Subgroups — C₅₃×#35056 #27242568

Order 13568.

2198 conjugacy classes of subgroups.

The subgroup lattice has 1622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2853	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2667	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2661	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2649	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2648	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2569	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2534	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2531	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2526	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2522	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2516	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2476	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2471	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2464	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2457	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2425	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2424	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, complemented
25	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2333	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2333	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₄×C₂²⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×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×#123×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
56	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#399	C₂²	1	1	yes	characteristic
61	C₅₃×#399	C₂²	1	1	yes	characteristic
62	C₅₃×#399	C₂²	1	1	yes	characteristic
63	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#397	C₂²	1	1	yes	characteristic
69	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#396	C₂²	1	1	yes	characteristic
74	C₅₃×#396	C₂²	1	1	yes	characteristic
75	C₅₃×#396	C₂²	1	1	yes	characteristic
76	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#394	C₂²	1	1	yes	characteristic
78	C₅₃×#394	C₂²	1	1	yes	characteristic
79	C₅₃×#394	C₂²	1	1	yes	characteristic
80	C₅₃×#394	C₂²	1	1	yes	characteristic
81	C₅₃×#394	C₂²	1	1	yes	characteristic
82	C₅₃×#394	C₂²	1	1	yes	characteristic
83	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#392	C₂²	1	1	yes	characteristic
86	C₅₃×#392	C₂²	1	1	yes	characteristic
87	C₅₃×#392	C₂²	1	1	yes	characteristic
88	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#390	C₂²	1	1	yes	characteristic
90	C₅₃×#390	C₂²	1	1	yes	characteristic
91	C₅₃×#390	C₂²	1	1	yes	characteristic
92	C₅₃×#390	C₂²	1	1	yes	characteristic
93	C₅₃×#390	C₂²	1	1	yes	characteristic
94	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
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, complemented
107	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#388	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×#386	C₂²	1	1	yes	characteristic
134	C₅₃×#386	C₂²	1	1	yes	characteristic
135	C₅₃×#386	C₂²	1	1	yes	characteristic
136	C₅₃×#386	C₂²	1	1	yes	characteristic
137	C₅₃×#386	C₂²	1	1	yes	characteristic
138	C₅₃×#386	C₂²	1	1	yes	characteristic
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
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×#386	C₂²	1	1	yes	characteristic
149	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
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, complemented
159	C₅₃×#381	C₂²	1	1	yes	characteristic
160	C₅₃×#381	C₂²	1	1	yes	characteristic
161	C₅₃×#381	C₂²	1	1	yes	characteristic
162	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
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×#380	C₂²	1	1	yes	characteristic
168	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
173	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
174	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
175	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
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	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
185	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
187	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×D₄×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	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₅₃	—	2	4	no	—
201	C₂³×C₄×C₅₃	—	4	2	no	—
202	C₂³×C₄×C₅₃	—	4	2	no	—
203	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
216	#123×C₅₃	—	2	4	no	—
217	#123×C₅₃	—	2	4	no	—
218	#123×C₅₃	—	4	2	no	—
219	#123×C₅₃	—	4	2	no	—
220	#123×C₅₃	—	4	2	no	—
221	#123×C₅₃	—	4	2	no	—
222	#121×C₅₃	—	2	4	no	—
223	#121×C₅₃	—	2	4	no	—
224	#121×C₅₃	—	2	4	no	—
225	#121×C₅₃	—	4	2	no	—
226	#121×C₅₃	—	4	2	no	—
227	#121×C₅₃	—	4	2	no	—
228	#120×C₅₃	—	4	2	no	—
229	#120×C₅₃	—	4	2	no	—
230	#120×C₅₃	—	4	2	no	—
231	C₄×D₄×C₅₃	—	2	4	no	—
232	C₄×D₄×C₅₃	—	4	2	no	—
233	C₄×D₄×C₅₃	—	4	2	no	—
234	C₄×D₄×C₅₃	—	4	2	no	—
235	#117×C₅₃	—	4	2	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₅₃	—	4	2	no	—
315	C₂×C₄²×C₅₃	—	4	2	no	—
316	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	C₂⁴×C₅₃	—	2	2	no	—
370	C₂⁴×C₅₃	—	2	2	no	—
371	C₂⁴×C₅₃	—	2	2	no	—
372	C₂⁴×C₅₃	—	2	2	no	—
373	C₂⁴×C₅₃	—	2	2	no	—
374	C₂⁴×C₅₃	—	4	1	no	—
375	C₂⁴×C₅₃	—	4	1	no	—
376	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
377	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
378	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
379	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
380	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
381	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
382	C₂×D₄×C₅₃	—	2	2	no	—
383	C₂×D₄×C₅₃	—	2	2	no	—
384	C₂×D₄×C₅₃	—	2	2	no	—
385	C₂×D₄×C₅₃	—	2	2	no	—
386	C₂×D₄×C₅₃	—	2	2	no	—
387	C₂×D₄×C₅₃	—	2	2	no	—
388	C₂×D₄×C₅₃	—	2	2	no	—
389	C₂×D₄×C₅₃	—	2	2	no	—
390	C₂×D₄×C₅₃	—	2	2	no	—
391	C₂×D₄×C₅₃	—	2	2	no	—
392	C₂×D₄×C₅₃	—	2	2	no	—
393	C₂×D₄×C₅₃	—	2	2	no	—
394	C₂×D₄×C₅₃	—	2	2	no	—
395	C₂×D₄×C₅₃	—	2	2	no	—
396	C₂×D₄×C₅₃	—	2	2	no	—
397	C₂×D₄×C₅₃	—	2	2	no	—
398	C₂×D₄×C₅₃	—	2	2	no	—
399	C₂×D₄×C₅₃	—	2	2	no	—
400	C₂×D₄×C₅₃	—	4	1	no	—
401	C₂×D₄×C₅₃	—	4	1	no	—
402	C₂×D₄×C₅₃	—	4	1	no	—
403	C₂×D₄×C₅₃	—	4	1	no	—
404	C₂×D₄×C₅₃	—	4	1	no	—
405	C₂×D₄×C₅₃	—	4	1	no	—
406	C₂×D₄×C₅₃	—	4	1	no	—
407	C₂×D₄×C₅₃	—	4	1	no	—
408	C₂×D₄×C₅₃	—	4	1	no	—
409	C₂×D₄×C₅₃	—	4	1	no	—
410	C₂×D₄×C₅₃	—	4	1	no	—
411	C₂×D₄×C₅₃	—	4	1	no	—
412	C₂×D₄×C₅₃	—	4	1	no	—
413	C₂×D₄×C₅₃	—	4	1	no	—
414	C₂×D₄×C₅₃	—	4	1	no	—
415	C₂×D₄×C₅₃	—	4	1	no	—
416	C₂×D₄×C₅₃	—	4	1	no	—
417	C₂×D₄×C₅₃	—	4	1	no	—
418	C₂²×C₄×C₅₃	—	2	2	no	—
419	C₂²×C₄×C₅₃	—	2	2	no	—
420	C₂²×C₄×C₅₃	—	2	2	no	—
421	C₂²×C₄×C₅₃	—	2	2	no	—
422	C₂²×C₄×C₅₃	—	2	2	no	—
423	C₂²×C₄×C₅₃	—	2	2	no	—
424	C₂²×C₄×C₅₃	—	2	2	no	—
425	C₂²×C₄×C₅₃	—	2	2	no	—
426	C₂²×C₄×C₅₃	—	2	2	no	—
427	C₂²×C₄×C₅₃	—	2	2	no	—
428	C₂²×C₄×C₅₃	—	2	2	no	—
429	C₂²×C₄×C₅₃	—	2	2	no	—
430	C₂²×C₄×C₅₃	—	2	2	no	—
431	C₂²×C₄×C₅₃	—	2	2	no	—
432	C₂²×C₄×C₅₃	—	2	2	no	—
433	C₂²×C₄×C₅₃	—	2	2	no	—
434	C₂²×C₄×C₅₃	—	2	2	no	—
435	C₂²×C₄×C₅₃	—	2	2	no	—
436	C₂²×C₄×C₅₃	—	2	2	no	—
437	C₂²×C₄×C₅₃	—	2	2	no	—
438	C₂²×C₄×C₅₃	—	4	1	no	—
439	C₂²×C₄×C₅₃	—	4	1	no	—
440	C₂²×C₄×C₅₃	—	4	1	no	—
441	C₂²×C₄×C₅₃	—	4	1	no	—
442	C₂²×C₄×C₅₃	—	4	1	no	—
443	C₂²×C₄×C₅₃	—	4	1	no	—
444	C₂²×C₄×C₅₃	—	4	1	no	—
445	C₂²×C₄×C₅₃	—	4	1	no	—
446	C₂²×C₄×C₅₃	—	4	1	no	—
447	C₂²×C₄×C₅₃	—	4	1	no	—
448	C₂²×C₄×C₅₃	—	4	1	no	—
449	C₂²×C₄×C₅₃	—	4	1	no	—
450	C₂²×C₄×C₅₃	—	4	1	no	—
451	C₂²×C₄×C₅₃	—	4	1	no	—
452	C₂²×C₄×C₅₃	—	4	1	no	—
453	C₂²×C₄×C₅₃	—	4	1	no	—
454	C₂²×C₄×C₅₃	—	4	1	no	—
455	C₂²×C₄×C₅₃	—	4	16	no	—
456	C₂²×C₄×C₅₃	#41	1	4	yes	—
457	C₂²×C₄×C₅₃	#41	1	4	yes	—
458	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
473	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
483	C₄⋊C₄×C₅₃	—	2	2	no	—
484	C₄⋊C₄×C₅₃	—	2	2	no	—
485	C₄⋊C₄×C₅₃	—	2	2	no	—
486	C₄⋊C₄×C₅₃	—	2	2	no	—
487	C₄⋊C₄×C₅₃	—	2	2	no	—
488	C₄⋊C₄×C₅₃	—	2	2	no	—
489	C₄⋊C₄×C₅₃	—	2	2	no	—
490	C₄⋊C₄×C₅₃	—	2	2	no	—
491	C₄⋊C₄×C₅₃	—	2	2	no	—
492	C₄⋊C₄×C₅₃	—	4	1	no	—
493	C₄⋊C₄×C₅₃	—	4	1	no	—
494	C₄⋊C₄×C₅₃	—	4	1	no	—
495	C₄⋊C₄×C₅₃	—	4	1	no	—
496	C₄⋊C₄×C₅₃	—	4	1	no	—
497	C₄⋊C₄×C₅₃	—	4	1	no	—
498	C₄⋊C₄×C₅₃	—	4	1	no	—
499	C₄⋊C₄×C₅₃	—	4	1	no	—
500	C₄⋊C₄×C₅₃	—	4	1	no	—
501	C₄⋊C₄×C₅₃	—	4	1	no	—
502	C₄⋊C₄×C₅₃	—	4	1	no	—
503	C₄⋊C₄×C₅₃	—	4	1	no	—
504	C₄⋊C₄×C₅₃	—	4	1	no	—
505	C₄⋊C₄×C₅₃	—	4	1	no	—
506	C₄⋊C₄×C₅₃	—	4	1	no	—
507	C₄⋊C₄×C₅₃	—	4	1	no	—
508	C₄⋊C₄×C₅₃	—	4	1	no	—
509	C₂²⋊C₄×C₅₃	—	2	2	no	—
510	C₂²⋊C₄×C₅₃	—	2	2	no	—
511	C₂²⋊C₄×C₅₃	—	2	2	no	—
512	C₂²⋊C₄×C₅₃	—	2	2	no	—
513	C₂²⋊C₄×C₅₃	—	2	2	no	—
514	C₂²⋊C₄×C₅₃	—	2	2	no	—
515	C₂²⋊C₄×C₅₃	—	2	2	no	—
516	C₂²⋊C₄×C₅₃	—	2	2	no	—
517	C₂²⋊C₄×C₅₃	—	2	2	no	—
518	C₂²⋊C₄×C₅₃	—	2	2	no	—
519	C₂²⋊C₄×C₅₃	—	2	2	no	—
520	C₂²⋊C₄×C₅₃	—	2	2	no	—
521	C₂²⋊C₄×C₅₃	—	2	2	no	—
522	C₂²⋊C₄×C₅₃	—	2	2	no	—
523	C₂²⋊C₄×C₅₃	—	2	2	no	—
524	C₂²⋊C₄×C₅₃	—	2	2	no	—
525	C₂²⋊C₄×C₅₃	—	2	2	no	—
526	C₂²⋊C₄×C₅₃	—	2	2	no	—
527	C₂²⋊C₄×C₅₃	—	2	2	no	—
528	C₂²⋊C₄×C₅₃	—	2	2	no	—
529	C₂²⋊C₄×C₅₃	—	2	2	no	—
530	C₂²⋊C₄×C₅₃	—	2	2	no	—
531	C₂²⋊C₄×C₅₃	—	2	2	no	—
532	C₂²⋊C₄×C₅₃	—	2	2	no	—
533	C₂²⋊C₄×C₅₃	—	2	2	no	—
534	C₂²⋊C₄×C₅₃	—	2	2	no	—
535	C₂²⋊C₄×C₅₃	—	4	1	no	—
536	C₂²⋊C₄×C₅₃	—	4	1	no	—
537	C₂²⋊C₄×C₅₃	—	4	1	no	—
538	C₂²⋊C₄×C₅₃	—	4	1	no	—
539	C₂²⋊C₄×C₅₃	—	4	1	no	—
540	C₂²⋊C₄×C₅₃	—	4	1	no	—
541	C₂²⋊C₄×C₅₃	—	4	1	no	—
542	C₂²⋊C₄×C₅₃	—	4	1	no	—
543	C₂²⋊C₄×C₅₃	—	4	1	no	—
544	C₂²⋊C₄×C₅₃	—	4	1	no	—
545	C₂²⋊C₄×C₅₃	—	4	1	no	—
546	C₂²⋊C₄×C₅₃	—	4	1	no	—
547	C₂²⋊C₄×C₅₃	—	4	1	no	—
548	C₂²⋊C₄×C₅₃	—	4	1	no	—
549	C₂²⋊C₄×C₅₃	—	4	1	no	—
550	C₂²⋊C₄×C₅₃	—	4	1	no	—
551	C₂²⋊C₄×C₅₃	—	4	1	no	—
552	C₂²⋊C₄×C₅₃	—	4	1	no	—
553	C₂²⋊C₄×C₅₃	—	4	1	no	—
554	C₂²⋊C₄×C₅₃	—	4	1	no	—
555	C₂²⋊C₄×C₅₃	—	4	1	no	—
556	C₂²⋊C₄×C₅₃	—	4	1	no	—
557	C₂²⋊C₄×C₅₃	—	4	1	no	—
558	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
559	C₄²×C₅₃	—	2	2	no	—
560	C₄²×C₅₃	—	2	2	no	—
561	C₄²×C₅₃	—	2	2	no	—
562	C₄²×C₅₃	—	4	1	no	—
563	C₄²×C₅₃	—	4	1	no	—
564	C₄²×C₅₃	—	4	1	no	—
565	C₄²×C₅₃	—	4	1	no	—
566	C₄²×C₅₃	—	4	1	no	—
567	C₄²×C₅₃	—	4	1	no	—
568	C₄²×C₅₃	—	4	1	no	—
569	C₄²×C₅₃	—	4	1	no	—
570	C₄²×C₅₃	—	4	1	no	—
571	C₄²×C₅₃	—	4	1	no	—
572	C₂³×C₅₃	—	2	1	no	—
573	C₂³×C₅₃	—	2	1	no	—
574	C₂³×C₅₃	—	2	1	no	—
575	C₂³×C₅₃	—	2	1	no	—
576	C₂³×C₅₃	—	2	8	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	2	1	no	—
581	C₂³×C₅₃	—	2	1	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	2	1	no	—
598	C₂³×C₅₃	—	2	1	no	—
599	C₂³×C₅₃	—	2	1	no	—
600	C₂³×C₅₃	—	2	1	no	—
601	C₂³×C₅₃	—	2	1	no	—
602	C₂³×C₅₃	—	2	1	no	—
603	C₂³×C₅₃	—	2	1	no	—
604	C₂³×C₅₃	—	2	1	no	—
605	C₂³×C₅₃	—	2	1	no	—
606	C₂³×C₅₃	—	2	1	no	—
607	C₂³×C₅₃	—	2	1	no	—
608	C₂³×C₅₃	—	2	1	no	—
609	C₂³×C₅₃	—	2	1	no	—
610	C₂³×C₅₃	—	4	4	no	—
611	C₂³×C₅₃	—	4	4	no	—
612	C₂³×C₅₃	—	4	4	no	—
613	C₂³×C₅₃	—	4	4	no	—
614	C₂³×C₅₃	—	4	4	no	—
615	C₂³×C₅₃	—	4	4	no	—
616	C₂³×C₅₃	C₂×#41	1	2	yes	—
617	C₂³×C₅₃	C₂×#41	1	2	yes	—
618	C₂³×C₅₃	C₂×#41	1	2	yes	—
619	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
620	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
621	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
622	D₄×C₅₃	—	4	4	no	—
623	D₄×C₅₃	—	4	4	no	—
624	D₄×C₅₃	—	4	4	no	—
625	D₄×C₅₃	—	4	4	no	—
626	D₄×C₅₃	—	8	2	no	—
627	D₄×C₅₃	—	8	2	no	—
628	D₄×C₅₃	—	8	2	no	—
629	D₄×C₅₃	—	8	2	no	—
630	D₄×C₅₃	—	8	2	no	—
631	D₄×C₅₃	—	8	2	no	—
632	D₄×C₅₃	—	8	2	no	—
633	D₄×C₅₃	—	8	2	no	—
634	C₂×C₄×C₅₃	—	2	8	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	—	2	1	no	—
639	C₂×C₄×C₅₃	—	2	1	no	—
640	C₂×C₄×C₅₃	—	2	1	no	—
641	C₂×C₄×C₅₃	—	2	1	no	—
642	C₂×C₄×C₅₃	—	2	1	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	1	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	2	1	no	—
683	C₂×C₄×C₅₃	—	2	1	no	—
684	C₂×C₄×C₅₃	—	2	1	no	—
685	C₂×C₄×C₅₃	—	2	1	no	—
686	C₂×C₄×C₅₃	—	2	1	no	—
687	C₂×C₄×C₅₃	—	2	1	no	—
688	C₂×C₄×C₅₃	—	2	1	no	—
689	C₂×C₄×C₅₃	—	2	1	no	—
690	C₂×C₄×C₅₃	—	2	1	no	—
691	C₂×C₄×C₅₃	—	2	1	no	—
692	C₂×C₄×C₅₃	—	2	1	no	—
693	C₂×C₄×C₅₃	—	2	1	no	—
694	C₂×C₄×C₅₃	—	2	1	no	—
695	C₂×C₄×C₅₃	—	2	1	no	—
696	C₂×C₄×C₅₃	—	2	1	no	—
697	C₂×C₄×C₅₃	—	2	1	no	—
698	C₂×C₄×C₅₃	—	2	1	no	—
699	C₂×C₄×C₅₃	—	2	1	no	—
700	C₂×C₄×C₅₃	—	2	1	no	—
701	C₂×C₄×C₅₃	—	2	1	no	—
702	C₂×C₄×C₅₃	—	2	1	no	—
703	C₂×C₄×C₅₃	—	4	4	no	—
704	C₂×C₄×C₅₃	—	4	4	no	—
705	C₂×C₄×C₅₃	—	4	4	no	—
706	C₂×C₄×C₅₃	—	4	4	no	—
707	C₂×C₄×C₅₃	—	4	4	no	—
708	C₂×C₄×C₅₃	—	4	4	no	—
709	C₂×C₄×C₅₃	—	4	4	no	—
710	C₂×C₄×C₅₃	—	4	4	no	—
711	C₂×C₄×C₅₃	—	4	4	no	—
712	C₂×C₄×C₅₃	—	4	4	no	—
713	C₂×C₄×C₅₃	—	8	2	no	—
714	C₂×C₄×C₅₃	—	8	2	no	—
715	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
716	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
717	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
718	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
719	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
720	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
721	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
722	#35056	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
723	C₂²×C₅₃	—	2	2	no	—
724	C₂²×C₅₃	—	2	2	no	—
725	C₂²×C₅₃	—	2	2	no	—
726	C₂²×C₅₃	—	2	2	no	—
727	C₂²×C₅₃	—	2	2	no	—
728	C₂²×C₅₃	—	2	2	no	—
729	C₂²×C₅₃	—	2	2	no	—
730	C₂²×C₅₃	—	2	2	no	—
731	C₂²×C₅₃	—	2	2	no	—
732	C₂²×C₅₃	—	2	2	no	—
733	C₂²×C₅₃	—	2	2	no	—
734	C₂²×C₅₃	—	2	2	no	—
735	C₂²×C₅₃	—	4	16	no	—
736	C₂²×C₅₃	—	4	1	no	—
737	C₂²×C₅₃	—	4	1	no	—
738	C₂²×C₅₃	—	4	1	no	—
739	C₂²×C₅₃	—	4	1	no	—
740	C₂²×C₅₃	—	4	1	no	—
741	C₂²×C₅₃	—	4	1	no	—
742	C₂²×C₅₃	—	4	1	no	—
743	C₂²×C₅₃	—	4	1	no	—
744	C₂²×C₅₃	—	4	1	no	—
745	C₂²×C₅₃	—	4	1	no	—
746	C₂²×C₅₃	—	4	1	no	—
747	C₂²×C₅₃	—	4	1	no	—
748	C₂²×C₅₃	—	4	1	no	—
749	C₂²×C₅₃	—	4	1	no	—
750	C₂²×C₅₃	—	4	1	no	—
751	C₂²×C₅₃	—	4	1	no	—
752	C₂²×C₅₃	—	4	1	no	—
753	C₂²×C₅₃	—	4	1	no	—
754	C₂²×C₅₃	—	4	1	no	—
755	C₂²×C₅₃	—	4	1	no	—
756	C₂²×C₅₃	—	4	1	no	—
757	C₂²×C₅₃	—	4	1	no	—
758	C₂²×C₅₃	—	4	1	no	—
759	C₂²×C₅₃	—	4	1	no	—
760	C₂²×C₅₃	—	4	1	no	—
761	C₂²×C₅₃	—	4	1	no	—
762	C₂²×C₅₃	—	4	1	no	—
763	C₂²×C₅₃	—	4	1	no	—
764	C₂²×C₅₃	—	4	1	no	—
765	C₂²×C₅₃	#540	1	4	yes	—
766	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
767	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
768	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
769	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
770	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
772	C₂²×C₅₃	#585	1	1	yes	characteristic
773	C₄×C₅₃	—	2	2	no	—
774	C₄×C₅₃	—	2	2	no	—
775	C₄×C₅₃	—	2	2	no	—
776	C₄×C₅₃	—	2	2	no	—
777	C₄×C₅₃	—	2	2	no	—
778	C₄×C₅₃	—	2	2	no	—
779	C₄×C₅₃	—	2	2	no	—
780	C₄×C₅₃	—	4	1	no	—
781	C₄×C₅₃	—	4	1	no	—
782	C₄×C₅₃	—	4	1	no	—
783	C₄×C₅₃	—	4	1	no	—
784	C₄×C₅₃	—	4	1	no	—
785	C₄×C₅₃	—	4	1	no	—
786	C₄×C₅₃	—	4	1	no	—
787	C₄×C₅₃	—	4	1	no	—
788	C₄×C₅₃	—	4	1	no	—
789	C₄×C₅₃	—	4	1	no	—
790	C₄×C₅₃	—	4	1	no	—
791	C₄×C₅₃	—	4	1	no	—
792	C₄×C₅₃	—	4	1	no	—
793	C₄×C₅₃	—	4	1	no	—
794	C₄×C₅₃	—	4	1	no	—
795	C₄×C₅₃	—	4	1	no	—
796	C₄×C₅₃	—	4	1	no	—
797	C₄×C₅₃	—	4	1	no	—
798	#2854	C₂×C₅₃	1	1	yes	characteristic, complemented
799	#2853	C₂×C₅₃	1	1	yes	characteristic, complemented
800	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
801	#2847	C₂×C₅₃	1	1	yes	characteristic, complemented
802	#2667	C₂×C₅₃	1	1	yes	characteristic, complemented
803	#2661	C₂×C₅₃	1	1	yes	characteristic, complemented
804	#2649	C₂×C₅₃	1	1	yes	characteristic, complemented
805	#2648	C₂×C₅₃	1	1	yes	characteristic, complemented
806	#2569	C₂×C₅₃	1	1	yes	characteristic, complemented
807	#2543	C₂×C₅₃	1	1	yes	characteristic, complemented
808	#2539	C₂×C₅₃	1	1	yes	characteristic, complemented
809	#2534	C₂×C₅₃	1	1	yes	characteristic, complemented
810	#2531	C₂×C₅₃	1	1	yes	characteristic, complemented
811	#2526	C₂×C₅₃	1	1	yes	characteristic, complemented
812	#2522	C₂×C₅₃	1	1	yes	characteristic, complemented
813	#2516	C₂×C₅₃	1	1	yes	characteristic, complemented
814	#2476	C₂×C₅₃	1	1	yes	characteristic, complemented
815	#2471	C₂×C₅₃	1	1	yes	characteristic, complemented
816	#2464	C₂×C₅₃	1	1	yes	characteristic, complemented
817	#2457	C₂×C₅₃	1	1	yes	characteristic, complemented
818	#2425	C₂×C₅₃	1	1	yes	characteristic, complemented
819	#2424	C₂×C₅₃	1	1	yes	characteristic, complemented
820	#2419	C₂×C₅₃	1	1	yes	characteristic, complemented
821	#2418	C₂×C₅₃	1	1	yes	characteristic, complemented
822	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
823	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
824	#2333	C₂×C₅₃	1	1	yes	characteristic, complemented
825	#2333	C₂×C₅₃	1	1	yes	characteristic, complemented
826	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
827	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
828	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
829	C₂×C₅₃	—	2	4	no	—
830	C₂×C₅₃	—	4	2	no	—
831	C₂×C₅₃	—	4	2	no	—
832	C₂×C₅₃	—	8	1	no	—
833	C₂×C₅₃	—	8	1	no	—
834	C₂×C₅₃	—	8	1	no	—
835	C₂×C₅₃	#3444	1	1	yes	characteristic
836	C₂×C₅₃	C₂×#540	1	1	yes	characteristic
837	C₂×C₅₃	#3459	1	1	yes	characteristic
838	C₂×C₅₃	#3490	1	1	yes	characteristic
839	C₂×C₅₃	#3494	1	1	yes	characteristic
840	C₂×C₅₃	#3513	1	1	yes	characteristic
841	C₂×C₅₃	#3519	1	1	yes	characteristic
842	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
843	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
844	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
845	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
846	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
847	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
848	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
849	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
850	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
851	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
852	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
853	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
854	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
855	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
856	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
857	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
858	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
859	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
860	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
861	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic, complemented
863	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
864	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
865	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
866	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
867	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	#399	C₂²×C₅₃	1	1	yes	characteristic
871	#399	C₂²×C₅₃	1	1	yes	characteristic
872	#399	C₂²×C₅₃	1	1	yes	characteristic
873	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
874	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
875	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
876	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#397	C₂²×C₅₃	1	1	yes	characteristic
879	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
881	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
882	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
883	#396	C₂²×C₅₃	1	1	yes	characteristic
884	#396	C₂²×C₅₃	1	1	yes	characteristic
885	#396	C₂²×C₅₃	1	1	yes	characteristic
886	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#394	C₂²×C₅₃	1	1	yes	characteristic
888	#394	C₂²×C₅₃	1	1	yes	characteristic
889	#394	C₂²×C₅₃	1	1	yes	characteristic
890	#394	C₂²×C₅₃	1	1	yes	characteristic
891	#394	C₂²×C₅₃	1	1	yes	characteristic
892	#394	C₂²×C₅₃	1	1	yes	characteristic
893	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
894	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#392	C₂²×C₅₃	1	1	yes	characteristic
896	#392	C₂²×C₅₃	1	1	yes	characteristic
897	#392	C₂²×C₅₃	1	1	yes	characteristic
898	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
899	#390	C₂²×C₅₃	1	1	yes	characteristic
900	#390	C₂²×C₅₃	1	1	yes	characteristic
901	#390	C₂²×C₅₃	1	1	yes	characteristic
902	#390	C₂²×C₅₃	1	1	yes	characteristic
903	#390	C₂²×C₅₃	1	1	yes	characteristic
904	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#388	C₂²×C₅₃	1	1	yes	characteristic
912	#388	C₂²×C₅₃	1	1	yes	characteristic
913	#388	C₂²×C₅₃	1	1	yes	characteristic
914	#388	C₂²×C₅₃	1	1	yes	characteristic
915	#388	C₂²×C₅₃	1	1	yes	characteristic
916	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#386	C₂²×C₅₃	1	1	yes	characteristic
944	#386	C₂²×C₅₃	1	1	yes	characteristic
945	#386	C₂²×C₅₃	1	1	yes	characteristic
946	#386	C₂²×C₅₃	1	1	yes	characteristic
947	#386	C₂²×C₅₃	1	1	yes	characteristic
948	#386	C₂²×C₅₃	1	1	yes	characteristic
949	#386	C₂²×C₅₃	1	1	yes	characteristic
950	#386	C₂²×C₅₃	1	1	yes	characteristic
951	#386	C₂²×C₅₃	1	1	yes	characteristic
952	#386	C₂²×C₅₃	1	1	yes	characteristic
953	#386	C₂²×C₅₃	1	1	yes	characteristic
954	#386	C₂²×C₅₃	1	1	yes	characteristic
955	#386	C₂²×C₅₃	1	1	yes	characteristic
956	#386	C₂²×C₅₃	1	1	yes	characteristic
957	#386	C₂²×C₅₃	1	1	yes	characteristic
958	#386	C₂²×C₅₃	1	1	yes	characteristic
959	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#385	C₂²×C₅₃	1	1	yes	characteristic
963	#385	C₂²×C₅₃	1	1	yes	characteristic
964	#385	C₂²×C₅₃	1	1	yes	characteristic
965	#385	C₂²×C₅₃	1	1	yes	characteristic
966	#385	C₂²×C₅₃	1	1	yes	characteristic
967	#385	C₂²×C₅₃	1	1	yes	characteristic
968	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#381	C₂²×C₅₃	1	1	yes	characteristic
970	#381	C₂²×C₅₃	1	1	yes	characteristic
971	#381	C₂²×C₅₃	1	1	yes	characteristic
972	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#380	C₂²×C₅₃	1	1	yes	characteristic
974	#380	C₂²×C₅₃	1	1	yes	characteristic
975	#380	C₂²×C₅₃	1	1	yes	characteristic
976	#380	C₂²×C₅₃	1	1	yes	characteristic
977	#380	C₂²×C₅₃	1	1	yes	characteristic
978	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#379	C₂²×C₅₃	1	1	yes	characteristic
980	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
983	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
984	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
985	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
986	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
987	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
988	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
989	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
990	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
991	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#376	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
996	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
997	C₅₃	#35056	1	1	yes	characteristic, direct product factor, Sylow
998	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
999	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂³×C₄	—	2	4	no	—
1012	C₂³×C₄	—	4	2	no	—
1013	C₂³×C₄	—	4	2	no	—
1014	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1027	#123	—	2	4	no	—
1028	#123	—	2	4	no	—
1029	#123	—	4	2	no	—
1030	#123	—	4	2	no	—
1031	#123	—	4	2	no	—
1032	#123	—	4	2	no	—
1033	#121	—	2	4	no	—
1034	#121	—	2	4	no	—
1035	#121	—	2	4	no	—
1036	#121	—	4	2	no	—
1037	#121	—	4	2	no	—
1038	#121	—	4	2	no	—
1039	#120	—	4	2	no	—
1040	#120	—	4	2	no	—
1041	#120	—	4	2	no	—
1042	C₄×D₄	—	2	4	no	—
1043	C₄×D₄	—	4	2	no	—
1044	C₄×D₄	—	4	2	no	—
1045	C₄×D₄	—	4	2	no	—
1046	#117	—	4	2	no	—
1047	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	—	2	4	no	—
1074	C₂×C₂²⋊C₄	—	2	4	no	—
1075	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×C₄²	—	4	2	no	—
1126	C₂×C₄²	—	4	2	no	—
1127	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1140	#95	C₂³×C₅₃	1	1	yes	characteristic
1141	#95	C₂³×C₅₃	1	1	yes	characteristic
1142	#95	C₂³×C₅₃	1	1	yes	characteristic
1143	#95	C₂³×C₅₃	1	1	yes	characteristic
1144	#95	C₂³×C₅₃	1	1	yes	characteristic
1145	#95	C₂³×C₅₃	1	1	yes	characteristic
1146	#95	C₂³×C₅₃	1	1	yes	characteristic
1147	#95	C₂³×C₅₃	1	1	yes	characteristic
1148	#95	C₂³×C₅₃	1	1	yes	characteristic
1149	#95	C₂³×C₅₃	1	1	yes	characteristic
1150	#95	C₂³×C₅₃	1	1	yes	characteristic
1151	#95	C₂³×C₅₃	1	1	yes	characteristic
1152	#95	C₂³×C₅₃	1	1	yes	characteristic
1153	#95	C₂³×C₅₃	1	1	yes	characteristic
1154	#95	C₂³×C₅₃	1	1	yes	characteristic
1155	#95	C₂³×C₅₃	1	1	yes	characteristic
1156	#95	C₂³×C₅₃	1	1	yes	characteristic
1157	#95	C₂³×C₅₃	1	1	yes	characteristic
1158	#95	C₂³×C₅₃	1	1	yes	characteristic
1159	#95	C₂³×C₅₃	1	1	yes	characteristic
1160	#95	C₂³×C₅₃	1	1	yes	characteristic
1161	#95	C₂³×C₅₃	1	1	yes	characteristic
1162	#95	C₂³×C₅₃	1	1	yes	characteristic
1163	#95	C₂³×C₅₃	1	1	yes	characteristic
1164	#95	C₂³×C₅₃	1	1	yes	characteristic
1165	#95	C₂³×C₅₃	1	1	yes	characteristic
1166	#95	C₂³×C₅₃	1	1	yes	characteristic
1167	#95	C₂³×C₅₃	1	1	yes	characteristic
1168	#95	C₂³×C₅₃	1	1	yes	characteristic
1169	#95	C₂³×C₅₃	1	1	yes	characteristic
1170	#95	C₂³×C₅₃	1	1	yes	characteristic
1171	#95	C₂³×C₅₃	1	1	yes	characteristic
1172	#95	C₂³×C₅₃	1	1	yes	characteristic
1173	#95	C₂³×C₅₃	1	1	yes	characteristic
1174	#95	C₂³×C₅₃	1	1	yes	characteristic
1175	#95	C₂³×C₅₃	1	1	yes	characteristic
1176	#95	C₂³×C₅₃	1	1	yes	characteristic
1177	#95	C₂³×C₅₃	1	1	yes	characteristic
1178	#95	C₂³×C₅₃	1	1	yes	characteristic
1179	#95	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂⁴	—	2	2	no	—
1181	C₂⁴	—	2	2	no	—
1182	C₂⁴	—	2	2	no	—
1183	C₂⁴	—	2	2	no	—
1184	C₂⁴	—	2	2	no	—
1185	C₂⁴	—	4	1	no	—
1186	C₂⁴	—	4	1	no	—
1187	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1188	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1189	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1190	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1191	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1192	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1193	C₂×D₄	—	2	2	no	—
1194	C₂×D₄	—	2	2	no	—
1195	C₂×D₄	—	2	2	no	—
1196	C₂×D₄	—	2	2	no	—
1197	C₂×D₄	—	2	2	no	—
1198	C₂×D₄	—	2	2	no	—
1199	C₂×D₄	—	2	2	no	—
1200	C₂×D₄	—	2	2	no	—
1201	C₂×D₄	—	2	2	no	—
1202	C₂×D₄	—	2	2	no	—
1203	C₂×D₄	—	2	2	no	—
1204	C₂×D₄	—	2	2	no	—
1205	C₂×D₄	—	2	2	no	—
1206	C₂×D₄	—	2	2	no	—
1207	C₂×D₄	—	2	2	no	—
1208	C₂×D₄	—	2	2	no	—
1209	C₂×D₄	—	2	2	no	—
1210	C₂×D₄	—	2	2	no	—
1211	C₂×D₄	—	4	1	no	—
1212	C₂×D₄	—	4	1	no	—
1213	C₂×D₄	—	4	1	no	—
1214	C₂×D₄	—	4	1	no	—
1215	C₂×D₄	—	4	1	no	—
1216	C₂×D₄	—	4	1	no	—
1217	C₂×D₄	—	4	1	no	—
1218	C₂×D₄	—	4	1	no	—
1219	C₂×D₄	—	4	1	no	—
1220	C₂×D₄	—	4	1	no	—
1221	C₂×D₄	—	4	1	no	—
1222	C₂×D₄	—	4	1	no	—
1223	C₂×D₄	—	4	1	no	—
1224	C₂×D₄	—	4	1	no	—
1225	C₂×D₄	—	4	1	no	—
1226	C₂×D₄	—	4	1	no	—
1227	C₂×D₄	—	4	1	no	—
1228	C₂×D₄	—	4	1	no	—
1229	C₂²×C₄	—	2	2	no	—
1230	C₂²×C₄	—	2	2	no	—
1231	C₂²×C₄	—	2	2	no	—
1232	C₂²×C₄	—	2	2	no	—
1233	C₂²×C₄	—	2	2	no	—
1234	C₂²×C₄	—	2	2	no	—
1235	C₂²×C₄	—	2	2	no	—
1236	C₂²×C₄	—	2	2	no	—
1237	C₂²×C₄	—	2	2	no	—
1238	C₂²×C₄	—	2	2	no	—
1239	C₂²×C₄	—	2	2	no	—
1240	C₂²×C₄	—	2	2	no	—
1241	C₂²×C₄	—	2	2	no	—
1242	C₂²×C₄	—	2	2	no	—
1243	C₂²×C₄	—	2	2	no	—
1244	C₂²×C₄	—	2	2	no	—
1245	C₂²×C₄	—	2	2	no	—
1246	C₂²×C₄	—	2	2	no	—
1247	C₂²×C₄	—	2	2	no	—
1248	C₂²×C₄	—	2	2	no	—
1249	C₂²×C₄	—	4	1	no	—
1250	C₂²×C₄	—	4	1	no	—
1251	C₂²×C₄	—	4	1	no	—
1252	C₂²×C₄	—	4	1	no	—
1253	C₂²×C₄	—	4	1	no	—
1254	C₂²×C₄	—	4	1	no	—
1255	C₂²×C₄	—	4	1	no	—
1256	C₂²×C₄	—	4	1	no	—
1257	C₂²×C₄	—	4	1	no	—
1258	C₂²×C₄	—	4	1	no	—
1259	C₂²×C₄	—	4	1	no	—
1260	C₂²×C₄	—	4	1	no	—
1261	C₂²×C₄	—	4	1	no	—
1262	C₂²×C₄	—	4	1	no	—
1263	C₂²×C₄	—	4	1	no	—
1264	C₂²×C₄	—	4	1	no	—
1265	C₂²×C₄	—	4	1	no	—
1266	C₂²×C₄	—	4	16	no	—
1267	C₂²×C₄	#41×C₅₃	1	4	yes	—
1268	C₂²×C₄	#41×C₅₃	1	4	yes	—
1269	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1270	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1271	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1272	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1273	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1274	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1275	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1276	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1277	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1278	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1279	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1280	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1281	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1282	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1283	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1284	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1285	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1286	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1287	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1288	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1289	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1290	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1291	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1292	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1293	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1294	C₄⋊C₄	—	2	2	no	—
1295	C₄⋊C₄	—	2	2	no	—
1296	C₄⋊C₄	—	2	2	no	—
1297	C₄⋊C₄	—	2	2	no	—
1298	C₄⋊C₄	—	2	2	no	—
1299	C₄⋊C₄	—	2	2	no	—
1300	C₄⋊C₄	—	2	2	no	—
1301	C₄⋊C₄	—	2	2	no	—
1302	C₄⋊C₄	—	2	2	no	—
1303	C₄⋊C₄	—	4	1	no	—
1304	C₄⋊C₄	—	4	1	no	—
1305	C₄⋊C₄	—	4	1	no	—
1306	C₄⋊C₄	—	4	1	no	—
1307	C₄⋊C₄	—	4	1	no	—
1308	C₄⋊C₄	—	4	1	no	—
1309	C₄⋊C₄	—	4	1	no	—
1310	C₄⋊C₄	—	4	1	no	—
1311	C₄⋊C₄	—	4	1	no	—
1312	C₄⋊C₄	—	4	1	no	—
1313	C₄⋊C₄	—	4	1	no	—
1314	C₄⋊C₄	—	4	1	no	—
1315	C₄⋊C₄	—	4	1	no	—
1316	C₄⋊C₄	—	4	1	no	—
1317	C₄⋊C₄	—	4	1	no	—
1318	C₄⋊C₄	—	4	1	no	—
1319	C₄⋊C₄	—	4	1	no	—
1320	C₂²⋊C₄	—	2	2	no	—
1321	C₂²⋊C₄	—	2	2	no	—
1322	C₂²⋊C₄	—	2	2	no	—
1323	C₂²⋊C₄	—	2	2	no	—
1324	C₂²⋊C₄	—	2	2	no	—
1325	C₂²⋊C₄	—	2	2	no	—
1326	C₂²⋊C₄	—	2	2	no	—
1327	C₂²⋊C₄	—	2	2	no	—
1328	C₂²⋊C₄	—	2	2	no	—
1329	C₂²⋊C₄	—	2	2	no	—
1330	C₂²⋊C₄	—	2	2	no	—
1331	C₂²⋊C₄	—	2	2	no	—
1332	C₂²⋊C₄	—	2	2	no	—
1333	C₂²⋊C₄	—	2	2	no	—
1334	C₂²⋊C₄	—	2	2	no	—
1335	C₂²⋊C₄	—	2	2	no	—
1336	C₂²⋊C₄	—	2	2	no	—
1337	C₂²⋊C₄	—	2	2	no	—
1338	C₂²⋊C₄	—	2	2	no	—
1339	C₂²⋊C₄	—	2	2	no	—
1340	C₂²⋊C₄	—	2	2	no	—
1341	C₂²⋊C₄	—	2	2	no	—
1342	C₂²⋊C₄	—	2	2	no	—
1343	C₂²⋊C₄	—	2	2	no	—
1344	C₂²⋊C₄	—	2	2	no	—
1345	C₂²⋊C₄	—	2	2	no	—
1346	C₂²⋊C₄	—	4	1	no	—
1347	C₂²⋊C₄	—	4	1	no	—
1348	C₂²⋊C₄	—	4	1	no	—
1349	C₂²⋊C₄	—	4	1	no	—
1350	C₂²⋊C₄	—	4	1	no	—
1351	C₂²⋊C₄	—	4	1	no	—
1352	C₂²⋊C₄	—	4	1	no	—
1353	C₂²⋊C₄	—	4	1	no	—
1354	C₂²⋊C₄	—	4	1	no	—
1355	C₂²⋊C₄	—	4	1	no	—
1356	C₂²⋊C₄	—	4	1	no	—
1357	C₂²⋊C₄	—	4	1	no	—
1358	C₂²⋊C₄	—	4	1	no	—
1359	C₂²⋊C₄	—	4	1	no	—
1360	C₂²⋊C₄	—	4	1	no	—
1361	C₂²⋊C₄	—	4	1	no	—
1362	C₂²⋊C₄	—	4	1	no	—
1363	C₂²⋊C₄	—	4	1	no	—
1364	C₂²⋊C₄	—	4	1	no	—
1365	C₂²⋊C₄	—	4	1	no	—
1366	C₂²⋊C₄	—	4	1	no	—
1367	C₂²⋊C₄	—	4	1	no	—
1368	C₂²⋊C₄	—	4	1	no	—
1369	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
1370	C₄²	—	2	2	no	—
1371	C₄²	—	2	2	no	—
1372	C₄²	—	2	2	no	—
1373	C₄²	—	4	1	no	—
1374	C₄²	—	4	1	no	—
1375	C₄²	—	4	1	no	—
1376	C₄²	—	4	1	no	—
1377	C₄²	—	4	1	no	—
1378	C₄²	—	4	1	no	—
1379	C₄²	—	4	1	no	—
1380	C₄²	—	4	1	no	—
1381	C₄²	—	4	1	no	—
1382	C₄²	—	4	1	no	—
1383	C₂³	—	2	1	no	—
1384	C₂³	—	2	1	no	—
1385	C₂³	—	2	1	no	—
1386	C₂³	—	2	1	no	—
1387	C₂³	—	2	8	no	—
1388	C₂³	—	2	1	no	—
1389	C₂³	—	2	1	no	—
1390	C₂³	—	2	1	no	—
1391	C₂³	—	2	1	no	—
1392	C₂³	—	2	1	no	—
1393	C₂³	—	2	1	no	—
1394	C₂³	—	2	1	no	—
1395	C₂³	—	2	1	no	—
1396	C₂³	—	2	1	no	—
1397	C₂³	—	2	1	no	—
1398	C₂³	—	2	1	no	—
1399	C₂³	—	2	1	no	—
1400	C₂³	—	2	1	no	—
1401	C₂³	—	2	1	no	—
1402	C₂³	—	2	1	no	—
1403	C₂³	—	2	1	no	—
1404	C₂³	—	2	1	no	—
1405	C₂³	—	2	1	no	—
1406	C₂³	—	2	1	no	—
1407	C₂³	—	2	1	no	—
1408	C₂³	—	2	1	no	—
1409	C₂³	—	2	1	no	—
1410	C₂³	—	2	1	no	—
1411	C₂³	—	2	1	no	—
1412	C₂³	—	2	1	no	—
1413	C₂³	—	2	1	no	—
1414	C₂³	—	2	1	no	—
1415	C₂³	—	2	1	no	—
1416	C₂³	—	2	1	no	—
1417	C₂³	—	2	1	no	—
1418	C₂³	—	2	1	no	—
1419	C₂³	—	2	1	no	—
1420	C₂³	—	2	1	no	—
1421	C₂³	—	4	4	no	—
1422	C₂³	—	4	4	no	—
1423	C₂³	—	4	4	no	—
1424	C₂³	—	4	4	no	—
1425	C₂³	—	4	4	no	—
1426	C₂³	—	4	4	no	—
1427	C₂³	C₂×#41×C₅₃	1	2	yes	—
1428	C₂³	C₂×#41×C₅₃	1	2	yes	—
1429	C₂³	C₂×#41×C₅₃	1	2	yes	—
1430	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1431	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1432	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1433	D₄	—	4	4	no	—
1434	D₄	—	4	4	no	—
1435	D₄	—	4	4	no	—
1436	D₄	—	4	4	no	—
1437	D₄	—	8	2	no	—
1438	D₄	—	8	2	no	—
1439	D₄	—	8	2	no	—
1440	D₄	—	8	2	no	—
1441	D₄	—	8	2	no	—
1442	D₄	—	8	2	no	—
1443	D₄	—	8	2	no	—
1444	D₄	—	8	2	no	—
1445	C₂×C₄	—	2	8	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	1	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	1	no	—
1462	C₂×C₄	—	2	1	no	—
1463	C₂×C₄	—	2	1	no	—
1464	C₂×C₄	—	2	1	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	2	1	no	—
1468	C₂×C₄	—	2	1	no	—
1469	C₂×C₄	—	2	1	no	—
1470	C₂×C₄	—	2	1	no	—
1471	C₂×C₄	—	2	1	no	—
1472	C₂×C₄	—	2	1	no	—
1473	C₂×C₄	—	2	1	no	—
1474	C₂×C₄	—	2	1	no	—
1475	C₂×C₄	—	2	1	no	—
1476	C₂×C₄	—	2	1	no	—
1477	C₂×C₄	—	2	1	no	—
1478	C₂×C₄	—	2	1	no	—
1479	C₂×C₄	—	2	1	no	—
1480	C₂×C₄	—	2	1	no	—
1481	C₂×C₄	—	2	1	no	—
1482	C₂×C₄	—	2	1	no	—
1483	C₂×C₄	—	2	1	no	—
1484	C₂×C₄	—	2	1	no	—
1485	C₂×C₄	—	2	1	no	—
1486	C₂×C₄	—	2	1	no	—
1487	C₂×C₄	—	2	1	no	—
1488	C₂×C₄	—	2	1	no	—
1489	C₂×C₄	—	2	1	no	—
1490	C₂×C₄	—	2	1	no	—
1491	C₂×C₄	—	2	1	no	—
1492	C₂×C₄	—	2	1	no	—
1493	C₂×C₄	—	2	1	no	—
1494	C₂×C₄	—	2	1	no	—
1495	C₂×C₄	—	2	1	no	—
1496	C₂×C₄	—	2	1	no	—
1497	C₂×C₄	—	2	1	no	—
1498	C₂×C₄	—	2	1	no	—
1499	C₂×C₄	—	2	1	no	—
1500	C₂×C₄	—	2	1	no	—
1501	C₂×C₄	—	2	1	no	—
1502	C₂×C₄	—	2	1	no	—
1503	C₂×C₄	—	2	1	no	—
1504	C₂×C₄	—	2	1	no	—
1505	C₂×C₄	—	2	1	no	—
1506	C₂×C₄	—	2	1	no	—
1507	C₂×C₄	—	2	1	no	—
1508	C₂×C₄	—	2	1	no	—
1509	C₂×C₄	—	2	1	no	—
1510	C₂×C₄	—	2	1	no	—
1511	C₂×C₄	—	2	1	no	—
1512	C₂×C₄	—	2	1	no	—
1513	C₂×C₄	—	2	1	no	—
1514	C₂×C₄	—	4	4	no	—
1515	C₂×C₄	—	4	4	no	—
1516	C₂×C₄	—	4	4	no	—
1517	C₂×C₄	—	4	4	no	—
1518	C₂×C₄	—	4	4	no	—
1519	C₂×C₄	—	4	4	no	—
1520	C₂×C₄	—	4	4	no	—
1521	C₂×C₄	—	4	4	no	—
1522	C₂×C₄	—	4	4	no	—
1523	C₂×C₄	—	4	4	no	—
1524	C₂×C₄	—	8	2	no	—
1525	C₂×C₄	—	8	2	no	—
1526	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1527	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1528	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1529	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1530	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1531	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1532	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1533	C₂²	—	2	2	no	—
1534	C₂²	—	2	2	no	—
1535	C₂²	—	2	2	no	—
1536	C₂²	—	2	2	no	—
1537	C₂²	—	2	2	no	—
1538	C₂²	—	2	2	no	—
1539	C₂²	—	2	2	no	—
1540	C₂²	—	2	2	no	—
1541	C₂²	—	2	2	no	—
1542	C₂²	—	2	2	no	—
1543	C₂²	—	2	2	no	—
1544	C₂²	—	2	2	no	—
1545	C₂²	—	4	16	no	—
1546	C₂²	—	4	1	no	—
1547	C₂²	—	4	1	no	—
1548	C₂²	—	4	1	no	—
1549	C₂²	—	4	1	no	—
1550	C₂²	—	4	1	no	—
1551	C₂²	—	4	1	no	—
1552	C₂²	—	4	1	no	—
1553	C₂²	—	4	1	no	—
1554	C₂²	—	4	1	no	—
1555	C₂²	—	4	1	no	—
1556	C₂²	—	4	1	no	—
1557	C₂²	—	4	1	no	—
1558	C₂²	—	4	1	no	—
1559	C₂²	—	4	1	no	—
1560	C₂²	—	4	1	no	—
1561	C₂²	—	4	1	no	—
1562	C₂²	—	4	1	no	—
1563	C₂²	—	4	1	no	—
1564	C₂²	—	4	1	no	—
1565	C₂²	—	4	1	no	—
1566	C₂²	—	4	1	no	—
1567	C₂²	—	4	1	no	—
1568	C₂²	—	4	1	no	—
1569	C₂²	—	4	1	no	—
1570	C₂²	—	4	1	no	—
1571	C₂²	—	4	1	no	—
1572	C₂²	—	4	1	no	—
1573	C₂²	—	4	1	no	—
1574	C₂²	—	4	1	no	—
1575	C₂²	C₅₃×#540	1	4	yes	—
1576	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1577	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1578	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1579	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1580	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1581	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1582	C₂²	C₅₃×#585	1	1	yes	characteristic
1583	C₄	—	2	2	no	—
1584	C₄	—	2	2	no	—
1585	C₄	—	2	2	no	—
1586	C₄	—	2	2	no	—
1587	C₄	—	2	2	no	—
1588	C₄	—	2	2	no	—
1589	C₄	—	2	2	no	—
1590	C₄	—	4	1	no	—
1591	C₄	—	4	1	no	—
1592	C₄	—	4	1	no	—
1593	C₄	—	4	1	no	—
1594	C₄	—	4	1	no	—
1595	C₄	—	4	1	no	—
1596	C₄	—	4	1	no	—
1597	C₄	—	4	1	no	—
1598	C₄	—	4	1	no	—
1599	C₄	—	4	1	no	—
1600	C₄	—	4	1	no	—
1601	C₄	—	4	1	no	—
1602	C₄	—	4	1	no	—
1603	C₄	—	4	1	no	—
1604	C₄	—	4	1	no	—
1605	C₄	—	4	1	no	—
1606	C₄	—	4	1	no	—
1607	C₄	—	4	1	no	—
1608	C₂	—	2	4	no	—
1609	C₂	—	4	2	no	—
1610	C₂	—	4	2	no	—
1611	C₂	—	8	1	no	—
1612	C₂	—	8	1	no	—
1613	C₂	—	8	1	no	—
1614	C₂	C₅₃×#3444	1	1	yes	characteristic
1615	C₂	C₂×C₅₃×#540	1	1	yes	characteristic
1616	C₂	C₅₃×#3459	1	1	yes	characteristic
1617	C₂	C₅₃×#3490	1	1	yes	characteristic
1618	C₂	C₅₃×#3494	1	1	yes	characteristic
1619	C₂	C₅₃×#3513	1	1	yes	characteristic
1620	C₂	C₅₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
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×#2854	C₂	semidirect
2. C₅₃×#2853	C₂	semidirect
3. C₅₃×#2849	C₂	semidirect
4. C₅₃×#2847	C₂	semidirect
5. C₅₃×#2667	C₂	semidirect
6. C₅₃×#2661	C₂	semidirect
7. C₅₃×#2649	C₂	semidirect
8. C₅₃×#2648	C₂	semidirect
9. C₅₃×#2569	C₂	semidirect
10. C₅₃×#2543	C₂	semidirect
11. C₅₃×#2539	C₂	semidirect
12. C₅₃×#2534	C₂	semidirect
13. C₅₃×#2531	C₂	semidirect
14. C₅₃×#2526	C₂	semidirect
15. C₅₃×#2522	C₂	semidirect
16. C₅₃×#2516	C₂	semidirect
17. C₅₃×#2476	C₂	semidirect
18. C₅₃×#2471	C₂	semidirect
19. C₅₃×#2464	C₂	semidirect
20. C₅₃×#2457	C₂	semidirect
21. C₅₃×#2425	C₂	semidirect
22. C₅₃×#2424	C₂	semidirect
23. C₅₃×#2419	C₂	semidirect
24. C₅₃×#2418	C₂	semidirect
25. C₅₃×#2335	C₂	semidirect
26. C₅₃×#2335	C₂	semidirect
27. C₅₃×#2333	C₂	semidirect
28. C₅₃×#2333	C₂	semidirect
29. C₄×#121×C₅₃	C₂	semidirect
30. C₅₃×#2290	C₂	semidirect
31. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
51. C₂×C₄×D₄×C₅₃	C₂²	semidirect
52. C₂×#117×C₅₃	C₂²	semidirect
57. C₅₃×#400	C₂²	semidirect
58. C₅₃×#400	C₂²	semidirect
59. C₅₃×#400	C₂²	semidirect
63. C₅₃×#398	C₂²	semidirect
64. C₅₃×#398	C₂²	semidirect
65. C₅₃×#398	C₂²	semidirect
66. C₅₃×#398	C₂²	semidirect
67. C₅₃×#398	C₂²	semidirect
69. C₅₃×#397	C₂²	semidirect
70. C₅₃×#397	C₂²	semidirect
71. C₅₃×#397	C₂²	semidirect
72. C₅₃×#397	C₂²	semidirect
76. C₅₃×#396	C₂²	semidirect
83. C₅₃×#394	C₂²	semidirect
84. C₅₃×#394	C₂²	semidirect
88. C₅₃×#392	C₂²	semidirect
94. C₅₃×#390	C₂²	semidirect
95. C₅₃×#390	C₂²	semidirect
96. C₅₃×#390	C₂²	semidirect
97. C₅₃×#389	C₂²	semidirect
98. C₅₃×#389	C₂²	semidirect
99. C₅₃×#389	C₂²	semidirect
100. C₅₃×#389	C₂²	semidirect
106. C₅₃×#388	C₂²	semidirect
107. C₅₃×#388	C₂²	semidirect
108. C₅₃×#388	C₂²	semidirect
109. C₅₃×#388	C₂²	semidirect
110. C₅₃×#388	C₂²	semidirect
111. C₅₃×#388	C₂²	semidirect
112. C₅₃×#388	C₂²	semidirect
113. C₅₃×#388	C₂²	semidirect
114. C₅₃×#388	C₂²	semidirect
115. C₅₃×#388	C₂²	semidirect
116. C₅₃×#388	C₂²	semidirect
117. C₅₃×#388	C₂²	semidirect
118. C₅₃×#388	C₂²	semidirect
119. C₅₃×#388	C₂²	semidirect
120. C₅₃×#388	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
149. C₅₃×#386	C₂²	semidirect
150. C₅₃×#386	C₂²	semidirect
151. C₅₃×#386	C₂²	semidirect
158. C₅₃×#385	C₂²	semidirect
162. C₅₃×#381	C₂²	semidirect
168. C₅₃×#380	C₂²	semidirect
170. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
171. 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
184. C₅₃×#376	C₂²	semidirect
722. #35056	C₅₃	direct (N × H)
798. #2854	C₂×C₅₃	semidirect
799. #2853	C₂×C₅₃	semidirect
800. #2849	C₂×C₅₃	semidirect
801. #2847	C₂×C₅₃	semidirect
802. #2667	C₂×C₅₃	semidirect
803. #2661	C₂×C₅₃	semidirect
804. #2649	C₂×C₅₃	semidirect
805. #2648	C₂×C₅₃	semidirect
806. #2569	C₂×C₅₃	semidirect
807. #2543	C₂×C₅₃	semidirect
808. #2539	C₂×C₅₃	semidirect
809. #2534	C₂×C₅₃	semidirect
810. #2531	C₂×C₅₃	semidirect
811. #2526	C₂×C₅₃	semidirect
812. #2522	C₂×C₅₃	semidirect
813. #2516	C₂×C₅₃	semidirect
814. #2476	C₂×C₅₃	semidirect
815. #2471	C₂×C₅₃	semidirect
816. #2464	C₂×C₅₃	semidirect
817. #2457	C₂×C₅₃	semidirect
818. #2425	C₂×C₅₃	semidirect
819. #2424	C₂×C₅₃	semidirect
820. #2419	C₂×C₅₃	semidirect
821. #2418	C₂×C₅₃	semidirect
822. #2335	C₂×C₅₃	semidirect
823. #2335	C₂×C₅₃	semidirect
824. #2333	C₂×C₅₃	semidirect
825. #2333	C₂×C₅₃	semidirect
826. C₄×#121	C₂×C₅₃	semidirect
827. #2290	C₂×C₅₃	semidirect
828. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
861. C₂×C₄×D₄	C₂²×C₅₃	semidirect
862. C₂×#117	C₂²×C₅₃	semidirect
867. #400	C₂²×C₅₃	semidirect
868. #400	C₂²×C₅₃	semidirect
869. #400	C₂²×C₅₃	semidirect
873. #398	C₂²×C₅₃	semidirect
874. #398	C₂²×C₅₃	semidirect
875. #398	C₂²×C₅₃	semidirect
876. #398	C₂²×C₅₃	semidirect
877. #398	C₂²×C₅₃	semidirect
879. #397	C₂²×C₅₃	semidirect
880. #397	C₂²×C₅₃	semidirect
881. #397	C₂²×C₅₃	semidirect
882. #397	C₂²×C₅₃	semidirect
886. #396	C₂²×C₅₃	semidirect
893. #394	C₂²×C₅₃	semidirect
894. #394	C₂²×C₅₃	semidirect
898. #392	C₂²×C₅₃	semidirect
904. #390	C₂²×C₅₃	semidirect
905. #390	C₂²×C₅₃	semidirect
906. #390	C₂²×C₅₃	semidirect
907. #389	C₂²×C₅₃	semidirect
908. #389	C₂²×C₅₃	semidirect
909. #389	C₂²×C₅₃	semidirect
910. #389	C₂²×C₅₃	semidirect
916. #388	C₂²×C₅₃	semidirect
917. #388	C₂²×C₅₃	semidirect
918. #388	C₂²×C₅₃	semidirect
919. #388	C₂²×C₅₃	semidirect
920. #388	C₂²×C₅₃	semidirect
921. #388	C₂²×C₅₃	semidirect
922. #388	C₂²×C₅₃	semidirect
923. #388	C₂²×C₅₃	semidirect
924. #388	C₂²×C₅₃	semidirect
925. #388	C₂²×C₅₃	semidirect
926. #388	C₂²×C₅₃	semidirect
927. #388	C₂²×C₅₃	semidirect
928. #388	C₂²×C₅₃	semidirect
929. #388	C₂²×C₅₃	semidirect
930. #388	C₂²×C₅₃	semidirect
931. #387	C₂²×C₅₃	semidirect
932. #387	C₂²×C₅₃	semidirect
933. #387	C₂²×C₅₃	semidirect
934. #387	C₂²×C₅₃	semidirect
935. #387	C₂²×C₅₃	semidirect
936. #387	C₂²×C₅₃	semidirect
937. #387	C₂²×C₅₃	semidirect
938. #387	C₂²×C₅₃	semidirect
939. #387	C₂²×C₅₃	semidirect
940. #387	C₂²×C₅₃	semidirect
941. #387	C₂²×C₅₃	semidirect
942. #387	C₂²×C₅₃	semidirect
959. #386	C₂²×C₅₃	semidirect
960. #386	C₂²×C₅₃	semidirect
961. #386	C₂²×C₅₃	semidirect
968. #385	C₂²×C₅₃	semidirect
972. #381	C₂²×C₅₃	semidirect
978. #380	C₂²×C₅₃	semidirect
980. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
981. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
991. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
992. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
993. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
994. #376	C₂²×C₅₃	semidirect
997. C₅₃	#35056	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×#2854	2
C₅₃×#2853	2
C₅₃×#2849	2
C₅₃×#2847	2
C₅₃×#2667	2
C₅₃×#2661	2
C₅₃×#2649	2
C₅₃×#2648	2
C₅₃×#2569	2
C₅₃×#2543	2
C₅₃×#2539	2
C₅₃×#2534	2
C₅₃×#2531	2
C₅₃×#2526	2
C₅₃×#2522	2
C₅₃×#2516	2
C₅₃×#2476	2
C₅₃×#2471	2
C₅₃×#2464	2
C₅₃×#2457	2
C₅₃×#2425	2
C₅₃×#2424	2
C₅₃×#2419	2
C₅₃×#2418	2
C₅₃×#2335	2
C₅₃×#2333	2
C₄×#121×C₅₃	2
C₅₃×#2290	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#35056	53

Subgroups — C53×#35056 #27242568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35056 #27242568