Subgroups — C₅₃×#62007 #27269519

Order 13568.

1966 conjugacy classes of subgroups.

The subgroup lattice has 1856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3513	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3309	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3268	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3264	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×#3259	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3224	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3220	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3122	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#560	—	2	1	no	—
39	C₅₃×#560	—	2	1	no	—
40	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#553	—	2	1	no	—
44	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#551	—	2	1	no	—
47	C₅₃×#551	—	2	1	no	—
48	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic
54	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
57	D₄²×C₅₃	—	2	1	no	—
58	D₄²×C₅₃	C₂²	1	1	yes	characteristic
59	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#540	—	2	1	no	—
64	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#539	—	2	1	no	—
68	C₅₃×#538	—	2	1	no	—
69	C₅₃×#535	—	2	1	no	—
70	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#534	—	2	1	no	—
73	C₅₃×#534	—	2	1	no	—
74	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#529	C₂²	1	1	yes	characteristic
76	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#525	—	2	1	no	—
79	C₂×#123×C₅₃	—	2	1	no	—
80	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×D₄×C₅₃	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×#496	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#486	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×#481	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#478	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×#476	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#466	C₂²	1	1	yes	characteristic
117	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#459	C₂²	1	1	yes	characteristic
139	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#447	C₂²	1	1	yes	characteristic
164	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
181	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₈×C₅₃	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×#435	C₂²	1	1	yes	characteristic, complemented
189	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
190	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
200	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
201	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×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	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×D₄×C₅₃	—	2	1	no	—
209	C₂²×D₄×C₅₃	—	2	1	no	—
210	C₂²×D₄×C₅₃	—	2	1	no	—
211	C₂²×D₄×C₅₃	—	2	1	no	—
212	C₂²×D₄×C₅₃	—	2	1	no	—
213	C₂²×D₄×C₅₃	—	2	1	no	—
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
220	C₂³×C₄×C₅₃	—	2	1	no	—
221	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
222	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
223	#135×C₅₃	—	4	2	no	—
224	C₂×Q₁₆×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×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×D₈×C₅₃	—	4	2	no	—
234	C₂×D₈×C₅₃	—	4	2	no	—
235	C₂×D₈×C₅₃	—	4	2	no	—
236	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
253	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
256	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	#127×C₅₃	—	2	1	no	—
259	#127×C₅₃	—	2	1	no	—
260	#127×C₅₃	—	2	1	no	—
261	#127×C₅₃	C₂³	1	1	yes	characteristic
262	#127×C₅₃	C₂³	1	1	yes	characteristic
263	#127×C₅₃	C₂³	1	1	yes	characteristic
264	#127×C₅₃	C₂³	1	1	yes	characteristic
265	#127×C₅₃	C₂³	1	1	yes	characteristic
266	#127×C₅₃	C₂³	1	1	yes	characteristic
267	#127×C₅₃	C₂³	1	1	yes	characteristic
268	#126×C₅₃	—	2	1	no	—
269	#126×C₅₃	—	2	1	no	—
270	#126×C₅₃	—	2	1	no	—
271	#126×C₅₃	—	2	1	no	—
272	#126×C₅₃	—	2	1	no	—
273	#126×C₅₃	D₄	1	1	yes	characteristic
274	#126×C₅₃	D₄	1	1	yes	characteristic
275	#125×C₅₃	—	2	1	no	—
276	#125×C₅₃	D₄	1	1	yes	characteristic
277	#125×C₅₃	C₂³	1	1	yes	characteristic
278	#125×C₅₃	C₂³	1	1	yes	characteristic
279	#125×C₅₃	C₂³	1	1	yes	characteristic
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	—	2	1	no	—
283	#124×C₅₃	D₄	1	1	yes	characteristic
284	#124×C₅₃	C₂³	1	1	yes	characteristic
285	#124×C₅₃	C₂³	1	1	yes	characteristic
286	#124×C₅₃	C₂³	1	1	yes	characteristic
287	#124×C₅₃	C₂³	1	1	yes	characteristic
288	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
294	#123×C₅₃	—	2	1	no	—
295	#123×C₅₃	—	2	1	no	—
296	#123×C₅₃	—	2	1	no	—
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	—	2	1	no	—
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	D₄	1	1	yes	characteristic
311	#123×C₅₃	D₄	1	1	yes	characteristic
312	C₂²⋊Q₈×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	—	2	1	no	—
315	C₂²⋊Q₈×C₅₃	—	2	1	no	—
316	C₂²⋊Q₈×C₅₃	—	2	1	no	—
317	C₂²⋊Q₈×C₅₃	D₄	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	—	2	1	no	—
329	#121×C₅₃	—	2	1	no	—
330	#121×C₅₃	—	2	1	no	—
331	#121×C₅₃	—	2	1	no	—
332	#121×C₅₃	—	2	1	no	—
333	#121×C₅₃	—	2	1	no	—
334	#121×C₅₃	—	2	1	no	—
335	#121×C₅₃	—	2	1	no	—
336	#121×C₅₃	—	2	1	no	—
337	#121×C₅₃	—	2	1	no	—
338	#121×C₅₃	—	2	1	no	—
339	#121×C₅₃	—	2	1	no	—
340	#121×C₅₃	—	2	1	no	—
341	#121×C₅₃	—	2	1	no	—
342	#121×C₅₃	—	2	1	no	—
343	#121×C₅₃	—	2	1	no	—
344	#121×C₅₃	—	2	1	no	—
345	#121×C₅₃	D₄	1	1	yes	characteristic
346	#121×C₅₃	C₂³	1	1	yes	characteristic
347	#121×C₅₃	C₂³	1	1	yes	characteristic
348	#121×C₅₃	C₂³	1	1	yes	characteristic
349	#121×C₅₃	C₂³	1	1	yes	characteristic
350	#121×C₅₃	C₂³	1	1	yes	characteristic
351	#121×C₅₃	C₂³	1	1	yes	characteristic
352	#121×C₅₃	C₂³	1	1	yes	characteristic
353	#121×C₅₃	C₂³	1	1	yes	characteristic
354	#121×C₅₃	C₂³	1	1	yes	characteristic
355	#120×C₅₃	—	2	1	no	—
356	#120×C₅₃	—	2	1	no	—
357	#120×C₅₃	—	2	1	no	—
358	#120×C₅₃	—	2	1	no	—
359	#120×C₅₃	—	2	1	no	—
360	#120×C₅₃	—	2	1	no	—
361	#120×C₅₃	—	2	1	no	—
362	#120×C₅₃	—	2	1	no	—
363	#120×C₅₃	—	2	1	no	—
364	#120×C₅₃	—	2	1	no	—
365	#120×C₅₃	—	2	1	no	—
366	#120×C₅₃	—	2	1	no	—
367	#120×C₅₃	—	2	1	no	—
368	#120×C₅₃	—	2	1	no	—
369	#120×C₅₃	—	2	1	no	—
370	#120×C₅₃	—	2	1	no	—
371	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₅₃	—	2	1	no	—
376	C₄×D₄×C₅₃	—	2	1	no	—
377	C₄×D₄×C₅₃	—	2	1	no	—
378	C₄×D₄×C₅₃	—	2	1	no	—
379	C₄×D₄×C₅₃	—	2	1	no	—
380	C₄×D₄×C₅₃	—	2	1	no	—
381	C₄×D₄×C₅₃	—	2	1	no	—
382	C₄×D₄×C₅₃	—	2	1	no	—
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	—	2	1	no	—
387	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
388	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
389	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
390	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
391	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
392	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
393	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
394	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
395	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
396	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
397	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
398	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
399	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
400	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
401	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
402	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
403	#117×C₅₃	—	2	1	no	—
404	#117×C₅₃	—	2	1	no	—
405	#117×C₅₃	—	2	1	no	—
406	#117×C₅₃	—	2	1	no	—
407	#117×C₅₃	C₂³	1	1	yes	characteristic
408	#117×C₅₃	C₂³	1	1	yes	characteristic
409	#117×C₅₃	C₂³	1	1	yes	characteristic
410	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
412	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
413	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
414	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#107×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#102×C₅₃	C₂³	1	1	yes	characteristic
447	#102×C₅₃	C₂³	1	1	yes	characteristic
448	#102×C₅₃	C₂³	1	1	yes	characteristic
449	#102×C₅₃	C₂³	1	1	yes	characteristic
450	#102×C₅₃	C₂³	1	1	yes	characteristic
451	#102×C₅₃	C₂³	1	1	yes	characteristic
452	#102×C₅₃	C₂³	1	1	yes	characteristic
453	#102×C₅₃	C₂³	1	1	yes	characteristic
454	#102×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	#97×C₅₃	C₂³	1	1	yes	characteristic
479	#97×C₅₃	C₂³	1	1	yes	characteristic
480	#97×C₅₃	C₂³	1	1	yes	characteristic
481	#97×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂⁴×C₅₃	—	2	1	no	—
485	C₂⁴×C₅₃	—	2	1	no	—
486	C₂⁴×C₅₃	—	2	1	no	—
487	C₂⁴×C₅₃	—	2	1	no	—
488	C₂⁴×C₅₃	—	2	1	no	—
489	C₂⁴×C₅₃	—	2	1	no	—
490	#41×C₅₃	—	2	2	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	4	1	no	—
493	#41×C₅₃	—	4	1	no	—
494	#41×C₅₃	—	4	1	no	—
495	#41×C₅₃	—	4	1	no	—
496	#41×C₅₃	—	8	2	no	—
497	#41×C₅₃	—	8	2	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	C₂×D₄	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	—	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	—	2	1	no	—
521	C₂×D₄×C₅₃	—	2	1	no	—
522	C₂×D₄×C₅₃	—	2	1	no	—
523	C₂×D₄×C₅₃	—	2	1	no	—
524	C₂×D₄×C₅₃	—	2	1	no	—
525	C₂×D₄×C₅₃	—	2	1	no	—
526	C₂×D₄×C₅₃	—	2	1	no	—
527	C₂×D₄×C₅₃	—	2	1	no	—
528	C₂×D₄×C₅₃	—	2	1	no	—
529	C₂×D₄×C₅₃	—	2	1	no	—
530	C₂×D₄×C₅₃	—	2	1	no	—
531	C₂×D₄×C₅₃	—	2	1	no	—
532	C₂×D₄×C₅₃	—	2	1	no	—
533	C₂×D₄×C₅₃	—	2	1	no	—
534	C₂×D₄×C₅₃	—	2	1	no	—
535	C₂×D₄×C₅₃	—	2	1	no	—
536	C₂×D₄×C₅₃	—	4	1	no	—
537	C₂×D₄×C₅₃	—	4	1	no	—
538	C₂×D₄×C₅₃	—	4	1	no	—
539	C₂×D₄×C₅₃	—	4	1	no	—
540	C₂×D₄×C₅₃	—	4	1	no	—
541	C₂×D₄×C₅₃	—	4	1	no	—
542	C₂×D₄×C₅₃	—	4	1	no	—
543	C₂×D₄×C₅₃	—	4	1	no	—
544	C₂×D₄×C₅₃	—	4	1	no	—
545	C₂×D₄×C₅₃	—	4	1	no	—
546	C₂×D₄×C₅₃	—	8	2	no	—
547	C₂×D₄×C₅₃	—	8	2	no	—
548	C₂×D₄×C₅₃	—	8	2	no	—
549	C₂×D₄×C₅₃	—	8	2	no	—
550	C₂×D₄×C₅₃	—	8	2	no	—
551	C₂×D₄×C₅₃	—	8	2	no	—
552	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
553	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
554	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
555	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
556	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
558	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
561	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
562	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	—	2	1	no	—
564	C₂²×C₄×C₅₃	—	2	1	no	—
565	C₂²×C₄×C₅₃	—	2	1	no	—
566	C₂²×C₄×C₅₃	—	2	1	no	—
567	C₂²×C₄×C₅₃	—	2	1	no	—
568	C₂²×C₄×C₅₃	—	2	1	no	—
569	C₂²×C₄×C₅₃	—	2	1	no	—
570	C₂²×C₄×C₅₃	—	2	1	no	—
571	C₂²×C₄×C₅₃	—	2	1	no	—
572	C₂²×C₄×C₅₃	—	2	1	no	—
573	C₂²×C₄×C₅₃	—	2	1	no	—
574	C₂²×C₄×C₅₃	—	2	1	no	—
575	C₂²×C₄×C₅₃	—	2	1	no	—
576	C₂²×C₄×C₅₃	—	2	1	no	—
577	C₂²×C₄×C₅₃	—	2	1	no	—
578	C₂²×C₄×C₅₃	—	2	1	no	—
579	C₂²×C₄×C₅₃	—	2	1	no	—
580	C₂²×C₄×C₅₃	—	2	1	no	—
581	C₂²×C₄×C₅₃	—	8	2	no	—
582	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
583	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
584	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
586	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
587	Q₁₆×C₅₃	—	4	1	no	—
588	SD₁₆×C₅₃	—	2	2	no	—
589	SD₁₆×C₅₃	—	4	1	no	—
590	SD₁₆×C₅₃	—	4	1	no	—
591	SD₁₆×C₅₃	—	4	1	no	—
592	SD₁₆×C₅₃	—	4	1	no	—
593	SD₁₆×C₅₃	—	4	1	no	—
594	SD₁₆×C₅₃	—	4	1	no	—
595	SD₁₆×C₅₃	—	4	1	no	—
596	D₈×C₅₃	—	2	2	no	—
597	D₈×C₅₃	—	2	2	no	—
598	D₈×C₅₃	—	2	2	no	—
599	D₈×C₅₃	—	2	2	no	—
600	D₈×C₅₃	—	2	2	no	—
601	D₈×C₅₃	—	4	1	no	—
602	D₈×C₅₃	—	4	1	no	—
603	D₈×C₅₃	—	4	1	no	—
604	D₈×C₅₃	—	4	1	no	—
605	D₈×C₅₃	—	4	1	no	—
606	D₈×C₅₃	—	4	1	no	—
607	D₈×C₅₃	—	4	1	no	—
608	D₈×C₅₃	—	4	1	no	—
609	D₈×C₅₃	—	4	1	no	—
610	D₈×C₅₃	—	4	1	no	—
611	M₁₆×C₅₃	—	4	1	no	—
612	M₁₆×C₅₃	—	4	1	no	—
613	C₂×C₈×C₅₃	—	4	1	no	—
614	C₂×C₈×C₅₃	—	4	1	no	—
615	C₂×C₈×C₅₃	—	4	1	no	—
616	C₂×C₈×C₅₃	—	4	1	no	—
617	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
618	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
619	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
620	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
621	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
622	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
623	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
624	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	—	2	1	no	—
627	C₄⋊C₄×C₅₃	—	2	1	no	—
628	C₄⋊C₄×C₅₃	—	2	1	no	—
629	C₄⋊C₄×C₅₃	—	2	1	no	—
630	C₄⋊C₄×C₅₃	—	2	1	no	—
631	C₄⋊C₄×C₅₃	—	2	1	no	—
632	C₄⋊C₄×C₅₃	—	2	1	no	—
633	C₄⋊C₄×C₅₃	—	2	1	no	—
634	C₄⋊C₄×C₅₃	—	2	1	no	—
635	C₄⋊C₄×C₅₃	—	2	1	no	—
636	C₄⋊C₄×C₅₃	—	2	1	no	—
637	C₄⋊C₄×C₅₃	—	2	1	no	—
638	C₄⋊C₄×C₅₃	—	2	1	no	—
639	C₄⋊C₄×C₅₃	—	2	1	no	—
640	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
642	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
643	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
644	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
645	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
646	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
647	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
648	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
649	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
650	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
651	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
652	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
653	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
654	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
655	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	—	2	1	no	—
670	C₂²⋊C₄×C₅₃	—	2	1	no	—
671	C₂²⋊C₄×C₅₃	—	2	1	no	—
672	C₂²⋊C₄×C₅₃	—	2	1	no	—
673	C₂²⋊C₄×C₅₃	—	2	1	no	—
674	C₂²⋊C₄×C₅₃	—	2	1	no	—
675	C₂²⋊C₄×C₅₃	—	2	1	no	—
676	C₂²⋊C₄×C₅₃	—	2	1	no	—
677	C₂²⋊C₄×C₅₃	—	2	1	no	—
678	C₂²⋊C₄×C₅₃	—	2	1	no	—
679	C₂²⋊C₄×C₅₃	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	—	2	1	no	—
682	C₂²⋊C₄×C₅₃	—	2	1	no	—
683	C₂²⋊C₄×C₅₃	—	2	1	no	—
684	C₂²⋊C₄×C₅₃	—	2	1	no	—
685	C₂²⋊C₄×C₅₃	—	2	1	no	—
686	C₂²⋊C₄×C₅₃	—	2	1	no	—
687	C₂²⋊C₄×C₅₃	—	2	1	no	—
688	C₂²⋊C₄×C₅₃	—	2	1	no	—
689	C₂²⋊C₄×C₅₃	—	2	1	no	—
690	C₂²⋊C₄×C₅₃	—	2	1	no	—
691	C₂²⋊C₄×C₅₃	—	2	1	no	—
692	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
693	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
694	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
695	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
696	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
697	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
698	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
699	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
700	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₅₃	—	2	1	no	—
703	C₄²×C₅₃	—	2	1	no	—
704	C₄²×C₅₃	—	2	1	no	—
705	C₄²×C₅₃	—	2	1	no	—
706	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
707	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
708	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
709	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
710	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
711	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
712	C₂³×C₅₃	—	2	1	no	—
713	C₂³×C₅₃	—	2	1	no	—
714	C₂³×C₅₃	—	2	1	no	—
715	C₂³×C₅₃	—	2	1	no	—
716	C₂³×C₅₃	—	2	1	no	—
717	C₂³×C₅₃	—	2	1	no	—
718	C₂³×C₅₃	—	2	1	no	—
719	C₂³×C₅₃	—	2	1	no	—
720	C₂³×C₅₃	—	4	2	no	—
721	C₂³×C₅₃	—	4	2	no	—
722	C₂³×C₅₃	—	4	2	no	—
723	C₂³×C₅₃	—	4	2	no	—
724	C₂³×C₅₃	—	4	2	no	—
725	C₂³×C₅₃	—	8	1	no	—
726	C₂³×C₅₃	—	8	1	no	—
727	C₂³×C₅₃	—	8	1	no	—
728	C₂³×C₅₃	—	8	1	no	—
729	C₂³×C₅₃	—	8	1	no	—
730	C₂³×C₅₃	—	8	1	no	—
731	C₂³×C₅₃	—	8	1	no	—
732	C₂³×C₅₃	—	8	1	no	—
733	C₂³×C₅₃	—	8	1	no	—
734	C₂³×C₅₃	—	8	1	no	—
735	C₂³×C₅₃	—	8	1	no	—
736	C₂³×C₅₃	—	8	1	no	—
737	C₂³×C₅₃	—	8	1	no	—
738	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
739	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
740	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
741	Q₈×C₅₃	—	2	1	no	—
742	Q₈×C₅₃	—	2	1	no	—
743	Q₈×C₅₃	—	2	1	no	—
744	Q₈×C₅₃	—	2	1	no	—
745	Q₈×C₅₃	—	4	1	no	—
746	Q₈×C₅₃	—	8	1	no	—
747	D₄×C₅₃	—	2	2	no	—
748	D₄×C₅₃	—	2	2	no	—
749	D₄×C₅₃	—	2	1	no	—
750	D₄×C₅₃	—	2	1	no	—
751	D₄×C₅₃	—	2	1	no	—
752	D₄×C₅₃	—	2	1	no	—
753	D₄×C₅₃	—	2	1	no	—
754	D₄×C₅₃	—	2	1	no	—
755	D₄×C₅₃	—	2	1	no	—
756	D₄×C₅₃	—	2	1	no	—
757	D₄×C₅₃	—	2	1	no	—
758	D₄×C₅₃	—	2	1	no	—
759	D₄×C₅₃	—	2	1	no	—
760	D₄×C₅₃	—	2	1	no	—
761	D₄×C₅₃	—	2	1	no	—
762	D₄×C₅₃	—	2	1	no	—
763	D₄×C₅₃	—	2	1	no	—
764	D₄×C₅₃	—	4	1	no	—
765	D₄×C₅₃	—	4	2	no	—
766	D₄×C₅₃	—	4	2	no	—
767	D₄×C₅₃	—	4	2	no	—
768	D₄×C₅₃	—	4	2	no	—
769	D₄×C₅₃	—	4	2	no	—
770	D₄×C₅₃	—	4	2	no	—
771	D₄×C₅₃	—	4	2	no	—
772	D₄×C₅₃	—	8	1	no	—
773	D₄×C₅₃	—	8	1	no	—
774	D₄×C₅₃	—	8	1	no	—
775	D₄×C₅₃	—	8	1	no	—
776	D₄×C₅₃	—	8	1	no	—
777	D₄×C₅₃	—	8	1	no	—
778	D₄×C₅₃	—	8	1	no	—
779	D₄×C₅₃	—	8	1	no	—
780	D₄×C₅₃	—	8	1	no	—
781	D₄×C₅₃	—	8	1	no	—
782	D₄×C₅₃	—	8	1	no	—
783	D₄×C₅₃	—	8	1	no	—
784	D₄×C₅₃	—	8	1	no	—
785	D₄×C₅₃	—	8	1	no	—
786	D₄×C₅₃	—	8	1	no	—
787	D₄×C₅₃	—	8	1	no	—
788	D₄×C₅₃	—	8	1	no	—
789	D₄×C₅₃	—	8	1	no	—
790	D₄×C₅₃	—	8	1	no	—
791	D₄×C₅₃	—	8	1	no	—
792	D₄×C₅₃	—	8	1	no	—
793	D₄×C₅₃	—	8	1	no	—
794	D₄×C₅₃	—	8	1	no	—
795	D₄×C₅₃	—	8	1	no	—
796	D₄×C₅₃	—	8	1	no	—
797	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
798	C₂×C₄×C₅₃	—	2	2	no	—
799	C₂×C₄×C₅₃	—	2	1	no	—
800	C₂×C₄×C₅₃	—	2	1	no	—
801	C₂×C₄×C₅₃	—	2	1	no	—
802	C₂×C₄×C₅₃	—	2	1	no	—
803	C₂×C₄×C₅₃	—	2	1	no	—
804	C₂×C₄×C₅₃	—	2	1	no	—
805	C₂×C₄×C₅₃	—	2	1	no	—
806	C₂×C₄×C₅₃	—	2	1	no	—
807	C₂×C₄×C₅₃	—	2	1	no	—
808	C₂×C₄×C₅₃	—	2	1	no	—
809	C₂×C₄×C₅₃	—	2	1	no	—
810	C₂×C₄×C₅₃	—	2	1	no	—
811	C₂×C₄×C₅₃	—	2	1	no	—
812	C₂×C₄×C₅₃	—	2	1	no	—
813	C₂×C₄×C₅₃	—	4	1	no	—
814	C₂×C₄×C₅₃	—	4	2	no	—
815	C₂×C₄×C₅₃	—	4	2	no	—
816	C₂×C₄×C₅₃	—	4	2	no	—
817	C₂×C₄×C₅₃	—	8	1	no	—
818	C₂×C₄×C₅₃	—	8	1	no	—
819	C₂×C₄×C₅₃	—	8	1	no	—
820	C₂×C₄×C₅₃	—	8	1	no	—
821	C₂×C₄×C₅₃	—	8	1	no	—
822	C₂×C₄×C₅₃	—	8	1	no	—
823	C₂×C₄×C₅₃	—	8	1	no	—
824	C₂×C₄×C₅₃	—	8	1	no	—
825	C₂×C₄×C₅₃	—	8	1	no	—
826	C₂×C₄×C₅₃	—	8	1	no	—
827	C₂×C₄×C₅₃	—	8	1	no	—
828	C₂×C₄×C₅₃	—	8	1	no	—
829	C₂×C₄×C₅₃	—	8	1	no	—
830	C₂×C₄×C₅₃	—	8	1	no	—
831	C₂×C₄×C₅₃	—	8	1	no	—
832	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
833	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
834	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
835	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
836	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
837	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
838	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
839	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
840	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
841	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
842	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
843	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
844	C₈×C₅₃	—	2	1	no	—
845	C₈×C₅₃	—	2	1	no	—
846	C₈×C₅₃	—	2	1	no	—
847	C₈×C₅₃	—	2	1	no	—
848	C₈×C₅₃	—	2	1	no	—
849	C₈×C₅₃	—	2	1	no	—
850	C₈×C₅₃	—	2	1	no	—
851	C₈×C₅₃	—	2	1	no	—
852	#62007	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
853	C₂²×C₅₃	—	2	1	no	—
854	C₂²×C₅₃	—	2	1	no	—
855	C₂²×C₅₃	—	2	1	no	—
856	C₂²×C₅₃	—	2	1	no	—
857	C₂²×C₅₃	—	2	1	no	—
858	C₂²×C₅₃	—	2	1	no	—
859	C₂²×C₅₃	—	2	2	no	—
860	C₂²×C₅₃	—	2	1	no	—
861	C₂²×C₅₃	—	2	1	no	—
862	C₂²×C₅₃	—	4	1	no	—
863	C₂²×C₅₃	—	4	1	no	—
864	C₂²×C₅₃	—	4	1	no	—
865	C₂²×C₅₃	—	4	1	no	—
866	C₂²×C₅₃	—	4	1	no	—
867	C₂²×C₅₃	—	4	1	no	—
868	C₂²×C₅₃	—	4	1	no	—
869	C₂²×C₅₃	—	4	1	no	—
870	C₂²×C₅₃	—	4	1	no	—
871	C₂²×C₅₃	—	4	1	no	—
872	C₂²×C₅₃	—	4	1	no	—
873	C₂²×C₅₃	—	4	1	no	—
874	C₂²×C₅₃	—	4	1	no	—
875	C₂²×C₅₃	—	4	1	no	—
876	C₂²×C₅₃	—	4	1	no	—
877	C₂²×C₅₃	—	4	1	no	—
878	C₂²×C₅₃	—	4	1	no	—
879	C₂²×C₅₃	—	4	1	no	—
880	C₂²×C₅₃	—	4	1	no	—
881	C₂²×C₅₃	—	4	1	no	—
882	C₂²×C₅₃	—	4	1	no	—
883	C₂²×C₅₃	—	4	1	no	—
884	C₂²×C₅₃	—	4	1	no	—
885	C₂²×C₅₃	—	8	4	no	—
886	C₂²×C₅₃	—	16	2	no	—
887	C₂²×C₅₃	—	16	2	no	—
888	C₂²×C₅₃	—	16	2	no	—
889	C₂²×C₅₃	—	16	2	no	—
890	C₂²×C₅₃	—	16	2	no	—
891	C₂²×C₅₃	#576	1	2	yes	—
892	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
893	C₄×C₅₃	—	2	1	no	—
894	C₄×C₅₃	—	2	1	no	—
895	C₄×C₅₃	—	2	1	no	—
896	C₄×C₅₃	—	2	1	no	—
897	C₄×C₅₃	—	2	1	no	—
898	C₄×C₅₃	—	2	1	no	—
899	C₄×C₅₃	—	2	1	no	—
900	C₄×C₅₃	—	2	1	no	—
901	C₄×C₅₃	—	2	1	no	—
902	C₄×C₅₃	—	2	1	no	—
903	C₄×C₅₃	—	2	1	no	—
904	C₄×C₅₃	—	4	1	no	—
905	C₄×C₅₃	—	4	1	no	—
906	C₄×C₅₃	—	4	1	no	—
907	C₄×C₅₃	—	4	1	no	—
908	C₄×C₅₃	—	4	1	no	—
909	C₄×C₅₃	—	4	1	no	—
910	C₄×C₅₃	—	4	1	no	—
911	C₄×C₅₃	—	4	1	no	—
912	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
913	C₄×C₅₃	#585	1	1	yes	characteristic
914	#3543	C₂×C₅₃	1	1	yes	characteristic, complemented
915	#3513	C₂×C₅₃	1	1	yes	characteristic, complemented
916	#3403	C₂×C₅₃	1	1	yes	characteristic, complemented
917	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
918	#3370	C₂×C₅₃	1	1	yes	characteristic, complemented
919	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
920	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
921	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
922	#3309	C₂×C₅₃	1	1	yes	characteristic, complemented
923	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
924	#3296	C₂×C₅₃	1	1	yes	characteristic, complemented
925	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
926	#3280	C₂×C₅₃	1	1	yes	characteristic, complemented
927	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
928	#3268	C₂×C₅₃	1	1	yes	characteristic, complemented
929	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
930	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
931	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
932	#3259	C₂×C₅₃	1	1	yes	characteristic, complemented
933	#3257	C₂×C₅₃	1	1	yes	characteristic, complemented
934	#3250	C₂×C₅₃	1	1	yes	characteristic, complemented
935	#3224	C₂×C₅₃	1	1	yes	characteristic, complemented
936	#3220	C₂×C₅₃	1	1	yes	characteristic, complemented
937	#3217	C₂×C₅₃	1	1	yes	characteristic, complemented
938	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
939	#3119	C₂×C₅₃	1	1	yes	characteristic, complemented
940	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
941	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
942	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
943	C₂×#459	C₂×C₅₃	1	1	yes	characteristic, complemented
944	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
945	C₂×C₅₃	—	2	2	no	—
946	C₂×C₅₃	—	4	1	no	—
947	C₂×C₅₃	—	4	1	no	—
948	C₂×C₅₃	—	4	2	no	—
949	C₂×C₅₃	—	8	1	no	—
950	C₂×C₅₃	—	8	1	no	—
951	C₂×C₅₃	—	8	1	no	—
952	C₂×C₅₃	—	8	1	no	—
953	C₂×C₅₃	—	8	1	no	—
954	C₂×C₅₃	—	8	1	no	—
955	C₂×C₅₃	—	8	1	no	—
956	C₂×C₅₃	#3488	1	1	yes	characteristic
957	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
958	C₂×C₅₃	#3585	1	1	yes	characteristic
959	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#560	—	2	1	no	—
966	#560	—	2	1	no	—
967	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#553	—	2	1	no	—
971	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#551	—	2	1	no	—
974	#551	—	2	1	no	—
975	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#546	—	2	1	no	—
979	#546	—	2	1	no	—
980	#546	C₂²×C₅₃	1	1	yes	characteristic
981	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	D₄²	—	2	1	no	—
985	D₄²	C₂²×C₅₃	1	1	yes	characteristic
986	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#540	—	2	1	no	—
991	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#539	—	2	1	no	—
995	#538	—	2	1	no	—
996	#535	—	2	1	no	—
997	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#534	—	2	1	no	—
1000	#534	—	2	1	no	—
1001	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#529	C₂²×C₅₃	1	1	yes	characteristic
1003	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#525	—	2	1	no	—
1006	C₂×#123	—	2	1	no	—
1007	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#466	C₂²×C₅₃	1	1	yes	characteristic
1044	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#459	C₂²×C₅₃	1	1	yes	characteristic
1066	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#447	C₂²×C₅₃	1	1	yes	characteristic
1091	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1106	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1107	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1115	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1117	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1118	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1125	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1126	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1127	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1128	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1129	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1130	C₅₃	#62007	1	1	yes	characteristic, direct product factor, Sylow
1131	C₂×#41	—	2	1	no	—
1132	C₂×#41	—	2	1	no	—
1133	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂²×D₄	—	2	1	no	—
1137	C₂²×D₄	—	2	1	no	—
1138	C₂²×D₄	—	2	1	no	—
1139	C₂²×D₄	—	2	1	no	—
1140	C₂²×D₄	—	2	1	no	—
1141	C₂²×D₄	—	2	1	no	—
1142	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂³×C₄	—	2	1	no	—
1149	AGL(1,ℤ/8)	—	4	2	no	—
1150	AGL(1,ℤ/8)	—	4	2	no	—
1151	#135	—	4	2	no	—
1152	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1159	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1160	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1161	C₂×D₈	—	4	2	no	—
1162	C₂×D₈	—	4	2	no	—
1163	C₂×D₈	—	4	2	no	—
1164	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1165	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1166	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1167	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1168	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1169	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1170	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1171	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1172	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1173	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1182	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1185	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1186	#127	—	2	1	no	—
1187	#127	—	2	1	no	—
1188	#127	—	2	1	no	—
1189	#127	C₂³×C₅₃	1	1	yes	characteristic
1190	#127	C₂³×C₅₃	1	1	yes	characteristic
1191	#127	C₂³×C₅₃	1	1	yes	characteristic
1192	#127	C₂³×C₅₃	1	1	yes	characteristic
1193	#127	C₂³×C₅₃	1	1	yes	characteristic
1194	#127	C₂³×C₅₃	1	1	yes	characteristic
1195	#127	C₂³×C₅₃	1	1	yes	characteristic
1196	#126	—	2	1	no	—
1197	#126	—	2	1	no	—
1198	#126	—	2	1	no	—
1199	#126	—	2	1	no	—
1200	#126	—	2	1	no	—
1201	#126	D₄×C₅₃	1	1	yes	characteristic
1202	#126	D₄×C₅₃	1	1	yes	characteristic
1203	#125	—	2	1	no	—
1204	#125	D₄×C₅₃	1	1	yes	characteristic
1205	#125	C₂³×C₅₃	1	1	yes	characteristic
1206	#125	C₂³×C₅₃	1	1	yes	characteristic
1207	#125	C₂³×C₅₃	1	1	yes	characteristic
1208	#124	—	2	1	no	—
1209	#124	—	2	1	no	—
1210	#124	—	2	1	no	—
1211	#124	D₄×C₅₃	1	1	yes	characteristic
1212	#124	C₂³×C₅₃	1	1	yes	characteristic
1213	#124	C₂³×C₅₃	1	1	yes	characteristic
1214	#124	C₂³×C₅₃	1	1	yes	characteristic
1215	#124	C₂³×C₅₃	1	1	yes	characteristic
1216	#124	C₂³×C₅₃	1	1	yes	characteristic
1217	#123	—	2	1	no	—
1218	#123	—	2	1	no	—
1219	#123	—	2	1	no	—
1220	#123	—	2	1	no	—
1221	#123	—	2	1	no	—
1222	#123	—	2	1	no	—
1223	#123	—	2	1	no	—
1224	#123	—	2	1	no	—
1225	#123	—	2	1	no	—
1226	#123	—	2	1	no	—
1227	#123	—	2	1	no	—
1228	#123	—	2	1	no	—
1229	#123	—	2	1	no	—
1230	#123	—	2	1	no	—
1231	#123	—	2	1	no	—
1232	#123	—	2	1	no	—
1233	#123	—	2	1	no	—
1234	#123	—	2	1	no	—
1235	#123	—	2	1	no	—
1236	#123	—	2	1	no	—
1237	#123	—	2	1	no	—
1238	#123	D₄×C₅₃	1	1	yes	characteristic
1239	#123	D₄×C₅₃	1	1	yes	characteristic
1240	C₂²⋊Q₈	—	2	1	no	—
1241	C₂²⋊Q₈	—	2	1	no	—
1242	C₂²⋊Q₈	—	2	1	no	—
1243	C₂²⋊Q₈	—	2	1	no	—
1244	C₂²⋊Q₈	—	2	1	no	—
1245	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1246	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1247	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1248	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1249	#121	—	2	1	no	—
1250	#121	—	2	1	no	—
1251	#121	—	2	1	no	—
1252	#121	—	2	1	no	—
1253	#121	—	2	1	no	—
1254	#121	—	2	1	no	—
1255	#121	—	2	1	no	—
1256	#121	—	2	1	no	—
1257	#121	—	2	1	no	—
1258	#121	—	2	1	no	—
1259	#121	—	2	1	no	—
1260	#121	—	2	1	no	—
1261	#121	—	2	1	no	—
1262	#121	—	2	1	no	—
1263	#121	—	2	1	no	—
1264	#121	—	2	1	no	—
1265	#121	—	2	1	no	—
1266	#121	—	2	1	no	—
1267	#121	—	2	1	no	—
1268	#121	—	2	1	no	—
1269	#121	—	2	1	no	—
1270	#121	—	2	1	no	—
1271	#121	—	2	1	no	—
1272	#121	—	2	1	no	—
1273	#121	D₄×C₅₃	1	1	yes	characteristic
1274	#121	C₂³×C₅₃	1	1	yes	characteristic
1275	#121	C₂³×C₅₃	1	1	yes	characteristic
1276	#121	C₂³×C₅₃	1	1	yes	characteristic
1277	#121	C₂³×C₅₃	1	1	yes	characteristic
1278	#121	C₂³×C₅₃	1	1	yes	characteristic
1279	#121	C₂³×C₅₃	1	1	yes	characteristic
1280	#121	C₂³×C₅₃	1	1	yes	characteristic
1281	#121	C₂³×C₅₃	1	1	yes	characteristic
1282	#121	C₂³×C₅₃	1	1	yes	characteristic
1283	#120	—	2	1	no	—
1284	#120	—	2	1	no	—
1285	#120	—	2	1	no	—
1286	#120	—	2	1	no	—
1287	#120	—	2	1	no	—
1288	#120	—	2	1	no	—
1289	#120	—	2	1	no	—
1290	#120	—	2	1	no	—
1291	#120	—	2	1	no	—
1292	#120	—	2	1	no	—
1293	#120	—	2	1	no	—
1294	#120	—	2	1	no	—
1295	#120	—	2	1	no	—
1296	#120	—	2	1	no	—
1297	#120	—	2	1	no	—
1298	#120	—	2	1	no	—
1299	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1300	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1301	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1302	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1303	C₄×D₄	—	2	1	no	—
1304	C₄×D₄	—	2	1	no	—
1305	C₄×D₄	—	2	1	no	—
1306	C₄×D₄	—	2	1	no	—
1307	C₄×D₄	—	2	1	no	—
1308	C₄×D₄	—	2	1	no	—
1309	C₄×D₄	—	2	1	no	—
1310	C₄×D₄	—	2	1	no	—
1311	C₄×D₄	—	2	1	no	—
1312	C₄×D₄	—	2	1	no	—
1313	C₄×D₄	—	2	1	no	—
1314	C₄×D₄	—	2	1	no	—
1315	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1316	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1317	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1318	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1319	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1320	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1321	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1322	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1323	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1324	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1325	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1326	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1327	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1328	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1329	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1330	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1331	#117	—	2	1	no	—
1332	#117	—	2	1	no	—
1333	#117	—	2	1	no	—
1334	#117	—	2	1	no	—
1335	#117	C₂³×C₅₃	1	1	yes	characteristic
1336	#117	C₂³×C₅₃	1	1	yes	characteristic
1337	#117	C₂³×C₅₃	1	1	yes	characteristic
1338	C₂×C₄⋊C₄	—	2	1	no	—
1339	C₂×C₄⋊C₄	—	2	1	no	—
1340	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1341	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1342	C₂×C₂²⋊C₄	—	2	1	no	—
1343	C₂×C₂²⋊C₄	—	2	1	no	—
1344	C₂×C₂²⋊C₄	—	2	1	no	—
1345	C₂×C₂²⋊C₄	—	2	1	no	—
1346	C₂×C₂²⋊C₄	—	2	1	no	—
1347	C₂×C₂²⋊C₄	—	2	1	no	—
1348	C₂×C₂²⋊C₄	—	2	1	no	—
1349	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1350	#107	C₂³×C₅₃	1	1	yes	characteristic
1351	#107	C₂³×C₅₃	1	1	yes	characteristic
1352	#107	C₂³×C₅₃	1	1	yes	characteristic
1353	#107	C₂³×C₅₃	1	1	yes	characteristic
1354	#106	C₂³×C₅₃	1	1	yes	characteristic
1355	#106	C₂³×C₅₃	1	1	yes	characteristic
1356	#106	C₂³×C₅₃	1	1	yes	characteristic
1357	#106	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	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1363	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1364	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1365	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1366	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1367	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1368	#103	C₂³×C₅₃	1	1	yes	characteristic
1369	#103	C₂³×C₅₃	1	1	yes	characteristic
1370	#103	C₂³×C₅₃	1	1	yes	characteristic
1371	#103	C₂³×C₅₃	1	1	yes	characteristic
1372	#103	C₂³×C₅₃	1	1	yes	characteristic
1373	#103	C₂³×C₅₃	1	1	yes	characteristic
1374	#102	C₂³×C₅₃	1	1	yes	characteristic
1375	#102	C₂³×C₅₃	1	1	yes	characteristic
1376	#102	C₂³×C₅₃	1	1	yes	characteristic
1377	#102	C₂³×C₅₃	1	1	yes	characteristic
1378	#102	C₂³×C₅₃	1	1	yes	characteristic
1379	#102	C₂³×C₅₃	1	1	yes	characteristic
1380	#102	C₂³×C₅₃	1	1	yes	characteristic
1381	#102	C₂³×C₅₃	1	1	yes	characteristic
1382	#102	C₂³×C₅₃	1	1	yes	characteristic
1383	#102	C₂³×C₅₃	1	1	yes	characteristic
1384	#102	C₂³×C₅₃	1	1	yes	characteristic
1385	#102	C₂³×C₅₃	1	1	yes	characteristic
1386	#102	C₂³×C₅₃	1	1	yes	characteristic
1387	#102	C₂³×C₅₃	1	1	yes	characteristic
1388	#102	C₂³×C₅₃	1	1	yes	characteristic
1389	#102	C₂³×C₅₃	1	1	yes	characteristic
1390	#102	C₂³×C₅₃	1	1	yes	characteristic
1391	#102	C₂³×C₅₃	1	1	yes	characteristic
1392	#102	C₂³×C₅₃	1	1	yes	characteristic
1393	#102	C₂³×C₅₃	1	1	yes	characteristic
1394	#102	C₂³×C₅₃	1	1	yes	characteristic
1395	#102	C₂³×C₅₃	1	1	yes	characteristic
1396	#102	C₂³×C₅₃	1	1	yes	characteristic
1397	#102	C₂³×C₅₃	1	1	yes	characteristic
1398	#102	C₂³×C₅₃	1	1	yes	characteristic
1399	#102	C₂³×C₅₃	1	1	yes	characteristic
1400	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1401	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1402	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1403	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1404	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1405	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1406	#97	C₂³×C₅₃	1	1	yes	characteristic
1407	#97	C₂³×C₅₃	1	1	yes	characteristic
1408	#97	C₂³×C₅₃	1	1	yes	characteristic
1409	#97	C₂³×C₅₃	1	1	yes	characteristic
1410	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1411	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1412	C₂⁴	—	2	1	no	—
1413	C₂⁴	—	2	1	no	—
1414	C₂⁴	—	2	1	no	—
1415	C₂⁴	—	2	1	no	—
1416	C₂⁴	—	2	1	no	—
1417	C₂⁴	—	2	1	no	—
1418	#41	—	2	2	no	—
1419	#41	—	4	1	no	—
1420	#41	—	4	1	no	—
1421	#41	—	4	1	no	—
1422	#41	—	4	1	no	—
1423	#41	—	4	1	no	—
1424	#41	—	8	2	no	—
1425	#41	—	8	2	no	—
1426	C₂×Q₈	—	2	1	no	—
1427	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1428	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1429	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1430	C₂×D₄	—	2	2	no	—
1431	C₂×D₄	—	2	2	no	—
1432	C₂×D₄	—	2	1	no	—
1433	C₂×D₄	—	2	1	no	—
1434	C₂×D₄	—	2	1	no	—
1435	C₂×D₄	—	2	1	no	—
1436	C₂×D₄	—	2	1	no	—
1437	C₂×D₄	—	2	1	no	—
1438	C₂×D₄	—	2	1	no	—
1439	C₂×D₄	—	2	1	no	—
1440	C₂×D₄	—	2	1	no	—
1441	C₂×D₄	—	2	1	no	—
1442	C₂×D₄	—	2	1	no	—
1443	C₂×D₄	—	2	1	no	—
1444	C₂×D₄	—	2	1	no	—
1445	C₂×D₄	—	2	1	no	—
1446	C₂×D₄	—	2	1	no	—
1447	C₂×D₄	—	2	1	no	—
1448	C₂×D₄	—	2	1	no	—
1449	C₂×D₄	—	2	1	no	—
1450	C₂×D₄	—	2	1	no	—
1451	C₂×D₄	—	2	1	no	—
1452	C₂×D₄	—	2	1	no	—
1453	C₂×D₄	—	2	1	no	—
1454	C₂×D₄	—	2	1	no	—
1455	C₂×D₄	—	2	1	no	—
1456	C₂×D₄	—	2	1	no	—
1457	C₂×D₄	—	2	1	no	—
1458	C₂×D₄	—	2	1	no	—
1459	C₂×D₄	—	2	1	no	—
1460	C₂×D₄	—	2	1	no	—
1461	C₂×D₄	—	2	1	no	—
1462	C₂×D₄	—	2	1	no	—
1463	C₂×D₄	—	2	1	no	—
1464	C₂×D₄	—	4	1	no	—
1465	C₂×D₄	—	4	1	no	—
1466	C₂×D₄	—	4	1	no	—
1467	C₂×D₄	—	4	1	no	—
1468	C₂×D₄	—	4	1	no	—
1469	C₂×D₄	—	4	1	no	—
1470	C₂×D₄	—	4	1	no	—
1471	C₂×D₄	—	4	1	no	—
1472	C₂×D₄	—	4	1	no	—
1473	C₂×D₄	—	4	1	no	—
1474	C₂×D₄	—	8	2	no	—
1475	C₂×D₄	—	8	2	no	—
1476	C₂×D₄	—	8	2	no	—
1477	C₂×D₄	—	8	2	no	—
1478	C₂×D₄	—	8	2	no	—
1479	C₂×D₄	—	8	2	no	—
1480	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1481	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1482	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1483	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1486	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1487	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1488	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1489	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1490	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	8	2	no	—
1510	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1511	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1512	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1513	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1514	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1515	Q₁₆	—	4	1	no	—
1516	SD₁₆	—	2	2	no	—
1517	SD₁₆	—	4	1	no	—
1518	SD₁₆	—	4	1	no	—
1519	SD₁₆	—	4	1	no	—
1520	SD₁₆	—	4	1	no	—
1521	SD₁₆	—	4	1	no	—
1522	SD₁₆	—	4	1	no	—
1523	SD₁₆	—	4	1	no	—
1524	D₈	—	2	2	no	—
1525	D₈	—	2	2	no	—
1526	D₈	—	2	2	no	—
1527	D₈	—	2	2	no	—
1528	D₈	—	2	2	no	—
1529	D₈	—	4	1	no	—
1530	D₈	—	4	1	no	—
1531	D₈	—	4	1	no	—
1532	D₈	—	4	1	no	—
1533	D₈	—	4	1	no	—
1534	D₈	—	4	1	no	—
1535	D₈	—	4	1	no	—
1536	D₈	—	4	1	no	—
1537	D₈	—	4	1	no	—
1538	D₈	—	4	1	no	—
1539	M₁₆	—	4	1	no	—
1540	M₁₆	—	4	1	no	—
1541	C₂×C₈	—	4	1	no	—
1542	C₂×C₈	—	4	1	no	—
1543	C₂×C₈	—	4	1	no	—
1544	C₂×C₈	—	4	1	no	—
1545	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1546	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1547	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1548	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1549	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1550	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1551	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1552	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1553	C₄⋊C₄	—	2	1	no	—
1554	C₄⋊C₄	—	2	1	no	—
1555	C₄⋊C₄	—	2	1	no	—
1556	C₄⋊C₄	—	2	1	no	—
1557	C₄⋊C₄	—	2	1	no	—
1558	C₄⋊C₄	—	2	1	no	—
1559	C₄⋊C₄	—	2	1	no	—
1560	C₄⋊C₄	—	2	1	no	—
1561	C₄⋊C₄	—	2	1	no	—
1562	C₄⋊C₄	—	2	1	no	—
1563	C₄⋊C₄	—	2	1	no	—
1564	C₄⋊C₄	—	2	1	no	—
1565	C₄⋊C₄	—	2	1	no	—
1566	C₄⋊C₄	—	2	1	no	—
1567	C₄⋊C₄	—	2	1	no	—
1568	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1569	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1570	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1571	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1572	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1573	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1574	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1575	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1576	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1577	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1578	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1579	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1580	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1581	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1582	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1583	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1584	C₂²⋊C₄	—	2	1	no	—
1585	C₂²⋊C₄	—	2	1	no	—
1586	C₂²⋊C₄	—	2	1	no	—
1587	C₂²⋊C₄	—	2	1	no	—
1588	C₂²⋊C₄	—	2	1	no	—
1589	C₂²⋊C₄	—	2	1	no	—
1590	C₂²⋊C₄	—	2	1	no	—
1591	C₂²⋊C₄	—	2	1	no	—
1592	C₂²⋊C₄	—	2	1	no	—
1593	C₂²⋊C₄	—	2	1	no	—
1594	C₂²⋊C₄	—	2	1	no	—
1595	C₂²⋊C₄	—	2	1	no	—
1596	C₂²⋊C₄	—	2	1	no	—
1597	C₂²⋊C₄	—	2	1	no	—
1598	C₂²⋊C₄	—	2	1	no	—
1599	C₂²⋊C₄	—	2	1	no	—
1600	C₂²⋊C₄	—	2	1	no	—
1601	C₂²⋊C₄	—	2	1	no	—
1602	C₂²⋊C₄	—	2	1	no	—
1603	C₂²⋊C₄	—	2	1	no	—
1604	C₂²⋊C₄	—	2	1	no	—
1605	C₂²⋊C₄	—	2	1	no	—
1606	C₂²⋊C₄	—	2	1	no	—
1607	C₂²⋊C₄	—	2	1	no	—
1608	C₂²⋊C₄	—	2	1	no	—
1609	C₂²⋊C₄	—	2	1	no	—
1610	C₂²⋊C₄	—	2	1	no	—
1611	C₂²⋊C₄	—	2	1	no	—
1612	C₂²⋊C₄	—	2	1	no	—
1613	C₂²⋊C₄	—	2	1	no	—
1614	C₂²⋊C₄	—	2	1	no	—
1615	C₂²⋊C₄	—	2	1	no	—
1616	C₂²⋊C₄	—	2	1	no	—
1617	C₂²⋊C₄	—	2	1	no	—
1618	C₂²⋊C₄	—	2	1	no	—
1619	C₂²⋊C₄	—	2	1	no	—
1620	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1621	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1622	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1623	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1624	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1625	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1626	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1627	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1628	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1629	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1630	C₄²	—	2	1	no	—
1631	C₄²	—	2	1	no	—
1632	C₄²	—	2	1	no	—
1633	C₄²	—	2	1	no	—
1634	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1635	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1636	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1637	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1638	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1639	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1640	C₂³	—	2	1	no	—
1641	C₂³	—	2	1	no	—
1642	C₂³	—	2	1	no	—
1643	C₂³	—	2	1	no	—
1644	C₂³	—	2	1	no	—
1645	C₂³	—	2	1	no	—
1646	C₂³	—	2	1	no	—
1647	C₂³	—	2	1	no	—
1648	C₂³	—	4	2	no	—
1649	C₂³	—	4	2	no	—
1650	C₂³	—	4	2	no	—
1651	C₂³	—	4	2	no	—
1652	C₂³	—	4	2	no	—
1653	C₂³	—	8	1	no	—
1654	C₂³	—	8	1	no	—
1655	C₂³	—	8	1	no	—
1656	C₂³	—	8	1	no	—
1657	C₂³	—	8	1	no	—
1658	C₂³	—	8	1	no	—
1659	C₂³	—	8	1	no	—
1660	C₂³	—	8	1	no	—
1661	C₂³	—	8	1	no	—
1662	C₂³	—	8	1	no	—
1663	C₂³	—	8	1	no	—
1664	C₂³	—	8	1	no	—
1665	C₂³	—	8	1	no	—
1666	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1667	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1668	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1669	Q₈	—	2	1	no	—
1670	Q₈	—	2	1	no	—
1671	Q₈	—	2	1	no	—
1672	Q₈	—	2	1	no	—
1673	Q₈	—	4	1	no	—
1674	Q₈	—	8	1	no	—
1675	D₄	—	2	2	no	—
1676	D₄	—	2	2	no	—
1677	D₄	—	2	1	no	—
1678	D₄	—	2	1	no	—
1679	D₄	—	2	1	no	—
1680	D₄	—	2	1	no	—
1681	D₄	—	2	1	no	—
1682	D₄	—	2	1	no	—
1683	D₄	—	2	1	no	—
1684	D₄	—	2	1	no	—
1685	D₄	—	2	1	no	—
1686	D₄	—	2	1	no	—
1687	D₄	—	2	1	no	—
1688	D₄	—	2	1	no	—
1689	D₄	—	2	1	no	—
1690	D₄	—	2	1	no	—
1691	D₄	—	2	1	no	—
1692	D₄	—	4	1	no	—
1693	D₄	—	4	2	no	—
1694	D₄	—	4	2	no	—
1695	D₄	—	4	2	no	—
1696	D₄	—	4	2	no	—
1697	D₄	—	4	2	no	—
1698	D₄	—	4	2	no	—
1699	D₄	—	4	2	no	—
1700	D₄	—	8	1	no	—
1701	D₄	—	8	1	no	—
1702	D₄	—	8	1	no	—
1703	D₄	—	8	1	no	—
1704	D₄	—	8	1	no	—
1705	D₄	—	8	1	no	—
1706	D₄	—	8	1	no	—
1707	D₄	—	8	1	no	—
1708	D₄	—	8	1	no	—
1709	D₄	—	8	1	no	—
1710	D₄	—	8	1	no	—
1711	D₄	—	8	1	no	—
1712	D₄	—	8	1	no	—
1713	D₄	—	8	1	no	—
1714	D₄	—	8	1	no	—
1715	D₄	—	8	1	no	—
1716	D₄	—	8	1	no	—
1717	D₄	—	8	1	no	—
1718	D₄	—	8	1	no	—
1719	D₄	—	8	1	no	—
1720	D₄	—	8	1	no	—
1721	D₄	—	8	1	no	—
1722	D₄	—	8	1	no	—
1723	D₄	—	8	1	no	—
1724	D₄	—	8	1	no	—
1725	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1726	C₂×C₄	—	2	2	no	—
1727	C₂×C₄	—	2	1	no	—
1728	C₂×C₄	—	2	1	no	—
1729	C₂×C₄	—	2	1	no	—
1730	C₂×C₄	—	2	1	no	—
1731	C₂×C₄	—	2	1	no	—
1732	C₂×C₄	—	2	1	no	—
1733	C₂×C₄	—	2	1	no	—
1734	C₂×C₄	—	2	1	no	—
1735	C₂×C₄	—	2	1	no	—
1736	C₂×C₄	—	2	1	no	—
1737	C₂×C₄	—	2	1	no	—
1738	C₂×C₄	—	2	1	no	—
1739	C₂×C₄	—	2	1	no	—
1740	C₂×C₄	—	2	1	no	—
1741	C₂×C₄	—	4	1	no	—
1742	C₂×C₄	—	4	2	no	—
1743	C₂×C₄	—	4	2	no	—
1744	C₂×C₄	—	4	2	no	—
1745	C₂×C₄	—	8	1	no	—
1746	C₂×C₄	—	8	1	no	—
1747	C₂×C₄	—	8	1	no	—
1748	C₂×C₄	—	8	1	no	—
1749	C₂×C₄	—	8	1	no	—
1750	C₂×C₄	—	8	1	no	—
1751	C₂×C₄	—	8	1	no	—
1752	C₂×C₄	—	8	1	no	—
1753	C₂×C₄	—	8	1	no	—
1754	C₂×C₄	—	8	1	no	—
1755	C₂×C₄	—	8	1	no	—
1756	C₂×C₄	—	8	1	no	—
1757	C₂×C₄	—	8	1	no	—
1758	C₂×C₄	—	8	1	no	—
1759	C₂×C₄	—	8	1	no	—
1760	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1761	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1762	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1763	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1764	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1765	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1766	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1767	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1768	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1769	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1770	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1771	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1772	C₈	—	2	1	no	—
1773	C₈	—	2	1	no	—
1774	C₈	—	2	1	no	—
1775	C₈	—	2	1	no	—
1776	C₈	—	2	1	no	—
1777	C₈	—	2	1	no	—
1778	C₈	—	2	1	no	—
1779	C₈	—	2	1	no	—
1780	C₂²	—	2	1	no	—
1781	C₂²	—	2	1	no	—
1782	C₂²	—	2	1	no	—
1783	C₂²	—	2	1	no	—
1784	C₂²	—	2	2	no	—
1785	C₂²	—	2	1	no	—
1786	C₂²	—	2	1	no	—
1787	C₂²	—	2	1	no	—
1788	C₂²	—	2	1	no	—
1789	C₂²	—	4	1	no	—
1790	C₂²	—	4	1	no	—
1791	C₂²	—	4	1	no	—
1792	C₂²	—	4	1	no	—
1793	C₂²	—	4	1	no	—
1794	C₂²	—	4	1	no	—
1795	C₂²	—	4	1	no	—
1796	C₂²	—	4	1	no	—
1797	C₂²	—	4	1	no	—
1798	C₂²	—	4	1	no	—
1799	C₂²	—	4	1	no	—
1800	C₂²	—	4	1	no	—
1801	C₂²	—	4	1	no	—
1802	C₂²	—	4	1	no	—
1803	C₂²	—	4	1	no	—
1804	C₂²	—	4	1	no	—
1805	C₂²	—	4	1	no	—
1806	C₂²	—	4	1	no	—
1807	C₂²	—	4	1	no	—
1808	C₂²	—	4	1	no	—
1809	C₂²	—	4	1	no	—
1810	C₂²	—	4	1	no	—
1811	C₂²	—	4	1	no	—
1812	C₂²	—	8	4	no	—
1813	C₂²	—	16	2	no	—
1814	C₂²	—	16	2	no	—
1815	C₂²	—	16	2	no	—
1816	C₂²	—	16	2	no	—
1817	C₂²	—	16	2	no	—
1818	C₂²	C₅₃×#576	1	2	yes	—
1819	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1820	C₄	—	2	1	no	—
1821	C₄	—	2	1	no	—
1822	C₄	—	2	1	no	—
1823	C₄	—	2	1	no	—
1824	C₄	—	2	1	no	—
1825	C₄	—	2	1	no	—
1826	C₄	—	2	1	no	—
1827	C₄	—	2	1	no	—
1828	C₄	—	2	1	no	—
1829	C₄	—	2	1	no	—
1830	C₄	—	2	1	no	—
1831	C₄	—	4	1	no	—
1832	C₄	—	4	1	no	—
1833	C₄	—	4	1	no	—
1834	C₄	—	4	1	no	—
1835	C₄	—	4	1	no	—
1836	C₄	—	4	1	no	—
1837	C₄	—	4	1	no	—
1838	C₄	—	4	1	no	—
1839	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1840	C₄	C₅₃×#585	1	1	yes	characteristic
1841	C₂	—	2	2	no	—
1842	C₂	—	4	1	no	—
1843	C₂	—	4	1	no	—
1844	C₂	—	4	2	no	—
1845	C₂	—	8	1	no	—
1846	C₂	—	8	1	no	—
1847	C₂	—	8	1	no	—
1848	C₂	—	8	1	no	—
1849	C₂	—	8	1	no	—
1850	C₂	—	8	1	no	—
1851	C₂	—	8	1	no	—
1852	C₂	C₅₃×#3488	1	1	yes	characteristic
1853	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1854	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×#3543	C₂	semidirect
2. C₅₃×#3513	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3399	C₂	semidirect
5. C₅₃×#3370	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3318	C₂	semidirect
8. C₅₃×#3310	C₂	semidirect
9. C₅₃×#3309	C₂	semidirect
10. C₅₃×#3306	C₂	semidirect
11. C₅₃×#3296	C₂	semidirect
12. C₅₃×#3294	C₂	semidirect
13. C₅₃×#3280	C₂	semidirect
14. D₄×D₈×C₅₃	C₂	semidirect
15. C₅₃×#3268	C₂	semidirect
16. C₅₃×#3264	C₂	semidirect
17. C₅₃×#3264	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3259	C₂	semidirect
20. C₅₃×#3257	C₂	semidirect
21. C₅₃×#3250	C₂	semidirect
22. C₅₃×#3224	C₂	semidirect
23. C₅₃×#3220	C₂	semidirect
24. C₅₃×#3217	C₂	semidirect
25. C₅₃×#3122	C₂	semidirect
26. C₅₃×#3119	C₂	semidirect
27. C₅₃×#3114	C₂	semidirect
28. C₅₃×#3045	C₂	semidirect
29. C₅₃×#3041	C₂	semidirect
30. C₂×C₅₃×#459	C₂	semidirect
31. C₅₃×#2992	C₂	semidirect
32. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
34. C₂×#135×C₅₃	C₂²	semidirect
35. C₂²×D₈×C₅₃	C₂²	semidirect
36. C₂²×D₈×C₅₃	C₂²	semidirect
37. C₂²×D₈×C₅₃	C₂²	semidirect
40. C₅₃×#559	C₂²	semidirect
41. C₅₃×#559	C₂²	semidirect
42. C₅₃×#554	C₂²	semidirect
44. C₅₃×#553	C₂²	semidirect
45. C₅₃×#552	C₂²	semidirect
48. C₅₃×#550	C₂²	semidirect
49. C₅₃×#550	C₂²	semidirect
50. C₅₃×#547	C₂²	semidirect
54. C₅₃×#546	C₂²	semidirect
55. C₅₃×#546	C₂²	semidirect
56. C₅₃×#546	C₂²	semidirect
59. D₄²×C₅₃	C₂²	semidirect
60. D₄²×C₅₃	C₂²	semidirect
61. D₄²×C₅₃	C₂²	semidirect
62. C₅₃×#542	C₂²	semidirect
64. C₅₃×#540	C₂²	semidirect
65. C₅₃×#540	C₂²	semidirect
66. C₅₃×#540	C₂²	semidirect
70. C₅₃×#535	C₂²	semidirect
71. C₅₃×#535	C₂²	semidirect
74. C₂×#127×C₅₃	C₂²	semidirect
76. C₅₃×#529	C₂²	semidirect
77. C₅₃×#529	C₂²	semidirect
80. C₅₃×#520	C₂²	semidirect
81. C₅₃×#518	C₂²	semidirect
82. C₂×C₄×D₄×C₅₃	C₂²	semidirect
83. C₅₃×#496	C₂²	semidirect
84. C₅₃×#496	C₂²	semidirect
85. C₅₃×#496	C₂²	semidirect
86. C₅₃×#496	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
88. C₅₃×#493	C₂²	semidirect
89. C₅₃×#490	C₂²	semidirect
90. C₅₃×#490	C₂²	semidirect
91. C₅₃×#490	C₂²	semidirect
92. C₅₃×#489	C₂²	semidirect
93. C₅₃×#488	C₂²	semidirect
94. C₅₃×#486	C₂²	semidirect
95. C₅₃×#483	C₂²	semidirect
96. C₅₃×#482	C₂²	semidirect
97. C₅₃×#482	C₂²	semidirect
98. C₅₃×#481	C₂²	semidirect
99. C₅₃×#480	C₂²	semidirect
100. C₅₃×#480	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
102. C₅₃×#479	C₂²	semidirect
103. C₅₃×#478	C₂²	semidirect
104. C₅₃×#478	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#476	C₂²	semidirect
110. C₅₃×#474	C₂²	semidirect
111. C₅₃×#469	C₂²	semidirect
112. C₅₃×#469	C₂²	semidirect
113. C₅₃×#469	C₂²	semidirect
114. C₅₃×#468	C₂²	semidirect
115. C₅₃×#467	C₂²	semidirect
117. C₅₃×#466	C₂²	semidirect
118. C₅₃×#466	C₂²	semidirect
119. C₅₃×#466	C₂²	semidirect
120. C₅₃×#465	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
123. C₅₃×#464	C₂²	semidirect
124. C₅₃×#464	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#463	C₂²	semidirect
127. C₅₃×#463	C₂²	semidirect
128. C₅₃×#463	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#463	C₂²	semidirect
135. C₅₃×#460	C₂²	semidirect
136. C₅₃×#460	C₂²	semidirect
137. C₅₃×#460	C₂²	semidirect
139. C₅₃×#459	C₂²	semidirect
140. C₅₃×#459	C₂²	semidirect
141. C₅₃×#459	C₂²	semidirect
142. C₅₃×#459	C₂²	semidirect
143. C₅₃×#459	C₂²	semidirect
144. C₅₃×#459	C₂²	semidirect
145. C₅₃×#459	C₂²	semidirect
146. C₅₃×#459	C₂²	semidirect
147. C₅₃×#459	C₂²	semidirect
148. C₅₃×#459	C₂²	semidirect
149. C₅₃×#459	C₂²	semidirect
150. C₅₃×#459	C₂²	semidirect
151. C₅₃×#459	C₂²	semidirect
152. C₅₃×#459	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#450	C₂²	semidirect
155. C₅₃×#450	C₂²	semidirect
156. C₅₃×#450	C₂²	semidirect
157. C₅₃×#450	C₂²	semidirect
158. C₅₃×#449	C₂²	semidirect
159. C₅₃×#449	C₂²	semidirect
160. C₅₃×#449	C₂²	semidirect
161. C₅₃×#449	C₂²	semidirect
162. C₅₃×#449	C₂²	semidirect
164. C₅₃×#447	C₂²	semidirect
165. C₅₃×#447	C₂²	semidirect
166. C₅₃×#447	C₂²	semidirect
167. C₅₃×#447	C₂²	semidirect
168. C₅₃×#447	C₂²	semidirect
169. C₅₃×#447	C₂²	semidirect
170. C₅₃×#447	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#442	C₂²	semidirect
175. C₅₃×#442	C₂²	semidirect
176. C₅₃×#442	C₂²	semidirect
177. C₅₃×#442	C₂²	semidirect
178. C₅₃×#440	C₂²	semidirect
179. C₅₃×#440	C₂²	semidirect
180. C₅₃×#440	C₂²	semidirect
181. C₄×SD₁₆×C₅₃	C₂²	semidirect
182. C₄×D₈×C₅₃	C₂²	semidirect
183. C₄×D₈×C₅₃	C₂²	semidirect
184. C₄×D₈×C₅₃	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₅₃×#435	C₂²	semidirect
187. C₅₃×#435	C₂²	semidirect
188. C₅₃×#435	C₂²	semidirect
189. C₈×D₄×C₅₃	C₂²	semidirect
190. C₈×D₄×C₅₃	C₂²	semidirect
191. C₅₃×#433	C₂²	semidirect
192. C₅₃×#433	C₂²	semidirect
193. C₅₃×#432	C₂²	semidirect
194. C₅₃×#424	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
197. C₅₃×#418	C₂²	semidirect
198. C₅₃×#417	C₂²	semidirect
199. C₅₃×#416	C₂²	semidirect
200. C₂×#102×C₅₃	C₂²	semidirect
201. C₂×#102×C₅₃	C₂²	semidirect
202. C₂×#102×C₅₃	C₂²	semidirect
852. #62007	C₅₃	direct (N × H)
914. #3543	C₂×C₅₃	semidirect
915. #3513	C₂×C₅₃	semidirect
916. #3403	C₂×C₅₃	semidirect
917. #3399	C₂×C₅₃	semidirect
918. #3370	C₂×C₅₃	semidirect
919. #3366	C₂×C₅₃	semidirect
920. #3318	C₂×C₅₃	semidirect
921. #3310	C₂×C₅₃	semidirect
922. #3309	C₂×C₅₃	semidirect
923. #3306	C₂×C₅₃	semidirect
924. #3296	C₂×C₅₃	semidirect
925. #3294	C₂×C₅₃	semidirect
926. #3280	C₂×C₅₃	semidirect
927. D₄×D₈	C₂×C₅₃	semidirect
928. #3268	C₂×C₅₃	semidirect
929. #3264	C₂×C₅₃	semidirect
930. #3264	C₂×C₅₃	semidirect
931. #3264	C₂×C₅₃	semidirect
932. #3259	C₂×C₅₃	semidirect
933. #3257	C₂×C₅₃	semidirect
934. #3250	C₂×C₅₃	semidirect
935. #3224	C₂×C₅₃	semidirect
936. #3220	C₂×C₅₃	semidirect
937. #3217	C₂×C₅₃	semidirect
938. #3122	C₂×C₅₃	semidirect
939. #3119	C₂×C₅₃	semidirect
940. #3114	C₂×C₅₃	semidirect
941. #3045	C₂×C₅₃	semidirect
942. #3041	C₂×C₅₃	semidirect
943. C₂×#459	C₂×C₅₃	semidirect
944. #2992	C₂×C₅₃	semidirect
959. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
960. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
961. C₂×#135	C₂²×C₅₃	semidirect
962. C₂²×D₈	C₂²×C₅₃	semidirect
963. C₂²×D₈	C₂²×C₅₃	semidirect
964. C₂²×D₈	C₂²×C₅₃	semidirect
967. #559	C₂²×C₅₃	semidirect
968. #559	C₂²×C₅₃	semidirect
969. #554	C₂²×C₅₃	semidirect
971. #553	C₂²×C₅₃	semidirect
972. #552	C₂²×C₅₃	semidirect
975. #550	C₂²×C₅₃	semidirect
976. #550	C₂²×C₅₃	semidirect
977. #547	C₂²×C₅₃	semidirect
981. #546	C₂²×C₅₃	semidirect
982. #546	C₂²×C₅₃	semidirect
983. #546	C₂²×C₅₃	semidirect
986. D₄²	C₂²×C₅₃	semidirect
987. D₄²	C₂²×C₅₃	semidirect
988. D₄²	C₂²×C₅₃	semidirect
989. #542	C₂²×C₅₃	semidirect
991. #540	C₂²×C₅₃	semidirect
992. #540	C₂²×C₅₃	semidirect
993. #540	C₂²×C₅₃	semidirect
997. #535	C₂²×C₅₃	semidirect
998. #535	C₂²×C₅₃	semidirect
1001. C₂×#127	C₂²×C₅₃	semidirect
1003. #529	C₂²×C₅₃	semidirect
1004. #529	C₂²×C₅₃	semidirect
1007. #520	C₂²×C₅₃	semidirect
1008. #518	C₂²×C₅₃	semidirect
1009. C₂×C₄×D₄	C₂²×C₅₃	semidirect
1010. #496	C₂²×C₅₃	semidirect
1011. #496	C₂²×C₅₃	semidirect
1012. #496	C₂²×C₅₃	semidirect
1013. #496	C₂²×C₅₃	semidirect
1014. #495	C₂²×C₅₃	semidirect
1015. #493	C₂²×C₅₃	semidirect
1016. #490	C₂²×C₅₃	semidirect
1017. #490	C₂²×C₅₃	semidirect
1018. #490	C₂²×C₅₃	semidirect
1019. #489	C₂²×C₅₃	semidirect
1020. #488	C₂²×C₅₃	semidirect
1021. #486	C₂²×C₅₃	semidirect
1022. #483	C₂²×C₅₃	semidirect
1023. #482	C₂²×C₅₃	semidirect
1024. #482	C₂²×C₅₃	semidirect
1025. #481	C₂²×C₅₃	semidirect
1026. #480	C₂²×C₅₃	semidirect
1027. #480	C₂²×C₅₃	semidirect
1028. #479	C₂²×C₅₃	semidirect
1029. #479	C₂²×C₅₃	semidirect
1030. #478	C₂²×C₅₃	semidirect
1031. #478	C₂²×C₅₃	semidirect
1032. #478	C₂²×C₅₃	semidirect
1033. #478	C₂²×C₅₃	semidirect
1034. #478	C₂²×C₅₃	semidirect
1035. #478	C₂²×C₅₃	semidirect
1036. #476	C₂²×C₅₃	semidirect
1037. #474	C₂²×C₅₃	semidirect
1038. #469	C₂²×C₅₃	semidirect
1039. #469	C₂²×C₅₃	semidirect
1040. #469	C₂²×C₅₃	semidirect
1041. #468	C₂²×C₅₃	semidirect
1042. #467	C₂²×C₅₃	semidirect
1044. #466	C₂²×C₅₃	semidirect
1045. #466	C₂²×C₅₃	semidirect
1046. #466	C₂²×C₅₃	semidirect
1047. #465	C₂²×C₅₃	semidirect
1048. #465	C₂²×C₅₃	semidirect
1049. #465	C₂²×C₅₃	semidirect
1050. #464	C₂²×C₅₃	semidirect
1051. #464	C₂²×C₅₃	semidirect
1052. #464	C₂²×C₅₃	semidirect
1053. #463	C₂²×C₅₃	semidirect
1054. #463	C₂²×C₅₃	semidirect
1055. #463	C₂²×C₅₃	semidirect
1056. #463	C₂²×C₅₃	semidirect
1057. #463	C₂²×C₅₃	semidirect
1058. #463	C₂²×C₅₃	semidirect
1059. #463	C₂²×C₅₃	semidirect
1060. #463	C₂²×C₅₃	semidirect
1061. #463	C₂²×C₅₃	semidirect
1062. #460	C₂²×C₅₃	semidirect
1063. #460	C₂²×C₅₃	semidirect
1064. #460	C₂²×C₅₃	semidirect
1066. #459	C₂²×C₅₃	semidirect
1067. #459	C₂²×C₅₃	semidirect
1068. #459	C₂²×C₅₃	semidirect
1069. #459	C₂²×C₅₃	semidirect
1070. #459	C₂²×C₅₃	semidirect
1071. #459	C₂²×C₅₃	semidirect
1072. #459	C₂²×C₅₃	semidirect
1073. #459	C₂²×C₅₃	semidirect
1074. #459	C₂²×C₅₃	semidirect
1075. #459	C₂²×C₅₃	semidirect
1076. #459	C₂²×C₅₃	semidirect
1077. #459	C₂²×C₅₃	semidirect
1078. #459	C₂²×C₅₃	semidirect
1079. #459	C₂²×C₅₃	semidirect
1080. #452	C₂²×C₅₃	semidirect
1081. #450	C₂²×C₅₃	semidirect
1082. #450	C₂²×C₅₃	semidirect
1083. #450	C₂²×C₅₃	semidirect
1084. #450	C₂²×C₅₃	semidirect
1085. #449	C₂²×C₅₃	semidirect
1086. #449	C₂²×C₅₃	semidirect
1087. #449	C₂²×C₅₃	semidirect
1088. #449	C₂²×C₅₃	semidirect
1089. #449	C₂²×C₅₃	semidirect
1091. #447	C₂²×C₅₃	semidirect
1092. #447	C₂²×C₅₃	semidirect
1093. #447	C₂²×C₅₃	semidirect
1094. #447	C₂²×C₅₃	semidirect
1095. #447	C₂²×C₅₃	semidirect
1096. #447	C₂²×C₅₃	semidirect
1097. #447	C₂²×C₅₃	semidirect
1098. #446	C₂²×C₅₃	semidirect
1099. #446	C₂²×C₅₃	semidirect
1100. #442	C₂²×C₅₃	semidirect
1101. #442	C₂²×C₅₃	semidirect
1102. #442	C₂²×C₅₃	semidirect
1103. #442	C₂²×C₅₃	semidirect
1104. #442	C₂²×C₅₃	semidirect
1105. #440	C₂²×C₅₃	semidirect
1106. #440	C₂²×C₅₃	semidirect
1107. #440	C₂²×C₅₃	semidirect
1108. C₄×SD₁₆	C₂²×C₅₃	semidirect
1109. C₄×D₈	C₂²×C₅₃	semidirect
1110. C₄×D₈	C₂²×C₅₃	semidirect
1111. C₄×D₈	C₂²×C₅₃	semidirect
1112. #435	C₂²×C₅₃	semidirect
1113. #435	C₂²×C₅₃	semidirect
1114. #435	C₂²×C₅₃	semidirect
1115. #435	C₂²×C₅₃	semidirect
1116. C₈×D₄	C₂²×C₅₃	semidirect
1117. C₈×D₄	C₂²×C₅₃	semidirect
1118. #433	C₂²×C₅₃	semidirect
1119. #433	C₂²×C₅₃	semidirect
1120. #432	C₂²×C₅₃	semidirect
1121. #424	C₂²×C₅₃	semidirect
1122. #424	C₂²×C₅₃	semidirect
1123. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1124. #418	C₂²×C₅₃	semidirect
1125. #417	C₂²×C₅₃	semidirect
1126. #416	C₂²×C₅₃	semidirect
1127. C₂×#102	C₂²×C₅₃	semidirect
1128. C₂×#102	C₂²×C₅₃	semidirect
1129. C₂×#102	C₂²×C₅₃	semidirect
1130. C₅₃	#62007	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅₃×#3543	2
C₅₃×#3513	2
C₅₃×#3403	2
C₅₃×#3399	2
C₅₃×#3370	2
C₅₃×#3366	2
C₅₃×#3318	2
C₅₃×#3310	2
C₅₃×#3309	2
C₅₃×#3306	2
C₅₃×#3296	2
C₅₃×#3294	2
C₅₃×#3280	2
D₄×D₈×C₅₃	2
C₅₃×#3268	2
C₅₃×#3264	2
C₅₃×#3259	2
C₅₃×#3257	2
C₅₃×#3250	2
C₅₃×#3224	2
C₅₃×#3220	2
C₅₃×#3217	2
C₅₃×#3122	2
C₅₃×#3119	2
C₅₃×#3114	2
C₅₃×#3045	2
C₅₃×#3041	2
C₂×C₅₃×#459	2
C₅₃×#2992	2
#62007	53

Subgroups — C53×#62007 #27269519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62007 #27269519