Subgroups — C₅₃×#34735 #27242247

Order 13568.

2562 conjugacy classes of subgroups.

The subgroup lattice has 1564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2479	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2478	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2475	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2469	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2462	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2461	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2449	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2443	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2438	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2430	C₂	1	1	yes	maximal, characteristic
15	C₅₃×#2425	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2419	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2413	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2406	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2399	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2396	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2395	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2392	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₂²⋊Q₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
25	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
26	C₄×#123×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
27	C₄×#121×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2290	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₄×C₄⋊C₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#529	—	2	8	no	—
34	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
38	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
40	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
41	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic
42	C₂×#123×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
45	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
46	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
47	C₄×#41×C₅₃	—	2	8	no	—
48	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
52	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
61	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×#117×C₅₃	C₂²	1	1	yes	characteristic
66	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
67	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
68	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
69	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
70	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
71	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
72	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic
73	C₅₃×#400	C₂²	1	1	yes	characteristic
74	C₅₃×#400	C₂²	1	1	yes	characteristic
75	C₅₃×#399	C₂²	1	1	yes	characteristic
76	C₅₃×#399	C₂²	1	1	yes	characteristic
77	C₅₃×#398	C₂²	1	1	yes	characteristic
78	C₅₃×#398	C₂²	1	1	yes	characteristic
79	C₅₃×#398	C₂²	1	1	yes	characteristic
80	C₅₃×#398	C₂²	1	1	yes	characteristic
81	C₅₃×#398	C₂²	1	1	yes	characteristic
82	C₅₃×#398	C₂²	1	1	yes	characteristic
83	C₅₃×#398	C₂²	1	1	yes	characteristic
84	C₅₃×#398	C₂²	1	1	yes	characteristic
85	C₅₃×#397	C₂²	1	1	yes	characteristic
86	C₅₃×#397	C₂²	1	1	yes	characteristic
87	C₅₃×#397	C₂²	1	1	yes	characteristic
88	C₅₃×#397	C₂²	1	1	yes	characteristic
89	C₅₃×#396	C₂²	1	1	yes	characteristic
90	C₅₃×#396	C₂²	1	1	yes	characteristic
91	C₅₃×#396	C₂²	1	1	yes	characteristic
92	C₅₃×#396	C₂²	1	1	yes	characteristic
93	C₅₃×#395	C₂²	1	1	yes	characteristic
94	C₅₃×#395	C₂²	1	1	yes	characteristic
95	C₅₃×#395	C₂²	1	1	yes	characteristic
96	C₅₃×#395	C₂²	1	1	yes	characteristic
97	C₅₃×#395	C₂²	1	1	yes	characteristic
98	C₅₃×#394	C₂²	1	1	yes	characteristic
99	C₅₃×#394	C₂²	1	1	yes	characteristic
100	C₅₃×#394	C₂²	1	1	yes	characteristic
101	C₅₃×#394	C₂²	1	1	yes	characteristic
102	C₅₃×#394	C₂²	1	1	yes	characteristic
103	C₅₃×#393	C₂²	1	1	yes	characteristic
104	C₅₃×#392	C₂²	1	1	yes	characteristic
105	C₅₃×#391	C₂²	1	1	yes	characteristic
106	C₅₃×#390	C₂²	1	1	yes	characteristic
107	C₅₃×#389	C₂²	1	1	yes	characteristic
108	C₅₃×#389	C₂²	1	1	yes	characteristic
109	C₅₃×#389	C₂²	1	1	yes	characteristic
110	C₅₃×#389	C₂²	1	1	yes	characteristic
111	C₅₃×#389	C₂²	1	1	yes	characteristic
112	C₅₃×#389	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×#387	C₂²	1	1	yes	characteristic
126	C₅₃×#387	C₂²	1	1	yes	characteristic
127	C₅₃×#387	C₂²	1	1	yes	characteristic
128	C₅₃×#387	C₂²	1	1	yes	characteristic
129	C₅₃×#387	C₂²	1	1	yes	characteristic
130	C₅₃×#387	C₂²	1	1	yes	characteristic
131	C₅₃×#387	C₂²	1	1	yes	characteristic
132	C₅₃×#387	C₂²	1	1	yes	characteristic
133	C₅₃×#387	C₂²	1	1	yes	characteristic
134	C₅₃×#387	C₂²	1	1	yes	characteristic
135	C₅₃×#387	C₂²	1	1	yes	characteristic
136	C₅₃×#387	C₂²	1	1	yes	characteristic
137	C₅₃×#386	C₂²	1	1	yes	characteristic
138	C₅₃×#386	C₂²	1	1	yes	characteristic
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
141	C₅₃×#386	C₂²	1	1	yes	characteristic
142	C₅₃×#386	C₂²	1	1	yes	characteristic
143	C₅₃×#386	C₂²	1	1	yes	characteristic
144	C₅₃×#386	C₂²	1	1	yes	characteristic
145	C₅₃×#386	C₂²	1	1	yes	characteristic
146	C₅₃×#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×#381	C₂²	1	1	yes	characteristic
160	C₅₃×#381	C₂²	1	1	yes	characteristic
161	C₅₃×#381	C₂²	1	1	yes	characteristic
162	C₅₃×#380	C₂²	1	1	yes	characteristic
163	C₅₃×#380	C₂²	1	1	yes	characteristic
164	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
165	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
166	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
167	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
168	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
169	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
170	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
171	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
172	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
173	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
174	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
175	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
180	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
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	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
186	C₅₃×#376	C₂²	1	1	yes	characteristic
187	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
188	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic
189	C₂×#41×C₅₃	—	2	4	no	—
190	C₂×#41×C₅₃	—	2	4	no	—
191	C₂×#41×C₅₃	—	2	4	no	—
192	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
194	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
195	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
196	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
197	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
198	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
199	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
214	#126×C₅₃	—	2	4	no	—
215	#126×C₅₃	—	2	4	no	—
216	#125×C₅₃	—	2	4	no	—
217	#124×C₅₃	—	2	4	no	—
218	#123×C₅₃	—	2	4	no	—
219	#123×C₅₃	—	2	4	no	—
220	#123×C₅₃	—	2	4	no	—
221	#123×C₅₃	—	2	4	no	—
222	#123×C₅₃	—	2	4	no	—
223	C₂²⋊Q₈×C₅₃	—	2	4	no	—
224	C₂²⋊Q₈×C₅₃	—	2	4	no	—
225	#121×C₅₃	—	2	4	no	—
226	#121×C₅₃	—	2	4	no	—
227	C₄×Q₈×C₅₃	—	2	4	no	—
228	C₄×Q₈×C₅₃	—	2	4	no	—
229	C₄×Q₈×C₅₃	—	2	4	no	—
230	C₄×D₄×C₅₃	—	2	4	no	—
231	C₄×D₄×C₅₃	—	2	4	no	—
232	C₄×D₄×C₅₃	—	2	4	no	—
233	C₄×D₄×C₅₃	—	2	4	no	—
234	C₄×D₄×C₅₃	—	2	4	no	—
235	C₄×D₄×C₅₃	—	2	4	no	—
236	C₄×D₄×C₅₃	—	2	4	no	—
237	C₄×D₄×C₅₃	—	2	4	no	—
238	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
239	#117×C₅₃	—	2	4	no	—
240	#117×C₅₃	—	2	4	no	—
241	#117×C₅₃	—	2	4	no	—
242	#117×C₅₃	—	2	4	no	—
243	#117×C₅₃	—	2	4	no	—
244	#117×C₅₃	—	2	4	no	—
245	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
246	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
272	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
274	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
275	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
276	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
277	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
278	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
285	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
297	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
298	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
299	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
300	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
301	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
302	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
304	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
307	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
308	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
314	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
315	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
316	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
317	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
318	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂×C₄²×C₅₃	—	2	4	no	—
320	C₂×C₄²×C₅₃	—	2	4	no	—
321	C₂×C₄²×C₅₃	—	2	4	no	—
322	C₂×C₄²×C₅₃	—	2	4	no	—
323	C₂×C₄²×C₅₃	—	2	4	no	—
324	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
345	#95×C₅₃	C₂³	1	1	yes	characteristic
346	#95×C₅₃	C₂³	1	1	yes	characteristic
347	#95×C₅₃	C₂³	1	1	yes	characteristic
348	#95×C₅₃	C₂³	1	1	yes	characteristic
349	#95×C₅₃	C₂³	1	1	yes	characteristic
350	#95×C₅₃	C₂³	1	1	yes	characteristic
351	#95×C₅₃	C₂³	1	1	yes	characteristic
352	#95×C₅₃	C₂³	1	1	yes	characteristic
353	#95×C₅₃	C₂³	1	1	yes	characteristic
354	#95×C₅₃	C₂³	1	1	yes	characteristic
355	#95×C₅₃	C₂³	1	1	yes	characteristic
356	#95×C₅₃	C₂³	1	1	yes	characteristic
357	#95×C₅₃	C₂³	1	1	yes	characteristic
358	#95×C₅₃	C₂³	1	1	yes	characteristic
359	#95×C₅₃	C₂³	1	1	yes	characteristic
360	#95×C₅₃	C₂³	1	1	yes	characteristic
361	#95×C₅₃	C₂³	1	1	yes	characteristic
362	#95×C₅₃	C₂³	1	1	yes	characteristic
363	#95×C₅₃	C₂³	1	1	yes	characteristic
364	#95×C₅₃	C₂³	1	1	yes	characteristic
365	#95×C₅₃	C₂³	1	1	yes	characteristic
366	#95×C₅₃	C₂³	1	1	yes	characteristic
367	#95×C₅₃	C₂³	1	1	yes	characteristic
368	#95×C₅₃	C₂³	1	1	yes	characteristic
369	#95×C₅₃	C₂³	1	1	yes	characteristic
370	#95×C₅₃	C₂³	1	1	yes	characteristic
371	#95×C₅₃	C₂³	1	1	yes	characteristic
372	#95×C₅₃	C₂³	1	1	yes	characteristic
373	#95×C₅₃	C₂³	1	1	yes	characteristic
374	#95×C₅₃	C₂³	1	1	yes	characteristic
375	#95×C₅₃	C₂³	1	1	yes	characteristic
376	#95×C₅₃	C₂³	1	1	yes	characteristic
377	#95×C₅₃	C₂³	1	1	yes	characteristic
378	#95×C₅₃	C₂³	1	1	yes	characteristic
379	#95×C₅₃	C₂³	1	1	yes	characteristic
380	#95×C₅₃	C₂³	1	1	yes	characteristic
381	#95×C₅₃	C₂³	1	1	yes	characteristic
382	#95×C₅₃	C₂³	1	1	yes	characteristic
383	#95×C₅₃	C₂³	1	1	yes	characteristic
384	#95×C₅₃	C₂³	1	1	yes	characteristic
385	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
389	#41×C₅₃	—	2	32	no	—
390	C₂×Q₈×C₅₃	—	2	2	no	—
391	C₂×Q₈×C₅₃	—	2	2	no	—
392	C₂×Q₈×C₅₃	—	2	2	no	—
393	C₂×Q₈×C₅₃	—	2	2	no	—
394	C₂×Q₈×C₅₃	—	2	2	no	—
395	C₂×Q₈×C₅₃	—	4	1	no	—
396	C₂×D₄×C₅₃	—	2	2	no	—
397	C₂×D₄×C₅₃	—	2	2	no	—
398	C₂×D₄×C₅₃	—	2	2	no	—
399	C₂×D₄×C₅₃	—	2	2	no	—
400	C₂×D₄×C₅₃	—	2	2	no	—
401	C₂×D₄×C₅₃	—	2	2	no	—
402	C₂×D₄×C₅₃	—	2	2	no	—
403	C₂×D₄×C₅₃	—	2	2	no	—
404	C₂×D₄×C₅₃	—	2	2	no	—
405	C₂×D₄×C₅₃	—	2	2	no	—
406	C₂×D₄×C₅₃	—	2	2	no	—
407	C₂×D₄×C₅₃	—	2	2	no	—
408	C₂×D₄×C₅₃	—	2	2	no	—
409	C₂×D₄×C₅₃	—	2	2	no	—
410	C₂×D₄×C₅₃	—	4	1	no	—
411	C₂×D₄×C₅₃	—	4	1	no	—
412	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
413	C₂×D₄×C₅₃	#41	1	4	yes	—
414	C₂²×C₄×C₅₃	—	2	2	no	—
415	C₂²×C₄×C₅₃	—	2	2	no	—
416	C₂²×C₄×C₅₃	—	2	2	no	—
417	C₂²×C₄×C₅₃	—	2	2	no	—
418	C₂²×C₄×C₅₃	—	2	2	no	—
419	C₂²×C₄×C₅₃	—	2	2	no	—
420	C₂²×C₄×C₅₃	—	2	2	no	—
421	C₂²×C₄×C₅₃	—	2	2	no	—
422	C₂²×C₄×C₅₃	—	2	2	no	—
423	C₂²×C₄×C₅₃	—	2	2	no	—
424	C₂²×C₄×C₅₃	—	2	2	no	—
425	C₂²×C₄×C₅₃	—	2	2	no	—
426	C₂²×C₄×C₅₃	—	2	2	no	—
427	C₂²×C₄×C₅₃	—	2	2	no	—
428	C₂²×C₄×C₅₃	—	2	2	no	—
429	C₂²×C₄×C₅₃	—	2	2	no	—
430	C₂²×C₄×C₅₃	—	2	2	no	—
431	C₂²×C₄×C₅₃	—	2	2	no	—
432	C₂²×C₄×C₅₃	—	2	2	no	—
433	C₂²×C₄×C₅₃	—	2	2	no	—
434	C₂²×C₄×C₅₃	—	2	2	no	—
435	C₂²×C₄×C₅₃	—	2	2	no	—
436	C₂²×C₄×C₅₃	—	2	2	no	—
437	C₂²×C₄×C₅₃	—	2	2	no	—
438	C₂²×C₄×C₅₃	—	2	2	no	—
439	C₂²×C₄×C₅₃	—	2	2	no	—
440	C₂²×C₄×C₅₃	—	2	2	no	—
441	C₂²×C₄×C₅₃	—	2	2	no	—
442	C₂²×C₄×C₅₃	—	2	2	no	—
443	C₂²×C₄×C₅₃	—	2	2	no	—
444	C₂²×C₄×C₅₃	—	2	2	no	—
445	C₂²×C₄×C₅₃	—	2	2	no	—
446	C₂²×C₄×C₅₃	—	2	2	no	—
447	C₂²×C₄×C₅₃	—	2	2	no	—
448	C₂²×C₄×C₅₃	—	4	1	no	—
449	C₂²×C₄×C₅₃	—	4	1	no	—
450	C₂²×C₄×C₅₃	—	4	1	no	—
451	C₂²×C₄×C₅₃	—	4	1	no	—
452	C₂²×C₄×C₅₃	—	4	1	no	—
453	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
454	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
455	C₂²×C₄×C₅₃	#41	1	4	yes	—
456	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
457	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
459	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
462	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
464	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
465	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
466	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
467	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
468	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
470	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
472	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
473	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
475	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
476	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
477	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
478	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
479	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
480	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
481	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
482	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
483	C₄⋊C₄×C₅₃	—	2	2	no	—
484	C₄⋊C₄×C₅₃	—	2	2	no	—
485	C₄⋊C₄×C₅₃	—	2	2	no	—
486	C₄⋊C₄×C₅₃	—	2	2	no	—
487	C₄⋊C₄×C₅₃	—	2	2	no	—
488	C₄⋊C₄×C₅₃	—	2	2	no	—
489	C₄⋊C₄×C₅₃	—	2	2	no	—
490	C₄⋊C₄×C₅₃	—	2	2	no	—
491	C₄⋊C₄×C₅₃	—	2	2	no	—
492	C₄⋊C₄×C₅₃	—	2	2	no	—
493	C₄⋊C₄×C₅₃	—	2	2	no	—
494	C₄⋊C₄×C₅₃	—	2	2	no	—
495	C₄⋊C₄×C₅₃	—	2	2	no	—
496	C₄⋊C₄×C₅₃	—	2	2	no	—
497	C₄⋊C₄×C₅₃	—	2	2	no	—
498	C₄⋊C₄×C₅₃	—	2	2	no	—
499	C₄⋊C₄×C₅₃	—	2	2	no	—
500	C₄⋊C₄×C₅₃	—	2	2	no	—
501	C₄⋊C₄×C₅₃	—	2	2	no	—
502	C₄⋊C₄×C₅₃	—	2	2	no	—
503	C₄⋊C₄×C₅₃	—	2	2	no	—
504	C₄⋊C₄×C₅₃	—	2	2	no	—
505	C₄⋊C₄×C₅₃	—	2	2	no	—
506	C₄⋊C₄×C₅₃	—	2	2	no	—
507	C₄⋊C₄×C₅₃	—	2	2	no	—
508	C₄⋊C₄×C₅₃	—	2	2	no	—
509	C₄⋊C₄×C₅₃	—	2	2	no	—
510	C₄⋊C₄×C₅₃	—	2	2	no	—
511	C₄⋊C₄×C₅₃	—	2	2	no	—
512	C₄⋊C₄×C₅₃	—	2	2	no	—
513	C₄⋊C₄×C₅₃	—	2	2	no	—
514	C₄⋊C₄×C₅₃	—	2	2	no	—
515	C₄⋊C₄×C₅₃	—	4	1	no	—
516	C₄⋊C₄×C₅₃	—	4	1	no	—
517	C₄⋊C₄×C₅₃	—	4	1	no	—
518	C₄⋊C₄×C₅₃	—	4	1	no	—
519	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
520	C₄⋊C₄×C₅₃	#41	1	4	yes	complemented
521	C₂²⋊C₄×C₅₃	—	2	2	no	—
522	C₂²⋊C₄×C₅₃	—	2	2	no	—
523	C₂²⋊C₄×C₅₃	—	2	2	no	—
524	C₂²⋊C₄×C₅₃	—	2	2	no	—
525	C₂²⋊C₄×C₅₃	—	2	2	no	—
526	C₂²⋊C₄×C₅₃	—	2	2	no	—
527	C₂²⋊C₄×C₅₃	—	2	2	no	—
528	C₂²⋊C₄×C₅₃	—	2	2	no	—
529	C₂²⋊C₄×C₅₃	—	2	2	no	—
530	C₂²⋊C₄×C₅₃	—	2	2	no	—
531	C₂²⋊C₄×C₅₃	—	2	2	no	—
532	C₂²⋊C₄×C₅₃	—	2	2	no	—
533	C₂²⋊C₄×C₅₃	—	2	2	no	—
534	C₂²⋊C₄×C₅₃	—	2	2	no	—
535	C₂²⋊C₄×C₅₃	—	2	2	no	—
536	C₂²⋊C₄×C₅₃	—	2	2	no	—
537	C₂²⋊C₄×C₅₃	—	2	2	no	—
538	C₂²⋊C₄×C₅₃	—	2	2	no	—
539	C₂²⋊C₄×C₅₃	—	2	2	no	—
540	C₂²⋊C₄×C₅₃	—	2	2	no	—
541	C₂²⋊C₄×C₅₃	—	2	2	no	—
542	C₂²⋊C₄×C₅₃	—	2	2	no	—
543	C₂²⋊C₄×C₅₃	—	2	2	no	—
544	C₂²⋊C₄×C₅₃	—	2	2	no	—
545	C₂²⋊C₄×C₅₃	—	2	2	no	—
546	C₂²⋊C₄×C₅₃	—	2	2	no	—
547	C₂²⋊C₄×C₅₃	—	2	2	no	—
548	C₂²⋊C₄×C₅₃	—	2	2	no	—
549	C₂²⋊C₄×C₅₃	—	2	2	no	—
550	C₂²⋊C₄×C₅₃	—	4	1	no	—
551	C₂²⋊C₄×C₅₃	—	4	1	no	—
552	C₂²⋊C₄×C₅₃	—	4	1	no	—
553	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
554	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
555	C₄²×C₅₃	—	2	2	no	—
556	C₄²×C₅₃	—	2	2	no	—
557	C₄²×C₅₃	—	2	2	no	—
558	C₄²×C₅₃	—	2	2	no	—
559	C₄²×C₅₃	—	2	2	no	—
560	C₄²×C₅₃	—	2	2	no	—
561	C₄²×C₅₃	—	2	2	no	—
562	C₄²×C₅₃	—	2	2	no	—
563	C₄²×C₅₃	—	2	2	no	—
564	C₄²×C₅₃	—	2	2	no	—
565	C₄²×C₅₃	—	2	2	no	—
566	C₄²×C₅₃	—	2	2	no	—
567	C₄²×C₅₃	—	2	2	no	—
568	C₄²×C₅₃	—	2	2	no	—
569	C₄²×C₅₃	—	2	2	no	—
570	C₄²×C₅₃	—	2	2	no	—
571	C₄²×C₅₃	—	2	2	no	—
572	C₄²×C₅₃	—	2	2	no	—
573	C₄²×C₅₃	—	2	2	no	—
574	C₄²×C₅₃	C₂×D₄	1	4	yes	—
575	C₄²×C₅₃	#41	1	4	yes	complemented
576	C₂³×C₅₃	—	2	1	no	—
577	C₂³×C₅₃	—	2	1	no	—
578	C₂³×C₅₃	—	2	1	no	—
579	C₂³×C₅₃	—	2	1	no	—
580	C₂³×C₅₃	—	2	1	no	—
581	C₂³×C₅₃	—	2	1	no	—
582	C₂³×C₅₃	—	2	1	no	—
583	C₂³×C₅₃	—	2	1	no	—
584	C₂³×C₅₃	—	2	1	no	—
585	C₂³×C₅₃	—	2	1	no	—
586	C₂³×C₅₃	—	2	1	no	—
587	C₂³×C₅₃	—	2	1	no	—
588	C₂³×C₅₃	—	2	1	no	—
589	C₂³×C₅₃	—	2	1	no	—
590	C₂³×C₅₃	—	2	1	no	—
591	C₂³×C₅₃	—	2	1	no	—
592	C₂³×C₅₃	—	2	1	no	—
593	C₂³×C₅₃	—	2	1	no	—
594	C₂³×C₅₃	—	2	1	no	—
595	C₂³×C₅₃	—	2	1	no	—
596	C₂³×C₅₃	—	2	1	no	—
597	C₂³×C₅₃	—	2	1	no	—
598	C₂³×C₅₃	—	2	1	no	—
599	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
600	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
601	C₂³×C₅₃	C₂×#41	1	2	yes	—
602	C₂³×C₅₃	C₂×#41	1	2	yes	—
603	C₂³×C₅₃	C₂×#41	1	2	yes	—
604	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
605	Q₈×C₅₃	—	2	8	no	—
606	Q₈×C₅₃	—	4	4	no	—
607	D₄×C₅₃	—	2	8	no	—
608	D₄×C₅₃	—	2	8	no	—
609	D₄×C₅₃	—	2	8	no	—
610	D₄×C₅₃	—	4	4	no	—
611	D₄×C₅₃	—	4	4	no	—
612	D₄×C₅₃	—	4	4	no	—
613	C₂×C₄×C₅₃	—	2	8	no	—
614	C₂×C₄×C₅₃	—	2	8	no	—
615	C₂×C₄×C₅₃	—	2	8	no	—
616	C₂×C₄×C₅₃	—	2	8	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	8	no	—
642	C₂×C₄×C₅₃	—	2	8	no	—
643	C₂×C₄×C₅₃	—	2	1	no	—
644	C₂×C₄×C₅₃	—	2	1	no	—
645	C₂×C₄×C₅₃	—	2	1	no	—
646	C₂×C₄×C₅₃	—	2	1	no	—
647	C₂×C₄×C₅₃	—	2	1	no	—
648	C₂×C₄×C₅₃	—	2	1	no	—
649	C₂×C₄×C₅₃	—	2	1	no	—
650	C₂×C₄×C₅₃	—	2	1	no	—
651	C₂×C₄×C₅₃	—	2	1	no	—
652	C₂×C₄×C₅₃	—	2	1	no	—
653	C₂×C₄×C₅₃	—	2	1	no	—
654	C₂×C₄×C₅₃	—	2	1	no	—
655	C₂×C₄×C₅₃	—	2	1	no	—
656	C₂×C₄×C₅₃	—	2	1	no	—
657	C₂×C₄×C₅₃	—	2	1	no	—
658	C₂×C₄×C₅₃	—	2	1	no	—
659	C₂×C₄×C₅₃	—	2	1	no	—
660	C₂×C₄×C₅₃	—	2	1	no	—
661	C₂×C₄×C₅₃	—	2	1	no	—
662	C₂×C₄×C₅₃	—	2	1	no	—
663	C₂×C₄×C₅₃	—	2	1	no	—
664	C₂×C₄×C₅₃	—	2	1	no	—
665	C₂×C₄×C₅₃	—	2	1	no	—
666	C₂×C₄×C₅₃	—	2	1	no	—
667	C₂×C₄×C₅₃	—	2	1	no	—
668	C₂×C₄×C₅₃	—	2	1	no	—
669	C₂×C₄×C₅₃	—	2	1	no	—
670	C₂×C₄×C₅₃	—	2	1	no	—
671	C₂×C₄×C₅₃	—	2	1	no	—
672	C₂×C₄×C₅₃	—	2	1	no	—
673	C₂×C₄×C₅₃	—	2	1	no	—
674	C₂×C₄×C₅₃	—	2	1	no	—
675	C₂×C₄×C₅₃	—	2	1	no	—
676	C₂×C₄×C₅₃	—	2	1	no	—
677	C₂×C₄×C₅₃	—	2	1	no	—
678	C₂×C₄×C₅₃	—	2	1	no	—
679	C₂×C₄×C₅₃	—	2	1	no	—
680	C₂×C₄×C₅₃	—	2	1	no	—
681	C₂×C₄×C₅₃	—	2	1	no	—
682	C₂×C₄×C₅₃	—	2	1	no	—
683	C₂×C₄×C₅₃	—	2	1	no	—
684	C₂×C₄×C₅₃	—	2	1	no	—
685	C₂×C₄×C₅₃	—	4	4	no	—
686	C₂×C₄×C₅₃	—	4	4	no	—
687	C₂×C₄×C₅₃	—	4	4	no	—
688	C₂×C₄×C₅₃	—	4	4	no	—
689	C₂×C₄×C₅₃	—	4	4	no	—
690	C₂×C₄×C₅₃	—	4	4	no	—
691	C₂×C₄×C₅₃	—	4	4	no	—
692	C₂×C₄×C₅₃	—	4	4	no	—
693	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
694	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
695	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
696	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
697	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
698	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
699	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
700	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
701	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
702	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
703	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
704	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
705	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
706	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
707	C₂×C₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
708	#34735	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
709	C₂²×C₅₃	—	2	2	no	—
710	C₂²×C₅₃	—	2	2	no	—
711	C₂²×C₅₃	—	2	2	no	—
712	C₂²×C₅₃	—	2	2	no	—
713	C₂²×C₅₃	—	2	2	no	—
714	C₂²×C₅₃	—	2	2	no	—
715	C₂²×C₅₃	—	2	2	no	—
716	C₂²×C₅₃	—	2	2	no	—
717	C₂²×C₅₃	—	2	2	no	—
718	C₂²×C₅₃	—	2	2	no	—
719	C₂²×C₅₃	—	2	2	no	—
720	C₂²×C₅₃	—	2	2	no	—
721	C₂²×C₅₃	—	4	1	no	—
722	C₂²×C₅₃	—	4	1	no	—
723	C₂²×C₅₃	—	4	1	no	—
724	C₂²×C₅₃	—	4	1	no	—
725	C₂²×C₅₃	—	4	1	no	—
726	C₂²×C₅₃	—	4	1	no	—
727	C₂²×C₅₃	—	4	1	no	—
728	C₂²×C₅₃	—	4	1	no	—
729	C₂²×C₅₃	—	4	1	no	—
730	C₂²×C₅₃	—	4	1	no	—
731	C₂²×C₅₃	—	4	1	no	—
732	C₂²×C₅₃	—	4	1	no	—
733	C₂²×C₅₃	—	4	1	no	—
734	C₂²×C₅₃	—	4	1	no	—
735	C₂²×C₅₃	—	4	1	no	—
736	C₂²×C₅₃	#525	1	4	yes	—
737	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
738	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
739	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
740	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
741	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
742	C₂²×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
743	C₂²×C₅₃	#585	1	1	yes	characteristic
744	C₄×C₅₃	—	2	2	no	—
745	C₄×C₅₃	—	2	2	no	—
746	C₄×C₅₃	—	2	2	no	—
747	C₄×C₅₃	—	2	2	no	—
748	C₄×C₅₃	—	2	2	no	—
749	C₄×C₅₃	—	2	2	no	—
750	C₄×C₅₃	—	2	2	no	—
751	C₄×C₅₃	—	2	2	no	—
752	C₄×C₅₃	—	2	2	no	—
753	C₄×C₅₃	—	2	2	no	—
754	C₄×C₅₃	—	2	2	no	—
755	C₄×C₅₃	—	2	2	no	—
756	C₄×C₅₃	—	4	1	no	—
757	C₄×C₅₃	—	4	1	no	—
758	C₄×C₅₃	—	4	1	no	—
759	C₄×C₅₃	—	4	1	no	—
760	C₄×C₅₃	—	4	1	no	—
761	C₄×C₅₃	—	4	1	no	—
762	C₄×C₅₃	—	4	1	no	—
763	C₄×C₅₃	—	4	1	no	—
764	C₄×C₅₃	—	4	1	no	—
765	C₄×C₅₃	—	4	1	no	—
766	C₄×C₅₃	—	4	1	no	—
767	C₄×C₅₃	—	4	1	no	—
768	C₄×C₅₃	—	4	1	no	—
769	C₄×C₅₃	—	4	1	no	—
770	C₄×C₅₃	#547	1	4	yes	—
771	C₂×#529	C₂×C₅₃	1	1	yes	characteristic, complemented
772	C₂×C₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
773	#2479	C₂×C₅₃	1	1	yes	characteristic, complemented
774	#2478	C₂×C₅₃	1	1	yes	characteristic, complemented
775	#2475	C₂×C₅₃	1	1	yes	characteristic, complemented
776	#2474	C₂×C₅₃	1	1	yes	characteristic, complemented
777	#2469	C₂×C₅₃	1	1	yes	characteristic, complemented
778	#2468	C₂×C₅₃	1	1	yes	characteristic, complemented
779	#2462	C₂×C₅₃	1	1	yes	characteristic, complemented
780	#2461	C₂×C₅₃	1	1	yes	characteristic, complemented
781	#2449	C₂×C₅₃	1	1	yes	characteristic, complemented
782	#2443	C₂×C₅₃	1	1	yes	characteristic, complemented
783	#2438	C₂×C₅₃	1	1	yes	characteristic, complemented
784	#2430	C₂×C₅₃	1	1	yes	characteristic
785	#2425	C₂×C₅₃	1	1	yes	characteristic, complemented
786	#2419	C₂×C₅₃	1	1	yes	characteristic, complemented
787	#2413	C₂×C₅₃	1	1	yes	characteristic, complemented
788	#2406	C₂×C₅₃	1	1	yes	characteristic, complemented
789	#2399	C₂×C₅₃	1	1	yes	characteristic, complemented
790	#2396	C₂×C₅₃	1	1	yes	characteristic, complemented
791	#2395	C₂×C₅₃	1	1	yes	characteristic, complemented
792	#2392	C₂×C₅₃	1	1	yes	characteristic, complemented
793	C₄×C₂²⋊Q₈	C₂×C₅₃	1	1	yes	characteristic, complemented
794	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
795	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
796	C₄×#123	C₂×C₅₃	1	1	yes	characteristic, complemented
797	C₄×#121	C₂×C₅₃	1	1	yes	characteristic, complemented
798	#2296	C₂×C₅₃	1	1	yes	characteristic, complemented
799	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
800	#2290	C₂×C₅₃	1	1	yes	characteristic, complemented
801	C₂×C₄×C₄⋊C₄	C₂×C₅₃	1	1	yes	characteristic, complemented
802	C₂×C₅₃	—	2	4	no	—
803	C₂×C₅₃	—	4	2	no	—
804	C₂×C₅₃	—	4	2	no	—
805	C₂×C₅₃	—	8	1	no	—
806	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
807	C₂×C₅₃	#3444	1	1	yes	characteristic
808	C₂×C₅₃	#3461	1	1	yes	characteristic
809	C₂×C₅₃	C₂×#547	1	1	yes	characteristic
810	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
811	C₂×C₅₃	#3475	1	1	yes	characteristic
812	C₂×C₅₃	#3482	1	1	yes	characteristic
813	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
814	#529	—	2	8	no	—
815	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
816	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic
817	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
818	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
819	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
820	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
821	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
822	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
823	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic
824	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
825	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic
826	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
827	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
828	C₄×#41	—	2	8	no	—
829	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
830	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
831	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
832	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
833	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
834	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
835	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
836	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
837	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
838	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
839	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
840	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
841	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
842	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
843	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
844	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
845	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
846	C₂×#117	C₂²×C₅₃	1	1	yes	characteristic
847	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
848	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
849	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
850	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
851	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
852	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
853	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic
854	#400	C₂²×C₅₃	1	1	yes	characteristic
855	#400	C₂²×C₅₃	1	1	yes	characteristic
856	#399	C₂²×C₅₃	1	1	yes	characteristic
857	#399	C₂²×C₅₃	1	1	yes	characteristic
858	#398	C₂²×C₅₃	1	1	yes	characteristic
859	#398	C₂²×C₅₃	1	1	yes	characteristic
860	#398	C₂²×C₅₃	1	1	yes	characteristic
861	#398	C₂²×C₅₃	1	1	yes	characteristic
862	#398	C₂²×C₅₃	1	1	yes	characteristic
863	#398	C₂²×C₅₃	1	1	yes	characteristic
864	#398	C₂²×C₅₃	1	1	yes	characteristic
865	#398	C₂²×C₅₃	1	1	yes	characteristic
866	#397	C₂²×C₅₃	1	1	yes	characteristic
867	#397	C₂²×C₅₃	1	1	yes	characteristic
868	#397	C₂²×C₅₃	1	1	yes	characteristic
869	#397	C₂²×C₅₃	1	1	yes	characteristic
870	#396	C₂²×C₅₃	1	1	yes	characteristic
871	#396	C₂²×C₅₃	1	1	yes	characteristic
872	#396	C₂²×C₅₃	1	1	yes	characteristic
873	#396	C₂²×C₅₃	1	1	yes	characteristic
874	#395	C₂²×C₅₃	1	1	yes	characteristic
875	#395	C₂²×C₅₃	1	1	yes	characteristic
876	#395	C₂²×C₅₃	1	1	yes	characteristic
877	#395	C₂²×C₅₃	1	1	yes	characteristic
878	#395	C₂²×C₅₃	1	1	yes	characteristic
879	#394	C₂²×C₅₃	1	1	yes	characteristic
880	#394	C₂²×C₅₃	1	1	yes	characteristic
881	#394	C₂²×C₅₃	1	1	yes	characteristic
882	#394	C₂²×C₅₃	1	1	yes	characteristic
883	#394	C₂²×C₅₃	1	1	yes	characteristic
884	#393	C₂²×C₅₃	1	1	yes	characteristic
885	#392	C₂²×C₅₃	1	1	yes	characteristic
886	#391	C₂²×C₅₃	1	1	yes	characteristic
887	#390	C₂²×C₅₃	1	1	yes	characteristic
888	#389	C₂²×C₅₃	1	1	yes	characteristic
889	#389	C₂²×C₅₃	1	1	yes	characteristic
890	#389	C₂²×C₅₃	1	1	yes	characteristic
891	#389	C₂²×C₅₃	1	1	yes	characteristic
892	#389	C₂²×C₅₃	1	1	yes	characteristic
893	#389	C₂²×C₅₃	1	1	yes	characteristic
894	#388	C₂²×C₅₃	1	1	yes	characteristic
895	#388	C₂²×C₅₃	1	1	yes	characteristic
896	#388	C₂²×C₅₃	1	1	yes	characteristic
897	#388	C₂²×C₅₃	1	1	yes	characteristic
898	#388	C₂²×C₅₃	1	1	yes	characteristic
899	#388	C₂²×C₅₃	1	1	yes	characteristic
900	#388	C₂²×C₅₃	1	1	yes	characteristic
901	#388	C₂²×C₅₃	1	1	yes	characteristic
902	#388	C₂²×C₅₃	1	1	yes	characteristic
903	#388	C₂²×C₅₃	1	1	yes	characteristic
904	#388	C₂²×C₅₃	1	1	yes	characteristic
905	#388	C₂²×C₅₃	1	1	yes	characteristic
906	#387	C₂²×C₅₃	1	1	yes	characteristic
907	#387	C₂²×C₅₃	1	1	yes	characteristic
908	#387	C₂²×C₅₃	1	1	yes	characteristic
909	#387	C₂²×C₅₃	1	1	yes	characteristic
910	#387	C₂²×C₅₃	1	1	yes	characteristic
911	#387	C₂²×C₅₃	1	1	yes	characteristic
912	#387	C₂²×C₅₃	1	1	yes	characteristic
913	#387	C₂²×C₅₃	1	1	yes	characteristic
914	#387	C₂²×C₅₃	1	1	yes	characteristic
915	#387	C₂²×C₅₃	1	1	yes	characteristic
916	#387	C₂²×C₅₃	1	1	yes	characteristic
917	#387	C₂²×C₅₃	1	1	yes	characteristic
918	#386	C₂²×C₅₃	1	1	yes	characteristic
919	#386	C₂²×C₅₃	1	1	yes	characteristic
920	#386	C₂²×C₅₃	1	1	yes	characteristic
921	#386	C₂²×C₅₃	1	1	yes	characteristic
922	#386	C₂²×C₅₃	1	1	yes	characteristic
923	#386	C₂²×C₅₃	1	1	yes	characteristic
924	#386	C₂²×C₅₃	1	1	yes	characteristic
925	#386	C₂²×C₅₃	1	1	yes	characteristic
926	#386	C₂²×C₅₃	1	1	yes	characteristic
927	#385	C₂²×C₅₃	1	1	yes	characteristic
928	#385	C₂²×C₅₃	1	1	yes	characteristic
929	#385	C₂²×C₅₃	1	1	yes	characteristic
930	#385	C₂²×C₅₃	1	1	yes	characteristic
931	#385	C₂²×C₅₃	1	1	yes	characteristic
932	#385	C₂²×C₅₃	1	1	yes	characteristic
933	#385	C₂²×C₅₃	1	1	yes	characteristic
934	#385	C₂²×C₅₃	1	1	yes	characteristic
935	#385	C₂²×C₅₃	1	1	yes	characteristic
936	#385	C₂²×C₅₃	1	1	yes	characteristic
937	#385	C₂²×C₅₃	1	1	yes	characteristic
938	#385	C₂²×C₅₃	1	1	yes	characteristic
939	#385	C₂²×C₅₃	1	1	yes	characteristic
940	#381	C₂²×C₅₃	1	1	yes	characteristic
941	#381	C₂²×C₅₃	1	1	yes	characteristic
942	#381	C₂²×C₅₃	1	1	yes	characteristic
943	#380	C₂²×C₅₃	1	1	yes	characteristic
944	#380	C₂²×C₅₃	1	1	yes	characteristic
945	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
946	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
947	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
948	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
949	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
950	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
951	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
952	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
953	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
954	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
955	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
956	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
957	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
958	C₄×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
959	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
960	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
961	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
962	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
963	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
964	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
965	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
966	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
967	#376	C₂²×C₅₃	1	1	yes	characteristic
968	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
969	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic
970	C₅₃	#34735	1	1	yes	characteristic, direct product factor, Sylow
971	C₂×#41	—	2	4	no	—
972	C₂×#41	—	2	4	no	—
973	C₂×#41	—	2	4	no	—
974	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
975	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
976	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
977	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
978	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
979	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
980	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
981	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
982	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
983	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
984	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
985	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
986	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
987	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
988	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
989	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
990	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
991	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
992	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
993	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
994	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
995	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
996	#126	—	2	4	no	—
997	#126	—	2	4	no	—
998	#125	—	2	4	no	—
999	#124	—	2	4	no	—
1000	#123	—	2	4	no	—
1001	#123	—	2	4	no	—
1002	#123	—	2	4	no	—
1003	#123	—	2	4	no	—
1004	#123	—	2	4	no	—
1005	C₂²⋊Q₈	—	2	4	no	—
1006	C₂²⋊Q₈	—	2	4	no	—
1007	#121	—	2	4	no	—
1008	#121	—	2	4	no	—
1009	C₄×Q₈	—	2	4	no	—
1010	C₄×Q₈	—	2	4	no	—
1011	C₄×Q₈	—	2	4	no	—
1012	C₄×D₄	—	2	4	no	—
1013	C₄×D₄	—	2	4	no	—
1014	C₄×D₄	—	2	4	no	—
1015	C₄×D₄	—	2	4	no	—
1016	C₄×D₄	—	2	4	no	—
1017	C₄×D₄	—	2	4	no	—
1018	C₄×D₄	—	2	4	no	—
1019	C₄×D₄	—	2	4	no	—
1020	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
1021	#117	—	2	4	no	—
1022	#117	—	2	4	no	—
1023	#117	—	2	4	no	—
1024	#117	—	2	4	no	—
1025	#117	—	2	4	no	—
1026	#117	—	2	4	no	—
1027	C₂×C₄⋊C₄	—	2	4	no	—
1028	C₂×C₄⋊C₄	—	2	4	no	—
1029	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1032	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1034	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1056	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1057	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1058	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×C₄²	—	2	4	no	—
1102	C₂×C₄²	—	2	4	no	—
1103	C₂×C₄²	—	2	4	no	—
1104	C₂×C₄²	—	2	4	no	—
1105	C₂×C₄²	—	2	4	no	—
1106	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1127	#95	C₂³×C₅₃	1	1	yes	characteristic
1128	#95	C₂³×C₅₃	1	1	yes	characteristic
1129	#95	C₂³×C₅₃	1	1	yes	characteristic
1130	#95	C₂³×C₅₃	1	1	yes	characteristic
1131	#95	C₂³×C₅₃	1	1	yes	characteristic
1132	#95	C₂³×C₅₃	1	1	yes	characteristic
1133	#95	C₂³×C₅₃	1	1	yes	characteristic
1134	#95	C₂³×C₅₃	1	1	yes	characteristic
1135	#95	C₂³×C₅₃	1	1	yes	characteristic
1136	#95	C₂³×C₅₃	1	1	yes	characteristic
1137	#95	C₂³×C₅₃	1	1	yes	characteristic
1138	#95	C₂³×C₅₃	1	1	yes	characteristic
1139	#95	C₂³×C₅₃	1	1	yes	characteristic
1140	#95	C₂³×C₅₃	1	1	yes	characteristic
1141	#95	C₂³×C₅₃	1	1	yes	characteristic
1142	#95	C₂³×C₅₃	1	1	yes	characteristic
1143	#95	C₂³×C₅₃	1	1	yes	characteristic
1144	#95	C₂³×C₅₃	1	1	yes	characteristic
1145	#95	C₂³×C₅₃	1	1	yes	characteristic
1146	#95	C₂³×C₅₃	1	1	yes	characteristic
1147	#95	C₂³×C₅₃	1	1	yes	characteristic
1148	#95	C₂³×C₅₃	1	1	yes	characteristic
1149	#95	C₂³×C₅₃	1	1	yes	characteristic
1150	#95	C₂³×C₅₃	1	1	yes	characteristic
1151	#95	C₂³×C₅₃	1	1	yes	characteristic
1152	#95	C₂³×C₅₃	1	1	yes	characteristic
1153	#95	C₂³×C₅₃	1	1	yes	characteristic
1154	#95	C₂³×C₅₃	1	1	yes	characteristic
1155	#95	C₂³×C₅₃	1	1	yes	characteristic
1156	#95	C₂³×C₅₃	1	1	yes	characteristic
1157	#95	C₂³×C₅₃	1	1	yes	characteristic
1158	#95	C₂³×C₅₃	1	1	yes	characteristic
1159	#95	C₂³×C₅₃	1	1	yes	characteristic
1160	#95	C₂³×C₅₃	1	1	yes	characteristic
1161	#95	C₂³×C₅₃	1	1	yes	characteristic
1162	#95	C₂³×C₅₃	1	1	yes	characteristic
1163	#95	C₂³×C₅₃	1	1	yes	characteristic
1164	#95	C₂³×C₅₃	1	1	yes	characteristic
1165	#95	C₂³×C₅₃	1	1	yes	characteristic
1166	#95	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1168	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1169	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1170	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1171	#41	—	2	32	no	—
1172	C₂×Q₈	—	2	2	no	—
1173	C₂×Q₈	—	2	2	no	—
1174	C₂×Q₈	—	2	2	no	—
1175	C₂×Q₈	—	2	2	no	—
1176	C₂×Q₈	—	2	2	no	—
1177	C₂×Q₈	—	4	1	no	—
1178	C₂×D₄	—	2	2	no	—
1179	C₂×D₄	—	2	2	no	—
1180	C₂×D₄	—	2	2	no	—
1181	C₂×D₄	—	2	2	no	—
1182	C₂×D₄	—	2	2	no	—
1183	C₂×D₄	—	2	2	no	—
1184	C₂×D₄	—	2	2	no	—
1185	C₂×D₄	—	2	2	no	—
1186	C₂×D₄	—	2	2	no	—
1187	C₂×D₄	—	2	2	no	—
1188	C₂×D₄	—	2	2	no	—
1189	C₂×D₄	—	2	2	no	—
1190	C₂×D₄	—	2	2	no	—
1191	C₂×D₄	—	2	2	no	—
1192	C₂×D₄	—	4	1	no	—
1193	C₂×D₄	—	4	1	no	—
1194	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
1195	C₂×D₄	#41×C₅₃	1	4	yes	—
1196	C₂²×C₄	—	2	2	no	—
1197	C₂²×C₄	—	2	2	no	—
1198	C₂²×C₄	—	2	2	no	—
1199	C₂²×C₄	—	2	2	no	—
1200	C₂²×C₄	—	2	2	no	—
1201	C₂²×C₄	—	2	2	no	—
1202	C₂²×C₄	—	2	2	no	—
1203	C₂²×C₄	—	2	2	no	—
1204	C₂²×C₄	—	2	2	no	—
1205	C₂²×C₄	—	2	2	no	—
1206	C₂²×C₄	—	2	2	no	—
1207	C₂²×C₄	—	2	2	no	—
1208	C₂²×C₄	—	2	2	no	—
1209	C₂²×C₄	—	2	2	no	—
1210	C₂²×C₄	—	2	2	no	—
1211	C₂²×C₄	—	2	2	no	—
1212	C₂²×C₄	—	2	2	no	—
1213	C₂²×C₄	—	2	2	no	—
1214	C₂²×C₄	—	2	2	no	—
1215	C₂²×C₄	—	2	2	no	—
1216	C₂²×C₄	—	2	2	no	—
1217	C₂²×C₄	—	2	2	no	—
1218	C₂²×C₄	—	2	2	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	—	4	1	no	—
1231	C₂²×C₄	—	4	1	no	—
1232	C₂²×C₄	—	4	1	no	—
1233	C₂²×C₄	—	4	1	no	—
1234	C₂²×C₄	—	4	1	no	—
1235	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1236	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1237	C₂²×C₄	#41×C₅₃	1	4	yes	—
1238	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1239	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1240	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1241	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1242	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1243	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1244	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1245	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1246	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1247	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1248	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1249	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1250	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1251	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1252	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1253	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1254	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1255	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1256	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1257	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1258	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1259	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1260	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1261	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1262	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1263	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1264	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1265	C₄⋊C₄	—	2	2	no	—
1266	C₄⋊C₄	—	2	2	no	—
1267	C₄⋊C₄	—	2	2	no	—
1268	C₄⋊C₄	—	2	2	no	—
1269	C₄⋊C₄	—	2	2	no	—
1270	C₄⋊C₄	—	2	2	no	—
1271	C₄⋊C₄	—	2	2	no	—
1272	C₄⋊C₄	—	2	2	no	—
1273	C₄⋊C₄	—	2	2	no	—
1274	C₄⋊C₄	—	2	2	no	—
1275	C₄⋊C₄	—	2	2	no	—
1276	C₄⋊C₄	—	2	2	no	—
1277	C₄⋊C₄	—	2	2	no	—
1278	C₄⋊C₄	—	2	2	no	—
1279	C₄⋊C₄	—	2	2	no	—
1280	C₄⋊C₄	—	2	2	no	—
1281	C₄⋊C₄	—	2	2	no	—
1282	C₄⋊C₄	—	2	2	no	—
1283	C₄⋊C₄	—	2	2	no	—
1284	C₄⋊C₄	—	2	2	no	—
1285	C₄⋊C₄	—	2	2	no	—
1286	C₄⋊C₄	—	2	2	no	—
1287	C₄⋊C₄	—	2	2	no	—
1288	C₄⋊C₄	—	2	2	no	—
1289	C₄⋊C₄	—	2	2	no	—
1290	C₄⋊C₄	—	2	2	no	—
1291	C₄⋊C₄	—	2	2	no	—
1292	C₄⋊C₄	—	2	2	no	—
1293	C₄⋊C₄	—	2	2	no	—
1294	C₄⋊C₄	—	2	2	no	—
1295	C₄⋊C₄	—	2	2	no	—
1296	C₄⋊C₄	—	2	2	no	—
1297	C₄⋊C₄	—	4	1	no	—
1298	C₄⋊C₄	—	4	1	no	—
1299	C₄⋊C₄	—	4	1	no	—
1300	C₄⋊C₄	—	4	1	no	—
1301	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1302	C₄⋊C₄	#41×C₅₃	1	4	yes	complemented
1303	C₂²⋊C₄	—	2	2	no	—
1304	C₂²⋊C₄	—	2	2	no	—
1305	C₂²⋊C₄	—	2	2	no	—
1306	C₂²⋊C₄	—	2	2	no	—
1307	C₂²⋊C₄	—	2	2	no	—
1308	C₂²⋊C₄	—	2	2	no	—
1309	C₂²⋊C₄	—	2	2	no	—
1310	C₂²⋊C₄	—	2	2	no	—
1311	C₂²⋊C₄	—	2	2	no	—
1312	C₂²⋊C₄	—	2	2	no	—
1313	C₂²⋊C₄	—	2	2	no	—
1314	C₂²⋊C₄	—	2	2	no	—
1315	C₂²⋊C₄	—	2	2	no	—
1316	C₂²⋊C₄	—	2	2	no	—
1317	C₂²⋊C₄	—	2	2	no	—
1318	C₂²⋊C₄	—	2	2	no	—
1319	C₂²⋊C₄	—	2	2	no	—
1320	C₂²⋊C₄	—	2	2	no	—
1321	C₂²⋊C₄	—	2	2	no	—
1322	C₂²⋊C₄	—	2	2	no	—
1323	C₂²⋊C₄	—	2	2	no	—
1324	C₂²⋊C₄	—	2	2	no	—
1325	C₂²⋊C₄	—	2	2	no	—
1326	C₂²⋊C₄	—	2	2	no	—
1327	C₂²⋊C₄	—	2	2	no	—
1328	C₂²⋊C₄	—	2	2	no	—
1329	C₂²⋊C₄	—	2	2	no	—
1330	C₂²⋊C₄	—	2	2	no	—
1331	C₂²⋊C₄	—	2	2	no	—
1332	C₂²⋊C₄	—	4	1	no	—
1333	C₂²⋊C₄	—	4	1	no	—
1334	C₂²⋊C₄	—	4	1	no	—
1335	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1336	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1337	C₄²	—	2	2	no	—
1338	C₄²	—	2	2	no	—
1339	C₄²	—	2	2	no	—
1340	C₄²	—	2	2	no	—
1341	C₄²	—	2	2	no	—
1342	C₄²	—	2	2	no	—
1343	C₄²	—	2	2	no	—
1344	C₄²	—	2	2	no	—
1345	C₄²	—	2	2	no	—
1346	C₄²	—	2	2	no	—
1347	C₄²	—	2	2	no	—
1348	C₄²	—	2	2	no	—
1349	C₄²	—	2	2	no	—
1350	C₄²	—	2	2	no	—
1351	C₄²	—	2	2	no	—
1352	C₄²	—	2	2	no	—
1353	C₄²	—	2	2	no	—
1354	C₄²	—	2	2	no	—
1355	C₄²	—	2	2	no	—
1356	C₄²	C₂×D₄×C₅₃	1	4	yes	—
1357	C₄²	#41×C₅₃	1	4	yes	complemented
1358	C₂³	—	2	1	no	—
1359	C₂³	—	2	1	no	—
1360	C₂³	—	2	1	no	—
1361	C₂³	—	2	1	no	—
1362	C₂³	—	2	1	no	—
1363	C₂³	—	2	1	no	—
1364	C₂³	—	2	1	no	—
1365	C₂³	—	2	1	no	—
1366	C₂³	—	2	1	no	—
1367	C₂³	—	2	1	no	—
1368	C₂³	—	2	1	no	—
1369	C₂³	—	2	1	no	—
1370	C₂³	—	2	1	no	—
1371	C₂³	—	2	1	no	—
1372	C₂³	—	2	1	no	—
1373	C₂³	—	2	1	no	—
1374	C₂³	—	2	1	no	—
1375	C₂³	—	2	1	no	—
1376	C₂³	—	2	1	no	—
1377	C₂³	—	2	1	no	—
1378	C₂³	—	2	1	no	—
1379	C₂³	—	2	1	no	—
1380	C₂³	—	2	1	no	—
1381	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1382	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1383	C₂³	C₂×#41×C₅₃	1	2	yes	—
1384	C₂³	C₂×#41×C₅₃	1	2	yes	—
1385	C₂³	C₂×#41×C₅₃	1	2	yes	—
1386	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1387	Q₈	—	2	8	no	—
1388	Q₈	—	4	4	no	—
1389	D₄	—	2	8	no	—
1390	D₄	—	2	8	no	—
1391	D₄	—	2	8	no	—
1392	D₄	—	4	4	no	—
1393	D₄	—	4	4	no	—
1394	D₄	—	4	4	no	—
1395	C₂×C₄	—	2	8	no	—
1396	C₂×C₄	—	2	8	no	—
1397	C₂×C₄	—	2	8	no	—
1398	C₂×C₄	—	2	8	no	—
1399	C₂×C₄	—	2	1	no	—
1400	C₂×C₄	—	2	1	no	—
1401	C₂×C₄	—	2	1	no	—
1402	C₂×C₄	—	2	1	no	—
1403	C₂×C₄	—	2	1	no	—
1404	C₂×C₄	—	2	1	no	—
1405	C₂×C₄	—	2	1	no	—
1406	C₂×C₄	—	2	1	no	—
1407	C₂×C₄	—	2	1	no	—
1408	C₂×C₄	—	2	1	no	—
1409	C₂×C₄	—	2	1	no	—
1410	C₂×C₄	—	2	1	no	—
1411	C₂×C₄	—	2	1	no	—
1412	C₂×C₄	—	2	1	no	—
1413	C₂×C₄	—	2	1	no	—
1414	C₂×C₄	—	2	1	no	—
1415	C₂×C₄	—	2	1	no	—
1416	C₂×C₄	—	2	1	no	—
1417	C₂×C₄	—	2	1	no	—
1418	C₂×C₄	—	2	1	no	—
1419	C₂×C₄	—	2	1	no	—
1420	C₂×C₄	—	2	1	no	—
1421	C₂×C₄	—	2	1	no	—
1422	C₂×C₄	—	2	1	no	—
1423	C₂×C₄	—	2	8	no	—
1424	C₂×C₄	—	2	8	no	—
1425	C₂×C₄	—	2	1	no	—
1426	C₂×C₄	—	2	1	no	—
1427	C₂×C₄	—	2	1	no	—
1428	C₂×C₄	—	2	1	no	—
1429	C₂×C₄	—	2	1	no	—
1430	C₂×C₄	—	2	1	no	—
1431	C₂×C₄	—	2	1	no	—
1432	C₂×C₄	—	2	1	no	—
1433	C₂×C₄	—	2	1	no	—
1434	C₂×C₄	—	2	1	no	—
1435	C₂×C₄	—	2	1	no	—
1436	C₂×C₄	—	2	1	no	—
1437	C₂×C₄	—	2	1	no	—
1438	C₂×C₄	—	2	1	no	—
1439	C₂×C₄	—	2	1	no	—
1440	C₂×C₄	—	2	1	no	—
1441	C₂×C₄	—	2	1	no	—
1442	C₂×C₄	—	2	1	no	—
1443	C₂×C₄	—	2	1	no	—
1444	C₂×C₄	—	2	1	no	—
1445	C₂×C₄	—	2	1	no	—
1446	C₂×C₄	—	2	1	no	—
1447	C₂×C₄	—	2	1	no	—
1448	C₂×C₄	—	2	1	no	—
1449	C₂×C₄	—	2	1	no	—
1450	C₂×C₄	—	2	1	no	—
1451	C₂×C₄	—	2	1	no	—
1452	C₂×C₄	—	2	1	no	—
1453	C₂×C₄	—	2	1	no	—
1454	C₂×C₄	—	2	1	no	—
1455	C₂×C₄	—	2	1	no	—
1456	C₂×C₄	—	2	1	no	—
1457	C₂×C₄	—	2	1	no	—
1458	C₂×C₄	—	2	1	no	—
1459	C₂×C₄	—	2	1	no	—
1460	C₂×C₄	—	2	1	no	—
1461	C₂×C₄	—	2	1	no	—
1462	C₂×C₄	—	2	1	no	—
1463	C₂×C₄	—	2	1	no	—
1464	C₂×C₄	—	2	1	no	—
1465	C₂×C₄	—	2	1	no	—
1466	C₂×C₄	—	2	1	no	—
1467	C₂×C₄	—	4	4	no	—
1468	C₂×C₄	—	4	4	no	—
1469	C₂×C₄	—	4	4	no	—
1470	C₂×C₄	—	4	4	no	—
1471	C₂×C₄	—	4	4	no	—
1472	C₂×C₄	—	4	4	no	—
1473	C₂×C₄	—	4	4	no	—
1474	C₂×C₄	—	4	4	no	—
1475	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1476	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1477	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1478	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1479	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1480	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1481	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1482	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1483	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1484	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1485	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1486	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1487	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1488	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1489	C₂×C₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1490	C₂²	—	2	2	no	—
1491	C₂²	—	2	2	no	—
1492	C₂²	—	2	2	no	—
1493	C₂²	—	2	2	no	—
1494	C₂²	—	2	2	no	—
1495	C₂²	—	2	2	no	—
1496	C₂²	—	2	2	no	—
1497	C₂²	—	2	2	no	—
1498	C₂²	—	2	2	no	—
1499	C₂²	—	2	2	no	—
1500	C₂²	—	2	2	no	—
1501	C₂²	—	2	2	no	—
1502	C₂²	—	4	1	no	—
1503	C₂²	—	4	1	no	—
1504	C₂²	—	4	1	no	—
1505	C₂²	—	4	1	no	—
1506	C₂²	—	4	1	no	—
1507	C₂²	—	4	1	no	—
1508	C₂²	—	4	1	no	—
1509	C₂²	—	4	1	no	—
1510	C₂²	—	4	1	no	—
1511	C₂²	—	4	1	no	—
1512	C₂²	—	4	1	no	—
1513	C₂²	—	4	1	no	—
1514	C₂²	—	4	1	no	—
1515	C₂²	—	4	1	no	—
1516	C₂²	—	4	1	no	—
1517	C₂²	C₅₃×#525	1	4	yes	—
1518	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1519	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1520	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1521	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1522	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1523	C₂²	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1524	C₂²	C₅₃×#585	1	1	yes	characteristic
1525	C₄	—	2	2	no	—
1526	C₄	—	2	2	no	—
1527	C₄	—	2	2	no	—
1528	C₄	—	2	2	no	—
1529	C₄	—	2	2	no	—
1530	C₄	—	2	2	no	—
1531	C₄	—	2	2	no	—
1532	C₄	—	2	2	no	—
1533	C₄	—	2	2	no	—
1534	C₄	—	2	2	no	—
1535	C₄	—	2	2	no	—
1536	C₄	—	2	2	no	—
1537	C₄	—	4	1	no	—
1538	C₄	—	4	1	no	—
1539	C₄	—	4	1	no	—
1540	C₄	—	4	1	no	—
1541	C₄	—	4	1	no	—
1542	C₄	—	4	1	no	—
1543	C₄	—	4	1	no	—
1544	C₄	—	4	1	no	—
1545	C₄	—	4	1	no	—
1546	C₄	—	4	1	no	—
1547	C₄	—	4	1	no	—
1548	C₄	—	4	1	no	—
1549	C₄	—	4	1	no	—
1550	C₄	—	4	1	no	—
1551	C₄	C₅₃×#547	1	4	yes	—
1552	C₂	—	2	4	no	—
1553	C₂	—	4	2	no	—
1554	C₂	—	4	2	no	—
1555	C₂	—	8	1	no	—
1556	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1557	C₂	C₅₃×#3444	1	1	yes	characteristic
1558	C₂	C₅₃×#3461	1	1	yes	characteristic
1559	C₂	C₂×C₅₃×#547	1	1	yes	characteristic
1560	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1561	C₂	C₅₃×#3475	1	1	yes	characteristic
1562	C₂	C₅₃×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
socle	C₂³×C₅₃	C₂⁵
prime radical	C₅₃×#2430	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#529	C₂	semidirect
2. C₂×C₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#2479	C₂	semidirect
4. C₅₃×#2478	C₂	semidirect
5. C₅₃×#2475	C₂	semidirect
6. C₅₃×#2474	C₂	semidirect
7. C₅₃×#2469	C₂	semidirect
8. C₅₃×#2468	C₂	semidirect
9. C₅₃×#2462	C₂	semidirect
10. C₅₃×#2461	C₂	semidirect
11. C₅₃×#2449	C₂	semidirect
12. C₅₃×#2443	C₂	semidirect
13. C₅₃×#2438	C₂	semidirect
15. C₅₃×#2425	C₂	semidirect
16. C₅₃×#2419	C₂	semidirect
17. C₅₃×#2413	C₂	semidirect
18. C₅₃×#2406	C₂	semidirect
19. C₅₃×#2399	C₂	semidirect
20. C₅₃×#2396	C₂	semidirect
21. C₅₃×#2395	C₂	semidirect
22. C₅₃×#2392	C₂	semidirect
23. C₄×C₂²⋊Q₈×C₅₃	C₂	semidirect
24. C₄×#123×C₅₃	C₂	semidirect
25. C₄×#123×C₅₃	C₂	semidirect
26. C₄×#123×C₅₃	C₂	semidirect
27. C₄×#121×C₅₃	C₂	semidirect
28. C₅₃×#2296	C₂	semidirect
29. C₅₃×#2290	C₂	semidirect
30. C₅₃×#2290	C₂	semidirect
31. C₂×C₄×C₄⋊C₄×C₅₃	C₂	semidirect
238. C₄×D₄×C₅₃	D₄	semidirect
520. C₄⋊C₄×C₅₃	#41	semidirect
575. C₄²×C₅₃	#41	semidirect
708. #34735	C₅₃	direct (N × H)
771. C₂×#529	C₂×C₅₃	semidirect
772. C₂×C₄×#41	C₂×C₅₃	semidirect
773. #2479	C₂×C₅₃	semidirect
774. #2478	C₂×C₅₃	semidirect
775. #2475	C₂×C₅₃	semidirect
776. #2474	C₂×C₅₃	semidirect
777. #2469	C₂×C₅₃	semidirect
778. #2468	C₂×C₅₃	semidirect
779. #2462	C₂×C₅₃	semidirect
780. #2461	C₂×C₅₃	semidirect
781. #2449	C₂×C₅₃	semidirect
782. #2443	C₂×C₅₃	semidirect
783. #2438	C₂×C₅₃	semidirect
785. #2425	C₂×C₅₃	semidirect
786. #2419	C₂×C₅₃	semidirect
787. #2413	C₂×C₅₃	semidirect
788. #2406	C₂×C₅₃	semidirect
789. #2399	C₂×C₅₃	semidirect
790. #2396	C₂×C₅₃	semidirect
791. #2395	C₂×C₅₃	semidirect
792. #2392	C₂×C₅₃	semidirect
793. C₄×C₂²⋊Q₈	C₂×C₅₃	semidirect
794. C₄×#123	C₂×C₅₃	semidirect
795. C₄×#123	C₂×C₅₃	semidirect
796. C₄×#123	C₂×C₅₃	semidirect
797. C₄×#121	C₂×C₅₃	semidirect
798. #2296	C₂×C₅₃	semidirect
799. #2290	C₂×C₅₃	semidirect
800. #2290	C₂×C₅₃	semidirect
801. C₂×C₄×C₄⋊C₄	C₂×C₅₃	semidirect
970. C₅₃	#34735	direct (N × H)
1020. C₄×D₄	D₄×C₅₃	semidirect
1302. C₄⋊C₄	#41×C₅₃	semidirect
1357. C₄²	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅₃×#529	2
C₂×C₄×#41×C₅₃	2
C₅₃×#2479	2
C₅₃×#2478	2
C₅₃×#2475	2
C₅₃×#2474	2
C₅₃×#2469	2
C₅₃×#2468	2
C₅₃×#2462	2
C₅₃×#2461	2
C₅₃×#2449	2
C₅₃×#2443	2
C₅₃×#2438	2
C₅₃×#2430	2
C₅₃×#2425	2
C₅₃×#2419	2
C₅₃×#2413	2
C₅₃×#2406	2
C₅₃×#2399	2
C₅₃×#2396	2
C₅₃×#2395	2
C₅₃×#2392	2
C₄×C₂²⋊Q₈×C₅₃	2
C₄×#123×C₅₃	2
C₄×#121×C₅₃	2
C₅₃×#2296	2
C₅₃×#2290	2
C₂×C₄×C₄⋊C₄×C₅₃	2
#34735	53

Subgroups — C53×#34735 #27242247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34735 #27242247