Subgroups — #20289334

Order 6784.

936 conjugacy classes of subgroups.

The subgroup lattice has 920 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	#16811374	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811373	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811372	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811345	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811333	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811327	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811314	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811303	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811302	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811298	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811297	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811250	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811248	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811239	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811237	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811235	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811231	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811231	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811230	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811219	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811215	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811214	C₂	1	1	yes	maximal, characteristic, complemented
27	#16811207	C₂	1	1	yes	maximal, characteristic
28	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811151	C₂	1	1	yes	maximal, characteristic, complemented
30	#126×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
32	#13133217	C₂²	1	1	yes	characteristic, complemented
33	#13133216	C₂²	1	1	yes	characteristic, complemented
34	#13133216	C₂²	1	1	yes	characteristic, complemented
35	#13133215	C₂²	1	1	yes	characteristic, complemented
36	#13133215	C₂²	1	1	yes	characteristic, complemented
37	#13133215	C₂²	1	1	yes	characteristic, complemented
38	#13133215	C₂²	1	1	yes	characteristic, complemented
39	#13133212	C₂²	1	1	yes	characteristic
40	#13133212	C₂²	1	1	yes	characteristic
41	#13133212	C₂²	1	1	yes	characteristic
42	#13133212	C₂²	1	1	yes	characteristic
43	#13133212	C₂²	1	1	yes	characteristic
44	#13133212	C₂²	1	1	yes	characteristic, complemented
45	#13133212	C₂²	1	1	yes	characteristic, complemented
46	#13133211	C₂²	1	1	yes	characteristic
47	#13133211	C₂²	1	1	yes	characteristic
48	#13133211	C₂²	1	1	yes	characteristic
49	#13133211	C₂²	1	1	yes	characteristic
50	#13133211	C₂²	1	1	yes	characteristic, complemented
51	#13133211	C₂²	1	1	yes	characteristic, complemented
52	#13133210	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, complemented
60	#13133210	C₂²	1	1	yes	characteristic, complemented
61	#13133209	C₂²	1	1	yes	characteristic, complemented
62	#13133209	C₂²	1	1	yes	characteristic, complemented
63	#13133209	C₂²	1	1	yes	characteristic, complemented
64	#13133209	C₂²	1	1	yes	characteristic, complemented
65	#13133209	C₂²	1	1	yes	characteristic, complemented
66	#13133208	C₂²	1	1	yes	characteristic, complemented
67	#13133208	C₂²	1	1	yes	characteristic, complemented
68	#13133208	C₂²	1	1	yes	characteristic, complemented
69	#13133207	C₂²	1	1	yes	characteristic, complemented
70	#13133207	C₂²	1	1	yes	characteristic, complemented
71	#13133207	C₂²	1	1	yes	characteristic, complemented
72	#13133207	C₂²	1	1	yes	characteristic, complemented
73	#13133207	C₂²	1	1	yes	characteristic, complemented
74	#13133207	C₂²	1	1	yes	characteristic, complemented
75	#13133207	C₂²	1	1	yes	characteristic, complemented
76	#13133207	C₂²	1	1	yes	characteristic, complemented
77	#13133207	C₂²	1	1	yes	characteristic, complemented
78	#13133207	C₂²	1	1	yes	characteristic, complemented
79	#13133207	C₂²	1	1	yes	characteristic, complemented
80	#13133206	C₂²	1	1	yes	characteristic
81	#13133205	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, complemented
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	#13133201	C₂²	1	1	yes	characteristic
90	#13133201	C₂²	1	1	yes	characteristic, complemented
91	#13133200	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	#13133199	C₂²	1	1	yes	characteristic, complemented
99	#13133198	C₂²	1	1	yes	characteristic
100	#13133198	C₂²	1	1	yes	characteristic
101	#13133197	C₂²	1	1	yes	characteristic
102	#13133197	C₂²	1	1	yes	characteristic
103	#13133197	C₂²	1	1	yes	characteristic
104	#13133196	C₂²	1	1	yes	characteristic
105	#13133196	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, complemented
114	#13133195	C₂²	1	1	yes	characteristic, complemented
115	#13133195	C₂²	1	1	yes	characteristic, complemented
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, complemented
120	#13133194	C₂²	1	1	yes	characteristic, complemented
121	#13133194	C₂²	1	1	yes	characteristic, complemented
122	#13133194	C₂²	1	1	yes	characteristic, complemented
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	#13133193	C₂²	1	1	yes	characteristic
128	#13133193	C₂²	1	1	yes	characteristic, complemented
129	#13133193	C₂²	1	1	yes	characteristic, complemented
130	#13133190	C₂²	1	1	yes	characteristic
131	#13133190	C₂²	1	1	yes	characteristic
132	#13133189	C₂²	1	1	yes	characteristic
133	#13133187	C₂²	1	1	yes	characteristic
134	#13133185	C₂²	1	1	yes	characteristic
135	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
136	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
137	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
138	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
139	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
140	#13133182	C₂²	1	1	yes	characteristic, complemented
141	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
142	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
143	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
144	#13133179	C₂²	1	1	yes	characteristic
145	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
146	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
147	#13133177	C₂²	1	1	yes	characteristic
148	#13133177	C₂²	1	1	yes	characteristic
149	#13133177	C₂²	1	1	yes	characteristic
150	#13133177	C₂²	1	1	yes	characteristic
151	#13133175	C₂²	1	1	yes	characteristic
152	#13133175	C₂²	1	1	yes	characteristic, complemented
153	#13133174	C₂²	1	1	yes	characteristic
154	#13133174	C₂²	1	1	yes	characteristic
155	#13133174	C₂²	1	1	yes	characteristic
156	#13133174	C₂²	1	1	yes	characteristic
157	#13133174	C₂²	1	1	yes	characteristic
158	#13133174	C₂²	1	1	yes	characteristic, complemented
159	#13133173	C₂²	1	1	yes	characteristic
160	#13133173	C₂²	1	1	yes	characteristic, complemented
161	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
162	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
163	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
164	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
165	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
166	C₂×#11719921	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
170	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
171	C₄²×D₅₃	C₂²	1	1	yes	characteristic
172	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	#126×C₅₃	C₂²	1	1	yes	characteristic
174	#126×C₅₃	C₂²	1	1	yes	characteristic
175	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	#124×C₅₃	C₂²	1	1	yes	characteristic
178	#124×C₅₃	C₂²	1	1	yes	characteristic
179	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
180	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
185	#117×C₅₃	C₂²	1	1	yes	characteristic
186	#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₅₃	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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₅₃	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	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×D₂₁₂	C₂³	1	1	yes	characteristic
202	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
203	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄×D₅₃	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×Dic₁₀₆	C₂³	1	1	yes	characteristic
215	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
216	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
217	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
218	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
219	C₂×Dic₁₀₆	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	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₄⋊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	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄²×C₅₃	C₂³	1	1	yes	characteristic
243	C₄²×C₅₃	C₂³	1	1	yes	characteristic
244	C₄²×C₅₃	C₂³	1	1	yes	characteristic
245	C₄²×C₅₃	C₂³	1	1	yes	characteristic
246	C₄²×C₅₃	C₂³	1	1	yes	characteristic
247	C₄²×C₅₃	C₂³	1	1	yes	characteristic
248	C₄²×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
250	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	#11719921	C₂³	1	1	yes	characteristic
258	#11719921	C₂³	1	1	yes	characteristic
259	#11719921	C₂³	1	1	yes	characteristic
260	#11719921	C₂³	1	1	yes	characteristic
261	#11719921	C₂³	1	1	yes	characteristic
262	#11719921	C₂³	1	1	yes	characteristic
263	#11719921	C₂³	1	1	yes	characteristic
264	#11719921	C₂³	1	1	yes	characteristic
265	#11719921	C₂³	1	1	yes	characteristic
266	#11719921	C₂³	1	1	yes	characteristic
267	#11719921	C₂³	1	1	yes	characteristic
268	#11719921	C₂³	1	1	yes	characteristic
269	#11719921	C₂³	1	1	yes	characteristic
270	#11719921	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	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
286	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
287	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
288	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
290	C₄⋊Dic₅₃	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	#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	#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	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	—	2	2	no	—
345	C₂²×D₅₃	—	4	1	no	—
346	C₂²×D₅₃	—	4	1	no	—
347	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
348	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
349	C₂²×D₅₃	C₂⁴	1	1	yes	characteristic
350	Q₈×C₅₃	—	4	1	no	—
351	Q₈×C₅₃	—	4	1	no	—
352	Q₈×C₅₃	—	4	1	no	—
353	D₄×C₅₃	—	4	1	no	—
354	C₂×C₄×C₅₃	—	4	1	no	—
355	C₂×C₄×C₅₃	—	4	1	no	—
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	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	C₂²⋊D₅₃	—	2	2	no	—
370	C₂²⋊D₅₃	—	4	1	no	—
371	C₂²⋊D₅₃	—	4	1	no	—
372	C₂²⋊D₅₃	—	4	1	no	—
373	C₂×Dic₅₃	—	4	1	no	—
374	C₂×Dic₅₃	—	4	1	no	—
375	C₂×Dic₅₃	—	4	1	no	—
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	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	D₂₁₂	—	2	2	no	—
390	D₂₁₂	—	4	1	no	—
391	C₄×D₅₃	—	2	2	no	—
392	C₄×D₅₃	—	2	2	no	—
393	C₄×D₅₃	—	4	1	no	—
394	C₄×D₅₃	—	4	1	no	—
395	C₄×D₅₃	—	4	1	no	—
396	C₄×D₅₃	—	4	1	no	—
397	C₄×D₅₃	—	4	1	no	—
398	C₄×D₅₃	—	4	1	no	—
399	C₄×D₅₃	—	4	1	no	—
400	C₄×D₅₃	—	4	1	no	—
401	C₄×D₅₃	—	4	1	no	—
402	Dic₁₀₆	—	4	1	no	—
403	Dic₁₀₆	—	4	1	no	—
404	Dic₁₀₆	—	4	1	no	—
405	Dic₁₀₆	—	4	1	no	—
406	Dic₁₀₆	—	4	1	no	—
407	Dic₁₀₆	—	4	1	no	—
408	C₂²×C₅₃	—	2	1	no	—
409	C₂²×C₅₃	—	2	1	no	—
410	C₂²×C₅₃	—	2	1	no	—
411	C₂²×C₅₃	—	2	1	no	—
412	C₂²×C₅₃	—	2	1	no	—
413	C₂²×C₅₃	—	2	1	no	—
414	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
415	C₂×D₅₃	—	2	1	no	—
416	C₂×D₅₃	—	2	1	no	—
417	C₂×D₅₃	—	2	1	no	—
418	C₂×D₅₃	—	2	1	no	—
419	C₂×D₅₃	—	2	1	no	—
420	C₂×D₅₃	—	2	1	no	—
421	C₂×D₅₃	—	2	1	no	—
422	C₂×D₅₃	—	2	1	no	—
423	C₂×D₅₃	—	8	2	no	—
424	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
425	C₄×C₅₃	—	2	1	no	—
426	C₄×C₅₃	—	2	1	no	—
427	C₄×C₅₃	—	2	1	no	—
428	C₄×C₅₃	—	2	1	no	—
429	C₄×C₅₃	—	2	1	no	—
430	C₄×C₅₃	—	2	1	no	—
431	C₄×C₅₃	—	2	1	no	—
432	C₄×C₅₃	—	2	1	no	—
433	C₄×C₅₃	—	2	1	no	—
434	C₄×C₅₃	—	2	1	no	—
435	C₄×C₅₃	—	2	1	no	—
436	C₄×C₅₃	—	2	1	no	—
437	C₄×C₅₃	—	2	1	no	—
438	Dic₅₃	—	2	1	no	—
439	Dic₅₃	—	2	1	no	—
440	Dic₅₃	—	2	1	no	—
441	Dic₅₃	—	2	1	no	—
442	Dic₅₃	—	2	1	no	—
443	Dic₅₃	—	2	1	no	—
444	Dic₅₃	—	2	1	no	—
445	Dic₅₃	—	2	1	no	—
446	Dic₅₃	—	2	1	no	—
447	Dic₅₃	—	2	1	no	—
448	Dic₅₃	—	2	1	no	—
449	Dic₅₃	—	2	1	no	—
450	Dic₅₃	—	2	1	no	—
451	#3564	—	53	1	no	maximal, Sylow
452	C₂×C₅₃	—	4	1	no	—
453	C₂×C₅₃	—	4	1	no	—
454	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
455	C₂×C₅₃	#585	1	1	yes	characteristic
456	C₂×C₅₃	#585	1	1	yes	characteristic
457	D₅₃	—	2	2	no	—
458	D₅₃	—	4	1	no	—
459	D₅₃	—	4	1	no	—
460	#563	—	53	1	no	—
461	#563	—	53	1	no	—
462	#563	—	53	1	no	—
463	#563	—	53	1	no	—
464	#556	—	53	1	no	—
465	#556	D₅₃	1	1	yes	characteristic, complemented
466	#554	—	53	1	no	—
467	#554	—	53	1	no	—
468	#552	—	53	1	no	—
469	#552	—	53	1	no	—
470	#552	—	53	1	no	—
471	#552	—	53	1	no	—
472	#551	—	53	1	no	—
473	#551	—	53	1	no	—
474	#551	—	53	1	no	—
475	#551	—	53	1	no	—
476	#544	—	53	1	no	—
477	#543	—	53	1	no	—
478	#542	—	53	1	no	—
479	#542	—	53	1	no	—
480	#541	—	53	1	no	—
481	#541	—	53	1	no	—
482	#541	—	53	1	no	—
483	#541	—	53	1	no	—
484	#539	—	53	1	no	—
485	#539	—	53	1	no	—
486	#539	—	53	1	no	—
487	#538	—	53	1	no	—
488	#533	—	53	1	no	—
489	#529	—	53	1	no	—
490	C₂×#126	—	53	1	no	—
491	C₅₃	#3564	1	1	yes	characteristic, complemented, Sylow
492	C₄⋊Q₈	—	53	1	no	—
493	C₄⋊Q₈	—	53	1	no	—
494	C₄⋊Q₈	—	53	1	no	—
495	C₄⋊Q₈	—	53	1	no	—
496	C₄⋊Q₈	—	53	1	no	—
497	C₄⋊Q₈	—	53	1	no	—
498	C₄⋊Q₈	—	53	1	no	—
499	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
500	#126	—	53	1	no	—
501	#126	—	53	1	no	—
502	#126	—	53	1	no	—
503	#126	—	53	1	no	—
504	#126	—	53	1	no	—
505	#126	—	53	1	no	—
506	#126	—	53	1	no	—
507	#126	—	53	1	no	—
508	#126	—	53	1	no	—
509	#126	—	53	1	no	—
510	#126	—	53	1	no	—
511	#126	—	53	1	no	—
512	#126	—	53	1	no	—
513	#126	—	53	1	no	—
514	#126	—	53	1	no	—
515	#126	—	53	1	no	—
516	#126	—	53	1	no	—
517	#126	—	53	1	no	—
518	#126	—	53	1	no	—
519	#126	—	53	1	no	—
520	#126	—	53	1	no	—
521	#126	—	53	1	no	—
522	#126	C₂×D₅₃	1	1	yes	characteristic
523	#126	C₂×D₅₃	1	1	yes	characteristic
524	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
525	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
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	#124	—	53	1	no	—
546	#124	—	53	1	no	—
547	#124	—	53	1	no	—
548	#124	—	53	1	no	—
549	#124	—	53	1	no	—
550	#124	C₂×D₅₃	1	1	yes	characteristic
551	#124	C₂×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
560	#123	—	53	1	no	—
561	#123	—	53	1	no	—
562	#123	—	53	1	no	—
563	#123	—	53	1	no	—
564	#123	—	53	1	no	—
565	#123	—	53	1	no	—
566	#123	—	53	1	no	—
567	#123	—	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	—	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	C₂×D₅₃	1	1	yes	characteristic
598	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
599	#121	—	53	1	no	—
600	#121	—	53	1	no	—
601	#121	—	53	1	no	—
602	#120	—	53	1	no	—
603	#120	—	53	1	no	—
604	C₄×Q₈	—	53	1	no	—
605	C₄×Q₈	—	53	1	no	—
606	C₄×Q₈	—	53	1	no	—
607	C₄×Q₈	—	53	1	no	—
608	C₄×Q₈	—	53	1	no	—
609	C₄×Q₈	—	53	1	no	—
610	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
611	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
612	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
613	C₄×D₄	—	53	1	no	—
614	C₄×D₄	—	53	1	no	—
615	C₄×D₄	—	53	1	no	—
616	C₄×D₄	—	53	1	no	—
617	C₄×D₄	—	53	1	no	—
618	C₄×D₄	—	53	1	no	—
619	C₄×D₄	—	53	1	no	—
620	C₄×D₄	—	53	1	no	—
621	C₄×D₄	—	53	1	no	—
622	C₄×D₄	—	53	1	no	—
623	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
624	#117	—	53	1	no	—
625	#117	—	53	1	no	—
626	#117	—	53	1	no	—
627	#117	—	53	1	no	—
628	#117	—	53	1	no	—
629	#117	—	53	1	no	—
630	#117	—	53	1	no	—
631	#117	—	53	1	no	—
632	#117	—	53	1	no	—
633	#117	—	53	1	no	—
634	#117	C₂×D₅₃	1	1	yes	characteristic
635	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
636	C₂×C₄⋊C₄	—	53	1	no	—
637	C₂×C₄⋊C₄	—	53	1	no	—
638	C₂×C₄⋊C₄	—	53	1	no	—
639	C₂×C₄⋊C₄	—	53	1	no	—
640	C₂×C₄⋊C₄	—	53	1	no	—
641	C₂×C₂²⋊C₄	—	53	1	no	—
642	C₂×C₂²⋊C₄	—	53	1	no	—
643	C₂×C₂²⋊C₄	—	53	1	no	—
644	C₂×C₂²⋊C₄	—	53	1	no	—
645	C₂×C₂²⋊C₄	—	53	1	no	—
646	C₂×C₄²	—	53	1	no	—
647	C₂⁴	—	53	1	no	—
648	C₂×Q₈	—	53	1	no	—
649	C₂×Q₈	—	53	1	no	—
650	C₂×Q₈	—	53	1	no	—
651	C₂×Q₈	—	53	1	no	—
652	C₂×Q₈	—	53	1	no	—
653	C₂×Q₈	—	53	1	no	—
654	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
655	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
656	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
657	C₂×D₄	—	53	1	no	—
658	C₂×D₄	—	53	1	no	—
659	C₂×D₄	—	53	1	no	—
660	C₂×D₄	—	53	1	no	—
661	C₂×D₄	—	53	1	no	—
662	C₂×D₄	—	53	1	no	—
663	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
664	C₂²×C₄	—	53	1	no	—
665	C₂²×C₄	—	53	1	no	—
666	C₂²×C₄	—	53	1	no	—
667	C₂²×C₄	—	53	1	no	—
668	C₂²×C₄	—	53	1	no	—
669	C₂²×C₄	—	53	1	no	—
670	C₂²×C₄	—	53	1	no	—
671	C₂²×C₄	—	53	1	no	—
672	C₂²×C₄	—	53	1	no	—
673	C₂²×C₄	—	53	1	no	—
674	C₂²×C₄	—	53	1	no	—
675	C₂²×C₄	—	53	1	no	—
676	C₂²×C₄	—	53	1	no	—
677	C₂²×C₄	—	53	1	no	—
678	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
679	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	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	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	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
738	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
739	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
740	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
741	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
756	C₂²⋊C₄	—	53	1	no	—
757	C₂²⋊C₄	—	53	1	no	—
758	C₂²⋊C₄	—	53	1	no	—
759	C₂²⋊C₄	—	53	1	no	—
760	C₂²⋊C₄	—	53	1	no	—
761	C₂²⋊C₄	—	53	1	no	—
762	C₂²⋊C₄	—	53	1	no	—
763	C₂²⋊C₄	—	53	1	no	—
764	C₂²⋊C₄	—	53	1	no	—
765	C₂²⋊C₄	—	53	1	no	—
766	C₂²⋊C₄	—	53	1	no	—
767	C₂²⋊C₄	—	53	1	no	—
768	C₂²⋊C₄	—	53	1	no	—
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	C₂²×D₅₃	1	1	yes	characteristic
775	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
776	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
777	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
778	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
779	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
780	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
781	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
782	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
784	C₄²	—	53	1	no	—
785	C₄²	—	53	1	no	—
786	C₄²	—	53	1	no	—
787	C₄²	—	53	1	no	—
788	C₄²	—	53	1	no	—
789	C₄²	—	53	1	no	—
790	C₄²	—	53	1	no	—
791	C₄²	—	53	1	no	—
792	C₄²	—	53	1	no	—
793	C₄²	—	53	1	no	—
794	C₄²	—	53	1	no	—
795	C₄²	C₂²×D₅₃	1	1	yes	characteristic
796	C₄²	C₂²×D₅₃	1	1	yes	characteristic
797	C₄²	C₂²×D₅₃	1	1	yes	characteristic
798	C₄²	C₂²×D₅₃	1	1	yes	characteristic
799	C₄²	C₂²×D₅₃	1	1	yes	characteristic
800	C₄²	C₂²×D₅₃	1	1	yes	characteristic
801	C₄²	C₂²×D₅₃	1	1	yes	characteristic
802	C₂³	—	53	1	no	—
803	C₂³	—	53	1	no	—
804	C₂³	—	53	1	no	—
805	C₂³	—	106	2	no	—
806	C₂³	—	212	1	no	—
807	C₂³	—	212	1	no	—
808	C₂³	C₂³×D₅₃	1	1	yes	characteristic
809	C₂³	C₂³×D₅₃	1	1	yes	characteristic
810	Q₈	—	4	1	no	—
811	Q₈	—	4	1	no	—
812	Q₈	—	4	1	no	—
813	Q₈	—	212	1	no	—
814	Q₈	—	212	1	no	—
815	Q₈	—	212	1	no	—
816	Q₈	—	212	1	no	—
817	Q₈	—	212	1	no	—
818	Q₈	—	212	1	no	—
819	D₄	—	4	1	no	—
820	D₄	—	106	2	no	—
821	D₄	—	106	2	no	—
822	D₄	—	212	1	no	—
823	D₄	—	212	1	no	—
824	D₄	—	212	1	no	—
825	D₄	—	212	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	1	no	—
828	C₂×C₄	—	53	1	no	—
829	C₂×C₄	—	53	1	no	—
830	C₂×C₄	—	53	1	no	—
831	C₂×C₄	—	53	1	no	—
832	C₂×C₄	—	53	1	no	—
833	C₂×C₄	—	53	1	no	—
834	C₂×C₄	—	53	1	no	—
835	C₂×C₄	—	53	1	no	—
836	C₂×C₄	—	53	1	no	—
837	C₂×C₄	—	53	1	no	—
838	C₂×C₄	—	53	1	no	—
839	C₂×C₄	—	53	1	no	—
840	C₂×C₄	—	53	1	no	—
841	C₂×C₄	—	106	2	no	—
842	C₂×C₄	—	106	2	no	—
843	C₂×C₄	—	212	1	no	—
844	C₂×C₄	—	212	1	no	—
845	C₂×C₄	—	212	1	no	—
846	C₂×C₄	—	212	1	no	—
847	C₂×C₄	—	212	1	no	—
848	C₂×C₄	—	212	1	no	—
849	C₂×C₄	—	212	1	no	—
850	C₂×C₄	—	212	1	no	—
851	C₂×C₄	—	212	1	no	—
852	C₂×C₄	—	212	1	no	—
853	C₂×C₄	—	212	1	no	—
854	C₂×C₄	—	212	1	no	—
855	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
856	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
857	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
858	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
859	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
860	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
861	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
862	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
863	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
864	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
865	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
866	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
867	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	1	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	53	2	no	—
875	C₂²	—	106	1	no	—
876	C₂²	—	106	1	no	—
877	C₂²	—	106	1	no	—
878	C₂²	—	106	1	no	—
879	C₂²	—	106	1	no	—
880	C₂²	—	106	1	no	—
881	C₂²	—	106	1	no	—
882	C₂²	—	106	1	no	—
883	C₂²	—	424	2	no	—
884	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	2	1	no	—
894	C₄	—	2	1	no	—
895	C₄	—	2	1	no	—
896	C₄	—	2	1	no	—
897	C₄	—	2	1	no	—
898	C₄	—	106	1	no	—
899	C₄	—	106	1	no	—
900	C₄	—	106	1	no	—
901	C₄	—	106	1	no	—
902	C₄	—	106	1	no	—
903	C₄	—	106	1	no	—
904	C₄	—	106	1	no	—
905	C₄	—	106	1	no	—
906	C₄	—	106	1	no	—
907	C₄	—	106	1	no	—
908	C₄	—	106	1	no	—
909	C₄	—	106	1	no	—
910	C₄	—	106	1	no	—
911	C₂	—	4	1	no	—
912	C₂	—	4	1	no	—
913	C₂	—	106	2	no	—
914	C₂	—	212	1	no	—
915	C₂	—	212	1	no	—
916	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
917	C₂	#16811459	1	1	yes	characteristic
918	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#556	C₂
hypercenter	#556	D₅₃
hypocenter	C₅₃	#3564
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #16811375	C₂	semidirect
2. #16811374	C₂	semidirect
3. #16811373	C₂	semidirect
4. #16811372	C₂	semidirect
5. #16811345	C₂	semidirect
6. #16811333	C₂	semidirect
7. #16811327	C₂	semidirect
8. #16811314	C₂	semidirect
9. #16811309	C₂	semidirect
10. #16811309	C₂	semidirect
11. #16811306	C₂	semidirect
12. #16811303	C₂	semidirect
13. #16811302	C₂	semidirect
14. #16811298	C₂	semidirect
15. #16811297	C₂	semidirect
16. #16811250	C₂	semidirect
17. #16811248	C₂	semidirect
18. #16811239	C₂	semidirect
19. #16811237	C₂	semidirect
20. #16811235	C₂	semidirect
21. #16811231	C₂	semidirect
22. #16811231	C₂	semidirect
23. #16811230	C₂	semidirect
24. #16811219	C₂	semidirect
25. #16811215	C₂	semidirect
26. #16811214	C₂	semidirect
28. #16811177	C₂	semidirect
29. #16811151	C₂	semidirect
30. #126×D₅₃	C₂	semidirect
31. C₅₃×#556	C₂	semidirect
32. #13133217	C₂²	semidirect
33. #13133216	C₂²	semidirect
34. #13133216	C₂²	semidirect
35. #13133215	C₂²	semidirect
36. #13133215	C₂²	semidirect
37. #13133215	C₂²	semidirect
38. #13133215	C₂²	semidirect
44. #13133212	C₂²	semidirect
45. #13133212	C₂²	semidirect
50. #13133211	C₂²	semidirect
51. #13133211	C₂²	semidirect
59. #13133210	C₂²	semidirect
60. #13133210	C₂²	semidirect
61. #13133209	C₂²	semidirect
62. #13133209	C₂²	semidirect
63. #13133209	C₂²	semidirect
64. #13133209	C₂²	semidirect
65. #13133209	C₂²	semidirect
66. #13133208	C₂²	semidirect
67. #13133208	C₂²	semidirect
68. #13133208	C₂²	semidirect
69. #13133207	C₂²	semidirect
70. #13133207	C₂²	semidirect
71. #13133207	C₂²	semidirect
72. #13133207	C₂²	semidirect
73. #13133207	C₂²	semidirect
74. #13133207	C₂²	semidirect
75. #13133207	C₂²	semidirect
76. #13133207	C₂²	semidirect
77. #13133207	C₂²	semidirect
78. #13133207	C₂²	semidirect
79. #13133207	C₂²	semidirect
84. #13133203	C₂²	semidirect
90. #13133201	C₂²	semidirect
98. #13133199	C₂²	semidirect
113. #13133195	C₂²	semidirect
114. #13133195	C₂²	semidirect
115. #13133195	C₂²	semidirect
119. #13133194	C₂²	semidirect
120. #13133194	C₂²	semidirect
121. #13133194	C₂²	semidirect
122. #13133194	C₂²	semidirect
128. #13133193	C₂²	semidirect
129. #13133193	C₂²	semidirect
135. C₄×Dic₁₀₆	C₂²	semidirect
136. C₄×Dic₁₀₆	C₂²	semidirect
137. C₄×Dic₁₀₆	C₂²	semidirect
138. C₄×Dic₁₀₆	C₂²	semidirect
139. C₄×Dic₁₀₆	C₂²	semidirect
140. #13133182	C₂²	semidirect
146. C₄×C₂²⋊D₅₃	C₂²	semidirect
152. #13133175	C₂²	semidirect
158. #13133174	C₂²	semidirect
160. #13133173	C₂²	semidirect
161. C₂×#11719919	C₂²	semidirect
165. C₄⋊C₄×D₅₃	C₂²	semidirect
172. C₄⋊Q₈×C₅₃	C₂²	semidirect
175. #126×C₅₃	C₂²	semidirect
176. #126×C₅₃	C₂²	semidirect
180. C₂²⋊Q₈×C₅₃	C₂²	semidirect
181. C₄×Q₈×C₅₃	C₂²	semidirect
182. C₄×Q₈×C₅₃	C₂²	semidirect
183. C₄×Q₈×C₅₃	C₂²	semidirect
186. #117×C₅₃	C₂²	semidirect
465. #556	D₅₃	semidirect
491. C₅₃	#3564	semidirect
499. C₄⋊Q₈	C₂×D₅₃	semidirect
524. #126	C₂×D₅₃	semidirect
525. #126	C₂×D₅₃	semidirect
598. C₂²⋊Q₈	C₂×D₅₃	semidirect
610. C₄×Q₈	C₂×D₅₃	semidirect
611. C₄×Q₈	C₂×D₅₃	semidirect
612. C₄×Q₈	C₂×D₅₃	semidirect
635. #117	C₂×D₅₃	semidirect