Subgroups — C₅₃×#62171 #27269683

Order 13568.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3348	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3347	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3343	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3339	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3307	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3260	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3244	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#562	—	2	1	no	—
33	C₅₃×#562	—	2	1	no	—
34	C₅₃×#556	C₂²	1	1	yes	characteristic
35	C₅₃×#556	C₂²	1	1	yes	characteristic
36	C₅₃×#555	C₂²	1	1	yes	characteristic
37	C₅₃×#555	C₂²	1	1	yes	characteristic
38	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#554	C₂²	1	1	yes	characteristic
40	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#553	—	2	1	no	—
42	C₅₃×#553	C₂²	1	1	yes	characteristic
43	C₅₃×#553	C₂²	1	1	yes	characteristic
44	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#552	—	2	1	no	—
46	C₅₃×#552	—	2	1	no	—
47	C₅₃×#552	C₂²	1	1	yes	characteristic
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#551	—	2	1	no	—
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#548	—	2	1	no	—
52	C₅₃×#547	C₂²	1	1	yes	characteristic
53	C₅₃×#547	C₂²	1	1	yes	characteristic
54	C₅₃×#546	C₂²	1	1	yes	characteristic
55	C₅₃×#546	C₂²	1	1	yes	characteristic
56	C₅₃×#544	C₂²	1	1	yes	characteristic
57	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#542	—	2	1	no	—
59	C₅₃×#542	—	2	1	no	—
60	C₅₃×#542	C₂²	1	1	yes	characteristic
61	C₅₃×#541	C₂²	1	1	yes	characteristic
62	C₅₃×#540	C₂²	1	1	yes	characteristic
63	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#539	—	2	1	no	—
65	C₅₃×#538	—	2	1	no	—
66	C₅₃×#537	—	2	1	no	—
67	C₅₃×#536	—	2	1	no	—
68	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#529	—	2	1	no	—
71	C₅₃×#529	C₂²	1	1	yes	characteristic
72	C₅₃×#529	C₂²	1	1	yes	characteristic
73	C₂×#126×C₅₃	—	2	1	no	—
74	C₅₃×#520	C₂²	1	1	yes	characteristic
75	C₅₃×#518	C₂²	1	1	yes	characteristic
76	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#489	C₂²	1	1	yes	characteristic
85	C₅₃×#489	C₂²	1	1	yes	characteristic
86	C₅₃×#489	C₂²	1	1	yes	characteristic
87	C₅₃×#488	C₂²	1	1	yes	characteristic
88	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#485	C₂²	1	1	yes	characteristic
90	C₅₃×#485	C₂²	1	1	yes	characteristic
91	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#484	C₂²	1	1	yes	characteristic
95	C₅₃×#483	C₂²	1	1	yes	characteristic
96	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#482	C₂²	1	1	yes	characteristic
98	C₅₃×#482	C₂²	1	1	yes	characteristic
99	C₅₃×#482	C₂²	1	1	yes	characteristic
100	C₅₃×#482	C₂²	1	1	yes	characteristic
101	C₅₃×#482	C₂²	1	1	yes	characteristic
102	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#481	C₂²	1	1	yes	characteristic
105	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#478	C₂²	1	1	yes	characteristic
113	C₅₃×#478	C₂²	1	1	yes	characteristic
114	C₅₃×#478	C₂²	1	1	yes	characteristic
115	C₅₃×#478	C₂²	1	1	yes	characteristic
116	C₅₃×#478	C₂²	1	1	yes	characteristic
117	C₅₃×#478	C₂²	1	1	yes	characteristic
118	C₅₃×#478	C₂²	1	1	yes	characteristic
119	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#476	C₂²	1	1	yes	characteristic
127	C₅₃×#476	C₂²	1	1	yes	characteristic
128	C₅₃×#476	C₂²	1	1	yes	characteristic
129	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#474	C₂²	1	1	yes	characteristic
133	C₅₃×#474	C₂²	1	1	yes	characteristic
134	C₅₃×#474	C₂²	1	1	yes	characteristic
135	C₅₃×#474	C₂²	1	1	yes	characteristic
136	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#469	C₂²	1	1	yes	characteristic
138	C₅₃×#468	C₂²	1	1	yes	characteristic
139	C₅₃×#468	C₂²	1	1	yes	characteristic
140	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#466	C₂²	1	1	yes	characteristic
142	C₅₃×#466	C₂²	1	1	yes	characteristic
143	C₅₃×#466	C₂²	1	1	yes	characteristic
144	C₅₃×#465	C₂²	1	1	yes	characteristic
145	C₅₃×#465	C₂²	1	1	yes	characteristic
146	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#463	C₂²	1	1	yes	characteristic
150	C₅₃×#463	C₂²	1	1	yes	characteristic
151	C₅₃×#463	C₂²	1	1	yes	characteristic
152	C₅₃×#463	C₂²	1	1	yes	characteristic
153	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#459	C₂²	1	1	yes	characteristic
158	C₅₃×#459	C₂²	1	1	yes	characteristic
159	C₅₃×#449	C₂²	1	1	yes	characteristic
160	C₅₃×#449	C₂²	1	1	yes	characteristic
161	C₅₃×#449	C₂²	1	1	yes	characteristic
162	C₅₃×#449	C₂²	1	1	yes	characteristic
163	C₅₃×#447	C₂²	1	1	yes	characteristic
164	C₅₃×#447	C₂²	1	1	yes	characteristic
165	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#442	C₂²	1	1	yes	characteristic
168	C₅₃×#442	C₂²	1	1	yes	characteristic
169	C₅₃×#442	C₂²	1	1	yes	characteristic
170	C₅₃×#442	C₂²	1	1	yes	characteristic
171	C₅₃×#442	C₂²	1	1	yes	characteristic
172	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
179	C₅₃×#435	C₂²	1	1	yes	characteristic
180	C₅₃×#435	C₂²	1	1	yes	characteristic
181	C₅₃×#435	C₂²	1	1	yes	characteristic
182	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
183	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#433	C₂²	1	1	yes	characteristic
186	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#428	C₂²	1	1	yes	characteristic
189	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#427	C₂²	1	1	yes	characteristic
191	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
193	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#418	C₂²	1	1	yes	characteristic
198	C₅₃×#417	C₂²	1	1	yes	characteristic
199	C₅₃×#416	C₂²	1	1	yes	characteristic
200	C₅₃×#416	C₂²	1	1	yes	characteristic
201	C₅₃×#416	C₂²	1	1	yes	characteristic
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	—	2	1	no	—
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₅₃	—	2	1	no	—
208	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
222	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₄⋊Q₈×C₅₃	—	2	1	no	—
224	C₄⋊Q₈×C₅₃	—	2	1	no	—
225	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
232	#127×C₅₃	C₂³	1	1	yes	characteristic
233	#126×C₅₃	—	2	1	no	—
234	#126×C₅₃	—	2	1	no	—
235	#126×C₅₃	—	2	1	no	—
236	#126×C₅₃	—	2	1	no	—
237	#126×C₅₃	—	2	1	no	—
238	#126×C₅₃	—	2	1	no	—
239	#126×C₅₃	—	2	1	no	—
240	#126×C₅₃	—	2	1	no	—
241	#126×C₅₃	—	2	1	no	—
242	#126×C₅₃	—	2	1	no	—
243	#126×C₅₃	—	2	1	no	—
244	#126×C₅₃	—	2	1	no	—
245	#126×C₅₃	D₄	1	1	yes	characteristic
246	#126×C₅₃	D₄	1	1	yes	characteristic
247	#125×C₅₃	—	2	1	no	—
248	#125×C₅₃	—	2	1	no	—
249	#125×C₅₃	—	2	1	no	—
250	#125×C₅₃	—	2	1	no	—
251	#125×C₅₃	—	2	1	no	—
252	#125×C₅₃	D₄	1	1	yes	characteristic
253	#125×C₅₃	C₂³	1	1	yes	characteristic
254	#125×C₅₃	C₂³	1	1	yes	characteristic
255	#125×C₅₃	C₂³	1	1	yes	characteristic
256	#125×C₅₃	C₂³	1	1	yes	characteristic
257	#125×C₅₃	C₂³	1	1	yes	characteristic
258	#125×C₅₃	C₂³	1	1	yes	characteristic
259	#124×C₅₃	—	2	1	no	—
260	#124×C₅₃	—	2	1	no	—
261	#124×C₅₃	—	2	1	no	—
262	#124×C₅₃	—	2	1	no	—
263	#124×C₅₃	—	2	1	no	—
264	#124×C₅₃	—	2	1	no	—
265	#124×C₅₃	—	2	1	no	—
266	#124×C₅₃	—	2	1	no	—
267	#124×C₅₃	—	2	1	no	—
268	#124×C₅₃	D₄	1	1	yes	characteristic
269	#124×C₅₃	C₂³	1	1	yes	characteristic
270	#124×C₅₃	C₂³	1	1	yes	characteristic
271	#123×C₅₃	—	2	1	no	—
272	#123×C₅₃	—	2	1	no	—
273	#123×C₅₃	—	2	1	no	—
274	#123×C₅₃	—	2	1	no	—
275	#123×C₅₃	—	2	1	no	—
276	#123×C₅₃	—	2	1	no	—
277	#123×C₅₃	—	2	1	no	—
278	#123×C₅₃	—	2	1	no	—
279	#123×C₅₃	—	2	1	no	—
280	#123×C₅₃	—	2	1	no	—
281	#123×C₅₃	—	2	1	no	—
282	#123×C₅₃	—	2	1	no	—
283	#123×C₅₃	—	2	1	no	—
284	#123×C₅₃	—	2	1	no	—
285	#123×C₅₃	—	2	1	no	—
286	#123×C₅₃	—	2	1	no	—
287	#123×C₅₃	D₄	1	1	yes	characteristic
288	#123×C₅₃	D₄	1	1	yes	characteristic
289	C₂²⋊Q₈×C₅₃	—	2	1	no	—
290	C₂²⋊Q₈×C₅₃	—	2	1	no	—
291	C₂²⋊Q₈×C₅₃	—	2	1	no	—
292	C₂²⋊Q₈×C₅₃	—	2	1	no	—
293	C₂²⋊Q₈×C₅₃	—	2	1	no	—
294	C₂²⋊Q₈×C₅₃	—	2	1	no	—
295	C₂²⋊Q₈×C₅₃	—	2	1	no	—
296	C₂²⋊Q₈×C₅₃	—	2	1	no	—
297	C₂²⋊Q₈×C₅₃	—	2	1	no	—
298	C₂²⋊Q₈×C₅₃	—	2	1	no	—
299	C₂²⋊Q₈×C₅₃	—	2	1	no	—
300	C₂²⋊Q₈×C₅₃	—	2	1	no	—
301	C₂²⋊Q₈×C₅₃	—	2	1	no	—
302	C₂²⋊Q₈×C₅₃	—	2	1	no	—
303	C₂²⋊Q₈×C₅₃	—	2	1	no	—
304	C₂²⋊Q₈×C₅₃	—	2	1	no	—
305	C₂²⋊Q₈×C₅₃	—	2	1	no	—
306	C₂²⋊Q₈×C₅₃	—	2	1	no	—
307	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
308	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
312	#121×C₅₃	—	2	1	no	—
313	#121×C₅₃	—	2	1	no	—
314	#121×C₅₃	—	2	1	no	—
315	#121×C₅₃	—	2	1	no	—
316	#121×C₅₃	—	2	1	no	—
317	#121×C₅₃	—	2	1	no	—
318	#121×C₅₃	—	2	1	no	—
319	#121×C₅₃	—	2	1	no	—
320	#121×C₅₃	—	2	1	no	—
321	#121×C₅₃	—	2	1	no	—
322	#121×C₅₃	—	2	1	no	—
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	—	2	1	no	—
325	#121×C₅₃	—	2	1	no	—
326	#121×C₅₃	D₄	1	1	yes	characteristic
327	#121×C₅₃	C₂³	1	1	yes	characteristic
328	#121×C₅₃	C₂³	1	1	yes	characteristic
329	#121×C₅₃	C₂³	1	1	yes	characteristic
330	#121×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	C₂³	1	1	yes	characteristic
332	#121×C₅₃	C₂³	1	1	yes	characteristic
333	#121×C₅₃	C₂³	1	1	yes	characteristic
334	#121×C₅₃	C₂³	1	1	yes	characteristic
335	#120×C₅₃	—	2	1	no	—
336	#120×C₅₃	—	2	1	no	—
337	C₄×Q₈×C₅₃	—	2	1	no	—
338	C₄×Q₈×C₅₃	—	2	1	no	—
339	C₄×Q₈×C₅₃	—	2	1	no	—
340	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
341	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
345	C₄×D₄×C₅₃	—	2	1	no	—
346	C₄×D₄×C₅₃	—	2	1	no	—
347	C₄×D₄×C₅₃	—	2	1	no	—
348	C₄×D₄×C₅₃	—	2	1	no	—
349	C₄×D₄×C₅₃	—	2	1	no	—
350	C₄×D₄×C₅₃	—	2	1	no	—
351	C₄×D₄×C₅₃	—	2	1	no	—
352	C₄×D₄×C₅₃	—	2	1	no	—
353	C₄×D₄×C₅₃	—	2	1	no	—
354	C₄×D₄×C₅₃	—	2	1	no	—
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
357	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
358	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
359	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
360	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
371	#117×C₅₃	—	2	1	no	—
372	#117×C₅₃	—	2	1	no	—
373	#117×C₅₃	—	2	1	no	—
374	#117×C₅₃	—	2	1	no	—
375	#117×C₅₃	—	2	1	no	—
376	#117×C₅₃	—	2	1	no	—
377	#117×C₅₃	—	2	1	no	—
378	#117×C₅₃	—	2	1	no	—
379	#117×C₅₃	C₂³	1	1	yes	characteristic
380	#117×C₅₃	C₂³	1	1	yes	characteristic
381	#117×C₅₃	C₂³	1	1	yes	characteristic
382	#117×C₅₃	C₂³	1	1	yes	characteristic
383	#117×C₅₃	C₂³	1	1	yes	characteristic
384	#117×C₅₃	C₂³	1	1	yes	characteristic
385	#117×C₅₃	C₂³	1	1	yes	characteristic
386	#117×C₅₃	C₂³	1	1	yes	characteristic
387	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
388	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
394	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
395	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
396	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
397	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
398	C₂×C₄²×C₅₃	—	2	1	no	—
399	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
400	#107×C₅₃	C₂³	1	1	yes	characteristic
401	#107×C₅₃	C₂³	1	1	yes	characteristic
402	#107×C₅₃	C₂³	1	1	yes	characteristic
403	#107×C₅₃	C₂³	1	1	yes	characteristic
404	#107×C₅₃	C₂³	1	1	yes	characteristic
405	#107×C₅₃	C₂³	1	1	yes	characteristic
406	#107×C₅₃	C₂³	1	1	yes	characteristic
407	#107×C₅₃	C₂³	1	1	yes	characteristic
408	#107×C₅₃	C₂³	1	1	yes	characteristic
409	#107×C₅₃	C₂³	1	1	yes	characteristic
410	#107×C₅₃	C₂³	1	1	yes	characteristic
411	#107×C₅₃	C₂³	1	1	yes	characteristic
412	#106×C₅₃	C₂³	1	1	yes	characteristic
413	#106×C₅₃	C₂³	1	1	yes	characteristic
414	#106×C₅₃	C₂³	1	1	yes	characteristic
415	#106×C₅₃	C₂³	1	1	yes	characteristic
416	#106×C₅₃	C₂³	1	1	yes	characteristic
417	#106×C₅₃	C₂³	1	1	yes	characteristic
418	#106×C₅₃	C₂³	1	1	yes	characteristic
419	#106×C₅₃	C₂³	1	1	yes	characteristic
420	#106×C₅₃	C₂³	1	1	yes	characteristic
421	#106×C₅₃	C₂³	1	1	yes	characteristic
422	#106×C₅₃	C₂³	1	1	yes	characteristic
423	#106×C₅₃	C₂³	1	1	yes	characteristic
424	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
425	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
426	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
427	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
428	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
429	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	#103×C₅₃	C₂³	1	1	yes	characteristic
435	#103×C₅₃	C₂³	1	1	yes	characteristic
436	#103×C₅₃	C₂³	1	1	yes	characteristic
437	#103×C₅₃	C₂³	1	1	yes	characteristic
438	#103×C₅₃	C₂³	1	1	yes	characteristic
439	#103×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×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	#102×C₅₃	C₂³	1	1	yes	characteristic
447	#102×C₅₃	C₂³	1	1	yes	characteristic
448	#102×C₅₃	C₂³	1	1	yes	characteristic
449	#102×C₅₃	C₂³	1	1	yes	characteristic
450	#102×C₅₃	C₂³	1	1	yes	characteristic
451	#102×C₅₃	C₂³	1	1	yes	characteristic
452	#102×C₅₃	C₂³	1	1	yes	characteristic
453	#102×C₅₃	C₂³	1	1	yes	characteristic
454	#102×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×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	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
467	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
468	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
469	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
470	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
471	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
472	#97×C₅₃	C₂³	1	1	yes	characteristic
473	#97×C₅₃	C₂³	1	1	yes	characteristic
474	#97×C₅₃	C₂³	1	1	yes	characteristic
475	#97×C₅₃	C₂³	1	1	yes	characteristic
476	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₂⁴×C₅₃	—	2	1	no	—
479	#41×C₅₃	—	2	2	no	—
480	#41×C₅₃	—	2	2	no	—
481	#41×C₅₃	—	4	1	no	—
482	#41×C₅₃	—	4	1	no	—
483	#41×C₅₃	—	8	2	no	—
484	#41×C₅₃	—	8	2	no	—
485	C₂×Q₈×C₅₃	—	2	1	no	—
486	C₂×Q₈×C₅₃	—	2	1	no	—
487	C₂×Q₈×C₅₃	—	2	1	no	—
488	C₂×Q₈×C₅₃	—	2	1	no	—
489	C₂×Q₈×C₅₃	—	2	1	no	—
490	C₂×Q₈×C₅₃	—	2	1	no	—
491	C₂×Q₈×C₅₃	—	8	2	no	—
492	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
493	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
494	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
495	C₂×D₄×C₅₃	—	2	2	no	—
496	C₂×D₄×C₅₃	—	2	1	no	—
497	C₂×D₄×C₅₃	—	2	1	no	—
498	C₂×D₄×C₅₃	—	2	1	no	—
499	C₂×D₄×C₅₃	—	2	1	no	—
500	C₂×D₄×C₅₃	—	2	1	no	—
501	C₂×D₄×C₅₃	—	2	1	no	—
502	C₂×D₄×C₅₃	—	2	1	no	—
503	C₂×D₄×C₅₃	—	2	1	no	—
504	C₂×D₄×C₅₃	—	2	1	no	—
505	C₂×D₄×C₅₃	—	2	1	no	—
506	C₂×D₄×C₅₃	—	2	1	no	—
507	C₂×D₄×C₅₃	—	2	1	no	—
508	C₂×D₄×C₅₃	—	2	1	no	—
509	C₂×D₄×C₅₃	—	4	1	no	—
510	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
511	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
512	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
513	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
515	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
516	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
517	C₂²×C₄×C₅₃	—	2	1	no	—
518	C₂²×C₄×C₅₃	—	2	1	no	—
519	C₂²×C₄×C₅₃	—	2	1	no	—
520	C₂²×C₄×C₅₃	—	2	1	no	—
521	C₂²×C₄×C₅₃	—	2	1	no	—
522	C₂²×C₄×C₅₃	—	2	1	no	—
523	C₂²×C₄×C₅₃	—	2	1	no	—
524	C₂²×C₄×C₅₃	—	2	1	no	—
525	C₂²×C₄×C₅₃	—	2	1	no	—
526	C₂²×C₄×C₅₃	—	2	1	no	—
527	C₂²×C₄×C₅₃	—	2	1	no	—
528	C₂²×C₄×C₅₃	—	2	1	no	—
529	C₂²×C₄×C₅₃	—	2	1	no	—
530	C₂²×C₄×C₅₃	—	2	1	no	—
531	C₂²×C₄×C₅₃	—	2	1	no	—
532	C₂²×C₄×C₅₃	—	2	1	no	—
533	C₂²×C₄×C₅₃	—	2	1	no	—
534	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
535	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
536	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
539	SD₁₆×C₅₃	—	4	1	no	—
540	SD₁₆×C₅₃	—	4	1	no	—
541	SD₁₆×C₅₃	—	4	1	no	—
542	SD₁₆×C₅₃	—	4	1	no	—
543	D₈×C₅₃	—	2	2	no	—
544	D₈×C₅₃	—	2	2	no	—
545	D₈×C₅₃	—	4	1	no	—
546	D₈×C₅₃	—	4	1	no	—
547	M₁₆×C₅₃	—	4	1	no	—
548	M₁₆×C₅₃	—	4	1	no	—
549	C₂×C₈×C₅₃	—	4	1	no	—
550	C₂×C₈×C₅₃	—	4	1	no	—
551	C₂×C₈×C₅₃	—	4	1	no	—
552	C₂×C₈×C₅₃	—	4	1	no	—
553	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
554	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
555	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
556	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
558	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
561	C₄⋊C₄×C₅₃	—	2	1	no	—
562	C₄⋊C₄×C₅₃	—	2	1	no	—
563	C₄⋊C₄×C₅₃	—	2	1	no	—
564	C₄⋊C₄×C₅₃	—	2	1	no	—
565	C₄⋊C₄×C₅₃	—	2	1	no	—
566	C₄⋊C₄×C₅₃	—	2	1	no	—
567	C₄⋊C₄×C₅₃	—	2	1	no	—
568	C₄⋊C₄×C₅₃	—	2	1	no	—
569	C₄⋊C₄×C₅₃	—	2	1	no	—
570	C₄⋊C₄×C₅₃	—	2	1	no	—
571	C₄⋊C₄×C₅₃	—	2	1	no	—
572	C₄⋊C₄×C₅₃	—	2	1	no	—
573	C₄⋊C₄×C₅₃	—	2	1	no	—
574	C₄⋊C₄×C₅₃	—	2	1	no	—
575	C₄⋊C₄×C₅₃	—	2	1	no	—
576	C₄⋊C₄×C₅₃	—	2	1	no	—
577	C₄⋊C₄×C₅₃	—	2	1	no	—
578	C₄⋊C₄×C₅₃	—	2	1	no	—
579	C₄⋊C₄×C₅₃	—	2	1	no	—
580	C₄⋊C₄×C₅₃	—	2	1	no	—
581	C₄⋊C₄×C₅₃	—	2	1	no	—
582	C₄⋊C₄×C₅₃	—	2	1	no	—
583	C₄⋊C₄×C₅₃	—	2	1	no	—
584	C₄⋊C₄×C₅₃	—	2	1	no	—
585	C₄⋊C₄×C₅₃	—	2	1	no	—
586	C₄⋊C₄×C₅₃	—	2	1	no	—
587	C₄⋊C₄×C₅₃	—	2	1	no	—
588	C₄⋊C₄×C₅₃	—	2	1	no	—
589	C₄⋊C₄×C₅₃	—	2	1	no	—
590	C₄⋊C₄×C₅₃	—	2	1	no	—
591	C₄⋊C₄×C₅₃	—	2	1	no	—
592	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
612	C₂²⋊C₄×C₅₃	—	2	1	no	—
613	C₂²⋊C₄×C₅₃	—	2	1	no	—
614	C₂²⋊C₄×C₅₃	—	2	1	no	—
615	C₂²⋊C₄×C₅₃	—	2	1	no	—
616	C₂²⋊C₄×C₅₃	—	2	1	no	—
617	C₂²⋊C₄×C₅₃	—	2	1	no	—
618	C₂²⋊C₄×C₅₃	—	2	1	no	—
619	C₂²⋊C₄×C₅₃	—	2	1	no	—
620	C₂²⋊C₄×C₅₃	—	2	1	no	—
621	C₂²⋊C₄×C₅₃	—	2	1	no	—
622	C₂²⋊C₄×C₅₃	—	2	1	no	—
623	C₂²⋊C₄×C₅₃	—	2	1	no	—
624	C₂²⋊C₄×C₅₃	—	2	1	no	—
625	C₂²⋊C₄×C₅₃	—	2	1	no	—
626	C₂²⋊C₄×C₅₃	—	2	1	no	—
627	C₂²⋊C₄×C₅₃	—	2	1	no	—
628	C₂²⋊C₄×C₅₃	—	2	1	no	—
629	C₂²⋊C₄×C₅₃	—	2	1	no	—
630	C₂²⋊C₄×C₅₃	—	2	1	no	—
631	C₂²⋊C₄×C₅₃	—	2	1	no	—
632	C₂²⋊C₄×C₅₃	—	2	1	no	—
633	C₂²⋊C₄×C₅₃	—	2	1	no	—
634	C₂²⋊C₄×C₅₃	—	2	1	no	—
635	C₂²⋊C₄×C₅₃	—	2	1	no	—
636	C₂²⋊C₄×C₅₃	—	2	1	no	—
637	C₂²⋊C₄×C₅₃	—	2	1	no	—
638	C₂²⋊C₄×C₅₃	—	2	1	no	—
639	C₂²⋊C₄×C₅₃	—	2	1	no	—
640	C₂²⋊C₄×C₅₃	—	2	1	no	—
641	C₂²⋊C₄×C₅₃	—	2	1	no	—
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
647	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
648	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
649	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
650	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
656	C₄²×C₅₃	—	2	1	no	—
657	C₄²×C₅₃	—	2	1	no	—
658	C₄²×C₅₃	—	2	1	no	—
659	C₄²×C₅₃	—	2	1	no	—
660	C₄²×C₅₃	—	2	1	no	—
661	C₄²×C₅₃	—	2	1	no	—
662	C₄²×C₅₃	—	2	1	no	—
663	C₄²×C₅₃	—	2	1	no	—
664	C₄²×C₅₃	—	2	1	no	—
665	C₄²×C₅₃	—	2	1	no	—
666	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
667	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
668	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
669	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
670	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
671	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
677	C₂³×C₅₃	—	8	1	no	—
678	C₂³×C₅₃	—	8	1	no	—
679	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
680	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
681	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
682	Q₈×C₅₃	—	2	1	no	—
683	Q₈×C₅₃	—	2	1	no	—
684	Q₈×C₅₃	—	2	1	no	—
685	Q₈×C₅₃	—	2	1	no	—
686	Q₈×C₅₃	—	4	1	no	—
687	Q₈×C₅₃	—	4	2	no	—
688	Q₈×C₅₃	—	8	1	no	—
689	Q₈×C₅₃	—	8	1	no	—
690	Q₈×C₅₃	—	8	1	no	—
691	Q₈×C₅₃	—	8	1	no	—
692	Q₈×C₅₃	—	8	1	no	—
693	D₄×C₅₃	—	2	1	no	—
694	D₄×C₅₃	—	2	1	no	—
695	D₄×C₅₃	—	2	1	no	—
696	D₄×C₅₃	—	2	1	no	—
697	D₄×C₅₃	—	2	1	no	—
698	D₄×C₅₃	—	2	1	no	—
699	D₄×C₅₃	—	2	1	no	—
700	D₄×C₅₃	—	4	1	no	—
701	D₄×C₅₃	—	4	1	no	—
702	D₄×C₅₃	—	4	1	no	—
703	D₄×C₅₃	—	4	2	no	—
704	D₄×C₅₃	—	4	2	no	—
705	D₄×C₅₃	—	4	2	no	—
706	D₄×C₅₃	—	8	1	no	—
707	D₄×C₅₃	—	8	1	no	—
708	D₄×C₅₃	—	8	1	no	—
709	D₄×C₅₃	—	8	1	no	—
710	D₄×C₅₃	—	8	1	no	—
711	D₄×C₅₃	—	8	1	no	—
712	D₄×C₅₃	—	8	1	no	—
713	D₄×C₅₃	—	8	1	no	—
714	D₄×C₅₃	—	8	1	no	—
715	D₄×C₅₃	—	8	1	no	—
716	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
717	C₂×C₄×C₅₃	—	2	1	no	—
718	C₂×C₄×C₅₃	—	2	1	no	—
719	C₂×C₄×C₅₃	—	2	1	no	—
720	C₂×C₄×C₅₃	—	2	1	no	—
721	C₂×C₄×C₅₃	—	2	1	no	—
722	C₂×C₄×C₅₃	—	2	1	no	—
723	C₂×C₄×C₅₃	—	2	1	no	—
724	C₂×C₄×C₅₃	—	2	1	no	—
725	C₂×C₄×C₅₃	—	2	1	no	—
726	C₂×C₄×C₅₃	—	2	1	no	—
727	C₂×C₄×C₅₃	—	2	1	no	—
728	C₂×C₄×C₅₃	—	2	1	no	—
729	C₂×C₄×C₅₃	—	2	1	no	—
730	C₂×C₄×C₅₃	—	2	1	no	—
731	C₂×C₄×C₅₃	—	2	1	no	—
732	C₂×C₄×C₅₃	—	2	1	no	—
733	C₂×C₄×C₅₃	—	2	1	no	—
734	C₂×C₄×C₅₃	—	2	1	no	—
735	C₂×C₄×C₅₃	—	4	1	no	—
736	C₂×C₄×C₅₃	—	4	1	no	—
737	C₂×C₄×C₅₃	—	4	2	no	—
738	C₂×C₄×C₅₃	—	4	2	no	—
739	C₂×C₄×C₅₃	—	4	2	no	—
740	C₂×C₄×C₅₃	—	4	2	no	—
741	C₂×C₄×C₅₃	—	8	1	no	—
742	C₂×C₄×C₅₃	—	8	1	no	—
743	C₂×C₄×C₅₃	—	8	1	no	—
744	C₂×C₄×C₅₃	—	8	1	no	—
745	C₂×C₄×C₅₃	—	8	1	no	—
746	C₂×C₄×C₅₃	—	8	1	no	—
747	C₂×C₄×C₅₃	—	8	1	no	—
748	C₂×C₄×C₅₃	—	8	1	no	—
749	C₂×C₄×C₅₃	—	8	1	no	—
750	C₂×C₄×C₅₃	—	8	1	no	—
751	C₂×C₄×C₅₃	—	8	1	no	—
752	C₂×C₄×C₅₃	—	8	1	no	—
753	C₂×C₄×C₅₃	—	8	1	no	—
754	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
755	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
756	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
757	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
758	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
759	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
760	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
761	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
762	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
763	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
764	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
765	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
766	C₈×C₅₃	—	2	1	no	—
767	C₈×C₅₃	—	2	1	no	—
768	C₈×C₅₃	—	2	1	no	—
769	C₈×C₅₃	—	2	1	no	—
770	C₈×C₅₃	—	2	1	no	—
771	C₈×C₅₃	—	2	1	no	—
772	C₈×C₅₃	—	2	1	no	—
773	C₈×C₅₃	—	2	1	no	—
774	#62171	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
775	C₂²×C₅₃	—	2	1	no	—
776	C₂²×C₅₃	—	2	1	no	—
777	C₂²×C₅₃	—	2	1	no	—
778	C₂²×C₅₃	—	2	1	no	—
779	C₂²×C₅₃	—	2	1	no	—
780	C₂²×C₅₃	—	2	1	no	—
781	C₂²×C₅₃	—	2	1	no	—
782	C₂²×C₅₃	—	2	1	no	—
783	C₂²×C₅₃	—	2	1	no	—
784	C₂²×C₅₃	—	2	2	no	—
785	C₂²×C₅₃	—	4	1	no	—
786	C₂²×C₅₃	—	4	1	no	—
787	C₂²×C₅₃	—	4	1	no	—
788	C₂²×C₅₃	—	4	1	no	—
789	C₂²×C₅₃	—	4	1	no	—
790	C₂²×C₅₃	—	4	1	no	—
791	C₂²×C₅₃	—	4	1	no	—
792	C₂²×C₅₃	—	4	1	no	—
793	C₂²×C₅₃	—	4	1	no	—
794	C₂²×C₅₃	—	4	1	no	—
795	C₂²×C₅₃	—	4	1	no	—
796	C₂²×C₅₃	—	16	2	no	—
797	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
798	C₄×C₅₃	—	2	1	no	—
799	C₄×C₅₃	—	2	1	no	—
800	C₄×C₅₃	—	2	1	no	—
801	C₄×C₅₃	—	2	1	no	—
802	C₄×C₅₃	—	2	1	no	—
803	C₄×C₅₃	—	2	1	no	—
804	C₄×C₅₃	—	2	1	no	—
805	C₄×C₅₃	—	2	1	no	—
806	C₄×C₅₃	—	2	1	no	—
807	C₄×C₅₃	—	2	1	no	—
808	C₄×C₅₃	—	2	1	no	—
809	C₄×C₅₃	—	4	1	no	—
810	C₄×C₅₃	—	4	1	no	—
811	C₄×C₅₃	—	4	1	no	—
812	C₄×C₅₃	—	4	1	no	—
813	C₄×C₅₃	—	4	1	no	—
814	C₄×C₅₃	—	4	1	no	—
815	C₄×C₅₃	—	4	1	no	—
816	C₄×C₅₃	—	4	1	no	—
817	C₄×C₅₃	—	4	1	no	—
818	C₄×C₅₃	—	4	1	no	—
819	C₄×C₅₃	—	4	1	no	—
820	C₄×C₅₃	—	4	1	no	—
821	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
822	C₄×C₅₃	#585	1	1	yes	characteristic
823	#3547	C₂×C₅₃	1	1	yes	characteristic, complemented
824	#3521	C₂×C₅₃	1	1	yes	characteristic, complemented
825	#3389	C₂×C₅₃	1	1	yes	characteristic, complemented
826	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
827	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
828	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
829	#3350	C₂×C₅₃	1	1	yes	characteristic, complemented
830	#3348	C₂×C₅₃	1	1	yes	characteristic, complemented
831	#3347	C₂×C₅₃	1	1	yes	characteristic, complemented
832	#3343	C₂×C₅₃	1	1	yes	characteristic, complemented
833	#3340	C₂×C₅₃	1	1	yes	characteristic, complemented
834	#3339	C₂×C₅₃	1	1	yes	characteristic, complemented
835	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
836	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
837	#3307	C₂×C₅₃	1	1	yes	characteristic, complemented
838	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
839	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
840	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
841	#3260	C₂×C₅₃	1	1	yes	characteristic, complemented
842	#3257	C₂×C₅₃	1	1	yes	characteristic, complemented
843	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
844	#3244	C₂×C₅₃	1	1	yes	characteristic, complemented
845	#3242	C₂×C₅₃	1	1	yes	characteristic, complemented
846	#3240	C₂×C₅₃	1	1	yes	characteristic, complemented
847	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
848	#3119	C₂×C₅₃	1	1	yes	characteristic, complemented
849	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
850	#3083	C₂×C₅₃	1	1	yes	characteristic, complemented
851	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
852	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
853	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
854	C₂×C₅₃	—	4	1	no	—
855	C₂×C₅₃	—	4	1	no	—
856	C₂×C₅₃	—	4	1	no	—
857	C₂×C₅₃	—	4	2	no	—
858	C₂×C₅₃	—	8	1	no	—
859	C₂×C₅₃	—	8	1	no	—
860	C₂×C₅₃	—	8	1	no	—
861	C₂×C₅₃	#3489	1	1	yes	characteristic
862	C₂×C₅₃	#3584	1	1	yes	characteristic
863	C₂×C₅₃	#3585	1	1	yes	characteristic
864	#562	—	2	1	no	—
865	#562	—	2	1	no	—
866	#556	C₂²×C₅₃	1	1	yes	characteristic
867	#556	C₂²×C₅₃	1	1	yes	characteristic
868	#555	C₂²×C₅₃	1	1	yes	characteristic
869	#555	C₂²×C₅₃	1	1	yes	characteristic
870	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
871	#554	C₂²×C₅₃	1	1	yes	characteristic
872	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
873	#553	—	2	1	no	—
874	#553	C₂²×C₅₃	1	1	yes	characteristic
875	#553	C₂²×C₅₃	1	1	yes	characteristic
876	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
877	#552	—	2	1	no	—
878	#552	—	2	1	no	—
879	#552	C₂²×C₅₃	1	1	yes	characteristic
880	#551	—	2	1	no	—
881	#551	—	2	1	no	—
882	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
883	#548	—	2	1	no	—
884	#547	C₂²×C₅₃	1	1	yes	characteristic
885	#547	C₂²×C₅₃	1	1	yes	characteristic
886	#546	C₂²×C₅₃	1	1	yes	characteristic
887	#546	C₂²×C₅₃	1	1	yes	characteristic
888	#544	C₂²×C₅₃	1	1	yes	characteristic
889	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
890	#542	—	2	1	no	—
891	#542	—	2	1	no	—
892	#542	C₂²×C₅₃	1	1	yes	characteristic
893	#541	C₂²×C₅₃	1	1	yes	characteristic
894	#540	C₂²×C₅₃	1	1	yes	characteristic
895	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
896	#539	—	2	1	no	—
897	#538	—	2	1	no	—
898	#537	—	2	1	no	—
899	#536	—	2	1	no	—
900	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#529	—	2	1	no	—
903	#529	C₂²×C₅₃	1	1	yes	characteristic
904	#529	C₂²×C₅₃	1	1	yes	characteristic
905	C₂×#126	—	2	1	no	—
906	#520	C₂²×C₅₃	1	1	yes	characteristic
907	#518	C₂²×C₅₃	1	1	yes	characteristic
908	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
909	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#499	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
915	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
916	#489	C₂²×C₅₃	1	1	yes	characteristic
917	#489	C₂²×C₅₃	1	1	yes	characteristic
918	#489	C₂²×C₅₃	1	1	yes	characteristic
919	#488	C₂²×C₅₃	1	1	yes	characteristic
920	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#485	C₂²×C₅₃	1	1	yes	characteristic
922	#485	C₂²×C₅₃	1	1	yes	characteristic
923	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#484	C₂²×C₅₃	1	1	yes	characteristic
927	#483	C₂²×C₅₃	1	1	yes	characteristic
928	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#482	C₂²×C₅₃	1	1	yes	characteristic
930	#482	C₂²×C₅₃	1	1	yes	characteristic
931	#482	C₂²×C₅₃	1	1	yes	characteristic
932	#482	C₂²×C₅₃	1	1	yes	characteristic
933	#482	C₂²×C₅₃	1	1	yes	characteristic
934	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#481	C₂²×C₅₃	1	1	yes	characteristic
937	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#478	C₂²×C₅₃	1	1	yes	characteristic
945	#478	C₂²×C₅₃	1	1	yes	characteristic
946	#478	C₂²×C₅₃	1	1	yes	characteristic
947	#478	C₂²×C₅₃	1	1	yes	characteristic
948	#478	C₂²×C₅₃	1	1	yes	characteristic
949	#478	C₂²×C₅₃	1	1	yes	characteristic
950	#478	C₂²×C₅₃	1	1	yes	characteristic
951	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#476	C₂²×C₅₃	1	1	yes	characteristic
959	#476	C₂²×C₅₃	1	1	yes	characteristic
960	#476	C₂²×C₅₃	1	1	yes	characteristic
961	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#474	C₂²×C₅₃	1	1	yes	characteristic
965	#474	C₂²×C₅₃	1	1	yes	characteristic
966	#474	C₂²×C₅₃	1	1	yes	characteristic
967	#474	C₂²×C₅₃	1	1	yes	characteristic
968	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#469	C₂²×C₅₃	1	1	yes	characteristic
970	#468	C₂²×C₅₃	1	1	yes	characteristic
971	#468	C₂²×C₅₃	1	1	yes	characteristic
972	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#466	C₂²×C₅₃	1	1	yes	characteristic
974	#466	C₂²×C₅₃	1	1	yes	characteristic
975	#466	C₂²×C₅₃	1	1	yes	characteristic
976	#465	C₂²×C₅₃	1	1	yes	characteristic
977	#465	C₂²×C₅₃	1	1	yes	characteristic
978	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#463	C₂²×C₅₃	1	1	yes	characteristic
982	#463	C₂²×C₅₃	1	1	yes	characteristic
983	#463	C₂²×C₅₃	1	1	yes	characteristic
984	#463	C₂²×C₅₃	1	1	yes	characteristic
985	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#459	C₂²×C₅₃	1	1	yes	characteristic
990	#459	C₂²×C₅₃	1	1	yes	characteristic
991	#449	C₂²×C₅₃	1	1	yes	characteristic
992	#449	C₂²×C₅₃	1	1	yes	characteristic
993	#449	C₂²×C₅₃	1	1	yes	characteristic
994	#449	C₂²×C₅₃	1	1	yes	characteristic
995	#447	C₂²×C₅₃	1	1	yes	characteristic
996	#447	C₂²×C₅₃	1	1	yes	characteristic
997	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#442	C₂²×C₅₃	1	1	yes	characteristic
1000	#442	C₂²×C₅₃	1	1	yes	characteristic
1001	#442	C₂²×C₅₃	1	1	yes	characteristic
1002	#442	C₂²×C₅₃	1	1	yes	characteristic
1003	#442	C₂²×C₅₃	1	1	yes	characteristic
1004	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1009	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1010	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1011	#435	C₂²×C₅₃	1	1	yes	characteristic
1012	#435	C₂²×C₅₃	1	1	yes	characteristic
1013	#435	C₂²×C₅₃	1	1	yes	characteristic
1014	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1016	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#433	C₂²×C₅₃	1	1	yes	characteristic
1018	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#428	C₂²×C₅₃	1	1	yes	characteristic
1021	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#427	C₂²×C₅₃	1	1	yes	characteristic
1023	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#424	C₂²×C₅₃	1	1	yes	characteristic
1027	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#418	C₂²×C₅₃	1	1	yes	characteristic
1030	#417	C₂²×C₅₃	1	1	yes	characteristic
1031	#416	C₂²×C₅₃	1	1	yes	characteristic
1032	#416	C₂²×C₅₃	1	1	yes	characteristic
1033	#416	C₂²×C₅₃	1	1	yes	characteristic
1034	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1035	C₅₃	#62171	1	1	yes	characteristic, direct product factor, Sylow
1036	C₂×#41	—	2	1	no	—
1037	C₂×#41	—	2	1	no	—
1038	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂²×Q₈	—	2	1	no	—
1041	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1048	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1049	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1050	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1051	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1052	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1053	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1054	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1055	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1056	C₄⋊Q₈	—	2	1	no	—
1057	C₄⋊Q₈	—	2	1	no	—
1058	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1059	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1060	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1061	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1062	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1063	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1064	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1065	#127	C₂³×C₅₃	1	1	yes	characteristic
1066	#126	—	2	1	no	—
1067	#126	—	2	1	no	—
1068	#126	—	2	1	no	—
1069	#126	—	2	1	no	—
1070	#126	—	2	1	no	—
1071	#126	—	2	1	no	—
1072	#126	—	2	1	no	—
1073	#126	—	2	1	no	—
1074	#126	—	2	1	no	—
1075	#126	—	2	1	no	—
1076	#126	—	2	1	no	—
1077	#126	—	2	1	no	—
1078	#126	D₄×C₅₃	1	1	yes	characteristic
1079	#126	D₄×C₅₃	1	1	yes	characteristic
1080	#125	—	2	1	no	—
1081	#125	—	2	1	no	—
1082	#125	—	2	1	no	—
1083	#125	—	2	1	no	—
1084	#125	—	2	1	no	—
1085	#125	D₄×C₅₃	1	1	yes	characteristic
1086	#125	C₂³×C₅₃	1	1	yes	characteristic
1087	#125	C₂³×C₅₃	1	1	yes	characteristic
1088	#125	C₂³×C₅₃	1	1	yes	characteristic
1089	#125	C₂³×C₅₃	1	1	yes	characteristic
1090	#125	C₂³×C₅₃	1	1	yes	characteristic
1091	#125	C₂³×C₅₃	1	1	yes	characteristic
1092	#124	—	2	1	no	—
1093	#124	—	2	1	no	—
1094	#124	—	2	1	no	—
1095	#124	—	2	1	no	—
1096	#124	—	2	1	no	—
1097	#124	—	2	1	no	—
1098	#124	—	2	1	no	—
1099	#124	—	2	1	no	—
1100	#124	—	2	1	no	—
1101	#124	D₄×C₅₃	1	1	yes	characteristic
1102	#124	C₂³×C₅₃	1	1	yes	characteristic
1103	#124	C₂³×C₅₃	1	1	yes	characteristic
1104	#123	—	2	1	no	—
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	—	2	1	no	—
1109	#123	—	2	1	no	—
1110	#123	—	2	1	no	—
1111	#123	—	2	1	no	—
1112	#123	—	2	1	no	—
1113	#123	—	2	1	no	—
1114	#123	—	2	1	no	—
1115	#123	—	2	1	no	—
1116	#123	—	2	1	no	—
1117	#123	—	2	1	no	—
1118	#123	—	2	1	no	—
1119	#123	—	2	1	no	—
1120	#123	D₄×C₅₃	1	1	yes	characteristic
1121	#123	D₄×C₅₃	1	1	yes	characteristic
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	—	2	1	no	—
1125	C₂²⋊Q₈	—	2	1	no	—
1126	C₂²⋊Q₈	—	2	1	no	—
1127	C₂²⋊Q₈	—	2	1	no	—
1128	C₂²⋊Q₈	—	2	1	no	—
1129	C₂²⋊Q₈	—	2	1	no	—
1130	C₂²⋊Q₈	—	2	1	no	—
1131	C₂²⋊Q₈	—	2	1	no	—
1132	C₂²⋊Q₈	—	2	1	no	—
1133	C₂²⋊Q₈	—	2	1	no	—
1134	C₂²⋊Q₈	—	2	1	no	—
1135	C₂²⋊Q₈	—	2	1	no	—
1136	C₂²⋊Q₈	—	2	1	no	—
1137	C₂²⋊Q₈	—	2	1	no	—
1138	C₂²⋊Q₈	—	2	1	no	—
1139	C₂²⋊Q₈	—	2	1	no	—
1140	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1141	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1145	#121	—	2	1	no	—
1146	#121	—	2	1	no	—
1147	#121	—	2	1	no	—
1148	#121	—	2	1	no	—
1149	#121	—	2	1	no	—
1150	#121	—	2	1	no	—
1151	#121	—	2	1	no	—
1152	#121	—	2	1	no	—
1153	#121	—	2	1	no	—
1154	#121	—	2	1	no	—
1155	#121	—	2	1	no	—
1156	#121	—	2	1	no	—
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	D₄×C₅₃	1	1	yes	characteristic
1160	#121	C₂³×C₅₃	1	1	yes	characteristic
1161	#121	C₂³×C₅₃	1	1	yes	characteristic
1162	#121	C₂³×C₅₃	1	1	yes	characteristic
1163	#121	C₂³×C₅₃	1	1	yes	characteristic
1164	#121	C₂³×C₅₃	1	1	yes	characteristic
1165	#121	C₂³×C₅₃	1	1	yes	characteristic
1166	#121	C₂³×C₅₃	1	1	yes	characteristic
1167	#121	C₂³×C₅₃	1	1	yes	characteristic
1168	#120	—	2	1	no	—
1169	#120	—	2	1	no	—
1170	C₄×Q₈	—	2	1	no	—
1171	C₄×Q₈	—	2	1	no	—
1172	C₄×Q₈	—	2	1	no	—
1173	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1176	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1177	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1178	C₄×D₄	—	2	1	no	—
1179	C₄×D₄	—	2	1	no	—
1180	C₄×D₄	—	2	1	no	—
1181	C₄×D₄	—	2	1	no	—
1182	C₄×D₄	—	2	1	no	—
1183	C₄×D₄	—	2	1	no	—
1184	C₄×D₄	—	2	1	no	—
1185	C₄×D₄	—	2	1	no	—
1186	C₄×D₄	—	2	1	no	—
1187	C₄×D₄	—	2	1	no	—
1188	C₄×D₄	—	2	1	no	—
1189	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1190	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1191	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1192	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1193	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1194	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1195	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1196	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1197	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1198	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1199	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1200	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1201	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1202	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1203	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1204	#117	—	2	1	no	—
1205	#117	—	2	1	no	—
1206	#117	—	2	1	no	—
1207	#117	—	2	1	no	—
1208	#117	—	2	1	no	—
1209	#117	—	2	1	no	—
1210	#117	—	2	1	no	—
1211	#117	—	2	1	no	—
1212	#117	C₂³×C₅₃	1	1	yes	characteristic
1213	#117	C₂³×C₅₃	1	1	yes	characteristic
1214	#117	C₂³×C₅₃	1	1	yes	characteristic
1215	#117	C₂³×C₅₃	1	1	yes	characteristic
1216	#117	C₂³×C₅₃	1	1	yes	characteristic
1217	#117	C₂³×C₅₃	1	1	yes	characteristic
1218	#117	C₂³×C₅₃	1	1	yes	characteristic
1219	#117	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂×C₄⋊C₄	—	2	1	no	—
1221	C₂×C₄⋊C₄	—	2	1	no	—
1222	C₂×C₄⋊C₄	—	2	1	no	—
1223	C₂×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
1228	C₂×C₂²⋊C₄	—	2	1	no	—
1229	C₂×C₂²⋊C₄	—	2	1	no	—
1230	C₂×C₂²⋊C₄	—	2	1	no	—
1231	C₂×C₄²	—	2	1	no	—
1232	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1233	#107	C₂³×C₅₃	1	1	yes	characteristic
1234	#107	C₂³×C₅₃	1	1	yes	characteristic
1235	#107	C₂³×C₅₃	1	1	yes	characteristic
1236	#107	C₂³×C₅₃	1	1	yes	characteristic
1237	#107	C₂³×C₅₃	1	1	yes	characteristic
1238	#107	C₂³×C₅₃	1	1	yes	characteristic
1239	#107	C₂³×C₅₃	1	1	yes	characteristic
1240	#107	C₂³×C₅₃	1	1	yes	characteristic
1241	#107	C₂³×C₅₃	1	1	yes	characteristic
1242	#107	C₂³×C₅₃	1	1	yes	characteristic
1243	#107	C₂³×C₅₃	1	1	yes	characteristic
1244	#107	C₂³×C₅₃	1	1	yes	characteristic
1245	#106	C₂³×C₅₃	1	1	yes	characteristic
1246	#106	C₂³×C₅₃	1	1	yes	characteristic
1247	#106	C₂³×C₅₃	1	1	yes	characteristic
1248	#106	C₂³×C₅₃	1	1	yes	characteristic
1249	#106	C₂³×C₅₃	1	1	yes	characteristic
1250	#106	C₂³×C₅₃	1	1	yes	characteristic
1251	#106	C₂³×C₅₃	1	1	yes	characteristic
1252	#106	C₂³×C₅₃	1	1	yes	characteristic
1253	#106	C₂³×C₅₃	1	1	yes	characteristic
1254	#106	C₂³×C₅₃	1	1	yes	characteristic
1255	#106	C₂³×C₅₃	1	1	yes	characteristic
1256	#106	C₂³×C₅₃	1	1	yes	characteristic
1257	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1258	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1259	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1260	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1261	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1262	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1263	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1264	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1267	#103	C₂³×C₅₃	1	1	yes	characteristic
1268	#103	C₂³×C₅₃	1	1	yes	characteristic
1269	#103	C₂³×C₅₃	1	1	yes	characteristic
1270	#103	C₂³×C₅₃	1	1	yes	characteristic
1271	#103	C₂³×C₅₃	1	1	yes	characteristic
1272	#103	C₂³×C₅₃	1	1	yes	characteristic
1273	#103	C₂³×C₅₃	1	1	yes	characteristic
1274	#103	C₂³×C₅₃	1	1	yes	characteristic
1275	#103	C₂³×C₅₃	1	1	yes	characteristic
1276	#103	C₂³×C₅₃	1	1	yes	characteristic
1277	#103	C₂³×C₅₃	1	1	yes	characteristic
1278	#103	C₂³×C₅₃	1	1	yes	characteristic
1279	#102	C₂³×C₅₃	1	1	yes	characteristic
1280	#102	C₂³×C₅₃	1	1	yes	characteristic
1281	#102	C₂³×C₅₃	1	1	yes	characteristic
1282	#102	C₂³×C₅₃	1	1	yes	characteristic
1283	#102	C₂³×C₅₃	1	1	yes	characteristic
1284	#102	C₂³×C₅₃	1	1	yes	characteristic
1285	#102	C₂³×C₅₃	1	1	yes	characteristic
1286	#102	C₂³×C₅₃	1	1	yes	characteristic
1287	#102	C₂³×C₅₃	1	1	yes	characteristic
1288	#102	C₂³×C₅₃	1	1	yes	characteristic
1289	#102	C₂³×C₅₃	1	1	yes	characteristic
1290	#102	C₂³×C₅₃	1	1	yes	characteristic
1291	#102	C₂³×C₅₃	1	1	yes	characteristic
1292	#102	C₂³×C₅₃	1	1	yes	characteristic
1293	#102	C₂³×C₅₃	1	1	yes	characteristic
1294	#102	C₂³×C₅₃	1	1	yes	characteristic
1295	#102	C₂³×C₅₃	1	1	yes	characteristic
1296	#102	C₂³×C₅₃	1	1	yes	characteristic
1297	#102	C₂³×C₅₃	1	1	yes	characteristic
1298	#102	C₂³×C₅₃	1	1	yes	characteristic
1299	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1300	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1301	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1302	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1303	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1304	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1305	#97	C₂³×C₅₃	1	1	yes	characteristic
1306	#97	C₂³×C₅₃	1	1	yes	characteristic
1307	#97	C₂³×C₅₃	1	1	yes	characteristic
1308	#97	C₂³×C₅₃	1	1	yes	characteristic
1309	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1310	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1311	C₂⁴	—	2	1	no	—
1312	#41	—	2	2	no	—
1313	#41	—	2	2	no	—
1314	#41	—	4	1	no	—
1315	#41	—	4	1	no	—
1316	#41	—	8	2	no	—
1317	#41	—	8	2	no	—
1318	C₂×Q₈	—	2	1	no	—
1319	C₂×Q₈	—	2	1	no	—
1320	C₂×Q₈	—	2	1	no	—
1321	C₂×Q₈	—	2	1	no	—
1322	C₂×Q₈	—	2	1	no	—
1323	C₂×Q₈	—	2	1	no	—
1324	C₂×Q₈	—	8	2	no	—
1325	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1326	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1327	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1328	C₂×D₄	—	2	2	no	—
1329	C₂×D₄	—	2	1	no	—
1330	C₂×D₄	—	2	1	no	—
1331	C₂×D₄	—	2	1	no	—
1332	C₂×D₄	—	2	1	no	—
1333	C₂×D₄	—	2	1	no	—
1334	C₂×D₄	—	2	1	no	—
1335	C₂×D₄	—	2	1	no	—
1336	C₂×D₄	—	2	1	no	—
1337	C₂×D₄	—	2	1	no	—
1338	C₂×D₄	—	2	1	no	—
1339	C₂×D₄	—	2	1	no	—
1340	C₂×D₄	—	2	1	no	—
1341	C₂×D₄	—	2	1	no	—
1342	C₂×D₄	—	4	1	no	—
1343	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1344	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1345	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1346	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1347	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1348	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1349	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1350	C₂²×C₄	—	2	1	no	—
1351	C₂²×C₄	—	2	1	no	—
1352	C₂²×C₄	—	2	1	no	—
1353	C₂²×C₄	—	2	1	no	—
1354	C₂²×C₄	—	2	1	no	—
1355	C₂²×C₄	—	2	1	no	—
1356	C₂²×C₄	—	2	1	no	—
1357	C₂²×C₄	—	2	1	no	—
1358	C₂²×C₄	—	2	1	no	—
1359	C₂²×C₄	—	2	1	no	—
1360	C₂²×C₄	—	2	1	no	—
1361	C₂²×C₄	—	2	1	no	—
1362	C₂²×C₄	—	2	1	no	—
1363	C₂²×C₄	—	2	1	no	—
1364	C₂²×C₄	—	2	1	no	—
1365	C₂²×C₄	—	2	1	no	—
1366	C₂²×C₄	—	2	1	no	—
1367	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1368	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1369	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1370	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1371	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1372	SD₁₆	—	4	1	no	—
1373	SD₁₆	—	4	1	no	—
1374	SD₁₆	—	4	1	no	—
1375	SD₁₆	—	4	1	no	—
1376	D₈	—	2	2	no	—
1377	D₈	—	2	2	no	—
1378	D₈	—	4	1	no	—
1379	D₈	—	4	1	no	—
1380	M₁₆	—	4	1	no	—
1381	M₁₆	—	4	1	no	—
1382	C₂×C₈	—	4	1	no	—
1383	C₂×C₈	—	4	1	no	—
1384	C₂×C₈	—	4	1	no	—
1385	C₂×C₈	—	4	1	no	—
1386	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1387	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1388	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1389	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1390	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1391	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1392	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1393	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1394	C₄⋊C₄	—	2	1	no	—
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	—	2	1	no	—
1400	C₄⋊C₄	—	2	1	no	—
1401	C₄⋊C₄	—	2	1	no	—
1402	C₄⋊C₄	—	2	1	no	—
1403	C₄⋊C₄	—	2	1	no	—
1404	C₄⋊C₄	—	2	1	no	—
1405	C₄⋊C₄	—	2	1	no	—
1406	C₄⋊C₄	—	2	1	no	—
1407	C₄⋊C₄	—	2	1	no	—
1408	C₄⋊C₄	—	2	1	no	—
1409	C₄⋊C₄	—	2	1	no	—
1410	C₄⋊C₄	—	2	1	no	—
1411	C₄⋊C₄	—	2	1	no	—
1412	C₄⋊C₄	—	2	1	no	—
1413	C₄⋊C₄	—	2	1	no	—
1414	C₄⋊C₄	—	2	1	no	—
1415	C₄⋊C₄	—	2	1	no	—
1416	C₄⋊C₄	—	2	1	no	—
1417	C₄⋊C₄	—	2	1	no	—
1418	C₄⋊C₄	—	2	1	no	—
1419	C₄⋊C₄	—	2	1	no	—
1420	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1426	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1427	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1428	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1429	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1430	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1431	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1432	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1433	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1434	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1435	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1436	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1437	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1438	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1439	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1440	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1441	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1442	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1443	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1444	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1445	C₂²⋊C₄	—	2	1	no	—
1446	C₂²⋊C₄	—	2	1	no	—
1447	C₂²⋊C₄	—	2	1	no	—
1448	C₂²⋊C₄	—	2	1	no	—
1449	C₂²⋊C₄	—	2	1	no	—
1450	C₂²⋊C₄	—	2	1	no	—
1451	C₂²⋊C₄	—	2	1	no	—
1452	C₂²⋊C₄	—	2	1	no	—
1453	C₂²⋊C₄	—	2	1	no	—
1454	C₂²⋊C₄	—	2	1	no	—
1455	C₂²⋊C₄	—	2	1	no	—
1456	C₂²⋊C₄	—	2	1	no	—
1457	C₂²⋊C₄	—	2	1	no	—
1458	C₂²⋊C₄	—	2	1	no	—
1459	C₂²⋊C₄	—	2	1	no	—
1460	C₂²⋊C₄	—	2	1	no	—
1461	C₂²⋊C₄	—	2	1	no	—
1462	C₂²⋊C₄	—	2	1	no	—
1463	C₂²⋊C₄	—	2	1	no	—
1464	C₂²⋊C₄	—	2	1	no	—
1465	C₂²⋊C₄	—	2	1	no	—
1466	C₂²⋊C₄	—	2	1	no	—
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1480	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1481	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1482	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1483	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1484	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1485	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1486	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1487	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1488	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1489	C₄²	—	2	1	no	—
1490	C₄²	—	2	1	no	—
1491	C₄²	—	2	1	no	—
1492	C₄²	—	2	1	no	—
1493	C₄²	—	2	1	no	—
1494	C₄²	—	2	1	no	—
1495	C₄²	—	2	1	no	—
1496	C₄²	—	2	1	no	—
1497	C₄²	—	2	1	no	—
1498	C₄²	—	2	1	no	—
1499	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1500	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1501	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1502	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1503	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1504	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1505	C₂³	—	2	1	no	—
1506	C₂³	—	2	1	no	—
1507	C₂³	—	2	1	no	—
1508	C₂³	—	2	1	no	—
1509	C₂³	—	4	2	no	—
1510	C₂³	—	8	1	no	—
1511	C₂³	—	8	1	no	—
1512	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1513	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1514	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1515	Q₈	—	2	1	no	—
1516	Q₈	—	2	1	no	—
1517	Q₈	—	2	1	no	—
1518	Q₈	—	2	1	no	—
1519	Q₈	—	4	1	no	—
1520	Q₈	—	4	2	no	—
1521	Q₈	—	8	1	no	—
1522	Q₈	—	8	1	no	—
1523	Q₈	—	8	1	no	—
1524	Q₈	—	8	1	no	—
1525	Q₈	—	8	1	no	—
1526	D₄	—	2	1	no	—
1527	D₄	—	2	1	no	—
1528	D₄	—	2	1	no	—
1529	D₄	—	2	1	no	—
1530	D₄	—	2	1	no	—
1531	D₄	—	2	1	no	—
1532	D₄	—	2	1	no	—
1533	D₄	—	4	1	no	—
1534	D₄	—	4	1	no	—
1535	D₄	—	4	1	no	—
1536	D₄	—	4	2	no	—
1537	D₄	—	4	2	no	—
1538	D₄	—	4	2	no	—
1539	D₄	—	8	1	no	—
1540	D₄	—	8	1	no	—
1541	D₄	—	8	1	no	—
1542	D₄	—	8	1	no	—
1543	D₄	—	8	1	no	—
1544	D₄	—	8	1	no	—
1545	D₄	—	8	1	no	—
1546	D₄	—	8	1	no	—
1547	D₄	—	8	1	no	—
1548	D₄	—	8	1	no	—
1549	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1550	C₂×C₄	—	2	1	no	—
1551	C₂×C₄	—	2	1	no	—
1552	C₂×C₄	—	2	1	no	—
1553	C₂×C₄	—	2	1	no	—
1554	C₂×C₄	—	2	1	no	—
1555	C₂×C₄	—	2	1	no	—
1556	C₂×C₄	—	2	1	no	—
1557	C₂×C₄	—	2	1	no	—
1558	C₂×C₄	—	2	1	no	—
1559	C₂×C₄	—	2	1	no	—
1560	C₂×C₄	—	2	1	no	—
1561	C₂×C₄	—	2	1	no	—
1562	C₂×C₄	—	2	1	no	—
1563	C₂×C₄	—	2	1	no	—
1564	C₂×C₄	—	2	1	no	—
1565	C₂×C₄	—	2	1	no	—
1566	C₂×C₄	—	2	1	no	—
1567	C₂×C₄	—	2	1	no	—
1568	C₂×C₄	—	4	1	no	—
1569	C₂×C₄	—	4	1	no	—
1570	C₂×C₄	—	4	2	no	—
1571	C₂×C₄	—	4	2	no	—
1572	C₂×C₄	—	4	2	no	—
1573	C₂×C₄	—	4	2	no	—
1574	C₂×C₄	—	8	1	no	—
1575	C₂×C₄	—	8	1	no	—
1576	C₂×C₄	—	8	1	no	—
1577	C₂×C₄	—	8	1	no	—
1578	C₂×C₄	—	8	1	no	—
1579	C₂×C₄	—	8	1	no	—
1580	C₂×C₄	—	8	1	no	—
1581	C₂×C₄	—	8	1	no	—
1582	C₂×C₄	—	8	1	no	—
1583	C₂×C₄	—	8	1	no	—
1584	C₂×C₄	—	8	1	no	—
1585	C₂×C₄	—	8	1	no	—
1586	C₂×C₄	—	8	1	no	—
1587	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1588	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1589	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1590	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1591	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1592	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1593	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1594	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1595	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1596	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1597	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1598	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1599	C₈	—	2	1	no	—
1600	C₈	—	2	1	no	—
1601	C₈	—	2	1	no	—
1602	C₈	—	2	1	no	—
1603	C₈	—	2	1	no	—
1604	C₈	—	2	1	no	—
1605	C₈	—	2	1	no	—
1606	C₈	—	2	1	no	—
1607	C₂²	—	2	1	no	—
1608	C₂²	—	2	1	no	—
1609	C₂²	—	2	1	no	—
1610	C₂²	—	2	2	no	—
1611	C₂²	—	2	1	no	—
1612	C₂²	—	2	1	no	—
1613	C₂²	—	2	1	no	—
1614	C₂²	—	2	1	no	—
1615	C₂²	—	2	1	no	—
1616	C₂²	—	2	1	no	—
1617	C₂²	—	4	1	no	—
1618	C₂²	—	4	1	no	—
1619	C₂²	—	4	1	no	—
1620	C₂²	—	4	1	no	—
1621	C₂²	—	4	1	no	—
1622	C₂²	—	4	1	no	—
1623	C₂²	—	4	1	no	—
1624	C₂²	—	4	1	no	—
1625	C₂²	—	4	1	no	—
1626	C₂²	—	4	1	no	—
1627	C₂²	—	4	1	no	—
1628	C₂²	—	16	2	no	—
1629	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1630	C₄	—	2	1	no	—
1631	C₄	—	2	1	no	—
1632	C₄	—	2	1	no	—
1633	C₄	—	2	1	no	—
1634	C₄	—	2	1	no	—
1635	C₄	—	2	1	no	—
1636	C₄	—	2	1	no	—
1637	C₄	—	2	1	no	—
1638	C₄	—	2	1	no	—
1639	C₄	—	2	1	no	—
1640	C₄	—	2	1	no	—
1641	C₄	—	4	1	no	—
1642	C₄	—	4	1	no	—
1643	C₄	—	4	1	no	—
1644	C₄	—	4	1	no	—
1645	C₄	—	4	1	no	—
1646	C₄	—	4	1	no	—
1647	C₄	—	4	1	no	—
1648	C₄	—	4	1	no	—
1649	C₄	—	4	1	no	—
1650	C₄	—	4	1	no	—
1651	C₄	—	4	1	no	—
1652	C₄	—	4	1	no	—
1653	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1654	C₄	C₅₃×#585	1	1	yes	characteristic
1655	C₂	—	4	1	no	—
1656	C₂	—	4	1	no	—
1657	C₂	—	4	1	no	—
1658	C₂	—	4	2	no	—
1659	C₂	—	8	1	no	—
1660	C₂	—	8	1	no	—
1661	C₂	—	8	1	no	—
1662	C₂	C₅₃×#3489	1	1	yes	characteristic
1663	C₂	C₅₃×#3584	1	1	yes	characteristic
1664	C₂	C₅₃×#3585	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 ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3547	C₂	semidirect
2. C₅₃×#3521	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3376	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3350	C₂	semidirect
8. C₅₃×#3348	C₂	semidirect
9. C₅₃×#3347	C₂	semidirect
10. C₅₃×#3343	C₂	semidirect
11. C₅₃×#3340	C₂	semidirect
12. C₅₃×#3339	C₂	semidirect
13. C₅₃×#3319	C₂	semidirect
14. C₅₃×#3319	C₂	semidirect
15. C₅₃×#3307	C₂	semidirect
16. C₅₃×#3306	C₂	semidirect
17. C₅₃×#3303	C₂	semidirect
18. C₅₃×#3297	C₂	semidirect
19. C₅₃×#3260	C₂	semidirect
20. C₅₃×#3257	C₂	semidirect
21. C₅₃×#3247	C₂	semidirect
22. C₅₃×#3244	C₂	semidirect
23. C₅₃×#3242	C₂	semidirect
24. C₅₃×#3240	C₂	semidirect
25. C₅₃×#3122	C₂	semidirect
26. C₅₃×#3119	C₂	semidirect
27. C₅₃×#3115	C₂	semidirect
28. C₅₃×#3083	C₂	semidirect
29. C₅₃×#3081	C₂	semidirect
30. C₅₃×#3076	C₂	semidirect
31. C₅₃×#2992	C₂	semidirect
38. C₅₃×#555	C₂²	semidirect
40. C₅₃×#554	C₂²	semidirect
44. C₅₃×#553	C₂²	semidirect
50. D₄×Q₈×C₅₃	C₂²	semidirect
57. C₅₃×#544	C₂²	semidirect
63. C₅₃×#540	C₂²	semidirect
68. C₅₃×#533	C₂²	semidirect
69. C₅₃×#532	C₂²	semidirect
77. C₅₃×#501	C₂²	semidirect
78. C₅₃×#501	C₂²	semidirect
79. C₅₃×#501	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#499	C₂²	semidirect
82. C₅₃×#498	C₂²	semidirect
83. C₅₃×#491	C₂²	semidirect
88. C₅₃×#487	C₂²	semidirect
91. C₅₃×#485	C₂²	semidirect
92. C₅₃×#485	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
96. C₅₃×#483	C₂²	semidirect
102. C₅₃×#482	C₂²	semidirect
103. C₅₃×#482	C₂²	semidirect
105. C₅₃×#481	C₂²	semidirect
106. C₅₃×#480	C₂²	semidirect
107. C₅₃×#479	C₂²	semidirect
108. C₅₃×#479	C₂²	semidirect
109. C₅₃×#479	C₂²	semidirect
110. C₅₃×#479	C₂²	semidirect
111. C₅₃×#479	C₂²	semidirect
119. C₅₃×#478	C₂²	semidirect
120. C₅₃×#478	C₂²	semidirect
121. C₅₃×#478	C₂²	semidirect
122. C₅₃×#478	C₂²	semidirect
123. C₅₃×#477	C₂²	semidirect
124. C₅₃×#477	C₂²	semidirect
125. C₅₃×#477	C₂²	semidirect
129. C₅₃×#476	C₂²	semidirect
130. C₅₃×#475	C₂²	semidirect
131. C₅₃×#475	C₂²	semidirect
136. C₅₃×#474	C₂²	semidirect
140. C₅₃×#468	C₂²	semidirect
146. C₅₃×#465	C₂²	semidirect
147. C₅₃×#465	C₂²	semidirect
148. C₅₃×#465	C₂²	semidirect
153. C₅₃×#461	C₂²	semidirect
154. C₅₃×#461	C₂²	semidirect
155. C₅₃×#460	C₂²	semidirect
156. C₅₃×#460	C₂²	semidirect
165. C₅₃×#446	C₂²	semidirect
166. C₅₃×#446	C₂²	semidirect
172. C₅₃×#440	C₂²	semidirect
173. C₅₃×#440	C₂²	semidirect
174. C₅₃×#440	C₂²	semidirect
175. C₄×SD₁₆×C₅₃	C₂²	semidirect
182. C₅₃×#435	C₂²	semidirect
184. C₈×D₄×C₅₃	C₂²	semidirect
186. C₅₃×#433	C₂²	semidirect
187. C₅₃×#432	C₂²	semidirect
189. C₅₃×#428	C₂²	semidirect
191. C₅₃×#427	C₂²	semidirect
192. C₅₃×#427	C₂²	semidirect
193. C₂×#107×C₅₃	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
774. #62171	C₅₃	direct (N × H)
823. #3547	C₂×C₅₃	semidirect
824. #3521	C₂×C₅₃	semidirect
825. #3389	C₂×C₅₃	semidirect
826. #3384	C₂×C₅₃	semidirect
827. #3376	C₂×C₅₃	semidirect
828. #3367	C₂×C₅₃	semidirect
829. #3350	C₂×C₅₃	semidirect
830. #3348	C₂×C₅₃	semidirect
831. #3347	C₂×C₅₃	semidirect
832. #3343	C₂×C₅₃	semidirect
833. #3340	C₂×C₅₃	semidirect
834. #3339	C₂×C₅₃	semidirect
835. #3319	C₂×C₅₃	semidirect
836. #3319	C₂×C₅₃	semidirect
837. #3307	C₂×C₅₃	semidirect
838. #3306	C₂×C₅₃	semidirect
839. #3303	C₂×C₅₃	semidirect
840. #3297	C₂×C₅₃	semidirect
841. #3260	C₂×C₅₃	semidirect
842. #3257	C₂×C₅₃	semidirect
843. #3247	C₂×C₅₃	semidirect
844. #3244	C₂×C₅₃	semidirect
845. #3242	C₂×C₅₃	semidirect
846. #3240	C₂×C₅₃	semidirect
847. #3122	C₂×C₅₃	semidirect
848. #3119	C₂×C₅₃	semidirect
849. #3115	C₂×C₅₃	semidirect
850. #3083	C₂×C₅₃	semidirect
851. #3081	C₂×C₅₃	semidirect
852. #3076	C₂×C₅₃	semidirect
853. #2992	C₂×C₅₃	semidirect
870. #555	C₂²×C₅₃	semidirect
872. #554	C₂²×C₅₃	semidirect
876. #553	C₂²×C₅₃	semidirect
882. D₄×Q₈	C₂²×C₅₃	semidirect
889. #544	C₂²×C₅₃	semidirect
895. #540	C₂²×C₅₃	semidirect
900. #533	C₂²×C₅₃	semidirect
901. #532	C₂²×C₅₃	semidirect
909. #501	C₂²×C₅₃	semidirect
910. #501	C₂²×C₅₃	semidirect
911. #501	C₂²×C₅₃	semidirect
912. #501	C₂²×C₅₃	semidirect
913. #499	C₂²×C₅₃	semidirect
914. #498	C₂²×C₅₃	semidirect
915. #491	C₂²×C₅₃	semidirect
920. #487	C₂²×C₅₃	semidirect
923. #485	C₂²×C₅₃	semidirect
924. #485	C₂²×C₅₃	semidirect
925. #485	C₂²×C₅₃	semidirect
928. #483	C₂²×C₅₃	semidirect
934. #482	C₂²×C₅₃	semidirect
935. #482	C₂²×C₅₃	semidirect
937. #481	C₂²×C₅₃	semidirect
938. #480	C₂²×C₅₃	semidirect
939. #479	C₂²×C₅₃	semidirect
940. #479	C₂²×C₅₃	semidirect
941. #479	C₂²×C₅₃	semidirect
942. #479	C₂²×C₅₃	semidirect
943. #479	C₂²×C₅₃	semidirect
951. #478	C₂²×C₅₃	semidirect
952. #478	C₂²×C₅₃	semidirect
953. #478	C₂²×C₅₃	semidirect
954. #478	C₂²×C₅₃	semidirect
955. #477	C₂²×C₅₃	semidirect
956. #477	C₂²×C₅₃	semidirect
957. #477	C₂²×C₅₃	semidirect
961. #476	C₂²×C₅₃	semidirect
962. #475	C₂²×C₅₃	semidirect
963. #475	C₂²×C₅₃	semidirect
968. #474	C₂²×C₅₃	semidirect
972. #468	C₂²×C₅₃	semidirect
978. #465	C₂²×C₅₃	semidirect
979. #465	C₂²×C₅₃	semidirect
980. #465	C₂²×C₅₃	semidirect
985. #461	C₂²×C₅₃	semidirect
986. #461	C₂²×C₅₃	semidirect
987. #460	C₂²×C₅₃	semidirect
988. #460	C₂²×C₅₃	semidirect
997. #446	C₂²×C₅₃	semidirect
998. #446	C₂²×C₅₃	semidirect
1004. #440	C₂²×C₅₃	semidirect
1005. #440	C₂²×C₅₃	semidirect
1006. #440	C₂²×C₅₃	semidirect
1007. C₄×SD₁₆	C₂²×C₅₃	semidirect
1014. #435	C₂²×C₅₃	semidirect
1016. C₈×D₄	C₂²×C₅₃	semidirect
1018. #433	C₂²×C₅₃	semidirect
1019. #432	C₂²×C₅₃	semidirect
1021. #428	C₂²×C₅₃	semidirect
1023. #427	C₂²×C₅₃	semidirect
1024. #427	C₂²×C₅₃	semidirect
1025. C₂×#107	C₂²×C₅₃	semidirect
1027. #424	C₂²×C₅₃	semidirect
1028. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1035. C₅₃	#62171	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×#3547	2
C₅₃×#3521	2
C₅₃×#3389	2
C₅₃×#3384	2
C₅₃×#3376	2
C₅₃×#3367	2
C₅₃×#3350	2
C₅₃×#3348	2
C₅₃×#3347	2
C₅₃×#3343	2
C₅₃×#3340	2
C₅₃×#3339	2
C₅₃×#3319	2
C₅₃×#3307	2
C₅₃×#3306	2
C₅₃×#3303	2
C₅₃×#3297	2
C₅₃×#3260	2
C₅₃×#3257	2
C₅₃×#3247	2
C₅₃×#3244	2
C₅₃×#3242	2
C₅₃×#3240	2
C₅₃×#3122	2
C₅₃×#3119	2
C₅₃×#3115	2
C₅₃×#3083	2
C₅₃×#3081	2
C₅₃×#3076	2
C₅₃×#2992	2
#62171	53

Subgroups — C53×#62171 #27269683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62171 #27269683