Subgroups — C₅₃×#61506 #27269018

Order 13568.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1762 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×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3355	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3350	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3348	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3322	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3307	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3179	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3174	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3171	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3119	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3115	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×#2948	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	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#555	C₂²	1	1	yes	characteristic
38	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#553	—	2	1	no	—
41	C₅₃×#553	—	2	1	no	—
42	C₅₃×#553	C₂²	1	1	yes	characteristic
43	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#552	—	2	1	no	—
46	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#551	—	2	1	no	—
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#546	—	2	1	no	—
52	C₅₃×#546	—	2	1	no	—
53	C₅₃×#546	—	2	1	no	—
54	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
56	D₄²×C₅₃	C₂²	1	1	yes	characteristic
57	D₄²×C₅₃	C₂²	1	1	yes	characteristic
58	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#540	C₂²	1	1	yes	characteristic
62	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#539	—	2	1	no	—
64	C₅₃×#538	—	2	1	no	—
65	C₅₃×#538	—	2	1	no	—
66	C₅₃×#538	—	2	1	no	—
67	C₅₃×#532	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, complemented
71	C₂×#126×C₅₃	—	2	1	no	—
72	C₅₃×#525	—	2	1	no	—
73	C₂×#121×C₅₃	—	2	1	no	—
74	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#518	C₂²	1	1	yes	characteristic
76	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
78	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
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×#499	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#490	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×#486	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×#483	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
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×#478	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#478	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×#469	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#463	C₂²	1	1	yes	characteristic
129	C₅₃×#463	C₂²	1	1	yes	characteristic
130	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#450	C₂²	1	1	yes	characteristic
141	C₅₃×#450	C₂²	1	1	yes	characteristic
142	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#447	C₂²	1	1	yes	characteristic
149	C₅₃×#447	C₂²	1	1	yes	characteristic
150	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
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, complemented
159	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#442	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×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×SD₁₆×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×D₈×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	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	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#418	C₂²	1	1	yes	characteristic
195	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
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	—	2	1	no	—
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂²×D₄×C₅₃	—	2	1	no	—
208	C₂²×D₄×C₅₃	—	2	1	no	—
209	C₂²×D₄×C₅₃	—	2	1	no	—
210	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₅₃	—	2	1	no	—
215	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
216	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
217	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×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×D₈×C₅₃	—	2	4	no	—
226	C₂×D₈×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×D₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
238	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₂²×C₈×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	#127×C₅₃	C₂³	1	1	yes	characteristic
244	#127×C₅₃	C₂³	1	1	yes	characteristic
245	#127×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
258	#126×C₅₃	D₄	1	1	yes	characteristic
259	#126×C₅₃	D₄	1	1	yes	characteristic
260	#125×C₅₃	—	2	1	no	—
261	#125×C₅₃	—	2	1	no	—
262	#125×C₅₃	—	2	1	no	—
263	#125×C₅₃	D₄	1	1	yes	characteristic
264	#125×C₅₃	C₂³	1	1	yes	characteristic
265	#125×C₅₃	C₂³	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	—	2	1	no	—
273	#124×C₅₃	D₄	1	1	yes	characteristic
274	#124×C₅₃	C₂³	1	1	yes	characteristic
275	#124×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
301	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
302	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
303	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
305	#121×C₅₃	—	2	1	no	—
306	#121×C₅₃	—	2	1	no	—
307	#121×C₅₃	—	2	1	no	—
308	#121×C₅₃	—	2	1	no	—
309	#121×C₅₃	—	2	1	no	—
310	#121×C₅₃	—	2	1	no	—
311	#121×C₅₃	—	2	1	no	—
312	#121×C₅₃	—	2	1	no	—
313	#121×C₅₃	—	2	1	no	—
314	#121×C₅₃	—	2	1	no	—
315	#121×C₅₃	—	2	1	no	—
316	#121×C₅₃	—	2	1	no	—
317	#121×C₅₃	—	2	1	no	—
318	#121×C₅₃	—	2	1	no	—
319	#121×C₅₃	—	2	1	no	—
320	#121×C₅₃	—	2	1	no	—
321	#121×C₅₃	—	2	1	no	—
322	#121×C₅₃	—	2	1	no	—
323	#121×C₅₃	D₄	1	1	yes	characteristic
324	#121×C₅₃	C₂³	1	1	yes	characteristic
325	#121×C₅₃	C₂³	1	1	yes	characteristic
326	#121×C₅₃	C₂³	1	1	yes	characteristic
327	#121×C₅₃	C₂³	1	1	yes	characteristic
328	#121×C₅₃	C₂³	1	1	yes	characteristic
329	#121×C₅₃	C₂³	1	1	yes	characteristic
330	#121×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	C₂³	1	1	yes	characteristic
332	#120×C₅₃	—	2	1	no	—
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	#120×C₅₃	—	2	1	no	—
338	#120×C₅₃	—	2	1	no	—
339	#120×C₅₃	—	2	1	no	—
340	C₄×Q₈×C₅₃	—	2	1	no	—
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×D₄×C₅₃	—	2	1	no	—
347	C₄×D₄×C₅₃	—	2	1	no	—
348	C₄×D₄×C₅₃	—	2	1	no	—
349	C₄×D₄×C₅₃	—	2	1	no	—
350	C₄×D₄×C₅₃	—	2	1	no	—
351	C₄×D₄×C₅₃	—	2	1	no	—
352	C₄×D₄×C₅₃	—	2	1	no	—
353	C₄×D₄×C₅₃	—	2	1	no	—
354	C₄×D₄×C₅₃	—	2	1	no	—
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	—	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	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	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	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	#117×C₅₃	C₂³	1	1	yes	characteristic
393	#117×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₅₃	—	2	1	no	—
401	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
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	#102×C₅₃	C₂³	1	1	yes	characteristic
442	#102×C₅₃	C₂³	1	1	yes	characteristic
443	#102×C₅₃	C₂³	1	1	yes	characteristic
444	#102×C₅₃	C₂³	1	1	yes	characteristic
445	#102×C₅₃	C₂³	1	1	yes	characteristic
446	#102×C₅₃	C₂³	1	1	yes	characteristic
447	#102×C₅₃	C₂³	1	1	yes	characteristic
448	#102×C₅₃	C₂³	1	1	yes	characteristic
449	#102×C₅₃	C₂³	1	1	yes	characteristic
450	#102×C₅₃	C₂³	1	1	yes	characteristic
451	#102×C₅₃	C₂³	1	1	yes	characteristic
452	#102×C₅₃	C₂³	1	1	yes	characteristic
453	#102×C₅₃	C₂³	1	1	yes	characteristic
454	#102×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	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	C₂⁴×C₅₃	—	2	1	no	—
484	C₂⁴×C₅₃	—	2	1	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	—	8	2	no	—
490	#41×C₅₃	—	8	2	no	—
491	C₂×Q₈×C₅₃	—	2	1	no	—
492	C₂×Q₈×C₅₃	—	2	1	no	—
493	C₂×Q₈×C₅₃	C₂×D₄	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	2	no	—
498	C₂×D₄×C₅₃	—	2	2	no	—
499	C₂×D₄×C₅₃	—	2	2	no	—
500	C₂×D₄×C₅₃	—	2	1	no	—
501	C₂×D₄×C₅₃	—	2	1	no	—
502	C₂×D₄×C₅₃	—	2	1	no	—
503	C₂×D₄×C₅₃	—	2	1	no	—
504	C₂×D₄×C₅₃	—	2	1	no	—
505	C₂×D₄×C₅₃	—	2	1	no	—
506	C₂×D₄×C₅₃	—	2	1	no	—
507	C₂×D₄×C₅₃	—	2	1	no	—
508	C₂×D₄×C₅₃	—	2	1	no	—
509	C₂×D₄×C₅₃	—	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	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	2	1	no	—
519	C₂×D₄×C₅₃	—	2	1	no	—
520	C₂×D₄×C₅₃	—	4	1	no	—
521	C₂×D₄×C₅₃	—	4	1	no	—
522	C₂×D₄×C₅₃	—	4	1	no	—
523	C₂×D₄×C₅₃	—	4	1	no	—
524	C₂×D₄×C₅₃	—	8	2	no	—
525	C₂×D₄×C₅₃	—	8	2	no	—
526	C₂×D₄×C₅₃	—	8	2	no	—
527	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
528	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
529	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
530	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
531	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
532	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
533	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
544	C₂²×C₄×C₅₃	—	2	1	no	—
545	C₂²×C₄×C₅₃	—	2	1	no	—
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	—	2	1	no	—
554	C₂²×C₄×C₅₃	—	2	1	no	—
555	C₂²×C₄×C₅₃	—	2	1	no	—
556	C₂²×C₄×C₅₃	—	8	2	no	—
557	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
559	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
561	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
562	SD₁₆×C₅₃	—	2	2	no	—
563	SD₁₆×C₅₃	—	2	2	no	—
564	SD₁₆×C₅₃	—	2	2	no	—
565	SD₁₆×C₅₃	—	2	2	no	—
566	SD₁₆×C₅₃	—	4	1	no	—
567	SD₁₆×C₅₃	—	4	1	no	—
568	SD₁₆×C₅₃	—	4	1	no	—
569	SD₁₆×C₅₃	—	4	1	no	—
570	D₈×C₅₃	—	2	2	no	—
571	D₈×C₅₃	—	2	2	no	—
572	D₈×C₅₃	—	2	2	no	—
573	D₈×C₅₃	—	2	2	no	—
574	D₈×C₅₃	—	2	2	no	—
575	D₈×C₅₃	—	4	1	no	—
576	D₈×C₅₃	—	4	1	no	—
577	D₈×C₅₃	#41	1	4	yes	complemented
578	M₁₆×C₅₃	—	2	2	no	—
579	M₁₆×C₅₃	—	2	2	no	—
580	M₁₆×C₅₃	—	4	1	no	—
581	M₁₆×C₅₃	—	4	1	no	—
582	C₂×C₈×C₅₃	—	2	2	no	—
583	C₂×C₈×C₅₃	—	4	1	no	—
584	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
586	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
587	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
588	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
589	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
590	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
591	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
622	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
623	C₄⋊C₄×C₅₃	C₂×D₄	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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
630	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
674	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
675	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
676	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
677	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
684	C₄²×C₅₃	—	2	1	no	—
685	C₄²×C₅₃	—	2	1	no	—
686	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
687	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
688	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
689	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
690	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
691	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
692	C₂³×C₅₃	—	2	1	no	—
693	C₂³×C₅₃	—	2	1	no	—
694	C₂³×C₅₃	—	2	1	no	—
695	C₂³×C₅₃	—	2	1	no	—
696	C₂³×C₅₃	—	2	1	no	—
697	C₂³×C₅₃	—	2	1	no	—
698	C₂³×C₅₃	—	4	2	no	—
699	C₂³×C₅₃	—	4	2	no	—
700	C₂³×C₅₃	—	4	2	no	—
701	C₂³×C₅₃	—	4	2	no	—
702	C₂³×C₅₃	—	4	2	no	—
703	C₂³×C₅₃	—	8	1	no	—
704	C₂³×C₅₃	—	8	1	no	—
705	C₂³×C₅₃	—	8	1	no	—
706	C₂³×C₅₃	—	8	1	no	—
707	C₂³×C₅₃	—	8	1	no	—
708	C₂³×C₅₃	—	8	1	no	—
709	C₂³×C₅₃	—	8	1	no	—
710	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
711	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
712	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
713	Q₈×C₅₃	—	2	1	no	—
714	Q₈×C₅₃	—	2	1	no	—
715	Q₈×C₅₃	—	2	1	no	—
716	Q₈×C₅₃	—	2	1	no	—
717	Q₈×C₅₃	—	4	1	no	—
718	Q₈×C₅₃	—	8	1	no	—
719	Q₈×C₅₃	—	8	1	no	—
720	D₄×C₅₃	—	2	1	no	—
721	D₄×C₅₃	—	2	1	no	—
722	D₄×C₅₃	—	2	1	no	—
723	D₄×C₅₃	—	2	1	no	—
724	D₄×C₅₃	—	2	1	no	—
725	D₄×C₅₃	—	2	1	no	—
726	D₄×C₅₃	—	2	1	no	—
727	D₄×C₅₃	—	2	1	no	—
728	D₄×C₅₃	—	2	1	no	—
729	D₄×C₅₃	—	2	1	no	—
730	D₄×C₅₃	—	4	1	no	—
731	D₄×C₅₃	—	4	1	no	—
732	D₄×C₅₃	—	4	1	no	—
733	D₄×C₅₃	—	4	2	no	—
734	D₄×C₅₃	—	4	2	no	—
735	D₄×C₅₃	—	4	2	no	—
736	D₄×C₅₃	—	4	2	no	—
737	D₄×C₅₃	—	4	2	no	—
738	D₄×C₅₃	—	4	2	no	—
739	D₄×C₅₃	—	4	2	no	—
740	D₄×C₅₃	—	4	2	no	—
741	D₄×C₅₃	—	4	2	no	—
742	D₄×C₅₃	—	8	1	no	—
743	D₄×C₅₃	—	8	1	no	—
744	D₄×C₅₃	—	8	1	no	—
745	D₄×C₅₃	—	8	1	no	—
746	D₄×C₅₃	—	8	1	no	—
747	D₄×C₅₃	—	8	1	no	—
748	D₄×C₅₃	—	8	1	no	—
749	D₄×C₅₃	—	8	1	no	—
750	D₄×C₅₃	—	8	1	no	—
751	D₄×C₅₃	—	8	1	no	—
752	D₄×C₅₃	—	8	1	no	—
753	D₄×C₅₃	C₂×#41	1	2	yes	—
754	D₄×C₅₃	C₂×#41	1	2	yes	—
755	C₂×C₄×C₅₃	—	2	1	no	—
756	C₂×C₄×C₅₃	—	2	1	no	—
757	C₂×C₄×C₅₃	—	2	1	no	—
758	C₂×C₄×C₅₃	—	2	1	no	—
759	C₂×C₄×C₅₃	—	2	1	no	—
760	C₂×C₄×C₅₃	—	2	1	no	—
761	C₂×C₄×C₅₃	—	2	1	no	—
762	C₂×C₄×C₅₃	—	2	1	no	—
763	C₂×C₄×C₅₃	—	2	1	no	—
764	C₂×C₄×C₅₃	—	2	1	no	—
765	C₂×C₄×C₅₃	—	2	1	no	—
766	C₂×C₄×C₅₃	—	2	1	no	—
767	C₂×C₄×C₅₃	—	2	1	no	—
768	C₂×C₄×C₅₃	—	2	1	no	—
769	C₂×C₄×C₅₃	—	2	1	no	—
770	C₂×C₄×C₅₃	—	2	1	no	—
771	C₂×C₄×C₅₃	—	4	1	no	—
772	C₂×C₄×C₅₃	—	4	1	no	—
773	C₂×C₄×C₅₃	—	4	2	no	—
774	C₂×C₄×C₅₃	—	4	2	no	—
775	C₂×C₄×C₅₃	—	4	2	no	—
776	C₂×C₄×C₅₃	—	4	2	no	—
777	C₂×C₄×C₅₃	—	8	1	no	—
778	C₂×C₄×C₅₃	—	8	1	no	—
779	C₂×C₄×C₅₃	—	8	1	no	—
780	C₂×C₄×C₅₃	—	8	1	no	—
781	C₂×C₄×C₅₃	—	8	1	no	—
782	C₂×C₄×C₅₃	—	8	1	no	—
783	C₂×C₄×C₅₃	—	8	1	no	—
784	C₂×C₄×C₅₃	—	8	1	no	—
785	C₂×C₄×C₅₃	—	8	1	no	—
786	C₂×C₄×C₅₃	—	8	1	no	—
787	C₂×C₄×C₅₃	—	8	1	no	—
788	C₂×C₄×C₅₃	—	8	1	no	—
789	C₂×C₄×C₅₃	—	8	1	no	—
790	C₂×C₄×C₅₃	—	8	1	no	—
791	C₂×C₄×C₅₃	—	8	1	no	—
792	C₂×C₄×C₅₃	—	8	1	no	—
793	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
794	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
795	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
796	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
797	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
798	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
803	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
804	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
805	C₈×C₅₃	—	2	1	no	—
806	C₈×C₅₃	—	2	1	no	—
807	C₈×C₅₃	—	2	1	no	—
808	C₈×C₅₃	—	2	1	no	—
809	C₈×C₅₃	—	2	1	no	—
810	C₈×C₅₃	—	2	1	no	—
811	C₈×C₅₃	—	2	1	no	—
812	C₈×C₅₃	C₂×#41	1	2	yes	—
813	#61506	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
814	C₂²×C₅₃	—	2	1	no	—
815	C₂²×C₅₃	—	2	1	no	—
816	C₂²×C₅₃	—	2	1	no	—
817	C₂²×C₅₃	—	2	1	no	—
818	C₂²×C₅₃	—	2	1	no	—
819	C₂²×C₅₃	—	2	1	no	—
820	C₂²×C₅₃	—	2	1	no	—
821	C₂²×C₅₃	—	2	1	no	—
822	C₂²×C₅₃	—	2	1	no	—
823	C₂²×C₅₃	—	2	2	no	—
824	C₂²×C₅₃	—	2	2	no	—
825	C₂²×C₅₃	—	4	1	no	—
826	C₂²×C₅₃	—	4	1	no	—
827	C₂²×C₅₃	—	4	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	—	4	1	no	—
832	C₂²×C₅₃	—	4	1	no	—
833	C₂²×C₅₃	—	4	1	no	—
834	C₂²×C₅₃	—	4	1	no	—
835	C₂²×C₅₃	—	4	1	no	—
836	C₂²×C₅₃	—	4	1	no	—
837	C₂²×C₅₃	—	4	1	no	—
838	C₂²×C₅₃	—	4	1	no	—
839	C₂²×C₅₃	—	4	1	no	—
840	C₂²×C₅₃	—	4	1	no	—
841	C₂²×C₅₃	—	8	4	no	—
842	C₂²×C₅₃	—	16	2	no	—
843	C₂²×C₅₃	—	16	2	no	—
844	C₂²×C₅₃	—	16	2	no	—
845	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
846	C₄×C₅₃	—	2	1	no	—
847	C₄×C₅₃	—	2	1	no	—
848	C₄×C₅₃	—	2	1	no	—
849	C₄×C₅₃	—	2	1	no	—
850	C₄×C₅₃	—	2	1	no	—
851	C₄×C₅₃	—	2	1	no	—
852	C₄×C₅₃	—	2	1	no	—
853	C₄×C₅₃	—	2	1	no	—
854	C₄×C₅₃	—	2	1	no	—
855	C₄×C₅₃	—	2	1	no	—
856	C₄×C₅₃	—	2	1	no	—
857	C₄×C₅₃	—	4	1	no	—
858	C₄×C₅₃	—	4	1	no	—
859	C₄×C₅₃	—	4	1	no	—
860	C₄×C₅₃	—	4	1	no	—
861	C₄×C₅₃	—	4	1	no	—
862	C₄×C₅₃	—	4	1	no	—
863	C₄×C₅₃	—	4	1	no	—
864	C₄×C₅₃	—	4	1	no	—
865	C₄×C₅₃	—	4	1	no	—
866	C₄×C₅₃	—	4	1	no	—
867	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
868	C₄×C₅₃	#585	1	1	yes	characteristic
869	#3521	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3389	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#3355	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3350	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3348	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3322	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3307	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3179	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3174	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3171	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3119	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#2967	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
899	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
900	C₂×C₅₃	—	4	1	no	—
901	C₂×C₅₃	—	4	1	no	—
902	C₂×C₅₃	—	4	1	no	—
903	C₂×C₅₃	—	4	2	no	—
904	C₂×C₅₃	—	4	2	no	—
905	C₂×C₅₃	—	8	1	no	—
906	C₂×C₅₃	—	8	1	no	—
907	C₂×C₅₃	—	8	1	no	—
908	C₂×C₅₃	—	8	1	no	—
909	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
910	C₂×C₅₃	#3585	1	1	yes	characteristic
911	C₂×C₅₃	#3585	1	1	yes	characteristic
912	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
913	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
914	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
915	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
916	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#555	C₂²×C₅₃	1	1	yes	characteristic
918	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#553	—	2	1	no	—
921	#553	—	2	1	no	—
922	#553	C₂²×C₅₃	1	1	yes	characteristic
923	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#552	—	2	1	no	—
926	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#551	—	2	1	no	—
928	#551	—	2	1	no	—
929	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#546	—	2	1	no	—
932	#546	—	2	1	no	—
933	#546	—	2	1	no	—
934	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	D₄²	C₂²×C₅₃	1	1	yes	characteristic
937	D₄²	C₂²×C₅₃	1	1	yes	characteristic
938	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#540	C₂²×C₅₃	1	1	yes	characteristic
942	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#539	—	2	1	no	—
944	#538	—	2	1	no	—
945	#538	—	2	1	no	—
946	#538	—	2	1	no	—
947	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#529	—	2	1	no	—
949	#529	C₂²×C₅₃	1	1	yes	characteristic
950	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	C₂×#126	—	2	1	no	—
952	#525	—	2	1	no	—
953	C₂×#121	—	2	1	no	—
954	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#518	C₂²×C₅₃	1	1	yes	characteristic
956	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#499	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#463	C₂²×C₅₃	1	1	yes	characteristic
1009	#463	C₂²×C₅₃	1	1	yes	characteristic
1010	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#450	C₂²×C₅₃	1	1	yes	characteristic
1021	#450	C₂²×C₅₃	1	1	yes	characteristic
1022	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#447	C₂²×C₅₃	1	1	yes	characteristic
1029	#447	C₂²×C₅₃	1	1	yes	characteristic
1030	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#442	C₂²×C₅₃	1	1	yes	characteristic
1035	#442	C₂²×C₅₃	1	1	yes	characteristic
1036	#442	C₂²×C₅₃	1	1	yes	characteristic
1037	#442	C₂²×C₅₃	1	1	yes	characteristic
1038	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1056	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1057	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#418	C₂²×C₅₃	1	1	yes	characteristic
1075	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	C₅₃	#61506	1	1	yes	characteristic, direct product factor, Sylow
1084	C₂×#41	—	2	1	no	—
1085	C₂×#41	—	2	1	no	—
1086	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂²×D₄	—	2	1	no	—
1089	C₂²×D₄	—	2	1	no	—
1090	C₂²×D₄	—	2	1	no	—
1091	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂³×C₄	—	2	1	no	—
1096	AGL(1,ℤ/8)	—	2	4	no	—
1097	AGL(1,ℤ/8)	—	2	4	no	—
1098	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×D₈	—	2	4	no	—
1107	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1121	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1122	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1123	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1124	#127	C₂³×C₅₃	1	1	yes	characteristic
1125	#127	C₂³×C₅₃	1	1	yes	characteristic
1126	#127	C₂³×C₅₃	1	1	yes	characteristic
1127	#126	—	2	1	no	—
1128	#126	—	2	1	no	—
1129	#126	—	2	1	no	—
1130	#126	—	2	1	no	—
1131	#126	—	2	1	no	—
1132	#126	—	2	1	no	—
1133	#126	—	2	1	no	—
1134	#126	—	2	1	no	—
1135	#126	—	2	1	no	—
1136	#126	—	2	1	no	—
1137	#126	—	2	1	no	—
1138	#126	—	2	1	no	—
1139	#126	D₄×C₅₃	1	1	yes	characteristic
1140	#126	D₄×C₅₃	1	1	yes	characteristic
1141	#125	—	2	1	no	—
1142	#125	—	2	1	no	—
1143	#125	—	2	1	no	—
1144	#125	D₄×C₅₃	1	1	yes	characteristic
1145	#125	C₂³×C₅₃	1	1	yes	characteristic
1146	#125	C₂³×C₅₃	1	1	yes	characteristic
1147	#125	C₂³×C₅₃	1	1	yes	characteristic
1148	#125	C₂³×C₅₃	1	1	yes	characteristic
1149	#124	—	2	1	no	—
1150	#124	—	2	1	no	—
1151	#124	—	2	1	no	—
1152	#124	—	2	1	no	—
1153	#124	—	2	1	no	—
1154	#124	D₄×C₅₃	1	1	yes	characteristic
1155	#124	C₂³×C₅₃	1	1	yes	characteristic
1156	#124	C₂³×C₅₃	1	1	yes	characteristic
1157	#123	—	2	1	no	—
1158	#123	—	2	1	no	—
1159	#123	—	2	1	no	—
1160	#123	—	2	1	no	—
1161	#123	—	2	1	no	—
1162	#123	—	2	1	no	—
1163	#123	—	2	1	no	—
1164	#123	—	2	1	no	—
1165	#123	—	2	1	no	—
1166	#123	—	2	1	no	—
1167	#123	—	2	1	no	—
1168	#123	—	2	1	no	—
1169	#123	—	2	1	no	—
1170	#123	—	2	1	no	—
1171	#123	D₄×C₅₃	1	1	yes	characteristic
1172	#123	D₄×C₅₃	1	1	yes	characteristic
1173	C₂²⋊Q₈	—	2	1	no	—
1174	C₂²⋊Q₈	—	2	1	no	—
1175	C₂²⋊Q₈	—	2	1	no	—
1176	C₂²⋊Q₈	—	2	1	no	—
1177	C₂²⋊Q₈	—	2	1	no	—
1178	C₂²⋊Q₈	—	2	1	no	—
1179	C₂²⋊Q₈	—	2	1	no	—
1180	C₂²⋊Q₈	—	2	1	no	—
1181	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1182	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1186	#121	—	2	1	no	—
1187	#121	—	2	1	no	—
1188	#121	—	2	1	no	—
1189	#121	—	2	1	no	—
1190	#121	—	2	1	no	—
1191	#121	—	2	1	no	—
1192	#121	—	2	1	no	—
1193	#121	—	2	1	no	—
1194	#121	—	2	1	no	—
1195	#121	—	2	1	no	—
1196	#121	—	2	1	no	—
1197	#121	—	2	1	no	—
1198	#121	—	2	1	no	—
1199	#121	—	2	1	no	—
1200	#121	—	2	1	no	—
1201	#121	—	2	1	no	—
1202	#121	—	2	1	no	—
1203	#121	—	2	1	no	—
1204	#121	D₄×C₅₃	1	1	yes	characteristic
1205	#121	C₂³×C₅₃	1	1	yes	characteristic
1206	#121	C₂³×C₅₃	1	1	yes	characteristic
1207	#121	C₂³×C₅₃	1	1	yes	characteristic
1208	#121	C₂³×C₅₃	1	1	yes	characteristic
1209	#121	C₂³×C₅₃	1	1	yes	characteristic
1210	#121	C₂³×C₅₃	1	1	yes	characteristic
1211	#121	C₂³×C₅₃	1	1	yes	characteristic
1212	#121	C₂³×C₅₃	1	1	yes	characteristic
1213	#120	—	2	1	no	—
1214	#120	—	2	1	no	—
1215	#120	—	2	1	no	—
1216	#120	—	2	1	no	—
1217	#120	—	2	1	no	—
1218	#120	—	2	1	no	—
1219	#120	—	2	1	no	—
1220	#120	—	2	1	no	—
1221	C₄×Q₈	—	2	1	no	—
1222	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1223	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1224	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1225	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1226	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1227	C₄×D₄	—	2	1	no	—
1228	C₄×D₄	—	2	1	no	—
1229	C₄×D₄	—	2	1	no	—
1230	C₄×D₄	—	2	1	no	—
1231	C₄×D₄	—	2	1	no	—
1232	C₄×D₄	—	2	1	no	—
1233	C₄×D₄	—	2	1	no	—
1234	C₄×D₄	—	2	1	no	—
1235	C₄×D₄	—	2	1	no	—
1236	C₄×D₄	—	2	1	no	—
1237	C₄×D₄	—	2	1	no	—
1238	C₄×D₄	—	2	1	no	—
1239	C₄×D₄	—	2	1	no	—
1240	C₄×D₄	—	2	1	no	—
1241	C₄×D₄	—	2	1	no	—
1242	C₄×D₄	—	2	1	no	—
1243	C₄×D₄	—	2	1	no	—
1244	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1245	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1246	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1247	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1248	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1249	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1250	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1251	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1252	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1253	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1254	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1255	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1256	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1257	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1258	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1259	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1260	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1261	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1262	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1263	#117	—	2	1	no	—
1264	#117	—	2	1	no	—
1265	#117	—	2	1	no	—
1266	#117	—	2	1	no	—
1267	#117	—	2	1	no	—
1268	#117	—	2	1	no	—
1269	#117	C₂³×C₅₃	1	1	yes	characteristic
1270	#117	C₂³×C₅₃	1	1	yes	characteristic
1271	#117	C₂³×C₅₃	1	1	yes	characteristic
1272	#117	C₂³×C₅₃	1	1	yes	characteristic
1273	#117	C₂³×C₅₃	1	1	yes	characteristic
1274	#117	C₂³×C₅₃	1	1	yes	characteristic
1275	C₂×C₄⋊C₄	—	2	1	no	—
1276	C₂×C₄⋊C₄	—	2	1	no	—
1277	C₂×C₄⋊C₄	—	2	1	no	—
1278	C₂×C₄⋊C₄	—	2	1	no	—
1279	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1280	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1281	C₂×C₂²⋊C₄	—	2	1	no	—
1282	C₂×C₂²⋊C₄	—	2	1	no	—
1283	C₂×C₂²⋊C₄	—	2	1	no	—
1284	C₂×C₂²⋊C₄	—	2	1	no	—
1285	C₂×C₂²⋊C₄	—	2	1	no	—
1286	C₂×C₂²⋊C₄	—	2	1	no	—
1287	C₂×C₂²⋊C₄	—	2	1	no	—
1288	C₂×C₂²⋊C₄	—	2	1	no	—
1289	C₂×C₂²⋊C₄	—	2	1	no	—
1290	C₂×C₄²	—	2	1	no	—
1291	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1292	#107	C₂³×C₅₃	1	1	yes	characteristic
1293	#107	C₂³×C₅₃	1	1	yes	characteristic
1294	#107	C₂³×C₅₃	1	1	yes	characteristic
1295	#107	C₂³×C₅₃	1	1	yes	characteristic
1296	#107	C₂³×C₅₃	1	1	yes	characteristic
1297	#107	C₂³×C₅₃	1	1	yes	characteristic
1298	#107	C₂³×C₅₃	1	1	yes	characteristic
1299	#107	C₂³×C₅₃	1	1	yes	characteristic
1300	#106	C₂³×C₅₃	1	1	yes	characteristic
1301	#106	C₂³×C₅₃	1	1	yes	characteristic
1302	#106	C₂³×C₅₃	1	1	yes	characteristic
1303	#106	C₂³×C₅₃	1	1	yes	characteristic
1304	#106	C₂³×C₅₃	1	1	yes	characteristic
1305	#106	C₂³×C₅₃	1	1	yes	characteristic
1306	#106	C₂³×C₅₃	1	1	yes	characteristic
1307	#106	C₂³×C₅₃	1	1	yes	characteristic
1308	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1309	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1310	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1311	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1312	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1313	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1314	#103	C₂³×C₅₃	1	1	yes	characteristic
1315	#103	C₂³×C₅₃	1	1	yes	characteristic
1316	#103	C₂³×C₅₃	1	1	yes	characteristic
1317	#103	C₂³×C₅₃	1	1	yes	characteristic
1318	#103	C₂³×C₅₃	1	1	yes	characteristic
1319	#103	C₂³×C₅₃	1	1	yes	characteristic
1320	#103	C₂³×C₅₃	1	1	yes	characteristic
1321	#103	C₂³×C₅₃	1	1	yes	characteristic
1322	#102	C₂³×C₅₃	1	1	yes	characteristic
1323	#102	C₂³×C₅₃	1	1	yes	characteristic
1324	#102	C₂³×C₅₃	1	1	yes	characteristic
1325	#102	C₂³×C₅₃	1	1	yes	characteristic
1326	#102	C₂³×C₅₃	1	1	yes	characteristic
1327	#102	C₂³×C₅₃	1	1	yes	characteristic
1328	#102	C₂³×C₅₃	1	1	yes	characteristic
1329	#102	C₂³×C₅₃	1	1	yes	characteristic
1330	#102	C₂³×C₅₃	1	1	yes	characteristic
1331	#102	C₂³×C₅₃	1	1	yes	characteristic
1332	#102	C₂³×C₅₃	1	1	yes	characteristic
1333	#102	C₂³×C₅₃	1	1	yes	characteristic
1334	#102	C₂³×C₅₃	1	1	yes	characteristic
1335	#102	C₂³×C₅₃	1	1	yes	characteristic
1336	#102	C₂³×C₅₃	1	1	yes	characteristic
1337	#102	C₂³×C₅₃	1	1	yes	characteristic
1338	#102	C₂³×C₅₃	1	1	yes	characteristic
1339	#102	C₂³×C₅₃	1	1	yes	characteristic
1340	#102	C₂³×C₅₃	1	1	yes	characteristic
1341	#102	C₂³×C₅₃	1	1	yes	characteristic
1342	#102	C₂³×C₅₃	1	1	yes	characteristic
1343	#102	C₂³×C₅₃	1	1	yes	characteristic
1344	#102	C₂³×C₅₃	1	1	yes	characteristic
1345	#102	C₂³×C₅₃	1	1	yes	characteristic
1346	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1347	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1348	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1349	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1350	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1351	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1352	#97	C₂³×C₅₃	1	1	yes	characteristic
1353	#97	C₂³×C₅₃	1	1	yes	characteristic
1354	#97	C₂³×C₅₃	1	1	yes	characteristic
1355	#97	C₂³×C₅₃	1	1	yes	characteristic
1356	#97	C₂³×C₅₃	1	1	yes	characteristic
1357	#97	C₂³×C₅₃	1	1	yes	characteristic
1358	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1359	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1360	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1361	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1362	C₂⁴	—	2	1	no	—
1363	C₂⁴	—	2	1	no	—
1364	C₂⁴	—	2	1	no	—
1365	C₂⁴	—	2	1	no	—
1366	#41	—	2	2	no	—
1367	#41	—	2	2	no	—
1368	#41	—	4	1	no	—
1369	#41	—	4	1	no	—
1370	#41	—	8	2	no	—
1371	#41	—	8	2	no	—
1372	C₂×Q₈	—	2	1	no	—
1373	C₂×Q₈	—	2	1	no	—
1374	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1375	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1376	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1377	C₂×D₄	—	2	2	no	—
1378	C₂×D₄	—	2	2	no	—
1379	C₂×D₄	—	2	2	no	—
1380	C₂×D₄	—	2	2	no	—
1381	C₂×D₄	—	2	1	no	—
1382	C₂×D₄	—	2	1	no	—
1383	C₂×D₄	—	2	1	no	—
1384	C₂×D₄	—	2	1	no	—
1385	C₂×D₄	—	2	1	no	—
1386	C₂×D₄	—	2	1	no	—
1387	C₂×D₄	—	2	1	no	—
1388	C₂×D₄	—	2	1	no	—
1389	C₂×D₄	—	2	1	no	—
1390	C₂×D₄	—	2	1	no	—
1391	C₂×D₄	—	2	1	no	—
1392	C₂×D₄	—	2	1	no	—
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	2	1	no	—
1396	C₂×D₄	—	2	1	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	—	2	1	no	—
1400	C₂×D₄	—	2	1	no	—
1401	C₂×D₄	—	4	1	no	—
1402	C₂×D₄	—	4	1	no	—
1403	C₂×D₄	—	4	1	no	—
1404	C₂×D₄	—	4	1	no	—
1405	C₂×D₄	—	8	2	no	—
1406	C₂×D₄	—	8	2	no	—
1407	C₂×D₄	—	8	2	no	—
1408	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1409	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1410	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1411	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1412	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1413	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1414	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1415	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1416	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	2	1	no	—
1420	C₂²×C₄	—	2	1	no	—
1421	C₂²×C₄	—	2	1	no	—
1422	C₂²×C₄	—	2	1	no	—
1423	C₂²×C₄	—	2	1	no	—
1424	C₂²×C₄	—	2	1	no	—
1425	C₂²×C₄	—	2	1	no	—
1426	C₂²×C₄	—	2	1	no	—
1427	C₂²×C₄	—	2	1	no	—
1428	C₂²×C₄	—	2	1	no	—
1429	C₂²×C₄	—	2	1	no	—
1430	C₂²×C₄	—	2	1	no	—
1431	C₂²×C₄	—	2	1	no	—
1432	C₂²×C₄	—	2	1	no	—
1433	C₂²×C₄	—	2	1	no	—
1434	C₂²×C₄	—	2	1	no	—
1435	C₂²×C₄	—	2	1	no	—
1436	C₂²×C₄	—	2	1	no	—
1437	C₂²×C₄	—	8	2	no	—
1438	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1439	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1440	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1441	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1442	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1443	SD₁₆	—	2	2	no	—
1444	SD₁₆	—	2	2	no	—
1445	SD₁₆	—	2	2	no	—
1446	SD₁₆	—	2	2	no	—
1447	SD₁₆	—	4	1	no	—
1448	SD₁₆	—	4	1	no	—
1449	SD₁₆	—	4	1	no	—
1450	SD₁₆	—	4	1	no	—
1451	D₈	—	2	2	no	—
1452	D₈	—	2	2	no	—
1453	D₈	—	2	2	no	—
1454	D₈	—	2	2	no	—
1455	D₈	—	2	2	no	—
1456	D₈	—	4	1	no	—
1457	D₈	—	4	1	no	—
1458	D₈	#41×C₅₃	1	4	yes	complemented
1459	M₁₆	—	2	2	no	—
1460	M₁₆	—	2	2	no	—
1461	M₁₆	—	4	1	no	—
1462	M₁₆	—	4	1	no	—
1463	C₂×C₈	—	2	2	no	—
1464	C₂×C₈	—	4	1	no	—
1465	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1466	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1467	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1468	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1469	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1470	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1471	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1472	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1473	C₄⋊C₄	—	2	1	no	—
1474	C₄⋊C₄	—	2	1	no	—
1475	C₄⋊C₄	—	2	1	no	—
1476	C₄⋊C₄	—	2	1	no	—
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1496	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1497	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1498	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1499	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1500	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1501	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1502	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1503	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1504	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1505	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1506	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1507	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1508	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1509	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1510	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1511	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1512	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1520	C₂²⋊C₄	—	2	1	no	—
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	—	2	1	no	—
1545	C₂²⋊C₄	—	2	1	no	—
1546	C₂²⋊C₄	—	2	1	no	—
1547	C₂²⋊C₄	—	2	1	no	—
1548	C₂²⋊C₄	—	2	1	no	—
1549	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1550	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1551	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1552	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1553	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1554	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1555	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1556	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1557	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1558	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1559	C₄²	—	2	1	no	—
1560	C₄²	—	2	1	no	—
1561	C₄²	—	2	1	no	—
1562	C₄²	—	2	1	no	—
1563	C₄²	—	2	1	no	—
1564	C₄²	—	2	1	no	—
1565	C₄²	—	2	1	no	—
1566	C₄²	—	2	1	no	—
1567	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1568	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1569	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1570	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1571	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1572	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1573	C₂³	—	2	1	no	—
1574	C₂³	—	2	1	no	—
1575	C₂³	—	2	1	no	—
1576	C₂³	—	2	1	no	—
1577	C₂³	—	2	1	no	—
1578	C₂³	—	2	1	no	—
1579	C₂³	—	4	2	no	—
1580	C₂³	—	4	2	no	—
1581	C₂³	—	4	2	no	—
1582	C₂³	—	4	2	no	—
1583	C₂³	—	4	2	no	—
1584	C₂³	—	8	1	no	—
1585	C₂³	—	8	1	no	—
1586	C₂³	—	8	1	no	—
1587	C₂³	—	8	1	no	—
1588	C₂³	—	8	1	no	—
1589	C₂³	—	8	1	no	—
1590	C₂³	—	8	1	no	—
1591	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1592	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1593	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1594	Q₈	—	2	1	no	—
1595	Q₈	—	2	1	no	—
1596	Q₈	—	2	1	no	—
1597	Q₈	—	2	1	no	—
1598	Q₈	—	4	1	no	—
1599	Q₈	—	8	1	no	—
1600	Q₈	—	8	1	no	—
1601	D₄	—	2	1	no	—
1602	D₄	—	2	1	no	—
1603	D₄	—	2	1	no	—
1604	D₄	—	2	1	no	—
1605	D₄	—	2	1	no	—
1606	D₄	—	2	1	no	—
1607	D₄	—	2	1	no	—
1608	D₄	—	2	1	no	—
1609	D₄	—	2	1	no	—
1610	D₄	—	2	1	no	—
1611	D₄	—	4	1	no	—
1612	D₄	—	4	1	no	—
1613	D₄	—	4	1	no	—
1614	D₄	—	4	2	no	—
1615	D₄	—	4	2	no	—
1616	D₄	—	4	2	no	—
1617	D₄	—	4	2	no	—
1618	D₄	—	4	2	no	—
1619	D₄	—	4	2	no	—
1620	D₄	—	4	2	no	—
1621	D₄	—	4	2	no	—
1622	D₄	—	4	2	no	—
1623	D₄	—	8	1	no	—
1624	D₄	—	8	1	no	—
1625	D₄	—	8	1	no	—
1626	D₄	—	8	1	no	—
1627	D₄	—	8	1	no	—
1628	D₄	—	8	1	no	—
1629	D₄	—	8	1	no	—
1630	D₄	—	8	1	no	—
1631	D₄	—	8	1	no	—
1632	D₄	—	8	1	no	—
1633	D₄	—	8	1	no	—
1634	D₄	C₂×#41×C₅₃	1	2	yes	—
1635	D₄	C₂×#41×C₅₃	1	2	yes	—
1636	C₂×C₄	—	2	1	no	—
1637	C₂×C₄	—	2	1	no	—
1638	C₂×C₄	—	2	1	no	—
1639	C₂×C₄	—	2	1	no	—
1640	C₂×C₄	—	2	1	no	—
1641	C₂×C₄	—	2	1	no	—
1642	C₂×C₄	—	2	1	no	—
1643	C₂×C₄	—	2	1	no	—
1644	C₂×C₄	—	2	1	no	—
1645	C₂×C₄	—	2	1	no	—
1646	C₂×C₄	—	2	1	no	—
1647	C₂×C₄	—	2	1	no	—
1648	C₂×C₄	—	2	1	no	—
1649	C₂×C₄	—	2	1	no	—
1650	C₂×C₄	—	2	1	no	—
1651	C₂×C₄	—	2	1	no	—
1652	C₂×C₄	—	4	1	no	—
1653	C₂×C₄	—	4	1	no	—
1654	C₂×C₄	—	4	2	no	—
1655	C₂×C₄	—	4	2	no	—
1656	C₂×C₄	—	4	2	no	—
1657	C₂×C₄	—	4	2	no	—
1658	C₂×C₄	—	8	1	no	—
1659	C₂×C₄	—	8	1	no	—
1660	C₂×C₄	—	8	1	no	—
1661	C₂×C₄	—	8	1	no	—
1662	C₂×C₄	—	8	1	no	—
1663	C₂×C₄	—	8	1	no	—
1664	C₂×C₄	—	8	1	no	—
1665	C₂×C₄	—	8	1	no	—
1666	C₂×C₄	—	8	1	no	—
1667	C₂×C₄	—	8	1	no	—
1668	C₂×C₄	—	8	1	no	—
1669	C₂×C₄	—	8	1	no	—
1670	C₂×C₄	—	8	1	no	—
1671	C₂×C₄	—	8	1	no	—
1672	C₂×C₄	—	8	1	no	—
1673	C₂×C₄	—	8	1	no	—
1674	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1675	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1676	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1677	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1678	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1679	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1680	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1681	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1682	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1683	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1684	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1685	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1686	C₈	—	2	1	no	—
1687	C₈	—	2	1	no	—
1688	C₈	—	2	1	no	—
1689	C₈	—	2	1	no	—
1690	C₈	—	2	1	no	—
1691	C₈	—	2	1	no	—
1692	C₈	—	2	1	no	—
1693	C₈	C₂×#41×C₅₃	1	2	yes	—
1694	C₂²	—	2	1	no	—
1695	C₂²	—	2	1	no	—
1696	C₂²	—	2	1	no	—
1697	C₂²	—	2	2	no	—
1698	C₂²	—	2	2	no	—
1699	C₂²	—	2	1	no	—
1700	C₂²	—	2	1	no	—
1701	C₂²	—	2	1	no	—
1702	C₂²	—	2	1	no	—
1703	C₂²	—	2	1	no	—
1704	C₂²	—	2	1	no	—
1705	C₂²	—	4	1	no	—
1706	C₂²	—	4	1	no	—
1707	C₂²	—	4	1	no	—
1708	C₂²	—	4	1	no	—
1709	C₂²	—	4	1	no	—
1710	C₂²	—	4	1	no	—
1711	C₂²	—	4	1	no	—
1712	C₂²	—	4	1	no	—
1713	C₂²	—	4	1	no	—
1714	C₂²	—	4	1	no	—
1715	C₂²	—	4	1	no	—
1716	C₂²	—	4	1	no	—
1717	C₂²	—	4	1	no	—
1718	C₂²	—	4	1	no	—
1719	C₂²	—	4	1	no	—
1720	C₂²	—	4	1	no	—
1721	C₂²	—	8	4	no	—
1722	C₂²	—	16	2	no	—
1723	C₂²	—	16	2	no	—
1724	C₂²	—	16	2	no	—
1725	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1726	C₄	—	2	1	no	—
1727	C₄	—	2	1	no	—
1728	C₄	—	2	1	no	—
1729	C₄	—	2	1	no	—
1730	C₄	—	2	1	no	—
1731	C₄	—	2	1	no	—
1732	C₄	—	2	1	no	—
1733	C₄	—	2	1	no	—
1734	C₄	—	2	1	no	—
1735	C₄	—	2	1	no	—
1736	C₄	—	2	1	no	—
1737	C₄	—	4	1	no	—
1738	C₄	—	4	1	no	—
1739	C₄	—	4	1	no	—
1740	C₄	—	4	1	no	—
1741	C₄	—	4	1	no	—
1742	C₄	—	4	1	no	—
1743	C₄	—	4	1	no	—
1744	C₄	—	4	1	no	—
1745	C₄	—	4	1	no	—
1746	C₄	—	4	1	no	—
1747	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1748	C₄	C₅₃×#585	1	1	yes	characteristic
1749	C₂	—	4	1	no	—
1750	C₂	—	4	1	no	—
1751	C₂	—	4	1	no	—
1752	C₂	—	4	2	no	—
1753	C₂	—	4	2	no	—
1754	C₂	—	8	1	no	—
1755	C₂	—	8	1	no	—
1756	C₂	—	8	1	no	—
1757	C₂	—	8	1	no	—
1758	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1759	C₂	C₅₃×#3585	1	1	yes	characteristic
1760	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3521	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3397	C₂	semidirect
4. C₅₃×#3389	C₂	semidirect
5. C₅₃×#3376	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3355	C₂	semidirect
8. C₅₃×#3350	C₂	semidirect
9. C₅₃×#3348	C₂	semidirect
10. C₅₃×#3324	C₂	semidirect
11. C₅₃×#3322	C₂	semidirect
12. C₅₃×#3319	C₂	semidirect
13. C₅₃×#3318	C₂	semidirect
14. C₅₃×#3310	C₂	semidirect
15. C₅₃×#3307	C₂	semidirect
16. C₅₃×#3272	C₂	semidirect
17. C₅₃×#3264	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3179	C₂	semidirect
20. C₅₃×#3174	C₂	semidirect
21. C₅₃×#3171	C₂	semidirect
22. C₅₃×#3123	C₂	semidirect
23. C₅₃×#3122	C₂	semidirect
24. C₅₃×#3119	C₂	semidirect
25. C₅₃×#3118	C₂	semidirect
26. C₅₃×#3115	C₂	semidirect
27. C₅₃×#3114	C₂	semidirect
28. C₅₃×#2967	C₂	semidirect
29. C₅₃×#2948	C₂	semidirect
30. C₅₃×#2946	C₂	semidirect
31. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
35. C₅₃×#556	C₂²	semidirect
36. C₅₃×#556	C₂²	semidirect
38. C₅₃×#554	C₂²	semidirect
39. C₅₃×#554	C₂²	semidirect
43. C₅₃×#553	C₂²	semidirect
44. C₅₃×#553	C₂²	semidirect
46. C₅₃×#552	C₂²	semidirect
49. C₅₃×#550	C₂²	semidirect
50. C₅₃×#547	C₂²	semidirect
54. C₅₃×#546	C₂²	semidirect
55. C₅₃×#546	C₂²	semidirect
58. D₄²×C₅₃	C₂²	semidirect
59. C₅₃×#542	C₂²	semidirect
60. C₅₃×#541	C₂²	semidirect
62. C₅₃×#540	C₂²	semidirect
67. C₅₃×#532	C₂²	semidirect
70. C₅₃×#529	C₂²	semidirect
74. C₅₃×#520	C₂²	semidirect
76. C₅₃×#518	C₂²	semidirect
77. C₅₃×#518	C₂²	semidirect
78. C₄×#41×C₅₃	C₂²	semidirect
79. C₂×C₄×D₄×C₅₃	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#501	C₂²	semidirect
82. C₅₃×#499	C₂²	semidirect
83. C₅₃×#496	C₂²	semidirect
84. C₅₃×#496	C₂²	semidirect
85. C₅₃×#492	C₂²	semidirect
86. C₅₃×#491	C₂²	semidirect
87. C₅₃×#490	C₂²	semidirect
88. C₅₃×#490	C₂²	semidirect
89. C₅₃×#489	C₂²	semidirect
90. C₅₃×#488	C₂²	semidirect
91. C₅₃×#486	C₂²	semidirect
92. C₅₃×#485	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#483	C₂²	semidirect
96. C₅₃×#482	C₂²	semidirect
97. C₅₃×#482	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#481	C₂²	semidirect
102. C₅₃×#480	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×#478	C₂²	semidirect
109. C₅₃×#478	C₂²	semidirect
110. C₅₃×#478	C₂²	semidirect
111. C₅₃×#478	C₂²	semidirect
112. C₅₃×#476	C₂²	semidirect
113. C₅₃×#475	C₂²	semidirect
114. C₅₃×#474	C₂²	semidirect
115. C₅₃×#474	C₂²	semidirect
116. C₅₃×#469	C₂²	semidirect
117. C₅₃×#469	C₂²	semidirect
118. C₅₃×#469	C₂²	semidirect
119. C₅₃×#468	C₂²	semidirect
120. C₅₃×#468	C₂²	semidirect
121. C₅₃×#468	C₂²	semidirect
122. C₅₃×#468	C₂²	semidirect
123. C₅₃×#468	C₂²	semidirect
124. C₅₃×#466	C₂²	semidirect
125. C₅₃×#465	C₂²	semidirect
126. C₅₃×#465	C₂²	semidirect
127. C₅₃×#465	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#461	C₂²	semidirect
133. C₅₃×#461	C₂²	semidirect
134. C₅₃×#460	C₂²	semidirect
135. C₅₃×#460	C₂²	semidirect
136. C₅₃×#459	C₂²	semidirect
137. C₅₃×#459	C₂²	semidirect
138. C₅₃×#459	C₂²	semidirect
139. C₅₃×#459	C₂²	semidirect
142. C₅₃×#450	C₂²	semidirect
143. C₅₃×#450	C₂²	semidirect
144. C₅₃×#449	C₂²	semidirect
145. C₅₃×#449	C₂²	semidirect
146. C₅₃×#449	C₂²	semidirect
147. C₅₃×#449	C₂²	semidirect
150. C₅₃×#447	C₂²	semidirect
151. C₅₃×#447	C₂²	semidirect
152. C₅₃×#446	C₂²	semidirect
153. C₅₃×#446	C₂²	semidirect
158. C₅₃×#442	C₂²	semidirect
159. C₅₃×#442	C₂²	semidirect
160. C₅₃×#442	C₂²	semidirect
161. C₅₃×#442	C₂²	semidirect
162. C₅₃×#442	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×SD₁₆×C₅₃	C₂²	semidirect
171. C₄×SD₁₆×C₅₃	C₂²	semidirect
172. C₄×SD₁₆×C₅₃	C₂²	semidirect
173. C₄×SD₁₆×C₅₃	C₂²	semidirect
174. C₄×SD₁₆×C₅₃	C₂²	semidirect
177. C₄×D₈×C₅₃	C₂²	semidirect
178. C₄×D₈×C₅₃	C₂²	semidirect
179. C₄×D₈×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
181. C₄×D₈×C₅₃	C₂²	semidirect
182. C₅₃×#436	C₂²	semidirect
183. C₅₃×#436	C₂²	semidirect
184. C₅₃×#435	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. C₅₃×#427	C₂²	semidirect
195. C₅₃×#418	C₂²	semidirect
196. C₅₃×#418	C₂²	semidirect
197. C₅₃×#417	C₂²	semidirect
198. C₅₃×#416	C₂²	semidirect
199. C₂×#102×C₅₃	C₂²	semidirect
200. C₅₃×#405	C₂²	semidirect
201. C₅₃×#405	C₂²	semidirect
202. C₄×M₁₆×C₅₃	C₂²	semidirect
577. D₈×C₅₃	#41	semidirect
813. #61506	C₅₃	direct (N × H)
869. #3521	C₂×C₅₃	semidirect
870. #3519	C₂×C₅₃	semidirect
871. #3397	C₂×C₅₃	semidirect
872. #3389	C₂×C₅₃	semidirect
873. #3376	C₂×C₅₃	semidirect
874. #3366	C₂×C₅₃	semidirect
875. #3355	C₂×C₅₃	semidirect
876. #3350	C₂×C₅₃	semidirect
877. #3348	C₂×C₅₃	semidirect
878. #3324	C₂×C₅₃	semidirect
879. #3322	C₂×C₅₃	semidirect
880. #3319	C₂×C₅₃	semidirect
881. #3318	C₂×C₅₃	semidirect
882. #3310	C₂×C₅₃	semidirect
883. #3307	C₂×C₅₃	semidirect
884. #3272	C₂×C₅₃	semidirect
885. #3264	C₂×C₅₃	semidirect
886. #3264	C₂×C₅₃	semidirect
887. #3179	C₂×C₅₃	semidirect
888. #3174	C₂×C₅₃	semidirect
889. #3171	C₂×C₅₃	semidirect
890. #3123	C₂×C₅₃	semidirect
891. #3122	C₂×C₅₃	semidirect
892. #3119	C₂×C₅₃	semidirect
893. #3118	C₂×C₅₃	semidirect
894. #3115	C₂×C₅₃	semidirect
895. #3114	C₂×C₅₃	semidirect
896. #2967	C₂×C₅₃	semidirect
897. #2948	C₂×C₅₃	semidirect
898. #2946	C₂×C₅₃	semidirect
899. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
915. #556	C₂²×C₅₃	semidirect
916. #556	C₂²×C₅₃	semidirect
918. #554	C₂²×C₅₃	semidirect
919. #554	C₂²×C₅₃	semidirect
923. #553	C₂²×C₅₃	semidirect
924. #553	C₂²×C₅₃	semidirect
926. #552	C₂²×C₅₃	semidirect
929. #550	C₂²×C₅₃	semidirect
930. #547	C₂²×C₅₃	semidirect
934. #546	C₂²×C₅₃	semidirect
935. #546	C₂²×C₅₃	semidirect
938. D₄²	C₂²×C₅₃	semidirect
939. #542	C₂²×C₅₃	semidirect
940. #541	C₂²×C₅₃	semidirect
942. #540	C₂²×C₅₃	semidirect
947. #532	C₂²×C₅₃	semidirect
950. #529	C₂²×C₅₃	semidirect
954. #520	C₂²×C₅₃	semidirect
956. #518	C₂²×C₅₃	semidirect
957. #518	C₂²×C₅₃	semidirect
958. C₄×#41	C₂²×C₅₃	semidirect
959. C₂×C₄×D₄	C₂²×C₅₃	semidirect
960. #501	C₂²×C₅₃	semidirect
961. #501	C₂²×C₅₃	semidirect
962. #499	C₂²×C₅₃	semidirect
963. #496	C₂²×C₅₃	semidirect
964. #496	C₂²×C₅₃	semidirect
965. #492	C₂²×C₅₃	semidirect
966. #491	C₂²×C₅₃	semidirect
967. #490	C₂²×C₅₃	semidirect
968. #490	C₂²×C₅₃	semidirect
969. #489	C₂²×C₅₃	semidirect
970. #488	C₂²×C₅₃	semidirect
971. #486	C₂²×C₅₃	semidirect
972. #485	C₂²×C₅₃	semidirect
973. #485	C₂²×C₅₃	semidirect
974. #485	C₂²×C₅₃	semidirect
975. #483	C₂²×C₅₃	semidirect
976. #482	C₂²×C₅₃	semidirect
977. #482	C₂²×C₅₃	semidirect
978. #482	C₂²×C₅₃	semidirect
979. #482	C₂²×C₅₃	semidirect
980. #482	C₂²×C₅₃	semidirect
981. #481	C₂²×C₅₃	semidirect
982. #480	C₂²×C₅₃	semidirect
983. #480	C₂²×C₅₃	semidirect
984. #479	C₂²×C₅₃	semidirect
985. #478	C₂²×C₅₃	semidirect
986. #478	C₂²×C₅₃	semidirect
987. #478	C₂²×C₅₃	semidirect
988. #478	C₂²×C₅₃	semidirect
989. #478	C₂²×C₅₃	semidirect
990. #478	C₂²×C₅₃	semidirect
991. #478	C₂²×C₅₃	semidirect
992. #476	C₂²×C₅₃	semidirect
993. #475	C₂²×C₅₃	semidirect
994. #474	C₂²×C₅₃	semidirect
995. #474	C₂²×C₅₃	semidirect
996. #469	C₂²×C₅₃	semidirect
997. #469	C₂²×C₅₃	semidirect
998. #469	C₂²×C₅₃	semidirect
999. #468	C₂²×C₅₃	semidirect
1000. #468	C₂²×C₅₃	semidirect
1001. #468	C₂²×C₅₃	semidirect
1002. #468	C₂²×C₅₃	semidirect
1003. #468	C₂²×C₅₃	semidirect
1004. #466	C₂²×C₅₃	semidirect
1005. #465	C₂²×C₅₃	semidirect
1006. #465	C₂²×C₅₃	semidirect
1007. #465	C₂²×C₅₃	semidirect
1010. #463	C₂²×C₅₃	semidirect
1011. #463	C₂²×C₅₃	semidirect
1012. #461	C₂²×C₅₃	semidirect
1013. #461	C₂²×C₅₃	semidirect
1014. #460	C₂²×C₅₃	semidirect
1015. #460	C₂²×C₅₃	semidirect
1016. #459	C₂²×C₅₃	semidirect
1017. #459	C₂²×C₅₃	semidirect
1018. #459	C₂²×C₅₃	semidirect
1019. #459	C₂²×C₅₃	semidirect
1022. #450	C₂²×C₅₃	semidirect
1023. #450	C₂²×C₅₃	semidirect
1024. #449	C₂²×C₅₃	semidirect
1025. #449	C₂²×C₅₃	semidirect
1026. #449	C₂²×C₅₃	semidirect
1027. #449	C₂²×C₅₃	semidirect
1030. #447	C₂²×C₅₃	semidirect
1031. #447	C₂²×C₅₃	semidirect
1032. #446	C₂²×C₅₃	semidirect
1033. #446	C₂²×C₅₃	semidirect
1038. #442	C₂²×C₅₃	semidirect
1039. #442	C₂²×C₅₃	semidirect
1040. #442	C₂²×C₅₃	semidirect
1041. #442	C₂²×C₅₃	semidirect
1042. #442	C₂²×C₅₃	semidirect
1043. #440	C₂²×C₅₃	semidirect
1044. #440	C₂²×C₅₃	semidirect
1045. #440	C₂²×C₅₃	semidirect
1046. #440	C₂²×C₅₃	semidirect
1047. #440	C₂²×C₅₃	semidirect
1048. #440	C₂²×C₅₃	semidirect
1049. #440	C₂²×C₅₃	semidirect
1050. C₄×SD₁₆	C₂²×C₅₃	semidirect
1051. C₄×SD₁₆	C₂²×C₅₃	semidirect
1052. C₄×SD₁₆	C₂²×C₅₃	semidirect
1053. C₄×SD₁₆	C₂²×C₅₃	semidirect
1054. C₄×SD₁₆	C₂²×C₅₃	semidirect
1057. C₄×D₈	C₂²×C₅₃	semidirect
1058. C₄×D₈	C₂²×C₅₃	semidirect
1059. C₄×D₈	C₂²×C₅₃	semidirect
1060. C₄×D₈	C₂²×C₅₃	semidirect
1061. C₄×D₈	C₂²×C₅₃	semidirect
1062. #436	C₂²×C₅₃	semidirect
1063. #436	C₂²×C₅₃	semidirect
1064. #435	C₂²×C₅₃	semidirect
1065. #435	C₂²×C₅₃	semidirect
1066. #435	C₂²×C₅₃	semidirect
1067. #435	C₂²×C₅₃	semidirect
1068. #433	C₂²×C₅₃	semidirect
1069. #433	C₂²×C₅₃	semidirect
1070. #432	C₂²×C₅₃	semidirect
1071. #428	C₂²×C₅₃	semidirect
1072. #428	C₂²×C₅₃	semidirect
1073. #427	C₂²×C₅₃	semidirect
1075. #418	C₂²×C₅₃	semidirect
1076. #418	C₂²×C₅₃	semidirect
1077. #417	C₂²×C₅₃	semidirect
1078. #416	C₂²×C₅₃	semidirect
1079. C₂×#102	C₂²×C₅₃	semidirect
1080. #405	C₂²×C₅₃	semidirect
1081. #405	C₂²×C₅₃	semidirect
1082. C₄×M₁₆	C₂²×C₅₃	semidirect
1083. C₅₃	#61506	direct (N × H)
1458. 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×#3519	2
C₅₃×#3397	2
C₅₃×#3389	2
C₅₃×#3376	2
C₅₃×#3366	2
C₅₃×#3355	2
C₅₃×#3350	2
C₅₃×#3348	2
C₅₃×#3324	2
C₅₃×#3322	2
C₅₃×#3319	2
C₅₃×#3318	2
C₅₃×#3310	2
C₅₃×#3307	2
C₅₃×#3272	2
C₅₃×#3264	2
C₅₃×#3179	2
C₅₃×#3174	2
C₅₃×#3171	2
C₅₃×#3123	2
C₅₃×#3122	2
C₅₃×#3119	2
C₅₃×#3118	2
C₅₃×#3115	2
C₅₃×#3114	2
C₅₃×#2967	2
C₅₃×#2948	2
C₅₃×#2946	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61506	53

Subgroups — C53×#61506 #27269018

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61506 #27269018