Subgroups — D₅₃×#2589 #27554383

Order 13568.

2334 conjugacy classes of subgroups.

The subgroup lattice has 1504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20280173	C₂	1	1	yes	maximal, characteristic, complemented
2	#20280172	C₂	1	1	yes	maximal, characteristic, complemented
3	#20280171	C₂	1	1	yes	maximal, characteristic, complemented
4	#20280170	C₂	1	1	yes	maximal, characteristic, complemented
5	#20280169	C₂	1	1	yes	maximal, characteristic, complemented
6	#20280168	C₂	1	1	yes	maximal, characteristic, complemented
7	#20280167	C₂	1	1	yes	maximal, characteristic, complemented
8	#20280166	C₂	1	1	yes	maximal, characteristic, complemented
9	#20280165	C₂	1	1	yes	maximal, characteristic, complemented
10	#20280164	C₂	1	1	yes	maximal, characteristic, complemented
11	#20280163	C₂	1	1	yes	maximal, characteristic, complemented
12	#20280162	C₂	1	1	yes	maximal, characteristic, complemented
13	#20280161	C₂	1	1	yes	maximal, characteristic, complemented
14	#20280160	C₂	1	1	yes	maximal, characteristic, complemented
15	#20280159	C₂	1	1	yes	maximal, characteristic, complemented
16	#400×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#399×D₅₃	C₂	1	1	yes	maximal, characteristic
18	#398×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#393×D₅₃	C₂	1	1	yes	maximal, characteristic
20	#391×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#391×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
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	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
26	#387×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	#385×D₅₃	C₂	1	1	yes	maximal, characteristic
28	#385×D₅₃	C₂	1	1	yes	maximal, characteristic
29	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×C₂²⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2589	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
53	#16810565	C₂²	1	1	yes	characteristic, complemented
54	#16810565	C₂²	1	1	yes	characteristic, complemented
55	#16810564	C₂²	1	1	yes	characteristic, complemented
56	#16810564	C₂²	1	1	yes	characteristic, complemented
57	#16810563	C₂²	1	1	yes	characteristic, complemented
58	#16810562	C₂²	1	1	yes	characteristic, complemented
59	#16810561	C₂²	1	1	yes	characteristic, complemented
60	#16810560	C₂²	1	1	yes	characteristic
61	#16810559	C₂²	1	1	yes	characteristic
62	#16810559	C₂²	1	1	yes	characteristic
63	#16810559	C₂²	1	1	yes	characteristic
64	#16810558	C₂²	1	1	yes	characteristic
65	#16810558	C₂²	1	1	yes	characteristic
66	#16810558	C₂²	1	1	yes	characteristic
67	#16810557	C₂²	1	1	yes	characteristic, complemented
68	#16810557	C₂²	1	1	yes	characteristic, complemented
69	#16810556	C₂²	1	1	yes	characteristic, complemented
70	#16810556	C₂²	1	1	yes	characteristic, complemented
71	#16810555	C₂²	1	1	yes	characteristic, complemented
72	#16810554	C₂²	1	1	yes	characteristic, complemented
73	#16810553	C₂²	1	1	yes	characteristic, complemented
74	#16810536	C₂²	1	1	yes	characteristic
75	#16810536	C₂²	1	1	yes	characteristic
76	#16810536	C₂²	1	1	yes	characteristic
77	#16810535	C₂²	1	1	yes	characteristic
78	#16810535	C₂²	1	1	yes	characteristic
79	#16810535	C₂²	1	1	yes	characteristic
80	#16810534	C₂²	1	1	yes	characteristic
81	#16810530	C₂²	1	1	yes	characteristic, complemented
82	#16810530	C₂²	1	1	yes	characteristic, complemented
83	#16810529	C₂²	1	1	yes	characteristic, complemented
84	#16810529	C₂²	1	1	yes	characteristic, complemented
85	#16810528	C₂²	1	1	yes	characteristic, complemented
86	#16810528	C₂²	1	1	yes	characteristic, complemented
87	#16810527	C₂²	1	1	yes	characteristic, complemented
88	#16810527	C₂²	1	1	yes	characteristic, complemented
89	#16810527	C₂²	1	1	yes	characteristic, complemented
90	#16810527	C₂²	1	1	yes	characteristic, complemented
91	#16810527	C₂²	1	1	yes	characteristic, complemented
92	#16810527	C₂²	1	1	yes	characteristic, complemented
93	#16810527	C₂²	1	1	yes	characteristic, complemented
94	#16810527	C₂²	1	1	yes	characteristic, complemented
95	#16810522	C₂²	1	1	yes	characteristic, complemented
96	#16810521	C₂²	1	1	yes	characteristic, complemented
97	#16810520	C₂²	1	1	yes	characteristic, complemented
98	#16810520	C₂²	1	1	yes	characteristic, complemented
99	#16810519	C₂²	1	1	yes	characteristic, complemented
100	#16810518	C₂²	1	1	yes	characteristic, complemented
101	#16810518	C₂²	1	1	yes	characteristic, complemented
102	#16810517	C₂²	1	1	yes	characteristic
103	#16810517	C₂²	1	1	yes	characteristic
104	#16810516	C₂²	1	1	yes	characteristic
105	#16810516	C₂²	1	1	yes	characteristic
106	#16810515	C₂²	1	1	yes	characteristic
107	#16810515	C₂²	1	1	yes	characteristic
108	#16810514	C₂²	1	1	yes	characteristic
109	#16810514	C₂²	1	1	yes	characteristic
110	#16810513	C₂²	1	1	yes	characteristic
111	#16810513	C₂²	1	1	yes	characteristic
112	#16810512	C₂²	1	1	yes	characteristic
113	#16810512	C₂²	1	1	yes	characteristic
114	#16810511	C₂²	1	1	yes	characteristic
115	#16810511	C₂²	1	1	yes	characteristic
116	#16810510	C₂²	1	1	yes	characteristic, complemented
117	#16810510	C₂²	1	1	yes	characteristic, complemented
118	#16810509	C₂²	1	1	yes	characteristic, complemented
119	#16810509	C₂²	1	1	yes	characteristic, complemented
120	#16810508	C₂²	1	1	yes	characteristic, complemented
121	#16810508	C₂²	1	1	yes	characteristic, complemented
122	#16810507	C₂²	1	1	yes	characteristic, complemented
123	#16810507	C₂²	1	1	yes	characteristic, complemented
124	#16810506	C₂²	1	1	yes	characteristic, complemented
125	#16810506	C₂²	1	1	yes	characteristic, complemented
126	#16810505	C₂²	1	1	yes	characteristic, complemented
127	#16810505	C₂²	1	1	yes	characteristic, complemented
128	#16810504	C₂²	1	1	yes	characteristic, complemented
129	#16810504	C₂²	1	1	yes	characteristic, complemented
130	#16810498	C₂²	1	1	yes	characteristic
131	#16810498	C₂²	1	1	yes	characteristic
132	#16810497	C₂²	1	1	yes	characteristic
133	#16810497	C₂²	1	1	yes	characteristic
134	#16810497	C₂²	1	1	yes	characteristic
135	#16810497	C₂²	1	1	yes	characteristic
136	#16810496	C₂²	1	1	yes	characteristic
137	#16810496	C₂²	1	1	yes	characteristic
138	#16810495	C₂²	1	1	yes	characteristic
139	#16810495	C₂²	1	1	yes	characteristic
140	#16810494	C₂²	1	1	yes	characteristic
141	#16810494	C₂²	1	1	yes	characteristic
142	#16810494	C₂²	1	1	yes	characteristic
143	#16810494	C₂²	1	1	yes	characteristic
144	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
145	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
146	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
147	C₄×#11719919	C₂²	1	1	yes	characteristic, complemented
148	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
149	#16810474	C₂²	1	1	yes	characteristic, complemented
150	#16810474	C₂²	1	1	yes	characteristic, complemented
151	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
152	C₂²⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
153	C₄×#11719921	C₂²	1	1	yes	characteristic
154	C₄×#11719921	C₂²	1	1	yes	characteristic
155	C₄×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic
156	#16810470	C₂²	1	1	yes	characteristic
157	#16810470	C₂²	1	1	yes	characteristic
158	#95×D₅₃	C₂²	1	1	yes	characteristic
159	#95×D₅₃	C₂²	1	1	yes	characteristic
160	#95×D₅₃	C₂²	1	1	yes	characteristic
161	#95×D₅₃	C₂²	1	1	yes	characteristic
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	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#399	C₂²	1	1	yes	characteristic
174	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#393	C₂²	1	1	yes	characteristic
176	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#388	C₂²	1	1	yes	characteristic
180	C₅₃×#388	C₂²	1	1	yes	characteristic
181	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#385	C₂²	1	1	yes	characteristic
184	C₅₃×#385	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂⁴×D₅₃	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	C₂×Q₈×D₅₃	—	2	4	no	—
192	C₂×Q₈×D₅₃	—	2	4	no	—
193	C₂×Q₈×D₅₃	—	4	2	no	—
194	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	—	2	4	no	—
196	C₂²×C₄×D₅₃	—	4	2	no	—
197	C₂²×C₄×D₅₃	—	4	2	no	—
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	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
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×#11719919	C₂³	1	1	yes	characteristic
224	C₂×#11719919	C₂³	1	1	yes	characteristic
225	C₂×#11719919	C₂³	1	1	yes	characteristic
226	C₂×#11719919	C₂³	1	1	yes	characteristic
227	C₂×#11719919	C₂³	1	1	yes	characteristic
228	C₂×#11719919	C₂³	1	1	yes	characteristic
229	C₂×#11719919	C₂³	1	1	yes	characteristic
230	C₂×#11719919	C₂³	1	1	yes	characteristic
231	C₂×#11719919	C₂³	1	1	yes	characteristic
232	C₂×#11719919	C₂³	1	1	yes	characteristic
233	C₂×#11719919	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	C₄⋊C₄×D₅₃	—	2	4	no	—
242	C₄⋊C₄×D₅₃	—	2	4	no	—
243	C₄⋊C₄×D₅₃	—	2	4	no	—
244	C₄⋊C₄×D₅₃	—	2	4	no	—
245	C₄⋊C₄×D₅₃	—	2	4	no	—
246	C₄⋊C₄×D₅₃	—	4	2	no	—
247	C₄⋊C₄×D₅₃	—	4	2	no	—
248	C₄⋊C₄×D₅₃	—	4	2	no	—
249	C₄⋊C₄×D₅₃	—	4	2	no	—
250	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	1	yes	characteristic
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	1	yes	characteristic
259	C₂×#11719921	C₂³	1	1	yes	characteristic
260	C₂×#11719921	C₂³	1	1	yes	characteristic
261	C₂×#11719921	C₂³	1	1	yes	characteristic
262	C₂×#11719921	C₂³	1	1	yes	characteristic
263	C₂×#11719921	C₂³	1	1	yes	characteristic
264	C₂×#11719921	C₂³	1	1	yes	characteristic
265	C₂×#11719921	C₂³	1	1	yes	characteristic
266	C₂×#11719921	C₂³	1	1	yes	characteristic
267	C₂×#11719921	C₂³	1	1	yes	characteristic
268	C₂²⋊C₄×D₅₃	—	2	4	no	—
269	C₂²⋊C₄×D₅₃	—	2	4	no	—
270	C₂²⋊C₄×D₅₃	—	2	4	no	—
271	C₂²⋊C₄×D₅₃	—	4	2	no	—
272	C₂²⋊C₄×D₅₃	—	4	2	no	—
273	C₂²⋊C₄×D₅₃	Q₈	1	8	yes	complemented
274	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄×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	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
286	C₄²×D₅₃	—	2	4	no	—
287	C₄²×D₅₃	—	4	2	no	—
288	C₄²×D₅₃	—	4	2	no	—
289	C₄²×D₅₃	—	4	2	no	—
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	#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	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
333	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄⋊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	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂³×D₅₃	—	2	2	no	—
369	C₂³×D₅₃	—	2	2	no	—
370	C₂³×D₅₃	—	2	2	no	—
371	C₂³×D₅₃	—	2	2	no	—
372	C₂³×D₅₃	—	2	2	no	—
373	C₂³×D₅₃	—	2	2	no	—
374	C₂³×D₅₃	C₂×Q₈	1	4	yes	—
375	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
376	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
377	C₂×Q₈×C₅₃	—	2	2	no	—
378	C₂×Q₈×C₅₃	—	2	2	no	—
379	C₂×Q₈×C₅₃	—	4	1	no	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	4	1	no	—
382	C₂²×C₄×C₅₃	—	4	1	no	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂²×Dic₅₃	—	2	2	no	—
398	C₂²×Dic₅₃	—	4	1	no	—
399	C₂²×Dic₅₃	—	4	1	no	—
400	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
414	Q₈×D₅₃	—	4	16	no	—
415	C₂×C₄×D₅₃	—	2	2	no	—
416	C₂×C₄×D₅₃	—	2	2	no	—
417	C₂×C₄×D₅₃	—	2	2	no	—
418	C₂×C₄×D₅₃	—	2	2	no	—
419	C₂×C₄×D₅₃	—	2	2	no	—
420	C₂×C₄×D₅₃	—	2	2	no	—
421	C₂×C₄×D₅₃	—	2	2	no	—
422	C₂×C₄×D₅₃	—	2	2	no	—
423	C₂×C₄×D₅₃	—	2	2	no	—
424	C₂×C₄×D₅₃	—	2	2	no	—
425	C₂×C₄×D₅₃	—	2	2	no	—
426	C₂×C₄×D₅₃	—	2	2	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	—	4	16	no	—
454	C₂×C₄×D₅₃	—	4	1	no	—
455	C₂×C₄×D₅₃	—	4	1	no	—
456	C₂×C₄×D₅₃	—	4	1	no	—
457	C₂×C₄×D₅₃	—	4	1	no	—
458	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
459	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
460	C₂×C₄×D₅₃	#41	1	4	yes	—
461	C₂×C₄×D₅₃	#41	1	4	yes	—
462	C₂×C₄×D₅₃	#41	1	4	yes	—
463	C₂×C₄×D₅₃	#41	1	4	yes	—
464	C₂×Dic₁₀₆	—	2	2	no	—
465	C₂×Dic₁₀₆	—	2	2	no	—
466	C₂×Dic₁₀₆	—	2	2	no	—
467	C₂×Dic₁₀₆	—	2	2	no	—
468	C₂×Dic₁₀₆	—	2	2	no	—
469	C₂×Dic₁₀₆	—	2	2	no	—
470	C₂×Dic₁₀₆	—	4	1	no	—
471	C₂×Dic₁₀₆	—	4	1	no	—
472	C₂×Dic₁₀₆	—	4	1	no	—
473	C₄⋊C₄×C₅₃	—	2	2	no	—
474	C₄⋊C₄×C₅₃	—	2	2	no	—
475	C₄⋊C₄×C₅₃	—	2	2	no	—
476	C₄⋊C₄×C₅₃	—	2	2	no	—
477	C₄⋊C₄×C₅₃	—	2	2	no	—
478	C₄⋊C₄×C₅₃	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	4	1	no	—
480	C₄⋊C₄×C₅₃	—	4	1	no	—
481	C₄⋊C₄×C₅₃	—	4	1	no	—
482	C₂²⋊C₄×C₅₃	—	2	2	no	—
483	C₂²⋊C₄×C₅₃	—	2	2	no	—
484	C₂²⋊C₄×C₅₃	—	2	2	no	—
485	C₂²⋊C₄×C₅₃	—	4	1	no	—
486	C₂²⋊C₄×C₅₃	—	4	1	no	—
487	C₂²⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
488	C₄²×C₅₃	—	2	2	no	—
489	C₄²×C₅₃	—	4	1	no	—
490	C₄²×C₅₃	—	4	1	no	—
491	C₄²×C₅₃	—	4	1	no	—
492	C₂²⋊Dic₅₃	—	2	2	no	—
493	C₂²⋊Dic₅₃	—	2	2	no	—
494	C₂²⋊Dic₅₃	—	2	2	no	—
495	C₂²⋊Dic₅₃	—	4	1	no	—
496	C₂²⋊Dic₅₃	—	4	1	no	—
497	C₂²⋊Dic₅₃	C₂×Q₈	1	4	yes	complemented
498	#11719921	—	2	2	no	—
499	#11719921	—	2	2	no	—
500	#11719921	—	2	2	no	—
501	#11719921	—	2	2	no	—
502	#11719921	—	2	2	no	—
503	#11719921	—	2	2	no	—
504	#11719921	—	4	1	no	—
505	#11719921	—	4	1	no	—
506	#11719921	—	4	1	no	—
507	#11719921	—	4	1	no	—
508	#11719921	C₂×Q₈	1	4	yes	complemented
509	#11719921	C₂×Q₈	1	4	yes	complemented
510	C₄⋊Dic₅₃	—	2	2	no	—
511	C₄⋊Dic₅₃	—	2	2	no	—
512	C₄⋊Dic₅₃	—	2	2	no	—
513	C₄⋊Dic₅₃	—	2	2	no	—
514	C₄⋊Dic₅₃	—	2	2	no	—
515	C₄⋊Dic₅₃	—	4	1	no	—
516	C₄⋊Dic₅₃	—	4	1	no	—
517	C₄⋊Dic₅₃	—	4	1	no	—
518	C₄⋊Dic₅₃	—	4	1	no	—
519	#11719919	—	2	2	no	—
520	#11719919	—	2	2	no	—
521	#11719919	—	2	2	no	—
522	#11719919	—	2	2	no	—
523	#11719919	—	2	2	no	—
524	#11719919	—	2	2	no	—
525	#11719919	—	2	2	no	—
526	#11719919	—	2	2	no	—
527	#11719919	—	2	2	no	—
528	#11719919	—	2	2	no	—
529	#11719919	—	4	1	no	—
530	#11719919	—	4	1	no	—
531	#11719919	—	4	1	no	—
532	#11719919	—	4	1	no	—
533	#11719919	—	4	1	no	—
534	#11719919	—	4	1	no	—
535	#11719919	—	4	1	no	—
536	#11719919	—	4	1	no	—
537	C₄×Dic₅₃	—	2	2	no	—
538	C₄×Dic₅₃	—	2	2	no	—
539	C₄×Dic₅₃	—	2	2	no	—
540	C₄×Dic₅₃	—	4	1	no	—
541	C₄×Dic₅₃	—	4	1	no	—
542	C₄×Dic₅₃	—	4	1	no	—
543	C₄×Dic₅₃	—	4	1	no	—
544	C₄×Dic₅₃	—	4	1	no	—
545	C₄×Dic₅₃	—	4	1	no	—
546	C₄×Dic₅₃	—	4	1	no	—
547	C₄×Dic₅₃	—	4	1	no	—
548	C₄×Dic₅₃	—	4	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	1	no	—
553	C₂³×C₅₃	—	2	1	no	—
554	C₂³×C₅₃	—	2	1	no	—
555	C₂³×C₅₃	C₂²×Q₈	1	2	yes	—
556	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
557	C₂²×D₅₃	—	2	1	no	—
558	C₂²×D₅₃	—	2	1	no	—
559	C₂²×D₅₃	—	2	1	no	—
560	C₂²×D₅₃	—	2	1	no	—
561	C₂²×D₅₃	—	2	1	no	—
562	C₂²×D₅₃	—	2	1	no	—
563	C₂²×D₅₃	—	2	8	no	—
564	C₂²×D₅₃	—	2	8	no	—
565	C₂²×D₅₃	—	2	8	no	—
566	C₂²×D₅₃	—	4	4	no	—
567	C₂²×D₅₃	—	4	4	no	—
568	C₂²×D₅₃	—	4	4	no	—
569	C₂²×D₅₃	—	4	4	no	—
570	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
571	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
572	C₂²×D₅₃	C₂×#41	1	2	yes	—
573	C₂²×D₅₃	C₂×#41	1	2	yes	—
574	C₂²×D₅₃	C₂×#41	1	2	yes	—
575	C₂²×D₅₃	C₂×#41	1	2	yes	—
576	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
577	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
578	Q₈×C₅₃	—	4	4	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	—	2	1	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	—	4	4	no	—
616	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
617	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
618	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
619	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
620	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
621	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
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	—	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	—	4	4	no	—
659	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
660	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
661	C₂×Dic₅₃	C₂×#41	1	2	yes	—
662	C₂×Dic₅₃	C₂×#41	1	2	yes	—
663	C₂×Dic₅₃	C₂×#41	1	2	yes	—
664	C₂×Dic₅₃	C₂×#41	1	2	yes	—
665	C₄×D₅₃	—	2	8	no	—
666	C₄×D₅₃	—	2	8	no	—
667	C₄×D₅₃	—	2	8	no	—
668	C₄×D₅₃	—	2	8	no	—
669	C₄×D₅₃	—	2	8	no	—
670	C₄×D₅₃	—	2	8	no	—
671	C₄×D₅₃	—	4	4	no	—
672	C₄×D₅₃	—	4	4	no	—
673	C₄×D₅₃	—	4	4	no	—
674	C₄×D₅₃	—	4	4	no	—
675	C₄×D₅₃	—	4	4	no	—
676	C₄×D₅₃	—	4	4	no	—
677	C₄×D₅₃	—	4	4	no	—
678	C₄×D₅₃	—	4	4	no	—
679	C₄×D₅₃	—	4	4	no	—
680	C₄×D₅₃	—	4	4	no	—
681	Dic₁₀₆	—	4	4	no	—
682	Dic₁₀₆	—	4	4	no	—
683	Dic₁₀₆	—	4	4	no	—
684	C₂×#2589	—	53	1	no	maximal, Sylow
685	C₂²×C₅₃	—	2	2	no	—
686	C₂²×C₅₃	—	2	2	no	—
687	C₂²×C₅₃	—	2	2	no	—
688	C₂²×C₅₃	—	4	1	no	—
689	C₂²×C₅₃	—	4	1	no	—
690	C₂²×C₅₃	—	4	1	no	—
691	C₂²×C₅₃	—	4	1	no	—
692	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
693	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
694	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
695	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
696	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
697	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
698	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
699	C₂×D₅₃	—	2	2	no	—
700	C₂×D₅₃	—	2	2	no	—
701	C₂×D₅₃	—	2	2	no	—
702	C₂×D₅₃	—	4	1	no	—
703	C₂×D₅₃	—	4	1	no	—
704	C₂×D₅₃	—	4	1	no	—
705	C₂×D₅₃	—	4	1	no	—
706	C₂×D₅₃	—	4	16	no	—
707	C₂×D₅₃	#529	1	4	yes	—
708	C₂×D₅₃	#533	1	4	yes	—
709	C₂×D₅₃	#538	1	4	yes	—
710	C₂×D₅₃	#551	1	4	yes	—
711	C₂×D₅₃	#554	1	4	yes	—
712	C₂×D₅₃	#554	1	4	yes	—
713	C₂×D₅₃	#559	1	4	yes	—
714	C₄×C₅₃	—	2	2	no	—
715	C₄×C₅₃	—	2	2	no	—
716	C₄×C₅₃	—	2	2	no	—
717	C₄×C₅₃	—	2	2	no	—
718	C₄×C₅₃	—	2	2	no	—
719	C₄×C₅₃	—	2	2	no	—
720	C₄×C₅₃	—	4	1	no	—
721	C₄×C₅₃	—	4	1	no	—
722	C₄×C₅₃	—	4	1	no	—
723	C₄×C₅₃	—	4	1	no	—
724	C₄×C₅₃	—	4	1	no	—
725	C₄×C₅₃	—	4	1	no	—
726	C₄×C₅₃	—	4	1	no	—
727	C₄×C₅₃	—	4	1	no	—
728	Dic₅₃	—	2	2	no	—
729	Dic₅₃	—	2	2	no	—
730	Dic₅₃	—	2	2	no	—
731	Dic₅₃	—	2	2	no	—
732	Dic₅₃	—	2	2	no	—
733	Dic₅₃	—	2	2	no	—
734	Dic₅₃	—	4	1	no	—
735	Dic₅₃	—	4	1	no	—
736	Dic₅₃	—	4	1	no	—
737	Dic₅₃	—	4	1	no	—
738	Dic₅₃	—	4	1	no	—
739	Dic₅₃	—	4	1	no	—
740	Dic₅₃	—	4	1	no	—
741	Dic₅₃	—	4	1	no	—
742	#2589	—	53	1	no	—
743	#2589	—	53	1	no	—
744	#2589	—	53	1	no	—
745	#2589	—	53	1	no	—
746	#2589	—	53	1	no	—
747	#2589	—	53	1	no	—
748	#2589	—	53	1	no	—
749	#2589	—	53	1	no	—
750	#2589	—	53	1	no	—
751	#2589	—	53	1	no	—
752	#2589	—	53	1	no	—
753	#2589	—	53	1	no	—
754	#2589	—	53	1	no	—
755	#2589	—	53	1	no	—
756	#2589	—	53	1	no	—
757	#2589	D₅₃	1	1	yes	characteristic, direct product factor
758	C₂×#400	—	53	1	no	—
759	C₂×#399	—	53	1	no	—
760	C₂×#398	—	53	1	no	—
761	C₂×#393	—	53	1	no	—
762	C₂×#391	—	53	1	no	—
763	C₂×#391	—	53	1	no	—
764	C₂×#389	—	53	1	no	—
765	C₂×#388	—	53	1	no	—
766	C₂×#388	—	53	1	no	—
767	C₂×#387	—	53	1	no	—
768	C₂×#387	—	53	1	no	—
769	C₂×#385	—	53	1	no	—
770	C₂×#385	—	53	1	no	—
771	C₂×C₄×C₄⋊C₄	—	53	1	no	—
772	C₂×C₄×C₂²⋊C₄	—	53	1	no	—
773	C₂×C₅₃	—	4	2	no	—
774	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
775	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
776	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
777	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
778	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
779	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
780	C₂×C₅₃	C₂×#559	1	1	yes	characteristic
781	D₅₃	—	4	2	no	—
782	D₅₃	#2589	1	8	yes	direct product factor
783	C₂³×Q₈	—	53	1	no	—
784	C₂⁴×C₄	—	53	1	no	—
785	C₂²×C₄⋊C₄	—	53	1	no	—
786	C₂²×C₄⋊C₄	—	53	1	no	—
787	C₂²×C₄⋊C₄	—	53	1	no	—
788	C₂²×C₄⋊C₄	—	53	1	no	—
789	C₂²×C₄⋊C₄	—	53	1	no	—
790	C₂²×C₄⋊C₄	—	53	1	no	—
791	C₂²×C₄⋊C₄	—	53	1	no	—
792	C₂²×C₄⋊C₄	—	53	1	no	—
793	C₂²×C₄⋊C₄	—	53	1	no	—
794	C₂²×C₂²⋊C₄	—	53	1	no	—
795	C₂²×C₂²⋊C₄	—	53	1	no	—
796	C₂²×C₂²⋊C₄	—	53	1	no	—
797	C₂²×C₂²⋊C₄	—	53	1	no	—
798	C₂²×C₂²⋊C₄	—	53	1	no	—
799	C₂²×C₂²⋊C₄	—	53	1	no	—
800	C₂²×C₄²	—	53	1	no	—
801	C₂²×C₄²	—	53	1	no	—
802	C₂²×C₄²	—	53	1	no	—
803	C₂²×C₄²	—	53	1	no	—
804	#400	—	53	1	no	—
805	#400	—	53	1	no	—
806	#400	—	53	1	no	—
807	#400	—	53	1	no	—
808	#400	—	53	1	no	—
809	#400	—	53	1	no	—
810	#400	—	53	1	no	—
811	#400	C₂×D₅₃	1	1	yes	characteristic, complemented
812	#399	—	53	1	no	—
813	#399	—	53	1	no	—
814	#399	—	53	1	no	—
815	#399	—	53	1	no	—
816	#399	—	53	1	no	—
817	#399	—	53	1	no	—
818	#399	—	53	1	no	—
819	#399	C₂×D₅₃	1	1	yes	characteristic
820	#398	—	53	1	no	—
821	#398	—	53	1	no	—
822	#398	—	53	1	no	—
823	#398	—	53	1	no	—
824	#398	—	53	1	no	—
825	#398	—	53	1	no	—
826	#398	—	53	1	no	—
827	#398	C₂×D₅₃	1	1	yes	characteristic, complemented
828	#393	—	53	1	no	—
829	#393	—	53	1	no	—
830	#393	—	53	1	no	—
831	#393	—	53	1	no	—
832	#393	—	53	1	no	—
833	#393	—	53	1	no	—
834	#393	—	53	1	no	—
835	#393	C₂×D₅₃	1	1	yes	characteristic
836	#391	—	53	1	no	—
837	#391	—	53	1	no	—
838	#391	—	53	1	no	—
839	#391	—	53	1	no	—
840	#391	—	53	1	no	—
841	#391	—	53	1	no	—
842	#391	—	53	1	no	—
843	#391	—	53	1	no	—
844	#391	—	53	1	no	—
845	#391	—	53	1	no	—
846	#391	—	53	1	no	—
847	#391	—	53	1	no	—
848	#391	—	53	1	no	—
849	#391	—	53	1	no	—
850	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
851	#391	C₂×D₅₃	1	1	yes	characteristic, complemented
852	#389	—	53	1	no	—
853	#389	—	53	1	no	—
854	#389	—	53	1	no	—
855	#389	—	53	1	no	—
856	#389	—	53	1	no	—
857	#389	—	53	1	no	—
858	#389	—	53	1	no	—
859	#389	C₂×D₅₃	1	1	yes	characteristic, complemented
860	#388	—	53	1	no	—
861	#388	—	53	1	no	—
862	#388	—	53	1	no	—
863	#388	—	53	1	no	—
864	#388	—	53	1	no	—
865	#388	—	53	1	no	—
866	#388	—	53	1	no	—
867	#388	—	53	1	no	—
868	#388	—	53	1	no	—
869	#388	—	53	1	no	—
870	#388	—	53	1	no	—
871	#388	—	53	1	no	—
872	#388	—	53	1	no	—
873	#388	—	53	1	no	—
874	#388	C₂×D₅₃	1	1	yes	characteristic
875	#388	C₂×D₅₃	1	1	yes	characteristic
876	#387	—	53	1	no	—
877	#387	—	53	1	no	—
878	#387	—	53	1	no	—
879	#387	—	53	1	no	—
880	#387	—	53	1	no	—
881	#387	—	53	1	no	—
882	#387	—	53	1	no	—
883	#387	—	53	1	no	—
884	#387	—	53	1	no	—
885	#387	—	53	1	no	—
886	#387	—	53	1	no	—
887	#387	—	53	1	no	—
888	#387	—	53	1	no	—
889	#387	—	53	1	no	—
890	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
891	#387	C₂×D₅₃	1	1	yes	characteristic, complemented
892	#385	—	53	1	no	—
893	#385	—	53	1	no	—
894	#385	—	53	1	no	—
895	#385	—	53	1	no	—
896	#385	—	53	1	no	—
897	#385	—	53	1	no	—
898	#385	—	53	1	no	—
899	#385	—	53	1	no	—
900	#385	—	53	1	no	—
901	#385	—	53	1	no	—
902	#385	—	53	1	no	—
903	#385	—	53	1	no	—
904	#385	—	53	1	no	—
905	#385	—	53	1	no	—
906	#385	C₂×D₅₃	1	1	yes	characteristic
907	#385	C₂×D₅₃	1	1	yes	characteristic
908	C₄×C₄⋊C₄	—	53	1	no	—
909	C₄×C₄⋊C₄	—	53	1	no	—
910	C₄×C₄⋊C₄	—	53	1	no	—
911	C₄×C₄⋊C₄	—	53	1	no	—
912	C₄×C₄⋊C₄	—	53	1	no	—
913	C₄×C₄⋊C₄	—	53	1	no	—
914	C₄×C₄⋊C₄	—	53	1	no	—
915	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
916	C₄×C₂²⋊C₄	—	53	1	no	—
917	C₄×C₂²⋊C₄	—	53	1	no	—
918	C₄×C₂²⋊C₄	—	53	1	no	—
919	C₄×C₂²⋊C₄	—	53	1	no	—
920	C₄×C₂²⋊C₄	—	53	1	no	—
921	C₄×C₂²⋊C₄	—	53	1	no	—
922	C₄×C₂²⋊C₄	—	53	1	no	—
923	C₄×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic
924	C₂×#95	—	53	1	no	—
925	C₂×#95	—	53	1	no	—
926	C₂×#95	—	53	1	no	—
927	C₂×#95	—	53	1	no	—
928	C₂×#95	—	53	1	no	—
929	C₂×#95	—	53	1	no	—
930	C₂×#95	—	53	1	no	—
931	C₂×#95	—	53	1	no	—
932	C₂×#95	—	53	1	no	—
933	C₂×#95	—	53	1	no	—
934	C₂×#95	—	53	1	no	—
935	C₂×#95	—	53	1	no	—
936	C₂×#95	—	53	1	no	—
937	C₂×#95	—	53	1	no	—
938	C₅₃	C₂×#2589	1	1	yes	characteristic, complemented, Sylow
939	C₂⁵	—	53	1	no	—
940	C₂²×Q₈	—	53	1	no	—
941	C₂²×Q₈	—	53	1	no	—
942	C₂²×Q₈	—	53	1	no	—
943	C₂²×Q₈	—	106	4	no	—
944	C₂²×Q₈	—	106	4	no	—
945	C₂²×Q₈	—	212	2	no	—
946	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
947	C₂³×C₄	—	53	1	no	—
948	C₂³×C₄	—	53	1	no	—
949	C₂³×C₄	—	53	1	no	—
950	C₂³×C₄	—	53	1	no	—
951	C₂³×C₄	—	53	1	no	—
952	C₂³×C₄	—	53	1	no	—
953	C₂³×C₄	—	53	1	no	—
954	C₂³×C₄	—	53	1	no	—
955	C₂³×C₄	—	53	1	no	—
956	C₂³×C₄	—	53	1	no	—
957	C₂³×C₄	—	53	1	no	—
958	C₂³×C₄	—	53	1	no	—
959	C₂³×C₄	—	53	1	no	—
960	C₂³×C₄	—	53	1	no	—
961	C₂³×C₄	—	53	1	no	—
962	C₂³×C₄	—	53	1	no	—
963	C₂³×C₄	—	53	1	no	—
964	C₂³×C₄	—	106	4	no	—
965	C₂³×C₄	—	212	2	no	—
966	C₂³×C₄	—	212	2	no	—
967	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
995	C₂×C₄⋊C₄	—	106	4	no	—
996	C₂×C₄⋊C₄	—	106	4	no	—
997	C₂×C₄⋊C₄	—	106	4	no	—
998	C₂×C₄⋊C₄	—	106	4	no	—
999	C₂×C₄⋊C₄	—	106	4	no	—
1000	C₂×C₄⋊C₄	—	212	2	no	—
1001	C₂×C₄⋊C₄	—	212	2	no	—
1002	C₂×C₄⋊C₄	—	212	2	no	—
1003	C₂×C₄⋊C₄	—	212	2	no	—
1004	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1005	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	8	no	—
1017	C₂×C₂²⋊C₄	—	53	1	no	—
1018	C₂×C₂²⋊C₄	—	53	1	no	—
1019	C₂×C₂²⋊C₄	—	53	1	no	—
1020	C₂×C₂²⋊C₄	—	53	1	no	—
1021	C₂×C₂²⋊C₄	—	53	1	no	—
1022	C₂×C₂²⋊C₄	—	53	1	no	—
1023	C₂×C₂²⋊C₄	—	53	1	no	—
1024	C₂×C₂²⋊C₄	—	53	1	no	—
1025	C₂×C₂²⋊C₄	—	53	1	no	—
1026	C₂×C₂²⋊C₄	—	53	1	no	—
1027	C₂×C₂²⋊C₄	—	53	1	no	—
1028	C₂×C₂²⋊C₄	—	53	1	no	—
1029	C₂×C₂²⋊C₄	—	53	1	no	—
1030	C₂×C₂²⋊C₄	—	53	1	no	—
1031	C₂×C₂²⋊C₄	—	53	1	no	—
1032	C₂×C₂²⋊C₄	—	106	4	no	—
1033	C₂×C₂²⋊C₄	—	106	4	no	—
1034	C₂×C₂²⋊C₄	—	106	4	no	—
1035	C₂×C₂²⋊C₄	—	212	2	no	—
1036	C₂×C₂²⋊C₄	—	212	2	no	—
1037	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
1043	C₂×C₄²	—	53	1	no	—
1044	C₂×C₄²	—	53	1	no	—
1045	C₂×C₄²	—	53	1	no	—
1046	C₂×C₄²	—	53	1	no	—
1047	C₂×C₄²	—	53	1	no	—
1048	C₂×C₄²	—	53	1	no	—
1049	C₂×C₄²	—	53	1	no	—
1050	C₂×C₄²	—	53	1	no	—
1051	C₂×C₄²	—	53	1	no	—
1052	C₂×C₄²	—	53	1	no	—
1053	C₂×C₄²	—	53	1	no	—
1054	C₂×C₄²	—	53	1	no	—
1055	C₂×C₄²	—	106	4	no	—
1056	C₂×C₄²	—	212	2	no	—
1057	C₂×C₄²	—	212	2	no	—
1058	C₂×C₄²	—	212	2	no	—
1059	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1060	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1061	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
1062	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
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	—	53	1	no	—
1083	#95	—	53	1	no	—
1084	#95	—	53	1	no	—
1085	#95	—	53	1	no	—
1086	#95	—	53	1	no	—
1087	#95	—	53	1	no	—
1088	#95	—	53	1	no	—
1089	#95	—	53	1	no	—
1090	#95	—	53	1	no	—
1091	#95	—	53	1	no	—
1092	#95	—	53	1	no	—
1093	#95	—	53	1	no	—
1094	#95	—	53	1	no	—
1095	#95	—	53	1	no	—
1096	#95	—	53	1	no	—
1097	#95	—	53	1	no	—
1098	#95	—	53	1	no	—
1099	#95	—	53	1	no	—
1100	#95	—	53	1	no	—
1101	#95	—	53	1	no	—
1102	#95	—	53	1	no	—
1103	#95	—	53	1	no	—
1104	#95	—	53	1	no	—
1105	#95	C₂²×D₅₃	1	1	yes	characteristic
1106	#95	C₂²×D₅₃	1	1	yes	characteristic
1107	#95	C₂²×D₅₃	1	1	yes	characteristic
1108	#95	C₂²×D₅₃	1	1	yes	characteristic
1109	#95	C₂²×D₅₃	1	1	yes	characteristic
1110	#95	C₂²×D₅₃	1	1	yes	characteristic
1111	#95	C₂²×D₅₃	1	1	yes	characteristic
1112	#95	C₂²×D₅₃	1	1	yes	characteristic
1113	#95	C₂²×D₅₃	1	1	yes	characteristic
1114	#95	C₂²×D₅₃	1	1	yes	characteristic
1115	#95	C₂²×D₅₃	1	1	yes	characteristic
1116	#95	C₂²×D₅₃	1	1	yes	characteristic
1117	#95	C₂²×D₅₃	1	1	yes	characteristic
1118	#95	C₂²×D₅₃	1	1	yes	characteristic
1119	C₂⁴	—	53	1	no	—
1120	C₂⁴	—	53	4	no	—
1121	C₂⁴	—	53	1	no	—
1122	C₂⁴	—	106	2	no	—
1123	C₂⁴	—	106	2	no	—
1124	C₂⁴	—	106	2	no	—
1125	C₂⁴	—	106	2	no	—
1126	C₂⁴	—	106	2	no	—
1127	C₂⁴	—	106	2	no	—
1128	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1129	C₂×Q₈	—	2	2	no	—
1130	C₂×Q₈	—	2	2	no	—
1131	C₂×Q₈	—	4	1	no	—
1132	C₂×Q₈	—	106	2	no	—
1133	C₂×Q₈	—	106	2	no	—
1134	C₂×Q₈	—	106	2	no	—
1135	C₂×Q₈	—	106	2	no	—
1136	C₂×Q₈	—	106	2	no	—
1137	C₂×Q₈	—	106	2	no	—
1138	C₂×Q₈	—	212	1	no	—
1139	C₂×Q₈	—	212	1	no	—
1140	C₂×Q₈	—	212	1	no	—
1141	C₂×Q₈	—	212	16	no	—
1142	C₂²×C₄	—	2	2	no	—
1143	C₂²×C₄	—	4	1	no	—
1144	C₂²×C₄	—	4	1	no	—
1145	C₂²×C₄	—	53	1	no	—
1146	C₂²×C₄	—	53	1	no	—
1147	C₂²×C₄	—	53	1	no	—
1148	C₂²×C₄	—	53	1	no	—
1149	C₂²×C₄	—	53	1	no	—
1150	C₂²×C₄	—	53	1	no	—
1151	C₂²×C₄	—	53	4	no	—
1152	C₂²×C₄	—	53	4	no	—
1153	C₂²×C₄	—	53	4	no	—
1154	C₂²×C₄	—	53	4	no	—
1155	C₂²×C₄	—	53	4	no	—
1156	C₂²×C₄	—	53	4	no	—
1157	C₂²×C₄	—	53	1	no	—
1158	C₂²×C₄	—	53	1	no	—
1159	C₂²×C₄	—	53	1	no	—
1160	C₂²×C₄	—	53	1	no	—
1161	C₂²×C₄	—	53	1	no	—
1162	C₂²×C₄	—	53	1	no	—
1163	C₂²×C₄	—	53	1	no	—
1164	C₂²×C₄	—	53	1	no	—
1165	C₂²×C₄	—	106	2	no	—
1166	C₂²×C₄	—	106	2	no	—
1167	C₂²×C₄	—	106	2	no	—
1168	C₂²×C₄	—	106	2	no	—
1169	C₂²×C₄	—	106	2	no	—
1170	C₂²×C₄	—	106	2	no	—
1171	C₂²×C₄	—	106	2	no	—
1172	C₂²×C₄	—	106	2	no	—
1173	C₂²×C₄	—	106	2	no	—
1174	C₂²×C₄	—	106	2	no	—
1175	C₂²×C₄	—	106	2	no	—
1176	C₂²×C₄	—	106	2	no	—
1177	C₂²×C₄	—	106	2	no	—
1178	C₂²×C₄	—	106	2	no	—
1179	C₂²×C₄	—	106	2	no	—
1180	C₂²×C₄	—	106	2	no	—
1181	C₂²×C₄	—	106	2	no	—
1182	C₂²×C₄	—	106	2	no	—
1183	C₂²×C₄	—	106	2	no	—
1184	C₂²×C₄	—	106	2	no	—
1185	C₂²×C₄	—	106	2	no	—
1186	C₂²×C₄	—	106	2	no	—
1187	C₂²×C₄	—	106	2	no	—
1188	C₂²×C₄	—	106	2	no	—
1189	C₂²×C₄	—	106	2	no	—
1190	C₂²×C₄	—	106	2	no	—
1191	C₂²×C₄	—	106	2	no	—
1192	C₂²×C₄	—	106	2	no	—
1193	C₂²×C₄	—	106	2	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	—	212	1	no	—
1205	C₂²×C₄	—	212	1	no	—
1206	C₂²×C₄	—	212	1	no	—
1207	C₂²×C₄	—	212	1	no	—
1208	C₂²×C₄	—	212	16	no	—
1209	C₂²×C₄	—	212	1	no	—
1210	C₂²×C₄	—	212	1	no	—
1211	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1223	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1224	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1225	C₄⋊C₄	—	2	2	no	—
1226	C₄⋊C₄	—	2	2	no	—
1227	C₄⋊C₄	—	2	2	no	—
1228	C₄⋊C₄	—	2	2	no	—
1229	C₄⋊C₄	—	2	2	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	1	no	—
1233	C₄⋊C₄	—	4	1	no	—
1234	C₄⋊C₄	—	106	2	no	—
1235	C₄⋊C₄	—	106	2	no	—
1236	C₄⋊C₄	—	106	2	no	—
1237	C₄⋊C₄	—	106	2	no	—
1238	C₄⋊C₄	—	106	2	no	—
1239	C₄⋊C₄	—	106	2	no	—
1240	C₄⋊C₄	—	106	2	no	—
1241	C₄⋊C₄	—	106	2	no	—
1242	C₄⋊C₄	—	106	2	no	—
1243	C₄⋊C₄	—	106	2	no	—
1244	C₄⋊C₄	—	106	2	no	—
1245	C₄⋊C₄	—	106	2	no	—
1246	C₄⋊C₄	—	106	2	no	—
1247	C₄⋊C₄	—	106	2	no	—
1248	C₄⋊C₄	—	106	2	no	—
1249	C₄⋊C₄	—	212	1	no	—
1250	C₄⋊C₄	—	212	1	no	—
1251	C₄⋊C₄	—	212	1	no	—
1252	C₄⋊C₄	—	212	1	no	—
1253	C₄⋊C₄	—	212	1	no	—
1254	C₄⋊C₄	—	212	1	no	—
1255	C₄⋊C₄	—	212	1	no	—
1256	C₄⋊C₄	—	212	1	no	—
1257	C₄⋊C₄	—	212	1	no	—
1258	C₄⋊C₄	—	212	1	no	—
1259	C₄⋊C₄	—	212	1	no	—
1260	C₄⋊C₄	—	212	1	no	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	4	1	no	—
1265	C₂²⋊C₄	—	4	1	no	—
1266	C₂²⋊C₄	—	53	4	no	—
1267	C₂²⋊C₄	—	53	4	no	—
1268	C₂²⋊C₄	—	53	4	no	—
1269	C₂²⋊C₄	—	106	2	no	—
1270	C₂²⋊C₄	—	106	2	no	—
1271	C₂²⋊C₄	—	106	2	no	—
1272	C₂²⋊C₄	—	106	2	no	—
1273	C₂²⋊C₄	—	106	2	no	—
1274	C₂²⋊C₄	—	106	2	no	—
1275	C₂²⋊C₄	—	106	2	no	—
1276	C₂²⋊C₄	—	106	2	no	—
1277	C₂²⋊C₄	—	106	2	no	—
1278	C₂²⋊C₄	—	212	1	no	—
1279	C₂²⋊C₄	—	212	1	no	—
1280	C₂²⋊C₄	—	212	1	no	—
1281	C₂²⋊C₄	—	212	1	no	—
1282	C₂²⋊C₄	—	212	1	no	—
1283	C₂²⋊C₄	—	212	1	no	—
1284	C₂²⋊C₄	Q₈×D₅₃	1	4	yes	complemented
1285	C₄²	—	2	2	no	—
1286	C₄²	—	4	1	no	—
1287	C₄²	—	4	1	no	—
1288	C₄²	—	4	1	no	—
1289	C₄²	—	106	2	no	—
1290	C₄²	—	106	2	no	—
1291	C₄²	—	106	2	no	—
1292	C₄²	—	212	1	no	—
1293	C₄²	—	212	1	no	—
1294	C₄²	—	212	1	no	—
1295	C₄²	—	212	1	no	—
1296	C₄²	—	212	1	no	—
1297	C₄²	—	212	1	no	—
1298	C₄²	—	212	1	no	—
1299	C₄²	—	212	1	no	—
1300	C₄²	—	212	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	2	1	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	2	1	no	—
1305	C₂³	—	2	1	no	—
1306	C₂³	—	2	1	no	—
1307	C₂³	—	53	2	no	—
1308	C₂³	—	53	2	no	—
1309	C₂³	—	53	2	no	—
1310	C₂³	—	53	2	no	—
1311	C₂³	—	53	2	no	—
1312	C₂³	—	53	2	no	—
1313	C₂³	—	53	2	no	—
1314	C₂³	—	53	2	no	—
1315	C₂³	—	106	8	no	—
1316	C₂³	—	106	8	no	—
1317	C₂³	—	106	8	no	—
1318	C₂³	—	106	1	no	—
1319	C₂³	—	106	1	no	—
1320	C₂³	—	106	1	no	—
1321	C₂³	—	106	1	no	—
1322	C₂³	—	106	1	no	—
1323	C₂³	—	106	1	no	—
1324	C₂³	—	212	4	no	—
1325	C₂³	—	212	4	no	—
1326	C₂³	—	212	4	no	—
1327	C₂³	—	212	4	no	—
1328	C₂³	C₂×Q₈×D₅₃	1	2	yes	—
1329	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1330	Q₈	—	4	4	no	—
1331	Q₈	—	212	4	no	—
1332	Q₈	—	212	4	no	—
1333	Q₈	—	212	4	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	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	—	4	4	no	—
1371	C₂×C₄	—	53	2	no	—
1372	C₂×C₄	—	53	2	no	—
1373	C₂×C₄	—	53	2	no	—
1374	C₂×C₄	—	53	2	no	—
1375	C₂×C₄	—	53	2	no	—
1376	C₂×C₄	—	53	2	no	—
1377	C₂×C₄	—	106	8	no	—
1378	C₂×C₄	—	106	8	no	—
1379	C₂×C₄	—	106	8	no	—
1380	C₂×C₄	—	106	8	no	—
1381	C₂×C₄	—	106	8	no	—
1382	C₂×C₄	—	106	8	no	—
1383	C₂×C₄	—	106	1	no	—
1384	C₂×C₄	—	106	1	no	—
1385	C₂×C₄	—	106	1	no	—
1386	C₂×C₄	—	106	1	no	—
1387	C₂×C₄	—	106	1	no	—
1388	C₂×C₄	—	106	1	no	—
1389	C₂×C₄	—	106	1	no	—
1390	C₂×C₄	—	106	1	no	—
1391	C₂×C₄	—	106	1	no	—
1392	C₂×C₄	—	106	1	no	—
1393	C₂×C₄	—	106	1	no	—
1394	C₂×C₄	—	106	1	no	—
1395	C₂×C₄	—	106	1	no	—
1396	C₂×C₄	—	106	1	no	—
1397	C₂×C₄	—	106	1	no	—
1398	C₂×C₄	—	106	1	no	—
1399	C₂×C₄	—	106	1	no	—
1400	C₂×C₄	—	106	1	no	—
1401	C₂×C₄	—	106	1	no	—
1402	C₂×C₄	—	106	1	no	—
1403	C₂×C₄	—	106	1	no	—
1404	C₂×C₄	—	106	1	no	—
1405	C₂×C₄	—	106	1	no	—
1406	C₂×C₄	—	106	1	no	—
1407	C₂×C₄	—	106	1	no	—
1408	C₂×C₄	—	106	1	no	—
1409	C₂×C₄	—	106	1	no	—
1410	C₂×C₄	—	106	1	no	—
1411	C₂×C₄	—	106	1	no	—
1412	C₂×C₄	—	106	1	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	—	212	4	no	—
1420	C₂×C₄	—	212	4	no	—
1421	C₂×C₄	—	212	4	no	—
1422	C₂×C₄	—	212	4	no	—
1423	C₂×C₄	—	212	4	no	—
1424	C₂×C₄	—	212	4	no	—
1425	C₂×C₄	—	212	4	no	—
1426	C₂×C₄	—	212	4	no	—
1427	C₂×C₄	—	212	4	no	—
1428	C₂×C₄	—	212	4	no	—
1429	C₂×C₄	—	212	4	no	—
1430	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1431	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1432	C₂×C₄	#41×D₅₃	1	2	yes	—
1433	C₂×C₄	#41×D₅₃	1	2	yes	—
1434	C₂×C₄	#41×D₅₃	1	2	yes	—
1435	C₂×C₄	#41×D₅₃	1	2	yes	—
1436	C₂²	—	2	2	no	—
1437	C₂²	—	2	2	no	—
1438	C₂²	—	2	2	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	4	1	no	—
1441	C₂²	—	4	1	no	—
1442	C₂²	—	4	1	no	—
1443	C₂²	—	53	4	no	—
1444	C₂²	—	53	4	no	—
1445	C₂²	—	53	4	no	—
1446	C₂²	—	53	4	no	—
1447	C₂²	—	53	4	no	—
1448	C₂²	—	53	4	no	—
1449	C₂²	—	53	4	no	—
1450	C₂²	—	106	2	no	—
1451	C₂²	—	106	2	no	—
1452	C₂²	—	106	2	no	—
1453	C₂²	—	212	16	no	—
1454	C₂²	—	212	1	no	—
1455	C₂²	—	212	1	no	—
1456	C₂²	—	212	1	no	—
1457	C₂²	—	212	1	no	—
1458	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1459	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1460	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1461	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1462	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1463	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1464	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1465	C₄	—	2	2	no	—
1466	C₄	—	2	2	no	—
1467	C₄	—	2	2	no	—
1468	C₄	—	2	2	no	—
1469	C₄	—	2	2	no	—
1470	C₄	—	2	2	no	—
1471	C₄	—	4	1	no	—
1472	C₄	—	4	1	no	—
1473	C₄	—	4	1	no	—
1474	C₄	—	4	1	no	—
1475	C₄	—	4	1	no	—
1476	C₄	—	4	1	no	—
1477	C₄	—	4	1	no	—
1478	C₄	—	4	1	no	—
1479	C₄	—	106	2	no	—
1480	C₄	—	106	2	no	—
1481	C₄	—	106	2	no	—
1482	C₄	—	106	2	no	—
1483	C₄	—	106	2	no	—
1484	C₄	—	106	2	no	—
1485	C₄	—	212	1	no	—
1486	C₄	—	212	1	no	—
1487	C₄	—	212	1	no	—
1488	C₄	—	212	1	no	—
1489	C₄	—	212	1	no	—
1490	C₄	—	212	1	no	—
1491	C₄	—	212	1	no	—
1492	C₄	—	212	1	no	—
1493	C₂	—	4	2	no	—
1494	C₂	—	53	8	no	—
1495	C₂	—	212	2	no	—
1496	C₂	#529×D₅₃	1	1	yes	characteristic
1497	C₂	#533×D₅₃	1	1	yes	characteristic
1498	C₂	#538×D₅₃	1	1	yes	characteristic
1499	C₂	#551×D₅₃	1	1	yes	characteristic
1500	C₂	#554×D₅₃	1	1	yes	characteristic
1501	C₂	#554×D₅₃	1	1	yes	characteristic
1502	C₂	#559×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2589	C₂
prime radical	C₂⁴×D₅₃	C₂³
hypercenter	#2589	D₅₃
hypocenter	C₅₃	C₂×#2589
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2589

Complements

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

N	H ≅ G/N	type
1. #20280173	C₂	semidirect
2. #20280172	C₂	semidirect
3. #20280171	C₂	semidirect
4. #20280170	C₂	semidirect
5. #20280169	C₂	semidirect
6. #20280168	C₂	semidirect
7. #20280167	C₂	semidirect
8. #20280166	C₂	semidirect
9. #20280165	C₂	semidirect
10. #20280164	C₂	semidirect
11. #20280163	C₂	semidirect
12. #20280162	C₂	semidirect
13. #20280161	C₂	semidirect
14. #20280160	C₂	semidirect
15. #20280159	C₂	semidirect
16. #400×D₅₃	C₂	semidirect
18. #398×D₅₃	C₂	semidirect
20. #391×D₅₃	C₂	semidirect
21. #391×D₅₃	C₂	semidirect
22. #389×D₅₃	C₂	semidirect
25. #387×D₅₃	C₂	semidirect
26. #387×D₅₃	C₂	semidirect
29. C₄×C₄⋊C₄×D₅₃	C₂	semidirect
31. C₅₃×#2589	C₂	semidirect
53. #16810565	C₂²	semidirect
54. #16810565	C₂²	semidirect
55. #16810564	C₂²	semidirect
56. #16810564	C₂²	semidirect
57. #16810563	C₂²	semidirect
58. #16810562	C₂²	semidirect
59. #16810561	C₂²	semidirect
67. #16810557	C₂²	semidirect
68. #16810557	C₂²	semidirect
69. #16810556	C₂²	semidirect
70. #16810556	C₂²	semidirect
71. #16810555	C₂²	semidirect
72. #16810554	C₂²	semidirect
73. #16810553	C₂²	semidirect
81. #16810530	C₂²	semidirect
82. #16810530	C₂²	semidirect
83. #16810529	C₂²	semidirect
84. #16810529	C₂²	semidirect
85. #16810528	C₂²	semidirect
86. #16810528	C₂²	semidirect
87. #16810527	C₂²	semidirect
88. #16810527	C₂²	semidirect
89. #16810527	C₂²	semidirect
90. #16810527	C₂²	semidirect
91. #16810527	C₂²	semidirect
92. #16810527	C₂²	semidirect
93. #16810527	C₂²	semidirect
94. #16810527	C₂²	semidirect
95. #16810522	C₂²	semidirect
96. #16810521	C₂²	semidirect
97. #16810520	C₂²	semidirect
98. #16810520	C₂²	semidirect
99. #16810519	C₂²	semidirect
100. #16810518	C₂²	semidirect
101. #16810518	C₂²	semidirect
116. #16810510	C₂²	semidirect
117. #16810510	C₂²	semidirect
118. #16810509	C₂²	semidirect
119. #16810509	C₂²	semidirect
120. #16810508	C₂²	semidirect
121. #16810508	C₂²	semidirect
122. #16810507	C₂²	semidirect
123. #16810507	C₂²	semidirect
124. #16810506	C₂²	semidirect
125. #16810506	C₂²	semidirect
126. #16810505	C₂²	semidirect
127. #16810505	C₂²	semidirect
128. #16810504	C₂²	semidirect
129. #16810504	C₂²	semidirect
144. C₄⋊C₄×Dic₅₃	C₂²	semidirect
145. C₄⋊C₄×Dic₅₃	C₂²	semidirect
146. C₄×#11719919	C₂²	semidirect
147. C₄×#11719919	C₂²	semidirect
148. C₄×C₄⋊Dic₅₃	C₂²	semidirect
149. #16810474	C₂²	semidirect
150. #16810474	C₂²	semidirect
172. C₅₃×#400	C₂²	semidirect
174. C₅₃×#398	C₂²	semidirect
176. C₅₃×#391	C₂²	semidirect
177. C₅₃×#391	C₂²	semidirect
178. C₅₃×#389	C₂²	semidirect
181. C₅₃×#387	C₂²	semidirect
182. C₅₃×#387	C₂²	semidirect
185. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
273. C₂²⋊C₄×D₅₃	Q₈	semidirect
487. C₂²⋊C₄×C₅₃	C₂×Q₈	semidirect
497. C₂²⋊Dic₅₃	C₂×Q₈	semidirect
508. #11719921	C₂×Q₈	semidirect
509. #11719921	C₂×Q₈	semidirect
757. #2589	D₅₃	direct (N × H)
782. D₅₃	#2589	direct (N × H)
811. #400	C₂×D₅₃	semidirect
827. #398	C₂×D₅₃	semidirect
850. #391	C₂×D₅₃	semidirect
851. #391	C₂×D₅₃	semidirect
859. #389	C₂×D₅₃	semidirect
890. #387	C₂×D₅₃	semidirect
891. #387	C₂×D₅₃	semidirect
915. C₄×C₄⋊C₄	C₂×D₅₃	semidirect
938. C₅₃	C₂×#2589	semidirect
1284. C₂²⋊C₄	Q₈×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20280173	2
#20280172	2
#20280171	2
#20280170	2
#20280169	2
#20280168	2
#20280167	2
#20280166	2
#20280165	2
#20280164	2
#20280163	2
#20280162	2
#20280161	2
#20280160	2
#20280159	2
#400×D₅₃	2
#399×D₅₃	2
#398×D₅₃	2
#393×D₅₃	2
#391×D₅₃	2
#389×D₅₃	2
#388×D₅₃	2
#387×D₅₃	2
#385×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₄×C₂²⋊C₄×D₅₃	2
C₅₃×#2589	2
C₂×#2589	53

Subgroups — D53×#2589 #27554383

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2589 #27554383