Subgroups — C₅₃×#62085 #27269597

Order 13568.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3516	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3402	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3322	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3309	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3275	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3266	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3265	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3262	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3251	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×#3219	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3121	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3112	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	C₅₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic, complemented
37	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#560	—	2	1	no	—
39	C₅₃×#560	—	2	1	no	—
40	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#556	—	2	1	no	—
42	C₅₃×#556	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
48	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#552	—	2	1	no	—
50	C₅₃×#552	C₂²	1	1	yes	characteristic
51	C₅₃×#550	C₂²	1	1	yes	characteristic
52	C₅₃×#550	C₂²	1	1	yes	characteristic
53	C₅₃×#550	C₂²	1	1	yes	characteristic
54	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#548	C₂²	1	1	yes	characteristic
56	C₅₃×#548	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#547	C₂²	1	1	yes	characteristic
58	C₅₃×#546	—	2	1	no	—
59	C₅₃×#546	C₂²	1	1	yes	characteristic
60	C₅₃×#546	C₂²	1	1	yes	characteristic
61	D₄²×C₅₃	C₂²	1	1	yes	characteristic
62	C₅₃×#542	—	2	1	no	—
63	C₅₃×#542	C₂²	1	1	yes	characteristic
64	C₅₃×#542	C₂²	1	1	yes	characteristic
65	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#541	—	2	1	no	—
67	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#538	—	2	1	no	—
69	C₅₃×#538	—	2	1	no	—
70	C₅₃×#537	—	2	1	no	—
71	C₅₃×#535	—	2	1	no	—
72	C₅₃×#535	C₂²	1	1	yes	characteristic
73	C₅₃×#535	C₂²	1	1	yes	characteristic
74	C₅₃×#532	C₂²	1	1	yes	characteristic
75	C₅₃×#532	C₂²	1	1	yes	characteristic
76	C₅₃×#529	—	2	1	no	—
77	C₅₃×#529	—	2	1	no	—
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
84	C₅₃×#497	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#496	C₂²	1	1	yes	characteristic
86	C₅₃×#496	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#495	C₂²	1	1	yes	characteristic
88	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#490	C₂²	1	1	yes	characteristic
91	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#489	C₂²	1	1	yes	characteristic
93	C₅₃×#488	C₂²	1	1	yes	characteristic
94	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#482	C₂²	1	1	yes	characteristic
98	C₅₃×#480	C₂²	1	1	yes	characteristic
99	C₅₃×#480	C₂²	1	1	yes	characteristic
100	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#478	C₂²	1	1	yes	characteristic
103	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#474	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×#469	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#468	C₂²	1	1	yes	characteristic
115	C₅₃×#468	C₂²	1	1	yes	characteristic
116	C₅₃×#468	C₂²	1	1	yes	characteristic
117	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#466	C₂²	1	1	yes	characteristic
122	C₅₃×#465	C₂²	1	1	yes	characteristic
123	C₅₃×#464	C₂²	1	1	yes	characteristic
124	C₅₃×#464	C₂²	1	1	yes	characteristic
125	C₅₃×#464	C₂²	1	1	yes	characteristic
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, complemented
136	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#460	C₂²	1	1	yes	characteristic
144	C₅₃×#460	C₂²	1	1	yes	characteristic
145	C₅₃×#460	C₂²	1	1	yes	characteristic
146	C₅₃×#460	C₂²	1	1	yes	characteristic
147	C₅₃×#460	C₂²	1	1	yes	characteristic
148	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#459	C₂²	1	1	yes	characteristic
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×#452	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#452	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
163	C₅₃×#449	C₂²	1	1	yes	characteristic
164	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#448	C₂²	1	1	yes	characteristic
168	C₅₃×#448	C₂²	1	1	yes	characteristic
169	C₅₃×#448	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#447	C₂²	1	1	yes	characteristic
171	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
172	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
173	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#440	C₂²	1	1	yes	characteristic
175	C₅₃×#440	C₂²	1	1	yes	characteristic
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×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₄×Q₁₆×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×#436	C₂²	1	1	yes	characteristic, complemented
186	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#435	C₂²	1	1	yes	characteristic
188	C₅₃×#435	C₂²	1	1	yes	characteristic
189	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#435	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	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#418	C₂²	1	1	yes	characteristic
198	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
199	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	—	2	1	no	—
205	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	C₂²×D₄×C₅₃	—	2	1	no	—
213	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
215	#137×C₅₃	—	4	2	no	—
216	#137×C₅₃	—	4	2	no	—
217	#137×C₅₃	—	4	2	no	—
218	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
219	#135×C₅₃	—	4	2	no	—
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×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
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×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	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
248	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
249	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
250	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₅₃	—	2	1	no	—
252	C₄⋊Q₈×C₅₃	—	2	1	no	—
253	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
257	#127×C₅₃	—	2	1	no	—
258	#127×C₅₃	—	2	1	no	—
259	#127×C₅₃	C₂³	1	1	yes	characteristic
260	#127×C₅₃	C₂³	1	1	yes	characteristic
261	#127×C₅₃	C₂³	1	1	yes	characteristic
262	#127×C₅₃	C₂³	1	1	yes	characteristic
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	#126×C₅₃	—	2	1	no	—
268	#126×C₅₃	—	2	1	no	—
269	#126×C₅₃	—	2	1	no	—
270	#126×C₅₃	—	2	1	no	—
271	#126×C₅₃	—	2	1	no	—
272	#126×C₅₃	—	2	1	no	—
273	#126×C₅₃	—	2	1	no	—
274	#126×C₅₃	—	2	1	no	—
275	#126×C₅₃	D₄	1	1	yes	characteristic
276	#126×C₅₃	D₄	1	1	yes	characteristic
277	#125×C₅₃	—	2	1	no	—
278	#125×C₅₃	—	2	1	no	—
279	#125×C₅₃	—	2	1	no	—
280	#125×C₅₃	—	2	1	no	—
281	#125×C₅₃	—	2	1	no	—
282	#125×C₅₃	—	2	1	no	—
283	#125×C₅₃	D₄	1	1	yes	characteristic
284	#125×C₅₃	C₂³	1	1	yes	characteristic
285	#125×C₅₃	C₂³	1	1	yes	characteristic
286	#124×C₅₃	—	2	1	no	—
287	#124×C₅₃	—	2	1	no	—
288	#124×C₅₃	—	2	1	no	—
289	#124×C₅₃	—	2	1	no	—
290	#124×C₅₃	—	2	1	no	—
291	#124×C₅₃	—	2	1	no	—
292	#124×C₅₃	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	#124×C₅₃	C₂³	1	1	yes	characteristic
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	D₄	1	1	yes	characteristic
310	#123×C₅₃	D₄	1	1	yes	characteristic
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	—	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	—	2	1	no	—
322	C₂²⋊Q₈×C₅₃	D₄	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	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
328	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
349	#121×C₅₃	—	2	1	no	—
350	#121×C₅₃	D₄	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	#121×C₅₃	C₂³	1	1	yes	characteristic
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	C₄×Q₈×C₅₃	—	2	1	no	—
366	C₄×Q₈×C₅₃	—	2	1	no	—
367	C₄×Q₈×C₅₃	—	2	1	no	—
368	C₄×Q₈×C₅₃	—	2	1	no	—
369	C₄×Q₈×C₅₃	—	2	1	no	—
370	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×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×D₄×C₅₃	—	2	1	no	—
382	C₄×D₄×C₅₃	—	2	1	no	—
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	—	2	1	no	—
387	C₄×D₄×C₅₃	—	2	1	no	—
388	C₄×D₄×C₅₃	—	2	1	no	—
389	C₄×D₄×C₅₃	—	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	#117×C₅₃	—	2	1	no	—
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	C₂³	1	1	yes	characteristic
411	#117×C₅₃	C₂³	1	1	yes	characteristic
412	#117×C₅₃	C₂³	1	1	yes	characteristic
413	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
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	#107×C₅₃	C₂³	1	1	yes	characteristic
427	#107×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	#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	#41×C₅₃	—	2	2	no	—
487	#41×C₅₃	—	4	1	no	—
488	#41×C₅₃	—	4	1	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	4	1	no	—
493	#41×C₅₃	—	4	1	no	—
494	#41×C₅₃	—	4	1	no	—
495	#41×C₅₃	—	4	1	no	—
496	#41×C₅₃	—	8	2	no	—
497	#41×C₅₃	—	8	2	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	—	2	1	no	—
500	C₂×Q₈×C₅₃	—	2	1	no	—
501	C₂×Q₈×C₅₃	—	2	1	no	—
502	C₂×Q₈×C₅₃	—	2	2	no	—
503	C₂×Q₈×C₅₃	—	2	2	no	—
504	C₂×Q₈×C₅₃	—	4	1	no	—
505	C₂×Q₈×C₅₃	—	4	1	no	—
506	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
507	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
508	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
512	C₂×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	—	8	2	no	—
538	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
539	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
540	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
541	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
544	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
545	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	—	2	1	no	—
554	C₂²×C₄×C₅₃	—	2	1	no	—
555	C₂²×C₄×C₅₃	—	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	C₂×D₄	1	1	yes	characteristic
562	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
563	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
564	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
565	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
566	Q₁₆×C₅₃	—	2	2	no	—
567	Q₁₆×C₅₃	—	2	2	no	—
568	Q₁₆×C₅₃	—	4	1	no	—
569	Q₁₆×C₅₃	—	4	1	no	—
570	Q₁₆×C₅₃	—	4	1	no	—
571	Q₁₆×C₅₃	—	4	1	no	—
572	SD₁₆×C₅₃	—	2	2	no	—
573	SD₁₆×C₅₃	—	2	2	no	—
574	SD₁₆×C₅₃	—	2	2	no	—
575	SD₁₆×C₅₃	—	2	2	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	SD₁₆×C₅₃	—	4	1	no	—
583	SD₁₆×C₅₃	—	4	1	no	—
584	SD₁₆×C₅₃	—	4	1	no	—
585	SD₁₆×C₅₃	—	4	1	no	—
586	D₈×C₅₃	—	4	1	no	—
587	D₈×C₅₃	—	4	1	no	—
588	D₈×C₅₃	—	4	1	no	—
589	D₈×C₅₃	—	4	1	no	—
590	M₁₆×C₅₃	—	4	1	no	—
591	M₁₆×C₅₃	—	4	1	no	—
592	M₁₆×C₅₃	—	4	1	no	—
593	M₁₆×C₅₃	—	4	1	no	—
594	C₂×C₈×C₅₃	—	4	1	no	—
595	C₂×C₈×C₅₃	—	4	1	no	—
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	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₅₃	—	2	1	no	—
605	C₄⋊C₄×C₅₃	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	—	2	1	no	—
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
614	C₄⋊C₄×C₅₃	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
619	C₄⋊C₄×C₅₃	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	—	2	1	no	—
627	C₄⋊C₄×C₅₃	—	2	1	no	—
628	C₄⋊C₄×C₅₃	—	2	1	no	—
629	C₄⋊C₄×C₅₃	—	2	1	no	—
630	C₄⋊C₄×C₅₃	—	2	1	no	—
631	C₄⋊C₄×C₅₃	—	2	1	no	—
632	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
640	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
642	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
643	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
644	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
645	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
646	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
647	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
648	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	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
688	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
697	C₄²×C₅₃	—	2	1	no	—
698	C₄²×C₅₃	—	2	1	no	—
699	C₄²×C₅₃	—	2	1	no	—
700	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
701	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
702	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
704	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
705	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
706	C₂³×C₅₃	—	2	1	no	—
707	C₂³×C₅₃	—	2	1	no	—
708	C₂³×C₅₃	—	2	1	no	—
709	C₂³×C₅₃	—	2	1	no	—
710	C₂³×C₅₃	—	2	1	no	—
711	C₂³×C₅₃	—	8	1	no	—
712	C₂³×C₅₃	—	8	1	no	—
713	C₂³×C₅₃	—	8	1	no	—
714	C₂³×C₅₃	—	8	1	no	—
715	C₂³×C₅₃	—	8	1	no	—
716	C₂³×C₅₃	—	8	1	no	—
717	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
718	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
719	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
720	Q₈×C₅₃	—	2	1	no	—
721	Q₈×C₅₃	—	2	1	no	—
722	Q₈×C₅₃	—	2	1	no	—
723	Q₈×C₅₃	—	2	1	no	—
724	Q₈×C₅₃	—	2	1	no	—
725	Q₈×C₅₃	—	2	1	no	—
726	Q₈×C₅₃	—	2	1	no	—
727	Q₈×C₅₃	—	2	1	no	—
728	Q₈×C₅₃	—	2	1	no	—
729	Q₈×C₅₃	—	4	1	no	—
730	Q₈×C₅₃	—	4	2	no	—
731	Q₈×C₅₃	—	4	2	no	—
732	Q₈×C₅₃	—	8	1	no	—
733	Q₈×C₅₃	—	8	1	no	—
734	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
735	D₄×C₅₃	—	2	1	no	—
736	D₄×C₅₃	—	2	1	no	—
737	D₄×C₅₃	—	2	1	no	—
738	D₄×C₅₃	—	2	1	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	—	4	1	no	—
746	D₄×C₅₃	—	4	1	no	—
747	D₄×C₅₃	—	4	1	no	—
748	D₄×C₅₃	—	4	2	no	—
749	D₄×C₅₃	—	4	2	no	—
750	D₄×C₅₃	—	4	2	no	—
751	D₄×C₅₃	—	8	1	no	—
752	D₄×C₅₃	—	8	1	no	—
753	D₄×C₅₃	—	8	1	no	—
754	D₄×C₅₃	—	8	1	no	—
755	D₄×C₅₃	—	8	1	no	—
756	D₄×C₅₃	—	8	1	no	—
757	D₄×C₅₃	—	8	1	no	—
758	D₄×C₅₃	—	8	1	no	—
759	D₄×C₅₃	—	8	1	no	—
760	D₄×C₅₃	—	8	1	no	—
761	D₄×C₅₃	—	8	1	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	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	—	2	1	no	—
783	C₂×C₄×C₅₃	—	2	1	no	—
784	C₂×C₄×C₅₃	—	2	1	no	—
785	C₂×C₄×C₅₃	—	2	1	no	—
786	C₂×C₄×C₅₃	—	4	1	no	—
787	C₂×C₄×C₅₃	—	4	1	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	—	8	1	no	—
794	C₂×C₄×C₅₃	—	8	1	no	—
795	C₂×C₄×C₅₃	—	8	1	no	—
796	C₂×C₄×C₅₃	—	8	1	no	—
797	C₂×C₄×C₅₃	—	8	1	no	—
798	C₂×C₄×C₅₃	—	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	#62085	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	1	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	—	4	1	no	—
848	C₂²×C₅₃	—	16	2	no	—
849	C₂²×C₅₃	—	16	2	no	—
850	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
851	C₄×C₅₃	—	2	1	no	—
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	2	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	C₂×H(5,𝔽₂)	1	1	yes	characteristic
874	C₄×C₅₃	#585	1	1	yes	characteristic
875	#3546	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3516	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3402	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3377	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3368	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3322	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3309	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3278	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3275	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#3271	C₂×C₅₃	1	1	yes	characteristic, complemented
890	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
891	#3266	C₂×C₅₃	1	1	yes	characteristic, complemented
892	#3265	C₂×C₅₃	1	1	yes	characteristic, complemented
893	#3262	C₂×C₅₃	1	1	yes	characteristic, complemented
894	#3258	C₂×C₅₃	1	1	yes	characteristic, complemented
895	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
896	#3224	C₂×C₅₃	1	1	yes	characteristic, complemented
897	#3222	C₂×C₅₃	1	1	yes	characteristic, complemented
898	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
899	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
900	#3121	C₂×C₅₃	1	1	yes	characteristic, complemented
901	#3112	C₂×C₅₃	1	1	yes	characteristic, complemented
902	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
903	#3043	C₂×C₅₃	1	1	yes	characteristic, complemented
904	#3037	C₂×C₅₃	1	1	yes	characteristic, complemented
905	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
906	C₂×C₅₃	—	4	1	no	—
907	C₂×C₅₃	—	4	1	no	—
908	C₂×C₅₃	—	4	1	no	—
909	C₂×C₅₃	—	8	1	no	—
910	C₂×C₅₃	—	8	1	no	—
911	C₂×C₅₃	—	8	1	no	—
912	C₂×C₅₃	—	8	1	no	—
913	C₂×C₅₃	—	8	1	no	—
914	C₂×C₅₃	#3488	1	1	yes	characteristic
915	C₂×C₅₃	#3585	1	1	yes	characteristic
916	C₂×C₅₃	#3586	1	1	yes	characteristic
917	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
921	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
923	#560	—	2	1	no	—
924	#560	—	2	1	no	—
925	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#556	—	2	1	no	—
927	#556	C₂²×C₅₃	1	1	yes	characteristic
928	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#554	—	2	1	no	—
930	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#553	—	2	1	no	—
932	#553	—	2	1	no	—
933	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#552	—	2	1	no	—
935	#552	C₂²×C₅₃	1	1	yes	characteristic
936	#550	C₂²×C₅₃	1	1	yes	characteristic
937	#550	C₂²×C₅₃	1	1	yes	characteristic
938	#550	C₂²×C₅₃	1	1	yes	characteristic
939	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#548	C₂²×C₅₃	1	1	yes	characteristic
941	#548	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#547	C₂²×C₅₃	1	1	yes	characteristic
943	#546	—	2	1	no	—
944	#546	C₂²×C₅₃	1	1	yes	characteristic
945	#546	C₂²×C₅₃	1	1	yes	characteristic
946	D₄²	C₂²×C₅₃	1	1	yes	characteristic
947	#542	—	2	1	no	—
948	#542	C₂²×C₅₃	1	1	yes	characteristic
949	#542	C₂²×C₅₃	1	1	yes	characteristic
950	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#541	—	2	1	no	—
952	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#538	—	2	1	no	—
954	#538	—	2	1	no	—
955	#537	—	2	1	no	—
956	#535	—	2	1	no	—
957	#535	C₂²×C₅₃	1	1	yes	characteristic
958	#535	C₂²×C₅₃	1	1	yes	characteristic
959	#532	C₂²×C₅₃	1	1	yes	characteristic
960	#532	C₂²×C₅₃	1	1	yes	characteristic
961	#529	—	2	1	no	—
962	#529	—	2	1	no	—
963	#529	C₂²×C₅₃	1	1	yes	characteristic
964	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#519	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#497	C₂²×C₅₃	1	1	yes	characteristic
969	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#496	C₂²×C₅₃	1	1	yes	characteristic
971	#496	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#495	C₂²×C₅₃	1	1	yes	characteristic
973	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#490	C₂²×C₅₃	1	1	yes	characteristic
976	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#489	C₂²×C₅₃	1	1	yes	characteristic
978	#488	C₂²×C₅₃	1	1	yes	characteristic
979	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#482	C₂²×C₅₃	1	1	yes	characteristic
983	#480	C₂²×C₅₃	1	1	yes	characteristic
984	#480	C₂²×C₅₃	1	1	yes	characteristic
985	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#478	C₂²×C₅₃	1	1	yes	characteristic
988	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#469	C₂²×C₅₃	1	1	yes	characteristic
998	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#468	C₂²×C₅₃	1	1	yes	characteristic
1000	#468	C₂²×C₅₃	1	1	yes	characteristic
1001	#468	C₂²×C₅₃	1	1	yes	characteristic
1002	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#466	C₂²×C₅₃	1	1	yes	characteristic
1007	#465	C₂²×C₅₃	1	1	yes	characteristic
1008	#464	C₂²×C₅₃	1	1	yes	characteristic
1009	#464	C₂²×C₅₃	1	1	yes	characteristic
1010	#464	C₂²×C₅₃	1	1	yes	characteristic
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	#463	C₂²×C₅₃	1	1	yes	characteristic
1019	#463	C₂²×C₅₃	1	1	yes	characteristic
1020	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1021	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#460	C₂²×C₅₃	1	1	yes	characteristic
1029	#460	C₂²×C₅₃	1	1	yes	characteristic
1030	#460	C₂²×C₅₃	1	1	yes	characteristic
1031	#460	C₂²×C₅₃	1	1	yes	characteristic
1032	#460	C₂²×C₅₃	1	1	yes	characteristic
1033	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#459	C₂²×C₅₃	1	1	yes	characteristic
1037	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
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	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#451	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#450	C₂²×C₅₃	1	1	yes	characteristic
1046	#450	C₂²×C₅₃	1	1	yes	characteristic
1047	#450	C₂²×C₅₃	1	1	yes	characteristic
1048	#449	C₂²×C₅₃	1	1	yes	characteristic
1049	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#448	C₂²×C₅₃	1	1	yes	characteristic
1053	#448	C₂²×C₅₃	1	1	yes	characteristic
1054	#448	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#447	C₂²×C₅₃	1	1	yes	characteristic
1056	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1059	#440	C₂²×C₅₃	1	1	yes	characteristic
1060	#440	C₂²×C₅₃	1	1	yes	characteristic
1061	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#440	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	C₄×Q₁₆	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×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1070	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1071	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1072	#435	C₂²×C₅₃	1	1	yes	characteristic
1073	#435	C₂²×C₅₃	1	1	yes	characteristic
1074	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1075	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1076	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1077	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1078	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1079	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1080	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1081	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1082	#418	C₂²×C₅₃	1	1	yes	characteristic
1083	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1084	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1085	#417	C₂²×C₅₃	1	1	yes	characteristic, complemented
1086	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1087	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1088	C₅₃	#62085	1	1	yes	characteristic, direct product factor, Sylow
1089	C₂×#41	—	2	1	no	—
1090	C₂×#41	—	2	1	no	—
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	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂²×D₄	—	2	1	no	—
1099	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1101	#137	—	4	2	no	—
1102	#137	—	4	2	no	—
1103	#137	—	4	2	no	—
1104	AGL(1,ℤ/8)	—	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×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂×SD₁₆	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×M₁₆	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	C₂×M₁₆	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	C₄⋊Q₈	—	2	1	no	—
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	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1143	#127	—	2	1	no	—
1144	#127	—	2	1	no	—
1145	#127	C₂³×C₅₃	1	1	yes	characteristic
1146	#127	C₂³×C₅₃	1	1	yes	characteristic
1147	#127	C₂³×C₅₃	1	1	yes	characteristic
1148	#127	C₂³×C₅₃	1	1	yes	characteristic
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	#126	—	2	1	no	—
1155	#126	—	2	1	no	—
1156	#126	—	2	1	no	—
1157	#126	—	2	1	no	—
1158	#126	—	2	1	no	—
1159	#126	—	2	1	no	—
1160	#126	—	2	1	no	—
1161	#126	D₄×C₅₃	1	1	yes	characteristic
1162	#126	D₄×C₅₃	1	1	yes	characteristic
1163	#125	—	2	1	no	—
1164	#125	—	2	1	no	—
1165	#125	—	2	1	no	—
1166	#125	—	2	1	no	—
1167	#125	—	2	1	no	—
1168	#125	—	2	1	no	—
1169	#125	D₄×C₅₃	1	1	yes	characteristic
1170	#125	C₂³×C₅₃	1	1	yes	characteristic
1171	#125	C₂³×C₅₃	1	1	yes	characteristic
1172	#124	—	2	1	no	—
1173	#124	—	2	1	no	—
1174	#124	—	2	1	no	—
1175	#124	—	2	1	no	—
1176	#124	—	2	1	no	—
1177	#124	—	2	1	no	—
1178	#124	D₄×C₅₃	1	1	yes	characteristic
1179	#124	C₂³×C₅₃	1	1	yes	characteristic
1180	#124	C₂³×C₅₃	1	1	yes	characteristic
1181	#124	C₂³×C₅₃	1	1	yes	characteristic
1182	#124	C₂³×C₅₃	1	1	yes	characteristic
1183	#124	C₂³×C₅₃	1	1	yes	characteristic
1184	#124	C₂³×C₅₃	1	1	yes	characteristic
1185	#123	—	2	1	no	—
1186	#123	—	2	1	no	—
1187	#123	—	2	1	no	—
1188	#123	—	2	1	no	—
1189	#123	—	2	1	no	—
1190	#123	—	2	1	no	—
1191	#123	—	2	1	no	—
1192	#123	—	2	1	no	—
1193	#123	—	2	1	no	—
1194	#123	—	2	1	no	—
1195	#123	D₄×C₅₃	1	1	yes	characteristic
1196	#123	D₄×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1204	C₂²⋊Q₈	—	2	1	no	—
1205	C₂²⋊Q₈	—	2	1	no	—
1206	C₂²⋊Q₈	—	2	1	no	—
1207	C₂²⋊Q₈	—	2	1	no	—
1208	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1209	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1210	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1211	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1212	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1213	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1214	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1222	#121	—	2	1	no	—
1223	#121	—	2	1	no	—
1224	#121	—	2	1	no	—
1225	#121	—	2	1	no	—
1226	#121	—	2	1	no	—
1227	#121	—	2	1	no	—
1228	#121	—	2	1	no	—
1229	#121	—	2	1	no	—
1230	#121	—	2	1	no	—
1231	#121	—	2	1	no	—
1232	#121	—	2	1	no	—
1233	#121	—	2	1	no	—
1234	#121	—	2	1	no	—
1235	#121	—	2	1	no	—
1236	#121	D₄×C₅₃	1	1	yes	characteristic
1237	#121	C₂³×C₅₃	1	1	yes	characteristic
1238	#121	C₂³×C₅₃	1	1	yes	characteristic
1239	#121	C₂³×C₅₃	1	1	yes	characteristic
1240	#121	C₂³×C₅₃	1	1	yes	characteristic
1241	#121	C₂³×C₅₃	1	1	yes	characteristic
1242	#121	C₂³×C₅₃	1	1	yes	characteristic
1243	#120	—	2	1	no	—
1244	#120	—	2	1	no	—
1245	#120	—	2	1	no	—
1246	#120	—	2	1	no	—
1247	#120	—	2	1	no	—
1248	#120	—	2	1	no	—
1249	#120	—	2	1	no	—
1250	#120	—	2	1	no	—
1251	C₄×Q₈	—	2	1	no	—
1252	C₄×Q₈	—	2	1	no	—
1253	C₄×Q₈	—	2	1	no	—
1254	C₄×Q₈	—	2	1	no	—
1255	C₄×Q₈	—	2	1	no	—
1256	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1257	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1258	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1259	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1260	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1261	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1262	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1263	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1264	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1267	C₄×D₄	—	2	1	no	—
1268	C₄×D₄	—	2	1	no	—
1269	C₄×D₄	—	2	1	no	—
1270	C₄×D₄	—	2	1	no	—
1271	C₄×D₄	—	2	1	no	—
1272	C₄×D₄	—	2	1	no	—
1273	C₄×D₄	—	2	1	no	—
1274	C₄×D₄	—	2	1	no	—
1275	C₄×D₄	—	2	1	no	—
1276	C₄×D₄	—	2	1	no	—
1277	C₄×D₄	—	2	1	no	—
1278	C₄×D₄	—	2	1	no	—
1279	C₄×D₄	—	2	1	no	—
1280	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1281	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1282	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1283	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1284	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1285	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1286	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1287	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1288	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1289	#117	—	2	1	no	—
1290	#117	—	2	1	no	—
1291	#117	—	2	1	no	—
1292	#117	—	2	1	no	—
1293	#117	—	2	1	no	—
1294	#117	—	2	1	no	—
1295	#117	—	2	1	no	—
1296	#117	C₂³×C₅₃	1	1	yes	characteristic
1297	#117	C₂³×C₅₃	1	1	yes	characteristic
1298	#117	C₂³×C₅₃	1	1	yes	characteristic
1299	C₂×C₄⋊C₄	—	2	1	no	—
1300	C₂×C₄⋊C₄	—	2	1	no	—
1301	C₂×C₄⋊C₄	—	2	1	no	—
1302	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1303	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1304	C₂×C₂²⋊C₄	—	2	1	no	—
1305	C₂×C₂²⋊C₄	—	2	1	no	—
1306	C₂×C₄²	—	2	1	no	—
1307	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1308	#107	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	#107	C₂³×C₅₃	1	1	yes	characteristic
1314	#106	C₂³×C₅₃	1	1	yes	characteristic
1315	#106	C₂³×C₅₃	1	1	yes	characteristic
1316	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1317	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1318	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	#103	C₂³×C₅₃	1	1	yes	characteristic
1327	#103	C₂³×C₅₃	1	1	yes	characteristic
1328	#103	C₂³×C₅₃	1	1	yes	characteristic
1329	#103	C₂³×C₅₃	1	1	yes	characteristic
1330	#103	C₂³×C₅₃	1	1	yes	characteristic
1331	#103	C₂³×C₅₃	1	1	yes	characteristic
1332	#103	C₂³×C₅₃	1	1	yes	characteristic
1333	#103	C₂³×C₅₃	1	1	yes	characteristic
1334	#103	C₂³×C₅₃	1	1	yes	characteristic
1335	#103	C₂³×C₅₃	1	1	yes	characteristic
1336	#103	C₂³×C₅₃	1	1	yes	characteristic
1337	#103	C₂³×C₅₃	1	1	yes	characteristic
1338	#103	C₂³×C₅₃	1	1	yes	characteristic
1339	#103	C₂³×C₅₃	1	1	yes	characteristic
1340	#102	C₂³×C₅₃	1	1	yes	characteristic
1341	#102	C₂³×C₅₃	1	1	yes	characteristic
1342	#102	C₂³×C₅₃	1	1	yes	characteristic
1343	#102	C₂³×C₅₃	1	1	yes	characteristic
1344	#102	C₂³×C₅₃	1	1	yes	characteristic
1345	#102	C₂³×C₅₃	1	1	yes	characteristic
1346	#102	C₂³×C₅₃	1	1	yes	characteristic
1347	#102	C₂³×C₅₃	1	1	yes	characteristic
1348	#102	C₂³×C₅₃	1	1	yes	characteristic
1349	#102	C₂³×C₅₃	1	1	yes	characteristic
1350	#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	C₂²⋊C₈	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	#97	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	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1369	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1370	C₂⁴	—	2	1	no	—
1371	C₂⁴	—	2	1	no	—
1372	#41	—	2	2	no	—
1373	#41	—	4	1	no	—
1374	#41	—	4	1	no	—
1375	#41	—	4	1	no	—
1376	#41	—	4	1	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	—	8	2	no	—
1383	#41	—	8	2	no	—
1384	C₂×Q₈	—	2	1	no	—
1385	C₂×Q₈	—	2	1	no	—
1386	C₂×Q₈	—	2	1	no	—
1387	C₂×Q₈	—	2	1	no	—
1388	C₂×Q₈	—	2	2	no	—
1389	C₂×Q₈	—	2	2	no	—
1390	C₂×Q₈	—	4	1	no	—
1391	C₂×Q₈	—	4	1	no	—
1392	C₂×Q₈	C₂×D₄×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×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1397	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	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	—	4	1	no	—
1420	C₂×D₄	—	4	1	no	—
1421	C₂×D₄	—	4	1	no	—
1422	C₂×D₄	—	4	1	no	—
1423	C₂×D₄	—	8	2	no	—
1424	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1425	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1426	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1427	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1428	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1429	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1430	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1431	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1442	C₂²×C₄	—	2	1	no	—
1443	C₂²×C₄	—	2	1	no	—
1444	C₂²×C₄	—	2	1	no	—
1445	C₂²×C₄	—	2	1	no	—
1446	C₂²×C₄	—	2	1	no	—
1447	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1448	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1449	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1450	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1451	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1452	Q₁₆	—	2	2	no	—
1453	Q₁₆	—	2	2	no	—
1454	Q₁₆	—	4	1	no	—
1455	Q₁₆	—	4	1	no	—
1456	Q₁₆	—	4	1	no	—
1457	Q₁₆	—	4	1	no	—
1458	SD₁₆	—	2	2	no	—
1459	SD₁₆	—	2	2	no	—
1460	SD₁₆	—	2	2	no	—
1461	SD₁₆	—	2	2	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	SD₁₆	—	4	1	no	—
1470	SD₁₆	—	4	1	no	—
1471	SD₁₆	—	4	1	no	—
1472	D₈	—	4	1	no	—
1473	D₈	—	4	1	no	—
1474	D₈	—	4	1	no	—
1475	D₈	—	4	1	no	—
1476	M₁₆	—	4	1	no	—
1477	M₁₆	—	4	1	no	—
1478	M₁₆	—	4	1	no	—
1479	M₁₆	—	4	1	no	—
1480	C₂×C₈	—	4	1	no	—
1481	C₂×C₈	—	4	1	no	—
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	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1516	C₄⋊C₄	—	2	1	no	—
1517	C₄⋊C₄	—	2	1	no	—
1518	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1519	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1520	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1522	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1523	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1524	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1525	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1526	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1527	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1528	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1529	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1530	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1531	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1532	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1533	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	C₂×D₄×C₅₃	1	1	yes	characteristic
1566	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1567	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1568	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1569	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1570	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	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1584	C₄²	—	2	1	no	—
1585	C₄²	—	2	1	no	—
1586	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1587	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1588	C₄²	C₂⁴×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	C₂³	—	2	1	no	—
1593	C₂³	—	2	1	no	—
1594	C₂³	—	2	1	no	—
1595	C₂³	—	2	1	no	—
1596	C₂³	—	2	1	no	—
1597	C₂³	—	8	1	no	—
1598	C₂³	—	8	1	no	—
1599	C₂³	—	8	1	no	—
1600	C₂³	—	8	1	no	—
1601	C₂³	—	8	1	no	—
1602	C₂³	—	8	1	no	—
1603	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1604	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1605	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1606	Q₈	—	2	1	no	—
1607	Q₈	—	2	1	no	—
1608	Q₈	—	2	1	no	—
1609	Q₈	—	2	1	no	—
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	—	4	1	no	—
1616	Q₈	—	4	2	no	—
1617	Q₈	—	4	2	no	—
1618	Q₈	—	8	1	no	—
1619	Q₈	—	8	1	no	—
1620	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1621	D₄	—	2	1	no	—
1622	D₄	—	2	1	no	—
1623	D₄	—	2	1	no	—
1624	D₄	—	2	1	no	—
1625	D₄	—	2	1	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	—	4	1	no	—
1632	D₄	—	4	1	no	—
1633	D₄	—	4	1	no	—
1634	D₄	—	4	2	no	—
1635	D₄	—	4	2	no	—
1636	D₄	—	4	2	no	—
1637	D₄	—	8	1	no	—
1638	D₄	—	8	1	no	—
1639	D₄	—	8	1	no	—
1640	D₄	—	8	1	no	—
1641	D₄	—	8	1	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	—	8	1	no	—
1651	D₄	—	8	1	no	—
1652	D₄	—	8	1	no	—
1653	D₄	—	8	1	no	—
1654	D₄	—	8	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	—	2	1	no	—
1670	C₂×C₄	—	2	1	no	—
1671	C₂×C₄	—	2	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	—	8	1	no	—
1680	C₂×C₄	—	8	1	no	—
1681	C₂×C₄	—	8	1	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	C₂²×D₄×C₅₃	1	1	yes	characteristic
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	C₂⁵×C₅₃	1	1	yes	characteristic
1701	C₈	—	2	1	no	—
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	C₂²	—	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	1	no	—
1715	C₂²	—	2	1	no	—
1716	C₂²	—	2	1	no	—
1717	C₂²	—	2	1	no	—
1718	C₂²	—	4	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	—	16	2	no	—
1734	C₂²	—	16	2	no	—
1735	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1736	C₄	—	2	1	no	—
1737	C₄	—	2	1	no	—
1738	C₄	—	2	1	no	—
1739	C₄	—	2	2	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	—	4	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	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1759	C₄	C₅₃×#585	1	1	yes	characteristic
1760	C₂	—	4	1	no	—
1761	C₂	—	4	1	no	—
1762	C₂	—	4	1	no	—
1763	C₂	—	8	1	no	—
1764	C₂	—	8	1	no	—
1765	C₂	—	8	1	no	—
1766	C₂	—	8	1	no	—
1767	C₂	—	8	1	no	—
1768	C₂	C₅₃×#3488	1	1	yes	characteristic
1769	C₂	C₅₃×#3585	1	1	yes	characteristic
1770	C₂	C₅₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3546	C₂	semidirect
2. C₅₃×#3516	C₂	semidirect
3. C₅₃×#3402	C₂	semidirect
4. C₅₃×#3397	C₂	semidirect
5. C₅₃×#3377	C₂	semidirect
6. C₅₃×#3368	C₂	semidirect
7. C₅₃×#3333	C₂	semidirect
8. C₅₃×#3322	C₂	semidirect
9. C₅₃×#3315	C₂	semidirect
10. C₅₃×#3314	C₂	semidirect
11. C₅₃×#3310	C₂	semidirect
12. C₅₃×#3309	C₂	semidirect
13. C₅₃×#3278	C₂	semidirect
14. C₅₃×#3275	C₂	semidirect
15. C₅₃×#3271	C₂	semidirect
16. C₅₃×#3269	C₂	semidirect
17. C₅₃×#3266	C₂	semidirect
18. C₅₃×#3265	C₂	semidirect
19. C₅₃×#3262	C₂	semidirect
20. C₅₃×#3258	C₂	semidirect
21. C₅₃×#3251	C₂	semidirect
22. C₅₃×#3224	C₂	semidirect
23. C₅₃×#3222	C₂	semidirect
24. C₅₃×#3219	C₂	semidirect
25. C₅₃×#3124	C₂	semidirect
26. C₅₃×#3121	C₂	semidirect
27. C₅₃×#3112	C₂	semidirect
28. C₅₃×#3045	C₂	semidirect
29. C₅₃×#3043	C₂	semidirect
30. C₅₃×#3037	C₂	semidirect
31. C₅₃×#2995	C₂	semidirect
32. C₂×#137×C₅₃	C₂²	semidirect
33. C₂×#137×C₅₃	C₂²	semidirect
34. C₂×#137×C₅₃	C₂²	semidirect
36. C₂×#135×C₅₃	C₂²	semidirect
40. C₅₃×#557	C₂²	semidirect
43. C₅₃×#556	C₂²	semidirect
45. C₅₃×#554	C₂²	semidirect
48. C₅₃×#553	C₂²	semidirect
54. D₄×Q₈×C₅₃	C₂²	semidirect
56. C₅₃×#548	C₂²	semidirect
65. C₅₃×#542	C₂²	semidirect
67. 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
84. C₅₃×#497	C₂²	semidirect
86. C₅₃×#496	C₂²	semidirect
88. C₅₃×#492	C₂²	semidirect
89. C₅₃×#491	C₂²	semidirect
91. C₅₃×#490	C₂²	semidirect
94. C₅₃×#486	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#484	C₂²	semidirect
100. C₅₃×#480	C₂²	semidirect
101. C₅₃×#479	C₂²	semidirect
103. C₅₃×#478	C₂²	semidirect
104. C₅₃×#478	C₂²	semidirect
105. C₅₃×#477	C₂²	semidirect
106. C₅₃×#477	C₂²	semidirect
107. C₅₃×#477	C₂²	semidirect
108. C₅₃×#475	C₂²	semidirect
109. C₅₃×#474	C₂²	semidirect
110. C₅₃×#474	C₂²	semidirect
111. C₅₃×#470	C₂²	semidirect
113. C₅₃×#469	C₂²	semidirect
117. C₅₃×#468	C₂²	semidirect
118. C₅₃×#468	C₂²	semidirect
119. C₅₃×#467	C₂²	semidirect
120. C₅₃×#467	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
135. C₅₃×#463	C₂²	semidirect
136. C₅₃×#463	C₂²	semidirect
137. C₅₃×#463	C₂²	semidirect
138. C₅₃×#463	C₂²	semidirect
139. C₅₃×#462	C₂²	semidirect
140. C₅₃×#462	C₂²	semidirect
141. C₅₃×#462	C₂²	semidirect
142. C₅₃×#461	C₂²	semidirect
148. C₅₃×#460	C₂²	semidirect
149. C₅₃×#460	C₂²	semidirect
150. C₅₃×#460	C₂²	semidirect
152. C₅₃×#459	C₂²	semidirect
153. C₅₃×#452	C₂²	semidirect
154. C₅₃×#452	C₂²	semidirect
155. C₅₃×#452	C₂²	semidirect
156. C₅₃×#452	C₂²	semidirect
157. C₅₃×#452	C₂²	semidirect
158. C₅₃×#452	C₂²	semidirect
159. C₅₃×#451	C₂²	semidirect
164. C₅₃×#449	C₂²	semidirect
165. C₅₃×#449	C₂²	semidirect
166. C₅₃×#449	C₂²	semidirect
169. C₅₃×#448	C₂²	semidirect
171. C₅₃×#446	C₂²	semidirect
172. C₅₃×#446	C₂²	semidirect
173. 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×Q₁₆×C₅₃	C₂²	semidirect
182. C₄×Q₁₆×C₅₃	C₂²	semidirect
183. C₄×SD₁₆×C₅₃	C₂²	semidirect
184. C₄×D₈×C₅₃	C₂²	semidirect
185. C₅₃×#436	C₂²	semidirect
186. C₅₃×#436	C₂²	semidirect
189. C₅₃×#435	C₂²	semidirect
190. C₅₃×#435	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. C₅₃×#423	C₂²	semidirect
198. C₅₃×#417	C₂²	semidirect
199. C₅₃×#417	C₂²	semidirect
200. C₅₃×#417	C₂²	semidirect
201. C₅₃×#416	C₂²	semidirect
823. #62085	C₅₃	direct (N × H)
875. #3546	C₂×C₅₃	semidirect
876. #3516	C₂×C₅₃	semidirect
877. #3402	C₂×C₅₃	semidirect
878. #3397	C₂×C₅₃	semidirect
879. #3377	C₂×C₅₃	semidirect
880. #3368	C₂×C₅₃	semidirect
881. #3333	C₂×C₅₃	semidirect
882. #3322	C₂×C₅₃	semidirect
883. #3315	C₂×C₅₃	semidirect
884. #3314	C₂×C₅₃	semidirect
885. #3310	C₂×C₅₃	semidirect
886. #3309	C₂×C₅₃	semidirect
887. #3278	C₂×C₅₃	semidirect
888. #3275	C₂×C₅₃	semidirect
889. #3271	C₂×C₅₃	semidirect
890. #3269	C₂×C₅₃	semidirect
891. #3266	C₂×C₅₃	semidirect
892. #3265	C₂×C₅₃	semidirect
893. #3262	C₂×C₅₃	semidirect
894. #3258	C₂×C₅₃	semidirect
895. #3251	C₂×C₅₃	semidirect
896. #3224	C₂×C₅₃	semidirect
897. #3222	C₂×C₅₃	semidirect
898. #3219	C₂×C₅₃	semidirect
899. #3124	C₂×C₅₃	semidirect
900. #3121	C₂×C₅₃	semidirect
901. #3112	C₂×C₅₃	semidirect
902. #3045	C₂×C₅₃	semidirect
903. #3043	C₂×C₅₃	semidirect
904. #3037	C₂×C₅₃	semidirect
905. #2995	C₂×C₅₃	semidirect
917. C₂×#137	C₂²×C₅₃	semidirect
918. C₂×#137	C₂²×C₅₃	semidirect
919. C₂×#137	C₂²×C₅₃	semidirect
921. C₂×#135	C₂²×C₅₃	semidirect
925. #557	C₂²×C₅₃	semidirect
928. #556	C₂²×C₅₃	semidirect
930. #554	C₂²×C₅₃	semidirect
933. #553	C₂²×C₅₃	semidirect
939. D₄×Q₈	C₂²×C₅₃	semidirect
941. #548	C₂²×C₅₃	semidirect
950. #542	C₂²×C₅₃	semidirect
952. #541	C₂²×C₅₃	semidirect
964. #529	C₂²×C₅₃	semidirect
965. #520	C₂²×C₅₃	semidirect
966. #519	C₂²×C₅₃	semidirect
967. C₂×C₄×Q₈	C₂²×C₅₃	semidirect
969. #497	C₂²×C₅₃	semidirect
971. #496	C₂²×C₅₃	semidirect
973. #492	C₂²×C₅₃	semidirect
974. #491	C₂²×C₅₃	semidirect
976. #490	C₂²×C₅₃	semidirect
979. #486	C₂²×C₅₃	semidirect
980. #485	C₂²×C₅₃	semidirect
981. #484	C₂²×C₅₃	semidirect
985. #480	C₂²×C₅₃	semidirect
986. #479	C₂²×C₅₃	semidirect
988. #478	C₂²×C₅₃	semidirect
989. #478	C₂²×C₅₃	semidirect
990. #477	C₂²×C₅₃	semidirect
991. #477	C₂²×C₅₃	semidirect
992. #477	C₂²×C₅₃	semidirect
993. #475	C₂²×C₅₃	semidirect
994. #474	C₂²×C₅₃	semidirect
995. #474	C₂²×C₅₃	semidirect
996. #470	C₂²×C₅₃	semidirect
998. #469	C₂²×C₅₃	semidirect
1002. #468	C₂²×C₅₃	semidirect
1003. #468	C₂²×C₅₃	semidirect
1004. #467	C₂²×C₅₃	semidirect
1005. #467	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
1020. #463	C₂²×C₅₃	semidirect
1021. #463	C₂²×C₅₃	semidirect
1022. #463	C₂²×C₅₃	semidirect
1023. #463	C₂²×C₅₃	semidirect
1024. #462	C₂²×C₅₃	semidirect
1025. #462	C₂²×C₅₃	semidirect
1026. #462	C₂²×C₅₃	semidirect
1027. #461	C₂²×C₅₃	semidirect
1033. #460	C₂²×C₅₃	semidirect
1034. #460	C₂²×C₅₃	semidirect
1035. #460	C₂²×C₅₃	semidirect
1037. #459	C₂²×C₅₃	semidirect
1038. #452	C₂²×C₅₃	semidirect
1039. #452	C₂²×C₅₃	semidirect
1040. #452	C₂²×C₅₃	semidirect
1041. #452	C₂²×C₅₃	semidirect
1042. #452	C₂²×C₅₃	semidirect
1043. #452	C₂²×C₅₃	semidirect
1044. #451	C₂²×C₅₃	semidirect
1049. #449	C₂²×C₅₃	semidirect
1050. #449	C₂²×C₅₃	semidirect
1051. #449	C₂²×C₅₃	semidirect
1054. #448	C₂²×C₅₃	semidirect
1056. #446	C₂²×C₅₃	semidirect
1057. #446	C₂²×C₅₃	semidirect
1058. #441	C₂²×C₅₃	semidirect
1061. #440	C₂²×C₅₃	semidirect
1062. #440	C₂²×C₅₃	semidirect
1063. #440	C₂²×C₅₃	semidirect
1064. #440	C₂²×C₅₃	semidirect
1065. #440	C₂²×C₅₃	semidirect
1066. C₄×Q₁₆	C₂²×C₅₃	semidirect
1067. C₄×Q₁₆	C₂²×C₅₃	semidirect
1068. C₄×SD₁₆	C₂²×C₅₃	semidirect
1069. C₄×D₈	C₂²×C₅₃	semidirect
1070. #436	C₂²×C₅₃	semidirect
1071. #436	C₂²×C₅₃	semidirect
1074. #435	C₂²×C₅₃	semidirect
1075. #435	C₂²×C₅₃	semidirect
1076. #433	C₂²×C₅₃	semidirect
1077. #433	C₂²×C₅₃	semidirect
1078. #432	C₂²×C₅₃	semidirect
1079. #424	C₂²×C₅₃	semidirect
1080. #424	C₂²×C₅₃	semidirect
1081. #423	C₂²×C₅₃	semidirect
1083. #417	C₂²×C₅₃	semidirect
1084. #417	C₂²×C₅₃	semidirect
1085. #417	C₂²×C₅₃	semidirect
1086. #416	C₂²×C₅₃	semidirect
1088. C₅₃	#62085	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×#3546	2
C₅₃×#3516	2
C₅₃×#3402	2
C₅₃×#3397	2
C₅₃×#3377	2
C₅₃×#3368	2
C₅₃×#3333	2
C₅₃×#3322	2
C₅₃×#3315	2
C₅₃×#3314	2
C₅₃×#3310	2
C₅₃×#3309	2
C₅₃×#3278	2
C₅₃×#3275	2
C₅₃×#3271	2
C₅₃×#3269	2
C₅₃×#3266	2
C₅₃×#3265	2
C₅₃×#3262	2
C₅₃×#3258	2
C₅₃×#3251	2
C₅₃×#3224	2
C₅₃×#3222	2
C₅₃×#3219	2
C₅₃×#3124	2
C₅₃×#3121	2
C₅₃×#3112	2
C₅₃×#3045	2
C₅₃×#3043	2
C₅₃×#3037	2
C₅₃×#2995	2
#62085	53

Subgroups — C53×#62085 #27269597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62085 #27269597