Subgroups — C₅₃×#62009 #27269521

Order 13568.

1896 conjugacy classes of subgroups.

The subgroup lattice has 1806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3516	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3371	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3317	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3295	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3282	C₂	1	1	yes	maximal, characteristic, complemented
14	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3260	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3250	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3224	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3217	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3126	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3119	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3117	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×C₅₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#560	—	2	1	no	—
39	C₅₃×#560	—	2	1	no	—
40	C₅₃×#559	C₂²	1	1	yes	characteristic
41	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#556	—	2	1	no	—
43	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#554	—	2	1	no	—
45	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#553	—	2	1	no	—
47	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#552	—	2	1	no	—
49	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
50	C₅₃×#550	C₂²	1	1	yes	characteristic
51	C₅₃×#550	C₂²	1	1	yes	characteristic
52	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#546	—	2	1	no	—
56	C₅₃×#546	C₂²	1	1	yes	characteristic
57	C₅₃×#546	C₂²	1	1	yes	characteristic
58	D₄²×C₅₃	—	2	1	no	—
59	D₄²×C₅₃	C₂²	1	1	yes	characteristic
60	D₄²×C₅₃	C₂²	1	1	yes	characteristic
61	D₄²×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#542	—	2	1	no	—
63	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#541	—	2	1	no	—
65	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#540	—	2	1	no	—
67	C₅₃×#540	C₂²	1	1	yes	characteristic
68	C₅₃×#540	C₂²	1	1	yes	characteristic
69	C₅₃×#535	—	2	1	no	—
70	C₅₃×#535	C₂²	1	1	yes	characteristic
71	C₅₃×#535	C₂²	1	1	yes	characteristic
72	C₅₃×#534	—	2	1	no	—
73	C₅₃×#534	—	2	1	no	—
74	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
75	C₅₃×#529	—	2	1	no	—
76	C₅₃×#529	—	2	1	no	—
77	C₅₃×#529	C₂²	1	1	yes	characteristic
78	C₅₃×#529	C₂²	1	1	yes	characteristic
79	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#519	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#496	C₂²	1	1	yes	characteristic
85	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#490	C₂²	1	1	yes	characteristic
90	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#490	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×#486	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#481	C₂²	1	1	yes	characteristic
99	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#478	C₂²	1	1	yes	characteristic, 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×#476	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
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×#466	C₂²	1	1	yes	characteristic
117	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#465	C₂²	1	1	yes	characteristic
119	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#464	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×#463	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#463	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×#460	C₂²	1	1	yes	characteristic
138	C₅₃×#460	C₂²	1	1	yes	characteristic
139	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#451	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
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×#447	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#447	C₂²	1	1	yes	characteristic, complemented
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, complemented
174	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
175	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
176	C₅₃×#440	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×SD₁₆×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, complemented
186	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
189	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
190	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
200	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
201	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
208	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×D₄×C₅₃	—	2	1	no	—
210	C₂²×D₄×C₅₃	—	2	1	no	—
211	C₂²×D₄×C₅₃	—	2	1	no	—
212	C₂²×D₄×C₅₃	—	2	1	no	—
213	C₂²×D₄×C₅₃	—	2	1	no	—
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
217	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
218	#137×C₅₃	—	4	2	no	—
219	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
220	#135×C₅₃	—	4	2	no	—
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×SD₁₆×C₅₃	—	4	2	no	—
225	C₂×SD₁₆×C₅₃	—	4	2	no	—
226	C₂×SD₁₆×C₅₃	—	4	2	no	—
227	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×SD₁₆×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×D₈×C₅₃	C₂³	1	1	yes	characteristic
246	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
252	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₅₃	—	2	1	no	—
255	C₄⋊Q₈×C₅₃	—	2	1	no	—
256	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
258	#127×C₅₃	—	2	1	no	—
259	#127×C₅₃	—	2	1	no	—
260	#127×C₅₃	—	2	1	no	—
261	#127×C₅₃	C₂³	1	1	yes	characteristic
262	#127×C₅₃	C₂³	1	1	yes	characteristic
263	#127×C₅₃	C₂³	1	1	yes	characteristic
264	#127×C₅₃	C₂³	1	1	yes	characteristic
265	#127×C₅₃	C₂³	1	1	yes	characteristic
266	#127×C₅₃	C₂³	1	1	yes	characteristic
267	#126×C₅₃	—	2	1	no	—
268	#126×C₅₃	—	2	1	no	—
269	#126×C₅₃	—	2	1	no	—
270	#126×C₅₃	—	2	1	no	—
271	#126×C₅₃	—	2	1	no	—
272	#126×C₅₃	—	2	1	no	—
273	#126×C₅₃	—	2	1	no	—
274	#126×C₅₃	—	2	1	no	—
275	#126×C₅₃	—	2	1	no	—
276	#126×C₅₃	D₄	1	1	yes	characteristic
277	#126×C₅₃	D₄	1	1	yes	characteristic
278	#125×C₅₃	—	2	1	no	—
279	#125×C₅₃	—	2	1	no	—
280	#125×C₅₃	—	2	1	no	—
281	#125×C₅₃	—	2	1	no	—
282	#125×C₅₃	—	2	1	no	—
283	#125×C₅₃	—	2	1	no	—
284	#125×C₅₃	D₄	1	1	yes	characteristic
285	#125×C₅₃	C₂³	1	1	yes	characteristic
286	#125×C₅₃	C₂³	1	1	yes	characteristic
287	#125×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
293	#124×C₅₃	C₂³	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
295	#124×C₅₃	C₂³	1	1	yes	characteristic
296	#124×C₅₃	C₂³	1	1	yes	characteristic
297	#124×C₅₃	C₂³	1	1	yes	characteristic
298	#123×C₅₃	—	2	1	no	—
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	—	2	1	no	—
311	#123×C₅₃	D₄	1	1	yes	characteristic
312	#123×C₅₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
317	C₂²⋊Q₈×C₅₃	—	2	1	no	—
318	C₂²⋊Q₈×C₅₃	—	2	1	no	—
319	C₂²⋊Q₈×C₅₃	—	2	1	no	—
320	C₂²⋊Q₈×C₅₃	—	2	1	no	—
321	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
322	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
325	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
326	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
335	#121×C₅₃	—	2	1	no	—
336	#121×C₅₃	—	2	1	no	—
337	#121×C₅₃	—	2	1	no	—
338	#121×C₅₃	—	2	1	no	—
339	#121×C₅₃	—	2	1	no	—
340	#121×C₅₃	—	2	1	no	—
341	#121×C₅₃	—	2	1	no	—
342	#121×C₅₃	—	2	1	no	—
343	#121×C₅₃	—	2	1	no	—
344	#121×C₅₃	—	2	1	no	—
345	#121×C₅₃	—	2	1	no	—
346	#121×C₅₃	—	2	1	no	—
347	#121×C₅₃	—	2	1	no	—
348	#121×C₅₃	D₄	1	1	yes	characteristic
349	#121×C₅₃	C₂³	1	1	yes	characteristic
350	#121×C₅₃	C₂³	1	1	yes	characteristic
351	#121×C₅₃	C₂³	1	1	yes	characteristic
352	#121×C₅₃	C₂³	1	1	yes	characteristic
353	#121×C₅₃	C₂³	1	1	yes	characteristic
354	#121×C₅₃	C₂³	1	1	yes	characteristic
355	#121×C₅₃	C₂³	1	1	yes	characteristic
356	#120×C₅₃	—	2	1	no	—
357	#120×C₅₃	—	2	1	no	—
358	#120×C₅₃	—	2	1	no	—
359	#120×C₅₃	—	2	1	no	—
360	#120×C₅₃	—	2	1	no	—
361	#120×C₅₃	—	2	1	no	—
362	#120×C₅₃	—	2	1	no	—
363	#120×C₅₃	—	2	1	no	—
364	#120×C₅₃	—	2	1	no	—
365	#120×C₅₃	—	2	1	no	—
366	#120×C₅₃	—	2	1	no	—
367	#120×C₅₃	—	2	1	no	—
368	C₄×Q₈×C₅₃	—	2	1	no	—
369	C₄×Q₈×C₅₃	—	2	1	no	—
370	C₄×Q₈×C₅₃	—	2	1	no	—
371	C₄×Q₈×C₅₃	—	2	1	no	—
372	C₄×Q₈×C₅₃	—	2	1	no	—
373	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
379	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
380	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
381	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
382	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	—	2	1	no	—
387	C₄×D₄×C₅₃	—	2	1	no	—
388	C₄×D₄×C₅₃	—	2	1	no	—
389	C₄×D₄×C₅₃	—	2	1	no	—
390	C₄×D₄×C₅₃	—	2	1	no	—
391	C₄×D₄×C₅₃	—	2	1	no	—
392	C₄×D₄×C₅₃	—	2	1	no	—
393	C₄×D₄×C₅₃	—	2	1	no	—
394	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
395	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
396	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
397	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
398	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
399	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
400	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
401	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
402	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
403	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
404	#117×C₅₃	—	2	1	no	—
405	#117×C₅₃	—	2	1	no	—
406	#117×C₅₃	—	2	1	no	—
407	#117×C₅₃	—	2	1	no	—
408	#117×C₅₃	—	2	1	no	—
409	#117×C₅₃	—	2	1	no	—
410	#117×C₅₃	—	2	1	no	—
411	#117×C₅₃	C₂³	1	1	yes	characteristic
412	#117×C₅₃	C₂³	1	1	yes	characteristic
413	#117×C₅₃	C₂³	1	1	yes	characteristic
414	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
417	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
418	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
419	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
420	C₂×C₄²×C₅₃	—	2	1	no	—
421	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#107×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#102×C₅₃	C₂³	1	1	yes	characteristic
451	#102×C₅₃	C₂³	1	1	yes	characteristic
452	#102×C₅₃	C₂³	1	1	yes	characteristic
453	#102×C₅₃	C₂³	1	1	yes	characteristic
454	#102×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#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	C₂⁴×C₅₃	—	2	1	no	—
488	#41×C₅₃	—	2	2	no	—
489	#41×C₅₃	—	4	1	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	—	8	2	no	—
495	C₂×Q₈×C₅₃	—	2	1	no	—
496	C₂×Q₈×C₅₃	—	2	1	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	2	2	no	—
499	C₂×Q₈×C₅₃	—	2	2	no	—
500	C₂×Q₈×C₅₃	—	4	1	no	—
501	C₂×Q₈×C₅₃	—	4	1	no	—
502	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
503	C₂×Q₈×C₅₃	C₂⁴	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×D₄×C₅₃	—	2	1	no	—
508	C₂×D₄×C₅₃	—	2	1	no	—
509	C₂×D₄×C₅₃	—	2	1	no	—
510	C₂×D₄×C₅₃	—	2	1	no	—
511	C₂×D₄×C₅₃	—	2	1	no	—
512	C₂×D₄×C₅₃	—	2	1	no	—
513	C₂×D₄×C₅₃	—	2	1	no	—
514	C₂×D₄×C₅₃	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	2	1	no	—
519	C₂×D₄×C₅₃	—	2	1	no	—
520	C₂×D₄×C₅₃	—	2	1	no	—
521	C₂×D₄×C₅₃	—	2	1	no	—
522	C₂×D₄×C₅₃	—	2	1	no	—
523	C₂×D₄×C₅₃	—	2	1	no	—
524	C₂×D₄×C₅₃	—	2	1	no	—
525	C₂×D₄×C₅₃	—	2	1	no	—
526	C₂×D₄×C₅₃	—	2	1	no	—
527	C₂×D₄×C₅₃	—	2	1	no	—
528	C₂×D₄×C₅₃	—	2	1	no	—
529	C₂×D₄×C₅₃	—	2	1	no	—
530	C₂×D₄×C₅₃	—	2	1	no	—
531	C₂×D₄×C₅₃	—	2	1	no	—
532	C₂×D₄×C₅₃	—	2	1	no	—
533	C₂×D₄×C₅₃	—	4	1	no	—
534	C₂×D₄×C₅₃	—	4	1	no	—
535	C₂×D₄×C₅₃	—	4	1	no	—
536	C₂×D₄×C₅₃	—	4	1	no	—
537	C₂×D₄×C₅₃	—	4	1	no	—
538	C₂×D₄×C₅₃	—	4	1	no	—
539	C₂×D₄×C₅₃	—	4	1	no	—
540	C₂×D₄×C₅₃	—	4	1	no	—
541	C₂×D₄×C₅₃	—	8	2	no	—
542	C₂×D₄×C₅₃	—	8	2	no	—
543	C₂×D₄×C₅₃	—	8	2	no	—
544	C₂×D₄×C₅₃	—	8	2	no	—
545	C₂×D₄×C₅₃	—	8	2	no	—
546	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
547	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
548	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
549	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
550	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
551	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
552	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
553	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
554	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
555	C₂²×C₄×C₅₃	—	2	1	no	—
556	C₂²×C₄×C₅₃	—	2	1	no	—
557	C₂²×C₄×C₅₃	—	2	1	no	—
558	C₂²×C₄×C₅₃	—	2	1	no	—
559	C₂²×C₄×C₅₃	—	2	1	no	—
560	C₂²×C₄×C₅₃	—	2	1	no	—
561	C₂²×C₄×C₅₃	—	2	1	no	—
562	C₂²×C₄×C₅₃	—	2	1	no	—
563	C₂²×C₄×C₅₃	—	2	1	no	—
564	C₂²×C₄×C₅₃	—	2	1	no	—
565	C₂²×C₄×C₅₃	—	2	1	no	—
566	C₂²×C₄×C₅₃	—	2	1	no	—
567	C₂²×C₄×C₅₃	—	2	1	no	—
568	C₂²×C₄×C₅₃	—	2	1	no	—
569	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
570	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
571	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
572	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
573	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
574	Q₁₆×C₅₃	—	2	2	no	—
575	Q₁₆×C₅₃	—	4	1	no	—
576	Q₁₆×C₅₃	—	4	1	no	—
577	SD₁₆×C₅₃	—	2	2	no	—
578	SD₁₆×C₅₃	—	2	2	no	—
579	SD₁₆×C₅₃	—	2	2	no	—
580	SD₁₆×C₅₃	—	2	2	no	—
581	SD₁₆×C₅₃	—	2	2	no	—
582	SD₁₆×C₅₃	—	4	1	no	—
583	SD₁₆×C₅₃	—	4	1	no	—
584	SD₁₆×C₅₃	—	4	1	no	—
585	SD₁₆×C₅₃	—	4	1	no	—
586	SD₁₆×C₅₃	—	4	1	no	—
587	SD₁₆×C₅₃	—	4	1	no	—
588	SD₁₆×C₅₃	—	4	1	no	—
589	SD₁₆×C₅₃	—	4	1	no	—
590	SD₁₆×C₅₃	—	4	1	no	—
591	SD₁₆×C₅₃	—	4	1	no	—
592	SD₁₆×C₅₃	—	4	1	no	—
593	D₈×C₅₃	—	4	1	no	—
594	D₈×C₅₃	—	4	1	no	—
595	D₈×C₅₃	—	4	1	no	—
596	D₈×C₅₃	—	4	1	no	—
597	D₈×C₅₃	—	4	1	no	—
598	M₁₆×C₅₃	—	4	1	no	—
599	M₁₆×C₅₃	—	4	1	no	—
600	C₂×C₈×C₅₃	—	4	1	no	—
601	C₂×C₈×C₅₃	—	4	1	no	—
602	C₂×C₈×C₅₃	—	4	1	no	—
603	C₂×C₈×C₅₃	—	4	1	no	—
604	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
605	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
606	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
607	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
614	C₄⋊C₄×C₅₃	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
619	C₄⋊C₄×C₅₃	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	—	2	1	no	—
627	C₄⋊C₄×C₅₃	—	2	1	no	—
628	C₄⋊C₄×C₅₃	—	2	1	no	—
629	C₄⋊C₄×C₅₃	—	2	1	no	—
630	C₄⋊C₄×C₅₃	—	2	1	no	—
631	C₄⋊C₄×C₅₃	—	2	1	no	—
632	C₄⋊C₄×C₅₃	—	2	1	no	—
633	C₄⋊C₄×C₅₃	—	2	1	no	—
634	C₄⋊C₄×C₅₃	—	2	1	no	—
635	C₄⋊C₄×C₅₃	—	2	1	no	—
636	C₄⋊C₄×C₅₃	—	2	1	no	—
637	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
642	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
643	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
644	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
645	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
646	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
647	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
648	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
649	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
650	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
651	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
652	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
668	C₂²⋊C₄×C₅₃	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	—	2	1	no	—
670	C₂²⋊C₄×C₅₃	—	2	1	no	—
671	C₂²⋊C₄×C₅₃	—	2	1	no	—
672	C₂²⋊C₄×C₅₃	—	2	1	no	—
673	C₂²⋊C₄×C₅₃	—	2	1	no	—
674	C₂²⋊C₄×C₅₃	—	2	1	no	—
675	C₂²⋊C₄×C₅₃	—	2	1	no	—
676	C₂²⋊C₄×C₅₃	—	2	1	no	—
677	C₂²⋊C₄×C₅₃	—	2	1	no	—
678	C₂²⋊C₄×C₅₃	—	2	1	no	—
679	C₂²⋊C₄×C₅₃	—	2	1	no	—
680	C₂²⋊C₄×C₅₃	—	2	1	no	—
681	C₂²⋊C₄×C₅₃	—	2	1	no	—
682	C₂²⋊C₄×C₅₃	—	2	1	no	—
683	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
685	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
686	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
687	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
688	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
689	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
690	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
691	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
692	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
693	C₄²×C₅₃	—	2	1	no	—
694	C₄²×C₅₃	—	2	1	no	—
695	C₄²×C₅₃	—	2	1	no	—
696	C₄²×C₅₃	—	2	1	no	—
697	C₄²×C₅₃	—	2	1	no	—
698	C₄²×C₅₃	—	2	1	no	—
699	C₄²×C₅₃	—	2	1	no	—
700	C₄²×C₅₃	—	2	1	no	—
701	C₄²×C₅₃	—	2	1	no	—
702	C₄²×C₅₃	—	2	1	no	—
703	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
704	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
705	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
707	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
708	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
709	C₂³×C₅₃	—	2	1	no	—
710	C₂³×C₅₃	—	2	1	no	—
711	C₂³×C₅₃	—	2	1	no	—
712	C₂³×C₅₃	—	2	1	no	—
713	C₂³×C₅₃	—	2	1	no	—
714	C₂³×C₅₃	—	2	1	no	—
715	C₂³×C₅₃	—	4	2	no	—
716	C₂³×C₅₃	—	4	2	no	—
717	C₂³×C₅₃	—	8	1	no	—
718	C₂³×C₅₃	—	8	1	no	—
719	C₂³×C₅₃	—	8	1	no	—
720	C₂³×C₅₃	—	8	1	no	—
721	C₂³×C₅₃	—	8	1	no	—
722	C₂³×C₅₃	—	8	1	no	—
723	C₂³×C₅₃	—	8	1	no	—
724	C₂³×C₅₃	—	8	1	no	—
725	C₂³×C₅₃	—	8	1	no	—
726	C₂³×C₅₃	—	8	1	no	—
727	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
728	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
729	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
730	Q₈×C₅₃	—	2	1	no	—
731	Q₈×C₅₃	—	2	1	no	—
732	Q₈×C₅₃	—	2	1	no	—
733	Q₈×C₅₃	—	2	1	no	—
734	Q₈×C₅₃	—	2	1	no	—
735	Q₈×C₅₃	—	2	1	no	—
736	Q₈×C₅₃	—	2	1	no	—
737	Q₈×C₅₃	—	4	1	no	—
738	Q₈×C₅₃	—	4	2	no	—
739	Q₈×C₅₃	—	4	2	no	—
740	Q₈×C₅₃	—	8	1	no	—
741	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
742	D₄×C₅₃	—	2	2	no	—
743	D₄×C₅₃	—	2	2	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	—	2	1	no	—
749	D₄×C₅₃	—	2	1	no	—
750	D₄×C₅₃	—	2	1	no	—
751	D₄×C₅₃	—	2	1	no	—
752	D₄×C₅₃	—	2	1	no	—
753	D₄×C₅₃	—	2	1	no	—
754	D₄×C₅₃	—	2	1	no	—
755	D₄×C₅₃	—	2	1	no	—
756	D₄×C₅₃	—	4	1	no	—
757	D₄×C₅₃	—	4	2	no	—
758	D₄×C₅₃	—	4	2	no	—
759	D₄×C₅₃	—	4	2	no	—
760	D₄×C₅₃	—	4	2	no	—
761	D₄×C₅₃	—	4	2	no	—
762	D₄×C₅₃	—	8	1	no	—
763	D₄×C₅₃	—	8	1	no	—
764	D₄×C₅₃	—	8	1	no	—
765	D₄×C₅₃	—	8	1	no	—
766	D₄×C₅₃	—	8	1	no	—
767	D₄×C₅₃	—	8	1	no	—
768	D₄×C₅₃	—	8	1	no	—
769	D₄×C₅₃	—	8	1	no	—
770	D₄×C₅₃	—	8	1	no	—
771	D₄×C₅₃	—	8	1	no	—
772	D₄×C₅₃	—	8	1	no	—
773	D₄×C₅₃	—	8	1	no	—
774	D₄×C₅₃	—	8	1	no	—
775	D₄×C₅₃	—	8	1	no	—
776	D₄×C₅₃	—	8	1	no	—
777	D₄×C₅₃	—	8	1	no	—
778	D₄×C₅₃	—	8	1	no	—
779	D₄×C₅₃	—	8	1	no	—
780	D₄×C₅₃	—	8	1	no	—
781	D₄×C₅₃	—	8	1	no	—
782	D₄×C₅₃	—	8	1	no	—
783	C₂×C₄×C₅₃	—	2	2	no	—
784	C₂×C₄×C₅₃	—	2	1	no	—
785	C₂×C₄×C₅₃	—	2	1	no	—
786	C₂×C₄×C₅₃	—	2	1	no	—
787	C₂×C₄×C₅₃	—	2	1	no	—
788	C₂×C₄×C₅₃	—	2	1	no	—
789	C₂×C₄×C₅₃	—	2	1	no	—
790	C₂×C₄×C₅₃	—	2	1	no	—
791	C₂×C₄×C₅₃	—	2	1	no	—
792	C₂×C₄×C₅₃	—	2	1	no	—
793	C₂×C₄×C₅₃	—	2	1	no	—
794	C₂×C₄×C₅₃	—	2	1	no	—
795	C₂×C₄×C₅₃	—	2	1	no	—
796	C₂×C₄×C₅₃	—	2	1	no	—
797	C₂×C₄×C₅₃	—	2	1	no	—
798	C₂×C₄×C₅₃	—	2	1	no	—
799	C₂×C₄×C₅₃	—	2	1	no	—
800	C₂×C₄×C₅₃	—	4	1	no	—
801	C₂×C₄×C₅₃	—	4	2	no	—
802	C₂×C₄×C₅₃	—	4	2	no	—
803	C₂×C₄×C₅₃	—	4	2	no	—
804	C₂×C₄×C₅₃	—	4	2	no	—
805	C₂×C₄×C₅₃	—	8	1	no	—
806	C₂×C₄×C₅₃	—	8	1	no	—
807	C₂×C₄×C₅₃	—	8	1	no	—
808	C₂×C₄×C₅₃	—	8	1	no	—
809	C₂×C₄×C₅₃	—	8	1	no	—
810	C₂×C₄×C₅₃	—	8	1	no	—
811	C₂×C₄×C₅₃	—	8	1	no	—
812	C₂×C₄×C₅₃	—	8	1	no	—
813	C₂×C₄×C₅₃	—	8	1	no	—
814	C₂×C₄×C₅₃	—	8	1	no	—
815	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
816	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
817	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
818	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
819	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
820	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
821	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
822	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
823	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
824	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
825	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
826	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
827	C₈×C₅₃	—	2	1	no	—
828	C₈×C₅₃	—	2	1	no	—
829	C₈×C₅₃	—	2	1	no	—
830	C₈×C₅₃	—	2	1	no	—
831	C₈×C₅₃	—	2	1	no	—
832	C₈×C₅₃	—	2	1	no	—
833	C₈×C₅₃	—	2	1	no	—
834	C₈×C₅₃	—	2	1	no	—
835	#62009	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
836	C₂²×C₅₃	—	2	1	no	—
837	C₂²×C₅₃	—	2	1	no	—
838	C₂²×C₅₃	—	2	1	no	—
839	C₂²×C₅₃	—	2	1	no	—
840	C₂²×C₅₃	—	2	1	no	—
841	C₂²×C₅₃	—	2	1	no	—
842	C₂²×C₅₃	—	2	1	no	—
843	C₂²×C₅₃	—	2	1	no	—
844	C₂²×C₅₃	—	4	1	no	—
845	C₂²×C₅₃	—	4	1	no	—
846	C₂²×C₅₃	—	4	1	no	—
847	C₂²×C₅₃	—	4	1	no	—
848	C₂²×C₅₃	—	4	1	no	—
849	C₂²×C₅₃	—	4	1	no	—
850	C₂²×C₅₃	—	4	1	no	—
851	C₂²×C₅₃	—	4	1	no	—
852	C₂²×C₅₃	—	4	1	no	—
853	C₂²×C₅₃	—	4	1	no	—
854	C₂²×C₅₃	—	4	1	no	—
855	C₂²×C₅₃	—	4	1	no	—
856	C₂²×C₅₃	—	4	1	no	—
857	C₂²×C₅₃	—	4	1	no	—
858	C₂²×C₅₃	—	4	1	no	—
859	C₂²×C₅₃	—	4	1	no	—
860	C₂²×C₅₃	—	4	1	no	—
861	C₂²×C₅₃	—	4	1	no	—
862	C₂²×C₅₃	—	16	2	no	—
863	C₂²×C₅₃	—	16	2	no	—
864	C₂²×C₅₃	—	16	2	no	—
865	C₂²×C₅₃	—	16	2	no	—
866	C₂²×C₅₃	#577	1	2	yes	—
867	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
868	C₄×C₅₃	—	2	1	no	—
869	C₄×C₅₃	—	2	1	no	—
870	C₄×C₅₃	—	2	1	no	—
871	C₄×C₅₃	—	2	1	no	—
872	C₄×C₅₃	—	2	1	no	—
873	C₄×C₅₃	—	2	1	no	—
874	C₄×C₅₃	—	2	1	no	—
875	C₄×C₅₃	—	2	2	no	—
876	C₄×C₅₃	—	2	1	no	—
877	C₄×C₅₃	—	2	1	no	—
878	C₄×C₅₃	—	2	1	no	—
879	C₄×C₅₃	—	2	1	no	—
880	C₄×C₅₃	—	4	1	no	—
881	C₄×C₅₃	—	4	1	no	—
882	C₄×C₅₃	—	4	1	no	—
883	C₄×C₅₃	—	4	1	no	—
884	C₄×C₅₃	—	4	1	no	—
885	C₄×C₅₃	—	4	1	no	—
886	C₄×C₅₃	—	4	1	no	—
887	C₄×C₅₃	—	4	1	no	—
888	C₄×C₅₃	—	4	1	no	—
889	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
890	C₄×C₅₃	#585	1	1	yes	characteristic
891	#3543	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3516	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3371	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3368	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#3317	C₂×C₅₃	1	1	yes	characteristic, complemented
899	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
900	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
901	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
902	#3295	C₂×C₅₃	1	1	yes	characteristic, complemented
903	#3282	C₂×C₅₃	1	1	yes	characteristic, complemented
904	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
905	#3271	C₂×C₅₃	1	1	yes	characteristic, complemented
906	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
907	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
908	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
909	#3260	C₂×C₅₃	1	1	yes	characteristic, complemented
910	#3257	C₂×C₅₃	1	1	yes	characteristic, complemented
911	#3250	C₂×C₅₃	1	1	yes	characteristic, complemented
912	#3224	C₂×C₅₃	1	1	yes	characteristic, complemented
913	#3222	C₂×C₅₃	1	1	yes	characteristic, complemented
914	#3217	C₂×C₅₃	1	1	yes	characteristic, complemented
915	#3126	C₂×C₅₃	1	1	yes	characteristic, complemented
916	#3119	C₂×C₅₃	1	1	yes	characteristic, complemented
917	#3117	C₂×C₅₃	1	1	yes	characteristic, complemented
918	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
919	#3043	C₂×C₅₃	1	1	yes	characteristic, complemented
920	C₂×#460	C₂×C₅₃	1	1	yes	characteristic, complemented
921	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
922	C₂×C₅₃	—	2	2	no	—
923	C₂×C₅₃	—	4	1	no	—
924	C₂×C₅₃	—	4	1	no	—
925	C₂×C₅₃	—	8	1	no	—
926	C₂×C₅₃	—	8	1	no	—
927	C₂×C₅₃	—	8	1	no	—
928	C₂×C₅₃	—	8	1	no	—
929	C₂×C₅₃	—	8	1	no	—
930	C₂×C₅₃	—	8	1	no	—
931	C₂×C₅₃	#3488	1	1	yes	characteristic
932	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
933	C₂×C₅₃	#3585	1	1	yes	characteristic
934	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#560	—	2	1	no	—
941	#560	—	2	1	no	—
942	#559	C₂²×C₅₃	1	1	yes	characteristic
943	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#556	—	2	1	no	—
945	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#554	—	2	1	no	—
947	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#553	—	2	1	no	—
949	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#552	—	2	1	no	—
951	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#550	C₂²×C₅₃	1	1	yes	characteristic
953	#550	C₂²×C₅₃	1	1	yes	characteristic
954	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#546	—	2	1	no	—
958	#546	C₂²×C₅₃	1	1	yes	characteristic
959	#546	C₂²×C₅₃	1	1	yes	characteristic
960	D₄²	—	2	1	no	—
961	D₄²	C₂²×C₅₃	1	1	yes	characteristic
962	D₄²	C₂²×C₅₃	1	1	yes	characteristic
963	D₄²	C₂²×C₅₃	1	1	yes	characteristic
964	#542	—	2	1	no	—
965	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#541	—	2	1	no	—
967	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#540	—	2	1	no	—
969	#540	C₂²×C₅₃	1	1	yes	characteristic
970	#540	C₂²×C₅₃	1	1	yes	characteristic
971	#535	—	2	1	no	—
972	#535	C₂²×C₅₃	1	1	yes	characteristic
973	#535	C₂²×C₅₃	1	1	yes	characteristic
974	#534	—	2	1	no	—
975	#534	—	2	1	no	—
976	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
977	#529	—	2	1	no	—
978	#529	—	2	1	no	—
979	#529	C₂²×C₅₃	1	1	yes	characteristic
980	#529	C₂²×C₅₃	1	1	yes	characteristic
981	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#496	C₂²×C₅₃	1	1	yes	characteristic
987	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#490	C₂²×C₅₃	1	1	yes	characteristic
992	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#481	C₂²×C₅₃	1	1	yes	characteristic
1001	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
1011	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
1012	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#466	C₂²×C₅₃	1	1	yes	characteristic
1019	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#465	C₂²×C₅₃	1	1	yes	characteristic
1021	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#460	C₂²×C₅₃	1	1	yes	characteristic
1040	#460	C₂²×C₅₃	1	1	yes	characteristic
1041	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1047	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1048	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	#448	C₂²×C₅₃	1	1	yes	characteristic
1068	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1069	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
1073	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1074	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1083	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1088	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1089	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1090	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1091	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1092	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1093	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1094	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1095	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1096	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1097	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1098	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1099	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1100	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1101	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1102	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1103	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1104	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1105	C₅₃	#62009	1	1	yes	characteristic, direct product factor, Sylow
1106	C₂×#41	—	2	1	no	—
1107	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂²×D₄	—	2	1	no	—
1113	C₂²×D₄	—	2	1	no	—
1114	C₂²×D₄	—	2	1	no	—
1115	C₂²×D₄	—	2	1	no	—
1116	C₂²×D₄	—	2	1	no	—
1117	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1118	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1119	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1120	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1121	#137	—	4	2	no	—
1122	AGL(1,ℤ/8)	—	4	2	no	—
1123	#135	—	4	2	no	—
1124	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1125	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂×SD₁₆	—	4	2	no	—
1128	C₂×SD₁₆	—	4	2	no	—
1129	C₂×SD₁₆	—	4	2	no	—
1130	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1135	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1136	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1137	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1138	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1139	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1140	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1141	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1142	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1143	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1144	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1145	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1146	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1147	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1148	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1149	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1150	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1151	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1152	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1153	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1154	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1157	C₄⋊Q₈	—	2	1	no	—
1158	C₄⋊Q₈	—	2	1	no	—
1159	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1160	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1161	#127	—	2	1	no	—
1162	#127	—	2	1	no	—
1163	#127	—	2	1	no	—
1164	#127	C₂³×C₅₃	1	1	yes	characteristic
1165	#127	C₂³×C₅₃	1	1	yes	characteristic
1166	#127	C₂³×C₅₃	1	1	yes	characteristic
1167	#127	C₂³×C₅₃	1	1	yes	characteristic
1168	#127	C₂³×C₅₃	1	1	yes	characteristic
1169	#127	C₂³×C₅₃	1	1	yes	characteristic
1170	#126	—	2	1	no	—
1171	#126	—	2	1	no	—
1172	#126	—	2	1	no	—
1173	#126	—	2	1	no	—
1174	#126	—	2	1	no	—
1175	#126	—	2	1	no	—
1176	#126	—	2	1	no	—
1177	#126	—	2	1	no	—
1178	#126	—	2	1	no	—
1179	#126	D₄×C₅₃	1	1	yes	characteristic
1180	#126	D₄×C₅₃	1	1	yes	characteristic
1181	#125	—	2	1	no	—
1182	#125	—	2	1	no	—
1183	#125	—	2	1	no	—
1184	#125	—	2	1	no	—
1185	#125	—	2	1	no	—
1186	#125	—	2	1	no	—
1187	#125	D₄×C₅₃	1	1	yes	characteristic
1188	#125	C₂³×C₅₃	1	1	yes	characteristic
1189	#125	C₂³×C₅₃	1	1	yes	characteristic
1190	#125	C₂³×C₅₃	1	1	yes	characteristic
1191	#124	—	2	1	no	—
1192	#124	—	2	1	no	—
1193	#124	—	2	1	no	—
1194	#124	—	2	1	no	—
1195	#124	D₄×C₅₃	1	1	yes	characteristic
1196	#124	C₂³×C₅₃	1	1	yes	characteristic
1197	#124	C₂³×C₅₃	1	1	yes	characteristic
1198	#124	C₂³×C₅₃	1	1	yes	characteristic
1199	#124	C₂³×C₅₃	1	1	yes	characteristic
1200	#124	C₂³×C₅₃	1	1	yes	characteristic
1201	#123	—	2	1	no	—
1202	#123	—	2	1	no	—
1203	#123	—	2	1	no	—
1204	#123	—	2	1	no	—
1205	#123	—	2	1	no	—
1206	#123	—	2	1	no	—
1207	#123	—	2	1	no	—
1208	#123	—	2	1	no	—
1209	#123	—	2	1	no	—
1210	#123	—	2	1	no	—
1211	#123	—	2	1	no	—
1212	#123	—	2	1	no	—
1213	#123	—	2	1	no	—
1214	#123	D₄×C₅₃	1	1	yes	characteristic
1215	#123	D₄×C₅₃	1	1	yes	characteristic
1216	C₂²⋊Q₈	—	2	1	no	—
1217	C₂²⋊Q₈	—	2	1	no	—
1218	C₂²⋊Q₈	—	2	1	no	—
1219	C₂²⋊Q₈	—	2	1	no	—
1220	C₂²⋊Q₈	—	2	1	no	—
1221	C₂²⋊Q₈	—	2	1	no	—
1222	C₂²⋊Q₈	—	2	1	no	—
1223	C₂²⋊Q₈	—	2	1	no	—
1224	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1225	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1226	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1227	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1228	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1229	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1230	#121	—	2	1	no	—
1231	#121	—	2	1	no	—
1232	#121	—	2	1	no	—
1233	#121	—	2	1	no	—
1234	#121	—	2	1	no	—
1235	#121	—	2	1	no	—
1236	#121	—	2	1	no	—
1237	#121	—	2	1	no	—
1238	#121	—	2	1	no	—
1239	#121	—	2	1	no	—
1240	#121	—	2	1	no	—
1241	#121	—	2	1	no	—
1242	#121	—	2	1	no	—
1243	#121	—	2	1	no	—
1244	#121	—	2	1	no	—
1245	#121	—	2	1	no	—
1246	#121	—	2	1	no	—
1247	#121	—	2	1	no	—
1248	#121	—	2	1	no	—
1249	#121	—	2	1	no	—
1250	#121	—	2	1	no	—
1251	#121	D₄×C₅₃	1	1	yes	characteristic
1252	#121	C₂³×C₅₃	1	1	yes	characteristic
1253	#121	C₂³×C₅₃	1	1	yes	characteristic
1254	#121	C₂³×C₅₃	1	1	yes	characteristic
1255	#121	C₂³×C₅₃	1	1	yes	characteristic
1256	#121	C₂³×C₅₃	1	1	yes	characteristic
1257	#121	C₂³×C₅₃	1	1	yes	characteristic
1258	#121	C₂³×C₅₃	1	1	yes	characteristic
1259	#120	—	2	1	no	—
1260	#120	—	2	1	no	—
1261	#120	—	2	1	no	—
1262	#120	—	2	1	no	—
1263	#120	—	2	1	no	—
1264	#120	—	2	1	no	—
1265	#120	—	2	1	no	—
1266	#120	—	2	1	no	—
1267	#120	—	2	1	no	—
1268	#120	—	2	1	no	—
1269	#120	—	2	1	no	—
1270	#120	—	2	1	no	—
1271	C₄×Q₈	—	2	1	no	—
1272	C₄×Q₈	—	2	1	no	—
1273	C₄×Q₈	—	2	1	no	—
1274	C₄×Q₈	—	2	1	no	—
1275	C₄×Q₈	—	2	1	no	—
1276	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1277	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1278	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1279	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1280	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1281	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1282	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1283	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1284	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1285	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1286	C₄×D₄	—	2	1	no	—
1287	C₄×D₄	—	2	1	no	—
1288	C₄×D₄	—	2	1	no	—
1289	C₄×D₄	—	2	1	no	—
1290	C₄×D₄	—	2	1	no	—
1291	C₄×D₄	—	2	1	no	—
1292	C₄×D₄	—	2	1	no	—
1293	C₄×D₄	—	2	1	no	—
1294	C₄×D₄	—	2	1	no	—
1295	C₄×D₄	—	2	1	no	—
1296	C₄×D₄	—	2	1	no	—
1297	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1298	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1299	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1300	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1301	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1302	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1303	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1304	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1305	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1306	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1307	#117	—	2	1	no	—
1308	#117	—	2	1	no	—
1309	#117	—	2	1	no	—
1310	#117	—	2	1	no	—
1311	#117	—	2	1	no	—
1312	#117	—	2	1	no	—
1313	#117	—	2	1	no	—
1314	#117	C₂³×C₅₃	1	1	yes	characteristic
1315	#117	C₂³×C₅₃	1	1	yes	characteristic
1316	#117	C₂³×C₅₃	1	1	yes	characteristic
1317	C₂×C₄⋊C₄	—	2	1	no	—
1318	C₂×C₄⋊C₄	—	2	1	no	—
1319	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1320	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1321	C₂×C₂²⋊C₄	—	2	1	no	—
1322	C₂×C₂²⋊C₄	—	2	1	no	—
1323	C₂×C₄²	—	2	1	no	—
1324	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1325	#107	C₂³×C₅₃	1	1	yes	characteristic
1326	#107	C₂³×C₅₃	1	1	yes	characteristic
1327	#107	C₂³×C₅₃	1	1	yes	characteristic
1328	#107	C₂³×C₅₃	1	1	yes	characteristic
1329	#106	C₂³×C₅₃	1	1	yes	characteristic
1330	#106	C₂³×C₅₃	1	1	yes	characteristic
1331	#106	C₂³×C₅₃	1	1	yes	characteristic
1332	#106	C₂³×C₅₃	1	1	yes	characteristic
1333	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1334	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1335	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1336	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1337	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1338	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1339	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1340	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1341	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1342	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1343	#103	C₂³×C₅₃	1	1	yes	characteristic
1344	#103	C₂³×C₅₃	1	1	yes	characteristic
1345	#103	C₂³×C₅₃	1	1	yes	characteristic
1346	#103	C₂³×C₅₃	1	1	yes	characteristic
1347	#103	C₂³×C₅₃	1	1	yes	characteristic
1348	#103	C₂³×C₅₃	1	1	yes	characteristic
1349	#103	C₂³×C₅₃	1	1	yes	characteristic
1350	#103	C₂³×C₅₃	1	1	yes	characteristic
1351	#103	C₂³×C₅₃	1	1	yes	characteristic
1352	#103	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	#102	C₂³×C₅₃	1	1	yes	characteristic
1360	#102	C₂³×C₅₃	1	1	yes	characteristic
1361	#102	C₂³×C₅₃	1	1	yes	characteristic
1362	#102	C₂³×C₅₃	1	1	yes	characteristic
1363	#102	C₂³×C₅₃	1	1	yes	characteristic
1364	#102	C₂³×C₅₃	1	1	yes	characteristic
1365	#102	C₂³×C₅₃	1	1	yes	characteristic
1366	#102	C₂³×C₅₃	1	1	yes	characteristic
1367	#102	C₂³×C₅₃	1	1	yes	characteristic
1368	#102	C₂³×C₅₃	1	1	yes	characteristic
1369	#102	C₂³×C₅₃	1	1	yes	characteristic
1370	#102	C₂³×C₅₃	1	1	yes	characteristic
1371	#102	C₂³×C₅₃	1	1	yes	characteristic
1372	#102	C₂³×C₅₃	1	1	yes	characteristic
1373	#102	C₂³×C₅₃	1	1	yes	characteristic
1374	#102	C₂³×C₅₃	1	1	yes	characteristic
1375	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1376	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1377	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1378	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1379	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1380	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1381	#97	C₂³×C₅₃	1	1	yes	characteristic
1382	#97	C₂³×C₅₃	1	1	yes	characteristic
1383	#97	C₂³×C₅₃	1	1	yes	characteristic
1384	#97	C₂³×C₅₃	1	1	yes	characteristic
1385	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1386	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1387	C₂⁴	—	2	1	no	—
1388	C₂⁴	—	2	1	no	—
1389	C₂⁴	—	2	1	no	—
1390	C₂⁴	—	2	1	no	—
1391	#41	—	2	2	no	—
1392	#41	—	4	1	no	—
1393	#41	—	4	1	no	—
1394	#41	—	4	1	no	—
1395	#41	—	4	1	no	—
1396	#41	—	4	1	no	—
1397	#41	—	8	2	no	—
1398	C₂×Q₈	—	2	1	no	—
1399	C₂×Q₈	—	2	1	no	—
1400	C₂×Q₈	—	2	1	no	—
1401	C₂×Q₈	—	2	2	no	—
1402	C₂×Q₈	—	2	2	no	—
1403	C₂×Q₈	—	4	1	no	—
1404	C₂×Q₈	—	4	1	no	—
1405	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1406	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1407	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1408	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1409	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1410	C₂×D₄	—	2	1	no	—
1411	C₂×D₄	—	2	1	no	—
1412	C₂×D₄	—	2	1	no	—
1413	C₂×D₄	—	2	1	no	—
1414	C₂×D₄	—	2	1	no	—
1415	C₂×D₄	—	2	1	no	—
1416	C₂×D₄	—	2	1	no	—
1417	C₂×D₄	—	2	1	no	—
1418	C₂×D₄	—	2	1	no	—
1419	C₂×D₄	—	2	1	no	—
1420	C₂×D₄	—	2	1	no	—
1421	C₂×D₄	—	2	1	no	—
1422	C₂×D₄	—	2	1	no	—
1423	C₂×D₄	—	2	1	no	—
1424	C₂×D₄	—	2	1	no	—
1425	C₂×D₄	—	2	1	no	—
1426	C₂×D₄	—	2	1	no	—
1427	C₂×D₄	—	2	1	no	—
1428	C₂×D₄	—	2	1	no	—
1429	C₂×D₄	—	2	1	no	—
1430	C₂×D₄	—	2	1	no	—
1431	C₂×D₄	—	2	1	no	—
1432	C₂×D₄	—	2	1	no	—
1433	C₂×D₄	—	2	1	no	—
1434	C₂×D₄	—	2	1	no	—
1435	C₂×D₄	—	2	1	no	—
1436	C₂×D₄	—	4	1	no	—
1437	C₂×D₄	—	4	1	no	—
1438	C₂×D₄	—	4	1	no	—
1439	C₂×D₄	—	4	1	no	—
1440	C₂×D₄	—	4	1	no	—
1441	C₂×D₄	—	4	1	no	—
1442	C₂×D₄	—	4	1	no	—
1443	C₂×D₄	—	4	1	no	—
1444	C₂×D₄	—	8	2	no	—
1445	C₂×D₄	—	8	2	no	—
1446	C₂×D₄	—	8	2	no	—
1447	C₂×D₄	—	8	2	no	—
1448	C₂×D₄	—	8	2	no	—
1449	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1450	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1451	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1452	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1453	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1454	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1455	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1456	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1457	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1458	C₂²×C₄	—	2	1	no	—
1459	C₂²×C₄	—	2	1	no	—
1460	C₂²×C₄	—	2	1	no	—
1461	C₂²×C₄	—	2	1	no	—
1462	C₂²×C₄	—	2	1	no	—
1463	C₂²×C₄	—	2	1	no	—
1464	C₂²×C₄	—	2	1	no	—
1465	C₂²×C₄	—	2	1	no	—
1466	C₂²×C₄	—	2	1	no	—
1467	C₂²×C₄	—	2	1	no	—
1468	C₂²×C₄	—	2	1	no	—
1469	C₂²×C₄	—	2	1	no	—
1470	C₂²×C₄	—	2	1	no	—
1471	C₂²×C₄	—	2	1	no	—
1472	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1473	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1474	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1475	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1476	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1477	Q₁₆	—	2	2	no	—
1478	Q₁₆	—	4	1	no	—
1479	Q₁₆	—	4	1	no	—
1480	SD₁₆	—	2	2	no	—
1481	SD₁₆	—	2	2	no	—
1482	SD₁₆	—	2	2	no	—
1483	SD₁₆	—	2	2	no	—
1484	SD₁₆	—	2	2	no	—
1485	SD₁₆	—	4	1	no	—
1486	SD₁₆	—	4	1	no	—
1487	SD₁₆	—	4	1	no	—
1488	SD₁₆	—	4	1	no	—
1489	SD₁₆	—	4	1	no	—
1490	SD₁₆	—	4	1	no	—
1491	SD₁₆	—	4	1	no	—
1492	SD₁₆	—	4	1	no	—
1493	SD₁₆	—	4	1	no	—
1494	SD₁₆	—	4	1	no	—
1495	SD₁₆	—	4	1	no	—
1496	D₈	—	4	1	no	—
1497	D₈	—	4	1	no	—
1498	D₈	—	4	1	no	—
1499	D₈	—	4	1	no	—
1500	D₈	—	4	1	no	—
1501	M₁₆	—	4	1	no	—
1502	M₁₆	—	4	1	no	—
1503	C₂×C₈	—	4	1	no	—
1504	C₂×C₈	—	4	1	no	—
1505	C₂×C₈	—	4	1	no	—
1506	C₂×C₈	—	4	1	no	—
1507	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1508	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1509	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1510	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1511	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1512	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1513	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1514	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1515	C₄⋊C₄	—	2	1	no	—
1516	C₄⋊C₄	—	2	1	no	—
1517	C₄⋊C₄	—	2	1	no	—
1518	C₄⋊C₄	—	2	1	no	—
1519	C₄⋊C₄	—	2	1	no	—
1520	C₄⋊C₄	—	2	1	no	—
1521	C₄⋊C₄	—	2	1	no	—
1522	C₄⋊C₄	—	2	1	no	—
1523	C₄⋊C₄	—	2	1	no	—
1524	C₄⋊C₄	—	2	1	no	—
1525	C₄⋊C₄	—	2	1	no	—
1526	C₄⋊C₄	—	2	1	no	—
1527	C₄⋊C₄	—	2	1	no	—
1528	C₄⋊C₄	—	2	1	no	—
1529	C₄⋊C₄	—	2	1	no	—
1530	C₄⋊C₄	—	2	1	no	—
1531	C₄⋊C₄	—	2	1	no	—
1532	C₄⋊C₄	—	2	1	no	—
1533	C₄⋊C₄	—	2	1	no	—
1534	C₄⋊C₄	—	2	1	no	—
1535	C₄⋊C₄	—	2	1	no	—
1536	C₄⋊C₄	—	2	1	no	—
1537	C₄⋊C₄	—	2	1	no	—
1538	C₄⋊C₄	—	2	1	no	—
1539	C₄⋊C₄	—	2	1	no	—
1540	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1541	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1542	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1543	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1544	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1545	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1546	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1547	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1548	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1549	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1550	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1551	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1552	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1553	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1554	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1555	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1569	C₂²⋊C₄	—	2	1	no	—
1570	C₂²⋊C₄	—	2	1	no	—
1571	C₂²⋊C₄	—	2	1	no	—
1572	C₂²⋊C₄	—	2	1	no	—
1573	C₂²⋊C₄	—	2	1	no	—
1574	C₂²⋊C₄	—	2	1	no	—
1575	C₂²⋊C₄	—	2	1	no	—
1576	C₂²⋊C₄	—	2	1	no	—
1577	C₂²⋊C₄	—	2	1	no	—
1578	C₂²⋊C₄	—	2	1	no	—
1579	C₂²⋊C₄	—	2	1	no	—
1580	C₂²⋊C₄	—	2	1	no	—
1581	C₂²⋊C₄	—	2	1	no	—
1582	C₂²⋊C₄	—	2	1	no	—
1583	C₂²⋊C₄	—	2	1	no	—
1584	C₂²⋊C₄	—	2	1	no	—
1585	C₂²⋊C₄	—	2	1	no	—
1586	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1587	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1588	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1589	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1590	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1591	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1592	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1593	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1594	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1595	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1596	C₄²	—	2	1	no	—
1597	C₄²	—	2	1	no	—
1598	C₄²	—	2	1	no	—
1599	C₄²	—	2	1	no	—
1600	C₄²	—	2	1	no	—
1601	C₄²	—	2	1	no	—
1602	C₄²	—	2	1	no	—
1603	C₄²	—	2	1	no	—
1604	C₄²	—	2	1	no	—
1605	C₄²	—	2	1	no	—
1606	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1607	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1608	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1609	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1610	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1611	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1612	C₂³	—	2	1	no	—
1613	C₂³	—	2	1	no	—
1614	C₂³	—	2	1	no	—
1615	C₂³	—	2	1	no	—
1616	C₂³	—	2	1	no	—
1617	C₂³	—	2	1	no	—
1618	C₂³	—	4	2	no	—
1619	C₂³	—	4	2	no	—
1620	C₂³	—	8	1	no	—
1621	C₂³	—	8	1	no	—
1622	C₂³	—	8	1	no	—
1623	C₂³	—	8	1	no	—
1624	C₂³	—	8	1	no	—
1625	C₂³	—	8	1	no	—
1626	C₂³	—	8	1	no	—
1627	C₂³	—	8	1	no	—
1628	C₂³	—	8	1	no	—
1629	C₂³	—	8	1	no	—
1630	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1631	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1632	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1633	Q₈	—	2	1	no	—
1634	Q₈	—	2	1	no	—
1635	Q₈	—	2	1	no	—
1636	Q₈	—	2	1	no	—
1637	Q₈	—	2	1	no	—
1638	Q₈	—	2	1	no	—
1639	Q₈	—	2	1	no	—
1640	Q₈	—	4	1	no	—
1641	Q₈	—	4	2	no	—
1642	Q₈	—	4	2	no	—
1643	Q₈	—	8	1	no	—
1644	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1645	D₄	—	2	2	no	—
1646	D₄	—	2	2	no	—
1647	D₄	—	2	1	no	—
1648	D₄	—	2	1	no	—
1649	D₄	—	2	1	no	—
1650	D₄	—	2	1	no	—
1651	D₄	—	2	1	no	—
1652	D₄	—	2	1	no	—
1653	D₄	—	2	1	no	—
1654	D₄	—	2	1	no	—
1655	D₄	—	2	1	no	—
1656	D₄	—	2	1	no	—
1657	D₄	—	2	1	no	—
1658	D₄	—	2	1	no	—
1659	D₄	—	4	1	no	—
1660	D₄	—	4	2	no	—
1661	D₄	—	4	2	no	—
1662	D₄	—	4	2	no	—
1663	D₄	—	4	2	no	—
1664	D₄	—	4	2	no	—
1665	D₄	—	8	1	no	—
1666	D₄	—	8	1	no	—
1667	D₄	—	8	1	no	—
1668	D₄	—	8	1	no	—
1669	D₄	—	8	1	no	—
1670	D₄	—	8	1	no	—
1671	D₄	—	8	1	no	—
1672	D₄	—	8	1	no	—
1673	D₄	—	8	1	no	—
1674	D₄	—	8	1	no	—
1675	D₄	—	8	1	no	—
1676	D₄	—	8	1	no	—
1677	D₄	—	8	1	no	—
1678	D₄	—	8	1	no	—
1679	D₄	—	8	1	no	—
1680	D₄	—	8	1	no	—
1681	D₄	—	8	1	no	—
1682	D₄	—	8	1	no	—
1683	D₄	—	8	1	no	—
1684	D₄	—	8	1	no	—
1685	D₄	—	8	1	no	—
1686	C₂×C₄	—	2	2	no	—
1687	C₂×C₄	—	2	1	no	—
1688	C₂×C₄	—	2	1	no	—
1689	C₂×C₄	—	2	1	no	—
1690	C₂×C₄	—	2	1	no	—
1691	C₂×C₄	—	2	1	no	—
1692	C₂×C₄	—	2	1	no	—
1693	C₂×C₄	—	2	1	no	—
1694	C₂×C₄	—	2	1	no	—
1695	C₂×C₄	—	2	1	no	—
1696	C₂×C₄	—	2	1	no	—
1697	C₂×C₄	—	2	1	no	—
1698	C₂×C₄	—	2	1	no	—
1699	C₂×C₄	—	2	1	no	—
1700	C₂×C₄	—	2	1	no	—
1701	C₂×C₄	—	2	1	no	—
1702	C₂×C₄	—	2	1	no	—
1703	C₂×C₄	—	4	1	no	—
1704	C₂×C₄	—	4	2	no	—
1705	C₂×C₄	—	4	2	no	—
1706	C₂×C₄	—	4	2	no	—
1707	C₂×C₄	—	4	2	no	—
1708	C₂×C₄	—	8	1	no	—
1709	C₂×C₄	—	8	1	no	—
1710	C₂×C₄	—	8	1	no	—
1711	C₂×C₄	—	8	1	no	—
1712	C₂×C₄	—	8	1	no	—
1713	C₂×C₄	—	8	1	no	—
1714	C₂×C₄	—	8	1	no	—
1715	C₂×C₄	—	8	1	no	—
1716	C₂×C₄	—	8	1	no	—
1717	C₂×C₄	—	8	1	no	—
1718	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1719	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1720	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1721	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1722	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1723	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1724	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1725	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1726	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1727	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1728	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1729	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1730	C₈	—	2	1	no	—
1731	C₈	—	2	1	no	—
1732	C₈	—	2	1	no	—
1733	C₈	—	2	1	no	—
1734	C₈	—	2	1	no	—
1735	C₈	—	2	1	no	—
1736	C₈	—	2	1	no	—
1737	C₈	—	2	1	no	—
1738	C₂²	—	2	1	no	—
1739	C₂²	—	2	1	no	—
1740	C₂²	—	2	1	no	—
1741	C₂²	—	2	1	no	—
1742	C₂²	—	2	1	no	—
1743	C₂²	—	2	1	no	—
1744	C₂²	—	2	1	no	—
1745	C₂²	—	2	1	no	—
1746	C₂²	—	4	1	no	—
1747	C₂²	—	4	1	no	—
1748	C₂²	—	4	1	no	—
1749	C₂²	—	4	1	no	—
1750	C₂²	—	4	1	no	—
1751	C₂²	—	4	1	no	—
1752	C₂²	—	4	1	no	—
1753	C₂²	—	4	1	no	—
1754	C₂²	—	4	1	no	—
1755	C₂²	—	4	1	no	—
1756	C₂²	—	4	1	no	—
1757	C₂²	—	4	1	no	—
1758	C₂²	—	4	1	no	—
1759	C₂²	—	4	1	no	—
1760	C₂²	—	4	1	no	—
1761	C₂²	—	4	1	no	—
1762	C₂²	—	4	1	no	—
1763	C₂²	—	4	1	no	—
1764	C₂²	—	16	2	no	—
1765	C₂²	—	16	2	no	—
1766	C₂²	—	16	2	no	—
1767	C₂²	—	16	2	no	—
1768	C₂²	C₅₃×#577	1	2	yes	—
1769	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1770	C₄	—	2	1	no	—
1771	C₄	—	2	1	no	—
1772	C₄	—	2	1	no	—
1773	C₄	—	2	2	no	—
1774	C₄	—	2	1	no	—
1775	C₄	—	2	1	no	—
1776	C₄	—	2	1	no	—
1777	C₄	—	2	1	no	—
1778	C₄	—	2	1	no	—
1779	C₄	—	2	1	no	—
1780	C₄	—	2	1	no	—
1781	C₄	—	2	1	no	—
1782	C₄	—	4	1	no	—
1783	C₄	—	4	1	no	—
1784	C₄	—	4	1	no	—
1785	C₄	—	4	1	no	—
1786	C₄	—	4	1	no	—
1787	C₄	—	4	1	no	—
1788	C₄	—	4	1	no	—
1789	C₄	—	4	1	no	—
1790	C₄	—	4	1	no	—
1791	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1792	C₄	C₅₃×#585	1	1	yes	characteristic
1793	C₂	—	2	2	no	—
1794	C₂	—	4	1	no	—
1795	C₂	—	4	1	no	—
1796	C₂	—	8	1	no	—
1797	C₂	—	8	1	no	—
1798	C₂	—	8	1	no	—
1799	C₂	—	8	1	no	—
1800	C₂	—	8	1	no	—
1801	C₂	—	8	1	no	—
1802	C₂	C₅₃×#3488	1	1	yes	characteristic
1803	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1804	C₂	C₅₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅₃ ◁ C₅₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3543	C₂	semidirect
2. C₅₃×#3516	C₂	semidirect
3. C₅₃×#3401	C₂	semidirect
4. C₅₃×#3397	C₂	semidirect
5. C₅₃×#3371	C₂	semidirect
6. C₅₃×#3368	C₂	semidirect
7. C₅₃×#3318	C₂	semidirect
8. C₅₃×#3317	C₂	semidirect
9. C₅₃×#3314	C₂	semidirect
10. C₅₃×#3310	C₂	semidirect
11. C₅₃×#3297	C₂	semidirect
12. C₅₃×#3295	C₂	semidirect
13. C₅₃×#3282	C₂	semidirect
14. D₄×SD₁₆×C₅₃	C₂	semidirect
15. C₅₃×#3271	C₂	semidirect
16. C₅₃×#3266	C₂	semidirect
17. C₅₃×#3265	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3260	C₂	semidirect
20. C₅₃×#3257	C₂	semidirect
21. C₅₃×#3250	C₂	semidirect
22. C₅₃×#3224	C₂	semidirect
23. C₅₃×#3222	C₂	semidirect
24. C₅₃×#3217	C₂	semidirect
25. C₅₃×#3126	C₂	semidirect
26. C₅₃×#3119	C₂	semidirect
27. C₅₃×#3117	C₂	semidirect
28. C₅₃×#3045	C₂	semidirect
29. C₅₃×#3043	C₂	semidirect
30. C₂×C₅₃×#460	C₂	semidirect
31. C₅₃×#2992	C₂	semidirect
32. C₂×#137×C₅₃	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
34. C₂×#135×C₅₃	C₂²	semidirect
35. C₂²×SD₁₆×C₅₃	C₂²	semidirect
36. C₂²×SD₁₆×C₅₃	C₂²	semidirect
37. C₂²×SD₁₆×C₅₃	C₂²	semidirect
41. C₅₃×#557	C₂²	semidirect
43. C₅₃×#556	C₂²	semidirect
45. C₅₃×#554	C₂²	semidirect
47. C₅₃×#553	C₂²	semidirect
49. C₅₃×#552	C₂²	semidirect
52. D₄×Q₈×C₅₃	C₂²	semidirect
53. C₅₃×#548	C₂²	semidirect
54. C₅₃×#548	C₂²	semidirect
63. C₅₃×#542	C₂²	semidirect
65. C₅₃×#541	C₂²	semidirect
79. C₅₃×#529	C₂²	semidirect
80. C₅₃×#520	C₂²	semidirect
81. C₅₃×#519	C₂²	semidirect
82. C₂×C₄×Q₈×C₅₃	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
85. C₅₃×#496	C₂²	semidirect
86. C₅₃×#496	C₂²	semidirect
87. C₅₃×#495	C₂²	semidirect
88. C₅₃×#492	C₂²	semidirect
90. C₅₃×#490	C₂²	semidirect
91. C₅₃×#490	C₂²	semidirect
92. C₅₃×#489	C₂²	semidirect
93. C₅₃×#488	C₂²	semidirect
94. C₅₃×#486	C₂²	semidirect
95. C₅₃×#484	C₂²	semidirect
96. C₅₃×#482	C₂²	semidirect
97. C₅₃×#482	C₂²	semidirect
99. C₅₃×#481	C₂²	semidirect
100. C₅₃×#480	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
102. C₅₃×#479	C₂²	semidirect
103. C₅₃×#479	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#478	C₂²	semidirect
109. C₅₃×#476	C₂²	semidirect
110. C₅₃×#474	C₂²	semidirect
111. C₅₃×#469	C₂²	semidirect
112. C₅₃×#468	C₂²	semidirect
113. C₅₃×#468	C₂²	semidirect
114. C₅₃×#468	C₂²	semidirect
115. C₅₃×#467	C₂²	semidirect
117. C₅₃×#466	C₂²	semidirect
119. C₅₃×#465	C₂²	semidirect
120. C₅₃×#465	C₂²	semidirect
121. C₅₃×#465	C₂²	semidirect
122. C₅₃×#465	C₂²	semidirect
123. C₅₃×#464	C₂²	semidirect
124. C₅₃×#464	C₂²	semidirect
125. C₅₃×#464	C₂²	semidirect
126. C₅₃×#464	C₂²	semidirect
127. C₅₃×#464	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
130. C₅₃×#463	C₂²	semidirect
131. C₅₃×#463	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#463	C₂²	semidirect
135. C₅₃×#461	C₂²	semidirect
136. C₅₃×#461	C₂²	semidirect
139. C₅₃×#460	C₂²	semidirect
140. C₅₃×#460	C₂²	semidirect
141. C₅₃×#460	C₂²	semidirect
142. C₅₃×#460	C₂²	semidirect
143. C₅₃×#460	C₂²	semidirect
144. C₅₃×#460	C₂²	semidirect
145. C₅₃×#460	C₂²	semidirect
146. C₅₃×#460	C₂²	semidirect
147. C₅₃×#460	C₂²	semidirect
148. C₅₃×#460	C₂²	semidirect
149. C₅₃×#460	C₂²	semidirect
150. C₅₃×#459	C₂²	semidirect
151. C₅₃×#459	C₂²	semidirect
152. C₅₃×#459	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#452	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#451	C₂²	semidirect
157. C₅₃×#450	C₂²	semidirect
158. C₅₃×#450	C₂²	semidirect
159. C₅₃×#450	C₂²	semidirect
160. C₅₃×#450	C₂²	semidirect
161. C₅₃×#450	C₂²	semidirect
162. C₅₃×#449	C₂²	semidirect
163. C₅₃×#449	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
166. C₅₃×#448	C₂²	semidirect
167. C₅₃×#448	C₂²	semidirect
168. C₅₃×#447	C₂²	semidirect
169. C₅₃×#447	C₂²	semidirect
170. C₅₃×#447	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
173. C₅₃×#442	C₂²	semidirect
174. C₅₃×#441	C₂²	semidirect
175. C₅₃×#441	C₂²	semidirect
176. C₅₃×#440	C₂²	semidirect
177. C₅₃×#440	C₂²	semidirect
178. C₅₃×#440	C₂²	semidirect
179. C₅₃×#440	C₂²	semidirect
180. C₅₃×#440	C₂²	semidirect
181. C₄×SD₁₆×C₅₃	C₂²	semidirect
182. C₄×SD₁₆×C₅₃	C₂²	semidirect
183. C₄×SD₁₆×C₅₃	C₂²	semidirect
184. C₄×D₈×C₅₃	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₅₃×#435	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×#433	C₂²	semidirect
192. C₅₃×#433	C₂²	semidirect
193. C₅₃×#432	C₂²	semidirect
194. C₅₃×#424	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
197. C₅₃×#418	C₂²	semidirect
198. C₅₃×#417	C₂²	semidirect
199. C₅₃×#416	C₂²	semidirect
200. C₂×#102×C₅₃	C₂²	semidirect
201. C₂×#102×C₅₃	C₂²	semidirect
202. C₂×#102×C₅₃	C₂²	semidirect
835. #62009	C₅₃	direct (N × H)
891. #3543	C₂×C₅₃	semidirect
892. #3516	C₂×C₅₃	semidirect
893. #3401	C₂×C₅₃	semidirect
894. #3397	C₂×C₅₃	semidirect
895. #3371	C₂×C₅₃	semidirect
896. #3368	C₂×C₅₃	semidirect
897. #3318	C₂×C₅₃	semidirect
898. #3317	C₂×C₅₃	semidirect
899. #3314	C₂×C₅₃	semidirect
900. #3310	C₂×C₅₃	semidirect
901. #3297	C₂×C₅₃	semidirect
902. #3295	C₂×C₅₃	semidirect
903. #3282	C₂×C₅₃	semidirect
904. D₄×SD₁₆	C₂×C₅₃	semidirect
905. #3271	C₂×C₅₃	semidirect
906. #3266	C₂×C₅₃	semidirect
907. #3265	C₂×C₅₃	semidirect
908. #3265	C₂×C₅₃	semidirect
909. #3260	C₂×C₅₃	semidirect
910. #3257	C₂×C₅₃	semidirect
911. #3250	C₂×C₅₃	semidirect
912. #3224	C₂×C₅₃	semidirect
913. #3222	C₂×C₅₃	semidirect
914. #3217	C₂×C₅₃	semidirect
915. #3126	C₂×C₅₃	semidirect
916. #3119	C₂×C₅₃	semidirect
917. #3117	C₂×C₅₃	semidirect
918. #3045	C₂×C₅₃	semidirect
919. #3043	C₂×C₅₃	semidirect
920. C₂×#460	C₂×C₅₃	semidirect
921. #2992	C₂×C₅₃	semidirect
934. C₂×#137	C₂²×C₅₃	semidirect
935. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
936. C₂×#135	C₂²×C₅₃	semidirect
937. C₂²×SD₁₆	C₂²×C₅₃	semidirect
938. C₂²×SD₁₆	C₂²×C₅₃	semidirect
939. C₂²×SD₁₆	C₂²×C₅₃	semidirect
943. #557	C₂²×C₅₃	semidirect
945. #556	C₂²×C₅₃	semidirect
947. #554	C₂²×C₅₃	semidirect
949. #553	C₂²×C₅₃	semidirect
951. #552	C₂²×C₅₃	semidirect
954. D₄×Q₈	C₂²×C₅₃	semidirect
955. #548	C₂²×C₅₃	semidirect
956. #548	C₂²×C₅₃	semidirect
965. #542	C₂²×C₅₃	semidirect
967. #541	C₂²×C₅₃	semidirect
981. #529	C₂²×C₅₃	semidirect
982. #520	C₂²×C₅₃	semidirect
983. #519	C₂²×C₅₃	semidirect
984. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
985. #497	C₂²×C₅₃	semidirect
987. #496	C₂²×C₅₃	semidirect
988. #496	C₂²×C₅₃	semidirect
989. #495	C₂²×C₅₃	semidirect
990. #492	C₂²×C₅₃	semidirect
992. #490	C₂²×C₅₃	semidirect
993. #490	C₂²×C₅₃	semidirect
994. #489	C₂²×C₅₃	semidirect
995. #488	C₂²×C₅₃	semidirect
996. #486	C₂²×C₅₃	semidirect
997. #484	C₂²×C₅₃	semidirect
998. #482	C₂²×C₅₃	semidirect
999. #482	C₂²×C₅₃	semidirect
1001. #481	C₂²×C₅₃	semidirect
1002. #480	C₂²×C₅₃	semidirect
1003. #479	C₂²×C₅₃	semidirect
1004. #479	C₂²×C₅₃	semidirect
1005. #479	C₂²×C₅₃	semidirect
1006. #479	C₂²×C₅₃	semidirect
1007. #478	C₂²×C₅₃	semidirect
1008. #478	C₂²×C₅₃	semidirect
1009. #478	C₂²×C₅₃	semidirect
1010. #478	C₂²×C₅₃	semidirect
1011. #476	C₂²×C₅₃	semidirect
1012. #474	C₂²×C₅₃	semidirect
1013. #469	C₂²×C₅₃	semidirect
1014. #468	C₂²×C₅₃	semidirect
1015. #468	C₂²×C₅₃	semidirect
1016. #468	C₂²×C₅₃	semidirect
1017. #467	C₂²×C₅₃	semidirect
1019. #466	C₂²×C₅₃	semidirect
1021. #465	C₂²×C₅₃	semidirect
1022. #465	C₂²×C₅₃	semidirect
1023. #465	C₂²×C₅₃	semidirect
1024. #465	C₂²×C₅₃	semidirect
1025. #464	C₂²×C₅₃	semidirect
1026. #464	C₂²×C₅₃	semidirect
1027. #464	C₂²×C₅₃	semidirect
1028. #464	C₂²×C₅₃	semidirect
1029. #464	C₂²×C₅₃	semidirect
1030. #464	C₂²×C₅₃	semidirect
1031. #464	C₂²×C₅₃	semidirect
1032. #463	C₂²×C₅₃	semidirect
1033. #463	C₂²×C₅₃	semidirect
1034. #463	C₂²×C₅₃	semidirect
1035. #463	C₂²×C₅₃	semidirect
1036. #463	C₂²×C₅₃	semidirect
1037. #461	C₂²×C₅₃	semidirect
1038. #461	C₂²×C₅₃	semidirect
1041. #460	C₂²×C₅₃	semidirect
1042. #460	C₂²×C₅₃	semidirect
1043. #460	C₂²×C₅₃	semidirect
1044. #460	C₂²×C₅₃	semidirect
1045. #460	C₂²×C₅₃	semidirect
1046. #460	C₂²×C₅₃	semidirect
1047. #460	C₂²×C₅₃	semidirect
1048. #460	C₂²×C₅₃	semidirect
1049. #460	C₂²×C₅₃	semidirect
1050. #460	C₂²×C₅₃	semidirect
1051. #460	C₂²×C₅₃	semidirect
1052. #459	C₂²×C₅₃	semidirect
1053. #459	C₂²×C₅₃	semidirect
1054. #459	C₂²×C₅₃	semidirect
1055. #452	C₂²×C₅₃	semidirect
1056. #452	C₂²×C₅₃	semidirect
1057. #452	C₂²×C₅₃	semidirect
1058. #451	C₂²×C₅₃	semidirect
1059. #450	C₂²×C₅₃	semidirect
1060. #450	C₂²×C₅₃	semidirect
1061. #450	C₂²×C₅₃	semidirect
1062. #450	C₂²×C₅₃	semidirect
1063. #450	C₂²×C₅₃	semidirect
1064. #449	C₂²×C₅₃	semidirect
1065. #449	C₂²×C₅₃	semidirect
1066. #449	C₂²×C₅₃	semidirect
1068. #448	C₂²×C₅₃	semidirect
1069. #448	C₂²×C₅₃	semidirect
1070. #447	C₂²×C₅₃	semidirect
1071. #447	C₂²×C₅₃	semidirect
1072. #447	C₂²×C₅₃	semidirect
1073. #446	C₂²×C₅₃	semidirect
1074. #446	C₂²×C₅₃	semidirect
1075. #442	C₂²×C₅₃	semidirect
1076. #441	C₂²×C₅₃	semidirect
1077. #441	C₂²×C₅₃	semidirect
1078. #440	C₂²×C₅₃	semidirect
1079. #440	C₂²×C₅₃	semidirect
1080. #440	C₂²×C₅₃	semidirect
1081. #440	C₂²×C₅₃	semidirect
1082. #440	C₂²×C₅₃	semidirect
1083. C₄×SD₁₆	C₂²×C₅₃	semidirect
1084. C₄×SD₁₆	C₂²×C₅₃	semidirect
1085. C₄×SD₁₆	C₂²×C₅₃	semidirect
1086. C₄×D₈	C₂²×C₅₃	semidirect
1087. #435	C₂²×C₅₃	semidirect
1088. #435	C₂²×C₅₃	semidirect
1089. #435	C₂²×C₅₃	semidirect
1090. #435	C₂²×C₅₃	semidirect
1091. C₈×D₄	C₂²×C₅₃	semidirect
1092. C₈×D₄	C₂²×C₅₃	semidirect
1093. #433	C₂²×C₅₃	semidirect
1094. #433	C₂²×C₅₃	semidirect
1095. #432	C₂²×C₅₃	semidirect
1096. #424	C₂²×C₅₃	semidirect
1097. #424	C₂²×C₅₃	semidirect
1098. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1099. #418	C₂²×C₅₃	semidirect
1100. #417	C₂²×C₅₃	semidirect
1101. #416	C₂²×C₅₃	semidirect
1102. C₂×#102	C₂²×C₅₃	semidirect
1103. C₂×#102	C₂²×C₅₃	semidirect
1104. C₂×#102	C₂²×C₅₃	semidirect
1105. C₅₃	#62009	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×#3543	2
C₅₃×#3516	2
C₅₃×#3401	2
C₅₃×#3397	2
C₅₃×#3371	2
C₅₃×#3368	2
C₅₃×#3318	2
C₅₃×#3317	2
C₅₃×#3314	2
C₅₃×#3310	2
C₅₃×#3297	2
C₅₃×#3295	2
C₅₃×#3282	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3271	2
C₅₃×#3266	2
C₅₃×#3265	2
C₅₃×#3260	2
C₅₃×#3257	2
C₅₃×#3250	2
C₅₃×#3224	2
C₅₃×#3222	2
C₅₃×#3217	2
C₅₃×#3126	2
C₅₃×#3119	2
C₅₃×#3117	2
C₅₃×#3045	2
C₅₃×#3043	2
C₂×C₅₃×#460	2
C₅₃×#2992	2
#62009	53

Subgroups — C53×#62009 #27269521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62009 #27269521