Subgroups — #27591703

Order 13568.

1858 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283000	C₂	1	1	yes	maximal, characteristic
2	#20283000	C₂	1	1	yes	maximal, characteristic
3	#20282682	C₂	1	1	yes	maximal, characteristic, complemented
4	#20282485	C₂	1	1	yes	maximal, characteristic, complemented
5	#20282480	C₂	1	1	yes	maximal, characteristic, complemented
6	#20282462	C₂	1	1	yes	maximal, characteristic, complemented
7	#20282458	C₂	1	1	yes	maximal, characteristic, complemented
8	#20282199	C₂	1	1	yes	maximal, characteristic, complemented
9	#20282196	C₂	1	1	yes	maximal, characteristic, complemented
10	#20282131	C₂	1	1	yes	maximal, characteristic, complemented
11	#20281841	C₂	1	1	yes	maximal, characteristic, complemented
12	#20281698	C₂	1	1	yes	maximal, characteristic, complemented
13	#20281694	C₂	1	1	yes	maximal, characteristic, complemented
14	#20281599	C₂	1	1	yes	maximal, characteristic, complemented
15	#20281592	C₂	1	1	yes	maximal, characteristic, complemented
16	#20281374	C₂	1	1	yes	maximal, characteristic, complemented
17	#20281370	C₂	1	1	yes	maximal, characteristic, complemented
18	#20281027	C₂	1	1	yes	maximal, characteristic, complemented
19	#20280524	C₂	1	1	yes	maximal, characteristic
20	#20280524	C₂	1	1	yes	maximal, characteristic
21	#20279940	C₂	1	1	yes	maximal, characteristic, complemented
22	#20279934	C₂	1	1	yes	maximal, characteristic, complemented
23	#20279727	C₂	1	1	yes	maximal, characteristic, complemented
24	#20279721	C₂	1	1	yes	maximal, characteristic, complemented
25	#20278440	C₂	1	1	yes	maximal, characteristic, complemented
26	#20278439	C₂	1	1	yes	maximal, characteristic, complemented
27	#20278418	C₂	1	1	yes	maximal, characteristic, complemented
28	#20278417	C₂	1	1	yes	maximal, characteristic, complemented
29	#20277313	C₂	1	1	yes	maximal, characteristic
30	C₂×#16810498	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2312	C₂	1	1	yes	maximal, characteristic
32	C₂⁴×Dic₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133217	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13133216	C₂²	1	1	yes	characteristic, complemented
35	C₂×#13133209	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13133208	C₂²	1	1	yes	characteristic, complemented
37	C₂×#13133194	C₂²	1	1	yes	characteristic
38	C₂×#13133194	C₂²	1	1	yes	characteristic
39	C₂×#13133194	C₂²	1	1	yes	characteristic
40	C₂×#13133194	C₂²	1	1	yes	characteristic
41	C₂×#13133194	C₂²	1	1	yes	characteristic
42	C₂×#13133194	C₂²	1	1	yes	characteristic
43	C₂×#13133194	C₂²	1	1	yes	characteristic
44	C₂×#13133194	C₂²	1	1	yes	characteristic
45	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
48	#16810565	C₂²	1	1	yes	characteristic, complemented
49	#16810565	C₂²	1	1	yes	characteristic, complemented
50	#16810565	C₂²	1	1	yes	characteristic, complemented
51	#16810565	C₂²	1	1	yes	characteristic, complemented
52	#16810565	C₂²	1	1	yes	characteristic, complemented
53	#16810565	C₂²	1	1	yes	characteristic, complemented
54	#16810562	C₂²	1	1	yes	characteristic, complemented
55	#16810562	C₂²	1	1	yes	characteristic, complemented
56	#16810559	C₂²	1	1	yes	characteristic
57	#16810559	C₂²	1	1	yes	characteristic
58	#16810559	C₂²	1	1	yes	characteristic
59	#16810559	C₂²	1	1	yes	characteristic
60	#16810557	C₂²	1	1	yes	characteristic, complemented
61	#16810557	C₂²	1	1	yes	characteristic, complemented
62	#16810557	C₂²	1	1	yes	characteristic, complemented
63	#16810557	C₂²	1	1	yes	characteristic, complemented
64	#16810557	C₂²	1	1	yes	characteristic, complemented
65	#16810557	C₂²	1	1	yes	characteristic, complemented
66	#16810556	C₂²	1	1	yes	characteristic, complemented
67	#16810556	C₂²	1	1	yes	characteristic, complemented
68	#16810556	C₂²	1	1	yes	characteristic, complemented
69	#16810556	C₂²	1	1	yes	characteristic, complemented
70	#16810555	C₂²	1	1	yes	characteristic, complemented
71	#16810555	C₂²	1	1	yes	characteristic, complemented
72	#16810555	C₂²	1	1	yes	characteristic, complemented
73	#16810555	C₂²	1	1	yes	characteristic, complemented
74	#16810555	C₂²	1	1	yes	characteristic, complemented
75	#16810555	C₂²	1	1	yes	characteristic, complemented
76	#16810546	C₂²	1	1	yes	characteristic
77	#16810546	C₂²	1	1	yes	characteristic
78	#16810546	C₂²	1	1	yes	characteristic
79	#16810546	C₂²	1	1	yes	characteristic
80	#16810546	C₂²	1	1	yes	characteristic
81	#16810546	C₂²	1	1	yes	characteristic
82	#16810546	C₂²	1	1	yes	characteristic
83	#16810546	C₂²	1	1	yes	characteristic
84	#16810544	C₂²	1	1	yes	characteristic, complemented
85	#16810544	C₂²	1	1	yes	characteristic, complemented
86	#16810544	C₂²	1	1	yes	characteristic, complemented
87	#16810544	C₂²	1	1	yes	characteristic, complemented
88	#16810544	C₂²	1	1	yes	characteristic, complemented
89	#16810544	C₂²	1	1	yes	characteristic, complemented
90	#16810543	C₂²	1	1	yes	characteristic, complemented
91	#16810543	C₂²	1	1	yes	characteristic, complemented
92	#16810535	C₂²	1	1	yes	characteristic
93	#16810535	C₂²	1	1	yes	characteristic
94	#16810535	C₂²	1	1	yes	characteristic
95	#16810535	C₂²	1	1	yes	characteristic
96	#16810529	C₂²	1	1	yes	characteristic, complemented
97	#16810529	C₂²	1	1	yes	characteristic, complemented
98	#16810527	C₂²	1	1	yes	characteristic, complemented
99	#16810527	C₂²	1	1	yes	characteristic, complemented
100	#16810522	C₂²	1	1	yes	characteristic, complemented
101	#16810522	C₂²	1	1	yes	characteristic, complemented
102	#16810521	C₂²	1	1	yes	characteristic, complemented
103	#16810521	C₂²	1	1	yes	characteristic, complemented
104	#16810521	C₂²	1	1	yes	characteristic, complemented
105	#16810521	C₂²	1	1	yes	characteristic, complemented
106	#16810521	C₂²	1	1	yes	characteristic, complemented
107	#16810521	C₂²	1	1	yes	characteristic, complemented
108	#16810520	C₂²	1	1	yes	characteristic, complemented
109	#16810520	C₂²	1	1	yes	characteristic, complemented
110	#16810519	C₂²	1	1	yes	characteristic, complemented
111	#16810519	C₂²	1	1	yes	characteristic, complemented
112	#16810516	C₂²	1	1	yes	characteristic
113	#16810516	C₂²	1	1	yes	characteristic
114	#16810516	C₂²	1	1	yes	characteristic
115	#16810516	C₂²	1	1	yes	characteristic
116	#16810516	C₂²	1	1	yes	characteristic
117	#16810516	C₂²	1	1	yes	characteristic
118	#16810516	C₂²	1	1	yes	characteristic
119	#16810516	C₂²	1	1	yes	characteristic
120	#16810510	C₂²	1	1	yes	characteristic, complemented
121	#16810510	C₂²	1	1	yes	characteristic, complemented
122	#16810507	C₂²	1	1	yes	characteristic, complemented
123	#16810507	C₂²	1	1	yes	characteristic, complemented
124	#16810507	C₂²	1	1	yes	characteristic, complemented
125	#16810507	C₂²	1	1	yes	characteristic, complemented
126	#16810506	C₂²	1	1	yes	characteristic, complemented
127	#16810506	C₂²	1	1	yes	characteristic, complemented
128	#16810498	C₂²	1	1	yes	characteristic
129	#16810498	C₂²	1	1	yes	characteristic
130	#16810498	C₂²	1	1	yes	characteristic
131	#16810498	C₂²	1	1	yes	characteristic
132	#16810498	C₂²	1	1	yes	characteristic
133	#16810498	C₂²	1	1	yes	characteristic
134	#16810498	C₂²	1	1	yes	characteristic
135	#16810498	C₂²	1	1	yes	characteristic
136	#16810498	C₂²	1	1	yes	characteristic
137	#16810498	C₂²	1	1	yes	characteristic
138	#16810498	C₂²	1	1	yes	characteristic
139	#16810498	C₂²	1	1	yes	characteristic
140	#16810498	C₂²	1	1	yes	characteristic
141	#16810498	C₂²	1	1	yes	characteristic
142	#16810498	C₂²	1	1	yes	characteristic
143	#16810498	C₂²	1	1	yes	characteristic
144	#16810495	C₂²	1	1	yes	characteristic
145	#16810495	C₂²	1	1	yes	characteristic
146	#16810495	C₂²	1	1	yes	characteristic
147	#16810495	C₂²	1	1	yes	characteristic
148	#16810495	C₂²	1	1	yes	characteristic
149	#16810495	C₂²	1	1	yes	characteristic
150	#16810495	C₂²	1	1	yes	characteristic
151	#16810495	C₂²	1	1	yes	characteristic
152	#16810493	C₂²	1	1	yes	characteristic, complemented
153	#16810492	C₂²	1	1	yes	characteristic, complemented
154	#16810489	C₂²	1	1	yes	characteristic, complemented
155	#16810488	C₂²	1	1	yes	characteristic, complemented
156	#16810483	C₂²	1	1	yes	characteristic
157	#16810483	C₂²	1	1	yes	characteristic
158	#16810481	C₂²	1	1	yes	characteristic
159	#16810481	C₂²	1	1	yes	characteristic
160	#16810481	C₂²	1	1	yes	characteristic
161	#16810481	C₂²	1	1	yes	characteristic
162	#16810481	C₂²	1	1	yes	characteristic
163	#16810481	C₂²	1	1	yes	characteristic
164	#16810481	C₂²	1	1	yes	characteristic
165	#16810481	C₂²	1	1	yes	characteristic
166	#16810479	C₂²	1	1	yes	characteristic
167	#16810479	C₂²	1	1	yes	characteristic
168	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
169	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
170	C₂×#13133124	C₂²	1	1	yes	characteristic
171	C₂×#13133124	C₂²	1	1	yes	characteristic
172	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
173	C₅₃×#388	C₂²	1	1	yes	characteristic
174	C₅₃×#388	C₂²	1	1	yes	characteristic
175	C₅₃×#388	C₂²	1	1	yes	characteristic
176	C₅₃×#388	C₂²	1	1	yes	characteristic
177	C₅₃×#388	C₂²	1	1	yes	characteristic
178	C₅₃×#388	C₂²	1	1	yes	characteristic
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#380	C₂²	1	1	yes	characteristic
182	C₅₃×#380	C₂²	1	1	yes	characteristic
183	C₅₃×#379	C₂²	1	1	yes	characteristic
184	C₅₃×#379	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂³×Dic₅₃	—	4	2	no	—
192	C₂³×Dic₅₃	—	4	2	no	—
193	C₂³×Dic₅₃	—	4	2	no	—
194	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
196	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
197	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
198	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
199	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
200	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
201	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
202	#13133217	—	4	2	no	—
203	#13133216	—	4	2	no	—
204	#13133209	—	4	2	no	—
205	#13133208	—	4	2	no	—
206	#13133194	—	4	2	no	—
207	#13133194	—	4	2	no	—
208	#13133194	—	4	2	no	—
209	#13133194	—	4	2	no	—
210	#13133194	—	4	2	no	—
211	#13133194	—	4	2	no	—
212	#13133194	—	4	2	no	—
213	#13133194	—	4	2	no	—
214	C₂×C₄⋊Dic₅₃	—	4	2	no	—
215	C₂×C₄⋊Dic₅₃	—	4	2	no	—
216	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
240	C₂×#11719919	C₂³	1	1	yes	characteristic
241	C₂×#11719919	C₂³	1	1	yes	characteristic
242	C₂×#11719919	C₂³	1	1	yes	characteristic
243	C₂×#11719919	C₂³	1	1	yes	characteristic
244	C₂×#11719919	C₂³	1	1	yes	characteristic
245	C₂×#11719919	C₂³	1	1	yes	characteristic
246	C₂×#11719919	C₂³	1	1	yes	characteristic
247	C₂×#11719919	C₂³	1	1	yes	characteristic
248	C₂×#11719919	C₂³	1	1	yes	characteristic
249	C₂×#11719919	C₂³	1	1	yes	characteristic
250	C₂×#11719919	C₂³	1	1	yes	characteristic
251	C₂×#11719919	C₂³	1	1	yes	characteristic
252	C₂×#11719919	C₂³	1	1	yes	characteristic
253	C₂×#11719919	C₂³	1	1	yes	characteristic
254	C₂×#11719919	C₂³	1	1	yes	characteristic
255	C₂×#11719919	C₂³	1	1	yes	characteristic
256	C₂×#11719919	C₂³	1	1	yes	characteristic
257	C₂×#11719919	C₂³	1	1	yes	characteristic
258	C₂×#11719919	C₂³	1	1	yes	characteristic
259	C₂×#11719919	C₂³	1	1	yes	characteristic
260	C₂×#11719919	C₂³	1	1	yes	characteristic
261	C₂×#11719919	C₂³	1	1	yes	characteristic
262	C₂×#11719919	C₂³	1	1	yes	characteristic
263	C₂×#11719919	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊Dic₅₃	—	4	2	no	—
265	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
285	#13133124	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
326	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₅₃	Q₈	1	8	yes	complemented
333	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	C₂⁴×C₅₃	—	2	2	no	—
362	C₂⁴×C₅₃	—	2	2	no	—
363	C₂⁴×C₅₃	—	4	1	no	—
364	C₂⁴×C₅₃	—	4	1	no	—
365	C₂⁴×C₅₃	—	4	1	no	—
366	C₂⁴×C₅₃	—	4	1	no	—
367	C₂⁴×C₅₃	C₂×Q₈	1	4	yes	—
368	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	—	4	1	no	—
372	C₂²×C₄×C₅₃	—	4	1	no	—
373	C₂²×C₄×C₅₃	—	4	1	no	—
374	C₂²×C₄×C₅₃	—	4	1	no	—
375	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
376	C₂²×C₄×C₅₃	C₂×Q₈	1	4	yes	—
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	—	2	2	no	—
390	C₂²×Dic₅₃	—	2	2	no	—
391	C₂²×Dic₅₃	—	2	2	no	—
392	C₂²×Dic₅₃	—	2	2	no	—
393	C₂²×Dic₅₃	—	2	2	no	—
394	C₂²×Dic₅₃	—	2	2	no	—
395	C₂²×Dic₅₃	—	2	2	no	—
396	C₂²×Dic₅₃	—	2	2	no	—
397	C₂²×Dic₅₃	—	2	2	no	—
398	C₂²×Dic₅₃	—	2	2	no	—
399	C₂²×Dic₅₃	—	4	1	no	—
400	C₂²×Dic₅₃	—	4	1	no	—
401	C₂²×Dic₅₃	—	4	1	no	—
402	C₂²×Dic₅₃	—	4	1	no	—
403	C₂²×Dic₅₃	—	4	1	no	—
404	C₂²×Dic₅₃	—	4	1	no	—
405	C₂²×Dic₅₃	—	4	1	no	—
406	C₂²×Dic₅₃	—	4	1	no	—
407	C₂²×Dic₅₃	—	4	1	no	—
408	C₂²×Dic₅₃	—	4	1	no	—
409	C₂²×Dic₅₃	—	4	1	no	—
410	C₂²×Dic₅₃	—	4	1	no	—
411	C₂²×Dic₅₃	—	4	1	no	—
412	C₂²×Dic₅₃	—	4	1	no	—
413	C₂²×Dic₅₃	—	4	16	no	—
414	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
430	C₂×Dic₁₀₆	—	2	2	no	—
431	C₂×Dic₁₀₆	—	2	2	no	—
432	C₂×Dic₁₀₆	—	4	1	no	—
433	C₂×Dic₁₀₆	—	4	1	no	—
434	C₂×Dic₁₀₆	—	4	1	no	—
435	C₂×Dic₁₀₆	—	4	1	no	—
436	C₂×Dic₁₀₆	—	4	1	no	—
437	C₂×Dic₁₀₆	—	4	1	no	—
438	C₂×Dic₁₀₆	—	4	1	no	—
439	C₂×Dic₁₀₆	—	4	1	no	—
440	C₂×Dic₁₀₆	—	4	1	no	—
441	C₂×Dic₁₀₆	—	4	1	no	—
442	C₄⋊C₄×C₅₃	—	4	1	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	4	1	no	—
451	C₂²⋊C₄×C₅₃	—	4	1	no	—
452	C₂²⋊C₄×C₅₃	—	4	1	no	—
453	C₂²⋊C₄×C₅₃	—	4	1	no	—
454	C₂²⋊C₄×C₅₃	—	4	1	no	—
455	C₂²⋊C₄×C₅₃	—	4	1	no	—
456	C₂²⋊C₄×C₅₃	—	4	1	no	—
457	C₂²⋊C₄×C₅₃	—	4	1	no	—
458	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
459	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
460	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
461	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	—
462	C₄²×C₅₃	—	4	1	no	—
463	C₄²×C₅₃	—	4	1	no	—
464	C₄²×C₅₃	—	4	1	no	—
465	C₄²×C₅₃	—	4	1	no	—
466	C₂²⋊Dic₅₃	—	2	2	no	—
467	C₂²⋊Dic₅₃	—	2	2	no	—
468	C₂²⋊Dic₅₃	—	2	2	no	—
469	C₂²⋊Dic₅₃	—	2	2	no	—
470	C₂²⋊Dic₅₃	—	4	1	no	—
471	C₂²⋊Dic₅₃	—	4	1	no	—
472	C₂²⋊Dic₅₃	—	4	1	no	—
473	C₂²⋊Dic₅₃	—	4	1	no	—
474	C₂²⋊Dic₅₃	—	4	1	no	—
475	C₂²⋊Dic₅₃	—	4	1	no	—
476	C₂²⋊Dic₅₃	—	4	1	no	—
477	C₂²⋊Dic₅₃	—	4	1	no	—
478	C₂²⋊Dic₅₃	—	4	1	no	—
479	C₂²⋊Dic₅₃	—	4	1	no	—
480	C₂²⋊Dic₅₃	—	4	1	no	—
481	C₂²⋊Dic₅₃	—	4	1	no	—
482	C₄⋊Dic₅₃	—	2	2	no	—
483	C₄⋊Dic₅₃	—	2	2	no	—
484	C₄⋊Dic₅₃	—	2	2	no	—
485	C₄⋊Dic₅₃	—	2	2	no	—
486	C₄⋊Dic₅₃	—	2	2	no	—
487	C₄⋊Dic₅₃	—	2	2	no	—
488	C₄⋊Dic₅₃	—	4	1	no	—
489	C₄⋊Dic₅₃	—	4	1	no	—
490	C₄⋊Dic₅₃	—	4	1	no	—
491	C₄⋊Dic₅₃	—	4	1	no	—
492	C₄⋊Dic₅₃	—	4	1	no	—
493	C₄⋊Dic₅₃	—	4	1	no	—
494	C₄⋊Dic₅₃	—	4	1	no	—
495	C₄⋊Dic₅₃	—	4	1	no	—
496	C₄⋊Dic₅₃	—	4	1	no	—
497	C₄⋊Dic₅₃	—	4	1	no	—
498	C₄⋊Dic₅₃	—	4	1	no	—
499	C₄⋊Dic₅₃	—	4	1	no	—
500	C₄⋊Dic₅₃	—	4	1	no	—
501	C₄⋊Dic₅₃	—	4	1	no	—
502	C₄⋊Dic₅₃	—	4	1	no	—
503	C₄⋊Dic₅₃	—	4	1	no	—
504	C₄⋊Dic₅₃	—	4	1	no	—
505	C₄⋊Dic₅₃	—	4	1	no	—
506	#11719919	—	2	2	no	—
507	#11719919	—	2	2	no	—
508	#11719919	—	2	2	no	—
509	#11719919	—	2	2	no	—
510	#11719919	—	4	1	no	—
511	#11719919	—	4	1	no	—
512	#11719919	—	4	1	no	—
513	#11719919	—	4	1	no	—
514	#11719919	—	4	1	no	—
515	#11719919	—	4	1	no	—
516	#11719919	—	4	1	no	—
517	#11719919	—	4	1	no	—
518	#11719919	—	4	1	no	—
519	#11719919	—	4	1	no	—
520	#11719919	—	4	1	no	—
521	#11719919	—	4	1	no	—
522	#11719919	—	4	1	no	—
523	#11719919	—	4	1	no	—
524	#11719919	—	4	1	no	—
525	#11719919	—	4	1	no	—
526	#11719919	—	4	1	no	—
527	#11719919	—	4	1	no	—
528	#11719919	—	4	1	no	—
529	#11719919	—	4	1	no	—
530	C₄×Dic₅₃	—	4	1	no	—
531	C₄×Dic₅₃	—	4	1	no	—
532	C₄×Dic₅₃	—	4	1	no	—
533	C₄×Dic₅₃	—	4	1	no	—
534	C₂³×C₅₃	—	2	1	no	—
535	C₂³×C₅₃	—	2	1	no	—
536	C₂³×C₅₃	—	2	1	no	—
537	C₂³×C₅₃	—	2	1	no	—
538	C₂³×C₅₃	—	2	8	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	1	no	—
547	C₂³×C₅₃	—	2	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	4	4	no	—
552	C₂³×C₅₃	—	4	4	no	—
553	C₂³×C₅₃	—	4	4	no	—
554	C₂³×C₅₃	—	4	4	no	—
555	C₂³×C₅₃	—	4	4	no	—
556	C₂³×C₅₃	—	4	4	no	—
557	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
558	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
559	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
560	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
561	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
562	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	4	4	no	—
596	C₂×C₄×C₅₃	—	4	4	no	—
597	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
598	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
599	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
600	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	—	2	1	no	—
607	C₂×Dic₅₃	—	2	1	no	—
608	C₂×Dic₅₃	—	2	1	no	—
609	C₂×Dic₅₃	—	2	1	no	—
610	C₂×Dic₅₃	—	2	1	no	—
611	C₂×Dic₅₃	—	2	1	no	—
612	C₂×Dic₅₃	—	2	1	no	—
613	C₂×Dic₅₃	—	2	1	no	—
614	C₂×Dic₅₃	—	2	1	no	—
615	C₂×Dic₅₃	—	2	1	no	—
616	C₂×Dic₅₃	—	2	1	no	—
617	C₂×Dic₅₃	—	2	1	no	—
618	C₂×Dic₅₃	—	2	1	no	—
619	C₂×Dic₅₃	—	2	1	no	—
620	C₂×Dic₅₃	—	2	1	no	—
621	C₂×Dic₅₃	—	2	1	no	—
622	C₂×Dic₅₃	—	2	1	no	—
623	C₂×Dic₅₃	—	2	1	no	—
624	C₂×Dic₅₃	—	2	1	no	—
625	C₂×Dic₅₃	—	2	1	no	—
626	C₂×Dic₅₃	—	2	1	no	—
627	C₂×Dic₅₃	—	2	1	no	—
628	C₂×Dic₅₃	—	2	1	no	—
629	C₂×Dic₅₃	—	2	1	no	—
630	C₂×Dic₅₃	—	2	1	no	—
631	C₂×Dic₅₃	—	2	1	no	—
632	C₂×Dic₅₃	—	2	1	no	—
633	C₂×Dic₅₃	—	2	1	no	—
634	C₂×Dic₅₃	—	2	1	no	—
635	C₂×Dic₅₃	—	2	1	no	—
636	C₂×Dic₅₃	—	2	1	no	—
637	C₂×Dic₅₃	—	2	1	no	—
638	C₂×Dic₅₃	—	2	1	no	—
639	C₂×Dic₅₃	—	2	1	no	—
640	C₂×Dic₅₃	—	2	1	no	—
641	C₂×Dic₅₃	—	2	1	no	—
642	C₂×Dic₅₃	—	2	1	no	—
643	C₂×Dic₅₃	—	2	1	no	—
644	C₂×Dic₅₃	—	2	1	no	—
645	C₂×Dic₅₃	—	2	1	no	—
646	C₂×Dic₅₃	—	2	1	no	—
647	C₂×Dic₅₃	—	4	4	no	—
648	C₂×Dic₅₃	—	4	4	no	—
649	C₂×Dic₅₃	—	4	4	no	—
650	C₂×Dic₅₃	—	4	4	no	—
651	C₂×Dic₅₃	—	4	4	no	—
652	C₂×Dic₅₃	—	4	4	no	—
653	C₂×Dic₅₃	—	8	2	no	—
654	C₂×Dic₅₃	—	8	2	no	—
655	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
656	C₂×Dic₅₃	H(5,𝔽₂)	1	2	yes	—
657	Dic₁₀₆	—	8	2	no	—
658	Dic₁₀₆	—	8	2	no	—
659	Dic₁₀₆	—	8	2	no	—
660	Dic₁₀₆	—	8	2	no	—
661	#36748	—	53	1	no	maximal, Sylow
662	C₂²×C₅₃	—	2	2	no	—
663	C₂²×C₅₃	—	2	2	no	—
664	C₂²×C₅₃	—	2	2	no	—
665	C₂²×C₅₃	—	2	2	no	—
666	C₂²×C₅₃	—	2	2	no	—
667	C₂²×C₅₃	—	2	2	no	—
668	C₂²×C₅₃	—	2	2	no	—
669	C₂²×C₅₃	—	2	2	no	—
670	C₂²×C₅₃	—	2	2	no	—
671	C₂²×C₅₃	—	2	2	no	—
672	C₂²×C₅₃	—	2	2	no	—
673	C₂²×C₅₃	—	2	2	no	—
674	C₂²×C₅₃	—	4	16	no	—
675	C₂²×C₅₃	—	4	1	no	—
676	C₂²×C₅₃	—	4	1	no	—
677	C₂²×C₅₃	—	4	1	no	—
678	C₂²×C₅₃	—	4	1	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	4	1	no	—
682	C₂²×C₅₃	—	4	1	no	—
683	C₂²×C₅₃	#544	1	4	yes	—
684	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
685	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
686	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
688	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
689	C₂²×C₅₃	#585	1	1	yes	characteristic
690	C₂²×C₅₃	#585	1	1	yes	characteristic
691	C₄×C₅₃	—	2	2	no	—
692	C₄×C₅₃	—	2	2	no	—
693	C₄×C₅₃	—	2	2	no	—
694	C₄×C₅₃	—	2	2	no	—
695	C₄×C₅₃	—	4	1	no	—
696	C₄×C₅₃	—	4	1	no	—
697	C₄×C₅₃	—	4	1	no	—
698	C₄×C₅₃	—	4	1	no	—
699	C₄×C₅₃	—	4	1	no	—
700	C₄×C₅₃	—	4	1	no	—
701	C₄×C₅₃	—	4	1	no	—
702	C₄×C₅₃	—	4	1	no	—
703	Dic₅₃	—	2	2	no	—
704	Dic₅₃	—	2	2	no	—
705	Dic₅₃	—	4	1	no	—
706	Dic₅₃	—	4	1	no	—
707	Dic₅₃	—	4	1	no	—
708	Dic₅₃	—	4	1	no	—
709	Dic₅₃	—	4	1	no	—
710	Dic₅₃	—	4	1	no	—
711	Dic₅₃	—	4	1	no	—
712	Dic₅₃	—	4	1	no	—
713	Dic₅₃	—	4	1	no	—
714	Dic₅₃	—	4	1	no	—
715	Dic₅₃	—	4	1	no	—
716	Dic₅₃	—	4	1	no	—
717	Dic₅₃	—	4	1	no	—
718	Dic₅₃	—	4	1	no	—
719	#2848	—	53	1	no	—
720	#2848	—	53	1	no	—
721	#2807	—	53	1	no	—
722	#2790	—	53	1	no	—
723	#2790	—	53	1	no	—
724	#2788	—	53	1	no	—
725	#2788	—	53	1	no	—
726	#2768	—	53	1	no	—
727	#2768	—	53	1	no	—
728	#2763	—	53	1	no	—
729	#2742	—	53	1	no	—
730	#2729	—	53	1	no	—
731	#2729	—	53	1	no	—
732	#2720	—	53	1	no	—
733	#2720	—	53	1	no	—
734	#2704	—	53	1	no	—
735	#2704	—	53	1	no	—
736	#2677	—	53	1	no	—
737	#2626	—	53	1	no	—
738	#2626	—	53	1	no	—
739	#2569	—	53	1	no	—
740	#2569	—	53	1	no	—
741	#2549	—	53	1	no	—
742	#2549	—	53	1	no	—
743	#2442	—	53	1	no	—
744	#2442	—	53	1	no	—
745	#2440	—	53	1	no	—
746	#2440	—	53	1	no	—
747	#2312	—	53	1	no	—
748	#2312	D₅₃	1	1	yes	characteristic
749	C₂×#385	—	53	1	no	—
750	C₂×C₅₃	—	2	4	no	—
751	C₂×C₅₃	—	4	2	no	—
752	C₂×C₅₃	—	4	2	no	—
753	C₂×C₅₃	C₂×#544	1	1	yes	characteristic
754	C₂×C₅₃	#3501	1	1	yes	characteristic
755	C₂×C₅₃	#3501	1	1	yes	characteristic
756	C₂×C₅₃	#3532	1	1	yes	characteristic
757	C₂×C₅₃	#3533	1	1	yes	characteristic
758	C₂×C₅₃	#3541	1	1	yes	characteristic
759	C₂×C₅₃	#3541	1	1	yes	characteristic
760	C₂⁴×C₄	—	53	1	no	—
761	C₂×C₄⋊Q₈	—	53	1	no	—
762	C₂×C₄⋊Q₈	—	53	1	no	—
763	C₂×#125	—	53	1	no	—
764	C₂×#125	—	53	1	no	—
765	C₂×C₂²⋊Q₈	—	53	1	no	—
766	C₂×C₂²⋊Q₈	—	53	1	no	—
767	C₂×C₂²⋊Q₈	—	53	1	no	—
768	C₂×C₂²⋊Q₈	—	53	1	no	—
769	C₂×C₂²⋊Q₈	—	53	1	no	—
770	C₂×C₂²⋊Q₈	—	53	1	no	—
771	C₂×C₂²⋊Q₈	—	53	1	no	—
772	C₂×C₂²⋊Q₈	—	53	1	no	—
773	C₂²×C₄⋊C₄	—	53	1	no	—
774	C₂²×C₄⋊C₄	—	53	1	no	—
775	C₂²×C₂²⋊C₄	—	53	1	no	—
776	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
777	#400	—	53	1	no	—
778	#400	—	53	1	no	—
779	#400	—	53	1	no	—
780	#400	—	53	1	no	—
781	#400	—	53	1	no	—
782	#400	—	53	1	no	—
783	#400	—	53	1	no	—
784	#400	—	53	1	no	—
785	#399	—	53	1	no	—
786	#399	—	53	1	no	—
787	#399	—	53	1	no	—
788	#399	—	53	1	no	—
789	#398	—	53	1	no	—
790	#398	—	53	1	no	—
791	#398	—	53	1	no	—
792	#398	—	53	1	no	—
793	#398	—	53	1	no	—
794	#398	—	53	1	no	—
795	#398	—	53	1	no	—
796	#398	—	53	1	no	—
797	#398	—	53	1	no	—
798	#398	—	53	1	no	—
799	#398	—	53	1	no	—
800	#398	—	53	1	no	—
801	#398	—	53	1	no	—
802	#398	—	53	1	no	—
803	#398	—	53	1	no	—
804	#398	—	53	1	no	—
805	#396	—	53	1	no	—
806	#396	—	53	1	no	—
807	#396	—	53	1	no	—
808	#396	—	53	1	no	—
809	#396	—	53	1	no	—
810	#396	—	53	1	no	—
811	#396	—	53	1	no	—
812	#396	—	53	1	no	—
813	#395	—	53	1	no	—
814	#395	—	53	1	no	—
815	#395	—	53	1	no	—
816	#395	—	53	1	no	—
817	#395	—	53	1	no	—
818	#395	—	53	1	no	—
819	#395	—	53	1	no	—
820	#395	—	53	1	no	—
821	#393	—	53	1	no	—
822	#393	—	53	1	no	—
823	#393	—	53	1	no	—
824	#393	—	53	1	no	—
825	#391	—	53	1	no	—
826	#391	—	53	1	no	—
827	#391	—	53	1	no	—
828	#391	—	53	1	no	—
829	#389	—	53	1	no	—
830	#389	—	53	1	no	—
831	#389	—	53	1	no	—
832	#389	—	53	1	no	—
833	#389	—	53	1	no	—
834	#389	—	53	1	no	—
835	#389	—	53	1	no	—
836	#389	—	53	1	no	—
837	#389	—	53	1	no	—
838	#389	—	53	1	no	—
839	#389	—	53	1	no	—
840	#389	—	53	1	no	—
841	#388	—	53	1	no	—
842	#388	—	53	1	no	—
843	#388	—	53	1	no	—
844	#388	—	53	1	no	—
845	#388	—	53	1	no	—
846	#388	—	53	1	no	—
847	#388	—	53	1	no	—
848	#388	—	53	1	no	—
849	#388	C₂×D₅₃	1	1	yes	characteristic
850	#388	C₂×D₅₃	1	1	yes	characteristic
851	#388	C₂×D₅₃	1	1	yes	characteristic
852	#388	C₂×D₅₃	1	1	yes	characteristic
853	#388	C₂×D₅₃	1	1	yes	characteristic
854	#388	C₂×D₅₃	1	1	yes	characteristic
855	#388	C₂×D₅₃	1	1	yes	characteristic
856	#388	C₂×D₅₃	1	1	yes	characteristic
857	#387	—	53	1	no	—
858	#387	—	53	1	no	—
859	#387	—	53	1	no	—
860	#387	—	53	1	no	—
861	#387	—	53	1	no	—
862	#387	—	53	1	no	—
863	#387	—	53	1	no	—
864	#387	—	53	1	no	—
865	#385	—	53	1	no	—
866	#385	—	53	1	no	—
867	#385	—	53	1	no	—
868	#385	—	53	1	no	—
869	#385	—	53	1	no	—
870	#385	—	53	1	no	—
871	#385	—	53	1	no	—
872	#385	—	53	1	no	—
873	#385	—	53	1	no	—
874	#385	—	53	1	no	—
875	#385	—	53	1	no	—
876	#385	—	53	1	no	—
877	#385	—	53	1	no	—
878	#385	—	53	1	no	—
879	#385	—	53	1	no	—
880	#385	—	53	1	no	—
881	#385	—	53	1	no	—
882	#385	—	53	1	no	—
883	#385	—	53	1	no	—
884	#385	—	53	1	no	—
885	#385	—	53	1	no	—
886	#385	—	53	1	no	—
887	#385	—	53	1	no	—
888	#385	—	53	1	no	—
889	#384	—	53	1	no	—
890	#384	—	53	1	no	—
891	#382	—	53	1	no	—
892	#382	—	53	1	no	—
893	#380	—	53	1	no	—
894	#380	—	53	1	no	—
895	#380	—	53	1	no	—
896	#380	—	53	1	no	—
897	#380	—	53	1	no	—
898	#380	—	53	1	no	—
899	#380	—	53	1	no	—
900	#380	—	53	1	no	—
901	#380	—	53	1	no	—
902	#380	—	53	1	no	—
903	#380	C₂×D₅₃	1	1	yes	characteristic
904	#380	C₂×D₅₃	1	1	yes	characteristic
905	#379	—	53	1	no	—
906	#379	—	53	1	no	—
907	#379	C₂×D₅₃	1	1	yes	characteristic
908	#379	C₂×D₅₃	1	1	yes	characteristic
909	C₄×C₂²⋊C₄	—	53	1	no	—
910	C₄×C₂²⋊C₄	—	53	1	no	—
911	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
912	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
913	C₂×#95	—	53	1	no	—
914	C₂×#95	—	53	1	no	—
915	C₅₃	#36748	1	1	yes	characteristic, complemented, Sylow
916	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
917	C₂²×Q₈	—	53	1	no	—
918	C₂²×Q₈	—	53	1	no	—
919	C₂²×Q₈	—	53	1	no	—
920	C₂²×Q₈	—	53	1	no	—
921	C₂³×C₄	—	53	1	no	—
922	C₂³×C₄	—	53	1	no	—
923	C₂³×C₄	—	53	1	no	—
924	C₂³×C₄	—	53	1	no	—
925	C₂³×C₄	—	53	1	no	—
926	C₂³×C₄	—	53	1	no	—
927	C₂³×C₄	—	53	1	no	—
928	C₂³×C₄	—	53	1	no	—
929	C₂³×C₄	—	212	2	no	—
930	C₂³×C₄	—	212	2	no	—
931	C₂³×C₄	—	212	2	no	—
932	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
933	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
934	C₄⋊Q₈	—	212	2	no	—
935	C₄⋊Q₈	—	212	2	no	—
936	#125	—	212	2	no	—
937	#125	—	212	2	no	—
938	C₂²⋊Q₈	—	212	2	no	—
939	C₂²⋊Q₈	—	212	2	no	—
940	C₂²⋊Q₈	—	212	2	no	—
941	C₂²⋊Q₈	—	212	2	no	—
942	C₂²⋊Q₈	—	212	2	no	—
943	C₂²⋊Q₈	—	212	2	no	—
944	C₂²⋊Q₈	—	212	2	no	—
945	C₂²⋊Q₈	—	212	2	no	—
946	C₂×C₄⋊C₄	—	53	1	no	—
947	C₂×C₄⋊C₄	—	53	1	no	—
948	C₂×C₄⋊C₄	—	53	1	no	—
949	C₂×C₄⋊C₄	—	53	1	no	—
950	C₂×C₄⋊C₄	—	53	1	no	—
951	C₂×C₄⋊C₄	—	53	1	no	—
952	C₂×C₄⋊C₄	—	53	1	no	—
953	C₂×C₄⋊C₄	—	53	1	no	—
954	C₂×C₄⋊C₄	—	53	1	no	—
955	C₂×C₄⋊C₄	—	53	1	no	—
956	C₂×C₄⋊C₄	—	53	1	no	—
957	C₂×C₄⋊C₄	—	53	1	no	—
958	C₂×C₄⋊C₄	—	53	1	no	—
959	C₂×C₄⋊C₄	—	53	1	no	—
960	C₂×C₄⋊C₄	—	53	1	no	—
961	C₂×C₄⋊C₄	—	53	1	no	—
962	C₂×C₄⋊C₄	—	53	1	no	—
963	C₂×C₄⋊C₄	—	53	1	no	—
964	C₂×C₄⋊C₄	—	53	1	no	—
965	C₂×C₄⋊C₄	—	53	1	no	—
966	C₂×C₄⋊C₄	—	53	1	no	—
967	C₂×C₄⋊C₄	—	53	1	no	—
968	C₂×C₄⋊C₄	—	53	1	no	—
969	C₂×C₄⋊C₄	—	53	1	no	—
970	C₂×C₄⋊C₄	—	53	1	no	—
971	C₂×C₄⋊C₄	—	53	1	no	—
972	C₂×C₄⋊C₄	—	53	1	no	—
973	C₂×C₄⋊C₄	—	53	1	no	—
974	C₂×C₄⋊C₄	—	53	1	no	—
975	C₂×C₄⋊C₄	—	53	1	no	—
976	C₂×C₄⋊C₄	—	53	1	no	—
977	C₂×C₄⋊C₄	—	53	1	no	—
978	C₂×C₄⋊C₄	—	53	1	no	—
979	C₂×C₄⋊C₄	—	53	1	no	—
980	C₂×C₄⋊C₄	—	53	1	no	—
981	C₂×C₄⋊C₄	—	53	1	no	—
982	C₂×C₄⋊C₄	—	53	1	no	—
983	C₂×C₄⋊C₄	—	53	1	no	—
984	C₂×C₄⋊C₄	—	53	1	no	—
985	C₂×C₄⋊C₄	—	53	1	no	—
986	C₂×C₄⋊C₄	—	53	1	no	—
987	C₂×C₄⋊C₄	—	53	1	no	—
988	C₂×C₄⋊C₄	—	53	1	no	—
989	C₂×C₄⋊C₄	—	53	1	no	—
990	C₂×C₄⋊C₄	—	53	1	no	—
991	C₂×C₄⋊C₄	—	53	1	no	—
992	C₂×C₄⋊C₄	—	53	1	no	—
993	C₂×C₄⋊C₄	—	53	1	no	—
994	C₂×C₄⋊C₄	—	212	2	no	—
995	C₂×C₄⋊C₄	—	212	2	no	—
996	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	—	53	1	no	—
1001	C₂×C₂²⋊C₄	—	53	1	no	—
1002	C₂×C₂²⋊C₄	—	53	1	no	—
1003	C₂×C₂²⋊C₄	—	53	1	no	—
1004	C₂×C₂²⋊C₄	—	53	1	no	—
1005	C₂×C₂²⋊C₄	—	53	1	no	—
1006	C₂×C₂²⋊C₄	—	53	1	no	—
1007	C₂×C₂²⋊C₄	—	53	1	no	—
1008	C₂×C₂²⋊C₄	—	53	1	no	—
1009	C₂×C₂²⋊C₄	—	53	1	no	—
1010	C₂×C₂²⋊C₄	—	53	1	no	—
1011	C₂×C₂²⋊C₄	—	53	1	no	—
1012	C₂×C₂²⋊C₄	—	53	1	no	—
1013	C₂×C₂²⋊C₄	—	53	1	no	—
1014	C₂×C₂²⋊C₄	—	53	1	no	—
1015	C₂×C₂²⋊C₄	—	53	1	no	—
1016	C₂×C₂²⋊C₄	—	212	2	no	—
1017	C₂×C₂²⋊C₄	Dic₁₀₆	1	8	yes	complemented
1018	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1024	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₄²	—	53	1	no	—
1035	C₂×C₄²	—	53	1	no	—
1036	C₂×C₄²	—	53	1	no	—
1037	C₂×C₄²	—	53	1	no	—
1038	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1042	#95	—	53	1	no	—
1043	#95	—	53	1	no	—
1044	#95	—	53	1	no	—
1045	#95	—	53	1	no	—
1046	#95	—	53	1	no	—
1047	#95	—	53	1	no	—
1048	#95	—	53	1	no	—
1049	#95	—	53	1	no	—
1050	#95	—	53	1	no	—
1051	#95	—	53	1	no	—
1052	#95	—	53	1	no	—
1053	#95	—	53	1	no	—
1054	#95	—	53	1	no	—
1055	#95	—	53	1	no	—
1056	#95	—	53	1	no	—
1057	#95	—	53	1	no	—
1058	#95	—	53	1	no	—
1059	#95	—	53	1	no	—
1060	#95	—	53	1	no	—
1061	#95	—	53	1	no	—
1062	#95	—	53	1	no	—
1063	#95	—	53	1	no	—
1064	#95	—	53	1	no	—
1065	#95	—	53	1	no	—
1066	#95	—	53	1	no	—
1067	#95	—	53	1	no	—
1068	#95	—	53	1	no	—
1069	#95	—	53	1	no	—
1070	#95	—	53	1	no	—
1071	#95	—	53	1	no	—
1072	#95	—	53	1	no	—
1073	#95	—	53	1	no	—
1074	#95	—	53	1	no	—
1075	#95	—	53	1	no	—
1076	#95	—	53	1	no	—
1077	#95	—	53	1	no	—
1078	#95	—	53	1	no	—
1079	#95	—	53	1	no	—
1080	#95	—	53	1	no	—
1081	#95	—	53	1	no	—
1082	#95	C₂²×D₅₃	1	1	yes	characteristic
1083	#95	C₂²×D₅₃	1	1	yes	characteristic
1084	#95	C₂²×D₅₃	1	1	yes	characteristic
1085	#95	C₂²×D₅₃	1	1	yes	characteristic
1086	#95	C₂²×D₅₃	1	1	yes	characteristic
1087	#95	C₂²×D₅₃	1	1	yes	characteristic
1088	#95	C₂²×D₅₃	1	1	yes	characteristic
1089	#95	C₂²×D₅₃	1	1	yes	characteristic
1090	C₂⁴	—	2	2	no	—
1091	C₂⁴	—	2	2	no	—
1092	C₂⁴	—	4	1	no	—
1093	C₂⁴	—	4	1	no	—
1094	C₂⁴	—	4	1	no	—
1095	C₂⁴	—	4	1	no	—
1096	C₂⁴	C₂×Dic₁₀₆	1	4	yes	—
1097	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1098	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1099	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1100	C₂×Q₈	—	106	2	no	—
1101	C₂×Q₈	—	106	2	no	—
1102	C₂×Q₈	—	212	1	no	—
1103	C₂×Q₈	—	212	1	no	—
1104	C₂×Q₈	—	212	1	no	—
1105	C₂×Q₈	—	212	1	no	—
1106	C₂×Q₈	—	212	1	no	—
1107	C₂×Q₈	—	212	1	no	—
1108	C₂×Q₈	—	212	1	no	—
1109	C₂×Q₈	—	212	1	no	—
1110	C₂×Q₈	—	212	1	no	—
1111	C₂×Q₈	—	212	1	no	—
1112	C₂²×C₄	—	4	1	no	—
1113	C₂²×C₄	—	4	1	no	—
1114	C₂²×C₄	—	4	1	no	—
1115	C₂²×C₄	—	4	1	no	—
1116	C₂²×C₄	—	53	1	no	—
1117	C₂²×C₄	—	53	1	no	—
1118	C₂²×C₄	—	53	1	no	—
1119	C₂²×C₄	—	53	1	no	—
1120	C₂²×C₄	—	53	1	no	—
1121	C₂²×C₄	—	53	1	no	—
1122	C₂²×C₄	—	53	1	no	—
1123	C₂²×C₄	—	53	1	no	—
1124	C₂²×C₄	—	53	1	no	—
1125	C₂²×C₄	—	53	1	no	—
1126	C₂²×C₄	—	53	1	no	—
1127	C₂²×C₄	—	53	1	no	—
1128	C₂²×C₄	—	53	1	no	—
1129	C₂²×C₄	—	53	1	no	—
1130	C₂²×C₄	—	53	1	no	—
1131	C₂²×C₄	—	53	1	no	—
1132	C₂²×C₄	—	106	2	no	—
1133	C₂²×C₄	—	106	2	no	—
1134	C₂²×C₄	—	106	2	no	—
1135	C₂²×C₄	—	106	2	no	—
1136	C₂²×C₄	—	106	2	no	—
1137	C₂²×C₄	—	106	2	no	—
1138	C₂²×C₄	—	106	2	no	—
1139	C₂²×C₄	—	106	2	no	—
1140	C₂²×C₄	—	106	2	no	—
1141	C₂²×C₄	—	106	2	no	—
1142	C₂²×C₄	—	212	1	no	—
1143	C₂²×C₄	—	212	1	no	—
1144	C₂²×C₄	—	212	1	no	—
1145	C₂²×C₄	—	212	1	no	—
1146	C₂²×C₄	—	212	1	no	—
1147	C₂²×C₄	—	212	1	no	—
1148	C₂²×C₄	—	212	1	no	—
1149	C₂²×C₄	—	212	1	no	—
1150	C₂²×C₄	—	212	1	no	—
1151	C₂²×C₄	—	212	1	no	—
1152	C₂²×C₄	—	212	1	no	—
1153	C₂²×C₄	—	212	1	no	—
1154	C₂²×C₄	—	212	1	no	—
1155	C₂²×C₄	—	212	1	no	—
1156	C₂²×C₄	—	212	16	no	—
1157	C₂²×C₄	C₂×Dic₁₀₆	1	4	yes	—
1158	C₂²×C₄	C₂×Dic₁₀₆	1	4	yes	—
1159	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1160	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1161	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1162	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1163	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1164	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1165	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1166	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1167	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1168	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1170	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1171	C₄⋊C₄	—	4	1	no	—
1172	C₄⋊C₄	—	4	1	no	—
1173	C₄⋊C₄	—	4	1	no	—
1174	C₄⋊C₄	—	4	1	no	—
1175	C₄⋊C₄	—	106	2	no	—
1176	C₄⋊C₄	—	106	2	no	—
1177	C₄⋊C₄	—	106	2	no	—
1178	C₄⋊C₄	—	106	2	no	—
1179	C₄⋊C₄	—	106	2	no	—
1180	C₄⋊C₄	—	106	2	no	—
1181	C₄⋊C₄	—	106	2	no	—
1182	C₄⋊C₄	—	106	2	no	—
1183	C₄⋊C₄	—	106	2	no	—
1184	C₄⋊C₄	—	106	2	no	—
1185	C₄⋊C₄	—	212	1	no	—
1186	C₄⋊C₄	—	212	1	no	—
1187	C₄⋊C₄	—	212	1	no	—
1188	C₄⋊C₄	—	212	1	no	—
1189	C₄⋊C₄	—	212	1	no	—
1190	C₄⋊C₄	—	212	1	no	—
1191	C₄⋊C₄	—	212	1	no	—
1192	C₄⋊C₄	—	212	1	no	—
1193	C₄⋊C₄	—	212	1	no	—
1194	C₄⋊C₄	—	212	1	no	—
1195	C₄⋊C₄	—	212	1	no	—
1196	C₄⋊C₄	—	212	1	no	—
1197	C₄⋊C₄	—	212	1	no	—
1198	C₄⋊C₄	—	212	1	no	—
1199	C₄⋊C₄	—	212	1	no	—
1200	C₄⋊C₄	—	212	1	no	—
1201	C₄⋊C₄	—	212	1	no	—
1202	C₄⋊C₄	—	212	1	no	—
1203	C₄⋊C₄	—	212	1	no	—
1204	C₄⋊C₄	—	212	1	no	—
1205	C₄⋊C₄	—	212	1	no	—
1206	C₄⋊C₄	—	212	1	no	—
1207	C₄⋊C₄	—	212	1	no	—
1208	C₄⋊C₄	—	212	1	no	—
1209	C₄⋊C₄	—	212	1	no	—
1210	C₄⋊C₄	—	212	1	no	—
1211	C₄⋊C₄	—	212	1	no	—
1212	C₄⋊C₄	—	212	1	no	—
1213	C₄⋊C₄	—	212	1	no	—
1214	C₄⋊C₄	—	212	1	no	—
1215	C₄⋊C₄	—	212	1	no	—
1216	C₄⋊C₄	—	212	1	no	—
1217	C₄⋊C₄	—	212	1	no	—
1218	C₄⋊C₄	—	212	1	no	—
1219	C₄⋊C₄	—	212	1	no	—
1220	C₄⋊C₄	—	212	1	no	—
1221	C₄⋊C₄	—	212	1	no	—
1222	C₄⋊C₄	—	212	1	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	—	2	2	no	—
1226	C₂²⋊C₄	—	2	2	no	—
1227	C₂²⋊C₄	—	4	1	no	—
1228	C₂²⋊C₄	—	4	1	no	—
1229	C₂²⋊C₄	—	4	1	no	—
1230	C₂²⋊C₄	—	4	1	no	—
1231	C₂²⋊C₄	—	4	1	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₂²⋊C₄	—	4	1	no	—
1235	C₂²⋊C₄	—	106	2	no	—
1236	C₂²⋊C₄	—	106	2	no	—
1237	C₂²⋊C₄	—	106	2	no	—
1238	C₂²⋊C₄	—	106	2	no	—
1239	C₂²⋊C₄	—	212	1	no	—
1240	C₂²⋊C₄	—	212	1	no	—
1241	C₂²⋊C₄	—	212	1	no	—
1242	C₂²⋊C₄	—	212	1	no	—
1243	C₂²⋊C₄	—	212	1	no	—
1244	C₂²⋊C₄	—	212	1	no	—
1245	C₂²⋊C₄	—	212	1	no	—
1246	C₂²⋊C₄	—	212	1	no	—
1247	C₂²⋊C₄	—	212	1	no	—
1248	C₂²⋊C₄	—	212	1	no	—
1249	C₂²⋊C₄	—	212	1	no	—
1250	C₂²⋊C₄	—	212	1	no	—
1251	C₂²⋊C₄	C₂×Dic₁₀₆	1	4	yes	—
1252	C₂²⋊C₄	C₂×Dic₁₀₆	1	4	yes	—
1253	C₂²⋊C₄	C₂×Dic₁₀₆	1	4	yes	—
1254	C₂²⋊C₄	C₂×Dic₁₀₆	1	4	yes	—
1255	C₄²	—	4	1	no	—
1256	C₄²	—	4	1	no	—
1257	C₄²	—	4	1	no	—
1258	C₄²	—	4	1	no	—
1259	C₄²	—	212	1	no	—
1260	C₄²	—	212	1	no	—
1261	C₄²	—	212	1	no	—
1262	C₄²	—	212	1	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	1	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	2	1	no	—
1268	C₂³	—	2	1	no	—
1269	C₂³	—	2	1	no	—
1270	C₂³	—	2	1	no	—
1271	C₂³	—	2	1	no	—
1272	C₂³	—	2	1	no	—
1273	C₂³	—	2	1	no	—
1274	C₂³	—	2	1	no	—
1275	C₂³	—	2	1	no	—
1276	C₂³	—	2	1	no	—
1277	C₂³	—	2	1	no	—
1278	C₂³	—	2	1	no	—
1279	C₂³	—	2	8	no	—
1280	C₂³	—	4	4	no	—
1281	C₂³	—	4	4	no	—
1282	C₂³	—	4	4	no	—
1283	C₂³	—	4	4	no	—
1284	C₂³	—	4	4	no	—
1285	C₂³	—	4	4	no	—
1286	C₂³	C₂²×Dic₁₀₆	1	2	yes	—
1287	C₂³	C₂²×Dic₁₀₆	1	2	yes	—
1288	C₂³	C₂²×Dic₁₀₆	1	2	yes	—
1289	C₂³	#13133263	1	2	yes	—
1290	C₂³	#13133264	1	2	yes	—
1291	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1292	Q₈	—	424	2	no	—
1293	Q₈	—	424	2	no	—
1294	Q₈	—	424	2	no	—
1295	Q₈	—	424	2	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	4	4	no	—
1329	C₂×C₄	—	4	4	no	—
1330	C₂×C₄	—	53	2	no	—
1331	C₂×C₄	—	53	2	no	—
1332	C₂×C₄	—	106	1	no	—
1333	C₂×C₄	—	106	1	no	—
1334	C₂×C₄	—	106	1	no	—
1335	C₂×C₄	—	106	1	no	—
1336	C₂×C₄	—	106	1	no	—
1337	C₂×C₄	—	106	1	no	—
1338	C₂×C₄	—	106	1	no	—
1339	C₂×C₄	—	106	1	no	—
1340	C₂×C₄	—	106	1	no	—
1341	C₂×C₄	—	106	1	no	—
1342	C₂×C₄	—	106	1	no	—
1343	C₂×C₄	—	106	1	no	—
1344	C₂×C₄	—	106	1	no	—
1345	C₂×C₄	—	106	1	no	—
1346	C₂×C₄	—	106	1	no	—
1347	C₂×C₄	—	106	1	no	—
1348	C₂×C₄	—	106	1	no	—
1349	C₂×C₄	—	106	1	no	—
1350	C₂×C₄	—	106	1	no	—
1351	C₂×C₄	—	106	1	no	—
1352	C₂×C₄	—	106	1	no	—
1353	C₂×C₄	—	106	1	no	—
1354	C₂×C₄	—	106	1	no	—
1355	C₂×C₄	—	106	1	no	—
1356	C₂×C₄	—	106	1	no	—
1357	C₂×C₄	—	106	1	no	—
1358	C₂×C₄	—	106	1	no	—
1359	C₂×C₄	—	106	1	no	—
1360	C₂×C₄	—	106	1	no	—
1361	C₂×C₄	—	106	1	no	—
1362	C₂×C₄	—	106	1	no	—
1363	C₂×C₄	—	106	1	no	—
1364	C₂×C₄	—	106	1	no	—
1365	C₂×C₄	—	106	1	no	—
1366	C₂×C₄	—	106	1	no	—
1367	C₂×C₄	—	106	1	no	—
1368	C₂×C₄	—	106	1	no	—
1369	C₂×C₄	—	106	1	no	—
1370	C₂×C₄	—	106	1	no	—
1371	C₂×C₄	—	106	1	no	—
1372	C₂×C₄	—	106	1	no	—
1373	C₂×C₄	—	106	1	no	—
1374	C₂×C₄	—	106	1	no	—
1375	C₂×C₄	—	106	1	no	—
1376	C₂×C₄	—	106	1	no	—
1377	C₂×C₄	—	106	1	no	—
1378	C₂×C₄	—	424	2	no	—
1379	C₂×C₄	—	424	2	no	—
1380	C₂×C₄	—	212	4	no	—
1381	C₂×C₄	—	212	4	no	—
1382	C₂×C₄	—	212	4	no	—
1383	C₂×C₄	—	212	4	no	—
1384	C₂×C₄	—	212	4	no	—
1385	C₂×C₄	—	212	4	no	—
1386	C₂×C₄	C₂²×Dic₁₀₆	1	2	yes	—
1387	C₂×C₄	C₂²×Dic₁₀₆	1	2	yes	—
1388	C₂×C₄	C₂²×Dic₁₀₆	1	2	yes	—
1389	C₂×C₄	C₂²×Dic₁₀₆	1	2	yes	—
1390	C₂²	—	2	2	no	—
1391	C₂²	—	2	2	no	—
1392	C₂²	—	2	2	no	—
1393	C₂²	—	2	2	no	—
1394	C₂²	—	2	2	no	—
1395	C₂²	—	2	2	no	—
1396	C₂²	—	2	2	no	—
1397	C₂²	—	2	2	no	—
1398	C₂²	—	2	2	no	—
1399	C₂²	—	2	2	no	—
1400	C₂²	—	2	2	no	—
1401	C₂²	—	2	2	no	—
1402	C₂²	—	4	16	no	—
1403	C₂²	—	4	1	no	—
1404	C₂²	—	4	1	no	—
1405	C₂²	—	4	1	no	—
1406	C₂²	—	4	1	no	—
1407	C₂²	—	4	1	no	—
1408	C₂²	—	4	1	no	—
1409	C₂²	—	4	1	no	—
1410	C₂²	—	4	1	no	—
1411	C₂²	#16811251	1	4	yes	—
1412	C₂²	C₂³×Dic₁₀₆	1	1	yes	characteristic
1413	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1414	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1415	C₂²	C₂×#13133263	1	1	yes	characteristic
1416	C₂²	C₂×#13133264	1	1	yes	characteristic
1417	C₂²	#16811458	1	1	yes	characteristic
1418	C₂²	#16811458	1	1	yes	characteristic
1419	C₄	—	2	2	no	—
1420	C₄	—	2	2	no	—
1421	C₄	—	2	2	no	—
1422	C₄	—	2	2	no	—
1423	C₄	—	4	1	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	1	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	4	1	no	—
1429	C₄	—	4	1	no	—
1430	C₄	—	4	1	no	—
1431	C₄	—	106	2	no	—
1432	C₄	—	106	2	no	—
1433	C₄	—	212	1	no	—
1434	C₄	—	212	1	no	—
1435	C₄	—	212	1	no	—
1436	C₄	—	212	1	no	—
1437	C₄	—	212	1	no	—
1438	C₄	—	212	1	no	—
1439	C₄	—	212	1	no	—
1440	C₄	—	212	1	no	—
1441	C₄	—	212	1	no	—
1442	C₄	—	212	1	no	—
1443	C₄	—	212	1	no	—
1444	C₄	—	212	1	no	—
1445	C₄	—	212	1	no	—
1446	C₄	—	212	1	no	—
1447	C₂	—	2	4	no	—
1448	C₂	—	4	2	no	—
1449	C₂	—	4	2	no	—
1450	C₂	C₂×#16811251	1	1	yes	characteristic
1451	C₂	#20288513	1	1	yes	characteristic
1452	C₂	#20288513	1	1	yes	characteristic
1453	C₂	#20288866	1	1	yes	characteristic
1454	C₂	#20288883	1	1	yes	characteristic
1455	C₂	#20288995	1	1	yes	characteristic
1456	C₂	#20289003	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2312	C₂
prime radical	C₂⁵×C₅₃	C₂³
hypercenter	#2312	D₅₃
hypocenter	C₅₃	#36748
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2312

Complements

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

N	H ≅ G/N	type
3. #20282682	C₂	semidirect
4. #20282485	C₂	semidirect
5. #20282480	C₂	semidirect
6. #20282462	C₂	semidirect
7. #20282458	C₂	semidirect
8. #20282199	C₂	semidirect
9. #20282196	C₂	semidirect
10. #20282131	C₂	semidirect
11. #20281841	C₂	semidirect
12. #20281698	C₂	semidirect
13. #20281694	C₂	semidirect
14. #20281599	C₂	semidirect
15. #20281592	C₂	semidirect
16. #20281374	C₂	semidirect
17. #20281370	C₂	semidirect
18. #20281027	C₂	semidirect
21. #20279940	C₂	semidirect
22. #20279934	C₂	semidirect
23. #20279727	C₂	semidirect
24. #20279721	C₂	semidirect
25. #20278440	C₂	semidirect
26. #20278439	C₂	semidirect
27. #20278418	C₂	semidirect
28. #20278417	C₂	semidirect
33. C₂×#13133217	C₂²	semidirect
34. C₂×#13133216	C₂²	semidirect
35. C₂×#13133209	C₂²	semidirect
36. C₂×#13133208	C₂²	semidirect
48. #16810565	C₂²	semidirect
49. #16810565	C₂²	semidirect
50. #16810565	C₂²	semidirect
51. #16810565	C₂²	semidirect
52. #16810565	C₂²	semidirect
53. #16810565	C₂²	semidirect
54. #16810562	C₂²	semidirect
55. #16810562	C₂²	semidirect
60. #16810557	C₂²	semidirect
61. #16810557	C₂²	semidirect
62. #16810557	C₂²	semidirect
63. #16810557	C₂²	semidirect
64. #16810557	C₂²	semidirect
65. #16810557	C₂²	semidirect
66. #16810556	C₂²	semidirect
67. #16810556	C₂²	semidirect
68. #16810556	C₂²	semidirect
69. #16810556	C₂²	semidirect
70. #16810555	C₂²	semidirect
71. #16810555	C₂²	semidirect
72. #16810555	C₂²	semidirect
73. #16810555	C₂²	semidirect
74. #16810555	C₂²	semidirect
75. #16810555	C₂²	semidirect
84. #16810544	C₂²	semidirect
85. #16810544	C₂²	semidirect
86. #16810544	C₂²	semidirect
87. #16810544	C₂²	semidirect
88. #16810544	C₂²	semidirect
89. #16810544	C₂²	semidirect
90. #16810543	C₂²	semidirect
91. #16810543	C₂²	semidirect
96. #16810529	C₂²	semidirect
97. #16810529	C₂²	semidirect
98. #16810527	C₂²	semidirect
99. #16810527	C₂²	semidirect
100. #16810522	C₂²	semidirect
101. #16810522	C₂²	semidirect
102. #16810521	C₂²	semidirect
103. #16810521	C₂²	semidirect
104. #16810521	C₂²	semidirect
105. #16810521	C₂²	semidirect
106. #16810521	C₂²	semidirect
107. #16810521	C₂²	semidirect
108. #16810520	C₂²	semidirect
109. #16810520	C₂²	semidirect
110. #16810519	C₂²	semidirect
111. #16810519	C₂²	semidirect
120. #16810510	C₂²	semidirect
121. #16810510	C₂²	semidirect
122. #16810507	C₂²	semidirect
123. #16810507	C₂²	semidirect
124. #16810507	C₂²	semidirect
125. #16810507	C₂²	semidirect
126. #16810506	C₂²	semidirect
127. #16810506	C₂²	semidirect
152. #16810493	C₂²	semidirect
153. #16810492	C₂²	semidirect
154. #16810489	C₂²	semidirect
155. #16810488	C₂²	semidirect
332. C₂×C₂²⋊C₄×C₅₃	Q₈	semidirect
915. C₅₃	#36748	semidirect
1017. C₂×C₂²⋊C₄	Dic₁₀₆	semidirect

Maximal subgroups

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

subgroup	index
#20283000	2
#20282682	2
#20282485	2
#20282480	2
#20282462	2
#20282458	2
#20282199	2
#20282196	2
#20282131	2
#20281841	2
#20281698	2
#20281694	2
#20281599	2
#20281592	2
#20281374	2
#20281370	2
#20281027	2
#20280524	2
#20279940	2
#20279934	2
#20279727	2
#20279721	2
#20278440	2
#20278439	2
#20278418	2
#20278417	2
#20277313	2
C₂×#16810498	2
C₅₃×#2312	2
#36748	53