Subgroups — #20289312

Order 6784.

912 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃⋊#564	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811375	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811374	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811351	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811332	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811327	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811310	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811310	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811308	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811253	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811252	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811252	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811251	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811235	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811232	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811232	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811231	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811230	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811230	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811217	C₂	1	1	yes	maximal, characteristic
27	#16811215	C₂	1	1	yes	maximal, characteristic
28	#16811176	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811150	C₂	1	1	yes	maximal, characteristic
30	C₂×#13133207	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
32	#13133217	C₂²	1	1	yes	characteristic
33	#13133217	C₂²	1	1	yes	characteristic
34	#13133216	C₂²	1	1	yes	characteristic
35	#13133216	C₂²	1	1	yes	characteristic
36	#13133216	C₂²	1	1	yes	characteristic
37	#13133216	C₂²	1	1	yes	characteristic
38	#13133216	C₂²	1	1	yes	characteristic
39	#13133216	C₂²	1	1	yes	characteristic
40	#13133216	C₂²	1	1	yes	characteristic
41	#13133215	C₂²	1	1	yes	characteristic
42	#13133215	C₂²	1	1	yes	characteristic
43	#13133215	C₂²	1	1	yes	characteristic
44	#13133212	C₂²	1	1	yes	characteristic
45	#13133212	C₂²	1	1	yes	characteristic
46	#13133212	C₂²	1	1	yes	characteristic
47	#13133212	C₂²	1	1	yes	characteristic
48	#13133212	C₂²	1	1	yes	characteristic
49	#13133212	C₂²	1	1	yes	characteristic
50	#13133211	C₂²	1	1	yes	characteristic
51	#13133211	C₂²	1	1	yes	characteristic
52	#13133211	C₂²	1	1	yes	characteristic
53	#13133210	C₂²	1	1	yes	characteristic
54	#13133210	C₂²	1	1	yes	characteristic
55	#13133210	C₂²	1	1	yes	characteristic
56	#13133210	C₂²	1	1	yes	characteristic
57	#13133210	C₂²	1	1	yes	characteristic
58	#13133210	C₂²	1	1	yes	characteristic
59	#13133210	C₂²	1	1	yes	characteristic
60	#13133209	C₂²	1	1	yes	characteristic
61	#13133209	C₂²	1	1	yes	characteristic
62	#13133209	C₂²	1	1	yes	characteristic
63	#13133209	C₂²	1	1	yes	characteristic
64	#13133209	C₂²	1	1	yes	characteristic
65	#13133209	C₂²	1	1	yes	characteristic
66	#13133208	C₂²	1	1	yes	characteristic
67	#13133208	C₂²	1	1	yes	characteristic
68	#13133208	C₂²	1	1	yes	characteristic
69	#13133208	C₂²	1	1	yes	characteristic
70	#13133208	C₂²	1	1	yes	characteristic
71	#13133208	C₂²	1	1	yes	characteristic
72	#13133208	C₂²	1	1	yes	characteristic
73	#13133208	C₂²	1	1	yes	characteristic
74	#13133208	C₂²	1	1	yes	characteristic
75	#13133207	C₂²	1	1	yes	characteristic
76	#13133207	C₂²	1	1	yes	characteristic
77	#13133207	C₂²	1	1	yes	characteristic
78	#13133207	C₂²	1	1	yes	characteristic
79	#13133207	C₂²	1	1	yes	characteristic
80	#13133207	C₂²	1	1	yes	characteristic
81	#13133207	C₂²	1	1	yes	characteristic
82	#13133207	C₂²	1	1	yes	characteristic
83	#13133207	C₂²	1	1	yes	characteristic
84	#13133207	C₂²	1	1	yes	characteristic
85	#13133207	C₂²	1	1	yes	characteristic
86	#13133207	C₂²	1	1	yes	characteristic
87	#13133207	C₂²	1	1	yes	characteristic
88	#13133207	C₂²	1	1	yes	characteristic
89	#13133207	C₂²	1	1	yes	characteristic
90	#13133207	C₂²	1	1	yes	characteristic
91	#13133207	C₂²	1	1	yes	characteristic
92	#13133207	C₂²	1	1	yes	characteristic
93	#13133207	C₂²	1	1	yes	characteristic
94	#13133207	C₂²	1	1	yes	characteristic
95	#13133207	C₂²	1	1	yes	characteristic
96	#13133207	C₂²	1	1	yes	characteristic
97	#13133207	C₂²	1	1	yes	characteristic
98	#13133207	C₂²	1	1	yes	characteristic
99	#13133207	C₂²	1	1	yes	characteristic
100	#13133207	C₂²	1	1	yes	characteristic
101	#13133207	C₂²	1	1	yes	characteristic
102	#13133203	C₂²	1	1	yes	characteristic
103	#13133201	C₂²	1	1	yes	characteristic
104	#13133201	C₂²	1	1	yes	characteristic
105	#13133200	C₂²	1	1	yes	characteristic
106	#13133200	C₂²	1	1	yes	characteristic
107	#13133200	C₂²	1	1	yes	characteristic
108	#13133199	C₂²	1	1	yes	characteristic
109	#13133199	C₂²	1	1	yes	characteristic
110	#13133198	C₂²	1	1	yes	characteristic
111	#13133197	C₂²	1	1	yes	characteristic
112	#13133197	C₂²	1	1	yes	characteristic
113	#13133196	C₂²	1	1	yes	characteristic
114	#13133196	C₂²	1	1	yes	characteristic
115	#13133196	C₂²	1	1	yes	characteristic
116	#13133195	C₂²	1	1	yes	characteristic
117	#13133195	C₂²	1	1	yes	characteristic
118	#13133195	C₂²	1	1	yes	characteristic
119	#13133195	C₂²	1	1	yes	characteristic
120	#13133195	C₂²	1	1	yes	characteristic
121	#13133194	C₂²	1	1	yes	characteristic
122	#13133194	C₂²	1	1	yes	characteristic
123	#13133194	C₂²	1	1	yes	characteristic
124	#13133194	C₂²	1	1	yes	characteristic
125	#13133194	C₂²	1	1	yes	characteristic
126	#13133194	C₂²	1	1	yes	characteristic
127	#13133194	C₂²	1	1	yes	characteristic
128	#13133194	C₂²	1	1	yes	characteristic
129	#13133194	C₂²	1	1	yes	characteristic
130	#13133194	C₂²	1	1	yes	characteristic
131	#13133194	C₂²	1	1	yes	characteristic
132	#13133194	C₂²	1	1	yes	characteristic
133	#13133193	C₂²	1	1	yes	characteristic
134	#13133189	C₂²	1	1	yes	characteristic
135	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
136	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
137	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
138	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
139	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
140	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
141	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
142	#13133182	C₂²	1	1	yes	characteristic
143	#13133182	C₂²	1	1	yes	characteristic
144	#13133182	C₂²	1	1	yes	characteristic
145	#13133182	C₂²	1	1	yes	characteristic
146	#13133182	C₂²	1	1	yes	characteristic
147	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
148	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
150	#13133177	C₂²	1	1	yes	characteristic
151	#13133177	C₂²	1	1	yes	characteristic
152	#13133177	C₂²	1	1	yes	characteristic
153	#13133176	C₂²	1	1	yes	characteristic
154	#13133176	C₂²	1	1	yes	characteristic
155	#13133175	C₂²	1	1	yes	characteristic
156	#13133175	C₂²	1	1	yes	characteristic
157	#13133174	C₂²	1	1	yes	characteristic
158	#13133174	C₂²	1	1	yes	characteristic
159	#13133173	C₂²	1	1	yes	characteristic
160	#13133173	C₂²	1	1	yes	characteristic
161	#13133173	C₂²	1	1	yes	characteristic
162	#13133173	C₂²	1	1	yes	characteristic
163	#13133173	C₂²	1	1	yes	characteristic
164	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
165	C₂×#11719919	C₂²	1	1	yes	characteristic
166	C₂×#11719919	C₂²	1	1	yes	characteristic
167	C₂×#11719919	C₂²	1	1	yes	characteristic
168	C₂×#11719919	C₂²	1	1	yes	characteristic
169	C₂×#11719919	C₂²	1	1	yes	characteristic
170	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
172	#126×C₅₃	C₂²	1	1	yes	characteristic
173	#126×C₅₃	C₂²	1	1	yes	characteristic
174	#125×C₅₃	C₂²	1	1	yes	characteristic
175	#125×C₅₃	C₂²	1	1	yes	characteristic
176	#125×C₅₃	C₂²	1	1	yes	characteristic
177	#123×C₅₃	C₂²	1	1	yes	characteristic
178	#123×C₅₃	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
180	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
183	#117×C₅₃	C₂²	1	1	yes	characteristic
184	#117×C₅₃	C₂²	1	1	yes	characteristic
185	#117×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
194	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
205	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
206	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
207	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
208	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
209	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
210	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
211	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
212	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₄²×C₅₃	C₂³	1	1	yes	characteristic
237	C₄²×C₅₃	C₂³	1	1	yes	characteristic
238	C₄²×C₅₃	C₂³	1	1	yes	characteristic
239	C₄²×C₅₃	C₂³	1	1	yes	characteristic
240	C₄²×C₅₃	C₂³	1	1	yes	characteristic
241	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
242	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
243	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
244	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
245	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
246	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
247	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
248	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
249	#11719921	C₂³	1	1	yes	characteristic
250	#11719921	C₂³	1	1	yes	characteristic
251	#11719921	C₂³	1	1	yes	characteristic
252	#11719921	C₂³	1	1	yes	characteristic
253	#11719921	C₂³	1	1	yes	characteristic
254	#11719921	C₂³	1	1	yes	characteristic
255	#11719921	C₂³	1	1	yes	characteristic
256	#11719921	C₂³	1	1	yes	characteristic
257	#11719921	C₂³	1	1	yes	characteristic
258	#11719921	C₂³	1	1	yes	characteristic
259	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
260	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
262	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
264	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
265	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
270	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
271	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
272	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
273	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
274	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
279	#11719919	C₂³	1	1	yes	characteristic
280	#11719919	C₂³	1	1	yes	characteristic
281	#11719919	C₂³	1	1	yes	characteristic
282	#11719919	C₂³	1	1	yes	characteristic
283	#11719919	C₂³	1	1	yes	characteristic
284	#11719919	C₂³	1	1	yes	characteristic
285	#11719919	C₂³	1	1	yes	characteristic
286	#11719919	C₂³	1	1	yes	characteristic
287	#11719919	C₂³	1	1	yes	characteristic
288	#11719919	C₂³	1	1	yes	characteristic
289	#11719919	C₂³	1	1	yes	characteristic
290	#11719919	C₂³	1	1	yes	characteristic
291	#11719919	C₂³	1	1	yes	characteristic
292	#11719919	C₂³	1	1	yes	characteristic
293	#11719919	C₂³	1	1	yes	characteristic
294	#11719919	C₂³	1	1	yes	characteristic
295	#11719919	C₂³	1	1	yes	characteristic
296	#11719919	C₂³	1	1	yes	characteristic
297	#11719919	C₂³	1	1	yes	characteristic
298	#11719919	C₂³	1	1	yes	characteristic
299	#11719919	C₂³	1	1	yes	characteristic
300	#11719919	C₂³	1	1	yes	characteristic
301	#11719919	C₂³	1	1	yes	characteristic
302	#11719919	C₂³	1	1	yes	characteristic
303	#11719919	C₂³	1	1	yes	characteristic
304	#11719919	C₂³	1	1	yes	characteristic
305	#11719919	C₂³	1	1	yes	characteristic
306	#11719919	C₂³	1	1	yes	characteristic
307	#11719919	C₂³	1	1	yes	characteristic
308	#11719919	C₂³	1	1	yes	characteristic
309	#11719919	C₂³	1	1	yes	characteristic
310	#11719919	C₂³	1	1	yes	characteristic
311	#11719919	C₂³	1	1	yes	characteristic
312	#11719919	C₂³	1	1	yes	characteristic
313	#11719919	C₂³	1	1	yes	characteristic
314	#11719919	C₂³	1	1	yes	characteristic
315	#11719919	C₂³	1	1	yes	characteristic
316	#11719919	C₂³	1	1	yes	characteristic
317	#11719919	C₂³	1	1	yes	characteristic
318	#11719919	C₂³	1	1	yes	characteristic
319	#11719919	C₂³	1	1	yes	characteristic
320	#11719919	C₂³	1	1	yes	characteristic
321	#11719919	C₂³	1	1	yes	characteristic
322	#11719919	C₂³	1	1	yes	characteristic
323	#11719919	C₂³	1	1	yes	characteristic
324	#11719919	C₂³	1	1	yes	characteristic
325	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
326	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
327	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
328	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
329	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
330	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
331	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
332	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
333	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
334	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
335	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
336	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
337	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
338	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
339	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
340	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
341	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
342	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
345	Q₈×C₅₃	—	4	1	no	—
346	D₄×C₅₃	—	2	2	no	—
347	C₂×C₄×C₅₃	—	2	2	no	—
348	C₂×C₄×C₅₃	—	2	2	no	—
349	C₂×C₄×C₅₃	—	4	1	no	—
350	C₂×C₄×C₅₃	—	4	1	no	—
351	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
357	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
359	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²⋊D₅₃	—	2	2	no	—
365	C₂²⋊D₅₃	—	4	1	no	—
366	C₂×Dic₅₃	—	2	2	no	—
367	C₂×Dic₅₃	—	2	2	no	—
368	C₂×Dic₅₃	—	2	2	no	—
369	C₂×Dic₅₃	—	4	1	no	—
370	C₂×Dic₅₃	—	4	1	no	—
371	C₂×Dic₅₃	—	4	1	no	—
372	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
374	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
378	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
379	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
380	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
381	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
387	C₄×D₅₃	—	2	2	no	—
388	C₄×D₅₃	—	4	1	no	—
389	C₄×D₅₃	—	4	1	no	—
390	Dic₁₀₆	—	2	2	no	—
391	Dic₁₀₆	—	2	2	no	—
392	Dic₁₀₆	—	4	1	no	—
393	Dic₁₀₆	—	4	1	no	—
394	Dic₁₀₆	—	4	1	no	—
395	Dic₁₀₆	—	4	1	no	—
396	Dic₁₀₆	—	4	1	no	—
397	Dic₁₀₆	—	4	1	no	—
398	C₂²×C₅₃	—	2	1	no	—
399	C₂²×C₅₃	—	2	1	no	—
400	C₂²×C₅₃	—	2	1	no	—
401	C₂²×C₅₃	—	2	1	no	—
402	C₂²×C₅₃	—	2	1	no	—
403	C₂²×C₅₃	2₋¹⁺⁴	1	2	yes	—
404	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
405	C₂×D₅₃	—	2	1	no	—
406	C₂×D₅₃	—	2	1	no	—
407	C₂×D₅₃	—	2	1	no	—
408	C₄×C₅₃	—	2	1	no	—
409	C₄×C₅₃	—	2	1	no	—
410	C₄×C₅₃	—	2	1	no	—
411	C₄×C₅₃	—	2	1	no	—
412	C₄×C₅₃	—	2	1	no	—
413	C₄×C₅₃	—	2	1	no	—
414	C₄×C₅₃	—	2	1	no	—
415	C₄×C₅₃	—	2	1	no	—
416	C₄×C₅₃	—	2	1	no	—
417	C₄×C₅₃	—	2	1	no	—
418	C₄×C₅₃	—	2	1	no	—
419	C₄×C₅₃	—	2	1	no	—
420	C₄×C₅₃	—	2	1	no	—
421	Dic₅₃	—	2	1	no	—
422	Dic₅₃	—	2	1	no	—
423	Dic₅₃	—	2	1	no	—
424	Dic₅₃	—	2	1	no	—
425	Dic₅₃	—	2	1	no	—
426	Dic₅₃	—	2	1	no	—
427	Dic₅₃	—	2	1	no	—
428	Dic₅₃	—	2	1	no	—
429	Dic₅₃	—	2	1	no	—
430	Dic₅₃	—	2	1	no	—
431	Dic₅₃	—	2	1	no	—
432	Dic₅₃	—	2	1	no	—
433	Dic₅₃	—	2	1	no	—
434	Dic₅₃	—	2	1	no	—
435	Dic₅₃	2₋¹⁺⁴	1	2	yes	—
436	#3563	—	53	1	no	maximal, Sylow
437	C₂×C₅₃	—	2	2	no	—
438	C₂×C₅₃	—	4	1	no	—
439	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
440	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
441	C₂×C₅₃	#585	1	1	yes	characteristic
442	D₅₃	—	4	1	no	—
443	#564	—	53	1	no	—
444	#564	—	53	1	no	—
445	#563	—	53	1	no	—
446	#563	—	53	1	no	—
447	#557	—	53	1	no	—
448	#557	—	53	1	no	—
449	#554	—	53	1	no	—
450	#554	—	53	1	no	—
451	#552	—	53	1	no	—
452	#552	—	53	1	no	—
453	#552	—	53	1	no	—
454	#552	—	53	1	no	—
455	#552	—	53	1	no	—
456	#552	—	53	1	no	—
457	#552	—	53	1	no	—
458	#552	D₅₃	1	1	yes	characteristic, complemented
459	#544	—	53	1	no	—
460	#544	—	53	1	no	—
461	#544	—	53	1	no	—
462	#544	—	53	1	no	—
463	#541	—	53	1	no	—
464	#541	—	53	1	no	—
465	#541	—	53	1	no	—
466	#541	—	53	1	no	—
467	#541	—	53	1	no	—
468	#541	—	53	1	no	—
469	#539	—	53	1	no	—
470	#539	—	53	1	no	—
471	#533	—	53	1	no	—
472	#529	—	53	1	no	—
473	C₂×#125	—	53	1	no	—
474	C₅₃	#3563	1	1	yes	characteristic, complemented, Sylow
475	C₄⋊Q₈	—	53	1	no	—
476	C₄⋊Q₈	—	53	1	no	—
477	C₄⋊Q₈	—	53	1	no	—
478	C₄⋊Q₈	—	53	1	no	—
479	C₄⋊Q₈	—	53	1	no	—
480	C₄⋊Q₈	—	53	1	no	—
481	C₄⋊Q₈	—	53	1	no	—
482	C₄⋊Q₈	—	53	1	no	—
483	C₄⋊Q₈	—	53	1	no	—
484	C₄⋊Q₈	—	53	1	no	—
485	C₄⋊Q₈	—	53	1	no	—
486	C₄⋊Q₈	—	53	1	no	—
487	#126	—	53	1	no	—
488	#126	—	53	1	no	—
489	#126	—	53	1	no	—
490	#126	—	53	1	no	—
491	#126	—	53	1	no	—
492	#126	—	53	1	no	—
493	#126	—	53	1	no	—
494	#126	—	53	1	no	—
495	#126	—	53	1	no	—
496	#126	—	53	1	no	—
497	#126	—	53	1	no	—
498	#126	—	53	1	no	—
499	#126	—	53	1	no	—
500	#126	—	53	1	no	—
501	#126	—	53	1	no	—
502	#126	—	53	1	no	—
503	#126	C₂×D₅₃	1	1	yes	characteristic
504	#126	C₂×D₅₃	1	1	yes	characteristic
505	#125	—	53	1	no	—
506	#125	—	53	1	no	—
507	#125	—	53	1	no	—
508	#125	—	53	1	no	—
509	#125	—	53	1	no	—
510	#125	—	53	1	no	—
511	#125	—	53	1	no	—
512	#125	—	53	1	no	—
513	#125	—	53	1	no	—
514	#125	—	53	1	no	—
515	#125	—	53	1	no	—
516	#125	—	53	1	no	—
517	#125	—	53	1	no	—
518	#125	—	53	1	no	—
519	#125	—	53	1	no	—
520	#125	—	53	1	no	—
521	#125	—	53	1	no	—
522	#125	—	53	1	no	—
523	#125	—	53	1	no	—
524	#125	—	53	1	no	—
525	#125	—	53	1	no	—
526	#125	—	53	1	no	—
527	#125	—	53	1	no	—
528	#125	—	53	1	no	—
529	#125	—	53	1	no	—
530	#125	—	53	1	no	—
531	#125	—	53	1	no	—
532	#125	—	53	1	no	—
533	#125	—	53	1	no	—
534	#125	—	53	1	no	—
535	#125	—	53	1	no	—
536	#125	—	53	1	no	—
537	#125	—	53	1	no	—
538	#125	—	53	1	no	—
539	#125	—	53	1	no	—
540	#125	—	53	1	no	—
541	#125	—	53	1	no	—
542	#125	—	53	1	no	—
543	#125	—	53	1	no	—
544	#125	—	53	1	no	—
545	#125	—	53	1	no	—
546	#125	—	53	1	no	—
547	#125	C₂×D₅₃	1	1	yes	characteristic
548	#125	C₂×D₅₃	1	1	yes	characteristic
549	#125	C₂×D₅₃	1	1	yes	characteristic
550	#124	—	53	1	no	—
551	#123	—	53	1	no	—
552	#123	—	53	1	no	—
553	#123	—	53	1	no	—
554	#123	—	53	1	no	—
555	#123	—	53	1	no	—
556	#123	—	53	1	no	—
557	#123	—	53	1	no	—
558	#123	—	53	1	no	—
559	#123	C₂×D₅₃	1	1	yes	characteristic
560	#123	C₂×D₅₃	1	1	yes	characteristic
561	C₂²⋊Q₈	—	53	1	no	—
562	C₂²⋊Q₈	—	53	1	no	—
563	C₂²⋊Q₈	—	53	1	no	—
564	C₂²⋊Q₈	—	53	1	no	—
565	C₂²⋊Q₈	—	53	1	no	—
566	C₂²⋊Q₈	—	53	1	no	—
567	C₂²⋊Q₈	—	53	1	no	—
568	C₂²⋊Q₈	—	53	1	no	—
569	C₂²⋊Q₈	—	53	1	no	—
570	C₂²⋊Q₈	—	53	1	no	—
571	C₂²⋊Q₈	—	53	1	no	—
572	C₂²⋊Q₈	—	53	1	no	—
573	C₂²⋊Q₈	—	53	1	no	—
574	C₂²⋊Q₈	—	53	1	no	—
575	C₂²⋊Q₈	—	53	1	no	—
576	C₂²⋊Q₈	—	53	1	no	—
577	C₂²⋊Q₈	—	53	1	no	—
578	C₂²⋊Q₈	—	53	1	no	—
579	C₂²⋊Q₈	—	53	1	no	—
580	C₂²⋊Q₈	—	53	1	no	—
581	C₂²⋊Q₈	—	53	1	no	—
582	C₂²⋊Q₈	—	53	1	no	—
583	C₂²⋊Q₈	—	53	1	no	—
584	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
585	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
586	#121	—	53	1	no	—
587	C₄×Q₈	—	53	1	no	—
588	C₄×Q₈	—	53	1	no	—
589	C₄×Q₈	—	53	1	no	—
590	C₄×Q₈	—	53	1	no	—
591	C₄×Q₈	—	53	1	no	—
592	C₄×Q₈	—	53	1	no	—
593	C₄×Q₈	—	53	1	no	—
594	C₄×Q₈	—	53	1	no	—
595	C₄×Q₈	—	53	1	no	—
596	C₄×Q₈	—	53	1	no	—
597	C₄×Q₈	—	53	1	no	—
598	C₄×Q₈	—	53	1	no	—
599	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
600	C₄×D₄	—	53	1	no	—
601	C₄×D₄	—	53	1	no	—
602	C₄×D₄	—	53	1	no	—
603	C₄×D₄	—	53	1	no	—
604	C₄×D₄	—	53	1	no	—
605	C₄×D₄	—	53	1	no	—
606	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
607	#117	—	53	1	no	—
608	#117	—	53	1	no	—
609	#117	—	53	1	no	—
610	#117	—	53	1	no	—
611	#117	—	53	1	no	—
612	#117	—	53	1	no	—
613	#117	—	53	1	no	—
614	#117	—	53	1	no	—
615	#117	—	53	1	no	—
616	#117	—	53	1	no	—
617	#117	—	53	1	no	—
618	#117	C₂×D₅₃	1	1	yes	characteristic
619	#117	C₂×D₅₃	1	1	yes	characteristic
620	#117	C₂×D₅₃	1	1	yes	characteristic
621	C₂×C₄⋊C₄	—	53	1	no	—
622	C₂×C₄⋊C₄	—	53	1	no	—
623	C₂×C₄⋊C₄	—	53	1	no	—
624	C₂×C₄⋊C₄	—	53	1	no	—
625	C₂×C₄⋊C₄	—	53	1	no	—
626	C₂×C₄⋊C₄	—	53	1	no	—
627	C₂×C₄⋊C₄	—	53	1	no	—
628	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
629	C₂×C₄²	—	53	1	no	—
630	C₂×Q₈	—	53	1	no	—
631	C₂×Q₈	—	53	1	no	—
632	C₂×Q₈	—	53	1	no	—
633	C₂×Q₈	—	53	1	no	—
634	C₂×Q₈	—	53	1	no	—
635	C₂×Q₈	—	53	1	no	—
636	C₂×Q₈	—	53	1	no	—
637	C₂×Q₈	—	53	1	no	—
638	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
639	C₂×D₄	—	53	1	no	—
640	C₂×D₄	—	53	1	no	—
641	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
642	C₂²×C₄	—	53	1	no	—
643	C₂²×C₄	—	53	1	no	—
644	C₂²×C₄	—	53	1	no	—
645	C₂²×C₄	—	53	1	no	—
646	C₂²×C₄	—	53	1	no	—
647	C₂²×C₄	—	53	1	no	—
648	C₂²×C₄	—	53	1	no	—
649	C₂²×C₄	—	53	1	no	—
650	C₂²×C₄	—	53	1	no	—
651	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
652	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
653	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
654	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
655	C₄⋊C₄	—	53	1	no	—
656	C₄⋊C₄	—	53	1	no	—
657	C₄⋊C₄	—	53	1	no	—
658	C₄⋊C₄	—	53	1	no	—
659	C₄⋊C₄	—	53	1	no	—
660	C₄⋊C₄	—	53	1	no	—
661	C₄⋊C₄	—	53	1	no	—
662	C₄⋊C₄	—	53	1	no	—
663	C₄⋊C₄	—	53	1	no	—
664	C₄⋊C₄	—	53	1	no	—
665	C₄⋊C₄	—	53	1	no	—
666	C₄⋊C₄	—	53	1	no	—
667	C₄⋊C₄	—	53	1	no	—
668	C₄⋊C₄	—	53	1	no	—
669	C₄⋊C₄	—	53	1	no	—
670	C₄⋊C₄	—	53	1	no	—
671	C₄⋊C₄	—	53	1	no	—
672	C₄⋊C₄	—	53	1	no	—
673	C₄⋊C₄	—	53	1	no	—
674	C₄⋊C₄	—	53	1	no	—
675	C₄⋊C₄	—	53	1	no	—
676	C₄⋊C₄	—	53	1	no	—
677	C₄⋊C₄	—	53	1	no	—
678	C₄⋊C₄	—	53	1	no	—
679	C₄⋊C₄	—	53	1	no	—
680	C₄⋊C₄	—	53	1	no	—
681	C₄⋊C₄	—	53	1	no	—
682	C₄⋊C₄	—	53	1	no	—
683	C₄⋊C₄	—	53	1	no	—
684	C₄⋊C₄	—	53	1	no	—
685	C₄⋊C₄	—	53	1	no	—
686	C₄⋊C₄	—	53	1	no	—
687	C₄⋊C₄	—	53	1	no	—
688	C₄⋊C₄	—	53	1	no	—
689	C₄⋊C₄	—	53	1	no	—
690	C₄⋊C₄	—	53	1	no	—
691	C₄⋊C₄	—	53	1	no	—
692	C₄⋊C₄	—	53	1	no	—
693	C₄⋊C₄	—	53	1	no	—
694	C₄⋊C₄	—	53	1	no	—
695	C₄⋊C₄	—	53	1	no	—
696	C₄⋊C₄	—	53	1	no	—
697	C₄⋊C₄	—	53	1	no	—
698	C₄⋊C₄	—	53	1	no	—
699	C₄⋊C₄	—	53	1	no	—
700	C₄⋊C₄	—	53	1	no	—
701	C₄⋊C₄	—	53	1	no	—
702	C₄⋊C₄	—	53	1	no	—
703	C₄⋊C₄	—	53	1	no	—
704	C₄⋊C₄	—	53	1	no	—
705	C₄⋊C₄	—	53	1	no	—
706	C₄⋊C₄	—	53	1	no	—
707	C₄⋊C₄	—	53	1	no	—
708	C₄⋊C₄	—	53	1	no	—
709	C₄⋊C₄	—	53	1	no	—
710	C₄⋊C₄	—	53	1	no	—
711	C₄⋊C₄	—	53	1	no	—
712	C₄⋊C₄	—	53	1	no	—
713	C₄⋊C₄	—	53	1	no	—
714	C₄⋊C₄	—	53	1	no	—
715	C₄⋊C₄	—	53	1	no	—
716	C₄⋊C₄	—	53	1	no	—
717	C₄⋊C₄	—	53	1	no	—
718	C₄⋊C₄	—	53	1	no	—
719	C₄⋊C₄	—	53	1	no	—
720	C₄⋊C₄	—	53	1	no	—
721	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
722	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
723	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
724	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
725	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
726	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
727	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
728	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
729	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
730	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
731	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
732	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
733	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
734	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
735	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
736	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
737	C₂²⋊C₄	—	53	1	no	—
738	C₂²⋊C₄	—	53	1	no	—
739	C₂²⋊C₄	—	53	1	no	—
740	C₂²⋊C₄	—	53	1	no	—
741	C₂²⋊C₄	—	53	1	no	—
742	C₂²⋊C₄	—	53	1	no	—
743	C₂²⋊C₄	—	53	1	no	—
744	C₂²⋊C₄	—	53	1	no	—
745	C₂²⋊C₄	—	53	1	no	—
746	C₂²⋊C₄	—	53	1	no	—
747	C₂²⋊C₄	—	53	1	no	—
748	C₂²⋊C₄	—	53	1	no	—
749	C₂²⋊C₄	—	53	1	no	—
750	C₂²⋊C₄	—	53	1	no	—
751	C₂²⋊C₄	—	53	1	no	—
752	C₂²⋊C₄	—	53	1	no	—
753	C₂²⋊C₄	—	53	1	no	—
754	C₂²⋊C₄	—	53	1	no	—
755	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
756	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
757	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
758	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
759	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
760	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
761	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
762	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
763	C₄²	—	53	1	no	—
764	C₄²	—	53	1	no	—
765	C₄²	—	53	1	no	—
766	C₄²	—	53	1	no	—
767	C₄²	—	53	1	no	—
768	C₄²	—	53	1	no	—
769	C₄²	—	53	1	no	—
770	C₄²	—	53	1	no	—
771	C₄²	—	53	1	no	—
772	C₄²	—	53	1	no	—
773	C₄²	—	53	1	no	—
774	C₄²	—	53	1	no	—
775	C₄²	—	53	1	no	—
776	C₄²	—	53	1	no	—
777	C₄²	—	53	1	no	—
778	C₄²	—	53	1	no	—
779	C₄²	—	53	1	no	—
780	C₄²	C₂²×D₅₃	1	1	yes	characteristic
781	C₄²	C₂²×D₅₃	1	1	yes	characteristic
782	C₄²	C₂²×D₅₃	1	1	yes	characteristic
783	C₄²	C₂²×D₅₃	1	1	yes	characteristic
784	C₄²	C₂²×D₅₃	1	1	yes	characteristic
785	C₂³	—	53	1	no	—
786	C₂³	C₂³×D₅₃	1	1	yes	characteristic
787	C₂³	C₂³×D₅₃	1	1	yes	characteristic
788	Q₈	—	4	1	no	—
789	Q₈	—	106	2	no	—
790	Q₈	—	106	2	no	—
791	Q₈	—	212	1	no	—
792	Q₈	—	212	1	no	—
793	Q₈	—	212	1	no	—
794	Q₈	—	212	1	no	—
795	Q₈	—	212	1	no	—
796	Q₈	—	212	1	no	—
797	D₄	—	2	2	no	—
798	D₄	—	106	2	no	—
799	D₄	—	212	1	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	4	1	no	—
803	C₂×C₄	—	4	1	no	—
804	C₂×C₄	—	53	1	no	—
805	C₂×C₄	—	53	1	no	—
806	C₂×C₄	—	53	1	no	—
807	C₂×C₄	—	53	1	no	—
808	C₂×C₄	—	53	1	no	—
809	C₂×C₄	—	53	1	no	—
810	C₂×C₄	—	53	1	no	—
811	C₂×C₄	—	53	1	no	—
812	C₂×C₄	—	53	1	no	—
813	C₂×C₄	—	53	1	no	—
814	C₂×C₄	—	53	1	no	—
815	C₂×C₄	—	53	1	no	—
816	C₂×C₄	—	53	1	no	—
817	C₂×C₄	—	53	1	no	—
818	C₂×C₄	—	53	1	no	—
819	C₂×C₄	—	106	2	no	—
820	C₂×C₄	—	106	2	no	—
821	C₂×C₄	—	106	2	no	—
822	C₂×C₄	—	106	2	no	—
823	C₂×C₄	—	212	1	no	—
824	C₂×C₄	—	212	1	no	—
825	C₂×C₄	—	212	1	no	—
826	C₂×C₄	—	212	1	no	—
827	C₂×C₄	—	212	1	no	—
828	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
829	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
830	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
831	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
832	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
833	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
834	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
835	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
836	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
837	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
838	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
839	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
840	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
841	C₂²	—	2	1	no	—
842	C₂²	—	2	1	no	—
843	C₂²	—	2	1	no	—
844	C₂²	—	2	1	no	—
845	C₂²	—	2	1	no	—
846	C₂²	—	106	1	no	—
847	C₂²	—	106	1	no	—
848	C₂²	—	106	1	no	—
849	C₂²	#13133264	1	2	yes	—
850	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
851	C₄	—	2	1	no	—
852	C₄	—	2	1	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	1	no	—
855	C₄	—	2	1	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	2	1	no	—
860	C₄	—	2	1	no	—
861	C₄	—	2	1	no	—
862	C₄	—	2	1	no	—
863	C₄	—	2	1	no	—
864	C₄	—	53	2	no	—
865	C₄	—	106	1	no	—
866	C₄	—	106	1	no	—
867	C₄	—	106	1	no	—
868	C₄	—	106	1	no	—
869	C₄	—	106	1	no	—
870	C₄	—	106	1	no	—
871	C₄	—	106	1	no	—
872	C₄	—	106	1	no	—
873	C₄	—	106	1	no	—
874	C₄	—	106	1	no	—
875	C₄	—	106	1	no	—
876	C₄	—	106	1	no	—
877	C₄	—	106	1	no	—
878	C₄	—	106	1	no	—
879	C₂	—	2	2	no	—
880	C₂	—	4	1	no	—
881	C₂	—	212	1	no	—
882	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
883	C₂	C₂×#13133264	1	1	yes	characteristic
884	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#552	C₂
hypercenter	#552	D₅₃
hypocenter	C₅₃	#3563
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₅₃⋊#564	C₂	semidirect
2. C₅₃⋊#564	C₂	semidirect
3. #16811375	C₂	semidirect
4. #16811374	C₂	semidirect
5. #16811351	C₂	semidirect
6. #16811350	C₂	semidirect
7. #16811332	C₂	semidirect
8. #16811327	C₂	semidirect
9. #16811310	C₂	semidirect
10. #16811310	C₂	semidirect
11. #16811309	C₂	semidirect
12. #16811308	C₂	semidirect
13. #16811306	C₂	semidirect
14. #16811306	C₂	semidirect
15. #16811306	C₂	semidirect
16. #16811253	C₂	semidirect
17. #16811252	C₂	semidirect
18. #16811252	C₂	semidirect
19. #16811251	C₂	semidirect
20. #16811235	C₂	semidirect
21. #16811232	C₂	semidirect
22. #16811232	C₂	semidirect
23. #16811231	C₂	semidirect
24. #16811230	C₂	semidirect
25. #16811230	C₂	semidirect
28. #16811176	C₂	semidirect
30. C₂×#13133207	C₂	semidirect
31. C₅₃×#552	C₂	semidirect
458. #552	D₅₃	semidirect
474. C₅₃	#3563	semidirect