Subgroups — C₅₃×#61627 #27269139

Order 13568.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3540	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3329	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3321	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3313	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3273	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3225	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3225	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3201	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3198	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3196	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3190	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3125	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3011	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3010	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3005	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3002	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2976	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×2₋¹⁺⁴×C₅₃	C₂²	1	1	yes	characteristic
33	C₂²×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
37	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
39	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
40	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
41	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×H(3,𝔽₄)	—	2	1	no	—
43	C₅₃×#560	—	2	1	no	—
44	C₅₃×#559	—	2	1	no	—
45	C₅₃×#556	C₂²	1	1	yes	characteristic
46	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
47	C₅₃×#555	C₂²	1	1	yes	characteristic
48	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#551	—	2	1	no	—
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
51	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
52	C₅₃×#548	C₂²	1	1	yes	characteristic
53	C₅₃×#548	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#547	—	2	1	no	—
57	C₅₃×#547	—	2	1	no	—
58	C₅₃×#547	C₂²	1	1	yes	characteristic
59	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#546	—	2	1	no	—
61	C₅₃×#546	—	2	1	no	—
62	C₅₃×#546	C₂²	1	1	yes	characteristic
63	C₅₃×#546	C₂²	1	1	yes	characteristic
64	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
65	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#542	—	2	1	no	—
67	C₅₃×#542	—	2	1	no	—
68	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#538	—	2	1	no	—
71	C₅₃×#538	—	2	1	no	—
72	C₅₃×#537	—	2	1	no	—
73	C₅₃×#537	C₂²	1	1	yes	characteristic
74	C₅₃×#536	—	2	1	no	—
75	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#536	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#535	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#525	—	2	1	no	—
79	C₅₃×#525	C₂²	1	1	yes	characteristic
80	C₅₃×#525	C₂²	1	1	yes	characteristic
81	C₅₃×#525	C₂²	1	1	yes	characteristic
82	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
83	C₂×C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	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×#485	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#468	C₂²	1	1	yes	characteristic
114	C₅₃×#468	C₂²	1	1	yes	characteristic
115	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#466	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×#465	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#465	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×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#452	C₂²	1	1	yes	characteristic
138	C₅₃×#452	C₂²	1	1	yes	characteristic
139	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#449	C₂²	1	1	yes	characteristic
158	C₅₃×#449	C₂²	1	1	yes	characteristic
159	C₅₃×#449	C₂²	1	1	yes	characteristic
160	C₅₃×#449	C₂²	1	1	yes	characteristic
161	C₅₃×#449	C₂²	1	1	yes	characteristic
162	C₅₃×#449	C₂²	1	1	yes	characteristic
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, complemented
167	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#447	C₂²	1	1	yes	characteristic
172	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
177	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
178	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#436	C₂²	1	1	yes	characteristic
182	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#435	C₂²	1	1	yes	characteristic
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#408	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#407	C₂²	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	2₋¹⁺⁴×C₅₃	—	4	2	no	—
204	2₋¹⁺⁴×C₅₃	—	4	2	no	—
205	C₂×#41×C₅₃	—	2	1	no	—
206	C₂×#41×C₅₃	—	2	1	no	—
207	C₂×#41×C₅₃	—	2	1	no	—
208	C₂×#41×C₅₃	—	2	1	no	—
209	C₂×#41×C₅₃	—	2	1	no	—
210	C₂×#41×C₅₃	—	4	2	no	—
211	C₂×#41×C₅₃	—	4	2	no	—
212	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
221	C₂²×Q₈×C₅₃	—	2	1	no	—
222	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
224	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₂²×D₄×C₅₃	—	2	1	no	—
228	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
229	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
230	C₂³×C₄×C₅₃	—	2	1	no	—
231	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic
232	#137×C₅₃	—	4	2	no	—
233	#137×C₅₃	—	4	2	no	—
234	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
235	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
236	#135×C₅₃	—	4	2	no	—
237	#135×C₅₃	—	4	2	no	—
238	C₂×Q₁₆×C₅₃	—	4	2	no	—
239	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×SD₁₆×C₅₃	—	4	2	no	—
248	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
250	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
251	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
252	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
253	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
254	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
255	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
256	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
258	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
259	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
260	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
261	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
263	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
264	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
266	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
267	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
268	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
269	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
272	C₄⋊Q₈×C₅₃	—	2	1	no	—
273	C₄⋊Q₈×C₅₃	—	2	1	no	—
274	C₄⋊Q₈×C₅₃	—	2	1	no	—
275	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
276	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
279	#127×C₅₃	—	2	1	no	—
280	#126×C₅₃	—	2	1	no	—
281	#126×C₅₃	—	2	1	no	—
282	#126×C₅₃	—	2	1	no	—
283	#126×C₅₃	—	2	1	no	—
284	#126×C₅₃	—	2	1	no	—
285	#126×C₅₃	—	2	1	no	—
286	#124×C₅₃	—	2	1	no	—
287	#124×C₅₃	—	2	1	no	—
288	#124×C₅₃	—	2	1	no	—
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	—	2	1	no	—
294	#124×C₅₃	—	2	1	no	—
295	#124×C₅₃	—	2	1	no	—
296	#124×C₅₃	—	2	1	no	—
297	#124×C₅₃	—	2	1	no	—
298	#124×C₅₃	—	2	1	no	—
299	#124×C₅₃	—	2	1	no	—
300	#124×C₅₃	C₂³	1	1	yes	characteristic
301	#124×C₅₃	C₂³	1	1	yes	characteristic
302	#124×C₅₃	C₂³	1	1	yes	characteristic
303	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
319	#123×C₅₃	—	2	1	no	—
320	#123×C₅₃	D₄	1	1	yes	characteristic
321	#123×C₅₃	D₄	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
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	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
347	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
348	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
350	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
356	#121×C₅₃	—	2	1	no	—
357	#121×C₅₃	—	2	1	no	—
358	#121×C₅₃	—	2	1	no	—
359	#121×C₅₃	—	2	1	no	—
360	#121×C₅₃	—	2	1	no	—
361	#121×C₅₃	—	2	1	no	—
362	#121×C₅₃	—	2	1	no	—
363	#121×C₅₃	—	2	1	no	—
364	#121×C₅₃	—	2	1	no	—
365	#121×C₅₃	—	2	1	no	—
366	#121×C₅₃	D₄	1	1	yes	characteristic
367	#121×C₅₃	D₄	1	1	yes	characteristic
368	#121×C₅₃	C₂³	1	1	yes	characteristic
369	#121×C₅₃	C₂³	1	1	yes	characteristic
370	#121×C₅₃	C₂³	1	1	yes	characteristic
371	#121×C₅₃	C₂³	1	1	yes	characteristic
372	#121×C₅₃	C₂³	1	1	yes	characteristic
373	#121×C₅₃	C₂³	1	1	yes	characteristic
374	#121×C₅₃	C₂³	1	1	yes	characteristic
375	#121×C₅₃	C₂³	1	1	yes	characteristic
376	#120×C₅₃	—	2	1	no	—
377	#120×C₅₃	—	2	1	no	—
378	#120×C₅₃	—	2	1	no	—
379	#120×C₅₃	—	2	1	no	—
380	#120×C₅₃	—	2	1	no	—
381	#120×C₅₃	—	2	1	no	—
382	#120×C₅₃	—	2	1	no	—
383	#120×C₅₃	—	2	1	no	—
384	#120×C₅₃	D₄	1	1	yes	characteristic
385	#120×C₅₃	D₄	1	1	yes	characteristic
386	C₄×Q₈×C₅₃	—	2	1	no	—
387	C₄×Q₈×C₅₃	—	2	1	no	—
388	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
389	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
390	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
391	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
392	C₄×D₄×C₅₃	—	2	1	no	—
393	C₄×D₄×C₅₃	—	2	1	no	—
394	C₄×D₄×C₅₃	—	2	1	no	—
395	C₄×D₄×C₅₃	—	2	1	no	—
396	C₄×D₄×C₅₃	—	2	1	no	—
397	C₄×D₄×C₅₃	—	2	1	no	—
398	C₄×D₄×C₅₃	—	2	1	no	—
399	C₄×D₄×C₅₃	—	2	1	no	—
400	C₄×D₄×C₅₃	—	2	1	no	—
401	C₄×D₄×C₅₃	—	2	1	no	—
402	C₄×D₄×C₅₃	—	2	1	no	—
403	C₄×D₄×C₅₃	—	2	1	no	—
404	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
405	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
406	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
407	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
408	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
409	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
410	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
411	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
412	#117×C₅₃	—	2	1	no	—
413	#117×C₅₃	—	2	1	no	—
414	#117×C₅₃	—	2	1	no	—
415	#117×C₅₃	C₂³	1	1	yes	characteristic
416	#117×C₅₃	C₂³	1	1	yes	characteristic
417	#117×C₅₃	C₂³	1	1	yes	characteristic
418	#117×C₅₃	C₂³	1	1	yes	characteristic
419	#117×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
422	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
423	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
424	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
425	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
430	#107×C₅₃	C₂³	1	1	yes	characteristic
431	#107×C₅₃	C₂³	1	1	yes	characteristic
432	#107×C₅₃	C₂³	1	1	yes	characteristic
433	#107×C₅₃	C₂³	1	1	yes	characteristic
434	#106×C₅₃	C₂³	1	1	yes	characteristic
435	#106×C₅₃	C₂³	1	1	yes	characteristic
436	#106×C₅₃	C₂³	1	1	yes	characteristic
437	#106×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	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
441	C₄⋊C₈×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	#102×C₅₃	C₂³	1	1	yes	characteristic
473	#102×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	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
482	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
485	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
486	#97×C₅₃	C₂³	1	1	yes	characteristic
487	#97×C₅₃	C₂³	1	1	yes	characteristic
488	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
489	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
490	C₂⁴×C₅₃	—	2	1	no	—
491	C₂⁴×C₅₃	—	2	1	no	—
492	C₂⁴×C₅₃	C₂×D₄	1	1	yes	characteristic
493	#41×C₅₃	—	2	2	no	—
494	#41×C₅₃	—	2	2	no	—
495	#41×C₅₃	—	2	2	no	—
496	#41×C₅₃	—	2	2	no	—
497	#41×C₅₃	—	2	2	no	—
498	#41×C₅₃	—	2	2	no	—
499	#41×C₅₃	—	4	1	no	—
500	#41×C₅₃	—	4	1	no	—
501	#41×C₅₃	—	4	1	no	—
502	#41×C₅₃	—	4	1	no	—
503	#41×C₅₃	—	4	1	no	—
504	#41×C₅₃	—	4	1	no	—
505	#41×C₅₃	—	4	1	no	—
506	#41×C₅₃	—	4	1	no	—
507	#41×C₅₃	—	4	4	no	—
508	#41×C₅₃	—	4	4	no	—
509	#41×C₅₃	—	4	1	no	—
510	#41×C₅₃	—	4	1	no	—
511	#41×C₅₃	—	4	1	no	—
512	#41×C₅₃	—	4	1	no	—
513	#41×C₅₃	—	4	4	no	—
514	#41×C₅₃	—	4	4	no	—
515	#41×C₅₃	—	4	4	no	—
516	C₂×Q₈×C₅₃	—	2	1	no	—
517	C₂×Q₈×C₅₃	—	2	1	no	—
518	C₂×Q₈×C₅₃	—	2	1	no	—
519	C₂×Q₈×C₅₃	—	2	1	no	—
520	C₂×Q₈×C₅₃	—	2	1	no	—
521	C₂×Q₈×C₅₃	—	2	1	no	—
522	C₂×Q₈×C₅₃	—	2	1	no	—
523	C₂×Q₈×C₅₃	—	2	2	no	—
524	C₂×Q₈×C₅₃	—	2	2	no	—
525	C₂×Q₈×C₅₃	—	2	2	no	—
526	C₂×Q₈×C₅₃	—	4	1	no	—
527	C₂×Q₈×C₅₃	—	4	1	no	—
528	C₂×Q₈×C₅₃	—	4	1	no	—
529	C₂×Q₈×C₅₃	—	4	1	no	—
530	C₂×Q₈×C₅₃	—	4	1	no	—
531	C₂×Q₈×C₅₃	—	4	4	no	—
532	C₂×Q₈×C₅₃	—	4	1	no	—
533	C₂×Q₈×C₅₃	—	4	1	no	—
534	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
535	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
539	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
540	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×D₄×C₅₃	—	2	1	no	—
542	C₂×D₄×C₅₃	—	2	2	no	—
543	C₂×D₄×C₅₃	—	2	1	no	—
544	C₂×D₄×C₅₃	—	2	1	no	—
545	C₂×D₄×C₅₃	—	2	1	no	—
546	C₂×D₄×C₅₃	—	2	1	no	—
547	C₂×D₄×C₅₃	—	2	1	no	—
548	C₂×D₄×C₅₃	—	2	1	no	—
549	C₂×D₄×C₅₃	—	2	1	no	—
550	C₂×D₄×C₅₃	—	2	1	no	—
551	C₂×D₄×C₅₃	—	2	1	no	—
552	C₂×D₄×C₅₃	—	2	1	no	—
553	C₂×D₄×C₅₃	—	2	1	no	—
554	C₂×D₄×C₅₃	—	2	1	no	—
555	C₂×D₄×C₅₃	—	2	1	no	—
556	C₂×D₄×C₅₃	—	2	1	no	—
557	C₂×D₄×C₅₃	—	2	1	no	—
558	C₂×D₄×C₅₃	—	2	1	no	—
559	C₂×D₄×C₅₃	—	2	1	no	—
560	C₂×D₄×C₅₃	—	4	1	no	—
561	C₂×D₄×C₅₃	—	4	1	no	—
562	C₂×D₄×C₅₃	—	4	1	no	—
563	C₂×D₄×C₅₃	—	4	4	no	—
564	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
565	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
566	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
567	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
568	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
569	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
570	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
571	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
572	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
573	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
574	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂²×C₄×C₅₃	—	2	1	no	—
576	C₂²×C₄×C₅₃	—	2	1	no	—
577	C₂²×C₄×C₅₃	—	2	1	no	—
578	C₂²×C₄×C₅₃	—	2	1	no	—
579	C₂²×C₄×C₅₃	—	2	1	no	—
580	C₂²×C₄×C₅₃	—	2	1	no	—
581	C₂²×C₄×C₅₃	—	2	1	no	—
582	C₂²×C₄×C₅₃	—	2	1	no	—
583	C₂²×C₄×C₅₃	—	2	1	no	—
584	C₂²×C₄×C₅₃	—	2	1	no	—
585	C₂²×C₄×C₅₃	—	2	1	no	—
586	C₂²×C₄×C₅₃	—	2	1	no	—
587	C₂²×C₄×C₅₃	—	2	1	no	—
588	C₂²×C₄×C₅₃	—	2	1	no	—
589	C₂²×C₄×C₅₃	—	2	1	no	—
590	C₂²×C₄×C₅₃	—	2	1	no	—
591	C₂²×C₄×C₅₃	—	2	1	no	—
592	C₂²×C₄×C₅₃	—	2	1	no	—
593	C₂²×C₄×C₅₃	—	4	1	no	—
594	C₂²×C₄×C₅₃	—	4	1	no	—
595	C₂²×C₄×C₅₃	—	4	4	no	—
596	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
597	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
598	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
599	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
601	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
602	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
604	Q₁₆×C₅₃	—	2	2	no	—
605	Q₁₆×C₅₃	—	2	2	no	—
606	Q₁₆×C₅₃	—	4	1	no	—
607	Q₁₆×C₅₃	—	4	1	no	—
608	Q₁₆×C₅₃	—	4	1	no	—
609	Q₁₆×C₅₃	—	4	1	no	—
610	Q₁₆×C₅₃	—	4	1	no	—
611	Q₁₆×C₅₃	—	4	1	no	—
612	SD₁₆×C₅₃	—	2	2	no	—
613	SD₁₆×C₅₃	—	2	2	no	—
614	SD₁₆×C₅₃	—	2	2	no	—
615	SD₁₆×C₅₃	—	2	2	no	—
616	SD₁₆×C₅₃	—	4	1	no	—
617	SD₁₆×C₅₃	—	4	1	no	—
618	SD₁₆×C₅₃	—	4	1	no	—
619	SD₁₆×C₅₃	—	4	1	no	—
620	SD₁₆×C₅₃	—	4	1	no	—
621	SD₁₆×C₅₃	—	4	1	no	—
622	SD₁₆×C₅₃	—	4	1	no	—
623	SD₁₆×C₅₃	—	4	1	no	—
624	D₈×C₅₃	—	2	2	no	—
625	D₈×C₅₃	—	2	2	no	—
626	D₈×C₅₃	—	4	1	no	—
627	D₈×C₅₃	—	4	1	no	—
628	M₁₆×C₅₃	—	4	1	no	—
629	M₁₆×C₅₃	—	4	1	no	—
630	M₁₆×C₅₃	—	4	1	no	—
631	M₁₆×C₅₃	—	4	1	no	—
632	C₂×C₈×C₅₃	—	4	1	no	—
633	C₂×C₈×C₅₃	—	4	1	no	—
634	C₂×C₈×C₅₃	—	4	1	no	—
635	C₂×C₈×C₅₃	—	4	1	no	—
636	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
637	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
640	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
641	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
642	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
643	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
644	C₄⋊C₄×C₅₃	—	2	1	no	—
645	C₄⋊C₄×C₅₃	—	2	1	no	—
646	C₄⋊C₄×C₅₃	—	2	1	no	—
647	C₄⋊C₄×C₅₃	—	2	1	no	—
648	C₄⋊C₄×C₅₃	—	2	1	no	—
649	C₄⋊C₄×C₅₃	—	2	1	no	—
650	C₄⋊C₄×C₅₃	—	2	1	no	—
651	C₄⋊C₄×C₅₃	—	2	1	no	—
652	C₄⋊C₄×C₅₃	—	2	1	no	—
653	C₄⋊C₄×C₅₃	—	2	1	no	—
654	C₄⋊C₄×C₅₃	—	2	1	no	—
655	C₄⋊C₄×C₅₃	—	2	1	no	—
656	C₄⋊C₄×C₅₃	—	2	1	no	—
657	C₄⋊C₄×C₅₃	—	2	1	no	—
658	C₄⋊C₄×C₅₃	—	2	1	no	—
659	C₄⋊C₄×C₅₃	—	2	1	no	—
660	C₄⋊C₄×C₅₃	—	2	1	no	—
661	C₄⋊C₄×C₅₃	—	2	1	no	—
662	C₄⋊C₄×C₅₃	—	2	1	no	—
663	C₄⋊C₄×C₅₃	—	2	1	no	—
664	C₄⋊C₄×C₅₃	—	2	1	no	—
665	C₄⋊C₄×C₅₃	—	2	1	no	—
666	C₄⋊C₄×C₅₃	—	2	1	no	—
667	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
668	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
669	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
670	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
671	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
672	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
673	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
674	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
675	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
676	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
677	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
678	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
679	C₂²⋊C₄×C₅₃	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	—	2	1	no	—
682	C₂²⋊C₄×C₅₃	—	2	1	no	—
683	C₂²⋊C₄×C₅₃	—	2	1	no	—
684	C₂²⋊C₄×C₅₃	—	2	1	no	—
685	C₂²⋊C₄×C₅₃	—	2	1	no	—
686	C₂²⋊C₄×C₅₃	—	2	1	no	—
687	C₂²⋊C₄×C₅₃	—	2	1	no	—
688	C₂²⋊C₄×C₅₃	—	2	1	no	—
689	C₂²⋊C₄×C₅₃	—	2	1	no	—
690	C₂²⋊C₄×C₅₃	—	2	1	no	—
691	C₂²⋊C₄×C₅₃	—	2	1	no	—
692	C₂²⋊C₄×C₅₃	—	2	1	no	—
693	C₂²⋊C₄×C₅₃	—	2	1	no	—
694	C₂²⋊C₄×C₅₃	—	2	1	no	—
695	C₂²⋊C₄×C₅₃	—	2	1	no	—
696	C₂²⋊C₄×C₅₃	—	2	1	no	—
697	C₂²⋊C₄×C₅₃	—	2	1	no	—
698	C₂²⋊C₄×C₅₃	—	2	1	no	—
699	C₂²⋊C₄×C₅₃	—	2	1	no	—
700	C₂²⋊C₄×C₅₃	—	2	1	no	—
701	C₂²⋊C₄×C₅₃	—	2	1	no	—
702	C₂²⋊C₄×C₅₃	—	2	1	no	—
703	C₂²⋊C₄×C₅₃	—	2	1	no	—
704	C₂²⋊C₄×C₅₃	—	2	1	no	—
705	C₂²⋊C₄×C₅₃	—	2	1	no	—
706	C₂²⋊C₄×C₅₃	—	2	1	no	—
707	C₂²⋊C₄×C₅₃	—	2	1	no	—
708	C₂²⋊C₄×C₅₃	—	2	1	no	—
709	C₂²⋊C₄×C₅₃	—	2	1	no	—
710	C₂²⋊C₄×C₅₃	—	2	1	no	—
711	C₂²⋊C₄×C₅₃	—	2	1	no	—
712	C₂²⋊C₄×C₅₃	—	2	1	no	—
713	C₂²⋊C₄×C₅₃	—	2	1	no	—
714	C₂²⋊C₄×C₅₃	—	2	1	no	—
715	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
716	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
717	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
718	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
719	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
720	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
721	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
722	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
723	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
724	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
725	C₄²×C₅₃	—	2	1	no	—
726	C₄²×C₅₃	—	2	1	no	—
727	C₄²×C₅₃	—	2	1	no	—
728	C₄²×C₅₃	—	2	1	no	—
729	C₄²×C₅₃	—	2	1	no	—
730	C₄²×C₅₃	—	2	1	no	—
731	C₄²×C₅₃	—	2	1	no	—
732	C₄²×C₅₃	—	2	1	no	—
733	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
734	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
735	C₂³×C₅₃	—	2	1	no	—
736	C₂³×C₅₃	—	2	1	no	—
737	C₂³×C₅₃	—	2	1	no	—
738	C₂³×C₅₃	—	2	1	no	—
739	C₂³×C₅₃	—	4	1	no	—
740	C₂³×C₅₃	—	4	1	no	—
741	C₂³×C₅₃	—	4	1	no	—
742	C₂³×C₅₃	—	4	2	no	—
743	C₂³×C₅₃	—	4	2	no	—
744	C₂³×C₅₃	—	8	1	no	—
745	C₂³×C₅₃	—	8	1	no	—
746	C₂³×C₅₃	—	8	1	no	—
747	C₂³×C₅₃	—	8	1	no	—
748	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
749	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
750	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
751	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
752	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
753	Q₈×C₅₃	—	2	1	no	—
754	Q₈×C₅₃	—	2	1	no	—
755	Q₈×C₅₃	—	2	1	no	—
756	Q₈×C₅₃	—	2	1	no	—
757	Q₈×C₅₃	—	2	1	no	—
758	Q₈×C₅₃	—	2	1	no	—
759	Q₈×C₅₃	—	2	1	no	—
760	Q₈×C₅₃	—	2	1	no	—
761	Q₈×C₅₃	—	2	1	no	—
762	Q₈×C₅₃	—	2	1	no	—
763	Q₈×C₅₃	—	2	1	no	—
764	Q₈×C₅₃	—	4	1	no	—
765	Q₈×C₅₃	—	4	2	no	—
766	Q₈×C₅₃	—	4	2	no	—
767	Q₈×C₅₃	—	4	2	no	—
768	Q₈×C₅₃	—	4	2	no	—
769	Q₈×C₅₃	—	8	1	no	—
770	Q₈×C₅₃	—	8	1	no	—
771	Q₈×C₅₃	—	8	1	no	—
772	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
773	D₄×C₅₃	—	2	4	no	—
774	D₄×C₅₃	—	2	1	no	—
775	D₄×C₅₃	—	2	1	no	—
776	D₄×C₅₃	—	2	1	no	—
777	D₄×C₅₃	—	2	1	no	—
778	D₄×C₅₃	—	2	1	no	—
779	D₄×C₅₃	—	2	1	no	—
780	D₄×C₅₃	—	2	1	no	—
781	D₄×C₅₃	—	4	1	no	—
782	D₄×C₅₃	—	4	1	no	—
783	D₄×C₅₃	—	4	1	no	—
784	D₄×C₅₃	—	4	1	no	—
785	D₄×C₅₃	—	4	1	no	—
786	D₄×C₅₃	—	4	1	no	—
787	D₄×C₅₃	—	4	1	no	—
788	D₄×C₅₃	—	4	2	no	—
789	D₄×C₅₃	—	4	2	no	—
790	D₄×C₅₃	—	4	2	no	—
791	D₄×C₅₃	—	4	2	no	—
792	D₄×C₅₃	—	4	2	no	—
793	D₄×C₅₃	—	4	2	no	—
794	D₄×C₅₃	—	8	1	no	—
795	D₄×C₅₃	—	8	1	no	—
796	D₄×C₅₃	—	8	1	no	—
797	D₄×C₅₃	—	8	1	no	—
798	D₄×C₅₃	—	8	1	no	—
799	D₄×C₅₃	—	8	1	no	—
800	D₄×C₅₃	—	8	1	no	—
801	D₄×C₅₃	—	8	1	no	—
802	D₄×C₅₃	—	8	1	no	—
803	D₄×C₅₃	—	8	1	no	—
804	D₄×C₅₃	—	8	1	no	—
805	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
806	C₂×C₄×C₅₃	—	2	4	no	—
807	C₂×C₄×C₅₃	—	2	1	no	—
808	C₂×C₄×C₅₃	—	2	1	no	—
809	C₂×C₄×C₅₃	—	2	1	no	—
810	C₂×C₄×C₅₃	—	2	1	no	—
811	C₂×C₄×C₅₃	—	2	1	no	—
812	C₂×C₄×C₅₃	—	2	1	no	—
813	C₂×C₄×C₅₃	—	2	1	no	—
814	C₂×C₄×C₅₃	—	2	1	no	—
815	C₂×C₄×C₅₃	—	2	1	no	—
816	C₂×C₄×C₅₃	—	2	1	no	—
817	C₂×C₄×C₅₃	—	2	1	no	—
818	C₂×C₄×C₅₃	—	2	1	no	—
819	C₂×C₄×C₅₃	—	2	1	no	—
820	C₂×C₄×C₅₃	—	2	1	no	—
821	C₂×C₄×C₅₃	—	2	1	no	—
822	C₂×C₄×C₅₃	—	2	1	no	—
823	C₂×C₄×C₅₃	—	2	1	no	—
824	C₂×C₄×C₅₃	—	2	1	no	—
825	C₂×C₄×C₅₃	—	2	1	no	—
826	C₂×C₄×C₅₃	—	2	1	no	—
827	C₂×C₄×C₅₃	—	2	1	no	—
828	C₂×C₄×C₅₃	—	2	1	no	—
829	C₂×C₄×C₅₃	—	4	1	no	—
830	C₂×C₄×C₅₃	—	4	1	no	—
831	C₂×C₄×C₅₃	—	4	1	no	—
832	C₂×C₄×C₅₃	—	4	2	no	—
833	C₂×C₄×C₅₃	—	4	2	no	—
834	C₂×C₄×C₅₃	—	4	2	no	—
835	C₂×C₄×C₅₃	—	4	2	no	—
836	C₂×C₄×C₅₃	—	4	2	no	—
837	C₂×C₄×C₅₃	—	4	2	no	—
838	C₂×C₄×C₅₃	—	4	2	no	—
839	C₂×C₄×C₅₃	—	4	2	no	—
840	C₂×C₄×C₅₃	—	4	2	no	—
841	C₂×C₄×C₅₃	—	8	1	no	—
842	C₂×C₄×C₅₃	—	8	1	no	—
843	C₂×C₄×C₅₃	—	8	1	no	—
844	C₂×C₄×C₅₃	—	8	1	no	—
845	C₂×C₄×C₅₃	—	8	1	no	—
846	C₂×C₄×C₅₃	—	8	1	no	—
847	C₂×C₄×C₅₃	—	8	1	no	—
848	C₂×C₄×C₅₃	—	8	1	no	—
849	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
850	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
851	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
852	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
853	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
854	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
855	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
856	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
857	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
858	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
859	C₈×C₅₃	—	2	1	no	—
860	C₈×C₅₃	—	2	1	no	—
861	C₈×C₅₃	—	2	1	no	—
862	C₈×C₅₃	—	2	1	no	—
863	C₈×C₅₃	—	2	1	no	—
864	C₈×C₅₃	—	2	1	no	—
865	C₈×C₅₃	—	2	1	no	—
866	C₈×C₅₃	—	2	1	no	—
867	#61627	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
868	C₂²×C₅₃	—	2	1	no	—
869	C₂²×C₅₃	—	2	1	no	—
870	C₂²×C₅₃	—	2	1	no	—
871	C₂²×C₅₃	—	2	1	no	—
872	C₂²×C₅₃	—	2	1	no	—
873	C₂²×C₅₃	—	2	1	no	—
874	C₂²×C₅₃	—	2	1	no	—
875	C₂²×C₅₃	—	2	1	no	—
876	C₂²×C₅₃	—	2	1	no	—
877	C₂²×C₅₃	—	2	1	no	—
878	C₂²×C₅₃	—	2	1	no	—
879	C₂²×C₅₃	—	2	2	no	—
880	C₂²×C₅₃	—	2	1	no	—
881	C₂²×C₅₃	—	2	1	no	—
882	C₂²×C₅₃	—	2	1	no	—
883	C₂²×C₅₃	—	2	1	no	—
884	C₂²×C₅₃	—	4	1	no	—
885	C₂²×C₅₃	—	4	1	no	—
886	C₂²×C₅₃	—	4	1	no	—
887	C₂²×C₅₃	—	4	1	no	—
888	C₂²×C₅₃	—	4	1	no	—
889	C₂²×C₅₃	—	4	1	no	—
890	C₂²×C₅₃	—	4	1	no	—
891	C₂²×C₅₃	—	4	1	no	—
892	C₂²×C₅₃	—	4	1	no	—
893	C₂²×C₅₃	—	4	1	no	—
894	C₂²×C₅₃	—	4	1	no	—
895	C₂²×C₅₃	—	8	2	no	—
896	C₂²×C₅₃	—	8	4	no	—
897	C₂²×C₅₃	—	16	2	no	—
898	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
899	C₄×C₅₃	—	2	1	no	—
900	C₄×C₅₃	—	2	1	no	—
901	C₄×C₅₃	—	2	1	no	—
902	C₄×C₅₃	—	2	1	no	—
903	C₄×C₅₃	—	2	1	no	—
904	C₄×C₅₃	—	2	2	no	—
905	C₄×C₅₃	—	2	1	no	—
906	C₄×C₅₃	—	2	1	no	—
907	C₄×C₅₃	—	2	1	no	—
908	C₄×C₅₃	—	2	1	no	—
909	C₄×C₅₃	—	4	1	no	—
910	C₄×C₅₃	—	4	1	no	—
911	C₄×C₅₃	—	4	1	no	—
912	C₄×C₅₃	—	4	1	no	—
913	C₄×C₅₃	—	4	1	no	—
914	C₄×C₅₃	—	4	1	no	—
915	C₄×C₅₃	—	4	1	no	—
916	C₄×C₅₃	—	4	1	no	—
917	C₄×C₅₃	—	4	1	no	—
918	C₄×C₅₃	—	4	1	no	—
919	C₄×C₅₃	—	4	1	no	—
920	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
921	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
922	#3540	C₂×C₅₃	1	1	yes	characteristic, complemented
923	#3489	C₂×C₅₃	1	1	yes	characteristic, complemented
924	#3329	C₂×C₅₃	1	1	yes	characteristic, complemented
925	#3328	C₂×C₅₃	1	1	yes	characteristic, complemented
926	#3321	C₂×C₅₃	1	1	yes	characteristic, complemented
927	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
928	#3313	C₂×C₅₃	1	1	yes	characteristic, complemented
929	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
930	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
931	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
932	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
933	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
934	#3275	C₂×C₅₃	1	1	yes	characteristic, complemented
935	#3273	C₂×C₅₃	1	1	yes	characteristic, complemented
936	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
937	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
938	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
939	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
940	#3225	C₂×C₅₃	1	1	yes	characteristic, complemented
941	#3225	C₂×C₅₃	1	1	yes	characteristic, complemented
942	#3201	C₂×C₅₃	1	1	yes	characteristic, complemented
943	#3198	C₂×C₅₃	1	1	yes	characteristic, complemented
944	#3196	C₂×C₅₃	1	1	yes	characteristic, complemented
945	#3190	C₂×C₅₃	1	1	yes	characteristic, complemented
946	#3125	C₂×C₅₃	1	1	yes	characteristic, complemented
947	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
948	#3011	C₂×C₅₃	1	1	yes	characteristic, complemented
949	#3010	C₂×C₅₃	1	1	yes	characteristic, complemented
950	#3005	C₂×C₅₃	1	1	yes	characteristic, complemented
951	#3002	C₂×C₅₃	1	1	yes	characteristic, complemented
952	#2976	C₂×C₅₃	1	1	yes	characteristic, complemented
953	C₂×C₅₃	—	4	1	no	—
954	C₂×C₅₃	—	4	1	no	—
955	C₂×C₅₃	—	4	1	no	—
956	C₂×C₅₃	—	4	1	no	—
957	C₂×C₅₃	—	4	1	no	—
958	C₂×C₅₃	—	4	2	no	—
959	C₂×C₅₃	—	8	1	no	—
960	C₂×C₅₃	—	8	1	no	—
961	C₂×C₅₃	—	8	1	no	—
962	C₂×C₅₃	#3484	1	1	yes	characteristic
963	C₂×C₅₃	#3584	1	1	yes	characteristic
964	C₂×C₅₃	#3586	1	1	yes	characteristic
965	C₂×2₋¹⁺⁴	C₂²×C₅₃	1	1	yes	characteristic
966	C₂²×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
968	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
970	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
972	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
973	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	H(3,𝔽₄)	—	2	1	no	—
976	#560	—	2	1	no	—
977	#559	—	2	1	no	—
978	#556	C₂²×C₅₃	1	1	yes	characteristic
979	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#555	C₂²×C₅₃	1	1	yes	characteristic
981	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#551	—	2	1	no	—
983	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
984	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#548	C₂²×C₅₃	1	1	yes	characteristic
986	#548	C₂²×C₅₃	1	1	yes	characteristic
987	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#547	—	2	1	no	—
990	#547	—	2	1	no	—
991	#547	C₂²×C₅₃	1	1	yes	characteristic
992	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#546	—	2	1	no	—
994	#546	—	2	1	no	—
995	#546	C₂²×C₅₃	1	1	yes	characteristic
996	#546	C₂²×C₅₃	1	1	yes	characteristic
997	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#542	—	2	1	no	—
1000	#542	—	2	1	no	—
1001	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#538	—	2	1	no	—
1004	#538	—	2	1	no	—
1005	#537	—	2	1	no	—
1006	#537	C₂²×C₅₃	1	1	yes	characteristic
1007	#536	—	2	1	no	—
1008	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#536	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#535	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#525	—	2	1	no	—
1012	#525	C₂²×C₅₃	1	1	yes	characteristic
1013	#525	C₂²×C₅₃	1	1	yes	characteristic
1014	#525	C₂²×C₅₃	1	1	yes	characteristic
1015	C₂×C₂²⋊Q₈	—	2	1	no	—
1016	C₂×C₂²⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#468	C₂²×C₅₃	1	1	yes	characteristic
1047	#468	C₂²×C₅₃	1	1	yes	characteristic
1048	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#452	C₂²×C₅₃	1	1	yes	characteristic
1071	#452	C₂²×C₅₃	1	1	yes	characteristic
1072	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#449	C₂²×C₅₃	1	1	yes	characteristic
1091	#449	C₂²×C₅₃	1	1	yes	characteristic
1092	#449	C₂²×C₅₃	1	1	yes	characteristic
1093	#449	C₂²×C₅₃	1	1	yes	characteristic
1094	#449	C₂²×C₅₃	1	1	yes	characteristic
1095	#449	C₂²×C₅₃	1	1	yes	characteristic
1096	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	#448	C₂²×C₅₃	1	1	yes	characteristic
1099	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	#447	C₂²×C₅₃	1	1	yes	characteristic
1105	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1106	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1107	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1108	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1109	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1110	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1111	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1112	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1113	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1114	#436	C₂²×C₅₃	1	1	yes	characteristic
1115	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1116	#435	C₂²×C₅₃	1	1	yes	characteristic
1117	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1118	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1119	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1120	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1121	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1122	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1123	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1124	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1125	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1126	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1127	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1128	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1129	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1130	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1131	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1132	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1133	#408	C₂²×C₅₃	1	1	yes	characteristic, complemented
1134	#407	C₂²×C₅₃	1	1	yes	characteristic, complemented
1135	C₂×C₂²⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1136	C₅₃	#61627	1	1	yes	characteristic, direct product factor, Sylow
1137	2₋¹⁺⁴	—	4	2	no	—
1138	2₋¹⁺⁴	—	4	2	no	—
1139	C₂×#41	—	2	1	no	—
1140	C₂×#41	—	2	1	no	—
1141	C₂×#41	—	2	1	no	—
1142	C₂×#41	—	2	1	no	—
1143	C₂×#41	—	2	1	no	—
1144	C₂×#41	—	4	2	no	—
1145	C₂×#41	—	4	2	no	—
1146	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1150	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂²×Q₈	—	2	1	no	—
1156	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1157	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1158	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1159	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1160	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1161	C₂²×D₄	—	2	1	no	—
1162	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1163	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1164	C₂³×C₄	—	2	1	no	—
1165	C₂³×C₄	C₂³×C₅₃	1	1	yes	characteristic
1166	#137	—	4	2	no	—
1167	#137	—	4	2	no	—
1168	AGL(1,ℤ/8)	—	4	2	no	—
1169	AGL(1,ℤ/8)	—	4	2	no	—
1170	#135	—	4	2	no	—
1171	#135	—	4	2	no	—
1172	C₂×Q₁₆	—	4	2	no	—
1173	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1179	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1180	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1181	C₂×SD₁₆	—	4	2	no	—
1182	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1183	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1184	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1185	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1186	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1187	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1188	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1189	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1190	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1191	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1192	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1193	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1194	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1195	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1196	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1197	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1199	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1200	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1201	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1206	C₄⋊Q₈	—	2	1	no	—
1207	C₄⋊Q₈	—	2	1	no	—
1208	C₄⋊Q₈	—	2	1	no	—
1209	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1210	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1211	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1212	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1213	#127	—	2	1	no	—
1214	#126	—	2	1	no	—
1215	#126	—	2	1	no	—
1216	#126	—	2	1	no	—
1217	#126	—	2	1	no	—
1218	#126	—	2	1	no	—
1219	#126	—	2	1	no	—
1220	#124	—	2	1	no	—
1221	#124	—	2	1	no	—
1222	#124	—	2	1	no	—
1223	#124	—	2	1	no	—
1224	#124	—	2	1	no	—
1225	#124	—	2	1	no	—
1226	#124	—	2	1	no	—
1227	#124	—	2	1	no	—
1228	#124	—	2	1	no	—
1229	#124	—	2	1	no	—
1230	#124	—	2	1	no	—
1231	#124	—	2	1	no	—
1232	#124	—	2	1	no	—
1233	#124	—	2	1	no	—
1234	#124	C₂³×C₅₃	1	1	yes	characteristic
1235	#124	C₂³×C₅₃	1	1	yes	characteristic
1236	#124	C₂³×C₅₃	1	1	yes	characteristic
1237	#124	C₂³×C₅₃	1	1	yes	characteristic
1238	#123	—	2	1	no	—
1239	#123	—	2	1	no	—
1240	#123	—	2	1	no	—
1241	#123	—	2	1	no	—
1242	#123	—	2	1	no	—
1243	#123	—	2	1	no	—
1244	#123	—	2	1	no	—
1245	#123	—	2	1	no	—
1246	#123	—	2	1	no	—
1247	#123	—	2	1	no	—
1248	#123	—	2	1	no	—
1249	#123	—	2	1	no	—
1250	#123	—	2	1	no	—
1251	#123	—	2	1	no	—
1252	#123	—	2	1	no	—
1253	#123	—	2	1	no	—
1254	#123	D₄×C₅₃	1	1	yes	characteristic
1255	#123	D₄×C₅₃	1	1	yes	characteristic
1256	C₂²⋊Q₈	—	2	1	no	—
1257	C₂²⋊Q₈	—	2	1	no	—
1258	C₂²⋊Q₈	—	2	1	no	—
1259	C₂²⋊Q₈	—	2	1	no	—
1260	C₂²⋊Q₈	—	2	1	no	—
1261	C₂²⋊Q₈	—	2	1	no	—
1262	C₂²⋊Q₈	—	2	1	no	—
1263	C₂²⋊Q₈	—	2	1	no	—
1264	C₂²⋊Q₈	—	2	1	no	—
1265	C₂²⋊Q₈	—	2	1	no	—
1266	C₂²⋊Q₈	—	2	1	no	—
1267	C₂²⋊Q₈	—	2	1	no	—
1268	C₂²⋊Q₈	—	2	1	no	—
1269	C₂²⋊Q₈	—	2	1	no	—
1270	C₂²⋊Q₈	—	2	1	no	—
1271	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1272	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1273	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1274	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1275	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1276	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1277	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1278	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1279	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1280	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1281	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1282	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1283	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1284	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1285	#121	—	2	1	no	—
1286	#121	—	2	1	no	—
1287	#121	—	2	1	no	—
1288	#121	—	2	1	no	—
1289	#121	—	2	1	no	—
1290	#121	—	2	1	no	—
1291	#121	—	2	1	no	—
1292	#121	—	2	1	no	—
1293	#121	—	2	1	no	—
1294	#121	—	2	1	no	—
1295	#121	—	2	1	no	—
1296	#121	—	2	1	no	—
1297	#121	—	2	1	no	—
1298	#121	—	2	1	no	—
1299	#121	—	2	1	no	—
1300	#121	D₄×C₅₃	1	1	yes	characteristic
1301	#121	D₄×C₅₃	1	1	yes	characteristic
1302	#121	C₂³×C₅₃	1	1	yes	characteristic
1303	#121	C₂³×C₅₃	1	1	yes	characteristic
1304	#121	C₂³×C₅₃	1	1	yes	characteristic
1305	#121	C₂³×C₅₃	1	1	yes	characteristic
1306	#121	C₂³×C₅₃	1	1	yes	characteristic
1307	#121	C₂³×C₅₃	1	1	yes	characteristic
1308	#121	C₂³×C₅₃	1	1	yes	characteristic
1309	#121	C₂³×C₅₃	1	1	yes	characteristic
1310	#120	—	2	1	no	—
1311	#120	—	2	1	no	—
1312	#120	—	2	1	no	—
1313	#120	—	2	1	no	—
1314	#120	—	2	1	no	—
1315	#120	—	2	1	no	—
1316	#120	—	2	1	no	—
1317	#120	—	2	1	no	—
1318	#120	D₄×C₅₃	1	1	yes	characteristic
1319	#120	D₄×C₅₃	1	1	yes	characteristic
1320	C₄×Q₈	—	2	1	no	—
1321	C₄×Q₈	—	2	1	no	—
1322	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1323	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1324	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1325	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1326	C₄×D₄	—	2	1	no	—
1327	C₄×D₄	—	2	1	no	—
1328	C₄×D₄	—	2	1	no	—
1329	C₄×D₄	—	2	1	no	—
1330	C₄×D₄	—	2	1	no	—
1331	C₄×D₄	—	2	1	no	—
1332	C₄×D₄	—	2	1	no	—
1333	C₄×D₄	—	2	1	no	—
1334	C₄×D₄	—	2	1	no	—
1335	C₄×D₄	—	2	1	no	—
1336	C₄×D₄	—	2	1	no	—
1337	C₄×D₄	—	2	1	no	—
1338	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1339	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1340	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1341	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1342	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1343	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1344	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1345	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1346	#117	—	2	1	no	—
1347	#117	—	2	1	no	—
1348	#117	—	2	1	no	—
1349	#117	C₂³×C₅₃	1	1	yes	characteristic
1350	#117	C₂³×C₅₃	1	1	yes	characteristic
1351	#117	C₂³×C₅₃	1	1	yes	characteristic
1352	#117	C₂³×C₅₃	1	1	yes	characteristic
1353	#117	C₂³×C₅₃	1	1	yes	characteristic
1354	C₂×C₄⋊C₄	—	2	1	no	—
1355	C₂×C₄⋊C₄	—	2	1	no	—
1356	C₂×C₄⋊C₄	—	2	1	no	—
1357	C₂×C₄⋊C₄	—	2	1	no	—
1358	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1359	C₂×C₂²⋊C₄	—	2	1	no	—
1360	C₂×C₂²⋊C₄	—	2	1	no	—
1361	C₂×C₂²⋊C₄	—	2	1	no	—
1362	C₂×C₂²⋊C₄	—	2	1	no	—
1363	C₂×C₂²⋊C₄	—	2	1	no	—
1364	#107	C₂³×C₅₃	1	1	yes	characteristic
1365	#107	C₂³×C₅₃	1	1	yes	characteristic
1366	#107	C₂³×C₅₃	1	1	yes	characteristic
1367	#107	C₂³×C₅₃	1	1	yes	characteristic
1368	#106	C₂³×C₅₃	1	1	yes	characteristic
1369	#106	C₂³×C₅₃	1	1	yes	characteristic
1370	#106	C₂³×C₅₃	1	1	yes	characteristic
1371	#106	C₂³×C₅₃	1	1	yes	characteristic
1372	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1373	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1374	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1375	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1376	#103	C₂³×C₅₃	1	1	yes	characteristic
1377	#103	C₂³×C₅₃	1	1	yes	characteristic
1378	#103	C₂³×C₅₃	1	1	yes	characteristic
1379	#103	C₂³×C₅₃	1	1	yes	characteristic
1380	#103	C₂³×C₅₃	1	1	yes	characteristic
1381	#103	C₂³×C₅₃	1	1	yes	characteristic
1382	#103	C₂³×C₅₃	1	1	yes	characteristic
1383	#103	C₂³×C₅₃	1	1	yes	characteristic
1384	#103	C₂³×C₅₃	1	1	yes	characteristic
1385	#103	C₂³×C₅₃	1	1	yes	characteristic
1386	#103	C₂³×C₅₃	1	1	yes	characteristic
1387	#103	C₂³×C₅₃	1	1	yes	characteristic
1388	#103	C₂³×C₅₃	1	1	yes	characteristic
1389	#103	C₂³×C₅₃	1	1	yes	characteristic
1390	#103	C₂³×C₅₃	1	1	yes	characteristic
1391	#103	C₂³×C₅₃	1	1	yes	characteristic
1392	#103	C₂³×C₅₃	1	1	yes	characteristic
1393	#103	C₂³×C₅₃	1	1	yes	characteristic
1394	#103	C₂³×C₅₃	1	1	yes	characteristic
1395	#103	C₂³×C₅₃	1	1	yes	characteristic
1396	#102	C₂³×C₅₃	1	1	yes	characteristic
1397	#102	C₂³×C₅₃	1	1	yes	characteristic
1398	#102	C₂³×C₅₃	1	1	yes	characteristic
1399	#102	C₂³×C₅₃	1	1	yes	characteristic
1400	#102	C₂³×C₅₃	1	1	yes	characteristic
1401	#102	C₂³×C₅₃	1	1	yes	characteristic
1402	#102	C₂³×C₅₃	1	1	yes	characteristic
1403	#102	C₂³×C₅₃	1	1	yes	characteristic
1404	#102	C₂³×C₅₃	1	1	yes	characteristic
1405	#102	C₂³×C₅₃	1	1	yes	characteristic
1406	#102	C₂³×C₅₃	1	1	yes	characteristic
1407	#102	C₂³×C₅₃	1	1	yes	characteristic
1408	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1409	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1410	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1411	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1412	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1413	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1414	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1415	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1416	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1417	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1418	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1419	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1420	#97	C₂³×C₅₃	1	1	yes	characteristic
1421	#97	C₂³×C₅₃	1	1	yes	characteristic
1422	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1423	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1424	C₂⁴	—	2	1	no	—
1425	C₂⁴	—	2	1	no	—
1426	C₂⁴	C₂×D₄×C₅₃	1	1	yes	characteristic
1427	#41	—	2	2	no	—
1428	#41	—	2	2	no	—
1429	#41	—	2	2	no	—
1430	#41	—	2	2	no	—
1431	#41	—	2	2	no	—
1432	#41	—	2	2	no	—
1433	#41	—	4	1	no	—
1434	#41	—	4	1	no	—
1435	#41	—	4	1	no	—
1436	#41	—	4	1	no	—
1437	#41	—	4	1	no	—
1438	#41	—	4	1	no	—
1439	#41	—	4	1	no	—
1440	#41	—	4	1	no	—
1441	#41	—	4	4	no	—
1442	#41	—	4	4	no	—
1443	#41	—	4	1	no	—
1444	#41	—	4	1	no	—
1445	#41	—	4	1	no	—
1446	#41	—	4	1	no	—
1447	#41	—	4	4	no	—
1448	#41	—	4	4	no	—
1449	#41	—	4	4	no	—
1450	C₂×Q₈	—	2	1	no	—
1451	C₂×Q₈	—	2	1	no	—
1452	C₂×Q₈	—	2	1	no	—
1453	C₂×Q₈	—	2	1	no	—
1454	C₂×Q₈	—	2	1	no	—
1455	C₂×Q₈	—	2	1	no	—
1456	C₂×Q₈	—	2	1	no	—
1457	C₂×Q₈	—	2	2	no	—
1458	C₂×Q₈	—	2	2	no	—
1459	C₂×Q₈	—	2	2	no	—
1460	C₂×Q₈	—	4	1	no	—
1461	C₂×Q₈	—	4	1	no	—
1462	C₂×Q₈	—	4	1	no	—
1463	C₂×Q₈	—	4	1	no	—
1464	C₂×Q₈	—	4	1	no	—
1465	C₂×Q₈	—	4	4	no	—
1466	C₂×Q₈	—	4	1	no	—
1467	C₂×Q₈	—	4	1	no	—
1468	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1469	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1470	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1471	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1472	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1473	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1474	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1475	C₂×D₄	—	2	1	no	—
1476	C₂×D₄	—	2	2	no	—
1477	C₂×D₄	—	2	1	no	—
1478	C₂×D₄	—	2	1	no	—
1479	C₂×D₄	—	2	1	no	—
1480	C₂×D₄	—	2	1	no	—
1481	C₂×D₄	—	2	1	no	—
1482	C₂×D₄	—	2	1	no	—
1483	C₂×D₄	—	2	1	no	—
1484	C₂×D₄	—	2	1	no	—
1485	C₂×D₄	—	2	1	no	—
1486	C₂×D₄	—	2	1	no	—
1487	C₂×D₄	—	2	1	no	—
1488	C₂×D₄	—	2	1	no	—
1489	C₂×D₄	—	2	1	no	—
1490	C₂×D₄	—	2	1	no	—
1491	C₂×D₄	—	2	1	no	—
1492	C₂×D₄	—	2	1	no	—
1493	C₂×D₄	—	2	1	no	—
1494	C₂×D₄	—	4	1	no	—
1495	C₂×D₄	—	4	1	no	—
1496	C₂×D₄	—	4	1	no	—
1497	C₂×D₄	—	4	4	no	—
1498	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1499	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1500	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1501	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1502	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1503	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1504	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1505	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1506	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1507	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1508	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	4	1	no	—
1528	C₂²×C₄	—	4	1	no	—
1529	C₂²×C₄	—	4	4	no	—
1530	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1531	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1532	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1533	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1534	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1535	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1536	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1537	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1538	Q₁₆	—	2	2	no	—
1539	Q₁₆	—	2	2	no	—
1540	Q₁₆	—	4	1	no	—
1541	Q₁₆	—	4	1	no	—
1542	Q₁₆	—	4	1	no	—
1543	Q₁₆	—	4	1	no	—
1544	Q₁₆	—	4	1	no	—
1545	Q₁₆	—	4	1	no	—
1546	SD₁₆	—	2	2	no	—
1547	SD₁₆	—	2	2	no	—
1548	SD₁₆	—	2	2	no	—
1549	SD₁₆	—	2	2	no	—
1550	SD₁₆	—	4	1	no	—
1551	SD₁₆	—	4	1	no	—
1552	SD₁₆	—	4	1	no	—
1553	SD₁₆	—	4	1	no	—
1554	SD₁₆	—	4	1	no	—
1555	SD₁₆	—	4	1	no	—
1556	SD₁₆	—	4	1	no	—
1557	SD₁₆	—	4	1	no	—
1558	D₈	—	2	2	no	—
1559	D₈	—	2	2	no	—
1560	D₈	—	4	1	no	—
1561	D₈	—	4	1	no	—
1562	M₁₆	—	4	1	no	—
1563	M₁₆	—	4	1	no	—
1564	M₁₆	—	4	1	no	—
1565	M₁₆	—	4	1	no	—
1566	C₂×C₈	—	4	1	no	—
1567	C₂×C₈	—	4	1	no	—
1568	C₂×C₈	—	4	1	no	—
1569	C₂×C₈	—	4	1	no	—
1570	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1571	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1572	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1573	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1574	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1575	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1576	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1577	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1578	C₄⋊C₄	—	2	1	no	—
1579	C₄⋊C₄	—	2	1	no	—
1580	C₄⋊C₄	—	2	1	no	—
1581	C₄⋊C₄	—	2	1	no	—
1582	C₄⋊C₄	—	2	1	no	—
1583	C₄⋊C₄	—	2	1	no	—
1584	C₄⋊C₄	—	2	1	no	—
1585	C₄⋊C₄	—	2	1	no	—
1586	C₄⋊C₄	—	2	1	no	—
1587	C₄⋊C₄	—	2	1	no	—
1588	C₄⋊C₄	—	2	1	no	—
1589	C₄⋊C₄	—	2	1	no	—
1590	C₄⋊C₄	—	2	1	no	—
1591	C₄⋊C₄	—	2	1	no	—
1592	C₄⋊C₄	—	2	1	no	—
1593	C₄⋊C₄	—	2	1	no	—
1594	C₄⋊C₄	—	2	1	no	—
1595	C₄⋊C₄	—	2	1	no	—
1596	C₄⋊C₄	—	2	1	no	—
1597	C₄⋊C₄	—	2	1	no	—
1598	C₄⋊C₄	—	2	1	no	—
1599	C₄⋊C₄	—	2	1	no	—
1600	C₄⋊C₄	—	2	1	no	—
1601	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1602	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1603	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1604	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1605	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1606	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1607	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1608	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1609	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1610	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1611	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1612	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1613	C₂²⋊C₄	—	2	1	no	—
1614	C₂²⋊C₄	—	2	1	no	—
1615	C₂²⋊C₄	—	2	1	no	—
1616	C₂²⋊C₄	—	2	1	no	—
1617	C₂²⋊C₄	—	2	1	no	—
1618	C₂²⋊C₄	—	2	1	no	—
1619	C₂²⋊C₄	—	2	1	no	—
1620	C₂²⋊C₄	—	2	1	no	—
1621	C₂²⋊C₄	—	2	1	no	—
1622	C₂²⋊C₄	—	2	1	no	—
1623	C₂²⋊C₄	—	2	1	no	—
1624	C₂²⋊C₄	—	2	1	no	—
1625	C₂²⋊C₄	—	2	1	no	—
1626	C₂²⋊C₄	—	2	1	no	—
1627	C₂²⋊C₄	—	2	1	no	—
1628	C₂²⋊C₄	—	2	1	no	—
1629	C₂²⋊C₄	—	2	1	no	—
1630	C₂²⋊C₄	—	2	1	no	—
1631	C₂²⋊C₄	—	2	1	no	—
1632	C₂²⋊C₄	—	2	1	no	—
1633	C₂²⋊C₄	—	2	1	no	—
1634	C₂²⋊C₄	—	2	1	no	—
1635	C₂²⋊C₄	—	2	1	no	—
1636	C₂²⋊C₄	—	2	1	no	—
1637	C₂²⋊C₄	—	2	1	no	—
1638	C₂²⋊C₄	—	2	1	no	—
1639	C₂²⋊C₄	—	2	1	no	—
1640	C₂²⋊C₄	—	2	1	no	—
1641	C₂²⋊C₄	—	2	1	no	—
1642	C₂²⋊C₄	—	2	1	no	—
1643	C₂²⋊C₄	—	2	1	no	—
1644	C₂²⋊C₄	—	2	1	no	—
1645	C₂²⋊C₄	—	2	1	no	—
1646	C₂²⋊C₄	—	2	1	no	—
1647	C₂²⋊C₄	—	2	1	no	—
1648	C₂²⋊C₄	—	2	1	no	—
1649	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1650	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1651	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1652	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1653	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1654	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1655	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1656	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1657	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1658	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1659	C₄²	—	2	1	no	—
1660	C₄²	—	2	1	no	—
1661	C₄²	—	2	1	no	—
1662	C₄²	—	2	1	no	—
1663	C₄²	—	2	1	no	—
1664	C₄²	—	2	1	no	—
1665	C₄²	—	2	1	no	—
1666	C₄²	—	2	1	no	—
1667	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1668	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1669	C₂³	—	2	1	no	—
1670	C₂³	—	2	1	no	—
1671	C₂³	—	2	1	no	—
1672	C₂³	—	2	1	no	—
1673	C₂³	—	4	1	no	—
1674	C₂³	—	4	1	no	—
1675	C₂³	—	4	1	no	—
1676	C₂³	—	4	2	no	—
1677	C₂³	—	4	2	no	—
1678	C₂³	—	8	1	no	—
1679	C₂³	—	8	1	no	—
1680	C₂³	—	8	1	no	—
1681	C₂³	—	8	1	no	—
1682	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1683	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1684	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1685	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1686	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1687	Q₈	—	2	1	no	—
1688	Q₈	—	2	1	no	—
1689	Q₈	—	2	1	no	—
1690	Q₈	—	2	1	no	—
1691	Q₈	—	2	1	no	—
1692	Q₈	—	2	1	no	—
1693	Q₈	—	2	1	no	—
1694	Q₈	—	2	1	no	—
1695	Q₈	—	2	1	no	—
1696	Q₈	—	2	1	no	—
1697	Q₈	—	2	1	no	—
1698	Q₈	—	4	1	no	—
1699	Q₈	—	4	2	no	—
1700	Q₈	—	4	2	no	—
1701	Q₈	—	4	2	no	—
1702	Q₈	—	4	2	no	—
1703	Q₈	—	8	1	no	—
1704	Q₈	—	8	1	no	—
1705	Q₈	—	8	1	no	—
1706	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1707	D₄	—	2	4	no	—
1708	D₄	—	2	1	no	—
1709	D₄	—	2	1	no	—
1710	D₄	—	2	1	no	—
1711	D₄	—	2	1	no	—
1712	D₄	—	2	1	no	—
1713	D₄	—	2	1	no	—
1714	D₄	—	2	1	no	—
1715	D₄	—	4	1	no	—
1716	D₄	—	4	1	no	—
1717	D₄	—	4	1	no	—
1718	D₄	—	4	1	no	—
1719	D₄	—	4	1	no	—
1720	D₄	—	4	1	no	—
1721	D₄	—	4	1	no	—
1722	D₄	—	4	2	no	—
1723	D₄	—	4	2	no	—
1724	D₄	—	4	2	no	—
1725	D₄	—	4	2	no	—
1726	D₄	—	4	2	no	—
1727	D₄	—	4	2	no	—
1728	D₄	—	8	1	no	—
1729	D₄	—	8	1	no	—
1730	D₄	—	8	1	no	—
1731	D₄	—	8	1	no	—
1732	D₄	—	8	1	no	—
1733	D₄	—	8	1	no	—
1734	D₄	—	8	1	no	—
1735	D₄	—	8	1	no	—
1736	D₄	—	8	1	no	—
1737	D₄	—	8	1	no	—
1738	D₄	—	8	1	no	—
1739	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1740	C₂×C₄	—	2	4	no	—
1741	C₂×C₄	—	2	1	no	—
1742	C₂×C₄	—	2	1	no	—
1743	C₂×C₄	—	2	1	no	—
1744	C₂×C₄	—	2	1	no	—
1745	C₂×C₄	—	2	1	no	—
1746	C₂×C₄	—	2	1	no	—
1747	C₂×C₄	—	2	1	no	—
1748	C₂×C₄	—	2	1	no	—
1749	C₂×C₄	—	2	1	no	—
1750	C₂×C₄	—	2	1	no	—
1751	C₂×C₄	—	2	1	no	—
1752	C₂×C₄	—	2	1	no	—
1753	C₂×C₄	—	2	1	no	—
1754	C₂×C₄	—	2	1	no	—
1755	C₂×C₄	—	2	1	no	—
1756	C₂×C₄	—	2	1	no	—
1757	C₂×C₄	—	2	1	no	—
1758	C₂×C₄	—	2	1	no	—
1759	C₂×C₄	—	2	1	no	—
1760	C₂×C₄	—	2	1	no	—
1761	C₂×C₄	—	2	1	no	—
1762	C₂×C₄	—	2	1	no	—
1763	C₂×C₄	—	4	1	no	—
1764	C₂×C₄	—	4	1	no	—
1765	C₂×C₄	—	4	1	no	—
1766	C₂×C₄	—	4	2	no	—
1767	C₂×C₄	—	4	2	no	—
1768	C₂×C₄	—	4	2	no	—
1769	C₂×C₄	—	4	2	no	—
1770	C₂×C₄	—	4	2	no	—
1771	C₂×C₄	—	4	2	no	—
1772	C₂×C₄	—	4	2	no	—
1773	C₂×C₄	—	4	2	no	—
1774	C₂×C₄	—	4	2	no	—
1775	C₂×C₄	—	8	1	no	—
1776	C₂×C₄	—	8	1	no	—
1777	C₂×C₄	—	8	1	no	—
1778	C₂×C₄	—	8	1	no	—
1779	C₂×C₄	—	8	1	no	—
1780	C₂×C₄	—	8	1	no	—
1781	C₂×C₄	—	8	1	no	—
1782	C₂×C₄	—	8	1	no	—
1783	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1784	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1785	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1786	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1787	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1788	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1789	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1790	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1791	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1792	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1793	C₈	—	2	1	no	—
1794	C₈	—	2	1	no	—
1795	C₈	—	2	1	no	—
1796	C₈	—	2	1	no	—
1797	C₈	—	2	1	no	—
1798	C₈	—	2	1	no	—
1799	C₈	—	2	1	no	—
1800	C₈	—	2	1	no	—
1801	C₂²	—	2	1	no	—
1802	C₂²	—	2	2	no	—
1803	C₂²	—	2	1	no	—
1804	C₂²	—	2	1	no	—
1805	C₂²	—	2	1	no	—
1806	C₂²	—	2	1	no	—
1807	C₂²	—	2	1	no	—
1808	C₂²	—	2	1	no	—
1809	C₂²	—	2	1	no	—
1810	C₂²	—	2	1	no	—
1811	C₂²	—	2	1	no	—
1812	C₂²	—	2	1	no	—
1813	C₂²	—	2	1	no	—
1814	C₂²	—	2	1	no	—
1815	C₂²	—	2	1	no	—
1816	C₂²	—	2	1	no	—
1817	C₂²	—	4	1	no	—
1818	C₂²	—	4	1	no	—
1819	C₂²	—	4	1	no	—
1820	C₂²	—	4	1	no	—
1821	C₂²	—	4	1	no	—
1822	C₂²	—	4	1	no	—
1823	C₂²	—	4	1	no	—
1824	C₂²	—	4	1	no	—
1825	C₂²	—	4	1	no	—
1826	C₂²	—	4	1	no	—
1827	C₂²	—	4	1	no	—
1828	C₂²	—	8	2	no	—
1829	C₂²	—	8	4	no	—
1830	C₂²	—	16	2	no	—
1831	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1832	C₄	—	2	1	no	—
1833	C₄	—	2	2	no	—
1834	C₄	—	2	1	no	—
1835	C₄	—	2	1	no	—
1836	C₄	—	2	1	no	—
1837	C₄	—	2	1	no	—
1838	C₄	—	2	1	no	—
1839	C₄	—	2	1	no	—
1840	C₄	—	2	1	no	—
1841	C₄	—	2	1	no	—
1842	C₄	—	4	1	no	—
1843	C₄	—	4	1	no	—
1844	C₄	—	4	1	no	—
1845	C₄	—	4	1	no	—
1846	C₄	—	4	1	no	—
1847	C₄	—	4	1	no	—
1848	C₄	—	4	1	no	—
1849	C₄	—	4	1	no	—
1850	C₄	—	4	1	no	—
1851	C₄	—	4	1	no	—
1852	C₄	—	4	1	no	—
1853	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1854	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1855	C₂	—	4	1	no	—
1856	C₂	—	4	1	no	—
1857	C₂	—	4	1	no	—
1858	C₂	—	4	1	no	—
1859	C₂	—	4	1	no	—
1860	C₂	—	4	2	no	—
1861	C₂	—	8	1	no	—
1862	C₂	—	8	1	no	—
1863	C₂	—	8	1	no	—
1864	C₂	C₅₃×#3484	1	1	yes	characteristic
1865	C₂	C₅₃×#3584	1	1	yes	characteristic
1866	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×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3540	C₂	semidirect
2. C₅₃×#3489	C₂	semidirect
3. C₅₃×#3329	C₂	semidirect
4. C₅₃×#3328	C₂	semidirect
5. C₅₃×#3321	C₂	semidirect
6. C₅₃×#3319	C₂	semidirect
7. C₅₃×#3313	C₂	semidirect
8. C₅₃×#3311	C₂	semidirect
9. C₅₃×#3303	C₂	semidirect
10. C₅₃×#3302	C₂	semidirect
11. C₅₃×#3285	C₂	semidirect
12. C₅₃×#3282	C₂	semidirect
13. C₅₃×#3275	C₂	semidirect
14. C₅₃×#3273	C₂	semidirect
15. C₅₃×#3270	C₂	semidirect
16. C₅₃×#3269	C₂	semidirect
17. C₅₃×#3267	C₂	semidirect
18. C₅₃×#3266	C₂	semidirect
19. C₅₃×#3225	C₂	semidirect
20. C₅₃×#3225	C₂	semidirect
21. C₅₃×#3201	C₂	semidirect
22. C₅₃×#3198	C₂	semidirect
23. C₅₃×#3196	C₂	semidirect
24. C₅₃×#3190	C₂	semidirect
25. C₅₃×#3125	C₂	semidirect
26. C₅₃×#3124	C₂	semidirect
27. C₅₃×#3011	C₂	semidirect
28. C₅₃×#3010	C₂	semidirect
29. C₅₃×#3005	C₂	semidirect
30. C₅₃×#3002	C₂	semidirect
31. C₅₃×#2976	C₂	semidirect
33. C₂²×#41×C₅₃	C₂²	semidirect
35. C₂×#137×C₅₃	C₂²	semidirect
37. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
40. C₂²×Q₁₆×C₅₃	C₂²	semidirect
41. C₂²×SD₁₆×C₅₃	C₂²	semidirect
46. C₅₃×#556	C₂²	semidirect
48. C₅₃×#555	C₂²	semidirect
51. D₄×Q₈×C₅₃	C₂²	semidirect
54. C₅₃×#548	C₂²	semidirect
55. C₅₃×#548	C₂²	semidirect
59. C₅₃×#547	C₂²	semidirect
64. C₅₃×#546	C₂²	semidirect
65. C₅₃×#546	C₂²	semidirect
68. C₅₃×#542	C₂²	semidirect
69. C₅₃×#542	C₂²	semidirect
75. C₅₃×#536	C₂²	semidirect
76. C₅₃×#536	C₂²	semidirect
77. C₅₃×#535	C₂²	semidirect
83. C₂×C₂²⋊Q₈×C₅₃	C₂²	semidirect
84. C₅₃×#520	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
86. C₅₃×#497	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
88. C₅₃×#495	C₂²	semidirect
89. C₅₃×#489	C₂²	semidirect
90. C₅₃×#489	C₂²	semidirect
91. C₅₃×#487	C₂²	semidirect
92. C₅₃×#487	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#485	C₂²	semidirect
98. C₅₃×#485	C₂²	semidirect
99. C₅₃×#484	C₂²	semidirect
100. C₅₃×#483	C₂²	semidirect
101. C₅₃×#482	C₂²	semidirect
102. C₅₃×#482	C₂²	semidirect
103. C₅₃×#481	C₂²	semidirect
104. C₅₃×#480	C₂²	semidirect
105. C₅₃×#477	C₂²	semidirect
106. C₅₃×#476	C₂²	semidirect
107. C₅₃×#475	C₂²	semidirect
108. C₅₃×#474	C₂²	semidirect
109. C₅₃×#470	C₂²	semidirect
110. C₅₃×#470	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
112. C₅₃×#469	C₂²	semidirect
115. C₅₃×#468	C₂²	semidirect
116. C₅₃×#468	C₂²	semidirect
117. C₅₃×#467	C₂²	semidirect
118. C₅₃×#467	C₂²	semidirect
119. C₅₃×#467	C₂²	semidirect
120. C₅₃×#466	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
123. C₅₃×#465	C₂²	semidirect
124. C₅₃×#465	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#463	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#462	C₂²	semidirect
134. C₅₃×#462	C₂²	semidirect
135. C₅₃×#461	C₂²	semidirect
136. C₅₃×#461	C₂²	semidirect
139. C₅₃×#452	C₂²	semidirect
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
142. C₅₃×#452	C₂²	semidirect
143. C₅₃×#452	C₂²	semidirect
144. C₅₃×#452	C₂²	semidirect
145. C₅₃×#452	C₂²	semidirect
146. C₅₃×#452	C₂²	semidirect
147. C₅₃×#452	C₂²	semidirect
148. C₅₃×#452	C₂²	semidirect
149. C₅₃×#451	C₂²	semidirect
150. C₅₃×#451	C₂²	semidirect
151. C₅₃×#451	C₂²	semidirect
152. C₅₃×#451	C₂²	semidirect
153. C₅₃×#451	C₂²	semidirect
154. C₅₃×#451	C₂²	semidirect
155. C₅₃×#450	C₂²	semidirect
156. C₅₃×#450	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
166. C₅₃×#448	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
168. C₅₃×#448	C₂²	semidirect
169. C₅₃×#448	C₂²	semidirect
170. C₅₃×#448	C₂²	semidirect
172. C₅₃×#447	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#440	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₄×Q₁₆×C₅₃	C₂²	semidirect
178. C₄×SD₁₆×C₅₃	C₂²	semidirect
179. C₄×SD₁₆×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
182. C₅₃×#436	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₅₃×#435	C₂²	semidirect
187. C₈×D₄×C₅₃	C₂²	semidirect
188. C₈×D₄×C₅₃	C₂²	semidirect
189. C₅₃×#433	C₂²	semidirect
190. C₅₃×#433	C₂²	semidirect
191. C₅₃×#419	C₂²	semidirect
192. C₅₃×#419	C₂²	semidirect
193. C₅₃×#419	C₂²	semidirect
194. C₅₃×#418	C₂²	semidirect
195. C₅₃×#416	C₂²	semidirect
196. C₅₃×#416	C₂²	semidirect
197. C₅₃×#416	C₂²	semidirect
198. C₅₃×#416	C₂²	semidirect
199. C₅₃×#408	C₂²	semidirect
200. C₅₃×#408	C₂²	semidirect
201. C₅₃×#407	C₂²	semidirect
202. C₂×C₂²⋊C₈×C₅₃	C₂²	semidirect
867. #61627	C₅₃	direct (N × H)
922. #3540	C₂×C₅₃	semidirect
923. #3489	C₂×C₅₃	semidirect
924. #3329	C₂×C₅₃	semidirect
925. #3328	C₂×C₅₃	semidirect
926. #3321	C₂×C₅₃	semidirect
927. #3319	C₂×C₅₃	semidirect
928. #3313	C₂×C₅₃	semidirect
929. #3311	C₂×C₅₃	semidirect
930. #3303	C₂×C₅₃	semidirect
931. #3302	C₂×C₅₃	semidirect
932. #3285	C₂×C₅₃	semidirect
933. #3282	C₂×C₅₃	semidirect
934. #3275	C₂×C₅₃	semidirect
935. #3273	C₂×C₅₃	semidirect
936. #3270	C₂×C₅₃	semidirect
937. #3269	C₂×C₅₃	semidirect
938. #3267	C₂×C₅₃	semidirect
939. #3266	C₂×C₅₃	semidirect
940. #3225	C₂×C₅₃	semidirect
941. #3225	C₂×C₅₃	semidirect
942. #3201	C₂×C₅₃	semidirect
943. #3198	C₂×C₅₃	semidirect
944. #3196	C₂×C₅₃	semidirect
945. #3190	C₂×C₅₃	semidirect
946. #3125	C₂×C₅₃	semidirect
947. #3124	C₂×C₅₃	semidirect
948. #3011	C₂×C₅₃	semidirect
949. #3010	C₂×C₅₃	semidirect
950. #3005	C₂×C₅₃	semidirect
951. #3002	C₂×C₅₃	semidirect
952. #2976	C₂×C₅₃	semidirect
966. C₂²×#41	C₂²×C₅₃	semidirect
968. C₂×#137	C₂²×C₅₃	semidirect
970. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
973. C₂²×Q₁₆	C₂²×C₅₃	semidirect
974. C₂²×SD₁₆	C₂²×C₅₃	semidirect
979. #556	C₂²×C₅₃	semidirect
981. #555	C₂²×C₅₃	semidirect
984. D₄×Q₈	C₂²×C₅₃	semidirect
987. #548	C₂²×C₅₃	semidirect
988. #548	C₂²×C₅₃	semidirect
992. #547	C₂²×C₅₃	semidirect
997. #546	C₂²×C₅₃	semidirect
998. #546	C₂²×C₅₃	semidirect
1001. #542	C₂²×C₅₃	semidirect
1002. #542	C₂²×C₅₃	semidirect
1008. #536	C₂²×C₅₃	semidirect
1009. #536	C₂²×C₅₃	semidirect
1010. #535	C₂²×C₅₃	semidirect
1016. C₂×C₂²⋊Q₈	C₂²×C₅₃	semidirect
1017. #520	C₂²×C₅₃	semidirect
1018. #497	C₂²×C₅₃	semidirect
1019. #497	C₂²×C₅₃	semidirect
1020. #495	C₂²×C₅₃	semidirect
1021. #495	C₂²×C₅₃	semidirect
1022. #489	C₂²×C₅₃	semidirect
1023. #489	C₂²×C₅₃	semidirect
1024. #487	C₂²×C₅₃	semidirect
1025. #487	C₂²×C₅₃	semidirect
1026. #485	C₂²×C₅₃	semidirect
1027. #485	C₂²×C₅₃	semidirect
1028. #485	C₂²×C₅₃	semidirect
1029. #485	C₂²×C₅₃	semidirect
1030. #485	C₂²×C₅₃	semidirect
1031. #485	C₂²×C₅₃	semidirect
1032. #484	C₂²×C₅₃	semidirect
1033. #483	C₂²×C₅₃	semidirect
1034. #482	C₂²×C₅₃	semidirect
1035. #482	C₂²×C₅₃	semidirect
1036. #481	C₂²×C₅₃	semidirect
1037. #480	C₂²×C₅₃	semidirect
1038. #477	C₂²×C₅₃	semidirect
1039. #476	C₂²×C₅₃	semidirect
1040. #475	C₂²×C₅₃	semidirect
1041. #474	C₂²×C₅₃	semidirect
1042. #470	C₂²×C₅₃	semidirect
1043. #470	C₂²×C₅₃	semidirect
1044. #470	C₂²×C₅₃	semidirect
1045. #469	C₂²×C₅₃	semidirect
1048. #468	C₂²×C₅₃	semidirect
1049. #468	C₂²×C₅₃	semidirect
1050. #467	C₂²×C₅₃	semidirect
1051. #467	C₂²×C₅₃	semidirect
1052. #467	C₂²×C₅₃	semidirect
1053. #466	C₂²×C₅₃	semidirect
1054. #465	C₂²×C₅₃	semidirect
1055. #465	C₂²×C₅₃	semidirect
1056. #465	C₂²×C₅₃	semidirect
1057. #465	C₂²×C₅₃	semidirect
1058. #464	C₂²×C₅₃	semidirect
1059. #464	C₂²×C₅₃	semidirect
1060. #464	C₂²×C₅₃	semidirect
1061. #464	C₂²×C₅₃	semidirect
1062. #463	C₂²×C₅₃	semidirect
1063. #463	C₂²×C₅₃	semidirect
1064. #463	C₂²×C₅₃	semidirect
1065. #463	C₂²×C₅₃	semidirect
1066. #462	C₂²×C₅₃	semidirect
1067. #462	C₂²×C₅₃	semidirect
1068. #461	C₂²×C₅₃	semidirect
1069. #461	C₂²×C₅₃	semidirect
1072. #452	C₂²×C₅₃	semidirect
1073. #452	C₂²×C₅₃	semidirect
1074. #452	C₂²×C₅₃	semidirect
1075. #452	C₂²×C₅₃	semidirect
1076. #452	C₂²×C₅₃	semidirect
1077. #452	C₂²×C₅₃	semidirect
1078. #452	C₂²×C₅₃	semidirect
1079. #452	C₂²×C₅₃	semidirect
1080. #452	C₂²×C₅₃	semidirect
1081. #452	C₂²×C₅₃	semidirect
1082. #451	C₂²×C₅₃	semidirect
1083. #451	C₂²×C₅₃	semidirect
1084. #451	C₂²×C₅₃	semidirect
1085. #451	C₂²×C₅₃	semidirect
1086. #451	C₂²×C₅₃	semidirect
1087. #451	C₂²×C₅₃	semidirect
1088. #450	C₂²×C₅₃	semidirect
1089. #450	C₂²×C₅₃	semidirect
1096. #449	C₂²×C₅₃	semidirect
1097. #449	C₂²×C₅₃	semidirect
1099. #448	C₂²×C₅₃	semidirect
1100. #448	C₂²×C₅₃	semidirect
1101. #448	C₂²×C₅₃	semidirect
1102. #448	C₂²×C₅₃	semidirect
1103. #448	C₂²×C₅₃	semidirect
1105. #447	C₂²×C₅₃	semidirect
1106. #442	C₂²×C₅₃	semidirect
1107. #441	C₂²×C₅₃	semidirect
1108. #440	C₂²×C₅₃	semidirect
1109. #440	C₂²×C₅₃	semidirect
1110. C₄×Q₁₆	C₂²×C₅₃	semidirect
1111. C₄×SD₁₆	C₂²×C₅₃	semidirect
1112. C₄×SD₁₆	C₂²×C₅₃	semidirect
1113. C₄×D₈	C₂²×C₅₃	semidirect
1115. #436	C₂²×C₅₃	semidirect
1117. #435	C₂²×C₅₃	semidirect
1118. #435	C₂²×C₅₃	semidirect
1119. #435	C₂²×C₅₃	semidirect
1120. C₈×D₄	C₂²×C₅₃	semidirect
1121. C₈×D₄	C₂²×C₅₃	semidirect
1122. #433	C₂²×C₅₃	semidirect
1123. #433	C₂²×C₅₃	semidirect
1124. #419	C₂²×C₅₃	semidirect
1125. #419	C₂²×C₅₃	semidirect
1126. #419	C₂²×C₅₃	semidirect
1127. #418	C₂²×C₅₃	semidirect
1128. #416	C₂²×C₅₃	semidirect
1129. #416	C₂²×C₅₃	semidirect
1130. #416	C₂²×C₅₃	semidirect
1131. #416	C₂²×C₅₃	semidirect
1132. #408	C₂²×C₅₃	semidirect
1133. #408	C₂²×C₅₃	semidirect
1134. #407	C₂²×C₅₃	semidirect
1135. C₂×C₂²⋊C₈	C₂²×C₅₃	semidirect
1136. C₅₃	#61627	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×#3540	2
C₅₃×#3489	2
C₅₃×#3329	2
C₅₃×#3328	2
C₅₃×#3321	2
C₅₃×#3319	2
C₅₃×#3313	2
C₅₃×#3311	2
C₅₃×#3303	2
C₅₃×#3302	2
C₅₃×#3285	2
C₅₃×#3282	2
C₅₃×#3275	2
C₅₃×#3273	2
C₅₃×#3270	2
C₅₃×#3269	2
C₅₃×#3267	2
C₅₃×#3266	2
C₅₃×#3225	2
C₅₃×#3201	2
C₅₃×#3198	2
C₅₃×#3196	2
C₅₃×#3190	2
C₅₃×#3125	2
C₅₃×#3124	2
C₅₃×#3011	2
C₅₃×#3010	2
C₅₃×#3005	2
C₅₃×#3002	2
C₅₃×#2976	2
#61627	53

Subgroups — C53×#61627 #27269139

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61627 #27269139