Subgroups — #28259576

Order 13568.

2878 conjugacy classes of subgroups.

The subgroup lattice has 2128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811432	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×AGL(1,ℤ/8)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288372	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288345	C₂	1	1	yes	maximal, characteristic, complemented
5	#20286345	C₂	1	1	yes	maximal, characteristic, complemented
6	#20286343	C₂	1	1	yes	maximal, characteristic, complemented
7	#20286340	C₂	1	1	yes	maximal, characteristic, complemented
8	#20286337	C₂	1	1	yes	maximal, characteristic, complemented
9	#20286336	C₂	1	1	yes	maximal, characteristic, complemented
10	#20286332	C₂	1	1	yes	maximal, characteristic, complemented
11	#20286329	C₂	1	1	yes	maximal, characteristic, complemented
12	#20286259	C₂	1	1	yes	maximal, characteristic, complemented
13	#20286258	C₂	1	1	yes	maximal, characteristic, complemented
14	#20286251	C₂	1	1	yes	maximal, characteristic, complemented
15	#20286250	C₂	1	1	yes	maximal, characteristic, complemented
16	#20286216	C₂	1	1	yes	maximal, characteristic, complemented
17	#20286211	C₂	1	1	yes	maximal, characteristic, complemented
18	#20286208	C₂	1	1	yes	maximal, characteristic, complemented
19	#20286203	C₂	1	1	yes	maximal, characteristic, complemented
20	#20285197	C₂	1	1	yes	maximal, characteristic, complemented
21	#20284361	C₂	1	1	yes	maximal, characteristic, complemented
22	#20284326	C₂	1	1	yes	maximal, characteristic, complemented
23	#20284234	C₂	1	1	yes	maximal, characteristic, complemented
24	#20284216	C₂	1	1	yes	maximal, characteristic, complemented
25	#20283996	C₂	1	1	yes	maximal, characteristic, complemented
26	#20283980	C₂	1	1	yes	maximal, characteristic, complemented
27	#20283958	C₂	1	1	yes	maximal, characteristic, complemented
28	#20283943	C₂	1	1	yes	maximal, characteristic, complemented
29	#20283569	C₂	1	1	yes	maximal, characteristic, complemented
30	#20283415	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133265	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13133263	C₂²	1	1	yes	characteristic
34	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
36	#16811432	—	2	8	no	—
37	C₂×#13133249	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13133249	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133245	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133245	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13133244	C₂²	1	1	yes	characteristic
42	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
47	C₂×#13133243	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13133242	C₂²	1	1	yes	characteristic, complemented
49	C₂×#13133241	C₂²	1	1	yes	characteristic, complemented
50	C₂×#13133241	C₂²	1	1	yes	characteristic, complemented
51	AGL(1,ℤ/8)×D₅₃	—	2	8	no	—
52	C₂×#13133240	C₂²	1	1	yes	characteristic, complemented
53	C₂×#13133240	C₂²	1	1	yes	characteristic, complemented
54	C₂×#13133237	C₂²	1	1	yes	characteristic, complemented
55	C₂²×#11719924	C₂²	1	1	yes	characteristic, complemented
56	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#13133225	C₂²	1	1	yes	characteristic, complemented
62	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
63	#16811295	C₂²	1	1	yes	characteristic, complemented
64	#16811294	—	2	1	no	—
65	#16811294	C₂²	1	1	yes	characteristic, complemented
66	#16811292	C₂²	1	1	yes	characteristic, complemented
67	#16811291	—	2	1	no	—
68	#16811291	C₂²	1	1	yes	characteristic, complemented
69	#16811284	C₂²	1	1	yes	characteristic, complemented
70	#16811283	—	2	1	no	—
71	#16811283	C₂²	1	1	yes	characteristic, complemented
72	#16811281	—	2	1	no	—
73	#16811281	C₂²	1	1	yes	characteristic, complemented
74	#16811266	C₂²	1	1	yes	characteristic, complemented
75	#16811265	—	2	1	no	—
76	#16811264	C₂²	1	1	yes	characteristic, complemented
77	#16811263	—	2	1	no	—
78	#16811261	C₂²	1	1	yes	characteristic, complemented
79	D₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
80	D₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
81	#16811257	—	2	1	no	—
82	#16811257	C₂²	1	1	yes	characteristic, complemented
83	D₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
84	#16811255	—	2	1	no	—
85	#16811191	—	2	1	no	—
86	#16811191	C₂²	1	1	yes	characteristic
87	#16811191	C₂²	1	1	yes	characteristic, complemented
88	#16811189	—	2	1	no	—
89	#16811189	C₂²	1	1	yes	characteristic
90	#16811189	C₂²	1	1	yes	characteristic, complemented
91	#16811184	—	2	1	no	—
92	#16811181	—	2	1	no	—
93	#16811136	—	2	1	no	—
94	#16811136	C₂²	1	1	yes	characteristic
95	#16811136	C₂²	1	1	yes	characteristic, complemented
96	#16811132	—	2	1	no	—
97	#16811132	C₂²	1	1	yes	characteristic
98	C₂×#13133187	—	2	1	no	—
99	#120×D₅₃	—	2	1	no	—
100	#16811099	C₂²	1	1	yes	characteristic, complemented
101	#16811095	C₂²	1	1	yes	characteristic
102	#16811013	C₂²	1	1	yes	characteristic, complemented
103	#16811013	C₂²	1	1	yes	characteristic, complemented
104	#16811009	C₂²	1	1	yes	characteristic, complemented
105	#16811009	C₂²	1	1	yes	characteristic, complemented
106	#16811008	C₂²	1	1	yes	characteristic, complemented
107	#16811000	C₂²	1	1	yes	characteristic, complemented
108	#16810998	C₂²	1	1	yes	characteristic, complemented
109	#16810878	C₂²	1	1	yes	characteristic, complemented
110	#16810877	C₂²	1	1	yes	characteristic, complemented
111	#16810877	C₂²	1	1	yes	characteristic, complemented
112	#16810876	C₂²	1	1	yes	characteristic, complemented
113	#16810876	C₂²	1	1	yes	characteristic, complemented
114	#16810873	C₂²	1	1	yes	characteristic, complemented
115	#16810872	C₂²	1	1	yes	characteristic, complemented
116	#16810872	C₂²	1	1	yes	characteristic, complemented
117	#16810871	C₂²	1	1	yes	characteristic, complemented
118	#16810871	C₂²	1	1	yes	characteristic, complemented
119	#16810858	C₂²	1	1	yes	characteristic, complemented
120	#16810858	C₂²	1	1	yes	characteristic, complemented
121	#16810857	C₂²	1	1	yes	characteristic, complemented
122	#16810857	C₂²	1	1	yes	characteristic, complemented
123	#16810848	C₂²	1	1	yes	characteristic, complemented
124	#16810847	C₂²	1	1	yes	characteristic, complemented
125	#16810842	C₂²	1	1	yes	characteristic, complemented
126	#16810841	C₂²	1	1	yes	characteristic, complemented
127	#16810840	C₂²	1	1	yes	characteristic, complemented
128	#16810835	C₂²	1	1	yes	characteristic, complemented
129	#16810824	C₂²	1	1	yes	characteristic, complemented
130	#16810823	C₂²	1	1	yes	characteristic, complemented
131	#16810822	C₂²	1	1	yes	characteristic, complemented
132	#16810821	C₂²	1	1	yes	characteristic, complemented
133	#16810819	C₂²	1	1	yes	characteristic, complemented
134	#16810818	C₂²	1	1	yes	characteristic, complemented
135	#16810817	C₂²	1	1	yes	characteristic, complemented
136	#16810816	C₂²	1	1	yes	characteristic, complemented
137	#16810784	C₂²	1	1	yes	characteristic, complemented
138	#16810783	C₂²	1	1	yes	characteristic, complemented
139	#16810782	C₂²	1	1	yes	characteristic, complemented
140	#16810773	C₂²	1	1	yes	characteristic, complemented
141	#16810772	C₂²	1	1	yes	characteristic, complemented
142	#16810772	C₂²	1	1	yes	characteristic, complemented
143	#16810771	C₂²	1	1	yes	characteristic, complemented
144	#16810771	C₂²	1	1	yes	characteristic, complemented
145	#16810771	C₂²	1	1	yes	characteristic, complemented
146	#16810770	C₂²	1	1	yes	characteristic, complemented
147	#16810770	C₂²	1	1	yes	characteristic, complemented
148	#16810769	C₂²	1	1	yes	characteristic, complemented
149	#16810768	C₂²	1	1	yes	characteristic, complemented
150	#16810768	C₂²	1	1	yes	characteristic, complemented
151	#16810767	C₂²	1	1	yes	characteristic, complemented
152	#16810767	C₂²	1	1	yes	characteristic, complemented
153	#16810766	C₂²	1	1	yes	characteristic, complemented
154	#16810763	C₂²	1	1	yes	characteristic, complemented
155	#16810762	C₂²	1	1	yes	characteristic, complemented
156	#16810760	C₂²	1	1	yes	characteristic, complemented
157	#16810759	C₂²	1	1	yes	characteristic, complemented
158	#16810759	C₂²	1	1	yes	characteristic, complemented
159	#16810758	C₂²	1	1	yes	characteristic, complemented
160	#16810758	C₂²	1	1	yes	characteristic, complemented
161	#16810758	C₂²	1	1	yes	characteristic, complemented
162	#16810757	C₂²	1	1	yes	characteristic, complemented
163	#16810756	C₂²	1	1	yes	characteristic, complemented
164	#16810755	C₂²	1	1	yes	characteristic, complemented
165	#16810726	C₂²	1	1	yes	characteristic, complemented
166	#16810723	C₂²	1	1	yes	characteristic, complemented
167	#16810721	C₂²	1	1	yes	characteristic, complemented
168	#16810720	C₂²	1	1	yes	characteristic, complemented
169	C₄×#11719913	C₂²	1	1	yes	characteristic, complemented
170	SD₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
171	#16810710	C₂²	1	1	yes	characteristic, complemented
172	#16810702	C₂²	1	1	yes	characteristic, complemented
173	#16810699	C₂²	1	1	yes	characteristic, complemented
174	#16810699	C₂²	1	1	yes	characteristic, complemented
175	#16810697	C₂²	1	1	yes	characteristic, complemented
176	#16810695	C₂²	1	1	yes	characteristic, complemented
177	#16810693	C₂²	1	1	yes	characteristic, complemented
178	#16810691	C₂²	1	1	yes	characteristic, complemented
179	#16810658	C₂²	1	1	yes	characteristic, complemented
180	#16810648	C₂²	1	1	yes	characteristic, complemented
181	#16810630	C₂²	1	1	yes	characteristic, complemented
182	#16810626	C₂²	1	1	yes	characteristic
183	#16810626	C₂²	1	1	yes	characteristic, complemented
184	#16810626	C₂²	1	1	yes	characteristic, complemented
185	#16810618	C₂²	1	1	yes	characteristic, complemented
186	#16810618	C₂²	1	1	yes	characteristic, complemented
187	#16810588	C₂²	1	1	yes	characteristic, complemented
188	#16810585	C₂²	1	1	yes	characteristic, complemented
189	#16810577	C₂²	1	1	yes	characteristic, complemented
190	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
202	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
203	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
204	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
205	C₂⁴×D₅₃	—	2	1	no	—
206	#13133265	—	2	4	no	—
207	#13133265	—	4	2	no	—
208	#13133263	—	2	4	no	—
209	#13133263	—	4	2	no	—
210	C₂×#11719949	—	2	1	no	—
211	C₂×#11719949	C₂³	1	1	yes	characteristic
212	C₂×#11719949	C₂³	1	1	yes	characteristic
213	C₂×#11719949	C₂³	1	1	yes	characteristic
214	C₂×#11719949	C₂³	1	1	yes	characteristic
215	C₂×#11719949	C₂³	1	1	yes	characteristic, complemented
216	C₂×#11719945	—	2	1	no	—
217	C₂×#11719945	—	2	1	no	—
218	C₂×#11719945	—	2	1	no	—
219	C₂×#11719945	—	2	1	no	—
220	C₂×#11719945	C₂³	1	1	yes	characteristic
221	C₂×#11719945	C₂³	1	1	yes	characteristic
222	C₂×#11719945	C₂³	1	1	yes	characteristic, complemented
223	C₂×#11719947	—	2	1	no	—
224	C₂×#11719947	C₂³	1	1	yes	characteristic
225	#41×D₅₃	—	2	4	no	—
226	#41×D₅₃	—	4	2	no	—
227	C₂×Q₈×D₅₃	—	2	1	no	—
228	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
229	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic, complemented
230	C₂²×D₂₁₂	—	2	1	no	—
231	C₂²×D₂₁₂	—	2	1	no	—
232	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
233	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
234	C₂²×C₂²⋊D₅₃	—	2	1	no	—
235	C₂²×C₂²⋊D₅₃	—	2	1	no	—
236	C₂×D₄×D₅₃	—	2	4	no	—
237	C₂×D₄×D₅₃	—	2	1	no	—
238	C₂×D₄×D₅₃	—	2	1	no	—
239	C₂×D₄×D₅₃	—	2	1	no	—
240	C₂×D₄×D₅₃	—	2	1	no	—
241	C₂×D₄×D₅₃	—	2	1	no	—
242	C₂×D₄×D₅₃	—	2	1	no	—
243	C₂×D₄×D₅₃	—	2	1	no	—
244	C₂×D₄×D₅₃	—	4	2	no	—
245	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
246	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
247	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
248	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
249	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
250	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
251	C₂²×C₄×D₅₃	—	2	1	no	—
252	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
253	#13133249	—	2	4	no	—
254	#13133249	—	2	4	no	—
255	#13133245	—	2	4	no	—
256	#13133245	—	2	4	no	—
257	#13133244	—	2	4	no	—
258	#13133244	—	2	4	no	—
259	#13133244	—	2	4	no	—
260	#13133244	—	2	4	no	—
261	#13133244	—	4	2	no	—
262	#13133244	—	4	2	no	—
263	#13133243	—	2	4	no	—
264	#13133242	—	2	4	no	—
265	#13133241	—	2	4	no	—
266	#13133241	—	2	4	no	—
267	#13133240	—	2	4	no	—
268	#13133240	—	2	4	no	—
269	#13133237	—	2	4	no	—
270	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
271	C₂×#11719913	C₂³	1	1	yes	characteristic
272	C₂×#11719913	C₂³	1	1	yes	characteristic
273	C₂×#11719913	C₂³	1	1	yes	characteristic, complemented
274	C₂×#11719923	C₂³	1	1	yes	characteristic
275	C₂×#11719923	C₂³	1	1	yes	characteristic
276	C₂×#11719924	—	2	4	no	—
277	C₂×#11719924	C₂³	1	1	yes	characteristic
278	C₂×#11719924	C₂³	1	1	yes	characteristic
279	C₂×#11719924	C₂³	1	1	yes	characteristic
280	C₂×#11719924	C₂³	1	1	yes	characteristic
281	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
282	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
283	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
284	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
285	SD₁₆×D₅₃	—	2	4	no	—
286	SD₁₆×D₅₃	—	2	4	no	—
287	SD₁₆×D₅₃	D₄	1	8	yes	complemented
288	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
289	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
290	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
291	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
292	C₂×D₄₂₄	C₂³	1	1	yes	characteristic, complemented
293	C₂×D₄₂₄	C₂³	1	1	yes	characteristic, complemented
294	C₂×#11719922	C₂³	1	1	yes	characteristic
295	C₂×#11719922	C₂³	1	1	yes	characteristic
296	C₂×#11719922	C₂³	1	1	yes	characteristic
297	C₂×#11719922	C₂³	1	1	yes	characteristic
298	C₂×#11719922	C₂³	1	1	yes	characteristic
299	C₂×#11719922	C₂³	1	1	yes	characteristic
300	C₂×#11719922	C₂³	1	1	yes	characteristic, complemented
301	D₈×D₅₃	—	2	4	no	—
302	D₈×D₅₃	—	2	4	no	—
303	#13133225	—	2	4	no	—
304	C₂×#11719917	C₂³	1	1	yes	characteristic
305	C₂×#11719912	C₂³	1	1	yes	characteristic
306	C₂×#11719912	C₂³	1	1	yes	characteristic
307	C₂×#11719912	C₂³	1	1	yes	characteristic
308	C₂×#11719912	C₂³	1	1	yes	characteristic
309	C₂×#11719912	C₂³	1	1	yes	characteristic, complemented
310	M₁₆×D₅₃	—	2	4	no	—
311	C₂²×#88322	C₂³	1	1	yes	characteristic, complemented
312	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic, complemented
315	#13133214	—	2	1	no	—
316	#13133214	C₂³	1	1	yes	characteristic
317	#13133214	C₂³	1	1	yes	characteristic, complemented
318	#13133213	—	2	1	no	—
319	#13133213	—	2	1	no	—
320	#13133213	—	2	1	no	—
321	#13133213	—	2	1	no	—
322	#13133213	—	2	1	no	—
323	#13133213	C₂³	1	1	yes	characteristic
324	#13133213	C₂³	1	1	yes	characteristic, complemented
325	#13133206	—	2	1	no	—
326	#13133206	C₂³	1	1	yes	characteristic
327	#13133206	C₂³	1	1	yes	characteristic, complemented
328	#13133203	—	2	1	no	—
329	#13133203	—	2	1	no	—
330	#13133203	—	2	1	no	—
331	#13133203	—	2	1	no	—
332	#13133202	—	2	1	no	—
333	#13133202	—	2	1	no	—
334	#13133202	—	2	1	no	—
335	#13133202	D₄	1	1	yes	characteristic
336	#13133200	—	2	1	no	—
337	#13133199	—	2	1	no	—
338	#13133199	D₄	1	1	yes	characteristic
339	#13133195	—	2	1	no	—
340	#13133195	D₄	1	1	yes	characteristic
341	#13133194	—	2	1	no	—
342	#13133194	D₄	1	1	yes	characteristic
343	#13133193	—	2	1	no	—
344	#13133193	C₂³	1	1	yes	characteristic
345	#13133193	C₂³	1	1	yes	characteristic
346	#13133192	—	2	1	no	—
347	#13133192	—	2	1	no	—
348	#13133192	—	2	1	no	—
349	#13133192	—	2	1	no	—
350	#13133192	C₂³	1	1	yes	characteristic
351	#13133192	C₂³	1	1	yes	characteristic
352	#13133192	C₂³	1	1	yes	characteristic
353	#13133192	C₂³	1	1	yes	characteristic, complemented
354	#13133191	—	2	1	no	—
355	#13133191	—	2	1	no	—
356	#13133191	—	2	1	no	—
357	#13133191	C₂³	1	1	yes	characteristic
358	#13133191	C₂³	1	1	yes	characteristic
359	#13133191	C₂³	1	1	yes	characteristic
360	#13133191	C₂³	1	1	yes	characteristic, complemented
361	#13133190	—	2	1	no	—
362	#13133190	—	2	1	no	—
363	#13133190	—	2	1	no	—
364	#13133190	—	2	1	no	—
365	#13133190	—	2	1	no	—
366	#13133190	—	2	1	no	—
367	#13133190	—	2	1	no	—
368	#13133190	—	2	1	no	—
369	#13133190	—	2	1	no	—
370	#13133190	—	2	1	no	—
371	#13133190	—	2	1	no	—
372	#13133190	D₄	1	1	yes	characteristic
373	#13133189	—	2	1	no	—
374	#13133189	—	2	1	no	—
375	#13133189	—	2	1	no	—
376	#13133189	D₄	1	1	yes	characteristic
377	#13133188	—	2	1	no	—
378	#13133188	C₂³	1	1	yes	characteristic
379	#13133188	C₂³	1	1	yes	characteristic, complemented
380	#13133187	—	2	1	no	—
381	#13133187	—	2	1	no	—
382	#13133187	—	2	1	no	—
383	#13133187	—	2	1	no	—
384	#13133187	—	2	1	no	—
385	#13133187	—	2	1	no	—
386	#13133187	—	2	1	no	—
387	#13133187	—	2	1	no	—
388	#13133187	—	2	1	no	—
389	#13133187	—	2	1	no	—
390	#13133187	—	2	1	no	—
391	#13133187	—	2	1	no	—
392	#13133187	—	2	1	no	—
393	#13133187	—	2	1	no	—
394	#13133187	—	2	1	no	—
395	#13133187	D₄	1	1	yes	characteristic
396	#13133186	—	2	1	no	—
397	#13133185	—	2	1	no	—
398	#13133185	—	2	1	no	—
399	#13133185	—	2	1	no	—
400	#13133185	—	2	1	no	—
401	#13133185	—	2	1	no	—
402	#13133185	D₄	1	1	yes	characteristic
403	Q₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
404	C₄×Dic₁₀₆	—	2	1	no	—
405	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
406	#13133182	—	2	1	no	—
407	#13133182	C₂³	1	1	yes	characteristic, complemented
408	C₄×D₂₁₂	—	2	1	no	—
409	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
410	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
411	D₄×Dic₅₃	C₂³	1	1	yes	characteristic
412	#13133179	—	2	1	no	—
413	#13133179	—	2	1	no	—
414	#13133179	—	2	1	no	—
415	#13133179	—	2	1	no	—
416	#13133179	C₂³	1	1	yes	characteristic
417	C₄×C₂²⋊D₅₃	—	2	1	no	—
418	C₄×C₂²⋊D₅₃	—	2	1	no	—
419	C₄×C₂²⋊D₅₃	—	2	1	no	—
420	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
421	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
422	#13133177	—	2	1	no	—
423	#13133177	—	2	1	no	—
424	#13133177	—	2	1	no	—
425	#13133177	—	2	1	no	—
426	#13133177	—	2	1	no	—
427	#13133175	—	2	1	no	—
428	#13133175	C₂³	1	1	yes	characteristic
429	#13133175	C₂³	1	1	yes	characteristic
430	#13133174	—	2	1	no	—
431	#13133174	C₂³	1	1	yes	characteristic
432	C₂×#11719921	—	2	1	no	—
433	C₂×#11719921	—	2	1	no	—
434	C₂²⋊C₄×D₅₃	—	2	1	no	—
435	C₂²⋊C₄×D₅₃	—	2	1	no	—
436	C₂²⋊C₄×D₅₃	—	2	1	no	—
437	#13133150	C₂³	1	1	yes	characteristic, complemented
438	#13133150	C₂³	1	1	yes	characteristic, complemented
439	#13133149	C₂³	1	1	yes	characteristic, complemented
440	C₄⋊#88322	C₂³	1	1	yes	characteristic, complemented
441	#13133146	C₂³	1	1	yes	characteristic, complemented
442	#13133146	C₂³	1	1	yes	characteristic, complemented
443	#13133142	C₂³	1	1	yes	characteristic, complemented
444	#13133141	C₂³	1	1	yes	characteristic, complemented
445	#13133141	C₂³	1	1	yes	characteristic, complemented
446	#13133141	C₂³	1	1	yes	characteristic, complemented
447	#13133140	C₂³	1	1	yes	characteristic, complemented
448	#13133139	C₂³	1	1	yes	characteristic
449	#13133139	C₂³	1	1	yes	characteristic
450	#13133139	C₂³	1	1	yes	characteristic, complemented
451	#13133139	C₂³	1	1	yes	characteristic, complemented
452	#13133139	C₂³	1	1	yes	characteristic, complemented
453	#13133138	C₂³	1	1	yes	characteristic
454	#13133138	C₂³	1	1	yes	characteristic
455	#13133138	C₂³	1	1	yes	characteristic, complemented
456	#13133137	C₂³	1	1	yes	characteristic
457	#13133137	C₂³	1	1	yes	characteristic
458	#13133137	C₂³	1	1	yes	characteristic, complemented
459	#13133137	C₂³	1	1	yes	characteristic, complemented
460	#13133137	C₂³	1	1	yes	characteristic, complemented
461	C₂²⋊#88322	C₂³	1	1	yes	characteristic
462	C₂²⋊#88322	C₂³	1	1	yes	characteristic, complemented
463	#13133129	C₂³	1	1	yes	characteristic
464	#13133129	C₂³	1	1	yes	characteristic
465	#13133129	C₂³	1	1	yes	characteristic, complemented
466	#13133129	C₂³	1	1	yes	characteristic, complemented
467	#13133128	C₂³	1	1	yes	characteristic, complemented
468	#13133127	C₂³	1	1	yes	characteristic, complemented
469	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
470	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
471	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
472	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
473	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
474	#137×C₅₃	—	2	4	no	—
475	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
476	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
477	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
478	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
479	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
480	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
481	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
482	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
483	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
485	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
486	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
487	#124×C₅₃	—	2	1	no	—
488	#124×C₅₃	C₂³	1	1	yes	characteristic
489	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
490	#123×C₅₃	—	2	1	no	—
491	C₂²⋊Q₈×C₅₃	—	2	1	no	—
492	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
493	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
494	#121×C₅₃	—	2	1	no	—
495	#121×C₅₃	—	2	1	no	—
496	#121×C₅₃	C₂³	1	1	yes	characteristic
497	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
498	#120×C₅₃	—	2	1	no	—
499	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
500	C₄×D₄×C₅₃	—	2	1	no	—
501	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
502	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
503	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
504	#106×C₅₃	C₂³	1	1	yes	characteristic, complemented
505	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
506	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
507	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
508	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
509	#102×C₅₃	C₂³	1	1	yes	characteristic
510	#102×C₅₃	C₂³	1	1	yes	characteristic
511	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
512	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
513	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
514	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
515	C₂⁴×C₅₃	—	2	1	no	—
516	C₂³×D₅₃	—	2	1	no	—
517	C₂³×D₅₃	—	2	1	no	—
518	C₂³×D₅₃	—	2	1	no	—
519	C₂³×D₅₃	—	2	1	no	—
520	C₂³×D₅₃	—	2	1	no	—
521	C₂³×D₅₃	—	2	1	no	—
522	C₂³×D₅₃	—	2	1	no	—
523	C₂³×D₅₃	—	2	1	no	—
524	C₂³×D₅₃	—	4	4	no	—
525	C₂³×D₅₃	—	8	2	no	—
526	C₂³×D₅₃	—	8	2	no	—
527	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
528	#41×C₅₃	—	2	2	no	—
529	#41×C₅₃	—	2	2	no	—
530	#41×C₅₃	—	4	1	no	—
531	#41×C₅₃	—	4	1	no	—
532	C₂×Q₈×C₅₃	—	2	1	no	—
533	C₂×Q₈×C₅₃	—	2	2	no	—
534	C₂×Q₈×C₅₃	—	4	1	no	—
535	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×D₄×C₅₃	—	2	2	no	—
539	C₂×D₄×C₅₃	—	2	1	no	—
540	C₂×D₄×C₅₃	—	2	1	no	—
541	C₂×D₄×C₅₃	—	2	1	no	—
542	C₂×D₄×C₅₃	—	2	1	no	—
543	C₂×D₄×C₅₃	—	2	1	no	—
544	C₂×D₄×C₅₃	—	4	1	no	—
545	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
546	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
547	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
548	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
554	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
555	C₂×C₂²⋊D₅₃	—	2	1	no	—
556	C₂×C₂²⋊D₅₃	—	2	1	no	—
557	C₂×C₂²⋊D₅₃	—	2	1	no	—
558	C₂×C₂²⋊D₅₃	—	2	1	no	—
559	C₂×C₂²⋊D₅₃	—	2	1	no	—
560	C₂×C₂²⋊D₅₃	—	2	1	no	—
561	C₂×C₂²⋊D₅₃	—	2	1	no	—
562	C₂×C₂²⋊D₅₃	—	2	1	no	—
563	C₂×C₂²⋊D₅₃	—	2	1	no	—
564	C₂×C₂²⋊D₅₃	—	2	1	no	—
565	C₂×C₂²⋊D₅₃	—	2	1	no	—
566	C₂×C₂²⋊D₅₃	—	2	1	no	—
567	C₂×C₂²⋊D₅₃	—	2	1	no	—
568	C₂×C₂²⋊D₅₃	—	2	1	no	—
569	C₂×C₂²⋊D₅₃	—	2	1	no	—
570	C₂×C₂²⋊D₅₃	—	2	1	no	—
571	C₂×C₂²⋊D₅₃	—	2	1	no	—
572	C₂×C₂²⋊D₅₃	—	2	1	no	—
573	C₂×C₂²⋊D₅₃	—	2	1	no	—
574	C₂×C₂²⋊D₅₃	—	4	4	no	—
575	C₂×C₂²⋊D₅₃	—	8	2	no	—
576	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
577	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
578	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
579	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
580	C₂²×Dic₅₃	—	2	1	no	—
581	C₂²×Dic₅₃	—	2	1	no	—
582	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
583	#11719949	—	2	2	no	—
584	#11719949	—	2	2	no	—
585	#11719949	—	2	2	no	—
586	#11719949	—	2	2	no	—
587	#11719949	—	2	2	no	—
588	#11719949	—	2	2	no	—
589	#11719949	—	2	2	no	—
590	#11719949	—	4	1	no	—
591	#11719949	—	4	1	no	—
592	#11719949	—	4	1	no	—
593	#11719949	—	4	4	no	—
594	Q₈×D₅₃	—	2	2	no	—
595	Q₈×D₅₃	—	2	2	no	—
596	Q₈×D₅₃	—	4	4	no	—
597	Q₈×D₅₃	—	4	1	no	—
598	Q₈×D₅₃	C₂×D₄	1	4	yes	complemented
599	#11719947	—	2	2	no	—
600	#11719947	—	4	1	no	—
601	#11719947	—	4	4	no	—
602	D₄×D₅₃	—	2	2	no	—
603	D₄×D₅₃	—	2	2	no	—
604	D₄×D₅₃	—	2	2	no	—
605	D₄×D₅₃	—	2	2	no	—
606	D₄×D₅₃	—	2	2	no	—
607	D₄×D₅₃	—	2	2	no	—
608	D₄×D₅₃	—	2	2	no	—
609	D₄×D₅₃	—	2	2	no	—
610	D₄×D₅₃	—	4	1	no	—
611	D₄×D₅₃	—	4	1	no	—
612	D₄×D₅₃	—	4	1	no	—
613	D₄×D₅₃	—	4	4	no	—
614	D₄×D₅₃	—	4	4	no	—
615	D₄×D₅₃	—	4	4	no	—
616	D₄×D₅₃	—	4	4	no	—
617	D₄×D₅₃	—	4	4	no	—
618	D₄×D₅₃	—	8	2	no	—
619	D₄×D₅₃	—	8	2	no	—
620	D₄×D₅₃	C₂×D₄	1	4	yes	—
621	#11719945	—	2	2	no	—
622	#11719945	—	2	2	no	—
623	#11719945	—	2	2	no	—
624	#11719945	—	2	2	no	—
625	#11719945	—	4	4	no	—
626	#11719945	—	4	1	no	—
627	#11719945	—	4	1	no	—
628	#11719945	—	4	4	no	—
629	#11719945	—	4	4	no	—
630	#11719945	—	4	4	no	—
631	C₂×D₂₁₂	—	2	2	no	—
632	C₂×D₂₁₂	—	2	2	no	—
633	C₂×D₂₁₂	—	2	1	no	—
634	C₂×D₂₁₂	—	2	1	no	—
635	C₂×D₂₁₂	—	2	1	no	—
636	C₂×D₂₁₂	—	2	1	no	—
637	C₂×D₂₁₂	—	2	1	no	—
638	C₂×D₂₁₂	—	2	1	no	—
639	C₂×D₂₁₂	—	2	1	no	—
640	C₂×D₂₁₂	—	2	1	no	—
641	C₂×D₂₁₂	—	2	1	no	—
642	C₂×D₂₁₂	—	2	1	no	—
643	C₂×D₂₁₂	—	2	1	no	—
644	C₂×D₂₁₂	—	2	1	no	—
645	C₂×D₂₁₂	—	2	1	no	—
646	C₂×D₂₁₂	—	2	1	no	—
647	C₂×D₂₁₂	—	2	1	no	—
648	C₂×D₂₁₂	—	4	1	no	—
649	C₂×D₂₁₂	—	4	1	no	—
650	C₂×D₂₁₂	—	4	4	no	—
651	C₂×D₂₁₂	—	8	2	no	—
652	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
653	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
654	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
655	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
656	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
657	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
658	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
659	C₂×C₄×D₅₃	—	2	1	no	—
660	C₂×C₄×D₅₃	—	2	2	no	—
661	C₂×C₄×D₅₃	—	2	2	no	—
662	C₂×C₄×D₅₃	—	2	1	no	—
663	C₂×C₄×D₅₃	—	2	1	no	—
664	C₂×C₄×D₅₃	—	2	1	no	—
665	C₂×C₄×D₅₃	—	2	1	no	—
666	C₂×C₄×D₅₃	—	2	1	no	—
667	C₂×C₄×D₅₃	—	2	1	no	—
668	C₂×C₄×D₅₃	—	2	1	no	—
669	C₂×C₄×D₅₃	—	2	1	no	—
670	C₂×C₄×D₅₃	—	2	1	no	—
671	C₂×C₄×D₅₃	—	2	1	no	—
672	C₂×C₄×D₅₃	—	4	4	no	—
673	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
674	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
675	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
676	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
677	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
678	C₂×Dic₁₀₆	—	2	1	no	—
679	C₂×Dic₁₀₆	—	2	1	no	—
680	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
681	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
682	Q₁₆×C₅₃	—	2	2	no	—
683	Q₁₆×C₅₃	—	2	2	no	—
684	SD₁₆×C₅₃	—	2	2	no	—
685	SD₁₆×C₅₃	—	2	2	no	—
686	SD₁₆×C₅₃	—	4	1	no	—
687	SD₁₆×C₅₃	—	4	1	no	—
688	SD₁₆×C₅₃	C₂×D₄	1	4	yes	complemented
689	D₈×C₅₃	—	2	2	no	—
690	D₈×C₅₃	—	2	2	no	—
691	M₁₆×C₅₃	—	2	2	no	—
692	M₁₆×C₅₃	—	2	2	no	—
693	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
694	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
695	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
696	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
697	C₄⋊C₄×C₅₃	—	2	1	no	—
698	C₄⋊C₄×C₅₃	—	2	1	no	—
699	C₄⋊C₄×C₅₃	—	2	1	no	—
700	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
702	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₂²⋊C₄×C₅₃	—	2	1	no	—
704	C₂²⋊C₄×C₅₃	—	2	1	no	—
705	C₂²⋊C₄×C₅₃	—	2	1	no	—
706	C₂²⋊C₄×C₅₃	—	2	1	no	—
707	C₂²⋊C₄×C₅₃	—	2	1	no	—
708	C₂²⋊C₄×C₅₃	—	2	1	no	—
709	C₂²⋊C₄×C₅₃	—	2	1	no	—
710	C₂²⋊C₄×C₅₃	—	2	1	no	—
711	C₂²⋊C₄×C₅₃	—	2	1	no	—
712	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
713	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
714	C₄²×C₅₃	—	2	1	no	—
715	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
716	C₂²⋊Dic₅₃	—	2	1	no	—
717	C₂²⋊Dic₅₃	—	2	1	no	—
718	C₂²⋊Dic₅₃	—	2	1	no	—
719	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
721	#11719925	—	2	2	no	—
722	#11719924	—	2	2	no	—
723	#11719924	—	2	2	no	—
724	#11719924	—	2	2	no	—
725	#11719924	—	2	2	no	—
726	#11719924	—	2	2	no	—
727	#11719924	—	4	1	no	—
728	#11719924	—	4	1	no	—
729	#11719924	C₂×D₄	1	4	yes	complemented
730	#11719923	—	2	2	no	—
731	#11719923	C₂×D₄	1	4	yes	complemented
732	#11719922	—	2	2	no	—
733	#11719922	—	2	2	no	—
734	#11719922	—	2	2	no	—
735	#11719922	—	2	2	no	—
736	#11719922	—	2	2	no	—
737	#11719922	—	4	1	no	—
738	#11719922	—	4	1	no	—
739	#11719921	—	2	1	no	—
740	#11719921	—	2	1	no	—
741	#11719921	—	2	1	no	—
742	#11719921	—	2	1	no	—
743	#11719921	—	2	1	no	—
744	#11719921	—	2	1	no	—
745	#11719921	—	2	1	no	—
746	#11719921	—	2	1	no	—
747	#11719921	—	2	1	no	—
748	#11719921	—	2	1	no	—
749	#11719921	—	2	1	no	—
750	#11719921	—	2	1	no	—
751	#11719921	—	2	1	no	—
752	#11719921	—	2	1	no	—
753	#11719921	—	2	1	no	—
754	#11719921	—	2	1	no	—
755	#11719921	—	2	1	no	—
756	#11719921	—	2	1	no	—
757	#11719921	C₂×D₄	1	1	yes	characteristic
758	#11719921	C₂×D₄	1	1	yes	characteristic
759	#11719921	C₂×D₄	1	1	yes	characteristic
760	#11719921	C₂×D₄	1	1	yes	characteristic
761	#11719921	C₂×D₄	1	1	yes	characteristic
762	#11719921	C₂×D₄	1	1	yes	characteristic
763	C₄⋊Dic₅₃	—	2	1	no	—
764	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
765	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
766	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
767	#11719919	—	2	1	no	—
768	#11719919	—	2	1	no	—
769	#11719919	—	2	1	no	—
770	#11719919	—	2	1	no	—
771	#11719919	C₂×D₄	1	1	yes	characteristic
772	#11719919	C₂×D₄	1	1	yes	characteristic
773	#11719919	C₂×D₄	1	1	yes	characteristic
774	#11719919	C₂×D₄	1	1	yes	characteristic
775	C₄×Dic₅₃	—	2	1	no	—
776	C₄×Dic₅₃	—	2	1	no	—
777	C₄×Dic₅₃	—	2	1	no	—
778	C₄×Dic₅₃	—	2	1	no	—
779	C₄×Dic₅₃	—	2	1	no	—
780	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
781	#11719917	—	2	2	no	—
782	C₂×#88322	—	2	2	no	—
783	C₂×#88322	C₂⁴	1	1	yes	characteristic
784	C₂×#88322	C₂⁴	1	1	yes	characteristic
785	C₂×#88322	C₂⁴	1	1	yes	characteristic
786	C₂×#88322	C₂⁴	1	1	yes	characteristic
787	D₄₂₄	—	2	2	no	—
788	D₄₂₄	—	2	2	no	—
789	D₄₂₄	—	2	2	no	—
790	D₄₂₄	—	2	2	no	—
791	D₄₂₄	—	4	1	no	—
792	D₄₂₄	—	4	1	no	—
793	#11719913	—	2	2	no	—
794	#11719913	—	2	2	no	—
795	#11719913	C₂×D₄	1	4	yes	complemented
796	#11719912	—	2	2	no	—
797	#11719912	—	2	2	no	—
798	#11719912	—	2	2	no	—
799	#11719912	—	2	2	no	—
800	#11719912	—	2	2	no	—
801	C₈×D₅₃	—	2	2	no	—
802	C₈×D₅₃	—	2	2	no	—
803	C₈×D₅₃	C₂×D₄	1	4	yes	complemented
804	C₂³×C₅₃	—	2	1	no	—
805	C₂³×C₅₃	—	2	1	no	—
806	C₂³×C₅₃	—	2	1	no	—
807	C₂³×C₅₃	—	4	2	no	—
808	C₂³×C₅₃	—	4	2	no	—
809	C₂³×C₅₃	—	8	1	no	—
810	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
811	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
812	C₂²×D₅₃	—	2	1	no	—
813	C₂²×D₅₃	—	2	2	no	—
814	C₂²×D₅₃	—	2	4	no	—
815	C₂²×D₅₃	—	2	1	no	—
816	C₂²×D₅₃	—	2	1	no	—
817	C₂²×D₅₃	—	2	1	no	—
818	C₂²×D₅₃	—	2	1	no	—
819	C₂²×D₅₃	—	4	1	no	—
820	C₂²×D₅₃	—	4	1	no	—
821	C₂²×D₅₃	—	4	2	no	—
822	C₂²×D₅₃	—	4	2	no	—
823	C₂²×D₅₃	—	4	2	no	—
824	C₂²×D₅₃	—	4	2	no	—
825	C₂²×D₅₃	—	4	2	no	—
826	C₂²×D₅₃	—	4	2	no	—
827	C₂²×D₅₃	—	4	2	no	—
828	C₂²×D₅₃	—	4	2	no	—
829	C₂²×D₅₃	—	4	2	no	—
830	C₂²×D₅₃	—	4	2	no	—
831	C₂²×D₅₃	—	8	1	no	—
832	C₂²×D₅₃	—	8	1	no	—
833	C₂²×D₅₃	—	8	1	no	—
834	C₂²×D₅₃	—	8	1	no	—
835	C₂²×D₅₃	—	8	1	no	—
836	C₂²×D₅₃	—	8	1	no	—
837	C₂²×D₅₃	—	8	1	no	—
838	C₂²×D₅₃	—	8	1	no	—
839	C₂²×D₅₃	—	8	1	no	—
840	C₂²×D₅₃	—	8	1	no	—
841	C₂²×D₅₃	—	8	1	no	—
842	C₂²×D₅₃	—	8	1	no	—
843	C₂²×D₅₃	—	8	1	no	—
844	C₂²×D₅₃	—	8	16	no	—
845	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
846	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
847	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
848	Q₈×C₅₃	—	2	1	no	—
849	Q₈×C₅₃	—	2	1	no	—
850	Q₈×C₅₃	—	2	1	no	—
851	Q₈×C₅₃	—	2	1	no	—
852	Q₈×C₅₃	—	2	1	no	—
853	Q₈×C₅₃	—	4	2	no	—
854	Q₈×C₅₃	C₂²×D₄	1	2	yes	—
855	D₄×C₅₃	—	2	1	no	—
856	D₄×C₅₃	—	2	1	no	—
857	D₄×C₅₃	—	2	1	no	—
858	D₄×C₅₃	—	2	1	no	—
859	D₄×C₅₃	—	2	1	no	—
860	D₄×C₅₃	—	4	1	no	—
861	D₄×C₅₃	—	4	2	no	—
862	D₄×C₅₃	—	4	2	no	—
863	D₄×C₅₃	—	4	2	no	—
864	D₄×C₅₃	—	8	1	no	—
865	D₄×C₅₃	—	8	1	no	—
866	D₄×C₅₃	C₂²×D₄	1	2	yes	—
867	C₂×C₄×C₅₃	—	2	1	no	—
868	C₂×C₄×C₅₃	—	2	1	no	—
869	C₂×C₄×C₅₃	—	2	1	no	—
870	C₂×C₄×C₅₃	—	2	1	no	—
871	C₂×C₄×C₅₃	—	2	1	no	—
872	C₂×C₄×C₅₃	—	2	1	no	—
873	C₂×C₄×C₅₃	—	2	1	no	—
874	C₂×C₄×C₅₃	—	2	1	no	—
875	C₂×C₄×C₅₃	—	2	1	no	—
876	C₂×C₄×C₅₃	—	4	2	no	—
877	C₂×C₄×C₅₃	—	4	2	no	—
878	C₂×C₄×C₅₃	—	4	2	no	—
879	C₂×C₄×C₅₃	—	8	1	no	—
880	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
881	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
882	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
883	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
884	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
885	C₂²⋊D₅₃	—	2	2	no	—
886	C₂²⋊D₅₃	—	2	2	no	—
887	C₂²⋊D₅₃	—	2	4	no	—
888	C₂²⋊D₅₃	—	4	1	no	—
889	C₂²⋊D₅₃	—	4	1	no	—
890	C₂²⋊D₅₃	—	4	2	no	—
891	C₂²⋊D₅₃	—	4	2	no	—
892	C₂²⋊D₅₃	—	4	2	no	—
893	C₂²⋊D₅₃	—	4	2	no	—
894	C₂²⋊D₅₃	—	4	2	no	—
895	C₂²⋊D₅₃	—	4	2	no	—
896	C₂²⋊D₅₃	—	4	2	no	—
897	C₂²⋊D₅₃	—	4	2	no	—
898	C₂²⋊D₅₃	—	4	2	no	—
899	C₂²⋊D₅₃	—	8	1	no	—
900	C₂²⋊D₅₃	—	8	1	no	—
901	C₂²⋊D₅₃	—	8	1	no	—
902	C₂²⋊D₅₃	—	8	1	no	—
903	C₂²⋊D₅₃	—	8	1	no	—
904	C₂²⋊D₅₃	—	8	1	no	—
905	C₂²⋊D₅₃	—	8	1	no	—
906	C₂²⋊D₅₃	—	8	1	no	—
907	C₂²⋊D₅₃	—	8	1	no	—
908	C₂×Dic₅₃	—	2	1	no	—
909	C₂×Dic₅₃	—	2	2	no	—
910	C₂×Dic₅₃	—	2	1	no	—
911	C₂×Dic₅₃	—	2	1	no	—
912	C₂×Dic₅₃	—	4	2	no	—
913	C₂×Dic₅₃	—	8	1	no	—
914	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
915	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
916	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
917	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
918	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
919	D₂₁₂	—	2	2	no	—
920	D₂₁₂	—	2	1	no	—
921	D₂₁₂	—	2	1	no	—
922	D₂₁₂	—	2	1	no	—
923	D₂₁₂	—	2	1	no	—
924	D₂₁₂	—	2	1	no	—
925	D₂₁₂	—	2	1	no	—
926	D₂₁₂	—	2	1	no	—
927	D₂₁₂	—	2	1	no	—
928	D₂₁₂	—	2	1	no	—
929	D₂₁₂	—	4	1	no	—
930	D₂₁₂	—	4	2	no	—
931	D₂₁₂	—	4	2	no	—
932	D₂₁₂	—	4	2	no	—
933	D₂₁₂	—	4	2	no	—
934	D₂₁₂	—	4	2	no	—
935	D₂₁₂	—	4	2	no	—
936	D₂₁₂	—	4	2	no	—
937	D₂₁₂	—	4	2	no	—
938	D₂₁₂	—	8	1	no	—
939	D₂₁₂	—	8	1	no	—
940	D₂₁₂	—	8	1	no	—
941	D₂₁₂	—	8	1	no	—
942	D₂₁₂	—	8	1	no	—
943	D₂₁₂	—	8	1	no	—
944	D₂₁₂	—	8	1	no	—
945	D₂₁₂	C₂²×D₄	1	2	yes	—
946	C₄×D₅₃	—	2	2	no	—
947	C₄×D₅₃	—	2	4	no	—
948	C₄×D₅₃	—	2	1	no	—
949	C₄×D₅₃	—	2	1	no	—
950	C₄×D₅₃	—	2	1	no	—
951	C₄×D₅₃	—	2	1	no	—
952	C₄×D₅₃	—	2	2	no	—
953	C₄×D₅₃	—	4	2	no	—
954	C₄×D₅₃	—	4	2	no	—
955	C₄×D₅₃	—	4	2	no	—
956	C₄×D₅₃	—	4	2	no	—
957	C₄×D₅₃	—	4	2	no	—
958	C₄×D₅₃	—	4	2	no	—
959	C₄×D₅₃	—	4	2	no	—
960	C₄×D₅₃	—	4	2	no	—
961	C₄×D₅₃	—	8	1	no	—
962	C₄×D₅₃	—	8	1	no	—
963	C₄×D₅₃	C₂²×D₄	1	2	yes	—
964	C₄×D₅₃	H(5,𝔽₂)	1	2	yes	—
965	Dic₁₀₆	—	2	1	no	—
966	Dic₁₀₆	—	2	4	no	—
967	Dic₁₀₆	—	2	2	no	—
968	Dic₁₀₆	—	4	2	no	—
969	Dic₁₀₆	C₂²×D₄	1	2	yes	—
970	C₈×C₅₃	—	2	1	no	—
971	C₈×C₅₃	—	2	1	no	—
972	C₈×C₅₃	—	2	1	no	—
973	C₈×C₅₃	C₂²×D₄	1	2	yes	—
974	#88322	—	2	1	no	—
975	#88322	—	2	1	no	—
976	#88322	—	2	1	no	—
977	#88322	C₂²×D₄	1	2	yes	—
978	#61059	—	53	1	no	maximal, Sylow
979	C₂²×C₅₃	—	2	1	no	—
980	C₂²×C₅₃	—	2	1	no	—
981	C₂²×C₅₃	—	2	1	no	—
982	C₂²×C₅₃	—	2	1	no	—
983	C₂²×C₅₃	—	2	1	no	—
984	C₂²×C₅₃	—	2	1	no	—
985	C₂²×C₅₃	—	2	2	no	—
986	C₂²×C₅₃	—	4	1	no	—
987	C₂²×C₅₃	—	4	1	no	—
988	C₂²×C₅₃	—	4	1	no	—
989	C₂²×C₅₃	—	4	1	no	—
990	C₂²×C₅₃	—	4	1	no	—
991	C₂²×C₅₃	—	4	1	no	—
992	C₂²×C₅₃	—	4	1	no	—
993	C₂²×C₅₃	—	4	1	no	—
994	C₂²×C₅₃	—	8	4	no	—
995	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
996	C₂×D₅₃	—	2	1	no	—
997	C₂×D₅₃	—	2	1	no	—
998	C₂×D₅₃	—	2	1	no	—
999	C₂×D₅₃	—	2	1	no	—
1000	C₂×D₅₃	—	2	1	no	—
1001	C₂×D₅₃	—	2	1	no	—
1002	C₂×D₅₃	—	2	1	no	—
1003	C₂×D₅₃	—	2	1	no	—
1004	C₂×D₅₃	—	2	2	no	—
1005	C₂×D₅₃	—	4	4	no	—
1006	C₂×D₅₃	—	4	1	no	—
1007	C₂×D₅₃	—	4	1	no	—
1008	C₂×D₅₃	—	4	1	no	—
1009	C₂×D₅₃	—	4	1	no	—
1010	C₂×D₅₃	—	4	1	no	—
1011	C₂×D₅₃	—	4	1	no	—
1012	C₂×D₅₃	—	4	1	no	—
1013	C₂×D₅₃	—	4	1	no	—
1014	C₂×D₅₃	—	4	1	no	—
1015	C₂×D₅₃	—	4	1	no	—
1016	C₂×D₅₃	—	4	1	no	—
1017	C₂×D₅₃	—	4	1	no	—
1018	C₂×D₅₃	—	4	1	no	—
1019	C₂×D₅₃	—	4	1	no	—
1020	C₂×D₅₃	—	8	4	no	—
1021	C₂×D₅₃	—	8	4	no	—
1022	C₂×D₅₃	—	8	4	no	—
1023	C₂×D₅₃	—	8	4	no	—
1024	C₂×D₅₃	—	8	4	no	—
1025	C₂×D₅₃	—	8	4	no	—
1026	C₂×D₅₃	—	16	2	no	—
1027	C₂×D₅₃	—	16	2	no	—
1028	C₂×D₅₃	D₄²	1	2	yes	—
1029	C₄×C₅₃	—	2	1	no	—
1030	C₄×C₅₃	—	2	1	no	—
1031	C₄×C₅₃	—	2	2	no	—
1032	C₄×C₅₃	—	2	1	no	—
1033	C₄×C₅₃	—	2	1	no	—
1034	C₄×C₅₃	—	4	1	no	—
1035	C₄×C₅₃	—	4	1	no	—
1036	C₄×C₅₃	—	4	1	no	—
1037	C₄×C₅₃	—	4	1	no	—
1038	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
1039	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1040	Dic₅₃	—	2	1	no	—
1041	Dic₅₃	—	2	1	no	—
1042	Dic₅₃	—	2	2	no	—
1043	Dic₅₃	—	2	1	no	—
1044	Dic₅₃	—	2	1	no	—
1045	Dic₅₃	—	4	1	no	—
1046	Dic₅₃	—	4	1	no	—
1047	Dic₅₃	D₄²	1	2	yes	—
1048	C₂×#577	—	53	1	no	—
1049	C₂²×AGL(1,ℤ/8)	—	53	1	no	—
1050	#3487	—	53	1	no	—
1051	#3484	—	53	1	no	—
1052	#3275	—	53	1	no	—
1053	#3275	—	53	1	no	—
1054	#3275	—	53	1	no	—
1055	#3275	D₅₃	1	1	yes	characteristic, complemented
1056	#3274	—	53	1	no	—
1057	#3274	—	53	1	no	—
1058	#3274	—	53	1	no	—
1059	#3274	—	53	1	no	—
1060	#3268	—	53	1	no	—
1061	#3268	—	53	1	no	—
1062	#3268	—	53	1	no	—
1063	#3268	—	53	1	no	—
1064	#3265	—	53	1	no	—
1065	#3265	—	53	1	no	—
1066	#3265	—	53	1	no	—
1067	#3265	—	53	1	no	—
1068	#3155	—	53	1	no	—
1069	#3058	—	53	1	no	—
1070	#3054	—	53	1	no	—
1071	#3043	—	53	1	no	—
1072	#3041	—	53	1	no	—
1073	#3010	—	53	1	no	—
1074	#3008	—	53	1	no	—
1075	#3005	—	53	1	no	—
1076	#3003	—	53	1	no	—
1077	#2949	—	53	1	no	—
1078	#2930	—	53	1	no	—
1079	C₂×C₅₃	—	4	1	no	—
1080	C₂×C₅₃	—	4	2	no	—
1081	C₂×C₅₃	—	4	1	no	—
1082	C₂×C₅₃	—	8	1	no	—
1083	C₂×C₅₃	—	8	1	no	—
1084	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
1085	C₂×C₅₃	#3585	1	1	yes	characteristic
1086	C₂×C₅₃	#3585	1	1	yes	characteristic
1087	D₅₃	—	2	2	no	—
1088	D₅₃	—	4	1	no	—
1089	D₅₃	—	4	1	no	—
1090	D₅₃	—	4	2	no	—
1091	D₅₃	—	8	1	no	—
1092	D₅₃	—	8	1	no	—
1093	D₅₃	—	8	1	no	—
1094	D₅₃	—	8	1	no	—
1095	C₂×2₋¹⁺⁴	—	53	1	no	—
1096	C₂×H(5,𝔽₂)	—	53	1	no	—
1097	C₂²×#41	—	53	1	no	—
1098	C₂³×D₄	—	53	1	no	—
1099	#577	—	106	8	no	—
1100	C₂×#137	—	53	1	no	—
1101	C₂×#137	—	53	1	no	—
1102	C₂×#137	C₂×D₅₃	1	1	yes	characteristic, complemented
1103	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1104	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1105	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1106	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1107	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1108	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1109	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1110	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1111	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1112	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1113	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1114	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1115	C₂×AGL(1,ℤ/8)	—	106	8	no	—
1116	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	1	yes	characteristic, complemented
1117	C₂×#135	—	53	1	no	—
1118	C₂×#135	—	53	1	no	—
1119	C₂×#135	—	53	1	no	—
1120	C₂²×SD₁₆	—	53	1	no	—
1121	C₂²×SD₁₆	—	53	1	no	—
1122	C₂²×SD₁₆	—	53	1	no	—
1123	C₂²×SD₁₆	—	53	1	no	—
1124	C₂²×D₈	—	53	1	no	—
1125	C₂²×D₈	—	53	1	no	—
1126	C₂×#131	—	53	1	no	—
1127	C₂²×M₁₆	—	53	1	no	—
1128	#550	—	53	1	no	—
1129	#550	—	53	1	no	—
1130	#550	—	53	1	no	—
1131	#550	—	53	1	no	—
1132	#550	—	106	1	no	—
1133	#550	—	106	1	no	—
1134	#548	—	53	1	no	—
1135	#548	—	53	1	no	—
1136	#548	—	53	1	no	—
1137	#548	—	106	1	no	—
1138	#548	—	106	1	no	—
1139	#548	C₂×D₅₃	1	1	yes	characteristic, complemented
1140	#546	—	53	1	no	—
1141	#546	—	53	1	no	—
1142	#546	—	53	1	no	—
1143	#546	—	106	1	no	—
1144	#546	—	106	1	no	—
1145	#546	C₂×D₅₃	1	1	yes	characteristic, complemented
1146	D₄²	—	53	1	no	—
1147	D₄²	—	53	1	no	—
1148	D₄²	—	53	1	no	—
1149	D₄²	—	53	1	no	—
1150	D₄²	—	106	1	no	—
1151	D₄²	—	106	1	no	—
1152	#535	—	53	1	no	—
1153	#535	—	53	1	no	—
1154	#535	—	53	1	no	—
1155	#535	—	53	1	no	—
1156	#535	—	106	1	no	—
1157	#535	—	106	1	no	—
1158	#534	—	106	1	no	—
1159	#534	—	106	1	no	—
1160	#525	—	53	1	no	—
1161	#525	—	53	1	no	—
1162	#525	—	53	1	no	—
1163	#525	—	106	1	no	—
1164	#525	—	106	1	no	—
1165	C₂×#120	—	106	1	no	—
1166	C₂×#120	—	106	1	no	—
1167	#519	—	53	1	no	—
1168	#518	—	53	1	no	—
1169	#496	—	53	1	no	—
1170	#496	—	53	1	no	—
1171	#496	—	53	1	no	—
1172	#496	—	53	1	no	—
1173	#495	—	53	1	no	—
1174	#495	C₂×D₅₃	1	1	yes	characteristic, complemented
1175	#493	—	53	1	no	—
1176	#493	—	53	1	no	—
1177	#470	—	53	1	no	—
1178	#470	C₂×D₅₃	1	1	yes	characteristic, complemented
1179	#469	—	53	1	no	—
1180	#469	—	53	1	no	—
1181	#469	—	53	1	no	—
1182	#469	—	53	1	no	—
1183	#469	—	53	1	no	—
1184	#469	C₂×D₅₃	1	1	yes	characteristic, complemented
1185	#468	—	53	1	no	—
1186	#468	—	53	1	no	—
1187	#468	—	53	1	no	—
1188	#468	—	53	1	no	—
1189	#466	—	53	1	no	—
1190	#466	—	53	1	no	—
1191	#466	—	53	1	no	—
1192	#466	—	53	1	no	—
1193	#464	—	53	1	no	—
1194	#464	—	53	1	no	—
1195	#464	—	53	1	no	—
1196	#464	C₂×D₅₃	1	1	yes	characteristic, complemented
1197	#463	—	53	1	no	—
1198	#463	—	53	1	no	—
1199	#463	—	53	1	no	—
1200	#463	C₂×D₅₃	1	1	yes	characteristic, complemented
1201	#460	—	53	1	no	—
1202	#460	—	53	1	no	—
1203	#460	—	53	1	no	—
1204	#460	—	53	1	no	—
1205	#459	—	53	1	no	—
1206	#459	—	53	1	no	—
1207	#459	—	53	1	no	—
1208	#459	—	53	1	no	—
1209	#452	—	53	1	no	—
1210	#452	—	53	1	no	—
1211	#452	—	53	1	no	—
1212	#452	C₂×D₅₃	1	1	yes	characteristic, complemented
1213	#450	—	53	1	no	—
1214	#450	—	53	1	no	—
1215	#450	—	53	1	no	—
1216	#450	C₂×D₅₃	1	1	yes	characteristic, complemented
1217	#449	—	53	1	no	—
1218	#449	—	53	1	no	—
1219	#449	—	53	1	no	—
1220	#449	—	53	1	no	—
1221	#449	—	53	1	no	—
1222	#449	—	53	1	no	—
1223	#449	—	53	1	no	—
1224	#449	—	53	1	no	—
1225	#449	—	53	1	no	—
1226	#449	—	53	1	no	—
1227	#449	—	53	1	no	—
1228	#449	C₂×D₅₃	1	1	yes	characteristic, complemented
1229	#448	—	53	1	no	—
1230	#448	—	53	1	no	—
1231	#448	—	53	1	no	—
1232	#448	C₂×D₅₃	1	1	yes	characteristic, complemented
1233	#447	—	53	1	no	—
1234	#447	—	53	1	no	—
1235	#447	—	53	1	no	—
1236	#447	—	53	1	no	—
1237	#447	—	53	1	no	—
1238	#447	—	53	1	no	—
1239	#447	—	53	1	no	—
1240	#447	—	53	1	no	—
1241	#440	—	53	1	no	—
1242	#440	—	53	1	no	—
1243	#440	—	53	1	no	—
1244	#440	—	53	1	no	—
1245	C₄×SD₁₆	—	53	1	no	—
1246	C₄×SD₁₆	—	53	1	no	—
1247	C₄×SD₁₆	—	53	1	no	—
1248	C₄×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
1249	#436	—	53	1	no	—
1250	#436	—	53	1	no	—
1251	#436	—	53	1	no	—
1252	#436	C₂×D₅₃	1	1	yes	characteristic, complemented
1253	#435	—	53	1	no	—
1254	#435	—	53	1	no	—
1255	#435	—	53	1	no	—
1256	#435	—	53	1	no	—
1257	#427	—	53	1	no	—
1258	#424	—	53	1	no	—
1259	#419	—	53	1	no	—
1260	#418	—	53	1	no	—
1261	#418	—	53	1	no	—
1262	#418	—	53	1	no	—
1263	#416	—	53	1	no	—
1264	#416	—	53	1	no	—
1265	#408	—	53	1	no	—
1266	#407	—	53	1	no	—
1267	#405	—	53	1	no	—
1268	C₅₃	#61059	1	1	yes	characteristic, complemented, Sylow
1269	C₂⁵	—	106	1	no	—
1270	2₋¹⁺⁴	—	106	4	no	—
1271	2₋¹⁺⁴	—	212	2	no	—
1272	H(5,𝔽₂)	—	106	4	no	—
1273	H(5,𝔽₂)	—	212	2	no	—
1274	C₂×#41	—	53	1	no	—
1275	C₂×#41	—	53	1	no	—
1276	C₂×#41	—	53	1	no	—
1277	C₂×#41	—	53	1	no	—
1278	C₂×#41	—	53	1	no	—
1279	C₂×#41	—	53	1	no	—
1280	C₂×#41	—	53	1	no	—
1281	C₂×#41	—	53	1	no	—
1282	C₂×#41	—	53	1	no	—
1283	C₂×#41	—	106	1	no	—
1284	C₂×#41	—	106	1	no	—
1285	C₂×#41	—	106	1	no	—
1286	C₂×#41	—	106	1	no	—
1287	C₂×#41	—	106	1	no	—
1288	C₂×#41	—	106	1	no	—
1289	C₂×#41	—	106	4	no	—
1290	C₂×#41	—	212	2	no	—
1291	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1292	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
1293	C₂²×Q₈	—	53	1	no	—
1294	C₂²×Q₈	—	53	1	no	—
1295	C₂²×Q₈	—	106	1	no	—
1296	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1297	C₂²×D₄	—	53	1	no	—
1298	C₂²×D₄	—	53	1	no	—
1299	C₂²×D₄	—	53	1	no	—
1300	C₂²×D₄	—	53	1	no	—
1301	C₂²×D₄	—	53	1	no	—
1302	C₂²×D₄	—	53	1	no	—
1303	C₂²×D₄	—	53	1	no	—
1304	C₂²×D₄	—	53	1	no	—
1305	C₂²×D₄	—	106	1	no	—
1306	C₂²×D₄	—	106	1	no	—
1307	C₂²×D₄	—	106	1	no	—
1308	C₂²×D₄	—	106	1	no	—
1309	C₂²×D₄	—	106	1	no	—
1310	C₂²×D₄	—	106	4	no	—
1311	C₂²×D₄	—	106	1	no	—
1312	C₂²×D₄	—	106	1	no	—
1313	C₂²×D₄	—	106	1	no	—
1314	C₂²×D₄	—	106	1	no	—
1315	C₂²×D₄	—	106	1	no	—
1316	C₂²×D₄	—	106	1	no	—
1317	C₂²×D₄	—	212	2	no	—
1318	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1319	C₂³×C₄	—	53	1	no	—
1320	C₂³×C₄	—	106	1	no	—
1321	#137	—	2	4	no	—
1322	#137	—	106	4	no	—
1323	#137	—	106	4	no	—
1324	AGL(1,ℤ/8)	—	2	4	no	—
1325	AGL(1,ℤ/8)	—	106	4	no	—
1326	AGL(1,ℤ/8)	—	106	4	no	—
1327	AGL(1,ℤ/8)	—	106	4	no	—
1328	AGL(1,ℤ/8)	—	106	4	no	—
1329	AGL(1,ℤ/8)	—	106	4	no	—
1330	AGL(1,ℤ/8)	—	106	4	no	—
1331	AGL(1,ℤ/8)	—	106	4	no	—
1332	AGL(1,ℤ/8)	—	106	4	no	—
1333	AGL(1,ℤ/8)	—	106	4	no	—
1334	AGL(1,ℤ/8)	—	106	4	no	—
1335	AGL(1,ℤ/8)	—	212	2	no	—
1336	AGL(1,ℤ/8)	—	212	2	no	—
1337	#135	—	106	4	no	—
1338	#135	—	106	4	no	—
1339	#135	—	106	4	no	—
1340	C₂×Q₁₆	—	53	1	no	—
1341	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1342	C₂×Q₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1343	C₂×SD₁₆	—	53	1	no	—
1344	C₂×SD₁₆	—	53	1	no	—
1345	C₂×SD₁₆	—	53	8	no	—
1346	C₂×SD₁₆	—	53	1	no	—
1347	C₂×SD₁₆	—	53	1	no	—
1348	C₂×SD₁₆	—	53	1	no	—
1349	C₂×SD₁₆	—	53	1	no	—
1350	C₂×SD₁₆	—	53	1	no	—
1351	C₂×SD₁₆	—	53	1	no	—
1352	C₂×SD₁₆	—	53	1	no	—
1353	C₂×SD₁₆	—	53	1	no	—
1354	C₂×SD₁₆	—	53	1	no	—
1355	C₂×SD₁₆	—	53	1	no	—
1356	C₂×SD₁₆	—	53	1	no	—
1357	C₂×SD₁₆	—	106	4	no	—
1358	C₂×SD₁₆	—	106	4	no	—
1359	C₂×SD₁₆	—	106	4	no	—
1360	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1361	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1362	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1363	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic
1364	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1365	C₂×D₈	—	53	1	no	—
1366	C₂×D₈	—	53	1	no	—
1367	C₂×D₈	—	53	1	no	—
1368	C₂×D₈	—	53	1	no	—
1369	C₂×D₈	—	53	1	no	—
1370	C₂×D₈	—	53	1	no	—
1371	C₂×D₈	—	53	1	no	—
1372	C₂×D₈	—	53	1	no	—
1373	C₂×D₈	—	53	1	no	—
1374	C₂×D₈	—	53	1	no	—
1375	C₂×D₈	—	53	1	no	—
1376	C₂×D₈	—	53	1	no	—
1377	C₂×D₈	—	53	1	no	—
1378	C₂×D₈	—	106	4	no	—
1379	C₂×D₈	—	106	4	no	—
1380	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1381	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1382	#131	—	106	4	no	—
1383	C₂×M₁₆	—	53	1	no	—
1384	C₂×M₁₆	—	53	1	no	—
1385	C₂×M₁₆	—	53	1	no	—
1386	C₂×M₁₆	—	53	1	no	—
1387	C₂×M₁₆	—	53	1	no	—
1388	C₂×M₁₆	—	53	1	no	—
1389	C₂×M₁₆	—	106	4	no	—
1390	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
1391	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1392	C₂²×C₈	—	53	1	no	—
1393	C₂²×C₈	—	53	1	no	—
1394	C₂²×C₈	—	53	1	no	—
1395	C₂²×C₈	—	53	1	no	—
1396	#127	—	53	1	no	—
1397	#127	—	53	1	no	—
1398	#127	—	53	1	no	—
1399	#127	—	53	1	no	—
1400	#127	—	106	1	no	—
1401	#127	—	106	1	no	—
1402	#127	—	106	1	no	—
1403	#127	—	106	1	no	—
1404	#127	—	106	1	no	—
1405	#127	—	106	1	no	—
1406	#124	—	2	1	no	—
1407	#124	—	53	1	no	—
1408	#124	—	53	1	no	—
1409	#124	—	106	1	no	—
1410	#124	—	106	1	no	—
1411	#124	—	106	1	no	—
1412	#124	—	106	1	no	—
1413	#124	—	106	1	no	—
1414	#124	C₂²×D₅₃	1	1	yes	characteristic
1415	#124	C₂²×D₅₃	1	1	yes	characteristic, complemented
1416	#123	—	2	1	no	—
1417	#123	—	53	1	no	—
1418	#123	—	53	1	no	—
1419	#123	—	106	1	no	—
1420	#123	—	106	1	no	—
1421	#123	—	106	1	no	—
1422	#123	—	106	1	no	—
1423	#123	—	106	1	no	—
1424	C₂²⋊Q₈	—	2	1	no	—
1425	C₂²⋊Q₈	—	53	1	no	—
1426	C₂²⋊Q₈	—	53	1	no	—
1427	C₂²⋊Q₈	—	53	1	no	—
1428	C₂²⋊Q₈	—	53	1	no	—
1429	C₂²⋊Q₈	—	106	1	no	—
1430	C₂²⋊Q₈	—	106	1	no	—
1431	C₂²⋊Q₈	—	106	1	no	—
1432	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
1433	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
1434	#121	—	2	1	no	—
1435	#121	—	2	1	no	—
1436	#121	—	53	1	no	—
1437	#121	—	53	1	no	—
1438	#121	—	53	1	no	—
1439	#121	—	53	1	no	—
1440	#121	—	53	1	no	—
1441	#121	—	53	1	no	—
1442	#121	—	53	1	no	—
1443	#121	—	53	1	no	—
1444	#121	—	53	1	no	—
1445	#121	—	53	1	no	—
1446	#121	—	53	1	no	—
1447	#121	—	53	1	no	—
1448	#121	—	106	1	no	—
1449	#121	—	106	1	no	—
1450	#121	—	106	1	no	—
1451	#121	—	106	1	no	—
1452	#121	—	106	1	no	—
1453	#121	—	106	1	no	—
1454	#121	—	106	1	no	—
1455	#121	—	106	1	no	—
1456	#121	—	106	1	no	—
1457	#121	—	106	1	no	—
1458	#121	—	106	1	no	—
1459	#121	—	106	1	no	—
1460	#121	—	106	1	no	—
1461	#121	—	106	1	no	—
1462	#121	—	106	1	no	—
1463	#121	—	106	1	no	—
1464	#121	—	106	1	no	—
1465	#121	—	106	1	no	—
1466	#121	—	106	1	no	—
1467	#121	—	106	1	no	—
1468	#121	—	106	1	no	—
1469	#121	—	106	1	no	—
1470	#121	C₂²×D₅₃	1	1	yes	characteristic
1471	#121	C₂²×D₅₃	1	1	yes	characteristic, complemented
1472	#120	—	2	1	no	—
1473	#120	—	53	1	no	—
1474	#120	—	53	1	no	—
1475	#120	—	106	1	no	—
1476	#120	—	106	1	no	—
1477	#120	—	106	1	no	—
1478	#120	—	106	1	no	—
1479	#120	—	106	1	no	—
1480	#120	—	106	1	no	—
1481	#120	—	106	1	no	—
1482	#120	—	106	1	no	—
1483	#120	—	106	1	no	—
1484	#120	—	106	1	no	—
1485	#120	—	106	1	no	—
1486	#120	—	106	1	no	—
1487	#120	—	106	1	no	—
1488	#120	—	106	1	no	—
1489	#120	—	106	1	no	—
1490	#120	—	106	1	no	—
1491	#120	—	106	1	no	—
1492	#120	—	106	1	no	—
1493	#120	—	106	1	no	—
1494	#120	—	106	1	no	—
1495	#120	—	106	1	no	—
1496	C₄×Q₈	—	53	1	no	—
1497	C₄×Q₈	—	53	1	no	—
1498	C₄×Q₈	—	53	1	no	—
1499	C₄×Q₈	—	106	1	no	—
1500	C₄×Q₈	—	106	1	no	—
1501	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1502	C₄×D₄	—	2	1	no	—
1503	C₄×D₄	—	53	1	no	—
1504	C₄×D₄	—	53	1	no	—
1505	C₄×D₄	—	53	1	no	—
1506	C₄×D₄	—	53	1	no	—
1507	C₄×D₄	—	53	1	no	—
1508	C₄×D₄	—	53	1	no	—
1509	C₄×D₄	—	106	1	no	—
1510	C₄×D₄	—	106	1	no	—
1511	C₄×D₄	—	106	1	no	—
1512	C₄×D₄	—	106	1	no	—
1513	C₄×D₄	—	106	1	no	—
1514	C₄×D₄	—	106	1	no	—
1515	C₄×D₄	—	106	1	no	—
1516	C₄×D₄	—	106	1	no	—
1517	C₄×D₄	—	106	1	no	—
1518	C₄×D₄	—	106	1	no	—
1519	C₄×D₄	—	106	1	no	—
1520	C₄×D₄	—	106	1	no	—
1521	C₄×D₄	—	106	1	no	—
1522	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1523	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1524	#117	—	53	1	no	—
1525	#117	—	53	1	no	—
1526	#117	—	53	1	no	—
1527	#117	—	106	1	no	—
1528	#117	—	106	1	no	—
1529	C₂×C₂²⋊C₄	—	2	1	no	—
1530	C₂×C₂²⋊C₄	—	106	1	no	—
1531	C₂×C₂²⋊C₄	—	106	1	no	—
1532	C₂×C₂²⋊C₄	—	106	1	no	—
1533	C₂×C₂²⋊C₄	—	106	1	no	—
1534	C₂×C₂²⋊C₄	—	106	1	no	—
1535	#107	—	53	1	no	—
1536	#107	—	53	1	no	—
1537	#106	—	53	1	no	—
1538	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
1539	C₄⋊C₈	—	53	1	no	—
1540	C₄⋊C₈	—	53	1	no	—
1541	C₄⋊C₈	—	53	1	no	—
1542	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1543	#103	—	53	1	no	—
1544	#103	—	53	1	no	—
1545	#103	—	53	1	no	—
1546	#103	—	53	1	no	—
1547	#103	—	53	1	no	—
1548	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1549	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1550	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1551	#102	—	53	1	no	—
1552	#102	—	53	1	no	—
1553	#102	—	53	1	no	—
1554	#102	—	53	1	no	—
1555	#102	—	53	1	no	—
1556	#102	—	53	1	no	—
1557	#102	—	53	1	no	—
1558	#102	—	53	1	no	—
1559	#102	—	53	1	no	—
1560	#102	—	53	1	no	—
1561	#102	—	53	1	no	—
1562	#102	—	53	1	no	—
1563	#102	—	53	1	no	—
1564	#102	C₂²×D₅₃	1	1	yes	characteristic
1565	#102	C₂²×D₅₃	1	1	yes	characteristic
1566	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1567	C₂²⋊C₈	—	53	1	no	—
1568	C₂²⋊C₈	—	53	1	no	—
1569	C₂²⋊C₈	—	53	1	no	—
1570	C₂²⋊C₈	—	53	1	no	—
1571	C₂²⋊C₈	—	53	1	no	—
1572	C₂²⋊C₈	—	53	1	no	—
1573	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1574	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1575	#97	—	53	1	no	—
1576	#97	—	53	1	no	—
1577	C₄×C₈	—	53	1	no	—
1578	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1579	C₂⁴	—	2	1	no	—
1580	C₂⁴	—	53	1	no	—
1581	C₂⁴	—	106	1	no	—
1582	C₂⁴	—	106	1	no	—
1583	C₂⁴	—	106	1	no	—
1584	C₂⁴	—	106	1	no	—
1585	C₂⁴	—	106	1	no	—
1586	C₂⁴	—	106	1	no	—
1587	C₂⁴	—	106	1	no	—
1588	C₂⁴	—	106	1	no	—
1589	C₂⁴	—	424	2	no	—
1590	C₂⁴	—	424	2	no	—
1591	C₂⁴	—	212	4	no	—
1592	#41	—	2	2	no	—
1593	#41	—	2	2	no	—
1594	#41	—	4	1	no	—
1595	#41	—	4	1	no	—
1596	#41	—	106	2	no	—
1597	#41	—	106	2	no	—
1598	#41	—	106	2	no	—
1599	#41	—	106	2	no	—
1600	#41	—	106	2	no	—
1601	#41	—	106	2	no	—
1602	#41	—	106	2	no	—
1603	#41	—	106	2	no	—
1604	#41	—	106	2	no	—
1605	#41	—	106	2	no	—
1606	#41	—	106	2	no	—
1607	#41	—	106	2	no	—
1608	#41	—	212	1	no	—
1609	#41	—	212	1	no	—
1610	#41	—	212	4	no	—
1611	#41	—	212	4	no	—
1612	#41	—	212	4	no	—
1613	#41	—	212	4	no	—
1614	#41	—	212	1	no	—
1615	#41	—	212	4	no	—
1616	#41	—	212	1	no	—
1617	#41	—	212	1	no	—
1618	#41	—	212	1	no	—
1619	#41	—	212	4	no	—
1620	C₂×Q₈	—	2	1	no	—
1621	C₂×Q₈	—	2	2	no	—
1622	C₂×Q₈	—	4	1	no	—
1623	C₂×Q₈	—	53	1	no	—
1624	C₂×Q₈	—	53	4	no	—
1625	C₂×Q₈	—	53	1	no	—
1626	C₂×Q₈	—	106	1	no	—
1627	C₂×Q₈	—	106	1	no	—
1628	C₂×Q₈	—	106	2	no	—
1629	C₂×Q₈	—	106	2	no	—
1630	C₂×Q₈	—	212	1	no	—
1631	C₂×Q₈	—	212	4	no	—
1632	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1633	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1634	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1635	C₂×D₄	—	2	2	no	—
1636	C₂×D₄	—	2	1	no	—
1637	C₂×D₄	—	2	1	no	—
1638	C₂×D₄	—	2	1	no	—
1639	C₂×D₄	—	2	1	no	—
1640	C₂×D₄	—	2	1	no	—
1641	C₂×D₄	—	4	1	no	—
1642	C₂×D₄	—	53	4	no	—
1643	C₂×D₄	—	53	1	no	—
1644	C₂×D₄	—	53	1	no	—
1645	C₂×D₄	—	53	1	no	—
1646	C₂×D₄	—	53	1	no	—
1647	C₂×D₄	—	53	1	no	—
1648	C₂×D₄	—	53	1	no	—
1649	C₂×D₄	—	53	1	no	—
1650	C₂×D₄	—	53	1	no	—
1651	C₂×D₄	—	53	1	no	—
1652	C₂×D₄	—	53	1	no	—
1653	C₂×D₄	—	53	1	no	—
1654	C₂×D₄	—	106	2	no	—
1655	C₂×D₄	—	106	2	no	—
1656	C₂×D₄	—	106	1	no	—
1657	C₂×D₄	—	106	1	no	—
1658	C₂×D₄	—	106	1	no	—
1659	C₂×D₄	—	106	1	no	—
1660	C₂×D₄	—	106	1	no	—
1661	C₂×D₄	—	106	1	no	—
1662	C₂×D₄	—	106	1	no	—
1663	C₂×D₄	—	106	1	no	—
1664	C₂×D₄	—	106	1	no	—
1665	C₂×D₄	—	106	2	no	—
1666	C₂×D₄	—	106	2	no	—
1667	C₂×D₄	—	106	2	no	—
1668	C₂×D₄	—	106	2	no	—
1669	C₂×D₄	—	106	2	no	—
1670	C₂×D₄	—	106	1	no	—
1671	C₂×D₄	—	106	1	no	—
1672	C₂×D₄	—	106	1	no	—
1673	C₂×D₄	—	106	1	no	—
1674	C₂×D₄	—	106	1	no	—
1675	C₂×D₄	—	106	1	no	—
1676	C₂×D₄	—	106	1	no	—
1677	C₂×D₄	—	106	1	no	—
1678	C₂×D₄	—	106	1	no	—
1679	C₂×D₄	—	106	1	no	—
1680	C₂×D₄	—	106	2	no	—
1681	C₂×D₄	—	106	2	no	—
1682	C₂×D₄	—	106	2	no	—
1683	C₂×D₄	—	106	1	no	—
1684	C₂×D₄	—	106	1	no	—
1685	C₂×D₄	—	106	1	no	—
1686	C₂×D₄	—	106	1	no	—
1687	C₂×D₄	—	106	1	no	—
1688	C₂×D₄	—	106	1	no	—
1689	C₂×D₄	—	106	1	no	—
1690	C₂×D₄	—	106	1	no	—
1691	C₂×D₄	—	106	1	no	—
1692	C₂×D₄	—	106	1	no	—
1693	C₂×D₄	—	106	1	no	—
1694	C₂×D₄	—	106	1	no	—
1695	C₂×D₄	—	106	1	no	—
1696	C₂×D₄	—	106	1	no	—
1697	C₂×D₄	—	106	1	no	—
1698	C₂×D₄	—	424	2	no	—
1699	C₂×D₄	—	424	2	no	—
1700	C₂×D₄	—	424	2	no	—
1701	C₂×D₄	—	424	2	no	—
1702	C₂×D₄	—	212	1	no	—
1703	C₂×D₄	—	212	1	no	—
1704	C₂×D₄	—	212	4	no	—
1705	C₂×D₄	—	212	1	no	—
1706	C₂×D₄	—	212	1	no	—
1707	C₂×D₄	—	212	1	no	—
1708	C₂×D₄	—	212	4	no	—
1709	C₂×D₄	—	212	4	no	—
1710	C₂×D₄	—	212	4	no	—
1711	C₂×D₄	—	212	4	no	—
1712	C₂×D₄	—	212	4	no	—
1713	C₂×D₄	—	212	4	no	—
1714	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
1715	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1716	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1717	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1718	C₂²×C₄	—	2	1	no	—
1719	C₂²×C₄	—	2	1	no	—
1720	C₂²×C₄	—	2	1	no	—
1721	C₂²×C₄	—	2	1	no	—
1722	C₂²×C₄	—	53	1	no	—
1723	C₂²×C₄	—	53	1	no	—
1724	C₂²×C₄	—	53	1	no	—
1725	C₂²×C₄	—	53	1	no	—
1726	C₂²×C₄	—	53	1	no	—
1727	C₂²×C₄	—	53	1	no	—
1728	C₂²×C₄	—	106	2	no	—
1729	C₂²×C₄	—	106	2	no	—
1730	C₂²×C₄	—	106	1	no	—
1731	C₂²×C₄	—	106	1	no	—
1732	C₂²×C₄	—	106	1	no	—
1733	C₂²×C₄	—	106	1	no	—
1734	C₂²×C₄	—	106	1	no	—
1735	C₂²×C₄	—	106	1	no	—
1736	C₂²×C₄	—	106	1	no	—
1737	C₂²×C₄	—	106	1	no	—
1738	C₂²×C₄	—	106	1	no	—
1739	C₂²×C₄	—	106	1	no	—
1740	C₂²×C₄	—	106	1	no	—
1741	C₂²×C₄	—	106	1	no	—
1742	C₂²×C₄	—	106	1	no	—
1743	C₂²×C₄	—	212	4	no	—
1744	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1745	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1746	Q₁₆	—	2	2	no	—
1747	Q₁₆	—	2	2	no	—
1748	Q₁₆	—	106	2	no	—
1749	SD₁₆	—	2	2	no	—
1750	SD₁₆	—	2	2	no	—
1751	SD₁₆	—	4	1	no	—
1752	SD₁₆	—	4	1	no	—
1753	SD₁₆	—	53	4	no	—
1754	SD₁₆	—	53	4	no	—
1755	SD₁₆	—	53	4	no	—
1756	SD₁₆	—	106	2	no	—
1757	SD₁₆	—	106	2	no	—
1758	SD₁₆	—	106	2	no	—
1759	SD₁₆	—	106	2	no	—
1760	SD₁₆	—	106	2	no	—
1761	SD₁₆	—	106	2	no	—
1762	SD₁₆	—	106	2	no	—
1763	SD₁₆	—	106	2	no	—
1764	SD₁₆	—	212	1	no	—
1765	SD₁₆	—	212	1	no	—
1766	SD₁₆	D₄×D₅₃	1	4	yes	complemented
1767	D₈	—	2	2	no	—
1768	D₈	—	2	2	no	—
1769	D₈	—	106	2	no	—
1770	D₈	—	106	2	no	—
1771	D₈	—	106	2	no	—
1772	D₈	—	106	2	no	—
1773	D₈	—	106	2	no	—
1774	D₈	—	106	2	no	—
1775	D₈	—	106	2	no	—
1776	D₈	—	106	2	no	—
1777	D₈	—	106	2	no	—
1778	D₈	—	212	1	no	—
1779	D₈	—	212	1	no	—
1780	D₈	—	212	1	no	—
1781	D₈	—	212	1	no	—
1782	M₁₆	—	2	2	no	—
1783	M₁₆	—	2	2	no	—
1784	M₁₆	—	106	2	no	—
1785	M₁₆	—	106	2	no	—
1786	M₁₆	—	106	2	no	—
1787	M₁₆	—	106	2	no	—
1788	M₁₆	—	106	2	no	—
1789	M₁₆	—	106	2	no	—
1790	C₂×C₈	—	53	1	no	—
1791	C₂×C₈	—	53	4	no	—
1792	C₂×C₈	—	53	1	no	—
1793	C₂×C₈	—	53	1	no	—
1794	C₂×C₈	—	53	1	no	—
1795	C₂×C₈	—	106	2	no	—
1796	C₂×C₈	—	106	2	no	—
1797	C₂×C₈	—	106	2	no	—
1798	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1799	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1800	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1801	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1802	C₄⋊C₄	—	2	1	no	—
1803	C₄⋊C₄	—	2	1	no	—
1804	C₄⋊C₄	—	2	1	no	—
1805	C₄⋊C₄	—	53	1	no	—
1806	C₄⋊C₄	—	53	1	no	—
1807	C₄⋊C₄	—	53	1	no	—
1808	C₄⋊C₄	—	53	1	no	—
1809	C₄⋊C₄	—	53	1	no	—
1810	C₄⋊C₄	—	53	1	no	—
1811	C₄⋊C₄	—	53	1	no	—
1812	C₄⋊C₄	—	106	1	no	—
1813	C₄⋊C₄	—	106	1	no	—
1814	C₄⋊C₄	—	106	1	no	—
1815	C₄⋊C₄	—	106	1	no	—
1816	C₄⋊C₄	—	106	1	no	—
1817	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1818	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1819	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1820	C₂²⋊C₄	—	2	1	no	—
1821	C₂²⋊C₄	—	2	1	no	—
1822	C₂²⋊C₄	—	2	1	no	—
1823	C₂²⋊C₄	—	2	1	no	—
1824	C₂²⋊C₄	—	2	1	no	—
1825	C₂²⋊C₄	—	2	1	no	—
1826	C₂²⋊C₄	—	2	1	no	—
1827	C₂²⋊C₄	—	2	1	no	—
1828	C₂²⋊C₄	—	2	1	no	—
1829	C₂²⋊C₄	—	53	1	no	—
1830	C₂²⋊C₄	—	53	1	no	—
1831	C₂²⋊C₄	—	53	1	no	—
1832	C₂²⋊C₄	—	53	1	no	—
1833	C₂²⋊C₄	—	53	1	no	—
1834	C₂²⋊C₄	—	53	1	no	—
1835	C₂²⋊C₄	—	53	1	no	—
1836	C₂²⋊C₄	—	53	1	no	—
1837	C₂²⋊C₄	—	106	1	no	—
1838	C₂²⋊C₄	—	106	1	no	—
1839	C₂²⋊C₄	—	106	1	no	—
1840	C₂²⋊C₄	—	106	1	no	—
1841	C₂²⋊C₄	—	106	1	no	—
1842	C₂²⋊C₄	—	106	1	no	—
1843	C₂²⋊C₄	—	106	1	no	—
1844	C₂²⋊C₄	—	106	1	no	—
1845	C₂²⋊C₄	—	106	1	no	—
1846	C₂²⋊C₄	—	106	1	no	—
1847	C₂²⋊C₄	—	106	1	no	—
1848	C₂²⋊C₄	—	106	1	no	—
1849	C₂²⋊C₄	—	106	1	no	—
1850	C₂²⋊C₄	—	106	1	no	—
1851	C₂²⋊C₄	—	106	1	no	—
1852	C₂²⋊C₄	—	106	1	no	—
1853	C₂²⋊C₄	—	106	1	no	—
1854	C₂²⋊C₄	—	106	1	no	—
1855	C₂²⋊C₄	—	106	1	no	—
1856	C₂²⋊C₄	—	106	1	no	—
1857	C₂²⋊C₄	—	106	1	no	—
1858	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1859	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1860	C₄²	—	2	1	no	—
1861	C₄²	—	53	1	no	—
1862	C₄²	—	106	1	no	—
1863	C₄²	—	106	1	no	—
1864	C₄²	—	106	1	no	—
1865	C₄²	—	106	1	no	—
1866	C₄²	—	106	1	no	—
1867	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1868	C₂³	—	2	1	no	—
1869	C₂³	—	2	1	no	—
1870	C₂³	—	2	1	no	—
1871	C₂³	—	4	2	no	—
1872	C₂³	—	4	2	no	—
1873	C₂³	—	8	1	no	—
1874	C₂³	—	53	1	no	—
1875	C₂³	—	53	1	no	—
1876	C₂³	—	53	1	no	—
1877	C₂³	—	106	4	no	—
1878	C₂³	—	106	2	no	—
1879	C₂³	—	106	1	no	—
1880	C₂³	—	106	1	no	—
1881	C₂³	—	106	1	no	—
1882	C₂³	—	106	1	no	—
1883	C₂³	—	106	1	no	—
1884	C₂³	—	424	1	no	—
1885	C₂³	—	424	1	no	—
1886	C₂³	—	424	1	no	—
1887	C₂³	—	424	1	no	—
1888	C₂³	—	424	1	no	—
1889	C₂³	—	424	1	no	—
1890	C₂³	—	424	1	no	—
1891	C₂³	—	424	1	no	—
1892	C₂³	—	424	1	no	—
1893	C₂³	—	424	1	no	—
1894	C₂³	—	424	1	no	—
1895	C₂³	—	424	1	no	—
1896	C₂³	—	424	1	no	—
1897	C₂³	—	424	16	no	—
1898	C₂³	—	212	2	no	—
1899	C₂³	—	212	2	no	—
1900	C₂³	—	212	1	no	—
1901	C₂³	—	212	1	no	—
1902	C₂³	—	212	2	no	—
1903	C₂³	—	212	2	no	—
1904	C₂³	—	212	2	no	—
1905	C₂³	—	212	2	no	—
1906	C₂³	—	212	2	no	—
1907	C₂³	—	212	2	no	—
1908	C₂³	—	212	2	no	—
1909	C₂³	—	212	2	no	—
1910	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1911	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1912	Q₈	—	2	1	no	—
1913	Q₈	—	2	1	no	—
1914	Q₈	—	2	1	no	—
1915	Q₈	—	2	1	no	—
1916	Q₈	—	2	1	no	—
1917	Q₈	—	4	2	no	—
1918	Q₈	—	53	2	no	—
1919	Q₈	—	106	4	no	—
1920	Q₈	—	106	2	no	—
1921	Q₈	—	106	1	no	—
1922	Q₈	—	212	2	no	—
1923	Q₈	C₂×D₄×D₅₃	1	2	yes	—
1924	D₄	—	2	1	no	—
1925	D₄	—	2	1	no	—
1926	D₄	—	2	1	no	—
1927	D₄	—	2	1	no	—
1928	D₄	—	2	1	no	—
1929	D₄	—	4	1	no	—
1930	D₄	—	4	2	no	—
1931	D₄	—	4	2	no	—
1932	D₄	—	4	2	no	—
1933	D₄	—	8	1	no	—
1934	D₄	—	8	1	no	—
1935	D₄	—	53	2	no	—
1936	D₄	—	106	2	no	—
1937	D₄	—	106	4	no	—
1938	D₄	—	106	2	no	—
1939	D₄	—	106	2	no	—
1940	D₄	—	106	1	no	—
1941	D₄	—	106	1	no	—
1942	D₄	—	106	1	no	—
1943	D₄	—	106	1	no	—
1944	D₄	—	106	1	no	—
1945	D₄	—	106	1	no	—
1946	D₄	—	106	1	no	—
1947	D₄	—	106	1	no	—
1948	D₄	—	106	1	no	—
1949	D₄	—	424	1	no	—
1950	D₄	—	424	1	no	—
1951	D₄	—	424	1	no	—
1952	D₄	—	424	1	no	—
1953	D₄	—	424	1	no	—
1954	D₄	—	424	1	no	—
1955	D₄	—	424	1	no	—
1956	D₄	—	424	1	no	—
1957	D₄	—	424	1	no	—
1958	D₄	—	424	1	no	—
1959	D₄	—	424	1	no	—
1960	D₄	—	424	1	no	—
1961	D₄	—	424	1	no	—
1962	D₄	—	424	1	no	—
1963	D₄	—	424	1	no	—
1964	D₄	—	424	1	no	—
1965	D₄	—	212	1	no	—
1966	D₄	—	212	2	no	—
1967	D₄	—	212	2	no	—
1968	D₄	—	212	2	no	—
1969	D₄	—	212	2	no	—
1970	D₄	—	212	2	no	—
1971	D₄	—	212	2	no	—
1972	D₄	—	212	2	no	—
1973	D₄	—	212	2	no	—
1974	D₄	—	212	2	no	—
1975	D₄	—	212	2	no	—
1976	D₄	—	212	1	no	—
1977	D₄	—	212	1	no	—
1978	D₄	—	212	2	no	—
1979	D₄	—	212	2	no	—
1980	D₄	—	212	2	no	—
1981	D₄	—	212	2	no	—
1982	D₄	—	212	2	no	—
1983	D₄	—	212	2	no	—
1984	D₄	—	212	2	no	—
1985	D₄	C₂×D₄×D₅₃	1	2	yes	—
1986	C₂×C₄	—	2	1	no	—
1987	C₂×C₄	—	2	1	no	—
1988	C₂×C₄	—	2	1	no	—
1989	C₂×C₄	—	2	1	no	—
1990	C₂×C₄	—	2	1	no	—
1991	C₂×C₄	—	2	1	no	—
1992	C₂×C₄	—	2	1	no	—
1993	C₂×C₄	—	2	1	no	—
1994	C₂×C₄	—	2	1	no	—
1995	C₂×C₄	—	4	2	no	—
1996	C₂×C₄	—	4	2	no	—
1997	C₂×C₄	—	4	2	no	—
1998	C₂×C₄	—	8	1	no	—
1999	C₂×C₄	—	53	1	no	—
2000	C₂×C₄	—	53	2	no	—
2001	C₂×C₄	—	53	2	no	—
2002	C₂×C₄	—	53	1	no	—
2003	C₂×C₄	—	53	1	no	—
2004	C₂×C₄	—	53	1	no	—
2005	C₂×C₄	—	53	1	no	—
2006	C₂×C₄	—	106	2	no	—
2007	C₂×C₄	—	106	2	no	—
2008	C₂×C₄	—	106	4	no	—
2009	C₂×C₄	—	106	2	no	—
2010	C₂×C₄	—	106	1	no	—
2011	C₂×C₄	—	106	1	no	—
2012	C₂×C₄	—	106	1	no	—
2013	C₂×C₄	—	106	1	no	—
2014	C₂×C₄	—	106	1	no	—
2015	C₂×C₄	—	106	1	no	—
2016	C₂×C₄	—	106	1	no	—
2017	C₂×C₄	—	424	1	no	—
2018	C₂×C₄	—	424	1	no	—
2019	C₂×C₄	—	424	1	no	—
2020	C₂×C₄	—	212	2	no	—
2021	C₂×C₄	—	212	2	no	—
2022	C₂×C₄	—	212	2	no	—
2023	C₂×C₄	—	212	2	no	—
2024	C₂×C₄	—	212	2	no	—
2025	C₂×C₄	—	212	2	no	—
2026	C₂×C₄	—	212	2	no	—
2027	C₂×C₄	—	212	2	no	—
2028	C₂×C₄	—	212	2	no	—
2029	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2030	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2031	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2032	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2033	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
2034	C₈	—	2	1	no	—
2035	C₈	—	2	1	no	—
2036	C₈	—	2	1	no	—
2037	C₈	—	53	2	no	—
2038	C₈	—	106	1	no	—
2039	C₈	—	106	1	no	—
2040	C₈	—	106	1	no	—
2041	C₈	C₂×D₄×D₅₃	1	2	yes	—
2042	C₂²	—	2	1	no	—
2043	C₂²	—	2	1	no	—
2044	C₂²	—	2	2	no	—
2045	C₂²	—	2	1	no	—
2046	C₂²	—	2	1	no	—
2047	C₂²	—	2	1	no	—
2048	C₂²	—	2	1	no	—
2049	C₂²	—	4	1	no	—
2050	C₂²	—	4	1	no	—
2051	C₂²	—	4	1	no	—
2052	C₂²	—	4	1	no	—
2053	C₂²	—	4	1	no	—
2054	C₂²	—	4	1	no	—
2055	C₂²	—	4	1	no	—
2056	C₂²	—	4	1	no	—
2057	C₂²	—	8	4	no	—
2058	C₂²	—	53	2	no	—
2059	C₂²	—	848	2	no	—
2060	C₂²	—	848	2	no	—
2061	C₂²	—	106	1	no	—
2062	C₂²	—	106	1	no	—
2063	C₂²	—	106	1	no	—
2064	C₂²	—	106	1	no	—
2065	C₂²	—	106	2	no	—
2066	C₂²	—	106	1	no	—
2067	C₂²	—	106	1	no	—
2068	C₂²	—	106	1	no	—
2069	C₂²	—	106	1	no	—
2070	C₂²	—	424	4	no	—
2071	C₂²	—	424	4	no	—
2072	C₂²	—	424	4	no	—
2073	C₂²	—	424	4	no	—
2074	C₂²	—	424	4	no	—
2075	C₂²	—	424	4	no	—
2076	C₂²	—	212	4	no	—
2077	C₂²	—	212	1	no	—
2078	C₂²	—	212	1	no	—
2079	C₂²	—	212	1	no	—
2080	C₂²	—	212	1	no	—
2081	C₂²	—	212	1	no	—
2082	C₂²	—	212	1	no	—
2083	C₂²	—	212	1	no	—
2084	C₂²	—	212	1	no	—
2085	C₂²	—	212	1	no	—
2086	C₂²	—	212	1	no	—
2087	C₂²	—	212	1	no	—
2088	C₂²	—	212	1	no	—
2089	C₂²	—	212	1	no	—
2090	C₂²	—	212	1	no	—
2091	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
2092	C₄	—	2	1	no	—
2093	C₄	—	2	1	no	—
2094	C₄	—	2	2	no	—
2095	C₄	—	2	1	no	—
2096	C₄	—	2	1	no	—
2097	C₄	—	4	1	no	—
2098	C₄	—	4	1	no	—
2099	C₄	—	4	1	no	—
2100	C₄	—	4	1	no	—
2101	C₄	—	53	2	no	—
2102	C₄	—	106	1	no	—
2103	C₄	—	106	1	no	—
2104	C₄	—	106	2	no	—
2105	C₄	—	106	1	no	—
2106	C₄	—	106	1	no	—
2107	C₄	—	212	1	no	—
2108	C₄	—	212	1	no	—
2109	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
2110	C₄	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
2111	C₂	—	4	1	no	—
2112	C₂	—	4	1	no	—
2113	C₂	—	4	2	no	—
2114	C₂	—	8	1	no	—
2115	C₂	—	8	1	no	—
2116	C₂	—	106	2	no	—
2117	C₂	—	424	1	no	—
2118	C₂	—	424	1	no	—
2119	C₂	—	424	1	no	—
2120	C₂	—	424	1	no	—
2121	C₂	—	212	1	no	—
2122	C₂	—	212	2	no	—
2123	C₂	—	212	1	no	—
2124	C₂	D₄²×D₅₃	1	1	yes	characteristic
2125	C₂	#20289492	1	1	yes	characteristic
2126	C₂	#20289493	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3275	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3275	D₅₃
hypocenter	C₅₃	#61059
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3275

Complements

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

N	H ≅ G/N	type
1. C₂×#16811432	C₂	semidirect
2. C₂×AGL(1,ℤ/8)×D₅₃	C₂	semidirect
3. #20288372	C₂	semidirect
4. #20288345	C₂	semidirect
5. #20286345	C₂	semidirect
6. #20286343	C₂	semidirect
7. #20286340	C₂	semidirect
8. #20286337	C₂	semidirect
9. #20286336	C₂	semidirect
10. #20286332	C₂	semidirect
11. #20286329	C₂	semidirect
12. #20286259	C₂	semidirect
13. #20286258	C₂	semidirect
14. #20286251	C₂	semidirect
15. #20286250	C₂	semidirect
16. #20286216	C₂	semidirect
17. #20286211	C₂	semidirect
18. #20286208	C₂	semidirect
19. #20286203	C₂	semidirect
20. #20285197	C₂	semidirect
21. #20284361	C₂	semidirect
22. #20284326	C₂	semidirect
23. #20284234	C₂	semidirect
24. #20284216	C₂	semidirect
25. #20283996	C₂	semidirect
26. #20283980	C₂	semidirect
27. #20283958	C₂	semidirect
28. #20283943	C₂	semidirect
29. #20283569	C₂	semidirect
30. #20283415	C₂	semidirect
31. C₅₃×#3275	C₂	semidirect
32. C₂×#13133265	C₂²	semidirect
34. C₂×#41×D₅₃	C₂²	semidirect
37. C₂×#13133249	C₂²	semidirect
38. C₂×#13133249	C₂²	semidirect
39. C₂×#13133245	C₂²	semidirect
40. C₂×#13133245	C₂²	semidirect
42. C₂×#13133244	C₂²	semidirect
43. C₂×#13133244	C₂²	semidirect
44. C₂×#13133244	C₂²	semidirect
45. C₂×#13133244	C₂²	semidirect
46. C₂×#13133244	C₂²	semidirect
47. C₂×#13133243	C₂²	semidirect
48. C₂×#13133242	C₂²	semidirect
49. C₂×#13133241	C₂²	semidirect
50. C₂×#13133241	C₂²	semidirect
52. C₂×#13133240	C₂²	semidirect
53. C₂×#13133240	C₂²	semidirect
54. C₂×#13133237	C₂²	semidirect
55. C₂²×#11719924	C₂²	semidirect
57. C₂×SD₁₆×D₅₃	C₂²	semidirect
58. C₂×SD₁₆×D₅₃	C₂²	semidirect
60. C₂×D₈×D₅₃	C₂²	semidirect
61. C₂×#13133225	C₂²	semidirect
62. C₂×M₁₆×D₅₃	C₂²	semidirect
63. #16811295	C₂²	semidirect
65. #16811294	C₂²	semidirect
66. #16811292	C₂²	semidirect
68. #16811291	C₂²	semidirect
69. #16811284	C₂²	semidirect
71. #16811283	C₂²	semidirect
73. #16811281	C₂²	semidirect
74. #16811266	C₂²	semidirect
76. #16811264	C₂²	semidirect
78. #16811261	C₂²	semidirect
79. D₄×D₂₁₂	C₂²	semidirect
80. D₄×D₂₁₂	C₂²	semidirect
82. #16811257	C₂²	semidirect
83. D₄×C₂²⋊D₅₃	C₂²	semidirect
87. #16811191	C₂²	semidirect
90. #16811189	C₂²	semidirect
95. #16811136	C₂²	semidirect
100. #16811099	C₂²	semidirect
102. #16811013	C₂²	semidirect
103. #16811013	C₂²	semidirect
104. #16811009	C₂²	semidirect
105. #16811009	C₂²	semidirect
106. #16811008	C₂²	semidirect
107. #16811000	C₂²	semidirect
108. #16810998	C₂²	semidirect
109. #16810878	C₂²	semidirect
110. #16810877	C₂²	semidirect
111. #16810877	C₂²	semidirect
112. #16810876	C₂²	semidirect
113. #16810876	C₂²	semidirect
114. #16810873	C₂²	semidirect
115. #16810872	C₂²	semidirect
116. #16810872	C₂²	semidirect
117. #16810871	C₂²	semidirect
118. #16810871	C₂²	semidirect
119. #16810858	C₂²	semidirect
120. #16810858	C₂²	semidirect
121. #16810857	C₂²	semidirect
122. #16810857	C₂²	semidirect
123. #16810848	C₂²	semidirect
124. #16810847	C₂²	semidirect
125. #16810842	C₂²	semidirect
126. #16810841	C₂²	semidirect
127. #16810840	C₂²	semidirect
128. #16810835	C₂²	semidirect
129. #16810824	C₂²	semidirect
130. #16810823	C₂²	semidirect
131. #16810822	C₂²	semidirect
132. #16810821	C₂²	semidirect
133. #16810819	C₂²	semidirect
134. #16810818	C₂²	semidirect
135. #16810817	C₂²	semidirect
136. #16810816	C₂²	semidirect
137. #16810784	C₂²	semidirect
138. #16810783	C₂²	semidirect
139. #16810782	C₂²	semidirect
140. #16810773	C₂²	semidirect
141. #16810772	C₂²	semidirect
142. #16810772	C₂²	semidirect
143. #16810771	C₂²	semidirect
144. #16810771	C₂²	semidirect
145. #16810771	C₂²	semidirect
146. #16810770	C₂²	semidirect
147. #16810770	C₂²	semidirect
148. #16810769	C₂²	semidirect
149. #16810768	C₂²	semidirect
150. #16810768	C₂²	semidirect
151. #16810767	C₂²	semidirect
152. #16810767	C₂²	semidirect
153. #16810766	C₂²	semidirect
154. #16810763	C₂²	semidirect
155. #16810762	C₂²	semidirect
156. #16810760	C₂²	semidirect
157. #16810759	C₂²	semidirect
158. #16810759	C₂²	semidirect
159. #16810758	C₂²	semidirect
160. #16810758	C₂²	semidirect
161. #16810758	C₂²	semidirect
162. #16810757	C₂²	semidirect
163. #16810756	C₂²	semidirect
164. #16810755	C₂²	semidirect
165. #16810726	C₂²	semidirect
166. #16810723	C₂²	semidirect
167. #16810721	C₂²	semidirect
168. #16810720	C₂²	semidirect
169. C₄×#11719913	C₂²	semidirect
170. SD₁₆×Dic₅₃	C₂²	semidirect
171. #16810710	C₂²	semidirect
172. #16810702	C₂²	semidirect
173. #16810699	C₂²	semidirect
174. #16810699	C₂²	semidirect
175. #16810697	C₂²	semidirect
176. #16810695	C₂²	semidirect
177. #16810693	C₂²	semidirect
178. #16810691	C₂²	semidirect
179. #16810658	C₂²	semidirect
180. #16810648	C₂²	semidirect
181. #16810630	C₂²	semidirect
183. #16810626	C₂²	semidirect
184. #16810626	C₂²	semidirect
185. #16810618	C₂²	semidirect
186. #16810618	C₂²	semidirect
187. #16810588	C₂²	semidirect
188. #16810585	C₂²	semidirect
189. #16810577	C₂²	semidirect
190. C₂×#137×C₅₃	C₂²	semidirect
191. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
192. C₅₃×#548	C₂²	semidirect
193. C₅₃×#546	C₂²	semidirect
194. C₅₃×#495	C₂²	semidirect
195. C₅₃×#470	C₂²	semidirect
196. C₅₃×#469	C₂²	semidirect
197. C₅₃×#464	C₂²	semidirect
198. C₅₃×#463	C₂²	semidirect
199. C₅₃×#452	C₂²	semidirect
200. C₅₃×#450	C₂²	semidirect
201. C₅₃×#449	C₂²	semidirect
202. C₅₃×#448	C₂²	semidirect
203. C₄×SD₁₆×C₅₃	C₂²	semidirect
204. C₅₃×#436	C₂²	semidirect
215. C₂×#11719949	C₂³	semidirect
222. C₂×#11719945	C₂³	semidirect
229. C₂×Q₈×D₅₃	C₂³	semidirect
270. C₂×#11719925	C₂³	semidirect
273. C₂×#11719913	C₂³	semidirect
281. C₂×#11719924	C₂³	semidirect
282. C₂×#11719924	C₂³	semidirect
283. C₂×#11719924	C₂³	semidirect
284. C₂×#11719924	C₂³	semidirect
287. SD₁₆×D₅₃	D₄	semidirect
292. C₂×D₄₂₄	C₂³	semidirect
293. C₂×D₄₂₄	C₂³	semidirect
300. C₂×#11719922	C₂³	semidirect
309. C₂×#11719912	C₂³	semidirect
311. C₂²×#88322	C₂³	semidirect
314. C₂×C₈×D₅₃	C₂³	semidirect
317. #13133214	C₂³	semidirect
324. #13133213	C₂³	semidirect
327. #13133206	C₂³	semidirect
353. #13133192	C₂³	semidirect
360. #13133191	C₂³	semidirect
379. #13133188	C₂³	semidirect
403. Q₈×Dic₅₃	C₂³	semidirect
405. C₄×Dic₁₀₆	C₂³	semidirect
407. #13133182	C₂³	semidirect
437. #13133150	C₂³	semidirect
438. #13133150	C₂³	semidirect
439. #13133149	C₂³	semidirect
440. C₄⋊#88322	C₂³	semidirect
441. #13133146	C₂³	semidirect
442. #13133146	C₂³	semidirect
443. #13133142	C₂³	semidirect
444. #13133141	C₂³	semidirect
445. #13133141	C₂³	semidirect
446. #13133141	C₂³	semidirect
447. #13133140	C₂³	semidirect
450. #13133139	C₂³	semidirect
451. #13133139	C₂³	semidirect
452. #13133139	C₂³	semidirect
455. #13133138	C₂³	semidirect
458. #13133137	C₂³	semidirect
459. #13133137	C₂³	semidirect
460. #13133137	C₂³	semidirect
462. C₂²⋊#88322	C₂³	semidirect
465. #13133129	C₂³	semidirect
466. #13133129	C₂³	semidirect
467. #13133128	C₂³	semidirect
468. #13133127	C₂³	semidirect
469. C₈×Dic₅₃	C₂³	semidirect
472. C₂²×Q₈×C₅₃	C₂³	semidirect
476. C₂×Q₁₆×C₅₃	C₂³	semidirect
477. C₂×Q₁₆×C₅₃	C₂³	semidirect
482. C₂×SD₁₆×C₅₃	C₂³	semidirect
486. C₂×M₁₆×C₅₃	C₂³	semidirect
489. #124×C₅₃	C₂³	semidirect
497. #121×C₅₃	C₂³	semidirect
499. C₄×Q₈×C₅₃	C₂³	semidirect
504. #106×C₅₃	C₂³	semidirect
505. C₄⋊C₈×C₅₃	C₂³	semidirect
506. #103×C₅₃	C₂³	semidirect
507. #103×C₅₃	C₂³	semidirect
508. #103×C₅₃	C₂³	semidirect
511. #102×C₅₃	C₂³	semidirect
513. C₂²⋊C₈×C₅₃	C₂³	semidirect
514. C₄×C₈×C₅₃	C₂³	semidirect
598. Q₈×D₅₃	C₂×D₄	semidirect
688. SD₁₆×C₅₃	C₂×D₄	semidirect
729. #11719924	C₂×D₄	semidirect
731. #11719923	C₂×D₄	semidirect
795. #11719913	C₂×D₄	semidirect
803. C₈×D₅₃	C₂×D₄	semidirect
1055. #3275	D₅₃	semidirect
1102. C₂×#137	C₂×D₅₃	semidirect
1116. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
1139. #548	C₂×D₅₃	semidirect
1145. #546	C₂×D₅₃	semidirect
1174. #495	C₂×D₅₃	semidirect
1178. #470	C₂×D₅₃	semidirect
1184. #469	C₂×D₅₃	semidirect
1196. #464	C₂×D₅₃	semidirect
1200. #463	C₂×D₅₃	semidirect
1212. #452	C₂×D₅₃	semidirect
1216. #450	C₂×D₅₃	semidirect
1228. #449	C₂×D₅₃	semidirect
1232. #448	C₂×D₅₃	semidirect
1248. C₄×SD₁₆	C₂×D₅₃	semidirect
1252. #436	C₂×D₅₃	semidirect
1268. C₅₃	#61059	semidirect
1296. C₂²×Q₈	C₂²×D₅₃	semidirect
1341. C₂×Q₁₆	C₂²×D₅₃	semidirect
1342. C₂×Q₁₆	C₂²×D₅₃	semidirect
1364. C₂×SD₁₆	C₂²×D₅₃	semidirect
1391. C₂×M₁₆	C₂²×D₅₃	semidirect
1415. #124	C₂²×D₅₃	semidirect
1471. #121	C₂²×D₅₃	semidirect
1501. C₄×Q₈	C₂²×D₅₃	semidirect
1538. #106	C₂²×D₅₃	semidirect
1542. C₄⋊C₈	C₂²×D₅₃	semidirect
1548. #103	C₂²×D₅₃	semidirect
1549. #103	C₂²×D₅₃	semidirect
1550. #103	C₂²×D₅₃	semidirect
1566. #102	C₂²×D₅₃	semidirect
1574. C₂²⋊C₈	C₂²×D₅₃	semidirect
1578. C₄×C₈	C₂²×D₅₃	semidirect
1766. SD₁₆	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811432	2
C₂×AGL(1,ℤ/8)×D₅₃	2
#20288372	2
#20288345	2
#20286345	2
#20286343	2
#20286340	2
#20286337	2
#20286336	2
#20286332	2
#20286329	2
#20286259	2
#20286258	2
#20286251	2
#20286250	2
#20286216	2
#20286211	2
#20286208	2
#20286203	2
#20285197	2
#20284361	2
#20284326	2
#20284234	2
#20284216	2
#20283996	2
#20283980	2
#20283958	2
#20283943	2
#20283569	2
#20283415	2
C₅₃×#3275	2
#61059	53