Subgroups — #28266836

Order 13568.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20288820	C₂	1	2	yes	maximal, complemented
2	#20287728	C₂	1	1	yes	maximal, characteristic, complemented
3	#20287607	C₂	1	1	yes	maximal, characteristic, complemented
4	#20287485	C₂	1	2	yes	maximal, complemented
5	#20287138	C₂	1	1	yes	maximal, characteristic, complemented
6	#20287118	C₂	1	1	yes	maximal, characteristic, complemented
7	#20287084	C₂	1	1	yes	maximal, characteristic, complemented
8	#20286970	C₂	1	2	yes	maximal, complemented
9	#20286903	C₂	1	2	yes	maximal, complemented
10	#20286843	C₂	1	2	yes	maximal, complemented
11	#20286475	C₂	1	1	yes	maximal, characteristic, complemented
12	#20286458	C₂	1	1	yes	maximal, characteristic, complemented
13	#20286458	C₂	1	1	yes	maximal, characteristic, complemented
14	#20285365	C₂	1	1	yes	maximal, characteristic, complemented
15	#20285354	C₂	1	1	yes	maximal, characteristic, complemented
16	#20285285	C₂	1	1	yes	maximal, characteristic, complemented
17	#20285007	C₂	1	2	yes	maximal, complemented
18	#20284994	C₂	1	2	yes	maximal, complemented
19	#20284826	C₂	1	2	yes	maximal, complemented
20	#20283592	C₂	1	1	yes	maximal, characteristic, complemented
21	#20283584	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13133239	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13133239	C₂²	1	1	yes	characteristic
25	C₂×#13133239	C₂²	1	1	yes	characteristic
26	C₂²×Dic₂₁₂	C₂²	1	1	yes	characteristic
27	#16811358	C₂²	1	2	yes	—
28	#16811357	—	2	2	no	—
29	#16811351	C₂²	1	2	yes	—
30	#16811338	C₂²	1	2	yes	—
31	#16811335	—	2	2	no	—
32	#16811319	C₂²	1	2	yes	—
33	#16811318	—	2	2	no	—
34	#16811313	C₂²	1	2	yes	—
35	#16811305	—	2	2	no	—
36	#16811294	C₂²	1	2	yes	—
37	#16811282	C₂²	1	2	yes	—
38	#16811282	C₂²	1	2	yes	—
39	#16811244	C₂²	1	2	yes	—
40	#16811243	—	2	2	no	—
41	#16811228	C₂²	1	2	yes	—
42	#16811223	—	2	2	no	—
43	#16811157	C₂²	1	2	yes	—
44	#16811156	—	2	2	no	—
45	#16811156	—	2	2	no	—
46	#16811103	C₂²	1	2	yes	—
47	#16811100	C₂²	1	2	yes	—
48	C₄×#11719945	C₂²	1	2	yes	—
49	#16811028	C₂²	1	1	yes	characteristic
50	#16811025	C₂²	1	1	yes	characteristic
51	#16811025	C₂²	1	1	yes	characteristic
52	#16811007	C₂²	1	1	yes	characteristic
53	#16811007	C₂²	1	1	yes	characteristic
54	#16811000	C₂²	1	1	yes	characteristic
55	#16810988	C₂²	1	2	yes	—
56	#16810983	C₂²	1	2	yes	—
57	#16810978	C₂²	1	2	yes	—
58	#16810965	C₂²	1	2	yes	—
59	#16810954	C₂²	1	2	yes	—
60	#16810948	C₂²	1	2	yes	—
61	#16810948	C₂²	1	2	yes	—
62	#16810948	C₂²	1	2	yes	—
63	#16810942	C₂²	1	2	yes	—
64	#16810931	C₂²	1	2	yes	—
65	#16810931	C₂²	1	2	yes	—
66	#16810931	C₂²	1	2	yes	—
67	#16810924	C₂²	1	2	yes	—
68	#16810914	C₂²	1	2	yes	—
69	#16810909	C₂²	1	2	yes	—
70	#16810876	C₂²	1	2	yes	—
71	#16810869	C₂²	1	2	yes	—
72	#16810864	C₂²	1	1	yes	characteristic
73	#16810864	C₂²	1	1	yes	characteristic
74	#16810859	C₂²	1	1	yes	characteristic
75	#16810859	C₂²	1	1	yes	characteristic
76	#16810859	C₂²	1	1	yes	characteristic
77	#16810859	C₂²	1	1	yes	characteristic
78	#16810852	C₂²	1	2	yes	—
79	#16810846	C₂²	1	2	yes	—
80	#16810846	C₂²	1	2	yes	—
81	#16810839	C₂²	1	2	yes	—
82	#16810839	C₂²	1	2	yes	—
83	#16810824	C₂²	1	2	yes	—
84	#16810824	C₂²	1	2	yes	—
85	#16810787	C₂²	1	2	yes	—
86	#16810787	C₂²	1	2	yes	—
87	#16810770	C₂²	1	2	yes	—
88	#16810770	C₂²	1	2	yes	—
89	#16810764	C₂²	1	2	yes	—
90	#16810764	C₂²	1	2	yes	—
91	#16810736	C₂²	1	2	yes	—
92	#16810731	C₂²	1	2	yes	—
93	#16810731	C₂²	1	2	yes	—
94	#16810725	C₂²	1	2	yes	—
95	#16810725	C₂²	1	2	yes	—
96	#16810725	C₂²	1	2	yes	—
97	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
98	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
99	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
100	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
101	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
102	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
103	C₄×#11719913	C₂²	1	2	yes	—
104	C₄×#11719913	C₂²	1	2	yes	—
105	C₄×#11719913	C₂²	1	2	yes	—
106	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
107	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
108	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
109	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
110	#16810661	C₂²	1	1	yes	characteristic
111	#16810661	C₂²	1	1	yes	characteristic
112	C₂×#13133151	C₂²	1	1	yes	characteristic
113	#16810633	C₂²	1	2	yes	—
114	#16810625	C₂²	1	2	yes	—
115	#16810620	C₂²	1	2	yes	—
116	C₅₃×#529	C₂²	1	1	yes	characteristic
117	C₅₃×#446	C₂²	1	1	yes	characteristic
118	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
119	C₅₃×#436	C₂²	1	1	yes	characteristic
120	C₅₃×#435	C₂²	1	1	yes	characteristic
121	C₅₃×#435	C₂²	1	1	yes	characteristic
122	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
125	C₅₃×#433	C₂²	1	1	yes	characteristic
126	C₅₃×#433	C₂²	1	1	yes	characteristic
127	C₅₃×#432	C₂²	1	1	yes	characteristic
128	C₅₃×#405	C₂²	1	1	yes	characteristic
129	C₅₃×#405	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#11719945	C₂³	1	2	yes	—
132	C₂×#11719945	C₂³	1	2	yes	—
133	C₂²×Dic₁₀₆	C₂³	1	2	yes	—
134	#13133239	—	2	4	no	—
135	#13133239	—	2	4	no	—
136	C₂×Dic₂₁₂	—	2	4	no	—
137	C₂×Dic₂₁₂	C₂³	1	2	yes	—
138	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
139	C₂×Dic₂₁₂	C₂³	1	1	yes	characteristic
140	C₂×#11719913	C₂³	1	2	yes	—
141	C₂×#11719913	C₂³	1	2	yes	—
142	C₂×#11719913	C₂³	1	2	yes	—
143	C₂×#11719913	C₂³	1	2	yes	—
144	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
145	C₂×D₄₂₄	C₂³	1	1	yes	characteristic
146	C₂×D₄₂₄	C₂³	1	2	yes	—
147	#13133217	C₂³	1	2	yes	—
148	#13133215	—	2	2	no	—
149	#13133214	C₂³	1	2	yes	—
150	#13133213	—	2	2	no	—
151	#13133212	—	2	2	no	—
152	#13133212	—	2	2	no	—
153	#13133211	—	2	2	no	—
154	#13133210	—	2	2	no	—
155	#13133209	C₂³	1	2	yes	—
156	#13133209	C₂³	1	2	yes	—
157	#13133207	—	2	2	no	—
158	#13133207	—	2	2	no	—
159	#13133207	—	2	2	no	—
160	#13133206	—	2	2	no	—
161	#13133205	C₂³	1	2	yes	—
162	#13133205	C₂³	1	2	yes	—
163	#13133203	—	2	2	no	—
164	#13133203	—	2	2	no	—
165	#13133203	—	2	2	no	—
166	#13133203	—	2	2	no	—
167	#13133203	—	2	2	no	—
168	#13133202	—	2	2	no	—
169	#13133202	—	2	2	no	—
170	#13133202	—	2	2	no	—
171	#13133202	—	2	2	no	—
172	#13133200	—	2	2	no	—
173	#13133199	—	2	2	no	—
174	#13133199	—	2	2	no	—
175	#13133198	—	2	2	no	—
176	#13133196	C₂³	1	2	yes	—
177	#13133196	C₂³	1	2	yes	—
178	#13133195	—	2	2	no	—
179	#13133195	—	2	2	no	—
180	#13133195	—	2	2	no	—
181	#13133191	C₂³	1	2	yes	—
182	#13133191	C₂³	1	2	yes	—
183	#13133191	C₂³	1	2	yes	—
184	#13133191	C₂³	1	2	yes	—
185	#13133190	—	2	2	no	—
186	#13133190	—	2	2	no	—
187	#13133190	—	2	2	no	—
188	#13133190	—	2	2	no	—
189	#13133189	—	2	2	no	—
190	#13133189	—	2	2	no	—
191	#13133189	—	2	2	no	—
192	#13133188	—	2	2	no	—
193	C₄×Dic₁₀₆	C₂³	1	2	yes	—
194	C₄×Dic₁₀₆	C₂³	1	2	yes	—
195	C₄×Dic₁₀₆	C₂³	1	2	yes	—
196	C₄×Dic₁₀₆	C₂³	1	2	yes	—
197	C₄×Dic₁₀₆	C₂³	1	2	yes	—
198	C₄×Dic₁₀₆	C₂³	1	2	yes	—
199	#13133182	—	2	2	no	—
200	#13133182	—	2	2	no	—
201	#13133182	—	2	2	no	—
202	C₄×D₂₁₂	C₂³	1	2	yes	—
203	C₄×D₂₁₂	C₂³	1	2	yes	—
204	C₄×D₂₁₂	C₂³	1	2	yes	—
205	C₄×D₂₁₂	C₂³	1	2	yes	—
206	#13133179	—	2	2	no	—
207	#13133179	—	2	2	no	—
208	C₄×C₂²⋊D₅₃	—	2	2	no	—
209	C₄×C₂²⋊D₅₃	—	2	2	no	—
210	C₄×C₂²⋊D₅₃	—	2	2	no	—
211	#13133177	—	2	2	no	—
212	#13133177	—	2	2	no	—
213	#13133177	—	2	2	no	—
214	#13133177	—	2	2	no	—
215	#13133177	—	2	2	no	—
216	#13133176	C₂³	1	2	yes	—
217	#13133176	C₂³	1	2	yes	—
218	#13133175	—	2	2	no	—
219	#13133175	—	2	2	no	—
220	#13133174	—	2	2	no	—
221	#13133174	—	2	2	no	—
222	#13133173	—	2	2	no	—
223	#13133173	—	2	2	no	—
224	#13133173	—	2	2	no	—
225	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
226	C₄⋊C₄×D₅₃	—	2	2	no	—
227	C₄²×D₅₃	—	2	2	no	—
228	#13133151	C₂³	1	1	yes	characteristic
229	#13133151	C₂³	1	1	yes	characteristic
230	#13133151	C₂³	1	1	yes	characteristic
231	#13133151	C₂³	1	2	yes	—
232	#13133151	C₂³	1	1	yes	characteristic
233	#13133151	C₂³	1	2	yes	—
234	#13133149	C₂³	1	2	yes	—
235	#13133149	C₂³	1	2	yes	—
236	#13133149	C₂³	1	2	yes	—
237	#13133149	C₂³	1	2	yes	—
238	#13133142	C₂³	1	2	yes	—
239	#13133142	C₂³	1	2	yes	—
240	#13133142	C₂³	1	2	yes	—
241	#13133142	C₂³	1	2	yes	—
242	#13133142	C₂³	1	2	yes	—
243	#13133142	C₂³	1	2	yes	—
244	#13133142	C₂³	1	2	yes	—
245	#13133142	C₂³	1	2	yes	—
246	#13133139	C₂³	1	2	yes	—
247	#13133139	C₂³	1	2	yes	—
248	#13133139	C₂³	1	2	yes	—
249	#13133139	C₂³	1	2	yes	—
250	#13133139	C₂³	1	2	yes	—
251	#13133139	C₂³	1	2	yes	—
252	#13133139	C₂³	1	2	yes	—
253	#13133139	C₂³	1	2	yes	—
254	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
260	#126×C₅₃	D₄	1	1	yes	characteristic
261	#126×C₅₃	D₄	1	1	yes	characteristic
262	#125×C₅₃	D₄	1	1	yes	characteristic
263	#124×C₅₃	D₄	1	1	yes	characteristic
264	#123×C₅₃	D₄	1	1	yes	characteristic
265	#123×C₅₃	D₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
267	#121×C₅₃	D₄	1	1	yes	characteristic
268	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
272	#117×C₅₃	C₂³	1	1	yes	characteristic
273	#117×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×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	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#97×C₅₃	C₂³	1	1	yes	characteristic
288	#97×C₅₃	C₂³	1	1	yes	characteristic
289	#97×C₅₃	C₂³	1	1	yes	characteristic
290	#97×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	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
298	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
299	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₅₃	—	2	2	no	—
307	C₂×C₂²⋊D₅₃	—	2	2	no	—
308	C₂×C₂²⋊D₅₃	—	2	2	no	—
309	C₂×C₂²⋊D₅₃	—	2	2	no	—
310	C₂×C₂²⋊D₅₃	—	2	2	no	—
311	C₂×C₂²⋊D₅₃	—	2	2	no	—
312	C₂²×Dic₅₃	—	2	2	no	—
313	C₂²×Dic₅₃	—	2	2	no	—
314	#11719945	—	2	4	no	—
315	#11719945	—	2	4	no	—
316	#11719945	—	4	2	no	—
317	#11719945	—	4	2	no	—
318	C₂×D₂₁₂	—	2	2	no	—
319	C₂×D₂₁₂	—	2	2	no	—
320	C₂×D₂₁₂	C₂⁴	1	2	yes	—
321	C₂×D₂₁₂	C₂⁴	1	2	yes	—
322	C₂×C₄×D₅₃	—	2	2	no	—
323	C₂×C₄×D₅₃	—	2	2	no	—
324	C₂×C₄×D₅₃	—	2	2	no	—
325	C₂×C₄×D₅₃	—	2	2	no	—
326	C₂×C₄×D₅₃	—	2	2	no	—
327	C₂×C₄×D₅₃	—	2	2	no	—
328	C₂×Dic₁₀₆	—	2	4	no	—
329	C₂×Dic₁₀₆	—	2	2	no	—
330	C₂×Dic₁₀₆	—	2	2	no	—
331	C₂×Dic₁₀₆	—	4	2	no	—
332	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
333	C₂×Dic₁₀₆	C₂⁴	1	2	yes	—
334	M₁₆×C₅₃	—	4	1	no	—
335	M₁₆×C₅₃	—	4	1	no	—
336	C₂×C₈×C₅₃	—	2	2	no	—
337	C₂×C₈×C₅₃	—	2	2	no	—
338	C₂×C₈×C₅₃	—	2	2	no	—
339	C₂×C₈×C₅₃	—	4	1	no	—
340	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
348	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
350	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
356	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
358	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
359	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
362	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
364	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
365	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
366	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
369	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
370	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²⋊Dic₅₃	—	2	2	no	—
375	C₂²⋊Dic₅₃	—	2	2	no	—
376	C₂²⋊Dic₅₃	—	2	2	no	—
377	C₂²⋊Dic₅₃	—	2	2	no	—
378	#11719921	—	2	2	no	—
379	#11719921	—	2	2	no	—
380	#11719921	—	2	2	no	—
381	#11719921	—	2	2	no	—
382	#11719921	—	2	2	no	—
383	#11719921	—	2	2	no	—
384	#11719921	—	2	2	no	—
385	#11719921	—	2	2	no	—
386	#11719921	—	2	2	no	—
387	#11719921	—	2	2	no	—
388	#11719921	—	2	2	no	—
389	#11719921	—	2	2	no	—
390	C₄⋊Dic₅₃	—	2	2	no	—
391	C₄⋊Dic₅₃	—	2	2	no	—
392	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
393	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
394	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
395	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
396	#11719919	—	2	2	no	—
397	#11719919	—	2	2	no	—
398	#11719919	—	2	2	no	—
399	#11719919	—	2	2	no	—
400	#11719919	—	2	2	no	—
401	#11719919	—	2	2	no	—
402	#11719919	—	2	2	no	—
403	#11719919	—	2	2	no	—
404	#11719919	—	2	2	no	—
405	#11719919	—	2	2	no	—
406	#11719919	—	2	2	no	—
407	#11719919	—	2	2	no	—
408	C₄×Dic₅₃	—	2	2	no	—
409	C₄×Dic₅₃	—	2	2	no	—
410	C₄×Dic₅₃	—	2	2	no	—
411	C₄×Dic₅₃	—	2	2	no	—
412	C₄×Dic₅₃	—	2	2	no	—
413	C₄×Dic₅₃	—	2	2	no	—
414	C₄×Dic₅₃	—	2	2	no	—
415	C₄×Dic₅₃	—	2	2	no	—
416	Dic₂₁₂	—	2	4	no	—
417	Dic₂₁₂	—	2	2	no	—
418	Dic₂₁₂	#41	1	4	yes	—
419	D₄₂₄	—	2	2	no	—
420	D₄₂₄	—	2	2	no	—
421	D₄₂₄	—	4	2	no	—
422	#11719913	—	2	4	no	—
423	#11719913	—	2	4	no	—
424	#11719913	—	4	2	no	—
425	#11719913	—	4	2	no	—
426	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
427	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
429	C₂²×D₅₃	—	2	2	no	—
430	C₂²×D₅₃	—	2	2	no	—
431	Q₈×C₅₃	—	4	1	no	—
432	D₄×C₅₃	—	4	1	no	—
433	D₄×C₅₃	—	4	1	no	—
434	D₄×C₅₃	—	4	1	no	—
435	C₂×C₄×C₅₃	—	2	1	no	—
436	C₂×C₄×C₅₃	—	2	1	no	—
437	C₂×C₄×C₅₃	—	2	1	no	—
438	C₂×C₄×C₅₃	—	2	1	no	—
439	C₂×C₄×C₅₃	—	2	1	no	—
440	C₂×C₄×C₅₃	—	2	1	no	—
441	C₂×C₄×C₅₃	—	4	1	no	—
442	C₂×C₄×C₅₃	—	4	1	no	—
443	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
444	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
455	C₂²⋊D₅₃	—	4	4	no	—
456	C₂²⋊D₅₃	—	4	4	no	—
457	C₂²⋊D₅₃	—	8	2	no	—
458	C₂²⋊D₅₃	—	8	2	no	—
459	C₂²⋊D₅₃	—	8	2	no	—
460	C₂²⋊D₅₃	—	8	2	no	—
461	C₂×Dic₅₃	—	2	2	no	—
462	C₂×Dic₅₃	—	2	2	no	—
463	C₂×Dic₅₃	—	2	2	no	—
464	C₂×Dic₅₃	—	2	2	no	—
465	C₂×Dic₅₃	—	2	2	no	—
466	C₂×Dic₅₃	—	2	2	no	—
467	C₂×Dic₅₃	—	4	4	no	—
468	C₂×Dic₅₃	—	8	2	no	—
469	D₂₁₂	—	2	2	no	—
470	D₂₁₂	—	2	2	no	—
471	D₂₁₂	—	2	2	no	—
472	D₂₁₂	—	2	2	no	—
473	D₂₁₂	—	8	2	no	—
474	D₂₁₂	—	8	2	no	—
475	C₄×D₅₃	—	4	4	no	—
476	C₄×D₅₃	—	4	4	no	—
477	C₄×D₅₃	—	8	2	no	—
478	C₄×D₅₃	—	8	2	no	—
479	C₄×D₅₃	—	8	2	no	—
480	C₄×D₅₃	—	8	2	no	—
481	Dic₁₀₆	—	2	2	no	—
482	Dic₁₀₆	—	2	2	no	—
483	Dic₁₀₆	—	2	2	no	—
484	Dic₁₀₆	—	4	4	no	—
485	Dic₁₀₆	—	8	2	no	—
486	Dic₁₀₆	C₂×#41	1	4	yes	—
487	C₈×C₅₃	—	2	1	no	—
488	C₈×C₅₃	—	2	1	no	—
489	C₈×C₅₃	—	2	1	no	—
490	C₈×C₅₃	—	2	1	no	—
491	C₈×C₅₃	—	2	1	no	—
492	C₈×C₅₃	—	2	1	no	—
493	C₈×C₅₃	—	2	1	no	—
494	C₈×C₅₃	C₂×#41	1	2	yes	—
495	#61488	—	53	1	no	maximal, Sylow
496	C₂²×C₅₃	—	2	1	no	—
497	C₂²×C₅₃	—	2	1	no	—
498	C₂²×C₅₃	—	2	1	no	—
499	C₂²×C₅₃	—	2	1	no	—
500	C₂²×C₅₃	—	2	1	no	—
501	C₂²×C₅₃	—	2	1	no	—
502	C₂²×C₅₃	—	2	1	no	—
503	C₂²×C₅₃	—	2	1	no	—
504	C₂²×C₅₃	—	2	1	no	—
505	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
506	C₂×D₅₃	—	4	2	no	—
507	C₂×D₅₃	—	4	2	no	—
508	C₂×D₅₃	—	4	2	no	—
509	C₂×D₅₃	—	4	2	no	—
510	C₂×D₅₃	—	4	2	no	—
511	C₂×D₅₃	—	4	2	no	—
512	C₄×C₅₃	—	2	1	no	—
513	C₄×C₅₃	—	2	1	no	—
514	C₄×C₅₃	—	2	1	no	—
515	C₄×C₅₃	—	2	1	no	—
516	C₄×C₅₃	—	2	1	no	—
517	C₄×C₅₃	—	2	1	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	C₂²×#41	1	1	yes	characteristic
524	C₄×C₅₃	#585	1	1	yes	characteristic
525	Dic₅₃	—	2	4	no	—
526	Dic₅₃	—	4	2	no	—
527	Dic₅₃	—	4	2	no	—
528	Dic₅₃	—	4	2	no	—
529	Dic₅₃	—	4	2	no	—
530	Dic₅₃	—	4	2	no	—
531	#3524	—	53	2	no	—
532	#3396	—	53	1	no	—
533	#3383	—	53	1	no	—
534	#3371	—	53	2	no	—
535	#3341	—	53	1	no	—
536	#3339	—	53	1	no	—
537	#3336	—	53	1	no	—
538	#3326	—	53	2	no	—
539	#3321	—	53	2	no	—
540	#3317	—	53	2	no	—
541	#3287	—	53	1	no	—
542	#3285	—	53	1	no	—
543	#3285	—	53	1	no	—
544	#3176	—	53	1	no	—
545	#3175	—	53	1	no	—
546	#3168	—	53	1	no	—
547	#3126	—	53	2	no	—
548	#3125	—	53	2	no	—
549	#3111	—	53	2	no	—
550	#2966	D₅₃	1	1	yes	characteristic, complemented
551	#2951	—	53	1	no	—
552	#2950	—	53	1	no	—
553	C₄×#135	—	53	1	no	—
554	C₂×C₅₃	—	4	1	no	—
555	C₂×C₅₃	—	4	1	no	—
556	C₂×C₅₃	—	4	1	no	—
557	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
558	C₂×C₅₃	#3584	1	1	yes	characteristic
559	C₂×C₅₃	#3584	1	1	yes	characteristic
560	D₅₃	—	8	2	no	—
561	D₅₃	—	8	2	no	—
562	C₂×#135	—	53	1	no	—
563	C₂×#135	—	53	1	no	—
564	C₂²×Q₁₆	—	53	1	no	—
565	#559	—	53	2	no	—
566	#559	—	106	2	no	—
567	#557	—	53	2	no	—
568	#555	—	53	2	no	—
569	#555	—	106	2	no	—
570	#553	—	53	2	no	—
571	#553	—	106	2	no	—
572	#552	—	53	2	no	—
573	#552	—	106	2	no	—
574	#550	—	53	2	no	—
575	#548	—	53	2	no	—
576	#548	—	53	2	no	—
577	#542	—	53	2	no	—
578	#542	—	106	2	no	—
579	#540	—	53	2	no	—
580	#540	—	106	2	no	—
581	#529	—	53	2	no	—
582	#529	—	106	2	no	—
583	#529	—	106	2	no	—
584	#529	C₂×D₅₃	1	1	yes	characteristic
585	#520	—	53	2	no	—
586	#519	—	53	2	no	—
587	C₄×#41	—	53	2	no	—
588	#500	—	53	1	no	—
589	#499	—	53	1	no	—
590	#499	—	53	1	no	—
591	#495	—	53	1	no	—
592	#495	—	53	1	no	—
593	#493	—	53	1	no	—
594	#490	—	53	2	no	—
595	#489	—	53	2	no	—
596	#488	—	53	2	no	—
597	#485	—	53	2	no	—
598	#483	—	53	2	no	—
599	#482	—	53	2	no	—
600	#482	—	53	2	no	—
601	#482	—	53	2	no	—
602	#481	—	53	2	no	—
603	#479	—	53	2	no	—
604	#479	—	53	2	no	—
605	#479	—	53	2	no	—
606	#478	—	53	2	no	—
607	#476	—	53	2	no	—
608	#475	—	53	2	no	—
609	#469	—	53	2	no	—
610	#468	—	53	2	no	—
611	#467	—	53	1	no	—
612	#467	—	53	1	no	—
613	#466	—	53	1	no	—
614	#466	—	53	1	no	—
615	#466	—	53	1	no	—
616	#466	—	53	1	no	—
617	#465	—	53	2	no	—
618	#464	—	53	2	no	—
619	#464	—	53	2	no	—
620	#463	—	53	2	no	—
621	#463	—	53	2	no	—
622	#460	—	53	2	no	—
623	#460	—	53	2	no	—
624	#452	—	53	2	no	—
625	#452	—	53	2	no	—
626	#449	—	53	2	no	—
627	#449	—	53	2	no	—
628	#448	—	53	2	no	—
629	#448	—	53	2	no	—
630	#446	C₂×D₅₃	1	1	yes	characteristic
631	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic
632	#442	—	53	2	no	—
633	#441	—	53	2	no	—
634	#441	—	53	2	no	—
635	#440	—	53	2	no	—
636	#440	—	53	2	no	—
637	#440	—	53	2	no	—
638	C₄×Q₁₆	—	53	1	no	—
639	C₄×Q₁₆	—	53	1	no	—
640	C₄×Q₁₆	—	53	1	no	—
641	C₄×Q₁₆	—	53	1	no	—
642	C₄×Q₁₆	—	53	1	no	—
643	C₄×Q₁₆	—	53	1	no	—
644	C₄×SD₁₆	—	53	2	no	—
645	C₄×SD₁₆	—	53	2	no	—
646	C₄×SD₁₆	—	53	2	no	—
647	C₄×D₈	—	53	1	no	—
648	C₄×D₈	—	53	1	no	—
649	C₄×D₈	—	53	1	no	—
650	C₄×D₈	—	53	1	no	—
651	#436	C₂×D₅₃	1	1	yes	characteristic
652	#435	C₂×D₅₃	1	1	yes	characteristic
653	#435	C₂×D₅₃	1	1	yes	characteristic
654	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
655	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
656	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
657	#433	C₂×D₅₃	1	1	yes	characteristic
658	#433	C₂×D₅₃	1	1	yes	characteristic
659	#432	C₂×D₅₃	1	1	yes	characteristic
660	#427	—	53	1	no	—
661	#427	—	53	1	no	—
662	C₂×#107	—	53	1	no	—
663	#419	—	53	2	no	—
664	#417	—	53	2	no	—
665	#416	—	53	2	no	—
666	#405	C₂×D₅₃	1	1	yes	characteristic
667	#405	C₂×D₅₃	1	1	yes	characteristic
668	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
669	C₅₃	#61488	1	1	yes	characteristic, complemented, Sylow
670	C₂×#41	—	53	2	no	—
671	C₂×#41	—	53	2	no	—
672	C₂²×Q₈	—	53	2	no	—
673	#135	—	106	4	no	—
674	#135	—	106	4	no	—
675	C₂×Q₁₆	—	53	1	no	—
676	C₂×Q₁₆	—	53	1	no	—
677	C₂×Q₁₆	—	53	2	no	—
678	C₂×Q₁₆	—	106	4	no	—
679	C₂×SD₁₆	—	53	2	no	—
680	C₂×SD₁₆	—	53	2	no	—
681	C₂×SD₁₆	—	53	2	no	—
682	C₂×SD₁₆	—	53	2	no	—
683	C₂×D₈	—	53	1	no	—
684	C₂×D₈	—	53	1	no	—
685	C₂×D₈	—	53	2	no	—
686	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
687	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
688	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
689	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
690	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
691	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
692	C₄⋊Q₈	—	53	2	no	—
693	C₄⋊Q₈	—	106	2	no	—
694	#127	—	53	2	no	—
695	#127	—	106	2	no	—
696	#126	—	106	2	no	—
697	#126	—	106	2	no	—
698	#126	—	106	2	no	—
699	#126	—	106	2	no	—
700	#126	D₂₁₂	1	1	yes	characteristic
701	#126	D₂₁₂	1	1	yes	characteristic
702	#125	—	53	2	no	—
703	#125	—	53	2	no	—
704	#125	—	106	2	no	—
705	#125	—	106	2	no	—
706	#125	—	106	2	no	—
707	#125	D₂₁₂	1	1	yes	characteristic
708	#124	—	53	2	no	—
709	#124	—	53	2	no	—
710	#124	—	106	2	no	—
711	#124	—	106	2	no	—
712	#124	—	106	2	no	—
713	#124	—	106	2	no	—
714	#124	—	106	2	no	—
715	#124	—	106	2	no	—
716	#124	D₂₁₂	1	1	yes	characteristic
717	#123	—	106	2	no	—
718	#123	—	106	2	no	—
719	#123	—	106	2	no	—
720	#123	—	106	2	no	—
721	#123	—	106	2	no	—
722	#123	—	106	2	no	—
723	#123	—	106	2	no	—
724	#123	—	106	2	no	—
725	#123	D₂₁₂	1	1	yes	characteristic
726	#123	D₂₁₂	1	1	yes	characteristic
727	C₂²⋊Q₈	—	53	2	no	—
728	C₂²⋊Q₈	—	53	2	no	—
729	C₂²⋊Q₈	—	106	2	no	—
730	C₂²⋊Q₈	—	106	2	no	—
731	C₂²⋊Q₈	—	106	2	no	—
732	C₂²⋊Q₈	D₂₁₂	1	1	yes	characteristic
733	#121	—	53	2	no	—
734	#121	—	53	2	no	—
735	#121	—	53	2	no	—
736	#121	—	53	2	no	—
737	#121	—	106	2	no	—
738	#121	—	106	2	no	—
739	#121	—	106	2	no	—
740	#121	—	106	2	no	—
741	#121	—	106	2	no	—
742	#121	—	106	2	no	—
743	#121	—	106	2	no	—
744	#121	—	106	2	no	—
745	#121	D₂₁₂	1	1	yes	characteristic
746	C₄×Q₈	—	53	2	no	—
747	C₄×Q₈	—	53	2	no	—
748	C₄×Q₈	—	53	2	no	—
749	C₄×Q₈	—	53	2	no	—
750	C₄×Q₈	—	53	2	no	—
751	C₄×Q₈	—	53	2	no	—
752	C₄×Q₈	—	106	2	no	—
753	C₄×Q₈	—	106	2	no	—
754	C₄×Q₈	—	106	2	no	—
755	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
756	C₄×D₄	—	53	2	no	—
757	C₄×D₄	—	53	2	no	—
758	C₄×D₄	—	53	2	no	—
759	C₄×D₄	—	53	2	no	—
760	C₄×D₄	—	106	2	no	—
761	C₄×D₄	—	106	2	no	—
762	C₄×D₄	—	106	2	no	—
763	C₄×D₄	—	106	2	no	—
764	C₄×D₄	—	106	2	no	—
765	C₄×D₄	—	106	2	no	—
766	C₄×D₄	—	106	2	no	—
767	C₄×D₄	—	106	2	no	—
768	C₄×D₄	—	106	2	no	—
769	C₄×D₄	—	106	2	no	—
770	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
771	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
772	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
773	#117	—	53	2	no	—
774	#117	—	53	2	no	—
775	#117	—	106	2	no	—
776	#117	—	106	2	no	—
777	#117	—	106	2	no	—
778	#117	—	106	2	no	—
779	#117	—	106	2	no	—
780	#117	—	106	2	no	—
781	#117	—	106	2	no	—
782	#117	C₂²×D₅₃	1	1	yes	characteristic
783	#117	C₂²×D₅₃	1	1	yes	characteristic
784	C₂×C₄⋊C₄	—	53	2	no	—
785	C₂×C₄⋊C₄	—	106	2	no	—
786	C₂×C₄²	—	106	2	no	—
787	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
788	#107	—	53	1	no	—
789	#107	—	53	1	no	—
790	#107	—	53	2	no	—
791	#107	—	53	1	no	—
792	#107	—	53	1	no	—
793	#107	—	53	2	no	—
794	#106	—	53	2	no	—
795	#106	—	53	2	no	—
796	#106	—	53	2	no	—
797	#106	—	53	2	no	—
798	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
799	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
800	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
801	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
802	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
803	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
804	#103	—	53	2	no	—
805	#103	—	53	2	no	—
806	#103	—	53	2	no	—
807	#103	—	53	2	no	—
808	#103	—	53	2	no	—
809	#103	—	53	2	no	—
810	#103	—	53	2	no	—
811	#103	—	53	2	no	—
812	#102	—	53	2	no	—
813	#102	—	53	2	no	—
814	#102	—	53	2	no	—
815	#102	—	53	2	no	—
816	#102	—	53	2	no	—
817	#102	—	53	2	no	—
818	#102	—	53	2	no	—
819	#102	—	53	2	no	—
820	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
821	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
822	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
823	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
824	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
825	C₂²⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
826	#97	C₂²×D₅₃	1	1	yes	characteristic
827	#97	C₂²×D₅₃	1	1	yes	characteristic
828	#97	C₂²×D₅₃	1	1	yes	characteristic
829	#97	C₂²×D₅₃	1	1	yes	characteristic
830	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
831	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
832	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
833	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
834	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
835	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
836	#41	—	106	4	no	—
837	#41	—	106	4	no	—
838	#41	—	212	2	no	—
839	#41	—	212	2	no	—
840	C₂×Q₈	—	53	2	no	—
841	C₂×Q₈	—	53	2	no	—
842	C₂×Q₈	—	106	4	no	—
843	C₂×Q₈	—	106	2	no	—
844	C₂×Q₈	—	106	2	no	—
845	C₂×Q₈	—	212	2	no	—
846	C₂×Q₈	C₂×D₂₁₂	1	1	yes	characteristic
847	C₂×D₄	—	53	2	no	—
848	C₂×D₄	—	53	2	no	—
849	C₂×D₄	—	106	2	no	—
850	C₂×D₄	—	106	2	no	—
851	C₂×D₄	—	106	2	no	—
852	C₂×D₄	—	106	2	no	—
853	C₂×D₄	—	106	2	no	—
854	C₂×D₄	—	106	2	no	—
855	C₂×D₄	—	106	2	no	—
856	C₂×D₄	—	106	2	no	—
857	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
858	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
859	C₂×D₄	C₂×D₂₁₂	1	1	yes	characteristic
860	C₂²×C₄	—	106	2	no	—
861	C₂²×C₄	—	106	2	no	—
862	C₂²×C₄	—	106	2	no	—
863	C₂²×C₄	—	106	2	no	—
864	C₂²×C₄	—	106	2	no	—
865	C₂²×C₄	—	106	2	no	—
866	C₂²×C₄	—	106	2	no	—
867	C₂²×C₄	—	106	2	no	—
868	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
869	C₂²×C₄	C₂×D₂₁₂	1	1	yes	characteristic
870	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
872	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
873	Q₁₆	—	53	4	no	—
874	Q₁₆	—	106	4	no	—
875	Q₁₆	—	106	2	no	—
876	SD₁₆	—	106	4	no	—
877	SD₁₆	—	106	4	no	—
878	SD₁₆	—	212	2	no	—
879	SD₁₆	—	212	2	no	—
880	D₈	—	106	2	no	—
881	D₈	—	106	2	no	—
882	D₈	—	212	2	no	—
883	M₁₆	—	4	1	no	—
884	M₁₆	—	4	1	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	2	2	no	—
888	C₂×C₈	—	4	1	no	—
889	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
892	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
896	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
897	C₄⋊C₄	—	53	2	no	—
898	C₄⋊C₄	—	53	2	no	—
899	C₄⋊C₄	—	53	2	no	—
900	C₄⋊C₄	—	53	2	no	—
901	C₄⋊C₄	—	106	2	no	—
902	C₄⋊C₄	—	106	2	no	—
903	C₄⋊C₄	—	106	2	no	—
904	C₄⋊C₄	—	106	2	no	—
905	C₄⋊C₄	—	106	2	no	—
906	C₄⋊C₄	—	106	2	no	—
907	C₄⋊C₄	—	106	2	no	—
908	C₄⋊C₄	—	106	2	no	—
909	C₄⋊C₄	—	106	2	no	—
910	C₄⋊C₄	—	106	2	no	—
911	C₄⋊C₄	—	106	2	no	—
912	C₄⋊C₄	—	106	2	no	—
913	C₄⋊C₄	—	106	2	no	—
914	C₄⋊C₄	—	106	2	no	—
915	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
916	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
922	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
925	C₂²⋊C₄	—	106	2	no	—
926	C₂²⋊C₄	—	106	2	no	—
927	C₂²⋊C₄	—	106	2	no	—
928	C₂²⋊C₄	—	106	2	no	—
929	C₂²⋊C₄	—	106	2	no	—
930	C₂²⋊C₄	—	106	2	no	—
931	C₂²⋊C₄	—	106	2	no	—
932	C₂²⋊C₄	—	106	2	no	—
933	C₂²⋊C₄	—	106	2	no	—
934	C₂²⋊C₄	—	106	2	no	—
935	C₂²⋊C₄	—	106	2	no	—
936	C₂²⋊C₄	—	106	2	no	—
937	C₂²⋊C₄	—	106	2	no	—
938	C₂²⋊C₄	—	106	2	no	—
939	C₂²⋊C₄	—	106	2	no	—
940	C₂²⋊C₄	—	106	2	no	—
941	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
942	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
943	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
944	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₂₁₂	1	1	yes	characteristic
951	C₄²	—	106	2	no	—
952	C₄²	—	106	2	no	—
953	C₄²	—	106	2	no	—
954	C₄²	—	106	2	no	—
955	C₄²	—	106	2	no	—
956	C₄²	—	106	2	no	—
957	C₄²	—	106	2	no	—
958	C₄²	—	106	2	no	—
959	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
960	C₄²	C₂×D₂₁₂	1	1	yes	characteristic
961	C₄²	C₂³×D₅₃	1	1	yes	characteristic
962	C₄²	C₂³×D₅₃	1	1	yes	characteristic
963	C₄²	C₂³×D₅₃	1	1	yes	characteristic
964	C₄²	C₂³×D₅₃	1	1	yes	characteristic
965	C₂³	—	106	2	no	—
966	C₂³	—	106	2	no	—
967	C₂³	C₂²×D₂₁₂	1	1	yes	characteristic
968	C₂³	C₂²×D₂₁₂	1	1	yes	characteristic
969	C₂³	C₂²×D₂₁₂	1	1	yes	characteristic
970	Q₈	—	4	1	no	—
971	Q₈	—	53	4	no	—
972	Q₈	—	106	2	no	—
973	Q₈	—	106	2	no	—
974	Q₈	—	106	2	no	—
975	Q₈	—	424	2	no	—
976	Q₈	—	212	4	no	—
977	D₄	—	4	1	no	—
978	D₄	—	4	1	no	—
979	D₄	—	4	1	no	—
980	D₄	—	106	2	no	—
981	D₄	—	106	2	no	—
982	D₄	—	106	2	no	—
983	D₄	—	106	2	no	—
984	D₄	—	424	2	no	—
985	D₄	—	424	2	no	—
986	D₄	—	424	2	no	—
987	D₄	—	424	2	no	—
988	D₄	—	424	2	no	—
989	D₄	—	424	2	no	—
990	D₄	—	212	4	no	—
991	D₄	—	212	4	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	106	2	no	—
1001	C₂×C₄	—	106	2	no	—
1002	C₂×C₄	—	106	2	no	—
1003	C₂×C₄	—	106	2	no	—
1004	C₂×C₄	—	106	2	no	—
1005	C₂×C₄	—	106	2	no	—
1006	C₂×C₄	—	424	2	no	—
1007	C₂×C₄	—	424	2	no	—
1008	C₂×C₄	—	424	2	no	—
1009	C₂×C₄	—	424	2	no	—
1010	C₂×C₄	—	424	2	no	—
1011	C₂×C₄	—	212	4	no	—
1012	C₂×C₄	—	212	4	no	—
1013	C₂×C₄	—	212	4	no	—
1014	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1015	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₂₁₂	1	1	yes	characteristic
1025	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1026	C₈	—	2	1	no	—
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	#41×D₅₃	1	2	yes	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	212	2	no	—
1044	C₂²	—	212	2	no	—
1045	C₂²	—	212	2	no	—
1046	C₂²	—	212	2	no	—
1047	C₂²	—	212	2	no	—
1048	C₂²	—	212	2	no	—
1049	C₂²	C₂³×D₂₁₂	1	1	yes	characteristic
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	106	4	no	—
1062	C₄	—	212	2	no	—
1063	C₄	—	212	2	no	—
1064	C₄	—	212	2	no	—
1065	C₄	—	212	2	no	—
1066	C₄	—	212	2	no	—
1067	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1068	C₄	#16811459	1	1	yes	characteristic
1069	C₂	—	4	1	no	—
1070	C₂	—	4	1	no	—
1071	C₂	—	4	1	no	—
1072	C₂	—	424	2	no	—
1073	C₂	—	424	2	no	—
1074	C₂	#41×D₂₁₂	1	1	yes	characteristic
1075	C₂	#20289489	1	1	yes	characteristic
1076	C₂	#20289489	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₂₁₂
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#2966	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#2966	D₅₃
hypocenter	C₅₃	#61488
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #20288820	C₂	semidirect
2. #20287728	C₂	semidirect
3. #20287607	C₂	semidirect
4. #20287485	C₂	semidirect
5. #20287138	C₂	semidirect
6. #20287118	C₂	semidirect
7. #20287084	C₂	semidirect
8. #20286970	C₂	semidirect
9. #20286903	C₂	semidirect
10. #20286843	C₂	semidirect
11. #20286475	C₂	semidirect
12. #20286458	C₂	semidirect
13. #20286458	C₂	semidirect
14. #20285365	C₂	semidirect
15. #20285354	C₂	semidirect
16. #20285285	C₂	semidirect
17. #20285007	C₂	semidirect
18. #20284994	C₂	semidirect
19. #20284826	C₂	semidirect
20. #20283592	C₂	semidirect
21. #20283584	C₂	semidirect
22. C₄×#13133239	C₂	semidirect
23. C₅₃×#2966	C₂	semidirect
550. #2966	D₅₃	semidirect
669. C₅₃	#61488	semidirect

Maximal subgroups

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

subgroup	index
#20288820	2
#20287728	2
#20287607	2
#20287485	2
#20287138	2
#20287118	2
#20287084	2
#20286970	2
#20286903	2
#20286843	2
#20286475	2
#20286458	2
#20285365	2
#20285354	2
#20285285	2
#20285007	2
#20284994	2
#20284826	2
#20283592	2
#20283584	2
C₄×#13133239	2
C₅₃×#2966	2
#61488	53