8	no	—
1349	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1350	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1351	C₂×C₄²	—	53	2	no	—
1352	C₂×C₄²	—	53	2	no	—
1353	C₂×C₄²	—	53	1	no	—
1354	C₂×C₄²	—	53	2	no	—
1355	C₂×C₄²	—	53	2	no	—
1356	C₂×C₄²	—	53	2	no	—
1357	C₂×C₄²	—	53	2	no	—
1358	C₂×C₄²	—	53	2	no	—
1359	C₂×C₄²	—	53	2	no	—
1360	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1361	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1362	C₂⁴	—	53	1	no	—
1363	C₂⁴	—	53	8	no	—
1364	C₂⁴	—	53	2	no	—
1365	C₂⁴	—	53	4	no	—
1366	C₂⁴	—	212	4	no	—
1367	C₂⁴	—	212	8	no	—
1368	C₂⁴	C₂³×D₅₃	1	2	yes	—
1369	C₂⁴	C₂³×D₅₃	1	4	yes	—
1370	#41	—	2	4	no	—
1371	#41	—	2	4	no	—
1372	#41	—	2	4	no	—
1373	#41	—	4	8	no	—
1374	#41	—	4	4	no	—
1375	#41	—	4	4	no	—
1376	#41	—	4	4	no	—
1377	#41	—	4	4	no	—
1378	#41	—	106	4	no	—
1379	#41	—	212	4	no	—
1380	#41	—	212	4	no	—
1381	#41	—	212	8	no	—
1382	#41	—	212	8	no	—
1383	#41	—	212	4	no	—
1384	#41	—	212	8	no	—
1385	#41	—	212	4	no	—
1386	C₂×Q₈	—	2	4	no	—
1387	C₂×Q₈	—	4	4	no	—
1388	C₂×Q₈	—	4	4	no	—
1389	C₂×Q₈	—	53	2	no	—
1390	C₂×Q₈	—	53	2	no	—
1391	C₂×Q₈	—	53	1	no	—
1392	C₂×Q₈	—	53	4	no	—
1393	C₂×Q₈	—	53	4	no	—
1394	C₂×Q₈	—	53	4	no	—
1395	C₂×Q₈	—	53	8	no	—
1396	C₂×Q₈	—	106	4	no	—
1397	C₂×Q₈	—	212	4	no	—
1398	C₂×Q₈	—	212	4	no	—
1399	C₂×Q₈	—	212	8	no	—
1400	C₂×Q₈	—	212	8	no	—
1401	C₂×Q₈	—	212	4	no	—
1402	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1403	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1404	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1405	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1406	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1407	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1408	C₂×D₄	—	2	4	no	—
1409	C₂×D₄	—	4	4	no	—
1410	C₂×D₄	—	4	4	no	—
1411	C₂×D₄	—	4	8	no	—
1412	C₂×D₄	—	53	4	no	—
1413	C₂×D₄	—	53	4	no	—
1414	C₂×D₄	—	53	4	no	—
1415	C₂×D₄	—	53	2	no	—
1416	C₂×D₄	—	53	4	no	—
1417	C₂×D₄	—	53	8	no	—
1418	C₂×D₄	—	53	8	no	—
1419	C₂×D₄	—	53	8	no	—
1420	C₂×D₄	—	53	4	no	—
1421	C₂×D₄	—	53	4	no	—
1422	C₂×D₄	—	53	8	no	—
1423	C₂×D₄	—	53	4	no	—
1424	C₂×D₄	—	53	2	no	—
1425	C₂×D₄	—	53	2	no	—
1426	C₂×D₄	—	53	1	no	—
1427	C₂×D₄	—	53	4	no	—
1428	C₂×D₄	—	106	4	no	—
1429	C₂×D₄	—	212	4	no	—
1430	C₂×D₄	—	212	8	no	—
1431	C₂×D₄	—	212	8	no	—
1432	C₂×D₄	—	212	4	no	—
1433	C₂×D₄	—	212	4	no	—
1434	C₂×D₄	—	212	8	no	—
1435	C₂×D₄	—	212	16	no	—
1436	C₂×D₄	—	212	16	no	—
1437	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1438	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1439	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1440	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1441	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1442	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1443	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1444	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1445	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1446	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1447	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1448	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1449	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1450	C₂²×C₄	—	53	1	no	—
1451	C₂²×C₄	—	53	2	no	—
1452	C₂²×C₄	—	53	2	no	—
1453	C₂²×C₄	—	53	4	no	—
1454	C₂²×C₄	—	53	4	no	—
1455	C₂²×C₄	—	53	8	no	—
1456	C₂²×C₄	—	53	4	no	—
1457	C₂²×C₄	—	53	2	no	—
1458	C₂²×C₄	—	53	2	no	—
1459	C₂²×C₄	—	53	2	no	—
1460	C₂²×C₄	—	53	2	no	—
1461	C₂²×C₄	—	53	2	no	—
1462	C₂²×C₄	—	53	2	no	—
1463	C₂²×C₄	—	53	2	no	—
1464	C₂²×C₄	—	53	4	no	—
1465	C₂²×C₄	—	53	8	no	—
1466	C₂²×C₄	—	53	8	no	—
1467	C₂²×C₄	—	53	4	no	—
1468	C₂²×C₄	—	53	4	no	—
1469	C₂²×C₄	—	106	4	no	—
1470	C₂²×C₄	—	212	4	no	—
1471	C₂²×C₄	—	212	4	no	—
1472	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1473	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1474	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1475	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1476	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1477	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1478	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1479	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1480	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1481	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1482	C₄⋊C₄	—	53	4	no	—
1483	C₄⋊C₄	—	53	4	no	—
1484	C₄⋊C₄	—	53	4	no	—
1485	C₄⋊C₄	—	53	4	no	—
1486	C₄⋊C₄	—	53	2	no	—
1487	C₄⋊C₄	—	53	2	no	—
1488	C₄⋊C₄	—	53	2	no	—
1489	C₄⋊C₄	—	53	8	no	—
1490	C₄⋊C₄	—	53	8	no	—
1491	C₄⋊C₄	—	53	8	no	—
1492	C₄⋊C₄	—	53	4	no	—
1493	C₄⋊C₄	—	53	4	no	—
1494	C₄⋊C₄	—	53	4	no	—
1495	C₄⋊C₄	—	53	4	no	—
1496	C₄⋊C₄	—	53	4	no	—
1497	C₄⋊C₄	—	53	4	no	—
1498	C₄⋊C₄	—	53	4	no	—
1499	C₄⋊C₄	—	53	4	no	—
1500	C₄⋊C₄	—	53	4	no	—
1501	C₄⋊C₄	—	53	4	no	—
1502	C₄⋊C₄	—	53	8	no	—
1503	C₄⋊C₄	—	53	8	no	—
1504	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1505	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1506	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1507	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1508	C₂²⋊C₄	—	53	8	no	—
1509	C₂²⋊C₄	—	53	8	no	—
1510	C₂²⋊C₄	—	53	2	no	—
1511	C₂²⋊C₄	—	53	2	no	—
1512	C₂²⋊C₄	—	53	2	no	—
1513	C₂²⋊C₄	—	53	4	no	—
1514	C₂²⋊C₄	—	53	8	no	—
1515	C₂²⋊C₄	—	53	8	no	—
1516	C₂²⋊C₄	—	53	8	no	—
1517	C₂²⋊C₄	—	53	8	no	—
1518	C₂²⋊C₄	—	53	4	no	—
1519	C₂²⋊C₄	—	53	4	no	—
1520	C₂²⋊C₄	—	53	4	no	—
1521	C₂²⋊C₄	—	53	4	no	—
1522	C₂²⋊C₄	—	53	4	no	—
1523	C₂²⋊C₄	—	53	8	no	—
1524	C₂²⋊C₄	—	53	8	no	—
1525	C₂²⋊C₄	—	53	8	no	—
1526	C₂²⋊C₄	—	53	8	no	—
1527	C₂²⋊C₄	—	53	4	no	—
1528	C₂²⋊C₄	—	53	4	no	—
1529	C₂²⋊C₄	—	53	4	no	—
1530	C₂²⋊C₄	—	53	4	no	—
1531	C₂²⋊C₄	—	53	4	no	—
1532	C₂²⋊C₄	—	53	8	no	—
1533	C₂²⋊C₄	—	53	8	no	—
1534	C₂²⋊C₄	—	53	8	no	—
1535	C₂²⋊C₄	—	53	8	no	—
1536	C₂²⋊C₄	—	53	4	no	—
1537	C₂²⋊C₄	—	53	4	no	—
1538	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1539	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1540	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1541	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1542	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1543	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1544	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1545	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1546	C₄²	—	53	1	no	—
1547	C₄²	—	53	2	no	—
1548	C₄²	—	53	1	no	—
1549	C₄²	—	53	2	no	—
1550	C₄²	—	53	2	no	—
1551	C₄²	—	53	2	no	—
1552	C₄²	—	53	2	no	—
1553	C₄²	—	53	4	no	—
1554	C₄²	—	53	4	no	—
1555	C₄²	—	53	4	no	—
1556	C₄²	—	53	2	no	—
1557	C₄²	—	53	2	no	—
1558	C₄²	—	53	2	no	—
1559	C₄²	—	53	8	no	—
1560	C₄²	—	53	8	no	—
1561	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1562	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1563	C₄²	C₂³×D₅₃	1	2	yes	—
1564	C₄²	C₂³×D₅₃	1	4	yes	—
1565	C₄²	C₂³×D₅₃	1	2	yes	—
1566	C₂³	—	2	4	no	—
1567	C₂³	—	4	4	no	—
1568	C₂³	—	4	4	no	—
1569	C₂³	—	4	8	no	—
1570	C₂³	—	53	2	no	—
1571	C₂³	—	53	4	no	—
1572	C₂³	—	53	2	no	—
1573	C₂³	—	106	4	no	—
1574	C₂³	—	106	16	no	—
1575	C₂³	—	106	2	no	—
1576	C₂³	—	106	4	no	—
1577	C₂³	—	424	16	no	—
1578	C₂³	—	212	4	no	—
1579	C₂³	—	212	8	no	—
1580	C₂³	—	212	8	no	—
1581	C₂³	—	212	4	no	—
1582	C₂³	—	212	8	no	—
1583	C₂³	C₂⁴×D₅₃	1	4	yes	—
1584	C₂³	C₂⁴×D₅₃	1	2	yes	—
1585	C₂³	C₂⁴×D₅₃	1	2	yes	—
1586	C₂³	C₂⁴×D₅₃	1	2	yes	—
1587	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1588	Q₈	—	2	4	no	—
1589	Q₈	—	2	4	no	—
1590	Q₈	—	2	2	no	—
1591	Q₈	—	2	2	no	—
1592	Q₈	—	2	2	no	—
1593	Q₈	—	4	4	no	—
1594	Q₈	—	106	4	no	—
1595	Q₈	—	106	4	no	—
1596	Q₈	—	106	2	no	—
1597	Q₈	—	212	8	no	—
1598	Q₈	—	212	4	no	—
1599	Q₈	—	212	4	no	—
1600	Q₈	—	212	4	no	—
1601	D₄	—	2	4	no	—
1602	D₄	—	2	4	no	—
1603	D₄	—	2	4	no	—
1604	D₄	—	2	4	no	—
1605	D₄	—	2	4	no	—
1606	D₄	—	2	2	no	—
1607	D₄	—	2	2	no	—
1608	D₄	—	2	2	no	—
1609	D₄	—	4	4	no	—
1610	D₄	—	4	4	no	—
1611	D₄	—	4	8	no	—
1612	D₄	—	4	4	no	—
1613	D₄	—	4	4	no	—
1614	D₄	—	106	8	no	—
1615	D₄	—	106	8	no	—
1616	D₄	—	106	8	no	—
1617	D₄	—	106	8	no	—
1618	D₄	—	106	4	no	—
1619	D₄	—	106	4	no	—
1620	D₄	—	106	4	no	—
1621	D₄	—	106	2	no	—
1622	D₄	—	212	4	no	—
1623	D₄	—	212	8	no	—
1624	D₄	—	212	8	no	—
1625	D₄	—	212	8	no	—
1626	D₄	—	212	8	no	—
1627	D₄	—	212	4	no	—
1628	D₄	—	212	4	no	—
1629	D₄	—	212	4	no	—
1630	C₂×C₄	—	2	4	no	—
1631	C₂×C₄	—	2	4	no	—
1632	C₂×C₄	—	2	4	no	—
1633	C₂×C₄	—	2	4	no	—
1634	C₂×C₄	—	4	2	no	—
1635	C₂×C₄	—	4	4	no	—
1636	C₂×C₄	—	4	4	no	—
1637	C₂×C₄	—	4	4	no	—
1638	C₂×C₄	—	4	4	no	—
1639	C₂×C₄	—	53	2	no	—
1640	C₂×C₄	—	53	2	no	—
1641	C₂×C₄	—	53	4	no	—
1642	C₂×C₄	—	53	4	no	—
1643	C₂×C₄	—	53	4	no	—
1644	C₂×C₄	—	53	2	no	—
1645	C₂×C₄	—	53	4	no	—
1646	C₂×C₄	—	53	2	no	—
1647	C₂×C₄	—	106	4	no	—
1648	C₂×C₄	—	106	4	no	—
1649	C₂×C₄	—	106	2	no	—
1650	C₂×C₄	—	106	4	no	—
1651	C₂×C₄	—	106	4	no	—
1652	C₂×C₄	—	106	4	no	—
1653	C₂×C₄	—	106	4	no	—
1654	C₂×C₄	—	212	2	no	—
1655	C₂×C₄	—	212	2	no	—
1656	C₂×C₄	—	212	8	no	—
1657	C₂×C₄	—	212	8	no	—
1658	C₂×C₄	—	212	4	no	—
1659	C₂×C₄	—	212	4	no	—
1660	C₂×C₄	—	212	4	no	—
1661	C₂×C₄	—	212	2	no	—
1662	C₂×C₄	—	212	8	no	—
1663	C₂×C₄	—	212	4	no	—
1664	C₂×C₄	—	212	4	no	—
1665	C₂×C₄	—	212	4	no	—
1666	C₂×C₄	#13133262	1	4	yes	—
1667	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1668	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1669	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1670	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1671	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1672	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1673	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1674	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1675	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1676	C₂²	—	2	2	no	—
1677	C₂²	—	2	2	no	—
1678	C₂²	—	2	2	no	—
1679	C₂²	—	2	2	no	—
1680	C₂²	—	2	4	no	—
1681	C₂²	—	2	4	no	—
1682	C₂²	—	2	4	no	—
1683	C₂²	—	2	4	no	—
1684	C₂²	—	2	8	no	—
1685	C₂²	—	8	4	no	—
1686	C₂²	—	16	4	no	—
1687	C₂²	—	53	4	no	—
1688	C₂²	—	848	4	no	—
1689	C₂²	—	106	8	no	—
1690	C₂²	—	106	2	no	—
1691	C₂²	—	106	2	no	—
1692	C₂²	—	106	2	no	—
1693	C₂²	—	106	4	no	—
1694	C₂²	—	106	4	no	—
1695	C₂²	—	106	8	no	—
1696	C₂²	—	424	4	no	—
1697	C₂²	—	424	16	no	—
1698	C₂²	C₂×#13133262	1	2	yes	—
1699	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1700	C₄	—	2	2	no	—
1701	C₄	—	2	2	no	—
1702	C₄	—	2	2	no	—
1703	C₄	—	2	4	no	—
1704	C₄	—	2	2	no	—
1705	C₄	—	2	2	no	—
1706	C₄	—	2	4	no	—
1707	C₄	—	106	2	no	—
1708	C₄	—	106	2	no	—
1709	C₄	—	106	4	no	—
1710	C₄	—	106	2	no	—
1711	C₄	—	106	2	no	—
1712	C₄	—	106	4	no	—
1713	C₄	—	106	4	no	—
1714	C₄	—	106	4	no	—
1715	C₄	C₂×#13133262	1	2	yes	—
1716	C₄	C₂×#13133262	1	2	yes	—
1717	C₂	—	2	2	no	—
1718	C₂	—	4	4	no	—
1719	C₂	—	4	2	no	—
1720	C₂	—	4	2	no	—
1721	C₂	—	4	2	no	—
1722	C₂	—	106	4	no	—
1723	C₂	—	212	2	no	—
1724	C₂	—	212	4	no	—
1725	C₂	C₂²×#13133262	1	1	yes	characteristic
1726	C₂	#585×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3500	C₂
hypercenter	#3500	D₅₃
hypocenter	C₅₃	#62824
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3500

Complements

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

N	H ≅ G/N	type
1. #20289278	C₂	semidirect
2. #20289276	C₂	semidirect
3. #20289233	C₂	semidirect
4. #20289224	C₂	semidirect
5. #20289062	C₂	semidirect
6. #20288673	C₂	semidirect
7. #20288671	C₂	semidirect
8. #20288670	C₂	semidirect
9. #20288669	C₂	semidirect
10. #20288614	C₂	semidirect
11. #20288611	C₂	semidirect
12. #20288610	C₂	semidirect
13. #20288609	C₂	semidirect
14. #20288509	C₂	semidirect
15. #20288503	C₂	semidirect
16. #20288502	C₂	semidirect
17. #20288397	C₂	semidirect
18. #20288364	C₂	semidirect
19. #20288363	C₂	semidirect
20. #20288349	C₂	semidirect
21. #20288346	C₂	semidirect
22. #20288010	C₂	semidirect
23. #20288008	C₂	semidirect
24. C₂×#124×D₅₃	C₂	semidirect
25. C₅₃×#3500	C₂	semidirect
26. C₂×#13133264	C₂²	semidirect
27. C₂×#13133263	C₂²	semidirect
28. C₂²×Q₈×D₅₃	C₂²	semidirect
30. #16811374	C₂²	semidirect
31. #16811370	C₂²	semidirect
32. #16811368	C₂²	semidirect
33. #16811366	C₂²	semidirect
34. #16811359	C₂²	semidirect
35. #16811356	C₂²	semidirect
36. #16811355	C₂²	semidirect
37. #16811355	C₂²	semidirect
38. #16811347	C₂²	semidirect
39. #16811345	C₂²	semidirect
40. #16811342	C₂²	semidirect
41. #16811342	C₂²	semidirect
42. #16811337	C₂²	semidirect
43. #16811335	C₂²	semidirect
44. #16811304	C₂²	semidirect
45. #16811303	C₂²	semidirect
46. #16811302	C₂²	semidirect
47. #16811302	C₂²	semidirect
48. #16811302	C₂²	semidirect
49. #16811301	C₂²	semidirect
50. #16811300	C₂²	semidirect
51. #16811299	C₂²	semidirect
52. #16811299	C₂²	semidirect
53. #16811296	C₂²	semidirect
54. #16811288	C₂²	semidirect
55. Q₈×C₂²⋊D₅₃	C₂²	semidirect
56. Q₈×C₂²⋊D₅₃	C₂²	semidirect
57. #16811286	C₂²	semidirect
58. #16811284	C₂²	semidirect
59. #16811283	C₂²	semidirect
60. #16811282	C₂²	semidirect
61. #16811281	C₂²	semidirect
62. #16811280	C₂²	semidirect
63. #16811280	C₂²	semidirect
64. #16811280	C₂²	semidirect
65. #16811270	C₂²	semidirect
66. #16811270	C₂²	semidirect
67. #16811269	C₂²	semidirect
68. #16811267	C₂²	semidirect
69. #16811267	C₂²	semidirect
70. #16811266	C₂²	semidirect
71. #16811263	C₂²	semidirect
72. #16811262	C₂²	semidirect
73. #16811262	C₂²	semidirect
74. #16811261	C₂²	semidirect
75. #16811261	C₂²	semidirect
76. #16811261	C₂²	semidirect
77. #16811261	C₂²	semidirect
78. #16811260	C₂²	semidirect
79. #16811258	C₂²	semidirect
80. #16811257	C₂²	semidirect
81. D₄×C₂²⋊D₅₃	C₂²	semidirect
82. D₄×C₂²⋊D₅₃	C₂²	semidirect
83. #16811248	C₂²	semidirect
84. #16811246	C₂²	semidirect
85. #16811244	C₂²	semidirect
86. #16811243	C₂²	semidirect
87. #16811242	C₂²	semidirect
88. #16811241	C₂²	semidirect
89. #16811240	C₂²	semidirect
90. #16811238	C₂²	semidirect
91. #16811237	C₂²	semidirect
92. #16811211	C₂²	semidirect
93. #16811210	C₂²	semidirect
94. #16811209	C₂²	semidirect
95. #16811208	C₂²	semidirect
96. #16811207	C₂²	semidirect
97. #16811205	C₂²	semidirect
98. #16811205	C₂²	semidirect
99. #16811205	C₂²	semidirect
100. #16811198	C₂²	semidirect
101. #16811197	C₂²	semidirect
102. #16811197	C₂²	semidirect
103. #16811195	C₂²	semidirect
104. #16811194	C₂²	semidirect
105. #16811194	C₂²	semidirect
106. #16811194	C₂²	semidirect
107. #16811194	C₂²	semidirect
109. #16811190	C₂²	semidirect
112. #16811187	C₂²	semidirect
113. #16811186	C₂²	semidirect
114. #16811183	C₂²	semidirect
115. #16811183	C₂²	semidirect
116. #16811182	C₂²	semidirect
117. #16811180	C₂²	semidirect
118. #16811178	C₂²	semidirect
119. #16811177	C₂²	semidirect
120. #16811176	C₂²	semidirect
121. #16811172	C₂²	semidirect
122. #16811171	C₂²	semidirect
123. #16811170	C₂²	semidirect
124. #16811169	C₂²	semidirect
125. #16811169	C₂²	semidirect
126. #16811169	C₂²	semidirect
127. #16811160	C₂²	semidirect
128. #16811159	C₂²	semidirect
129. #16811157	C₂²	semidirect
130. #16811155	C₂²	semidirect
131. #16811155	C₂²	semidirect
132. #16811154	C₂²	semidirect
133. #16811154	C₂²	semidirect
134. #16811153	C₂²	semidirect
135. #16811152	C₂²	semidirect
136. #16811152	C₂²	semidirect
137. #16811152	C₂²	semidirect
138. #16811151	C₂²	semidirect
139. C₂×#13133206	C₂²	semidirect
140. C₂×#13133206	C₂²	semidirect
141. C₂×#13133205	C₂²	semidirect
142. C₂×#13133204	C₂²	semidirect
143. C₂×#13133204	C₂²	semidirect
144. C₂×#13133203	C₂²	semidirect
145. #124×D₅₃	C₂²	semidirect
146. #124×D₅₃	C₂²	semidirect
147. #124×D₅₃	C₂²	semidirect
148. #124×D₅₃	C₂²	semidirect
149. #124×D₅₃	C₂²	semidirect
150. #16811135	C₂²	semidirect
151. #16811133	C₂²	semidirect
152. #16811132	C₂²	semidirect
153. #16811131	C₂²	semidirect
154. #16811130	C₂²	semidirect
155. #16811130	C₂²	semidirect
156. #16811130	C₂²	semidirect
157. #16811130	C₂²	semidirect
158. C₂×#13133185	C₂²	semidirect
159. #120×D₅₃	C₂²	semidirect
160. #16811101	C₂²	semidirect
161. #16811100	C₂²	semidirect
162. #16811098	C₂²	semidirect
163. #16811097	C₂²	semidirect
164. #16811096	C₂²	semidirect
165. #16811095	C₂²	semidirect
166. #41×Dic₅₃	C₂²	semidirect
167. #41×Dic₅₃	C₂²	semidirect
168. C₄×#11719945	C₂²	semidirect
169. C₄×#11719945	C₂²	semidirect
170. C₄×#11719947	C₂²	semidirect
171. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
172. C₂×C₄²×D₅₃	C₂²	semidirect
173. C₂×2₋¹⁺⁴×C₅₃	C₂²	semidirect
174. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
175. C₅₃×#548	C₂²	semidirect
176. C₅₃×#546	C₂²	semidirect
177. C₅₃×#546	C₂²	semidirect
178. C₅₃×#536	C₂²	semidirect
179. C₅₃×#536	C₂²	semidirect
181. C₅₃×#535	C₂²	semidirect
182. C₅₃×#532	C₂²	semidirect
183. C₅₃×#532	C₂²	semidirect
184. C₂×#124×C₅₃	C₂²	semidirect
185. C₂×#124×C₅₃	C₂²	semidirect
186. C₄×#41×C₅₃	C₂²	semidirect
194. C₂×#11719945	C₂³	semidirect
197. C₂×#11719947	C₂³	semidirect
200. C₂²×Dic₁₀₆	C₂³	semidirect
204. C₂×Q₈×D₅₃	C₂³	semidirect
218. #13133217	C₂³	semidirect
219. #13133216	C₂³	semidirect
220. #13133216	C₂³	semidirect
221. #13133215	C₂³	semidirect
222. #13133215	C₂³	semidirect
223. #13133215	C₂³	semidirect
224. #13133215	C₂³	semidirect
225. #13133215	C₂³	semidirect
229. #13133213	C₂³	semidirect
230. #13133212	C₂³	semidirect
231. #13133212	C₂³	semidirect
232. #13133212	C₂³	semidirect
233. #13133212	C₂³	semidirect
234. #13133211	C₂³	semidirect
235. #13133210	C₂³	semidirect
236. #13133210	C₂³	semidirect
237. #13133210	C₂³	semidirect
238. #13133210	C₂³	semidirect
239. #13133210	C₂³	semidirect
240. #13133210	C₂³	semidirect
241. #13133210	C₂³	semidirect
242. #13133209	C₂³	semidirect
243. #13133208	C₂³	semidirect
244. #13133208	C₂³	semidirect
245. #13133207	C₂³	semidirect
251. #13133206	C₂³	semidirect
252. #13133206	C₂³	semidirect
253. #13133206	C₂³	semidirect
261. #13133204	C₂³	semidirect
262. #13133204	C₂³	semidirect
263. #13133204	C₂³	semidirect
264. #13133204	C₂³	semidirect
265. #13133204	C₂³	semidirect
266. #13133204	C₂³	semidirect
267. #13133204	C₂³	semidirect
272. #13133203	C₂³	semidirect
273. #13133203	C₂³	semidirect
274. #13133203	C₂³	semidirect
275. #13133203	C₂³	semidirect
276. #13133203	C₂³	semidirect
277. #13133203	C₂³	semidirect
279. #13133202	C₂³	semidirect
281. #13133201	C₂³	semidirect
282. #13133201	C₂³	semidirect
285. #13133200	C₂³	semidirect
286. #13133200	C₂³	semidirect
291. #13133199	C₂³	semidirect
292. #13133199	C₂³	semidirect
293. #13133199	C₂³	semidirect
299. #13133198	C₂³	semidirect
300. #13133198	C₂³	semidirect
301. #13133198	C₂³	semidirect
304. #13133197	C₂³	semidirect
306. #13133196	C₂³	semidirect
307. #13133196	C₂³	semidirect
308. #13133196	C₂³	semidirect
309. #13133196	C₂³	semidirect
310. #13133196	C₂³	semidirect
313. #13133195	C₂³	semidirect
314. #13133195	C₂³	semidirect
315. #13133195	C₂³	semidirect
317. #13133194	C₂³	semidirect
318. #13133194	C₂³	semidirect
319. #13133194	C₂³	semidirect
324. #13133193	C₂³	semidirect
325. #13133193	C₂³	semidirect
329. #13133191	C₂³	semidirect
333. #13133190	C₂³	semidirect
337. #13133189	C₂³	semidirect
338. #13133189	C₂³	semidirect
339. #13133189	C₂³	semidirect
347. #13133188	C₂³	semidirect
352. #13133186	C₂³	semidirect
362. #13133185	C₂³	semidirect
363. #13133185	C₂³	semidirect
364. Q₈×Dic₅₃	C₂³	semidirect
365. Q₈×Dic₅₃	C₂³	semidirect
366. Q₈×Dic₅₃	C₂³	semidirect
367. Q₈×Dic₅₃	C₂³	semidirect
368. C₄×Dic₁₀₆	C₂³	semidirect
369. C₄×Dic₁₀₆	C₂³	semidirect
370. C₄×Dic₁₀₆	C₂³	semidirect
371. C₄×Dic₁₀₆	C₂³	semidirect
372. C₄×Dic₁₀₆	C₂³	semidirect
373. #13133182	C₂³	semidirect
374. #13133182	C₂³	semidirect
378. C₄×D₂₁₂	C₂³	semidirect
383. D₄×Dic₅₃	C₂³	semidirect
384. D₄×Dic₅₃	C₂³	semidirect
385. D₄×Dic₅₃	C₂³	semidirect
386. D₄×Dic₅₃	C₂³	semidirect
396. C₄×C₂²⋊D₅₃	C₂³	semidirect
397. C₄×C₂²⋊D₅₃	C₂³	semidirect
398. C₄×C₂²⋊D₅₃	C₂³	semidirect
399. C₄×C₂²⋊D₅₃	C₂³	semidirect
400. C₄×C₂²⋊D₅₃	C₂³	semidirect
404. #13133177	C₂³	semidirect
405. #13133177	C₂³	semidirect
406. #13133177	C₂³	semidirect
411. #13133176	C₂³	semidirect
412. #13133176	C₂³	semidirect
413. #13133176	C₂³	semidirect
415. #13133175	C₂³	semidirect
417. #13133174	C₂³	semidirect
418. #13133174	C₂³	semidirect
419. #13133174	C₂³	semidirect
421. #13133173	C₂³	semidirect
422. #13133173	C₂³	semidirect
423. #13133173	C₂³	semidirect
424. #13133173	C₂³	semidirect
427. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
431. C₂×#11719921	C₂³	semidirect
438. C₂²⋊C₄×D₅₃	C₂³	semidirect
441. C₂×C₄×Dic₅₃	C₂³	semidirect
442. C₂×C₄×Dic₅₃	C₂³	semidirect
447. C₄²×D₅₃	C₂³	semidirect
456. C₂×#41×C₅₃	C₂³	semidirect
457. C₂×#41×C₅₃	C₂³	semidirect
459. C₂²×Q₈×C₅₃	C₂³	semidirect
460. C₂²×Q₈×C₅₃	C₂³	semidirect
465. C₄⋊Q₈×C₅₃	C₂³	semidirect
466. C₄⋊Q₈×C₅₃	C₂³	semidirect
468. #127×C₅₃	C₂³	semidirect
473. #124×C₅₃	C₂³	semidirect
474. #124×C₅₃	C₂³	semidirect
475. #124×C₅₃	C₂³	semidirect
476. #124×C₅₃	C₂³	semidirect
478. #123×C₅₃	C₂³	semidirect
479. C₂²⋊Q₈×C₅₃	C₂³	semidirect
480. C₂²⋊Q₈×C₅₃	C₂³	semidirect
483. #121×C₅₃	C₂³	semidirect
484. #121×C₅₃	C₂³	semidirect
486. #120×C₅₃	C₂³	semidirect
487. C₄×Q₈×C₅₃	C₂³	semidirect
489. C₄×D₄×C₅₃	C₂³	semidirect
490. C₄×D₄×C₅₃	C₂³	semidirect
491. C₄×D₄×C₅₃	C₂³	semidirect
493. #117×C₅₃	C₂³	semidirect
495. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
497. C₂×C₄²×C₅₃	C₂³	semidirect
870. #3500	D₅₃	semidirect
890. C₂×2₋¹⁺⁴	C₂×D₅₃	semidirect
892. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
930. #548	C₂×D₅₃	semidirect
945. #546	C₂×D₅₃	semidirect
946. #546	C₂×D₅₃	semidirect
976. #536	C₂×D₅₃	semidirect
977. #536	C₂×D₅₃	semidirect
985. #535	C₂×D₅₃	semidirect
999. #532	C₂×D₅₃	semidirect
1000. #532	C₂×D₅₃	semidirect
1024. C₂×#124	C₂×D₅₃	semidirect
1025. C₂×#124	C₂×D₅₃	semidirect
1047. C₄×#41	C₂×D₅₃	semidirect
1050. C₅₃	#62824	semidirect
1070. C₂×#41	C₂²×D₅₃	semidirect
1071. C₂×#41	C₂²×D₅₃	semidirect
1080. C₂²×Q₈	C₂²×D₅₃	semidirect
1081. C₂²×Q₈	C₂²×D₅₃	semidirect
1107. C₄⋊Q₈	C₂²×D₅₃	semidirect
1108. C₄⋊Q₈	C₂²×D₅₃	semidirect
1114. #127	C₂²×D₅₃	semidirect
1167. #124	C₂²×D₅₃	semidirect
1168. #124	C₂²×D₅₃	semidirect
1169. #124	C₂²×D₅₃	semidirect
1170. #124	C₂²×D₅₃	semidirect
1196. #123	C₂²×D₅₃	semidirect
1221. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1222. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1247. #121	C₂²×D₅₃	semidirect
1248. #121	C₂²×D₅₃	semidirect
1266. #120	C₂²×D₅₃	semidirect
1278. C₄×Q₈	C₂²×D₅₃	semidirect
1312. C₄×D₄	C₂²×D₅₃	semidirect
1313. C₄×D₄	C₂²×D₅₃	semidirect
1314. C₄×D₄	C₂²×D₅₃	semidirect
1334. #117	C₂²×D₅₃	semidirect
1350. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1361. 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
#20289278	2
#20289276	2
#20289233	2
#20289224	2
#20289062	2
#20288673	2
#20288671	2
#20288670	2
#20288669	2
#20288614	2
#20288611	2
#20288610	2
#20288609	2
#20288509	2
#20288503	2
#20288502	2
#20288397	2
#20288364	2
#20288363	2
#20288349	2
#20288346	2
#20288010	2
#20288008	2
C₂×#124×D₅₃	2
C₅₃×#3500	2
#62824	53