Subgroups — #28252188

Order 13568.

2192 conjugacy classes of subgroups.

The subgroup lattice has 1764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288008	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#41×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20284799	C₂	1	1	yes	maximal, characteristic, complemented
4	#20284793	C₂	1	1	yes	maximal, characteristic, complemented
5	#20284784	C₂	1	1	yes	maximal, characteristic, complemented
6	#20284782	C₂	1	1	yes	maximal, characteristic, complemented
7	#20284773	C₂	1	1	yes	maximal, characteristic, complemented
8	#20284771	C₂	1	1	yes	maximal, characteristic, complemented
9	#20284766	C₂	1	1	yes	maximal, characteristic, complemented
10	#20284760	C₂	1	1	yes	maximal, characteristic, complemented
11	#20284752	C₂	1	1	yes	maximal, characteristic, complemented
12	#20284744	C₂	1	1	yes	maximal, characteristic, complemented
13	#20284739	C₂	1	1	yes	maximal, characteristic, complemented
14	#20284737	C₂	1	1	yes	maximal, characteristic, complemented
15	#20284731	C₂	1	1	yes	maximal, characteristic, complemented
16	#20284729	C₂	1	1	yes	maximal, characteristic, complemented
17	#20284721	C₂	1	1	yes	maximal, characteristic, complemented
18	#20284713	C₂	1	1	yes	maximal, characteristic, complemented
19	#20284632	C₂	1	1	yes	maximal, characteristic, complemented
20	#20284626	C₂	1	1	yes	maximal, characteristic, complemented
21	#20284501	C₂	1	1	yes	maximal, characteristic, complemented
22	#20284499	C₂	1	1	yes	maximal, characteristic, complemented
23	#20284168	C₂	1	1	yes	maximal, characteristic, complemented
24	#20284166	C₂	1	1	yes	maximal, characteristic, complemented
25	#20283935	C₂	1	1	yes	maximal, characteristic, complemented
26	#20283929	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#13133239	C₂	1	1	yes	maximal, characteristic, complemented
28	C₄×#13133237	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#13133237	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#16810674	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#135×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133239	C₂²	1	1	yes	characteristic
34	C₂×#13133237	C₂²	1	1	yes	characteristic
35	C₂×#13133237	C₂²	1	1	yes	characteristic
36	#16811177	C₂²	1	1	yes	characteristic
37	#16811177	C₂²	1	1	yes	characteristic, complemented
38	#16811176	C₂²	1	1	yes	characteristic, complemented
39	#16811170	C₂²	1	1	yes	characteristic
40	#16811170	C₂²	1	1	yes	characteristic, complemented
41	#16811169	C₂²	1	1	yes	characteristic, complemented
42	#16811160	C₂²	1	1	yes	characteristic
43	#16811160	C₂²	1	1	yes	characteristic, complemented
44	#16811155	C₂²	1	1	yes	characteristic
45	#16811155	C₂²	1	1	yes	characteristic, complemented
46	#16811153	—	2	1	no	—
47	#16811153	—	2	1	no	—
48	#16811151	—	2	1	no	—
49	#16811151	—	2	1	no	—
50	#16811135	C₂²	1	1	yes	characteristic
51	#16811132	—	2	1	no	—
52	#16811132	—	2	1	no	—
53	#16811130	C₂²	1	1	yes	characteristic
54	#41×Dic₅₃	C₂²	1	1	yes	characteristic
55	C₄×#11719949	C₂²	1	1	yes	characteristic
56	C₄×#11719949	C₂²	1	1	yes	characteristic
57	C₄×#11719945	—	2	1	no	—
58	C₄×#11719945	—	2	1	no	—
59	C₄×#11719945	—	2	1	no	—
60	C₄×#11719945	C₂²	1	1	yes	characteristic
61	C₄×#11719945	C₂²	1	1	yes	characteristic, complemented
62	#16811091	—	2	1	no	—
63	#16811091	C₂²	1	1	yes	characteristic
64	C₄×#11719947	—	2	1	no	—
65	C₄×#11719947	—	2	1	no	—
66	C₄×#11719947	C₂²	1	1	yes	characteristic
67	C₄×#11719947	C₂²	1	1	yes	characteristic
68	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
69	C₄×Q₈×D₅₃	C₂²	1	1	yes	characteristic
70	C₄×D₄×D₅₃	—	2	1	no	—
71	C₄×D₄×D₅₃	—	2	1	no	—
72	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
73	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
74	#117×D₅₃	—	2	1	no	—
75	#117×D₅₃	C₂²	1	1	yes	characteristic
76	C₂×C₄²×D₅₃	—	2	1	no	—
77	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
78	#16810967	C₂²	1	1	yes	characteristic, complemented
79	#16810966	C₂²	1	1	yes	characteristic, complemented
80	#16810963	C₂²	1	1	yes	characteristic, complemented
81	#16810962	C₂²	1	1	yes	characteristic, complemented
82	#16810960	C₂²	1	1	yes	characteristic
83	#16810957	C₂²	1	1	yes	characteristic
84	#16810955	C₂²	1	1	yes	characteristic
85	#16810952	C₂²	1	1	yes	characteristic
86	#16810950	C₂²	1	1	yes	characteristic, complemented
87	#16810949	C₂²	1	1	yes	characteristic, complemented
88	#16810946	C₂²	1	1	yes	characteristic, complemented
89	#16810945	C₂²	1	1	yes	characteristic, complemented
90	#16810943	C₂²	1	1	yes	characteristic
91	#16810940	C₂²	1	1	yes	characteristic
92	#16810938	C₂²	1	1	yes	characteristic
93	#16810935	C₂²	1	1	yes	characteristic
94	#16810933	C₂²	1	1	yes	characteristic, complemented
95	#16810932	C₂²	1	1	yes	characteristic, complemented
96	#16810929	C₂²	1	1	yes	characteristic, complemented
97	#16810928	C₂²	1	1	yes	characteristic, complemented
98	#16810926	C₂²	1	1	yes	characteristic, complemented
99	#16810925	C₂²	1	1	yes	characteristic, complemented
100	#16810922	C₂²	1	1	yes	characteristic, complemented
101	#16810921	C₂²	1	1	yes	characteristic, complemented
102	#16810917	C₂²	1	1	yes	characteristic, complemented
103	#16810916	C₂²	1	1	yes	characteristic, complemented
104	#16810912	C₂²	1	1	yes	characteristic, complemented
105	#16810911	C₂²	1	1	yes	characteristic, complemented
106	#16810907	C₂²	1	1	yes	characteristic, complemented
107	#16810906	C₂²	1	1	yes	characteristic, complemented
108	#16810902	C₂²	1	1	yes	characteristic, complemented
109	#16810901	C₂²	1	1	yes	characteristic, complemented
110	#16810848	C₂²	1	1	yes	characteristic, complemented
111	#16810847	C₂²	1	1	yes	characteristic, complemented
112	#16810844	C₂²	1	1	yes	characteristic, complemented
113	#16810843	C₂²	1	1	yes	characteristic, complemented
114	#16810841	C₂²	1	1	yes	characteristic, complemented
115	#16810840	C₂²	1	1	yes	characteristic, complemented
116	#16810837	C₂²	1	1	yes	characteristic, complemented
117	#16810836	C₂²	1	1	yes	characteristic, complemented
118	#16810832	C₂²	1	1	yes	characteristic, complemented
119	#16810831	C₂²	1	1	yes	characteristic, complemented
120	#16810827	C₂²	1	1	yes	characteristic, complemented
121	#16810826	C₂²	1	1	yes	characteristic, complemented
122	#16810822	C₂²	1	1	yes	characteristic, complemented
123	#16810821	C₂²	1	1	yes	characteristic, complemented
124	#16810817	C₂²	1	1	yes	characteristic, complemented
125	#16810816	C₂²	1	1	yes	characteristic, complemented
126	#16810788	C₂²	1	1	yes	characteristic
127	#16810786	C₂²	1	1	yes	characteristic
128	#16810784	C₂²	1	1	yes	characteristic
129	#16810782	C₂²	1	1	yes	characteristic
130	#16810780	C₂²	1	1	yes	characteristic
131	#16810777	C₂²	1	1	yes	characteristic
132	#16810775	C₂²	1	1	yes	characteristic
133	#16810772	C₂²	1	1	yes	characteristic
134	#16810771	C₂²	1	1	yes	characteristic
135	#16810769	C₂²	1	1	yes	characteristic
136	#16810767	C₂²	1	1	yes	characteristic
137	#16810765	C₂²	1	1	yes	characteristic
138	#16810763	C₂²	1	1	yes	characteristic
139	#16810760	C₂²	1	1	yes	characteristic
140	#16810758	C₂²	1	1	yes	characteristic
141	#16810755	C₂²	1	1	yes	characteristic
142	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic, complemented
143	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic, complemented
144	C₄×#11719925	C₂²	1	1	yes	characteristic, complemented
145	C₄×#11719925	C₂²	1	1	yes	characteristic, complemented
146	C₄×#11719925	C₂²	1	1	yes	characteristic, complemented
147	C₄×#11719925	C₂²	1	1	yes	characteristic, complemented
148	C₄×#11719913	C₂²	1	1	yes	characteristic, complemented
149	C₄×#11719913	C₂²	1	1	yes	characteristic, complemented
150	C₄×#11719913	C₂²	1	1	yes	characteristic, complemented
151	C₄×#11719913	C₂²	1	1	yes	characteristic, complemented
152	C₄×#11719924	C₂²	1	1	yes	characteristic, complemented
153	C₄×#11719924	C₂²	1	1	yes	characteristic, complemented
154	C₄×#11719924	C₂²	1	1	yes	characteristic, complemented
155	C₄×#11719924	C₂²	1	1	yes	characteristic, complemented
156	C₄×#11719923	C₂²	1	1	yes	characteristic, complemented
157	C₄×#11719923	C₂²	1	1	yes	characteristic, complemented
158	C₄×#11719923	C₂²	1	1	yes	characteristic, complemented
159	C₄×#11719923	C₂²	1	1	yes	characteristic, complemented
160	C₄×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
161	C₄×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
162	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
163	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
164	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
165	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
166	#16810674	C₂²	1	1	yes	characteristic
167	#16810674	C₂²	1	1	yes	characteristic
168	#16810674	C₂²	1	1	yes	characteristic
169	#16810674	C₂²	1	1	yes	characteristic
170	#16810674	C₂²	1	1	yes	characteristic, complemented
171	#16810674	C₂²	1	1	yes	characteristic, complemented
172	#16810674	C₂²	1	1	yes	characteristic, complemented
173	#16810674	C₂²	1	1	yes	characteristic, complemented
174	#16810661	C₂²	1	1	yes	characteristic, complemented
175	#16810659	C₂²	1	1	yes	characteristic, complemented
176	#16810659	C₂²	1	1	yes	characteristic, complemented
177	C₂×#13133146	C₂²	1	1	yes	characteristic, complemented
178	C₂×#13133146	C₂²	1	1	yes	characteristic, complemented
179	#16810620	C₂²	1	1	yes	characteristic
180	#16810620	C₂²	1	1	yes	characteristic, complemented
181	#16810619	C₂²	1	1	yes	characteristic
182	#16810619	C₂²	1	1	yes	characteristic, complemented
183	#16810617	C₂²	1	1	yes	characteristic
184	#16810617	C₂²	1	1	yes	characteristic, complemented
185	C₂×#13133129	C₂²	1	1	yes	characteristic
186	C₂×#13133129	C₂²	1	1	yes	characteristic
187	C₂×C₄×#88322	C₂²	1	1	yes	characteristic, complemented
188	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
189	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
190	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
192	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
193	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
195	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
196	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#416	C₂²	1	1	yes	characteristic
201	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#11719949	C₂³	1	1	yes	characteristic
204	C₂×#11719945	—	2	1	no	—
205	C₂×#11719945	—	2	1	no	—
206	C₂×#11719945	—	2	1	no	—
207	C₂×#11719945	C₂³	1	1	yes	characteristic
208	C₂×#11719945	C₂³	1	1	yes	characteristic
209	C₂×#11719947	—	2	1	no	—
210	C₂×#11719947	C₂³	1	1	yes	characteristic
211	#41×D₅₃	—	2	4	no	—
212	#41×D₅₃	—	2	4	no	—
213	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
214	C₂×D₄×D₅₃	—	2	1	no	—
215	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
216	C₂²×C₄×D₅₃	—	2	1	no	—
217	C₂²×C₄×D₅₃	—	2	1	no	—
218	C₂²×C₄×D₅₃	—	2	1	no	—
219	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
220	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
221	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
222	#13133239	—	2	4	no	—
223	#13133237	—	2	4	no	—
224	#13133237	—	2	4	no	—
225	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
226	C₂×#11719925	C₂³	1	1	yes	characteristic
227	C₂×#11719925	C₂³	1	1	yes	characteristic
228	C₂×#11719913	C₂³	1	1	yes	characteristic
229	C₂×#11719913	C₂³	1	1	yes	characteristic
230	C₂×#11719923	C₂³	1	1	yes	characteristic
231	C₂×#11719923	C₂³	1	1	yes	characteristic
232	C₂×#11719924	C₂³	1	1	yes	characteristic
233	C₂×#11719924	C₂³	1	1	yes	characteristic
234	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
235	C₂×#11719922	C₂³	1	1	yes	characteristic
236	C₂×#11719922	C₂³	1	1	yes	characteristic
237	C₂²×#88322	C₂³	1	1	yes	characteristic
238	C₂²×#88322	C₂³	1	1	yes	characteristic
239	#13133216	C₂³	1	1	yes	characteristic
240	#13133216	C₂³	1	1	yes	characteristic
241	#13133215	C₂³	1	1	yes	characteristic
242	#13133213	C₂³	1	1	yes	characteristic
243	#13133212	—	2	1	no	—
244	#13133212	—	2	1	no	—
245	#13133210	—	2	1	no	—
246	#13133210	—	2	1	no	—
247	#13133208	C₂³	1	1	yes	characteristic
248	#13133208	C₂³	1	1	yes	characteristic
249	#13133207	—	2	1	no	—
250	#13133207	—	2	1	no	—
251	#13133206	C₂³	1	1	yes	characteristic
252	#13133204	C₂³	1	1	yes	characteristic
253	#13133203	—	2	1	no	—
254	#13133203	—	2	1	no	—
255	#13133202	—	2	1	no	—
256	#13133202	—	2	1	no	—
257	#13133201	—	2	1	no	—
258	#13133199	—	2	1	no	—
259	#13133199	—	2	1	no	—
260	#13133198	—	2	1	no	—
261	#13133197	C₂³	1	1	yes	characteristic
262	#13133197	C₂³	1	1	yes	characteristic
263	#13133195	—	2	1	no	—
264	#13133195	—	2	1	no	—
265	#13133194	—	2	1	no	—
266	#13133194	—	2	1	no	—
267	#13133193	C₂³	1	1	yes	characteristic
268	#13133193	C₂³	1	1	yes	characteristic
269	#13133192	C₂³	1	1	yes	characteristic
270	#13133192	C₂³	1	1	yes	characteristic
271	#13133190	—	2	1	no	—
272	#13133190	—	2	1	no	—
273	#13133189	—	2	1	no	—
274	#13133189	—	2	1	no	—
275	#13133188	C₂³	1	1	yes	characteristic
276	#13133188	C₂³	1	1	yes	characteristic
277	#13133187	—	2	1	no	—
278	#13133185	—	2	1	no	—
279	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic
280	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic
281	C₄×Dic₁₀₆	—	2	1	no	—
282	C₄×Dic₁₀₆	—	2	1	no	—
283	C₄×Dic₁₀₆	—	2	1	no	—
284	C₄×Dic₁₀₆	—	2	1	no	—
285	C₄×Dic₁₀₆	—	2	1	no	—
286	C₄×Dic₁₀₆	—	2	1	no	—
287	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
288	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
289	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
290	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
291	#13133182	—	2	1	no	—
292	#13133182	—	2	1	no	—
293	#13133182	C₂³	1	1	yes	characteristic
294	#13133182	C₂³	1	1	yes	characteristic
295	C₄×D₂₁₂	—	2	1	no	—
296	C₄×D₂₁₂	—	2	1	no	—
297	C₄×D₂₁₂	—	2	1	no	—
298	C₄×D₂₁₂	—	2	1	no	—
299	C₄×D₂₁₂	—	2	1	no	—
300	C₄×D₂₁₂	—	2	1	no	—
301	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
302	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
303	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
304	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
305	D₄×Dic₅₃	—	2	1	no	—
306	D₄×Dic₅₃	—	2	1	no	—
307	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
308	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
309	#13133179	—	2	1	no	—
310	#13133179	—	2	1	no	—
311	#13133179	C₂³	1	1	yes	characteristic
312	#13133179	C₂³	1	1	yes	characteristic
313	C₄×C₂²⋊D₅₃	—	2	1	no	—
314	C₄×C₂²⋊D₅₃	—	2	1	no	—
315	C₄×C₂²⋊D₅₃	—	2	1	no	—
316	C₄×C₂²⋊D₅₃	—	2	1	no	—
317	C₄×C₂²⋊D₅₃	—	2	1	no	—
318	C₄×C₂²⋊D₅₃	—	2	1	no	—
319	C₄×C₂²⋊D₅₃	—	2	1	no	—
320	C₄×C₂²⋊D₅₃	—	2	1	no	—
321	C₄×C₂²⋊D₅₃	—	2	1	no	—
322	C₄×C₂²⋊D₅₃	—	2	1	no	—
323	C₄×C₂²⋊D₅₃	—	2	1	no	—
324	C₄×C₂²⋊D₅₃	—	2	1	no	—
325	C₄×C₂²⋊D₅₃	—	2	1	no	—
326	C₄×C₂²⋊D₅₃	—	2	1	no	—
327	C₄×C₂²⋊D₅₃	—	2	1	no	—
328	C₄×C₂²⋊D₅₃	—	2	1	no	—
329	#13133177	—	2	1	no	—
330	#13133177	—	2	1	no	—
331	#13133177	—	2	1	no	—
332	#13133177	—	2	1	no	—
333	#13133177	—	2	1	no	—
334	#13133177	—	2	1	no	—
335	#13133176	—	2	1	no	—
336	#13133176	—	2	1	no	—
337	#13133176	—	2	1	no	—
338	#13133176	C₂³	1	1	yes	characteristic
339	#13133176	C₂³	1	1	yes	characteristic
340	#13133175	—	2	1	no	—
341	#13133175	—	2	1	no	—
342	#13133175	C₂³	1	1	yes	characteristic
343	#13133175	C₂³	1	1	yes	characteristic
344	#13133174	—	2	1	no	—
345	#13133174	—	2	1	no	—
346	#13133174	—	2	1	no	—
347	#13133174	—	2	1	no	—
348	#13133174	—	2	1	no	—
349	#13133174	—	2	1	no	—
350	#13133174	—	2	1	no	—
351	#13133174	—	2	1	no	—
352	#13133173	—	2	1	no	—
353	#13133173	—	2	1	no	—
354	#13133173	—	2	1	no	—
355	C₄⋊C₄×D₅₃	—	2	1	no	—
356	C₄⋊C₄×D₅₃	—	2	1	no	—
357	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
358	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
359	C₂²⋊C₄×D₅₃	—	2	1	no	—
360	C₂²⋊C₄×D₅₃	—	2	1	no	—
361	C₂²⋊C₄×D₅₃	—	2	1	no	—
362	C₂×C₄×Dic₅₃	—	2	1	no	—
363	C₂×C₄×Dic₅₃	—	2	1	no	—
364	C₂×C₄×Dic₅₃	—	2	1	no	—
365	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
366	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
367	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
368	C₄²×D₅₃	—	2	1	no	—
369	C₄²×D₅₃	—	2	1	no	—
370	C₄²×D₅₃	—	2	1	no	—
371	C₄²×D₅₃	—	2	1	no	—
372	C₄²×D₅₃	—	2	1	no	—
373	C₄²×D₅₃	—	2	1	no	—
374	C₄²×D₅₃	—	2	1	no	—
375	C₄²×D₅₃	—	2	1	no	—
376	C₄²×D₅₃	D₄	1	1	yes	characteristic
377	C₄²×D₅₃	D₄	1	1	yes	characteristic
378	C₄²×D₅₃	D₄	1	1	yes	characteristic
379	C₄²×D₅₃	D₄	1	1	yes	characteristic
380	C₄²×D₅₃	C₂³	1	1	yes	characteristic
381	C₄²×D₅₃	C₂³	1	1	yes	characteristic
382	C₄²×D₅₃	C₂³	1	1	yes	characteristic
383	C₄²×D₅₃	C₂³	1	1	yes	characteristic
384	#13133151	C₂³	1	1	yes	characteristic
385	#13133151	C₂³	1	1	yes	characteristic
386	#13133150	C₂³	1	1	yes	characteristic
387	#13133150	C₂³	1	1	yes	characteristic
388	#13133150	C₂³	1	1	yes	characteristic
389	#13133150	C₂³	1	1	yes	characteristic
390	#13133149	C₂³	1	1	yes	characteristic
391	#13133149	C₂³	1	1	yes	characteristic
392	#13133148	C₂³	1	1	yes	characteristic
393	#13133148	C₂³	1	1	yes	characteristic
394	#13133148	C₂³	1	1	yes	characteristic
395	#13133148	C₂³	1	1	yes	characteristic
396	#13133146	C₂³	1	1	yes	characteristic
397	#13133146	C₂³	1	1	yes	characteristic
398	#13133146	C₂³	1	1	yes	characteristic
399	#13133146	C₂³	1	1	yes	characteristic
400	#13133146	C₂³	1	1	yes	characteristic
401	#13133146	C₂³	1	1	yes	characteristic
402	#13133146	C₂³	1	1	yes	characteristic
403	#13133146	C₂³	1	1	yes	characteristic
404	#13133142	C₂³	1	1	yes	characteristic
405	#13133142	C₂³	1	1	yes	characteristic
406	#13133142	C₂³	1	1	yes	characteristic
407	#13133142	C₂³	1	1	yes	characteristic
408	#13133141	C₂³	1	1	yes	characteristic
409	#13133141	C₂³	1	1	yes	characteristic
410	#13133141	C₂³	1	1	yes	characteristic
411	#13133141	C₂³	1	1	yes	characteristic
412	#13133140	C₂³	1	1	yes	characteristic
413	#13133140	C₂³	1	1	yes	characteristic
414	#13133140	C₂³	1	1	yes	characteristic
415	#13133140	C₂³	1	1	yes	characteristic
416	#13133139	C₂³	1	1	yes	characteristic
417	#13133139	C₂³	1	1	yes	characteristic
418	#13133139	C₂³	1	1	yes	characteristic
419	#13133139	C₂³	1	1	yes	characteristic
420	#13133138	C₂³	1	1	yes	characteristic
421	#13133138	C₂³	1	1	yes	characteristic
422	#13133138	C₂³	1	1	yes	characteristic
423	#13133138	C₂³	1	1	yes	characteristic
424	#13133137	C₂³	1	1	yes	characteristic
425	#13133137	C₂³	1	1	yes	characteristic
426	#13133137	C₂³	1	1	yes	characteristic
427	#13133137	C₂³	1	1	yes	characteristic
428	#13133129	C₂³	1	1	yes	characteristic
429	#13133129	C₂³	1	1	yes	characteristic
430	#13133129	C₂³	1	1	yes	characteristic
431	#13133129	C₂³	1	1	yes	characteristic
432	#13133129	C₂³	1	1	yes	characteristic
433	#13133129	C₂³	1	1	yes	characteristic
434	#13133129	C₂³	1	1	yes	characteristic
435	#13133129	C₂³	1	1	yes	characteristic
436	C₄×#88322	C₂³	1	1	yes	characteristic
437	C₄×#88322	C₂³	1	1	yes	characteristic
438	C₄×#88322	C₂³	1	1	yes	characteristic
439	C₄×#88322	C₂³	1	1	yes	characteristic
440	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
441	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
442	#135×C₅₃	—	2	4	no	—
443	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
444	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
445	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
446	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
447	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
448	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
449	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
450	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
451	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
452	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
453	C₄×D₄×C₅₃	—	2	1	no	—
454	C₄×D₄×C₅₃	—	2	1	no	—
455	C₄×D₄×C₅₃	—	2	1	no	—
456	C₄×D₄×C₅₃	—	2	1	no	—
457	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
458	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
459	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
460	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
461	#117×C₅₃	—	2	1	no	—
462	#117×C₅₃	—	2	1	no	—
463	#117×C₅₃	C₂³	1	1	yes	characteristic
464	#117×C₅₃	C₂³	1	1	yes	characteristic
465	C₂×C₄²×C₅₃	—	2	1	no	—
466	C₂×C₄²×C₅₃	—	2	1	no	—
467	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
468	#107×C₅₃	C₂³	1	1	yes	characteristic
469	#107×C₅₃	C₂³	1	1	yes	characteristic
470	#106×C₅₃	C₂³	1	1	yes	characteristic
471	#106×C₅₃	C₂³	1	1	yes	characteristic
472	#103×C₅₃	C₂³	1	1	yes	characteristic
473	#103×C₅₃	C₂³	1	1	yes	characteristic
474	#103×C₅₃	C₂³	1	1	yes	characteristic
475	#103×C₅₃	C₂³	1	1	yes	characteristic
476	#102×C₅₃	C₂³	1	1	yes	characteristic
477	#102×C₅₃	C₂³	1	1	yes	characteristic
478	#102×C₅₃	C₂³	1	1	yes	characteristic
479	#102×C₅₃	C₂³	1	1	yes	characteristic
480	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂³×D₅₃	—	2	1	no	—
485	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
486	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	2	2	no	—
488	#41×C₅₃	—	2	2	no	—
489	#41×C₅₃	#41	1	4	yes	complemented
490	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
491	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
492	C₂×D₄×C₅₃	—	2	1	no	—
493	C₂×D₄×C₅₃	—	2	1	no	—
494	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
496	C₂²×C₄×C₅₃	—	2	1	no	—
497	C₂²×C₄×C₅₃	—	2	1	no	—
498	C₂²×C₄×C₅₃	—	2	1	no	—
499	C₂²×C₄×C₅₃	—	2	1	no	—
500	C₂²×C₄×C₅₃	—	2	1	no	—
501	C₂²×C₄×C₅₃	—	2	1	no	—
502	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
503	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
504	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₂×C₂²⋊D₅₃	—	2	1	no	—
506	C₂×C₂²⋊D₅₃	—	2	1	no	—
507	C₂×C₂²⋊D₅₃	—	2	1	no	—
508	C₂×C₂²⋊D₅₃	—	2	1	no	—
509	C₂×C₂²⋊D₅₃	—	2	1	no	—
510	C₂×C₂²⋊D₅₃	—	2	1	no	—
511	C₂×C₂²⋊D₅₃	—	2	1	no	—
512	C₂×C₂²⋊D₅₃	—	2	1	no	—
513	C₂²×Dic₅₃	—	2	1	no	—
514	C₂²×Dic₅₃	—	2	1	no	—
515	C₂²×Dic₅₃	—	2	1	no	—
516	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
517	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
519	#11719949	—	2	2	no	—
520	#11719949	—	2	2	no	—
521	Q₈×D₅₃	—	2	2	no	—
522	Q₈×D₅₃	—	2	2	no	—
523	#11719947	—	2	8	no	—
524	#11719947	—	2	2	no	—
525	#11719947	—	2	2	no	—
526	D₄×D₅₃	—	2	8	no	—
527	D₄×D₅₃	—	2	2	no	—
528	D₄×D₅₃	—	2	2	no	—
529	#11719945	—	2	8	no	—
530	#11719945	—	2	2	no	—
531	#11719945	—	2	2	no	—
532	#11719945	—	2	2	no	—
533	#11719945	—	4	4	no	—
534	#11719945	—	4	4	no	—
535	#11719945	#41	1	4	yes	complemented
536	C₂×D₂₁₂	—	2	1	no	—
537	C₂×D₂₁₂	—	2	1	no	—
538	C₂×D₂₁₂	—	2	1	no	—
539	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
540	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
541	C₂×C₄×D₅₃	—	2	8	no	—
542	C₂×C₄×D₅₃	—	2	1	no	—
543	C₂×C₄×D₅₃	—	2	1	no	—
544	C₂×C₄×D₅₃	—	2	2	no	—
545	C₂×C₄×D₅₃	—	2	2	no	—
546	C₂×C₄×D₅₃	—	2	1	no	—
547	C₂×C₄×D₅₃	—	2	4	no	—
548	C₂×C₄×D₅₃	—	2	1	no	—
549	C₂×C₄×D₅₃	—	2	1	no	—
550	C₂×C₄×D₅₃	—	2	1	no	—
551	C₂×C₄×D₅₃	—	2	1	no	—
552	C₂×C₄×D₅₃	—	2	1	no	—
553	C₂×C₄×D₅₃	—	2	1	no	—
554	C₂×C₄×D₅₃	—	2	1	no	—
555	C₂×C₄×D₅₃	—	2	1	no	—
556	C₂×C₄×D₅₃	—	2	1	no	—
557	C₂×C₄×D₅₃	—	4	2	no	—
558	C₂×C₄×D₅₃	—	4	4	no	—
559	C₂×C₄×D₅₃	—	4	4	no	—
560	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
561	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
562	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
563	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
564	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
565	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
566	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
567	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
568	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
569	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
570	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
571	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
572	C₂×Dic₁₀₆	—	2	1	no	—
573	C₂×Dic₁₀₆	—	2	1	no	—
574	C₂×Dic₁₀₆	—	2	1	no	—
575	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
576	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
577	Q₁₆×C₅₃	—	2	2	no	—
578	SD₁₆×C₅₃	—	2	2	no	—
579	SD₁₆×C₅₃	—	2	2	no	—
580	D₈×C₅₃	—	2	2	no	—
581	C₂×C₈×C₅₃	—	2	2	no	—
582	C₂×C₈×C₅₃	—	2	2	no	—
583	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
584	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
586	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
587	C₄⋊C₄×C₅₃	—	2	1	no	—
588	C₄⋊C₄×C₅₃	—	2	1	no	—
589	C₄⋊C₄×C₅₃	—	2	1	no	—
590	C₄⋊C₄×C₅₃	—	2	1	no	—
591	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
592	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
593	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
594	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂²⋊C₄×C₅₃	—	2	1	no	—
596	C₂²⋊C₄×C₅₃	—	2	1	no	—
597	C₂²⋊C₄×C₅₃	—	2	1	no	—
598	C₂²⋊C₄×C₅₃	—	2	1	no	—
599	C₂²⋊C₄×C₅₃	—	2	1	no	—
600	C₂²⋊C₄×C₅₃	—	2	1	no	—
601	C₄²×C₅₃	—	2	1	no	—
602	C₄²×C₅₃	—	2	1	no	—
603	C₄²×C₅₃	—	2	1	no	—
604	C₄²×C₅₃	—	2	1	no	—
605	C₄²×C₅₃	—	2	1	no	—
606	C₄²×C₅₃	—	2	1	no	—
607	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
608	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
609	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₂²⋊Dic₅₃	—	2	1	no	—
612	C₂²⋊Dic₅₃	—	2	1	no	—
613	C₂²⋊Dic₅₃	—	2	1	no	—
614	C₂²⋊Dic₅₃	—	2	1	no	—
615	C₂²⋊Dic₅₃	—	2	1	no	—
616	C₂²⋊Dic₅₃	—	2	1	no	—
617	C₂²⋊Dic₅₃	—	2	1	no	—
618	C₂²⋊Dic₅₃	—	2	1	no	—
619	#11719925	—	2	2	no	—
620	#11719925	—	2	2	no	—
621	#11719924	—	2	2	no	—
622	#11719924	—	2	2	no	—
623	#11719923	—	2	2	no	—
624	#11719923	—	2	2	no	—
625	#11719922	—	2	2	no	—
626	#11719922	—	2	2	no	—
627	#11719921	—	2	1	no	—
628	#11719921	—	2	1	no	—
629	#11719921	—	2	1	no	—
630	#11719921	—	2	1	no	—
631	#11719921	—	2	1	no	—
632	#11719921	—	2	1	no	—
633	#11719921	—	2	1	no	—
634	#11719921	—	2	1	no	—
635	#11719921	—	2	1	no	—
636	#11719921	—	2	1	no	—
637	#11719921	—	2	1	no	—
638	#11719921	—	2	1	no	—
639	#11719921	—	2	1	no	—
640	#11719921	—	2	1	no	—
641	#11719921	—	2	1	no	—
642	#11719921	—	2	1	no	—
643	C₄⋊Dic₅₃	—	2	1	no	—
644	C₄⋊Dic₅₃	—	2	1	no	—
645	C₄⋊Dic₅₃	—	2	1	no	—
646	C₄⋊Dic₅₃	—	2	1	no	—
647	C₄⋊Dic₅₃	—	2	1	no	—
648	C₄⋊Dic₅₃	—	2	1	no	—
649	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
650	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
651	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
652	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
653	#11719919	—	2	1	no	—
654	#11719919	—	2	1	no	—
655	#11719919	—	2	1	no	—
656	#11719919	—	2	1	no	—
657	#11719919	—	2	1	no	—
658	#11719919	—	2	1	no	—
659	#11719919	—	2	1	no	—
660	#11719919	—	2	1	no	—
661	#11719919	—	2	1	no	—
662	#11719919	—	2	1	no	—
663	#11719919	—	2	1	no	—
664	#11719919	—	2	1	no	—
665	#11719919	—	2	1	no	—
666	#11719919	—	2	1	no	—
667	#11719919	—	2	1	no	—
668	#11719919	—	2	1	no	—
669	C₄×Dic₅₃	—	2	1	no	—
670	C₄×Dic₅₃	—	2	1	no	—
671	C₄×Dic₅₃	—	2	1	no	—
672	C₄×Dic₅₃	—	2	1	no	—
673	C₄×Dic₅₃	—	2	1	no	—
674	C₄×Dic₅₃	—	2	1	no	—
675	C₄×Dic₅₃	—	2	1	no	—
676	C₄×Dic₅₃	—	2	1	no	—
677	C₄×Dic₅₃	—	2	1	no	—
678	C₄×Dic₅₃	—	2	1	no	—
679	C₄×Dic₅₃	—	2	1	no	—
680	C₄×Dic₅₃	—	2	1	no	—
681	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
682	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
683	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
684	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
685	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
686	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
687	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
688	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
689	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
690	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
691	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
692	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
693	C₂×#88322	—	2	2	no	—
694	C₂×#88322	—	2	2	no	—
695	C₂×#88322	C₂⁴	1	1	yes	characteristic
696	C₂×#88322	C₂⁴	1	1	yes	characteristic
697	C₂×#88322	C₂⁴	1	1	yes	characteristic
698	C₂×#88322	C₂⁴	1	1	yes	characteristic
699	Dic₂₁₂	—	2	2	no	—
700	D₄₂₄	—	2	2	no	—
701	#11719913	—	2	2	no	—
702	#11719913	—	2	2	no	—
703	C₂³×C₅₃	—	2	1	no	—
704	C₂³×C₅₃	—	2	1	no	—
705	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
706	C₂²×D₅₃	—	2	4	no	—
707	C₂²×D₅₃	—	2	2	no	—
708	C₂²×D₅₃	—	2	1	no	—
709	C₂²×D₅₃	—	2	2	no	—
710	C₂²×D₅₃	—	2	1	no	—
711	C₂²×D₅₃	—	4	1	no	—
712	C₂²×D₅₃	—	4	2	no	—
713	C₂²×D₅₃	—	4	2	no	—
714	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
715	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
716	Q₈×C₅₃	—	2	1	no	—
717	Q₈×C₅₃	—	2	1	no	—
718	Q₈×C₅₃	—	2	1	no	—
719	Q₈×C₅₃	C₂×#41	1	2	yes	—
720	D₄×C₅₃	—	2	4	no	—
721	D₄×C₅₃	—	2	1	no	—
722	D₄×C₅₃	—	2	1	no	—
723	D₄×C₅₃	—	2	1	no	—
724	D₄×C₅₃	—	4	2	no	—
725	D₄×C₅₃	C₂×#41	1	2	yes	—
726	C₂×C₄×C₅₃	—	2	1	no	—
727	C₂×C₄×C₅₃	—	2	4	no	—
728	C₂×C₄×C₅₃	—	2	2	no	—
729	C₂×C₄×C₅₃	—	2	2	no	—
730	C₂×C₄×C₅₃	—	2	1	no	—
731	C₂×C₄×C₅₃	—	2	1	no	—
732	C₂×C₄×C₅₃	—	2	1	no	—
733	C₂×C₄×C₅₃	—	2	1	no	—
734	C₂×C₄×C₅₃	—	2	1	no	—
735	C₂×C₄×C₅₃	—	4	2	no	—
736	C₂×C₄×C₅₃	—	4	2	no	—
737	C₂×C₄×C₅₃	—	4	2	no	—
738	C₂×C₄×C₅₃	—	4	2	no	—
739	C₂×C₄×C₅₃	—	4	2	no	—
740	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
741	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
742	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
746	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
747	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
748	C₂²⋊D₅₃	—	2	4	no	—
749	C₂²⋊D₅₃	—	2	4	no	—
750	C₂²⋊D₅₃	—	2	4	no	—
751	C₂²⋊D₅₃	—	4	2	no	—
752	C₂²⋊D₅₃	—	4	2	no	—
753	C₂²⋊D₅₃	—	4	2	no	—
754	C₂²⋊D₅₃	—	4	2	no	—
755	C₂²⋊D₅₃	—	4	2	no	—
756	C₂×Dic₅₃	—	2	4	no	—
757	C₂×Dic₅₃	—	2	2	no	—
758	C₂×Dic₅₃	—	2	1	no	—
759	C₂×Dic₅₃	—	2	2	no	—
760	C₂×Dic₅₃	—	2	1	no	—
761	C₂×Dic₅₃	—	2	1	no	—
762	C₂×Dic₅₃	—	2	1	no	—
763	C₂×Dic₅₃	—	2	1	no	—
764	C₂×Dic₅₃	—	2	1	no	—
765	C₂×Dic₅₃	—	4	1	no	—
766	C₂×Dic₅₃	—	4	2	no	—
767	C₂×Dic₅₃	—	4	2	no	—
768	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
769	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
770	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
771	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
772	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
773	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
774	D₂₁₂	—	2	4	no	—
775	D₂₁₂	—	2	1	no	—
776	D₂₁₂	—	2	1	no	—
777	D₂₁₂	—	2	1	no	—
778	D₂₁₂	—	4	2	no	—
779	D₂₁₂	—	4	2	no	—
780	D₂₁₂	C₂×#41	1	2	yes	—
781	C₄×D₅₃	—	2	4	no	—
782	C₄×D₅₃	—	2	4	no	—
783	C₄×D₅₃	—	2	2	no	—
784	C₄×D₅₃	—	2	2	no	—
785	C₄×D₅₃	—	2	4	no	—
786	C₄×D₅₃	—	2	2	no	—
787	C₄×D₅₃	—	2	2	no	—
788	C₄×D₅₃	—	2	2	no	—
789	C₄×D₅₃	—	2	2	no	—
790	C₄×D₅₃	—	2	1	no	—
791	C₄×D₅₃	—	2	1	no	—
792	C₄×D₅₃	—	2	1	no	—
793	C₄×D₅₃	—	2	1	no	—
794	C₄×D₅₃	—	2	2	no	—
795	C₄×D₅₃	—	4	1	no	—
796	C₄×D₅₃	—	4	1	no	—
797	C₄×D₅₃	—	4	2	no	—
798	C₄×D₅₃	—	4	2	no	—
799	C₄×D₅₃	—	4	2	no	—
800	C₄×D₅₃	—	4	2	no	—
801	C₄×D₅₃	—	4	2	no	—
802	C₄×D₅₃	—	4	2	no	—
803	C₄×D₅₃	—	4	2	no	—
804	C₄×D₅₃	—	4	2	no	—
805	C₄×D₅₃	—	4	2	no	—
806	C₄×D₅₃	#135	1	4	yes	complemented
807	Dic₁₀₆	—	2	4	no	—
808	Dic₁₀₆	—	2	1	no	—
809	Dic₁₀₆	—	2	1	no	—
810	Dic₁₀₆	—	2	1	no	—
811	Dic₁₀₆	—	4	2	no	—
812	Dic₁₀₆	—	4	2	no	—
813	Dic₁₀₆	C₂×#41	1	2	yes	—
814	C₈×C₅₃	—	2	1	no	—
815	C₈×C₅₃	—	2	1	no	—
816	C₈×C₅₃	—	2	1	no	—
817	C₈×C₅₃	—	2	1	no	—
818	#88322	—	2	1	no	—
819	#88322	—	2	1	no	—
820	#88322	—	2	1	no	—
821	#88322	—	2	1	no	—
822	#60536	—	53	1	no	maximal, Sylow
823	C₂²×C₅₃	—	2	1	no	—
824	C₂²×C₅₃	—	2	1	no	—
825	C₂²×C₅₃	—	2	2	no	—
826	C₂²×C₅₃	—	4	1	no	—
827	C₂²×C₅₃	—	4	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	#525	1	2	yes	—
832	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
833	C₂×D₅₃	—	2	1	no	—
834	C₂×D₅₃	—	2	1	no	—
835	C₂×D₅₃	—	2	1	no	—
836	C₂×D₅₃	—	2	2	no	—
837	C₂×D₅₃	—	2	1	no	—
838	C₂×D₅₃	—	2	1	no	—
839	C₂×D₅₃	—	4	4	no	—
840	C₂×D₅₃	—	4	8	no	—
841	C₂×D₅₃	—	4	1	no	—
842	C₂×D₅₃	—	4	1	no	—
843	C₂×D₅₃	—	4	1	no	—
844	C₂×D₅₃	—	4	1	no	—
845	C₂×D₅₃	—	4	1	no	—
846	C₂×D₅₃	C₂×#135	1	2	yes	—
847	C₄×C₅₃	—	2	2	no	—
848	C₄×C₅₃	—	2	1	no	—
849	C₄×C₅₃	—	2	1	no	—
850	C₄×C₅₃	—	4	1	no	—
851	C₄×C₅₃	—	4	1	no	—
852	C₄×C₅₃	—	4	1	no	—
853	C₄×C₅₃	—	4	1	no	—
854	C₄×C₅₃	—	4	1	no	—
855	C₄×C₅₃	#525	1	2	yes	—
856	C₄×C₅₃	C₂×#135	1	2	yes	—
857	C₄×C₅₃	#575	1	2	yes	—
858	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
859	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
860	Dic₅₃	—	2	1	no	—
861	Dic₅₃	—	2	2	no	—
862	Dic₅₃	—	2	1	no	—
863	Dic₅₃	—	2	1	no	—
864	Dic₅₃	—	2	1	no	—
865	Dic₅₃	—	2	1	no	—
866	Dic₅₃	—	4	1	no	—
867	Dic₅₃	—	4	1	no	—
868	Dic₅₃	—	4	1	no	—
869	Dic₅₃	—	4	1	no	—
870	Dic₅₃	—	4	1	no	—
871	Dic₅₃	C₂×#135	1	2	yes	—
872	#3444	—	53	1	no	—
873	C₂×C₄×#41	—	53	1	no	—
874	#3108	—	53	1	no	—
875	#3108	—	53	1	no	—
876	#3107	—	53	1	no	—
877	#3107	—	53	1	no	—
878	#3106	—	53	1	no	—
879	#3106	—	53	1	no	—
880	#3105	—	53	1	no	—
881	#3105	—	53	1	no	—
882	#3104	—	53	1	no	—
883	#3103	—	53	1	no	—
884	#3102	—	53	1	no	—
885	#3102	—	53	1	no	—
886	#3102	—	53	1	no	—
887	#3102	—	53	1	no	—
888	#3101	—	53	1	no	—
889	#3100	—	53	1	no	—
890	#3091	—	53	1	no	—
891	#3091	—	53	1	no	—
892	#3076	—	53	1	no	—
893	#3076	—	53	1	no	—
894	#3035	—	53	1	no	—
895	#3035	—	53	1	no	—
896	#3002	—	53	1	no	—
897	#3002	—	53	1	no	—
898	C₄×#135	—	53	1	no	—
899	C₄×#135	—	53	1	no	—
900	C₄×#135	—	53	1	no	—
901	C₄×#135	D₅₃	1	1	yes	characteristic, complemented
902	C₂×#431	—	53	1	no	—
903	C₂×C₅₃	—	2	2	no	—
904	C₂×C₅₃	—	4	2	no	—
905	C₂×C₅₃	—	8	1	no	—
906	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
907	C₂×C₅₃	C₂²×#135	1	1	yes	characteristic
908	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
909	D₅₃	—	2	2	no	—
910	D₅₃	—	4	1	no	—
911	D₅₃	—	4	2	no	—
912	D₅₃	—	8	1	no	—
913	C₂²×#41	—	53	1	no	—
914	C₂×#135	—	53	1	no	—
915	C₂×#135	—	53	1	no	—
916	C₂×#135	—	53	1	no	—
917	C₂×#135	C₂×D₅₃	1	1	yes	characteristic
918	#533	—	53	1	no	—
919	#533	—	53	1	no	—
920	#533	—	53	1	no	—
921	#532	—	53	1	no	—
922	#532	—	53	1	no	—
923	#532	—	53	1	no	—
924	#529	—	53	1	no	—
925	#529	—	53	1	no	—
926	#529	—	53	1	no	—
927	#529	—	53	1	no	—
928	#529	—	106	1	no	—
929	#529	—	106	1	no	—
930	#529	—	106	1	no	—
931	#529	—	106	1	no	—
932	#525	—	53	1	no	—
933	#525	—	53	1	no	—
934	#525	—	106	1	no	—
935	#525	—	106	1	no	—
936	C₄×#41	—	53	1	no	—
937	C₄×#41	—	53	1	no	—
938	C₄×#41	—	53	1	no	—
939	C₄×#41	—	53	1	no	—
940	C₄×#41	—	53	1	no	—
941	C₄×#41	—	53	1	no	—
942	C₄×#41	—	53	1	no	—
943	C₄×#41	—	53	1	no	—
944	C₄×#41	—	106	1	no	—
945	C₄×#41	—	106	1	no	—
946	C₄×#41	—	106	1	no	—
947	C₄×#41	—	106	1	no	—
948	C₄×#41	—	106	1	no	—
949	C₄×#41	—	106	1	no	—
950	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
951	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
952	C₂×C₄×Q₈	—	53	1	no	—
953	C₂×C₄×Q₈	—	53	1	no	—
954	C₂×C₄×D₄	—	53	1	no	—
955	C₂×C₄×D₄	—	53	1	no	—
956	C₂×C₄×D₄	—	106	1	no	—
957	C₂×C₄×D₄	—	106	1	no	—
958	C₂×#117	—	53	1	no	—
959	C₂×#117	—	106	1	no	—
960	C₂²×C₄²	—	53	1	no	—
961	C₂²×C₄²	—	106	1	no	—
962	#485	—	53	1	no	—
963	#485	—	53	1	no	—
964	#485	—	53	1	no	—
965	#485	—	53	1	no	—
966	#484	—	53	1	no	—
967	#484	—	53	1	no	—
968	#483	—	53	1	no	—
969	#483	—	53	1	no	—
970	#482	—	53	1	no	—
971	#482	—	53	1	no	—
972	#482	—	53	1	no	—
973	#482	—	53	1	no	—
974	#481	—	53	1	no	—
975	#481	—	53	1	no	—
976	#480	—	53	1	no	—
977	#480	—	53	1	no	—
978	#479	—	53	1	no	—
979	#479	—	53	1	no	—
980	#479	—	53	1	no	—
981	#479	—	53	1	no	—
982	#478	—	53	1	no	—
983	#478	—	53	1	no	—
984	#478	—	53	1	no	—
985	#478	—	53	1	no	—
986	#477	—	53	1	no	—
987	#477	—	53	1	no	—
988	#476	—	53	1	no	—
989	#476	—	53	1	no	—
990	#475	—	53	1	no	—
991	#475	—	53	1	no	—
992	#474	—	53	1	no	—
993	#474	—	53	1	no	—
994	#464	—	53	1	no	—
995	#464	—	53	1	no	—
996	#464	—	53	1	no	—
997	#464	—	53	1	no	—
998	#463	—	53	1	no	—
999	#463	—	53	1	no	—
1000	#463	—	53	1	no	—
1001	#463	—	53	1	no	—
1002	#462	—	53	1	no	—
1003	#462	—	53	1	no	—
1004	#461	—	53	1	no	—
1005	#461	—	53	1	no	—
1006	#460	—	53	1	no	—
1007	#460	—	53	1	no	—
1008	#459	—	53	1	no	—
1009	#459	—	53	1	no	—
1010	#452	—	53	1	no	—
1011	#452	—	53	1	no	—
1012	#452	—	53	1	no	—
1013	#452	—	53	1	no	—
1014	#451	—	53	1	no	—
1015	#451	—	53	1	no	—
1016	#450	—	53	1	no	—
1017	#450	—	53	1	no	—
1018	#449	—	53	1	no	—
1019	#449	—	53	1	no	—
1020	#449	—	53	1	no	—
1021	#449	—	53	1	no	—
1022	#448	—	53	1	no	—
1023	#448	—	53	1	no	—
1024	#447	—	53	1	no	—
1025	#447	—	53	1	no	—
1026	C₄×Q₁₆	—	53	1	no	—
1027	C₄×Q₁₆	—	53	1	no	—
1028	C₄×Q₁₆	—	53	1	no	—
1029	C₄×Q₁₆	—	53	1	no	—
1030	C₄×Q₁₆	—	53	1	no	—
1031	C₄×Q₁₆	—	53	1	no	—
1032	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1033	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1034	C₄×SD₁₆	—	53	1	no	—
1035	C₄×SD₁₆	—	53	1	no	—
1036	C₄×SD₁₆	—	53	1	no	—
1037	C₄×SD₁₆	—	53	1	no	—
1038	C₄×SD₁₆	—	53	1	no	—
1039	C₄×SD₁₆	—	53	1	no	—
1040	C₄×SD₁₆	—	53	1	no	—
1041	C₄×SD₁₆	—	53	1	no	—
1042	C₄×SD₁₆	—	53	1	no	—
1043	C₄×SD₁₆	—	53	1	no	—
1044	C₄×SD₁₆	—	53	1	no	—
1045	C₄×SD₁₆	—	53	1	no	—
1046	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1047	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1048	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1049	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1050	C₄×D₈	—	53	1	no	—
1051	C₄×D₈	—	53	1	no	—
1052	C₄×D₈	—	53	1	no	—
1053	C₄×D₈	—	53	1	no	—
1054	C₄×D₈	—	53	1	no	—
1055	C₄×D₈	—	53	1	no	—
1056	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1057	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1058	#431	—	53	1	no	—
1059	#431	—	53	1	no	—
1060	#431	—	53	1	no	—
1061	#431	—	53	1	no	—
1062	#431	—	53	1	no	—
1063	#431	—	53	1	no	—
1064	#431	—	53	1	no	—
1065	#431	—	53	1	no	—
1066	#427	—	53	1	no	—
1067	#427	—	53	1	no	—
1068	#427	—	53	1	no	—
1069	#427	C₂×D₅₃	1	1	yes	characteristic, complemented
1070	C₂×C₄⋊C₈	—	53	1	no	—
1071	C₂×C₄⋊C₈	—	53	1	no	—
1072	#416	—	53	1	no	—
1073	#416	—	53	1	no	—
1074	#416	—	53	1	no	—
1075	#416	—	53	1	no	—
1076	#416	—	53	1	no	—
1077	#416	—	53	1	no	—
1078	#416	C₂×D₅₃	1	1	yes	characteristic
1079	#416	C₂×D₅₃	1	1	yes	characteristic, complemented
1080	C₂×C₂²⋊C₈	—	53	1	no	—
1081	C₂×C₂²⋊C₈	—	53	1	no	—
1082	C₂×C₄×C₈	—	53	1	no	—
1083	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1084	C₅₃	#60536	1	1	yes	characteristic, complemented, Sylow
1085	C₂×#41	—	53	1	no	—
1086	C₂×#41	—	53	1	no	—
1087	C₂×#41	—	53	1	no	—
1088	C₂×#41	—	53	1	no	—
1089	C₂×#41	—	106	1	no	—
1090	C₂×#41	—	106	1	no	—
1091	C₂×#41	—	106	1	no	—
1092	C₂×#41	—	106	1	no	—
1093	C₂×#41	—	106	4	no	—
1094	C₂×#41	—	106	4	no	—
1095	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1096	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1097	C₂²×Q₈	—	53	1	no	—
1098	C₂²×D₄	—	53	1	no	—
1099	C₂²×D₄	—	106	1	no	—
1100	C₂³×C₄	—	53	1	no	—
1101	C₂³×C₄	—	53	1	no	—
1102	C₂³×C₄	—	53	1	no	—
1103	C₂³×C₄	—	106	1	no	—
1104	C₂³×C₄	—	106	1	no	—
1105	C₂³×C₄	—	106	1	no	—
1106	#135	—	2	4	no	—
1107	#135	—	106	4	no	—
1108	#135	—	106	4	no	—
1109	#135	—	106	4	no	—
1110	C₂×Q₁₆	—	53	1	no	—
1111	C₂×Q₁₆	—	53	1	no	—
1112	C₂×Q₁₆	—	53	1	no	—
1113	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic
1114	C₂×SD₁₆	—	53	1	no	—
1115	C₂×SD₁₆	—	53	1	no	—
1116	C₂×SD₁₆	—	53	1	no	—
1117	C₂×SD₁₆	—	53	1	no	—
1118	C₂×SD₁₆	—	53	1	no	—
1119	C₂×SD₁₆	—	53	1	no	—
1120	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1121	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1122	C₂×D₈	—	53	1	no	—
1123	C₂×D₈	—	53	1	no	—
1124	C₂×D₈	—	53	1	no	—
1125	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1126	C₂²×C₈	—	53	1	no	—
1127	C₂²×C₈	—	53	1	no	—
1128	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1129	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1130	C₄⋊Q₈	—	53	1	no	—
1131	C₄⋊Q₈	—	53	1	no	—
1132	C₄⋊Q₈	—	53	1	no	—
1133	#127	—	53	1	no	—
1134	#126	—	106	1	no	—
1135	#126	—	106	1	no	—
1136	#126	—	106	1	no	—
1137	#126	—	106	1	no	—
1138	#125	—	53	1	no	—
1139	#125	—	53	1	no	—
1140	#125	—	106	1	no	—
1141	#125	—	106	1	no	—
1142	#124	—	53	1	no	—
1143	#124	—	53	1	no	—
1144	#124	—	106	1	no	—
1145	#124	—	106	1	no	—
1146	#123	—	106	1	no	—
1147	#123	—	106	1	no	—
1148	#123	—	106	1	no	—
1149	#123	—	106	1	no	—
1150	#123	—	106	1	no	—
1151	#123	—	106	1	no	—
1152	C₂²⋊Q₈	—	53	1	no	—
1153	C₂²⋊Q₈	—	53	1	no	—
1154	C₂²⋊Q₈	—	53	1	no	—
1155	C₂²⋊Q₈	—	53	1	no	—
1156	C₂²⋊Q₈	—	106	1	no	—
1157	C₂²⋊Q₈	—	106	1	no	—
1158	C₂²⋊Q₈	—	106	1	no	—
1159	C₂²⋊Q₈	—	106	1	no	—
1160	#121	—	53	1	no	—
1161	#121	—	53	1	no	—
1162	#121	—	53	1	no	—
1163	#121	—	53	1	no	—
1164	#121	—	106	1	no	—
1165	#121	—	106	1	no	—
1166	#121	—	106	1	no	—
1167	#121	—	106	1	no	—
1168	#120	—	106	1	no	—
1169	#120	—	106	1	no	—
1170	C₄×Q₈	—	53	1	no	—
1171	C₄×Q₈	—	53	1	no	—
1172	C₄×Q₈	—	53	1	no	—
1173	C₄×Q₈	—	53	1	no	—
1174	C₄×Q₈	—	53	1	no	—
1175	C₄×Q₈	—	53	1	no	—
1176	C₄×Q₈	—	53	1	no	—
1177	C₄×Q₈	—	53	1	no	—
1178	C₄×Q₈	—	106	1	no	—
1179	C₄×Q₈	—	106	1	no	—
1180	C₄×Q₈	—	106	1	no	—
1181	C₄×Q₈	—	106	1	no	—
1182	C₄×Q₈	—	106	1	no	—
1183	C₄×Q₈	—	106	1	no	—
1184	C₄×Q₈	—	106	1	no	—
1185	C₄×Q₈	—	106	1	no	—
1186	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1187	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1188	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1189	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
1190	C₄×D₄	—	2	1	no	—
1191	C₄×D₄	—	2	1	no	—
1192	C₄×D₄	—	2	1	no	—
1193	C₄×D₄	—	2	1	no	—
1194	C₄×D₄	—	53	1	no	—
1195	C₄×D₄	—	53	1	no	—
1196	C₄×D₄	—	53	1	no	—
1197	C₄×D₄	—	53	1	no	—
1198	C₄×D₄	—	53	1	no	—
1199	C₄×D₄	—	53	1	no	—
1200	C₄×D₄	—	53	1	no	—
1201	C₄×D₄	—	53	1	no	—
1202	C₄×D₄	—	106	1	no	—
1203	C₄×D₄	—	106	1	no	—
1204	C₄×D₄	—	106	1	no	—
1205	C₄×D₄	—	106	1	no	—
1206	C₄×D₄	—	106	1	no	—
1207	C₄×D₄	—	106	1	no	—
1208	C₄×D₄	—	106	1	no	—
1209	C₄×D₄	—	106	1	no	—
1210	C₄×D₄	—	106	1	no	—
1211	C₄×D₄	—	106	1	no	—
1212	C₄×D₄	—	106	1	no	—
1213	C₄×D₄	—	106	1	no	—
1214	C₄×D₄	—	106	1	no	—
1215	C₄×D₄	—	106	1	no	—
1216	C₄×D₄	—	106	1	no	—
1217	C₄×D₄	—	106	1	no	—
1218	C₄×D₄	—	106	1	no	—
1219	C₄×D₄	—	106	1	no	—
1220	C₄×D₄	—	106	1	no	—
1221	C₄×D₄	—	106	1	no	—
1222	C₄×D₄	—	106	1	no	—
1223	C₄×D₄	—	106	1	no	—
1224	C₄×D₄	—	106	1	no	—
1225	C₄×D₄	—	106	1	no	—
1226	C₄×D₄	—	106	1	no	—
1227	C₄×D₄	—	106	1	no	—
1228	C₄×D₄	—	106	1	no	—
1229	C₄×D₄	—	106	1	no	—
1230	C₄×D₄	—	106	1	no	—
1231	C₄×D₄	—	106	1	no	—
1232	C₄×D₄	—	106	1	no	—
1233	C₄×D₄	—	106	1	no	—
1234	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1235	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1236	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1237	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1238	#117	—	2	1	no	—
1239	#117	—	2	1	no	—
1240	#117	—	53	1	no	—
1241	#117	—	53	1	no	—
1242	#117	—	53	1	no	—
1243	#117	—	53	1	no	—
1244	#117	—	106	1	no	—
1245	#117	—	106	1	no	—
1246	#117	—	106	1	no	—
1247	#117	—	106	1	no	—
1248	#117	—	106	1	no	—
1249	#117	—	106	1	no	—
1250	#117	—	106	1	no	—
1251	#117	—	106	1	no	—
1252	#117	—	106	1	no	—
1253	#117	—	106	1	no	—
1254	#117	—	106	1	no	—
1255	#117	—	106	1	no	—
1256	#117	—	106	1	no	—
1257	#117	—	106	1	no	—
1258	#117	—	106	1	no	—
1259	#117	—	106	1	no	—
1260	#117	C₂²×D₅₃	1	1	yes	characteristic
1261	#117	C₂²×D₅₃	1	1	yes	characteristic
1262	C₂×C₄⋊C₄	—	53	1	no	—
1263	C₂×C₄⋊C₄	—	53	1	no	—
1264	C₂×C₄⋊C₄	—	106	1	no	—
1265	C₂×C₄⋊C₄	—	106	1	no	—
1266	C₂×C₂²⋊C₄	—	106	1	no	—
1267	C₂×C₂²⋊C₄	—	106	1	no	—
1268	C₂×C₂²⋊C₄	—	106	1	no	—
1269	C₂×C₄²	—	2	1	no	—
1270	C₂×C₄²	—	2	1	no	—
1271	C₂×C₄²	—	53	1	no	—
1272	C₂×C₄²	—	53	1	no	—
1273	C₂×C₄²	—	53	1	no	—
1274	C₂×C₄²	—	53	1	no	—
1275	C₂×C₄²	—	53	1	no	—
1276	C₂×C₄²	—	53	1	no	—
1277	C₂×C₄²	—	53	1	no	—
1278	C₂×C₄²	—	53	1	no	—
1279	C₂×C₄²	—	53	1	no	—
1280	C₂×C₄²	—	53	1	no	—
1281	C₂×C₄²	—	53	1	no	—
1282	C₂×C₄²	—	106	1	no	—
1283	C₂×C₄²	—	106	1	no	—
1284	C₂×C₄²	—	106	1	no	—
1285	C₂×C₄²	—	106	1	no	—
1286	C₂×C₄²	—	106	1	no	—
1287	C₂×C₄²	—	106	1	no	—
1288	C₂×C₄²	—	106	1	no	—
1289	C₂×C₄²	—	106	1	no	—
1290	C₂×C₄²	—	106	1	no	—
1291	C₂×C₄²	—	106	1	no	—
1292	C₂×C₄²	—	106	1	no	—
1293	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1294	#107	—	53	1	no	—
1295	#107	—	53	1	no	—
1296	#107	—	53	1	no	—
1297	#107	—	53	1	no	—
1298	#107	—	53	1	no	—
1299	#107	—	53	1	no	—
1300	#107	C₂²×D₅₃	1	1	yes	characteristic
1301	#107	C₂²×D₅₃	1	1	yes	characteristic
1302	#106	—	53	1	no	—
1303	#106	—	53	1	no	—
1304	#106	—	53	1	no	—
1305	#106	—	53	1	no	—
1306	#106	—	53	1	no	—
1307	#106	—	53	1	no	—
1308	#106	C₂²×D₅₃	1	1	yes	characteristic
1309	#106	C₂²×D₅₃	1	1	yes	characteristic
1310	C₄⋊C₈	—	53	1	no	—
1311	C₄⋊C₈	—	53	1	no	—
1312	C₄⋊C₈	—	53	1	no	—
1313	C₄⋊C₈	—	53	1	no	—
1314	C₄⋊C₈	—	53	1	no	—
1315	C₄⋊C₈	—	53	1	no	—
1316	C₄⋊C₈	—	53	1	no	—
1317	C₄⋊C₈	—	53	1	no	—
1318	#103	—	53	1	no	—
1319	#103	—	53	1	no	—
1320	#103	—	53	1	no	—
1321	#103	—	53	1	no	—
1322	#103	—	53	1	no	—
1323	#103	—	53	1	no	—
1324	#103	—	53	1	no	—
1325	#103	—	53	1	no	—
1326	#103	—	53	1	no	—
1327	#103	—	53	1	no	—
1328	#103	—	53	1	no	—
1329	#103	—	53	1	no	—
1330	#103	C₂²×D₅₃	1	1	yes	characteristic
1331	#103	C₂²×D₅₃	1	1	yes	characteristic
1332	#103	C₂²×D₅₃	1	1	yes	characteristic
1333	#103	C₂²×D₅₃	1	1	yes	characteristic
1334	#102	—	53	1	no	—
1335	#102	—	53	1	no	—
1336	#102	—	53	1	no	—
1337	#102	—	53	1	no	—
1338	#102	—	53	1	no	—
1339	#102	—	53	1	no	—
1340	#102	—	53	1	no	—
1341	#102	—	53	1	no	—
1342	#102	—	53	1	no	—
1343	#102	—	53	1	no	—
1344	#102	—	53	1	no	—
1345	#102	—	53	1	no	—
1346	#102	C₂²×D₅₃	1	1	yes	characteristic
1347	#102	C₂²×D₅₃	1	1	yes	characteristic
1348	#102	C₂²×D₅₃	1	1	yes	characteristic
1349	#102	C₂²×D₅₃	1	1	yes	characteristic
1350	C₂²⋊C₈	—	53	1	no	—
1351	C₂²⋊C₈	—	53	1	no	—
1352	C₂²⋊C₈	—	53	1	no	—
1353	C₂²⋊C₈	—	53	1	no	—
1354	C₂²⋊C₈	—	53	1	no	—
1355	C₂²⋊C₈	—	53	1	no	—
1356	C₂²⋊C₈	—	53	1	no	—
1357	C₂²⋊C₈	—	53	1	no	—
1358	C₄×C₈	—	53	1	no	—
1359	C₄×C₈	—	53	1	no	—
1360	C₄×C₈	—	53	1	no	—
1361	C₄×C₈	—	53	1	no	—
1362	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1363	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1364	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1365	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
1366	C₂⁴	—	53	1	no	—
1367	C₂⁴	—	106	1	no	—
1368	#41	—	2	2	no	—
1369	#41	—	2	2	no	—
1370	#41	—	2	2	no	—
1371	#41	—	53	4	no	—
1372	#41	—	106	8	no	—
1373	#41	—	106	2	no	—
1374	#41	—	106	8	no	—
1375	#41	—	106	2	no	—
1376	#41	—	106	2	no	—
1377	#41	—	106	2	no	—
1378	#41	—	106	2	no	—
1379	#41	—	106	2	no	—
1380	#41	—	106	2	no	—
1381	#41	—	212	4	no	—
1382	#41	—	212	4	no	—
1383	#41	#11719945	1	4	yes	complemented
1384	C₂×Q₈	—	53	1	no	—
1385	C₂×Q₈	—	53	1	no	—
1386	C₂×Q₈	—	106	1	no	—
1387	C₂×Q₈	—	106	1	no	—
1388	C₂×Q₈	—	106	1	no	—
1389	C₂×Q₈	—	106	2	no	—
1390	C₂×Q₈	—	106	2	no	—
1391	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1392	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	53	1	no	—
1396	C₂×D₄	—	53	1	no	—
1397	C₂×D₄	—	106	1	no	—
1398	C₂×D₄	—	106	1	no	—
1399	C₂×D₄	—	106	1	no	—
1400	C₂×D₄	—	106	1	no	—
1401	C₂×D₄	—	106	1	no	—
1402	C₂×D₄	—	106	1	no	—
1403	C₂×D₄	—	106	2	no	—
1404	C₂×D₄	—	106	8	no	—
1405	C₂×D₄	—	106	1	no	—
1406	C₂×D₄	—	106	1	no	—
1407	C₂×D₄	—	106	2	no	—
1408	C₂×D₄	—	106	1	no	—
1409	C₂×D₄	—	106	1	no	—
1410	C₂×D₄	—	106	1	no	—
1411	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1412	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1413	C₂²×C₄	—	2	1	no	—
1414	C₂²×C₄	—	2	1	no	—
1415	C₂²×C₄	—	2	1	no	—
1416	C₂²×C₄	—	2	1	no	—
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	53	1	no	—
1420	C₂²×C₄	—	53	1	no	—
1421	C₂²×C₄	—	53	1	no	—
1422	C₂²×C₄	—	53	1	no	—
1423	C₂²×C₄	—	53	1	no	—
1424	C₂²×C₄	—	53	1	no	—
1425	C₂²×C₄	—	53	1	no	—
1426	C₂²×C₄	—	53	1	no	—
1427	C₂²×C₄	—	53	1	no	—
1428	C₂²×C₄	—	53	1	no	—
1429	C₂²×C₄	—	53	1	no	—
1430	C₂²×C₄	—	53	1	no	—
1431	C₂²×C₄	—	53	1	no	—
1432	C₂²×C₄	—	53	1	no	—
1433	C₂²×C₄	—	53	1	no	—
1434	C₂²×C₄	—	106	1	no	—
1435	C₂²×C₄	—	106	4	no	—
1436	C₂²×C₄	—	106	1	no	—
1437	C₂²×C₄	—	106	1	no	—
1438	C₂²×C₄	—	106	1	no	—
1439	C₂²×C₄	—	106	8	no	—
1440	C₂²×C₄	—	106	1	no	—
1441	C₂²×C₄	—	106	1	no	—
1442	C₂²×C₄	—	106	1	no	—
1443	C₂²×C₄	—	106	1	no	—
1444	C₂²×C₄	—	106	1	no	—
1445	C₂²×C₄	—	106	1	no	—
1446	C₂²×C₄	—	106	2	no	—
1447	C₂²×C₄	—	106	2	no	—
1448	C₂²×C₄	—	106	1	no	—
1449	C₂²×C₄	—	106	1	no	—
1450	C₂²×C₄	—	106	1	no	—
1451	C₂²×C₄	—	106	1	no	—
1452	C₂²×C₄	—	106	1	no	—
1453	C₂²×C₄	—	212	2	no	—
1454	C₂²×C₄	—	212	4	no	—
1455	C₂²×C₄	—	212	4	no	—
1456	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
1457	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
1458	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1459	Q₁₆	—	2	2	no	—
1460	Q₁₆	—	106	2	no	—
1461	Q₁₆	—	106	2	no	—
1462	Q₁₆	—	106	2	no	—
1463	SD₁₆	—	2	2	no	—
1464	SD₁₆	—	2	2	no	—
1465	SD₁₆	—	106	2	no	—
1466	SD₁₆	—	106	2	no	—
1467	SD₁₆	—	106	2	no	—
1468	SD₁₆	—	106	2	no	—
1469	SD₁₆	—	106	2	no	—
1470	SD₁₆	—	106	2	no	—
1471	D₈	—	2	2	no	—
1472	D₈	—	106	2	no	—
1473	D₈	—	106	2	no	—
1474	D₈	—	106	2	no	—
1475	C₂×C₈	—	2	2	no	—
1476	C₂×C₈	—	2	2	no	—
1477	C₂×C₈	—	53	1	no	—
1478	C₂×C₈	—	53	1	no	—
1479	C₂×C₈	—	53	1	no	—
1480	C₂×C₈	—	53	1	no	—
1481	C₂×C₈	—	106	2	no	—
1482	C₂×C₈	—	106	2	no	—
1483	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1484	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1485	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1486	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	53	1	no	—
1492	C₄⋊C₄	—	53	1	no	—
1493	C₄⋊C₄	—	53	1	no	—
1494	C₄⋊C₄	—	53	1	no	—
1495	C₄⋊C₄	—	106	1	no	—
1496	C₄⋊C₄	—	106	1	no	—
1497	C₄⋊C₄	—	106	1	no	—
1498	C₄⋊C₄	—	106	1	no	—
1499	C₄⋊C₄	—	106	1	no	—
1500	C₄⋊C₄	—	106	1	no	—
1501	C₄⋊C₄	—	106	1	no	—
1502	C₄⋊C₄	—	106	1	no	—
1503	C₄⋊C₄	—	106	1	no	—
1504	C₄⋊C₄	—	106	1	no	—
1505	C₄⋊C₄	—	106	1	no	—
1506	C₄⋊C₄	—	106	1	no	—
1507	C₄⋊C₄	—	106	1	no	—
1508	C₄⋊C₄	—	106	1	no	—
1509	C₄⋊C₄	—	106	1	no	—
1510	C₄⋊C₄	—	106	1	no	—
1511	C₄⋊C₄	—	106	1	no	—
1512	C₄⋊C₄	—	106	1	no	—
1513	C₄⋊C₄	—	106	1	no	—
1514	C₄⋊C₄	—	106	1	no	—
1515	C₄⋊C₄	—	106	1	no	—
1516	C₄⋊C₄	—	106	1	no	—
1517	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1518	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1519	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1520	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	106	1	no	—
1528	C₂²⋊C₄	—	106	1	no	—
1529	C₂²⋊C₄	—	106	1	no	—
1530	C₂²⋊C₄	—	106	1	no	—
1531	C₂²⋊C₄	—	106	1	no	—
1532	C₂²⋊C₄	—	106	1	no	—
1533	C₂²⋊C₄	—	106	1	no	—
1534	C₂²⋊C₄	—	106	1	no	—
1535	C₂²⋊C₄	—	106	1	no	—
1536	C₂²⋊C₄	—	106	1	no	—
1537	C₂²⋊C₄	—	106	1	no	—
1538	C₂²⋊C₄	—	106	1	no	—
1539	C₂²⋊C₄	—	106	1	no	—
1540	C₂²⋊C₄	—	106	1	no	—
1541	C₂²⋊C₄	—	106	1	no	—
1542	C₂²⋊C₄	—	106	1	no	—
1543	C₂²⋊C₄	—	106	1	no	—
1544	C₂²⋊C₄	—	106	1	no	—
1545	C₂²⋊C₄	—	106	1	no	—
1546	C₂²⋊C₄	—	106	1	no	—
1547	C₂²⋊C₄	—	106	1	no	—
1548	C₂²⋊C₄	—	106	1	no	—
1549	C₂²⋊C₄	—	106	1	no	—
1550	C₂²⋊C₄	—	106	1	no	—
1551	C₄²	—	2	1	no	—
1552	C₄²	—	2	1	no	—
1553	C₄²	—	2	1	no	—
1554	C₄²	—	2	1	no	—
1555	C₄²	—	2	1	no	—
1556	C₄²	—	2	1	no	—
1557	C₄²	—	53	1	no	—
1558	C₄²	—	53	1	no	—
1559	C₄²	—	53	1	no	—
1560	C₄²	—	53	1	no	—
1561	C₄²	—	53	1	no	—
1562	C₄²	—	53	1	no	—
1563	C₄²	—	53	1	no	—
1564	C₄²	—	53	1	no	—
1565	C₄²	—	53	1	no	—
1566	C₄²	—	53	1	no	—
1567	C₄²	—	53	1	no	—
1568	C₄²	—	53	1	no	—
1569	C₄²	—	106	1	no	—
1570	C₄²	—	106	1	no	—
1571	C₄²	—	106	1	no	—
1572	C₄²	—	106	1	no	—
1573	C₄²	—	106	1	no	—
1574	C₄²	—	106	1	no	—
1575	C₄²	—	106	1	no	—
1576	C₄²	—	106	1	no	—
1577	C₄²	—	106	1	no	—
1578	C₄²	—	106	1	no	—
1579	C₄²	—	106	1	no	—
1580	C₄²	—	106	1	no	—
1581	C₄²	D₄×D₅₃	1	1	yes	characteristic
1582	C₄²	D₄×D₅₃	1	1	yes	characteristic
1583	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1584	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1585	C₂³	—	2	1	no	—
1586	C₂³	—	2	1	no	—
1587	C₂³	—	53	1	no	—
1588	C₂³	—	53	1	no	—
1589	C₂³	—	106	2	no	—
1590	C₂³	—	106	4	no	—
1591	C₂³	—	106	2	no	—
1592	C₂³	—	106	1	no	—
1593	C₂³	—	106	1	no	—
1594	C₂³	—	212	1	no	—
1595	C₂³	—	212	2	no	—
1596	C₂³	—	212	2	no	—
1597	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1598	Q₈	—	2	1	no	—
1599	Q₈	—	2	1	no	—
1600	Q₈	—	2	1	no	—
1601	Q₈	—	53	2	no	—
1602	Q₈	—	106	4	no	—
1603	Q₈	—	106	1	no	—
1604	Q₈	—	106	1	no	—
1605	Q₈	—	106	1	no	—
1606	Q₈	—	212	2	no	—
1607	Q₈	—	212	2	no	—
1608	Q₈	C₂×#11719945	1	2	yes	—
1609	D₄	—	2	4	no	—
1610	D₄	—	2	1	no	—
1611	D₄	—	2	1	no	—
1612	D₄	—	2	1	no	—
1613	D₄	—	4	2	no	—
1614	D₄	—	53	2	no	—
1615	D₄	—	106	4	no	—
1616	D₄	—	106	4	no	—
1617	D₄	—	106	4	no	—
1618	D₄	—	106	4	no	—
1619	D₄	—	106	1	no	—
1620	D₄	—	106	1	no	—
1621	D₄	—	106	1	no	—
1622	D₄	—	212	2	no	—
1623	D₄	—	212	2	no	—
1624	D₄	—	212	2	no	—
1625	D₄	—	212	2	no	—
1626	D₄	—	212	2	no	—
1627	D₄	—	212	2	no	—
1628	D₄	—	212	2	no	—
1629	D₄	C₂×#11719945	1	2	yes	—
1630	C₂×C₄	—	2	1	no	—
1631	C₂×C₄	—	2	4	no	—
1632	C₂×C₄	—	2	2	no	—
1633	C₂×C₄	—	2	2	no	—
1634	C₂×C₄	—	2	1	no	—
1635	C₂×C₄	—	2	1	no	—
1636	C₂×C₄	—	2	1	no	—
1637	C₂×C₄	—	2	1	no	—
1638	C₂×C₄	—	2	1	no	—
1639	C₂×C₄	—	4	2	no	—
1640	C₂×C₄	—	4	2	no	—
1641	C₂×C₄	—	4	2	no	—
1642	C₂×C₄	—	4	2	no	—
1643	C₂×C₄	—	4	2	no	—
1644	C₂×C₄	—	53	1	no	—
1645	C₂×C₄	—	53	4	no	—
1646	C₂×C₄	—	53	1	no	—
1647	C₂×C₄	—	53	1	no	—
1648	C₂×C₄	—	53	1	no	—
1649	C₂×C₄	—	53	1	no	—
1650	C₂×C₄	—	53	1	no	—
1651	C₂×C₄	—	106	2	no	—
1652	C₂×C₄	—	106	2	no	—
1653	C₂×C₄	—	106	4	no	—
1654	C₂×C₄	—	106	4	no	—
1655	C₂×C₄	—	106	2	no	—
1656	C₂×C₄	—	106	4	no	—
1657	C₂×C₄	—	106	2	no	—
1658	C₂×C₄	—	106	1	no	—
1659	C₂×C₄	—	106	2	no	—
1660	C₂×C₄	—	106	2	no	—
1661	C₂×C₄	—	106	4	no	—
1662	C₂×C₄	—	106	2	no	—
1663	C₂×C₄	—	106	2	no	—
1664	C₂×C₄	—	106	2	no	—
1665	C₂×C₄	—	106	1	no	—
1666	C₂×C₄	—	106	1	no	—
1667	C₂×C₄	—	106	1	no	—
1668	C₂×C₄	—	106	1	no	—
1669	C₂×C₄	—	106	1	no	—
1670	C₂×C₄	—	106	1	no	—
1671	C₂×C₄	—	106	1	no	—
1672	C₂×C₄	—	106	1	no	—
1673	C₂×C₄	—	106	1	no	—
1674	C₂×C₄	—	212	1	no	—
1675	C₂×C₄	—	212	1	no	—
1676	C₂×C₄	—	212	2	no	—
1677	C₂×C₄	—	212	2	no	—
1678	C₂×C₄	—	212	2	no	—
1679	C₂×C₄	—	212	2	no	—
1680	C₂×C₄	—	212	2	no	—
1681	C₂×C₄	—	212	1	no	—
1682	C₂×C₄	—	212	2	no	—
1683	C₂×C₄	—	212	2	no	—
1684	C₂×C₄	—	212	2	no	—
1685	C₂×C₄	—	212	2	no	—
1686	C₂×C₄	—	212	2	no	—
1687	C₂×C₄	—	212	2	no	—
1688	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1689	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1690	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1691	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1692	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1693	C₂×C₄	#41×D₅₃	1	2	yes	—
1694	C₂×C₄	C₂×#11719945	1	2	yes	—
1695	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1696	C₈	—	2	1	no	—
1697	C₈	—	2	1	no	—
1698	C₈	—	2	1	no	—
1699	C₈	—	2	1	no	—
1700	C₈	—	106	1	no	—
1701	C₈	—	106	1	no	—
1702	C₈	—	106	1	no	—
1703	C₈	—	106	1	no	—
1704	C₂²	—	2	1	no	—
1705	C₂²	—	2	1	no	—
1706	C₂²	—	2	2	no	—
1707	C₂²	—	4	1	no	—
1708	C₂²	—	4	1	no	—
1709	C₂²	—	4	1	no	—
1710	C₂²	—	4	1	no	—
1711	C₂²	—	4	1	no	—
1712	C₂²	—	53	2	no	—
1713	C₂²	—	106	1	no	—
1714	C₂²	—	106	1	no	—
1715	C₂²	—	106	1	no	—
1716	C₂²	—	106	1	no	—
1717	C₂²	—	106	2	no	—
1718	C₂²	—	106	1	no	—
1719	C₂²	—	212	4	no	—
1720	C₂²	—	212	8	no	—
1721	C₂²	—	212	1	no	—
1722	C₂²	—	212	1	no	—
1723	C₂²	—	212	1	no	—
1724	C₂²	—	212	1	no	—
1725	C₂²	—	212	1	no	—
1726	C₂²	#16811132	1	2	yes	—
1727	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1728	C₄	—	2	1	no	—
1729	C₄	—	2	1	no	—
1730	C₄	—	2	2	no	—
1731	C₄	—	4	1	no	—
1732	C₄	—	4	1	no	—
1733	C₄	—	4	1	no	—
1734	C₄	—	4	1	no	—
1735	C₄	—	4	1	no	—
1736	C₄	—	53	2	no	—
1737	C₄	—	106	1	no	—
1738	C₄	—	106	1	no	—
1739	C₄	—	106	1	no	—
1740	C₄	—	106	1	no	—
1741	C₄	—	106	1	no	—
1742	C₄	—	106	2	no	—
1743	C₄	—	212	1	no	—
1744	C₄	—	212	1	no	—
1745	C₄	—	212	1	no	—
1746	C₄	—	212	1	no	—
1747	C₄	—	212	1	no	—
1748	C₄	#16811132	1	2	yes	—
1749	C₄	#135×D₅₃	1	2	yes	—
1750	C₄	#16811420	1	2	yes	—
1751	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1752	C₄	C₂²×#11719945	1	1	yes	characteristic
1753	C₂	—	2	2	no	—
1754	C₂	—	4	2	no	—
1755	C₂	—	8	1	no	—
1756	C₂	—	106	2	no	—
1757	C₂	—	424	1	no	—
1758	C₂	—	212	1	no	—
1759	C₂	—	212	2	no	—
1760	C₂	C₂×#16811132	1	1	yes	characteristic
1761	C₂	C₂×#135×D₅₃	1	1	yes	characteristic
1762	C₂	C₂×#16811420	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₄×#135×C₅₃	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	C₄×#135	D₅₃
hypocenter	C₅₃	#60536
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #20288008	C₂	semidirect
2. C₄×#41×D₅₃	C₂	semidirect
3. #20284799	C₂	semidirect
4. #20284793	C₂	semidirect
5. #20284784	C₂	semidirect
6. #20284782	C₂	semidirect
7. #20284773	C₂	semidirect
8. #20284771	C₂	semidirect
9. #20284766	C₂	semidirect
10. #20284760	C₂	semidirect
11. #20284752	C₂	semidirect
12. #20284744	C₂	semidirect
13. #20284739	C₂	semidirect
14. #20284737	C₂	semidirect
15. #20284731	C₂	semidirect
16. #20284729	C₂	semidirect
17. #20284721	C₂	semidirect
18. #20284713	C₂	semidirect
19. #20284632	C₂	semidirect
20. #20284626	C₂	semidirect
21. #20284501	C₂	semidirect
22. #20284499	C₂	semidirect
23. #20284168	C₂	semidirect
24. #20284166	C₂	semidirect
25. #20283935	C₂	semidirect
26. #20283929	C₂	semidirect
27. C₄×#13133239	C₂	semidirect
28. C₄×#13133237	C₂	semidirect
29. C₄×#13133237	C₂	semidirect
30. C₂×#16810674	C₂	semidirect
31. C₄×#135×C₅₃	C₂	semidirect
37. #16811177	C₂²	semidirect
38. #16811176	C₂²	semidirect
40. #16811170	C₂²	semidirect
41. #16811169	C₂²	semidirect
43. #16811160	C₂²	semidirect
45. #16811155	C₂²	semidirect
61. C₄×#11719945	C₂²	semidirect
78. #16810967	C₂²	semidirect
79. #16810966	C₂²	semidirect
80. #16810963	C₂²	semidirect
81. #16810962	C₂²	semidirect
86. #16810950	C₂²	semidirect
87. #16810949	C₂²	semidirect
88. #16810946	C₂²	semidirect
89. #16810945	C₂²	semidirect
94. #16810933	C₂²	semidirect
95. #16810932	C₂²	semidirect
96. #16810929	C₂²	semidirect
97. #16810928	C₂²	semidirect
98. #16810926	C₂²	semidirect
99. #16810925	C₂²	semidirect
100. #16810922	C₂²	semidirect
101. #16810921	C₂²	semidirect
102. #16810917	C₂²	semidirect
103. #16810916	C₂²	semidirect
104. #16810912	C₂²	semidirect
105. #16810911	C₂²	semidirect
106. #16810907	C₂²	semidirect
107. #16810906	C₂²	semidirect
108. #16810902	C₂²	semidirect
109. #16810901	C₂²	semidirect
110. #16810848	C₂²	semidirect
111. #16810847	C₂²	semidirect
112. #16810844	C₂²	semidirect
113. #16810843	C₂²	semidirect
114. #16810841	C₂²	semidirect
115. #16810840	C₂²	semidirect
116. #16810837	C₂²	semidirect
117. #16810836	C₂²	semidirect
118. #16810832	C₂²	semidirect
119. #16810831	C₂²	semidirect
120. #16810827	C₂²	semidirect
121. #16810826	C₂²	semidirect
122. #16810822	C₂²	semidirect
123. #16810821	C₂²	semidirect
124. #16810817	C₂²	semidirect
125. #16810816	C₂²	semidirect
142. C₄×Dic₂₁₂	C₂²	semidirect
143. C₄×Dic₂₁₂	C₂²	semidirect
144. C₄×#11719925	C₂²	semidirect
145. C₄×#11719925	C₂²	semidirect
146. C₄×#11719925	C₂²	semidirect
147. C₄×#11719925	C₂²	semidirect
148. C₄×#11719913	C₂²	semidirect
149. C₄×#11719913	C₂²	semidirect
150. C₄×#11719913	C₂²	semidirect
151. C₄×#11719913	C₂²	semidirect
152. C₄×#11719924	C₂²	semidirect
153. C₄×#11719924	C₂²	semidirect
154. C₄×#11719924	C₂²	semidirect
155. C₄×#11719924	C₂²	semidirect
156. C₄×#11719923	C₂²	semidirect
157. C₄×#11719923	C₂²	semidirect
158. C₄×#11719923	C₂²	semidirect
159. C₄×#11719923	C₂²	semidirect
160. C₄×D₄₂₄	C₂²	semidirect
161. C₄×D₄₂₄	C₂²	semidirect
162. C₄×#11719922	C₂²	semidirect
163. C₄×#11719922	C₂²	semidirect
164. C₄×#11719922	C₂²	semidirect
165. C₄×#11719922	C₂²	semidirect
170. #16810674	C₂²	semidirect
171. #16810674	C₂²	semidirect
172. #16810674	C₂²	semidirect
173. #16810674	C₂²	semidirect
174. #16810661	C₂²	semidirect
175. #16810659	C₂²	semidirect
176. #16810659	C₂²	semidirect
177. C₂×#13133146	C₂²	semidirect
178. C₂×#13133146	C₂²	semidirect
180. #16810620	C₂²	semidirect
182. #16810619	C₂²	semidirect
184. #16810617	C₂²	semidirect
187. C₂×C₄×#88322	C₂²	semidirect
190. C₄×#41×C₅₃	C₂²	semidirect
191. C₄×Q₁₆×C₅₃	C₂²	semidirect
192. C₄×Q₁₆×C₅₃	C₂²	semidirect
193. C₄×SD₁₆×C₅₃	C₂²	semidirect
194. C₄×SD₁₆×C₅₃	C₂²	semidirect
195. C₄×SD₁₆×C₅₃	C₂²	semidirect
196. C₄×SD₁₆×C₅₃	C₂²	semidirect
197. C₄×D₈×C₅₃	C₂²	semidirect
198. C₄×D₈×C₅₃	C₂²	semidirect
199. C₅₃×#427	C₂²	semidirect
201. C₅₃×#416	C₂²	semidirect
202. C₂×C₄×C₈×C₅₃	C₂²	semidirect
489. #41×C₅₃	#41	semidirect
535. #11719945	#41	semidirect
806. C₄×D₅₃	#135	semidirect
901. C₄×#135	D₅₃	semidirect
951. C₄×#41	C₂×D₅₃	semidirect
1032. C₄×Q₁₆	C₂×D₅₃	semidirect
1033. C₄×Q₁₆	C₂×D₅₃	semidirect
1046. C₄×SD₁₆	C₂×D₅₃	semidirect
1047. C₄×SD₁₆	C₂×D₅₃	semidirect
1048. C₄×SD₁₆	C₂×D₅₃	semidirect
1049. C₄×SD₁₆	C₂×D₅₃	semidirect
1056. C₄×D₈	C₂×D₅₃	semidirect
1057. C₄×D₈	C₂×D₅₃	semidirect
1069. #427	C₂×D₅₃	semidirect
1079. #416	C₂×D₅₃	semidirect
1083. C₂×C₄×C₈	C₂×D₅₃	semidirect
1084. C₅₃	#60536	semidirect
1383. #41	#11719945	semidirect

Maximal subgroups

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

subgroup	index
#20288008	2
C₄×#41×D₅₃	2
#20284799	2
#20284793	2
#20284784	2
#20284782	2
#20284773	2
#20284771	2
#20284766	2
#20284760	2
#20284752	2
#20284744	2
#20284739	2
#20284737	2
#20284731	2
#20284729	2
#20284721	2
#20284713	2
#20284632	2
#20284626	2
#20284501	2
#20284499	2
#20284168	2
#20284166	2
#20283935	2
#20283929	2
C₄×#13133239	2
C₄×#13133237	2
C₂×#16810674	2
C₄×#135×C₅₃	2
#60536	53