Subgroups — C₅₃×#61522 #27269034

Order 13568.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3513	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3345	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3335	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3307	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3306	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3181	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3179	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3173	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3125	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×#3101	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2952	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	C₂×#135×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×#556	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#554	C₂²	1	1	yes	characteristic
38	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#553	—	2	1	no	—
41	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#552	—	2	1	no	—
43	C₅₃×#552	C₂²	1	1	yes	characteristic
44	C₅₃×#551	—	2	1	no	—
45	C₅₃×#551	—	2	1	no	—
46	C₅₃×#551	—	2	1	no	—
47	C₅₃×#551	—	2	1	no	—
48	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#548	—	2	1	no	—
50	C₅₃×#547	C₂²	1	1	yes	characteristic
51	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#546	—	2	1	no	—
54	C₅₃×#546	C₂²	1	1	yes	characteristic
55	C₅₃×#546	C₂²	1	1	yes	characteristic
56	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
58	D₄²×C₅₃	C₂²	1	1	yes	characteristic
59	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#540	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#539	—	2	1	no	—
64	C₅₃×#539	—	2	1	no	—
65	C₅₃×#539	—	2	1	no	—
66	C₅₃×#538	—	2	1	no	—
67	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#529	C₂²	1	1	yes	characteristic
69	C₅₃×#529	C₂²	1	1	yes	characteristic
70	C₅₃×#525	—	2	1	no	—
71	C₅₃×#525	—	2	1	no	—
72	C₂×#123×C₅₃	—	2	1	no	—
73	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
74	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
79	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#498	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#496	C₂²	1	1	yes	characteristic
85	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#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×#483	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#481	C₂²	1	1	yes	characteristic
100	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#481	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×#476	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#469	C₂²	1	1	yes	characteristic
118	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#465	C₂²	1	1	yes	characteristic
124	C₅₃×#465	C₂²	1	1	yes	characteristic
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×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic
131	C₅₃×#463	C₂²	1	1	yes	characteristic
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#459	C₂²	1	1	yes	characteristic
140	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#450	C₂²	1	1	yes	characteristic
143	C₅₃×#450	C₂²	1	1	yes	characteristic
144	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#449	C₂²	1	1	yes	characteristic
147	C₅₃×#449	C₂²	1	1	yes	characteristic
148	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#447	C₂²	1	1	yes	characteristic
151	C₅₃×#447	C₂²	1	1	yes	characteristic
152	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#442	C₂²	1	1	yes	characteristic
155	C₅₃×#442	C₂²	1	1	yes	characteristic
156	C₅₃×#442	C₂²	1	1	yes	characteristic
157	C₅₃×#442	C₂²	1	1	yes	characteristic
158	C₅₃×#442	C₂²	1	1	yes	characteristic
159	C₅₃×#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×#441	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
170	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
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
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
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	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
193	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
197	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₅₃	—	2	1	no	—
209	C₂²×D₄×C₅₃	—	2	1	no	—
210	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂³×C₄×C₅₃	—	2	1	no	—
214	C₂³×C₄×C₅₃	—	2	1	no	—
215	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
216	#135×C₅₃	—	2	4	no	—
217	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×D₈×C₅₃	—	2	4	no	—
228	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
243	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	#126×C₅₃	—	2	1	no	—
247	#126×C₅₃	—	2	1	no	—
248	#126×C₅₃	—	2	1	no	—
249	#126×C₅₃	—	2	1	no	—
250	#126×C₅₃	—	2	1	no	—
251	#126×C₅₃	—	2	1	no	—
252	#126×C₅₃	—	2	1	no	—
253	#126×C₅₃	—	2	1	no	—
254	#126×C₅₃	D₄	1	1	yes	characteristic
255	#126×C₅₃	D₄	1	1	yes	characteristic
256	#125×C₅₃	—	2	1	no	—
257	#125×C₅₃	—	2	1	no	—
258	#125×C₅₃	—	2	1	no	—
259	#125×C₅₃	—	2	1	no	—
260	#125×C₅₃	D₄	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	D₄	1	1	yes	characteristic
268	#124×C₅₃	C₂³	1	1	yes	characteristic
269	#124×C₅₃	C₂³	1	1	yes	characteristic
270	#124×C₅₃	C₂³	1	1	yes	characteristic
271	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
290	#123×C₅₃	—	2	1	no	—
291	#123×C₅₃	—	2	1	no	—
292	#123×C₅₃	D₄	1	1	yes	characteristic
293	#123×C₅₃	D₄	1	1	yes	characteristic
294	C₂²⋊Q₈×C₅₃	—	2	1	no	—
295	C₂²⋊Q₈×C₅₃	—	2	1	no	—
296	C₂²⋊Q₈×C₅₃	—	2	1	no	—
297	C₂²⋊Q₈×C₅₃	—	2	1	no	—
298	C₂²⋊Q₈×C₅₃	—	2	1	no	—
299	C₂²⋊Q₈×C₅₃	—	2	1	no	—
300	C₂²⋊Q₈×C₅₃	—	2	1	no	—
301	C₂²⋊Q₈×C₅₃	—	2	1	no	—
302	C₂²⋊Q₈×C₅₃	—	2	1	no	—
303	C₂²⋊Q₈×C₅₃	—	2	1	no	—
304	C₂²⋊Q₈×C₅₃	—	2	1	no	—
305	C₂²⋊Q₈×C₅₃	—	2	1	no	—
306	C₂²⋊Q₈×C₅₃	—	2	1	no	—
307	C₂²⋊Q₈×C₅₃	—	2	1	no	—
308	C₂²⋊Q₈×C₅₃	—	2	1	no	—
309	C₂²⋊Q₈×C₅₃	—	2	1	no	—
310	C₂²⋊Q₈×C₅₃	—	2	1	no	—
311	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
312	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
318	#121×C₅₃	—	2	1	no	—
319	#121×C₅₃	—	2	1	no	—
320	#121×C₅₃	—	2	1	no	—
321	#121×C₅₃	—	2	1	no	—
322	#121×C₅₃	—	2	1	no	—
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	—	2	1	no	—
325	#121×C₅₃	—	2	1	no	—
326	#121×C₅₃	—	2	1	no	—
327	#121×C₅₃	D₄	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	#121×C₅₃	C₂³	1	1	yes	characteristic
334	#120×C₅₃	—	2	1	no	—
335	#120×C₅₃	—	2	1	no	—
336	#120×C₅₃	—	2	1	no	—
337	#120×C₅₃	—	2	1	no	—
338	#120×C₅₃	—	2	1	no	—
339	#120×C₅₃	—	2	1	no	—
340	C₄×Q₈×C₅₃	—	2	1	no	—
341	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
346	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
348	C₄×D₄×C₅₃	—	2	1	no	—
349	C₄×D₄×C₅₃	—	2	1	no	—
350	C₄×D₄×C₅₃	—	2	1	no	—
351	C₄×D₄×C₅₃	—	2	1	no	—
352	C₄×D₄×C₅₃	—	2	1	no	—
353	C₄×D₄×C₅₃	—	2	1	no	—
354	C₄×D₄×C₅₃	—	2	1	no	—
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	—	2	1	no	—
357	C₄×D₄×C₅₃	—	2	1	no	—
358	C₄×D₄×C₅₃	—	2	1	no	—
359	C₄×D₄×C₅₃	—	2	1	no	—
360	C₄×D₄×C₅₃	—	2	1	no	—
361	C₄×D₄×C₅₃	—	2	1	no	—
362	C₄×D₄×C₅₃	—	2	1	no	—
363	C₄×D₄×C₅₃	—	2	1	no	—
364	C₄×D₄×C₅₃	—	2	1	no	—
365	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
379	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
382	#117×C₅₃	—	2	1	no	—
383	#117×C₅₃	—	2	1	no	—
384	#117×C₅₃	—	2	1	no	—
385	#117×C₅₃	—	2	1	no	—
386	#117×C₅₃	—	2	1	no	—
387	#117×C₅₃	—	2	1	no	—
388	#117×C₅₃	—	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	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
394	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₂×C₄⋊C₄×C₅₃	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×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
401	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
402	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
403	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
404	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
405	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
406	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
407	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂×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	#106×C₅₃	C₂³	1	1	yes	characteristic
416	#106×C₅₃	C₂³	1	1	yes	characteristic
417	#106×C₅₃	C₂³	1	1	yes	characteristic
418	#106×C₅₃	C₂³	1	1	yes	characteristic
419	#106×C₅₃	C₂³	1	1	yes	characteristic
420	#106×C₅₃	C₂³	1	1	yes	characteristic
421	#106×C₅₃	C₂³	1	1	yes	characteristic
422	#106×C₅₃	C₂³	1	1	yes	characteristic
423	#106×C₅₃	C₂³	1	1	yes	characteristic
424	#106×C₅₃	C₂³	1	1	yes	characteristic
425	#106×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
428	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
429	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	#103×C₅₃	C₂³	1	1	yes	characteristic
434	#103×C₅₃	C₂³	1	1	yes	characteristic
435	#103×C₅₃	C₂³	1	1	yes	characteristic
436	#103×C₅₃	C₂³	1	1	yes	characteristic
437	#103×C₅₃	C₂³	1	1	yes	characteristic
438	#103×C₅₃	C₂³	1	1	yes	characteristic
439	#103×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#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	#41×C₅₃	—	2	2	no	—
485	#41×C₅₃	—	2	2	no	—
486	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	4	1	no	—
488	#41×C₅₃	—	4	1	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	8	2	no	—
491	#41×C₅₃	—	8	2	no	—
492	C₂×Q₈×C₅₃	—	2	1	no	—
493	C₂×Q₈×C₅₃	—	2	1	no	—
494	C₂×Q₈×C₅₃	—	2	1	no	—
495	C₂×Q₈×C₅₃	—	2	1	no	—
496	C₂×Q₈×C₅₃	—	8	2	no	—
497	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
498	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
500	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
501	C₂×D₄×C₅₃	—	2	2	no	—
502	C₂×D₄×C₅₃	—	2	2	no	—
503	C₂×D₄×C₅₃	—	2	2	no	—
504	C₂×D₄×C₅₃	—	2	1	no	—
505	C₂×D₄×C₅₃	—	2	1	no	—
506	C₂×D₄×C₅₃	—	2	1	no	—
507	C₂×D₄×C₅₃	—	2	1	no	—
508	C₂×D₄×C₅₃	—	2	1	no	—
509	C₂×D₄×C₅₃	—	2	1	no	—
510	C₂×D₄×C₅₃	—	2	1	no	—
511	C₂×D₄×C₅₃	—	2	1	no	—
512	C₂×D₄×C₅₃	—	2	1	no	—
513	C₂×D₄×C₅₃	—	2	1	no	—
514	C₂×D₄×C₅₃	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	4	1	no	—
519	C₂×D₄×C₅₃	—	4	1	no	—
520	C₂×D₄×C₅₃	—	4	1	no	—
521	C₂×D₄×C₅₃	—	8	2	no	—
522	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
523	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
524	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
525	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
526	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
527	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
528	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
529	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
530	C₂²×C₄×C₅₃	—	2	1	no	—
531	C₂²×C₄×C₅₃	—	2	1	no	—
532	C₂²×C₄×C₅₃	—	2	1	no	—
533	C₂²×C₄×C₅₃	—	2	1	no	—
534	C₂²×C₄×C₅₃	—	2	1	no	—
535	C₂²×C₄×C₅₃	—	2	1	no	—
536	C₂²×C₄×C₅₃	—	2	1	no	—
537	C₂²×C₄×C₅₃	—	2	1	no	—
538	C₂²×C₄×C₅₃	—	2	1	no	—
539	C₂²×C₄×C₅₃	—	2	1	no	—
540	C₂²×C₄×C₅₃	—	2	1	no	—
541	C₂²×C₄×C₅₃	—	2	1	no	—
542	C₂²×C₄×C₅₃	—	2	1	no	—
543	C₂²×C₄×C₅₃	—	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	—	8	2	no	—
553	C₂²×C₄×C₅₃	—	8	2	no	—
554	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
556	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	Q₁₆×C₅₃	—	2	2	no	—
560	Q₁₆×C₅₃	—	4	1	no	—
561	SD₁₆×C₅₃	—	2	2	no	—
562	SD₁₆×C₅₃	—	2	2	no	—
563	SD₁₆×C₅₃	—	2	2	no	—
564	SD₁₆×C₅₃	—	2	2	no	—
565	SD₁₆×C₅₃	—	4	1	no	—
566	SD₁₆×C₅₃	—	4	1	no	—
567	SD₁₆×C₅₃	—	4	1	no	—
568	SD₁₆×C₅₃	—	4	1	no	—
569	D₈×C₅₃	—	2	2	no	—
570	D₈×C₅₃	—	2	2	no	—
571	D₈×C₅₃	—	2	2	no	—
572	D₈×C₅₃	—	2	2	no	—
573	D₈×C₅₃	—	4	1	no	—
574	D₈×C₅₃	#41	1	4	yes	complemented
575	M₁₆×C₅₃	—	2	2	no	—
576	M₁₆×C₅₃	—	4	1	no	—
577	C₂×C₈×C₅₃	—	2	2	no	—
578	C₂×C₈×C₅₃	—	2	2	no	—
579	C₂×C₈×C₅₃	—	4	1	no	—
580	C₂×C₈×C₅₃	—	4	1	no	—
581	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
582	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
583	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
584	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
585	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
586	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
587	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
588	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
589	C₄⋊C₄×C₅₃	—	2	1	no	—
590	C₄⋊C₄×C₅₃	—	2	1	no	—
591	C₄⋊C₄×C₅₃	—	2	1	no	—
592	C₄⋊C₄×C₅₃	—	2	1	no	—
593	C₄⋊C₄×C₅₃	—	2	1	no	—
594	C₄⋊C₄×C₅₃	—	2	1	no	—
595	C₄⋊C₄×C₅₃	—	2	1	no	—
596	C₄⋊C₄×C₅₃	—	2	1	no	—
597	C₄⋊C₄×C₅₃	—	2	1	no	—
598	C₄⋊C₄×C₅₃	—	2	1	no	—
599	C₄⋊C₄×C₅₃	—	2	1	no	—
600	C₄⋊C₄×C₅₃	—	2	1	no	—
601	C₄⋊C₄×C₅₃	—	2	1	no	—
602	C₄⋊C₄×C₅₃	—	2	1	no	—
603	C₄⋊C₄×C₅₃	—	2	1	no	—
604	C₄⋊C₄×C₅₃	—	2	1	no	—
605	C₄⋊C₄×C₅₃	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	—	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	C₂×D₄	1	1	yes	characteristic
617	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
618	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
619	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
620	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
621	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
622	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
623	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
624	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
625	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
626	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
627	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
628	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
629	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
630	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
634	C₂²⋊C₄×C₅₃	—	2	1	no	—
635	C₂²⋊C₄×C₅₃	—	2	1	no	—
636	C₂²⋊C₄×C₅₃	—	2	1	no	—
637	C₂²⋊C₄×C₅₃	—	2	1	no	—
638	C₂²⋊C₄×C₅₃	—	2	1	no	—
639	C₂²⋊C₄×C₅₃	—	2	1	no	—
640	C₂²⋊C₄×C₅₃	—	2	1	no	—
641	C₂²⋊C₄×C₅₃	—	2	1	no	—
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
668	C₂²⋊C₄×C₅₃	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
670	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
671	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
672	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
673	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
674	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
675	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
676	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
677	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
678	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
679	C₄²×C₅₃	—	2	1	no	—
680	C₄²×C₅₃	—	2	1	no	—
681	C₄²×C₅₃	—	2	1	no	—
682	C₄²×C₅₃	—	2	1	no	—
683	C₄²×C₅₃	—	2	1	no	—
684	C₄²×C₅₃	—	2	1	no	—
685	C₄²×C₅₃	—	2	1	no	—
686	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
687	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
688	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
689	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
690	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
691	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
692	C₂³×C₅₃	—	2	1	no	—
693	C₂³×C₅₃	—	2	1	no	—
694	C₂³×C₅₃	—	2	1	no	—
695	C₂³×C₅₃	—	2	1	no	—
696	C₂³×C₅₃	—	2	1	no	—
697	C₂³×C₅₃	—	4	2	no	—
698	C₂³×C₅₃	—	4	2	no	—
699	C₂³×C₅₃	—	4	2	no	—
700	C₂³×C₅₃	—	4	2	no	—
701	C₂³×C₅₃	—	4	2	no	—
702	C₂³×C₅₃	—	8	1	no	—
703	C₂³×C₅₃	—	8	1	no	—
704	C₂³×C₅₃	—	8	1	no	—
705	C₂³×C₅₃	—	8	1	no	—
706	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
707	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
708	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
709	Q₈×C₅₃	—	2	1	no	—
710	Q₈×C₅₃	—	2	1	no	—
711	Q₈×C₅₃	—	2	1	no	—
712	Q₈×C₅₃	—	2	1	no	—
713	Q₈×C₅₃	—	2	1	no	—
714	Q₈×C₅₃	—	2	1	no	—
715	Q₈×C₅₃	—	4	1	no	—
716	Q₈×C₅₃	—	4	2	no	—
717	Q₈×C₅₃	—	8	1	no	—
718	Q₈×C₅₃	—	8	1	no	—
719	Q₈×C₅₃	—	8	1	no	—
720	D₄×C₅₃	—	2	2	no	—
721	D₄×C₅₃	—	2	2	no	—
722	D₄×C₅₃	—	2	1	no	—
723	D₄×C₅₃	—	2	1	no	—
724	D₄×C₅₃	—	2	1	no	—
725	D₄×C₅₃	—	2	1	no	—
726	D₄×C₅₃	—	2	1	no	—
727	D₄×C₅₃	—	2	1	no	—
728	D₄×C₅₃	—	2	1	no	—
729	D₄×C₅₃	—	2	1	no	—
730	D₄×C₅₃	—	4	1	no	—
731	D₄×C₅₃	—	4	2	no	—
732	D₄×C₅₃	—	4	2	no	—
733	D₄×C₅₃	—	4	2	no	—
734	D₄×C₅₃	—	4	2	no	—
735	D₄×C₅₃	—	4	2	no	—
736	D₄×C₅₃	—	4	2	no	—
737	D₄×C₅₃	—	4	2	no	—
738	D₄×C₅₃	—	8	1	no	—
739	D₄×C₅₃	—	8	1	no	—
740	D₄×C₅₃	—	8	1	no	—
741	D₄×C₅₃	—	8	1	no	—
742	D₄×C₅₃	—	8	1	no	—
743	D₄×C₅₃	—	8	1	no	—
744	D₄×C₅₃	—	8	1	no	—
745	D₄×C₅₃	C₂×#41	1	2	yes	—
746	D₄×C₅₃	C₂×#41	1	2	yes	—
747	C₂×C₄×C₅₃	—	2	2	no	—
748	C₂×C₄×C₅₃	—	2	1	no	—
749	C₂×C₄×C₅₃	—	2	1	no	—
750	C₂×C₄×C₅₃	—	2	1	no	—
751	C₂×C₄×C₅₃	—	2	1	no	—
752	C₂×C₄×C₅₃	—	2	1	no	—
753	C₂×C₄×C₅₃	—	2	1	no	—
754	C₂×C₄×C₅₃	—	2	1	no	—
755	C₂×C₄×C₅₃	—	2	1	no	—
756	C₂×C₄×C₅₃	—	2	1	no	—
757	C₂×C₄×C₅₃	—	2	1	no	—
758	C₂×C₄×C₅₃	—	2	1	no	—
759	C₂×C₄×C₅₃	—	2	1	no	—
760	C₂×C₄×C₅₃	—	2	1	no	—
761	C₂×C₄×C₅₃	—	2	1	no	—
762	C₂×C₄×C₅₃	—	2	1	no	—
763	C₂×C₄×C₅₃	—	2	1	no	—
764	C₂×C₄×C₅₃	—	2	1	no	—
765	C₂×C₄×C₅₃	—	4	1	no	—
766	C₂×C₄×C₅₃	—	4	2	no	—
767	C₂×C₄×C₅₃	—	4	2	no	—
768	C₂×C₄×C₅₃	—	4	2	no	—
769	C₂×C₄×C₅₃	—	4	2	no	—
770	C₂×C₄×C₅₃	—	4	2	no	—
771	C₂×C₄×C₅₃	—	4	2	no	—
772	C₂×C₄×C₅₃	—	8	1	no	—
773	C₂×C₄×C₅₃	—	8	1	no	—
774	C₂×C₄×C₅₃	—	8	1	no	—
775	C₂×C₄×C₅₃	—	8	1	no	—
776	C₂×C₄×C₅₃	—	8	1	no	—
777	C₂×C₄×C₅₃	—	8	1	no	—
778	C₂×C₄×C₅₃	—	8	1	no	—
779	C₂×C₄×C₅₃	—	8	1	no	—
780	C₂×C₄×C₅₃	—	8	1	no	—
781	C₂×C₄×C₅₃	—	8	1	no	—
782	C₂×C₄×C₅₃	—	8	1	no	—
783	C₂×C₄×C₅₃	—	8	1	no	—
784	C₂×C₄×C₅₃	—	8	1	no	—
785	C₂×C₄×C₅₃	—	8	1	no	—
786	C₂×C₄×C₅₃	—	8	1	no	—
787	C₂×C₄×C₅₃	—	8	1	no	—
788	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
790	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
791	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
792	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
793	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
794	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
795	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
796	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
797	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
798	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
800	C₈×C₅₃	—	2	1	no	—
801	C₈×C₅₃	—	2	1	no	—
802	C₈×C₅₃	—	2	1	no	—
803	C₈×C₅₃	—	2	1	no	—
804	C₈×C₅₃	—	2	1	no	—
805	C₈×C₅₃	—	2	1	no	—
806	C₈×C₅₃	—	2	1	no	—
807	C₈×C₅₃	C₂×#41	1	2	yes	—
808	#61522	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
809	C₂²×C₅₃	—	2	1	no	—
810	C₂²×C₅₃	—	2	1	no	—
811	C₂²×C₅₃	—	2	1	no	—
812	C₂²×C₅₃	—	2	1	no	—
813	C₂²×C₅₃	—	2	1	no	—
814	C₂²×C₅₃	—	2	1	no	—
815	C₂²×C₅₃	—	2	2	no	—
816	C₂²×C₅₃	—	2	2	no	—
817	C₂²×C₅₃	—	2	1	no	—
818	C₂²×C₅₃	—	2	1	no	—
819	C₂²×C₅₃	—	4	1	no	—
820	C₂²×C₅₃	—	4	1	no	—
821	C₂²×C₅₃	—	4	1	no	—
822	C₂²×C₅₃	—	4	1	no	—
823	C₂²×C₅₃	—	4	1	no	—
824	C₂²×C₅₃	—	4	1	no	—
825	C₂²×C₅₃	—	4	1	no	—
826	C₂²×C₅₃	—	4	1	no	—
827	C₂²×C₅₃	—	4	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	—	4	1	no	—
832	C₂²×C₅₃	—	8	4	no	—
833	C₂²×C₅₃	—	8	4	no	—
834	C₂²×C₅₃	—	16	2	no	—
835	C₂²×C₅₃	#577	1	2	yes	—
836	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
837	C₄×C₅₃	—	2	1	no	—
838	C₄×C₅₃	—	2	1	no	—
839	C₄×C₅₃	—	2	1	no	—
840	C₄×C₅₃	—	2	1	no	—
841	C₄×C₅₃	—	2	1	no	—
842	C₄×C₅₃	—	2	1	no	—
843	C₄×C₅₃	—	2	1	no	—
844	C₄×C₅₃	—	2	1	no	—
845	C₄×C₅₃	—	2	1	no	—
846	C₄×C₅₃	—	2	1	no	—
847	C₄×C₅₃	—	2	1	no	—
848	C₄×C₅₃	—	4	1	no	—
849	C₄×C₅₃	—	4	1	no	—
850	C₄×C₅₃	—	4	1	no	—
851	C₄×C₅₃	—	4	1	no	—
852	C₄×C₅₃	—	4	1	no	—
853	C₄×C₅₃	—	4	1	no	—
854	C₄×C₅₃	—	4	1	no	—
855	C₄×C₅₃	—	4	1	no	—
856	C₄×C₅₃	—	4	1	no	—
857	C₄×C₅₃	—	4	1	no	—
858	C₄×C₅₃	—	4	1	no	—
859	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
860	C₄×C₅₃	#585	1	1	yes	characteristic
861	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#3513	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#3345	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#3344	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#3335	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3307	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#3306	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#3296	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3280	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3181	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3179	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3173	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3119	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3105	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#2968	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#2952	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
891	C₂×#442	C₂×C₅₃	1	1	yes	characteristic, complemented
892	C₂×C₅₃	—	2	2	no	—
893	C₂×C₅₃	—	4	1	no	—
894	C₂×C₅₃	—	4	1	no	—
895	C₂×C₅₃	—	4	2	no	—
896	C₂×C₅₃	—	4	2	no	—
897	C₂×C₅₃	—	8	1	no	—
898	C₂×C₅₃	—	8	1	no	—
899	C₂×C₅₃	—	8	1	no	—
900	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
901	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
902	C₂×C₅₃	#3585	1	1	yes	characteristic
903	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
904	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
905	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
906	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#554	C₂²×C₅₃	1	1	yes	characteristic
909	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#553	—	2	1	no	—
912	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
913	#552	—	2	1	no	—
914	#552	C₂²×C₅₃	1	1	yes	characteristic
915	#551	—	2	1	no	—
916	#551	—	2	1	no	—
917	#551	—	2	1	no	—
918	#551	—	2	1	no	—
919	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#548	—	2	1	no	—
921	#547	C₂²×C₅₃	1	1	yes	characteristic
922	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#546	—	2	1	no	—
925	#546	C₂²×C₅₃	1	1	yes	characteristic
926	#546	C₂²×C₅₃	1	1	yes	characteristic
927	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	D₄²	C₂²×C₅₃	1	1	yes	characteristic
930	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#540	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#539	—	2	1	no	—
935	#539	—	2	1	no	—
936	#539	—	2	1	no	—
937	#538	—	2	1	no	—
938	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#529	C₂²×C₅₃	1	1	yes	characteristic
940	#529	C₂²×C₅₃	1	1	yes	characteristic
941	#525	—	2	1	no	—
942	#525	—	2	1	no	—
943	C₂×#123	—	2	1	no	—
944	C₂×C₂²⋊Q₈	—	2	1	no	—
945	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
950	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#496	C₂²×C₅₃	1	1	yes	characteristic
956	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#481	C₂²×C₅₃	1	1	yes	characteristic
971	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#469	C₂²×C₅₃	1	1	yes	characteristic
989	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#465	C₂²×C₅₃	1	1	yes	characteristic
995	#465	C₂²×C₅₃	1	1	yes	characteristic
996	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#463	C₂²×C₅₃	1	1	yes	characteristic
1002	#463	C₂²×C₅₃	1	1	yes	characteristic
1003	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#459	C₂²×C₅₃	1	1	yes	characteristic
1011	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#450	C₂²×C₅₃	1	1	yes	characteristic
1014	#450	C₂²×C₅₃	1	1	yes	characteristic
1015	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#449	C₂²×C₅₃	1	1	yes	characteristic
1018	#449	C₂²×C₅₃	1	1	yes	characteristic
1019	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#447	C₂²×C₅₃	1	1	yes	characteristic
1022	#447	C₂²×C₅₃	1	1	yes	characteristic
1023	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#442	C₂²×C₅₃	1	1	yes	characteristic
1026	#442	C₂²×C₅₃	1	1	yes	characteristic
1027	#442	C₂²×C₅₃	1	1	yes	characteristic
1028	#442	C₂²×C₅₃	1	1	yes	characteristic
1029	#442	C₂²×C₅₃	1	1	yes	characteristic
1030	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1051	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#435	C₂²×C₅₃	1	1	yes	characteristic
1054	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1058	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1069	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	C₅₃	#61522	1	1	yes	characteristic, direct product factor, Sylow
1075	C₂×#41	—	2	1	no	—
1076	C₂×#41	—	2	1	no	—
1077	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂²×Q₈	—	2	1	no	—
1081	C₂²×D₄	—	2	1	no	—
1082	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂³×C₄	—	2	1	no	—
1086	C₂³×C₄	—	2	1	no	—
1087	AGL(1,ℤ/8)	—	2	4	no	—
1088	#135	—	2	4	no	—
1089	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×D₈	—	2	4	no	—
1100	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1112	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1113	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1114	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1115	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1116	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1117	#127	C₂³×C₅₃	1	1	yes	characteristic
1118	#126	—	2	1	no	—
1119	#126	—	2	1	no	—
1120	#126	—	2	1	no	—
1121	#126	—	2	1	no	—
1122	#126	—	2	1	no	—
1123	#126	—	2	1	no	—
1124	#126	—	2	1	no	—
1125	#126	—	2	1	no	—
1126	#126	D₄×C₅₃	1	1	yes	characteristic
1127	#126	D₄×C₅₃	1	1	yes	characteristic
1128	#125	—	2	1	no	—
1129	#125	—	2	1	no	—
1130	#125	—	2	1	no	—
1131	#125	—	2	1	no	—
1132	#125	D₄×C₅₃	1	1	yes	characteristic
1133	#125	C₂³×C₅₃	1	1	yes	characteristic
1134	#125	C₂³×C₅₃	1	1	yes	characteristic
1135	#124	—	2	1	no	—
1136	#124	—	2	1	no	—
1137	#124	—	2	1	no	—
1138	#124	—	2	1	no	—
1139	#124	D₄×C₅₃	1	1	yes	characteristic
1140	#124	C₂³×C₅₃	1	1	yes	characteristic
1141	#124	C₂³×C₅₃	1	1	yes	characteristic
1142	#124	C₂³×C₅₃	1	1	yes	characteristic
1143	#124	C₂³×C₅₃	1	1	yes	characteristic
1144	#123	—	2	1	no	—
1145	#123	—	2	1	no	—
1146	#123	—	2	1	no	—
1147	#123	—	2	1	no	—
1148	#123	—	2	1	no	—
1149	#123	—	2	1	no	—
1150	#123	—	2	1	no	—
1151	#123	—	2	1	no	—
1152	#123	—	2	1	no	—
1153	#123	—	2	1	no	—
1154	#123	—	2	1	no	—
1155	#123	—	2	1	no	—
1156	#123	—	2	1	no	—
1157	#123	—	2	1	no	—
1158	#123	—	2	1	no	—
1159	#123	—	2	1	no	—
1160	#123	—	2	1	no	—
1161	#123	—	2	1	no	—
1162	#123	—	2	1	no	—
1163	#123	—	2	1	no	—
1164	#123	D₄×C₅₃	1	1	yes	characteristic
1165	#123	D₄×C₅₃	1	1	yes	characteristic
1166	C₂²⋊Q₈	—	2	1	no	—
1167	C₂²⋊Q₈	—	2	1	no	—
1168	C₂²⋊Q₈	—	2	1	no	—
1169	C₂²⋊Q₈	—	2	1	no	—
1170	C₂²⋊Q₈	—	2	1	no	—
1171	C₂²⋊Q₈	—	2	1	no	—
1172	C₂²⋊Q₈	—	2	1	no	—
1173	C₂²⋊Q₈	—	2	1	no	—
1174	C₂²⋊Q₈	—	2	1	no	—
1175	C₂²⋊Q₈	—	2	1	no	—
1176	C₂²⋊Q₈	—	2	1	no	—
1177	C₂²⋊Q₈	—	2	1	no	—
1178	C₂²⋊Q₈	—	2	1	no	—
1179	C₂²⋊Q₈	—	2	1	no	—
1180	C₂²⋊Q₈	—	2	1	no	—
1181	C₂²⋊Q₈	—	2	1	no	—
1182	C₂²⋊Q₈	—	2	1	no	—
1183	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1184	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1188	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1189	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1190	#121	—	2	1	no	—
1191	#121	—	2	1	no	—
1192	#121	—	2	1	no	—
1193	#121	—	2	1	no	—
1194	#121	—	2	1	no	—
1195	#121	—	2	1	no	—
1196	#121	—	2	1	no	—
1197	#121	—	2	1	no	—
1198	#121	—	2	1	no	—
1199	#121	D₄×C₅₃	1	1	yes	characteristic
1200	#121	C₂³×C₅₃	1	1	yes	characteristic
1201	#121	C₂³×C₅₃	1	1	yes	characteristic
1202	#121	C₂³×C₅₃	1	1	yes	characteristic
1203	#121	C₂³×C₅₃	1	1	yes	characteristic
1204	#121	C₂³×C₅₃	1	1	yes	characteristic
1205	#121	C₂³×C₅₃	1	1	yes	characteristic
1206	#120	—	2	1	no	—
1207	#120	—	2	1	no	—
1208	#120	—	2	1	no	—
1209	#120	—	2	1	no	—
1210	#120	—	2	1	no	—
1211	#120	—	2	1	no	—
1212	C₄×Q₈	—	2	1	no	—
1213	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1214	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1215	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1216	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1217	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1218	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1219	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1220	C₄×D₄	—	2	1	no	—
1221	C₄×D₄	—	2	1	no	—
1222	C₄×D₄	—	2	1	no	—
1223	C₄×D₄	—	2	1	no	—
1224	C₄×D₄	—	2	1	no	—
1225	C₄×D₄	—	2	1	no	—
1226	C₄×D₄	—	2	1	no	—
1227	C₄×D₄	—	2	1	no	—
1228	C₄×D₄	—	2	1	no	—
1229	C₄×D₄	—	2	1	no	—
1230	C₄×D₄	—	2	1	no	—
1231	C₄×D₄	—	2	1	no	—
1232	C₄×D₄	—	2	1	no	—
1233	C₄×D₄	—	2	1	no	—
1234	C₄×D₄	—	2	1	no	—
1235	C₄×D₄	—	2	1	no	—
1236	C₄×D₄	—	2	1	no	—
1237	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1240	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1243	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1244	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1245	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1246	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1247	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1248	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1249	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1250	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1251	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1252	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1253	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1254	#117	—	2	1	no	—
1255	#117	—	2	1	no	—
1256	#117	—	2	1	no	—
1257	#117	—	2	1	no	—
1258	#117	—	2	1	no	—
1259	#117	—	2	1	no	—
1260	#117	—	2	1	no	—
1261	#117	C₂³×C₅₃	1	1	yes	characteristic
1262	#117	C₂³×C₅₃	1	1	yes	characteristic
1263	#117	C₂³×C₅₃	1	1	yes	characteristic
1264	C₂×C₄⋊C₄	—	2	1	no	—
1265	C₂×C₄⋊C₄	—	2	1	no	—
1266	C₂×C₄⋊C₄	—	2	1	no	—
1267	C₂×C₄⋊C₄	—	2	1	no	—
1268	C₂×C₄⋊C₄	—	2	1	no	—
1269	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1271	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1272	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1273	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1274	C₂×C₂²⋊C₄	—	2	1	no	—
1275	C₂×C₂²⋊C₄	—	2	1	no	—
1276	C₂×C₂²⋊C₄	—	2	1	no	—
1277	C₂×C₂²⋊C₄	—	2	1	no	—
1278	C₂×C₂²⋊C₄	—	2	1	no	—
1279	C₂×C₂²⋊C₄	—	2	1	no	—
1280	C₂×C₂²⋊C₄	—	2	1	no	—
1281	C₂×C₂²⋊C₄	—	2	1	no	—
1282	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1283	#107	C₂³×C₅₃	1	1	yes	characteristic
1284	#107	C₂³×C₅₃	1	1	yes	characteristic
1285	#107	C₂³×C₅₃	1	1	yes	characteristic
1286	#107	C₂³×C₅₃	1	1	yes	characteristic
1287	#106	C₂³×C₅₃	1	1	yes	characteristic
1288	#106	C₂³×C₅₃	1	1	yes	characteristic
1289	#106	C₂³×C₅₃	1	1	yes	characteristic
1290	#106	C₂³×C₅₃	1	1	yes	characteristic
1291	#106	C₂³×C₅₃	1	1	yes	characteristic
1292	#106	C₂³×C₅₃	1	1	yes	characteristic
1293	#106	C₂³×C₅₃	1	1	yes	characteristic
1294	#106	C₂³×C₅₃	1	1	yes	characteristic
1295	#106	C₂³×C₅₃	1	1	yes	characteristic
1296	#106	C₂³×C₅₃	1	1	yes	characteristic
1297	#106	C₂³×C₅₃	1	1	yes	characteristic
1298	#106	C₂³×C₅₃	1	1	yes	characteristic
1299	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1300	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1301	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1302	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1303	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1304	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1305	#103	C₂³×C₅₃	1	1	yes	characteristic
1306	#103	C₂³×C₅₃	1	1	yes	characteristic
1307	#103	C₂³×C₅₃	1	1	yes	characteristic
1308	#103	C₂³×C₅₃	1	1	yes	characteristic
1309	#103	C₂³×C₅₃	1	1	yes	characteristic
1310	#103	C₂³×C₅₃	1	1	yes	characteristic
1311	#103	C₂³×C₅₃	1	1	yes	characteristic
1312	#103	C₂³×C₅₃	1	1	yes	characteristic
1313	#103	C₂³×C₅₃	1	1	yes	characteristic
1314	#103	C₂³×C₅₃	1	1	yes	characteristic
1315	#103	C₂³×C₅₃	1	1	yes	characteristic
1316	#103	C₂³×C₅₃	1	1	yes	characteristic
1317	#102	C₂³×C₅₃	1	1	yes	characteristic
1318	#102	C₂³×C₅₃	1	1	yes	characteristic
1319	#102	C₂³×C₅₃	1	1	yes	characteristic
1320	#102	C₂³×C₅₃	1	1	yes	characteristic
1321	#102	C₂³×C₅₃	1	1	yes	characteristic
1322	#102	C₂³×C₅₃	1	1	yes	characteristic
1323	#102	C₂³×C₅₃	1	1	yes	characteristic
1324	#102	C₂³×C₅₃	1	1	yes	characteristic
1325	#102	C₂³×C₅₃	1	1	yes	characteristic
1326	#102	C₂³×C₅₃	1	1	yes	characteristic
1327	#102	C₂³×C₅₃	1	1	yes	characteristic
1328	#102	C₂³×C₅₃	1	1	yes	characteristic
1329	#102	C₂³×C₅₃	1	1	yes	characteristic
1330	#102	C₂³×C₅₃	1	1	yes	characteristic
1331	#102	C₂³×C₅₃	1	1	yes	characteristic
1332	#102	C₂³×C₅₃	1	1	yes	characteristic
1333	#102	C₂³×C₅₃	1	1	yes	characteristic
1334	#102	C₂³×C₅₃	1	1	yes	characteristic
1335	#102	C₂³×C₅₃	1	1	yes	characteristic
1336	#102	C₂³×C₅₃	1	1	yes	characteristic
1337	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1338	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1339	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1340	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1341	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1342	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1343	#97	C₂³×C₅₃	1	1	yes	characteristic
1344	#97	C₂³×C₅₃	1	1	yes	characteristic
1345	#97	C₂³×C₅₃	1	1	yes	characteristic
1346	#97	C₂³×C₅₃	1	1	yes	characteristic
1347	#97	C₂³×C₅₃	1	1	yes	characteristic
1348	#97	C₂³×C₅₃	1	1	yes	characteristic
1349	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1350	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1351	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1352	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1353	C₂⁴	—	2	1	no	—
1354	C₂⁴	—	2	1	no	—
1355	C₂⁴	—	2	1	no	—
1356	#41	—	2	2	no	—
1357	#41	—	2	2	no	—
1358	#41	—	2	2	no	—
1359	#41	—	4	1	no	—
1360	#41	—	4	1	no	—
1361	#41	—	4	1	no	—
1362	#41	—	8	2	no	—
1363	#41	—	8	2	no	—
1364	C₂×Q₈	—	2	1	no	—
1365	C₂×Q₈	—	2	1	no	—
1366	C₂×Q₈	—	2	1	no	—
1367	C₂×Q₈	—	2	1	no	—
1368	C₂×Q₈	—	8	2	no	—
1369	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1370	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1371	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1372	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1373	C₂×D₄	—	2	2	no	—
1374	C₂×D₄	—	2	2	no	—
1375	C₂×D₄	—	2	2	no	—
1376	C₂×D₄	—	2	1	no	—
1377	C₂×D₄	—	2	1	no	—
1378	C₂×D₄	—	2	1	no	—
1379	C₂×D₄	—	2	1	no	—
1380	C₂×D₄	—	2	1	no	—
1381	C₂×D₄	—	2	1	no	—
1382	C₂×D₄	—	2	1	no	—
1383	C₂×D₄	—	2	1	no	—
1384	C₂×D₄	—	2	1	no	—
1385	C₂×D₄	—	2	1	no	—
1386	C₂×D₄	—	2	1	no	—
1387	C₂×D₄	—	2	1	no	—
1388	C₂×D₄	—	2	1	no	—
1389	C₂×D₄	—	2	1	no	—
1390	C₂×D₄	—	4	1	no	—
1391	C₂×D₄	—	4	1	no	—
1392	C₂×D₄	—	4	1	no	—
1393	C₂×D₄	—	8	2	no	—
1394	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1395	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1396	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1397	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1398	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1399	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1400	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1401	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1402	C₂²×C₄	—	2	1	no	—
1403	C₂²×C₄	—	2	1	no	—
1404	C₂²×C₄	—	2	1	no	—
1405	C₂²×C₄	—	2	1	no	—
1406	C₂²×C₄	—	2	1	no	—
1407	C₂²×C₄	—	2	1	no	—
1408	C₂²×C₄	—	2	1	no	—
1409	C₂²×C₄	—	2	1	no	—
1410	C₂²×C₄	—	2	1	no	—
1411	C₂²×C₄	—	2	1	no	—
1412	C₂²×C₄	—	2	1	no	—
1413	C₂²×C₄	—	2	1	no	—
1414	C₂²×C₄	—	2	1	no	—
1415	C₂²×C₄	—	2	1	no	—
1416	C₂²×C₄	—	2	1	no	—
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	2	1	no	—
1420	C₂²×C₄	—	2	1	no	—
1421	C₂²×C₄	—	2	1	no	—
1422	C₂²×C₄	—	2	1	no	—
1423	C₂²×C₄	—	2	1	no	—
1424	C₂²×C₄	—	8	2	no	—
1425	C₂²×C₄	—	8	2	no	—
1426	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1427	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1428	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1429	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1430	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1431	Q₁₆	—	2	2	no	—
1432	Q₁₆	—	4	1	no	—
1433	SD₁₆	—	2	2	no	—
1434	SD₁₆	—	2	2	no	—
1435	SD₁₆	—	2	2	no	—
1436	SD₁₆	—	2	2	no	—
1437	SD₁₆	—	4	1	no	—
1438	SD₁₆	—	4	1	no	—
1439	SD₁₆	—	4	1	no	—
1440	SD₁₆	—	4	1	no	—
1441	D₈	—	2	2	no	—
1442	D₈	—	2	2	no	—
1443	D₈	—	2	2	no	—
1444	D₈	—	2	2	no	—
1445	D₈	—	4	1	no	—
1446	D₈	#41×C₅₃	1	4	yes	complemented
1447	M₁₆	—	2	2	no	—
1448	M₁₆	—	4	1	no	—
1449	C₂×C₈	—	2	2	no	—
1450	C₂×C₈	—	2	2	no	—
1451	C₂×C₈	—	4	1	no	—
1452	C₂×C₈	—	4	1	no	—
1453	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1454	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1455	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1456	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1457	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1458	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1459	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1460	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1461	C₄⋊C₄	—	2	1	no	—
1462	C₄⋊C₄	—	2	1	no	—
1463	C₄⋊C₄	—	2	1	no	—
1464	C₄⋊C₄	—	2	1	no	—
1465	C₄⋊C₄	—	2	1	no	—
1466	C₄⋊C₄	—	2	1	no	—
1467	C₄⋊C₄	—	2	1	no	—
1468	C₄⋊C₄	—	2	1	no	—
1469	C₄⋊C₄	—	2	1	no	—
1470	C₄⋊C₄	—	2	1	no	—
1471	C₄⋊C₄	—	2	1	no	—
1472	C₄⋊C₄	—	2	1	no	—
1473	C₄⋊C₄	—	2	1	no	—
1474	C₄⋊C₄	—	2	1	no	—
1475	C₄⋊C₄	—	2	1	no	—
1476	C₄⋊C₄	—	2	1	no	—
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1489	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1490	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1491	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1492	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1493	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1494	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1495	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1496	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1497	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1498	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1499	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1500	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1501	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1502	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1503	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1504	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1505	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1506	C₂²⋊C₄	—	2	1	no	—
1507	C₂²⋊C₄	—	2	1	no	—
1508	C₂²⋊C₄	—	2	1	no	—
1509	C₂²⋊C₄	—	2	1	no	—
1510	C₂²⋊C₄	—	2	1	no	—
1511	C₂²⋊C₄	—	2	1	no	—
1512	C₂²⋊C₄	—	2	1	no	—
1513	C₂²⋊C₄	—	2	1	no	—
1514	C₂²⋊C₄	—	2	1	no	—
1515	C₂²⋊C₄	—	2	1	no	—
1516	C₂²⋊C₄	—	2	1	no	—
1517	C₂²⋊C₄	—	2	1	no	—
1518	C₂²⋊C₄	—	2	1	no	—
1519	C₂²⋊C₄	—	2	1	no	—
1520	C₂²⋊C₄	—	2	1	no	—
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1542	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1543	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1544	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1545	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1546	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1547	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1548	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1549	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1550	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1551	C₄²	—	2	1	no	—
1552	C₄²	—	2	1	no	—
1553	C₄²	—	2	1	no	—
1554	C₄²	—	2	1	no	—
1555	C₄²	—	2	1	no	—
1556	C₄²	—	2	1	no	—
1557	C₄²	—	2	1	no	—
1558	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1559	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1560	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1561	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1562	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1563	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1564	C₂³	—	2	1	no	—
1565	C₂³	—	2	1	no	—
1566	C₂³	—	2	1	no	—
1567	C₂³	—	2	1	no	—
1568	C₂³	—	2	1	no	—
1569	C₂³	—	4	2	no	—
1570	C₂³	—	4	2	no	—
1571	C₂³	—	4	2	no	—
1572	C₂³	—	4	2	no	—
1573	C₂³	—	4	2	no	—
1574	C₂³	—	8	1	no	—
1575	C₂³	—	8	1	no	—
1576	C₂³	—	8	1	no	—
1577	C₂³	—	8	1	no	—
1578	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1579	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1580	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1581	Q₈	—	2	1	no	—
1582	Q₈	—	2	1	no	—
1583	Q₈	—	2	1	no	—
1584	Q₈	—	2	1	no	—
1585	Q₈	—	2	1	no	—
1586	Q₈	—	2	1	no	—
1587	Q₈	—	4	1	no	—
1588	Q₈	—	4	2	no	—
1589	Q₈	—	8	1	no	—
1590	Q₈	—	8	1	no	—
1591	Q₈	—	8	1	no	—
1592	D₄	—	2	2	no	—
1593	D₄	—	2	2	no	—
1594	D₄	—	2	1	no	—
1595	D₄	—	2	1	no	—
1596	D₄	—	2	1	no	—
1597	D₄	—	2	1	no	—
1598	D₄	—	2	1	no	—
1599	D₄	—	2	1	no	—
1600	D₄	—	2	1	no	—
1601	D₄	—	2	1	no	—
1602	D₄	—	4	1	no	—
1603	D₄	—	4	2	no	—
1604	D₄	—	4	2	no	—
1605	D₄	—	4	2	no	—
1606	D₄	—	4	2	no	—
1607	D₄	—	4	2	no	—
1608	D₄	—	4	2	no	—
1609	D₄	—	4	2	no	—
1610	D₄	—	8	1	no	—
1611	D₄	—	8	1	no	—
1612	D₄	—	8	1	no	—
1613	D₄	—	8	1	no	—
1614	D₄	—	8	1	no	—
1615	D₄	—	8	1	no	—
1616	D₄	—	8	1	no	—
1617	D₄	C₂×#41×C₅₃	1	2	yes	—
1618	D₄	C₂×#41×C₅₃	1	2	yes	—
1619	C₂×C₄	—	2	2	no	—
1620	C₂×C₄	—	2	1	no	—
1621	C₂×C₄	—	2	1	no	—
1622	C₂×C₄	—	2	1	no	—
1623	C₂×C₄	—	2	1	no	—
1624	C₂×C₄	—	2	1	no	—
1625	C₂×C₄	—	2	1	no	—
1626	C₂×C₄	—	2	1	no	—
1627	C₂×C₄	—	2	1	no	—
1628	C₂×C₄	—	2	1	no	—
1629	C₂×C₄	—	2	1	no	—
1630	C₂×C₄	—	2	1	no	—
1631	C₂×C₄	—	2	1	no	—
1632	C₂×C₄	—	2	1	no	—
1633	C₂×C₄	—	2	1	no	—
1634	C₂×C₄	—	2	1	no	—
1635	C₂×C₄	—	2	1	no	—
1636	C₂×C₄	—	2	1	no	—
1637	C₂×C₄	—	4	1	no	—
1638	C₂×C₄	—	4	2	no	—
1639	C₂×C₄	—	4	2	no	—
1640	C₂×C₄	—	4	2	no	—
1641	C₂×C₄	—	4	2	no	—
1642	C₂×C₄	—	4	2	no	—
1643	C₂×C₄	—	4	2	no	—
1644	C₂×C₄	—	8	1	no	—
1645	C₂×C₄	—	8	1	no	—
1646	C₂×C₄	—	8	1	no	—
1647	C₂×C₄	—	8	1	no	—
1648	C₂×C₄	—	8	1	no	—
1649	C₂×C₄	—	8	1	no	—
1650	C₂×C₄	—	8	1	no	—
1651	C₂×C₄	—	8	1	no	—
1652	C₂×C₄	—	8	1	no	—
1653	C₂×C₄	—	8	1	no	—
1654	C₂×C₄	—	8	1	no	—
1655	C₂×C₄	—	8	1	no	—
1656	C₂×C₄	—	8	1	no	—
1657	C₂×C₄	—	8	1	no	—
1658	C₂×C₄	—	8	1	no	—
1659	C₂×C₄	—	8	1	no	—
1660	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1661	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1662	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1663	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1664	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1665	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1666	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1667	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1668	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1669	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1670	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1671	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1672	C₈	—	2	1	no	—
1673	C₈	—	2	1	no	—
1674	C₈	—	2	1	no	—
1675	C₈	—	2	1	no	—
1676	C₈	—	2	1	no	—
1677	C₈	—	2	1	no	—
1678	C₈	—	2	1	no	—
1679	C₈	C₂×#41×C₅₃	1	2	yes	—
1680	C₂²	—	2	1	no	—
1681	C₂²	—	2	1	no	—
1682	C₂²	—	2	1	no	—
1683	C₂²	—	2	1	no	—
1684	C₂²	—	2	2	no	—
1685	C₂²	—	2	2	no	—
1686	C₂²	—	2	1	no	—
1687	C₂²	—	2	1	no	—
1688	C₂²	—	2	1	no	—
1689	C₂²	—	2	1	no	—
1690	C₂²	—	4	1	no	—
1691	C₂²	—	4	1	no	—
1692	C₂²	—	4	1	no	—
1693	C₂²	—	4	1	no	—
1694	C₂²	—	4	1	no	—
1695	C₂²	—	4	1	no	—
1696	C₂²	—	4	1	no	—
1697	C₂²	—	4	1	no	—
1698	C₂²	—	4	1	no	—
1699	C₂²	—	4	1	no	—
1700	C₂²	—	4	1	no	—
1701	C₂²	—	4	1	no	—
1702	C₂²	—	4	1	no	—
1703	C₂²	—	8	4	no	—
1704	C₂²	—	8	4	no	—
1705	C₂²	—	16	2	no	—
1706	C₂²	C₅₃×#577	1	2	yes	—
1707	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1708	C₄	—	2	1	no	—
1709	C₄	—	2	1	no	—
1710	C₄	—	2	1	no	—
1711	C₄	—	2	1	no	—
1712	C₄	—	2	1	no	—
1713	C₄	—	2	1	no	—
1714	C₄	—	2	1	no	—
1715	C₄	—	2	1	no	—
1716	C₄	—	2	1	no	—
1717	C₄	—	2	1	no	—
1718	C₄	—	2	1	no	—
1719	C₄	—	4	1	no	—
1720	C₄	—	4	1	no	—
1721	C₄	—	4	1	no	—
1722	C₄	—	4	1	no	—
1723	C₄	—	4	1	no	—
1724	C₄	—	4	1	no	—
1725	C₄	—	4	1	no	—
1726	C₄	—	4	1	no	—
1727	C₄	—	4	1	no	—
1728	C₄	—	4	1	no	—
1729	C₄	—	4	1	no	—
1730	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1731	C₄	C₅₃×#585	1	1	yes	characteristic
1732	C₂	—	2	2	no	—
1733	C₂	—	4	1	no	—
1734	C₂	—	4	1	no	—
1735	C₂	—	4	2	no	—
1736	C₂	—	4	2	no	—
1737	C₂	—	8	1	no	—
1738	C₂	—	8	1	no	—
1739	C₂	—	8	1	no	—
1740	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1741	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1742	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×#3520	C₂	semidirect
2. C₅₃×#3513	C₂	semidirect
3. C₅₃×#3401	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3376	C₂	semidirect
6. C₅₃×#3373	C₂	semidirect
7. C₅₃×#3345	C₂	semidirect
8. C₅₃×#3344	C₂	semidirect
9. C₅₃×#3335	C₂	semidirect
10. C₅₃×#3314	C₂	semidirect
11. C₅₃×#3307	C₂	semidirect
12. C₅₃×#3306	C₂	semidirect
13. C₅₃×#3306	C₂	semidirect
14. C₅₃×#3296	C₂	semidirect
15. C₅₃×#3295	C₂	semidirect
16. C₅₃×#3280	C₂	semidirect
17. C₅₃×#3267	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3181	C₂	semidirect
20. C₅₃×#3179	C₂	semidirect
21. C₅₃×#3173	C₂	semidirect
22. C₅₃×#3125	C₂	semidirect
23. C₅₃×#3125	C₂	semidirect
24. C₅₃×#3119	C₂	semidirect
25. C₅₃×#3118	C₂	semidirect
26. C₅₃×#3105	C₂	semidirect
27. C₅₃×#3101	C₂	semidirect
28. C₅₃×#2968	C₂	semidirect
29. C₅₃×#2952	C₂	semidirect
30. C₅₃×#2946	C₂	semidirect
31. C₂×C₅₃×#442	C₂	semidirect
35. C₅₃×#559	C₂²	semidirect
36. C₅₃×#556	C₂²	semidirect
38. C₅₃×#554	C₂²	semidirect
39. C₅₃×#554	C₂²	semidirect
41. C₅₃×#553	C₂²	semidirect
48. D₄×Q₈×C₅₃	C₂²	semidirect
51. C₅₃×#547	C₂²	semidirect
52. C₅₃×#547	C₂²	semidirect
56. C₅₃×#546	C₂²	semidirect
57. C₅₃×#546	C₂²	semidirect
59. C₅₃×#542	C₂²	semidirect
60. C₅₃×#542	C₂²	semidirect
61. C₅₃×#542	C₂²	semidirect
62. C₅₃×#540	C₂²	semidirect
67. C₅₃×#533	C₂²	semidirect
74. C₅₃×#520	C₂²	semidirect
75. C₅₃×#520	C₂²	semidirect
76. C₅₃×#520	C₂²	semidirect
77. C₅₃×#518	C₂²	semidirect
79. C₂×C₄×D₄×C₅₃	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#501	C₂²	semidirect
82. C₅₃×#498	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
85. C₅₃×#495	C₂²	semidirect
86. C₅₃×#491	C₂²	semidirect
87. C₅₃×#489	C₂²	semidirect
88. C₅₃×#489	C₂²	semidirect
89. C₅₃×#489	C₂²	semidirect
90. C₅₃×#488	C₂²	semidirect
91. C₅₃×#486	C₂²	semidirect
92. C₅₃×#485	C₂²	semidirect
93. C₅₃×#484	C₂²	semidirect
94. C₅₃×#483	C₂²	semidirect
95. C₅₃×#483	C₂²	semidirect
96. C₅₃×#483	C₂²	semidirect
97. C₅₃×#483	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
100. C₅₃×#481	C₂²	semidirect
101. C₅₃×#481	C₂²	semidirect
102. C₅₃×#481	C₂²	semidirect
103. C₅₃×#480	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#476	C₂²	semidirect
109. C₅₃×#476	C₂²	semidirect
110. C₅₃×#476	C₂²	semidirect
111. C₅₃×#476	C₂²	semidirect
112. C₅₃×#476	C₂²	semidirect
113. C₅₃×#475	C₂²	semidirect
114. C₅₃×#475	C₂²	semidirect
115. C₅₃×#474	C₂²	semidirect
116. C₅₃×#470	C₂²	semidirect
118. C₅₃×#469	C₂²	semidirect
119. C₅₃×#468	C₂²	semidirect
120. C₅₃×#467	C₂²	semidirect
121. C₅₃×#467	C₂²	semidirect
122. C₅₃×#466	C₂²	semidirect
125. C₅₃×#465	C₂²	semidirect
126. C₅₃×#465	C₂²	semidirect
127. C₅₃×#465	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#463	C₂²	semidirect
135. C₅₃×#463	C₂²	semidirect
136. C₅₃×#461	C₂²	semidirect
137. C₅₃×#461	C₂²	semidirect
138. C₅₃×#460	C₂²	semidirect
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
144. C₅₃×#450	C₂²	semidirect
145. C₅₃×#450	C₂²	semidirect
148. C₅₃×#449	C₂²	semidirect
149. C₅₃×#449	C₂²	semidirect
152. C₅₃×#446	C₂²	semidirect
153. C₅₃×#446	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×#441	C₂²	semidirect
165. C₅₃×#441	C₂²	semidirect
166. C₅₃×#441	C₂²	semidirect
167. C₅₃×#440	C₂²	semidirect
168. C₅₃×#440	C₂²	semidirect
169. C₅₃×#440	C₂²	semidirect
170. C₄×SD₁₆×C₅₃	C₂²	semidirect
171. C₄×SD₁₆×C₅₃	C₂²	semidirect
172. C₄×SD₁₆×C₅₃	C₂²	semidirect
173. C₄×SD₁₆×C₅₃	C₂²	semidirect
174. C₄×SD₁₆×C₅₃	C₂²	semidirect
175. C₄×SD₁₆×C₅₃	C₂²	semidirect
176. C₄×SD₁₆×C₅₃	C₂²	semidirect
177. C₄×SD₁₆×C₅₃	C₂²	semidirect
178. C₄×SD₁₆×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
181. C₄×D₈×C₅₃	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#435	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. C₂×#106×C₅₃	C₂²	semidirect
193. C₂×#106×C₅₃	C₂²	semidirect
194. C₅₃×#417	C₂²	semidirect
195. C₅₃×#417	C₂²	semidirect
196. C₅₃×#416	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
574. D₈×C₅₃	#41	semidirect
808. #61522	C₅₃	direct (N × H)
861. #3520	C₂×C₅₃	semidirect
862. #3513	C₂×C₅₃	semidirect
863. #3401	C₂×C₅₃	semidirect
864. #3384	C₂×C₅₃	semidirect
865. #3376	C₂×C₅₃	semidirect
866. #3373	C₂×C₅₃	semidirect
867. #3345	C₂×C₅₃	semidirect
868. #3344	C₂×C₅₃	semidirect
869. #3335	C₂×C₅₃	semidirect
870. #3314	C₂×C₅₃	semidirect
871. #3307	C₂×C₅₃	semidirect
872. #3306	C₂×C₅₃	semidirect
873. #3306	C₂×C₅₃	semidirect
874. #3296	C₂×C₅₃	semidirect
875. #3295	C₂×C₅₃	semidirect
876. #3280	C₂×C₅₃	semidirect
877. #3267	C₂×C₅₃	semidirect
878. #3264	C₂×C₅₃	semidirect
879. #3181	C₂×C₅₃	semidirect
880. #3179	C₂×C₅₃	semidirect
881. #3173	C₂×C₅₃	semidirect
882. #3125	C₂×C₅₃	semidirect
883. #3125	C₂×C₅₃	semidirect
884. #3119	C₂×C₅₃	semidirect
885. #3118	C₂×C₅₃	semidirect
886. #3105	C₂×C₅₃	semidirect
887. #3101	C₂×C₅₃	semidirect
888. #2968	C₂×C₅₃	semidirect
889. #2952	C₂×C₅₃	semidirect
890. #2946	C₂×C₅₃	semidirect
891. C₂×#442	C₂×C₅₃	semidirect
906. #559	C₂²×C₅₃	semidirect
907. #556	C₂²×C₅₃	semidirect
909. #554	C₂²×C₅₃	semidirect
910. #554	C₂²×C₅₃	semidirect
912. #553	C₂²×C₅₃	semidirect
919. D₄×Q₈	C₂²×C₅₃	semidirect
922. #547	C₂²×C₅₃	semidirect
923. #547	C₂²×C₅₃	semidirect
927. #546	C₂²×C₅₃	semidirect
928. #546	C₂²×C₅₃	semidirect
930. #542	C₂²×C₅₃	semidirect
931. #542	C₂²×C₅₃	semidirect
932. #542	C₂²×C₅₃	semidirect
933. #540	C₂²×C₅₃	semidirect
938. #533	C₂²×C₅₃	semidirect
945. #520	C₂²×C₅₃	semidirect
946. #520	C₂²×C₅₃	semidirect
947. #520	C₂²×C₅₃	semidirect
948. #518	C₂²×C₅₃	semidirect
950. C₂×C₄×D₄	C₂²×C₅₃	semidirect
951. #501	C₂²×C₅₃	semidirect
952. #501	C₂²×C₅₃	semidirect
953. #498	C₂²×C₅₃	semidirect
954. #497	C₂²×C₅₃	semidirect
956. #495	C₂²×C₅₃	semidirect
957. #491	C₂²×C₅₃	semidirect
958. #489	C₂²×C₅₃	semidirect
959. #489	C₂²×C₅₃	semidirect
960. #489	C₂²×C₅₃	semidirect
961. #488	C₂²×C₅₃	semidirect
962. #486	C₂²×C₅₃	semidirect
963. #485	C₂²×C₅₃	semidirect
964. #484	C₂²×C₅₃	semidirect
965. #483	C₂²×C₅₃	semidirect
966. #483	C₂²×C₅₃	semidirect
967. #483	C₂²×C₅₃	semidirect
968. #483	C₂²×C₅₃	semidirect
969. #482	C₂²×C₅₃	semidirect
971. #481	C₂²×C₅₃	semidirect
972. #481	C₂²×C₅₃	semidirect
973. #481	C₂²×C₅₃	semidirect
974. #480	C₂²×C₅₃	semidirect
975. #479	C₂²×C₅₃	semidirect
976. #478	C₂²×C₅₃	semidirect
977. #478	C₂²×C₅₃	semidirect
978. #478	C₂²×C₅₃	semidirect
979. #476	C₂²×C₅₃	semidirect
980. #476	C₂²×C₅₃	semidirect
981. #476	C₂²×C₅₃	semidirect
982. #476	C₂²×C₅₃	semidirect
983. #476	C₂²×C₅₃	semidirect
984. #475	C₂²×C₅₃	semidirect
985. #475	C₂²×C₅₃	semidirect
986. #474	C₂²×C₅₃	semidirect
987. #470	C₂²×C₅₃	semidirect
989. #469	C₂²×C₅₃	semidirect
990. #468	C₂²×C₅₃	semidirect
991. #467	C₂²×C₅₃	semidirect
992. #467	C₂²×C₅₃	semidirect
993. #466	C₂²×C₅₃	semidirect
996. #465	C₂²×C₅₃	semidirect
997. #465	C₂²×C₅₃	semidirect
998. #465	C₂²×C₅₃	semidirect
999. #464	C₂²×C₅₃	semidirect
1000. #464	C₂²×C₅₃	semidirect
1003. #463	C₂²×C₅₃	semidirect
1004. #463	C₂²×C₅₃	semidirect
1005. #463	C₂²×C₅₃	semidirect
1006. #463	C₂²×C₅₃	semidirect
1007. #461	C₂²×C₅₃	semidirect
1008. #461	C₂²×C₅₃	semidirect
1009. #460	C₂²×C₅₃	semidirect
1011. #452	C₂²×C₅₃	semidirect
1012. #452	C₂²×C₅₃	semidirect
1015. #450	C₂²×C₅₃	semidirect
1016. #450	C₂²×C₅₃	semidirect
1019. #449	C₂²×C₅₃	semidirect
1020. #449	C₂²×C₅₃	semidirect
1023. #446	C₂²×C₅₃	semidirect
1024. #446	C₂²×C₅₃	semidirect
1030. #442	C₂²×C₅₃	semidirect
1031. #442	C₂²×C₅₃	semidirect
1032. #442	C₂²×C₅₃	semidirect
1033. #442	C₂²×C₅₃	semidirect
1034. #442	C₂²×C₅₃	semidirect
1035. #441	C₂²×C₅₃	semidirect
1036. #441	C₂²×C₅₃	semidirect
1037. #441	C₂²×C₅₃	semidirect
1038. #440	C₂²×C₅₃	semidirect
1039. #440	C₂²×C₅₃	semidirect
1040. #440	C₂²×C₅₃	semidirect
1041. C₄×SD₁₆	C₂²×C₅₃	semidirect
1042. C₄×SD₁₆	C₂²×C₅₃	semidirect
1043. C₄×SD₁₆	C₂²×C₅₃	semidirect
1044. C₄×SD₁₆	C₂²×C₅₃	semidirect
1045. C₄×SD₁₆	C₂²×C₅₃	semidirect
1046. C₄×SD₁₆	C₂²×C₅₃	semidirect
1047. C₄×SD₁₆	C₂²×C₅₃	semidirect
1048. C₄×SD₁₆	C₂²×C₅₃	semidirect
1049. C₄×SD₁₆	C₂²×C₅₃	semidirect
1051. C₄×D₈	C₂²×C₅₃	semidirect
1052. C₄×D₈	C₂²×C₅₃	semidirect
1054. #435	C₂²×C₅₃	semidirect
1055. #435	C₂²×C₅₃	semidirect
1056. #435	C₂²×C₅₃	semidirect
1058. C₈×D₄	C₂²×C₅₃	semidirect
1059. #433	C₂²×C₅₃	semidirect
1060. #433	C₂²×C₅₃	semidirect
1061. #431	C₂²×C₅₃	semidirect
1062. #428	C₂²×C₅₃	semidirect
1063. C₂×#106	C₂²×C₅₃	semidirect
1064. C₂×#106	C₂²×C₅₃	semidirect
1065. #417	C₂²×C₅₃	semidirect
1066. #417	C₂²×C₅₃	semidirect
1067. #416	C₂²×C₅₃	semidirect
1069. C₂×#102	C₂²×C₅₃	semidirect
1070. C₂×#102	C₂²×C₅₃	semidirect
1071. #405	C₂²×C₅₃	semidirect
1072. #405	C₂²×C₅₃	semidirect
1073. C₂×#97	C₂²×C₅₃	semidirect
1074. C₅₃	#61522	direct (N × H)
1446. 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×#3520	2
C₅₃×#3513	2
C₅₃×#3401	2
C₅₃×#3384	2
C₅₃×#3376	2
C₅₃×#3373	2
C₅₃×#3345	2
C₅₃×#3344	2
C₅₃×#3335	2
C₅₃×#3314	2
C₅₃×#3307	2
C₅₃×#3306	2
C₅₃×#3296	2
C₅₃×#3295	2
C₅₃×#3280	2
C₅₃×#3267	2
C₅₃×#3264	2
C₅₃×#3181	2
C₅₃×#3179	2
C₅₃×#3173	2
C₅₃×#3125	2
C₅₃×#3119	2
C₅₃×#3118	2
C₅₃×#3105	2
C₅₃×#3101	2
C₅₃×#2968	2
C₅₃×#2952	2
C₅₃×#2946	2
C₂×C₅₃×#442	2
#61522	53

Subgroups — C53×#61522 #27269034

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61522 #27269034