Subgroups — #28259396

Order 13568.

3074 conjugacy classes of subgroups.

The subgroup lattice has 2204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811427	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288345	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288343	C₂	1	1	yes	maximal, characteristic, complemented
5	#20286398	C₂	1	1	yes	maximal, characteristic, complemented
6	#20286396	C₂	1	1	yes	maximal, characteristic, complemented
7	#20286395	C₂	1	1	yes	maximal, characteristic, complemented
8	#20286393	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×#11719922	C₂	1	1	yes	maximal, characteristic, complemented
10	#20286387	C₂	1	1	yes	maximal, characteristic, complemented
11	#20286385	C₂	1	1	yes	maximal, characteristic, complemented
12	#20286385	C₂	1	1	yes	maximal, characteristic, complemented
13	#20286202	C₂	1	1	yes	maximal, characteristic, complemented
14	#20286200	C₂	1	1	yes	maximal, characteristic, complemented
15	#20286197	C₂	1	1	yes	maximal, characteristic, complemented
16	#20286195	C₂	1	1	yes	maximal, characteristic, complemented
17	#20286194	C₂	1	1	yes	maximal, characteristic, complemented
18	#20286192	C₂	1	1	yes	maximal, characteristic, complemented
19	#20286189	C₂	1	1	yes	maximal, characteristic, complemented
20	#20285199	C₂	1	1	yes	maximal, characteristic, complemented
21	#20284361	C₂	1	1	yes	maximal, characteristic, complemented
22	#20284291	C₂	1	1	yes	maximal, characteristic, complemented
23	#20284216	C₂	1	1	yes	maximal, characteristic, complemented
24	#20284213	C₂	1	1	yes	maximal, characteristic, complemented
25	#20283980	C₂	1	1	yes	maximal, characteristic, complemented
26	#20283978	C₂	1	1	yes	maximal, characteristic, complemented
27	#20283943	C₂	1	1	yes	maximal, characteristic, complemented
28	#20283939	C₂	1	1	yes	maximal, characteristic, complemented
29	#20283564	C₂	1	1	yes	maximal, characteristic, complemented
30	#20283406	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#13133263	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
34	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
36	#16811427	—	2	8	no	—
37	C₂×#13133245	C₂²	1	1	yes	characteristic, complemented
38	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
39	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
40	C₂×#13133244	C₂²	1	1	yes	characteristic, complemented
41	C₂×#13133241	C₂²	1	1	yes	characteristic, complemented
42	C₂×#13133241	C₂²	1	1	yes	characteristic, complemented
43	C₂×#13133241	C₂²	1	1	yes	characteristic, complemented
44	C₂×#13133238	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13133238	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133237	C₂²	1	1	yes	characteristic, complemented
47	C₂²×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
48	C₂²×#11719922	C₂²	1	1	yes	characteristic, complemented
49	C₂²×#11719922	C₂²	1	1	yes	characteristic, complemented
50	C₂²×#11719922	C₂²	1	1	yes	characteristic, complemented
51	C₂×D₈×D₅₃	—	2	8	no	—
52	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
56	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×D₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#13133225	C₂²	1	1	yes	characteristic, complemented
62	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
63	#16811270	C₂²	1	1	yes	characteristic, complemented
64	#16811269	C₂²	1	1	yes	characteristic, complemented
65	#16811268	C₂²	1	1	yes	characteristic, complemented
66	#16811267	C₂²	1	1	yes	characteristic, complemented
67	#16811266	C₂²	1	1	yes	characteristic, complemented
68	#16811265	—	2	1	no	—
69	#16811264	C₂²	1	1	yes	characteristic, complemented
70	#16811263	—	2	1	no	—
71	#16811262	—	2	1	no	—
72	#16811261	C₂²	1	1	yes	characteristic, complemented
73	#16811260	—	2	1	no	—
74	D₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
75	D₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
76	#16811258	C₂²	1	1	yes	characteristic, complemented
77	#16811257	—	2	1	no	—
78	#16811257	C₂²	1	1	yes	characteristic, complemented
79	#16811257	C₂²	1	1	yes	characteristic, complemented
80	D₄×C₂²⋊D₅₃	—	2	1	no	—
81	D₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
82	D₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic, complemented
83	#16811255	—	2	1	no	—
84	#16811255	—	2	1	no	—
85	#16811191	C₂²	1	1	yes	characteristic, complemented
86	#16811189	C₂²	1	1	yes	characteristic, complemented
87	#16811189	C₂²	1	1	yes	characteristic, complemented
88	#16811186	C₂²	1	1	yes	characteristic, complemented
89	#16811184	—	2	1	no	—
90	#16811183	—	2	1	no	—
91	#16811181	—	2	1	no	—
92	#16811181	—	2	1	no	—
93	#16811136	C₂²	1	1	yes	characteristic, complemented
94	#16811133	C₂²	1	1	yes	characteristic, complemented
95	#16811132	C₂²	1	1	yes	characteristic
96	C₂×#13133187	—	2	1	no	—
97	C₂×#13133185	—	2	1	no	—
98	#120×D₅₃	—	2	1	no	—
99	#120×D₅₃	—	2	1	no	—
100	#16811095	C₂²	1	1	yes	characteristic, complemented
101	#16811095	C₂²	1	1	yes	characteristic, complemented
102	#16811012	C₂²	1	1	yes	characteristic, complemented
103	#16811011	C₂²	1	1	yes	characteristic, complemented
104	#16811009	C₂²	1	1	yes	characteristic, complemented
105	#16811005	C₂²	1	1	yes	characteristic, complemented
106	#16811004	C₂²	1	1	yes	characteristic, complemented
107	#16810999	C₂²	1	1	yes	characteristic, complemented
108	#16810998	C₂²	1	1	yes	characteristic, complemented
109	#16810877	C₂²	1	1	yes	characteristic, complemented
110	#16810876	C₂²	1	1	yes	characteristic, complemented
111	#16810873	C₂²	1	1	yes	characteristic, complemented
112	#16810863	C₂²	1	1	yes	characteristic, complemented
113	#16810862	C₂²	1	1	yes	characteristic, complemented
114	#16810858	C₂²	1	1	yes	characteristic, complemented
115	#16810858	C₂²	1	1	yes	characteristic, complemented
116	#16810858	C₂²	1	1	yes	characteristic, complemented
117	#16810857	C₂²	1	1	yes	characteristic, complemented
118	#16810857	C₂²	1	1	yes	characteristic, complemented
119	#16810857	C₂²	1	1	yes	characteristic, complemented
120	#16810853	C₂²	1	1	yes	characteristic, complemented
121	#16810852	C₂²	1	1	yes	characteristic, complemented
122	#16810849	C₂²	1	1	yes	characteristic, complemented
123	#16810841	C₂²	1	1	yes	characteristic, complemented
124	#16810840	C₂²	1	1	yes	characteristic, complemented
125	#16810839	C₂²	1	1	yes	characteristic, complemented
126	#16810838	C₂²	1	1	yes	characteristic, complemented
127	#16810837	C₂²	1	1	yes	characteristic, complemented
128	#16810836	C₂²	1	1	yes	characteristic, complemented
129	#16810835	C₂²	1	1	yes	characteristic, complemented
130	#16810819	C₂²	1	1	yes	characteristic, complemented
131	#16810818	C₂²	1	1	yes	characteristic, complemented
132	#16810817	C₂²	1	1	yes	characteristic, complemented
133	#16810817	C₂²	1	1	yes	characteristic, complemented
134	#16810816	C₂²	1	1	yes	characteristic, complemented
135	#16810816	C₂²	1	1	yes	characteristic, complemented
136	#16810815	C₂²	1	1	yes	characteristic, complemented
137	#16810776	C₂²	1	1	yes	characteristic, complemented
138	#16810775	C₂²	1	1	yes	characteristic, complemented
139	#16810775	C₂²	1	1	yes	characteristic, complemented
140	#16810774	C₂²	1	1	yes	characteristic, complemented
141	#16810773	C₂²	1	1	yes	characteristic, complemented
142	#16810772	C₂²	1	1	yes	characteristic, complemented
143	#16810772	C₂²	1	1	yes	characteristic, complemented
144	#16810771	C₂²	1	1	yes	characteristic, complemented
145	#16810770	C₂²	1	1	yes	characteristic, complemented
146	#16810769	C₂²	1	1	yes	characteristic, complemented
147	#16810768	C₂²	1	1	yes	characteristic, complemented
148	#16810767	C₂²	1	1	yes	characteristic, complemented
149	#16810766	C₂²	1	1	yes	characteristic, complemented
150	#16810765	C₂²	1	1	yes	characteristic, complemented
151	#16810759	C₂²	1	1	yes	characteristic, complemented
152	#16810759	C₂²	1	1	yes	characteristic, complemented
153	#16810758	C₂²	1	1	yes	characteristic, complemented
154	#16810758	C₂²	1	1	yes	characteristic, complemented
155	#16810758	C₂²	1	1	yes	characteristic, complemented
156	#16810758	C₂²	1	1	yes	characteristic, complemented
157	#16810757	C₂²	1	1	yes	characteristic, complemented
158	#16810757	C₂²	1	1	yes	characteristic, complemented
159	#16810756	C₂²	1	1	yes	characteristic, complemented
160	#16810756	C₂²	1	1	yes	characteristic, complemented
161	#16810755	C₂²	1	1	yes	characteristic, complemented
162	#16810755	C₂²	1	1	yes	characteristic, complemented
163	#16810755	C₂²	1	1	yes	characteristic, complemented
164	#16810755	C₂²	1	1	yes	characteristic, complemented
165	#16810736	C₂²	1	1	yes	characteristic, complemented
166	#16810735	C₂²	1	1	yes	characteristic, complemented
167	#16810734	C₂²	1	1	yes	characteristic, complemented
168	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
169	C₄×#11719922	C₂²	1	1	yes	characteristic, complemented
170	#16810703	C₂²	1	1	yes	characteristic, complemented
171	#16810703	C₂²	1	1	yes	characteristic, complemented
172	#16810696	C₂²	1	1	yes	characteristic, complemented
173	#16810694	C₂²	1	1	yes	characteristic, complemented
174	#16810692	C₂²	1	1	yes	characteristic, complemented
175	D₄×#88322	C₂²	1	1	yes	characteristic, complemented
176	#16810688	C₂²	1	1	yes	characteristic, complemented
177	#16810686	C₂²	1	1	yes	characteristic, complemented
178	#16810686	C₂²	1	1	yes	characteristic, complemented
179	#16810658	C₂²	1	1	yes	characteristic, complemented
180	#16810648	C₂²	1	1	yes	characteristic, complemented
181	#16810626	C₂²	1	1	yes	characteristic, complemented
182	#16810626	C₂²	1	1	yes	characteristic, complemented
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	#16810616	C₂²	1	1	yes	characteristic, complemented
187	#16810588	C₂²	1	1	yes	characteristic, complemented
188	#16810585	C₂²	1	1	yes	characteristic, complemented
189	#16810580	C₂²	1	1	yes	characteristic, complemented
190	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
193	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
202	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
203	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
204	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
205	C₂⁴×D₅₃	—	2	1	no	—
206	C₂⁴×D₅₃	—	2	1	no	—
207	#13133263	—	2	4	no	—
208	#13133263	—	4	2	no	—
209	#13133262	—	2	4	no	—
210	#13133262	—	4	2	no	—
211	C₂×#11719949	C₂³	1	1	yes	characteristic
212	C₂×#11719949	C₂³	1	1	yes	characteristic, complemented
213	C₂×#11719945	—	2	1	no	—
214	C₂×#11719945	C₂³	1	1	yes	characteristic
215	C₂×#11719945	C₂³	1	1	yes	characteristic, complemented
216	C₂×#11719947	—	2	1	no	—
217	C₂×#11719947	C₂³	1	1	yes	characteristic
218	C₂×#11719947	C₂³	1	1	yes	characteristic, complemented
219	C₂²×D₂₁₂	—	2	1	no	—
220	C₂²×D₂₁₂	—	2	1	no	—
221	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
222	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
223	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
224	C₂²×C₂²⋊D₅₃	—	2	1	no	—
225	C₂²×C₂²⋊D₅₃	—	2	1	no	—
226	C₂²×C₂²⋊D₅₃	—	2	1	no	—
227	C₂²×C₂²⋊D₅₃	—	2	1	no	—
228	C₂²×C₂²⋊D₅₃	—	2	1	no	—
229	C₂²×C₂²⋊D₅₃	—	2	1	no	—
230	C₂×D₄×D₅₃	—	2	4	no	—
231	C₂×D₄×D₅₃	—	2	4	no	—
232	C₂×D₄×D₅₃	—	2	1	no	—
233	C₂×D₄×D₅₃	—	2	1	no	—
234	C₂×D₄×D₅₃	—	2	1	no	—
235	C₂×D₄×D₅₃	—	2	1	no	—
236	C₂×D₄×D₅₃	—	2	1	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	—	4	2	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	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
252	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
253	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
254	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
255	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
256	#13133245	—	2	4	no	—
257	#13133244	—	2	4	no	—
258	#13133244	—	2	4	no	—
259	#13133244	—	4	2	no	—
260	#13133241	—	2	4	no	—
261	#13133241	—	2	4	no	—
262	#13133241	—	4	2	no	—
263	#13133238	—	2	4	no	—
264	#13133238	—	2	4	no	—
265	#13133237	—	2	4	no	—
266	C₂×#11719925	C₂³	1	1	yes	characteristic, complemented
267	C₂×#11719913	C₂³	1	1	yes	characteristic, complemented
268	C₂×#11719913	C₂³	1	1	yes	characteristic, complemented
269	C₂×#11719913	C₂³	1	1	yes	characteristic, complemented
270	C₂×#11719923	C₂³	1	1	yes	characteristic, complemented
271	C₂×#11719923	C₂³	1	1	yes	characteristic, complemented
272	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
273	C₂×#11719924	C₂³	1	1	yes	characteristic, complemented
274	C₂×D₄₂₄	—	2	4	no	—
275	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
276	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
277	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
278	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
279	C₂×D₄₂₄	C₂³	1	1	yes	characteristic, complemented
280	C₂×D₄₂₄	C₂³	1	1	yes	characteristic, complemented
281	C₂×#11719922	—	2	4	no	—
282	C₂×#11719922	—	2	4	no	—
283	C₂×#11719922	—	2	4	no	—
284	C₂×#11719922	C₂³	1	1	yes	characteristic
285	C₂×#11719922	C₂³	1	1	yes	characteristic
286	C₂×#11719922	C₂³	1	1	yes	characteristic
287	C₂×#11719922	C₂³	1	1	yes	characteristic
288	C₂×#11719922	C₂³	1	1	yes	characteristic
289	C₂×#11719922	C₂³	1	1	yes	characteristic
290	C₂×#11719922	C₂³	1	1	yes	characteristic
291	C₂×#11719922	C₂³	1	1	yes	characteristic
292	C₂×#11719922	C₂³	1	1	yes	characteristic, complemented
293	C₂×#11719922	C₂³	1	1	yes	characteristic, complemented
294	C₂×#11719922	C₂³	1	1	yes	characteristic, complemented
295	C₂×#11719922	C₂³	1	1	yes	characteristic, complemented
296	C₂×#11719922	C₂³	1	1	yes	characteristic, complemented
297	D₈×D₅₃	—	2	4	no	—
298	D₈×D₅₃	—	2	4	no	—
299	D₈×D₅₃	—	2	4	no	—
300	D₈×D₅₃	—	2	4	no	—
301	D₈×D₅₃	—	2	4	no	—
302	D₈×D₅₃	—	2	4	no	—
303	D₈×D₅₃	—	2	4	no	—
304	D₈×D₅₃	—	2	4	no	—
305	D₈×D₅₃	D₄	1	8	yes	complemented
306	#13133225	—	2	4	no	—
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	C₂²×#88322	C₂³	1	1	yes	characteristic
311	C₂²×#88322	C₂³	1	1	yes	characteristic, complemented
312	C₂×C₈×D₅₃	—	2	4	no	—
313	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic, complemented
318	#13133214	C₂³	1	1	yes	characteristic, complemented
319	#13133213	—	2	1	no	—
320	#13133213	—	2	1	no	—
321	#13133213	C₂³	1	1	yes	characteristic, complemented
322	#13133213	C₂³	1	1	yes	characteristic, complemented
323	#13133206	C₂³	1	1	yes	characteristic, complemented
324	#13133205	C₂³	1	1	yes	characteristic, complemented
325	#13133204	C₂³	1	1	yes	characteristic, complemented
326	#13133203	—	2	1	no	—
327	#13133203	—	2	1	no	—
328	#13133202	—	2	1	no	—
329	#13133202	—	2	1	no	—
330	#13133202	—	2	1	no	—
331	#13133202	D₄	1	1	yes	characteristic
332	#13133201	—	2	1	no	—
333	#13133200	—	2	1	no	—
334	#13133199	—	2	1	no	—
335	#13133199	—	2	1	no	—
336	#13133199	—	2	1	no	—
337	#13133199	D₄	1	1	yes	characteristic
338	#13133198	—	2	1	no	—
339	#13133197	C₂³	1	1	yes	characteristic
340	#13133196	C₂³	1	1	yes	characteristic
341	#13133195	D₄	1	1	yes	characteristic
342	#13133194	D₄	1	1	yes	characteristic
343	#13133193	C₂³	1	1	yes	characteristic
344	#13133192	—	2	1	no	—
345	#13133192	—	2	1	no	—
346	#13133192	C₂³	1	1	yes	characteristic
347	#13133192	C₂³	1	1	yes	characteristic, complemented
348	#13133192	C₂³	1	1	yes	characteristic, complemented
349	#13133191	—	2	1	no	—
350	#13133191	—	2	1	no	—
351	#13133191	C₂³	1	1	yes	characteristic
352	#13133191	C₂³	1	1	yes	characteristic, complemented
353	#13133191	C₂³	1	1	yes	characteristic, complemented
354	#13133190	—	2	1	no	—
355	#13133190	—	2	1	no	—
356	#13133190	—	2	1	no	—
357	#13133190	—	2	1	no	—
358	#13133190	—	2	1	no	—
359	#13133190	—	2	1	no	—
360	#13133190	D₄	1	1	yes	characteristic
361	#13133189	—	2	1	no	—
362	#13133189	—	2	1	no	—
363	#13133189	—	2	1	no	—
364	#13133189	—	2	1	no	—
365	#13133189	—	2	1	no	—
366	#13133189	—	2	1	no	—
367	#13133189	D₄	1	1	yes	characteristic
368	#13133188	—	2	1	no	—
369	#13133188	—	2	1	no	—
370	#13133188	C₂³	1	1	yes	characteristic
371	#13133188	C₂³	1	1	yes	characteristic, complemented
372	#13133188	C₂³	1	1	yes	characteristic, complemented
373	#13133187	—	2	1	no	—
374	#13133187	—	2	1	no	—
375	#13133187	—	2	1	no	—
376	#13133187	—	2	1	no	—
377	#13133187	—	2	1	no	—
378	#13133187	—	2	1	no	—
379	#13133187	—	2	1	no	—
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	D₄	1	1	yes	characteristic
388	#13133186	—	2	1	no	—
389	#13133186	—	2	1	no	—
390	#13133186	—	2	1	no	—
391	#13133185	—	2	1	no	—
392	#13133185	—	2	1	no	—
393	#13133185	—	2	1	no	—
394	#13133185	—	2	1	no	—
395	#13133185	—	2	1	no	—
396	#13133185	—	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	—	2	1	no	—
403	#13133185	—	2	1	no	—
404	#13133185	—	2	1	no	—
405	#13133185	D₄	1	1	yes	characteristic
406	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
407	C₄×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
408	C₄×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
409	D₄×Dic₅₃	—	2	1	no	—
410	D₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
411	D₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
412	#13133179	—	2	1	no	—
413	#13133179	C₂³	1	1	yes	characteristic, complemented
414	#13133179	C₂³	1	1	yes	characteristic, complemented
415	C₄×C₂²⋊D₅₃	—	2	1	no	—
416	C₄×C₂²⋊D₅₃	—	2	1	no	—
417	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
418	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
419	#13133177	—	2	1	no	—
420	#13133177	—	2	1	no	—
421	#13133177	—	2	1	no	—
422	#13133177	—	2	1	no	—
423	#13133175	C₂³	1	1	yes	characteristic
424	#13133175	C₂³	1	1	yes	characteristic
425	#13133174	C₂³	1	1	yes	characteristic
426	C₂×C₂²⋊Dic₅₃	—	2	1	no	—
427	C₂×#11719921	—	2	1	no	—
428	C₂×#11719921	—	2	1	no	—
429	C₂×#11719921	—	2	1	no	—
430	C₂×#11719921	—	2	1	no	—
431	C₂²⋊C₄×D₅₃	—	2	1	no	—
432	C₂²⋊C₄×D₅₃	—	2	1	no	—
433	C₂²⋊C₄×D₅₃	—	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	#13133140	C₂³	1	1	yes	characteristic, complemented
446	#13133139	C₂³	1	1	yes	characteristic, complemented
447	#13133139	C₂³	1	1	yes	characteristic, complemented
448	#13133139	C₂³	1	1	yes	characteristic, complemented
449	#13133139	C₂³	1	1	yes	characteristic, complemented
450	#13133139	C₂³	1	1	yes	characteristic, complemented
451	#13133138	C₂³	1	1	yes	characteristic, complemented
452	#13133138	C₂³	1	1	yes	characteristic, complemented
453	#13133138	C₂³	1	1	yes	characteristic, complemented
454	#13133138	C₂³	1	1	yes	characteristic, complemented
455	#13133138	C₂³	1	1	yes	characteristic, complemented
456	#13133137	C₂³	1	1	yes	characteristic, complemented
457	#13133137	C₂³	1	1	yes	characteristic, complemented
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	#13133127	C₂³	1	1	yes	characteristic, complemented
468	C₄×#88322	C₂³	1	1	yes	characteristic, complemented
469	C₈×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
470	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic, complemented
471	C₂²×D₄×C₅₃	—	2	1	no	—
472	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
475	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
476	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
477	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
478	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
479	C₂×D₈×C₅₃	—	2	4	no	—
480	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
485	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
486	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
487	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
488	#127×C₅₃	C₂³	1	1	yes	characteristic, complemented
489	#124×C₅₃	C₂³	1	1	yes	characteristic, complemented
490	#123×C₅₃	—	2	1	no	—
491	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
492	#121×C₅₃	—	2	1	no	—
493	#121×C₅₃	—	2	1	no	—
494	#121×C₅₃	C₂³	1	1	yes	characteristic
495	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
496	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
497	#120×C₅₃	—	2	1	no	—
498	#120×C₅₃	—	2	1	no	—
499	#120×C₅₃	—	2	1	no	—
500	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
501	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
502	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
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	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
508	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
509	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
510	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
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	#97×C₅₃	C₂³	1	1	yes	characteristic, complemented
515	C₂⁴×C₅₃	—	2	1	no	—
516	C₂⁴×C₅₃	—	2	1	no	—
517	C₂⁴×C₅₃	—	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	—	2	1	no	—
525	C₂³×D₅₃	—	2	1	no	—
526	C₂³×D₅₃	—	2	1	no	—
527	C₂³×D₅₃	—	2	1	no	—
528	C₂³×D₅₃	—	2	1	no	—
529	C₂³×D₅₃	—	2	1	no	—
530	C₂³×D₅₃	—	2	1	no	—
531	C₂³×D₅₃	—	4	4	no	—
532	C₂³×D₅₃	—	4	4	no	—
533	C₂³×D₅₃	—	8	2	no	—
534	C₂³×D₅₃	—	8	2	no	—
535	C₂³×D₅₃	—	8	2	no	—
536	C₂³×D₅₃	—	8	2	no	—
537	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
538	#41×C₅₃	—	2	2	no	—
539	#41×C₅₃	—	4	1	no	—
540	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×D₄×C₅₃	—	2	2	no	—
542	C₂×D₄×C₅₃	—	2	2	no	—
543	C₂×D₄×C₅₃	—	2	2	no	—
544	C₂×D₄×C₅₃	—	2	1	no	—
545	C₂×D₄×C₅₃	—	2	1	no	—
546	C₂×D₄×C₅₃	—	2	1	no	—
547	C₂×D₄×C₅₃	—	2	1	no	—
548	C₂×D₄×C₅₃	—	2	1	no	—
549	C₂×D₄×C₅₃	—	2	1	no	—
550	C₂×D₄×C₅₃	—	2	1	no	—
551	C₂×D₄×C₅₃	—	2	1	no	—
552	C₂×D₄×C₅₃	—	2	1	no	—
553	C₂×D₄×C₅₃	—	4	1	no	—
554	C₂×D₄×C₅₃	—	4	1	no	—
555	C₂×D₄×C₅₃	—	4	1	no	—
556	C₂×D₄×C₅₃	—	8	2	no	—
557	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
558	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
561	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
562	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	—	2	1	no	—
564	C₂²×C₄×C₅₃	—	2	1	no	—
565	C₂²×C₄×C₅₃	—	2	1	no	—
566	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
567	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
575	C₂×C₂²⋊D₅₃	—	2	1	no	—
576	C₂×C₂²⋊D₅₃	—	2	1	no	—
577	C₂×C₂²⋊D₅₃	—	2	1	no	—
578	C₂×C₂²⋊D₅₃	—	2	1	no	—
579	C₂×C₂²⋊D₅₃	—	2	1	no	—
580	C₂×C₂²⋊D₅₃	—	2	1	no	—
581	C₂×C₂²⋊D₅₃	—	2	1	no	—
582	C₂×C₂²⋊D₅₃	—	2	1	no	—
583	C₂×C₂²⋊D₅₃	—	2	1	no	—
584	C₂×C₂²⋊D₅₃	—	2	1	no	—
585	C₂×C₂²⋊D₅₃	—	2	1	no	—
586	C₂×C₂²⋊D₅₃	—	2	1	no	—
587	C₂×C₂²⋊D₅₃	—	2	1	no	—
588	C₂×C₂²⋊D₅₃	—	2	1	no	—
589	C₂×C₂²⋊D₅₃	—	2	1	no	—
590	C₂×C₂²⋊D₅₃	—	2	1	no	—
591	C₂×C₂²⋊D₅₃	—	4	4	no	—
592	C₂×C₂²⋊D₅₃	—	4	4	no	—
593	C₂×C₂²⋊D₅₃	—	4	4	no	—
594	C₂×C₂²⋊D₅₃	—	4	4	no	—
595	C₂×C₂²⋊D₅₃	—	8	2	no	—
596	C₂×C₂²⋊D₅₃	—	8	2	no	—
597	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
598	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
599	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
600	C₂×C₂²⋊D₅₃	C₂×D₄	1	1	yes	characteristic
601	C₂²×Dic₅₃	—	2	1	no	—
602	C₂²×Dic₅₃	—	2	1	no	—
603	C₂²×Dic₅₃	—	2	1	no	—
604	C₂²×Dic₅₃	—	2	1	no	—
605	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
606	#11719949	—	2	2	no	—
607	#11719949	—	2	2	no	—
608	#11719949	—	2	2	no	—
609	#11719949	—	4	1	no	—
610	#11719947	—	2	2	no	—
611	#11719947	—	2	2	no	—
612	#11719947	—	2	2	no	—
613	#11719947	—	4	1	no	—
614	#11719947	—	4	4	no	—
615	D₄×D₅₃	—	2	2	no	—
616	D₄×D₅₃	—	2	2	no	—
617	D₄×D₅₃	—	2	2	no	—
618	D₄×D₅₃	—	2	2	no	—
619	D₄×D₅₃	—	2	2	no	—
620	D₄×D₅₃	—	2	2	no	—
621	D₄×D₅₃	—	2	2	no	—
622	D₄×D₅₃	—	2	2	no	—
623	D₄×D₅₃	—	2	2	no	—
624	D₄×D₅₃	—	2	2	no	—
625	D₄×D₅₃	—	2	2	no	—
626	D₄×D₅₃	—	2	2	no	—
627	D₄×D₅₃	—	4	1	no	—
628	D₄×D₅₃	—	4	1	no	—
629	D₄×D₅₃	—	4	1	no	—
630	D₄×D₅₃	—	4	1	no	—
631	D₄×D₅₃	—	4	1	no	—
632	D₄×D₅₃	—	4	1	no	—
633	D₄×D₅₃	—	4	4	no	—
634	D₄×D₅₃	—	4	4	no	—
635	D₄×D₅₃	—	4	4	no	—
636	D₄×D₅₃	—	4	4	no	—
637	D₄×D₅₃	—	4	4	no	—
638	D₄×D₅₃	—	4	4	no	—
639	D₄×D₅₃	—	4	4	no	—
640	D₄×D₅₃	—	8	2	no	—
641	D₄×D₅₃	—	8	2	no	—
642	D₄×D₅₃	—	8	2	no	—
643	D₄×D₅₃	—	8	2	no	—
644	D₄×D₅₃	C₂×D₄	1	4	yes	complemented
645	D₄×D₅₃	C₂×D₄	1	4	yes	complemented
646	#11719945	—	2	2	no	—
647	#11719945	—	2	2	no	—
648	#11719945	—	2	2	no	—
649	#11719945	—	4	1	no	—
650	#11719945	—	4	4	no	—
651	C₂×D₂₁₂	—	2	2	no	—
652	C₂×D₂₁₂	—	2	2	no	—
653	C₂×D₂₁₂	—	2	2	no	—
654	C₂×D₂₁₂	—	2	1	no	—
655	C₂×D₂₁₂	—	2	1	no	—
656	C₂×D₂₁₂	—	2	1	no	—
657	C₂×D₂₁₂	—	2	1	no	—
658	C₂×D₂₁₂	—	2	1	no	—
659	C₂×D₂₁₂	—	2	1	no	—
660	C₂×D₂₁₂	—	2	1	no	—
661	C₂×D₂₁₂	—	2	1	no	—
662	C₂×D₂₁₂	—	2	1	no	—
663	C₂×D₂₁₂	—	2	1	no	—
664	C₂×D₂₁₂	—	4	1	no	—
665	C₂×D₂₁₂	—	4	1	no	—
666	C₂×D₂₁₂	—	4	1	no	—
667	C₂×D₂₁₂	—	4	4	no	—
668	C₂×D₂₁₂	—	8	2	no	—
669	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
670	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
671	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
672	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
673	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
674	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
675	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
676	C₂×C₄×D₅₃	—	2	2	no	—
677	C₂×C₄×D₅₃	—	2	2	no	—
678	C₂×C₄×D₅₃	—	2	1	no	—
679	C₂×C₄×D₅₃	—	2	1	no	—
680	C₂×C₄×D₅₃	—	2	1	no	—
681	C₂×C₄×D₅₃	—	2	1	no	—
682	C₂×C₄×D₅₃	—	2	1	no	—
683	C₂×C₄×D₅₃	—	2	1	no	—
684	C₂×C₄×D₅₃	—	2	1	no	—
685	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
686	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
687	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
688	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
689	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
690	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
691	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
692	SD₁₆×C₅₃	—	2	2	no	—
693	SD₁₆×C₅₃	—	2	2	no	—
694	SD₁₆×C₅₃	—	4	1	no	—
695	D₈×C₅₃	—	2	2	no	—
696	D₈×C₅₃	—	2	2	no	—
697	D₈×C₅₃	—	2	2	no	—
698	D₈×C₅₃	—	2	2	no	—
699	D₈×C₅₃	—	4	1	no	—
700	D₈×C₅₃	C₂×D₄	1	4	yes	complemented
701	M₁₆×C₅₃	—	2	2	no	—
702	C₂×C₈×C₅₃	—	2	2	no	—
703	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
704	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
705	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
707	C₄⋊C₄×C₅₃	—	2	1	no	—
708	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
709	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
710	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
711	C₂²⋊C₄×C₅₃	—	2	1	no	—
712	C₂²⋊C₄×C₅₃	—	2	1	no	—
713	C₂²⋊C₄×C₅₃	—	2	1	no	—
714	C₂²⋊C₄×C₅₃	—	2	1	no	—
715	C₂²⋊C₄×C₅₃	—	2	1	no	—
716	C₂²⋊C₄×C₅₃	—	2	1	no	—
717	C₂²⋊C₄×C₅₃	—	2	1	no	—
718	C₂²⋊C₄×C₅₃	—	2	1	no	—
719	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
721	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
722	C₂²⋊Dic₅₃	—	2	1	no	—
723	C₂²⋊Dic₅₃	—	2	1	no	—
724	C₂²⋊Dic₅₃	—	2	1	no	—
725	C₂²⋊Dic₅₃	—	2	1	no	—
726	C₂²⋊Dic₅₃	—	2	1	no	—
727	C₂²⋊Dic₅₃	—	2	1	no	—
728	C₂²⋊Dic₅₃	—	2	1	no	—
729	C₂²⋊Dic₅₃	—	2	1	no	—
730	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
731	C₂²⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
732	#11719925	—	2	2	no	—
733	#11719924	—	2	2	no	—
734	#11719924	—	4	1	no	—
735	#11719923	—	2	2	no	—
736	#11719923	—	4	1	no	—
737	#11719922	—	2	2	no	—
738	#11719922	—	2	2	no	—
739	#11719922	—	2	2	no	—
740	#11719922	—	2	2	no	—
741	#11719922	—	2	2	no	—
742	#11719922	—	2	2	no	—
743	#11719922	—	2	2	no	—
744	#11719922	—	2	2	no	—
745	#11719922	—	2	2	no	—
746	#11719922	—	4	1	no	—
747	#11719922	—	4	1	no	—
748	#11719922	C₂×D₄	1	4	yes	complemented
749	#11719922	C₂×D₄	1	4	yes	complemented
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	—	2	1	no	—
758	#11719921	—	2	1	no	—
759	#11719921	—	2	1	no	—
760	#11719921	—	2	1	no	—
761	#11719921	—	2	1	no	—
762	#11719921	—	2	1	no	—
763	#11719921	—	2	1	no	—
764	#11719921	—	2	1	no	—
765	#11719921	—	2	1	no	—
766	#11719921	—	2	1	no	—
767	#11719921	—	2	1	no	—
768	#11719921	C₂×D₄	1	1	yes	characteristic
769	#11719921	C₂×D₄	1	1	yes	characteristic
770	#11719921	C₂×D₄	1	1	yes	characteristic
771	#11719921	C₂×D₄	1	1	yes	characteristic
772	#11719921	C₂×D₄	1	1	yes	characteristic
773	#11719921	C₂×D₄	1	1	yes	characteristic
774	C₄⋊Dic₅₃	—	2	1	no	—
775	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
776	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
777	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
778	#11719919	—	2	1	no	—
779	#11719919	—	2	1	no	—
780	#11719919	C₂×D₄	1	1	yes	characteristic
781	#11719919	C₂×D₄	1	1	yes	characteristic
782	#11719919	C₂×D₄	1	1	yes	characteristic
783	#11719919	C₂×D₄	1	1	yes	characteristic
784	C₄×Dic₅₃	—	2	1	no	—
785	C₄×Dic₅₃	—	2	1	no	—
786	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
787	C₂×#88322	—	2	2	no	—
788	C₂×#88322	—	2	2	no	—
789	C₂×#88322	C₂⁴	1	1	yes	characteristic
790	C₂×#88322	C₂⁴	1	1	yes	characteristic
791	C₂×#88322	C₂⁴	1	1	yes	characteristic
792	C₂×#88322	C₂⁴	1	1	yes	characteristic
793	D₄₂₄	—	2	2	no	—
794	D₄₂₄	—	2	2	no	—
795	D₄₂₄	—	2	2	no	—
796	D₄₂₄	—	2	2	no	—
797	D₄₂₄	—	4	1	no	—
798	D₄₂₄	C₂×D₄	1	4	yes	complemented
799	#11719913	—	2	2	no	—
800	#11719913	—	2	2	no	—
801	#11719913	—	4	1	no	—
802	#11719912	—	2	2	no	—
803	#11719912	—	2	2	no	—
804	#11719912	—	2	2	no	—
805	C₈×D₅₃	—	2	2	no	—
806	C₈×D₅₃	—	2	2	no	—
807	C₈×D₅₃	—	2	2	no	—
808	C₈×D₅₃	—	2	2	no	—
809	C₈×D₅₃	C₂×D₄	1	4	yes	complemented
810	C₂³×C₅₃	—	2	1	no	—
811	C₂³×C₅₃	—	2	1	no	—
812	C₂³×C₅₃	—	2	1	no	—
813	C₂³×C₅₃	—	2	1	no	—
814	C₂³×C₅₃	—	2	1	no	—
815	C₂³×C₅₃	—	4	2	no	—
816	C₂³×C₅₃	—	4	2	no	—
817	C₂³×C₅₃	—	4	2	no	—
818	C₂³×C₅₃	—	4	2	no	—
819	C₂³×C₅₃	—	4	2	no	—
820	C₂³×C₅₃	—	8	1	no	—
821	C₂³×C₅₃	—	8	1	no	—
822	C₂³×C₅₃	—	8	1	no	—
823	C₂³×C₅₃	—	8	1	no	—
824	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
825	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
826	C₂²×D₅₃	—	2	2	no	—
827	C₂²×D₅₃	—	2	2	no	—
828	C₂²×D₅₃	—	2	2	no	—
829	C₂²×D₅₃	—	2	1	no	—
830	C₂²×D₅₃	—	2	1	no	—
831	C₂²×D₅₃	—	2	4	no	—
832	C₂²×D₅₃	—	2	4	no	—
833	C₂²×D₅₃	—	2	1	no	—
834	C₂²×D₅₃	—	2	1	no	—
835	C₂²×D₅₃	—	2	1	no	—
836	C₂²×D₅₃	—	4	2	no	—
837	C₂²×D₅₃	—	4	2	no	—
838	C₂²×D₅₃	—	4	2	no	—
839	C₂²×D₅₃	—	4	2	no	—
840	C₂²×D₅₃	—	4	2	no	—
841	C₂²×D₅₃	—	4	2	no	—
842	C₂²×D₅₃	—	4	2	no	—
843	C₂²×D₅₃	—	4	2	no	—
844	C₂²×D₅₃	—	4	2	no	—
845	C₂²×D₅₃	—	4	2	no	—
846	C₂²×D₅₃	—	4	2	no	—
847	C₂²×D₅₃	—	4	2	no	—
848	C₂²×D₅₃	—	4	2	no	—
849	C₂²×D₅₃	—	4	2	no	—
850	C₂²×D₅₃	—	4	2	no	—
851	C₂²×D₅₃	—	4	2	no	—
852	C₂²×D₅₃	—	4	2	no	—
853	C₂²×D₅₃	—	8	1	no	—
854	C₂²×D₅₃	—	8	1	no	—
855	C₂²×D₅₃	—	8	1	no	—
856	C₂²×D₅₃	—	8	1	no	—
857	C₂²×D₅₃	—	8	1	no	—
858	C₂²×D₅₃	—	8	1	no	—
859	C₂²×D₅₃	—	8	1	no	—
860	C₂²×D₅₃	—	8	1	no	—
861	C₂²×D₅₃	—	8	1	no	—
862	C₂²×D₅₃	—	8	1	no	—
863	C₂²×D₅₃	—	8	1	no	—
864	C₂²×D₅₃	—	8	1	no	—
865	C₂²×D₅₃	—	8	1	no	—
866	C₂²×D₅₃	—	8	1	no	—
867	C₂²×D₅₃	—	8	1	no	—
868	C₂²×D₅₃	—	8	1	no	—
869	C₂²×D₅₃	—	8	16	no	—
870	C₂²×D₅₃	—	8	16	no	—
871	C₂²×D₅₃	—	8	1	no	—
872	C₂²×D₅₃	—	8	1	no	—
873	C₂²×D₅₃	—	8	1	no	—
874	C₂²×D₅₃	—	8	1	no	—
875	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
876	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
877	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
878	Q₈×C₅₃	—	2	1	no	—
879	Q₈×C₅₃	—	2	1	no	—
880	D₄×C₅₃	—	2	2	no	—
881	D₄×C₅₃	—	2	1	no	—
882	D₄×C₅₃	—	2	1	no	—
883	D₄×C₅₃	—	2	1	no	—
884	D₄×C₅₃	—	2	1	no	—
885	D₄×C₅₃	—	2	1	no	—
886	D₄×C₅₃	—	2	1	no	—
887	D₄×C₅₃	—	2	1	no	—
888	D₄×C₅₃	—	2	1	no	—
889	D₄×C₅₃	—	4	2	no	—
890	D₄×C₅₃	—	4	2	no	—
891	D₄×C₅₃	—	4	2	no	—
892	D₄×C₅₃	—	4	2	no	—
893	D₄×C₅₃	—	4	2	no	—
894	D₄×C₅₃	—	8	1	no	—
895	D₄×C₅₃	—	8	1	no	—
896	D₄×C₅₃	—	8	1	no	—
897	D₄×C₅₃	—	8	1	no	—
898	D₄×C₅₃	C₂²×D₄	1	2	yes	—
899	D₄×C₅₃	C₂²×D₄	1	2	yes	—
900	C₂×C₄×C₅₃	—	2	1	no	—
901	C₂×C₄×C₅₃	—	2	1	no	—
902	C₂×C₄×C₅₃	—	2	1	no	—
903	C₂×C₄×C₅₃	—	2	1	no	—
904	C₂×C₄×C₅₃	—	2	1	no	—
905	C₂×C₄×C₅₃	—	2	1	no	—
906	C₂×C₄×C₅₃	—	2	1	no	—
907	C₂×C₄×C₅₃	—	4	2	no	—
908	C₂×C₄×C₅₃	—	8	1	no	—
909	C₂×C₄×C₅₃	—	8	1	no	—
910	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
911	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
912	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
913	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
914	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
915	C₂²⋊D₅₃	—	2	2	no	—
916	C₂²⋊D₅₃	—	2	2	no	—
917	C₂²⋊D₅₃	—	2	2	no	—
918	C₂²⋊D₅₃	—	2	2	no	—
919	C₂²⋊D₅₃	—	2	4	no	—
920	C₂²⋊D₅₃	—	2	4	no	—
921	C₂²⋊D₅₃	—	4	2	no	—
922	C₂²⋊D₅₃	—	4	2	no	—
923	C₂²⋊D₅₃	—	4	2	no	—
924	C₂²⋊D₅₃	—	4	2	no	—
925	C₂²⋊D₅₃	—	4	2	no	—
926	C₂²⋊D₅₃	—	4	2	no	—
927	C₂²⋊D₅₃	—	4	2	no	—
928	C₂²⋊D₅₃	—	4	2	no	—
929	C₂²⋊D₅₃	—	4	2	no	—
930	C₂²⋊D₅₃	—	4	2	no	—
931	C₂²⋊D₅₃	—	4	2	no	—
932	C₂²⋊D₅₃	—	4	2	no	—
933	C₂²⋊D₅₃	—	4	2	no	—
934	C₂²⋊D₅₃	—	8	1	no	—
935	C₂²⋊D₅₃	—	8	1	no	—
936	C₂²⋊D₅₃	—	8	1	no	—
937	C₂²⋊D₅₃	—	8	1	no	—
938	C₂²⋊D₅₃	—	8	1	no	—
939	C₂²⋊D₅₃	—	8	1	no	—
940	C₂²⋊D₅₃	—	8	1	no	—
941	C₂²⋊D₅₃	—	8	1	no	—
942	C₂×Dic₅₃	—	2	2	no	—
943	C₂×Dic₅₃	—	2	1	no	—
944	C₂×Dic₅₃	—	2	1	no	—
945	C₂×Dic₅₃	—	2	1	no	—
946	C₂×Dic₅₃	—	4	2	no	—
947	C₂×Dic₅₃	—	4	2	no	—
948	C₂×Dic₅₃	—	8	1	no	—
949	C₂×Dic₅₃	—	8	1	no	—
950	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
951	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
952	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
953	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
954	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
955	D₂₁₂	—	2	2	no	—
956	D₂₁₂	—	2	2	no	—
957	D₂₁₂	—	2	1	no	—
958	D₂₁₂	—	2	1	no	—
959	D₂₁₂	—	2	1	no	—
960	D₂₁₂	—	2	1	no	—
961	D₂₁₂	—	2	1	no	—
962	D₂₁₂	—	2	1	no	—
963	D₂₁₂	—	2	1	no	—
964	D₂₁₂	—	2	1	no	—
965	D₂₁₂	—	4	2	no	—
966	D₂₁₂	—	4	2	no	—
967	D₂₁₂	—	4	2	no	—
968	D₂₁₂	—	4	2	no	—
969	D₂₁₂	—	4	2	no	—
970	D₂₁₂	—	4	2	no	—
971	D₂₁₂	—	8	1	no	—
972	D₂₁₂	—	8	1	no	—
973	D₂₁₂	—	8	1	no	—
974	D₂₁₂	—	8	1	no	—
975	D₂₁₂	C₂²×D₄	1	2	yes	—
976	D₂₁₂	C₂²×D₄	1	2	yes	—
977	C₄×D₅₃	—	2	2	no	—
978	C₄×D₅₃	—	2	1	no	—
979	C₄×D₅₃	—	2	1	no	—
980	C₄×D₅₃	—	2	1	no	—
981	C₄×D₅₃	—	2	1	no	—
982	C₄×D₅₃	—	2	2	no	—
983	C₄×D₅₃	—	4	2	no	—
984	C₄×D₅₃	—	4	2	no	—
985	C₄×D₅₃	—	4	2	no	—
986	C₄×D₅₃	—	8	1	no	—
987	C₄×D₅₃	—	8	1	no	—
988	C₄×D₅₃	—	8	1	no	—
989	C₄×D₅₃	—	8	1	no	—
990	C₄×D₅₃	C₂²×D₄	1	2	yes	—
991	C₄×D₅₃	H(5,𝔽₂)	1	2	yes	—
992	Dic₁₀₆	—	2	2	no	—
993	Dic₁₀₆	—	2	1	no	—
994	Dic₁₀₆	—	2	1	no	—
995	C₈×C₅₃	—	2	1	no	—
996	C₈×C₅₃	—	2	1	no	—
997	C₈×C₅₃	—	2	1	no	—
998	C₈×C₅₃	C₂²×D₄	1	2	yes	—
999	#88322	—	2	1	no	—
1000	#88322	—	2	1	no	—
1001	#88322	—	2	1	no	—
1002	#88322	C₂²×D₄	1	2	yes	—
1003	#61049	—	53	1	no	maximal, Sylow
1004	C₂²×C₅₃	—	2	1	no	—
1005	C₂²×C₅₃	—	2	1	no	—
1006	C₂²×C₅₃	—	2	2	no	—
1007	C₂²×C₅₃	—	2	1	no	—
1008	C₂²×C₅₃	—	2	2	no	—
1009	C₂²×C₅₃	—	2	1	no	—
1010	C₂²×C₅₃	—	2	1	no	—
1011	C₂²×C₅₃	—	4	1	no	—
1012	C₂²×C₅₃	—	4	1	no	—
1013	C₂²×C₅₃	—	4	1	no	—
1014	C₂²×C₅₃	—	4	1	no	—
1015	C₂²×C₅₃	—	4	1	no	—
1016	C₂²×C₅₃	—	4	1	no	—
1017	C₂²×C₅₃	—	4	1	no	—
1018	C₂²×C₅₃	—	4	1	no	—
1019	C₂²×C₅₃	—	4	1	no	—
1020	C₂²×C₅₃	—	4	1	no	—
1021	C₂²×C₅₃	—	4	1	no	—
1022	C₂²×C₅₃	—	4	1	no	—
1023	C₂²×C₅₃	—	4	1	no	—
1024	C₂²×C₅₃	—	8	4	no	—
1025	C₂²×C₅₃	—	8	4	no	—
1026	C₂²×C₅₃	—	16	2	no	—
1027	C₂²×C₅₃	#576	1	2	yes	complemented
1028	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
1029	C₂×D₅₃	—	2	8	no	—
1030	C₂×D₅₃	—	2	1	no	—
1031	C₂×D₅₃	—	2	1	no	—
1032	C₂×D₅₃	—	2	1	no	—
1033	C₂×D₅₃	—	2	1	no	—
1034	C₂×D₅₃	—	2	1	no	—
1035	C₂×D₅₃	—	2	2	no	—
1036	C₂×D₅₃	—	2	2	no	—
1037	C₂×D₅₃	—	2	1	no	—
1038	C₂×D₅₃	—	2	1	no	—
1039	C₂×D₅₃	—	4	1	no	—
1040	C₂×D₅₃	—	4	1	no	—
1041	C₂×D₅₃	—	4	1	no	—
1042	C₂×D₅₃	—	4	1	no	—
1043	C₂×D₅₃	—	4	1	no	—
1044	C₂×D₅₃	—	4	1	no	—
1045	C₂×D₅₃	—	4	1	no	—
1046	C₂×D₅₃	—	4	1	no	—
1047	C₂×D₅₃	—	4	1	no	—
1048	C₂×D₅₃	—	4	1	no	—
1049	C₂×D₅₃	—	4	1	no	—
1050	C₂×D₅₃	—	4	1	no	—
1051	C₂×D₅₃	—	4	1	no	—
1052	C₂×D₅₃	—	8	4	no	—
1053	C₂×D₅₃	—	8	4	no	—
1054	C₂×D₅₃	—	8	4	no	—
1055	C₂×D₅₃	—	8	4	no	—
1056	C₂×D₅₃	—	8	4	no	—
1057	C₂×D₅₃	—	8	4	no	—
1058	C₂×D₅₃	—	8	4	no	—
1059	C₂×D₅₃	—	8	4	no	—
1060	C₂×D₅₃	—	8	4	no	—
1061	C₂×D₅₃	—	8	4	no	—
1062	C₂×D₅₃	—	16	2	no	—
1063	C₂×D₅₃	—	16	2	no	—
1064	C₂×D₅₃	—	16	2	no	—
1065	C₂×D₅₃	D₄²	1	2	yes	—
1066	C₂×D₅₃	#576	1	2	yes	complemented
1067	C₄×C₅₃	—	2	1	no	—
1068	C₄×C₅₃	—	2	1	no	—
1069	C₄×C₅₃	—	2	1	no	—
1070	C₄×C₅₃	—	2	1	no	—
1071	C₄×C₅₃	—	4	1	no	—
1072	C₄×C₅₃	—	4	1	no	—
1073	C₄×C₅₃	—	4	1	no	—
1074	C₄×C₅₃	C₂³×D₄	1	1	yes	characteristic
1075	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
1076	Dic₅₃	—	2	1	no	—
1077	Dic₅₃	—	2	1	no	—
1078	Dic₅₃	—	2	1	no	—
1079	Dic₅₃	—	2	1	no	—
1080	Dic₅₃	—	4	1	no	—
1081	Dic₅₃	—	4	1	no	—
1082	Dic₅₃	—	4	1	no	—
1083	Dic₅₃	D₄²	1	2	yes	—
1084	C₂×#576	—	53	1	no	—
1085	C₂³×D₈	—	53	1	no	—
1086	#3484	—	53	1	no	—
1087	#3484	—	53	1	no	—
1088	#3280	—	53	1	no	—
1089	#3280	—	53	1	no	—
1090	#3280	—	53	1	no	—
1091	#3280	—	53	1	no	—
1092	D₄×D₈	—	53	1	no	—
1093	D₄×D₈	—	53	1	no	—
1094	D₄×D₈	—	53	1	no	—
1095	D₄×D₈	—	53	1	no	—
1096	#3264	—	53	1	no	—
1097	#3264	—	53	1	no	—
1098	#3264	—	53	1	no	—
1099	#3264	—	53	1	no	—
1100	#3264	—	53	1	no	—
1101	#3264	—	53	1	no	—
1102	#3264	—	53	1	no	—
1103	#3264	D₅₃	1	1	yes	characteristic, complemented
1104	#3155	—	53	1	no	—
1105	#3058	—	53	1	no	—
1106	#3050	—	53	1	no	—
1107	#3041	—	53	1	no	—
1108	#3041	—	53	1	no	—
1109	#3008	—	53	1	no	—
1110	#3008	—	53	1	no	—
1111	#3003	—	53	1	no	—
1112	#3003	—	53	1	no	—
1113	#2948	—	53	1	no	—
1114	#2929	—	53	1	no	—
1115	C₂×C₅₃	—	2	2	no	—
1116	C₂×C₅₃	—	4	2	no	—
1117	C₂×C₅₃	—	4	2	no	—
1118	C₂×C₅₃	—	4	1	no	—
1119	C₂×C₅₃	—	8	1	no	—
1120	C₂×C₅₃	—	8	1	no	—
1121	C₂×C₅₃	—	8	1	no	—
1122	C₂×C₅₃	C₂×D₄²	1	1	yes	characteristic
1123	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
1124	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
1125	D₅₃	—	2	2	no	—
1126	D₅₃	—	2	2	no	—
1127	D₅₃	—	4	1	no	—
1128	D₅₃	—	4	2	no	—
1129	D₅₃	—	4	2	no	—
1130	D₅₃	—	8	1	no	—
1131	D₅₃	—	8	1	no	—
1132	D₅₃	—	8	1	no	—
1133	C₂×H(5,𝔽₂)	—	53	1	no	—
1134	C₂×H(5,𝔽₂)	—	53	1	no	—
1135	C₂³×D₄	—	53	1	no	—
1136	C₂³×D₄	—	53	1	no	—
1137	#576	—	106	8	no	—
1138	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1139	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1140	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1141	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1142	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1143	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1144	C₂×AGL(1,ℤ/8)	—	53	1	no	—
1145	C₂×AGL(1,ℤ/8)	C₂×D₅₃	1	1	yes	characteristic, complemented
1146	C₂×#135	—	53	1	no	—
1147	C₂×#135	—	53	1	no	—
1148	C₂×#135	—	53	1	no	—
1149	C₂²×D₈	—	53	1	no	—
1150	C₂²×D₈	—	53	1	no	—
1151	C₂²×D₈	—	53	1	no	—
1152	C₂²×D₈	—	53	1	no	—
1153	C₂²×D₈	—	53	1	no	—
1154	C₂²×D₈	—	53	1	no	—
1155	C₂²×D₈	—	53	1	no	—
1156	C₂²×D₈	—	53	1	no	—
1157	C₂²×D₈	—	53	1	no	—
1158	C₂²×D₈	—	53	1	no	—
1159	C₂²×D₈	—	53	1	no	—
1160	C₂²×D₈	—	53	1	no	—
1161	C₂²×D₈	—	53	1	no	—
1162	C₂²×D₈	—	106	8	no	—
1163	C₂²×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
1164	C₂×#131	—	53	1	no	—
1165	C₂³×C₈	—	53	1	no	—
1166	#546	—	53	1	no	—
1167	#546	—	53	1	no	—
1168	#546	—	53	1	no	—
1169	#546	—	53	1	no	—
1170	#546	—	53	1	no	—
1171	#546	—	53	1	no	—
1172	#546	—	53	1	no	—
1173	#546	—	106	1	no	—
1174	#546	—	106	1	no	—
1175	#546	—	106	1	no	—
1176	#546	—	106	1	no	—
1177	#546	C₂×D₅₃	1	1	yes	characteristic, complemented
1178	D₄²	—	53	1	no	—
1179	D₄²	—	53	1	no	—
1180	D₄²	—	53	1	no	—
1181	D₄²	—	53	1	no	—
1182	D₄²	—	53	1	no	—
1183	D₄²	—	53	1	no	—
1184	D₄²	—	53	1	no	—
1185	D₄²	—	106	1	no	—
1186	D₄²	—	106	1	no	—
1187	D₄²	—	106	1	no	—
1188	D₄²	—	106	1	no	—
1189	D₄²	C₂×D₅₃	1	1	yes	characteristic, complemented
1190	#535	—	53	1	no	—
1191	#535	—	53	1	no	—
1192	#535	—	53	1	no	—
1193	#535	—	53	1	no	—
1194	#534	—	106	1	no	—
1195	#534	—	106	1	no	—
1196	#534	—	106	1	no	—
1197	#534	—	106	1	no	—
1198	#525	—	53	1	no	—
1199	#525	—	53	1	no	—
1200	#525	—	53	1	no	—
1201	C₂×#120	—	106	1	no	—
1202	C₂×#120	—	106	1	no	—
1203	C₂×#120	—	106	1	no	—
1204	C₂×#120	—	106	1	no	—
1205	#518	—	53	1	no	—
1206	#518	—	53	1	no	—
1207	#496	—	53	1	no	—
1208	#496	—	53	1	no	—
1209	#496	—	53	1	no	—
1210	#496	C₂×D₅₃	1	1	yes	characteristic, complemented
1211	#495	—	53	1	no	—
1212	#495	—	53	1	no	—
1213	#493	—	53	1	no	—
1214	#493	—	53	1	no	—
1215	#469	—	53	1	no	—
1216	#469	—	53	1	no	—
1217	#469	—	53	1	no	—
1218	#469	C₂×D₅₃	1	1	yes	characteristic, complemented
1219	#467	—	53	1	no	—
1220	#467	—	53	1	no	—
1221	#466	—	53	1	no	—
1222	#466	—	53	1	no	—
1223	#466	—	53	1	no	—
1224	#466	—	53	1	no	—
1225	#466	—	53	1	no	—
1226	#466	—	53	1	no	—
1227	#465	—	53	1	no	—
1228	#465	—	53	1	no	—
1229	#465	—	53	1	no	—
1230	#465	C₂×D₅₃	1	1	yes	characteristic, complemented
1231	#463	—	53	1	no	—
1232	#463	—	53	1	no	—
1233	#463	—	53	1	no	—
1234	#463	—	53	1	no	—
1235	#463	—	53	1	no	—
1236	#463	—	53	1	no	—
1237	#463	—	53	1	no	—
1238	#463	C₂×D₅₃	1	1	yes	characteristic, complemented
1239	#459	—	53	1	no	—
1240	#459	—	53	1	no	—
1241	#459	—	53	1	no	—
1242	#459	—	53	1	no	—
1243	#459	—	53	1	no	—
1244	#459	—	53	1	no	—
1245	#459	—	53	1	no	—
1246	#459	C₂×D₅₃	1	1	yes	characteristic, complemented
1247	#450	—	53	1	no	—
1248	#450	—	53	1	no	—
1249	#450	—	53	1	no	—
1250	#450	—	53	1	no	—
1251	#450	—	53	1	no	—
1252	#450	—	53	1	no	—
1253	#450	—	53	1	no	—
1254	#450	C₂×D₅₃	1	1	yes	characteristic, complemented
1255	#449	—	53	1	no	—
1256	#449	—	53	1	no	—
1257	#449	—	53	1	no	—
1258	#449	—	53	1	no	—
1259	#449	—	53	1	no	—
1260	#449	—	53	1	no	—
1261	#449	—	53	1	no	—
1262	#449	C₂×D₅₃	1	1	yes	characteristic, complemented
1263	#447	—	53	1	no	—
1264	#447	—	53	1	no	—
1265	#447	—	53	1	no	—
1266	#447	—	53	1	no	—
1267	#447	—	53	1	no	—
1268	#447	—	53	1	no	—
1269	#447	—	53	1	no	—
1270	#447	—	53	1	no	—
1271	#447	—	53	1	no	—
1272	#447	—	53	1	no	—
1273	#447	—	53	1	no	—
1274	#447	—	53	1	no	—
1275	#447	—	53	1	no	—
1276	#447	—	53	1	no	—
1277	#447	C₂×D₅₃	1	1	yes	characteristic, complemented
1278	#447	C₂×D₅₃	1	1	yes	characteristic, complemented
1279	#442	—	53	1	no	—
1280	#442	—	53	1	no	—
1281	#442	—	53	1	no	—
1282	#442	C₂×D₅₃	1	1	yes	characteristic, complemented
1283	C₄×D₈	—	53	1	no	—
1284	C₄×D₈	—	53	1	no	—
1285	C₄×D₈	—	53	1	no	—
1286	C₄×D₈	—	53	1	no	—
1287	#435	—	53	1	no	—
1288	#435	—	53	1	no	—
1289	#435	—	53	1	no	—
1290	#435	C₂×D₅₃	1	1	yes	characteristic, complemented
1291	C₈×D₄	—	53	1	no	—
1292	C₈×D₄	—	53	1	no	—
1293	C₈×D₄	—	53	1	no	—
1294	C₈×D₄	—	53	1	no	—
1295	#427	—	53	1	no	—
1296	#424	—	53	1	no	—
1297	#418	—	53	1	no	—
1298	#418	—	53	1	no	—
1299	#418	—	53	1	no	—
1300	#418	—	53	1	no	—
1301	#416	—	53	1	no	—
1302	#416	—	53	1	no	—
1303	#408	—	53	1	no	—
1304	#407	—	53	1	no	—
1305	#405	—	53	1	no	—
1306	C₅₃	#61049	1	1	yes	characteristic, complemented, Sylow
1307	C₂⁵	—	106	1	no	—
1308	C₂⁵	—	106	1	no	—
1309	H(5,𝔽₂)	—	106	4	no	—
1310	H(5,𝔽₂)	—	106	4	no	—
1311	H(5,𝔽₂)	—	212	2	no	—
1312	H(5,𝔽₂)	—	212	2	no	—
1313	C₂×#41	—	53	1	no	—
1314	C₂×#41	—	53	1	no	—
1315	C₂×#41	—	53	1	no	—
1316	C₂×#41	—	53	1	no	—
1317	C₂×#41	—	53	1	no	—
1318	C₂×#41	—	53	1	no	—
1319	C₂×#41	—	106	1	no	—
1320	C₂×#41	—	106	1	no	—
1321	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic, complemented
1322	C₂²×D₄	—	2	1	no	—
1323	C₂²×D₄	—	53	1	no	—
1324	C₂²×D₄	—	53	1	no	—
1325	C₂²×D₄	—	53	1	no	—
1326	C₂²×D₄	—	53	1	no	—
1327	C₂²×D₄	—	53	1	no	—
1328	C₂²×D₄	—	53	1	no	—
1329	C₂²×D₄	—	53	1	no	—
1330	C₂²×D₄	—	53	1	no	—
1331	C₂²×D₄	—	53	1	no	—
1332	C₂²×D₄	—	53	1	no	—
1333	C₂²×D₄	—	53	1	no	—
1334	C₂²×D₄	—	53	1	no	—
1335	C₂²×D₄	—	53	1	no	—
1336	C₂²×D₄	—	106	1	no	—
1337	C₂²×D₄	—	106	1	no	—
1338	C₂²×D₄	—	106	1	no	—
1339	C₂²×D₄	—	106	1	no	—
1340	C₂²×D₄	—	106	1	no	—
1341	C₂²×D₄	—	106	1	no	—
1342	C₂²×D₄	—	106	1	no	—
1343	C₂²×D₄	—	106	1	no	—
1344	C₂²×D₄	—	106	4	no	—
1345	C₂²×D₄	—	106	4	no	—
1346	C₂²×D₄	—	106	1	no	—
1347	C₂²×D₄	—	106	1	no	—
1348	C₂²×D₄	—	106	1	no	—
1349	C₂²×D₄	—	106	1	no	—
1350	C₂²×D₄	—	106	1	no	—
1351	C₂²×D₄	—	106	1	no	—
1352	C₂²×D₄	—	106	1	no	—
1353	C₂²×D₄	—	106	1	no	—
1354	C₂²×D₄	—	106	1	no	—
1355	C₂²×D₄	—	106	1	no	—
1356	C₂²×D₄	—	106	1	no	—
1357	C₂²×D₄	—	212	2	no	—
1358	C₂²×D₄	—	212	2	no	—
1359	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1360	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
1361	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1362	C₂³×C₄	—	53	1	no	—
1363	AGL(1,ℤ/8)	—	2	4	no	—
1364	AGL(1,ℤ/8)	—	106	4	no	—
1365	AGL(1,ℤ/8)	—	106	4	no	—
1366	AGL(1,ℤ/8)	—	106	4	no	—
1367	AGL(1,ℤ/8)	—	106	4	no	—
1368	AGL(1,ℤ/8)	—	106	4	no	—
1369	AGL(1,ℤ/8)	—	212	2	no	—
1370	AGL(1,ℤ/8)	—	212	2	no	—
1371	#135	—	106	4	no	—
1372	#135	—	106	4	no	—
1373	#135	—	106	4	no	—
1374	C₂×Q₁₆	—	53	1	no	—
1375	C₂×SD₁₆	—	53	1	no	—
1376	C₂×SD₁₆	—	53	1	no	—
1377	C₂×SD₁₆	—	53	1	no	—
1378	C₂×SD₁₆	—	53	1	no	—
1379	C₂×SD₁₆	—	53	1	no	—
1380	C₂×SD₁₆	—	53	1	no	—
1381	C₂×SD₁₆	—	53	1	no	—
1382	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1383	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1384	C₂×SD₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1385	C₂×D₈	—	2	4	no	—
1386	C₂×D₈	—	53	1	no	—
1387	C₂×D₈	—	53	1	no	—
1388	C₂×D₈	—	53	8	no	—
1389	C₂×D₈	—	53	1	no	—
1390	C₂×D₈	—	53	1	no	—
1391	C₂×D₈	—	53	1	no	—
1392	C₂×D₈	—	53	1	no	—
1393	C₂×D₈	—	53	1	no	—
1394	C₂×D₈	—	53	1	no	—
1395	C₂×D₈	—	53	1	no	—
1396	C₂×D₈	—	53	1	no	—
1397	C₂×D₈	—	53	1	no	—
1398	C₂×D₈	—	53	1	no	—
1399	C₂×D₈	—	53	1	no	—
1400	C₂×D₈	—	53	1	no	—
1401	C₂×D₈	—	53	1	no	—
1402	C₂×D₈	—	53	1	no	—
1403	C₂×D₈	—	53	1	no	—
1404	C₂×D₈	—	53	1	no	—
1405	C₂×D₈	—	53	1	no	—
1406	C₂×D₈	—	106	4	no	—
1407	C₂×D₈	—	106	4	no	—
1408	C₂×D₈	—	106	4	no	—
1409	C₂×D₈	—	106	4	no	—
1410	C₂×D₈	—	106	4	no	—
1411	C₂×D₈	—	106	4	no	—
1412	C₂×D₈	—	106	4	no	—
1413	C₂×D₈	—	106	4	no	—
1414	C₂×D₈	—	106	4	no	—
1415	C₂×D₈	—	106	4	no	—
1416	C₂×D₈	—	106	4	no	—
1417	C₂×D₈	—	106	4	no	—
1418	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1419	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1420	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1421	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic
1422	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1423	C₂×D₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1424	#131	—	106	4	no	—
1425	C₂×M₁₆	—	53	1	no	—
1426	C₂×M₁₆	—	53	1	no	—
1427	C₂×M₁₆	—	53	1	no	—
1428	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
1429	C₂²×C₈	—	53	1	no	—
1430	C₂²×C₈	—	53	1	no	—
1431	C₂²×C₈	—	53	1	no	—
1432	C₂²×C₈	—	53	1	no	—
1433	C₂²×C₈	—	53	1	no	—
1434	C₂²×C₈	—	53	1	no	—
1435	C₂²×C₈	—	53	1	no	—
1436	C₂²×C₈	—	106	4	no	—
1437	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
1438	#127	—	53	1	no	—
1439	#127	—	53	1	no	—
1440	#127	—	53	1	no	—
1441	#127	—	106	1	no	—
1442	#127	—	106	1	no	—
1443	#127	C₂²×D₅₃	1	1	yes	characteristic, complemented
1444	#124	—	53	1	no	—
1445	#124	—	53	1	no	—
1446	#124	—	53	1	no	—
1447	#124	—	106	1	no	—
1448	#124	—	106	1	no	—
1449	#124	C₂²×D₅₃	1	1	yes	characteristic, complemented
1450	#123	—	2	1	no	—
1451	#123	—	53	1	no	—
1452	#123	—	53	1	no	—
1453	#123	—	106	1	no	—
1454	#123	—	106	1	no	—
1455	#123	—	106	1	no	—
1456	#123	—	106	1	no	—
1457	#123	—	106	1	no	—
1458	#123	—	106	1	no	—
1459	#123	—	106	1	no	—
1460	#123	—	106	1	no	—
1461	#123	—	106	1	no	—
1462	C₂²⋊Q₈	—	53	1	no	—
1463	C₂²⋊Q₈	—	53	1	no	—
1464	C₂²⋊Q₈	—	53	1	no	—
1465	C₂²⋊Q₈	—	53	1	no	—
1466	C₂²⋊Q₈	—	53	1	no	—
1467	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
1468	#121	—	2	1	no	—
1469	#121	—	2	1	no	—
1470	#121	—	53	1	no	—
1471	#121	—	53	1	no	—
1472	#121	—	53	1	no	—
1473	#121	—	53	1	no	—
1474	#121	—	53	1	no	—
1475	#121	—	53	1	no	—
1476	#121	—	53	1	no	—
1477	#121	—	53	1	no	—
1478	#121	—	53	1	no	—
1479	#121	—	53	1	no	—
1480	#121	—	53	1	no	—
1481	#121	—	106	1	no	—
1482	#121	—	106	1	no	—
1483	#121	—	106	1	no	—
1484	#121	—	106	1	no	—
1485	#121	—	106	1	no	—
1486	#121	—	106	1	no	—
1487	#121	—	106	1	no	—
1488	#121	—	106	1	no	—
1489	#121	—	106	1	no	—
1490	#121	—	106	1	no	—
1491	#121	—	106	1	no	—
1492	#121	—	106	1	no	—
1493	#121	—	106	1	no	—
1494	#121	—	106	1	no	—
1495	#121	—	106	1	no	—
1496	#121	—	106	1	no	—
1497	#121	—	106	1	no	—
1498	#121	—	106	1	no	—
1499	#121	C₂²×D₅₃	1	1	yes	characteristic
1500	#121	C₂²×D₅₃	1	1	yes	characteristic, complemented
1501	#121	C₂²×D₅₃	1	1	yes	characteristic, complemented
1502	#120	—	2	1	no	—
1503	#120	—	2	1	no	—
1504	#120	—	2	1	no	—
1505	#120	—	53	1	no	—
1506	#120	—	53	1	no	—
1507	#120	—	106	1	no	—
1508	#120	—	106	1	no	—
1509	#120	—	106	1	no	—
1510	#120	—	106	1	no	—
1511	#120	—	106	1	no	—
1512	#120	—	106	1	no	—
1513	#120	—	106	1	no	—
1514	#120	—	106	1	no	—
1515	#120	—	106	1	no	—
1516	#120	—	106	1	no	—
1517	#120	—	106	1	no	—
1518	#120	—	106	1	no	—
1519	#120	—	106	1	no	—
1520	#120	—	106	1	no	—
1521	#120	—	106	1	no	—
1522	#120	—	106	1	no	—
1523	#120	—	106	1	no	—
1524	#120	—	106	1	no	—
1525	#120	—	106	1	no	—
1526	#120	—	106	1	no	—
1527	#120	—	106	1	no	—
1528	#120	—	106	1	no	—
1529	#120	—	106	1	no	—
1530	#120	—	106	1	no	—
1531	#120	—	106	1	no	—
1532	#120	—	106	1	no	—
1533	#120	—	106	1	no	—
1534	#120	—	106	1	no	—
1535	#120	—	106	1	no	—
1536	#120	—	106	1	no	—
1537	#120	—	106	1	no	—
1538	C₄×D₄	—	53	1	no	—
1539	C₄×D₄	—	53	1	no	—
1540	C₄×D₄	—	53	1	no	—
1541	C₄×D₄	—	53	1	no	—
1542	C₄×D₄	—	53	1	no	—
1543	C₄×D₄	—	53	1	no	—
1544	C₄×D₄	—	53	1	no	—
1545	C₄×D₄	—	53	1	no	—
1546	C₄×D₄	—	53	1	no	—
1547	C₄×D₄	—	106	1	no	—
1548	C₄×D₄	—	106	1	no	—
1549	C₄×D₄	—	106	1	no	—
1550	C₄×D₄	—	106	1	no	—
1551	C₄×D₄	—	106	1	no	—
1552	C₄×D₄	—	106	1	no	—
1553	C₄×D₄	—	106	1	no	—
1554	C₄×D₄	—	106	1	no	—
1555	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
1556	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1557	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1558	#117	—	53	1	no	—
1559	#117	—	53	1	no	—
1560	#117	—	53	1	no	—
1561	C₂×C₂²⋊C₄	—	2	1	no	—
1562	C₂×C₂²⋊C₄	—	106	1	no	—
1563	C₂×C₂²⋊C₄	—	106	1	no	—
1564	C₂×C₂²⋊C₄	—	106	1	no	—
1565	C₂×C₂²⋊C₄	—	106	1	no	—
1566	C₂×C₂²⋊C₄	—	106	1	no	—
1567	C₂×C₂²⋊C₄	—	106	1	no	—
1568	C₂×C₂²⋊C₄	—	106	1	no	—
1569	C₂×C₂²⋊C₄	—	106	1	no	—
1570	C₂×C₂²⋊C₄	—	106	1	no	—
1571	C₂×C₂²⋊C₄	—	106	1	no	—
1572	C₂×C₂²⋊C₄	—	106	1	no	—
1573	#107	—	53	1	no	—
1574	#107	—	53	1	no	—
1575	#106	—	53	1	no	—
1576	#106	C₂²×D₅₃	1	1	yes	characteristic, complemented
1577	C₄⋊C₈	—	53	1	no	—
1578	C₄⋊C₈	—	53	1	no	—
1579	C₄⋊C₈	—	53	1	no	—
1580	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1581	#103	—	53	1	no	—
1582	#103	—	53	1	no	—
1583	#103	—	53	1	no	—
1584	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
1585	#102	—	53	1	no	—
1586	#102	—	53	1	no	—
1587	#102	—	53	1	no	—
1588	#102	—	53	1	no	—
1589	#102	—	53	1	no	—
1590	#102	—	53	1	no	—
1591	#102	—	53	1	no	—
1592	#102	—	53	1	no	—
1593	#102	—	53	1	no	—
1594	#102	—	53	1	no	—
1595	#102	—	53	1	no	—
1596	#102	—	53	1	no	—
1597	#102	—	53	1	no	—
1598	#102	—	53	1	no	—
1599	#102	—	53	1	no	—
1600	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1601	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1602	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1603	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1604	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
1605	C₂²⋊C₈	—	53	1	no	—
1606	C₂²⋊C₈	—	53	1	no	—
1607	C₂²⋊C₈	—	53	1	no	—
1608	C₂²⋊C₈	—	53	1	no	—
1609	C₂²⋊C₈	—	53	1	no	—
1610	C₂²⋊C₈	—	53	1	no	—
1611	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
1612	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
1613	#97	—	53	1	no	—
1614	#97	C₂²×D₅₃	1	1	yes	characteristic, complemented
1615	C₄×C₈	—	53	1	no	—
1616	C₄×C₈	—	53	1	no	—
1617	C₂⁴	—	2	1	no	—
1618	C₂⁴	—	2	1	no	—
1619	C₂⁴	—	2	1	no	—
1620	C₂⁴	—	53	1	no	—
1621	C₂⁴	—	106	1	no	—
1622	C₂⁴	—	106	1	no	—
1623	C₂⁴	—	106	1	no	—
1624	C₂⁴	—	106	1	no	—
1625	C₂⁴	—	106	1	no	—
1626	C₂⁴	—	106	1	no	—
1627	C₂⁴	—	106	1	no	—
1628	C₂⁴	—	106	1	no	—
1629	C₂⁴	—	106	1	no	—
1630	C₂⁴	—	106	1	no	—
1631	C₂⁴	—	106	1	no	—
1632	C₂⁴	—	106	1	no	—
1633	C₂⁴	—	106	1	no	—
1634	C₂⁴	—	424	2	no	—
1635	C₂⁴	—	424	2	no	—
1636	C₂⁴	—	424	2	no	—
1637	C₂⁴	—	424	2	no	—
1638	C₂⁴	—	212	4	no	—
1639	C₂⁴	—	212	4	no	—
1640	#41	—	2	2	no	—
1641	#41	—	4	1	no	—
1642	#41	—	106	2	no	—
1643	#41	—	106	2	no	—
1644	#41	—	106	2	no	—
1645	#41	—	106	2	no	—
1646	#41	—	106	2	no	—
1647	#41	—	106	2	no	—
1648	#41	—	106	2	no	—
1649	#41	—	106	2	no	—
1650	#41	—	106	2	no	—
1651	#41	—	212	1	no	—
1652	#41	—	212	4	no	—
1653	#41	—	212	1	no	—
1654	#41	—	212	1	no	—
1655	#41	—	212	4	no	—
1656	C₂×Q₈	—	53	1	no	—
1657	C₂×Q₈	—	53	1	no	—
1658	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1659	C₂×D₄	—	2	2	no	—
1660	C₂×D₄	—	2	2	no	—
1661	C₂×D₄	—	2	2	no	—
1662	C₂×D₄	—	2	1	no	—
1663	C₂×D₄	—	2	1	no	—
1664	C₂×D₄	—	2	1	no	—
1665	C₂×D₄	—	2	1	no	—
1666	C₂×D₄	—	2	1	no	—
1667	C₂×D₄	—	2	1	no	—
1668	C₂×D₄	—	2	1	no	—
1669	C₂×D₄	—	2	1	no	—
1670	C₂×D₄	—	2	1	no	—
1671	C₂×D₄	—	4	1	no	—
1672	C₂×D₄	—	4	1	no	—
1673	C₂×D₄	—	4	1	no	—
1674	C₂×D₄	—	8	2	no	—
1675	C₂×D₄	—	53	4	no	—
1676	C₂×D₄	—	53	4	no	—
1677	C₂×D₄	—	53	1	no	—
1678	C₂×D₄	—	53	1	no	—
1679	C₂×D₄	—	53	1	no	—
1680	C₂×D₄	—	53	1	no	—
1681	C₂×D₄	—	53	1	no	—
1682	C₂×D₄	—	53	1	no	—
1683	C₂×D₄	—	53	1	no	—
1684	C₂×D₄	—	53	1	no	—
1685	C₂×D₄	—	53	1	no	—
1686	C₂×D₄	—	53	1	no	—
1687	C₂×D₄	—	53	1	no	—
1688	C₂×D₄	—	106	2	no	—
1689	C₂×D₄	—	106	2	no	—
1690	C₂×D₄	—	106	2	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	2	no	—
1697	C₂×D₄	—	106	2	no	—
1698	C₂×D₄	—	106	2	no	—
1699	C₂×D₄	—	106	2	no	—
1700	C₂×D₄	—	106	2	no	—
1701	C₂×D₄	—	106	2	no	—
1702	C₂×D₄	—	106	1	no	—
1703	C₂×D₄	—	106	1	no	—
1704	C₂×D₄	—	106	1	no	—
1705	C₂×D₄	—	106	1	no	—
1706	C₂×D₄	—	106	1	no	—
1707	C₂×D₄	—	106	1	no	—
1708	C₂×D₄	—	106	1	no	—
1709	C₂×D₄	—	106	1	no	—
1710	C₂×D₄	—	106	1	no	—
1711	C₂×D₄	—	106	1	no	—
1712	C₂×D₄	—	106	1	no	—
1713	C₂×D₄	—	106	1	no	—
1714	C₂×D₄	—	106	1	no	—
1715	C₂×D₄	—	106	1	no	—
1716	C₂×D₄	—	106	2	no	—
1717	C₂×D₄	—	106	2	no	—
1718	C₂×D₄	—	106	2	no	—
1719	C₂×D₄	—	106	2	no	—
1720	C₂×D₄	—	106	2	no	—
1721	C₂×D₄	—	106	2	no	—
1722	C₂×D₄	—	106	1	no	—
1723	C₂×D₄	—	106	1	no	—
1724	C₂×D₄	—	106	1	no	—
1725	C₂×D₄	—	106	1	no	—
1726	C₂×D₄	—	106	1	no	—
1727	C₂×D₄	—	106	1	no	—
1728	C₂×D₄	—	106	1	no	—
1729	C₂×D₄	—	106	1	no	—
1730	C₂×D₄	—	106	1	no	—
1731	C₂×D₄	—	106	1	no	—
1732	C₂×D₄	—	106	1	no	—
1733	C₂×D₄	—	106	1	no	—
1734	C₂×D₄	—	106	1	no	—
1735	C₂×D₄	—	106	1	no	—
1736	C₂×D₄	—	424	2	no	—
1737	C₂×D₄	—	424	2	no	—
1738	C₂×D₄	—	424	2	no	—
1739	C₂×D₄	—	424	2	no	—
1740	C₂×D₄	—	424	2	no	—
1741	C₂×D₄	—	424	2	no	—
1742	C₂×D₄	—	424	2	no	—
1743	C₂×D₄	—	212	1	no	—
1744	C₂×D₄	—	212	1	no	—
1745	C₂×D₄	—	212	1	no	—
1746	C₂×D₄	—	212	4	no	—
1747	C₂×D₄	—	212	1	no	—
1748	C₂×D₄	—	212	1	no	—
1749	C₂×D₄	—	212	1	no	—
1750	C₂×D₄	—	212	1	no	—
1751	C₂×D₄	—	212	1	no	—
1752	C₂×D₄	—	212	1	no	—
1753	C₂×D₄	—	212	4	no	—
1754	C₂×D₄	—	212	4	no	—
1755	C₂×D₄	—	212	4	no	—
1756	C₂×D₄	—	212	4	no	—
1757	C₂×D₄	—	212	4	no	—
1758	C₂×D₄	—	212	4	no	—
1759	C₂×D₄	—	212	4	no	—
1760	C₂×D₄	—	212	4	no	—
1761	C₂×D₄	—	212	4	no	—
1762	C₂×D₄	—	212	4	no	—
1763	C₂×D₄	—	212	4	no	—
1764	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
1765	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1766	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1767	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1768	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1769	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1770	C₂²×C₄	—	2	1	no	—
1771	C₂²×C₄	—	2	1	no	—
1772	C₂²×C₄	—	2	1	no	—
1773	C₂²×C₄	—	53	1	no	—
1774	C₂²×C₄	—	53	1	no	—
1775	C₂²×C₄	—	53	1	no	—
1776	C₂²×C₄	—	53	1	no	—
1777	C₂²×C₄	—	53	1	no	—
1778	C₂²×C₄	—	53	1	no	—
1779	C₂²×C₄	—	106	2	no	—
1780	C₂²×C₄	—	106	2	no	—
1781	C₂²×C₄	—	106	1	no	—
1782	C₂²×C₄	—	106	1	no	—
1783	C₂²×C₄	—	106	1	no	—
1784	C₂²×C₄	—	106	1	no	—
1785	C₂²×C₄	—	106	1	no	—
1786	C₂²×C₄	—	106	1	no	—
1787	C₂²×C₄	—	106	1	no	—
1788	C₂²×C₄	—	106	1	no	—
1789	C₂²×C₄	—	106	1	no	—
1790	C₂²×C₄	—	106	1	no	—
1791	C₂²×C₄	—	106	1	no	—
1792	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1793	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1794	Q₁₆	—	106	2	no	—
1795	SD₁₆	—	2	2	no	—
1796	SD₁₆	—	2	2	no	—
1797	SD₁₆	—	4	1	no	—
1798	SD₁₆	—	106	2	no	—
1799	SD₁₆	—	106	2	no	—
1800	SD₁₆	—	106	2	no	—
1801	SD₁₆	—	106	2	no	—
1802	SD₁₆	—	212	1	no	—
1803	SD₁₆	—	212	1	no	—
1804	SD₁₆	—	212	1	no	—
1805	D₈	—	2	2	no	—
1806	D₈	—	2	2	no	—
1807	D₈	—	2	2	no	—
1808	D₈	—	2	2	no	—
1809	D₈	—	4	1	no	—
1810	D₈	—	53	4	no	—
1811	D₈	—	53	4	no	—
1812	D₈	—	53	4	no	—
1813	D₈	—	106	2	no	—
1814	D₈	—	106	2	no	—
1815	D₈	—	106	2	no	—
1816	D₈	—	106	2	no	—
1817	D₈	—	106	2	no	—
1818	D₈	—	106	2	no	—
1819	D₈	—	106	2	no	—
1820	D₈	—	106	2	no	—
1821	D₈	—	106	2	no	—
1822	D₈	—	106	2	no	—
1823	D₈	—	106	2	no	—
1824	D₈	—	106	2	no	—
1825	D₈	—	106	2	no	—
1826	D₈	—	212	1	no	—
1827	D₈	—	212	1	no	—
1828	D₈	—	212	1	no	—
1829	D₈	D₄×D₅₃	1	4	yes	complemented
1830	M₁₆	—	2	2	no	—
1831	M₁₆	—	106	2	no	—
1832	M₁₆	—	106	2	no	—
1833	M₁₆	—	106	2	no	—
1834	C₂×C₈	—	2	2	no	—
1835	C₂×C₈	—	53	1	no	—
1836	C₂×C₈	—	53	4	no	—
1837	C₂×C₈	—	53	1	no	—
1838	C₂×C₈	—	53	1	no	—
1839	C₂×C₈	—	53	1	no	—
1840	C₂×C₈	—	106	2	no	—
1841	C₂×C₈	—	106	2	no	—
1842	C₂×C₈	—	106	2	no	—
1843	C₂×C₈	—	106	2	no	—
1844	C₂×C₈	—	106	2	no	—
1845	C₂×C₈	—	106	2	no	—
1846	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1847	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1848	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1849	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1850	C₄⋊C₄	—	2	1	no	—
1851	C₄⋊C₄	—	53	1	no	—
1852	C₄⋊C₄	—	53	1	no	—
1853	C₄⋊C₄	—	53	1	no	—
1854	C₄⋊C₄	—	53	1	no	—
1855	C₄⋊C₄	—	53	1	no	—
1856	C₄⋊C₄	—	53	1	no	—
1857	C₄⋊C₄	—	53	1	no	—
1858	C₄⋊C₄	—	106	1	no	—
1859	C₄⋊C₄	—	106	1	no	—
1860	C₄⋊C₄	—	106	1	no	—
1861	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1862	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1863	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1864	C₂²⋊C₄	—	2	1	no	—
1865	C₂²⋊C₄	—	2	1	no	—
1866	C₂²⋊C₄	—	2	1	no	—
1867	C₂²⋊C₄	—	2	1	no	—
1868	C₂²⋊C₄	—	2	1	no	—
1869	C₂²⋊C₄	—	2	1	no	—
1870	C₂²⋊C₄	—	2	1	no	—
1871	C₂²⋊C₄	—	2	1	no	—
1872	C₂²⋊C₄	—	53	1	no	—
1873	C₂²⋊C₄	—	53	1	no	—
1874	C₂²⋊C₄	—	53	1	no	—
1875	C₂²⋊C₄	—	53	1	no	—
1876	C₂²⋊C₄	—	53	1	no	—
1877	C₂²⋊C₄	—	53	1	no	—
1878	C₂²⋊C₄	—	53	1	no	—
1879	C₂²⋊C₄	—	53	1	no	—
1880	C₂²⋊C₄	—	106	1	no	—
1881	C₂²⋊C₄	—	106	1	no	—
1882	C₂²⋊C₄	—	106	1	no	—
1883	C₂²⋊C₄	—	106	1	no	—
1884	C₂²⋊C₄	—	106	1	no	—
1885	C₂²⋊C₄	—	106	1	no	—
1886	C₂²⋊C₄	—	106	1	no	—
1887	C₂²⋊C₄	—	106	1	no	—
1888	C₂²⋊C₄	—	106	1	no	—
1889	C₂²⋊C₄	—	106	1	no	—
1890	C₂²⋊C₄	—	106	1	no	—
1891	C₂²⋊C₄	—	106	1	no	—
1892	C₂²⋊C₄	—	106	1	no	—
1893	C₂²⋊C₄	—	106	1	no	—
1894	C₂²⋊C₄	—	106	1	no	—
1895	C₂²⋊C₄	—	106	1	no	—
1896	C₂²⋊C₄	—	106	1	no	—
1897	C₂²⋊C₄	—	106	1	no	—
1898	C₂²⋊C₄	—	106	1	no	—
1899	C₂²⋊C₄	—	106	1	no	—
1900	C₂²⋊C₄	—	106	1	no	—
1901	C₂²⋊C₄	—	106	1	no	—
1902	C₂²⋊C₄	—	106	1	no	—
1903	C₂²⋊C₄	—	106	1	no	—
1904	C₂²⋊C₄	—	106	1	no	—
1905	C₂²⋊C₄	—	106	1	no	—
1906	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1907	C₂²⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1908	C₄²	—	53	1	no	—
1909	C₄²	—	106	1	no	—
1910	C₄²	—	106	1	no	—
1911	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1912	C₂³	—	2	1	no	—
1913	C₂³	—	2	1	no	—
1914	C₂³	—	2	1	no	—
1915	C₂³	—	2	1	no	—
1916	C₂³	—	2	1	no	—
1917	C₂³	—	4	2	no	—
1918	C₂³	—	4	2	no	—
1919	C₂³	—	4	2	no	—
1920	C₂³	—	4	2	no	—
1921	C₂³	—	4	2	no	—
1922	C₂³	—	8	1	no	—
1923	C₂³	—	8	1	no	—
1924	C₂³	—	8	1	no	—
1925	C₂³	—	8	1	no	—
1926	C₂³	—	53	1	no	—
1927	C₂³	—	53	1	no	—
1928	C₂³	—	53	1	no	—
1929	C₂³	—	106	2	no	—
1930	C₂³	—	106	2	no	—
1931	C₂³	—	106	4	no	—
1932	C₂³	—	106	4	no	—
1933	C₂³	—	106	2	no	—
1934	C₂³	—	106	1	no	—
1935	C₂³	—	106	1	no	—
1936	C₂³	—	106	1	no	—
1937	C₂³	—	106	1	no	—
1938	C₂³	—	106	1	no	—
1939	C₂³	—	424	1	no	—
1940	C₂³	—	424	1	no	—
1941	C₂³	—	424	1	no	—
1942	C₂³	—	424	1	no	—
1943	C₂³	—	424	1	no	—
1944	C₂³	—	424	1	no	—
1945	C₂³	—	424	1	no	—
1946	C₂³	—	424	1	no	—
1947	C₂³	—	424	1	no	—
1948	C₂³	—	424	1	no	—
1949	C₂³	—	424	1	no	—
1950	C₂³	—	424	1	no	—
1951	C₂³	—	424	1	no	—
1952	C₂³	—	424	1	no	—
1953	C₂³	—	424	1	no	—
1954	C₂³	—	424	1	no	—
1955	C₂³	—	424	1	no	—
1956	C₂³	—	424	1	no	—
1957	C₂³	—	424	1	no	—
1958	C₂³	—	424	1	no	—
1959	C₂³	—	424	16	no	—
1960	C₂³	—	424	16	no	—
1961	C₂³	—	212	2	no	—
1962	C₂³	—	212	2	no	—
1963	C₂³	—	212	2	no	—
1964	C₂³	—	212	2	no	—
1965	C₂³	—	212	2	no	—
1966	C₂³	—	212	2	no	—
1967	C₂³	—	212	2	no	—
1968	C₂³	—	212	2	no	—
1969	C₂³	—	212	2	no	—
1970	C₂³	—	212	2	no	—
1971	C₂³	—	212	2	no	—
1972	C₂³	—	212	2	no	—
1973	C₂³	—	212	2	no	—
1974	C₂³	—	212	2	no	—
1975	C₂³	—	212	2	no	—
1976	C₂³	—	212	2	no	—
1977	C₂³	—	212	2	no	—
1978	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1979	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1980	Q₈	—	2	1	no	—
1981	Q₈	—	2	1	no	—
1982	Q₈	—	106	2	no	—
1983	Q₈	—	106	1	no	—
1984	Q₈	—	106	1	no	—
1985	D₄	—	2	2	no	—
1986	D₄	—	2	1	no	—
1987	D₄	—	2	1	no	—
1988	D₄	—	2	1	no	—
1989	D₄	—	2	1	no	—
1990	D₄	—	2	1	no	—
1991	D₄	—	2	1	no	—
1992	D₄	—	2	1	no	—
1993	D₄	—	2	1	no	—
1994	D₄	—	4	2	no	—
1995	D₄	—	4	2	no	—
1996	D₄	—	4	2	no	—
1997	D₄	—	4	2	no	—
1998	D₄	—	4	2	no	—
1999	D₄	—	8	1	no	—
2000	D₄	—	8	1	no	—
2001	D₄	—	8	1	no	—
2002	D₄	—	8	1	no	—
2003	D₄	—	53	2	no	—
2004	D₄	—	53	2	no	—
2005	D₄	—	106	2	no	—
2006	D₄	—	106	2	no	—
2007	D₄	—	106	4	no	—
2008	D₄	—	106	4	no	—
2009	D₄	—	106	2	no	—
2010	D₄	—	106	2	no	—
2011	D₄	—	106	2	no	—
2012	D₄	—	106	2	no	—
2013	D₄	—	106	1	no	—
2014	D₄	—	106	1	no	—
2015	D₄	—	106	1	no	—
2016	D₄	—	106	1	no	—
2017	D₄	—	106	1	no	—
2018	D₄	—	106	1	no	—
2019	D₄	—	106	1	no	—
2020	D₄	—	106	1	no	—
2021	D₄	—	424	1	no	—
2022	D₄	—	424	1	no	—
2023	D₄	—	424	1	no	—
2024	D₄	—	424	1	no	—
2025	D₄	—	424	1	no	—
2026	D₄	—	424	1	no	—
2027	D₄	—	424	1	no	—
2028	D₄	—	424	1	no	—
2029	D₄	—	424	1	no	—
2030	D₄	—	424	1	no	—
2031	D₄	—	424	1	no	—
2032	D₄	—	424	1	no	—
2033	D₄	—	212	2	no	—
2034	D₄	—	212	2	no	—
2035	D₄	—	212	2	no	—
2036	D₄	—	212	2	no	—
2037	D₄	—	212	2	no	—
2038	D₄	—	212	2	no	—
2039	D₄	—	212	2	no	—
2040	D₄	—	212	2	no	—
2041	D₄	—	212	2	no	—
2042	D₄	—	212	2	no	—
2043	D₄	—	212	2	no	—
2044	D₄	—	212	2	no	—
2045	D₄	—	212	2	no	—
2046	D₄	—	212	2	no	—
2047	D₄	—	212	2	no	—
2048	D₄	—	212	2	no	—
2049	D₄	—	212	2	no	—
2050	D₄	—	212	2	no	—
2051	D₄	—	212	2	no	—
2052	D₄	C₂×D₄×D₅₃	1	2	yes	—
2053	D₄	C₂×D₄×D₅₃	1	2	yes	—
2054	C₂×C₄	—	2	1	no	—
2055	C₂×C₄	—	2	1	no	—
2056	C₂×C₄	—	2	1	no	—
2057	C₂×C₄	—	2	1	no	—
2058	C₂×C₄	—	2	1	no	—
2059	C₂×C₄	—	2	1	no	—
2060	C₂×C₄	—	2	1	no	—
2061	C₂×C₄	—	4	2	no	—
2062	C₂×C₄	—	8	1	no	—
2063	C₂×C₄	—	8	1	no	—
2064	C₂×C₄	—	53	1	no	—
2065	C₂×C₄	—	53	2	no	—
2066	C₂×C₄	—	53	2	no	—
2067	C₂×C₄	—	53	1	no	—
2068	C₂×C₄	—	53	1	no	—
2069	C₂×C₄	—	53	1	no	—
2070	C₂×C₄	—	53	1	no	—
2071	C₂×C₄	—	106	2	no	—
2072	C₂×C₄	—	106	2	no	—
2073	C₂×C₄	—	106	2	no	—
2074	C₂×C₄	—	106	1	no	—
2075	C₂×C₄	—	106	1	no	—
2076	C₂×C₄	—	106	1	no	—
2077	C₂×C₄	—	106	1	no	—
2078	C₂×C₄	—	106	1	no	—
2079	C₂×C₄	—	106	1	no	—
2080	C₂×C₄	—	106	1	no	—
2081	C₂×C₄	—	424	1	no	—
2082	C₂×C₄	—	424	1	no	—
2083	C₂×C₄	—	424	1	no	—
2084	C₂×C₄	—	424	1	no	—
2085	C₂×C₄	—	424	1	no	—
2086	C₂×C₄	—	424	1	no	—
2087	C₂×C₄	—	212	2	no	—
2088	C₂×C₄	—	212	2	no	—
2089	C₂×C₄	—	212	2	no	—
2090	C₂×C₄	—	212	2	no	—
2091	C₂×C₄	—	212	2	no	—
2092	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2093	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2094	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2095	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
2096	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
2097	C₈	—	2	1	no	—
2098	C₈	—	2	1	no	—
2099	C₈	—	2	1	no	—
2100	C₈	—	53	2	no	—
2101	C₈	—	106	1	no	—
2102	C₈	—	106	1	no	—
2103	C₈	—	106	1	no	—
2104	C₈	C₂×D₄×D₅₃	1	2	yes	—
2105	C₂²	—	2	1	no	—
2106	C₂²	—	2	1	no	—
2107	C₂²	—	2	1	no	—
2108	C₂²	—	2	2	no	—
2109	C₂²	—	2	2	no	—
2110	C₂²	—	2	1	no	—
2111	C₂²	—	2	1	no	—
2112	C₂²	—	4	1	no	—
2113	C₂²	—	4	1	no	—
2114	C₂²	—	4	1	no	—
2115	C₂²	—	4	1	no	—
2116	C₂²	—	4	1	no	—
2117	C₂²	—	4	1	no	—
2118	C₂²	—	4	1	no	—
2119	C₂²	—	4	1	no	—
2120	C₂²	—	4	1	no	—
2121	C₂²	—	4	1	no	—
2122	C₂²	—	4	1	no	—
2123	C₂²	—	4	1	no	—
2124	C₂²	—	4	1	no	—
2125	C₂²	—	8	4	no	—
2126	C₂²	—	8	4	no	—
2127	C₂²	—	16	2	no	—
2128	C₂²	—	53	2	no	—
2129	C₂²	—	53	2	no	—
2130	C₂²	—	848	2	no	—
2131	C₂²	—	848	2	no	—
2132	C₂²	—	848	2	no	—
2133	C₂²	—	106	8	no	—
2134	C₂²	—	106	1	no	—
2135	C₂²	—	106	1	no	—
2136	C₂²	—	106	1	no	—
2137	C₂²	—	106	1	no	—
2138	C₂²	—	106	1	no	—
2139	C₂²	—	106	2	no	—
2140	C₂²	—	106	2	no	—
2141	C₂²	—	106	1	no	—
2142	C₂²	—	106	1	no	—
2143	C₂²	—	424	4	no	—
2144	C₂²	—	424	4	no	—
2145	C₂²	—	424	4	no	—
2146	C₂²	—	424	4	no	—
2147	C₂²	—	424	4	no	—
2148	C₂²	—	424	4	no	—
2149	C₂²	—	424	4	no	—
2150	C₂²	—	424	4	no	—
2151	C₂²	—	424	4	no	—
2152	C₂²	—	424	4	no	—
2153	C₂²	—	212	1	no	—
2154	C₂²	—	212	1	no	—
2155	C₂²	—	212	1	no	—
2156	C₂²	—	212	1	no	—
2157	C₂²	—	212	1	no	—
2158	C₂²	—	212	1	no	—
2159	C₂²	—	212	1	no	—
2160	C₂²	—	212	1	no	—
2161	C₂²	—	212	1	no	—
2162	C₂²	—	212	1	no	—
2163	C₂²	—	212	1	no	—
2164	C₂²	—	212	1	no	—
2165	C₂²	—	212	1	no	—
2166	C₂²	#16811427	1	2	yes	complemented
2167	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
2168	C₄	—	2	1	no	—
2169	C₄	—	2	1	no	—
2170	C₄	—	2	1	no	—
2171	C₄	—	2	1	no	—
2172	C₄	—	4	1	no	—
2173	C₄	—	4	1	no	—
2174	C₄	—	4	1	no	—
2175	C₄	—	53	2	no	—
2176	C₄	—	106	1	no	—
2177	C₄	—	106	1	no	—
2178	C₄	—	106	1	no	—
2179	C₄	—	106	1	no	—
2180	C₄	—	212	1	no	—
2181	C₄	—	212	1	no	—
2182	C₄	—	212	1	no	—
2183	C₄	C₂²×D₄×D₅₃	1	1	yes	characteristic
2184	C₄	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
2185	C₂	—	2	2	no	—
2186	C₂	—	4	1	no	—
2187	C₂	—	4	2	no	—
2188	C₂	—	4	2	no	—
2189	C₂	—	8	1	no	—
2190	C₂	—	8	1	no	—
2191	C₂	—	8	1	no	—
2192	C₂	—	106	2	no	—
2193	C₂	—	106	2	no	—
2194	C₂	—	424	1	no	—
2195	C₂	—	424	1	no	—
2196	C₂	—	424	1	no	—
2197	C₂	—	212	1	no	—
2198	C₂	—	212	2	no	—
2199	C₂	—	212	2	no	—
2200	C₂	D₄²×D₅₃	1	1	yes	characteristic
2201	C₂	#576×D₅₃	1	1	yes	characteristic
2202	C₂	C₂×#16811427	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×#3264	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3264	D₅₃
hypocenter	C₅₃	#61049
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3264

Complements

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

N	H ≅ G/N	type
1. C₂×#16811427	C₂	semidirect
2. C₂²×D₈×D₅₃	C₂	semidirect
3. #20288345	C₂	semidirect
4. #20288343	C₂	semidirect
5. #20286398	C₂	semidirect
6. #20286396	C₂	semidirect
7. #20286395	C₂	semidirect
8. #20286393	C₂	semidirect
9. D₄×#11719922	C₂	semidirect
10. #20286387	C₂	semidirect
11. #20286385	C₂	semidirect
12. #20286385	C₂	semidirect
13. #20286202	C₂	semidirect
14. #20286200	C₂	semidirect
15. #20286197	C₂	semidirect
16. #20286195	C₂	semidirect
17. #20286194	C₂	semidirect
18. #20286192	C₂	semidirect
19. #20286189	C₂	semidirect
20. #20285199	C₂	semidirect
21. #20284361	C₂	semidirect
22. #20284291	C₂	semidirect
23. #20284216	C₂	semidirect
24. #20284213	C₂	semidirect
25. #20283980	C₂	semidirect
26. #20283978	C₂	semidirect
27. #20283943	C₂	semidirect
28. #20283939	C₂	semidirect
29. #20283564	C₂	semidirect
30. #20283406	C₂	semidirect
31. C₅₃×#3264	C₂	semidirect
32. C₂×#13133263	C₂²	semidirect
33. C₂×#13133262	C₂²	semidirect
34. C₂²×D₄×D₅₃	C₂²	semidirect
35. C₂²×D₄×D₅₃	C₂²	semidirect
37. C₂×#13133245	C₂²	semidirect
38. C₂×#13133244	C₂²	semidirect
39. C₂×#13133244	C₂²	semidirect
40. C₂×#13133244	C₂²	semidirect
41. C₂×#13133241	C₂²	semidirect
42. C₂×#13133241	C₂²	semidirect
43. C₂×#13133241	C₂²	semidirect
44. C₂×#13133238	C₂²	semidirect
45. C₂×#13133238	C₂²	semidirect
46. C₂×#13133237	C₂²	semidirect
47. C₂²×D₄₂₄	C₂²	semidirect
48. C₂²×#11719922	C₂²	semidirect
49. C₂²×#11719922	C₂²	semidirect
50. C₂²×#11719922	C₂²	semidirect
53. C₂×D₈×D₅₃	C₂²	semidirect
54. C₂×D₈×D₅₃	C₂²	semidirect
55. C₂×D₈×D₅₃	C₂²	semidirect
56. C₂×D₈×D₅₃	C₂²	semidirect
57. C₂×D₈×D₅₃	C₂²	semidirect
58. C₂×D₈×D₅₃	C₂²	semidirect
59. C₂×D₈×D₅₃	C₂²	semidirect
60. C₂×D₈×D₅₃	C₂²	semidirect
61. C₂×#13133225	C₂²	semidirect
62. C₂²×C₈×D₅₃	C₂²	semidirect
63. #16811270	C₂²	semidirect
64. #16811269	C₂²	semidirect
65. #16811268	C₂²	semidirect
66. #16811267	C₂²	semidirect
67. #16811266	C₂²	semidirect
69. #16811264	C₂²	semidirect
72. #16811261	C₂²	semidirect
74. D₄×D₂₁₂	C₂²	semidirect
75. D₄×D₂₁₂	C₂²	semidirect
76. #16811258	C₂²	semidirect
78. #16811257	C₂²	semidirect
79. #16811257	C₂²	semidirect
81. D₄×C₂²⋊D₅₃	C₂²	semidirect
82. D₄×C₂²⋊D₅₃	C₂²	semidirect
85. #16811191	C₂²	semidirect
86. #16811189	C₂²	semidirect
87. #16811189	C₂²	semidirect
88. #16811186	C₂²	semidirect
93. #16811136	C₂²	semidirect
94. #16811133	C₂²	semidirect
100. #16811095	C₂²	semidirect
101. #16811095	C₂²	semidirect
102. #16811012	C₂²	semidirect
103. #16811011	C₂²	semidirect
104. #16811009	C₂²	semidirect
105. #16811005	C₂²	semidirect
106. #16811004	C₂²	semidirect
107. #16810999	C₂²	semidirect
108. #16810998	C₂²	semidirect
109. #16810877	C₂²	semidirect
110. #16810876	C₂²	semidirect
111. #16810873	C₂²	semidirect
112. #16810863	C₂²	semidirect
113. #16810862	C₂²	semidirect
114. #16810858	C₂²	semidirect
115. #16810858	C₂²	semidirect
116. #16810858	C₂²	semidirect
117. #16810857	C₂²	semidirect
118. #16810857	C₂²	semidirect
119. #16810857	C₂²	semidirect
120. #16810853	C₂²	semidirect
121. #16810852	C₂²	semidirect
122. #16810849	C₂²	semidirect
123. #16810841	C₂²	semidirect
124. #16810840	C₂²	semidirect
125. #16810839	C₂²	semidirect
126. #16810838	C₂²	semidirect
127. #16810837	C₂²	semidirect
128. #16810836	C₂²	semidirect
129. #16810835	C₂²	semidirect
130. #16810819	C₂²	semidirect
131. #16810818	C₂²	semidirect
132. #16810817	C₂²	semidirect
133. #16810817	C₂²	semidirect
134. #16810816	C₂²	semidirect
135. #16810816	C₂²	semidirect
136. #16810815	C₂²	semidirect
137. #16810776	C₂²	semidirect
138. #16810775	C₂²	semidirect
139. #16810775	C₂²	semidirect
140. #16810774	C₂²	semidirect
141. #16810773	C₂²	semidirect
142. #16810772	C₂²	semidirect
143. #16810772	C₂²	semidirect
144. #16810771	C₂²	semidirect
145. #16810770	C₂²	semidirect
146. #16810769	C₂²	semidirect
147. #16810768	C₂²	semidirect
148. #16810767	C₂²	semidirect
149. #16810766	C₂²	semidirect
150. #16810765	C₂²	semidirect
151. #16810759	C₂²	semidirect
152. #16810759	C₂²	semidirect
153. #16810758	C₂²	semidirect
154. #16810758	C₂²	semidirect
155. #16810758	C₂²	semidirect
156. #16810758	C₂²	semidirect
157. #16810757	C₂²	semidirect
158. #16810757	C₂²	semidirect
159. #16810756	C₂²	semidirect
160. #16810756	C₂²	semidirect
161. #16810755	C₂²	semidirect
162. #16810755	C₂²	semidirect
163. #16810755	C₂²	semidirect
164. #16810755	C₂²	semidirect
165. #16810736	C₂²	semidirect
166. #16810735	C₂²	semidirect
167. #16810734	C₂²	semidirect
168. C₄×#11719922	C₂²	semidirect
169. C₄×#11719922	C₂²	semidirect
170. #16810703	C₂²	semidirect
171. #16810703	C₂²	semidirect
172. #16810696	C₂²	semidirect
173. #16810694	C₂²	semidirect
174. #16810692	C₂²	semidirect
175. D₄×#88322	C₂²	semidirect
176. #16810688	C₂²	semidirect
177. #16810686	C₂²	semidirect
178. #16810686	C₂²	semidirect
179. #16810658	C₂²	semidirect
180. #16810648	C₂²	semidirect
181. #16810626	C₂²	semidirect
182. #16810626	C₂²	semidirect
183. #16810626	C₂²	semidirect
184. #16810626	C₂²	semidirect
185. #16810618	C₂²	semidirect
186. #16810616	C₂²	semidirect
187. #16810588	C₂²	semidirect
188. #16810585	C₂²	semidirect
189. #16810580	C₂²	semidirect
190. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
191. C₂²×D₈×C₅₃	C₂²	semidirect
192. C₅₃×#546	C₂²	semidirect
193. D₄²×C₅₃	C₂²	semidirect
194. C₅₃×#496	C₂²	semidirect
195. C₅₃×#469	C₂²	semidirect
196. C₅₃×#465	C₂²	semidirect
197. C₅₃×#463	C₂²	semidirect
198. C₅₃×#459	C₂²	semidirect
199. C₅₃×#450	C₂²	semidirect
200. C₅₃×#449	C₂²	semidirect
201. C₅₃×#447	C₂²	semidirect
202. C₅₃×#447	C₂²	semidirect
203. C₅₃×#442	C₂²	semidirect
204. C₅₃×#435	C₂²	semidirect
212. C₂×#11719949	C₂³	semidirect
215. C₂×#11719945	C₂³	semidirect
218. C₂×#11719947	C₂³	semidirect
223. C₂²×D₂₁₂	C₂³	semidirect
253. C₂×D₄×D₅₃	C₂³	semidirect
254. C₂×D₄×D₅₃	C₂³	semidirect
266. C₂×#11719925	C₂³	semidirect
267. C₂×#11719913	C₂³	semidirect
268. C₂×#11719913	C₂³	semidirect
269. C₂×#11719913	C₂³	semidirect
270. C₂×#11719923	C₂³	semidirect
271. C₂×#11719923	C₂³	semidirect
272. C₂×#11719924	C₂³	semidirect
273. C₂×#11719924	C₂³	semidirect
279. C₂×D₄₂₄	C₂³	semidirect
280. C₂×D₄₂₄	C₂³	semidirect
292. C₂×#11719922	C₂³	semidirect
293. C₂×#11719922	C₂³	semidirect
294. C₂×#11719922	C₂³	semidirect
295. C₂×#11719922	C₂³	semidirect
296. C₂×#11719922	C₂³	semidirect
305. D₈×D₅₃	D₄	semidirect
309. C₂×#11719912	C₂³	semidirect
311. C₂²×#88322	C₂³	semidirect
317. C₂×C₈×D₅₃	C₂³	semidirect
318. #13133214	C₂³	semidirect
321. #13133213	C₂³	semidirect
322. #13133213	C₂³	semidirect
323. #13133206	C₂³	semidirect
324. #13133205	C₂³	semidirect
325. #13133204	C₂³	semidirect
347. #13133192	C₂³	semidirect
348. #13133192	C₂³	semidirect
352. #13133191	C₂³	semidirect
353. #13133191	C₂³	semidirect
371. #13133188	C₂³	semidirect
372. #13133188	C₂³	semidirect
407. C₄×D₂₁₂	C₂³	semidirect
408. C₄×D₂₁₂	C₂³	semidirect
410. D₄×Dic₅₃	C₂³	semidirect
411. D₄×Dic₅₃	C₂³	semidirect
413. #13133179	C₂³	semidirect
414. #13133179	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. #13133140	C₂³	semidirect
446. #13133139	C₂³	semidirect
447. #13133139	C₂³	semidirect
448. #13133139	C₂³	semidirect
449. #13133139	C₂³	semidirect
450. #13133139	C₂³	semidirect
451. #13133138	C₂³	semidirect
452. #13133138	C₂³	semidirect
453. #13133138	C₂³	semidirect
454. #13133138	C₂³	semidirect
455. #13133138	C₂³	semidirect
456. #13133137	C₂³	semidirect
457. #13133137	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. #13133127	C₂³	semidirect
468. C₄×#88322	C₂³	semidirect
469. C₈×Dic₅₃	C₂³	semidirect
470. C₂×#41×C₅₃	C₂³	semidirect
474. C₂²×D₄×C₅₃	C₂³	semidirect
476. C₂×SD₁₆×C₅₃	C₂³	semidirect
477. C₂×SD₁₆×C₅₃	C₂³	semidirect
478. C₂×SD₁₆×C₅₃	C₂³	semidirect
484. C₂×D₈×C₅₃	C₂³	semidirect
485. C₂×D₈×C₅₃	C₂³	semidirect
486. C₂×M₁₆×C₅₃	C₂³	semidirect
488. #127×C₅₃	C₂³	semidirect
489. #124×C₅₃	C₂³	semidirect
495. #121×C₅₃	C₂³	semidirect
496. #121×C₅₃	C₂³	semidirect
501. C₄×D₄×C₅₃	C₂³	semidirect
502. C₄×D₄×C₅₃	C₂³	semidirect
504. #106×C₅₃	C₂³	semidirect
505. C₄⋊C₈×C₅₃	C₂³	semidirect
506. #103×C₅₃	C₂³	semidirect
507. #102×C₅₃	C₂³	semidirect
508. #102×C₅₃	C₂³	semidirect
509. #102×C₅₃	C₂³	semidirect
510. #102×C₅₃	C₂³	semidirect
511. #102×C₅₃	C₂³	semidirect
513. C₂²⋊C₈×C₅₃	C₂³	semidirect
514. #97×C₅₃	C₂³	semidirect
644. D₄×D₅₃	C₂×D₄	semidirect
645. D₄×D₅₃	C₂×D₄	semidirect
700. D₈×C₅₃	C₂×D₄	semidirect
748. #11719922	C₂×D₄	semidirect
749. #11719922	C₂×D₄	semidirect
798. D₄₂₄	C₂×D₄	semidirect
809. C₈×D₅₃	C₂×D₄	semidirect
1027. C₂²×C₅₃	#576	semidirect
1066. C₂×D₅₃	#576	semidirect
1103. #3264	D₅₃	semidirect
1145. C₂×AGL(1,ℤ/8)	C₂×D₅₃	semidirect
1163. C₂²×D₈	C₂×D₅₃	semidirect
1177. #546	C₂×D₅₃	semidirect
1189. D₄²	C₂×D₅₃	semidirect
1210. #496	C₂×D₅₃	semidirect
1218. #469	C₂×D₅₃	semidirect
1230. #465	C₂×D₅₃	semidirect
1238. #463	C₂×D₅₃	semidirect
1246. #459	C₂×D₅₃	semidirect
1254. #450	C₂×D₅₃	semidirect
1262. #449	C₂×D₅₃	semidirect
1277. #447	C₂×D₅₃	semidirect
1278. #447	C₂×D₅₃	semidirect
1282. #442	C₂×D₅₃	semidirect
1290. #435	C₂×D₅₃	semidirect
1306. C₅₃	#61049	semidirect
1321. C₂×#41	C₂²×D₅₃	semidirect
1361. C₂²×D₄	C₂²×D₅₃	semidirect
1382. C₂×SD₁₆	C₂²×D₅₃	semidirect
1383. C₂×SD₁₆	C₂²×D₅₃	semidirect
1384. C₂×SD₁₆	C₂²×D₅₃	semidirect
1422. C₂×D₈	C₂²×D₅₃	semidirect
1423. C₂×D₈	C₂²×D₅₃	semidirect
1428. C₂×M₁₆	C₂²×D₅₃	semidirect
1443. #127	C₂²×D₅₃	semidirect
1449. #124	C₂²×D₅₃	semidirect
1500. #121	C₂²×D₅₃	semidirect
1501. #121	C₂²×D₅₃	semidirect
1556. C₄×D₄	C₂²×D₅₃	semidirect
1557. C₄×D₄	C₂²×D₅₃	semidirect
1576. #106	C₂²×D₅₃	semidirect
1580. C₄⋊C₈	C₂²×D₅₃	semidirect
1584. #103	C₂²×D₅₃	semidirect
1600. #102	C₂²×D₅₃	semidirect
1601. #102	C₂²×D₅₃	semidirect
1602. #102	C₂²×D₅₃	semidirect
1603. #102	C₂²×D₅₃	semidirect
1604. #102	C₂²×D₅₃	semidirect
1612. C₂²⋊C₈	C₂²×D₅₃	semidirect
1614. #97	C₂²×D₅₃	semidirect
1829. D₈	D₄×D₅₃	semidirect
2166. C₂²	#16811427	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811427	2
C₂²×D₈×D₅₃	2
#20288345	2
#20288343	2
#20286398	2
#20286396	2
#20286395	2
#20286393	2
D₄×#11719922	2
#20286387	2
#20286385	2
#20286202	2
#20286200	2
#20286197	2
#20286195	2
#20286194	2
#20286192	2
#20286189	2
#20285199	2
#20284361	2
#20284291	2
#20284216	2
#20284213	2
#20283980	2
#20283978	2
#20283943	2
#20283939	2
#20283564	2
#20283406	2
C₅₃×#3264	2
#61049	53