Subgroups — #28293341

Order 13568.

7466 conjugacy classes of subgroups.

The subgroup lattice has 1386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20289269	C₂	1	4	yes	maximal, complemented
2	#20289267	C₂	1	4	yes	maximal, complemented
3	#20289236	C₂	1	4	yes	maximal, complemented
4	#20289234	C₂	1	4	yes	maximal, complemented
5	#20288950	C₂	1	4	yes	maximal, complemented
6	#20288947	C₂	1	4	yes	maximal, complemented
7	#20288909	C₂	1	4	yes	maximal, complemented
8	#20288906	C₂	1	4	yes	maximal, complemented
9	#20288883	C₂	1	8	yes	maximal, complemented
10	#20288866	C₂	1	8	yes	maximal, complemented
11	#20288556	C₂	1	2	yes	maximal, complemented
12	#20288554	C₂	1	2	yes	maximal, complemented
13	#20288479	C₂	1	2	yes	maximal, complemented
14	#20288472	C₂	1	2	yes	maximal, complemented
15	#20288344	C₂	1	4	yes	maximal, complemented
16	C₂×#16811211	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#16811185	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#13133262	C₂²	1	4	yes	complemented
20	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
21	#16811375	C₂²	1	8	yes	complemented
22	#16811370	C₂²	1	8	yes	complemented
23	#16811367	C₂²	1	8	yes	complemented
24	#16811365	C₂²	1	8	yes	complemented
25	#16811364	C₂²	1	8	yes	complemented
26	#16811363	C₂²	1	8	yes	complemented
27	#16811361	C₂²	1	8	yes	complemented
28	#16811361	C₂²	1	8	yes	complemented
29	#16811355	C₂²	1	8	yes	complemented
30	#16811325	C₂²	1	8	yes	complemented
31	#16811324	C₂²	1	8	yes	complemented
32	#16811322	C₂²	1	8	yes	complemented
33	#16811321	C₂²	1	4	yes	complemented
34	#16811321	C₂²	1	8	yes	complemented
35	#16811319	C₂²	1	4	yes	complemented
36	#16811315	C₂²	1	4	yes	complemented
37	#16811313	C₂²	1	4	yes	complemented
38	#16811302	C₂²	1	8	yes	complemented
39	#16811300	C₂²	1	8	yes	complemented
40	#16811298	C₂²	1	8	yes	complemented
41	#16811296	C₂²	1	8	yes	complemented
42	#16811284	C₂²	1	4	yes	complemented
43	#16811282	C₂²	1	4	yes	complemented
44	#16811277	C₂²	1	4	yes	complemented
45	#16811277	C₂²	1	4	yes	complemented
46	#16811274	C₂²	1	4	yes	complemented
47	#16811273	C₂²	1	4	yes	complemented
48	#16811269	C₂²	1	4	yes	complemented
49	#16811268	C₂²	1	8	yes	complemented
50	#16811268	C₂²	1	8	yes	complemented
51	#16811266	C₂²	1	8	yes	complemented
52	#16811265	C₂²	1	8	yes	complemented
53	#16811264	C₂²	1	4	yes	complemented
54	#16811263	C₂²	1	8	yes	complemented
55	#16811263	C₂²	1	8	yes	complemented
56	#16811263	C₂²	1	8	yes	complemented
57	#16811262	C₂²	1	8	yes	complemented
58	#16811260	C₂²	1	8	yes	complemented
59	#16811260	C₂²	1	8	yes	complemented
60	D₄×D₂₁₂	C₂²	1	4	yes	complemented
61	D₄×D₂₁₂	C₂²	1	4	yes	complemented
62	#16811257	C₂²	1	4	yes	complemented
63	#16811257	C₂²	1	8	yes	complemented
64	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
65	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
66	D₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
67	#16811255	C₂²	1	8	yes	complemented
68	#16811255	C₂²	1	8	yes	complemented
69	#16811242	C₂²	1	8	yes	complemented
70	#16811239	C₂²	1	8	yes	complemented
71	#16811226	C₂²	1	8	yes	complemented
72	#16811225	C₂²	1	8	yes	complemented
73	#16811222	C₂²	1	4	yes	complemented
74	#16811220	C₂²	1	4	yes	complemented
75	#16811217	C₂²	1	8	yes	complemented
76	#16811214	C₂²	1	8	yes	complemented
77	#16811213	C₂²	1	4	yes	complemented
78	#16811212	C₂²	1	8	yes	complemented
79	#16811212	C₂²	1	8	yes	complemented
80	#16811211	C₂²	1	8	yes	complemented
81	#16811211	C₂²	1	4	yes	complemented
82	#16811211	C₂²	1	4	yes	complemented
83	#16811211	C₂²	1	4	yes	complemented
84	#16811210	C₂²	1	8	yes	complemented
85	#16811209	C₂²	1	8	yes	complemented
86	#16811207	C₂²	1	8	yes	complemented
87	#16811207	C₂²	1	8	yes	complemented
88	#16811204	C₂²	1	4	yes	complemented
89	#16811200	C₂²	1	4	yes	complemented
90	#16811191	C₂²	1	8	yes	complemented
91	#16811189	C₂²	1	8	yes	complemented
92	#16811188	C₂²	1	8	yes	complemented
93	#16811185	C₂²	1	4	yes	complemented
94	#16811185	C₂²	1	4	yes	complemented
95	#16811185	C₂²	1	4	yes	complemented
96	#16811185	C₂²	1	4	yes	complemented
97	#16811185	C₂²	1	4	yes	complemented
98	#16811185	C₂²	1	4	yes	complemented
99	#16811184	C₂²	1	8	yes	complemented
100	#16811183	C₂²	1	8	yes	complemented
101	#16811182	C₂²	1	4	yes	complemented
102	#16811181	C₂²	1	8	yes	complemented
103	#16811181	C₂²	1	4	yes	complemented
104	#16811173	C₂²	1	4	yes	complemented
105	#16811168	C₂²	1	4	yes	complemented
106	#16811159	C₂²	1	4	yes	complemented
107	#16811157	C₂²	1	4	yes	complemented
108	C₂×#13133210	C₂²	1	2	yes	complemented
109	C₂×#13133203	C₂²	1	2	yes	complemented
110	#16811136	C₂²	1	4	yes	complemented
111	#16811134	C₂²	1	4	yes	complemented
112	#16811129	C₂²	1	8	yes	complemented
113	C₂×#13133201	C₂²	1	4	yes	complemented
114	C₂×#13133199	C₂²	1	2	yes	complemented
115	C₂×#13133196	C₂²	1	1	yes	characteristic, complemented
116	C₂×#13133191	C₂²	1	2	yes	complemented
117	C₂×#13133191	C₂²	1	2	yes	complemented
118	C₂×#13133191	C₂²	1	1	yes	characteristic, complemented
119	C₂×#13133191	C₂²	1	4	yes	complemented
120	C₂×#13133190	C₂²	1	2	yes	complemented
121	#121×D₅₃	C₂²	1	4	yes	complemented
122	C₂×#13133187	C₂²	1	4	yes	complemented
123	C₂×#13133186	C₂²	1	2	yes	complemented
124	#120×D₅₃	C₂²	1	8	yes	complemented
125	#16811096	C₂²	1	4	yes	complemented
126	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
127	C₅₃×#538	C₂²	1	8	yes	complemented
128	C₅₃×#538	C₂²	1	4	yes	complemented
129	C₅₃×#538	C₂²	1	4	yes	complemented
130	C₂×#126×C₅₃	C₂²	1	2	yes	complemented
131	C₂×#124×C₅₃	C₂²	1	2	yes	complemented
132	C₂×#123×C₅₃	C₂²	1	2	yes	complemented
133	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×#121×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
136	C₂×#120×C₅₃	C₂²	1	2	yes	complemented
137	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	complemented
138	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
139	C₂⁴×D₅₃	C₂³	1	2	yes	—
140	#13133262	—	4	16	no	—
141	C₂×#11719949	C₂³	1	4	yes	complemented
142	C₂×#11719945	C₂³	1	8	yes	complemented
143	C₂×#11719945	C₂³	1	4	yes	complemented
144	C₂×#11719947	C₂³	1	8	yes	—
145	C₂×#11719947	C₂³	1	8	yes	complemented
146	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic, complemented
147	C₂²×D₂₁₂	C₂³	1	2	yes	—
148	C₂²×D₂₁₂	C₂³	1	2	yes	—
149	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
150	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
151	C₂²×C₂²⋊D₅₃	—	4	8	no	—
152	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
153	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
154	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
155	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
156	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
157	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
158	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
159	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
160	C₂×D₄×D₅₃	C₂³	1	8	yes	—
161	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
162	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
163	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
164	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
165	C₂³×Dic₅₃	C₂³	1	2	yes	—
166	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
167	#13133217	C₂³	1	4	yes	complemented
168	#13133216	C₂³	1	4	yes	complemented
169	#13133214	C₂³	1	4	yes	complemented
170	#13133213	C₂³	1	8	yes	—
171	#13133213	C₂³	1	8	yes	—
172	#13133213	C₂³	1	4	yes	complemented
173	#13133212	C₂³	1	8	yes	complemented
174	#13133212	C₂³	1	8	yes	complemented
175	#13133212	C₂³	1	8	yes	complemented
176	#13133212	C₂³	1	8	yes	complemented
177	#13133211	C₂³	1	8	yes	complemented
178	#13133210	C₂³	1	8	yes	complemented
179	#13133210	C₂³	1	8	yes	complemented
180	#13133210	C₂³	1	8	yes	complemented
181	#13133209	C₂³	1	4	yes	complemented
182	#13133208	C₂³	1	8	yes	complemented
183	#13133208	C₂³	1	4	yes	complemented
184	#13133207	C₂³	1	8	yes	complemented
185	#13133206	C₂³	1	4	yes	complemented
186	#13133206	C₂³	1	8	yes	complemented
187	#13133205	C₂³	1	8	yes	complemented
188	#13133205	C₂³	1	4	yes	complemented
189	#13133203	C₂³	1	8	yes	—
190	#13133203	C₂³	1	8	yes	—
191	#13133203	C₂³	1	8	yes	complemented
192	#13133203	C₂³	1	8	yes	complemented
193	#13133203	C₂³	1	8	yes	complemented
194	#13133203	C₂³	1	8	yes	complemented
195	#13133202	C₂³	1	8	yes	complemented
196	#13133202	C₂³	1	8	yes	complemented
197	#13133202	C₂³	1	8	yes	complemented
198	#13133202	C₂³	1	8	yes	complemented
199	#13133202	C₂³	1	8	yes	complemented
200	#13133201	C₂³	1	8	yes	—
201	#13133201	C₂³	1	8	yes	—
202	#13133201	C₂³	1	8	yes	—
203	#13133201	C₂³	1	8	yes	—
204	#13133201	C₂³	1	8	yes	—
205	#13133201	C₂³	1	8	yes	complemented
206	#13133201	C₂³	1	8	yes	complemented
207	#13133201	C₂³	1	8	yes	complemented
208	#13133200	C₂³	1	8	yes	complemented
209	#13133200	C₂³	1	8	yes	complemented
210	#13133199	C₂³	1	8	yes	—
211	#13133199	C₂³	1	8	yes	—
212	#13133199	C₂³	1	8	yes	complemented
213	#13133199	C₂³	1	8	yes	complemented
214	#13133199	C₂³	1	8	yes	complemented
215	#13133199	C₂³	1	8	yes	complemented
216	#13133198	C₂³	1	8	yes	—
217	#13133197	C₂³	1	8	yes	complemented
218	#13133197	C₂³	1	8	yes	complemented
219	#13133196	C₂³	1	4	yes	—
220	#13133196	C₂³	1	4	yes	complemented
221	#13133196	C₂³	1	4	yes	complemented
222	#13133195	C₂³	1	8	yes	complemented
223	#13133195	C₂³	1	8	yes	complemented
224	#13133194	C₂³	1	8	yes	complemented
225	#13133194	C₂³	1	8	yes	complemented
226	#13133194	C₂³	1	8	yes	complemented
227	#13133193	C₂³	1	8	yes	complemented
228	#13133193	C₂³	1	4	yes	complemented
229	#13133192	C₂³	1	4	yes	complemented
230	#13133192	C₂³	1	8	yes	complemented
231	#13133192	C₂³	1	8	yes	complemented
232	#13133192	C₂³	1	8	yes	complemented
233	#13133192	C₂³	1	4	yes	complemented
234	#13133191	C₂³	1	4	yes	—
235	#13133191	C₂³	1	4	yes	—
236	#13133191	C₂³	1	4	yes	—
237	#13133191	C₂³	1	4	yes	—
238	#13133191	C₂³	1	4	yes	—
239	#13133191	C₂³	1	4	yes	—
240	#13133191	C₂³	1	4	yes	—
241	#13133191	C₂³	1	4	yes	—
242	#13133191	C₂³	1	4	yes	—
243	#13133191	C₂³	1	8	yes	complemented
244	#13133191	C₂³	1	4	yes	complemented
245	#13133191	C₂³	1	4	yes	complemented
246	#13133191	C₂³	1	4	yes	complemented
247	#13133191	C₂³	1	8	yes	complemented
248	#13133191	C₂³	1	8	yes	complemented
249	#13133191	C₂³	1	4	yes	complemented
250	#13133190	C₂³	1	8	yes	—
251	#13133190	C₂³	1	8	yes	—
252	#13133190	C₂³	1	8	yes	—
253	#13133190	C₂³	1	8	yes	—
254	#13133190	C₂³	1	8	yes	complemented
255	#13133190	C₂³	1	8	yes	complemented
256	#13133190	C₂³	1	8	yes	complemented
257	#13133190	C₂³	1	8	yes	complemented
258	#13133190	C₂³	1	8	yes	complemented
259	#13133189	C₂³	1	8	yes	—
260	#13133189	C₂³	1	8	yes	—
261	#13133189	C₂³	1	8	yes	complemented
262	#13133189	C₂³	1	8	yes	complemented
263	#13133189	C₂³	1	8	yes	complemented
264	#13133189	C₂³	1	8	yes	complemented
265	#13133189	C₂³	1	8	yes	complemented
266	#13133188	C₂³	1	8	yes	—
267	#13133188	C₂³	1	8	yes	—
268	#13133188	C₂³	1	4	yes	complemented
269	#13133187	C₂³	1	8	yes	—
270	#13133187	C₂³	1	8	yes	—
271	#13133187	C₂³	1	8	yes	—
272	#13133187	C₂³	1	8	yes	—
273	#13133187	C₂³	1	8	yes	—
274	#13133187	C₂³	1	8	yes	complemented
275	#13133187	C₂³	1	8	yes	complemented
276	#13133187	C₂³	1	8	yes	complemented
277	#13133187	C₂³	1	8	yes	complemented
278	#13133187	C₂³	1	8	yes	complemented
279	#13133187	C₂³	1	8	yes	complemented
280	#13133186	C₂³	1	8	yes	—
281	#13133186	C₂³	1	8	yes	—
282	#13133186	C₂³	1	8	yes	complemented
283	#13133185	C₂³	1	8	yes	—
284	#13133185	C₂³	1	8	yes	—
285	#13133185	C₂³	1	8	yes	—
286	#13133185	C₂³	1	8	yes	complemented
287	#13133185	C₂³	1	8	yes	complemented
288	#13133185	C₂³	1	8	yes	complemented
289	Q₈×Dic₅₃	C₂³	1	4	yes	complemented
290	C₄×Dic₁₀₆	C₂³	1	4	yes	complemented
291	C₄×D₂₁₂	C₂³	1	4	yes	complemented
292	C₄×D₂₁₂	C₂³	1	8	yes	complemented
293	C₄×D₂₁₂	C₂³	1	4	yes	complemented
294	C₄×D₂₁₂	C₂³	1	4	yes	complemented
295	D₄×Dic₅₃	C₂³	1	4	yes	complemented
296	D₄×Dic₅₃	C₂³	1	8	yes	complemented
297	D₄×Dic₅₃	C₂³	1	8	yes	complemented
298	#13133179	C₂³	1	4	yes	complemented
299	#13133179	C₂³	1	4	yes	complemented
300	#13133179	C₂³	1	8	yes	complemented
301	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
302	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	—
303	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
304	C₄×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
305	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
306	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
307	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
308	#13133177	C₂³	1	8	yes	complemented
309	#13133177	C₂³	1	8	yes	complemented
310	#13133177	C₂³	1	8	yes	complemented
311	#13133177	C₂³	1	8	yes	complemented
312	#13133177	C₂³	1	8	yes	complemented
313	#13133176	C₂³	1	4	yes	complemented
314	#13133175	C₂³	1	4	yes	complemented
315	#13133175	C₂³	1	8	yes	complemented
316	#13133174	C₂³	1	8	yes	complemented
317	#13133173	C₂³	1	8	yes	—
318	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
319	C₂×C₄⋊Dic₅₃	C₂³	1	2	yes	—
320	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
321	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
322	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
323	C₂×#11719919	C₂³	1	2	yes	complemented
324	C₂×#11719919	C₂³	1	2	yes	complemented
325	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
326	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
327	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
328	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
329	C₂×#11719921	C₂³	1	4	yes	—
330	C₂×#11719921	C₂³	1	4	yes	—
331	C₂×#11719921	C₂³	1	8	yes	complemented
332	C₂×#11719921	C₂³	1	2	yes	complemented
333	C₂×#11719921	C₂³	1	2	yes	complemented
334	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
335	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
336	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
337	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
338	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
339	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
340	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic, complemented
341	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
342	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
343	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
344	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
345	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
348	#126×C₅₃	C₂³	1	8	yes	complemented
349	#126×C₅₃	C₂³	1	8	yes	complemented
350	#124×C₅₃	C₂³	1	8	yes	complemented
351	#124×C₅₃	C₂³	1	8	yes	complemented
352	#123×C₅₃	C₂³	1	8	yes	complemented
353	#123×C₅₃	C₂³	1	8	yes	complemented
354	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	—
355	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
356	#121×C₅₃	C₂³	1	4	yes	—
357	#121×C₅₃	C₂³	1	8	yes	complemented
358	#121×C₅₃	C₂³	1	4	yes	complemented
359	#121×C₅₃	C₂³	1	8	yes	complemented
360	#120×C₅₃	C₂³	1	8	yes	—
361	#120×C₅₃	C₂³	1	8	yes	—
362	C₄×D₄×C₅₃	C₂³	1	4	yes	—
363	C₄×D₄×C₅₃	C₂³	1	4	yes	—
364	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
365	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
366	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
367	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
368	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	complemented
369	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
370	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
371	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
372	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	—
373	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
374	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
375	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
376	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
377	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
378	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
379	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
380	C₂×C₄²×C₅₃	C₂³	1	2	yes	complemented
381	C₂⁴×C₅₃	—	2	4	no	—
382	C₂⁴×C₅₃	—	8	1	no	—
383	C₂⁴×C₅₃	—	8	1	no	—
384	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
385	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
386	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
387	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
388	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂³×D₅₃	—	4	4	no	—
390	C₂³×D₅₃	—	8	2	no	—
391	C₂³×D₅₃	—	8	2	no	—
392	C₂³×D₅₃	C₂⁴	1	4	yes	—
393	C₂³×D₅₃	C₂⁴	1	2	yes	—
394	C₂³×D₅₃	C₂⁴	1	8	yes	—
395	C₂³×D₅₃	C₂⁴	1	8	yes	—
396	C₂×Q₈×C₅₃	—	8	1	no	—
397	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
398	C₂×D₄×C₅₃	—	2	8	no	—
399	C₂×D₄×C₅₃	—	8	2	no	—
400	C₂×D₄×C₅₃	—	8	2	no	—
401	C₂×D₄×C₅₃	—	8	1	no	—
402	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
403	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
404	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
405	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
406	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
407	C₂²×C₄×C₅₃	—	8	1	no	—
408	C₂²×C₄×C₅₃	—	8	1	no	—
409	C₂²×C₄×C₅₃	—	8	2	no	—
410	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
411	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
412	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
416	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
420	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
421	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
422	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
423	C₂×C₂²⋊D₅₃	—	2	16	no	—
424	C₂×C₂²⋊D₅₃	—	2	8	no	—
425	C₂×C₂²⋊D₅₃	—	4	8	no	—
426	C₂×C₂²⋊D₅₃	—	4	16	no	—
427	C₂×C₂²⋊D₅₃	—	4	16	no	—
428	C₂×C₂²⋊D₅₃	—	4	16	no	—
429	C₂×C₂²⋊D₅₃	—	8	2	no	—
430	C₂×C₂²⋊D₅₃	—	8	2	no	—
431	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
432	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
433	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
434	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
435	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
436	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
437	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
438	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
439	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
440	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
441	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
442	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
443	C₂²×Dic₅₃	—	4	4	no	—
444	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
445	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
446	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
447	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
448	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
449	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
450	#11719949	—	8	4	no	—
451	#11719947	—	4	16	no	—
452	#11719947	—	4	16	no	—
453	D₄×D₅₃	—	4	16	no	—
454	D₄×D₅₃	—	4	16	no	—
455	D₄×D₅₃	—	8	4	no	—
456	D₄×D₅₃	—	8	8	no	—
457	D₄×D₅₃	—	8	8	no	—
458	#11719945	—	4	16	no	—
459	#11719945	—	8	4	no	—
460	C₂×D₂₁₂	—	8	2	no	—
461	C₂×D₂₁₂	—	8	2	no	—
462	C₂×D₂₁₂	—	8	1	no	—
463	C₂×D₂₁₂	—	8	4	no	—
464	C₂×D₂₁₂	C₂⁴	1	4	yes	—
465	C₂×D₂₁₂	C₂⁴	1	4	yes	—
466	C₂×D₂₁₂	C₂⁴	1	8	yes	—
467	C₂×D₂₁₂	C₂⁴	1	4	yes	—
468	C₂×D₂₁₂	C₂⁴	1	4	yes	—
469	C₂×D₂₁₂	C₂⁴	1	8	yes	—
470	C₂×D₂₁₂	C₂⁴	1	4	yes	—
471	C₂×D₂₁₂	C₂⁴	1	8	yes	—
472	C₂×C₄×D₅₃	—	8	2	no	—
473	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
474	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
475	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
476	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
477	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
478	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
479	C₂×Dic₁₀₆	—	8	1	no	—
480	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
481	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
482	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
483	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
484	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
485	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
486	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
487	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
488	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
489	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
490	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
491	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
492	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
493	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
494	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
495	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
496	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
497	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
498	C₄²×C₅₃	C₂⁴	1	4	yes	—
499	C₄²×C₅₃	C₂⁴	1	4	yes	—
500	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
501	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
502	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
503	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
504	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
505	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
506	#11719921	C₂⁴	1	8	yes	—
507	#11719921	C₂⁴	1	8	yes	—
508	#11719921	C₂⁴	1	8	yes	—
509	#11719921	C₂⁴	1	8	yes	—
510	#11719921	C₂⁴	1	8	yes	—
511	#11719921	C₂⁴	1	8	yes	—
512	#11719921	C₂⁴	1	8	yes	—
513	#11719921	C₂⁴	1	8	yes	—
514	#11719921	C₂⁴	1	8	yes	—
515	#11719921	C₂⁴	1	8	yes	—
516	#11719921	C₂⁴	1	8	yes	—
517	#11719921	C₂⁴	1	8	yes	—
518	#11719921	C₂⁴	1	4	yes	—
519	#11719921	C₂⁴	1	4	yes	—
520	#11719921	C₂⁴	1	8	yes	—
521	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
522	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
523	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
524	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
525	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
526	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
527	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
528	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
529	#11719919	C₂⁴	1	8	yes	—
530	#11719919	C₂⁴	1	8	yes	—
531	#11719919	C₂⁴	1	4	yes	—
532	#11719919	C₂⁴	1	4	yes	—
533	#11719919	C₂⁴	1	8	yes	—
534	#11719919	C₂⁴	1	8	yes	—
535	#11719919	C₂⁴	1	8	yes	—
536	C₄×Dic₅₃	C₂⁴	1	4	yes	—
537	C₄×Dic₅₃	C₂⁴	1	4	yes	—
538	C₄×Dic₅₃	C₂⁴	1	8	yes	—
539	C₄×Dic₅₃	C₂⁴	1	8	yes	—
540	C₂³×C₅₃	—	2	4	no	—
541	C₂³×C₅₃	—	2	4	no	—
542	C₂³×C₅₃	—	2	4	no	—
543	C₂³×C₅₃	—	2	4	no	—
544	C₂³×C₅₃	—	4	1	no	—
545	C₂³×C₅₃	—	4	1	no	—
546	C₂³×C₅₃	—	4	2	no	—
547	C₂³×C₅₃	—	4	2	no	—
548	C₂³×C₅₃	—	4	2	no	—
549	C₂³×C₅₃	—	4	2	no	—
550	C₂³×C₅₃	—	4	2	no	—
551	C₂³×C₅₃	—	4	2	no	—
552	C₂³×C₅₃	—	4	2	no	—
553	C₂³×C₅₃	—	4	2	no	—
554	C₂³×C₅₃	—	8	8	no	—
555	C₂³×C₅₃	H(5,𝔽₂)	1	4	yes	—
556	C₂³×C₅₃	C₂⁵	1	4	yes	—
557	C₂³×C₅₃	C₂⁵	1	4	yes	—
558	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
559	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
560	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
561	C₂²×D₅₃	—	2	4	no	—
562	C₂²×D₅₃	—	2	8	no	—
563	C₂²×D₅₃	—	4	2	no	—
564	C₂²×D₅₃	—	4	2	no	—
565	C₂²×D₅₃	—	4	4	no	—
566	C₂²×D₅₃	—	4	4	no	—
567	C₂²×D₅₃	—	4	8	no	—
568	C₂²×D₅₃	—	4	8	no	—
569	C₂²×D₅₃	—	4	8	no	—
570	C₂²×D₅₃	—	4	8	no	—
571	C₂²×D₅₃	—	4	8	no	—
572	C₂²×D₅₃	—	4	8	no	—
573	C₂²×D₅₃	—	8	16	no	—
574	C₂²×D₅₃	C₂⁵	1	4	yes	—
575	C₂²×D₅₃	C₂⁵	1	8	yes	—
576	Q₈×C₅₃	—	4	4	no	—
577	D₄×C₅₃	—	2	8	no	—
578	D₄×C₅₃	—	2	8	no	—
579	D₄×C₅₃	—	4	8	no	—
580	D₄×C₅₃	—	4	4	no	—
581	D₄×C₅₃	—	4	8	no	—
582	C₂×C₄×C₅₃	—	2	4	no	—
583	C₂×C₄×C₅₃	—	4	1	no	—
584	C₂×C₄×C₅₃	—	4	2	no	—
585	C₂×C₄×C₅₃	—	4	2	no	—
586	C₂×C₄×C₅₃	—	4	2	no	—
587	C₂×C₄×C₅₃	—	4	4	no	—
588	C₂×C₄×C₅₃	—	4	1	no	—
589	C₂×C₄×C₅₃	—	4	4	no	—
590	C₂×C₄×C₅₃	—	4	2	no	—
591	C₂×C₄×C₅₃	—	4	1	no	—
592	C₂×C₄×C₅₃	—	4	2	no	—
593	C₂×C₄×C₅₃	—	4	1	no	—
594	C₂×C₄×C₅₃	—	4	2	no	—
595	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
596	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
597	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
598	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
599	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
600	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
601	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
602	C₂²⋊D₅₃	—	2	8	no	—
603	C₂²⋊D₅₃	—	2	16	no	—
604	C₂²⋊D₅₃	—	2	8	no	—
605	C₂²⋊D₅₃	—	2	16	no	—
606	C₂²⋊D₅₃	—	4	8	no	—
607	C₂²⋊D₅₃	—	4	8	no	—
608	C₂²⋊D₅₃	—	4	8	no	—
609	C₂²⋊D₅₃	—	4	8	no	—
610	C₂²⋊D₅₃	—	4	8	no	—
611	C₂²⋊D₅₃	—	4	8	no	—
612	C₂²⋊D₅₃	—	4	8	no	—
613	C₂²⋊D₅₃	—	4	8	no	—
614	C₂×Dic₅₃	—	2	4	no	—
615	C₂×Dic₅₃	—	2	8	no	—
616	C₂×Dic₅₃	—	4	2	no	—
617	C₂×Dic₅₃	—	4	2	no	—
618	C₂×Dic₅₃	—	4	8	no	—
619	C₂×Dic₅₃	—	4	8	no	—
620	C₂×Dic₅₃	C₂⁵	1	4	yes	—
621	C₂×Dic₅₃	C₂⁵	1	4	yes	—
622	C₂×Dic₅₃	C₂⁵	1	8	yes	—
623	C₂×Dic₅₃	C₂⁵	1	4	yes	—
624	D₂₁₂	—	4	4	no	—
625	D₂₁₂	—	4	4	no	—
626	D₂₁₂	—	4	4	no	—
627	D₂₁₂	—	4	4	no	—
628	D₂₁₂	—	4	8	no	—
629	D₂₁₂	—	4	4	no	—
630	D₂₁₂	—	4	8	no	—
631	D₂₁₂	—	4	8	no	—
632	C₄×D₅₃	—	4	4	no	—
633	C₄×D₅₃	—	4	4	no	—
634	C₄×D₅₃	—	4	8	no	—
635	C₄×D₅₃	—	4	8	no	—
636	C₄×D₅₃	—	4	8	no	—
637	C₄×D₅₃	—	4	8	no	—
638	Dic₁₀₆	—	4	4	no	—
639	Dic₁₀₆	—	4	8	no	—
640	#62863	—	53	1	no	maximal, Sylow
641	C₂²×C₅₃	—	2	1	no	—
642	C₂²×C₅₃	—	2	1	no	—
643	C₂²×C₅₃	—	2	1	no	—
644	C₂²×C₅₃	—	2	1	no	—
645	C₂²×C₅₃	—	2	1	no	—
646	C₂²×C₅₃	—	2	1	no	—
647	C₂²×C₅₃	—	2	4	no	—
648	C₂²×C₅₃	—	2	4	no	—
649	C₂²×C₅₃	—	2	4	no	—
650	C₂²×C₅₃	—	2	4	no	—
651	C₂²×C₅₃	—	2	4	no	—
652	C₂²×C₅₃	—	2	4	no	—
653	C₂²×C₅₃	—	4	4	no	—
654	C₂²×C₅₃	—	4	8	no	—
655	C₂²×C₅₃	—	8	4	no	—
656	C₂²×C₅₃	—	8	4	no	—
657	C₂²×C₅₃	—	8	4	no	—
658	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
659	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
660	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
661	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
662	C₂×D₅₃	—	2	4	no	—
663	C₂×D₅₃	—	2	8	no	—
664	C₂×D₅₃	—	2	4	no	—
665	C₂×D₅₃	—	2	8	no	—
666	C₂×D₅₃	—	2	8	no	—
667	C₂×D₅₃	—	2	4	no	—
668	C₂×D₅₃	—	8	4	no	—
669	C₂×D₅₃	—	8	8	no	—
670	C₂×D₅₃	—	8	16	no	—
671	C₂×D₅₃	—	16	8	no	—
672	C₄×C₅₃	—	2	4	no	—
673	C₄×C₅₃	—	2	2	no	—
674	C₄×C₅₃	—	2	2	no	—
675	C₄×C₅₃	—	2	4	no	—
676	C₄×C₅₃	—	2	2	no	—
677	C₄×C₅₃	—	2	4	no	—
678	C₄×C₅₃	—	2	2	no	—
679	Dic₅₃	—	2	4	no	—
680	Dic₅₃	—	2	8	no	—
681	Dic₅₃	—	2	4	no	—
682	Dic₅₃	—	2	4	no	—
683	#3560	—	53	4	no	—
684	#3560	—	53	4	no	—
685	#3558	—	53	4	no	—
686	#3558	—	53	4	no	—
687	#3537	—	53	4	no	—
688	#3537	—	53	4	no	—
689	#3534	—	53	4	no	—
690	#3534	—	53	4	no	—
691	#3533	—	53	8	no	—
692	#3532	—	53	8	no	—
693	#3505	—	53	2	no	—
694	#3505	—	53	2	no	—
695	#3496	—	53	2	no	—
696	#3496	—	53	2	no	—
697	#3484	—	53	4	no	—
698	C₂×#538	—	53	1	no	—
699	C₂×#538	D₅₃	1	1	yes	characteristic, complemented
700	C₂×#534	—	53	1	no	—
701	C₂×C₅₃	—	2	2	no	—
702	C₂×C₅₃	—	2	2	no	—
703	C₂×C₅₃	—	2	2	no	—
704	C₂×C₅₃	—	4	4	no	—
705	C₂×C₅₃	—	4	4	no	—
706	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
708	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
709	D₅₃	—	4	8	no	—
710	D₅₃	—	4	4	no	—
711	C₂×H(5,𝔽₂)	—	53	4	no	—
712	C₂³×D₄	—	53	2	no	—
713	#563	—	53	8	no	—
714	#562	—	53	8	no	—
715	#562	—	53	8	no	—
716	H(3,𝔽₄)	—	53	8	no	—
717	#560	—	53	8	no	—
718	#560	—	53	8	no	—
719	#560	—	53	8	no	—
720	#560	—	53	8	no	—
721	#559	—	53	8	no	—
722	#553	—	53	8	no	—
723	#553	—	53	8	no	—
724	#553	—	53	4	no	—
725	#553	—	53	8	no	—
726	#553	—	53	4	no	—
727	#553	—	53	8	no	—
728	#552	—	53	4	no	—
729	#552	—	53	4	no	—
730	#551	—	53	8	no	—
731	#551	—	53	8	no	—
732	#551	—	53	8	no	—
733	#551	—	53	8	no	—
734	#548	—	53	4	no	—
735	#548	—	53	4	no	—
736	#547	—	53	4	no	—
737	#547	—	53	4	no	—
738	#547	—	53	4	no	—
739	#547	—	53	4	no	—
740	#546	—	53	8	no	—
741	#546	—	53	8	no	—
742	#546	—	53	4	no	—
743	#546	—	53	8	no	—
744	#546	—	53	8	no	—
745	#546	—	53	8	no	—
746	#546	—	53	8	no	—
747	#546	—	53	4	no	—
748	#546	—	53	8	no	—
749	#546	—	53	8	no	—
750	#546	—	53	8	no	—
751	#546	—	53	8	no	—
752	D₄²	—	53	8	no	—
753	D₄²	—	53	8	no	—
754	D₄²	—	53	4	no	—
755	D₄²	—	53	4	no	—
756	D₄²	—	53	8	no	—
757	D₄²	—	53	8	no	—
758	D₄²	—	53	8	no	—
759	D₄²	—	53	4	no	—
760	D₄²	—	53	4	no	—
761	#542	—	53	8	no	—
762	#542	—	53	8	no	—
763	#540	—	53	8	no	—
764	#540	—	53	8	no	—
765	#539	—	53	8	no	—
766	#539	—	53	8	no	—
767	#539	—	53	4	no	—
768	#539	—	53	4	no	—
769	#538	—	53	8	no	—
770	#538	—	53	8	no	—
771	#538	—	53	8	no	—
772	#538	—	53	8	no	—
773	#538	—	53	8	no	—
774	#538	—	53	4	no	—
775	#538	—	53	8	no	—
776	#538	—	53	8	no	—
777	#538	—	53	4	no	—
778	#538	—	53	4	no	—
779	#538	—	53	4	no	—
780	#538	C₂×D₅₃	1	8	yes	complemented
781	#538	C₂×D₅₃	1	4	yes	complemented
782	#538	C₂×D₅₃	1	4	yes	complemented
783	#537	—	53	4	no	—
784	#537	—	53	4	no	—
785	#535	—	53	8	no	—
786	#535	—	53	8	no	—
787	#535	—	53	8	no	—
788	#534	—	53	4	no	—
789	#534	—	53	8	no	—
790	#534	—	53	4	no	—
791	#534	—	53	8	no	—
792	#534	—	53	8	no	—
793	#534	—	53	4	no	—
794	#534	—	53	4	no	—
795	#534	—	53	4	no	—
796	#534	—	53	4	no	—
797	#534	—	53	4	no	—
798	#534	—	53	4	no	—
799	#532	—	53	4	no	—
800	#532	—	53	4	no	—
801	#529	—	53	4	no	—
802	#529	—	53	4	no	—
803	C₂×#126	—	53	2	no	—
804	C₂×#126	C₂×D₅₃	1	2	yes	complemented
805	C₂×#124	—	53	2	no	—
806	C₂×#124	C₂×D₅₃	1	2	yes	complemented
807	#525	—	53	4	no	—
808	#525	—	53	4	no	—
809	#525	—	53	8	no	—
810	C₂×#123	—	53	4	no	—
811	C₂×#123	—	53	2	no	—
812	C₂×#123	C₂×D₅₃	1	2	yes	complemented
813	C₂×C₂²⋊Q₈	—	53	1	no	—
814	C₂×C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
815	C₂×#121	—	53	2	no	—
816	C₂×#121	—	53	2	no	—
817	C₂×#121	—	53	1	no	—
818	C₂×#121	—	53	4	no	—
819	C₂×#121	—	53	4	no	—
820	C₂×#121	—	53	2	no	—
821	C₂×#121	C₂×D₅₃	1	2	yes	complemented
822	C₂×#121	C₂×D₅₃	1	1	yes	characteristic, complemented
823	C₂×#120	—	53	2	no	—
824	C₂×#120	—	53	8	no	—
825	C₂×#120	—	53	4	no	—
826	C₂×#120	C₂×D₅₃	1	2	yes	complemented
827	#518	—	53	4	no	—
828	C₂×C₄×D₄	—	53	2	no	—
829	C₂×C₄×D₄	C₂×D₅₃	1	2	yes	complemented
830	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
831	C₅₃	#62863	1	1	yes	characteristic, complemented, Sylow
832	C₂⁵	—	53	2	no	—
833	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
834	H(5,𝔽₂)	—	212	16	no	—
835	C₂×#41	—	53	4	no	—
836	C₂×#41	—	53	8	no	—
837	C₂×#41	—	53	8	no	—
838	C₂×#41	—	53	4	no	—
839	C₂×#41	—	53	8	no	—
840	C₂²×Q₈	—	53	1	no	—
841	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic, complemented
842	C₂²×D₄	—	53	2	no	—
843	C₂²×D₄	—	53	4	no	—
844	C₂²×D₄	—	53	2	no	—
845	C₂²×D₄	—	53	2	no	—
846	C₂²×D₄	—	53	4	no	—
847	C₂²×D₄	—	53	8	no	—
848	C₂²×D₄	—	53	8	no	—
849	C₂²×D₄	—	53	8	no	—
850	C₂²×D₄	—	53	8	no	—
851	C₂²×D₄	—	53	8	no	—
852	C₂²×D₄	—	53	4	no	—
853	C₂²×D₄	—	53	8	no	—
854	C₂²×D₄	—	53	8	no	—
855	C₂²×D₄	—	53	2	no	—
856	C₂²×D₄	—	53	2	no	—
857	C₂²×D₄	—	53	1	no	—
858	C₂²×D₄	—	53	4	no	—
859	C₂²×D₄	—	212	8	no	—
860	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
861	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
862	C₂²×D₄	C₂²×D₅₃	1	2	yes	—
863	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
864	C₂³×C₄	—	53	2	no	—
865	C₂³×C₄	—	53	2	no	—
866	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
867	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
868	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
869	C₄⋊Q₈	—	53	4	no	—
870	C₄⋊Q₈	—	53	4	no	—
871	#127	—	53	4	no	—
872	#127	—	53	8	no	—
873	#127	—	53	8	no	—
874	#127	—	53	4	no	—
875	#126	—	53	8	no	—
876	#126	—	53	8	no	—
877	#126	—	53	8	no	—
878	#126	—	53	8	no	—
879	#126	—	53	8	no	—
880	#126	—	53	8	no	—
881	#126	—	53	8	no	—
882	#126	—	53	8	no	—
883	#126	C₂²×D₅₃	1	8	yes	complemented
884	#126	C₂²×D₅₃	1	8	yes	complemented
885	#125	—	53	4	no	—
886	#125	—	53	8	no	—
887	#125	—	53	8	no	—
888	#125	—	53	4	no	—
889	#124	—	53	4	no	—
890	#124	—	53	8	no	—
891	#124	—	53	8	no	—
892	#124	—	53	8	no	—
893	#124	—	53	8	no	—
894	#124	—	53	8	no	—
895	#124	—	53	8	no	—
896	#124	—	53	8	no	—
897	#124	—	53	4	no	—
898	#124	—	53	8	no	—
899	#124	C₂²×D₅₃	1	8	yes	complemented
900	#124	C₂²×D₅₃	1	8	yes	complemented
901	#123	—	53	8	no	—
902	#123	—	53	8	no	—
903	#123	—	53	8	no	—
904	#123	—	53	8	no	—
905	#123	—	53	8	no	—
906	#123	—	53	8	no	—
907	#123	—	53	8	no	—
908	#123	—	53	8	no	—
909	#123	—	53	8	no	—
910	#123	—	53	8	no	—
911	#123	—	53	8	no	—
912	#123	—	53	8	no	—
913	#123	—	53	8	no	—
914	#123	—	53	8	no	—
915	#123	—	53	8	no	—
916	#123	—	53	8	no	—
917	#123	—	53	8	no	—
918	#123	—	53	8	no	—
919	#123	—	53	8	no	—
920	#123	—	53	8	no	—
921	#123	—	53	8	no	—
922	#123	—	53	8	no	—
923	#123	C₂²×D₅₃	1	8	yes	complemented
924	#123	C₂²×D₅₃	1	8	yes	complemented
925	C₂²⋊Q₈	—	53	4	no	—
926	C₂²⋊Q₈	—	53	8	no	—
927	C₂²⋊Q₈	—	53	4	no	—
928	C₂²⋊Q₈	—	53	4	no	—
929	C₂²⋊Q₈	—	53	4	no	—
930	C₂²⋊Q₈	—	53	8	no	—
931	C₂²⋊Q₈	—	53	8	no	—
932	C₂²⋊Q₈	—	53	8	no	—
933	C₂²⋊Q₈	—	53	8	no	—
934	C₂²⋊Q₈	—	53	8	no	—
935	C₂²⋊Q₈	—	53	8	no	—
936	C₂²⋊Q₈	—	53	8	no	—
937	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	—
938	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
939	#121	—	53	8	no	—
940	#121	—	53	4	no	—
941	#121	—	53	8	no	—
942	#121	—	53	8	no	—
943	#121	—	53	8	no	—
944	#121	—	53	8	no	—
945	#121	—	53	8	no	—
946	#121	—	53	8	no	—
947	#121	—	53	8	no	—
948	#121	—	53	8	no	—
949	#121	—	53	4	no	—
950	#121	—	53	4	no	—
951	#121	—	53	4	no	—
952	#121	—	53	4	no	—
953	#121	—	53	4	no	—
954	#121	—	53	4	no	—
955	#121	—	53	4	no	—
956	#121	—	53	4	no	—
957	#121	—	53	4	no	—
958	#121	—	53	8	no	—
959	#121	—	53	8	no	—
960	#121	—	53	4	no	—
961	#121	—	53	4	no	—
962	#121	—	53	4	no	—
963	#121	—	53	4	no	—
964	#121	—	53	8	no	—
965	#121	—	53	4	no	—
966	#121	—	53	4	no	—
967	#121	—	53	8	no	—
968	#121	—	53	8	no	—
969	#121	—	53	8	no	—
970	#121	—	53	8	no	—
971	#121	—	53	8	no	—
972	#121	—	53	8	no	—
973	#121	—	53	8	no	—
974	#121	—	53	8	no	—
975	#121	—	53	8	no	—
976	#121	—	53	8	no	—
977	#121	—	53	8	no	—
978	#121	—	53	8	no	—
979	#121	C₂²×D₅₃	1	4	yes	—
980	#121	C₂²×D₅₃	1	4	yes	complemented
981	#121	C₂²×D₅₃	1	8	yes	complemented
982	#121	C₂²×D₅₃	1	8	yes	complemented
983	#120	—	53	8	no	—
984	#120	—	53	8	no	—
985	#120	—	53	8	no	—
986	#120	—	53	8	no	—
987	#120	—	53	8	no	—
988	#120	—	53	8	no	—
989	#120	—	53	8	no	—
990	#120	—	53	8	no	—
991	#120	—	53	8	no	—
992	#120	—	53	8	no	—
993	#120	—	53	8	no	—
994	#120	—	53	8	no	—
995	#120	—	53	8	no	—
996	#120	—	53	8	no	—
997	#120	—	53	8	no	—
998	#120	—	53	8	no	—
999	#120	—	53	8	no	—
1000	#120	—	53	8	no	—
1001	#120	—	53	8	no	—
1002	#120	—	53	8	no	—
1003	#120	C₂²×D₅₃	1	8	yes	—
1004	#120	C₂²×D₅₃	1	8	yes	—
1005	C₄×Q₈	—	53	4	no	—
1006	C₄×Q₈	—	53	4	no	—
1007	C₄×D₄	—	53	8	no	—
1008	C₄×D₄	—	53	8	no	—
1009	C₄×D₄	—	53	4	no	—
1010	C₄×D₄	—	53	4	no	—
1011	C₄×D₄	—	53	4	no	—
1012	C₄×D₄	—	53	4	no	—
1013	C₄×D₄	—	53	4	no	—
1014	C₄×D₄	—	53	8	no	—
1015	C₄×D₄	—	53	8	no	—
1016	C₄×D₄	—	53	8	no	—
1017	C₄×D₄	—	53	8	no	—
1018	C₄×D₄	—	53	4	no	—
1019	C₄×D₄	—	53	4	no	—
1020	C₄×D₄	—	53	8	no	—
1021	C₄×D₄	—	53	8	no	—
1022	C₄×D₄	—	53	8	no	—
1023	C₄×D₄	—	53	8	no	—
1024	C₄×D₄	—	53	8	no	—
1025	C₄×D₄	—	53	4	no	—
1026	C₄×D₄	—	53	4	no	—
1027	C₄×D₄	—	53	4	no	—
1028	C₄×D₄	—	53	8	no	—
1029	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1030	C₄×D₄	C₂²×D₅₃	1	4	yes	—
1031	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1032	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
1033	#117	—	53	4	no	—
1034	#117	—	53	4	no	—
1035	#117	—	53	8	no	—
1036	#117	—	53	8	no	—
1037	#117	—	53	8	no	—
1038	C₂×C₄⋊C₄	—	53	2	no	—
1039	C₂×C₄⋊C₄	—	53	2	no	—
1040	C₂×C₄⋊C₄	—	53	2	no	—
1041	C₂×C₄⋊C₄	—	53	2	no	—
1042	C₂×C₄⋊C₄	—	53	1	no	—
1043	C₂×C₄⋊C₄	—	53	4	no	—
1044	C₂×C₄⋊C₄	—	53	1	no	—
1045	C₂×C₄⋊C₄	—	53	4	no	—
1046	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1047	C₂×C₄⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1048	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1049	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
1050	C₂×C₂²⋊C₄	—	53	2	no	—
1051	C₂×C₂²⋊C₄	—	53	2	no	—
1052	C₂×C₂²⋊C₄	—	53	2	no	—
1053	C₂×C₂²⋊C₄	—	53	2	no	—
1054	C₂×C₂²⋊C₄	—	53	4	no	—
1055	C₂×C₂²⋊C₄	—	53	4	no	—
1056	C₂×C₂²⋊C₄	—	53	2	no	—
1057	C₂×C₂²⋊C₄	—	53	8	no	—
1058	C₂×C₂²⋊C₄	—	53	8	no	—
1059	C₂×C₂²⋊C₄	—	53	8	no	—
1060	C₂×C₂²⋊C₄	—	53	8	no	—
1061	C₂×C₂²⋊C₄	—	53	8	no	—
1062	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	—
1063	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1064	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1065	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1066	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1067	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1068	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1069	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
1070	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1071	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
1072	C₂×C₄²	—	53	2	no	—
1073	C₂×C₄²	C₂²×D₅₃	1	2	yes	complemented
1074	C₂⁴	—	2	4	no	—
1075	C₂⁴	—	8	1	no	—
1076	C₂⁴	—	8	1	no	—
1077	C₂⁴	—	53	4	no	—
1078	C₂⁴	—	53	2	no	—
1079	C₂⁴	—	53	8	no	—
1080	C₂⁴	—	53	8	no	—
1081	C₂⁴	—	424	2	no	—
1082	C₂⁴	—	424	2	no	—
1083	C₂⁴	—	212	4	no	—
1084	C₂⁴	C₂³×D₅₃	1	2	yes	—
1085	C₂⁴	C₂³×D₅₃	1	2	yes	—
1086	C₂⁴	C₂³×D₅₃	1	2	yes	—
1087	C₂⁴	C₂³×D₅₃	1	2	yes	—
1088	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1089	#41	—	424	4	no	—
1090	#41	—	424	4	no	—
1091	#41	—	212	16	no	—
1092	#41	—	212	16	no	—
1093	#41	—	212	16	no	—
1094	C₂×Q₈	—	8	1	no	—
1095	C₂×Q₈	—	53	4	no	—
1096	C₂×Q₈	—	53	8	no	—
1097	C₂×Q₈	—	424	1	no	—
1098	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1099	C₂×D₄	—	2	8	no	—
1100	C₂×D₄	—	8	2	no	—
1101	C₂×D₄	—	8	2	no	—
1102	C₂×D₄	—	8	1	no	—
1103	C₂×D₄	—	53	4	no	—
1104	C₂×D₄	—	53	4	no	—
1105	C₂×D₄	—	53	8	no	—
1106	C₂×D₄	—	53	8	no	—
1107	C₂×D₄	—	53	8	no	—
1108	C₂×D₄	—	53	8	no	—
1109	C₂×D₄	—	53	8	no	—
1110	C₂×D₄	—	53	8	no	—
1111	C₂×D₄	—	53	8	no	—
1112	C₂×D₄	—	53	8	no	—
1113	C₂×D₄	—	53	8	no	—
1114	C₂×D₄	—	53	8	no	—
1115	C₂×D₄	—	53	4	no	—
1116	C₂×D₄	—	53	4	no	—
1117	C₂×D₄	—	53	8	no	—
1118	C₂×D₄	—	53	4	no	—
1119	C₂×D₄	—	53	4	no	—
1120	C₂×D₄	—	53	8	no	—
1121	C₂×D₄	—	53	4	no	—
1122	C₂×D₄	—	53	8	no	—
1123	C₂×D₄	—	106	16	no	—
1124	C₂×D₄	—	106	8	no	—
1125	C₂×D₄	—	424	4	no	—
1126	C₂×D₄	—	424	1	no	—
1127	C₂×D₄	—	424	2	no	—
1128	C₂×D₄	—	424	2	no	—
1129	C₂×D₄	—	424	4	no	—
1130	C₂×D₄	—	424	8	no	—
1131	C₂×D₄	—	424	8	no	—
1132	C₂×D₄	—	424	2	no	—
1133	C₂×D₄	—	424	2	no	—
1134	C₂×D₄	—	212	8	no	—
1135	C₂×D₄	—	212	16	no	—
1136	C₂×D₄	—	212	16	no	—
1137	C₂×D₄	—	212	16	no	—
1138	C₂×D₄	—	212	16	no	—
1139	C₂×D₄	—	212	16	no	—
1140	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1141	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1142	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1143	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1144	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1145	C₂²×C₄	—	8	1	no	—
1146	C₂²×C₄	—	8	1	no	—
1147	C₂²×C₄	—	8	2	no	—
1148	C₂²×C₄	—	53	2	no	—
1149	C₂²×C₄	—	53	4	no	—
1150	C₂²×C₄	—	53	2	no	—
1151	C₂²×C₄	—	53	2	no	—
1152	C₂²×C₄	—	53	8	no	—
1153	C₂²×C₄	—	53	8	no	—
1154	C₂²×C₄	—	53	8	no	—
1155	C₂²×C₄	—	53	8	no	—
1156	C₂²×C₄	—	53	4	no	—
1157	C₂²×C₄	—	53	8	no	—
1158	C₂²×C₄	—	53	8	no	—
1159	C₂²×C₄	—	53	4	no	—
1160	C₂²×C₄	—	424	2	no	—
1161	C₂²×C₄	—	212	4	no	—
1162	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1163	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1164	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1165	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1166	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1167	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1168	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1170	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1171	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1173	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1174	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1175	C₄⋊C₄	—	53	4	no	—
1176	C₄⋊C₄	—	53	4	no	—
1177	C₄⋊C₄	—	53	4	no	—
1178	C₄⋊C₄	—	53	8	no	—
1179	C₄⋊C₄	—	53	8	no	—
1180	C₄⋊C₄	—	53	8	no	—
1181	C₄⋊C₄	—	53	4	no	—
1182	C₄⋊C₄	—	53	4	no	—
1183	C₄⋊C₄	—	53	4	no	—
1184	C₄⋊C₄	—	53	4	no	—
1185	C₄⋊C₄	—	53	4	no	—
1186	C₄⋊C₄	—	53	8	no	—
1187	C₄⋊C₄	—	53	8	no	—
1188	C₄⋊C₄	—	53	8	no	—
1189	C₄⋊C₄	—	53	8	no	—
1190	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1191	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1192	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1193	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1194	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1195	C₂²⋊C₄	—	53	4	no	—
1196	C₂²⋊C₄	—	53	8	no	—
1197	C₂²⋊C₄	—	53	8	no	—
1198	C₂²⋊C₄	—	53	8	no	—
1199	C₂²⋊C₄	—	53	4	no	—
1200	C₂²⋊C₄	—	53	8	no	—
1201	C₂²⋊C₄	—	53	8	no	—
1202	C₂²⋊C₄	—	53	8	no	—
1203	C₂²⋊C₄	—	53	8	no	—
1204	C₂²⋊C₄	—	53	8	no	—
1205	C₂²⋊C₄	—	53	8	no	—
1206	C₂²⋊C₄	—	53	8	no	—
1207	C₂²⋊C₄	—	53	8	no	—
1208	C₂²⋊C₄	—	53	8	no	—
1209	C₂²⋊C₄	—	53	8	no	—
1210	C₂²⋊C₄	—	53	8	no	—
1211	C₂²⋊C₄	—	53	8	no	—
1212	C₂²⋊C₄	—	53	8	no	—
1213	C₂²⋊C₄	—	53	4	no	—
1214	C₂²⋊C₄	—	53	4	no	—
1215	C₂²⋊C₄	—	53	8	no	—
1216	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1217	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1218	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1219	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1220	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1221	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1222	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1223	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1224	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1225	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1226	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1227	C₄²	—	53	4	no	—
1228	C₄²	—	53	4	no	—
1229	C₄²	—	53	8	no	—
1230	C₄²	—	53	8	no	—
1231	C₄²	C₂³×D₅₃	1	4	yes	—
1232	C₄²	C₂³×D₅₃	1	4	yes	—
1233	C₂³	—	2	4	no	—
1234	C₂³	—	2	4	no	—
1235	C₂³	—	2	4	no	—
1236	C₂³	—	2	4	no	—
1237	C₂³	—	4	1	no	—
1238	C₂³	—	4	1	no	—
1239	C₂³	—	4	2	no	—
1240	C₂³	—	4	2	no	—
1241	C₂³	—	4	2	no	—
1242	C₂³	—	4	2	no	—
1243	C₂³	—	4	2	no	—
1244	C₂³	—	4	2	no	—
1245	C₂³	—	4	2	no	—
1246	C₂³	—	4	2	no	—
1247	C₂³	—	8	8	no	—
1248	C₂³	—	53	8	no	—
1249	C₂³	—	53	4	no	—
1250	C₂³	—	106	4	no	—
1251	C₂³	—	106	8	no	—
1252	C₂³	—	424	16	no	—
1253	C₂³	—	212	8	no	—
1254	C₂³	—	212	8	no	—
1255	C₂³	—	212	8	no	—
1256	C₂³	—	212	2	no	—
1257	C₂³	—	212	2	no	—
1258	C₂³	—	212	4	no	—
1259	C₂³	—	212	4	no	—
1260	C₂³	—	212	8	no	—
1261	C₂³	—	212	8	no	—
1262	C₂³	—	212	8	no	—
1263	C₂³	#13133263	1	4	yes	—
1264	C₂³	C₂⁴×D₅₃	1	4	yes	—
1265	C₂³	C₂⁴×D₅₃	1	4	yes	—
1266	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1267	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1268	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1269	Q₈	—	4	4	no	—
1270	Q₈	—	212	4	no	—
1271	Q₈	—	212	8	no	—
1272	D₄	—	2	8	no	—
1273	D₄	—	2	8	no	—
1274	D₄	—	4	8	no	—
1275	D₄	—	4	4	no	—
1276	D₄	—	4	8	no	—
1277	D₄	—	106	16	no	—
1278	D₄	—	106	16	no	—
1279	D₄	—	106	8	no	—
1280	D₄	—	106	8	no	—
1281	D₄	—	212	4	no	—
1282	D₄	—	212	4	no	—
1283	D₄	—	212	4	no	—
1284	D₄	—	212	8	no	—
1285	D₄	—	212	4	no	—
1286	D₄	—	212	4	no	—
1287	D₄	—	212	8	no	—
1288	D₄	—	212	8	no	—
1289	D₄	—	212	8	no	—
1290	D₄	—	212	8	no	—
1291	D₄	—	212	8	no	—
1292	D₄	—	212	8	no	—
1293	D₄	—	212	8	no	—
1294	D₄	—	212	8	no	—
1295	D₄	—	212	8	no	—
1296	D₄	—	212	8	no	—
1297	C₂×C₄	—	2	4	no	—
1298	C₂×C₄	—	4	2	no	—
1299	C₂×C₄	—	4	2	no	—
1300	C₂×C₄	—	4	1	no	—
1301	C₂×C₄	—	4	2	no	—
1302	C₂×C₄	—	4	1	no	—
1303	C₂×C₄	—	4	2	no	—
1304	C₂×C₄	—	4	4	no	—
1305	C₂×C₄	—	4	2	no	—
1306	C₂×C₄	—	4	1	no	—
1307	C₂×C₄	—	4	1	no	—
1308	C₂×C₄	—	4	4	no	—
1309	C₂×C₄	—	4	2	no	—
1310	C₂×C₄	—	53	4	no	—
1311	C₂×C₄	—	53	4	no	—
1312	C₂×C₄	—	53	4	no	—
1313	C₂×C₄	—	53	8	no	—
1314	C₂×C₄	—	106	8	no	—
1315	C₂×C₄	—	106	4	no	—
1316	C₂×C₄	—	212	4	no	—
1317	C₂×C₄	—	212	4	no	—
1318	C₂×C₄	—	212	8	no	—
1319	C₂×C₄	—	212	8	no	—
1320	C₂×C₄	—	212	8	no	—
1321	C₂×C₄	—	212	8	no	—
1322	C₂×C₄	—	212	2	no	—
1323	C₂×C₄	—	212	8	no	—
1324	C₂×C₄	—	212	2	no	—
1325	C₂×C₄	—	212	8	no	—
1326	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1327	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1328	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1329	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1330	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1331	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1332	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1333	C₂²	—	2	1	no	—
1334	C₂²	—	2	1	no	—
1335	C₂²	—	2	1	no	—
1336	C₂²	—	2	1	no	—
1337	C₂²	—	2	1	no	—
1338	C₂²	—	2	1	no	—
1339	C₂²	—	2	4	no	—
1340	C₂²	—	2	4	no	—
1341	C₂²	—	2	4	no	—
1342	C₂²	—	2	4	no	—
1343	C₂²	—	2	4	no	—
1344	C₂²	—	2	4	no	—
1345	C₂²	—	4	4	no	—
1346	C₂²	—	4	8	no	—
1347	C₂²	—	8	4	no	—
1348	C₂²	—	8	4	no	—
1349	C₂²	—	8	4	no	—
1350	C₂²	—	848	8	no	—
1351	C₂²	—	106	4	no	—
1352	C₂²	—	106	8	no	—
1353	C₂²	—	106	4	no	—
1354	C₂²	—	106	8	no	—
1355	C₂²	—	106	8	no	—
1356	C₂²	—	106	4	no	—
1357	C₂²	—	424	8	no	—
1358	C₂²	—	424	4	no	—
1359	C₂²	—	424	16	no	—
1360	C₂²	C₂×#13133263	1	2	yes	—
1361	C₂²	C₂×#13133263	1	2	yes	—
1362	C₂²	C₂×#13133263	1	2	yes	—
1363	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1364	C₄	—	2	4	no	—
1365	C₄	—	2	2	no	—
1366	C₄	—	2	2	no	—
1367	C₄	—	2	2	no	—
1368	C₄	—	2	4	no	—
1369	C₄	—	2	2	no	—
1370	C₄	—	2	4	no	—
1371	C₄	—	106	8	no	—
1372	C₄	—	106	4	no	—
1373	C₄	—	106	4	no	—
1374	C₄	—	106	4	no	—
1375	C₂	—	2	2	no	—
1376	C₂	—	2	2	no	—
1377	C₂	—	2	2	no	—
1378	C₂	—	4	4	no	—
1379	C₂	—	4	4	no	—
1380	C₂	—	212	4	no	—
1381	C₂	—	212	8	no	—
1382	C₂	C₂²×#13133263	1	1	yes	characteristic
1383	C₂	#20289525	1	1	yes	characteristic
1384	C₂	#20289525	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#538	C₂
hypercenter	C₂×#538	D₅₃
hypocenter	C₅₃	#62863
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#538

Complements

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

N	H ≅ G/N	type
1. #20289269	C₂	semidirect
2. #20289267	C₂	semidirect
3. #20289236	C₂	semidirect
4. #20289234	C₂	semidirect
5. #20288950	C₂	semidirect
6. #20288947	C₂	semidirect
7. #20288909	C₂	semidirect
8. #20288906	C₂	semidirect
9. #20288883	C₂	semidirect
10. #20288866	C₂	semidirect
11. #20288556	C₂	semidirect
12. #20288554	C₂	semidirect
13. #20288479	C₂	semidirect
14. #20288472	C₂	semidirect
15. #20288344	C₂	semidirect
16. C₂×#16811211	C₂	semidirect
17. C₂×#16811185	C₂	semidirect
18. C₂×C₅₃×#538	C₂	semidirect
19. C₂×#13133262	C₂²	semidirect
20. C₂³×C₂²⋊D₅₃	C₂²	semidirect
21. #16811375	C₂²	semidirect
22. #16811370	C₂²	semidirect
23. #16811367	C₂²	semidirect
24. #16811365	C₂²	semidirect
25. #16811364	C₂²	semidirect
26. #16811363	C₂²	semidirect
27. #16811361	C₂²	semidirect
28. #16811361	C₂²	semidirect
29. #16811355	C₂²	semidirect
30. #16811325	C₂²	semidirect
31. #16811324	C₂²	semidirect
32. #16811322	C₂²	semidirect
33. #16811321	C₂²	semidirect
34. #16811321	C₂²	semidirect
35. #16811319	C₂²	semidirect
36. #16811315	C₂²	semidirect
37. #16811313	C₂²	semidirect
38. #16811302	C₂²	semidirect
39. #16811300	C₂²	semidirect
40. #16811298	C₂²	semidirect
41. #16811296	C₂²	semidirect
42. #16811284	C₂²	semidirect
43. #16811282	C₂²	semidirect
44. #16811277	C₂²	semidirect
45. #16811277	C₂²	semidirect
46. #16811274	C₂²	semidirect
47. #16811273	C₂²	semidirect
48. #16811269	C₂²	semidirect
49. #16811268	C₂²	semidirect
50. #16811268	C₂²	semidirect
51. #16811266	C₂²	semidirect
52. #16811265	C₂²	semidirect
53. #16811264	C₂²	semidirect
54. #16811263	C₂²	semidirect
55. #16811263	C₂²	semidirect
56. #16811263	C₂²	semidirect
57. #16811262	C₂²	semidirect
58. #16811260	C₂²	semidirect
59. #16811260	C₂²	semidirect
60. D₄×D₂₁₂	C₂²	semidirect
61. D₄×D₂₁₂	C₂²	semidirect
62. #16811257	C₂²	semidirect
63. #16811257	C₂²	semidirect
64. D₄×C₂²⋊D₅₃	C₂²	semidirect
65. D₄×C₂²⋊D₅₃	C₂²	semidirect
66. D₄×C₂²⋊D₅₃	C₂²	semidirect
67. #16811255	C₂²	semidirect
68. #16811255	C₂²	semidirect
69. #16811242	C₂²	semidirect
70. #16811239	C₂²	semidirect
71. #16811226	C₂²	semidirect
72. #16811225	C₂²	semidirect
73. #16811222	C₂²	semidirect
74. #16811220	C₂²	semidirect
75. #16811217	C₂²	semidirect
76. #16811214	C₂²	semidirect
77. #16811213	C₂²	semidirect
78. #16811212	C₂²	semidirect
79. #16811212	C₂²	semidirect
80. #16811211	C₂²	semidirect
81. #16811211	C₂²	semidirect
82. #16811211	C₂²	semidirect
83. #16811211	C₂²	semidirect
84. #16811210	C₂²	semidirect
85. #16811209	C₂²	semidirect
86. #16811207	C₂²	semidirect
87. #16811207	C₂²	semidirect
88. #16811204	C₂²	semidirect
89. #16811200	C₂²	semidirect
90. #16811191	C₂²	semidirect
91. #16811189	C₂²	semidirect
92. #16811188	C₂²	semidirect
93. #16811185	C₂²	semidirect
94. #16811185	C₂²	semidirect
95. #16811185	C₂²	semidirect
96. #16811185	C₂²	semidirect
97. #16811185	C₂²	semidirect
98. #16811185	C₂²	semidirect
99. #16811184	C₂²	semidirect
100. #16811183	C₂²	semidirect
101. #16811182	C₂²	semidirect
102. #16811181	C₂²	semidirect
103. #16811181	C₂²	semidirect
104. #16811173	C₂²	semidirect
105. #16811168	C₂²	semidirect
106. #16811159	C₂²	semidirect
107. #16811157	C₂²	semidirect
108. C₂×#13133210	C₂²	semidirect
109. C₂×#13133203	C₂²	semidirect
110. #16811136	C₂²	semidirect
111. #16811134	C₂²	semidirect
112. #16811129	C₂²	semidirect
113. C₂×#13133201	C₂²	semidirect
114. C₂×#13133199	C₂²	semidirect
115. C₂×#13133196	C₂²	semidirect
116. C₂×#13133191	C₂²	semidirect
117. C₂×#13133191	C₂²	semidirect
118. C₂×#13133191	C₂²	semidirect
119. C₂×#13133191	C₂²	semidirect
120. C₂×#13133190	C₂²	semidirect
121. #121×D₅₃	C₂²	semidirect
122. C₂×#13133187	C₂²	semidirect
123. C₂×#13133186	C₂²	semidirect
124. #120×D₅₃	C₂²	semidirect
125. #16811096	C₂²	semidirect
126. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
127. C₅₃×#538	C₂²	semidirect
128. C₅₃×#538	C₂²	semidirect
129. C₅₃×#538	C₂²	semidirect
130. C₂×#126×C₅₃	C₂²	semidirect
131. C₂×#124×C₅₃	C₂²	semidirect
132. C₂×#123×C₅₃	C₂²	semidirect
133. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
134. C₂×#121×C₅₃	C₂²	semidirect
135. C₂×#121×C₅₃	C₂²	semidirect
136. C₂×#120×C₅₃	C₂²	semidirect
137. C₂×C₄×D₄×C₅₃	C₂²	semidirect
138. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
141. C₂×#11719949	C₂³	semidirect
142. C₂×#11719945	C₂³	semidirect
143. C₂×#11719945	C₂³	semidirect
145. C₂×#11719947	C₂³	semidirect
146. C₂²×Dic₁₀₆	C₂³	semidirect
149. C₂²×D₂₁₂	C₂³	semidirect
150. C₂²×D₂₁₂	C₂³	semidirect
159. C₂²×C₂²⋊D₅₃	C₂³	semidirect
161. C₂×D₄×D₅₃	C₂³	semidirect
162. C₂×D₄×D₅₃	C₂³	semidirect
163. C₂×D₄×D₅₃	C₂³	semidirect
164. C₂×D₄×D₅₃	C₂³	semidirect
166. C₂²×C₄×D₅₃	C₂³	semidirect
167. #13133217	C₂³	semidirect
168. #13133216	C₂³	semidirect
169. #13133214	C₂³	semidirect
172. #13133213	C₂³	semidirect
173. #13133212	C₂³	semidirect
174. #13133212	C₂³	semidirect
175. #13133212	C₂³	semidirect
176. #13133212	C₂³	semidirect
177. #13133211	C₂³	semidirect
178. #13133210	C₂³	semidirect
179. #13133210	C₂³	semidirect
180. #13133210	C₂³	semidirect
181. #13133209	C₂³	semidirect
182. #13133208	C₂³	semidirect
183. #13133208	C₂³	semidirect
184. #13133207	C₂³	semidirect
185. #13133206	C₂³	semidirect
186. #13133206	C₂³	semidirect
187. #13133205	C₂³	semidirect
188. #13133205	C₂³	semidirect
191. #13133203	C₂³	semidirect
192. #13133203	C₂³	semidirect
193. #13133203	C₂³	semidirect
194. #13133203	C₂³	semidirect
195. #13133202	C₂³	semidirect
196. #13133202	C₂³	semidirect
197. #13133202	C₂³	semidirect
198. #13133202	C₂³	semidirect
199. #13133202	C₂³	semidirect
205. #13133201	C₂³	semidirect
206. #13133201	C₂³	semidirect
207. #13133201	C₂³	semidirect
208. #13133200	C₂³	semidirect
209. #13133200	C₂³	semidirect
212. #13133199	C₂³	semidirect
213. #13133199	C₂³	semidirect
214. #13133199	C₂³	semidirect
215. #13133199	C₂³	semidirect
217. #13133197	C₂³	semidirect
218. #13133197	C₂³	semidirect
220. #13133196	C₂³	semidirect
221. #13133196	C₂³	semidirect
222. #13133195	C₂³	semidirect
223. #13133195	C₂³	semidirect
224. #13133194	C₂³	semidirect
225. #13133194	C₂³	semidirect
226. #13133194	C₂³	semidirect
227. #13133193	C₂³	semidirect
228. #13133193	C₂³	semidirect
229. #13133192	C₂³	semidirect
230. #13133192	C₂³	semidirect
231. #13133192	C₂³	semidirect
232. #13133192	C₂³	semidirect
233. #13133192	C₂³	semidirect
243. #13133191	C₂³	semidirect
244. #13133191	C₂³	semidirect
245. #13133191	C₂³	semidirect
246. #13133191	C₂³	semidirect
247. #13133191	C₂³	semidirect
248. #13133191	C₂³	semidirect
249. #13133191	C₂³	semidirect
254. #13133190	C₂³	semidirect
255. #13133190	C₂³	semidirect
256. #13133190	C₂³	semidirect
257. #13133190	C₂³	semidirect
258. #13133190	C₂³	semidirect
261. #13133189	C₂³	semidirect
262. #13133189	C₂³	semidirect
263. #13133189	C₂³	semidirect
264. #13133189	C₂³	semidirect
265. #13133189	C₂³	semidirect
268. #13133188	C₂³	semidirect
274. #13133187	C₂³	semidirect
275. #13133187	C₂³	semidirect
276. #13133187	C₂³	semidirect
277. #13133187	C₂³	semidirect
278. #13133187	C₂³	semidirect
279. #13133187	C₂³	semidirect
282. #13133186	C₂³	semidirect
286. #13133185	C₂³	semidirect
287. #13133185	C₂³	semidirect
288. #13133185	C₂³	semidirect
289. Q₈×Dic₅₃	C₂³	semidirect
290. C₄×Dic₁₀₆	C₂³	semidirect
291. C₄×D₂₁₂	C₂³	semidirect
292. C₄×D₂₁₂	C₂³	semidirect
293. C₄×D₂₁₂	C₂³	semidirect
294. C₄×D₂₁₂	C₂³	semidirect
295. D₄×Dic₅₃	C₂³	semidirect
296. D₄×Dic₅₃	C₂³	semidirect
297. D₄×Dic₅₃	C₂³	semidirect
298. #13133179	C₂³	semidirect
299. #13133179	C₂³	semidirect
300. #13133179	C₂³	semidirect
303. C₄×C₂²⋊D₅₃	C₂³	semidirect
304. C₄×C₂²⋊D₅₃	C₂³	semidirect
305. C₄×C₂²⋊D₅₃	C₂³	semidirect
306. C₄×C₂²⋊D₅₃	C₂³	semidirect
307. C₄×C₂²⋊D₅₃	C₂³	semidirect
308. #13133177	C₂³	semidirect
309. #13133177	C₂³	semidirect
310. #13133177	C₂³	semidirect
311. #13133177	C₂³	semidirect
312. #13133177	C₂³	semidirect
313. #13133176	C₂³	semidirect
314. #13133175	C₂³	semidirect
315. #13133175	C₂³	semidirect
316. #13133174	C₂³	semidirect
320. C₂×C₄⋊Dic₅₃	C₂³	semidirect
321. C₂×C₄⋊Dic₅₃	C₂³	semidirect
322. C₂×C₄⋊Dic₅₃	C₂³	semidirect
323. C₂×#11719919	C₂³	semidirect
324. C₂×#11719919	C₂³	semidirect
325. C₄⋊C₄×D₅₃	C₂³	semidirect
331. C₂×#11719921	C₂³	semidirect
332. C₂×#11719921	C₂³	semidirect
333. C₂×#11719921	C₂³	semidirect
335. C₂²⋊C₄×D₅₃	C₂³	semidirect
336. C₂²⋊C₄×D₅₃	C₂³	semidirect
337. C₂²⋊C₄×D₅₃	C₂³	semidirect
338. C₂×C₄×Dic₅₃	C₂³	semidirect
340. C₂²×Q₈×C₅₃	C₂³	semidirect
344. C₂²×D₄×C₅₃	C₂³	semidirect
347. C₂³×C₄×C₅₃	C₂³	semidirect
348. #126×C₅₃	C₂³	semidirect
349. #126×C₅₃	C₂³	semidirect
350. #124×C₅₃	C₂³	semidirect
351. #124×C₅₃	C₂³	semidirect
352. #123×C₅₃	C₂³	semidirect
353. #123×C₅₃	C₂³	semidirect
355. C₂²⋊Q₈×C₅₃	C₂³	semidirect
357. #121×C₅₃	C₂³	semidirect
358. #121×C₅₃	C₂³	semidirect
359. #121×C₅₃	C₂³	semidirect
364. C₄×D₄×C₅₃	C₂³	semidirect
365. C₄×D₄×C₅₃	C₂³	semidirect
366. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
367. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
368. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
369. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
378. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
379. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
380. C₂×C₄²×C₅₃	C₂³	semidirect
699. C₂×#538	D₅₃	semidirect
780. #538	C₂×D₅₃	semidirect
781. #538	C₂×D₅₃	semidirect
782. #538	C₂×D₅₃	semidirect
804. C₂×#126	C₂×D₅₃	semidirect
806. C₂×#124	C₂×D₅₃	semidirect
812. C₂×#123	C₂×D₅₃	semidirect
814. C₂×C₂²⋊Q₈	C₂×D₅₃	semidirect
821. C₂×#121	C₂×D₅₃	semidirect
822. C₂×#121	C₂×D₅₃	semidirect
826. C₂×#120	C₂×D₅₃	semidirect
829. C₂×C₄×D₄	C₂×D₅₃	semidirect
830. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
831. C₅₃	#62863	semidirect
841. C₂²×Q₈	C₂²×D₅₃	semidirect
863. C₂²×D₄	C₂²×D₅₃	semidirect
868. C₂³×C₄	C₂²×D₅₃	semidirect
883. #126	C₂²×D₅₃	semidirect
884. #126	C₂²×D₅₃	semidirect
899. #124	C₂²×D₅₃	semidirect
900. #124	C₂²×D₅₃	semidirect
923. #123	C₂²×D₅₃	semidirect
924. #123	C₂²×D₅₃	semidirect
938. C₂²⋊Q₈	C₂²×D₅₃	semidirect
980. #121	C₂²×D₅₃	semidirect
981. #121	C₂²×D₅₃	semidirect
982. #121	C₂²×D₅₃	semidirect
1031. C₄×D₄	C₂²×D₅₃	semidirect
1032. C₄×D₄	C₂²×D₅₃	semidirect
1046. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1047. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1048. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1049. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
1070. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1071. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1073. C₂×C₄²	C₂²×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20289269	2
#20289267	2
#20289236	2
#20289234	2
#20288950	2
#20288947	2
#20288909	2
#20288906	2
#20288883	2
#20288866	2
#20288556	2
#20288554	2
#20288479	2
#20288472	2
#20288344	2
C₂×#16811211	2
C₂×#16811185	2
C₂×C₅₃×#538	2
#62863	53