Subgroups — C₅₃×#35074 #27242586

Order 13568.

2062 conjugacy classes of subgroups.

The subgroup lattice has 1542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2652	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×#2597	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2595	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2589	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2587	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2578	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2576	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2559	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2557	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2493	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2488	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2480	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2472	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
23	C₅₃×#2419	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2418	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2337	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2335	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2334	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2333	C₂	1	1	yes	maximal, characteristic, complemented
29	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#123×C₅₃	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×#126×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#124×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×#123×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×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×#120×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#401	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×#400	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#399	C₂²	1	1	yes	characteristic
59	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
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×#397	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#396	C₂²	1	1	yes	characteristic
71	C₅₃×#396	C₂²	1	1	yes	characteristic
72	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
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×#394	C₂²	1	1	yes	characteristic
77	C₅₃×#394	C₂²	1	1	yes	characteristic
78	C₅₃×#394	C₂²	1	1	yes	characteristic
79	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#393	C₂²	1	1	yes	characteristic
81	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#392	C₂²	1	1	yes	characteristic
83	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#390	C₂²	1	1	yes	characteristic
87	C₅₃×#390	C₂²	1	1	yes	characteristic
88	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
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, complemented
104	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
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×#387	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#387	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×#386	C₂²	1	1	yes	characteristic
128	C₅₃×#386	C₂²	1	1	yes	characteristic
129	C₅₃×#386	C₂²	1	1	yes	characteristic
130	C₅₃×#386	C₂²	1	1	yes	characteristic
131	C₅₃×#386	C₂²	1	1	yes	characteristic
132	C₅₃×#386	C₂²	1	1	yes	characteristic
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, complemented
142	C₅₃×#385	C₂²	1	1	yes	characteristic
143	C₅₃×#385	C₂²	1	1	yes	characteristic
144	C₅₃×#385	C₂²	1	1	yes	characteristic
145	C₅₃×#385	C₂²	1	1	yes	characteristic
146	C₅₃×#385	C₂²	1	1	yes	characteristic
147	C₅₃×#385	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
153	C₅₃×#385	C₂²	1	1	yes	characteristic
154	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#381	C₂²	1	1	yes	characteristic
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, complemented
165	C₅₃×#379	C₂²	1	1	yes	characteristic
166	C₅₃×#379	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
168	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
169	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
170	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
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	C₄×C₂²⋊C₄×C₅₃	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×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	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	C₂³×C₄×C₅₃	—	2	4	no	—
197	C₂³×C₄×C₅₃	—	4	2	no	—
198	C₂³×C₄×C₅₃	—	4	2	no	—
199	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
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	#126×C₅₃	—	2	4	no	—
212	#124×C₅₃	—	2	4	no	—
213	#123×C₅₃	—	2	4	no	—
214	#123×C₅₃	—	2	4	no	—
215	#123×C₅₃	—	2	4	no	—
216	#123×C₅₃	—	4	2	no	—
217	#123×C₅₃	—	4	2	no	—
218	C₂²⋊Q₈×C₅₃	—	4	2	no	—
219	#121×C₅₃	—	2	4	no	—
220	#121×C₅₃	—	4	2	no	—
221	#120×C₅₃	—	4	2	no	—
222	#120×C₅₃	—	4	2	no	—
223	C₄×D₄×C₅₃	—	4	2	no	—
224	C₄×D₄×C₅₃	—	4	2	no	—
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
252	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
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×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×C₄²×C₅₃	—	4	2	no	—
300	C₂×C₄²×C₅₃	—	4	2	no	—
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	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×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	#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	C₂⁴×C₅₃	—	2	2	no	—
364	C₂⁴×C₅₃	—	2	2	no	—
365	C₂⁴×C₅₃	—	2	2	no	—
366	C₂⁴×C₅₃	—	2	2	no	—
367	C₂⁴×C₅₃	—	2	2	no	—
368	C₂⁴×C₅₃	—	4	1	no	—
369	C₂⁴×C₅₃	—	4	1	no	—
370	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
371	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
372	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
373	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
374	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
375	C₂×Q₈×C₅₃	—	2	2	no	—
376	C₂×Q₈×C₅₃	—	4	1	no	—
377	C₂×Q₈×C₅₃	—	4	1	no	—
378	C₂×D₄×C₅₃	—	2	2	no	—
379	C₂×D₄×C₅₃	—	2	2	no	—
380	C₂×D₄×C₅₃	—	2	2	no	—
381	C₂×D₄×C₅₃	—	2	2	no	—
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	—	4	1	no	—
390	C₂×D₄×C₅₃	—	4	1	no	—
391	C₂×D₄×C₅₃	—	4	1	no	—
392	C₂×D₄×C₅₃	—	4	1	no	—
393	C₂×D₄×C₅₃	—	4	1	no	—
394	C₂×D₄×C₅₃	—	4	1	no	—
395	C₂×D₄×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	4	1	no	—
397	C₂×D₄×C₅₃	—	4	1	no	—
398	C₂×D₄×C₅₃	—	4	1	no	—
399	C₂²×C₄×C₅₃	—	2	2	no	—
400	C₂²×C₄×C₅₃	—	2	2	no	—
401	C₂²×C₄×C₅₃	—	2	2	no	—
402	C₂²×C₄×C₅₃	—	2	2	no	—
403	C₂²×C₄×C₅₃	—	2	2	no	—
404	C₂²×C₄×C₅₃	—	2	2	no	—
405	C₂²×C₄×C₅₃	—	2	2	no	—
406	C₂²×C₄×C₅₃	—	2	2	no	—
407	C₂²×C₄×C₅₃	—	2	2	no	—
408	C₂²×C₄×C₅₃	—	2	2	no	—
409	C₂²×C₄×C₅₃	—	2	2	no	—
410	C₂²×C₄×C₅₃	—	2	2	no	—
411	C₂²×C₄×C₅₃	—	2	2	no	—
412	C₂²×C₄×C₅₃	—	2	2	no	—
413	C₂²×C₄×C₅₃	—	2	2	no	—
414	C₂²×C₄×C₅₃	—	2	2	no	—
415	C₂²×C₄×C₅₃	—	2	2	no	—
416	C₂²×C₄×C₅₃	—	2	2	no	—
417	C₂²×C₄×C₅₃	—	2	2	no	—
418	C₂²×C₄×C₅₃	—	4	1	no	—
419	C₂²×C₄×C₅₃	—	4	1	no	—
420	C₂²×C₄×C₅₃	—	4	1	no	—
421	C₂²×C₄×C₅₃	—	4	1	no	—
422	C₂²×C₄×C₅₃	—	4	1	no	—
423	C₂²×C₄×C₅₃	—	4	1	no	—
424	C₂²×C₄×C₅₃	—	4	1	no	—
425	C₂²×C₄×C₅₃	—	4	1	no	—
426	C₂²×C₄×C₅₃	—	4	1	no	—
427	C₂²×C₄×C₅₃	—	4	1	no	—
428	C₂²×C₄×C₅₃	—	4	1	no	—
429	C₂²×C₄×C₅₃	—	4	1	no	—
430	C₂²×C₄×C₅₃	—	4	1	no	—
431	C₂²×C₄×C₅₃	—	4	1	no	—
432	C₂²×C₄×C₅₃	—	4	1	no	—
433	C₂²×C₄×C₅₃	—	4	1	no	—
434	C₂²×C₄×C₅₃	—	4	16	no	—
435	C₂²×C₄×C₅₃	#41	1	4	yes	—
436	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
442	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
445	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
446	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
447	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
448	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
449	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
450	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
451	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
452	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
453	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
454	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
455	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	—	2	2	no	—
463	C₄⋊C₄×C₅₃	—	2	2	no	—
464	C₄⋊C₄×C₅₃	—	2	2	no	—
465	C₄⋊C₄×C₅₃	—	2	2	no	—
466	C₄⋊C₄×C₅₃	—	2	2	no	—
467	C₄⋊C₄×C₅₃	—	2	2	no	—
468	C₄⋊C₄×C₅₃	—	2	2	no	—
469	C₄⋊C₄×C₅₃	—	2	2	no	—
470	C₄⋊C₄×C₅₃	—	2	2	no	—
471	C₄⋊C₄×C₅₃	—	2	2	no	—
472	C₄⋊C₄×C₅₃	—	4	1	no	—
473	C₄⋊C₄×C₅₃	—	4	1	no	—
474	C₄⋊C₄×C₅₃	—	4	1	no	—
475	C₄⋊C₄×C₅₃	—	4	1	no	—
476	C₄⋊C₄×C₅₃	—	4	1	no	—
477	C₄⋊C₄×C₅₃	—	4	1	no	—
478	C₄⋊C₄×C₅₃	—	4	1	no	—
479	C₄⋊C₄×C₅₃	—	4	1	no	—
480	C₄⋊C₄×C₅₃	—	4	1	no	—
481	C₄⋊C₄×C₅₃	—	4	1	no	—
482	C₄⋊C₄×C₅₃	—	4	1	no	—
483	C₄⋊C₄×C₅₃	—	4	1	no	—
484	C₄⋊C₄×C₅₃	—	4	1	no	—
485	C₄⋊C₄×C₅₃	—	4	1	no	—
486	C₄⋊C₄×C₅₃	—	4	1	no	—
487	C₄⋊C₄×C₅₃	—	4	1	no	—
488	C₂²⋊C₄×C₅₃	—	2	2	no	—
489	C₂²⋊C₄×C₅₃	—	2	2	no	—
490	C₂²⋊C₄×C₅₃	—	2	2	no	—
491	C₂²⋊C₄×C₅₃	—	2	2	no	—
492	C₂²⋊C₄×C₅₃	—	2	2	no	—
493	C₂²⋊C₄×C₅₃	—	2	2	no	—
494	C₂²⋊C₄×C₅₃	—	2	2	no	—
495	C₂²⋊C₄×C₅₃	—	2	2	no	—
496	C₂²⋊C₄×C₅₃	—	2	2	no	—
497	C₂²⋊C₄×C₅₃	—	2	2	no	—
498	C₂²⋊C₄×C₅₃	—	2	2	no	—
499	C₂²⋊C₄×C₅₃	—	2	2	no	—
500	C₂²⋊C₄×C₅₃	—	2	2	no	—
501	C₂²⋊C₄×C₅₃	—	2	2	no	—
502	C₂²⋊C₄×C₅₃	—	2	2	no	—
503	C₂²⋊C₄×C₅₃	—	2	2	no	—
504	C₂²⋊C₄×C₅₃	—	2	2	no	—
505	C₂²⋊C₄×C₅₃	—	2	2	no	—
506	C₂²⋊C₄×C₅₃	—	2	2	no	—
507	C₂²⋊C₄×C₅₃	—	2	2	no	—
508	C₂²⋊C₄×C₅₃	—	2	2	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	—	4	1	no	—
513	C₂²⋊C₄×C₅₃	—	4	1	no	—
514	C₂²⋊C₄×C₅₃	—	4	1	no	—
515	C₂²⋊C₄×C₅₃	—	4	1	no	—
516	C₂²⋊C₄×C₅₃	—	4	1	no	—
517	C₂²⋊C₄×C₅₃	—	4	1	no	—
518	C₂²⋊C₄×C₅₃	—	4	1	no	—
519	C₂²⋊C₄×C₅₃	—	4	1	no	—
520	C₂²⋊C₄×C₅₃	—	4	1	no	—
521	C₂²⋊C₄×C₅₃	—	4	1	no	—
522	C₂²⋊C₄×C₅₃	—	4	1	no	—
523	C₂²⋊C₄×C₅₃	—	4	1	no	—
524	C₂²⋊C₄×C₅₃	—	4	1	no	—
525	C₂²⋊C₄×C₅₃	—	4	1	no	—
526	C₂²⋊C₄×C₅₃	—	4	1	no	—
527	C₂²⋊C₄×C₅₃	—	4	1	no	—
528	C₂²⋊C₄×C₅₃	—	4	1	no	—
529	C₂²⋊C₄×C₅₃	—	4	1	no	—
530	C₂²⋊C₄×C₅₃	—	4	1	no	—
531	C₂²⋊C₄×C₅₃	—	4	1	no	—
532	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
533	C₂²⋊C₄×C₅₃	#41	1	4	yes	—
534	C₄²×C₅₃	—	2	2	no	—
535	C₄²×C₅₃	—	2	2	no	—
536	C₄²×C₅₃	—	4	1	no	—
537	C₄²×C₅₃	—	4	1	no	—
538	C₄²×C₅₃	—	4	1	no	—
539	C₄²×C₅₃	—	4	1	no	—
540	C₄²×C₅₃	—	4	1	no	—
541	C₄²×C₅₃	—	4	1	no	—
542	C₄²×C₅₃	—	4	1	no	—
543	C₄²×C₅₃	—	4	1	no	—
544	C₄²×C₅₃	—	4	1	no	—
545	C₄²×C₅₃	—	4	1	no	—
546	C₄²×C₅₃	—	4	1	no	—
547	C₄²×C₅₃	—	4	1	no	—
548	C₂³×C₅₃	—	2	1	no	—
549	C₂³×C₅₃	—	2	1	no	—
550	C₂³×C₅₃	—	2	1	no	—
551	C₂³×C₅₃	—	2	1	no	—
552	C₂³×C₅₃	—	2	8	no	—
553	C₂³×C₅₃	—	2	1	no	—
554	C₂³×C₅₃	—	2	1	no	—
555	C₂³×C₅₃	—	2	1	no	—
556	C₂³×C₅₃	—	2	1	no	—
557	C₂³×C₅₃	—	2	1	no	—
558	C₂³×C₅₃	—	2	1	no	—
559	C₂³×C₅₃	—	2	1	no	—
560	C₂³×C₅₃	—	2	1	no	—
561	C₂³×C₅₃	—	2	1	no	—
562	C₂³×C₅₃	—	2	1	no	—
563	C₂³×C₅₃	—	2	1	no	—
564	C₂³×C₅₃	—	2	1	no	—
565	C₂³×C₅₃	—	2	1	no	—
566	C₂³×C₅₃	—	2	1	no	—
567	C₂³×C₅₃	—	2	1	no	—
568	C₂³×C₅₃	—	2	1	no	—
569	C₂³×C₅₃	—	2	1	no	—
570	C₂³×C₅₃	—	2	1	no	—
571	C₂³×C₅₃	—	2	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	1	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	4	4	no	—
580	C₂³×C₅₃	—	4	4	no	—
581	C₂³×C₅₃	—	4	4	no	—
582	C₂³×C₅₃	—	4	4	no	—
583	C₂³×C₅₃	—	4	4	no	—
584	C₂³×C₅₃	—	4	4	no	—
585	C₂³×C₅₃	C₂×#41	1	2	yes	—
586	C₂³×C₅₃	C₂×#41	1	2	yes	—
587	C₂³×C₅₃	C₂×#41	1	2	yes	—
588	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
589	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
590	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
591	Q₈×C₅₃	—	8	2	no	—
592	D₄×C₅₃	—	4	4	no	—
593	D₄×C₅₃	—	4	4	no	—
594	D₄×C₅₃	—	8	2	no	—
595	D₄×C₅₃	—	8	2	no	—
596	D₄×C₅₃	—	8	2	no	—
597	D₄×C₅₃	—	8	2	no	—
598	D₄×C₅₃	—	8	2	no	—
599	C₂×C₄×C₅₃	—	2	8	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	—	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	—	4	4	no	—
673	C₂×C₄×C₅₃	—	4	4	no	—
674	C₂×C₄×C₅₃	—	4	4	no	—
675	C₂×C₄×C₅₃	—	4	4	no	—
676	C₂×C₄×C₅₃	—	4	4	no	—
677	C₂×C₄×C₅₃	—	4	4	no	—
678	C₂×C₄×C₅₃	—	4	4	no	—
679	C₂×C₄×C₅₃	—	4	4	no	—
680	C₂×C₄×C₅₃	—	4	4	no	—
681	C₂×C₄×C₅₃	—	8	2	no	—
682	C₂×C₄×C₅₃	—	8	2	no	—
683	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
684	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
685	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
686	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
687	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
688	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
689	#35074	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
690	C₂²×C₅₃	—	2	2	no	—
691	C₂²×C₅₃	—	2	2	no	—
692	C₂²×C₅₃	—	2	2	no	—
693	C₂²×C₅₃	—	2	2	no	—
694	C₂²×C₅₃	—	2	2	no	—
695	C₂²×C₅₃	—	2	2	no	—
696	C₂²×C₅₃	—	2	2	no	—
697	C₂²×C₅₃	—	2	2	no	—
698	C₂²×C₅₃	—	2	2	no	—
699	C₂²×C₅₃	—	2	2	no	—
700	C₂²×C₅₃	—	2	2	no	—
701	C₂²×C₅₃	—	2	2	no	—
702	C₂²×C₅₃	—	4	16	no	—
703	C₂²×C₅₃	—	4	1	no	—
704	C₂²×C₅₃	—	4	1	no	—
705	C₂²×C₅₃	—	4	1	no	—
706	C₂²×C₅₃	—	4	1	no	—
707	C₂²×C₅₃	—	4	1	no	—
708	C₂²×C₅₃	—	4	1	no	—
709	C₂²×C₅₃	—	4	1	no	—
710	C₂²×C₅₃	—	4	1	no	—
711	C₂²×C₅₃	—	4	1	no	—
712	C₂²×C₅₃	—	4	1	no	—
713	C₂²×C₅₃	—	4	1	no	—
714	C₂²×C₅₃	—	4	1	no	—
715	C₂²×C₅₃	—	4	1	no	—
716	C₂²×C₅₃	—	4	1	no	—
717	C₂²×C₅₃	—	4	1	no	—
718	C₂²×C₅₃	—	4	1	no	—
719	C₂²×C₅₃	—	4	1	no	—
720	C₂²×C₅₃	—	4	1	no	—
721	C₂²×C₅₃	—	4	1	no	—
722	C₂²×C₅₃	—	4	1	no	—
723	C₂²×C₅₃	—	4	1	no	—
724	C₂²×C₅₃	—	4	1	no	—
725	C₂²×C₅₃	#538	1	4	yes	—
726	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
727	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
728	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
729	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
730	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
731	C₂²×C₅₃	#585	1	1	yes	characteristic
732	C₂²×C₅₃	#585	1	1	yes	characteristic
733	C₄×C₅₃	—	2	2	no	—
734	C₄×C₅₃	—	2	2	no	—
735	C₄×C₅₃	—	2	2	no	—
736	C₄×C₅₃	—	2	2	no	—
737	C₄×C₅₃	—	2	2	no	—
738	C₄×C₅₃	—	2	2	no	—
739	C₄×C₅₃	—	4	1	no	—
740	C₄×C₅₃	—	4	1	no	—
741	C₄×C₅₃	—	4	1	no	—
742	C₄×C₅₃	—	4	1	no	—
743	C₄×C₅₃	—	4	1	no	—
744	C₄×C₅₃	—	4	1	no	—
745	C₄×C₅₃	—	4	1	no	—
746	C₄×C₅₃	—	4	1	no	—
747	C₄×C₅₃	—	4	1	no	—
748	C₄×C₅₃	—	4	1	no	—
749	C₄×C₅₃	—	4	1	no	—
750	C₄×C₅₃	—	4	1	no	—
751	C₄×C₅₃	—	4	1	no	—
752	C₄×C₅₃	—	4	1	no	—
753	C₄×C₅₃	—	4	1	no	—
754	C₄×C₅₃	—	4	1	no	—
755	C₄×C₅₃	—	4	1	no	—
756	C₄×C₅₃	—	4	1	no	—
757	C₄×C₅₃	—	4	1	no	—
758	C₄×C₅₃	—	4	1	no	—
759	#2855	C₂×C₅₃	1	1	yes	characteristic, complemented
760	#2854	C₂×C₅₃	1	1	yes	characteristic, complemented
761	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
762	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
763	#2653	C₂×C₅₃	1	1	yes	characteristic, complemented
764	#2652	C₂×C₅₃	1	1	yes	characteristic, complemented
765	#2649	C₂×C₅₃	1	1	yes	characteristic, complemented
766	#2648	C₂×C₅₃	1	1	yes	characteristic, complemented
767	#2597	C₂×C₅₃	1	1	yes	characteristic, complemented
768	#2595	C₂×C₅₃	1	1	yes	characteristic, complemented
769	#2589	C₂×C₅₃	1	1	yes	characteristic, complemented
770	#2587	C₂×C₅₃	1	1	yes	characteristic, complemented
771	#2578	C₂×C₅₃	1	1	yes	characteristic, complemented
772	#2576	C₂×C₅₃	1	1	yes	characteristic, complemented
773	#2559	C₂×C₅₃	1	1	yes	characteristic, complemented
774	#2557	C₂×C₅₃	1	1	yes	characteristic, complemented
775	#2493	C₂×C₅₃	1	1	yes	characteristic, complemented
776	#2488	C₂×C₅₃	1	1	yes	characteristic, complemented
777	#2480	C₂×C₅₃	1	1	yes	characteristic, complemented
778	#2472	C₂×C₅₃	1	1	yes	characteristic, complemented
779	#2425	C₂×C₅₃	1	1	yes	characteristic, complemented
780	#2424	C₂×C₅₃	1	1	yes	characteristic
781	#2419	C₂×C₅₃	1	1	yes	characteristic, complemented
782	#2418	C₂×C₅₃	1	1	yes	characteristic, complemented
783	#2337	C₂×C₅₃	1	1	yes	characteristic, complemented
784	#2335	C₂×C₅₃	1	1	yes	characteristic, complemented
785	#2334	C₂×C₅₃	1	1	yes	characteristic, complemented
786	#2333	C₂×C₅₃	1	1	yes	characteristic, complemented
787	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
788	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
789	C₂×C₄×C₂²⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
790	C₂×C₅₃	—	2	4	no	—
791	C₂×C₅₃	—	4	2	no	—
792	C₂×C₅₃	—	4	2	no	—
793	C₂×C₅₃	—	8	1	no	—
794	C₂×C₅₃	—	8	1	no	—
795	C₂×C₅₃	#3444	1	1	yes	characteristic
796	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
797	C₂×C₅₃	#3455	1	1	yes	characteristic
798	C₂×C₅₃	#3513	1	1	yes	characteristic
799	C₂×C₅₃	#3513	1	1	yes	characteristic
800	C₂×C₅₃	#3513	1	1	yes	characteristic
801	C₂×C₅₃	#3513	1	1	yes	characteristic
802	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
803	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
804	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
805	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
806	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
807	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
808	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
809	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
810	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
811	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
812	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
813	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
814	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
815	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
816	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
817	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
818	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
819	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
820	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
821	#401	C₂²×C₅₃	1	1	yes	characteristic, complemented
822	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
823	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
824	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
825	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
826	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
827	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
828	#399	C₂²×C₅₃	1	1	yes	characteristic
829	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
830	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
831	#397	C₂²×C₅₃	1	1	yes	characteristic
832	#397	C₂²×C₅₃	1	1	yes	characteristic
833	#397	C₂²×C₅₃	1	1	yes	characteristic
834	#397	C₂²×C₅₃	1	1	yes	characteristic
835	#397	C₂²×C₅₃	1	1	yes	characteristic
836	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
837	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
838	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
839	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
840	#396	C₂²×C₅₃	1	1	yes	characteristic
841	#396	C₂²×C₅₃	1	1	yes	characteristic
842	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
843	#394	C₂²×C₅₃	1	1	yes	characteristic
844	#394	C₂²×C₅₃	1	1	yes	characteristic
845	#394	C₂²×C₅₃	1	1	yes	characteristic
846	#394	C₂²×C₅₃	1	1	yes	characteristic
847	#394	C₂²×C₅₃	1	1	yes	characteristic
848	#394	C₂²×C₅₃	1	1	yes	characteristic
849	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
850	#393	C₂²×C₅₃	1	1	yes	characteristic
851	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
852	#392	C₂²×C₅₃	1	1	yes	characteristic
853	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
854	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
855	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
856	#390	C₂²×C₅₃	1	1	yes	characteristic
857	#390	C₂²×C₅₃	1	1	yes	characteristic
858	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
860	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
861	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
862	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
863	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
864	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
865	#388	C₂²×C₅₃	1	1	yes	characteristic
866	#388	C₂²×C₅₃	1	1	yes	characteristic
867	#388	C₂²×C₅₃	1	1	yes	characteristic
868	#388	C₂²×C₅₃	1	1	yes	characteristic
869	#388	C₂²×C₅₃	1	1	yes	characteristic
870	#388	C₂²×C₅₃	1	1	yes	characteristic
871	#388	C₂²×C₅₃	1	1	yes	characteristic
872	#388	C₂²×C₅₃	1	1	yes	characteristic
873	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
874	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
875	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
876	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
879	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
880	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
881	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
882	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
883	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
884	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
885	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
886	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
888	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
889	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
890	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
891	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
892	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
893	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
894	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
896	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
897	#386	C₂²×C₅₃	1	1	yes	characteristic
898	#386	C₂²×C₅₃	1	1	yes	characteristic
899	#386	C₂²×C₅₃	1	1	yes	characteristic
900	#386	C₂²×C₅₃	1	1	yes	characteristic
901	#386	C₂²×C₅₃	1	1	yes	characteristic
902	#386	C₂²×C₅₃	1	1	yes	characteristic
903	#386	C₂²×C₅₃	1	1	yes	characteristic
904	#386	C₂²×C₅₃	1	1	yes	characteristic
905	#386	C₂²×C₅₃	1	1	yes	characteristic
906	#386	C₂²×C₅₃	1	1	yes	characteristic
907	#386	C₂²×C₅₃	1	1	yes	characteristic
908	#386	C₂²×C₅₃	1	1	yes	characteristic
909	#386	C₂²×C₅₃	1	1	yes	characteristic
910	#386	C₂²×C₅₃	1	1	yes	characteristic
911	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#385	C₂²×C₅₃	1	1	yes	characteristic
913	#385	C₂²×C₅₃	1	1	yes	characteristic
914	#385	C₂²×C₅₃	1	1	yes	characteristic
915	#385	C₂²×C₅₃	1	1	yes	characteristic
916	#385	C₂²×C₅₃	1	1	yes	characteristic
917	#385	C₂²×C₅₃	1	1	yes	characteristic
918	#385	C₂²×C₅₃	1	1	yes	characteristic
919	#385	C₂²×C₅₃	1	1	yes	characteristic
920	#385	C₂²×C₅₃	1	1	yes	characteristic
921	#385	C₂²×C₅₃	1	1	yes	characteristic
922	#385	C₂²×C₅₃	1	1	yes	characteristic
923	#385	C₂²×C₅₃	1	1	yes	characteristic
924	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#381	C₂²×C₅₃	1	1	yes	characteristic
928	#381	C₂²×C₅₃	1	1	yes	characteristic
929	#381	C₂²×C₅₃	1	1	yes	characteristic
930	#381	C₂²×C₅₃	1	1	yes	characteristic
931	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#380	C₂²×C₅₃	1	1	yes	characteristic
933	#380	C₂²×C₅₃	1	1	yes	characteristic
934	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#379	C₂²×C₅₃	1	1	yes	characteristic
936	#379	C₂²×C₅₃	1	1	yes	characteristic
937	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
942	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
943	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
944	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
945	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
946	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
947	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
948	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
949	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
950	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
951	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
956	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
957	C₅₃	#35074	1	1	yes	characteristic, direct product factor, Sylow
958	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
959	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
960	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
961	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
962	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
963	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
964	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
965	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂³×C₄	—	2	4	no	—
968	C₂³×C₄	—	4	2	no	—
969	C₂³×C₄	—	4	2	no	—
970	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
979	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
980	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
981	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
982	#126	—	2	4	no	—
983	#124	—	2	4	no	—
984	#123	—	2	4	no	—
985	#123	—	2	4	no	—
986	#123	—	2	4	no	—
987	#123	—	4	2	no	—
988	#123	—	4	2	no	—
989	C₂²⋊Q₈	—	4	2	no	—
990	#121	—	2	4	no	—
991	#121	—	4	2	no	—
992	#120	—	4	2	no	—
993	#120	—	4	2	no	—
994	C₄×D₄	—	4	2	no	—
995	C₄×D₄	—	4	2	no	—
996	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
998	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	—	2	4	no	—
1023	C₂×C₂²⋊C₄	—	2	4	no	—
1024	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1032	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1034	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₄²	—	4	2	no	—
1071	C₂×C₄²	—	4	2	no	—
1072	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1086	#95	C₂³×C₅₃	1	1	yes	characteristic
1087	#95	C₂³×C₅₃	1	1	yes	characteristic
1088	#95	C₂³×C₅₃	1	1	yes	characteristic
1089	#95	C₂³×C₅₃	1	1	yes	characteristic
1090	#95	C₂³×C₅₃	1	1	yes	characteristic
1091	#95	C₂³×C₅₃	1	1	yes	characteristic
1092	#95	C₂³×C₅₃	1	1	yes	characteristic
1093	#95	C₂³×C₅₃	1	1	yes	characteristic
1094	#95	C₂³×C₅₃	1	1	yes	characteristic
1095	#95	C₂³×C₅₃	1	1	yes	characteristic
1096	#95	C₂³×C₅₃	1	1	yes	characteristic
1097	#95	C₂³×C₅₃	1	1	yes	characteristic
1098	#95	C₂³×C₅₃	1	1	yes	characteristic
1099	#95	C₂³×C₅₃	1	1	yes	characteristic
1100	#95	C₂³×C₅₃	1	1	yes	characteristic
1101	#95	C₂³×C₅₃	1	1	yes	characteristic
1102	#95	C₂³×C₅₃	1	1	yes	characteristic
1103	#95	C₂³×C₅₃	1	1	yes	characteristic
1104	#95	C₂³×C₅₃	1	1	yes	characteristic
1105	#95	C₂³×C₅₃	1	1	yes	characteristic
1106	#95	C₂³×C₅₃	1	1	yes	characteristic
1107	#95	C₂³×C₅₃	1	1	yes	characteristic
1108	#95	C₂³×C₅₃	1	1	yes	characteristic
1109	#95	C₂³×C₅₃	1	1	yes	characteristic
1110	#95	C₂³×C₅₃	1	1	yes	characteristic
1111	#95	C₂³×C₅₃	1	1	yes	characteristic
1112	#95	C₂³×C₅₃	1	1	yes	characteristic
1113	#95	C₂³×C₅₃	1	1	yes	characteristic
1114	#95	C₂³×C₅₃	1	1	yes	characteristic
1115	#95	C₂³×C₅₃	1	1	yes	characteristic
1116	#95	C₂³×C₅₃	1	1	yes	characteristic
1117	#95	C₂³×C₅₃	1	1	yes	characteristic
1118	#95	C₂³×C₅₃	1	1	yes	characteristic
1119	#95	C₂³×C₅₃	1	1	yes	characteristic
1120	#95	C₂³×C₅₃	1	1	yes	characteristic
1121	#95	C₂³×C₅₃	1	1	yes	characteristic
1122	#95	C₂³×C₅₃	1	1	yes	characteristic
1123	#95	C₂³×C₅₃	1	1	yes	characteristic
1124	#95	C₂³×C₅₃	1	1	yes	characteristic
1125	#95	C₂³×C₅₃	1	1	yes	characteristic
1126	#95	C₂³×C₅₃	1	1	yes	characteristic
1127	#95	C₂³×C₅₃	1	1	yes	characteristic
1128	#95	C₂³×C₅₃	1	1	yes	characteristic
1129	#95	C₂³×C₅₃	1	1	yes	characteristic
1130	#95	C₂³×C₅₃	1	1	yes	characteristic
1131	#95	C₂³×C₅₃	1	1	yes	characteristic
1132	#95	C₂³×C₅₃	1	1	yes	characteristic
1133	#95	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂⁴	—	2	2	no	—
1135	C₂⁴	—	2	2	no	—
1136	C₂⁴	—	2	2	no	—
1137	C₂⁴	—	2	2	no	—
1138	C₂⁴	—	2	2	no	—
1139	C₂⁴	—	4	1	no	—
1140	C₂⁴	—	4	1	no	—
1141	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1142	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1143	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1144	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1145	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1146	C₂×Q₈	—	2	2	no	—
1147	C₂×Q₈	—	4	1	no	—
1148	C₂×Q₈	—	4	1	no	—
1149	C₂×D₄	—	2	2	no	—
1150	C₂×D₄	—	2	2	no	—
1151	C₂×D₄	—	2	2	no	—
1152	C₂×D₄	—	2	2	no	—
1153	C₂×D₄	—	2	2	no	—
1154	C₂×D₄	—	2	2	no	—
1155	C₂×D₄	—	2	2	no	—
1156	C₂×D₄	—	2	2	no	—
1157	C₂×D₄	—	2	2	no	—
1158	C₂×D₄	—	2	2	no	—
1159	C₂×D₄	—	2	2	no	—
1160	C₂×D₄	—	4	1	no	—
1161	C₂×D₄	—	4	1	no	—
1162	C₂×D₄	—	4	1	no	—
1163	C₂×D₄	—	4	1	no	—
1164	C₂×D₄	—	4	1	no	—
1165	C₂×D₄	—	4	1	no	—
1166	C₂×D₄	—	4	1	no	—
1167	C₂×D₄	—	4	1	no	—
1168	C₂×D₄	—	4	1	no	—
1169	C₂×D₄	—	4	1	no	—
1170	C₂²×C₄	—	2	2	no	—
1171	C₂²×C₄	—	2	2	no	—
1172	C₂²×C₄	—	2	2	no	—
1173	C₂²×C₄	—	2	2	no	—
1174	C₂²×C₄	—	2	2	no	—
1175	C₂²×C₄	—	2	2	no	—
1176	C₂²×C₄	—	2	2	no	—
1177	C₂²×C₄	—	2	2	no	—
1178	C₂²×C₄	—	2	2	no	—
1179	C₂²×C₄	—	2	2	no	—
1180	C₂²×C₄	—	2	2	no	—
1181	C₂²×C₄	—	2	2	no	—
1182	C₂²×C₄	—	2	2	no	—
1183	C₂²×C₄	—	2	2	no	—
1184	C₂²×C₄	—	2	2	no	—
1185	C₂²×C₄	—	2	2	no	—
1186	C₂²×C₄	—	2	2	no	—
1187	C₂²×C₄	—	2	2	no	—
1188	C₂²×C₄	—	2	2	no	—
1189	C₂²×C₄	—	4	1	no	—
1190	C₂²×C₄	—	4	1	no	—
1191	C₂²×C₄	—	4	1	no	—
1192	C₂²×C₄	—	4	1	no	—
1193	C₂²×C₄	—	4	1	no	—
1194	C₂²×C₄	—	4	1	no	—
1195	C₂²×C₄	—	4	1	no	—
1196	C₂²×C₄	—	4	1	no	—
1197	C₂²×C₄	—	4	1	no	—
1198	C₂²×C₄	—	4	1	no	—
1199	C₂²×C₄	—	4	1	no	—
1200	C₂²×C₄	—	4	1	no	—
1201	C₂²×C₄	—	4	1	no	—
1202	C₂²×C₄	—	4	1	no	—
1203	C₂²×C₄	—	4	1	no	—
1204	C₂²×C₄	—	4	1	no	—
1205	C₂²×C₄	—	4	16	no	—
1206	C₂²×C₄	#41×C₅₃	1	4	yes	—
1207	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1208	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1209	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1210	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1211	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1212	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1213	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1214	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1215	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1216	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1217	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1218	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1219	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1220	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1221	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1222	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1223	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1224	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1225	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1226	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1227	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1228	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1229	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1230	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1231	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1232	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1233	C₄⋊C₄	—	2	2	no	—
1234	C₄⋊C₄	—	2	2	no	—
1235	C₄⋊C₄	—	2	2	no	—
1236	C₄⋊C₄	—	2	2	no	—
1237	C₄⋊C₄	—	2	2	no	—
1238	C₄⋊C₄	—	2	2	no	—
1239	C₄⋊C₄	—	2	2	no	—
1240	C₄⋊C₄	—	2	2	no	—
1241	C₄⋊C₄	—	2	2	no	—
1242	C₄⋊C₄	—	2	2	no	—
1243	C₄⋊C₄	—	4	1	no	—
1244	C₄⋊C₄	—	4	1	no	—
1245	C₄⋊C₄	—	4	1	no	—
1246	C₄⋊C₄	—	4	1	no	—
1247	C₄⋊C₄	—	4	1	no	—
1248	C₄⋊C₄	—	4	1	no	—
1249	C₄⋊C₄	—	4	1	no	—
1250	C₄⋊C₄	—	4	1	no	—
1251	C₄⋊C₄	—	4	1	no	—
1252	C₄⋊C₄	—	4	1	no	—
1253	C₄⋊C₄	—	4	1	no	—
1254	C₄⋊C₄	—	4	1	no	—
1255	C₄⋊C₄	—	4	1	no	—
1256	C₄⋊C₄	—	4	1	no	—
1257	C₄⋊C₄	—	4	1	no	—
1258	C₄⋊C₄	—	4	1	no	—
1259	C₂²⋊C₄	—	2	2	no	—
1260	C₂²⋊C₄	—	2	2	no	—
1261	C₂²⋊C₄	—	2	2	no	—
1262	C₂²⋊C₄	—	2	2	no	—
1263	C₂²⋊C₄	—	2	2	no	—
1264	C₂²⋊C₄	—	2	2	no	—
1265	C₂²⋊C₄	—	2	2	no	—
1266	C₂²⋊C₄	—	2	2	no	—
1267	C₂²⋊C₄	—	2	2	no	—
1268	C₂²⋊C₄	—	2	2	no	—
1269	C₂²⋊C₄	—	2	2	no	—
1270	C₂²⋊C₄	—	2	2	no	—
1271	C₂²⋊C₄	—	2	2	no	—
1272	C₂²⋊C₄	—	2	2	no	—
1273	C₂²⋊C₄	—	2	2	no	—
1274	C₂²⋊C₄	—	2	2	no	—
1275	C₂²⋊C₄	—	2	2	no	—
1276	C₂²⋊C₄	—	2	2	no	—
1277	C₂²⋊C₄	—	2	2	no	—
1278	C₂²⋊C₄	—	2	2	no	—
1279	C₂²⋊C₄	—	2	2	no	—
1280	C₂²⋊C₄	—	2	2	no	—
1281	C₂²⋊C₄	—	2	2	no	—
1282	C₂²⋊C₄	—	2	2	no	—
1283	C₂²⋊C₄	—	4	1	no	—
1284	C₂²⋊C₄	—	4	1	no	—
1285	C₂²⋊C₄	—	4	1	no	—
1286	C₂²⋊C₄	—	4	1	no	—
1287	C₂²⋊C₄	—	4	1	no	—
1288	C₂²⋊C₄	—	4	1	no	—
1289	C₂²⋊C₄	—	4	1	no	—
1290	C₂²⋊C₄	—	4	1	no	—
1291	C₂²⋊C₄	—	4	1	no	—
1292	C₂²⋊C₄	—	4	1	no	—
1293	C₂²⋊C₄	—	4	1	no	—
1294	C₂²⋊C₄	—	4	1	no	—
1295	C₂²⋊C₄	—	4	1	no	—
1296	C₂²⋊C₄	—	4	1	no	—
1297	C₂²⋊C₄	—	4	1	no	—
1298	C₂²⋊C₄	—	4	1	no	—
1299	C₂²⋊C₄	—	4	1	no	—
1300	C₂²⋊C₄	—	4	1	no	—
1301	C₂²⋊C₄	—	4	1	no	—
1302	C₂²⋊C₄	—	4	1	no	—
1303	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
1304	C₂²⋊C₄	#41×C₅₃	1	4	yes	—
1305	C₄²	—	2	2	no	—
1306	C₄²	—	2	2	no	—
1307	C₄²	—	4	1	no	—
1308	C₄²	—	4	1	no	—
1309	C₄²	—	4	1	no	—
1310	C₄²	—	4	1	no	—
1311	C₄²	—	4	1	no	—
1312	C₄²	—	4	1	no	—
1313	C₄²	—	4	1	no	—
1314	C₄²	—	4	1	no	—
1315	C₄²	—	4	1	no	—
1316	C₄²	—	4	1	no	—
1317	C₄²	—	4	1	no	—
1318	C₄²	—	4	1	no	—
1319	C₂³	—	2	1	no	—
1320	C₂³	—	2	1	no	—
1321	C₂³	—	2	1	no	—
1322	C₂³	—	2	1	no	—
1323	C₂³	—	2	8	no	—
1324	C₂³	—	2	1	no	—
1325	C₂³	—	2	1	no	—
1326	C₂³	—	2	1	no	—
1327	C₂³	—	2	1	no	—
1328	C₂³	—	2	1	no	—
1329	C₂³	—	2	1	no	—
1330	C₂³	—	2	1	no	—
1331	C₂³	—	2	1	no	—
1332	C₂³	—	2	1	no	—
1333	C₂³	—	2	1	no	—
1334	C₂³	—	2	1	no	—
1335	C₂³	—	2	1	no	—
1336	C₂³	—	2	1	no	—
1337	C₂³	—	2	1	no	—
1338	C₂³	—	2	1	no	—
1339	C₂³	—	2	1	no	—
1340	C₂³	—	2	1	no	—
1341	C₂³	—	2	1	no	—
1342	C₂³	—	2	1	no	—
1343	C₂³	—	2	1	no	—
1344	C₂³	—	2	1	no	—
1345	C₂³	—	2	1	no	—
1346	C₂³	—	2	1	no	—
1347	C₂³	—	2	1	no	—
1348	C₂³	—	2	1	no	—
1349	C₂³	—	2	1	no	—
1350	C₂³	—	4	4	no	—
1351	C₂³	—	4	4	no	—
1352	C₂³	—	4	4	no	—
1353	C₂³	—	4	4	no	—
1354	C₂³	—	4	4	no	—
1355	C₂³	—	4	4	no	—
1356	C₂³	C₂×#41×C₅₃	1	2	yes	—
1357	C₂³	C₂×#41×C₅₃	1	2	yes	—
1358	C₂³	C₂×#41×C₅₃	1	2	yes	—
1359	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1360	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1361	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1362	Q₈	—	8	2	no	—
1363	D₄	—	4	4	no	—
1364	D₄	—	4	4	no	—
1365	D₄	—	8	2	no	—
1366	D₄	—	8	2	no	—
1367	D₄	—	8	2	no	—
1368	D₄	—	8	2	no	—
1369	D₄	—	8	2	no	—
1370	C₂×C₄	—	2	8	no	—
1371	C₂×C₄	—	2	1	no	—
1372	C₂×C₄	—	2	1	no	—
1373	C₂×C₄	—	2	1	no	—
1374	C₂×C₄	—	2	1	no	—
1375	C₂×C₄	—	2	1	no	—
1376	C₂×C₄	—	2	1	no	—
1377	C₂×C₄	—	2	1	no	—
1378	C₂×C₄	—	2	1	no	—
1379	C₂×C₄	—	2	1	no	—
1380	C₂×C₄	—	2	1	no	—
1381	C₂×C₄	—	2	1	no	—
1382	C₂×C₄	—	2	1	no	—
1383	C₂×C₄	—	2	1	no	—
1384	C₂×C₄	—	2	1	no	—
1385	C₂×C₄	—	2	1	no	—
1386	C₂×C₄	—	2	1	no	—
1387	C₂×C₄	—	2	1	no	—
1388	C₂×C₄	—	2	1	no	—
1389	C₂×C₄	—	2	1	no	—
1390	C₂×C₄	—	2	1	no	—
1391	C₂×C₄	—	2	1	no	—
1392	C₂×C₄	—	2	1	no	—
1393	C₂×C₄	—	2	1	no	—
1394	C₂×C₄	—	2	1	no	—
1395	C₂×C₄	—	2	1	no	—
1396	C₂×C₄	—	2	1	no	—
1397	C₂×C₄	—	2	1	no	—
1398	C₂×C₄	—	2	1	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	1	no	—
1424	C₂×C₄	—	2	1	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	4	4	no	—
1444	C₂×C₄	—	4	4	no	—
1445	C₂×C₄	—	4	4	no	—
1446	C₂×C₄	—	4	4	no	—
1447	C₂×C₄	—	4	4	no	—
1448	C₂×C₄	—	4	4	no	—
1449	C₂×C₄	—	4	4	no	—
1450	C₂×C₄	—	4	4	no	—
1451	C₂×C₄	—	4	4	no	—
1452	C₂×C₄	—	8	2	no	—
1453	C₂×C₄	—	8	2	no	—
1454	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1455	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1456	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1457	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1458	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1459	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1460	C₂²	—	2	2	no	—
1461	C₂²	—	2	2	no	—
1462	C₂²	—	2	2	no	—
1463	C₂²	—	2	2	no	—
1464	C₂²	—	2	2	no	—
1465	C₂²	—	2	2	no	—
1466	C₂²	—	2	2	no	—
1467	C₂²	—	2	2	no	—
1468	C₂²	—	2	2	no	—
1469	C₂²	—	2	2	no	—
1470	C₂²	—	2	2	no	—
1471	C₂²	—	2	2	no	—
1472	C₂²	—	4	16	no	—
1473	C₂²	—	4	1	no	—
1474	C₂²	—	4	1	no	—
1475	C₂²	—	4	1	no	—
1476	C₂²	—	4	1	no	—
1477	C₂²	—	4	1	no	—
1478	C₂²	—	4	1	no	—
1479	C₂²	—	4	1	no	—
1480	C₂²	—	4	1	no	—
1481	C₂²	—	4	1	no	—
1482	C₂²	—	4	1	no	—
1483	C₂²	—	4	1	no	—
1484	C₂²	—	4	1	no	—
1485	C₂²	—	4	1	no	—
1486	C₂²	—	4	1	no	—
1487	C₂²	—	4	1	no	—
1488	C₂²	—	4	1	no	—
1489	C₂²	—	4	1	no	—
1490	C₂²	—	4	1	no	—
1491	C₂²	—	4	1	no	—
1492	C₂²	—	4	1	no	—
1493	C₂²	—	4	1	no	—
1494	C₂²	—	4	1	no	—
1495	C₂²	C₅₃×#538	1	4	yes	—
1496	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1497	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1498	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1499	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1500	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1501	C₂²	C₅₃×#585	1	1	yes	characteristic
1502	C₂²	C₅₃×#585	1	1	yes	characteristic
1503	C₄	—	2	2	no	—
1504	C₄	—	2	2	no	—
1505	C₄	—	2	2	no	—
1506	C₄	—	2	2	no	—
1507	C₄	—	2	2	no	—
1508	C₄	—	2	2	no	—
1509	C₄	—	4	1	no	—
1510	C₄	—	4	1	no	—
1511	C₄	—	4	1	no	—
1512	C₄	—	4	1	no	—
1513	C₄	—	4	1	no	—
1514	C₄	—	4	1	no	—
1515	C₄	—	4	1	no	—
1516	C₄	—	4	1	no	—
1517	C₄	—	4	1	no	—
1518	C₄	—	4	1	no	—
1519	C₄	—	4	1	no	—
1520	C₄	—	4	1	no	—
1521	C₄	—	4	1	no	—
1522	C₄	—	4	1	no	—
1523	C₄	—	4	1	no	—
1524	C₄	—	4	1	no	—
1525	C₄	—	4	1	no	—
1526	C₄	—	4	1	no	—
1527	C₄	—	4	1	no	—
1528	C₄	—	4	1	no	—
1529	C₂	—	2	4	no	—
1530	C₂	—	4	2	no	—
1531	C₂	—	4	2	no	—
1532	C₂	—	8	1	no	—
1533	C₂	—	8	1	no	—
1534	C₂	C₅₃×#3444	1	1	yes	characteristic
1535	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
1536	C₂	C₅₃×#3455	1	1	yes	characteristic
1537	C₂	C₅₃×#3513	1	1	yes	characteristic
1538	C₂	C₅₃×#3513	1	1	yes	characteristic
1539	C₂	C₅₃×#3513	1	1	yes	characteristic
1540	C₂	C₅₃×#3513	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2424	C₂
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×#2855	C₂	semidirect
2. C₅₃×#2854	C₂	semidirect
3. C₅₃×#2849	C₂	semidirect
4. C₅₃×#2849	C₂	semidirect
5. C₅₃×#2653	C₂	semidirect
6. C₅₃×#2652	C₂	semidirect
7. C₅₃×#2649	C₂	semidirect
8. C₅₃×#2648	C₂	semidirect
9. C₅₃×#2597	C₂	semidirect
10. C₅₃×#2595	C₂	semidirect
11. C₅₃×#2589	C₂	semidirect
12. C₅₃×#2587	C₂	semidirect
13. C₅₃×#2578	C₂	semidirect
14. C₅₃×#2576	C₂	semidirect
15. C₅₃×#2559	C₂	semidirect
16. C₅₃×#2557	C₂	semidirect
17. C₅₃×#2493	C₂	semidirect
18. C₅₃×#2488	C₂	semidirect
19. C₅₃×#2480	C₂	semidirect
20. C₅₃×#2472	C₂	semidirect
21. C₅₃×#2425	C₂	semidirect
23. C₅₃×#2419	C₂	semidirect
24. C₅₃×#2418	C₂	semidirect
25. C₅₃×#2337	C₂	semidirect
26. C₅₃×#2335	C₂	semidirect
27. C₅₃×#2334	C₂	semidirect
28. C₅₃×#2333	C₂	semidirect
29. C₄×#123×C₅₃	C₂	semidirect
30. C₄×#123×C₅₃	C₂	semidirect
31. C₂×C₄×C₂²⋊C₄×C₅₃	C₂	semidirect
51. C₅₃×#401	C₂²	semidirect
52. C₅₃×#400	C₂²	semidirect
53. C₅₃×#400	C₂²	semidirect
54. C₅₃×#400	C₂²	semidirect
55. C₅₃×#400	C₂²	semidirect
56. C₅₃×#400	C₂²	semidirect
57. C₅₃×#400	C₂²	semidirect
59. C₅₃×#398	C₂²	semidirect
60. C₅₃×#398	C₂²	semidirect
66. C₅₃×#397	C₂²	semidirect
67. C₅₃×#397	C₂²	semidirect
68. C₅₃×#397	C₂²	semidirect
69. C₅₃×#397	C₂²	semidirect
72. C₅₃×#396	C₂²	semidirect
79. C₅₃×#394	C₂²	semidirect
81. C₅₃×#393	C₂²	semidirect
83. C₅₃×#391	C₂²	semidirect
84. C₅₃×#391	C₂²	semidirect
85. C₅₃×#391	C₂²	semidirect
88. C₅₃×#390	C₂²	semidirect
89. C₅₃×#390	C₂²	semidirect
90. C₅₃×#389	C₂²	semidirect
91. C₅₃×#389	C₂²	semidirect
92. C₅₃×#389	C₂²	semidirect
93. C₅₃×#389	C₂²	semidirect
94. C₅₃×#389	C₂²	semidirect
103. C₅₃×#388	C₂²	semidirect
104. C₅₃×#388	C₂²	semidirect
105. C₅₃×#388	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×#387	C₂²	semidirect
115. C₅₃×#387	C₂²	semidirect
116. C₅₃×#387	C₂²	semidirect
117. C₅₃×#387	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
141. C₅₃×#386	C₂²	semidirect
154. C₅₃×#385	C₂²	semidirect
155. C₅₃×#383	C₂²	semidirect
156. C₅₃×#382	C₂²	semidirect
161. C₅₃×#381	C₂²	semidirect
164. C₅₃×#380	C₂²	semidirect
167. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
168. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
169. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
170. 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. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
689. #35074	C₅₃	direct (N × H)
759. #2855	C₂×C₅₃	semidirect
760. #2854	C₂×C₅₃	semidirect
761. #2849	C₂×C₅₃	semidirect
762. #2849	C₂×C₅₃	semidirect
763. #2653	C₂×C₅₃	semidirect
764. #2652	C₂×C₅₃	semidirect
765. #2649	C₂×C₅₃	semidirect
766. #2648	C₂×C₅₃	semidirect
767. #2597	C₂×C₅₃	semidirect
768. #2595	C₂×C₅₃	semidirect
769. #2589	C₂×C₅₃	semidirect
770. #2587	C₂×C₅₃	semidirect
771. #2578	C₂×C₅₃	semidirect
772. #2576	C₂×C₅₃	semidirect
773. #2559	C₂×C₅₃	semidirect
774. #2557	C₂×C₅₃	semidirect
775. #2493	C₂×C₅₃	semidirect
776. #2488	C₂×C₅₃	semidirect
777. #2480	C₂×C₅₃	semidirect
778. #2472	C₂×C₅₃	semidirect
779. #2425	C₂×C₅₃	semidirect
781. #2419	C₂×C₅₃	semidirect
782. #2418	C₂×C₅₃	semidirect
783. #2337	C₂×C₅₃	semidirect
784. #2335	C₂×C₅₃	semidirect
785. #2334	C₂×C₅₃	semidirect
786. #2333	C₂×C₅₃	semidirect
787. C₄×#123	C₂×C₅₃	semidirect
788. C₄×#123	C₂×C₅₃	semidirect
789. C₂×C₄×C₂²⋊C₄	C₂×C₅₃	semidirect
821. #401	C₂²×C₅₃	semidirect
822. #400	C₂²×C₅₃	semidirect
823. #400	C₂²×C₅₃	semidirect
824. #400	C₂²×C₅₃	semidirect
825. #400	C₂²×C₅₃	semidirect
826. #400	C₂²×C₅₃	semidirect
827. #400	C₂²×C₅₃	semidirect
829. #398	C₂²×C₅₃	semidirect
830. #398	C₂²×C₅₃	semidirect
836. #397	C₂²×C₅₃	semidirect
837. #397	C₂²×C₅₃	semidirect
838. #397	C₂²×C₅₃	semidirect
839. #397	C₂²×C₅₃	semidirect
842. #396	C₂²×C₅₃	semidirect
849. #394	C₂²×C₅₃	semidirect
851. #393	C₂²×C₅₃	semidirect
853. #391	C₂²×C₅₃	semidirect
854. #391	C₂²×C₅₃	semidirect
855. #391	C₂²×C₅₃	semidirect
858. #390	C₂²×C₅₃	semidirect
859. #390	C₂²×C₅₃	semidirect
860. #389	C₂²×C₅₃	semidirect
861. #389	C₂²×C₅₃	semidirect
862. #389	C₂²×C₅₃	semidirect
863. #389	C₂²×C₅₃	semidirect
864. #389	C₂²×C₅₃	semidirect
873. #388	C₂²×C₅₃	semidirect
874. #388	C₂²×C₅₃	semidirect
875. #388	C₂²×C₅₃	semidirect
876. #388	C₂²×C₅₃	semidirect
877. #388	C₂²×C₅₃	semidirect
878. #388	C₂²×C₅₃	semidirect
879. #388	C₂²×C₅₃	semidirect
880. #388	C₂²×C₅₃	semidirect
881. #388	C₂²×C₅₃	semidirect
882. #388	C₂²×C₅₃	semidirect
883. #388	C₂²×C₅₃	semidirect
884. #387	C₂²×C₅₃	semidirect
885. #387	C₂²×C₅₃	semidirect
886. #387	C₂²×C₅₃	semidirect
887. #387	C₂²×C₅₃	semidirect
888. #387	C₂²×C₅₃	semidirect
889. #387	C₂²×C₅₃	semidirect
890. #387	C₂²×C₅₃	semidirect
891. #387	C₂²×C₅₃	semidirect
892. #387	C₂²×C₅₃	semidirect
893. #387	C₂²×C₅₃	semidirect
894. #387	C₂²×C₅₃	semidirect
895. #387	C₂²×C₅₃	semidirect
896. #387	C₂²×C₅₃	semidirect
911. #386	C₂²×C₅₃	semidirect
924. #385	C₂²×C₅₃	semidirect
925. #383	C₂²×C₅₃	semidirect
926. #382	C₂²×C₅₃	semidirect
931. #381	C₂²×C₅₃	semidirect
934. #380	C₂²×C₅₃	semidirect
937. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
938. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
939. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
940. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
951. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
952. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
953. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
954. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
957. C₅₃	#35074	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×#2855	2
C₅₃×#2854	2
C₅₃×#2849	2
C₅₃×#2653	2
C₅₃×#2652	2
C₅₃×#2649	2
C₅₃×#2648	2
C₅₃×#2597	2
C₅₃×#2595	2
C₅₃×#2589	2
C₅₃×#2587	2
C₅₃×#2578	2
C₅₃×#2576	2
C₅₃×#2559	2
C₅₃×#2557	2
C₅₃×#2493	2
C₅₃×#2488	2
C₅₃×#2480	2
C₅₃×#2472	2
C₅₃×#2425	2
C₅₃×#2424	2
C₅₃×#2419	2
C₅₃×#2418	2
C₅₃×#2337	2
C₅₃×#2335	2
C₅₃×#2334	2
C₅₃×#2333	2
C₄×#123×C₅₃	2
C₂×C₄×C₂²⋊C₄×C₅₃	2
#35074	53

Subgroups — C53×#35074 #27242586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#35074 #27242586