Subgroups — C₅₃×#62008 #27269520

Order 13568.

1838 conjugacy classes of subgroups.

The subgroup lattice has 1756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3552	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×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3312	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3308	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3307	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3300	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3260	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3225	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3221	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3218	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3120	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
35	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
36	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#563	—	2	1	no	—
39	C₅₃×#563	—	2	1	no	—
40	C₅₃×#559	C₂²	1	1	yes	characteristic
41	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#554	—	2	1	no	—
44	C₅₃×#554	C₂²	1	1	yes	characteristic
45	C₅₃×#553	—	2	1	no	—
46	C₅₃×#553	—	2	1	no	—
47	C₅₃×#553	C₂²	1	1	yes	characteristic
48	C₅₃×#552	C₂²	1	1	yes	characteristic
49	C₅₃×#551	—	2	1	no	—
50	C₅₃×#551	—	2	1	no	—
51	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
52	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#548	C₂²	1	1	yes	characteristic
55	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#547	C₂²	1	1	yes	characteristic
57	C₅₃×#547	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×#544	—	2	1	no	—
63	C₅₃×#542	—	2	1	no	—
64	C₅₃×#542	C₂²	1	1	yes	characteristic
65	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#540	C₂²	1	1	yes	characteristic
68	C₅₃×#539	—	2	1	no	—
69	C₅₃×#539	—	2	1	no	—
70	C₅₃×#539	—	2	1	no	—
71	C₅₃×#538	—	2	1	no	—
72	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
74	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#529	C₂²	1	1	yes	characteristic
76	C₅₃×#529	C₂²	1	1	yes	characteristic
77	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#525	—	2	1	no	—
79	C₂×#123×C₅₃	—	2	1	no	—
80	C₅₃×#520	C₂²	1	1	yes	characteristic
81	C₅₃×#518	C₂²	1	1	yes	characteristic
82	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
83	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#496	C₂²	1	1	yes	characteristic
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#492	C₂²	1	1	yes	characteristic
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#487	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×#483	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#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×#475	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#468	C₂²	1	1	yes	characteristic
113	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#466	C₂²	1	1	yes	characteristic
118	C₅₃×#465	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, complemented
124	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#463	C₂²	1	1	yes	characteristic
129	C₅₃×#463	C₂²	1	1	yes	characteristic
130	C₅₃×#463	C₂²	1	1	yes	characteristic
131	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#461	C₂²	1	1	yes	characteristic
139	C₅₃×#461	C₂²	1	1	yes	characteristic
140	C₅₃×#461	C₂²	1	1	yes	characteristic
141	C₅₃×#461	C₂²	1	1	yes	characteristic
142	C₅₃×#461	C₂²	1	1	yes	characteristic
143	C₅₃×#461	C₂²	1	1	yes	characteristic
144	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#460	C₂²	1	1	yes	characteristic
152	C₅₃×#460	C₂²	1	1	yes	characteristic
153	C₅₃×#452	C₂²	1	1	yes	characteristic
154	C₅₃×#452	C₂²	1	1	yes	characteristic
155	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#451	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×#450	C₂²	1	1	yes	characteristic
161	C₅₃×#450	C₂²	1	1	yes	characteristic
162	C₅₃×#449	C₂²	1	1	yes	characteristic
163	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#448	C₂²	1	1	yes	characteristic
166	C₅₃×#448	C₂²	1	1	yes	characteristic
167	C₅₃×#448	C₂²	1	1	yes	characteristic
168	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
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×#442	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	C₂²	1	1	yes	characteristic
177	C₅₃×#440	C₂²	1	1	yes	characteristic
178	C₅₃×#440	C₂²	1	1	yes	characteristic
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
183	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
189	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
190	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
200	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
201	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×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×D₄×C₅₃	—	2	1	no	—
212	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂³×C₄×C₅₃	—	2	1	no	—
215	#137×C₅₃	—	4	2	no	—
216	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
217	#135×C₅₃	—	4	2	no	—
218	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
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×SD₁₆×C₅₃	—	4	2	no	—
224	C₂×SD₁₆×C₅₃	—	4	2	no	—
225	C₂×SD₁₆×C₅₃	—	4	2	no	—
226	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×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×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×SD₁₆×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	—	2	1	no	—
254	C₄⋊Q₈×C₅₃	—	2	1	no	—
255	C₄⋊Q₈×C₅₃	—	2	1	no	—
256	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
259	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
260	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
261	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
262	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
263	#127×C₅₃	C₂³	1	1	yes	characteristic
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	#126×C₅₃	—	2	1	no	—
270	#126×C₅₃	—	2	1	no	—
271	#126×C₅₃	—	2	1	no	—
272	#126×C₅₃	—	2	1	no	—
273	#126×C₅₃	—	2	1	no	—
274	#126×C₅₃	—	2	1	no	—
275	#126×C₅₃	D₄	1	1	yes	characteristic
276	#126×C₅₃	D₄	1	1	yes	characteristic
277	#125×C₅₃	—	2	1	no	—
278	#125×C₅₃	—	2	1	no	—
279	#125×C₅₃	—	2	1	no	—
280	#125×C₅₃	—	2	1	no	—
281	#125×C₅₃	—	2	1	no	—
282	#125×C₅₃	—	2	1	no	—
283	#125×C₅₃	—	2	1	no	—
284	#125×C₅₃	—	2	1	no	—
285	#125×C₅₃	D₄	1	1	yes	characteristic
286	#125×C₅₃	C₂³	1	1	yes	characteristic
287	#125×C₅₃	C₂³	1	1	yes	characteristic
288	#125×C₅₃	C₂³	1	1	yes	characteristic
289	#124×C₅₃	—	2	1	no	—
290	#124×C₅₃	—	2	1	no	—
291	#124×C₅₃	—	2	1	no	—
292	#124×C₅₃	—	2	1	no	—
293	#124×C₅₃	D₄	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
295	#124×C₅₃	C₂³	1	1	yes	characteristic
296	#124×C₅₃	C₂³	1	1	yes	characteristic
297	#124×C₅₃	C₂³	1	1	yes	characteristic
298	#124×C₅₃	C₂³	1	1	yes	characteristic
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	—	2	1	no	—
311	#123×C₅₃	—	2	1	no	—
312	#123×C₅₃	—	2	1	no	—
313	#123×C₅₃	—	2	1	no	—
314	#123×C₅₃	—	2	1	no	—
315	#123×C₅₃	—	2	1	no	—
316	#123×C₅₃	—	2	1	no	—
317	#123×C₅₃	—	2	1	no	—
318	#123×C₅₃	D₄	1	1	yes	characteristic
319	#123×C₅₃	D₄	1	1	yes	characteristic
320	C₂²⋊Q₈×C₅₃	—	2	1	no	—
321	C₂²⋊Q₈×C₅₃	—	2	1	no	—
322	C₂²⋊Q₈×C₅₃	—	2	1	no	—
323	C₂²⋊Q₈×C₅₃	—	2	1	no	—
324	C₂²⋊Q₈×C₅₃	—	2	1	no	—
325	C₂²⋊Q₈×C₅₃	—	2	1	no	—
326	C₂²⋊Q₈×C₅₃	—	2	1	no	—
327	C₂²⋊Q₈×C₅₃	—	2	1	no	—
328	C₂²⋊Q₈×C₅₃	—	2	1	no	—
329	C₂²⋊Q₈×C₅₃	—	2	1	no	—
330	C₂²⋊Q₈×C₅₃	—	2	1	no	—
331	C₂²⋊Q₈×C₅₃	—	2	1	no	—
332	C₂²⋊Q₈×C₅₃	—	2	1	no	—
333	C₂²⋊Q₈×C₅₃	—	2	1	no	—
334	C₂²⋊Q₈×C₅₃	—	2	1	no	—
335	C₂²⋊Q₈×C₅₃	—	2	1	no	—
336	C₂²⋊Q₈×C₅₃	—	2	1	no	—
337	C₂²⋊Q₈×C₅₃	—	2	1	no	—
338	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
339	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
340	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
341	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
343	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
344	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
345	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
346	#121×C₅₃	—	2	1	no	—
347	#121×C₅₃	—	2	1	no	—
348	#121×C₅₃	—	2	1	no	—
349	#121×C₅₃	—	2	1	no	—
350	#121×C₅₃	—	2	1	no	—
351	#121×C₅₃	—	2	1	no	—
352	#121×C₅₃	—	2	1	no	—
353	#121×C₅₃	—	2	1	no	—
354	#121×C₅₃	—	2	1	no	—
355	#121×C₅₃	D₄	1	1	yes	characteristic
356	#121×C₅₃	C₂³	1	1	yes	characteristic
357	#121×C₅₃	C₂³	1	1	yes	characteristic
358	#121×C₅₃	C₂³	1	1	yes	characteristic
359	#121×C₅₃	C₂³	1	1	yes	characteristic
360	#121×C₅₃	C₂³	1	1	yes	characteristic
361	#120×C₅₃	—	2	1	no	—
362	#120×C₅₃	—	2	1	no	—
363	#120×C₅₃	—	2	1	no	—
364	#120×C₅₃	—	2	1	no	—
365	C₄×Q₈×C₅₃	—	2	1	no	—
366	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×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	—	2	1	no	—
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	—	2	1	no	—
387	C₄×D₄×C₅₃	—	2	1	no	—
388	C₄×D₄×C₅₃	—	2	1	no	—
389	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
390	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
391	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
392	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
393	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
394	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
395	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
396	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
397	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
398	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
399	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
400	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
401	#117×C₅₃	—	2	1	no	—
402	#117×C₅₃	—	2	1	no	—
403	#117×C₅₃	—	2	1	no	—
404	#117×C₅₃	—	2	1	no	—
405	#117×C₅₃	—	2	1	no	—
406	#117×C₅₃	C₂³	1	1	yes	characteristic
407	#117×C₅₃	C₂³	1	1	yes	characteristic
408	#117×C₅₃	C₂³	1	1	yes	characteristic
409	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
410	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
412	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
413	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
415	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
416	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
418	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#107×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#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	#103×C₅₃	C₂³	1	1	yes	characteristic
457	#103×C₅₃	C₂³	1	1	yes	characteristic
458	#103×C₅₃	C₂³	1	1	yes	characteristic
459	#103×C₅₃	C₂³	1	1	yes	characteristic
460	#103×C₅₃	C₂³	1	1	yes	characteristic
461	#103×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	—	4	1	no	—
488	#41×C₅₃	—	4	1	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	8	2	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	—	2	1	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	4	1	no	—
499	C₂×Q₈×C₅₃	—	4	1	no	—
500	C₂×Q₈×C₅₃	—	4	1	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×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
513	C₂×D₄×C₅₃	—	2	2	no	—
514	C₂×D₄×C₅₃	—	2	2	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	—	4	1	no	—
528	C₂×D₄×C₅₃	—	4	1	no	—
529	C₂×D₄×C₅₃	—	8	2	no	—
530	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
531	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂²×C₄×C₅₃	—	2	1	no	—
538	C₂²×C₄×C₅₃	—	2	1	no	—
539	C₂²×C₄×C₅₃	—	2	1	no	—
540	C₂²×C₄×C₅₃	—	2	1	no	—
541	C₂²×C₄×C₅₃	—	2	1	no	—
542	C₂²×C₄×C₅₃	—	2	1	no	—
543	C₂²×C₄×C₅₃	—	2	1	no	—
544	C₂²×C₄×C₅₃	—	2	1	no	—
545	C₂²×C₄×C₅₃	—	2	1	no	—
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	—	2	1	no	—
554	C₂²×C₄×C₅₃	—	2	1	no	—
555	C₂²×C₄×C₅₃	—	8	2	no	—
556	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
557	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
559	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
561	Q₁₆×C₅₃	—	4	1	no	—
562	Q₁₆×C₅₃	—	4	1	no	—
563	Q₁₆×C₅₃	—	4	1	no	—
564	Q₁₆×C₅₃	—	4	1	no	—
565	Q₁₆×C₅₃	—	4	1	no	—
566	SD₁₆×C₅₃	—	2	2	no	—
567	SD₁₆×C₅₃	—	2	2	no	—
568	SD₁₆×C₅₃	—	2	2	no	—
569	SD₁₆×C₅₃	—	2	2	no	—
570	SD₁₆×C₅₃	—	2	2	no	—
571	SD₁₆×C₅₃	—	4	1	no	—
572	SD₁₆×C₅₃	—	4	1	no	—
573	SD₁₆×C₅₃	—	4	1	no	—
574	SD₁₆×C₅₃	—	4	1	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	D₈×C₅₃	—	2	2	no	—
583	D₈×C₅₃	—	4	1	no	—
584	D₈×C₅₃	—	4	1	no	—
585	M₁₆×C₅₃	—	4	1	no	—
586	M₁₆×C₅₃	—	4	1	no	—
587	C₂×C₈×C₅₃	—	4	1	no	—
588	C₂×C₈×C₅₃	—	4	1	no	—
589	C₂×C₈×C₅₃	—	4	1	no	—
590	C₂×C₈×C₅₃	—	4	1	no	—
591	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
592	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
593	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
594	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
599	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	—	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	—	2	1	no	—
629	C₄⋊C₄×C₅₃	—	2	1	no	—
630	C₄⋊C₄×C₅₃	—	2	1	no	—
631	C₄⋊C₄×C₅₃	—	2	1	no	—
632	C₄⋊C₄×C₅₃	—	2	1	no	—
633	C₄⋊C₄×C₅₃	—	2	1	no	—
634	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
642	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
643	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
644	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
645	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
646	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
647	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
648	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
649	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
686	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
687	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
688	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
689	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
690	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
691	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
697	C₄²×C₅₃	—	2	1	no	—
698	C₄²×C₅₃	—	2	1	no	—
699	C₄²×C₅₃	—	2	1	no	—
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	—	4	2	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	C₂²×D₄	1	1	yes	characteristic
717	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
718	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
719	Q₈×C₅₃	—	2	1	no	—
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	—	2	1	no	—
730	Q₈×C₅₃	—	2	1	no	—
731	Q₈×C₅₃	—	4	1	no	—
732	Q₈×C₅₃	—	8	1	no	—
733	Q₈×C₅₃	—	8	1	no	—
734	Q₈×C₅₃	—	8	1	no	—
735	Q₈×C₅₃	—	8	1	no	—
736	Q₈×C₅₃	—	8	1	no	—
737	D₄×C₅₃	—	2	2	no	—
738	D₄×C₅₃	—	2	2	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	—	4	1	no	—
747	D₄×C₅₃	—	4	2	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	—	8	1	no	—
753	D₄×C₅₃	—	8	1	no	—
754	D₄×C₅₃	—	8	1	no	—
755	D₄×C₅₃	—	8	1	no	—
756	D₄×C₅₃	—	8	1	no	—
757	D₄×C₅₃	—	8	1	no	—
758	D₄×C₅₃	—	8	1	no	—
759	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
760	C₂×C₄×C₅₃	—	2	2	no	—
761	C₂×C₄×C₅₃	—	2	1	no	—
762	C₂×C₄×C₅₃	—	2	1	no	—
763	C₂×C₄×C₅₃	—	2	1	no	—
764	C₂×C₄×C₅₃	—	2	1	no	—
765	C₂×C₄×C₅₃	—	2	1	no	—
766	C₂×C₄×C₅₃	—	2	1	no	—
767	C₂×C₄×C₅₃	—	2	1	no	—
768	C₂×C₄×C₅₃	—	2	1	no	—
769	C₂×C₄×C₅₃	—	2	1	no	—
770	C₂×C₄×C₅₃	—	2	1	no	—
771	C₂×C₄×C₅₃	—	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	—	4	1	no	—
780	C₂×C₄×C₅₃	—	4	2	no	—
781	C₂×C₄×C₅₃	—	4	2	no	—
782	C₂×C₄×C₅₃	—	4	2	no	—
783	C₂×C₄×C₅₃	—	8	1	no	—
784	C₂×C₄×C₅₃	—	8	1	no	—
785	C₂×C₄×C₅₃	—	8	1	no	—
786	C₂×C₄×C₅₃	—	8	1	no	—
787	C₂×C₄×C₅₃	—	8	1	no	—
788	C₂×C₄×C₅₃	—	8	1	no	—
789	C₂×C₄×C₅₃	—	8	1	no	—
790	C₂×C₄×C₅₃	—	8	1	no	—
791	C₂×C₄×C₅₃	—	8	1	no	—
792	C₂×C₄×C₅₃	—	8	1	no	—
793	C₂×C₄×C₅₃	—	8	1	no	—
794	C₂×C₄×C₅₃	—	8	1	no	—
795	C₂×C₄×C₅₃	—	8	1	no	—
796	C₂×C₄×C₅₃	—	8	1	no	—
797	C₂×C₄×C₅₃	—	8	1	no	—
798	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
803	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
804	C₂×C₄×C₅₃	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	C₂⁵	1	1	yes	characteristic
810	C₈×C₅₃	—	2	1	no	—
811	C₈×C₅₃	—	2	1	no	—
812	C₈×C₅₃	—	2	1	no	—
813	C₈×C₅₃	—	2	1	no	—
814	C₈×C₅₃	—	2	1	no	—
815	C₈×C₅₃	—	2	1	no	—
816	C₈×C₅₃	—	2	1	no	—
817	C₈×C₅₃	—	2	1	no	—
818	#62008	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
819	C₂²×C₅₃	—	2	1	no	—
820	C₂²×C₅₃	—	2	1	no	—
821	C₂²×C₅₃	—	2	1	no	—
822	C₂²×C₅₃	—	2	1	no	—
823	C₂²×C₅₃	—	2	1	no	—
824	C₂²×C₅₃	—	2	1	no	—
825	C₂²×C₅₃	—	2	2	no	—
826	C₂²×C₅₃	—	2	1	no	—
827	C₂²×C₅₃	—	2	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	—	4	1	no	—
832	C₂²×C₅₃	—	4	1	no	—
833	C₂²×C₅₃	—	4	1	no	—
834	C₂²×C₅₃	—	4	1	no	—
835	C₂²×C₅₃	—	4	1	no	—
836	C₂²×C₅₃	—	4	1	no	—
837	C₂²×C₅₃	—	4	1	no	—
838	C₂²×C₅₃	—	4	1	no	—
839	C₂²×C₅₃	—	8	4	no	—
840	C₂²×C₅₃	—	16	2	no	—
841	C₂²×C₅₃	#577	1	2	yes	—
842	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
849	C₄×C₅₃	—	2	1	no	—
850	C₄×C₅₃	—	2	1	no	—
851	C₄×C₅₃	—	2	1	no	—
852	C₄×C₅₃	—	2	1	no	—
853	C₄×C₅₃	—	2	1	no	—
854	C₄×C₅₃	—	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	—	4	1	no	—
860	C₄×C₅₃	—	4	1	no	—
861	C₄×C₅₃	—	4	1	no	—
862	C₄×C₅₃	—	4	1	no	—
863	C₄×C₅₃	—	4	1	no	—
864	C₄×C₅₃	—	4	1	no	—
865	C₄×C₅₃	—	4	1	no	—
866	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
867	C₄×C₅₃	#585	1	1	yes	characteristic
868	#3552	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#3513	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3400	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#3372	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#3312	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3308	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3307	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3300	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3298	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
881	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3260	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3258	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3250	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3225	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3221	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3218	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3120	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3042	C₂×C₅₃	1	1	yes	characteristic, complemented
897	C₂×#461	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
899	C₂×C₅₃	—	2	2	no	—
900	C₂×C₅₃	—	4	1	no	—
901	C₂×C₅₃	—	4	1	no	—
902	C₂×C₅₃	—	4	2	no	—
903	C₂×C₅₃	—	8	1	no	—
904	C₂×C₅₃	—	8	1	no	—
905	C₂×C₅₃	—	8	1	no	—
906	C₂×C₅₃	#3488	1	1	yes	characteristic
907	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
908	C₂×C₅₃	#3586	1	1	yes	characteristic
909	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
910	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
911	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
912	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
913	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
914	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
915	#563	—	2	1	no	—
916	#563	—	2	1	no	—
917	#559	C₂²×C₅₃	1	1	yes	characteristic
918	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#554	—	2	1	no	—
921	#554	C₂²×C₅₃	1	1	yes	characteristic
922	#553	—	2	1	no	—
923	#553	—	2	1	no	—
924	#553	C₂²×C₅₃	1	1	yes	characteristic
925	#552	C₂²×C₅₃	1	1	yes	characteristic
926	#551	—	2	1	no	—
927	#551	—	2	1	no	—
928	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
929	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#548	C₂²×C₅₃	1	1	yes	characteristic
932	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#547	C₂²×C₅₃	1	1	yes	characteristic
934	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#546	—	2	1	no	—
936	#546	C₂²×C₅₃	1	1	yes	characteristic
937	#546	C₂²×C₅₃	1	1	yes	characteristic
938	D₄²	C₂²×C₅₃	1	1	yes	characteristic
939	#544	—	2	1	no	—
940	#542	—	2	1	no	—
941	#542	C₂²×C₅₃	1	1	yes	characteristic
942	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#540	C₂²×C₅₃	1	1	yes	characteristic
945	#539	—	2	1	no	—
946	#539	—	2	1	no	—
947	#539	—	2	1	no	—
948	#538	—	2	1	no	—
949	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#529	C₂²×C₅₃	1	1	yes	characteristic
953	#529	C₂²×C₅₃	1	1	yes	characteristic
954	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#525	—	2	1	no	—
956	C₂×#123	—	2	1	no	—
957	#520	C₂²×C₅₃	1	1	yes	characteristic
958	#518	C₂²×C₅₃	1	1	yes	characteristic
959	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
960	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#496	C₂²×C₅₃	1	1	yes	characteristic
964	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#492	C₂²×C₅₃	1	1	yes	characteristic
966	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#478	C₂²×C₅₃	1	1	yes	characteristic
983	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#468	C₂²×C₅₃	1	1	yes	characteristic
990	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#466	C₂²×C₅₃	1	1	yes	characteristic
995	#465	C₂²×C₅₃	1	1	yes	characteristic
996	#465	C₂²×C₅₃	1	1	yes	characteristic
997	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#463	C₂²×C₅₃	1	1	yes	characteristic
1006	#463	C₂²×C₅₃	1	1	yes	characteristic
1007	#463	C₂²×C₅₃	1	1	yes	characteristic
1008	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#461	C₂²×C₅₃	1	1	yes	characteristic
1016	#461	C₂²×C₅₃	1	1	yes	characteristic
1017	#461	C₂²×C₅₃	1	1	yes	characteristic
1018	#461	C₂²×C₅₃	1	1	yes	characteristic
1019	#461	C₂²×C₅₃	1	1	yes	characteristic
1020	#461	C₂²×C₅₃	1	1	yes	characteristic
1021	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#460	C₂²×C₅₃	1	1	yes	characteristic
1029	#460	C₂²×C₅₃	1	1	yes	characteristic
1030	#452	C₂²×C₅₃	1	1	yes	characteristic
1031	#452	C₂²×C₅₃	1	1	yes	characteristic
1032	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#450	C₂²×C₅₃	1	1	yes	characteristic
1037	#450	C₂²×C₅₃	1	1	yes	characteristic
1038	#450	C₂²×C₅₃	1	1	yes	characteristic
1039	#449	C₂²×C₅₃	1	1	yes	characteristic
1040	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#448	C₂²×C₅₃	1	1	yes	characteristic
1043	#448	C₂²×C₅₃	1	1	yes	characteristic
1044	#448	C₂²×C₅₃	1	1	yes	characteristic
1045	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#447	C₂²×C₅₃	1	1	yes	characteristic
1048	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#442	C₂²×C₅₃	1	1	yes	characteristic
1051	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#440	C₂²×C₅₃	1	1	yes	characteristic
1054	#440	C₂²×C₅₃	1	1	yes	characteristic
1055	#440	C₂²×C₅₃	1	1	yes	characteristic
1056	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
1060	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
1061	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#435	C₂²×C₅₃	1	1	yes	characteristic
1063	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1067	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	C₅₃	#62008	1	1	yes	characteristic, direct product factor, Sylow
1081	C₂×#41	—	2	1	no	—
1082	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂²×D₄	—	2	1	no	—
1090	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂³×C₄	—	2	1	no	—
1093	#137	—	4	2	no	—
1094	AGL(1,ℤ/8)	—	4	2	no	—
1095	#135	—	4	2	no	—
1096	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×SD₁₆	—	4	2	no	—
1102	C₂×SD₁₆	—	4	2	no	—
1103	C₂×SD₁₆	—	4	2	no	—
1104	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
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×D₈	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1129	C₄⋊Q₈	—	2	1	no	—
1130	C₄⋊Q₈	—	2	1	no	—
1131	C₄⋊Q₈	—	2	1	no	—
1132	C₄⋊Q₈	—	2	1	no	—
1133	C₄⋊Q₈	—	2	1	no	—
1134	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1135	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1136	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1137	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1138	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1139	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1140	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1141	#127	C₂³×C₅₃	1	1	yes	characteristic
1142	#126	—	2	1	no	—
1143	#126	—	2	1	no	—
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	D₄×C₅₃	1	1	yes	characteristic
1154	#126	D₄×C₅₃	1	1	yes	characteristic
1155	#125	—	2	1	no	—
1156	#125	—	2	1	no	—
1157	#125	—	2	1	no	—
1158	#125	—	2	1	no	—
1159	#125	—	2	1	no	—
1160	#125	—	2	1	no	—
1161	#125	—	2	1	no	—
1162	#125	—	2	1	no	—
1163	#125	D₄×C₅₃	1	1	yes	characteristic
1164	#125	C₂³×C₅₃	1	1	yes	characteristic
1165	#125	C₂³×C₅₃	1	1	yes	characteristic
1166	#125	C₂³×C₅₃	1	1	yes	characteristic
1167	#124	—	2	1	no	—
1168	#124	—	2	1	no	—
1169	#124	—	2	1	no	—
1170	#124	—	2	1	no	—
1171	#124	D₄×C₅₃	1	1	yes	characteristic
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	#123	—	2	1	no	—
1178	#123	—	2	1	no	—
1179	#123	—	2	1	no	—
1180	#123	—	2	1	no	—
1181	#123	—	2	1	no	—
1182	#123	—	2	1	no	—
1183	#123	—	2	1	no	—
1184	#123	—	2	1	no	—
1185	#123	—	2	1	no	—
1186	#123	—	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	#123	—	2	1	no	—
1195	#123	—	2	1	no	—
1196	#123	D₄×C₅₃	1	1	yes	characteristic
1197	#123	D₄×C₅₃	1	1	yes	characteristic
1198	C₂²⋊Q₈	—	2	1	no	—
1199	C₂²⋊Q₈	—	2	1	no	—
1200	C₂²⋊Q₈	—	2	1	no	—
1201	C₂²⋊Q₈	—	2	1	no	—
1202	C₂²⋊Q₈	—	2	1	no	—
1203	C₂²⋊Q₈	—	2	1	no	—
1204	C₂²⋊Q₈	—	2	1	no	—
1205	C₂²⋊Q₈	—	2	1	no	—
1206	C₂²⋊Q₈	—	2	1	no	—
1207	C₂²⋊Q₈	—	2	1	no	—
1208	C₂²⋊Q₈	—	2	1	no	—
1209	C₂²⋊Q₈	—	2	1	no	—
1210	C₂²⋊Q₈	—	2	1	no	—
1211	C₂²⋊Q₈	—	2	1	no	—
1212	C₂²⋊Q₈	—	2	1	no	—
1213	C₂²⋊Q₈	—	2	1	no	—
1214	C₂²⋊Q₈	—	2	1	no	—
1215	C₂²⋊Q₈	—	2	1	no	—
1216	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1217	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1218	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1219	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1220	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1221	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1222	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1223	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1224	#121	—	2	1	no	—
1225	#121	—	2	1	no	—
1226	#121	—	2	1	no	—
1227	#121	—	2	1	no	—
1228	#121	—	2	1	no	—
1229	#121	—	2	1	no	—
1230	#121	—	2	1	no	—
1231	#121	—	2	1	no	—
1232	#121	—	2	1	no	—
1233	#121	D₄×C₅₃	1	1	yes	characteristic
1234	#121	C₂³×C₅₃	1	1	yes	characteristic
1235	#121	C₂³×C₅₃	1	1	yes	characteristic
1236	#121	C₂³×C₅₃	1	1	yes	characteristic
1237	#121	C₂³×C₅₃	1	1	yes	characteristic
1238	#121	C₂³×C₅₃	1	1	yes	characteristic
1239	#120	—	2	1	no	—
1240	#120	—	2	1	no	—
1241	#120	—	2	1	no	—
1242	#120	—	2	1	no	—
1243	C₄×Q₈	—	2	1	no	—
1244	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1245	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1246	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1247	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1248	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1249	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1250	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1251	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
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	C₂³×C₅₃	1	1	yes	characteristic
1268	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1271	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1272	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1273	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1274	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1275	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1276	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1277	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1278	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1279	#117	—	2	1	no	—
1280	#117	—	2	1	no	—
1281	#117	—	2	1	no	—
1282	#117	—	2	1	no	—
1283	#117	—	2	1	no	—
1284	#117	C₂³×C₅₃	1	1	yes	characteristic
1285	#117	C₂³×C₅₃	1	1	yes	characteristic
1286	#117	C₂³×C₅₃	1	1	yes	characteristic
1287	C₂×C₄⋊C₄	—	2	1	no	—
1288	C₂×C₄⋊C₄	—	2	1	no	—
1289	C₂×C₄⋊C₄	—	2	1	no	—
1290	C₂×C₄⋊C₄	—	2	1	no	—
1291	C₂×C₄⋊C₄	—	2	1	no	—
1292	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1293	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1294	C₂×C₂²⋊C₄	—	2	1	no	—
1295	C₂×C₂²⋊C₄	—	2	1	no	—
1296	C₂×C₂²⋊C₄	—	2	1	no	—
1297	C₂×C₂²⋊C₄	—	2	1	no	—
1298	C₂×C₂²⋊C₄	—	2	1	no	—
1299	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1300	#107	C₂³×C₅₃	1	1	yes	characteristic
1301	#107	C₂³×C₅₃	1	1	yes	characteristic
1302	#107	C₂³×C₅₃	1	1	yes	characteristic
1303	#107	C₂³×C₅₃	1	1	yes	characteristic
1304	#106	C₂³×C₅₃	1	1	yes	characteristic
1305	#106	C₂³×C₅₃	1	1	yes	characteristic
1306	#106	C₂³×C₅₃	1	1	yes	characteristic
1307	#106	C₂³×C₅₃	1	1	yes	characteristic
1308	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1309	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1310	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1311	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1312	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1313	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1314	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1315	C₄⋊C₈	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	#103	C₂³×C₅₃	1	1	yes	characteristic
1319	#103	C₂³×C₅₃	1	1	yes	characteristic
1320	#103	C₂³×C₅₃	1	1	yes	characteristic
1321	#103	C₂³×C₅₃	1	1	yes	characteristic
1322	#103	C₂³×C₅₃	1	1	yes	characteristic
1323	#103	C₂³×C₅₃	1	1	yes	characteristic
1324	#103	C₂³×C₅₃	1	1	yes	characteristic
1325	#103	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	#102	C₂³×C₅₃	1	1	yes	characteristic
1341	#102	C₂³×C₅₃	1	1	yes	characteristic
1342	#102	C₂³×C₅₃	1	1	yes	characteristic
1343	#102	C₂³×C₅₃	1	1	yes	characteristic
1344	#102	C₂³×C₅₃	1	1	yes	characteristic
1345	#102	C₂³×C₅₃	1	1	yes	characteristic
1346	#102	C₂³×C₅₃	1	1	yes	characteristic
1347	#102	C₂³×C₅₃	1	1	yes	characteristic
1348	#102	C₂³×C₅₃	1	1	yes	characteristic
1349	#102	C₂³×C₅₃	1	1	yes	characteristic
1350	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1351	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1352	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1353	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1354	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1355	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1356	#97	C₂³×C₅₃	1	1	yes	characteristic
1357	#97	C₂³×C₅₃	1	1	yes	characteristic
1358	#97	C₂³×C₅₃	1	1	yes	characteristic
1359	#97	C₂³×C₅₃	1	1	yes	characteristic
1360	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1361	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1362	C₂⁴	—	2	1	no	—
1363	C₂⁴	—	2	1	no	—
1364	#41	—	2	2	no	—
1365	#41	—	4	1	no	—
1366	#41	—	4	1	no	—
1367	#41	—	4	1	no	—
1368	#41	—	4	1	no	—
1369	#41	—	4	1	no	—
1370	#41	—	8	2	no	—
1371	C₂×Q₈	—	2	1	no	—
1372	C₂×Q₈	—	2	1	no	—
1373	C₂×Q₈	—	2	1	no	—
1374	C₂×Q₈	—	2	1	no	—
1375	C₂×Q₈	—	2	1	no	—
1376	C₂×Q₈	—	4	1	no	—
1377	C₂×Q₈	—	4	1	no	—
1378	C₂×Q₈	—	4	1	no	—
1379	C₂×Q₈	—	4	1	no	—
1380	C₂×Q₈	—	4	1	no	—
1381	C₂×Q₈	—	4	1	no	—
1382	C₂×Q₈	—	4	1	no	—
1383	C₂×Q₈	—	4	1	no	—
1384	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1385	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1386	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1387	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1388	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1389	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1390	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1391	C₂×D₄	—	2	2	no	—
1392	C₂×D₄	—	2	2	no	—
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	2	1	no	—
1396	C₂×D₄	—	2	1	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	—	2	1	no	—
1400	C₂×D₄	—	2	1	no	—
1401	C₂×D₄	—	2	1	no	—
1402	C₂×D₄	—	2	1	no	—
1403	C₂×D₄	—	2	1	no	—
1404	C₂×D₄	—	2	1	no	—
1405	C₂×D₄	—	4	1	no	—
1406	C₂×D₄	—	4	1	no	—
1407	C₂×D₄	—	8	2	no	—
1408	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1409	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1410	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1411	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1412	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1413	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1414	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1415	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	—	2	1	no	—
1425	C₂²×C₄	—	2	1	no	—
1426	C₂²×C₄	—	2	1	no	—
1427	C₂²×C₄	—	2	1	no	—
1428	C₂²×C₄	—	2	1	no	—
1429	C₂²×C₄	—	2	1	no	—
1430	C₂²×C₄	—	2	1	no	—
1431	C₂²×C₄	—	2	1	no	—
1432	C₂²×C₄	—	2	1	no	—
1433	C₂²×C₄	—	8	2	no	—
1434	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1435	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1436	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1437	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1438	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1439	Q₁₆	—	4	1	no	—
1440	Q₁₆	—	4	1	no	—
1441	Q₁₆	—	4	1	no	—
1442	Q₁₆	—	4	1	no	—
1443	Q₁₆	—	4	1	no	—
1444	SD₁₆	—	2	2	no	—
1445	SD₁₆	—	2	2	no	—
1446	SD₁₆	—	2	2	no	—
1447	SD₁₆	—	2	2	no	—
1448	SD₁₆	—	2	2	no	—
1449	SD₁₆	—	4	1	no	—
1450	SD₁₆	—	4	1	no	—
1451	SD₁₆	—	4	1	no	—
1452	SD₁₆	—	4	1	no	—
1453	SD₁₆	—	4	1	no	—
1454	SD₁₆	—	4	1	no	—
1455	SD₁₆	—	4	1	no	—
1456	SD₁₆	—	4	1	no	—
1457	SD₁₆	—	4	1	no	—
1458	SD₁₆	—	4	1	no	—
1459	SD₁₆	—	4	1	no	—
1460	D₈	—	2	2	no	—
1461	D₈	—	4	1	no	—
1462	D₈	—	4	1	no	—
1463	M₁₆	—	4	1	no	—
1464	M₁₆	—	4	1	no	—
1465	C₂×C₈	—	4	1	no	—
1466	C₂×C₈	—	4	1	no	—
1467	C₂×C₈	—	4	1	no	—
1468	C₂×C₈	—	4	1	no	—
1469	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1470	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1471	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1472	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1473	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1474	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1475	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1476	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	—	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	C₂×D₄×C₅₃	1	1	yes	characteristic
1513	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₄⋊C₄	C₂×D₄×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	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1527	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1561	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1562	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1563	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1564	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	C₄²	—	2	1	no	—
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1579	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1580	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1581	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1582	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1583	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1584	C₂³	—	2	1	no	—
1585	C₂³	—	2	1	no	—
1586	C₂³	—	2	1	no	—
1587	C₂³	—	2	1	no	—
1588	C₂³	—	4	2	no	—
1589	C₂³	—	4	2	no	—
1590	C₂³	—	4	2	no	—
1591	C₂³	—	8	1	no	—
1592	C₂³	—	8	1	no	—
1593	C₂³	—	8	1	no	—
1594	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1595	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1596	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1597	Q₈	—	2	1	no	—
1598	Q₈	—	2	1	no	—
1599	Q₈	—	2	1	no	—
1600	Q₈	—	2	1	no	—
1601	Q₈	—	2	1	no	—
1602	Q₈	—	2	1	no	—
1603	Q₈	—	2	1	no	—
1604	Q₈	—	2	1	no	—
1605	Q₈	—	2	1	no	—
1606	Q₈	—	2	1	no	—
1607	Q₈	—	2	1	no	—
1608	Q₈	—	2	1	no	—
1609	Q₈	—	4	1	no	—
1610	Q₈	—	8	1	no	—
1611	Q₈	—	8	1	no	—
1612	Q₈	—	8	1	no	—
1613	Q₈	—	8	1	no	—
1614	Q₈	—	8	1	no	—
1615	D₄	—	2	2	no	—
1616	D₄	—	2	2	no	—
1617	D₄	—	2	1	no	—
1618	D₄	—	2	1	no	—
1619	D₄	—	2	1	no	—
1620	D₄	—	2	1	no	—
1621	D₄	—	2	1	no	—
1622	D₄	—	2	1	no	—
1623	D₄	—	2	1	no	—
1624	D₄	—	4	1	no	—
1625	D₄	—	4	2	no	—
1626	D₄	—	4	2	no	—
1627	D₄	—	4	2	no	—
1628	D₄	—	4	2	no	—
1629	D₄	—	4	2	no	—
1630	D₄	—	8	1	no	—
1631	D₄	—	8	1	no	—
1632	D₄	—	8	1	no	—
1633	D₄	—	8	1	no	—
1634	D₄	—	8	1	no	—
1635	D₄	—	8	1	no	—
1636	D₄	—	8	1	no	—
1637	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1638	C₂×C₄	—	2	2	no	—
1639	C₂×C₄	—	2	1	no	—
1640	C₂×C₄	—	2	1	no	—
1641	C₂×C₄	—	2	1	no	—
1642	C₂×C₄	—	2	1	no	—
1643	C₂×C₄	—	2	1	no	—
1644	C₂×C₄	—	2	1	no	—
1645	C₂×C₄	—	2	1	no	—
1646	C₂×C₄	—	2	1	no	—
1647	C₂×C₄	—	2	1	no	—
1648	C₂×C₄	—	2	1	no	—
1649	C₂×C₄	—	2	1	no	—
1650	C₂×C₄	—	2	1	no	—
1651	C₂×C₄	—	2	1	no	—
1652	C₂×C₄	—	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	—	4	1	no	—
1658	C₂×C₄	—	4	2	no	—
1659	C₂×C₄	—	4	2	no	—
1660	C₂×C₄	—	4	2	no	—
1661	C₂×C₄	—	8	1	no	—
1662	C₂×C₄	—	8	1	no	—
1663	C₂×C₄	—	8	1	no	—
1664	C₂×C₄	—	8	1	no	—
1665	C₂×C₄	—	8	1	no	—
1666	C₂×C₄	—	8	1	no	—
1667	C₂×C₄	—	8	1	no	—
1668	C₂×C₄	—	8	1	no	—
1669	C₂×C₄	—	8	1	no	—
1670	C₂×C₄	—	8	1	no	—
1671	C₂×C₄	—	8	1	no	—
1672	C₂×C₄	—	8	1	no	—
1673	C₂×C₄	—	8	1	no	—
1674	C₂×C₄	—	8	1	no	—
1675	C₂×C₄	—	8	1	no	—
1676	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1677	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1678	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1679	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1680	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1681	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1682	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1683	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1684	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1685	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1686	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1687	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1688	C₈	—	2	1	no	—
1689	C₈	—	2	1	no	—
1690	C₈	—	2	1	no	—
1691	C₈	—	2	1	no	—
1692	C₈	—	2	1	no	—
1693	C₈	—	2	1	no	—
1694	C₈	—	2	1	no	—
1695	C₈	—	2	1	no	—
1696	C₂²	—	2	1	no	—
1697	C₂²	—	2	1	no	—
1698	C₂²	—	2	1	no	—
1699	C₂²	—	2	1	no	—
1700	C₂²	—	2	2	no	—
1701	C₂²	—	2	1	no	—
1702	C₂²	—	2	1	no	—
1703	C₂²	—	2	1	no	—
1704	C₂²	—	2	1	no	—
1705	C₂²	—	4	1	no	—
1706	C₂²	—	4	1	no	—
1707	C₂²	—	4	1	no	—
1708	C₂²	—	4	1	no	—
1709	C₂²	—	4	1	no	—
1710	C₂²	—	4	1	no	—
1711	C₂²	—	4	1	no	—
1712	C₂²	—	4	1	no	—
1713	C₂²	—	4	1	no	—
1714	C₂²	—	4	1	no	—
1715	C₂²	—	4	1	no	—
1716	C₂²	—	8	4	no	—
1717	C₂²	—	16	2	no	—
1718	C₂²	C₅₃×#577	1	2	yes	—
1719	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1720	C₄	—	2	1	no	—
1721	C₄	—	2	1	no	—
1722	C₄	—	2	1	no	—
1723	C₄	—	2	1	no	—
1724	C₄	—	2	1	no	—
1725	C₄	—	2	1	no	—
1726	C₄	—	2	1	no	—
1727	C₄	—	2	1	no	—
1728	C₄	—	2	1	no	—
1729	C₄	—	2	1	no	—
1730	C₄	—	2	1	no	—
1731	C₄	—	4	1	no	—
1732	C₄	—	4	1	no	—
1733	C₄	—	4	1	no	—
1734	C₄	—	4	1	no	—
1735	C₄	—	4	1	no	—
1736	C₄	—	4	1	no	—
1737	C₄	—	4	1	no	—
1738	C₄	—	4	1	no	—
1739	C₄	—	4	1	no	—
1740	C₄	—	4	1	no	—
1741	C₄	—	4	1	no	—
1742	C₄	—	4	1	no	—
1743	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1744	C₄	C₅₃×#585	1	1	yes	characteristic
1745	C₂	—	2	2	no	—
1746	C₂	—	4	1	no	—
1747	C₂	—	4	1	no	—
1748	C₂	—	4	2	no	—
1749	C₂	—	8	1	no	—
1750	C₂	—	8	1	no	—
1751	C₂	—	8	1	no	—
1752	C₂	C₅₃×#3488	1	1	yes	characteristic
1753	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1754	C₂	C₅₃×#3586	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×#3552	C₂	semidirect
2. C₅₃×#3513	C₂	semidirect
3. C₅₃×#3401	C₂	semidirect
4. C₅₃×#3400	C₂	semidirect
5. C₅₃×#3376	C₂	semidirect
6. C₅₃×#3372	C₂	semidirect
7. C₅₃×#3320	C₂	semidirect
8. C₅₃×#3312	C₂	semidirect
9. C₅₃×#3308	C₂	semidirect
10. C₅₃×#3307	C₂	semidirect
11. C₅₃×#3300	C₂	semidirect
12. C₅₃×#3298	C₂	semidirect
13. C₅₃×#3282	C₂	semidirect
14. D₄×SD₁₆×C₅₃	C₂	semidirect
15. C₅₃×#3267	C₂	semidirect
16. C₅₃×#3266	C₂	semidirect
17. C₅₃×#3266	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3260	C₂	semidirect
20. C₅₃×#3258	C₂	semidirect
21. C₅₃×#3250	C₂	semidirect
22. C₅₃×#3225	C₂	semidirect
23. C₅₃×#3221	C₂	semidirect
24. C₅₃×#3218	C₂	semidirect
25. C₅₃×#3123	C₂	semidirect
26. C₅₃×#3120	C₂	semidirect
27. C₅₃×#3114	C₂	semidirect
28. C₅₃×#3046	C₂	semidirect
29. C₅₃×#3042	C₂	semidirect
30. C₂×C₅₃×#461	C₂	semidirect
31. C₅₃×#2992	C₂	semidirect
41. C₅₃×#557	C₂²	semidirect
42. C₅₃×#556	C₂²	semidirect
52. D₄×Q₈×C₅₃	C₂²	semidirect
53. D₄×Q₈×C₅₃	C₂²	semidirect
55. C₅₃×#548	C₂²	semidirect
57. C₅₃×#547	C₂²	semidirect
65. C₅₃×#541	C₂²	semidirect
66. C₅₃×#541	C₂²	semidirect
72. C₅₃×#536	C₂²	semidirect
73. C₅₃×#536	C₂²	semidirect
74. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
77. C₅₃×#529	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
84. C₅₃×#497	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
90. C₅₃×#491	C₂²	semidirect
91. C₅₃×#491	C₂²	semidirect
92. C₅₃×#489	C₂²	semidirect
93. C₅₃×#488	C₂²	semidirect
94. C₅₃×#487	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#484	C₂²	semidirect
98. C₅₃×#483	C₂²	semidirect
99. C₅₃×#483	C₂²	semidirect
100. C₅₃×#480	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×#475	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
113. C₅₃×#468	C₂²	semidirect
114. C₅₃×#468	C₂²	semidirect
115. C₅₃×#467	C₂²	semidirect
116. C₅₃×#467	C₂²	semidirect
120. C₅₃×#465	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
123. C₅₃×#464	C₂²	semidirect
124. C₅₃×#464	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#463	C₂²	semidirect
135. C₅₃×#462	C₂²	semidirect
136. C₅₃×#462	C₂²	semidirect
137. C₅₃×#462	C₂²	semidirect
144. C₅₃×#461	C₂²	semidirect
145. C₅₃×#461	C₂²	semidirect
146. C₅₃×#461	C₂²	semidirect
147. C₅₃×#461	C₂²	semidirect
148. C₅₃×#461	C₂²	semidirect
149. C₅₃×#461	C₂²	semidirect
150. C₅₃×#461	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#451	C₂²	semidirect
157. C₅₃×#451	C₂²	semidirect
158. C₅₃×#451	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
168. C₅₃×#448	C₂²	semidirect
169. C₅₃×#448	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
174. C₅₃×#442	C₂²	semidirect
175. C₅₃×#441	C₂²	semidirect
179. C₅₃×#440	C₂²	semidirect
180. C₅₃×#440	C₂²	semidirect
181. C₄×Q₁₆×C₅₃	C₂²	semidirect
184. C₄×SD₁₆×C₅₃	C₂²	semidirect
186. C₅₃×#435	C₂²	semidirect
187. C₅₃×#435	C₂²	semidirect
188. C₅₃×#435	C₂²	semidirect
190. C₈×D₄×C₅₃	C₂²	semidirect
191. C₅₃×#433	C₂²	semidirect
192. C₅₃×#433	C₂²	semidirect
193. C₅₃×#432	C₂²	semidirect
194. C₅₃×#424	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
197. C₅₃×#419	C₂²	semidirect
198. C₅₃×#417	C₂²	semidirect
199. C₅₃×#416	C₂²	semidirect
200. C₂×#103×C₅₃	C₂²	semidirect
201. C₂×#103×C₅₃	C₂²	semidirect
202. C₂×#103×C₅₃	C₂²	semidirect
818. #62008	C₅₃	direct (N × H)
868. #3552	C₂×C₅₃	semidirect
869. #3513	C₂×C₅₃	semidirect
870. #3401	C₂×C₅₃	semidirect
871. #3400	C₂×C₅₃	semidirect
872. #3376	C₂×C₅₃	semidirect
873. #3372	C₂×C₅₃	semidirect
874. #3320	C₂×C₅₃	semidirect
875. #3312	C₂×C₅₃	semidirect
876. #3308	C₂×C₅₃	semidirect
877. #3307	C₂×C₅₃	semidirect
878. #3300	C₂×C₅₃	semidirect
879. #3298	C₂×C₅₃	semidirect
880. #3282	C₂×C₅₃	semidirect
881. D₄×SD₁₆	C₂×C₅₃	semidirect
882. #3267	C₂×C₅₃	semidirect
883. #3266	C₂×C₅₃	semidirect
884. #3266	C₂×C₅₃	semidirect
885. #3265	C₂×C₅₃	semidirect
886. #3260	C₂×C₅₃	semidirect
887. #3258	C₂×C₅₃	semidirect
888. #3250	C₂×C₅₃	semidirect
889. #3225	C₂×C₅₃	semidirect
890. #3221	C₂×C₅₃	semidirect
891. #3218	C₂×C₅₃	semidirect
892. #3123	C₂×C₅₃	semidirect
893. #3120	C₂×C₅₃	semidirect
894. #3114	C₂×C₅₃	semidirect
895. #3046	C₂×C₅₃	semidirect
896. #3042	C₂×C₅₃	semidirect
897. C₂×#461	C₂×C₅₃	semidirect
898. #2992	C₂×C₅₃	semidirect
918. #557	C₂²×C₅₃	semidirect
919. #556	C₂²×C₅₃	semidirect
929. D₄×Q₈	C₂²×C₅₃	semidirect
930. D₄×Q₈	C₂²×C₅₃	semidirect
932. #548	C₂²×C₅₃	semidirect
934. #547	C₂²×C₅₃	semidirect
942. #541	C₂²×C₅₃	semidirect
943. #541	C₂²×C₅₃	semidirect
949. #536	C₂²×C₅₃	semidirect
950. #536	C₂²×C₅₃	semidirect
951. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
954. #529	C₂²×C₅₃	semidirect
960. #497	C₂²×C₅₃	semidirect
961. #497	C₂²×C₅₃	semidirect
962. #497	C₂²×C₅₃	semidirect
964. #495	C₂²×C₅₃	semidirect
966. #491	C₂²×C₅₃	semidirect
967. #491	C₂²×C₅₃	semidirect
968. #491	C₂²×C₅₃	semidirect
969. #489	C₂²×C₅₃	semidirect
970. #488	C₂²×C₅₃	semidirect
971. #487	C₂²×C₅₃	semidirect
972. #485	C₂²×C₅₃	semidirect
973. #485	C₂²×C₅₃	semidirect
974. #484	C₂²×C₅₃	semidirect
975. #483	C₂²×C₅₃	semidirect
976. #483	C₂²×C₅₃	semidirect
977. #480	C₂²×C₅₃	semidirect
978. #479	C₂²×C₅₃	semidirect
979. #479	C₂²×C₅₃	semidirect
980. #479	C₂²×C₅₃	semidirect
981. #479	C₂²×C₅₃	semidirect
983. #478	C₂²×C₅₃	semidirect
984. #478	C₂²×C₅₃	semidirect
985. #478	C₂²×C₅₃	semidirect
986. #477	C₂²×C₅₃	semidirect
987. #475	C₂²×C₅₃	semidirect
988. #470	C₂²×C₅₃	semidirect
990. #468	C₂²×C₅₃	semidirect
991. #468	C₂²×C₅₃	semidirect
992. #467	C₂²×C₅₃	semidirect
993. #467	C₂²×C₅₃	semidirect
997. #465	C₂²×C₅₃	semidirect
998. #465	C₂²×C₅₃	semidirect
999. #465	C₂²×C₅₃	semidirect
1000. #464	C₂²×C₅₃	semidirect
1001. #464	C₂²×C₅₃	semidirect
1002. #464	C₂²×C₅₃	semidirect
1003. #464	C₂²×C₅₃	semidirect
1004. #464	C₂²×C₅₃	semidirect
1008. #463	C₂²×C₅₃	semidirect
1009. #463	C₂²×C₅₃	semidirect
1010. #463	C₂²×C₅₃	semidirect
1011. #463	C₂²×C₅₃	semidirect
1012. #462	C₂²×C₅₃	semidirect
1013. #462	C₂²×C₅₃	semidirect
1014. #462	C₂²×C₅₃	semidirect
1021. #461	C₂²×C₅₃	semidirect
1022. #461	C₂²×C₅₃	semidirect
1023. #461	C₂²×C₅₃	semidirect
1024. #461	C₂²×C₅₃	semidirect
1025. #461	C₂²×C₅₃	semidirect
1026. #461	C₂²×C₅₃	semidirect
1027. #461	C₂²×C₅₃	semidirect
1032. #452	C₂²×C₅₃	semidirect
1033. #451	C₂²×C₅₃	semidirect
1034. #451	C₂²×C₅₃	semidirect
1035. #451	C₂²×C₅₃	semidirect
1040. #449	C₂²×C₅₃	semidirect
1041. #449	C₂²×C₅₃	semidirect
1045. #448	C₂²×C₅₃	semidirect
1046. #448	C₂²×C₅₃	semidirect
1048. #446	C₂²×C₅₃	semidirect
1049. #446	C₂²×C₅₃	semidirect
1051. #442	C₂²×C₅₃	semidirect
1052. #441	C₂²×C₅₃	semidirect
1056. #440	C₂²×C₅₃	semidirect
1057. #440	C₂²×C₅₃	semidirect
1058. C₄×Q₁₆	C₂²×C₅₃	semidirect
1061. C₄×SD₁₆	C₂²×C₅₃	semidirect
1063. #435	C₂²×C₅₃	semidirect
1064. #435	C₂²×C₅₃	semidirect
1065. #435	C₂²×C₅₃	semidirect
1067. C₈×D₄	C₂²×C₅₃	semidirect
1068. #433	C₂²×C₅₃	semidirect
1069. #433	C₂²×C₅₃	semidirect
1070. #432	C₂²×C₅₃	semidirect
1071. #424	C₂²×C₅₃	semidirect
1072. #424	C₂²×C₅₃	semidirect
1073. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1074. #419	C₂²×C₅₃	semidirect
1075. #417	C₂²×C₅₃	semidirect
1076. #416	C₂²×C₅₃	semidirect
1077. C₂×#103	C₂²×C₅₃	semidirect
1078. C₂×#103	C₂²×C₅₃	semidirect
1079. C₂×#103	C₂²×C₅₃	semidirect
1080. C₅₃	#62008	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×#3552	2
C₅₃×#3513	2
C₅₃×#3401	2
C₅₃×#3400	2
C₅₃×#3376	2
C₅₃×#3372	2
C₅₃×#3320	2
C₅₃×#3312	2
C₅₃×#3308	2
C₅₃×#3307	2
C₅₃×#3300	2
C₅₃×#3298	2
C₅₃×#3282	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3267	2
C₅₃×#3266	2
C₅₃×#3265	2
C₅₃×#3260	2
C₅₃×#3258	2
C₅₃×#3250	2
C₅₃×#3225	2
C₅₃×#3221	2
C₅₃×#3218	2
C₅₃×#3123	2
C₅₃×#3120	2
C₅₃×#3114	2
C₅₃×#3046	2
C₅₃×#3042	2
C₂×C₅₃×#461	2
C₅₃×#2992	2
#62008	53

Subgroups — C53×#62008 #27269520

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62008 #27269520