Subgroups — #28293223

Order 13568.

7370 conjugacy classes of subgroups.

The subgroup lattice has 1698 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288613	C₂	1	1	yes	maximal, characteristic, complemented
2	#20288611	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288610	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288608	C₂	1	4	yes	maximal, complemented
5	#20288606	C₂	1	1	yes	maximal, characteristic, complemented
6	#20288590	C₂	1	1	yes	maximal, characteristic, complemented
7	#20288589	C₂	1	1	yes	maximal, characteristic, complemented
8	#20288586	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288585	C₂	1	4	yes	maximal, complemented
10	#20288563	C₂	1	4	yes	maximal, complemented
11	#20288559	C₂	1	4	yes	maximal, complemented
12	#20288445	C₂	1	4	yes	maximal, complemented
13	#20288442	C₂	1	4	yes	maximal, complemented
14	#20288437	C₂	1	8	yes	maximal, complemented
15	#20288397	C₂	1	8	yes	maximal, complemented
16	#20288130	C₂	1	4	yes	maximal, complemented
17	#20288129	C₂	1	4	yes	maximal, complemented
18	#20288118	C₂	1	1	yes	maximal, characteristic, complemented
19	#20288046	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#16811186	C₂	1	1	yes	maximal, characteristic, complemented
21	#535×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#20287914	C₂	1	1	yes	maximal, characteristic, complemented
23	#20287913	C₂	1	1	yes	maximal, characteristic, complemented
24	#518×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂²×#11719947	C₂²	1	1	yes	characteristic
27	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
28	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
29	#16811359	C₂²	1	4	yes	complemented
30	#16811359	C₂²	1	4	yes	complemented
31	#16811358	C₂²	1	4	yes	complemented
32	#16811356	C₂²	1	4	yes	complemented
33	#16811356	C₂²	1	4	yes	complemented
34	#16811356	C₂²	1	4	yes	complemented
35	#16811355	C₂²	1	4	yes	complemented
36	#16811346	C₂²	1	4	yes	complemented
37	#16811345	C₂²	1	4	yes	complemented
38	#16811343	C₂²	1	4	yes	complemented
39	#16811342	C₂²	1	4	yes	complemented
40	#16811337	C₂²	1	8	yes	complemented
41	#16811335	C₂²	1	8	yes	complemented
42	#16811322	C₂²	1	8	yes	complemented
43	#16811318	C₂²	1	8	yes	complemented
44	#16811316	C₂²	1	8	yes	complemented
45	#16811316	C₂²	1	8	yes	complemented
46	#16811304	C₂²	1	8	yes	complemented
47	#16811303	C₂²	1	8	yes	complemented
48	#16811302	C₂²	1	8	yes	complemented
49	#16811302	C₂²	1	8	yes	complemented
50	#16811301	C₂²	1	8	yes	complemented
51	#16811300	C₂²	1	8	yes	complemented
52	#16811299	C₂²	1	8	yes	complemented
53	#16811296	C₂²	1	8	yes	complemented
54	#16811294	C₂²	1	4	yes	complemented
55	#16811293	C₂²	1	4	yes	complemented
56	#16811293	C₂²	1	4	yes	complemented
57	#16811272	C₂²	1	8	yes	complemented
58	#16811271	C₂²	1	8	yes	complemented
59	#16811270	C₂²	1	8	yes	complemented
60	#16811267	C₂²	1	8	yes	complemented
61	#16811263	C₂²	1	8	yes	complemented
62	#16811262	C₂²	1	8	yes	complemented
63	#16811262	C₂²	1	8	yes	complemented
64	#16811261	C₂²	1	8	yes	complemented
65	#16811260	C₂²	1	8	yes	complemented
66	#16811253	C₂²	1	2	yes	complemented
67	#16811253	C₂²	1	2	yes	complemented
68	#16811252	C₂²	1	4	yes	complemented
69	#16811250	C₂²	1	2	yes	complemented
70	#16811250	C₂²	1	2	yes	complemented
71	#16811248	C₂²	1	4	yes	—
72	#16811247	C₂²	1	4	yes	complemented
73	#16811244	C₂²	1	4	yes	complemented
74	#16811241	C₂²	1	8	yes	complemented
75	#16811240	C₂²	1	4	yes	complemented
76	#16811238	C₂²	1	4	yes	complemented
77	#16811237	C₂²	1	8	yes	complemented
78	#16811227	C₂²	1	4	yes	complemented
79	#16811226	C₂²	1	4	yes	complemented
80	#16811224	C₂²	1	4	yes	complemented
81	#16811223	C₂²	1	8	yes	complemented
82	#16811223	C₂²	1	8	yes	complemented
83	#16811209	C₂²	1	8	yes	complemented
84	#16811207	C₂²	1	8	yes	complemented
85	#16811205	C₂²	1	8	yes	complemented
86	#16811205	C₂²	1	8	yes	complemented
87	#16811202	C₂²	1	4	yes	complemented
88	#16811199	C₂²	1	1	yes	characteristic, complemented
89	#16811194	C₂²	1	1	yes	characteristic, complemented
90	#16811193	C₂²	1	2	yes	complemented
91	#16811192	C₂²	1	1	yes	characteristic
92	#16811191	C₂²	1	2	yes	complemented
93	#16811190	C₂²	1	1	yes	characteristic
94	#16811190	C₂²	1	1	yes	characteristic, complemented
95	#16811189	C₂²	1	4	yes	complemented
96	#16811188	C₂²	1	4	yes	—
97	#16811187	C₂²	1	1	yes	characteristic
98	#16811186	C₂²	1	4	yes	—
99	#16811186	C₂²	1	2	yes	—
100	#16811186	C₂²	1	2	yes	—
101	#16811186	C₂²	1	2	yes	complemented
102	#16811186	C₂²	1	4	yes	complemented
103	#16811186	C₂²	1	2	yes	complemented
104	#16811186	C₂²	1	2	yes	complemented
105	#16811186	C₂²	1	2	yes	complemented
106	#16811183	C₂²	1	4	yes	—
107	#16811180	C₂²	1	1	yes	characteristic, complemented
108	#16811177	C₂²	1	4	yes	complemented
109	#16811177	C₂²	1	4	yes	complemented
110	#16811176	C₂²	1	1	yes	characteristic, complemented
111	#16811176	C₂²	1	1	yes	characteristic, complemented
112	#16811172	C₂²	1	2	yes	complemented
113	#16811171	C₂²	1	4	yes	complemented
114	#16811171	C₂²	1	2	yes	complemented
115	#16811170	C₂²	1	4	yes	complemented
116	#16811169	C₂²	1	8	yes	complemented
117	#16811168	C₂²	1	8	yes	complemented
118	#16811168	C₂²	1	4	yes	complemented
119	C₂×#13133213	C₂²	1	1	yes	characteristic, complemented
120	#127×D₅₃	C₂²	1	2	yes	complemented
121	#16811158	C₂²	1	4	yes	complemented
122	#16811157	C₂²	1	4	yes	complemented
123	#16811155	C₂²	1	4	yes	complemented
124	#16811154	C₂²	1	4	yes	complemented
125	#16811153	C₂²	1	8	yes	complemented
126	#16811150	C₂²	1	8	yes	complemented
127	C₂×#13133205	C₂²	1	1	yes	characteristic, complemented
128	C₂×#13133204	C₂²	1	1	yes	characteristic, complemented
129	#124×D₅₃	C₂²	1	2	yes	complemented
130	#16811133	C₂²	1	4	yes	complemented
131	#16811133	C₂²	1	8	yes	complemented
132	#16811132	C₂²	1	8	yes	complemented
133	#16811131	C₂²	1	8	yes	complemented
134	#16811130	C₂²	1	8	yes	complemented
135	#16811129	C₂²	1	4	yes	complemented
136	C₂×#13133189	C₂²	1	4	yes	complemented
137	#121×D₅₃	C₂²	1	4	yes	complemented
138	C₂×#13133185	C₂²	1	4	yes	—
139	#120×D₅₃	C₂²	1	4	yes	—
140	#16811105	C₂²	1	2	yes	complemented
141	#16811102	C₂²	1	4	yes	complemented
142	#16811102	C₂²	1	2	yes	complemented
143	#16811102	C₂²	1	4	yes	complemented
144	#16811102	C₂²	1	4	yes	complemented
145	#16811100	C₂²	1	1	yes	characteristic, complemented
146	#16811100	C₂²	1	1	yes	characteristic, complemented
147	#16811099	C₂²	1	2	yes	complemented
148	#16811098	C₂²	1	1	yes	characteristic, complemented
149	#16811098	C₂²	1	1	yes	characteristic, complemented
150	#16811097	C₂²	1	1	yes	characteristic, complemented
151	#16811097	C₂²	1	1	yes	characteristic, complemented
152	#16811096	C₂²	1	4	yes	—
153	#16811096	C₂²	1	4	yes	complemented
154	#16811095	C₂²	1	4	yes	—
155	#16811095	C₂²	1	4	yes	complemented
156	#16811095	C₂²	1	4	yes	complemented
157	#16811095	C₂²	1	2	yes	complemented
158	#41×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
159	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
160	C₄×#11719945	C₂²	1	2	yes	complemented
161	#16811091	C₂²	1	1	yes	characteristic, complemented
162	#16811091	C₂²	1	2	yes	complemented
163	C₄×#11719947	C₂²	1	4	yes	complemented
164	C₄×#11719947	C₂²	1	4	yes	complemented
165	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
166	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
167	C₂×#13133174	C₂²	1	1	yes	characteristic
168	C₂×#13133174	C₂²	1	2	yes	complemented
169	C₂×#13133173	C₂²	1	4	yes	complemented
170	#117×D₅₃	C₂²	1	1	yes	characteristic
171	#117×D₅₃	C₂²	1	1	yes	characteristic
172	#117×D₅₃	C₂²	1	1	yes	characteristic
173	#117×D₅₃	C₂²	1	2	yes	complemented
174	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	—
175	C₅₃×#559	C₂²	1	4	yes	complemented
176	C₅₃×#550	C₂²	1	4	yes	complemented
177	C₅₃×#546	C₂²	1	8	yes	complemented
178	C₅₃×#540	C₂²	1	4	yes	complemented
179	C₅₃×#535	C₂²	1	1	yes	characteristic
180	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#532	C₂²	1	4	yes	complemented
183	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#518	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	C₂×#11719949	C₂³	1	1	yes	characteristic
189	C₂×#11719945	C₂³	1	2	yes	—
190	C₂×#11719945	C₂³	1	1	yes	characteristic
191	C₂×#11719945	C₂³	1	8	yes	complemented
192	C₂×#11719947	—	2	8	no	—
193	C₂×#11719947	C₂³	1	2	yes	—
194	C₂×#11719947	C₂³	1	2	yes	—
195	C₂×#11719947	C₂³	1	2	yes	—
196	C₂×#11719947	C₂³	1	2	yes	—
197	C₂×#11719947	C₂³	1	1	yes	characteristic
198	C₂×#11719947	C₂³	1	2	yes	—
199	C₂×#11719947	C₂³	1	8	yes	complemented
200	C₂×#11719947	C₂³	1	8	yes	complemented
201	#41×D₅₃	—	2	8	no	—
202	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
203	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
205	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
206	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
207	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
208	C₂×D₄×D₅₃	—	2	8	no	—
209	C₂×D₄×D₅₃	C₂³	1	2	yes	—
210	C₂×D₄×D₅₃	C₂³	1	2	yes	—
211	C₂×D₄×D₅₃	C₂³	1	2	yes	—
212	C₂×D₄×D₅₃	C₂³	1	2	yes	—
213	C₂×D₄×D₅₃	C₂³	1	2	yes	—
214	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
215	C₂×D₄×D₅₃	C₂³	1	8	yes	—
216	C₂³×Dic₅₃	C₂³	1	2	yes	—
217	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
218	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
219	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
220	#13133217	C₂³	1	2	yes	complemented
221	#13133217	C₂³	1	2	yes	complemented
222	#13133216	C₂³	1	4	yes	complemented
223	#13133216	C₂³	1	2	yes	complemented
224	#13133216	C₂³	1	4	yes	complemented
225	#13133216	C₂³	1	2	yes	complemented
226	#13133215	C₂³	1	4	yes	complemented
227	#13133215	C₂³	1	2	yes	complemented
228	#13133215	C₂³	1	4	yes	complemented
229	#13133214	C₂³	1	2	yes	—
230	#13133213	C₂³	1	2	yes	—
231	#13133213	C₂³	1	2	yes	—
232	#13133213	C₂³	1	4	yes	—
233	#13133213	C₂³	1	8	yes	—
234	#13133213	C₂³	1	2	yes	—
235	#13133213	C₂³	1	2	yes	—
236	#13133213	C₂³	1	2	yes	complemented
237	#13133212	C₂³	1	8	yes	complemented
238	#13133212	C₂³	1	8	yes	complemented
239	#13133212	C₂³	1	8	yes	complemented
240	#13133211	C₂³	1	8	yes	complemented
241	#13133210	C₂³	1	8	yes	complemented
242	#13133210	C₂³	1	8	yes	complemented
243	#13133210	C₂³	1	8	yes	complemented
244	#13133210	C₂³	1	8	yes	complemented
245	#13133209	C₂³	1	2	yes	complemented
246	#13133208	C₂³	1	2	yes	complemented
247	#13133208	C₂³	1	2	yes	complemented
248	#13133207	C₂³	1	4	yes	complemented
249	#13133207	C₂³	1	4	yes	complemented
250	#13133207	C₂³	1	4	yes	complemented
251	#13133207	C₂³	1	4	yes	complemented
252	#13133206	C₂³	1	2	yes	—
253	#13133206	C₂³	1	8	yes	complemented
254	#13133205	C₂³	1	4	yes	—
255	#13133205	C₂³	1	2	yes	—
256	#13133205	C₂³	1	2	yes	—
257	#13133205	C₂³	1	2	yes	—
258	#13133205	C₂³	1	2	yes	complemented
259	#13133204	C₂³	1	4	yes	—
260	#13133204	C₂³	1	2	yes	—
261	#13133204	C₂³	1	2	yes	—
262	#13133204	C₂³	1	2	yes	—
263	#13133204	C₂³	1	8	yes	complemented
264	#13133204	C₂³	1	8	yes	complemented
265	#13133204	C₂³	1	2	yes	complemented
266	#13133204	C₂³	1	2	yes	complemented
267	#13133203	C₂³	1	8	yes	—
268	#13133203	C₂³	1	8	yes	complemented
269	#13133203	C₂³	1	8	yes	complemented
270	#13133203	C₂³	1	8	yes	complemented
271	#13133203	C₂³	1	8	yes	complemented
272	#13133202	C₂³	1	8	yes	complemented
273	#13133202	C₂³	1	8	yes	complemented
274	#13133201	C₂³	1	4	yes	—
275	#13133201	C₂³	1	8	yes	complemented
276	#13133200	C₂³	1	8	yes	complemented
277	#13133200	C₂³	1	8	yes	complemented
278	#13133200	C₂³	1	8	yes	complemented
279	#13133199	C₂³	1	8	yes	—
280	#13133199	C₂³	1	8	yes	complemented
281	#13133199	C₂³	1	8	yes	complemented
282	#13133199	C₂³	1	8	yes	complemented
283	#13133199	C₂³	1	8	yes	complemented
284	#13133198	C₂³	1	4	yes	—
285	#13133198	C₂³	1	8	yes	complemented
286	#13133198	C₂³	1	8	yes	complemented
287	#13133198	C₂³	1	8	yes	complemented
288	#13133198	C₂³	1	8	yes	complemented
289	#13133197	C₂³	1	4	yes	—
290	#13133197	C₂³	1	4	yes	—
291	#13133197	C₂³	1	4	yes	complemented
292	#13133196	C₂³	1	4	yes	—
293	#13133196	C₂³	1	8	yes	complemented
294	#13133196	C₂³	1	4	yes	complemented
295	#13133195	C₂³	1	4	yes	—
296	#13133195	C₂³	1	4	yes	—
297	#13133195	C₂³	1	4	yes	—
298	#13133195	C₂³	1	4	yes	—
299	#13133195	C₂³	1	8	yes	complemented
300	#13133194	C₂³	1	4	yes	—
301	#13133194	C₂³	1	4	yes	—
302	#13133194	C₂³	1	8	yes	complemented
303	#13133194	C₂³	1	8	yes	complemented
304	#13133193	C₂³	1	4	yes	—
305	#13133193	C₂³	1	4	yes	—
306	#13133193	C₂³	1	8	yes	complemented
307	#13133192	C₂³	1	4	yes	—
308	#13133191	C₂³	1	4	yes	—
309	#13133191	C₂³	1	8	yes	complemented
310	#13133190	C₂³	1	8	yes	—
311	#13133190	C₂³	1	8	yes	—
312	#13133190	C₂³	1	8	yes	complemented
313	#13133190	C₂³	1	8	yes	complemented
314	#13133189	C₂³	1	8	yes	—
315	#13133189	C₂³	1	8	yes	—
316	#13133189	C₂³	1	8	yes	—
317	#13133189	C₂³	1	8	yes	—
318	#13133189	C₂³	1	8	yes	—
319	#13133189	C₂³	1	8	yes	complemented
320	#13133189	C₂³	1	8	yes	complemented
321	#13133189	C₂³	1	8	yes	complemented
322	#13133189	C₂³	1	8	yes	complemented
323	#13133189	C₂³	1	8	yes	complemented
324	#13133188	C₂³	1	4	yes	—
325	#13133188	C₂³	1	8	yes	—
326	#13133188	C₂³	1	8	yes	complemented
327	#13133188	C₂³	1	8	yes	complemented
328	#13133188	C₂³	1	4	yes	complemented
329	#13133187	C₂³	1	4	yes	—
330	#13133187	C₂³	1	8	yes	—
331	#13133186	C₂³	1	4	yes	—
332	#13133186	C₂³	1	4	yes	—
333	#13133185	C₂³	1	8	yes	—
334	#13133185	C₂³	1	8	yes	—
335	#13133185	C₂³	1	4	yes	—
336	#13133185	C₂³	1	8	yes	—
337	#13133185	C₂³	1	8	yes	—
338	#13133185	C₂³	1	8	yes	—
339	#13133185	C₂³	1	8	yes	—
340	Q₈×Dic₅₃	C₂³	1	2	yes	complemented
341	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
342	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
343	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
344	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
345	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
346	C₄×Dic₁₀₆	C₂³	1	2	yes	complemented
347	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
348	#13133182	C₂³	1	2	yes	complemented
349	#13133182	C₂³	1	4	yes	complemented
350	#13133182	C₂³	1	4	yes	complemented
351	#13133182	C₂³	1	4	yes	complemented
352	C₄×D₂₁₂	C₂³	1	4	yes	—
353	C₄×D₂₁₂	C₂³	1	4	yes	—
354	C₄×D₂₁₂	C₂³	1	4	yes	—
355	C₄×D₂₁₂	C₂³	1	2	yes	complemented
356	D₄×Dic₅₃	C₂³	1	4	yes	—
357	D₄×Dic₅₃	C₂³	1	4	yes	—
358	D₄×Dic₅₃	C₂³	1	4	yes	—
359	D₄×Dic₅₃	C₂³	1	8	yes	complemented
360	D₄×Dic₅₃	C₂³	1	8	yes	complemented
361	D₄×Dic₅₃	C₂³	1	4	yes	complemented
362	D₄×Dic₅₃	C₂³	1	2	yes	complemented
363	D₄×Dic₅₃	C₂³	1	8	yes	complemented
364	D₄×Dic₅₃	C₂³	1	4	yes	complemented
365	#13133179	C₂³	1	4	yes	—
366	#13133179	C₂³	1	4	yes	—
367	#13133179	C₂³	1	4	yes	—
368	#13133179	C₂³	1	8	yes	complemented
369	#13133179	C₂³	1	2	yes	complemented
370	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
371	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
372	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
373	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
374	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	—
375	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
376	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
377	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
378	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
379	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
380	#13133177	C₂³	1	8	yes	—
381	#13133177	C₂³	1	8	yes	—
382	#13133177	C₂³	1	4	yes	—
383	#13133177	C₂³	1	8	yes	—
384	#13133177	C₂³	1	8	yes	—
385	#13133177	C₂³	1	4	yes	—
386	#13133177	C₂³	1	8	yes	complemented
387	#13133177	C₂³	1	8	yes	complemented
388	#13133177	C₂³	1	4	yes	complemented
389	#13133176	C₂³	1	1	yes	characteristic
390	#13133176	C₂³	1	1	yes	characteristic
391	#13133176	C₂³	1	1	yes	characteristic
392	#13133176	C₂³	1	8	yes	complemented
393	#13133176	C₂³	1	2	yes	complemented
394	#13133175	C₂³	1	4	yes	—
395	#13133175	C₂³	1	2	yes	—
396	#13133175	C₂³	1	2	yes	—
397	#13133175	C₂³	1	2	yes	—
398	#13133175	C₂³	1	8	yes	complemented
399	#13133174	C₂³	1	4	yes	—
400	#13133174	C₂³	1	2	yes	—
401	#13133174	C₂³	1	2	yes	—
402	#13133174	C₂³	1	2	yes	—
403	#13133174	C₂³	1	1	yes	characteristic
404	#13133174	C₂³	1	1	yes	characteristic
405	#13133174	C₂³	1	1	yes	characteristic
406	#13133174	C₂³	1	1	yes	characteristic
407	#13133174	C₂³	1	2	yes	—
408	#13133174	C₂³	1	2	yes	—
409	#13133174	C₂³	1	8	yes	complemented
410	#13133174	C₂³	1	4	yes	complemented
411	#13133174	C₂³	1	2	yes	complemented
412	#13133174	C₂³	1	2	yes	complemented
413	#13133173	C₂³	1	4	yes	—
414	#13133173	C₂³	1	4	yes	—
415	#13133173	C₂³	1	2	yes	—
416	#13133173	C₂³	1	2	yes	—
417	#13133173	C₂³	1	2	yes	—
418	#13133173	C₂³	1	8	yes	complemented
419	#13133173	C₂³	1	4	yes	complemented
420	#13133173	C₂³	1	8	yes	complemented
421	#13133173	C₂³	1	8	yes	complemented
422	C₂×#11719919	C₂³	1	2	yes	—
423	C₂×#11719919	C₂³	1	8	yes	complemented
424	C₂×#11719919	C₂³	1	4	yes	complemented
425	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
426	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
427	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
428	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
429	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
430	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
431	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	—
432	C₂×#11719921	C₂³	1	8	yes	—
433	C₂×#11719921	C₂³	1	4	yes	—
434	C₂×#11719921	C₂³	1	2	yes	—
435	C₂×#11719921	C₂³	1	4	yes	—
436	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
437	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
438	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
439	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
440	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
441	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
442	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
443	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
444	C₂²⋊C₄×D₅₃	C₂³	1	2	yes	—
445	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
446	C₂×C₄×Dic₅₃	C₂³	1	8	yes	complemented
447	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
448	C₄²×D₅₃	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	complemented
452	C₄²×D₅₃	C₂³	1	2	yes	complemented
453	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
454	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
455	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
456	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
457	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
458	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
459	#127×C₅₃	C₂³	1	4	yes	—
460	#127×C₅₃	C₂³	1	2	yes	—
461	#127×C₅₃	C₂³	1	2	yes	—
462	#127×C₅₃	C₂³	1	2	yes	—
463	#127×C₅₃	C₂³	1	2	yes	complemented
464	#125×C₅₃	C₂³	1	2	yes	complemented
465	#124×C₅₃	C₂³	1	2	yes	—
466	#124×C₅₃	C₂³	1	8	yes	complemented
467	#124×C₅₃	C₂³	1	2	yes	complemented
468	#123×C₅₃	C₂³	1	8	yes	complemented
469	#123×C₅₃	C₂³	1	8	yes	complemented
470	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
471	#121×C₅₃	C₂³	1	4	yes	—
472	#121×C₅₃	C₂³	1	8	yes	complemented
473	#121×C₅₃	C₂³	1	4	yes	complemented
474	#121×C₅₃	C₂³	1	8	yes	complemented
475	#121×C₅₃	C₂³	1	8	yes	complemented
476	#120×C₅₃	C₂³	1	4	yes	—
477	#120×C₅₃	C₂³	1	4	yes	—
478	C₄×Q₈×C₅₃	C₂³	1	2	yes	complemented
479	C₄×Q₈×C₅₃	C₂³	1	4	yes	complemented
480	C₄×D₄×C₅₃	C₂³	1	4	yes	—
481	C₄×D₄×C₅₃	C₂³	1	4	yes	—
482	C₄×D₄×C₅₃	C₂³	1	4	yes	—
483	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
484	C₄×D₄×C₅₃	C₂³	1	2	yes	complemented
485	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
486	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
487	#117×C₅₃	C₂³	1	1	yes	characteristic
488	#117×C₅₃	C₂³	1	1	yes	characteristic
489	#117×C₅₃	C₂³	1	1	yes	characteristic
490	#117×C₅₃	C₂³	1	2	yes	complemented
491	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
492	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
493	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
494	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
495	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
496	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
497	C₂³×D₅₃	—	2	8	no	—
498	C₂³×D₅₃	—	8	4	no	—
499	C₂³×D₅₃	C₂⁴	1	4	yes	—
500	C₂³×D₅₃	C₂⁴	1	2	yes	—
501	C₂³×D₅₃	C₂⁴	1	2	yes	—
502	C₂³×D₅₃	C₂⁴	1	4	yes	—
503	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
504	#41×C₅₃	—	2	4	no	—
505	#41×C₅₃	—	8	8	no	—
506	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
507	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
508	C₂×D₄×C₅₃	—	2	4	no	—
509	C₂×D₄×C₅₃	—	2	4	no	—
510	C₂×D₄×C₅₃	—	8	4	no	—
511	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
512	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
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	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
519	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
520	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
521	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
522	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
523	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
524	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
525	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
526	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
527	C₂×C₂²⋊D₅₃	—	2	8	no	—
528	C₂×C₂²⋊D₅₃	—	2	8	no	—
529	C₂×C₂²⋊D₅₃	—	8	4	no	—
530	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
531	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
532	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
533	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
534	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
535	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
536	C₂×C₂²⋊D₅₃	C₂⁴	1	2	yes	—
537	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
538	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
539	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
540	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
541	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
542	C₂²×Dic₅₃	—	2	8	no	—
543	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
544	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
545	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
546	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
547	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
548	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
549	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
550	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
551	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
552	#11719949	—	2	4	no	—
553	Q₈×D₅₃	—	2	4	no	—
554	#11719947	—	2	8	no	—
555	#11719947	—	2	4	no	—
556	#11719947	—	2	8	no	—
557	#11719947	—	2	8	no	—
558	#11719947	—	2	8	no	—
559	#11719947	—	2	8	no	—
560	#11719947	—	8	8	no	—
561	#11719947	—	8	8	no	—
562	D₄×D₅₃	—	2	8	no	—
563	D₄×D₅₃	—	2	8	no	—
564	D₄×D₅₃	—	2	8	no	—
565	D₄×D₅₃	—	2	8	no	—
566	D₄×D₅₃	—	2	8	no	—
567	D₄×D₅₃	—	2	4	no	—
568	D₄×D₅₃	—	8	8	no	—
569	#11719945	—	2	4	no	—
570	#11719945	—	2	8	no	—
571	#11719945	—	8	8	no	—
572	C₂×D₂₁₂	—	2	4	no	—
573	C₂×D₂₁₂	C₂⁴	1	2	yes	—
574	C₂×D₂₁₂	C₂⁴	1	2	yes	—
575	C₂×D₂₁₂	C₂⁴	1	2	yes	—
576	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
577	C₂×D₂₁₂	C₂⁴	1	8	yes	—
578	C₂×C₄×D₅₃	—	2	8	no	—
579	C₂×C₄×D₅₃	—	8	8	no	—
580	C₂×C₄×D₅₃	#41	1	8	yes	complemented
581	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
582	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
583	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
584	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
585	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
586	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
587	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
588	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
589	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
590	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
591	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
592	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
593	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
594	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
595	C₂×Dic₁₀₆	—	2	4	no	—
596	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
597	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
598	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
599	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
600	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
601	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
602	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
603	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
604	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
605	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
606	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
607	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
608	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
609	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
610	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
611	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
612	C₂²⋊C₄×C₅₃	C₂⁴	1	2	yes	—
613	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
614	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
615	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
616	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
617	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
618	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
619	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
620	C₄²×C₅₃	C₂⁴	1	2	yes	—
621	C₄²×C₅₃	C₂⁴	1	2	yes	—
622	C₄²×C₅₃	C₂⁴	1	4	yes	—
623	C₄²×C₅₃	C₂⁴	1	2	yes	—
624	C₄²×C₅₃	C₂⁴	1	2	yes	—
625	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
626	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
627	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
628	C₂²⋊Dic₅₃	C₂⁴	1	2	yes	—
629	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
630	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
631	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
632	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
633	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
634	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
635	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
636	#11719921	C₂⁴	1	4	yes	—
637	#11719921	C₂⁴	1	4	yes	—
638	#11719921	C₂⁴	1	2	yes	—
639	#11719921	C₂⁴	1	8	yes	—
640	#11719921	C₂⁴	1	8	yes	—
641	#11719921	C₂⁴	1	4	yes	—
642	#11719921	C₂⁴	1	8	yes	—
643	#11719921	C₂⁴	1	8	yes	—
644	#11719921	C₂⁴	1	2	yes	—
645	#11719921	C₂⁴	1	2	yes	—
646	#11719921	C₂⁴	1	2	yes	—
647	#11719921	C₂⁴	1	4	yes	—
648	#11719921	C₂⁴	1	4	yes	—
649	#11719921	C₂⁴	1	8	yes	—
650	#11719921	C₂⁴	1	8	yes	—
651	#11719921	C₂⁴	1	8	yes	—
652	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
653	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
654	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
655	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
656	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
657	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
658	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
659	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
660	#11719919	C₂⁴	1	4	yes	—
661	#11719919	C₂⁴	1	4	yes	—
662	#11719919	C₂⁴	1	4	yes	—
663	#11719919	C₂⁴	1	2	yes	—
664	#11719919	C₂⁴	1	2	yes	—
665	#11719919	C₂⁴	1	2	yes	—
666	#11719919	C₂⁴	1	2	yes	—
667	#11719919	C₂⁴	1	8	yes	—
668	#11719919	C₂⁴	1	8	yes	—
669	#11719919	C₂⁴	1	4	yes	—
670	#11719919	C₂⁴	1	4	yes	—
671	#11719919	C₂⁴	1	4	yes	—
672	#11719919	C₂⁴	1	8	yes	—
673	#11719919	C₂⁴	1	4	yes	—
674	#11719919	C₂⁴	1	4	yes	—
675	#11719919	C₂⁴	1	4	yes	—
676	#11719919	C₂⁴	1	4	yes	—
677	#11719919	C₂⁴	1	4	yes	—
678	C₄×Dic₅₃	C₂⁴	1	2	yes	—
679	C₄×Dic₅₃	C₂⁴	1	4	yes	—
680	C₄×Dic₅₃	C₂⁴	1	4	yes	—
681	C₄×Dic₅₃	C₂⁴	1	4	yes	—
682	C₄×Dic₅₃	C₂⁴	1	2	yes	—
683	C₄×Dic₅₃	C₂⁴	1	2	yes	—
684	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
685	C₄×Dic₅₃	C₂⁴	1	4	yes	—
686	C₄×Dic₅₃	C₂⁴	1	4	yes	—
687	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
688	C₄×Dic₅₃	C₂⁴	1	2	yes	—
689	C₄×Dic₅₃	C₂⁴	1	8	yes	—
690	C₄×Dic₅₃	C₂⁴	1	8	yes	—
691	C₄×Dic₅₃	C₂⁴	1	4	yes	—
692	C₂³×C₅₃	—	2	4	no	—
693	C₂³×C₅₃	—	2	4	no	—
694	C₂³×C₅₃	—	4	4	no	—
695	C₂³×C₅₃	—	4	4	no	—
696	C₂³×C₅₃	C₂⁵	1	4	yes	—
697	C₂³×C₅₃	C₂⁵	1	2	yes	—
698	C₂³×C₅₃	C₂⁵	1	4	yes	—
699	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
700	C₂²×D₅₃	—	2	4	no	—
701	C₂²×D₅₃	—	2	8	no	—
702	C₂²×D₅₃	—	2	4	no	—
703	C₂²×D₅₃	—	2	8	no	—
704	C₂²×D₅₃	—	4	8	no	—
705	C₂²×D₅₃	—	4	2	no	—
706	C₂²×D₅₃	—	4	4	no	—
707	C₂²×D₅₃	—	4	8	no	—
708	C₂²×D₅₃	—	4	4	no	—
709	C₂²×D₅₃	—	8	16	no	—
710	C₂²×D₅₃	C₂×#41	1	4	yes	—
711	C₂²×D₅₃	C₂⁵	1	2	yes	—
712	C₂²×D₅₃	C₂⁵	1	4	yes	—
713	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
714	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
715	Q₈×C₅₃	—	2	2	no	—
716	Q₈×C₅₃	—	4	4	no	—
717	D₄×C₅₃	—	2	4	no	—
718	D₄×C₅₃	—	2	4	no	—
719	D₄×C₅₃	—	2	4	no	—
720	D₄×C₅₃	—	2	2	no	—
721	D₄×C₅₃	—	2	4	no	—
722	D₄×C₅₃	—	2	4	no	—
723	D₄×C₅₃	—	4	8	no	—
724	D₄×C₅₃	—	4	8	no	—
725	D₄×C₅₃	—	4	8	no	—
726	D₄×C₅₃	—	4	8	no	—
727	C₂×C₄×C₅₃	—	2	4	no	—
728	C₂×C₄×C₅₃	—	4	8	no	—
729	C₂×C₄×C₅₃	—	4	8	no	—
730	C₂×C₄×C₅₃	—	4	2	no	—
731	C₂×C₄×C₅₃	—	4	4	no	—
732	C₂×C₄×C₅₃	C₂×#41	1	4	yes	—
733	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
734	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
735	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
736	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
737	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
738	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
739	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
740	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
741	C₂²⋊D₅₃	—	2	4	no	—
742	C₂²⋊D₅₃	—	2	4	no	—
743	C₂²⋊D₅₃	—	2	8	no	—
744	C₂²⋊D₅₃	—	2	8	no	—
745	C₂²⋊D₅₃	—	2	4	no	—
746	C₂²⋊D₅₃	—	2	8	no	—
747	C₂²⋊D₅₃	—	2	8	no	—
748	C₂²⋊D₅₃	—	4	8	no	—
749	C₂²⋊D₅₃	—	4	8	no	—
750	C₂²⋊D₅₃	—	4	8	no	—
751	C₂²⋊D₅₃	—	4	8	no	—
752	C₂²⋊D₅₃	—	4	8	no	—
753	C₂×Dic₅₃	—	2	4	no	—
754	C₂×Dic₅₃	—	2	4	no	—
755	C₂×Dic₅₃	—	2	8	no	—
756	C₂×Dic₅₃	—	2	8	no	—
757	C₂×Dic₅₃	—	4	8	no	—
758	C₂×Dic₅₃	—	4	8	no	—
759	C₂×Dic₅₃	—	4	4	no	—
760	C₂×Dic₅₃	—	4	2	no	—
761	C₂×Dic₅₃	C₂×#41	1	4	yes	—
762	C₂×Dic₅₃	C₂⁵	1	4	yes	—
763	C₂×Dic₅₃	C₂⁵	1	2	yes	—
764	C₂×Dic₅₃	C₂⁵	1	2	yes	—
765	C₂×Dic₅₃	C₂⁵	1	4	yes	—
766	C₂×Dic₅₃	C₂⁵	1	2	yes	—
767	C₂×Dic₅₃	C₂⁵	1	4	yes	—
768	C₂×Dic₅₃	C₂⁵	1	4	yes	—
769	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
770	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
771	D₂₁₂	—	2	4	no	—
772	D₂₁₂	—	2	4	no	—
773	D₂₁₂	—	2	4	no	—
774	D₂₁₂	—	2	2	no	—
775	D₂₁₂	—	4	8	no	—
776	C₄×D₅₃	—	2	4	no	—
777	C₄×D₅₃	—	2	4	no	—
778	C₄×D₅₃	—	2	4	no	—
779	C₄×D₅₃	—	4	4	no	—
780	C₄×D₅₃	—	4	4	no	—
781	C₄×D₅₃	—	4	8	no	—
782	C₄×D₅₃	—	4	8	no	—
783	C₄×D₅₃	—	4	4	no	—
784	C₄×D₅₃	—	4	4	no	—
785	C₄×D₅₃	—	4	4	no	—
786	C₄×D₅₃	C₂×#41	1	4	yes	—
787	C₄×D₅₃	C₂×#41	1	4	yes	—
788	C₄×D₅₃	C₂×#41	1	4	yes	—
789	C₄×D₅₃	C₂×#41	1	4	yes	—
790	Dic₁₀₆	—	2	4	no	—
791	Dic₁₀₆	—	2	4	no	—
792	Dic₁₀₆	—	2	2	no	—
793	Dic₁₀₆	—	2	4	no	—
794	Dic₁₀₆	—	4	4	no	—
795	Dic₁₀₆	—	4	4	no	—
796	Dic₁₀₆	—	4	4	no	—
797	#62855	—	53	1	no	maximal, Sylow
798	C₂²×C₅₃	—	2	2	no	—
799	C₂²×C₅₃	—	2	4	no	—
800	C₂²×C₅₃	—	2	2	no	—
801	C₂²×C₅₃	—	2	4	no	—
802	C₂²×C₅₃	—	2	8	no	—
803	C₂²×C₅₃	—	2	4	no	—
804	C₂²×C₅₃	—	2	8	no	—
805	C₂²×C₅₃	—	8	4	no	—
806	C₂²×C₅₃	—	8	4	no	—
807	C₂²×C₅₃	C₂²×#41	1	2	yes	—
808	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
809	C₂×D₅₃	—	2	2	no	—
810	C₂×D₅₃	—	2	2	no	—
811	C₂×D₅₃	—	2	2	no	—
812	C₂×D₅₃	—	2	4	no	—
813	C₂×D₅₃	—	2	4	no	—
814	C₂×D₅₃	—	2	8	no	—
815	C₂×D₅₃	—	4	4	no	—
816	C₂×D₅₃	—	4	16	no	—
817	C₂×D₅₃	—	8	4	no	—
818	C₂×D₅₃	—	8	8	no	—
819	C₂×D₅₃	—	8	4	no	—
820	C₂×D₅₃	C₂²×#41	1	2	yes	—
821	C₂×D₅₃	C₂²×#41	1	2	yes	—
822	C₄×C₅₃	—	2	2	no	—
823	C₄×C₅₃	—	2	2	no	—
824	C₄×C₅₃	—	2	4	no	—
825	C₄×C₅₃	—	2	4	no	—
826	C₄×C₅₃	—	2	4	no	—
827	C₄×C₅₃	—	2	2	no	—
828	C₄×C₅₃	C₂²×#41	1	2	yes	—
829	C₄×C₅₃	C₂²×#41	1	2	yes	—
830	Dic₅₃	—	2	2	no	—
831	Dic₅₃	—	2	4	no	—
832	Dic₅₃	—	2	4	no	—
833	Dic₅₃	—	2	2	no	—
834	Dic₅₃	—	2	4	no	—
835	Dic₅₃	—	2	2	no	—
836	Dic₅₃	—	2	4	no	—
837	Dic₅₃	C₂²×#41	1	2	yes	—
838	Dic₅₃	C₂²×#41	1	2	yes	—
839	#3510	—	53	4	no	—
840	#3510	—	53	1	no	—
841	#3510	—	53	1	no	—
842	#3510	—	53	1	no	—
843	#3510	—	53	1	no	—
844	#3508	—	53	4	no	—
845	#3508	—	53	1	no	—
846	#3508	—	53	1	no	—
847	#3508	—	53	1	no	—
848	#3508	D₅₃	1	1	yes	characteristic, complemented
849	#3506	—	53	4	no	—
850	#3506	—	53	4	no	—
851	#3494	—	53	8	no	—
852	#3494	—	53	4	no	—
853	#3494	—	53	4	no	—
854	#3490	—	53	8	no	—
855	#3460	—	53	4	no	—
856	#3460	—	53	4	no	—
857	#3458	—	53	1	no	—
858	#3449	—	53	1	no	—
859	C₂×#535	—	53	1	no	—
860	C₂×#535	—	53	1	no	—
861	#3428	—	53	1	no	—
862	#3428	—	53	1	no	—
863	C₂×#518	—	53	1	no	—
864	C₂×C₅₃	—	2	2	no	—
865	C₂×C₅₃	—	4	4	no	—
866	C₂×C₅₃	—	4	2	no	—
867	C₂×C₅₃	—	4	4	no	—
868	C₂×C₅₃	C₂³×#41	1	1	yes	characteristic
869	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
870	D₅₃	—	2	2	no	—
871	D₅₃	—	2	2	no	—
872	D₅₃	—	4	4	no	—
873	D₅₃	—	4	2	no	—
874	C₂²×#41	—	53	1	no	—
875	C₂²×#41	—	53	1	no	—
876	C₂³×D₄	—	53	1	no	—
877	#559	—	53	4	no	—
878	#559	—	53	4	no	—
879	#559	—	53	4	no	—
880	#559	—	53	4	no	—
881	#559	—	53	4	no	—
882	#559	—	53	4	no	—
883	#559	—	53	4	no	—
884	#559	C₂×D₅₃	1	4	yes	complemented
885	#556	—	53	4	no	—
886	#556	—	53	4	no	—
887	#556	—	53	4	no	—
888	#556	—	53	4	no	—
889	#555	—	53	8	no	—
890	#555	—	53	8	no	—
891	#553	—	53	8	no	—
892	#553	—	53	8	no	—
893	#553	—	53	8	no	—
894	#553	—	53	8	no	—
895	#551	—	53	8	no	—
896	#551	—	53	8	no	—
897	#551	—	53	8	no	—
898	#551	—	53	8	no	—
899	#551	—	53	8	no	—
900	#551	—	53	8	no	—
901	#551	—	53	8	no	—
902	#551	—	53	8	no	—
903	#550	—	53	4	no	—
904	#550	—	53	4	no	—
905	#550	—	53	4	no	—
906	#550	C₂×D₅₃	1	4	yes	complemented
907	#547	—	53	8	no	—
908	#547	—	53	8	no	—
909	#546	—	53	8	no	—
910	#546	—	53	8	no	—
911	#546	—	53	8	no	—
912	#546	—	53	8	no	—
913	#546	—	53	8	no	—
914	#546	—	53	8	no	—
915	#546	—	53	8	no	—
916	#546	C₂×D₅₃	1	8	yes	complemented
917	#544	—	53	2	no	—
918	#544	—	53	2	no	—
919	#544	—	53	2	no	—
920	#544	—	53	2	no	—
921	#544	—	53	4	no	—
922	#543	—	53	4	no	—
923	#542	—	53	4	no	—
924	#542	—	53	8	no	—
925	#542	—	53	8	no	—
926	#542	—	53	4	no	—
927	#542	—	53	4	no	—
928	#542	—	53	4	no	—
929	#540	—	53	4	no	—
930	#540	—	53	8	no	—
931	#540	—	53	8	no	—
932	#540	—	53	4	no	—
933	#540	—	53	4	no	—
934	#540	C₂×D₅₃	1	4	yes	complemented
935	#538	—	53	8	no	—
936	#538	—	53	8	no	—
937	#538	—	53	8	no	—
938	#538	—	53	8	no	—
939	#537	—	53	4	no	—
940	#536	—	53	1	no	—
941	#536	—	53	2	no	—
942	#536	—	53	1	no	—
943	#535	—	53	1	no	—
944	#535	—	53	1	no	—
945	#535	—	53	1	no	—
946	#535	—	53	2	no	—
947	#535	—	53	2	no	—
948	#535	—	53	2	no	—
949	#535	—	53	2	no	—
950	#535	—	53	2	no	—
951	#535	—	53	4	no	—
952	#535	—	53	4	no	—
953	#535	—	53	2	no	—
954	#535	—	53	2	no	—
955	#535	—	53	4	no	—
956	#535	—	53	4	no	—
957	#535	—	53	1	no	—
958	#535	C₂×D₅₃	1	1	yes	characteristic
959	#535	C₂×D₅₃	1	1	yes	characteristic, complemented
960	#534	—	53	4	no	—
961	#533	—	53	4	no	—
962	#533	—	53	4	no	—
963	#533	—	53	1	no	—
964	#533	—	53	1	no	—
965	#533	—	53	1	no	—
966	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
967	#532	—	53	8	no	—
968	#532	—	53	4	no	—
969	#532	—	53	2	no	—
970	#532	—	53	2	no	—
971	#532	—	53	4	no	—
972	#532	—	53	8	no	—
973	#532	—	53	4	no	—
974	#532	C₂×D₅₃	1	4	yes	complemented
975	C₂×#127	—	53	1	no	—
976	C₂×#127	—	53	2	no	—
977	C₂×#127	C₂×D₅₃	1	1	yes	characteristic, complemented
978	#529	—	53	4	no	—
979	#529	—	53	8	no	—
980	#529	—	53	4	no	—
981	#529	—	53	4	no	—
982	#529	—	53	8	no	—
983	#529	—	53	4	no	—
984	C₂×#124	—	53	1	no	—
985	C₂×#124	—	53	2	no	—
986	C₂×#124	—	53	1	no	—
987	#525	—	53	8	no	—
988	#525	—	53	8	no	—
989	#525	—	53	4	no	—
990	#525	—	53	8	no	—
991	#525	—	53	4	no	—
992	#525	—	53	8	no	—
993	C₂×#121	—	53	4	no	—
994	C₂×#121	—	53	4	no	—
995	C₂×#120	—	53	4	no	—
996	C₂×#120	—	53	4	no	—
997	#520	—	53	2	no	—
998	#520	—	53	4	no	—
999	#520	—	53	4	no	—
1000	#520	—	53	4	no	—
1001	#520	—	53	2	no	—
1002	#519	—	53	2	no	—
1003	#519	—	53	1	no	—
1004	#519	—	53	1	no	—
1005	#518	—	53	1	no	—
1006	#518	—	53	1	no	—
1007	#518	—	53	4	no	—
1008	#518	—	53	4	no	—
1009	#518	—	53	4	no	—
1010	#518	—	53	2	no	—
1011	#518	—	53	1	no	—
1012	#518	—	53	1	no	—
1013	#518	—	53	4	no	—
1014	#518	—	53	4	no	—
1015	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
1016	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
1017	C₄×#41	—	53	1	no	—
1018	C₄×#41	—	53	4	no	—
1019	C₄×#41	—	53	4	no	—
1020	C₄×#41	—	53	1	no	—
1021	C₄×#41	—	53	2	no	—
1022	C₄×#41	—	53	1	no	—
1023	C₄×#41	—	53	2	no	—
1024	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
1025	C₂×C₄×D₄	—	53	4	no	—
1026	C₂×C₄×D₄	—	53	4	no	—
1027	C₂×#117	—	53	1	no	—
1028	C₂×#117	—	53	1	no	—
1029	C₂×#117	—	53	1	no	—
1030	C₂×#117	—	53	2	no	—
1031	C₂×#117	—	53	4	no	—
1032	C₂×#117	—	53	1	no	—
1033	C₂×#117	—	53	2	no	—
1034	C₂²×C₂²⋊C₄	—	53	4	no	—
1035	C₅₃	#62855	1	1	yes	characteristic, complemented, Sylow
1036	C₂⁵	—	53	2	no	—
1037	C₂×#41	—	53	1	no	—
1038	C₂×#41	—	53	2	no	—
1039	C₂×#41	—	53	2	no	—
1040	C₂×#41	—	53	2	no	—
1041	C₂×#41	—	53	2	no	—
1042	C₂×#41	—	53	1	no	—
1043	C₂×#41	—	53	2	no	—
1044	C₂×#41	—	53	8	no	—
1045	C₂×#41	—	53	8	no	—
1046	C₂×#41	—	53	1	no	—
1047	C₂×#41	—	53	2	no	—
1048	C₂×#41	—	53	8	no	—
1049	C₂×#41	—	106	8	no	—
1050	C₂×#41	—	106	8	no	—
1051	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1052	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
1053	C₂²×Q₈	—	53	1	no	—
1054	C₂²×Q₈	—	53	1	no	—
1055	C₂²×D₄	—	53	2	no	—
1056	C₂²×D₄	—	53	2	no	—
1057	C₂²×D₄	—	53	4	no	—
1058	C₂²×D₄	—	53	2	no	—
1059	C₂²×D₄	—	53	2	no	—
1060	C₂²×D₄	—	53	2	no	—
1061	C₂²×D₄	—	53	2	no	—
1062	C₂²×D₄	—	53	2	no	—
1063	C₂²×D₄	—	53	1	no	—
1064	C₂²×D₄	—	53	8	no	—
1065	C₂²×D₄	—	53	1	no	—
1066	C₂²×D₄	—	106	8	no	—
1067	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1068	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1069	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
1070	C₂³×C₄	—	53	1	no	—
1071	C₂³×C₄	—	53	2	no	—
1072	C₂³×C₄	—	53	2	no	—
1073	C₂³×C₄	—	53	8	no	—
1074	C₄⋊Q₈	—	53	4	no	—
1075	C₄⋊Q₈	—	53	2	no	—
1076	C₄⋊Q₈	—	53	4	no	—
1077	C₄⋊Q₈	—	53	4	no	—
1078	C₄⋊Q₈	—	53	2	no	—
1079	C₄⋊Q₈	—	53	2	no	—
1080	C₄⋊Q₈	—	53	4	no	—
1081	C₄⋊Q₈	—	53	2	no	—
1082	C₄⋊Q₈	—	53	2	no	—
1083	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
1084	#127	—	53	8	no	—
1085	#127	—	53	2	no	—
1086	#127	—	53	2	no	—
1087	#127	—	53	2	no	—
1088	#127	—	53	4	no	—
1089	#127	—	53	2	no	—
1090	#127	—	53	2	no	—
1091	#127	—	53	2	no	—
1092	#127	C₂²×D₅₃	1	2	yes	—
1093	#127	C₂²×D₅₃	1	2	yes	—
1094	#127	C₂²×D₅₃	1	2	yes	—
1095	#127	C₂²×D₅₃	1	4	yes	—
1096	#127	C₂²×D₅₃	1	2	yes	complemented
1097	#126	—	53	8	no	—
1098	#126	—	53	8	no	—
1099	#126	—	53	8	no	—
1100	#126	—	53	8	no	—
1101	#126	—	53	8	no	—
1102	#126	—	53	8	no	—
1103	#126	—	53	8	no	—
1104	#126	—	53	8	no	—
1105	#125	—	53	4	no	—
1106	#125	—	53	4	no	—
1107	#125	—	53	2	no	—
1108	#125	—	53	2	no	—
1109	#125	—	53	4	no	—
1110	#125	—	53	4	no	—
1111	#125	—	53	2	no	—
1112	#125	C₂²×D₅₃	1	2	yes	complemented
1113	#124	—	53	2	no	—
1114	#124	—	53	8	no	—
1115	#124	—	53	2	no	—
1116	#124	—	53	2	no	—
1117	#124	—	53	4	no	—
1118	#124	—	53	2	no	—
1119	#124	—	53	2	no	—
1120	#124	—	53	2	no	—
1121	#124	—	53	8	no	—
1122	#124	—	53	8	no	—
1123	#124	—	53	8	no	—
1124	#124	—	53	8	no	—
1125	#124	—	53	8	no	—
1126	#124	—	53	8	no	—
1127	#124	—	53	8	no	—
1128	#124	—	53	2	no	—
1129	#124	—	53	2	no	—
1130	#124	—	53	2	no	—
1131	#124	—	53	4	no	—
1132	#124	—	53	2	no	—
1133	#124	C₂²×D₅₃	1	2	yes	—
1134	#124	C₂²×D₅₃	1	2	yes	complemented
1135	#124	C₂²×D₅₃	1	8	yes	complemented
1136	#123	—	53	4	no	—
1137	#123	—	53	8	no	—
1138	#123	—	53	8	no	—
1139	#123	—	53	8	no	—
1140	#123	—	53	8	no	—
1141	#123	—	53	8	no	—
1142	#123	—	53	8	no	—
1143	#123	—	53	8	no	—
1144	#123	—	53	8	no	—
1145	#123	—	53	8	no	—
1146	#123	—	53	8	no	—
1147	#123	—	53	4	no	—
1148	#123	—	53	8	no	—
1149	#123	—	53	8	no	—
1150	#123	—	53	8	no	—
1151	#123	—	53	8	no	—
1152	#123	—	53	8	no	—
1153	#123	C₂²×D₅₃	1	8	yes	complemented
1154	#123	C₂²×D₅₃	1	8	yes	complemented
1155	C₂²⋊Q₈	—	53	4	no	—
1156	C₂²⋊Q₈	—	53	8	no	—
1157	C₂²⋊Q₈	—	53	4	no	—
1158	C₂²⋊Q₈	—	53	4	no	—
1159	C₂²⋊Q₈	—	53	8	no	—
1160	C₂²⋊Q₈	—	53	4	no	—
1161	C₂²⋊Q₈	—	53	4	no	—
1162	C₂²⋊Q₈	—	53	4	no	—
1163	C₂²⋊Q₈	—	53	4	no	—
1164	C₂²⋊Q₈	—	53	4	no	—
1165	C₂²⋊Q₈	—	53	8	no	—
1166	C₂²⋊Q₈	—	53	4	no	—
1167	C₂²⋊Q₈	—	53	4	no	—
1168	C₂²⋊Q₈	—	53	4	no	—
1169	C₂²⋊Q₈	—	53	8	no	—
1170	C₂²⋊Q₈	—	53	8	no	—
1171	C₂²⋊Q₈	—	53	4	no	—
1172	C₂²⋊Q₈	—	53	4	no	—
1173	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
1174	#121	—	53	4	no	—
1175	#121	—	53	8	no	—
1176	#121	—	53	8	no	—
1177	#121	—	53	8	no	—
1178	#121	—	53	8	no	—
1179	#121	—	53	8	no	—
1180	#121	—	53	8	no	—
1181	#121	—	53	4	no	—
1182	#121	—	53	8	no	—
1183	#121	—	53	8	no	—
1184	#121	—	53	8	no	—
1185	#121	—	53	8	no	—
1186	#121	—	53	8	no	—
1187	#121	—	53	8	no	—
1188	#121	—	53	8	no	—
1189	#121	—	53	4	no	—
1190	#121	—	53	8	no	—
1191	#121	—	53	4	no	—
1192	#121	—	53	8	no	—
1193	#121	—	53	8	no	—
1194	#121	—	53	8	no	—
1195	#121	—	53	8	no	—
1196	#121	C₂²×D₅₃	1	4	yes	—
1197	#121	C₂²×D₅₃	1	4	yes	complemented
1198	#121	C₂²×D₅₃	1	8	yes	complemented
1199	#121	C₂²×D₅₃	1	8	yes	complemented
1200	#121	C₂²×D₅₃	1	8	yes	complemented
1201	#120	—	53	4	no	—
1202	#120	—	53	4	no	—
1203	#120	—	53	8	no	—
1204	#120	—	53	8	no	—
1205	#120	—	53	8	no	—
1206	#120	—	53	4	no	—
1207	#120	—	53	8	no	—
1208	#120	—	53	8	no	—
1209	#120	—	53	8	no	—
1210	#120	—	53	8	no	—
1211	#120	—	53	4	no	—
1212	#120	C₂²×D₅₃	1	4	yes	—
1213	#120	C₂²×D₅₃	1	4	yes	—
1214	C₄×Q₈	—	53	2	no	—
1215	C₄×Q₈	—	53	4	no	—
1216	C₄×Q₈	—	53	4	no	—
1217	C₄×Q₈	—	53	4	no	—
1218	C₄×Q₈	—	53	2	no	—
1219	C₄×Q₈	—	53	4	no	—
1220	C₄×Q₈	—	53	4	no	—
1221	C₄×Q₈	—	53	4	no	—
1222	C₄×Q₈	—	53	2	no	—
1223	C₄×Q₈	—	53	4	no	—
1224	C₄×Q₈	—	53	4	no	—
1225	C₄×Q₈	—	53	4	no	—
1226	C₄×Q₈	C₂²×D₅₃	1	2	yes	complemented
1227	C₄×Q₈	C₂²×D₅₃	1	4	yes	complemented
1228	C₄×D₄	—	53	4	no	—
1229	C₄×D₄	—	53	4	no	—
1230	C₄×D₄	—	53	4	no	—
1231	C₄×D₄	—	53	4	no	—
1232	C₄×D₄	—	53	2	no	—
1233	C₄×D₄	—	53	4	no	—
1234	C₄×D₄	—	53	8	no	—
1235	C₄×D₄	—	53	8	no	—
1236	C₄×D₄	—	53	8	no	—
1237	C₄×D₄	—	53	8	no	—
1238	C₄×D₄	—	53	8	no	—
1239	C₄×D₄	—	53	8	no	—
1240	C₄×D₄	—	53	4	no	—
1241	C₄×D₄	—	53	4	no	—
1242	C₄×D₄	—	53	4	no	—
1243	C₄×D₄	—	53	8	no	—
1244	C₄×D₄	—	53	8	no	—
1245	C₄×D₄	—	53	8	no	—
1246	C₄×D₄	—	53	8	no	—
1247	C₄×D₄	—	53	4	no	—
1248	C₄×D₄	—	53	4	no	—
1249	C₄×D₄	—	53	4	no	—
1250	C₄×D₄	—	53	2	no	—
1251	C₄×D₄	—	53	8	no	—
1252	C₄×D₄	—	53	8	no	—
1253	C₄×D₄	—	53	8	no	—
1254	C₄×D₄	—	53	4	no	—
1255	C₄×D₄	—	53	8	no	—
1256	C₄×D₄	—	53	4	no	—
1257	C₄×D₄	—	53	8	no	—
1258	C₄×D₄	—	53	4	no	—
1259	C₄×D₄	—	53	8	no	—
1260	C₄×D₄	—	53	8	no	—
1261	C₄×D₄	—	53	4	no	—
1262	C₄×D₄	—	53	4	no	—
1263	C₄×D₄	—	53	4	no	—
1264	C₄×D₄	—	53	2	no	—
1265	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1266	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1267	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1268	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1269	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1270	C₄×D₄	C₂²×D₅₃	1	2	yes	complemented
1271	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1272	#117	—	53	1	no	—
1273	#117	—	53	2	no	—
1274	#117	—	53	1	no	—
1275	#117	—	53	1	no	—
1276	#117	—	53	8	no	—
1277	#117	—	53	2	no	—
1278	#117	—	53	2	no	—
1279	#117	—	53	2	no	—
1280	#117	—	53	4	no	—
1281	#117	—	53	8	no	—
1282	#117	—	53	2	no	—
1283	#117	—	53	2	no	—
1284	#117	—	53	8	no	—
1285	#117	—	53	2	no	—
1286	#117	—	53	4	no	—
1287	#117	—	53	4	no	—
1288	#117	—	53	4	no	—
1289	#117	—	53	8	no	—
1290	#117	—	53	8	no	—
1291	#117	—	53	2	no	—
1292	#117	—	53	1	no	—
1293	#117	—	53	1	no	—
1294	#117	—	53	1	no	—
1295	#117	—	53	1	no	—
1296	#117	—	53	2	no	—
1297	#117	—	53	2	no	—
1298	#117	—	53	2	no	—
1299	#117	—	53	2	no	—
1300	#117	—	53	4	no	—
1301	#117	—	53	2	no	—
1302	#117	—	53	2	no	—
1303	#117	—	53	4	no	—
1304	#117	—	53	8	no	—
1305	#117	C₂²×D₅₃	1	1	yes	characteristic
1306	#117	C₂²×D₅₃	1	1	yes	characteristic
1307	#117	C₂²×D₅₃	1	1	yes	characteristic
1308	#117	C₂²×D₅₃	1	2	yes	complemented
1309	C₂×C₄⋊C₄	—	53	2	no	—
1310	C₂×C₄⋊C₄	—	53	8	no	—
1311	C₂×C₄⋊C₄	—	53	4	no	—
1312	C₂×C₄⋊C₄	—	53	2	no	—
1313	C₂×C₄⋊C₄	—	53	2	no	—
1314	C₂×C₄⋊C₄	—	53	2	no	—
1315	C₂×C₄⋊C₄	—	53	4	no	—
1316	C₂×C₂²⋊C₄	—	53	4	no	—
1317	C₂×C₂²⋊C₄	—	53	4	no	—
1318	C₂×C₂²⋊C₄	—	53	4	no	—
1319	C₂×C₂²⋊C₄	—	53	8	no	—
1320	C₂×C₂²⋊C₄	—	53	2	no	—
1321	C₂×C₂²⋊C₄	—	53	4	no	—
1322	C₂×C₂²⋊C₄	—	53	4	no	—
1323	C₂×C₂²⋊C₄	—	53	2	no	—
1324	C₂×C₂²⋊C₄	—	53	2	no	—
1325	C₂×C₂²⋊C₄	—	53	8	no	—
1326	C₂×C₂²⋊C₄	—	53	4	no	—
1327	C₂×C₂²⋊C₄	—	53	4	no	—
1328	C₂×C₂²⋊C₄	—	53	8	no	—
1329	C₂×C₂²⋊C₄	—	53	2	no	—
1330	C₂×C₂²⋊C₄	—	53	4	no	—
1331	C₂×C₂²⋊C₄	—	53	8	no	—
1332	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1333	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1334	C₂×C₄²	—	53	1	no	—
1335	C₂×C₄²	—	53	8	no	—
1336	C₂×C₄²	—	53	2	no	—
1337	C₂×C₄²	—	53	2	no	—
1338	C₂×C₄²	—	53	2	no	—
1339	C₂×C₄²	—	53	2	no	—
1340	C₂×C₄²	—	53	2	no	—
1341	C₂×C₄²	—	53	2	no	—
1342	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1343	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1344	C₂⁴	—	53	1	no	—
1345	C₂⁴	—	53	4	no	—
1346	C₂⁴	—	53	2	no	—
1347	C₂⁴	—	53	2	no	—
1348	C₂⁴	—	53	4	no	—
1349	C₂⁴	—	106	8	no	—
1350	C₂⁴	—	424	4	no	—
1351	C₂⁴	C₂³×D₅₃	1	2	yes	—
1352	C₂⁴	C₂³×D₅₃	1	2	yes	—
1353	#41	—	2	4	no	—
1354	#41	—	8	8	no	—
1355	#41	—	106	8	no	—
1356	#41	—	106	8	no	—
1357	#41	—	106	8	no	—
1358	#41	—	106	8	no	—
1359	#41	—	106	8	no	—
1360	#41	—	106	8	no	—
1361	#41	—	106	4	no	—
1362	#41	—	106	4	no	—
1363	#41	—	106	4	no	—
1364	#41	—	424	8	no	—
1365	#41	—	424	8	no	—
1366	#41	—	424	8	no	—
1367	C₂×Q₈	—	53	2	no	—
1368	C₂×Q₈	—	53	2	no	—
1369	C₂×Q₈	—	53	1	no	—
1370	C₂×Q₈	—	53	2	no	—
1371	C₂×Q₈	—	53	4	no	—
1372	C₂×Q₈	—	53	4	no	—
1373	C₂×Q₈	—	53	4	no	—
1374	C₂×Q₈	—	106	4	no	—
1375	C₂×Q₈	—	106	4	no	—
1376	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1377	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1378	C₂×D₄	—	2	4	no	—
1379	C₂×D₄	—	2	4	no	—
1380	C₂×D₄	—	8	4	no	—
1381	C₂×D₄	—	53	4	no	—
1382	C₂×D₄	—	53	2	no	—
1383	C₂×D₄	—	53	2	no	—
1384	C₂×D₄	—	53	4	no	—
1385	C₂×D₄	—	53	4	no	—
1386	C₂×D₄	—	53	4	no	—
1387	C₂×D₄	—	53	2	no	—
1388	C₂×D₄	—	53	8	no	—
1389	C₂×D₄	—	53	8	no	—
1390	C₂×D₄	—	53	8	no	—
1391	C₂×D₄	—	53	8	no	—
1392	C₂×D₄	—	53	8	no	—
1393	C₂×D₄	—	53	2	no	—
1394	C₂×D₄	—	53	2	no	—
1395	C₂×D₄	—	53	2	no	—
1396	C₂×D₄	—	53	1	no	—
1397	C₂×D₄	—	53	8	no	—
1398	C₂×D₄	—	106	8	no	—
1399	C₂×D₄	—	106	8	no	—
1400	C₂×D₄	—	106	8	no	—
1401	C₂×D₄	—	106	8	no	—
1402	C₂×D₄	—	106	4	no	—
1403	C₂×D₄	—	106	8	no	—
1404	C₂×D₄	—	106	8	no	—
1405	C₂×D₄	—	106	8	no	—
1406	C₂×D₄	—	106	4	no	—
1407	C₂×D₄	—	424	8	no	—
1408	C₂×D₄	—	424	4	no	—
1409	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1410	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1411	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1412	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1413	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1414	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1415	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1416	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1417	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1418	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1419	C₂²×C₄	—	53	1	no	—
1420	C₂²×C₄	—	53	8	no	—
1421	C₂²×C₄	—	53	1	no	—
1422	C₂²×C₄	—	53	1	no	—
1423	C₂²×C₄	—	53	1	no	—
1424	C₂²×C₄	—	53	1	no	—
1425	C₂²×C₄	—	53	4	no	—
1426	C₂²×C₄	—	53	2	no	—
1427	C₂²×C₄	—	53	2	no	—
1428	C₂²×C₄	—	53	4	no	—
1429	C₂²×C₄	—	53	2	no	—
1430	C₂²×C₄	—	53	4	no	—
1431	C₂²×C₄	—	53	8	no	—
1432	C₂²×C₄	—	53	8	no	—
1433	C₂²×C₄	—	53	2	no	—
1434	C₂²×C₄	—	53	2	no	—
1435	C₂²×C₄	—	53	2	no	—
1436	C₂²×C₄	—	53	4	no	—
1437	C₂²×C₄	—	53	4	no	—
1438	C₂²×C₄	—	53	4	no	—
1439	C₂²×C₄	—	53	4	no	—
1440	C₂²×C₄	—	53	4	no	—
1441	C₂²×C₄	—	53	8	no	—
1442	C₂²×C₄	—	53	8	no	—
1443	C₂²×C₄	—	106	8	no	—
1444	C₂²×C₄	—	106	8	no	—
1445	C₂²×C₄	—	424	8	no	—
1446	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1447	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1448	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1449	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1450	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1451	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1452	C₄⋊C₄	—	53	4	no	—
1453	C₄⋊C₄	—	53	4	no	—
1454	C₄⋊C₄	—	53	2	no	—
1455	C₄⋊C₄	—	53	2	no	—
1456	C₄⋊C₄	—	53	2	no	—
1457	C₄⋊C₄	—	53	4	no	—
1458	C₄⋊C₄	—	53	2	no	—
1459	C₄⋊C₄	—	53	2	no	—
1460	C₄⋊C₄	—	53	2	no	—
1461	C₄⋊C₄	—	53	2	no	—
1462	C₄⋊C₄	—	53	8	no	—
1463	C₄⋊C₄	—	53	4	no	—
1464	C₄⋊C₄	—	53	8	no	—
1465	C₄⋊C₄	—	53	4	no	—
1466	C₄⋊C₄	—	53	4	no	—
1467	C₄⋊C₄	—	53	8	no	—
1468	C₄⋊C₄	—	53	8	no	—
1469	C₄⋊C₄	—	53	4	no	—
1470	C₄⋊C₄	—	53	4	no	—
1471	C₄⋊C₄	—	53	4	no	—
1472	C₄⋊C₄	—	53	4	no	—
1473	C₄⋊C₄	—	53	4	no	—
1474	C₄⋊C₄	—	53	4	no	—
1475	C₄⋊C₄	—	53	4	no	—
1476	C₄⋊C₄	—	53	4	no	—
1477	C₄⋊C₄	—	53	4	no	—
1478	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1479	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1480	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1481	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1482	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1483	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1484	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1485	C₂²⋊C₄	—	53	2	no	—
1486	C₂²⋊C₄	—	53	2	no	—
1487	C₂²⋊C₄	—	53	2	no	—
1488	C₂²⋊C₄	—	53	8	no	—
1489	C₂²⋊C₄	—	53	4	no	—
1490	C₂²⋊C₄	—	53	8	no	—
1491	C₂²⋊C₄	—	53	8	no	—
1492	C₂²⋊C₄	—	53	8	no	—
1493	C₂²⋊C₄	—	53	8	no	—
1494	C₂²⋊C₄	—	53	8	no	—
1495	C₂²⋊C₄	—	53	8	no	—
1496	C₂²⋊C₄	—	53	4	no	—
1497	C₂²⋊C₄	—	53	4	no	—
1498	C₂²⋊C₄	—	53	2	no	—
1499	C₂²⋊C₄	—	53	2	no	—
1500	C₂²⋊C₄	—	53	8	no	—
1501	C₂²⋊C₄	—	53	8	no	—
1502	C₂²⋊C₄	—	53	4	no	—
1503	C₂²⋊C₄	—	53	2	no	—
1504	C₂²⋊C₄	—	53	2	no	—
1505	C₂²⋊C₄	—	53	4	no	—
1506	C₂²⋊C₄	—	53	4	no	—
1507	C₂²⋊C₄	—	53	8	no	—
1508	C₂²⋊C₄	—	53	8	no	—
1509	C₂²⋊C₄	—	53	8	no	—
1510	C₂²⋊C₄	—	53	8	no	—
1511	C₂²⋊C₄	—	53	8	no	—
1512	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1513	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1514	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1515	C₂²⋊C₄	C₂³×D₅₃	1	2	yes	—
1516	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1517	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1518	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1519	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1520	C₄²	—	53	4	no	—
1521	C₄²	—	53	2	no	—
1522	C₄²	—	53	4	no	—
1523	C₄²	—	53	1	no	—
1524	C₄²	—	53	1	no	—
1525	C₄²	—	53	8	no	—
1526	C₄²	—	53	4	no	—
1527	C₄²	—	53	4	no	—
1528	C₄²	—	53	8	no	—
1529	C₄²	—	53	4	no	—
1530	C₄²	—	53	4	no	—
1531	C₄²	—	53	2	no	—
1532	C₄²	—	53	2	no	—
1533	C₄²	—	53	2	no	—
1534	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1535	C₄²	C₂³×D₅₃	1	2	yes	—
1536	C₄²	C₂³×D₅₃	1	2	yes	—
1537	C₄²	C₂³×D₅₃	1	2	yes	—
1538	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1539	C₄²	C₂³×D₅₃	1	2	yes	—
1540	C₄²	C₂³×D₅₃	1	4	yes	—
1541	C₂³	—	2	4	no	—
1542	C₂³	—	2	4	no	—
1543	C₂³	—	4	4	no	—
1544	C₂³	—	4	4	no	—
1545	C₂³	—	53	1	no	—
1546	C₂³	—	53	1	no	—
1547	C₂³	—	53	4	no	—
1548	C₂³	—	53	4	no	—
1549	C₂³	—	53	2	no	—
1550	C₂³	—	106	4	no	—
1551	C₂³	—	106	8	no	—
1552	C₂³	—	106	8	no	—
1553	C₂³	—	106	4	no	—
1554	C₂³	—	424	16	no	—
1555	C₂³	—	212	4	no	—
1556	C₂³	—	212	4	no	—
1557	C₂³	—	212	8	no	—
1558	C₂³	—	212	8	no	—
1559	C₂³	—	212	2	no	—
1560	C₂³	C₂⁴×D₅₃	1	4	yes	—
1561	C₂³	C₂⁴×D₅₃	1	2	yes	—
1562	C₂³	C₂⁴×D₅₃	1	4	yes	—
1563	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1564	Q₈	—	2	2	no	—
1565	Q₈	—	4	4	no	—
1566	Q₈	—	106	4	no	—
1567	Q₈	—	106	4	no	—
1568	Q₈	—	106	4	no	—
1569	Q₈	—	106	2	no	—
1570	Q₈	—	212	4	no	—
1571	Q₈	—	212	4	no	—
1572	Q₈	—	212	4	no	—
1573	D₄	—	2	4	no	—
1574	D₄	—	2	4	no	—
1575	D₄	—	2	4	no	—
1576	D₄	—	2	4	no	—
1577	D₄	—	2	4	no	—
1578	D₄	—	2	2	no	—
1579	D₄	—	4	8	no	—
1580	D₄	—	4	8	no	—
1581	D₄	—	4	8	no	—
1582	D₄	—	4	8	no	—
1583	D₄	—	106	4	no	—
1584	D₄	—	106	8	no	—
1585	D₄	—	106	8	no	—
1586	D₄	—	106	4	no	—
1587	D₄	—	106	4	no	—
1588	D₄	—	106	8	no	—
1589	D₄	—	106	8	no	—
1590	D₄	—	106	4	no	—
1591	D₄	—	106	4	no	—
1592	D₄	—	106	4	no	—
1593	D₄	—	106	2	no	—
1594	D₄	—	212	8	no	—
1595	D₄	—	212	8	no	—
1596	D₄	—	212	8	no	—
1597	D₄	—	212	8	no	—
1598	D₄	—	212	8	no	—
1599	D₄	—	212	8	no	—
1600	C₂×C₄	—	2	4	no	—
1601	C₂×C₄	—	4	8	no	—
1602	C₂×C₄	—	4	2	no	—
1603	C₂×C₄	—	4	4	no	—
1604	C₂×C₄	—	4	8	no	—
1605	C₂×C₄	—	53	4	no	—
1606	C₂×C₄	—	53	1	no	—
1607	C₂×C₄	—	53	1	no	—
1608	C₂×C₄	—	53	4	no	—
1609	C₂×C₄	—	53	4	no	—
1610	C₂×C₄	—	53	4	no	—
1611	C₂×C₄	—	53	4	no	—
1612	C₂×C₄	—	53	4	no	—
1613	C₂×C₄	—	53	2	no	—
1614	C₂×C₄	—	53	4	no	—
1615	C₂×C₄	—	53	2	no	—
1616	C₂×C₄	—	53	4	no	—
1617	C₂×C₄	—	53	2	no	—
1618	C₂×C₄	—	53	4	no	—
1619	C₂×C₄	—	106	4	no	—
1620	C₂×C₄	—	106	4	no	—
1621	C₂×C₄	—	106	4	no	—
1622	C₂×C₄	—	106	8	no	—
1623	C₂×C₄	—	106	8	no	—
1624	C₂×C₄	—	106	4	no	—
1625	C₂×C₄	—	106	4	no	—
1626	C₂×C₄	—	212	4	no	—
1627	C₂×C₄	—	212	4	no	—
1628	C₂×C₄	—	212	8	no	—
1629	C₂×C₄	—	212	8	no	—
1630	C₂×C₄	—	212	4	no	—
1631	C₂×C₄	—	212	4	no	—
1632	C₂×C₄	—	212	4	no	—
1633	C₂×C₄	—	212	8	no	—
1634	C₂×C₄	—	212	2	no	—
1635	C₂×C₄	—	212	4	no	—
1636	C₂×C₄	—	212	8	no	—
1637	C₂×C₄	#41×D₅₃	1	4	yes	—
1638	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1639	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1640	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1641	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1642	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1643	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1644	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1645	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1646	C₂²	—	2	2	no	—
1647	C₂²	—	2	2	no	—
1648	C₂²	—	2	4	no	—
1649	C₂²	—	2	4	no	—
1650	C₂²	—	2	4	no	—
1651	C₂²	—	2	8	no	—
1652	C₂²	—	2	8	no	—
1653	C₂²	—	8	4	no	—
1654	C₂²	—	8	4	no	—
1655	C₂²	—	53	2	no	—
1656	C₂²	—	53	2	no	—
1657	C₂²	—	106	2	no	—
1658	C₂²	—	106	2	no	—
1659	C₂²	—	106	2	no	—
1660	C₂²	—	106	4	no	—
1661	C₂²	—	106	4	no	—
1662	C₂²	—	106	8	no	—
1663	C₂²	—	424	4	no	—
1664	C₂²	—	424	8	no	—
1665	C₂²	—	424	4	no	—
1666	C₂²	—	212	4	no	—
1667	C₂²	—	212	16	no	—
1668	C₂²	C₂×#41×D₅₃	1	2	yes	—
1669	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1670	C₄	—	2	2	no	—
1671	C₄	—	2	4	no	—
1672	C₄	—	2	2	no	—
1673	C₄	—	2	4	no	—
1674	C₄	—	2	4	no	—
1675	C₄	—	2	2	no	—
1676	C₄	—	53	2	no	—
1677	C₄	—	53	2	no	—
1678	C₄	—	106	2	no	—
1679	C₄	—	106	4	no	—
1680	C₄	—	106	4	no	—
1681	C₄	—	106	4	no	—
1682	C₄	—	106	4	no	—
1683	C₄	—	106	2	no	—
1684	C₄	—	106	2	no	—
1685	C₄	C₂×#41×D₅₃	1	2	yes	—
1686	C₄	C₂×#41×D₅₃	1	2	yes	—
1687	C₂	—	2	2	no	—
1688	C₂	—	4	4	no	—
1689	C₂	—	4	4	no	—
1690	C₂	—	4	2	no	—
1691	C₂	—	106	2	no	—
1692	C₂	—	106	2	no	—
1693	C₂	—	212	4	no	—
1694	C₂	—	212	2	no	—
1695	C₂	C₂²×#41×D₅₃	1	1	yes	characteristic
1696	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3508	C₂
hypercenter	#3508	D₅₃
hypocenter	C₅₃	#62855
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3508

Complements

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

N	H ≅ G/N	type
1. #20288613	C₂	semidirect
2. #20288611	C₂	semidirect
3. #20288610	C₂	semidirect
4. #20288608	C₂	semidirect
5. #20288606	C₂	semidirect
6. #20288590	C₂	semidirect
7. #20288589	C₂	semidirect
8. #20288586	C₂	semidirect
9. #20288585	C₂	semidirect
10. #20288563	C₂	semidirect
11. #20288559	C₂	semidirect
12. #20288445	C₂	semidirect
13. #20288442	C₂	semidirect
14. #20288437	C₂	semidirect
15. #20288397	C₂	semidirect
16. #20288130	C₂	semidirect
17. #20288129	C₂	semidirect
18. #20288118	C₂	semidirect
19. #20288046	C₂	semidirect
20. C₂×#16811186	C₂	semidirect
21. #535×D₅₃	C₂	semidirect
22. #20287914	C₂	semidirect
23. #20287913	C₂	semidirect
24. #518×D₅₃	C₂	semidirect
25. C₅₃×#3508	C₂	semidirect
29. #16811359	C₂²	semidirect
30. #16811359	C₂²	semidirect
31. #16811358	C₂²	semidirect
32. #16811356	C₂²	semidirect
33. #16811356	C₂²	semidirect
34. #16811356	C₂²	semidirect
35. #16811355	C₂²	semidirect
36. #16811346	C₂²	semidirect
37. #16811345	C₂²	semidirect
38. #16811343	C₂²	semidirect
39. #16811342	C₂²	semidirect
40. #16811337	C₂²	semidirect
41. #16811335	C₂²	semidirect
42. #16811322	C₂²	semidirect
43. #16811318	C₂²	semidirect
44. #16811316	C₂²	semidirect
45. #16811316	C₂²	semidirect
46. #16811304	C₂²	semidirect
47. #16811303	C₂²	semidirect
48. #16811302	C₂²	semidirect
49. #16811302	C₂²	semidirect
50. #16811301	C₂²	semidirect
51. #16811300	C₂²	semidirect
52. #16811299	C₂²	semidirect
53. #16811296	C₂²	semidirect
54. #16811294	C₂²	semidirect
55. #16811293	C₂²	semidirect
56. #16811293	C₂²	semidirect
57. #16811272	C₂²	semidirect
58. #16811271	C₂²	semidirect
59. #16811270	C₂²	semidirect
60. #16811267	C₂²	semidirect
61. #16811263	C₂²	semidirect
62. #16811262	C₂²	semidirect
63. #16811262	C₂²	semidirect
64. #16811261	C₂²	semidirect
65. #16811260	C₂²	semidirect
66. #16811253	C₂²	semidirect
67. #16811253	C₂²	semidirect
68. #16811252	C₂²	semidirect
69. #16811250	C₂²	semidirect
70. #16811250	C₂²	semidirect
72. #16811247	C₂²	semidirect
73. #16811244	C₂²	semidirect
74. #16811241	C₂²	semidirect
75. #16811240	C₂²	semidirect
76. #16811238	C₂²	semidirect
77. #16811237	C₂²	semidirect
78. #16811227	C₂²	semidirect
79. #16811226	C₂²	semidirect
80. #16811224	C₂²	semidirect
81. #16811223	C₂²	semidirect
82. #16811223	C₂²	semidirect
83. #16811209	C₂²	semidirect
84. #16811207	C₂²	semidirect
85. #16811205	C₂²	semidirect
86. #16811205	C₂²	semidirect
87. #16811202	C₂²	semidirect
88. #16811199	C₂²	semidirect
89. #16811194	C₂²	semidirect
90. #16811193	C₂²	semidirect
92. #16811191	C₂²	semidirect
94. #16811190	C₂²	semidirect
95. #16811189	C₂²	semidirect
101. #16811186	C₂²	semidirect
102. #16811186	C₂²	semidirect
103. #16811186	C₂²	semidirect
104. #16811186	C₂²	semidirect
105. #16811186	C₂²	semidirect
107. #16811180	C₂²	semidirect
108. #16811177	C₂²	semidirect
109. #16811177	C₂²	semidirect
110. #16811176	C₂²	semidirect
111. #16811176	C₂²	semidirect
112. #16811172	C₂²	semidirect
113. #16811171	C₂²	semidirect
114. #16811171	C₂²	semidirect
115. #16811170	C₂²	semidirect
116. #16811169	C₂²	semidirect
117. #16811168	C₂²	semidirect
118. #16811168	C₂²	semidirect
119. C₂×#13133213	C₂²	semidirect
120. #127×D₅₃	C₂²	semidirect
121. #16811158	C₂²	semidirect
122. #16811157	C₂²	semidirect
123. #16811155	C₂²	semidirect
124. #16811154	C₂²	semidirect
125. #16811153	C₂²	semidirect
126. #16811150	C₂²	semidirect
127. C₂×#13133205	C₂²	semidirect
128. C₂×#13133204	C₂²	semidirect
129. #124×D₅₃	C₂²	semidirect
130. #16811133	C₂²	semidirect
131. #16811133	C₂²	semidirect
132. #16811132	C₂²	semidirect
133. #16811131	C₂²	semidirect
134. #16811130	C₂²	semidirect
135. #16811129	C₂²	semidirect
136. C₂×#13133189	C₂²	semidirect
137. #121×D₅₃	C₂²	semidirect
140. #16811105	C₂²	semidirect
141. #16811102	C₂²	semidirect
142. #16811102	C₂²	semidirect
143. #16811102	C₂²	semidirect
144. #16811102	C₂²	semidirect
145. #16811100	C₂²	semidirect
146. #16811100	C₂²	semidirect
147. #16811099	C₂²	semidirect
148. #16811098	C₂²	semidirect
149. #16811098	C₂²	semidirect
150. #16811097	C₂²	semidirect
151. #16811097	C₂²	semidirect
153. #16811096	C₂²	semidirect
155. #16811095	C₂²	semidirect
156. #16811095	C₂²	semidirect
157. #16811095	C₂²	semidirect
158. #41×Dic₅₃	C₂²	semidirect
159. C₄×#11719945	C₂²	semidirect
160. C₄×#11719945	C₂²	semidirect
161. #16811091	C₂²	semidirect
162. #16811091	C₂²	semidirect
163. C₄×#11719947	C₂²	semidirect
164. C₄×#11719947	C₂²	semidirect
165. C₄×D₄×D₅₃	C₂²	semidirect
166. C₄×D₄×D₅₃	C₂²	semidirect
168. C₂×#13133174	C₂²	semidirect
169. C₂×#13133173	C₂²	semidirect
173. #117×D₅₃	C₂²	semidirect
175. C₅₃×#559	C₂²	semidirect
176. C₅₃×#550	C₂²	semidirect
177. C₅₃×#546	C₂²	semidirect
178. C₅₃×#540	C₂²	semidirect
180. C₅₃×#535	C₂²	semidirect
181. C₅₃×#533	C₂²	semidirect
182. C₅₃×#532	C₂²	semidirect
183. C₂×#127×C₅₃	C₂²	semidirect
184. C₅₃×#518	C₂²	semidirect
185. C₅₃×#518	C₂²	semidirect
186. C₄×#41×C₅₃	C₂²	semidirect
191. C₂×#11719945	C₂³	semidirect
199. C₂×#11719947	C₂³	semidirect
200. C₂×#11719947	C₂³	semidirect
220. #13133217	C₂³	semidirect
221. #13133217	C₂³	semidirect
222. #13133216	C₂³	semidirect
223. #13133216	C₂³	semidirect
224. #13133216	C₂³	semidirect
225. #13133216	C₂³	semidirect
226. #13133215	C₂³	semidirect
227. #13133215	C₂³	semidirect
228. #13133215	C₂³	semidirect
236. #13133213	C₂³	semidirect
237. #13133212	C₂³	semidirect
238. #13133212	C₂³	semidirect
239. #13133212	C₂³	semidirect
240. #13133211	C₂³	semidirect
241. #13133210	C₂³	semidirect
242. #13133210	C₂³	semidirect
243. #13133210	C₂³	semidirect
244. #13133210	C₂³	semidirect
245. #13133209	C₂³	semidirect
246. #13133208	C₂³	semidirect
247. #13133208	C₂³	semidirect
248. #13133207	C₂³	semidirect
249. #13133207	C₂³	semidirect
250. #13133207	C₂³	semidirect
251. #13133207	C₂³	semidirect
253. #13133206	C₂³	semidirect
258. #13133205	C₂³	semidirect
263. #13133204	C₂³	semidirect
264. #13133204	C₂³	semidirect
265. #13133204	C₂³	semidirect
266. #13133204	C₂³	semidirect
268. #13133203	C₂³	semidirect
269. #13133203	C₂³	semidirect
270. #13133203	C₂³	semidirect
271. #13133203	C₂³	semidirect
272. #13133202	C₂³	semidirect
273. #13133202	C₂³	semidirect
275. #13133201	C₂³	semidirect
276. #13133200	C₂³	semidirect
277. #13133200	C₂³	semidirect
278. #13133200	C₂³	semidirect
280. #13133199	C₂³	semidirect
281. #13133199	C₂³	semidirect
282. #13133199	C₂³	semidirect
283. #13133199	C₂³	semidirect
285. #13133198	C₂³	semidirect
286. #13133198	C₂³	semidirect
287. #13133198	C₂³	semidirect
288. #13133198	C₂³	semidirect
291. #13133197	C₂³	semidirect
293. #13133196	C₂³	semidirect
294. #13133196	C₂³	semidirect
299. #13133195	C₂³	semidirect
302. #13133194	C₂³	semidirect
303. #13133194	C₂³	semidirect
306. #13133193	C₂³	semidirect
309. #13133191	C₂³	semidirect
312. #13133190	C₂³	semidirect
313. #13133190	C₂³	semidirect
319. #13133189	C₂³	semidirect
320. #13133189	C₂³	semidirect
321. #13133189	C₂³	semidirect
322. #13133189	C₂³	semidirect
323. #13133189	C₂³	semidirect
326. #13133188	C₂³	semidirect
327. #13133188	C₂³	semidirect
328. #13133188	C₂³	semidirect
340. Q₈×Dic₅₃	C₂³	semidirect
341. C₄×Dic₁₀₆	C₂³	semidirect
342. C₄×Dic₁₀₆	C₂³	semidirect
343. C₄×Dic₁₀₆	C₂³	semidirect
344. C₄×Dic₁₀₆	C₂³	semidirect
345. C₄×Dic₁₀₆	C₂³	semidirect
346. C₄×Dic₁₀₆	C₂³	semidirect
347. C₄×Dic₁₀₆	C₂³	semidirect
348. #13133182	C₂³	semidirect
349. #13133182	C₂³	semidirect
350. #13133182	C₂³	semidirect
351. #13133182	C₂³	semidirect
355. C₄×D₂₁₂	C₂³	semidirect
359. D₄×Dic₅₃	C₂³	semidirect
360. D₄×Dic₅₃	C₂³	semidirect
361. D₄×Dic₅₃	C₂³	semidirect
362. D₄×Dic₅₃	C₂³	semidirect
363. D₄×Dic₅₃	C₂³	semidirect
364. D₄×Dic₅₃	C₂³	semidirect
368. #13133179	C₂³	semidirect
369. #13133179	C₂³	semidirect
376. C₄×C₂²⋊D₅₃	C₂³	semidirect
377. C₄×C₂²⋊D₅₃	C₂³	semidirect
378. C₄×C₂²⋊D₅₃	C₂³	semidirect
379. C₄×C₂²⋊D₅₃	C₂³	semidirect
386. #13133177	C₂³	semidirect
387. #13133177	C₂³	semidirect
388. #13133177	C₂³	semidirect
392. #13133176	C₂³	semidirect
393. #13133176	C₂³	semidirect
398. #13133175	C₂³	semidirect
409. #13133174	C₂³	semidirect
410. #13133174	C₂³	semidirect
411. #13133174	C₂³	semidirect
412. #13133174	C₂³	semidirect
418. #13133173	C₂³	semidirect
419. #13133173	C₂³	semidirect
420. #13133173	C₂³	semidirect
421. #13133173	C₂³	semidirect
423. C₂×#11719919	C₂³	semidirect
424. C₂×#11719919	C₂³	semidirect
428. C₄⋊C₄×D₅₃	C₂³	semidirect
446. C₂×C₄×Dic₅₃	C₂³	semidirect
447. C₂×C₄×Dic₅₃	C₂³	semidirect
451. C₄²×D₅₃	C₂³	semidirect
452. C₄²×D₅₃	C₂³	semidirect
454. C₂×#41×C₅₃	C₂³	semidirect
458. C₄⋊Q₈×C₅₃	C₂³	semidirect
463. #127×C₅₃	C₂³	semidirect
464. #125×C₅₃	C₂³	semidirect
466. #124×C₅₃	C₂³	semidirect
467. #124×C₅₃	C₂³	semidirect
468. #123×C₅₃	C₂³	semidirect
469. #123×C₅₃	C₂³	semidirect
472. #121×C₅₃	C₂³	semidirect
473. #121×C₅₃	C₂³	semidirect
474. #121×C₅₃	C₂³	semidirect
475. #121×C₅₃	C₂³	semidirect
478. C₄×Q₈×C₅₃	C₂³	semidirect
479. C₄×Q₈×C₅₃	C₂³	semidirect
483. C₄×D₄×C₅₃	C₂³	semidirect
484. C₄×D₄×C₅₃	C₂³	semidirect
485. C₄×D₄×C₅₃	C₂³	semidirect
486. C₄×D₄×C₅₃	C₂³	semidirect
490. #117×C₅₃	C₂³	semidirect
494. C₂×C₄²×C₅₃	C₂³	semidirect
580. C₂×C₄×D₅₃	#41	semidirect
848. #3508	D₅₃	semidirect
884. #559	C₂×D₅₃	semidirect
906. #550	C₂×D₅₃	semidirect
916. #546	C₂×D₅₃	semidirect
934. #540	C₂×D₅₃	semidirect
959. #535	C₂×D₅₃	semidirect
966. #533	C₂×D₅₃	semidirect
974. #532	C₂×D₅₃	semidirect
977. C₂×#127	C₂×D₅₃	semidirect
1015. #518	C₂×D₅₃	semidirect
1016. #518	C₂×D₅₃	semidirect
1024. C₄×#41	C₂×D₅₃	semidirect
1035. C₅₃	#62855	semidirect
1052. C₂×#41	C₂²×D₅₃	semidirect
1083. C₄⋊Q₈	C₂²×D₅₃	semidirect
1096. #127	C₂²×D₅₃	semidirect
1112. #125	C₂²×D₅₃	semidirect
1134. #124	C₂²×D₅₃	semidirect
1135. #124	C₂²×D₅₃	semidirect
1153. #123	C₂²×D₅₃	semidirect
1154. #123	C₂²×D₅₃	semidirect
1197. #121	C₂²×D₅₃	semidirect
1198. #121	C₂²×D₅₃	semidirect
1199. #121	C₂²×D₅₃	semidirect
1200. #121	C₂²×D₅₃	semidirect
1226. C₄×Q₈	C₂²×D₅₃	semidirect
1227. C₄×Q₈	C₂²×D₅₃	semidirect
1268. C₄×D₄	C₂²×D₅₃	semidirect
1269. C₄×D₄	C₂²×D₅₃	semidirect
1270. C₄×D₄	C₂²×D₅₃	semidirect
1271. C₄×D₄	C₂²×D₅₃	semidirect
1308. #117	C₂²×D₅₃	semidirect
1343. 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
#20288613	2
#20288611	2
#20288610	2
#20288608	2
#20288606	2
#20288590	2
#20288589	2
#20288586	2
#20288585	2
#20288563	2
#20288559	2
#20288445	2
#20288442	2
#20288437	2
#20288397	2
#20288130	2
#20288129	2
#20288118	2
#20288046	2
C₂×#16811186	2
#535×D₅₃	2
#20287914	2
#20287913	2
#518×D₅₃	2
C₅₃×#3508	2
#62855	53