Subgroups — C₅₃×#35027 #27242539

Order 13568.

1840 conjugacy classes of subgroups.

The subgroup lattice has 1456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2866	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2865	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2853	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2852	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2654	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2650	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2649	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2597	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2596	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2595	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2594	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2569	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2564	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2534	C₂	1	1	yes	maximal, characteristic
17	C₅₃×#2525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2516	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2493	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2480	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2469	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2458	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2419	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2418	C₂	1	1	yes	maximal, characteristic
25	C₅₃×#2322	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic
27	C₅₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2312	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#388	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄²×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
41	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#401	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#399	C₂²	1	1	yes	characteristic
56	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#397	C₂²	1	1	yes	characteristic
61	C₅₃×#397	C₂²	1	1	yes	characteristic
62	C₅₃×#397	C₂²	1	1	yes	characteristic
63	C₅₃×#397	C₂²	1	1	yes	characteristic
64	C₅₃×#397	C₂²	1	1	yes	characteristic
65	C₅₃×#397	C₂²	1	1	yes	characteristic
66	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#396	C₂²	1	1	yes	characteristic
69	C₅₃×#396	C₂²	1	1	yes	characteristic
70	C₅₃×#396	C₂²	1	1	yes	characteristic
71	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#394	C₂²	1	1	yes	characteristic
73	C₅₃×#394	C₂²	1	1	yes	characteristic
74	C₅₃×#394	C₂²	1	1	yes	characteristic
75	C₅₃×#394	C₂²	1	1	yes	characteristic
76	C₅₃×#393	C₂²	1	1	yes	characteristic
77	C₅₃×#393	C₂²	1	1	yes	characteristic
78	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#390	C₂²	1	1	yes	characteristic
81	C₅₃×#390	C₂²	1	1	yes	characteristic
82	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#388	C₂²	1	1	yes	characteristic
86	C₅₃×#388	C₂²	1	1	yes	characteristic
87	C₅₃×#388	C₂²	1	1	yes	characteristic
88	C₅₃×#388	C₂²	1	1	yes	characteristic
89	C₅₃×#388	C₂²	1	1	yes	characteristic
90	C₅₃×#388	C₂²	1	1	yes	characteristic
91	C₅₃×#388	C₂²	1	1	yes	characteristic
92	C₅₃×#388	C₂²	1	1	yes	characteristic
93	C₅₃×#388	C₂²	1	1	yes	characteristic
94	C₅₃×#388	C₂²	1	1	yes	characteristic
95	C₅₃×#388	C₂²	1	1	yes	characteristic
96	C₅₃×#388	C₂²	1	1	yes	characteristic
97	C₅₃×#388	C₂²	1	1	yes	characteristic
98	C₅₃×#388	C₂²	1	1	yes	characteristic
99	C₅₃×#388	C₂²	1	1	yes	characteristic
100	C₅₃×#388	C₂²	1	1	yes	characteristic
101	C₅₃×#388	C₂²	1	1	yes	characteristic
102	C₅₃×#388	C₂²	1	1	yes	characteristic
103	C₅₃×#388	C₂²	1	1	yes	characteristic
104	C₅₃×#388	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×#388	C₂²	1	1	yes	characteristic
115	C₅₃×#388	C₂²	1	1	yes	characteristic
116	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#386	C₂²	1	1	yes	characteristic
142	C₅₃×#386	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×#385	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, complemented
153	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#381	C₂²	1	1	yes	characteristic
159	C₅₃×#381	C₂²	1	1	yes	characteristic
160	C₅₃×#381	C₂²	1	1	yes	characteristic
161	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#380	C₂²	1	1	yes	characteristic
163	C₅₃×#380	C₂²	1	1	yes	characteristic
164	C₅₃×#380	C₂²	1	1	yes	characteristic
165	C₅₃×#380	C₂²	1	1	yes	characteristic
166	C₅₃×#380	C₂²	1	1	yes	characteristic
167	C₅₃×#379	C₂²	1	1	yes	characteristic
168	C₅₃×#379	C₂²	1	1	yes	characteristic
169	C₅₃×#379	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₅₃	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, complemented
182	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
186	C₄³×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×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	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	#126×C₅₃	—	4	2	no	—
202	#123×C₅₃	—	2	4	no	—
203	#123×C₅₃	—	4	2	no	—
204	C₂²⋊Q₈×C₅₃	—	2	4	no	—
205	#120×C₅₃	—	2	4	no	—
206	C₄×Q₈×C₅₃	—	4	2	no	—
207	C₄×D₄×C₅₃	—	2	4	no	—
208	C₄×D₄×C₅₃	—	2	4	no	—
209	C₄×D₄×C₅₃	—	2	4	no	—
210	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
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×C₂²⋊C₄×C₅₃	—	2	4	no	—
242	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
243	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
244	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₅₃	—	4	2	no	—
287	C₂×C₄²×C₅₃	—	4	2	no	—
288	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₄²×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	#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	C₂⁴×C₅₃	—	2	2	no	—
358	C₂⁴×C₅₃	—	2	2	no	—
359	C₂⁴×C₅₃	—	2	2	no	—
360	C₂⁴×C₅₃	—	4	1	no	—
361	C₂⁴×C₅₃	—	4	1	no	—
362	C₂⁴×C₅₃	—	4	1	no	—
363	C₂⁴×C₅₃	—	4	1	no	—
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×Q₈×C₅₃	—	2	2	no	—
369	C₂×Q₈×C₅₃	—	4	1	no	—
370	C₂×Q₈×C₅₃	—	4	1	no	—
371	C₂×D₄×C₅₃	—	2	2	no	—
372	C₂×D₄×C₅₃	—	2	2	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	4	1	no	—
376	C₂×D₄×C₅₃	—	4	1	no	—
377	C₂×D₄×C₅₃	—	4	1	no	—
378	C₂×D₄×C₅₃	—	4	1	no	—
379	C₂×D₄×C₅₃	#41	1	4	yes	—
380	C₂²×C₄×C₅₃	—	2	2	no	—
381	C₂²×C₄×C₅₃	—	2	2	no	—
382	C₂²×C₄×C₅₃	—	2	2	no	—
383	C₂²×C₄×C₅₃	—	2	2	no	—
384	C₂²×C₄×C₅₃	—	2	2	no	—
385	C₂²×C₄×C₅₃	—	2	2	no	—
386	C₂²×C₄×C₅₃	—	2	2	no	—
387	C₂²×C₄×C₅₃	—	2	2	no	—
388	C₂²×C₄×C₅₃	—	2	2	no	—
389	C₂²×C₄×C₅₃	—	2	2	no	—
390	C₂²×C₄×C₅₃	—	2	2	no	—
391	C₂²×C₄×C₅₃	—	4	1	no	—
392	C₂²×C₄×C₅₃	—	4	1	no	—
393	C₂²×C₄×C₅₃	—	4	1	no	—
394	C₂²×C₄×C₅₃	—	4	1	no	—
395	C₂²×C₄×C₅₃	—	4	1	no	—
396	C₂²×C₄×C₅₃	—	4	1	no	—
397	C₂²×C₄×C₅₃	—	4	1	no	—
398	C₂²×C₄×C₅₃	—	4	1	no	—
399	C₂²×C₄×C₅₃	—	4	1	no	—
400	C₂²×C₄×C₅₃	—	4	1	no	—
401	C₂²×C₄×C₅₃	—	4	1	no	—
402	C₂²×C₄×C₅₃	—	4	1	no	—
403	C₂²×C₄×C₅₃	—	4	1	no	—
404	C₂²×C₄×C₅₃	—	4	1	no	—
405	C₂²×C₄×C₅₃	#41	1	4	yes	—
406	C₂²×C₄×C₅₃	#41	1	4	yes	—
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₅₃	—	2	2	no	—
435	C₄⋊C₄×C₅₃	—	2	2	no	—
436	C₄⋊C₄×C₅₃	—	2	2	no	—
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	—	2	2	no	—
444	C₄⋊C₄×C₅₃	—	2	2	no	—
445	C₄⋊C₄×C₅₃	—	2	2	no	—
446	C₄⋊C₄×C₅₃	—	2	2	no	—
447	C₄⋊C₄×C₅₃	—	2	2	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	C₄⋊C₄×C₅₃	—	4	1	no	—
459	C₄⋊C₄×C₅₃	—	4	1	no	—
460	C₄⋊C₄×C₅₃	—	4	1	no	—
461	C₄⋊C₄×C₅₃	—	4	1	no	—
462	C₄⋊C₄×C₅₃	—	4	1	no	—
463	C₄⋊C₄×C₅₃	—	4	1	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	—	2	2	no	—
468	C₂²⋊C₄×C₅₃	—	2	2	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	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	—	2	2	no	—
486	C₂²⋊C₄×C₅₃	—	2	2	no	—
487	C₂²⋊C₄×C₅₃	—	2	2	no	—
488	C₂²⋊C₄×C₅₃	—	4	1	no	—
489	C₂²⋊C₄×C₅₃	—	4	1	no	—
490	C₂²⋊C₄×C₅₃	—	4	1	no	—
491	C₂²⋊C₄×C₅₃	—	4	1	no	—
492	C₂²⋊C₄×C₅₃	—	4	1	no	—
493	C₂²⋊C₄×C₅₃	—	4	1	no	—
494	C₂²⋊C₄×C₅₃	—	4	1	no	—
495	C₂²⋊C₄×C₅₃	—	4	1	no	—
496	C₂²⋊C₄×C₅₃	—	4	1	no	—
497	C₂²⋊C₄×C₅₃	—	4	1	no	—
498	C₂²⋊C₄×C₅₃	—	4	1	no	—
499	C₂²⋊C₄×C₅₃	—	4	1	no	—
500	C₂²⋊C₄×C₅₃	—	4	1	no	—
501	C₂²⋊C₄×C₅₃	—	4	1	no	—
502	C₂²⋊C₄×C₅₃	—	4	1	no	—
503	C₂²⋊C₄×C₅₃	—	4	1	no	—
504	C₂²⋊C₄×C₅₃	—	4	1	no	—
505	C₂²⋊C₄×C₅₃	—	4	1	no	—
506	C₄²×C₅₃	—	2	2	no	—
507	C₄²×C₅₃	—	2	2	no	—
508	C₄²×C₅₃	—	2	2	no	—
509	C₄²×C₅₃	—	2	2	no	—
510	C₄²×C₅₃	—	2	2	no	—
511	C₄²×C₅₃	—	2	2	no	—
512	C₄²×C₅₃	—	4	1	no	—
513	C₄²×C₅₃	—	4	1	no	—
514	C₄²×C₅₃	—	4	1	no	—
515	C₄²×C₅₃	—	4	1	no	—
516	C₄²×C₅₃	—	4	1	no	—
517	C₄²×C₅₃	—	4	1	no	—
518	C₄²×C₅₃	—	4	1	no	—
519	C₄²×C₅₃	—	4	1	no	—
520	C₄²×C₅₃	—	4	1	no	—
521	C₄²×C₅₃	—	4	1	no	—
522	C₄²×C₅₃	—	4	1	no	—
523	C₂³×C₅₃	—	2	1	no	—
524	C₂³×C₅₃	—	2	1	no	—
525	C₂³×C₅₃	—	2	1	no	—
526	C₂³×C₅₃	—	2	1	no	—
527	C₂³×C₅₃	—	2	1	no	—
528	C₂³×C₅₃	—	2	1	no	—
529	C₂³×C₅₃	—	2	1	no	—
530	C₂³×C₅₃	—	2	1	no	—
531	C₂³×C₅₃	—	2	1	no	—
532	C₂³×C₅₃	—	2	1	no	—
533	C₂³×C₅₃	—	2	1	no	—
534	C₂³×C₅₃	—	2	1	no	—
535	C₂³×C₅₃	—	2	1	no	—
536	C₂³×C₅₃	—	2	1	no	—
537	C₂³×C₅₃	—	2	1	no	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	1	no	—
547	C₂³×C₅₃	—	4	4	no	—
548	C₂³×C₅₃	—	4	4	no	—
549	C₂³×C₅₃	—	4	4	no	—
550	C₂³×C₅₃	—	8	2	no	—
551	C₂³×C₅₃	—	8	2	no	—
552	C₂³×C₅₃	—	8	2	no	—
553	C₂³×C₅₃	—	8	2	no	—
554	C₂³×C₅₃	C₂×#41	1	2	yes	—
555	C₂³×C₅₃	C₂×#41	1	2	yes	—
556	C₂³×C₅₃	C₂×#41	1	2	yes	—
557	C₂³×C₅₃	C₂×#41	1	2	yes	—
558	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
559	Q₈×C₅₃	—	4	4	no	—
560	D₄×C₅₃	—	2	8	no	—
561	D₄×C₅₃	—	8	2	no	—
562	D₄×C₅₃	—	8	2	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	—	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	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	4	4	no	—
639	C₂×C₄×C₅₃	—	4	4	no	—
640	C₂×C₄×C₅₃	—	4	4	no	—
641	C₂×C₄×C₅₃	—	4	4	no	—
642	C₂×C₄×C₅₃	—	4	4	no	—
643	C₂×C₄×C₅₃	—	4	4	no	—
644	C₂×C₄×C₅₃	—	4	4	no	—
645	C₂×C₄×C₅₃	—	8	2	no	—
646	C₂×C₄×C₅₃	—	8	2	no	—
647	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
648	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
649	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
650	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
651	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
652	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
653	#35027	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
654	C₂²×C₅₃	—	2	2	no	—
655	C₂²×C₅₃	—	2	2	no	—
656	C₂²×C₅₃	—	2	2	no	—
657	C₂²×C₅₃	—	2	2	no	—
658	C₂²×C₅₃	—	2	2	no	—
659	C₂²×C₅₃	—	2	2	no	—
660	C₂²×C₅₃	—	2	2	no	—
661	C₂²×C₅₃	—	2	2	no	—
662	C₂²×C₅₃	—	2	2	no	—
663	C₂²×C₅₃	—	4	1	no	—
664	C₂²×C₅₃	—	4	1	no	—
665	C₂²×C₅₃	—	4	1	no	—
666	C₂²×C₅₃	—	4	1	no	—
667	C₂²×C₅₃	—	4	1	no	—
668	C₂²×C₅₃	—	4	1	no	—
669	C₂²×C₅₃	—	4	1	no	—
670	C₂²×C₅₃	—	4	1	no	—
671	C₂²×C₅₃	—	4	1	no	—
672	C₂²×C₅₃	—	4	1	no	—
673	C₂²×C₅₃	—	4	1	no	—
674	C₂²×C₅₃	—	4	1	no	—
675	C₂²×C₅₃	—	4	1	no	—
676	C₂²×C₅₃	—	4	1	no	—
677	C₂²×C₅₃	—	4	1	no	—
678	C₂²×C₅₃	—	4	1	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	8	8	no	—
682	C₂²×C₅₃	#529	1	4	yes	—
683	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
684	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
685	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
686	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂²×C₅₃	#585	1	1	yes	characteristic
688	C₂²×C₅₃	#585	1	1	yes	characteristic
689	C₂²×C₅₃	#585	1	1	yes	characteristic
690	C₄×C₅₃	—	2	2	no	—
691	C₄×C₅₃	—	2	2	no	—
692	C₄×C₅₃	—	2	2	no	—
693	C₄×C₅₃	—	2	2	no	—
694	C₄×C₅₃	—	2	2	no	—
695	C₄×C₅₃	—	2	2	no	—
696	C₄×C₅₃	—	4	1	no	—
697	C₄×C₅₃	—	4	1	no	—
698	C₄×C₅₃	—	4	1	no	—
699	C₄×C₅₃	—	4	1	no	—
700	C₄×C₅₃	—	4	1	no	—
701	C₄×C₅₃	—	4	1	no	—
702	C₄×C₅₃	—	4	1	no	—
703	C₄×C₅₃	—	4	1	no	—
704	C₄×C₅₃	—	4	1	no	—
705	C₄×C₅₃	—	4	1	no	—
706	C₄×C₅₃	—	4	1	no	—
707	C₄×C₅₃	—	4	1	no	—
708	C₄×C₅₃	—	4	1	no	—
709	C₄×C₅₃	—	4	1	no	—
710	C₄×C₅₃	—	4	1	no	—
711	C₄×C₅₃	—	4	1	no	—
712	C₄×C₅₃	—	4	1	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	#2866	C₂×C₅₃	1	1	yes	characteristic, complemented
718	#2865	C₂×C₅₃	1	1	yes	characteristic, complemented
719	#2853	C₂×C₅₃	1	1	yes	characteristic, complemented
720	#2852	C₂×C₅₃	1	1	yes	characteristic, complemented
721	#2654	C₂×C₅₃	1	1	yes	characteristic, complemented
722	#2653	C₂×C₅₃	1	1	yes	characteristic, complemented
723	#2650	C₂×C₅₃	1	1	yes	characteristic, complemented
724	#2649	C₂×C₅₃	1	1	yes	characteristic, complemented
725	#2597	C₂×C₅₃	1	1	yes	characteristic, complemented
726	#2596	C₂×C₅₃	1	1	yes	characteristic, complemented
727	#2595	C₂×C₅₃	1	1	yes	characteristic, complemented
728	#2594	C₂×C₅₃	1	1	yes	characteristic, complemented
729	#2569	C₂×C₅₃	1	1	yes	characteristic, complemented
730	#2564	C₂×C₅₃	1	1	yes	characteristic, complemented
731	#2561	C₂×C₅₃	1	1	yes	characteristic, complemented
732	#2534	C₂×C₅₃	1	1	yes	characteristic
733	#2525	C₂×C₅₃	1	1	yes	characteristic, complemented
734	#2516	C₂×C₅₃	1	1	yes	characteristic, complemented
735	#2493	C₂×C₅₃	1	1	yes	characteristic, complemented
736	#2480	C₂×C₅₃	1	1	yes	characteristic, complemented
737	#2469	C₂×C₅₃	1	1	yes	characteristic, complemented
738	#2458	C₂×C₅₃	1	1	yes	characteristic, complemented
739	#2419	C₂×C₅₃	1	1	yes	characteristic, complemented
740	#2418	C₂×C₅₃	1	1	yes	characteristic
741	#2322	C₂×C₅₃	1	1	yes	characteristic, complemented
742	#2321	C₂×C₅₃	1	1	yes	characteristic
743	#2313	C₂×C₅₃	1	1	yes	characteristic, complemented
744	#2312	C₂×C₅₃	1	1	yes	characteristic, complemented
745	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
746	C₂×#388	C₂×C₅₃	1	1	yes	characteristic, complemented
747	C₄²×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
748	C₂×C₅₃	—	2	4	no	—
749	C₂×C₅₃	—	4	2	no	—
750	C₂×C₅₃	—	8	1	no	—
751	C₂×C₅₃	—	8	1	no	—
752	C₂×C₅₃	C₂×#529	1	1	yes	characteristic
753	C₂×C₅₃	#3455	1	1	yes	characteristic
754	C₂×C₅₃	#3459	1	1	yes	characteristic
755	C₂×C₅₃	#3505	1	1	yes	characteristic
756	C₂×C₅₃	#3510	1	1	yes	characteristic
757	C₂×C₅₃	#3513	1	1	yes	characteristic
758	C₂×C₅₃	#3521	1	1	yes	characteristic
759	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
760	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
761	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
762	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
763	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
764	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
765	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
766	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
767	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
768	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
769	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
770	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
771	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
772	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
773	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
774	#401	C₂²×C₅₃	1	1	yes	characteristic, complemented
775	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
776	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
777	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
778	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
779	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
780	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
781	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
782	#399	C₂²×C₅₃	1	1	yes	characteristic
783	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
785	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
786	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
787	#397	C₂²×C₅₃	1	1	yes	characteristic
788	#397	C₂²×C₅₃	1	1	yes	characteristic
789	#397	C₂²×C₅₃	1	1	yes	characteristic
790	#397	C₂²×C₅₃	1	1	yes	characteristic
791	#397	C₂²×C₅₃	1	1	yes	characteristic
792	#397	C₂²×C₅₃	1	1	yes	characteristic
793	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
794	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
795	#396	C₂²×C₅₃	1	1	yes	characteristic
796	#396	C₂²×C₅₃	1	1	yes	characteristic
797	#396	C₂²×C₅₃	1	1	yes	characteristic
798	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
799	#394	C₂²×C₅₃	1	1	yes	characteristic
800	#394	C₂²×C₅₃	1	1	yes	characteristic
801	#394	C₂²×C₅₃	1	1	yes	characteristic
802	#394	C₂²×C₅₃	1	1	yes	characteristic
803	#393	C₂²×C₅₃	1	1	yes	characteristic
804	#393	C₂²×C₅₃	1	1	yes	characteristic
805	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
806	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
807	#390	C₂²×C₅₃	1	1	yes	characteristic
808	#390	C₂²×C₅₃	1	1	yes	characteristic
809	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
810	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
811	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
812	#388	C₂²×C₅₃	1	1	yes	characteristic
813	#388	C₂²×C₅₃	1	1	yes	characteristic
814	#388	C₂²×C₅₃	1	1	yes	characteristic
815	#388	C₂²×C₅₃	1	1	yes	characteristic
816	#388	C₂²×C₅₃	1	1	yes	characteristic
817	#388	C₂²×C₅₃	1	1	yes	characteristic
818	#388	C₂²×C₅₃	1	1	yes	characteristic
819	#388	C₂²×C₅₃	1	1	yes	characteristic
820	#388	C₂²×C₅₃	1	1	yes	characteristic
821	#388	C₂²×C₅₃	1	1	yes	characteristic
822	#388	C₂²×C₅₃	1	1	yes	characteristic
823	#388	C₂²×C₅₃	1	1	yes	characteristic
824	#388	C₂²×C₅₃	1	1	yes	characteristic
825	#388	C₂²×C₅₃	1	1	yes	characteristic
826	#388	C₂²×C₅₃	1	1	yes	characteristic
827	#388	C₂²×C₅₃	1	1	yes	characteristic
828	#388	C₂²×C₅₃	1	1	yes	characteristic
829	#388	C₂²×C₅₃	1	1	yes	characteristic
830	#388	C₂²×C₅₃	1	1	yes	characteristic
831	#388	C₂²×C₅₃	1	1	yes	characteristic
832	#388	C₂²×C₅₃	1	1	yes	characteristic
833	#388	C₂²×C₅₃	1	1	yes	characteristic
834	#388	C₂²×C₅₃	1	1	yes	characteristic
835	#388	C₂²×C₅₃	1	1	yes	characteristic
836	#388	C₂²×C₅₃	1	1	yes	characteristic
837	#388	C₂²×C₅₃	1	1	yes	characteristic
838	#388	C₂²×C₅₃	1	1	yes	characteristic
839	#388	C₂²×C₅₃	1	1	yes	characteristic
840	#388	C₂²×C₅₃	1	1	yes	characteristic
841	#388	C₂²×C₅₃	1	1	yes	characteristic
842	#388	C₂²×C₅₃	1	1	yes	characteristic
843	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
844	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
845	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
848	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
849	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
850	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
851	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
852	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
853	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
854	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
855	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
856	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
857	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
858	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
860	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
861	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
863	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
864	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
865	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
866	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
867	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#386	C₂²×C₅₃	1	1	yes	characteristic
869	#386	C₂²×C₅₃	1	1	yes	characteristic
870	#386	C₂²×C₅₃	1	1	yes	characteristic
871	#386	C₂²×C₅₃	1	1	yes	characteristic
872	#386	C₂²×C₅₃	1	1	yes	characteristic
873	#386	C₂²×C₅₃	1	1	yes	characteristic
874	#386	C₂²×C₅₃	1	1	yes	characteristic
875	#385	C₂²×C₅₃	1	1	yes	characteristic
876	#385	C₂²×C₅₃	1	1	yes	characteristic
877	#385	C₂²×C₅₃	1	1	yes	characteristic
878	#385	C₂²×C₅₃	1	1	yes	characteristic
879	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
881	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
882	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
883	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
884	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
885	#381	C₂²×C₅₃	1	1	yes	characteristic
886	#381	C₂²×C₅₃	1	1	yes	characteristic
887	#381	C₂²×C₅₃	1	1	yes	characteristic
888	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
889	#380	C₂²×C₅₃	1	1	yes	characteristic
890	#380	C₂²×C₅₃	1	1	yes	characteristic
891	#380	C₂²×C₅₃	1	1	yes	characteristic
892	#380	C₂²×C₅₃	1	1	yes	characteristic
893	#380	C₂²×C₅₃	1	1	yes	characteristic
894	#379	C₂²×C₅₃	1	1	yes	characteristic
895	#379	C₂²×C₅₃	1	1	yes	characteristic
896	#379	C₂²×C₅₃	1	1	yes	characteristic
897	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
898	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
899	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
900	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
904	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
905	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
906	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
907	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
908	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
912	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
913	C₄³	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	C₅₃	#35027	1	1	yes	characteristic, direct product factor, Sylow
915	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
916	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
917	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
918	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
919	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
920	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
921	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
922	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
923	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
924	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
925	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
926	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
927	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
928	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
929	#126	—	4	2	no	—
930	#123	—	2	4	no	—
931	#123	—	4	2	no	—
932	C₂²⋊Q₈	—	2	4	no	—
933	#120	—	2	4	no	—
934	C₄×Q₈	—	4	2	no	—
935	C₄×D₄	—	2	4	no	—
936	C₄×D₄	—	2	4	no	—
937	C₄×D₄	—	2	4	no	—
938	C₂×C₄⋊C₄	—	2	4	no	—
939	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
940	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
941	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
942	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
943	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
944	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
945	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
946	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
947	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
948	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
949	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
950	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
951	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
952	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
953	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
954	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
955	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
956	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
957	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
958	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
959	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
960	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
961	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
962	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
963	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
964	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
969	C₂×C₂²⋊C₄	—	2	4	no	—
970	C₂×C₂²⋊C₄	—	2	4	no	—
971	C₂×C₂²⋊C₄	—	4	2	no	—
972	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
979	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
980	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
981	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
982	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
983	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
984	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
985	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
986	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
987	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
990	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
991	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
992	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
993	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₄²	—	4	2	no	—
1015	C₂×C₄²	—	4	2	no	—
1016	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1032	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1033	#95	C₂³×C₅₃	1	1	yes	characteristic
1034	#95	C₂³×C₅₃	1	1	yes	characteristic
1035	#95	C₂³×C₅₃	1	1	yes	characteristic
1036	#95	C₂³×C₅₃	1	1	yes	characteristic
1037	#95	C₂³×C₅₃	1	1	yes	characteristic
1038	#95	C₂³×C₅₃	1	1	yes	characteristic
1039	#95	C₂³×C₅₃	1	1	yes	characteristic
1040	#95	C₂³×C₅₃	1	1	yes	characteristic
1041	#95	C₂³×C₅₃	1	1	yes	characteristic
1042	#95	C₂³×C₅₃	1	1	yes	characteristic
1043	#95	C₂³×C₅₃	1	1	yes	characteristic
1044	#95	C₂³×C₅₃	1	1	yes	characteristic
1045	#95	C₂³×C₅₃	1	1	yes	characteristic
1046	#95	C₂³×C₅₃	1	1	yes	characteristic
1047	#95	C₂³×C₅₃	1	1	yes	characteristic
1048	#95	C₂³×C₅₃	1	1	yes	characteristic
1049	#95	C₂³×C₅₃	1	1	yes	characteristic
1050	#95	C₂³×C₅₃	1	1	yes	characteristic
1051	#95	C₂³×C₅₃	1	1	yes	characteristic
1052	#95	C₂³×C₅₃	1	1	yes	characteristic
1053	#95	C₂³×C₅₃	1	1	yes	characteristic
1054	#95	C₂³×C₅₃	1	1	yes	characteristic
1055	#95	C₂³×C₅₃	1	1	yes	characteristic
1056	#95	C₂³×C₅₃	1	1	yes	characteristic
1057	#95	C₂³×C₅₃	1	1	yes	characteristic
1058	#95	C₂³×C₅₃	1	1	yes	characteristic
1059	#95	C₂³×C₅₃	1	1	yes	characteristic
1060	#95	C₂³×C₅₃	1	1	yes	characteristic
1061	#95	C₂³×C₅₃	1	1	yes	characteristic
1062	#95	C₂³×C₅₃	1	1	yes	characteristic
1063	#95	C₂³×C₅₃	1	1	yes	characteristic
1064	#95	C₂³×C₅₃	1	1	yes	characteristic
1065	#95	C₂³×C₅₃	1	1	yes	characteristic
1066	#95	C₂³×C₅₃	1	1	yes	characteristic
1067	#95	C₂³×C₅₃	1	1	yes	characteristic
1068	#95	C₂³×C₅₃	1	1	yes	characteristic
1069	#95	C₂³×C₅₃	1	1	yes	characteristic
1070	#95	C₂³×C₅₃	1	1	yes	characteristic
1071	#95	C₂³×C₅₃	1	1	yes	characteristic
1072	#95	C₂³×C₅₃	1	1	yes	characteristic
1073	#95	C₂³×C₅₃	1	1	yes	characteristic
1074	#95	C₂³×C₅₃	1	1	yes	characteristic
1075	#95	C₂³×C₅₃	1	1	yes	characteristic
1076	#95	C₂³×C₅₃	1	1	yes	characteristic
1077	#95	C₂³×C₅₃	1	1	yes	characteristic
1078	#95	C₂³×C₅₃	1	1	yes	characteristic
1079	#95	C₂³×C₅₃	1	1	yes	characteristic
1080	#95	C₂³×C₅₃	1	1	yes	characteristic
1081	#95	C₂³×C₅₃	1	1	yes	characteristic
1082	#95	C₂³×C₅₃	1	1	yes	characteristic
1083	#95	C₂³×C₅₃	1	1	yes	characteristic
1084	#95	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂⁴	—	2	2	no	—
1086	C₂⁴	—	2	2	no	—
1087	C₂⁴	—	2	2	no	—
1088	C₂⁴	—	4	1	no	—
1089	C₂⁴	—	4	1	no	—
1090	C₂⁴	—	4	1	no	—
1091	C₂⁴	—	4	1	no	—
1092	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1093	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1094	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1095	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1096	C₂×Q₈	—	2	2	no	—
1097	C₂×Q₈	—	4	1	no	—
1098	C₂×Q₈	—	4	1	no	—
1099	C₂×D₄	—	2	2	no	—
1100	C₂×D₄	—	2	2	no	—
1101	C₂×D₄	—	2	2	no	—
1102	C₂×D₄	—	2	2	no	—
1103	C₂×D₄	—	4	1	no	—
1104	C₂×D₄	—	4	1	no	—
1105	C₂×D₄	—	4	1	no	—
1106	C₂×D₄	—	4	1	no	—
1107	C₂×D₄	#41×C₅₃	1	4	yes	—
1108	C₂²×C₄	—	2	2	no	—
1109	C₂²×C₄	—	2	2	no	—
1110	C₂²×C₄	—	2	2	no	—
1111	C₂²×C₄	—	2	2	no	—
1112	C₂²×C₄	—	2	2	no	—
1113	C₂²×C₄	—	2	2	no	—
1114	C₂²×C₄	—	2	2	no	—
1115	C₂²×C₄	—	2	2	no	—
1116	C₂²×C₄	—	2	2	no	—
1117	C₂²×C₄	—	2	2	no	—
1118	C₂²×C₄	—	2	2	no	—
1119	C₂²×C₄	—	4	1	no	—
1120	C₂²×C₄	—	4	1	no	—
1121	C₂²×C₄	—	4	1	no	—
1122	C₂²×C₄	—	4	1	no	—
1123	C₂²×C₄	—	4	1	no	—
1124	C₂²×C₄	—	4	1	no	—
1125	C₂²×C₄	—	4	1	no	—
1126	C₂²×C₄	—	4	1	no	—
1127	C₂²×C₄	—	4	1	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	#41×C₅₃	1	4	yes	—
1134	C₂²×C₄	#41×C₅₃	1	4	yes	—
1135	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1136	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1137	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1138	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1139	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1140	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1141	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1142	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1143	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1144	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1145	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1146	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1147	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1148	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1149	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1150	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1151	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1152	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1153	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1154	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1155	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1156	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1157	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1158	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1159	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1160	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1161	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1162	C₄⋊C₄	—	2	2	no	—
1163	C₄⋊C₄	—	2	2	no	—
1164	C₄⋊C₄	—	2	2	no	—
1165	C₄⋊C₄	—	2	2	no	—
1166	C₄⋊C₄	—	2	2	no	—
1167	C₄⋊C₄	—	2	2	no	—
1168	C₄⋊C₄	—	2	2	no	—
1169	C₄⋊C₄	—	2	2	no	—
1170	C₄⋊C₄	—	2	2	no	—
1171	C₄⋊C₄	—	2	2	no	—
1172	C₄⋊C₄	—	2	2	no	—
1173	C₄⋊C₄	—	2	2	no	—
1174	C₄⋊C₄	—	2	2	no	—
1175	C₄⋊C₄	—	2	2	no	—
1176	C₄⋊C₄	—	4	1	no	—
1177	C₄⋊C₄	—	4	1	no	—
1178	C₄⋊C₄	—	4	1	no	—
1179	C₄⋊C₄	—	4	1	no	—
1180	C₄⋊C₄	—	4	1	no	—
1181	C₄⋊C₄	—	4	1	no	—
1182	C₄⋊C₄	—	4	1	no	—
1183	C₄⋊C₄	—	4	1	no	—
1184	C₄⋊C₄	—	4	1	no	—
1185	C₄⋊C₄	—	4	1	no	—
1186	C₄⋊C₄	—	4	1	no	—
1187	C₄⋊C₄	—	4	1	no	—
1188	C₄⋊C₄	—	4	1	no	—
1189	C₄⋊C₄	—	4	1	no	—
1190	C₄⋊C₄	—	4	1	no	—
1191	C₄⋊C₄	—	4	1	no	—
1192	C₂²⋊C₄	—	2	2	no	—
1193	C₂²⋊C₄	—	2	2	no	—
1194	C₂²⋊C₄	—	2	2	no	—
1195	C₂²⋊C₄	—	2	2	no	—
1196	C₂²⋊C₄	—	2	2	no	—
1197	C₂²⋊C₄	—	2	2	no	—
1198	C₂²⋊C₄	—	2	2	no	—
1199	C₂²⋊C₄	—	2	2	no	—
1200	C₂²⋊C₄	—	2	2	no	—
1201	C₂²⋊C₄	—	2	2	no	—
1202	C₂²⋊C₄	—	2	2	no	—
1203	C₂²⋊C₄	—	2	2	no	—
1204	C₂²⋊C₄	—	2	2	no	—
1205	C₂²⋊C₄	—	2	2	no	—
1206	C₂²⋊C₄	—	2	2	no	—
1207	C₂²⋊C₄	—	2	2	no	—
1208	C₂²⋊C₄	—	2	2	no	—
1209	C₂²⋊C₄	—	2	2	no	—
1210	C₂²⋊C₄	—	2	2	no	—
1211	C₂²⋊C₄	—	2	2	no	—
1212	C₂²⋊C₄	—	2	2	no	—
1213	C₂²⋊C₄	—	2	2	no	—
1214	C₂²⋊C₄	—	2	2	no	—
1215	C₂²⋊C₄	—	2	2	no	—
1216	C₂²⋊C₄	—	4	1	no	—
1217	C₂²⋊C₄	—	4	1	no	—
1218	C₂²⋊C₄	—	4	1	no	—
1219	C₂²⋊C₄	—	4	1	no	—
1220	C₂²⋊C₄	—	4	1	no	—
1221	C₂²⋊C₄	—	4	1	no	—
1222	C₂²⋊C₄	—	4	1	no	—
1223	C₂²⋊C₄	—	4	1	no	—
1224	C₂²⋊C₄	—	4	1	no	—
1225	C₂²⋊C₄	—	4	1	no	—
1226	C₂²⋊C₄	—	4	1	no	—
1227	C₂²⋊C₄	—	4	1	no	—
1228	C₂²⋊C₄	—	4	1	no	—
1229	C₂²⋊C₄	—	4	1	no	—
1230	C₂²⋊C₄	—	4	1	no	—
1231	C₂²⋊C₄	—	4	1	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₄²	—	2	2	no	—
1235	C₄²	—	2	2	no	—
1236	C₄²	—	2	2	no	—
1237	C₄²	—	2	2	no	—
1238	C₄²	—	2	2	no	—
1239	C₄²	—	2	2	no	—
1240	C₄²	—	4	1	no	—
1241	C₄²	—	4	1	no	—
1242	C₄²	—	4	1	no	—
1243	C₄²	—	4	1	no	—
1244	C₄²	—	4	1	no	—
1245	C₄²	—	4	1	no	—
1246	C₄²	—	4	1	no	—
1247	C₄²	—	4	1	no	—
1248	C₄²	—	4	1	no	—
1249	C₄²	—	4	1	no	—
1250	C₄²	—	4	1	no	—
1251	C₂³	—	2	1	no	—
1252	C₂³	—	2	1	no	—
1253	C₂³	—	2	1	no	—
1254	C₂³	—	2	1	no	—
1255	C₂³	—	2	1	no	—
1256	C₂³	—	2	1	no	—
1257	C₂³	—	2	1	no	—
1258	C₂³	—	2	1	no	—
1259	C₂³	—	2	1	no	—
1260	C₂³	—	2	1	no	—
1261	C₂³	—	2	1	no	—
1262	C₂³	—	2	1	no	—
1263	C₂³	—	2	1	no	—
1264	C₂³	—	2	1	no	—
1265	C₂³	—	2	1	no	—
1266	C₂³	—	2	1	no	—
1267	C₂³	—	2	1	no	—
1268	C₂³	—	2	1	no	—
1269	C₂³	—	2	1	no	—
1270	C₂³	—	2	1	no	—
1271	C₂³	—	2	1	no	—
1272	C₂³	—	2	1	no	—
1273	C₂³	—	2	1	no	—
1274	C₂³	—	2	1	no	—
1275	C₂³	—	4	4	no	—
1276	C₂³	—	4	4	no	—
1277	C₂³	—	4	4	no	—
1278	C₂³	—	8	2	no	—
1279	C₂³	—	8	2	no	—
1280	C₂³	—	8	2	no	—
1281	C₂³	—	8	2	no	—
1282	C₂³	C₂×#41×C₅₃	1	2	yes	—
1283	C₂³	C₂×#41×C₅₃	1	2	yes	—
1284	C₂³	C₂×#41×C₅₃	1	2	yes	—
1285	C₂³	C₂×#41×C₅₃	1	2	yes	—
1286	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1287	Q₈	—	4	4	no	—
1288	D₄	—	2	8	no	—
1289	D₄	—	8	2	no	—
1290	D₄	—	8	2	no	—
1291	C₂×C₄	—	2	1	no	—
1292	C₂×C₄	—	2	1	no	—
1293	C₂×C₄	—	2	1	no	—
1294	C₂×C₄	—	2	1	no	—
1295	C₂×C₄	—	2	1	no	—
1296	C₂×C₄	—	2	1	no	—
1297	C₂×C₄	—	2	1	no	—
1298	C₂×C₄	—	2	1	no	—
1299	C₂×C₄	—	2	1	no	—
1300	C₂×C₄	—	2	1	no	—
1301	C₂×C₄	—	2	1	no	—
1302	C₂×C₄	—	2	1	no	—
1303	C₂×C₄	—	2	1	no	—
1304	C₂×C₄	—	2	1	no	—
1305	C₂×C₄	—	2	1	no	—
1306	C₂×C₄	—	2	1	no	—
1307	C₂×C₄	—	2	1	no	—
1308	C₂×C₄	—	2	1	no	—
1309	C₂×C₄	—	2	1	no	—
1310	C₂×C₄	—	2	1	no	—
1311	C₂×C₄	—	2	1	no	—
1312	C₂×C₄	—	2	1	no	—
1313	C₂×C₄	—	2	1	no	—
1314	C₂×C₄	—	2	1	no	—
1315	C₂×C₄	—	2	1	no	—
1316	C₂×C₄	—	2	1	no	—
1317	C₂×C₄	—	2	1	no	—
1318	C₂×C₄	—	2	1	no	—
1319	C₂×C₄	—	2	1	no	—
1320	C₂×C₄	—	2	1	no	—
1321	C₂×C₄	—	2	1	no	—
1322	C₂×C₄	—	2	1	no	—
1323	C₂×C₄	—	2	1	no	—
1324	C₂×C₄	—	2	1	no	—
1325	C₂×C₄	—	2	1	no	—
1326	C₂×C₄	—	2	1	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	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	—	4	4	no	—
1367	C₂×C₄	—	4	4	no	—
1368	C₂×C₄	—	4	4	no	—
1369	C₂×C₄	—	4	4	no	—
1370	C₂×C₄	—	4	4	no	—
1371	C₂×C₄	—	4	4	no	—
1372	C₂×C₄	—	4	4	no	—
1373	C₂×C₄	—	8	2	no	—
1374	C₂×C₄	—	8	2	no	—
1375	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1376	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1377	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1378	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1379	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1380	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1381	C₂²	—	2	2	no	—
1382	C₂²	—	2	2	no	—
1383	C₂²	—	2	2	no	—
1384	C₂²	—	2	2	no	—
1385	C₂²	—	2	2	no	—
1386	C₂²	—	2	2	no	—
1387	C₂²	—	2	2	no	—
1388	C₂²	—	2	2	no	—
1389	C₂²	—	2	2	no	—
1390	C₂²	—	4	1	no	—
1391	C₂²	—	4	1	no	—
1392	C₂²	—	4	1	no	—
1393	C₂²	—	4	1	no	—
1394	C₂²	—	4	1	no	—
1395	C₂²	—	4	1	no	—
1396	C₂²	—	4	1	no	—
1397	C₂²	—	4	1	no	—
1398	C₂²	—	4	1	no	—
1399	C₂²	—	4	1	no	—
1400	C₂²	—	4	1	no	—
1401	C₂²	—	4	1	no	—
1402	C₂²	—	4	1	no	—
1403	C₂²	—	4	1	no	—
1404	C₂²	—	4	1	no	—
1405	C₂²	—	4	1	no	—
1406	C₂²	—	4	1	no	—
1407	C₂²	—	4	1	no	—
1408	C₂²	—	8	8	no	—
1409	C₂²	C₅₃×#529	1	4	yes	—
1410	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1411	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1412	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1413	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1414	C₂²	C₅₃×#585	1	1	yes	characteristic
1415	C₂²	C₅₃×#585	1	1	yes	characteristic
1416	C₂²	C₅₃×#585	1	1	yes	characteristic
1417	C₄	—	2	2	no	—
1418	C₄	—	2	2	no	—
1419	C₄	—	2	2	no	—
1420	C₄	—	2	2	no	—
1421	C₄	—	2	2	no	—
1422	C₄	—	2	2	no	—
1423	C₄	—	4	1	no	—
1424	C₄	—	4	1	no	—
1425	C₄	—	4	1	no	—
1426	C₄	—	4	1	no	—
1427	C₄	—	4	1	no	—
1428	C₄	—	4	1	no	—
1429	C₄	—	4	1	no	—
1430	C₄	—	4	1	no	—
1431	C₄	—	4	1	no	—
1432	C₄	—	4	1	no	—
1433	C₄	—	4	1	no	—
1434	C₄	—	4	1	no	—
1435	C₄	—	4	1	no	—
1436	C₄	—	4	1	no	—
1437	C₄	—	4	1	no	—
1438	C₄	—	4	1	no	—
1439	C₄	—	4	1	no	—
1440	C₄	—	4	1	no	—
1441	C₄	—	4	1	no	—
1442	C₄	—	4	1	no	—
1443	C₄	—	4	1	no	—
1444	C₂	—	2	4	no	—
1445	C₂	—	4	2	no	—
1446	C₂	—	8	1	no	—
1447	C₂	—	8	1	no	—
1448	C₂	C₂×C₅₃×#529	1	1	yes	characteristic
1449	C₂	C₅₃×#3455	1	1	yes	characteristic
1450	C₂	C₅₃×#3459	1	1	yes	characteristic
1451	C₂	C₅₃×#3505	1	1	yes	characteristic
1452	C₂	C₅₃×#3510	1	1	yes	characteristic
1453	C₂	C₅₃×#3513	1	1	yes	characteristic
1454	C₂	C₅₃×#3521	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×#120×C₅₃	C₂²
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
1. C₅₃×#2866	C₂	semidirect
2. C₅₃×#2865	C₂	semidirect
3. C₅₃×#2853	C₂	semidirect
4. C₅₃×#2852	C₂	semidirect
5. C₅₃×#2654	C₂	semidirect
6. C₅₃×#2653	C₂	semidirect
7. C₅₃×#2650	C₂	semidirect
8. C₅₃×#2649	C₂	semidirect
9. C₅₃×#2597	C₂	semidirect
10. C₅₃×#2596	C₂	semidirect
11. C₅₃×#2595	C₂	semidirect
12. C₅₃×#2594	C₂	semidirect
13. C₅₃×#2569	C₂	semidirect
14. C₅₃×#2564	C₂	semidirect
15. C₅₃×#2561	C₂	semidirect
17. C₅₃×#2525	C₂	semidirect
18. C₅₃×#2516	C₂	semidirect
19. C₅₃×#2493	C₂	semidirect
20. C₅₃×#2480	C₂	semidirect
21. C₅₃×#2469	C₂	semidirect
22. C₅₃×#2458	C₂	semidirect
23. C₅₃×#2419	C₂	semidirect
25. C₅₃×#2322	C₂	semidirect
27. C₅₃×#2313	C₂	semidirect
28. C₅₃×#2312	C₂	semidirect
29. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
30. C₂×C₅₃×#388	C₂	semidirect
31. C₄²×D₄×C₅₃	C₂	semidirect
37. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
46. C₂²×C₄²×C₅₃	C₂²	semidirect
47. C₅₃×#401	C₂²	semidirect
48. C₅₃×#400	C₂²	semidirect
49. C₅₃×#400	C₂²	semidirect
50. C₅₃×#400	C₂²	semidirect
51. C₅₃×#400	C₂²	semidirect
52. C₅₃×#400	C₂²	semidirect
53. C₅₃×#400	C₂²	semidirect
54. C₅₃×#400	C₂²	semidirect
56. C₅₃×#399	C₂²	semidirect
57. C₅₃×#398	C₂²	semidirect
58. C₅₃×#398	C₂²	semidirect
59. C₅₃×#398	C₂²	semidirect
66. C₅₃×#397	C₂²	semidirect
67. C₅₃×#397	C₂²	semidirect
71. C₅₃×#395	C₂²	semidirect
78. C₅₃×#393	C₂²	semidirect
79. C₅₃×#391	C₂²	semidirect
82. C₅₃×#389	C₂²	semidirect
83. C₅₃×#389	C₂²	semidirect
84. C₅₃×#389	C₂²	semidirect
116. C₅₃×#388	C₂²	semidirect
117. C₅₃×#388	C₂²	semidirect
118. C₅₃×#387	C₂²	semidirect
119. C₅₃×#387	C₂²	semidirect
120. C₅₃×#387	C₂²	semidirect
121. C₅₃×#387	C₂²	semidirect
122. C₅₃×#387	C₂²	semidirect
123. C₅₃×#387	C₂²	semidirect
124. C₅₃×#387	C₂²	semidirect
125. C₅₃×#387	C₂²	semidirect
126. C₅₃×#387	C₂²	semidirect
127. C₅₃×#387	C₂²	semidirect
128. C₅₃×#387	C₂²	semidirect
129. C₅₃×#387	C₂²	semidirect
130. C₅₃×#387	C₂²	semidirect
131. C₅₃×#387	C₂²	semidirect
132. C₅₃×#387	C₂²	semidirect
133. C₅₃×#387	C₂²	semidirect
134. C₅₃×#387	C₂²	semidirect
135. C₅₃×#387	C₂²	semidirect
136. C₅₃×#387	C₂²	semidirect
137. C₅₃×#387	C₂²	semidirect
138. C₅₃×#387	C₂²	semidirect
139. C₅₃×#387	C₂²	semidirect
140. C₅₃×#387	C₂²	semidirect
152. C₅₃×#385	C₂²	semidirect
153. C₅₃×#385	C₂²	semidirect
154. C₅₃×#385	C₂²	semidirect
155. C₅₃×#385	C₂²	semidirect
156. C₅₃×#385	C₂²	semidirect
157. C₅₃×#383	C₂²	semidirect
161. C₅₃×#381	C₂²	semidirect
170. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
171. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
172. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
173. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
174. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
175. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
181. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
182. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
183. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₄³×C₅₃	C₂²	semidirect
653. #35027	C₅₃	direct (N × H)
717. #2866	C₂×C₅₃	semidirect
718. #2865	C₂×C₅₃	semidirect
719. #2853	C₂×C₅₃	semidirect
720. #2852	C₂×C₅₃	semidirect
721. #2654	C₂×C₅₃	semidirect
722. #2653	C₂×C₅₃	semidirect
723. #2650	C₂×C₅₃	semidirect
724. #2649	C₂×C₅₃	semidirect
725. #2597	C₂×C₅₃	semidirect
726. #2596	C₂×C₅₃	semidirect
727. #2595	C₂×C₅₃	semidirect
728. #2594	C₂×C₅₃	semidirect
729. #2569	C₂×C₅₃	semidirect
730. #2564	C₂×C₅₃	semidirect
731. #2561	C₂×C₅₃	semidirect
733. #2525	C₂×C₅₃	semidirect
734. #2516	C₂×C₅₃	semidirect
735. #2493	C₂×C₅₃	semidirect
736. #2480	C₂×C₅₃	semidirect
737. #2469	C₂×C₅₃	semidirect
738. #2458	C₂×C₅₃	semidirect
739. #2419	C₂×C₅₃	semidirect
741. #2322	C₂×C₅₃	semidirect
743. #2313	C₂×C₅₃	semidirect
744. #2312	C₂×C₅₃	semidirect
745. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
746. C₂×#388	C₂×C₅₃	semidirect
747. C₄²×D₄	C₂×C₅₃	semidirect
764. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
773. C₂²×C₄²	C₂²×C₅₃	semidirect
774. #401	C₂²×C₅₃	semidirect
775. #400	C₂²×C₅₃	semidirect
776. #400	C₂²×C₅₃	semidirect
777. #400	C₂²×C₅₃	semidirect
778. #400	C₂²×C₅₃	semidirect
779. #400	C₂²×C₅₃	semidirect
780. #400	C₂²×C₅₃	semidirect
781. #400	C₂²×C₅₃	semidirect
783. #399	C₂²×C₅₃	semidirect
784. #398	C₂²×C₅₃	semidirect
785. #398	C₂²×C₅₃	semidirect
786. #398	C₂²×C₅₃	semidirect
793. #397	C₂²×C₅₃	semidirect
794. #397	C₂²×C₅₃	semidirect
798. #395	C₂²×C₅₃	semidirect
805. #393	C₂²×C₅₃	semidirect
806. #391	C₂²×C₅₃	semidirect
809. #389	C₂²×C₅₃	semidirect
810. #389	C₂²×C₅₃	semidirect
811. #389	C₂²×C₅₃	semidirect
843. #388	C₂²×C₅₃	semidirect
844. #388	C₂²×C₅₃	semidirect
845. #387	C₂²×C₅₃	semidirect
846. #387	C₂²×C₅₃	semidirect
847. #387	C₂²×C₅₃	semidirect
848. #387	C₂²×C₅₃	semidirect
849. #387	C₂²×C₅₃	semidirect
850. #387	C₂²×C₅₃	semidirect
851. #387	C₂²×C₅₃	semidirect
852. #387	C₂²×C₅₃	semidirect
853. #387	C₂²×C₅₃	semidirect
854. #387	C₂²×C₅₃	semidirect
855. #387	C₂²×C₅₃	semidirect
856. #387	C₂²×C₅₃	semidirect
857. #387	C₂²×C₅₃	semidirect
858. #387	C₂²×C₅₃	semidirect
859. #387	C₂²×C₅₃	semidirect
860. #387	C₂²×C₅₃	semidirect
861. #387	C₂²×C₅₃	semidirect
862. #387	C₂²×C₅₃	semidirect
863. #387	C₂²×C₅₃	semidirect
864. #387	C₂²×C₅₃	semidirect
865. #387	C₂²×C₅₃	semidirect
866. #387	C₂²×C₅₃	semidirect
867. #387	C₂²×C₅₃	semidirect
879. #385	C₂²×C₅₃	semidirect
880. #385	C₂²×C₅₃	semidirect
881. #385	C₂²×C₅₃	semidirect
882. #385	C₂²×C₅₃	semidirect
883. #385	C₂²×C₅₃	semidirect
884. #383	C₂²×C₅₃	semidirect
888. #381	C₂²×C₅₃	semidirect
897. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
898. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
899. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
900. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
901. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
902. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
908. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
909. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
910. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
913. C₄³	C₂²×C₅₃	semidirect
914. C₅₃	#35027	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×#2866	2
C₅₃×#2865	2
C₅₃×#2853	2
C₅₃×#2852	2
C₅₃×#2654	2
C₅₃×#2653	2
C₅₃×#2650	2
C₅₃×#2649	2
C₅₃×#2597	2
C₅₃×#2596	2
C₅₃×#2595	2
C₅₃×#2594	2
C₅₃×#2569	2
C₅₃×#2564	2
C₅₃×#2561	2
C₅₃×#2534	2
C₅₃×#2525	2
C₅₃×#2516	2
C₅₃×#2493	2
C₅₃×#2480	2
C₅₃×#2469	2
C₅₃×#2458	2
C₅₃×#2419	2
C₅₃×#2418	2
C₅₃×#2322	2
C₅₃×#2321	2
C₅₃×#2313	2
C₅₃×#2312	2
C₄×C₂²⋊Q₈×C₅₃	2
C₂×C₅₃×#388	2
C₄²×D₄×C₅₃	2
#35027	53

Subgroups — C53×#35027 #27242539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35027 #27242539