Subgroups — C₅₃×#61529 #27269041

Order 13568.

1846 conjugacy classes of subgroups.

The subgroup lattice has 1730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3521	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3401	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3384	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3349	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3347	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3340	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3319	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3297	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3280	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3267	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3264	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3180	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3178	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3173	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3106	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#2968	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
34	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
35	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#556	C₂²	1	1	yes	characteristic
37	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#555	C₂²	1	1	yes	characteristic
40	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
42	C₅₃×#553	—	2	1	no	—
43	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#552	—	2	1	no	—
45	C₅₃×#552	C₂²	1	1	yes	characteristic
46	C₅₃×#551	—	2	1	no	—
47	C₅₃×#551	—	2	1	no	—
48	C₅₃×#551	—	2	1	no	—
49	C₅₃×#551	—	2	1	no	—
50	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#548	—	2	1	no	—
52	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#546	—	2	1	no	—
54	C₅₃×#546	C₂²	1	1	yes	characteristic
55	C₅₃×#546	C₂²	1	1	yes	characteristic
56	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#546	C₂²	1	1	yes	characteristic, complemented
58	D₄²×C₅₃	C₂²	1	1	yes	characteristic
59	C₅₃×#542	C₂²	1	1	yes	characteristic
60	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#539	—	2	1	no	—
64	C₅₃×#538	—	2	1	no	—
65	C₅₃×#538	—	2	1	no	—
66	C₅₃×#538	—	2	1	no	—
67	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#529	—	2	1	no	—
69	C₅₃×#529	—	2	1	no	—
70	C₅₃×#529	C₂²	1	1	yes	characteristic
71	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
72	C₂×#126×C₅₃	—	2	1	no	—
73	C₂×#124×C₅₃	—	2	1	no	—
74	C₅₃×#520	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#518	C₂²	1	1	yes	characteristic
76	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
78	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#498	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×#495	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#489	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#488	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#480	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×#477	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#469	C₂²	1	1	yes	characteristic
119	C₅₃×#468	C₂²	1	1	yes	characteristic
120	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#465	C₂²	1	1	yes	characteristic
124	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#465	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
131	C₅₃×#463	C₂²	1	1	yes	characteristic
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×#463	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#459	C₂²	1	1	yes	characteristic
140	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#450	C₂²	1	1	yes	characteristic
143	C₅₃×#450	C₂²	1	1	yes	characteristic
144	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#450	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#449	C₂²	1	1	yes	characteristic
147	C₅₃×#449	C₂²	1	1	yes	characteristic
148	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#449	C₂²	1	1	yes	characteristic, complemented
150	C₅₃×#447	C₂²	1	1	yes	characteristic
151	C₅₃×#447	C₂²	1	1	yes	characteristic
152	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#442	C₂²	1	1	yes	characteristic
155	C₅₃×#442	C₂²	1	1	yes	characteristic
156	C₅₃×#442	C₂²	1	1	yes	characteristic
157	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
160	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
161	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
162	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
163	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
164	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
165	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
170	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
171	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
172	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
173	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
174	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
179	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#435	C₂²	1	1	yes	characteristic
183	C₅₃×#435	C₂²	1	1	yes	characteristic
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
186	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
187	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
189	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#418	C₂²	1	1	yes	characteristic
195	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
198	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
199	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
200	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
201	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
202	C₂×#97×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	—	2	1	no	—
208	C₂²×D₄×C₅₃	—	2	1	no	—
209	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
212	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
213	#135×C₅₃	—	2	4	no	—
214	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×D₈×C₅₃	—	2	4	no	—
225	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
234	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
235	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	#127×C₅₃	C₂³	1	1	yes	characteristic
243	#126×C₅₃	—	2	1	no	—
244	#126×C₅₃	—	2	1	no	—
245	#126×C₅₃	—	2	1	no	—
246	#126×C₅₃	—	2	1	no	—
247	#126×C₅₃	—	2	1	no	—
248	#126×C₅₃	—	2	1	no	—
249	#126×C₅₃	—	2	1	no	—
250	#126×C₅₃	—	2	1	no	—
251	#126×C₅₃	—	2	1	no	—
252	#126×C₅₃	—	2	1	no	—
253	#126×C₅₃	—	2	1	no	—
254	#126×C₅₃	—	2	1	no	—
255	#126×C₅₃	—	2	1	no	—
256	#126×C₅₃	—	2	1	no	—
257	#126×C₅₃	D₄	1	1	yes	characteristic
258	#126×C₅₃	D₄	1	1	yes	characteristic
259	#125×C₅₃	—	2	1	no	—
260	#125×C₅₃	—	2	1	no	—
261	#125×C₅₃	—	2	1	no	—
262	#125×C₅₃	D₄	1	1	yes	characteristic
263	#125×C₅₃	C₂³	1	1	yes	characteristic
264	#125×C₅₃	C₂³	1	1	yes	characteristic
265	#124×C₅₃	—	2	1	no	—
266	#124×C₅₃	—	2	1	no	—
267	#124×C₅₃	—	2	1	no	—
268	#124×C₅₃	—	2	1	no	—
269	#124×C₅₃	—	2	1	no	—
270	#124×C₅₃	—	2	1	no	—
271	#124×C₅₃	—	2	1	no	—
272	#124×C₅₃	—	2	1	no	—
273	#124×C₅₃	—	2	1	no	—
274	#124×C₅₃	—	2	1	no	—
275	#124×C₅₃	—	2	1	no	—
276	#124×C₅₃	D₄	1	1	yes	characteristic
277	#124×C₅₃	C₂³	1	1	yes	characteristic
278	#124×C₅₃	C₂³	1	1	yes	characteristic
279	#124×C₅₃	C₂³	1	1	yes	characteristic
280	#124×C₅₃	C₂³	1	1	yes	characteristic
281	#123×C₅₃	—	2	1	no	—
282	#123×C₅₃	—	2	1	no	—
283	#123×C₅₃	—	2	1	no	—
284	#123×C₅₃	—	2	1	no	—
285	#123×C₅₃	—	2	1	no	—
286	#123×C₅₃	—	2	1	no	—
287	#123×C₅₃	—	2	1	no	—
288	#123×C₅₃	—	2	1	no	—
289	#123×C₅₃	—	2	1	no	—
290	#123×C₅₃	—	2	1	no	—
291	#123×C₅₃	—	2	1	no	—
292	#123×C₅₃	—	2	1	no	—
293	#123×C₅₃	—	2	1	no	—
294	#123×C₅₃	—	2	1	no	—
295	#123×C₅₃	D₄	1	1	yes	characteristic
296	#123×C₅₃	D₄	1	1	yes	characteristic
297	C₂²⋊Q₈×C₅₃	—	2	1	no	—
298	C₂²⋊Q₈×C₅₃	—	2	1	no	—
299	C₂²⋊Q₈×C₅₃	—	2	1	no	—
300	C₂²⋊Q₈×C₅₃	—	2	1	no	—
301	C₂²⋊Q₈×C₅₃	—	2	1	no	—
302	C₂²⋊Q₈×C₅₃	—	2	1	no	—
303	C₂²⋊Q₈×C₅₃	—	2	1	no	—
304	C₂²⋊Q₈×C₅₃	—	2	1	no	—
305	C₂²⋊Q₈×C₅₃	—	2	1	no	—
306	C₂²⋊Q₈×C₅₃	—	2	1	no	—
307	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
308	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
311	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
312	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
314	#121×C₅₃	—	2	1	no	—
315	#121×C₅₃	—	2	1	no	—
316	#121×C₅₃	—	2	1	no	—
317	#121×C₅₃	—	2	1	no	—
318	#121×C₅₃	—	2	1	no	—
319	#121×C₅₃	—	2	1	no	—
320	#121×C₅₃	—	2	1	no	—
321	#121×C₅₃	—	2	1	no	—
322	#121×C₅₃	—	2	1	no	—
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	D₄	1	1	yes	characteristic
325	#121×C₅₃	C₂³	1	1	yes	characteristic
326	#121×C₅₃	C₂³	1	1	yes	characteristic
327	#121×C₅₃	C₂³	1	1	yes	characteristic
328	#121×C₅₃	C₂³	1	1	yes	characteristic
329	#121×C₅₃	C₂³	1	1	yes	characteristic
330	#121×C₅₃	C₂³	1	1	yes	characteristic
331	#120×C₅₃	—	2	1	no	—
332	#120×C₅₃	—	2	1	no	—
333	#120×C₅₃	—	2	1	no	—
334	#120×C₅₃	—	2	1	no	—
335	#120×C₅₃	—	2	1	no	—
336	#120×C₅₃	—	2	1	no	—
337	C₄×Q₈×C₅₃	—	2	1	no	—
338	C₄×Q₈×C₅₃	—	2	1	no	—
339	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
340	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
341	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
342	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
343	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
344	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
345	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
346	C₄×D₄×C₅₃	—	2	1	no	—
347	C₄×D₄×C₅₃	—	2	1	no	—
348	C₄×D₄×C₅₃	—	2	1	no	—
349	C₄×D₄×C₅₃	—	2	1	no	—
350	C₄×D₄×C₅₃	—	2	1	no	—
351	C₄×D₄×C₅₃	—	2	1	no	—
352	C₄×D₄×C₅₃	—	2	1	no	—
353	C₄×D₄×C₅₃	—	2	1	no	—
354	C₄×D₄×C₅₃	—	2	1	no	—
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	—	2	1	no	—
357	C₄×D₄×C₅₃	—	2	1	no	—
358	C₄×D₄×C₅₃	—	2	1	no	—
359	C₄×D₄×C₅₃	—	2	1	no	—
360	C₄×D₄×C₅₃	—	2	1	no	—
361	C₄×D₄×C₅₃	—	2	1	no	—
362	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
379	#117×C₅₃	—	2	1	no	—
380	#117×C₅₃	—	2	1	no	—
381	#117×C₅₃	—	2	1	no	—
382	#117×C₅₃	—	2	1	no	—
383	#117×C₅₃	—	2	1	no	—
384	#117×C₅₃	—	2	1	no	—
385	#117×C₅₃	—	2	1	no	—
386	#117×C₅₃	—	2	1	no	—
387	#117×C₅₃	C₂³	1	1	yes	characteristic
388	#117×C₅₃	C₂³	1	1	yes	characteristic
389	#117×C₅₃	C₂³	1	1	yes	characteristic
390	#117×C₅₃	C₂³	1	1	yes	characteristic
391	#117×C₅₃	C₂³	1	1	yes	characteristic
392	#117×C₅₃	C₂³	1	1	yes	characteristic
393	#117×C₅₃	C₂³	1	1	yes	characteristic
394	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
397	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
398	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
399	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
400	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
401	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
402	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
403	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
404	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
405	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
406	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
407	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
408	C₂×C₄²×C₅₃	—	2	1	no	—
409	C₂×C₄²×C₅₃	—	2	1	no	—
410	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
411	#107×C₅₃	C₂³	1	1	yes	characteristic
412	#107×C₅₃	C₂³	1	1	yes	characteristic
413	#107×C₅₃	C₂³	1	1	yes	characteristic
414	#107×C₅₃	C₂³	1	1	yes	characteristic
415	#107×C₅₃	C₂³	1	1	yes	characteristic
416	#107×C₅₃	C₂³	1	1	yes	characteristic
417	#107×C₅₃	C₂³	1	1	yes	characteristic
418	#107×C₅₃	C₂³	1	1	yes	characteristic
419	#106×C₅₃	C₂³	1	1	yes	characteristic
420	#106×C₅₃	C₂³	1	1	yes	characteristic
421	#106×C₅₃	C₂³	1	1	yes	characteristic
422	#106×C₅₃	C₂³	1	1	yes	characteristic
423	#106×C₅₃	C₂³	1	1	yes	characteristic
424	#106×C₅₃	C₂³	1	1	yes	characteristic
425	#106×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
428	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
429	C₄⋊C₈×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	#103×C₅₃	C₂³	1	1	yes	characteristic
434	#103×C₅₃	C₂³	1	1	yes	characteristic
435	#103×C₅₃	C₂³	1	1	yes	characteristic
436	#103×C₅₃	C₂³	1	1	yes	characteristic
437	#103×C₅₃	C₂³	1	1	yes	characteristic
438	#103×C₅₃	C₂³	1	1	yes	characteristic
439	#103×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	#102×C₅₃	C₂³	1	1	yes	characteristic
446	#102×C₅₃	C₂³	1	1	yes	characteristic
447	#102×C₅₃	C₂³	1	1	yes	characteristic
448	#102×C₅₃	C₂³	1	1	yes	characteristic
449	#102×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	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
466	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
467	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
468	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
469	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
470	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
471	#97×C₅₃	C₂³	1	1	yes	characteristic
472	#97×C₅₃	C₂³	1	1	yes	characteristic
473	#97×C₅₃	C₂³	1	1	yes	characteristic
474	#97×C₅₃	C₂³	1	1	yes	characteristic
475	#97×C₅₃	C₂³	1	1	yes	characteristic
476	#97×C₅₃	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
479	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
480	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
481	C₂⁴×C₅₃	—	2	1	no	—
482	C₂⁴×C₅₃	—	2	1	no	—
483	C₂⁴×C₅₃	—	2	1	no	—
484	#41×C₅₃	—	2	2	no	—
485	#41×C₅₃	—	2	2	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	—	8	2	no	—
491	C₂×Q₈×C₅₃	—	2	1	no	—
492	C₂×Q₈×C₅₃	—	2	1	no	—
493	C₂×Q₈×C₅₃	—	2	1	no	—
494	C₂×Q₈×C₅₃	—	2	1	no	—
495	C₂×Q₈×C₅₃	—	8	2	no	—
496	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
497	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
498	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
499	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
500	C₂×D₄×C₅₃	—	2	2	no	—
501	C₂×D₄×C₅₃	—	2	2	no	—
502	C₂×D₄×C₅₃	—	2	2	no	—
503	C₂×D₄×C₅₃	—	2	1	no	—
504	C₂×D₄×C₅₃	—	2	1	no	—
505	C₂×D₄×C₅₃	—	2	1	no	—
506	C₂×D₄×C₅₃	—	2	1	no	—
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	—	4	1	no	—
518	C₂×D₄×C₅₃	—	4	1	no	—
519	C₂×D₄×C₅₃	—	4	1	no	—
520	C₂×D₄×C₅₃	—	8	2	no	—
521	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
522	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
523	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
524	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
525	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
526	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
527	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
528	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
529	C₂²×C₄×C₅₃	—	2	1	no	—
530	C₂²×C₄×C₅₃	—	2	1	no	—
531	C₂²×C₄×C₅₃	—	2	1	no	—
532	C₂²×C₄×C₅₃	—	2	1	no	—
533	C₂²×C₄×C₅₃	—	2	1	no	—
534	C₂²×C₄×C₅₃	—	2	1	no	—
535	C₂²×C₄×C₅₃	—	2	1	no	—
536	C₂²×C₄×C₅₃	—	2	1	no	—
537	C₂²×C₄×C₅₃	—	2	1	no	—
538	C₂²×C₄×C₅₃	—	2	1	no	—
539	C₂²×C₄×C₅₃	—	2	1	no	—
540	C₂²×C₄×C₅₃	—	2	1	no	—
541	C₂²×C₄×C₅₃	—	2	1	no	—
542	C₂²×C₄×C₅₃	—	2	1	no	—
543	C₂²×C₄×C₅₃	—	2	1	no	—
544	C₂²×C₄×C₅₃	—	2	1	no	—
545	C₂²×C₄×C₅₃	—	2	1	no	—
546	C₂²×C₄×C₅₃	—	2	1	no	—
547	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
548	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
549	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
550	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
551	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
552	Q₁₆×C₅₃	—	2	2	no	—
553	Q₁₆×C₅₃	—	4	1	no	—
554	SD₁₆×C₅₃	—	2	2	no	—
555	SD₁₆×C₅₃	—	2	2	no	—
556	SD₁₆×C₅₃	—	2	2	no	—
557	SD₁₆×C₅₃	—	2	2	no	—
558	SD₁₆×C₅₃	—	4	1	no	—
559	SD₁₆×C₅₃	—	4	1	no	—
560	SD₁₆×C₅₃	—	4	1	no	—
561	SD₁₆×C₅₃	—	4	1	no	—
562	D₈×C₅₃	—	2	2	no	—
563	D₈×C₅₃	—	2	2	no	—
564	D₈×C₅₃	—	2	2	no	—
565	D₈×C₅₃	—	2	2	no	—
566	D₈×C₅₃	—	4	1	no	—
567	D₈×C₅₃	#41	1	4	yes	complemented
568	M₁₆×C₅₃	—	2	2	no	—
569	M₁₆×C₅₃	—	4	1	no	—
570	C₂×C₈×C₅₃	—	2	2	no	—
571	C₂×C₈×C₅₃	—	2	2	no	—
572	C₂×C₈×C₅₃	—	4	1	no	—
573	C₂×C₈×C₅₃	—	4	1	no	—
574	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
575	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
576	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
577	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
578	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
579	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
580	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
581	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
582	C₄⋊C₄×C₅₃	—	2	1	no	—
583	C₄⋊C₄×C₅₃	—	2	1	no	—
584	C₄⋊C₄×C₅₃	—	2	1	no	—
585	C₄⋊C₄×C₅₃	—	2	1	no	—
586	C₄⋊C₄×C₅₃	—	2	1	no	—
587	C₄⋊C₄×C₅₃	—	2	1	no	—
588	C₄⋊C₄×C₅₃	—	2	1	no	—
589	C₄⋊C₄×C₅₃	—	2	1	no	—
590	C₄⋊C₄×C₅₃	—	2	1	no	—
591	C₄⋊C₄×C₅₃	—	2	1	no	—
592	C₄⋊C₄×C₅₃	—	2	1	no	—
593	C₄⋊C₄×C₅₃	—	2	1	no	—
594	C₄⋊C₄×C₅₃	—	2	1	no	—
595	C₄⋊C₄×C₅₃	—	2	1	no	—
596	C₄⋊C₄×C₅₃	—	2	1	no	—
597	C₄⋊C₄×C₅₃	—	2	1	no	—
598	C₄⋊C₄×C₅₃	—	2	1	no	—
599	C₄⋊C₄×C₅₃	—	2	1	no	—
600	C₄⋊C₄×C₅₃	—	2	1	no	—
601	C₄⋊C₄×C₅₃	—	2	1	no	—
602	C₄⋊C₄×C₅₃	—	2	1	no	—
603	C₄⋊C₄×C₅₃	—	2	1	no	—
604	C₄⋊C₄×C₅₃	—	2	1	no	—
605	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
608	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
609	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
610	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
611	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
612	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
613	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
614	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
615	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
617	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
618	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
619	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
620	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
621	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
622	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
623	C₂²⋊C₄×C₅₃	—	2	1	no	—
624	C₂²⋊C₄×C₅₃	—	2	1	no	—
625	C₂²⋊C₄×C₅₃	—	2	1	no	—
626	C₂²⋊C₄×C₅₃	—	2	1	no	—
627	C₂²⋊C₄×C₅₃	—	2	1	no	—
628	C₂²⋊C₄×C₅₃	—	2	1	no	—
629	C₂²⋊C₄×C₅₃	—	2	1	no	—
630	C₂²⋊C₄×C₅₃	—	2	1	no	—
631	C₂²⋊C₄×C₅₃	—	2	1	no	—
632	C₂²⋊C₄×C₅₃	—	2	1	no	—
633	C₂²⋊C₄×C₅₃	—	2	1	no	—
634	C₂²⋊C₄×C₅₃	—	2	1	no	—
635	C₂²⋊C₄×C₅₃	—	2	1	no	—
636	C₂²⋊C₄×C₅₃	—	2	1	no	—
637	C₂²⋊C₄×C₅₃	—	2	1	no	—
638	C₂²⋊C₄×C₅₃	—	2	1	no	—
639	C₂²⋊C₄×C₅₃	—	2	1	no	—
640	C₂²⋊C₄×C₅₃	—	2	1	no	—
641	C₂²⋊C₄×C₅₃	—	2	1	no	—
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
663	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
664	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
665	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
666	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
667	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
668	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
669	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
670	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
671	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
672	C₄²×C₅₃	—	2	1	no	—
673	C₄²×C₅₃	—	2	1	no	—
674	C₄²×C₅₃	—	2	1	no	—
675	C₄²×C₅₃	—	2	1	no	—
676	C₄²×C₅₃	—	2	1	no	—
677	C₄²×C₅₃	—	2	1	no	—
678	C₄²×C₅₃	—	2	1	no	—
679	C₄²×C₅₃	—	2	1	no	—
680	C₄²×C₅₃	—	2	1	no	—
681	C₄²×C₅₃	—	2	1	no	—
682	C₄²×C₅₃	—	2	1	no	—
683	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
685	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
686	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
687	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
688	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
689	C₂³×C₅₃	—	2	1	no	—
690	C₂³×C₅₃	—	2	1	no	—
691	C₂³×C₅₃	—	2	1	no	—
692	C₂³×C₅₃	—	2	1	no	—
693	C₂³×C₅₃	—	2	1	no	—
694	C₂³×C₅₃	—	4	2	no	—
695	C₂³×C₅₃	—	4	2	no	—
696	C₂³×C₅₃	—	4	2	no	—
697	C₂³×C₅₃	—	8	1	no	—
698	C₂³×C₅₃	—	8	1	no	—
699	C₂³×C₅₃	—	8	1	no	—
700	C₂³×C₅₃	—	8	1	no	—
701	C₂³×C₅₃	—	8	1	no	—
702	C₂³×C₅₃	—	8	1	no	—
703	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
704	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
705	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
706	Q₈×C₅₃	—	2	1	no	—
707	Q₈×C₅₃	—	2	1	no	—
708	Q₈×C₅₃	—	2	1	no	—
709	Q₈×C₅₃	—	2	1	no	—
710	Q₈×C₅₃	—	2	1	no	—
711	Q₈×C₅₃	—	2	1	no	—
712	Q₈×C₅₃	—	4	1	no	—
713	Q₈×C₅₃	—	4	2	no	—
714	Q₈×C₅₃	—	8	1	no	—
715	Q₈×C₅₃	—	8	1	no	—
716	Q₈×C₅₃	—	8	1	no	—
717	D₄×C₅₃	—	2	1	no	—
718	D₄×C₅₃	—	2	1	no	—
719	D₄×C₅₃	—	2	1	no	—
720	D₄×C₅₃	—	2	1	no	—
721	D₄×C₅₃	—	2	1	no	—
722	D₄×C₅₃	—	2	1	no	—
723	D₄×C₅₃	—	2	1	no	—
724	D₄×C₅₃	—	2	1	no	—
725	D₄×C₅₃	—	4	1	no	—
726	D₄×C₅₃	—	4	1	no	—
727	D₄×C₅₃	—	4	1	no	—
728	D₄×C₅₃	—	4	2	no	—
729	D₄×C₅₃	—	4	2	no	—
730	D₄×C₅₃	—	4	2	no	—
731	D₄×C₅₃	—	4	2	no	—
732	D₄×C₅₃	—	4	2	no	—
733	D₄×C₅₃	—	4	2	no	—
734	D₄×C₅₃	—	4	2	no	—
735	D₄×C₅₃	—	8	1	no	—
736	D₄×C₅₃	—	8	1	no	—
737	D₄×C₅₃	—	8	1	no	—
738	D₄×C₅₃	—	8	1	no	—
739	D₄×C₅₃	—	8	1	no	—
740	D₄×C₅₃	—	8	1	no	—
741	D₄×C₅₃	—	8	1	no	—
742	D₄×C₅₃	C₂×#41	1	2	yes	—
743	D₄×C₅₃	C₂×#41	1	2	yes	—
744	C₂×C₄×C₅₃	—	2	1	no	—
745	C₂×C₄×C₅₃	—	2	1	no	—
746	C₂×C₄×C₅₃	—	2	1	no	—
747	C₂×C₄×C₅₃	—	2	1	no	—
748	C₂×C₄×C₅₃	—	2	1	no	—
749	C₂×C₄×C₅₃	—	2	1	no	—
750	C₂×C₄×C₅₃	—	2	1	no	—
751	C₂×C₄×C₅₃	—	2	1	no	—
752	C₂×C₄×C₅₃	—	2	1	no	—
753	C₂×C₄×C₅₃	—	2	1	no	—
754	C₂×C₄×C₅₃	—	2	1	no	—
755	C₂×C₄×C₅₃	—	2	1	no	—
756	C₂×C₄×C₅₃	—	2	1	no	—
757	C₂×C₄×C₅₃	—	2	1	no	—
758	C₂×C₄×C₅₃	—	2	1	no	—
759	C₂×C₄×C₅₃	—	2	1	no	—
760	C₂×C₄×C₅₃	—	2	1	no	—
761	C₂×C₄×C₅₃	—	4	1	no	—
762	C₂×C₄×C₅₃	—	4	1	no	—
763	C₂×C₄×C₅₃	—	4	2	no	—
764	C₂×C₄×C₅₃	—	4	2	no	—
765	C₂×C₄×C₅₃	—	4	2	no	—
766	C₂×C₄×C₅₃	—	4	2	no	—
767	C₂×C₄×C₅₃	—	8	1	no	—
768	C₂×C₄×C₅₃	—	8	1	no	—
769	C₂×C₄×C₅₃	—	8	1	no	—
770	C₂×C₄×C₅₃	—	8	1	no	—
771	C₂×C₄×C₅₃	—	8	1	no	—
772	C₂×C₄×C₅₃	—	8	1	no	—
773	C₂×C₄×C₅₃	—	8	1	no	—
774	C₂×C₄×C₅₃	—	8	1	no	—
775	C₂×C₄×C₅₃	—	8	1	no	—
776	C₂×C₄×C₅₃	—	8	1	no	—
777	C₂×C₄×C₅₃	—	8	1	no	—
778	C₂×C₄×C₅₃	—	8	1	no	—
779	C₂×C₄×C₅₃	—	8	1	no	—
780	C₂×C₄×C₅₃	—	8	1	no	—
781	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
782	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
783	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
784	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
785	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
786	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
787	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
788	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
789	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
790	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
791	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
792	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
793	C₈×C₅₃	—	2	1	no	—
794	C₈×C₅₃	—	2	1	no	—
795	C₈×C₅₃	—	2	1	no	—
796	C₈×C₅₃	—	2	1	no	—
797	C₈×C₅₃	—	2	1	no	—
798	C₈×C₅₃	—	2	1	no	—
799	C₈×C₅₃	—	2	1	no	—
800	C₈×C₅₃	C₂×#41	1	2	yes	—
801	#61529	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
802	C₂²×C₅₃	—	2	1	no	—
803	C₂²×C₅₃	—	2	1	no	—
804	C₂²×C₅₃	—	2	1	no	—
805	C₂²×C₅₃	—	2	1	no	—
806	C₂²×C₅₃	—	2	1	no	—
807	C₂²×C₅₃	—	2	1	no	—
808	C₂²×C₅₃	—	2	1	no	—
809	C₂²×C₅₃	—	2	1	no	—
810	C₂²×C₅₃	—	2	1	no	—
811	C₂²×C₅₃	—	2	2	no	—
812	C₂²×C₅₃	—	2	2	no	—
813	C₂²×C₅₃	—	4	1	no	—
814	C₂²×C₅₃	—	4	1	no	—
815	C₂²×C₅₃	—	4	1	no	—
816	C₂²×C₅₃	—	4	1	no	—
817	C₂²×C₅₃	—	4	1	no	—
818	C₂²×C₅₃	—	4	1	no	—
819	C₂²×C₅₃	—	4	1	no	—
820	C₂²×C₅₃	—	4	1	no	—
821	C₂²×C₅₃	—	4	1	no	—
822	C₂²×C₅₃	—	4	1	no	—
823	C₂²×C₅₃	—	4	1	no	—
824	C₂²×C₅₃	—	4	1	no	—
825	C₂²×C₅₃	—	4	1	no	—
826	C₂²×C₅₃	—	16	2	no	—
827	C₂²×C₅₃	—	16	2	no	—
828	C₂²×C₅₃	—	16	2	no	—
829	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
830	C₄×C₅₃	—	2	1	no	—
831	C₄×C₅₃	—	2	1	no	—
832	C₄×C₅₃	—	2	1	no	—
833	C₄×C₅₃	—	2	1	no	—
834	C₄×C₅₃	—	2	1	no	—
835	C₄×C₅₃	—	2	1	no	—
836	C₄×C₅₃	—	2	1	no	—
837	C₄×C₅₃	—	2	1	no	—
838	C₄×C₅₃	—	2	1	no	—
839	C₄×C₅₃	—	2	1	no	—
840	C₄×C₅₃	—	2	1	no	—
841	C₄×C₅₃	—	4	1	no	—
842	C₄×C₅₃	—	4	1	no	—
843	C₄×C₅₃	—	4	1	no	—
844	C₄×C₅₃	—	4	1	no	—
845	C₄×C₅₃	—	4	1	no	—
846	C₄×C₅₃	—	4	1	no	—
847	C₄×C₅₃	—	4	1	no	—
848	C₄×C₅₃	—	4	1	no	—
849	C₄×C₅₃	—	4	1	no	—
850	C₄×C₅₃	—	4	1	no	—
851	C₄×C₅₃	—	4	1	no	—
852	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
853	C₄×C₅₃	#585	1	1	yes	characteristic
854	#3521	C₂×C₅₃	1	1	yes	characteristic, complemented
855	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
856	#3401	C₂×C₅₃	1	1	yes	characteristic, complemented
857	#3384	C₂×C₅₃	1	1	yes	characteristic, complemented
858	#3370	C₂×C₅₃	1	1	yes	characteristic, complemented
859	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
860	#3349	C₂×C₅₃	1	1	yes	characteristic, complemented
861	#3347	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#3340	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#3319	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#3297	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#3280	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3267	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3264	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3180	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#3178	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#3173	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3106	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#2968	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#2948	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#2943	C₂×C₅₃	1	1	yes	characteristic, complemented
885	C₂×C₅₃	—	4	1	no	—
886	C₂×C₅₃	—	4	1	no	—
887	C₂×C₅₃	—	4	1	no	—
888	C₂×C₅₃	—	4	2	no	—
889	C₂×C₅₃	—	4	2	no	—
890	C₂×C₅₃	—	8	1	no	—
891	C₂×C₅₃	—	8	1	no	—
892	C₂×C₅₃	—	8	1	no	—
893	C₂×C₅₃	D₄×#41	1	1	yes	characteristic
894	C₂×C₅₃	#3584	1	1	yes	characteristic
895	C₂×C₅₃	#3585	1	1	yes	characteristic
896	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
897	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
898	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
899	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
900	#556	C₂²×C₅₃	1	1	yes	characteristic
901	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
902	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#555	C₂²×C₅₃	1	1	yes	characteristic
904	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#553	—	2	1	no	—
907	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
908	#552	—	2	1	no	—
909	#552	C₂²×C₅₃	1	1	yes	characteristic
910	#551	—	2	1	no	—
911	#551	—	2	1	no	—
912	#551	—	2	1	no	—
913	#551	—	2	1	no	—
914	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
915	#548	—	2	1	no	—
916	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#546	—	2	1	no	—
918	#546	C₂²×C₅₃	1	1	yes	characteristic
919	#546	C₂²×C₅₃	1	1	yes	characteristic
920	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#546	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	D₄²	C₂²×C₅₃	1	1	yes	characteristic
923	#542	C₂²×C₅₃	1	1	yes	characteristic
924	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
926	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#539	—	2	1	no	—
928	#538	—	2	1	no	—
929	#538	—	2	1	no	—
930	#538	—	2	1	no	—
931	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#529	—	2	1	no	—
933	#529	—	2	1	no	—
934	#529	C₂²×C₅₃	1	1	yes	characteristic
935	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	C₂×#126	—	2	1	no	—
937	C₂×#124	—	2	1	no	—
938	#520	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#518	C₂²×C₅₃	1	1	yes	characteristic
940	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#518	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#498	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#497	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#496	C₂²×C₅₃	1	1	yes	characteristic
949	#495	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#489	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#488	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
959	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
960	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
961	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
962	#482	C₂²×C₅₃	1	1	yes	characteristic
963	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
973	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
974	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
980	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
981	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#469	C₂²×C₅₃	1	1	yes	characteristic
983	#468	C₂²×C₅₃	1	1	yes	characteristic
984	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#465	C₂²×C₅₃	1	1	yes	characteristic
988	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#463	C₂²×C₅₃	1	1	yes	characteristic
995	#463	C₂²×C₅₃	1	1	yes	characteristic
996	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#459	C₂²×C₅₃	1	1	yes	characteristic
1004	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#450	C₂²×C₅₃	1	1	yes	characteristic
1007	#450	C₂²×C₅₃	1	1	yes	characteristic
1008	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1009	#450	C₂²×C₅₃	1	1	yes	characteristic, complemented
1010	#449	C₂²×C₅₃	1	1	yes	characteristic
1011	#449	C₂²×C₅₃	1	1	yes	characteristic
1012	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1013	#449	C₂²×C₅₃	1	1	yes	characteristic, complemented
1014	#447	C₂²×C₅₃	1	1	yes	characteristic
1015	#447	C₂²×C₅₃	1	1	yes	characteristic
1016	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1017	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1018	#442	C₂²×C₅₃	1	1	yes	characteristic
1019	#442	C₂²×C₅₃	1	1	yes	characteristic
1020	#442	C₂²×C₅₃	1	1	yes	characteristic
1021	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1022	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1025	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
1027	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1041	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1042	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1043	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#435	C₂²×C₅₃	1	1	yes	characteristic
1047	#435	C₂²×C₅₃	1	1	yes	characteristic
1048	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1049	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1050	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1051	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
1052	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1053	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1054	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
1055	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1056	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1057	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1058	#418	C₂²×C₅₃	1	1	yes	characteristic
1059	#418	C₂²×C₅₃	1	1	yes	characteristic, complemented
1060	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1061	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1062	#416	C₂²×C₅₃	1	1	yes	characteristic, complemented
1063	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic, complemented
1064	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1065	#405	C₂²×C₅₃	1	1	yes	characteristic, complemented
1066	C₂×#97	C₂²×C₅₃	1	1	yes	characteristic, complemented
1067	C₅₃	#61529	1	1	yes	characteristic, direct product factor, Sylow
1068	C₂×#41	—	2	1	no	—
1069	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂²×Q₈	—	2	1	no	—
1073	C₂²×D₄	—	2	1	no	—
1074	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1077	AGL(1,ℤ/8)	—	2	4	no	—
1078	#135	—	2	4	no	—
1079	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1081	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1082	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1083	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1084	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1085	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1086	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1087	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×D₈	—	2	4	no	—
1090	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1102	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1103	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1104	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1105	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1106	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1107	#127	C₂³×C₅₃	1	1	yes	characteristic
1108	#126	—	2	1	no	—
1109	#126	—	2	1	no	—
1110	#126	—	2	1	no	—
1111	#126	—	2	1	no	—
1112	#126	—	2	1	no	—
1113	#126	—	2	1	no	—
1114	#126	—	2	1	no	—
1115	#126	—	2	1	no	—
1116	#126	—	2	1	no	—
1117	#126	—	2	1	no	—
1118	#126	—	2	1	no	—
1119	#126	—	2	1	no	—
1120	#126	—	2	1	no	—
1121	#126	—	2	1	no	—
1122	#126	D₄×C₅₃	1	1	yes	characteristic
1123	#126	D₄×C₅₃	1	1	yes	characteristic
1124	#125	—	2	1	no	—
1125	#125	—	2	1	no	—
1126	#125	—	2	1	no	—
1127	#125	D₄×C₅₃	1	1	yes	characteristic
1128	#125	C₂³×C₅₃	1	1	yes	characteristic
1129	#125	C₂³×C₅₃	1	1	yes	characteristic
1130	#124	—	2	1	no	—
1131	#124	—	2	1	no	—
1132	#124	—	2	1	no	—
1133	#124	—	2	1	no	—
1134	#124	—	2	1	no	—
1135	#124	—	2	1	no	—
1136	#124	—	2	1	no	—
1137	#124	—	2	1	no	—
1138	#124	—	2	1	no	—
1139	#124	—	2	1	no	—
1140	#124	—	2	1	no	—
1141	#124	D₄×C₅₃	1	1	yes	characteristic
1142	#124	C₂³×C₅₃	1	1	yes	characteristic
1143	#124	C₂³×C₅₃	1	1	yes	characteristic
1144	#124	C₂³×C₅₃	1	1	yes	characteristic
1145	#124	C₂³×C₅₃	1	1	yes	characteristic
1146	#123	—	2	1	no	—
1147	#123	—	2	1	no	—
1148	#123	—	2	1	no	—
1149	#123	—	2	1	no	—
1150	#123	—	2	1	no	—
1151	#123	—	2	1	no	—
1152	#123	—	2	1	no	—
1153	#123	—	2	1	no	—
1154	#123	—	2	1	no	—
1155	#123	—	2	1	no	—
1156	#123	—	2	1	no	—
1157	#123	—	2	1	no	—
1158	#123	—	2	1	no	—
1159	#123	—	2	1	no	—
1160	#123	D₄×C₅₃	1	1	yes	characteristic
1161	#123	D₄×C₅₃	1	1	yes	characteristic
1162	C₂²⋊Q₈	—	2	1	no	—
1163	C₂²⋊Q₈	—	2	1	no	—
1164	C₂²⋊Q₈	—	2	1	no	—
1165	C₂²⋊Q₈	—	2	1	no	—
1166	C₂²⋊Q₈	—	2	1	no	—
1167	C₂²⋊Q₈	—	2	1	no	—
1168	C₂²⋊Q₈	—	2	1	no	—
1169	C₂²⋊Q₈	—	2	1	no	—
1170	C₂²⋊Q₈	—	2	1	no	—
1171	C₂²⋊Q₈	—	2	1	no	—
1172	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1173	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1174	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1175	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1176	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1177	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1178	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1179	#121	—	2	1	no	—
1180	#121	—	2	1	no	—
1181	#121	—	2	1	no	—
1182	#121	—	2	1	no	—
1183	#121	—	2	1	no	—
1184	#121	—	2	1	no	—
1185	#121	—	2	1	no	—
1186	#121	—	2	1	no	—
1187	#121	—	2	1	no	—
1188	#121	—	2	1	no	—
1189	#121	D₄×C₅₃	1	1	yes	characteristic
1190	#121	C₂³×C₅₃	1	1	yes	characteristic
1191	#121	C₂³×C₅₃	1	1	yes	characteristic
1192	#121	C₂³×C₅₃	1	1	yes	characteristic
1193	#121	C₂³×C₅₃	1	1	yes	characteristic
1194	#121	C₂³×C₅₃	1	1	yes	characteristic
1195	#121	C₂³×C₅₃	1	1	yes	characteristic
1196	#120	—	2	1	no	—
1197	#120	—	2	1	no	—
1198	#120	—	2	1	no	—
1199	#120	—	2	1	no	—
1200	#120	—	2	1	no	—
1201	#120	—	2	1	no	—
1202	C₄×Q₈	—	2	1	no	—
1203	C₄×Q₈	—	2	1	no	—
1204	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1205	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1206	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1207	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1208	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1209	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1210	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1211	C₄×D₄	—	2	1	no	—
1212	C₄×D₄	—	2	1	no	—
1213	C₄×D₄	—	2	1	no	—
1214	C₄×D₄	—	2	1	no	—
1215	C₄×D₄	—	2	1	no	—
1216	C₄×D₄	—	2	1	no	—
1217	C₄×D₄	—	2	1	no	—
1218	C₄×D₄	—	2	1	no	—
1219	C₄×D₄	—	2	1	no	—
1220	C₄×D₄	—	2	1	no	—
1221	C₄×D₄	—	2	1	no	—
1222	C₄×D₄	—	2	1	no	—
1223	C₄×D₄	—	2	1	no	—
1224	C₄×D₄	—	2	1	no	—
1225	C₄×D₄	—	2	1	no	—
1226	C₄×D₄	—	2	1	no	—
1227	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1228	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1229	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1230	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1231	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1232	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1233	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1234	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1235	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1236	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1237	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1240	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1243	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1244	#117	—	2	1	no	—
1245	#117	—	2	1	no	—
1246	#117	—	2	1	no	—
1247	#117	—	2	1	no	—
1248	#117	—	2	1	no	—
1249	#117	—	2	1	no	—
1250	#117	—	2	1	no	—
1251	#117	—	2	1	no	—
1252	#117	C₂³×C₅₃	1	1	yes	characteristic
1253	#117	C₂³×C₅₃	1	1	yes	characteristic
1254	#117	C₂³×C₅₃	1	1	yes	characteristic
1255	#117	C₂³×C₅₃	1	1	yes	characteristic
1256	#117	C₂³×C₅₃	1	1	yes	characteristic
1257	#117	C₂³×C₅₃	1	1	yes	characteristic
1258	#117	C₂³×C₅₃	1	1	yes	characteristic
1259	C₂×C₄⋊C₄	—	2	1	no	—
1260	C₂×C₄⋊C₄	—	2	1	no	—
1261	C₂×C₄⋊C₄	—	2	1	no	—
1262	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1263	C₂×C₂²⋊C₄	—	2	1	no	—
1264	C₂×C₂²⋊C₄	—	2	1	no	—
1265	C₂×C₂²⋊C₄	—	2	1	no	—
1266	C₂×C₂²⋊C₄	—	2	1	no	—
1267	C₂×C₂²⋊C₄	—	2	1	no	—
1268	C₂×C₂²⋊C₄	—	2	1	no	—
1269	C₂×C₂²⋊C₄	—	2	1	no	—
1270	C₂×C₂²⋊C₄	—	2	1	no	—
1271	C₂×C₂²⋊C₄	—	2	1	no	—
1272	C₂×C₂²⋊C₄	—	2	1	no	—
1273	C₂×C₄²	—	2	1	no	—
1274	C₂×C₄²	—	2	1	no	—
1275	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1276	#107	C₂³×C₅₃	1	1	yes	characteristic
1277	#107	C₂³×C₅₃	1	1	yes	characteristic
1278	#107	C₂³×C₅₃	1	1	yes	characteristic
1279	#107	C₂³×C₅₃	1	1	yes	characteristic
1280	#107	C₂³×C₅₃	1	1	yes	characteristic
1281	#107	C₂³×C₅₃	1	1	yes	characteristic
1282	#107	C₂³×C₅₃	1	1	yes	characteristic
1283	#107	C₂³×C₅₃	1	1	yes	characteristic
1284	#106	C₂³×C₅₃	1	1	yes	characteristic
1285	#106	C₂³×C₅₃	1	1	yes	characteristic
1286	#106	C₂³×C₅₃	1	1	yes	characteristic
1287	#106	C₂³×C₅₃	1	1	yes	characteristic
1288	#106	C₂³×C₅₃	1	1	yes	characteristic
1289	#106	C₂³×C₅₃	1	1	yes	characteristic
1290	#106	C₂³×C₅₃	1	1	yes	characteristic
1291	#106	C₂³×C₅₃	1	1	yes	characteristic
1292	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1293	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1294	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1295	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1296	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1297	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1298	#103	C₂³×C₅₃	1	1	yes	characteristic
1299	#103	C₂³×C₅₃	1	1	yes	characteristic
1300	#103	C₂³×C₅₃	1	1	yes	characteristic
1301	#103	C₂³×C₅₃	1	1	yes	characteristic
1302	#103	C₂³×C₅₃	1	1	yes	characteristic
1303	#103	C₂³×C₅₃	1	1	yes	characteristic
1304	#103	C₂³×C₅₃	1	1	yes	characteristic
1305	#103	C₂³×C₅₃	1	1	yes	characteristic
1306	#103	C₂³×C₅₃	1	1	yes	characteristic
1307	#103	C₂³×C₅₃	1	1	yes	characteristic
1308	#103	C₂³×C₅₃	1	1	yes	characteristic
1309	#103	C₂³×C₅₃	1	1	yes	characteristic
1310	#102	C₂³×C₅₃	1	1	yes	characteristic
1311	#102	C₂³×C₅₃	1	1	yes	characteristic
1312	#102	C₂³×C₅₃	1	1	yes	characteristic
1313	#102	C₂³×C₅₃	1	1	yes	characteristic
1314	#102	C₂³×C₅₃	1	1	yes	characteristic
1315	#102	C₂³×C₅₃	1	1	yes	characteristic
1316	#102	C₂³×C₅₃	1	1	yes	characteristic
1317	#102	C₂³×C₅₃	1	1	yes	characteristic
1318	#102	C₂³×C₅₃	1	1	yes	characteristic
1319	#102	C₂³×C₅₃	1	1	yes	characteristic
1320	#102	C₂³×C₅₃	1	1	yes	characteristic
1321	#102	C₂³×C₅₃	1	1	yes	characteristic
1322	#102	C₂³×C₅₃	1	1	yes	characteristic
1323	#102	C₂³×C₅₃	1	1	yes	characteristic
1324	#102	C₂³×C₅₃	1	1	yes	characteristic
1325	#102	C₂³×C₅₃	1	1	yes	characteristic
1326	#102	C₂³×C₅₃	1	1	yes	characteristic
1327	#102	C₂³×C₅₃	1	1	yes	characteristic
1328	#102	C₂³×C₅₃	1	1	yes	characteristic
1329	#102	C₂³×C₅₃	1	1	yes	characteristic
1330	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1331	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1332	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1333	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1334	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1335	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1336	#97	C₂³×C₅₃	1	1	yes	characteristic
1337	#97	C₂³×C₅₃	1	1	yes	characteristic
1338	#97	C₂³×C₅₃	1	1	yes	characteristic
1339	#97	C₂³×C₅₃	1	1	yes	characteristic
1340	#97	C₂³×C₅₃	1	1	yes	characteristic
1341	#97	C₂³×C₅₃	1	1	yes	characteristic
1342	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1343	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1344	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1345	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1346	C₂⁴	—	2	1	no	—
1347	C₂⁴	—	2	1	no	—
1348	C₂⁴	—	2	1	no	—
1349	#41	—	2	2	no	—
1350	#41	—	2	2	no	—
1351	#41	—	2	2	no	—
1352	#41	—	4	1	no	—
1353	#41	—	4	1	no	—
1354	#41	—	4	1	no	—
1355	#41	—	8	2	no	—
1356	C₂×Q₈	—	2	1	no	—
1357	C₂×Q₈	—	2	1	no	—
1358	C₂×Q₈	—	2	1	no	—
1359	C₂×Q₈	—	2	1	no	—
1360	C₂×Q₈	—	8	2	no	—
1361	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1362	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1363	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1364	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1365	C₂×D₄	—	2	2	no	—
1366	C₂×D₄	—	2	2	no	—
1367	C₂×D₄	—	2	2	no	—
1368	C₂×D₄	—	2	1	no	—
1369	C₂×D₄	—	2	1	no	—
1370	C₂×D₄	—	2	1	no	—
1371	C₂×D₄	—	2	1	no	—
1372	C₂×D₄	—	2	1	no	—
1373	C₂×D₄	—	2	1	no	—
1374	C₂×D₄	—	2	1	no	—
1375	C₂×D₄	—	2	1	no	—
1376	C₂×D₄	—	2	1	no	—
1377	C₂×D₄	—	2	1	no	—
1378	C₂×D₄	—	2	1	no	—
1379	C₂×D₄	—	2	1	no	—
1380	C₂×D₄	—	2	1	no	—
1381	C₂×D₄	—	2	1	no	—
1382	C₂×D₄	—	4	1	no	—
1383	C₂×D₄	—	4	1	no	—
1384	C₂×D₄	—	4	1	no	—
1385	C₂×D₄	—	8	2	no	—
1386	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1387	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1388	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1389	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1390	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1391	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1392	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1393	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1394	C₂²×C₄	—	2	1	no	—
1395	C₂²×C₄	—	2	1	no	—
1396	C₂²×C₄	—	2	1	no	—
1397	C₂²×C₄	—	2	1	no	—
1398	C₂²×C₄	—	2	1	no	—
1399	C₂²×C₄	—	2	1	no	—
1400	C₂²×C₄	—	2	1	no	—
1401	C₂²×C₄	—	2	1	no	—
1402	C₂²×C₄	—	2	1	no	—
1403	C₂²×C₄	—	2	1	no	—
1404	C₂²×C₄	—	2	1	no	—
1405	C₂²×C₄	—	2	1	no	—
1406	C₂²×C₄	—	2	1	no	—
1407	C₂²×C₄	—	2	1	no	—
1408	C₂²×C₄	—	2	1	no	—
1409	C₂²×C₄	—	2	1	no	—
1410	C₂²×C₄	—	2	1	no	—
1411	C₂²×C₄	—	2	1	no	—
1412	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1413	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1414	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1415	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1416	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1417	Q₁₆	—	2	2	no	—
1418	Q₁₆	—	4	1	no	—
1419	SD₁₆	—	2	2	no	—
1420	SD₁₆	—	2	2	no	—
1421	SD₁₆	—	2	2	no	—
1422	SD₁₆	—	2	2	no	—
1423	SD₁₆	—	4	1	no	—
1424	SD₁₆	—	4	1	no	—
1425	SD₁₆	—	4	1	no	—
1426	SD₁₆	—	4	1	no	—
1427	D₈	—	2	2	no	—
1428	D₈	—	2	2	no	—
1429	D₈	—	2	2	no	—
1430	D₈	—	2	2	no	—
1431	D₈	—	4	1	no	—
1432	D₈	#41×C₅₃	1	4	yes	complemented
1433	M₁₆	—	2	2	no	—
1434	M₁₆	—	4	1	no	—
1435	C₂×C₈	—	2	2	no	—
1436	C₂×C₈	—	2	2	no	—
1437	C₂×C₈	—	4	1	no	—
1438	C₂×C₈	—	4	1	no	—
1439	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1440	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1441	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1442	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1443	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1444	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1445	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1446	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1447	C₄⋊C₄	—	2	1	no	—
1448	C₄⋊C₄	—	2	1	no	—
1449	C₄⋊C₄	—	2	1	no	—
1450	C₄⋊C₄	—	2	1	no	—
1451	C₄⋊C₄	—	2	1	no	—
1452	C₄⋊C₄	—	2	1	no	—
1453	C₄⋊C₄	—	2	1	no	—
1454	C₄⋊C₄	—	2	1	no	—
1455	C₄⋊C₄	—	2	1	no	—
1456	C₄⋊C₄	—	2	1	no	—
1457	C₄⋊C₄	—	2	1	no	—
1458	C₄⋊C₄	—	2	1	no	—
1459	C₄⋊C₄	—	2	1	no	—
1460	C₄⋊C₄	—	2	1	no	—
1461	C₄⋊C₄	—	2	1	no	—
1462	C₄⋊C₄	—	2	1	no	—
1463	C₄⋊C₄	—	2	1	no	—
1464	C₄⋊C₄	—	2	1	no	—
1465	C₄⋊C₄	—	2	1	no	—
1466	C₄⋊C₄	—	2	1	no	—
1467	C₄⋊C₄	—	2	1	no	—
1468	C₄⋊C₄	—	2	1	no	—
1469	C₄⋊C₄	—	2	1	no	—
1470	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1471	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1472	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1473	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1474	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1475	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1476	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1477	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1478	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1479	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1480	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1481	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1482	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1483	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1484	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1485	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1486	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1487	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	—	2	1	no	—
1496	C₂²⋊C₄	—	2	1	no	—
1497	C₂²⋊C₄	—	2	1	no	—
1498	C₂²⋊C₄	—	2	1	no	—
1499	C₂²⋊C₄	—	2	1	no	—
1500	C₂²⋊C₄	—	2	1	no	—
1501	C₂²⋊C₄	—	2	1	no	—
1502	C₂²⋊C₄	—	2	1	no	—
1503	C₂²⋊C₄	—	2	1	no	—
1504	C₂²⋊C₄	—	2	1	no	—
1505	C₂²⋊C₄	—	2	1	no	—
1506	C₂²⋊C₄	—	2	1	no	—
1507	C₂²⋊C₄	—	2	1	no	—
1508	C₂²⋊C₄	—	2	1	no	—
1509	C₂²⋊C₄	—	2	1	no	—
1510	C₂²⋊C₄	—	2	1	no	—
1511	C₂²⋊C₄	—	2	1	no	—
1512	C₂²⋊C₄	—	2	1	no	—
1513	C₂²⋊C₄	—	2	1	no	—
1514	C₂²⋊C₄	—	2	1	no	—
1515	C₂²⋊C₄	—	2	1	no	—
1516	C₂²⋊C₄	—	2	1	no	—
1517	C₂²⋊C₄	—	2	1	no	—
1518	C₂²⋊C₄	—	2	1	no	—
1519	C₂²⋊C₄	—	2	1	no	—
1520	C₂²⋊C₄	—	2	1	no	—
1521	C₂²⋊C₄	—	2	1	no	—
1522	C₂²⋊C₄	—	2	1	no	—
1523	C₂²⋊C₄	—	2	1	no	—
1524	C₂²⋊C₄	—	2	1	no	—
1525	C₂²⋊C₄	—	2	1	no	—
1526	C₂²⋊C₄	—	2	1	no	—
1527	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1528	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1529	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1530	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1531	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1532	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1533	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1534	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1535	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1536	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1537	C₄²	—	2	1	no	—
1538	C₄²	—	2	1	no	—
1539	C₄²	—	2	1	no	—
1540	C₄²	—	2	1	no	—
1541	C₄²	—	2	1	no	—
1542	C₄²	—	2	1	no	—
1543	C₄²	—	2	1	no	—
1544	C₄²	—	2	1	no	—
1545	C₄²	—	2	1	no	—
1546	C₄²	—	2	1	no	—
1547	C₄²	—	2	1	no	—
1548	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1549	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1550	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1551	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1552	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1553	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1554	C₂³	—	2	1	no	—
1555	C₂³	—	2	1	no	—
1556	C₂³	—	2	1	no	—
1557	C₂³	—	2	1	no	—
1558	C₂³	—	2	1	no	—
1559	C₂³	—	4	2	no	—
1560	C₂³	—	4	2	no	—
1561	C₂³	—	4	2	no	—
1562	C₂³	—	8	1	no	—
1563	C₂³	—	8	1	no	—
1564	C₂³	—	8	1	no	—
1565	C₂³	—	8	1	no	—
1566	C₂³	—	8	1	no	—
1567	C₂³	—	8	1	no	—
1568	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1569	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1570	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1571	Q₈	—	2	1	no	—
1572	Q₈	—	2	1	no	—
1573	Q₈	—	2	1	no	—
1574	Q₈	—	2	1	no	—
1575	Q₈	—	2	1	no	—
1576	Q₈	—	2	1	no	—
1577	Q₈	—	4	1	no	—
1578	Q₈	—	4	2	no	—
1579	Q₈	—	8	1	no	—
1580	Q₈	—	8	1	no	—
1581	Q₈	—	8	1	no	—
1582	D₄	—	2	1	no	—
1583	D₄	—	2	1	no	—
1584	D₄	—	2	1	no	—
1585	D₄	—	2	1	no	—
1586	D₄	—	2	1	no	—
1587	D₄	—	2	1	no	—
1588	D₄	—	2	1	no	—
1589	D₄	—	2	1	no	—
1590	D₄	—	4	1	no	—
1591	D₄	—	4	1	no	—
1592	D₄	—	4	1	no	—
1593	D₄	—	4	2	no	—
1594	D₄	—	4	2	no	—
1595	D₄	—	4	2	no	—
1596	D₄	—	4	2	no	—
1597	D₄	—	4	2	no	—
1598	D₄	—	4	2	no	—
1599	D₄	—	4	2	no	—
1600	D₄	—	8	1	no	—
1601	D₄	—	8	1	no	—
1602	D₄	—	8	1	no	—
1603	D₄	—	8	1	no	—
1604	D₄	—	8	1	no	—
1605	D₄	—	8	1	no	—
1606	D₄	—	8	1	no	—
1607	D₄	C₂×#41×C₅₃	1	2	yes	—
1608	D₄	C₂×#41×C₅₃	1	2	yes	—
1609	C₂×C₄	—	2	1	no	—
1610	C₂×C₄	—	2	1	no	—
1611	C₂×C₄	—	2	1	no	—
1612	C₂×C₄	—	2	1	no	—
1613	C₂×C₄	—	2	1	no	—
1614	C₂×C₄	—	2	1	no	—
1615	C₂×C₄	—	2	1	no	—
1616	C₂×C₄	—	2	1	no	—
1617	C₂×C₄	—	2	1	no	—
1618	C₂×C₄	—	2	1	no	—
1619	C₂×C₄	—	2	1	no	—
1620	C₂×C₄	—	2	1	no	—
1621	C₂×C₄	—	2	1	no	—
1622	C₂×C₄	—	2	1	no	—
1623	C₂×C₄	—	2	1	no	—
1624	C₂×C₄	—	2	1	no	—
1625	C₂×C₄	—	2	1	no	—
1626	C₂×C₄	—	4	1	no	—
1627	C₂×C₄	—	4	1	no	—
1628	C₂×C₄	—	4	2	no	—
1629	C₂×C₄	—	4	2	no	—
1630	C₂×C₄	—	4	2	no	—
1631	C₂×C₄	—	4	2	no	—
1632	C₂×C₄	—	8	1	no	—
1633	C₂×C₄	—	8	1	no	—
1634	C₂×C₄	—	8	1	no	—
1635	C₂×C₄	—	8	1	no	—
1636	C₂×C₄	—	8	1	no	—
1637	C₂×C₄	—	8	1	no	—
1638	C₂×C₄	—	8	1	no	—
1639	C₂×C₄	—	8	1	no	—
1640	C₂×C₄	—	8	1	no	—
1641	C₂×C₄	—	8	1	no	—
1642	C₂×C₄	—	8	1	no	—
1643	C₂×C₄	—	8	1	no	—
1644	C₂×C₄	—	8	1	no	—
1645	C₂×C₄	—	8	1	no	—
1646	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1647	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1648	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1649	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1650	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1651	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1652	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1653	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1654	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1655	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1656	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1657	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1658	C₈	—	2	1	no	—
1659	C₈	—	2	1	no	—
1660	C₈	—	2	1	no	—
1661	C₈	—	2	1	no	—
1662	C₈	—	2	1	no	—
1663	C₈	—	2	1	no	—
1664	C₈	—	2	1	no	—
1665	C₈	C₂×#41×C₅₃	1	2	yes	—
1666	C₂²	—	2	1	no	—
1667	C₂²	—	2	1	no	—
1668	C₂²	—	2	1	no	—
1669	C₂²	—	2	2	no	—
1670	C₂²	—	2	2	no	—
1671	C₂²	—	2	1	no	—
1672	C₂²	—	2	1	no	—
1673	C₂²	—	2	1	no	—
1674	C₂²	—	2	1	no	—
1675	C₂²	—	2	1	no	—
1676	C₂²	—	2	1	no	—
1677	C₂²	—	4	1	no	—
1678	C₂²	—	4	1	no	—
1679	C₂²	—	4	1	no	—
1680	C₂²	—	4	1	no	—
1681	C₂²	—	4	1	no	—
1682	C₂²	—	4	1	no	—
1683	C₂²	—	4	1	no	—
1684	C₂²	—	4	1	no	—
1685	C₂²	—	4	1	no	—
1686	C₂²	—	4	1	no	—
1687	C₂²	—	4	1	no	—
1688	C₂²	—	4	1	no	—
1689	C₂²	—	4	1	no	—
1690	C₂²	—	16	2	no	—
1691	C₂²	—	16	2	no	—
1692	C₂²	—	16	2	no	—
1693	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1694	C₄	—	2	1	no	—
1695	C₄	—	2	1	no	—
1696	C₄	—	2	1	no	—
1697	C₄	—	2	1	no	—
1698	C₄	—	2	1	no	—
1699	C₄	—	2	1	no	—
1700	C₄	—	2	1	no	—
1701	C₄	—	2	1	no	—
1702	C₄	—	2	1	no	—
1703	C₄	—	2	1	no	—
1704	C₄	—	2	1	no	—
1705	C₄	—	4	1	no	—
1706	C₄	—	4	1	no	—
1707	C₄	—	4	1	no	—
1708	C₄	—	4	1	no	—
1709	C₄	—	4	1	no	—
1710	C₄	—	4	1	no	—
1711	C₄	—	4	1	no	—
1712	C₄	—	4	1	no	—
1713	C₄	—	4	1	no	—
1714	C₄	—	4	1	no	—
1715	C₄	—	4	1	no	—
1716	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1717	C₄	C₅₃×#585	1	1	yes	characteristic
1718	C₂	—	4	1	no	—
1719	C₂	—	4	1	no	—
1720	C₂	—	4	1	no	—
1721	C₂	—	4	2	no	—
1722	C₂	—	4	2	no	—
1723	C₂	—	8	1	no	—
1724	C₂	—	8	1	no	—
1725	C₂	—	8	1	no	—
1726	C₂	D₄×#41×C₅₃	1	1	yes	characteristic
1727	C₂	C₅₃×#3584	1	1	yes	characteristic
1728	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×#3521	C₂	semidirect
2. C₅₃×#3514	C₂	semidirect
3. C₅₃×#3401	C₂	semidirect
4. C₅₃×#3384	C₂	semidirect
5. C₅₃×#3370	C₂	semidirect
6. C₅₃×#3367	C₂	semidirect
7. C₅₃×#3349	C₂	semidirect
8. C₅₃×#3347	C₂	semidirect
9. C₅₃×#3340	C₂	semidirect
10. C₅₃×#3319	C₂	semidirect
11. C₅₃×#3311	C₂	semidirect
12. C₅₃×#3311	C₂	semidirect
13. C₅₃×#3310	C₂	semidirect
14. C₅₃×#3303	C₂	semidirect
15. C₅₃×#3297	C₂	semidirect
16. C₅₃×#3280	C₂	semidirect
17. C₅₃×#3267	C₂	semidirect
18. C₅₃×#3264	C₂	semidirect
19. C₅₃×#3180	C₂	semidirect
20. C₅₃×#3178	C₂	semidirect
21. C₅₃×#3173	C₂	semidirect
22. C₅₃×#3124	C₂	semidirect
23. C₅₃×#3123	C₂	semidirect
24. C₅₃×#3118	C₂	semidirect
25. C₅₃×#3118	C₂	semidirect
26. C₅₃×#3106	C₂	semidirect
27. C₅₃×#3102	C₂	semidirect
28. C₅₃×#2968	C₂	semidirect
29. C₅₃×#2948	C₂	semidirect
30. C₅₃×#2946	C₂	semidirect
31. C₅₃×#2943	C₂	semidirect
35. C₅₃×#559	C₂²	semidirect
37. C₅₃×#556	C₂²	semidirect
38. C₅₃×#556	C₂²	semidirect
40. C₅₃×#555	C₂²	semidirect
41. C₅₃×#554	C₂²	semidirect
43. C₅₃×#553	C₂²	semidirect
50. D₄×Q₈×C₅₃	C₂²	semidirect
52. C₅₃×#547	C₂²	semidirect
56. C₅₃×#546	C₂²	semidirect
57. C₅₃×#546	C₂²	semidirect
60. C₅₃×#542	C₂²	semidirect
61. C₅₃×#542	C₂²	semidirect
62. C₅₃×#541	C₂²	semidirect
67. C₅₃×#532	C₂²	semidirect
71. C₅₃×#529	C₂²	semidirect
74. C₅₃×#520	C₂²	semidirect
76. C₅₃×#518	C₂²	semidirect
77. C₅₃×#518	C₂²	semidirect
78. C₄×#41×C₅₃	C₂²	semidirect
79. C₄×#41×C₅₃	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#501	C₂²	semidirect
82. C₅₃×#498	C₂²	semidirect
83. C₅₃×#497	C₂²	semidirect
85. C₅₃×#495	C₂²	semidirect
86. C₅₃×#490	C₂²	semidirect
87. C₅₃×#489	C₂²	semidirect
88. C₅₃×#489	C₂²	semidirect
89. C₅₃×#489	C₂²	semidirect
90. C₅₃×#488	C₂²	semidirect
91. C₅₃×#487	C₂²	semidirect
92. C₅₃×#485	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#484	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#482	C₂²	semidirect
102. C₅₃×#482	C₂²	semidirect
103. C₅₃×#480	C₂²	semidirect
104. C₅₃×#479	C₂²	semidirect
105. C₅₃×#478	C₂²	semidirect
106. C₅₃×#478	C₂²	semidirect
107. C₅₃×#478	C₂²	semidirect
108. C₅₃×#477	C₂²	semidirect
109. C₅₃×#477	C₂²	semidirect
110. C₅₃×#476	C₂²	semidirect
111. C₅₃×#476	C₂²	semidirect
112. C₅₃×#476	C₂²	semidirect
113. C₅₃×#474	C₂²	semidirect
114. C₅₃×#474	C₂²	semidirect
115. C₅₃×#474	C₂²	semidirect
116. C₅₃×#470	C₂²	semidirect
117. C₅₃×#470	C₂²	semidirect
120. C₅₃×#467	C₂²	semidirect
121. C₅₃×#466	C₂²	semidirect
122. C₅₃×#466	C₂²	semidirect
124. C₅₃×#465	C₂²	semidirect
125. C₅₃×#465	C₂²	semidirect
126. C₅₃×#465	C₂²	semidirect
127. C₅₃×#465	C₂²	semidirect
128. C₅₃×#464	C₂²	semidirect
129. C₅₃×#464	C₂²	semidirect
132. C₅₃×#463	C₂²	semidirect
133. C₅₃×#463	C₂²	semidirect
134. C₅₃×#463	C₂²	semidirect
135. C₅₃×#463	C₂²	semidirect
136. C₅₃×#461	C₂²	semidirect
137. C₅₃×#461	C₂²	semidirect
138. C₅₃×#460	C₂²	semidirect
140. C₅₃×#452	C₂²	semidirect
141. C₅₃×#452	C₂²	semidirect
144. C₅₃×#450	C₂²	semidirect
145. C₅₃×#450	C₂²	semidirect
148. C₅₃×#449	C₂²	semidirect
149. C₅₃×#449	C₂²	semidirect
152. C₅₃×#446	C₂²	semidirect
153. C₅₃×#446	C₂²	semidirect
157. C₅₃×#442	C₂²	semidirect
158. C₅₃×#442	C₂²	semidirect
159. C₅₃×#442	C₂²	semidirect
160. C₅₃×#442	C₂²	semidirect
161. C₅₃×#441	C₂²	semidirect
162. C₅₃×#441	C₂²	semidirect
163. C₅₃×#440	C₂²	semidirect
164. C₅₃×#440	C₂²	semidirect
165. C₅₃×#440	C₂²	semidirect
166. C₅₃×#440	C₂²	semidirect
167. C₅₃×#440	C₂²	semidirect
168. C₅₃×#440	C₂²	semidirect
169. C₅₃×#440	C₂²	semidirect
170. C₄×Q₁₆×C₅₃	C₂²	semidirect
171. C₄×SD₁₆×C₅₃	C₂²	semidirect
172. C₄×SD₁₆×C₅₃	C₂²	semidirect
173. C₄×SD₁₆×C₅₃	C₂²	semidirect
174. C₄×SD₁₆×C₅₃	C₂²	semidirect
175. C₄×SD₁₆×C₅₃	C₂²	semidirect
179. C₄×D₈×C₅₃	C₂²	semidirect
180. C₄×D₈×C₅₃	C₂²	semidirect
181. C₄×D₈×C₅₃	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#435	C₂²	semidirect
186. C₈×D₄×C₅₃	C₂²	semidirect
187. C₈×D₄×C₅₃	C₂²	semidirect
188. C₅₃×#433	C₂²	semidirect
189. C₅₃×#433	C₂²	semidirect
190. C₅₃×#431	C₂²	semidirect
191. C₅₃×#428	C₂²	semidirect
192. C₅₃×#427	C₂²	semidirect
193. C₅₃×#427	C₂²	semidirect
195. C₅₃×#418	C₂²	semidirect
196. C₅₃×#416	C₂²	semidirect
197. C₅₃×#416	C₂²	semidirect
198. C₅₃×#416	C₂²	semidirect
199. C₂×#102×C₅₃	C₂²	semidirect
200. C₅₃×#405	C₂²	semidirect
201. C₅₃×#405	C₂²	semidirect
202. C₂×#97×C₅₃	C₂²	semidirect
567. D₈×C₅₃	#41	semidirect
801. #61529	C₅₃	direct (N × H)
854. #3521	C₂×C₅₃	semidirect
855. #3514	C₂×C₅₃	semidirect
856. #3401	C₂×C₅₃	semidirect
857. #3384	C₂×C₅₃	semidirect
858. #3370	C₂×C₅₃	semidirect
859. #3367	C₂×C₅₃	semidirect
860. #3349	C₂×C₅₃	semidirect
861. #3347	C₂×C₅₃	semidirect
862. #3340	C₂×C₅₃	semidirect
863. #3319	C₂×C₅₃	semidirect
864. #3311	C₂×C₅₃	semidirect
865. #3311	C₂×C₅₃	semidirect
866. #3310	C₂×C₅₃	semidirect
867. #3303	C₂×C₅₃	semidirect
868. #3297	C₂×C₅₃	semidirect
869. #3280	C₂×C₅₃	semidirect
870. #3267	C₂×C₅₃	semidirect
871. #3264	C₂×C₅₃	semidirect
872. #3180	C₂×C₅₃	semidirect
873. #3178	C₂×C₅₃	semidirect
874. #3173	C₂×C₅₃	semidirect
875. #3124	C₂×C₅₃	semidirect
876. #3123	C₂×C₅₃	semidirect
877. #3118	C₂×C₅₃	semidirect
878. #3118	C₂×C₅₃	semidirect
879. #3106	C₂×C₅₃	semidirect
880. #3102	C₂×C₅₃	semidirect
881. #2968	C₂×C₅₃	semidirect
882. #2948	C₂×C₅₃	semidirect
883. #2946	C₂×C₅₃	semidirect
884. #2943	C₂×C₅₃	semidirect
899. #559	C₂²×C₅₃	semidirect
901. #556	C₂²×C₅₃	semidirect
902. #556	C₂²×C₅₃	semidirect
904. #555	C₂²×C₅₃	semidirect
905. #554	C₂²×C₅₃	semidirect
907. #553	C₂²×C₅₃	semidirect
914. D₄×Q₈	C₂²×C₅₃	semidirect
916. #547	C₂²×C₅₃	semidirect
920. #546	C₂²×C₅₃	semidirect
921. #546	C₂²×C₅₃	semidirect
924. #542	C₂²×C₅₃	semidirect
925. #542	C₂²×C₅₃	semidirect
926. #541	C₂²×C₅₃	semidirect
931. #532	C₂²×C₅₃	semidirect
935. #529	C₂²×C₅₃	semidirect
938. #520	C₂²×C₅₃	semidirect
940. #518	C₂²×C₅₃	semidirect
941. #518	C₂²×C₅₃	semidirect
942. C₄×#41	C₂²×C₅₃	semidirect
943. C₄×#41	C₂²×C₅₃	semidirect
944. #501	C₂²×C₅₃	semidirect
945. #501	C₂²×C₅₃	semidirect
946. #498	C₂²×C₅₃	semidirect
947. #497	C₂²×C₅₃	semidirect
949. #495	C₂²×C₅₃	semidirect
950. #490	C₂²×C₅₃	semidirect
951. #489	C₂²×C₅₃	semidirect
952. #489	C₂²×C₅₃	semidirect
953. #489	C₂²×C₅₃	semidirect
954. #488	C₂²×C₅₃	semidirect
955. #487	C₂²×C₅₃	semidirect
956. #485	C₂²×C₅₃	semidirect
957. #485	C₂²×C₅₃	semidirect
958. #485	C₂²×C₅₃	semidirect
959. #485	C₂²×C₅₃	semidirect
960. #485	C₂²×C₅₃	semidirect
961. #484	C₂²×C₅₃	semidirect
963. #482	C₂²×C₅₃	semidirect
964. #482	C₂²×C₅₃	semidirect
965. #482	C₂²×C₅₃	semidirect
966. #482	C₂²×C₅₃	semidirect
967. #480	C₂²×C₅₃	semidirect
968. #479	C₂²×C₅₃	semidirect
969. #478	C₂²×C₅₃	semidirect
970. #478	C₂²×C₅₃	semidirect
971. #478	C₂²×C₅₃	semidirect
972. #477	C₂²×C₅₃	semidirect
973. #477	C₂²×C₅₃	semidirect
974. #476	C₂²×C₅₃	semidirect
975. #476	C₂²×C₅₃	semidirect
976. #476	C₂²×C₅₃	semidirect
977. #474	C₂²×C₅₃	semidirect
978. #474	C₂²×C₅₃	semidirect
979. #474	C₂²×C₅₃	semidirect
980. #470	C₂²×C₅₃	semidirect
981. #470	C₂²×C₅₃	semidirect
984. #467	C₂²×C₅₃	semidirect
985. #466	C₂²×C₅₃	semidirect
986. #466	C₂²×C₅₃	semidirect
988. #465	C₂²×C₅₃	semidirect
989. #465	C₂²×C₅₃	semidirect
990. #465	C₂²×C₅₃	semidirect
991. #465	C₂²×C₅₃	semidirect
992. #464	C₂²×C₅₃	semidirect
993. #464	C₂²×C₅₃	semidirect
996. #463	C₂²×C₅₃	semidirect
997. #463	C₂²×C₅₃	semidirect
998. #463	C₂²×C₅₃	semidirect
999. #463	C₂²×C₅₃	semidirect
1000. #461	C₂²×C₅₃	semidirect
1001. #461	C₂²×C₅₃	semidirect
1002. #460	C₂²×C₅₃	semidirect
1004. #452	C₂²×C₅₃	semidirect
1005. #452	C₂²×C₅₃	semidirect
1008. #450	C₂²×C₅₃	semidirect
1009. #450	C₂²×C₅₃	semidirect
1012. #449	C₂²×C₅₃	semidirect
1013. #449	C₂²×C₅₃	semidirect
1016. #446	C₂²×C₅₃	semidirect
1017. #446	C₂²×C₅₃	semidirect
1021. #442	C₂²×C₅₃	semidirect
1022. #442	C₂²×C₅₃	semidirect
1023. #442	C₂²×C₅₃	semidirect
1024. #442	C₂²×C₅₃	semidirect
1025. #441	C₂²×C₅₃	semidirect
1026. #441	C₂²×C₅₃	semidirect
1027. #440	C₂²×C₅₃	semidirect
1028. #440	C₂²×C₅₃	semidirect
1029. #440	C₂²×C₅₃	semidirect
1030. #440	C₂²×C₅₃	semidirect
1031. #440	C₂²×C₅₃	semidirect
1032. #440	C₂²×C₅₃	semidirect
1033. #440	C₂²×C₅₃	semidirect
1034. C₄×Q₁₆	C₂²×C₅₃	semidirect
1035. C₄×SD₁₆	C₂²×C₅₃	semidirect
1036. C₄×SD₁₆	C₂²×C₅₃	semidirect
1037. C₄×SD₁₆	C₂²×C₅₃	semidirect
1038. C₄×SD₁₆	C₂²×C₅₃	semidirect
1039. C₄×SD₁₆	C₂²×C₅₃	semidirect
1043. C₄×D₈	C₂²×C₅₃	semidirect
1044. C₄×D₈	C₂²×C₅₃	semidirect
1045. C₄×D₈	C₂²×C₅₃	semidirect
1048. #435	C₂²×C₅₃	semidirect
1049. #435	C₂²×C₅₃	semidirect
1050. C₈×D₄	C₂²×C₅₃	semidirect
1051. C₈×D₄	C₂²×C₅₃	semidirect
1052. #433	C₂²×C₅₃	semidirect
1053. #433	C₂²×C₅₃	semidirect
1054. #431	C₂²×C₅₃	semidirect
1055. #428	C₂²×C₅₃	semidirect
1056. #427	C₂²×C₅₃	semidirect
1057. #427	C₂²×C₅₃	semidirect
1059. #418	C₂²×C₅₃	semidirect
1060. #416	C₂²×C₅₃	semidirect
1061. #416	C₂²×C₅₃	semidirect
1062. #416	C₂²×C₅₃	semidirect
1063. C₂×#102	C₂²×C₅₃	semidirect
1064. #405	C₂²×C₅₃	semidirect
1065. #405	C₂²×C₅₃	semidirect
1066. C₂×#97	C₂²×C₅₃	semidirect
1067. C₅₃	#61529	direct (N × H)
1432. D₈	#41×C₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₅₃×#3521	2
C₅₃×#3514	2
C₅₃×#3401	2
C₅₃×#3384	2
C₅₃×#3370	2
C₅₃×#3367	2
C₅₃×#3349	2
C₅₃×#3347	2
C₅₃×#3340	2
C₅₃×#3319	2
C₅₃×#3311	2
C₅₃×#3310	2
C₅₃×#3303	2
C₅₃×#3297	2
C₅₃×#3280	2
C₅₃×#3267	2
C₅₃×#3264	2
C₅₃×#3180	2
C₅₃×#3178	2
C₅₃×#3173	2
C₅₃×#3124	2
C₅₃×#3123	2
C₅₃×#3118	2
C₅₃×#3106	2
C₅₃×#3102	2
C₅₃×#2968	2
C₅₃×#2948	2
C₅₃×#2946	2
C₅₃×#2943	2
#61529	53

Subgroups — C53×#61529 #27269041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61529 #27269041