Subgroups — #20289379

Order 6784.

954 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16811373	C₂	1	1	yes	maximal, characteristic, complemented
2	#16811368	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811368	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811362	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811355	C₂	1	1	yes	maximal, characteristic, complemented
6	#16811342	C₂	1	1	yes	maximal, characteristic, complemented
7	#16811335	C₂	1	1	yes	maximal, characteristic, complemented
8	#16811325	C₂	1	1	yes	maximal, characteristic, complemented
9	#16811323	C₂	1	1	yes	maximal, characteristic, complemented
10	#16811320	C₂	1	1	yes	maximal, characteristic, complemented
11	#16811313	C₂	1	1	yes	maximal, characteristic, complemented
12	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
13	#16811309	C₂	1	1	yes	maximal, characteristic, complemented
14	#16811304	C₂	1	1	yes	maximal, characteristic, complemented
15	#16811299	C₂	1	1	yes	maximal, characteristic, complemented
16	#16811299	C₂	1	1	yes	maximal, characteristic, complemented
17	#16811243	C₂	1	1	yes	maximal, characteristic, complemented
18	#16811241	C₂	1	1	yes	maximal, characteristic, complemented
19	#16811238	C₂	1	1	yes	maximal, characteristic, complemented
20	#16811233	C₂	1	1	yes	maximal, characteristic, complemented
21	#16811230	C₂	1	1	yes	maximal, characteristic, complemented
22	#16811223	C₂	1	1	yes	maximal, characteristic, complemented
23	#16811217	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	#16811208	C₂	1	1	yes	maximal, characteristic, complemented
27	#16811208	C₂	1	1	yes	maximal, characteristic, complemented
28	#16811154	C₂	1	1	yes	maximal, characteristic, complemented
29	#16811153	C₂	1	1	yes	maximal, characteristic, complemented
30	#16811150	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
32	#13133216	C₂²	1	1	yes	characteristic, complemented
33	#13133215	C₂²	1	1	yes	characteristic, complemented
34	#13133215	C₂²	1	1	yes	characteristic, complemented
35	#13133213	C₂²	1	1	yes	characteristic
36	#13133212	C₂²	1	1	yes	characteristic, complemented
37	#13133212	C₂²	1	1	yes	characteristic, complemented
38	#13133210	C₂²	1	1	yes	characteristic
39	#13133210	C₂²	1	1	yes	characteristic
40	#13133210	C₂²	1	1	yes	characteristic
41	#13133210	C₂²	1	1	yes	characteristic
42	#13133210	C₂²	1	1	yes	characteristic
43	#13133210	C₂²	1	1	yes	characteristic
44	#13133210	C₂²	1	1	yes	characteristic
45	#13133210	C₂²	1	1	yes	characteristic
46	#13133210	C₂²	1	1	yes	characteristic
47	#13133210	C₂²	1	1	yes	characteristic
48	#13133210	C₂²	1	1	yes	characteristic
49	#13133210	C₂²	1	1	yes	characteristic
50	#13133210	C₂²	1	1	yes	characteristic, complemented
51	#13133210	C₂²	1	1	yes	characteristic, complemented
52	#13133210	C₂²	1	1	yes	characteristic, complemented
53	#13133210	C₂²	1	1	yes	characteristic, complemented
54	#13133209	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	#13133208	C₂²	1	1	yes	characteristic, complemented
59	#13133208	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	#13133206	C₂²	1	1	yes	characteristic, complemented
67	#13133204	C₂²	1	1	yes	characteristic
68	#13133204	C₂²	1	1	yes	characteristic
69	#13133204	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
73	#13133203	C₂²	1	1	yes	characteristic
74	#13133203	C₂²	1	1	yes	characteristic, complemented
75	#13133203	C₂²	1	1	yes	characteristic, complemented
76	#13133202	C₂²	1	1	yes	characteristic, complemented
77	#13133201	C₂²	1	1	yes	characteristic
78	#13133201	C₂²	1	1	yes	characteristic
79	#13133201	C₂²	1	1	yes	characteristic, complemented
80	#13133200	C₂²	1	1	yes	characteristic
81	#13133200	C₂²	1	1	yes	characteristic
82	#13133200	C₂²	1	1	yes	characteristic, complemented
83	#13133200	C₂²	1	1	yes	characteristic, complemented
84	#13133199	C₂²	1	1	yes	characteristic
85	#13133199	C₂²	1	1	yes	characteristic
86	#13133199	C₂²	1	1	yes	characteristic
87	#13133199	C₂²	1	1	yes	characteristic
88	#13133199	C₂²	1	1	yes	characteristic
89	#13133199	C₂²	1	1	yes	characteristic
90	#13133199	C₂²	1	1	yes	characteristic, complemented
91	#13133198	C₂²	1	1	yes	characteristic
92	#13133198	C₂²	1	1	yes	characteristic
93	#13133198	C₂²	1	1	yes	characteristic
94	#13133198	C₂²	1	1	yes	characteristic
95	#13133198	C₂²	1	1	yes	characteristic
96	#13133198	C₂²	1	1	yes	characteristic
97	#13133198	C₂²	1	1	yes	characteristic, complemented
98	#13133197	C₂²	1	1	yes	characteristic, complemented
99	#13133196	C₂²	1	1	yes	characteristic
100	#13133196	C₂²	1	1	yes	characteristic
101	#13133196	C₂²	1	1	yes	characteristic, complemented
102	#13133196	C₂²	1	1	yes	characteristic, complemented
103	#13133195	C₂²	1	1	yes	characteristic, complemented
104	#13133195	C₂²	1	1	yes	characteristic, complemented
105	#13133195	C₂²	1	1	yes	characteristic, complemented
106	#13133194	C₂²	1	1	yes	characteristic
107	#13133194	C₂²	1	1	yes	characteristic
108	#13133194	C₂²	1	1	yes	characteristic
109	#13133194	C₂²	1	1	yes	characteristic
110	#13133194	C₂²	1	1	yes	characteristic
111	#13133194	C₂²	1	1	yes	characteristic
112	#13133194	C₂²	1	1	yes	characteristic, complemented
113	#13133194	C₂²	1	1	yes	characteristic, complemented
114	#13133194	C₂²	1	1	yes	characteristic, complemented
115	#13133190	C₂²	1	1	yes	characteristic
116	#13133190	C₂²	1	1	yes	characteristic
117	#13133190	C₂²	1	1	yes	characteristic, complemented
118	#13133189	C₂²	1	1	yes	characteristic
119	#13133189	C₂²	1	1	yes	characteristic
120	#13133189	C₂²	1	1	yes	characteristic
121	#13133189	C₂²	1	1	yes	characteristic
122	#13133189	C₂²	1	1	yes	characteristic
123	#13133189	C₂²	1	1	yes	characteristic
124	#13133189	C₂²	1	1	yes	characteristic, complemented
125	#13133188	C₂²	1	1	yes	characteristic
126	#13133188	C₂²	1	1	yes	characteristic
127	#13133188	C₂²	1	1	yes	characteristic
128	#13133188	C₂²	1	1	yes	characteristic
129	#13133188	C₂²	1	1	yes	characteristic, complemented
130	#13133186	C₂²	1	1	yes	characteristic
131	#13133186	C₂²	1	1	yes	characteristic
132	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
134	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
135	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
136	#13133182	C₂²	1	1	yes	characteristic, complemented
137	#13133182	C₂²	1	1	yes	characteristic, complemented
138	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
139	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
140	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
141	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
142	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
143	D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
144	C₄×C₂²⋊D₅₃	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	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
148	#13133177	C₂²	1	1	yes	characteristic
149	#13133177	C₂²	1	1	yes	characteristic
150	#13133177	C₂²	1	1	yes	characteristic
151	#13133177	C₂²	1	1	yes	characteristic
152	#13133177	C₂²	1	1	yes	characteristic, complemented
153	#13133177	C₂²	1	1	yes	characteristic, complemented
154	#13133176	C₂²	1	1	yes	characteristic
155	#13133176	C₂²	1	1	yes	characteristic
156	#13133175	C₂²	1	1	yes	characteristic, complemented
157	#13133175	C₂²	1	1	yes	characteristic, complemented
158	#13133174	C₂²	1	1	yes	characteristic, complemented
159	#13133174	C₂²	1	1	yes	characteristic, complemented
160	#13133173	C₂²	1	1	yes	characteristic
161	#13133173	C₂²	1	1	yes	characteristic
162	#13133173	C₂²	1	1	yes	characteristic
163	#13133173	C₂²	1	1	yes	characteristic
164	#13133173	C₂²	1	1	yes	characteristic, complemented
165	#13133173	C₂²	1	1	yes	characteristic, complemented
166	C₂×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
167	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
169	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
170	C₂×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
171	C₂×C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
172	#126×C₅₃	C₂²	1	1	yes	characteristic
173	#126×C₅₃	C₂²	1	1	yes	characteristic
174	#124×C₅₃	C₂²	1	1	yes	characteristic
175	#124×C₅₃	C₂²	1	1	yes	characteristic
176	#123×C₅₃	C₂²	1	1	yes	characteristic
177	#123×C₅₃	C₂²	1	1	yes	characteristic
178	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
179	#121×C₅₃	C₂²	1	1	yes	characteristic
180	#121×C₅₃	C₂²	1	1	yes	characteristic
181	#121×C₅₃	C₂²	1	1	yes	characteristic
182	#120×C₅₃	C₂²	1	1	yes	characteristic
183	#120×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂⁴×C₅₃	C₂³	1	1	yes	characteristic
188	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
210	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
214	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
216	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂²×Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×D₂₁₂	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×C₄×D₅₃	C₂³	1	1	yes	characteristic
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	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	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	C₂²⋊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	C₄²×C₅₃	C₂³	1	1	yes	characteristic
251	C₄²×C₅₃	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	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	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂²⋊Dic₅₃	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	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₅₃	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	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	#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	C₂³×C₅₃	—	4	1	no	—
343	C₂³×C₅₃	—	4	1	no	—
344	C₂³×C₅₃	—	4	1	no	—
345	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂³×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂³×C₅₃	C₂⁴	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	Q₈×C₅₃	—	4	1	no	—
353	D₄×C₅₃	—	4	1	no	—
354	D₄×C₅₃	—	4	1	no	—
355	D₄×C₅₃	—	4	1	no	—
356	D₄×C₅₃	—	4	1	no	—
357	D₄×C₅₃	—	4	1	no	—
358	D₄×C₅₃	—	4	1	no	—
359	D₄×C₅₃	—	4	1	no	—
360	C₂×C₄×C₅₃	—	4	1	no	—
361	C₂×C₄×C₅₃	—	4	1	no	—
362	C₂×C₄×C₅₃	—	4	1	no	—
363	C₂×C₄×C₅₃	—	4	1	no	—
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	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²⋊D₅₃	—	4	1	no	—
375	C₂²⋊D₅₃	—	4	1	no	—
376	C₂²⋊D₅₃	—	4	1	no	—
377	C₂²⋊D₅₃	—	4	1	no	—
378	C₂²⋊D₅₃	—	4	1	no	—
379	C₂²⋊D₅₃	—	4	1	no	—
380	C₂²⋊D₅₃	—	4	1	no	—
381	C₂²⋊D₅₃	—	4	1	no	—
382	C₂²⋊D₅₃	—	4	1	no	—
383	C₂²⋊D₅₃	—	4	1	no	—
384	C₂×Dic₅₃	—	4	1	no	—
385	C₂×Dic₅₃	—	4	1	no	—
386	C₂×Dic₅₃	—	4	1	no	—
387	C₂×Dic₅₃	—	4	1	no	—
388	C₂×Dic₅₃	—	4	1	no	—
389	C₂×Dic₅₃	—	4	1	no	—
390	C₂×Dic₅₃	—	4	1	no	—
391	C₂×Dic₅₃	—	4	1	no	—
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	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	D₂₁₂	—	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	C₄×D₅₃	—	4	1	no	—
412	C₄×D₅₃	—	4	1	no	—
413	Dic₁₀₆	—	4	1	no	—
414	Dic₁₀₆	—	4	1	no	—
415	Dic₁₀₆	—	4	1	no	—
416	Dic₁₀₆	—	4	1	no	—
417	Dic₁₀₆	—	4	1	no	—
418	C₂²×C₅₃	—	2	1	no	—
419	C₂²×C₅₃	—	2	1	no	—
420	C₂²×C₅₃	—	2	1	no	—
421	C₂²×C₅₃	—	2	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	—	2	1	no	—
429	C₂²×C₅₃	—	2	1	no	—
430	C₂²×C₅₃	—	2	1	no	—
431	C₂²×C₅₃	—	2	1	no	—
432	C₂²×C₅₃	—	2	1	no	—
433	C₂²×C₅₃	—	8	2	no	—
434	C₂²×C₅₃	C₂⁵	1	1	yes	characteristic
435	C₂×D₅₃	—	2	1	no	—
436	C₂×D₅₃	—	2	1	no	—
437	C₂×D₅₃	—	2	1	no	—
438	C₂×D₅₃	—	2	1	no	—
439	C₂×D₅₃	—	2	1	no	—
440	C₂×D₅₃	—	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	—	2	1	no	—
463	Dic₅₃	—	2	1	no	—
464	Dic₅₃	—	2	1	no	—
465	#3566	—	53	1	no	maximal, Sylow
466	C₂×C₅₃	—	4	1	no	—
467	C₂×C₅₃	—	4	1	no	—
468	C₂×C₅₃	—	4	1	no	—
469	C₂×C₅₃	—	4	1	no	—
470	C₂×C₅₃	—	4	1	no	—
471	C₂×C₅₃	#585	1	1	yes	characteristic
472	C₂×C₅₃	#585	1	1	yes	characteristic
473	C₂×C₅₃	#585	1	1	yes	characteristic
474	D₅₃	—	4	1	no	—
475	D₅₃	—	4	1	no	—
476	#563	—	53	1	no	—
477	#562	—	53	1	no	—
478	#562	—	53	1	no	—
479	#560	—	53	1	no	—
480	#559	—	53	1	no	—
481	#556	—	53	1	no	—
482	#555	—	53	1	no	—
483	#553	—	53	1	no	—
484	#553	—	53	1	no	—
485	#553	—	53	1	no	—
486	#552	—	53	1	no	—
487	#552	—	53	1	no	—
488	#552	—	53	1	no	—
489	#551	—	53	1	no	—
490	#551	—	53	1	no	—
491	#551	—	53	1	no	—
492	#542	—	53	1	no	—
493	#542	—	53	1	no	—
494	#542	—	53	1	no	—
495	#541	—	53	1	no	—
496	#541	—	53	1	no	—
497	#540	—	53	1	no	—
498	#539	—	53	1	no	—
499	#539	—	53	1	no	—
500	#539	—	53	1	no	—
501	#538	—	53	1	no	—
502	#538	—	53	1	no	—
503	#538	D₅₃	1	1	yes	characteristic, complemented
504	#529	—	53	1	no	—
505	#529	—	53	1	no	—
506	#529	—	53	1	no	—
507	C₅₃	#3566	1	1	yes	characteristic, complemented, Sylow
508	C₄⋊Q₈	—	53	1	no	—
509	C₄⋊Q₈	—	53	1	no	—
510	C₄⋊Q₈	—	53	1	no	—
511	#127	—	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	—	53	1	no	—
523	#126	—	53	1	no	—
524	#126	—	53	1	no	—
525	#126	—	53	1	no	—
526	#126	—	53	1	no	—
527	#126	—	53	1	no	—
528	#126	—	53	1	no	—
529	#126	—	53	1	no	—
530	#126	C₂×D₅₃	1	1	yes	characteristic
531	#126	C₂×D₅₃	1	1	yes	characteristic
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	#124	—	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	—	53	1	no	—
551	#124	—	53	1	no	—
552	#124	—	53	1	no	—
553	#124	—	53	1	no	—
554	#124	C₂×D₅₃	1	1	yes	characteristic
555	#124	C₂×D₅₃	1	1	yes	characteristic
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	#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	C₂×D₅₃	1	1	yes	characteristic
579	#123	C₂×D₅₃	1	1	yes	characteristic
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	#121	—	53	1	no	—
599	#121	—	53	1	no	—
600	#121	—	53	1	no	—
601	#121	—	53	1	no	—
602	#121	—	53	1	no	—
603	#121	—	53	1	no	—
604	#121	—	53	1	no	—
605	#121	—	53	1	no	—
606	#121	—	53	1	no	—
607	#121	—	53	1	no	—
608	#121	—	53	1	no	—
609	#121	—	53	1	no	—
610	#121	—	53	1	no	—
611	#121	—	53	1	no	—
612	#121	—	53	1	no	—
613	#121	C₂×D₅₃	1	1	yes	characteristic
614	#121	C₂×D₅₃	1	1	yes	characteristic
615	#121	C₂×D₅₃	1	1	yes	characteristic
616	#120	—	53	1	no	—
617	#120	—	53	1	no	—
618	#120	C₂×D₅₃	1	1	yes	characteristic
619	#120	C₂×D₅₃	1	1	yes	characteristic
620	C₄×Q₈	—	53	1	no	—
621	C₄×Q₈	—	53	1	no	—
622	C₄×Q₈	—	53	1	no	—
623	C₄×Q₈	—	53	1	no	—
624	C₄×Q₈	—	53	1	no	—
625	C₄×Q₈	—	53	1	no	—
626	C₄×D₄	—	53	1	no	—
627	C₄×D₄	—	53	1	no	—
628	C₄×D₄	—	53	1	no	—
629	C₄×D₄	—	53	1	no	—
630	C₄×D₄	—	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	C₂×D₅₃	1	1	yes	characteristic
643	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
644	#117	—	53	1	no	—
645	#117	—	53	1	no	—
646	#117	—	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	#117	—	53	1	no	—
654	#117	—	53	1	no	—
655	#117	—	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×C₂²⋊C₄	—	53	1	no	—
660	C₂×C₂²⋊C₄	—	53	1	no	—
661	C₂×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
662	C₂×C₄²	—	53	1	no	—
663	C₂⁴	C₂²×D₅₃	1	1	yes	characteristic
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	C₂²×D₅₃	1	1	yes	characteristic
670	C₂×D₄	—	53	1	no	—
671	C₂×D₄	—	53	1	no	—
672	C₂×D₄	—	53	1	no	—
673	C₂×D₄	—	53	1	no	—
674	C₂×D₄	—	53	1	no	—
675	C₂×D₄	—	53	1	no	—
676	C₂×D₄	—	53	1	no	—
677	C₂×D₄	—	53	1	no	—
678	C₂×D₄	—	53	1	no	—
679	C₂×D₄	—	53	1	no	—
680	C₂×D₄	—	53	1	no	—
681	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
682	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
683	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
684	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
685	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
686	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
687	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
688	C₂²×C₄	—	53	1	no	—
689	C₂²×C₄	—	53	1	no	—
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	C₂²×D₅₃	1	1	yes	characteristic
703	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
704	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
705	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	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	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	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
753	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	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	C₂²×D₅₃	1	1	yes	characteristic
789	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
790	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
791	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
792	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
793	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
794	C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	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	—	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	C₂²×D₅₃	1	1	yes	characteristic
817	C₄²	C₂²×D₅₃	1	1	yes	characteristic
818	C₂³	—	4	1	no	—
819	C₂³	—	4	1	no	—
820	C₂³	—	4	1	no	—
821	C₂³	—	53	1	no	—
822	C₂³	—	53	1	no	—
823	C₂³	C₂³×D₅₃	1	1	yes	characteristic
824	C₂³	C₂³×D₅₃	1	1	yes	characteristic
825	C₂³	C₂³×D₅₃	1	1	yes	characteristic
826	C₂³	C₂³×D₅₃	1	1	yes	characteristic
827	C₂³	C₂³×D₅₃	1	1	yes	characteristic
828	Q₈	—	4	1	no	—
829	Q₈	—	212	1	no	—
830	Q₈	—	212	1	no	—
831	Q₈	—	212	1	no	—
832	Q₈	—	212	1	no	—
833	Q₈	—	212	1	no	—
834	D₄	—	4	1	no	—
835	D₄	—	4	1	no	—
836	D₄	—	4	1	no	—
837	D₄	—	4	1	no	—
838	D₄	—	4	1	no	—
839	D₄	—	4	1	no	—
840	D₄	—	4	1	no	—
841	D₄	—	212	1	no	—
842	D₄	—	212	1	no	—
843	D₄	—	212	1	no	—
844	D₄	—	212	1	no	—
845	D₄	—	212	1	no	—
846	D₄	—	212	1	no	—
847	D₄	—	212	1	no	—
848	D₄	—	212	1	no	—
849	D₄	—	212	1	no	—
850	D₄	—	212	1	no	—
851	D₄	—	212	1	no	—
852	C₂×C₄	—	4	1	no	—
853	C₂×C₄	—	4	1	no	—
854	C₂×C₄	—	4	1	no	—
855	C₂×C₄	—	4	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	—	53	1	no	—
866	C₂×C₄	—	53	1	no	—
867	C₂×C₄	—	53	1	no	—
868	C₂×C₄	—	53	1	no	—
869	C₂×C₄	—	53	1	no	—
870	C₂×C₄	—	212	1	no	—
871	C₂×C₄	—	212	1	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	—	212	1	no	—
883	C₂×C₄	—	212	1	no	—
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	C₂²	—	2	1	no	—
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	—	2	1	no	—
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	1	no	—
905	C₂²	—	2	1	no	—
906	C₂²	—	2	1	no	—
907	C₂²	—	2	1	no	—
908	C₂²	—	2	1	no	—
909	C₂²	—	8	2	no	—
910	C₂²	—	106	1	no	—
911	C₂²	—	106	1	no	—
912	C₂²	—	106	1	no	—
913	C₂²	—	106	1	no	—
914	C₂²	—	106	1	no	—
915	C₂²	—	106	1	no	—
916	C₂²	C₂⁴×D₅₃	1	1	yes	characteristic
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	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	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	C₄	—	106	1	no	—
938	C₄	—	106	1	no	—
939	C₄	—	106	1	no	—
940	C₄	—	106	1	no	—
941	C₂	—	4	1	no	—
942	C₂	—	4	1	no	—
943	C₂	—	4	1	no	—
944	C₂	—	4	1	no	—
945	C₂	—	4	1	no	—
946	C₂	—	212	1	no	—
947	C₂	—	212	1	no	—
948	C₂	#16811458	1	1	yes	characteristic
949	C₂	#16811458	1	1	yes	characteristic
950	C₂	#16811459	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁵
Fitting	C₅₃×#538	C₂
hypercenter	#538	D₅₃
hypocenter	C₅₃	#3566
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #16811373	C₂	semidirect
2. #16811368	C₂	semidirect
3. #16811368	C₂	semidirect
4. #16811362	C₂	semidirect
5. #16811355	C₂	semidirect
6. #16811342	C₂	semidirect
7. #16811335	C₂	semidirect
8. #16811325	C₂	semidirect
9. #16811323	C₂	semidirect
10. #16811320	C₂	semidirect
11. #16811313	C₂	semidirect
12. #16811309	C₂	semidirect
13. #16811309	C₂	semidirect
14. #16811304	C₂	semidirect
15. #16811299	C₂	semidirect
16. #16811299	C₂	semidirect
17. #16811243	C₂	semidirect
18. #16811241	C₂	semidirect
19. #16811238	C₂	semidirect
20. #16811233	C₂	semidirect
21. #16811230	C₂	semidirect
22. #16811223	C₂	semidirect
23. #16811217	C₂	semidirect
24. #16811216	C₂	semidirect
25. #16811214	C₂	semidirect
26. #16811208	C₂	semidirect
27. #16811208	C₂	semidirect
28. #16811154	C₂	semidirect
29. #16811153	C₂	semidirect
30. #16811150	C₂	semidirect
31. C₅₃×#538	C₂	semidirect
32. #13133216	C₂²	semidirect
33. #13133215	C₂²	semidirect
34. #13133215	C₂²	semidirect
36. #13133212	C₂²	semidirect
37. #13133212	C₂²	semidirect
50. #13133210	C₂²	semidirect
51. #13133210	C₂²	semidirect
52. #13133210	C₂²	semidirect
53. #13133210	C₂²	semidirect
54. #13133209	C₂²	semidirect
55. #13133209	C₂²	semidirect
56. #13133208	C₂²	semidirect
57. #13133208	C₂²	semidirect
58. #13133208	C₂²	semidirect
59. #13133208	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. #13133206	C₂²	semidirect
74. #13133203	C₂²	semidirect
75. #13133203	C₂²	semidirect
76. #13133202	C₂²	semidirect
79. #13133201	C₂²	semidirect
82. #13133200	C₂²	semidirect
83. #13133200	C₂²	semidirect
90. #13133199	C₂²	semidirect
97. #13133198	C₂²	semidirect
98. #13133197	C₂²	semidirect
101. #13133196	C₂²	semidirect
102. #13133196	C₂²	semidirect
103. #13133195	C₂²	semidirect
104. #13133195	C₂²	semidirect
105. #13133195	C₂²	semidirect
112. #13133194	C₂²	semidirect
113. #13133194	C₂²	semidirect
114. #13133194	C₂²	semidirect
117. #13133190	C₂²	semidirect
124. #13133189	C₂²	semidirect
129. #13133188	C₂²	semidirect
132. Q₈×Dic₅₃	C₂²	semidirect
133. C₄×Dic₁₀₆	C₂²	semidirect
134. C₄×Dic₁₀₆	C₂²	semidirect
135. C₄×Dic₁₀₆	C₂²	semidirect
136. #13133182	C₂²	semidirect
137. #13133182	C₂²	semidirect
138. C₄×D₂₁₂	C₂²	semidirect
143. D₄×Dic₅₃	C₂²	semidirect
146. C₄×C₂²⋊D₅₃	C₂²	semidirect
147. C₄×C₂²⋊D₅₃	C₂²	semidirect
152. #13133177	C₂²	semidirect
153. #13133177	C₂²	semidirect
156. #13133175	C₂²	semidirect
157. #13133175	C₂²	semidirect
158. #13133174	C₂²	semidirect
159. #13133174	C₂²	semidirect
164. #13133173	C₂²	semidirect
165. #13133173	C₂²	semidirect
166. C₂×C₄⋊Dic₅₃	C₂²	semidirect
167. C₄⋊C₄×D₅₃	C₂²	semidirect
168. C₄⋊C₄×D₅₃	C₂²	semidirect
171. C₂×C₄×Dic₅₃	C₂²	semidirect
503. #538	D₅₃	semidirect
507. C₅₃	#3566	semidirect