Subgroups — C₅₃×#36889 #27244401

Order 13568.

1740 conjugacy classes of subgroups.

The subgroup lattice has 1500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2853	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#2852	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2808	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2797	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2795	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2780	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2775	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2753	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2747	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2740	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2735	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2721	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2707	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2686	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2685	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2684	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2678	C₂	1	1	yes	maximal, characteristic
19	C₅₃×#2636	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2630	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2531	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2529	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2517	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2480	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2469	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2460	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2458	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2418	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2326	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#124×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×#121×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#399	C₂²	1	1	yes	characteristic
51	C₅₃×#399	C₂²	1	1	yes	characteristic
52	C₅₃×#399	C₂²	1	1	yes	characteristic
53	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#397	C₂²	1	1	yes	characteristic
58	C₅₃×#397	C₂²	1	1	yes	characteristic
59	C₅₃×#397	C₂²	1	1	yes	characteristic
60	C₅₃×#397	C₂²	1	1	yes	characteristic
61	C₅₃×#397	C₂²	1	1	yes	characteristic
62	C₅₃×#397	C₂²	1	1	yes	characteristic
63	C₅₃×#397	C₂²	1	1	yes	characteristic
64	C₅₃×#397	C₂²	1	1	yes	characteristic
65	C₅₃×#397	C₂²	1	1	yes	characteristic
66	C₅₃×#397	C₂²	1	1	yes	characteristic
67	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#396	C₂²	1	1	yes	characteristic
70	C₅₃×#396	C₂²	1	1	yes	characteristic
71	C₅₃×#396	C₂²	1	1	yes	characteristic
72	C₅₃×#396	C₂²	1	1	yes	characteristic
73	C₅₃×#396	C₂²	1	1	yes	characteristic
74	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
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
84	C₅₃×#394	C₂²	1	1	yes	characteristic
85	C₅₃×#394	C₂²	1	1	yes	characteristic
86	C₅₃×#394	C₂²	1	1	yes	characteristic
87	C₅₃×#394	C₂²	1	1	yes	characteristic
88	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#393	C₂²	1	1	yes	characteristic
91	C₅₃×#393	C₂²	1	1	yes	characteristic
92	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#392	C₂²	1	1	yes	characteristic
94	C₅₃×#392	C₂²	1	1	yes	characteristic
95	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#390	C₂²	1	1	yes	characteristic
97	C₅₃×#390	C₂²	1	1	yes	characteristic
98	C₅₃×#390	C₂²	1	1	yes	characteristic
99	C₅₃×#390	C₂²	1	1	yes	characteristic
100	C₅₃×#390	C₂²	1	1	yes	characteristic
101	C₅₃×#390	C₂²	1	1	yes	characteristic
102	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#388	C₂²	1	1	yes	characteristic
106	C₅₃×#388	C₂²	1	1	yes	characteristic
107	C₅₃×#388	C₂²	1	1	yes	characteristic
108	C₅₃×#388	C₂²	1	1	yes	characteristic
109	C₅₃×#388	C₂²	1	1	yes	characteristic
110	C₅₃×#388	C₂²	1	1	yes	characteristic
111	C₅₃×#388	C₂²	1	1	yes	characteristic
112	C₅₃×#388	C₂²	1	1	yes	characteristic
113	C₅₃×#388	C₂²	1	1	yes	characteristic
114	C₅₃×#388	C₂²	1	1	yes	characteristic
115	C₅₃×#388	C₂²	1	1	yes	characteristic
116	C₅₃×#388	C₂²	1	1	yes	characteristic
117	C₅₃×#388	C₂²	1	1	yes	characteristic
118	C₅₃×#388	C₂²	1	1	yes	characteristic
119	C₅₃×#388	C₂²	1	1	yes	characteristic
120	C₅₃×#388	C₂²	1	1	yes	characteristic
121	C₅₃×#388	C₂²	1	1	yes	characteristic
122	C₅₃×#388	C₂²	1	1	yes	characteristic
123	C₅₃×#388	C₂²	1	1	yes	characteristic
124	C₅₃×#388	C₂²	1	1	yes	characteristic
125	C₅₃×#388	C₂²	1	1	yes	characteristic
126	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#386	C₂²	1	1	yes	characteristic
150	C₅₃×#386	C₂²	1	1	yes	characteristic
151	C₅₃×#386	C₂²	1	1	yes	characteristic
152	C₅₃×#386	C₂²	1	1	yes	characteristic
153	C₅₃×#386	C₂²	1	1	yes	characteristic
154	C₅₃×#386	C₂²	1	1	yes	characteristic
155	C₅₃×#386	C₂²	1	1	yes	characteristic
156	C₅₃×#386	C₂²	1	1	yes	characteristic
157	C₅₃×#386	C₂²	1	1	yes	characteristic
158	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#385	C₂²	1	1	yes	characteristic
160	C₅₃×#385	C₂²	1	1	yes	characteristic
161	C₅₃×#385	C₂²	1	1	yes	characteristic
162	C₅₃×#385	C₂²	1	1	yes	characteristic
163	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#380	C₂²	1	1	yes	characteristic
175	C₅₃×#380	C₂²	1	1	yes	characteristic
176	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#379	C₂²	1	1	yes	characteristic
179	C₅₃×#379	C₂²	1	1	yes	characteristic
180	C₅₃×#379	C₂²	1	1	yes	characteristic
181	C₅₃×#379	C₂²	1	1	yes	characteristic
182	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#376	C₂²	1	1	yes	characteristic, complemented
187	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
191	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
192	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	C₂³	1	1	yes	characteristic
197	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	#126×C₅₃	—	4	2	no	—
203	#126×C₅₃	—	4	2	no	—
204	#125×C₅₃	—	4	2	no	—
205	#124×C₅₃	—	2	4	no	—
206	#123×C₅₃	—	4	2	no	—
207	#123×C₅₃	—	4	2	no	—
208	#121×C₅₃	—	2	4	no	—
209	#120×C₅₃	—	2	4	no	—
210	#120×C₅₃	—	4	2	no	—
211	C₄×Q₈×C₅₃	—	4	2	no	—
212	C₄×D₄×C₅₃	—	4	2	no	—
213	C₄×D₄×C₅₃	—	4	2	no	—
214	C₄×D₄×C₅₃	—	4	2	no	—
215	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
248	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×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×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	#95×C₅₃	C₂³	1	1	yes	characteristic
314	#95×C₅₃	C₂³	1	1	yes	characteristic
315	#95×C₅₃	C₂³	1	1	yes	characteristic
316	#95×C₅₃	C₂³	1	1	yes	characteristic
317	#95×C₅₃	C₂³	1	1	yes	characteristic
318	#95×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	C₂⁴×C₅₃	—	2	2	no	—
358	C₂⁴×C₅₃	—	4	1	no	—
359	C₂⁴×C₅₃	—	4	1	no	—
360	C₂⁴×C₅₃	—	4	1	no	—
361	C₂⁴×C₅₃	—	4	1	no	—
362	C₂⁴×C₅₃	—	4	1	no	—
363	C₂⁴×C₅₃	—	4	1	no	—
364	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
369	C₂×Q₈×C₅₃	—	2	2	no	—
370	C₂×Q₈×C₅₃	—	4	1	no	—
371	C₂×Q₈×C₅₃	—	4	1	no	—
372	C₂×D₄×C₅₃	—	2	2	no	—
373	C₂×D₄×C₅₃	—	2	2	no	—
374	C₂×D₄×C₅₃	—	2	2	no	—
375	C₂×D₄×C₅₃	—	2	2	no	—
376	C₂×D₄×C₅₃	—	2	2	no	—
377	C₂×D₄×C₅₃	—	4	1	no	—
378	C₂×D₄×C₅₃	—	4	1	no	—
379	C₂×D₄×C₅₃	—	4	1	no	—
380	C₂×D₄×C₅₃	—	4	1	no	—
381	C₂×D₄×C₅₃	—	4	1	no	—
382	C₂×D₄×C₅₃	—	4	1	no	—
383	C₂×D₄×C₅₃	—	4	1	no	—
384	C₂×D₄×C₅₃	—	4	1	no	—
385	C₂×D₄×C₅₃	—	4	1	no	—
386	C₂×D₄×C₅₃	—	4	1	no	—
387	C₂×D₄×C₅₃	—	4	1	no	—
388	C₂×D₄×C₅₃	—	4	1	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	#41	1	4	yes	—
393	C₂²×C₄×C₅₃	—	2	2	no	—
394	C₂²×C₄×C₅₃	—	2	2	no	—
395	C₂²×C₄×C₅₃	—	2	2	no	—
396	C₂²×C₄×C₅₃	—	2	2	no	—
397	C₂²×C₄×C₅₃	—	2	2	no	—
398	C₂²×C₄×C₅₃	—	4	1	no	—
399	C₂²×C₄×C₅₃	—	4	1	no	—
400	C₂²×C₄×C₅₃	—	4	1	no	—
401	C₂²×C₄×C₅₃	—	4	1	no	—
402	C₂²×C₄×C₅₃	—	4	1	no	—
403	C₂²×C₄×C₅₃	—	4	1	no	—
404	C₂²×C₄×C₅₃	—	4	1	no	—
405	C₂²×C₄×C₅₃	—	4	1	no	—
406	C₂²×C₄×C₅₃	—	4	1	no	—
407	C₂²×C₄×C₅₃	—	4	1	no	—
408	C₂²×C₄×C₅₃	—	4	1	no	—
409	C₂²×C₄×C₅₃	—	4	1	no	—
410	C₂²×C₄×C₅₃	—	4	1	no	—
411	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
414	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
415	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₅₃	—	2	2	no	—
438	C₄⋊C₄×C₅₃	—	2	2	no	—
439	C₄⋊C₄×C₅₃	—	2	2	no	—
440	C₄⋊C₄×C₅₃	—	2	2	no	—
441	C₄⋊C₄×C₅₃	—	2	2	no	—
442	C₄⋊C₄×C₅₃	—	2	2	no	—
443	C₄⋊C₄×C₅₃	—	4	1	no	—
444	C₄⋊C₄×C₅₃	—	4	1	no	—
445	C₄⋊C₄×C₅₃	—	4	1	no	—
446	C₄⋊C₄×C₅₃	—	4	1	no	—
447	C₄⋊C₄×C₅₃	—	4	1	no	—
448	C₄⋊C₄×C₅₃	—	4	1	no	—
449	C₄⋊C₄×C₅₃	—	4	1	no	—
450	C₄⋊C₄×C₅₃	—	4	1	no	—
451	C₄⋊C₄×C₅₃	—	4	1	no	—
452	C₄⋊C₄×C₅₃	—	4	1	no	—
453	C₄⋊C₄×C₅₃	—	4	1	no	—
454	C₄⋊C₄×C₅₃	—	4	1	no	—
455	C₄⋊C₄×C₅₃	—	4	1	no	—
456	C₄⋊C₄×C₅₃	—	4	1	no	—
457	C₄⋊C₄×C₅₃	—	4	1	no	—
458	C₄⋊C₄×C₅₃	—	4	1	no	—
459	C₄⋊C₄×C₅₃	—	4	1	no	—
460	C₄⋊C₄×C₅₃	—	4	1	no	—
461	C₄⋊C₄×C₅₃	—	4	1	no	—
462	C₄⋊C₄×C₅₃	—	4	1	no	—
463	C₄⋊C₄×C₅₃	—	4	1	no	—
464	C₄⋊C₄×C₅₃	—	4	1	no	—
465	C₄⋊C₄×C₅₃	—	4	1	no	—
466	C₄⋊C₄×C₅₃	—	4	1	no	—
467	C₄⋊C₄×C₅₃	—	4	1	no	—
468	C₄⋊C₄×C₅₃	—	4	1	no	—
469	C₂²⋊C₄×C₅₃	—	2	2	no	—
470	C₂²⋊C₄×C₅₃	—	2	2	no	—
471	C₂²⋊C₄×C₅₃	—	2	2	no	—
472	C₂²⋊C₄×C₅₃	—	2	2	no	—
473	C₂²⋊C₄×C₅₃	—	2	2	no	—
474	C₂²⋊C₄×C₅₃	—	2	2	no	—
475	C₂²⋊C₄×C₅₃	—	2	2	no	—
476	C₂²⋊C₄×C₅₃	—	2	2	no	—
477	C₂²⋊C₄×C₅₃	—	2	2	no	—
478	C₂²⋊C₄×C₅₃	—	2	2	no	—
479	C₂²⋊C₄×C₅₃	—	2	2	no	—
480	C₂²⋊C₄×C₅₃	—	2	2	no	—
481	C₂²⋊C₄×C₅₃	—	2	2	no	—
482	C₂²⋊C₄×C₅₃	—	4	1	no	—
483	C₂²⋊C₄×C₅₃	—	4	1	no	—
484	C₂²⋊C₄×C₅₃	—	4	1	no	—
485	C₂²⋊C₄×C₅₃	—	4	1	no	—
486	C₂²⋊C₄×C₅₃	—	4	1	no	—
487	C₂²⋊C₄×C₅₃	—	4	1	no	—
488	C₂²⋊C₄×C₅₃	—	4	1	no	—
489	C₂²⋊C₄×C₅₃	—	4	1	no	—
490	C₂²⋊C₄×C₅₃	—	4	1	no	—
491	C₂²⋊C₄×C₅₃	—	4	1	no	—
492	C₂²⋊C₄×C₅₃	—	4	1	no	—
493	C₂²⋊C₄×C₅₃	—	4	1	no	—
494	C₂²⋊C₄×C₅₃	—	4	1	no	—
495	C₂²⋊C₄×C₅₃	—	4	1	no	—
496	C₂²⋊C₄×C₅₃	—	4	1	no	—
497	C₂²⋊C₄×C₅₃	—	4	1	no	—
498	C₂²⋊C₄×C₅₃	—	4	1	no	—
499	C₂²⋊C₄×C₅₃	—	4	1	no	—
500	C₂²⋊C₄×C₅₃	—	4	1	no	—
501	C₂²⋊C₄×C₅₃	—	4	1	no	—
502	C₂²⋊C₄×C₅₃	—	4	1	no	—
503	C₂²⋊C₄×C₅₃	—	4	1	no	—
504	C₂²⋊C₄×C₅₃	—	4	1	no	—
505	C₂²⋊C₄×C₅₃	—	4	1	no	—
506	C₂²⋊C₄×C₅₃	—	4	1	no	—
507	C₂²⋊C₄×C₅₃	—	4	1	no	—
508	C₂²⋊C₄×C₅₃	—	4	1	no	—
509	C₂²⋊C₄×C₅₃	—	4	1	no	—
510	C₂²⋊C₄×C₅₃	—	4	1	no	—
511	C₂²⋊C₄×C₅₃	—	4	1	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	C₄²×C₅₃	—	2	2	no	—
522	C₄²×C₅₃	—	2	2	no	—
523	C₄²×C₅₃	—	2	2	no	—
524	C₄²×C₅₃	—	2	2	no	—
525	C₄²×C₅₃	—	2	2	no	—
526	C₄²×C₅₃	—	4	1	no	—
527	C₄²×C₅₃	—	4	1	no	—
528	C₄²×C₅₃	—	4	1	no	—
529	C₄²×C₅₃	—	4	1	no	—
530	C₄²×C₅₃	—	4	1	no	—
531	C₄²×C₅₃	—	4	1	no	—
532	C₄²×C₅₃	—	4	1	no	—
533	C₂³×C₅₃	—	2	1	no	—
534	C₂³×C₅₃	—	2	1	no	—
535	C₂³×C₅₃	—	2	1	no	—
536	C₂³×C₅₃	—	2	1	no	—
537	C₂³×C₅₃	—	2	1	no	—
538	C₂³×C₅₃	—	2	1	no	—
539	C₂³×C₅₃	—	2	1	no	—
540	C₂³×C₅₃	—	2	1	no	—
541	C₂³×C₅₃	—	2	1	no	—
542	C₂³×C₅₃	—	2	1	no	—
543	C₂³×C₅₃	—	2	1	no	—
544	C₂³×C₅₃	—	2	1	no	—
545	C₂³×C₅₃	—	2	1	no	—
546	C₂³×C₅₃	—	2	1	no	—
547	C₂³×C₅₃	—	2	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	1	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	—	4	4	no	—
567	C₂³×C₅₃	—	8	2	no	—
568	C₂³×C₅₃	—	8	2	no	—
569	C₂³×C₅₃	—	8	2	no	—
570	C₂³×C₅₃	—	8	2	no	—
571	C₂³×C₅₃	—	8	2	no	—
572	C₂³×C₅₃	—	8	2	no	—
573	C₂³×C₅₃	C₂×#41	1	2	yes	—
574	C₂³×C₅₃	C₂×#41	1	2	yes	—
575	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
576	Q₈×C₅₃	—	4	4	no	—
577	D₄×C₅₃	—	4	4	no	—
578	D₄×C₅₃	—	4	4	no	—
579	D₄×C₅₃	—	4	4	no	—
580	D₄×C₅₃	—	8	2	no	—
581	D₄×C₅₃	—	8	2	no	—
582	D₄×C₅₃	—	8	2	no	—
583	D₄×C₅₃	—	8	2	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	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	—	4	4	no	—
660	C₂×C₄×C₅₃	—	4	4	no	—
661	C₂×C₄×C₅₃	—	4	4	no	—
662	C₂×C₄×C₅₃	—	8	2	no	—
663	C₂×C₄×C₅₃	—	8	2	no	—
664	C₂×C₄×C₅₃	—	8	2	no	—
665	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
666	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
667	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
668	#36889	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
669	C₂²×C₅₃	—	2	2	no	—
670	C₂²×C₅₃	—	2	2	no	—
671	C₂²×C₅₃	—	2	2	no	—
672	C₂²×C₅₃	—	2	2	no	—
673	C₂²×C₅₃	—	2	2	no	—
674	C₂²×C₅₃	—	2	2	no	—
675	C₂²×C₅₃	—	4	1	no	—
676	C₂²×C₅₃	—	4	1	no	—
677	C₂²×C₅₃	—	4	1	no	—
678	C₂²×C₅₃	—	4	1	no	—
679	C₂²×C₅₃	—	4	1	no	—
680	C₂²×C₅₃	—	4	1	no	—
681	C₂²×C₅₃	—	4	1	no	—
682	C₂²×C₅₃	—	4	1	no	—
683	C₂²×C₅₃	—	4	1	no	—
684	C₂²×C₅₃	—	4	1	no	—
685	C₂²×C₅₃	—	4	1	no	—
686	C₂²×C₅₃	—	4	1	no	—
687	C₂²×C₅₃	—	4	1	no	—
688	C₂²×C₅₃	—	4	1	no	—
689	C₂²×C₅₃	—	4	1	no	—
690	C₂²×C₅₃	—	4	1	no	—
691	C₂²×C₅₃	—	4	1	no	—
692	C₂²×C₅₃	—	4	1	no	—
693	C₂²×C₅₃	—	4	1	no	—
694	C₂²×C₅₃	—	4	1	no	—
695	C₂²×C₅₃	—	4	1	no	—
696	C₂²×C₅₃	—	4	1	no	—
697	C₂²×C₅₃	—	4	1	no	—
698	C₂²×C₅₃	—	4	1	no	—
699	C₂²×C₅₃	—	4	1	no	—
700	C₂²×C₅₃	—	4	1	no	—
701	C₂²×C₅₃	—	4	1	no	—
702	C₂²×C₅₃	—	4	1	no	—
703	C₂²×C₅₃	—	4	1	no	—
704	C₂²×C₅₃	—	8	8	no	—
705	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
706	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
707	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
708	C₂²×C₅₃	#585	1	1	yes	characteristic
709	C₂²×C₅₃	#585	1	1	yes	characteristic
710	C₂²×C₅₃	#585	1	1	yes	characteristic
711	C₂²×C₅₃	#585	1	1	yes	characteristic
712	C₄×C₅₃	—	2	2	no	—
713	C₄×C₅₃	—	2	2	no	—
714	C₄×C₅₃	—	2	2	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	C₄×C₅₃	—	4	1	no	—
718	C₄×C₅₃	—	4	1	no	—
719	C₄×C₅₃	—	4	1	no	—
720	C₄×C₅₃	—	4	1	no	—
721	C₄×C₅₃	—	4	1	no	—
722	C₄×C₅₃	—	4	1	no	—
723	C₄×C₅₃	—	4	1	no	—
724	C₄×C₅₃	—	4	1	no	—
725	C₄×C₅₃	—	4	1	no	—
726	C₄×C₅₃	—	4	1	no	—
727	C₄×C₅₃	—	4	1	no	—
728	C₄×C₅₃	—	4	1	no	—
729	C₄×C₅₃	—	4	1	no	—
730	C₄×C₅₃	—	4	1	no	—
731	C₄×C₅₃	—	4	1	no	—
732	C₄×C₅₃	—	4	1	no	—
733	C₄×C₅₃	—	4	1	no	—
734	C₄×C₅₃	—	4	1	no	—
735	C₄×C₅₃	—	4	1	no	—
736	C₄×C₅₃	—	4	1	no	—
737	C₄×C₅₃	—	4	1	no	—
738	#2853	C₂×C₅₃	1	1	yes	characteristic, complemented
739	#2852	C₂×C₅₃	1	1	yes	characteristic, complemented
740	#2808	C₂×C₅₃	1	1	yes	characteristic, complemented
741	#2797	C₂×C₅₃	1	1	yes	characteristic, complemented
742	#2795	C₂×C₅₃	1	1	yes	characteristic, complemented
743	#2780	C₂×C₅₃	1	1	yes	characteristic, complemented
744	#2775	C₂×C₅₃	1	1	yes	characteristic, complemented
745	#2757	C₂×C₅₃	1	1	yes	characteristic, complemented
746	#2753	C₂×C₅₃	1	1	yes	characteristic, complemented
747	#2747	C₂×C₅₃	1	1	yes	characteristic, complemented
748	#2740	C₂×C₅₃	1	1	yes	characteristic, complemented
749	#2735	C₂×C₅₃	1	1	yes	characteristic, complemented
750	#2721	C₂×C₅₃	1	1	yes	characteristic, complemented
751	#2707	C₂×C₅₃	1	1	yes	characteristic, complemented
752	#2686	C₂×C₅₃	1	1	yes	characteristic, complemented
753	#2685	C₂×C₅₃	1	1	yes	characteristic, complemented
754	#2684	C₂×C₅₃	1	1	yes	characteristic, complemented
755	#2678	C₂×C₅₃	1	1	yes	characteristic
756	#2636	C₂×C₅₃	1	1	yes	characteristic, complemented
757	#2630	C₂×C₅₃	1	1	yes	characteristic, complemented
758	#2531	C₂×C₅₃	1	1	yes	characteristic, complemented
759	#2529	C₂×C₅₃	1	1	yes	characteristic, complemented
760	#2517	C₂×C₅₃	1	1	yes	characteristic, complemented
761	#2480	C₂×C₅₃	1	1	yes	characteristic, complemented
762	#2469	C₂×C₅₃	1	1	yes	characteristic, complemented
763	#2460	C₂×C₅₃	1	1	yes	characteristic, complemented
764	#2458	C₂×C₅₃	1	1	yes	characteristic, complemented
765	#2418	C₂×C₅₃	1	1	yes	characteristic, complemented
766	#2326	C₂×C₅₃	1	1	yes	characteristic, complemented
767	#2321	C₂×C₅₃	1	1	yes	characteristic, complemented
768	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
769	C₂×C₅₃	—	4	2	no	—
770	C₂×C₅₃	—	4	2	no	—
771	C₂×C₅₃	—	8	1	no	—
772	C₂×C₅₃	—	8	1	no	—
773	C₂×C₅₃	—	8	1	no	—
774	C₂×C₅₃	#3459	1	1	yes	characteristic
775	C₂×C₅₃	#3513	1	1	yes	characteristic
776	C₂×C₅₃	#3521	1	1	yes	characteristic
777	C₂×C₅₃	#3540	1	1	yes	characteristic
778	C₂×C₅₃	#3542	1	1	yes	characteristic
779	C₂×C₅₃	#3551	1	1	yes	characteristic
780	C₂×C₅₃	#3566	1	1	yes	characteristic
781	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
782	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
783	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic, complemented
784	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
785	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
786	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
787	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
788	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
789	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
790	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
791	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
792	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
793	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
794	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
795	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
796	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
797	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
798	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
799	#399	C₂²×C₅₃	1	1	yes	characteristic
800	#399	C₂²×C₅₃	1	1	yes	characteristic
801	#399	C₂²×C₅₃	1	1	yes	characteristic
802	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
803	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
804	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
805	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
806	#397	C₂²×C₅₃	1	1	yes	characteristic
807	#397	C₂²×C₅₃	1	1	yes	characteristic
808	#397	C₂²×C₅₃	1	1	yes	characteristic
809	#397	C₂²×C₅₃	1	1	yes	characteristic
810	#397	C₂²×C₅₃	1	1	yes	characteristic
811	#397	C₂²×C₅₃	1	1	yes	characteristic
812	#397	C₂²×C₅₃	1	1	yes	characteristic
813	#397	C₂²×C₅₃	1	1	yes	characteristic
814	#397	C₂²×C₅₃	1	1	yes	characteristic
815	#397	C₂²×C₅₃	1	1	yes	characteristic
816	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
817	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
818	#396	C₂²×C₅₃	1	1	yes	characteristic
819	#396	C₂²×C₅₃	1	1	yes	characteristic
820	#396	C₂²×C₅₃	1	1	yes	characteristic
821	#396	C₂²×C₅₃	1	1	yes	characteristic
822	#396	C₂²×C₅₃	1	1	yes	characteristic
823	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
824	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
825	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
826	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
827	#394	C₂²×C₅₃	1	1	yes	characteristic
828	#394	C₂²×C₅₃	1	1	yes	characteristic
829	#394	C₂²×C₅₃	1	1	yes	characteristic
830	#394	C₂²×C₅₃	1	1	yes	characteristic
831	#394	C₂²×C₅₃	1	1	yes	characteristic
832	#394	C₂²×C₅₃	1	1	yes	characteristic
833	#394	C₂²×C₅₃	1	1	yes	characteristic
834	#394	C₂²×C₅₃	1	1	yes	characteristic
835	#394	C₂²×C₅₃	1	1	yes	characteristic
836	#394	C₂²×C₅₃	1	1	yes	characteristic
837	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
838	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
839	#393	C₂²×C₅₃	1	1	yes	characteristic
840	#393	C₂²×C₅₃	1	1	yes	characteristic
841	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
842	#392	C₂²×C₅₃	1	1	yes	characteristic
843	#392	C₂²×C₅₃	1	1	yes	characteristic
844	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
845	#390	C₂²×C₅₃	1	1	yes	characteristic
846	#390	C₂²×C₅₃	1	1	yes	characteristic
847	#390	C₂²×C₅₃	1	1	yes	characteristic
848	#390	C₂²×C₅₃	1	1	yes	characteristic
849	#390	C₂²×C₅₃	1	1	yes	characteristic
850	#390	C₂²×C₅₃	1	1	yes	characteristic
851	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
852	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
853	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
854	#388	C₂²×C₅₃	1	1	yes	characteristic
855	#388	C₂²×C₅₃	1	1	yes	characteristic
856	#388	C₂²×C₅₃	1	1	yes	characteristic
857	#388	C₂²×C₅₃	1	1	yes	characteristic
858	#388	C₂²×C₅₃	1	1	yes	characteristic
859	#388	C₂²×C₅₃	1	1	yes	characteristic
860	#388	C₂²×C₅₃	1	1	yes	characteristic
861	#388	C₂²×C₅₃	1	1	yes	characteristic
862	#388	C₂²×C₅₃	1	1	yes	characteristic
863	#388	C₂²×C₅₃	1	1	yes	characteristic
864	#388	C₂²×C₅₃	1	1	yes	characteristic
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
874	#388	C₂²×C₅₃	1	1	yes	characteristic
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	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
883	#387	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	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
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, complemented
908	#385	C₂²×C₅₃	1	1	yes	characteristic
909	#385	C₂²×C₅₃	1	1	yes	characteristic
910	#385	C₂²×C₅₃	1	1	yes	characteristic
911	#385	C₂²×C₅₃	1	1	yes	characteristic
912	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
915	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
916	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#380	C₂²×C₅₃	1	1	yes	characteristic
924	#380	C₂²×C₅₃	1	1	yes	characteristic
925	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#379	C₂²×C₅₃	1	1	yes	characteristic
928	#379	C₂²×C₅₃	1	1	yes	characteristic
929	#379	C₂²×C₅₃	1	1	yes	characteristic
930	#379	C₂²×C₅₃	1	1	yes	characteristic
931	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
933	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
934	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#376	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	C₅₃	#36889	1	1	yes	characteristic, direct product factor, Sylow
937	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
938	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
939	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
940	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
941	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
942	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
943	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
944	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
945	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
946	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
947	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
948	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
949	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
950	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
951	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
952	#126	—	4	2	no	—
953	#126	—	4	2	no	—
954	#125	—	4	2	no	—
955	#124	—	2	4	no	—
956	#123	—	4	2	no	—
957	#123	—	4	2	no	—
958	#121	—	2	4	no	—
959	#120	—	2	4	no	—
960	#120	—	4	2	no	—
961	C₄×Q₈	—	4	2	no	—
962	C₄×D₄	—	4	2	no	—
963	C₄×D₄	—	4	2	no	—
964	C₄×D₄	—	4	2	no	—
965	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
966	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
967	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
968	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
969	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
970	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
971	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
972	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
973	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
974	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
975	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
976	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
979	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
980	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
981	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
982	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
983	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
984	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
985	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
986	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
987	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
990	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
991	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
992	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
993	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
996	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
997	C₂×C₂²⋊C₄	—	4	2	no	—
998	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
999	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1000	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1001	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1002	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1003	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1004	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1005	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1006	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1007	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1008	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1009	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1010	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1011	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1012	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1013	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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×C₄²	—	4	2	no	—
1051	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1063	#95	C₂³×C₅₃	1	1	yes	characteristic
1064	#95	C₂³×C₅₃	1	1	yes	characteristic
1065	#95	C₂³×C₅₃	1	1	yes	characteristic
1066	#95	C₂³×C₅₃	1	1	yes	characteristic
1067	#95	C₂³×C₅₃	1	1	yes	characteristic
1068	#95	C₂³×C₅₃	1	1	yes	characteristic
1069	#95	C₂³×C₅₃	1	1	yes	characteristic
1070	#95	C₂³×C₅₃	1	1	yes	characteristic
1071	#95	C₂³×C₅₃	1	1	yes	characteristic
1072	#95	C₂³×C₅₃	1	1	yes	characteristic
1073	#95	C₂³×C₅₃	1	1	yes	characteristic
1074	#95	C₂³×C₅₃	1	1	yes	characteristic
1075	#95	C₂³×C₅₃	1	1	yes	characteristic
1076	#95	C₂³×C₅₃	1	1	yes	characteristic
1077	#95	C₂³×C₅₃	1	1	yes	characteristic
1078	#95	C₂³×C₅₃	1	1	yes	characteristic
1079	#95	C₂³×C₅₃	1	1	yes	characteristic
1080	#95	C₂³×C₅₃	1	1	yes	characteristic
1081	#95	C₂³×C₅₃	1	1	yes	characteristic
1082	#95	C₂³×C₅₃	1	1	yes	characteristic
1083	#95	C₂³×C₅₃	1	1	yes	characteristic
1084	#95	C₂³×C₅₃	1	1	yes	characteristic
1085	#95	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	C₂⁴	—	2	2	no	—
1108	C₂⁴	—	4	1	no	—
1109	C₂⁴	—	4	1	no	—
1110	C₂⁴	—	4	1	no	—
1111	C₂⁴	—	4	1	no	—
1112	C₂⁴	—	4	1	no	—
1113	C₂⁴	—	4	1	no	—
1114	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1115	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1116	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1117	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1118	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1119	C₂×Q₈	—	2	2	no	—
1120	C₂×Q₈	—	4	1	no	—
1121	C₂×Q₈	—	4	1	no	—
1122	C₂×D₄	—	2	2	no	—
1123	C₂×D₄	—	2	2	no	—
1124	C₂×D₄	—	2	2	no	—
1125	C₂×D₄	—	2	2	no	—
1126	C₂×D₄	—	2	2	no	—
1127	C₂×D₄	—	4	1	no	—
1128	C₂×D₄	—	4	1	no	—
1129	C₂×D₄	—	4	1	no	—
1130	C₂×D₄	—	4	1	no	—
1131	C₂×D₄	—	4	1	no	—
1132	C₂×D₄	—	4	1	no	—
1133	C₂×D₄	—	4	1	no	—
1134	C₂×D₄	—	4	1	no	—
1135	C₂×D₄	—	4	1	no	—
1136	C₂×D₄	—	4	1	no	—
1137	C₂×D₄	—	4	1	no	—
1138	C₂×D₄	—	4	1	no	—
1139	C₂×D₄	—	4	1	no	—
1140	C₂×D₄	—	4	1	no	—
1141	C₂×D₄	—	4	1	no	—
1142	C₂×D₄	#41×C₅₃	1	4	yes	—
1143	C₂²×C₄	—	2	2	no	—
1144	C₂²×C₄	—	2	2	no	—
1145	C₂²×C₄	—	2	2	no	—
1146	C₂²×C₄	—	2	2	no	—
1147	C₂²×C₄	—	2	2	no	—
1148	C₂²×C₄	—	4	1	no	—
1149	C₂²×C₄	—	4	1	no	—
1150	C₂²×C₄	—	4	1	no	—
1151	C₂²×C₄	—	4	1	no	—
1152	C₂²×C₄	—	4	1	no	—
1153	C₂²×C₄	—	4	1	no	—
1154	C₂²×C₄	—	4	1	no	—
1155	C₂²×C₄	—	4	1	no	—
1156	C₂²×C₄	—	4	1	no	—
1157	C₂²×C₄	—	4	1	no	—
1158	C₂²×C₄	—	4	1	no	—
1159	C₂²×C₄	—	4	1	no	—
1160	C₂²×C₄	—	4	1	no	—
1161	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1162	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1163	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1164	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1165	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1166	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1167	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1168	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1169	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1170	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1171	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1172	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1173	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1174	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1175	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1176	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1177	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1178	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1179	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1180	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1181	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1182	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1183	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1184	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1185	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1186	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1187	C₄⋊C₄	—	2	2	no	—
1188	C₄⋊C₄	—	2	2	no	—
1189	C₄⋊C₄	—	2	2	no	—
1190	C₄⋊C₄	—	2	2	no	—
1191	C₄⋊C₄	—	2	2	no	—
1192	C₄⋊C₄	—	2	2	no	—
1193	C₄⋊C₄	—	4	1	no	—
1194	C₄⋊C₄	—	4	1	no	—
1195	C₄⋊C₄	—	4	1	no	—
1196	C₄⋊C₄	—	4	1	no	—
1197	C₄⋊C₄	—	4	1	no	—
1198	C₄⋊C₄	—	4	1	no	—
1199	C₄⋊C₄	—	4	1	no	—
1200	C₄⋊C₄	—	4	1	no	—
1201	C₄⋊C₄	—	4	1	no	—
1202	C₄⋊C₄	—	4	1	no	—
1203	C₄⋊C₄	—	4	1	no	—
1204	C₄⋊C₄	—	4	1	no	—
1205	C₄⋊C₄	—	4	1	no	—
1206	C₄⋊C₄	—	4	1	no	—
1207	C₄⋊C₄	—	4	1	no	—
1208	C₄⋊C₄	—	4	1	no	—
1209	C₄⋊C₄	—	4	1	no	—
1210	C₄⋊C₄	—	4	1	no	—
1211	C₄⋊C₄	—	4	1	no	—
1212	C₄⋊C₄	—	4	1	no	—
1213	C₄⋊C₄	—	4	1	no	—
1214	C₄⋊C₄	—	4	1	no	—
1215	C₄⋊C₄	—	4	1	no	—
1216	C₄⋊C₄	—	4	1	no	—
1217	C₄⋊C₄	—	4	1	no	—
1218	C₄⋊C₄	—	4	1	no	—
1219	C₂²⋊C₄	—	2	2	no	—
1220	C₂²⋊C₄	—	2	2	no	—
1221	C₂²⋊C₄	—	2	2	no	—
1222	C₂²⋊C₄	—	2	2	no	—
1223	C₂²⋊C₄	—	2	2	no	—
1224	C₂²⋊C₄	—	2	2	no	—
1225	C₂²⋊C₄	—	2	2	no	—
1226	C₂²⋊C₄	—	2	2	no	—
1227	C₂²⋊C₄	—	2	2	no	—
1228	C₂²⋊C₄	—	2	2	no	—
1229	C₂²⋊C₄	—	2	2	no	—
1230	C₂²⋊C₄	—	2	2	no	—
1231	C₂²⋊C₄	—	2	2	no	—
1232	C₂²⋊C₄	—	4	1	no	—
1233	C₂²⋊C₄	—	4	1	no	—
1234	C₂²⋊C₄	—	4	1	no	—
1235	C₂²⋊C₄	—	4	1	no	—
1236	C₂²⋊C₄	—	4	1	no	—
1237	C₂²⋊C₄	—	4	1	no	—
1238	C₂²⋊C₄	—	4	1	no	—
1239	C₂²⋊C₄	—	4	1	no	—
1240	C₂²⋊C₄	—	4	1	no	—
1241	C₂²⋊C₄	—	4	1	no	—
1242	C₂²⋊C₄	—	4	1	no	—
1243	C₂²⋊C₄	—	4	1	no	—
1244	C₂²⋊C₄	—	4	1	no	—
1245	C₂²⋊C₄	—	4	1	no	—
1246	C₂²⋊C₄	—	4	1	no	—
1247	C₂²⋊C₄	—	4	1	no	—
1248	C₂²⋊C₄	—	4	1	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	1	no	—
1267	C₂²⋊C₄	—	4	1	no	—
1268	C₂²⋊C₄	—	4	1	no	—
1269	C₂²⋊C₄	—	4	1	no	—
1270	C₂²⋊C₄	—	4	1	no	—
1271	C₄²	—	2	2	no	—
1272	C₄²	—	2	2	no	—
1273	C₄²	—	2	2	no	—
1274	C₄²	—	2	2	no	—
1275	C₄²	—	2	2	no	—
1276	C₄²	—	4	1	no	—
1277	C₄²	—	4	1	no	—
1278	C₄²	—	4	1	no	—
1279	C₄²	—	4	1	no	—
1280	C₄²	—	4	1	no	—
1281	C₄²	—	4	1	no	—
1282	C₄²	—	4	1	no	—
1283	C₂³	—	2	1	no	—
1284	C₂³	—	2	1	no	—
1285	C₂³	—	2	1	no	—
1286	C₂³	—	2	1	no	—
1287	C₂³	—	2	1	no	—
1288	C₂³	—	2	1	no	—
1289	C₂³	—	2	1	no	—
1290	C₂³	—	2	1	no	—
1291	C₂³	—	2	1	no	—
1292	C₂³	—	2	1	no	—
1293	C₂³	—	2	1	no	—
1294	C₂³	—	2	1	no	—
1295	C₂³	—	2	1	no	—
1296	C₂³	—	2	1	no	—
1297	C₂³	—	2	1	no	—
1298	C₂³	—	2	1	no	—
1299	C₂³	—	2	1	no	—
1300	C₂³	—	2	1	no	—
1301	C₂³	—	2	1	no	—
1302	C₂³	—	2	1	no	—
1303	C₂³	—	2	1	no	—
1304	C₂³	—	2	1	no	—
1305	C₂³	—	2	1	no	—
1306	C₂³	—	2	1	no	—
1307	C₂³	—	2	1	no	—
1308	C₂³	—	2	1	no	—
1309	C₂³	—	2	1	no	—
1310	C₂³	—	2	1	no	—
1311	C₂³	—	2	1	no	—
1312	C₂³	—	2	1	no	—
1313	C₂³	—	2	1	no	—
1314	C₂³	—	2	1	no	—
1315	C₂³	—	2	1	no	—
1316	C₂³	—	4	4	no	—
1317	C₂³	—	8	2	no	—
1318	C₂³	—	8	2	no	—
1319	C₂³	—	8	2	no	—
1320	C₂³	—	8	2	no	—
1321	C₂³	—	8	2	no	—
1322	C₂³	—	8	2	no	—
1323	C₂³	C₂×#41×C₅₃	1	2	yes	—
1324	C₂³	C₂×#41×C₅₃	1	2	yes	—
1325	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1326	Q₈	—	4	4	no	—
1327	D₄	—	4	4	no	—
1328	D₄	—	4	4	no	—
1329	D₄	—	4	4	no	—
1330	D₄	—	8	2	no	—
1331	D₄	—	8	2	no	—
1332	D₄	—	8	2	no	—
1333	D₄	—	8	2	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	2	1	no	—
1367	C₂×C₄	—	2	1	no	—
1368	C₂×C₄	—	2	1	no	—
1369	C₂×C₄	—	2	1	no	—
1370	C₂×C₄	—	2	1	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	—	4	4	no	—
1410	C₂×C₄	—	4	4	no	—
1411	C₂×C₄	—	4	4	no	—
1412	C₂×C₄	—	8	2	no	—
1413	C₂×C₄	—	8	2	no	—
1414	C₂×C₄	—	8	2	no	—
1415	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1416	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1417	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1418	C₂²	—	2	2	no	—
1419	C₂²	—	2	2	no	—
1420	C₂²	—	2	2	no	—
1421	C₂²	—	2	2	no	—
1422	C₂²	—	2	2	no	—
1423	C₂²	—	2	2	no	—
1424	C₂²	—	4	1	no	—
1425	C₂²	—	4	1	no	—
1426	C₂²	—	4	1	no	—
1427	C₂²	—	4	1	no	—
1428	C₂²	—	4	1	no	—
1429	C₂²	—	4	1	no	—
1430	C₂²	—	4	1	no	—
1431	C₂²	—	4	1	no	—
1432	C₂²	—	4	1	no	—
1433	C₂²	—	4	1	no	—
1434	C₂²	—	4	1	no	—
1435	C₂²	—	4	1	no	—
1436	C₂²	—	4	1	no	—
1437	C₂²	—	4	1	no	—
1438	C₂²	—	4	1	no	—
1439	C₂²	—	4	1	no	—
1440	C₂²	—	4	1	no	—
1441	C₂²	—	4	1	no	—
1442	C₂²	—	4	1	no	—
1443	C₂²	—	4	1	no	—
1444	C₂²	—	4	1	no	—
1445	C₂²	—	4	1	no	—
1446	C₂²	—	4	1	no	—
1447	C₂²	—	4	1	no	—
1448	C₂²	—	4	1	no	—
1449	C₂²	—	4	1	no	—
1450	C₂²	—	4	1	no	—
1451	C₂²	—	4	1	no	—
1452	C₂²	—	4	1	no	—
1453	C₂²	—	8	8	no	—
1454	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1455	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1456	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1457	C₂²	C₅₃×#585	1	1	yes	characteristic
1458	C₂²	C₅₃×#585	1	1	yes	characteristic
1459	C₂²	C₅₃×#585	1	1	yes	characteristic
1460	C₂²	C₅₃×#585	1	1	yes	characteristic
1461	C₄	—	2	2	no	—
1462	C₄	—	2	2	no	—
1463	C₄	—	2	2	no	—
1464	C₄	—	4	1	no	—
1465	C₄	—	4	1	no	—
1466	C₄	—	4	1	no	—
1467	C₄	—	4	1	no	—
1468	C₄	—	4	1	no	—
1469	C₄	—	4	1	no	—
1470	C₄	—	4	1	no	—
1471	C₄	—	4	1	no	—
1472	C₄	—	4	1	no	—
1473	C₄	—	4	1	no	—
1474	C₄	—	4	1	no	—
1475	C₄	—	4	1	no	—
1476	C₄	—	4	1	no	—
1477	C₄	—	4	1	no	—
1478	C₄	—	4	1	no	—
1479	C₄	—	4	1	no	—
1480	C₄	—	4	1	no	—
1481	C₄	—	4	1	no	—
1482	C₄	—	4	1	no	—
1483	C₄	—	4	1	no	—
1484	C₄	—	4	1	no	—
1485	C₄	—	4	1	no	—
1486	C₄	—	4	1	no	—
1487	C₂	—	4	2	no	—
1488	C₂	—	4	2	no	—
1489	C₂	—	8	1	no	—
1490	C₂	—	8	1	no	—
1491	C₂	—	8	1	no	—
1492	C₂	C₅₃×#3459	1	1	yes	characteristic
1493	C₂	C₅₃×#3513	1	1	yes	characteristic
1494	C₂	C₅₃×#3521	1	1	yes	characteristic
1495	C₂	C₅₃×#3540	1	1	yes	characteristic
1496	C₂	C₅₃×#3542	1	1	yes	characteristic
1497	C₂	C₅₃×#3551	1	1	yes	characteristic
1498	C₂	C₅₃×#3566	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₅₃×#2678	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×#2853	C₂	semidirect
2. C₅₃×#2852	C₂	semidirect
3. C₅₃×#2808	C₂	semidirect
4. C₅₃×#2797	C₂	semidirect
5. C₅₃×#2795	C₂	semidirect
6. C₅₃×#2780	C₂	semidirect
7. C₅₃×#2775	C₂	semidirect
8. C₅₃×#2757	C₂	semidirect
9. C₅₃×#2753	C₂	semidirect
10. C₅₃×#2747	C₂	semidirect
11. C₅₃×#2740	C₂	semidirect
12. C₅₃×#2735	C₂	semidirect
13. C₅₃×#2721	C₂	semidirect
14. C₅₃×#2707	C₂	semidirect
15. C₅₃×#2686	C₂	semidirect
16. C₅₃×#2685	C₂	semidirect
17. C₅₃×#2684	C₂	semidirect
19. C₅₃×#2636	C₂	semidirect
20. C₅₃×#2630	C₂	semidirect
21. C₅₃×#2531	C₂	semidirect
22. C₅₃×#2529	C₂	semidirect
23. C₅₃×#2517	C₂	semidirect
24. C₅₃×#2480	C₂	semidirect
25. C₅₃×#2469	C₂	semidirect
26. C₅₃×#2460	C₂	semidirect
27. C₅₃×#2458	C₂	semidirect
28. C₅₃×#2418	C₂	semidirect
29. C₅₃×#2326	C₂	semidirect
30. C₅₃×#2321	C₂	semidirect
31. C₄×#121×C₅₃	C₂	semidirect
34. C₂×#125×C₅₃	C₂²	semidirect
41. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
44. C₂×C₄×D₄×C₅₃	C₂²	semidirect
46. C₂²×C₄²×C₅₃	C₂²	semidirect
47. C₅₃×#400	C₂²	semidirect
48. C₅₃×#400	C₂²	semidirect
49. C₅₃×#400	C₂²	semidirect
53. C₅₃×#398	C₂²	semidirect
54. C₅₃×#398	C₂²	semidirect
55. C₅₃×#398	C₂²	semidirect
56. C₅₃×#398	C₂²	semidirect
67. C₅₃×#397	C₂²	semidirect
68. C₅₃×#397	C₂²	semidirect
74. C₅₃×#396	C₂²	semidirect
75. C₅₃×#396	C₂²	semidirect
76. C₅₃×#396	C₂²	semidirect
77. C₅₃×#395	C₂²	semidirect
88. C₅₃×#394	C₂²	semidirect
89. C₅₃×#394	C₂²	semidirect
92. C₅₃×#393	C₂²	semidirect
95. C₅₃×#391	C₂²	semidirect
102. C₅₃×#389	C₂²	semidirect
103. C₅₃×#389	C₂²	semidirect
104. C₅₃×#389	C₂²	semidirect
126. C₅₃×#388	C₂²	semidirect
127. C₅₃×#388	C₂²	semidirect
128. C₅₃×#388	C₂²	semidirect
129. C₅₃×#388	C₂²	semidirect
130. C₅₃×#388	C₂²	semidirect
131. C₅₃×#388	C₂²	semidirect
132. C₅₃×#388	C₂²	semidirect
133. C₅₃×#387	C₂²	semidirect
134. C₅₃×#387	C₂²	semidirect
135. C₅₃×#387	C₂²	semidirect
136. C₅₃×#387	C₂²	semidirect
137. C₅₃×#387	C₂²	semidirect
138. C₅₃×#387	C₂²	semidirect
139. C₅₃×#387	C₂²	semidirect
140. C₅₃×#387	C₂²	semidirect
141. C₅₃×#387	C₂²	semidirect
142. C₅₃×#387	C₂²	semidirect
143. C₅₃×#387	C₂²	semidirect
144. C₅₃×#387	C₂²	semidirect
145. C₅₃×#387	C₂²	semidirect
146. C₅₃×#387	C₂²	semidirect
147. C₅₃×#387	C₂²	semidirect
148. C₅₃×#387	C₂²	semidirect
158. C₅₃×#386	C₂²	semidirect
163. C₅₃×#385	C₂²	semidirect
164. C₅₃×#385	C₂²	semidirect
165. C₅₃×#385	C₂²	semidirect
166. C₅₃×#385	C₂²	semidirect
167. C₅₃×#385	C₂²	semidirect
168. C₅₃×#385	C₂²	semidirect
169. C₅₃×#384	C₂²	semidirect
170. C₅₃×#383	C₂²	semidirect
171. C₅₃×#382	C₂²	semidirect
172. C₅₃×#382	C₂²	semidirect
173. C₅₃×#381	C₂²	semidirect
176. C₅₃×#380	C₂²	semidirect
177. C₅₃×#380	C₂²	semidirect
182. C₄×C₄⋊C₄×C₅₃	C₂²	semidirect
185. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₅₃×#376	C₂²	semidirect
668. #36889	C₅₃	direct (N × H)
738. #2853	C₂×C₅₃	semidirect
739. #2852	C₂×C₅₃	semidirect
740. #2808	C₂×C₅₃	semidirect
741. #2797	C₂×C₅₃	semidirect
742. #2795	C₂×C₅₃	semidirect
743. #2780	C₂×C₅₃	semidirect
744. #2775	C₂×C₅₃	semidirect
745. #2757	C₂×C₅₃	semidirect
746. #2753	C₂×C₅₃	semidirect
747. #2747	C₂×C₅₃	semidirect
748. #2740	C₂×C₅₃	semidirect
749. #2735	C₂×C₅₃	semidirect
750. #2721	C₂×C₅₃	semidirect
751. #2707	C₂×C₅₃	semidirect
752. #2686	C₂×C₅₃	semidirect
753. #2685	C₂×C₅₃	semidirect
754. #2684	C₂×C₅₃	semidirect
756. #2636	C₂×C₅₃	semidirect
757. #2630	C₂×C₅₃	semidirect
758. #2531	C₂×C₅₃	semidirect
759. #2529	C₂×C₅₃	semidirect
760. #2517	C₂×C₅₃	semidirect
761. #2480	C₂×C₅₃	semidirect
762. #2469	C₂×C₅₃	semidirect
763. #2460	C₂×C₅₃	semidirect
764. #2458	C₂×C₅₃	semidirect
765. #2418	C₂×C₅₃	semidirect
766. #2326	C₂×C₅₃	semidirect
767. #2321	C₂×C₅₃	semidirect
768. C₄×#121	C₂×C₅₃	semidirect
783. C₂×#125	C₂²×C₅₃	semidirect
790. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
793. C₂×C₄×D₄	C₂²×C₅₃	semidirect
795. C₂²×C₄²	C₂²×C₅₃	semidirect
796. #400	C₂²×C₅₃	semidirect
797. #400	C₂²×C₅₃	semidirect
798. #400	C₂²×C₅₃	semidirect
802. #398	C₂²×C₅₃	semidirect
803. #398	C₂²×C₅₃	semidirect
804. #398	C₂²×C₅₃	semidirect
805. #398	C₂²×C₅₃	semidirect
816. #397	C₂²×C₅₃	semidirect
817. #397	C₂²×C₅₃	semidirect
823. #396	C₂²×C₅₃	semidirect
824. #396	C₂²×C₅₃	semidirect
825. #396	C₂²×C₅₃	semidirect
826. #395	C₂²×C₅₃	semidirect
837. #394	C₂²×C₅₃	semidirect
838. #394	C₂²×C₅₃	semidirect
841. #393	C₂²×C₅₃	semidirect
844. #391	C₂²×C₅₃	semidirect
851. #389	C₂²×C₅₃	semidirect
852. #389	C₂²×C₅₃	semidirect
853. #389	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. #387	C₂²×C₅₃	semidirect
883. #387	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
897. #387	C₂²×C₅₃	semidirect
907. #386	C₂²×C₅₃	semidirect
912. #385	C₂²×C₅₃	semidirect
913. #385	C₂²×C₅₃	semidirect
914. #385	C₂²×C₅₃	semidirect
915. #385	C₂²×C₅₃	semidirect
916. #385	C₂²×C₅₃	semidirect
917. #385	C₂²×C₅₃	semidirect
918. #384	C₂²×C₅₃	semidirect
919. #383	C₂²×C₅₃	semidirect
920. #382	C₂²×C₅₃	semidirect
921. #382	C₂²×C₅₃	semidirect
922. #381	C₂²×C₅₃	semidirect
925. #380	C₂²×C₅₃	semidirect
926. #380	C₂²×C₅₃	semidirect
931. C₄×C₄⋊C₄	C₂²×C₅₃	semidirect
934. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
935. #376	C₂²×C₅₃	semidirect
936. C₅₃	#36889	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×#2853	2
C₅₃×#2852	2
C₅₃×#2808	2
C₅₃×#2797	2
C₅₃×#2795	2
C₅₃×#2780	2
C₅₃×#2775	2
C₅₃×#2757	2
C₅₃×#2753	2
C₅₃×#2747	2
C₅₃×#2740	2
C₅₃×#2735	2
C₅₃×#2721	2
C₅₃×#2707	2
C₅₃×#2686	2
C₅₃×#2685	2
C₅₃×#2684	2
C₅₃×#2678	2
C₅₃×#2636	2
C₅₃×#2630	2
C₅₃×#2531	2
C₅₃×#2529	2
C₅₃×#2517	2
C₅₃×#2480	2
C₅₃×#2469	2
C₅₃×#2460	2
C₅₃×#2458	2
C₅₃×#2418	2
C₅₃×#2326	2
C₅₃×#2321	2
C₄×#121×C₅₃	2
#36889	53

Subgroups — C53×#36889 #27244401

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36889 #27244401