Subgroups — D₅₃×#2469 #27552294

Order 13568.

2594 conjugacy classes of subgroups.

The subgroup lattice has 1530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#126×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20278803	C₂	1	1	yes	maximal, characteristic, complemented
4	#20278802	C₂	1	1	yes	maximal, characteristic, complemented
5	#20278801	C₂	1	1	yes	maximal, characteristic, complemented
6	#20278800	C₂	1	1	yes	maximal, characteristic, complemented
7	#20278799	C₂	1	1	yes	maximal, characteristic, complemented
8	#20278798	C₂	1	1	yes	maximal, characteristic, complemented
9	#20278797	C₂	1	1	yes	maximal, characteristic, complemented
10	#20278796	C₂	1	1	yes	maximal, characteristic, complemented
11	#20278795	C₂	1	1	yes	maximal, characteristic, complemented
12	#20278794	C₂	1	1	yes	maximal, characteristic, complemented
13	#20278793	C₂	1	1	yes	maximal, characteristic, complemented
14	#20278792	C₂	1	1	yes	maximal, characteristic, complemented
15	#20278791	C₂	1	1	yes	maximal, characteristic, complemented
16	#20278790	C₂	1	1	yes	maximal, characteristic, complemented
17	#20278789	C₂	1	1	yes	maximal, characteristic, complemented
18	#400×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#396×D₅₃	C₂	1	1	yes	maximal, characteristic
20	#395×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#393×D₅₃	C₂	1	1	yes	maximal, characteristic
22	#389×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
24	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
25	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
26	#388×D₅₃	C₂	1	1	yes	maximal, characteristic
27	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
29	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2469	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×#13133212	C₂²	1	1	yes	characteristic
34	C₂×#13133212	C₂²	1	1	yes	characteristic
35	C₂×#13133212	C₂²	1	1	yes	characteristic
36	C₂×#13133211	C₂²	1	1	yes	characteristic
37	C₂×#13133210	C₂²	1	1	yes	characteristic
38	C₂×#13133210	C₂²	1	1	yes	characteristic
39	C₂×#13133210	C₂²	1	1	yes	characteristic
40	#126×D₅₃	—	2	8	no	—
41	C₂×Q₈×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
45	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
47	C₂×#13133182	C₂²	1	1	yes	characteristic, complemented
48	C₄×Q₈×D₅₃	—	2	8	no	—
49	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
66	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
67	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
68	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
69	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
70	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
71	#16810565	C₂²	1	1	yes	characteristic, complemented
72	#16810565	C₂²	1	1	yes	characteristic, complemented
73	#16810564	C₂²	1	1	yes	characteristic, complemented
74	#16810564	C₂²	1	1	yes	characteristic, complemented
75	#16810563	C₂²	1	1	yes	characteristic, complemented
76	#16810562	C₂²	1	1	yes	characteristic, complemented
77	#16810561	C₂²	1	1	yes	characteristic, complemented
78	#16810547	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	#16810545	C₂²	1	1	yes	characteristic
83	#16810545	C₂²	1	1	yes	characteristic
84	#16810545	C₂²	1	1	yes	characteristic
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	#16810543	C₂²	1	1	yes	characteristic, complemented
89	#16810543	C₂²	1	1	yes	characteristic, complemented
90	#16810543	C₂²	1	1	yes	characteristic, complemented
91	#16810542	C₂²	1	1	yes	characteristic, complemented
92	#16810536	C₂²	1	1	yes	characteristic
93	#16810536	C₂²	1	1	yes	characteristic
94	#16810536	C₂²	1	1	yes	characteristic
95	#16810535	C₂²	1	1	yes	characteristic
96	#16810535	C₂²	1	1	yes	characteristic
97	#16810535	C₂²	1	1	yes	characteristic
98	#16810534	C₂²	1	1	yes	characteristic
99	#16810522	C₂²	1	1	yes	characteristic, complemented
100	#16810521	C₂²	1	1	yes	characteristic, complemented
101	#16810520	C₂²	1	1	yes	characteristic, complemented
102	#16810520	C₂²	1	1	yes	characteristic, complemented
103	#16810519	C₂²	1	1	yes	characteristic, complemented
104	#16810518	C₂²	1	1	yes	characteristic, complemented
105	#16810518	C₂²	1	1	yes	characteristic, complemented
106	#16810517	C₂²	1	1	yes	characteristic
107	#16810517	C₂²	1	1	yes	characteristic
108	#16810517	C₂²	1	1	yes	characteristic
109	#16810517	C₂²	1	1	yes	characteristic
110	#16810516	C₂²	1	1	yes	characteristic
111	#16810516	C₂²	1	1	yes	characteristic
112	#16810516	C₂²	1	1	yes	characteristic
113	#16810516	C₂²	1	1	yes	characteristic
114	#16810515	C₂²	1	1	yes	characteristic
115	#16810515	C₂²	1	1	yes	characteristic
116	#16810515	C₂²	1	1	yes	characteristic
117	#16810515	C₂²	1	1	yes	characteristic
118	#16810514	C₂²	1	1	yes	characteristic
119	#16810514	C₂²	1	1	yes	characteristic
120	#16810514	C₂²	1	1	yes	characteristic
121	#16810514	C₂²	1	1	yes	characteristic
122	#16810513	C₂²	1	1	yes	characteristic
123	#16810513	C₂²	1	1	yes	characteristic
124	#16810513	C₂²	1	1	yes	characteristic
125	#16810513	C₂²	1	1	yes	characteristic
126	#16810512	C₂²	1	1	yes	characteristic
127	#16810512	C₂²	1	1	yes	characteristic
128	#16810512	C₂²	1	1	yes	characteristic
129	#16810512	C₂²	1	1	yes	characteristic
130	#16810511	C₂²	1	1	yes	characteristic
131	#16810511	C₂²	1	1	yes	characteristic
132	#16810511	C₂²	1	1	yes	characteristic
133	#16810511	C₂²	1	1	yes	characteristic
134	#16810510	C₂²	1	1	yes	characteristic, complemented
135	#16810510	C₂²	1	1	yes	characteristic, complemented
136	#16810510	C₂²	1	1	yes	characteristic, complemented
137	#16810509	C₂²	1	1	yes	characteristic, complemented
138	#16810509	C₂²	1	1	yes	characteristic, complemented
139	#16810509	C₂²	1	1	yes	characteristic, complemented
140	#16810508	C₂²	1	1	yes	characteristic, complemented
141	#16810508	C₂²	1	1	yes	characteristic, complemented
142	#16810508	C₂²	1	1	yes	characteristic, complemented
143	#16810507	C₂²	1	1	yes	characteristic, complemented
144	#16810507	C₂²	1	1	yes	characteristic, complemented
145	#16810507	C₂²	1	1	yes	characteristic, complemented
146	#16810506	C₂²	1	1	yes	characteristic, complemented
147	#16810506	C₂²	1	1	yes	characteristic, complemented
148	#16810506	C₂²	1	1	yes	characteristic, complemented
149	#16810505	C₂²	1	1	yes	characteristic, complemented
150	#16810505	C₂²	1	1	yes	characteristic, complemented
151	#16810505	C₂²	1	1	yes	characteristic, complemented
152	#16810504	C₂²	1	1	yes	characteristic, complemented
153	#16810504	C₂²	1	1	yes	characteristic, complemented
154	#16810504	C₂²	1	1	yes	characteristic, complemented
155	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
156	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
157	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
158	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
159	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
160	#16810474	C₂²	1	1	yes	characteristic, complemented
161	#16810474	C₂²	1	1	yes	characteristic, complemented
162	#95×D₅₃	C₂²	1	1	yes	characteristic
163	#95×D₅₃	C₂²	1	1	yes	characteristic
164	#95×D₅₃	C₂²	1	1	yes	characteristic
165	#95×D₅₃	C₂²	1	1	yes	characteristic
166	#95×D₅₃	C₂²	1	1	yes	characteristic
167	#95×D₅₃	C₂²	1	1	yes	characteristic
168	#95×D₅₃	C₂²	1	1	yes	characteristic
169	#95×D₅₃	C₂²	1	1	yes	characteristic
170	#95×D₅₃	C₂²	1	1	yes	characteristic
171	#95×D₅₃	C₂²	1	1	yes	characteristic
172	#95×D₅₃	C₂²	1	1	yes	characteristic
173	#95×D₅₃	C₂²	1	1	yes	characteristic
174	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
175	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#396	C₂²	1	1	yes	characteristic
178	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#393	C₂²	1	1	yes	characteristic
180	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#388	C₂²	1	1	yes	characteristic
182	C₅₃×#388	C₂²	1	1	yes	characteristic
183	C₅₃×#388	C₂²	1	1	yes	characteristic
184	C₅₃×#388	C₂²	1	1	yes	characteristic
185	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
188	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
191	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
192	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
193	C₂×Q₈×D₅₃	—	2	4	no	—
194	C₂×Q₈×D₅₃	—	2	4	no	—
195	C₂×Q₈×D₅₃	—	2	4	no	—
196	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
197	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
198	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
199	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
200	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
201	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
202	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
203	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
204	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
205	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
206	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
207	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
208	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
209	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
210	#13133212	—	2	4	no	—
211	#13133212	—	2	4	no	—
212	#13133212	—	2	4	no	—
213	#13133211	—	2	4	no	—
214	#13133210	—	2	4	no	—
215	#13133210	—	2	4	no	—
216	#13133210	—	2	4	no	—
217	Q₈×Dic₅₃	—	2	4	no	—
218	C₄×Dic₁₀₆	—	2	4	no	—
219	C₄×Dic₁₀₆	—	2	4	no	—
220	C₄×Dic₁₀₆	—	2	4	no	—
221	#13133182	—	2	4	no	—
222	#13133182	—	2	4	no	—
223	#13133182	—	2	4	no	—
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×#11719919	C₂³	1	1	yes	characteristic
235	C₂×#11719919	C₂³	1	1	yes	characteristic
236	C₂×#11719919	C₂³	1	1	yes	characteristic
237	C₂×#11719919	C₂³	1	1	yes	characteristic
238	C₂×#11719919	C₂³	1	1	yes	characteristic
239	C₂×#11719919	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	C₄⋊C₄×D₅₃	—	2	4	no	—
255	C₄⋊C₄×D₅₃	—	2	4	no	—
256	C₄⋊C₄×D₅₃	—	2	4	no	—
257	C₄⋊C₄×D₅₃	—	2	4	no	—
258	C₄⋊C₄×D₅₃	—	2	4	no	—
259	C₄⋊C₄×D₅₃	—	2	4	no	—
260	C₄⋊C₄×D₅₃	—	2	4	no	—
261	C₄⋊C₄×D₅₃	—	2	4	no	—
262	C₄⋊C₄×D₅₃	—	2	4	no	—
263	C₄⋊C₄×D₅₃	D₄	1	8	yes	—
264	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
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×#11719921	C₂³	1	1	yes	characteristic
272	C₂×#11719921	C₂³	1	1	yes	characteristic
273	C₂×#11719921	C₂³	1	1	yes	characteristic
274	C₂×#11719921	C₂³	1	1	yes	characteristic
275	C₂×#11719921	C₂³	1	1	yes	characteristic
276	C₂×#11719921	C₂³	1	1	yes	characteristic
277	C₂×#11719921	C₂³	1	1	yes	characteristic
278	C₂×#11719921	C₂³	1	1	yes	characteristic
279	C₂×#11719921	C₂³	1	1	yes	characteristic
280	C₂×#11719921	C₂³	1	1	yes	characteristic
281	C₂×#11719921	C₂³	1	1	yes	characteristic
282	C₂×#11719921	C₂³	1	1	yes	characteristic
283	C₂×#11719921	C₂³	1	1	yes	characteristic
284	C₂×#11719921	C₂³	1	1	yes	characteristic
285	C₂²⋊C₄×D₅₃	—	2	4	no	—
286	C₂²⋊C₄×D₅₃	—	2	4	no	—
287	C₂²⋊C₄×D₅₃	—	2	4	no	—
288	C₂²⋊C₄×D₅₃	—	2	4	no	—
289	C₂²⋊C₄×D₅₃	—	2	4	no	—
290	C₂²⋊C₄×D₅₃	—	2	4	no	—
291	C₂²⋊C₄×D₅₃	—	2	4	no	—
292	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
307	C₄²×D₅₃	—	2	4	no	—
308	C₄²×D₅₃	—	2	4	no	—
309	C₄²×D₅₃	—	2	4	no	—
310	C₄²×D₅₃	—	2	4	no	—
311	C₄²×D₅₃	—	2	4	no	—
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	#13133124	C₂³	1	1	yes	characteristic
326	#13133124	C₂³	1	1	yes	characteristic
327	#13133124	C₂³	1	1	yes	characteristic
328	#13133124	C₂³	1	1	yes	characteristic
329	#13133124	C₂³	1	1	yes	characteristic
330	#13133124	C₂³	1	1	yes	characteristic
331	#13133124	C₂³	1	1	yes	characteristic
332	#13133124	C₂³	1	1	yes	characteristic
333	#13133124	C₂³	1	1	yes	characteristic
334	#13133124	C₂³	1	1	yes	characteristic
335	#13133124	C₂³	1	1	yes	characteristic
336	#13133124	C₂³	1	1	yes	characteristic
337	#13133124	C₂³	1	1	yes	characteristic
338	#13133124	C₂³	1	1	yes	characteristic
339	#13133124	C₂³	1	1	yes	characteristic
340	#13133124	C₂³	1	1	yes	characteristic
341	#13133124	C₂³	1	1	yes	characteristic
342	#13133124	C₂³	1	1	yes	characteristic
343	#13133124	C₂³	1	1	yes	characteristic
344	#13133124	C₂³	1	1	yes	characteristic
345	#13133124	C₂³	1	1	yes	characteristic
346	#13133124	C₂³	1	1	yes	characteristic
347	#13133124	C₂³	1	1	yes	characteristic
348	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	#126×C₅₃	—	2	4	no	—
350	C₄×Q₈×C₅₃	—	2	4	no	—
351	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
369	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
370	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
371	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
372	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂³×D₅₃	—	2	2	no	—
387	C₂³×D₅₃	—	2	2	no	—
388	C₂³×D₅₃	—	2	2	no	—
389	C₂³×D₅₃	—	2	2	no	—
390	C₂³×D₅₃	—	2	2	no	—
391	C₂³×D₅₃	—	2	2	no	—
392	C₂³×D₅₃	—	2	2	no	—
393	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
394	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×Q₈×C₅₃	—	2	2	no	—
396	C₂×Q₈×C₅₃	—	2	2	no	—
397	C₂×Q₈×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
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	Q₈×D₅₃	—	2	32	no	—
427	C₂×C₄×D₅₃	—	2	2	no	—
428	C₂×C₄×D₅₃	—	2	2	no	—
429	C₂×C₄×D₅₃	—	2	2	no	—
430	C₂×C₄×D₅₃	—	2	2	no	—
431	C₂×C₄×D₅₃	—	2	2	no	—
432	C₂×C₄×D₅₃	—	2	2	no	—
433	C₂×C₄×D₅₃	—	2	2	no	—
434	C₂×C₄×D₅₃	—	2	2	no	—
435	C₂×C₄×D₅₃	—	2	2	no	—
436	C₂×C₄×D₅₃	—	2	2	no	—
437	C₂×C₄×D₅₃	—	2	2	no	—
438	C₂×C₄×D₅₃	—	2	2	no	—
439	C₂×C₄×D₅₃	—	2	2	no	—
440	C₂×C₄×D₅₃	—	2	2	no	—
441	C₂×C₄×D₅₃	—	2	2	no	—
442	C₂×C₄×D₅₃	—	2	2	no	—
443	C₂×C₄×D₅₃	—	2	2	no	—
444	C₂×C₄×D₅₃	—	2	2	no	—
445	C₂×C₄×D₅₃	—	2	2	no	—
446	C₂×C₄×D₅₃	—	2	2	no	—
447	C₂×C₄×D₅₃	—	2	2	no	—
448	C₂×C₄×D₅₃	—	2	2	no	—
449	C₂×C₄×D₅₃	—	2	2	no	—
450	C₂×C₄×D₅₃	—	2	2	no	—
451	C₂×C₄×D₅₃	—	2	2	no	—
452	C₂×C₄×D₅₃	—	2	2	no	—
453	C₂×C₄×D₅₃	—	2	2	no	—
454	C₂×C₄×D₅₃	—	2	2	no	—
455	C₂×C₄×D₅₃	—	2	2	no	—
456	C₂×C₄×D₅₃	—	2	2	no	—
457	C₂×C₄×D₅₃	—	2	2	no	—
458	C₂×C₄×D₅₃	—	2	2	no	—
459	C₂×C₄×D₅₃	—	2	2	no	—
460	C₂×C₄×D₅₃	—	2	2	no	—
461	C₂×C₄×D₅₃	—	2	2	no	—
462	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
463	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
464	C₂×C₄×D₅₃	C₂×D₄	1	4	yes	—
465	C₂×C₄×D₅₃	#41	1	4	yes	—
466	C₂×C₄×D₅₃	#41	1	4	yes	—
467	C₂×C₄×D₅₃	#41	1	4	yes	—
468	C₂×C₄×D₅₃	#41	1	4	yes	—
469	C₂×Dic₁₀₆	—	2	2	no	—
470	C₂×Dic₁₀₆	—	2	2	no	—
471	C₂×Dic₁₀₆	—	2	2	no	—
472	C₂×Dic₁₀₆	—	2	2	no	—
473	C₂×Dic₁₀₆	—	2	2	no	—
474	C₂×Dic₁₀₆	—	2	2	no	—
475	C₂×Dic₁₀₆	—	2	2	no	—
476	C₂×Dic₁₀₆	—	2	2	no	—
477	C₂×Dic₁₀₆	—	2	2	no	—
478	C₄⋊C₄×C₅₃	—	2	2	no	—
479	C₄⋊C₄×C₅₃	—	2	2	no	—
480	C₄⋊C₄×C₅₃	—	2	2	no	—
481	C₄⋊C₄×C₅₃	—	2	2	no	—
482	C₄⋊C₄×C₅₃	—	2	2	no	—
483	C₄⋊C₄×C₅₃	—	2	2	no	—
484	C₄⋊C₄×C₅₃	—	2	2	no	—
485	C₄⋊C₄×C₅₃	—	2	2	no	—
486	C₄⋊C₄×C₅₃	—	2	2	no	—
487	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
488	C₂²⋊C₄×C₅₃	—	2	2	no	—
489	C₂²⋊C₄×C₅₃	—	2	2	no	—
490	C₂²⋊C₄×C₅₃	—	2	2	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	2	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₄²×C₅₃	—	2	2	no	—
496	C₄²×C₅₃	—	2	2	no	—
497	C₄²×C₅₃	—	2	2	no	—
498	C₄²×C₅₃	—	2	2	no	—
499	C₄²×C₅₃	—	2	2	no	—
500	C₂²⋊Dic₅₃	—	2	2	no	—
501	C₂²⋊Dic₅₃	—	2	2	no	—
502	C₂²⋊Dic₅₃	—	2	2	no	—
503	C₂²⋊Dic₅₃	—	2	2	no	—
504	C₂²⋊Dic₅₃	—	2	2	no	—
505	C₂²⋊Dic₅₃	—	2	2	no	—
506	C₂²⋊Dic₅₃	—	2	2	no	—
507	#11719921	—	2	2	no	—
508	#11719921	—	2	2	no	—
509	#11719921	—	2	2	no	—
510	#11719921	—	2	2	no	—
511	#11719921	—	2	2	no	—
512	#11719921	—	2	2	no	—
513	#11719921	—	2	2	no	—
514	#11719921	—	2	2	no	—
515	#11719921	—	2	2	no	—
516	#11719921	—	2	2	no	—
517	#11719921	—	2	2	no	—
518	#11719921	—	2	2	no	—
519	#11719921	—	2	2	no	—
520	#11719921	—	2	2	no	—
521	C₄⋊Dic₅₃	—	2	2	no	—
522	C₄⋊Dic₅₃	—	2	2	no	—
523	C₄⋊Dic₅₃	—	2	2	no	—
524	C₄⋊Dic₅₃	—	2	2	no	—
525	C₄⋊Dic₅₃	—	2	2	no	—
526	C₄⋊Dic₅₃	—	2	2	no	—
527	C₄⋊Dic₅₃	—	2	2	no	—
528	C₄⋊Dic₅₃	—	2	2	no	—
529	C₄⋊Dic₅₃	—	2	2	no	—
530	C₄⋊Dic₅₃	C₂×D₄	1	4	yes	—
531	#11719919	—	2	2	no	—
532	#11719919	—	2	2	no	—
533	#11719919	—	2	2	no	—
534	#11719919	—	2	2	no	—
535	#11719919	—	2	2	no	—
536	#11719919	—	2	2	no	—
537	#11719919	—	2	2	no	—
538	#11719919	—	2	2	no	—
539	#11719919	—	2	2	no	—
540	#11719919	—	2	2	no	—
541	#11719919	—	2	2	no	—
542	#11719919	—	2	2	no	—
543	#11719919	—	2	2	no	—
544	#11719919	—	2	2	no	—
545	#11719919	—	2	2	no	—
546	#11719919	—	2	2	no	—
547	#11719919	—	2	2	no	—
548	#11719919	—	2	2	no	—
549	#11719919	C₂×D₄	1	4	yes	—
550	#11719919	C₂×D₄	1	4	yes	—
551	C₄×Dic₅₃	—	2	2	no	—
552	C₄×Dic₅₃	—	2	2	no	—
553	C₄×Dic₅₃	—	2	2	no	—
554	C₄×Dic₅₃	—	2	2	no	—
555	C₄×Dic₅₃	—	2	2	no	—
556	C₄×Dic₅₃	—	2	2	no	—
557	C₄×Dic₅₃	—	2	2	no	—
558	C₄×Dic₅₃	—	2	2	no	—
559	C₄×Dic₅₃	—	2	2	no	—
560	C₄×Dic₅₃	—	2	2	no	—
561	C₄×Dic₅₃	—	2	2	no	—
562	C₄×Dic₅₃	—	2	2	no	—
563	C₄×Dic₅₃	—	2	2	no	—
564	C₄×Dic₅₃	—	2	2	no	—
565	C₄×Dic₅₃	—	2	2	no	—
566	C₂³×C₅₃	—	2	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
574	C₂²×D₅₃	—	2	1	no	—
575	C₂²×D₅₃	—	2	1	no	—
576	C₂²×D₅₃	—	2	1	no	—
577	C₂²×D₅₃	—	2	1	no	—
578	C₂²×D₅₃	—	2	1	no	—
579	C₂²×D₅₃	—	2	1	no	—
580	C₂²×D₅₃	—	2	1	no	—
581	C₂²×D₅₃	—	4	4	no	—
582	C₂²×D₅₃	—	4	4	no	—
583	C₂²×D₅₃	—	4	4	no	—
584	C₂²×D₅₃	—	4	4	no	—
585	C₂²×D₅₃	—	4	4	no	—
586	C₂²×D₅₃	—	4	4	no	—
587	C₂²×D₅₃	—	4	4	no	—
588	C₂²×D₅₃	C₂²×D₄	1	2	yes	—
589	C₂²×D₅₃	C₂×#41	1	2	yes	—
590	C₂²×D₅₃	C₂×#41	1	2	yes	—
591	C₂²×D₅₃	C₂×#41	1	2	yes	—
592	C₂²×D₅₃	C₂×#41	1	2	yes	—
593	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
594	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
595	Q₈×C₅₃	—	2	8	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
632	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
633	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
634	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
635	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
636	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
637	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
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	—	2	1	no	—
648	C₂×Dic₅₃	—	2	1	no	—
649	C₂×Dic₅₃	—	2	1	no	—
650	C₂×Dic₅₃	—	2	1	no	—
651	C₂×Dic₅₃	—	2	1	no	—
652	C₂×Dic₅₃	—	2	1	no	—
653	C₂×Dic₅₃	—	2	1	no	—
654	C₂×Dic₅₃	—	2	1	no	—
655	C₂×Dic₅₃	—	2	1	no	—
656	C₂×Dic₅₃	—	2	1	no	—
657	C₂×Dic₅₃	—	2	1	no	—
658	C₂×Dic₅₃	—	2	1	no	—
659	C₂×Dic₅₃	—	2	1	no	—
660	C₂×Dic₅₃	—	2	1	no	—
661	C₂×Dic₅₃	—	2	1	no	—
662	C₂×Dic₅₃	—	2	1	no	—
663	C₂×Dic₅₃	—	2	1	no	—
664	C₂×Dic₅₃	—	2	1	no	—
665	C₂×Dic₅₃	—	2	1	no	—
666	C₂×Dic₅₃	—	2	1	no	—
667	C₂×Dic₅₃	—	2	1	no	—
668	C₂×Dic₅₃	—	2	1	no	—
669	C₂×Dic₅₃	—	2	1	no	—
670	C₂×Dic₅₃	—	2	1	no	—
671	C₂×Dic₅₃	—	2	1	no	—
672	C₂×Dic₅₃	—	2	1	no	—
673	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
674	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
675	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
676	C₂×Dic₅₃	C₂×#41	1	2	yes	—
677	C₂×Dic₅₃	C₂×#41	1	2	yes	—
678	C₂×Dic₅₃	C₂×#41	1	2	yes	—
679	C₂×Dic₅₃	C₂×#41	1	2	yes	—
680	C₄×D₅₃	—	2	8	no	—
681	C₄×D₅₃	—	2	8	no	—
682	C₄×D₅₃	—	2	8	no	—
683	C₄×D₅₃	—	2	8	no	—
684	C₄×D₅₃	—	2	8	no	—
685	C₄×D₅₃	—	2	8	no	—
686	C₄×D₅₃	—	2	8	no	—
687	C₄×D₅₃	—	4	4	no	—
688	C₄×D₅₃	—	4	4	no	—
689	C₄×D₅₃	—	4	4	no	—
690	C₄×D₅₃	—	4	4	no	—
691	C₄×D₅₃	—	4	4	no	—
692	C₄×D₅₃	—	4	4	no	—
693	C₄×D₅₃	—	4	4	no	—
694	Dic₁₀₆	—	2	8	no	—
695	Dic₁₀₆	—	2	8	no	—
696	Dic₁₀₆	—	2	8	no	—
697	C₂×#2469	—	53	1	no	maximal, Sylow
698	C₂²×C₅₃	—	4	1	no	—
699	C₂²×C₅₃	—	4	1	no	—
700	C₂²×C₅₃	—	4	1	no	—
701	C₂²×C₅₃	—	4	1	no	—
702	C₂²×C₅₃	—	4	1	no	—
703	C₂²×C₅₃	—	4	1	no	—
704	C₂²×C₅₃	—	4	1	no	—
705	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
706	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
707	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
708	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
709	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
710	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
711	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
712	C₂×D₅₃	—	4	1	no	—
713	C₂×D₅₃	—	4	1	no	—
714	C₂×D₅₃	—	4	1	no	—
715	C₂×D₅₃	—	4	1	no	—
716	C₂×D₅₃	—	4	1	no	—
717	C₂×D₅₃	—	4	1	no	—
718	C₂×D₅₃	—	4	1	no	—
719	C₂×D₅₃	—	8	8	no	—
720	C₂×D₅₃	#525	1	4	yes	—
721	C₂×D₅₃	#529	1	4	yes	—
722	C₂×D₅₃	#541	1	4	yes	—
723	C₂×D₅₃	#547	1	4	yes	—
724	C₂×D₅₃	#548	1	4	yes	—
725	C₂×D₅₃	#556	1	4	yes	—
726	C₂×D₅₃	#556	1	4	yes	—
727	C₄×C₅₃	—	2	2	no	—
728	C₄×C₅₃	—	2	2	no	—
729	C₄×C₅₃	—	2	2	no	—
730	C₄×C₅₃	—	2	2	no	—
731	C₄×C₅₃	—	2	2	no	—
732	C₄×C₅₃	—	2	2	no	—
733	C₄×C₅₃	—	2	2	no	—
734	C₄×C₅₃	—	4	1	no	—
735	C₄×C₅₃	—	4	1	no	—
736	C₄×C₅₃	—	4	1	no	—
737	C₄×C₅₃	—	4	1	no	—
738	C₄×C₅₃	—	4	1	no	—
739	C₄×C₅₃	—	4	1	no	—
740	C₄×C₅₃	—	4	1	no	—
741	Dic₅₃	—	2	2	no	—
742	Dic₅₃	—	2	2	no	—
743	Dic₅₃	—	2	2	no	—
744	Dic₅₃	—	2	2	no	—
745	Dic₅₃	—	2	2	no	—
746	Dic₅₃	—	2	2	no	—
747	Dic₅₃	—	2	2	no	—
748	Dic₅₃	—	4	1	no	—
749	Dic₅₃	—	4	1	no	—
750	Dic₅₃	—	4	1	no	—
751	Dic₅₃	—	4	1	no	—
752	Dic₅₃	—	4	1	no	—
753	Dic₅₃	—	4	1	no	—
754	Dic₅₃	—	4	1	no	—
755	C₂²×#126	—	53	1	no	—
756	C₂²×C₄×Q₈	—	53	1	no	—
757	#2469	—	53	1	no	—
758	#2469	—	53	1	no	—
759	#2469	—	53	1	no	—
760	#2469	—	53	1	no	—
761	#2469	—	53	1	no	—
762	#2469	—	53	1	no	—
763	#2469	—	53	1	no	—
764	#2469	—	53	1	no	—
765	#2469	—	53	1	no	—
766	#2469	—	53	1	no	—
767	#2469	—	53	1	no	—
768	#2469	—	53	1	no	—
769	#2469	—	53	1	no	—
770	#2469	—	53	1	no	—
771	#2469	—	53	1	no	—
772	#2469	D₅₃	1	1	yes	characteristic, direct product factor
773	C₂×#400	—	53	1	no	—
774	C₂×#396	—	53	1	no	—
775	C₂×#395	—	53	1	no	—
776	C₂×#393	—	53	1	no	—
777	C₂×#389	—	53	1	no	—
778	C₂×#388	—	53	1	no	—
779	C₂×#388	—	53	1	no	—
780	C₂×#388	—	53	1	no	—
781	C₂×#388	—	53	1	no	—
782	C₂×#387	—	53	1	no	—
783	C₂×#387	—	53	1	no	—
784	C₂×#387	—	53	1	no	—
785	C₂×C₄×C₄⋊C₄	—	53	1	no	—
786	C₂×C₅₃	—	8	1	no	—
787	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
788	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
789	C₂×C₅₃	C₂×#541	1	1	yes	characteristic
790	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
791	C₂×C₅₃	C₂×#548	1	1	yes	characteristic
792	C₂×C₅₃	C₂×#556	1	1	yes	characteristic
793	C₂×C₅₃	C₂×#556	1	1	yes	characteristic
794	D₅₃	—	8	1	no	—
795	D₅₃	#2469	1	8	yes	direct product factor
796	C₂³×Q₈	—	53	1	no	—
797	C₂×#126	—	53	1	no	—
798	C₂×#126	—	53	1	no	—
799	C₂×#126	—	53	1	no	—
800	C₂×#126	—	53	1	no	—
801	C₂×#126	—	53	1	no	—
802	C₂×#126	—	53	1	no	—
803	C₂×#126	—	53	1	no	—
804	C₂×#126	—	106	8	no	—
805	C₂×#126	C₂×D₅₃	1	1	yes	characteristic
806	C₂×C₄×Q₈	—	53	1	no	—
807	C₂×C₄×Q₈	—	53	1	no	—
808	C₂×C₄×Q₈	—	53	1	no	—
809	C₂×C₄×Q₈	—	53	1	no	—
810	C₂×C₄×Q₈	—	53	1	no	—
811	C₂×C₄×Q₈	—	53	1	no	—
812	C₂×C₄×Q₈	—	53	1	no	—
813	C₂×C₄×Q₈	—	106	8	no	—
814	C₂×C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
815	C₂²×C₄⋊C₄	—	53	1	no	—
816	C₂²×C₄⋊C₄	—	53	1	no	—
817	C₂²×C₄⋊C₄	—	53	1	no	—
818	C₂²×C₄⋊C₄	—	53	1	no	—
819	C₂²×C₄⋊C₄	—	53	1	no	—
820	C₂²×C₄⋊C₄	—	53	1	no	—
821	C₂²×C₄⋊C₄	—	53	1	no	—
822	C₂²×C₄⋊C₄	—	53	1	no	—
823	C₂²×C₄⋊C₄	—	53	1	no	—
824	C₂²×C₄⋊C₄	—	53	1	no	—
825	C₂²×C₂²⋊C₄	—	53	1	no	—
826	C₂²×C₂²⋊C₄	—	53	1	no	—
827	C₂²×C₂²⋊C₄	—	53	1	no	—
828	C₂²×C₂²⋊C₄	—	53	1	no	—
829	C₂²×C₂²⋊C₄	—	53	1	no	—
830	C₂²×C₂²⋊C₄	—	53	1	no	—
831	C₂²×C₂²⋊C₄	—	53	1	no	—
832	C₂²×C₄²	—	53	1	no	—
833	C₂²×C₄²	—	53	1	no	—
834	C₂²×C₄²	—	53	1	no	—
835	C₂²×C₄²	—	53	1	no	—
836	C₂²×C₄²	—	53	1	no	—
837	#400	—	53	1	no	—
838	#400	—	53	1	no	—
839	#400	—	53	1	no	—
840	#400	—	53	1	no	—
841	#400	—	53	1	no	—
842	#400	—	53	1	no	—
843	#400	—	53	1	no	—
844	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
845	#396	—	53	1	no	—
846	#396	—	53	1	no	—
847	#396	—	53	1	no	—
848	#396	—	53	1	no	—
849	#396	—	53	1	no	—
850	#396	—	53	1	no	—
851	#396	—	53	1	no	—
852	#396	C₂×D₅₃	1	1	yes	characteristic
853	#395	—	53	1	no	—
854	#395	—	53	1	no	—
855	#395	—	53	1	no	—
856	#395	—	53	1	no	—
857	#395	—	53	1	no	—
858	#395	—	53	1	no	—
859	#395	—	53	1	no	—
860	#395	C₂×D₅₃	1	1	yes	characteristic, complemented
861	#393	—	53	1	no	—
862	#393	—	53	1	no	—
863	#393	—	53	1	no	—
864	#393	—	53	1	no	—
865	#393	—	53	1	no	—
866	#393	—	53	1	no	—
867	#393	—	53	1	no	—
868	#393	C₂×D₅₃	1	1	yes	characteristic
869	#389	—	53	1	no	—
870	#389	—	53	1	no	—
871	#389	—	53	1	no	—
872	#389	—	53	1	no	—
873	#389	—	53	1	no	—
874	#389	—	53	1	no	—
875	#389	—	53	1	no	—
876	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
877	#388	—	53	1	no	—
878	#388	—	53	1	no	—
879	#388	—	53	1	no	—
880	#388	—	53	1	no	—
881	#388	—	53	1	no	—
882	#388	—	53	1	no	—
883	#388	—	53	1	no	—
884	#388	—	53	1	no	—
885	#388	—	53	1	no	—
886	#388	—	53	1	no	—
887	#388	—	53	1	no	—
888	#388	—	53	1	no	—
889	#388	—	53	1	no	—
890	#388	—	53	1	no	—
891	#388	—	53	1	no	—
892	#388	—	53	1	no	—
893	#388	—	53	1	no	—
894	#388	—	53	1	no	—
895	#388	—	53	1	no	—
896	#388	—	53	1	no	—
897	#388	—	53	1	no	—
898	#388	—	53	1	no	—
899	#388	—	53	1	no	—
900	#388	—	53	1	no	—
901	#388	—	53	1	no	—
902	#388	—	53	1	no	—
903	#388	—	53	1	no	—
904	#388	—	53	1	no	—
905	#388	C₂×D₅₃	1	1	yes	characteristic
906	#388	C₂×D₅₃	1	1	yes	characteristic
907	#388	C₂×D₅₃	1	1	yes	characteristic
908	#388	C₂×D₅₃	1	1	yes	characteristic
909	#387	—	53	1	no	—
910	#387	—	53	1	no	—
911	#387	—	53	1	no	—
912	#387	—	53	1	no	—
913	#387	—	53	1	no	—
914	#387	—	53	1	no	—
915	#387	—	53	1	no	—
916	#387	—	53	1	no	—
917	#387	—	53	1	no	—
918	#387	—	53	1	no	—
919	#387	—	53	1	no	—
920	#387	—	53	1	no	—
921	#387	—	53	1	no	—
922	#387	—	53	1	no	—
923	#387	—	53	1	no	—
924	#387	—	53	1	no	—
925	#387	—	53	1	no	—
926	#387	—	53	1	no	—
927	#387	—	53	1	no	—
928	#387	—	53	1	no	—
929	#387	—	53	1	no	—
930	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
931	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
932	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
933	C₄×C₄⋊C₄	—	53	1	no	—
934	C₄×C₄⋊C₄	—	53	1	no	—
935	C₄×C₄⋊C₄	—	53	1	no	—
936	C₄×C₄⋊C₄	—	53	1	no	—
937	C₄×C₄⋊C₄	—	53	1	no	—
938	C₄×C₄⋊C₄	—	53	1	no	—
939	C₄×C₄⋊C₄	—	53	1	no	—
940	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
941	C₂×#95	—	53	1	no	—
942	C₂×#95	—	53	1	no	—
943	C₂×#95	—	53	1	no	—
944	C₂×#95	—	53	1	no	—
945	C₂×#95	—	53	1	no	—
946	C₂×#95	—	53	1	no	—
947	C₂×#95	—	53	1	no	—
948	C₂×#95	—	53	1	no	—
949	C₂×#95	—	53	1	no	—
950	C₂×#95	—	53	1	no	—
951	C₂×#95	—	53	1	no	—
952	C₂×#95	—	53	1	no	—
953	C₅₃	C₂×#2469	1	1	yes	characteristic, complemented, Sylow
954	C₂⁵	—	53	1	no	—
955	C₂²×Q₈	—	53	1	no	—
956	C₂²×Q₈	—	53	1	no	—
957	C₂²×Q₈	—	53	1	no	—
958	C₂²×Q₈	—	106	4	no	—
959	C₂²×Q₈	—	106	4	no	—
960	C₂²×Q₈	—	106	4	no	—
961	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
962	C₂³×C₄	—	53	1	no	—
963	C₂³×C₄	—	53	1	no	—
964	C₂³×C₄	—	53	1	no	—
965	C₂³×C₄	—	53	1	no	—
966	C₂³×C₄	—	53	1	no	—
967	C₂³×C₄	—	53	1	no	—
968	C₂³×C₄	—	53	1	no	—
969	C₂³×C₄	—	53	1	no	—
970	C₂³×C₄	—	53	1	no	—
971	C₂³×C₄	—	53	1	no	—
972	C₂³×C₄	—	53	1	no	—
973	C₂³×C₄	—	53	1	no	—
974	C₂³×C₄	—	53	1	no	—
975	C₂³×C₄	—	53	1	no	—
976	#126	—	2	4	no	—
977	#126	—	106	4	no	—
978	#126	—	106	4	no	—
979	#126	—	106	4	no	—
980	#126	—	106	4	no	—
981	#126	—	106	4	no	—
982	#126	—	106	4	no	—
983	#126	—	106	4	no	—
984	C₄×Q₈	—	2	4	no	—
985	C₄×Q₈	—	106	4	no	—
986	C₄×Q₈	—	106	4	no	—
987	C₄×Q₈	—	106	4	no	—
988	C₄×Q₈	—	106	4	no	—
989	C₄×Q₈	—	106	4	no	—
990	C₄×Q₈	—	106	4	no	—
991	C₄×Q₈	—	106	4	no	—
992	C₂×C₄⋊C₄	—	53	1	no	—
993	C₂×C₄⋊C₄	—	53	1	no	—
994	C₂×C₄⋊C₄	—	53	1	no	—
995	C₂×C₄⋊C₄	—	53	8	no	—
996	C₂×C₄⋊C₄	—	53	1	no	—
997	C₂×C₄⋊C₄	—	53	1	no	—
998	C₂×C₄⋊C₄	—	53	1	no	—
999	C₂×C₄⋊C₄	—	53	1	no	—
1000	C₂×C₄⋊C₄	—	53	1	no	—
1001	C₂×C₄⋊C₄	—	53	1	no	—
1002	C₂×C₄⋊C₄	—	53	1	no	—
1003	C₂×C₄⋊C₄	—	53	1	no	—
1004	C₂×C₄⋊C₄	—	53	1	no	—
1005	C₂×C₄⋊C₄	—	53	1	no	—
1006	C₂×C₄⋊C₄	—	53	1	no	—
1007	C₂×C₄⋊C₄	—	53	1	no	—
1008	C₂×C₄⋊C₄	—	53	1	no	—
1009	C₂×C₄⋊C₄	—	53	1	no	—
1010	C₂×C₄⋊C₄	—	53	1	no	—
1011	C₂×C₄⋊C₄	—	53	1	no	—
1012	C₂×C₄⋊C₄	—	53	1	no	—
1013	C₂×C₄⋊C₄	—	53	1	no	—
1014	C₂×C₄⋊C₄	—	53	1	no	—
1015	C₂×C₄⋊C₄	—	53	1	no	—
1016	C₂×C₄⋊C₄	—	53	1	no	—
1017	C₂×C₄⋊C₄	—	53	1	no	—
1018	C₂×C₄⋊C₄	—	53	1	no	—
1019	C₂×C₄⋊C₄	—	53	1	no	—
1020	C₂×C₄⋊C₄	—	53	1	no	—
1021	C₂×C₄⋊C₄	—	53	1	no	—
1022	C₂×C₄⋊C₄	—	53	1	no	—
1023	C₂×C₄⋊C₄	—	106	4	no	—
1024	C₂×C₄⋊C₄	—	106	4	no	—
1025	C₂×C₄⋊C₄	—	106	4	no	—
1026	C₂×C₄⋊C₄	—	106	4	no	—
1027	C₂×C₄⋊C₄	—	106	4	no	—
1028	C₂×C₄⋊C₄	—	106	4	no	—
1029	C₂×C₄⋊C₄	—	106	4	no	—
1030	C₂×C₄⋊C₄	—	106	4	no	—
1031	C₂×C₄⋊C₄	—	106	4	no	—
1032	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1033	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1034	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1035	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1036	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1037	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1038	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	—	53	1	no	—
1043	C₂×C₂²⋊C₄	—	53	1	no	—
1044	C₂×C₂²⋊C₄	—	53	1	no	—
1045	C₂×C₂²⋊C₄	—	53	1	no	—
1046	C₂×C₂²⋊C₄	—	53	1	no	—
1047	C₂×C₂²⋊C₄	—	53	1	no	—
1048	C₂×C₂²⋊C₄	—	53	1	no	—
1049	C₂×C₂²⋊C₄	—	53	1	no	—
1050	C₂×C₂²⋊C₄	—	53	1	no	—
1051	C₂×C₂²⋊C₄	—	53	1	no	—
1052	C₂×C₂²⋊C₄	—	53	1	no	—
1053	C₂×C₂²⋊C₄	—	53	1	no	—
1054	C₂×C₂²⋊C₄	—	53	1	no	—
1055	C₂×C₂²⋊C₄	—	53	1	no	—
1056	C₂×C₂²⋊C₄	—	53	1	no	—
1057	C₂×C₂²⋊C₄	—	53	1	no	—
1058	C₂×C₂²⋊C₄	—	53	1	no	—
1059	C₂×C₂²⋊C₄	—	53	1	no	—
1060	C₂×C₂²⋊C₄	—	53	1	no	—
1061	C₂×C₂²⋊C₄	—	53	1	no	—
1062	C₂×C₂²⋊C₄	—	53	1	no	—
1063	C₂×C₂²⋊C₄	—	106	4	no	—
1064	C₂×C₂²⋊C₄	—	106	4	no	—
1065	C₂×C₂²⋊C₄	—	106	4	no	—
1066	C₂×C₂²⋊C₄	—	106	4	no	—
1067	C₂×C₂²⋊C₄	—	106	4	no	—
1068	C₂×C₂²⋊C₄	—	106	4	no	—
1069	C₂×C₂²⋊C₄	—	106	4	no	—
1070	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1076	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1077	C₂×C₄²	—	53	1	no	—
1078	C₂×C₄²	—	53	1	no	—
1079	C₂×C₄²	—	53	1	no	—
1080	C₂×C₄²	—	53	1	no	—
1081	C₂×C₄²	—	53	1	no	—
1082	C₂×C₄²	—	53	1	no	—
1083	C₂×C₄²	—	53	1	no	—
1084	C₂×C₄²	—	53	1	no	—
1085	C₂×C₄²	—	53	1	no	—
1086	C₂×C₄²	—	53	1	no	—
1087	C₂×C₄²	—	53	1	no	—
1088	C₂×C₄²	—	53	1	no	—
1089	C₂×C₄²	—	53	1	no	—
1090	C₂×C₄²	—	53	1	no	—
1091	C₂×C₄²	—	53	1	no	—
1092	C₂×C₄²	—	106	4	no	—
1093	C₂×C₄²	—	106	4	no	—
1094	C₂×C₄²	—	106	4	no	—
1095	C₂×C₄²	—	106	4	no	—
1096	C₂×C₄²	—	106	4	no	—
1097	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1098	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1099	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1100	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1101	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1102	#95	—	53	1	no	—
1103	#95	—	53	1	no	—
1104	#95	—	53	1	no	—
1105	#95	—	53	1	no	—
1106	#95	—	53	1	no	—
1107	#95	—	53	1	no	—
1108	#95	—	53	1	no	—
1109	#95	—	53	1	no	—
1110	#95	—	53	1	no	—
1111	#95	—	53	1	no	—
1112	#95	—	53	1	no	—
1113	#95	—	53	1	no	—
1114	#95	—	53	1	no	—
1115	#95	—	53	1	no	—
1116	#95	—	53	1	no	—
1117	#95	—	53	1	no	—
1118	#95	—	53	1	no	—
1119	#95	—	53	1	no	—
1120	#95	—	53	1	no	—
1121	#95	—	53	1	no	—
1122	#95	—	53	1	no	—
1123	#95	—	53	1	no	—
1124	#95	—	53	1	no	—
1125	#95	—	53	1	no	—
1126	#95	—	53	1	no	—
1127	#95	—	53	1	no	—
1128	#95	—	53	1	no	—
1129	#95	—	53	1	no	—
1130	#95	—	53	1	no	—
1131	#95	—	53	1	no	—
1132	#95	—	53	1	no	—
1133	#95	—	53	1	no	—
1134	#95	—	53	1	no	—
1135	#95	—	53	1	no	—
1136	#95	—	53	1	no	—
1137	#95	—	53	1	no	—
1138	#95	C₂²×D₅₃	1	1	yes	characteristic
1139	#95	C₂²×D₅₃	1	1	yes	characteristic
1140	#95	C₂²×D₅₃	1	1	yes	characteristic
1141	#95	C₂²×D₅₃	1	1	yes	characteristic
1142	#95	C₂²×D₅₃	1	1	yes	characteristic
1143	#95	C₂²×D₅₃	1	1	yes	characteristic
1144	#95	C₂²×D₅₃	1	1	yes	characteristic
1145	#95	C₂²×D₅₃	1	1	yes	characteristic
1146	#95	C₂²×D₅₃	1	1	yes	characteristic
1147	#95	C₂²×D₅₃	1	1	yes	characteristic
1148	#95	C₂²×D₅₃	1	1	yes	characteristic
1149	#95	C₂²×D₅₃	1	1	yes	characteristic
1150	C₂⁴	—	53	1	no	—
1151	C₂⁴	—	53	1	no	—
1152	C₂⁴	—	106	2	no	—
1153	C₂⁴	—	106	2	no	—
1154	C₂⁴	—	106	2	no	—
1155	C₂⁴	—	106	2	no	—
1156	C₂⁴	—	106	2	no	—
1157	C₂⁴	—	106	2	no	—
1158	C₂⁴	—	106	2	no	—
1159	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1160	C₂×Q₈	—	2	2	no	—
1161	C₂×Q₈	—	2	2	no	—
1162	C₂×Q₈	—	2	2	no	—
1163	C₂×Q₈	—	106	2	no	—
1164	C₂×Q₈	—	106	2	no	—
1165	C₂×Q₈	—	106	2	no	—
1166	C₂×Q₈	—	106	2	no	—
1167	C₂×Q₈	—	106	2	no	—
1168	C₂×Q₈	—	106	2	no	—
1169	C₂×Q₈	—	106	32	no	—
1170	C₂×Q₈	—	106	2	no	—
1171	C₂×Q₈	—	106	2	no	—
1172	C₂×Q₈	—	106	2	no	—
1173	C₂²×C₄	—	53	1	no	—
1174	C₂²×C₄	—	53	1	no	—
1175	C₂²×C₄	—	53	1	no	—
1176	C₂²×C₄	—	53	1	no	—
1177	C₂²×C₄	—	53	1	no	—
1178	C₂²×C₄	—	53	1	no	—
1179	C₂²×C₄	—	53	1	no	—
1180	C₂²×C₄	—	53	4	no	—
1181	C₂²×C₄	—	53	4	no	—
1182	C₂²×C₄	—	53	4	no	—
1183	C₂²×C₄	—	53	4	no	—
1184	C₂²×C₄	—	53	4	no	—
1185	C₂²×C₄	—	53	4	no	—
1186	C₂²×C₄	—	53	4	no	—
1187	C₂²×C₄	—	53	1	no	—
1188	C₂²×C₄	—	53	1	no	—
1189	C₂²×C₄	—	53	1	no	—
1190	C₂²×C₄	—	53	1	no	—
1191	C₂²×C₄	—	53	1	no	—
1192	C₂²×C₄	—	53	1	no	—
1193	C₂²×C₄	—	53	1	no	—
1194	C₂²×C₄	—	106	2	no	—
1195	C₂²×C₄	—	106	2	no	—
1196	C₂²×C₄	—	106	2	no	—
1197	C₂²×C₄	—	106	2	no	—
1198	C₂²×C₄	—	106	2	no	—
1199	C₂²×C₄	—	106	2	no	—
1200	C₂²×C₄	—	106	2	no	—
1201	C₂²×C₄	—	106	2	no	—
1202	C₂²×C₄	—	106	2	no	—
1203	C₂²×C₄	—	106	2	no	—
1204	C₂²×C₄	—	106	2	no	—
1205	C₂²×C₄	—	106	2	no	—
1206	C₂²×C₄	—	106	2	no	—
1207	C₂²×C₄	—	106	2	no	—
1208	C₂²×C₄	—	106	2	no	—
1209	C₂²×C₄	—	106	2	no	—
1210	C₂²×C₄	—	106	2	no	—
1211	C₂²×C₄	—	106	2	no	—
1212	C₂²×C₄	—	106	2	no	—
1213	C₂²×C₄	—	106	2	no	—
1214	C₂²×C₄	—	106	2	no	—
1215	C₂²×C₄	—	106	2	no	—
1216	C₂²×C₄	—	106	2	no	—
1217	C₂²×C₄	—	106	2	no	—
1218	C₂²×C₄	—	106	2	no	—
1219	C₂²×C₄	—	106	2	no	—
1220	C₂²×C₄	—	106	2	no	—
1221	C₂²×C₄	—	106	2	no	—
1222	C₂²×C₄	—	106	2	no	—
1223	C₂²×C₄	—	106	2	no	—
1224	C₂²×C₄	—	106	2	no	—
1225	C₂²×C₄	—	106	2	no	—
1226	C₂²×C₄	—	106	2	no	—
1227	C₂²×C₄	—	106	2	no	—
1228	C₂²×C₄	—	106	2	no	—
1229	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1230	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1231	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1232	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1233	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1234	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1235	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1236	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1237	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1238	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1239	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1240	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1241	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1242	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1243	C₄⋊C₄	—	2	2	no	—
1244	C₄⋊C₄	—	2	2	no	—
1245	C₄⋊C₄	—	2	2	no	—
1246	C₄⋊C₄	—	2	2	no	—
1247	C₄⋊C₄	—	2	2	no	—
1248	C₄⋊C₄	—	2	2	no	—
1249	C₄⋊C₄	—	2	2	no	—
1250	C₄⋊C₄	—	2	2	no	—
1251	C₄⋊C₄	—	2	2	no	—
1252	C₄⋊C₄	—	53	4	no	—
1253	C₄⋊C₄	—	53	4	no	—
1254	C₄⋊C₄	—	53	4	no	—
1255	C₄⋊C₄	—	106	2	no	—
1256	C₄⋊C₄	—	106	2	no	—
1257	C₄⋊C₄	—	106	2	no	—
1258	C₄⋊C₄	—	106	2	no	—
1259	C₄⋊C₄	—	106	2	no	—
1260	C₄⋊C₄	—	106	2	no	—
1261	C₄⋊C₄	—	106	2	no	—
1262	C₄⋊C₄	—	106	2	no	—
1263	C₄⋊C₄	—	106	2	no	—
1264	C₄⋊C₄	—	106	2	no	—
1265	C₄⋊C₄	—	106	2	no	—
1266	C₄⋊C₄	—	106	2	no	—
1267	C₄⋊C₄	—	106	2	no	—
1268	C₄⋊C₄	—	106	2	no	—
1269	C₄⋊C₄	—	106	2	no	—
1270	C₄⋊C₄	—	106	2	no	—
1271	C₄⋊C₄	—	106	2	no	—
1272	C₄⋊C₄	—	106	2	no	—
1273	C₄⋊C₄	—	106	2	no	—
1274	C₄⋊C₄	—	106	2	no	—
1275	C₄⋊C₄	—	106	2	no	—
1276	C₄⋊C₄	—	106	2	no	—
1277	C₄⋊C₄	—	106	2	no	—
1278	C₄⋊C₄	—	106	2	no	—
1279	C₄⋊C₄	—	106	2	no	—
1280	C₄⋊C₄	—	106	2	no	—
1281	C₄⋊C₄	—	106	2	no	—
1282	C₄⋊C₄	D₄×D₅₃	1	4	yes	—
1283	C₂²⋊C₄	—	2	2	no	—
1284	C₂²⋊C₄	—	2	2	no	—
1285	C₂²⋊C₄	—	2	2	no	—
1286	C₂²⋊C₄	—	2	2	no	—
1287	C₂²⋊C₄	—	2	2	no	—
1288	C₂²⋊C₄	—	2	2	no	—
1289	C₂²⋊C₄	—	2	2	no	—
1290	C₂²⋊C₄	—	106	2	no	—
1291	C₂²⋊C₄	—	106	2	no	—
1292	C₂²⋊C₄	—	106	2	no	—
1293	C₂²⋊C₄	—	106	2	no	—
1294	C₂²⋊C₄	—	106	2	no	—
1295	C₂²⋊C₄	—	106	2	no	—
1296	C₂²⋊C₄	—	106	2	no	—
1297	C₂²⋊C₄	—	106	2	no	—
1298	C₂²⋊C₄	—	106	2	no	—
1299	C₂²⋊C₄	—	106	2	no	—
1300	C₂²⋊C₄	—	106	2	no	—
1301	C₂²⋊C₄	—	106	2	no	—
1302	C₂²⋊C₄	—	106	2	no	—
1303	C₂²⋊C₄	—	106	2	no	—
1304	C₂²⋊C₄	—	106	2	no	—
1305	C₂²⋊C₄	—	106	2	no	—
1306	C₂²⋊C₄	—	106	2	no	—
1307	C₂²⋊C₄	—	106	2	no	—
1308	C₂²⋊C₄	—	106	2	no	—
1309	C₂²⋊C₄	—	106	2	no	—
1310	C₂²⋊C₄	—	106	2	no	—
1311	C₄²	—	2	2	no	—
1312	C₄²	—	2	2	no	—
1313	C₄²	—	2	2	no	—
1314	C₄²	—	2	2	no	—
1315	C₄²	—	2	2	no	—
1316	C₄²	—	106	2	no	—
1317	C₄²	—	106	2	no	—
1318	C₄²	—	106	2	no	—
1319	C₄²	—	106	2	no	—
1320	C₄²	—	106	2	no	—
1321	C₄²	—	106	2	no	—
1322	C₄²	—	106	2	no	—
1323	C₄²	—	106	2	no	—
1324	C₄²	—	106	2	no	—
1325	C₄²	—	106	2	no	—
1326	C₄²	—	106	2	no	—
1327	C₄²	—	106	2	no	—
1328	C₄²	—	106	2	no	—
1329	C₄²	—	106	2	no	—
1330	C₄²	—	106	2	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	—	2	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	1	no	—
1336	C₂³	—	2	1	no	—
1337	C₂³	—	2	1	no	—
1338	C₂³	—	53	2	no	—
1339	C₂³	—	53	2	no	—
1340	C₂³	—	53	2	no	—
1341	C₂³	—	53	2	no	—
1342	C₂³	—	53	2	no	—
1343	C₂³	—	53	2	no	—
1344	C₂³	—	53	2	no	—
1345	C₂³	—	106	1	no	—
1346	C₂³	—	106	1	no	—
1347	C₂³	—	106	1	no	—
1348	C₂³	—	106	1	no	—
1349	C₂³	—	106	1	no	—
1350	C₂³	—	106	1	no	—
1351	C₂³	—	106	1	no	—
1352	C₂³	—	212	4	no	—
1353	C₂³	—	212	4	no	—
1354	C₂³	—	212	4	no	—
1355	C₂³	—	212	4	no	—
1356	C₂³	—	212	4	no	—
1357	C₂³	—	212	4	no	—
1358	C₂³	—	212	4	no	—
1359	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1360	Q₈	—	2	8	no	—
1361	Q₈	—	106	8	no	—
1362	Q₈	—	106	8	no	—
1363	Q₈	—	106	8	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	53	2	no	—
1400	C₂×C₄	—	53	2	no	—
1401	C₂×C₄	—	53	2	no	—
1402	C₂×C₄	—	53	2	no	—
1403	C₂×C₄	—	53	2	no	—
1404	C₂×C₄	—	53	2	no	—
1405	C₂×C₄	—	53	2	no	—
1406	C₂×C₄	—	106	8	no	—
1407	C₂×C₄	—	106	8	no	—
1408	C₂×C₄	—	106	8	no	—
1409	C₂×C₄	—	106	8	no	—
1410	C₂×C₄	—	106	8	no	—
1411	C₂×C₄	—	106	8	no	—
1412	C₂×C₄	—	106	8	no	—
1413	C₂×C₄	—	106	1	no	—
1414	C₂×C₄	—	106	1	no	—
1415	C₂×C₄	—	106	1	no	—
1416	C₂×C₄	—	106	1	no	—
1417	C₂×C₄	—	106	1	no	—
1418	C₂×C₄	—	106	1	no	—
1419	C₂×C₄	—	106	1	no	—
1420	C₂×C₄	—	106	1	no	—
1421	C₂×C₄	—	106	1	no	—
1422	C₂×C₄	—	106	1	no	—
1423	C₂×C₄	—	106	1	no	—
1424	C₂×C₄	—	106	1	no	—
1425	C₂×C₄	—	106	1	no	—
1426	C₂×C₄	—	106	1	no	—
1427	C₂×C₄	—	106	1	no	—
1428	C₂×C₄	—	106	1	no	—
1429	C₂×C₄	—	106	1	no	—
1430	C₂×C₄	—	106	1	no	—
1431	C₂×C₄	—	106	1	no	—
1432	C₂×C₄	—	106	1	no	—
1433	C₂×C₄	—	106	1	no	—
1434	C₂×C₄	—	106	1	no	—
1435	C₂×C₄	—	106	1	no	—
1436	C₂×C₄	—	106	1	no	—
1437	C₂×C₄	—	106	1	no	—
1438	C₂×C₄	—	106	1	no	—
1439	C₂×C₄	—	106	1	no	—
1440	C₂×C₄	—	106	1	no	—
1441	C₂×C₄	—	106	1	no	—
1442	C₂×C₄	—	106	1	no	—
1443	C₂×C₄	—	106	1	no	—
1444	C₂×C₄	—	106	1	no	—
1445	C₂×C₄	—	106	1	no	—
1446	C₂×C₄	—	106	1	no	—
1447	C₂×C₄	—	106	1	no	—
1448	C₂×C₄	—	212	4	no	—
1449	C₂×C₄	—	212	4	no	—
1450	C₂×C₄	—	212	4	no	—
1451	C₂×C₄	—	212	4	no	—
1452	C₂×C₄	—	212	4	no	—
1453	C₂×C₄	—	212	4	no	—
1454	C₂×C₄	—	212	4	no	—
1455	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1456	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1457	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1458	C₂×C₄	#41×D₅₃	1	2	yes	—
1459	C₂×C₄	#41×D₅₃	1	2	yes	—
1460	C₂×C₄	#41×D₅₃	1	2	yes	—
1461	C₂×C₄	#41×D₅₃	1	2	yes	—
1462	C₂²	—	4	1	no	—
1463	C₂²	—	4	1	no	—
1464	C₂²	—	4	1	no	—
1465	C₂²	—	4	1	no	—
1466	C₂²	—	4	1	no	—
1467	C₂²	—	4	1	no	—
1468	C₂²	—	4	1	no	—
1469	C₂²	—	53	4	no	—
1470	C₂²	—	53	4	no	—
1471	C₂²	—	53	4	no	—
1472	C₂²	—	53	4	no	—
1473	C₂²	—	53	4	no	—
1474	C₂²	—	53	4	no	—
1475	C₂²	—	53	4	no	—
1476	C₂²	—	424	8	no	—
1477	C₂²	—	212	1	no	—
1478	C₂²	—	212	1	no	—
1479	C₂²	—	212	1	no	—
1480	C₂²	—	212	1	no	—
1481	C₂²	—	212	1	no	—
1482	C₂²	—	212	1	no	—
1483	C₂²	—	212	1	no	—
1484	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1485	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1486	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1487	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1488	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1489	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1490	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1491	C₄	—	2	2	no	—
1492	C₄	—	2	2	no	—
1493	C₄	—	2	2	no	—
1494	C₄	—	2	2	no	—
1495	C₄	—	2	2	no	—
1496	C₄	—	2	2	no	—
1497	C₄	—	2	2	no	—
1498	C₄	—	4	1	no	—
1499	C₄	—	4	1	no	—
1500	C₄	—	4	1	no	—
1501	C₄	—	4	1	no	—
1502	C₄	—	4	1	no	—
1503	C₄	—	4	1	no	—
1504	C₄	—	4	1	no	—
1505	C₄	—	106	2	no	—
1506	C₄	—	106	2	no	—
1507	C₄	—	106	2	no	—
1508	C₄	—	106	2	no	—
1509	C₄	—	106	2	no	—
1510	C₄	—	106	2	no	—
1511	C₄	—	106	2	no	—
1512	C₄	—	212	1	no	—
1513	C₄	—	212	1	no	—
1514	C₄	—	212	1	no	—
1515	C₄	—	212	1	no	—
1516	C₄	—	212	1	no	—
1517	C₄	—	212	1	no	—
1518	C₄	—	212	1	no	—
1519	C₂	—	8	1	no	—
1520	C₂	—	53	8	no	—
1521	C₂	—	424	1	no	—
1522	C₂	#525×D₅₃	1	1	yes	characteristic
1523	C₂	#529×D₅₃	1	1	yes	characteristic
1524	C₂	#541×D₅₃	1	1	yes	characteristic
1525	C₂	#547×D₅₃	1	1	yes	characteristic
1526	C₂	#548×D₅₃	1	1	yes	characteristic
1527	C₂	#556×D₅₃	1	1	yes	characteristic
1528	C₂	#556×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2469	C₂
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2469	D₅₃
hypocenter	C₅₃	C₂×#2469
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2469

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₈×D₅₃	C₂	semidirect
3. #20278803	C₂	semidirect
4. #20278802	C₂	semidirect
5. #20278801	C₂	semidirect
6. #20278800	C₂	semidirect
7. #20278799	C₂	semidirect
8. #20278798	C₂	semidirect
9. #20278797	C₂	semidirect
10. #20278796	C₂	semidirect
11. #20278795	C₂	semidirect
12. #20278794	C₂	semidirect
13. #20278793	C₂	semidirect
14. #20278792	C₂	semidirect
15. #20278791	C₂	semidirect
16. #20278790	C₂	semidirect
17. #20278789	C₂	semidirect
18. #400×D₅₃	C₂	semidirect
20. #395×D₅₃	C₂	semidirect
22. #389×D₅₃	C₂	semidirect
27. #387×D₅₃	C₂	semidirect
28. #387×D₅₃	C₂	semidirect
29. #387×D₅₃	C₂	semidirect
30. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2469	C₂	semidirect
41. C₂×Q₈×Dic₅₃	C₂²	semidirect
42. C₂×C₄×Dic₁₀₆	C₂²	semidirect
43. C₂×C₄×Dic₁₀₆	C₂²	semidirect
44. C₂×C₄×Dic₁₀₆	C₂²	semidirect
45. C₂×#13133182	C₂²	semidirect
46. C₂×#13133182	C₂²	semidirect
47. C₂×#13133182	C₂²	semidirect
71. #16810565	C₂²	semidirect
72. #16810565	C₂²	semidirect
73. #16810564	C₂²	semidirect
74. #16810564	C₂²	semidirect
75. #16810563	C₂²	semidirect
76. #16810562	C₂²	semidirect
77. #16810561	C₂²	semidirect
85. #16810544	C₂²	semidirect
86. #16810544	C₂²	semidirect
87. #16810544	C₂²	semidirect
88. #16810543	C₂²	semidirect
89. #16810543	C₂²	semidirect
90. #16810543	C₂²	semidirect
91. #16810542	C₂²	semidirect
99. #16810522	C₂²	semidirect
100. #16810521	C₂²	semidirect
101. #16810520	C₂²	semidirect
102. #16810520	C₂²	semidirect
103. #16810519	C₂²	semidirect
104. #16810518	C₂²	semidirect
105. #16810518	C₂²	semidirect
134. #16810510	C₂²	semidirect
135. #16810510	C₂²	semidirect
136. #16810510	C₂²	semidirect
137. #16810509	C₂²	semidirect
138. #16810509	C₂²	semidirect
139. #16810509	C₂²	semidirect
140. #16810508	C₂²	semidirect
141. #16810508	C₂²	semidirect
142. #16810508	C₂²	semidirect
143. #16810507	C₂²	semidirect
144. #16810507	C₂²	semidirect
145. #16810507	C₂²	semidirect
146. #16810506	C₂²	semidirect
147. #16810506	C₂²	semidirect
148. #16810506	C₂²	semidirect
149. #16810505	C₂²	semidirect
150. #16810505	C₂²	semidirect
151. #16810505	C₂²	semidirect
152. #16810504	C₂²	semidirect
153. #16810504	C₂²	semidirect
154. #16810504	C₂²	semidirect
155. C₄⋊C₄×Dic₅₃	C₂²	semidirect
156. C₄⋊C₄×Dic₅₃	C₂²	semidirect
157. C₄×#11719919	C₂²	semidirect
158. C₄×#11719919	C₂²	semidirect
159. C₄×C₄⋊Dic₅₃	C₂²	semidirect
160. #16810474	C₂²	semidirect
161. #16810474	C₂²	semidirect
175. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
176. C₅₃×#400	C₂²	semidirect
178. C₅₃×#395	C₂²	semidirect
180. C₅₃×#389	C₂²	semidirect
185. C₅₃×#387	C₂²	semidirect
186. C₅₃×#387	C₂²	semidirect
187. C₅₃×#387	C₂²	semidirect
188. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
772. #2469	D₅₃	direct (N × H)
795. D₅₃	#2469	direct (N × H)
814. C₂×C₄×Q₈	C₂×D₅₃	semidirect
844. #400	C₂×D₅₃	semidirect
860. #395	C₂×D₅₃	semidirect
876. #389	C₂×D₅₃	semidirect
930. #387	C₂×D₅₃	semidirect
931. #387	C₂×D₅₃	semidirect
932. #387	C₂×D₅₃	semidirect
940. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
953. C₅₃	C₂×#2469	semidirect

Maximal subgroups

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

subgroup	index
C₂×#126×D₅₃	2
C₂×C₄×Q₈×D₅₃	2
#20278803	2
#20278802	2
#20278801	2
#20278800	2
#20278799	2
#20278798	2
#20278797	2
#20278796	2
#20278795	2
#20278794	2
#20278793	2
#20278792	2
#20278791	2
#20278790	2
#20278789	2
#400×D₅₃	2
#396×D₅₃	2
#395×D₅₃	2
#393×D₅₃	2
#389×D₅₃	2
#388×D₅₃	2
#387×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₅₃×#2469	2
C₂×#2469	53

Subgroups — D53×#2469 #27552294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2469 #27552294