Subgroups — C₅₃×#61510 #27269022

Order 13568.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3521	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3402	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×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3346	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3343	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3322	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3178	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3173	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3172	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3120	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2967	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2951	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
31	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#556	C₂²	1	1	yes	characteristic
36	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#554	C₂²	1	1	yes	characteristic
39	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
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×#552	—	2	1	no	—
44	C₅₃×#552	—	2	1	no	—
45	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#551	—	2	1	no	—
47	C₅₃×#551	—	2	1	no	—
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×#547	C₂²	1	1	yes	characteristic
55	C₅₃×#546	C₂²	1	1	yes	characteristic
56	C₅₃×#546	C₂²	1	1	yes	characteristic
57	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#542	C₂²	1	1	yes	characteristic
60	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#539	—	2	1	no	—
64	C₅₃×#539	—	2	1	no	—
65	C₅₃×#539	—	2	1	no	—
66	C₅₃×#538	—	2	1	no	—
67	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#529	—	2	1	no	—
69	C₅₃×#529	C₂²	1	1	yes	characteristic
70	C₅₃×#529	C₂²	1	1	yes	characteristic
71	C₂×#126×C₅₃	—	2	1	no	—
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, complemented
76	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
78	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#495	C₂²	1	1	yes	characteristic
86	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#487	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×#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, complemented
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×#481	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#480	C₂²	1	1	yes	characteristic
103	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#469	C₂²	1	1	yes	characteristic
121	C₅₃×#468	C₂²	1	1	yes	characteristic
122	C₅₃×#468	C₂²	1	1	yes	characteristic
123	C₅₃×#468	C₂²	1	1	yes	characteristic
124	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#465	C₂²	1	1	yes	characteristic
126	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic
131	C₅₃×#463	C₂²	1	1	yes	characteristic
132	C₅₃×#463	C₂²	1	1	yes	characteristic
133	C₅₃×#463	C₂²	1	1	yes	characteristic
134	C₅₃×#463	C₂²	1	1	yes	characteristic
135	C₅₃×#463	C₂²	1	1	yes	characteristic
136	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#452	C₂²	1	1	yes	characteristic
141	C₅₃×#452	C₂²	1	1	yes	characteristic
142	C₅₃×#452	C₂²	1	1	yes	characteristic
143	C₅₃×#452	C₂²	1	1	yes	characteristic
144	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#449	C₂²	1	1	yes	characteristic
149	C₅₃×#449	C₂²	1	1	yes	characteristic
150	C₅₃×#447	C₂²	1	1	yes	characteristic
151	C₅₃×#447	C₂²	1	1	yes	characteristic
152	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#442	C₂²	1	1	yes	characteristic
155	C₅₃×#442	C₂²	1	1	yes	characteristic
156	C₅₃×#442	C₂²	1	1	yes	characteristic
157	C₅₃×#442	C₂²	1	1	yes	characteristic
158	C₅₃×#442	C₂²	1	1	yes	characteristic
159	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
170	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
181	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
182	C₅₃×#436	C₂²	1	1	yes	characteristic
183	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic
185	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
193	C₂×#107×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#417	C₂²	1	1	yes	characteristic
196	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#416	C₂²	1	1	yes	characteristic
199	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
202	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
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	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₅₃	—	2	1	no	—
209	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	—	2	1	no	—
212	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
213	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
214	#135×C₅₃	—	2	4	no	—
215	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
248	#126×C₅₃	—	2	1	no	—
249	#126×C₅₃	—	2	1	no	—
250	#126×C₅₃	—	2	1	no	—
251	#126×C₅₃	—	2	1	no	—
252	#126×C₅₃	—	2	1	no	—
253	#126×C₅₃	—	2	1	no	—
254	#126×C₅₃	—	2	1	no	—
255	#126×C₅₃	—	2	1	no	—
256	#126×C₅₃	—	2	1	no	—
257	#126×C₅₃	D₄	1	1	yes	characteristic
258	#126×C₅₃	D₄	1	1	yes	characteristic
259	#125×C₅₃	—	2	1	no	—
260	#125×C₅₃	—	2	1	no	—
261	#125×C₅₃	—	2	1	no	—
262	#125×C₅₃	—	2	1	no	—
263	#125×C₅₃	—	2	1	no	—
264	#125×C₅₃	—	2	1	no	—
265	#125×C₅₃	D₄	1	1	yes	characteristic
266	#125×C₅₃	C₂³	1	1	yes	characteristic
267	#125×C₅₃	C₂³	1	1	yes	characteristic
268	#124×C₅₃	—	2	1	no	—
269	#124×C₅₃	—	2	1	no	—
270	#124×C₅₃	—	2	1	no	—
271	#124×C₅₃	—	2	1	no	—
272	#124×C₅₃	D₄	1	1	yes	characteristic
273	#124×C₅₃	C₂³	1	1	yes	characteristic
274	#124×C₅₃	C₂³	1	1	yes	characteristic
275	#124×C₅₃	C₂³	1	1	yes	characteristic
276	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
291	#123×C₅₃	—	2	1	no	—
292	#123×C₅₃	—	2	1	no	—
293	#123×C₅₃	D₄	1	1	yes	characteristic
294	#123×C₅₃	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
313	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊Q₈×C₅₃	C₂³	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	#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	—	2	1	no	—
327	#121×C₅₃	—	2	1	no	—
328	#121×C₅₃	D₄	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	#120×C₅₃	—	2	1	no	—
334	#120×C₅₃	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
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×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×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	—	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	—	2	1	no	—
362	C₄×D₄×C₅₃	—	2	1	no	—
363	C₄×D₄×C₅₃	—	2	1	no	—
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	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
379	#117×C₅₃	—	2	1	no	—
380	#117×C₅₃	—	2	1	no	—
381	#117×C₅₃	—	2	1	no	—
382	#117×C₅₃	—	2	1	no	—
383	#117×C₅₃	—	2	1	no	—
384	#117×C₅₃	—	2	1	no	—
385	#117×C₅₃	—	2	1	no	—
386	#117×C₅₃	—	2	1	no	—
387	#117×C₅₃	—	2	1	no	—
388	#117×C₅₃	C₂³	1	1	yes	characteristic
389	#117×C₅₃	C₂³	1	1	yes	characteristic
390	#117×C₅₃	C₂³	1	1	yes	characteristic
391	#117×C₅₃	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
398	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
399	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
400	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
401	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
402	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
403	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
404	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
405	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
406	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
407	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂×C₄²×C₅₃	—	2	1	no	—
410	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
411	#107×C₅₃	C₂³	1	1	yes	characteristic
412	#107×C₅₃	C₂³	1	1	yes	characteristic
413	#107×C₅₃	C₂³	1	1	yes	characteristic
414	#107×C₅₃	C₂³	1	1	yes	characteristic
415	#107×C₅₃	C₂³	1	1	yes	characteristic
416	#107×C₅₃	C₂³	1	1	yes	characteristic
417	#107×C₅₃	C₂³	1	1	yes	characteristic
418	#107×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	#106×C₅₃	C₂³	1	1	yes	characteristic
425	#106×C₅₃	C₂³	1	1	yes	characteristic
426	#106×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	#103×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	#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	C₂²⋊C₈×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	#97×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	#97×C₅₃	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂⁴×C₅₃	—	2	1	no	—
482	C₂⁴×C₅₃	—	2	1	no	—
483	#41×C₅₃	—	2	2	no	—
484	#41×C₅₃	—	2	2	no	—
485	#41×C₅₃	—	2	2	no	—
486	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	4	1	no	—
488	#41×C₅₃	—	4	1	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	8	2	no	—
492	C₂×Q₈×C₅₃	—	2	1	no	—
493	C₂×Q₈×C₅₃	—	2	1	no	—
494	C₂×Q₈×C₅₃	—	2	1	no	—
495	C₂×Q₈×C₅₃	—	2	1	no	—
496	C₂×Q₈×C₅₃	—	8	2	no	—
497	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
498	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
500	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
501	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
502	C₂×D₄×C₅₃	—	2	2	no	—
503	C₂×D₄×C₅₃	—	2	2	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	—	2	1	no	—
510	C₂×D₄×C₅₃	—	2	1	no	—
511	C₂×D₄×C₅₃	—	2	1	no	—
512	C₂×D₄×C₅₃	—	2	1	no	—
513	C₂×D₄×C₅₃	—	2	1	no	—
514	C₂×D₄×C₅₃	—	4	1	no	—
515	C₂×D₄×C₅₃	—	4	1	no	—
516	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
517	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
520	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
522	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
535	C₂²×C₄×C₅₃	—	2	1	no	—
536	C₂²×C₄×C₅₃	—	2	1	no	—
537	C₂²×C₄×C₅₃	—	2	1	no	—
538	C₂²×C₄×C₅₃	—	2	1	no	—
539	C₂²×C₄×C₅₃	—	2	1	no	—
540	C₂²×C₄×C₅₃	—	2	1	no	—
541	C₂²×C₄×C₅₃	—	2	1	no	—
542	C₂²×C₄×C₅₃	—	2	1	no	—
543	C₂²×C₄×C₅₃	—	8	2	no	—
544	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
545	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
546	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
547	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
548	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
549	Q₁₆×C₅₃	—	2	2	no	—
550	Q₁₆×C₅₃	—	4	1	no	—
551	Q₁₆×C₅₃	—	4	1	no	—
552	Q₁₆×C₅₃	—	4	1	no	—
553	SD₁₆×C₅₃	—	2	2	no	—
554	SD₁₆×C₅₃	—	2	2	no	—
555	SD₁₆×C₅₃	—	2	2	no	—
556	SD₁₆×C₅₃	—	2	2	no	—
557	SD₁₆×C₅₃	—	2	2	no	—
558	SD₁₆×C₅₃	—	2	2	no	—
559	SD₁₆×C₅₃	—	4	1	no	—
560	SD₁₆×C₅₃	—	4	1	no	—
561	D₈×C₅₃	—	2	2	no	—
562	D₈×C₅₃	—	2	2	no	—
563	D₈×C₅₃	—	4	1	no	—
564	D₈×C₅₃	#41	1	4	yes	complemented
565	M₁₆×C₅₃	—	2	2	no	—
566	M₁₆×C₅₃	—	2	2	no	—
567	M₁₆×C₅₃	—	4	1	no	—
568	M₁₆×C₅₃	—	4	1	no	—
569	C₂×C₈×C₅₃	—	2	2	no	—
570	C₂×C₈×C₅₃	—	4	1	no	—
571	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
572	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
573	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
574	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
576	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
577	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
578	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
595	C₄⋊C₄×C₅₃	—	2	1	no	—
596	C₄⋊C₄×C₅₃	—	2	1	no	—
597	C₄⋊C₄×C₅₃	—	2	1	no	—
598	C₄⋊C₄×C₅₃	—	2	1	no	—
599	C₄⋊C₄×C₅₃	—	2	1	no	—
600	C₄⋊C₄×C₅₃	—	2	1	no	—
601	C₄⋊C₄×C₅₃	—	2	1	no	—
602	C₄⋊C₄×C₅₃	—	2	1	no	—
603	C₄⋊C₄×C₅₃	—	2	1	no	—
604	C₄⋊C₄×C₅₃	—	2	1	no	—
605	C₄⋊C₄×C₅₃	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
616	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
617	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
618	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
619	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
620	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
621	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
622	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
623	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
624	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
625	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
626	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
627	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
628	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
664	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
665	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
666	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
667	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
668	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
669	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
670	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
671	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
672	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
673	C₄²×C₅₃	—	2	1	no	—
674	C₄²×C₅₃	—	2	1	no	—
675	C₄²×C₅₃	—	2	1	no	—
676	C₄²×C₅₃	—	2	1	no	—
677	C₄²×C₅₃	—	2	1	no	—
678	C₄²×C₅₃	—	2	1	no	—
679	C₄²×C₅₃	—	2	1	no	—
680	C₄²×C₅₃	—	2	1	no	—
681	C₄²×C₅₃	—	2	1	no	—
682	C₄²×C₅₃	—	2	1	no	—
683	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
685	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
686	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
687	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
688	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
689	C₂³×C₅₃	—	2	1	no	—
690	C₂³×C₅₃	—	2	1	no	—
691	C₂³×C₅₃	—	2	1	no	—
692	C₂³×C₅₃	—	2	1	no	—
693	C₂³×C₅₃	—	4	2	no	—
694	C₂³×C₅₃	—	4	2	no	—
695	C₂³×C₅₃	—	4	2	no	—
696	C₂³×C₅₃	—	8	1	no	—
697	C₂³×C₅₃	—	8	1	no	—
698	C₂³×C₅₃	—	8	1	no	—
699	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
700	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
701	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
702	Q₈×C₅₃	—	2	1	no	—
703	Q₈×C₅₃	—	2	1	no	—
704	Q₈×C₅₃	—	2	1	no	—
705	Q₈×C₅₃	—	2	1	no	—
706	Q₈×C₅₃	—	2	1	no	—
707	Q₈×C₅₃	—	2	1	no	—
708	Q₈×C₅₃	—	2	1	no	—
709	Q₈×C₅₃	—	2	1	no	—
710	Q₈×C₅₃	—	4	1	no	—
711	Q₈×C₅₃	—	4	2	no	—
712	Q₈×C₅₃	—	8	1	no	—
713	Q₈×C₅₃	—	8	1	no	—
714	Q₈×C₅₃	—	8	1	no	—
715	D₄×C₅₃	—	2	1	no	—
716	D₄×C₅₃	—	2	1	no	—
717	D₄×C₅₃	—	2	1	no	—
718	D₄×C₅₃	—	2	1	no	—
719	D₄×C₅₃	—	2	1	no	—
720	D₄×C₅₃	—	2	1	no	—
721	D₄×C₅₃	—	4	1	no	—
722	D₄×C₅₃	—	4	1	no	—
723	D₄×C₅₃	—	4	1	no	—
724	D₄×C₅₃	—	4	2	no	—
725	D₄×C₅₃	—	4	2	no	—
726	D₄×C₅₃	—	4	2	no	—
727	D₄×C₅₃	—	4	2	no	—
728	D₄×C₅₃	—	4	2	no	—
729	D₄×C₅₃	—	4	2	no	—
730	D₄×C₅₃	—	8	1	no	—
731	D₄×C₅₃	—	8	1	no	—
732	D₄×C₅₃	—	8	1	no	—
733	D₄×C₅₃	—	8	1	no	—
734	D₄×C₅₃	C₂×#41	1	2	yes	—
735	D₄×C₅₃	C₂×#41	1	2	yes	—
736	C₂×C₄×C₅₃	—	2	1	no	—
737	C₂×C₄×C₅₃	—	2	1	no	—
738	C₂×C₄×C₅₃	—	2	1	no	—
739	C₂×C₄×C₅₃	—	2	1	no	—
740	C₂×C₄×C₅₃	—	2	1	no	—
741	C₂×C₄×C₅₃	—	2	1	no	—
742	C₂×C₄×C₅₃	—	2	1	no	—
743	C₂×C₄×C₅₃	—	2	1	no	—
744	C₂×C₄×C₅₃	—	2	1	no	—
745	C₂×C₄×C₅₃	—	2	1	no	—
746	C₂×C₄×C₅₃	—	2	1	no	—
747	C₂×C₄×C₅₃	—	2	1	no	—
748	C₂×C₄×C₅₃	—	2	1	no	—
749	C₂×C₄×C₅₃	—	2	1	no	—
750	C₂×C₄×C₅₃	—	2	1	no	—
751	C₂×C₄×C₅₃	—	2	1	no	—
752	C₂×C₄×C₅₃	—	2	1	no	—
753	C₂×C₄×C₅₃	—	2	1	no	—
754	C₂×C₄×C₅₃	—	4	1	no	—
755	C₂×C₄×C₅₃	—	4	1	no	—
756	C₂×C₄×C₅₃	—	4	2	no	—
757	C₂×C₄×C₅₃	—	4	2	no	—
758	C₂×C₄×C₅₃	—	4	2	no	—
759	C₂×C₄×C₅₃	—	4	2	no	—
760	C₂×C₄×C₅₃	—	4	2	no	—
761	C₂×C₄×C₅₃	—	4	2	no	—
762	C₂×C₄×C₅₃	—	8	1	no	—
763	C₂×C₄×C₅₃	—	8	1	no	—
764	C₂×C₄×C₅₃	—	8	1	no	—
765	C₂×C₄×C₅₃	—	8	1	no	—
766	C₂×C₄×C₅₃	—	8	1	no	—
767	C₂×C₄×C₅₃	—	8	1	no	—
768	C₂×C₄×C₅₃	—	8	1	no	—
769	C₂×C₄×C₅₃	—	8	1	no	—
770	C₂×C₄×C₅₃	—	8	1	no	—
771	C₂×C₄×C₅₃	—	8	1	no	—
772	C₂×C₄×C₅₃	—	8	1	no	—
773	C₂×C₄×C₅₃	—	8	1	no	—
774	C₂×C₄×C₅₃	—	8	1	no	—
775	C₂×C₄×C₅₃	—	8	1	no	—
776	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
777	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
778	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
779	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
780	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
781	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
788	C₈×C₅₃	—	2	1	no	—
789	C₈×C₅₃	—	2	1	no	—
790	C₈×C₅₃	—	2	1	no	—
791	C₈×C₅₃	—	2	1	no	—
792	C₈×C₅₃	—	2	1	no	—
793	C₈×C₅₃	—	2	1	no	—
794	C₈×C₅₃	—	2	1	no	—
795	C₈×C₅₃	C₂×#41	1	2	yes	—
796	#61510	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
797	C₂²×C₅₃	—	2	1	no	—
798	C₂²×C₅₃	—	2	1	no	—
799	C₂²×C₅₃	—	2	1	no	—
800	C₂²×C₅₃	—	2	1	no	—
801	C₂²×C₅₃	—	2	1	no	—
802	C₂²×C₅₃	—	2	1	no	—
803	C₂²×C₅₃	—	2	1	no	—
804	C₂²×C₅₃	—	2	1	no	—
805	C₂²×C₅₃	—	2	1	no	—
806	C₂²×C₅₃	—	2	2	no	—
807	C₂²×C₅₃	—	2	2	no	—
808	C₂²×C₅₃	—	4	1	no	—
809	C₂²×C₅₃	—	4	1	no	—
810	C₂²×C₅₃	—	4	1	no	—
811	C₂²×C₅₃	—	4	1	no	—
812	C₂²×C₅₃	—	4	1	no	—
813	C₂²×C₅₃	—	4	1	no	—
814	C₂²×C₅₃	—	4	1	no	—
815	C₂²×C₅₃	—	4	1	no	—
816	C₂²×C₅₃	—	4	1	no	—
817	C₂²×C₅₃	—	4	1	no	—
818	C₂²×C₅₃	—	8	4	no	—
819	C₂²×C₅₃	—	16	2	no	—
820	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
821	C₄×C₅₃	—	2	1	no	—
822	C₄×C₅₃	—	2	1	no	—
823	C₄×C₅₃	—	2	1	no	—
824	C₄×C₅₃	—	2	1	no	—
825	C₄×C₅₃	—	2	1	no	—
826	C₄×C₅₃	—	2	1	no	—
827	C₄×C₅₃	—	2	1	no	—
828	C₄×C₅₃	—	2	1	no	—
829	C₄×C₅₃	—	2	1	no	—
830	C₄×C₅₃	—	2	1	no	—
831	C₄×C₅₃	—	2	1	no	—
832	C₄×C₅₃	—	4	1	no	—
833	C₄×C₅₃	—	4	1	no	—
834	C₄×C₅₃	—	4	1	no	—
835	C₄×C₅₃	—	4	1	no	—
836	C₄×C₅₃	—	4	1	no	—
837	C₄×C₅₃	—	4	1	no	—
838	C₄×C₅₃	—	4	1	no	—
839	C₄×C₅₃	—	4	1	no	—
840	C₄×C₅₃	—	4	1	no	—
841	C₄×C₅₃	—	4	1	no	—
842	C₄×C₅₃	—	4	1	no	—
843	C₄×C₅₃	—	4	1	no	—
844	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
845	C₄×C₅₃	#585	1	1	yes	characteristic
846	#3521	C₂×C₅₃	1	1	yes	characteristic, complemented
847	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
848	#3402	C₂×C₅₃	1	1	yes	characteristic, complemented
849	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
850	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
851	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
852	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
853	#3346	C₂×C₅₃	1	1	yes	characteristic, complemented
854	#3343	C₂×C₅₃	1	1	yes	characteristic, complemented
855	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
856	#3322	C₂×C₅₃	1	1	yes	characteristic, complemented
857	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
858	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
859	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
860	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
861	#3273	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#3178	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#3173	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#3172	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#3120	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#2967	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#2951	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
876	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
877	C₂×C₅₃	—	4	1	no	—
878	C₂×C₅₃	—	4	1	no	—
879	C₂×C₅₃	—	4	1	no	—
880	C₂×C₅₃	—	4	2	no	—
881	C₂×C₅₃	—	4	2	no	—
882	C₂×C₅₃	—	8	1	no	—
883	C₂×C₅₃	—	8	1	no	—
884	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
885	C₂×C₅₃	#3585	1	1	yes	characteristic
886	C₂×C₅₃	#3586	1	1	yes	characteristic
887	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
888	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
889	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
890	#556	C₂²×C₅₃	1	1	yes	characteristic
891	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
892	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
893	#554	C₂²×C₅₃	1	1	yes	characteristic
894	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
896	#553	—	2	1	no	—
897	#553	C₂²×C₅₃	1	1	yes	characteristic
898	#552	—	2	1	no	—
899	#552	—	2	1	no	—
900	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
901	#551	—	2	1	no	—
902	#551	—	2	1	no	—
903	#551	—	2	1	no	—
904	#551	—	2	1	no	—
905	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#548	—	2	1	no	—
907	#547	C₂²×C₅₃	1	1	yes	characteristic
908	#547	C₂²×C₅₃	1	1	yes	characteristic
909	#547	C₂²×C₅₃	1	1	yes	characteristic
910	#546	C₂²×C₅₃	1	1	yes	characteristic
911	#546	C₂²×C₅₃	1	1	yes	characteristic
912	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
914	#542	C₂²×C₅₃	1	1	yes	characteristic
915	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
916	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#539	—	2	1	no	—
919	#539	—	2	1	no	—
920	#539	—	2	1	no	—
921	#538	—	2	1	no	—
922	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#529	—	2	1	no	—
924	#529	C₂²×C₅₃	1	1	yes	characteristic
925	#529	C₂²×C₅₃	1	1	yes	characteristic
926	C₂×#126	—	2	1	no	—
927	#525	—	2	1	no	—
928	C₂×C₂²⋊Q₈	—	2	1	no	—
929	#520	C₂²×C₅₃	1	1	yes	characteristic
930	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
934	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#495	C₂²×C₅₃	1	1	yes	characteristic
941	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#482	C₂²×C₅₃	1	1	yes	characteristic
956	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#480	C₂²×C₅₃	1	1	yes	characteristic
958	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#469	C₂²×C₅₃	1	1	yes	characteristic
976	#468	C₂²×C₅₃	1	1	yes	characteristic
977	#468	C₂²×C₅₃	1	1	yes	characteristic
978	#468	C₂²×C₅₃	1	1	yes	characteristic
979	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#465	C₂²×C₅₃	1	1	yes	characteristic
981	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#463	C₂²×C₅₃	1	1	yes	characteristic
986	#463	C₂²×C₅₃	1	1	yes	characteristic
987	#463	C₂²×C₅₃	1	1	yes	characteristic
988	#463	C₂²×C₅₃	1	1	yes	characteristic
989	#463	C₂²×C₅₃	1	1	yes	characteristic
990	#463	C₂²×C₅₃	1	1	yes	characteristic
991	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#452	C₂²×C₅₃	1	1	yes	characteristic
996	#452	C₂²×C₅₃	1	1	yes	characteristic
997	#452	C₂²×C₅₃	1	1	yes	characteristic
998	#452	C₂²×C₅₃	1	1	yes	characteristic
999	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#449	C₂²×C₅₃	1	1	yes	characteristic
1004	#449	C₂²×C₅₃	1	1	yes	characteristic
1005	#447	C₂²×C₅₃	1	1	yes	characteristic
1006	#447	C₂²×C₅₃	1	1	yes	characteristic
1007	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#442	C₂²×C₅₃	1	1	yes	characteristic
1010	#442	C₂²×C₅₃	1	1	yes	characteristic
1011	#442	C₂²×C₅₃	1	1	yes	characteristic
1012	#442	C₂²×C₅₃	1	1	yes	characteristic
1013	#442	C₂²×C₅₃	1	1	yes	characteristic
1014	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1034	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1035	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1036	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1037	#436	C₂²×C₅₃	1	1	yes	characteristic
1038	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#435	C₂²×C₅₃	1	1	yes	characteristic
1040	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	C₂×#107	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#417	C₂²×C₅₃	1	1	yes	characteristic
1051	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#416	C₂²×C₅₃	1	1	yes	characteristic
1054	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	C₅₃	#61510	1	1	yes	characteristic, direct product factor, Sylow
1059	C₂×#41	—	2	1	no	—
1060	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1062	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂²×Q₈	—	2	1	no	—
1065	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂³×C₄	—	2	1	no	—
1068	AGL(1,ℤ/8)	—	2	4	no	—
1069	AGL(1,ℤ/8)	—	2	4	no	—
1070	#135	—	2	4	no	—
1071	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1093	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1094	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1095	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1096	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1097	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1098	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1099	#126	—	2	1	no	—
1100	#126	—	2	1	no	—
1101	#126	—	2	1	no	—
1102	#126	—	2	1	no	—
1103	#126	—	2	1	no	—
1104	#126	—	2	1	no	—
1105	#126	—	2	1	no	—
1106	#126	—	2	1	no	—
1107	#126	—	2	1	no	—
1108	#126	—	2	1	no	—
1109	#126	—	2	1	no	—
1110	#126	—	2	1	no	—
1111	#126	—	2	1	no	—
1112	#126	—	2	1	no	—
1113	#126	D₄×C₅₃	1	1	yes	characteristic
1114	#126	D₄×C₅₃	1	1	yes	characteristic
1115	#125	—	2	1	no	—
1116	#125	—	2	1	no	—
1117	#125	—	2	1	no	—
1118	#125	—	2	1	no	—
1119	#125	—	2	1	no	—
1120	#125	—	2	1	no	—
1121	#125	D₄×C₅₃	1	1	yes	characteristic
1122	#125	C₂³×C₅₃	1	1	yes	characteristic
1123	#125	C₂³×C₅₃	1	1	yes	characteristic
1124	#124	—	2	1	no	—
1125	#124	—	2	1	no	—
1126	#124	—	2	1	no	—
1127	#124	—	2	1	no	—
1128	#124	D₄×C₅₃	1	1	yes	characteristic
1129	#124	C₂³×C₅₃	1	1	yes	characteristic
1130	#124	C₂³×C₅₃	1	1	yes	characteristic
1131	#124	C₂³×C₅₃	1	1	yes	characteristic
1132	#124	C₂³×C₅₃	1	1	yes	characteristic
1133	#123	—	2	1	no	—
1134	#123	—	2	1	no	—
1135	#123	—	2	1	no	—
1136	#123	—	2	1	no	—
1137	#123	—	2	1	no	—
1138	#123	—	2	1	no	—
1139	#123	—	2	1	no	—
1140	#123	—	2	1	no	—
1141	#123	—	2	1	no	—
1142	#123	—	2	1	no	—
1143	#123	—	2	1	no	—
1144	#123	—	2	1	no	—
1145	#123	—	2	1	no	—
1146	#123	—	2	1	no	—
1147	#123	—	2	1	no	—
1148	#123	—	2	1	no	—
1149	#123	D₄×C₅₃	1	1	yes	characteristic
1150	#123	D₄×C₅₃	1	1	yes	characteristic
1151	C₂²⋊Q₈	—	2	1	no	—
1152	C₂²⋊Q₈	—	2	1	no	—
1153	C₂²⋊Q₈	—	2	1	no	—
1154	C₂²⋊Q₈	—	2	1	no	—
1155	C₂²⋊Q₈	—	2	1	no	—
1156	C₂²⋊Q₈	—	2	1	no	—
1157	C₂²⋊Q₈	—	2	1	no	—
1158	C₂²⋊Q₈	—	2	1	no	—
1159	C₂²⋊Q₈	—	2	1	no	—
1160	C₂²⋊Q₈	—	2	1	no	—
1161	C₂²⋊Q₈	—	2	1	no	—
1162	C₂²⋊Q₈	—	2	1	no	—
1163	C₂²⋊Q₈	—	2	1	no	—
1164	C₂²⋊Q₈	—	2	1	no	—
1165	C₂²⋊Q₈	—	2	1	no	—
1166	C₂²⋊Q₈	—	2	1	no	—
1167	C₂²⋊Q₈	—	2	1	no	—
1168	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1169	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1177	#121	—	2	1	no	—
1178	#121	—	2	1	no	—
1179	#121	—	2	1	no	—
1180	#121	—	2	1	no	—
1181	#121	—	2	1	no	—
1182	#121	—	2	1	no	—
1183	#121	—	2	1	no	—
1184	#121	D₄×C₅₃	1	1	yes	characteristic
1185	#121	C₂³×C₅₃	1	1	yes	characteristic
1186	#121	C₂³×C₅₃	1	1	yes	characteristic
1187	#121	C₂³×C₅₃	1	1	yes	characteristic
1188	#121	C₂³×C₅₃	1	1	yes	characteristic
1189	#120	—	2	1	no	—
1190	#120	—	2	1	no	—
1191	#120	—	2	1	no	—
1192	#120	—	2	1	no	—
1193	C₄×Q₈	—	2	1	no	—
1194	C₄×Q₈	—	2	1	no	—
1195	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1196	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1197	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1198	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1199	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1200	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1201	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1202	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1203	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	—	2	1	no	—
1208	C₄×D₄	—	2	1	no	—
1209	C₄×D₄	—	2	1	no	—
1210	C₄×D₄	—	2	1	no	—
1211	C₄×D₄	—	2	1	no	—
1212	C₄×D₄	—	2	1	no	—
1213	C₄×D₄	—	2	1	no	—
1214	C₄×D₄	—	2	1	no	—
1215	C₄×D₄	—	2	1	no	—
1216	C₄×D₄	—	2	1	no	—
1217	C₄×D₄	—	2	1	no	—
1218	C₄×D₄	—	2	1	no	—
1219	C₄×D₄	—	2	1	no	—
1220	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1221	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1222	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1223	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1224	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1225	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1226	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1227	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1228	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1229	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1230	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1231	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1232	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1233	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1234	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1235	#117	—	2	1	no	—
1236	#117	—	2	1	no	—
1237	#117	—	2	1	no	—
1238	#117	—	2	1	no	—
1239	#117	—	2	1	no	—
1240	#117	—	2	1	no	—
1241	#117	—	2	1	no	—
1242	#117	—	2	1	no	—
1243	#117	—	2	1	no	—
1244	#117	C₂³×C₅₃	1	1	yes	characteristic
1245	#117	C₂³×C₅₃	1	1	yes	characteristic
1246	#117	C₂³×C₅₃	1	1	yes	characteristic
1247	#117	C₂³×C₅₃	1	1	yes	characteristic
1248	C₂×C₄⋊C₄	—	2	1	no	—
1249	C₂×C₄⋊C₄	—	2	1	no	—
1250	C₂×C₄⋊C₄	—	2	1	no	—
1251	C₂×C₄⋊C₄	—	2	1	no	—
1252	C₂×C₄⋊C₄	—	2	1	no	—
1253	C₂×C₄⋊C₄	—	2	1	no	—
1254	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1255	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1256	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1257	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1258	C₂×C₂²⋊C₄	—	2	1	no	—
1259	C₂×C₂²⋊C₄	—	2	1	no	—
1260	C₂×C₂²⋊C₄	—	2	1	no	—
1261	C₂×C₂²⋊C₄	—	2	1	no	—
1262	C₂×C₂²⋊C₄	—	2	1	no	—
1263	C₂×C₂²⋊C₄	—	2	1	no	—
1264	C₂×C₂²⋊C₄	—	2	1	no	—
1265	C₂×C₄²	—	2	1	no	—
1266	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1267	#107	C₂³×C₅₃	1	1	yes	characteristic
1268	#107	C₂³×C₅₃	1	1	yes	characteristic
1269	#107	C₂³×C₅₃	1	1	yes	characteristic
1270	#107	C₂³×C₅₃	1	1	yes	characteristic
1271	#107	C₂³×C₅₃	1	1	yes	characteristic
1272	#107	C₂³×C₅₃	1	1	yes	characteristic
1273	#107	C₂³×C₅₃	1	1	yes	characteristic
1274	#107	C₂³×C₅₃	1	1	yes	characteristic
1275	#106	C₂³×C₅₃	1	1	yes	characteristic
1276	#106	C₂³×C₅₃	1	1	yes	characteristic
1277	#106	C₂³×C₅₃	1	1	yes	characteristic
1278	#106	C₂³×C₅₃	1	1	yes	characteristic
1279	#106	C₂³×C₅₃	1	1	yes	characteristic
1280	#106	C₂³×C₅₃	1	1	yes	characteristic
1281	#106	C₂³×C₅₃	1	1	yes	characteristic
1282	#106	C₂³×C₅₃	1	1	yes	characteristic
1283	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1284	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1285	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1286	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1287	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1288	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1289	#103	C₂³×C₅₃	1	1	yes	characteristic
1290	#103	C₂³×C₅₃	1	1	yes	characteristic
1291	#103	C₂³×C₅₃	1	1	yes	characteristic
1292	#103	C₂³×C₅₃	1	1	yes	characteristic
1293	#103	C₂³×C₅₃	1	1	yes	characteristic
1294	#103	C₂³×C₅₃	1	1	yes	characteristic
1295	#103	C₂³×C₅₃	1	1	yes	characteristic
1296	#103	C₂³×C₅₃	1	1	yes	characteristic
1297	#103	C₂³×C₅₃	1	1	yes	characteristic
1298	#103	C₂³×C₅₃	1	1	yes	characteristic
1299	#103	C₂³×C₅₃	1	1	yes	characteristic
1300	#103	C₂³×C₅₃	1	1	yes	characteristic
1301	#103	C₂³×C₅₃	1	1	yes	characteristic
1302	#103	C₂³×C₅₃	1	1	yes	characteristic
1303	#103	C₂³×C₅₃	1	1	yes	characteristic
1304	#103	C₂³×C₅₃	1	1	yes	characteristic
1305	#102	C₂³×C₅₃	1	1	yes	characteristic
1306	#102	C₂³×C₅₃	1	1	yes	characteristic
1307	#102	C₂³×C₅₃	1	1	yes	characteristic
1308	#102	C₂³×C₅₃	1	1	yes	characteristic
1309	#102	C₂³×C₅₃	1	1	yes	characteristic
1310	#102	C₂³×C₅₃	1	1	yes	characteristic
1311	#102	C₂³×C₅₃	1	1	yes	characteristic
1312	#102	C₂³×C₅₃	1	1	yes	characteristic
1313	#102	C₂³×C₅₃	1	1	yes	characteristic
1314	#102	C₂³×C₅₃	1	1	yes	characteristic
1315	#102	C₂³×C₅₃	1	1	yes	characteristic
1316	#102	C₂³×C₅₃	1	1	yes	characteristic
1317	#102	C₂³×C₅₃	1	1	yes	characteristic
1318	#102	C₂³×C₅₃	1	1	yes	characteristic
1319	#102	C₂³×C₅₃	1	1	yes	characteristic
1320	#102	C₂³×C₅₃	1	1	yes	characteristic
1321	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1322	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1323	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1324	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1325	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1326	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1327	#97	C₂³×C₅₃	1	1	yes	characteristic
1328	#97	C₂³×C₅₃	1	1	yes	characteristic
1329	#97	C₂³×C₅₃	1	1	yes	characteristic
1330	#97	C₂³×C₅₃	1	1	yes	characteristic
1331	#97	C₂³×C₅₃	1	1	yes	characteristic
1332	#97	C₂³×C₅₃	1	1	yes	characteristic
1333	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1334	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1335	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1336	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1337	C₂⁴	—	2	1	no	—
1338	C₂⁴	—	2	1	no	—
1339	#41	—	2	2	no	—
1340	#41	—	2	2	no	—
1341	#41	—	2	2	no	—
1342	#41	—	2	2	no	—
1343	#41	—	4	1	no	—
1344	#41	—	4	1	no	—
1345	#41	—	4	1	no	—
1346	#41	—	4	1	no	—
1347	#41	—	8	2	no	—
1348	C₂×Q₈	—	2	1	no	—
1349	C₂×Q₈	—	2	1	no	—
1350	C₂×Q₈	—	2	1	no	—
1351	C₂×Q₈	—	2	1	no	—
1352	C₂×Q₈	—	8	2	no	—
1353	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1354	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1355	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1356	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1357	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1358	C₂×D₄	—	2	2	no	—
1359	C₂×D₄	—	2	2	no	—
1360	C₂×D₄	—	2	1	no	—
1361	C₂×D₄	—	2	1	no	—
1362	C₂×D₄	—	2	1	no	—
1363	C₂×D₄	—	2	1	no	—
1364	C₂×D₄	—	2	1	no	—
1365	C₂×D₄	—	2	1	no	—
1366	C₂×D₄	—	2	1	no	—
1367	C₂×D₄	—	2	1	no	—
1368	C₂×D₄	—	2	1	no	—
1369	C₂×D₄	—	2	1	no	—
1370	C₂×D₄	—	4	1	no	—
1371	C₂×D₄	—	4	1	no	—
1372	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1373	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1374	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1375	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1376	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1377	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1378	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1379	C₂²×C₄	—	2	1	no	—
1380	C₂²×C₄	—	2	1	no	—
1381	C₂²×C₄	—	2	1	no	—
1382	C₂²×C₄	—	2	1	no	—
1383	C₂²×C₄	—	2	1	no	—
1384	C₂²×C₄	—	2	1	no	—
1385	C₂²×C₄	—	2	1	no	—
1386	C₂²×C₄	—	2	1	no	—
1387	C₂²×C₄	—	2	1	no	—
1388	C₂²×C₄	—	2	1	no	—
1389	C₂²×C₄	—	2	1	no	—
1390	C₂²×C₄	—	2	1	no	—
1391	C₂²×C₄	—	2	1	no	—
1392	C₂²×C₄	—	2	1	no	—
1393	C₂²×C₄	—	2	1	no	—
1394	C₂²×C₄	—	2	1	no	—
1395	C₂²×C₄	—	2	1	no	—
1396	C₂²×C₄	—	2	1	no	—
1397	C₂²×C₄	—	2	1	no	—
1398	C₂²×C₄	—	2	1	no	—
1399	C₂²×C₄	—	8	2	no	—
1400	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1401	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1402	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1403	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1404	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1405	Q₁₆	—	2	2	no	—
1406	Q₁₆	—	4	1	no	—
1407	Q₁₆	—	4	1	no	—
1408	Q₁₆	—	4	1	no	—
1409	SD₁₆	—	2	2	no	—
1410	SD₁₆	—	2	2	no	—
1411	SD₁₆	—	2	2	no	—
1412	SD₁₆	—	2	2	no	—
1413	SD₁₆	—	2	2	no	—
1414	SD₁₆	—	2	2	no	—
1415	SD₁₆	—	4	1	no	—
1416	SD₁₆	—	4	1	no	—
1417	D₈	—	2	2	no	—
1418	D₈	—	2	2	no	—
1419	D₈	—	4	1	no	—
1420	D₈	#41×C₅₃	1	4	yes	complemented
1421	M₁₆	—	2	2	no	—
1422	M₁₆	—	2	2	no	—
1423	M₁₆	—	4	1	no	—
1424	M₁₆	—	4	1	no	—
1425	C₂×C₈	—	2	2	no	—
1426	C₂×C₈	—	4	1	no	—
1427	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1428	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1429	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1430	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1431	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1432	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1433	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1434	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	—	2	1	no	—
1450	C₄⋊C₄	—	2	1	no	—
1451	C₄⋊C₄	—	2	1	no	—
1452	C₄⋊C₄	—	2	1	no	—
1453	C₄⋊C₄	—	2	1	no	—
1454	C₄⋊C₄	—	2	1	no	—
1455	C₄⋊C₄	—	2	1	no	—
1456	C₄⋊C₄	—	2	1	no	—
1457	C₄⋊C₄	—	2	1	no	—
1458	C₄⋊C₄	—	2	1	no	—
1459	C₄⋊C₄	—	2	1	no	—
1460	C₄⋊C₄	—	2	1	no	—
1461	C₄⋊C₄	—	2	1	no	—
1462	C₄⋊C₄	—	2	1	no	—
1463	C₄⋊C₄	—	2	1	no	—
1464	C₄⋊C₄	—	2	1	no	—
1465	C₄⋊C₄	—	2	1	no	—
1466	C₄⋊C₄	—	2	1	no	—
1467	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1468	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1469	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1470	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1471	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1472	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1473	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1474	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1475	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1476	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1477	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1478	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1479	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1480	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1481	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1482	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂²⋊C₄	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	—	2	1	no	—
1496	C₂²⋊C₄	—	2	1	no	—
1497	C₂²⋊C₄	—	2	1	no	—
1498	C₂²⋊C₄	—	2	1	no	—
1499	C₂²⋊C₄	—	2	1	no	—
1500	C₂²⋊C₄	—	2	1	no	—
1501	C₂²⋊C₄	—	2	1	no	—
1502	C₂²⋊C₄	—	2	1	no	—
1503	C₂²⋊C₄	—	2	1	no	—
1504	C₂²⋊C₄	—	2	1	no	—
1505	C₂²⋊C₄	—	2	1	no	—
1506	C₂²⋊C₄	—	2	1	no	—
1507	C₂²⋊C₄	—	2	1	no	—
1508	C₂²⋊C₄	—	2	1	no	—
1509	C₂²⋊C₄	—	2	1	no	—
1510	C₂²⋊C₄	—	2	1	no	—
1511	C₂²⋊C₄	—	2	1	no	—
1512	C₂²⋊C₄	—	2	1	no	—
1513	C₂²⋊C₄	—	2	1	no	—
1514	C₂²⋊C₄	—	2	1	no	—
1515	C₂²⋊C₄	—	2	1	no	—
1516	C₂²⋊C₄	—	2	1	no	—
1517	C₂²⋊C₄	—	2	1	no	—
1518	C₂²⋊C₄	—	2	1	no	—
1519	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1520	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1522	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1523	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1524	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1525	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1526	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1527	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1528	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1529	C₄²	—	2	1	no	—
1530	C₄²	—	2	1	no	—
1531	C₄²	—	2	1	no	—
1532	C₄²	—	2	1	no	—
1533	C₄²	—	2	1	no	—
1534	C₄²	—	2	1	no	—
1535	C₄²	—	2	1	no	—
1536	C₄²	—	2	1	no	—
1537	C₄²	—	2	1	no	—
1538	C₄²	—	2	1	no	—
1539	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1540	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1541	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1542	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1543	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1544	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1545	C₂³	—	2	1	no	—
1546	C₂³	—	2	1	no	—
1547	C₂³	—	2	1	no	—
1548	C₂³	—	2	1	no	—
1549	C₂³	—	4	2	no	—
1550	C₂³	—	4	2	no	—
1551	C₂³	—	4	2	no	—
1552	C₂³	—	8	1	no	—
1553	C₂³	—	8	1	no	—
1554	C₂³	—	8	1	no	—
1555	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1556	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1557	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1558	Q₈	—	2	1	no	—
1559	Q₈	—	2	1	no	—
1560	Q₈	—	2	1	no	—
1561	Q₈	—	2	1	no	—
1562	Q₈	—	2	1	no	—
1563	Q₈	—	2	1	no	—
1564	Q₈	—	2	1	no	—
1565	Q₈	—	2	1	no	—
1566	Q₈	—	4	1	no	—
1567	Q₈	—	4	2	no	—
1568	Q₈	—	8	1	no	—
1569	Q₈	—	8	1	no	—
1570	Q₈	—	8	1	no	—
1571	D₄	—	2	1	no	—
1572	D₄	—	2	1	no	—
1573	D₄	—	2	1	no	—
1574	D₄	—	2	1	no	—
1575	D₄	—	2	1	no	—
1576	D₄	—	2	1	no	—
1577	D₄	—	4	1	no	—
1578	D₄	—	4	1	no	—
1579	D₄	—	4	1	no	—
1580	D₄	—	4	2	no	—
1581	D₄	—	4	2	no	—
1582	D₄	—	4	2	no	—
1583	D₄	—	4	2	no	—
1584	D₄	—	4	2	no	—
1585	D₄	—	4	2	no	—
1586	D₄	—	8	1	no	—
1587	D₄	—	8	1	no	—
1588	D₄	—	8	1	no	—
1589	D₄	—	8	1	no	—
1590	D₄	C₂×#41×C₅₃	1	2	yes	—
1591	D₄	C₂×#41×C₅₃	1	2	yes	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	2	1	no	—
1599	C₂×C₄	—	2	1	no	—
1600	C₂×C₄	—	2	1	no	—
1601	C₂×C₄	—	2	1	no	—
1602	C₂×C₄	—	2	1	no	—
1603	C₂×C₄	—	2	1	no	—
1604	C₂×C₄	—	2	1	no	—
1605	C₂×C₄	—	2	1	no	—
1606	C₂×C₄	—	2	1	no	—
1607	C₂×C₄	—	2	1	no	—
1608	C₂×C₄	—	2	1	no	—
1609	C₂×C₄	—	2	1	no	—
1610	C₂×C₄	—	4	1	no	—
1611	C₂×C₄	—	4	1	no	—
1612	C₂×C₄	—	4	2	no	—
1613	C₂×C₄	—	4	2	no	—
1614	C₂×C₄	—	4	2	no	—
1615	C₂×C₄	—	4	2	no	—
1616	C₂×C₄	—	4	2	no	—
1617	C₂×C₄	—	4	2	no	—
1618	C₂×C₄	—	8	1	no	—
1619	C₂×C₄	—	8	1	no	—
1620	C₂×C₄	—	8	1	no	—
1621	C₂×C₄	—	8	1	no	—
1622	C₂×C₄	—	8	1	no	—
1623	C₂×C₄	—	8	1	no	—
1624	C₂×C₄	—	8	1	no	—
1625	C₂×C₄	—	8	1	no	—
1626	C₂×C₄	—	8	1	no	—
1627	C₂×C₄	—	8	1	no	—
1628	C₂×C₄	—	8	1	no	—
1629	C₂×C₄	—	8	1	no	—
1630	C₂×C₄	—	8	1	no	—
1631	C₂×C₄	—	8	1	no	—
1632	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1633	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1634	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1635	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1636	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1637	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1638	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1639	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1640	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1641	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1642	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1643	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1644	C₈	—	2	1	no	—
1645	C₈	—	2	1	no	—
1646	C₈	—	2	1	no	—
1647	C₈	—	2	1	no	—
1648	C₈	—	2	1	no	—
1649	C₈	—	2	1	no	—
1650	C₈	—	2	1	no	—
1651	C₈	C₂×#41×C₅₃	1	2	yes	—
1652	C₂²	—	2	1	no	—
1653	C₂²	—	2	1	no	—
1654	C₂²	—	2	1	no	—
1655	C₂²	—	2	2	no	—
1656	C₂²	—	2	2	no	—
1657	C₂²	—	2	1	no	—
1658	C₂²	—	2	1	no	—
1659	C₂²	—	2	1	no	—
1660	C₂²	—	2	1	no	—
1661	C₂²	—	2	1	no	—
1662	C₂²	—	2	1	no	—
1663	C₂²	—	4	1	no	—
1664	C₂²	—	4	1	no	—
1665	C₂²	—	4	1	no	—
1666	C₂²	—	4	1	no	—
1667	C₂²	—	4	1	no	—
1668	C₂²	—	4	1	no	—
1669	C₂²	—	4	1	no	—
1670	C₂²	—	4	1	no	—
1671	C₂²	—	4	1	no	—
1672	C₂²	—	4	1	no	—
1673	C₂²	—	8	4	no	—
1674	C₂²	—	16	2	no	—
1675	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1676	C₄	—	2	1	no	—
1677	C₄	—	2	1	no	—
1678	C₄	—	2	1	no	—
1679	C₄	—	2	1	no	—
1680	C₄	—	2	1	no	—
1681	C₄	—	2	1	no	—
1682	C₄	—	2	1	no	—
1683	C₄	—	2	1	no	—
1684	C₄	—	2	1	no	—
1685	C₄	—	2	1	no	—
1686	C₄	—	2	1	no	—
1687	C₄	—	4	1	no	—
1688	C₄	—	4	1	no	—
1689	C₄	—	4	1	no	—
1690	C₄	—	4	1	no	—
1691	C₄	—	4	1	no	—
1692	C₄	—	4	1	no	—
1693	C₄	—	4	1	no	—
1694	C₄	—	4	1	no	—
1695	C₄	—	4	1	no	—
1696	C₄	—	4	1	no	—
1697	C₄	—	4	1	no	—
1698	C₄	—	4	1	no	—
1699	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1700	C₄	C₅₃×#585	1	1	yes	characteristic
1701	C₂	—	4	1	no	—
1702	C₂	—	4	1	no	—
1703	C₂	—	4	1	no	—
1704	C₂	—	4	2	no	—
1705	C₂	—	4	2	no	—
1706	C₂	—	8	1	no	—
1707	C₂	—	8	1	no	—
1708	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1709	C₂	C₅₃×#3585	1	1	yes	characteristic
1710	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×#3521	C₂	semidirect
2. C₅₃×#3520	C₂	semidirect
3. C₅₃×#3402	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3376	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3346	C₂	semidirect
9. C₅₃×#3343	C₂	semidirect
10. C₅₃×#3331	C₂	semidirect
11. C₅₃×#3322	C₂	semidirect
12. C₅₃×#3315	C₂	semidirect
13. C₅₃×#3314	C₂	semidirect
14. C₅₃×#3311	C₂	semidirect
15. C₅₃×#3306	C₂	semidirect
16. C₅₃×#3273	C₂	semidirect
17. C₅₃×#3267	C₂	semidirect
18. C₅₃×#3267	C₂	semidirect
19. C₅₃×#3178	C₂	semidirect
20. C₅₃×#3173	C₂	semidirect
21. C₅₃×#3172	C₂	semidirect
22. C₅₃×#3125	C₂	semidirect
23. C₅₃×#3124	C₂	semidirect
24. C₅₃×#3120	C₂	semidirect
25. C₅₃×#3118	C₂	semidirect
26. C₅₃×#3116	C₂	semidirect
27. C₅₃×#3114	C₂	semidirect
28. C₅₃×#2967	C₂	semidirect
29. C₅₃×#2951	C₂	semidirect
30. C₅₃×#2946	C₂	semidirect
31. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
36. C₅₃×#556	C₂²	semidirect
37. C₅₃×#556	C₂²	semidirect
39. C₅₃×#554	C₂²	semidirect
40. C₅₃×#554	C₂²	semidirect
45. C₅₃×#552	C₂²	semidirect
50. D₄×Q₈×C₅₃	C₂²	semidirect
57. C₅₃×#546	C₂²	semidirect
58. C₅₃×#546	C₂²	semidirect
60. C₅₃×#542	C₂²	semidirect
61. C₅₃×#542	C₂²	semidirect
62. C₅₃×#541	C₂²	semidirect
67. C₅₃×#533	C₂²	semidirect
75. C₅₃×#520	C₂²	semidirect
76. C₅₃×#520	C₂²	semidirect
77. C₅₃×#518	C₂²	semidirect
79. C₂×C₄×D₄×C₅₃	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#501	C₂²	semidirect
82. C₅₃×#498	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
84. C₅₃×#497	C₂²	semidirect
86. C₅₃×#491	C₂²	semidirect
87. C₅₃×#489	C₂²	semidirect
88. C₅₃×#489	C₂²	semidirect
89. C₅₃×#489	C₂²	semidirect
90. C₅₃×#488	C₂²	semidirect
91. C₅₃×#487	C₂²	semidirect
92. C₅₃×#485	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#484	C₂²	semidirect
96. C₅₃×#484	C₂²	semidirect
97. C₅₃×#483	C₂²	semidirect
98. C₅₃×#483	C₂²	semidirect
99. C₅₃×#483	C₂²	semidirect
101. C₅₃×#481	C₂²	semidirect
103. C₅₃×#480	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#477	C₂²	semidirect
109. C₅₃×#477	C₂²	semidirect
110. C₅₃×#476	C₂²	semidirect
111. C₅₃×#476	C₂²	semidirect
112. C₅₃×#476	C₂²	semidirect
113. C₅₃×#475	C₂²	semidirect
114. C₅₃×#474	C₂²	semidirect
115. C₅₃×#474	C₂²	semidirect
116. C₅₃×#470	C₂²	semidirect
117. C₅₃×#470	C₂²	semidirect
118. C₅₃×#470	C₂²	semidirect
119. C₅₃×#470	C₂²	semidirect
124. C₅₃×#467	C₂²	semidirect
126. C₅₃×#465	C₂²	semidirect
127. C₅₃×#465	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
136. C₅₃×#462	C₂²	semidirect
137. C₅₃×#462	C₂²	semidirect
138. C₅₃×#461	C₂²	semidirect
139. C₅₃×#461	C₂²	semidirect
144. C₅₃×#452	C₂²	semidirect
145. C₅₃×#452	C₂²	semidirect
146. C₅₃×#450	C₂²	semidirect
147. C₅₃×#450	C₂²	semidirect
152. C₅₃×#446	C₂²	semidirect
153. C₅₃×#446	C₂²	semidirect
159. C₅₃×#441	C₂²	semidirect
160. C₅₃×#441	C₂²	semidirect
161. C₅₃×#440	C₂²	semidirect
162. C₅₃×#440	C₂²	semidirect
163. C₅₃×#440	C₂²	semidirect
164. C₅₃×#440	C₂²	semidirect
165. C₅₃×#440	C₂²	semidirect
166. C₅₃×#440	C₂²	semidirect
167. C₅₃×#440	C₂²	semidirect
168. C₅₃×#440	C₂²	semidirect
169. C₅₃×#440	C₂²	semidirect
170. C₄×Q₁₆×C₅₃	C₂²	semidirect
171. C₄×Q₁₆×C₅₃	C₂²	semidirect
172. C₄×Q₁₆×C₅₃	C₂²	semidirect
173. C₄×SD₁₆×C₅₃	C₂²	semidirect
174. C₄×SD₁₆×C₅₃	C₂²	semidirect
175. C₄×SD₁₆×C₅₃	C₂²	semidirect
176. C₄×SD₁₆×C₅₃	C₂²	semidirect
177. C₄×SD₁₆×C₅₃	C₂²	semidirect
183. C₅₃×#436	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₅₃×#435	C₂²	semidirect
187. C₅₃×#435	C₂²	semidirect
188. C₅₃×#433	C₂²	semidirect
189. C₅₃×#433	C₂²	semidirect
190. C₅₃×#432	C₂²	semidirect
191. C₅₃×#428	C₂²	semidirect
192. C₅₃×#428	C₂²	semidirect
193. C₂×#107×C₅₃	C₂²	semidirect
194. C₅₃×#418	C₂²	semidirect
196. C₅₃×#417	C₂²	semidirect
197. C₅₃×#417	C₂²	semidirect
199. C₂×#102×C₅₃	C₂²	semidirect
200. C₅₃×#405	C₂²	semidirect
201. C₅₃×#405	C₂²	semidirect
202. C₄×M₁₆×C₅₃	C₂²	semidirect
564. D₈×C₅₃	#41	semidirect
796. #61510	C₅₃	direct (N × H)
846. #3521	C₂×C₅₃	semidirect
847. #3520	C₂×C₅₃	semidirect
848. #3402	C₂×C₅₃	semidirect
849. #3384	C₂×C₅₃	semidirect
850. #3376	C₂×C₅₃	semidirect
851. #3367	C₂×C₅₃	semidirect
852. #3356	C₂×C₅₃	semidirect
853. #3346	C₂×C₅₃	semidirect
854. #3343	C₂×C₅₃	semidirect
855. #3331	C₂×C₅₃	semidirect
856. #3322	C₂×C₅₃	semidirect
857. #3315	C₂×C₅₃	semidirect
858. #3314	C₂×C₅₃	semidirect
859. #3311	C₂×C₅₃	semidirect
860. #3306	C₂×C₅₃	semidirect
861. #3273	C₂×C₅₃	semidirect
862. #3267	C₂×C₅₃	semidirect
863. #3267	C₂×C₅₃	semidirect
864. #3178	C₂×C₅₃	semidirect
865. #3173	C₂×C₅₃	semidirect
866. #3172	C₂×C₅₃	semidirect
867. #3125	C₂×C₅₃	semidirect
868. #3124	C₂×C₅₃	semidirect
869. #3120	C₂×C₅₃	semidirect
870. #3118	C₂×C₅₃	semidirect
871. #3116	C₂×C₅₃	semidirect
872. #3114	C₂×C₅₃	semidirect
873. #2967	C₂×C₅₃	semidirect
874. #2951	C₂×C₅₃	semidirect
875. #2946	C₂×C₅₃	semidirect
876. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
891. #556	C₂²×C₅₃	semidirect
892. #556	C₂²×C₅₃	semidirect
894. #554	C₂²×C₅₃	semidirect
895. #554	C₂²×C₅₃	semidirect
900. #552	C₂²×C₅₃	semidirect
905. D₄×Q₈	C₂²×C₅₃	semidirect
912. #546	C₂²×C₅₃	semidirect
913. #546	C₂²×C₅₃	semidirect
915. #542	C₂²×C₅₃	semidirect
916. #542	C₂²×C₅₃	semidirect
917. #541	C₂²×C₅₃	semidirect
922. #533	C₂²×C₅₃	semidirect
930. #520	C₂²×C₅₃	semidirect
931. #520	C₂²×C₅₃	semidirect
932. #518	C₂²×C₅₃	semidirect
934. C₂×C₄×D₄	C₂²×C₅₃	semidirect
935. #501	C₂²×C₅₃	semidirect
936. #501	C₂²×C₅₃	semidirect
937. #498	C₂²×C₅₃	semidirect
938. #497	C₂²×C₅₃	semidirect
939. #497	C₂²×C₅₃	semidirect
941. #491	C₂²×C₅₃	semidirect
942. #489	C₂²×C₅₃	semidirect
943. #489	C₂²×C₅₃	semidirect
944. #489	C₂²×C₅₃	semidirect
945. #488	C₂²×C₅₃	semidirect
946. #487	C₂²×C₅₃	semidirect
947. #485	C₂²×C₅₃	semidirect
948. #485	C₂²×C₅₃	semidirect
949. #485	C₂²×C₅₃	semidirect
950. #484	C₂²×C₅₃	semidirect
951. #484	C₂²×C₅₃	semidirect
952. #483	C₂²×C₅₃	semidirect
953. #483	C₂²×C₅₃	semidirect
954. #483	C₂²×C₅₃	semidirect
956. #481	C₂²×C₅₃	semidirect
958. #480	C₂²×C₅₃	semidirect
959. #479	C₂²×C₅₃	semidirect
960. #478	C₂²×C₅₃	semidirect
961. #478	C₂²×C₅₃	semidirect
962. #478	C₂²×C₅₃	semidirect
963. #477	C₂²×C₅₃	semidirect
964. #477	C₂²×C₅₃	semidirect
965. #476	C₂²×C₅₃	semidirect
966. #476	C₂²×C₅₃	semidirect
967. #476	C₂²×C₅₃	semidirect
968. #475	C₂²×C₅₃	semidirect
969. #474	C₂²×C₅₃	semidirect
970. #474	C₂²×C₅₃	semidirect
971. #470	C₂²×C₅₃	semidirect
972. #470	C₂²×C₅₃	semidirect
973. #470	C₂²×C₅₃	semidirect
974. #470	C₂²×C₅₃	semidirect
979. #467	C₂²×C₅₃	semidirect
981. #465	C₂²×C₅₃	semidirect
982. #465	C₂²×C₅₃	semidirect
983. #464	C₂²×C₅₃	semidirect
984. #464	C₂²×C₅₃	semidirect
991. #462	C₂²×C₅₃	semidirect
992. #462	C₂²×C₅₃	semidirect
993. #461	C₂²×C₅₃	semidirect
994. #461	C₂²×C₅₃	semidirect
999. #452	C₂²×C₅₃	semidirect
1000. #452	C₂²×C₅₃	semidirect
1001. #450	C₂²×C₅₃	semidirect
1002. #450	C₂²×C₅₃	semidirect
1007. #446	C₂²×C₅₃	semidirect
1008. #446	C₂²×C₅₃	semidirect
1014. #441	C₂²×C₅₃	semidirect
1015. #441	C₂²×C₅₃	semidirect
1016. #440	C₂²×C₅₃	semidirect
1017. #440	C₂²×C₅₃	semidirect
1018. #440	C₂²×C₅₃	semidirect
1019. #440	C₂²×C₅₃	semidirect
1020. #440	C₂²×C₅₃	semidirect
1021. #440	C₂²×C₅₃	semidirect
1022. #440	C₂²×C₅₃	semidirect
1023. #440	C₂²×C₅₃	semidirect
1024. #440	C₂²×C₅₃	semidirect
1025. C₄×Q₁₆	C₂²×C₅₃	semidirect
1026. C₄×Q₁₆	C₂²×C₅₃	semidirect
1027. C₄×Q₁₆	C₂²×C₅₃	semidirect
1028. C₄×SD₁₆	C₂²×C₅₃	semidirect
1029. C₄×SD₁₆	C₂²×C₅₃	semidirect
1030. C₄×SD₁₆	C₂²×C₅₃	semidirect
1031. C₄×SD₁₆	C₂²×C₅₃	semidirect
1032. C₄×SD₁₆	C₂²×C₅₃	semidirect
1038. #436	C₂²×C₅₃	semidirect
1040. #435	C₂²×C₅₃	semidirect
1041. #435	C₂²×C₅₃	semidirect
1042. #435	C₂²×C₅₃	semidirect
1043. #433	C₂²×C₅₃	semidirect
1044. #433	C₂²×C₅₃	semidirect
1045. #432	C₂²×C₅₃	semidirect
1046. #428	C₂²×C₅₃	semidirect
1047. #428	C₂²×C₅₃	semidirect
1048. C₂×#107	C₂²×C₅₃	semidirect
1049. #418	C₂²×C₅₃	semidirect
1051. #417	C₂²×C₅₃	semidirect
1052. #417	C₂²×C₅₃	semidirect
1054. C₂×#102	C₂²×C₅₃	semidirect
1055. #405	C₂²×C₅₃	semidirect
1056. #405	C₂²×C₅₃	semidirect
1057. C₄×M₁₆	C₂²×C₅₃	semidirect
1058. C₅₃	#61510	direct (N × H)
1420. D₈	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3521	2
C₅₃×#3520	2
C₅₃×#3402	2
C₅₃×#3384	2
C₅₃×#3376	2
C₅₃×#3367	2
C₅₃×#3356	2
C₅₃×#3346	2
C₅₃×#3343	2
C₅₃×#3331	2
C₅₃×#3322	2
C₅₃×#3315	2
C₅₃×#3314	2
C₅₃×#3311	2
C₅₃×#3306	2
C₅₃×#3273	2
C₅₃×#3267	2
C₅₃×#3178	2
C₅₃×#3173	2
C₅₃×#3172	2
C₅₃×#3125	2
C₅₃×#3124	2
C₅₃×#3120	2
C₅₃×#3118	2
C₅₃×#3116	2
C₅₃×#3114	2
C₅₃×#2967	2
C₅₃×#2951	2
C₅₃×#2946	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61510	53

Subgroups — C53×#61510 #27269022

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61510 #27269022