Subgroups — C₅₃×#61992 #27269504

Order 13568.

1870 conjugacy classes of subgroups.

The subgroup lattice has 1772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3301	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3268	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3256	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3213	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3111	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#559	—	2	1	no	—
39	C₅₃×#559	C₂²	1	1	yes	characteristic
40	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#556	—	2	1	no	—
43	C₅₃×#556	C₂²	1	1	yes	characteristic
44	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#555	—	2	1	no	—
46	C₅₃×#553	—	2	1	no	—
47	C₅₃×#553	—	2	1	no	—
48	C₅₃×#553	C₂²	1	1	yes	characteristic
49	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#551	—	2	1	no	—
51	C₅₃×#551	—	2	1	no	—
52	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
53	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic
55	C₅₃×#548	C₂²	1	1	yes	characteristic
56	C₅₃×#548	C₂²	1	1	yes	characteristic
57	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#546	—	2	1	no	—
59	C₅₃×#546	C₂²	1	1	yes	characteristic
60	C₅₃×#546	C₂²	1	1	yes	characteristic
61	D₄²×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#542	—	2	1	no	—
63	C₅₃×#538	—	2	1	no	—
64	C₅₃×#538	—	2	1	no	—
65	C₅₃×#532	—	2	1	no	—
66	C₅₃×#532	C₂²	1	1	yes	characteristic
67	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#529	—	2	1	no	—
69	C₅₃×#529	—	2	1	no	—
70	C₅₃×#529	C₂²	1	1	yes	characteristic
71	C₅₃×#529	C₂²	1	1	yes	characteristic
72	C₅₃×#529	C₂²	1	1	yes	characteristic
73	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
74	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
75	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
76	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#518	—	2	1	no	—
78	C₄×#41×C₅₃	—	2	1	no	—
79	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
80	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#496	C₂²	1	1	yes	characteristic
85	C₅₃×#496	C₂²	1	1	yes	characteristic
86	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic
88	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#490	C₂²	1	1	yes	characteristic
91	C₅₃×#489	C₂²	1	1	yes	characteristic
92	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#488	C₂²	1	1	yes	characteristic
94	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic
99	C₅₃×#482	C₂²	1	1	yes	characteristic
100	C₅₃×#481	C₂²	1	1	yes	characteristic
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#478	C₂²	1	1	yes	characteristic
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×#477	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#469	C₂²	1	1	yes	characteristic
113	C₅₃×#468	C₂²	1	1	yes	characteristic
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
118	C₅₃×#466	C₂²	1	1	yes	characteristic
119	C₅₃×#465	C₂²	1	1	yes	characteristic
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
124	C₅₃×#464	C₂²	1	1	yes	characteristic
125	C₅₃×#464	C₂²	1	1	yes	characteristic
126	C₅₃×#464	C₂²	1	1	yes	characteristic
127	C₅₃×#464	C₂²	1	1	yes	characteristic
128	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#463	C₂²	1	1	yes	characteristic
138	C₅₃×#463	C₂²	1	1	yes	characteristic
139	C₅₃×#463	C₂²	1	1	yes	characteristic
140	C₅₃×#463	C₂²	1	1	yes	characteristic
141	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#460	C₂²	1	1	yes	characteristic
150	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#459	C₂²	1	1	yes	characteristic
152	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#450	C₂²	1	1	yes	characteristic
160	C₅₃×#449	C₂²	1	1	yes	characteristic
161	C₅₃×#449	C₂²	1	1	yes	characteristic
162	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#448	C₂²	1	1	yes	characteristic
165	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#447	C₂²	1	1	yes	characteristic
169	C₅₃×#447	C₂²	1	1	yes	characteristic
170	C₅₃×#447	C₂²	1	1	yes	characteristic
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
174	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#440	C₂²	1	1	yes	characteristic
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×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×SD₁₆×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
186	C₅₃×#435	C₂²	1	1	yes	characteristic
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×#432	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
195	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#418	C₂²	1	1	yes	characteristic
199	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
201	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	—	2	1	no	—
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	#137×C₅₃	—	4	2	no	—
216	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
217	#135×C₅₃	—	4	2	no	—
218	#135×C₅₃	—	4	2	no	—
219	C₂×Q₁₆×C₅₃	—	4	2	no	—
220	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×C₅₃	—	4	2	no	—
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×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×SD₁₆×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×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
248	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₅₃	—	2	1	no	—
252	C₄⋊Q₈×C₅₃	—	2	1	no	—
253	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
255	#127×C₅₃	—	2	1	no	—
256	#127×C₅₃	C₂³	1	1	yes	characteristic
257	#127×C₅₃	C₂³	1	1	yes	characteristic
258	#126×C₅₃	—	2	1	no	—
259	#126×C₅₃	—	2	1	no	—
260	#126×C₅₃	—	2	1	no	—
261	#126×C₅₃	—	2	1	no	—
262	#126×C₅₃	—	2	1	no	—
263	#126×C₅₃	—	2	1	no	—
264	#126×C₅₃	—	2	1	no	—
265	#126×C₅₃	—	2	1	no	—
266	#126×C₅₃	—	2	1	no	—
267	#126×C₅₃	—	2	1	no	—
268	#126×C₅₃	—	2	1	no	—
269	#125×C₅₃	—	2	1	no	—
270	#125×C₅₃	—	2	1	no	—
271	#125×C₅₃	C₂³	1	1	yes	characteristic
272	#125×C₅₃	C₂³	1	1	yes	characteristic
273	#125×C₅₃	C₂³	1	1	yes	characteristic
274	#124×C₅₃	—	2	1	no	—
275	#124×C₅₃	—	2	1	no	—
276	#124×C₅₃	—	2	1	no	—
277	#124×C₅₃	—	2	1	no	—
278	#124×C₅₃	—	2	1	no	—
279	#124×C₅₃	—	2	1	no	—
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	—	2	1	no	—
283	#124×C₅₃	—	2	1	no	—
284	#124×C₅₃	—	2	1	no	—
285	#124×C₅₃	—	2	1	no	—
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	#124×C₅₃	C₂³	1	1	yes	characteristic
290	#124×C₅₃	C₂³	1	1	yes	characteristic
291	#124×C₅₃	C₂³	1	1	yes	characteristic
292	#124×C₅₃	C₂³	1	1	yes	characteristic
293	#124×C₅₃	C₂³	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
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	C₂²⋊Q₈×C₅₃	—	2	1	no	—
309	C₂²⋊Q₈×C₅₃	—	2	1	no	—
310	C₂²⋊Q₈×C₅₃	—	2	1	no	—
311	C₂²⋊Q₈×C₅₃	—	2	1	no	—
312	C₂²⋊Q₈×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	—	2	1	no	—
315	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
320	#121×C₅₃	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
335	#121×C₅₃	C₂³	1	1	yes	characteristic
336	#121×C₅₃	C₂³	1	1	yes	characteristic
337	#121×C₅₃	C₂³	1	1	yes	characteristic
338	#121×C₅₃	C₂³	1	1	yes	characteristic
339	#121×C₅₃	C₂³	1	1	yes	characteristic
340	#121×C₅₃	C₂³	1	1	yes	characteristic
341	#120×C₅₃	—	2	1	no	—
342	#120×C₅₃	—	2	1	no	—
343	#120×C₅₃	—	2	1	no	—
344	#120×C₅₃	—	2	1	no	—
345	C₄×Q₈×C₅₃	—	2	1	no	—
346	C₄×Q₈×C₅₃	—	2	1	no	—
347	C₄×Q₈×C₅₃	—	2	1	no	—
348	C₄×Q₈×C₅₃	—	2	1	no	—
349	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
350	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
355	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
356	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
357	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
358	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
359	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
365	C₄×D₄×C₅₃	—	2	1	no	—
366	C₄×D₄×C₅₃	—	2	1	no	—
367	C₄×D₄×C₅₃	—	2	1	no	—
368	C₄×D₄×C₅₃	—	2	1	no	—
369	C₄×D₄×C₅₃	—	2	1	no	—
370	C₄×D₄×C₅₃	—	2	1	no	—
371	C₄×D₄×C₅₃	—	2	1	no	—
372	C₄×D₄×C₅₃	—	2	1	no	—
373	C₄×D₄×C₅₃	—	2	1	no	—
374	C₄×D₄×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
383	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
384	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
385	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
386	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
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	#117×C₅₃	—	2	1	no	—
396	#117×C₅₃	—	2	1	no	—
397	#117×C₅₃	—	2	1	no	—
398	#117×C₅₃	—	2	1	no	—
399	#117×C₅₃	—	2	1	no	—
400	#117×C₅₃	—	2	1	no	—
401	#117×C₅₃	—	2	1	no	—
402	#117×C₅₃	—	2	1	no	—
403	#117×C₅₃	D₄	1	1	yes	characteristic
404	#117×C₅₃	D₄	1	1	yes	characteristic
405	#117×C₅₃	D₄	1	1	yes	characteristic
406	#117×C₅₃	C₂³	1	1	yes	characteristic
407	#117×C₅₃	C₂³	1	1	yes	characteristic
408	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
410	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₄²×C₅₃	—	2	1	no	—
417	C₂×C₄²×C₅₃	—	2	1	no	—
418	C₂×C₄²×C₅₃	—	2	1	no	—
419	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
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	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#103×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	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	2	2	no	—
488	#41×C₅₃	—	4	2	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	4	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	C₂×Q₈×C₅₃	—	2	1	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	—	2	1	no	—
500	C₂×Q₈×C₅₃	—	2	2	no	—
501	C₂×Q₈×C₅₃	—	4	1	no	—
502	C₂×Q₈×C₅₃	—	4	1	no	—
503	C₂×Q₈×C₅₃	—	4	1	no	—
504	C₂×Q₈×C₅₃	—	4	1	no	—
505	C₂×Q₈×C₅₃	—	4	1	no	—
506	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
507	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
508	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	4	1	no	—
530	C₂×D₄×C₅₃	—	4	1	no	—
531	C₂×D₄×C₅₃	—	4	1	no	—
532	C₂×D₄×C₅₃	—	4	1	no	—
533	C₂×D₄×C₅₃	—	4	4	no	—
534	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
536	C₂×D₄×C₅₃	C₂×D₄	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	C₂²×C₄×C₅₃	—	2	1	no	—
543	C₂²×C₄×C₅₃	—	2	1	no	—
544	C₂²×C₄×C₅₃	—	2	1	no	—
545	C₂²×C₄×C₅₃	—	2	1	no	—
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	—	2	1	no	—
554	C₂²×C₄×C₅₃	—	2	1	no	—
555	C₂²×C₄×C₅₃	—	2	1	no	—
556	C₂²×C₄×C₅₃	—	2	1	no	—
557	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
559	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
561	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
562	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
564	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
565	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
566	Q₁₆×C₅₃	—	2	2	no	—
567	Q₁₆×C₅₃	—	2	2	no	—
568	Q₁₆×C₅₃	—	2	2	no	—
569	Q₁₆×C₅₃	—	4	1	no	—
570	Q₁₆×C₅₃	—	4	1	no	—
571	Q₁₆×C₅₃	—	4	1	no	—
572	SD₁₆×C₅₃	—	2	2	no	—
573	SD₁₆×C₅₃	—	2	2	no	—
574	SD₁₆×C₅₃	—	2	2	no	—
575	SD₁₆×C₅₃	—	4	1	no	—
576	SD₁₆×C₅₃	—	4	1	no	—
577	SD₁₆×C₅₃	—	4	1	no	—
578	SD₁₆×C₅₃	—	4	1	no	—
579	SD₁₆×C₅₃	—	4	1	no	—
580	SD₁₆×C₅₃	—	4	1	no	—
581	SD₁₆×C₅₃	—	4	1	no	—
582	SD₁₆×C₅₃	—	4	1	no	—
583	SD₁₆×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	—	4	1	no	—
588	D₈×C₅₃	—	4	1	no	—
589	D₈×C₅₃	—	4	1	no	—
590	M₁₆×C₅₃	—	4	1	no	—
591	M₁₆×C₅₃	—	4	1	no	—
592	C₂×C₈×C₅₃	—	4	1	no	—
593	C₂×C₈×C₅₃	—	4	1	no	—
594	C₂×C₈×C₅₃	—	4	1	no	—
595	C₂×C₈×C₅₃	—	4	1	no	—
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	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂×D₄	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	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	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	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	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
690	C₄²×C₅₃	—	2	1	no	—
691	C₄²×C₅₃	—	2	1	no	—
692	C₄²×C₅₃	—	2	1	no	—
693	C₄²×C₅₃	—	2	1	no	—
694	C₄²×C₅₃	—	2	1	no	—
695	C₄²×C₅₃	—	2	1	no	—
696	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
697	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
698	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
699	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
700	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
704	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
705	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₂³×C₅₃	—	2	1	no	—
707	C₂³×C₅₃	—	2	1	no	—
708	C₂³×C₅₃	—	2	1	no	—
709	C₂³×C₅₃	—	2	1	no	—
710	C₂³×C₅₃	—	2	1	no	—
711	C₂³×C₅₃	—	4	2	no	—
712	C₂³×C₅₃	—	4	2	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	—	2	1	no	—
723	Q₈×C₅₃	—	2	1	no	—
724	Q₈×C₅₃	—	2	1	no	—
725	Q₈×C₅₃	—	2	1	no	—
726	Q₈×C₅₃	—	2	1	no	—
727	Q₈×C₅₃	—	2	1	no	—
728	Q₈×C₅₃	—	2	1	no	—
729	Q₈×C₅₃	—	4	1	no	—
730	Q₈×C₅₃	—	4	2	no	—
731	Q₈×C₅₃	—	4	2	no	—
732	Q₈×C₅₃	—	8	1	no	—
733	Q₈×C₅₃	—	8	1	no	—
734	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
735	D₄×C₅₃	—	2	2	no	—
736	D₄×C₅₃	—	2	2	no	—
737	D₄×C₅₃	—	2	1	no	—
738	D₄×C₅₃	—	2	1	no	—
739	D₄×C₅₃	—	2	1	no	—
740	D₄×C₅₃	—	2	1	no	—
741	D₄×C₅₃	—	2	1	no	—
742	D₄×C₅₃	—	2	1	no	—
743	D₄×C₅₃	—	2	1	no	—
744	D₄×C₅₃	—	2	1	no	—
745	D₄×C₅₃	—	2	1	no	—
746	D₄×C₅₃	—	2	1	no	—
747	D₄×C₅₃	—	4	1	no	—
748	D₄×C₅₃	—	4	2	no	—
749	D₄×C₅₃	—	4	2	no	—
750	D₄×C₅₃	—	4	2	no	—
751	D₄×C₅₃	—	4	2	no	—
752	D₄×C₅₃	—	4	2	no	—
753	D₄×C₅₃	—	4	2	no	—
754	D₄×C₅₃	—	4	2	no	—
755	D₄×C₅₃	—	4	2	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	—	8	1	no	—
765	C₂×C₄×C₅₃	—	2	2	no	—
766	C₂×C₄×C₅₃	—	2	1	no	—
767	C₂×C₄×C₅₃	—	2	1	no	—
768	C₂×C₄×C₅₃	—	2	1	no	—
769	C₂×C₄×C₅₃	—	2	1	no	—
770	C₂×C₄×C₅₃	—	2	1	no	—
771	C₂×C₄×C₅₃	—	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	—	2	1	no	—
783	C₂×C₄×C₅₃	—	4	1	no	—
784	C₂×C₄×C₅₃	—	4	1	no	—
785	C₂×C₄×C₅₃	—	4	1	no	—
786	C₂×C₄×C₅₃	—	4	1	no	—
787	C₂×C₄×C₅₃	—	4	1	no	—
788	C₂×C₄×C₅₃	—	4	2	no	—
789	C₂×C₄×C₅₃	—	4	2	no	—
790	C₂×C₄×C₅₃	—	4	2	no	—
791	C₂×C₄×C₅₃	—	4	2	no	—
792	C₂×C₄×C₅₃	—	4	2	no	—
793	C₂×C₄×C₅₃	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
804	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
815	C₈×C₅₃	—	2	1	no	—
816	C₈×C₅₃	—	2	1	no	—
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	#61992	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
824	C₂²×C₅₃	—	2	1	no	—
825	C₂²×C₅₃	—	2	1	no	—
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	—	4	1	no	—
833	C₂²×C₅₃	—	4	1	no	—
834	C₂²×C₅₃	—	4	1	no	—
835	C₂²×C₅₃	—	4	1	no	—
836	C₂²×C₅₃	—	4	1	no	—
837	C₂²×C₅₃	—	4	1	no	—
838	C₂²×C₅₃	—	4	1	no	—
839	C₂²×C₅₃	—	4	1	no	—
840	C₂²×C₅₃	—	4	1	no	—
841	C₂²×C₅₃	—	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	—	16	2	no	—
848	C₂²×C₅₃	—	16	2	no	—
849	C₂²×C₅₃	#575	1	2	yes	—
850	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
851	C₄×C₅₃	—	2	1	no	—
852	C₄×C₅₃	—	2	1	no	—
853	C₄×C₅₃	—	2	1	no	—
854	C₄×C₅₃	—	2	1	no	—
855	C₄×C₅₃	—	2	1	no	—
856	C₄×C₅₃	—	2	1	no	—
857	C₄×C₅₃	—	2	1	no	—
858	C₄×C₅₃	—	2	2	no	—
859	C₄×C₅₃	—	2	1	no	—
860	C₄×C₅₃	—	2	1	no	—
861	C₄×C₅₃	—	2	1	no	—
862	C₄×C₅₃	—	2	1	no	—
863	C₄×C₅₃	—	4	1	no	—
864	C₄×C₅₃	—	4	1	no	—
865	C₄×C₅₃	—	4	1	no	—
866	C₄×C₅₃	—	4	1	no	—
867	C₄×C₅₃	—	4	1	no	—
868	C₄×C₅₃	—	4	1	no	—
869	C₄×C₅₃	—	4	1	no	—
870	C₄×C₅₃	—	4	1	no	—
871	C₄×C₅₃	—	4	1	no	—
872	C₄×C₅₃	—	4	1	no	—
873	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
874	C₄×C₅₃	#585	1	1	yes	characteristic
875	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3480	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3403	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3377	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3371	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3313	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3301	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3271	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3268	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3256	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3250	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#3213	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#3211	C₂×C₅₃	1	1	yes	characteristic, complemented
899	#3117	C₂×C₅₃	1	1	yes	characteristic, complemented
900	#3111	C₂×C₅₃	1	1	yes	characteristic, complemented
901	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
902	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
903	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
904	C₂×#464	C₂×C₅₃	1	1	yes	characteristic, complemented
905	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
906	C₂×C₅₃	—	2	2	no	—
907	C₂×C₅₃	—	4	1	no	—
908	C₂×C₅₃	—	4	1	no	—
909	C₂×C₅₃	—	8	1	no	—
910	C₂×C₅₃	—	8	1	no	—
911	C₂×C₅₃	—	8	1	no	—
912	C₂×C₅₃	—	8	1	no	—
913	C₂×C₅₃	—	8	1	no	—
914	C₂×C₅₃	#3488	1	1	yes	characteristic
915	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
916	C₂×C₅₃	#3584	1	1	yes	characteristic
917	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
919	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
923	#559	—	2	1	no	—
924	#559	C₂²×C₅₃	1	1	yes	characteristic
925	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#556	—	2	1	no	—
928	#556	C₂²×C₅₃	1	1	yes	characteristic
929	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#555	—	2	1	no	—
931	#553	—	2	1	no	—
932	#553	—	2	1	no	—
933	#553	C₂²×C₅₃	1	1	yes	characteristic
934	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#551	—	2	1	no	—
936	#551	—	2	1	no	—
937	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
939	#548	C₂²×C₅₃	1	1	yes	characteristic
940	#548	C₂²×C₅₃	1	1	yes	characteristic
941	#548	C₂²×C₅₃	1	1	yes	characteristic
942	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#546	—	2	1	no	—
944	#546	C₂²×C₅₃	1	1	yes	characteristic
945	#546	C₂²×C₅₃	1	1	yes	characteristic
946	D₄²	C₂²×C₅₃	1	1	yes	characteristic
947	#542	—	2	1	no	—
948	#538	—	2	1	no	—
949	#538	—	2	1	no	—
950	#532	—	2	1	no	—
951	#532	C₂²×C₅₃	1	1	yes	characteristic
952	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#529	—	2	1	no	—
954	#529	—	2	1	no	—
955	#529	C₂²×C₅₃	1	1	yes	characteristic
956	#529	C₂²×C₅₃	1	1	yes	characteristic
957	#529	C₂²×C₅₃	1	1	yes	characteristic
958	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
961	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
962	#518	—	2	1	no	—
963	C₄×#41	—	2	1	no	—
964	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
965	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#496	C₂²×C₅₃	1	1	yes	characteristic
970	#496	C₂²×C₅₃	1	1	yes	characteristic
971	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#495	C₂²×C₅₃	1	1	yes	characteristic
973	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#490	C₂²×C₅₃	1	1	yes	characteristic
976	#489	C₂²×C₅₃	1	1	yes	characteristic
977	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#488	C₂²×C₅₃	1	1	yes	characteristic
979	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#482	C₂²×C₅₃	1	1	yes	characteristic
984	#482	C₂²×C₅₃	1	1	yes	characteristic
985	#481	C₂²×C₅₃	1	1	yes	characteristic
986	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#478	C₂²×C₅₃	1	1	yes	characteristic
991	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#469	C₂²×C₅₃	1	1	yes	characteristic
998	#468	C₂²×C₅₃	1	1	yes	characteristic
999	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#466	C₂²×C₅₃	1	1	yes	characteristic
1002	#466	C₂²×C₅₃	1	1	yes	characteristic
1003	#466	C₂²×C₅₃	1	1	yes	characteristic
1004	#465	C₂²×C₅₃	1	1	yes	characteristic
1005	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#464	C₂²×C₅₃	1	1	yes	characteristic
1009	#464	C₂²×C₅₃	1	1	yes	characteristic
1010	#464	C₂²×C₅₃	1	1	yes	characteristic
1011	#464	C₂²×C₅₃	1	1	yes	characteristic
1012	#464	C₂²×C₅₃	1	1	yes	characteristic
1013	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#463	C₂²×C₅₃	1	1	yes	characteristic
1023	#463	C₂²×C₅₃	1	1	yes	characteristic
1024	#463	C₂²×C₅₃	1	1	yes	characteristic
1025	#463	C₂²×C₅₃	1	1	yes	characteristic
1026	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#460	C₂²×C₅₃	1	1	yes	characteristic
1035	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#459	C₂²×C₅₃	1	1	yes	characteristic
1037	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#450	C₂²×C₅₃	1	1	yes	characteristic
1045	#449	C₂²×C₅₃	1	1	yes	characteristic
1046	#449	C₂²×C₅₃	1	1	yes	characteristic
1047	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#448	C₂²×C₅₃	1	1	yes	characteristic
1050	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#447	C₂²×C₅₃	1	1	yes	characteristic
1054	#447	C₂²×C₅₃	1	1	yes	characteristic
1055	#447	C₂²×C₅₃	1	1	yes	characteristic
1056	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#442	C₂²×C₅₃	1	1	yes	characteristic
1059	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#440	C₂²×C₅₃	1	1	yes	characteristic
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×Q₁₆	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, complemented
1070	#435	C₂²×C₅₃	1	1	yes	characteristic
1071	#435	C₂²×C₅₃	1	1	yes	characteristic
1072	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#418	C₂²×C₅₃	1	1	yes	characteristic
1084	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1088	C₅₃	#61992	1	1	yes	characteristic, direct product factor, Sylow
1089	C₂×#41	—	2	1	no	—
1090	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
1091	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂²×D₄	—	2	1	no	—
1099	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1101	#137	—	4	2	no	—
1102	AGL(1,ℤ/8)	—	4	2	no	—
1103	#135	—	4	2	no	—
1104	#135	—	4	2	no	—
1105	C₂×Q₁₆	—	4	2	no	—
1106	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×SD₁₆	—	4	2	no	—
1113	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
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×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×SD₁₆	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×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1137	C₄⋊Q₈	—	2	1	no	—
1138	C₄⋊Q₈	—	2	1	no	—
1139	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1140	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1141	#127	—	2	1	no	—
1142	#127	C₂³×C₅₃	1	1	yes	characteristic
1143	#127	C₂³×C₅₃	1	1	yes	characteristic
1144	#126	—	2	1	no	—
1145	#126	—	2	1	no	—
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	—	2	1	no	—
1153	#126	—	2	1	no	—
1154	#126	—	2	1	no	—
1155	#125	—	2	1	no	—
1156	#125	—	2	1	no	—
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	—	2	1	no	—
1166	#124	—	2	1	no	—
1167	#124	—	2	1	no	—
1168	#124	—	2	1	no	—
1169	#124	—	2	1	no	—
1170	#124	—	2	1	no	—
1171	#124	—	2	1	no	—
1172	#124	C₂³×C₅₃	1	1	yes	characteristic
1173	#124	C₂³×C₅₃	1	1	yes	characteristic
1174	#124	C₂³×C₅₃	1	1	yes	characteristic
1175	#124	C₂³×C₅₃	1	1	yes	characteristic
1176	#124	C₂³×C₅₃	1	1	yes	characteristic
1177	#124	C₂³×C₅₃	1	1	yes	characteristic
1178	#124	C₂³×C₅₃	1	1	yes	characteristic
1179	#124	C₂³×C₅₃	1	1	yes	characteristic
1180	#124	C₂³×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1187	#123	—	2	1	no	—
1188	#123	—	2	1	no	—
1189	#123	—	2	1	no	—
1190	#123	—	2	1	no	—
1191	#123	—	2	1	no	—
1192	#123	—	2	1	no	—
1193	#123	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	—	2	1	no	—
1197	C₂²⋊Q₈	—	2	1	no	—
1198	C₂²⋊Q₈	—	2	1	no	—
1199	C₂²⋊Q₈	—	2	1	no	—
1200	C₂²⋊Q₈	—	2	1	no	—
1201	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
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	#120	—	2	1	no	—
1228	#120	—	2	1	no	—
1229	#120	—	2	1	no	—
1230	#120	—	2	1	no	—
1231	C₄×Q₈	—	2	1	no	—
1232	C₄×Q₈	—	2	1	no	—
1233	C₄×Q₈	—	2	1	no	—
1234	C₄×Q₈	—	2	1	no	—
1235	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
1236	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1237	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
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×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1244	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1245	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1262	C₄×D₄	—	2	1	no	—
1263	C₄×D₄	—	2	1	no	—
1264	C₄×D₄	—	2	1	no	—
1265	C₄×D₄	—	2	1	no	—
1266	C₄×D₄	—	2	1	no	—
1267	C₄×D₄	—	2	1	no	—
1268	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1270	C₄×D₄	D₄×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	#117	—	2	1	no	—
1282	#117	—	2	1	no	—
1283	#117	—	2	1	no	—
1284	#117	—	2	1	no	—
1285	#117	—	2	1	no	—
1286	#117	—	2	1	no	—
1287	#117	—	2	1	no	—
1288	#117	—	2	1	no	—
1289	#117	D₄×C₅₃	1	1	yes	characteristic
1290	#117	D₄×C₅₃	1	1	yes	characteristic
1291	#117	D₄×C₅₃	1	1	yes	characteristic
1292	#117	C₂³×C₅₃	1	1	yes	characteristic
1293	#117	C₂³×C₅₃	1	1	yes	characteristic
1294	C₂×C₄⋊C₄	—	2	1	no	—
1295	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1296	C₂×C₂²⋊C₄	—	2	1	no	—
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×C₄²	—	2	1	no	—
1303	C₂×C₄²	—	2	1	no	—
1304	C₂×C₄²	—	2	1	no	—
1305	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1306	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
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	#106	C₂³×C₅₃	1	1	yes	characteristic
1313	#106	C₂³×C₅₃	1	1	yes	characteristic
1314	#106	C₂³×C₅₃	1	1	yes	characteristic
1315	#106	C₂³×C₅₃	1	1	yes	characteristic
1316	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1317	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1318	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1319	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1320	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1321	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1322	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1323	C₄⋊C₈	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	#103	C₂³×C₅₃	1	1	yes	characteristic
1327	#103	C₂³×C₅₃	1	1	yes	characteristic
1328	#103	C₂³×C₅₃	1	1	yes	characteristic
1329	#103	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	#103	C₂³×C₅₃	1	1	yes	characteristic
1335	#103	C₂³×C₅₃	1	1	yes	characteristic
1336	#103	C₂³×C₅₃	1	1	yes	characteristic
1337	#103	C₂³×C₅₃	1	1	yes	characteristic
1338	#103	C₂³×C₅₃	1	1	yes	characteristic
1339	#103	C₂³×C₅₃	1	1	yes	characteristic
1340	#103	C₂³×C₅₃	1	1	yes	characteristic
1341	#103	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	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1359	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1360	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1361	C₂²⋊C₈	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	#97	C₂³×C₅₃	1	1	yes	characteristic
1365	#97	C₂³×C₅₃	1	1	yes	characteristic
1366	#97	C₂³×C₅₃	1	1	yes	characteristic
1367	#97	C₂³×C₅₃	1	1	yes	characteristic
1368	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1369	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1370	C₂⁴	—	2	1	no	—
1371	C₂⁴	—	2	1	no	—
1372	#41	—	2	2	no	—
1373	#41	—	2	2	no	—
1374	#41	—	4	2	no	—
1375	#41	—	4	1	no	—
1376	#41	—	4	1	no	—
1377	#41	—	4	4	no	—
1378	#41	—	4	1	no	—
1379	#41	—	4	1	no	—
1380	#41	—	4	1	no	—
1381	#41	—	4	1	no	—
1382	C₂×Q₈	—	2	1	no	—
1383	C₂×Q₈	—	2	1	no	—
1384	C₂×Q₈	—	2	1	no	—
1385	C₂×Q₈	—	2	1	no	—
1386	C₂×Q₈	—	2	2	no	—
1387	C₂×Q₈	—	4	1	no	—
1388	C₂×Q₈	—	4	1	no	—
1389	C₂×Q₈	—	4	1	no	—
1390	C₂×Q₈	—	4	1	no	—
1391	C₂×Q₈	—	4	1	no	—
1392	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1393	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1394	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1395	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1396	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1397	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	4	1	no	—
1416	C₂×D₄	—	4	1	no	—
1417	C₂×D₄	—	4	1	no	—
1418	C₂×D₄	—	4	1	no	—
1419	C₂×D₄	—	4	4	no	—
1420	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1421	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1422	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1423	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1424	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1425	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1426	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1427	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1428	C₂²×C₄	—	2	1	no	—
1429	C₂²×C₄	—	2	1	no	—
1430	C₂²×C₄	—	2	1	no	—
1431	C₂²×C₄	—	2	1	no	—
1432	C₂²×C₄	—	2	1	no	—
1433	C₂²×C₄	—	2	1	no	—
1434	C₂²×C₄	—	2	1	no	—
1435	C₂²×C₄	—	2	1	no	—
1436	C₂²×C₄	—	2	1	no	—
1437	C₂²×C₄	—	2	1	no	—
1438	C₂²×C₄	—	2	1	no	—
1439	C₂²×C₄	—	2	1	no	—
1440	C₂²×C₄	—	2	1	no	—
1441	C₂²×C₄	—	2	1	no	—
1442	C₂²×C₄	—	2	1	no	—
1443	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1444	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1445	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1446	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1447	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1448	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1449	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1450	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1451	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1452	Q₁₆	—	2	2	no	—
1453	Q₁₆	—	2	2	no	—
1454	Q₁₆	—	2	2	no	—
1455	Q₁₆	—	4	1	no	—
1456	Q₁₆	—	4	1	no	—
1457	Q₁₆	—	4	1	no	—
1458	SD₁₆	—	2	2	no	—
1459	SD₁₆	—	2	2	no	—
1460	SD₁₆	—	2	2	no	—
1461	SD₁₆	—	4	1	no	—
1462	SD₁₆	—	4	1	no	—
1463	SD₁₆	—	4	1	no	—
1464	SD₁₆	—	4	1	no	—
1465	SD₁₆	—	4	1	no	—
1466	SD₁₆	—	4	1	no	—
1467	SD₁₆	—	4	1	no	—
1468	SD₁₆	—	4	1	no	—
1469	SD₁₆	—	4	1	no	—
1470	D₈	—	4	1	no	—
1471	D₈	—	4	1	no	—
1472	D₈	—	4	1	no	—
1473	D₈	—	4	1	no	—
1474	D₈	—	4	1	no	—
1475	D₈	—	4	1	no	—
1476	M₁₆	—	4	1	no	—
1477	M₁₆	—	4	1	no	—
1478	C₂×C₈	—	4	1	no	—
1479	C₂×C₈	—	4	1	no	—
1480	C₂×C₈	—	4	1	no	—
1481	C₂×C₈	—	4	1	no	—
1482	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1486	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1487	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1488	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1489	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	—	2	1	no	—
1496	C₄⋊C₄	—	2	1	no	—
1497	C₄⋊C₄	—	2	1	no	—
1498	C₄⋊C₄	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1515	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	C₂⁴×C₅₃	1	1	yes	characteristic
1521	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1522	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1523	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1524	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1525	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	—	2	1	no	—
1545	C₂²⋊C₄	—	2	1	no	—
1546	C₂²⋊C₄	—	2	1	no	—
1547	C₂²⋊C₄	—	2	1	no	—
1548	C₂²⋊C₄	—	2	1	no	—
1549	C₂²⋊C₄	—	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	C₂×D₄×C₅₃	1	1	yes	characteristic
1566	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1567	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1568	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1569	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1570	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1571	C₄²	—	2	1	no	—
1572	C₄²	—	2	1	no	—
1573	C₄²	—	2	1	no	—
1574	C₄²	—	2	1	no	—
1575	C₄²	—	2	1	no	—
1576	C₄²	—	2	1	no	—
1577	C₄²	—	2	1	no	—
1578	C₄²	—	2	1	no	—
1579	C₄²	—	2	1	no	—
1580	C₄²	—	2	1	no	—
1581	C₄²	—	2	1	no	—
1582	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1583	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1584	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1585	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
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	—	4	2	no	—
1598	C₂³	—	4	2	no	—
1599	C₂³	—	8	1	no	—
1600	C₂³	—	8	1	no	—
1601	C₂³	—	8	1	no	—
1602	C₂³	—	8	1	no	—
1603	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1604	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1605	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1606	Q₈	—	2	1	no	—
1607	Q₈	—	2	1	no	—
1608	Q₈	—	2	1	no	—
1609	Q₈	—	2	1	no	—
1610	Q₈	—	2	1	no	—
1611	Q₈	—	2	1	no	—
1612	Q₈	—	2	1	no	—
1613	Q₈	—	2	1	no	—
1614	Q₈	—	2	1	no	—
1615	Q₈	—	4	1	no	—
1616	Q₈	—	4	2	no	—
1617	Q₈	—	4	2	no	—
1618	Q₈	—	8	1	no	—
1619	Q₈	—	8	1	no	—
1620	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1621	D₄	—	2	2	no	—
1622	D₄	—	2	2	no	—
1623	D₄	—	2	1	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	—	4	1	no	—
1634	D₄	—	4	2	no	—
1635	D₄	—	4	2	no	—
1636	D₄	—	4	2	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	—	8	1	no	—
1643	D₄	—	8	1	no	—
1644	D₄	—	8	1	no	—
1645	D₄	—	8	1	no	—
1646	D₄	—	8	1	no	—
1647	D₄	—	8	1	no	—
1648	D₄	—	8	1	no	—
1649	D₄	—	8	1	no	—
1650	D₄	—	8	1	no	—
1651	C₂×C₄	—	2	2	no	—
1652	C₂×C₄	—	2	1	no	—
1653	C₂×C₄	—	2	1	no	—
1654	C₂×C₄	—	2	1	no	—
1655	C₂×C₄	—	2	1	no	—
1656	C₂×C₄	—	2	1	no	—
1657	C₂×C₄	—	2	1	no	—
1658	C₂×C₄	—	2	1	no	—
1659	C₂×C₄	—	2	1	no	—
1660	C₂×C₄	—	2	1	no	—
1661	C₂×C₄	—	2	1	no	—
1662	C₂×C₄	—	2	1	no	—
1663	C₂×C₄	—	2	1	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	—	4	1	no	—
1670	C₂×C₄	—	4	1	no	—
1671	C₂×C₄	—	4	1	no	—
1672	C₂×C₄	—	4	1	no	—
1673	C₂×C₄	—	4	1	no	—
1674	C₂×C₄	—	4	2	no	—
1675	C₂×C₄	—	4	2	no	—
1676	C₂×C₄	—	4	2	no	—
1677	C₂×C₄	—	4	2	no	—
1678	C₂×C₄	—	4	2	no	—
1679	C₂×C₄	—	4	2	no	—
1680	C₂×C₄	—	8	1	no	—
1681	C₂×C₄	—	8	1	no	—
1682	C₂×C₄	—	8	1	no	—
1683	C₂×C₄	—	8	1	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	C₂²×D₄×C₅₃	1	1	yes	characteristic
1690	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1691	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1692	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1693	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1694	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1695	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1696	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1697	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1698	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1699	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1700	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1701	C₈	—	2	1	no	—
1702	C₈	—	2	1	no	—
1703	C₈	—	2	1	no	—
1704	C₈	—	2	1	no	—
1705	C₈	—	2	1	no	—
1706	C₈	—	2	1	no	—
1707	C₈	—	2	1	no	—
1708	C₈	—	2	1	no	—
1709	C₂²	—	2	1	no	—
1710	C₂²	—	2	1	no	—
1711	C₂²	—	2	1	no	—
1712	C₂²	—	2	1	no	—
1713	C₂²	—	2	1	no	—
1714	C₂²	—	2	1	no	—
1715	C₂²	—	2	1	no	—
1716	C₂²	—	2	1	no	—
1717	C₂²	—	4	1	no	—
1718	C₂²	—	4	1	no	—
1719	C₂²	—	4	1	no	—
1720	C₂²	—	4	1	no	—
1721	C₂²	—	4	1	no	—
1722	C₂²	—	4	1	no	—
1723	C₂²	—	4	1	no	—
1724	C₂²	—	4	1	no	—
1725	C₂²	—	4	1	no	—
1726	C₂²	—	4	1	no	—
1727	C₂²	—	4	1	no	—
1728	C₂²	—	4	1	no	—
1729	C₂²	—	4	1	no	—
1730	C₂²	—	4	1	no	—
1731	C₂²	—	4	1	no	—
1732	C₂²	—	16	2	no	—
1733	C₂²	—	16	2	no	—
1734	C₂²	C₅₃×#575	1	2	yes	—
1735	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1736	C₄	—	2	1	no	—
1737	C₄	—	2	1	no	—
1738	C₄	—	2	1	no	—
1739	C₄	—	2	2	no	—
1740	C₄	—	2	1	no	—
1741	C₄	—	2	1	no	—
1742	C₄	—	2	1	no	—
1743	C₄	—	2	1	no	—
1744	C₄	—	2	1	no	—
1745	C₄	—	2	1	no	—
1746	C₄	—	2	1	no	—
1747	C₄	—	2	1	no	—
1748	C₄	—	4	1	no	—
1749	C₄	—	4	1	no	—
1750	C₄	—	4	1	no	—
1751	C₄	—	4	1	no	—
1752	C₄	—	4	1	no	—
1753	C₄	—	4	1	no	—
1754	C₄	—	4	1	no	—
1755	C₄	—	4	1	no	—
1756	C₄	—	4	1	no	—
1757	C₄	—	4	1	no	—
1758	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1759	C₄	C₅₃×#585	1	1	yes	characteristic
1760	C₂	—	2	2	no	—
1761	C₂	—	4	1	no	—
1762	C₂	—	4	1	no	—
1763	C₂	—	8	1	no	—
1764	C₂	—	8	1	no	—
1765	C₂	—	8	1	no	—
1766	C₂	—	8	1	no	—
1767	C₂	—	8	1	no	—
1768	C₂	C₅₃×#3488	1	1	yes	characteristic
1769	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1770	C₂	C₅₃×#3584	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3514	C₂	semidirect
2. C₅₃×#3480	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3401	C₂	semidirect
5. C₅₃×#3377	C₂	semidirect
6. C₅₃×#3371	C₂	semidirect
7. C₅₃×#3320	C₂	semidirect
8. C₅₃×#3318	C₂	semidirect
9. C₅₃×#3313	C₂	semidirect
10. C₅₃×#3311	C₂	semidirect
11. C₅₃×#3301	C₂	semidirect
12. C₅₃×#3297	C₂	semidirect
13. C₅₃×#3285	C₂	semidirect
14. C₅₃×#3282	C₂	semidirect
15. C₅₃×#3271	C₂	semidirect
16. C₅₃×#3270	C₂	semidirect
17. C₅₃×#3268	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3256	C₂	semidirect
20. C₅₃×#3250	C₂	semidirect
21. C₅₃×#3247	C₂	semidirect
22. C₅₃×#3219	C₂	semidirect
23. C₅₃×#3213	C₂	semidirect
24. C₅₃×#3211	C₂	semidirect
25. C₅₃×#3117	C₂	semidirect
26. C₅₃×#3111	C₂	semidirect
27. C₅₃×#3102	C₂	semidirect
28. C₅₃×#3040	C₂	semidirect
29. C₅₃×#3035	C₂	semidirect
30. C₂×C₅₃×#464	C₂	semidirect
31. C₅₃×#2990	C₂	semidirect
32. C₂×#137×C₅₃	C₂²	semidirect
34. C₂×#135×C₅₃	C₂²	semidirect
35. C₂×#135×C₅₃	C₂²	semidirect
36. C₂²×Q₁₆×C₅₃	C₂²	semidirect
40. C₅₃×#559	C₂²	semidirect
41. C₅₃×#557	C₂²	semidirect
44. C₅₃×#556	C₂²	semidirect
49. C₅₃×#553	C₂²	semidirect
52. C₅₃×#550	C₂²	semidirect
57. C₅₃×#548	C₂²	semidirect
67. C₅₃×#532	C₂²	semidirect
73. C₅₃×#529	C₂²	semidirect
74. C₅₃×#529	C₂²	semidirect
80. C₄×#41×C₅₃	C₂²	semidirect
81. C₄×#41×C₅₃	C₂²	semidirect
82. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
86. C₅₃×#496	C₂²	semidirect
88. C₅₃×#495	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
92. C₅₃×#489	C₂²	semidirect
94. C₅₃×#488	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#484	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
102. C₅₃×#479	C₂²	semidirect
103. C₅₃×#479	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#477	C₂²	semidirect
110. C₅₃×#476	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
114. C₅₃×#468	C₂²	semidirect
115. C₅₃×#467	C₂²	semidirect
120. C₅₃×#465	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
130. C₅₃×#464	C₂²	semidirect
131. C₅₃×#464	C₂²	semidirect
132. C₅₃×#464	C₂²	semidirect
133. C₅₃×#464	C₂²	semidirect
134. C₅₃×#464	C₂²	semidirect
135. C₅₃×#464	C₂²	semidirect
136. C₅₃×#464	C₂²	semidirect
141. C₅₃×#463	C₂²	semidirect
142. C₅₃×#463	C₂²	semidirect
143. C₅₃×#463	C₂²	semidirect
144. C₅₃×#463	C₂²	semidirect
145. C₅₃×#463	C₂²	semidirect
146. C₅₃×#463	C₂²	semidirect
147. C₅₃×#462	C₂²	semidirect
148. C₅₃×#461	C₂²	semidirect
150. C₅₃×#460	C₂²	semidirect
152. C₅₃×#459	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#452	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#452	C₂²	semidirect
157. C₅₃×#451	C₂²	semidirect
158. C₅₃×#451	C₂²	semidirect
162. C₅₃×#449	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
165. C₅₃×#448	C₂²	semidirect
166. C₅₃×#448	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#441	C₂²	semidirect
176. C₅₃×#441	C₂²	semidirect
178. C₅₃×#440	C₂²	semidirect
179. C₅₃×#440	C₂²	semidirect
180. C₅₃×#440	C₂²	semidirect
181. C₄×Q₁₆×C₅₃	C₂²	semidirect
182. C₄×SD₁₆×C₅₃	C₂²	semidirect
183. C₄×SD₁₆×C₅₃	C₂²	semidirect
184. C₄×D₈×C₅₃	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×#432	C₂²	semidirect
192. C₅₃×#432	C₂²	semidirect
193. C₅₃×#431	C₂²	semidirect
194. C₅₃×#423	C₂²	semidirect
195. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
197. C₅₃×#419	C₂²	semidirect
199. C₅₃×#416	C₂²	semidirect
200. C₅₃×#416	C₂²	semidirect
201. C₂×#103×C₅₃	C₂²	semidirect
823. #61992	C₅₃	direct (N × H)
875. #3514	C₂×C₅₃	semidirect
876. #3480	C₂×C₅₃	semidirect
877. #3403	C₂×C₅₃	semidirect
878. #3401	C₂×C₅₃	semidirect
879. #3377	C₂×C₅₃	semidirect
880. #3371	C₂×C₅₃	semidirect
881. #3320	C₂×C₅₃	semidirect
882. #3318	C₂×C₅₃	semidirect
883. #3313	C₂×C₅₃	semidirect
884. #3311	C₂×C₅₃	semidirect
885. #3301	C₂×C₅₃	semidirect
886. #3297	C₂×C₅₃	semidirect
887. #3285	C₂×C₅₃	semidirect
888. #3282	C₂×C₅₃	semidirect
889. #3271	C₂×C₅₃	semidirect
890. #3270	C₂×C₅₃	semidirect
891. #3268	C₂×C₅₃	semidirect
892. #3265	C₂×C₅₃	semidirect
893. #3256	C₂×C₅₃	semidirect
894. #3250	C₂×C₅₃	semidirect
895. #3247	C₂×C₅₃	semidirect
896. #3219	C₂×C₅₃	semidirect
897. #3213	C₂×C₅₃	semidirect
898. #3211	C₂×C₅₃	semidirect
899. #3117	C₂×C₅₃	semidirect
900. #3111	C₂×C₅₃	semidirect
901. #3102	C₂×C₅₃	semidirect
902. #3040	C₂×C₅₃	semidirect
903. #3035	C₂×C₅₃	semidirect
904. C₂×#464	C₂×C₅₃	semidirect
905. #2990	C₂×C₅₃	semidirect
917. C₂×#137	C₂²×C₅₃	semidirect
919. C₂×#135	C₂²×C₅₃	semidirect
920. C₂×#135	C₂²×C₅₃	semidirect
921. C₂²×Q₁₆	C₂²×C₅₃	semidirect
925. #559	C₂²×C₅₃	semidirect
926. #557	C₂²×C₅₃	semidirect
929. #556	C₂²×C₅₃	semidirect
934. #553	C₂²×C₅₃	semidirect
937. #550	C₂²×C₅₃	semidirect
942. #548	C₂²×C₅₃	semidirect
952. #532	C₂²×C₅₃	semidirect
958. #529	C₂²×C₅₃	semidirect
959. #529	C₂²×C₅₃	semidirect
965. C₄×#41	C₂²×C₅₃	semidirect
966. C₄×#41	C₂²×C₅₃	semidirect
967. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
968. #497	C₂²×C₅₃	semidirect
971. #496	C₂²×C₅₃	semidirect
973. #495	C₂²×C₅₃	semidirect
974. #491	C₂²×C₅₃	semidirect
977. #489	C₂²×C₅₃	semidirect
979. #488	C₂²×C₅₃	semidirect
980. #485	C₂²×C₅₃	semidirect
981. #485	C₂²×C₅₃	semidirect
982. #484	C₂²×C₅₃	semidirect
986. #479	C₂²×C₅₃	semidirect
987. #479	C₂²×C₅₃	semidirect
988. #479	C₂²×C₅₃	semidirect
989. #479	C₂²×C₅₃	semidirect
991. #478	C₂²×C₅₃	semidirect
992. #478	C₂²×C₅₃	semidirect
993. #478	C₂²×C₅₃	semidirect
994. #477	C₂²×C₅₃	semidirect
995. #476	C₂²×C₅₃	semidirect
996. #470	C₂²×C₅₃	semidirect
999. #468	C₂²×C₅₃	semidirect
1000. #467	C₂²×C₅₃	semidirect
1005. #465	C₂²×C₅₃	semidirect
1006. #465	C₂²×C₅₃	semidirect
1007. #465	C₂²×C₅₃	semidirect
1013. #464	C₂²×C₅₃	semidirect
1014. #464	C₂²×C₅₃	semidirect
1015. #464	C₂²×C₅₃	semidirect
1016. #464	C₂²×C₅₃	semidirect
1017. #464	C₂²×C₅₃	semidirect
1018. #464	C₂²×C₅₃	semidirect
1019. #464	C₂²×C₅₃	semidirect
1020. #464	C₂²×C₅₃	semidirect
1021. #464	C₂²×C₅₃	semidirect
1026. #463	C₂²×C₅₃	semidirect
1027. #463	C₂²×C₅₃	semidirect
1028. #463	C₂²×C₅₃	semidirect
1029. #463	C₂²×C₅₃	semidirect
1030. #463	C₂²×C₅₃	semidirect
1031. #463	C₂²×C₅₃	semidirect
1032. #462	C₂²×C₅₃	semidirect
1033. #461	C₂²×C₅₃	semidirect
1035. #460	C₂²×C₅₃	semidirect
1037. #459	C₂²×C₅₃	semidirect
1038. #452	C₂²×C₅₃	semidirect
1039. #452	C₂²×C₅₃	semidirect
1040. #452	C₂²×C₅₃	semidirect
1041. #452	C₂²×C₅₃	semidirect
1042. #451	C₂²×C₅₃	semidirect
1043. #451	C₂²×C₅₃	semidirect
1047. #449	C₂²×C₅₃	semidirect
1048. #449	C₂²×C₅₃	semidirect
1050. #448	C₂²×C₅₃	semidirect
1051. #448	C₂²×C₅₃	semidirect
1052. #448	C₂²×C₅₃	semidirect
1056. #446	C₂²×C₅₃	semidirect
1057. #446	C₂²×C₅₃	semidirect
1059. #441	C₂²×C₅₃	semidirect
1060. #441	C₂²×C₅₃	semidirect
1061. #441	C₂²×C₅₃	semidirect
1063. #440	C₂²×C₅₃	semidirect
1064. #440	C₂²×C₅₃	semidirect
1065. #440	C₂²×C₅₃	semidirect
1066. C₄×Q₁₆	C₂²×C₅₃	semidirect
1067. C₄×SD₁₆	C₂²×C₅₃	semidirect
1068. C₄×SD₁₆	C₂²×C₅₃	semidirect
1069. C₄×D₈	C₂²×C₅₃	semidirect
1072. #435	C₂²×C₅₃	semidirect
1073. #435	C₂²×C₅₃	semidirect
1074. C₈×D₄	C₂²×C₅₃	semidirect
1075. C₈×D₄	C₂²×C₅₃	semidirect
1076. #432	C₂²×C₅₃	semidirect
1077. #432	C₂²×C₅₃	semidirect
1078. #431	C₂²×C₅₃	semidirect
1079. #423	C₂²×C₅₃	semidirect
1080. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1081. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1082. #419	C₂²×C₅₃	semidirect
1084. #416	C₂²×C₅₃	semidirect
1085. #416	C₂²×C₅₃	semidirect
1086. C₂×#103	C₂²×C₅₃	semidirect
1088. C₅₃	#61992	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×#3514	2
C₅₃×#3480	2
C₅₃×#3403	2
C₅₃×#3401	2
C₅₃×#3377	2
C₅₃×#3371	2
C₅₃×#3320	2
C₅₃×#3318	2
C₅₃×#3313	2
C₅₃×#3311	2
C₅₃×#3301	2
C₅₃×#3297	2
C₅₃×#3285	2
C₅₃×#3282	2
C₅₃×#3271	2
C₅₃×#3270	2
C₅₃×#3268	2
C₅₃×#3265	2
C₅₃×#3256	2
C₅₃×#3250	2
C₅₃×#3247	2
C₅₃×#3219	2
C₅₃×#3213	2
C₅₃×#3211	2
C₅₃×#3117	2
C₅₃×#3111	2
C₅₃×#3102	2
C₅₃×#3040	2
C₅₃×#3035	2
C₂×C₅₃×#464	2
C₅₃×#2990	2
#61992	53

Subgroups — C53×#61992 #27269504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61992 #27269504