Subgroups — #20288458

Order 6784.

1022 conjugacy classes of subgroups.

The subgroup lattice has 934 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811345	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811340	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811329	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811327	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811310	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811308	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811306	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811305	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811305	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811302	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811300	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811297	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811296	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811252	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811243	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811239	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811232	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811232	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811195	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811179	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811177	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811156	C₂	1	1	yes	maximal, characteristic, complemented
25	#16811151	C₂	1	1	yes	maximal, characteristic, complemented
26	#16811131	C₂	1	1	yes	maximal, characteristic
27	C₂×#13133195	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811102	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811100	C₂	1	1	yes	maximal, characteristic, complemented
30	#117×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#11719947	C₂²	1	1	yes	characteristic
33	C₂²×Dic₁₀₆	C₂²	1	1	yes	characteristic
34	C₂²×C₄×D₅₃	C₂²	1	1	yes	characteristic
35	#13133216	C₂²	1	1	yes	characteristic, complemented
36	#13133216	C₂²	1	1	yes	characteristic, complemented
37	#13133216	C₂²	1	1	yes	characteristic, complemented
38	#13133216	C₂²	1	1	yes	characteristic, complemented
39	#13133215	C₂²	1	1	yes	characteristic, complemented
40	#13133215	C₂²	1	1	yes	characteristic, complemented
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
45	#13133212	C₂²	1	1	yes	characteristic
46	#13133212	C₂²	1	1	yes	characteristic
47	#13133212	C₂²	1	1	yes	characteristic, complemented
48	#13133212	C₂²	1	1	yes	characteristic, complemented
49	#13133212	C₂²	1	1	yes	characteristic, complemented
50	#13133211	C₂²	1	1	yes	characteristic
51	#13133211	C₂²	1	1	yes	characteristic
52	#13133211	C₂²	1	1	yes	characteristic, complemented
53	#13133210	C₂²	1	1	yes	characteristic, complemented
54	#13133210	C₂²	1	1	yes	characteristic, complemented
55	#13133209	C₂²	1	1	yes	characteristic, complemented
56	#13133208	C₂²	1	1	yes	characteristic, complemented
57	#13133208	C₂²	1	1	yes	characteristic, complemented
58	#13133207	C₂²	1	1	yes	characteristic, complemented
59	#13133207	C₂²	1	1	yes	characteristic, complemented
60	#13133207	C₂²	1	1	yes	characteristic, complemented
61	#13133207	C₂²	1	1	yes	characteristic, complemented
62	#13133207	C₂²	1	1	yes	characteristic, complemented
63	#13133207	C₂²	1	1	yes	characteristic, complemented
64	#13133207	C₂²	1	1	yes	characteristic, complemented
65	#13133207	C₂²	1	1	yes	characteristic, complemented
66	#13133207	C₂²	1	1	yes	characteristic, complemented
67	#13133207	C₂²	1	1	yes	characteristic, complemented
68	#13133206	C₂²	1	1	yes	characteristic
69	#13133205	C₂²	1	1	yes	characteristic
70	#13133203	C₂²	1	1	yes	characteristic
71	#13133203	C₂²	1	1	yes	characteristic
72	#13133203	C₂²	1	1	yes	characteristic, complemented
73	#13133203	C₂²	1	1	yes	characteristic, complemented
74	#13133202	C₂²	1	1	yes	characteristic
75	#13133202	C₂²	1	1	yes	characteristic
76	#13133202	C₂²	1	1	yes	characteristic
77	#13133202	C₂²	1	1	yes	characteristic
78	#13133201	C₂²	1	1	yes	characteristic
79	#13133201	C₂²	1	1	yes	characteristic
80	#13133200	C₂²	1	1	yes	characteristic
81	#13133200	C₂²	1	1	yes	characteristic
82	#13133200	C₂²	1	1	yes	characteristic
83	#13133199	C₂²	1	1	yes	characteristic
84	#13133199	C₂²	1	1	yes	characteristic
85	#13133198	C₂²	1	1	yes	characteristic
86	#13133197	C₂²	1	1	yes	characteristic
87	#13133197	C₂²	1	1	yes	characteristic, complemented
88	#13133196	C₂²	1	1	yes	characteristic
89	#13133195	C₂²	1	1	yes	characteristic
90	#13133195	C₂²	1	1	yes	characteristic
91	#13133195	C₂²	1	1	yes	characteristic
92	#13133195	C₂²	1	1	yes	characteristic
93	#13133195	C₂²	1	1	yes	characteristic
94	#13133195	C₂²	1	1	yes	characteristic
95	#13133195	C₂²	1	1	yes	characteristic
96	#13133195	C₂²	1	1	yes	characteristic
97	#13133195	C₂²	1	1	yes	characteristic
98	#13133195	C₂²	1	1	yes	characteristic
99	#13133195	C₂²	1	1	yes	characteristic
100	#13133195	C₂²	1	1	yes	characteristic
101	#13133195	C₂²	1	1	yes	characteristic, complemented
102	#13133195	C₂²	1	1	yes	characteristic, complemented
103	#13133195	C₂²	1	1	yes	characteristic, complemented
104	#13133194	C₂²	1	1	yes	characteristic
105	#13133194	C₂²	1	1	yes	characteristic
106	#13133194	C₂²	1	1	yes	characteristic, complemented
107	#13133194	C₂²	1	1	yes	characteristic, complemented
108	#13133194	C₂²	1	1	yes	characteristic, complemented
109	#13133193	C₂²	1	1	yes	characteristic
110	#13133190	C₂²	1	1	yes	characteristic
111	#13133190	C₂²	1	1	yes	characteristic
112	#13133187	C₂²	1	1	yes	characteristic
113	#13133185	C₂²	1	1	yes	characteristic
114	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
115	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
116	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
117	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
118	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
120	#13133182	C₂²	1	1	yes	characteristic, complemented
121	#13133182	C₂²	1	1	yes	characteristic, complemented
122	#13133182	C₂²	1	1	yes	characteristic, complemented
123	#13133182	C₂²	1	1	yes	characteristic, complemented
124	#13133182	C₂²	1	1	yes	characteristic, complemented
125	#13133182	C₂²	1	1	yes	characteristic, complemented
126	#13133182	C₂²	1	1	yes	characteristic, complemented
127	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
128	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
129	#13133179	C₂²	1	1	yes	characteristic
130	#13133179	C₂²	1	1	yes	characteristic
131	#13133179	C₂²	1	1	yes	characteristic
132	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
133	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
134	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
135	#13133177	C₂²	1	1	yes	characteristic
136	#13133177	C₂²	1	1	yes	characteristic
137	#13133177	C₂²	1	1	yes	characteristic
138	#13133177	C₂²	1	1	yes	characteristic
139	#13133177	C₂²	1	1	yes	characteristic, complemented
140	#13133176	C₂²	1	1	yes	characteristic
141	#13133176	C₂²	1	1	yes	characteristic
142	#13133175	C₂²	1	1	yes	characteristic
143	#13133175	C₂²	1	1	yes	characteristic
144	#13133175	C₂²	1	1	yes	characteristic
145	#13133175	C₂²	1	1	yes	characteristic
146	#13133175	C₂²	1	1	yes	characteristic, complemented
147	#13133174	C₂²	1	1	yes	characteristic
148	#13133174	C₂²	1	1	yes	characteristic
149	#13133174	C₂²	1	1	yes	characteristic
150	#13133174	C₂²	1	1	yes	characteristic
151	#13133174	C₂²	1	1	yes	characteristic, complemented
152	#13133174	C₂²	1	1	yes	characteristic, complemented
153	#13133173	C₂²	1	1	yes	characteristic
154	#13133173	C₂²	1	1	yes	characteristic
155	#13133173	C₂²	1	1	yes	characteristic
156	#13133173	C₂²	1	1	yes	characteristic
157	#13133173	C₂²	1	1	yes	characteristic
158	#13133173	C₂²	1	1	yes	characteristic, complemented
159	#13133173	C₂²	1	1	yes	characteristic, complemented
160	C₂×#11719919	C₂²	1	1	yes	characteristic
161	C₂×#11719919	C₂²	1	1	yes	characteristic
162	C₂×#11719919	C₂²	1	1	yes	characteristic, complemented
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	C₂×#11719921	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
169	C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
170	C₄²×D₅₃	C₂²	1	1	yes	characteristic
171	C₄²×D₅₃	C₂²	1	1	yes	characteristic
172	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
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, complemented
181	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
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, complemented
186	C₂×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂³×D₅₃	C₂³	1	1	yes	characteristic
188	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂×D₄×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	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	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
202	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
203	#11719947	—	2	4	no	—
204	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
205	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
206	C₂×C₄×D₅₃	—	2	4	no	—
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×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×Dic₁₀₆	—	2	4	no	—
219	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
220	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
221	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
222	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
223	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
224	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
225	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
226	C₂×Dic₁₀₆	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	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₄⋊C₄×C₅₃	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	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₄²×C₅₃	C₂³	1	1	yes	characteristic
252	C₄²×C₅₃	C₂³	1	1	yes	characteristic
253	C₄²×C₅₃	C₂³	1	1	yes	characteristic
254	C₄²×C₅₃	C₂³	1	1	yes	characteristic
255	C₄²×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂²⋊Dic₅₃	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	#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	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	C₄⋊Dic₅₃	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	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	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
343	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
344	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
345	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂²×D₅₃	—	2	2	no	—
348	C₂²×D₅₃	—	2	2	no	—
349	C₂²×D₅₃	—	4	1	no	—
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	D₄×C₅₃	—	2	2	no	—
355	C₂×C₄×C₅₃	—	2	2	no	—
356	C₂×C₄×C₅₃	—	2	2	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	—	4	1	no	—
376	C₂×Dic₅₃	—	2	2	no	—
377	C₂×Dic₅₃	—	2	2	no	—
378	C₂×Dic₅₃	—	4	1	no	—
379	C₂×Dic₅₃	—	4	1	no	—
380	C₂×Dic₅₃	#41	1	4	yes	—
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	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	D₂₁₂	—	2	2	no	—
395	D₂₁₂	—	4	1	no	—
396	C₄×D₅₃	—	2	2	no	—
397	C₄×D₅₃	—	2	2	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	Dic₁₀₆	—	2	2	no	—
408	Dic₁₀₆	—	2	2	no	—
409	Dic₁₀₆	—	2	2	no	—
410	Dic₁₀₆	—	2	2	no	—
411	Dic₁₀₆	—	2	2	no	—
412	Dic₁₀₆	—	4	1	no	—
413	Dic₁₀₆	—	4	1	no	—
414	Dic₁₀₆	—	4	1	no	—
415	C₂²×C₅₃	—	2	1	no	—
416	C₂²×C₅₃	—	2	1	no	—
417	C₂²×C₅₃	—	2	1	no	—
418	C₂²×C₅₃	—	2	1	no	—
419	C₂²×C₅₃	—	2	1	no	—
420	C₂²×C₅₃	C₂×#41	1	2	yes	—
421	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
422	C₂×D₅₃	—	2	1	no	—
423	C₂×D₅₃	—	2	1	no	—
424	C₂×D₅₃	—	2	1	no	—
425	C₂×D₅₃	—	2	1	no	—
426	C₂×D₅₃	—	2	1	no	—
427	C₂×D₅₃	—	2	1	no	—
428	C₂×D₅₃	—	2	1	no	—
429	C₂×D₅₃	—	2	1	no	—
430	C₂×D₅₃	—	4	4	no	—
431	C₂×D₅₃	2₋¹⁺⁴	1	2	yes	—
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	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	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	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	C₂×#41	1	2	yes	—
457	Dic₅₃	C₂×#41	1	2	yes	—
458	#3495	—	53	1	no	maximal, Sylow
459	C₂×C₅₃	—	2	2	no	—
460	C₂×C₅₃	—	4	1	no	—
461	C₂×C₅₃	C₂²×#41	1	1	yes	characteristic
462	C₂×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
463	C₂×C₅₃	#585	1	1	yes	characteristic
464	D₅₃	—	2	2	no	—
465	D₅₃	—	4	1	no	—
466	D₅₃	—	4	1	no	—
467	#556	—	53	1	no	—
468	#556	—	53	1	no	—
469	#554	—	53	1	no	—
470	#554	—	53	1	no	—
471	#552	—	53	1	no	—
472	#552	—	53	1	no	—
473	#552	—	53	1	no	—
474	#552	—	53	1	no	—
475	#552	—	53	1	no	—
476	#552	—	53	1	no	—
477	#552	—	53	1	no	—
478	#552	D₅₃	1	1	yes	characteristic, complemented
479	#551	—	53	1	no	—
480	#551	—	53	1	no	—
481	#551	—	53	1	no	—
482	#551	—	53	1	no	—
483	#544	—	53	1	no	—
484	#542	—	53	1	no	—
485	#542	—	53	1	no	—
486	#541	—	53	1	no	—
487	#541	—	53	1	no	—
488	#536	—	53	1	no	—
489	#533	—	53	1	no	—
490	#533	—	53	1	no	—
491	#529	—	53	1	no	—
492	#529	—	53	1	no	—
493	#525	—	53	1	no	—
494	C₂×C₂²⋊Q₈	—	53	1	no	—
495	#520	—	53	1	no	—
496	#519	—	53	1	no	—
497	C₂×#117	—	53	1	no	—
498	C₅₃	#3495	1	1	yes	characteristic, complemented, Sylow
499	C₂×#41	—	53	1	no	—
500	C₂²×Q₈	—	53	1	no	—
501	C₂³×C₄	—	53	1	no	—
502	C₄⋊Q₈	—	53	1	no	—
503	C₄⋊Q₈	—	53	1	no	—
504	C₄⋊Q₈	—	53	1	no	—
505	C₄⋊Q₈	—	53	1	no	—
506	C₄⋊Q₈	—	53	1	no	—
507	C₄⋊Q₈	—	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, complemented
523	#126	C₂×D₅₃	1	1	yes	characteristic, complemented
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	C₂×D₅₃	1	1	yes	characteristic, complemented
538	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
539	#125	C₂×D₅₃	1	1	yes	characteristic, complemented
540	#124	—	53	1	no	—
541	#124	—	53	1	no	—
542	#124	—	53	1	no	—
543	#124	—	53	1	no	—
544	#124	—	53	1	no	—
545	#124	—	53	1	no	—
546	#123	—	53	1	no	—
547	#123	—	53	1	no	—
548	#123	—	53	1	no	—
549	#123	—	53	1	no	—
550	#123	—	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	C₂×D₅₃	1	1	yes	characteristic
559	#123	C₂×D₅₃	1	1	yes	characteristic
560	C₂²⋊Q₈	—	53	1	no	—
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, complemented
586	#121	—	53	1	no	—
587	#121	—	53	1	no	—
588	#120	—	53	1	no	—
589	#120	—	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	—	53	1	no	—
600	C₄×Q₈	—	53	1	no	—
601	C₄×Q₈	—	53	1	no	—
602	C₄×Q₈	—	53	1	no	—
603	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
604	C₄×D₄	—	53	1	no	—
605	C₄×D₄	—	53	1	no	—
606	C₄×D₄	—	53	1	no	—
607	C₄×D₄	—	53	1	no	—
608	C₄×D₄	—	53	1	no	—
609	C₄×D₄	—	53	1	no	—
610	C₄×D₄	—	53	1	no	—
611	C₄×D₄	—	53	1	no	—
612	C₄×D₄	—	53	1	no	—
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	C₂×D₅₃	1	1	yes	characteristic
618	#117	—	53	1	no	—
619	#117	—	53	1	no	—
620	#117	—	53	1	no	—
621	#117	—	53	1	no	—
622	#117	—	53	1	no	—
623	#117	—	53	1	no	—
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	—	53	1	no	—
635	#117	—	53	1	no	—
636	#117	—	53	1	no	—
637	#117	—	53	1	no	—
638	#117	C₂×D₅₃	1	1	yes	characteristic
639	#117	C₂×D₅₃	1	1	yes	characteristic
640	#117	C₂×D₅₃	1	1	yes	characteristic, complemented
641	C₂×C₄⋊C₄	—	53	1	no	—
642	C₂×C₄⋊C₄	—	53	1	no	—
643	C₂×C₄⋊C₄	—	53	1	no	—
644	C₂×C₄⋊C₄	—	53	1	no	—
645	C₂×C₄⋊C₄	—	53	1	no	—
646	C₂×C₄⋊C₄	—	53	1	no	—
647	C₂×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
648	C₂×C₂²⋊C₄	—	53	1	no	—
649	C₂×C₂²⋊C₄	—	53	1	no	—
650	C₂×C₂²⋊C₄	—	53	1	no	—
651	C₂×C₂²⋊C₄	—	53	1	no	—
652	C₂×C₄²	—	53	1	no	—
653	C₂×C₄²	—	53	1	no	—
654	C₂⁴	—	53	1	no	—
655	#41	—	106	4	no	—
656	C₂×Q₈	—	53	1	no	—
657	C₂×Q₈	—	53	1	no	—
658	C₂×Q₈	—	53	1	no	—
659	C₂×Q₈	—	53	1	no	—
660	C₂×Q₈	—	53	1	no	—
661	C₂×Q₈	—	53	1	no	—
662	C₂×Q₈	—	53	1	no	—
663	C₂×Q₈	—	53	1	no	—
664	C₂×Q₈	—	106	4	no	—
665	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
666	C₂×D₄	—	53	1	no	—
667	C₂×D₄	—	53	1	no	—
668	C₂×D₄	—	53	1	no	—
669	C₂×D₄	—	53	1	no	—
670	C₂×D₄	—	53	1	no	—
671	C₂×D₄	—	53	1	no	—
672	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
679	C₂²×C₄	—	53	1	no	—
680	C₂²×C₄	—	53	1	no	—
681	C₂²×C₄	—	53	1	no	—
682	C₂²×C₄	—	53	1	no	—
683	C₂²×C₄	—	53	1	no	—
684	C₂²×C₄	—	53	1	no	—
685	C₂²×C₄	—	53	1	no	—
686	C₂²×C₄	—	53	1	no	—
687	C₂²×C₄	—	53	1	no	—
688	C₂²×C₄	—	53	1	no	—
689	C₂²×C₄	—	106	4	no	—
690	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
691	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
692	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
693	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	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	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	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
743	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
745	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
746	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
747	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
748	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
749	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
750	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
751	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	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	C₂²×D₅₃	1	1	yes	characteristic
783	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
784	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
785	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
786	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
787	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
788	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
796	C₄²	—	53	1	no	—
797	C₄²	—	53	1	no	—
798	C₄²	—	53	1	no	—
799	C₄²	—	53	1	no	—
800	C₄²	—	53	1	no	—
801	C₄²	—	53	1	no	—
802	C₄²	—	53	1	no	—
803	C₄²	—	53	1	no	—
804	C₄²	—	53	1	no	—
805	C₄²	—	53	1	no	—
806	C₄²	—	53	1	no	—
807	C₄²	C₂²×D₅₃	1	1	yes	characteristic
808	C₄²	C₂²×D₅₃	1	1	yes	characteristic
809	C₄²	C₂²×D₅₃	1	1	yes	characteristic
810	C₄²	C₂²×D₅₃	1	1	yes	characteristic
811	C₄²	C₂²×D₅₃	1	1	yes	characteristic
812	C₂³	—	53	1	no	—
813	C₂³	—	53	1	no	—
814	C₂³	—	53	1	no	—
815	C₂³	—	106	2	no	—
816	C₂³	—	106	2	no	—
817	C₂³	—	212	1	no	—
818	C₂³	C₂³×D₅₃	1	1	yes	characteristic
819	C₂³	C₂³×D₅₃	1	1	yes	characteristic
820	Q₈	—	4	1	no	—
821	Q₈	—	106	2	no	—
822	Q₈	—	106	2	no	—
823	Q₈	—	106	2	no	—
824	Q₈	—	106	2	no	—
825	Q₈	—	106	2	no	—
826	Q₈	—	212	1	no	—
827	Q₈	—	212	1	no	—
828	Q₈	—	212	1	no	—
829	D₄	—	2	2	no	—
830	D₄	—	106	2	no	—
831	D₄	—	106	2	no	—
832	D₄	—	106	2	no	—
833	D₄	—	106	2	no	—
834	D₄	—	212	1	no	—
835	D₄	—	212	1	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	2	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	53	4	no	—
841	C₂×C₄	—	53	1	no	—
842	C₂×C₄	—	53	1	no	—
843	C₂×C₄	—	53	1	no	—
844	C₂×C₄	—	53	1	no	—
845	C₂×C₄	—	53	1	no	—
846	C₂×C₄	—	53	1	no	—
847	C₂×C₄	—	53	1	no	—
848	C₂×C₄	—	53	1	no	—
849	C₂×C₄	—	53	1	no	—
850	C₂×C₄	—	53	1	no	—
851	C₂×C₄	—	53	1	no	—
852	C₂×C₄	—	53	1	no	—
853	C₂×C₄	—	53	1	no	—
854	C₂×C₄	—	106	2	no	—
855	C₂×C₄	—	106	2	no	—
856	C₂×C₄	—	106	2	no	—
857	C₂×C₄	—	106	2	no	—
858	C₂×C₄	—	106	2	no	—
859	C₂×C₄	—	106	2	no	—
860	C₂×C₄	—	106	2	no	—
861	C₂×C₄	—	106	2	no	—
862	C₂×C₄	—	106	2	no	—
863	C₂×C₄	—	212	1	no	—
864	C₂×C₄	—	212	1	no	—
865	C₂×C₄	—	212	1	no	—
866	C₂×C₄	—	212	1	no	—
867	C₂×C₄	—	212	1	no	—
868	C₂×C₄	—	212	1	no	—
869	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
870	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
871	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
872	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
873	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
874	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
875	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
876	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
877	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
878	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
879	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
880	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
881	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
882	C₂²	—	2	1	no	—
883	C₂²	—	2	1	no	—
884	C₂²	—	2	1	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	53	2	no	—
888	C₂²	—	106	1	no	—
889	C₂²	—	106	1	no	—
890	C₂²	—	106	1	no	—
891	C₂²	—	106	1	no	—
892	C₂²	—	106	1	no	—
893	C₂²	—	106	1	no	—
894	C₂²	—	106	1	no	—
895	C₂²	—	106	1	no	—
896	C₂²	—	212	4	no	—
897	C₂²	#41×D₅₃	1	2	yes	—
898	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
899	C₄	—	2	1	no	—
900	C₄	—	2	1	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	2	1	no	—
904	C₄	—	2	1	no	—
905	C₄	—	2	1	no	—
906	C₄	—	2	1	no	—
907	C₄	—	2	1	no	—
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	1	no	—
911	C₄	—	2	1	no	—
912	C₄	—	53	2	no	—
913	C₄	—	53	2	no	—
914	C₄	—	106	1	no	—
915	C₄	—	106	1	no	—
916	C₄	—	106	1	no	—
917	C₄	—	106	1	no	—
918	C₄	—	106	1	no	—
919	C₄	—	106	1	no	—
920	C₄	—	106	1	no	—
921	C₄	—	106	1	no	—
922	C₄	—	106	1	no	—
923	C₄	—	106	1	no	—
924	C₄	—	106	1	no	—
925	C₂	—	2	2	no	—
926	C₂	—	4	1	no	—
927	C₂	—	106	2	no	—
928	C₂	—	212	1	no	—
929	C₂	—	212	1	no	—
930	C₂	C₂×#41×D₅₃	1	1	yes	characteristic
931	C₂	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
932	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	#3495
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. #16811345	C₂	semidirect
2. #16811340	C₂	semidirect
3. #16811329	C₂	semidirect
4. #16811327	C₂	semidirect
5. #16811310	C₂	semidirect
6. #16811309	C₂	semidirect
7. #16811308	C₂	semidirect
8. #16811306	C₂	semidirect
9. #16811306	C₂	semidirect
10. #16811305	C₂	semidirect
11. #16811305	C₂	semidirect
12. #16811302	C₂	semidirect
13. #16811300	C₂	semidirect
14. #16811297	C₂	semidirect
15. #16811296	C₂	semidirect
16. #16811252	C₂	semidirect
17. #16811243	C₂	semidirect
18. #16811239	C₂	semidirect
19. #16811232	C₂	semidirect
20. #16811232	C₂	semidirect
21. #16811195	C₂	semidirect
22. #16811179	C₂	semidirect
23. #16811177	C₂	semidirect
24. #16811156	C₂	semidirect
25. #16811151	C₂	semidirect
27. C₂×#13133195	C₂	semidirect
28. #16811102	C₂	semidirect
29. #16811100	C₂	semidirect
30. #117×D₅₃	C₂	semidirect
31. C₅₃×#552	C₂	semidirect
35. #13133216	C₂²	semidirect
36. #13133216	C₂²	semidirect
37. #13133216	C₂²	semidirect
38. #13133216	C₂²	semidirect
39. #13133215	C₂²	semidirect
40. #13133215	C₂²	semidirect
47. #13133212	C₂²	semidirect
48. #13133212	C₂²	semidirect
49. #13133212	C₂²	semidirect
52. #13133211	C₂²	semidirect
53. #13133210	C₂²	semidirect
54. #13133210	C₂²	semidirect
55. #13133209	C₂²	semidirect
56. #13133208	C₂²	semidirect
57. #13133208	C₂²	semidirect
58. #13133207	C₂²	semidirect
59. #13133207	C₂²	semidirect
60. #13133207	C₂²	semidirect
61. #13133207	C₂²	semidirect
62. #13133207	C₂²	semidirect
63. #13133207	C₂²	semidirect
64. #13133207	C₂²	semidirect
65. #13133207	C₂²	semidirect
66. #13133207	C₂²	semidirect
67. #13133207	C₂²	semidirect
72. #13133203	C₂²	semidirect
73. #13133203	C₂²	semidirect
87. #13133197	C₂²	semidirect
101. #13133195	C₂²	semidirect
102. #13133195	C₂²	semidirect
103. #13133195	C₂²	semidirect
106. #13133194	C₂²	semidirect
107. #13133194	C₂²	semidirect
108. #13133194	C₂²	semidirect
114. C₄×Dic₁₀₆	C₂²	semidirect
115. C₄×Dic₁₀₆	C₂²	semidirect
116. C₄×Dic₁₀₆	C₂²	semidirect
117. C₄×Dic₁₀₆	C₂²	semidirect
118. C₄×Dic₁₀₆	C₂²	semidirect
119. C₄×Dic₁₀₆	C₂²	semidirect
120. #13133182	C₂²	semidirect
121. #13133182	C₂²	semidirect
122. #13133182	C₂²	semidirect
123. #13133182	C₂²	semidirect
124. #13133182	C₂²	semidirect
125. #13133182	C₂²	semidirect
126. #13133182	C₂²	semidirect
134. C₄×C₂²⋊D₅₃	C₂²	semidirect
139. #13133177	C₂²	semidirect
146. #13133175	C₂²	semidirect
151. #13133174	C₂²	semidirect
152. #13133174	C₂²	semidirect
158. #13133173	C₂²	semidirect
159. #13133173	C₂²	semidirect
162. C₂×#11719919	C₂²	semidirect
165. C₄⋊C₄×D₅₃	C₂²	semidirect
172. #126×C₅₃	C₂²	semidirect
173. #126×C₅₃	C₂²	semidirect
174. #125×C₅₃	C₂²	semidirect
175. #125×C₅₃	C₂²	semidirect
176. #125×C₅₃	C₂²	semidirect
180. C₂²⋊Q₈×C₅₃	C₂²	semidirect
181. C₄×Q₈×C₅₃	C₂²	semidirect
185. #117×C₅₃	C₂²	semidirect
478. #552	D₅₃	semidirect
498. C₅₃	#3495	semidirect
522. #126	C₂×D₅₃	semidirect
523. #126	C₂×D₅₃	semidirect
537. #125	C₂×D₅₃	semidirect
538. #125	C₂×D₅₃	semidirect
539. #125	C₂×D₅₃	semidirect
585. C₂²⋊Q₈	C₂×D₅₃	semidirect
603. C₄×Q₈	C₂×D₅₃	semidirect
640. #117	C₂×D₅₃	semidirect