Subgroups — #28261084

Order 13568.

2254 conjugacy classes of subgroups.

The subgroup lattice has 1424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16811269	C₂	1	1	yes	maximal, characteristic, complemented
2	#20286925	C₂	1	2	yes	maximal, complemented
3	#20286910	C₂	1	2	yes	maximal, complemented
4	#20286865	C₂	1	2	yes	maximal, complemented
5	#20286790	C₂	1	2	yes	maximal, complemented
6	#20286745	C₂	1	2	yes	maximal, complemented
7	#20286670	C₂	1	2	yes	maximal, complemented
8	#20286559	C₂	1	2	yes	maximal, complemented
9	#20286544	C₂	1	2	yes	maximal, complemented
10	#20285104	C₂	1	1	yes	maximal, characteristic, complemented
11	#20284663	C₂	1	1	yes	maximal, characteristic, complemented
12	#20284655	C₂	1	1	yes	maximal, characteristic, complemented
13	#20284508	C₂	1	1	yes	maximal, characteristic, complemented
14	#20284347	C₂	1	1	yes	maximal, characteristic, complemented
15	#20284336	C₂	1	1	yes	maximal, characteristic, complemented
16	#20284209	C₂	1	1	yes	maximal, characteristic, complemented
17	#20283955	C₂	1	1	yes	maximal, characteristic, complemented
18	#20283941	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13133242	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×#11719917	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283232	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16810627	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11719945	C₂²	1	1	yes	characteristic
25	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic
26	C₂×#13133247	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13133242	C₂²	1	1	yes	characteristic
28	C₂×#13133242	C₂²	1	1	yes	characteristic
29	C₂²×#11719917	C₂²	1	1	yes	characteristic
30	C₂²×#11719917	C₂²	1	1	yes	characteristic, complemented
31	#16811269	—	2	1	no	—
32	#16811269	—	2	1	no	—
33	#16811269	—	2	1	no	—
34	#16811269	—	2	1	no	—
35	#16811269	C₂²	1	2	yes	—
36	#16811269	C₂²	1	2	yes	—
37	#16811269	C₂²	1	2	yes	—
38	#16811269	C₂²	1	2	yes	—
39	C₂×#13133205	C₂²	1	1	yes	characteristic
40	C₂×#13133202	—	2	1	no	—
41	C₂×#13133196	C₂²	1	1	yes	characteristic
42	C₂×#13133191	C₂²	1	1	yes	characteristic
43	C₂×#13133190	—	2	1	no	—
44	C₂×#13133185	—	2	1	no	—
45	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₅₃	—	2	1	no	—
47	#16810985	C₂²	1	2	yes	complemented
48	#16810985	C₂²	1	2	yes	complemented
49	#16810980	C₂²	1	2	yes	complemented
50	#16810980	C₂²	1	2	yes	complemented
51	#16810964	C₂²	1	2	yes	complemented
52	#16810964	C₂²	1	2	yes	complemented
53	#16810958	C₂²	1	2	yes	complemented
54	#16810953	C₂²	1	2	yes	complemented
55	#16810947	C₂²	1	2	yes	complemented
56	#16810947	C₂²	1	2	yes	complemented
57	#16810941	C₂²	1	2	yes	complemented
58	#16810936	C₂²	1	2	yes	complemented
59	#16810920	C₂²	1	2	yes	complemented
60	#16810920	C₂²	1	2	yes	complemented
61	#16810910	C₂²	1	2	yes	complemented
62	#16810900	C₂²	1	2	yes	complemented
63	#16810879	C₂²	1	2	yes	complemented
64	#16810874	C₂²	1	2	yes	complemented
65	#16810871	C₂²	1	2	yes	complemented
66	#16810867	C₂²	1	2	yes	complemented
67	#16810862	C₂²	1	2	yes	complemented
68	#16810857	C₂²	1	2	yes	complemented
69	#16810854	C₂²	1	2	yes	complemented
70	#16810850	C₂²	1	2	yes	complemented
71	#16810845	C₂²	1	2	yes	complemented
72	#16810845	C₂²	1	2	yes	complemented
73	#16810838	C₂²	1	2	yes	complemented
74	#16810838	C₂²	1	2	yes	complemented
75	#16810783	C₂²	1	2	yes	complemented
76	#16810783	C₂²	1	2	yes	complemented
77	#16810773	C₂²	1	2	yes	complemented
78	#16810773	C₂²	1	2	yes	complemented
79	#16810766	C₂²	1	2	yes	complemented
80	#16810766	C₂²	1	2	yes	complemented
81	#16810756	C₂²	1	2	yes	complemented
82	#16810756	C₂²	1	2	yes	complemented
83	#16810733	C₂²	1	2	yes	complemented
84	#16810721	C₂²	1	2	yes	complemented
85	C₄×#11719924	C₂²	1	2	yes	complemented
86	C₄×#11719922	C₂²	1	2	yes	complemented
87	#16810701	C₂²	1	2	yes	complemented
88	#16810695	C₂²	1	2	yes	complemented
89	#16810695	C₂²	1	2	yes	complemented
90	D₄×#88322	C₂²	1	2	yes	complemented
91	#16810666	C₂²	1	1	yes	characteristic, complemented
92	#16810666	C₂²	1	1	yes	characteristic, complemented
93	#16810666	C₂²	1	1	yes	characteristic, complemented
94	#16810647	C₂²	1	1	yes	characteristic, complemented
95	#16810631	C₂²	1	1	yes	characteristic, complemented
96	#16810631	C₂²	1	1	yes	characteristic, complemented
97	#16810631	C₂²	1	1	yes	characteristic, complemented
98	#16810627	C₂²	1	1	yes	characteristic
99	#16810627	C₂²	1	1	yes	characteristic
100	#16810627	C₂²	1	1	yes	characteristic
101	#16810627	C₂²	1	1	yes	characteristic
102	#16810627	C₂²	1	1	yes	characteristic
103	#16810627	C₂²	1	1	yes	characteristic
104	#16810627	C₂²	1	2	yes	complemented
105	#16810627	C₂²	1	2	yes	complemented
106	#16810624	C₂²	1	1	yes	characteristic, complemented
107	#16810622	C₂²	1	2	yes	complemented
108	#16810622	C₂²	1	2	yes	complemented
109	#16810617	C₂²	1	2	yes	complemented
110	#16810617	C₂²	1	2	yes	complemented
111	C₂×#13133137	C₂²	1	2	yes	complemented
112	C₂×#13133137	C₂²	1	2	yes	complemented
113	#16810587	C₂²	1	1	yes	characteristic
114	#16810587	C₂²	1	1	yes	characteristic, complemented
115	C₄×#11719917	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#552	—	2	1	no	—
122	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#551	—	2	1	no	—
125	C₅₃×#551	—	2	1	no	—
126	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#546	—	2	1	no	—
128	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#529	—	2	1	no	—
130	C₅₃×#529	—	2	1	no	—
131	C₅₃×#529	—	2	1	no	—
132	C₅₃×#525	C₂²	1	1	yes	characteristic
133	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
134	C₄×#41×C₅₃	—	2	1	no	—
135	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
137	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
138	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₅₃	—	2	1	no	—
140	C₂×#11719945	—	2	1	no	—
141	C₂×#11719945	—	2	1	no	—
142	C₂×#11719945	—	2	4	no	—
143	C₂×#11719945	—	4	2	no	—
144	C₂×#11719945	C₂³	1	2	yes	—
145	C₂×#11719945	C₂³	1	2	yes	—
146	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
147	C₂²×D₂₁₂	—	2	4	no	—
148	C₂²×D₂₁₂	—	2	1	no	—
149	C₂²×D₂₁₂	—	2	1	no	—
150	C₂²×D₂₁₂	—	2	1	no	—
151	C₂²×D₂₁₂	—	4	2	no	—
152	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
153	C₂²×D₂₁₂	C₂³	1	2	yes	—
154	C₂²×D₂₁₂	C₂³	1	2	yes	—
155	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
156	C₂²×C₂²⋊D₅₃	—	2	1	no	—
157	C₂²×C₂²⋊D₅₃	—	2	1	no	—
158	C₂²×C₄×D₅₃	—	2	1	no	—
159	C₂²×C₄×D₅₃	—	2	1	no	—
160	#13133247	—	4	2	no	—
161	#13133242	—	2	4	no	—
162	#13133242	—	4	2	no	—
163	C₂×#11719925	C₂³	1	2	yes	complemented
164	C₂×#11719923	C₂³	1	2	yes	complemented
165	C₂×#11719924	C₂³	1	2	yes	—
166	C₂×#11719924	C₂³	1	2	yes	—
167	C₂×#11719922	C₂³	1	2	yes	—
168	C₂×#11719922	C₂³	1	2	yes	—
169	C₂×#11719917	—	4	2	no	—
170	C₂×#11719917	—	4	2	no	—
171	C₂×#11719917	C₂³	1	1	yes	characteristic
172	C₂×#11719917	C₂³	1	1	yes	characteristic
173	C₂×#11719917	C₂³	1	1	yes	characteristic
174	C₂×#11719917	C₂³	1	1	yes	characteristic
175	C₂×#11719917	C₂³	1	2	yes	—
176	C₂×#11719917	C₂³	1	2	yes	complemented
177	C₂²×#88322	C₂³	1	2	yes	—
178	C₂²×#88322	C₂³	1	2	yes	complemented
179	#13133205	—	2	1	no	—
180	#13133205	—	2	1	no	—
181	#13133205	C₂³	1	2	yes	—
182	#13133205	C₂³	1	2	yes	—
183	#13133202	—	2	2	no	—
184	#13133202	—	2	2	no	—
185	#13133202	—	2	2	no	—
186	#13133202	—	2	2	no	—
187	#13133196	—	2	1	no	—
188	#13133196	—	2	1	no	—
189	#13133196	C₂³	1	2	yes	—
190	#13133196	C₂³	1	2	yes	—
191	#13133191	—	2	1	no	—
192	#13133191	—	2	1	no	—
193	#13133191	C₂³	1	2	yes	—
194	#13133191	C₂³	1	2	yes	—
195	#13133190	—	2	2	no	—
196	#13133190	—	2	2	no	—
197	#13133190	—	2	2	no	—
198	#13133190	—	2	2	no	—
199	#13133185	—	2	2	no	—
200	#13133185	—	2	2	no	—
201	#13133185	—	2	2	no	—
202	#13133185	—	2	2	no	—
203	C₄×D₂₁₂	—	2	1	no	—
204	C₄×D₂₁₂	—	2	1	no	—
205	C₄×D₂₁₂	C₂³	1	2	yes	—
206	C₄×D₂₁₂	C₂³	1	2	yes	—
207	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
208	C₂×#11719919	—	2	1	no	—
209	C₂×C₂²⋊Dic₅₃	—	2	1	no	—
210	C₂×#11719921	—	2	1	no	—
211	C₂×#11719921	—	2	1	no	—
212	C₂×#11719921	—	2	1	no	—
213	C₂×#11719921	—	2	1	no	—
214	C₂²⋊C₄×D₅₃	—	2	2	no	—
215	C₂²⋊C₄×D₅₃	—	2	2	no	—
216	C₂²⋊C₄×D₅₃	—	2	2	no	—
217	C₂²⋊C₄×D₅₃	—	2	2	no	—
218	#13133150	C₂³	1	2	yes	complemented
219	#13133150	C₂³	1	2	yes	complemented
220	#13133150	C₂³	1	2	yes	complemented
221	#13133148	C₂³	1	2	yes	complemented
222	#13133148	C₂³	1	2	yes	complemented
223	#13133148	C₂³	1	2	yes	complemented
224	C₄⋊#88322	C₂³	1	2	yes	complemented
225	C₄⋊#88322	C₂³	1	2	yes	complemented
226	#13133141	C₂³	1	2	yes	complemented
227	#13133140	C₂³	1	2	yes	complemented
228	#13133140	C₂³	1	2	yes	complemented
229	#13133140	C₂³	1	2	yes	complemented
230	#13133140	C₂³	1	2	yes	complemented
231	#13133140	C₂³	1	2	yes	complemented
232	#13133140	C₂³	1	2	yes	complemented
233	#13133138	C₂³	1	2	yes	complemented
234	#13133137	C₂³	1	2	yes	—
235	#13133137	C₂³	1	2	yes	—
236	#13133137	C₂³	1	2	yes	—
237	#13133137	C₂³	1	2	yes	—
238	#13133137	C₂³	1	2	yes	—
239	#13133137	C₂³	1	2	yes	—
240	#13133137	C₂³	1	2	yes	—
241	#13133137	C₂³	1	2	yes	—
242	#13133137	C₂³	1	2	yes	—
243	#13133137	C₂³	1	2	yes	—
244	#13133137	C₂³	1	2	yes	—
245	#13133137	C₂³	1	2	yes	—
246	C₂²⋊#88322	C₂³	1	2	yes	—
247	C₂²⋊#88322	C₂³	1	2	yes	—
248	C₂²⋊#88322	C₂³	1	2	yes	complemented
249	C₂²⋊#88322	C₂³	1	2	yes	complemented
250	#13133128	C₂³	1	2	yes	complemented
251	C₄×#88322	C₂³	1	2	yes	complemented
252	C₂×#41×C₅₃	—	2	1	no	—
253	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
254	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
255	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
258	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
259	#126×C₅₃	—	2	1	no	—
260	#126×C₅₃	—	2	1	no	—
261	#126×C₅₃	—	2	1	no	—
262	#126×C₅₃	—	2	1	no	—
263	#126×C₅₃	—	2	1	no	—
264	#126×C₅₃	—	2	1	no	—
265	#125×C₅₃	—	2	1	no	—
266	#125×C₅₃	—	2	1	no	—
267	#125×C₅₃	—	2	1	no	—
268	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
269	#125×C₅₃	C₂³	1	1	yes	characteristic, complemented
270	#124×C₅₃	—	2	1	no	—
271	#124×C₅₃	—	2	1	no	—
272	#124×C₅₃	—	2	1	no	—
273	#123×C₅₃	—	2	1	no	—
274	#123×C₅₃	—	2	1	no	—
275	#123×C₅₃	—	2	1	no	—
276	#123×C₅₃	—	2	1	no	—
277	#123×C₅₃	—	2	1	no	—
278	#123×C₅₃	—	2	1	no	—
279	#123×C₅₃	—	2	1	no	—
280	#123×C₅₃	—	2	1	no	—
281	C₂²⋊Q₈×C₅₃	—	2	1	no	—
282	C₂²⋊Q₈×C₅₃	—	2	1	no	—
283	C₂²⋊Q₈×C₅₃	—	2	1	no	—
284	C₂²⋊Q₈×C₅₃	—	2	1	no	—
285	C₂²⋊Q₈×C₅₃	—	2	1	no	—
286	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
287	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
288	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
289	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
290	#121×C₅₃	—	2	1	no	—
291	#121×C₅₃	—	2	1	no	—
292	#121×C₅₃	—	2	1	no	—
293	#121×C₅₃	C₂³	1	1	yes	characteristic
294	#121×C₅₃	C₂³	1	1	yes	characteristic
295	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
296	#121×C₅₃	C₂³	1	1	yes	characteristic, complemented
297	#120×C₅₃	—	2	1	no	—
298	#120×C₅₃	—	2	1	no	—
299	C₄×Q₈×C₅₃	—	2	1	no	—
300	C₄×Q₈×C₅₃	—	2	1	no	—
301	C₄×Q₈×C₅₃	—	2	1	no	—
302	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
303	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
304	C₄×D₄×C₅₃	—	2	1	no	—
305	C₄×D₄×C₅₃	—	2	1	no	—
306	C₄×D₄×C₅₃	—	2	1	no	—
307	C₄×D₄×C₅₃	—	2	1	no	—
308	C₄×D₄×C₅₃	—	2	1	no	—
309	C₄×D₄×C₅₃	—	2	1	no	—
310	C₄×D₄×C₅₃	—	2	1	no	—
311	C₄×D₄×C₅₃	—	2	1	no	—
312	C₄×D₄×C₅₃	—	2	1	no	—
313	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
314	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
315	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
316	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
317	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
322	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
323	#117×C₅₃	—	2	1	no	—
324	#117×C₅₃	—	2	1	no	—
325	#117×C₅₃	—	2	1	no	—
326	#117×C₅₃	—	2	1	no	—
327	#117×C₅₃	—	2	1	no	—
328	#117×C₅₃	—	2	1	no	—
329	#117×C₅₃	—	2	1	no	—
330	#117×C₅₃	—	2	1	no	—
331	#117×C₅₃	C₂³	1	1	yes	characteristic
332	#117×C₅₃	C₂³	1	1	yes	characteristic
333	#117×C₅₃	C₂³	1	1	yes	characteristic
334	#117×C₅₃	C₂³	1	1	yes	characteristic
335	#117×C₅₃	C₂³	1	1	yes	characteristic
336	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
337	#117×C₅₃	C₂³	1	1	yes	characteristic, complemented
338	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
342	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
343	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
344	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
345	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	—	2	1	no	—
348	C₂×C₄²×C₅₃	—	2	1	no	—
349	C₂×C₄²×C₅₃	—	2	1	no	—
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₂³×D₅₃	—	2	1	no	—
354	C₂³×D₅₃	—	2	1	no	—
355	C₂³×D₅₃	—	2	2	no	—
356	C₂³×D₅₃	—	2	2	no	—
357	C₂³×D₅₃	—	4	4	no	—
358	C₂³×D₅₃	—	4	4	no	—
359	C₂³×D₅₃	—	8	2	no	—
360	#41×C₅₃	—	2	2	no	—
361	#41×C₅₃	—	2	2	no	—
362	#41×C₅₃	—	4	4	no	—
363	C₂×Q₈×C₅₃	—	2	1	no	—
364	C₂×Q₈×C₅₃	—	2	1	no	—
365	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₅₃	—	2	1	no	—
367	C₂×D₄×C₅₃	—	2	1	no	—
368	C₂×D₄×C₅₃	—	2	1	no	—
369	C₂×D₄×C₅₃	—	2	1	no	—
370	C₂×D₄×C₅₃	—	2	1	no	—
371	C₂×D₄×C₅₃	—	4	2	no	—
372	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
374	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
375	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
376	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	1	no	—
382	C₂²×C₄×C₅₃	—	2	1	no	—
383	C₂²×C₄×C₅₃	—	2	1	no	—
384	C₂²×C₄×C₅₃	—	2	1	no	—
385	C₂²×C₄×C₅₃	—	2	1	no	—
386	C₂²×C₄×C₅₃	—	2	1	no	—
387	C₂²×C₄×C₅₃	—	2	1	no	—
388	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
389	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₂²⋊D₅₃	—	2	2	no	—
402	C₂×C₂²⋊D₅₃	—	2	2	no	—
403	C₂×C₂²⋊D₅₃	—	2	2	no	—
404	C₂×C₂²⋊D₅₃	—	2	2	no	—
405	C₂×C₂²⋊D₅₃	—	4	4	no	—
406	C₂×C₂²⋊D₅₃	—	8	2	no	—
407	C₂²×Dic₅₃	—	2	1	no	—
408	C₂²×Dic₅₃	—	2	1	no	—
409	#11719945	—	2	4	no	—
410	#11719945	—	2	4	no	—
411	#11719945	—	4	2	no	—
412	#11719945	—	4	2	no	—
413	#11719945	—	4	4	no	—
414	#11719945	—	4	4	no	—
415	C₂×D₂₁₂	—	2	1	no	—
416	C₂×D₂₁₂	—	2	2	no	—
417	C₂×D₂₁₂	—	2	2	no	—
418	C₂×D₂₁₂	—	2	2	no	—
419	C₂×D₂₁₂	—	2	4	no	—
420	C₂×D₂₁₂	—	2	4	no	—
421	C₂×D₂₁₂	—	2	2	no	—
422	C₂×D₂₁₂	—	2	2	no	—
423	C₂×D₂₁₂	—	2	1	no	—
424	C₂×D₂₁₂	—	4	2	no	—
425	C₂×D₂₁₂	—	4	2	no	—
426	C₂×D₂₁₂	—	4	4	no	—
427	C₂×D₂₁₂	—	4	4	no	—
428	C₂×D₂₁₂	—	4	4	no	—
429	C₂×D₂₁₂	#41	1	4	yes	complemented
430	C₂×D₂₁₂	C₂⁴	1	2	yes	—
431	C₂×D₂₁₂	C₂⁴	1	2	yes	—
432	C₂×C₄×D₅₃	—	2	2	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	4	4	no	—
437	C₂×C₄×D₅₃	—	8	2	no	—
438	C₂×Dic₁₀₆	—	2	2	no	—
439	C₂×Dic₁₀₆	—	2	2	no	—
440	C₂×Dic₁₀₆	—	2	1	no	—
441	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
442	C₄⋊C₄×C₅₃	—	2	1	no	—
443	C₄⋊C₄×C₅₃	—	2	1	no	—
444	C₄⋊C₄×C₅₃	—	2	1	no	—
445	C₄⋊C₄×C₅₃	—	2	1	no	—
446	C₄⋊C₄×C₅₃	—	2	1	no	—
447	C₄⋊C₄×C₅₃	—	2	1	no	—
448	C₄⋊C₄×C₅₃	—	2	1	no	—
449	C₄⋊C₄×C₅₃	—	2	1	no	—
450	C₄⋊C₄×C₅₃	—	2	1	no	—
451	C₄⋊C₄×C₅₃	—	2	1	no	—
452	C₄⋊C₄×C₅₃	—	2	1	no	—
453	C₄⋊C₄×C₅₃	—	2	1	no	—
454	C₄⋊C₄×C₅₃	—	2	1	no	—
455	C₄⋊C₄×C₅₃	—	2	1	no	—
456	C₄⋊C₄×C₅₃	—	2	1	no	—
457	C₄⋊C₄×C₅₃	—	2	1	no	—
458	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
460	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
461	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
462	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂²⋊C₄×C₅₃	—	2	1	no	—
469	C₂²⋊C₄×C₅₃	—	2	1	no	—
470	C₂²⋊C₄×C₅₃	—	2	1	no	—
471	C₂²⋊C₄×C₅₃	—	2	1	no	—
472	C₂²⋊C₄×C₅₃	—	2	1	no	—
473	C₂²⋊C₄×C₅₃	—	2	1	no	—
474	C₂²⋊C₄×C₅₃	—	2	1	no	—
475	C₂²⋊C₄×C₅₃	—	2	1	no	—
476	C₂²⋊C₄×C₅₃	—	2	1	no	—
477	C₂²⋊C₄×C₅₃	—	2	1	no	—
478	C₂²⋊C₄×C₅₃	—	2	1	no	—
479	C₂²⋊C₄×C₅₃	—	2	1	no	—
480	C₂²⋊C₄×C₅₃	—	2	1	no	—
481	C₂²⋊C₄×C₅₃	—	2	1	no	—
482	C₂²⋊C₄×C₅₃	—	2	1	no	—
483	C₂²⋊C₄×C₅₃	—	2	1	no	—
484	C₂²⋊C₄×C₅₃	—	2	1	no	—
485	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
486	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
487	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
488	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
489	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
490	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
491	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
492	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
493	C₄²×C₅₃	—	2	1	no	—
494	C₄²×C₅₃	—	2	1	no	—
495	C₄²×C₅₃	—	2	1	no	—
496	C₄²×C₅₃	—	2	1	no	—
497	C₄²×C₅₃	—	2	1	no	—
498	C₄²×C₅₃	—	2	1	no	—
499	C₄²×C₅₃	—	2	1	no	—
500	C₄²×C₅₃	—	2	1	no	—
501	C₄²×C₅₃	—	2	1	no	—
502	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
503	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
504	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
506	C₂²⋊Dic₅₃	—	2	2	no	—
507	C₂²⋊Dic₅₃	—	2	2	no	—
508	#11719925	—	4	2	no	—
509	#11719924	—	2	4	no	—
510	#11719924	—	4	2	no	—
511	#11719923	—	4	2	no	—
512	#11719922	—	2	4	no	—
513	#11719922	—	4	2	no	—
514	#11719921	—	2	2	no	—
515	#11719921	—	2	2	no	—
516	#11719921	—	2	2	no	—
517	#11719921	—	2	2	no	—
518	#11719921	—	2	2	no	—
519	#11719921	—	2	2	no	—
520	#11719921	—	2	2	no	—
521	#11719921	—	2	2	no	—
522	C₄⋊Dic₅₃	—	2	1	no	—
523	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
524	#11719919	—	2	2	no	—
525	#11719919	—	2	2	no	—
526	#11719917	—	2	2	no	—
527	#11719917	—	2	2	no	—
528	#11719917	—	2	2	no	—
529	#11719917	—	2	2	no	—
530	#11719917	—	4	2	no	—
531	#11719917	—	4	2	no	—
532	C₂×#88322	—	4	2	no	—
533	C₂×#88322	—	4	2	no	—
534	C₂×#88322	C₂⁴	1	2	yes	—
535	C₂×#88322	C₂⁴	1	2	yes	—
536	C₂×#88322	C₂⁴	1	2	yes	—
537	C₂×#88322	C₂⁴	1	2	yes	—
538	C₂³×C₅₃	—	2	2	no	—
539	C₂³×C₅₃	—	2	2	no	—
540	C₂³×C₅₃	—	2	2	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	4	1	no	—
543	C₂³×C₅₃	—	4	1	no	—
544	C₂³×C₅₃	—	4	1	no	—
545	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
546	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
547	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
548	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
549	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
550	C₂²×D₅₃	—	2	4	no	—
551	C₂²×D₅₃	—	2	2	no	—
552	C₂²×D₅₃	—	2	2	no	—
553	C₂²×D₅₃	—	4	4	no	—
554	C₂²×D₅₃	—	4	4	no	—
555	C₂²×D₅₃	—	4	2	no	—
556	C₂²×D₅₃	—	4	2	no	—
557	C₂²×D₅₃	—	4	2	no	—
558	C₂²×D₅₃	—	4	4	no	—
559	C₂²×D₅₃	—	4	2	no	—
560	C₂²×D₅₃	—	4	2	no	—
561	C₂²×D₅₃	—	4	4	no	—
562	C₂²×D₅₃	—	8	2	no	—
563	C₂²×D₅₃	—	8	2	no	—
564	C₂²×D₅₃	—	8	16	no	—
565	Q₈×C₅₃	—	2	1	no	—
566	Q₈×C₅₃	—	2	1	no	—
567	Q₈×C₅₃	—	4	2	no	—
568	Q₈×C₅₃	—	8	1	no	—
569	D₄×C₅₃	—	2	2	no	—
570	D₄×C₅₃	—	2	2	no	—
571	D₄×C₅₃	—	2	1	no	—
572	D₄×C₅₃	—	2	1	no	—
573	D₄×C₅₃	—	4	1	no	—
574	D₄×C₅₃	—	4	1	no	—
575	D₄×C₅₃	—	4	2	no	—
576	D₄×C₅₃	—	4	2	no	—
577	D₄×C₅₃	—	4	2	no	—
578	D₄×C₅₃	—	8	1	no	—
579	D₄×C₅₃	—	8	1	no	—
580	C₂×C₄×C₅₃	—	2	2	no	—
581	C₂×C₄×C₅₃	—	2	2	no	—
582	C₂×C₄×C₅₃	—	2	2	no	—
583	C₂×C₄×C₅₃	—	2	2	no	—
584	C₂×C₄×C₅₃	—	2	2	no	—
585	C₂×C₄×C₅₃	—	2	2	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	4	1	no	—
602	C₂×C₄×C₅₃	—	4	1	no	—
603	C₂×C₄×C₅₃	—	4	2	no	—
604	C₂×C₄×C₅₃	—	4	2	no	—
605	C₂×C₄×C₅₃	—	4	2	no	—
606	C₂×C₄×C₅₃	—	4	2	no	—
607	C₂×C₄×C₅₃	—	8	1	no	—
608	C₂×C₄×C₅₃	—	8	1	no	—
609	C₂×C₄×C₅₃	—	8	1	no	—
610	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
611	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
614	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
615	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
616	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
618	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
620	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
621	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
622	C₂²⋊D₅₃	—	4	4	no	—
623	C₂²⋊D₅₃	—	4	4	no	—
624	C₂²⋊D₅₃	—	8	2	no	—
625	C₂²⋊D₅₃	—	8	2	no	—
626	C₂×Dic₅₃	—	2	2	no	—
627	C₂×Dic₅₃	—	2	2	no	—
628	C₂×Dic₅₃	—	4	2	no	—
629	C₂×Dic₅₃	—	4	2	no	—
630	D₂₁₂	—	2	4	no	—
631	D₂₁₂	—	2	2	no	—
632	D₂₁₂	—	2	2	no	—
633	D₂₁₂	—	2	2	no	—
634	D₂₁₂	—	4	4	no	—
635	D₂₁₂	—	4	4	no	—
636	D₂₁₂	—	4	2	no	—
637	D₂₁₂	C₂×#41	1	4	yes	—
638	C₄×D₅₃	—	4	4	no	—
639	C₄×D₅₃	—	4	4	no	—
640	C₄×D₅₃	—	8	2	no	—
641	C₄×D₅₃	—	8	2	no	—
642	Dic₁₀₆	—	2	2	no	—
643	Dic₁₀₆	—	2	2	no	—
644	Dic₁₀₆	—	4	2	no	—
645	#88322	—	2	2	no	—
646	#88322	—	2	2	no	—
647	#88322	—	2	2	no	—
648	#88322	—	2	2	no	—
649	#61156	—	53	1	no	maximal, Sylow
650	C₂²×C₅₃	—	2	1	no	—
651	C₂²×C₅₃	—	2	1	no	—
652	C₂²×C₅₃	—	2	1	no	—
653	C₂²×C₅₃	—	2	1	no	—
654	C₂²×C₅₃	—	2	1	no	—
655	C₂²×C₅₃	—	2	1	no	—
656	C₂²×C₅₃	—	2	1	no	—
657	C₂²×C₅₃	—	2	1	no	—
658	C₂²×C₅₃	—	2	1	no	—
659	C₂²×C₅₃	—	2	1	no	—
660	C₂²×C₅₃	—	2	1	no	—
661	C₂²×C₅₃	—	2	1	no	—
662	C₂²×C₅₃	—	2	1	no	—
663	C₂²×C₅₃	—	4	4	no	—
664	C₂²×C₅₃	—	4	1	no	—
665	C₂²×C₅₃	—	4	1	no	—
666	C₂²×C₅₃	—	4	1	no	—
667	C₂²×C₅₃	—	8	2	no	—
668	C₂²×C₅₃	#546	1	2	yes	—
669	C₂²×C₅₃	#575	1	2	yes	—
670	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
671	C₂×D₅₃	—	2	4	no	—
672	C₂×D₅₃	—	4	8	no	—
673	C₂×D₅₃	—	4	2	no	—
674	C₂×D₅₃	—	4	2	no	—
675	C₂×D₅₃	—	4	2	no	—
676	C₂×D₅₃	—	4	2	no	—
677	C₂×D₅₃	—	4	2	no	—
678	C₂×D₅₃	—	8	8	no	—
679	C₂×D₅₃	—	8	8	no	—
680	C₂×D₅₃	—	8	4	no	—
681	C₄×C₅₃	—	2	1	no	—
682	C₄×C₅₃	—	2	1	no	—
683	C₄×C₅₃	—	2	1	no	—
684	C₄×C₅₃	—	2	1	no	—
685	C₄×C₅₃	—	2	1	no	—
686	C₄×C₅₃	—	2	1	no	—
687	C₄×C₅₃	—	2	1	no	—
688	C₄×C₅₃	—	2	1	no	—
689	C₄×C₅₃	—	4	1	no	—
690	C₄×C₅₃	—	4	1	no	—
691	C₄×C₅₃	—	4	1	no	—
692	C₄×C₅₃	—	4	1	no	—
693	C₄×C₅₃	—	4	1	no	—
694	C₄×C₅₃	—	4	1	no	—
695	C₄×C₅₃	—	4	1	no	—
696	C₄×C₅₃	#546	1	2	yes	—
697	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
698	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
699	Dic₅₃	—	4	2	no	—
700	Dic₅₃	—	4	2	no	—
701	#3475	D₅₃	1	1	yes	characteristic, complemented
702	C₂×#546	—	53	1	no	—
703	#3323	—	53	2	no	—
704	#3322	—	53	2	no	—
705	#3319	—	53	2	no	—
706	#3314	—	53	2	no	—
707	#3311	—	53	2	no	—
708	#3306	—	53	2	no	—
709	#3297	—	53	2	no	—
710	#3296	—	53	2	no	—
711	#3140	—	53	1	no	—
712	#3095	—	53	1	no	—
713	#3094	—	53	1	no	—
714	#3077	—	53	1	no	—
715	#3056	—	53	1	no	—
716	#3055	—	53	1	no	—
717	#3040	—	53	1	no	—
718	#3005	—	53	1	no	—
719	#3003	—	53	1	no	—
720	C₄×AGL(1,ℤ/8)	—	53	1	no	—
721	D₄×M₁₆	—	53	1	no	—
722	#2896	—	53	1	no	—
723	C₂×#418	—	53	1	no	—
724	C₂×C₅₃	—	2	2	no	—
725	C₂×C₅₃	—	2	2	no	—
726	C₂×C₅₃	—	4	1	no	—
727	C₂×C₅₃	—	4	1	no	—
728	C₂×C₅₃	—	4	1	no	—
729	C₂×C₅₃	—	8	1	no	—
730	C₂×C₅₃	C₂×#546	1	1	yes	characteristic
731	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
732	C₂×C₅₃	#3585	1	1	yes	characteristic
733	D₅₃	—	4	4	no	—
734	D₅₃	—	8	2	no	—
735	C₂²×#41	—	53	1	no	—
736	C₂³×D₄	—	53	1	no	—
737	C₂×#137	—	53	1	no	—
738	C₂×AGL(1,ℤ/8)	—	53	1	no	—
739	C₂×AGL(1,ℤ/8)	—	53	1	no	—
740	C₂²×M₁₆	—	53	1	no	—
741	C₂²×M₁₆	—	53	1	no	—
742	#556	C₂×D₅₃	1	1	yes	characteristic, complemented
743	#555	C₂×D₅₃	1	1	yes	characteristic, complemented
744	#554	C₂×D₅₃	1	1	yes	characteristic, complemented
745	#553	C₂×D₅₃	1	1	yes	characteristic, complemented
746	#553	C₂×D₅₃	1	1	yes	characteristic, complemented
747	#552	—	2	1	no	—
748	#552	C₂×D₅₃	1	1	yes	characteristic, complemented
749	#552	C₂×D₅₃	1	1	yes	characteristic, complemented
750	#551	—	2	1	no	—
751	#551	—	2	1	no	—
752	#547	C₂×D₅₃	1	1	yes	characteristic, complemented
753	#546	—	2	1	no	—
754	#546	—	53	2	no	—
755	#546	—	53	2	no	—
756	#546	—	53	2	no	—
757	#546	—	53	2	no	—
758	#546	—	106	1	no	—
759	#546	—	106	1	no	—
760	#546	—	106	1	no	—
761	#546	—	106	1	no	—
762	#533	C₂×D₅₃	1	1	yes	characteristic, complemented
763	#529	—	2	1	no	—
764	#529	—	2	1	no	—
765	#529	—	2	1	no	—
766	C₂×#124	—	53	1	no	—
767	#525	C₂×D₅₃	1	1	yes	characteristic
768	#525	C₂×D₅₃	1	1	yes	characteristic, complemented
769	C₂×#123	—	106	1	no	—
770	C₂×C₂²⋊Q₈	—	53	1	no	—
771	C₂×#121	—	53	1	no	—
772	C₂×#121	—	106	1	no	—
773	C₂×#120	—	106	1	no	—
774	C₄×#41	—	2	1	no	—
775	C₄×#41	C₂×D₅₃	1	1	yes	characteristic, complemented
776	C₂×C₄×D₄	—	53	1	no	—
777	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic
778	C₂×#117	C₂×D₅₃	1	1	yes	characteristic
779	C₂×#117	C₂×D₅₃	1	1	yes	characteristic, complemented
780	C₂²×C₂²⋊C₄	—	106	1	no	—
781	#489	—	53	2	no	—
782	#489	—	53	2	no	—
783	#488	—	53	2	no	—
784	#488	—	53	2	no	—
785	#485	—	53	2	no	—
786	#485	—	53	2	no	—
787	#484	—	53	2	no	—
788	#483	—	53	2	no	—
789	#482	—	53	2	no	—
790	#482	—	53	2	no	—
791	#481	—	53	2	no	—
792	#480	—	53	2	no	—
793	#478	—	53	2	no	—
794	#478	—	53	2	no	—
795	#476	—	53	2	no	—
796	#474	—	53	2	no	—
797	#470	—	53	2	no	—
798	#469	—	53	2	no	—
799	#468	—	53	2	no	—
800	#468	—	53	2	no	—
801	#467	—	53	2	no	—
802	#466	—	53	2	no	—
803	#465	—	53	2	no	—
804	#465	—	53	2	no	—
805	#464	—	53	2	no	—
806	#464	—	53	2	no	—
807	#463	—	53	2	no	—
808	#463	—	53	2	no	—
809	#452	—	53	2	no	—
810	#452	—	53	2	no	—
811	#450	—	53	2	no	—
812	#450	—	53	2	no	—
813	#449	—	53	2	no	—
814	#449	—	53	2	no	—
815	#447	—	53	2	no	—
816	#447	—	53	2	no	—
817	#442	—	53	2	no	—
818	#440	—	53	2	no	—
819	C₄×SD₁₆	—	53	2	no	—
820	C₄×D₈	—	53	2	no	—
821	#436	—	53	2	no	—
822	#435	—	53	2	no	—
823	#435	—	53	2	no	—
824	C₈×D₄	—	53	2	no	—
825	#428	—	53	1	no	—
826	#428	—	53	1	no	—
827	#428	—	53	1	no	—
828	#423	—	53	1	no	—
829	#419	—	53	1	no	—
830	#419	—	53	1	no	—
831	#419	—	53	1	no	—
832	#418	—	53	1	no	—
833	#418	—	53	1	no	—
834	#418	—	53	1	no	—
835	#418	—	53	1	no	—
836	#418	—	53	1	no	—
837	#418	—	53	1	no	—
838	#418	—	53	2	no	—
839	#418	—	53	2	no	—
840	#417	—	53	1	no	—
841	#417	—	53	2	no	—
842	#417	—	53	2	no	—
843	#416	—	53	2	no	—
844	#416	—	53	2	no	—
845	C₂×#102	—	53	2	no	—
846	C₂×#102	—	53	2	no	—
847	#407	—	53	1	no	—
848	#407	—	53	1	no	—
849	C₄×M₁₆	—	53	1	no	—
850	C₅₃	#61156	1	1	yes	characteristic, complemented, Sylow
851	C₂⁵	—	106	1	no	—
852	C₂×#41	—	2	1	no	—
853	C₂×#41	—	53	2	no	—
854	C₂×#41	—	53	2	no	—
855	C₂×#41	—	106	4	no	—
856	C₂×#41	—	106	1	no	—
857	C₂×#41	—	106	1	no	—
858	C₂×#41	—	212	2	no	—
859	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
860	C₂²×Q₈	—	53	1	no	—
861	C₂²×D₄	—	53	1	no	—
862	C₂²×D₄	—	53	1	no	—
863	C₂²×D₄	—	53	2	no	—
864	C₂²×D₄	—	53	2	no	—
865	C₂²×D₄	—	106	4	no	—
866	C₂²×D₄	—	106	1	no	—
867	C₂²×D₄	—	106	1	no	—
868	C₂²×D₄	—	106	1	no	—
869	C₂²×D₄	—	106	1	no	—
870	C₂²×D₄	—	106	1	no	—
871	C₂²×D₄	—	212	2	no	—
872	C₂²×D₄	C₂²⋊D₅₃	1	1	yes	characteristic
873	C₂³×C₄	—	106	1	no	—
874	C₂³×C₄	—	106	1	no	—
875	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
876	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
877	#137	—	212	2	no	—
878	AGL(1,ℤ/8)	—	106	4	no	—
879	AGL(1,ℤ/8)	—	212	2	no	—
880	C₂×Q₁₆	—	53	2	no	—
881	C₂×SD₁₆	—	53	2	no	—
882	C₂×SD₁₆	—	53	2	no	—
883	C₂×SD₁₆	—	53	2	no	—
884	C₂×D₈	—	53	2	no	—
885	C₂×D₈	—	53	2	no	—
886	C₂×M₁₆	—	53	1	no	—
887	C₂×M₁₆	—	53	1	no	—
888	C₂×M₁₆	—	53	1	no	—
889	C₂×M₁₆	—	53	1	no	—
890	C₂×M₁₆	—	53	2	no	—
891	C₂×M₁₆	—	53	2	no	—
892	C₂×M₁₆	—	212	2	no	—
893	C₂×M₁₆	—	212	2	no	—
894	C₂²×C₈	—	53	2	no	—
895	C₂²×C₈	—	53	2	no	—
896	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
897	C₄⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
898	#126	—	2	1	no	—
899	#126	—	2	1	no	—
900	#126	—	2	1	no	—
901	#126	—	2	1	no	—
902	#126	—	2	1	no	—
903	#126	—	2	1	no	—
904	#125	—	2	1	no	—
905	#125	—	2	1	no	—
906	#125	—	2	1	no	—
907	#125	C₂²×D₅₃	1	1	yes	characteristic, complemented
908	#125	C₂²×D₅₃	1	1	yes	characteristic, complemented
909	#124	—	2	1	no	—
910	#124	—	2	1	no	—
911	#124	—	2	1	no	—
912	#124	—	53	2	no	—
913	#124	—	53	2	no	—
914	#124	—	106	1	no	—
915	#124	—	106	1	no	—
916	#123	—	2	1	no	—
917	#123	—	2	1	no	—
918	#123	—	2	1	no	—
919	#123	—	2	1	no	—
920	#123	—	2	1	no	—
921	#123	—	2	1	no	—
922	#123	—	2	1	no	—
923	#123	—	2	1	no	—
924	#123	—	106	2	no	—
925	#123	—	106	2	no	—
926	#123	—	106	2	no	—
927	#123	—	106	2	no	—
928	C₂²⋊Q₈	—	2	1	no	—
929	C₂²⋊Q₈	—	2	1	no	—
930	C₂²⋊Q₈	—	2	1	no	—
931	C₂²⋊Q₈	—	2	1	no	—
932	C₂²⋊Q₈	—	2	1	no	—
933	C₂²⋊Q₈	—	53	2	no	—
934	C₂²⋊Q₈	—	53	2	no	—
935	C₂²⋊Q₈	—	106	1	no	—
936	C₂²⋊Q₈	—	106	1	no	—
937	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
938	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic
939	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
940	C₂²⋊Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
941	#121	—	2	1	no	—
942	#121	—	2	1	no	—
943	#121	—	2	1	no	—
944	#121	—	53	2	no	—
945	#121	—	53	2	no	—
946	#121	—	106	1	no	—
947	#121	—	106	1	no	—
948	#121	—	106	2	no	—
949	#121	—	106	2	no	—
950	#121	—	106	2	no	—
951	#121	—	106	2	no	—
952	#121	C₂²×D₅₃	1	1	yes	characteristic
953	#121	C₂²×D₅₃	1	1	yes	characteristic
954	#121	C₂²×D₅₃	1	1	yes	characteristic, complemented
955	#121	C₂²×D₅₃	1	1	yes	characteristic, complemented
956	#120	—	2	1	no	—
957	#120	—	2	1	no	—
958	#120	—	106	2	no	—
959	#120	—	106	2	no	—
960	#120	—	106	2	no	—
961	#120	—	106	2	no	—
962	C₄×Q₈	—	2	1	no	—
963	C₄×Q₈	—	2	1	no	—
964	C₄×Q₈	—	2	1	no	—
965	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
966	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
967	C₄×D₄	—	2	1	no	—
968	C₄×D₄	—	2	1	no	—
969	C₄×D₄	—	2	1	no	—
970	C₄×D₄	—	2	1	no	—
971	C₄×D₄	—	2	1	no	—
972	C₄×D₄	—	2	1	no	—
973	C₄×D₄	—	2	1	no	—
974	C₄×D₄	—	2	1	no	—
975	C₄×D₄	—	2	1	no	—
976	C₄×D₄	—	53	2	no	—
977	C₄×D₄	—	53	2	no	—
978	C₄×D₄	—	106	1	no	—
979	C₄×D₄	—	106	1	no	—
980	C₄×D₄	C₂²⋊D₅₃	1	1	yes	characteristic
981	C₄×D₄	C₂²⋊D₅₃	1	1	yes	characteristic
982	C₄×D₄	C₂²⋊D₅₃	1	1	yes	characteristic
983	C₄×D₄	C₂²⋊D₅₃	1	1	yes	characteristic
984	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
985	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
986	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
987	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
988	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
989	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
990	#117	—	2	1	no	—
991	#117	—	2	1	no	—
992	#117	—	2	1	no	—
993	#117	—	2	1	no	—
994	#117	—	2	1	no	—
995	#117	—	2	1	no	—
996	#117	—	2	1	no	—
997	#117	—	2	1	no	—
998	#117	C₂²×D₅₃	1	1	yes	characteristic
999	#117	C₂²×D₅₃	1	1	yes	characteristic
1000	#117	C₂²×D₅₃	1	1	yes	characteristic
1001	#117	C₂²×D₅₃	1	1	yes	characteristic
1002	#117	C₂²×D₅₃	1	1	yes	characteristic
1003	#117	C₂²×D₅₃	1	1	yes	characteristic, complemented
1004	#117	C₂²×D₅₃	1	1	yes	characteristic, complemented
1005	C₂×C₄⋊C₄	—	53	1	no	—
1006	C₂×C₄⋊C₄	—	106	1	no	—
1007	C₂×C₄⋊C₄	C₂²⋊D₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1011	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1012	C₂×C₂²⋊C₄	—	2	1	no	—
1013	C₂×C₂²⋊C₄	—	2	1	no	—
1014	C₂×C₂²⋊C₄	—	106	1	no	—
1015	C₂×C₂²⋊C₄	—	106	1	no	—
1016	C₂×C₂²⋊C₄	—	106	1	no	—
1017	C₂×C₂²⋊C₄	—	106	1	no	—
1018	C₂×C₂²⋊C₄	—	106	1	no	—
1019	C₂×C₂²⋊C₄	—	106	2	no	—
1020	C₂×C₂²⋊C₄	—	106	2	no	—
1021	C₂×C₂²⋊C₄	—	106	2	no	—
1022	C₂×C₂²⋊C₄	—	106	2	no	—
1023	C₂×C₂²⋊C₄	C₂²⋊D₅₃	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂²⋊D₅₃	1	1	yes	characteristic
1025	C₂×C₄²	—	2	1	no	—
1026	C₂×C₄²	—	2	1	no	—
1027	C₂×C₄²	—	2	1	no	—
1028	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1029	#107	—	53	2	no	—
1030	#107	—	53	2	no	—
1031	#107	—	53	2	no	—
1032	#106	—	53	2	no	—
1033	#106	—	53	2	no	—
1034	#106	—	53	2	no	—
1035	C₄⋊C₈	—	53	2	no	—
1036	C₄⋊C₈	—	53	2	no	—
1037	#103	—	53	2	no	—
1038	#103	—	53	2	no	—
1039	#103	—	53	2	no	—
1040	#103	—	53	2	no	—
1041	#103	—	53	2	no	—
1042	#103	—	53	2	no	—
1043	#103	—	53	2	no	—
1044	#102	—	53	2	no	—
1045	#102	—	53	2	no	—
1046	#102	—	53	2	no	—
1047	#102	—	53	2	no	—
1048	#102	—	53	2	no	—
1049	#102	—	53	2	no	—
1050	#102	—	53	2	no	—
1051	#102	—	53	2	no	—
1052	#102	—	53	2	no	—
1053	#102	—	53	2	no	—
1054	#102	—	53	2	no	—
1055	#102	—	53	2	no	—
1056	#102	—	53	2	no	—
1057	C₂²⋊C₈	—	53	2	no	—
1058	C₂²⋊C₈	—	53	2	no	—
1059	C₂²⋊C₈	—	53	2	no	—
1060	C₂²⋊C₈	—	53	2	no	—
1061	#97	—	53	2	no	—
1062	C₄×C₈	—	53	2	no	—
1063	C₂⁴	—	106	1	no	—
1064	C₂⁴	—	106	2	no	—
1065	C₂⁴	—	106	2	no	—
1066	C₂⁴	—	106	1	no	—
1067	C₂⁴	—	424	2	no	—
1068	C₂⁴	—	212	4	no	—
1069	C₂⁴	—	212	4	no	—
1070	C₂⁴	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1071	C₂⁴	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1072	#41	—	2	2	no	—
1073	#41	—	2	2	no	—
1074	#41	—	4	4	no	—
1075	#41	—	106	4	no	—
1076	#41	—	106	4	no	—
1077	#41	—	212	2	no	—
1078	#41	—	212	2	no	—
1079	#41	—	212	4	no	—
1080	#41	—	212	4	no	—
1081	C₂×Q₈	—	2	1	no	—
1082	C₂×Q₈	—	2	1	no	—
1083	C₂×Q₈	—	53	2	no	—
1084	C₂×Q₈	—	106	1	no	—
1085	C₂×Q₈	—	106	2	no	—
1086	C₂×Q₈	—	106	2	no	—
1087	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
1088	C₂×D₄	—	2	1	no	—
1089	C₂×D₄	—	2	1	no	—
1090	C₂×D₄	—	2	1	no	—
1091	C₂×D₄	—	2	1	no	—
1092	C₂×D₄	—	2	1	no	—
1093	C₂×D₄	—	4	2	no	—
1094	C₂×D₄	—	53	4	no	—
1095	C₂×D₄	—	53	2	no	—
1096	C₂×D₄	—	53	2	no	—
1097	C₂×D₄	—	106	4	no	—
1098	C₂×D₄	—	106	4	no	—
1099	C₂×D₄	—	106	2	no	—
1100	C₂×D₄	—	106	2	no	—
1101	C₂×D₄	—	106	2	no	—
1102	C₂×D₄	—	106	2	no	—
1103	C₂×D₄	—	106	1	no	—
1104	C₂×D₄	—	106	2	no	—
1105	C₂×D₄	—	106	2	no	—
1106	C₂×D₄	—	106	1	no	—
1107	C₂×D₄	—	106	2	no	—
1108	C₂×D₄	—	106	2	no	—
1109	C₂×D₄	—	106	2	no	—
1110	C₂×D₄	—	424	2	no	—
1111	C₂×D₄	—	212	2	no	—
1112	C₂×D₄	—	212	2	no	—
1113	C₂×D₄	—	212	4	no	—
1114	C₂×D₄	—	212	4	no	—
1115	C₂×D₄	—	212	4	no	—
1116	C₂×D₄	—	212	4	no	—
1117	C₂×D₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1118	C₂×D₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1119	C₂×D₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1120	C₂×D₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1121	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1122	C₂²×C₄	—	2	2	no	—
1123	C₂²×C₄	—	2	2	no	—
1124	C₂²×C₄	—	2	2	no	—
1125	C₂²×C₄	—	2	2	no	—
1126	C₂²×C₄	—	2	1	no	—
1127	C₂²×C₄	—	2	1	no	—
1128	C₂²×C₄	—	2	1	no	—
1129	C₂²×C₄	—	2	1	no	—
1130	C₂²×C₄	—	2	1	no	—
1131	C₂²×C₄	—	2	1	no	—
1132	C₂²×C₄	—	2	1	no	—
1133	C₂²×C₄	—	106	1	no	—
1134	C₂²×C₄	—	106	1	no	—
1135	C₂²×C₄	—	106	2	no	—
1136	C₂²×C₄	—	106	2	no	—
1137	C₂²×C₄	—	106	2	no	—
1138	C₂²×C₄	—	106	2	no	—
1139	C₂²×C₄	—	424	2	no	—
1140	C₂²×C₄	—	212	4	no	—
1141	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1143	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1147	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1148	C₂²×C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1150	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1151	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1152	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1153	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1154	Q₁₆	—	212	2	no	—
1155	SD₁₆	—	106	4	no	—
1156	SD₁₆	—	212	2	no	—
1157	SD₁₆	—	212	2	no	—
1158	D₈	—	106	4	no	—
1159	D₈	—	212	2	no	—
1160	M₁₆	—	106	2	no	—
1161	M₁₆	—	106	2	no	—
1162	M₁₆	—	106	2	no	—
1163	M₁₆	—	106	2	no	—
1164	M₁₆	—	212	2	no	—
1165	M₁₆	—	212	2	no	—
1166	C₂×C₈	—	53	2	no	—
1167	C₂×C₈	—	53	2	no	—
1168	C₂×C₈	—	53	2	no	—
1169	C₂×C₈	—	53	2	no	—
1170	C₂×C₈	—	212	2	no	—
1171	C₂×C₈	—	212	2	no	—
1172	C₄⋊C₄	—	2	1	no	—
1173	C₄⋊C₄	—	2	1	no	—
1174	C₄⋊C₄	—	2	1	no	—
1175	C₄⋊C₄	—	2	1	no	—
1176	C₄⋊C₄	—	2	1	no	—
1177	C₄⋊C₄	—	2	1	no	—
1178	C₄⋊C₄	—	2	1	no	—
1179	C₄⋊C₄	—	2	1	no	—
1180	C₄⋊C₄	—	2	1	no	—
1181	C₄⋊C₄	—	2	1	no	—
1182	C₄⋊C₄	—	2	1	no	—
1183	C₄⋊C₄	—	2	1	no	—
1184	C₄⋊C₄	—	2	1	no	—
1185	C₄⋊C₄	—	2	1	no	—
1186	C₄⋊C₄	—	2	1	no	—
1187	C₄⋊C₄	—	2	1	no	—
1188	C₄⋊C₄	—	53	2	no	—
1189	C₄⋊C₄	—	106	1	no	—
1190	C₄⋊C₄	—	106	2	no	—
1191	C₄⋊C₄	—	106	2	no	—
1192	C₄⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1193	C₄⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1194	C₄⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1195	C₄⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1196	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1197	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1198	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1199	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1200	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1201	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1202	C₂²⋊C₄	—	2	1	no	—
1203	C₂²⋊C₄	—	2	1	no	—
1204	C₂²⋊C₄	—	2	1	no	—
1205	C₂²⋊C₄	—	2	1	no	—
1206	C₂²⋊C₄	—	2	1	no	—
1207	C₂²⋊C₄	—	2	1	no	—
1208	C₂²⋊C₄	—	2	1	no	—
1209	C₂²⋊C₄	—	2	1	no	—
1210	C₂²⋊C₄	—	2	1	no	—
1211	C₂²⋊C₄	—	2	1	no	—
1212	C₂²⋊C₄	—	2	1	no	—
1213	C₂²⋊C₄	—	2	1	no	—
1214	C₂²⋊C₄	—	2	1	no	—
1215	C₂²⋊C₄	—	2	1	no	—
1216	C₂²⋊C₄	—	2	1	no	—
1217	C₂²⋊C₄	—	2	1	no	—
1218	C₂²⋊C₄	—	2	1	no	—
1219	C₂²⋊C₄	—	106	2	no	—
1220	C₂²⋊C₄	—	106	2	no	—
1221	C₂²⋊C₄	—	106	2	no	—
1222	C₂²⋊C₄	—	106	2	no	—
1223	C₂²⋊C₄	—	106	2	no	—
1224	C₂²⋊C₄	—	106	2	no	—
1225	C₂²⋊C₄	—	106	2	no	—
1226	C₂²⋊C₄	—	106	2	no	—
1227	C₂²⋊C₄	—	106	2	no	—
1228	C₂²⋊C₄	—	106	2	no	—
1229	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1230	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1231	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1232	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1233	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1234	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1235	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1236	C₂²⋊C₄	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1237	C₄²	—	2	1	no	—
1238	C₄²	—	2	1	no	—
1239	C₄²	—	2	1	no	—
1240	C₄²	—	2	1	no	—
1241	C₄²	—	2	1	no	—
1242	C₄²	—	2	1	no	—
1243	C₄²	—	2	1	no	—
1244	C₄²	—	2	1	no	—
1245	C₄²	—	2	1	no	—
1246	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1247	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
1248	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1249	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1250	C₂³	—	2	2	no	—
1251	C₂³	—	2	2	no	—
1252	C₂³	—	2	2	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	4	1	no	—
1255	C₂³	—	4	1	no	—
1256	C₂³	—	4	1	no	—
1257	C₂³	—	106	2	no	—
1258	C₂³	—	106	4	no	—
1259	C₂³	—	106	2	no	—
1260	C₂³	—	424	2	no	—
1261	C₂³	—	424	2	no	—
1262	C₂³	—	424	16	no	—
1263	C₂³	—	212	4	no	—
1264	C₂³	—	212	4	no	—
1265	C₂³	—	212	2	no	—
1266	C₂³	—	212	2	no	—
1267	C₂³	—	212	4	no	—
1268	C₂³	—	212	2	no	—
1269	C₂³	—	212	2	no	—
1270	C₂³	—	212	4	no	—
1271	C₂³	—	212	2	no	—
1272	C₂³	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1273	C₂³	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1274	C₂³	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1275	C₂³	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1276	C₂³	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1277	Q₈	—	2	1	no	—
1278	Q₈	—	2	1	no	—
1279	Q₈	—	4	2	no	—
1280	Q₈	—	8	1	no	—
1281	Q₈	—	106	2	no	—
1282	Q₈	—	106	2	no	—
1283	Q₈	—	212	2	no	—
1284	D₄	—	2	2	no	—
1285	D₄	—	2	2	no	—
1286	D₄	—	2	1	no	—
1287	D₄	—	2	1	no	—
1288	D₄	—	4	1	no	—
1289	D₄	—	4	1	no	—
1290	D₄	—	4	2	no	—
1291	D₄	—	4	2	no	—
1292	D₄	—	4	2	no	—
1293	D₄	—	8	1	no	—
1294	D₄	—	8	1	no	—
1295	D₄	—	53	4	no	—
1296	D₄	—	106	2	no	—
1297	D₄	—	106	2	no	—
1298	D₄	—	106	2	no	—
1299	D₄	—	106	4	no	—
1300	D₄	—	424	2	no	—
1301	D₄	—	424	2	no	—
1302	D₄	—	212	4	no	—
1303	D₄	—	212	4	no	—
1304	D₄	—	212	4	no	—
1305	D₄	—	212	4	no	—
1306	D₄	—	212	2	no	—
1307	C₂×C₄	—	2	2	no	—
1308	C₂×C₄	—	2	2	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	2	no	—
1318	C₂×C₄	—	2	2	no	—
1319	C₂×C₄	—	2	2	no	—
1320	C₂×C₄	—	2	2	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	4	1	no	—
1329	C₂×C₄	—	4	1	no	—
1330	C₂×C₄	—	4	2	no	—
1331	C₂×C₄	—	4	2	no	—
1332	C₂×C₄	—	4	2	no	—
1333	C₂×C₄	—	4	2	no	—
1334	C₂×C₄	—	8	1	no	—
1335	C₂×C₄	—	8	1	no	—
1336	C₂×C₄	—	8	1	no	—
1337	C₂×C₄	—	106	2	no	—
1338	C₂×C₄	—	106	2	no	—
1339	C₂×C₄	—	424	2	no	—
1340	C₂×C₄	—	424	2	no	—
1341	C₂×C₄	—	212	4	no	—
1342	C₂×C₄	—	212	4	no	—
1343	C₂×C₄	—	212	2	no	—
1344	C₂×C₄	—	212	2	no	—
1345	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1346	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1347	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1348	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1349	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1350	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1351	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1352	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1353	C₂×C₄	C₂²×C₂²⋊D₅₃	1	1	yes	characteristic
1354	C₂×C₄	#41×D₅₃	1	2	yes	—
1355	C₂×C₄	#13133263	1	2	yes	—
1356	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1357	C₈	—	106	2	no	—
1358	C₈	—	106	2	no	—
1359	C₈	—	106	2	no	—
1360	C₈	—	106	2	no	—
1361	C₂²	—	2	1	no	—
1362	C₂²	—	2	1	no	—
1363	C₂²	—	2	1	no	—
1364	C₂²	—	2	1	no	—
1365	C₂²	—	2	1	no	—
1366	C₂²	—	2	1	no	—
1367	C₂²	—	2	1	no	—
1368	C₂²	—	2	1	no	—
1369	C₂²	—	2	1	no	—
1370	C₂²	—	2	1	no	—
1371	C₂²	—	2	1	no	—
1372	C₂²	—	2	1	no	—
1373	C₂²	—	2	1	no	—
1374	C₂²	—	4	4	no	—
1375	C₂²	—	4	1	no	—
1376	C₂²	—	4	1	no	—
1377	C₂²	—	4	1	no	—
1378	C₂²	—	8	2	no	—
1379	C₂²	—	106	4	no	—
1380	C₂²	—	424	4	no	—
1381	C₂²	—	424	8	no	—
1382	C₂²	—	424	8	no	—
1383	C₂²	—	212	8	no	—
1384	C₂²	—	212	2	no	—
1385	C₂²	—	212	2	no	—
1386	C₂²	—	212	2	no	—
1387	C₂²	—	212	2	no	—
1388	C₂²	—	212	2	no	—
1389	C₂²	#16811261	1	2	yes	—
1390	C₂²	#16811421	1	2	yes	—
1391	C₂²	C₂³×C₂²⋊D₅₃	1	1	yes	characteristic
1392	C₄	—	2	1	no	—
1393	C₄	—	2	1	no	—
1394	C₄	—	2	1	no	—
1395	C₄	—	2	1	no	—
1396	C₄	—	2	1	no	—
1397	C₄	—	2	1	no	—
1398	C₄	—	2	1	no	—
1399	C₄	—	2	1	no	—
1400	C₄	—	4	1	no	—
1401	C₄	—	4	1	no	—
1402	C₄	—	4	1	no	—
1403	C₄	—	4	1	no	—
1404	C₄	—	4	1	no	—
1405	C₄	—	4	1	no	—
1406	C₄	—	4	1	no	—
1407	C₄	—	212	2	no	—
1408	C₄	—	212	2	no	—
1409	C₄	#16811261	1	2	yes	—
1410	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1411	C₄	C₂×#13133263	1	1	yes	characteristic
1412	C₂	—	2	2	no	—
1413	C₂	—	2	2	no	—
1414	C₂	—	4	1	no	—
1415	C₂	—	4	1	no	—
1416	C₂	—	4	1	no	—
1417	C₂	—	8	1	no	—
1418	C₂	—	424	2	no	—
1419	C₂	—	212	4	no	—
1420	C₂	C₂×#16811261	1	1	yes	characteristic
1421	C₂	C₂×#16811421	1	1	yes	characteristic
1422	C₂	#20289494	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3475	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3475	D₅₃
hypocenter	C₅₃	#61156
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄×D₄ ◁ #3475

Complements

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

N	H ≅ G/N	type
1. C₂×#16811269	C₂	semidirect
2. #20286925	C₂	semidirect
3. #20286910	C₂	semidirect
4. #20286865	C₂	semidirect
5. #20286790	C₂	semidirect
6. #20286745	C₂	semidirect
7. #20286670	C₂	semidirect
8. #20286559	C₂	semidirect
9. #20286544	C₂	semidirect
10. #20285104	C₂	semidirect
11. #20284663	C₂	semidirect
12. #20284655	C₂	semidirect
13. #20284508	C₂	semidirect
14. #20284347	C₂	semidirect
15. #20284336	C₂	semidirect
16. #20284209	C₂	semidirect
17. #20283955	C₂	semidirect
18. #20283941	C₂	semidirect
19. C₄×#13133242	C₂	semidirect
20. D₄×#11719917	C₂	semidirect
21. #20283232	C₂	semidirect
22. C₂×#16810627	C₂	semidirect
23. C₅₃×#3475	C₂	semidirect
26. C₂×#13133247	C₂²	semidirect
30. C₂²×#11719917	C₂²	semidirect
47. #16810985	C₂²	semidirect
48. #16810985	C₂²	semidirect
49. #16810980	C₂²	semidirect
50. #16810980	C₂²	semidirect
51. #16810964	C₂²	semidirect
52. #16810964	C₂²	semidirect
53. #16810958	C₂²	semidirect
54. #16810953	C₂²	semidirect
55. #16810947	C₂²	semidirect
56. #16810947	C₂²	semidirect
57. #16810941	C₂²	semidirect
58. #16810936	C₂²	semidirect
59. #16810920	C₂²	semidirect
60. #16810920	C₂²	semidirect
61. #16810910	C₂²	semidirect
62. #16810900	C₂²	semidirect
63. #16810879	C₂²	semidirect
64. #16810874	C₂²	semidirect
65. #16810871	C₂²	semidirect
66. #16810867	C₂²	semidirect
67. #16810862	C₂²	semidirect
68. #16810857	C₂²	semidirect
69. #16810854	C₂²	semidirect
70. #16810850	C₂²	semidirect
71. #16810845	C₂²	semidirect
72. #16810845	C₂²	semidirect
73. #16810838	C₂²	semidirect
74. #16810838	C₂²	semidirect
75. #16810783	C₂²	semidirect
76. #16810783	C₂²	semidirect
77. #16810773	C₂²	semidirect
78. #16810773	C₂²	semidirect
79. #16810766	C₂²	semidirect
80. #16810766	C₂²	semidirect
81. #16810756	C₂²	semidirect
82. #16810756	C₂²	semidirect
83. #16810733	C₂²	semidirect
84. #16810721	C₂²	semidirect
85. C₄×#11719924	C₂²	semidirect
86. C₄×#11719922	C₂²	semidirect
87. #16810701	C₂²	semidirect
88. #16810695	C₂²	semidirect
89. #16810695	C₂²	semidirect
90. D₄×#88322	C₂²	semidirect
91. #16810666	C₂²	semidirect
92. #16810666	C₂²	semidirect
93. #16810666	C₂²	semidirect
94. #16810647	C₂²	semidirect
95. #16810631	C₂²	semidirect
96. #16810631	C₂²	semidirect
97. #16810631	C₂²	semidirect
104. #16810627	C₂²	semidirect
105. #16810627	C₂²	semidirect
106. #16810624	C₂²	semidirect
107. #16810622	C₂²	semidirect
108. #16810622	C₂²	semidirect
109. #16810617	C₂²	semidirect
110. #16810617	C₂²	semidirect
111. C₂×#13133137	C₂²	semidirect
112. C₂×#13133137	C₂²	semidirect
114. #16810587	C₂²	semidirect
115. C₄×#11719917	C₂²	semidirect
116. C₅₃×#556	C₂²	semidirect
117. C₅₃×#555	C₂²	semidirect
118. C₅₃×#554	C₂²	semidirect
119. C₅₃×#553	C₂²	semidirect
120. C₅₃×#553	C₂²	semidirect
122. C₅₃×#552	C₂²	semidirect
123. C₅₃×#552	C₂²	semidirect
126. C₅₃×#547	C₂²	semidirect
128. C₅₃×#533	C₂²	semidirect
133. C₅₃×#525	C₂²	semidirect
135. C₄×#41×C₅₃	C₂²	semidirect
138. C₂×#117×C₅₃	C₂²	semidirect
163. C₂×#11719925	C₂³	semidirect
164. C₂×#11719923	C₂³	semidirect
176. C₂×#11719917	C₂³	semidirect
178. C₂²×#88322	C₂³	semidirect
218. #13133150	C₂³	semidirect
219. #13133150	C₂³	semidirect
220. #13133150	C₂³	semidirect
221. #13133148	C₂³	semidirect
222. #13133148	C₂³	semidirect
223. #13133148	C₂³	semidirect
224. C₄⋊#88322	C₂³	semidirect
225. C₄⋊#88322	C₂³	semidirect
226. #13133141	C₂³	semidirect
227. #13133140	C₂³	semidirect
228. #13133140	C₂³	semidirect
229. #13133140	C₂³	semidirect
230. #13133140	C₂³	semidirect
231. #13133140	C₂³	semidirect
232. #13133140	C₂³	semidirect
233. #13133138	C₂³	semidirect
248. C₂²⋊#88322	C₂³	semidirect
249. C₂²⋊#88322	C₂³	semidirect
250. #13133128	C₂³	semidirect
251. C₄×#88322	C₂³	semidirect
257. C₄⋊Q₈×C₅₃	C₂³	semidirect
258. C₄⋊Q₈×C₅₃	C₂³	semidirect
268. #125×C₅₃	C₂³	semidirect
269. #125×C₅₃	C₂³	semidirect
288. C₂²⋊Q₈×C₅₃	C₂³	semidirect
289. C₂²⋊Q₈×C₅₃	C₂³	semidirect
295. #121×C₅₃	C₂³	semidirect
296. #121×C₅₃	C₂³	semidirect
302. C₄×Q₈×C₅₃	C₂³	semidirect
303. C₄×Q₈×C₅₃	C₂³	semidirect
321. C₄×D₄×C₅₃	C₂³	semidirect
322. C₄×D₄×C₅₃	C₂³	semidirect
336. #117×C₅₃	C₂³	semidirect
337. #117×C₅₃	C₂³	semidirect
341. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
342. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
429. C₂×D₂₁₂	#41	semidirect
701. #3475	D₅₃	semidirect
742. #556	C₂×D₅₃	semidirect
743. #555	C₂×D₅₃	semidirect
744. #554	C₂×D₅₃	semidirect
745. #553	C₂×D₅₃	semidirect
746. #553	C₂×D₅₃	semidirect
748. #552	C₂×D₅₃	semidirect
749. #552	C₂×D₅₃	semidirect
752. #547	C₂×D₅₃	semidirect
762. #533	C₂×D₅₃	semidirect
768. #525	C₂×D₅₃	semidirect
775. C₄×#41	C₂×D₅₃	semidirect
779. C₂×#117	C₂×D₅₃	semidirect
850. C₅₃	#61156	semidirect
896. C₄⋊Q₈	C₂²×D₅₃	semidirect
897. C₄⋊Q₈	C₂²×D₅₃	semidirect
907. #125	C₂²×D₅₃	semidirect
908. #125	C₂²×D₅₃	semidirect
939. C₂²⋊Q₈	C₂²×D₅₃	semidirect
940. C₂²⋊Q₈	C₂²×D₅₃	semidirect
954. #121	C₂²×D₅₃	semidirect
955. #121	C₂²×D₅₃	semidirect
965. C₄×Q₈	C₂²×D₅₃	semidirect
966. C₄×Q₈	C₂²×D₅₃	semidirect
988. C₄×D₄	C₂²×D₅₃	semidirect
989. C₄×D₄	C₂²×D₅₃	semidirect
1003. #117	C₂²×D₅₃	semidirect
1004. #117	C₂²×D₅₃	semidirect
1010. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1011. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16811269	2
#20286925	2
#20286910	2
#20286865	2
#20286790	2
#20286745	2
#20286670	2
#20286559	2
#20286544	2
#20285104	2
#20284663	2
#20284655	2
#20284508	2
#20284347	2
#20284336	2
#20284209	2
#20283955	2
#20283941	2
C₄×#13133242	2
D₄×#11719917	2
#20283232	2
C₂×#16810627	2
C₅₃×#3475	2
#61156	53