Subgroups — #28249100

Order 13568.

1626 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288118	C₂	1	1	yes	maximal, characteristic
2	#20283818	C₂	1	2	yes	maximal, complemented
3	#20283818	C₂	1	2	yes	maximal, complemented
4	#20283815	C₂	1	2	yes	maximal, complemented
5	#20283813	C₂	1	2	yes	maximal, complemented
6	#20283811	C₂	1	2	yes	maximal, complemented
7	#20283808	C₂	1	2	yes	maximal, complemented
8	#20283808	C₂	1	2	yes	maximal, complemented
9	#20283806	C₂	1	2	yes	maximal, complemented
10	#20283664	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283662	C₂	1	1	yes	maximal, characteristic, complemented
12	#20283658	C₂	1	1	yes	maximal, characteristic, complemented
13	#20283654	C₂	1	1	yes	maximal, characteristic, complemented
14	#20283653	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283648	C₂	1	1	yes	maximal, characteristic, complemented
16	#20283647	C₂	1	1	yes	maximal, characteristic, complemented
17	#20283372	C₂	1	1	yes	maximal, characteristic
18	#20283372	C₂	1	1	yes	maximal, characteristic
19	#20283370	C₂	1	1	yes	maximal, characteristic
20	#20283370	C₂	1	1	yes	maximal, characteristic
21	#20283351	C₂	1	1	yes	maximal, characteristic
22	C₂×#16810683	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811253	C₄	1	1	yes	characteristic
25	#16811253	C₄	1	1	yes	characteristic
26	#16811253	C₄	1	1	yes	characteristic
27	#16811253	C₄	1	1	yes	characteristic
28	#16811252	C₄	1	2	yes	—
29	#16811252	C₄	1	2	yes	—
30	#16811250	C₄	1	1	yes	characteristic
31	#16811250	C₄	1	1	yes	characteristic
32	#16811250	C₄	1	1	yes	characteristic
33	#16811250	C₄	1	1	yes	characteristic
34	#16811248	C₄	1	2	yes	—
35	#16811248	C₄	1	2	yes	—
36	#16811180	C₂²	1	1	yes	characteristic
37	#16811177	C₂²	1	2	yes	—
38	#16811177	C₂²	1	2	yes	—
39	#16811177	C₂²	1	2	yes	—
40	#16811177	C₂²	1	2	yes	—
41	#16811176	C₂²	1	1	yes	characteristic
42	#16811176	C₂²	1	1	yes	characteristic
43	C₂×#13133174	C₂²	1	1	yes	characteristic
44	#117×D₅₃	C₂²	1	1	yes	characteristic
45	#117×D₅₃	C₂²	1	1	yes	characteristic
46	#16810754	C₂²	1	2	yes	complemented
47	#16810754	C₂²	1	2	yes	complemented
48	#16810754	C₂²	1	2	yes	complemented
49	#16810753	C₂²	1	2	yes	complemented
50	#16810753	C₂²	1	2	yes	complemented
51	#16810753	C₂²	1	2	yes	complemented
52	#16810752	C₂²	1	2	yes	complemented
53	#16810752	C₂²	1	2	yes	complemented
54	#16810752	C₂²	1	2	yes	complemented
55	#16810752	C₂²	1	2	yes	complemented
56	#16810752	C₂²	1	2	yes	complemented
57	#16810752	C₂²	1	2	yes	complemented
58	#16810751	C₂²	1	2	yes	complemented
59	#16810751	C₂²	1	2	yes	complemented
60	#16810751	C₂²	1	2	yes	complemented
61	#16810751	C₂²	1	2	yes	complemented
62	#16810751	C₂²	1	2	yes	complemented
63	#16810751	C₂²	1	2	yes	complemented
64	#16810750	C₂²	1	2	yes	complemented
65	#16810750	C₂²	1	2	yes	complemented
66	#16810750	C₂²	1	2	yes	complemented
67	Q₈×#88322	C₂²	1	2	yes	complemented
68	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
69	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
70	C₈×Dic₁₀₆	C₂²	1	2	yes	complemented
71	#16810747	C₂²	1	2	yes	complemented
72	#16810747	C₂²	1	2	yes	complemented
73	#16810747	C₂²	1	2	yes	complemented
74	#16810685	C₂²	1	2	yes	—
75	#16810685	C₂²	1	2	yes	—
76	#16810685	C₂²	1	2	yes	—
77	#16810685	C₂²	1	2	yes	—
78	#16810683	C₂²	1	1	yes	characteristic
79	#16810683	C₂²	1	2	yes	—
80	#16810683	C₂²	1	1	yes	characteristic
81	#16810683	C₂²	1	1	yes	characteristic
82	#16810683	C₂²	1	2	yes	—
83	#16810683	C₂²	1	2	yes	—
84	#16810683	C₂²	1	1	yes	characteristic
85	#16810683	C₂²	1	2	yes	—
86	#16810683	C₂²	1	1	yes	characteristic
87	#16810683	C₂²	1	1	yes	characteristic
88	#16810683	C₂²	1	1	yes	characteristic
89	#16810683	C₂²	1	1	yes	characteristic
90	#16810682	C₂²	1	2	yes	—
91	#16810682	C₂²	1	2	yes	—
92	#16810682	C₂²	1	2	yes	—
93	#16810682	C₂²	1	2	yes	—
94	#16810679	C₂²	1	2	yes	—
95	#16810679	C₂²	1	2	yes	—
96	#16810678	C₂²	1	2	yes	—
97	#16810678	C₂²	1	2	yes	—
98	#16810675	C₂²	1	2	yes	—
99	#16810675	C₂²	1	2	yes	—
100	#16810674	C₂²	1	2	yes	—
101	#16810674	C₂²	1	2	yes	—
102	#16810651	C₂²	1	1	yes	characteristic
103	#16810651	C₂²	1	1	yes	characteristic
104	#16810650	C₂²	1	1	yes	characteristic
105	#16810650	C₂²	1	1	yes	characteristic
106	#16810649	C₂²	1	1	yes	characteristic
107	#16810649	C₂²	1	1	yes	characteristic
108	#16810646	C₂²	1	1	yes	characteristic
109	#16810646	C₂²	1	1	yes	characteristic
110	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
111	#16810586	C₂²	1	1	yes	characteristic
112	#16810586	C₂²	1	1	yes	characteristic
113	C₂×#13133129	C₂²	1	1	yes	characteristic
114	C₂×#13133129	C₂²	1	1	yes	characteristic
115	#16810581	C₂²	1	1	yes	characteristic
116	#16810581	C₂²	1	1	yes	characteristic
117	#16810579	C₂²	1	1	yes	characteristic
118	#16810579	C₂²	1	1	yes	characteristic
119	#16810578	C₂²	1	1	yes	characteristic
120	#16810578	C₂²	1	1	yes	characteristic
121	C₄×#11719917	C₂²	1	1	yes	characteristic
122	C₂×#13133127	C₂²	1	1	yes	characteristic
123	C₂×C₈×Dic₅₃	C₂²	1	1	yes	characteristic
124	C₅₃×#533	C₂²	1	1	yes	characteristic
125	C₅₃×#446	C₂²	1	2	yes	complemented
126	C₅₃×#446	C₂²	1	2	yes	complemented
127	C₅₃×#446	C₂²	1	2	yes	complemented
128	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
129	C₅₃×#424	C₂²	1	1	yes	characteristic
130	C₅₃×#424	C₂²	1	1	yes	characteristic
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#405	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
135	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
136	C₂×#11719917	C₂³	1	1	yes	characteristic
137	C₂×#11719917	C₂³	1	1	yes	characteristic
138	C₂²×#88322	C₂³	1	1	yes	characteristic
139	C₂²×#88322	C₂³	1	1	yes	characteristic
140	#13133217	C₂×C₄	1	1	yes	characteristic
141	#13133217	C₂×C₄	1	1	yes	characteristic
142	#13133216	C₂×C₄	1	1	yes	characteristic
143	#13133216	C₂×C₄	1	1	yes	characteristic
144	#13133216	C₂×C₄	1	1	yes	characteristic
145	#13133216	C₂×C₄	1	1	yes	characteristic
146	#13133216	C₂×C₄	1	2	yes	—
147	#13133216	C₂×C₄	1	2	yes	—
148	#13133216	C₂×C₄	1	2	yes	—
149	#13133216	C₂×C₄	1	2	yes	—
150	#13133215	C₂×C₄	1	2	yes	—
151	#13133215	C₂×C₄	1	2	yes	—
152	#13133215	C₂×C₄	1	2	yes	—
153	#13133215	C₂×C₄	1	2	yes	—
154	#13133209	C₂×C₄	1	1	yes	characteristic
155	#13133209	C₂×C₄	1	1	yes	characteristic
156	#13133208	C₂×C₄	1	1	yes	characteristic
157	#13133208	C₂×C₄	1	1	yes	characteristic
158	#13133208	C₂×C₄	1	1	yes	characteristic
159	#13133208	C₂×C₄	1	1	yes	characteristic
160	#13133207	C₂×C₄	1	2	yes	—
161	#13133207	C₂×C₄	1	2	yes	—
162	#13133207	C₂×C₄	1	2	yes	—
163	#13133207	C₂×C₄	1	2	yes	—
164	#13133207	C₂×C₄	1	2	yes	—
165	#13133207	C₂×C₄	1	2	yes	—
166	#13133207	C₂×C₄	1	2	yes	—
167	#13133207	C₂×C₄	1	2	yes	—
168	#13133197	C₂×C₄	1	2	yes	—
169	#13133197	C₂×C₄	1	2	yes	—
170	#13133197	C₂×C₄	1	2	yes	—
171	#13133197	C₂×C₄	1	2	yes	—
172	#13133196	C₂×C₄	1	2	yes	—
173	#13133196	C₂×C₄	1	2	yes	—
174	#13133195	C₂×C₄	1	2	yes	—
175	#13133195	C₂×C₄	1	2	yes	—
176	#13133195	C₂×C₄	1	2	yes	—
177	#13133195	C₂×C₄	1	2	yes	—
178	#13133195	C₂×C₄	1	2	yes	—
179	#13133195	C₂×C₄	1	2	yes	—
180	#13133195	C₂×C₄	1	2	yes	—
181	#13133195	C₂×C₄	1	2	yes	—
182	#13133194	C₂×C₄	1	2	yes	—
183	#13133194	C₂×C₄	1	2	yes	—
184	#13133194	C₂×C₄	1	2	yes	—
185	#13133194	C₂×C₄	1	2	yes	—
186	#13133193	C₂×C₄	1	2	yes	—
187	#13133193	C₂×C₄	1	2	yes	—
188	#13133193	C₂×C₄	1	2	yes	—
189	#13133193	C₂×C₄	1	2	yes	—
190	C₄×Dic₁₀₆	C₂³	1	2	yes	—
191	C₄×Dic₁₀₆	C₂³	1	2	yes	—
192	C₄×Dic₁₀₆	C₂³	1	2	yes	—
193	C₄×Dic₁₀₆	C₂³	1	2	yes	—
194	C₄×Dic₁₀₆	C₂³	1	2	yes	—
195	C₄×Dic₁₀₆	C₂³	1	2	yes	—
196	#13133176	C₂³	1	1	yes	characteristic
197	#13133176	C₂³	1	1	yes	characteristic
198	#13133175	C₂×C₄	1	1	yes	characteristic
199	#13133175	C₂×C₄	1	1	yes	characteristic
200	#13133175	C₂×C₄	1	1	yes	characteristic
201	#13133175	C₂×C₄	1	1	yes	characteristic
202	#13133174	C₂×C₄	1	1	yes	characteristic
203	#13133174	C₂×C₄	1	1	yes	characteristic
204	#13133174	C₂×C₄	1	1	yes	characteristic
205	#13133174	C₂×C₄	1	1	yes	characteristic
206	#13133174	C₂³	1	2	yes	—
207	#13133174	C₂³	1	2	yes	—
208	#13133174	C₂³	1	1	yes	characteristic
209	#13133174	C₂³	1	1	yes	characteristic
210	#13133174	C₂³	1	1	yes	characteristic
211	#13133174	C₂³	1	1	yes	characteristic
212	#13133173	C₂×C₄	1	2	yes	—
213	#13133173	C₂×C₄	1	2	yes	—
214	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
215	C₂×#11719919	C₂×C₄	1	1	yes	characteristic
216	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
217	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
218	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
219	C₄⋊C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
220	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
221	C₂×#11719921	C₂×C₄	1	1	yes	characteristic
222	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
223	C₂²⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
224	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
225	C₄²×D₅₃	C₂³	1	2	yes	—
226	C₄²×D₅₃	C₂³	1	2	yes	—
227	C₄⋊#88322	C₂³	1	1	yes	characteristic
228	C₄⋊#88322	C₂³	1	2	yes	—
229	C₄⋊#88322	C₂³	1	2	yes	—
230	C₄⋊#88322	C₂³	1	1	yes	characteristic
231	C₄⋊#88322	C₂³	1	1	yes	characteristic
232	C₄⋊#88322	C₂³	1	2	yes	—
233	C₄⋊#88322	C₂³	1	2	yes	—
234	C₄⋊#88322	C₂³	1	1	yes	characteristic
235	#13133146	C₂³	1	2	yes	—
236	#13133146	C₂³	1	2	yes	—
237	#13133146	C₂³	1	2	yes	—
238	#13133146	C₂³	1	2	yes	—
239	#13133146	C₂³	1	2	yes	—
240	#13133146	C₂³	1	2	yes	—
241	#13133146	C₂³	1	2	yes	—
242	#13133146	C₂³	1	2	yes	—
243	#13133146	C₂³	1	2	yes	—
244	#13133146	C₂³	1	2	yes	—
245	#13133146	C₂³	1	2	yes	—
246	#13133146	C₂³	1	2	yes	—
247	#13133129	C₂³	1	1	yes	characteristic
248	#13133129	C₂³	1	1	yes	characteristic
249	#13133129	C₂³	1	1	yes	characteristic
250	#13133129	C₂³	1	1	yes	characteristic
251	#13133129	C₂³	1	1	yes	characteristic
252	#13133129	C₂³	1	1	yes	characteristic
253	#13133129	C₂³	1	1	yes	characteristic
254	#13133129	C₂³	1	1	yes	characteristic
255	#13133129	C₂³	1	2	yes	—
256	#13133129	C₂³	1	2	yes	—
257	#13133129	C₂³	1	2	yes	—
258	#13133129	C₂³	1	2	yes	—
259	#13133128	C₂³	1	2	yes	—
260	#13133128	C₂³	1	2	yes	—
261	#13133128	C₂³	1	2	yes	—
262	#13133127	C₂³	1	1	yes	characteristic
263	#13133127	C₂³	1	2	yes	—
264	#13133127	C₂³	1	1	yes	characteristic
265	#13133127	C₂³	1	2	yes	—
266	#13133127	C₂³	1	2	yes	—
267	#13133127	C₂³	1	1	yes	characteristic
268	#13133127	C₂³	1	2	yes	—
269	#13133127	C₂³	1	1	yes	characteristic
270	C₄×#88322	C₂³	1	2	yes	—
271	C₄×#88322	C₂³	1	2	yes	—
272	C₄×#88322	C₂³	1	2	yes	—
273	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
274	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₈×Dic₅₃	C₂³	1	2	yes	—
276	C₈×Dic₅₃	C₂³	1	2	yes	—
277	C₈×Dic₅₃	C₂³	1	2	yes	—
278	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₈×Dic₅₃	C₂³	1	2	yes	—
281	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
286	C₄⋊Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
287	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
288	#125×C₅₃	C₂×C₄	1	1	yes	characteristic
289	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
290	C₂²⋊Q₈×C₅₃	C₂×C₄	1	2	yes	—
291	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
292	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
293	#117×C₅₃	C₂³	1	1	yes	characteristic
294	#117×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
296	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
297	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
299	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
300	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
301	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
302	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
304	#97×C₅₃	C₂³	1	2	yes	—
305	#97×C₅₃	C₂³	1	2	yes	—
306	#97×C₅₃	C₂³	1	2	yes	—
307	C₄×C₈×C₅₃	C₂³	1	2	yes	—
308	C₄×C₈×C₅₃	C₂³	1	2	yes	—
309	C₄×C₈×C₅₃	C₂³	1	2	yes	—
310	C₂³×D₅₃	C₂²×C₄	1	1	yes	characteristic
311	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
312	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
314	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
316	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
317	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₂²×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
319	C₂×C₄×D₅₃	—	2	2	no	—
320	C₂×C₄×D₅₃	—	2	2	no	—
321	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
322	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
323	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
324	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
325	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
326	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
327	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
329	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
330	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
331	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
332	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
333	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
334	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
335	M₁₆×C₅₃	—	2	2	no	—
336	M₁₆×C₅₃	—	2	2	no	—
337	C₂×C₈×C₅₃	—	2	2	no	—
338	C₂×C₈×C₅₃	—	2	2	no	—
339	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
340	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
343	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
346	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
347	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
348	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
349	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
350	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
351	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
352	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
353	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
354	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
355	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
356	C₂²⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
357	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
358	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
359	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₄²×C₅₃	C₂⁴	1	2	yes	—
361	C₄²×C₅₃	C₂⁴	1	2	yes	—
362	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
364	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
365	#11719921	C₂²×C₄	1	2	yes	—
366	#11719921	C₂²×C₄	1	2	yes	—
367	#11719921	C₂²×C₄	1	2	yes	—
368	#11719921	C₂²×C₄	1	2	yes	—
369	#11719921	C₂²×C₄	1	1	yes	characteristic
370	#11719921	C₂²×C₄	1	1	yes	characteristic
371	#11719921	C₂²×C₄	1	1	yes	characteristic
372	#11719921	C₂²×C₄	1	1	yes	characteristic
373	#11719921	C₂²×C₄	1	1	yes	characteristic
374	#11719921	C₂²×C₄	1	1	yes	characteristic
375	#11719921	C₂²×C₄	1	1	yes	characteristic
376	#11719921	C₂²×C₄	1	1	yes	characteristic
377	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
378	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
379	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
380	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
381	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
382	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
383	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
384	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
385	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
386	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
387	#11719919	C₂²×C₄	1	2	yes	—
388	#11719919	C₂²×C₄	1	2	yes	—
389	#11719919	C₂²×C₄	1	2	yes	—
390	#11719919	C₂²×C₄	1	2	yes	—
391	#11719919	C₂²×C₄	1	1	yes	characteristic
392	#11719919	C₂²×C₄	1	1	yes	characteristic
393	#11719919	C₂²×C₄	1	1	yes	characteristic
394	#11719919	C₂²×C₄	1	1	yes	characteristic
395	#11719919	C₂²×C₄	1	1	yes	characteristic
396	#11719919	C₂²×C₄	1	1	yes	characteristic
397	#11719919	C₂²×C₄	1	1	yes	characteristic
398	#11719919	C₂²×C₄	1	1	yes	characteristic
399	#11719919	C₂²×C₄	1	2	yes	—
400	#11719919	C₂²×C₄	1	2	yes	—
401	#11719919	C₂²×C₄	1	2	yes	—
402	#11719919	C₂²×C₄	1	2	yes	—
403	#11719919	C₂²×C₄	1	2	yes	—
404	#11719919	C₂²×C₄	1	2	yes	—
405	#11719919	C₂²×C₄	1	2	yes	—
406	#11719919	C₂²×C₄	1	2	yes	—
407	#11719919	C₂²×C₄	1	2	yes	—
408	#11719919	C₂²×C₄	1	2	yes	—
409	#11719919	C₂²×C₄	1	2	yes	—
410	#11719919	C₂²×C₄	1	2	yes	—
411	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
412	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
413	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
414	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
415	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
416	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
417	C₄×Dic₅₃	C₂⁴	1	2	yes	—
418	C₄×Dic₅₃	C₂⁴	1	2	yes	—
419	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	#11719917	—	2	2	no	—
422	#11719917	—	2	2	no	—
423	C₂×#88322	—	2	2	no	—
424	C₂×#88322	—	2	2	no	—
425	C₂×#88322	C₂⁴	1	1	yes	characteristic
426	C₂×#88322	C₂⁴	1	2	yes	—
427	C₂×#88322	C₂⁴	1	1	yes	characteristic
428	C₂×#88322	C₂⁴	1	1	yes	characteristic
429	C₂×#88322	C₂⁴	1	2	yes	—
430	C₂×#88322	C₂⁴	1	1	yes	characteristic
431	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
432	C₂²×D₅₃	—	2	2	no	—
433	C₂²×D₅₃	—	4	1	no	—
434	C₂²×D₅₃	—	4	1	no	—
435	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
436	C₂²×D₅₃	C₂³×C₄	1	1	yes	characteristic
437	Q₈×C₅₃	—	4	2	no	—
438	Q₈×C₅₃	—	4	2	no	—
439	C₂×C₄×C₅₃	—	4	1	no	—
440	C₂×C₄×C₅₃	—	4	1	no	—
441	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
442	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
443	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
444	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
445	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
446	C₂×C₄×C₅₃	C₂³×C₄	1	2	yes	—
447	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
448	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
449	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
450	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
451	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
452	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
453	C₂×Dic₅₃	—	2	2	no	—
454	C₂×Dic₅₃	—	4	1	no	—
455	C₂×Dic₅₃	—	4	1	no	—
456	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
457	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
458	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
459	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
460	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
461	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
462	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
463	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
464	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
465	C₂×Dic₅₃	C₂³×C₄	1	1	yes	characteristic
466	C₄×D₅₃	—	2	2	no	—
467	C₄×D₅₃	—	2	2	no	—
468	C₄×D₅₃	—	2	1	no	—
469	C₄×D₅₃	—	2	1	no	—
470	C₄×D₅₃	—	2	1	no	—
471	C₄×D₅₃	—	2	1	no	—
472	C₄×D₅₃	—	4	2	no	—
473	C₄×D₅₃	—	4	2	no	—
474	C₄×D₅₃	—	4	2	no	—
475	C₄×D₅₃	—	4	2	no	—
476	Dic₁₀₆	—	4	2	no	—
477	Dic₁₀₆	—	4	2	no	—
478	Dic₁₀₆	—	4	2	no	—
479	Dic₁₀₆	—	4	2	no	—
480	Dic₁₀₆	—	4	2	no	—
481	Dic₁₀₆	—	4	2	no	—
482	C₈×C₅₃	—	2	1	no	—
483	C₈×C₅₃	—	2	1	no	—
484	C₈×C₅₃	—	2	1	no	—
485	C₈×C₅₃	—	2	1	no	—
486	C₈×C₅₃	—	2	2	no	—
487	C₈×C₅₃	—	2	2	no	—
488	#88322	—	2	1	no	—
489	#88322	—	2	1	no	—
490	#88322	—	2	1	no	—
491	#88322	—	2	1	no	—
492	#88322	—	2	2	no	—
493	#88322	—	2	2	no	—
494	#60252	—	53	1	no	maximal, Sylow
495	C₂²×C₅₃	—	2	1	no	—
496	C₂²×C₅₃	—	2	1	no	—
497	C₂²×C₅₃	#519	1	2	yes	—
498	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
499	C₂×D₅₃	—	2	1	no	—
500	C₂×D₅₃	—	2	1	no	—
501	C₂×D₅₃	—	2	1	no	—
502	C₂×D₅₃	—	2	1	no	—
503	C₂×D₅₃	—	2	1	no	—
504	C₂×D₅₃	—	2	1	no	—
505	C₂×D₅₃	—	8	2	no	—
506	C₄×C₅₃	—	2	1	no	—
507	C₄×C₅₃	—	2	1	no	—
508	C₄×C₅₃	—	2	2	no	—
509	C₄×C₅₃	—	2	2	no	—
510	C₄×C₅₃	—	2	2	no	—
511	C₄×C₅₃	—	2	2	no	—
512	C₄×C₅₃	—	2	1	no	—
513	C₄×C₅₃	—	2	1	no	—
514	C₄×C₅₃	#519	1	2	yes	—
515	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
517	Dic₅₃	—	2	1	no	—
518	Dic₅₃	—	2	1	no	—
519	Dic₅₃	—	2	2	no	—
520	Dic₅₃	—	2	2	no	—
521	Dic₅₃	—	2	2	no	—
522	Dic₅₃	—	2	2	no	—
523	Dic₅₃	—	2	1	no	—
524	Dic₅₃	—	2	1	no	—
525	Dic₅₃	—	2	1	no	—
526	Dic₅₃	—	2	1	no	—
527	#3458	—	53	1	no	—
528	#2987	—	53	2	no	—
529	#2987	—	53	2	no	—
530	#2986	—	53	2	no	—
531	#2986	—	53	2	no	—
532	#2985	—	53	2	no	—
533	#2985	—	53	2	no	—
534	#2985	—	53	2	no	—
535	#2985	—	53	2	no	—
536	#2962	—	53	1	no	—
537	#2962	—	53	1	no	—
538	#2962	—	53	1	no	—
539	#2962	D₅₃	1	1	yes	characteristic, complemented
540	#2961	—	53	1	no	—
541	#2961	—	53	1	no	—
542	#2960	—	53	1	no	—
543	#2960	—	53	1	no	—
544	#2924	—	53	1	no	—
545	#2924	—	53	1	no	—
546	#2924	—	53	1	no	—
547	#2924	—	53	1	no	—
548	#2921	—	53	1	no	—
549	C₂×#433	—	53	1	no	—
550	C₂×C₅₃	—	2	2	no	—
551	C₂×C₅₃	C₂×#519	1	1	yes	characteristic
552	C₂×C₅₃	#3573	1	1	yes	characteristic
553	C₂×C₅₃	#3573	1	1	yes	characteristic
554	D₅₃	—	4	1	no	—
555	D₅₃	—	4	1	no	—
556	#544	—	53	1	no	—
557	#544	—	53	1	no	—
558	#544	—	53	1	no	—
559	#544	—	53	1	no	—
560	#544	—	53	1	no	—
561	#544	—	53	1	no	—
562	#544	—	53	1	no	—
563	#544	—	53	1	no	—
564	#544	—	53	2	no	—
565	#544	—	53	2	no	—
566	#543	—	53	2	no	—
567	#543	—	53	2	no	—
568	#533	—	53	2	no	—
569	#533	—	53	2	no	—
570	#533	—	53	2	no	—
571	#533	—	53	2	no	—
572	#533	—	53	1	no	—
573	#533	—	53	1	no	—
574	#533	—	53	1	no	—
575	#533	C₂×D₅₃	1	1	yes	characteristic
576	C₂×#117	—	53	1	no	—
577	C₂×#117	—	53	1	no	—
578	C₂×#117	—	53	1	no	—
579	#446	—	53	2	no	—
580	#446	—	53	2	no	—
581	#446	—	53	2	no	—
582	#446	—	53	2	no	—
583	#446	—	53	2	no	—
584	#446	—	53	2	no	—
585	#446	—	53	2	no	—
586	#446	—	53	2	no	—
587	#446	—	53	2	no	—
588	#446	—	53	2	no	—
589	#446	—	53	2	no	—
590	#446	—	53	2	no	—
591	#446	—	53	2	no	—
592	#446	—	53	2	no	—
593	#446	—	53	2	no	—
594	#446	—	53	2	no	—
595	#446	—	53	2	no	—
596	#446	—	53	2	no	—
597	#446	—	53	2	no	—
598	#446	—	53	2	no	—
599	#446	—	53	2	no	—
600	#446	C₂×D₅₃	1	2	yes	complemented
601	#446	C₂×D₅₃	1	2	yes	complemented
602	#446	C₂×D₅₃	1	2	yes	complemented
603	C₈×Q₈	—	53	2	no	—
604	C₈×Q₈	—	53	2	no	—
605	C₈×Q₈	—	53	2	no	—
606	C₈×Q₈	—	53	2	no	—
607	C₈×Q₈	—	53	2	no	—
608	C₈×Q₈	—	53	2	no	—
609	C₈×Q₈	—	53	2	no	—
610	C₈×Q₈	C₂×D₅₃	1	2	yes	complemented
611	#433	—	53	1	no	—
612	#433	—	53	1	no	—
613	#433	—	53	1	no	—
614	#433	—	53	1	no	—
615	#433	—	53	1	no	—
616	#433	—	53	1	no	—
617	#433	—	53	1	no	—
618	#433	—	53	1	no	—
619	#433	—	53	2	no	—
620	#433	—	53	2	no	—
621	#433	—	53	2	no	—
622	#433	—	53	2	no	—
623	#433	—	53	2	no	—
624	#433	—	53	2	no	—
625	#433	—	53	2	no	—
626	#433	—	53	2	no	—
627	#433	—	53	2	no	—
628	#433	—	53	2	no	—
629	#433	—	53	2	no	—
630	#433	—	53	2	no	—
631	#432	—	53	2	no	—
632	#432	—	53	2	no	—
633	#432	—	53	2	no	—
634	#432	—	53	2	no	—
635	#431	—	53	2	no	—
636	#431	—	53	2	no	—
637	#431	—	53	2	no	—
638	#431	—	53	2	no	—
639	#424	—	53	1	no	—
640	#424	—	53	1	no	—
641	#424	—	53	1	no	—
642	#424	—	53	1	no	—
643	#424	—	53	1	no	—
644	#424	—	53	1	no	—
645	#424	C₂×D₅₃	1	1	yes	characteristic
646	#424	C₂×D₅₃	1	1	yes	characteristic
647	#423	—	53	1	no	—
648	#423	—	53	1	no	—
649	C₂×C₄⋊C₈	—	53	1	no	—
650	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
651	#407	—	53	1	no	—
652	#407	—	53	1	no	—
653	C₂×C₂²⋊C₈	—	53	1	no	—
654	C₂×C₂²⋊C₈	—	53	1	no	—
655	#405	—	53	1	no	—
656	#405	—	53	1	no	—
657	#405	—	53	1	no	—
658	#405	—	53	1	no	—
659	#405	—	53	1	no	—
660	#405	—	53	1	no	—
661	#405	C₂×D₅₃	1	1	yes	characteristic
662	#405	C₂×D₅₃	1	1	yes	characteristic
663	C₄×M₁₆	—	53	1	no	—
664	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
665	C₂×#97	—	53	1	no	—
666	C₂×C₄×C₈	—	53	1	no	—
667	C₅₃	#60252	1	1	yes	characteristic, complemented, Sylow
668	C₂³×C₄	—	53	1	no	—
669	C₂×M₁₆	—	53	1	no	—
670	C₂×M₁₆	—	53	1	no	—
671	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
672	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
673	C₂²×C₈	—	53	1	no	—
674	C₂²×C₈	—	53	1	no	—
675	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
676	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
677	C₄⋊Q₈	—	53	2	no	—
678	C₄⋊Q₈	—	53	2	no	—
679	C₄⋊Q₈	—	53	2	no	—
680	C₄⋊Q₈	—	53	2	no	—
681	C₄⋊Q₈	—	53	2	no	—
682	C₄⋊Q₈	—	53	2	no	—
683	C₄⋊Q₈	—	53	2	no	—
684	C₄⋊Q₈	—	53	2	no	—
685	C₄⋊Q₈	—	53	1	no	—
686	C₄⋊Q₈	—	53	1	no	—
687	C₄⋊Q₈	—	53	1	no	—
688	C₄⋊Q₈	—	53	1	no	—
689	C₄⋊Q₈	—	53	1	no	—
690	C₄⋊Q₈	—	53	1	no	—
691	C₄⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
692	C₄⋊Q₈	C₄×D₅₃	1	1	yes	characteristic
693	#125	—	53	2	no	—
694	#125	—	53	2	no	—
695	#125	—	53	2	no	—
696	#125	—	53	2	no	—
697	#125	—	53	2	no	—
698	#125	—	53	2	no	—
699	#125	—	53	2	no	—
700	#125	—	53	2	no	—
701	#125	—	53	1	no	—
702	#125	—	53	1	no	—
703	#125	—	53	1	no	—
704	#125	—	53	1	no	—
705	#125	—	53	1	no	—
706	#125	—	53	1	no	—
707	#125	C₄×D₅₃	1	1	yes	characteristic
708	#125	C₄×D₅₃	1	1	yes	characteristic
709	C₂²⋊Q₈	—	53	2	no	—
710	C₂²⋊Q₈	—	53	2	no	—
711	C₂²⋊Q₈	—	53	2	no	—
712	C₂²⋊Q₈	—	53	2	no	—
713	C₂²⋊Q₈	—	53	2	no	—
714	C₂²⋊Q₈	—	53	2	no	—
715	C₂²⋊Q₈	—	53	2	no	—
716	C₂²⋊Q₈	—	53	2	no	—
717	C₂²⋊Q₈	—	53	2	no	—
718	C₂²⋊Q₈	—	53	2	no	—
719	C₂²⋊Q₈	—	53	2	no	—
720	C₂²⋊Q₈	—	53	2	no	—
721	C₂²⋊Q₈	—	53	2	no	—
722	C₂²⋊Q₈	—	53	2	no	—
723	C₂²⋊Q₈	—	53	2	no	—
724	C₂²⋊Q₈	—	53	2	no	—
725	C₂²⋊Q₈	—	53	2	no	—
726	C₂²⋊Q₈	—	53	2	no	—
727	C₂²⋊Q₈	—	53	2	no	—
728	C₂²⋊Q₈	—	53	2	no	—
729	C₂²⋊Q₈	—	53	2	no	—
730	C₂²⋊Q₈	—	53	2	no	—
731	C₂²⋊Q₈	C₄×D₅₃	1	2	yes	—
732	C₂²⋊Q₈	C₄×D₅₃	1	2	yes	—
733	C₄×Q₈	—	53	2	no	—
734	C₄×Q₈	—	53	2	no	—
735	C₄×Q₈	—	53	2	no	—
736	C₄×Q₈	—	53	2	no	—
737	C₄×Q₈	—	53	2	no	—
738	C₄×Q₈	—	53	2	no	—
739	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
740	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
741	#117	—	53	1	no	—
742	#117	—	53	1	no	—
743	#117	—	53	1	no	—
744	#117	—	53	1	no	—
745	#117	—	53	1	no	—
746	#117	—	53	1	no	—
747	#117	—	53	2	no	—
748	#117	—	53	2	no	—
749	#117	—	53	1	no	—
750	#117	—	53	1	no	—
751	#117	—	53	1	no	—
752	#117	—	53	1	no	—
753	#117	—	53	1	no	—
754	#117	—	53	1	no	—
755	#117	—	53	2	no	—
756	#117	—	53	2	no	—
757	#117	—	53	1	no	—
758	#117	—	53	1	no	—
759	#117	C₂²×D₅₃	1	1	yes	characteristic
760	#117	C₂²×D₅₃	1	1	yes	characteristic
761	C₂×C₄⋊C₄	—	53	1	no	—
762	C₂×C₄⋊C₄	—	53	1	no	—
763	C₂×C₄⋊C₄	—	53	1	no	—
764	C₂×C₄⋊C₄	—	53	1	no	—
765	C₂×C₄⋊C₄	—	53	1	no	—
766	C₂×C₄⋊C₄	—	53	1	no	—
767	C₂×C₂²⋊C₄	—	53	1	no	—
768	C₂×C₂²⋊C₄	—	53	1	no	—
769	C₂×C₂²⋊C₄	—	53	2	no	—
770	C₂×C₂²⋊C₄	—	53	2	no	—
771	C₂×C₄²	—	53	1	no	—
772	C₂×C₄²	—	53	2	no	—
773	C₂×C₄²	—	53	2	no	—
774	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
775	C₄⋊C₈	—	53	2	no	—
776	C₄⋊C₈	—	53	2	no	—
777	C₄⋊C₈	—	53	2	no	—
778	C₄⋊C₈	—	53	2	no	—
779	C₄⋊C₈	—	53	2	no	—
780	C₄⋊C₈	—	53	2	no	—
781	C₄⋊C₈	—	53	2	no	—
782	C₄⋊C₈	—	53	2	no	—
783	C₄⋊C₈	—	53	2	no	—
784	C₄⋊C₈	—	53	2	no	—
785	C₄⋊C₈	—	53	2	no	—
786	C₄⋊C₈	—	53	2	no	—
787	C₄⋊C₈	—	53	1	no	—
788	C₄⋊C₈	—	53	1	no	—
789	C₄⋊C₈	—	53	1	no	—
790	C₄⋊C₈	—	53	1	no	—
791	C₄⋊C₈	—	53	2	no	—
792	C₄⋊C₈	—	53	2	no	—
793	C₄⋊C₈	—	53	2	no	—
794	C₄⋊C₈	—	53	2	no	—
795	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
796	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
797	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
798	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
799	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
800	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
801	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
802	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
803	C₂²⋊C₈	—	53	1	no	—
804	C₂²⋊C₈	—	53	1	no	—
805	C₂²⋊C₈	—	53	1	no	—
806	C₂²⋊C₈	—	53	1	no	—
807	C₂²⋊C₈	—	53	1	no	—
808	C₂²⋊C₈	—	53	1	no	—
809	C₂²⋊C₈	—	53	1	no	—
810	C₂²⋊C₈	—	53	1	no	—
811	C₂²⋊C₈	—	53	2	no	—
812	C₂²⋊C₈	—	53	2	no	—
813	C₂²⋊C₈	—	53	2	no	—
814	C₂²⋊C₈	—	53	2	no	—
815	#97	—	53	1	no	—
816	#97	—	53	1	no	—
817	#97	—	53	1	no	—
818	#97	—	53	1	no	—
819	#97	—	53	2	no	—
820	#97	—	53	2	no	—
821	#97	—	53	2	no	—
822	#97	—	53	2	no	—
823	#97	—	53	2	no	—
824	#97	—	53	2	no	—
825	#97	—	53	2	no	—
826	#97	C₂²×D₅₃	1	2	yes	—
827	#97	C₂²×D₅₃	1	2	yes	—
828	#97	C₂²×D₅₃	1	2	yes	—
829	C₄×C₈	—	53	1	no	—
830	C₄×C₈	—	53	1	no	—
831	C₄×C₈	—	53	1	no	—
832	C₄×C₈	—	53	1	no	—
833	C₄×C₈	—	53	2	no	—
834	C₄×C₈	—	53	2	no	—
835	C₄×C₈	—	53	2	no	—
836	C₄×C₈	—	53	2	no	—
837	C₄×C₈	—	53	2	no	—
838	C₄×C₈	—	53	2	no	—
839	C₄×C₈	—	53	2	no	—
840	C₄×C₈	C₂²×D₅₃	1	2	yes	—
841	C₄×C₈	C₂²×D₅₃	1	2	yes	—
842	C₄×C₈	C₂²×D₅₃	1	2	yes	—
843	C₂⁴	—	53	1	no	—
844	C₂×Q₈	—	53	2	no	—
845	C₂×Q₈	—	53	2	no	—
846	C₂×Q₈	—	53	2	no	—
847	C₂×Q₈	—	53	2	no	—
848	C₂×Q₈	—	53	2	no	—
849	C₂×Q₈	—	53	2	no	—
850	C₂×Q₈	C₂×C₄×D₅₃	1	2	yes	—
851	C₂×Q₈	C₂×C₄×D₅₃	1	2	yes	—
852	C₂²×C₄	—	53	1	no	—
853	C₂²×C₄	—	53	1	no	—
854	C₂²×C₄	—	53	1	no	—
855	C₂²×C₄	—	53	1	no	—
856	C₂²×C₄	—	53	1	no	—
857	C₂²×C₄	—	53	1	no	—
858	C₂²×C₄	—	53	1	no	—
859	C₂²×C₄	—	53	2	no	—
860	C₂²×C₄	—	53	2	no	—
861	C₂²×C₄	—	53	2	no	—
862	C₂²×C₄	—	53	2	no	—
863	C₂²×C₄	—	106	2	no	—
864	C₂²×C₄	—	106	2	no	—
865	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
866	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
867	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
868	M₁₆	—	2	2	no	—
869	M₁₆	—	2	2	no	—
870	M₁₆	—	106	2	no	—
871	M₁₆	—	106	2	no	—
872	C₂×C₈	—	2	2	no	—
873	C₂×C₈	—	2	2	no	—
874	C₂×C₈	—	53	1	no	—
875	C₂×C₈	—	53	2	no	—
876	C₂×C₈	—	53	2	no	—
877	C₂×C₈	—	53	1	no	—
878	C₂×C₈	—	53	1	no	—
879	C₂×C₈	—	53	1	no	—
880	C₂×C₈	—	106	2	no	—
881	C₂×C₈	—	106	2	no	—
882	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
883	C₂×C₈	C₂³×D₅₃	1	2	yes	—
884	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
885	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
886	C₂×C₈	C₂³×D₅₃	1	2	yes	—
887	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
888	C₄⋊C₄	—	53	2	no	—
889	C₄⋊C₄	—	53	2	no	—
890	C₄⋊C₄	—	53	2	no	—
891	C₄⋊C₄	—	53	2	no	—
892	C₄⋊C₄	—	53	1	no	—
893	C₄⋊C₄	—	53	1	no	—
894	C₄⋊C₄	—	53	1	no	—
895	C₄⋊C₄	—	53	1	no	—
896	C₄⋊C₄	—	53	1	no	—
897	C₄⋊C₄	—	53	1	no	—
898	C₄⋊C₄	—	53	1	no	—
899	C₄⋊C₄	—	53	1	no	—
900	C₄⋊C₄	—	53	1	no	—
901	C₄⋊C₄	—	53	1	no	—
902	C₄⋊C₄	—	53	1	no	—
903	C₄⋊C₄	—	53	1	no	—
904	C₄⋊C₄	—	53	2	no	—
905	C₄⋊C₄	—	53	2	no	—
906	C₄⋊C₄	—	53	2	no	—
907	C₄⋊C₄	—	53	2	no	—
908	C₄⋊C₄	—	53	2	no	—
909	C₄⋊C₄	—	53	2	no	—
910	C₄⋊C₄	—	53	2	no	—
911	C₄⋊C₄	—	53	2	no	—
912	C₄⋊C₄	—	53	2	no	—
913	C₄⋊C₄	—	53	2	no	—
914	C₄⋊C₄	—	53	2	no	—
915	C₄⋊C₄	—	53	2	no	—
916	C₄⋊C₄	—	53	2	no	—
917	C₄⋊C₄	—	53	2	no	—
918	C₄⋊C₄	—	53	2	no	—
919	C₄⋊C₄	—	53	2	no	—
920	C₄⋊C₄	—	53	2	no	—
921	C₄⋊C₄	—	53	2	no	—
922	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
923	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
925	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
926	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
927	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
928	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
929	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
930	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
931	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
932	C₂²⋊C₄	—	53	2	no	—
933	C₂²⋊C₄	—	53	2	no	—
934	C₂²⋊C₄	—	53	2	no	—
935	C₂²⋊C₄	—	53	2	no	—
936	C₂²⋊C₄	—	53	2	no	—
937	C₂²⋊C₄	—	53	2	no	—
938	C₂²⋊C₄	—	53	1	no	—
939	C₂²⋊C₄	—	53	1	no	—
940	C₂²⋊C₄	—	53	1	no	—
941	C₂²⋊C₄	—	53	1	no	—
942	C₂²⋊C₄	—	53	1	no	—
943	C₂²⋊C₄	—	53	1	no	—
944	C₂²⋊C₄	—	53	1	no	—
945	C₂²⋊C₄	—	53	1	no	—
946	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
947	C₂²⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
948	C₄²	—	53	2	no	—
949	C₄²	—	53	2	no	—
950	C₄²	—	53	2	no	—
951	C₄²	—	53	2	no	—
952	C₄²	—	53	1	no	—
953	C₄²	—	53	1	no	—
954	C₄²	—	53	1	no	—
955	C₄²	—	53	1	no	—
956	C₄²	—	53	2	no	—
957	C₄²	—	53	2	no	—
958	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
959	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
960	C₄²	C₂³×D₅₃	1	1	yes	characteristic
961	C₄²	C₂³×D₅₃	1	2	yes	—
962	C₄²	C₂³×D₅₃	1	2	yes	—
963	C₄²	C₂³×D₅₃	1	1	yes	characteristic
964	C₂³	—	53	1	no	—
965	C₂³	—	53	1	no	—
966	C₂³	—	106	2	no	—
967	C₂³	—	212	1	no	—
968	C₂³	—	212	1	no	—
969	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	212	2	no	—
973	Q₈	—	212	2	no	—
974	Q₈	—	212	2	no	—
975	Q₈	—	212	2	no	—
976	Q₈	—	212	2	no	—
977	Q₈	—	212	2	no	—
978	C₂×C₄	—	4	1	no	—
979	C₂×C₄	—	4	1	no	—
980	C₂×C₄	—	53	1	no	—
981	C₂×C₄	—	53	1	no	—
982	C₂×C₄	—	53	2	no	—
983	C₂×C₄	—	53	2	no	—
984	C₂×C₄	—	53	1	no	—
985	C₂×C₄	—	53	1	no	—
986	C₂×C₄	—	53	2	no	—
987	C₂×C₄	—	53	2	no	—
988	C₂×C₄	—	53	1	no	—
989	C₂×C₄	—	53	1	no	—
990	C₂×C₄	—	106	2	no	—
991	C₂×C₄	—	106	2	no	—
992	C₂×C₄	—	106	2	no	—
993	C₂×C₄	—	106	1	no	—
994	C₂×C₄	—	106	1	no	—
995	C₂×C₄	—	106	1	no	—
996	C₂×C₄	—	106	1	no	—
997	C₂×C₄	—	212	2	no	—
998	C₂×C₄	—	212	2	no	—
999	C₂×C₄	—	212	2	no	—
1000	C₂×C₄	—	212	2	no	—
1001	C₂×C₄	—	212	1	no	—
1002	C₂×C₄	—	212	1	no	—
1003	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1004	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1005	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1006	C₂×C₄	C₂²×C₄×D₅₃	1	2	yes	—
1007	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1008	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1009	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1010	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1011	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1012	C₂×C₄	#13133264	1	2	yes	—
1013	C₂×C₄	#13133265	1	2	yes	—
1014	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1015	C₈	—	2	1	no	—
1016	C₈	—	2	1	no	—
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	2	no	—
1020	C₈	—	2	2	no	—
1021	C₈	—	106	2	no	—
1022	C₈	—	106	1	no	—
1023	C₈	—	106	1	no	—
1024	C₈	—	106	1	no	—
1025	C₈	—	106	1	no	—
1026	C₈	—	106	2	no	—
1027	C₂²	—	2	1	no	—
1028	C₂²	—	2	1	no	—
1029	C₂²	—	106	1	no	—
1030	C₂²	—	106	1	no	—
1031	C₂²	—	106	1	no	—
1032	C₂²	—	106	1	no	—
1033	C₂²	—	106	1	no	—
1034	C₂²	—	106	1	no	—
1035	C₂²	—	424	2	no	—
1036	C₂²	#16811099	1	2	yes	—
1037	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	2	no	—
1041	C₄	—	2	2	no	—
1042	C₄	—	2	1	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	106	2	no	—
1047	C₄	—	106	2	no	—
1048	C₄	—	106	1	no	—
1049	C₄	—	106	1	no	—
1050	C₄	—	106	2	no	—
1051	C₄	—	106	2	no	—
1052	C₄	—	106	1	no	—
1053	C₄	—	106	1	no	—
1054	C₄	—	106	1	no	—
1055	C₄	—	106	1	no	—
1056	C₄	#16811099	1	2	yes	—
1057	C₄	C₂×#13133264	1	1	yes	characteristic
1058	C₄	C₂×#13133265	1	1	yes	characteristic
1059	C₂	—	2	2	no	—
1060	C₂	—	212	1	no	—
1061	C₂	—	212	1	no	—
1062	C₂	C₂×#16811099	1	1	yes	characteristic
1063	C₂	#20289426	1	1	yes	characteristic
1064	C₂	#20289428	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2962	C₂
prime radical	C₂³×D₅₃	C₂²×C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2962	D₅₃
hypocenter	C₅₃	#60252
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #2962

Complements

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

N	H ≅ G/N	type
2. #20283818	C₂	semidirect
3. #20283818	C₂	semidirect
4. #20283815	C₂	semidirect
5. #20283813	C₂	semidirect
6. #20283811	C₂	semidirect
7. #20283808	C₂	semidirect
8. #20283808	C₂	semidirect
9. #20283806	C₂	semidirect
10. #20283664	C₂	semidirect
11. #20283662	C₂	semidirect
12. #20283658	C₂	semidirect
13. #20283654	C₂	semidirect
14. #20283653	C₂	semidirect
15. #20283648	C₂	semidirect
16. #20283647	C₂	semidirect
23. C₅₃×#2962	C₂	semidirect
46. #16810754	C₂²	semidirect
47. #16810754	C₂²	semidirect
48. #16810754	C₂²	semidirect
49. #16810753	C₂²	semidirect
50. #16810753	C₂²	semidirect
51. #16810753	C₂²	semidirect
52. #16810752	C₂²	semidirect
53. #16810752	C₂²	semidirect
54. #16810752	C₂²	semidirect
55. #16810752	C₂²	semidirect
56. #16810752	C₂²	semidirect
57. #16810752	C₂²	semidirect
58. #16810751	C₂²	semidirect
59. #16810751	C₂²	semidirect
60. #16810751	C₂²	semidirect
61. #16810751	C₂²	semidirect
62. #16810751	C₂²	semidirect
63. #16810751	C₂²	semidirect
64. #16810750	C₂²	semidirect
65. #16810750	C₂²	semidirect
66. #16810750	C₂²	semidirect
67. Q₈×#88322	C₂²	semidirect
68. C₈×Dic₁₀₆	C₂²	semidirect
69. C₈×Dic₁₀₆	C₂²	semidirect
70. C₈×Dic₁₀₆	C₂²	semidirect
71. #16810747	C₂²	semidirect
72. #16810747	C₂²	semidirect
73. #16810747	C₂²	semidirect
125. C₅₃×#446	C₂²	semidirect
126. C₅₃×#446	C₂²	semidirect
127. C₅₃×#446	C₂²	semidirect
128. C₈×Q₈×C₅₃	C₂²	semidirect
539. #2962	D₅₃	semidirect
600. #446	C₂×D₅₃	semidirect
601. #446	C₂×D₅₃	semidirect
602. #446	C₂×D₅₃	semidirect
610. C₈×Q₈	C₂×D₅₃	semidirect
667. C₅₃	#60252	semidirect

Maximal subgroups

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

subgroup	index
#20288118	2
#20283818	2
#20283815	2
#20283813	2
#20283811	2
#20283808	2
#20283806	2
#20283664	2
#20283662	2
#20283658	2
#20283654	2
#20283653	2
#20283648	2
#20283647	2
#20283372	2
#20283370	2
#20283351	2
C₂×#16810683	2
C₅₃×#2962	2
#60252	53