Subgroups — #28248678

Order 13568.

1952 conjugacy classes of subgroups.

The subgroup lattice has 1406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288008	C₂	1	1	yes	maximal, characteristic
2	#20283733	C₂	1	1	yes	maximal, characteristic, complemented
3	#20283732	C₂	1	1	yes	maximal, characteristic, complemented
4	#20283729	C₂	1	1	yes	maximal, characteristic, complemented
5	#20283726	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283726	C₂	1	1	yes	maximal, characteristic, complemented
7	#20283724	C₂	1	1	yes	maximal, characteristic, complemented
8	#20283724	C₂	1	1	yes	maximal, characteristic, complemented
9	#20283699	C₂	1	2	yes	maximal, complemented
10	#20283697	C₂	1	2	yes	maximal, complemented
11	#20283685	C₂	1	2	yes	maximal, complemented
12	#20283683	C₂	1	2	yes	maximal, complemented
13	#20283660	C₂	1	2	yes	maximal, complemented
14	#20283456	C₂	1	2	yes	maximal, complemented
15	#20283441	C₂	1	2	yes	maximal, complemented
16	#20283435	C₂	1	2	yes	maximal, complemented
17	#20283361	C₂	1	1	yes	maximal, characteristic, complemented
18	#20283361	C₂	1	1	yes	maximal, characteristic, complemented
19	#432×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283144	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283140	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#16810575	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2970	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133225	C₂²	1	2	yes	—
25	C₂×#13133223	C₂²	1	2	yes	—
26	C₂²×#11719912	C₂²	1	2	yes	—
27	#16811177	C₄	1	1	yes	characteristic
28	#16811177	C₂²	1	1	yes	characteristic
29	#16811176	C₄	1	1	yes	characteristic
30	#16811170	C₄	1	1	yes	characteristic
31	#16811170	C₂²	1	1	yes	characteristic
32	#16811169	C₄	1	1	yes	characteristic
33	#16811160	C₄	1	1	yes	characteristic
34	#16811160	C₂²	1	1	yes	characteristic
35	#16811155	C₄	1	1	yes	characteristic
36	#16811155	C₂²	1	1	yes	characteristic
37	#16811153	C₄	1	1	yes	characteristic
38	#16811153	C₄	1	1	yes	characteristic
39	#16811153	C₂²	1	1	yes	characteristic
40	#16811153	C₂²	1	1	yes	characteristic
41	#16811151	C₄	1	1	yes	characteristic
42	#16811151	C₄	1	1	yes	characteristic
43	#16811151	C₄	1	1	yes	characteristic
44	#16811151	C₄	1	1	yes	characteristic
45	#16811135	C₄	1	1	yes	characteristic
46	#16811132	C₄	1	1	yes	characteristic
47	#16811132	C₄	1	1	yes	characteristic
48	#16811132	C₂²	1	1	yes	characteristic
49	#16811132	C₂²	1	1	yes	characteristic
50	#16811130	C₄	1	1	yes	characteristic
51	C₄×#11719945	C₂²	1	1	yes	characteristic
52	C₄×#11719945	C₂²	1	1	yes	characteristic
53	C₄×#11719945	C₂²	1	1	yes	characteristic
54	C₄×#11719945	C₂²	1	1	yes	characteristic
55	C₄×#11719945	C₂²	1	1	yes	characteristic
56	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
57	#16810754	C₂²	1	2	yes	complemented
58	#16810752	C₂²	1	2	yes	complemented
59	#16810752	C₂²	1	2	yes	complemented
60	#16810751	C₂²	1	2	yes	complemented
61	#16810751	C₂²	1	2	yes	complemented
62	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
63	#16810747	C₂²	1	2	yes	complemented
64	#16810702	C₂²	1	2	yes	—
65	#16810700	C₂²	1	2	yes	—
66	#16810699	C₂²	1	2	yes	—
67	#16810699	C₂²	1	2	yes	complemented
68	#16810698	C₂²	1	2	yes	—
69	#16810698	C₂²	1	2	yes	complemented
70	#16810696	C₂²	1	2	yes	—
71	#16810696	C₂²	1	2	yes	complemented
72	#16810695	C₂²	1	2	yes	—
73	#16810695	C₂²	1	2	yes	complemented
74	#16810694	C₂²	1	2	yes	—
75	#16810694	C₂²	1	2	yes	—
76	#16810693	C₂²	1	2	yes	—
77	#16810693	C₂²	1	2	yes	complemented
78	#16810691	C₂²	1	2	yes	—
79	#16810691	C₂²	1	2	yes	—
80	D₄×#88322	C₂²	1	2	yes	—
81	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
82	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
83	#16810686	C₂²	1	2	yes	—
84	#16810686	C₂²	1	2	yes	complemented
85	#16810683	C₂²	1	2	yes	complemented
86	#16810683	C₂²	1	2	yes	complemented
87	#16810681	C₂²	1	2	yes	complemented
88	#16810681	C₂²	1	2	yes	complemented
89	#16810680	C₂²	1	1	yes	characteristic
90	#16810680	C₂²	1	1	yes	characteristic, complemented
91	#16810680	C₂²	1	1	yes	characteristic, complemented
92	#16810679	C₂²	1	2	yes	—
93	#16810678	C₂²	1	1	yes	characteristic
94	#16810678	C₂²	1	1	yes	characteristic
95	#16810678	C₂²	1	1	yes	characteristic, complemented
96	#16810678	C₂²	1	1	yes	characteristic, complemented
97	#16810678	C₂²	1	1	yes	characteristic, complemented
98	#16810678	C₂²	1	1	yes	characteristic, complemented
99	#16810677	C₂²	1	2	yes	—
100	#16810648	C₂²	1	2	yes	—
101	#16810648	C₂²	1	2	yes	—
102	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
103	#16810588	C₂²	1	2	yes	—
104	#16810588	C₂²	1	2	yes	—
105	C₂²⋊C₈×D₅₃	C₂²	1	2	yes	—
106	#16810581	C₂²	1	2	yes	complemented
107	#16810580	C₂²	1	2	yes	—
108	#16810580	C₂²	1	2	yes	complemented
109	#16810578	C₂²	1	2	yes	complemented
110	#16810577	C₂²	1	2	yes	—
111	#16810577	C₂²	1	2	yes	complemented
112	C₄×#11719917	C₂²	1	1	yes	characteristic, complemented
113	#16810575	C₂²	1	1	yes	characteristic
114	#16810575	C₂²	1	2	yes	—
115	#16810575	C₂²	1	2	yes	—
116	#16810575	C₂²	1	1	yes	characteristic
117	#16810575	C₂²	1	1	yes	characteristic
118	#16810575	C₂²	1	1	yes	characteristic
119	#16810575	C₂²	1	1	yes	characteristic, complemented
120	#16810575	C₂²	1	1	yes	characteristic, complemented
121	C₂×#13133128	C₂²	1	1	yes	characteristic
122	C₂×#13133128	C₂²	1	1	yes	characteristic, complemented
123	#97×D₅₃	C₂²	1	1	yes	characteristic
124	#97×D₅₃	C₂²	1	1	yes	characteristic
125	#97×D₅₃	C₂²	1	1	yes	characteristic, complemented
126	#97×D₅₃	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₈×Dic₅₃	C₂²	1	2	yes	—
128	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
129	C₅₃×#446	C₂²	1	2	yes	complemented
130	C₅₃×#435	C₂²	1	2	yes	—
131	C₅₃×#435	C₂²	1	2	yes	complemented
132	C₈×D₄×C₅₃	C₂²	1	2	yes	—
133	C₅₃×#432	C₂²	1	1	yes	characteristic
134	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
136	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
137	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic
138	C₂×#97×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
140	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
141	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
142	C₂×#11719945	C₂³	1	1	yes	characteristic
143	C₂×#11719945	C₂³	1	1	yes	characteristic
144	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
145	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
146	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
147	#13133225	—	2	8	no	—
148	#13133223	—	2	8	no	—
149	C₂×#11719917	C₂³	1	2	yes	—
150	C₂×#11719912	—	2	8	no	—
151	C₂×#11719912	C₂³	1	2	yes	—
152	C₂×#11719912	C₂³	1	2	yes	—
153	C₂×#11719912	C₂³	1	2	yes	—
154	C₂×#11719912	C₂³	1	2	yes	—
155	C₂×#11719912	C₂³	1	2	yes	—
156	C₂×#11719912	C₂³	1	2	yes	—
157	C₂²×#88322	C₂³	1	2	yes	—
158	C₂²×#88322	C₂³	1	2	yes	—
159	C₂×C₈×D₅₃	C₂³	1	2	yes	—
160	C₂×C₈×D₅₃	C₂³	1	2	yes	—
161	C₂×C₈×D₅₃	C₂³	1	2	yes	—
162	C₂×C₈×D₅₃	C₂³	1	2	yes	—
163	#13133216	C₂×C₄	1	1	yes	characteristic
164	#13133216	C₂×C₄	1	1	yes	characteristic
165	#13133215	C₂×C₄	1	1	yes	characteristic
166	#13133213	C₂×C₄	1	1	yes	characteristic
167	#13133212	C₂×C₄	1	1	yes	characteristic
168	#13133212	C₂×C₄	1	1	yes	characteristic
169	#13133212	C₂×C₄	1	1	yes	characteristic
170	#13133212	C₂×C₄	1	1	yes	characteristic
171	#13133210	C₂×C₄	1	1	yes	characteristic
172	#13133210	C₂×C₄	1	1	yes	characteristic
173	#13133210	C₂×C₄	1	1	yes	characteristic
174	#13133210	C₂×C₄	1	1	yes	characteristic
175	#13133208	C₂×C₄	1	1	yes	characteristic
176	#13133208	C₂×C₄	1	1	yes	characteristic
177	#13133207	C₂×C₄	1	1	yes	characteristic
178	#13133207	C₂×C₄	1	1	yes	characteristic
179	#13133207	C₂×C₄	1	1	yes	characteristic
180	#13133207	C₂×C₄	1	1	yes	characteristic
181	#13133206	C₂×C₄	1	1	yes	characteristic
182	#13133204	C₂×C₄	1	1	yes	characteristic
183	#13133203	C₂×C₄	1	1	yes	characteristic
184	#13133203	C₂×C₄	1	1	yes	characteristic
185	#13133203	C₂×C₄	1	1	yes	characteristic
186	#13133203	C₂×C₄	1	1	yes	characteristic
187	#13133202	C₂×C₄	1	1	yes	characteristic
188	#13133202	C₂×C₄	1	1	yes	characteristic
189	#13133202	C₂×C₄	1	1	yes	characteristic
190	#13133202	C₂×C₄	1	1	yes	characteristic
191	#13133201	C₂×C₄	1	1	yes	characteristic
192	#13133201	C₂×C₄	1	1	yes	characteristic
193	#13133199	C₂×C₄	1	1	yes	characteristic
194	#13133199	C₂×C₄	1	1	yes	characteristic
195	#13133199	C₂×C₄	1	1	yes	characteristic
196	#13133199	C₂×C₄	1	1	yes	characteristic
197	#13133198	C₂×C₄	1	1	yes	characteristic
198	#13133198	C₂×C₄	1	1	yes	characteristic
199	#13133197	C₂×C₄	1	1	yes	characteristic
200	#13133197	C₂×C₄	1	1	yes	characteristic
201	#13133195	C₂×C₄	1	1	yes	characteristic
202	#13133195	C₂×C₄	1	1	yes	characteristic
203	#13133195	C₂×C₄	1	1	yes	characteristic
204	#13133195	C₂×C₄	1	1	yes	characteristic
205	#13133194	C₂×C₄	1	1	yes	characteristic
206	#13133194	C₂×C₄	1	1	yes	characteristic
207	#13133194	C₂×C₄	1	1	yes	characteristic
208	#13133194	C₂×C₄	1	1	yes	characteristic
209	#13133193	C₂×C₄	1	1	yes	characteristic
210	#13133193	C₂×C₄	1	1	yes	characteristic
211	#13133192	C₂×C₄	1	1	yes	characteristic
212	#13133192	C₂×C₄	1	1	yes	characteristic
213	#13133190	C₂×C₄	1	1	yes	characteristic
214	#13133190	C₂×C₄	1	1	yes	characteristic
215	#13133190	C₂×C₄	1	1	yes	characteristic
216	#13133190	C₂×C₄	1	1	yes	characteristic
217	#13133189	C₂×C₄	1	1	yes	characteristic
218	#13133189	C₂×C₄	1	1	yes	characteristic
219	#13133189	C₂×C₄	1	1	yes	characteristic
220	#13133189	C₂×C₄	1	1	yes	characteristic
221	#13133188	C₂×C₄	1	1	yes	characteristic
222	#13133188	C₂×C₄	1	1	yes	characteristic
223	#13133187	C₂×C₄	1	1	yes	characteristic
224	#13133187	C₂×C₄	1	1	yes	characteristic
225	#13133185	C₂×C₄	1	1	yes	characteristic
226	#13133185	C₂×C₄	1	1	yes	characteristic
227	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
228	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
229	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
230	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
231	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
232	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
233	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
234	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
235	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
236	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
237	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
238	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
239	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
240	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
241	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
242	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
243	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
244	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
245	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
246	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
247	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
248	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
249	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
250	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
251	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
252	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
253	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
254	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
255	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
256	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
257	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
258	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
259	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
260	C₄×C₂²⋊D₅₃	C₂×C₄	1	1	yes	characteristic
261	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
262	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
263	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
264	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
265	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
266	C₄×C₂²⋊D₅₃	C₂³	1	1	yes	characteristic
267	#13133176	C₂×C₄	1	1	yes	characteristic
268	#13133176	C₂×C₄	1	1	yes	characteristic
269	#13133176	C₂×C₄	1	1	yes	characteristic
270	#13133176	C₂³	1	1	yes	characteristic
271	#13133176	C₂³	1	1	yes	characteristic
272	#13133174	C₂×C₄	1	1	yes	characteristic
273	#13133174	C₂×C₄	1	1	yes	characteristic
274	#13133174	C₂×C₄	1	1	yes	characteristic
275	#13133174	C₂×C₄	1	1	yes	characteristic
276	#13133174	C₂×C₄	1	1	yes	characteristic
277	#13133174	C₂×C₄	1	1	yes	characteristic
278	#13133174	C₂³	1	1	yes	characteristic
279	#13133174	C₂³	1	1	yes	characteristic
280	#13133174	C₂³	1	1	yes	characteristic
281	#13133174	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
286	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
287	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
288	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
289	C₄²×D₅₃	C₂³	1	1	yes	characteristic
290	C₄²×D₅₃	C₂³	1	1	yes	characteristic
291	C₄²×D₅₃	C₂³	1	1	yes	characteristic
292	C₄²×D₅₃	C₂³	1	1	yes	characteristic
293	C₄²×D₅₃	C₂³	1	1	yes	characteristic
294	C₄²×D₅₃	C₂³	1	1	yes	characteristic
295	C₄⋊#88322	C₂³	1	2	yes	—
296	C₄⋊#88322	C₂³	1	2	yes	—
297	C₄⋊#88322	C₂³	1	2	yes	—
298	#13133146	C₂³	1	2	yes	—
299	#13133146	C₂³	1	2	yes	—
300	#13133146	C₂³	1	2	yes	—
301	#13133146	C₂³	1	2	yes	—
302	#13133146	C₂³	1	2	yes	—
303	#13133146	C₂³	1	2	yes	—
304	C₂²⋊#88322	C₂³	1	2	yes	—
305	C₂²⋊#88322	C₂³	1	2	yes	—
306	C₂²⋊#88322	C₂³	1	2	yes	—
307	#13133129	C₂³	1	2	yes	—
308	#13133129	C₂³	1	2	yes	—
309	#13133129	C₂³	1	2	yes	—
310	#13133129	C₂³	1	2	yes	—
311	#13133129	C₂³	1	2	yes	—
312	#13133129	C₂³	1	2	yes	—
313	#13133128	C₂³	1	2	yes	—
314	#13133128	C₂³	1	2	yes	—
315	#13133128	C₂³	1	1	yes	characteristic
316	#13133128	C₂³	1	1	yes	characteristic
317	#13133128	C₂³	1	1	yes	characteristic
318	#13133128	C₂³	1	1	yes	characteristic
319	#13133127	C₂³	1	2	yes	—
320	#13133127	C₂³	1	2	yes	—
321	#13133127	C₂³	1	2	yes	—
322	#13133127	C₂³	1	2	yes	—
323	C₄×#88322	C₂³	1	2	yes	—
324	C₈×Dic₅₃	C₂³	1	2	yes	—
325	C₈×Dic₅₃	C₂³	1	2	yes	—
326	C₈×Dic₅₃	C₂³	1	2	yes	—
327	C₈×Dic₅₃	C₂³	1	2	yes	—
328	C₈×Dic₅₃	C₂³	1	2	yes	—
329	C₈×Dic₅₃	C₂³	1	2	yes	—
330	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
331	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
332	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
333	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
334	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
335	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
336	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
337	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
338	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
339	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
342	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
343	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
344	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
345	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
348	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
349	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
350	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
351	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
352	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
353	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
354	#97×C₅₃	C₂³	1	1	yes	characteristic
355	#97×C₅₃	C₂³	1	1	yes	characteristic
356	#97×C₅₃	C₂³	1	1	yes	characteristic
357	#97×C₅₃	C₂³	1	1	yes	characteristic
358	#97×C₅₃	C₂³	1	2	yes	—
359	#97×C₅₃	C₂³	1	2	yes	—
360	C₄×C₈×C₅₃	C₂³	1	2	yes	—
361	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
362	#41×C₅₃	—	4	2	no	—
363	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
364	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
365	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
366	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
377	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
378	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
379	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
380	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
382	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
383	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
384	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
385	C₂×C₂²⋊D₅₃	C₂²×C₄	1	1	yes	characteristic
386	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
387	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
388	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
389	#11719945	—	2	4	no	—
390	#11719945	—	2	4	no	—
391	#11719945	—	4	2	no	—
392	#11719945	—	4	2	no	—
393	#11719945	—	4	2	no	—
394	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
395	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
396	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
397	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
398	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
399	C₂×C₄×D₅₃	—	2	4	no	—
400	C₂×C₄×D₅₃	—	4	2	no	—
401	C₂×C₄×D₅₃	—	4	2	no	—
402	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
403	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
404	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
405	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
406	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
407	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
408	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
409	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
410	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
411	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
412	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
413	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
414	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
415	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
416	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
421	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
422	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
423	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
424	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
425	M₁₆×C₅₃	—	2	4	no	—
426	C₂×C₈×C₅₃	—	2	4	no	—
427	C₂×C₈×C₅₃	—	2	4	no	—
428	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
429	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
430	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
431	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
433	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
434	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
435	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
436	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
438	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
439	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
440	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
441	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
442	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
443	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
444	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
445	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
446	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
447	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
448	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
449	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
450	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
455	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
456	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
457	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
458	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
459	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
460	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
461	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
462	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
463	C₂²⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
464	#11719921	C₂²×C₄	1	1	yes	characteristic
465	#11719921	C₂²×C₄	1	1	yes	characteristic
466	#11719921	C₂²×C₄	1	1	yes	characteristic
467	#11719921	C₂²×C₄	1	1	yes	characteristic
468	#11719921	C₂²×C₄	1	1	yes	characteristic
469	#11719921	C₂²×C₄	1	1	yes	characteristic
470	#11719921	C₂²×C₄	1	1	yes	characteristic
471	#11719921	C₂²×C₄	1	1	yes	characteristic
472	#11719921	C₂²×C₄	1	1	yes	characteristic
473	#11719921	C₂²×C₄	1	1	yes	characteristic
474	#11719921	C₂²×C₄	1	1	yes	characteristic
475	#11719921	C₂²×C₄	1	1	yes	characteristic
476	#11719921	C₂²×C₄	1	1	yes	characteristic
477	#11719921	C₂²×C₄	1	1	yes	characteristic
478	#11719921	C₂²×C₄	1	1	yes	characteristic
479	#11719921	C₂²×C₄	1	1	yes	characteristic
480	#11719921	C₂²×C₄	1	1	yes	characteristic
481	#11719921	C₂²×C₄	1	1	yes	characteristic
482	#11719921	C₂²×C₄	1	1	yes	characteristic
483	#11719921	C₂²×C₄	1	1	yes	characteristic
484	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
485	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
486	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
487	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
488	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
489	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
490	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
491	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
492	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
493	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
494	#11719919	C₂²×C₄	1	1	yes	characteristic
495	#11719919	C₂²×C₄	1	1	yes	characteristic
496	#11719919	C₂²×C₄	1	1	yes	characteristic
497	#11719919	C₂²×C₄	1	1	yes	characteristic
498	#11719919	C₂²×C₄	1	1	yes	characteristic
499	#11719919	C₂²×C₄	1	1	yes	characteristic
500	#11719919	C₂²×C₄	1	1	yes	characteristic
501	#11719919	C₂²×C₄	1	1	yes	characteristic
502	#11719919	C₂²×C₄	1	1	yes	characteristic
503	#11719919	C₂²×C₄	1	1	yes	characteristic
504	#11719919	C₂²×C₄	1	1	yes	characteristic
505	#11719919	C₂²×C₄	1	1	yes	characteristic
506	#11719919	C₂²×C₄	1	1	yes	characteristic
507	#11719919	C₂²×C₄	1	1	yes	characteristic
508	#11719919	C₂²×C₄	1	1	yes	characteristic
509	#11719919	C₂²×C₄	1	1	yes	characteristic
510	#11719919	C₂²×C₄	1	1	yes	characteristic
511	#11719919	C₂²×C₄	1	1	yes	characteristic
512	#11719919	C₂²×C₄	1	1	yes	characteristic
513	#11719919	C₂²×C₄	1	1	yes	characteristic
514	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
515	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
516	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
517	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
518	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
519	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
520	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
521	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
522	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
523	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
524	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
525	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
526	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
527	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
528	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
529	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
530	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
531	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
532	#11719917	—	2	4	no	—
533	C₂×#88322	—	2	4	no	—
534	C₂×#88322	—	2	4	no	—
535	C₂×#88322	C₂⁴	1	2	yes	—
536	C₂×#88322	C₂⁴	1	2	yes	—
537	C₂×#88322	C₂⁴	1	2	yes	—
538	C₂×#88322	C₂⁴	1	2	yes	—
539	#11719912	—	2	4	no	—
540	#11719912	—	2	4	no	—
541	#11719912	—	2	4	no	—
542	#11719912	—	2	4	no	—
543	#11719912	—	2	4	no	—
544	#11719912	#41	1	8	yes	complemented
545	C₈×D₅₃	—	2	4	no	—
546	C₈×D₅₃	—	2	4	no	—
547	C₈×D₅₃	—	2	4	no	—
548	C₈×D₅₃	—	2	4	no	—
549	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
550	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
551	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
552	C₂²×D₅₃	—	2	2	no	—
553	C₂²×D₅₃	—	2	2	no	—
554	C₂²×D₅₃	—	4	1	no	—
555	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
556	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
557	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
558	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
559	Q₈×C₅₃	—	4	1	no	—
560	D₄×C₅₃	—	2	2	no	—
561	D₄×C₅₃	—	2	2	no	—
562	D₄×C₅₃	—	4	1	no	—
563	C₂×C₄×C₅₃	—	2	2	no	—
564	C₂×C₄×C₅₃	—	2	2	no	—
565	C₂×C₄×C₅₃	—	2	2	no	—
566	C₂×C₄×C₅₃	—	2	2	no	—
567	C₂×C₄×C₅₃	—	4	1	no	—
568	C₂×C₄×C₅₃	—	4	1	no	—
569	C₂×C₄×C₅₃	—	4	1	no	—
570	C₂×C₄×C₅₃	—	4	1	no	—
571	C₂×C₄×C₅₃	—	4	1	no	—
572	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
573	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
574	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
575	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
576	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
577	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
578	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
579	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
580	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
581	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
582	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
583	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
584	C₂²⋊D₅₃	—	2	2	no	—
585	C₂²⋊D₅₃	—	2	2	no	—
586	C₂²⋊D₅₃	—	2	2	no	—
587	C₂²⋊D₅₃	—	2	2	no	—
588	C₂²⋊D₅₃	—	2	2	no	—
589	C₂²⋊D₅₃	—	2	2	no	—
590	C₂²⋊D₅₃	—	2	2	no	—
591	C₂²⋊D₅₃	—	2	2	no	—
592	C₂²⋊D₅₃	—	4	1	no	—
593	C₂²⋊D₅₃	—	4	1	no	—
594	C₂×Dic₅₃	—	2	2	no	—
595	C₂×Dic₅₃	—	2	2	no	—
596	C₂×Dic₅₃	—	2	2	no	—
597	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
598	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
599	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
600	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
601	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
602	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
603	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
604	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
605	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
606	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
607	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
608	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
609	D₂₁₂	—	2	2	no	—
610	D₂₁₂	—	2	2	no	—
611	D₂₁₂	—	4	1	no	—
612	D₂₁₂	—	4	1	no	—
613	D₂₁₂	—	4	1	no	—
614	C₄×D₅₃	—	2	2	no	—
615	C₄×D₅₃	—	2	2	no	—
616	C₄×D₅₃	—	2	2	no	—
617	C₄×D₅₃	—	2	2	no	—
618	C₄×D₅₃	—	2	2	no	—
619	C₄×D₅₃	—	2	2	no	—
620	C₄×D₅₃	—	2	2	no	—
621	C₄×D₅₃	—	4	1	no	—
622	C₄×D₅₃	—	4	1	no	—
623	C₄×D₅₃	—	4	1	no	—
624	C₄×D₅₃	—	4	1	no	—
625	C₄×D₅₃	—	4	1	no	—
626	C₄×D₅₃	—	4	1	no	—
627	C₄×D₅₃	—	4	1	no	—
628	C₄×D₅₃	—	4	1	no	—
629	C₄×D₅₃	—	4	1	no	—
630	C₄×D₅₃	—	4	1	no	—
631	C₄×D₅₃	C₂×#41	1	4	yes	—
632	Dic₁₀₆	—	2	2	no	—
633	Dic₁₀₆	—	2	2	no	—
634	Dic₁₀₆	—	2	2	no	—
635	Dic₁₀₆	—	2	2	no	—
636	Dic₁₀₆	—	4	1	no	—
637	C₈×C₅₃	—	2	2	no	—
638	C₈×C₅₃	—	2	2	no	—
639	C₈×C₅₃	—	2	2	no	—
640	C₈×C₅₃	C₂×#41	1	4	yes	—
641	#88322	—	2	2	no	—
642	#88322	—	2	2	no	—
643	#88322	—	2	2	no	—
644	#88322	C₂×#41	1	4	yes	—
645	#60211	—	53	1	no	maximal, Sylow
646	C₂²×C₅₃	—	2	1	no	—
647	C₂²×C₅₃	—	2	1	no	—
648	C₂²×C₅₃	—	2	1	no	—
649	C₂²×C₅₃	—	2	1	no	—
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	#568	1	2	yes	—
655	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
656	C₂×D₅₃	—	2	1	no	—
657	C₂×D₅₃	—	2	1	no	—
658	C₂×D₅₃	—	2	1	no	—
659	C₂×D₅₃	—	2	1	no	—
660	C₂×D₅₃	—	2	1	no	—
661	C₂×D₅₃	—	2	1	no	—
662	C₂×D₅₃	—	2	1	no	—
663	C₂×D₅₃	—	2	1	no	—
664	C₂×D₅₃	—	2	1	no	—
665	C₂×D₅₃	—	2	1	no	—
666	C₂×D₅₃	—	2	1	no	—
667	C₂×D₅₃	—	4	4	no	—
668	C₂×D₅₃	C₄×#41	1	2	yes	—
669	C₄×C₅₃	—	2	1	no	—
670	C₄×C₅₃	—	2	1	no	—
671	C₄×C₅₃	—	2	1	no	—
672	C₄×C₅₃	—	2	1	no	—
673	C₄×C₅₃	—	2	1	no	—
674	C₄×C₅₃	—	2	1	no	—
675	C₄×C₅₃	—	2	1	no	—
676	C₄×C₅₃	—	2	1	no	—
677	C₄×C₅₃	—	2	1	no	—
678	C₄×C₅₃	—	2	1	no	—
679	C₄×C₅₃	—	2	1	no	—
680	C₄×C₅₃	C₂²×#41	1	2	yes	—
681	Dic₅₃	—	2	1	no	—
682	Dic₅₃	—	2	1	no	—
683	Dic₅₃	—	2	1	no	—
684	Dic₅₃	—	2	1	no	—
685	Dic₅₃	—	2	1	no	—
686	Dic₅₃	—	2	1	no	—
687	Dic₅₃	—	2	1	no	—
688	Dic₅₃	—	2	1	no	—
689	Dic₅₃	—	2	1	no	—
690	Dic₅₃	—	2	1	no	—
691	Dic₅₃	C₄×#41	1	2	yes	—
692	Dic₅₃	#568	1	2	yes	—
693	#3444	—	53	1	no	—
694	#2971	—	53	1	no	—
695	#2971	—	53	1	no	—
696	#2970	—	53	1	no	—
697	#2970	—	53	1	no	—
698	#2970	—	53	1	no	—
699	#2970	—	53	1	no	—
700	#2970	—	53	1	no	—
701	#2970	D₅₃	1	1	yes	characteristic, complemented
702	#2967	—	53	2	no	—
703	#2967	—	53	2	no	—
704	#2966	—	53	2	no	—
705	#2966	—	53	2	no	—
706	#2962	—	53	2	no	—
707	#2935	—	53	2	no	—
708	#2933	—	53	2	no	—
709	#2933	—	53	2	no	—
710	#2923	—	53	1	no	—
711	#2923	—	53	1	no	—
712	C₂×#432	—	53	1	no	—
713	#2875	—	53	1	no	—
714	#2875	—	53	1	no	—
715	C₂×C₄×M₁₆	—	53	1	no	—
716	C₂×C₅₃	—	2	2	no	—
717	C₂×C₅₃	—	4	1	no	—
718	C₂×C₅₃	—	4	1	no	—
719	C₂×C₅₃	C₂×C₄×#41	1	1	yes	characteristic
720	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
721	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
722	D₅₃	—	2	2	no	—
723	D₅₃	—	4	1	no	—
724	D₅₃	—	4	1	no	—
725	D₅₃	—	4	1	no	—
726	C₂×#131	—	53	2	no	—
727	C₂×#131	—	53	2	no	—
728	C₂²×M₁₆	—	53	2	no	—
729	#533	—	53	1	no	—
730	#533	—	53	1	no	—
731	#533	—	53	1	no	—
732	#532	—	53	1	no	—
733	#532	—	53	1	no	—
734	#532	—	53	1	no	—
735	#529	—	53	1	no	—
736	#529	—	53	1	no	—
737	#529	—	53	1	no	—
738	#529	—	53	1	no	—
739	#529	—	53	1	no	—
740	#529	—	53	1	no	—
741	#529	—	53	1	no	—
742	#529	—	53	1	no	—
743	#529	—	53	1	no	—
744	#529	—	53	1	no	—
745	#529	—	53	1	no	—
746	#529	—	53	1	no	—
747	#525	—	53	1	no	—
748	#525	—	53	1	no	—
749	#525	—	53	1	no	—
750	#525	—	53	1	no	—
751	#525	—	53	1	no	—
752	#525	—	53	1	no	—
753	C₄×#41	—	53	1	no	—
754	C₄×#41	—	53	1	no	—
755	C₄×#41	—	53	1	no	—
756	C₄×#41	—	53	1	no	—
757	C₄×#41	—	53	1	no	—
758	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
759	C₂²×C₄²	—	53	1	no	—
760	#446	—	53	2	no	—
761	#446	—	53	2	no	—
762	#446	—	53	2	no	—
763	#446	—	53	2	no	—
764	#446	—	53	2	no	—
765	#446	C₂×D₅₃	1	2	yes	complemented
766	C₈×Q₈	—	53	2	no	—
767	C₈×Q₈	—	53	2	no	—
768	#436	—	53	2	no	—
769	#436	—	53	2	no	—
770	#436	—	53	2	no	—
771	#436	—	53	2	no	—
772	#436	—	53	2	no	—
773	#436	—	53	2	no	—
774	#435	—	53	2	no	—
775	#435	—	53	2	no	—
776	#435	—	53	2	no	—
777	#435	—	53	2	no	—
778	#435	—	53	2	no	—
779	#435	—	53	2	no	—
780	#435	—	53	2	no	—
781	#435	—	53	2	no	—
782	#435	—	53	2	no	—
783	#435	—	53	2	no	—
784	#435	C₂×D₅₃	1	2	yes	—
785	#435	C₂×D₅₃	1	2	yes	complemented
786	C₈×D₄	—	53	2	no	—
787	C₈×D₄	—	53	2	no	—
788	C₈×D₄	—	53	2	no	—
789	C₈×D₄	—	53	2	no	—
790	C₈×D₄	—	53	2	no	—
791	C₈×D₄	C₂×D₅₃	1	2	yes	—
792	#433	—	53	2	no	—
793	#433	—	53	2	no	—
794	#433	—	53	2	no	—
795	#433	—	53	2	no	—
796	#432	—	53	1	no	—
797	#432	—	53	1	no	—
798	#432	—	53	1	no	—
799	#432	—	53	2	no	—
800	#432	—	53	2	no	—
801	#432	—	53	1	no	—
802	#432	—	53	1	no	—
803	#432	—	53	1	no	—
804	#432	—	53	1	no	—
805	#432	—	53	1	no	—
806	#432	—	53	1	no	—
807	#432	C₂×D₅₃	1	1	yes	characteristic
808	#432	C₂×D₅₃	1	1	yes	characteristic, complemented
809	#432	C₂×D₅₃	1	1	yes	characteristic, complemented
810	#424	—	53	2	no	—
811	#424	—	53	2	no	—
812	C₂×C₄⋊C₈	—	53	2	no	—
813	#408	—	53	2	no	—
814	#408	—	53	2	no	—
815	C₂×C₂²⋊C₈	—	53	2	no	—
816	#405	—	53	2	no	—
817	#405	—	53	2	no	—
818	#405	—	53	2	no	—
819	#405	—	53	2	no	—
820	#405	—	53	2	no	—
821	#405	—	53	2	no	—
822	C₄×M₁₆	—	53	1	no	—
823	C₄×M₁₆	—	53	1	no	—
824	C₄×M₁₆	—	53	1	no	—
825	C₄×M₁₆	—	53	2	no	—
826	C₄×M₁₆	—	53	2	no	—
827	C₄×M₁₆	—	53	1	no	—
828	C₄×M₁₆	—	53	1	no	—
829	C₄×M₁₆	—	53	1	no	—
830	C₄×M₁₆	—	53	1	no	—
831	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
832	C₂×#97	—	53	1	no	—
833	C₂×#97	—	53	1	no	—
834	C₂×#97	—	53	1	no	—
835	C₂×#97	—	53	1	no	—
836	C₂×#97	—	53	1	no	—
837	C₂×#97	—	53	1	no	—
838	C₂×#97	C₂×D₅₃	1	1	yes	characteristic
839	C₂×#97	C₂×D₅₃	1	1	yes	characteristic, complemented
840	C₂×C₄×C₈	—	53	2	no	—
841	C₅₃	#60211	1	1	yes	characteristic, complemented, Sylow
842	C₂×#41	—	53	1	no	—
843	C₂×#41	—	53	1	no	—
844	C₂×#41	—	53	1	no	—
845	C₂×#41	—	53	1	no	—
846	C₂×#41	—	53	1	no	—
847	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
848	C₂³×C₄	—	53	1	no	—
849	C₂³×C₄	—	53	1	no	—
850	C₂³×C₄	—	53	1	no	—
851	#131	—	106	8	no	—
852	#131	—	106	8	no	—
853	C₂×M₁₆	—	53	2	no	—
854	C₂×M₁₆	—	53	2	no	—
855	C₂×M₁₆	—	53	2	no	—
856	C₂×M₁₆	—	53	2	no	—
857	C₂×M₁₆	—	53	2	no	—
858	C₂×M₁₆	—	53	2	no	—
859	C₂×M₁₆	—	53	2	no	—
860	C₂×M₁₆	—	106	8	no	—
861	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
862	C₂²×C₈	—	53	2	no	—
863	C₂²×C₈	—	53	2	no	—
864	C₂²×C₈	—	53	2	no	—
865	C₂²×C₈	—	53	2	no	—
866	C₂²×C₈	—	53	2	no	—
867	C₂²×C₈	—	53	2	no	—
868	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
869	C₂²×C₈	C₂²×D₅₃	1	2	yes	—
870	C₄⋊Q₈	—	53	1	no	—
871	C₄⋊Q₈	—	53	1	no	—
872	C₄⋊Q₈	—	53	1	no	—
873	#127	—	53	1	no	—
874	#126	—	53	1	no	—
875	#126	—	53	1	no	—
876	#126	—	53	1	no	—
877	#126	—	53	1	no	—
878	#126	—	53	1	no	—
879	#126	—	53	1	no	—
880	#126	—	53	1	no	—
881	#126	—	53	1	no	—
882	#125	—	53	1	no	—
883	#125	—	53	1	no	—
884	#125	—	53	1	no	—
885	#125	—	53	1	no	—
886	#125	—	53	1	no	—
887	#125	—	53	1	no	—
888	#124	—	53	1	no	—
889	#124	—	53	1	no	—
890	#124	—	53	1	no	—
891	#124	—	53	1	no	—
892	#124	—	53	1	no	—
893	#124	—	53	1	no	—
894	#123	—	53	1	no	—
895	#123	—	53	1	no	—
896	#123	—	53	1	no	—
897	#123	—	53	1	no	—
898	#123	—	53	1	no	—
899	#123	—	53	1	no	—
900	#123	—	53	1	no	—
901	#123	—	53	1	no	—
902	#123	—	53	1	no	—
903	#123	—	53	1	no	—
904	#123	—	53	1	no	—
905	#123	—	53	1	no	—
906	C₂²⋊Q₈	—	53	1	no	—
907	C₂²⋊Q₈	—	53	1	no	—
908	C₂²⋊Q₈	—	53	1	no	—
909	C₂²⋊Q₈	—	53	1	no	—
910	C₂²⋊Q₈	—	53	1	no	—
911	C₂²⋊Q₈	—	53	1	no	—
912	C₂²⋊Q₈	—	53	1	no	—
913	C₂²⋊Q₈	—	53	1	no	—
914	C₂²⋊Q₈	—	53	1	no	—
915	C₂²⋊Q₈	—	53	1	no	—
916	C₂²⋊Q₈	—	53	1	no	—
917	C₂²⋊Q₈	—	53	1	no	—
918	#121	—	53	1	no	—
919	#121	—	53	1	no	—
920	#121	—	53	1	no	—
921	#121	—	53	1	no	—
922	#121	—	53	1	no	—
923	#121	—	53	1	no	—
924	#121	—	53	1	no	—
925	#121	—	53	1	no	—
926	#121	—	53	1	no	—
927	#121	—	53	1	no	—
928	#121	—	53	1	no	—
929	#121	—	53	1	no	—
930	#120	—	53	1	no	—
931	#120	—	53	1	no	—
932	#120	—	53	1	no	—
933	#120	—	53	1	no	—
934	C₄×Q₈	—	53	1	no	—
935	C₄×Q₈	—	53	1	no	—
936	C₄×Q₈	—	53	1	no	—
937	C₄×Q₈	—	53	1	no	—
938	C₄×Q₈	—	53	1	no	—
939	C₄×Q₈	—	53	1	no	—
940	C₄×Q₈	—	53	1	no	—
941	C₄×Q₈	—	53	1	no	—
942	C₄×Q₈	—	53	1	no	—
943	C₄×Q₈	—	53	1	no	—
944	C₄×Q₈	C₄×D₅₃	1	1	yes	characteristic
945	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
946	C₄×D₄	—	53	1	no	—
947	C₄×D₄	—	53	1	no	—
948	C₄×D₄	—	53	1	no	—
949	C₄×D₄	—	53	1	no	—
950	C₄×D₄	—	53	1	no	—
951	C₄×D₄	—	53	1	no	—
952	C₄×D₄	—	53	1	no	—
953	C₄×D₄	—	53	1	no	—
954	C₄×D₄	—	53	1	no	—
955	C₄×D₄	—	53	1	no	—
956	C₄×D₄	—	53	1	no	—
957	C₄×D₄	—	53	1	no	—
958	C₄×D₄	—	53	1	no	—
959	C₄×D₄	—	53	1	no	—
960	C₄×D₄	—	53	1	no	—
961	C₄×D₄	—	53	1	no	—
962	C₄×D₄	—	53	1	no	—
963	C₄×D₄	—	53	1	no	—
964	C₄×D₄	—	53	1	no	—
965	C₄×D₄	—	53	1	no	—
966	C₄×D₄	—	53	1	no	—
967	C₄×D₄	—	53	1	no	—
968	C₄×D₄	—	53	1	no	—
969	C₄×D₄	—	53	1	no	—
970	C₄×D₄	—	53	1	no	—
971	C₄×D₄	—	53	1	no	—
972	C₄×D₄	—	53	1	no	—
973	C₄×D₄	—	53	1	no	—
974	C₄×D₄	—	53	1	no	—
975	C₄×D₄	—	53	1	no	—
976	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
977	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
978	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
979	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
980	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
981	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
982	#117	—	53	1	no	—
983	#117	—	53	1	no	—
984	#117	—	53	1	no	—
985	#117	—	53	1	no	—
986	#117	—	53	1	no	—
987	#117	—	53	1	no	—
988	#117	—	53	1	no	—
989	#117	—	53	1	no	—
990	#117	—	53	1	no	—
991	#117	—	53	1	no	—
992	#117	—	53	1	no	—
993	#117	—	53	1	no	—
994	#117	—	53	1	no	—
995	#117	—	53	1	no	—
996	#117	—	53	1	no	—
997	#117	C₄×D₅₃	1	1	yes	characteristic
998	#117	C₄×D₅₃	1	1	yes	characteristic
999	#117	C₄×D₅₃	1	1	yes	characteristic
1000	C₂×C₄²	—	53	1	no	—
1001	C₂×C₄²	—	53	1	no	—
1002	C₂×C₄²	—	53	1	no	—
1003	C₂×C₄²	—	53	1	no	—
1004	C₂×C₄²	—	53	1	no	—
1005	C₂×C₄²	—	53	1	no	—
1006	C₂×C₄²	—	53	1	no	—
1007	C₂×C₄²	—	53	1	no	—
1008	C₂×C₄²	—	53	1	no	—
1009	C₂×C₄²	—	53	1	no	—
1010	C₂×C₄²	—	53	1	no	—
1011	C₂×C₄²	—	53	1	no	—
1012	C₂×C₄²	—	53	1	no	—
1013	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1014	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1015	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1016	C₄⋊C₈	—	53	2	no	—
1017	C₄⋊C₈	—	53	2	no	—
1018	C₄⋊C₈	—	53	2	no	—
1019	C₄⋊C₈	—	53	2	no	—
1020	C₄⋊C₈	—	53	2	no	—
1021	C₄⋊C₈	—	53	2	no	—
1022	C₄⋊C₈	—	53	2	no	—
1023	C₄⋊C₈	—	53	2	no	—
1024	C₄⋊C₈	—	53	2	no	—
1025	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
1026	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
1027	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
1028	C₂²⋊C₈	—	53	2	no	—
1029	C₂²⋊C₈	—	53	2	no	—
1030	C₂²⋊C₈	—	53	2	no	—
1031	C₂²⋊C₈	—	53	2	no	—
1032	C₂²⋊C₈	—	53	2	no	—
1033	C₂²⋊C₈	—	53	2	no	—
1034	C₂²⋊C₈	—	53	2	no	—
1035	C₂²⋊C₈	—	53	2	no	—
1036	C₂²⋊C₈	—	53	2	no	—
1037	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1038	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1039	C₂²⋊C₈	C₂²×D₅₃	1	2	yes	—
1040	#97	—	53	2	no	—
1041	#97	—	53	2	no	—
1042	#97	—	53	2	no	—
1043	#97	—	53	2	no	—
1044	#97	—	53	1	no	—
1045	#97	—	53	1	no	—
1046	#97	—	53	1	no	—
1047	#97	—	53	1	no	—
1048	#97	—	53	2	no	—
1049	#97	—	53	2	no	—
1050	#97	C₂²×D₅₃	1	1	yes	characteristic
1051	#97	C₂²×D₅₃	1	1	yes	characteristic
1052	#97	C₂²×D₅₃	1	1	yes	characteristic
1053	#97	C₂²×D₅₃	1	1	yes	characteristic
1054	#97	C₂²×D₅₃	1	2	yes	—
1055	#97	C₂²×D₅₃	1	2	yes	—
1056	C₄×C₈	—	53	2	no	—
1057	C₄×C₈	—	53	2	no	—
1058	C₄×C₈	—	53	2	no	—
1059	C₄×C₈	—	53	2	no	—
1060	C₄×C₈	—	53	2	no	—
1061	C₄×C₈	—	53	2	no	—
1062	C₄×C₈	—	53	2	no	—
1063	C₄×C₈	C₂²×D₅₃	1	2	yes	—
1064	C₂⁴	—	53	1	no	—
1065	#41	—	4	2	no	—
1066	#41	—	106	4	no	—
1067	#41	—	106	4	no	—
1068	#41	—	212	2	no	—
1069	#41	—	212	2	no	—
1070	#41	—	212	2	no	—
1071	C₂×Q₈	—	53	1	no	—
1072	C₂×Q₈	—	53	1	no	—
1073	C₂×Q₈	—	53	1	no	—
1074	C₂×Q₈	—	53	1	no	—
1075	C₂×Q₈	—	53	1	no	—
1076	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
1077	C₂×D₄	—	53	1	no	—
1078	C₂×D₄	—	53	1	no	—
1079	C₂×D₄	—	53	1	no	—
1080	C₂×D₄	—	53	1	no	—
1081	C₂×D₄	—	53	1	no	—
1082	C₂×D₄	—	53	1	no	—
1083	C₂×D₄	—	53	1	no	—
1084	C₂×D₄	—	53	1	no	—
1085	C₂×D₄	—	53	1	no	—
1086	C₂×D₄	—	53	1	no	—
1087	C₂×D₄	—	53	1	no	—
1088	C₂×D₄	—	53	1	no	—
1089	C₂×D₄	—	53	1	no	—
1090	C₂×D₄	—	53	1	no	—
1091	C₂×D₄	—	53	1	no	—
1092	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1093	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1094	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1095	C₂²×C₄	—	53	1	no	—
1096	C₂²×C₄	—	53	1	no	—
1097	C₂²×C₄	—	53	1	no	—
1098	C₂²×C₄	—	53	1	no	—
1099	C₂²×C₄	—	53	1	no	—
1100	C₂²×C₄	—	53	1	no	—
1101	C₂²×C₄	—	53	1	no	—
1102	C₂²×C₄	—	53	1	no	—
1103	C₂²×C₄	—	53	1	no	—
1104	C₂²×C₄	—	53	1	no	—
1105	C₂²×C₄	—	53	1	no	—
1106	C₂²×C₄	—	53	1	no	—
1107	C₂²×C₄	—	53	1	no	—
1108	C₂²×C₄	—	53	1	no	—
1109	C₂²×C₄	—	53	1	no	—
1110	C₂²×C₄	—	53	1	no	—
1111	C₂²×C₄	—	53	1	no	—
1112	C₂²×C₄	—	53	1	no	—
1113	C₂²×C₄	—	53	1	no	—
1114	C₂²×C₄	—	53	1	no	—
1115	C₂²×C₄	—	53	1	no	—
1116	C₂²×C₄	—	106	4	no	—
1117	C₂²×C₄	—	212	2	no	—
1118	C₂²×C₄	—	212	2	no	—
1119	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1120	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1123	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1128	M₁₆	—	2	4	no	—
1129	M₁₆	—	53	8	no	—
1130	M₁₆	—	106	4	no	—
1131	M₁₆	—	106	4	no	—
1132	M₁₆	—	106	4	no	—
1133	M₁₆	—	106	4	no	—
1134	M₁₆	—	106	4	no	—
1135	M₁₆	—	106	4	no	—
1136	C₂×C₈	—	2	4	no	—
1137	C₂×C₈	—	2	4	no	—
1138	C₂×C₈	—	53	2	no	—
1139	C₂×C₈	—	53	2	no	—
1140	C₂×C₈	—	53	2	no	—
1141	C₂×C₈	—	53	2	no	—
1142	C₂×C₈	—	106	4	no	—
1143	C₂×C₈	—	106	4	no	—
1144	C₂×C₈	—	106	4	no	—
1145	C₂×C₈	—	106	4	no	—
1146	C₂×C₈	—	106	4	no	—
1147	C₂×C₈	—	106	4	no	—
1148	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1149	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1150	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1151	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1152	C₄⋊C₄	—	53	1	no	—
1153	C₄⋊C₄	—	53	1	no	—
1154	C₄⋊C₄	—	53	1	no	—
1155	C₄⋊C₄	—	53	1	no	—
1156	C₄⋊C₄	—	53	1	no	—
1157	C₄⋊C₄	—	53	1	no	—
1158	C₄⋊C₄	—	53	1	no	—
1159	C₄⋊C₄	—	53	1	no	—
1160	C₄⋊C₄	—	53	1	no	—
1161	C₄⋊C₄	—	53	1	no	—
1162	C₄⋊C₄	—	53	1	no	—
1163	C₄⋊C₄	—	53	1	no	—
1164	C₄⋊C₄	—	53	1	no	—
1165	C₄⋊C₄	—	53	1	no	—
1166	C₄⋊C₄	—	53	1	no	—
1167	C₄⋊C₄	—	53	1	no	—
1168	C₄⋊C₄	—	53	1	no	—
1169	C₄⋊C₄	—	53	1	no	—
1170	C₄⋊C₄	—	53	1	no	—
1171	C₄⋊C₄	—	53	1	no	—
1172	C₄⋊C₄	—	53	1	no	—
1173	C₄⋊C₄	—	53	1	no	—
1174	C₄⋊C₄	—	53	1	no	—
1175	C₄⋊C₄	—	53	1	no	—
1176	C₄⋊C₄	—	53	1	no	—
1177	C₄⋊C₄	—	53	1	no	—
1178	C₄⋊C₄	—	53	1	no	—
1179	C₄⋊C₄	—	53	1	no	—
1180	C₄⋊C₄	—	53	1	no	—
1181	C₄⋊C₄	—	53	1	no	—
1182	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1183	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1184	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1185	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1186	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1187	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1188	C₂²⋊C₄	—	53	1	no	—
1189	C₂²⋊C₄	—	53	1	no	—
1190	C₂²⋊C₄	—	53	1	no	—
1191	C₂²⋊C₄	—	53	1	no	—
1192	C₂²⋊C₄	—	53	1	no	—
1193	C₂²⋊C₄	—	53	1	no	—
1194	C₂²⋊C₄	—	53	1	no	—
1195	C₂²⋊C₄	—	53	1	no	—
1196	C₂²⋊C₄	—	53	1	no	—
1197	C₂²⋊C₄	—	53	1	no	—
1198	C₂²⋊C₄	—	53	1	no	—
1199	C₂²⋊C₄	—	53	1	no	—
1200	C₂²⋊C₄	—	53	1	no	—
1201	C₂²⋊C₄	—	53	1	no	—
1202	C₂²⋊C₄	—	53	1	no	—
1203	C₂²⋊C₄	—	53	1	no	—
1204	C₂²⋊C₄	—	53	1	no	—
1205	C₂²⋊C₄	—	53	1	no	—
1206	C₂²⋊C₄	—	53	1	no	—
1207	C₂²⋊C₄	—	53	1	no	—
1208	C₂²⋊C₄	—	53	1	no	—
1209	C₂²⋊C₄	—	53	1	no	—
1210	C₂²⋊C₄	—	53	1	no	—
1211	C₂²⋊C₄	—	53	1	no	—
1212	C₂²⋊C₄	—	53	1	no	—
1213	C₂²⋊C₄	—	53	1	no	—
1214	C₂²⋊C₄	—	53	1	no	—
1215	C₂²⋊C₄	—	53	1	no	—
1216	C₂²⋊C₄	—	53	1	no	—
1217	C₂²⋊C₄	—	53	1	no	—
1218	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1219	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1220	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1221	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1222	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1223	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
1224	C₄²	—	53	1	no	—
1225	C₄²	—	53	1	no	—
1226	C₄²	—	53	1	no	—
1227	C₄²	—	53	1	no	—
1228	C₄²	—	53	1	no	—
1229	C₄²	—	53	1	no	—
1230	C₄²	—	53	1	no	—
1231	C₄²	—	53	1	no	—
1232	C₄²	—	53	1	no	—
1233	C₄²	—	53	1	no	—
1234	C₄²	—	53	1	no	—
1235	C₄²	—	53	1	no	—
1236	C₄²	—	53	1	no	—
1237	C₄²	—	53	1	no	—
1238	C₄²	—	53	1	no	—
1239	C₄²	—	53	1	no	—
1240	C₄²	—	53	1	no	—
1241	C₄²	—	53	1	no	—
1242	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1243	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1244	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1245	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1246	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1247	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
1248	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1249	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1250	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1251	C₄²	C₂³×D₅₃	1	1	yes	characteristic
1252	C₂³	—	53	1	no	—
1253	C₂³	—	53	1	no	—
1254	C₂³	—	53	1	no	—
1255	C₂³	—	53	1	no	—
1256	C₂³	—	106	2	no	—
1257	C₂³	—	106	2	no	—
1258	C₂³	—	212	1	no	—
1259	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1260	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1261	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
1262	Q₈	—	4	1	no	—
1263	Q₈	—	106	2	no	—
1264	Q₈	—	106	2	no	—
1265	Q₈	—	106	2	no	—
1266	Q₈	—	106	2	no	—
1267	Q₈	—	212	1	no	—
1268	D₄	—	2	2	no	—
1269	D₄	—	2	2	no	—
1270	D₄	—	4	1	no	—
1271	D₄	—	106	2	no	—
1272	D₄	—	106	2	no	—
1273	D₄	—	106	2	no	—
1274	D₄	—	106	2	no	—
1275	D₄	—	106	2	no	—
1276	D₄	—	106	2	no	—
1277	D₄	—	106	2	no	—
1278	D₄	—	106	2	no	—
1279	D₄	—	106	2	no	—
1280	D₄	—	106	2	no	—
1281	D₄	—	212	1	no	—
1282	D₄	—	212	1	no	—
1283	D₄	—	212	1	no	—
1284	D₄	—	212	1	no	—
1285	D₄	—	212	1	no	—
1286	C₂×C₄	—	2	2	no	—
1287	C₂×C₄	—	2	2	no	—
1288	C₂×C₄	—	2	2	no	—
1289	C₂×C₄	—	2	2	no	—
1290	C₂×C₄	—	4	1	no	—
1291	C₂×C₄	—	4	1	no	—
1292	C₂×C₄	—	4	1	no	—
1293	C₂×C₄	—	4	1	no	—
1294	C₂×C₄	—	4	1	no	—
1295	C₂×C₄	—	53	1	no	—
1296	C₂×C₄	—	53	1	no	—
1297	C₂×C₄	—	53	4	no	—
1298	C₂×C₄	—	53	1	no	—
1299	C₂×C₄	—	53	1	no	—
1300	C₂×C₄	—	53	1	no	—
1301	C₂×C₄	—	53	1	no	—
1302	C₂×C₄	—	53	1	no	—
1303	C₂×C₄	—	53	1	no	—
1304	C₂×C₄	—	53	1	no	—
1305	C₂×C₄	—	53	1	no	—
1306	C₂×C₄	—	53	1	no	—
1307	C₂×C₄	—	53	1	no	—
1308	C₂×C₄	—	106	2	no	—
1309	C₂×C₄	—	106	2	no	—
1310	C₂×C₄	—	106	2	no	—
1311	C₂×C₄	—	106	2	no	—
1312	C₂×C₄	—	106	2	no	—
1313	C₂×C₄	—	106	2	no	—
1314	C₂×C₄	—	106	2	no	—
1315	C₂×C₄	—	106	2	no	—
1316	C₂×C₄	—	106	2	no	—
1317	C₂×C₄	—	106	2	no	—
1318	C₂×C₄	—	212	1	no	—
1319	C₂×C₄	—	212	1	no	—
1320	C₂×C₄	—	212	1	no	—
1321	C₂×C₄	—	212	1	no	—
1322	C₂×C₄	—	212	1	no	—
1323	C₂×C₄	—	212	1	no	—
1324	C₂×C₄	—	212	1	no	—
1325	C₂×C₄	—	212	1	no	—
1326	C₂×C₄	—	212	1	no	—
1327	C₂×C₄	—	212	1	no	—
1328	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1329	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1330	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1331	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1332	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1333	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1334	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1335	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1336	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1337	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1338	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1339	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1340	C₈	—	2	2	no	—
1341	C₈	—	2	2	no	—
1342	C₈	—	2	2	no	—
1343	C₈	—	53	4	no	—
1344	C₈	—	106	2	no	—
1345	C₈	—	106	2	no	—
1346	C₈	—	106	2	no	—
1347	C₈	#41×D₅₃	1	4	yes	—
1348	C₂²	—	2	1	no	—
1349	C₂²	—	2	1	no	—
1350	C₂²	—	2	1	no	—
1351	C₂²	—	2	1	no	—
1352	C₂²	—	2	1	no	—
1353	C₂²	—	2	1	no	—
1354	C₂²	—	2	1	no	—
1355	C₂²	—	2	1	no	—
1356	C₂²	—	53	2	no	—
1357	C₂²	—	106	1	no	—
1358	C₂²	—	106	1	no	—
1359	C₂²	—	106	1	no	—
1360	C₂²	—	106	1	no	—
1361	C₂²	—	106	1	no	—
1362	C₂²	—	106	1	no	—
1363	C₂²	—	106	1	no	—
1364	C₂²	—	106	1	no	—
1365	C₂²	—	106	1	no	—
1366	C₂²	—	106	1	no	—
1367	C₂²	—	106	1	no	—
1368	C₂²	—	212	4	no	—
1369	C₂²	#16811389	1	2	yes	—
1370	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1371	C₄	—	2	1	no	—
1372	C₄	—	2	1	no	—
1373	C₄	—	2	1	no	—
1374	C₄	—	2	1	no	—
1375	C₄	—	2	1	no	—
1376	C₄	—	2	1	no	—
1377	C₄	—	2	1	no	—
1378	C₄	—	2	1	no	—
1379	C₄	—	2	1	no	—
1380	C₄	—	2	1	no	—
1381	C₄	—	2	1	no	—
1382	C₄	—	53	2	no	—
1383	C₄	—	53	2	no	—
1384	C₄	—	106	1	no	—
1385	C₄	—	106	1	no	—
1386	C₄	—	106	1	no	—
1387	C₄	—	106	1	no	—
1388	C₄	—	106	1	no	—
1389	C₄	—	106	1	no	—
1390	C₄	—	106	1	no	—
1391	C₄	—	106	1	no	—
1392	C₄	—	106	1	no	—
1393	C₄	—	106	1	no	—
1394	C₄	C₂×#41×D₅₃	1	2	yes	—
1395	C₂	—	2	2	no	—
1396	C₂	—	4	1	no	—
1397	C₂	—	4	1	no	—
1398	C₂	—	106	2	no	—
1399	C₂	—	212	1	no	—
1400	C₂	—	212	1	no	—
1401	C₂	—	212	1	no	—
1402	C₂	C₄×#41×D₅₃	1	1	yes	characteristic
1403	C₂	#568×D₅₃	1	1	yes	characteristic
1404	C₂	C₂×#16811389	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2970	C₂
prime radical	#20288008	C₂
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2970	D₅₃
hypocenter	C₅₃	#60211
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #2970

Complements

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

N	H ≅ G/N	type
2. #20283733	C₂	semidirect
3. #20283732	C₂	semidirect
4. #20283729	C₂	semidirect
5. #20283726	C₂	semidirect
6. #20283726	C₂	semidirect
7. #20283724	C₂	semidirect
8. #20283724	C₂	semidirect
9. #20283699	C₂	semidirect
10. #20283697	C₂	semidirect
11. #20283685	C₂	semidirect
12. #20283683	C₂	semidirect
13. #20283660	C₂	semidirect
14. #20283456	C₂	semidirect
15. #20283441	C₂	semidirect
16. #20283435	C₂	semidirect
17. #20283361	C₂	semidirect
18. #20283361	C₂	semidirect
19. #432×D₅₃	C₂	semidirect
20. #20283144	C₂	semidirect
21. #20283140	C₂	semidirect
22. C₂×#16810575	C₂	semidirect
23. C₅₃×#2970	C₂	semidirect
57. #16810754	C₂²	semidirect
58. #16810752	C₂²	semidirect
59. #16810752	C₂²	semidirect
60. #16810751	C₂²	semidirect
61. #16810751	C₂²	semidirect
62. C₈×Dic₁₀₆	C₂²	semidirect
63. #16810747	C₂²	semidirect
67. #16810699	C₂²	semidirect
69. #16810698	C₂²	semidirect
71. #16810696	C₂²	semidirect
73. #16810695	C₂²	semidirect
77. #16810693	C₂²	semidirect
82. C₈×C₂²⋊D₅₃	C₂²	semidirect
84. #16810686	C₂²	semidirect
85. #16810683	C₂²	semidirect
86. #16810683	C₂²	semidirect
87. #16810681	C₂²	semidirect
88. #16810681	C₂²	semidirect
90. #16810680	C₂²	semidirect
91. #16810680	C₂²	semidirect
95. #16810678	C₂²	semidirect
96. #16810678	C₂²	semidirect
97. #16810678	C₂²	semidirect
98. #16810678	C₂²	semidirect
106. #16810581	C₂²	semidirect
108. #16810580	C₂²	semidirect
109. #16810578	C₂²	semidirect
111. #16810577	C₂²	semidirect
112. C₄×#11719917	C₂²	semidirect
119. #16810575	C₂²	semidirect
120. #16810575	C₂²	semidirect
122. C₂×#13133128	C₂²	semidirect
125. #97×D₅₃	C₂²	semidirect
126. #97×D₅₃	C₂²	semidirect
129. C₅₃×#446	C₂²	semidirect
131. C₅₃×#435	C₂²	semidirect
134. C₅₃×#432	C₂²	semidirect
135. C₅₃×#432	C₂²	semidirect
136. C₄×M₁₆×C₅₃	C₂²	semidirect
138. C₂×#97×C₅₃	C₂²	semidirect
544. #11719912	#41	semidirect
701. #2970	D₅₃	semidirect
765. #446	C₂×D₅₃	semidirect
785. #435	C₂×D₅₃	semidirect
808. #432	C₂×D₅₃	semidirect
809. #432	C₂×D₅₃	semidirect
831. C₄×M₁₆	C₂×D₅₃	semidirect
839. C₂×#97	C₂×D₅₃	semidirect
841. C₅₃	#60211	semidirect

Maximal subgroups

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

subgroup	index
#20288008	2
#20283733	2
#20283732	2
#20283729	2
#20283726	2
#20283724	2
#20283699	2
#20283697	2
#20283685	2
#20283683	2
#20283660	2
#20283456	2
#20283441	2
#20283435	2
#20283361	2
#432×D₅₃	2
#20283144	2
#20283140	2
C₂×#16810575	2
C₅₃×#2970	2
#60211	53