Subgroups — #28292808

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	#20289286	C₂	1	4	yes	maximal, complemented
2	#20289284	C₂	1	4	yes	maximal, complemented
3	#20289235	C₂	1	4	yes	maximal, complemented
4	#20289230	C₂	1	4	yes	maximal, complemented
5	#20289071	C₂	1	8	yes	maximal, complemented
6	#20288679	C₂	1	4	yes	maximal, complemented
7	#20288678	C₂	1	4	yes	maximal, complemented
8	#20288675	C₂	1	4	yes	maximal, complemented
9	#20288664	C₂	1	4	yes	maximal, complemented
10	#20288613	C₂	1	1	yes	maximal, characteristic, complemented
11	#20288612	C₂	1	1	yes	maximal, characteristic, complemented
12	#20288606	C₂	1	1	yes	maximal, characteristic, complemented
13	#20288508	C₂	1	1	yes	maximal, characteristic, complemented
14	#20288507	C₂	1	1	yes	maximal, characteristic, complemented
15	#20288505	C₂	1	1	yes	maximal, characteristic, complemented
16	#20288504	C₂	1	1	yes	maximal, characteristic, complemented
17	#20288399	C₂	1	8	yes	maximal, complemented
18	#20288367	C₂	1	1	yes	maximal, characteristic, complemented
19	#20288364	C₂	1	1	yes	maximal, characteristic, complemented
20	#20288351	C₂	1	1	yes	maximal, characteristic, complemented
21	#20288349	C₂	1	1	yes	maximal, characteristic, complemented
22	#20288012	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×#3510	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#13133265	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13133264	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
30	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
31	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
32	#16811375	C₂²	1	8	yes	complemented
33	#16811370	C₂²	1	8	yes	complemented
34	#16811369	C₂²	1	8	yes	complemented
35	#16811365	C₂²	1	8	yes	complemented
36	#16811358	C₂²	1	4	yes	complemented
37	#16811358	C₂²	1	4	yes	complemented
38	#16811356	C₂²	1	4	yes	complemented
39	#16811346	C₂²	1	4	yes	complemented
40	#16811345	C₂²	1	4	yes	complemented
41	#16811343	C₂²	1	4	yes	complemented
42	#16811338	C₂²	1	8	yes	complemented
43	#16811336	C₂²	1	8	yes	complemented
44	#16811300	C₂²	1	8	yes	complemented
45	#16811299	C₂²	1	8	yes	complemented
46	#16811298	C₂²	1	8	yes	complemented
47	#16811298	C₂²	1	8	yes	complemented
48	#16811298	C₂²	1	8	yes	complemented
49	#16811297	C₂²	1	8	yes	complemented
50	#16811297	C₂²	1	8	yes	complemented
51	#16811296	C₂²	1	8	yes	complemented
52	#16811296	C₂²	1	8	yes	complemented
53	Q₈×D₂₁₂	C₂²	1	4	yes	complemented
54	Q₈×D₂₁₂	C₂²	1	4	yes	complemented
55	#16811288	C₂²	1	4	yes	complemented
56	#16811286	C₂²	1	4	yes	complemented
57	#16811285	C₂²	1	4	yes	complemented
58	#16811285	C₂²	1	4	yes	complemented
59	#16811285	C₂²	1	4	yes	complemented
60	#16811283	C₂²	1	4	yes	complemented
61	#16811283	C₂²	1	4	yes	complemented
62	#16811281	C₂²	1	4	yes	complemented
63	#16811281	C₂²	1	4	yes	complemented
64	#16811279	C₂²	1	4	yes	complemented
65	#16811270	C₂²	1	4	yes	complemented
66	#16811270	C₂²	1	4	yes	complemented
67	#16811269	C₂²	1	8	yes	complemented
68	#16811268	C₂²	1	4	yes	complemented
69	#16811268	C₂²	1	4	yes	complemented
70	#16811268	C₂²	1	8	yes	complemented
71	#16811268	C₂²	1	4	yes	complemented
72	#16811266	C₂²	1	4	yes	complemented
73	#16811266	C₂²	1	4	yes	complemented
74	#16811266	C₂²	1	8	yes	complemented
75	#16811265	C₂²	1	8	yes	complemented
76	#16811265	C₂²	1	8	yes	complemented
77	#16811264	C₂²	1	8	yes	complemented
78	#16811264	C₂²	1	4	yes	complemented
79	#16811263	C₂²	1	8	yes	complemented
80	#16811260	C₂²	1	8	yes	complemented
81	D₄×D₂₁₂	C₂²	1	4	yes	complemented
82	D₄×D₂₁₂	C₂²	1	4	yes	complemented
83	#16811258	C₂²	1	4	yes	complemented
84	#16811257	C₂²	1	4	yes	complemented
85	#16811248	C₂²	1	8	yes	complemented
86	#16811247	C₂²	1	4	yes	complemented
87	#16811246	C₂²	1	8	yes	complemented
88	#16811245	C₂²	1	4	yes	complemented
89	#16811244	C₂²	1	8	yes	complemented
90	#16811242	C₂²	1	8	yes	complemented
91	#16811239	C₂²	1	8	yes	complemented
92	#16811238	C₂²	1	4	yes	complemented
93	#16811212	C₂²	1	8	yes	complemented
94	#16811212	C₂²	1	8	yes	complemented
95	#16811212	C₂²	1	8	yes	complemented
96	#16811209	C₂²	1	8	yes	complemented
97	#16811209	C₂²	1	8	yes	complemented
98	#16811209	C₂²	1	8	yes	complemented
99	#16811207	C₂²	1	8	yes	complemented
100	#16811206	C₂²	1	8	yes	complemented
101	#16811199	C₂²	1	4	yes	complemented
102	#16811199	C₂²	1	1	yes	characteristic, complemented
103	#16811199	C₂²	1	1	yes	characteristic, complemented
104	#16811199	C₂²	1	2	yes	complemented
105	#16811198	C₂²	1	2	yes	complemented
106	#16811197	C₂²	1	1	yes	characteristic, complemented
107	#16811195	C₂²	1	4	yes	complemented
108	#16811193	C₂²	1	2	yes	complemented
109	#16811193	C₂²	1	2	yes	complemented
110	#16811192	C₂²	1	1	yes	characteristic
111	#16811192	C₂²	1	1	yes	characteristic
112	#16811192	C₂²	1	2	yes	complemented
113	#16811191	C₂²	1	2	yes	complemented
114	#16811191	C₂²	1	2	yes	complemented
115	#16811190	C₂²	1	1	yes	characteristic
116	#16811186	C₂²	1	2	yes	complemented
117	#16811185	C₂²	1	4	yes	complemented
118	#16811184	C₂²	1	8	yes	complemented
119	#16811183	C₂²	1	4	yes	complemented
120	#16811178	C₂²	1	2	yes	complemented
121	#16811177	C₂²	1	2	yes	complemented
122	#16811176	C₂²	1	1	yes	characteristic, complemented
123	#16811174	C₂²	1	2	yes	complemented
124	#16811174	C₂²	1	2	yes	complemented
125	#16811173	C₂²	1	1	yes	characteristic, complemented
126	#16811173	C₂²	1	2	yes	complemented
127	#16811172	C₂²	1	2	yes	complemented
128	#16811171	C₂²	1	2	yes	complemented
129	#16811170	C₂²	1	2	yes	complemented
130	#16811169	C₂²	1	1	yes	characteristic, complemented
131	#16811160	C₂²	1	4	yes	complemented
132	#16811160	C₂²	1	2	yes	complemented
133	#16811160	C₂²	1	4	yes	complemented
134	#16811159	C₂²	1	4	yes	complemented
135	#16811158	C₂²	1	2	yes	complemented
136	#16811158	C₂²	1	2	yes	complemented
137	#16811158	C₂²	1	4	yes	complemented
138	#16811155	C₂²	1	4	yes	complemented
139	#16811155	C₂²	1	2	yes	complemented
140	#16811153	C₂²	1	4	yes	complemented
141	#16811151	C₂²	1	4	yes	complemented
142	C₂×#13133206	C₂²	1	1	yes	characteristic, complemented
143	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
144	C₂×#13133205	C₂²	1	2	yes	complemented
145	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
146	C₂×#13133203	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	4	yes	complemented
150	#124×D₅₃	C₂²	1	4	yes	complemented
151	#124×D₅₃	C₂²	1	2	yes	complemented
152	#124×D₅₃	C₂²	1	2	yes	complemented
153	#124×D₅₃	C₂²	1	2	yes	complemented
154	#16811136	C₂²	1	4	yes	complemented
155	#16811135	C₂²	1	1	yes	characteristic, complemented
156	#16811135	C₂²	1	1	yes	characteristic, complemented
157	#16811135	C₂²	1	1	yes	characteristic, complemented
158	#16811135	C₂²	1	4	yes	complemented
159	#16811132	C₂²	1	4	yes	complemented
160	#16811131	C₂²	1	4	yes	complemented
161	#16811130	C₂²	1	1	yes	characteristic, complemented
162	C₂×#13133187	C₂²	1	4	yes	complemented
163	#120×D₅₃	C₂²	1	4	yes	complemented
164	#16811100	C₂²	1	1	yes	characteristic, complemented
165	#16811097	C₂²	1	1	yes	characteristic, complemented
166	#16811097	C₂²	1	8	yes	complemented
167	#16811095	C₂²	1	8	yes	complemented
168	C₄×#11719949	C₂²	1	4	yes	complemented
169	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
170	C₄×#11719945	C₂²	1	4	yes	complemented
171	#16811091	C₂²	1	1	yes	characteristic, complemented
172	#16811091	C₂²	1	1	yes	characteristic, complemented
173	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
174	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#559	C₂²	1	4	yes	complemented
176	C₅₃×#556	C₂²	1	4	yes	complemented
177	C₅₃×#551	C₂²	1	8	yes	complemented
178	C₅₃×#542	C₂²	1	4	yes	complemented
179	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#535	C₂²	1	1	yes	characteristic
181	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#529	C₂²	1	4	yes	complemented
183	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
186	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁴×D₅₃	C₂³	1	2	yes	—
188	#13133265	—	4	4	no	—
189	#13133264	—	4	4	no	—
190	#13133263	—	4	4	no	—
191	#13133262	—	4	4	no	—
192	C₂×#11719949	C₂³	1	4	yes	—
193	C₂×#11719949	C₂³	1	2	yes	—
194	C₂×#11719949	C₂³	1	2	yes	complemented
195	C₂×#11719949	C₂³	1	2	yes	complemented
196	C₂×#11719945	C₂³	1	1	yes	characteristic
197	C₂×#11719945	C₂³	1	1	yes	characteristic
198	C₂×#11719945	C₂³	1	1	yes	characteristic
199	C₂×#11719945	C₂³	1	4	yes	—
200	C₂×#11719945	C₂³	1	4	yes	—
201	C₂×#11719945	C₂³	1	2	yes	—
202	C₂×#11719945	C₂³	1	2	yes	complemented
203	C₂×#11719947	C₂³	1	2	yes	—
204	C₂×#11719947	C₂³	1	2	yes	—
205	C₂×#11719947	C₂³	1	4	yes	—
206	C₂×#11719947	C₂³	1	2	yes	complemented
207	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
208	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
209	C₂²×Dic₁₀₆	C₂³	1	2	yes	complemented
210	C₂×Q₈×D₅₃	—	4	4	no	—
211	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
212	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
213	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
214	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
215	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
216	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
217	C₂²×D₂₁₂	C₂³	1	2	yes	—
218	C₂²×D₂₁₂	C₂³	1	8	yes	—
219	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
220	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
221	C₂×D₄×D₅₃	—	4	4	no	—
222	C₂×D₄×D₅₃	C₂³	1	4	yes	—
223	C₂×D₄×D₅₃	C₂³	1	8	yes	—
224	C₂×D₄×D₅₃	C₂³	1	2	yes	—
225	C₂×D₄×D₅₃	C₂³	1	4	yes	—
226	C₂×D₄×D₅₃	C₂³	1	2	yes	—
227	C₂×D₄×D₅₃	C₂³	1	4	yes	—
228	C₂×D₄×D₅₃	C₂³	1	2	yes	—
229	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
230	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
231	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
232	#13133217	C₂³	1	8	yes	complemented
233	#13133217	C₂³	1	2	yes	complemented
234	#13133217	C₂³	1	2	yes	complemented
235	#13133217	C₂³	1	1	yes	characteristic, complemented
236	#13133216	C₂³	1	8	yes	complemented
237	#13133216	C₂³	1	2	yes	complemented
238	#13133215	C₂³	1	2	yes	complemented
239	#13133215	C₂³	1	1	yes	characteristic, complemented
240	#13133214	C₂³	1	2	yes	—
241	#13133214	C₂³	1	2	yes	—
242	#13133214	C₂³	1	1	yes	characteristic, complemented
243	#13133213	C₂³	1	2	yes	—
244	#13133213	C₂³	1	1	yes	characteristic, complemented
245	#13133212	C₂³	1	8	yes	complemented
246	#13133212	C₂³	1	8	yes	complemented
247	#13133212	C₂³	1	8	yes	complemented
248	#13133212	C₂³	1	4	yes	complemented
249	#13133212	C₂³	1	4	yes	complemented
250	#13133212	C₂³	1	4	yes	complemented
251	#13133211	C₂³	1	8	yes	complemented
252	#13133210	C₂³	1	8	yes	complemented
253	#13133210	C₂³	1	8	yes	complemented
254	#13133210	C₂³	1	4	yes	complemented
255	#13133208	C₂³	1	4	yes	complemented
256	#13133208	C₂³	1	2	yes	complemented
257	#13133207	C₂³	1	4	yes	complemented
258	#13133206	C₂³	1	4	yes	—
259	#13133206	C₂³	1	2	yes	—
260	#13133206	C₂³	1	2	yes	—
261	#13133206	C₂³	1	8	yes	complemented
262	#13133206	C₂³	1	2	yes	complemented
263	#13133206	C₂³	1	4	yes	complemented
264	#13133206	C₂³	1	1	yes	characteristic, complemented
265	#13133205	C₂³	1	2	yes	—
266	#13133205	C₂³	1	2	yes	—
267	#13133205	C₂³	1	4	yes	—
268	#13133205	C₂³	1	2	yes	—
269	#13133205	C₂³	1	2	yes	—
270	#13133205	C₂³	1	8	yes	complemented
271	#13133205	C₂³	1	8	yes	complemented
272	#13133205	C₂³	1	8	yes	complemented
273	#13133205	C₂³	1	2	yes	complemented
274	#13133205	C₂³	1	2	yes	complemented
275	#13133205	C₂³	1	1	yes	characteristic, complemented
276	#13133205	C₂³	1	1	yes	characteristic, complemented
277	#13133204	C₂³	1	2	yes	—
278	#13133204	C₂³	1	4	yes	—
279	#13133204	C₂³	1	2	yes	—
280	#13133204	C₂³	1	2	yes	—
281	#13133204	C₂³	1	1	yes	characteristic, complemented
282	#13133203	C₂³	1	8	yes	—
283	#13133203	C₂³	1	8	yes	—
284	#13133203	C₂³	1	8	yes	—
285	#13133203	C₂³	1	8	yes	—
286	#13133203	C₂³	1	8	yes	complemented
287	#13133203	C₂³	1	8	yes	complemented
288	#13133203	C₂³	1	8	yes	complemented
289	#13133203	C₂³	1	8	yes	complemented
290	#13133203	C₂³	1	8	yes	complemented
291	#13133203	C₂³	1	4	yes	complemented
292	#13133202	C₂³	1	4	yes	—
293	#13133202	C₂³	1	4	yes	—
294	#13133202	C₂³	1	4	yes	—
295	#13133202	C₂³	1	8	yes	complemented
296	#13133202	C₂³	1	8	yes	complemented
297	#13133202	C₂³	1	8	yes	complemented
298	#13133202	C₂³	1	8	yes	complemented
299	#13133202	C₂³	1	8	yes	complemented
300	#13133201	C₂³	1	8	yes	—
301	#13133201	C₂³	1	4	yes	—
302	#13133201	C₂³	1	4	yes	—
303	#13133201	C₂³	1	2	yes	—
304	#13133201	C₂³	1	2	yes	—
305	#13133201	C₂³	1	2	yes	—
306	#13133201	C₂³	1	8	yes	complemented
307	#13133200	C₂³	1	4	yes	—
308	#13133200	C₂³	1	8	yes	complemented
309	#13133199	C₂³	1	4	yes	—
310	#13133199	C₂³	1	8	yes	—
311	#13133199	C₂³	1	8	yes	complemented
312	#13133199	C₂³	1	8	yes	complemented
313	#13133199	C₂³	1	8	yes	complemented
314	#13133198	C₂³	1	2	yes	—
315	#13133197	C₂³	1	2	yes	—
316	#13133197	C₂³	1	2	yes	—
317	#13133197	C₂³	1	2	yes	—
318	#13133197	C₂³	1	8	yes	—
319	#13133197	C₂³	1	4	yes	complemented
320	#13133197	C₂³	1	8	yes	complemented
321	#13133197	C₂³	1	4	yes	complemented
322	#13133197	C₂³	1	8	yes	complemented
323	#13133197	C₂³	1	8	yes	complemented
324	#13133196	C₂³	1	8	yes	complemented
325	#13133195	C₂³	1	8	yes	—
326	#13133195	C₂³	1	4	yes	—
327	#13133195	C₂³	1	8	yes	complemented
328	#13133195	C₂³	1	8	yes	complemented
329	#13133195	C₂³	1	8	yes	complemented
330	#13133194	C₂³	1	4	yes	—
331	#13133194	C₂³	1	8	yes	complemented
332	#13133194	C₂³	1	8	yes	complemented
333	#13133194	C₂³	1	8	yes	complemented
334	#13133193	C₂³	1	2	yes	—
335	#13133193	C₂³	1	4	yes	—
336	#13133193	C₂³	1	4	yes	complemented
337	#13133193	C₂³	1	8	yes	complemented
338	#13133192	C₂³	1	8	yes	—
339	#13133192	C₂³	1	4	yes	—
340	#13133192	C₂³	1	4	yes	—
341	#13133192	C₂³	1	2	yes	—
342	#13133192	C₂³	1	2	yes	—
343	#13133192	C₂³	1	2	yes	—
344	#13133192	C₂³	1	4	yes	—
345	#13133192	C₂³	1	8	yes	complemented
346	#13133192	C₂³	1	8	yes	complemented
347	#13133191	C₂³	1	4	yes	—
348	#13133191	C₂³	1	8	yes	—
349	#13133191	C₂³	1	8	yes	—
350	#13133191	C₂³	1	8	yes	complemented
351	#13133190	C₂³	1	8	yes	—
352	#13133190	C₂³	1	8	yes	—
353	#13133190	C₂³	1	4	yes	—
354	#13133190	C₂³	1	8	yes	complemented
355	#13133190	C₂³	1	8	yes	complemented
356	#13133190	C₂³	1	8	yes	complemented
357	#13133189	C₂³	1	4	yes	—
358	#13133189	C₂³	1	8	yes	complemented
359	#13133188	C₂³	1	4	yes	—
360	#13133188	C₂³	1	8	yes	—
361	#13133188	C₂³	1	2	yes	—
362	#13133188	C₂³	1	8	yes	complemented
363	#13133187	C₂³	1	8	yes	—
364	#13133187	C₂³	1	4	yes	—
365	#13133187	C₂³	1	8	yes	—
366	#13133187	C₂³	1	8	yes	—
367	#13133187	C₂³	1	4	yes	—
368	#13133187	C₂³	1	8	yes	—
369	#13133187	C₂³	1	2	yes	—
370	#13133187	C₂³	1	2	yes	—
371	#13133187	C₂³	1	2	yes	—
372	#13133187	C₂³	1	8	yes	complemented
373	#13133187	C₂³	1	8	yes	complemented
374	#13133187	C₂³	1	8	yes	complemented
375	#13133186	C₂³	1	4	yes	—
376	#13133185	C₂³	1	8	yes	—
377	#13133185	C₂³	1	8	yes	—
378	#13133185	C₂³	1	2	yes	—
379	#13133185	C₂³	1	8	yes	complemented
380	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
381	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
382	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
383	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
384	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
385	#13133182	C₂³	1	2	yes	complemented
386	#13133182	C₂³	1	2	yes	complemented
387	#13133182	C₂³	1	4	yes	complemented
388	C₄×D₂₁₂	C₂³	1	8	yes	—
389	C₄×D₂₁₂	C₂³	1	4	yes	—
390	C₄×D₂₁₂	C₂³	1	4	yes	—
391	C₄×D₂₁₂	C₂³	1	4	yes	—
392	C₄×D₂₁₂	C₂³	1	4	yes	—
393	C₄×D₂₁₂	C₂³	1	8	yes	—
394	C₄×D₂₁₂	C₂³	1	4	yes	—
395	C₄×D₂₁₂	C₂³	1	2	yes	complemented
396	C₄×D₂₁₂	C₂³	1	4	yes	complemented
397	C₄×D₂₁₂	C₂³	1	8	yes	complemented
398	C₄×D₂₁₂	C₂³	1	8	yes	complemented
399	D₄×Dic₅₃	C₂³	1	8	yes	complemented
400	#13133179	C₂³	1	8	yes	—
401	#13133179	C₂³	1	4	yes	—
402	#13133179	C₂³	1	4	yes	—
403	#13133179	C₂³	1	4	yes	—
404	#13133179	C₂³	1	2	yes	complemented
405	#13133179	C₂³	1	8	yes	complemented
406	#13133179	C₂³	1	8	yes	complemented
407	#13133179	C₂³	1	2	yes	complemented
408	#13133179	C₂³	1	4	yes	complemented
409	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
410	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
411	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
412	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
413	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
414	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
415	#13133177	C₂³	1	4	yes	—
416	#13133177	C₂³	1	8	yes	—
417	#13133177	C₂³	1	4	yes	—
418	#13133177	C₂³	1	8	yes	complemented
419	#13133176	C₂³	1	1	yes	characteristic
420	#13133176	C₂³	1	4	yes	complemented
421	#13133176	C₂³	1	8	yes	complemented
422	#13133175	C₂³	1	4	yes	—
423	#13133175	C₂³	1	4	yes	complemented
424	#13133175	C₂³	1	4	yes	complemented
425	#13133175	C₂³	1	8	yes	complemented
426	#13133174	C₂³	1	4	yes	—
427	#13133174	C₂³	1	8	yes	complemented
428	#13133174	C₂³	1	4	yes	complemented
429	#13133174	C₂³	1	2	yes	complemented
430	#13133174	C₂³	1	2	yes	complemented
431	#13133174	C₂³	1	2	yes	complemented
432	#13133173	C₂³	1	4	yes	—
433	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
434	C₂×#11719921	C₂³	1	4	yes	—
435	C₂×#11719921	C₂³	1	8	yes	—
436	C₂×#11719921	C₂³	1	4	yes	—
437	C₂×#11719921	C₂³	1	8	yes	complemented
438	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
439	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
440	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
441	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
442	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
443	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
444	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
445	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
446	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
447	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
448	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
449	C₄²×D₅₃	C₂³	1	2	yes	—
450	C₄²×D₅₃	C₂³	1	2	yes	—
451	C₄²×D₅₃	C₂³	1	2	yes	—
452	C₄²×D₅₃	C₂³	1	2	yes	—
453	C₄²×D₅₃	C₂³	1	2	yes	complemented
454	C₄²×D₅₃	C₂³	1	2	yes	complemented
455	C₄²×D₅₃	C₂³	1	2	yes	complemented
456	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
457	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
458	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
459	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
460	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
461	#127×C₅₃	C₂³	1	2	yes	—
462	#126×C₅₃	C₂³	1	8	yes	complemented
463	#126×C₅₃	C₂³	1	8	yes	complemented
464	#125×C₅₃	C₂³	1	2	yes	complemented
465	#124×C₅₃	C₂³	1	2	yes	—
466	#124×C₅₃	C₂³	1	4	yes	—
467	#124×C₅₃	C₂³	1	2	yes	—
468	#124×C₅₃	C₂³	1	2	yes	—
469	#124×C₅₃	C₂³	1	8	yes	complemented
470	#124×C₅₃	C₂³	1	2	yes	complemented
471	#123×C₅₃	C₂³	1	4	yes	—
472	#123×C₅₃	C₂³	1	8	yes	complemented
473	#123×C₅₃	C₂³	1	8	yes	complemented
474	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
475	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
476	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
477	#121×C₅₃	C₂³	1	4	yes	—
478	#120×C₅₃	C₂³	1	4	yes	—
479	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
480	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
481	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
482	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
483	C₄×D₄×C₅₃	C₂³	1	4	yes	—
484	C₄×D₄×C₅₃	C₂³	1	4	yes	—
485	C₄×D₄×C₅₃	C₂³	1	4	yes	—
486	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
487	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
488	#117×C₅₃	C₂³	1	1	yes	characteristic
489	#117×C₅₃	C₂³	1	1	yes	characteristic
490	#117×C₅₃	C₂³	1	4	yes	—
491	#117×C₅₃	C₂³	1	1	yes	characteristic
492	#117×C₅₃	C₂³	1	2	yes	complemented
493	#117×C₅₃	C₂³	1	8	yes	complemented
494	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
495	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
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	C₂³×D₅₃	—	4	8	no	—
500	C₂³×D₅₃	—	4	4	no	—
501	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
502	C₂³×D₅₃	C₂⁴	1	8	yes	—
503	C₂³×D₅₃	C₂⁴	1	2	yes	—
504	C₂³×D₅₃	C₂⁴	1	4	yes	—
505	C₂³×D₅₃	C₂⁴	1	4	yes	—
506	#41×C₅₃	—	2	4	no	—
507	C₂×Q₈×C₅₃	—	2	4	no	—
508	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
509	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
510	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
512	C₂×D₄×C₅₃	—	2	4	no	—
513	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
514	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
515	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
516	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
517	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
518	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
519	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
520	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
521	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
522	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
523	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
524	C₂×C₂²⋊D₅₃	—	4	4	no	—
525	C₂×C₂²⋊D₅₃	—	4	8	no	—
526	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
527	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
528	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
529	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
530	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
531	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
532	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
533	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
534	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
535	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
536	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
537	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
538	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
539	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
540	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
541	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
542	#11719949	—	4	8	no	—
543	#11719949	—	4	4	no	—
544	#11719949	—	4	4	no	—
545	#11719949	—	4	4	no	—
546	Q₈×D₅₃	—	4	8	no	—
547	Q₈×D₅₃	—	4	8	no	—
548	Q₈×D₅₃	—	4	4	no	—
549	Q₈×D₅₃	—	4	4	no	—
550	Q₈×D₅₃	—	4	4	no	—
551	#11719947	—	4	4	no	—
552	#11719947	—	4	4	no	—
553	#11719947	—	4	4	no	—
554	#11719947	—	4	8	no	—
555	D₄×D₅₃	—	4	8	no	—
556	D₄×D₅₃	—	4	8	no	—
557	D₄×D₅₃	—	4	4	no	—
558	D₄×D₅₃	—	4	4	no	—
559	D₄×D₅₃	—	4	4	no	—
560	D₄×D₅₃	—	4	16	no	—
561	D₄×D₅₃	—	4	8	no	—
562	#11719945	—	2	4	no	—
563	#11719945	—	2	4	no	—
564	#11719945	—	2	4	no	—
565	#11719945	—	4	4	no	—
566	#11719945	—	4	4	no	—
567	#11719945	—	4	8	no	—
568	#11719945	—	4	8	no	—
569	C₂×D₂₁₂	—	2	4	no	—
570	C₂×D₂₁₂	—	4	4	no	—
571	C₂×D₂₁₂	—	4	16	no	—
572	C₂×D₂₁₂	C₂⁴	1	4	yes	—
573	C₂×D₂₁₂	C₂⁴	1	2	yes	—
574	C₂×D₂₁₂	C₂⁴	1	4	yes	—
575	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
576	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
577	C₂×D₂₁₂	C₂⁴	1	4	yes	—
578	C₂×D₂₁₂	C₂⁴	1	2	yes	—
579	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
580	C₂×D₂₁₂	C₂⁴	1	8	yes	—
581	C₂×D₂₁₂	C₂⁴	1	4	yes	—
582	C₂×D₂₁₂	C₂⁴	1	8	yes	—
583	C₂×D₂₁₂	C₂⁴	1	4	yes	—
584	C₂×D₂₁₂	C₂⁴	1	4	yes	—
585	C₂×C₄×D₅₃	—	2	4	no	—
586	C₂×C₄×D₅₃	—	4	4	no	—
587	C₂×C₄×D₅₃	—	4	4	no	—
588	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
589	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
590	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
591	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
592	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
593	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
594	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
595	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
596	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
597	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
598	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
599	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
600	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
601	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
602	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
603	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
604	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
605	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
606	C₂×Dic₁₀₆	—	2	4	no	—
607	C₂×Dic₁₀₆	—	4	4	no	—
608	C₂×Dic₁₀₆	—	4	4	no	—
609	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
610	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
611	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
612	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
613	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
614	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
615	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
616	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
617	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
618	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
619	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
620	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
621	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
622	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
623	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
624	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
625	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
626	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
627	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
628	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
629	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
630	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
631	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
632	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
633	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
634	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
635	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
636	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
637	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄²×C₅₃	C₂⁴	1	2	yes	—
639	C₄²×C₅₃	C₂⁴	1	2	yes	—
640	C₄²×C₅₃	C₂⁴	1	4	yes	—
641	C₄²×C₅₃	C₂⁴	1	8	yes	—
642	C₄²×C₅₃	C₂⁴	1	2	yes	—
643	C₄²×C₅₃	C₂⁴	1	2	yes	—
644	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
645	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
646	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
647	C₂²⋊Dic₅₃	C₂⁴	1	8	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	4	yes	—
658	#11719921	C₂⁴	1	4	yes	—
659	#11719921	C₂⁴	1	8	yes	—
660	#11719921	C₂⁴	1	8	yes	—
661	#11719921	C₂⁴	1	8	yes	—
662	#11719921	C₂⁴	1	4	yes	—
663	#11719921	C₂⁴	1	4	yes	—
664	#11719921	C₂⁴	1	8	yes	—
665	#11719921	C₂⁴	1	4	yes	—
666	#11719921	C₂⁴	1	8	yes	—
667	#11719921	C₂⁴	1	4	yes	—
668	#11719921	C₂⁴	1	4	yes	—
669	#11719921	C₂⁴	1	4	yes	—
670	#11719921	C₂⁴	1	4	yes	—
671	#11719921	C₂⁴	1	4	yes	—
672	#11719921	C₂⁴	1	4	yes	—
673	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
674	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
675	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
676	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
677	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
678	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
679	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
680	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
681	#11719919	C₂⁴	1	8	yes	—
682	#11719919	C₂⁴	1	4	yes	—
683	#11719919	C₂⁴	1	4	yes	—
684	#11719919	C₂⁴	1	4	yes	—
685	#11719919	C₂⁴	1	8	yes	—
686	#11719919	C₂⁴	1	4	yes	—
687	#11719919	C₂⁴	1	4	yes	—
688	#11719919	C₂⁴	1	4	yes	—
689	#11719919	C₂⁴	1	4	yes	—
690	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
691	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
692	C₄×Dic₅₃	C₂⁴	1	2	yes	—
693	C₄×Dic₅₃	C₂⁴	1	2	yes	—
694	C₄×Dic₅₃	C₂⁴	1	2	yes	—
695	C₄×Dic₅₃	C₂⁴	1	2	yes	—
696	C₄×Dic₅₃	C₂⁴	1	2	yes	—
697	C₄×Dic₅₃	C₂⁴	1	4	yes	—
698	C₄×Dic₅₃	C₂⁴	1	4	yes	—
699	C₄×Dic₅₃	C₂⁴	1	2	yes	—
700	C₄×Dic₅₃	C₂⁴	1	4	yes	—
701	C₄×Dic₅₃	C₂⁴	1	8	yes	—
702	C₂³×C₅₃	—	2	4	no	—
703	C₂³×C₅₃	—	4	4	no	—
704	C₂³×C₅₃	C₂⁵	1	2	yes	—
705	C₂³×C₅₃	C₂⁵	1	4	yes	—
706	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
707	C₂²×D₅₃	—	2	2	no	—
708	C₂²×D₅₃	—	2	4	no	—
709	C₂²×D₅₃	—	2	4	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	C₂²×D₅₃	—	4	4	no	—
717	C₂²×D₅₃	—	4	8	no	—
718	C₂²×D₅₃	—	8	16	no	—
719	C₂²×D₅₃	C₂⁵	1	2	yes	—
720	C₂²×D₅₃	C₂⁵	1	2	yes	—
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	—	4	4	no	—
728	D₄×C₅₃	—	2	4	no	—
729	D₄×C₅₃	—	2	4	no	—
730	D₄×C₅₃	—	2	4	no	—
731	D₄×C₅₃	—	2	2	no	—
732	D₄×C₅₃	—	4	8	no	—
733	C₂×C₄×C₅₃	—	2	4	no	—
734	C₂×C₄×C₅₃	—	2	4	no	—
735	C₂×C₄×C₅₃	—	4	2	no	—
736	C₂×C₄×C₅₃	—	4	8	no	—
737	C₂×C₄×C₅₃	—	4	4	no	—
738	C₂×C₄×C₅₃	H(5,𝔽₂)	1	4	yes	—
739	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
740	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
741	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
742	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
743	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
744	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
745	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
746	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
747	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
748	C₂²⋊D₅₃	—	2	4	no	—
749	C₂²⋊D₅₃	—	2	4	no	—
750	C₂²⋊D₅₃	—	2	4	no	—
751	C₂²⋊D₅₃	—	2	8	no	—
752	C₂²⋊D₅₃	—	4	4	no	—
753	C₂²⋊D₅₃	—	4	4	no	—
754	C₂²⋊D₅₃	—	4	4	no	—
755	C₂²⋊D₅₃	—	4	8	no	—
756	C₂²⋊D₅₃	—	4	4	no	—
757	C₂²⋊D₅₃	—	4	4	no	—
758	C₂²⋊D₅₃	—	4	8	no	—
759	C₂×Dic₅₃	—	2	4	no	—
760	C₂×Dic₅₃	—	2	2	no	—
761	C₂×Dic₅₃	—	4	4	no	—
762	C₂×Dic₅₃	—	4	2	no	—
763	C₂×Dic₅₃	—	4	4	no	—
764	C₂×Dic₅₃	C₂⁵	1	4	yes	—
765	C₂×Dic₅₃	C₂⁵	1	2	yes	—
766	C₂×Dic₅₃	C₂⁵	1	2	yes	—
767	C₂×Dic₅₃	C₂⁵	1	2	yes	—
768	C₂×Dic₅₃	C₂⁵	1	2	yes	—
769	C₂×Dic₅₃	C₂⁵	1	2	yes	—
770	C₂×Dic₅₃	C₂⁵	1	4	yes	—
771	C₂×Dic₅₃	C₂⁵	1	2	yes	—
772	D₂₁₂	—	2	8	no	—
773	D₂₁₂	—	2	8	no	—
774	D₂₁₂	—	2	8	no	—
775	D₂₁₂	—	2	4	no	—
776	D₂₁₂	—	2	4	no	—
777	D₂₁₂	—	2	2	no	—
778	D₂₁₂	—	2	2	no	—
779	D₂₁₂	—	2	2	no	—
780	D₂₁₂	—	4	8	no	—
781	D₂₁₂	—	4	8	no	—
782	D₂₁₂	—	4	4	no	—
783	D₂₁₂	—	4	4	no	—
784	D₂₁₂	—	4	4	no	—
785	C₄×D₅₃	—	2	4	no	—
786	C₄×D₅₃	—	2	4	no	—
787	C₄×D₅₃	—	2	4	no	—
788	C₄×D₅₃	—	2	4	no	—
789	C₄×D₅₃	—	2	4	no	—
790	C₄×D₅₃	—	2	4	no	—
791	C₄×D₅₃	—	2	4	no	—
792	C₄×D₅₃	—	4	2	no	—
793	C₄×D₅₃	—	4	2	no	—
794	C₄×D₅₃	—	4	8	no	—
795	C₄×D₅₃	—	4	4	no	—
796	C₄×D₅₃	—	4	4	no	—
797	C₄×D₅₃	—	4	4	no	—
798	C₄×D₅₃	—	4	4	no	—
799	C₄×D₅₃	—	4	4	no	—
800	C₄×D₅₃	—	4	8	no	—
801	C₄×D₅₃	—	4	4	no	—
802	C₄×D₅₃	—	4	4	no	—
803	Dic₁₀₆	—	2	4	no	—
804	Dic₁₀₆	—	2	4	no	—
805	Dic₁₀₆	—	2	2	no	—
806	Dic₁₀₆	—	2	2	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	4	no	—
816	C₂²×C₅₃	—	2	4	no	—
817	C₂²×C₅₃	—	2	8	no	—
818	C₂²×C₅₃	—	8	4	no	—
819	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
820	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
821	C₂×D₅₃	—	2	8	no	—
822	C₂×D₅₃	—	2	2	no	—
823	C₂×D₅₃	—	2	2	no	—
824	C₂×D₅₃	—	2	2	no	—
825	C₂×D₅₃	—	2	2	no	—
826	C₂×D₅₃	—	2	2	no	—
827	C₂×D₅₃	—	2	4	no	—
828	C₂×D₅₃	—	2	4	no	—
829	C₂×D₅₃	—	2	4	no	—
830	C₂×D₅₃	—	2	4	no	—
831	C₂×D₅₃	—	2	8	no	—
832	C₂×D₅₃	—	8	16	no	—
833	C₂×D₅₃	—	8	4	no	—
834	C₂×D₅₃	—	16	4	no	—
835	C₂×D₅₃	—	16	4	no	—
836	C₂×D₅₃	#585	1	4	yes	—
837	C₄×C₅₃	—	2	4	no	—
838	C₄×C₅₃	—	2	2	no	—
839	C₄×C₅₃	—	2	4	no	—
840	C₄×C₅₃	—	2	2	no	—
841	C₄×C₅₃	—	2	2	no	—
842	C₄×C₅₃	—	2	4	no	—
843	C₄×C₅₃	—	2	4	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	2	no	—
851	Dic₅₃	—	2	2	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	D₅₃	1	1	yes	characteristic, complemented
867	#3500	—	53	1	no	—
868	#3500	—	53	1	no	—
869	#3500	—	53	1	no	—
870	#3500	—	53	1	no	—
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	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
883	C₂×C₅₃	C₂×#585	1	2	yes	—
884	D₅₃	—	2	4	no	—
885	D₅₃	—	4	4	no	—
886	D₅₃	—	4	2	no	—
887	D₅₃	—	4	2	no	—
888	D₅₃	—	4	2	no	—
889	C₂×2₋¹⁺⁴	—	53	1	no	—
890	C₂×2₋¹⁺⁴	—	53	1	no	—
891	C₂×H(5,𝔽₂)	—	53	1	no	—
892	C₂×H(5,𝔽₂)	—	53	1	no	—
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	C₂×D₅₃	1	4	yes	complemented
903	#556	—	53	4	no	—
904	#556	—	53	4	no	—
905	#556	—	53	4	no	—
906	#556	C₂×D₅₃	1	4	yes	complemented
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	C₂×D₅₃	1	8	yes	complemented
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	—	53	4	no	—
931	#546	—	53	4	no	—
932	#546	—	53	4	no	—
933	#546	—	53	8	no	—
934	#546	—	53	8	no	—
935	#546	—	53	8	no	—
936	#546	—	53	8	no	—
937	#546	—	53	4	no	—
938	#546	—	53	4	no	—
939	#546	—	53	4	no	—
940	#546	—	53	8	no	—
941	#546	—	53	4	no	—
942	#546	—	53	4	no	—
943	#546	—	53	8	no	—
944	#546	—	53	4	no	—
945	#546	—	53	8	no	—
946	#546	—	53	8	no	—
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	8	no	—
956	#542	—	53	4	no	—
957	#542	—	53	4	no	—
958	#542	—	53	8	no	—
959	#542	C₂×D₅₃	1	4	yes	complemented
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	2	no	—
970	#536	—	53	2	no	—
971	#536	—	53	2	no	—
972	#536	—	53	4	no	—
973	#536	—	53	1	no	—
974	#536	—	53	1	no	—
975	#536	—	53	4	no	—
976	#536	—	53	2	no	—
977	#536	C₂×D₅₃	1	1	yes	characteristic, complemented
978	#535	—	53	1	no	—
979	#535	—	53	2	no	—
980	#535	—	53	2	no	—
981	#535	—	53	2	no	—
982	#535	—	53	1	no	—
983	#535	—	53	1	no	—
984	#535	—	53	2	no	—
985	#535	C₂×D₅₃	1	1	yes	characteristic
986	#534	—	53	8	no	—
987	#534	—	53	4	no	—
988	#534	—	53	4	no	—
989	#533	—	53	2	no	—
990	#533	—	53	2	no	—
991	#533	—	53	1	no	—
992	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
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	—	53	1	no	—
1000	#532	—	53	2	no	—
1001	#529	—	53	2	no	—
1002	#529	—	53	2	no	—
1003	#529	—	53	4	no	—
1004	#529	—	53	4	no	—
1005	#529	—	53	2	no	—
1006	#529	—	53	4	no	—
1007	#529	—	53	4	no	—
1008	#529	—	53	4	no	—
1009	#529	—	53	4	no	—
1010	#529	—	53	2	no	—
1011	#529	—	53	4	no	—
1012	#529	C₂×D₅₃	1	4	yes	complemented
1013	C₂×#124	—	53	1	no	—
1014	C₂×#124	—	53	1	no	—
1015	C₂×#124	—	53	4	no	—
1016	C₂×#124	—	53	4	no	—
1017	C₂×#124	—	53	4	no	—
1018	C₂×#124	—	53	4	no	—
1019	C₂×#124	—	53	2	no	—
1020	C₂×#124	—	53	2	no	—
1021	C₂×#124	—	53	2	no	—
1022	C₂×#124	—	53	4	no	—
1023	C₂×#124	—	53	1	no	—
1024	C₂×#124	—	53	2	no	—
1025	C₂×#124	C₂×D₅₃	1	1	yes	characteristic, complemented
1026	#525	—	53	1	no	—
1027	#525	—	53	4	no	—
1028	#525	—	53	4	no	—
1029	#525	—	53	4	no	—
1030	#525	—	53	1	no	—
1031	#525	—	53	1	no	—
1032	#525	—	53	1	no	—
1033	#525	—	53	4	no	—
1034	C₂×#120	—	53	4	no	—
1035	C₂×#120	—	53	4	no	—
1036	#519	—	53	1	no	—
1037	#519	C₂×D₅₃	1	1	yes	characteristic, complemented
1038	#518	—	53	8	no	—
1039	#518	—	53	1	no	—
1040	#518	—	53	8	no	—
1041	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
1042	C₄×#41	—	53	4	no	—
1043	C₄×#41	—	53	1	no	—
1044	C₄×#41	—	53	1	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	—	212	4	no	—
1053	2₋¹⁺⁴	—	212	4	no	—
1054	H(5,𝔽₂)	—	212	4	no	—
1055	H(5,𝔽₂)	—	212	4	no	—
1056	C₂×#41	—	53	4	no	—
1057	C₂×#41	—	53	2	no	—
1058	C₂×#41	—	53	2	no	—
1059	C₂×#41	—	53	2	no	—
1060	C₂×#41	—	53	4	no	—
1061	C₂×#41	—	53	2	no	—
1062	C₂×#41	—	53	2	no	—
1063	C₂×#41	—	53	2	no	—
1064	C₂×#41	—	53	1	no	—
1065	C₂×#41	—	53	1	no	—
1066	C₂×#41	—	53	1	no	—
1067	C₂×#41	—	53	4	no	—
1068	C₂×#41	—	53	4	no	—
1069	C₂×#41	—	53	2	no	—
1070	C₂×#41	—	53	2	no	—
1071	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1072	C₂²×Q₈	—	53	4	no	—
1073	C₂²×Q₈	—	53	4	no	—
1074	C₂²×Q₈	—	53	2	no	—
1075	C₂²×Q₈	—	53	2	no	—
1076	C₂²×Q₈	—	53	2	no	—
1077	C₂²×Q₈	—	53	1	no	—
1078	C₂²×Q₈	—	53	2	no	—
1079	C₂²×Q₈	—	53	2	no	—
1080	C₂²×Q₈	—	212	4	no	—
1081	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1082	C₂²×D₄	—	53	4	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	2	no	—
1090	C₂²×D₄	—	53	2	no	—
1091	C₂²×D₄	—	53	1	no	—
1092	C₂²×D₄	—	53	8	no	—
1093	C₂²×D₄	—	53	2	no	—
1094	C₂²×D₄	—	212	4	no	—
1095	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
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	8	no	—
1103	C₄⋊Q₈	—	53	1	no	—
1104	C₄⋊Q₈	—	53	2	no	—
1105	C₄⋊Q₈	—	53	2	no	—
1106	C₄⋊Q₈	—	53	8	no	—
1107	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1108	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1109	#127	—	53	1	no	—
1110	#127	—	53	2	no	—
1111	#127	—	53	1	no	—
1112	#127	—	53	2	no	—
1113	#127	—	53	2	no	—
1114	#127	C₂²×D₅₃	1	2	yes	—
1115	#126	—	53	4	no	—
1116	#126	—	53	4	no	—
1117	#126	—	53	4	no	—
1118	#126	—	53	8	no	—
1119	#126	—	53	8	no	—
1120	#126	—	53	8	no	—
1121	#126	—	53	4	no	—
1122	#126	—	53	8	no	—
1123	#126	—	53	8	no	—
1124	#126	—	53	8	no	—
1125	#126	C₂²×D₅₃	1	8	yes	complemented
1126	#126	C₂²×D₅₃	1	8	yes	complemented
1127	#125	—	53	2	no	—
1128	#125	—	53	4	no	—
1129	#125	—	53	4	no	—
1130	#125	C₂²×D₅₃	1	2	yes	complemented
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	4	no	—
1137	#124	—	53	8	no	—
1138	#124	—	53	2	no	—
1139	#124	—	53	2	no	—
1140	#124	—	53	4	no	—
1141	#124	—	53	1	no	—
1142	#124	—	53	2	no	—
1143	#124	—	53	8	no	—
1144	#124	—	53	8	no	—
1145	#124	—	53	8	no	—
1146	#124	—	53	8	no	—
1147	#124	—	53	8	no	—
1148	#124	—	53	8	no	—
1149	#124	—	53	8	no	—
1150	#124	—	53	4	no	—
1151	#124	—	53	8	no	—
1152	#124	—	53	8	no	—
1153	#124	—	53	2	no	—
1154	#124	—	53	2	no	—
1155	#124	—	53	4	no	—
1156	#124	—	53	1	no	—
1157	#124	—	53	1	no	—
1158	#124	—	53	2	no	—
1159	#124	—	53	2	no	—
1160	#124	—	53	2	no	—
1161	#124	—	53	2	no	—
1162	#124	—	53	8	no	—
1163	#124	—	53	8	no	—
1164	#124	—	53	8	no	—
1165	#124	C₂²×D₅₃	1	2	yes	—
1166	#124	C₂²×D₅₃	1	2	yes	—
1167	#124	C₂²×D₅₃	1	4	yes	—
1168	#124	C₂²×D₅₃	1	2	yes	—
1169	#124	C₂²×D₅₃	1	2	yes	complemented
1170	#124	C₂²×D₅₃	1	8	yes	complemented
1171	#123	—	53	2	no	—
1172	#123	—	53	4	no	—
1173	#123	—	53	8	no	—
1174	#123	—	53	4	no	—
1175	#123	—	53	4	no	—
1176	#123	—	53	4	no	—
1177	#123	—	53	8	no	—
1178	#123	—	53	8	no	—
1179	#123	—	53	8	no	—
1180	#123	—	53	8	no	—
1181	#123	—	53	8	no	—
1182	#123	—	53	2	no	—
1183	#123	—	53	2	no	—
1184	#123	—	53	2	no	—
1185	#123	—	53	4	no	—
1186	#123	—	53	4	no	—
1187	#123	—	53	4	no	—
1188	#123	—	53	8	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	C₂²×D₅₃	1	4	yes	—
1195	#123	C₂²×D₅₃	1	8	yes	complemented
1196	#123	C₂²×D₅₃	1	8	yes	complemented
1197	C₂²⋊Q₈	—	53	4	no	—
1198	C₂²⋊Q₈	—	53	2	no	—
1199	C₂²⋊Q₈	—	53	4	no	—
1200	C₂²⋊Q₈	—	53	8	no	—
1201	C₂²⋊Q₈	—	53	8	no	—
1202	C₂²⋊Q₈	—	53	4	no	—
1203	C₂²⋊Q₈	—	53	2	no	—
1204	C₂²⋊Q₈	—	53	2	no	—
1205	C₂²⋊Q₈	—	53	2	no	—
1206	C₂²⋊Q₈	—	53	8	no	—
1207	C₂²⋊Q₈	—	53	8	no	—
1208	C₂²⋊Q₈	—	53	4	no	—
1209	C₂²⋊Q₈	—	53	4	no	—
1210	C₂²⋊Q₈	—	53	8	no	—
1211	C₂²⋊Q₈	—	53	8	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	4	no	—
1217	C₂²⋊Q₈	—	53	8	no	—
1218	C₂²⋊Q₈	—	53	8	no	—
1219	C₂²⋊Q₈	—	53	8	no	—
1220	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
1221	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1222	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
1223	#121	—	53	2	no	—
1224	#121	—	53	4	no	—
1225	#121	—	53	4	no	—
1226	#121	—	53	8	no	—
1227	#121	—	53	8	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	4	no	—
1234	#121	—	53	2	no	—
1235	#121	—	53	2	no	—
1236	#121	—	53	2	no	—
1237	#121	—	53	8	no	—
1238	#121	—	53	4	no	—
1239	#121	—	53	4	no	—
1240	#121	—	53	8	no	—
1241	#121	—	53	8	no	—
1242	#121	—	53	4	no	—
1243	#121	—	53	8	no	—
1244	#121	—	53	8	no	—
1245	#121	—	53	8	no	—
1246	#121	—	53	8	no	—
1247	#121	—	53	8	no	—
1248	#121	C₂²×D₅₃	1	4	yes	—
1249	#120	—	53	4	no	—
1250	#120	—	53	2	no	—
1251	#120	—	53	8	no	—
1252	#120	—	53	8	no	—
1253	#120	—	53	8	no	—
1254	#120	—	53	2	no	—
1255	#120	—	53	2	no	—
1256	#120	—	53	2	no	—
1257	#120	—	53	4	no	—
1258	#120	—	53	4	no	—
1259	#120	—	53	8	no	—
1260	#120	—	53	8	no	—
1261	#120	—	53	8	no	—
1262	#120	—	53	8	no	—
1263	#120	—	53	8	no	—
1264	#120	—	53	8	no	—
1265	#120	—	53	8	no	—
1266	#120	C₂²×D₅₃	1	4	yes	—
1267	C₄×Q₈	—	53	4	no	—
1268	C₄×Q₈	—	53	2	no	—
1269	C₄×Q₈	—	53	2	no	—
1270	C₄×Q₈	—	53	4	no	—
1271	C₄×Q₈	—	53	4	no	—
1272	C₄×Q₈	—	53	2	no	—
1273	C₄×Q₈	—	53	4	no	—
1274	C₄×Q₈	—	53	4	no	—
1275	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1276	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1277	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1278	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1279	C₄×D₄	—	53	8	no	—
1280	C₄×D₄	—	53	4	no	—
1281	C₄×D₄	—	53	4	no	—
1282	C₄×D₄	—	53	4	no	—
1283	C₄×D₄	—	53	4	no	—
1284	C₄×D₄	—	53	4	no	—
1285	C₄×D₄	—	53	8	no	—
1286	C₄×D₄	—	53	4	no	—
1287	C₄×D₄	—	53	4	no	—
1288	C₄×D₄	—	53	4	no	—
1289	C₄×D₄	—	53	2	no	—
1290	C₄×D₄	—	53	2	no	—
1291	C₄×D₄	—	53	8	no	—
1292	C₄×D₄	—	53	8	no	—
1293	C₄×D₄	—	53	4	no	—
1294	C₄×D₄	—	53	8	no	—
1295	C₄×D₄	—	53	4	no	—
1296	C₄×D₄	—	53	4	no	—
1297	C₄×D₄	—	53	8	no	—
1298	C₄×D₄	—	53	8	no	—
1299	C₄×D₄	—	53	4	no	—
1300	C₄×D₄	—	53	4	no	—
1301	C₄×D₄	—	53	4	no	—
1302	C₄×D₄	—	53	4	no	—
1303	C₄×D₄	—	53	4	no	—
1304	C₄×D₄	—	53	2	no	—
1305	C₄×D₄	—	53	8	no	—
1306	C₄×D₄	—	53	8	no	—
1307	C₄×D₄	—	53	8	no	—
1308	C₄×D₄	—	53	4	no	—
1309	C₄×D₄	—	53	8	no	—
1310	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1311	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1312	C₄×D₄	C₂²×D₅₃	1	4	yes	—
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	4	no	—
1317	#117	—	53	8	no	—
1318	#117	—	53	4	no	—
1319	#117	—	53	4	no	—
1320	#117	—	53	4	no	—
1321	#117	—	53	8	no	—
1322	#117	—	53	4	no	—
1323	#117	—	53	4	no	—
1324	#117	—	53	2	no	—
1325	#117	—	53	2	no	—
1326	#117	—	53	2	no	—
1327	#117	—	53	4	no	—
1328	#117	—	53	8	no	—
1329	#117	C₂²×D₅₃	1	1	yes	characteristic
1330	#117	C₂²×D₅₃	1	1	yes	characteristic
1331	#117	C₂²×D₅₃	1	1	yes	characteristic
1332	#117	C₂²×D₅₃	1	4	yes	—
1333	#117	C₂²×D₅₃	1	2	yes	complemented
1334	#117	C₂²×D₅₃	1	8	yes	complemented
1335	C₂×C₂²⋊C₄	—	53	4	no	—
1336	C₂×C₂²⋊C₄	—	53	4	no	—
1337	C₂×C₂²⋊C₄	—	53	4	no	—
1338	C₂×C₂²⋊C₄	—	53	8	no	—
1339	C₂×C₂²⋊C₄	—	53	8	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	4	no	—
1345	C₂×C₂²⋊C₄	—	53	8	no	—
1346	C₂×C₂²⋊C₄	—	53	8	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	4	yes	—
1351	C₂×C₄²	—	53	1	no	—
1352	C₂×C₄²	—	53	2	no	—
1353	C₂×C₄²	—	53	2	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	—	53	4	no	—
1367	C₂⁴	—	212	4	no	—
1368	C₂⁴	—	212	8	no	—
1369	C₂⁴	C₂³×D₅₃	1	2	yes	—
1370	#41	—	2	4	no	—
1371	#41	—	106	4	no	—
1372	#41	—	106	4	no	—
1373	#41	—	106	4	no	—
1374	#41	—	212	8	no	—
1375	#41	—	212	4	no	—
1376	#41	—	212	4	no	—
1377	#41	—	212	8	no	—
1378	#41	—	212	8	no	—
1379	#41	—	212	4	no	—
1380	#41	—	212	4	no	—
1381	#41	—	212	4	no	—
1382	#41	—	212	8	no	—
1383	#41	—	212	4	no	—
1384	#41	—	212	4	no	—
1385	#41	—	212	4	no	—
1386	C₂×Q₈	—	2	4	no	—
1387	C₂×Q₈	—	53	2	no	—
1388	C₂×Q₈	—	53	2	no	—
1389	C₂×Q₈	—	53	1	no	—
1390	C₂×Q₈	—	53	1	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	—	212	4	no	—
1403	C₂×Q₈	—	212	4	no	—
1404	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1405	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1406	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1407	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1408	C₂×D₄	—	2	4	no	—
1409	C₂×D₄	—	53	4	no	—
1410	C₂×D₄	—	53	2	no	—
1411	C₂×D₄	—	53	2	no	—
1412	C₂×D₄	—	53	2	no	—
1413	C₂×D₄	—	53	4	no	—
1414	C₂×D₄	—	53	8	no	—
1415	C₂×D₄	—	53	4	no	—
1416	C₂×D₄	—	53	4	no	—
1417	C₂×D₄	—	53	4	no	—
1418	C₂×D₄	—	53	4	no	—
1419	C₂×D₄	—	53	8	no	—
1420	C₂×D₄	—	53	4	no	—
1421	C₂×D₄	—	53	4	no	—
1422	C₂×D₄	—	53	4	no	—
1423	C₂×D₄	—	53	2	no	—
1424	C₂×D₄	—	53	2	no	—
1425	C₂×D₄	—	53	1	no	—
1426	C₂×D₄	—	53	1	no	—
1427	C₂×D₄	—	53	1	no	—
1428	C₂×D₄	—	53	4	no	—
1429	C₂×D₄	—	53	8	no	—
1430	C₂×D₄	—	53	8	no	—
1431	C₂×D₄	—	53	4	no	—
1432	C₂×D₄	—	53	4	no	—
1433	C₂×D₄	—	106	4	no	—
1434	C₂×D₄	—	212	4	no	—
1435	C₂×D₄	—	212	16	no	—
1436	C₂×D₄	—	212	8	no	—
1437	C₂×D₄	—	212	8	no	—
1438	C₂×D₄	—	212	4	no	—
1439	C₂×D₄	—	212	4	no	—
1440	C₂×D₄	—	212	4	no	—
1441	C₂×D₄	—	212	4	no	—
1442	C₂×D₄	—	212	8	no	—
1443	C₂×D₄	—	212	16	no	—
1444	C₂×D₄	—	212	8	no	—
1445	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1446	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1447	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1448	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1449	C₂×D₄	C₂³×D₅₃	1	8	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	2	no	—
1456	C₂²×C₄	—	53	2	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	4	no	—
1466	C₂²×C₄	—	53	4	no	—
1467	C₂²×C₄	—	53	8	no	—
1468	C₂²×C₄	—	53	8	no	—
1469	C₂²×C₄	—	53	4	no	—
1470	C₂²×C₄	—	53	4	no	—
1471	C₂²×C₄	—	53	4	no	—
1472	C₂²×C₄	—	53	4	no	—
1473	C₂²×C₄	—	106	4	no	—
1474	C₂²×C₄	—	212	4	no	—
1475	C₂²×C₄	—	212	4	no	—
1476	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1477	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1478	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1479	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1480	C₂²×C₄	C₂³×D₅₃	1	8	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	2	no	—
1485	C₄⋊C₄	—	53	8	no	—
1486	C₄⋊C₄	—	53	8	no	—
1487	C₄⋊C₄	—	53	8	no	—
1488	C₄⋊C₄	—	53	4	no	—
1489	C₄⋊C₄	—	53	4	no	—
1490	C₄⋊C₄	—	53	4	no	—
1491	C₄⋊C₄	—	53	4	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	8	no	—
1499	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1500	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1501	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1502	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1503	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1504	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1505	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1506	C₄⋊C₄	C₂³×D₅₃	1	8	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	4	no	—
1512	C₂²⋊C₄	—	53	8	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	4	no	—
1524	C₂²⋊C₄	—	53	4	no	—
1525	C₂²⋊C₄	—	53	8	no	—
1526	C₂²⋊C₄	—	53	8	no	—
1527	C₂²⋊C₄	—	53	8	no	—
1528	C₂²⋊C₄	—	53	8	no	—
1529	C₂²⋊C₄	—	53	8	no	—
1530	C₂²⋊C₄	—	53	8	no	—
1531	C₂²⋊C₄	—	53	4	no	—
1532	C₂²⋊C₄	—	53	4	no	—
1533	C₂²⋊C₄	—	53	4	no	—
1534	C₂²⋊C₄	—	53	4	no	—
1535	C₂²⋊C₄	—	53	4	no	—
1536	C₂²⋊C₄	—	53	4	no	—
1537	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1538	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1539	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1540	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1541	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1542	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1543	C₂²⋊C₄	C₂³×D₅₃	1	2	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	8	no	—
1558	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1559	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1560	C₄²	C₂³×D₅₃	1	2	yes	—
1561	C₄²	C₂³×D₅₃	1	2	yes	—
1562	C₄²	C₂³×D₅₃	1	2	yes	—
1563	C₄²	C₂³×D₅₃	1	4	yes	—
1564	C₄²	C₂³×D₅₃	1	2	yes	—
1565	C₄²	C₂³×D₅₃	1	8	yes	—
1566	C₂³	—	2	4	no	—
1567	C₂³	—	4	4	no	—
1568	C₂³	—	53	2	no	—
1569	C₂³	—	53	4	no	—
1570	C₂³	—	53	2	no	—
1571	C₂³	—	53	2	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	4	no	—
1580	C₂³	—	212	8	no	—
1581	C₂³	—	212	8	no	—
1582	C₂³	—	212	8	no	—
1583	C₂³	—	212	4	no	—
1584	C₂³	—	212	8	no	—
1585	C₂³	C₂⁴×D₅₃	1	4	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	—	4	4	no	—
1592	Q₈	—	106	4	no	—
1593	Q₈	—	106	4	no	—
1594	Q₈	—	106	2	no	—
1595	Q₈	—	106	2	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	2	no	—
1605	D₄	—	4	8	no	—
1606	D₄	—	106	8	no	—
1607	D₄	—	106	8	no	—
1608	D₄	—	106	8	no	—
1609	D₄	—	106	8	no	—
1610	D₄	—	106	4	no	—
1611	D₄	—	106	4	no	—
1612	D₄	—	106	4	no	—
1613	D₄	—	106	4	no	—
1614	D₄	—	106	4	no	—
1615	D₄	—	106	2	no	—
1616	D₄	—	106	2	no	—
1617	D₄	—	106	2	no	—
1618	D₄	—	212	8	no	—
1619	D₄	—	212	8	no	—
1620	D₄	—	212	4	no	—
1621	D₄	—	212	4	no	—
1622	D₄	—	212	4	no	—
1623	D₄	—	212	8	no	—
1624	D₄	—	212	8	no	—
1625	D₄	—	212	4	no	—
1626	D₄	—	212	4	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	—	4	2	no	—
1633	C₂×C₄	—	4	8	no	—
1634	C₂×C₄	—	4	4	no	—
1635	C₂×C₄	—	53	2	no	—
1636	C₂×C₄	—	53	2	no	—
1637	C₂×C₄	—	53	4	no	—
1638	C₂×C₄	—	53	2	no	—
1639	C₂×C₄	—	53	4	no	—
1640	C₂×C₄	—	53	2	no	—
1641	C₂×C₄	—	53	2	no	—
1642	C₂×C₄	—	53	2	no	—
1643	C₂×C₄	—	106	4	no	—
1644	C₂×C₄	—	106	4	no	—
1645	C₂×C₄	—	106	2	no	—
1646	C₂×C₄	—	106	4	no	—
1647	C₂×C₄	—	106	4	no	—
1648	C₂×C₄	—	106	4	no	—
1649	C₂×C₄	—	106	4	no	—
1650	C₂×C₄	—	106	4	no	—
1651	C₂×C₄	—	106	4	no	—
1652	C₂×C₄	—	212	2	no	—
1653	C₂×C₄	—	212	2	no	—
1654	C₂×C₄	—	212	8	no	—
1655	C₂×C₄	—	212	8	no	—
1656	C₂×C₄	—	212	4	no	—
1657	C₂×C₄	—	212	4	no	—
1658	C₂×C₄	—	212	4	no	—
1659	C₂×C₄	—	212	4	no	—
1660	C₂×C₄	—	212	4	no	—
1661	C₂×C₄	—	212	4	no	—
1662	C₂×C₄	—	212	4	no	—
1663	C₂×C₄	—	212	2	no	—
1664	C₂×C₄	—	212	4	no	—
1665	C₂×C₄	—	212	4	no	—
1666	C₂×C₄	#13133263	1	4	yes	—
1667	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1668	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1669	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1670	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1671	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1672	C₂×C₄	C₂⁴×D₅₃	1	4	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	4	no	—
1679	C₂²	—	2	4	no	—
1680	C₂²	—	2	8	no	—
1681	C₂²	—	8	4	no	—
1682	C₂²	—	53	4	no	—
1683	C₂²	—	848	4	no	—
1684	C₂²	—	848	4	no	—
1685	C₂²	—	106	8	no	—
1686	C₂²	—	106	2	no	—
1687	C₂²	—	106	2	no	—
1688	C₂²	—	106	2	no	—
1689	C₂²	—	106	2	no	—
1690	C₂²	—	106	2	no	—
1691	C₂²	—	106	4	no	—
1692	C₂²	—	106	4	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×#13133263	1	2	yes	—
1699	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1700	C₄	—	2	2	no	—
1701	C₄	—	2	4	no	—
1702	C₄	—	2	2	no	—
1703	C₄	—	2	4	no	—
1704	C₄	—	2	4	no	—
1705	C₄	—	2	2	no	—
1706	C₄	—	2	4	no	—
1707	C₄	—	106	2	no	—
1708	C₄	—	106	2	no	—
1709	C₄	—	106	2	no	—
1710	C₄	—	106	2	no	—
1711	C₄	—	106	4	no	—
1712	C₄	—	106	2	no	—
1713	C₄	—	106	2	no	—
1714	C₄	—	106	4	no	—
1715	C₄	C₂×#13133263	1	2	yes	—
1716	C₄	C₂×#13133263	1	2	yes	—
1717	C₂	—	2	2	no	—
1718	C₂	—	4	4	no	—
1719	C₂	—	4	2	no	—
1720	C₂	—	106	4	no	—
1721	C₂	—	212	2	no	—
1722	C₂	—	212	2	no	—
1723	C₂	—	212	2	no	—
1724	C₂	—	212	4	no	—
1725	C₂	C₂²×#13133263	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×#3510	C₂
hypercenter	#3510	D₅₃
hypocenter	C₅₃	#62824
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3510

Complements

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

N	H ≅ G/N	type
1. #20289286	C₂	semidirect
2. #20289284	C₂	semidirect
3. #20289235	C₂	semidirect
4. #20289230	C₂	semidirect
5. #20289071	C₂	semidirect
6. #20288679	C₂	semidirect
7. #20288678	C₂	semidirect
8. #20288675	C₂	semidirect
9. #20288664	C₂	semidirect
10. #20288613	C₂	semidirect
11. #20288612	C₂	semidirect
12. #20288606	C₂	semidirect
13. #20288508	C₂	semidirect
14. #20288507	C₂	semidirect
15. #20288505	C₂	semidirect
16. #20288504	C₂	semidirect
17. #20288399	C₂	semidirect
18. #20288367	C₂	semidirect
19. #20288364	C₂	semidirect
20. #20288351	C₂	semidirect
21. #20288349	C₂	semidirect
22. #20288012	C₂	semidirect
23. #20288008	C₂	semidirect
24. C₂×#124×D₅₃	C₂	semidirect
25. C₅₃×#3510	C₂	semidirect
26. C₂×#13133265	C₂²	semidirect
27. C₂×#13133264	C₂²	semidirect
28. C₂×#13133263	C₂²	semidirect
29. C₂×#13133262	C₂²	semidirect
30. C₂²×Q₈×D₅₃	C₂²	semidirect
32. #16811375	C₂²	semidirect
33. #16811370	C₂²	semidirect
34. #16811369	C₂²	semidirect
35. #16811365	C₂²	semidirect
36. #16811358	C₂²	semidirect
37. #16811358	C₂²	semidirect
38. #16811356	C₂²	semidirect
39. #16811346	C₂²	semidirect
40. #16811345	C₂²	semidirect
41. #16811343	C₂²	semidirect
42. #16811338	C₂²	semidirect
43. #16811336	C₂²	semidirect
44. #16811300	C₂²	semidirect
45. #16811299	C₂²	semidirect
46. #16811298	C₂²	semidirect
47. #16811298	C₂²	semidirect
48. #16811298	C₂²	semidirect
49. #16811297	C₂²	semidirect
50. #16811297	C₂²	semidirect
51. #16811296	C₂²	semidirect
52. #16811296	C₂²	semidirect
53. Q₈×D₂₁₂	C₂²	semidirect
54. Q₈×D₂₁₂	C₂²	semidirect
55. #16811288	C₂²	semidirect
56. #16811286	C₂²	semidirect
57. #16811285	C₂²	semidirect
58. #16811285	C₂²	semidirect
59. #16811285	C₂²	semidirect
60. #16811283	C₂²	semidirect
61. #16811283	C₂²	semidirect
62. #16811281	C₂²	semidirect
63. #16811281	C₂²	semidirect
64. #16811279	C₂²	semidirect
65. #16811270	C₂²	semidirect
66. #16811270	C₂²	semidirect
67. #16811269	C₂²	semidirect
68. #16811268	C₂²	semidirect
69. #16811268	C₂²	semidirect
70. #16811268	C₂²	semidirect
71. #16811268	C₂²	semidirect
72. #16811266	C₂²	semidirect
73. #16811266	C₂²	semidirect
74. #16811266	C₂²	semidirect
75. #16811265	C₂²	semidirect
76. #16811265	C₂²	semidirect
77. #16811264	C₂²	semidirect
78. #16811264	C₂²	semidirect
79. #16811263	C₂²	semidirect
80. #16811260	C₂²	semidirect
81. D₄×D₂₁₂	C₂²	semidirect
82. D₄×D₂₁₂	C₂²	semidirect
83. #16811258	C₂²	semidirect
84. #16811257	C₂²	semidirect
85. #16811248	C₂²	semidirect
86. #16811247	C₂²	semidirect
87. #16811246	C₂²	semidirect
88. #16811245	C₂²	semidirect
89. #16811244	C₂²	semidirect
90. #16811242	C₂²	semidirect
91. #16811239	C₂²	semidirect
92. #16811238	C₂²	semidirect
93. #16811212	C₂²	semidirect
94. #16811212	C₂²	semidirect
95. #16811212	C₂²	semidirect
96. #16811209	C₂²	semidirect
97. #16811209	C₂²	semidirect
98. #16811209	C₂²	semidirect
99. #16811207	C₂²	semidirect
100. #16811206	C₂²	semidirect
101. #16811199	C₂²	semidirect
102. #16811199	C₂²	semidirect
103. #16811199	C₂²	semidirect
104. #16811199	C₂²	semidirect
105. #16811198	C₂²	semidirect
106. #16811197	C₂²	semidirect
107. #16811195	C₂²	semidirect
108. #16811193	C₂²	semidirect
109. #16811193	C₂²	semidirect
112. #16811192	C₂²	semidirect
113. #16811191	C₂²	semidirect
114. #16811191	C₂²	semidirect
116. #16811186	C₂²	semidirect
117. #16811185	C₂²	semidirect
118. #16811184	C₂²	semidirect
119. #16811183	C₂²	semidirect
120. #16811178	C₂²	semidirect
121. #16811177	C₂²	semidirect
122. #16811176	C₂²	semidirect
123. #16811174	C₂²	semidirect
124. #16811174	C₂²	semidirect
125. #16811173	C₂²	semidirect
126. #16811173	C₂²	semidirect
127. #16811172	C₂²	semidirect
128. #16811171	C₂²	semidirect
129. #16811170	C₂²	semidirect
130. #16811169	C₂²	semidirect
131. #16811160	C₂²	semidirect
132. #16811160	C₂²	semidirect
133. #16811160	C₂²	semidirect
134. #16811159	C₂²	semidirect
135. #16811158	C₂²	semidirect
136. #16811158	C₂²	semidirect
137. #16811158	C₂²	semidirect
138. #16811155	C₂²	semidirect
139. #16811155	C₂²	semidirect
140. #16811153	C₂²	semidirect
141. #16811151	C₂²	semidirect
142. C₂×#13133206	C₂²	semidirect
143. C₂×#13133205	C₂²	semidirect
144. C₂×#13133205	C₂²	semidirect
145. C₂×#13133204	C₂²	semidirect
146. C₂×#13133203	C₂²	semidirect
147. #124×D₅₃	C₂²	semidirect
148. #124×D₅₃	C₂²	semidirect
149. #124×D₅₃	C₂²	semidirect
150. #124×D₅₃	C₂²	semidirect
151. #124×D₅₃	C₂²	semidirect
152. #124×D₅₃	C₂²	semidirect
153. #124×D₅₃	C₂²	semidirect
154. #16811136	C₂²	semidirect
155. #16811135	C₂²	semidirect
156. #16811135	C₂²	semidirect
157. #16811135	C₂²	semidirect
158. #16811135	C₂²	semidirect
159. #16811132	C₂²	semidirect
160. #16811131	C₂²	semidirect
161. #16811130	C₂²	semidirect
162. C₂×#13133187	C₂²	semidirect
163. #120×D₅₃	C₂²	semidirect
164. #16811100	C₂²	semidirect
165. #16811097	C₂²	semidirect
166. #16811097	C₂²	semidirect
167. #16811095	C₂²	semidirect
168. C₄×#11719949	C₂²	semidirect
169. C₄×#11719945	C₂²	semidirect
170. C₄×#11719945	C₂²	semidirect
171. #16811091	C₂²	semidirect
172. #16811091	C₂²	semidirect
173. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
174. C₂×C₄²×D₅₃	C₂²	semidirect
175. C₅₃×#559	C₂²	semidirect
176. C₅₃×#556	C₂²	semidirect
177. C₅₃×#551	C₂²	semidirect
178. C₅₃×#542	C₂²	semidirect
179. C₅₃×#536	C₂²	semidirect
181. C₅₃×#533	C₂²	semidirect
182. C₅₃×#529	C₂²	semidirect
183. C₂×#124×C₅₃	C₂²	semidirect
184. C₅₃×#519	C₂²	semidirect
185. C₅₃×#518	C₂²	semidirect
186. C₄×#41×C₅₃	C₂²	semidirect
194. C₂×#11719949	C₂³	semidirect
195. C₂×#11719949	C₂³	semidirect
202. C₂×#11719945	C₂³	semidirect
206. C₂×#11719947	C₂³	semidirect
209. C₂²×Dic₁₀₆	C₂³	semidirect
213. C₂×Q₈×D₅₃	C₂³	semidirect
214. C₂×Q₈×D₅₃	C₂³	semidirect
215. C₂×Q₈×D₅₃	C₂³	semidirect
232. #13133217	C₂³	semidirect
233. #13133217	C₂³	semidirect
234. #13133217	C₂³	semidirect
235. #13133217	C₂³	semidirect
236. #13133216	C₂³	semidirect
237. #13133216	C₂³	semidirect
238. #13133215	C₂³	semidirect
239. #13133215	C₂³	semidirect
242. #13133214	C₂³	semidirect
244. #13133213	C₂³	semidirect
245. #13133212	C₂³	semidirect
246. #13133212	C₂³	semidirect
247. #13133212	C₂³	semidirect
248. #13133212	C₂³	semidirect
249. #13133212	C₂³	semidirect
250. #13133212	C₂³	semidirect
251. #13133211	C₂³	semidirect
252. #13133210	C₂³	semidirect
253. #13133210	C₂³	semidirect
254. #13133210	C₂³	semidirect
255. #13133208	C₂³	semidirect
256. #13133208	C₂³	semidirect
257. #13133207	C₂³	semidirect
261. #13133206	C₂³	semidirect
262. #13133206	C₂³	semidirect
263. #13133206	C₂³	semidirect
264. #13133206	C₂³	semidirect
270. #13133205	C₂³	semidirect
271. #13133205	C₂³	semidirect
272. #13133205	C₂³	semidirect
273. #13133205	C₂³	semidirect
274. #13133205	C₂³	semidirect
275. #13133205	C₂³	semidirect
276. #13133205	C₂³	semidirect
281. #13133204	C₂³	semidirect
286. #13133203	C₂³	semidirect
287. #13133203	C₂³	semidirect
288. #13133203	C₂³	semidirect
289. #13133203	C₂³	semidirect
290. #13133203	C₂³	semidirect
291. #13133203	C₂³	semidirect
295. #13133202	C₂³	semidirect
296. #13133202	C₂³	semidirect
297. #13133202	C₂³	semidirect
298. #13133202	C₂³	semidirect
299. #13133202	C₂³	semidirect
306. #13133201	C₂³	semidirect
308. #13133200	C₂³	semidirect
311. #13133199	C₂³	semidirect
312. #13133199	C₂³	semidirect
313. #13133199	C₂³	semidirect
319. #13133197	C₂³	semidirect
320. #13133197	C₂³	semidirect
321. #13133197	C₂³	semidirect
322. #13133197	C₂³	semidirect
323. #13133197	C₂³	semidirect
324. #13133196	C₂³	semidirect
327. #13133195	C₂³	semidirect
328. #13133195	C₂³	semidirect
329. #13133195	C₂³	semidirect
331. #13133194	C₂³	semidirect
332. #13133194	C₂³	semidirect
333. #13133194	C₂³	semidirect
336. #13133193	C₂³	semidirect
337. #13133193	C₂³	semidirect
345. #13133192	C₂³	semidirect
346. #13133192	C₂³	semidirect
350. #13133191	C₂³	semidirect
354. #13133190	C₂³	semidirect
355. #13133190	C₂³	semidirect
356. #13133190	C₂³	semidirect
358. #13133189	C₂³	semidirect
362. #13133188	C₂³	semidirect
372. #13133187	C₂³	semidirect
373. #13133187	C₂³	semidirect
374. #13133187	C₂³	semidirect
379. #13133185	C₂³	semidirect
380. Q₈×Dic₅₃	C₂³	semidirect
381. C₄×Dic₁₀₆	C₂³	semidirect
382. C₄×Dic₁₀₆	C₂³	semidirect
383. C₄×Dic₁₀₆	C₂³	semidirect
384. C₄×Dic₁₀₆	C₂³	semidirect
385. #13133182	C₂³	semidirect
386. #13133182	C₂³	semidirect
387. #13133182	C₂³	semidirect
395. C₄×D₂₁₂	C₂³	semidirect
396. C₄×D₂₁₂	C₂³	semidirect
397. C₄×D₂₁₂	C₂³	semidirect
398. C₄×D₂₁₂	C₂³	semidirect
399. D₄×Dic₅₃	C₂³	semidirect
404. #13133179	C₂³	semidirect
405. #13133179	C₂³	semidirect
406. #13133179	C₂³	semidirect
407. #13133179	C₂³	semidirect
408. #13133179	C₂³	semidirect
412. C₄×C₂²⋊D₅₃	C₂³	semidirect
413. C₄×C₂²⋊D₅₃	C₂³	semidirect
414. C₄×C₂²⋊D₅₃	C₂³	semidirect
418. #13133177	C₂³	semidirect
420. #13133176	C₂³	semidirect
421. #13133176	C₂³	semidirect
423. #13133175	C₂³	semidirect
424. #13133175	C₂³	semidirect
425. #13133175	C₂³	semidirect
427. #13133174	C₂³	semidirect
428. #13133174	C₂³	semidirect
429. #13133174	C₂³	semidirect
430. #13133174	C₂³	semidirect
431. #13133174	C₂³	semidirect
437. C₂×#11719921	C₂³	semidirect
444. C₂²⋊C₄×D₅₃	C₂³	semidirect
445. C₂²⋊C₄×D₅₃	C₂³	semidirect
446. C₂²⋊C₄×D₅₃	C₂³	semidirect
453. C₄²×D₅₃	C₂³	semidirect
454. C₄²×D₅₃	C₂³	semidirect
455. C₄²×D₅₃	C₂³	semidirect
459. C₄⋊Q₈×C₅₃	C₂³	semidirect
460. C₄⋊Q₈×C₅₃	C₂³	semidirect
462. #126×C₅₃	C₂³	semidirect
463. #126×C₅₃	C₂³	semidirect
464. #125×C₅₃	C₂³	semidirect
469. #124×C₅₃	C₂³	semidirect
470. #124×C₅₃	C₂³	semidirect
472. #123×C₅₃	C₂³	semidirect
473. #123×C₅₃	C₂³	semidirect
475. C₂²⋊Q₈×C₅₃	C₂³	semidirect
476. C₂²⋊Q₈×C₅₃	C₂³	semidirect
479. C₄×Q₈×C₅₃	C₂³	semidirect
480. C₄×Q₈×C₅₃	C₂³	semidirect
481. C₄×Q₈×C₅₃	C₂³	semidirect
482. C₄×Q₈×C₅₃	C₂³	semidirect
486. C₄×D₄×C₅₃	C₂³	semidirect
487. C₄×D₄×C₅₃	C₂³	semidirect
492. #117×C₅₃	C₂³	semidirect
493. #117×C₅₃	C₂³	semidirect
497. C₂×C₄²×C₅₃	C₂³	semidirect
866. #3510	D₅₃	semidirect
902. #559	C₂×D₅₃	semidirect
906. #556	C₂×D₅₃	semidirect
918. #551	C₂×D₅₃	semidirect
959. #542	C₂×D₅₃	semidirect
977. #536	C₂×D₅₃	semidirect
992. #533	C₂×D₅₃	semidirect
1012. #529	C₂×D₅₃	semidirect
1025. C₂×#124	C₂×D₅₃	semidirect
1037. #519	C₂×D₅₃	semidirect
1041. #518	C₂×D₅₃	semidirect
1047. C₄×#41	C₂×D₅₃	semidirect
1050. C₅₃	#62824	semidirect
1107. C₄⋊Q₈	C₂²×D₅₃	semidirect
1108. C₄⋊Q₈	C₂²×D₅₃	semidirect
1125. #126	C₂²×D₅₃	semidirect
1126. #126	C₂²×D₅₃	semidirect
1130. #125	C₂²×D₅₃	semidirect
1169. #124	C₂²×D₅₃	semidirect
1170. #124	C₂²×D₅₃	semidirect
1195. #123	C₂²×D₅₃	semidirect
1196. #123	C₂²×D₅₃	semidirect
1221. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1222. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1275. C₄×Q₈	C₂²×D₅₃	semidirect
1276. C₄×Q₈	C₂²×D₅₃	semidirect
1277. C₄×Q₈	C₂²×D₅₃	semidirect
1278. C₄×Q₈	C₂²×D₅₃	semidirect
1313. C₄×D₄	C₂²×D₅₃	semidirect
1314. C₄×D₄	C₂²×D₅₃	semidirect
1333. #117	C₂²×D₅₃	semidirect
1334. #117	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
#20289286	2
#20289284	2
#20289235	2
#20289230	2
#20289071	2
#20288679	2
#20288678	2
#20288675	2
#20288664	2
#20288613	2
#20288612	2
#20288606	2
#20288508	2
#20288507	2
#20288505	2
#20288504	2
#20288399	2
#20288367	2
#20288364	2
#20288351	2
#20288349	2
#20288012	2
#20288008	2
C₂×#124×D₅₃	2
C₅₃×#3510	2
#62824	53