Subgroups — C₅₃×#61990 #27269502

Order 13568.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3370	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3321	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3312	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3300	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3256	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3215	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3211	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3111	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3040	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2990	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#555	—	2	1	no	—
42	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#553	—	2	1	no	—
45	C₅₃×#552	—	2	1	no	—
46	C₅₃×#552	C₂²	1	1	yes	characteristic
47	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#551	—	2	1	no	—
50	C₅₃×#551	—	2	1	no	—
51	C₅₃×#551	—	2	1	no	—
52	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
53	C₅₃×#548	C₂²	1	1	yes	characteristic
54	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
56	C₅₃×#546	—	2	1	no	—
57	C₅₃×#546	C₂²	1	1	yes	characteristic
58	C₅₃×#546	C₂²	1	1	yes	characteristic
59	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
61	D₄²×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#542	—	2	1	no	—
63	C₅₃×#538	—	2	1	no	—
64	C₅₃×#538	—	2	1	no	—
65	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#529	—	2	1	no	—
68	C₅₃×#529	—	2	1	no	—
69	C₅₃×#529	C₂²	1	1	yes	characteristic
70	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
74	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
75	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#525	—	2	1	no	—
77	C₅₃×#518	—	2	1	no	—
78	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
79	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
81	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
82	C₂×#117×C₅₃	—	2	1	no	—
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
88	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#489	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×#488	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#480	C₂²	1	1	yes	characteristic
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#469	C₂²	1	1	yes	characteristic
113	C₅₃×#468	C₂²	1	1	yes	characteristic, 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×#467	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#466	C₂²	1	1	yes	characteristic
119	C₅₃×#465	C₂²	1	1	yes	characteristic
120	C₅₃×#465	C₂²	1	1	yes	characteristic
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×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#463	C₂²	1	1	yes	characteristic
134	C₅₃×#463	C₂²	1	1	yes	characteristic
135	C₅₃×#463	C₂²	1	1	yes	characteristic
136	C₅₃×#463	C₂²	1	1	yes	characteristic
137	C₅₃×#463	C₂²	1	1	yes	characteristic
138	C₅₃×#463	C₂²	1	1	yes	characteristic
139	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#462	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, complemented
152	C₅₃×#459	C₂²	1	1	yes	characteristic
153	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#450	C₂²	1	1	yes	characteristic
161	C₅₃×#450	C₂²	1	1	yes	characteristic
162	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#449	C₂²	1	1	yes	characteristic
165	C₅₃×#449	C₂²	1	1	yes	characteristic
166	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#447	C₂²	1	1	yes	characteristic
170	C₅₃×#447	C₂²	1	1	yes	characteristic
171	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#442	C₂²	1	1	yes	characteristic
174	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
177	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
178	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
181	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
183	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
184	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic
186	C₅₃×#435	C₂²	1	1	yes	characteristic
187	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
189	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
190	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
195	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#419	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
201	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
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	C₂×#41×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×D₄×C₅₃	—	2	1	no	—
211	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	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	#135×C₅₃	—	4	2	no	—
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×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
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×D₈×C₅₃	—	4	2	no	—
239	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
247	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
248	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₅₃	—	2	1	no	—
252	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
255	#127×C₅₃	C₂³	1	1	yes	characteristic
256	#126×C₅₃	—	2	1	no	—
257	#126×C₅₃	—	2	1	no	—
258	#126×C₅₃	—	2	1	no	—
259	#126×C₅₃	—	2	1	no	—
260	#126×C₅₃	—	2	1	no	—
261	#126×C₅₃	—	2	1	no	—
262	#126×C₅₃	—	2	1	no	—
263	#126×C₅₃	—	2	1	no	—
264	#126×C₅₃	—	2	1	no	—
265	#126×C₅₃	—	2	1	no	—
266	#126×C₅₃	—	2	1	no	—
267	#125×C₅₃	—	2	1	no	—
268	#125×C₅₃	—	2	1	no	—
269	#125×C₅₃	—	2	1	no	—
270	#125×C₅₃	C₂³	1	1	yes	characteristic
271	#125×C₅₃	C₂³	1	1	yes	characteristic
272	#125×C₅₃	C₂³	1	1	yes	characteristic
273	#124×C₅₃	—	2	1	no	—
274	#124×C₅₃	—	2	1	no	—
275	#124×C₅₃	—	2	1	no	—
276	#124×C₅₃	—	2	1	no	—
277	#124×C₅₃	—	2	1	no	—
278	#124×C₅₃	—	2	1	no	—
279	#124×C₅₃	—	2	1	no	—
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	C₂³	1	1	yes	characteristic
283	#124×C₅₃	C₂³	1	1	yes	characteristic
284	#124×C₅₃	C₂³	1	1	yes	characteristic
285	#124×C₅₃	C₂³	1	1	yes	characteristic
286	#124×C₅₃	C₂³	1	1	yes	characteristic
287	#124×C₅₃	C₂³	1	1	yes	characteristic
288	#124×C₅₃	C₂³	1	1	yes	characteristic
289	#124×C₅₃	C₂³	1	1	yes	characteristic
290	#124×C₅₃	C₂³	1	1	yes	characteristic
291	#123×C₅₃	—	2	1	no	—
292	#123×C₅₃	—	2	1	no	—
293	#123×C₅₃	—	2	1	no	—
294	#123×C₅₃	—	2	1	no	—
295	#123×C₅₃	—	2	1	no	—
296	#123×C₅₃	—	2	1	no	—
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	—	2	1	no	—
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	C₂²⋊Q₈×C₅₃	—	2	1	no	—
307	C₂²⋊Q₈×C₅₃	—	2	1	no	—
308	C₂²⋊Q₈×C₅₃	—	2	1	no	—
309	C₂²⋊Q₈×C₅₃	—	2	1	no	—
310	C₂²⋊Q₈×C₅₃	—	2	1	no	—
311	C₂²⋊Q₈×C₅₃	—	2	1	no	—
312	C₂²⋊Q₈×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	—	2	1	no	—
315	C₂²⋊Q₈×C₅₃	—	2	1	no	—
316	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	—	2	1	no	—
325	#121×C₅₃	—	2	1	no	—
326	#121×C₅₃	—	2	1	no	—
327	#121×C₅₃	—	2	1	no	—
328	#121×C₅₃	—	2	1	no	—
329	#121×C₅₃	—	2	1	no	—
330	#121×C₅₃	—	2	1	no	—
331	#121×C₅₃	—	2	1	no	—
332	#121×C₅₃	—	2	1	no	—
333	#121×C₅₃	—	2	1	no	—
334	#121×C₅₃	C₂³	1	1	yes	characteristic
335	#121×C₅₃	C₂³	1	1	yes	characteristic
336	#121×C₅₃	C₂³	1	1	yes	characteristic
337	#121×C₅₃	C₂³	1	1	yes	characteristic
338	#121×C₅₃	C₂³	1	1	yes	characteristic
339	#120×C₅₃	—	2	1	no	—
340	#120×C₅₃	—	2	1	no	—
341	#120×C₅₃	—	2	1	no	—
342	#120×C₅₃	—	2	1	no	—
343	#120×C₅₃	—	2	1	no	—
344	#120×C₅₃	—	2	1	no	—
345	C₄×Q₈×C₅₃	—	2	1	no	—
346	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
347	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
354	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	—	2	1	no	—
357	C₄×D₄×C₅₃	—	2	1	no	—
358	C₄×D₄×C₅₃	—	2	1	no	—
359	C₄×D₄×C₅₃	—	2	1	no	—
360	C₄×D₄×C₅₃	—	2	1	no	—
361	C₄×D₄×C₅₃	—	2	1	no	—
362	C₄×D₄×C₅₃	—	2	1	no	—
363	C₄×D₄×C₅₃	—	2	1	no	—
364	C₄×D₄×C₅₃	—	2	1	no	—
365	C₄×D₄×C₅₃	—	2	1	no	—
366	C₄×D₄×C₅₃	—	2	1	no	—
367	C₄×D₄×C₅₃	—	2	1	no	—
368	C₄×D₄×C₅₃	—	2	1	no	—
369	C₄×D₄×C₅₃	—	2	1	no	—
370	C₄×D₄×C₅₃	—	2	1	no	—
371	C₄×D₄×C₅₃	—	2	1	no	—
372	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
373	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
374	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
375	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
379	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
380	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
381	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
382	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
383	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
384	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
385	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
386	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
387	#117×C₅₃	—	2	1	no	—
388	#117×C₅₃	—	2	1	no	—
389	#117×C₅₃	—	2	1	no	—
390	#117×C₅₃	—	2	1	no	—
391	#117×C₅₃	—	2	1	no	—
392	#117×C₅₃	—	2	1	no	—
393	#117×C₅₃	—	2	1	no	—
394	#117×C₅₃	—	2	1	no	—
395	#117×C₅₃	—	2	1	no	—
396	#117×C₅₃	—	2	1	no	—
397	#117×C₅₃	—	2	1	no	—
398	#117×C₅₃	—	2	1	no	—
399	#117×C₅₃	—	2	1	no	—
400	#117×C₅₃	D₄	1	1	yes	characteristic
401	#117×C₅₃	D₄	1	1	yes	characteristic
402	#117×C₅₃	D₄	1	1	yes	characteristic
403	#117×C₅₃	C₂³	1	1	yes	characteristic
404	#117×C₅₃	C₂³	1	1	yes	characteristic
405	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
408	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
409	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
412	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
414	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
417	C₂×C₄²×C₅₃	—	2	1	no	—
418	C₂×C₄²×C₅₃	—	2	1	no	—
419	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
421	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#107×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#103×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	#97×C₅₃	C₂³	1	1	yes	characteristic
479	#97×C₅₃	C₂³	1	1	yes	characteristic
480	#97×C₅₃	C₂³	1	1	yes	characteristic
481	#97×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	C₂⁴×C₅₃	—	2	1	no	—
485	C₂⁴×C₅₃	—	2	1	no	—
486	C₂⁴×C₅₃	—	2	1	no	—
487	#41×C₅₃	—	2	2	no	—
488	#41×C₅₃	—	2	2	no	—
489	#41×C₅₃	—	4	2	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	4	1	no	—
493	#41×C₅₃	—	4	1	no	—
494	#41×C₅₃	—	4	1	no	—
495	#41×C₅₃	—	4	1	no	—
496	C₂×Q₈×C₅₃	—	2	1	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	—	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	C₂×D₄	1	1	yes	characteristic
504	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
506	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
507	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
508	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
509	C₂×D₄×C₅₃	—	2	2	no	—
510	C₂×D₄×C₅₃	—	2	1	no	—
511	C₂×D₄×C₅₃	—	2	1	no	—
512	C₂×D₄×C₅₃	—	2	1	no	—
513	C₂×D₄×C₅₃	—	2	1	no	—
514	C₂×D₄×C₅₃	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	2	1	no	—
519	C₂×D₄×C₅₃	—	2	1	no	—
520	C₂×D₄×C₅₃	—	2	1	no	—
521	C₂×D₄×C₅₃	—	2	1	no	—
522	C₂×D₄×C₅₃	—	2	1	no	—
523	C₂×D₄×C₅₃	—	2	1	no	—
524	C₂×D₄×C₅₃	—	4	1	no	—
525	C₂×D₄×C₅₃	—	4	1	no	—
526	C₂×D₄×C₅₃	—	4	1	no	—
527	C₂×D₄×C₅₃	—	4	1	no	—
528	C₂×D₄×C₅₃	—	4	1	no	—
529	C₂×D₄×C₅₃	—	4	4	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	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	4	4	no	—
555	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
556	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
557	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
558	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
559	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
560	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
561	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
562	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
564	Q₁₆×C₅₃	—	4	1	no	—
565	Q₁₆×C₅₃	—	4	1	no	—
566	Q₁₆×C₅₃	—	4	1	no	—
567	Q₁₆×C₅₃	—	4	1	no	—
568	Q₁₆×C₅₃	—	4	1	no	—
569	Q₁₆×C₅₃	—	4	1	no	—
570	SD₁₆×C₅₃	—	2	2	no	—
571	SD₁₆×C₅₃	—	2	2	no	—
572	SD₁₆×C₅₃	—	2	2	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	—	2	2	no	—
584	D₈×C₅₃	—	2	2	no	—
585	D₈×C₅₃	—	4	1	no	—
586	D₈×C₅₃	—	4	1	no	—
587	D₈×C₅₃	—	4	1	no	—
588	M₁₆×C₅₃	—	4	1	no	—
589	M₁₆×C₅₃	—	4	1	no	—
590	C₂×C₈×C₅₃	—	4	1	no	—
591	C₂×C₈×C₅₃	—	4	1	no	—
592	C₂×C₈×C₅₃	—	4	1	no	—
593	C₂×C₈×C₅₃	—	4	1	no	—
594	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
596	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
597	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
598	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
599	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
601	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
602	C₄⋊C₄×C₅₃	—	2	1	no	—
603	C₄⋊C₄×C₅₃	—	2	1	no	—
604	C₄⋊C₄×C₅₃	—	2	1	no	—
605	C₄⋊C₄×C₅₃	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	—	2	1	no	—
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
614	C₄⋊C₄×C₅₃	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
619	C₄⋊C₄×C₅₃	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	—	2	1	no	—
627	C₄⋊C₄×C₅₃	—	2	1	no	—
628	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
637	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
640	C₂²⋊C₄×C₅₃	—	2	1	no	—
641	C₂²⋊C₄×C₅₃	—	2	1	no	—
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
668	C₂²⋊C₄×C₅₃	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	—	2	1	no	—
670	C₂²⋊C₄×C₅₃	—	2	1	no	—
671	C₂²⋊C₄×C₅₃	—	2	1	no	—
672	C₂²⋊C₄×C₅₃	—	2	1	no	—
673	C₂²⋊C₄×C₅₃	—	2	1	no	—
674	C₂²⋊C₄×C₅₃	—	2	1	no	—
675	C₂²⋊C₄×C₅₃	—	2	1	no	—
676	C₂²⋊C₄×C₅₃	—	2	1	no	—
677	C₂²⋊C₄×C₅₃	—	2	1	no	—
678	C₂²⋊C₄×C₅₃	—	2	1	no	—
679	C₂²⋊C₄×C₅₃	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
685	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
686	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
687	C₄²×C₅₃	—	2	1	no	—
688	C₄²×C₅₃	—	2	1	no	—
689	C₄²×C₅₃	—	2	1	no	—
690	C₄²×C₅₃	—	2	1	no	—
691	C₄²×C₅₃	—	2	1	no	—
692	C₄²×C₅₃	—	2	1	no	—
693	C₄²×C₅₃	—	2	1	no	—
694	C₄²×C₅₃	—	2	1	no	—
695	C₄²×C₅₃	—	2	1	no	—
696	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
697	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
698	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
699	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
700	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
704	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
705	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₂³×C₅₃	—	2	1	no	—
707	C₂³×C₅₃	—	2	1	no	—
708	C₂³×C₅₃	—	2	1	no	—
709	C₂³×C₅₃	—	2	1	no	—
710	C₂³×C₅₃	—	2	1	no	—
711	C₂³×C₅₃	—	4	2	no	—
712	C₂³×C₅₃	—	4	2	no	—
713	C₂³×C₅₃	—	4	2	no	—
714	C₂³×C₅₃	—	4	2	no	—
715	C₂³×C₅₃	—	8	1	no	—
716	C₂³×C₅₃	—	8	1	no	—
717	C₂³×C₅₃	—	8	1	no	—
718	C₂³×C₅₃	—	8	1	no	—
719	C₂³×C₅₃	—	8	1	no	—
720	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
721	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
722	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
732	Q₈×C₅₃	—	2	1	no	—
733	Q₈×C₅₃	—	4	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	—	2	1	no	—
747	D₄×C₅₃	—	2	1	no	—
748	D₄×C₅₃	—	4	1	no	—
749	D₄×C₅₃	—	4	2	no	—
750	D₄×C₅₃	—	4	2	no	—
751	D₄×C₅₃	—	4	2	no	—
752	D₄×C₅₃	—	4	2	no	—
753	D₄×C₅₃	—	4	2	no	—
754	D₄×C₅₃	—	4	2	no	—
755	D₄×C₅₃	—	8	1	no	—
756	D₄×C₅₃	—	8	1	no	—
757	D₄×C₅₃	—	8	1	no	—
758	D₄×C₅₃	—	8	1	no	—
759	D₄×C₅₃	—	8	1	no	—
760	D₄×C₅₃	—	8	1	no	—
761	D₄×C₅₃	—	8	1	no	—
762	D₄×C₅₃	—	8	1	no	—
763	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
764	C₂×C₄×C₅₃	—	2	2	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	—	2	1	no	—
780	C₂×C₄×C₅₃	—	2	1	no	—
781	C₂×C₄×C₅₃	—	2	1	no	—
782	C₂×C₄×C₅₃	—	4	1	no	—
783	C₂×C₄×C₅₃	—	4	1	no	—
784	C₂×C₄×C₅₃	—	4	1	no	—
785	C₂×C₄×C₅₃	—	4	1	no	—
786	C₂×C₄×C₅₃	—	4	1	no	—
787	C₂×C₄×C₅₃	—	4	2	no	—
788	C₂×C₄×C₅₃	—	4	2	no	—
789	C₂×C₄×C₅₃	—	4	2	no	—
790	C₂×C₄×C₅₃	—	4	2	no	—
791	C₂×C₄×C₅₃	—	4	2	no	—
792	C₂×C₄×C₅₃	—	4	2	no	—
793	C₂×C₄×C₅₃	—	4	2	no	—
794	C₂×C₄×C₅₃	—	4	2	no	—
795	C₂×C₄×C₅₃	—	8	1	no	—
796	C₂×C₄×C₅₃	—	8	1	no	—
797	C₂×C₄×C₅₃	—	8	1	no	—
798	C₂×C₄×C₅₃	—	8	1	no	—
799	C₂×C₄×C₅₃	—	8	1	no	—
800	C₂×C₄×C₅₃	—	8	1	no	—
801	C₂×C₄×C₅₃	—	8	1	no	—
802	C₂×C₄×C₅₃	—	8	1	no	—
803	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
804	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
805	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
806	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
807	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
808	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
809	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
810	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
811	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
812	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
813	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
814	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
815	C₈×C₅₃	—	2	1	no	—
816	C₈×C₅₃	—	2	1	no	—
817	C₈×C₅₃	—	2	1	no	—
818	C₈×C₅₃	—	2	1	no	—
819	C₈×C₅₃	—	2	1	no	—
820	C₈×C₅₃	—	2	1	no	—
821	C₈×C₅₃	—	2	1	no	—
822	C₈×C₅₃	—	2	1	no	—
823	#61990	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
824	C₂²×C₅₃	—	2	1	no	—
825	C₂²×C₅₃	—	2	1	no	—
826	C₂²×C₅₃	—	2	1	no	—
827	C₂²×C₅₃	—	2	1	no	—
828	C₂²×C₅₃	—	2	1	no	—
829	C₂²×C₅₃	—	2	1	no	—
830	C₂²×C₅₃	—	2	2	no	—
831	C₂²×C₅₃	—	2	1	no	—
832	C₂²×C₅₃	—	2	1	no	—
833	C₂²×C₅₃	—	4	1	no	—
834	C₂²×C₅₃	—	4	1	no	—
835	C₂²×C₅₃	—	4	1	no	—
836	C₂²×C₅₃	—	4	1	no	—
837	C₂²×C₅₃	—	4	1	no	—
838	C₂²×C₅₃	—	4	1	no	—
839	C₂²×C₅₃	—	4	1	no	—
840	C₂²×C₅₃	—	4	1	no	—
841	C₂²×C₅₃	—	4	1	no	—
842	C₂²×C₅₃	—	4	1	no	—
843	C₂²×C₅₃	—	4	1	no	—
844	C₂²×C₅₃	—	4	1	no	—
845	C₂²×C₅₃	—	4	1	no	—
846	C₂²×C₅₃	—	4	1	no	—
847	C₂²×C₅₃	—	8	4	no	—
848	C₂²×C₅₃	—	16	2	no	—
849	C₂²×C₅₃	—	16	2	no	—
850	C₂²×C₅₃	#575	1	2	yes	—
851	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
852	C₄×C₅₃	—	2	1	no	—
853	C₄×C₅₃	—	2	1	no	—
854	C₄×C₅₃	—	2	1	no	—
855	C₄×C₅₃	—	2	1	no	—
856	C₄×C₅₃	—	2	1	no	—
857	C₄×C₅₃	—	2	1	no	—
858	C₄×C₅₃	—	2	1	no	—
859	C₄×C₅₃	—	2	1	no	—
860	C₄×C₅₃	—	2	1	no	—
861	C₄×C₅₃	—	2	1	no	—
862	C₄×C₅₃	—	2	1	no	—
863	C₄×C₅₃	—	4	1	no	—
864	C₄×C₅₃	—	4	1	no	—
865	C₄×C₅₃	—	4	1	no	—
866	C₄×C₅₃	—	4	1	no	—
867	C₄×C₅₃	—	4	1	no	—
868	C₄×C₅₃	—	4	1	no	—
869	C₄×C₅₃	—	4	1	no	—
870	C₄×C₅₃	—	4	1	no	—
871	C₄×C₅₃	—	4	1	no	—
872	C₄×C₅₃	—	4	1	no	—
873	C₄×C₅₃	—	4	1	no	—
874	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
875	C₄×C₅₃	#585	1	1	yes	characteristic
876	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3475	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3402	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3376	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3370	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3321	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3312	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3300	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3296	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3280	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3256	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3250	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#3215	C₂×C₅₃	1	1	yes	characteristic, complemented
899	#3211	C₂×C₅₃	1	1	yes	characteristic, complemented
900	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
901	#3111	C₂×C₅₃	1	1	yes	characteristic, complemented
902	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
903	#3040	C₂×C₅₃	1	1	yes	characteristic, complemented
904	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
905	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
906	#2990	C₂×C₅₃	1	1	yes	characteristic, complemented
907	C₂×C₅₃	—	2	2	no	—
908	C₂×C₅₃	—	4	1	no	—
909	C₂×C₅₃	—	4	1	no	—
910	C₂×C₅₃	—	4	2	no	—
911	C₂×C₅₃	—	8	1	no	—
912	C₂×C₅₃	—	8	1	no	—
913	C₂×C₅₃	—	8	1	no	—
914	C₂×C₅₃	—	8	1	no	—
915	C₂×C₅₃	#3488	1	1	yes	characteristic
916	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
917	C₂×C₅₃	#3584	1	1	yes	characteristic
918	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
920	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
924	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#555	—	2	1	no	—
928	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#553	—	2	1	no	—
931	#552	—	2	1	no	—
932	#552	C₂²×C₅₃	1	1	yes	characteristic
933	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#551	—	2	1	no	—
935	#551	—	2	1	no	—
936	#551	—	2	1	no	—
937	#551	—	2	1	no	—
938	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
939	#548	C₂²×C₅₃	1	1	yes	characteristic
940	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#546	—	2	1	no	—
943	#546	C₂²×C₅₃	1	1	yes	characteristic
944	#546	C₂²×C₅₃	1	1	yes	characteristic
945	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	D₄²	C₂²×C₅₃	1	1	yes	characteristic
948	#542	—	2	1	no	—
949	#538	—	2	1	no	—
950	#538	—	2	1	no	—
951	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#529	—	2	1	no	—
954	#529	—	2	1	no	—
955	#529	C₂²×C₅₃	1	1	yes	characteristic
956	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
961	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#525	—	2	1	no	—
963	#518	—	2	1	no	—
964	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
965	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	C₂×#117	—	2	1	no	—
969	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#496	C₂²×C₅₃	1	1	yes	characteristic
973	#495	C₂²×C₅₃	1	1	yes	characteristic
974	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#480	C₂²×C₅₃	1	1	yes	characteristic
987	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#469	C₂²×C₅₃	1	1	yes	characteristic
999	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#466	C₂²×C₅₃	1	1	yes	characteristic
1005	#465	C₂²×C₅₃	1	1	yes	characteristic
1006	#465	C₂²×C₅₃	1	1	yes	characteristic
1007	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#463	C₂²×C₅₃	1	1	yes	characteristic
1020	#463	C₂²×C₅₃	1	1	yes	characteristic
1021	#463	C₂²×C₅₃	1	1	yes	characteristic
1022	#463	C₂²×C₅₃	1	1	yes	characteristic
1023	#463	C₂²×C₅₃	1	1	yes	characteristic
1024	#463	C₂²×C₅₃	1	1	yes	characteristic
1025	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#459	C₂²×C₅₃	1	1	yes	characteristic
1039	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#450	C₂²×C₅₃	1	1	yes	characteristic
1047	#450	C₂²×C₅₃	1	1	yes	characteristic
1048	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#449	C₂²×C₅₃	1	1	yes	characteristic
1051	#449	C₂²×C₅₃	1	1	yes	characteristic
1052	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#447	C₂²×C₅₃	1	1	yes	characteristic
1056	#447	C₂²×C₅₃	1	1	yes	characteristic
1057	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#442	C₂²×C₅₃	1	1	yes	characteristic
1060	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1068	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#435	C₂²×C₅₃	1	1	yes	characteristic
1072	#435	C₂²×C₅₃	1	1	yes	characteristic
1073	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	#419	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1089	C₅₃	#61990	1	1	yes	characteristic, direct product factor, Sylow
1090	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
1091	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂²×D₄	—	2	1	no	—
1098	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂³×C₄	—	2	1	no	—
1102	#137	—	4	2	no	—
1103	AGL(1,ℤ/8)	—	4	2	no	—
1104	#135	—	4	2	no	—
1105	#135	—	4	2	no	—
1106	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×SD₁₆	—	4	2	no	—
1113	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1117	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1121	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1122	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1123	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1124	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×D₈	—	4	2	no	—
1126	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1138	C₄⋊Q₈	—	2	1	no	—
1139	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1140	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1141	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1142	#127	C₂³×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1154	#125	—	2	1	no	—
1155	#125	—	2	1	no	—
1156	#125	—	2	1	no	—
1157	#125	C₂³×C₅₃	1	1	yes	characteristic
1158	#125	C₂³×C₅₃	1	1	yes	characteristic
1159	#125	C₂³×C₅₃	1	1	yes	characteristic
1160	#124	—	2	1	no	—
1161	#124	—	2	1	no	—
1162	#124	—	2	1	no	—
1163	#124	—	2	1	no	—
1164	#124	—	2	1	no	—
1165	#124	—	2	1	no	—
1166	#124	—	2	1	no	—
1167	#124	—	2	1	no	—
1168	#124	—	2	1	no	—
1169	#124	C₂³×C₅₃	1	1	yes	characteristic
1170	#124	C₂³×C₅₃	1	1	yes	characteristic
1171	#124	C₂³×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	#124	C₂³×C₅₃	1	1	yes	characteristic
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	C₂²⋊Q₈	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	—	2	1	no	—
1197	C₂²⋊Q₈	—	2	1	no	—
1198	C₂²⋊Q₈	—	2	1	no	—
1199	C₂²⋊Q₈	—	2	1	no	—
1200	C₂²⋊Q₈	—	2	1	no	—
1201	C₂²⋊Q₈	—	2	1	no	—
1202	C₂²⋊Q₈	—	2	1	no	—
1203	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1207	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1208	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1209	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1210	#121	—	2	1	no	—
1211	#121	—	2	1	no	—
1212	#121	—	2	1	no	—
1213	#121	—	2	1	no	—
1214	#121	—	2	1	no	—
1215	#121	—	2	1	no	—
1216	#121	—	2	1	no	—
1217	#121	—	2	1	no	—
1218	#121	—	2	1	no	—
1219	#121	—	2	1	no	—
1220	#121	—	2	1	no	—
1221	#121	C₂³×C₅₃	1	1	yes	characteristic
1222	#121	C₂³×C₅₃	1	1	yes	characteristic
1223	#121	C₂³×C₅₃	1	1	yes	characteristic
1224	#121	C₂³×C₅₃	1	1	yes	characteristic
1225	#121	C₂³×C₅₃	1	1	yes	characteristic
1226	#120	—	2	1	no	—
1227	#120	—	2	1	no	—
1228	#120	—	2	1	no	—
1229	#120	—	2	1	no	—
1230	#120	—	2	1	no	—
1231	#120	—	2	1	no	—
1232	C₄×Q₈	—	2	1	no	—
1233	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
1234	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1235	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1236	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1237	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1240	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄×D₄	—	2	1	no	—
1243	C₄×D₄	—	2	1	no	—
1244	C₄×D₄	—	2	1	no	—
1245	C₄×D₄	—	2	1	no	—
1246	C₄×D₄	—	2	1	no	—
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	—	2	1	no	—
1249	C₄×D₄	—	2	1	no	—
1250	C₄×D₄	—	2	1	no	—
1251	C₄×D₄	—	2	1	no	—
1252	C₄×D₄	—	2	1	no	—
1253	C₄×D₄	—	2	1	no	—
1254	C₄×D₄	—	2	1	no	—
1255	C₄×D₄	—	2	1	no	—
1256	C₄×D₄	—	2	1	no	—
1257	C₄×D₄	—	2	1	no	—
1258	C₄×D₄	—	2	1	no	—
1259	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1260	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1261	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
1262	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1263	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1264	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1267	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1268	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1271	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1272	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1273	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1274	#117	—	2	1	no	—
1275	#117	—	2	1	no	—
1276	#117	—	2	1	no	—
1277	#117	—	2	1	no	—
1278	#117	—	2	1	no	—
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	—	2	1	no	—
1285	#117	—	2	1	no	—
1286	#117	—	2	1	no	—
1287	#117	D₄×C₅₃	1	1	yes	characteristic
1288	#117	D₄×C₅₃	1	1	yes	characteristic
1289	#117	D₄×C₅₃	1	1	yes	characteristic
1290	#117	C₂³×C₅₃	1	1	yes	characteristic
1291	#117	C₂³×C₅₃	1	1	yes	characteristic
1292	C₂×C₄⋊C₄	—	2	1	no	—
1293	C₂×C₄⋊C₄	—	2	1	no	—
1294	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1295	C₂×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×C₂²⋊C₄	—	2	1	no	—
1300	C₂×C₂²⋊C₄	—	2	1	no	—
1301	C₂×C₂²⋊C₄	—	2	1	no	—
1302	C₂×C₂²⋊C₄	—	2	1	no	—
1303	C₂×C₂²⋊C₄	—	2	1	no	—
1304	C₂×C₄²	—	2	1	no	—
1305	C₂×C₄²	—	2	1	no	—
1306	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1307	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1308	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1309	#107	C₂³×C₅₃	1	1	yes	characteristic
1310	#107	C₂³×C₅₃	1	1	yes	characteristic
1311	#107	C₂³×C₅₃	1	1	yes	characteristic
1312	#107	C₂³×C₅₃	1	1	yes	characteristic
1313	#106	C₂³×C₅₃	1	1	yes	characteristic
1314	#106	C₂³×C₅₃	1	1	yes	characteristic
1315	#106	C₂³×C₅₃	1	1	yes	characteristic
1316	#106	C₂³×C₅₃	1	1	yes	characteristic
1317	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1318	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1319	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1320	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1321	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1322	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1323	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1324	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1325	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1326	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1327	#103	C₂³×C₅₃	1	1	yes	characteristic
1328	#103	C₂³×C₅₃	1	1	yes	characteristic
1329	#103	C₂³×C₅₃	1	1	yes	characteristic
1330	#103	C₂³×C₅₃	1	1	yes	characteristic
1331	#103	C₂³×C₅₃	1	1	yes	characteristic
1332	#103	C₂³×C₅₃	1	1	yes	characteristic
1333	#103	C₂³×C₅₃	1	1	yes	characteristic
1334	#103	C₂³×C₅₃	1	1	yes	characteristic
1335	#103	C₂³×C₅₃	1	1	yes	characteristic
1336	#103	C₂³×C₅₃	1	1	yes	characteristic
1337	#103	C₂³×C₅₃	1	1	yes	characteristic
1338	#103	C₂³×C₅₃	1	1	yes	characteristic
1339	#103	C₂³×C₅₃	1	1	yes	characteristic
1340	#103	C₂³×C₅₃	1	1	yes	characteristic
1341	#103	C₂³×C₅₃	1	1	yes	characteristic
1342	#103	C₂³×C₅₃	1	1	yes	characteristic
1343	#102	C₂³×C₅₃	1	1	yes	characteristic
1344	#102	C₂³×C₅₃	1	1	yes	characteristic
1345	#102	C₂³×C₅₃	1	1	yes	characteristic
1346	#102	C₂³×C₅₃	1	1	yes	characteristic
1347	#102	C₂³×C₅₃	1	1	yes	characteristic
1348	#102	C₂³×C₅₃	1	1	yes	characteristic
1349	#102	C₂³×C₅₃	1	1	yes	characteristic
1350	#102	C₂³×C₅₃	1	1	yes	characteristic
1351	#102	C₂³×C₅₃	1	1	yes	characteristic
1352	#102	C₂³×C₅₃	1	1	yes	characteristic
1353	#102	C₂³×C₅₃	1	1	yes	characteristic
1354	#102	C₂³×C₅₃	1	1	yes	characteristic
1355	#102	C₂³×C₅₃	1	1	yes	characteristic
1356	#102	C₂³×C₅₃	1	1	yes	characteristic
1357	#102	C₂³×C₅₃	1	1	yes	characteristic
1358	#102	C₂³×C₅₃	1	1	yes	characteristic
1359	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1360	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1361	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1362	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1363	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1364	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1365	#97	C₂³×C₅₃	1	1	yes	characteristic
1366	#97	C₂³×C₅₃	1	1	yes	characteristic
1367	#97	C₂³×C₅₃	1	1	yes	characteristic
1368	#97	C₂³×C₅₃	1	1	yes	characteristic
1369	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1370	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1371	C₂⁴	—	2	1	no	—
1372	C₂⁴	—	2	1	no	—
1373	C₂⁴	—	2	1	no	—
1374	#41	—	2	2	no	—
1375	#41	—	2	2	no	—
1376	#41	—	4	2	no	—
1377	#41	—	4	1	no	—
1378	#41	—	4	1	no	—
1379	#41	—	4	1	no	—
1380	#41	—	4	1	no	—
1381	#41	—	4	1	no	—
1382	#41	—	4	1	no	—
1383	C₂×Q₈	—	2	1	no	—
1384	C₂×Q₈	—	2	1	no	—
1385	C₂×Q₈	—	2	1	no	—
1386	C₂×Q₈	—	4	1	no	—
1387	C₂×Q₈	—	4	1	no	—
1388	C₂×Q₈	—	4	1	no	—
1389	C₂×Q₈	—	4	1	no	—
1390	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1391	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1392	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1393	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1394	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1395	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1396	C₂×D₄	—	2	2	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	—	2	1	no	—
1400	C₂×D₄	—	2	1	no	—
1401	C₂×D₄	—	2	1	no	—
1402	C₂×D₄	—	2	1	no	—
1403	C₂×D₄	—	2	1	no	—
1404	C₂×D₄	—	2	1	no	—
1405	C₂×D₄	—	2	1	no	—
1406	C₂×D₄	—	2	1	no	—
1407	C₂×D₄	—	2	1	no	—
1408	C₂×D₄	—	2	1	no	—
1409	C₂×D₄	—	2	1	no	—
1410	C₂×D₄	—	2	1	no	—
1411	C₂×D₄	—	4	1	no	—
1412	C₂×D₄	—	4	1	no	—
1413	C₂×D₄	—	4	1	no	—
1414	C₂×D₄	—	4	1	no	—
1415	C₂×D₄	—	4	1	no	—
1416	C₂×D₄	—	4	4	no	—
1417	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1418	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1419	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1420	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1421	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1422	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1423	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1424	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1434	C₂²×C₄	—	2	1	no	—
1435	C₂²×C₄	—	2	1	no	—
1436	C₂²×C₄	—	2	1	no	—
1437	C₂²×C₄	—	2	1	no	—
1438	C₂²×C₄	—	2	1	no	—
1439	C₂²×C₄	—	2	1	no	—
1440	C₂²×C₄	—	2	1	no	—
1441	C₂²×C₄	—	4	4	no	—
1442	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1443	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1444	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1445	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1446	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1447	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1448	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1449	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1450	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1451	Q₁₆	—	4	1	no	—
1452	Q₁₆	—	4	1	no	—
1453	Q₁₆	—	4	1	no	—
1454	Q₁₆	—	4	1	no	—
1455	Q₁₆	—	4	1	no	—
1456	Q₁₆	—	4	1	no	—
1457	SD₁₆	—	2	2	no	—
1458	SD₁₆	—	2	2	no	—
1459	SD₁₆	—	2	2	no	—
1460	SD₁₆	—	4	1	no	—
1461	SD₁₆	—	4	1	no	—
1462	SD₁₆	—	4	1	no	—
1463	SD₁₆	—	4	1	no	—
1464	SD₁₆	—	4	1	no	—
1465	SD₁₆	—	4	1	no	—
1466	SD₁₆	—	4	1	no	—
1467	SD₁₆	—	4	1	no	—
1468	SD₁₆	—	4	1	no	—
1469	D₈	—	2	2	no	—
1470	D₈	—	2	2	no	—
1471	D₈	—	2	2	no	—
1472	D₈	—	4	1	no	—
1473	D₈	—	4	1	no	—
1474	D₈	—	4	1	no	—
1475	M₁₆	—	4	1	no	—
1476	M₁₆	—	4	1	no	—
1477	C₂×C₈	—	4	1	no	—
1478	C₂×C₈	—	4	1	no	—
1479	C₂×C₈	—	4	1	no	—
1480	C₂×C₈	—	4	1	no	—
1481	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1482	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1486	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1487	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1488	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1489	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	—	2	1	no	—
1513	C₄⋊C₄	—	2	1	no	—
1514	C₄⋊C₄	—	2	1	no	—
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	C₂⁴×C₅₃	1	1	yes	characteristic
1522	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1523	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1524	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1525	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1526	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1527	C₂²⋊C₄	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	—	2	1	no	—
1545	C₂²⋊C₄	—	2	1	no	—
1546	C₂²⋊C₄	—	2	1	no	—
1547	C₂²⋊C₄	—	2	1	no	—
1548	C₂²⋊C₄	—	2	1	no	—
1549	C₂²⋊C₄	—	2	1	no	—
1550	C₂²⋊C₄	—	2	1	no	—
1551	C₂²⋊C₄	—	2	1	no	—
1552	C₂²⋊C₄	—	2	1	no	—
1553	C₂²⋊C₄	—	2	1	no	—
1554	C₂²⋊C₄	—	2	1	no	—
1555	C₂²⋊C₄	—	2	1	no	—
1556	C₂²⋊C₄	—	2	1	no	—
1557	C₂²⋊C₄	—	2	1	no	—
1558	C₂²⋊C₄	—	2	1	no	—
1559	C₂²⋊C₄	—	2	1	no	—
1560	C₂²⋊C₄	—	2	1	no	—
1561	C₂²⋊C₄	—	2	1	no	—
1562	C₂²⋊C₄	—	2	1	no	—
1563	C₂²⋊C₄	—	2	1	no	—
1564	C₂²⋊C₄	—	2	1	no	—
1565	C₂²⋊C₄	—	2	1	no	—
1566	C₂²⋊C₄	—	2	1	no	—
1567	C₂²⋊C₄	—	2	1	no	—
1568	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1569	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1570	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1571	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1572	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1573	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1574	C₄²	—	2	1	no	—
1575	C₄²	—	2	1	no	—
1576	C₄²	—	2	1	no	—
1577	C₄²	—	2	1	no	—
1578	C₄²	—	2	1	no	—
1579	C₄²	—	2	1	no	—
1580	C₄²	—	2	1	no	—
1581	C₄²	—	2	1	no	—
1582	C₄²	—	2	1	no	—
1583	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1584	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1585	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1586	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1587	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1588	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1589	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1590	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1591	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1592	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1593	C₂³	—	2	1	no	—
1594	C₂³	—	2	1	no	—
1595	C₂³	—	2	1	no	—
1596	C₂³	—	2	1	no	—
1597	C₂³	—	2	1	no	—
1598	C₂³	—	4	2	no	—
1599	C₂³	—	4	2	no	—
1600	C₂³	—	4	2	no	—
1601	C₂³	—	4	2	no	—
1602	C₂³	—	8	1	no	—
1603	C₂³	—	8	1	no	—
1604	C₂³	—	8	1	no	—
1605	C₂³	—	8	1	no	—
1606	C₂³	—	8	1	no	—
1607	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1608	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1609	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1610	Q₈	—	2	1	no	—
1611	Q₈	—	2	1	no	—
1612	Q₈	—	2	1	no	—
1613	Q₈	—	2	1	no	—
1614	Q₈	—	2	1	no	—
1615	Q₈	—	2	1	no	—
1616	Q₈	—	2	1	no	—
1617	Q₈	—	2	1	no	—
1618	Q₈	—	2	1	no	—
1619	Q₈	—	2	1	no	—
1620	Q₈	—	4	1	no	—
1621	Q₈	—	8	1	no	—
1622	Q₈	—	8	1	no	—
1623	Q₈	—	8	1	no	—
1624	D₄	—	2	2	no	—
1625	D₄	—	2	2	no	—
1626	D₄	—	2	1	no	—
1627	D₄	—	2	1	no	—
1628	D₄	—	2	1	no	—
1629	D₄	—	2	1	no	—
1630	D₄	—	2	1	no	—
1631	D₄	—	2	1	no	—
1632	D₄	—	2	1	no	—
1633	D₄	—	2	1	no	—
1634	D₄	—	2	1	no	—
1635	D₄	—	4	1	no	—
1636	D₄	—	4	2	no	—
1637	D₄	—	4	2	no	—
1638	D₄	—	4	2	no	—
1639	D₄	—	4	2	no	—
1640	D₄	—	4	2	no	—
1641	D₄	—	4	2	no	—
1642	D₄	—	8	1	no	—
1643	D₄	—	8	1	no	—
1644	D₄	—	8	1	no	—
1645	D₄	—	8	1	no	—
1646	D₄	—	8	1	no	—
1647	D₄	—	8	1	no	—
1648	D₄	—	8	1	no	—
1649	D₄	—	8	1	no	—
1650	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1651	C₂×C₄	—	2	2	no	—
1652	C₂×C₄	—	2	1	no	—
1653	C₂×C₄	—	2	1	no	—
1654	C₂×C₄	—	2	1	no	—
1655	C₂×C₄	—	2	1	no	—
1656	C₂×C₄	—	2	1	no	—
1657	C₂×C₄	—	2	1	no	—
1658	C₂×C₄	—	2	1	no	—
1659	C₂×C₄	—	2	1	no	—
1660	C₂×C₄	—	2	1	no	—
1661	C₂×C₄	—	2	1	no	—
1662	C₂×C₄	—	2	1	no	—
1663	C₂×C₄	—	2	1	no	—
1664	C₂×C₄	—	2	1	no	—
1665	C₂×C₄	—	2	1	no	—
1666	C₂×C₄	—	2	1	no	—
1667	C₂×C₄	—	2	1	no	—
1668	C₂×C₄	—	2	1	no	—
1669	C₂×C₄	—	4	1	no	—
1670	C₂×C₄	—	4	1	no	—
1671	C₂×C₄	—	4	1	no	—
1672	C₂×C₄	—	4	1	no	—
1673	C₂×C₄	—	4	1	no	—
1674	C₂×C₄	—	4	2	no	—
1675	C₂×C₄	—	4	2	no	—
1676	C₂×C₄	—	4	2	no	—
1677	C₂×C₄	—	4	2	no	—
1678	C₂×C₄	—	4	2	no	—
1679	C₂×C₄	—	4	2	no	—
1680	C₂×C₄	—	4	2	no	—
1681	C₂×C₄	—	4	2	no	—
1682	C₂×C₄	—	8	1	no	—
1683	C₂×C₄	—	8	1	no	—
1684	C₂×C₄	—	8	1	no	—
1685	C₂×C₄	—	8	1	no	—
1686	C₂×C₄	—	8	1	no	—
1687	C₂×C₄	—	8	1	no	—
1688	C₂×C₄	—	8	1	no	—
1689	C₂×C₄	—	8	1	no	—
1690	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1691	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1692	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1693	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1694	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1695	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1696	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1697	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1698	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1699	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1700	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1701	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1702	C₈	—	2	1	no	—
1703	C₈	—	2	1	no	—
1704	C₈	—	2	1	no	—
1705	C₈	—	2	1	no	—
1706	C₈	—	2	1	no	—
1707	C₈	—	2	1	no	—
1708	C₈	—	2	1	no	—
1709	C₈	—	2	1	no	—
1710	C₂²	—	2	1	no	—
1711	C₂²	—	2	1	no	—
1712	C₂²	—	2	1	no	—
1713	C₂²	—	2	1	no	—
1714	C₂²	—	2	2	no	—
1715	C₂²	—	2	1	no	—
1716	C₂²	—	2	1	no	—
1717	C₂²	—	2	1	no	—
1718	C₂²	—	2	1	no	—
1719	C₂²	—	4	1	no	—
1720	C₂²	—	4	1	no	—
1721	C₂²	—	4	1	no	—
1722	C₂²	—	4	1	no	—
1723	C₂²	—	4	1	no	—
1724	C₂²	—	4	1	no	—
1725	C₂²	—	4	1	no	—
1726	C₂²	—	4	1	no	—
1727	C₂²	—	4	1	no	—
1728	C₂²	—	4	1	no	—
1729	C₂²	—	4	1	no	—
1730	C₂²	—	4	1	no	—
1731	C₂²	—	4	1	no	—
1732	C₂²	—	4	1	no	—
1733	C₂²	—	8	4	no	—
1734	C₂²	—	16	2	no	—
1735	C₂²	—	16	2	no	—
1736	C₂²	C₅₃×#575	1	2	yes	—
1737	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1738	C₄	—	2	1	no	—
1739	C₄	—	2	1	no	—
1740	C₄	—	2	1	no	—
1741	C₄	—	2	1	no	—
1742	C₄	—	2	1	no	—
1743	C₄	—	2	1	no	—
1744	C₄	—	2	1	no	—
1745	C₄	—	2	1	no	—
1746	C₄	—	2	1	no	—
1747	C₄	—	2	1	no	—
1748	C₄	—	2	1	no	—
1749	C₄	—	4	1	no	—
1750	C₄	—	4	1	no	—
1751	C₄	—	4	1	no	—
1752	C₄	—	4	1	no	—
1753	C₄	—	4	1	no	—
1754	C₄	—	4	1	no	—
1755	C₄	—	4	1	no	—
1756	C₄	—	4	1	no	—
1757	C₄	—	4	1	no	—
1758	C₄	—	4	1	no	—
1759	C₄	—	4	1	no	—
1760	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1761	C₄	C₅₃×#585	1	1	yes	characteristic
1762	C₂	—	2	2	no	—
1763	C₂	—	4	1	no	—
1764	C₂	—	4	1	no	—
1765	C₂	—	4	2	no	—
1766	C₂	—	8	1	no	—
1767	C₂	—	8	1	no	—
1768	C₂	—	8	1	no	—
1769	C₂	—	8	1	no	—
1770	C₂	C₅₃×#3488	1	1	yes	characteristic
1771	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1772	C₂	C₅₃×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3514	C₂	semidirect
2. C₅₃×#3475	C₂	semidirect
3. C₅₃×#3402	C₂	semidirect
4. C₅₃×#3401	C₂	semidirect
5. C₅₃×#3376	C₂	semidirect
6. C₅₃×#3370	C₂	semidirect
7. C₅₃×#3321	C₂	semidirect
8. C₅₃×#3319	C₂	semidirect
9. C₅₃×#3312	C₂	semidirect
10. C₅₃×#3310	C₂	semidirect
11. C₅₃×#3300	C₂	semidirect
12. C₅₃×#3296	C₂	semidirect
13. C₅₃×#3282	C₂	semidirect
14. C₅₃×#3280	C₂	semidirect
15. C₅₃×#3269	C₂	semidirect
16. C₅₃×#3267	C₂	semidirect
17. C₅₃×#3266	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3256	C₂	semidirect
20. C₅₃×#3250	C₂	semidirect
21. C₅₃×#3248	C₂	semidirect
22. C₅₃×#3219	C₂	semidirect
23. C₅₃×#3215	C₂	semidirect
24. C₅₃×#3211	C₂	semidirect
25. C₅₃×#3114	C₂	semidirect
26. C₅₃×#3111	C₂	semidirect
27. C₅₃×#3102	C₂	semidirect
28. C₅₃×#3040	C₂	semidirect
29. C₅₃×#3035	C₂	semidirect
30. C₂×C₅₃×#463	C₂	semidirect
31. C₅₃×#2990	C₂	semidirect
32. C₂×#137×C₅₃	C₂²	semidirect
34. C₂×#135×C₅₃	C₂²	semidirect
35. C₂×#135×C₅₃	C₂²	semidirect
36. C₂²×SD₁₆×C₅₃	C₂²	semidirect
38. C₅₃×#559	C₂²	semidirect
39. C₅₃×#556	C₂²	semidirect
40. C₅₃×#556	C₂²	semidirect
42. C₅₃×#555	C₂²	semidirect
43. C₅₃×#554	C₂²	semidirect
47. C₅₃×#552	C₂²	semidirect
54. C₅₃×#548	C₂²	semidirect
55. C₅₃×#547	C₂²	semidirect
59. C₅₃×#546	C₂²	semidirect
60. C₅₃×#546	C₂²	semidirect
65. C₅₃×#533	C₂²	semidirect
66. C₅₃×#532	C₂²	semidirect
70. C₅₃×#529	C₂²	semidirect
71. C₅₃×#529	C₂²	semidirect
72. C₅₃×#529	C₂²	semidirect
73. C₅₃×#529	C₂²	semidirect
75. C₂×#124×C₅₃	C₂²	semidirect
79. C₄×#41×C₅₃	C₂²	semidirect
80. C₄×#41×C₅₃	C₂²	semidirect
81. C₂×C₄×D₄×C₅₃	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
84. C₅₃×#497	C₂²	semidirect
85. C₅₃×#497	C₂²	semidirect
88. C₅₃×#495	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
90. C₅₃×#490	C₂²	semidirect
91. C₅₃×#489	C₂²	semidirect
92. C₅₃×#489	C₂²	semidirect
93. C₅₃×#488	C₂²	semidirect
94. C₅₃×#488	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#483	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
102. C₅₃×#479	C₂²	semidirect
103. C₅₃×#479	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#475	C₂²	semidirect
110. C₅₃×#474	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
117. C₅₃×#467	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
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
130. C₅₃×#464	C₂²	semidirect
131. C₅₃×#464	C₂²	semidirect
132. C₅₃×#464	C₂²	semidirect
139. C₅₃×#463	C₂²	semidirect
140. C₅₃×#463	C₂²	semidirect
141. C₅₃×#463	C₂²	semidirect
142. C₅₃×#463	C₂²	semidirect
143. C₅₃×#463	C₂²	semidirect
144. C₅₃×#463	C₂²	semidirect
145. C₅₃×#463	C₂²	semidirect
146. C₅₃×#463	C₂²	semidirect
147. C₅₃×#462	C₂²	semidirect
148. C₅₃×#462	C₂²	semidirect
149. C₅₃×#461	C₂²	semidirect
150. C₅₃×#461	C₂²	semidirect
151. C₅₃×#460	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#452	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#452	C₂²	semidirect
157. C₅₃×#451	C₂²	semidirect
158. C₅₃×#451	C₂²	semidirect
159. C₅₃×#451	C₂²	semidirect
162. C₅₃×#450	C₂²	semidirect
163. C₅₃×#450	C₂²	semidirect
166. C₅₃×#449	C₂²	semidirect
167. C₅₃×#449	C₂²	semidirect
168. C₅₃×#448	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
174. C₅₃×#442	C₂²	semidirect
175. C₅₃×#442	C₂²	semidirect
176. C₅₃×#441	C₂²	semidirect
177. C₅₃×#440	C₂²	semidirect
178. C₅₃×#440	C₂²	semidirect
179. C₅₃×#440	C₂²	semidirect
180. C₅₃×#440	C₂²	semidirect
181. C₄×Q₁₆×C₅₃	C₂²	semidirect
182. C₄×SD₁₆×C₅₃	C₂²	semidirect
183. C₄×SD₁₆×C₅₃	C₂²	semidirect
184. C₄×D₈×C₅₃	C₂²	semidirect
187. C₅₃×#435	C₂²	semidirect
188. C₅₃×#435	C₂²	semidirect
189. C₈×D₄×C₅₃	C₂²	semidirect
190. C₈×D₄×C₅₃	C₂²	semidirect
191. C₅₃×#432	C₂²	semidirect
192. C₅₃×#432	C₂²	semidirect
193. C₅₃×#431	C₂²	semidirect
194. C₅₃×#423	C₂²	semidirect
195. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
197. C₅₃×#419	C₂²	semidirect
198. C₅₃×#418	C₂²	semidirect
199. C₅₃×#416	C₂²	semidirect
200. C₅₃×#416	C₂²	semidirect
201. C₂×#103×C₅₃	C₂²	semidirect
823. #61990	C₅₃	direct (N × H)
876. #3514	C₂×C₅₃	semidirect
877. #3475	C₂×C₅₃	semidirect
878. #3402	C₂×C₅₃	semidirect
879. #3401	C₂×C₅₃	semidirect
880. #3376	C₂×C₅₃	semidirect
881. #3370	C₂×C₅₃	semidirect
882. #3321	C₂×C₅₃	semidirect
883. #3319	C₂×C₅₃	semidirect
884. #3312	C₂×C₅₃	semidirect
885. #3310	C₂×C₅₃	semidirect
886. #3300	C₂×C₅₃	semidirect
887. #3296	C₂×C₅₃	semidirect
888. #3282	C₂×C₅₃	semidirect
889. #3280	C₂×C₅₃	semidirect
890. #3269	C₂×C₅₃	semidirect
891. #3267	C₂×C₅₃	semidirect
892. #3266	C₂×C₅₃	semidirect
893. #3264	C₂×C₅₃	semidirect
894. #3256	C₂×C₅₃	semidirect
895. #3250	C₂×C₅₃	semidirect
896. #3248	C₂×C₅₃	semidirect
897. #3219	C₂×C₅₃	semidirect
898. #3215	C₂×C₅₃	semidirect
899. #3211	C₂×C₅₃	semidirect
900. #3114	C₂×C₅₃	semidirect
901. #3111	C₂×C₅₃	semidirect
902. #3102	C₂×C₅₃	semidirect
903. #3040	C₂×C₅₃	semidirect
904. #3035	C₂×C₅₃	semidirect
905. C₂×#463	C₂×C₅₃	semidirect
906. #2990	C₂×C₅₃	semidirect
918. C₂×#137	C₂²×C₅₃	semidirect
920. C₂×#135	C₂²×C₅₃	semidirect
921. C₂×#135	C₂²×C₅₃	semidirect
922. C₂²×SD₁₆	C₂²×C₅₃	semidirect
924. #559	C₂²×C₅₃	semidirect
925. #556	C₂²×C₅₃	semidirect
926. #556	C₂²×C₅₃	semidirect
928. #555	C₂²×C₅₃	semidirect
929. #554	C₂²×C₅₃	semidirect
933. #552	C₂²×C₅₃	semidirect
940. #548	C₂²×C₅₃	semidirect
941. #547	C₂²×C₅₃	semidirect
945. #546	C₂²×C₅₃	semidirect
946. #546	C₂²×C₅₃	semidirect
951. #533	C₂²×C₅₃	semidirect
952. #532	C₂²×C₅₃	semidirect
956. #529	C₂²×C₅₃	semidirect
957. #529	C₂²×C₅₃	semidirect
958. #529	C₂²×C₅₃	semidirect
959. #529	C₂²×C₅₃	semidirect
961. C₂×#124	C₂²×C₅₃	semidirect
965. C₄×#41	C₂²×C₅₃	semidirect
966. C₄×#41	C₂²×C₅₃	semidirect
967. C₂×C₄×D₄	C₂²×C₅₃	semidirect
969. #497	C₂²×C₅₃	semidirect
970. #497	C₂²×C₅₃	semidirect
971. #497	C₂²×C₅₃	semidirect
974. #495	C₂²×C₅₃	semidirect
975. #491	C₂²×C₅₃	semidirect
976. #490	C₂²×C₅₃	semidirect
977. #489	C₂²×C₅₃	semidirect
978. #489	C₂²×C₅₃	semidirect
979. #488	C₂²×C₅₃	semidirect
980. #488	C₂²×C₅₃	semidirect
981. #485	C₂²×C₅₃	semidirect
982. #485	C₂²×C₅₃	semidirect
983. #483	C₂²×C₅₃	semidirect
984. #482	C₂²×C₅₃	semidirect
985. #482	C₂²×C₅₃	semidirect
987. #479	C₂²×C₅₃	semidirect
988. #479	C₂²×C₅₃	semidirect
989. #479	C₂²×C₅₃	semidirect
990. #479	C₂²×C₅₃	semidirect
991. #478	C₂²×C₅₃	semidirect
992. #478	C₂²×C₅₃	semidirect
993. #478	C₂²×C₅₃	semidirect
994. #478	C₂²×C₅₃	semidirect
995. #475	C₂²×C₅₃	semidirect
996. #474	C₂²×C₅₃	semidirect
997. #470	C₂²×C₅₃	semidirect
999. #468	C₂²×C₅₃	semidirect
1000. #468	C₂²×C₅₃	semidirect
1001. #467	C₂²×C₅₃	semidirect
1002. #467	C₂²×C₅₃	semidirect
1003. #467	C₂²×C₅₃	semidirect
1007. #465	C₂²×C₅₃	semidirect
1008. #465	C₂²×C₅₃	semidirect
1009. #464	C₂²×C₅₃	semidirect
1010. #464	C₂²×C₅₃	semidirect
1011. #464	C₂²×C₅₃	semidirect
1012. #464	C₂²×C₅₃	semidirect
1013. #464	C₂²×C₅₃	semidirect
1014. #464	C₂²×C₅₃	semidirect
1015. #464	C₂²×C₅₃	semidirect
1016. #464	C₂²×C₅₃	semidirect
1017. #464	C₂²×C₅₃	semidirect
1018. #464	C₂²×C₅₃	semidirect
1025. #463	C₂²×C₅₃	semidirect
1026. #463	C₂²×C₅₃	semidirect
1027. #463	C₂²×C₅₃	semidirect
1028. #463	C₂²×C₅₃	semidirect
1029. #463	C₂²×C₅₃	semidirect
1030. #463	C₂²×C₅₃	semidirect
1031. #463	C₂²×C₅₃	semidirect
1032. #463	C₂²×C₅₃	semidirect
1033. #462	C₂²×C₅₃	semidirect
1034. #462	C₂²×C₅₃	semidirect
1035. #461	C₂²×C₅₃	semidirect
1036. #461	C₂²×C₅₃	semidirect
1037. #460	C₂²×C₅₃	semidirect
1039. #452	C₂²×C₅₃	semidirect
1040. #452	C₂²×C₅₃	semidirect
1041. #452	C₂²×C₅₃	semidirect
1042. #452	C₂²×C₅₃	semidirect
1043. #451	C₂²×C₅₃	semidirect
1044. #451	C₂²×C₅₃	semidirect
1045. #451	C₂²×C₅₃	semidirect
1048. #450	C₂²×C₅₃	semidirect
1049. #450	C₂²×C₅₃	semidirect
1052. #449	C₂²×C₅₃	semidirect
1053. #449	C₂²×C₅₃	semidirect
1054. #448	C₂²×C₅₃	semidirect
1057. #446	C₂²×C₅₃	semidirect
1058. #446	C₂²×C₅₃	semidirect
1060. #442	C₂²×C₅₃	semidirect
1061. #442	C₂²×C₅₃	semidirect
1062. #441	C₂²×C₅₃	semidirect
1063. #440	C₂²×C₅₃	semidirect
1064. #440	C₂²×C₅₃	semidirect
1065. #440	C₂²×C₅₃	semidirect
1066. #440	C₂²×C₅₃	semidirect
1067. C₄×Q₁₆	C₂²×C₅₃	semidirect
1068. C₄×SD₁₆	C₂²×C₅₃	semidirect
1069. C₄×SD₁₆	C₂²×C₅₃	semidirect
1070. C₄×D₈	C₂²×C₅₃	semidirect
1073. #435	C₂²×C₅₃	semidirect
1074. #435	C₂²×C₅₃	semidirect
1075. C₈×D₄	C₂²×C₅₃	semidirect
1076. C₈×D₄	C₂²×C₅₃	semidirect
1077. #432	C₂²×C₅₃	semidirect
1078. #432	C₂²×C₅₃	semidirect
1079. #431	C₂²×C₅₃	semidirect
1080. #423	C₂²×C₅₃	semidirect
1081. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1082. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1083. #419	C₂²×C₅₃	semidirect
1084. #418	C₂²×C₅₃	semidirect
1085. #416	C₂²×C₅₃	semidirect
1086. #416	C₂²×C₅₃	semidirect
1087. C₂×#103	C₂²×C₅₃	semidirect
1089. C₅₃	#61990	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3514	2
C₅₃×#3475	2
C₅₃×#3402	2
C₅₃×#3401	2
C₅₃×#3376	2
C₅₃×#3370	2
C₅₃×#3321	2
C₅₃×#3319	2
C₅₃×#3312	2
C₅₃×#3310	2
C₅₃×#3300	2
C₅₃×#3296	2
C₅₃×#3282	2
C₅₃×#3280	2
C₅₃×#3269	2
C₅₃×#3267	2
C₅₃×#3266	2
C₅₃×#3264	2
C₅₃×#3256	2
C₅₃×#3250	2
C₅₃×#3248	2
C₅₃×#3219	2
C₅₃×#3215	2
C₅₃×#3211	2
C₅₃×#3114	2
C₅₃×#3111	2
C₅₃×#3102	2
C₅₃×#3040	2
C₅₃×#3035	2
C₂×C₅₃×#463	2
C₅₃×#2990	2
#61990	53

Subgroups — C53×#61990 #27269502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61990 #27269502