Subgroups — D₅₃×#2520 #27553292

Order 13568.

2030 conjugacy classes of subgroups.

The subgroup lattice has 1368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20279410	C₂	1	1	yes	maximal, characteristic, complemented
2	#20279409	C₂	1	1	yes	maximal, characteristic, complemented
3	#20279408	C₂	1	1	yes	maximal, characteristic, complemented
4	#20279407	C₂	1	1	yes	maximal, characteristic, complemented
5	#20279406	C₂	1	1	yes	maximal, characteristic, complemented
6	#20279405	C₂	1	1	yes	maximal, characteristic, complemented
7	#20279404	C₂	1	1	yes	maximal, characteristic, complemented
8	#20279403	C₂	1	1	yes	maximal, characteristic, complemented
9	#20279402	C₂	1	1	yes	maximal, characteristic, complemented
10	#20279401	C₂	1	1	yes	maximal, characteristic, complemented
11	#20279400	C₂	1	1	yes	maximal, characteristic, complemented
12	#20279399	C₂	1	1	yes	maximal, characteristic, complemented
13	#20279398	C₂	1	1	yes	maximal, characteristic, complemented
14	#20279397	C₂	1	1	yes	maximal, characteristic, complemented
15	#20279396	C₂	1	1	yes	maximal, characteristic, complemented
16	#400×D₅₃	C₂	1	1	yes	maximal, characteristic
17	#398×D₅₃	C₂	1	1	yes	maximal, characteristic
18	#398×D₅₃	C₂	1	1	yes	maximal, characteristic
19	#395×D₅₃	C₂	1	1	yes	maximal, characteristic
20	#391×D₅₃	C₂	1	1	yes	maximal, characteristic
21	#391×D₅₃	C₂	1	1	yes	maximal, characteristic
22	#387×D₅₃	C₂	1	1	yes	maximal, characteristic
23	#387×D₅₃	C₂	1	1	yes	maximal, characteristic
24	#387×D₅₃	C₂	1	1	yes	maximal, characteristic
25	#387×D₅₃	C₂	1	1	yes	maximal, characteristic
26	#387×D₅₃	C₂	1	1	yes	maximal, characteristic
27	#387×D₅₃	C₂	1	1	yes	maximal, characteristic
28	#382×D₅₃	C₂	1	1	yes	maximal, characteristic
29	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
30	C₄×C₄⋊C₄×D₅₃	C₂	1	1	yes	maximal, characteristic
31	C₅₃×#2520	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×Q₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊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×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
47	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
49	#16810565	C₂²	1	1	yes	characteristic
50	#16810565	C₂²	1	1	yes	characteristic
51	#16810564	C₂²	1	1	yes	characteristic
52	#16810564	C₂²	1	1	yes	characteristic
53	#16810563	C₂²	1	1	yes	characteristic
54	#16810562	C₂²	1	1	yes	characteristic
55	#16810561	C₂²	1	1	yes	characteristic
56	#16810557	C₂²	1	1	yes	characteristic
57	#16810557	C₂²	1	1	yes	characteristic
58	#16810557	C₂²	1	1	yes	characteristic
59	#16810557	C₂²	1	1	yes	characteristic
60	#16810556	C₂²	1	1	yes	characteristic
61	#16810556	C₂²	1	1	yes	characteristic
62	#16810556	C₂²	1	1	yes	characteristic
63	#16810556	C₂²	1	1	yes	characteristic
64	#16810555	C₂²	1	1	yes	characteristic
65	#16810555	C₂²	1	1	yes	characteristic
66	#16810554	C₂²	1	1	yes	characteristic
67	#16810554	C₂²	1	1	yes	characteristic
68	#16810553	C₂²	1	1	yes	characteristic
69	#16810553	C₂²	1	1	yes	characteristic
70	#16810544	C₂²	1	1	yes	characteristic
71	#16810544	C₂²	1	1	yes	characteristic
72	#16810544	C₂²	1	1	yes	characteristic
73	#16810543	C₂²	1	1	yes	characteristic
74	#16810543	C₂²	1	1	yes	characteristic
75	#16810543	C₂²	1	1	yes	characteristic
76	#16810542	C₂²	1	1	yes	characteristic
77	#16810530	C₂²	1	1	yes	characteristic
78	#16810530	C₂²	1	1	yes	characteristic
79	#16810529	C₂²	1	1	yes	characteristic
80	#16810529	C₂²	1	1	yes	characteristic
81	#16810528	C₂²	1	1	yes	characteristic
82	#16810528	C₂²	1	1	yes	characteristic
83	#16810527	C₂²	1	1	yes	characteristic
84	#16810527	C₂²	1	1	yes	characteristic
85	#16810527	C₂²	1	1	yes	characteristic
86	#16810527	C₂²	1	1	yes	characteristic
87	#16810527	C₂²	1	1	yes	characteristic
88	#16810527	C₂²	1	1	yes	characteristic
89	#16810527	C₂²	1	1	yes	characteristic
90	#16810527	C₂²	1	1	yes	characteristic
91	#16810510	C₂²	1	1	yes	characteristic
92	#16810510	C₂²	1	1	yes	characteristic
93	#16810510	C₂²	1	1	yes	characteristic
94	#16810510	C₂²	1	1	yes	characteristic
95	#16810510	C₂²	1	1	yes	characteristic
96	#16810510	C₂²	1	1	yes	characteristic
97	#16810509	C₂²	1	1	yes	characteristic
98	#16810509	C₂²	1	1	yes	characteristic
99	#16810509	C₂²	1	1	yes	characteristic
100	#16810509	C₂²	1	1	yes	characteristic
101	#16810509	C₂²	1	1	yes	characteristic
102	#16810509	C₂²	1	1	yes	characteristic
103	#16810508	C₂²	1	1	yes	characteristic
104	#16810508	C₂²	1	1	yes	characteristic
105	#16810508	C₂²	1	1	yes	characteristic
106	#16810508	C₂²	1	1	yes	characteristic
107	#16810508	C₂²	1	1	yes	characteristic
108	#16810508	C₂²	1	1	yes	characteristic
109	#16810507	C₂²	1	1	yes	characteristic
110	#16810507	C₂²	1	1	yes	characteristic
111	#16810507	C₂²	1	1	yes	characteristic
112	#16810507	C₂²	1	1	yes	characteristic
113	#16810507	C₂²	1	1	yes	characteristic
114	#16810507	C₂²	1	1	yes	characteristic
115	#16810506	C₂²	1	1	yes	characteristic
116	#16810506	C₂²	1	1	yes	characteristic
117	#16810506	C₂²	1	1	yes	characteristic
118	#16810506	C₂²	1	1	yes	characteristic
119	#16810506	C₂²	1	1	yes	characteristic
120	#16810506	C₂²	1	1	yes	characteristic
121	#16810505	C₂²	1	1	yes	characteristic
122	#16810505	C₂²	1	1	yes	characteristic
123	#16810505	C₂²	1	1	yes	characteristic
124	#16810505	C₂²	1	1	yes	characteristic
125	#16810505	C₂²	1	1	yes	characteristic
126	#16810505	C₂²	1	1	yes	characteristic
127	#16810504	C₂²	1	1	yes	characteristic
128	#16810504	C₂²	1	1	yes	characteristic
129	#16810504	C₂²	1	1	yes	characteristic
130	#16810504	C₂²	1	1	yes	characteristic
131	#16810504	C₂²	1	1	yes	characteristic
132	#16810504	C₂²	1	1	yes	characteristic
133	#16810489	C₂²	1	1	yes	characteristic
134	#16810488	C₂²	1	1	yes	characteristic
135	#16810488	C₂²	1	1	yes	characteristic
136	#16810487	C₂²	1	1	yes	characteristic
137	#16810487	C₂²	1	1	yes	characteristic
138	#16810487	C₂²	1	1	yes	characteristic
139	#16810487	C₂²	1	1	yes	characteristic
140	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
141	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
142	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
143	C₄⋊C₄×Dic₅₃	C₂²	1	1	yes	characteristic
144	C₄×#11719919	C₂²	1	1	yes	characteristic
145	C₄×#11719919	C₂²	1	1	yes	characteristic
146	C₄×#11719919	C₂²	1	1	yes	characteristic
147	C₄×#11719919	C₂²	1	1	yes	characteristic
148	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
149	C₄×C₄⋊Dic₅₃	C₂²	1	1	yes	characteristic
150	#16810474	C₂²	1	1	yes	characteristic
151	#16810474	C₂²	1	1	yes	characteristic
152	#16810474	C₂²	1	1	yes	characteristic
153	#16810474	C₂²	1	1	yes	characteristic
154	#95×D₅₃	C₂²	1	1	yes	characteristic
155	#95×D₅₃	C₂²	1	1	yes	characteristic
156	#95×D₅₃	C₂²	1	1	yes	characteristic
157	#95×D₅₃	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
173	C₅₃×#398	C₂²	1	1	yes	characteristic
174	C₅₃×#398	C₂²	1	1	yes	characteristic
175	C₅₃×#395	C₂²	1	1	yes	characteristic
176	C₅₃×#391	C₂²	1	1	yes	characteristic
177	C₅₃×#391	C₂²	1	1	yes	characteristic
178	C₅₃×#387	C₂²	1	1	yes	characteristic
179	C₅₃×#387	C₂²	1	1	yes	characteristic
180	C₅₃×#387	C₂²	1	1	yes	characteristic
181	C₅₃×#387	C₂²	1	1	yes	characteristic
182	C₅₃×#387	C₂²	1	1	yes	characteristic
183	C₅₃×#387	C₂²	1	1	yes	characteristic
184	C₅₃×#382	C₂²	1	1	yes	characteristic
185	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
188	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
189	C₂²×Dic₁₀₆	C₂³	1	1	yes	characteristic
190	C₂×Q₈×D₅₃	—	2	4	no	—
191	C₂×Q₈×D₅₃	—	2	4	no	—
192	C₂×Q₈×D₅₃	—	4	2	no	—
193	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
194	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
195	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
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	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊Dic₅₃	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×#11719919	C₂³	1	1	yes	characteristic
220	C₂×#11719919	C₂³	1	1	yes	characteristic
221	C₂×#11719919	C₂³	1	1	yes	characteristic
222	C₂×#11719919	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	—	2	4	no	—
247	C₄⋊C₄×D₅₃	—	2	4	no	—
248	C₄⋊C₄×D₅₃	—	4	2	no	—
249	C₄⋊C₄×D₅₃	—	4	2	no	—
250	C₄⋊C₄×D₅₃	—	4	2	no	—
251	C₄⋊C₄×D₅₃	Q₈	1	8	yes	complemented
252	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
267	C₄²×D₅₃	—	2	4	no	—
268	C₄²×D₅₃	—	2	4	no	—
269	C₄²×D₅₃	—	2	4	no	—
270	C₄²×D₅₃	—	4	2	no	—
271	C₄²×D₅₃	—	4	2	no	—
272	#13133124	C₂³	1	1	yes	characteristic
273	#13133124	C₂³	1	1	yes	characteristic
274	#13133124	C₂³	1	1	yes	characteristic
275	#13133124	C₂³	1	1	yes	characteristic
276	#13133124	C₂³	1	1	yes	characteristic
277	#13133124	C₂³	1	1	yes	characteristic
278	#13133124	C₂³	1	1	yes	characteristic
279	#13133124	C₂³	1	1	yes	characteristic
280	#13133124	C₂³	1	1	yes	characteristic
281	#13133124	C₂³	1	1	yes	characteristic
282	#13133124	C₂³	1	1	yes	characteristic
283	#13133124	C₂³	1	1	yes	characteristic
284	#13133124	C₂³	1	1	yes	characteristic
285	#13133124	C₂³	1	1	yes	characteristic
286	#13133124	C₂³	1	1	yes	characteristic
287	#13133124	C₂³	1	1	yes	characteristic
288	#13133124	C₂³	1	1	yes	characteristic
289	#13133124	C₂³	1	1	yes	characteristic
290	#13133124	C₂³	1	1	yes	characteristic
291	#13133124	C₂³	1	1	yes	characteristic
292	#13133124	C₂³	1	1	yes	characteristic
293	#13133124	C₂³	1	1	yes	characteristic
294	#13133124	C₂³	1	1	yes	characteristic
295	#13133124	C₂³	1	1	yes	characteristic
296	#13133124	C₂³	1	1	yes	characteristic
297	#13133124	C₂³	1	1	yes	characteristic
298	#13133124	C₂³	1	1	yes	characteristic
299	#13133124	C₂³	1	1	yes	characteristic
300	#13133124	C₂³	1	1	yes	characteristic
301	#13133124	C₂³	1	1	yes	characteristic
302	#13133124	C₂³	1	1	yes	characteristic
303	#13133124	C₂³	1	1	yes	characteristic
304	#13133124	C₂³	1	1	yes	characteristic
305	#13133124	C₂³	1	1	yes	characteristic
306	#13133124	C₂³	1	1	yes	characteristic
307	#13133124	C₂³	1	1	yes	characteristic
308	#13133124	C₂³	1	1	yes	characteristic
309	#13133124	C₂³	1	1	yes	characteristic
310	#13133124	C₂³	1	1	yes	characteristic
311	#13133124	C₂³	1	1	yes	characteristic
312	#13133124	C₂³	1	1	yes	characteristic
313	#13133124	C₂³	1	1	yes	characteristic
314	#13133124	C₂³	1	1	yes	characteristic
315	#13133124	C₂³	1	1	yes	characteristic
316	#13133124	C₂³	1	1	yes	characteristic
317	#13133124	C₂³	1	1	yes	characteristic
318	#13133124	C₂³	1	1	yes	characteristic
319	#13133124	C₂³	1	1	yes	characteristic
320	#13133124	C₂³	1	1	yes	characteristic
321	#13133124	C₂³	1	1	yes	characteristic
322	#13133124	C₂³	1	1	yes	characteristic
323	#13133124	C₂³	1	1	yes	characteristic
324	#13133124	C₂³	1	1	yes	characteristic
325	#13133124	C₂³	1	1	yes	characteristic
326	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄⋊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×C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×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	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
362	C₂×Q₈×C₅₃	—	2	2	no	—
363	C₂×Q₈×C₅₃	—	2	2	no	—
364	C₂×Q₈×C₅₃	—	4	1	no	—
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
381	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
382	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
386	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
387	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
389	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
392	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
393	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
394	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
395	Q₈×D₅₃	—	4	16	no	—
396	C₂×C₄×D₅₃	—	2	2	no	—
397	C₂×C₄×D₅₃	—	2	2	no	—
398	C₂×C₄×D₅₃	—	2	2	no	—
399	C₂×C₄×D₅₃	—	2	2	no	—
400	C₂×C₄×D₅₃	—	2	2	no	—
401	C₂×C₄×D₅₃	—	2	2	no	—
402	C₂×C₄×D₅₃	—	2	2	no	—
403	C₂×C₄×D₅₃	—	2	2	no	—
404	C₂×C₄×D₅₃	—	2	2	no	—
405	C₂×C₄×D₅₃	—	2	2	no	—
406	C₂×C₄×D₅₃	—	2	2	no	—
407	C₂×C₄×D₅₃	—	2	2	no	—
408	C₂×C₄×D₅₃	—	2	2	no	—
409	C₂×C₄×D₅₃	—	2	2	no	—
410	C₂×C₄×D₅₃	—	2	2	no	—
411	C₂×C₄×D₅₃	—	2	2	no	—
412	C₂×C₄×D₅₃	—	2	2	no	—
413	C₂×C₄×D₅₃	—	2	2	no	—
414	C₂×C₄×D₅₃	—	2	2	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	C₂×Q₈	1	4	yes	—
435	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
436	C₂×C₄×D₅₃	C₂×Q₈	1	4	yes	—
437	C₂×C₄×D₅₃	#41	1	4	yes	—
438	C₂×C₄×D₅₃	#41	1	4	yes	—
439	C₂×C₄×D₅₃	#41	1	4	yes	—
440	C₂×C₄×D₅₃	#41	1	4	yes	—
441	C₂×Dic₁₀₆	—	2	2	no	—
442	C₂×Dic₁₀₆	—	2	2	no	—
443	C₂×Dic₁₀₆	—	2	2	no	—
444	C₂×Dic₁₀₆	—	2	2	no	—
445	C₂×Dic₁₀₆	—	2	2	no	—
446	C₂×Dic₁₀₆	—	2	2	no	—
447	C₂×Dic₁₀₆	—	4	1	no	—
448	C₂×Dic₁₀₆	—	4	1	no	—
449	C₂×Dic₁₀₆	—	4	1	no	—
450	C₄⋊C₄×C₅₃	—	2	2	no	—
451	C₄⋊C₄×C₅₃	—	2	2	no	—
452	C₄⋊C₄×C₅₃	—	2	2	no	—
453	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	—	2	2	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	4	1	no	—
458	C₄⋊C₄×C₅₃	—	4	1	no	—
459	C₄⋊C₄×C₅₃	—	4	1	no	—
460	C₄⋊C₄×C₅₃	C₂×Q₈	1	4	yes	complemented
461	C₄²×C₅₃	—	2	2	no	—
462	C₄²×C₅₃	—	2	2	no	—
463	C₄²×C₅₃	—	2	2	no	—
464	C₄²×C₅₃	—	4	1	no	—
465	C₄²×C₅₃	—	4	1	no	—
466	C₄⋊Dic₅₃	—	2	2	no	—
467	C₄⋊Dic₅₃	—	2	2	no	—
468	C₄⋊Dic₅₃	—	2	2	no	—
469	C₄⋊Dic₅₃	—	2	2	no	—
470	C₄⋊Dic₅₃	—	2	2	no	—
471	C₄⋊Dic₅₃	—	2	2	no	—
472	C₄⋊Dic₅₃	—	2	2	no	—
473	C₄⋊Dic₅₃	—	4	1	no	—
474	C₄⋊Dic₅₃	—	4	1	no	—
475	C₄⋊Dic₅₃	—	4	1	no	—
476	C₄⋊Dic₅₃	C₂×Q₈	1	4	yes	complemented
477	#11719919	—	2	2	no	—
478	#11719919	—	2	2	no	—
479	#11719919	—	2	2	no	—
480	#11719919	—	2	2	no	—
481	#11719919	—	2	2	no	—
482	#11719919	—	2	2	no	—
483	#11719919	—	2	2	no	—
484	#11719919	—	2	2	no	—
485	#11719919	—	2	2	no	—
486	#11719919	—	2	2	no	—
487	#11719919	—	2	2	no	—
488	#11719919	—	2	2	no	—
489	#11719919	—	2	2	no	—
490	#11719919	—	2	2	no	—
491	#11719919	—	4	1	no	—
492	#11719919	—	4	1	no	—
493	#11719919	—	4	1	no	—
494	#11719919	—	4	1	no	—
495	#11719919	—	4	1	no	—
496	#11719919	—	4	1	no	—
497	#11719919	C₂×Q₈	1	4	yes	complemented
498	#11719919	C₂×Q₈	1	4	yes	complemented
499	C₄×Dic₅₃	—	2	2	no	—
500	C₄×Dic₅₃	—	2	2	no	—
501	C₄×Dic₅₃	—	2	2	no	—
502	C₄×Dic₅₃	—	2	2	no	—
503	C₄×Dic₅₃	—	2	2	no	—
504	C₄×Dic₅₃	—	2	2	no	—
505	C₄×Dic₅₃	—	2	2	no	—
506	C₄×Dic₅₃	—	2	2	no	—
507	C₄×Dic₅₃	—	2	2	no	—
508	C₄×Dic₅₃	—	4	1	no	—
509	C₄×Dic₅₃	—	4	1	no	—
510	C₄×Dic₅₃	—	4	1	no	—
511	C₄×Dic₅₃	—	4	1	no	—
512	C₄×Dic₅₃	—	4	1	no	—
513	C₄×Dic₅₃	—	4	1	no	—
514	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
515	C₂²×D₅₃	C₂²×Q₈	1	2	yes	—
516	C₂²×D₅₃	C₂×#41	1	2	yes	—
517	C₂²×D₅₃	C₂×#41	1	2	yes	—
518	C₂²×D₅₃	C₂×#41	1	2	yes	—
519	C₂²×D₅₃	C₂×#41	1	2	yes	—
520	C₂²×D₅₃	H(5,𝔽₂)	1	2	yes	—
521	C₂²×D₅₃	2₋¹⁺⁴	1	2	yes	—
522	Q₈×C₅₃	—	4	4	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	2	1	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	2	1	no	—
532	C₂×C₄×C₅₃	—	2	1	no	—
533	C₂×C₄×C₅₃	—	2	1	no	—
534	C₂×C₄×C₅₃	—	2	1	no	—
535	C₂×C₄×C₅₃	—	2	1	no	—
536	C₂×C₄×C₅₃	—	2	1	no	—
537	C₂×C₄×C₅₃	—	2	1	no	—
538	C₂×C₄×C₅₃	—	2	1	no	—
539	C₂×C₄×C₅₃	—	2	1	no	—
540	C₂×C₄×C₅₃	—	2	1	no	—
541	C₂×C₄×C₅₃	—	2	1	no	—
542	C₂×C₄×C₅₃	—	2	1	no	—
543	C₂×C₄×C₅₃	—	2	1	no	—
544	C₂×C₄×C₅₃	—	2	1	no	—
545	C₂×C₄×C₅₃	—	2	1	no	—
546	C₂×C₄×C₅₃	—	2	1	no	—
547	C₂×C₄×C₅₃	—	2	1	no	—
548	C₂×C₄×C₅₃	—	2	1	no	—
549	C₂×C₄×C₅₃	—	2	1	no	—
550	C₂×C₄×C₅₃	—	2	1	no	—
551	C₂×C₄×C₅₃	—	2	1	no	—
552	C₂×C₄×C₅₃	—	2	1	no	—
553	C₂×C₄×C₅₃	—	2	1	no	—
554	C₂×C₄×C₅₃	—	2	1	no	—
555	C₂×C₄×C₅₃	—	2	1	no	—
556	C₂×C₄×C₅₃	—	2	1	no	—
557	C₂×C₄×C₅₃	—	2	1	no	—
558	C₂×C₄×C₅₃	—	2	1	no	—
559	C₂×C₄×C₅₃	—	2	1	no	—
560	C₂×C₄×C₅₃	—	2	1	no	—
561	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
562	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
563	C₂×C₄×C₅₃	C₂²×Q₈	1	2	yes	—
564	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
565	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
566	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
567	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
568	C₂×Dic₅₃	—	2	1	no	—
569	C₂×Dic₅₃	—	2	1	no	—
570	C₂×Dic₅₃	—	2	1	no	—
571	C₂×Dic₅₃	—	2	1	no	—
572	C₂×Dic₅₃	—	2	1	no	—
573	C₂×Dic₅₃	—	2	1	no	—
574	C₂×Dic₅₃	—	2	1	no	—
575	C₂×Dic₅₃	—	2	1	no	—
576	C₂×Dic₅₃	—	2	1	no	—
577	C₂×Dic₅₃	—	2	1	no	—
578	C₂×Dic₅₃	—	2	1	no	—
579	C₂×Dic₅₃	—	2	1	no	—
580	C₂×Dic₅₃	—	2	1	no	—
581	C₂×Dic₅₃	—	2	1	no	—
582	C₂×Dic₅₃	—	2	1	no	—
583	C₂×Dic₅₃	—	2	1	no	—
584	C₂×Dic₅₃	—	2	1	no	—
585	C₂×Dic₅₃	—	2	1	no	—
586	C₂×Dic₅₃	—	2	1	no	—
587	C₂×Dic₅₃	—	2	1	no	—
588	C₂×Dic₅₃	—	2	1	no	—
589	C₂×Dic₅₃	—	2	1	no	—
590	C₂×Dic₅₃	—	2	1	no	—
591	C₂×Dic₅₃	—	2	1	no	—
592	C₂×Dic₅₃	—	2	1	no	—
593	C₂×Dic₅₃	—	2	1	no	—
594	C₂×Dic₅₃	—	2	1	no	—
595	C₂×Dic₅₃	—	2	1	no	—
596	C₂×Dic₅₃	—	2	1	no	—
597	C₂×Dic₅₃	—	2	1	no	—
598	C₂×Dic₅₃	—	2	1	no	—
599	C₂×Dic₅₃	—	2	1	no	—
600	C₂×Dic₅₃	—	2	1	no	—
601	C₂×Dic₅₃	—	2	1	no	—
602	C₂×Dic₅₃	—	2	1	no	—
603	C₂×Dic₅₃	—	2	1	no	—
604	C₂×Dic₅₃	—	2	1	no	—
605	C₂×Dic₅₃	—	2	1	no	—
606	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
607	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
608	C₂×Dic₅₃	C₂²×Q₈	1	2	yes	—
609	C₂×Dic₅₃	C₂×#41	1	2	yes	—
610	C₂×Dic₅₃	C₂×#41	1	2	yes	—
611	C₂×Dic₅₃	C₂×#41	1	2	yes	—
612	C₂×Dic₅₃	C₂×#41	1	2	yes	—
613	C₄×D₅₃	—	2	8	no	—
614	C₄×D₅₃	—	2	8	no	—
615	C₄×D₅₃	—	2	8	no	—
616	C₄×D₅₃	—	2	8	no	—
617	C₄×D₅₃	—	2	8	no	—
618	C₄×D₅₃	—	2	8	no	—
619	C₄×D₅₃	—	2	8	no	—
620	C₄×D₅₃	—	4	4	no	—
621	C₄×D₅₃	—	4	4	no	—
622	C₄×D₅₃	—	4	4	no	—
623	C₄×D₅₃	—	4	4	no	—
624	C₄×D₅₃	—	4	4	no	—
625	C₄×D₅₃	—	4	4	no	—
626	C₄×D₅₃	—	4	4	no	—
627	C₄×D₅₃	—	4	4	no	—
628	Dic₁₀₆	—	4	4	no	—
629	Dic₁₀₆	—	4	4	no	—
630	Dic₁₀₆	—	4	4	no	—
631	C₂×#2520	—	53	1	no	maximal, Sylow
632	C₂²×C₅₃	C₂³×Q₈	1	1	yes	characteristic
633	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
634	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
635	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
636	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
637	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
638	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
639	C₂×D₅₃	#529	1	4	yes	—
640	C₂×D₅₃	#533	1	4	yes	—
641	C₂×D₅₃	#542	1	4	yes	—
642	C₂×D₅₃	#551	1	4	yes	—
643	C₂×D₅₃	#552	1	4	yes	—
644	C₂×D₅₃	#554	1	4	yes	—
645	C₂×D₅₃	#557	1	4	yes	—
646	C₄×C₅₃	—	2	2	no	—
647	C₄×C₅₃	—	2	2	no	—
648	C₄×C₅₃	—	2	2	no	—
649	C₄×C₅₃	—	2	2	no	—
650	C₄×C₅₃	—	2	2	no	—
651	C₄×C₅₃	—	2	2	no	—
652	C₄×C₅₃	—	2	2	no	—
653	C₄×C₅₃	—	4	1	no	—
654	C₄×C₅₃	—	4	1	no	—
655	C₄×C₅₃	—	4	1	no	—
656	C₄×C₅₃	—	4	1	no	—
657	C₄×C₅₃	—	4	1	no	—
658	C₄×C₅₃	—	4	1	no	—
659	C₄×C₅₃	—	4	1	no	—
660	C₄×C₅₃	—	4	1	no	—
661	Dic₅₃	—	2	2	no	—
662	Dic₅₃	—	2	2	no	—
663	Dic₅₃	—	2	2	no	—
664	Dic₅₃	—	2	2	no	—
665	Dic₅₃	—	2	2	no	—
666	Dic₅₃	—	2	2	no	—
667	Dic₅₃	—	2	2	no	—
668	Dic₅₃	—	4	1	no	—
669	Dic₅₃	—	4	1	no	—
670	Dic₅₃	—	4	1	no	—
671	Dic₅₃	—	4	1	no	—
672	Dic₅₃	—	4	1	no	—
673	Dic₅₃	—	4	1	no	—
674	Dic₅₃	—	4	1	no	—
675	Dic₅₃	—	4	1	no	—
676	#2520	—	53	1	no	—
677	#2520	—	53	1	no	—
678	#2520	—	53	1	no	—
679	#2520	—	53	1	no	—
680	#2520	—	53	1	no	—
681	#2520	—	53	1	no	—
682	#2520	—	53	1	no	—
683	#2520	—	53	1	no	—
684	#2520	—	53	1	no	—
685	#2520	—	53	1	no	—
686	#2520	—	53	1	no	—
687	#2520	—	53	1	no	—
688	#2520	—	53	1	no	—
689	#2520	—	53	1	no	—
690	#2520	—	53	1	no	—
691	#2520	D₅₃	1	1	yes	characteristic, direct product factor
692	C₂×#400	—	53	1	no	—
693	C₂×#398	—	53	1	no	—
694	C₂×#398	—	53	1	no	—
695	C₂×#395	—	53	1	no	—
696	C₂×#391	—	53	1	no	—
697	C₂×#391	—	53	1	no	—
698	C₂×#387	—	53	1	no	—
699	C₂×#387	—	53	1	no	—
700	C₂×#387	—	53	1	no	—
701	C₂×#387	—	53	1	no	—
702	C₂×#387	—	53	1	no	—
703	C₂×#387	—	53	1	no	—
704	C₂×#382	—	53	1	no	—
705	C₂×C₄×C₄⋊C₄	—	53	1	no	—
706	C₂×C₄×C₄⋊C₄	—	53	1	no	—
707	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
708	C₂×C₅₃	C₂×#533	1	1	yes	characteristic
709	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
710	C₂×C₅₃	C₂×#551	1	1	yes	characteristic
711	C₂×C₅₃	C₂×#552	1	1	yes	characteristic
712	C₂×C₅₃	C₂×#554	1	1	yes	characteristic
713	C₂×C₅₃	C₂×#557	1	1	yes	characteristic
714	D₅₃	#2520	1	8	yes	direct product factor
715	C₂³×Q₈	—	53	1	no	—
716	C₂²×C₄⋊C₄	—	53	1	no	—
717	C₂²×C₄⋊C₄	—	53	1	no	—
718	C₂²×C₄⋊C₄	—	53	1	no	—
719	C₂²×C₄⋊C₄	—	53	1	no	—
720	C₂²×C₄⋊C₄	—	53	1	no	—
721	C₂²×C₄⋊C₄	—	53	1	no	—
722	C₂²×C₄⋊C₄	—	53	1	no	—
723	C₂²×C₄⋊C₄	—	53	1	no	—
724	C₂²×C₄⋊C₄	—	53	1	no	—
725	C₂²×C₄⋊C₄	—	53	1	no	—
726	C₂²×C₄⋊C₄	—	53	1	no	—
727	C₂²×C₄²	—	53	1	no	—
728	C₂²×C₄²	—	53	1	no	—
729	C₂²×C₄²	—	53	1	no	—
730	C₂²×C₄²	—	53	1	no	—
731	C₂²×C₄²	—	53	1	no	—
732	#400	—	53	1	no	—
733	#400	—	53	1	no	—
734	#400	—	53	1	no	—
735	#400	—	53	1	no	—
736	#400	—	53	1	no	—
737	#400	—	53	1	no	—
738	#400	—	53	1	no	—
739	#400	C₂×D₅₃	1	1	yes	characteristic
740	#398	—	53	1	no	—
741	#398	—	53	1	no	—
742	#398	—	53	1	no	—
743	#398	—	53	1	no	—
744	#398	—	53	1	no	—
745	#398	—	53	1	no	—
746	#398	—	53	1	no	—
747	#398	—	53	1	no	—
748	#398	—	53	1	no	—
749	#398	—	53	1	no	—
750	#398	—	53	1	no	—
751	#398	—	53	1	no	—
752	#398	—	53	1	no	—
753	#398	—	53	1	no	—
754	#398	C₂×D₅₃	1	1	yes	characteristic
755	#398	C₂×D₅₃	1	1	yes	characteristic
756	#395	—	53	1	no	—
757	#395	—	53	1	no	—
758	#395	—	53	1	no	—
759	#395	—	53	1	no	—
760	#395	—	53	1	no	—
761	#395	—	53	1	no	—
762	#395	—	53	1	no	—
763	#395	C₂×D₅₃	1	1	yes	characteristic
764	#391	—	53	1	no	—
765	#391	—	53	1	no	—
766	#391	—	53	1	no	—
767	#391	—	53	1	no	—
768	#391	—	53	1	no	—
769	#391	—	53	1	no	—
770	#391	—	53	1	no	—
771	#391	—	53	1	no	—
772	#391	—	53	1	no	—
773	#391	—	53	1	no	—
774	#391	—	53	1	no	—
775	#391	—	53	1	no	—
776	#391	—	53	1	no	—
777	#391	—	53	1	no	—
778	#391	C₂×D₅₃	1	1	yes	characteristic
779	#391	C₂×D₅₃	1	1	yes	characteristic
780	#387	—	53	1	no	—
781	#387	—	53	1	no	—
782	#387	—	53	1	no	—
783	#387	—	53	1	no	—
784	#387	—	53	1	no	—
785	#387	—	53	1	no	—
786	#387	—	53	1	no	—
787	#387	—	53	1	no	—
788	#387	—	53	1	no	—
789	#387	—	53	1	no	—
790	#387	—	53	1	no	—
791	#387	—	53	1	no	—
792	#387	—	53	1	no	—
793	#387	—	53	1	no	—
794	#387	—	53	1	no	—
795	#387	—	53	1	no	—
796	#387	—	53	1	no	—
797	#387	—	53	1	no	—
798	#387	—	53	1	no	—
799	#387	—	53	1	no	—
800	#387	—	53	1	no	—
801	#387	—	53	1	no	—
802	#387	—	53	1	no	—
803	#387	—	53	1	no	—
804	#387	—	53	1	no	—
805	#387	—	53	1	no	—
806	#387	—	53	1	no	—
807	#387	—	53	1	no	—
808	#387	—	53	1	no	—
809	#387	—	53	1	no	—
810	#387	—	53	1	no	—
811	#387	—	53	1	no	—
812	#387	—	53	1	no	—
813	#387	—	53	1	no	—
814	#387	—	53	1	no	—
815	#387	—	53	1	no	—
816	#387	—	53	1	no	—
817	#387	—	53	1	no	—
818	#387	—	53	1	no	—
819	#387	—	53	1	no	—
820	#387	—	53	1	no	—
821	#387	—	53	1	no	—
822	#387	C₂×D₅₃	1	1	yes	characteristic
823	#387	C₂×D₅₃	1	1	yes	characteristic
824	#387	C₂×D₅₃	1	1	yes	characteristic
825	#387	C₂×D₅₃	1	1	yes	characteristic
826	#387	C₂×D₅₃	1	1	yes	characteristic
827	#387	C₂×D₅₃	1	1	yes	characteristic
828	#382	—	53	1	no	—
829	#382	—	53	1	no	—
830	#382	—	53	1	no	—
831	#382	—	53	1	no	—
832	#382	—	53	1	no	—
833	#382	—	53	1	no	—
834	#382	—	53	1	no	—
835	#382	C₂×D₅₃	1	1	yes	characteristic
836	C₄×C₄⋊C₄	—	53	1	no	—
837	C₄×C₄⋊C₄	—	53	1	no	—
838	C₄×C₄⋊C₄	—	53	1	no	—
839	C₄×C₄⋊C₄	—	53	1	no	—
840	C₄×C₄⋊C₄	—	53	1	no	—
841	C₄×C₄⋊C₄	—	53	1	no	—
842	C₄×C₄⋊C₄	—	53	1	no	—
843	C₄×C₄⋊C₄	—	53	1	no	—
844	C₄×C₄⋊C₄	—	53	1	no	—
845	C₄×C₄⋊C₄	—	53	1	no	—
846	C₄×C₄⋊C₄	—	53	1	no	—
847	C₄×C₄⋊C₄	—	53	1	no	—
848	C₄×C₄⋊C₄	—	53	1	no	—
849	C₄×C₄⋊C₄	—	53	1	no	—
850	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
851	C₄×C₄⋊C₄	C₂×D₅₃	1	1	yes	characteristic
852	C₂×#95	—	53	1	no	—
853	C₂×#95	—	53	1	no	—
854	C₂×#95	—	53	1	no	—
855	C₂×#95	—	53	1	no	—
856	C₂×#95	—	53	1	no	—
857	C₂×#95	—	53	1	no	—
858	C₂×#95	—	53	1	no	—
859	C₂×#95	—	53	1	no	—
860	C₂×#95	—	53	1	no	—
861	C₂×#95	—	53	1	no	—
862	C₂×#95	—	53	1	no	—
863	C₂×#95	—	53	1	no	—
864	C₂×#95	—	53	1	no	—
865	C₂×#95	—	53	1	no	—
866	C₂×#95	—	53	1	no	—
867	C₂×#95	—	53	1	no	—
868	C₂×#95	—	53	1	no	—
869	C₂×#95	—	53	1	no	—
870	C₅₃	C₂×#2520	1	1	yes	characteristic, complemented, Sylow
871	C₂²×Q₈	—	53	1	no	—
872	C₂²×Q₈	—	53	1	no	—
873	C₂²×Q₈	—	53	1	no	—
874	C₂²×Q₈	—	106	4	no	—
875	C₂²×Q₈	—	106	4	no	—
876	C₂²×Q₈	—	212	2	no	—
877	C₂²×Q₈	C₂²×D₅₃	1	1	yes	characteristic
878	C₂³×C₄	—	53	1	no	—
879	C₂³×C₄	—	53	1	no	—
880	C₂³×C₄	—	53	1	no	—
881	C₂³×C₄	—	53	1	no	—
882	C₂³×C₄	—	53	1	no	—
883	C₂³×C₄	—	53	1	no	—
884	C₂³×C₄	—	53	1	no	—
885	C₂³×C₄	—	53	1	no	—
886	C₂³×C₄	—	53	1	no	—
887	C₂³×C₄	—	53	1	no	—
888	C₂³×C₄	—	53	1	no	—
889	C₂³×C₄	—	53	1	no	—
890	C₂³×C₄	—	53	1	no	—
891	C₂³×C₄	—	53	1	no	—
892	C₂³×C₄	—	53	1	no	—
893	C₂×C₄⋊C₄	—	53	1	no	—
894	C₂×C₄⋊C₄	—	53	1	no	—
895	C₂×C₄⋊C₄	—	53	1	no	—
896	C₂×C₄⋊C₄	—	53	8	no	—
897	C₂×C₄⋊C₄	—	53	1	no	—
898	C₂×C₄⋊C₄	—	53	1	no	—
899	C₂×C₄⋊C₄	—	53	1	no	—
900	C₂×C₄⋊C₄	—	53	1	no	—
901	C₂×C₄⋊C₄	—	53	1	no	—
902	C₂×C₄⋊C₄	—	53	1	no	—
903	C₂×C₄⋊C₄	—	53	1	no	—
904	C₂×C₄⋊C₄	—	53	1	no	—
905	C₂×C₄⋊C₄	—	53	1	no	—
906	C₂×C₄⋊C₄	—	53	1	no	—
907	C₂×C₄⋊C₄	—	53	1	no	—
908	C₂×C₄⋊C₄	—	53	1	no	—
909	C₂×C₄⋊C₄	—	53	1	no	—
910	C₂×C₄⋊C₄	—	53	1	no	—
911	C₂×C₄⋊C₄	—	53	1	no	—
912	C₂×C₄⋊C₄	—	53	1	no	—
913	C₂×C₄⋊C₄	—	53	1	no	—
914	C₂×C₄⋊C₄	—	53	1	no	—
915	C₂×C₄⋊C₄	—	53	1	no	—
916	C₂×C₄⋊C₄	—	53	1	no	—
917	C₂×C₄⋊C₄	—	53	1	no	—
918	C₂×C₄⋊C₄	—	53	1	no	—
919	C₂×C₄⋊C₄	—	53	1	no	—
920	C₂×C₄⋊C₄	—	53	1	no	—
921	C₂×C₄⋊C₄	—	53	1	no	—
922	C₂×C₄⋊C₄	—	53	1	no	—
923	C₂×C₄⋊C₄	—	53	1	no	—
924	C₂×C₄⋊C₄	—	53	1	no	—
925	C₂×C₄⋊C₄	—	53	1	no	—
926	C₂×C₄⋊C₄	—	53	1	no	—
927	C₂×C₄⋊C₄	—	106	4	no	—
928	C₂×C₄⋊C₄	—	106	4	no	—
929	C₂×C₄⋊C₄	—	106	4	no	—
930	C₂×C₄⋊C₄	—	106	4	no	—
931	C₂×C₄⋊C₄	—	106	4	no	—
932	C₂×C₄⋊C₄	—	106	4	no	—
933	C₂×C₄⋊C₄	—	106	4	no	—
934	C₂×C₄⋊C₄	—	212	2	no	—
935	C₂×C₄⋊C₄	—	212	2	no	—
936	C₂×C₄⋊C₄	—	212	2	no	—
937	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
938	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
939	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
948	C₂×C₄²	—	53	1	no	—
949	C₂×C₄²	—	53	1	no	—
950	C₂×C₄²	—	53	1	no	—
951	C₂×C₄²	—	53	1	no	—
952	C₂×C₄²	—	53	1	no	—
953	C₂×C₄²	—	53	1	no	—
954	C₂×C₄²	—	53	1	no	—
955	C₂×C₄²	—	53	1	no	—
956	C₂×C₄²	—	53	1	no	—
957	C₂×C₄²	—	53	1	no	—
958	C₂×C₄²	—	53	1	no	—
959	C₂×C₄²	—	53	1	no	—
960	C₂×C₄²	—	53	1	no	—
961	C₂×C₄²	—	53	1	no	—
962	C₂×C₄²	—	53	1	no	—
963	C₂×C₄²	—	106	4	no	—
964	C₂×C₄²	—	106	4	no	—
965	C₂×C₄²	—	106	4	no	—
966	C₂×C₄²	—	212	2	no	—
967	C₂×C₄²	—	212	2	no	—
968	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
969	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
970	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
971	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
972	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
973	#95	—	53	1	no	—
974	#95	—	53	1	no	—
975	#95	—	53	1	no	—
976	#95	—	53	1	no	—
977	#95	—	53	1	no	—
978	#95	—	53	1	no	—
979	#95	—	53	1	no	—
980	#95	—	53	1	no	—
981	#95	—	53	1	no	—
982	#95	—	53	1	no	—
983	#95	—	53	1	no	—
984	#95	—	53	1	no	—
985	#95	—	53	1	no	—
986	#95	—	53	1	no	—
987	#95	—	53	1	no	—
988	#95	—	53	1	no	—
989	#95	—	53	1	no	—
990	#95	—	53	1	no	—
991	#95	—	53	1	no	—
992	#95	—	53	1	no	—
993	#95	—	53	1	no	—
994	#95	—	53	1	no	—
995	#95	—	53	1	no	—
996	#95	—	53	1	no	—
997	#95	—	53	1	no	—
998	#95	—	53	1	no	—
999	#95	—	53	1	no	—
1000	#95	—	53	1	no	—
1001	#95	—	53	1	no	—
1002	#95	—	53	1	no	—
1003	#95	—	53	1	no	—
1004	#95	—	53	1	no	—
1005	#95	—	53	1	no	—
1006	#95	—	53	1	no	—
1007	#95	—	53	1	no	—
1008	#95	—	53	1	no	—
1009	#95	—	53	1	no	—
1010	#95	—	53	1	no	—
1011	#95	—	53	1	no	—
1012	#95	—	53	1	no	—
1013	#95	—	53	1	no	—
1014	#95	—	53	1	no	—
1015	#95	—	53	1	no	—
1016	#95	—	53	1	no	—
1017	#95	—	53	1	no	—
1018	#95	—	53	1	no	—
1019	#95	—	53	1	no	—
1020	#95	—	53	1	no	—
1021	#95	—	53	1	no	—
1022	#95	—	53	1	no	—
1023	#95	—	53	1	no	—
1024	#95	—	53	1	no	—
1025	#95	—	53	1	no	—
1026	#95	—	53	1	no	—
1027	#95	C₂²×D₅₃	1	1	yes	characteristic
1028	#95	C₂²×D₅₃	1	1	yes	characteristic
1029	#95	C₂²×D₅₃	1	1	yes	characteristic
1030	#95	C₂²×D₅₃	1	1	yes	characteristic
1031	#95	C₂²×D₅₃	1	1	yes	characteristic
1032	#95	C₂²×D₅₃	1	1	yes	characteristic
1033	#95	C₂²×D₅₃	1	1	yes	characteristic
1034	#95	C₂²×D₅₃	1	1	yes	characteristic
1035	#95	C₂²×D₅₃	1	1	yes	characteristic
1036	#95	C₂²×D₅₃	1	1	yes	characteristic
1037	#95	C₂²×D₅₃	1	1	yes	characteristic
1038	#95	C₂²×D₅₃	1	1	yes	characteristic
1039	#95	C₂²×D₅₃	1	1	yes	characteristic
1040	#95	C₂²×D₅₃	1	1	yes	characteristic
1041	#95	C₂²×D₅₃	1	1	yes	characteristic
1042	#95	C₂²×D₅₃	1	1	yes	characteristic
1043	#95	C₂²×D₅₃	1	1	yes	characteristic
1044	#95	C₂²×D₅₃	1	1	yes	characteristic
1045	C₂⁴	—	53	1	no	—
1046	C₂×Q₈	—	2	2	no	—
1047	C₂×Q₈	—	2	2	no	—
1048	C₂×Q₈	—	4	1	no	—
1049	C₂×Q₈	—	106	2	no	—
1050	C₂×Q₈	—	106	2	no	—
1051	C₂×Q₈	—	106	2	no	—
1052	C₂×Q₈	—	106	2	no	—
1053	C₂×Q₈	—	106	2	no	—
1054	C₂×Q₈	—	106	2	no	—
1055	C₂×Q₈	—	212	1	no	—
1056	C₂×Q₈	—	212	1	no	—
1057	C₂×Q₈	—	212	1	no	—
1058	C₂×Q₈	—	212	16	no	—
1059	C₂²×C₄	—	53	1	no	—
1060	C₂²×C₄	—	53	1	no	—
1061	C₂²×C₄	—	53	1	no	—
1062	C₂²×C₄	—	53	1	no	—
1063	C₂²×C₄	—	53	1	no	—
1064	C₂²×C₄	—	53	1	no	—
1065	C₂²×C₄	—	53	1	no	—
1066	C₂²×C₄	—	53	4	no	—
1067	C₂²×C₄	—	53	4	no	—
1068	C₂²×C₄	—	53	4	no	—
1069	C₂²×C₄	—	53	4	no	—
1070	C₂²×C₄	—	53	4	no	—
1071	C₂²×C₄	—	53	4	no	—
1072	C₂²×C₄	—	53	4	no	—
1073	C₂²×C₄	—	53	1	no	—
1074	C₂²×C₄	—	53	1	no	—
1075	C₂²×C₄	—	53	1	no	—
1076	C₂²×C₄	—	53	1	no	—
1077	C₂²×C₄	—	53	1	no	—
1078	C₂²×C₄	—	53	1	no	—
1079	C₂²×C₄	—	53	1	no	—
1080	C₂²×C₄	—	53	1	no	—
1081	C₂²×C₄	—	106	2	no	—
1082	C₂²×C₄	—	106	2	no	—
1083	C₂²×C₄	—	106	2	no	—
1084	C₂²×C₄	—	106	2	no	—
1085	C₂²×C₄	—	106	2	no	—
1086	C₂²×C₄	—	106	2	no	—
1087	C₂²×C₄	—	106	2	no	—
1088	C₂²×C₄	—	106	2	no	—
1089	C₂²×C₄	—	106	2	no	—
1090	C₂²×C₄	—	106	2	no	—
1091	C₂²×C₄	—	106	2	no	—
1092	C₂²×C₄	—	106	2	no	—
1093	C₂²×C₄	—	106	2	no	—
1094	C₂²×C₄	—	106	2	no	—
1095	C₂²×C₄	—	106	2	no	—
1096	C₂²×C₄	—	106	2	no	—
1097	C₂²×C₄	—	106	2	no	—
1098	C₂²×C₄	—	106	2	no	—
1099	C₂²×C₄	—	106	2	no	—
1100	C₂²×C₄	—	106	2	no	—
1101	C₂²×C₄	—	106	2	no	—
1102	C₂²×C₄	—	106	2	no	—
1103	C₂²×C₄	—	106	2	no	—
1104	C₂²×C₄	—	106	2	no	—
1105	C₂²×C₄	—	106	2	no	—
1106	C₂²×C₄	—	106	2	no	—
1107	C₂²×C₄	—	106	2	no	—
1108	C₂²×C₄	—	106	2	no	—
1109	C₂²×C₄	—	106	2	no	—
1110	C₂²×C₄	—	106	2	no	—
1111	C₂²×C₄	—	106	2	no	—
1112	C₂²×C₄	—	106	2	no	—
1113	C₂²×C₄	—	106	2	no	—
1114	C₂²×C₄	—	106	2	no	—
1115	C₂²×C₄	—	106	2	no	—
1116	C₂²×C₄	—	106	2	no	—
1117	C₂²×C₄	—	106	2	no	—
1118	C₂²×C₄	—	106	2	no	—
1119	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1120	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1121	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1122	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1123	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1124	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1125	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1126	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1127	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1128	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1129	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1130	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1131	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1132	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1133	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1134	C₄⋊C₄	—	2	2	no	—
1135	C₄⋊C₄	—	2	2	no	—
1136	C₄⋊C₄	—	2	2	no	—
1137	C₄⋊C₄	—	2	2	no	—
1138	C₄⋊C₄	—	2	2	no	—
1139	C₄⋊C₄	—	2	2	no	—
1140	C₄⋊C₄	—	2	2	no	—
1141	C₄⋊C₄	—	4	1	no	—
1142	C₄⋊C₄	—	4	1	no	—
1143	C₄⋊C₄	—	4	1	no	—
1144	C₄⋊C₄	—	53	4	no	—
1145	C₄⋊C₄	—	53	4	no	—
1146	C₄⋊C₄	—	53	4	no	—
1147	C₄⋊C₄	—	106	2	no	—
1148	C₄⋊C₄	—	106	2	no	—
1149	C₄⋊C₄	—	106	2	no	—
1150	C₄⋊C₄	—	106	2	no	—
1151	C₄⋊C₄	—	106	2	no	—
1152	C₄⋊C₄	—	106	2	no	—
1153	C₄⋊C₄	—	106	2	no	—
1154	C₄⋊C₄	—	106	2	no	—
1155	C₄⋊C₄	—	106	2	no	—
1156	C₄⋊C₄	—	106	2	no	—
1157	C₄⋊C₄	—	106	2	no	—
1158	C₄⋊C₄	—	106	2	no	—
1159	C₄⋊C₄	—	106	2	no	—
1160	C₄⋊C₄	—	106	2	no	—
1161	C₄⋊C₄	—	106	2	no	—
1162	C₄⋊C₄	—	106	2	no	—
1163	C₄⋊C₄	—	106	2	no	—
1164	C₄⋊C₄	—	106	2	no	—
1165	C₄⋊C₄	—	106	2	no	—
1166	C₄⋊C₄	—	106	2	no	—
1167	C₄⋊C₄	—	106	2	no	—
1168	C₄⋊C₄	—	212	1	no	—
1169	C₄⋊C₄	—	212	1	no	—
1170	C₄⋊C₄	—	212	1	no	—
1171	C₄⋊C₄	—	212	1	no	—
1172	C₄⋊C₄	—	212	1	no	—
1173	C₄⋊C₄	—	212	1	no	—
1174	C₄⋊C₄	—	212	1	no	—
1175	C₄⋊C₄	—	212	1	no	—
1176	C₄⋊C₄	—	212	1	no	—
1177	C₄⋊C₄	Q₈×D₅₃	1	4	yes	complemented
1178	C₄²	—	2	2	no	—
1179	C₄²	—	2	2	no	—
1180	C₄²	—	2	2	no	—
1181	C₄²	—	4	1	no	—
1182	C₄²	—	4	1	no	—
1183	C₄²	—	106	2	no	—
1184	C₄²	—	106	2	no	—
1185	C₄²	—	106	2	no	—
1186	C₄²	—	106	2	no	—
1187	C₄²	—	106	2	no	—
1188	C₄²	—	106	2	no	—
1189	C₄²	—	106	2	no	—
1190	C₄²	—	106	2	no	—
1191	C₄²	—	106	2	no	—
1192	C₄²	—	212	1	no	—
1193	C₄²	—	212	1	no	—
1194	C₄²	—	212	1	no	—
1195	C₄²	—	212	1	no	—
1196	C₄²	—	212	1	no	—
1197	C₄²	—	212	1	no	—
1198	C₂³	—	53	2	no	—
1199	C₂³	—	53	2	no	—
1200	C₂³	—	53	2	no	—
1201	C₂³	—	53	2	no	—
1202	C₂³	—	53	2	no	—
1203	C₂³	—	53	2	no	—
1204	C₂³	—	53	2	no	—
1205	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1206	Q₈	—	4	4	no	—
1207	Q₈	—	212	4	no	—
1208	Q₈	—	212	4	no	—
1209	Q₈	—	212	4	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	1	no	—
1215	C₂×C₄	—	2	1	no	—
1216	C₂×C₄	—	2	1	no	—
1217	C₂×C₄	—	2	1	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	1	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	1	no	—
1227	C₂×C₄	—	2	1	no	—
1228	C₂×C₄	—	2	1	no	—
1229	C₂×C₄	—	2	1	no	—
1230	C₂×C₄	—	2	1	no	—
1231	C₂×C₄	—	2	1	no	—
1232	C₂×C₄	—	2	1	no	—
1233	C₂×C₄	—	2	1	no	—
1234	C₂×C₄	—	2	1	no	—
1235	C₂×C₄	—	2	1	no	—
1236	C₂×C₄	—	2	1	no	—
1237	C₂×C₄	—	2	1	no	—
1238	C₂×C₄	—	2	1	no	—
1239	C₂×C₄	—	2	1	no	—
1240	C₂×C₄	—	2	1	no	—
1241	C₂×C₄	—	2	1	no	—
1242	C₂×C₄	—	2	1	no	—
1243	C₂×C₄	—	2	1	no	—
1244	C₂×C₄	—	2	1	no	—
1245	C₂×C₄	—	2	1	no	—
1246	C₂×C₄	—	2	1	no	—
1247	C₂×C₄	—	2	1	no	—
1248	C₂×C₄	—	53	2	no	—
1249	C₂×C₄	—	53	2	no	—
1250	C₂×C₄	—	53	2	no	—
1251	C₂×C₄	—	53	2	no	—
1252	C₂×C₄	—	53	2	no	—
1253	C₂×C₄	—	53	2	no	—
1254	C₂×C₄	—	53	2	no	—
1255	C₂×C₄	—	106	8	no	—
1256	C₂×C₄	—	106	8	no	—
1257	C₂×C₄	—	106	8	no	—
1258	C₂×C₄	—	106	8	no	—
1259	C₂×C₄	—	106	8	no	—
1260	C₂×C₄	—	106	8	no	—
1261	C₂×C₄	—	106	8	no	—
1262	C₂×C₄	—	106	1	no	—
1263	C₂×C₄	—	106	1	no	—
1264	C₂×C₄	—	106	1	no	—
1265	C₂×C₄	—	106	1	no	—
1266	C₂×C₄	—	106	1	no	—
1267	C₂×C₄	—	106	1	no	—
1268	C₂×C₄	—	106	1	no	—
1269	C₂×C₄	—	106	1	no	—
1270	C₂×C₄	—	106	1	no	—
1271	C₂×C₄	—	106	1	no	—
1272	C₂×C₄	—	106	1	no	—
1273	C₂×C₄	—	106	1	no	—
1274	C₂×C₄	—	106	1	no	—
1275	C₂×C₄	—	106	1	no	—
1276	C₂×C₄	—	106	1	no	—
1277	C₂×C₄	—	106	1	no	—
1278	C₂×C₄	—	106	1	no	—
1279	C₂×C₄	—	106	1	no	—
1280	C₂×C₄	—	106	1	no	—
1281	C₂×C₄	—	106	1	no	—
1282	C₂×C₄	—	106	1	no	—
1283	C₂×C₄	—	106	1	no	—
1284	C₂×C₄	—	106	1	no	—
1285	C₂×C₄	—	106	1	no	—
1286	C₂×C₄	—	106	1	no	—
1287	C₂×C₄	—	106	1	no	—
1288	C₂×C₄	—	106	1	no	—
1289	C₂×C₄	—	106	1	no	—
1290	C₂×C₄	—	106	1	no	—
1291	C₂×C₄	—	106	1	no	—
1292	C₂×C₄	—	106	1	no	—
1293	C₂×C₄	—	106	1	no	—
1294	C₂×C₄	—	106	1	no	—
1295	C₂×C₄	—	106	1	no	—
1296	C₂×C₄	—	106	1	no	—
1297	C₂×C₄	—	106	1	no	—
1298	C₂×C₄	—	106	1	no	—
1299	C₂×C₄	—	106	1	no	—
1300	C₂×C₄	—	212	4	no	—
1301	C₂×C₄	—	212	4	no	—
1302	C₂×C₄	—	212	4	no	—
1303	C₂×C₄	—	212	4	no	—
1304	C₂×C₄	—	212	4	no	—
1305	C₂×C₄	—	212	4	no	—
1306	C₂×C₄	—	212	4	no	—
1307	C₂×C₄	—	212	4	no	—
1308	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1309	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1310	C₂×C₄	C₂×Q₈×D₅₃	1	2	yes	—
1311	C₂×C₄	#41×D₅₃	1	2	yes	—
1312	C₂×C₄	#41×D₅₃	1	2	yes	—
1313	C₂×C₄	#41×D₅₃	1	2	yes	—
1314	C₂×C₄	#41×D₅₃	1	2	yes	—
1315	C₂²	—	53	4	no	—
1316	C₂²	—	53	4	no	—
1317	C₂²	—	53	4	no	—
1318	C₂²	—	53	4	no	—
1319	C₂²	—	53	4	no	—
1320	C₂²	—	53	4	no	—
1321	C₂²	—	53	4	no	—
1322	C₂²	C₂²×Q₈×D₅₃	1	1	yes	characteristic
1323	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1324	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1325	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1326	C₂²	C₂×#41×D₅₃	1	1	yes	characteristic
1327	C₂²	H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1328	C₂²	2₋¹⁺⁴×D₅₃	1	1	yes	characteristic
1329	C₄	—	2	2	no	—
1330	C₄	—	2	2	no	—
1331	C₄	—	2	2	no	—
1332	C₄	—	2	2	no	—
1333	C₄	—	2	2	no	—
1334	C₄	—	2	2	no	—
1335	C₄	—	2	2	no	—
1336	C₄	—	4	1	no	—
1337	C₄	—	4	1	no	—
1338	C₄	—	4	1	no	—
1339	C₄	—	4	1	no	—
1340	C₄	—	4	1	no	—
1341	C₄	—	4	1	no	—
1342	C₄	—	4	1	no	—
1343	C₄	—	4	1	no	—
1344	C₄	—	106	2	no	—
1345	C₄	—	106	2	no	—
1346	C₄	—	106	2	no	—
1347	C₄	—	106	2	no	—
1348	C₄	—	106	2	no	—
1349	C₄	—	106	2	no	—
1350	C₄	—	106	2	no	—
1351	C₄	—	212	1	no	—
1352	C₄	—	212	1	no	—
1353	C₄	—	212	1	no	—
1354	C₄	—	212	1	no	—
1355	C₄	—	212	1	no	—
1356	C₄	—	212	1	no	—
1357	C₄	—	212	1	no	—
1358	C₄	—	212	1	no	—
1359	C₂	—	53	8	no	—
1360	C₂	#529×D₅₃	1	1	yes	characteristic
1361	C₂	#533×D₅₃	1	1	yes	characteristic
1362	C₂	#542×D₅₃	1	1	yes	characteristic
1363	C₂	#551×D₅₃	1	1	yes	characteristic
1364	C₂	#552×D₅₃	1	1	yes	characteristic
1365	C₂	#554×D₅₃	1	1	yes	characteristic
1366	C₂	#557×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₅₃
commutator, socle, cosocle	C₂³×C₅₃	C₂⁵
Fitting	C₅₃×#2520	C₂
prime radical	C₂³×D₅₃	C₂⁴
hypercenter	#2520	D₅₃
hypocenter	C₅₃	C₂×#2520
LCS	G ▷ C₂³×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂³ ◁ #2520

Complements

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

N	H ≅ G/N	type
1. #20279410	C₂	semidirect
2. #20279409	C₂	semidirect
3. #20279408	C₂	semidirect
4. #20279407	C₂	semidirect
5. #20279406	C₂	semidirect
6. #20279405	C₂	semidirect
7. #20279404	C₂	semidirect
8. #20279403	C₂	semidirect
9. #20279402	C₂	semidirect
10. #20279401	C₂	semidirect
11. #20279400	C₂	semidirect
12. #20279399	C₂	semidirect
13. #20279398	C₂	semidirect
14. #20279397	C₂	semidirect
15. #20279396	C₂	semidirect
31. C₅₃×#2520	C₂	semidirect
251. C₄⋊C₄×D₅₃	Q₈	semidirect
460. C₄⋊C₄×C₅₃	C₂×Q₈	semidirect
476. C₄⋊Dic₅₃	C₂×Q₈	semidirect
497. #11719919	C₂×Q₈	semidirect
498. #11719919	C₂×Q₈	semidirect
691. #2520	D₅₃	direct (N × H)
714. D₅₃	#2520	direct (N × H)
870. C₅₃	C₂×#2520	semidirect
1177. C₄⋊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
#20279410	2
#20279409	2
#20279408	2
#20279407	2
#20279406	2
#20279405	2
#20279404	2
#20279403	2
#20279402	2
#20279401	2
#20279400	2
#20279399	2
#20279398	2
#20279397	2
#20279396	2
#400×D₅₃	2
#398×D₅₃	2
#395×D₅₃	2
#391×D₅₃	2
#387×D₅₃	2
#382×D₅₃	2
C₄×C₄⋊C₄×D₅₃	2
C₅₃×#2520	2
C₂×#2520	53

Subgroups — D53×#2520 #27553292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2520 #27553292