Subgroups — C₅₃×#62224 #27269736

Order 13568.

1698 conjugacy classes of subgroups.

The subgroup lattice has 1650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3565	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3386	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3346	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3345	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3344	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3343	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3323	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3322	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3307	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3263	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3262	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3252	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3244	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3243	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3237	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3083	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#563	—	2	1	no	—
33	C₅₃×#562	—	2	1	no	—
34	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#556	—	2	1	no	—
36	C₅₃×#556	C₂²	1	1	yes	characteristic
37	C₅₃×#556	C₂²	1	1	yes	characteristic
38	C₅₃×#555	C₂²	1	1	yes	characteristic
39	C₅₃×#554	C₂²	1	1	yes	characteristic
40	C₅₃×#554	C₂²	1	1	yes	characteristic
41	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#553	C₂²	1	1	yes	characteristic
43	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#552	—	2	1	no	—
45	C₅₃×#552	—	2	1	no	—
46	C₅₃×#552	C₂²	1	1	yes	characteristic
47	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#551	—	2	1	no	—
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
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, complemented
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×#542	C₂²	1	1	yes	characteristic
62	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#541	—	2	1	no	—
65	C₅₃×#539	—	2	1	no	—
66	C₅₃×#539	—	2	1	no	—
67	C₅₃×#539	—	2	1	no	—
68	C₅₃×#533	C₂²	1	1	yes	characteristic
69	C₅₃×#533	C₂²	1	1	yes	characteristic
70	C₅₃×#529	C₂²	1	1	yes	characteristic
71	C₅₃×#529	C₂²	1	1	yes	characteristic
72	C₅₃×#525	—	2	1	no	—
73	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
74	C₅₃×#520	C₂²	1	1	yes	characteristic
75	C₅₃×#520	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×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×#500	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×#491	C₂²	1	1	yes	characteristic, complemented
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×#488	C₂²	1	1	yes	characteristic
89	C₅₃×#485	C₂²	1	1	yes	characteristic
90	C₅₃×#485	C₂²	1	1	yes	characteristic
91	C₅₃×#485	C₂²	1	1	yes	characteristic
92	C₅₃×#485	C₂²	1	1	yes	characteristic
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#483	C₂²	1	1	yes	characteristic
98	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic
101	C₅₃×#482	C₂²	1	1	yes	characteristic
102	C₅₃×#481	C₂²	1	1	yes	characteristic
103	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#480	C₂²	1	1	yes	characteristic
105	C₅₃×#480	C₂²	1	1	yes	characteristic
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×#478	C₂²	1	1	yes	characteristic
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×#477	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#476	C₂²	1	1	yes	characteristic
125	C₅₃×#476	C₂²	1	1	yes	characteristic
126	C₅₃×#476	C₂²	1	1	yes	characteristic
127	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#475	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×#475	C₂²	1	1	yes	characteristic, complemented
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×#470	C₂²	1	1	yes	characteristic
138	C₅₃×#470	C₂²	1	1	yes	characteristic
139	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#469	C₂²	1	1	yes	characteristic
141	C₅₃×#468	C₂²	1	1	yes	characteristic
142	C₅₃×#468	C₂²	1	1	yes	characteristic
143	C₅₃×#468	C₂²	1	1	yes	characteristic
144	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#466	C₂²	1	1	yes	characteristic
147	C₅₃×#465	C₂²	1	1	yes	characteristic
148	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#464	C₂²	1	1	yes	characteristic
150	C₅₃×#464	C₂²	1	1	yes	characteristic
151	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#463	C₂²	1	1	yes	characteristic
154	C₅₃×#463	C₂²	1	1	yes	characteristic
155	C₅₃×#463	C₂²	1	1	yes	characteristic
156	C₅₃×#463	C₂²	1	1	yes	characteristic
157	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#452	C₂²	1	1	yes	characteristic
160	C₅₃×#452	C₂²	1	1	yes	characteristic
161	C₅₃×#450	C₂²	1	1	yes	characteristic
162	C₅₃×#449	C₂²	1	1	yes	characteristic
163	C₅₃×#449	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×#441	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#440	C₂²	1	1	yes	characteristic
172	C₅₃×#440	C₂²	1	1	yes	characteristic
173	C₅₃×#440	C₂²	1	1	yes	characteristic
174	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
179	C₅₃×#436	C₂²	1	1	yes	characteristic
180	C₅₃×#436	C₂²	1	1	yes	characteristic
181	C₅₃×#435	C₂²	1	1	yes	characteristic
182	C₅₃×#435	C₂²	1	1	yes	characteristic
183	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#432	C₂²	1	1	yes	characteristic
188	C₅₃×#428	C₂²	1	1	yes	characteristic
189	C₅₃×#428	C₂²	1	1	yes	characteristic
190	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
192	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
193	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#423	C₂²	1	1	yes	characteristic
197	C₅₃×#418	C₂²	1	1	yes	characteristic
198	C₅₃×#418	C₂²	1	1	yes	characteristic
199	C₅₃×#417	C₂²	1	1	yes	characteristic
200	C₅₃×#417	C₂²	1	1	yes	characteristic
201	C₅₃×#416	C₂²	1	1	yes	characteristic
202	C₅₃×#416	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂²×Q₈×C₅₃	—	2	1	no	—
207	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
208	C₂³×C₄×C₅₃	—	2	1	no	—
209	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×Q₁₆×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×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×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	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×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	—	2	1	no	—
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	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
246	#126×C₅₃	—	2	1	no	—
247	#126×C₅₃	D₄	1	1	yes	characteristic
248	#126×C₅₃	D₄	1	1	yes	characteristic
249	#125×C₅₃	—	2	1	no	—
250	#125×C₅₃	—	2	1	no	—
251	#125×C₅₃	—	2	1	no	—
252	#125×C₅₃	—	2	1	no	—
253	#125×C₅₃	—	2	1	no	—
254	#125×C₅₃	—	2	1	no	—
255	#125×C₅₃	—	2	1	no	—
256	#125×C₅₃	—	2	1	no	—
257	#125×C₅₃	—	2	1	no	—
258	#125×C₅₃	D₄	1	1	yes	characteristic
259	#125×C₅₃	C₂³	1	1	yes	characteristic
260	#125×C₅₃	C₂³	1	1	yes	characteristic
261	#125×C₅₃	C₂³	1	1	yes	characteristic
262	#125×C₅₃	C₂³	1	1	yes	characteristic
263	#125×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
269	#124×C₅₃	—	2	1	no	—
270	#124×C₅₃	—	2	1	no	—
271	#124×C₅₃	D₄	1	1	yes	characteristic
272	#124×C₅₃	C₂³	1	1	yes	characteristic
273	#124×C₅₃	C₂³	1	1	yes	characteristic
274	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
288	#123×C₅₃	—	2	1	no	—
289	#123×C₅₃	—	2	1	no	—
290	#123×C₅₃	D₄	1	1	yes	characteristic
291	#123×C₅₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
308	C₂²⋊Q₈×C₅₃	—	2	1	no	—
309	C₂²⋊Q₈×C₅₃	—	2	1	no	—
310	C₂²⋊Q₈×C₅₃	—	2	1	no	—
311	C₂²⋊Q₈×C₅₃	—	2	1	no	—
312	C₂²⋊Q₈×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	—	2	1	no	—
315	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
316	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	—	2	1	no	—
325	#121×C₅₃	—	2	1	no	—
326	#121×C₅₃	—	2	1	no	—
327	#121×C₅₃	—	2	1	no	—
328	#121×C₅₃	—	2	1	no	—
329	#121×C₅₃	D₄	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	—	2	1	no	—
341	C₄×Q₈×C₅₃	—	2	1	no	—
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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
357	C₄×D₄×C₅₃	—	2	1	no	—
358	C₄×D₄×C₅₃	—	2	1	no	—
359	C₄×D₄×C₅₃	—	2	1	no	—
360	C₄×D₄×C₅₃	—	2	1	no	—
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	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
380	#117×C₅₃	—	2	1	no	—
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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
395	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
396	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
397	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
398	C₂×C₂²⋊C₄×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	#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	#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	C₂×Q₈×C₅₃	—	2	1	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×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
496	C₂×D₄×C₅₃	—	2	2	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	—	4	1	no	—
506	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
507	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
508	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
509	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
510	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
512	C₂²×C₄×C₅₃	—	2	1	no	—
513	C₂²×C₄×C₅₃	—	2	1	no	—
514	C₂²×C₄×C₅₃	—	2	1	no	—
515	C₂²×C₄×C₅₃	—	2	1	no	—
516	C₂²×C₄×C₅₃	—	2	1	no	—
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	—	8	2	no	—
529	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
530	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
531	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
532	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
533	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
534	Q₁₆×C₅₃	—	4	1	no	—
535	Q₁₆×C₅₃	—	4	1	no	—
536	SD₁₆×C₅₃	—	2	2	no	—
537	SD₁₆×C₅₃	—	4	1	no	—
538	SD₁₆×C₅₃	—	4	1	no	—
539	SD₁₆×C₅₃	—	4	1	no	—
540	D₈×C₅₃	—	2	2	no	—
541	D₈×C₅₃	—	4	1	no	—
542	M₁₆×C₅₃	—	4	1	no	—
543	M₁₆×C₅₃	—	4	1	no	—
544	M₁₆×C₅₃	—	4	1	no	—
545	M₁₆×C₅₃	—	4	1	no	—
546	C₂×C₈×C₅₃	—	4	1	no	—
547	C₂×C₈×C₅₃	—	4	1	no	—
548	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
549	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
550	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
551	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
552	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₅₃	—	2	1	no	—
557	C₄⋊C₄×C₅₃	—	2	1	no	—
558	C₄⋊C₄×C₅₃	—	2	1	no	—
559	C₄⋊C₄×C₅₃	—	2	1	no	—
560	C₄⋊C₄×C₅₃	—	2	1	no	—
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	—	2	1	no	—
593	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₅₃	C₂×D₄	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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₅₃	—	2	1	no	—
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	—	4	2	no	—
676	C₂³×C₅₃	—	4	2	no	—
677	C₂³×C₅₃	—	8	1	no	—
678	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
679	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
680	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
681	Q₈×C₅₃	—	2	1	no	—
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	—	2	1	no	—
687	Q₈×C₅₃	—	4	1	no	—
688	Q₈×C₅₃	—	4	2	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	Q₈×C₅₃	—	8	1	no	—
694	Q₈×C₅₃	—	8	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	2₋¹⁺⁴	1	2	yes	—
712	C₂×C₄×C₅₃	—	2	1	no	—
713	C₂×C₄×C₅₃	—	2	1	no	—
714	C₂×C₄×C₅₃	—	2	1	no	—
715	C₂×C₄×C₅₃	—	2	1	no	—
716	C₂×C₄×C₅₃	—	2	1	no	—
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	—	4	1	no	—
732	C₂×C₄×C₅₃	—	4	1	no	—
733	C₂×C₄×C₅₃	—	4	2	no	—
734	C₂×C₄×C₅₃	—	4	2	no	—
735	C₂×C₄×C₅₃	—	4	2	no	—
736	C₂×C₄×C₅₃	—	4	2	no	—
737	C₂×C₄×C₅₃	—	8	1	no	—
738	C₂×C₄×C₅₃	—	8	1	no	—
739	C₂×C₄×C₅₃	—	8	1	no	—
740	C₂×C₄×C₅₃	—	8	1	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	C₂²×D₄	1	1	yes	characteristic
750	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
751	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
752	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
753	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
761	C₈×C₅₃	—	2	1	no	—
762	C₈×C₅₃	—	2	1	no	—
763	C₈×C₅₃	—	2	1	no	—
764	C₈×C₅₃	—	2	1	no	—
765	C₈×C₅₃	—	2	1	no	—
766	C₈×C₅₃	—	2	1	no	—
767	C₈×C₅₃	—	2	1	no	—
768	C₈×C₅₃	—	2	1	no	—
769	#62224	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
770	C₂²×C₅₃	—	2	1	no	—
771	C₂²×C₅₃	—	2	1	no	—
772	C₂²×C₅₃	—	2	1	no	—
773	C₂²×C₅₃	—	2	1	no	—
774	C₂²×C₅₃	—	2	1	no	—
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	2	no	—
780	C₂²×C₅₃	—	4	1	no	—
781	C₂²×C₅₃	—	4	1	no	—
782	C₂²×C₅₃	—	4	1	no	—
783	C₂²×C₅₃	—	4	1	no	—
784	C₂²×C₅₃	—	4	1	no	—
785	C₂²×C₅₃	—	4	1	no	—
786	C₂²×C₅₃	—	4	1	no	—
787	C₂²×C₅₃	—	4	1	no	—
788	C₂²×C₅₃	—	8	4	no	—
789	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
790	C₄×C₅₃	—	2	1	no	—
791	C₄×C₅₃	—	2	1	no	—
792	C₄×C₅₃	—	2	1	no	—
793	C₄×C₅₃	—	2	1	no	—
794	C₄×C₅₃	—	2	1	no	—
795	C₄×C₅₃	—	2	1	no	—
796	C₄×C₅₃	—	2	1	no	—
797	C₄×C₅₃	—	2	1	no	—
798	C₄×C₅₃	—	2	1	no	—
799	C₄×C₅₃	—	2	1	no	—
800	C₄×C₅₃	—	2	1	no	—
801	C₄×C₅₃	—	4	1	no	—
802	C₄×C₅₃	—	4	1	no	—
803	C₄×C₅₃	—	4	1	no	—
804	C₄×C₅₃	—	4	1	no	—
805	C₄×C₅₃	—	4	1	no	—
806	C₄×C₅₃	—	4	1	no	—
807	C₄×C₅₃	—	4	1	no	—
808	C₄×C₅₃	—	4	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	C₂×2₋¹⁺⁴	1	1	yes	characteristic
815	C₄×C₅₃	#585	1	1	yes	characteristic
816	#3565	C₂×C₅₃	1	1	yes	characteristic, complemented
817	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
818	#3386	C₂×C₅₃	1	1	yes	characteristic, complemented
819	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
820	#3377	C₂×C₅₃	1	1	yes	characteristic, complemented
821	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
822	#3357	C₂×C₅₃	1	1	yes	characteristic, complemented
823	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
824	#3346	C₂×C₅₃	1	1	yes	characteristic, complemented
825	#3345	C₂×C₅₃	1	1	yes	characteristic, complemented
826	#3344	C₂×C₅₃	1	1	yes	characteristic, complemented
827	#3343	C₂×C₅₃	1	1	yes	characteristic, complemented
828	#3323	C₂×C₅₃	1	1	yes	characteristic, complemented
829	#3322	C₂×C₅₃	1	1	yes	characteristic, complemented
830	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
831	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
832	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
833	#3307	C₂×C₅₃	1	1	yes	characteristic, complemented
834	#3263	C₂×C₅₃	1	1	yes	characteristic, complemented
835	#3262	C₂×C₅₃	1	1	yes	characteristic, complemented
836	#3252	C₂×C₅₃	1	1	yes	characteristic, complemented
837	#3244	C₂×C₅₃	1	1	yes	characteristic, complemented
838	#3243	C₂×C₅₃	1	1	yes	characteristic, complemented
839	#3237	C₂×C₅₃	1	1	yes	characteristic, complemented
840	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
841	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
842	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
843	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
844	#3083	C₂×C₅₃	1	1	yes	characteristic, complemented
845	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
846	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
847	C₂×C₅₃	—	4	1	no	—
848	C₂×C₅₃	—	4	1	no	—
849	C₂×C₅₃	—	4	1	no	—
850	C₂×C₅₃	—	4	2	no	—
851	C₂×C₅₃	—	8	1	no	—
852	C₂×C₅₃	—	8	1	no	—
853	C₂×C₅₃	#3489	1	1	yes	characteristic
854	C₂×C₅₃	#3585	1	1	yes	characteristic
855	C₂×C₅₃	#3586	1	1	yes	characteristic
856	#563	—	2	1	no	—
857	#562	—	2	1	no	—
858	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
859	#556	—	2	1	no	—
860	#556	C₂²×C₅₃	1	1	yes	characteristic
861	#556	C₂²×C₅₃	1	1	yes	characteristic
862	#555	C₂²×C₅₃	1	1	yes	characteristic
863	#554	C₂²×C₅₃	1	1	yes	characteristic
864	#554	C₂²×C₅₃	1	1	yes	characteristic
865	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
866	#553	C₂²×C₅₃	1	1	yes	characteristic
867	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
868	#552	—	2	1	no	—
869	#552	—	2	1	no	—
870	#552	C₂²×C₅₃	1	1	yes	characteristic
871	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
872	#551	—	2	1	no	—
873	#551	—	2	1	no	—
874	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
875	#548	—	2	1	no	—
876	#547	C₂²×C₅₃	1	1	yes	characteristic
877	#547	C₂²×C₅₃	1	1	yes	characteristic
878	#546	C₂²×C₅₃	1	1	yes	characteristic
879	#546	C₂²×C₅₃	1	1	yes	characteristic
880	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
881	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
882	#542	—	2	1	no	—
883	#542	—	2	1	no	—
884	#542	C₂²×C₅₃	1	1	yes	characteristic
885	#542	C₂²×C₅₃	1	1	yes	characteristic
886	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
888	#541	—	2	1	no	—
889	#539	—	2	1	no	—
890	#539	—	2	1	no	—
891	#539	—	2	1	no	—
892	#533	C₂²×C₅₃	1	1	yes	characteristic
893	#533	C₂²×C₅₃	1	1	yes	characteristic
894	#529	C₂²×C₅₃	1	1	yes	characteristic
895	#529	C₂²×C₅₃	1	1	yes	characteristic
896	#525	—	2	1	no	—
897	C₂×C₂²⋊Q₈	—	2	1	no	—
898	#520	C₂²×C₅₃	1	1	yes	characteristic
899	#520	C₂²×C₅₃	1	1	yes	characteristic
900	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
901	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
904	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#489	C₂²×C₅₃	1	1	yes	characteristic
910	#489	C₂²×C₅₃	1	1	yes	characteristic
911	#488	C₂²×C₅₃	1	1	yes	characteristic
912	#488	C₂²×C₅₃	1	1	yes	characteristic
913	#485	C₂²×C₅₃	1	1	yes	characteristic
914	#485	C₂²×C₅₃	1	1	yes	characteristic
915	#485	C₂²×C₅₃	1	1	yes	characteristic
916	#485	C₂²×C₅₃	1	1	yes	characteristic
917	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#483	C₂²×C₅₃	1	1	yes	characteristic
922	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#482	C₂²×C₅₃	1	1	yes	characteristic
925	#482	C₂²×C₅₃	1	1	yes	characteristic
926	#481	C₂²×C₅₃	1	1	yes	characteristic
927	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#480	C₂²×C₅₃	1	1	yes	characteristic
929	#480	C₂²×C₅₃	1	1	yes	characteristic
930	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#478	C₂²×C₅₃	1	1	yes	characteristic
936	#478	C₂²×C₅₃	1	1	yes	characteristic
937	#478	C₂²×C₅₃	1	1	yes	characteristic
938	#478	C₂²×C₅₃	1	1	yes	characteristic
939	#478	C₂²×C₅₃	1	1	yes	characteristic
940	#478	C₂²×C₅₃	1	1	yes	characteristic
941	#478	C₂²×C₅₃	1	1	yes	characteristic
942	#478	C₂²×C₅₃	1	1	yes	characteristic
943	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#476	C₂²×C₅₃	1	1	yes	characteristic
949	#476	C₂²×C₅₃	1	1	yes	characteristic
950	#476	C₂²×C₅₃	1	1	yes	characteristic
951	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#474	C₂²×C₅₃	1	1	yes	characteristic
958	#474	C₂²×C₅₃	1	1	yes	characteristic
959	#474	C₂²×C₅₃	1	1	yes	characteristic
960	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#470	C₂²×C₅₃	1	1	yes	characteristic
962	#470	C₂²×C₅₃	1	1	yes	characteristic
963	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#469	C₂²×C₅₃	1	1	yes	characteristic
965	#468	C₂²×C₅₃	1	1	yes	characteristic
966	#468	C₂²×C₅₃	1	1	yes	characteristic
967	#468	C₂²×C₅₃	1	1	yes	characteristic
968	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#466	C₂²×C₅₃	1	1	yes	characteristic
971	#465	C₂²×C₅₃	1	1	yes	characteristic
972	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#464	C₂²×C₅₃	1	1	yes	characteristic
974	#464	C₂²×C₅₃	1	1	yes	characteristic
975	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#463	C₂²×C₅₃	1	1	yes	characteristic
978	#463	C₂²×C₅₃	1	1	yes	characteristic
979	#463	C₂²×C₅₃	1	1	yes	characteristic
980	#463	C₂²×C₅₃	1	1	yes	characteristic
981	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#452	C₂²×C₅₃	1	1	yes	characteristic
984	#452	C₂²×C₅₃	1	1	yes	characteristic
985	#450	C₂²×C₅₃	1	1	yes	characteristic
986	#449	C₂²×C₅₃	1	1	yes	characteristic
987	#449	C₂²×C₅₃	1	1	yes	characteristic
988	#447	C₂²×C₅₃	1	1	yes	characteristic
989	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#442	C₂²×C₅₃	1	1	yes	characteristic
992	#442	C₂²×C₅₃	1	1	yes	characteristic
993	#442	C₂²×C₅₃	1	1	yes	characteristic
994	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#440	C₂²×C₅₃	1	1	yes	characteristic
996	#440	C₂²×C₅₃	1	1	yes	characteristic
997	#440	C₂²×C₅₃	1	1	yes	characteristic
998	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
1001	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1003	#436	C₂²×C₅₃	1	1	yes	characteristic
1004	#436	C₂²×C₅₃	1	1	yes	characteristic
1005	#435	C₂²×C₅₃	1	1	yes	characteristic
1006	#435	C₂²×C₅₃	1	1	yes	characteristic
1007	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#432	C₂²×C₅₃	1	1	yes	characteristic
1012	#428	C₂²×C₅₃	1	1	yes	characteristic
1013	#428	C₂²×C₅₃	1	1	yes	characteristic
1014	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#423	C₂²×C₅₃	1	1	yes	characteristic
1021	#418	C₂²×C₅₃	1	1	yes	characteristic
1022	#418	C₂²×C₅₃	1	1	yes	characteristic
1023	#417	C₂²×C₅₃	1	1	yes	characteristic
1024	#417	C₂²×C₅₃	1	1	yes	characteristic
1025	#416	C₂²×C₅₃	1	1	yes	characteristic
1026	#416	C₂²×C₅₃	1	1	yes	characteristic
1027	C₅₃	#62224	1	1	yes	characteristic, direct product factor, Sylow
1028	C₂×#41	—	2	1	no	—
1029	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1030	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1031	C₂²×Q₈	—	2	1	no	—
1032	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1033	C₂³×C₄	—	2	1	no	—
1034	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1035	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1036	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1037	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1038	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1039	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1040	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1041	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1042	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1043	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1044	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1045	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1046	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1047	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1048	C₄⋊Q₈	—	2	1	no	—
1049	C₄⋊Q₈	—	2	1	no	—
1050	C₄⋊Q₈	—	2	1	no	—
1051	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1052	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1053	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1054	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1055	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1056	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1057	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1058	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1059	#126	—	2	1	no	—
1060	#126	—	2	1	no	—
1061	#126	—	2	1	no	—
1062	#126	—	2	1	no	—
1063	#126	—	2	1	no	—
1064	#126	—	2	1	no	—
1065	#126	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1073	#126	D₄×C₅₃	1	1	yes	characteristic
1074	#125	—	2	1	no	—
1075	#125	—	2	1	no	—
1076	#125	—	2	1	no	—
1077	#125	—	2	1	no	—
1078	#125	—	2	1	no	—
1079	#125	—	2	1	no	—
1080	#125	—	2	1	no	—
1081	#125	—	2	1	no	—
1082	#125	—	2	1	no	—
1083	#125	D₄×C₅₃	1	1	yes	characteristic
1084	#125	C₂³×C₅₃	1	1	yes	characteristic
1085	#125	C₂³×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	#124	—	2	1	no	—
1090	#124	—	2	1	no	—
1091	#124	—	2	1	no	—
1092	#124	—	2	1	no	—
1093	#124	—	2	1	no	—
1094	#124	—	2	1	no	—
1095	#124	—	2	1	no	—
1096	#124	D₄×C₅₃	1	1	yes	characteristic
1097	#124	C₂³×C₅₃	1	1	yes	characteristic
1098	#124	C₂³×C₅₃	1	1	yes	characteristic
1099	#124	C₂³×C₅₃	1	1	yes	characteristic
1100	#123	—	2	1	no	—
1101	#123	—	2	1	no	—
1102	#123	—	2	1	no	—
1103	#123	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1116	#123	D₄×C₅₃	1	1	yes	characteristic
1117	C₂²⋊Q₈	—	2	1	no	—
1118	C₂²⋊Q₈	—	2	1	no	—
1119	C₂²⋊Q₈	—	2	1	no	—
1120	C₂²⋊Q₈	—	2	1	no	—
1121	C₂²⋊Q₈	—	2	1	no	—
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	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
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	D₄×C₅₃	1	1	yes	characteristic
1155	#121	C₂³×C₅₃	1	1	yes	characteristic
1156	#121	C₂³×C₅₃	1	1	yes	characteristic
1157	#121	C₂³×C₅₃	1	1	yes	characteristic
1158	#121	C₂³×C₅₃	1	1	yes	characteristic
1159	#121	C₂³×C₅₃	1	1	yes	characteristic
1160	#120	—	2	1	no	—
1161	#120	—	2	1	no	—
1162	C₄×Q₈	—	2	1	no	—
1163	C₄×Q₈	—	2	1	no	—
1164	C₄×Q₈	—	2	1	no	—
1165	C₄×Q₈	—	2	1	no	—
1166	C₄×Q₈	—	2	1	no	—
1167	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1168	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1169	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1170	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1171	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1172	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1173	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₄×D₄	—	2	1	no	—
1176	C₄×D₄	—	2	1	no	—
1177	C₄×D₄	—	2	1	no	—
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	C₂³×C₅₃	1	1	yes	characteristic
1187	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1188	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
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	#117	—	2	1	no	—
1199	#117	—	2	1	no	—
1200	#117	—	2	1	no	—
1201	#117	—	2	1	no	—
1202	#117	—	2	1	no	—
1203	#117	—	2	1	no	—
1204	#117	—	2	1	no	—
1205	#117	—	2	1	no	—
1206	#117	C₂³×C₅₃	1	1	yes	characteristic
1207	#117	C₂³×C₅₃	1	1	yes	characteristic
1208	#117	C₂³×C₅₃	1	1	yes	characteristic
1209	#117	C₂³×C₅₃	1	1	yes	characteristic
1210	#117	C₂³×C₅₃	1	1	yes	characteristic
1211	#117	C₂³×C₅₃	1	1	yes	characteristic
1212	C₂×C₄⋊C₄	—	2	1	no	—
1213	C₂×C₄⋊C₄	—	2	1	no	—
1214	C₂×C₄⋊C₄	—	2	1	no	—
1215	C₂×C₄⋊C₄	—	2	1	no	—
1216	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1217	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1218	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1219	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1221	C₂×C₂²⋊C₄	—	2	1	no	—
1222	C₂×C₂²⋊C₄	—	2	1	no	—
1223	C₂×C₂²⋊C₄	—	2	1	no	—
1224	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1225	#107	C₂³×C₅₃	1	1	yes	characteristic
1226	#107	C₂³×C₅₃	1	1	yes	characteristic
1227	#107	C₂³×C₅₃	1	1	yes	characteristic
1228	#107	C₂³×C₅₃	1	1	yes	characteristic
1229	#107	C₂³×C₅₃	1	1	yes	characteristic
1230	#107	C₂³×C₅₃	1	1	yes	characteristic
1231	#107	C₂³×C₅₃	1	1	yes	characteristic
1232	#107	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	#106	C₂³×C₅₃	1	1	yes	characteristic
1238	#106	C₂³×C₅₃	1	1	yes	characteristic
1239	#106	C₂³×C₅₃	1	1	yes	characteristic
1240	#106	C₂³×C₅₃	1	1	yes	characteristic
1241	#106	C₂³×C₅₃	1	1	yes	characteristic
1242	#106	C₂³×C₅₃	1	1	yes	characteristic
1243	#106	C₂³×C₅₃	1	1	yes	characteristic
1244	#106	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	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1250	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1251	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1252	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1253	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1254	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1255	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1256	C₄⋊C₈	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	#103	C₂³×C₅₃	1	1	yes	characteristic
1260	#103	C₂³×C₅₃	1	1	yes	characteristic
1261	#103	C₂³×C₅₃	1	1	yes	characteristic
1262	#103	C₂³×C₅₃	1	1	yes	characteristic
1263	#103	C₂³×C₅₃	1	1	yes	characteristic
1264	#103	C₂³×C₅₃	1	1	yes	characteristic
1265	#103	C₂³×C₅₃	1	1	yes	characteristic
1266	#103	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	#102	C₂³×C₅₃	1	1	yes	characteristic
1276	#102	C₂³×C₅₃	1	1	yes	characteristic
1277	#102	C₂³×C₅₃	1	1	yes	characteristic
1278	#102	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	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1292	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1293	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1294	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1295	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1296	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1297	#97	C₂³×C₅₃	1	1	yes	characteristic
1298	#97	C₂³×C₅₃	1	1	yes	characteristic
1299	#97	C₂³×C₅₃	1	1	yes	characteristic
1300	#97	C₂³×C₅₃	1	1	yes	characteristic
1301	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1302	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1303	C₂⁴	—	2	1	no	—
1304	#41	—	2	2	no	—
1305	#41	—	2	2	no	—
1306	#41	—	4	1	no	—
1307	#41	—	4	1	no	—
1308	#41	—	8	2	no	—
1309	C₂×Q₈	—	2	1	no	—
1310	C₂×Q₈	—	2	1	no	—
1311	C₂×Q₈	—	2	1	no	—
1312	C₂×Q₈	—	2	1	no	—
1313	C₂×Q₈	—	2	1	no	—
1314	C₂×Q₈	—	2	1	no	—
1315	C₂×Q₈	—	2	1	no	—
1316	C₂×Q₈	—	8	2	no	—
1317	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1318	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1319	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1320	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1321	C₂×D₄	—	2	2	no	—
1322	C₂×D₄	—	2	1	no	—
1323	C₂×D₄	—	2	1	no	—
1324	C₂×D₄	—	2	1	no	—
1325	C₂×D₄	—	2	1	no	—
1326	C₂×D₄	—	2	1	no	—
1327	C₂×D₄	—	2	1	no	—
1328	C₂×D₄	—	2	1	no	—
1329	C₂×D₄	—	2	1	no	—
1330	C₂×D₄	—	4	1	no	—
1331	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1332	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1333	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1334	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1335	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1336	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1337	C₂²×C₄	—	2	1	no	—
1338	C₂²×C₄	—	2	1	no	—
1339	C₂²×C₄	—	2	1	no	—
1340	C₂²×C₄	—	2	1	no	—
1341	C₂²×C₄	—	2	1	no	—
1342	C₂²×C₄	—	2	1	no	—
1343	C₂²×C₄	—	2	1	no	—
1344	C₂²×C₄	—	2	1	no	—
1345	C₂²×C₄	—	2	1	no	—
1346	C₂²×C₄	—	2	1	no	—
1347	C₂²×C₄	—	2	1	no	—
1348	C₂²×C₄	—	2	1	no	—
1349	C₂²×C₄	—	2	1	no	—
1350	C₂²×C₄	—	2	1	no	—
1351	C₂²×C₄	—	2	1	no	—
1352	C₂²×C₄	—	2	1	no	—
1353	C₂²×C₄	—	8	2	no	—
1354	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1355	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1356	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1357	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1358	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1359	Q₁₆	—	4	1	no	—
1360	Q₁₆	—	4	1	no	—
1361	SD₁₆	—	2	2	no	—
1362	SD₁₆	—	4	1	no	—
1363	SD₁₆	—	4	1	no	—
1364	SD₁₆	—	4	1	no	—
1365	D₈	—	2	2	no	—
1366	D₈	—	4	1	no	—
1367	M₁₆	—	4	1	no	—
1368	M₁₆	—	4	1	no	—
1369	M₁₆	—	4	1	no	—
1370	M₁₆	—	4	1	no	—
1371	C₂×C₈	—	4	1	no	—
1372	C₂×C₈	—	4	1	no	—
1373	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1374	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1375	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1376	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1377	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1378	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1379	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1380	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1381	C₄⋊C₄	—	2	1	no	—
1382	C₄⋊C₄	—	2	1	no	—
1383	C₄⋊C₄	—	2	1	no	—
1384	C₄⋊C₄	—	2	1	no	—
1385	C₄⋊C₄	—	2	1	no	—
1386	C₄⋊C₄	—	2	1	no	—
1387	C₄⋊C₄	—	2	1	no	—
1388	C₄⋊C₄	—	2	1	no	—
1389	C₄⋊C₄	—	2	1	no	—
1390	C₄⋊C₄	—	2	1	no	—
1391	C₄⋊C₄	—	2	1	no	—
1392	C₄⋊C₄	—	2	1	no	—
1393	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1420	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1421	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1422	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1423	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1424	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	C₂⁴×C₅₃	1	1	yes	characteristic
1430	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1431	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1432	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1433	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1434	C₄⋊C₄	C₂⁴×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	C₂²⋊C₄	—	2	1	no	—
1440	C₂²⋊C₄	—	2	1	no	—
1441	C₂²⋊C₄	—	2	1	no	—
1442	C₂²⋊C₄	—	2	1	no	—
1443	C₂²⋊C₄	—	2	1	no	—
1444	C₂²⋊C₄	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1471	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1472	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1473	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1474	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1475	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1476	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1477	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1478	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1479	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1480	C₄²	—	2	1	no	—
1481	C₄²	—	2	1	no	—
1482	C₄²	—	2	1	no	—
1483	C₄²	—	2	1	no	—
1484	C₄²	—	2	1	no	—
1485	C₄²	—	2	1	no	—
1486	C₄²	—	2	1	no	—
1487	C₄²	—	2	1	no	—
1488	C₄²	—	2	1	no	—
1489	C₄²	—	2	1	no	—
1490	C₄²	—	2	1	no	—
1491	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1492	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1493	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1494	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1495	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1496	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1497	C₂³	—	2	1	no	—
1498	C₂³	—	2	1	no	—
1499	C₂³	—	2	1	no	—
1500	C₂³	—	4	2	no	—
1501	C₂³	—	4	2	no	—
1502	C₂³	—	8	1	no	—
1503	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1504	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1505	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1506	Q₈	—	2	1	no	—
1507	Q₈	—	2	1	no	—
1508	Q₈	—	2	1	no	—
1509	Q₈	—	2	1	no	—
1510	Q₈	—	2	1	no	—
1511	Q₈	—	2	1	no	—
1512	Q₈	—	4	1	no	—
1513	Q₈	—	4	2	no	—
1514	Q₈	—	8	1	no	—
1515	Q₈	—	8	1	no	—
1516	Q₈	—	8	1	no	—
1517	Q₈	—	8	1	no	—
1518	Q₈	—	8	1	no	—
1519	Q₈	—	8	1	no	—
1520	D₄	—	2	1	no	—
1521	D₄	—	2	1	no	—
1522	D₄	—	2	1	no	—
1523	D₄	—	2	1	no	—
1524	D₄	—	2	1	no	—
1525	D₄	—	4	1	no	—
1526	D₄	—	4	1	no	—
1527	D₄	—	4	1	no	—
1528	D₄	—	4	2	no	—
1529	D₄	—	4	2	no	—
1530	D₄	—	4	2	no	—
1531	D₄	—	8	1	no	—
1532	D₄	—	8	1	no	—
1533	D₄	—	8	1	no	—
1534	D₄	—	8	1	no	—
1535	D₄	—	8	1	no	—
1536	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1537	C₂×C₄	—	2	1	no	—
1538	C₂×C₄	—	2	1	no	—
1539	C₂×C₄	—	2	1	no	—
1540	C₂×C₄	—	2	1	no	—
1541	C₂×C₄	—	2	1	no	—
1542	C₂×C₄	—	2	1	no	—
1543	C₂×C₄	—	2	1	no	—
1544	C₂×C₄	—	2	1	no	—
1545	C₂×C₄	—	2	1	no	—
1546	C₂×C₄	—	2	1	no	—
1547	C₂×C₄	—	2	1	no	—
1548	C₂×C₄	—	2	1	no	—
1549	C₂×C₄	—	2	1	no	—
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	—	4	1	no	—
1557	C₂×C₄	—	4	1	no	—
1558	C₂×C₄	—	4	2	no	—
1559	C₂×C₄	—	4	2	no	—
1560	C₂×C₄	—	4	2	no	—
1561	C₂×C₄	—	4	2	no	—
1562	C₂×C₄	—	8	1	no	—
1563	C₂×C₄	—	8	1	no	—
1564	C₂×C₄	—	8	1	no	—
1565	C₂×C₄	—	8	1	no	—
1566	C₂×C₄	—	8	1	no	—
1567	C₂×C₄	—	8	1	no	—
1568	C₂×C₄	—	8	1	no	—
1569	C₂×C₄	—	8	1	no	—
1570	C₂×C₄	—	8	1	no	—
1571	C₂×C₄	—	8	1	no	—
1572	C₂×C₄	—	8	1	no	—
1573	C₂×C₄	—	8	1	no	—
1574	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1575	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1576	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1577	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1578	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1579	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1580	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1581	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1582	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1583	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1584	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1585	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1586	C₈	—	2	1	no	—
1587	C₈	—	2	1	no	—
1588	C₈	—	2	1	no	—
1589	C₈	—	2	1	no	—
1590	C₈	—	2	1	no	—
1591	C₈	—	2	1	no	—
1592	C₈	—	2	1	no	—
1593	C₈	—	2	1	no	—
1594	C₂²	—	2	1	no	—
1595	C₂²	—	2	1	no	—
1596	C₂²	—	2	1	no	—
1597	C₂²	—	2	2	no	—
1598	C₂²	—	2	1	no	—
1599	C₂²	—	2	1	no	—
1600	C₂²	—	2	1	no	—
1601	C₂²	—	2	1	no	—
1602	C₂²	—	2	1	no	—
1603	C₂²	—	2	1	no	—
1604	C₂²	—	4	1	no	—
1605	C₂²	—	4	1	no	—
1606	C₂²	—	4	1	no	—
1607	C₂²	—	4	1	no	—
1608	C₂²	—	4	1	no	—
1609	C₂²	—	4	1	no	—
1610	C₂²	—	4	1	no	—
1611	C₂²	—	4	1	no	—
1612	C₂²	—	8	4	no	—
1613	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1614	C₄	—	2	1	no	—
1615	C₄	—	2	1	no	—
1616	C₄	—	2	1	no	—
1617	C₄	—	2	1	no	—
1618	C₄	—	2	1	no	—
1619	C₄	—	2	1	no	—
1620	C₄	—	2	1	no	—
1621	C₄	—	2	1	no	—
1622	C₄	—	2	1	no	—
1623	C₄	—	2	1	no	—
1624	C₄	—	2	1	no	—
1625	C₄	—	4	1	no	—
1626	C₄	—	4	1	no	—
1627	C₄	—	4	1	no	—
1628	C₄	—	4	1	no	—
1629	C₄	—	4	1	no	—
1630	C₄	—	4	1	no	—
1631	C₄	—	4	1	no	—
1632	C₄	—	4	1	no	—
1633	C₄	—	4	1	no	—
1634	C₄	—	4	1	no	—
1635	C₄	—	4	1	no	—
1636	C₄	—	4	1	no	—
1637	C₄	—	4	1	no	—
1638	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1639	C₄	C₅₃×#585	1	1	yes	characteristic
1640	C₂	—	4	1	no	—
1641	C₂	—	4	1	no	—
1642	C₂	—	4	1	no	—
1643	C₂	—	4	2	no	—
1644	C₂	—	8	1	no	—
1645	C₂	—	8	1	no	—
1646	C₂	C₅₃×#3489	1	1	yes	characteristic
1647	C₂	C₅₃×#3585	1	1	yes	characteristic
1648	C₂	C₅₃×#3586	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×#3565	C₂	semidirect
2. C₅₃×#3520	C₂	semidirect
3. C₅₃×#3386	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3377	C₂	semidirect
6. C₅₃×#3376	C₂	semidirect
7. C₅₃×#3357	C₂	semidirect
8. C₅₃×#3356	C₂	semidirect
9. C₅₃×#3346	C₂	semidirect
10. C₅₃×#3345	C₂	semidirect
11. C₅₃×#3344	C₂	semidirect
12. C₅₃×#3343	C₂	semidirect
13. C₅₃×#3323	C₂	semidirect
14. C₅₃×#3322	C₂	semidirect
15. C₅₃×#3319	C₂	semidirect
16. C₅₃×#3315	C₂	semidirect
17. C₅₃×#3311	C₂	semidirect
18. C₅₃×#3307	C₂	semidirect
19. C₅₃×#3263	C₂	semidirect
20. C₅₃×#3262	C₂	semidirect
21. C₅₃×#3252	C₂	semidirect
22. C₅₃×#3244	C₂	semidirect
23. C₅₃×#3243	C₂	semidirect
24. C₅₃×#3237	C₂	semidirect
25. C₅₃×#3125	C₂	semidirect
26. C₅₃×#3124	C₂	semidirect
27. C₅₃×#3114	C₂	semidirect
28. C₅₃×#3084	C₂	semidirect
29. C₅₃×#3083	C₂	semidirect
30. C₅₃×#3077	C₂	semidirect
31. C₅₃×#2995	C₂	semidirect
34. C₅₃×#557	C₂²	semidirect
41. C₅₃×#554	C₂²	semidirect
43. C₅₃×#553	C₂²	semidirect
47. C₅₃×#552	C₂²	semidirect
56. C₅₃×#544	C₂²	semidirect
57. C₅₃×#544	C₂²	semidirect
62. C₅₃×#542	C₂²	semidirect
63. C₅₃×#542	C₂²	semidirect
77. C₅₃×#501	C₂²	semidirect
78. C₅₃×#501	C₂²	semidirect
79. C₅₃×#501	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#500	C₂²	semidirect
82. C₅₃×#498	C₂²	semidirect
83. C₅₃×#491	C₂²	semidirect
84. C₅₃×#491	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#484	C₂²	semidirect
96. C₅₃×#484	C₂²	semidirect
98. C₅₃×#483	C₂²	semidirect
99. C₅₃×#483	C₂²	semidirect
103. 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
119. C₅₃×#477	C₂²	semidirect
120. C₅₃×#477	C₂²	semidirect
121. C₅₃×#477	C₂²	semidirect
122. C₅₃×#477	C₂²	semidirect
123. C₅₃×#477	C₂²	semidirect
127. C₅₃×#476	C₂²	semidirect
128. C₅₃×#476	C₂²	semidirect
129. C₅₃×#475	C₂²	semidirect
130. C₅₃×#475	C₂²	semidirect
131. C₅₃×#475	C₂²	semidirect
132. C₅₃×#475	C₂²	semidirect
136. C₅₃×#474	C₂²	semidirect
139. C₅₃×#470	C₂²	semidirect
144. C₅₃×#468	C₂²	semidirect
145. C₅₃×#467	C₂²	semidirect
148. C₅₃×#465	C₂²	semidirect
151. C₅₃×#464	C₂²	semidirect
152. C₅₃×#464	C₂²	semidirect
157. C₅₃×#462	C₂²	semidirect
158. C₅₃×#461	C₂²	semidirect
165. C₅₃×#446	C₂²	semidirect
166. C₅₃×#446	C₂²	semidirect
170. C₅₃×#441	C₂²	semidirect
174. C₅₃×#440	C₂²	semidirect
175. C₄×Q₁₆×C₅₃	C₂²	semidirect
177. C₄×SD₁₆×C₅₃	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#433	C₂²	semidirect
186. C₅₃×#433	C₂²	semidirect
190. C₅₃×#428	C₂²	semidirect
191. C₅₃×#428	C₂²	semidirect
192. C₂×#107×C₅₃	C₂²	semidirect
193. C₂×#106×C₅₃	C₂²	semidirect
194. C₅₃×#424	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
769. #62224	C₅₃	direct (N × H)
816. #3565	C₂×C₅₃	semidirect
817. #3520	C₂×C₅₃	semidirect
818. #3386	C₂×C₅₃	semidirect
819. #3384	C₂×C₅₃	semidirect
820. #3377	C₂×C₅₃	semidirect
821. #3376	C₂×C₅₃	semidirect
822. #3357	C₂×C₅₃	semidirect
823. #3356	C₂×C₅₃	semidirect
824. #3346	C₂×C₅₃	semidirect
825. #3345	C₂×C₅₃	semidirect
826. #3344	C₂×C₅₃	semidirect
827. #3343	C₂×C₅₃	semidirect
828. #3323	C₂×C₅₃	semidirect
829. #3322	C₂×C₅₃	semidirect
830. #3319	C₂×C₅₃	semidirect
831. #3315	C₂×C₅₃	semidirect
832. #3311	C₂×C₅₃	semidirect
833. #3307	C₂×C₅₃	semidirect
834. #3263	C₂×C₅₃	semidirect
835. #3262	C₂×C₅₃	semidirect
836. #3252	C₂×C₅₃	semidirect
837. #3244	C₂×C₅₃	semidirect
838. #3243	C₂×C₅₃	semidirect
839. #3237	C₂×C₅₃	semidirect
840. #3125	C₂×C₅₃	semidirect
841. #3124	C₂×C₅₃	semidirect
842. #3114	C₂×C₅₃	semidirect
843. #3084	C₂×C₅₃	semidirect
844. #3083	C₂×C₅₃	semidirect
845. #3077	C₂×C₅₃	semidirect
846. #2995	C₂×C₅₃	semidirect
858. #557	C₂²×C₅₃	semidirect
865. #554	C₂²×C₅₃	semidirect
867. #553	C₂²×C₅₃	semidirect
871. #552	C₂²×C₅₃	semidirect
880. #544	C₂²×C₅₃	semidirect
881. #544	C₂²×C₅₃	semidirect
886. #542	C₂²×C₅₃	semidirect
887. #542	C₂²×C₅₃	semidirect
901. #501	C₂²×C₅₃	semidirect
902. #501	C₂²×C₅₃	semidirect
903. #501	C₂²×C₅₃	semidirect
904. #501	C₂²×C₅₃	semidirect
905. #500	C₂²×C₅₃	semidirect
906. #498	C₂²×C₅₃	semidirect
907. #491	C₂²×C₅₃	semidirect
908. #491	C₂²×C₅₃	semidirect
917. #485	C₂²×C₅₃	semidirect
918. #485	C₂²×C₅₃	semidirect
919. #484	C₂²×C₅₃	semidirect
920. #484	C₂²×C₅₃	semidirect
922. #483	C₂²×C₅₃	semidirect
923. #483	C₂²×C₅₃	semidirect
927. #481	C₂²×C₅₃	semidirect
930. #480	C₂²×C₅₃	semidirect
931. #479	C₂²×C₅₃	semidirect
932. #479	C₂²×C₅₃	semidirect
933. #479	C₂²×C₅₃	semidirect
934. #479	C₂²×C₅₃	semidirect
943. #477	C₂²×C₅₃	semidirect
944. #477	C₂²×C₅₃	semidirect
945. #477	C₂²×C₅₃	semidirect
946. #477	C₂²×C₅₃	semidirect
947. #477	C₂²×C₅₃	semidirect
951. #476	C₂²×C₅₃	semidirect
952. #476	C₂²×C₅₃	semidirect
953. #475	C₂²×C₅₃	semidirect
954. #475	C₂²×C₅₃	semidirect
955. #475	C₂²×C₅₃	semidirect
956. #475	C₂²×C₅₃	semidirect
960. #474	C₂²×C₅₃	semidirect
963. #470	C₂²×C₅₃	semidirect
968. #468	C₂²×C₅₃	semidirect
969. #467	C₂²×C₅₃	semidirect
972. #465	C₂²×C₅₃	semidirect
975. #464	C₂²×C₅₃	semidirect
976. #464	C₂²×C₅₃	semidirect
981. #462	C₂²×C₅₃	semidirect
982. #461	C₂²×C₅₃	semidirect
989. #446	C₂²×C₅₃	semidirect
990. #446	C₂²×C₅₃	semidirect
994. #441	C₂²×C₅₃	semidirect
998. #440	C₂²×C₅₃	semidirect
999. C₄×Q₁₆	C₂²×C₅₃	semidirect
1001. C₄×SD₁₆	C₂²×C₅₃	semidirect
1007. #435	C₂²×C₅₃	semidirect
1008. #435	C₂²×C₅₃	semidirect
1009. #433	C₂²×C₅₃	semidirect
1010. #433	C₂²×C₅₃	semidirect
1014. #428	C₂²×C₅₃	semidirect
1015. #428	C₂²×C₅₃	semidirect
1016. C₂×#107	C₂²×C₅₃	semidirect
1017. C₂×#106	C₂²×C₅₃	semidirect
1018. #424	C₂²×C₅₃	semidirect
1019. #424	C₂²×C₅₃	semidirect
1027. C₅₃	#62224	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×#3565	2
C₅₃×#3520	2
C₅₃×#3386	2
C₅₃×#3384	2
C₅₃×#3377	2
C₅₃×#3376	2
C₅₃×#3357	2
C₅₃×#3356	2
C₅₃×#3346	2
C₅₃×#3345	2
C₅₃×#3344	2
C₅₃×#3343	2
C₅₃×#3323	2
C₅₃×#3322	2
C₅₃×#3319	2
C₅₃×#3315	2
C₅₃×#3311	2
C₅₃×#3307	2
C₅₃×#3263	2
C₅₃×#3262	2
C₅₃×#3252	2
C₅₃×#3244	2
C₅₃×#3243	2
C₅₃×#3237	2
C₅₃×#3125	2
C₅₃×#3124	2
C₅₃×#3114	2
C₅₃×#3084	2
C₅₃×#3083	2
C₅₃×#3077	2
C₅₃×#2995	2
#62224	53

Subgroups — C53×#62224 #27269736

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62224 #27269736