Subgroups — #28249218

Order 13568.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811153	C₂	1	1	yes	maximal, characteristic
2	#20283886	C₂	1	2	yes	maximal, complemented
3	#20283879	C₂	1	2	yes	maximal, complemented
4	#20283872	C₂	1	2	yes	maximal, complemented
5	#20283868	C₂	1	2	yes	maximal, complemented
6	#20283861	C₂	1	2	yes	maximal, complemented
7	#20283857	C₂	1	2	yes	maximal, complemented
8	#20283855	C₂	1	2	yes	maximal, complemented
9	#20283848	C₂	1	2	yes	maximal, complemented
10	M₁₆×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283666	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄×#11719917	C₂	1	1	yes	maximal, characteristic, complemented
13	M₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283447	C₂	1	1	yes	maximal, characteristic, complemented
16	#20283447	C₂	1	1	yes	maximal, characteristic, complemented
17	#20283351	C₂	1	1	yes	maximal, characteristic, complemented
18	#20283350	C₂	1	1	yes	maximal, characteristic, complemented
19	#20283344	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283278	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283277	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16810646	C₂	1	1	yes	maximal, characteristic, complemented
23	D₄×M₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11719917	C₂²	1	1	yes	characteristic
25	C₂²×#11719917	C₂²	1	1	yes	characteristic
26	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
28	#16811153	C₄	1	1	yes	characteristic
29	#16811153	C₄	1	1	yes	characteristic
30	#16811153	C₄	1	1	yes	characteristic
31	#16811153	C₄	1	1	yes	characteristic
32	#16811153	C₄	1	1	yes	characteristic
33	#16811153	C₄	1	1	yes	characteristic
34	#16811153	C₄	1	1	yes	characteristic
35	#16811153	C₄	1	1	yes	characteristic
36	#16811153	C₂²	1	1	yes	characteristic
37	#16811153	C₂²	1	1	yes	characteristic
38	#16811153	C₂²	1	1	yes	characteristic
39	#16811153	C₂²	1	1	yes	characteristic
40	#16811153	C₂²	1	1	yes	characteristic
41	#16811153	C₂²	1	1	yes	characteristic
42	#16811153	C₂²	1	1	yes	characteristic
43	#16811153	C₂²	1	1	yes	characteristic
44	C₂×#13133212	C₄	1	1	yes	characteristic
45	C₂×#13133210	C₄	1	1	yes	characteristic
46	C₂×#13133207	C₄	1	1	yes	characteristic
47	C₂×#13133203	C₄	1	1	yes	characteristic
48	C₂×#13133201	C₄	1	1	yes	characteristic
49	C₂×#13133198	C₄	1	1	yes	characteristic
50	C₂×#13133194	C₄	1	1	yes	characteristic
51	C₂×#13133189	C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
55	C₂×#13133176	C₂²	1	1	yes	characteristic
56	C₂×#13133174	C₂²	1	1	yes	characteristic
57	C₂²×C₄×Dic₅₃	C₂²	1	1	yes	characteristic
58	#16810753	C₂²	1	2	yes	complemented
59	#16810752	C₂²	1	2	yes	complemented
60	#16810752	C₂²	1	2	yes	complemented
61	#16810751	C₂²	1	2	yes	complemented
62	#16810751	C₂²	1	2	yes	complemented
63	#16810750	C₂²	1	2	yes	complemented
64	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
65	#16810747	C₂²	1	2	yes	complemented
66	#16810701	C₂²	1	2	yes	complemented
67	#16810699	C₂²	1	2	yes	complemented
68	#16810699	C₂²	1	2	yes	complemented
69	#16810698	C₂²	1	2	yes	complemented
70	#16810698	C₂²	1	2	yes	complemented
71	#16810697	C₂²	1	2	yes	complemented
72	#16810697	C₂²	1	2	yes	complemented
73	#16810695	C₂²	1	2	yes	complemented
74	#16810695	C₂²	1	2	yes	complemented
75	#16810694	C₂²	1	2	yes	complemented
76	#16810694	C₂²	1	2	yes	complemented
77	#16810692	C₂²	1	2	yes	complemented
78	#16810692	C₂²	1	2	yes	complemented
79	#16810691	C₂²	1	2	yes	complemented
80	#16810691	C₂²	1	2	yes	complemented
81	D₄×#88322	C₂²	1	2	yes	complemented
82	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
83	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
84	#16810686	C₂²	1	2	yes	complemented
85	#16810686	C₂²	1	2	yes	complemented
86	#16810685	C₂²	1	2	yes	complemented
87	#16810685	C₂²	1	2	yes	complemented
88	#16810682	C₂²	1	2	yes	complemented
89	#16810682	C₂²	1	2	yes	complemented
90	#16810681	C₂²	1	2	yes	complemented
91	#16810681	C₂²	1	2	yes	complemented
92	#16810681	C₂²	1	2	yes	complemented
93	#16810681	C₂²	1	2	yes	complemented
94	#16810677	C₂²	1	2	yes	complemented
95	#16810677	C₂²	1	2	yes	complemented
96	#16810673	C₂²	1	2	yes	complemented
97	#16810673	C₂²	1	2	yes	complemented
98	#16810651	C₂²	1	2	yes	complemented
99	#16810651	C₂²	1	2	yes	complemented
100	#16810649	C₂²	1	2	yes	complemented
101	#16810649	C₂²	1	2	yes	complemented
102	#16810648	C₂²	1	2	yes	complemented
103	#16810648	C₂²	1	2	yes	complemented
104	#16810648	C₂²	1	2	yes	complemented
105	#16810648	C₂²	1	2	yes	complemented
106	#16810647	C₂²	1	1	yes	characteristic
107	#16810646	C₂²	1	1	yes	characteristic
108	#16810646	C₂²	1	1	yes	characteristic
109	#16810646	C₂²	1	1	yes	characteristic
110	#16810646	C₂²	1	1	yes	characteristic
111	#16810646	C₂²	1	1	yes	characteristic
112	#16810646	C₂²	1	1	yes	characteristic
113	#16810646	C₂²	1	1	yes	characteristic
114	#16810646	C₂²	1	1	yes	characteristic
115	#16810646	C₂²	1	2	yes	complemented
116	#16810646	C₂²	1	2	yes	complemented
117	C₂×#13133146	C₂²	1	2	yes	complemented
118	C₂×#13133146	C₂²	1	2	yes	complemented
119	#16810587	C₂²	1	1	yes	characteristic
120	#16810587	C₂²	1	1	yes	characteristic
121	#16810586	C₂²	1	1	yes	characteristic
122	#16810586	C₂²	1	1	yes	characteristic
123	C₄×#11719917	C₂²	1	1	yes	characteristic
124	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
125	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
126	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
127	M₁₆×Dic₅₃	C₂²	1	1	yes	characteristic
128	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
129	C₂²×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
130	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
131	C₅₃×#436	C₂²	1	2	yes	complemented
132	C₅₃×#435	C₂²	1	2	yes	complemented
133	C₅₃×#435	C₂²	1	2	yes	complemented
134	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
135	C₅₃×#423	C₂²	1	1	yes	characteristic
136	C₅₃×#407	C₂²	1	1	yes	characteristic
137	C₅₃×#407	C₂²	1	1	yes	characteristic
138	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
139	C₂²×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
140	C₂²×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
141	C₂²×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
142	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
143	C₂³×Dic₅₃	C₂×C₄	1	1	yes	characteristic
144	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
145	C₂×#11719917	—	4	2	no	—
146	C₂×#11719917	—	4	2	no	—
147	C₂×#11719917	C₂³	1	1	yes	characteristic
148	C₂×#11719917	C₂³	1	1	yes	characteristic
149	C₂×#11719917	C₂³	1	1	yes	characteristic
150	C₂×#11719917	C₂³	1	1	yes	characteristic
151	C₂×#11719917	C₂³	1	2	yes	—
152	C₂×#11719917	C₂³	1	2	yes	—
153	C₂×#11719912	C₂³	1	2	yes	—
154	C₂×#11719912	C₂³	1	2	yes	—
155	M₁₆×D₅₃	—	4	2	no	—
156	M₁₆×D₅₃	—	4	2	no	—
157	C₂²×#88322	C₂³	1	2	yes	—
158	C₂²×#88322	C₂³	1	2	yes	—
159	C₂×C₈×D₅₃	C₂³	1	2	yes	—
160	C₂×C₈×D₅₃	C₂³	1	2	yes	—
161	#13133212	C₂×C₄	1	1	yes	characteristic
162	#13133212	C₂×C₄	1	1	yes	characteristic
163	#13133212	C₂×C₄	1	1	yes	characteristic
164	#13133212	C₂×C₄	1	1	yes	characteristic
165	#13133212	C₂×C₄	1	1	yes	characteristic
166	#13133212	C₂×C₄	1	1	yes	characteristic
167	#13133212	C₂×C₄	1	1	yes	characteristic
168	#13133212	C₂×C₄	1	1	yes	characteristic
169	#13133210	C₂×C₄	1	1	yes	characteristic
170	#13133210	C₂×C₄	1	1	yes	characteristic
171	#13133210	C₂×C₄	1	1	yes	characteristic
172	#13133210	C₂×C₄	1	1	yes	characteristic
173	#13133210	C₂×C₄	1	1	yes	characteristic
174	#13133210	C₂×C₄	1	1	yes	characteristic
175	#13133210	C₂×C₄	1	1	yes	characteristic
176	#13133210	C₂×C₄	1	1	yes	characteristic
177	#13133207	C₂×C₄	1	1	yes	characteristic
178	#13133207	C₂×C₄	1	1	yes	characteristic
179	#13133207	C₂×C₄	1	1	yes	characteristic
180	#13133207	C₂×C₄	1	1	yes	characteristic
181	#13133207	C₂×C₄	1	1	yes	characteristic
182	#13133207	C₂×C₄	1	1	yes	characteristic
183	#13133207	C₂×C₄	1	1	yes	characteristic
184	#13133207	C₂×C₄	1	1	yes	characteristic
185	#13133203	C₂×C₄	1	1	yes	characteristic
186	#13133203	C₂×C₄	1	1	yes	characteristic
187	#13133203	C₂×C₄	1	1	yes	characteristic
188	#13133203	C₂×C₄	1	1	yes	characteristic
189	#13133203	C₂×C₄	1	1	yes	characteristic
190	#13133203	C₂×C₄	1	1	yes	characteristic
191	#13133203	C₂×C₄	1	1	yes	characteristic
192	#13133203	C₂×C₄	1	1	yes	characteristic
193	#13133201	C₂×C₄	1	1	yes	characteristic
194	#13133201	C₂×C₄	1	1	yes	characteristic
195	#13133201	C₂×C₄	1	1	yes	characteristic
196	#13133201	C₂×C₄	1	1	yes	characteristic
197	#13133201	C₂×C₄	1	1	yes	characteristic
198	#13133201	C₂×C₄	1	1	yes	characteristic
199	#13133201	C₂×C₄	1	1	yes	characteristic
200	#13133201	C₂×C₄	1	1	yes	characteristic
201	#13133198	C₂×C₄	1	1	yes	characteristic
202	#13133198	C₂×C₄	1	1	yes	characteristic
203	#13133198	C₂×C₄	1	1	yes	characteristic
204	#13133198	C₂×C₄	1	1	yes	characteristic
205	#13133198	C₂×C₄	1	1	yes	characteristic
206	#13133198	C₂×C₄	1	1	yes	characteristic
207	#13133198	C₂×C₄	1	1	yes	characteristic
208	#13133198	C₂×C₄	1	1	yes	characteristic
209	#13133194	C₂×C₄	1	1	yes	characteristic
210	#13133194	C₂×C₄	1	1	yes	characteristic
211	#13133194	C₂×C₄	1	1	yes	characteristic
212	#13133194	C₂×C₄	1	1	yes	characteristic
213	#13133194	C₂×C₄	1	1	yes	characteristic
214	#13133194	C₂×C₄	1	1	yes	characteristic
215	#13133194	C₂×C₄	1	1	yes	characteristic
216	#13133194	C₂×C₄	1	1	yes	characteristic
217	#13133189	C₂×C₄	1	1	yes	characteristic
218	#13133189	C₂×C₄	1	1	yes	characteristic
219	#13133189	C₂×C₄	1	1	yes	characteristic
220	#13133189	C₂×C₄	1	1	yes	characteristic
221	#13133189	C₂×C₄	1	1	yes	characteristic
222	#13133189	C₂×C₄	1	1	yes	characteristic
223	#13133189	C₂×C₄	1	1	yes	characteristic
224	#13133189	C₂×C₄	1	1	yes	characteristic
225	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
226	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
227	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
228	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
229	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
230	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
231	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
232	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
233	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
234	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
235	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
236	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
237	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
238	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
239	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
240	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
241	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
242	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
243	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
244	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
245	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
246	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
247	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
248	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
249	#13133176	C₂×C₄	1	1	yes	characteristic
250	#13133176	C₂×C₄	1	1	yes	characteristic
251	#13133176	C₂×C₄	1	1	yes	characteristic
252	#13133176	C₂×C₄	1	1	yes	characteristic
253	#13133176	C₂³	1	1	yes	characteristic
254	#13133176	C₂³	1	1	yes	characteristic
255	#13133176	C₂³	1	1	yes	characteristic
256	#13133176	C₂³	1	1	yes	characteristic
257	#13133174	C₂×C₄	1	1	yes	characteristic
258	#13133174	C₂×C₄	1	1	yes	characteristic
259	#13133174	C₂×C₄	1	1	yes	characteristic
260	#13133174	C₂×C₄	1	1	yes	characteristic
261	#13133174	C₂³	1	1	yes	characteristic
262	#13133174	C₂³	1	1	yes	characteristic
263	#13133174	C₂³	1	1	yes	characteristic
264	#13133174	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
266	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
267	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
268	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
269	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
270	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
271	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
272	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
273	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
274	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
275	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
276	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
278	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
279	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
280	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
281	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
285	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
286	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
287	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
288	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₄⋊#88322	C₂³	1	2	yes	—
296	C₄⋊#88322	C₂³	1	2	yes	—
297	#13133146	C₂³	1	2	yes	—
298	#13133146	C₂³	1	2	yes	—
299	#13133146	C₂³	1	2	yes	—
300	#13133146	C₂³	1	2	yes	—
301	#13133146	C₂³	1	2	yes	—
302	#13133146	C₂³	1	2	yes	—
303	#13133146	C₂³	1	2	yes	—
304	#13133146	C₂³	1	2	yes	—
305	#13133146	C₂³	1	2	yes	—
306	#13133146	C₂³	1	2	yes	—
307	#13133146	C₂³	1	2	yes	—
308	#13133146	C₂³	1	2	yes	—
309	#13133146	C₂³	1	2	yes	—
310	#13133146	C₂³	1	2	yes	—
311	#13133146	C₂³	1	2	yes	—
312	#13133146	C₂³	1	2	yes	—
313	C₂²⋊#88322	C₂³	1	2	yes	—
314	C₂²⋊#88322	C₂³	1	2	yes	—
315	C₂²⋊#88322	C₂³	1	2	yes	—
316	C₂²⋊#88322	C₂³	1	2	yes	—
317	#13133129	C₂³	1	2	yes	—
318	#13133129	C₂³	1	2	yes	—
319	#13133129	C₂³	1	2	yes	—
320	#13133129	C₂³	1	2	yes	—
321	#13133128	C₂³	1	2	yes	—
322	#13133127	C₂³	1	2	yes	—
323	#13133127	C₂³	1	2	yes	—
324	#13133127	C₂³	1	2	yes	—
325	#13133127	C₂³	1	2	yes	—
326	C₄×#88322	C₂³	1	2	yes	—
327	C₈×Dic₅₃	C₂³	1	2	yes	—
328	C₈×Dic₅₃	C₂³	1	2	yes	—
329	C₈×Dic₅₃	C₂³	1	2	yes	—
330	C₈×Dic₅₃	C₂³	1	2	yes	—
331	C₂²×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
332	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×M₁₆×C₅₃	—	4	2	no	—
335	C₂×M₁₆×C₅₃	—	4	2	no	—
336	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
341	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
342	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
343	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
344	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
345	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
346	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
347	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
348	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₅₃	C₂×C₄	1	1	yes	characteristic
355	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
356	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
357	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
358	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
359	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
360	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
361	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
362	#97×C₅₃	C₂³	1	2	yes	—
363	C₄×C₈×C₅₃	C₂³	1	2	yes	—
364	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
365	C₂⁴×C₅₃	C₂²×C₄	1	1	yes	characteristic
366	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
367	C₂×D₄×C₅₃	—	4	2	no	—
368	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
369	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
370	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
371	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	2	2	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₂²⋊D₅₃	—	4	2	no	—
390	C₂×C₂²⋊D₅₃	—	4	2	no	—
391	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
392	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
393	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
394	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
395	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
396	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
397	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
398	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
399	C₂²×Dic₅₃	—	4	2	no	—
400	C₂²×Dic₅₃	—	4	2	no	—
401	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
404	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
405	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
408	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
410	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
414	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
416	C₂×C₄×D₅₃	—	2	2	no	—
417	C₂×C₄×D₅₃	—	2	2	no	—
418	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
419	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
420	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₁₀₆	—	4	2	no	—
423	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
424	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
425	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
426	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
427	M₁₆×C₅₃	—	2	2	no	—
428	M₁₆×C₅₃	—	2	2	no	—
429	M₁₆×C₅₃	—	2	2	no	—
430	M₁₆×C₅₃	—	2	2	no	—
431	M₁₆×C₅₃	—	4	2	no	—
432	M₁₆×C₅₃	—	4	2	no	—
433	C₂×C₈×C₅₃	—	4	2	no	—
434	C₂×C₈×C₅₃	—	4	2	no	—
435	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
436	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
437	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
438	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
439	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
440	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
441	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
442	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
443	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
444	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
445	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
446	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
447	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
448	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
449	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
450	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
451	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
452	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
453	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
456	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
457	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
458	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
459	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
460	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
461	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
462	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
463	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
464	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
465	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
466	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
467	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
468	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
469	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
470	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
471	#11719921	C₂²×C₄	1	1	yes	characteristic
472	#11719921	C₂²×C₄	1	1	yes	characteristic
473	#11719921	C₂²×C₄	1	1	yes	characteristic
474	#11719921	C₂²×C₄	1	1	yes	characteristic
475	#11719921	C₂²×C₄	1	1	yes	characteristic
476	#11719921	C₂²×C₄	1	1	yes	characteristic
477	#11719921	C₂²×C₄	1	1	yes	characteristic
478	#11719921	C₂²×C₄	1	1	yes	characteristic
479	#11719921	C₂²×C₄	1	1	yes	characteristic
480	#11719921	C₂²×C₄	1	1	yes	characteristic
481	#11719921	C₂²×C₄	1	1	yes	characteristic
482	#11719921	C₂²×C₄	1	1	yes	characteristic
483	#11719921	C₂²×C₄	1	1	yes	characteristic
484	#11719921	C₂²×C₄	1	1	yes	characteristic
485	#11719921	C₂²×C₄	1	1	yes	characteristic
486	#11719921	C₂²×C₄	1	1	yes	characteristic
487	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
488	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
489	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
490	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
491	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
492	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
493	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
494	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
495	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
496	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
497	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
498	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
499	#11719919	C₂²×C₄	1	1	yes	characteristic
500	#11719919	C₂²×C₄	1	1	yes	characteristic
501	#11719919	C₂²×C₄	1	1	yes	characteristic
502	#11719919	C₂²×C₄	1	1	yes	characteristic
503	#11719919	C₂²×C₄	1	1	yes	characteristic
504	#11719919	C₂²×C₄	1	1	yes	characteristic
505	#11719919	C₂²×C₄	1	1	yes	characteristic
506	#11719919	C₂²×C₄	1	1	yes	characteristic
507	#11719919	C₂²×C₄	1	1	yes	characteristic
508	#11719919	C₂²×C₄	1	1	yes	characteristic
509	#11719919	C₂²×C₄	1	1	yes	characteristic
510	#11719919	C₂²×C₄	1	1	yes	characteristic
511	#11719919	C₂²×C₄	1	1	yes	characteristic
512	#11719919	C₂²×C₄	1	1	yes	characteristic
513	#11719919	C₂²×C₄	1	1	yes	characteristic
514	#11719919	C₂²×C₄	1	1	yes	characteristic
515	#11719919	C₂²×C₄	1	1	yes	characteristic
516	#11719919	C₂²×C₄	1	1	yes	characteristic
517	#11719919	C₂²×C₄	1	1	yes	characteristic
518	#11719919	C₂²×C₄	1	1	yes	characteristic
519	#11719919	C₂²×C₄	1	1	yes	characteristic
520	#11719919	C₂²×C₄	1	1	yes	characteristic
521	#11719919	C₂²×C₄	1	1	yes	characteristic
522	#11719919	C₂²×C₄	1	1	yes	characteristic
523	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
524	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
525	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
526	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
527	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
528	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
529	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
530	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
531	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
532	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
533	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
534	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
535	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
536	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
537	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
538	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
539	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
540	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
541	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
542	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
543	#11719917	—	2	2	no	—
544	#11719917	—	2	2	no	—
545	#11719917	—	2	2	no	—
546	#11719917	—	2	2	no	—
547	#11719917	—	4	2	no	—
548	#11719917	—	4	2	no	—
549	C₂×#88322	—	4	2	no	—
550	C₂×#88322	—	4	2	no	—
551	C₂×#88322	C₂⁴	1	2	yes	—
552	C₂×#88322	C₂⁴	1	2	yes	—
553	C₂×#88322	C₂⁴	1	2	yes	—
554	C₂×#88322	C₂⁴	1	2	yes	—
555	#11719912	—	4	2	no	—
556	#11719912	—	4	2	no	—
557	C₈×D₅₃	—	4	2	no	—
558	C₈×D₅₃	—	4	2	no	—
559	C₂³×C₅₃	—	2	2	no	—
560	C₂³×C₅₃	—	2	2	no	—
561	C₂³×C₅₃	—	2	2	no	—
562	C₂³×C₅₃	—	4	1	no	—
563	C₂³×C₅₃	—	4	1	no	—
564	C₂³×C₅₃	—	4	1	no	—
565	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
566	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
567	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
568	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
569	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
570	C₂²×D₅₃	—	2	2	no	—
571	C₂²×D₅₃	—	4	1	no	—
572	C₂²×D₅₃	—	4	1	no	—
573	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
574	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
575	D₄×C₅₃	—	2	2	no	—
576	D₄×C₅₃	—	2	2	no	—
577	D₄×C₅₃	—	4	1	no	—
578	D₄×C₅₃	—	4	1	no	—
579	C₂×C₄×C₅₃	—	2	2	no	—
580	C₂×C₄×C₅₃	—	2	2	no	—
581	C₂×C₄×C₅₃	—	2	2	no	—
582	C₂×C₄×C₅₃	—	2	2	no	—
583	C₂×C₄×C₅₃	—	2	2	no	—
584	C₂×C₄×C₅₃	—	2	2	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	4	1	no	—
594	C₂×C₄×C₅₃	—	4	1	no	—
595	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
596	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
597	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
598	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
599	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
600	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
601	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
602	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
603	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
604	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
605	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
606	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
607	C₂²⋊D₅₃	—	2	2	no	—
608	C₂²⋊D₅₃	—	2	2	no	—
609	C₂²⋊D₅₃	—	2	2	no	—
610	C₂²⋊D₅₃	—	2	2	no	—
611	C₂²⋊D₅₃	—	4	1	no	—
612	C₂²⋊D₅₃	—	4	1	no	—
613	C₂²⋊D₅₃	—	4	1	no	—
614	C₂²⋊D₅₃	—	4	1	no	—
615	C₂×Dic₅₃	—	2	2	no	—
616	C₂×Dic₅₃	—	2	2	no	—
617	C₂×Dic₅₃	—	2	2	no	—
618	C₂×Dic₅₃	—	2	2	no	—
619	C₂×Dic₅₃	—	2	2	no	—
620	C₂×Dic₅₃	—	2	2	no	—
621	C₂×Dic₅₃	—	4	1	no	—
622	C₂×Dic₅₃	—	4	1	no	—
623	C₂×Dic₅₃	—	4	1	no	—
624	C₂×Dic₅₃	—	4	1	no	—
625	C₂×Dic₅₃	—	4	1	no	—
626	C₂×Dic₅₃	—	4	1	no	—
627	C₂×Dic₅₃	—	4	1	no	—
628	C₂×Dic₅₃	—	4	1	no	—
629	C₂×Dic₅₃	—	4	1	no	—
630	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
631	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
632	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
633	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
634	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
635	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
636	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
637	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
638	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
639	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
640	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
641	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
642	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
643	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
644	C₄×D₅₃	—	2	2	no	—
645	C₄×D₅₃	—	2	2	no	—
646	C₄×D₅₃	—	2	1	no	—
647	C₄×D₅₃	—	2	1	no	—
648	C₄×D₅₃	—	2	1	no	—
649	C₄×D₅₃	—	2	1	no	—
650	Dic₁₀₆	—	2	2	no	—
651	Dic₁₀₆	—	2	2	no	—
652	Dic₁₀₆	—	4	1	no	—
653	Dic₁₀₆	—	4	1	no	—
654	C₈×C₅₃	—	2	2	no	—
655	C₈×C₅₃	—	2	2	no	—
656	C₈×C₅₃	—	2	2	no	—
657	C₈×C₅₃	—	2	2	no	—
658	#88322	—	2	2	no	—
659	#88322	—	2	2	no	—
660	#88322	—	2	2	no	—
661	#88322	—	2	2	no	—
662	#60264	—	53	1	no	maximal, Sylow
663	C₂²×C₅₃	—	2	1	no	—
664	C₂²×C₅₃	—	2	1	no	—
665	C₂²×C₅₃	—	2	1	no	—
666	C₂²×C₅₃	—	2	1	no	—
667	C₂²×C₅₃	—	2	1	no	—
668	C₂²×C₅₃	—	2	1	no	—
669	C₂²×C₅₃	—	2	1	no	—
670	C₂²×C₅₃	—	2	1	no	—
671	C₂²×C₅₃	—	2	1	no	—
672	C₂²×C₅₃	—	2	1	no	—
673	C₂²×C₅₃	—	2	1	no	—
674	C₂²×C₅₃	—	2	1	no	—
675	C₂²×C₅₃	—	2	1	no	—
676	C₂²×C₅₃	—	4	4	no	—
677	C₂²×C₅₃	—	8	2	no	—
678	C₂²×C₅₃	#520	1	2	yes	—
679	C₂²×C₅₃	#568	1	2	yes	—
680	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
681	C₂×D₅₃	—	2	1	no	—
682	C₂×D₅₃	—	2	1	no	—
683	C₂×D₅₃	—	2	1	no	—
684	C₂×D₅₃	—	2	1	no	—
685	C₂×D₅₃	—	2	1	no	—
686	C₂×D₅₃	—	2	1	no	—
687	C₂×D₅₃	—	8	2	no	—
688	C₄×C₅₃	—	2	1	no	—
689	C₄×C₅₃	—	2	1	no	—
690	C₄×C₅₃	—	2	1	no	—
691	C₄×C₅₃	—	2	1	no	—
692	C₄×C₅₃	—	2	1	no	—
693	C₄×C₅₃	—	2	1	no	—
694	C₄×C₅₃	—	2	1	no	—
695	C₄×C₅₃	—	2	1	no	—
696	C₄×C₅₃	#520	1	2	yes	—
697	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
698	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
699	Dic₅₃	—	2	1	no	—
700	Dic₅₃	—	2	1	no	—
701	Dic₅₃	—	2	1	no	—
702	Dic₅₃	—	2	1	no	—
703	Dic₅₃	—	2	1	no	—
704	Dic₅₃	—	2	1	no	—
705	Dic₅₃	—	2	1	no	—
706	Dic₅₃	—	2	1	no	—
707	Dic₅₃	—	2	1	no	—
708	Dic₅₃	—	2	1	no	—
709	Dic₅₃	—	2	1	no	—
710	Dic₅₃	—	2	1	no	—
711	Dic₅₃	—	2	1	no	—
712	Dic₅₃	#568	1	2	yes	—
713	C₂×#529	—	53	1	no	—
714	#2995	—	53	2	no	—
715	#2995	—	53	2	no	—
716	#2994	—	53	2	no	—
717	#2994	—	53	2	no	—
718	#2993	—	53	2	no	—
719	#2993	—	53	2	no	—
720	#2992	—	53	2	no	—
721	#2992	—	53	2	no	—
722	Q₈×M₁₆	—	53	1	no	—
723	Q₈×M₁₆	—	53	1	no	—
724	D₄×M₁₆	—	53	1	no	—
725	D₄×M₁₆	—	53	1	no	—
726	D₄×M₁₆	—	53	1	no	—
727	D₄×M₁₆	—	53	1	no	—
728	D₄×M₁₆	—	53	1	no	—
729	D₄×M₁₆	D₅₃	1	1	yes	characteristic, complemented
730	#2921	—	53	1	no	—
731	#2921	—	53	1	no	—
732	#2920	—	53	1	no	—
733	#2905	—	53	1	no	—
734	#2905	—	53	1	no	—
735	C₂×#423	—	53	1	no	—
736	C₂×C₅₃	—	2	2	no	—
737	C₂×C₅₃	—	2	2	no	—
738	C₂×C₅₃	—	4	1	no	—
739	C₂×C₅₃	—	4	1	no	—
740	C₂×C₅₃	—	4	1	no	—
741	C₂×C₅₃	C₂×#520	1	1	yes	characteristic
742	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
743	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
744	D₅₃	—	4	1	no	—
745	D₅₃	—	4	1	no	—
746	C₂²×M₁₆	—	53	1	no	—
747	C₂²×M₁₆	—	53	1	no	—
748	C₂²×M₁₆	—	53	1	no	—
749	C₂²×M₁₆	—	53	1	no	—
750	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
751	C₂²×M₁₆	C₂×D₅₃	1	1	yes	characteristic
752	#529	—	53	1	no	—
753	#529	—	53	1	no	—
754	#529	—	53	1	no	—
755	#529	—	53	1	no	—
756	#529	—	53	1	no	—
757	#529	—	53	1	no	—
758	#529	—	53	1	no	—
759	#529	—	53	1	no	—
760	#529	—	53	1	no	—
761	#529	—	53	1	no	—
762	#529	—	53	1	no	—
763	#529	—	53	1	no	—
764	#529	—	53	1	no	—
765	#529	—	53	1	no	—
766	#529	—	53	1	no	—
767	#529	—	53	1	no	—
768	C₂×#126	—	53	1	no	—
769	C₂×#126	—	53	1	no	—
770	C₂×#125	—	53	1	no	—
771	C₂×#124	—	53	1	no	—
772	C₂×#123	—	53	1	no	—
773	C₂×#123	—	53	1	no	—
774	C₂×C₂²⋊Q₈	—	53	1	no	—
775	C₂×#121	—	53	1	no	—
776	C₂×C₄×Q₈	—	53	1	no	—
777	C₂×C₄×D₄	—	53	1	no	—
778	C₂×C₄×D₄	—	53	1	no	—
779	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
780	C₂×#117	—	53	1	no	—
781	C₂×#117	—	53	1	no	—
782	C₂²×C₄²	—	53	1	no	—
783	#446	—	53	2	no	—
784	#446	—	53	2	no	—
785	#446	—	53	2	no	—
786	#446	—	53	2	no	—
787	#446	—	53	2	no	—
788	#446	—	53	2	no	—
789	C₈×Q₈	—	53	2	no	—
790	C₈×Q₈	—	53	2	no	—
791	#436	—	53	2	no	—
792	#436	—	53	2	no	—
793	#436	—	53	2	no	—
794	#436	—	53	2	no	—
795	#436	—	53	2	no	—
796	#436	C₂×D₅₃	1	2	yes	complemented
797	#435	—	53	2	no	—
798	#435	—	53	2	no	—
799	#435	—	53	2	no	—
800	#435	—	53	2	no	—
801	#435	—	53	2	no	—
802	#435	—	53	2	no	—
803	#435	—	53	2	no	—
804	#435	—	53	2	no	—
805	#435	—	53	2	no	—
806	#435	—	53	2	no	—
807	#435	C₂×D₅₃	1	2	yes	complemented
808	#435	C₂×D₅₃	1	2	yes	complemented
809	C₈×D₄	—	53	2	no	—
810	C₈×D₄	—	53	2	no	—
811	C₈×D₄	—	53	2	no	—
812	C₈×D₄	—	53	2	no	—
813	C₈×D₄	—	53	2	no	—
814	C₈×D₄	C₂×D₅₃	1	2	yes	complemented
815	#433	—	53	2	no	—
816	#433	—	53	2	no	—
817	#433	—	53	2	no	—
818	#433	—	53	2	no	—
819	#433	—	53	2	no	—
820	#433	—	53	2	no	—
821	#433	—	53	2	no	—
822	#433	—	53	2	no	—
823	#432	—	53	2	no	—
824	#432	—	53	2	no	—
825	#431	—	53	2	no	—
826	#431	—	53	2	no	—
827	#424	—	53	2	no	—
828	#424	—	53	2	no	—
829	#424	—	53	2	no	—
830	#424	—	53	2	no	—
831	#424	—	53	2	no	—
832	#424	—	53	2	no	—
833	#424	—	53	2	no	—
834	#424	—	53	2	no	—
835	#423	—	53	1	no	—
836	#423	—	53	1	no	—
837	#423	—	53	1	no	—
838	#423	—	53	1	no	—
839	#423	—	53	2	no	—
840	#423	—	53	2	no	—
841	#423	—	53	1	no	—
842	#423	—	53	1	no	—
843	#423	—	53	1	no	—
844	#423	—	53	1	no	—
845	#423	—	53	1	no	—
846	#423	C₂×D₅₃	1	1	yes	characteristic
847	C₂×C₄⋊C₈	—	53	2	no	—
848	C₂×C₄⋊C₈	—	53	2	no	—
849	#407	—	53	1	no	—
850	#407	—	53	1	no	—
851	#407	—	53	1	no	—
852	#407	—	53	1	no	—
853	#407	C₂×D₅₃	1	1	yes	characteristic
854	#407	C₂×D₅₃	1	1	yes	characteristic
855	C₄×M₁₆	—	53	1	no	—
856	C₄×M₁₆	—	53	1	no	—
857	C₄×M₁₆	—	53	1	no	—
858	C₄×M₁₆	—	53	1	no	—
859	C₄×M₁₆	—	53	1	no	—
860	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
861	C₅₃	#60264	1	1	yes	characteristic, complemented, Sylow
862	C₂²×Q₈	—	53	1	no	—
863	C₂²×D₄	—	53	1	no	—
864	C₂²×D₄	—	53	1	no	—
865	C₂²×D₄	C₄×D₅₃	1	1	yes	characteristic
866	C₂³×C₄	—	53	1	no	—
867	C₂³×C₄	—	53	1	no	—
868	C₂³×C₄	—	53	1	no	—
869	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
870	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
871	C₂×M₁₆	—	4	2	no	—
872	C₂×M₁₆	—	4	2	no	—
873	C₂×M₁₆	—	53	1	no	—
874	C₂×M₁₆	—	53	1	no	—
875	C₂×M₁₆	—	53	1	no	—
876	C₂×M₁₆	—	53	1	no	—
877	C₂×M₁₆	—	53	2	no	—
878	C₂×M₁₆	—	53	2	no	—
879	C₂×M₁₆	—	53	2	no	—
880	C₂×M₁₆	—	53	2	no	—
881	C₂×M₁₆	—	212	2	no	—
882	C₂×M₁₆	—	212	2	no	—
883	C₂×M₁₆	—	212	2	no	—
884	C₂×M₁₆	—	212	2	no	—
885	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
886	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
887	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
888	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
889	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
890	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
891	C₂²×C₈	—	53	2	no	—
892	C₂²×C₈	—	53	2	no	—
893	C₂²×C₈	—	53	2	no	—
894	C₂²×C₈	—	53	2	no	—
895	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
896	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
897	#126	—	53	1	no	—
898	#126	—	53	1	no	—
899	#126	—	53	1	no	—
900	#126	—	53	1	no	—
901	#126	—	53	1	no	—
902	#126	—	53	1	no	—
903	#126	—	53	1	no	—
904	#126	—	53	1	no	—
905	#126	—	53	1	no	—
906	#126	—	53	1	no	—
907	#126	—	53	1	no	—
908	#126	—	53	1	no	—
909	#126	—	53	1	no	—
910	#126	—	53	1	no	—
911	#126	—	53	1	no	—
912	#126	—	53	1	no	—
913	#125	—	53	1	no	—
914	#125	—	53	1	no	—
915	#125	—	53	1	no	—
916	#125	—	53	1	no	—
917	#125	—	53	1	no	—
918	#125	—	53	1	no	—
919	#125	—	53	1	no	—
920	#125	—	53	1	no	—
921	#124	—	53	1	no	—
922	#124	—	53	1	no	—
923	#124	—	53	1	no	—
924	#124	—	53	1	no	—
925	#124	—	53	1	no	—
926	#124	—	53	1	no	—
927	#124	—	53	1	no	—
928	#124	—	53	1	no	—
929	#123	—	53	1	no	—
930	#123	—	53	1	no	—
931	#123	—	53	1	no	—
932	#123	—	53	1	no	—
933	#123	—	53	1	no	—
934	#123	—	53	1	no	—
935	#123	—	53	1	no	—
936	#123	—	53	1	no	—
937	#123	—	53	1	no	—
938	#123	—	53	1	no	—
939	#123	—	53	1	no	—
940	#123	—	53	1	no	—
941	#123	—	53	1	no	—
942	#123	—	53	1	no	—
943	#123	—	53	1	no	—
944	#123	—	53	1	no	—
945	C₂²⋊Q₈	—	53	1	no	—
946	C₂²⋊Q₈	—	53	1	no	—
947	C₂²⋊Q₈	—	53	1	no	—
948	C₂²⋊Q₈	—	53	1	no	—
949	C₂²⋊Q₈	—	53	1	no	—
950	C₂²⋊Q₈	—	53	1	no	—
951	C₂²⋊Q₈	—	53	1	no	—
952	C₂²⋊Q₈	—	53	1	no	—
953	#121	—	53	1	no	—
954	#121	—	53	1	no	—
955	#121	—	53	1	no	—
956	#121	—	53	1	no	—
957	#121	—	53	1	no	—
958	#121	—	53	1	no	—
959	#121	—	53	1	no	—
960	#121	—	53	1	no	—
961	C₄×Q₈	—	53	1	no	—
962	C₄×Q₈	—	53	1	no	—
963	C₄×Q₈	—	53	1	no	—
964	C₄×Q₈	—	53	1	no	—
965	C₄×Q₈	—	53	1	no	—
966	C₄×Q₈	—	53	1	no	—
967	C₄×Q₈	—	53	1	no	—
968	C₄×Q₈	—	53	1	no	—
969	C₄×D₄	—	53	1	no	—
970	C₄×D₄	—	53	1	no	—
971	C₄×D₄	—	53	1	no	—
972	C₄×D₄	—	53	1	no	—
973	C₄×D₄	—	53	1	no	—
974	C₄×D₄	—	53	1	no	—
975	C₄×D₄	—	53	1	no	—
976	C₄×D₄	—	53	1	no	—
977	C₄×D₄	—	53	1	no	—
978	C₄×D₄	—	53	1	no	—
979	C₄×D₄	—	53	1	no	—
980	C₄×D₄	—	53	1	no	—
981	C₄×D₄	—	53	1	no	—
982	C₄×D₄	—	53	1	no	—
983	C₄×D₄	—	53	1	no	—
984	C₄×D₄	—	53	1	no	—
985	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
986	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
987	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
988	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
989	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
990	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
991	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
992	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
993	#117	—	53	1	no	—
994	#117	—	53	1	no	—
995	#117	—	53	1	no	—
996	#117	—	53	1	no	—
997	#117	—	53	1	no	—
998	#117	—	53	1	no	—
999	#117	—	53	1	no	—
1000	#117	—	53	1	no	—
1001	#117	—	53	1	no	—
1002	#117	—	53	1	no	—
1003	#117	—	53	1	no	—
1004	#117	—	53	1	no	—
1005	#117	—	53	1	no	—
1006	#117	—	53	1	no	—
1007	#117	—	53	1	no	—
1008	#117	—	53	1	no	—
1009	C₂×C₄⋊C₄	—	53	1	no	—
1010	C₂×C₄⋊C₄	—	53	1	no	—
1011	C₂×C₄⋊C₄	—	53	1	no	—
1012	C₂×C₄⋊C₄	—	53	1	no	—
1013	C₂×C₄⋊C₄	—	53	1	no	—
1014	C₂×C₄⋊C₄	—	53	1	no	—
1015	C₂×C₄⋊C₄	—	53	1	no	—
1016	C₂×C₄⋊C₄	—	53	1	no	—
1017	C₂×C₄⋊C₄	—	53	1	no	—
1018	C₂×C₄⋊C₄	C₄×D₅₃	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	53	1	no	—
1023	C₂×C₂²⋊C₄	—	53	1	no	—
1024	C₂×C₂²⋊C₄	—	53	1	no	—
1025	C₂×C₂²⋊C₄	—	53	1	no	—
1026	C₂×C₂²⋊C₄	—	53	1	no	—
1027	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₄×D₅₃	1	1	yes	characteristic
1029	C₂×C₄²	—	53	1	no	—
1030	C₂×C₄²	—	53	1	no	—
1031	C₂×C₄²	—	53	1	no	—
1032	C₂×C₄²	—	53	1	no	—
1033	C₂×C₄²	—	53	1	no	—
1034	C₂×C₄²	—	53	1	no	—
1035	C₂×C₄²	—	53	1	no	—
1036	C₂×C₄²	—	53	1	no	—
1037	C₂×C₄²	—	53	1	no	—
1038	C₂×C₄²	—	53	1	no	—
1039	C₂×C₄²	—	53	1	no	—
1040	C₂×C₄²	—	53	1	no	—
1041	C₂×C₄²	—	53	1	no	—
1042	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1043	C₄⋊C₈	—	53	2	no	—
1044	C₄⋊C₈	—	53	2	no	—
1045	C₄⋊C₈	—	53	2	no	—
1046	C₄⋊C₈	—	53	2	no	—
1047	C₄⋊C₈	—	53	2	no	—
1048	C₄⋊C₈	—	53	2	no	—
1049	C₄⋊C₈	—	53	2	no	—
1050	C₄⋊C₈	—	53	2	no	—
1051	C₄⋊C₈	—	53	2	no	—
1052	C₄⋊C₈	—	53	2	no	—
1053	C₄⋊C₈	—	53	2	no	—
1054	C₄⋊C₈	—	53	2	no	—
1055	C₄⋊C₈	—	53	2	no	—
1056	C₄⋊C₈	—	53	2	no	—
1057	C₄⋊C₈	—	53	2	no	—
1058	C₄⋊C₈	—	53	2	no	—
1059	C₄⋊C₈	—	53	2	no	—
1060	C₄⋊C₈	—	53	2	no	—
1061	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
1062	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
1063	C₂²⋊C₈	—	53	2	no	—
1064	C₂²⋊C₈	—	53	2	no	—
1065	C₂²⋊C₈	—	53	2	no	—
1066	C₂²⋊C₈	—	53	2	no	—
1067	C₂²⋊C₈	—	53	2	no	—
1068	C₂²⋊C₈	—	53	2	no	—
1069	C₂²⋊C₈	—	53	2	no	—
1070	C₂²⋊C₈	—	53	2	no	—
1071	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1072	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1073	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1074	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1075	#97	—	53	2	no	—
1076	#97	—	53	2	no	—
1077	#97	—	53	2	no	—
1078	#97	—	53	2	no	—
1079	#97	—	53	2	no	—
1080	#97	C₂²×D₅₃	1	2	yes	—
1081	C₄×C₈	—	53	2	no	—
1082	C₄×C₈	—	53	2	no	—
1083	C₄×C₈	—	53	2	no	—
1084	C₄×C₈	—	53	2	no	—
1085	C₄×C₈	—	53	2	no	—
1086	C₄×C₈	C₂²×D₅₃	1	2	yes	—
1087	C₂⁴	—	53	1	no	—
1088	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
1089	C₂⁴	C₂×C₄×D₅₃	1	1	yes	characteristic
1090	C₂×Q₈	—	53	1	no	—
1091	C₂×Q₈	—	53	1	no	—
1092	C₂×Q₈	—	53	1	no	—
1093	C₂×Q₈	—	53	1	no	—
1094	C₂×Q₈	—	212	2	no	—
1095	C₂×D₄	—	4	2	no	—
1096	C₂×D₄	—	53	1	no	—
1097	C₂×D₄	—	53	1	no	—
1098	C₂×D₄	—	53	1	no	—
1099	C₂×D₄	—	53	1	no	—
1100	C₂×D₄	—	53	1	no	—
1101	C₂×D₄	—	53	1	no	—
1102	C₂×D₄	—	53	1	no	—
1103	C₂×D₄	—	53	1	no	—
1104	C₂×D₄	—	212	2	no	—
1105	C₂×D₄	—	212	2	no	—
1106	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1107	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1108	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1109	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1110	C₂²×C₄	—	2	2	no	—
1111	C₂²×C₄	—	2	2	no	—
1112	C₂²×C₄	—	2	2	no	—
1113	C₂²×C₄	—	2	2	no	—
1114	C₂²×C₄	—	53	1	no	—
1115	C₂²×C₄	—	53	1	no	—
1116	C₂²×C₄	—	53	1	no	—
1117	C₂²×C₄	—	53	1	no	—
1118	C₂²×C₄	—	53	1	no	—
1119	C₂²×C₄	—	53	1	no	—
1120	C₂²×C₄	—	53	1	no	—
1121	C₂²×C₄	—	53	1	no	—
1122	C₂²×C₄	—	53	1	no	—
1123	C₂²×C₄	—	53	1	no	—
1124	C₂²×C₄	—	53	1	no	—
1125	C₂²×C₄	—	53	1	no	—
1126	C₂²×C₄	—	53	1	no	—
1127	C₂²×C₄	—	53	1	no	—
1128	C₂²×C₄	—	53	1	no	—
1129	C₂²×C₄	—	53	1	no	—
1130	C₂²×C₄	—	53	1	no	—
1131	C₂²×C₄	—	53	1	no	—
1132	C₂²×C₄	—	53	1	no	—
1133	C₂²×C₄	—	106	2	no	—
1134	C₂²×C₄	—	106	2	no	—
1135	C₂²×C₄	—	212	2	no	—
1136	C₂²×C₄	—	212	2	no	—
1137	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1138	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1140	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1143	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1147	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1148	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1150	M₁₆	—	2	2	no	—
1151	M₁₆	—	2	2	no	—
1152	M₁₆	—	2	2	no	—
1153	M₁₆	—	2	2	no	—
1154	M₁₆	—	4	2	no	—
1155	M₁₆	—	4	2	no	—
1156	M₁₆	—	106	2	no	—
1157	M₁₆	—	106	2	no	—
1158	M₁₆	—	106	2	no	—
1159	M₁₆	—	106	2	no	—
1160	M₁₆	—	212	2	no	—
1161	M₁₆	—	212	2	no	—
1162	M₁₆	—	212	2	no	—
1163	M₁₆	—	212	2	no	—
1164	C₂×C₈	—	4	2	no	—
1165	C₂×C₈	—	4	2	no	—
1166	C₂×C₈	—	53	2	no	—
1167	C₂×C₈	—	53	2	no	—
1168	C₂×C₈	—	53	2	no	—
1169	C₂×C₈	—	53	2	no	—
1170	C₂×C₈	—	212	2	no	—
1171	C₂×C₈	—	212	2	no	—
1172	C₂×C₈	—	212	2	no	—
1173	C₂×C₈	—	212	2	no	—
1174	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1175	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1176	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1177	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1178	C₄⋊C₄	—	53	1	no	—
1179	C₄⋊C₄	—	53	1	no	—
1180	C₄⋊C₄	—	53	1	no	—
1181	C₄⋊C₄	—	53	1	no	—
1182	C₄⋊C₄	—	53	1	no	—
1183	C₄⋊C₄	—	53	1	no	—
1184	C₄⋊C₄	—	53	1	no	—
1185	C₄⋊C₄	—	53	1	no	—
1186	C₄⋊C₄	—	53	1	no	—
1187	C₄⋊C₄	—	53	1	no	—
1188	C₄⋊C₄	—	53	1	no	—
1189	C₄⋊C₄	—	53	1	no	—
1190	C₄⋊C₄	—	53	1	no	—
1191	C₄⋊C₄	—	53	1	no	—
1192	C₄⋊C₄	—	53	1	no	—
1193	C₄⋊C₄	—	53	1	no	—
1194	C₄⋊C₄	—	53	1	no	—
1195	C₄⋊C₄	—	53	1	no	—
1196	C₄⋊C₄	—	53	1	no	—
1197	C₄⋊C₄	—	53	1	no	—
1198	C₄⋊C₄	—	53	1	no	—
1199	C₄⋊C₄	—	53	1	no	—
1200	C₄⋊C₄	—	53	1	no	—
1201	C₄⋊C₄	—	53	1	no	—
1202	C₄⋊C₄	—	53	1	no	—
1203	C₄⋊C₄	—	53	1	no	—
1204	C₄⋊C₄	—	53	1	no	—
1205	C₄⋊C₄	—	53	1	no	—
1206	C₄⋊C₄	—	53	1	no	—
1207	C₄⋊C₄	—	53	1	no	—
1208	C₄⋊C₄	—	53	1	no	—
1209	C₄⋊C₄	—	53	1	no	—
1210	C₄⋊C₄	—	53	1	no	—
1211	C₄⋊C₄	—	53	1	no	—
1212	C₄⋊C₄	—	53	1	no	—
1213	C₄⋊C₄	—	53	1	no	—
1214	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1215	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1216	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1217	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1218	C₂²⋊C₄	—	53	1	no	—
1219	C₂²⋊C₄	—	53	1	no	—
1220	C₂²⋊C₄	—	53	1	no	—
1221	C₂²⋊C₄	—	53	1	no	—
1222	C₂²⋊C₄	—	53	1	no	—
1223	C₂²⋊C₄	—	53	1	no	—
1224	C₂²⋊C₄	—	53	1	no	—
1225	C₂²⋊C₄	—	53	1	no	—
1226	C₂²⋊C₄	—	53	1	no	—
1227	C₂²⋊C₄	—	53	1	no	—
1228	C₂²⋊C₄	—	53	1	no	—
1229	C₂²⋊C₄	—	53	1	no	—
1230	C₂²⋊C₄	—	53	1	no	—
1231	C₂²⋊C₄	—	53	1	no	—
1232	C₂²⋊C₄	—	53	1	no	—
1233	C₂²⋊C₄	—	53	1	no	—
1234	C₂²⋊C₄	—	53	1	no	—
1235	C₂²⋊C₄	—	53	1	no	—
1236	C₂²⋊C₄	—	53	1	no	—
1237	C₂²⋊C₄	—	53	1	no	—
1238	C₂²⋊C₄	—	53	1	no	—
1239	C₂²⋊C₄	—	53	1	no	—
1240	C₂²⋊C₄	—	53	1	no	—
1241	C₂²⋊C₄	—	53	1	no	—
1242	C₂²⋊C₄	—	53	1	no	—
1243	C₂²⋊C₄	—	53	1	no	—
1244	C₂²⋊C₄	—	53	1	no	—
1245	C₂²⋊C₄	—	53	1	no	—
1246	C₂²⋊C₄	—	53	1	no	—
1247	C₂²⋊C₄	—	53	1	no	—
1248	C₂²⋊C₄	—	53	1	no	—
1249	C₂²⋊C₄	—	53	1	no	—
1250	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1251	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1252	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1253	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1254	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1255	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1256	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1257	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1258	C₄²	—	53	1	no	—
1259	C₄²	—	53	1	no	—
1260	C₄²	—	53	1	no	—
1261	C₄²	—	53	1	no	—
1262	C₄²	—	53	1	no	—
1263	C₄²	—	53	1	no	—
1264	C₄²	—	53	1	no	—
1265	C₄²	—	53	1	no	—
1266	C₄²	—	53	1	no	—
1267	C₄²	—	53	1	no	—
1268	C₄²	—	53	1	no	—
1269	C₄²	—	53	1	no	—
1270	C₄²	—	53	1	no	—
1271	C₄²	—	53	1	no	—
1272	C₄²	—	53	1	no	—
1273	C₄²	—	53	1	no	—
1274	C₄²	—	53	1	no	—
1275	C₄²	—	53	1	no	—
1276	C₄²	—	53	1	no	—
1277	C₄²	—	53	1	no	—
1278	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1279	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1280	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1281	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1282	C₂³	—	2	2	no	—
1283	C₂³	—	2	2	no	—
1284	C₂³	—	2	2	no	—
1285	C₂³	—	4	1	no	—
1286	C₂³	—	4	1	no	—
1287	C₂³	—	4	1	no	—
1288	C₂³	—	53	1	no	—
1289	C₂³	—	53	1	no	—
1290	C₂³	—	106	2	no	—
1291	C₂³	—	212	1	no	—
1292	C₂³	—	212	1	no	—
1293	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1294	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1295	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1296	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1297	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1298	Q₈	—	106	2	no	—
1299	Q₈	—	106	2	no	—
1300	Q₈	—	212	1	no	—
1301	Q₈	—	212	1	no	—
1302	D₄	—	2	2	no	—
1303	D₄	—	2	2	no	—
1304	D₄	—	4	1	no	—
1305	D₄	—	4	1	no	—
1306	D₄	—	106	2	no	—
1307	D₄	—	106	2	no	—
1308	D₄	—	106	2	no	—
1309	D₄	—	106	2	no	—
1310	D₄	—	212	1	no	—
1311	D₄	—	212	1	no	—
1312	D₄	—	212	1	no	—
1313	D₄	—	212	1	no	—
1314	C₂×C₄	—	2	2	no	—
1315	C₂×C₄	—	2	2	no	—
1316	C₂×C₄	—	2	2	no	—
1317	C₂×C₄	—	2	2	no	—
1318	C₂×C₄	—	2	2	no	—
1319	C₂×C₄	—	2	2	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	4	1	no	—
1329	C₂×C₄	—	4	1	no	—
1330	C₂×C₄	—	53	1	no	—
1331	C₂×C₄	—	53	1	no	—
1332	C₂×C₄	—	53	1	no	—
1333	C₂×C₄	—	53	1	no	—
1334	C₂×C₄	—	53	1	no	—
1335	C₂×C₄	—	53	1	no	—
1336	C₂×C₄	—	53	1	no	—
1337	C₂×C₄	—	53	1	no	—
1338	C₂×C₄	—	53	1	no	—
1339	C₂×C₄	—	53	1	no	—
1340	C₂×C₄	—	53	1	no	—
1341	C₂×C₄	—	53	1	no	—
1342	C₂×C₄	—	53	1	no	—
1343	C₂×C₄	—	53	1	no	—
1344	C₂×C₄	—	106	2	no	—
1345	C₂×C₄	—	106	2	no	—
1346	C₂×C₄	—	106	2	no	—
1347	C₂×C₄	—	106	2	no	—
1348	C₂×C₄	—	106	2	no	—
1349	C₂×C₄	—	106	2	no	—
1350	C₂×C₄	—	106	2	no	—
1351	C₂×C₄	—	106	2	no	—
1352	C₂×C₄	—	106	1	no	—
1353	C₂×C₄	—	106	1	no	—
1354	C₂×C₄	—	106	1	no	—
1355	C₂×C₄	—	106	1	no	—
1356	C₂×C₄	—	212	1	no	—
1357	C₂×C₄	—	212	1	no	—
1358	C₂×C₄	—	212	1	no	—
1359	C₂×C₄	—	212	1	no	—
1360	C₂×C₄	—	212	1	no	—
1361	C₂×C₄	—	212	1	no	—
1362	C₂×C₄	—	212	1	no	—
1363	C₂×C₄	—	212	1	no	—
1364	C₂×C₄	—	212	1	no	—
1365	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1366	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1367	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1368	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1369	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1370	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1371	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1372	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1373	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1374	C₂×C₄	#13133262	1	2	yes	—
1375	C₂×C₄	#13133264	1	2	yes	—
1376	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1377	C₈	—	2	2	no	—
1378	C₈	—	2	2	no	—
1379	C₈	—	2	2	no	—
1380	C₈	—	2	2	no	—
1381	C₈	—	106	2	no	—
1382	C₈	—	106	2	no	—
1383	C₈	—	106	2	no	—
1384	C₈	—	106	2	no	—
1385	C₂²	—	2	1	no	—
1386	C₂²	—	2	1	no	—
1387	C₂²	—	2	1	no	—
1388	C₂²	—	2	1	no	—
1389	C₂²	—	2	1	no	—
1390	C₂²	—	2	1	no	—
1391	C₂²	—	2	1	no	—
1392	C₂²	—	2	1	no	—
1393	C₂²	—	2	1	no	—
1394	C₂²	—	2	1	no	—
1395	C₂²	—	2	1	no	—
1396	C₂²	—	2	1	no	—
1397	C₂²	—	2	1	no	—
1398	C₂²	—	4	4	no	—
1399	C₂²	—	8	2	no	—
1400	C₂²	—	106	1	no	—
1401	C₂²	—	106	1	no	—
1402	C₂²	—	106	1	no	—
1403	C₂²	—	106	1	no	—
1404	C₂²	—	106	1	no	—
1405	C₂²	—	106	1	no	—
1406	C₂²	—	424	2	no	—
1407	C₂²	#16811102	1	2	yes	—
1408	C₂²	#16811389	1	2	yes	—
1409	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1410	C₄	—	2	1	no	—
1411	C₄	—	2	1	no	—
1412	C₄	—	2	1	no	—
1413	C₄	—	2	1	no	—
1414	C₄	—	2	1	no	—
1415	C₄	—	2	1	no	—
1416	C₄	—	2	1	no	—
1417	C₄	—	2	1	no	—
1418	C₄	—	53	2	no	—
1419	C₄	—	106	1	no	—
1420	C₄	—	106	1	no	—
1421	C₄	—	106	1	no	—
1422	C₄	—	106	1	no	—
1423	C₄	—	106	1	no	—
1424	C₄	—	106	1	no	—
1425	C₄	—	106	1	no	—
1426	C₄	—	106	1	no	—
1427	C₄	—	106	1	no	—
1428	C₄	—	106	1	no	—
1429	C₄	—	106	1	no	—
1430	C₄	—	106	1	no	—
1431	C₄	—	106	1	no	—
1432	C₄	#16811102	1	2	yes	—
1433	C₄	C₂×#13133262	1	1	yes	characteristic
1434	C₄	C₂×#13133264	1	1	yes	characteristic
1435	C₂	—	2	2	no	—
1436	C₂	—	2	2	no	—
1437	C₂	—	4	1	no	—
1438	C₂	—	4	1	no	—
1439	C₂	—	4	1	no	—
1440	C₂	—	212	1	no	—
1441	C₂	—	212	1	no	—
1442	C₂	C₂×#16811102	1	1	yes	characteristic
1443	C₂	#568×D₅₃	1	1	yes	characteristic
1444	C₂	C₂×#16811389	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	D₄×M₁₆×C₅₃	C₂
prime radical	C₂×#13133189	C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	D₄×M₁₆	D₅₃
hypocenter	C₅₃	#60264
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ D₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #20283886	C₂	semidirect
3. #20283879	C₂	semidirect
4. #20283872	C₂	semidirect
5. #20283868	C₂	semidirect
6. #20283861	C₂	semidirect
7. #20283857	C₂	semidirect
8. #20283855	C₂	semidirect
9. #20283848	C₂	semidirect
10. M₁₆×Dic₁₀₆	C₂	semidirect
11. #20283666	C₂	semidirect
12. D₄×#11719917	C₂	semidirect
13. M₁₆×C₂²⋊D₅₃	C₂	semidirect
14. M₁₆×C₂²⋊D₅₃	C₂	semidirect
15. #20283447	C₂	semidirect
16. #20283447	C₂	semidirect
17. #20283351	C₂	semidirect
18. #20283350	C₂	semidirect
19. #20283344	C₂	semidirect
20. #20283278	C₂	semidirect
21. #20283277	C₂	semidirect
22. C₂×#16810646	C₂	semidirect
23. D₄×M₁₆×C₅₃	C₂	semidirect
58. #16810753	C₂²	semidirect
59. #16810752	C₂²	semidirect
60. #16810752	C₂²	semidirect
61. #16810751	C₂²	semidirect
62. #16810751	C₂²	semidirect
63. #16810750	C₂²	semidirect
64. C₈×Dic₁₀₆	C₂²	semidirect
65. #16810747	C₂²	semidirect
66. #16810701	C₂²	semidirect
67. #16810699	C₂²	semidirect
68. #16810699	C₂²	semidirect
69. #16810698	C₂²	semidirect
70. #16810698	C₂²	semidirect
71. #16810697	C₂²	semidirect
72. #16810697	C₂²	semidirect
73. #16810695	C₂²	semidirect
74. #16810695	C₂²	semidirect
75. #16810694	C₂²	semidirect
76. #16810694	C₂²	semidirect
77. #16810692	C₂²	semidirect
78. #16810692	C₂²	semidirect
79. #16810691	C₂²	semidirect
80. #16810691	C₂²	semidirect
81. D₄×#88322	C₂²	semidirect
82. C₈×C₂²⋊D₅₃	C₂²	semidirect
83. C₈×C₂²⋊D₅₃	C₂²	semidirect
84. #16810686	C₂²	semidirect
85. #16810686	C₂²	semidirect
86. #16810685	C₂²	semidirect
87. #16810685	C₂²	semidirect
88. #16810682	C₂²	semidirect
89. #16810682	C₂²	semidirect
90. #16810681	C₂²	semidirect
91. #16810681	C₂²	semidirect
92. #16810681	C₂²	semidirect
93. #16810681	C₂²	semidirect
94. #16810677	C₂²	semidirect
95. #16810677	C₂²	semidirect
96. #16810673	C₂²	semidirect
97. #16810673	C₂²	semidirect
98. #16810651	C₂²	semidirect
99. #16810651	C₂²	semidirect
100. #16810649	C₂²	semidirect
101. #16810649	C₂²	semidirect
102. #16810648	C₂²	semidirect
103. #16810648	C₂²	semidirect
104. #16810648	C₂²	semidirect
105. #16810648	C₂²	semidirect
115. #16810646	C₂²	semidirect
116. #16810646	C₂²	semidirect
117. C₂×#13133146	C₂²	semidirect
118. C₂×#13133146	C₂²	semidirect
131. C₅₃×#436	C₂²	semidirect
132. C₅₃×#435	C₂²	semidirect
133. C₅₃×#435	C₂²	semidirect
134. C₈×D₄×C₅₃	C₂²	semidirect
729. D₄×M₁₆	D₅₃	semidirect
796. #436	C₂×D₅₃	semidirect
807. #435	C₂×D₅₃	semidirect
808. #435	C₂×D₅₃	semidirect
814. C₈×D₄	C₂×D₅₃	semidirect
861. C₅₃	#60264	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#16811153	2
#20283886	2
#20283879	2
#20283872	2
#20283868	2
#20283861	2
#20283857	2
#20283855	2
#20283848	2
M₁₆×Dic₁₀₆	2
#20283666	2
D₄×#11719917	2
M₁₆×C₂²⋊D₅₃	2
#20283447	2
#20283351	2
#20283350	2
#20283344	2
#20283278	2
#20283277	2
C₂×#16810646	2
D₄×M₁₆×C₅₃	2
#60264	53