Subgroups — C₅₃×#61519 #27269031

Order 13568.

1956 conjugacy classes of subgroups.

The subgroup lattice has 1794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3513	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3389	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×#3347	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3345	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3337	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
16	D₄×D₈×C₅₃	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×#3180	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3179	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3122	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×#3105	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2968	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	C₂×C₅₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#553	—	2	1	no	—
40	C₅₃×#553	—	2	1	no	—
41	C₅₃×#553	C₂²	1	1	yes	characteristic
42	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#551	—	2	1	no	—
46	C₅₃×#551	—	2	1	no	—
47	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#546	—	2	1	no	—
50	C₅₃×#546	—	2	1	no	—
51	C₅₃×#546	—	2	1	no	—
52	C₅₃×#546	—	2	1	no	—
53	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
55	D₄²×C₅₃	C₂²	1	1	yes	characteristic
56	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
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	C₂²	1	1	yes	characteristic
69	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#525	—	2	1	no	—
71	C₅₃×#525	—	2	1	no	—
72	C₂×#123×C₅₃	—	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, complemented
76	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×D₄×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×#493	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#490	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×#484	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#482	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×#481	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#480	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×#474	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×#466	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#466	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, 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×#460	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#459	C₂²	1	1	yes	characteristic
134	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#459	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, complemented
141	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#447	C₂²	1	1	yes	characteristic
145	C₅₃×#447	C₂²	1	1	yes	characteristic
146	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
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, complemented
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×#442	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#442	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×D₈×C₅₃	C₂²	1	1	yes	characteristic
174	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
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×#435	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#435	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	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄×C₅₃	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×#431	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
193	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
197	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
198	C₂×#102×C₅₃	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	C₂×#97×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	—	2	1	no	—
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	—	2	1	no	—
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	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂³×C₄×C₅₃	—	2	1	no	—
217	C₂³×C₄×C₅₃	—	2	1	no	—
218	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
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×D₈×C₅₃	—	2	4	no	—
224	C₂×D₈×C₅₃	—	2	4	no	—
225	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
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×D₈×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
239	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
245	#127×C₅₃	C₂³	1	1	yes	characteristic
246	#127×C₅₃	C₂³	1	1	yes	characteristic
247	#127×C₅₃	C₂³	1	1	yes	characteristic
248	#127×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
256	#126×C₅₃	D₄	1	1	yes	characteristic
257	#125×C₅₃	—	2	1	no	—
258	#125×C₅₃	D₄	1	1	yes	characteristic
259	#125×C₅₃	C₂³	1	1	yes	characteristic
260	#125×C₅₃	C₂³	1	1	yes	characteristic
261	#125×C₅₃	C₂³	1	1	yes	characteristic
262	#125×C₅₃	C₂³	1	1	yes	characteristic
263	#124×C₅₃	—	2	1	no	—
264	#124×C₅₃	—	2	1	no	—
265	#124×C₅₃	—	2	1	no	—
266	#124×C₅₃	—	2	1	no	—
267	#124×C₅₃	—	2	1	no	—
268	#124×C₅₃	D₄	1	1	yes	characteristic
269	#124×C₅₃	C₂³	1	1	yes	characteristic
270	#124×C₅₃	C₂³	1	1	yes	characteristic
271	#123×C₅₃	—	2	1	no	—
272	#123×C₅₃	—	2	1	no	—
273	#123×C₅₃	—	2	1	no	—
274	#123×C₅₃	—	2	1	no	—
275	#123×C₅₃	—	2	1	no	—
276	#123×C₅₃	—	2	1	no	—
277	#123×C₅₃	—	2	1	no	—
278	#123×C₅₃	—	2	1	no	—
279	#123×C₅₃	—	2	1	no	—
280	#123×C₅₃	—	2	1	no	—
281	#123×C₅₃	—	2	1	no	—
282	#123×C₅₃	—	2	1	no	—
283	#123×C₅₃	—	2	1	no	—
284	#123×C₅₃	—	2	1	no	—
285	#123×C₅₃	—	2	1	no	—
286	#123×C₅₃	—	2	1	no	—
287	#123×C₅₃	—	2	1	no	—
288	#123×C₅₃	—	2	1	no	—
289	#123×C₅₃	D₄	1	1	yes	characteristic
290	#123×C₅₃	D₄	1	1	yes	characteristic
291	C₂²⋊Q₈×C₅₃	—	2	1	no	—
292	C₂²⋊Q₈×C₅₃	—	2	1	no	—
293	C₂²⋊Q₈×C₅₃	—	2	1	no	—
294	C₂²⋊Q₈×C₅₃	—	2	1	no	—
295	C₂²⋊Q₈×C₅₃	—	2	1	no	—
296	C₂²⋊Q₈×C₅₃	—	2	1	no	—
297	C₂²⋊Q₈×C₅₃	—	2	1	no	—
298	C₂²⋊Q₈×C₅₃	—	2	1	no	—
299	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
300	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
301	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
302	#121×C₅₃	—	2	1	no	—
303	#121×C₅₃	—	2	1	no	—
304	#121×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
323	#121×C₅₃	C₂³	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	#121×C₅₃	C₂³	1	1	yes	characteristic
333	#120×C₅₃	—	2	1	no	—
334	#120×C₅₃	—	2	1	no	—
335	#120×C₅₃	—	2	1	no	—
336	#120×C₅₃	—	2	1	no	—
337	#120×C₅₃	—	2	1	no	—
338	#120×C₅₃	—	2	1	no	—
339	#120×C₅₃	—	2	1	no	—
340	#120×C₅₃	—	2	1	no	—
341	#120×C₅₃	—	2	1	no	—
342	#120×C₅₃	—	2	1	no	—
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	—	2	1	no	—
364	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
379	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	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
383	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
384	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
385	#117×C₅₃	—	2	1	no	—
386	#117×C₅₃	—	2	1	no	—
387	#117×C₅₃	—	2	1	no	—
388	#117×C₅₃	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×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	#102×C₅₃	C₂³	1	1	yes	characteristic
438	#102×C₅₃	C₂³	1	1	yes	characteristic
439	#102×C₅₃	C₂³	1	1	yes	characteristic
440	#102×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	C₂⁴×C₅₃	—	2	1	no	—
486	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	4	1	no	—
488	#41×C₅₃	—	8	2	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×D₄×C₅₃	—	2	2	no	—
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	—	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	—	4	1	no	—
525	C₂×D₄×C₅₃	—	4	1	no	—
526	C₂×D₄×C₅₃	—	4	1	no	—
527	C₂×D₄×C₅₃	—	4	1	no	—
528	C₂×D₄×C₅₃	—	4	1	no	—
529	C₂×D₄×C₅₃	—	8	2	no	—
530	C₂×D₄×C₅₃	—	8	2	no	—
531	C₂×D₄×C₅₃	—	8	2	no	—
532	C₂×D₄×C₅₃	—	8	2	no	—
533	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
534	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
536	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
539	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
540	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
557	C₂²×C₄×C₅₃	—	2	1	no	—
558	C₂²×C₄×C₅₃	—	2	1	no	—
559	C₂²×C₄×C₅₃	—	2	1	no	—
560	C₂²×C₄×C₅₃	—	2	1	no	—
561	C₂²×C₄×C₅₃	—	2	1	no	—
562	C₂²×C₄×C₅₃	—	2	1	no	—
563	C₂²×C₄×C₅₃	—	2	1	no	—
564	C₂²×C₄×C₅₃	—	2	1	no	—
565	C₂²×C₄×C₅₃	—	8	2	no	—
566	C₂²×C₄×C₅₃	—	8	2	no	—
567	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
568	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
569	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
570	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
571	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
572	SD₁₆×C₅₃	—	2	2	no	—
573	SD₁₆×C₅₃	—	2	2	no	—
574	SD₁₆×C₅₃	—	4	1	no	—
575	SD₁₆×C₅₃	—	4	1	no	—
576	D₈×C₅₃	—	2	2	no	—
577	D₈×C₅₃	—	2	2	no	—
578	D₈×C₅₃	—	2	2	no	—
579	D₈×C₅₃	—	2	2	no	—
580	D₈×C₅₃	—	2	2	no	—
581	D₈×C₅₃	—	2	2	no	—
582	D₈×C₅₃	—	2	2	no	—
583	D₈×C₅₃	—	4	1	no	—
584	D₈×C₅₃	—	4	1	no	—
585	D₈×C₅₃	—	4	1	no	—
586	D₈×C₅₃	—	4	1	no	—
587	D₈×C₅₃	#41	1	4	yes	complemented
588	M₁₆×C₅₃	—	2	2	no	—
589	M₁₆×C₅₃	—	4	1	no	—
590	C₂×C₈×C₅₃	—	2	2	no	—
591	C₂×C₈×C₅₃	—	2	2	no	—
592	C₂×C₈×C₅₃	—	4	1	no	—
593	C₂×C₈×C₅₃	—	4	1	no	—
594	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
599	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
601	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
625	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
626	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
627	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
628	C₄⋊C₄×C₅₃	C₂×D₄	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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
634	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	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	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	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
679	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
681	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₄²×C₅₃	—	2	1	no	—
685	C₄²×C₅₃	—	2	1	no	—
686	C₄²×C₅₃	—	2	1	no	—
687	C₄²×C₅₃	—	2	1	no	—
688	C₄²×C₅₃	—	2	1	no	—
689	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
690	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
691	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
692	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
693	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
694	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
695	C₂³×C₅₃	—	2	1	no	—
696	C₂³×C₅₃	—	2	1	no	—
697	C₂³×C₅₃	—	2	1	no	—
698	C₂³×C₅₃	—	2	1	no	—
699	C₂³×C₅₃	—	2	1	no	—
700	C₂³×C₅₃	—	2	1	no	—
701	C₂³×C₅₃	—	2	1	no	—
702	C₂³×C₅₃	—	4	2	no	—
703	C₂³×C₅₃	—	4	2	no	—
704	C₂³×C₅₃	—	4	2	no	—
705	C₂³×C₅₃	—	4	2	no	—
706	C₂³×C₅₃	—	4	2	no	—
707	C₂³×C₅₃	—	4	2	no	—
708	C₂³×C₅₃	—	4	2	no	—
709	C₂³×C₅₃	—	8	1	no	—
710	C₂³×C₅₃	—	8	1	no	—
711	C₂³×C₅₃	—	8	1	no	—
712	C₂³×C₅₃	—	8	1	no	—
713	C₂³×C₅₃	—	8	1	no	—
714	C₂³×C₅₃	—	8	1	no	—
715	C₂³×C₅₃	—	8	1	no	—
716	C₂³×C₅₃	—	8	1	no	—
717	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
718	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
719	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
720	Q₈×C₅₃	—	2	1	no	—
721	Q₈×C₅₃	—	2	1	no	—
722	Q₈×C₅₃	—	4	1	no	—
723	Q₈×C₅₃	—	8	1	no	—
724	Q₈×C₅₃	—	8	1	no	—
725	D₄×C₅₃	—	2	2	no	—
726	D₄×C₅₃	—	2	2	no	—
727	D₄×C₅₃	—	2	1	no	—
728	D₄×C₅₃	—	2	1	no	—
729	D₄×C₅₃	—	2	1	no	—
730	D₄×C₅₃	—	2	1	no	—
731	D₄×C₅₃	—	2	1	no	—
732	D₄×C₅₃	—	2	1	no	—
733	D₄×C₅₃	—	2	1	no	—
734	D₄×C₅₃	—	2	1	no	—
735	D₄×C₅₃	—	2	1	no	—
736	D₄×C₅₃	—	2	1	no	—
737	D₄×C₅₃	—	2	1	no	—
738	D₄×C₅₃	—	2	1	no	—
739	D₄×C₅₃	—	4	1	no	—
740	D₄×C₅₃	—	4	2	no	—
741	D₄×C₅₃	—	4	2	no	—
742	D₄×C₅₃	—	4	2	no	—
743	D₄×C₅₃	—	4	2	no	—
744	D₄×C₅₃	—	4	2	no	—
745	D₄×C₅₃	—	4	2	no	—
746	D₄×C₅₃	—	4	2	no	—
747	D₄×C₅₃	—	4	2	no	—
748	D₄×C₅₃	—	4	2	no	—
749	D₄×C₅₃	—	4	2	no	—
750	D₄×C₅₃	—	8	1	no	—
751	D₄×C₅₃	—	8	1	no	—
752	D₄×C₅₃	—	8	1	no	—
753	D₄×C₅₃	—	8	1	no	—
754	D₄×C₅₃	—	8	1	no	—
755	D₄×C₅₃	—	8	1	no	—
756	D₄×C₅₃	—	8	1	no	—
757	D₄×C₅₃	—	8	1	no	—
758	D₄×C₅₃	—	8	1	no	—
759	D₄×C₅₃	—	8	1	no	—
760	D₄×C₅₃	—	8	1	no	—
761	D₄×C₅₃	—	8	1	no	—
762	D₄×C₅₃	—	8	1	no	—
763	D₄×C₅₃	—	8	1	no	—
764	D₄×C₅₃	C₂×#41	1	2	yes	—
765	D₄×C₅₃	C₂×#41	1	2	yes	—
766	C₂×C₄×C₅₃	—	2	2	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	—	2	1	no	—
772	C₂×C₄×C₅₃	—	2	1	no	—
773	C₂×C₄×C₅₃	—	2	1	no	—
774	C₂×C₄×C₅₃	—	2	1	no	—
775	C₂×C₄×C₅₃	—	2	1	no	—
776	C₂×C₄×C₅₃	—	2	1	no	—
777	C₂×C₄×C₅₃	—	2	1	no	—
778	C₂×C₄×C₅₃	—	2	1	no	—
779	C₂×C₄×C₅₃	—	2	1	no	—
780	C₂×C₄×C₅₃	—	2	1	no	—
781	C₂×C₄×C₅₃	—	2	1	no	—
782	C₂×C₄×C₅₃	—	4	1	no	—
783	C₂×C₄×C₅₃	—	4	2	no	—
784	C₂×C₄×C₅₃	—	4	2	no	—
785	C₂×C₄×C₅₃	—	4	2	no	—
786	C₂×C₄×C₅₃	—	4	2	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	—	8	1	no	—
794	C₂×C₄×C₅₃	—	8	1	no	—
795	C₂×C₄×C₅₃	—	8	1	no	—
796	C₂×C₄×C₅₃	—	8	1	no	—
797	C₂×C₄×C₅₃	—	8	1	no	—
798	C₂×C₄×C₅₃	—	8	1	no	—
799	C₂×C₄×C₅₃	—	8	1	no	—
800	C₂×C₄×C₅₃	—	8	1	no	—
801	C₂×C₄×C₅₃	—	8	1	no	—
802	C₂×C₄×C₅₃	—	8	1	no	—
803	C₂×C₄×C₅₃	—	8	1	no	—
804	C₂×C₄×C₅₃	—	8	1	no	—
805	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
806	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
807	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
808	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
810	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
811	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
812	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
813	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
814	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
815	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
816	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
817	C₈×C₅₃	—	2	1	no	—
818	C₈×C₅₃	—	2	1	no	—
819	C₈×C₅₃	—	2	1	no	—
820	C₈×C₅₃	—	2	1	no	—
821	C₈×C₅₃	—	2	1	no	—
822	C₈×C₅₃	—	2	1	no	—
823	C₈×C₅₃	—	2	1	no	—
824	C₈×C₅₃	C₂×#41	1	2	yes	—
825	#61519	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
826	C₂²×C₅₃	—	2	1	no	—
827	C₂²×C₅₃	—	2	1	no	—
828	C₂²×C₅₃	—	2	1	no	—
829	C₂²×C₅₃	—	2	1	no	—
830	C₂²×C₅₃	—	2	1	no	—
831	C₂²×C₅₃	—	2	1	no	—
832	C₂²×C₅₃	—	2	2	no	—
833	C₂²×C₅₃	—	2	2	no	—
834	C₂²×C₅₃	—	2	1	no	—
835	C₂²×C₅₃	—	2	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	—	4	1	no	—
842	C₂²×C₅₃	—	4	1	no	—
843	C₂²×C₅₃	—	4	1	no	—
844	C₂²×C₅₃	—	4	1	no	—
845	C₂²×C₅₃	—	4	1	no	—
846	C₂²×C₅₃	—	4	1	no	—
847	C₂²×C₅₃	—	4	1	no	—
848	C₂²×C₅₃	—	4	1	no	—
849	C₂²×C₅₃	—	4	1	no	—
850	C₂²×C₅₃	—	4	1	no	—
851	C₂²×C₅₃	—	4	1	no	—
852	C₂²×C₅₃	—	4	1	no	—
853	C₂²×C₅₃	—	4	1	no	—
854	C₂²×C₅₃	—	4	1	no	—
855	C₂²×C₅₃	—	8	4	no	—
856	C₂²×C₅₃	—	8	4	no	—
857	C₂²×C₅₃	—	16	2	no	—
858	C₂²×C₅₃	—	16	2	no	—
859	C₂²×C₅₃	—	16	2	no	—
860	C₂²×C₅₃	#576	1	2	yes	—
861	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
862	C₄×C₅₃	—	2	1	no	—
863	C₄×C₅₃	—	2	1	no	—
864	C₄×C₅₃	—	2	1	no	—
865	C₄×C₅₃	—	2	1	no	—
866	C₄×C₅₃	—	2	1	no	—
867	C₄×C₅₃	—	2	1	no	—
868	C₄×C₅₃	—	2	1	no	—
869	C₄×C₅₃	—	2	1	no	—
870	C₄×C₅₃	—	2	1	no	—
871	C₄×C₅₃	—	2	1	no	—
872	C₄×C₅₃	—	2	1	no	—
873	C₄×C₅₃	—	4	1	no	—
874	C₄×C₅₃	—	4	1	no	—
875	C₄×C₅₃	—	4	1	no	—
876	C₄×C₅₃	—	4	1	no	—
877	C₄×C₅₃	—	4	1	no	—
878	C₄×C₅₃	—	4	1	no	—
879	C₄×C₅₃	—	4	1	no	—
880	C₄×C₅₃	—	4	1	no	—
881	C₄×C₅₃	—	4	1	no	—
882	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
883	C₄×C₅₃	#585	1	1	yes	characteristic
884	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3513	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3389	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3370	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3347	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3345	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3337	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
899	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
900	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
901	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
902	#3180	C₂×C₅₃	1	1	yes	characteristic, complemented
903	#3179	C₂×C₅₃	1	1	yes	characteristic, complemented
904	#3176	C₂×C₅₃	1	1	yes	characteristic, complemented
905	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
906	#3122	C₂×C₅₃	1	1	yes	characteristic, complemented
907	#3119	C₂×C₅₃	1	1	yes	characteristic, complemented
908	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
909	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
910	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
911	#2968	C₂×C₅₃	1	1	yes	characteristic, complemented
912	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
913	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
914	C₂×#442	C₂×C₅₃	1	1	yes	characteristic, complemented
915	C₂×C₅₃	—	2	2	no	—
916	C₂×C₅₃	—	4	1	no	—
917	C₂×C₅₃	—	4	1	no	—
918	C₂×C₅₃	—	4	2	no	—
919	C₂×C₅₃	—	4	2	no	—
920	C₂×C₅₃	—	8	1	no	—
921	C₂×C₅₃	—	8	1	no	—
922	C₂×C₅₃	—	8	1	no	—
923	C₂×C₅₃	—	8	1	no	—
924	C₂×C₅₃	—	8	1	no	—
925	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
926	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
927	C₂×C₅₃	#3585	1	1	yes	characteristic
928	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
929	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
930	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
931	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#553	—	2	1	no	—
936	#553	—	2	1	no	—
937	#553	C₂²×C₅₃	1	1	yes	characteristic
938	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#551	—	2	1	no	—
942	#551	—	2	1	no	—
943	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#546	—	2	1	no	—
946	#546	—	2	1	no	—
947	#546	—	2	1	no	—
948	#546	—	2	1	no	—
949	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	D₄²	C₂²×C₅₃	1	1	yes	characteristic
952	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#539	—	2	1	no	—
960	#538	—	2	1	no	—
961	#538	—	2	1	no	—
962	#538	—	2	1	no	—
963	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#529	C₂²×C₅₃	1	1	yes	characteristic
965	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#525	—	2	1	no	—
967	#525	—	2	1	no	—
968	C₂×#123	—	2	1	no	—
969	C₂×#121	—	2	1	no	—
970	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#499	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#459	C₂²×C₅₃	1	1	yes	characteristic
1030	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#447	C₂²×C₅₃	1	1	yes	characteristic
1041	#447	C₂²×C₅₃	1	1	yes	characteristic
1042	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#442	C₂²×C₅₃	1	1	yes	characteristic
1051	#442	C₂²×C₅₃	1	1	yes	characteristic
1052	#442	C₂²×C₅₃	1	1	yes	characteristic
1053	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1070	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	C₅₃	#61519	1	1	yes	characteristic, direct product factor, Sylow
1100	C₂×#41	—	2	1	no	—
1101	C₂×#41	—	2	1	no	—
1102	C₂×#41	—	2	1	no	—
1103	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂²×D₄	—	2	1	no	—
1105	C₂²×D₄	—	2	1	no	—
1106	C₂²×D₄	—	2	1	no	—
1107	C₂²×D₄	—	2	1	no	—
1108	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂³×C₄	—	2	1	no	—
1114	C₂³×C₄	—	2	1	no	—
1115	AGL(1,ℤ/8)	—	2	4	no	—
1116	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×D₈	—	2	4	no	—
1121	C₂×D₈	—	2	4	no	—
1122	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1140	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1141	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1142	#127	C₂³×C₅₃	1	1	yes	characteristic
1143	#127	C₂³×C₅₃	1	1	yes	characteristic
1144	#127	C₂³×C₅₃	1	1	yes	characteristic
1145	#127	C₂³×C₅₃	1	1	yes	characteristic
1146	#126	—	2	1	no	—
1147	#126	—	2	1	no	—
1148	#126	—	2	1	no	—
1149	#126	—	2	1	no	—
1150	#126	—	2	1	no	—
1151	#126	—	2	1	no	—
1152	#126	D₄×C₅₃	1	1	yes	characteristic
1153	#126	D₄×C₅₃	1	1	yes	characteristic
1154	#125	—	2	1	no	—
1155	#125	D₄×C₅₃	1	1	yes	characteristic
1156	#125	C₂³×C₅₃	1	1	yes	characteristic
1157	#125	C₂³×C₅₃	1	1	yes	characteristic
1158	#125	C₂³×C₅₃	1	1	yes	characteristic
1159	#125	C₂³×C₅₃	1	1	yes	characteristic
1160	#124	—	2	1	no	—
1161	#124	—	2	1	no	—
1162	#124	—	2	1	no	—
1163	#124	—	2	1	no	—
1164	#124	—	2	1	no	—
1165	#124	D₄×C₅₃	1	1	yes	characteristic
1166	#124	C₂³×C₅₃	1	1	yes	characteristic
1167	#124	C₂³×C₅₃	1	1	yes	characteristic
1168	#123	—	2	1	no	—
1169	#123	—	2	1	no	—
1170	#123	—	2	1	no	—
1171	#123	—	2	1	no	—
1172	#123	—	2	1	no	—
1173	#123	—	2	1	no	—
1174	#123	—	2	1	no	—
1175	#123	—	2	1	no	—
1176	#123	—	2	1	no	—
1177	#123	—	2	1	no	—
1178	#123	—	2	1	no	—
1179	#123	—	2	1	no	—
1180	#123	—	2	1	no	—
1181	#123	—	2	1	no	—
1182	#123	—	2	1	no	—
1183	#123	—	2	1	no	—
1184	#123	—	2	1	no	—
1185	#123	—	2	1	no	—
1186	#123	D₄×C₅₃	1	1	yes	characteristic
1187	#123	D₄×C₅₃	1	1	yes	characteristic
1188	C₂²⋊Q₈	—	2	1	no	—
1189	C₂²⋊Q₈	—	2	1	no	—
1190	C₂²⋊Q₈	—	2	1	no	—
1191	C₂²⋊Q₈	—	2	1	no	—
1192	C₂²⋊Q₈	—	2	1	no	—
1193	C₂²⋊Q₈	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1197	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1205	#121	—	2	1	no	—
1206	#121	—	2	1	no	—
1207	#121	—	2	1	no	—
1208	#121	—	2	1	no	—
1209	#121	—	2	1	no	—
1210	#121	—	2	1	no	—
1211	#121	—	2	1	no	—
1212	#121	—	2	1	no	—
1213	#121	—	2	1	no	—
1214	#121	—	2	1	no	—
1215	#121	—	2	1	no	—
1216	#121	—	2	1	no	—
1217	#121	—	2	1	no	—
1218	#121	—	2	1	no	—
1219	#121	D₄×C₅₃	1	1	yes	characteristic
1220	#121	C₂³×C₅₃	1	1	yes	characteristic
1221	#121	C₂³×C₅₃	1	1	yes	characteristic
1222	#121	C₂³×C₅₃	1	1	yes	characteristic
1223	#121	C₂³×C₅₃	1	1	yes	characteristic
1224	#121	C₂³×C₅₃	1	1	yes	characteristic
1225	#121	C₂³×C₅₃	1	1	yes	characteristic
1226	#121	C₂³×C₅₃	1	1	yes	characteristic
1227	#121	C₂³×C₅₃	1	1	yes	characteristic
1228	#121	C₂³×C₅₃	1	1	yes	characteristic
1229	#121	C₂³×C₅₃	1	1	yes	characteristic
1230	#120	—	2	1	no	—
1231	#120	—	2	1	no	—
1232	#120	—	2	1	no	—
1233	#120	—	2	1	no	—
1234	#120	—	2	1	no	—
1235	#120	—	2	1	no	—
1236	#120	—	2	1	no	—
1237	#120	—	2	1	no	—
1238	#120	—	2	1	no	—
1239	#120	—	2	1	no	—
1240	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1243	C₄×D₄	—	2	1	no	—
1244	C₄×D₄	—	2	1	no	—
1245	C₄×D₄	—	2	1	no	—
1246	C₄×D₄	—	2	1	no	—
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	—	2	1	no	—
1249	C₄×D₄	—	2	1	no	—
1250	C₄×D₄	—	2	1	no	—
1251	C₄×D₄	—	2	1	no	—
1252	C₄×D₄	—	2	1	no	—
1253	C₄×D₄	—	2	1	no	—
1254	C₄×D₄	—	2	1	no	—
1255	C₄×D₄	—	2	1	no	—
1256	C₄×D₄	—	2	1	no	—
1257	C₄×D₄	—	2	1	no	—
1258	C₄×D₄	—	2	1	no	—
1259	C₄×D₄	—	2	1	no	—
1260	C₄×D₄	—	2	1	no	—
1261	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1262	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1263	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1264	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1267	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1268	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1271	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1272	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1273	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1274	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1275	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1276	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1277	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1278	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1279	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1280	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1281	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1282	#117	—	2	1	no	—
1283	#117	—	2	1	no	—
1284	#117	—	2	1	no	—
1285	#117	—	2	1	no	—
1286	#117	C₂³×C₅₃	1	1	yes	characteristic
1287	#117	C₂³×C₅₃	1	1	yes	characteristic
1288	#117	C₂³×C₅₃	1	1	yes	characteristic
1289	#117	C₂³×C₅₃	1	1	yes	characteristic
1290	#117	C₂³×C₅₃	1	1	yes	characteristic
1291	C₂×C₄⋊C₄	—	2	1	no	—
1292	C₂×C₄⋊C₄	—	2	1	no	—
1293	C₂×C₄⋊C₄	—	2	1	no	—
1294	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1295	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1296	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1297	C₂×C₂²⋊C₄	—	2	1	no	—
1298	C₂×C₂²⋊C₄	—	2	1	no	—
1299	C₂×C₂²⋊C₄	—	2	1	no	—
1300	C₂×C₂²⋊C₄	—	2	1	no	—
1301	C₂×C₂²⋊C₄	—	2	1	no	—
1302	C₂×C₂²⋊C₄	—	2	1	no	—
1303	C₂×C₂²⋊C₄	—	2	1	no	—
1304	C₂×C₂²⋊C₄	—	2	1	no	—
1305	C₂×C₂²⋊C₄	—	2	1	no	—
1306	C₂×C₂²⋊C₄	—	2	1	no	—
1307	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1308	#107	C₂³×C₅₃	1	1	yes	characteristic
1309	#107	C₂³×C₅₃	1	1	yes	characteristic
1310	#107	C₂³×C₅₃	1	1	yes	characteristic
1311	#107	C₂³×C₅₃	1	1	yes	characteristic
1312	#107	C₂³×C₅₃	1	1	yes	characteristic
1313	#107	C₂³×C₅₃	1	1	yes	characteristic
1314	#107	C₂³×C₅₃	1	1	yes	characteristic
1315	#107	C₂³×C₅₃	1	1	yes	characteristic
1316	#106	C₂³×C₅₃	1	1	yes	characteristic
1317	#106	C₂³×C₅₃	1	1	yes	characteristic
1318	#106	C₂³×C₅₃	1	1	yes	characteristic
1319	#106	C₂³×C₅₃	1	1	yes	characteristic
1320	#106	C₂³×C₅₃	1	1	yes	characteristic
1321	#106	C₂³×C₅₃	1	1	yes	characteristic
1322	#106	C₂³×C₅₃	1	1	yes	characteristic
1323	#106	C₂³×C₅₃	1	1	yes	characteristic
1324	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1325	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1326	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1327	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1328	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1329	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1330	#103	C₂³×C₅₃	1	1	yes	characteristic
1331	#103	C₂³×C₅₃	1	1	yes	characteristic
1332	#103	C₂³×C₅₃	1	1	yes	characteristic
1333	#103	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	#102	C₂³×C₅₃	1	1	yes	characteristic
1347	#102	C₂³×C₅₃	1	1	yes	characteristic
1348	#102	C₂³×C₅₃	1	1	yes	characteristic
1349	#102	C₂³×C₅₃	1	1	yes	characteristic
1350	#102	C₂³×C₅₃	1	1	yes	characteristic
1351	#102	C₂³×C₅₃	1	1	yes	characteristic
1352	#102	C₂³×C₅₃	1	1	yes	characteristic
1353	#102	C₂³×C₅₃	1	1	yes	characteristic
1354	#102	C₂³×C₅₃	1	1	yes	characteristic
1355	#102	C₂³×C₅₃	1	1	yes	characteristic
1356	#102	C₂³×C₅₃	1	1	yes	characteristic
1357	#102	C₂³×C₅₃	1	1	yes	characteristic
1358	#102	C₂³×C₅₃	1	1	yes	characteristic
1359	#102	C₂³×C₅₃	1	1	yes	characteristic
1360	#102	C₂³×C₅₃	1	1	yes	characteristic
1361	#102	C₂³×C₅₃	1	1	yes	characteristic
1362	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1363	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1364	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1365	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1366	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1367	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1368	#97	C₂³×C₅₃	1	1	yes	characteristic
1369	#97	C₂³×C₅₃	1	1	yes	characteristic
1370	#97	C₂³×C₅₃	1	1	yes	characteristic
1371	#97	C₂³×C₅₃	1	1	yes	characteristic
1372	#97	C₂³×C₅₃	1	1	yes	characteristic
1373	#97	C₂³×C₅₃	1	1	yes	characteristic
1374	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1375	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1376	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1377	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1378	C₂⁴	—	2	1	no	—
1379	C₂⁴	—	2	1	no	—
1380	C₂⁴	—	2	1	no	—
1381	C₂⁴	—	2	1	no	—
1382	C₂⁴	—	2	1	no	—
1383	#41	—	2	2	no	—
1384	#41	—	4	1	no	—
1385	#41	—	8	2	no	—
1386	#41	—	8	2	no	—
1387	#41	—	8	2	no	—
1388	C₂×Q₈	—	2	1	no	—
1389	C₂×Q₈	—	2	1	no	—
1390	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1391	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1392	C₂×D₄	—	2	2	no	—
1393	C₂×D₄	—	2	2	no	—
1394	C₂×D₄	—	2	2	no	—
1395	C₂×D₄	—	2	2	no	—
1396	C₂×D₄	—	2	2	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	—	2	1	no	—
1402	C₂×D₄	—	2	1	no	—
1403	C₂×D₄	—	2	1	no	—
1404	C₂×D₄	—	2	1	no	—
1405	C₂×D₄	—	2	1	no	—
1406	C₂×D₄	—	2	1	no	—
1407	C₂×D₄	—	2	1	no	—
1408	C₂×D₄	—	2	1	no	—
1409	C₂×D₄	—	2	1	no	—
1410	C₂×D₄	—	2	1	no	—
1411	C₂×D₄	—	2	1	no	—
1412	C₂×D₄	—	2	1	no	—
1413	C₂×D₄	—	2	1	no	—
1414	C₂×D₄	—	2	1	no	—
1415	C₂×D₄	—	2	1	no	—
1416	C₂×D₄	—	2	1	no	—
1417	C₂×D₄	—	2	1	no	—
1418	C₂×D₄	—	2	1	no	—
1419	C₂×D₄	—	2	1	no	—
1420	C₂×D₄	—	2	1	no	—
1421	C₂×D₄	—	4	1	no	—
1422	C₂×D₄	—	4	1	no	—
1423	C₂×D₄	—	4	1	no	—
1424	C₂×D₄	—	4	1	no	—
1425	C₂×D₄	—	4	1	no	—
1426	C₂×D₄	—	8	2	no	—
1427	C₂×D₄	—	8	2	no	—
1428	C₂×D₄	—	8	2	no	—
1429	C₂×D₄	—	8	2	no	—
1430	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1431	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1432	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1433	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1434	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1435	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1436	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1437	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1438	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1439	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1440	C₂²×C₄	—	2	1	no	—
1441	C₂²×C₄	—	2	1	no	—
1442	C₂²×C₄	—	2	1	no	—
1443	C₂²×C₄	—	2	1	no	—
1444	C₂²×C₄	—	2	1	no	—
1445	C₂²×C₄	—	2	1	no	—
1446	C₂²×C₄	—	2	1	no	—
1447	C₂²×C₄	—	2	1	no	—
1448	C₂²×C₄	—	2	1	no	—
1449	C₂²×C₄	—	2	1	no	—
1450	C₂²×C₄	—	2	1	no	—
1451	C₂²×C₄	—	2	1	no	—
1452	C₂²×C₄	—	2	1	no	—
1453	C₂²×C₄	—	2	1	no	—
1454	C₂²×C₄	—	2	1	no	—
1455	C₂²×C₄	—	2	1	no	—
1456	C₂²×C₄	—	2	1	no	—
1457	C₂²×C₄	—	2	1	no	—
1458	C₂²×C₄	—	2	1	no	—
1459	C₂²×C₄	—	2	1	no	—
1460	C₂²×C₄	—	2	1	no	—
1461	C₂²×C₄	—	2	1	no	—
1462	C₂²×C₄	—	8	2	no	—
1463	C₂²×C₄	—	8	2	no	—
1464	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1465	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1466	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1467	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1468	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1469	SD₁₆	—	2	2	no	—
1470	SD₁₆	—	2	2	no	—
1471	SD₁₆	—	4	1	no	—
1472	SD₁₆	—	4	1	no	—
1473	D₈	—	2	2	no	—
1474	D₈	—	2	2	no	—
1475	D₈	—	2	2	no	—
1476	D₈	—	2	2	no	—
1477	D₈	—	2	2	no	—
1478	D₈	—	2	2	no	—
1479	D₈	—	2	2	no	—
1480	D₈	—	4	1	no	—
1481	D₈	—	4	1	no	—
1482	D₈	—	4	1	no	—
1483	D₈	—	4	1	no	—
1484	D₈	#41×C₅₃	1	4	yes	complemented
1485	M₁₆	—	2	2	no	—
1486	M₁₆	—	4	1	no	—
1487	C₂×C₈	—	2	2	no	—
1488	C₂×C₈	—	2	2	no	—
1489	C₂×C₈	—	4	1	no	—
1490	C₂×C₈	—	4	1	no	—
1491	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1492	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1493	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1494	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1495	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1496	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1497	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1498	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1499	C₄⋊C₄	—	2	1	no	—
1500	C₄⋊C₄	—	2	1	no	—
1501	C₄⋊C₄	—	2	1	no	—
1502	C₄⋊C₄	—	2	1	no	—
1503	C₄⋊C₄	—	2	1	no	—
1504	C₄⋊C₄	—	2	1	no	—
1505	C₄⋊C₄	—	2	1	no	—
1506	C₄⋊C₄	—	2	1	no	—
1507	C₄⋊C₄	—	2	1	no	—
1508	C₄⋊C₄	—	2	1	no	—
1509	C₄⋊C₄	—	2	1	no	—
1510	C₄⋊C₄	—	2	1	no	—
1511	C₄⋊C₄	—	2	1	no	—
1512	C₄⋊C₄	—	2	1	no	—
1513	C₄⋊C₄	—	2	1	no	—
1514	C₄⋊C₄	—	2	1	no	—
1515	C₄⋊C₄	—	2	1	no	—
1516	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1517	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1518	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1519	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1520	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1522	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1523	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1524	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1525	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1526	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1527	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1528	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1529	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1530	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1531	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1532	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1533	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1550	C₂²⋊C₄	—	2	1	no	—
1551	C₂²⋊C₄	—	2	1	no	—
1552	C₂²⋊C₄	—	2	1	no	—
1553	C₂²⋊C₄	—	2	1	no	—
1554	C₂²⋊C₄	—	2	1	no	—
1555	C₂²⋊C₄	—	2	1	no	—
1556	C₂²⋊C₄	—	2	1	no	—
1557	C₂²⋊C₄	—	2	1	no	—
1558	C₂²⋊C₄	—	2	1	no	—
1559	C₂²⋊C₄	—	2	1	no	—
1560	C₂²⋊C₄	—	2	1	no	—
1561	C₂²⋊C₄	—	2	1	no	—
1562	C₂²⋊C₄	—	2	1	no	—
1563	C₂²⋊C₄	—	2	1	no	—
1564	C₂²⋊C₄	—	2	1	no	—
1565	C₂²⋊C₄	—	2	1	no	—
1566	C₂²⋊C₄	—	2	1	no	—
1567	C₂²⋊C₄	—	2	1	no	—
1568	C₂²⋊C₄	—	2	1	no	—
1569	C₂²⋊C₄	—	2	1	no	—
1570	C₂²⋊C₄	—	2	1	no	—
1571	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1572	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1573	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1574	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1575	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1576	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1577	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1578	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1579	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1580	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1581	C₄²	—	2	1	no	—
1582	C₄²	—	2	1	no	—
1583	C₄²	—	2	1	no	—
1584	C₄²	—	2	1	no	—
1585	C₄²	—	2	1	no	—
1586	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1587	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1588	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1589	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1590	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1591	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1592	C₂³	—	2	1	no	—
1593	C₂³	—	2	1	no	—
1594	C₂³	—	2	1	no	—
1595	C₂³	—	2	1	no	—
1596	C₂³	—	2	1	no	—
1597	C₂³	—	2	1	no	—
1598	C₂³	—	2	1	no	—
1599	C₂³	—	4	2	no	—
1600	C₂³	—	4	2	no	—
1601	C₂³	—	4	2	no	—
1602	C₂³	—	4	2	no	—
1603	C₂³	—	4	2	no	—
1604	C₂³	—	4	2	no	—
1605	C₂³	—	4	2	no	—
1606	C₂³	—	8	1	no	—
1607	C₂³	—	8	1	no	—
1608	C₂³	—	8	1	no	—
1609	C₂³	—	8	1	no	—
1610	C₂³	—	8	1	no	—
1611	C₂³	—	8	1	no	—
1612	C₂³	—	8	1	no	—
1613	C₂³	—	8	1	no	—
1614	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1615	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1616	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1617	Q₈	—	2	1	no	—
1618	Q₈	—	2	1	no	—
1619	Q₈	—	4	1	no	—
1620	Q₈	—	8	1	no	—
1621	Q₈	—	8	1	no	—
1622	D₄	—	2	2	no	—
1623	D₄	—	2	2	no	—
1624	D₄	—	2	1	no	—
1625	D₄	—	2	1	no	—
1626	D₄	—	2	1	no	—
1627	D₄	—	2	1	no	—
1628	D₄	—	2	1	no	—
1629	D₄	—	2	1	no	—
1630	D₄	—	2	1	no	—
1631	D₄	—	2	1	no	—
1632	D₄	—	2	1	no	—
1633	D₄	—	2	1	no	—
1634	D₄	—	2	1	no	—
1635	D₄	—	2	1	no	—
1636	D₄	—	4	1	no	—
1637	D₄	—	4	2	no	—
1638	D₄	—	4	2	no	—
1639	D₄	—	4	2	no	—
1640	D₄	—	4	2	no	—
1641	D₄	—	4	2	no	—
1642	D₄	—	4	2	no	—
1643	D₄	—	4	2	no	—
1644	D₄	—	4	2	no	—
1645	D₄	—	4	2	no	—
1646	D₄	—	4	2	no	—
1647	D₄	—	8	1	no	—
1648	D₄	—	8	1	no	—
1649	D₄	—	8	1	no	—
1650	D₄	—	8	1	no	—
1651	D₄	—	8	1	no	—
1652	D₄	—	8	1	no	—
1653	D₄	—	8	1	no	—
1654	D₄	—	8	1	no	—
1655	D₄	—	8	1	no	—
1656	D₄	—	8	1	no	—
1657	D₄	—	8	1	no	—
1658	D₄	—	8	1	no	—
1659	D₄	—	8	1	no	—
1660	D₄	—	8	1	no	—
1661	D₄	C₂×#41×C₅₃	1	2	yes	—
1662	D₄	C₂×#41×C₅₃	1	2	yes	—
1663	C₂×C₄	—	2	2	no	—
1664	C₂×C₄	—	2	1	no	—
1665	C₂×C₄	—	2	1	no	—
1666	C₂×C₄	—	2	1	no	—
1667	C₂×C₄	—	2	1	no	—
1668	C₂×C₄	—	2	1	no	—
1669	C₂×C₄	—	2	1	no	—
1670	C₂×C₄	—	2	1	no	—
1671	C₂×C₄	—	2	1	no	—
1672	C₂×C₄	—	2	1	no	—
1673	C₂×C₄	—	2	1	no	—
1674	C₂×C₄	—	2	1	no	—
1675	C₂×C₄	—	2	1	no	—
1676	C₂×C₄	—	2	1	no	—
1677	C₂×C₄	—	2	1	no	—
1678	C₂×C₄	—	2	1	no	—
1679	C₂×C₄	—	4	1	no	—
1680	C₂×C₄	—	4	2	no	—
1681	C₂×C₄	—	4	2	no	—
1682	C₂×C₄	—	4	2	no	—
1683	C₂×C₄	—	4	2	no	—
1684	C₂×C₄	—	8	1	no	—
1685	C₂×C₄	—	8	1	no	—
1686	C₂×C₄	—	8	1	no	—
1687	C₂×C₄	—	8	1	no	—
1688	C₂×C₄	—	8	1	no	—
1689	C₂×C₄	—	8	1	no	—
1690	C₂×C₄	—	8	1	no	—
1691	C₂×C₄	—	8	1	no	—
1692	C₂×C₄	—	8	1	no	—
1693	C₂×C₄	—	8	1	no	—
1694	C₂×C₄	—	8	1	no	—
1695	C₂×C₄	—	8	1	no	—
1696	C₂×C₄	—	8	1	no	—
1697	C₂×C₄	—	8	1	no	—
1698	C₂×C₄	—	8	1	no	—
1699	C₂×C₄	—	8	1	no	—
1700	C₂×C₄	—	8	1	no	—
1701	C₂×C₄	—	8	1	no	—
1702	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1703	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1704	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1705	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1706	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1707	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1708	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1709	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1710	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1711	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1712	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1713	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1714	C₈	—	2	1	no	—
1715	C₈	—	2	1	no	—
1716	C₈	—	2	1	no	—
1717	C₈	—	2	1	no	—
1718	C₈	—	2	1	no	—
1719	C₈	—	2	1	no	—
1720	C₈	—	2	1	no	—
1721	C₈	C₂×#41×C₅₃	1	2	yes	—
1722	C₂²	—	2	1	no	—
1723	C₂²	—	2	1	no	—
1724	C₂²	—	2	1	no	—
1725	C₂²	—	2	1	no	—
1726	C₂²	—	2	2	no	—
1727	C₂²	—	2	2	no	—
1728	C₂²	—	2	1	no	—
1729	C₂²	—	2	1	no	—
1730	C₂²	—	2	1	no	—
1731	C₂²	—	2	1	no	—
1732	C₂²	—	4	1	no	—
1733	C₂²	—	4	1	no	—
1734	C₂²	—	4	1	no	—
1735	C₂²	—	4	1	no	—
1736	C₂²	—	4	1	no	—
1737	C₂²	—	4	1	no	—
1738	C₂²	—	4	1	no	—
1739	C₂²	—	4	1	no	—
1740	C₂²	—	4	1	no	—
1741	C₂²	—	4	1	no	—
1742	C₂²	—	4	1	no	—
1743	C₂²	—	4	1	no	—
1744	C₂²	—	4	1	no	—
1745	C₂²	—	4	1	no	—
1746	C₂²	—	4	1	no	—
1747	C₂²	—	4	1	no	—
1748	C₂²	—	4	1	no	—
1749	C₂²	—	4	1	no	—
1750	C₂²	—	4	1	no	—
1751	C₂²	—	8	4	no	—
1752	C₂²	—	8	4	no	—
1753	C₂²	—	16	2	no	—
1754	C₂²	—	16	2	no	—
1755	C₂²	—	16	2	no	—
1756	C₂²	C₅₃×#576	1	2	yes	—
1757	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1758	C₄	—	2	1	no	—
1759	C₄	—	2	1	no	—
1760	C₄	—	2	1	no	—
1761	C₄	—	2	1	no	—
1762	C₄	—	2	1	no	—
1763	C₄	—	2	1	no	—
1764	C₄	—	2	1	no	—
1765	C₄	—	2	1	no	—
1766	C₄	—	2	1	no	—
1767	C₄	—	2	1	no	—
1768	C₄	—	2	1	no	—
1769	C₄	—	4	1	no	—
1770	C₄	—	4	1	no	—
1771	C₄	—	4	1	no	—
1772	C₄	—	4	1	no	—
1773	C₄	—	4	1	no	—
1774	C₄	—	4	1	no	—
1775	C₄	—	4	1	no	—
1776	C₄	—	4	1	no	—
1777	C₄	—	4	1	no	—
1778	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1779	C₄	C₅₃×#585	1	1	yes	characteristic
1780	C₂	—	2	2	no	—
1781	C₂	—	4	1	no	—
1782	C₂	—	4	1	no	—
1783	C₂	—	4	2	no	—
1784	C₂	—	4	2	no	—
1785	C₂	—	8	1	no	—
1786	C₂	—	8	1	no	—
1787	C₂	—	8	1	no	—
1788	C₂	—	8	1	no	—
1789	C₂	—	8	1	no	—
1790	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1791	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1792	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×#3519	C₂	semidirect
2. C₅₃×#3513	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3389	C₂	semidirect
5. C₅₃×#3370	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3347	C₂	semidirect
8. C₅₃×#3345	C₂	semidirect
9. C₅₃×#3337	C₂	semidirect
10. C₅₃×#3319	C₂	semidirect
11. C₅₃×#3318	C₂	semidirect
12. C₅₃×#3318	C₂	semidirect
13. C₅₃×#3310	C₂	semidirect
14. C₅₃×#3297	C₂	semidirect
15. C₅₃×#3294	C₂	semidirect
16. D₄×D₈×C₅₃	C₂	semidirect
17. C₅₃×#3264	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3180	C₂	semidirect
20. C₅₃×#3179	C₂	semidirect
21. C₅₃×#3176	C₂	semidirect
22. C₅₃×#3122	C₂	semidirect
23. C₅₃×#3122	C₂	semidirect
24. C₅₃×#3119	C₂	semidirect
25. C₅₃×#3118	C₂	semidirect
26. C₅₃×#3105	C₂	semidirect
27. C₅₃×#3100	C₂	semidirect
28. C₅₃×#2968	C₂	semidirect
29. C₅₃×#2948	C₂	semidirect
30. C₅₃×#2946	C₂	semidirect
31. C₂×C₅₃×#442	C₂	semidirect
35. C₅₃×#559	C₂²	semidirect
36. C₅₃×#555	C₂²	semidirect
37. C₅₃×#554	C₂²	semidirect
38. C₅₃×#554	C₂²	semidirect
42. C₅₃×#553	C₂²	semidirect
43. C₅₃×#553	C₂²	semidirect
44. C₅₃×#552	C₂²	semidirect
47. C₅₃×#550	C₂²	semidirect
48. C₅₃×#547	C₂²	semidirect
53. C₅₃×#546	C₂²	semidirect
54. C₅₃×#546	C₂²	semidirect
56. D₄²×C₅₃	C₂²	semidirect
57. D₄²×C₅₃	C₂²	semidirect
58. D₄²×C₅₃	C₂²	semidirect
59. C₅₃×#542	C₂²	semidirect
60. C₅₃×#540	C₂²	semidirect
61. C₅₃×#540	C₂²	semidirect
62. C₅₃×#540	C₂²	semidirect
67. C₅₃×#532	C₂²	semidirect
69. C₅₃×#529	C₂²	semidirect
74. C₅₃×#520	C₂²	semidirect
75. C₅₃×#518	C₂²	semidirect
76. C₅₃×#518	C₂²	semidirect
77. C₅₃×#518	C₂²	semidirect
78. C₂×C₄×D₄×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×#493	C₂²	semidirect
86. C₅₃×#490	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×#484	C₂²	semidirect
94. C₅₃×#482	C₂²	semidirect
95. C₅₃×#482	C₂²	semidirect
96. C₅₃×#482	C₂²	semidirect
97. C₅₃×#482	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#481	C₂²	semidirect
100. C₅₃×#481	C₂²	semidirect
101. C₅₃×#480	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×#474	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×#466	C₂²	semidirect
121. C₅₃×#466	C₂²	semidirect
122. C₅₃×#466	C₂²	semidirect
123. C₅₃×#466	C₂²	semidirect
124. C₅₃×#466	C₂²	semidirect
125. C₅₃×#465	C₂²	semidirect
126. C₅₃×#465	C₂²	semidirect
127. C₅₃×#465	C₂²	semidirect
128. C₅₃×#463	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#460	C₂²	semidirect
134. C₅₃×#459	C₂²	semidirect
135. C₅₃×#459	C₂²	semidirect
136. C₅₃×#459	C₂²	semidirect
137. C₅₃×#459	C₂²	semidirect
138. C₅₃×#459	C₂²	semidirect
139. C₅₃×#459	C₂²	semidirect
140. C₅₃×#450	C₂²	semidirect
141. C₅₃×#450	C₂²	semidirect
142. C₅₃×#449	C₂²	semidirect
143. C₅₃×#449	C₂²	semidirect
146. C₅₃×#447	C₂²	semidirect
147. C₅₃×#447	C₂²	semidirect
148. C₅₃×#447	C₂²	semidirect
149. C₅₃×#447	C₂²	semidirect
150. C₅₃×#447	C₂²	semidirect
151. C₅₃×#447	C₂²	semidirect
152. C₅₃×#446	C₂²	semidirect
153. C₅₃×#446	C₂²	semidirect
157. C₅₃×#442	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×#442	C₂²	semidirect
164. C₅₃×#442	C₂²	semidirect
165. C₅₃×#442	C₂²	semidirect
166. C₅₃×#442	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
174. C₄×D₈×C₅₃	C₂²	semidirect
175. C₄×D₈×C₅₃	C₂²	semidirect
176. C₄×D₈×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×#435	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₈×D₄×C₅₃	C₂²	semidirect
187. C₈×D₄×C₅₃	C₂²	semidirect
188. C₅₃×#433	C₂²	semidirect
189. C₅₃×#433	C₂²	semidirect
190. C₅₃×#431	C₂²	semidirect
191. C₅₃×#428	C₂²	semidirect
192. C₅₃×#427	C₂²	semidirect
193. C₂×#106×C₅₃	C₂²	semidirect
194. C₅₃×#418	C₂²	semidirect
195. C₅₃×#418	C₂²	semidirect
196. C₅₃×#416	C₂²	semidirect
197. C₂×#102×C₅₃	C₂²	semidirect
198. C₂×#102×C₅₃	C₂²	semidirect
199. C₂×#102×C₅₃	C₂²	semidirect
200. C₅₃×#405	C₂²	semidirect
201. C₅₃×#405	C₂²	semidirect
202. C₂×#97×C₅₃	C₂²	semidirect
587. D₈×C₅₃	#41	semidirect
825. #61519	C₅₃	direct (N × H)
884. #3519	C₂×C₅₃	semidirect
885. #3513	C₂×C₅₃	semidirect
886. #3399	C₂×C₅₃	semidirect
887. #3389	C₂×C₅₃	semidirect
888. #3370	C₂×C₅₃	semidirect
889. #3366	C₂×C₅₃	semidirect
890. #3347	C₂×C₅₃	semidirect
891. #3345	C₂×C₅₃	semidirect
892. #3337	C₂×C₅₃	semidirect
893. #3319	C₂×C₅₃	semidirect
894. #3318	C₂×C₅₃	semidirect
895. #3318	C₂×C₅₃	semidirect
896. #3310	C₂×C₅₃	semidirect
897. #3297	C₂×C₅₃	semidirect
898. #3294	C₂×C₅₃	semidirect
899. D₄×D₈	C₂×C₅₃	semidirect
900. #3264	C₂×C₅₃	semidirect
901. #3264	C₂×C₅₃	semidirect
902. #3180	C₂×C₅₃	semidirect
903. #3179	C₂×C₅₃	semidirect
904. #3176	C₂×C₅₃	semidirect
905. #3122	C₂×C₅₃	semidirect
906. #3122	C₂×C₅₃	semidirect
907. #3119	C₂×C₅₃	semidirect
908. #3118	C₂×C₅₃	semidirect
909. #3105	C₂×C₅₃	semidirect
910. #3100	C₂×C₅₃	semidirect
911. #2968	C₂×C₅₃	semidirect
912. #2948	C₂×C₅₃	semidirect
913. #2946	C₂×C₅₃	semidirect
914. C₂×#442	C₂×C₅₃	semidirect
931. #559	C₂²×C₅₃	semidirect
932. #555	C₂²×C₅₃	semidirect
933. #554	C₂²×C₅₃	semidirect
934. #554	C₂²×C₅₃	semidirect
938. #553	C₂²×C₅₃	semidirect
939. #553	C₂²×C₅₃	semidirect
940. #552	C₂²×C₅₃	semidirect
943. #550	C₂²×C₅₃	semidirect
944. #547	C₂²×C₅₃	semidirect
949. #546	C₂²×C₅₃	semidirect
950. #546	C₂²×C₅₃	semidirect
952. D₄²	C₂²×C₅₃	semidirect
953. D₄²	C₂²×C₅₃	semidirect
954. D₄²	C₂²×C₅₃	semidirect
955. #542	C₂²×C₅₃	semidirect
956. #540	C₂²×C₅₃	semidirect
957. #540	C₂²×C₅₃	semidirect
958. #540	C₂²×C₅₃	semidirect
963. #532	C₂²×C₅₃	semidirect
965. #529	C₂²×C₅₃	semidirect
970. #520	C₂²×C₅₃	semidirect
971. #518	C₂²×C₅₃	semidirect
972. #518	C₂²×C₅₃	semidirect
973. #518	C₂²×C₅₃	semidirect
974. C₂×C₄×D₄	C₂²×C₅₃	semidirect
975. C₂×C₄×D₄	C₂²×C₅₃	semidirect
976. #501	C₂²×C₅₃	semidirect
977. #501	C₂²×C₅₃	semidirect
978. #499	C₂²×C₅₃	semidirect
979. #496	C₂²×C₅₃	semidirect
980. #496	C₂²×C₅₃	semidirect
981. #493	C₂²×C₅₃	semidirect
982. #490	C₂²×C₅₃	semidirect
983. #490	C₂²×C₅₃	semidirect
984. #490	C₂²×C₅₃	semidirect
985. #489	C₂²×C₅₃	semidirect
986. #488	C₂²×C₅₃	semidirect
987. #486	C₂²×C₅₃	semidirect
988. #485	C₂²×C₅₃	semidirect
989. #484	C₂²×C₅₃	semidirect
990. #482	C₂²×C₅₃	semidirect
991. #482	C₂²×C₅₃	semidirect
992. #482	C₂²×C₅₃	semidirect
993. #482	C₂²×C₅₃	semidirect
994. #482	C₂²×C₅₃	semidirect
995. #481	C₂²×C₅₃	semidirect
996. #481	C₂²×C₅₃	semidirect
997. #480	C₂²×C₅₃	semidirect
998. #480	C₂²×C₅₃	semidirect
999. #480	C₂²×C₅₃	semidirect
1000. #479	C₂²×C₅₃	semidirect
1001. #478	C₂²×C₅₃	semidirect
1002. #478	C₂²×C₅₃	semidirect
1003. #478	C₂²×C₅₃	semidirect
1004. #478	C₂²×C₅₃	semidirect
1005. #478	C₂²×C₅₃	semidirect
1006. #478	C₂²×C₅₃	semidirect
1007. #478	C₂²×C₅₃	semidirect
1008. #476	C₂²×C₅₃	semidirect
1009. #474	C₂²×C₅₃	semidirect
1010. #474	C₂²×C₅₃	semidirect
1011. #474	C₂²×C₅₃	semidirect
1012. #469	C₂²×C₅₃	semidirect
1013. #469	C₂²×C₅₃	semidirect
1014. #469	C₂²×C₅₃	semidirect
1015. #468	C₂²×C₅₃	semidirect
1016. #466	C₂²×C₅₃	semidirect
1017. #466	C₂²×C₅₃	semidirect
1018. #466	C₂²×C₅₃	semidirect
1019. #466	C₂²×C₅₃	semidirect
1020. #466	C₂²×C₅₃	semidirect
1021. #465	C₂²×C₅₃	semidirect
1022. #465	C₂²×C₅₃	semidirect
1023. #465	C₂²×C₅₃	semidirect
1024. #463	C₂²×C₅₃	semidirect
1025. #463	C₂²×C₅₃	semidirect
1026. #463	C₂²×C₅₃	semidirect
1027. #463	C₂²×C₅₃	semidirect
1028. #460	C₂²×C₅₃	semidirect
1030. #459	C₂²×C₅₃	semidirect
1031. #459	C₂²×C₅₃	semidirect
1032. #459	C₂²×C₅₃	semidirect
1033. #459	C₂²×C₅₃	semidirect
1034. #459	C₂²×C₅₃	semidirect
1035. #459	C₂²×C₅₃	semidirect
1036. #450	C₂²×C₅₃	semidirect
1037. #450	C₂²×C₅₃	semidirect
1038. #449	C₂²×C₅₃	semidirect
1039. #449	C₂²×C₅₃	semidirect
1042. #447	C₂²×C₅₃	semidirect
1043. #447	C₂²×C₅₃	semidirect
1044. #447	C₂²×C₅₃	semidirect
1045. #447	C₂²×C₅₃	semidirect
1046. #447	C₂²×C₅₃	semidirect
1047. #447	C₂²×C₅₃	semidirect
1048. #446	C₂²×C₅₃	semidirect
1049. #446	C₂²×C₅₃	semidirect
1053. #442	C₂²×C₅₃	semidirect
1054. #442	C₂²×C₅₃	semidirect
1055. #442	C₂²×C₅₃	semidirect
1056. #442	C₂²×C₅₃	semidirect
1057. #442	C₂²×C₅₃	semidirect
1058. #442	C₂²×C₅₃	semidirect
1059. #442	C₂²×C₅₃	semidirect
1060. #442	C₂²×C₅₃	semidirect
1061. #442	C₂²×C₅₃	semidirect
1062. #442	C₂²×C₅₃	semidirect
1063. #440	C₂²×C₅₃	semidirect
1064. #440	C₂²×C₅₃	semidirect
1065. #440	C₂²×C₅₃	semidirect
1066. C₄×SD₁₆	C₂²×C₅₃	semidirect
1067. C₄×SD₁₆	C₂²×C₅₃	semidirect
1068. C₄×SD₁₆	C₂²×C₅₃	semidirect
1070. C₄×D₈	C₂²×C₅₃	semidirect
1071. C₄×D₈	C₂²×C₅₃	semidirect
1072. C₄×D₈	C₂²×C₅₃	semidirect
1073. C₄×D₈	C₂²×C₅₃	semidirect
1074. C₄×D₈	C₂²×C₅₃	semidirect
1075. C₄×D₈	C₂²×C₅₃	semidirect
1076. C₄×D₈	C₂²×C₅₃	semidirect
1077. C₄×D₈	C₂²×C₅₃	semidirect
1078. #435	C₂²×C₅₃	semidirect
1079. #435	C₂²×C₅₃	semidirect
1080. #435	C₂²×C₅₃	semidirect
1081. #435	C₂²×C₅₃	semidirect
1082. C₈×D₄	C₂²×C₅₃	semidirect
1083. C₈×D₄	C₂²×C₅₃	semidirect
1084. #433	C₂²×C₅₃	semidirect
1085. #433	C₂²×C₅₃	semidirect
1086. #431	C₂²×C₅₃	semidirect
1087. #428	C₂²×C₅₃	semidirect
1088. #427	C₂²×C₅₃	semidirect
1089. C₂×#106	C₂²×C₅₃	semidirect
1090. #418	C₂²×C₅₃	semidirect
1091. #418	C₂²×C₅₃	semidirect
1092. #416	C₂²×C₅₃	semidirect
1093. C₂×#102	C₂²×C₅₃	semidirect
1094. C₂×#102	C₂²×C₅₃	semidirect
1095. C₂×#102	C₂²×C₅₃	semidirect
1096. #405	C₂²×C₅₃	semidirect
1097. #405	C₂²×C₅₃	semidirect
1098. C₂×#97	C₂²×C₅₃	semidirect
1099. C₅₃	#61519	direct (N × H)
1484. 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×#3519	2
C₅₃×#3513	2
C₅₃×#3399	2
C₅₃×#3389	2
C₅₃×#3370	2
C₅₃×#3366	2
C₅₃×#3347	2
C₅₃×#3345	2
C₅₃×#3337	2
C₅₃×#3319	2
C₅₃×#3318	2
C₅₃×#3310	2
C₅₃×#3297	2
C₅₃×#3294	2
D₄×D₈×C₅₃	2
C₅₃×#3264	2
C₅₃×#3180	2
C₅₃×#3179	2
C₅₃×#3176	2
C₅₃×#3122	2
C₅₃×#3119	2
C₅₃×#3118	2
C₅₃×#3105	2
C₅₃×#3100	2
C₅₃×#2968	2
C₅₃×#2948	2
C₅₃×#2946	2
C₂×C₅₃×#442	2
#61519	53

Subgroups — C53×#61519 #27269031

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61519 #27269031