Subgroups — #28260344

Order 13568.

2656 conjugacy classes of subgroups.

The subgroup lattice has 1648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289493	C₂	1	2	yes	maximal, complemented
2	#20289485	C₂	1	1	yes	maximal, characteristic, complemented
3	#576×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#20286515	C₂	1	1	yes	maximal, characteristic, complemented
5	#20286515	C₂	1	1	yes	maximal, characteristic, complemented
6	#20286513	C₂	1	1	yes	maximal, characteristic, complemented
7	#20286512	C₂	1	1	yes	maximal, characteristic, complemented
8	#20286504	C₂	1	1	yes	maximal, characteristic, complemented
9	#20286501	C₂	1	1	yes	maximal, characteristic, complemented
10	#20286500	C₂	1	1	yes	maximal, characteristic, complemented
11	#20286484	C₂	1	2	yes	maximal, complemented
12	#20286483	C₂	1	2	yes	maximal, complemented
13	#20286480	C₂	1	2	yes	maximal, complemented
14	#20286477	C₂	1	2	yes	maximal, complemented
15	#20285197	C₂	1	1	yes	maximal, characteristic, complemented
16	#20284438	C₂	1	2	yes	maximal, complemented
17	#20284437	C₂	1	1	yes	maximal, characteristic, complemented
18	#472×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#20284085	C₂	1	2	yes	maximal, complemented
20	#20284073	C₂	1	2	yes	maximal, complemented
21	#20283627	C₂	1	1	yes	maximal, characteristic, complemented
22	#20283613	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3290	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811460	C₂²	1	2	yes	complemented
25	H(5,𝔽₂)×D₅₃	C₂²	1	2	yes	complemented
26	#16811436	—	2	1	no	—
27	#16811436	C₂²	1	1	yes	characteristic, complemented
28	#16811432	—	2	2	no	—
29	#16811432	—	2	2	no	—
30	#16811432	C₂²	1	2	yes	complemented
31	#16811432	C₂²	1	2	yes	complemented
32	#16811431	C₂²	1	2	yes	complemented
33	#16811431	C₂²	1	2	yes	complemented
34	#16811429	—	2	2	no	—
35	#16811429	C₂²	1	2	yes	complemented
36	#16811428	C₂²	1	1	yes	characteristic, complemented
37	#16811428	C₂²	1	2	yes	complemented
38	#16811428	C₂²	1	1	yes	characteristic, complemented
39	#16811427	—	2	2	no	—
40	#16811427	—	2	2	no	—
41	#16811427	C₂²	1	2	yes	complemented
42	#16811427	C₂²	1	2	yes	complemented
43	#16811426	C₂²	1	2	yes	complemented
44	#16811426	C₂²	1	2	yes	complemented
45	#16811425	—	2	2	no	—
46	#16811425	—	2	1	no	—
47	#16811425	—	2	1	no	—
48	#16811425	C₂²	1	1	yes	characteristic, complemented
49	#16811425	C₂²	1	2	yes	complemented
50	#16811425	C₂²	1	1	yes	characteristic, complemented
51	#16811424	—	2	1	no	—
52	#16811424	C₂²	1	1	yes	characteristic, complemented
53	#16811422	—	2	2	no	—
54	#16811422	—	2	2	no	—
55	#16811422	C₂²	1	2	yes	complemented
56	#16811422	C₂²	1	2	yes	complemented
57	#16811420	—	2	2	no	—
58	#16811420	C₂²	1	1	yes	characteristic
59	C₂×#13133244	—	2	2	no	—
60	C₂×#13133244	C₂²	1	2	yes	complemented
61	AGL(1,ℤ/8)×D₅₃	—	2	2	no	—
62	AGL(1,ℤ/8)×D₅₃	—	2	2	no	—
63	AGL(1,ℤ/8)×D₅₃	C₂²	1	2	yes	complemented
64	AGL(1,ℤ/8)×D₅₃	C₂²	1	2	yes	complemented
65	C₂×#13133240	—	2	1	no	—
66	C₂×#13133240	C₂²	1	1	yes	characteristic, complemented
67	#135×D₅₃	—	2	1	no	—
68	#135×D₅₃	—	2	1	no	—
69	#135×D₅₃	C₂²	1	1	yes	characteristic
70	C₂×D₈×D₅₃	—	2	1	no	—
71	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
72	#16811388	C₂²	1	2	yes	complemented
73	#131×D₅₃	C₂²	1	1	yes	characteristic, complemented
74	#131×D₅₃	C₂²	1	1	yes	characteristic, complemented
75	#16811191	C₂²	1	2	yes	complemented
76	#16811013	C₂²	1	2	yes	complemented
77	#16811009	C₂²	1	2	yes	complemented
78	#16811008	C₂²	1	1	yes	characteristic, complemented
79	#16811000	C₂²	1	1	yes	characteristic, complemented
80	#16810998	C₂²	1	1	yes	characteristic, complemented
81	#16810895	C₂²	1	1	yes	characteristic, complemented
82	#16810894	C₂²	1	1	yes	characteristic, complemented
83	#16810894	C₂²	1	1	yes	characteristic, complemented
84	#16810894	C₂²	1	2	yes	complemented
85	#16810893	C₂²	1	1	yes	characteristic, complemented
86	#16810893	C₂²	1	1	yes	characteristic, complemented
87	#16810893	C₂²	1	2	yes	complemented
88	#16810892	C₂²	1	2	yes	complemented
89	#16810892	C₂²	1	2	yes	complemented
90	#16810891	C₂²	1	2	yes	complemented
91	#16810891	C₂²	1	2	yes	complemented
92	#16810890	C₂²	1	1	yes	characteristic, complemented
93	#16810889	C₂²	1	2	yes	complemented
94	#16810889	C₂²	1	2	yes	complemented
95	#16810888	C₂²	1	2	yes	complemented
96	#16810888	C₂²	1	2	yes	complemented
97	#16810883	C₂²	1	2	yes	complemented
98	#16810800	C₂²	1	2	yes	complemented
99	#16810799	C₂²	1	2	yes	complemented
100	#16810799	C₂²	1	2	yes	complemented
101	#16810798	C₂²	1	2	yes	complemented
102	#16810796	C₂²	1	2	yes	complemented
103	#16810795	C₂²	1	2	yes	complemented
104	#16810793	C₂²	1	2	yes	complemented
105	#16810792	C₂²	1	2	yes	complemented
106	#16810792	C₂²	1	2	yes	complemented
107	#16810792	C₂²	1	2	yes	complemented
108	#16810792	C₂²	1	2	yes	complemented
109	#16810791	C₂²	1	2	yes	complemented
110	#16810789	C₂²	1	2	yes	complemented
111	#16810789	C₂²	1	2	yes	complemented
112	#16810745	C₂²	1	1	yes	characteristic, complemented
113	#16810744	C₂²	1	1	yes	characteristic, complemented
114	#16810743	C₂²	1	2	yes	complemented
115	#16810742	C₂²	1	1	yes	characteristic, complemented
116	#16810742	C₂²	1	1	yes	characteristic, complemented
117	#16810742	C₂²	1	2	yes	complemented
118	#16810741	C₂²	1	1	yes	characteristic, complemented
119	#16810741	C₂²	1	1	yes	characteristic, complemented
120	#16810740	C₂²	1	1	yes	characteristic, complemented
121	#16810739	C₂²	1	1	yes	characteristic, complemented
122	#16810738	C₂²	1	1	yes	characteristic, complemented
123	#16810738	C₂²	1	1	yes	characteristic, complemented
124	#16810670	C₂²	1	1	yes	characteristic, complemented
125	#108×D₅₃	C₂²	1	1	yes	characteristic, complemented
126	#16810638	C₂²	1	1	yes	characteristic, complemented
127	#16810638	C₂²	1	2	yes	complemented
128	#16810638	C₂²	1	1	yes	characteristic, complemented
129	#16810606	C₂²	1	2	yes	complemented
130	#100×D₅₃	C₂²	1	2	yes	complemented
131	#16810577	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#578	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#577	C₂²	1	2	yes	complemented
134	C₅₃×#576	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#473	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#472	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#471	C₂²	1	2	yes	complemented
139	C₅₃×#455	C₂²	1	2	yes	complemented
140	C₅₃×#454	C₂²	1	2	yes	complemented
141	C₅₃×#443	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#443	C₂²	1	1	yes	characteristic, complemented
143	#13133265	—	2	2	no	—
144	#13133265	—	2	2	no	—
145	#13133265	C₂³	1	2	yes	complemented
146	#13133263	—	2	2	no	—
147	#13133263	—	2	2	no	—
148	#13133263	—	2	2	no	—
149	#13133263	—	2	2	no	—
150	#13133263	—	4	2	no	—
151	#13133263	C₂³	1	2	yes	—
152	#13133263	C₂³	1	2	yes	—
153	#13133263	C₂³	1	2	yes	complemented
154	#13133263	C₂³	1	2	yes	complemented
155	#13133262	—	2	2	no	—
156	#13133262	—	2	2	no	—
157	#13133262	—	4	2	no	—
158	#13133262	C₂³	1	2	yes	—
159	C₂×#11719949	—	2	2	no	—
160	C₂×#11719949	—	2	2	no	—
161	C₂×#11719949	C₂³	1	2	yes	—
162	#41×D₅₃	—	2	2	no	—
163	#41×D₅₃	—	2	2	no	—
164	#41×D₅₃	—	2	2	no	—
165	#41×D₅₃	—	2	2	no	—
166	#41×D₅₃	—	4	2	no	—
167	#41×D₅₃	C₂³	1	1	yes	characteristic
168	#41×D₅₃	C₂³	1	1	yes	characteristic
169	#41×D₅₃	C₂³	1	2	yes	—
170	C₂×D₄×D₅₃	—	2	2	no	—
171	C₂×D₄×D₅₃	—	2	2	no	—
172	C₂×D₄×D₅₃	—	4	2	no	—
173	C₂×D₄×D₅₃	C₂³	1	2	yes	—
174	#13133249	—	2	2	no	—
175	#13133249	—	2	2	no	—
176	#13133249	—	2	2	no	—
177	#13133249	—	2	2	no	—
178	#13133249	—	2	2	no	—
179	#13133249	D₄	1	1	yes	characteristic, complemented
180	#13133249	D₄	1	1	yes	characteristic, complemented
181	#13133248	—	2	2	no	—
182	#13133248	—	2	2	no	—
183	#13133248	C₂³	1	2	yes	—
184	#13133248	C₂³	1	2	yes	complemented
185	#13133246	—	2	2	no	—
186	#13133246	D₄	1	1	yes	characteristic, complemented
187	#13133246	D₄	1	1	yes	characteristic, complemented
188	#13133245	—	2	2	no	—
189	#13133245	—	2	2	no	—
190	#13133245	—	2	2	no	—
191	#13133245	—	2	2	no	—
192	#13133245	C₂³	1	2	yes	—
193	#13133245	C₂³	1	2	yes	—
194	#13133245	C₂³	1	2	yes	complemented
195	#13133245	C₂³	1	2	yes	complemented
196	#13133244	—	2	2	no	—
197	#13133244	—	2	2	no	—
198	#13133244	—	2	2	no	—
199	#13133244	—	2	2	no	—
200	#13133244	—	2	2	no	—
201	#13133244	—	2	2	no	—
202	#13133244	—	2	2	no	—
203	#13133244	—	2	2	no	—
204	#13133244	—	2	2	no	—
205	#13133244	—	2	2	no	—
206	#13133244	—	2	2	no	—
207	#13133244	—	2	2	no	—
208	#13133244	—	2	2	no	—
209	#13133244	—	2	2	no	—
210	#13133244	—	2	2	no	—
211	#13133244	—	2	2	no	—
212	#13133244	—	2	2	no	—
213	#13133244	D₄	1	1	yes	characteristic, complemented
214	#13133244	D₄	1	1	yes	characteristic, complemented
215	#13133243	—	2	2	no	—
216	#13133243	—	2	2	no	—
217	#13133243	C₂³	1	2	yes	—
218	#13133243	C₂³	1	2	yes	complemented
219	#13133242	—	2	2	no	—
220	#13133242	—	2	2	no	—
221	#13133242	—	2	2	no	—
222	#13133242	—	2	2	no	—
223	#13133242	C₂³	1	2	yes	—
224	#13133242	C₂³	1	2	yes	—
225	#13133242	C₂³	1	2	yes	complemented
226	#13133242	C₂³	1	2	yes	complemented
227	#13133241	—	2	2	no	—
228	#13133241	—	2	2	no	—
229	#13133241	—	2	2	no	—
230	#13133241	—	2	2	no	—
231	#13133241	—	2	2	no	—
232	#13133241	D₄	1	1	yes	characteristic, complemented
233	#13133241	D₄	1	1	yes	characteristic, complemented
234	#13133240	—	2	1	no	—
235	#13133240	—	2	1	no	—
236	#13133240	—	2	2	no	—
237	#13133240	—	2	2	no	—
238	#13133240	—	2	2	no	—
239	#13133240	—	2	1	no	—
240	#13133240	—	2	1	no	—
241	#13133240	—	2	1	no	—
242	#13133240	—	2	1	no	—
243	#13133240	—	2	1	no	—
244	#13133240	—	2	2	no	—
245	#13133240	—	2	2	no	—
246	#13133240	D₄	1	1	yes	characteristic, complemented
247	#13133239	—	2	1	no	—
248	#13133239	—	2	1	no	—
249	#13133239	—	2	2	no	—
250	#13133239	C₂³	1	1	yes	characteristic
251	#13133239	C₂³	1	1	yes	characteristic
252	#13133238	—	2	2	no	—
253	#13133238	—	2	2	no	—
254	#13133238	—	2	2	no	—
255	#13133238	—	2	2	no	—
256	#13133238	—	2	2	no	—
257	#13133238	D₄	1	2	yes	complemented
258	#13133237	—	2	2	no	—
259	#13133237	—	2	2	no	—
260	#13133237	—	2	2	no	—
261	#13133237	—	2	2	no	—
262	#13133237	C₂³	1	2	yes	—
263	#13133237	C₂³	1	1	yes	characteristic
264	#13133237	C₂³	1	1	yes	characteristic
265	#13133236	—	2	1	no	—
266	#13133236	D₄	1	1	yes	characteristic, complemented
267	Q₁₆×D₅₃	—	2	1	no	—
268	Q₁₆×D₅₃	D₄	1	1	yes	characteristic, complemented
269	C₂×#11719924	—	2	2	no	—
270	C₂×#11719924	—	2	2	no	—
271	C₂×#11719924	C₂³	1	2	yes	complemented
272	C₂×#11719924	C₂³	1	2	yes	complemented
273	SD₁₆×D₅₃	—	2	2	no	—
274	SD₁₆×D₅₃	—	2	2	no	—
275	SD₁₆×D₅₃	—	2	2	no	—
276	SD₁₆×D₅₃	—	2	2	no	—
277	SD₁₆×D₅₃	—	2	2	no	—
278	SD₁₆×D₅₃	D₄	1	2	yes	complemented
279	C₂×D₄₂₄	—	2	1	no	—
280	C₂×D₄₂₄	—	2	1	no	—
281	C₂×D₄₂₄	—	2	2	no	—
282	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
283	C₂×D₄₂₄	C₂³	1	2	yes	complemented
284	C₂×D₄₂₄	C₂³	1	1	yes	characteristic, complemented
285	C₂×#11719922	—	2	2	no	—
286	C₂×#11719922	—	2	2	no	—
287	C₂×#11719922	C₂³	1	2	yes	—
288	C₂×#11719922	C₂³	1	2	yes	complemented
289	D₈×D₅₃	—	2	1	no	—
290	D₈×D₅₃	—	2	1	no	—
291	D₈×D₅₃	—	2	2	no	—
292	D₈×D₅₃	—	2	2	no	—
293	D₈×D₅₃	—	2	2	no	—
294	D₈×D₅₃	—	2	1	no	—
295	D₈×D₅₃	—	2	1	no	—
296	D₈×D₅₃	—	2	1	no	—
297	D₈×D₅₃	—	2	1	no	—
298	D₈×D₅₃	—	2	1	no	—
299	D₈×D₅₃	—	2	2	no	—
300	D₈×D₅₃	—	2	2	no	—
301	D₈×D₅₃	D₄	1	1	yes	characteristic, complemented
302	#13133225	—	2	2	no	—
303	#13133225	—	2	1	no	—
304	#13133225	—	2	1	no	—
305	#13133225	C₂³	1	1	yes	characteristic
306	#13133225	C₂³	1	1	yes	characteristic, complemented
307	#13133225	C₂³	1	2	yes	complemented
308	#13133224	C₂³	1	1	yes	characteristic
309	#13133224	C₂³	1	1	yes	characteristic, complemented
310	#13133224	C₂³	1	2	yes	complemented
311	#13133223	—	2	2	no	—
312	#13133223	—	2	1	no	—
313	#13133223	—	2	1	no	—
314	#13133223	C₂³	1	1	yes	characteristic
315	#13133223	C₂³	1	1	yes	characteristic, complemented
316	#13133223	C₂³	1	2	yes	complemented
317	C₂×#11719912	—	2	2	no	—
318	C₂×#11719912	C₂³	1	1	yes	characteristic
319	M₁₆×D₅₃	—	2	2	no	—
320	M₁₆×D₅₃	—	2	1	no	—
321	M₁₆×D₅₃	—	2	1	no	—
322	M₁₆×D₅₃	C₂³	1	1	yes	characteristic
323	M₁₆×D₅₃	C₂³	1	2	yes	—
324	M₁₆×D₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₈×D₅₃	—	2	1	no	—
326	C₂×C₈×D₅₃	—	2	1	no	—
327	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
328	#13133214	C₂³	1	2	yes	complemented
329	#13133213	C₂³	1	2	yes	complemented
330	#13133206	C₂³	1	2	yes	complemented
331	#13133190	—	4	2	no	—
332	#13133187	—	4	2	no	—
333	#13133174	C₂³	1	1	yes	characteristic
334	#13133153	C₂³	1	1	yes	characteristic, complemented
335	#13133153	C₂³	1	1	yes	characteristic, complemented
336	#13133152	C₂³	1	1	yes	characteristic, complemented
337	#13133152	C₂³	1	2	yes	complemented
338	#13133152	C₂³	1	1	yes	characteristic, complemented
339	#13133145	C₂³	1	1	yes	characteristic
340	#13133145	C₂³	1	1	yes	characteristic, complemented
341	#13133145	C₂³	1	2	yes	complemented
342	#13133144	C₂³	1	1	yes	characteristic
343	#13133144	C₂³	1	1	yes	characteristic, complemented
344	#13133144	C₂³	1	2	yes	complemented
345	#13133143	C₂³	1	1	yes	characteristic
346	#13133143	C₂³	1	1	yes	characteristic, complemented
347	#13133143	C₂³	1	2	yes	complemented
348	#13133136	C₂³	1	2	yes	complemented
349	#13133134	C₂³	1	2	yes	complemented
350	#13133133	C₂³	1	2	yes	complemented
351	#13133133	C₂³	1	2	yes	complemented
352	#13133133	C₂³	1	2	yes	complemented
353	#13133133	C₂³	1	2	yes	complemented
354	#13133128	C₂³	1	1	yes	characteristic, complemented
355	#13133127	C₂³	1	1	yes	characteristic, complemented
356	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
357	2₋¹⁺⁴×C₅₃	C₂³	1	2	yes	complemented
358	H(5,𝔽₂)×C₅₃	C₂³	1	2	yes	—
359	#137×C₅₃	—	2	2	no	—
360	#137×C₅₃	—	2	2	no	—
361	#137×C₅₃	C₂³	1	2	yes	—
362	#137×C₅₃	C₂³	1	2	yes	complemented
363	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
364	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
365	AGL(1,ℤ/8)×C₅₃	C₂³	1	2	yes	—
366	AGL(1,ℤ/8)×C₅₃	C₂³	1	2	yes	complemented
367	#135×C₅₃	—	2	1	no	—
368	#135×C₅₃	—	2	2	no	—
369	#135×C₅₃	—	2	1	no	—
370	#135×C₅₃	C₂³	1	1	yes	characteristic
371	#135×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×Q₁₆×C₅₃	—	2	1	no	—
373	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
374	C₂×SD₁₆×C₅₃	—	2	2	no	—
375	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	complemented
376	C₂×D₈×C₅₃	—	2	1	no	—
377	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
378	#131×C₅₃	C₂³	1	1	yes	characteristic
379	#131×C₅₃	C₂³	1	2	yes	complemented
380	#131×C₅₃	C₂³	1	1	yes	characteristic, complemented
381	#124×C₅₃	C₂³	1	2	yes	complemented
382	#108×C₅₃	C₂³	1	1	yes	characteristic, complemented
383	#108×C₅₃	C₂³	1	1	yes	characteristic, complemented
384	#104×C₅₃	C₂³	1	1	yes	characteristic
385	#104×C₅₃	C₂³	1	1	yes	characteristic, complemented
386	#104×C₅₃	C₂³	1	2	yes	complemented
387	#101×C₅₃	C₂³	1	2	yes	complemented
388	#100×C₅₃	C₂³	1	2	yes	complemented
389	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	4	2	no	—
392	#41×C₅₃	—	2	2	no	—
393	#41×C₅₃	—	2	2	no	—
394	#41×C₅₃	—	2	2	no	—
395	#41×C₅₃	—	2	2	no	—
396	#41×C₅₃	—	4	2	no	—
397	#41×C₅₃	C₂⁴	1	1	yes	characteristic
398	#41×C₅₃	C₂⁴	1	2	yes	—
399	#41×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×Q₈×C₅₃	—	2	2	no	—
401	C₂×Q₈×C₅₃	—	2	2	no	—
402	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
403	C₂×D₄×C₅₃	—	2	2	no	—
404	C₂×D₄×C₅₃	—	2	2	no	—
405	C₂×D₄×C₅₃	—	4	2	no	—
406	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
407	C₂×C₂²⋊D₅₃	—	2	2	no	—
408	C₂×C₂²⋊D₅₃	—	4	2	no	—
409	C₂×C₂²⋊D₅₃	—	4	2	no	—
410	C₂×C₂²⋊D₅₃	—	4	2	no	—
411	C₂×C₂²⋊D₅₃	—	4	2	no	—
412	C₂×C₂²⋊D₅₃	—	4	2	no	—
413	#11719949	—	2	2	no	—
414	#11719949	—	2	2	no	—
415	#11719949	—	2	2	no	—
416	#11719949	—	2	2	no	—
417	#11719949	—	2	2	no	—
418	#11719949	—	2	2	no	—
419	#11719949	—	2	2	no	—
420	#11719949	—	2	2	no	—
421	#11719949	—	2	2	no	—
422	#11719949	—	2	2	no	—
423	#11719949	—	4	2	no	—
424	#11719949	—	4	2	no	—
425	#11719949	—	4	2	no	—
426	#11719949	C₂×D₄	1	2	yes	—
427	#11719949	C₂×D₄	1	1	yes	characteristic
428	#11719949	C₂×D₄	1	1	yes	characteristic
429	Q₈×D₅₃	—	2	2	no	—
430	Q₈×D₅₃	—	2	2	no	—
431	Q₈×D₅₃	—	4	2	no	—
432	Q₈×D₅₃	C₂×D₄	1	1	yes	characteristic
433	Q₈×D₅₃	C₂×D₄	1	2	yes	—
434	Q₈×D₅₃	C₂×D₄	1	1	yes	characteristic
435	#11719947	—	2	1	no	—
436	#11719947	—	2	2	no	—
437	#11719947	—	2	1	no	—
438	#11719947	—	2	2	no	—
439	#11719947	—	2	2	no	—
440	#11719947	—	4	2	no	—
441	#11719947	—	4	2	no	—
442	#11719947	—	4	2	no	—
443	#11719947	C₂×D₄	1	2	yes	—
444	#11719947	C₂×D₄	1	1	yes	characteristic
445	#11719947	C₂×D₄	1	1	yes	characteristic
446	D₄×D₅₃	—	2	1	no	—
447	D₄×D₅₃	—	2	2	no	—
448	D₄×D₅₃	—	2	1	no	—
449	D₄×D₅₃	—	2	2	no	—
450	D₄×D₅₃	—	2	2	no	—
451	D₄×D₅₃	—	2	2	no	—
452	D₄×D₅₃	—	2	2	no	—
453	D₄×D₅₃	—	2	2	no	—
454	D₄×D₅₃	—	2	2	no	—
455	D₄×D₅₃	—	2	2	no	—
456	D₄×D₅₃	—	2	2	no	—
457	D₄×D₅₃	—	2	2	no	—
458	D₄×D₅₃	—	2	2	no	—
459	D₄×D₅₃	—	4	2	no	—
460	D₄×D₅₃	—	4	2	no	—
461	D₄×D₅₃	—	4	2	no	—
462	D₄×D₅₃	—	4	2	no	—
463	D₄×D₅₃	—	4	2	no	—
464	D₄×D₅₃	—	4	2	no	—
465	D₄×D₅₃	—	4	2	no	—
466	D₄×D₅₃	—	4	2	no	—
467	D₄×D₅₃	—	4	2	no	—
468	D₄×D₅₃	—	4	2	no	—
469	D₄×D₅₃	—	4	2	no	—
470	D₄×D₅₃	—	4	2	no	—
471	D₄×D₅₃	—	4	2	no	—
472	D₄×D₅₃	C₂×D₄	1	1	yes	characteristic
473	D₄×D₅₃	C₂×D₄	1	2	yes	—
474	D₄×D₅₃	C₂×D₄	1	1	yes	characteristic
475	#11719945	—	2	1	no	—
476	#11719945	—	2	2	no	—
477	#11719945	—	2	1	no	—
478	#11719945	—	2	2	no	—
479	#11719945	—	2	2	no	—
480	#11719945	—	2	2	no	—
481	#11719945	—	2	2	no	—
482	#11719945	—	4	2	no	—
483	#11719945	—	4	2	no	—
484	#11719945	—	4	2	no	—
485	#11719945	—	4	2	no	—
486	#11719945	—	4	2	no	—
487	#11719945	—	4	2	no	—
488	#11719945	—	4	2	no	—
489	#11719945	C₂⁴	1	1	yes	characteristic
490	#11719945	C₂⁴	1	2	yes	—
491	#11719945	C₂⁴	1	1	yes	characteristic
492	C₂×D₂₁₂	—	2	2	no	—
493	C₂×D₂₁₂	—	2	2	no	—
494	C₂×D₂₁₂	—	2	2	no	—
495	C₂×D₂₁₂	—	2	2	no	—
496	C₂×D₂₁₂	—	2	2	no	—
497	C₂×D₂₁₂	—	4	2	no	—
498	C₂×D₂₁₂	—	4	2	no	—
499	C₂×D₂₁₂	—	4	2	no	—
500	C₂×D₂₁₂	—	4	2	no	—
501	C₂×D₂₁₂	C₂⁴	1	2	yes	—
502	C₂×D₂₁₂	C₂⁴	1	2	yes	—
503	C₂×C₄×D₅₃	—	2	1	no	—
504	C₂×C₄×D₅₃	—	2	1	no	—
505	C₂×C₄×D₅₃	—	2	2	no	—
506	C₂×C₄×D₅₃	—	2	2	no	—
507	C₂×C₄×D₅₃	—	4	2	no	—
508	C₂×C₄×D₅₃	—	4	2	no	—
509	C₂×C₄×D₅₃	—	4	2	no	—
510	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
511	Q₁₆×C₅₃	—	2	2	no	—
512	Q₁₆×C₅₃	—	2	2	no	—
513	Q₁₆×C₅₃	—	2	1	no	—
514	Q₁₆×C₅₃	—	2	1	no	—
515	Q₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
516	Q₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
517	SD₁₆×C₅₃	—	2	2	no	—
518	SD₁₆×C₅₃	—	2	2	no	—
519	SD₁₆×C₅₃	—	2	2	no	—
520	SD₁₆×C₅₃	—	2	2	no	—
521	SD₁₆×C₅₃	—	2	2	no	—
522	SD₁₆×C₅₃	—	2	2	no	—
523	SD₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
524	SD₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
525	SD₁₆×C₅₃	C₂×D₄	1	2	yes	—
526	D₈×C₅₃	—	2	2	no	—
527	D₈×C₅₃	—	2	2	no	—
528	D₈×C₅₃	—	2	1	no	—
529	D₈×C₅₃	—	2	1	no	—
530	D₈×C₅₃	C₂×D₄	1	1	yes	characteristic
531	D₈×C₅₃	C₂×D₄	1	1	yes	characteristic
532	M₁₆×C₅₃	—	2	1	no	—
533	M₁₆×C₅₃	—	2	2	no	—
534	M₁₆×C₅₃	—	2	1	no	—
535	M₁₆×C₅₃	C₂⁴	1	1	yes	characteristic
536	M₁₆×C₅₃	C₂⁴	1	2	yes	—
537	M₁₆×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×C₈×C₅₃	—	2	1	no	—
539	C₂×C₈×C₅₃	—	2	2	no	—
540	C₂×C₈×C₅₃	—	2	1	no	—
541	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂²⋊C₄×C₅₃	—	4	2	no	—
544	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
545	#11719925	—	2	2	no	—
546	#11719925	—	2	2	no	—
547	#11719925	C₂×D₄	1	2	yes	—
548	#11719925	C₂×D₄	1	1	yes	characteristic
549	#11719925	C₂×D₄	1	1	yes	characteristic
550	#11719924	—	2	2	no	—
551	#11719924	—	2	2	no	—
552	#11719924	—	2	2	no	—
553	#11719924	—	2	2	no	—
554	#11719924	—	2	2	no	—
555	#11719924	—	2	2	no	—
556	#11719924	—	2	2	no	—
557	#11719924	—	2	2	no	—
558	#11719924	—	2	2	no	—
559	#11719924	—	2	2	no	—
560	#11719924	C₂×D₄	1	2	yes	—
561	#11719924	C₂×D₄	1	1	yes	characteristic
562	#11719924	C₂×D₄	1	1	yes	characteristic
563	#11719923	—	2	2	no	—
564	#11719923	—	2	2	no	—
565	#11719923	C₂×D₄	1	1	yes	characteristic
566	#11719923	C₂×D₄	1	2	yes	—
567	#11719923	C₂×D₄	1	1	yes	characteristic
568	#11719922	—	2	2	no	—
569	#11719922	—	2	2	no	—
570	#11719922	—	2	2	no	—
571	#11719922	—	2	2	no	—
572	#11719922	—	2	2	no	—
573	#11719922	—	2	2	no	—
574	#11719922	—	2	2	no	—
575	#11719922	—	2	2	no	—
576	#11719922	—	2	2	no	—
577	#11719922	—	2	2	no	—
578	#11719922	C₂×D₄	1	1	yes	characteristic
579	#11719922	C₂×D₄	1	2	yes	—
580	#11719922	C₂×D₄	1	1	yes	characteristic
581	#11719921	—	2	1	no	—
582	#11719921	—	4	2	no	—
583	#11719919	—	2	1	no	—
584	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
585	#11719917	—	2	1	no	—
586	#11719917	—	2	2	no	—
587	#11719917	—	2	1	no	—
588	#11719917	C₂⁴	1	1	yes	characteristic
589	#11719917	C₂⁴	1	2	yes	—
590	#11719917	C₂⁴	1	1	yes	characteristic
591	C₂×#88322	—	2	1	no	—
592	C₂×#88322	—	2	1	no	—
593	C₂×#88322	—	2	2	no	—
594	C₂×#88322	C₂⁴	1	1	yes	characteristic
595	C₂×#88322	C₂⁴	1	1	yes	characteristic
596	Dic₂₁₂	C₂×D₄	1	1	yes	characteristic
597	Dic₂₁₂	C₂×D₄	1	1	yes	characteristic
598	D₄₂₄	—	2	2	no	—
599	D₄₂₄	—	2	2	no	—
600	D₄₂₄	—	2	2	no	—
601	D₄₂₄	—	2	2	no	—
602	D₄₂₄	—	2	1	no	—
603	D₄₂₄	—	2	1	no	—
604	D₄₂₄	—	2	1	no	—
605	D₄₂₄	—	2	2	no	—
606	D₄₂₄	—	2	2	no	—
607	D₄₂₄	—	2	1	no	—
608	D₄₂₄	C₂×D₄	1	1	yes	characteristic
609	D₄₂₄	C₂×D₄	1	1	yes	characteristic
610	#11719913	—	2	2	no	—
611	#11719913	—	2	2	no	—
612	#11719913	—	2	2	no	—
613	#11719913	—	2	2	no	—
614	#11719913	C₂×D₄	1	1	yes	characteristic
615	#11719913	C₂×D₄	1	2	yes	—
616	#11719913	C₂×D₄	1	1	yes	characteristic
617	#11719912	—	2	2	no	—
618	#11719912	—	2	1	no	—
619	#11719912	—	2	1	no	—
620	#11719912	—	2	1	no	—
621	#11719912	—	2	1	no	—
622	#11719912	—	2	2	no	—
623	#11719912	—	2	1	no	—
624	#11719912	—	2	1	no	—
625	#11719912	—	2	2	no	—
626	#11719912	C₂×D₄	1	1	yes	characteristic
627	#11719912	C₂×D₄	1	1	yes	characteristic
628	#11719912	C₂×D₄	1	1	yes	characteristic
629	#11719912	C₂×D₄	1	1	yes	characteristic
630	C₈×D₅₃	—	2	1	no	—
631	C₈×D₅₃	—	2	1	no	—
632	C₈×D₅₃	—	2	2	no	—
633	C₈×D₅₃	—	2	1	no	—
634	C₈×D₅₃	—	2	1	no	—
635	C₈×D₅₃	—	2	2	no	—
636	C₈×D₅₃	—	2	1	no	—
637	C₈×D₅₃	—	2	1	no	—
638	C₈×D₅₃	—	2	2	no	—
639	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
640	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
641	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
642	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
643	C₂³×C₅₃	—	2	2	no	—
644	C₂³×C₅₃	—	4	2	no	—
645	C₂²×D₅₃	—	2	1	no	—
646	C₂²×D₅₃	—	2	1	no	—
647	C₂²×D₅₃	—	2	2	no	—
648	C₂²×D₅₃	—	2	2	no	—
649	C₂²×D₅₃	—	2	2	no	—
650	C₂²×D₅₃	—	4	2	no	—
651	C₂²×D₅₃	—	4	2	no	—
652	C₂²×D₅₃	—	4	2	no	—
653	C₂²×D₅₃	—	4	2	no	—
654	C₂²×D₅₃	—	4	2	no	—
655	C₂²×D₅₃	—	4	2	no	—
656	C₂²×D₅₃	—	4	2	no	—
657	C₂²×D₅₃	—	16	2	no	—
658	C₂²×D₅₃	—	16	4	no	—
659	C₂²×D₅₃	H(5,𝔽₂)	1	1	yes	characteristic
660	Q₈×C₅₃	—	2	2	no	—
661	Q₈×C₅₃	—	2	2	no	—
662	Q₈×C₅₃	—	4	2	no	—
663	Q₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
664	Q₈×C₅₃	C₂²×D₄	1	2	yes	—
665	Q₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
666	D₄×C₅₃	—	2	1	no	—
667	D₄×C₅₃	—	2	2	no	—
668	D₄×C₅₃	—	2	1	no	—
669	D₄×C₅₃	—	2	2	no	—
670	D₄×C₅₃	—	2	2	no	—
671	D₄×C₅₃	—	4	2	no	—
672	D₄×C₅₃	—	4	2	no	—
673	D₄×C₅₃	—	4	2	no	—
674	D₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
675	D₄×C₅₃	C₂²×D₄	1	2	yes	—
676	D₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	2	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	2	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	4	2	no	—
683	C₂×C₄×C₅₃	—	4	2	no	—
684	C₂×C₄×C₅₃	—	4	2	no	—
685	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
686	C₂²⋊D₅₃	—	2	1	no	—
687	C₂²⋊D₅₃	—	2	2	no	—
688	C₂²⋊D₅₃	—	2	1	no	—
689	C₂²⋊D₅₃	—	2	1	no	—
690	C₂²⋊D₅₃	—	2	2	no	—
691	C₂²⋊D₅₃	—	2	1	no	—
692	C₂²⋊D₅₃	—	2	1	no	—
693	C₂²⋊D₅₃	—	2	2	no	—
694	C₂²⋊D₅₃	—	2	1	no	—
695	C₂²⋊D₅₃	—	4	2	no	—
696	C₂²⋊D₅₃	—	4	2	no	—
697	C₂²⋊D₅₃	—	4	2	no	—
698	C₂²⋊D₅₃	—	4	2	no	—
699	C₂²⋊D₅₃	—	4	2	no	—
700	C₂²⋊D₅₃	—	4	2	no	—
701	C₂²⋊D₅₃	—	4	2	no	—
702	C₂²⋊D₅₃	—	4	2	no	—
703	C₂²⋊D₅₃	—	16	2	no	—
704	C₂×Dic₅₃	—	2	1	no	—
705	C₂×Dic₅₃	—	2	2	no	—
706	C₂×Dic₅₃	—	2	1	no	—
707	C₂×Dic₅₃	—	2	1	no	—
708	C₂×Dic₅₃	—	4	2	no	—
709	C₂×Dic₅₃	H(5,𝔽₂)	1	1	yes	characteristic
710	D₂₁₂	—	2	1	no	—
711	D₂₁₂	—	2	2	no	—
712	D₂₁₂	—	2	1	no	—
713	D₂₁₂	—	2	2	no	—
714	D₂₁₂	—	2	2	no	—
715	D₂₁₂	—	2	2	no	—
716	D₂₁₂	—	2	2	no	—
717	D₂₁₂	—	4	2	no	—
718	D₂₁₂	—	4	2	no	—
719	D₂₁₂	—	4	2	no	—
720	D₂₁₂	—	4	2	no	—
721	D₂₁₂	—	4	2	no	—
722	D₂₁₂	—	4	2	no	—
723	D₂₁₂	—	4	2	no	—
724	D₂₁₂	—	16	2	no	—
725	D₂₁₂	C₂²×D₄	1	1	yes	characteristic
726	D₂₁₂	C₂²×D₄	1	2	yes	—
727	D₂₁₂	C₂²×D₄	1	1	yes	characteristic
728	C₄×D₅₃	—	2	1	no	—
729	C₄×D₅₃	—	2	2	no	—
730	C₄×D₅₃	—	2	1	no	—
731	C₄×D₅₃	—	2	1	no	—
732	C₄×D₅₃	—	2	2	no	—
733	C₄×D₅₃	—	2	1	no	—
734	C₄×D₅₃	—	2	1	no	—
735	C₄×D₅₃	—	2	2	no	—
736	C₄×D₅₃	—	2	1	no	—
737	C₄×D₅₃	—	4	2	no	—
738	C₄×D₅₃	—	4	2	no	—
739	C₄×D₅₃	—	4	2	no	—
740	C₄×D₅₃	—	4	2	no	—
741	C₄×D₅₃	—	4	2	no	—
742	C₄×D₅₃	—	4	2	no	—
743	C₄×D₅₃	—	4	2	no	—
744	C₄×D₅₃	—	4	2	no	—
745	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
746	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
747	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
748	C₄×D₅₃	C₂²×D₄	1	1	yes	characteristic
749	Dic₁₀₆	—	2	1	no	—
750	Dic₁₀₆	—	2	2	no	—
751	Dic₁₀₆	—	2	1	no	—
752	Dic₁₀₆	—	4	2	no	—
753	Dic₁₀₆	C₂²×D₄	1	1	yes	characteristic
754	Dic₁₀₆	C₂²×D₄	1	2	yes	—
755	Dic₁₀₆	C₂²×D₄	1	1	yes	characteristic
756	C₈×C₅₃	—	2	1	no	—
757	C₈×C₅₃	—	2	2	no	—
758	C₈×C₅₃	—	2	1	no	—
759	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
760	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
761	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
762	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
763	#88322	—	2	1	no	—
764	#88322	—	2	2	no	—
765	#88322	—	2	1	no	—
766	#88322	C₂²×D₄	1	1	yes	characteristic
767	#88322	C₂²×D₄	1	1	yes	characteristic
768	#88322	C₂²×D₄	1	1	yes	characteristic
769	#88322	C₂²×D₄	1	1	yes	characteristic
770	#61106	—	53	1	no	maximal, Sylow
771	C₂²×C₅₃	—	2	1	no	—
772	C₂²×C₅₃	—	2	2	no	—
773	C₂²×C₅₃	—	2	1	no	—
774	C₂²×C₅₃	—	4	2	no	—
775	C₂²×C₅₃	—	8	2	no	—
776	C₂²×C₅₃	—	16	2	no	—
777	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
778	C₂×D₅₃	—	2	1	no	—
779	C₂×D₅₃	—	2	2	no	—
780	C₂×D₅₃	—	2	1	no	—
781	C₂×D₅₃	—	4	1	no	—
782	C₂×D₅₃	—	4	2	no	—
783	C₂×D₅₃	—	4	2	no	—
784	C₂×D₅₃	—	4	2	no	—
785	C₂×D₅₃	—	8	1	no	—
786	C₂×D₅₃	—	8	2	no	—
787	C₂×D₅₃	—	8	4	no	—
788	C₂×D₅₃	—	8	2	no	—
789	C₂×D₅₃	—	8	2	no	—
790	C₂×D₅₃	—	16	2	no	—
791	C₂×D₅₃	—	16	2	no	—
792	C₂×D₅₃	—	16	2	no	—
793	C₂×D₅₃	—	16	2	no	—
794	C₂×D₅₃	—	16	2	no	—
795	C₂×D₅₃	—	16	2	no	—
796	C₂×D₅₃	D₄²	1	1	yes	characteristic
797	C₂×D₅₃	D₄²	1	1	yes	characteristic
798	C₄×C₅₃	—	2	1	no	—
799	C₄×C₅₃	—	2	2	no	—
800	C₄×C₅₃	—	2	1	no	—
801	C₄×C₅₃	—	4	1	no	—
802	C₄×C₅₃	—	4	2	no	—
803	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
804	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
805	Dic₅₃	—	2	1	no	—
806	Dic₅₃	—	2	2	no	—
807	Dic₅₃	—	2	1	no	—
808	Dic₅₃	—	4	1	no	—
809	Dic₅₃	D₄²	1	1	yes	characteristic
810	Dic₅₃	D₄²	1	1	yes	characteristic
811	#3585	—	53	2	no	—
812	#3584	—	53	1	no	—
813	C₂×#576	—	53	1	no	—
814	#3292	—	53	1	no	—
815	#3292	—	53	1	no	—
816	#3292	—	53	1	no	—
817	#3292	—	53	1	no	—
818	#3290	—	53	1	no	—
819	#3290	—	53	1	no	—
820	#3290	—	53	1	no	—
821	#3290	D₅₃	1	1	yes	characteristic, complemented
822	#3288	—	53	2	no	—
823	#3288	—	53	2	no	—
824	#3288	—	53	2	no	—
825	#3288	—	53	2	no	—
826	#3155	—	53	1	no	—
827	#3068	—	53	2	no	—
828	#3067	—	53	1	no	—
829	C₂×#472	—	53	1	no	—
830	#3021	—	53	2	no	—
831	#3019	—	53	2	no	—
832	#2957	—	53	1	no	—
833	#2955	—	53	1	no	—
834	C₂×C₅₃	—	2	1	no	—
835	C₂×C₅₃	—	4	1	no	—
836	C₂×C₅₃	—	4	1	no	—
837	C₂×C₅₃	—	4	2	no	—
838	C₂×C₅₃	—	8	2	no	—
839	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
840	D₅₃	—	2	1	no	—
841	D₅₃	—	2	1	no	—
842	D₅₃	—	4	1	no	—
843	D₅₃	—	4	1	no	—
844	D₅₃	—	4	2	no	—
845	D₅₃	—	8	2	no	—
846	D₅₃	—	8	2	no	—
847	#585	—	53	2	no	—
848	C₂×H(5,𝔽₂)	—	53	2	no	—
849	#578	—	53	1	no	—
850	#578	—	106	1	no	—
851	#578	C₂×D₅₃	1	1	yes	characteristic, complemented
852	#577	—	53	2	no	—
853	#577	—	53	2	no	—
854	#577	—	53	2	no	—
855	#577	—	53	2	no	—
856	#577	—	53	2	no	—
857	#577	—	106	2	no	—
858	#577	—	106	2	no	—
859	#577	—	106	2	no	—
860	#577	C₂×D₅₃	1	2	yes	complemented
861	#576	—	53	2	no	—
862	#576	—	53	2	no	—
863	#576	—	53	2	no	—
864	#576	—	53	2	no	—
865	#576	—	53	1	no	—
866	#576	—	53	2	no	—
867	#576	—	53	1	no	—
868	#576	—	53	1	no	—
869	#576	—	53	1	no	—
870	#576	—	53	1	no	—
871	#576	—	53	2	no	—
872	#576	—	106	1	no	—
873	#576	—	106	1	no	—
874	#576	—	106	1	no	—
875	#576	—	106	2	no	—
876	#576	—	106	2	no	—
877	#576	—	106	2	no	—
878	#576	C₂×D₅₃	1	1	yes	characteristic, complemented
879	#575	—	53	1	no	—
880	#575	—	53	2	no	—
881	#575	—	53	2	no	—
882	#575	—	106	2	no	—
883	#575	—	106	2	no	—
884	#575	—	106	2	no	—
885	C₂×AGL(1,ℤ/8)	—	53	2	no	—
886	C₂×AGL(1,ℤ/8)	—	53	2	no	—
887	C₂×AGL(1,ℤ/8)	—	53	2	no	—
888	C₂×AGL(1,ℤ/8)	—	106	2	no	—
889	C₂×AGL(1,ℤ/8)	—	106	2	no	—
890	C₂×AGL(1,ℤ/8)	—	106	2	no	—
891	C₂×#135	—	53	1	no	—
892	C₂×#135	—	53	1	no	—
893	C₂×#135	—	106	1	no	—
894	C₂×#135	—	106	1	no	—
895	C₂×#135	—	106	1	no	—
896	C₂²×D₈	—	53	1	no	—
897	C₂²×D₈	—	106	1	no	—
898	#568	—	53	2	no	—
899	C₂×#131	—	53	1	no	—
900	C₂×#131	—	53	1	no	—
901	#535	—	53	2	no	—
902	#496	—	53	2	no	—
903	#496	—	53	2	no	—
904	#495	—	53	1	no	—
905	#495	C₂×D₅₃	1	1	yes	characteristic, complemented
906	#493	—	53	1	no	—
907	#493	—	53	1	no	—
908	#473	—	53	1	no	—
909	#473	C₂×D₅₃	1	1	yes	characteristic, complemented
910	#472	—	53	2	no	—
911	#472	—	53	2	no	—
912	#472	—	53	1	no	—
913	#472	—	53	1	no	—
914	#472	—	53	2	no	—
915	#472	—	53	1	no	—
916	#472	—	53	2	no	—
917	#472	—	53	1	no	—
918	#472	—	53	1	no	—
919	#472	—	53	2	no	—
920	#472	—	53	2	no	—
921	#472	C₂×D₅₃	1	1	yes	characteristic, complemented
922	#471	—	53	2	no	—
923	#471	—	53	2	no	—
924	#471	—	53	2	no	—
925	#471	—	53	2	no	—
926	#471	—	53	2	no	—
927	#471	C₂×D₅₃	1	2	yes	complemented
928	#455	—	53	2	no	—
929	#455	—	53	2	no	—
930	#455	—	53	2	no	—
931	#455	C₂×D₅₃	1	2	yes	complemented
932	#454	—	53	2	no	—
933	#454	—	53	2	no	—
934	#454	—	53	2	no	—
935	#454	C₂×D₅₃	1	2	yes	complemented
936	#453	—	53	2	no	—
937	#453	—	53	2	no	—
938	#453	—	53	2	no	—
939	#453	—	53	2	no	—
940	#453	—	53	2	no	—
941	#453	—	53	2	no	—
942	#453	—	53	2	no	—
943	#453	—	53	2	no	—
944	#444	—	53	1	no	—
945	#444	—	53	2	no	—
946	#444	—	53	1	no	—
947	#444	—	53	1	no	—
948	#444	—	53	1	no	—
949	#444	—	53	2	no	—
950	#443	—	53	1	no	—
951	#443	—	53	1	no	—
952	#443	—	53	1	no	—
953	#443	—	53	1	no	—
954	#443	—	53	1	no	—
955	#443	—	53	1	no	—
956	#443	C₂×D₅₃	1	1	yes	characteristic, complemented
957	#443	C₂×D₅₃	1	1	yes	characteristic, complemented
958	#430	—	53	1	no	—
959	C₂×#108	—	53	1	no	—
960	#421	—	53	1	no	—
961	#421	—	53	1	no	—
962	#421	—	53	2	no	—
963	#413	—	53	2	no	—
964	C₂×#100	—	53	2	no	—
965	#405	—	53	1	no	—
966	C₅₃	#61106	1	1	yes	characteristic, complemented, Sylow
967	2₋¹⁺⁴	—	53	2	no	—
968	2₋¹⁺⁴	—	106	2	no	—
969	2₋¹⁺⁴	—	106	2	no	—
970	2₋¹⁺⁴	C₂²×D₅₃	1	2	yes	complemented
971	H(5,𝔽₂)	—	53	2	no	—
972	H(5,𝔽₂)	—	53	2	no	—
973	H(5,𝔽₂)	—	53	2	no	—
974	H(5,𝔽₂)	—	53	2	no	—
975	H(5,𝔽₂)	—	53	2	no	—
976	H(5,𝔽₂)	—	106	2	no	—
977	H(5,𝔽₂)	—	106	2	no	—
978	H(5,𝔽₂)	—	106	2	no	—
979	H(5,𝔽₂)	—	106	2	no	—
980	H(5,𝔽₂)	—	106	2	no	—
981	H(5,𝔽₂)	—	106	2	no	—
982	H(5,𝔽₂)	—	212	2	no	—
983	H(5,𝔽₂)	—	212	2	no	—
984	H(5,𝔽₂)	C₂²×D₅₃	1	2	yes	—
985	C₂×#41	—	53	1	no	—
986	C₂×#41	—	53	1	no	—
987	C₂×#41	—	53	2	no	—
988	C₂×#41	—	53	2	no	—
989	C₂×#41	—	106	2	no	—
990	C₂×#41	—	106	2	no	—
991	C₂×#41	—	106	2	no	—
992	C₂×#41	—	106	2	no	—
993	C₂×#41	—	106	2	no	—
994	C₂×#41	—	106	2	no	—
995	C₂×#41	—	212	2	no	—
996	C₂²×D₄	—	53	2	no	—
997	C₂²×D₄	—	106	2	no	—
998	C₂²×D₄	—	106	2	no	—
999	C₂²×D₄	—	212	2	no	—
1000	#137	—	2	2	no	—
1001	#137	—	2	2	no	—
1002	#137	—	53	1	no	—
1003	#137	—	53	1	no	—
1004	#137	—	53	1	no	—
1005	#137	—	53	1	no	—
1006	#137	—	53	2	no	—
1007	#137	—	53	2	no	—
1008	#137	—	106	2	no	—
1009	#137	—	106	2	no	—
1010	#137	—	106	2	no	—
1011	#137	—	106	2	no	—
1012	#137	—	106	2	no	—
1013	#137	—	106	2	no	—
1014	#137	—	106	2	no	—
1015	#137	—	106	2	no	—
1016	#137	C₂²×D₅₃	1	2	yes	—
1017	#137	C₂²×D₅₃	1	2	yes	complemented
1018	AGL(1,ℤ/8)	—	2	2	no	—
1019	AGL(1,ℤ/8)	—	2	2	no	—
1020	AGL(1,ℤ/8)	—	53	1	no	—
1021	AGL(1,ℤ/8)	—	53	1	no	—
1022	AGL(1,ℤ/8)	—	53	1	no	—
1023	AGL(1,ℤ/8)	—	53	1	no	—
1024	AGL(1,ℤ/8)	—	53	2	no	—
1025	AGL(1,ℤ/8)	—	53	2	no	—
1026	AGL(1,ℤ/8)	—	53	2	no	—
1027	AGL(1,ℤ/8)	—	53	2	no	—
1028	AGL(1,ℤ/8)	—	53	2	no	—
1029	AGL(1,ℤ/8)	—	53	2	no	—
1030	AGL(1,ℤ/8)	—	53	2	no	—
1031	AGL(1,ℤ/8)	—	53	2	no	—
1032	AGL(1,ℤ/8)	—	53	2	no	—
1033	AGL(1,ℤ/8)	—	53	2	no	—
1034	AGL(1,ℤ/8)	—	106	2	no	—
1035	AGL(1,ℤ/8)	—	106	2	no	—
1036	AGL(1,ℤ/8)	—	106	2	no	—
1037	AGL(1,ℤ/8)	—	106	2	no	—
1038	AGL(1,ℤ/8)	—	106	2	no	—
1039	AGL(1,ℤ/8)	—	106	2	no	—
1040	AGL(1,ℤ/8)	—	106	2	no	—
1041	AGL(1,ℤ/8)	—	106	2	no	—
1042	AGL(1,ℤ/8)	—	106	2	no	—
1043	AGL(1,ℤ/8)	—	106	2	no	—
1044	AGL(1,ℤ/8)	—	106	2	no	—
1045	AGL(1,ℤ/8)	—	106	2	no	—
1046	AGL(1,ℤ/8)	—	106	2	no	—
1047	AGL(1,ℤ/8)	—	106	2	no	—
1048	AGL(1,ℤ/8)	—	106	2	no	—
1049	AGL(1,ℤ/8)	—	106	2	no	—
1050	AGL(1,ℤ/8)	—	106	2	no	—
1051	AGL(1,ℤ/8)	—	106	2	no	—
1052	AGL(1,ℤ/8)	—	106	2	no	—
1053	AGL(1,ℤ/8)	—	106	2	no	—
1054	AGL(1,ℤ/8)	—	106	2	no	—
1055	AGL(1,ℤ/8)	—	106	2	no	—
1056	AGL(1,ℤ/8)	—	106	2	no	—
1057	AGL(1,ℤ/8)	—	106	2	no	—
1058	AGL(1,ℤ/8)	—	106	2	no	—
1059	AGL(1,ℤ/8)	—	106	2	no	—
1060	AGL(1,ℤ/8)	—	106	2	no	—
1061	AGL(1,ℤ/8)	—	106	2	no	—
1062	AGL(1,ℤ/8)	—	106	2	no	—
1063	AGL(1,ℤ/8)	—	106	2	no	—
1064	AGL(1,ℤ/8)	—	106	2	no	—
1065	AGL(1,ℤ/8)	—	106	2	no	—
1066	AGL(1,ℤ/8)	C₂²×D₅₃	1	2	yes	—
1067	AGL(1,ℤ/8)	C₂²×D₅₃	1	2	yes	complemented
1068	#135	—	2	1	no	—
1069	#135	—	2	2	no	—
1070	#135	—	2	1	no	—
1071	#135	—	53	2	no	—
1072	#135	—	53	1	no	—
1073	#135	—	53	1	no	—
1074	#135	—	53	1	no	—
1075	#135	—	53	2	no	—
1076	#135	—	53	1	no	—
1077	#135	—	53	1	no	—
1078	#135	—	53	1	no	—
1079	#135	—	106	1	no	—
1080	#135	—	106	1	no	—
1081	#135	—	106	2	no	—
1082	#135	—	106	1	no	—
1083	#135	—	106	1	no	—
1084	#135	—	106	1	no	—
1085	#135	—	106	1	no	—
1086	#135	—	106	1	no	—
1087	#135	—	106	1	no	—
1088	#135	—	106	2	no	—
1089	#135	—	106	2	no	—
1090	#135	—	106	2	no	—
1091	#135	—	106	2	no	—
1092	#135	—	106	2	no	—
1093	#135	—	106	2	no	—
1094	#135	—	106	2	no	—
1095	#135	—	106	2	no	—
1096	#135	—	106	2	no	—
1097	#135	—	106	2	no	—
1098	#135	—	106	2	no	—
1099	#135	—	106	2	no	—
1100	#135	—	106	2	no	—
1101	#135	—	106	1	no	—
1102	#135	—	106	1	no	—
1103	#135	—	106	2	no	—
1104	#135	C₂²×D₅₃	1	1	yes	characteristic
1105	#135	C₂²×D₅₃	1	1	yes	characteristic
1106	C₂×Q₁₆	—	2	1	no	—
1107	C₂×Q₁₆	—	53	1	no	—
1108	C₂×Q₁₆	—	106	1	no	—
1109	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1110	C₂×SD₁₆	—	2	2	no	—
1111	C₂×SD₁₆	—	53	2	no	—
1112	C₂×SD₁₆	—	53	2	no	—
1113	C₂×SD₁₆	—	53	2	no	—
1114	C₂×SD₁₆	—	106	2	no	—
1115	C₂×SD₁₆	—	106	2	no	—
1116	C₂×SD₁₆	—	106	2	no	—
1117	C₂×SD₁₆	—	106	2	no	—
1118	C₂×SD₁₆	—	106	2	no	—
1119	C₂×SD₁₆	—	106	2	no	—
1120	C₂×SD₁₆	—	106	2	no	—
1121	C₂×SD₁₆	C₂²×D₅₃	1	2	yes	complemented
1122	C₂×D₈	—	2	1	no	—
1123	C₂×D₈	—	53	1	no	—
1124	C₂×D₈	—	53	2	no	—
1125	C₂×D₈	—	53	2	no	—
1126	C₂×D₈	—	53	1	no	—
1127	C₂×D₈	—	53	1	no	—
1128	C₂×D₈	—	53	2	no	—
1129	C₂×D₈	—	106	1	no	—
1130	C₂×D₈	—	106	1	no	—
1131	C₂×D₈	—	106	2	no	—
1132	C₂×D₈	—	106	1	no	—
1133	C₂×D₈	—	106	1	no	—
1134	C₂×D₈	—	106	1	no	—
1135	C₂×D₈	—	106	1	no	—
1136	C₂×D₈	—	106	2	no	—
1137	C₂×D₈	—	106	1	no	—
1138	C₂×D₈	—	106	2	no	—
1139	C₂×D₈	—	106	2	no	—
1140	C₂×D₈	—	106	2	no	—
1141	C₂×D₈	—	106	2	no	—
1142	C₂×D₈	—	106	2	no	—
1143	C₂×D₈	—	106	1	no	—
1144	C₂×D₈	—	106	1	no	—
1145	C₂×D₈	—	106	2	no	—
1146	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1147	#131	—	53	1	no	—
1148	#131	—	53	1	no	—
1149	#131	—	53	2	no	—
1150	#131	—	53	1	no	—
1151	#131	—	53	1	no	—
1152	#131	—	53	2	no	—
1153	#131	—	53	1	no	—
1154	#131	—	53	1	no	—
1155	#131	—	53	2	no	—
1156	#131	—	106	1	no	—
1157	#131	—	106	1	no	—
1158	#131	—	106	2	no	—
1159	#131	—	106	1	no	—
1160	#131	—	106	1	no	—
1161	#131	—	106	2	no	—
1162	#131	C₂²×D₅₃	1	1	yes	characteristic
1163	#131	C₂²×D₅₃	1	1	yes	characteristic, complemented
1164	#131	C₂²×D₅₃	1	2	yes	complemented
1165	C₂×M₁₆	—	53	1	no	—
1166	C₂×M₁₆	—	53	1	no	—
1167	C₂×M₁₆	—	53	1	no	—
1168	C₂×M₁₆	—	53	2	no	—
1169	C₂×M₁₆	—	106	2	no	—
1170	C₂×M₁₆	—	106	1	no	—
1171	C₂×M₁₆	—	106	1	no	—
1172	C₂×M₁₆	—	106	2	no	—
1173	C₂²×C₈	—	53	1	no	—
1174	C₂²×C₈	—	106	1	no	—
1175	C₂²×C₈	—	106	1	no	—
1176	#127	—	53	2	no	—
1177	#127	—	53	2	no	—
1178	#124	—	53	2	no	—
1179	#124	C₂²×D₅₃	1	2	yes	complemented
1180	#121	—	212	2	no	—
1181	#120	—	212	2	no	—
1182	#117	—	53	1	no	—
1183	#108	—	53	2	no	—
1184	#108	—	53	1	no	—
1185	#108	—	53	1	no	—
1186	#108	—	53	1	no	—
1187	#108	—	53	1	no	—
1188	#108	C₂²×D₅₃	1	1	yes	characteristic, complemented
1189	#108	C₂²×D₅₃	1	1	yes	characteristic, complemented
1190	#104	—	53	1	no	—
1191	#104	—	53	1	no	—
1192	#104	—	53	2	no	—
1193	#104	—	53	1	no	—
1194	#104	—	53	1	no	—
1195	#104	—	53	2	no	—
1196	#104	—	53	1	no	—
1197	#104	—	53	1	no	—
1198	#104	—	53	2	no	—
1199	#104	C₂²×D₅₃	1	1	yes	characteristic
1200	#104	C₂²×D₅₃	1	1	yes	characteristic, complemented
1201	#104	C₂²×D₅₃	1	2	yes	complemented
1202	#101	—	53	2	no	—
1203	#101	C₂²×D₅₃	1	2	yes	complemented
1204	#100	—	53	2	no	—
1205	#100	—	53	2	no	—
1206	#100	—	53	2	no	—
1207	#100	—	53	2	no	—
1208	#100	—	53	2	no	—
1209	#100	C₂²×D₅₃	1	2	yes	complemented
1210	#97	—	53	1	no	—
1211	#97	—	53	1	no	—
1212	C₄×C₈	—	53	1	no	—
1213	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1214	C₂⁴	—	106	2	no	—
1215	C₂⁴	—	212	2	no	—
1216	#41	—	2	2	no	—
1217	#41	—	2	2	no	—
1218	#41	—	2	2	no	—
1219	#41	—	2	2	no	—
1220	#41	—	4	2	no	—
1221	#41	—	53	2	no	—
1222	#41	—	53	1	no	—
1223	#41	—	53	1	no	—
1224	#41	—	53	2	no	—
1225	#41	—	53	1	no	—
1226	#41	—	53	1	no	—
1227	#41	—	53	1	no	—
1228	#41	—	53	2	no	—
1229	#41	—	53	1	no	—
1230	#41	—	106	1	no	—
1231	#41	—	106	2	no	—
1232	#41	—	106	1	no	—
1233	#41	—	106	2	no	—
1234	#41	—	106	2	no	—
1235	#41	—	106	2	no	—
1236	#41	—	106	2	no	—
1237	#41	—	106	1	no	—
1238	#41	—	106	2	no	—
1239	#41	—	106	1	no	—
1240	#41	—	106	2	no	—
1241	#41	—	106	2	no	—
1242	#41	—	106	2	no	—
1243	#41	—	106	2	no	—
1244	#41	—	106	2	no	—
1245	#41	—	106	2	no	—
1246	#41	—	106	2	no	—
1247	#41	—	106	2	no	—
1248	#41	—	106	2	no	—
1249	#41	—	106	2	no	—
1250	#41	—	106	2	no	—
1251	#41	—	106	2	no	—
1252	#41	—	212	2	no	—
1253	#41	—	212	2	no	—
1254	#41	—	212	2	no	—
1255	#41	—	212	2	no	—
1256	#41	—	212	2	no	—
1257	#41	—	212	2	no	—
1258	#41	—	212	2	no	—
1259	#41	—	212	2	no	—
1260	#41	—	212	2	no	—
1261	#41	—	212	2	no	—
1262	#41	—	212	2	no	—
1263	#41	—	212	2	no	—
1264	#41	—	212	2	no	—
1265	#41	C₂³×D₅₃	1	1	yes	characteristic
1266	#41	C₂³×D₅₃	1	2	yes	—
1267	#41	C₂³×D₅₃	1	1	yes	characteristic
1268	C₂×Q₈	—	2	2	no	—
1269	C₂×Q₈	—	2	2	no	—
1270	C₂×Q₈	—	53	2	no	—
1271	C₂×Q₈	—	53	1	no	—
1272	C₂×Q₈	—	53	1	no	—
1273	C₂×Q₈	—	106	2	no	—
1274	C₂×Q₈	—	106	2	no	—
1275	C₂×Q₈	—	212	2	no	—
1276	C₂×Q₈	C₂³×D₅₃	1	2	yes	—
1277	C₂×D₄	—	2	2	no	—
1278	C₂×D₄	—	2	2	no	—
1279	C₂×D₄	—	4	2	no	—
1280	C₂×D₄	—	53	2	no	—
1281	C₂×D₄	—	53	1	no	—
1282	C₂×D₄	—	53	1	no	—
1283	C₂×D₄	—	53	2	no	—
1284	C₂×D₄	—	53	2	no	—
1285	C₂×D₄	—	106	2	no	—
1286	C₂×D₄	—	106	2	no	—
1287	C₂×D₄	—	106	2	no	—
1288	C₂×D₄	—	106	2	no	—
1289	C₂×D₄	—	106	2	no	—
1290	C₂×D₄	—	106	2	no	—
1291	C₂×D₄	—	106	2	no	—
1292	C₂×D₄	—	106	2	no	—
1293	C₂×D₄	—	106	2	no	—
1294	C₂×D₄	—	106	2	no	—
1295	C₂×D₄	—	106	2	no	—
1296	C₂×D₄	—	106	2	no	—
1297	C₂×D₄	—	106	1	no	—
1298	C₂×D₄	—	106	2	no	—
1299	C₂×D₄	—	106	1	no	—
1300	C₂×D₄	—	106	2	no	—
1301	C₂×D₄	—	106	2	no	—
1302	C₂×D₄	—	106	2	no	—
1303	C₂×D₄	—	106	2	no	—
1304	C₂×D₄	—	212	2	no	—
1305	C₂×D₄	—	212	2	no	—
1306	C₂×D₄	—	212	2	no	—
1307	C₂×D₄	—	212	2	no	—
1308	C₂×D₄	—	212	2	no	—
1309	C₂×D₄	—	212	2	no	—
1310	C₂×D₄	—	212	2	no	—
1311	C₂×D₄	—	212	2	no	—
1312	C₂×D₄	—	212	2	no	—
1313	C₂×D₄	—	212	2	no	—
1314	C₂×D₄	—	212	2	no	—
1315	C₂×D₄	—	212	2	no	—
1316	C₂×D₄	—	212	2	no	—
1317	C₂×D₄	—	212	2	no	—
1318	C₂×D₄	—	212	2	no	—
1319	C₂×D₄	—	212	2	no	—
1320	C₂×D₄	—	212	2	no	—
1321	C₂×D₄	—	212	2	no	—
1322	C₂×D₄	—	212	2	no	—
1323	C₂×D₄	—	212	2	no	—
1324	C₂×D₄	—	212	2	no	—
1325	C₂×D₄	—	212	2	no	—
1326	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1327	C₂²×C₄	—	53	1	no	—
1328	C₂²×C₄	—	106	1	no	—
1329	C₂²×C₄	—	106	1	no	—
1330	C₂²×C₄	—	106	2	no	—
1331	C₂²×C₄	—	106	2	no	—
1332	C₂²×C₄	—	212	2	no	—
1333	C₂²×C₄	—	212	2	no	—
1334	C₂²×C₄	—	212	2	no	—
1335	Q₁₆	—	2	2	no	—
1336	Q₁₆	—	2	2	no	—
1337	Q₁₆	—	2	1	no	—
1338	Q₁₆	—	2	1	no	—
1339	Q₁₆	—	53	2	no	—
1340	Q₁₆	—	53	1	no	—
1341	Q₁₆	—	53	1	no	—
1342	Q₁₆	—	53	1	no	—
1343	Q₁₆	—	53	1	no	—
1344	Q₁₆	—	106	2	no	—
1345	Q₁₆	—	106	2	no	—
1346	Q₁₆	D₄×D₅₃	1	1	yes	characteristic
1347	Q₁₆	D₄×D₅₃	1	1	yes	characteristic
1348	SD₁₆	—	2	2	no	—
1349	SD₁₆	—	2	2	no	—
1350	SD₁₆	—	2	2	no	—
1351	SD₁₆	—	2	2	no	—
1352	SD₁₆	—	2	2	no	—
1353	SD₁₆	—	2	2	no	—
1354	SD₁₆	—	53	2	no	—
1355	SD₁₆	—	53	1	no	—
1356	SD₁₆	—	53	1	no	—
1357	SD₁₆	—	53	2	no	—
1358	SD₁₆	—	53	1	no	—
1359	SD₁₆	—	53	1	no	—
1360	SD₁₆	—	53	2	no	—
1361	SD₁₆	—	53	1	no	—
1362	SD₁₆	—	53	1	no	—
1363	SD₁₆	—	106	2	no	—
1364	SD₁₆	—	106	2	no	—
1365	SD₁₆	—	106	2	no	—
1366	SD₁₆	—	106	2	no	—
1367	SD₁₆	—	106	2	no	—
1368	SD₁₆	—	106	2	no	—
1369	SD₁₆	—	106	2	no	—
1370	SD₁₆	—	106	2	no	—
1371	SD₁₆	—	106	2	no	—
1372	SD₁₆	—	106	2	no	—
1373	SD₁₆	—	106	2	no	—
1374	SD₁₆	—	106	2	no	—
1375	SD₁₆	—	106	2	no	—
1376	SD₁₆	—	106	2	no	—
1377	SD₁₆	—	106	2	no	—
1378	SD₁₆	—	106	2	no	—
1379	SD₁₆	D₄×D₅₃	1	1	yes	characteristic
1380	SD₁₆	D₄×D₅₃	1	2	yes	—
1381	SD₁₆	D₄×D₅₃	1	1	yes	characteristic
1382	D₈	—	2	2	no	—
1383	D₈	—	2	2	no	—
1384	D₈	—	2	1	no	—
1385	D₈	—	2	1	no	—
1386	D₈	—	53	2	no	—
1387	D₈	—	53	1	no	—
1388	D₈	—	53	1	no	—
1389	D₈	—	53	1	no	—
1390	D₈	—	53	1	no	—
1391	D₈	—	106	2	no	—
1392	D₈	—	106	2	no	—
1393	D₈	—	106	2	no	—
1394	D₈	—	106	2	no	—
1395	D₈	—	106	2	no	—
1396	D₈	—	106	2	no	—
1397	D₈	—	106	2	no	—
1398	D₈	—	106	2	no	—
1399	D₈	—	106	2	no	—
1400	D₈	—	106	2	no	—
1401	D₈	—	106	2	no	—
1402	D₈	—	106	2	no	—
1403	D₈	—	106	2	no	—
1404	D₈	—	106	2	no	—
1405	D₈	—	106	1	no	—
1406	D₈	—	106	1	no	—
1407	D₈	—	106	1	no	—
1408	D₈	—	106	2	no	—
1409	D₈	—	106	2	no	—
1410	D₈	—	106	1	no	—
1411	D₈	D₄×D₅₃	1	1	yes	characteristic
1412	D₈	D₄×D₅₃	1	1	yes	characteristic
1413	M₁₆	—	2	1	no	—
1414	M₁₆	—	2	2	no	—
1415	M₁₆	—	2	1	no	—
1416	M₁₆	—	53	1	no	—
1417	M₁₆	—	53	1	no	—
1418	M₁₆	—	53	1	no	—
1419	M₁₆	—	53	1	no	—
1420	M₁₆	—	53	1	no	—
1421	M₁₆	—	53	2	no	—
1422	M₁₆	—	53	1	no	—
1423	M₁₆	—	106	1	no	—
1424	M₁₆	—	106	2	no	—
1425	M₁₆	—	106	1	no	—
1426	M₁₆	—	106	2	no	—
1427	M₁₆	—	106	1	no	—
1428	M₁₆	—	106	1	no	—
1429	M₁₆	—	106	1	no	—
1430	M₁₆	—	106	2	no	—
1431	M₁₆	—	106	1	no	—
1432	M₁₆	—	106	1	no	—
1433	M₁₆	—	106	2	no	—
1434	M₁₆	—	106	1	no	—
1435	M₁₆	C₂³×D₅₃	1	1	yes	characteristic
1436	M₁₆	C₂³×D₅₃	1	2	yes	—
1437	M₁₆	C₂³×D₅₃	1	1	yes	characteristic
1438	C₂×C₈	—	2	1	no	—
1439	C₂×C₈	—	2	1	no	—
1440	C₂×C₈	—	2	2	no	—
1441	C₂×C₈	—	53	1	no	—
1442	C₂×C₈	—	53	1	no	—
1443	C₂×C₈	—	53	1	no	—
1444	C₂×C₈	—	53	1	no	—
1445	C₂×C₈	—	53	1	no	—
1446	C₂×C₈	—	53	1	no	—
1447	C₂×C₈	—	106	1	no	—
1448	C₂×C₈	—	106	1	no	—
1449	C₂×C₈	—	106	2	no	—
1450	C₂×C₈	—	106	1	no	—
1451	C₂×C₈	—	106	1	no	—
1452	C₂×C₈	—	106	2	no	—
1453	C₂×C₈	—	106	1	no	—
1454	C₂×C₈	—	106	1	no	—
1455	C₂×C₈	—	106	2	no	—
1456	C₂×C₈	—	106	1	no	—
1457	C₂×C₈	—	106	1	no	—
1458	C₂×C₈	—	106	2	no	—
1459	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1460	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1461	C₄⋊C₄	—	106	1	no	—
1462	C₂²⋊C₄	—	4	2	no	—
1463	C₂²⋊C₄	—	106	1	no	—
1464	C₂²⋊C₄	—	212	2	no	—
1465	C₄²	—	53	1	no	—
1466	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1467	C₂³	—	2	2	no	—
1468	C₂³	—	4	2	no	—
1469	C₂³	—	53	1	no	—
1470	C₂³	—	848	2	no	—
1471	C₂³	—	848	4	no	—
1472	C₂³	—	106	1	no	—
1473	C₂³	—	106	2	no	—
1474	C₂³	—	106	1	no	—
1475	C₂³	—	106	2	no	—
1476	C₂³	—	106	2	no	—
1477	C₂³	—	212	2	no	—
1478	C₂³	—	212	2	no	—
1479	C₂³	—	212	2	no	—
1480	C₂³	—	212	2	no	—
1481	C₂³	—	212	2	no	—
1482	C₂³	—	212	2	no	—
1483	C₂³	—	212	2	no	—
1484	Q₈	—	2	2	no	—
1485	Q₈	—	2	2	no	—
1486	Q₈	—	4	2	no	—
1487	Q₈	—	53	1	no	—
1488	Q₈	—	53	2	no	—
1489	Q₈	—	53	1	no	—
1490	Q₈	—	106	1	no	—
1491	Q₈	—	106	2	no	—
1492	Q₈	—	106	1	no	—
1493	Q₈	—	212	2	no	—
1494	Q₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1495	Q₈	C₂×D₄×D₅₃	1	2	yes	—
1496	Q₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1497	D₄	—	2	1	no	—
1498	D₄	—	2	2	no	—
1499	D₄	—	2	1	no	—
1500	D₄	—	2	2	no	—
1501	D₄	—	2	2	no	—
1502	D₄	—	4	2	no	—
1503	D₄	—	4	2	no	—
1504	D₄	—	4	2	no	—
1505	D₄	—	53	1	no	—
1506	D₄	—	53	2	no	—
1507	D₄	—	53	1	no	—
1508	D₄	—	848	2	no	—
1509	D₄	—	848	2	no	—
1510	D₄	—	106	1	no	—
1511	D₄	—	106	2	no	—
1512	D₄	—	106	1	no	—
1513	D₄	—	106	1	no	—
1514	D₄	—	106	2	no	—
1515	D₄	—	106	1	no	—
1516	D₄	—	106	1	no	—
1517	D₄	—	106	2	no	—
1518	D₄	—	106	1	no	—
1519	D₄	—	106	1	no	—
1520	D₄	—	106	2	no	—
1521	D₄	—	106	1	no	—
1522	D₄	—	106	2	no	—
1523	D₄	—	106	2	no	—
1524	D₄	—	106	2	no	—
1525	D₄	—	106	2	no	—
1526	D₄	—	212	2	no	—
1527	D₄	—	212	2	no	—
1528	D₄	—	212	2	no	—
1529	D₄	—	212	2	no	—
1530	D₄	—	212	2	no	—
1531	D₄	—	212	2	no	—
1532	D₄	—	212	2	no	—
1533	D₄	—	212	2	no	—
1534	D₄	—	212	2	no	—
1535	D₄	—	212	2	no	—
1536	D₄	—	212	2	no	—
1537	D₄	—	212	2	no	—
1538	D₄	—	212	2	no	—
1539	D₄	—	212	2	no	—
1540	D₄	—	212	2	no	—
1541	D₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1542	D₄	C₂×D₄×D₅₃	1	2	yes	—
1543	D₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1544	C₂×C₄	—	2	1	no	—
1545	C₂×C₄	—	2	2	no	—
1546	C₂×C₄	—	2	1	no	—
1547	C₂×C₄	—	2	1	no	—
1548	C₂×C₄	—	2	2	no	—
1549	C₂×C₄	—	4	2	no	—
1550	C₂×C₄	—	4	2	no	—
1551	C₂×C₄	—	4	2	no	—
1552	C₂×C₄	—	53	1	no	—
1553	C₂×C₄	—	53	1	no	—
1554	C₂×C₄	—	53	1	no	—
1555	C₂×C₄	—	53	1	no	—
1556	C₂×C₄	—	53	1	no	—
1557	C₂×C₄	—	106	1	no	—
1558	C₂×C₄	—	106	2	no	—
1559	C₂×C₄	—	106	1	no	—
1560	C₂×C₄	—	106	1	no	—
1561	C₂×C₄	—	106	2	no	—
1562	C₂×C₄	—	106	1	no	—
1563	C₂×C₄	—	106	1	no	—
1564	C₂×C₄	—	106	2	no	—
1565	C₂×C₄	—	106	1	no	—
1566	C₂×C₄	—	106	1	no	—
1567	C₂×C₄	—	106	2	no	—
1568	C₂×C₄	—	106	1	no	—
1569	C₂×C₄	—	106	1	no	—
1570	C₂×C₄	—	212	2	no	—
1571	C₂×C₄	—	212	2	no	—
1572	C₂×C₄	—	212	2	no	—
1573	C₂×C₄	—	212	2	no	—
1574	C₂×C₄	—	212	2	no	—
1575	C₂×C₄	—	212	2	no	—
1576	C₂×C₄	—	212	2	no	—
1577	C₂×C₄	—	212	2	no	—
1578	C₂×C₄	—	212	2	no	—
1579	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1580	C₈	—	2	1	no	—
1581	C₈	—	2	2	no	—
1582	C₈	—	2	1	no	—
1583	C₈	—	53	1	no	—
1584	C₈	—	53	1	no	—
1585	C₈	—	53	1	no	—
1586	C₈	—	53	1	no	—
1587	C₈	—	106	1	no	—
1588	C₈	—	106	2	no	—
1589	C₈	—	106	1	no	—
1590	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1591	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1592	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1593	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
1594	C₂²	—	2	1	no	—
1595	C₂²	—	2	2	no	—
1596	C₂²	—	2	1	no	—
1597	C₂²	—	4	2	no	—
1598	C₂²	—	8	2	no	—
1599	C₂²	—	16	2	no	—
1600	C₂²	—	53	1	no	—
1601	C₂²	—	53	1	no	—
1602	C₂²	—	848	2	no	—
1603	C₂²	—	848	2	no	—
1604	C₂²	—	848	2	no	—
1605	C₂²	—	848	2	no	—
1606	C₂²	—	848	2	no	—
1607	C₂²	—	848	2	no	—
1608	C₂²	—	106	1	no	—
1609	C₂²	—	106	2	no	—
1610	C₂²	—	106	1	no	—
1611	C₂²	—	424	2	no	—
1612	C₂²	—	424	2	no	—
1613	C₂²	—	424	2	no	—
1614	C₂²	—	424	1	no	—
1615	C₂²	—	424	4	no	—
1616	C₂²	—	212	1	no	—
1617	C₂²	—	212	2	no	—
1618	C₂²	—	212	2	no	—
1619	C₂²	—	212	2	no	—
1620	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1621	C₄	—	2	1	no	—
1622	C₄	—	2	2	no	—
1623	C₄	—	2	1	no	—
1624	C₄	—	4	1	no	—
1625	C₄	—	4	2	no	—
1626	C₄	—	53	1	no	—
1627	C₄	—	53	1	no	—
1628	C₄	—	106	1	no	—
1629	C₄	—	106	2	no	—
1630	C₄	—	106	1	no	—
1631	C₄	—	212	1	no	—
1632	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1633	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
1634	C₂	—	2	1	no	—
1635	C₂	—	4	1	no	—
1636	C₂	—	4	2	no	—
1637	C₂	—	4	1	no	—
1638	C₂	—	8	2	no	—
1639	C₂	—	106	1	no	—
1640	C₂	—	106	1	no	—
1641	C₂	—	424	2	no	—
1642	C₂	—	424	2	no	—
1643	C₂	—	212	1	no	—
1644	C₂	—	212	2	no	—
1645	C₂	—	212	1	no	—
1646	C₂	D₄²×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄²×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3290	C₂
socle	C₂×C₅₃	C₂×D₄²
hypercenter	#3290	D₅₃
hypocenter	C₅₃	#61106
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #3290

Complements

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

N	H ≅ G/N	type
1. #20289493	C₂	semidirect
2. #20289485	C₂	semidirect
3. #576×D₅₃	C₂	semidirect
4. #20286515	C₂	semidirect
5. #20286515	C₂	semidirect
6. #20286513	C₂	semidirect
7. #20286512	C₂	semidirect
8. #20286504	C₂	semidirect
9. #20286501	C₂	semidirect
10. #20286500	C₂	semidirect
11. #20286484	C₂	semidirect
12. #20286483	C₂	semidirect
13. #20286480	C₂	semidirect
14. #20286477	C₂	semidirect
15. #20285197	C₂	semidirect
16. #20284438	C₂	semidirect
17. #20284437	C₂	semidirect
18. #472×D₅₃	C₂	semidirect
19. #20284085	C₂	semidirect
20. #20284073	C₂	semidirect
21. #20283627	C₂	semidirect
22. #20283613	C₂	semidirect
23. C₅₃×#3290	C₂	semidirect
24. #16811460	C₂²	semidirect
25. H(5,𝔽₂)×D₅₃	C₂²	semidirect
27. #16811436	C₂²	semidirect
30. #16811432	C₂²	semidirect
31. #16811432	C₂²	semidirect
32. #16811431	C₂²	semidirect
33. #16811431	C₂²	semidirect
35. #16811429	C₂²	semidirect
36. #16811428	C₂²	semidirect
37. #16811428	C₂²	semidirect
38. #16811428	C₂²	semidirect
41. #16811427	C₂²	semidirect
42. #16811427	C₂²	semidirect
43. #16811426	C₂²	semidirect
44. #16811426	C₂²	semidirect
48. #16811425	C₂²	semidirect
49. #16811425	C₂²	semidirect
50. #16811425	C₂²	semidirect
52. #16811424	C₂²	semidirect
55. #16811422	C₂²	semidirect
56. #16811422	C₂²	semidirect
60. C₂×#13133244	C₂²	semidirect
63. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
64. AGL(1,ℤ/8)×D₅₃	C₂²	semidirect
66. C₂×#13133240	C₂²	semidirect
71. C₂×D₈×D₅₃	C₂²	semidirect
72. #16811388	C₂²	semidirect
73. #131×D₅₃	C₂²	semidirect
74. #131×D₅₃	C₂²	semidirect
75. #16811191	C₂²	semidirect
76. #16811013	C₂²	semidirect
77. #16811009	C₂²	semidirect
78. #16811008	C₂²	semidirect
79. #16811000	C₂²	semidirect
80. #16810998	C₂²	semidirect
81. #16810895	C₂²	semidirect
82. #16810894	C₂²	semidirect
83. #16810894	C₂²	semidirect
84. #16810894	C₂²	semidirect
85. #16810893	C₂²	semidirect
86. #16810893	C₂²	semidirect
87. #16810893	C₂²	semidirect
88. #16810892	C₂²	semidirect
89. #16810892	C₂²	semidirect
90. #16810891	C₂²	semidirect
91. #16810891	C₂²	semidirect
92. #16810890	C₂²	semidirect
93. #16810889	C₂²	semidirect
94. #16810889	C₂²	semidirect
95. #16810888	C₂²	semidirect
96. #16810888	C₂²	semidirect
97. #16810883	C₂²	semidirect
98. #16810800	C₂²	semidirect
99. #16810799	C₂²	semidirect
100. #16810799	C₂²	semidirect
101. #16810798	C₂²	semidirect
102. #16810796	C₂²	semidirect
103. #16810795	C₂²	semidirect
104. #16810793	C₂²	semidirect
105. #16810792	C₂²	semidirect
106. #16810792	C₂²	semidirect
107. #16810792	C₂²	semidirect
108. #16810792	C₂²	semidirect
109. #16810791	C₂²	semidirect
110. #16810789	C₂²	semidirect
111. #16810789	C₂²	semidirect
112. #16810745	C₂²	semidirect
113. #16810744	C₂²	semidirect
114. #16810743	C₂²	semidirect
115. #16810742	C₂²	semidirect
116. #16810742	C₂²	semidirect
117. #16810742	C₂²	semidirect
118. #16810741	C₂²	semidirect
119. #16810741	C₂²	semidirect
120. #16810740	C₂²	semidirect
121. #16810739	C₂²	semidirect
122. #16810738	C₂²	semidirect
123. #16810738	C₂²	semidirect
124. #16810670	C₂²	semidirect
125. #108×D₅₃	C₂²	semidirect
126. #16810638	C₂²	semidirect
127. #16810638	C₂²	semidirect
128. #16810638	C₂²	semidirect
129. #16810606	C₂²	semidirect
130. #100×D₅₃	C₂²	semidirect
131. #16810577	C₂²	semidirect
132. C₅₃×#578	C₂²	semidirect
133. C₅₃×#577	C₂²	semidirect
134. C₅₃×#576	C₂²	semidirect
135. C₅₃×#495	C₂²	semidirect
136. C₅₃×#473	C₂²	semidirect
137. C₅₃×#472	C₂²	semidirect
138. C₅₃×#471	C₂²	semidirect
139. C₅₃×#455	C₂²	semidirect
140. C₅₃×#454	C₂²	semidirect
141. C₅₃×#443	C₂²	semidirect
142. C₅₃×#443	C₂²	semidirect
145. #13133265	C₂³	semidirect
153. #13133263	C₂³	semidirect
154. #13133263	C₂³	semidirect
179. #13133249	D₄	semidirect
180. #13133249	D₄	semidirect
184. #13133248	C₂³	semidirect
186. #13133246	D₄	semidirect
187. #13133246	D₄	semidirect
194. #13133245	C₂³	semidirect
195. #13133245	C₂³	semidirect
213. #13133244	D₄	semidirect
214. #13133244	D₄	semidirect
218. #13133243	C₂³	semidirect
225. #13133242	C₂³	semidirect
226. #13133242	C₂³	semidirect
232. #13133241	D₄	semidirect
233. #13133241	D₄	semidirect
246. #13133240	D₄	semidirect
257. #13133238	D₄	semidirect
266. #13133236	D₄	semidirect
268. Q₁₆×D₅₃	D₄	semidirect
271. C₂×#11719924	C₂³	semidirect
272. C₂×#11719924	C₂³	semidirect
278. SD₁₆×D₅₃	D₄	semidirect
283. C₂×D₄₂₄	C₂³	semidirect
284. C₂×D₄₂₄	C₂³	semidirect
288. C₂×#11719922	C₂³	semidirect
301. D₈×D₅₃	D₄	semidirect
306. #13133225	C₂³	semidirect
307. #13133225	C₂³	semidirect
309. #13133224	C₂³	semidirect
310. #13133224	C₂³	semidirect
315. #13133223	C₂³	semidirect
316. #13133223	C₂³	semidirect
328. #13133214	C₂³	semidirect
329. #13133213	C₂³	semidirect
330. #13133206	C₂³	semidirect
334. #13133153	C₂³	semidirect
335. #13133153	C₂³	semidirect
336. #13133152	C₂³	semidirect
337. #13133152	C₂³	semidirect
338. #13133152	C₂³	semidirect
340. #13133145	C₂³	semidirect
341. #13133145	C₂³	semidirect
343. #13133144	C₂³	semidirect
344. #13133144	C₂³	semidirect
346. #13133143	C₂³	semidirect
347. #13133143	C₂³	semidirect
348. #13133136	C₂³	semidirect
349. #13133134	C₂³	semidirect
350. #13133133	C₂³	semidirect
351. #13133133	C₂³	semidirect
352. #13133133	C₂³	semidirect
353. #13133133	C₂³	semidirect
354. #13133128	C₂³	semidirect
355. #13133127	C₂³	semidirect
356. C₈×Dic₅₃	C₂³	semidirect
357. 2₋¹⁺⁴×C₅₃	C₂³	semidirect
362. #137×C₅₃	C₂³	semidirect
366. AGL(1,ℤ/8)×C₅₃	C₂³	semidirect
373. C₂×Q₁₆×C₅₃	C₂³	semidirect
375. C₂×SD₁₆×C₅₃	C₂³	semidirect
379. #131×C₅₃	C₂³	semidirect
380. #131×C₅₃	C₂³	semidirect
381. #124×C₅₃	C₂³	semidirect
382. #108×C₅₃	C₂³	semidirect
383. #108×C₅₃	C₂³	semidirect
385. #104×C₅₃	C₂³	semidirect
386. #104×C₅₃	C₂³	semidirect
387. #101×C₅₃	C₂³	semidirect
388. #100×C₅₃	C₂³	semidirect
389. C₄×C₈×C₅₃	C₂³	semidirect
821. #3290	D₅₃	semidirect
851. #578	C₂×D₅₃	semidirect
860. #577	C₂×D₅₃	semidirect
878. #576	C₂×D₅₃	semidirect
905. #495	C₂×D₅₃	semidirect
909. #473	C₂×D₅₃	semidirect
921. #472	C₂×D₅₃	semidirect
927. #471	C₂×D₅₃	semidirect
931. #455	C₂×D₅₃	semidirect
935. #454	C₂×D₅₃	semidirect
956. #443	C₂×D₅₃	semidirect
957. #443	C₂×D₅₃	semidirect
966. C₅₃	#61106	semidirect
970. 2₋¹⁺⁴	C₂²×D₅₃	semidirect
1017. #137	C₂²×D₅₃	semidirect
1067. AGL(1,ℤ/8)	C₂²×D₅₃	semidirect
1109. C₂×Q₁₆	C₂²×D₅₃	semidirect
1121. C₂×SD₁₆	C₂²×D₅₃	semidirect
1163. #131	C₂²×D₅₃	semidirect
1164. #131	C₂²×D₅₃	semidirect
1179. #124	C₂²×D₅₃	semidirect
1188. #108	C₂²×D₅₃	semidirect
1189. #108	C₂²×D₅₃	semidirect
1200. #104	C₂²×D₅₃	semidirect
1201. #104	C₂²×D₅₃	semidirect
1203. #101	C₂²×D₅₃	semidirect
1209. #100	C₂²×D₅₃	semidirect
1213. C₄×C₈	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289493	2
#20289485	2
#576×D₅₃	2
#20286515	2
#20286513	2
#20286512	2
#20286504	2
#20286501	2
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C₅₃×#3290	2
#61106	53