Subgroups — C₅₃×#34990 #27242502

Order 13568.

3146 conjugacy classes of subgroups.

The subgroup lattice has 1872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅₃×#538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#2852	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#2849	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#2636	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#2635	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#2631	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#2630	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2481	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#2472	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#2467	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#2459	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#2456	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#2456	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#2450	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#2444	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2443	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2437	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2424	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2424	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#2410	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#2410	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#2403	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#2325	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2321	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2318	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×#120×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
31	C₂×C₅₃×#386	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
33	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic
34	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic
35	C₂⁴×C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#538	—	2	8	no	—
37	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#126×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂×#123×C₅₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
47	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
48	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
49	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic
50	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
54	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
57	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₂×#120×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂×C₄×D₄×C₅₃	—	2	8	no	—
61	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
62	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
63	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
64	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
68	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
69	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
72	C₂²×C₄⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
73	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
74	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic
75	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
77	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
78	C₂²×C₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#400	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#399	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#398	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#397	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#396	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#394	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#393	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#392	C₂²	1	1	yes	characteristic
103	C₅₃×#392	C₂²	1	1	yes	characteristic
104	C₅₃×#392	C₂²	1	1	yes	characteristic
105	C₅₃×#392	C₂²	1	1	yes	characteristic
106	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#392	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#391	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#390	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#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×#388	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#388	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#387	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#386	C₂²	1	1	yes	characteristic
134	C₅₃×#386	C₂²	1	1	yes	characteristic
135	C₅₃×#386	C₂²	1	1	yes	characteristic
136	C₅₃×#386	C₂²	1	1	yes	characteristic
137	C₅₃×#386	C₂²	1	1	yes	characteristic
138	C₅₃×#386	C₂²	1	1	yes	characteristic
139	C₅₃×#386	C₂²	1	1	yes	characteristic
140	C₅₃×#386	C₂²	1	1	yes	characteristic
141	C₅₃×#386	C₂²	1	1	yes	characteristic
142	C₅₃×#386	C₂²	1	1	yes	characteristic
143	C₅₃×#386	C₂²	1	1	yes	characteristic
144	C₅₃×#386	C₂²	1	1	yes	characteristic
145	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#386	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#385	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#383	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#382	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#381	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#380	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#379	C₂²	1	1	yes	characteristic
182	C₅₃×#379	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#379	C₂²	1	1	yes	characteristic, complemented
184	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
186	C₄×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₂×#95×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
190	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
191	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
192	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
193	C₂²×D₄×C₅₃	—	2	4	no	—
194	C₂²×D₄×C₅₃	—	2	4	no	—
195	C₂²×D₄×C₅₃	—	2	4	no	—
196	C₂²×D₄×C₅₃	—	2	4	no	—
197	C₂²×D₄×C₅₃	—	4	2	no	—
198	C₂²×D₄×C₅₃	—	4	2	no	—
199	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
201	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
202	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
203	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
204	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
207	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂³×C₄×C₅₃	—	2	4	no	—
219	C₂³×C₄×C₅₃	—	2	4	no	—
220	C₂³×C₄×C₅₃	—	4	2	no	—
221	C₂³×C₄×C₅₃	—	4	2	no	—
222	C₂³×C₄×C₅₃	—	4	2	no	—
223	C₂³×C₄×C₅₃	—	4	2	no	—
224	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
225	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
226	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
227	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
228	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
232	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
233	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
235	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
238	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
239	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
241	#126×C₅₃	—	2	4	no	—
242	#126×C₅₃	—	2	4	no	—
243	#124×C₅₃	—	2	4	no	—
244	#124×C₅₃	—	2	4	no	—
245	#123×C₅₃	—	2	4	no	—
246	#123×C₅₃	—	2	4	no	—
247	#123×C₅₃	—	4	2	no	—
248	C₂²⋊Q₈×C₅₃	—	2	4	no	—
249	C₂²⋊Q₈×C₅₃	—	4	2	no	—
250	#121×C₅₃	—	2	4	no	—
251	#121×C₅₃	—	2	4	no	—
252	#121×C₅₃	—	2	4	no	—
253	#121×C₅₃	—	2	4	no	—
254	#121×C₅₃	—	4	2	no	—
255	#121×C₅₃	—	4	2	no	—
256	#121×C₅₃	—	4	2	no	—
257	#120×C₅₃	—	2	4	no	—
258	#120×C₅₃	—	2	4	no	—
259	#120×C₅₃	—	2	4	no	—
260	#120×C₅₃	—	2	4	no	—
261	#120×C₅₃	—	4	2	no	—
262	#120×C₅₃	—	4	2	no	—
263	#120×C₅₃	—	4	2	no	—
264	C₄×D₄×C₅₃	—	2	4	no	—
265	C₄×D₄×C₅₃	—	2	4	no	—
266	C₄×D₄×C₅₃	—	2	4	no	—
267	C₄×D₄×C₅₃	—	2	4	no	—
268	C₄×D₄×C₅₃	—	2	4	no	—
269	C₄×D₄×C₅₃	—	2	4	no	—
270	C₄×D₄×C₅₃	—	2	4	no	—
271	C₄×D₄×C₅₃	—	2	4	no	—
272	C₄×D₄×C₅₃	—	4	2	no	—
273	C₄×D₄×C₅₃	—	4	2	no	—
274	C₄×D₄×C₅₃	D₄	1	8	yes	complemented
275	C₂×C₄⋊C₄×C₅₃	—	2	4	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
286	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
287	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
288	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
289	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
290	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
295	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
297	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
298	C₂×C₂²⋊C₄×C₅₃	—	2	4	no	—
299	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
300	C₂×C₂²⋊C₄×C₅₃	—	4	2	no	—
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×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
320	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
321	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
322	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
323	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
324	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
325	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
327	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
329	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
330	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
333	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
334	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
335	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
337	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
338	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
339	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
340	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
343	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
344	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
345	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
346	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
347	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
348	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
349	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
350	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
351	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
352	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
353	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
354	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
355	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
356	C₂×C₂²⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₂×C₄²×C₅₃	—	2	4	no	—
358	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
359	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
360	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
361	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
362	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
363	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
364	C₂×C₄²×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	#95×C₅₃	C₂³	1	1	yes	characteristic
386	#95×C₅₃	C₂³	1	1	yes	characteristic
387	#95×C₅₃	C₂³	1	1	yes	characteristic
388	#95×C₅₃	C₂³	1	1	yes	characteristic
389	#95×C₅₃	C₂³	1	1	yes	characteristic
390	#95×C₅₃	C₂³	1	1	yes	characteristic
391	#95×C₅₃	C₂³	1	1	yes	characteristic
392	#95×C₅₃	C₂³	1	1	yes	characteristic
393	#95×C₅₃	C₂³	1	1	yes	characteristic
394	#95×C₅₃	C₂³	1	1	yes	characteristic
395	#95×C₅₃	C₂³	1	1	yes	characteristic
396	#95×C₅₃	C₂³	1	1	yes	characteristic
397	C₂⁴×C₅₃	—	2	2	no	—
398	C₂⁴×C₅₃	—	2	2	no	—
399	C₂⁴×C₅₃	—	2	2	no	—
400	C₂⁴×C₅₃	—	2	2	no	—
401	C₂⁴×C₅₃	—	2	2	no	—
402	C₂⁴×C₅₃	—	2	2	no	—
403	C₂⁴×C₅₃	—	2	2	no	—
404	C₂⁴×C₅₃	—	2	2	no	—
405	C₂⁴×C₅₃	—	2	2	no	—
406	C₂⁴×C₅₃	—	2	2	no	—
407	C₂⁴×C₅₃	—	2	2	no	—
408	C₂⁴×C₅₃	—	2	2	no	—
409	C₂⁴×C₅₃	—	4	1	no	—
410	C₂⁴×C₅₃	—	4	1	no	—
411	C₂⁴×C₅₃	—	4	1	no	—
412	C₂⁴×C₅₃	—	4	1	no	—
413	C₂⁴×C₅₃	—	4	1	no	—
414	C₂⁴×C₅₃	—	4	1	no	—
415	C₂⁴×C₅₃	—	4	1	no	—
416	C₂⁴×C₅₃	—	4	1	no	—
417	C₂⁴×C₅₃	#41	1	4	yes	—
418	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
419	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
426	C₂×Q₈×C₅₃	—	2	2	no	—
427	C₂×Q₈×C₅₃	—	4	1	no	—
428	C₂×Q₈×C₅₃	—	4	1	no	—
429	C₂×D₄×C₅₃	—	2	32	no	—
430	C₂×D₄×C₅₃	—	2	2	no	—
431	C₂×D₄×C₅₃	—	2	2	no	—
432	C₂×D₄×C₅₃	—	2	2	no	—
433	C₂×D₄×C₅₃	—	2	2	no	—
434	C₂×D₄×C₅₃	—	2	2	no	—
435	C₂×D₄×C₅₃	—	2	2	no	—
436	C₂×D₄×C₅₃	—	2	2	no	—
437	C₂×D₄×C₅₃	—	2	2	no	—
438	C₂×D₄×C₅₃	—	2	2	no	—
439	C₂×D₄×C₅₃	—	2	2	no	—
440	C₂×D₄×C₅₃	—	2	2	no	—
441	C₂×D₄×C₅₃	—	2	2	no	—
442	C₂×D₄×C₅₃	—	2	2	no	—
443	C₂×D₄×C₅₃	—	2	2	no	—
444	C₂×D₄×C₅₃	—	2	2	no	—
445	C₂×D₄×C₅₃	—	2	2	no	—
446	C₂×D₄×C₅₃	—	2	2	no	—
447	C₂×D₄×C₅₃	—	2	2	no	—
448	C₂×D₄×C₅₃	—	2	2	no	—
449	C₂×D₄×C₅₃	—	2	2	no	—
450	C₂×D₄×C₅₃	—	2	2	no	—
451	C₂×D₄×C₅₃	—	2	2	no	—
452	C₂×D₄×C₅₃	—	2	2	no	—
453	C₂×D₄×C₅₃	—	2	2	no	—
454	C₂×D₄×C₅₃	—	2	2	no	—
455	C₂×D₄×C₅₃	—	2	2	no	—
456	C₂×D₄×C₅₃	—	2	2	no	—
457	C₂×D₄×C₅₃	—	2	2	no	—
458	C₂×D₄×C₅₃	—	2	2	no	—
459	C₂×D₄×C₅₃	—	2	2	no	—
460	C₂×D₄×C₅₃	—	2	2	no	—
461	C₂×D₄×C₅₃	—	2	2	no	—
462	C₂×D₄×C₅₃	—	2	2	no	—
463	C₂×D₄×C₅₃	—	4	1	no	—
464	C₂×D₄×C₅₃	—	4	1	no	—
465	C₂×D₄×C₅₃	—	4	1	no	—
466	C₂×D₄×C₅₃	—	4	1	no	—
467	C₂×D₄×C₅₃	—	4	1	no	—
468	C₂×D₄×C₅₃	—	4	1	no	—
469	C₂×D₄×C₅₃	—	4	1	no	—
470	C₂×D₄×C₅₃	—	4	1	no	—
471	C₂×D₄×C₅₃	—	4	1	no	—
472	C₂×D₄×C₅₃	—	4	1	no	—
473	C₂×D₄×C₅₃	—	4	1	no	—
474	C₂×D₄×C₅₃	—	4	1	no	—
475	C₂×D₄×C₅₃	—	4	1	no	—
476	C₂×D₄×C₅₃	—	4	1	no	—
477	C₂×D₄×C₅₃	—	4	1	no	—
478	C₂×D₄×C₅₃	—	4	1	no	—
479	C₂×D₄×C₅₃	—	4	1	no	—
480	C₂×D₄×C₅₃	—	4	1	no	—
481	C₂×D₄×C₅₃	—	4	1	no	—
482	C₂×D₄×C₅₃	—	4	1	no	—
483	C₂×D₄×C₅₃	—	4	1	no	—
484	C₂×D₄×C₅₃	—	4	1	no	—
485	C₂×D₄×C₅₃	—	4	16	no	—
486	C₂×D₄×C₅₃	C₂×D₄	1	4	yes	—
487	C₂×D₄×C₅₃	#41	1	4	yes	—
488	C₂²×C₄×C₅₃	—	2	2	no	—
489	C₂²×C₄×C₅₃	—	2	2	no	—
490	C₂²×C₄×C₅₃	—	2	2	no	—
491	C₂²×C₄×C₅₃	—	2	2	no	—
492	C₂²×C₄×C₅₃	—	2	2	no	—
493	C₂²×C₄×C₅₃	—	2	2	no	—
494	C₂²×C₄×C₅₃	—	2	2	no	—
495	C₂²×C₄×C₅₃	—	2	2	no	—
496	C₂²×C₄×C₅₃	—	2	2	no	—
497	C₂²×C₄×C₅₃	—	2	2	no	—
498	C₂²×C₄×C₅₃	—	2	2	no	—
499	C₂²×C₄×C₅₃	—	2	2	no	—
500	C₂²×C₄×C₅₃	—	2	2	no	—
501	C₂²×C₄×C₅₃	—	2	2	no	—
502	C₂²×C₄×C₅₃	—	2	2	no	—
503	C₂²×C₄×C₅₃	—	2	2	no	—
504	C₂²×C₄×C₅₃	—	2	2	no	—
505	C₂²×C₄×C₅₃	—	2	2	no	—
506	C₂²×C₄×C₅₃	—	2	2	no	—
507	C₂²×C₄×C₅₃	—	2	2	no	—
508	C₂²×C₄×C₅₃	—	2	2	no	—
509	C₂²×C₄×C₅₃	—	2	2	no	—
510	C₂²×C₄×C₅₃	—	2	2	no	—
511	C₂²×C₄×C₅₃	—	2	2	no	—
512	C₂²×C₄×C₅₃	—	2	2	no	—
513	C₂²×C₄×C₅₃	—	2	2	no	—
514	C₂²×C₄×C₅₃	—	4	1	no	—
515	C₂²×C₄×C₅₃	—	4	1	no	—
516	C₂²×C₄×C₅₃	—	4	1	no	—
517	C₂²×C₄×C₅₃	—	4	1	no	—
518	C₂²×C₄×C₅₃	—	4	1	no	—
519	C₂²×C₄×C₅₃	—	4	1	no	—
520	C₂²×C₄×C₅₃	—	4	1	no	—
521	C₂²×C₄×C₅₃	—	4	1	no	—
522	C₂²×C₄×C₅₃	—	4	1	no	—
523	C₂²×C₄×C₅₃	—	4	1	no	—
524	C₂²×C₄×C₅₃	—	4	1	no	—
525	C₂²×C₄×C₅₃	—	4	1	no	—
526	C₂²×C₄×C₅₃	—	4	1	no	—
527	C₂²×C₄×C₅₃	—	4	1	no	—
528	C₂²×C₄×C₅₃	—	4	1	no	—
529	C₂²×C₄×C₅₃	—	4	1	no	—
530	C₂²×C₄×C₅₃	—	4	1	no	—
531	C₂²×C₄×C₅₃	—	4	1	no	—
532	C₂²×C₄×C₅₃	—	4	1	no	—
533	C₂²×C₄×C₅₃	—	4	1	no	—
534	C₂²×C₄×C₅₃	—	4	1	no	—
535	C₂²×C₄×C₅₃	—	4	1	no	—
536	C₂²×C₄×C₅₃	—	4	1	no	—
537	C₂²×C₄×C₅₃	—	4	16	no	—
538	C₂²×C₄×C₅₃	—	4	16	no	—
539	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	—
540	C₂²×C₄×C₅₃	C₂×D₄	1	4	yes	complemented
541	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
544	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
545	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
547	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
548	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
549	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
550	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
551	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
552	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
553	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
554	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
555	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
556	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
561	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
562	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
564	C₄⋊C₄×C₅₃	—	2	2	no	—
565	C₄⋊C₄×C₅₃	—	2	2	no	—
566	C₄⋊C₄×C₅₃	—	2	2	no	—
567	C₄⋊C₄×C₅₃	—	2	2	no	—
568	C₄⋊C₄×C₅₃	—	2	2	no	—
569	C₄⋊C₄×C₅₃	—	2	2	no	—
570	C₄⋊C₄×C₅₃	—	2	2	no	—
571	C₄⋊C₄×C₅₃	—	2	2	no	—
572	C₄⋊C₄×C₅₃	—	2	2	no	—
573	C₄⋊C₄×C₅₃	—	2	2	no	—
574	C₄⋊C₄×C₅₃	—	4	1	no	—
575	C₄⋊C₄×C₅₃	—	4	1	no	—
576	C₄⋊C₄×C₅₃	—	4	1	no	—
577	C₄⋊C₄×C₅₃	—	4	1	no	—
578	C₄⋊C₄×C₅₃	—	4	1	no	—
579	C₄⋊C₄×C₅₃	—	4	1	no	—
580	C₄⋊C₄×C₅₃	—	4	1	no	—
581	C₄⋊C₄×C₅₃	—	4	1	no	—
582	C₄⋊C₄×C₅₃	—	4	1	no	—
583	C₄⋊C₄×C₅₃	C₂×D₄	1	4	yes	complemented
584	C₂²⋊C₄×C₅₃	—	2	2	no	—
585	C₂²⋊C₄×C₅₃	—	2	2	no	—
586	C₂²⋊C₄×C₅₃	—	2	2	no	—
587	C₂²⋊C₄×C₅₃	—	2	2	no	—
588	C₂²⋊C₄×C₅₃	—	2	2	no	—
589	C₂²⋊C₄×C₅₃	—	2	2	no	—
590	C₂²⋊C₄×C₅₃	—	2	2	no	—
591	C₂²⋊C₄×C₅₃	—	2	2	no	—
592	C₂²⋊C₄×C₅₃	—	2	2	no	—
593	C₂²⋊C₄×C₅₃	—	2	2	no	—
594	C₂²⋊C₄×C₅₃	—	2	2	no	—
595	C₂²⋊C₄×C₅₃	—	2	2	no	—
596	C₂²⋊C₄×C₅₃	—	2	2	no	—
597	C₂²⋊C₄×C₅₃	—	2	2	no	—
598	C₂²⋊C₄×C₅₃	—	2	2	no	—
599	C₂²⋊C₄×C₅₃	—	2	2	no	—
600	C₂²⋊C₄×C₅₃	—	2	2	no	—
601	C₂²⋊C₄×C₅₃	—	2	2	no	—
602	C₂²⋊C₄×C₅₃	—	2	2	no	—
603	C₂²⋊C₄×C₅₃	—	2	2	no	—
604	C₂²⋊C₄×C₅₃	—	2	2	no	—
605	C₂²⋊C₄×C₅₃	—	2	2	no	—
606	C₂²⋊C₄×C₅₃	—	2	2	no	—
607	C₂²⋊C₄×C₅₃	—	2	2	no	—
608	C₂²⋊C₄×C₅₃	—	2	2	no	—
609	C₂²⋊C₄×C₅₃	—	2	2	no	—
610	C₂²⋊C₄×C₅₃	—	2	2	no	—
611	C₂²⋊C₄×C₅₃	—	2	2	no	—
612	C₂²⋊C₄×C₅₃	—	2	2	no	—
613	C₂²⋊C₄×C₅₃	—	2	2	no	—
614	C₂²⋊C₄×C₅₃	—	2	2	no	—
615	C₂²⋊C₄×C₅₃	—	2	2	no	—
616	C₂²⋊C₄×C₅₃	—	2	2	no	—
617	C₂²⋊C₄×C₅₃	—	4	1	no	—
618	C₂²⋊C₄×C₅₃	—	4	1	no	—
619	C₂²⋊C₄×C₅₃	—	4	1	no	—
620	C₂²⋊C₄×C₅₃	—	4	1	no	—
621	C₂²⋊C₄×C₅₃	—	4	1	no	—
622	C₂²⋊C₄×C₅₃	—	4	1	no	—
623	C₂²⋊C₄×C₅₃	—	4	1	no	—
624	C₂²⋊C₄×C₅₃	—	4	1	no	—
625	C₂²⋊C₄×C₅₃	—	4	1	no	—
626	C₂²⋊C₄×C₅₃	—	4	1	no	—
627	C₂²⋊C₄×C₅₃	—	4	1	no	—
628	C₂²⋊C₄×C₅₃	—	4	1	no	—
629	C₂²⋊C₄×C₅₃	—	4	1	no	—
630	C₂²⋊C₄×C₅₃	—	4	1	no	—
631	C₂²⋊C₄×C₅₃	—	4	1	no	—
632	C₂²⋊C₄×C₅₃	—	4	1	no	—
633	C₂²⋊C₄×C₅₃	—	4	1	no	—
634	C₂²⋊C₄×C₅₃	—	4	1	no	—
635	C₂²⋊C₄×C₅₃	—	4	1	no	—
636	C₂²⋊C₄×C₅₃	—	4	1	no	—
637	C₂²⋊C₄×C₅₃	—	4	1	no	—
638	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	—
639	C₂²⋊C₄×C₅₃	C₂×D₄	1	4	yes	complemented
640	C₄²×C₅₃	—	2	2	no	—
641	C₄²×C₅₃	—	2	2	no	—
642	C₄²×C₅₃	—	2	2	no	—
643	C₄²×C₅₃	—	2	2	no	—
644	C₄²×C₅₃	—	4	1	no	—
645	C₄²×C₅₃	—	4	1	no	—
646	C₄²×C₅₃	C₂×D₄	1	4	yes	complemented
647	C₂³×C₅₃	—	2	1	no	—
648	C₂³×C₅₃	—	2	1	no	—
649	C₂³×C₅₃	—	2	1	no	—
650	C₂³×C₅₃	—	2	1	no	—
651	C₂³×C₅₃	—	2	1	no	—
652	C₂³×C₅₃	—	2	1	no	—
653	C₂³×C₅₃	—	2	1	no	—
654	C₂³×C₅₃	—	2	1	no	—
655	C₂³×C₅₃	—	2	8	no	—
656	C₂³×C₅₃	—	2	8	no	—
657	C₂³×C₅₃	—	2	8	no	—
658	C₂³×C₅₃	—	2	1	no	—
659	C₂³×C₅₃	—	2	1	no	—
660	C₂³×C₅₃	—	2	1	no	—
661	C₂³×C₅₃	—	2	1	no	—
662	C₂³×C₅₃	—	2	1	no	—
663	C₂³×C₅₃	—	2	1	no	—
664	C₂³×C₅₃	—	2	1	no	—
665	C₂³×C₅₃	—	2	1	no	—
666	C₂³×C₅₃	—	2	1	no	—
667	C₂³×C₅₃	—	2	1	no	—
668	C₂³×C₅₃	—	2	1	no	—
669	C₂³×C₅₃	—	2	1	no	—
670	C₂³×C₅₃	—	2	1	no	—
671	C₂³×C₅₃	—	2	1	no	—
672	C₂³×C₅₃	—	2	1	no	—
673	C₂³×C₅₃	—	2	1	no	—
674	C₂³×C₅₃	—	2	1	no	—
675	C₂³×C₅₃	—	2	1	no	—
676	C₂³×C₅₃	—	2	1	no	—
677	C₂³×C₅₃	—	2	1	no	—
678	C₂³×C₅₃	—	2	1	no	—
679	C₂³×C₅₃	—	2	1	no	—
680	C₂³×C₅₃	—	2	1	no	—
681	C₂³×C₅₃	—	2	1	no	—
682	C₂³×C₅₃	—	2	1	no	—
683	C₂³×C₅₃	—	2	1	no	—
684	C₂³×C₅₃	—	2	1	no	—
685	C₂³×C₅₃	—	2	1	no	—
686	C₂³×C₅₃	—	2	1	no	—
687	C₂³×C₅₃	—	2	1	no	—
688	C₂³×C₅₃	—	2	1	no	—
689	C₂³×C₅₃	—	2	1	no	—
690	C₂³×C₅₃	—	2	1	no	—
691	C₂³×C₅₃	—	2	1	no	—
692	C₂³×C₅₃	—	2	1	no	—
693	C₂³×C₅₃	—	2	1	no	—
694	C₂³×C₅₃	—	2	1	no	—
695	C₂³×C₅₃	—	2	1	no	—
696	C₂³×C₅₃	—	2	1	no	—
697	C₂³×C₅₃	—	4	4	no	—
698	C₂³×C₅₃	—	4	4	no	—
699	C₂³×C₅₃	—	4	4	no	—
700	C₂³×C₅₃	—	4	4	no	—
701	C₂³×C₅₃	—	4	4	no	—
702	C₂³×C₅₃	—	4	4	no	—
703	C₂³×C₅₃	—	4	4	no	—
704	C₂³×C₅₃	—	4	4	no	—
705	C₂³×C₅₃	—	4	4	no	—
706	C₂³×C₅₃	—	4	4	no	—
707	C₂³×C₅₃	—	4	4	no	—
708	C₂³×C₅₃	—	4	4	no	—
709	C₂³×C₅₃	—	4	4	no	—
710	C₂³×C₅₃	—	4	4	no	—
711	C₂³×C₅₃	—	8	2	no	—
712	C₂³×C₅₃	—	8	2	no	—
713	C₂³×C₅₃	—	8	2	no	—
714	C₂³×C₅₃	—	8	2	no	—
715	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
716	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
717	C₂³×C₅₃	C₂×#41	1	2	yes	—
718	C₂³×C₅₃	C₂×#41	1	2	yes	—
719	C₂³×C₅₃	C₂×#41	1	2	yes	—
720	C₂³×C₅₃	C₂×#41	1	2	yes	—
721	C₂³×C₅₃	C₂×#41	1	2	yes	—
722	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
723	C₂³×C₅₃	H(5,𝔽₂)	1	2	yes	—
724	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
725	Q₈×C₅₃	—	8	2	no	—
726	D₄×C₅₃	—	2	8	no	—
727	D₄×C₅₃	—	2	8	no	—
728	D₄×C₅₃	—	2	8	no	—
729	D₄×C₅₃	—	2	8	no	—
730	D₄×C₅₃	—	4	4	no	—
731	D₄×C₅₃	—	4	4	no	—
732	D₄×C₅₃	—	4	4	no	—
733	D₄×C₅₃	—	4	4	no	—
734	D₄×C₅₃	—	4	4	no	—
735	D₄×C₅₃	—	4	4	no	—
736	D₄×C₅₃	—	4	4	no	—
737	D₄×C₅₃	—	8	2	no	—
738	D₄×C₅₃	—	8	2	no	—
739	D₄×C₅₃	—	8	2	no	—
740	D₄×C₅₃	—	8	2	no	—
741	D₄×C₅₃	—	8	2	no	—
742	D₄×C₅₃	—	8	2	no	—
743	D₄×C₅₃	—	8	2	no	—
744	D₄×C₅₃	—	8	2	no	—
745	C₂×C₄×C₅₃	—	2	8	no	—
746	C₂×C₄×C₅₃	—	2	8	no	—
747	C₂×C₄×C₅₃	—	2	1	no	—
748	C₂×C₄×C₅₃	—	2	1	no	—
749	C₂×C₄×C₅₃	—	2	1	no	—
750	C₂×C₄×C₅₃	—	2	1	no	—
751	C₂×C₄×C₅₃	—	2	1	no	—
752	C₂×C₄×C₅₃	—	2	1	no	—
753	C₂×C₄×C₅₃	—	2	1	no	—
754	C₂×C₄×C₅₃	—	2	1	no	—
755	C₂×C₄×C₅₃	—	2	1	no	—
756	C₂×C₄×C₅₃	—	2	1	no	—
757	C₂×C₄×C₅₃	—	2	1	no	—
758	C₂×C₄×C₅₃	—	2	1	no	—
759	C₂×C₄×C₅₃	—	2	1	no	—
760	C₂×C₄×C₅₃	—	2	1	no	—
761	C₂×C₄×C₅₃	—	2	1	no	—
762	C₂×C₄×C₅₃	—	2	1	no	—
763	C₂×C₄×C₅₃	—	2	1	no	—
764	C₂×C₄×C₅₃	—	2	1	no	—
765	C₂×C₄×C₅₃	—	2	1	no	—
766	C₂×C₄×C₅₃	—	2	1	no	—
767	C₂×C₄×C₅₃	—	2	1	no	—
768	C₂×C₄×C₅₃	—	2	1	no	—
769	C₂×C₄×C₅₃	—	2	1	no	—
770	C₂×C₄×C₅₃	—	2	1	no	—
771	C₂×C₄×C₅₃	—	2	1	no	—
772	C₂×C₄×C₅₃	—	2	1	no	—
773	C₂×C₄×C₅₃	—	2	1	no	—
774	C₂×C₄×C₅₃	—	2	1	no	—
775	C₂×C₄×C₅₃	—	2	1	no	—
776	C₂×C₄×C₅₃	—	2	1	no	—
777	C₂×C₄×C₅₃	—	2	1	no	—
778	C₂×C₄×C₅₃	—	2	1	no	—
779	C₂×C₄×C₅₃	—	2	1	no	—
780	C₂×C₄×C₅₃	—	2	1	no	—
781	C₂×C₄×C₅₃	—	2	1	no	—
782	C₂×C₄×C₅₃	—	2	1	no	—
783	C₂×C₄×C₅₃	—	2	1	no	—
784	C₂×C₄×C₅₃	—	2	1	no	—
785	C₂×C₄×C₅₃	—	2	1	no	—
786	C₂×C₄×C₅₃	—	2	1	no	—
787	C₂×C₄×C₅₃	—	2	1	no	—
788	C₂×C₄×C₅₃	—	2	1	no	—
789	C₂×C₄×C₅₃	—	2	1	no	—
790	C₂×C₄×C₅₃	—	2	1	no	—
791	C₂×C₄×C₅₃	—	2	1	no	—
792	C₂×C₄×C₅₃	—	2	1	no	—
793	C₂×C₄×C₅₃	—	2	1	no	—
794	C₂×C₄×C₅₃	—	2	1	no	—
795	C₂×C₄×C₅₃	—	2	1	no	—
796	C₂×C₄×C₅₃	—	2	1	no	—
797	C₂×C₄×C₅₃	—	2	1	no	—
798	C₂×C₄×C₅₃	—	2	1	no	—
799	C₂×C₄×C₅₃	—	2	1	no	—
800	C₂×C₄×C₅₃	—	2	1	no	—
801	C₂×C₄×C₅₃	—	2	1	no	—
802	C₂×C₄×C₅₃	—	2	1	no	—
803	C₂×C₄×C₅₃	—	2	1	no	—
804	C₂×C₄×C₅₃	—	2	1	no	—
805	C₂×C₄×C₅₃	—	2	1	no	—
806	C₂×C₄×C₅₃	—	2	1	no	—
807	C₂×C₄×C₅₃	—	2	1	no	—
808	C₂×C₄×C₅₃	—	2	1	no	—
809	C₂×C₄×C₅₃	—	4	4	no	—
810	C₂×C₄×C₅₃	—	4	4	no	—
811	C₂×C₄×C₅₃	—	4	4	no	—
812	C₂×C₄×C₅₃	—	4	4	no	—
813	C₂×C₄×C₅₃	—	4	4	no	—
814	C₂×C₄×C₅₃	—	4	4	no	—
815	C₂×C₄×C₅₃	—	4	4	no	—
816	C₂×C₄×C₅₃	—	4	4	no	—
817	C₂×C₄×C₅₃	—	4	4	no	—
818	C₂×C₄×C₅₃	—	4	4	no	—
819	C₂×C₄×C₅₃	—	4	4	no	—
820	C₂×C₄×C₅₃	—	4	4	no	—
821	C₂×C₄×C₅₃	—	8	2	no	—
822	C₂×C₄×C₅₃	—	8	2	no	—
823	C₂×C₄×C₅₃	—	8	2	no	—
824	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
825	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
826	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
827	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
828	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
829	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
830	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
831	#34990	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
832	C₂²×C₅₃	—	2	2	no	—
833	C₂²×C₅₃	—	2	2	no	—
834	C₂²×C₅₃	—	2	2	no	—
835	C₂²×C₅₃	—	2	2	no	—
836	C₂²×C₅₃	—	2	2	no	—
837	C₂²×C₅₃	—	2	2	no	—
838	C₂²×C₅₃	—	2	2	no	—
839	C₂²×C₅₃	—	2	2	no	—
840	C₂²×C₅₃	—	2	2	no	—
841	C₂²×C₅₃	—	2	2	no	—
842	C₂²×C₅₃	—	2	2	no	—
843	C₂²×C₅₃	—	2	2	no	—
844	C₂²×C₅₃	—	2	2	no	—
845	C₂²×C₅₃	—	2	2	no	—
846	C₂²×C₅₃	—	2	2	no	—
847	C₂²×C₅₃	—	2	2	no	—
848	C₂²×C₅₃	—	2	2	no	—
849	C₂²×C₅₃	—	2	2	no	—
850	C₂²×C₅₃	—	2	2	no	—
851	C₂²×C₅₃	—	2	2	no	—
852	C₂²×C₅₃	—	2	2	no	—
853	C₂²×C₅₃	—	4	16	no	—
854	C₂²×C₅₃	—	4	16	no	—
855	C₂²×C₅₃	—	4	1	no	—
856	C₂²×C₅₃	—	4	1	no	—
857	C₂²×C₅₃	—	4	1	no	—
858	C₂²×C₅₃	—	4	1	no	—
859	C₂²×C₅₃	—	4	1	no	—
860	C₂²×C₅₃	—	4	1	no	—
861	C₂²×C₅₃	—	4	1	no	—
862	C₂²×C₅₃	—	4	1	no	—
863	C₂²×C₅₃	—	4	1	no	—
864	C₂²×C₅₃	—	4	1	no	—
865	C₂²×C₅₃	—	4	1	no	—
866	C₂²×C₅₃	—	4	1	no	—
867	C₂²×C₅₃	—	4	1	no	—
868	C₂²×C₅₃	—	4	1	no	—
869	C₂²×C₅₃	—	4	1	no	—
870	C₂²×C₅₃	—	4	1	no	—
871	C₂²×C₅₃	—	4	1	no	—
872	C₂²×C₅₃	—	4	1	no	—
873	C₂²×C₅₃	—	4	1	no	—
874	C₂²×C₅₃	—	4	1	no	—
875	C₂²×C₅₃	—	4	1	no	—
876	C₂²×C₅₃	—	4	1	no	—
877	C₂²×C₅₃	—	4	1	no	—
878	C₂²×C₅₃	—	4	1	no	—
879	C₂²×C₅₃	—	4	1	no	—
880	C₂²×C₅₃	—	4	1	no	—
881	C₂²×C₅₃	—	4	1	no	—
882	C₂²×C₅₃	—	4	1	no	—
883	C₂²×C₅₃	—	4	1	no	—
884	C₂²×C₅₃	—	4	1	no	—
885	C₂²×C₅₃	—	4	1	no	—
886	C₂²×C₅₃	—	4	1	no	—
887	C₂²×C₅₃	—	4	1	no	—
888	C₂²×C₅₃	—	8	8	no	—
889	C₂²×C₅₃	#525	1	4	yes	—
890	C₂²×C₅₃	#538	1	4	yes	complemented
891	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
892	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
893	C₂²×C₅₃	C₂²×#41	1	1	yes	characteristic
894	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
895	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
896	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
897	C₂²×C₅₃	#585	1	1	yes	characteristic
898	C₄×C₅₃	—	2	2	no	—
899	C₄×C₅₃	—	2	2	no	—
900	C₄×C₅₃	—	2	2	no	—
901	C₄×C₅₃	—	2	2	no	—
902	C₄×C₅₃	—	2	2	no	—
903	C₄×C₅₃	—	2	2	no	—
904	C₄×C₅₃	—	2	2	no	—
905	C₄×C₅₃	—	4	1	no	—
906	C₄×C₅₃	—	4	1	no	—
907	C₄×C₅₃	—	4	1	no	—
908	C₄×C₅₃	—	4	1	no	—
909	C₄×C₅₃	—	4	1	no	—
910	C₄×C₅₃	—	4	1	no	—
911	C₄×C₅₃	—	4	1	no	—
912	C₄×C₅₃	—	4	1	no	—
913	C₄×C₅₃	—	4	1	no	—
914	C₄×C₅₃	—	4	1	no	—
915	C₄×C₅₃	—	4	1	no	—
916	C₄×C₅₃	—	4	1	no	—
917	C₄×C₅₃	—	4	1	no	—
918	C₄×C₅₃	—	4	1	no	—
919	C₄×C₅₃	—	4	1	no	—
920	C₄×C₅₃	—	4	1	no	—
921	C₂×#538	C₂×C₅₃	1	1	yes	characteristic, complemented
922	C₂²×C₄×D₄	C₂×C₅₃	1	1	yes	characteristic, complemented
923	#2852	C₂×C₅₃	1	1	yes	characteristic, complemented
924	#2850	C₂×C₅₃	1	1	yes	characteristic, complemented
925	#2849	C₂×C₅₃	1	1	yes	characteristic, complemented
926	#2847	C₂×C₅₃	1	1	yes	characteristic, complemented
927	#2636	C₂×C₅₃	1	1	yes	characteristic, complemented
928	#2635	C₂×C₅₃	1	1	yes	characteristic, complemented
929	#2631	C₂×C₅₃	1	1	yes	characteristic, complemented
930	#2630	C₂×C₅₃	1	1	yes	characteristic, complemented
931	#2481	C₂×C₅₃	1	1	yes	characteristic, complemented
932	#2472	C₂×C₅₃	1	1	yes	characteristic, complemented
933	#2467	C₂×C₅₃	1	1	yes	characteristic, complemented
934	#2459	C₂×C₅₃	1	1	yes	characteristic, complemented
935	#2456	C₂×C₅₃	1	1	yes	characteristic, complemented
936	#2456	C₂×C₅₃	1	1	yes	characteristic, complemented
937	#2450	C₂×C₅₃	1	1	yes	characteristic, complemented
938	#2444	C₂×C₅₃	1	1	yes	characteristic, complemented
939	#2443	C₂×C₅₃	1	1	yes	characteristic, complemented
940	#2437	C₂×C₅₃	1	1	yes	characteristic, complemented
941	#2424	C₂×C₅₃	1	1	yes	characteristic, complemented
942	#2424	C₂×C₅₃	1	1	yes	characteristic, complemented
943	#2418	C₂×C₅₃	1	1	yes	characteristic, complemented
944	#2410	C₂×C₅₃	1	1	yes	characteristic, complemented
945	#2410	C₂×C₅₃	1	1	yes	characteristic, complemented
946	#2403	C₂×C₅₃	1	1	yes	characteristic, complemented
947	#2325	C₂×C₅₃	1	1	yes	characteristic, complemented
948	#2321	C₂×C₅₃	1	1	yes	characteristic, complemented
949	#2318	C₂×C₅₃	1	1	yes	characteristic, complemented
950	C₄×#120	C₂×C₅₃	1	1	yes	characteristic, complemented
951	C₂×#386	C₂×C₅₃	1	1	yes	characteristic, complemented
952	C₂×C₅₃	—	2	4	no	—
953	C₂×C₅₃	—	2	4	no	—
954	C₂×C₅₃	—	4	2	no	—
955	C₂×C₅₃	—	4	2	no	—
956	C₂×C₅₃	—	4	2	no	—
957	C₂×C₅₃	—	8	1	no	—
958	C₂×C₅₃	—	8	1	no	—
959	C₂×C₅₃	—	8	1	no	—
960	C₂×C₅₃	C₂×#525	1	1	yes	characteristic
961	C₂×C₅₃	C₂×#538	1	1	yes	characteristic
962	C₂×C₅₃	#3459	1	1	yes	characteristic
963	C₂×C₅₃	#3484	1	1	yes	characteristic
964	C₂×C₅₃	#3488	1	1	yes	characteristic
965	C₂×C₅₃	#3513	1	1	yes	characteristic
966	C₂×C₅₃	#3519	1	1	yes	characteristic
967	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
968	C₂³×D₄	C₂²×C₅₃	1	1	yes	characteristic
969	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic
970	C₂⁴×C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#538	—	2	8	no	—
972	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	C₂×#126	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	C₂×#123	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
982	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
983	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
984	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic
985	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
989	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
990	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
991	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
992	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic
993	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	C₂×#120	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	C₂×C₄×D₄	—	2	8	no	—
996	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
997	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
998	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
999	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1000	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	C₂²×C₄⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1009	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic
1010	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	C₂²×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	C₂²×C₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#400	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#399	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#398	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#397	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#396	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#394	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#393	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#392	C₂²×C₅₃	1	1	yes	characteristic
1038	#392	C₂²×C₅₃	1	1	yes	characteristic
1039	#392	C₂²×C₅₃	1	1	yes	characteristic
1040	#392	C₂²×C₅₃	1	1	yes	characteristic
1041	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#392	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#391	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#390	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#388	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#387	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#386	C₂²×C₅₃	1	1	yes	characteristic
1069	#386	C₂²×C₅₃	1	1	yes	characteristic
1070	#386	C₂²×C₅₃	1	1	yes	characteristic
1071	#386	C₂²×C₅₃	1	1	yes	characteristic
1072	#386	C₂²×C₅₃	1	1	yes	characteristic
1073	#386	C₂²×C₅₃	1	1	yes	characteristic
1074	#386	C₂²×C₅₃	1	1	yes	characteristic
1075	#386	C₂²×C₅₃	1	1	yes	characteristic
1076	#386	C₂²×C₅₃	1	1	yes	characteristic
1077	#386	C₂²×C₅₃	1	1	yes	characteristic
1078	#386	C₂²×C₅₃	1	1	yes	characteristic
1079	#386	C₂²×C₅₃	1	1	yes	characteristic
1080	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#386	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1106	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1107	#385	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#383	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#382	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	#381	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	#380	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	#379	C₂²×C₅₃	1	1	yes	characteristic
1117	#379	C₂²×C₅₃	1	1	yes	characteristic, complemented
1118	#379	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	C₄×C₂²⋊C₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	C₂×#95	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	C₅₃	#34990	1	1	yes	characteristic, direct product factor, Sylow
1125	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂⁵	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂²×D₄	—	2	4	no	—
1130	C₂²×D₄	—	2	4	no	—
1131	C₂²×D₄	—	2	4	no	—
1132	C₂²×D₄	—	2	4	no	—
1133	C₂²×D₄	—	4	2	no	—
1134	C₂²×D₄	—	4	2	no	—
1135	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1150	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂³×C₄	—	2	4	no	—
1155	C₂³×C₄	—	2	4	no	—
1156	C₂³×C₄	—	4	2	no	—
1157	C₂³×C₄	—	4	2	no	—
1158	C₂³×C₄	—	4	2	no	—
1159	C₂³×C₄	—	4	2	no	—
1160	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1161	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1162	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1164	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1168	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1177	#126	—	2	4	no	—
1178	#126	—	2	4	no	—
1179	#124	—	2	4	no	—
1180	#124	—	2	4	no	—
1181	#123	—	2	4	no	—
1182	#123	—	2	4	no	—
1183	#123	—	4	2	no	—
1184	C₂²⋊Q₈	—	2	4	no	—
1185	C₂²⋊Q₈	—	4	2	no	—
1186	#121	—	2	4	no	—
1187	#121	—	2	4	no	—
1188	#121	—	2	4	no	—
1189	#121	—	2	4	no	—
1190	#121	—	4	2	no	—
1191	#121	—	4	2	no	—
1192	#121	—	4	2	no	—
1193	#120	—	2	4	no	—
1194	#120	—	2	4	no	—
1195	#120	—	2	4	no	—
1196	#120	—	2	4	no	—
1197	#120	—	4	2	no	—
1198	#120	—	4	2	no	—
1199	#120	—	4	2	no	—
1200	C₄×D₄	—	2	4	no	—
1201	C₄×D₄	—	2	4	no	—
1202	C₄×D₄	—	2	4	no	—
1203	C₄×D₄	—	2	4	no	—
1204	C₄×D₄	—	2	4	no	—
1205	C₄×D₄	—	2	4	no	—
1206	C₄×D₄	—	2	4	no	—
1207	C₄×D₄	—	2	4	no	—
1208	C₄×D₄	—	4	2	no	—
1209	C₄×D₄	—	4	2	no	—
1210	C₄×D₄	D₄×C₅₃	1	8	yes	complemented
1211	C₂×C₄⋊C₄	—	2	4	no	—
1212	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1213	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1214	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1215	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1216	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1217	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1218	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1219	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1221	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1222	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1223	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1224	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1225	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1226	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1227	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1228	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1229	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1230	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1231	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1232	C₂×C₂²⋊C₄	—	2	4	no	—
1233	C₂×C₂²⋊C₄	—	2	4	no	—
1234	C₂×C₂²⋊C₄	—	2	4	no	—
1235	C₂×C₂²⋊C₄	—	4	2	no	—
1236	C₂×C₂²⋊C₄	—	4	2	no	—
1237	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1238	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1239	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1240	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1241	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1242	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1243	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1244	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1245	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1246	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1247	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1248	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1249	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1250	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1251	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1252	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1253	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1254	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1255	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1256	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1257	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1258	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1259	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1260	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1261	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1262	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1263	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1264	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1265	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1266	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1267	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1268	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1269	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1271	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1272	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1273	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1274	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1275	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1276	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1277	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1278	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1279	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1280	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1281	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1282	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1283	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1284	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1285	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1286	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1287	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1288	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1289	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1290	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1291	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1292	C₂×C₂²⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1293	C₂×C₄²	—	2	4	no	—
1294	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1295	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1296	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1297	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1298	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1299	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1300	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1301	#95	C₂³×C₅₃	1	1	yes	characteristic
1302	#95	C₂³×C₅₃	1	1	yes	characteristic
1303	#95	C₂³×C₅₃	1	1	yes	characteristic
1304	#95	C₂³×C₅₃	1	1	yes	characteristic
1305	#95	C₂³×C₅₃	1	1	yes	characteristic
1306	#95	C₂³×C₅₃	1	1	yes	characteristic
1307	#95	C₂³×C₅₃	1	1	yes	characteristic
1308	#95	C₂³×C₅₃	1	1	yes	characteristic
1309	#95	C₂³×C₅₃	1	1	yes	characteristic
1310	#95	C₂³×C₅₃	1	1	yes	characteristic
1311	#95	C₂³×C₅₃	1	1	yes	characteristic
1312	#95	C₂³×C₅₃	1	1	yes	characteristic
1313	#95	C₂³×C₅₃	1	1	yes	characteristic
1314	#95	C₂³×C₅₃	1	1	yes	characteristic
1315	#95	C₂³×C₅₃	1	1	yes	characteristic
1316	#95	C₂³×C₅₃	1	1	yes	characteristic
1317	#95	C₂³×C₅₃	1	1	yes	characteristic
1318	#95	C₂³×C₅₃	1	1	yes	characteristic
1319	#95	C₂³×C₅₃	1	1	yes	characteristic
1320	#95	C₂³×C₅₃	1	1	yes	characteristic
1321	#95	C₂³×C₅₃	1	1	yes	characteristic
1322	#95	C₂³×C₅₃	1	1	yes	characteristic
1323	#95	C₂³×C₅₃	1	1	yes	characteristic
1324	#95	C₂³×C₅₃	1	1	yes	characteristic
1325	#95	C₂³×C₅₃	1	1	yes	characteristic
1326	#95	C₂³×C₅₃	1	1	yes	characteristic
1327	#95	C₂³×C₅₃	1	1	yes	characteristic
1328	#95	C₂³×C₅₃	1	1	yes	characteristic
1329	#95	C₂³×C₅₃	1	1	yes	characteristic
1330	#95	C₂³×C₅₃	1	1	yes	characteristic
1331	#95	C₂³×C₅₃	1	1	yes	characteristic
1332	#95	C₂³×C₅₃	1	1	yes	characteristic
1333	C₂⁴	—	2	2	no	—
1334	C₂⁴	—	2	2	no	—
1335	C₂⁴	—	2	2	no	—
1336	C₂⁴	—	2	2	no	—
1337	C₂⁴	—	2	2	no	—
1338	C₂⁴	—	2	2	no	—
1339	C₂⁴	—	2	2	no	—
1340	C₂⁴	—	2	2	no	—
1341	C₂⁴	—	2	2	no	—
1342	C₂⁴	—	2	2	no	—
1343	C₂⁴	—	2	2	no	—
1344	C₂⁴	—	2	2	no	—
1345	C₂⁴	—	4	1	no	—
1346	C₂⁴	—	4	1	no	—
1347	C₂⁴	—	4	1	no	—
1348	C₂⁴	—	4	1	no	—
1349	C₂⁴	—	4	1	no	—
1350	C₂⁴	—	4	1	no	—
1351	C₂⁴	—	4	1	no	—
1352	C₂⁴	—	4	1	no	—
1353	C₂⁴	#41×C₅₃	1	4	yes	—
1354	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1355	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1356	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1357	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1358	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1359	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1360	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1361	C₂⁴	C₂⁴×C₅₃	1	1	yes	characteristic
1362	C₂×Q₈	—	2	2	no	—
1363	C₂×Q₈	—	4	1	no	—
1364	C₂×Q₈	—	4	1	no	—
1365	C₂×D₄	—	2	32	no	—
1366	C₂×D₄	—	2	2	no	—
1367	C₂×D₄	—	2	2	no	—
1368	C₂×D₄	—	2	2	no	—
1369	C₂×D₄	—	2	2	no	—
1370	C₂×D₄	—	2	2	no	—
1371	C₂×D₄	—	2	2	no	—
1372	C₂×D₄	—	2	2	no	—
1373	C₂×D₄	—	2	2	no	—
1374	C₂×D₄	—	2	2	no	—
1375	C₂×D₄	—	2	2	no	—
1376	C₂×D₄	—	2	2	no	—
1377	C₂×D₄	—	2	2	no	—
1378	C₂×D₄	—	2	2	no	—
1379	C₂×D₄	—	2	2	no	—
1380	C₂×D₄	—	2	2	no	—
1381	C₂×D₄	—	2	2	no	—
1382	C₂×D₄	—	2	2	no	—
1383	C₂×D₄	—	2	2	no	—
1384	C₂×D₄	—	2	2	no	—
1385	C₂×D₄	—	2	2	no	—
1386	C₂×D₄	—	2	2	no	—
1387	C₂×D₄	—	2	2	no	—
1388	C₂×D₄	—	2	2	no	—
1389	C₂×D₄	—	2	2	no	—
1390	C₂×D₄	—	2	2	no	—
1391	C₂×D₄	—	2	2	no	—
1392	C₂×D₄	—	2	2	no	—
1393	C₂×D₄	—	2	2	no	—
1394	C₂×D₄	—	2	2	no	—
1395	C₂×D₄	—	2	2	no	—
1396	C₂×D₄	—	2	2	no	—
1397	C₂×D₄	—	2	2	no	—
1398	C₂×D₄	—	2	2	no	—
1399	C₂×D₄	—	4	1	no	—
1400	C₂×D₄	—	4	1	no	—
1401	C₂×D₄	—	4	1	no	—
1402	C₂×D₄	—	4	1	no	—
1403	C₂×D₄	—	4	1	no	—
1404	C₂×D₄	—	4	1	no	—
1405	C₂×D₄	—	4	1	no	—
1406	C₂×D₄	—	4	1	no	—
1407	C₂×D₄	—	4	1	no	—
1408	C₂×D₄	—	4	1	no	—
1409	C₂×D₄	—	4	1	no	—
1410	C₂×D₄	—	4	1	no	—
1411	C₂×D₄	—	4	1	no	—
1412	C₂×D₄	—	4	1	no	—
1413	C₂×D₄	—	4	1	no	—
1414	C₂×D₄	—	4	1	no	—
1415	C₂×D₄	—	4	1	no	—
1416	C₂×D₄	—	4	1	no	—
1417	C₂×D₄	—	4	1	no	—
1418	C₂×D₄	—	4	1	no	—
1419	C₂×D₄	—	4	1	no	—
1420	C₂×D₄	—	4	1	no	—
1421	C₂×D₄	—	4	16	no	—
1422	C₂×D₄	C₂×D₄×C₅₃	1	4	yes	—
1423	C₂×D₄	#41×C₅₃	1	4	yes	—
1424	C₂²×C₄	—	2	2	no	—
1425	C₂²×C₄	—	2	2	no	—
1426	C₂²×C₄	—	2	2	no	—
1427	C₂²×C₄	—	2	2	no	—
1428	C₂²×C₄	—	2	2	no	—
1429	C₂²×C₄	—	2	2	no	—
1430	C₂²×C₄	—	2	2	no	—
1431	C₂²×C₄	—	2	2	no	—
1432	C₂²×C₄	—	2	2	no	—
1433	C₂²×C₄	—	2	2	no	—
1434	C₂²×C₄	—	2	2	no	—
1435	C₂²×C₄	—	2	2	no	—
1436	C₂²×C₄	—	2	2	no	—
1437	C₂²×C₄	—	2	2	no	—
1438	C₂²×C₄	—	2	2	no	—
1439	C₂²×C₄	—	2	2	no	—
1440	C₂²×C₄	—	2	2	no	—
1441	C₂²×C₄	—	2	2	no	—
1442	C₂²×C₄	—	2	2	no	—
1443	C₂²×C₄	—	2	2	no	—
1444	C₂²×C₄	—	2	2	no	—
1445	C₂²×C₄	—	2	2	no	—
1446	C₂²×C₄	—	2	2	no	—
1447	C₂²×C₄	—	2	2	no	—
1448	C₂²×C₄	—	2	2	no	—
1449	C₂²×C₄	—	2	2	no	—
1450	C₂²×C₄	—	4	1	no	—
1451	C₂²×C₄	—	4	1	no	—
1452	C₂²×C₄	—	4	1	no	—
1453	C₂²×C₄	—	4	1	no	—
1454	C₂²×C₄	—	4	1	no	—
1455	C₂²×C₄	—	4	1	no	—
1456	C₂²×C₄	—	4	1	no	—
1457	C₂²×C₄	—	4	1	no	—
1458	C₂²×C₄	—	4	1	no	—
1459	C₂²×C₄	—	4	1	no	—
1460	C₂²×C₄	—	4	1	no	—
1461	C₂²×C₄	—	4	1	no	—
1462	C₂²×C₄	—	4	1	no	—
1463	C₂²×C₄	—	4	1	no	—
1464	C₂²×C₄	—	4	1	no	—
1465	C₂²×C₄	—	4	1	no	—
1466	C₂²×C₄	—	4	1	no	—
1467	C₂²×C₄	—	4	1	no	—
1468	C₂²×C₄	—	4	1	no	—
1469	C₂²×C₄	—	4	1	no	—
1470	C₂²×C₄	—	4	1	no	—
1471	C₂²×C₄	—	4	1	no	—
1472	C₂²×C₄	—	4	1	no	—
1473	C₂²×C₄	—	4	16	no	—
1474	C₂²×C₄	—	4	16	no	—
1475	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	—
1476	C₂²×C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1477	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1478	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1479	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1480	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1481	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1482	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1486	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1487	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1488	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1489	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1490	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1491	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1492	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1493	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1494	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1495	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1496	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1497	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1498	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1499	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1500	C₄⋊C₄	—	2	2	no	—
1501	C₄⋊C₄	—	2	2	no	—
1502	C₄⋊C₄	—	2	2	no	—
1503	C₄⋊C₄	—	2	2	no	—
1504	C₄⋊C₄	—	2	2	no	—
1505	C₄⋊C₄	—	2	2	no	—
1506	C₄⋊C₄	—	2	2	no	—
1507	C₄⋊C₄	—	2	2	no	—
1508	C₄⋊C₄	—	2	2	no	—
1509	C₄⋊C₄	—	2	2	no	—
1510	C₄⋊C₄	—	4	1	no	—
1511	C₄⋊C₄	—	4	1	no	—
1512	C₄⋊C₄	—	4	1	no	—
1513	C₄⋊C₄	—	4	1	no	—
1514	C₄⋊C₄	—	4	1	no	—
1515	C₄⋊C₄	—	4	1	no	—
1516	C₄⋊C₄	—	4	1	no	—
1517	C₄⋊C₄	—	4	1	no	—
1518	C₄⋊C₄	—	4	1	no	—
1519	C₄⋊C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1520	C₂²⋊C₄	—	2	2	no	—
1521	C₂²⋊C₄	—	2	2	no	—
1522	C₂²⋊C₄	—	2	2	no	—
1523	C₂²⋊C₄	—	2	2	no	—
1524	C₂²⋊C₄	—	2	2	no	—
1525	C₂²⋊C₄	—	2	2	no	—
1526	C₂²⋊C₄	—	2	2	no	—
1527	C₂²⋊C₄	—	2	2	no	—
1528	C₂²⋊C₄	—	2	2	no	—
1529	C₂²⋊C₄	—	2	2	no	—
1530	C₂²⋊C₄	—	2	2	no	—
1531	C₂²⋊C₄	—	2	2	no	—
1532	C₂²⋊C₄	—	2	2	no	—
1533	C₂²⋊C₄	—	2	2	no	—
1534	C₂²⋊C₄	—	2	2	no	—
1535	C₂²⋊C₄	—	2	2	no	—
1536	C₂²⋊C₄	—	2	2	no	—
1537	C₂²⋊C₄	—	2	2	no	—
1538	C₂²⋊C₄	—	2	2	no	—
1539	C₂²⋊C₄	—	2	2	no	—
1540	C₂²⋊C₄	—	2	2	no	—
1541	C₂²⋊C₄	—	2	2	no	—
1542	C₂²⋊C₄	—	2	2	no	—
1543	C₂²⋊C₄	—	2	2	no	—
1544	C₂²⋊C₄	—	2	2	no	—
1545	C₂²⋊C₄	—	2	2	no	—
1546	C₂²⋊C₄	—	2	2	no	—
1547	C₂²⋊C₄	—	2	2	no	—
1548	C₂²⋊C₄	—	2	2	no	—
1549	C₂²⋊C₄	—	2	2	no	—
1550	C₂²⋊C₄	—	2	2	no	—
1551	C₂²⋊C₄	—	2	2	no	—
1552	C₂²⋊C₄	—	2	2	no	—
1553	C₂²⋊C₄	—	4	1	no	—
1554	C₂²⋊C₄	—	4	1	no	—
1555	C₂²⋊C₄	—	4	1	no	—
1556	C₂²⋊C₄	—	4	1	no	—
1557	C₂²⋊C₄	—	4	1	no	—
1558	C₂²⋊C₄	—	4	1	no	—
1559	C₂²⋊C₄	—	4	1	no	—
1560	C₂²⋊C₄	—	4	1	no	—
1561	C₂²⋊C₄	—	4	1	no	—
1562	C₂²⋊C₄	—	4	1	no	—
1563	C₂²⋊C₄	—	4	1	no	—
1564	C₂²⋊C₄	—	4	1	no	—
1565	C₂²⋊C₄	—	4	1	no	—
1566	C₂²⋊C₄	—	4	1	no	—
1567	C₂²⋊C₄	—	4	1	no	—
1568	C₂²⋊C₄	—	4	1	no	—
1569	C₂²⋊C₄	—	4	1	no	—
1570	C₂²⋊C₄	—	4	1	no	—
1571	C₂²⋊C₄	—	4	1	no	—
1572	C₂²⋊C₄	—	4	1	no	—
1573	C₂²⋊C₄	—	4	1	no	—
1574	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	—
1575	C₂²⋊C₄	C₂×D₄×C₅₃	1	4	yes	complemented
1576	C₄²	—	2	2	no	—
1577	C₄²	—	2	2	no	—
1578	C₄²	—	2	2	no	—
1579	C₄²	—	2	2	no	—
1580	C₄²	—	4	1	no	—
1581	C₄²	—	4	1	no	—
1582	C₄²	C₂×D₄×C₅₃	1	4	yes	complemented
1583	C₂³	—	2	1	no	—
1584	C₂³	—	2	1	no	—
1585	C₂³	—	2	1	no	—
1586	C₂³	—	2	1	no	—
1587	C₂³	—	2	1	no	—
1588	C₂³	—	2	1	no	—
1589	C₂³	—	2	1	no	—
1590	C₂³	—	2	1	no	—
1591	C₂³	—	2	8	no	—
1592	C₂³	—	2	8	no	—
1593	C₂³	—	2	8	no	—
1594	C₂³	—	2	1	no	—
1595	C₂³	—	2	1	no	—
1596	C₂³	—	2	1	no	—
1597	C₂³	—	2	1	no	—
1598	C₂³	—	2	1	no	—
1599	C₂³	—	2	1	no	—
1600	C₂³	—	2	1	no	—
1601	C₂³	—	2	1	no	—
1602	C₂³	—	2	1	no	—
1603	C₂³	—	2	1	no	—
1604	C₂³	—	2	1	no	—
1605	C₂³	—	2	1	no	—
1606	C₂³	—	2	1	no	—
1607	C₂³	—	2	1	no	—
1608	C₂³	—	2	1	no	—
1609	C₂³	—	2	1	no	—
1610	C₂³	—	2	1	no	—
1611	C₂³	—	2	1	no	—
1612	C₂³	—	2	1	no	—
1613	C₂³	—	2	1	no	—
1614	C₂³	—	2	1	no	—
1615	C₂³	—	2	1	no	—
1616	C₂³	—	2	1	no	—
1617	C₂³	—	2	1	no	—
1618	C₂³	—	2	1	no	—
1619	C₂³	—	2	1	no	—
1620	C₂³	—	2	1	no	—
1621	C₂³	—	2	1	no	—
1622	C₂³	—	2	1	no	—
1623	C₂³	—	2	1	no	—
1624	C₂³	—	2	1	no	—
1625	C₂³	—	2	1	no	—
1626	C₂³	—	2	1	no	—
1627	C₂³	—	2	1	no	—
1628	C₂³	—	2	1	no	—
1629	C₂³	—	2	1	no	—
1630	C₂³	—	2	1	no	—
1631	C₂³	—	2	1	no	—
1632	C₂³	—	2	1	no	—
1633	C₂³	—	4	4	no	—
1634	C₂³	—	4	4	no	—
1635	C₂³	—	4	4	no	—
1636	C₂³	—	4	4	no	—
1637	C₂³	—	4	4	no	—
1638	C₂³	—	4	4	no	—
1639	C₂³	—	4	4	no	—
1640	C₂³	—	4	4	no	—
1641	C₂³	—	4	4	no	—
1642	C₂³	—	4	4	no	—
1643	C₂³	—	4	4	no	—
1644	C₂³	—	4	4	no	—
1645	C₂³	—	4	4	no	—
1646	C₂³	—	4	4	no	—
1647	C₂³	—	8	2	no	—
1648	C₂³	—	8	2	no	—
1649	C₂³	—	8	2	no	—
1650	C₂³	—	8	2	no	—
1651	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1652	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1653	C₂³	C₂×#41×C₅₃	1	2	yes	—
1654	C₂³	C₂×#41×C₅₃	1	2	yes	—
1655	C₂³	C₂×#41×C₅₃	1	2	yes	—
1656	C₂³	C₂×#41×C₅₃	1	2	yes	—
1657	C₂³	C₂×#41×C₅₃	1	2	yes	—
1658	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1659	C₂³	H(5,𝔽₂)×C₅₃	1	2	yes	—
1660	C₂³	C₂⁵×C₅₃	1	1	yes	characteristic
1661	Q₈	—	8	2	no	—
1662	D₄	—	2	8	no	—
1663	D₄	—	2	8	no	—
1664	D₄	—	2	8	no	—
1665	D₄	—	2	8	no	—
1666	D₄	—	4	4	no	—
1667	D₄	—	4	4	no	—
1668	D₄	—	4	4	no	—
1669	D₄	—	4	4	no	—
1670	D₄	—	4	4	no	—
1671	D₄	—	4	4	no	—
1672	D₄	—	4	4	no	—
1673	D₄	—	8	2	no	—
1674	D₄	—	8	2	no	—
1675	D₄	—	8	2	no	—
1676	D₄	—	8	2	no	—
1677	D₄	—	8	2	no	—
1678	D₄	—	8	2	no	—
1679	D₄	—	8	2	no	—
1680	D₄	—	8	2	no	—
1681	C₂×C₄	—	2	8	no	—
1682	C₂×C₄	—	2	8	no	—
1683	C₂×C₄	—	2	1	no	—
1684	C₂×C₄	—	2	1	no	—
1685	C₂×C₄	—	2	1	no	—
1686	C₂×C₄	—	2	1	no	—
1687	C₂×C₄	—	2	1	no	—
1688	C₂×C₄	—	2	1	no	—
1689	C₂×C₄	—	2	1	no	—
1690	C₂×C₄	—	2	1	no	—
1691	C₂×C₄	—	2	1	no	—
1692	C₂×C₄	—	2	1	no	—
1693	C₂×C₄	—	2	1	no	—
1694	C₂×C₄	—	2	1	no	—
1695	C₂×C₄	—	2	1	no	—
1696	C₂×C₄	—	2	1	no	—
1697	C₂×C₄	—	2	1	no	—
1698	C₂×C₄	—	2	1	no	—
1699	C₂×C₄	—	2	1	no	—
1700	C₂×C₄	—	2	1	no	—
1701	C₂×C₄	—	2	1	no	—
1702	C₂×C₄	—	2	1	no	—
1703	C₂×C₄	—	2	1	no	—
1704	C₂×C₄	—	2	1	no	—
1705	C₂×C₄	—	2	1	no	—
1706	C₂×C₄	—	2	1	no	—
1707	C₂×C₄	—	2	1	no	—
1708	C₂×C₄	—	2	1	no	—
1709	C₂×C₄	—	2	1	no	—
1710	C₂×C₄	—	2	1	no	—
1711	C₂×C₄	—	2	1	no	—
1712	C₂×C₄	—	2	1	no	—
1713	C₂×C₄	—	2	1	no	—
1714	C₂×C₄	—	2	1	no	—
1715	C₂×C₄	—	2	1	no	—
1716	C₂×C₄	—	2	1	no	—
1717	C₂×C₄	—	2	1	no	—
1718	C₂×C₄	—	2	1	no	—
1719	C₂×C₄	—	2	1	no	—
1720	C₂×C₄	—	2	1	no	—
1721	C₂×C₄	—	2	1	no	—
1722	C₂×C₄	—	2	1	no	—
1723	C₂×C₄	—	2	1	no	—
1724	C₂×C₄	—	2	1	no	—
1725	C₂×C₄	—	2	1	no	—
1726	C₂×C₄	—	2	1	no	—
1727	C₂×C₄	—	2	1	no	—
1728	C₂×C₄	—	2	1	no	—
1729	C₂×C₄	—	2	1	no	—
1730	C₂×C₄	—	2	1	no	—
1731	C₂×C₄	—	2	1	no	—
1732	C₂×C₄	—	2	1	no	—
1733	C₂×C₄	—	2	1	no	—
1734	C₂×C₄	—	2	1	no	—
1735	C₂×C₄	—	2	1	no	—
1736	C₂×C₄	—	2	1	no	—
1737	C₂×C₄	—	2	1	no	—
1738	C₂×C₄	—	2	1	no	—
1739	C₂×C₄	—	2	1	no	—
1740	C₂×C₄	—	2	1	no	—
1741	C₂×C₄	—	2	1	no	—
1742	C₂×C₄	—	2	1	no	—
1743	C₂×C₄	—	2	1	no	—
1744	C₂×C₄	—	2	1	no	—
1745	C₂×C₄	—	4	4	no	—
1746	C₂×C₄	—	4	4	no	—
1747	C₂×C₄	—	4	4	no	—
1748	C₂×C₄	—	4	4	no	—
1749	C₂×C₄	—	4	4	no	—
1750	C₂×C₄	—	4	4	no	—
1751	C₂×C₄	—	4	4	no	—
1752	C₂×C₄	—	4	4	no	—
1753	C₂×C₄	—	4	4	no	—
1754	C₂×C₄	—	4	4	no	—
1755	C₂×C₄	—	4	4	no	—
1756	C₂×C₄	—	4	4	no	—
1757	C₂×C₄	—	8	2	no	—
1758	C₂×C₄	—	8	2	no	—
1759	C₂×C₄	—	8	2	no	—
1760	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1761	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1762	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1763	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1764	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1765	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1766	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1767	C₂²	—	2	2	no	—
1768	C₂²	—	2	2	no	—
1769	C₂²	—	2	2	no	—
1770	C₂²	—	2	2	no	—
1771	C₂²	—	2	2	no	—
1772	C₂²	—	2	2	no	—
1773	C₂²	—	2	2	no	—
1774	C₂²	—	2	2	no	—
1775	C₂²	—	2	2	no	—
1776	C₂²	—	2	2	no	—
1777	C₂²	—	2	2	no	—
1778	C₂²	—	2	2	no	—
1779	C₂²	—	2	2	no	—
1780	C₂²	—	2	2	no	—
1781	C₂²	—	2	2	no	—
1782	C₂²	—	2	2	no	—
1783	C₂²	—	2	2	no	—
1784	C₂²	—	2	2	no	—
1785	C₂²	—	2	2	no	—
1786	C₂²	—	2	2	no	—
1787	C₂²	—	2	2	no	—
1788	C₂²	—	4	16	no	—
1789	C₂²	—	4	16	no	—
1790	C₂²	—	4	1	no	—
1791	C₂²	—	4	1	no	—
1792	C₂²	—	4	1	no	—
1793	C₂²	—	4	1	no	—
1794	C₂²	—	4	1	no	—
1795	C₂²	—	4	1	no	—
1796	C₂²	—	4	1	no	—
1797	C₂²	—	4	1	no	—
1798	C₂²	—	4	1	no	—
1799	C₂²	—	4	1	no	—
1800	C₂²	—	4	1	no	—
1801	C₂²	—	4	1	no	—
1802	C₂²	—	4	1	no	—
1803	C₂²	—	4	1	no	—
1804	C₂²	—	4	1	no	—
1805	C₂²	—	4	1	no	—
1806	C₂²	—	4	1	no	—
1807	C₂²	—	4	1	no	—
1808	C₂²	—	4	1	no	—
1809	C₂²	—	4	1	no	—
1810	C₂²	—	4	1	no	—
1811	C₂²	—	4	1	no	—
1812	C₂²	—	4	1	no	—
1813	C₂²	—	4	1	no	—
1814	C₂²	—	4	1	no	—
1815	C₂²	—	4	1	no	—
1816	C₂²	—	4	1	no	—
1817	C₂²	—	4	1	no	—
1818	C₂²	—	4	1	no	—
1819	C₂²	—	4	1	no	—
1820	C₂²	—	4	1	no	—
1821	C₂²	—	4	1	no	—
1822	C₂²	—	4	1	no	—
1823	C₂²	—	8	8	no	—
1824	C₂²	C₅₃×#525	1	4	yes	—
1825	C₂²	C₅₃×#538	1	4	yes	complemented
1826	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1827	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1828	C₂²	C₂²×#41×C₅₃	1	1	yes	characteristic
1829	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1830	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1831	C₂²	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1832	C₂²	C₅₃×#585	1	1	yes	characteristic
1833	C₄	—	2	2	no	—
1834	C₄	—	2	2	no	—
1835	C₄	—	2	2	no	—
1836	C₄	—	2	2	no	—
1837	C₄	—	2	2	no	—
1838	C₄	—	2	2	no	—
1839	C₄	—	2	2	no	—
1840	C₄	—	4	1	no	—
1841	C₄	—	4	1	no	—
1842	C₄	—	4	1	no	—
1843	C₄	—	4	1	no	—
1844	C₄	—	4	1	no	—
1845	C₄	—	4	1	no	—
1846	C₄	—	4	1	no	—
1847	C₄	—	4	1	no	—
1848	C₄	—	4	1	no	—
1849	C₄	—	4	1	no	—
1850	C₄	—	4	1	no	—
1851	C₄	—	4	1	no	—
1852	C₄	—	4	1	no	—
1853	C₄	—	4	1	no	—
1854	C₄	—	4	1	no	—
1855	C₄	—	4	1	no	—
1856	C₂	—	2	4	no	—
1857	C₂	—	2	4	no	—
1858	C₂	—	4	2	no	—
1859	C₂	—	4	2	no	—
1860	C₂	—	4	2	no	—
1861	C₂	—	8	1	no	—
1862	C₂	—	8	1	no	—
1863	C₂	—	8	1	no	—
1864	C₂	C₂×C₅₃×#525	1	1	yes	characteristic
1865	C₂	C₂×C₅₃×#538	1	1	yes	characteristic
1866	C₂	C₅₃×#3459	1	1	yes	characteristic
1867	C₂	C₅₃×#3484	1	1	yes	characteristic
1868	C₂	C₅₃×#3488	1	1	yes	characteristic
1869	C₂	C₅₃×#3513	1	1	yes	characteristic
1870	C₂	C₅₃×#3519	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₅₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅₃×#538	C₂	semidirect
2. C₂²×C₄×D₄×C₅₃	C₂	semidirect
3. C₅₃×#2852	C₂	semidirect
4. C₅₃×#2850	C₂	semidirect
5. C₅₃×#2849	C₂	semidirect
6. C₅₃×#2847	C₂	semidirect
7. C₅₃×#2636	C₂	semidirect
8. C₅₃×#2635	C₂	semidirect
9. C₅₃×#2631	C₂	semidirect
10. C₅₃×#2630	C₂	semidirect
11. C₅₃×#2481	C₂	semidirect
12. C₅₃×#2472	C₂	semidirect
13. C₅₃×#2467	C₂	semidirect
14. C₅₃×#2459	C₂	semidirect
15. C₅₃×#2456	C₂	semidirect
16. C₅₃×#2456	C₂	semidirect
17. C₅₃×#2450	C₂	semidirect
18. C₅₃×#2444	C₂	semidirect
19. C₅₃×#2443	C₂	semidirect
20. C₅₃×#2437	C₂	semidirect
21. C₅₃×#2424	C₂	semidirect
22. C₅₃×#2424	C₂	semidirect
23. C₅₃×#2418	C₂	semidirect
24. C₅₃×#2410	C₂	semidirect
25. C₅₃×#2410	C₂	semidirect
26. C₅₃×#2403	C₂	semidirect
27. C₅₃×#2325	C₂	semidirect
28. C₅₃×#2321	C₂	semidirect
29. C₅₃×#2318	C₂	semidirect
30. C₄×#120×C₅₃	C₂	semidirect
31. C₂×C₅₃×#386	C₂	semidirect
35. C₂⁴×C₄×C₅₃	C₂²	semidirect
37. C₂×#126×C₅₃	C₂²	semidirect
38. C₂×#126×C₅₃	C₂²	semidirect
39. C₂×#124×C₅₃	C₂²	semidirect
40. C₂×#124×C₅₃	C₂²	semidirect
41. C₂×#123×C₅₃	C₂²	semidirect
42. C₂×#123×C₅₃	C₂²	semidirect
43. C₂×#123×C₅₃	C₂²	semidirect
44. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
45. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
50. C₂×#121×C₅₃	C₂²	semidirect
51. C₂×#121×C₅₃	C₂²	semidirect
52. C₂×#121×C₅₃	C₂²	semidirect
58. C₂×#120×C₅₃	C₂²	semidirect
59. C₂×#120×C₅₃	C₂²	semidirect
65. C₂×C₄×D₄×C₅₃	C₂²	semidirect
66. C₂×C₄×D₄×C₅₃	C₂²	semidirect
67. C₂×C₄×D₄×C₅₃	C₂²	semidirect
68. C₂×C₄×D₄×C₅₃	C₂²	semidirect
69. C₂×C₄×D₄×C₅₃	C₂²	semidirect
70. C₂×C₄×D₄×C₅₃	C₂²	semidirect
71. C₂×C₄×D₄×C₅₃	C₂²	semidirect
72. C₂²×C₄⋊C₄×C₅₃	C₂²	semidirect
75. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
76. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
77. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
78. C₂²×C₄²×C₅₃	C₂²	semidirect
79. C₅₃×#400	C₂²	semidirect
80. C₅₃×#400	C₂²	semidirect
81. C₅₃×#399	C₂²	semidirect
82. C₅₃×#399	C₂²	semidirect
83. C₅₃×#398	C₂²	semidirect
84. C₅₃×#397	C₂²	semidirect
85. C₅₃×#397	C₂²	semidirect
86. C₅₃×#397	C₂²	semidirect
87. C₅₃×#396	C₂²	semidirect
88. C₅₃×#396	C₂²	semidirect
89. C₅₃×#396	C₂²	semidirect
90. C₅₃×#396	C₂²	semidirect
91. C₅₃×#394	C₂²	semidirect
92. C₅₃×#394	C₂²	semidirect
93. C₅₃×#394	C₂²	semidirect
94. C₅₃×#394	C₂²	semidirect
95. C₅₃×#394	C₂²	semidirect
96. C₅₃×#394	C₂²	semidirect
97. C₅₃×#394	C₂²	semidirect
98. C₅₃×#394	C₂²	semidirect
99. C₅₃×#394	C₂²	semidirect
100. C₅₃×#393	C₂²	semidirect
101. C₅₃×#393	C₂²	semidirect
106. C₅₃×#392	C₂²	semidirect
107. C₅₃×#392	C₂²	semidirect
108. C₅₃×#392	C₂²	semidirect
109. C₅₃×#392	C₂²	semidirect
110. C₅₃×#392	C₂²	semidirect
111. C₅₃×#391	C₂²	semidirect
112. C₅₃×#390	C₂²	semidirect
113. C₅₃×#390	C₂²	semidirect
114. C₅₃×#390	C₂²	semidirect
115. C₅₃×#388	C₂²	semidirect
116. C₅₃×#388	C₂²	semidirect
117. C₅₃×#388	C₂²	semidirect
118. C₅₃×#388	C₂²	semidirect
119. C₅₃×#388	C₂²	semidirect
120. C₅₃×#388	C₂²	semidirect
121. C₅₃×#388	C₂²	semidirect
122. C₅₃×#388	C₂²	semidirect
123. C₅₃×#388	C₂²	semidirect
124. C₅₃×#388	C₂²	semidirect
125. C₅₃×#388	C₂²	semidirect
126. C₅₃×#388	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
145. C₅₃×#386	C₂²	semidirect
146. C₅₃×#386	C₂²	semidirect
147. C₅₃×#386	C₂²	semidirect
148. C₅₃×#386	C₂²	semidirect
149. C₅₃×#386	C₂²	semidirect
150. C₅₃×#386	C₂²	semidirect
151. C₅₃×#386	C₂²	semidirect
152. C₅₃×#386	C₂²	semidirect
153. C₅₃×#386	C₂²	semidirect
154. C₅₃×#386	C₂²	semidirect
155. C₅₃×#386	C₂²	semidirect
156. C₅₃×#386	C₂²	semidirect
157. C₅₃×#386	C₂²	semidirect
158. C₅₃×#386	C₂²	semidirect
159. C₅₃×#386	C₂²	semidirect
160. C₅₃×#386	C₂²	semidirect
161. C₅₃×#385	C₂²	semidirect
162. C₅₃×#385	C₂²	semidirect
163. C₅₃×#385	C₂²	semidirect
164. C₅₃×#385	C₂²	semidirect
165. C₅₃×#385	C₂²	semidirect
166. C₅₃×#385	C₂²	semidirect
167. C₅₃×#385	C₂²	semidirect
168. C₅₃×#385	C₂²	semidirect
169. C₅₃×#385	C₂²	semidirect
170. C₅₃×#385	C₂²	semidirect
171. C₅₃×#385	C₂²	semidirect
172. C₅₃×#385	C₂²	semidirect
173. C₅₃×#383	C₂²	semidirect
174. C₅₃×#382	C₂²	semidirect
175. C₅₃×#381	C₂²	semidirect
176. C₅₃×#381	C₂²	semidirect
177. C₅₃×#380	C₂²	semidirect
178. C₅₃×#380	C₂²	semidirect
179. C₅₃×#380	C₂²	semidirect
180. C₅₃×#380	C₂²	semidirect
182. C₅₃×#379	C₂²	semidirect
183. C₅₃×#379	C₂²	semidirect
184. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
185. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
186. C₄×C₂²⋊C₄×C₅₃	C₂²	semidirect
187. C₂×#95×C₅₃	C₂²	semidirect
188. C₂×#95×C₅₃	C₂²	semidirect
274. C₄×D₄×C₅₃	D₄	semidirect
540. C₂²×C₄×C₅₃	C₂×D₄	semidirect
583. C₄⋊C₄×C₅₃	C₂×D₄	semidirect
639. C₂²⋊C₄×C₅₃	C₂×D₄	semidirect
646. C₄²×C₅₃	C₂×D₄	semidirect
831. #34990	C₅₃	direct (N × H)
890. C₂²×C₅₃	#538	semidirect
921. C₂×#538	C₂×C₅₃	semidirect
922. C₂²×C₄×D₄	C₂×C₅₃	semidirect
923. #2852	C₂×C₅₃	semidirect
924. #2850	C₂×C₅₃	semidirect
925. #2849	C₂×C₅₃	semidirect
926. #2847	C₂×C₅₃	semidirect
927. #2636	C₂×C₅₃	semidirect
928. #2635	C₂×C₅₃	semidirect
929. #2631	C₂×C₅₃	semidirect
930. #2630	C₂×C₅₃	semidirect
931. #2481	C₂×C₅₃	semidirect
932. #2472	C₂×C₅₃	semidirect
933. #2467	C₂×C₅₃	semidirect
934. #2459	C₂×C₅₃	semidirect
935. #2456	C₂×C₅₃	semidirect
936. #2456	C₂×C₅₃	semidirect
937. #2450	C₂×C₅₃	semidirect
938. #2444	C₂×C₅₃	semidirect
939. #2443	C₂×C₅₃	semidirect
940. #2437	C₂×C₅₃	semidirect
941. #2424	C₂×C₅₃	semidirect
942. #2424	C₂×C₅₃	semidirect
943. #2418	C₂×C₅₃	semidirect
944. #2410	C₂×C₅₃	semidirect
945. #2410	C₂×C₅₃	semidirect
946. #2403	C₂×C₅₃	semidirect
947. #2325	C₂×C₅₃	semidirect
948. #2321	C₂×C₅₃	semidirect
949. #2318	C₂×C₅₃	semidirect
950. C₄×#120	C₂×C₅₃	semidirect
951. C₂×#386	C₂×C₅₃	semidirect
970. C₂⁴×C₄	C₂²×C₅₃	semidirect
972. C₂×#126	C₂²×C₅₃	semidirect
973. C₂×#126	C₂²×C₅₃	semidirect
974. C₂×#124	C₂²×C₅₃	semidirect
975. C₂×#124	C₂²×C₅₃	semidirect
976. C₂×#123	C₂²×C₅₃	semidirect
977. C₂×#123	C₂²×C₅₃	semidirect
978. C₂×#123	C₂²×C₅₃	semidirect
979. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
980. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
985. C₂×#121	C₂²×C₅₃	semidirect
986. C₂×#121	C₂²×C₅₃	semidirect
987. C₂×#121	C₂²×C₅₃	semidirect
993. C₂×#120	C₂²×C₅₃	semidirect
994. C₂×#120	C₂²×C₅₃	semidirect
1000. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1001. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1002. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1003. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1004. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1005. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1006. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1007. C₂²×C₄⋊C₄	C₂²×C₅₃	semidirect
1010. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
1011. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
1012. C₂²×C₂²⋊C₄	C₂²×C₅₃	semidirect
1013. C₂²×C₄²	C₂²×C₅₃	semidirect
1014. #400	C₂²×C₅₃	semidirect
1015. #400	C₂²×C₅₃	semidirect
1016. #399	C₂²×C₅₃	semidirect
1017. #399	C₂²×C₅₃	semidirect
1018. #398	C₂²×C₅₃	semidirect
1019. #397	C₂²×C₅₃	semidirect
1020. #397	C₂²×C₅₃	semidirect
1021. #397	C₂²×C₅₃	semidirect
1022. #396	C₂²×C₅₃	semidirect
1023. #396	C₂²×C₅₃	semidirect
1024. #396	C₂²×C₅₃	semidirect
1025. #396	C₂²×C₅₃	semidirect
1026. #394	C₂²×C₅₃	semidirect
1027. #394	C₂²×C₅₃	semidirect
1028. #394	C₂²×C₅₃	semidirect
1029. #394	C₂²×C₅₃	semidirect
1030. #394	C₂²×C₅₃	semidirect
1031. #394	C₂²×C₅₃	semidirect
1032. #394	C₂²×C₅₃	semidirect
1033. #394	C₂²×C₅₃	semidirect
1034. #394	C₂²×C₅₃	semidirect
1035. #393	C₂²×C₅₃	semidirect
1036. #393	C₂²×C₅₃	semidirect
1041. #392	C₂²×C₅₃	semidirect
1042. #392	C₂²×C₅₃	semidirect
1043. #392	C₂²×C₅₃	semidirect
1044. #392	C₂²×C₅₃	semidirect
1045. #392	C₂²×C₅₃	semidirect
1046. #391	C₂²×C₅₃	semidirect
1047. #390	C₂²×C₅₃	semidirect
1048. #390	C₂²×C₅₃	semidirect
1049. #390	C₂²×C₅₃	semidirect
1050. #388	C₂²×C₅₃	semidirect
1051. #388	C₂²×C₅₃	semidirect
1052. #388	C₂²×C₅₃	semidirect
1053. #388	C₂²×C₅₃	semidirect
1054. #388	C₂²×C₅₃	semidirect
1055. #388	C₂²×C₅₃	semidirect
1056. #388	C₂²×C₅₃	semidirect
1057. #388	C₂²×C₅₃	semidirect
1058. #388	C₂²×C₅₃	semidirect
1059. #388	C₂²×C₅₃	semidirect
1060. #388	C₂²×C₅₃	semidirect
1061. #388	C₂²×C₅₃	semidirect
1062. #387	C₂²×C₅₃	semidirect
1063. #387	C₂²×C₅₃	semidirect
1064. #387	C₂²×C₅₃	semidirect
1065. #387	C₂²×C₅₃	semidirect
1066. #387	C₂²×C₅₃	semidirect
1067. #387	C₂²×C₅₃	semidirect
1080. #386	C₂²×C₅₃	semidirect
1081. #386	C₂²×C₅₃	semidirect
1082. #386	C₂²×C₅₃	semidirect
1083. #386	C₂²×C₅₃	semidirect
1084. #386	C₂²×C₅₃	semidirect
1085. #386	C₂²×C₅₃	semidirect
1086. #386	C₂²×C₅₃	semidirect
1087. #386	C₂²×C₅₃	semidirect
1088. #386	C₂²×C₅₃	semidirect
1089. #386	C₂²×C₅₃	semidirect
1090. #386	C₂²×C₅₃	semidirect
1091. #386	C₂²×C₅₃	semidirect
1092. #386	C₂²×C₅₃	semidirect
1093. #386	C₂²×C₅₃	semidirect
1094. #386	C₂²×C₅₃	semidirect
1095. #386	C₂²×C₅₃	semidirect
1096. #385	C₂²×C₅₃	semidirect
1097. #385	C₂²×C₅₃	semidirect
1098. #385	C₂²×C₅₃	semidirect
1099. #385	C₂²×C₅₃	semidirect
1100. #385	C₂²×C₅₃	semidirect
1101. #385	C₂²×C₅₃	semidirect
1102. #385	C₂²×C₅₃	semidirect
1103. #385	C₂²×C₅₃	semidirect
1104. #385	C₂²×C₅₃	semidirect
1105. #385	C₂²×C₅₃	semidirect
1106. #385	C₂²×C₅₃	semidirect
1107. #385	C₂²×C₅₃	semidirect
1108. #383	C₂²×C₅₃	semidirect
1109. #382	C₂²×C₅₃	semidirect
1110. #381	C₂²×C₅₃	semidirect
1111. #381	C₂²×C₅₃	semidirect
1112. #380	C₂²×C₅₃	semidirect
1113. #380	C₂²×C₅₃	semidirect
1114. #380	C₂²×C₅₃	semidirect
1115. #380	C₂²×C₅₃	semidirect
1117. #379	C₂²×C₅₃	semidirect
1118. #379	C₂²×C₅₃	semidirect
1119. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1120. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1121. C₄×C₂²⋊C₄	C₂²×C₅₃	semidirect
1122. C₂×#95	C₂²×C₅₃	semidirect
1123. C₂×#95	C₂²×C₅₃	semidirect
1124. C₅₃	#34990	direct (N × H)
1210. C₄×D₄	D₄×C₅₃	semidirect
1476. C₂²×C₄	C₂×D₄×C₅₃	semidirect
1519. C₄⋊C₄	C₂×D₄×C₅₃	semidirect
1575. C₂²⋊C₄	C₂×D₄×C₅₃	semidirect
1582. C₄²	C₂×D₄×C₅₃	semidirect
1825. C₂²	C₅₃×#538	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅₃×#538	2
C₂²×C₄×D₄×C₅₃	2
C₅₃×#2852	2
C₅₃×#2850	2
C₅₃×#2849	2
C₅₃×#2847	2
C₅₃×#2636	2
C₅₃×#2635	2
C₅₃×#2631	2
C₅₃×#2630	2
C₅₃×#2481	2
C₅₃×#2472	2
C₅₃×#2467	2
C₅₃×#2459	2
C₅₃×#2456	2
C₅₃×#2450	2
C₅₃×#2444	2
C₅₃×#2443	2
C₅₃×#2437	2
C₅₃×#2424	2
C₅₃×#2418	2
C₅₃×#2410	2
C₅₃×#2403	2
C₅₃×#2325	2
C₅₃×#2321	2
C₅₃×#2318	2
C₄×#120×C₅₃	2
C₂×C₅₃×#386	2
#34990	53

Subgroups — C53×#34990 #27242502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#34990 #27242502