Subgroups — C₅₃×#61606 #27269118

Order 13568.

2138 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3505	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#41×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3327	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3323	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3317	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3301	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3268	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3212	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3197	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3191	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3188	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3111	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3006	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2974	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#553	—	2	1	no	—
43	C₅₃×#553	—	2	1	no	—
44	C₅₃×#553	C₂²	1	1	yes	characteristic
45	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#551	—	2	1	no	—
50	C₅₃×#550	C₂²	1	1	yes	characteristic
51	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#548	C₂²	1	1	yes	characteristic
53	C₅₃×#548	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#547	—	2	1	no	—
57	C₅₃×#547	C₂²	1	1	yes	characteristic
58	C₅₃×#546	—	2	1	no	—
59	C₅₃×#546	—	2	1	no	—
60	C₅₃×#546	C₂²	1	1	yes	characteristic
61	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
64	D₄²×C₅₃	—	2	1	no	—
65	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#539	—	2	1	no	—
67	C₅₃×#538	—	2	1	no	—
68	C₅₃×#534	—	2	1	no	—
69	C₅₃×#532	—	2	1	no	—
70	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#525	—	2	1	no	—
74	C₅₃×#525	—	2	1	no	—
75	C₅₃×#525	C₂²	1	1	yes	characteristic
76	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#525	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₂×#121×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#518	—	2	1	no	—
82	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₂×C₄×D₄×C₅₃	—	2	1	no	—
84	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
85	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#449	C₂²	1	1	yes	characteristic
156	C₅₃×#449	C₂²	1	1	yes	characteristic
157	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
197	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
201	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	—	2	1	no	—
205	C₂×#41×C₅₃	—	2	1	no	—
206	C₂×#41×C₅₃	—	2	1	no	—
207	C₂×#41×C₅₃	—	4	2	no	—
208	C₂×#41×C₅₃	—	4	2	no	—
209	C₂×#41×C₅₃	—	4	2	no	—
210	C₂×#41×C₅₃	—	4	2	no	—
211	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₂²×D₄×C₅₃	—	2	1	no	—
224	C₂²×D₄×C₅₃	—	2	1	no	—
225	C₂²×D₄×C₅₃	—	2	1	no	—
226	C₂²×D₄×C₅₃	—	2	1	no	—
227	C₂²×D₄×C₅₃	D₄	1	1	yes	characteristic
228	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
231	C₂³×C₄×C₅₃	—	2	1	no	—
232	C₂³×C₄×C₅₃	—	2	1	no	—
233	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
234	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
235	#137×C₅₃	—	4	2	no	—
236	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
237	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
238	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
239	#135×C₅₃	—	4	2	no	—
240	#135×C₅₃	—	4	2	no	—
241	C₂×Q₁₆×C₅₃	—	4	2	no	—
242	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×SD₁₆×C₅₃	—	4	2	no	—
249	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
268	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
275	C₄⋊Q₈×C₅₃	—	2	1	no	—
276	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
277	#127×C₅₃	—	2	1	no	—
278	#127×C₅₃	C₂³	1	1	yes	characteristic
279	#126×C₅₃	—	2	1	no	—
280	#126×C₅₃	—	2	1	no	—
281	#126×C₅₃	—	2	1	no	—
282	#126×C₅₃	—	2	1	no	—
283	#126×C₅₃	—	2	1	no	—
284	#126×C₅₃	—	2	1	no	—
285	#125×C₅₃	—	2	1	no	—
286	#125×C₅₃	—	2	1	no	—
287	#125×C₅₃	C₂³	1	1	yes	characteristic
288	#125×C₅₃	C₂³	1	1	yes	characteristic
289	#124×C₅₃	—	2	1	no	—
290	#124×C₅₃	—	2	1	no	—
291	#124×C₅₃	—	2	1	no	—
292	#124×C₅₃	—	2	1	no	—
293	#124×C₅₃	C₂³	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
295	#124×C₅₃	C₂³	1	1	yes	characteristic
296	#124×C₅₃	C₂³	1	1	yes	characteristic
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	—	2	1	no	—
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	—	2	1	no	—
311	#123×C₅₃	—	2	1	no	—
312	#123×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	—	2	1	no	—
315	C₂²⋊Q₈×C₅₃	—	2	1	no	—
316	C₂²⋊Q₈×C₅₃	—	2	1	no	—
317	C₂²⋊Q₈×C₅₃	—	2	1	no	—
318	C₂²⋊Q₈×C₅₃	—	2	1	no	—
319	C₂²⋊Q₈×C₅₃	—	2	1	no	—
320	C₂²⋊Q₈×C₅₃	—	2	1	no	—
321	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
325	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
326	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
327	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
328	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
329	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
330	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	—	2	1	no	—
332	#121×C₅₃	—	2	1	no	—
333	#121×C₅₃	—	2	1	no	—
334	#121×C₅₃	—	2	1	no	—
335	#121×C₅₃	—	2	1	no	—
336	#121×C₅₃	—	2	1	no	—
337	#121×C₅₃	—	2	1	no	—
338	#121×C₅₃	—	2	1	no	—
339	#121×C₅₃	—	2	1	no	—
340	#121×C₅₃	—	2	1	no	—
341	#121×C₅₃	—	2	1	no	—
342	#121×C₅₃	—	2	1	no	—
343	#121×C₅₃	—	2	1	no	—
344	#121×C₅₃	—	2	1	no	—
345	#121×C₅₃	—	2	1	no	—
346	#121×C₅₃	—	2	1	no	—
347	#121×C₅₃	—	2	1	no	—
348	#121×C₅₃	—	2	1	no	—
349	#121×C₅₃	C₂³	1	1	yes	characteristic
350	#121×C₅₃	C₂³	1	1	yes	characteristic
351	#121×C₅₃	C₂³	1	1	yes	characteristic
352	#121×C₅₃	C₂³	1	1	yes	characteristic
353	#121×C₅₃	C₂³	1	1	yes	characteristic
354	#121×C₅₃	C₂³	1	1	yes	characteristic
355	#121×C₅₃	C₂³	1	1	yes	characteristic
356	#121×C₅₃	C₂³	1	1	yes	characteristic
357	#121×C₅₃	C₂³	1	1	yes	characteristic
358	#121×C₅₃	C₂³	1	1	yes	characteristic
359	#120×C₅₃	—	2	1	no	—
360	#120×C₅₃	—	2	1	no	—
361	#120×C₅₃	—	2	1	no	—
362	#120×C₅₃	—	2	1	no	—
363	#120×C₅₃	—	2	1	no	—
364	#120×C₅₃	—	2	1	no	—
365	#120×C₅₃	—	2	1	no	—
366	#120×C₅₃	—	2	1	no	—
367	#120×C₅₃	—	2	1	no	—
368	#120×C₅₃	—	2	1	no	—
369	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₅₃	—	2	1	no	—
374	C₄×D₄×C₅₃	—	2	1	no	—
375	C₄×D₄×C₅₃	—	2	1	no	—
376	C₄×D₄×C₅₃	—	2	1	no	—
377	C₄×D₄×C₅₃	—	2	1	no	—
378	C₄×D₄×C₅₃	—	2	1	no	—
379	C₄×D₄×C₅₃	—	2	1	no	—
380	C₄×D₄×C₅₃	—	2	1	no	—
381	C₄×D₄×C₅₃	—	2	1	no	—
382	C₄×D₄×C₅₃	—	2	1	no	—
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	—	2	1	no	—
387	C₄×D₄×C₅₃	—	2	1	no	—
388	C₄×D₄×C₅₃	—	2	1	no	—
389	C₄×D₄×C₅₃	—	2	1	no	—
390	C₄×D₄×C₅₃	—	2	1	no	—
391	C₄×D₄×C₅₃	—	2	1	no	—
392	C₄×D₄×C₅₃	—	2	1	no	—
393	C₄×D₄×C₅₃	—	2	1	no	—
394	C₄×D₄×C₅₃	—	2	1	no	—
395	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
396	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
397	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
398	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
399	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
400	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
401	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
402	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
403	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
404	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
405	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
406	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
407	#117×C₅₃	—	2	1	no	—
408	#117×C₅₃	—	2	1	no	—
409	#117×C₅₃	—	2	1	no	—
410	#117×C₅₃	—	2	1	no	—
411	#117×C₅₃	—	2	1	no	—
412	#117×C₅₃	C₂³	1	1	yes	characteristic
413	#117×C₅₃	C₂³	1	1	yes	characteristic
414	#117×C₅₃	C₂³	1	1	yes	characteristic
415	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₂×C₄⋊C₄×C₅₃	D₄	1	1	yes	characteristic
418	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
419	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
425	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
427	C₂×C₂²⋊C₄×C₅₃	D₄	1	1	yes	characteristic
428	C₂×C₄²×C₅₃	—	2	1	no	—
429	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
430	#107×C₅₃	C₂³	1	1	yes	characteristic
431	#107×C₅₃	C₂³	1	1	yes	characteristic
432	#107×C₅₃	C₂³	1	1	yes	characteristic
433	#107×C₅₃	C₂³	1	1	yes	characteristic
434	#106×C₅₃	C₂³	1	1	yes	characteristic
435	#106×C₅₃	C₂³	1	1	yes	characteristic
436	#106×C₅₃	C₂³	1	1	yes	characteristic
437	#106×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
441	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#103×C₅₃	C₂³	1	1	yes	characteristic
456	#103×C₅₃	C₂³	1	1	yes	characteristic
457	#103×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	#102×C₅₃	C₂³	1	1	yes	characteristic
473	#102×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
485	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
486	#97×C₅₃	C₂³	1	1	yes	characteristic
487	#97×C₅₃	C₂³	1	1	yes	characteristic
488	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
489	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
490	C₂⁴×C₅₃	—	2	1	no	—
491	C₂⁴×C₅₃	—	2	1	no	—
492	C₂⁴×C₅₃	—	2	1	no	—
493	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
494	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
495	#41×C₅₃	—	2	2	no	—
496	#41×C₅₃	—	2	2	no	—
497	#41×C₅₃	—	2	2	no	—
498	#41×C₅₃	—	2	2	no	—
499	#41×C₅₃	—	2	2	no	—
500	#41×C₅₃	—	2	2	no	—
501	#41×C₅₃	—	4	1	no	—
502	#41×C₅₃	—	4	1	no	—
503	#41×C₅₃	—	4	1	no	—
504	#41×C₅₃	—	4	1	no	—
505	#41×C₅₃	—	4	1	no	—
506	#41×C₅₃	—	4	1	no	—
507	#41×C₅₃	—	4	1	no	—
508	#41×C₅₃	—	4	1	no	—
509	#41×C₅₃	—	4	4	no	—
510	#41×C₅₃	—	4	4	no	—
511	#41×C₅₃	—	4	1	no	—
512	#41×C₅₃	—	4	1	no	—
513	#41×C₅₃	—	4	1	no	—
514	#41×C₅₃	—	4	1	no	—
515	#41×C₅₃	—	4	4	no	—
516	#41×C₅₃	—	4	4	no	—
517	C₂×Q₈×C₅₃	—	2	1	no	—
518	C₂×Q₈×C₅₃	—	2	1	no	—
519	C₂×Q₈×C₅₃	—	2	1	no	—
520	C₂×Q₈×C₅₃	—	2	2	no	—
521	C₂×Q₈×C₅₃	—	2	2	no	—
522	C₂×Q₈×C₅₃	—	4	1	no	—
523	C₂×Q₈×C₅₃	—	4	1	no	—
524	C₂×Q₈×C₅₃	—	4	1	no	—
525	C₂×Q₈×C₅₃	—	4	1	no	—
526	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
527	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
528	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
529	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
530	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
531	C₂×D₄×C₅₃	—	2	1	no	—
532	C₂×D₄×C₅₃	—	2	2	no	—
533	C₂×D₄×C₅₃	—	2	2	no	—
534	C₂×D₄×C₅₃	—	2	1	no	—
535	C₂×D₄×C₅₃	—	2	1	no	—
536	C₂×D₄×C₅₃	—	2	1	no	—
537	C₂×D₄×C₅₃	—	2	1	no	—
538	C₂×D₄×C₅₃	—	2	1	no	—
539	C₂×D₄×C₅₃	—	2	1	no	—
540	C₂×D₄×C₅₃	—	2	1	no	—
541	C₂×D₄×C₅₃	—	2	1	no	—
542	C₂×D₄×C₅₃	—	2	1	no	—
543	C₂×D₄×C₅₃	—	2	1	no	—
544	C₂×D₄×C₅₃	—	2	1	no	—
545	C₂×D₄×C₅₃	—	2	1	no	—
546	C₂×D₄×C₅₃	—	2	1	no	—
547	C₂×D₄×C₅₃	—	2	1	no	—
548	C₂×D₄×C₅₃	—	2	1	no	—
549	C₂×D₄×C₅₃	—	2	1	no	—
550	C₂×D₄×C₅₃	—	2	1	no	—
551	C₂×D₄×C₅₃	—	2	1	no	—
552	C₂×D₄×C₅₃	—	2	1	no	—
553	C₂×D₄×C₅₃	—	2	1	no	—
554	C₂×D₄×C₅₃	—	2	1	no	—
555	C₂×D₄×C₅₃	—	2	1	no	—
556	C₂×D₄×C₅₃	—	2	1	no	—
557	C₂×D₄×C₅₃	—	4	1	no	—
558	C₂×D₄×C₅₃	—	4	1	no	—
559	C₂×D₄×C₅₃	—	4	1	no	—
560	C₂×D₄×C₅₃	—	4	1	no	—
561	C₂×D₄×C₅₃	—	4	2	no	—
562	C₂×D₄×C₅₃	—	4	4	no	—
563	C₂×D₄×C₅₃	—	4	4	no	—
564	C₂×D₄×C₅₃	—	4	4	no	—
565	C₂×D₄×C₅₃	—	4	4	no	—
566	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
567	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
568	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
569	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
570	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
571	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
572	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
573	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
574	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂²×C₄×C₅₃	—	2	1	no	—
576	C₂²×C₄×C₅₃	—	2	1	no	—
577	C₂²×C₄×C₅₃	—	2	1	no	—
578	C₂²×C₄×C₅₃	—	2	1	no	—
579	C₂²×C₄×C₅₃	—	2	1	no	—
580	C₂²×C₄×C₅₃	—	2	1	no	—
581	C₂²×C₄×C₅₃	—	2	1	no	—
582	C₂²×C₄×C₅₃	—	2	1	no	—
583	C₂²×C₄×C₅₃	—	2	1	no	—
584	C₂²×C₄×C₅₃	—	2	1	no	—
585	C₂²×C₄×C₅₃	—	2	1	no	—
586	C₂²×C₄×C₅₃	—	2	1	no	—
587	C₂²×C₄×C₅₃	—	2	1	no	—
588	C₂²×C₄×C₅₃	—	2	1	no	—
589	C₂²×C₄×C₅₃	—	2	1	no	—
590	C₂²×C₄×C₅₃	—	2	1	no	—
591	C₂²×C₄×C₅₃	—	2	1	no	—
592	C₂²×C₄×C₅₃	—	2	1	no	—
593	C₂²×C₄×C₅₃	—	4	1	no	—
594	C₂²×C₄×C₅₃	—	4	1	no	—
595	C₂²×C₄×C₅₃	—	4	1	no	—
596	C₂²×C₄×C₅₃	—	4	1	no	—
597	C₂²×C₄×C₅₃	—	4	4	no	—
598	C₂²×C₄×C₅₃	—	4	4	no	—
599	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
600	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
601	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
602	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
603	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
604	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
605	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
606	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
607	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
612	Q₁₆×C₅₃	—	2	2	no	—
613	Q₁₆×C₅₃	—	2	2	no	—
614	Q₁₆×C₅₃	—	4	1	no	—
615	Q₁₆×C₅₃	—	4	1	no	—
616	Q₁₆×C₅₃	—	4	1	no	—
617	Q₁₆×C₅₃	—	4	1	no	—
618	SD₁₆×C₅₃	—	2	2	no	—
619	SD₁₆×C₅₃	—	2	2	no	—
620	SD₁₆×C₅₃	—	2	2	no	—
621	SD₁₆×C₅₃	—	2	2	no	—
622	SD₁₆×C₅₃	—	4	1	no	—
623	SD₁₆×C₅₃	—	4	1	no	—
624	SD₁₆×C₅₃	—	4	1	no	—
625	SD₁₆×C₅₃	—	4	1	no	—
626	SD₁₆×C₅₃	—	4	1	no	—
627	SD₁₆×C₅₃	—	4	1	no	—
628	SD₁₆×C₅₃	—	4	1	no	—
629	SD₁₆×C₅₃	—	4	1	no	—
630	D₈×C₅₃	—	2	2	no	—
631	D₈×C₅₃	—	2	2	no	—
632	D₈×C₅₃	—	4	1	no	—
633	D₈×C₅₃	—	4	1	no	—
634	D₈×C₅₃	—	4	1	no	—
635	D₈×C₅₃	—	4	1	no	—
636	M₁₆×C₅₃	—	4	1	no	—
637	M₁₆×C₅₃	—	4	1	no	—
638	M₁₆×C₅₃	—	4	1	no	—
639	M₁₆×C₅₃	—	4	1	no	—
640	C₂×C₈×C₅₃	—	4	1	no	—
641	C₂×C₈×C₅₃	—	4	1	no	—
642	C₂×C₈×C₅₃	—	4	1	no	—
643	C₂×C₈×C₅₃	—	4	1	no	—
644	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
645	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
646	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
647	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
648	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
649	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
650	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
651	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
652	C₄⋊C₄×C₅₃	—	2	1	no	—
653	C₄⋊C₄×C₅₃	—	2	1	no	—
654	C₄⋊C₄×C₅₃	—	2	1	no	—
655	C₄⋊C₄×C₅₃	—	2	1	no	—
656	C₄⋊C₄×C₅₃	—	2	1	no	—
657	C₄⋊C₄×C₅₃	—	2	1	no	—
658	C₄⋊C₄×C₅₃	—	2	1	no	—
659	C₄⋊C₄×C₅₃	—	2	1	no	—
660	C₄⋊C₄×C₅₃	—	2	1	no	—
661	C₄⋊C₄×C₅₃	—	2	1	no	—
662	C₄⋊C₄×C₅₃	—	2	1	no	—
663	C₄⋊C₄×C₅₃	—	2	1	no	—
664	C₄⋊C₄×C₅₃	—	2	1	no	—
665	C₄⋊C₄×C₅₃	—	2	1	no	—
666	C₄⋊C₄×C₅₃	—	2	1	no	—
667	C₄⋊C₄×C₅₃	—	2	1	no	—
668	C₄⋊C₄×C₅₃	—	2	1	no	—
669	C₄⋊C₄×C₅₃	—	2	1	no	—
670	C₄⋊C₄×C₅₃	—	2	1	no	—
671	C₄⋊C₄×C₅₃	—	2	1	no	—
672	C₄⋊C₄×C₅₃	—	2	1	no	—
673	C₄⋊C₄×C₅₃	—	2	1	no	—
674	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
675	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
676	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
677	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
678	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
679	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
680	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
681	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
682	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
683	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
684	C₂²⋊C₄×C₅₃	—	2	1	no	—
685	C₂²⋊C₄×C₅₃	—	2	1	no	—
686	C₂²⋊C₄×C₅₃	—	2	1	no	—
687	C₂²⋊C₄×C₅₃	—	2	1	no	—
688	C₂²⋊C₄×C₅₃	—	2	1	no	—
689	C₂²⋊C₄×C₅₃	—	2	1	no	—
690	C₂²⋊C₄×C₅₃	—	2	1	no	—
691	C₂²⋊C₄×C₅₃	—	2	1	no	—
692	C₂²⋊C₄×C₅₃	—	2	1	no	—
693	C₂²⋊C₄×C₅₃	—	2	1	no	—
694	C₂²⋊C₄×C₅₃	—	2	1	no	—
695	C₂²⋊C₄×C₅₃	—	2	1	no	—
696	C₂²⋊C₄×C₅₃	—	2	1	no	—
697	C₂²⋊C₄×C₅₃	—	2	1	no	—
698	C₂²⋊C₄×C₅₃	—	2	1	no	—
699	C₂²⋊C₄×C₅₃	—	2	1	no	—
700	C₂²⋊C₄×C₅₃	—	2	1	no	—
701	C₂²⋊C₄×C₅₃	—	2	1	no	—
702	C₂²⋊C₄×C₅₃	—	2	1	no	—
703	C₂²⋊C₄×C₅₃	—	2	1	no	—
704	C₂²⋊C₄×C₅₃	—	2	1	no	—
705	C₂²⋊C₄×C₅₃	—	2	1	no	—
706	C₂²⋊C₄×C₅₃	—	2	1	no	—
707	C₂²⋊C₄×C₅₃	—	2	1	no	—
708	C₂²⋊C₄×C₅₃	—	2	1	no	—
709	C₂²⋊C₄×C₅₃	—	2	1	no	—
710	C₂²⋊C₄×C₅₃	—	2	1	no	—
711	C₂²⋊C₄×C₅₃	—	2	1	no	—
712	C₂²⋊C₄×C₅₃	—	2	1	no	—
713	C₂²⋊C₄×C₅₃	—	2	1	no	—
714	C₂²⋊C₄×C₅₃	—	2	1	no	—
715	C₂²⋊C₄×C₅₃	—	2	1	no	—
716	C₂²⋊C₄×C₅₃	—	2	1	no	—
717	C₂²⋊C₄×C₅₃	—	2	1	no	—
718	C₂²⋊C₄×C₅₃	—	2	1	no	—
719	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
721	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
722	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
723	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
724	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
725	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
726	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
727	C₄²×C₅₃	—	2	1	no	—
728	C₄²×C₅₃	—	2	1	no	—
729	C₄²×C₅₃	—	2	1	no	—
730	C₄²×C₅₃	—	2	1	no	—
731	C₄²×C₅₃	—	2	1	no	—
732	C₄²×C₅₃	—	2	1	no	—
733	C₄²×C₅₃	—	2	1	no	—
734	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
735	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
736	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
737	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
738	C₂³×C₅₃	—	2	1	no	—
739	C₂³×C₅₃	—	2	2	no	—
740	C₂³×C₅₃	—	2	1	no	—
741	C₂³×C₅₃	—	2	1	no	—
742	C₂³×C₅₃	—	2	1	no	—
743	C₂³×C₅₃	—	2	1	no	—
744	C₂³×C₅₃	—	4	1	no	—
745	C₂³×C₅₃	—	4	1	no	—
746	C₂³×C₅₃	—	4	1	no	—
747	C₂³×C₅₃	—	4	1	no	—
748	C₂³×C₅₃	—	4	1	no	—
749	C₂³×C₅₃	—	4	2	no	—
750	C₂³×C₅₃	—	4	2	no	—
751	C₂³×C₅₃	—	4	2	no	—
752	C₂³×C₅₃	—	4	2	no	—
753	C₂³×C₅₃	—	4	2	no	—
754	C₂³×C₅₃	—	8	1	no	—
755	C₂³×C₅₃	—	8	1	no	—
756	C₂³×C₅₃	—	8	1	no	—
757	C₂³×C₅₃	—	8	1	no	—
758	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
759	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
760	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
761	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
762	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
763	Q₈×C₅₃	—	2	1	no	—
764	Q₈×C₅₃	—	2	1	no	—
765	Q₈×C₅₃	—	2	1	no	—
766	Q₈×C₅₃	—	2	1	no	—
767	Q₈×C₅₃	—	2	1	no	—
768	Q₈×C₅₃	—	2	1	no	—
769	Q₈×C₅₃	—	2	1	no	—
770	Q₈×C₅₃	—	2	1	no	—
771	Q₈×C₅₃	—	2	1	no	—
772	Q₈×C₅₃	—	4	2	no	—
773	Q₈×C₅₃	—	4	2	no	—
774	Q₈×C₅₃	—	8	1	no	—
775	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
776	D₄×C₅₃	—	2	4	no	—
777	D₄×C₅₃	—	2	2	no	—
778	D₄×C₅₃	—	2	2	no	—
779	D₄×C₅₃	—	2	1	no	—
780	D₄×C₅₃	—	2	1	no	—
781	D₄×C₅₃	—	2	1	no	—
782	D₄×C₅₃	—	2	1	no	—
783	D₄×C₅₃	—	2	1	no	—
784	D₄×C₅₃	—	2	1	no	—
785	D₄×C₅₃	—	2	1	no	—
786	D₄×C₅₃	—	2	1	no	—
787	D₄×C₅₃	—	2	1	no	—
788	D₄×C₅₃	—	4	1	no	—
789	D₄×C₅₃	—	4	1	no	—
790	D₄×C₅₃	—	4	2	no	—
791	D₄×C₅₃	—	4	2	no	—
792	D₄×C₅₃	—	4	2	no	—
793	D₄×C₅₃	—	4	2	no	—
794	D₄×C₅₃	—	4	2	no	—
795	D₄×C₅₃	—	4	2	no	—
796	D₄×C₅₃	—	4	2	no	—
797	D₄×C₅₃	—	4	2	no	—
798	D₄×C₅₃	—	4	2	no	—
799	D₄×C₅₃	—	4	2	no	—
800	D₄×C₅₃	—	4	2	no	—
801	D₄×C₅₃	—	4	2	no	—
802	D₄×C₅₃	—	4	2	no	—
803	D₄×C₅₃	—	4	2	no	—
804	D₄×C₅₃	—	4	2	no	—
805	D₄×C₅₃	—	8	1	no	—
806	D₄×C₅₃	—	8	1	no	—
807	D₄×C₅₃	—	8	1	no	—
808	D₄×C₅₃	—	8	1	no	—
809	D₄×C₅₃	—	8	1	no	—
810	D₄×C₅₃	—	8	1	no	—
811	D₄×C₅₃	—	8	1	no	—
812	D₄×C₅₃	—	8	1	no	—
813	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
814	C₂×C₄×C₅₃	—	2	4	no	—
815	C₂×C₄×C₅₃	—	2	1	no	—
816	C₂×C₄×C₅₃	—	2	1	no	—
817	C₂×C₄×C₅₃	—	2	1	no	—
818	C₂×C₄×C₅₃	—	2	1	no	—
819	C₂×C₄×C₅₃	—	2	1	no	—
820	C₂×C₄×C₅₃	—	2	1	no	—
821	C₂×C₄×C₅₃	—	2	1	no	—
822	C₂×C₄×C₅₃	—	2	1	no	—
823	C₂×C₄×C₅₃	—	2	1	no	—
824	C₂×C₄×C₅₃	—	2	1	no	—
825	C₂×C₄×C₅₃	—	2	1	no	—
826	C₂×C₄×C₅₃	—	2	1	no	—
827	C₂×C₄×C₅₃	—	2	1	no	—
828	C₂×C₄×C₅₃	—	2	1	no	—
829	C₂×C₄×C₅₃	—	2	1	no	—
830	C₂×C₄×C₅₃	—	2	1	no	—
831	C₂×C₄×C₅₃	—	2	1	no	—
832	C₂×C₄×C₅₃	—	2	1	no	—
833	C₂×C₄×C₅₃	—	2	1	no	—
834	C₂×C₄×C₅₃	—	2	1	no	—
835	C₂×C₄×C₅₃	—	2	1	no	—
836	C₂×C₄×C₅₃	—	4	1	no	—
837	C₂×C₄×C₅₃	—	4	1	no	—
838	C₂×C₄×C₅₃	—	4	1	no	—
839	C₂×C₄×C₅₃	—	4	1	no	—
840	C₂×C₄×C₅₃	—	4	1	no	—
841	C₂×C₄×C₅₃	—	4	1	no	—
842	C₂×C₄×C₅₃	—	4	1	no	—
843	C₂×C₄×C₅₃	—	4	1	no	—
844	C₂×C₄×C₅₃	—	4	2	no	—
845	C₂×C₄×C₅₃	—	4	2	no	—
846	C₂×C₄×C₅₃	—	4	2	no	—
847	C₂×C₄×C₅₃	—	4	2	no	—
848	C₂×C₄×C₅₃	—	4	2	no	—
849	C₂×C₄×C₅₃	—	4	2	no	—
850	C₂×C₄×C₅₃	—	4	2	no	—
851	C₂×C₄×C₅₃	—	4	2	no	—
852	C₂×C₄×C₅₃	—	4	2	no	—
853	C₂×C₄×C₅₃	—	4	2	no	—
854	C₂×C₄×C₅₃	—	8	1	no	—
855	C₂×C₄×C₅₃	—	8	1	no	—
856	C₂×C₄×C₅₃	—	8	1	no	—
857	C₂×C₄×C₅₃	—	8	1	no	—
858	C₂×C₄×C₅₃	—	8	1	no	—
859	C₂×C₄×C₅₃	—	8	1	no	—
860	C₂×C₄×C₅₃	—	8	1	no	—
861	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
862	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
863	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
864	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
865	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
866	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
867	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
868	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
869	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
870	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
871	C₈×C₅₃	—	2	1	no	—
872	C₈×C₅₃	—	2	1	no	—
873	C₈×C₅₃	—	2	1	no	—
874	C₈×C₅₃	—	2	1	no	—
875	C₈×C₅₃	—	2	1	no	—
876	C₈×C₅₃	—	2	1	no	—
877	C₈×C₅₃	—	2	1	no	—
878	C₈×C₅₃	—	2	1	no	—
879	#61606	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
880	C₂²×C₅₃	—	2	1	no	—
881	C₂²×C₅₃	—	2	1	no	—
882	C₂²×C₅₃	—	2	1	no	—
883	C₂²×C₅₃	—	2	1	no	—
884	C₂²×C₅₃	—	2	1	no	—
885	C₂²×C₅₃	—	2	1	no	—
886	C₂²×C₅₃	—	2	1	no	—
887	C₂²×C₅₃	—	2	1	no	—
888	C₂²×C₅₃	—	2	2	no	—
889	C₂²×C₅₃	—	2	1	no	—
890	C₂²×C₅₃	—	2	1	no	—
891	C₂²×C₅₃	—	2	1	no	—
892	C₂²×C₅₃	—	2	1	no	—
893	C₂²×C₅₃	—	2	1	no	—
894	C₂²×C₅₃	—	2	1	no	—
895	C₂²×C₅₃	—	4	1	no	—
896	C₂²×C₅₃	—	4	1	no	—
897	C₂²×C₅₃	—	4	1	no	—
898	C₂²×C₅₃	—	4	1	no	—
899	C₂²×C₅₃	—	4	1	no	—
900	C₂²×C₅₃	—	4	1	no	—
901	C₂²×C₅₃	—	4	1	no	—
902	C₂²×C₅₃	—	4	1	no	—
903	C₂²×C₅₃	—	4	1	no	—
904	C₂²×C₅₃	—	4	1	no	—
905	C₂²×C₅₃	—	4	1	no	—
906	C₂²×C₅₃	—	4	1	no	—
907	C₂²×C₅₃	—	4	1	no	—
908	C₂²×C₅₃	—	4	1	no	—
909	C₂²×C₅₃	—	8	2	no	—
910	C₂²×C₅₃	—	8	4	no	—
911	C₂²×C₅₃	—	8	2	no	—
912	C₂²×C₅₃	—	8	4	no	—
913	C₂²×C₅₃	—	16	2	no	—
914	C₂²×C₅₃	#575	1	2	yes	—
915	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
916	C₄×C₅₃	—	2	1	no	—
917	C₄×C₅₃	—	2	1	no	—
918	C₄×C₅₃	—	2	1	no	—
919	C₄×C₅₃	—	2	2	no	—
920	C₄×C₅₃	—	2	1	no	—
921	C₄×C₅₃	—	2	1	no	—
922	C₄×C₅₃	—	2	1	no	—
923	C₄×C₅₃	—	2	1	no	—
924	C₄×C₅₃	—	2	1	no	—
925	C₄×C₅₃	—	2	1	no	—
926	C₄×C₅₃	—	4	1	no	—
927	C₄×C₅₃	—	4	1	no	—
928	C₄×C₅₃	—	4	1	no	—
929	C₄×C₅₃	—	4	1	no	—
930	C₄×C₅₃	—	4	1	no	—
931	C₄×C₅₃	—	4	1	no	—
932	C₄×C₅₃	—	4	1	no	—
933	C₄×C₅₃	—	4	1	no	—
934	C₄×C₅₃	—	4	1	no	—
935	C₄×C₅₃	—	4	1	no	—
936	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
937	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
938	#3505	C₂×C₅₃	1	1	yes	characteristic, complemented
939	D₄×#41	C₂×C₅₃	1	1	yes	characteristic, complemented
940	#3327	C₂×C₅₃	1	1	yes	characteristic, complemented
941	#3323	C₂×C₅₃	1	1	yes	characteristic, complemented
942	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
943	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
944	#3317	C₂×C₅₃	1	1	yes	characteristic, complemented
945	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
946	#3301	C₂×C₅₃	1	1	yes	characteristic, complemented
947	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
948	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
949	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
950	#3275	C₂×C₅₃	1	1	yes	characteristic, complemented
951	#3273	C₂×C₅₃	1	1	yes	characteristic, complemented
952	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
953	#3268	C₂×C₅₃	1	1	yes	characteristic, complemented
954	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
955	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
956	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
957	#3212	C₂×C₅₃	1	1	yes	characteristic, complemented
958	#3197	C₂×C₅₃	1	1	yes	characteristic, complemented
959	#3196	C₂×C₅₃	1	1	yes	characteristic, complemented
960	#3191	C₂×C₅₃	1	1	yes	characteristic, complemented
961	#3188	C₂×C₅₃	1	1	yes	characteristic, complemented
962	#3111	C₂×C₅₃	1	1	yes	characteristic, complemented
963	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
964	#3006	C₂×C₅₃	1	1	yes	characteristic, complemented
965	#3005	C₂×C₅₃	1	1	yes	characteristic, complemented
966	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
967	C₂×#452	C₂×C₅₃	1	1	yes	characteristic, complemented
968	#2974	C₂×C₅₃	1	1	yes	characteristic, complemented
969	C₂×C₅₃	—	2	2	no	—
970	C₂×C₅₃	—	4	1	no	—
971	C₂×C₅₃	—	4	1	no	—
972	C₂×C₅₃	—	4	1	no	—
973	C₂×C₅₃	—	4	1	no	—
974	C₂×C₅₃	—	4	2	no	—
975	C₂×C₅₃	—	8	1	no	—
976	C₂×C₅₃	—	8	1	no	—
977	C₂×C₅₃	—	8	1	no	—
978	C₂×C₅₃	—	8	1	no	—
979	C₂×C₅₃	#3484	1	1	yes	characteristic
980	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
981	C₂×C₅₃	#3584	1	1	yes	characteristic
982	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic
983	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#553	—	2	1	no	—
993	#553	—	2	1	no	—
994	#553	C₂²×C₅₃	1	1	yes	characteristic
995	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#551	—	2	1	no	—
999	#551	—	2	1	no	—
1000	#550	C₂²×C₅₃	1	1	yes	characteristic
1001	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#548	C₂²×C₅₃	1	1	yes	characteristic
1003	#548	C₂²×C₅₃	1	1	yes	characteristic
1004	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#547	—	2	1	no	—
1007	#547	C₂²×C₅₃	1	1	yes	characteristic
1008	#546	—	2	1	no	—
1009	#546	—	2	1	no	—
1010	#546	C₂²×C₅₃	1	1	yes	characteristic
1011	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	D₄²	—	2	1	no	—
1015	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#539	—	2	1	no	—
1017	#538	—	2	1	no	—
1018	#534	—	2	1	no	—
1019	#532	—	2	1	no	—
1020	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#525	—	2	1	no	—
1024	#525	—	2	1	no	—
1025	#525	C₂²×C₅₃	1	1	yes	characteristic
1026	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#525	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	C₂×#121	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#518	—	2	1	no	—
1032	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	C₂×C₄×D₄	—	2	1	no	—
1034	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
1035	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#449	C₂²×C₅₃	1	1	yes	characteristic
1106	#449	C₂²×C₅₃	1	1	yes	characteristic
1107	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1117	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1118	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1125	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1126	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1127	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1128	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1129	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1130	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1131	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1132	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1133	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1134	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1135	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1136	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1137	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1138	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1139	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1140	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1141	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1142	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1143	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1144	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1145	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1146	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1147	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1148	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1149	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
1150	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
1151	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1152	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1153	C₅₃	#61606	1	1	yes	characteristic, direct product factor, Sylow
1154	C₂×#41	—	2	1	no	—
1155	C₂×#41	—	2	1	no	—
1156	C₂×#41	—	2	1	no	—
1157	C₂×#41	—	2	1	no	—
1158	C₂×#41	—	4	2	no	—
1159	C₂×#41	—	4	2	no	—
1160	C₂×#41	—	4	2	no	—
1161	C₂×#41	—	4	2	no	—
1162	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1164	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1168	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂²×D₄	—	2	1	no	—
1175	C₂²×D₄	—	2	1	no	—
1176	C₂²×D₄	—	2	1	no	—
1177	C₂²×D₄	—	2	1	no	—
1178	C₂²×D₄	D₄×C₅₃	1	1	yes	characteristic
1179	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂³×C₄	—	2	1	no	—
1183	C₂³×C₄	—	2	1	no	—
1184	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1186	#137	—	4	2	no	—
1187	AGL(1,ℤ/8)	—	4	2	no	—
1188	AGL(1,ℤ/8)	—	4	2	no	—
1189	AGL(1,ℤ/8)	—	4	2	no	—
1190	#135	—	4	2	no	—
1191	#135	—	4	2	no	—
1192	C₂×Q₁₆	—	4	2	no	—
1193	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1197	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1199	C₂×SD₁₆	—	4	2	no	—
1200	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1207	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1208	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1209	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1210	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1211	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1212	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1213	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1214	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1215	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1216	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1217	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1218	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1219	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1221	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1222	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1223	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1224	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1225	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1226	C₄⋊Q₈	—	2	1	no	—
1227	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1228	#127	—	2	1	no	—
1229	#127	C₂³×C₅₃	1	1	yes	characteristic
1230	#126	—	2	1	no	—
1231	#126	—	2	1	no	—
1232	#126	—	2	1	no	—
1233	#126	—	2	1	no	—
1234	#126	—	2	1	no	—
1235	#126	—	2	1	no	—
1236	#125	—	2	1	no	—
1237	#125	—	2	1	no	—
1238	#125	C₂³×C₅₃	1	1	yes	characteristic
1239	#125	C₂³×C₅₃	1	1	yes	characteristic
1240	#124	—	2	1	no	—
1241	#124	—	2	1	no	—
1242	#124	—	2	1	no	—
1243	#124	—	2	1	no	—
1244	#124	C₂³×C₅₃	1	1	yes	characteristic
1245	#124	C₂³×C₅₃	1	1	yes	characteristic
1246	#124	C₂³×C₅₃	1	1	yes	characteristic
1247	#124	C₂³×C₅₃	1	1	yes	characteristic
1248	#123	—	2	1	no	—
1249	#123	—	2	1	no	—
1250	#123	—	2	1	no	—
1251	#123	—	2	1	no	—
1252	#123	—	2	1	no	—
1253	#123	—	2	1	no	—
1254	#123	—	2	1	no	—
1255	#123	—	2	1	no	—
1256	#123	—	2	1	no	—
1257	#123	—	2	1	no	—
1258	#123	—	2	1	no	—
1259	#123	—	2	1	no	—
1260	#123	—	2	1	no	—
1261	#123	—	2	1	no	—
1262	#123	—	2	1	no	—
1263	#123	—	2	1	no	—
1264	C₂²⋊Q₈	—	2	1	no	—
1265	C₂²⋊Q₈	—	2	1	no	—
1266	C₂²⋊Q₈	—	2	1	no	—
1267	C₂²⋊Q₈	—	2	1	no	—
1268	C₂²⋊Q₈	—	2	1	no	—
1269	C₂²⋊Q₈	—	2	1	no	—
1270	C₂²⋊Q₈	—	2	1	no	—
1271	C₂²⋊Q₈	—	2	1	no	—
1272	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1273	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1274	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1275	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1276	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1277	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1278	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1279	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1280	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1281	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1282	#121	—	2	1	no	—
1283	#121	—	2	1	no	—
1284	#121	—	2	1	no	—
1285	#121	—	2	1	no	—
1286	#121	—	2	1	no	—
1287	#121	—	2	1	no	—
1288	#121	—	2	1	no	—
1289	#121	—	2	1	no	—
1290	#121	—	2	1	no	—
1291	#121	—	2	1	no	—
1292	#121	—	2	1	no	—
1293	#121	—	2	1	no	—
1294	#121	—	2	1	no	—
1295	#121	—	2	1	no	—
1296	#121	—	2	1	no	—
1297	#121	—	2	1	no	—
1298	#121	—	2	1	no	—
1299	#121	—	2	1	no	—
1300	#121	C₂³×C₅₃	1	1	yes	characteristic
1301	#121	C₂³×C₅₃	1	1	yes	characteristic
1302	#121	C₂³×C₅₃	1	1	yes	characteristic
1303	#121	C₂³×C₅₃	1	1	yes	characteristic
1304	#121	C₂³×C₅₃	1	1	yes	characteristic
1305	#121	C₂³×C₅₃	1	1	yes	characteristic
1306	#121	C₂³×C₅₃	1	1	yes	characteristic
1307	#121	C₂³×C₅₃	1	1	yes	characteristic
1308	#121	C₂³×C₅₃	1	1	yes	characteristic
1309	#121	C₂³×C₅₃	1	1	yes	characteristic
1310	#120	—	2	1	no	—
1311	#120	—	2	1	no	—
1312	#120	—	2	1	no	—
1313	#120	—	2	1	no	—
1314	#120	—	2	1	no	—
1315	#120	—	2	1	no	—
1316	#120	—	2	1	no	—
1317	#120	—	2	1	no	—
1318	#120	—	2	1	no	—
1319	#120	—	2	1	no	—
1320	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1321	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1322	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1323	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1324	C₄×D₄	—	2	1	no	—
1325	C₄×D₄	—	2	1	no	—
1326	C₄×D₄	—	2	1	no	—
1327	C₄×D₄	—	2	1	no	—
1328	C₄×D₄	—	2	1	no	—
1329	C₄×D₄	—	2	1	no	—
1330	C₄×D₄	—	2	1	no	—
1331	C₄×D₄	—	2	1	no	—
1332	C₄×D₄	—	2	1	no	—
1333	C₄×D₄	—	2	1	no	—
1334	C₄×D₄	—	2	1	no	—
1335	C₄×D₄	—	2	1	no	—
1336	C₄×D₄	—	2	1	no	—
1337	C₄×D₄	—	2	1	no	—
1338	C₄×D₄	—	2	1	no	—
1339	C₄×D₄	—	2	1	no	—
1340	C₄×D₄	—	2	1	no	—
1341	C₄×D₄	—	2	1	no	—
1342	C₄×D₄	—	2	1	no	—
1343	C₄×D₄	—	2	1	no	—
1344	C₄×D₄	—	2	1	no	—
1345	C₄×D₄	—	2	1	no	—
1346	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1347	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1348	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1349	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1350	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1351	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1352	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1353	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1354	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1355	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1356	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1357	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1358	#117	—	2	1	no	—
1359	#117	—	2	1	no	—
1360	#117	—	2	1	no	—
1361	#117	—	2	1	no	—
1362	#117	—	2	1	no	—
1363	#117	C₂³×C₅₃	1	1	yes	characteristic
1364	#117	C₂³×C₅₃	1	1	yes	characteristic
1365	#117	C₂³×C₅₃	1	1	yes	characteristic
1366	C₂×C₄⋊C₄	—	2	1	no	—
1367	C₂×C₄⋊C₄	—	2	1	no	—
1368	C₂×C₄⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1369	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1370	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1371	C₂×C₂²⋊C₄	—	2	1	no	—
1372	C₂×C₂²⋊C₄	—	2	1	no	—
1373	C₂×C₂²⋊C₄	—	2	1	no	—
1374	C₂×C₂²⋊C₄	—	2	1	no	—
1375	C₂×C₂²⋊C₄	—	2	1	no	—
1376	C₂×C₂²⋊C₄	—	2	1	no	—
1377	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1378	C₂×C₂²⋊C₄	D₄×C₅₃	1	1	yes	characteristic
1379	C₂×C₄²	—	2	1	no	—
1380	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1381	#107	C₂³×C₅₃	1	1	yes	characteristic
1382	#107	C₂³×C₅₃	1	1	yes	characteristic
1383	#107	C₂³×C₅₃	1	1	yes	characteristic
1384	#107	C₂³×C₅₃	1	1	yes	characteristic
1385	#106	C₂³×C₅₃	1	1	yes	characteristic
1386	#106	C₂³×C₅₃	1	1	yes	characteristic
1387	#106	C₂³×C₅₃	1	1	yes	characteristic
1388	#106	C₂³×C₅₃	1	1	yes	characteristic
1389	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1390	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1391	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1392	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1393	#103	C₂³×C₅₃	1	1	yes	characteristic
1394	#103	C₂³×C₅₃	1	1	yes	characteristic
1395	#103	C₂³×C₅₃	1	1	yes	characteristic
1396	#103	C₂³×C₅₃	1	1	yes	characteristic
1397	#103	C₂³×C₅₃	1	1	yes	characteristic
1398	#103	C₂³×C₅₃	1	1	yes	characteristic
1399	#103	C₂³×C₅₃	1	1	yes	characteristic
1400	#103	C₂³×C₅₃	1	1	yes	characteristic
1401	#103	C₂³×C₅₃	1	1	yes	characteristic
1402	#103	C₂³×C₅₃	1	1	yes	characteristic
1403	#103	C₂³×C₅₃	1	1	yes	characteristic
1404	#103	C₂³×C₅₃	1	1	yes	characteristic
1405	#103	C₂³×C₅₃	1	1	yes	characteristic
1406	#103	C₂³×C₅₃	1	1	yes	characteristic
1407	#103	C₂³×C₅₃	1	1	yes	characteristic
1408	#103	C₂³×C₅₃	1	1	yes	characteristic
1409	#102	C₂³×C₅₃	1	1	yes	characteristic
1410	#102	C₂³×C₅₃	1	1	yes	characteristic
1411	#102	C₂³×C₅₃	1	1	yes	characteristic
1412	#102	C₂³×C₅₃	1	1	yes	characteristic
1413	#102	C₂³×C₅₃	1	1	yes	characteristic
1414	#102	C₂³×C₅₃	1	1	yes	characteristic
1415	#102	C₂³×C₅₃	1	1	yes	characteristic
1416	#102	C₂³×C₅₃	1	1	yes	characteristic
1417	#102	C₂³×C₅₃	1	1	yes	characteristic
1418	#102	C₂³×C₅₃	1	1	yes	characteristic
1419	#102	C₂³×C₅₃	1	1	yes	characteristic
1420	#102	C₂³×C₅₃	1	1	yes	characteristic
1421	#102	C₂³×C₅₃	1	1	yes	characteristic
1422	#102	C₂³×C₅₃	1	1	yes	characteristic
1423	#102	C₂³×C₅₃	1	1	yes	characteristic
1424	#102	C₂³×C₅₃	1	1	yes	characteristic
1425	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1426	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1427	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1428	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1429	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1430	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1431	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1432	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1433	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1434	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1435	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1436	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1437	#97	C₂³×C₅₃	1	1	yes	characteristic
1438	#97	C₂³×C₅₃	1	1	yes	characteristic
1439	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1440	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1441	C₂⁴	—	2	1	no	—
1442	C₂⁴	—	2	1	no	—
1443	C₂⁴	—	2	1	no	—
1444	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1445	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1446	#41	—	2	2	no	—
1447	#41	—	2	2	no	—
1448	#41	—	2	2	no	—
1449	#41	—	2	2	no	—
1450	#41	—	2	2	no	—
1451	#41	—	2	2	no	—
1452	#41	—	4	1	no	—
1453	#41	—	4	1	no	—
1454	#41	—	4	1	no	—
1455	#41	—	4	1	no	—
1456	#41	—	4	1	no	—
1457	#41	—	4	1	no	—
1458	#41	—	4	1	no	—
1459	#41	—	4	1	no	—
1460	#41	—	4	4	no	—
1461	#41	—	4	4	no	—
1462	#41	—	4	1	no	—
1463	#41	—	4	1	no	—
1464	#41	—	4	1	no	—
1465	#41	—	4	1	no	—
1466	#41	—	4	4	no	—
1467	#41	—	4	4	no	—
1468	C₂×Q₈	—	2	1	no	—
1469	C₂×Q₈	—	2	1	no	—
1470	C₂×Q₈	—	2	1	no	—
1471	C₂×Q₈	—	2	2	no	—
1472	C₂×Q₈	—	2	2	no	—
1473	C₂×Q₈	—	4	1	no	—
1474	C₂×Q₈	—	4	1	no	—
1475	C₂×Q₈	—	4	1	no	—
1476	C₂×Q₈	—	4	1	no	—
1477	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1478	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1479	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1480	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1481	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1482	C₂×D₄	—	2	1	no	—
1483	C₂×D₄	—	2	2	no	—
1484	C₂×D₄	—	2	2	no	—
1485	C₂×D₄	—	2	1	no	—
1486	C₂×D₄	—	2	1	no	—
1487	C₂×D₄	—	2	1	no	—
1488	C₂×D₄	—	2	1	no	—
1489	C₂×D₄	—	2	1	no	—
1490	C₂×D₄	—	2	1	no	—
1491	C₂×D₄	—	2	1	no	—
1492	C₂×D₄	—	2	1	no	—
1493	C₂×D₄	—	2	1	no	—
1494	C₂×D₄	—	2	1	no	—
1495	C₂×D₄	—	2	1	no	—
1496	C₂×D₄	—	2	1	no	—
1497	C₂×D₄	—	2	1	no	—
1498	C₂×D₄	—	2	1	no	—
1499	C₂×D₄	—	2	1	no	—
1500	C₂×D₄	—	2	1	no	—
1501	C₂×D₄	—	2	1	no	—
1502	C₂×D₄	—	2	1	no	—
1503	C₂×D₄	—	2	1	no	—
1504	C₂×D₄	—	2	1	no	—
1505	C₂×D₄	—	2	1	no	—
1506	C₂×D₄	—	2	1	no	—
1507	C₂×D₄	—	2	1	no	—
1508	C₂×D₄	—	4	1	no	—
1509	C₂×D₄	—	4	1	no	—
1510	C₂×D₄	—	4	1	no	—
1511	C₂×D₄	—	4	1	no	—
1512	C₂×D₄	—	4	2	no	—
1513	C₂×D₄	—	4	4	no	—
1514	C₂×D₄	—	4	4	no	—
1515	C₂×D₄	—	4	4	no	—
1516	C₂×D₄	—	4	4	no	—
1517	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1518	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1519	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1520	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1522	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1523	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1524	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1525	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1526	C₂²×C₄	—	2	1	no	—
1527	C₂²×C₄	—	2	1	no	—
1528	C₂²×C₄	—	2	1	no	—
1529	C₂²×C₄	—	2	1	no	—
1530	C₂²×C₄	—	2	1	no	—
1531	C₂²×C₄	—	2	1	no	—
1532	C₂²×C₄	—	2	1	no	—
1533	C₂²×C₄	—	2	1	no	—
1534	C₂²×C₄	—	2	1	no	—
1535	C₂²×C₄	—	2	1	no	—
1536	C₂²×C₄	—	2	1	no	—
1537	C₂²×C₄	—	2	1	no	—
1538	C₂²×C₄	—	2	1	no	—
1539	C₂²×C₄	—	2	1	no	—
1540	C₂²×C₄	—	2	1	no	—
1541	C₂²×C₄	—	2	1	no	—
1542	C₂²×C₄	—	2	1	no	—
1543	C₂²×C₄	—	2	1	no	—
1544	C₂²×C₄	—	4	1	no	—
1545	C₂²×C₄	—	4	1	no	—
1546	C₂²×C₄	—	4	1	no	—
1547	C₂²×C₄	—	4	1	no	—
1548	C₂²×C₄	—	4	4	no	—
1549	C₂²×C₄	—	4	4	no	—
1550	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1551	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1552	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1553	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1554	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1555	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1556	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1557	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1558	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1559	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1560	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1561	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1562	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1563	Q₁₆	—	2	2	no	—
1564	Q₁₆	—	2	2	no	—
1565	Q₁₆	—	4	1	no	—
1566	Q₁₆	—	4	1	no	—
1567	Q₁₆	—	4	1	no	—
1568	Q₁₆	—	4	1	no	—
1569	SD₁₆	—	2	2	no	—
1570	SD₁₆	—	2	2	no	—
1571	SD₁₆	—	2	2	no	—
1572	SD₁₆	—	2	2	no	—
1573	SD₁₆	—	4	1	no	—
1574	SD₁₆	—	4	1	no	—
1575	SD₁₆	—	4	1	no	—
1576	SD₁₆	—	4	1	no	—
1577	SD₁₆	—	4	1	no	—
1578	SD₁₆	—	4	1	no	—
1579	SD₁₆	—	4	1	no	—
1580	SD₁₆	—	4	1	no	—
1581	D₈	—	2	2	no	—
1582	D₈	—	2	2	no	—
1583	D₈	—	4	1	no	—
1584	D₈	—	4	1	no	—
1585	D₈	—	4	1	no	—
1586	D₈	—	4	1	no	—
1587	M₁₆	—	4	1	no	—
1588	M₁₆	—	4	1	no	—
1589	M₁₆	—	4	1	no	—
1590	M₁₆	—	4	1	no	—
1591	C₂×C₈	—	4	1	no	—
1592	C₂×C₈	—	4	1	no	—
1593	C₂×C₈	—	4	1	no	—
1594	C₂×C₈	—	4	1	no	—
1595	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1596	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1597	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1598	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1599	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1600	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1601	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1602	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1603	C₄⋊C₄	—	2	1	no	—
1604	C₄⋊C₄	—	2	1	no	—
1605	C₄⋊C₄	—	2	1	no	—
1606	C₄⋊C₄	—	2	1	no	—
1607	C₄⋊C₄	—	2	1	no	—
1608	C₄⋊C₄	—	2	1	no	—
1609	C₄⋊C₄	—	2	1	no	—
1610	C₄⋊C₄	—	2	1	no	—
1611	C₄⋊C₄	—	2	1	no	—
1612	C₄⋊C₄	—	2	1	no	—
1613	C₄⋊C₄	—	2	1	no	—
1614	C₄⋊C₄	—	2	1	no	—
1615	C₄⋊C₄	—	2	1	no	—
1616	C₄⋊C₄	—	2	1	no	—
1617	C₄⋊C₄	—	2	1	no	—
1618	C₄⋊C₄	—	2	1	no	—
1619	C₄⋊C₄	—	2	1	no	—
1620	C₄⋊C₄	—	2	1	no	—
1621	C₄⋊C₄	—	2	1	no	—
1622	C₄⋊C₄	—	2	1	no	—
1623	C₄⋊C₄	—	2	1	no	—
1624	C₄⋊C₄	—	2	1	no	—
1625	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1626	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1627	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1628	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1629	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1630	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1631	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1632	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1633	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1634	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1635	C₂²⋊C₄	—	2	1	no	—
1636	C₂²⋊C₄	—	2	1	no	—
1637	C₂²⋊C₄	—	2	1	no	—
1638	C₂²⋊C₄	—	2	1	no	—
1639	C₂²⋊C₄	—	2	1	no	—
1640	C₂²⋊C₄	—	2	1	no	—
1641	C₂²⋊C₄	—	2	1	no	—
1642	C₂²⋊C₄	—	2	1	no	—
1643	C₂²⋊C₄	—	2	1	no	—
1644	C₂²⋊C₄	—	2	1	no	—
1645	C₂²⋊C₄	—	2	1	no	—
1646	C₂²⋊C₄	—	2	1	no	—
1647	C₂²⋊C₄	—	2	1	no	—
1648	C₂²⋊C₄	—	2	1	no	—
1649	C₂²⋊C₄	—	2	1	no	—
1650	C₂²⋊C₄	—	2	1	no	—
1651	C₂²⋊C₄	—	2	1	no	—
1652	C₂²⋊C₄	—	2	1	no	—
1653	C₂²⋊C₄	—	2	1	no	—
1654	C₂²⋊C₄	—	2	1	no	—
1655	C₂²⋊C₄	—	2	1	no	—
1656	C₂²⋊C₄	—	2	1	no	—
1657	C₂²⋊C₄	—	2	1	no	—
1658	C₂²⋊C₄	—	2	1	no	—
1659	C₂²⋊C₄	—	2	1	no	—
1660	C₂²⋊C₄	—	2	1	no	—
1661	C₂²⋊C₄	—	2	1	no	—
1662	C₂²⋊C₄	—	2	1	no	—
1663	C₂²⋊C₄	—	2	1	no	—
1664	C₂²⋊C₄	—	2	1	no	—
1665	C₂²⋊C₄	—	2	1	no	—
1666	C₂²⋊C₄	—	2	1	no	—
1667	C₂²⋊C₄	—	2	1	no	—
1668	C₂²⋊C₄	—	2	1	no	—
1669	C₂²⋊C₄	—	2	1	no	—
1670	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1671	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1672	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1673	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1674	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1675	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1676	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1677	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1678	C₄²	—	2	1	no	—
1679	C₄²	—	2	1	no	—
1680	C₄²	—	2	1	no	—
1681	C₄²	—	2	1	no	—
1682	C₄²	—	2	1	no	—
1683	C₄²	—	2	1	no	—
1684	C₄²	—	2	1	no	—
1685	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1686	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1687	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1688	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1689	C₂³	—	2	1	no	—
1690	C₂³	—	2	2	no	—
1691	C₂³	—	2	1	no	—
1692	C₂³	—	2	1	no	—
1693	C₂³	—	2	1	no	—
1694	C₂³	—	2	1	no	—
1695	C₂³	—	4	1	no	—
1696	C₂³	—	4	1	no	—
1697	C₂³	—	4	1	no	—
1698	C₂³	—	4	1	no	—
1699	C₂³	—	4	1	no	—
1700	C₂³	—	4	2	no	—
1701	C₂³	—	4	2	no	—
1702	C₂³	—	4	2	no	—
1703	C₂³	—	4	2	no	—
1704	C₂³	—	4	2	no	—
1705	C₂³	—	8	1	no	—
1706	C₂³	—	8	1	no	—
1707	C₂³	—	8	1	no	—
1708	C₂³	—	8	1	no	—
1709	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1710	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1711	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1712	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1713	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1714	Q₈	—	2	1	no	—
1715	Q₈	—	2	1	no	—
1716	Q₈	—	2	1	no	—
1717	Q₈	—	2	1	no	—
1718	Q₈	—	2	1	no	—
1719	Q₈	—	2	1	no	—
1720	Q₈	—	2	1	no	—
1721	Q₈	—	2	1	no	—
1722	Q₈	—	2	1	no	—
1723	Q₈	—	4	2	no	—
1724	Q₈	—	4	2	no	—
1725	Q₈	—	8	1	no	—
1726	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1727	D₄	—	2	4	no	—
1728	D₄	—	2	2	no	—
1729	D₄	—	2	2	no	—
1730	D₄	—	2	1	no	—
1731	D₄	—	2	1	no	—
1732	D₄	—	2	1	no	—
1733	D₄	—	2	1	no	—
1734	D₄	—	2	1	no	—
1735	D₄	—	2	1	no	—
1736	D₄	—	2	1	no	—
1737	D₄	—	2	1	no	—
1738	D₄	—	2	1	no	—
1739	D₄	—	4	1	no	—
1740	D₄	—	4	1	no	—
1741	D₄	—	4	2	no	—
1742	D₄	—	4	2	no	—
1743	D₄	—	4	2	no	—
1744	D₄	—	4	2	no	—
1745	D₄	—	4	2	no	—
1746	D₄	—	4	2	no	—
1747	D₄	—	4	2	no	—
1748	D₄	—	4	2	no	—
1749	D₄	—	4	2	no	—
1750	D₄	—	4	2	no	—
1751	D₄	—	4	2	no	—
1752	D₄	—	4	2	no	—
1753	D₄	—	4	2	no	—
1754	D₄	—	4	2	no	—
1755	D₄	—	4	2	no	—
1756	D₄	—	8	1	no	—
1757	D₄	—	8	1	no	—
1758	D₄	—	8	1	no	—
1759	D₄	—	8	1	no	—
1760	D₄	—	8	1	no	—
1761	D₄	—	8	1	no	—
1762	D₄	—	8	1	no	—
1763	D₄	—	8	1	no	—
1764	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1765	C₂×C₄	—	2	4	no	—
1766	C₂×C₄	—	2	1	no	—
1767	C₂×C₄	—	2	1	no	—
1768	C₂×C₄	—	2	1	no	—
1769	C₂×C₄	—	2	1	no	—
1770	C₂×C₄	—	2	1	no	—
1771	C₂×C₄	—	2	1	no	—
1772	C₂×C₄	—	2	1	no	—
1773	C₂×C₄	—	2	1	no	—
1774	C₂×C₄	—	2	1	no	—
1775	C₂×C₄	—	2	1	no	—
1776	C₂×C₄	—	2	1	no	—
1777	C₂×C₄	—	2	1	no	—
1778	C₂×C₄	—	2	1	no	—
1779	C₂×C₄	—	2	1	no	—
1780	C₂×C₄	—	2	1	no	—
1781	C₂×C₄	—	2	1	no	—
1782	C₂×C₄	—	2	1	no	—
1783	C₂×C₄	—	2	1	no	—
1784	C₂×C₄	—	2	1	no	—
1785	C₂×C₄	—	2	1	no	—
1786	C₂×C₄	—	2	1	no	—
1787	C₂×C₄	—	4	1	no	—
1788	C₂×C₄	—	4	1	no	—
1789	C₂×C₄	—	4	1	no	—
1790	C₂×C₄	—	4	1	no	—
1791	C₂×C₄	—	4	1	no	—
1792	C₂×C₄	—	4	1	no	—
1793	C₂×C₄	—	4	1	no	—
1794	C₂×C₄	—	4	1	no	—
1795	C₂×C₄	—	4	2	no	—
1796	C₂×C₄	—	4	2	no	—
1797	C₂×C₄	—	4	2	no	—
1798	C₂×C₄	—	4	2	no	—
1799	C₂×C₄	—	4	2	no	—
1800	C₂×C₄	—	4	2	no	—
1801	C₂×C₄	—	4	2	no	—
1802	C₂×C₄	—	4	2	no	—
1803	C₂×C₄	—	4	2	no	—
1804	C₂×C₄	—	4	2	no	—
1805	C₂×C₄	—	8	1	no	—
1806	C₂×C₄	—	8	1	no	—
1807	C₂×C₄	—	8	1	no	—
1808	C₂×C₄	—	8	1	no	—
1809	C₂×C₄	—	8	1	no	—
1810	C₂×C₄	—	8	1	no	—
1811	C₂×C₄	—	8	1	no	—
1812	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1813	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1814	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1815	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1816	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1817	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1818	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1819	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1820	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1821	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1822	C₈	—	2	1	no	—
1823	C₈	—	2	1	no	—
1824	C₈	—	2	1	no	—
1825	C₈	—	2	1	no	—
1826	C₈	—	2	1	no	—
1827	C₈	—	2	1	no	—
1828	C₈	—	2	1	no	—
1829	C₈	—	2	1	no	—
1830	C₂²	—	2	1	no	—
1831	C₂²	—	2	1	no	—
1832	C₂²	—	2	1	no	—
1833	C₂²	—	2	1	no	—
1834	C₂²	—	2	2	no	—
1835	C₂²	—	2	1	no	—
1836	C₂²	—	2	1	no	—
1837	C₂²	—	2	1	no	—
1838	C₂²	—	2	1	no	—
1839	C₂²	—	2	1	no	—
1840	C₂²	—	2	1	no	—
1841	C₂²	—	2	1	no	—
1842	C₂²	—	2	1	no	—
1843	C₂²	—	2	1	no	—
1844	C₂²	—	2	1	no	—
1845	C₂²	—	4	1	no	—
1846	C₂²	—	4	1	no	—
1847	C₂²	—	4	1	no	—
1848	C₂²	—	4	1	no	—
1849	C₂²	—	4	1	no	—
1850	C₂²	—	4	1	no	—
1851	C₂²	—	4	1	no	—
1852	C₂²	—	4	1	no	—
1853	C₂²	—	4	1	no	—
1854	C₂²	—	4	1	no	—
1855	C₂²	—	4	1	no	—
1856	C₂²	—	4	1	no	—
1857	C₂²	—	4	1	no	—
1858	C₂²	—	4	1	no	—
1859	C₂²	—	8	2	no	—
1860	C₂²	—	8	4	no	—
1861	C₂²	—	8	2	no	—
1862	C₂²	—	8	4	no	—
1863	C₂²	—	16	2	no	—
1864	C₂²	C₅₃×#575	1	2	yes	—
1865	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1866	C₄	—	2	1	no	—
1867	C₄	—	2	2	no	—
1868	C₄	—	2	1	no	—
1869	C₄	—	2	1	no	—
1870	C₄	—	2	1	no	—
1871	C₄	—	2	1	no	—
1872	C₄	—	2	1	no	—
1873	C₄	—	2	1	no	—
1874	C₄	—	2	1	no	—
1875	C₄	—	2	1	no	—
1876	C₄	—	4	1	no	—
1877	C₄	—	4	1	no	—
1878	C₄	—	4	1	no	—
1879	C₄	—	4	1	no	—
1880	C₄	—	4	1	no	—
1881	C₄	—	4	1	no	—
1882	C₄	—	4	1	no	—
1883	C₄	—	4	1	no	—
1884	C₄	—	4	1	no	—
1885	C₄	—	4	1	no	—
1886	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1887	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1888	C₂	—	2	2	no	—
1889	C₂	—	4	1	no	—
1890	C₂	—	4	1	no	—
1891	C₂	—	4	1	no	—
1892	C₂	—	4	1	no	—
1893	C₂	—	4	2	no	—
1894	C₂	—	8	1	no	—
1895	C₂	—	8	1	no	—
1896	C₂	—	8	1	no	—
1897	C₂	—	8	1	no	—
1898	C₂	C₅₃×#3484	1	1	yes	characteristic
1899	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1900	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₂×C₄×D₄×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3505	C₂	semidirect
2. D₄×#41×C₅₃	C₂	semidirect
3. C₅₃×#3327	C₂	semidirect
4. C₅₃×#3323	C₂	semidirect
5. C₅₃×#3320	C₂	semidirect
6. C₅₃×#3318	C₂	semidirect
7. C₅₃×#3317	C₂	semidirect
8. C₅₃×#3315	C₂	semidirect
9. C₅₃×#3301	C₂	semidirect
10. C₅₃×#3297	C₂	semidirect
11. C₅₃×#3285	C₂	semidirect
12. C₅₃×#3282	C₂	semidirect
13. C₅₃×#3275	C₂	semidirect
14. C₅₃×#3273	C₂	semidirect
15. C₅₃×#3270	C₂	semidirect
16. C₅₃×#3268	C₂	semidirect
17. C₅₃×#3267	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3219	C₂	semidirect
20. C₅₃×#3212	C₂	semidirect
21. C₅₃×#3197	C₂	semidirect
22. C₅₃×#3196	C₂	semidirect
23. C₅₃×#3191	C₂	semidirect
24. C₅₃×#3188	C₂	semidirect
25. C₅₃×#3111	C₂	semidirect
26. C₅₃×#3102	C₂	semidirect
27. C₅₃×#3006	C₂	semidirect
28. C₅₃×#3005	C₂	semidirect
29. C₅₃×#3002	C₂	semidirect
30. C₂×C₅₃×#452	C₂	semidirect
31. C₅₃×#2974	C₂	semidirect
33. C₂²×#41×C₅₃	C₂²	semidirect
34. C₂×#137×C₅₃	C₂²	semidirect
35. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
36. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
38. C₂×#135×C₅₃	C₂²	semidirect
39. C₂×#135×C₅₃	C₂²	semidirect
40. C₂²×Q₁₆×C₅₃	C₂²	semidirect
41. C₂²×SD₁₆×C₅₃	C₂²	semidirect
45. C₅₃×#553	C₂²	semidirect
46. C₅₃×#552	C₂²	semidirect
47. C₅₃×#552	C₂²	semidirect
51. D₄×Q₈×C₅₃	C₂²	semidirect
54. C₅₃×#548	C₂²	semidirect
55. C₅₃×#548	C₂²	semidirect
61. C₅₃×#546	C₂²	semidirect
62. C₅₃×#546	C₂²	semidirect
63. C₅₃×#546	C₂²	semidirect
65. D₄²×C₅₃	C₂²	semidirect
70. C₅₃×#532	C₂²	semidirect
71. C₅₃×#529	C₂²	semidirect
72. C₅₃×#529	C₂²	semidirect
76. C₅₃×#525	C₂²	semidirect
77. C₅₃×#525	C₂²	semidirect
78. C₅₃×#525	C₂²	semidirect
79. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
80. C₂×#121×C₅₃	C₂²	semidirect
82. C₄×#41×C₅₃	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
86. C₅₃×#496	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
88. C₅₃×#495	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
90. C₅₃×#490	C₂²	semidirect
91. C₅₃×#488	C₂²	semidirect
92. C₅₃×#488	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#484	C₂²	semidirect
98. C₅₃×#484	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#482	C₂²	semidirect
102. C₅₃×#482	C₂²	semidirect
103. C₅₃×#481	C₂²	semidirect
104. C₅₃×#481	C₂²	semidirect
105. C₅₃×#479	C₂²	semidirect
106. C₅₃×#479	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#470	C₂²	semidirect
110. C₅₃×#470	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
112. C₅₃×#469	C₂²	semidirect
113. C₅₃×#468	C₂²	semidirect
114. C₅₃×#468	C₂²	semidirect
115. C₅₃×#468	C₂²	semidirect
116. C₅₃×#468	C₂²	semidirect
117. C₅₃×#467	C₂²	semidirect
118. C₅₃×#466	C₂²	semidirect
119. C₅₃×#466	C₂²	semidirect
120. C₅₃×#466	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
123. C₅₃×#465	C₂²	semidirect
124. C₅₃×#465	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#462	C₂²	semidirect
134. C₅₃×#461	C₂²	semidirect
135. C₅₃×#460	C₂²	semidirect
136. C₅₃×#459	C₂²	semidirect
137. C₅₃×#452	C₂²	semidirect
138. C₅₃×#452	C₂²	semidirect
139. C₅₃×#452	C₂²	semidirect
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
142. C₅₃×#452	C₂²	semidirect
143. C₅₃×#452	C₂²	semidirect
144. C₅₃×#452	C₂²	semidirect
145. C₅₃×#452	C₂²	semidirect
146. C₅₃×#452	C₂²	semidirect
147. C₅₃×#452	C₂²	semidirect
148. C₅₃×#452	C₂²	semidirect
149. C₅₃×#452	C₂²	semidirect
150. C₅₃×#452	C₂²	semidirect
151. C₅₃×#451	C₂²	semidirect
152. C₅₃×#451	C₂²	semidirect
153. C₅₃×#450	C₂²	semidirect
154. C₅₃×#450	C₂²	semidirect
157. C₅₃×#449	C₂²	semidirect
158. C₅₃×#449	C₂²	semidirect
159. C₅₃×#449	C₂²	semidirect
160. C₅₃×#449	C₂²	semidirect
161. C₅₃×#449	C₂²	semidirect
162. C₅₃×#449	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
165. C₅₃×#448	C₂²	semidirect
166. C₅₃×#448	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
168. C₅₃×#448	C₂²	semidirect
169. C₅₃×#447	C₂²	semidirect
170. C₅₃×#447	C₂²	semidirect
171. C₅₃×#447	C₂²	semidirect
172. C₅₃×#447	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#440	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₄×Q₁₆×C₅₃	C₂²	semidirect
178. C₄×SD₁₆×C₅₃	C₂²	semidirect
179. C₄×SD₁₆×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
181. C₅₃×#436	C₂²	semidirect
182. C₅₃×#436	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₅₃×#435	C₂²	semidirect
187. C₈×D₄×C₅₃	C₂²	semidirect
188. C₈×D₄×C₅₃	C₂²	semidirect
189. C₅₃×#432	C₂²	semidirect
190. C₅₃×#431	C₂²	semidirect
191. C₅₃×#419	C₂²	semidirect
192. C₅₃×#418	C₂²	semidirect
193. C₅₃×#417	C₂²	semidirect
194. C₅₃×#417	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
196. C₅₃×#416	C₂²	semidirect
197. C₂×#103×C₅₃	C₂²	semidirect
198. C₂×#102×C₅₃	C₂²	semidirect
199. C₅₃×#407	C₂²	semidirect
200. C₅₃×#407	C₂²	semidirect
201. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
202. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
879. #61606	C₅₃	direct (N × H)
938. #3505	C₂×C₅₃	semidirect
939. D₄×#41	C₂×C₅₃	semidirect
940. #3327	C₂×C₅₃	semidirect
941. #3323	C₂×C₅₃	semidirect
942. #3320	C₂×C₅₃	semidirect
943. #3318	C₂×C₅₃	semidirect
944. #3317	C₂×C₅₃	semidirect
945. #3315	C₂×C₅₃	semidirect
946. #3301	C₂×C₅₃	semidirect
947. #3297	C₂×C₅₃	semidirect
948. #3285	C₂×C₅₃	semidirect
949. #3282	C₂×C₅₃	semidirect
950. #3275	C₂×C₅₃	semidirect
951. #3273	C₂×C₅₃	semidirect
952. #3270	C₂×C₅₃	semidirect
953. #3268	C₂×C₅₃	semidirect
954. #3267	C₂×C₅₃	semidirect
955. #3265	C₂×C₅₃	semidirect
956. #3219	C₂×C₅₃	semidirect
957. #3212	C₂×C₅₃	semidirect
958. #3197	C₂×C₅₃	semidirect
959. #3196	C₂×C₅₃	semidirect
960. #3191	C₂×C₅₃	semidirect
961. #3188	C₂×C₅₃	semidirect
962. #3111	C₂×C₅₃	semidirect
963. #3102	C₂×C₅₃	semidirect
964. #3006	C₂×C₅₃	semidirect
965. #3005	C₂×C₅₃	semidirect
966. #3002	C₂×C₅₃	semidirect
967. C₂×#452	C₂×C₅₃	semidirect
968. #2974	C₂×C₅₃	semidirect
983. C₂²×#41	C₂²×C₅₃	semidirect
984. C₂×#137	C₂²×C₅₃	semidirect
985. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
986. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
987. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
988. C₂×#135	C₂²×C₅₃	semidirect
989. C₂×#135	C₂²×C₅₃	semidirect
990. C₂²×Q₁₆	C₂²×C₅₃	semidirect
991. C₂²×SD₁₆	C₂²×C₅₃	semidirect
995. #553	C₂²×C₅₃	semidirect
996. #552	C₂²×C₅₃	semidirect
997. #552	C₂²×C₅₃	semidirect
1001. D₄×Q₈	C₂²×C₅₃	semidirect
1004. #548	C₂²×C₅₃	semidirect
1005. #548	C₂²×C₅₃	semidirect
1011. #546	C₂²×C₅₃	semidirect
1012. #546	C₂²×C₅₃	semidirect
1013. #546	C₂²×C₅₃	semidirect
1015. D₄²	C₂²×C₅₃	semidirect
1020. #532	C₂²×C₅₃	semidirect
1021. #529	C₂²×C₅₃	semidirect
1022. #529	C₂²×C₅₃	semidirect
1026. #525	C₂²×C₅₃	semidirect
1027. #525	C₂²×C₅₃	semidirect
1028. #525	C₂²×C₅₃	semidirect
1029. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1030. C₂×#121	C₂²×C₅₃	semidirect
1032. C₄×#41	C₂²×C₅₃	semidirect
1035. #497	C₂²×C₅₃	semidirect
1036. #496	C₂²×C₅₃	semidirect
1037. #495	C₂²×C₅₃	semidirect
1038. #495	C₂²×C₅₃	semidirect
1039. #491	C₂²×C₅₃	semidirect
1040. #490	C₂²×C₅₃	semidirect
1041. #488	C₂²×C₅₃	semidirect
1042. #488	C₂²×C₅₃	semidirect
1043. #485	C₂²×C₅₃	semidirect
1044. #485	C₂²×C₅₃	semidirect
1045. #485	C₂²×C₅₃	semidirect
1046. #485	C₂²×C₅₃	semidirect
1047. #484	C₂²×C₅₃	semidirect
1048. #484	C₂²×C₅₃	semidirect
1049. #482	C₂²×C₅₃	semidirect
1050. #482	C₂²×C₅₃	semidirect
1051. #482	C₂²×C₅₃	semidirect
1052. #482	C₂²×C₅₃	semidirect
1053. #481	C₂²×C₅₃	semidirect
1054. #481	C₂²×C₅₃	semidirect
1055. #479	C₂²×C₅₃	semidirect
1056. #479	C₂²×C₅₃	semidirect
1057. #478	C₂²×C₅₃	semidirect
1058. #478	C₂²×C₅₃	semidirect
1059. #470	C₂²×C₅₃	semidirect
1060. #470	C₂²×C₅₃	semidirect
1061. #470	C₂²×C₅₃	semidirect
1062. #469	C₂²×C₅₃	semidirect
1063. #468	C₂²×C₅₃	semidirect
1064. #468	C₂²×C₅₃	semidirect
1065. #468	C₂²×C₅₃	semidirect
1066. #468	C₂²×C₅₃	semidirect
1067. #467	C₂²×C₅₃	semidirect
1068. #466	C₂²×C₅₃	semidirect
1069. #466	C₂²×C₅₃	semidirect
1070. #466	C₂²×C₅₃	semidirect
1071. #465	C₂²×C₅₃	semidirect
1072. #465	C₂²×C₅₃	semidirect
1073. #465	C₂²×C₅₃	semidirect
1074. #465	C₂²×C₅₃	semidirect
1075. #464	C₂²×C₅₃	semidirect
1076. #464	C₂²×C₅₃	semidirect
1077. #464	C₂²×C₅₃	semidirect
1078. #464	C₂²×C₅₃	semidirect
1079. #463	C₂²×C₅₃	semidirect
1080. #463	C₂²×C₅₃	semidirect
1081. #463	C₂²×C₅₃	semidirect
1082. #463	C₂²×C₅₃	semidirect
1083. #462	C₂²×C₅₃	semidirect
1084. #461	C₂²×C₅₃	semidirect
1085. #460	C₂²×C₅₃	semidirect
1086. #459	C₂²×C₅₃	semidirect
1087. #452	C₂²×C₅₃	semidirect
1088. #452	C₂²×C₅₃	semidirect
1089. #452	C₂²×C₅₃	semidirect
1090. #452	C₂²×C₅₃	semidirect
1091. #452	C₂²×C₅₃	semidirect
1092. #452	C₂²×C₅₃	semidirect
1093. #452	C₂²×C₅₃	semidirect
1094. #452	C₂²×C₅₃	semidirect
1095. #452	C₂²×C₅₃	semidirect
1096. #452	C₂²×C₅₃	semidirect
1097. #452	C₂²×C₅₃	semidirect
1098. #452	C₂²×C₅₃	semidirect
1099. #452	C₂²×C₅₃	semidirect
1100. #452	C₂²×C₅₃	semidirect
1101. #451	C₂²×C₅₃	semidirect
1102. #451	C₂²×C₅₃	semidirect
1103. #450	C₂²×C₅₃	semidirect
1104. #450	C₂²×C₅₃	semidirect
1107. #449	C₂²×C₅₃	semidirect
1108. #449	C₂²×C₅₃	semidirect
1109. #449	C₂²×C₅₃	semidirect
1110. #449	C₂²×C₅₃	semidirect
1111. #449	C₂²×C₅₃	semidirect
1112. #449	C₂²×C₅₃	semidirect
1113. #449	C₂²×C₅₃	semidirect
1114. #449	C₂²×C₅₃	semidirect
1115. #448	C₂²×C₅₃	semidirect
1116. #448	C₂²×C₅₃	semidirect
1117. #448	C₂²×C₅₃	semidirect
1118. #448	C₂²×C₅₃	semidirect
1119. #447	C₂²×C₅₃	semidirect
1120. #447	C₂²×C₅₃	semidirect
1121. #447	C₂²×C₅₃	semidirect
1122. #447	C₂²×C₅₃	semidirect
1123. #442	C₂²×C₅₃	semidirect
1124. #441	C₂²×C₅₃	semidirect
1125. #440	C₂²×C₅₃	semidirect
1126. #440	C₂²×C₅₃	semidirect
1127. C₄×Q₁₆	C₂²×C₅₃	semidirect
1128. C₄×SD₁₆	C₂²×C₅₃	semidirect
1129. C₄×SD₁₆	C₂²×C₅₃	semidirect
1130. C₄×D₈	C₂²×C₅₃	semidirect
1131. #436	C₂²×C₅₃	semidirect
1132. #436	C₂²×C₅₃	semidirect
1133. #435	C₂²×C₅₃	semidirect
1134. #435	C₂²×C₅₃	semidirect
1135. #435	C₂²×C₅₃	semidirect
1136. #435	C₂²×C₅₃	semidirect
1137. C₈×D₄	C₂²×C₅₃	semidirect
1138. C₈×D₄	C₂²×C₅₃	semidirect
1139. #432	C₂²×C₅₃	semidirect
1140. #431	C₂²×C₅₃	semidirect
1141. #419	C₂²×C₅₃	semidirect
1142. #418	C₂²×C₅₃	semidirect
1143. #417	C₂²×C₅₃	semidirect
1144. #417	C₂²×C₅₃	semidirect
1145. #416	C₂²×C₅₃	semidirect
1146. #416	C₂²×C₅₃	semidirect
1147. C₂×#103	C₂²×C₅₃	semidirect
1148. C₂×#102	C₂²×C₅₃	semidirect
1149. #407	C₂²×C₅₃	semidirect
1150. #407	C₂²×C₅₃	semidirect
1151. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1152. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1153. C₅₃	#61606	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3505	2
D₄×#41×C₅₃	2
C₅₃×#3327	2
C₅₃×#3323	2
C₅₃×#3320	2
C₅₃×#3318	2
C₅₃×#3317	2
C₅₃×#3315	2
C₅₃×#3301	2
C₅₃×#3297	2
C₅₃×#3285	2
C₅₃×#3282	2
C₅₃×#3275	2
C₅₃×#3273	2
C₅₃×#3270	2
C₅₃×#3268	2
C₅₃×#3267	2
C₅₃×#3265	2
C₅₃×#3219	2
C₅₃×#3212	2
C₅₃×#3197	2
C₅₃×#3196	2
C₅₃×#3191	2
C₅₃×#3188	2
C₅₃×#3111	2
C₅₃×#3102	2
C₅₃×#3006	2
C₅₃×#3005	2
C₅₃×#3002	2
C₂×C₅₃×#452	2
C₅₃×#2974	2
#61606	53

Subgroups — C53×#61606 #27269118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61606 #27269118