Subgroups — C₅₃×#36782 #27244294

Order 13568.

1518 conjugacy classes of subgroups.

The subgroup lattice has 1322 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2852	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2783	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2783	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2776	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2776	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2772	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2769	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2766	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2766	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2762	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2747	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2744	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2725	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2719	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2690	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2689	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2643	C₂	1	1	yes	maximal, characteristic
21	C₅₃×#2583	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2579	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#2510	C₂	1	1	yes	maximal, characteristic
24	C₅₃×#2510	C₂	1	1	yes	maximal, characteristic
25	C₅₃×#2505	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2505	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2442	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2417	C₂	1	1	yes	maximal, characteristic
29	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2318	C₂	1	1	yes	maximal, characteristic
31	C₂×C₅₃×#387	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
38	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#401	C₂²	1	1	yes	characteristic
42	C₅₃×#401	C₂²	1	1	yes	characteristic
43	C₅₃×#401	C₂²	1	1	yes	characteristic
44	C₅₃×#400	C₂²	1	1	yes	characteristic
45	C₅₃×#400	C₂²	1	1	yes	characteristic
46	C₅₃×#400	C₂²	1	1	yes	characteristic
47	C₅₃×#400	C₂²	1	1	yes	characteristic
48	C₅₃×#400	C₂²	1	1	yes	characteristic
49	C₅₃×#400	C₂²	1	1	yes	characteristic
50	C₅₃×#400	C₂²	1	1	yes	characteristic
51	C₅₃×#400	C₂²	1	1	yes	characteristic
52	C₅₃×#400	C₂²	1	1	yes	characteristic
53	C₅₃×#400	C₂²	1	1	yes	characteristic
54	C₅₃×#400	C₂²	1	1	yes	characteristic
55	C₅₃×#400	C₂²	1	1	yes	characteristic
56	C₅₃×#400	C₂²	1	1	yes	characteristic
57	C₅₃×#400	C₂²	1	1	yes	characteristic
58	C₅₃×#400	C₂²	1	1	yes	characteristic
59	C₅₃×#400	C₂²	1	1	yes	characteristic
60	C₅₃×#400	C₂²	1	1	yes	characteristic
61	C₅₃×#398	C₂²	1	1	yes	characteristic
62	C₅₃×#398	C₂²	1	1	yes	characteristic
63	C₅₃×#398	C₂²	1	1	yes	characteristic
64	C₅₃×#398	C₂²	1	1	yes	characteristic
65	C₅₃×#398	C₂²	1	1	yes	characteristic
66	C₅₃×#398	C₂²	1	1	yes	characteristic
67	C₅₃×#398	C₂²	1	1	yes	characteristic
68	C₅₃×#398	C₂²	1	1	yes	characteristic
69	C₅₃×#398	C₂²	1	1	yes	characteristic
70	C₅₃×#398	C₂²	1	1	yes	characteristic
71	C₅₃×#398	C₂²	1	1	yes	characteristic
72	C₅₃×#398	C₂²	1	1	yes	characteristic
73	C₅₃×#398	C₂²	1	1	yes	characteristic
74	C₅₃×#398	C₂²	1	1	yes	characteristic
75	C₅₃×#397	C₂²	1	1	yes	characteristic
76	C₅₃×#397	C₂²	1	1	yes	characteristic
77	C₅₃×#397	C₂²	1	1	yes	characteristic
78	C₅₃×#397	C₂²	1	1	yes	characteristic
79	C₅₃×#397	C₂²	1	1	yes	characteristic
80	C₅₃×#397	C₂²	1	1	yes	characteristic
81	C₅₃×#397	C₂²	1	1	yes	characteristic
82	C₅₃×#396	C₂²	1	1	yes	characteristic
83	C₅₃×#396	C₂²	1	1	yes	characteristic
84	C₅₃×#396	C₂²	1	1	yes	characteristic
85	C₅₃×#396	C₂²	1	1	yes	characteristic
86	C₅₃×#396	C₂²	1	1	yes	characteristic
87	C₅₃×#395	C₂²	1	1	yes	characteristic
88	C₅₃×#395	C₂²	1	1	yes	characteristic
89	C₅₃×#391	C₂²	1	1	yes	characteristic
90	C₅₃×#391	C₂²	1	1	yes	characteristic
91	C₅₃×#391	C₂²	1	1	yes	characteristic
92	C₅₃×#389	C₂²	1	1	yes	characteristic
93	C₅₃×#389	C₂²	1	1	yes	characteristic
94	C₅₃×#389	C₂²	1	1	yes	characteristic
95	C₅₃×#389	C₂²	1	1	yes	characteristic
96	C₅₃×#389	C₂²	1	1	yes	characteristic
97	C₅₃×#389	C₂²	1	1	yes	characteristic
98	C₅₃×#389	C₂²	1	1	yes	characteristic
99	C₅₃×#389	C₂²	1	1	yes	characteristic
100	C₅₃×#389	C₂²	1	1	yes	characteristic
101	C₅₃×#389	C₂²	1	1	yes	characteristic
102	C₅₃×#389	C₂²	1	1	yes	characteristic
103	C₅₃×#389	C₂²	1	1	yes	characteristic
104	C₅₃×#389	C₂²	1	1	yes	characteristic
105	C₅₃×#388	C₂²	1	1	yes	characteristic
106	C₅₃×#388	C₂²	1	1	yes	characteristic
107	C₅₃×#388	C₂²	1	1	yes	characteristic
108	C₅₃×#388	C₂²	1	1	yes	characteristic
109	C₅₃×#388	C₂²	1	1	yes	characteristic
110	C₅₃×#388	C₂²	1	1	yes	characteristic
111	C₅₃×#388	C₂²	1	1	yes	characteristic
112	C₅₃×#388	C₂²	1	1	yes	characteristic
113	C₅₃×#388	C₂²	1	1	yes	characteristic
114	C₅₃×#387	C₂²	1	1	yes	characteristic
115	C₅₃×#387	C₂²	1	1	yes	characteristic
116	C₅₃×#387	C₂²	1	1	yes	characteristic
117	C₅₃×#387	C₂²	1	1	yes	characteristic
118	C₅₃×#387	C₂²	1	1	yes	characteristic
119	C₅₃×#387	C₂²	1	1	yes	characteristic
120	C₅₃×#387	C₂²	1	1	yes	characteristic
121	C₅₃×#387	C₂²	1	1	yes	characteristic
122	C₅₃×#387	C₂²	1	1	yes	characteristic
123	C₅₃×#387	C₂²	1	1	yes	characteristic
124	C₅₃×#387	C₂²	1	1	yes	characteristic
125	C₅₃×#387	C₂²	1	1	yes	characteristic
126	C₅₃×#387	C₂²	1	1	yes	characteristic
127	C₅₃×#387	C₂²	1	1	yes	characteristic
128	C₅₃×#387	C₂²	1	1	yes	characteristic
129	C₅₃×#387	C₂²	1	1	yes	characteristic
130	C₅₃×#387	C₂²	1	1	yes	characteristic
131	C₅₃×#387	C₂²	1	1	yes	characteristic
132	C₅₃×#387	C₂²	1	1	yes	characteristic
133	C₅₃×#387	C₂²	1	1	yes	characteristic
134	C₅₃×#387	C₂²	1	1	yes	characteristic
135	C₅₃×#387	C₂²	1	1	yes	characteristic
136	C₅₃×#387	C₂²	1	1	yes	characteristic
137	C₅₃×#387	C₂²	1	1	yes	characteristic
138	C₅₃×#387	C₂²	1	1	yes	characteristic
139	C₅₃×#387	C₂²	1	1	yes	characteristic
140	C₅₃×#387	C₂²	1	1	yes	characteristic
141	C₅₃×#387	C₂²	1	1	yes	characteristic
142	C₅₃×#387	C₂²	1	1	yes	characteristic
143	C₅₃×#386	C₂²	1	1	yes	characteristic
144	C₅₃×#386	C₂²	1	1	yes	characteristic
145	C₅₃×#386	C₂²	1	1	yes	characteristic
146	C₅₃×#386	C₂²	1	1	yes	characteristic
147	C₅₃×#386	C₂²	1	1	yes	characteristic
148	C₅₃×#386	C₂²	1	1	yes	characteristic
149	C₅₃×#385	C₂²	1	1	yes	characteristic
150	C₅₃×#385	C₂²	1	1	yes	characteristic
151	C₅₃×#385	C₂²	1	1	yes	characteristic
152	C₅₃×#385	C₂²	1	1	yes	characteristic
153	C₅₃×#385	C₂²	1	1	yes	characteristic
154	C₅₃×#385	C₂²	1	1	yes	characteristic
155	C₅₃×#385	C₂²	1	1	yes	characteristic
156	C₅₃×#385	C₂²	1	1	yes	characteristic
157	C₅₃×#385	C₂²	1	1	yes	characteristic
158	C₅₃×#385	C₂²	1	1	yes	characteristic
159	C₅₃×#385	C₂²	1	1	yes	characteristic
160	C₅₃×#385	C₂²	1	1	yes	characteristic
161	C₅₃×#385	C₂²	1	1	yes	characteristic
162	C₅₃×#385	C₂²	1	1	yes	characteristic
163	C₅₃×#383	C₂²	1	1	yes	characteristic
164	C₅₃×#383	C₂²	1	1	yes	characteristic
165	C₅₃×#383	C₂²	1	1	yes	characteristic
166	C₅₃×#383	C₂²	1	1	yes	characteristic
167	C₅₃×#382	C₂²	1	1	yes	characteristic
168	C₅₃×#382	C₂²	1	1	yes	characteristic
169	C₅₃×#382	C₂²	1	1	yes	characteristic
170	C₅₃×#382	C₂²	1	1	yes	characteristic
171	C₅₃×#382	C₂²	1	1	yes	characteristic
172	C₅₃×#381	C₂²	1	1	yes	characteristic
173	C₅₃×#380	C₂²	1	1	yes	characteristic
174	C₅₃×#380	C₂²	1	1	yes	characteristic
175	C₅₃×#380	C₂²	1	1	yes	characteristic
176	C₅₃×#380	C₂²	1	1	yes	characteristic
177	C₅₃×#380	C₂²	1	1	yes	characteristic
178	C₅₃×#380	C₂²	1	1	yes	characteristic
179	C₅₃×#380	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
184	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
187	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
189	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
192	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
197	#126×C₅₃	—	4	2	no	—
198	#125×C₅₃	—	4	2	no	—
199	#125×C₅₃	—	4	2	no	—
200	C₂²⋊Q₈×C₅₃	—	2	4	no	—
201	C₂²⋊Q₈×C₅₃	—	4	2	no	—
202	C₄×D₄×C₅₃	—	2	4	no	—
203	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
204	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
205	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄²×C₅₃	—	4	2	no	—
272	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
283	#95×C₅₃	C₂³	1	1	yes	characteristic
284	#95×C₅₃	C₂³	1	1	yes	characteristic
285	#95×C₅₃	C₂³	1	1	yes	characteristic
286	#95×C₅₃	C₂³	1	1	yes	characteristic
287	#95×C₅₃	C₂³	1	1	yes	characteristic
288	#95×C₅₃	C₂³	1	1	yes	characteristic
289	#95×C₅₃	C₂³	1	1	yes	characteristic
290	#95×C₅₃	C₂³	1	1	yes	characteristic
291	#95×C₅₃	C₂³	1	1	yes	characteristic
292	#95×C₅₃	C₂³	1	1	yes	characteristic
293	#95×C₅₃	C₂³	1	1	yes	characteristic
294	#95×C₅₃	C₂³	1	1	yes	characteristic
295	#95×C₅₃	C₂³	1	1	yes	characteristic
296	#95×C₅₃	C₂³	1	1	yes	characteristic
297	#95×C₅₃	C₂³	1	1	yes	characteristic
298	#95×C₅₃	C₂³	1	1	yes	characteristic
299	#95×C₅₃	C₂³	1	1	yes	characteristic
300	#95×C₅₃	C₂³	1	1	yes	characteristic
301	#95×C₅₃	C₂³	1	1	yes	characteristic
302	#95×C₅₃	C₂³	1	1	yes	characteristic
303	#95×C₅₃	C₂³	1	1	yes	characteristic
304	#95×C₅₃	C₂³	1	1	yes	characteristic
305	#95×C₅₃	C₂³	1	1	yes	characteristic
306	#95×C₅₃	C₂³	1	1	yes	characteristic
307	#95×C₅₃	C₂³	1	1	yes	characteristic
308	#95×C₅₃	C₂³	1	1	yes	characteristic
309	#95×C₅₃	C₂³	1	1	yes	characteristic
310	#95×C₅₃	C₂³	1	1	yes	characteristic
311	#95×C₅₃	C₂³	1	1	yes	characteristic
312	#95×C₅₃	C₂³	1	1	yes	characteristic
313	#95×C₅₃	C₂³	1	1	yes	characteristic
314	#95×C₅₃	C₂³	1	1	yes	characteristic
315	#95×C₅₃	C₂³	1	1	yes	characteristic
316	#95×C₅₃	C₂³	1	1	yes	characteristic
317	#95×C₅₃	C₂³	1	1	yes	characteristic
318	#95×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×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	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×Q₈×C₅₃	—	2	2	no	—
354	C₂×Q₈×C₅₃	—	4	1	no	—
355	C₂×Q₈×C₅₃	—	4	1	no	—
356	C₂×D₄×C₅₃	—	2	2	no	—
357	C₂×D₄×C₅₃	—	2	2	no	—
358	C₂×D₄×C₅₃	—	2	2	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	2	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	4	1	no	—
368	C₂²×C₄×C₅₃	—	4	1	no	—
369	C₂²×C₄×C₅₃	—	4	1	no	—
370	C₂²×C₄×C₅₃	—	4	1	no	—
371	C₂²×C₄×C₅₃	—	4	1	no	—
372	C₂²×C₄×C₅₃	—	4	1	no	—
373	C₂²×C₄×C₅₃	—	4	1	no	—
374	C₂²×C₄×C₅₃	—	4	1	no	—
375	C₂²×C₄×C₅₃	—	4	1	no	—
376	C₂²×C₄×C₅₃	—	4	1	no	—
377	C₂²×C₄×C₅₃	—	4	1	no	—
378	C₂²×C₄×C₅₃	—	4	1	no	—
379	C₂²×C₄×C₅₃	—	4	1	no	—
380	C₂²×C₄×C₅₃	—	4	1	no	—
381	C₂²×C₄×C₅₃	—	4	1	no	—
382	C₂²×C₄×C₅₃	#41	1	4	yes	—
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×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	2	no	—
414	C₄⋊C₄×C₅₃	—	2	2	no	—
415	C₄⋊C₄×C₅₃	—	2	2	no	—
416	C₄⋊C₄×C₅₃	—	2	2	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	—	2	2	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	2	no	—
421	C₄⋊C₄×C₅₃	—	2	2	no	—
422	C₄⋊C₄×C₅₃	—	2	2	no	—
423	C₄⋊C₄×C₅₃	—	2	2	no	—
424	C₄⋊C₄×C₅₃	—	2	2	no	—
425	C₄⋊C₄×C₅₃	—	4	1	no	—
426	C₄⋊C₄×C₅₃	—	4	1	no	—
427	C₄⋊C₄×C₅₃	—	4	1	no	—
428	C₄⋊C₄×C₅₃	—	4	1	no	—
429	C₄⋊C₄×C₅₃	—	4	1	no	—
430	C₄⋊C₄×C₅₃	—	4	1	no	—
431	C₄⋊C₄×C₅₃	—	4	1	no	—
432	C₄⋊C₄×C₅₃	—	4	1	no	—
433	C₄⋊C₄×C₅₃	—	4	1	no	—
434	C₄⋊C₄×C₅₃	—	4	1	no	—
435	C₄⋊C₄×C₅₃	—	4	1	no	—
436	C₄⋊C₄×C₅₃	—	4	1	no	—
437	C₄⋊C₄×C₅₃	—	4	1	no	—
438	C₄⋊C₄×C₅₃	—	4	1	no	—
439	C₄⋊C₄×C₅₃	—	4	1	no	—
440	C₄⋊C₄×C₅₃	—	4	1	no	—
441	C₄⋊C₄×C₅₃	—	4	1	no	—
442	C₄⋊C₄×C₅₃	—	4	1	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₄⋊C₄×C₅₃	—	4	1	no	—
447	C₄⋊C₄×C₅₃	—	4	1	no	—
448	C₄⋊C₄×C₅₃	—	4	1	no	—
449	C₄⋊C₄×C₅₃	—	4	1	no	—
450	C₄⋊C₄×C₅₃	—	4	1	no	—
451	C₄⋊C₄×C₅₃	—	4	1	no	—
452	C₄⋊C₄×C₅₃	—	4	1	no	—
453	C₄⋊C₄×C₅₃	—	4	1	no	—
454	C₄⋊C₄×C₅₃	—	4	1	no	—
455	C₄⋊C₄×C₅₃	—	4	1	no	—
456	C₄⋊C₄×C₅₃	—	4	1	no	—
457	C₄⋊C₄×C₅₃	—	4	1	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	—	2	2	no	—
460	C₂²⋊C₄×C₅₃	—	2	2	no	—
461	C₂²⋊C₄×C₅₃	—	2	2	no	—
462	C₂²⋊C₄×C₅₃	—	2	2	no	—
463	C₂²⋊C₄×C₅₃	—	2	2	no	—
464	C₂²⋊C₄×C₅₃	—	2	2	no	—
465	C₂²⋊C₄×C₅₃	—	2	2	no	—
466	C₂²⋊C₄×C₅₃	—	2	2	no	—
467	C₂²⋊C₄×C₅₃	—	4	1	no	—
468	C₂²⋊C₄×C₅₃	—	4	1	no	—
469	C₂²⋊C₄×C₅₃	—	4	1	no	—
470	C₂²⋊C₄×C₅₃	—	4	1	no	—
471	C₂²⋊C₄×C₅₃	—	4	1	no	—
472	C₂²⋊C₄×C₅₃	—	4	1	no	—
473	C₂²⋊C₄×C₅₃	—	4	1	no	—
474	C₂²⋊C₄×C₅₃	—	4	1	no	—
475	C₂²⋊C₄×C₅₃	—	4	1	no	—
476	C₂²⋊C₄×C₅₃	—	4	1	no	—
477	C₂²⋊C₄×C₅₃	—	4	1	no	—
478	C₄²×C₅₃	—	2	2	no	—
479	C₄²×C₅₃	—	2	2	no	—
480	C₄²×C₅₃	—	2	2	no	—
481	C₄²×C₅₃	—	4	1	no	—
482	C₄²×C₅₃	—	4	1	no	—
483	C₄²×C₅₃	—	4	1	no	—
484	C₄²×C₅₃	—	4	1	no	—
485	C₄²×C₅₃	—	4	1	no	—
486	C₄²×C₅₃	—	4	1	no	—
487	C₄²×C₅₃	—	4	1	no	—
488	C₄²×C₅₃	—	4	1	no	—
489	C₂³×C₅₃	—	2	1	no	—
490	C₂³×C₅₃	—	2	1	no	—
491	C₂³×C₅₃	—	2	1	no	—
492	C₂³×C₅₃	—	2	1	no	—
493	C₂³×C₅₃	—	2	1	no	—
494	C₂³×C₅₃	—	2	1	no	—
495	C₂³×C₅₃	—	2	1	no	—
496	C₂³×C₅₃	—	2	1	no	—
497	C₂³×C₅₃	—	2	1	no	—
498	C₂³×C₅₃	—	2	1	no	—
499	C₂³×C₅₃	—	2	1	no	—
500	C₂³×C₅₃	C₂×#41	1	2	yes	—
501	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
502	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
503	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
504	Q₈×C₅₃	—	8	2	no	—
505	D₄×C₅₃	—	4	4	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	1	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	2	1	no	—
519	C₂×C₄×C₅₃	—	2	1	no	—
520	C₂×C₄×C₅₃	—	2	1	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	1	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	—	2	1	no	—
562	C₂×C₄×C₅₃	—	2	1	no	—
563	C₂×C₄×C₅₃	—	2	1	no	—
564	C₂×C₄×C₅₃	—	2	1	no	—
565	C₂×C₄×C₅₃	—	2	1	no	—
566	C₂×C₄×C₅₃	—	2	1	no	—
567	C₂×C₄×C₅₃	—	2	1	no	—
568	C₂×C₄×C₅₃	—	2	1	no	—
569	C₂×C₄×C₅₃	—	2	1	no	—
570	C₂×C₄×C₅₃	—	2	1	no	—
571	C₂×C₄×C₅₃	—	2	1	no	—
572	C₂×C₄×C₅₃	—	2	1	no	—
573	C₂×C₄×C₅₃	—	2	1	no	—
574	C₂×C₄×C₅₃	—	2	1	no	—
575	C₂×C₄×C₅₃	—	2	1	no	—
576	C₂×C₄×C₅₃	—	2	1	no	—
577	C₂×C₄×C₅₃	—	2	1	no	—
578	C₂×C₄×C₅₃	—	2	1	no	—
579	C₂×C₄×C₅₃	—	2	1	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	4	4	no	—
591	C₂×C₄×C₅₃	—	4	4	no	—
592	C₂×C₄×C₅₃	—	4	4	no	—
593	C₂×C₄×C₅₃	—	4	4	no	—
594	C₂×C₄×C₅₃	—	4	4	no	—
595	C₂×C₄×C₅₃	—	8	2	no	—
596	C₂×C₄×C₅₃	—	8	2	no	—
597	C₂×C₄×C₅₃	—	8	2	no	—
598	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
599	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
600	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
601	#36782	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
602	C₂²×C₅₃	—	2	2	no	—
603	C₂²×C₅₃	—	2	2	no	—
604	C₂²×C₅₃	—	2	2	no	—
605	C₂²×C₅₃	—	2	2	no	—
606	C₂²×C₅₃	—	2	2	no	—
607	C₂²×C₅₃	—	2	2	no	—
608	C₂²×C₅₃	—	4	1	no	—
609	C₂²×C₅₃	—	4	1	no	—
610	C₂²×C₅₃	—	4	1	no	—
611	C₂²×C₅₃	—	4	1	no	—
612	C₂²×C₅₃	—	4	1	no	—
613	C₂²×C₅₃	—	4	1	no	—
614	C₂²×C₅₃	—	4	1	no	—
615	C₂²×C₅₃	#541	1	4	yes	—
616	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
617	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
618	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
619	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
620	C₂²×C₅₃	#585	1	1	yes	characteristic
621	C₂²×C₅₃	#585	1	1	yes	characteristic
622	C₂²×C₅₃	#585	1	1	yes	characteristic
623	C₄×C₅₃	—	2	2	no	—
624	C₄×C₅₃	—	2	2	no	—
625	C₄×C₅₃	—	2	2	no	—
626	C₄×C₅₃	—	4	1	no	—
627	C₄×C₅₃	—	4	1	no	—
628	C₄×C₅₃	—	4	1	no	—
629	C₄×C₅₃	—	4	1	no	—
630	C₄×C₅₃	—	4	1	no	—
631	C₄×C₅₃	—	4	1	no	—
632	C₄×C₅₃	—	4	1	no	—
633	C₄×C₅₃	—	4	1	no	—
634	C₄×C₅₃	—	4	1	no	—
635	C₄×C₅₃	—	4	1	no	—
636	C₄×C₅₃	—	4	1	no	—
637	C₄×C₅₃	—	4	1	no	—
638	C₄×C₅₃	—	4	1	no	—
639	C₄×C₅₃	—	4	1	no	—
640	C₄×C₅₃	—	4	1	no	—
641	C₄×C₅₃	—	4	1	no	—
642	C₄×C₅₃	—	4	1	no	—
643	C₄×C₅₃	—	4	1	no	—
644	C₄×C₅₃	—	4	1	no	—
645	C₄×C₅₃	—	4	1	no	—
646	C₄×C₅₃	—	4	1	no	—
647	C₄×C₅₃	—	4	1	no	—
648	C₄×C₅₃	—	4	1	no	—
649	C₄×C₅₃	—	4	1	no	—
650	C₄×C₅₃	—	4	1	no	—
651	C₄×C₅₃	—	4	1	no	—
652	#2852	C₂×C₅₃	1	1	yes	characteristic
653	#2851	C₂×C₅₃	1	1	yes	characteristic, complemented
654	#2783	C₂×C₅₃	1	1	yes	characteristic, complemented
655	#2783	C₂×C₅₃	1	1	yes	characteristic, complemented
656	#2776	C₂×C₅₃	1	1	yes	characteristic, complemented
657	#2776	C₂×C₅₃	1	1	yes	characteristic, complemented
658	#2772	C₂×C₅₃	1	1	yes	characteristic, complemented
659	#2769	C₂×C₅₃	1	1	yes	characteristic, complemented
660	#2766	C₂×C₅₃	1	1	yes	characteristic, complemented
661	#2766	C₂×C₅₃	1	1	yes	characteristic, complemented
662	#2762	C₂×C₅₃	1	1	yes	characteristic, complemented
663	#2762	C₂×C₅₃	1	1	yes	characteristic, complemented
664	#2747	C₂×C₅₃	1	1	yes	characteristic, complemented
665	#2744	C₂×C₅₃	1	1	yes	characteristic, complemented
666	#2725	C₂×C₅₃	1	1	yes	characteristic, complemented
667	#2719	C₂×C₅₃	1	1	yes	characteristic, complemented
668	#2690	C₂×C₅₃	1	1	yes	characteristic, complemented
669	#2689	C₂×C₅₃	1	1	yes	characteristic, complemented
670	#2646	C₂×C₅₃	1	1	yes	characteristic, complemented
671	#2643	C₂×C₅₃	1	1	yes	characteristic
672	#2583	C₂×C₅₃	1	1	yes	characteristic, complemented
673	#2579	C₂×C₅₃	1	1	yes	characteristic
674	#2510	C₂×C₅₃	1	1	yes	characteristic
675	#2510	C₂×C₅₃	1	1	yes	characteristic
676	#2505	C₂×C₅₃	1	1	yes	characteristic, complemented
677	#2505	C₂×C₅₃	1	1	yes	characteristic, complemented
678	#2442	C₂×C₅₃	1	1	yes	characteristic, complemented
679	#2417	C₂×C₅₃	1	1	yes	characteristic
680	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
681	#2318	C₂×C₅₃	1	1	yes	characteristic
682	C₂×#387	C₂×C₅₃	1	1	yes	characteristic, complemented
683	C₂×C₅₃	—	2	4	no	—
684	C₂×C₅₃	—	8	1	no	—
685	C₂×C₅₃	C₂×#541	1	1	yes	characteristic
686	C₂×C₅₃	#3493	1	1	yes	characteristic
687	C₂×C₅₃	#3505	1	1	yes	characteristic
688	C₂×C₅₃	#3535	1	1	yes	characteristic
689	C₂×C₅₃	#3541	1	1	yes	characteristic
690	C₂×C₅₃	#3553	1	1	yes	characteristic
691	C₂×C₅₃	#3564	1	1	yes	characteristic
692	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
693	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
694	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
695	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
696	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
697	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
698	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
699	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
700	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
701	#401	C₂²×C₅₃	1	1	yes	characteristic
702	#401	C₂²×C₅₃	1	1	yes	characteristic
703	#401	C₂²×C₅₃	1	1	yes	characteristic
704	#400	C₂²×C₅₃	1	1	yes	characteristic
705	#400	C₂²×C₅₃	1	1	yes	characteristic
706	#400	C₂²×C₅₃	1	1	yes	characteristic
707	#400	C₂²×C₅₃	1	1	yes	characteristic
708	#400	C₂²×C₅₃	1	1	yes	characteristic
709	#400	C₂²×C₅₃	1	1	yes	characteristic
710	#400	C₂²×C₅₃	1	1	yes	characteristic
711	#400	C₂²×C₅₃	1	1	yes	characteristic
712	#400	C₂²×C₅₃	1	1	yes	characteristic
713	#400	C₂²×C₅₃	1	1	yes	characteristic
714	#400	C₂²×C₅₃	1	1	yes	characteristic
715	#400	C₂²×C₅₃	1	1	yes	characteristic
716	#400	C₂²×C₅₃	1	1	yes	characteristic
717	#400	C₂²×C₅₃	1	1	yes	characteristic
718	#400	C₂²×C₅₃	1	1	yes	characteristic
719	#400	C₂²×C₅₃	1	1	yes	characteristic
720	#400	C₂²×C₅₃	1	1	yes	characteristic
721	#398	C₂²×C₅₃	1	1	yes	characteristic
722	#398	C₂²×C₅₃	1	1	yes	characteristic
723	#398	C₂²×C₅₃	1	1	yes	characteristic
724	#398	C₂²×C₅₃	1	1	yes	characteristic
725	#398	C₂²×C₅₃	1	1	yes	characteristic
726	#398	C₂²×C₅₃	1	1	yes	characteristic
727	#398	C₂²×C₅₃	1	1	yes	characteristic
728	#398	C₂²×C₅₃	1	1	yes	characteristic
729	#398	C₂²×C₅₃	1	1	yes	characteristic
730	#398	C₂²×C₅₃	1	1	yes	characteristic
731	#398	C₂²×C₅₃	1	1	yes	characteristic
732	#398	C₂²×C₅₃	1	1	yes	characteristic
733	#398	C₂²×C₅₃	1	1	yes	characteristic
734	#398	C₂²×C₅₃	1	1	yes	characteristic
735	#397	C₂²×C₅₃	1	1	yes	characteristic
736	#397	C₂²×C₅₃	1	1	yes	characteristic
737	#397	C₂²×C₅₃	1	1	yes	characteristic
738	#397	C₂²×C₅₃	1	1	yes	characteristic
739	#397	C₂²×C₅₃	1	1	yes	characteristic
740	#397	C₂²×C₅₃	1	1	yes	characteristic
741	#397	C₂²×C₅₃	1	1	yes	characteristic
742	#396	C₂²×C₅₃	1	1	yes	characteristic
743	#396	C₂²×C₅₃	1	1	yes	characteristic
744	#396	C₂²×C₅₃	1	1	yes	characteristic
745	#396	C₂²×C₅₃	1	1	yes	characteristic
746	#396	C₂²×C₅₃	1	1	yes	characteristic
747	#395	C₂²×C₅₃	1	1	yes	characteristic
748	#395	C₂²×C₅₃	1	1	yes	characteristic
749	#391	C₂²×C₅₃	1	1	yes	characteristic
750	#391	C₂²×C₅₃	1	1	yes	characteristic
751	#391	C₂²×C₅₃	1	1	yes	characteristic
752	#389	C₂²×C₅₃	1	1	yes	characteristic
753	#389	C₂²×C₅₃	1	1	yes	characteristic
754	#389	C₂²×C₅₃	1	1	yes	characteristic
755	#389	C₂²×C₅₃	1	1	yes	characteristic
756	#389	C₂²×C₅₃	1	1	yes	characteristic
757	#389	C₂²×C₅₃	1	1	yes	characteristic
758	#389	C₂²×C₅₃	1	1	yes	characteristic
759	#389	C₂²×C₅₃	1	1	yes	characteristic
760	#389	C₂²×C₅₃	1	1	yes	characteristic
761	#389	C₂²×C₅₃	1	1	yes	characteristic
762	#389	C₂²×C₅₃	1	1	yes	characteristic
763	#389	C₂²×C₅₃	1	1	yes	characteristic
764	#389	C₂²×C₅₃	1	1	yes	characteristic
765	#388	C₂²×C₅₃	1	1	yes	characteristic
766	#388	C₂²×C₅₃	1	1	yes	characteristic
767	#388	C₂²×C₅₃	1	1	yes	characteristic
768	#388	C₂²×C₅₃	1	1	yes	characteristic
769	#388	C₂²×C₅₃	1	1	yes	characteristic
770	#388	C₂²×C₅₃	1	1	yes	characteristic
771	#388	C₂²×C₅₃	1	1	yes	characteristic
772	#388	C₂²×C₅₃	1	1	yes	characteristic
773	#388	C₂²×C₅₃	1	1	yes	characteristic
774	#387	C₂²×C₅₃	1	1	yes	characteristic
775	#387	C₂²×C₅₃	1	1	yes	characteristic
776	#387	C₂²×C₅₃	1	1	yes	characteristic
777	#387	C₂²×C₅₃	1	1	yes	characteristic
778	#387	C₂²×C₅₃	1	1	yes	characteristic
779	#387	C₂²×C₅₃	1	1	yes	characteristic
780	#387	C₂²×C₅₃	1	1	yes	characteristic
781	#387	C₂²×C₅₃	1	1	yes	characteristic
782	#387	C₂²×C₅₃	1	1	yes	characteristic
783	#387	C₂²×C₅₃	1	1	yes	characteristic
784	#387	C₂²×C₅₃	1	1	yes	characteristic
785	#387	C₂²×C₅₃	1	1	yes	characteristic
786	#387	C₂²×C₅₃	1	1	yes	characteristic
787	#387	C₂²×C₅₃	1	1	yes	characteristic
788	#387	C₂²×C₅₃	1	1	yes	characteristic
789	#387	C₂²×C₅₃	1	1	yes	characteristic
790	#387	C₂²×C₅₃	1	1	yes	characteristic
791	#387	C₂²×C₅₃	1	1	yes	characteristic
792	#387	C₂²×C₅₃	1	1	yes	characteristic
793	#387	C₂²×C₅₃	1	1	yes	characteristic
794	#387	C₂²×C₅₃	1	1	yes	characteristic
795	#387	C₂²×C₅₃	1	1	yes	characteristic
796	#387	C₂²×C₅₃	1	1	yes	characteristic
797	#387	C₂²×C₅₃	1	1	yes	characteristic
798	#387	C₂²×C₅₃	1	1	yes	characteristic
799	#387	C₂²×C₅₃	1	1	yes	characteristic
800	#387	C₂²×C₅₃	1	1	yes	characteristic
801	#387	C₂²×C₅₃	1	1	yes	characteristic
802	#387	C₂²×C₅₃	1	1	yes	characteristic
803	#386	C₂²×C₅₃	1	1	yes	characteristic
804	#386	C₂²×C₅₃	1	1	yes	characteristic
805	#386	C₂²×C₅₃	1	1	yes	characteristic
806	#386	C₂²×C₅₃	1	1	yes	characteristic
807	#386	C₂²×C₅₃	1	1	yes	characteristic
808	#386	C₂²×C₅₃	1	1	yes	characteristic
809	#385	C₂²×C₅₃	1	1	yes	characteristic
810	#385	C₂²×C₅₃	1	1	yes	characteristic
811	#385	C₂²×C₅₃	1	1	yes	characteristic
812	#385	C₂²×C₅₃	1	1	yes	characteristic
813	#385	C₂²×C₅₃	1	1	yes	characteristic
814	#385	C₂²×C₅₃	1	1	yes	characteristic
815	#385	C₂²×C₅₃	1	1	yes	characteristic
816	#385	C₂²×C₅₃	1	1	yes	characteristic
817	#385	C₂²×C₅₃	1	1	yes	characteristic
818	#385	C₂²×C₅₃	1	1	yes	characteristic
819	#385	C₂²×C₅₃	1	1	yes	characteristic
820	#385	C₂²×C₅₃	1	1	yes	characteristic
821	#385	C₂²×C₅₃	1	1	yes	characteristic
822	#385	C₂²×C₅₃	1	1	yes	characteristic
823	#383	C₂²×C₅₃	1	1	yes	characteristic
824	#383	C₂²×C₅₃	1	1	yes	characteristic
825	#383	C₂²×C₅₃	1	1	yes	characteristic
826	#383	C₂²×C₅₃	1	1	yes	characteristic
827	#382	C₂²×C₅₃	1	1	yes	characteristic
828	#382	C₂²×C₅₃	1	1	yes	characteristic
829	#382	C₂²×C₅₃	1	1	yes	characteristic
830	#382	C₂²×C₅₃	1	1	yes	characteristic
831	#382	C₂²×C₅₃	1	1	yes	characteristic
832	#381	C₂²×C₅₃	1	1	yes	characteristic
833	#380	C₂²×C₅₃	1	1	yes	characteristic
834	#380	C₂²×C₅₃	1	1	yes	characteristic
835	#380	C₂²×C₅₃	1	1	yes	characteristic
836	#380	C₂²×C₅₃	1	1	yes	characteristic
837	#380	C₂²×C₅₃	1	1	yes	characteristic
838	#380	C₂²×C₅₃	1	1	yes	characteristic
839	#380	C₂²×C₅₃	1	1	yes	characteristic
840	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
841	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
842	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
843	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
844	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
845	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
846	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
847	C₅₃	#36782	1	1	yes	characteristic, direct product factor, Sylow
848	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
850	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
851	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
853	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
854	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
855	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
856	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
857	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
858	#126	—	4	2	no	—
859	#125	—	4	2	no	—
860	#125	—	4	2	no	—
861	C₂²⋊Q₈	—	2	4	no	—
862	C₂²⋊Q₈	—	4	2	no	—
863	C₄×D₄	—	2	4	no	—
864	C₂×C₄⋊C₄	—	2	4	no	—
865	C₂×C₄⋊C₄	—	4	2	no	—
866	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
868	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
869	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
871	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
872	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
873	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
875	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
880	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
886	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
890	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
891	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
896	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
897	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
898	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
899	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
900	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
901	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
902	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
903	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
904	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
905	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
906	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
907	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
908	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
909	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
910	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
911	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
912	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
913	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
914	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
915	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
916	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
917	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
918	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
919	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
920	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
921	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
922	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
923	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
924	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
925	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
926	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
927	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
928	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
929	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
930	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
931	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
932	C₂×C₄²	—	4	2	no	—
933	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
934	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
935	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
936	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
937	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
938	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
939	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
940	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
941	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
942	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
943	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
944	#95	C₂³×C₅₃	1	1	yes	characteristic
945	#95	C₂³×C₅₃	1	1	yes	characteristic
946	#95	C₂³×C₅₃	1	1	yes	characteristic
947	#95	C₂³×C₅₃	1	1	yes	characteristic
948	#95	C₂³×C₅₃	1	1	yes	characteristic
949	#95	C₂³×C₅₃	1	1	yes	characteristic
950	#95	C₂³×C₅₃	1	1	yes	characteristic
951	#95	C₂³×C₅₃	1	1	yes	characteristic
952	#95	C₂³×C₅₃	1	1	yes	characteristic
953	#95	C₂³×C₅₃	1	1	yes	characteristic
954	#95	C₂³×C₅₃	1	1	yes	characteristic
955	#95	C₂³×C₅₃	1	1	yes	characteristic
956	#95	C₂³×C₅₃	1	1	yes	characteristic
957	#95	C₂³×C₅₃	1	1	yes	characteristic
958	#95	C₂³×C₅₃	1	1	yes	characteristic
959	#95	C₂³×C₅₃	1	1	yes	characteristic
960	#95	C₂³×C₅₃	1	1	yes	characteristic
961	#95	C₂³×C₅₃	1	1	yes	characteristic
962	#95	C₂³×C₅₃	1	1	yes	characteristic
963	#95	C₂³×C₅₃	1	1	yes	characteristic
964	#95	C₂³×C₅₃	1	1	yes	characteristic
965	#95	C₂³×C₅₃	1	1	yes	characteristic
966	#95	C₂³×C₅₃	1	1	yes	characteristic
967	#95	C₂³×C₅₃	1	1	yes	characteristic
968	#95	C₂³×C₅₃	1	1	yes	characteristic
969	#95	C₂³×C₅₃	1	1	yes	characteristic
970	#95	C₂³×C₅₃	1	1	yes	characteristic
971	#95	C₂³×C₅₃	1	1	yes	characteristic
972	#95	C₂³×C₅₃	1	1	yes	characteristic
973	#95	C₂³×C₅₃	1	1	yes	characteristic
974	#95	C₂³×C₅₃	1	1	yes	characteristic
975	#95	C₂³×C₅₃	1	1	yes	characteristic
976	#95	C₂³×C₅₃	1	1	yes	characteristic
977	#95	C₂³×C₅₃	1	1	yes	characteristic
978	#95	C₂³×C₅₃	1	1	yes	characteristic
979	#95	C₂³×C₅₃	1	1	yes	characteristic
980	#95	C₂³×C₅₃	1	1	yes	characteristic
981	#95	C₂³×C₅₃	1	1	yes	characteristic
982	#95	C₂³×C₅₃	1	1	yes	characteristic
983	#95	C₂³×C₅₃	1	1	yes	characteristic
984	#95	C₂³×C₅₃	1	1	yes	characteristic
985	#95	C₂³×C₅₃	1	1	yes	characteristic
986	#95	C₂³×C₅₃	1	1	yes	characteristic
987	#95	C₂³×C₅₃	1	1	yes	characteristic
988	#95	C₂³×C₅₃	1	1	yes	characteristic
989	#95	C₂³×C₅₃	1	1	yes	characteristic
990	#95	C₂³×C₅₃	1	1	yes	characteristic
991	#95	C₂³×C₅₃	1	1	yes	characteristic
992	#95	C₂³×C₅₃	1	1	yes	characteristic
993	#95	C₂³×C₅₃	1	1	yes	characteristic
994	#95	C₂³×C₅₃	1	1	yes	characteristic
995	#95	C₂³×C₅₃	1	1	yes	characteristic
996	#95	C₂³×C₅₃	1	1	yes	characteristic
997	#95	C₂³×C₅₃	1	1	yes	characteristic
998	#95	C₂³×C₅₃	1	1	yes	characteristic
999	#95	C₂³×C₅₃	1	1	yes	characteristic
1000	#95	C₂³×C₅₃	1	1	yes	characteristic
1001	#95	C₂³×C₅₃	1	1	yes	characteristic
1002	#95	C₂³×C₅₃	1	1	yes	characteristic
1003	#95	C₂³×C₅₃	1	1	yes	characteristic
1004	#95	C₂³×C₅₃	1	1	yes	characteristic
1005	#95	C₂³×C₅₃	1	1	yes	characteristic
1006	#95	C₂³×C₅₃	1	1	yes	characteristic
1007	#95	C₂³×C₅₃	1	1	yes	characteristic
1008	#95	C₂³×C₅₃	1	1	yes	characteristic
1009	#95	C₂³×C₅₃	1	1	yes	characteristic
1010	#95	C₂³×C₅₃	1	1	yes	characteristic
1011	#95	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₂×Q₈	—	2	2	no	—
1015	C₂×Q₈	—	4	1	no	—
1016	C₂×Q₈	—	4	1	no	—
1017	C₂×D₄	—	2	2	no	—
1018	C₂×D₄	—	2	2	no	—
1019	C₂×D₄	—	2	2	no	—
1020	C₂²×C₄	—	2	2	no	—
1021	C₂²×C₄	—	2	2	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	2	no	—
1028	C₂²×C₄	—	4	1	no	—
1029	C₂²×C₄	—	4	1	no	—
1030	C₂²×C₄	—	4	1	no	—
1031	C₂²×C₄	—	4	1	no	—
1032	C₂²×C₄	—	4	1	no	—
1033	C₂²×C₄	—	4	1	no	—
1034	C₂²×C₄	—	4	1	no	—
1035	C₂²×C₄	—	4	1	no	—
1036	C₂²×C₄	—	4	1	no	—
1037	C₂²×C₄	—	4	1	no	—
1038	C₂²×C₄	—	4	1	no	—
1039	C₂²×C₄	—	4	1	no	—
1040	C₂²×C₄	—	4	1	no	—
1041	C₂²×C₄	—	4	1	no	—
1042	C₂²×C₄	—	4	1	no	—
1043	C₂²×C₄	#41×C₅₃	1	4	yes	—
1044	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1046	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1047	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1050	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1055	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1056	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1057	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1058	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1059	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1060	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1061	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1062	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1063	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1064	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1065	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1066	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1068	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1069	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1070	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1071	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1072	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	2	no	—
1086	C₄⋊C₄	—	4	1	no	—
1087	C₄⋊C₄	—	4	1	no	—
1088	C₄⋊C₄	—	4	1	no	—
1089	C₄⋊C₄	—	4	1	no	—
1090	C₄⋊C₄	—	4	1	no	—
1091	C₄⋊C₄	—	4	1	no	—
1092	C₄⋊C₄	—	4	1	no	—
1093	C₄⋊C₄	—	4	1	no	—
1094	C₄⋊C₄	—	4	1	no	—
1095	C₄⋊C₄	—	4	1	no	—
1096	C₄⋊C₄	—	4	1	no	—
1097	C₄⋊C₄	—	4	1	no	—
1098	C₄⋊C₄	—	4	1	no	—
1099	C₄⋊C₄	—	4	1	no	—
1100	C₄⋊C₄	—	4	1	no	—
1101	C₄⋊C₄	—	4	1	no	—
1102	C₄⋊C₄	—	4	1	no	—
1103	C₄⋊C₄	—	4	1	no	—
1104	C₄⋊C₄	—	4	1	no	—
1105	C₄⋊C₄	—	4	1	no	—
1106	C₄⋊C₄	—	4	1	no	—
1107	C₄⋊C₄	—	4	1	no	—
1108	C₄⋊C₄	—	4	1	no	—
1109	C₄⋊C₄	—	4	1	no	—
1110	C₄⋊C₄	—	4	1	no	—
1111	C₄⋊C₄	—	4	1	no	—
1112	C₄⋊C₄	—	4	1	no	—
1113	C₄⋊C₄	—	4	1	no	—
1114	C₄⋊C₄	—	4	1	no	—
1115	C₄⋊C₄	—	4	1	no	—
1116	C₄⋊C₄	—	4	1	no	—
1117	C₄⋊C₄	—	4	1	no	—
1118	C₄⋊C₄	—	4	1	no	—
1119	C₂²⋊C₄	—	2	2	no	—
1120	C₂²⋊C₄	—	2	2	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	2	no	—
1128	C₂²⋊C₄	—	4	1	no	—
1129	C₂²⋊C₄	—	4	1	no	—
1130	C₂²⋊C₄	—	4	1	no	—
1131	C₂²⋊C₄	—	4	1	no	—
1132	C₂²⋊C₄	—	4	1	no	—
1133	C₂²⋊C₄	—	4	1	no	—
1134	C₂²⋊C₄	—	4	1	no	—
1135	C₂²⋊C₄	—	4	1	no	—
1136	C₂²⋊C₄	—	4	1	no	—
1137	C₂²⋊C₄	—	4	1	no	—
1138	C₂²⋊C₄	—	4	1	no	—
1139	C₄²	—	2	2	no	—
1140	C₄²	—	2	2	no	—
1141	C₄²	—	2	2	no	—
1142	C₄²	—	4	1	no	—
1143	C₄²	—	4	1	no	—
1144	C₄²	—	4	1	no	—
1145	C₄²	—	4	1	no	—
1146	C₄²	—	4	1	no	—
1147	C₄²	—	4	1	no	—
1148	C₄²	—	4	1	no	—
1149	C₄²	—	4	1	no	—
1150	C₂³	—	2	1	no	—
1151	C₂³	—	2	1	no	—
1152	C₂³	—	2	1	no	—
1153	C₂³	—	2	1	no	—
1154	C₂³	—	2	1	no	—
1155	C₂³	—	2	1	no	—
1156	C₂³	—	2	1	no	—
1157	C₂³	—	2	1	no	—
1158	C₂³	—	2	1	no	—
1159	C₂³	—	2	1	no	—
1160	C₂³	—	2	1	no	—
1161	C₂³	C₂×#41×C₅₃	1	2	yes	—
1162	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1163	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1164	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1165	Q₈	—	8	2	no	—
1166	D₄	—	4	4	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	1	no	—
1172	C₂×C₄	—	2	1	no	—
1173	C₂×C₄	—	2	1	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	1	no	—
1178	C₂×C₄	—	2	1	no	—
1179	C₂×C₄	—	2	1	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	1	no	—
1189	C₂×C₄	—	2	1	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	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	—	2	1	no	—
1249	C₂×C₄	—	2	1	no	—
1250	C₂×C₄	—	2	1	no	—
1251	C₂×C₄	—	4	4	no	—
1252	C₂×C₄	—	4	4	no	—
1253	C₂×C₄	—	4	4	no	—
1254	C₂×C₄	—	4	4	no	—
1255	C₂×C₄	—	4	4	no	—
1256	C₂×C₄	—	8	2	no	—
1257	C₂×C₄	—	8	2	no	—
1258	C₂×C₄	—	8	2	no	—
1259	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1260	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1261	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1262	C₂²	—	2	2	no	—
1263	C₂²	—	2	2	no	—
1264	C₂²	—	2	2	no	—
1265	C₂²	—	2	2	no	—
1266	C₂²	—	2	2	no	—
1267	C₂²	—	2	2	no	—
1268	C₂²	—	4	1	no	—
1269	C₂²	—	4	1	no	—
1270	C₂²	—	4	1	no	—
1271	C₂²	—	4	1	no	—
1272	C₂²	—	4	1	no	—
1273	C₂²	—	4	1	no	—
1274	C₂²	—	4	1	no	—
1275	C₂²	C₅₃×#541	1	4	yes	—
1276	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1277	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1278	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1279	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1280	C₂²	C₅₃×#585	1	1	yes	characteristic
1281	C₂²	C₅₃×#585	1	1	yes	characteristic
1282	C₂²	C₅₃×#585	1	1	yes	characteristic
1283	C₄	—	2	2	no	—
1284	C₄	—	2	2	no	—
1285	C₄	—	2	2	no	—
1286	C₄	—	4	1	no	—
1287	C₄	—	4	1	no	—
1288	C₄	—	4	1	no	—
1289	C₄	—	4	1	no	—
1290	C₄	—	4	1	no	—
1291	C₄	—	4	1	no	—
1292	C₄	—	4	1	no	—
1293	C₄	—	4	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	1	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	1	no	—
1299	C₄	—	4	1	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	—	4	1	no	—
1305	C₄	—	4	1	no	—
1306	C₄	—	4	1	no	—
1307	C₄	—	4	1	no	—
1308	C₄	—	4	1	no	—
1309	C₄	—	4	1	no	—
1310	C₄	—	4	1	no	—
1311	C₄	—	4	1	no	—
1312	C₂	—	2	4	no	—
1313	C₂	—	8	1	no	—
1314	C₂	C₂×C₅₃×#541	1	1	yes	characteristic
1315	C₂	C₅₃×#3493	1	1	yes	characteristic
1316	C₂	C₅₃×#3505	1	1	yes	characteristic
1317	C₂	C₅₃×#3535	1	1	yes	characteristic
1318	C₂	C₅₃×#3541	1	1	yes	characteristic
1319	C₂	C₅₃×#3553	1	1	yes	characteristic
1320	C₂	C₅₃×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂²×D₄×C₅₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2851	C₂	semidirect
3. C₅₃×#2783	C₂	semidirect
4. C₅₃×#2783	C₂	semidirect
5. C₅₃×#2776	C₂	semidirect
6. C₅₃×#2776	C₂	semidirect
7. C₅₃×#2772	C₂	semidirect
8. C₅₃×#2769	C₂	semidirect
9. C₅₃×#2766	C₂	semidirect
10. C₅₃×#2766	C₂	semidirect
11. C₅₃×#2762	C₂	semidirect
12. C₅₃×#2762	C₂	semidirect
13. C₅₃×#2747	C₂	semidirect
14. C₅₃×#2744	C₂	semidirect
15. C₅₃×#2725	C₂	semidirect
16. C₅₃×#2719	C₂	semidirect
17. C₅₃×#2690	C₂	semidirect
18. C₅₃×#2689	C₂	semidirect
19. C₅₃×#2646	C₂	semidirect
21. C₅₃×#2583	C₂	semidirect
25. C₅₃×#2505	C₂	semidirect
26. C₅₃×#2505	C₂	semidirect
27. C₅₃×#2442	C₂	semidirect
29. C₅₃×#2329	C₂	semidirect
31. C₂×C₅₃×#387	C₂	semidirect
601. #36782	C₅₃	direct (N × H)
653. #2851	C₂×C₅₃	semidirect
654. #2783	C₂×C₅₃	semidirect
655. #2783	C₂×C₅₃	semidirect
656. #2776	C₂×C₅₃	semidirect
657. #2776	C₂×C₅₃	semidirect
658. #2772	C₂×C₅₃	semidirect
659. #2769	C₂×C₅₃	semidirect
660. #2766	C₂×C₅₃	semidirect
661. #2766	C₂×C₅₃	semidirect
662. #2762	C₂×C₅₃	semidirect
663. #2762	C₂×C₅₃	semidirect
664. #2747	C₂×C₅₃	semidirect
665. #2744	C₂×C₅₃	semidirect
666. #2725	C₂×C₅₃	semidirect
667. #2719	C₂×C₅₃	semidirect
668. #2690	C₂×C₅₃	semidirect
669. #2689	C₂×C₅₃	semidirect
670. #2646	C₂×C₅₃	semidirect
672. #2583	C₂×C₅₃	semidirect
676. #2505	C₂×C₅₃	semidirect
677. #2505	C₂×C₅₃	semidirect
678. #2442	C₂×C₅₃	semidirect
680. #2329	C₂×C₅₃	semidirect
682. C₂×#387	C₂×C₅₃	semidirect
847. C₅₃	#36782	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#2852	2
C₅₃×#2851	2
C₅₃×#2783	2
C₅₃×#2776	2
C₅₃×#2772	2
C₅₃×#2769	2
C₅₃×#2766	2
C₅₃×#2762	2
C₅₃×#2747	2
C₅₃×#2744	2
C₅₃×#2725	2
C₅₃×#2719	2
C₅₃×#2690	2
C₅₃×#2689	2
C₅₃×#2646	2
C₅₃×#2643	2
C₅₃×#2583	2
C₅₃×#2579	2
C₅₃×#2510	2
C₅₃×#2505	2
C₅₃×#2442	2
C₅₃×#2417	2
C₅₃×#2329	2
C₅₃×#2318	2
C₂×C₅₃×#387	2
#36782	53

Subgroups — C53×#36782 #27244294

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36782 #27244294