Subgroups — #20289149

Order 6784.

1004 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811375	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811375	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811372	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811350	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811340	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811327	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811324	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811318	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811288	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811286	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811283	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811281	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811271	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811252	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811250	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811243	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811237	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811232	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811230	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811221	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811219	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811216	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811214	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811196	C₂	1	1	yes	maximal, characteristic, complemented
27	#16811195	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811156	C₂	1	1	yes	maximal, characteristic, complemented
30	#16811156	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#563	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719945	C₂²	1	1	yes	characteristic
33	C₂×#11719947	C₂²	1	1	yes	characteristic
34	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic
35	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
37	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
38	#13133217	C₂²	1	1	yes	characteristic
39	#13133216	C₂²	1	1	yes	characteristic
40	#13133216	C₂²	1	1	yes	characteristic
41	#13133216	C₂²	1	1	yes	characteristic
42	#13133216	C₂²	1	1	yes	characteristic
43	#13133216	C₂²	1	1	yes	characteristic
44	#13133216	C₂²	1	1	yes	characteristic
45	#13133216	C₂²	1	1	yes	characteristic
46	#13133216	C₂²	1	1	yes	characteristic
47	#13133216	C₂²	1	1	yes	characteristic
48	#13133215	C₂²	1	1	yes	characteristic
49	#13133215	C₂²	1	1	yes	characteristic
50	#13133215	C₂²	1	1	yes	characteristic
51	#13133215	C₂²	1	1	yes	characteristic
52	#13133212	C₂²	1	1	yes	characteristic
53	#13133212	C₂²	1	1	yes	characteristic
54	#13133212	C₂²	1	1	yes	characteristic
55	#13133212	C₂²	1	1	yes	characteristic
56	#13133212	C₂²	1	1	yes	characteristic
57	#13133211	C₂²	1	1	yes	characteristic
58	#13133211	C₂²	1	1	yes	characteristic
59	#13133211	C₂²	1	1	yes	characteristic
60	#13133210	C₂²	1	1	yes	characteristic
61	#13133210	C₂²	1	1	yes	characteristic
62	#13133210	C₂²	1	1	yes	characteristic
63	#13133210	C₂²	1	1	yes	characteristic
64	#13133209	C₂²	1	1	yes	characteristic
65	#13133208	C₂²	1	1	yes	characteristic
66	#13133208	C₂²	1	1	yes	characteristic
67	#13133208	C₂²	1	1	yes	characteristic
68	#13133207	C₂²	1	1	yes	characteristic
69	#13133207	C₂²	1	1	yes	characteristic
70	#13133207	C₂²	1	1	yes	characteristic
71	#13133207	C₂²	1	1	yes	characteristic
72	#13133207	C₂²	1	1	yes	characteristic
73	#13133207	C₂²	1	1	yes	characteristic
74	#13133207	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	#13133206	C₂²	1	1	yes	characteristic
79	#13133203	C₂²	1	1	yes	characteristic
80	#13133203	C₂²	1	1	yes	characteristic
81	#13133203	C₂²	1	1	yes	characteristic
82	#13133203	C₂²	1	1	yes	characteristic
83	#13133203	C₂²	1	1	yes	characteristic
84	#13133203	C₂²	1	1	yes	characteristic
85	#13133202	C₂²	1	1	yes	characteristic
86	#13133202	C₂²	1	1	yes	characteristic
87	#13133202	C₂²	1	1	yes	characteristic
88	#13133202	C₂²	1	1	yes	characteristic
89	#13133202	C₂²	1	1	yes	characteristic
90	#13133201	C₂²	1	1	yes	characteristic
91	#13133201	C₂²	1	1	yes	characteristic
92	#13133200	C₂²	1	1	yes	characteristic
93	#13133199	C₂²	1	1	yes	characteristic
94	#13133199	C₂²	1	1	yes	characteristic
95	#13133199	C₂²	1	1	yes	characteristic
96	#13133199	C₂²	1	1	yes	characteristic
97	#13133199	C₂²	1	1	yes	characteristic
98	#13133198	C₂²	1	1	yes	characteristic
99	#13133197	C₂²	1	1	yes	characteristic
100	#13133197	C₂²	1	1	yes	characteristic
101	#13133197	C₂²	1	1	yes	characteristic
102	#13133196	C₂²	1	1	yes	characteristic
103	#13133195	C₂²	1	1	yes	characteristic
104	#13133195	C₂²	1	1	yes	characteristic
105	#13133195	C₂²	1	1	yes	characteristic
106	#13133195	C₂²	1	1	yes	characteristic
107	#13133195	C₂²	1	1	yes	characteristic
108	#13133195	C₂²	1	1	yes	characteristic
109	#13133195	C₂²	1	1	yes	characteristic
110	#13133195	C₂²	1	1	yes	characteristic
111	#13133195	C₂²	1	1	yes	characteristic
112	#13133195	C₂²	1	1	yes	characteristic
113	#13133195	C₂²	1	1	yes	characteristic
114	#13133195	C₂²	1	1	yes	characteristic
115	#13133194	C₂²	1	1	yes	characteristic
116	#13133194	C₂²	1	1	yes	characteristic
117	#13133194	C₂²	1	1	yes	characteristic
118	#13133194	C₂²	1	1	yes	characteristic
119	#13133194	C₂²	1	1	yes	characteristic
120	#13133194	C₂²	1	1	yes	characteristic
121	#13133194	C₂²	1	1	yes	characteristic
122	#13133194	C₂²	1	1	yes	characteristic
123	#13133193	C₂²	1	1	yes	characteristic
124	#13133193	C₂²	1	1	yes	characteristic
125	#13133193	C₂²	1	1	yes	characteristic
126	#13133193	C₂²	1	1	yes	characteristic
127	#13133192	C₂²	1	1	yes	characteristic
128	#13133190	C₂²	1	1	yes	characteristic
129	#13133190	C₂²	1	1	yes	characteristic
130	#13133190	C₂²	1	1	yes	characteristic
131	#13133190	C₂²	1	1	yes	characteristic
132	#13133190	C₂²	1	1	yes	characteristic
133	#13133189	C₂²	1	1	yes	characteristic
134	#13133188	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	#13133182	C₂²	1	1	yes	characteristic
139	#13133182	C₂²	1	1	yes	characteristic
140	#13133182	C₂²	1	1	yes	characteristic
141	#13133182	C₂²	1	1	yes	characteristic
142	#13133182	C₂²	1	1	yes	characteristic
143	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
144	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
145	#13133179	C₂²	1	1	yes	characteristic
146	#13133179	C₂²	1	1	yes	characteristic
147	#13133179	C₂²	1	1	yes	characteristic
148	#13133179	C₂²	1	1	yes	characteristic
149	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
150	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
151	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
152	#13133177	C₂²	1	1	yes	characteristic
153	#13133177	C₂²	1	1	yes	characteristic
154	#13133177	C₂²	1	1	yes	characteristic
155	#13133177	C₂²	1	1	yes	characteristic
156	#13133177	C₂²	1	1	yes	characteristic
157	#13133177	C₂²	1	1	yes	characteristic
158	#13133177	C₂²	1	1	yes	characteristic
159	#13133175	C₂²	1	1	yes	characteristic
160	#13133175	C₂²	1	1	yes	characteristic
161	#13133174	C₂²	1	1	yes	characteristic
162	#13133173	C₂²	1	1	yes	characteristic
163	#13133173	C₂²	1	1	yes	characteristic
164	#13133173	C₂²	1	1	yes	characteristic
165	C₂×#11719919	C₂²	1	1	yes	characteristic
166	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
167	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
168	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
169	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
170	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
171	C₄²×D₅₃	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
173	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
174	#126×C₅₃	C₂²	1	1	yes	characteristic
175	#126×C₅₃	C₂²	1	1	yes	characteristic
176	#126×C₅₃	C₂²	1	1	yes	characteristic
177	#126×C₅₃	C₂²	1	1	yes	characteristic
178	#125×C₅₃	C₂²	1	1	yes	characteristic
179	#125×C₅₃	C₂²	1	1	yes	characteristic
180	#124×C₅₃	C₂²	1	1	yes	characteristic
181	#123×C₅₃	C₂²	1	1	yes	characteristic
182	#123×C₅₃	C₂²	1	1	yes	characteristic
183	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
184	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
185	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
186	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
187	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×D₄×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	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
196	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
197	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
198	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
203	Q₈×D₅₃	—	4	2	no	—
204	Q₈×D₅₃	—	4	2	no	—
205	Q₈×D₅₃	—	4	2	no	—
206	#11719947	—	4	2	no	—
207	#11719945	—	4	2	no	—
208	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
209	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
210	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
211	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
224	C₂×Dic₁₀₆	—	4	2	no	—
225	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
226	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
227	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
228	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
229	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
230	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
231	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
232	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
233	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
234	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
235	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₄²×C₅₃	C₂³	1	1	yes	characteristic
263	C₄²×C₅₃	C₂³	1	1	yes	characteristic
264	C₄²×C₅₃	C₂³	1	1	yes	characteristic
265	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
271	#11719921	C₂³	1	1	yes	characteristic
272	#11719921	C₂³	1	1	yes	characteristic
273	#11719921	C₂³	1	1	yes	characteristic
274	#11719921	C₂³	1	1	yes	characteristic
275	#11719921	C₂³	1	1	yes	characteristic
276	#11719921	C₂³	1	1	yes	characteristic
277	#11719921	C₂³	1	1	yes	characteristic
278	#11719921	C₂³	1	1	yes	characteristic
279	#11719921	C₂³	1	1	yes	characteristic
280	#11719921	C₂³	1	1	yes	characteristic
281	#11719921	C₂³	1	1	yes	characteristic
282	#11719921	C₂³	1	1	yes	characteristic
283	#11719921	C₂³	1	1	yes	characteristic
284	#11719921	C₂³	1	1	yes	characteristic
285	#11719921	C₂³	1	1	yes	characteristic
286	#11719921	C₂³	1	1	yes	characteristic
287	#11719921	C₂³	1	1	yes	characteristic
288	#11719921	C₂³	1	1	yes	characteristic
289	#11719921	C₂³	1	1	yes	characteristic
290	#11719921	C₂³	1	1	yes	characteristic
291	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
294	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
295	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
296	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
297	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
298	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
299	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
300	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
301	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
302	C₄⋊Dic₅₃	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	#11719919	C₂³	1	1	yes	characteristic
326	#11719919	C₂³	1	1	yes	characteristic
327	#11719919	C₂³	1	1	yes	characteristic
328	#11719919	C₂³	1	1	yes	characteristic
329	#11719919	C₂³	1	1	yes	characteristic
330	#11719919	C₂³	1	1	yes	characteristic
331	#11719919	C₂³	1	1	yes	characteristic
332	#11719919	C₂³	1	1	yes	characteristic
333	#11719919	C₂³	1	1	yes	characteristic
334	#11719919	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	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
345	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
346	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
347	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
348	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
351	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
352	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
353	Q₈×C₅₃	—	4	1	no	—
354	Q₈×C₅₃	—	4	1	no	—
355	Q₈×C₅₃	—	4	1	no	—
356	D₄×C₅₃	—	4	1	no	—
357	C₂×C₄×C₅₃	—	4	1	no	—
358	C₂×C₄×C₅₃	—	4	1	no	—
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	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²⋊D₅₃	—	2	2	no	—
373	C₂²⋊D₅₃	—	2	2	no	—
374	C₂²⋊D₅₃	—	2	2	no	—
375	C₂²⋊D₅₃	—	2	2	no	—
376	C₂²⋊D₅₃	—	4	1	no	—
377	C₂²⋊D₅₃	—	4	1	no	—
378	C₂×Dic₅₃	—	2	2	no	—
379	C₂×Dic₅₃	—	2	2	no	—
380	C₂×Dic₅₃	—	4	1	no	—
381	C₂×Dic₅₃	—	4	1	no	—
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	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
392	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	D₂₁₂	—	2	2	no	—
396	D₂₁₂	—	2	2	no	—
397	D₂₁₂	—	4	1	no	—
398	C₄×D₅₃	—	2	2	no	—
399	C₄×D₅₃	—	2	2	no	—
400	C₄×D₅₃	—	2	2	no	—
401	C₄×D₅₃	—	2	2	no	—
402	C₄×D₅₃	—	2	2	no	—
403	C₄×D₅₃	—	4	1	no	—
404	C₄×D₅₃	—	4	1	no	—
405	C₄×D₅₃	—	4	1	no	—
406	C₄×D₅₃	—	4	1	no	—
407	C₄×D₅₃	—	4	1	no	—
408	C₄×D₅₃	—	4	1	no	—
409	C₄×D₅₃	—	4	1	no	—
410	C₄×D₅₃	—	4	1	no	—
411	Dic₁₀₆	—	2	2	no	—
412	Dic₁₀₆	—	2	2	no	—
413	Dic₁₀₆	—	2	2	no	—
414	Dic₁₀₆	—	2	2	no	—
415	Dic₁₀₆	—	2	2	no	—
416	Dic₁₀₆	—	2	2	no	—
417	Dic₁₀₆	—	4	1	no	—
418	Dic₁₀₆	—	4	1	no	—
419	Dic₁₀₆	—	4	1	no	—
420	Dic₁₀₆	—	4	1	no	—
421	Dic₁₀₆	—	4	1	no	—
422	C₂²×C₅₃	—	2	1	no	—
423	C₂²×C₅₃	—	2	1	no	—
424	C₂²×C₅₃	—	2	1	no	—
425	C₂²×C₅₃	—	2	1	no	—
426	C₂²×C₅₃	—	2	1	no	—
427	C₂²×C₅₃	—	2	1	no	—
428	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
429	C₂×D₅₃	—	2	1	no	—
430	C₂×D₅₃	—	2	1	no	—
431	C₂×D₅₃	—	2	1	no	—
432	C₂×D₅₃	—	2	1	no	—
433	C₂×D₅₃	—	2	1	no	—
434	C₂×D₅₃	—	2	1	no	—
435	C₂×D₅₃	—	2	1	no	—
436	C₂×D₅₃	—	2	1	no	—
437	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
438	C₄×C₅₃	—	2	1	no	—
439	C₄×C₅₃	—	2	1	no	—
440	C₄×C₅₃	—	2	1	no	—
441	C₄×C₅₃	—	2	1	no	—
442	C₄×C₅₃	—	2	1	no	—
443	C₄×C₅₃	—	2	1	no	—
444	C₄×C₅₃	—	2	1	no	—
445	C₄×C₅₃	—	2	1	no	—
446	C₄×C₅₃	—	2	1	no	—
447	C₄×C₅₃	—	2	1	no	—
448	C₄×C₅₃	—	2	1	no	—
449	C₄×C₅₃	—	2	1	no	—
450	C₄×C₅₃	—	2	1	no	—
451	Dic₅₃	—	2	1	no	—
452	Dic₅₃	—	2	1	no	—
453	Dic₅₃	—	2	1	no	—
454	Dic₅₃	—	2	1	no	—
455	Dic₅₃	—	2	1	no	—
456	Dic₅₃	—	2	1	no	—
457	Dic₅₃	—	2	1	no	—
458	Dic₅₃	—	2	1	no	—
459	Dic₅₃	—	2	1	no	—
460	Dic₅₃	—	2	1	no	—
461	Dic₅₃	—	2	1	no	—
462	Dic₅₃	H(5,𝔽₂)	1	2	yes	—
463	Dic₅₃	2₋¹⁺⁴	1	2	yes	—
464	#3552	—	53	1	no	maximal, Sylow
465	C₂×C₅₃	—	4	1	no	—
466	C₂×C₅₃	—	4	1	no	—
467	C₂×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
469	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
470	D₅₃	—	2	2	no	—
471	D₅₃	—	4	1	no	—
472	D₅₃	—	4	1	no	—
473	#563	—	53	1	no	—
474	#563	—	53	1	no	—
475	#563	—	53	1	no	—
476	#563	D₅₃	1	1	yes	characteristic, complemented
477	#557	—	53	1	no	—
478	#556	—	53	1	no	—
479	#554	—	53	1	no	—
480	#554	—	53	1	no	—
481	#553	—	53	1	no	—
482	#553	—	53	1	no	—
483	D₄×Q₈	—	53	1	no	—
484	D₄×Q₈	—	53	1	no	—
485	D₄×Q₈	—	53	1	no	—
486	#548	—	53	1	no	—
487	#548	—	53	1	no	—
488	#547	—	53	1	no	—
489	#544	—	53	1	no	—
490	#544	—	53	1	no	—
491	#542	—	53	1	no	—
492	#542	—	53	1	no	—
493	#541	—	53	1	no	—
494	#541	—	53	1	no	—
495	#539	—	53	1	no	—
496	#539	—	53	1	no	—
497	#539	—	53	1	no	—
498	#539	—	53	1	no	—
499	#536	—	53	1	no	—
500	#536	—	53	1	no	—
501	C₂×C₄⋊Q₈	—	53	1	no	—
502	#529	—	53	1	no	—
503	#529	—	53	1	no	—
504	C₅₃	#3552	1	1	yes	characteristic, complemented, Sylow
505	C₂×#41	—	53	1	no	—
506	C₂×#41	—	53	1	no	—
507	C₂²×Q₈	—	53	1	no	—
508	C₂²×Q₈	—	53	1	no	—
509	C₂²×Q₈	—	53	1	no	—
510	C₂²×Q₈	—	53	1	no	—
511	C₄⋊Q₈	—	53	1	no	—
512	C₄⋊Q₈	—	53	1	no	—
513	C₄⋊Q₈	—	53	1	no	—
514	C₄⋊Q₈	—	53	1	no	—
515	C₄⋊Q₈	—	53	1	no	—
516	C₄⋊Q₈	—	53	1	no	—
517	C₄⋊Q₈	—	53	1	no	—
518	C₄⋊Q₈	—	53	1	no	—
519	C₄⋊Q₈	—	53	1	no	—
520	C₄⋊Q₈	—	53	1	no	—
521	C₄⋊Q₈	—	53	1	no	—
522	C₄⋊Q₈	—	53	1	no	—
523	C₄⋊Q₈	—	53	1	no	—
524	C₄⋊Q₈	—	53	1	no	—
525	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
526	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
527	#126	—	53	1	no	—
528	#126	—	53	1	no	—
529	#126	—	53	1	no	—
530	#126	—	53	1	no	—
531	#126	—	53	1	no	—
532	#126	—	53	1	no	—
533	#126	—	53	1	no	—
534	#126	—	53	1	no	—
535	#126	—	53	1	no	—
536	#126	—	53	1	no	—
537	#126	—	53	1	no	—
538	#126	—	53	1	no	—
539	#126	C₂×D₅₃	1	1	yes	characteristic
540	#126	C₂×D₅₃	1	1	yes	characteristic
541	#126	C₂×D₅₃	1	1	yes	characteristic
542	#126	C₂×D₅₃	1	1	yes	characteristic
543	#125	—	53	1	no	—
544	#125	—	53	1	no	—
545	#125	—	53	1	no	—
546	#125	—	53	1	no	—
547	#125	—	53	1	no	—
548	#125	—	53	1	no	—
549	#125	—	53	1	no	—
550	#125	—	53	1	no	—
551	#125	—	53	1	no	—
552	#125	—	53	1	no	—
553	#125	—	53	1	no	—
554	#125	—	53	1	no	—
555	#125	—	53	1	no	—
556	#125	—	53	1	no	—
557	#125	C₂×D₅₃	1	1	yes	characteristic
558	#125	C₂×D₅₃	1	1	yes	characteristic
559	#124	—	53	1	no	—
560	#124	—	53	1	no	—
561	#124	—	53	1	no	—
562	#124	—	53	1	no	—
563	#124	—	53	1	no	—
564	#124	—	53	1	no	—
565	#124	—	53	1	no	—
566	#124	C₂×D₅₃	1	1	yes	characteristic
567	#123	—	53	1	no	—
568	#123	—	53	1	no	—
569	#123	—	53	1	no	—
570	#123	—	53	1	no	—
571	#123	—	53	1	no	—
572	#123	—	53	1	no	—
573	#123	—	53	1	no	—
574	#123	—	53	1	no	—
575	#123	—	53	1	no	—
576	#123	—	53	1	no	—
577	#123	—	53	1	no	—
578	#123	—	53	1	no	—
579	#123	—	53	1	no	—
580	#123	—	53	1	no	—
581	#123	C₂×D₅₃	1	1	yes	characteristic
582	#123	C₂×D₅₃	1	1	yes	characteristic
583	C₂²⋊Q₈	—	53	1	no	—
584	C₂²⋊Q₈	—	53	1	no	—
585	C₂²⋊Q₈	—	53	1	no	—
586	C₂²⋊Q₈	—	53	1	no	—
587	C₂²⋊Q₈	—	53	1	no	—
588	C₂²⋊Q₈	—	53	1	no	—
589	C₂²⋊Q₈	—	53	1	no	—
590	C₂²⋊Q₈	—	53	1	no	—
591	C₂²⋊Q₈	—	53	1	no	—
592	C₂²⋊Q₈	—	53	1	no	—
593	C₂²⋊Q₈	—	53	1	no	—
594	C₂²⋊Q₈	—	53	1	no	—
595	C₂²⋊Q₈	—	53	1	no	—
596	C₂²⋊Q₈	—	53	1	no	—
597	C₂²⋊Q₈	—	53	1	no	—
598	C₂²⋊Q₈	—	53	1	no	—
599	C₂²⋊Q₈	—	53	1	no	—
600	C₂²⋊Q₈	—	53	1	no	—
601	C₂²⋊Q₈	—	53	1	no	—
602	C₂²⋊Q₈	—	53	1	no	—
603	C₂²⋊Q₈	—	53	1	no	—
604	C₂²⋊Q₈	—	53	1	no	—
605	C₂²⋊Q₈	—	53	1	no	—
606	C₂²⋊Q₈	—	53	1	no	—
607	C₂²⋊Q₈	—	53	1	no	—
608	C₂²⋊Q₈	—	53	1	no	—
609	C₂²⋊Q₈	—	53	1	no	—
610	C₂²⋊Q₈	—	53	1	no	—
611	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
612	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
613	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
614	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
615	#121	—	53	1	no	—
616	#121	—	53	1	no	—
617	#121	—	53	1	no	—
618	#121	—	53	1	no	—
619	#121	—	53	1	no	—
620	#121	—	53	1	no	—
621	#121	—	53	1	no	—
622	#121	—	53	1	no	—
623	C₄×Q₈	—	53	1	no	—
624	C₄×Q₈	—	53	1	no	—
625	C₄×Q₈	—	53	1	no	—
626	C₄×Q₈	—	53	1	no	—
627	C₄×Q₈	—	53	1	no	—
628	C₄×Q₈	—	53	1	no	—
629	C₄×Q₈	—	53	1	no	—
630	C₄×Q₈	—	53	1	no	—
631	C₄×D₄	—	53	1	no	—
632	C₄×D₄	—	53	1	no	—
633	C₄×D₄	—	53	1	no	—
634	C₄×D₄	—	53	1	no	—
635	C₄×D₄	—	53	1	no	—
636	C₄×D₄	—	53	1	no	—
637	C₄×D₄	—	53	1	no	—
638	C₄×D₄	—	53	1	no	—
639	C₄×D₄	—	53	1	no	—
640	C₄×D₄	—	53	1	no	—
641	C₄×D₄	—	53	1	no	—
642	C₄×D₄	—	53	1	no	—
643	C₄×D₄	—	53	1	no	—
644	C₄×D₄	—	53	1	no	—
645	C₄×D₄	—	53	1	no	—
646	C₄×D₄	—	53	1	no	—
647	#117	—	53	1	no	—
648	#117	—	53	1	no	—
649	#117	—	53	1	no	—
650	#117	—	53	1	no	—
651	#117	—	53	1	no	—
652	#117	—	53	1	no	—
653	C₂×C₄⋊C₄	—	53	1	no	—
654	C₂×C₄⋊C₄	—	53	1	no	—
655	C₂×C₄⋊C₄	—	53	1	no	—
656	C₂×C₄⋊C₄	—	53	1	no	—
657	C₂×C₄⋊C₄	—	53	1	no	—
658	C₂×C₄⋊C₄	—	53	1	no	—
659	C₂×C₄²	—	53	1	no	—
660	#41	—	212	2	no	—
661	#41	—	212	2	no	—
662	C₂×Q₈	—	53	1	no	—
663	C₂×Q₈	—	53	1	no	—
664	C₂×Q₈	—	53	1	no	—
665	C₂×Q₈	—	53	1	no	—
666	C₂×Q₈	—	53	1	no	—
667	C₂×Q₈	—	53	1	no	—
668	C₂×Q₈	—	53	1	no	—
669	C₂×Q₈	—	53	1	no	—
670	C₂×Q₈	—	53	1	no	—
671	C₂×Q₈	—	53	1	no	—
672	C₂×Q₈	—	53	1	no	—
673	C₂×Q₈	—	212	2	no	—
674	C₂×Q₈	—	212	2	no	—
675	C₂×Q₈	—	212	2	no	—
676	C₂×Q₈	—	212	2	no	—
677	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
678	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
679	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
680	C₂×D₄	—	53	1	no	—
681	C₂×D₄	—	53	1	no	—
682	C₂×D₄	—	53	1	no	—
683	C₂×D₄	—	53	1	no	—
684	C₂×D₄	—	53	1	no	—
685	C₂×D₄	—	53	1	no	—
686	C₂×D₄	—	53	1	no	—
687	C₂×D₄	—	53	1	no	—
688	C₂×D₄	—	53	1	no	—
689	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
690	C₂²×C₄	—	53	1	no	—
691	C₂²×C₄	—	53	1	no	—
692	C₂²×C₄	—	53	1	no	—
693	C₂²×C₄	—	53	1	no	—
694	C₂²×C₄	—	53	1	no	—
695	C₂²×C₄	—	53	1	no	—
696	C₂²×C₄	—	53	1	no	—
697	C₂²×C₄	—	53	1	no	—
698	C₂²×C₄	—	53	1	no	—
699	C₂²×C₄	—	53	1	no	—
700	C₂²×C₄	—	53	1	no	—
701	C₂²×C₄	—	53	1	no	—
702	C₂²×C₄	—	53	1	no	—
703	C₂²×C₄	—	53	1	no	—
704	C₂²×C₄	—	53	1	no	—
705	C₂²×C₄	—	53	1	no	—
706	C₂²×C₄	—	53	1	no	—
707	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
708	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
722	C₄⋊C₄	—	53	1	no	—
723	C₄⋊C₄	—	53	1	no	—
724	C₄⋊C₄	—	53	1	no	—
725	C₄⋊C₄	—	53	1	no	—
726	C₄⋊C₄	—	53	1	no	—
727	C₄⋊C₄	—	53	1	no	—
728	C₄⋊C₄	—	53	1	no	—
729	C₄⋊C₄	—	53	1	no	—
730	C₄⋊C₄	—	53	1	no	—
731	C₄⋊C₄	—	53	1	no	—
732	C₄⋊C₄	—	53	1	no	—
733	C₄⋊C₄	—	53	1	no	—
734	C₄⋊C₄	—	53	1	no	—
735	C₄⋊C₄	—	53	1	no	—
736	C₄⋊C₄	—	53	1	no	—
737	C₄⋊C₄	—	53	1	no	—
738	C₄⋊C₄	—	53	1	no	—
739	C₄⋊C₄	—	53	1	no	—
740	C₄⋊C₄	—	53	1	no	—
741	C₄⋊C₄	—	53	1	no	—
742	C₄⋊C₄	—	53	1	no	—
743	C₄⋊C₄	—	53	1	no	—
744	C₄⋊C₄	—	53	1	no	—
745	C₄⋊C₄	—	53	1	no	—
746	C₄⋊C₄	—	53	1	no	—
747	C₄⋊C₄	—	53	1	no	—
748	C₄⋊C₄	—	53	1	no	—
749	C₄⋊C₄	—	53	1	no	—
750	C₄⋊C₄	—	53	1	no	—
751	C₄⋊C₄	—	53	1	no	—
752	C₄⋊C₄	—	53	1	no	—
753	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
754	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
755	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
756	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
757	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
760	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
761	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
762	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
763	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
764	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
765	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
766	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
767	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
769	C₂²⋊C₄	—	53	1	no	—
770	C₂²⋊C₄	—	53	1	no	—
771	C₂²⋊C₄	—	53	1	no	—
772	C₂²⋊C₄	—	53	1	no	—
773	C₂²⋊C₄	—	53	1	no	—
774	C₂²⋊C₄	—	53	1	no	—
775	C₂²⋊C₄	—	53	1	no	—
776	C₂²⋊C₄	—	53	1	no	—
777	C₂²⋊C₄	—	53	1	no	—
778	C₂²⋊C₄	—	53	1	no	—
779	C₂²⋊C₄	—	53	1	no	—
780	C₂²⋊C₄	—	53	1	no	—
781	C₂²⋊C₄	—	53	1	no	—
782	C₂²⋊C₄	—	53	1	no	—
783	C₂²⋊C₄	—	53	1	no	—
784	C₂²⋊C₄	—	53	1	no	—
785	C₂²⋊C₄	—	53	1	no	—
786	C₂²⋊C₄	—	53	1	no	—
787	C₂²⋊C₄	—	53	1	no	—
788	C₂²⋊C₄	—	53	1	no	—
789	C₂²⋊C₄	—	53	1	no	—
790	C₂²⋊C₄	—	53	1	no	—
791	C₂²⋊C₄	—	53	1	no	—
792	C₂²⋊C₄	—	53	1	no	—
793	C₂²⋊C₄	—	53	1	no	—
794	C₂²⋊C₄	—	53	1	no	—
795	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
796	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
797	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
798	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
799	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
800	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
801	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
802	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
803	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
804	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
805	C₄²	—	53	1	no	—
806	C₄²	—	53	1	no	—
807	C₄²	—	53	1	no	—
808	C₄²	—	53	1	no	—
809	C₄²	—	53	1	no	—
810	C₄²	—	53	1	no	—
811	C₄²	—	53	1	no	—
812	C₄²	—	53	1	no	—
813	C₄²	—	53	1	no	—
814	C₄²	—	53	1	no	—
815	C₄²	—	53	1	no	—
816	C₄²	—	53	1	no	—
817	C₄²	—	53	1	no	—
818	C₄²	C₂²×D₅₃	1	1	yes	characteristic
819	C₄²	C₂²×D₅₃	1	1	yes	characteristic
820	C₄²	C₂²×D₅₃	1	1	yes	characteristic
821	C₂³	—	53	1	no	—
822	C₂³	—	53	1	no	—
823	C₂³	—	53	1	no	—
824	C₂³	C₂³×D₅₃	1	1	yes	characteristic
825	C₂³	C₂³×D₅₃	1	1	yes	characteristic
826	Q₈	—	4	1	no	—
827	Q₈	—	4	1	no	—
828	Q₈	—	4	1	no	—
829	Q₈	—	106	2	no	—
830	Q₈	—	106	2	no	—
831	Q₈	—	106	2	no	—
832	Q₈	—	106	2	no	—
833	Q₈	—	106	2	no	—
834	Q₈	—	106	2	no	—
835	Q₈	—	212	1	no	—
836	Q₈	—	212	1	no	—
837	Q₈	—	212	1	no	—
838	Q₈	—	212	1	no	—
839	Q₈	—	212	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	106	2	no	—
842	D₄	—	106	2	no	—
843	D₄	—	106	2	no	—
844	D₄	—	106	2	no	—
845	D₄	—	106	2	no	—
846	D₄	—	106	2	no	—
847	D₄	—	212	1	no	—
848	D₄	—	212	1	no	—
849	D₄	—	212	1	no	—
850	C₂×C₄	—	4	1	no	—
851	C₂×C₄	—	4	1	no	—
852	C₂×C₄	—	53	1	no	—
853	C₂×C₄	—	53	1	no	—
854	C₂×C₄	—	53	1	no	—
855	C₂×C₄	—	53	1	no	—
856	C₂×C₄	—	53	1	no	—
857	C₂×C₄	—	53	1	no	—
858	C₂×C₄	—	53	1	no	—
859	C₂×C₄	—	53	1	no	—
860	C₂×C₄	—	53	1	no	—
861	C₂×C₄	—	53	1	no	—
862	C₂×C₄	—	53	1	no	—
863	C₂×C₄	—	53	1	no	—
864	C₂×C₄	—	53	1	no	—
865	C₂×C₄	—	106	2	no	—
866	C₂×C₄	—	106	2	no	—
867	C₂×C₄	—	106	2	no	—
868	C₂×C₄	—	106	2	no	—
869	C₂×C₄	—	106	2	no	—
870	C₂×C₄	—	106	2	no	—
871	C₂×C₄	—	106	2	no	—
872	C₂×C₄	—	212	1	no	—
873	C₂×C₄	—	212	1	no	—
874	C₂×C₄	—	212	1	no	—
875	C₂×C₄	—	212	1	no	—
876	C₂×C₄	—	212	1	no	—
877	C₂×C₄	—	212	1	no	—
878	C₂×C₄	—	212	1	no	—
879	C₂×C₄	—	212	1	no	—
880	C₂×C₄	—	212	1	no	—
881	C₂×C₄	—	212	1	no	—
882	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
883	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
884	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
885	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
886	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
887	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
888	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
889	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
890	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
891	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
892	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
893	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
894	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
895	C₂²	—	2	1	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	2	1	no	—
899	C₂²	—	2	1	no	—
900	C₂²	—	2	1	no	—
901	C₂²	—	53	2	no	—
902	C₂²	—	106	1	no	—
903	C₂²	—	106	1	no	—
904	C₂²	—	106	1	no	—
905	C₂²	—	106	1	no	—
906	C₂²	—	106	1	no	—
907	C₂²	—	106	1	no	—
908	C₂²	—	106	1	no	—
909	C₂²	—	106	1	no	—
910	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
911	C₄	—	2	1	no	—
912	C₄	—	2	1	no	—
913	C₄	—	2	1	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	1	no	—
916	C₄	—	2	1	no	—
917	C₄	—	2	1	no	—
918	C₄	—	2	1	no	—
919	C₄	—	2	1	no	—
920	C₄	—	2	1	no	—
921	C₄	—	2	1	no	—
922	C₄	—	2	1	no	—
923	C₄	—	2	1	no	—
924	C₄	—	53	2	no	—
925	C₄	—	53	2	no	—
926	C₄	—	106	1	no	—
927	C₄	—	106	1	no	—
928	C₄	—	106	1	no	—
929	C₄	—	106	1	no	—
930	C₄	—	106	1	no	—
931	C₄	—	106	1	no	—
932	C₄	—	106	1	no	—
933	C₄	—	106	1	no	—
934	C₄	—	106	1	no	—
935	C₄	—	106	1	no	—
936	C₄	—	106	1	no	—
937	C₂	—	4	1	no	—
938	C₂	—	4	1	no	—
939	C₂	—	106	2	no	—
940	C₂	—	212	1	no	—
941	C₂	—	212	1	no	—
942	C₂	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
943	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
944	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#563	C₂
hypercenter	#563	D₅₃
hypocenter	C₅₃	#3552
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #563

Complements

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

N	H ≅ G/N	type
1. #16811375	C₂	semidirect
2. #16811375	C₂	semidirect
3. #16811372	C₂	semidirect
4. #16811350	C₂	semidirect
5. #16811340	C₂	semidirect
6. #16811329	C₂	semidirect
7. #16811327	C₂	semidirect
8. #16811324	C₂	semidirect
9. #16811318	C₂	semidirect
10. #16811288	C₂	semidirect
11. #16811286	C₂	semidirect
12. #16811286	C₂	semidirect
13. #16811283	C₂	semidirect
14. #16811281	C₂	semidirect
15. #16811271	C₂	semidirect
16. #16811252	C₂	semidirect
17. #16811250	C₂	semidirect
18. #16811243	C₂	semidirect
19. #16811237	C₂	semidirect
20. #16811232	C₂	semidirect
21. #16811230	C₂	semidirect
22. #16811221	C₂	semidirect
23. #16811219	C₂	semidirect
24. #16811216	C₂	semidirect
25. #16811214	C₂	semidirect
26. #16811196	C₂	semidirect
27. #16811195	C₂	semidirect
28. C₄⋊Q₈×D₅₃	C₂	semidirect
29. #16811156	C₂	semidirect
30. #16811156	C₂	semidirect
31. C₅₃×#563	C₂	semidirect
476. #563	D₅₃	semidirect
504. C₅₃	#3552	semidirect