Subgroups — C₅₃×#36778 #27244290

Order 13568.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic
2	C₅₃×#2848	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2790	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2779	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2770	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2765	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2764	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2763	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2757	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2746	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2739	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2729	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2718	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2717	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2698	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2692	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2687	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2674	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2627	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2623	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2561	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2534	C₂	1	1	yes	maximal, characteristic
23	C₅₃×#2493	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2488	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2480	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2472	C₂	1	1	yes	maximal, characteristic
27	C₅₃×#2440	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2417	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2329	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#385	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
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×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
44	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
47	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
48	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×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×#400	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#397	C₂²	1	1	yes	characteristic
74	C₅₃×#397	C₂²	1	1	yes	characteristic
75	C₅₃×#397	C₂²	1	1	yes	characteristic
76	C₅₃×#397	C₂²	1	1	yes	characteristic
77	C₅₃×#397	C₂²	1	1	yes	characteristic
78	C₅₃×#397	C₂²	1	1	yes	characteristic
79	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#396	C₂²	1	1	yes	characteristic
83	C₅₃×#396	C₂²	1	1	yes	characteristic
84	C₅₃×#396	C₂²	1	1	yes	characteristic
85	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#395	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#394	C₂²	1	1	yes	characteristic
92	C₅₃×#394	C₂²	1	1	yes	characteristic
93	C₅₃×#394	C₂²	1	1	yes	characteristic
94	C₅₃×#394	C₂²	1	1	yes	characteristic
95	C₅₃×#393	C₂²	1	1	yes	characteristic
96	C₅₃×#393	C₂²	1	1	yes	characteristic
97	C₅₃×#393	C₂²	1	1	yes	characteristic
98	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#390	C₂²	1	1	yes	characteristic
104	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#389	C₂²	1	1	yes	characteristic, complemented
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, complemented
121	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#386	C₂²	1	1	yes	characteristic
134	C₅₃×#386	C₂²	1	1	yes	characteristic
135	C₅₃×#386	C₂²	1	1	yes	characteristic
136	C₅₃×#386	C₂²	1	1	yes	characteristic
137	C₅₃×#386	C₂²	1	1	yes	characteristic
138	C₅₃×#386	C₂²	1	1	yes	characteristic
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
141	C₅₃×#385	C₂²	1	1	yes	characteristic
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
155	C₅₃×#385	C₂²	1	1	yes	characteristic
156	C₅₃×#385	C₂²	1	1	yes	characteristic
157	C₅₃×#385	C₂²	1	1	yes	characteristic
158	C₅₃×#385	C₂²	1	1	yes	characteristic
159	C₅₃×#385	C₂²	1	1	yes	characteristic
160	C₅₃×#385	C₂²	1	1	yes	characteristic
161	C₅₃×#384	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#381	C₂²	1	1	yes	characteristic
167	C₅₃×#381	C₂²	1	1	yes	characteristic
168	C₅₃×#381	C₂²	1	1	yes	characteristic
169	C₅₃×#381	C₂²	1	1	yes	characteristic
170	C₅₃×#381	C₂²	1	1	yes	characteristic
171	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#380	C₂²	1	1	yes	characteristic
173	C₅₃×#380	C₂²	1	1	yes	characteristic
174	C₅₃×#380	C₂²	1	1	yes	characteristic
175	C₅₃×#380	C₂²	1	1	yes	characteristic
176	C₅₃×#380	C₂²	1	1	yes	characteristic
177	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
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×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
185	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
186	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
187	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
188	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
189	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
190	C₂²×Q₈×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	C₂³×C₄×C₅₃	—	4	2	no	—
195	C₂³×C₄×C₅₃	—	4	2	no	—
196	C₂³×C₄×C₅₃	—	4	2	no	—
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	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	C₄⋊Q₈×C₅₃	—	4	2	no	—
209	#126×C₅₃	—	4	2	no	—
210	#124×C₅₃	—	4	2	no	—
211	#123×C₅₃	—	4	2	no	—
212	#123×C₅₃	—	4	2	no	—
213	#123×C₅₃	—	4	2	no	—
214	C₂²⋊Q₈×C₅₃	—	2	4	no	—
215	C₂²⋊Q₈×C₅₃	—	4	2	no	—
216	C₂²⋊Q₈×C₅₃	—	4	2	no	—
217	C₂²⋊Q₈×C₅₃	—	4	2	no	—
218	C₂²⋊Q₈×C₅₃	—	4	2	no	—
219	C₂²⋊Q₈×C₅₃	—	4	2	no	—
220	#120×C₅₃	—	4	2	no	—
221	C₄×D₄×C₅₃	—	2	4	no	—
222	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
223	C₂×C₄⋊C₄×C₅₃	—	4	2	no	—
224	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
263	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
264	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×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	#95×C₅₃	C₂³	1	1	yes	characteristic
312	#95×C₅₃	C₂³	1	1	yes	characteristic
313	#95×C₅₃	C₂³	1	1	yes	characteristic
314	#95×C₅₃	C₂³	1	1	yes	characteristic
315	#95×C₅₃	C₂³	1	1	yes	characteristic
316	#95×C₅₃	C₂³	1	1	yes	characteristic
317	#95×C₅₃	C₂³	1	1	yes	characteristic
318	#95×C₅₃	C₂³	1	1	yes	characteristic
319	#95×C₅₃	C₂³	1	1	yes	characteristic
320	#95×C₅₃	C₂³	1	1	yes	characteristic
321	#95×C₅₃	C₂³	1	1	yes	characteristic
322	#95×C₅₃	C₂³	1	1	yes	characteristic
323	#95×C₅₃	C₂³	1	1	yes	characteristic
324	#95×C₅₃	C₂³	1	1	yes	characteristic
325	#95×C₅₃	C₂³	1	1	yes	characteristic
326	#95×C₅₃	C₂³	1	1	yes	characteristic
327	#95×C₅₃	C₂³	1	1	yes	characteristic
328	#95×C₅₃	C₂³	1	1	yes	characteristic
329	#95×C₅₃	C₂³	1	1	yes	characteristic
330	#95×C₅₃	C₂³	1	1	yes	characteristic
331	#95×C₅₃	C₂³	1	1	yes	characteristic
332	#95×C₅₃	C₂³	1	1	yes	characteristic
333	#95×C₅₃	C₂³	1	1	yes	characteristic
334	#95×C₅₃	C₂³	1	1	yes	characteristic
335	#95×C₅₃	C₂³	1	1	yes	characteristic
336	#95×C₅₃	C₂³	1	1	yes	characteristic
337	#95×C₅₃	C₂³	1	1	yes	characteristic
338	#95×C₅₃	C₂³	1	1	yes	characteristic
339	#95×C₅₃	C₂³	1	1	yes	characteristic
340	#95×C₅₃	C₂³	1	1	yes	characteristic
341	#95×C₅₃	C₂³	1	1	yes	characteristic
342	#95×C₅₃	C₂³	1	1	yes	characteristic
343	#95×C₅₃	C₂³	1	1	yes	characteristic
344	#95×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#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	C₂×Q₈×C₅₃	—	2	2	no	—
375	C₂×Q₈×C₅₃	—	2	2	no	—
376	C₂×Q₈×C₅₃	—	4	1	no	—
377	C₂×Q₈×C₅₃	—	4	1	no	—
378	C₂×Q₈×C₅₃	—	4	1	no	—
379	C₂×Q₈×C₅₃	—	4	1	no	—
380	C₂×Q₈×C₅₃	—	4	1	no	—
381	C₂×Q₈×C₅₃	—	4	1	no	—
382	C₂×Q₈×C₅₃	—	4	1	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	—	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	C₂²×C₄×C₅₃	—	2	2	no	—
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	—	2	2	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	—	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	—	4	1	no	—
412	C₂²×C₄×C₅₃	—	4	1	no	—
413	C₂²×C₄×C₅₃	—	4	1	no	—
414	C₂²×C₄×C₅₃	—	4	1	no	—
415	C₂²×C₄×C₅₃	—	4	1	no	—
416	C₂²×C₄×C₅₃	—	4	1	no	—
417	C₂²×C₄×C₅₃	—	4	1	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	16	no	—
425	C₂²×C₄×C₅₃	#41	1	4	yes	—
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	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	C₄⋊C₄×C₅₃	—	2	2	no	—
454	C₄⋊C₄×C₅₃	—	2	2	no	—
455	C₄⋊C₄×C₅₃	—	2	2	no	—
456	C₄⋊C₄×C₅₃	—	2	2	no	—
457	C₄⋊C₄×C₅₃	—	2	2	no	—
458	C₄⋊C₄×C₅₃	—	2	2	no	—
459	C₄⋊C₄×C₅₃	—	2	2	no	—
460	C₄⋊C₄×C₅₃	—	2	2	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	C₄⋊C₄×C₅₃	—	4	1	no	—
470	C₄⋊C₄×C₅₃	—	4	1	no	—
471	C₄⋊C₄×C₅₃	—	4	1	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	C₄⋊C₄×C₅₃	—	4	1	no	—
489	C₄⋊C₄×C₅₃	—	4	1	no	—
490	C₄⋊C₄×C₅₃	—	4	1	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	C₄²×C₅₃	—	2	2	no	—
532	C₄²×C₅₃	—	4	1	no	—
533	C₄²×C₅₃	—	4	1	no	—
534	C₄²×C₅₃	—	4	1	no	—
535	C₄²×C₅₃	—	4	1	no	—
536	C₄²×C₅₃	—	4	1	no	—
537	C₄²×C₅₃	—	4	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	8	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	—	4	4	no	—
563	C₂³×C₅₃	—	4	4	no	—
564	C₂³×C₅₃	—	4	4	no	—
565	C₂³×C₅₃	—	4	4	no	—
566	C₂³×C₅₃	—	4	4	no	—
567	C₂³×C₅₃	—	4	4	no	—
568	C₂³×C₅₃	C₂×#41	1	2	yes	—
569	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
570	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
571	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
572	C₂³×C₅₃	2₋¹⁺⁴	1	2	yes	—
573	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
574	Q₈×C₅₃	—	8	2	no	—
575	Q₈×C₅₃	—	8	2	no	—
576	Q₈×C₅₃	—	8	2	no	—
577	D₄×C₅₃	—	4	4	no	—
578	D₄×C₅₃	—	8	2	no	—
579	D₄×C₅₃	—	8	2	no	—
580	C₂×C₄×C₅₃	—	2	1	no	—
581	C₂×C₄×C₅₃	—	2	1	no	—
582	C₂×C₄×C₅₃	—	2	1	no	—
583	C₂×C₄×C₅₃	—	2	1	no	—
584	C₂×C₄×C₅₃	—	2	1	no	—
585	C₂×C₄×C₅₃	—	2	1	no	—
586	C₂×C₄×C₅₃	—	2	1	no	—
587	C₂×C₄×C₅₃	—	2	1	no	—
588	C₂×C₄×C₅₃	—	2	1	no	—
589	C₂×C₄×C₅₃	—	2	1	no	—
590	C₂×C₄×C₅₃	—	2	1	no	—
591	C₂×C₄×C₅₃	—	2	1	no	—
592	C₂×C₄×C₅₃	—	2	1	no	—
593	C₂×C₄×C₅₃	—	2	1	no	—
594	C₂×C₄×C₅₃	—	2	1	no	—
595	C₂×C₄×C₅₃	—	2	1	no	—
596	C₂×C₄×C₅₃	—	2	1	no	—
597	C₂×C₄×C₅₃	—	2	1	no	—
598	C₂×C₄×C₅₃	—	2	1	no	—
599	C₂×C₄×C₅₃	—	2	1	no	—
600	C₂×C₄×C₅₃	—	2	1	no	—
601	C₂×C₄×C₅₃	—	2	1	no	—
602	C₂×C₄×C₅₃	—	2	1	no	—
603	C₂×C₄×C₅₃	—	2	1	no	—
604	C₂×C₄×C₅₃	—	2	1	no	—
605	C₂×C₄×C₅₃	—	2	1	no	—
606	C₂×C₄×C₅₃	—	2	1	no	—
607	C₂×C₄×C₅₃	—	2	1	no	—
608	C₂×C₄×C₅₃	—	2	1	no	—
609	C₂×C₄×C₅₃	—	2	1	no	—
610	C₂×C₄×C₅₃	—	2	1	no	—
611	C₂×C₄×C₅₃	—	2	1	no	—
612	C₂×C₄×C₅₃	—	2	1	no	—
613	C₂×C₄×C₅₃	—	2	1	no	—
614	C₂×C₄×C₅₃	—	2	1	no	—
615	C₂×C₄×C₅₃	—	2	1	no	—
616	C₂×C₄×C₅₃	—	2	1	no	—
617	C₂×C₄×C₅₃	—	2	1	no	—
618	C₂×C₄×C₅₃	—	2	1	no	—
619	C₂×C₄×C₅₃	—	2	1	no	—
620	C₂×C₄×C₅₃	—	2	1	no	—
621	C₂×C₄×C₅₃	—	2	1	no	—
622	C₂×C₄×C₅₃	—	2	1	no	—
623	C₂×C₄×C₅₃	—	2	1	no	—
624	C₂×C₄×C₅₃	—	2	1	no	—
625	C₂×C₄×C₅₃	—	2	1	no	—
626	C₂×C₄×C₅₃	—	2	1	no	—
627	C₂×C₄×C₅₃	—	2	1	no	—
628	C₂×C₄×C₅₃	—	2	1	no	—
629	C₂×C₄×C₅₃	—	2	1	no	—
630	C₂×C₄×C₅₃	—	2	1	no	—
631	C₂×C₄×C₅₃	—	2	1	no	—
632	C₂×C₄×C₅₃	—	2	1	no	—
633	C₂×C₄×C₅₃	—	2	1	no	—
634	C₂×C₄×C₅₃	—	2	1	no	—
635	C₂×C₄×C₅₃	—	2	1	no	—
636	C₂×C₄×C₅₃	—	2	1	no	—
637	C₂×C₄×C₅₃	—	2	1	no	—
638	C₂×C₄×C₅₃	—	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	—	4	4	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	—	4	4	no	—
663	C₂×C₄×C₅₃	—	4	4	no	—
664	C₂×C₄×C₅₃	—	4	4	no	—
665	C₂×C₄×C₅₃	—	4	4	no	—
666	C₂×C₄×C₅₃	—	8	2	no	—
667	C₂×C₄×C₅₃	—	8	2	no	—
668	C₂×C₄×C₅₃	—	8	2	no	—
669	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
670	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
671	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
672	#36778	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
673	C₂²×C₅₃	—	2	2	no	—
674	C₂²×C₅₃	—	2	2	no	—
675	C₂²×C₅₃	—	2	2	no	—
676	C₂²×C₅₃	—	2	2	no	—
677	C₂²×C₅₃	—	2	2	no	—
678	C₂²×C₅₃	—	2	2	no	—
679	C₂²×C₅₃	—	2	2	no	—
680	C₂²×C₅₃	—	2	2	no	—
681	C₂²×C₅₃	—	2	2	no	—
682	C₂²×C₅₃	—	2	2	no	—
683	C₂²×C₅₃	—	2	2	no	—
684	C₂²×C₅₃	—	2	2	no	—
685	C₂²×C₅₃	—	4	16	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	#542	1	4	yes	—
702	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
703	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
704	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
705	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
707	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
708	C₂²×C₅₃	#585	1	1	yes	characteristic
709	C₄×C₅₃	—	2	2	no	—
710	C₄×C₅₃	—	2	2	no	—
711	C₄×C₅₃	—	2	2	no	—
712	C₄×C₅₃	—	4	1	no	—
713	C₄×C₅₃	—	4	1	no	—
714	C₄×C₅₃	—	4	1	no	—
715	C₄×C₅₃	—	4	1	no	—
716	C₄×C₅₃	—	4	1	no	—
717	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	#2849	C₂×C₅₃	1	1	yes	characteristic
737	#2848	C₂×C₅₃	1	1	yes	characteristic, complemented
738	#2790	C₂×C₅₃	1	1	yes	characteristic, complemented
739	#2779	C₂×C₅₃	1	1	yes	characteristic, complemented
740	#2770	C₂×C₅₃	1	1	yes	characteristic, complemented
741	#2765	C₂×C₅₃	1	1	yes	characteristic, complemented
742	#2764	C₂×C₅₃	1	1	yes	characteristic, complemented
743	#2763	C₂×C₅₃	1	1	yes	characteristic, complemented
744	#2757	C₂×C₅₃	1	1	yes	characteristic, complemented
745	#2746	C₂×C₅₃	1	1	yes	characteristic, complemented
746	#2739	C₂×C₅₃	1	1	yes	characteristic, complemented
747	#2729	C₂×C₅₃	1	1	yes	characteristic, complemented
748	#2718	C₂×C₅₃	1	1	yes	characteristic, complemented
749	#2717	C₂×C₅₃	1	1	yes	characteristic, complemented
750	#2698	C₂×C₅₃	1	1	yes	characteristic, complemented
751	#2692	C₂×C₅₃	1	1	yes	characteristic, complemented
752	#2687	C₂×C₅₃	1	1	yes	characteristic, complemented
753	#2674	C₂×C₅₃	1	1	yes	characteristic, complemented
754	#2627	C₂×C₅₃	1	1	yes	characteristic, complemented
755	#2623	C₂×C₅₃	1	1	yes	characteristic, complemented
756	#2561	C₂×C₅₃	1	1	yes	characteristic, complemented
757	#2534	C₂×C₅₃	1	1	yes	characteristic
758	#2493	C₂×C₅₃	1	1	yes	characteristic, complemented
759	#2488	C₂×C₅₃	1	1	yes	characteristic, complemented
760	#2480	C₂×C₅₃	1	1	yes	characteristic, complemented
761	#2472	C₂×C₅₃	1	1	yes	characteristic
762	#2440	C₂×C₅₃	1	1	yes	characteristic, complemented
763	#2417	C₂×C₅₃	1	1	yes	characteristic, complemented
764	#2329	C₂×C₅₃	1	1	yes	characteristic, complemented
765	#2318	C₂×C₅₃	1	1	yes	characteristic, complemented
766	C₂×#385	C₂×C₅₃	1	1	yes	characteristic, complemented
767	C₂×C₅₃	—	2	4	no	—
768	C₂×C₅₃	—	4	2	no	—
769	C₂×C₅₃	—	4	2	no	—
770	C₂×C₅₃	—	8	1	no	—
771	C₂×C₅₃	C₂×#542	1	1	yes	characteristic
772	C₂×C₅₃	#3492	1	1	yes	characteristic
773	C₂×C₅₃	#3505	1	1	yes	characteristic
774	C₂×C₅₃	#3532	1	1	yes	characteristic
775	C₂×C₅₃	#3535	1	1	yes	characteristic
776	C₂×C₅₃	#3535	1	1	yes	characteristic
777	C₂×C₅₃	#3538	1	1	yes	characteristic
778	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
779	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
780	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
781	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
782	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
783	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
784	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
785	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
786	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
787	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
788	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
789	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
790	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
791	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
792	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
793	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
794	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
795	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
796	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
797	#401	C₂²×C₅₃	1	1	yes	characteristic, complemented
798	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
799	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
800	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
801	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
802	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
803	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
804	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
805	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
806	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
807	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
808	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
809	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
810	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
811	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
812	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
813	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
814	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
815	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
816	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
817	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
818	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
819	#397	C₂²×C₅₃	1	1	yes	characteristic
820	#397	C₂²×C₅₃	1	1	yes	characteristic
821	#397	C₂²×C₅₃	1	1	yes	characteristic
822	#397	C₂²×C₅₃	1	1	yes	characteristic
823	#397	C₂²×C₅₃	1	1	yes	characteristic
824	#397	C₂²×C₅₃	1	1	yes	characteristic
825	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
826	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
827	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
828	#396	C₂²×C₅₃	1	1	yes	characteristic
829	#396	C₂²×C₅₃	1	1	yes	characteristic
830	#396	C₂²×C₅₃	1	1	yes	characteristic
831	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
832	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
833	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
834	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
835	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
836	#395	C₂²×C₅₃	1	1	yes	characteristic, complemented
837	#394	C₂²×C₅₃	1	1	yes	characteristic
838	#394	C₂²×C₅₃	1	1	yes	characteristic
839	#394	C₂²×C₅₃	1	1	yes	characteristic
840	#394	C₂²×C₅₃	1	1	yes	characteristic
841	#393	C₂²×C₅₃	1	1	yes	characteristic
842	#393	C₂²×C₅₃	1	1	yes	characteristic
843	#393	C₂²×C₅₃	1	1	yes	characteristic
844	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
845	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
847	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
848	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
849	#390	C₂²×C₅₃	1	1	yes	characteristic
850	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
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	#389	C₂²×C₅₃	1	1	yes	characteristic, complemented
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, complemented
867	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
869	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
870	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
872	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
873	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
874	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
875	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
876	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
879	#386	C₂²×C₅₃	1	1	yes	characteristic
880	#386	C₂²×C₅₃	1	1	yes	characteristic
881	#386	C₂²×C₅₃	1	1	yes	characteristic
882	#386	C₂²×C₅₃	1	1	yes	characteristic
883	#386	C₂²×C₅₃	1	1	yes	characteristic
884	#386	C₂²×C₅₃	1	1	yes	characteristic
885	#386	C₂²×C₅₃	1	1	yes	characteristic
886	#386	C₂²×C₅₃	1	1	yes	characteristic
887	#385	C₂²×C₅₃	1	1	yes	characteristic
888	#385	C₂²×C₅₃	1	1	yes	characteristic
889	#385	C₂²×C₅₃	1	1	yes	characteristic
890	#385	C₂²×C₅₃	1	1	yes	characteristic
891	#385	C₂²×C₅₃	1	1	yes	characteristic
892	#385	C₂²×C₅₃	1	1	yes	characteristic
893	#385	C₂²×C₅₃	1	1	yes	characteristic
894	#385	C₂²×C₅₃	1	1	yes	characteristic
895	#385	C₂²×C₅₃	1	1	yes	characteristic
896	#385	C₂²×C₅₃	1	1	yes	characteristic
897	#385	C₂²×C₅₃	1	1	yes	characteristic
898	#385	C₂²×C₅₃	1	1	yes	characteristic
899	#385	C₂²×C₅₃	1	1	yes	characteristic
900	#385	C₂²×C₅₃	1	1	yes	characteristic
901	#385	C₂²×C₅₃	1	1	yes	characteristic
902	#385	C₂²×C₅₃	1	1	yes	characteristic
903	#385	C₂²×C₅₃	1	1	yes	characteristic
904	#385	C₂²×C₅₃	1	1	yes	characteristic
905	#385	C₂²×C₅₃	1	1	yes	characteristic
906	#385	C₂²×C₅₃	1	1	yes	characteristic
907	#384	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#381	C₂²×C₅₃	1	1	yes	characteristic
913	#381	C₂²×C₅₃	1	1	yes	characteristic
914	#381	C₂²×C₅₃	1	1	yes	characteristic
915	#381	C₂²×C₅₃	1	1	yes	characteristic
916	#381	C₂²×C₅₃	1	1	yes	characteristic
917	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#380	C₂²×C₅₃	1	1	yes	characteristic
919	#380	C₂²×C₅₃	1	1	yes	characteristic
920	#380	C₂²×C₅₃	1	1	yes	characteristic
921	#380	C₂²×C₅₃	1	1	yes	characteristic
922	#380	C₂²×C₅₃	1	1	yes	characteristic
923	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#379	C₂²×C₅₃	1	1	yes	characteristic
926	#379	C₂²×C₅₃	1	1	yes	characteristic
927	#379	C₂²×C₅₃	1	1	yes	characteristic
928	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
929	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
930	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
931	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
932	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
933	C₅₃	#36778	1	1	yes	characteristic, direct product factor, Sylow
934	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
935	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
936	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
937	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
938	C₂²×D₄	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	C₂³×C₄	—	4	2	no	—
942	C₂³×C₄	—	4	2	no	—
943	C₂³×C₄	—	4	2	no	—
944	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
945	C₂³×C₄	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	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
953	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
954	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
955	C₄⋊Q₈	—	4	2	no	—
956	#126	—	4	2	no	—
957	#124	—	4	2	no	—
958	#123	—	4	2	no	—
959	#123	—	4	2	no	—
960	#123	—	4	2	no	—
961	C₂²⋊Q₈	—	2	4	no	—
962	C₂²⋊Q₈	—	4	2	no	—
963	C₂²⋊Q₈	—	4	2	no	—
964	C₂²⋊Q₈	—	4	2	no	—
965	C₂²⋊Q₈	—	4	2	no	—
966	C₂²⋊Q₈	—	4	2	no	—
967	#120	—	4	2	no	—
968	C₄×D₄	—	2	4	no	—
969	C₂×C₄⋊C₄	—	4	2	no	—
970	C₂×C₄⋊C₄	—	4	2	no	—
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×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×C₂²⋊C₄	—	2	4	no	—
1010	C₂×C₂²⋊C₄	—	4	2	no	—
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×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
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	#95	C₂³×C₅₃	1	1	yes	characteristic
1059	#95	C₂³×C₅₃	1	1	yes	characteristic
1060	#95	C₂³×C₅₃	1	1	yes	characteristic
1061	#95	C₂³×C₅₃	1	1	yes	characteristic
1062	#95	C₂³×C₅₃	1	1	yes	characteristic
1063	#95	C₂³×C₅₃	1	1	yes	characteristic
1064	#95	C₂³×C₅₃	1	1	yes	characteristic
1065	#95	C₂³×C₅₃	1	1	yes	characteristic
1066	#95	C₂³×C₅₃	1	1	yes	characteristic
1067	#95	C₂³×C₅₃	1	1	yes	characteristic
1068	#95	C₂³×C₅₃	1	1	yes	characteristic
1069	#95	C₂³×C₅₃	1	1	yes	characteristic
1070	#95	C₂³×C₅₃	1	1	yes	characteristic
1071	#95	C₂³×C₅₃	1	1	yes	characteristic
1072	#95	C₂³×C₅₃	1	1	yes	characteristic
1073	#95	C₂³×C₅₃	1	1	yes	characteristic
1074	#95	C₂³×C₅₃	1	1	yes	characteristic
1075	#95	C₂³×C₅₃	1	1	yes	characteristic
1076	#95	C₂³×C₅₃	1	1	yes	characteristic
1077	#95	C₂³×C₅₃	1	1	yes	characteristic
1078	#95	C₂³×C₅₃	1	1	yes	characteristic
1079	#95	C₂³×C₅₃	1	1	yes	characteristic
1080	#95	C₂³×C₅₃	1	1	yes	characteristic
1081	#95	C₂³×C₅₃	1	1	yes	characteristic
1082	#95	C₂³×C₅₃	1	1	yes	characteristic
1083	#95	C₂³×C₅₃	1	1	yes	characteristic
1084	#95	C₂³×C₅₃	1	1	yes	characteristic
1085	#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	#95	C₂³×C₅₃	1	1	yes	characteristic
1108	#95	C₂³×C₅₃	1	1	yes	characteristic
1109	#95	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂⁴	—	2	2	no	—
1111	C₂⁴	—	2	2	no	—
1112	C₂⁴	—	2	2	no	—
1113	C₂⁴	—	2	2	no	—
1114	C₂⁴	—	2	2	no	—
1115	C₂⁴	—	4	1	no	—
1116	C₂⁴	—	4	1	no	—
1117	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1118	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1119	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1120	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1121	C₂×Q₈	—	2	2	no	—
1122	C₂×Q₈	—	2	2	no	—
1123	C₂×Q₈	—	4	1	no	—
1124	C₂×Q₈	—	4	1	no	—
1125	C₂×Q₈	—	4	1	no	—
1126	C₂×Q₈	—	4	1	no	—
1127	C₂×Q₈	—	4	1	no	—
1128	C₂×Q₈	—	4	1	no	—
1129	C₂×Q₈	—	4	1	no	—
1130	C₂×D₄	—	2	2	no	—
1131	C₂×D₄	—	2	2	no	—
1132	C₂×D₄	—	2	2	no	—
1133	C₂×D₄	—	2	2	no	—
1134	C₂×D₄	—	2	2	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	C₂²×C₄	—	2	2	no	—
1140	C₂²×C₄	—	2	2	no	—
1141	C₂²×C₄	—	2	2	no	—
1142	C₂²×C₄	—	2	2	no	—
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	—	2	2	no	—
1149	C₂²×C₄	—	2	2	no	—
1150	C₂²×C₄	—	2	2	no	—
1151	C₂²×C₄	—	2	2	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	—	4	1	no	—
1162	C₂²×C₄	—	4	1	no	—
1163	C₂²×C₄	—	4	1	no	—
1164	C₂²×C₄	—	4	1	no	—
1165	C₂²×C₄	—	4	1	no	—
1166	C₂²×C₄	—	4	1	no	—
1167	C₂²×C₄	—	4	1	no	—
1168	C₂²×C₄	—	4	1	no	—
1169	C₂²×C₄	—	4	1	no	—
1170	C₂²×C₄	—	4	1	no	—
1171	C₂²×C₄	—	4	16	no	—
1172	C₂²×C₄	#41×C₅₃	1	4	yes	—
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	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1188	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1189	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1190	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1191	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1192	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1193	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1194	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1195	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1196	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1197	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1198	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1199	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1200	C₄⋊C₄	—	2	2	no	—
1201	C₄⋊C₄	—	2	2	no	—
1202	C₄⋊C₄	—	2	2	no	—
1203	C₄⋊C₄	—	2	2	no	—
1204	C₄⋊C₄	—	2	2	no	—
1205	C₄⋊C₄	—	2	2	no	—
1206	C₄⋊C₄	—	2	2	no	—
1207	C₄⋊C₄	—	2	2	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	C₄⋊C₄	—	4	1	no	—
1220	C₄⋊C₄	—	4	1	no	—
1221	C₄⋊C₄	—	4	1	no	—
1222	C₄⋊C₄	—	4	1	no	—
1223	C₄⋊C₄	—	4	1	no	—
1224	C₄⋊C₄	—	4	1	no	—
1225	C₄⋊C₄	—	4	1	no	—
1226	C₄⋊C₄	—	4	1	no	—
1227	C₄⋊C₄	—	4	1	no	—
1228	C₄⋊C₄	—	4	1	no	—
1229	C₄⋊C₄	—	4	1	no	—
1230	C₄⋊C₄	—	4	1	no	—
1231	C₄⋊C₄	—	4	1	no	—
1232	C₄⋊C₄	—	4	1	no	—
1233	C₄⋊C₄	—	4	1	no	—
1234	C₄⋊C₄	—	4	1	no	—
1235	C₄⋊C₄	—	4	1	no	—
1236	C₄⋊C₄	—	4	1	no	—
1237	C₄⋊C₄	—	4	1	no	—
1238	C₂²⋊C₄	—	2	2	no	—
1239	C₂²⋊C₄	—	2	2	no	—
1240	C₂²⋊C₄	—	2	2	no	—
1241	C₂²⋊C₄	—	2	2	no	—
1242	C₂²⋊C₄	—	2	2	no	—
1243	C₂²⋊C₄	—	2	2	no	—
1244	C₂²⋊C₄	—	2	2	no	—
1245	C₂²⋊C₄	—	2	2	no	—
1246	C₂²⋊C₄	—	2	2	no	—
1247	C₂²⋊C₄	—	2	2	no	—
1248	C₂²⋊C₄	—	2	2	no	—
1249	C₂²⋊C₄	—	2	2	no	—
1250	C₂²⋊C₄	—	2	2	no	—
1251	C₂²⋊C₄	—	2	2	no	—
1252	C₂²⋊C₄	—	2	2	no	—
1253	C₂²⋊C₄	—	2	2	no	—
1254	C₂²⋊C₄	—	2	2	no	—
1255	C₂²⋊C₄	—	2	2	no	—
1256	C₂²⋊C₄	—	2	2	no	—
1257	C₂²⋊C₄	—	2	2	no	—
1258	C₂²⋊C₄	—	2	2	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	C₂²⋊C₄	—	4	1	no	—
1272	C₂²⋊C₄	—	4	1	no	—
1273	C₂²⋊C₄	—	4	1	no	—
1274	C₂²⋊C₄	—	4	1	no	—
1275	C₂²⋊C₄	—	4	1	no	—
1276	C₂²⋊C₄	—	4	1	no	—
1277	C₂²⋊C₄	—	4	1	no	—
1278	C₄²	—	2	2	no	—
1279	C₄²	—	4	1	no	—
1280	C₄²	—	4	1	no	—
1281	C₄²	—	4	1	no	—
1282	C₄²	—	4	1	no	—
1283	C₄²	—	4	1	no	—
1284	C₄²	—	4	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	8	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	—	4	4	no	—
1310	C₂³	—	4	4	no	—
1311	C₂³	—	4	4	no	—
1312	C₂³	—	4	4	no	—
1313	C₂³	—	4	4	no	—
1314	C₂³	—	4	4	no	—
1315	C₂³	C₂×#41×C₅₃	1	2	yes	—
1316	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1317	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1318	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1319	C₂³	2₋¹⁺⁴×C₅₃	1	2	yes	—
1320	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1321	Q₈	—	8	2	no	—
1322	Q₈	—	8	2	no	—
1323	Q₈	—	8	2	no	—
1324	D₄	—	4	4	no	—
1325	D₄	—	8	2	no	—
1326	D₄	—	8	2	no	—
1327	C₂×C₄	—	2	1	no	—
1328	C₂×C₄	—	2	1	no	—
1329	C₂×C₄	—	2	1	no	—
1330	C₂×C₄	—	2	1	no	—
1331	C₂×C₄	—	2	1	no	—
1332	C₂×C₄	—	2	1	no	—
1333	C₂×C₄	—	2	1	no	—
1334	C₂×C₄	—	2	1	no	—
1335	C₂×C₄	—	2	1	no	—
1336	C₂×C₄	—	2	1	no	—
1337	C₂×C₄	—	2	1	no	—
1338	C₂×C₄	—	2	1	no	—
1339	C₂×C₄	—	2	1	no	—
1340	C₂×C₄	—	2	1	no	—
1341	C₂×C₄	—	2	1	no	—
1342	C₂×C₄	—	2	1	no	—
1343	C₂×C₄	—	2	1	no	—
1344	C₂×C₄	—	2	1	no	—
1345	C₂×C₄	—	2	1	no	—
1346	C₂×C₄	—	2	1	no	—
1347	C₂×C₄	—	2	1	no	—
1348	C₂×C₄	—	2	1	no	—
1349	C₂×C₄	—	2	1	no	—
1350	C₂×C₄	—	2	1	no	—
1351	C₂×C₄	—	2	1	no	—
1352	C₂×C₄	—	2	1	no	—
1353	C₂×C₄	—	2	1	no	—
1354	C₂×C₄	—	2	1	no	—
1355	C₂×C₄	—	2	1	no	—
1356	C₂×C₄	—	2	1	no	—
1357	C₂×C₄	—	2	1	no	—
1358	C₂×C₄	—	2	1	no	—
1359	C₂×C₄	—	2	1	no	—
1360	C₂×C₄	—	2	1	no	—
1361	C₂×C₄	—	2	1	no	—
1362	C₂×C₄	—	2	1	no	—
1363	C₂×C₄	—	2	1	no	—
1364	C₂×C₄	—	2	1	no	—
1365	C₂×C₄	—	2	1	no	—
1366	C₂×C₄	—	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	—	4	4	no	—
1406	C₂×C₄	—	4	4	no	—
1407	C₂×C₄	—	4	4	no	—
1408	C₂×C₄	—	4	4	no	—
1409	C₂×C₄	—	4	4	no	—
1410	C₂×C₄	—	4	4	no	—
1411	C₂×C₄	—	4	4	no	—
1412	C₂×C₄	—	4	4	no	—
1413	C₂×C₄	—	8	2	no	—
1414	C₂×C₄	—	8	2	no	—
1415	C₂×C₄	—	8	2	no	—
1416	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1417	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1418	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
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	—	2	2	no	—
1425	C₂²	—	2	2	no	—
1426	C₂²	—	2	2	no	—
1427	C₂²	—	2	2	no	—
1428	C₂²	—	2	2	no	—
1429	C₂²	—	2	2	no	—
1430	C₂²	—	2	2	no	—
1431	C₂²	—	4	16	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	C₅₃×#542	1	4	yes	—
1448	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1449	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1450	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1451	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1452	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1453	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1454	C₂²	C₅₃×#585	1	1	yes	characteristic
1455	C₄	—	2	2	no	—
1456	C₄	—	2	2	no	—
1457	C₄	—	2	2	no	—
1458	C₄	—	4	1	no	—
1459	C₄	—	4	1	no	—
1460	C₄	—	4	1	no	—
1461	C₄	—	4	1	no	—
1462	C₄	—	4	1	no	—
1463	C₄	—	4	1	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	C₂	—	2	4	no	—
1483	C₂	—	4	2	no	—
1484	C₂	—	4	2	no	—
1485	C₂	—	8	1	no	—
1486	C₂	C₂×C₅₃×#542	1	1	yes	characteristic
1487	C₂	C₅₃×#3492	1	1	yes	characteristic
1488	C₂	C₅₃×#3505	1	1	yes	characteristic
1489	C₂	C₅₃×#3532	1	1	yes	characteristic
1490	C₂	C₅₃×#3535	1	1	yes	characteristic
1491	C₂	C₅₃×#3535	1	1	yes	characteristic
1492	C₂	C₅₃×#3538	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
prime radical	C₂×#120×C₅₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅₃×#2848	C₂	semidirect
3. C₅₃×#2790	C₂	semidirect
4. C₅₃×#2779	C₂	semidirect
5. C₅₃×#2770	C₂	semidirect
6. C₅₃×#2765	C₂	semidirect
7. C₅₃×#2764	C₂	semidirect
8. C₅₃×#2763	C₂	semidirect
9. C₅₃×#2757	C₂	semidirect
10. C₅₃×#2746	C₂	semidirect
11. C₅₃×#2739	C₂	semidirect
12. C₅₃×#2729	C₂	semidirect
13. C₅₃×#2718	C₂	semidirect
14. C₅₃×#2717	C₂	semidirect
15. C₅₃×#2698	C₂	semidirect
16. C₅₃×#2692	C₂	semidirect
17. C₅₃×#2687	C₂	semidirect
18. C₅₃×#2674	C₂	semidirect
19. C₅₃×#2627	C₂	semidirect
20. C₅₃×#2623	C₂	semidirect
21. C₅₃×#2561	C₂	semidirect
23. C₅₃×#2493	C₂	semidirect
24. C₅₃×#2488	C₂	semidirect
25. C₅₃×#2480	C₂	semidirect
27. C₅₃×#2440	C₂	semidirect
28. C₅₃×#2417	C₂	semidirect
29. C₅₃×#2329	C₂	semidirect
30. C₅₃×#2318	C₂	semidirect
31. C₂×C₅₃×#385	C₂	semidirect
33. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₅₃	C₂²	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
58. C₅₃×#400	C₂²	semidirect
59. C₅₃×#400	C₂²	semidirect
60. C₅₃×#400	C₂²	semidirect
61. C₅₃×#399	C₂²	semidirect
62. C₅₃×#399	C₂²	semidirect
63. C₅₃×#398	C₂²	semidirect
64. C₅₃×#398	C₂²	semidirect
65. C₅₃×#398	C₂²	semidirect
66. C₅₃×#398	C₂²	semidirect
67. C₅₃×#398	C₂²	semidirect
68. C₅₃×#398	C₂²	semidirect
69. C₅₃×#398	C₂²	semidirect
70. C₅₃×#398	C₂²	semidirect
71. C₅₃×#398	C₂²	semidirect
72. C₅₃×#398	C₂²	semidirect
79. C₅₃×#397	C₂²	semidirect
80. C₅₃×#397	C₂²	semidirect
81. C₅₃×#397	C₂²	semidirect
85. C₅₃×#396	C₂²	semidirect
86. C₅₃×#396	C₂²	semidirect
87. C₅₃×#395	C₂²	semidirect
88. C₅₃×#395	C₂²	semidirect
89. C₅₃×#395	C₂²	semidirect
90. C₅₃×#395	C₂²	semidirect
98. C₅₃×#393	C₂²	semidirect
99. C₅₃×#391	C₂²	semidirect
100. C₅₃×#391	C₂²	semidirect
101. C₅₃×#391	C₂²	semidirect
102. C₅₃×#391	C₂²	semidirect
104. C₅₃×#389	C₂²	semidirect
105. C₅₃×#389	C₂²	semidirect
106. C₅₃×#389	C₂²	semidirect
107. C₅₃×#389	C₂²	semidirect
108. C₅₃×#389	C₂²	semidirect
120. C₅₃×#388	C₂²	semidirect
121. C₅₃×#388	C₂²	semidirect
122. C₅₃×#388	C₂²	semidirect
123. C₅₃×#388	C₂²	semidirect
124. C₅₃×#387	C₂²	semidirect
125. C₅₃×#387	C₂²	semidirect
126. C₅₃×#387	C₂²	semidirect
127. C₅₃×#387	C₂²	semidirect
128. C₅₃×#387	C₂²	semidirect
129. C₅₃×#387	C₂²	semidirect
130. C₅₃×#387	C₂²	semidirect
131. C₅₃×#387	C₂²	semidirect
132. C₅₃×#387	C₂²	semidirect
161. C₅₃×#384	C₂²	semidirect
162. C₅₃×#383	C₂²	semidirect
163. C₅₃×#383	C₂²	semidirect
164. C₅₃×#382	C₂²	semidirect
165. C₅₃×#382	C₂²	semidirect
171. C₅₃×#381	C₂²	semidirect
177. C₅₃×#380	C₂²	semidirect
178. C₅₃×#380	C₂²	semidirect
672. #36778	C₅₃	direct (N × H)
737. #2848	C₂×C₅₃	semidirect
738. #2790	C₂×C₅₃	semidirect
739. #2779	C₂×C₅₃	semidirect
740. #2770	C₂×C₅₃	semidirect
741. #2765	C₂×C₅₃	semidirect
742. #2764	C₂×C₅₃	semidirect
743. #2763	C₂×C₅₃	semidirect
744. #2757	C₂×C₅₃	semidirect
745. #2746	C₂×C₅₃	semidirect
746. #2739	C₂×C₅₃	semidirect
747. #2729	C₂×C₅₃	semidirect
748. #2718	C₂×C₅₃	semidirect
749. #2717	C₂×C₅₃	semidirect
750. #2698	C₂×C₅₃	semidirect
751. #2692	C₂×C₅₃	semidirect
752. #2687	C₂×C₅₃	semidirect
753. #2674	C₂×C₅₃	semidirect
754. #2627	C₂×C₅₃	semidirect
755. #2623	C₂×C₅₃	semidirect
756. #2561	C₂×C₅₃	semidirect
758. #2493	C₂×C₅₃	semidirect
759. #2488	C₂×C₅₃	semidirect
760. #2480	C₂×C₅₃	semidirect
762. #2440	C₂×C₅₃	semidirect
763. #2417	C₂×C₅₃	semidirect
764. #2329	C₂×C₅₃	semidirect
765. #2318	C₂×C₅₃	semidirect
766. C₂×#385	C₂×C₅₃	semidirect
779. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
790. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
797. #401	C₂²×C₅₃	semidirect
798. #400	C₂²×C₅₃	semidirect
799. #400	C₂²×C₅₃	semidirect
800. #400	C₂²×C₅₃	semidirect
801. #400	C₂²×C₅₃	semidirect
802. #400	C₂²×C₅₃	semidirect
803. #400	C₂²×C₅₃	semidirect
804. #400	C₂²×C₅₃	semidirect
805. #400	C₂²×C₅₃	semidirect
806. #400	C₂²×C₅₃	semidirect
807. #399	C₂²×C₅₃	semidirect
808. #399	C₂²×C₅₃	semidirect
809. #398	C₂²×C₅₃	semidirect
810. #398	C₂²×C₅₃	semidirect
811. #398	C₂²×C₅₃	semidirect
812. #398	C₂²×C₅₃	semidirect
813. #398	C₂²×C₅₃	semidirect
814. #398	C₂²×C₅₃	semidirect
815. #398	C₂²×C₅₃	semidirect
816. #398	C₂²×C₅₃	semidirect
817. #398	C₂²×C₅₃	semidirect
818. #398	C₂²×C₅₃	semidirect
825. #397	C₂²×C₅₃	semidirect
826. #397	C₂²×C₅₃	semidirect
827. #397	C₂²×C₅₃	semidirect
831. #396	C₂²×C₅₃	semidirect
832. #396	C₂²×C₅₃	semidirect
833. #395	C₂²×C₅₃	semidirect
834. #395	C₂²×C₅₃	semidirect
835. #395	C₂²×C₅₃	semidirect
836. #395	C₂²×C₅₃	semidirect
844. #393	C₂²×C₅₃	semidirect
845. #391	C₂²×C₅₃	semidirect
846. #391	C₂²×C₅₃	semidirect
847. #391	C₂²×C₅₃	semidirect
848. #391	C₂²×C₅₃	semidirect
850. #389	C₂²×C₅₃	semidirect
851. #389	C₂²×C₅₃	semidirect
852. #389	C₂²×C₅₃	semidirect
853. #389	C₂²×C₅₃	semidirect
854. #389	C₂²×C₅₃	semidirect
866. #388	C₂²×C₅₃	semidirect
867. #388	C₂²×C₅₃	semidirect
868. #388	C₂²×C₅₃	semidirect
869. #388	C₂²×C₅₃	semidirect
870. #387	C₂²×C₅₃	semidirect
871. #387	C₂²×C₅₃	semidirect
872. #387	C₂²×C₅₃	semidirect
873. #387	C₂²×C₅₃	semidirect
874. #387	C₂²×C₅₃	semidirect
875. #387	C₂²×C₅₃	semidirect
876. #387	C₂²×C₅₃	semidirect
877. #387	C₂²×C₅₃	semidirect
878. #387	C₂²×C₅₃	semidirect
907. #384	C₂²×C₅₃	semidirect
908. #383	C₂²×C₅₃	semidirect
909. #383	C₂²×C₅₃	semidirect
910. #382	C₂²×C₅₃	semidirect
911. #382	C₂²×C₅₃	semidirect
917. #381	C₂²×C₅₃	semidirect
923. #380	C₂²×C₅₃	semidirect
924. #380	C₂²×C₅₃	semidirect
933. C₅₃	#36778	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×#2849	2
C₅₃×#2848	2
C₅₃×#2790	2
C₅₃×#2779	2
C₅₃×#2770	2
C₅₃×#2765	2
C₅₃×#2764	2
C₅₃×#2763	2
C₅₃×#2757	2
C₅₃×#2746	2
C₅₃×#2739	2
C₅₃×#2729	2
C₅₃×#2718	2
C₅₃×#2717	2
C₅₃×#2698	2
C₅₃×#2692	2
C₅₃×#2687	2
C₅₃×#2674	2
C₅₃×#2627	2
C₅₃×#2623	2
C₅₃×#2561	2
C₅₃×#2534	2
C₅₃×#2493	2
C₅₃×#2488	2
C₅₃×#2480	2
C₅₃×#2472	2
C₅₃×#2440	2
C₅₃×#2417	2
C₅₃×#2329	2
C₅₃×#2318	2
C₂×C₅₃×#385	2
#36778	53

Subgroups — C53×#36778 #27244290

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#36778 #27244290