Subgroups — #28250349

Order 13568.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1090 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288142	C₂	1	1	yes	maximal, characteristic
2	#20283886	C₂	1	2	yes	maximal, complemented
3	#20283881	C₂	1	2	yes	maximal, complemented
4	#20283877	C₂	1	1	yes	maximal, characteristic, complemented
5	#20283866	C₂	1	1	yes	maximal, characteristic, complemented
6	#20283861	C₂	1	2	yes	maximal, complemented
7	#20283844	C₂	1	1	yes	maximal, characteristic, complemented
8	#20283832	C₂	1	1	yes	maximal, characteristic, complemented
9	#20283816	C₂	1	1	yes	maximal, characteristic, complemented
10	#20283809	C₂	1	1	yes	maximal, characteristic, complemented
11	#20283808	C₂	1	2	yes	maximal, complemented
12	#20283802	C₂	1	1	yes	maximal, characteristic, complemented
13	#20283730	C₂	1	1	yes	maximal, characteristic, complemented
14	#20283719	C₂	1	1	yes	maximal, characteristic, complemented
15	#20283712	C₂	1	2	yes	maximal, complemented
16	#20283706	C₂	1	2	yes	maximal, complemented
17	#20283701	C₂	1	2	yes	maximal, complemented
18	#20283690	C₂	1	1	yes	maximal, characteristic, complemented
19	M₁₆×Dic₁₀₆	C₂	1	1	yes	maximal, characteristic, complemented
20	#20283662	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283651	C₂	1	2	yes	maximal, complemented
22	#20283649	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2965	C₂	1	1	yes	maximal, characteristic, complemented
24	#16811251	C₄	1	1	yes	characteristic
25	#16811244	C₄	1	1	yes	characteristic
26	#16811244	C₄	1	1	yes	characteristic
27	#16811238	C₄	1	2	yes	—
28	#16811235	C₄	1	1	yes	characteristic
29	#16811235	C₄	1	1	yes	characteristic
30	#16811231	C₄	1	2	yes	—
31	#16811215	C₄	1	2	yes	—
32	#16811215	C₄	1	2	yes	—
33	#16811201	C₄	1	1	yes	characteristic
34	#16811199	C₄	1	1	yes	characteristic
35	#16811194	C₄	1	1	yes	characteristic
36	#16811180	C₂²	1	1	yes	characteristic
37	#16811180	C₂²	1	1	yes	characteristic
38	#16811177	C₂²	1	2	yes	—
39	#16811157	C₂²	1	1	yes	characteristic
40	#16811157	C₂²	1	1	yes	characteristic
41	#16811155	C₂²	1	2	yes	—
42	#16811153	C₂²	1	2	yes	—
43	#16811153	C₂²	1	2	yes	—
44	C₄×#11719945	C₂²	1	1	yes	characteristic
45	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
46	#16810754	C₂²	1	2	yes	—
47	#16810753	C₂²	1	2	yes	—
48	#16810753	C₂²	1	1	yes	characteristic
49	#16810753	C₂²	1	1	yes	characteristic
50	#16810753	C₂²	1	1	yes	characteristic
51	#16810753	C₂²	1	1	yes	characteristic
52	#16810753	C₂²	1	1	yes	characteristic
53	#16810753	C₂²	1	1	yes	characteristic
54	#16810752	C₂²	1	2	yes	—
55	#16810752	C₂²	1	2	yes	—
56	#16810752	C₂²	1	2	yes	—
57	#16810752	C₂²	1	2	yes	—
58	#16810751	C₂²	1	2	yes	—
59	#16810751	C₂²	1	2	yes	—
60	#16810751	C₂²	1	2	yes	—
61	#16810751	C₂²	1	2	yes	—
62	#16810750	C₂²	1	2	yes	—
63	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
64	C₈×Dic₁₀₆	C₂²	1	2	yes	—
65	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
66	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
67	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
68	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
69	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic
70	#16810747	C₂²	1	2	yes	—
71	#16810702	C₂²	1	1	yes	characteristic
72	#16810702	C₂²	1	1	yes	characteristic
73	#16810701	C₂²	1	2	yes	—
74	#16810699	C₂²	1	2	yes	—
75	#16810698	C₂²	1	2	yes	—
76	#16810698	C₂²	1	2	yes	—
77	#16810698	C₂²	1	2	yes	—
78	#16810697	C₂²	1	2	yes	—
79	#16810695	C₂²	1	2	yes	—
80	#16810695	C₂²	1	2	yes	—
81	#16810694	C₂²	1	2	yes	—
82	#16810692	C₂²	1	2	yes	—
83	#16810692	C₂²	1	2	yes	—
84	#16810692	C₂²	1	2	yes	—
85	#16810691	C₂²	1	2	yes	—
86	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
87	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
88	C₈×C₂²⋊D₅₃	C₂²	1	2	yes	—
89	#16810686	C₂²	1	2	yes	—
90	#16810685	C₂²	1	2	yes	—
91	#16810683	C₂²	1	2	yes	—
92	#16810683	C₂²	1	2	yes	—
93	#16810682	C₂²	1	2	yes	—
94	#16810681	C₂²	1	2	yes	—
95	#16810681	C₂²	1	2	yes	—
96	#16810681	C₂²	1	2	yes	—
97	#16810681	C₂²	1	2	yes	—
98	#16810680	C₂²	1	1	yes	characteristic
99	#16810680	C₂²	1	1	yes	characteristic
100	#16810678	C₂²	1	2	yes	—
101	#16810677	C₂²	1	2	yes	—
102	#16810676	C₂²	1	1	yes	characteristic
103	#16810675	C₂²	1	2	yes	—
104	#16810673	C₂²	1	2	yes	—
105	#16810651	C₂²	1	2	yes	—
106	#16810649	C₂²	1	2	yes	—
107	#16810648	C₂²	1	2	yes	—
108	#16810648	C₂²	1	2	yes	—
109	#16810647	C₂²	1	1	yes	characteristic
110	#16810647	C₂²	1	1	yes	characteristic
111	#16810646	C₂²	1	2	yes	—
112	#16810645	C₂²	1	2	yes	—
113	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
114	#16810581	C₂²	1	2	yes	—
115	#16810580	C₂²	1	2	yes	—
116	#16810578	C₂²	1	2	yes	—
117	#16810577	C₂²	1	2	yes	—
118	M₁₆×Dic₅₃	C₂²	1	2	yes	—
119	#97×D₅₃	C₂²	1	2	yes	—
120	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
121	C₅₃×#446	C₂²	1	1	yes	characteristic
122	C₅₃×#446	C₂²	1	1	yes	characteristic
123	C₅₃×#436	C₂²	1	1	yes	characteristic
124	C₅₃×#436	C₂²	1	1	yes	characteristic
125	C₅₃×#435	C₂²	1	1	yes	characteristic
126	C₅₃×#435	C₂²	1	1	yes	characteristic
127	C₅₃×#435	C₂²	1	1	yes	characteristic
128	C₅₃×#435	C₂²	1	1	yes	characteristic
129	C₅₃×#431	C₂²	1	1	yes	characteristic
130	C₅₃×#431	C₂²	1	1	yes	characteristic
131	C₅₃×#431	C₂²	1	1	yes	characteristic
132	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#11719945	C₂×C₄	1	1	yes	characteristic
136	C₂²×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
137	C₂×#11719917	C₂³	1	2	yes	—
138	C₂×#11719917	C₂³	1	2	yes	—
139	C₂×#11719912	C₂³	1	2	yes	—
140	C₂×#11719912	C₂³	1	2	yes	—
141	C₂²×#88322	C₂³	1	2	yes	—
142	C₂×C₈×D₅₃	C₂³	1	2	yes	—
143	C₂×C₈×D₅₃	C₂³	1	2	yes	—
144	#13133217	C₂×C₄	1	1	yes	characteristic
145	#13133217	C₂×C₄	1	1	yes	characteristic
146	#13133217	C₂×C₄	1	1	yes	characteristic
147	#13133217	C₂×C₄	1	1	yes	characteristic
148	#13133216	C₂×C₄	1	2	yes	—
149	#13133215	C₂×C₄	1	2	yes	—
150	#13133212	C₂×C₄	1	2	yes	—
151	#13133212	C₂×C₄	1	2	yes	—
152	#13133211	C₂×C₄	1	2	yes	—
153	#13133211	C₂×C₄	1	2	yes	—
154	#13133210	C₂×C₄	1	2	yes	—
155	#13133210	C₂×C₄	1	2	yes	—
156	#13133210	C₂×C₄	1	2	yes	—
157	#13133210	C₂×C₄	1	2	yes	—
158	#13133209	C₂×C₄	1	1	yes	characteristic
159	#13133209	C₂×C₄	1	1	yes	characteristic
160	#13133209	C₂×C₄	1	2	yes	—
161	#13133209	C₂×C₄	1	2	yes	—
162	#13133208	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	#13133205	C₂×C₄	1	1	yes	characteristic
168	#13133205	C₂×C₄	1	1	yes	characteristic
169	#13133204	C₂×C₄	1	2	yes	—
170	#13133203	C₂×C₄	1	2	yes	—
171	#13133203	C₂×C₄	1	2	yes	—
172	#13133201	C₂×C₄	1	2	yes	—
173	#13133201	C₂×C₄	1	2	yes	—
174	#13133200	C₂×C₄	1	2	yes	—
175	#13133200	C₂×C₄	1	2	yes	—
176	#13133199	C₂×C₄	1	2	yes	—
177	#13133199	C₂×C₄	1	2	yes	—
178	#13133198	C₂×C₄	1	2	yes	—
179	#13133198	C₂×C₄	1	2	yes	—
180	#13133197	C₂×C₄	1	2	yes	—
181	#13133197	C₂×C₄	1	2	yes	—
182	#13133196	C₂×C₄	1	1	yes	characteristic
183	#13133196	C₂×C₄	1	1	yes	characteristic
184	#13133196	C₂×C₄	1	1	yes	characteristic
185	#13133196	C₂×C₄	1	1	yes	characteristic
186	#13133196	C₂×C₄	1	1	yes	characteristic
187	#13133196	C₂×C₄	1	1	yes	characteristic
188	#13133196	C₂×C₄	1	2	yes	—
189	#13133196	C₂×C₄	1	2	yes	—
190	#13133195	C₂×C₄	1	2	yes	—
191	#13133195	C₂×C₄	1	2	yes	—
192	#13133194	C₂×C₄	1	2	yes	—
193	#13133194	C₂×C₄	1	2	yes	—
194	#13133193	C₂×C₄	1	2	yes	—
195	#13133191	C₂×C₄	1	1	yes	characteristic
196	#13133191	C₂×C₄	1	1	yes	characteristic
197	#13133189	C₂×C₄	1	2	yes	—
198	#13133189	C₂×C₄	1	2	yes	—
199	#13133188	C₂×C₄	1	2	yes	—
200	C₄×Dic₁₀₆	C₂×C₄	1	2	yes	—
201	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
202	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
203	C₄×Dic₁₀₆	C₂×C₄	1	1	yes	characteristic
204	C₄×Dic₁₀₆	C₂³	1	2	yes	—
205	C₄×Dic₁₀₆	C₂³	1	2	yes	—
206	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
207	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
208	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
209	C₄×Dic₁₀₆	C₂³	1	2	yes	—
210	C₄×D₂₁₂	C₂×C₄	1	1	yes	characteristic
211	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
212	C₄×C₂²⋊D₅₃	C₂×C₄	1	2	yes	—
213	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
214	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₅₃	C₂³	1	2	yes	—
216	#13133176	C₂×C₄	1	1	yes	characteristic
217	#13133176	C₂³	1	2	yes	—
218	#13133176	C₂³	1	2	yes	—
219	#13133174	C₂×C₄	1	2	yes	—
220	#13133174	C₂³	1	2	yes	—
221	#13133174	C₂³	1	2	yes	—
222	C₂×C₄⋊Dic₅₃	C₂×C₄	1	1	yes	characteristic
223	C₂×#11719919	C₂×C₄	1	2	yes	—
224	C₂×C₄×Dic₅₃	C₂³	1	2	yes	—
225	C₄²×D₅₃	C₂³	1	2	yes	—
226	C₄⋊#88322	C₂³	1	1	yes	characteristic
227	C₄⋊#88322	C₂³	1	1	yes	characteristic
228	C₄⋊#88322	C₂³	1	2	yes	—
229	C₄⋊#88322	C₂³	1	1	yes	characteristic
230	C₄⋊#88322	C₂³	1	1	yes	characteristic
231	C₄⋊#88322	C₂³	1	2	yes	—
232	C₄⋊#88322	C₂³	1	2	yes	—
233	#13133146	C₂³	1	2	yes	—
234	#13133146	C₂³	1	2	yes	—
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	C₂²⋊#88322	C₂³	1	2	yes	—
246	C₂²⋊#88322	C₂³	1	2	yes	—
247	C₂²⋊#88322	C₂³	1	2	yes	—
248	#13133129	C₂³	1	2	yes	—
249	#13133129	C₂³	1	2	yes	—
250	#13133129	C₂³	1	2	yes	—
251	#13133129	C₂³	1	2	yes	—
252	#13133128	C₂³	1	2	yes	—
253	#13133128	C₂³	1	2	yes	—
254	#13133127	C₂³	1	2	yes	—
255	#13133127	C₂³	1	2	yes	—
256	#13133127	C₂³	1	2	yes	—
257	#13133127	C₂³	1	2	yes	—
258	#13133127	C₂³	1	2	yes	—
259	#13133127	C₂³	1	2	yes	—
260	C₄×#88322	C₂³	1	2	yes	—
261	C₈×Dic₅₃	C₂³	1	2	yes	—
262	C₈×Dic₅₃	C₂³	1	2	yes	—
263	C₈×Dic₅₃	C₂³	1	2	yes	—
264	C₈×Dic₅₃	C₂³	1	2	yes	—
265	C₈×Dic₅₃	C₂³	1	2	yes	—
266	C₈×Dic₅₃	C₂³	1	2	yes	—
267	C₂×#41×C₅₃	C₂×C₄	1	1	yes	characteristic
268	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
274	C₄×Q₈×C₅₃	C₂×C₄	1	1	yes	characteristic
275	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
277	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
278	C₄×D₄×C₅₃	C₂×C₄	1	1	yes	characteristic
279	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
282	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
283	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
284	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
285	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
291	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
296	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
297	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
298	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
299	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
300	#97×C₅₃	C₂³	1	1	yes	characteristic
301	#97×C₅₃	C₂³	1	1	yes	characteristic
302	#97×C₅₃	C₂³	1	1	yes	characteristic
303	#97×C₅₃	C₂³	1	1	yes	characteristic
304	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	#41×C₅₃	—	4	2	no	—
311	C₂×Q₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
312	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
313	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
314	C₂×D₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
316	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
317	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
318	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
319	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
320	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
321	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
324	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
325	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
326	C₂×C₂²⋊D₅₃	C₂²×C₄	1	2	yes	—
327	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
328	C₂²×Dic₅₃	C₂²×C₄	1	2	yes	—
329	#11719945	—	4	2	no	—
330	C₂×D₂₁₂	C₂²×C₄	1	1	yes	characteristic
331	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
332	C₂×C₄×D₅₃	C₂²×C₄	1	2	yes	—
333	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
334	C₂×Dic₁₀₆	—	4	2	no	—
335	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
336	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
337	C₂×Dic₁₀₆	C₂²×C₄	1	1	yes	characteristic
338	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
339	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
340	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
341	M₁₆×C₅₃	—	2	2	no	—
342	M₁₆×C₅₃	—	2	2	no	—
343	M₁₆×C₅₃	—	4	1	no	—
344	M₁₆×C₅₃	—	4	1	no	—
345	C₂×C₈×C₅₃	—	2	2	no	—
346	C₂×C₈×C₅₃	—	4	1	no	—
347	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
356	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
357	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
358	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
359	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
360	C₄⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
361	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
362	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
363	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
364	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
365	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
366	C₂²⋊C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
367	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
368	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
369	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
370	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
371	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
372	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
373	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
378	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
379	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
380	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
381	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
382	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊Dic₅₃	C₂²×C₄	1	2	yes	—
384	#11719921	C₂²×C₄	1	2	yes	—
385	#11719921	C₂²×C₄	1	2	yes	—
386	#11719921	C₂²×C₄	1	2	yes	—
387	#11719921	C₂²×C₄	1	2	yes	—
388	#11719921	C₂²×C₄	1	2	yes	—
389	#11719921	C₂²×C₄	1	2	yes	—
390	#11719921	C₂²×C₄	1	2	yes	—
391	#11719921	C₂²×C₄	1	2	yes	—
392	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
393	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
394	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
395	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
396	C₄⋊Dic₅₃	C₂²×C₄	1	1	yes	characteristic
397	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
398	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
399	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
400	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
401	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
402	C₄⋊Dic₅₃	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	#11719919	C₂²×C₄	1	2	yes	—
412	#11719919	C₂²×C₄	1	2	yes	—
413	#11719919	C₂²×C₄	1	2	yes	—
414	#11719919	C₂²×C₄	1	2	yes	—
415	#11719919	C₂²×C₄	1	2	yes	—
416	#11719919	C₂²×C₄	1	2	yes	—
417	#11719919	C₂²×C₄	1	2	yes	—
418	#11719919	C₂²×C₄	1	2	yes	—
419	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
420	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
421	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
422	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
423	C₄×Dic₅₃	C₂⁴	1	2	yes	—
424	C₄×Dic₅₃	C₂⁴	1	2	yes	—
425	C₄×Dic₅₃	C₂⁴	1	2	yes	—
426	#11719917	—	4	2	no	—
427	#11719917	—	4	2	no	—
428	C₂×#88322	—	4	2	no	—
429	C₂×#88322	C₂⁴	1	2	yes	—
430	C₂×#88322	C₂⁴	1	2	yes	—
431	C₂×#88322	C₂⁴	1	2	yes	—
432	C₂×#88322	C₂⁴	1	2	yes	—
433	#11719912	—	4	2	no	—
434	#11719912	—	4	2	no	—
435	C₈×D₅₃	—	2	4	no	—
436	C₈×D₅₃	—	4	2	no	—
437	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
438	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
439	C₂³×C₅₃	C₂³×C₄	1	1	yes	characteristic
440	C₂²×D₅₃	C₂³×C₄	1	2	yes	—
441	Q₈×C₅₃	—	4	1	no	—
442	D₄×C₅₃	—	4	1	no	—
443	D₄×C₅₃	—	4	1	no	—
444	D₄×C₅₃	—	4	1	no	—
445	C₂×C₄×C₅₃	—	2	2	no	—
446	C₂×C₄×C₅₃	—	2	2	no	—
447	C₂×C₄×C₅₃	—	2	2	no	—
448	C₂×C₄×C₅₃	—	2	1	no	—
449	C₂×C₄×C₅₃	—	2	1	no	—
450	C₂×C₄×C₅₃	—	2	1	no	—
451	C₂×C₄×C₅₃	—	2	1	no	—
452	C₂×C₄×C₅₃	—	2	1	no	—
453	C₂×C₄×C₅₃	—	2	1	no	—
454	C₂×C₄×C₅₃	—	4	1	no	—
455	C₂×C₄×C₅₃	—	4	1	no	—
456	C₂×C₄×C₅₃	—	4	1	no	—
457	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
459	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
461	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
462	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
463	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
464	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
465	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
466	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
467	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
468	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₅₃	—	4	2	no	—
470	C₂²⋊D₅₃	—	4	2	no	—
471	C₂²⋊D₅₃	—	4	2	no	—
472	C₂×Dic₅₃	—	4	2	no	—
473	C₂×Dic₅₃	—	4	2	no	—
474	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
475	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
476	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
477	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
478	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
479	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
480	C₂×Dic₅₃	C₂³×C₄	1	2	yes	—
481	D₂₁₂	—	2	2	no	—
482	C₄×D₅₃	—	2	2	no	—
483	C₄×D₅₃	—	2	2	no	—
484	C₄×D₅₃	—	4	2	no	—
485	C₄×D₅₃	—	4	2	no	—
486	Dic₁₀₆	—	2	2	no	—
487	Dic₁₀₆	—	2	2	no	—
488	Dic₁₀₆	—	2	2	no	—
489	Dic₁₀₆	—	4	2	no	—
490	Dic₁₀₆	—	4	2	no	—
491	Dic₁₀₆	—	4	2	no	—
492	C₈×C₅₃	—	2	1	no	—
493	C₈×C₅₃	—	2	1	no	—
494	C₈×C₅₃	—	2	1	no	—
495	C₈×C₅₃	—	2	1	no	—
496	C₈×C₅₃	—	2	1	no	—
497	C₈×C₅₃	—	2	1	no	—
498	C₈×C₅₃	—	2	1	no	—
499	C₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
500	#88322	—	2	2	no	—
501	#88322	—	2	2	no	—
502	#88322	—	2	2	no	—
503	#88322	—	2	2	no	—
504	#60344	—	53	1	no	maximal, Sylow
505	C₂²×C₅₃	—	2	1	no	—
506	C₂²×C₅₃	—	2	1	no	—
507	C₂²×C₅₃	—	2	1	no	—
508	C₂²×C₅₃	—	2	1	no	—
509	C₂²×C₅₃	—	2	1	no	—
510	C₂²×C₅₃	—	2	1	no	—
511	C₂²×C₅₃	—	2	1	no	—
512	C₂²×C₅₃	—	2	1	no	—
513	C₂²×C₅₃	—	2	1	no	—
514	C₂²×C₅₃	C₂⁴×C₄	1	1	yes	characteristic
515	C₂×D₅₃	—	2	2	no	—
516	C₂×D₅₃	—	2	2	no	—
517	C₂×D₅₃	—	2	2	no	—
518	C₄×C₅₃	—	2	1	no	—
519	C₄×C₅₃	—	2	1	no	—
520	C₄×C₅₃	—	2	1	no	—
521	C₄×C₅₃	—	2	1	no	—
522	C₄×C₅₃	—	2	1	no	—
523	C₄×C₅₃	—	2	1	no	—
524	C₄×C₅₃	—	2	1	no	—
525	C₄×C₅₃	—	2	1	no	—
526	C₄×C₅₃	—	2	1	no	—
527	C₄×C₅₃	—	2	1	no	—
528	C₄×C₅₃	#568	1	2	yes	—
529	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄×C₅₃	#585	1	1	yes	characteristic
531	Dic₅₃	—	2	2	no	—
532	Dic₅₃	—	2	2	no	—
533	Dic₅₃	—	2	2	no	—
534	Dic₅₃	—	2	2	no	—
535	Dic₅₃	—	2	2	no	—
536	Dic₅₃	—	2	2	no	—
537	Dic₅₃	—	2	2	no	—
538	#3461	—	53	1	no	—
539	#2995	—	53	2	no	—
540	#2995	—	53	2	no	—
541	#2994	—	53	1	no	—
542	#2993	—	53	2	no	—
543	#2993	—	53	1	no	—
544	#2991	—	53	1	no	—
545	#2989	—	53	1	no	—
546	#2986	—	53	1	no	—
547	#2985	—	53	2	no	—
548	#2985	—	53	1	no	—
549	#2984	—	53	1	no	—
550	#2970	—	53	1	no	—
551	#2969	—	53	2	no	—
552	#2969	—	53	1	no	—
553	#2968	—	53	2	no	—
554	#2967	—	53	2	no	—
555	#2966	—	53	1	no	—
556	#2965	D₅₃	1	1	yes	characteristic, complemented
557	Q₈×M₁₆	—	53	1	no	—
558	#2962	—	53	1	no	—
559	#2961	—	53	2	no	—
560	#2960	—	53	1	no	—
561	C₂×C₅₃	—	4	1	no	—
562	C₂×C₅₃	—	4	1	no	—
563	C₂×C₅₃	—	4	1	no	—
564	C₂×C₅₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
565	C₂×C₅₃	C₂×#568	1	1	yes	characteristic
566	C₂×C₅₃	#3573	1	1	yes	characteristic
567	D₅₃	—	4	2	no	—
568	#544	—	53	1	no	—
569	#542	—	53	2	no	—
570	#542	—	53	1	no	—
571	#542	—	53	1	no	—
572	#541	—	53	2	no	—
573	#541	—	53	1	no	—
574	#541	—	53	1	no	—
575	#539	—	53	2	no	—
576	#539	—	53	2	no	—
577	#537	—	53	1	no	—
578	#536	—	53	1	no	—
579	#536	—	53	1	no	—
580	#533	—	53	2	no	—
581	#533	—	53	1	no	—
582	#533	—	53	1	no	—
583	#529	—	53	2	no	—
584	#529	—	53	2	no	—
585	#529	—	53	2	no	—
586	#529	—	53	1	no	—
587	#529	—	53	1	no	—
588	C₄×#41	—	53	1	no	—
589	C₄×#41	C₂×D₅₃	1	1	yes	characteristic
590	C₂×C₄×Q₈	—	53	1	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	—	53	2	no	—
601	#446	—	53	2	no	—
602	#446	—	53	1	no	—
603	#446	—	53	1	no	—
604	#446	—	53	1	no	—
605	#446	—	53	1	no	—
606	#446	—	53	1	no	—
607	#446	—	53	1	no	—
608	#446	C₂×D₅₃	1	1	yes	characteristic
609	#446	C₂×D₅₃	1	1	yes	characteristic
610	C₈×Q₈	—	53	2	no	—
611	C₈×Q₈	—	53	1	no	—
612	C₈×Q₈	—	53	2	no	—
613	C₈×Q₈	—	53	1	no	—
614	C₈×Q₈	—	53	1	no	—
615	C₈×Q₈	—	53	1	no	—
616	C₈×Q₈	—	53	1	no	—
617	C₈×Q₈	—	53	1	no	—
618	#436	—	53	2	no	—
619	#436	—	53	2	no	—
620	#436	—	53	2	no	—
621	#436	—	53	2	no	—
622	#436	—	53	2	no	—
623	#436	—	53	1	no	—
624	#436	—	53	1	no	—
625	#436	C₂×D₅₃	1	1	yes	characteristic
626	#436	C₂×D₅₃	1	1	yes	characteristic
627	#435	—	53	2	no	—
628	#435	—	53	2	no	—
629	#435	—	53	2	no	—
630	#435	—	53	2	no	—
631	#435	—	53	2	no	—
632	#435	—	53	2	no	—
633	#435	—	53	2	no	—
634	#435	—	53	2	no	—
635	#435	C₂×D₅₃	1	1	yes	characteristic
636	#435	C₂×D₅₃	1	1	yes	characteristic
637	#435	C₂×D₅₃	1	1	yes	characteristic
638	#435	C₂×D₅₃	1	1	yes	characteristic
639	C₈×D₄	—	53	2	no	—
640	C₈×D₄	—	53	2	no	—
641	C₈×D₄	—	53	1	no	—
642	C₈×D₄	—	53	1	no	—
643	#433	—	53	2	no	—
644	#433	—	53	2	no	—
645	#433	—	53	2	no	—
646	#433	—	53	2	no	—
647	#433	—	53	2	no	—
648	#433	—	53	2	no	—
649	#433	—	53	2	no	—
650	#433	—	53	2	no	—
651	#432	—	53	1	no	—
652	#432	—	53	1	no	—
653	#432	—	53	2	no	—
654	#432	—	53	2	no	—
655	#431	—	53	1	no	—
656	#431	—	53	2	no	—
657	#431	—	53	2	no	—
658	#431	C₂×D₅₃	1	1	yes	characteristic
659	#431	C₂×D₅₃	1	1	yes	characteristic
660	#431	C₂×D₅₃	1	1	yes	characteristic
661	#424	—	53	2	no	—
662	#424	—	53	2	no	—
663	#424	—	53	2	no	—
664	#424	—	53	2	no	—
665	#423	—	53	2	no	—
666	#423	—	53	1	no	—
667	#423	—	53	1	no	—
668	#423	—	53	2	no	—
669	C₂×C₄⋊C₈	—	53	1	no	—
670	#405	—	53	2	no	—
671	#405	—	53	2	no	—
672	#405	—	53	2	no	—
673	#405	—	53	2	no	—
674	C₄×M₁₆	—	53	2	no	—
675	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
676	C₄×M₁₆	C₂×D₅₃	1	1	yes	characteristic
677	C₂×#97	—	53	2	no	—
678	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
679	C₅₃	#60344	1	1	yes	characteristic, complemented, Sylow
680	C₂×#41	—	53	1	no	—
681	C₂×#41	C₄×D₅₃	1	1	yes	characteristic
682	C₂²×Q₈	—	53	1	no	—
683	C₂×M₁₆	—	53	2	no	—
684	C₂×M₁₆	—	53	2	no	—
685	C₂×M₁₆	—	53	2	no	—
686	C₂×M₁₆	—	53	2	no	—
687	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
688	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
689	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
690	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
691	C₂²×C₈	—	53	2	no	—
692	C₂²×C₈	—	53	2	no	—
693	C₂²×C₈	—	53	2	no	—
694	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
695	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
696	C₄⋊Q₈	—	53	2	no	—
697	C₄⋊Q₈	—	53	2	no	—
698	C₄⋊Q₈	—	53	1	no	—
699	C₄⋊Q₈	—	53	1	no	—
700	C₄⋊Q₈	—	53	1	no	—
701	C₄⋊Q₈	—	53	1	no	—
702	#126	—	53	2	no	—
703	#126	—	53	2	no	—
704	#126	—	53	2	no	—
705	#126	—	53	2	no	—
706	#126	—	53	2	no	—
707	#126	—	53	2	no	—
708	#126	—	53	2	no	—
709	#126	—	53	2	no	—
710	#125	—	53	2	no	—
711	#125	—	53	2	no	—
712	#125	—	53	2	no	—
713	#125	—	53	2	no	—
714	#125	—	53	2	no	—
715	#125	—	53	1	no	—
716	#125	—	53	1	no	—
717	#125	—	53	2	no	—
718	#125	—	53	2	no	—
719	#124	—	53	2	no	—
720	#124	—	53	2	no	—
721	#124	—	53	2	no	—
722	#124	—	53	1	no	—
723	#124	—	53	1	no	—
724	#123	—	53	2	no	—
725	#123	—	53	2	no	—
726	#123	—	53	2	no	—
727	#123	—	53	2	no	—
728	#123	—	53	2	no	—
729	#123	—	53	2	no	—
730	#123	—	53	2	no	—
731	#123	—	53	2	no	—
732	C₂²⋊Q₈	—	53	2	no	—
733	C₂²⋊Q₈	—	53	1	no	—
734	C₂²⋊Q₈	—	53	1	no	—
735	C₂²⋊Q₈	—	53	1	no	—
736	C₂²⋊Q₈	—	53	1	no	—
737	C₂²⋊Q₈	—	53	1	no	—
738	C₂²⋊Q₈	—	53	1	no	—
739	C₂²⋊Q₈	—	53	2	no	—
740	C₂²⋊Q₈	—	53	2	no	—
741	C₂²⋊Q₈	—	53	2	no	—
742	C₂²⋊Q₈	—	53	2	no	—
743	C₂²⋊Q₈	—	53	2	no	—
744	C₂²⋊Q₈	—	53	2	no	—
745	C₂²⋊Q₈	—	53	2	no	—
746	C₂²⋊Q₈	—	53	2	no	—
747	#121	—	53	2	no	—
748	#121	—	53	2	no	—
749	#121	—	53	2	no	—
750	#121	—	53	1	no	—
751	#121	—	53	1	no	—
752	C₄×Q₈	—	53	2	no	—
753	C₄×Q₈	—	53	1	no	—
754	C₄×Q₈	—	53	1	no	—
755	C₄×Q₈	—	53	1	no	—
756	C₄×Q₈	—	53	1	no	—
757	C₄×Q₈	—	53	1	no	—
758	C₄×Q₈	—	53	2	no	—
759	C₄×Q₈	—	53	1	no	—
760	C₄×Q₈	—	53	2	no	—
761	C₄×Q₈	—	53	2	no	—
762	C₄×Q₈	C₄×D₅₃	1	1	yes	characteristic
763	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
764	C₄×D₄	—	53	2	no	—
765	C₄×D₄	—	53	2	no	—
766	C₄×D₄	—	53	2	no	—
767	C₄×D₄	—	53	2	no	—
768	C₄×D₄	—	53	1	no	—
769	C₄×D₄	—	53	1	no	—
770	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
771	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
772	C₄×D₄	C₄×D₅₃	1	1	yes	characteristic
773	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
774	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
775	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
776	#117	—	53	1	no	—
777	#117	—	53	2	no	—
778	#117	—	53	2	no	—
779	#117	—	53	2	no	—
780	#117	—	53	2	no	—
781	#117	—	53	2	no	—
782	#117	C₄×D₅₃	1	1	yes	characteristic
783	#117	C₄×D₅₃	1	1	yes	characteristic
784	#117	C₄×D₅₃	1	1	yes	characteristic
785	C₂×C₄⋊C₄	—	53	1	no	—
786	C₂×C₄⋊C₄	—	53	2	no	—
787	C₂×C₄²	—	53	2	no	—
788	C₂×C₄²	—	53	2	no	—
789	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
790	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
791	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
792	C₄⋊C₈	—	53	2	no	—
793	C₄⋊C₈	—	53	2	no	—
794	C₄⋊C₈	—	53	2	no	—
795	C₄⋊C₈	—	53	2	no	—
796	C₄⋊C₈	—	53	2	no	—
797	C₄⋊C₈	—	53	2	no	—
798	C₄⋊C₈	—	53	2	no	—
799	C₄⋊C₈	—	53	2	no	—
800	C₄⋊C₈	—	53	2	no	—
801	C₄⋊C₈	—	53	2	no	—
802	C₄⋊C₈	—	53	2	no	—
803	C₄⋊C₈	—	53	2	no	—
804	C₄⋊C₈	—	53	1	no	—
805	C₄⋊C₈	—	53	1	no	—
806	C₄⋊C₈	—	53	2	no	—
807	C₄⋊C₈	—	53	2	no	—
808	C₄⋊C₈	—	53	1	no	—
809	C₄⋊C₈	—	53	2	no	—
810	C₄⋊C₈	—	53	1	no	—
811	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
812	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
814	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
815	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
816	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
817	C₂²⋊C₈	—	53	2	no	—
818	C₂²⋊C₈	—	53	2	no	—
819	C₂²⋊C₈	—	53	2	no	—
820	C₂²⋊C₈	—	53	2	no	—
821	C₂²⋊C₈	—	53	2	no	—
822	C₂²⋊C₈	—	53	2	no	—
823	C₂²⋊C₈	—	53	2	no	—
824	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
825	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
826	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
827	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
828	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
829	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
830	#97	—	53	2	no	—
831	#97	—	53	2	no	—
832	#97	—	53	2	no	—
833	#97	—	53	2	no	—
834	#97	—	53	2	no	—
835	#97	—	53	2	no	—
836	#97	—	53	2	no	—
837	#97	—	53	2	no	—
838	#97	C₂²×D₅₃	1	1	yes	characteristic
839	#97	C₂²×D₅₃	1	1	yes	characteristic
840	#97	C₂²×D₅₃	1	1	yes	characteristic
841	#97	C₂²×D₅₃	1	1	yes	characteristic
842	C₄×C₈	—	53	2	no	—
843	C₄×C₈	—	53	2	no	—
844	C₄×C₈	—	53	2	no	—
845	C₄×C₈	—	53	2	no	—
846	C₄×C₈	—	53	2	no	—
847	C₄×C₈	—	53	2	no	—
848	C₄×C₈	—	53	2	no	—
849	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
850	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
852	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
853	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
854	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
855	#41	—	4	2	no	—
856	#41	—	212	2	no	—
857	C₂×Q₈	—	53	1	no	—
858	C₂×Q₈	—	53	1	no	—
859	C₂×Q₈	—	53	1	no	—
860	C₂×Q₈	—	53	2	no	—
861	C₂×Q₈	—	53	2	no	—
862	C₂×Q₈	—	53	2	no	—
863	C₂×Q₈	—	212	2	no	—
864	C₂×Q₈	C₂×C₄×D₅₃	1	1	yes	characteristic
865	C₂×D₄	—	53	2	no	—
866	C₂×D₄	—	53	2	no	—
867	C₂×D₄	—	53	2	no	—
868	C₂×D₄	—	53	1	no	—
869	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
870	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
871	C₂×D₄	C₂×C₄×D₅₃	1	1	yes	characteristic
872	C₂²×C₄	—	53	2	no	—
873	C₂²×C₄	—	53	2	no	—
874	C₂²×C₄	—	53	2	no	—
875	C₂²×C₄	—	53	2	no	—
876	C₂²×C₄	—	53	2	no	—
877	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
878	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
879	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
880	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
881	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
882	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
883	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
884	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
885	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
886	M₁₆	—	2	2	no	—
887	M₁₆	—	2	2	no	—
888	M₁₆	—	4	1	no	—
889	M₁₆	—	4	1	no	—
890	M₁₆	—	212	2	no	—
891	M₁₆	—	212	2	no	—
892	M₁₆	—	212	2	no	—
893	M₁₆	—	212	2	no	—
894	C₂×C₈	—	2	2	no	—
895	C₂×C₈	—	4	1	no	—
896	C₂×C₈	—	53	2	no	—
897	C₂×C₈	—	53	2	no	—
898	C₂×C₈	—	53	2	no	—
899	C₂×C₈	—	53	2	no	—
900	C₂×C₈	—	106	4	no	—
901	C₂×C₈	—	212	2	no	—
902	C₂×C₈	—	212	2	no	—
903	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
904	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
905	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
906	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
907	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
908	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
909	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
910	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
911	C₄⋊C₄	—	53	2	no	—
912	C₄⋊C₄	—	53	1	no	—
913	C₄⋊C₄	—	53	1	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	1	no	—
920	C₄⋊C₄	—	53	1	no	—
921	C₄⋊C₄	—	53	2	no	—
922	C₄⋊C₄	—	53	2	no	—
923	C₄⋊C₄	—	53	2	no	—
924	C₄⋊C₄	—	53	2	no	—
925	C₄⋊C₄	—	53	2	no	—
926	C₄⋊C₄	—	53	2	no	—
927	C₄⋊C₄	—	53	2	no	—
928	C₄⋊C₄	—	53	2	no	—
929	C₄⋊C₄	—	53	2	no	—
930	C₄⋊C₄	—	53	2	no	—
931	C₄⋊C₄	—	53	2	no	—
932	C₄⋊C₄	—	53	2	no	—
933	C₄⋊C₄	—	53	2	no	—
934	C₄⋊C₄	—	53	2	no	—
935	C₄⋊C₄	—	53	2	no	—
936	C₄⋊C₄	—	53	2	no	—
937	C₄⋊C₄	—	53	2	no	—
938	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
944	C₂²⋊C₄	—	53	2	no	—
945	C₂²⋊C₄	—	53	2	no	—
946	C₂²⋊C₄	—	53	2	no	—
947	C₂²⋊C₄	—	53	2	no	—
948	C₂²⋊C₄	—	53	2	no	—
949	C₂²⋊C₄	—	53	2	no	—
950	C₂²⋊C₄	—	53	2	no	—
951	C₂²⋊C₄	—	53	2	no	—
952	C₂²⋊C₄	—	53	2	no	—
953	C₂²⋊C₄	—	53	2	no	—
954	C₂²⋊C₄	—	53	2	no	—
955	C₂²⋊C₄	—	53	2	no	—
956	C₂²⋊C₄	—	53	2	no	—
957	C₂²⋊C₄	—	53	2	no	—
958	C₂²⋊C₄	—	53	2	no	—
959	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
960	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
961	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
962	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
963	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
964	C₂²⋊C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
965	C₄²	—	53	2	no	—
966	C₄²	—	53	2	no	—
967	C₄²	—	53	2	no	—
968	C₄²	—	53	2	no	—
969	C₄²	—	53	2	no	—
970	C₄²	—	53	2	no	—
971	C₄²	—	53	2	no	—
972	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
973	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
974	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
975	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
976	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
977	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
978	C₄²	C₂³×D₅₃	1	1	yes	characteristic
979	C₄²	C₂³×D₅₃	1	1	yes	characteristic
980	C₄²	C₂³×D₅₃	1	1	yes	characteristic
981	C₄²	C₂³×D₅₃	1	1	yes	characteristic
982	C₂³	—	53	2	no	—
983	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
984	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
985	C₂³	C₂²×C₄×D₅₃	1	1	yes	characteristic
986	Q₈	—	4	1	no	—
987	Q₈	—	106	2	no	—
988	Q₈	—	106	2	no	—
989	Q₈	—	106	2	no	—
990	Q₈	—	212	2	no	—
991	Q₈	—	212	2	no	—
992	Q₈	—	212	2	no	—
993	D₄	—	4	1	no	—
994	D₄	—	4	1	no	—
995	D₄	—	4	1	no	—
996	D₄	—	106	2	no	—
997	D₄	—	212	2	no	—
998	D₄	—	212	2	no	—
999	D₄	—	212	2	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	4	1	no	—
1010	C₂×C₄	—	4	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	53	2	no	—
1013	C₂×C₄	—	53	2	no	—
1014	C₂×C₄	—	53	2	no	—
1015	C₂×C₄	—	53	2	no	—
1016	C₂×C₄	—	53	2	no	—
1017	C₂×C₄	—	53	2	no	—
1018	C₂×C₄	—	53	2	no	—
1019	C₂×C₄	—	106	2	no	—
1020	C₂×C₄	—	106	2	no	—
1021	C₂×C₄	—	212	2	no	—
1022	C₂×C₄	—	212	2	no	—
1023	C₂×C₄	—	212	2	no	—
1024	C₂×C₄	—	212	2	no	—
1025	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1026	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1027	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1028	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1029	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1030	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1031	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1032	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1033	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1034	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1035	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
1036	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1037	C₈	—	2	1	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	106	2	no	—
1045	C₈	—	106	2	no	—
1046	C₈	—	106	2	no	—
1047	C₈	—	106	2	no	—
1048	C₈	#13133264	1	2	yes	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	106	2	no	—
1059	C₂²	—	106	2	no	—
1060	C₂²	—	106	2	no	—
1061	C₂²	C₂³×C₄×D₅₃	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	106	2	no	—
1073	C₄	—	106	2	no	—
1074	C₄	—	106	2	no	—
1075	C₄	—	106	2	no	—
1076	C₄	—	106	2	no	—
1077	C₄	—	106	2	no	—
1078	C₄	—	106	2	no	—
1079	C₄	#16811389	1	2	yes	—
1080	C₄	C₂×#13133264	1	1	yes	characteristic
1081	C₄	#16811459	1	1	yes	characteristic
1082	C₂	—	4	1	no	—
1083	C₂	—	4	1	no	—
1084	C₂	—	4	1	no	—
1085	C₂	—	212	2	no	—
1086	C₂	C₄×#13133264	1	1	yes	characteristic
1087	C₂	C₂×#16811389	1	1	yes	characteristic
1088	C₂	#20289426	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₅₃
commutator, socle	C₂²×C₅₃	C₂⁴×C₄
Fitting	C₅₃×#2965	C₂
prime radical	#16811201	C₄
cosocle	C₂×C₄×C₅₃	C₂⁵
hypercenter	#2965	D₅₃
hypocenter	C₅₃	#60344
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ #2965

Complements

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

N	H ≅ G/N	type
2. #20283886	C₂	semidirect
3. #20283881	C₂	semidirect
4. #20283877	C₂	semidirect
5. #20283866	C₂	semidirect
6. #20283861	C₂	semidirect
7. #20283844	C₂	semidirect
8. #20283832	C₂	semidirect
9. #20283816	C₂	semidirect
10. #20283809	C₂	semidirect
11. #20283808	C₂	semidirect
12. #20283802	C₂	semidirect
13. #20283730	C₂	semidirect
14. #20283719	C₂	semidirect
15. #20283712	C₂	semidirect
16. #20283706	C₂	semidirect
17. #20283701	C₂	semidirect
18. #20283690	C₂	semidirect
19. M₁₆×Dic₁₀₆	C₂	semidirect
20. #20283662	C₂	semidirect
21. #20283651	C₂	semidirect
22. #20283649	C₂	semidirect
23. C₅₃×#2965	C₂	semidirect
556. #2965	D₅₃	semidirect
679. C₅₃	#60344	semidirect

Maximal subgroups

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

subgroup	index
#20288142	2
#20283886	2
#20283881	2
#20283877	2
#20283866	2
#20283861	2
#20283844	2
#20283832	2
#20283816	2
#20283809	2
#20283808	2
#20283802	2
#20283730	2
#20283719	2
#20283712	2
#20283706	2
#20283701	2
#20283690	2
M₁₆×Dic₁₀₆	2
#20283662	2
#20283651	2
#20283649	2
C₅₃×#2965	2
#60344	53