Subgroups — C₅₃×#62172 #27269684

Order 13568.

1652 conjugacy classes of subgroups.

The subgroup lattice has 1620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3521	C₂	1	1	yes	maximal, characteristic
3	C₅₃×#3388	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3349	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3349	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3344	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3337	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3314	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3311	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3296	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3261	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3258	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3243	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3242	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3240	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3123	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3120	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3084	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#563	—	2	1	no	—
33	C₅₃×#563	—	2	1	no	—
34	Q₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#557	—	2	1	no	—
36	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#556	—	2	1	no	—
38	C₅₃×#556	C₂²	1	1	yes	characteristic
39	C₅₃×#556	C₂²	1	1	yes	characteristic
40	C₅₃×#556	C₂²	1	1	yes	characteristic
41	C₅₃×#556	C₂²	1	1	yes	characteristic
42	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#554	C₂²	1	1	yes	characteristic
44	C₅₃×#554	C₂²	1	1	yes	characteristic
45	C₅₃×#553	—	2	1	no	—
46	C₅₃×#553	C₂²	1	1	yes	characteristic
47	C₅₃×#552	—	2	1	no	—
48	C₅₃×#552	C₂²	1	1	yes	characteristic
49	C₅₃×#552	C₂²	1	1	yes	characteristic
50	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
51	C₅₃×#551	—	2	1	no	—
52	C₅₃×#551	—	2	1	no	—
53	C₅₃×#547	C₂²	1	1	yes	characteristic
54	C₅₃×#546	C₂²	1	1	yes	characteristic
55	C₅₃×#546	C₂²	1	1	yes	characteristic
56	C₅₃×#544	C₂²	1	1	yes	characteristic
57	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#542	—	2	1	no	—
59	C₅₃×#542	C₂²	1	1	yes	characteristic
60	C₅₃×#541	—	2	1	no	—
61	C₅₃×#541	—	2	1	no	—
62	C₅₃×#541	—	2	1	no	—
63	C₅₃×#541	C₂²	1	1	yes	characteristic
64	C₅₃×#541	C₂²	1	1	yes	characteristic
65	C₅₃×#541	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#539	—	2	1	no	—
67	C₅₃×#538	—	2	1	no	—
68	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
70	C₅₃×#529	—	2	1	no	—
71	C₅₃×#529	C₂²	1	1	yes	characteristic
72	C₅₃×#529	C₂²	1	1	yes	characteristic
73	C₂×#126×C₅₃	—	2	1	no	—
74	C₅₃×#520	C₂²	1	1	yes	characteristic
75	C₅₃×#518	C₂²	1	1	yes	characteristic
76	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
77	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#501	C₂²	1	1	yes	characteristic, complemented
81	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#491	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#489	C₂²	1	1	yes	characteristic
85	C₅₃×#489	C₂²	1	1	yes	characteristic
86	C₅₃×#489	C₂²	1	1	yes	characteristic
87	C₅₃×#488	C₂²	1	1	yes	characteristic
88	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#485	C₂²	1	1	yes	characteristic
90	C₅₃×#485	C₂²	1	1	yes	characteristic
91	C₅₃×#485	C₂²	1	1	yes	characteristic
92	C₅₃×#485	C₂²	1	1	yes	characteristic
93	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#484	C₂²	1	1	yes	characteristic
99	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#484	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#483	C₂²	1	1	yes	characteristic
102	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#482	C₂²	1	1	yes	characteristic
104	C₅₃×#482	C₂²	1	1	yes	characteristic
105	C₅₃×#482	C₂²	1	1	yes	characteristic
106	C₅₃×#480	C₂²	1	1	yes	characteristic
107	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
110	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
111	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
112	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
113	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
114	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#478	C₂²	1	1	yes	characteristic
117	C₅₃×#478	C₂²	1	1	yes	characteristic
118	C₅₃×#478	C₂²	1	1	yes	characteristic
119	C₅₃×#478	C₂²	1	1	yes	characteristic
120	C₅₃×#478	C₂²	1	1	yes	characteristic
121	C₅₃×#478	C₂²	1	1	yes	characteristic
122	C₅₃×#478	C₂²	1	1	yes	characteristic
123	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#476	C₂²	1	1	yes	characteristic
127	C₅₃×#476	C₂²	1	1	yes	characteristic
128	C₅₃×#476	C₂²	1	1	yes	characteristic
129	C₅₃×#476	C₂²	1	1	yes	characteristic
130	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#474	C₂²	1	1	yes	characteristic
135	C₅₃×#474	C₂²	1	1	yes	characteristic
136	C₅₃×#474	C₂²	1	1	yes	characteristic
137	C₅₃×#470	C₂²	1	1	yes	characteristic
138	C₅₃×#470	C₂²	1	1	yes	characteristic
139	C₅₃×#470	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#468	C₂²	1	1	yes	characteristic
141	C₅₃×#467	C₂²	1	1	yes	characteristic
142	C₅₃×#467	C₂²	1	1	yes	characteristic
143	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#467	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#465	C₂²	1	1	yes	characteristic
147	C₅₃×#465	C₂²	1	1	yes	characteristic
148	C₅₃×#465	C₂²	1	1	yes	characteristic
149	C₅₃×#464	C₂²	1	1	yes	characteristic
150	C₅₃×#464	C₂²	1	1	yes	characteristic
151	C₅₃×#464	C₂²	1	1	yes	characteristic
152	C₅₃×#464	C₂²	1	1	yes	characteristic
153	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#461	C₂²	1	1	yes	characteristic
158	C₅₃×#461	C₂²	1	1	yes	characteristic
159	C₅₃×#452	C₂²	1	1	yes	characteristic
160	C₅₃×#452	C₂²	1	1	yes	characteristic
161	C₅₃×#452	C₂²	1	1	yes	characteristic
162	C₅₃×#452	C₂²	1	1	yes	characteristic
163	C₅₃×#450	C₂²	1	1	yes	characteristic
164	C₅₃×#450	C₂²	1	1	yes	characteristic
165	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
166	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
167	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
168	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
169	C₅₃×#441	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#440	C₂²	1	1	yes	characteristic
171	C₅₃×#440	C₂²	1	1	yes	characteristic
172	C₅₃×#440	C₂²	1	1	yes	characteristic
173	C₅₃×#440	C₂²	1	1	yes	characteristic
174	C₅₃×#440	C₂²	1	1	yes	characteristic
175	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
176	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
177	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
179	C₅₃×#435	C₂²	1	1	yes	characteristic
180	C₅₃×#435	C₂²	1	1	yes	characteristic
181	C₅₃×#435	C₂²	1	1	yes	characteristic
182	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
183	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
184	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#433	C₂²	1	1	yes	characteristic
186	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
187	C₅₃×#432	C₂²	1	1	yes	characteristic, complemented
188	C₅₃×#428	C₂²	1	1	yes	characteristic
189	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#427	C₂²	1	1	yes	characteristic
191	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
193	C₂×#106×C₅₃	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#418	C₂²	1	1	yes	characteristic
198	C₅₃×#417	C₂²	1	1	yes	characteristic
199	C₅₃×#416	C₂²	1	1	yes	characteristic
200	C₅₃×#416	C₂²	1	1	yes	characteristic
201	C₅₃×#416	C₂²	1	1	yes	characteristic
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
204	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
205	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
209	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
210	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
211	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
212	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
216	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄⋊Q₈×C₅₃	—	2	1	no	—
221	C₄⋊Q₈×C₅₃	—	2	1	no	—
222	C₄⋊Q₈×C₅₃	—	2	1	no	—
223	C₄⋊Q₈×C₅₃	—	2	1	no	—
224	C₄⋊Q₈×C₅₃	—	2	1	no	—
225	C₄⋊Q₈×C₅₃	—	2	1	no	—
226	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
230	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
231	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
232	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
233	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
234	#126×C₅₃	—	2	1	no	—
235	#126×C₅₃	—	2	1	no	—
236	#126×C₅₃	—	2	1	no	—
237	#126×C₅₃	—	2	1	no	—
238	#126×C₅₃	—	2	1	no	—
239	#126×C₅₃	—	2	1	no	—
240	#126×C₅₃	—	2	1	no	—
241	#126×C₅₃	—	2	1	no	—
242	#126×C₅₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
257	#126×C₅₃	D₄	1	1	yes	characteristic
258	#125×C₅₃	—	2	1	no	—
259	#125×C₅₃	—	2	1	no	—
260	#125×C₅₃	—	2	1	no	—
261	#125×C₅₃	—	2	1	no	—
262	#125×C₅₃	—	2	1	no	—
263	#125×C₅₃	—	2	1	no	—
264	#125×C₅₃	—	2	1	no	—
265	#125×C₅₃	—	2	1	no	—
266	#125×C₅₃	—	2	1	no	—
267	#125×C₅₃	—	2	1	no	—
268	#125×C₅₃	—	2	1	no	—
269	#125×C₅₃	—	2	1	no	—
270	#125×C₅₃	—	2	1	no	—
271	#125×C₅₃	—	2	1	no	—
272	#125×C₅₃	—	2	1	no	—
273	#125×C₅₃	D₄	1	1	yes	characteristic
274	#125×C₅₃	C₂³	1	1	yes	characteristic
275	#125×C₅₃	C₂³	1	1	yes	characteristic
276	#125×C₅₃	C₂³	1	1	yes	characteristic
277	#125×C₅₃	C₂³	1	1	yes	characteristic
278	#125×C₅₃	C₂³	1	1	yes	characteristic
279	#125×C₅₃	C₂³	1	1	yes	characteristic
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	—	2	1	no	—
283	#124×C₅₃	—	2	1	no	—
284	#124×C₅₃	—	2	1	no	—
285	#124×C₅₃	D₄	1	1	yes	characteristic
286	#124×C₅₃	C₂³	1	1	yes	characteristic
287	#124×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
296	#123×C₅₃	—	2	1	no	—
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	D₄	1	1	yes	characteristic
299	#123×C₅₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
308	C₂²⋊Q₈×C₅₃	—	2	1	no	—
309	C₂²⋊Q₈×C₅₃	—	2	1	no	—
310	C₂²⋊Q₈×C₅₃	—	2	1	no	—
311	C₂²⋊Q₈×C₅₃	—	2	1	no	—
312	C₂²⋊Q₈×C₅₃	—	2	1	no	—
313	C₂²⋊Q₈×C₅₃	—	2	1	no	—
314	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
315	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
316	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
317	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
318	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
320	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
321	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
322	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
323	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
324	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
325	#121×C₅₃	—	2	1	no	—
326	#121×C₅₃	—	2	1	no	—
327	#121×C₅₃	—	2	1	no	—
328	#121×C₅₃	—	2	1	no	—
329	#121×C₅₃	D₄	1	1	yes	characteristic
330	#121×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	C₂³	1	1	yes	characteristic
332	#120×C₅₃	—	2	1	no	—
333	#120×C₅₃	—	2	1	no	—
334	C₄×Q₈×C₅₃	—	2	1	no	—
335	C₄×Q₈×C₅₃	—	2	1	no	—
336	C₄×Q₈×C₅₃	—	2	1	no	—
337	C₄×Q₈×C₅₃	—	2	1	no	—
338	C₄×Q₈×C₅₃	—	2	1	no	—
339	C₄×Q₈×C₅₃	—	2	1	no	—
340	C₄×Q₈×C₅₃	—	2	1	no	—
341	C₄×Q₈×C₅₃	—	2	1	no	—
342	C₄×Q₈×C₅₃	—	2	1	no	—
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×Q₈×C₅₃	C₂³	1	1	yes	characteristic
347	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
348	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
349	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
350	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
351	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
352	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
353	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
354	C₄×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	—	2	1	no	—
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	#117×C₅₃	—	2	1	no	—
373	#117×C₅₃	—	2	1	no	—
374	#117×C₅₃	—	2	1	no	—
375	#117×C₅₃	—	2	1	no	—
376	#117×C₅₃	—	2	1	no	—
377	#117×C₅₃	—	2	1	no	—
378	#117×C₅₃	—	2	1	no	—
379	#117×C₅₃	—	2	1	no	—
380	#117×C₅₃	C₂³	1	1	yes	characteristic
381	#117×C₅₃	C₂³	1	1	yes	characteristic
382	#117×C₅₃	C₂³	1	1	yes	characteristic
383	#117×C₅₃	C₂³	1	1	yes	characteristic
384	#117×C₅₃	C₂³	1	1	yes	characteristic
385	#117×C₅₃	C₂³	1	1	yes	characteristic
386	#117×C₅₃	C₂³	1	1	yes	characteristic
387	#117×C₅₃	C₂³	1	1	yes	characteristic
388	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
392	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
393	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
394	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
395	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
396	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
397	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
398	C₂×C₄²×C₅₃	—	2	1	no	—
399	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
400	#107×C₅₃	C₂³	1	1	yes	characteristic
401	#107×C₅₃	C₂³	1	1	yes	characteristic
402	#107×C₅₃	C₂³	1	1	yes	characteristic
403	#107×C₅₃	C₂³	1	1	yes	characteristic
404	#107×C₅₃	C₂³	1	1	yes	characteristic
405	#107×C₅₃	C₂³	1	1	yes	characteristic
406	#107×C₅₃	C₂³	1	1	yes	characteristic
407	#107×C₅₃	C₂³	1	1	yes	characteristic
408	#107×C₅₃	C₂³	1	1	yes	characteristic
409	#107×C₅₃	C₂³	1	1	yes	characteristic
410	#107×C₅₃	C₂³	1	1	yes	characteristic
411	#107×C₅₃	C₂³	1	1	yes	characteristic
412	#106×C₅₃	C₂³	1	1	yes	characteristic
413	#106×C₅₃	C₂³	1	1	yes	characteristic
414	#106×C₅₃	C₂³	1	1	yes	characteristic
415	#106×C₅₃	C₂³	1	1	yes	characteristic
416	#106×C₅₃	C₂³	1	1	yes	characteristic
417	#106×C₅₃	C₂³	1	1	yes	characteristic
418	#106×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	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
425	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
426	C₄⋊C₈×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	C₄⋊C₈×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	#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	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	C₂²⋊C₈×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	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
478	C₂⁴×C₅₃	—	2	1	no	—
479	#41×C₅₃	—	2	2	no	—
480	#41×C₅₃	—	2	2	no	—
481	#41×C₅₃	—	4	1	no	—
482	#41×C₅₃	—	4	1	no	—
483	C₂×Q₈×C₅₃	—	2	1	no	—
484	C₂×Q₈×C₅₃	—	2	1	no	—
485	C₂×Q₈×C₅₃	—	2	1	no	—
486	C₂×Q₈×C₅₃	—	2	1	no	—
487	C₂×Q₈×C₅₃	—	2	1	no	—
488	C₂×Q₈×C₅₃	—	2	1	no	—
489	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
490	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
491	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
492	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
493	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
494	C₂×D₄×C₅₃	—	2	2	no	—
495	C₂×D₄×C₅₃	—	2	1	no	—
496	C₂×D₄×C₅₃	—	2	1	no	—
497	C₂×D₄×C₅₃	—	2	1	no	—
498	C₂×D₄×C₅₃	—	2	1	no	—
499	C₂×D₄×C₅₃	—	2	1	no	—
500	C₂×D₄×C₅₃	—	4	1	no	—
501	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
502	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
503	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
504	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
505	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
506	C₂²×C₄×C₅₃	—	2	1	no	—
507	C₂²×C₄×C₅₃	—	2	1	no	—
508	C₂²×C₄×C₅₃	—	2	1	no	—
509	C₂²×C₄×C₅₃	—	2	1	no	—
510	C₂²×C₄×C₅₃	—	2	1	no	—
511	C₂²×C₄×C₅₃	—	2	1	no	—
512	C₂²×C₄×C₅₃	—	2	1	no	—
513	C₂²×C₄×C₅₃	—	2	1	no	—
514	C₂²×C₄×C₅₃	—	2	1	no	—
515	C₂²×C₄×C₅₃	—	2	1	no	—
516	C₂²×C₄×C₅₃	—	2	1	no	—
517	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
519	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
520	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
522	Q₁₆×C₅₃	—	4	1	no	—
523	Q₁₆×C₅₃	—	4	1	no	—
524	Q₁₆×C₅₃	—	4	1	no	—
525	Q₁₆×C₅₃	—	4	1	no	—
526	SD₁₆×C₅₃	—	2	2	no	—
527	SD₁₆×C₅₃	—	2	2	no	—
528	SD₁₆×C₅₃	—	4	1	no	—
529	SD₁₆×C₅₃	—	4	1	no	—
530	M₁₆×C₅₃	—	4	1	no	—
531	M₁₆×C₅₃	—	4	1	no	—
532	C₂×C₈×C₅₃	—	4	1	no	—
533	C₂×C₈×C₅₃	—	4	1	no	—
534	C₂×C₈×C₅₃	—	4	1	no	—
535	C₂×C₈×C₅₃	—	4	1	no	—
536	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
537	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
538	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
539	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
540	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
541	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
542	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
543	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
544	C₄⋊C₄×C₅₃	—	2	1	no	—
545	C₄⋊C₄×C₅₃	—	2	1	no	—
546	C₄⋊C₄×C₅₃	—	2	1	no	—
547	C₄⋊C₄×C₅₃	—	2	1	no	—
548	C₄⋊C₄×C₅₃	—	2	1	no	—
549	C₄⋊C₄×C₅₃	—	2	1	no	—
550	C₄⋊C₄×C₅₃	—	2	1	no	—
551	C₄⋊C₄×C₅₃	—	2	1	no	—
552	C₄⋊C₄×C₅₃	—	2	1	no	—
553	C₄⋊C₄×C₅₃	—	2	1	no	—
554	C₄⋊C₄×C₅₃	—	2	1	no	—
555	C₄⋊C₄×C₅₃	—	2	1	no	—
556	C₄⋊C₄×C₅₃	—	2	1	no	—
557	C₄⋊C₄×C₅₃	—	2	1	no	—
558	C₄⋊C₄×C₅₃	—	2	1	no	—
559	C₄⋊C₄×C₅₃	—	2	1	no	—
560	C₄⋊C₄×C₅₃	—	2	1	no	—
561	C₄⋊C₄×C₅₃	—	2	1	no	—
562	C₄⋊C₄×C₅₃	—	2	1	no	—
563	C₄⋊C₄×C₅₃	—	2	1	no	—
564	C₄⋊C₄×C₅₃	—	2	1	no	—
565	C₄⋊C₄×C₅₃	—	2	1	no	—
566	C₄⋊C₄×C₅₃	—	2	1	no	—
567	C₄⋊C₄×C₅₃	—	2	1	no	—
568	C₄⋊C₄×C₅₃	—	2	1	no	—
569	C₄⋊C₄×C₅₃	—	2	1	no	—
570	C₄⋊C₄×C₅₃	—	2	1	no	—
571	C₄⋊C₄×C₅₃	—	2	1	no	—
572	C₄⋊C₄×C₅₃	—	2	1	no	—
573	C₄⋊C₄×C₅₃	—	2	1	no	—
574	C₄⋊C₄×C₅₃	—	2	1	no	—
575	C₄⋊C₄×C₅₃	—	2	1	no	—
576	C₄⋊C₄×C₅₃	—	2	1	no	—
577	C₄⋊C₄×C₅₃	—	2	1	no	—
578	C₄⋊C₄×C₅₃	—	2	1	no	—
579	C₄⋊C₄×C₅₃	—	2	1	no	—
580	C₄⋊C₄×C₅₃	—	2	1	no	—
581	C₄⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
590	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
591	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
592	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
593	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
594	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
595	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
596	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
597	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
600	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
601	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
602	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
603	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
604	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
605	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
606	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
607	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₂²⋊C₄×C₅₃	—	2	1	no	—
610	C₂²⋊C₄×C₅₃	—	2	1	no	—
611	C₂²⋊C₄×C₅₃	—	2	1	no	—
612	C₂²⋊C₄×C₅₃	—	2	1	no	—
613	C₂²⋊C₄×C₅₃	—	2	1	no	—
614	C₂²⋊C₄×C₅₃	—	2	1	no	—
615	C₂²⋊C₄×C₅₃	—	2	1	no	—
616	C₂²⋊C₄×C₅₃	—	2	1	no	—
617	C₂²⋊C₄×C₅₃	—	2	1	no	—
618	C₂²⋊C₄×C₅₃	—	2	1	no	—
619	C₂²⋊C₄×C₅₃	—	2	1	no	—
620	C₂²⋊C₄×C₅₃	—	2	1	no	—
621	C₂²⋊C₄×C₅₃	—	2	1	no	—
622	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
638	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
639	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
640	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
641	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
642	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
643	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
644	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
645	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
646	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
647	C₄²×C₅₃	—	2	1	no	—
648	C₄²×C₅₃	—	2	1	no	—
649	C₄²×C₅₃	—	2	1	no	—
650	C₄²×C₅₃	—	2	1	no	—
651	C₄²×C₅₃	—	2	1	no	—
652	C₄²×C₅₃	—	2	1	no	—
653	C₄²×C₅₃	—	2	1	no	—
654	C₄²×C₅₃	—	2	1	no	—
655	C₄²×C₅₃	—	2	1	no	—
656	C₄²×C₅₃	—	2	1	no	—
657	C₄²×C₅₃	—	2	1	no	—
658	C₄²×C₅₃	—	2	1	no	—
659	C₄²×C₅₃	—	2	1	no	—
660	C₄²×C₅₃	—	2	1	no	—
661	C₄²×C₅₃	—	2	1	no	—
662	C₄²×C₅₃	—	2	1	no	—
663	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
664	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
665	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
666	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
667	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
668	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
669	C₂³×C₅₃	—	2	1	no	—
670	C₂³×C₅₃	—	2	1	no	—
671	C₂³×C₅₃	—	4	2	no	—
672	C₂³×C₅₃	—	8	1	no	—
673	C₂³×C₅₃	—	8	1	no	—
674	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
675	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
676	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
677	Q₈×C₅₃	—	2	1	no	—
678	Q₈×C₅₃	—	2	1	no	—
679	Q₈×C₅₃	—	2	1	no	—
680	Q₈×C₅₃	—	2	1	no	—
681	Q₈×C₅₃	—	2	1	no	—
682	Q₈×C₅₃	—	2	1	no	—
683	Q₈×C₅₃	—	2	1	no	—
684	Q₈×C₅₃	—	2	1	no	—
685	Q₈×C₅₃	—	4	1	no	—
686	Q₈×C₅₃	—	4	2	no	—
687	Q₈×C₅₃	—	8	1	no	—
688	Q₈×C₅₃	—	8	1	no	—
689	Q₈×C₅₃	—	8	1	no	—
690	Q₈×C₅₃	—	8	1	no	—
691	Q₈×C₅₃	—	8	1	no	—
692	D₄×C₅₃	—	2	1	no	—
693	D₄×C₅₃	—	2	1	no	—
694	D₄×C₅₃	—	2	1	no	—
695	D₄×C₅₃	—	4	1	no	—
696	D₄×C₅₃	—	4	1	no	—
697	D₄×C₅₃	—	4	1	no	—
698	D₄×C₅₃	—	4	2	no	—
699	D₄×C₅₃	—	4	2	no	—
700	D₄×C₅₃	—	4	2	no	—
701	D₄×C₅₃	—	8	1	no	—
702	D₄×C₅₃	—	8	1	no	—
703	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
704	C₂×C₄×C₅₃	—	2	1	no	—
705	C₂×C₄×C₅₃	—	2	1	no	—
706	C₂×C₄×C₅₃	—	2	1	no	—
707	C₂×C₄×C₅₃	—	2	1	no	—
708	C₂×C₄×C₅₃	—	2	1	no	—
709	C₂×C₄×C₅₃	—	2	1	no	—
710	C₂×C₄×C₅₃	—	2	1	no	—
711	C₂×C₄×C₅₃	—	2	1	no	—
712	C₂×C₄×C₅₃	—	2	1	no	—
713	C₂×C₄×C₅₃	—	2	1	no	—
714	C₂×C₄×C₅₃	—	2	1	no	—
715	C₂×C₄×C₅₃	—	2	1	no	—
716	C₂×C₄×C₅₃	—	2	1	no	—
717	C₂×C₄×C₅₃	—	2	1	no	—
718	C₂×C₄×C₅₃	—	2	1	no	—
719	C₂×C₄×C₅₃	—	2	1	no	—
720	C₂×C₄×C₅₃	—	2	1	no	—
721	C₂×C₄×C₅₃	—	2	1	no	—
722	C₂×C₄×C₅₃	—	2	1	no	—
723	C₂×C₄×C₅₃	—	2	1	no	—
724	C₂×C₄×C₅₃	—	4	1	no	—
725	C₂×C₄×C₅₃	—	4	1	no	—
726	C₂×C₄×C₅₃	—	4	2	no	—
727	C₂×C₄×C₅₃	—	4	2	no	—
728	C₂×C₄×C₅₃	—	8	1	no	—
729	C₂×C₄×C₅₃	—	8	1	no	—
730	C₂×C₄×C₅₃	—	8	1	no	—
731	C₂×C₄×C₅₃	—	8	1	no	—
732	C₂×C₄×C₅₃	—	8	1	no	—
733	C₂×C₄×C₅₃	—	8	1	no	—
734	C₂×C₄×C₅₃	—	8	1	no	—
735	C₂×C₄×C₅₃	—	8	1	no	—
736	C₂×C₄×C₅₃	—	8	1	no	—
737	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
738	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
739	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
740	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
741	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
742	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
743	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
744	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
745	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
746	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
747	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
748	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
749	C₈×C₅₃	—	2	1	no	—
750	C₈×C₅₃	—	2	1	no	—
751	C₈×C₅₃	—	2	1	no	—
752	C₈×C₅₃	—	2	1	no	—
753	C₈×C₅₃	—	2	1	no	—
754	C₈×C₅₃	—	2	1	no	—
755	C₈×C₅₃	—	2	1	no	—
756	C₈×C₅₃	—	2	1	no	—
757	#62172	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
758	C₂²×C₅₃	—	2	1	no	—
759	C₂²×C₅₃	—	2	1	no	—
760	C₂²×C₅₃	—	2	1	no	—
761	C₂²×C₅₃	—	2	1	no	—
762	C₂²×C₅₃	—	2	1	no	—
763	C₂²×C₅₃	—	2	1	no	—
764	C₂²×C₅₃	—	2	1	no	—
765	C₂²×C₅₃	—	2	1	no	—
766	C₂²×C₅₃	—	2	1	no	—
767	C₂²×C₅₃	—	2	2	no	—
768	C₂²×C₅₃	—	4	1	no	—
769	C₂²×C₅₃	—	4	1	no	—
770	C₂²×C₅₃	—	4	1	no	—
771	C₂²×C₅₃	—	4	1	no	—
772	C₂²×C₅₃	—	4	1	no	—
773	C₂²×C₅₃	—	16	2	no	—
774	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
775	C₄×C₅₃	—	2	1	no	—
776	C₄×C₅₃	—	2	1	no	—
777	C₄×C₅₃	—	2	1	no	—
778	C₄×C₅₃	—	2	1	no	—
779	C₄×C₅₃	—	2	1	no	—
780	C₄×C₅₃	—	2	1	no	—
781	C₄×C₅₃	—	2	1	no	—
782	C₄×C₅₃	—	2	1	no	—
783	C₄×C₅₃	—	2	1	no	—
784	C₄×C₅₃	—	2	1	no	—
785	C₄×C₅₃	—	2	1	no	—
786	C₄×C₅₃	—	4	1	no	—
787	C₄×C₅₃	—	4	1	no	—
788	C₄×C₅₃	—	4	1	no	—
789	C₄×C₅₃	—	4	1	no	—
790	C₄×C₅₃	—	4	1	no	—
791	C₄×C₅₃	—	4	1	no	—
792	C₄×C₅₃	—	4	1	no	—
793	C₄×C₅₃	—	4	1	no	—
794	C₄×C₅₃	—	4	1	no	—
795	C₄×C₅₃	—	4	1	no	—
796	C₄×C₅₃	—	4	1	no	—
797	C₄×C₅₃	—	4	1	no	—
798	C₄×C₅₃	—	4	1	no	—
799	C₄×C₅₃	—	4	1	no	—
800	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
801	C₄×C₅₃	#585	1	1	yes	characteristic
802	#3555	C₂×C₅₃	1	1	yes	characteristic, complemented
803	#3521	C₂×C₅₃	1	1	yes	characteristic
804	#3388	C₂×C₅₃	1	1	yes	characteristic, complemented
805	#3385	C₂×C₅₃	1	1	yes	characteristic, complemented
806	#3377	C₂×C₅₃	1	1	yes	characteristic, complemented
807	#3369	C₂×C₅₃	1	1	yes	characteristic, complemented
808	#3350	C₂×C₅₃	1	1	yes	characteristic, complemented
809	#3349	C₂×C₅₃	1	1	yes	characteristic, complemented
810	#3349	C₂×C₅₃	1	1	yes	characteristic, complemented
811	#3344	C₂×C₅₃	1	1	yes	characteristic, complemented
812	#3342	C₂×C₅₃	1	1	yes	characteristic, complemented
813	#3337	C₂×C₅₃	1	1	yes	characteristic, complemented
814	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
815	#3314	C₂×C₅₃	1	1	yes	characteristic, complemented
816	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
817	#3311	C₂×C₅₃	1	1	yes	characteristic, complemented
818	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
819	#3296	C₂×C₅₃	1	1	yes	characteristic, complemented
820	#3261	C₂×C₅₃	1	1	yes	characteristic, complemented
821	#3258	C₂×C₅₃	1	1	yes	characteristic, complemented
822	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
823	#3243	C₂×C₅₃	1	1	yes	characteristic, complemented
824	#3242	C₂×C₅₃	1	1	yes	characteristic, complemented
825	#3240	C₂×C₅₃	1	1	yes	characteristic, complemented
826	#3123	C₂×C₅₃	1	1	yes	characteristic, complemented
827	#3120	C₂×C₅₃	1	1	yes	characteristic, complemented
828	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
829	#3084	C₂×C₅₃	1	1	yes	characteristic, complemented
830	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
831	#3076	C₂×C₅₃	1	1	yes	characteristic, complemented
832	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
833	C₂×C₅₃	—	4	1	no	—
834	C₂×C₅₃	—	4	1	no	—
835	C₂×C₅₃	—	4	1	no	—
836	C₂×C₅₃	—	4	2	no	—
837	C₂×C₅₃	—	8	1	no	—
838	C₂×C₅₃	#3489	1	1	yes	characteristic
839	C₂×C₅₃	#3584	1	1	yes	characteristic
840	C₂×C₅₃	#3586	1	1	yes	characteristic
841	#563	—	2	1	no	—
842	#563	—	2	1	no	—
843	Q₈²	C₂²×C₅₃	1	1	yes	characteristic, complemented
844	#557	—	2	1	no	—
845	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
846	#556	—	2	1	no	—
847	#556	C₂²×C₅₃	1	1	yes	characteristic
848	#556	C₂²×C₅₃	1	1	yes	characteristic
849	#556	C₂²×C₅₃	1	1	yes	characteristic
850	#556	C₂²×C₅₃	1	1	yes	characteristic
851	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
852	#554	C₂²×C₅₃	1	1	yes	characteristic
853	#554	C₂²×C₅₃	1	1	yes	characteristic
854	#553	—	2	1	no	—
855	#553	C₂²×C₅₃	1	1	yes	characteristic
856	#552	—	2	1	no	—
857	#552	C₂²×C₅₃	1	1	yes	characteristic
858	#552	C₂²×C₅₃	1	1	yes	characteristic
859	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
860	#551	—	2	1	no	—
861	#551	—	2	1	no	—
862	#547	C₂²×C₅₃	1	1	yes	characteristic
863	#546	C₂²×C₅₃	1	1	yes	characteristic
864	#546	C₂²×C₅₃	1	1	yes	characteristic
865	#544	C₂²×C₅₃	1	1	yes	characteristic
866	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
867	#542	—	2	1	no	—
868	#542	C₂²×C₅₃	1	1	yes	characteristic
869	#541	—	2	1	no	—
870	#541	—	2	1	no	—
871	#541	—	2	1	no	—
872	#541	C₂²×C₅₃	1	1	yes	characteristic
873	#541	C₂²×C₅₃	1	1	yes	characteristic
874	#541	C₂²×C₅₃	1	1	yes	characteristic, complemented
875	#539	—	2	1	no	—
876	#538	—	2	1	no	—
877	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
878	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
879	#529	—	2	1	no	—
880	#529	C₂²×C₅₃	1	1	yes	characteristic
881	#529	C₂²×C₅₃	1	1	yes	characteristic
882	C₂×#126	—	2	1	no	—
883	#520	C₂²×C₅₃	1	1	yes	characteristic
884	#518	C₂²×C₅₃	1	1	yes	characteristic
885	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
886	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
887	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
888	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
889	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
890	#500	C₂²×C₅₃	1	1	yes	characteristic, complemented
891	#499	C₂²×C₅₃	1	1	yes	characteristic, complemented
892	#491	C₂²×C₅₃	1	1	yes	characteristic, complemented
893	#489	C₂²×C₅₃	1	1	yes	characteristic
894	#489	C₂²×C₅₃	1	1	yes	characteristic
895	#489	C₂²×C₅₃	1	1	yes	characteristic
896	#488	C₂²×C₅₃	1	1	yes	characteristic
897	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
898	#485	C₂²×C₅₃	1	1	yes	characteristic
899	#485	C₂²×C₅₃	1	1	yes	characteristic
900	#485	C₂²×C₅₃	1	1	yes	characteristic
901	#485	C₂²×C₅₃	1	1	yes	characteristic
902	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
903	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
904	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
905	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#484	C₂²×C₅₃	1	1	yes	characteristic
908	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
909	#484	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#483	C₂²×C₅₃	1	1	yes	characteristic
911	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
912	#482	C₂²×C₅₃	1	1	yes	characteristic
913	#482	C₂²×C₅₃	1	1	yes	characteristic
914	#482	C₂²×C₅₃	1	1	yes	characteristic
915	#480	C₂²×C₅₃	1	1	yes	characteristic
916	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
917	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
919	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
920	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
922	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
923	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
924	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
925	#478	C₂²×C₅₃	1	1	yes	characteristic
926	#478	C₂²×C₅₃	1	1	yes	characteristic
927	#478	C₂²×C₅₃	1	1	yes	characteristic
928	#478	C₂²×C₅₃	1	1	yes	characteristic
929	#478	C₂²×C₅₃	1	1	yes	characteristic
930	#478	C₂²×C₅₃	1	1	yes	characteristic
931	#478	C₂²×C₅₃	1	1	yes	characteristic
932	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#476	C₂²×C₅₃	1	1	yes	characteristic
936	#476	C₂²×C₅₃	1	1	yes	characteristic
937	#476	C₂²×C₅₃	1	1	yes	characteristic
938	#476	C₂²×C₅₃	1	1	yes	characteristic
939	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#474	C₂²×C₅₃	1	1	yes	characteristic
944	#474	C₂²×C₅₃	1	1	yes	characteristic
945	#474	C₂²×C₅₃	1	1	yes	characteristic
946	#470	C₂²×C₅₃	1	1	yes	characteristic
947	#470	C₂²×C₅₃	1	1	yes	characteristic
948	#470	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#468	C₂²×C₅₃	1	1	yes	characteristic
950	#467	C₂²×C₅₃	1	1	yes	characteristic
951	#467	C₂²×C₅₃	1	1	yes	characteristic
952	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#467	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#465	C₂²×C₅₃	1	1	yes	characteristic
956	#465	C₂²×C₅₃	1	1	yes	characteristic
957	#465	C₂²×C₅₃	1	1	yes	characteristic
958	#464	C₂²×C₅₃	1	1	yes	characteristic
959	#464	C₂²×C₅₃	1	1	yes	characteristic
960	#464	C₂²×C₅₃	1	1	yes	characteristic
961	#464	C₂²×C₅₃	1	1	yes	characteristic
962	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
963	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#461	C₂²×C₅₃	1	1	yes	characteristic
967	#461	C₂²×C₅₃	1	1	yes	characteristic
968	#452	C₂²×C₅₃	1	1	yes	characteristic
969	#452	C₂²×C₅₃	1	1	yes	characteristic
970	#452	C₂²×C₅₃	1	1	yes	characteristic
971	#452	C₂²×C₅₃	1	1	yes	characteristic
972	#450	C₂²×C₅₃	1	1	yes	characteristic
973	#450	C₂²×C₅₃	1	1	yes	characteristic
974	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#441	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#440	C₂²×C₅₃	1	1	yes	characteristic
980	#440	C₂²×C₅₃	1	1	yes	characteristic
981	#440	C₂²×C₅₃	1	1	yes	characteristic
982	#440	C₂²×C₅₃	1	1	yes	characteristic
983	#440	C₂²×C₅₃	1	1	yes	characteristic
984	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
986	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
987	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
988	#435	C₂²×C₅₃	1	1	yes	characteristic
989	#435	C₂²×C₅₃	1	1	yes	characteristic
990	#435	C₂²×C₅₃	1	1	yes	characteristic
991	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
993	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#433	C₂²×C₅₃	1	1	yes	characteristic
995	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#428	C₂²×C₅₃	1	1	yes	characteristic
998	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
999	#427	C₂²×C₅₃	1	1	yes	characteristic
1000	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	C₂×#106	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#424	C₂²×C₅₃	1	1	yes	characteristic
1004	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#418	C₂²×C₅₃	1	1	yes	characteristic
1007	#417	C₂²×C₅₃	1	1	yes	characteristic
1008	#416	C₂²×C₅₃	1	1	yes	characteristic
1009	#416	C₂²×C₅₃	1	1	yes	characteristic
1010	#416	C₂²×C₅₃	1	1	yes	characteristic
1011	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1012	C₅₃	#62172	1	1	yes	characteristic, direct product factor, Sylow
1013	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1014	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1015	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1016	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1017	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1018	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1019	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1020	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1021	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1022	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1023	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1024	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1025	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1026	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1027	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1028	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1029	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1030	C₄⋊Q₈	—	2	1	no	—
1031	C₄⋊Q₈	—	2	1	no	—
1032	C₄⋊Q₈	—	2	1	no	—
1033	C₄⋊Q₈	—	2	1	no	—
1034	C₄⋊Q₈	—	2	1	no	—
1035	C₄⋊Q₈	—	2	1	no	—
1036	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1037	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1038	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1039	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1040	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1041	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1042	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1043	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1044	#126	—	2	1	no	—
1045	#126	—	2	1	no	—
1046	#126	—	2	1	no	—
1047	#126	—	2	1	no	—
1048	#126	—	2	1	no	—
1049	#126	—	2	1	no	—
1050	#126	—	2	1	no	—
1051	#126	—	2	1	no	—
1052	#126	—	2	1	no	—
1053	#126	—	2	1	no	—
1054	#126	—	2	1	no	—
1055	#126	—	2	1	no	—
1056	#126	—	2	1	no	—
1057	#126	—	2	1	no	—
1058	#126	—	2	1	no	—
1059	#126	—	2	1	no	—
1060	#126	—	2	1	no	—
1061	#126	—	2	1	no	—
1062	#126	—	2	1	no	—
1063	#126	—	2	1	no	—
1064	#126	—	2	1	no	—
1065	#126	—	2	1	no	—
1066	#126	D₄×C₅₃	1	1	yes	characteristic
1067	#126	D₄×C₅₃	1	1	yes	characteristic
1068	#125	—	2	1	no	—
1069	#125	—	2	1	no	—
1070	#125	—	2	1	no	—
1071	#125	—	2	1	no	—
1072	#125	—	2	1	no	—
1073	#125	—	2	1	no	—
1074	#125	—	2	1	no	—
1075	#125	—	2	1	no	—
1076	#125	—	2	1	no	—
1077	#125	—	2	1	no	—
1078	#125	—	2	1	no	—
1079	#125	—	2	1	no	—
1080	#125	—	2	1	no	—
1081	#125	—	2	1	no	—
1082	#125	—	2	1	no	—
1083	#125	D₄×C₅₃	1	1	yes	characteristic
1084	#125	C₂³×C₅₃	1	1	yes	characteristic
1085	#125	C₂³×C₅₃	1	1	yes	characteristic
1086	#125	C₂³×C₅₃	1	1	yes	characteristic
1087	#125	C₂³×C₅₃	1	1	yes	characteristic
1088	#125	C₂³×C₅₃	1	1	yes	characteristic
1089	#125	C₂³×C₅₃	1	1	yes	characteristic
1090	#124	—	2	1	no	—
1091	#124	—	2	1	no	—
1092	#124	—	2	1	no	—
1093	#124	—	2	1	no	—
1094	#124	—	2	1	no	—
1095	#124	D₄×C₅₃	1	1	yes	characteristic
1096	#124	C₂³×C₅₃	1	1	yes	characteristic
1097	#124	C₂³×C₅₃	1	1	yes	characteristic
1098	#123	—	2	1	no	—
1099	#123	—	2	1	no	—
1100	#123	—	2	1	no	—
1101	#123	—	2	1	no	—
1102	#123	—	2	1	no	—
1103	#123	—	2	1	no	—
1104	#123	—	2	1	no	—
1105	#123	—	2	1	no	—
1106	#123	—	2	1	no	—
1107	#123	—	2	1	no	—
1108	#123	D₄×C₅₃	1	1	yes	characteristic
1109	#123	D₄×C₅₃	1	1	yes	characteristic
1110	C₂²⋊Q₈	—	2	1	no	—
1111	C₂²⋊Q₈	—	2	1	no	—
1112	C₂²⋊Q₈	—	2	1	no	—
1113	C₂²⋊Q₈	—	2	1	no	—
1114	C₂²⋊Q₈	—	2	1	no	—
1115	C₂²⋊Q₈	—	2	1	no	—
1116	C₂²⋊Q₈	—	2	1	no	—
1117	C₂²⋊Q₈	—	2	1	no	—
1118	C₂²⋊Q₈	—	2	1	no	—
1119	C₂²⋊Q₈	—	2	1	no	—
1120	C₂²⋊Q₈	—	2	1	no	—
1121	C₂²⋊Q₈	—	2	1	no	—
1122	C₂²⋊Q₈	—	2	1	no	—
1123	C₂²⋊Q₈	—	2	1	no	—
1124	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1125	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1126	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1127	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1128	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1129	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1130	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1131	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1132	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1133	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1134	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1135	#121	—	2	1	no	—
1136	#121	—	2	1	no	—
1137	#121	—	2	1	no	—
1138	#121	—	2	1	no	—
1139	#121	D₄×C₅₃	1	1	yes	characteristic
1140	#121	C₂³×C₅₃	1	1	yes	characteristic
1141	#121	C₂³×C₅₃	1	1	yes	characteristic
1142	#120	—	2	1	no	—
1143	#120	—	2	1	no	—
1144	C₄×Q₈	—	2	1	no	—
1145	C₄×Q₈	—	2	1	no	—
1146	C₄×Q₈	—	2	1	no	—
1147	C₄×Q₈	—	2	1	no	—
1148	C₄×Q₈	—	2	1	no	—
1149	C₄×Q₈	—	2	1	no	—
1150	C₄×Q₈	—	2	1	no	—
1151	C₄×Q₈	—	2	1	no	—
1152	C₄×Q₈	—	2	1	no	—
1153	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1154	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1155	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1156	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1157	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1158	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1159	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1160	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1161	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1162	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1163	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1164	C₄×D₄	—	2	1	no	—
1165	C₄×D₄	—	2	1	no	—
1166	C₄×D₄	—	2	1	no	—
1167	C₄×D₄	—	2	1	no	—
1168	C₄×D₄	—	2	1	no	—
1169	C₄×D₄	—	2	1	no	—
1170	C₄×D₄	—	2	1	no	—
1171	C₄×D₄	—	2	1	no	—
1172	C₄×D₄	—	2	1	no	—
1173	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1174	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1175	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1176	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1177	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1178	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1179	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1180	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1181	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1182	#117	—	2	1	no	—
1183	#117	—	2	1	no	—
1184	#117	—	2	1	no	—
1185	#117	—	2	1	no	—
1186	#117	—	2	1	no	—
1187	#117	—	2	1	no	—
1188	#117	—	2	1	no	—
1189	#117	—	2	1	no	—
1190	#117	C₂³×C₅₃	1	1	yes	characteristic
1191	#117	C₂³×C₅₃	1	1	yes	characteristic
1192	#117	C₂³×C₅₃	1	1	yes	characteristic
1193	#117	C₂³×C₅₃	1	1	yes	characteristic
1194	#117	C₂³×C₅₃	1	1	yes	characteristic
1195	#117	C₂³×C₅₃	1	1	yes	characteristic
1196	#117	C₂³×C₅₃	1	1	yes	characteristic
1197	#117	C₂³×C₅₃	1	1	yes	characteristic
1198	C₂×C₄⋊C₄	—	2	1	no	—
1199	C₂×C₄⋊C₄	—	2	1	no	—
1200	C₂×C₄⋊C₄	—	2	1	no	—
1201	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1202	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂×C₂²⋊C₄	—	2	1	no	—
1205	C₂×C₂²⋊C₄	—	2	1	no	—
1206	C₂×C₂²⋊C₄	—	2	1	no	—
1207	C₂×C₂²⋊C₄	—	2	1	no	—
1208	C₂×C₄²	—	2	1	no	—
1209	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1210	#107	C₂³×C₅₃	1	1	yes	characteristic
1211	#107	C₂³×C₅₃	1	1	yes	characteristic
1212	#107	C₂³×C₅₃	1	1	yes	characteristic
1213	#107	C₂³×C₅₃	1	1	yes	characteristic
1214	#107	C₂³×C₅₃	1	1	yes	characteristic
1215	#107	C₂³×C₅₃	1	1	yes	characteristic
1216	#107	C₂³×C₅₃	1	1	yes	characteristic
1217	#107	C₂³×C₅₃	1	1	yes	characteristic
1218	#107	C₂³×C₅₃	1	1	yes	characteristic
1219	#107	C₂³×C₅₃	1	1	yes	characteristic
1220	#107	C₂³×C₅₃	1	1	yes	characteristic
1221	#107	C₂³×C₅₃	1	1	yes	characteristic
1222	#106	C₂³×C₅₃	1	1	yes	characteristic
1223	#106	C₂³×C₅₃	1	1	yes	characteristic
1224	#106	C₂³×C₅₃	1	1	yes	characteristic
1225	#106	C₂³×C₅₃	1	1	yes	characteristic
1226	#106	C₂³×C₅₃	1	1	yes	characteristic
1227	#106	C₂³×C₅₃	1	1	yes	characteristic
1228	#106	C₂³×C₅₃	1	1	yes	characteristic
1229	#106	C₂³×C₅₃	1	1	yes	characteristic
1230	#106	C₂³×C₅₃	1	1	yes	characteristic
1231	#106	C₂³×C₅₃	1	1	yes	characteristic
1232	#106	C₂³×C₅₃	1	1	yes	characteristic
1233	#106	C₂³×C₅₃	1	1	yes	characteristic
1234	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1235	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1236	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1237	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1240	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1243	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1244	#103	C₂³×C₅₃	1	1	yes	characteristic
1245	#103	C₂³×C₅₃	1	1	yes	characteristic
1246	#103	C₂³×C₅₃	1	1	yes	characteristic
1247	#103	C₂³×C₅₃	1	1	yes	characteristic
1248	#103	C₂³×C₅₃	1	1	yes	characteristic
1249	#103	C₂³×C₅₃	1	1	yes	characteristic
1250	#103	C₂³×C₅₃	1	1	yes	characteristic
1251	#103	C₂³×C₅₃	1	1	yes	characteristic
1252	#103	C₂³×C₅₃	1	1	yes	characteristic
1253	#103	C₂³×C₅₃	1	1	yes	characteristic
1254	#103	C₂³×C₅₃	1	1	yes	characteristic
1255	#103	C₂³×C₅₃	1	1	yes	characteristic
1256	#103	C₂³×C₅₃	1	1	yes	characteristic
1257	#103	C₂³×C₅₃	1	1	yes	characteristic
1258	#103	C₂³×C₅₃	1	1	yes	characteristic
1259	#103	C₂³×C₅₃	1	1	yes	characteristic
1260	#103	C₂³×C₅₃	1	1	yes	characteristic
1261	#103	C₂³×C₅₃	1	1	yes	characteristic
1262	#103	C₂³×C₅₃	1	1	yes	characteristic
1263	#103	C₂³×C₅₃	1	1	yes	characteristic
1264	#102	C₂³×C₅₃	1	1	yes	characteristic
1265	#102	C₂³×C₅₃	1	1	yes	characteristic
1266	#102	C₂³×C₅₃	1	1	yes	characteristic
1267	#102	C₂³×C₅₃	1	1	yes	characteristic
1268	#102	C₂³×C₅₃	1	1	yes	characteristic
1269	#102	C₂³×C₅₃	1	1	yes	characteristic
1270	#102	C₂³×C₅₃	1	1	yes	characteristic
1271	#102	C₂³×C₅₃	1	1	yes	characteristic
1272	#102	C₂³×C₅₃	1	1	yes	characteristic
1273	#102	C₂³×C₅₃	1	1	yes	characteristic
1274	#102	C₂³×C₅₃	1	1	yes	characteristic
1275	#102	C₂³×C₅₃	1	1	yes	characteristic
1276	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1277	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1278	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1279	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1280	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1281	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1282	#97	C₂³×C₅₃	1	1	yes	characteristic
1283	#97	C₂³×C₅₃	1	1	yes	characteristic
1284	#97	C₂³×C₅₃	1	1	yes	characteristic
1285	#97	C₂³×C₅₃	1	1	yes	characteristic
1286	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1287	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1288	C₂⁴	—	2	1	no	—
1289	#41	—	2	2	no	—
1290	#41	—	2	2	no	—
1291	#41	—	4	1	no	—
1292	#41	—	4	1	no	—
1293	C₂×Q₈	—	2	1	no	—
1294	C₂×Q₈	—	2	1	no	—
1295	C₂×Q₈	—	2	1	no	—
1296	C₂×Q₈	—	2	1	no	—
1297	C₂×Q₈	—	2	1	no	—
1298	C₂×Q₈	—	2	1	no	—
1299	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1300	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1301	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1302	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1303	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1304	C₂×D₄	—	2	2	no	—
1305	C₂×D₄	—	2	1	no	—
1306	C₂×D₄	—	2	1	no	—
1307	C₂×D₄	—	2	1	no	—
1308	C₂×D₄	—	2	1	no	—
1309	C₂×D₄	—	2	1	no	—
1310	C₂×D₄	—	4	1	no	—
1311	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1312	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1313	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1314	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1315	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1316	C₂²×C₄	—	2	1	no	—
1317	C₂²×C₄	—	2	1	no	—
1318	C₂²×C₄	—	2	1	no	—
1319	C₂²×C₄	—	2	1	no	—
1320	C₂²×C₄	—	2	1	no	—
1321	C₂²×C₄	—	2	1	no	—
1322	C₂²×C₄	—	2	1	no	—
1323	C₂²×C₄	—	2	1	no	—
1324	C₂²×C₄	—	2	1	no	—
1325	C₂²×C₄	—	2	1	no	—
1326	C₂²×C₄	—	2	1	no	—
1327	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1328	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1329	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1330	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1331	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1332	Q₁₆	—	4	1	no	—
1333	Q₁₆	—	4	1	no	—
1334	Q₁₆	—	4	1	no	—
1335	Q₁₆	—	4	1	no	—
1336	SD₁₆	—	2	2	no	—
1337	SD₁₆	—	2	2	no	—
1338	SD₁₆	—	4	1	no	—
1339	SD₁₆	—	4	1	no	—
1340	M₁₆	—	4	1	no	—
1341	M₁₆	—	4	1	no	—
1342	C₂×C₈	—	4	1	no	—
1343	C₂×C₈	—	4	1	no	—
1344	C₂×C₈	—	4	1	no	—
1345	C₂×C₈	—	4	1	no	—
1346	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1347	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1348	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1349	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1350	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1351	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1352	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1353	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1354	C₄⋊C₄	—	2	1	no	—
1355	C₄⋊C₄	—	2	1	no	—
1356	C₄⋊C₄	—	2	1	no	—
1357	C₄⋊C₄	—	2	1	no	—
1358	C₄⋊C₄	—	2	1	no	—
1359	C₄⋊C₄	—	2	1	no	—
1360	C₄⋊C₄	—	2	1	no	—
1361	C₄⋊C₄	—	2	1	no	—
1362	C₄⋊C₄	—	2	1	no	—
1363	C₄⋊C₄	—	2	1	no	—
1364	C₄⋊C₄	—	2	1	no	—
1365	C₄⋊C₄	—	2	1	no	—
1366	C₄⋊C₄	—	2	1	no	—
1367	C₄⋊C₄	—	2	1	no	—
1368	C₄⋊C₄	—	2	1	no	—
1369	C₄⋊C₄	—	2	1	no	—
1370	C₄⋊C₄	—	2	1	no	—
1371	C₄⋊C₄	—	2	1	no	—
1372	C₄⋊C₄	—	2	1	no	—
1373	C₄⋊C₄	—	2	1	no	—
1374	C₄⋊C₄	—	2	1	no	—
1375	C₄⋊C₄	—	2	1	no	—
1376	C₄⋊C₄	—	2	1	no	—
1377	C₄⋊C₄	—	2	1	no	—
1378	C₄⋊C₄	—	2	1	no	—
1379	C₄⋊C₄	—	2	1	no	—
1380	C₄⋊C₄	—	2	1	no	—
1381	C₄⋊C₄	—	2	1	no	—
1382	C₄⋊C₄	—	2	1	no	—
1383	C₄⋊C₄	—	2	1	no	—
1384	C₄⋊C₄	—	2	1	no	—
1385	C₄⋊C₄	—	2	1	no	—
1386	C₄⋊C₄	—	2	1	no	—
1387	C₄⋊C₄	—	2	1	no	—
1388	C₄⋊C₄	—	2	1	no	—
1389	C₄⋊C₄	—	2	1	no	—
1390	C₄⋊C₄	—	2	1	no	—
1391	C₄⋊C₄	—	2	1	no	—
1392	C₄⋊C₄	—	2	1	no	—
1393	C₄⋊C₄	—	2	1	no	—
1394	C₄⋊C₄	—	2	1	no	—
1395	C₄⋊C₄	—	2	1	no	—
1396	C₄⋊C₄	—	2	1	no	—
1397	C₄⋊C₄	—	2	1	no	—
1398	C₄⋊C₄	—	2	1	no	—
1399	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1400	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1401	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1402	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1403	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1404	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1405	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1406	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1407	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1408	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1409	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1410	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1411	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1412	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1413	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1414	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1415	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1416	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1417	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1418	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1419	C₂²⋊C₄	—	2	1	no	—
1420	C₂²⋊C₄	—	2	1	no	—
1421	C₂²⋊C₄	—	2	1	no	—
1422	C₂²⋊C₄	—	2	1	no	—
1423	C₂²⋊C₄	—	2	1	no	—
1424	C₂²⋊C₄	—	2	1	no	—
1425	C₂²⋊C₄	—	2	1	no	—
1426	C₂²⋊C₄	—	2	1	no	—
1427	C₂²⋊C₄	—	2	1	no	—
1428	C₂²⋊C₄	—	2	1	no	—
1429	C₂²⋊C₄	—	2	1	no	—
1430	C₂²⋊C₄	—	2	1	no	—
1431	C₂²⋊C₄	—	2	1	no	—
1432	C₂²⋊C₄	—	2	1	no	—
1433	C₂²⋊C₄	—	2	1	no	—
1434	C₂²⋊C₄	—	2	1	no	—
1435	C₂²⋊C₄	—	2	1	no	—
1436	C₂²⋊C₄	—	2	1	no	—
1437	C₂²⋊C₄	—	2	1	no	—
1438	C₂²⋊C₄	—	2	1	no	—
1439	C₂²⋊C₄	—	2	1	no	—
1440	C₂²⋊C₄	—	2	1	no	—
1441	C₂²⋊C₄	—	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	C₂×D₄×C₅₃	1	1	yes	characteristic
1450	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1451	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1452	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1453	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1454	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1455	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1456	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1457	C₄²	—	2	1	no	—
1458	C₄²	—	2	1	no	—
1459	C₄²	—	2	1	no	—
1460	C₄²	—	2	1	no	—
1461	C₄²	—	2	1	no	—
1462	C₄²	—	2	1	no	—
1463	C₄²	—	2	1	no	—
1464	C₄²	—	2	1	no	—
1465	C₄²	—	2	1	no	—
1466	C₄²	—	2	1	no	—
1467	C₄²	—	2	1	no	—
1468	C₄²	—	2	1	no	—
1469	C₄²	—	2	1	no	—
1470	C₄²	—	2	1	no	—
1471	C₄²	—	2	1	no	—
1472	C₄²	—	2	1	no	—
1473	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1474	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1475	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1476	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1477	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1478	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1479	C₂³	—	2	1	no	—
1480	C₂³	—	2	1	no	—
1481	C₂³	—	4	2	no	—
1482	C₂³	—	8	1	no	—
1483	C₂³	—	8	1	no	—
1484	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1485	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1486	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1487	Q₈	—	2	1	no	—
1488	Q₈	—	2	1	no	—
1489	Q₈	—	2	1	no	—
1490	Q₈	—	2	1	no	—
1491	Q₈	—	2	1	no	—
1492	Q₈	—	2	1	no	—
1493	Q₈	—	2	1	no	—
1494	Q₈	—	2	1	no	—
1495	Q₈	—	4	1	no	—
1496	Q₈	—	4	2	no	—
1497	Q₈	—	8	1	no	—
1498	Q₈	—	8	1	no	—
1499	Q₈	—	8	1	no	—
1500	Q₈	—	8	1	no	—
1501	Q₈	—	8	1	no	—
1502	D₄	—	2	1	no	—
1503	D₄	—	2	1	no	—
1504	D₄	—	2	1	no	—
1505	D₄	—	4	1	no	—
1506	D₄	—	4	1	no	—
1507	D₄	—	4	1	no	—
1508	D₄	—	4	2	no	—
1509	D₄	—	4	2	no	—
1510	D₄	—	4	2	no	—
1511	D₄	—	8	1	no	—
1512	D₄	—	8	1	no	—
1513	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1514	C₂×C₄	—	2	1	no	—
1515	C₂×C₄	—	2	1	no	—
1516	C₂×C₄	—	2	1	no	—
1517	C₂×C₄	—	2	1	no	—
1518	C₂×C₄	—	2	1	no	—
1519	C₂×C₄	—	2	1	no	—
1520	C₂×C₄	—	2	1	no	—
1521	C₂×C₄	—	2	1	no	—
1522	C₂×C₄	—	2	1	no	—
1523	C₂×C₄	—	2	1	no	—
1524	C₂×C₄	—	2	1	no	—
1525	C₂×C₄	—	2	1	no	—
1526	C₂×C₄	—	2	1	no	—
1527	C₂×C₄	—	2	1	no	—
1528	C₂×C₄	—	2	1	no	—
1529	C₂×C₄	—	2	1	no	—
1530	C₂×C₄	—	2	1	no	—
1531	C₂×C₄	—	2	1	no	—
1532	C₂×C₄	—	2	1	no	—
1533	C₂×C₄	—	2	1	no	—
1534	C₂×C₄	—	4	1	no	—
1535	C₂×C₄	—	4	1	no	—
1536	C₂×C₄	—	4	2	no	—
1537	C₂×C₄	—	4	2	no	—
1538	C₂×C₄	—	8	1	no	—
1539	C₂×C₄	—	8	1	no	—
1540	C₂×C₄	—	8	1	no	—
1541	C₂×C₄	—	8	1	no	—
1542	C₂×C₄	—	8	1	no	—
1543	C₂×C₄	—	8	1	no	—
1544	C₂×C₄	—	8	1	no	—
1545	C₂×C₄	—	8	1	no	—
1546	C₂×C₄	—	8	1	no	—
1547	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1548	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1549	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1550	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1551	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1552	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1553	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1554	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1555	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1556	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1557	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1558	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1559	C₈	—	2	1	no	—
1560	C₈	—	2	1	no	—
1561	C₈	—	2	1	no	—
1562	C₈	—	2	1	no	—
1563	C₈	—	2	1	no	—
1564	C₈	—	2	1	no	—
1565	C₈	—	2	1	no	—
1566	C₈	—	2	1	no	—
1567	C₂²	—	2	1	no	—
1568	C₂²	—	2	1	no	—
1569	C₂²	—	2	1	no	—
1570	C₂²	—	2	2	no	—
1571	C₂²	—	2	1	no	—
1572	C₂²	—	2	1	no	—
1573	C₂²	—	2	1	no	—
1574	C₂²	—	2	1	no	—
1575	C₂²	—	2	1	no	—
1576	C₂²	—	2	1	no	—
1577	C₂²	—	4	1	no	—
1578	C₂²	—	4	1	no	—
1579	C₂²	—	4	1	no	—
1580	C₂²	—	4	1	no	—
1581	C₂²	—	4	1	no	—
1582	C₂²	—	16	2	no	—
1583	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1584	C₄	—	2	1	no	—
1585	C₄	—	2	1	no	—
1586	C₄	—	2	1	no	—
1587	C₄	—	2	1	no	—
1588	C₄	—	2	1	no	—
1589	C₄	—	2	1	no	—
1590	C₄	—	2	1	no	—
1591	C₄	—	2	1	no	—
1592	C₄	—	2	1	no	—
1593	C₄	—	2	1	no	—
1594	C₄	—	2	1	no	—
1595	C₄	—	4	1	no	—
1596	C₄	—	4	1	no	—
1597	C₄	—	4	1	no	—
1598	C₄	—	4	1	no	—
1599	C₄	—	4	1	no	—
1600	C₄	—	4	1	no	—
1601	C₄	—	4	1	no	—
1602	C₄	—	4	1	no	—
1603	C₄	—	4	1	no	—
1604	C₄	—	4	1	no	—
1605	C₄	—	4	1	no	—
1606	C₄	—	4	1	no	—
1607	C₄	—	4	1	no	—
1608	C₄	—	4	1	no	—
1609	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1610	C₄	C₅₃×#585	1	1	yes	characteristic
1611	C₂	—	4	1	no	—
1612	C₂	—	4	1	no	—
1613	C₂	—	4	1	no	—
1614	C₂	—	4	2	no	—
1615	C₂	—	8	1	no	—
1616	C₂	C₅₃×#3489	1	1	yes	characteristic
1617	C₂	C₅₃×#3584	1	1	yes	characteristic
1618	C₂	C₅₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅₃
prime radical	C₅₃×#3521	C₂
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×#3555	C₂	semidirect
3. C₅₃×#3388	C₂	semidirect
4. C₅₃×#3385	C₂	semidirect
5. C₅₃×#3377	C₂	semidirect
6. C₅₃×#3369	C₂	semidirect
7. C₅₃×#3350	C₂	semidirect
8. C₅₃×#3349	C₂	semidirect
9. C₅₃×#3349	C₂	semidirect
10. C₅₃×#3344	C₂	semidirect
11. C₅₃×#3342	C₂	semidirect
12. C₅₃×#3337	C₂	semidirect
13. C₅₃×#3315	C₂	semidirect
14. C₅₃×#3314	C₂	semidirect
15. C₅₃×#3311	C₂	semidirect
16. C₅₃×#3311	C₂	semidirect
17. C₅₃×#3302	C₂	semidirect
18. C₅₃×#3296	C₂	semidirect
19. C₅₃×#3261	C₂	semidirect
20. C₅₃×#3258	C₂	semidirect
21. C₅₃×#3248	C₂	semidirect
22. C₅₃×#3243	C₂	semidirect
23. C₅₃×#3242	C₂	semidirect
24. C₅₃×#3240	C₂	semidirect
25. C₅₃×#3123	C₂	semidirect
26. C₅₃×#3120	C₂	semidirect
27. C₅₃×#3116	C₂	semidirect
28. C₅₃×#3084	C₂	semidirect
29. C₅₃×#3081	C₂	semidirect
30. C₅₃×#3076	C₂	semidirect
31. C₅₃×#2992	C₂	semidirect
34. Q₈²×C₅₃	C₂²	semidirect
36. C₅₃×#557	C₂²	semidirect
42. C₅₃×#556	C₂²	semidirect
50. C₅₃×#552	C₂²	semidirect
57. C₅₃×#544	C₂²	semidirect
65. C₅₃×#541	C₂²	semidirect
68. C₅₃×#533	C₂²	semidirect
69. C₅₃×#533	C₂²	semidirect
77. C₅₃×#501	C₂²	semidirect
78. C₅₃×#501	C₂²	semidirect
79. C₅₃×#501	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#500	C₂²	semidirect
82. C₅₃×#499	C₂²	semidirect
83. C₅₃×#491	C₂²	semidirect
88. C₅₃×#487	C₂²	semidirect
93. C₅₃×#485	C₂²	semidirect
94. C₅₃×#485	C₂²	semidirect
95. C₅₃×#485	C₂²	semidirect
96. C₅₃×#485	C₂²	semidirect
97. C₅₃×#485	C₂²	semidirect
99. C₅₃×#484	C₂²	semidirect
100. C₅₃×#484	C₂²	semidirect
102. C₅₃×#483	C₂²	semidirect
107. C₅₃×#479	C₂²	semidirect
108. C₅₃×#479	C₂²	semidirect
109. C₅₃×#479	C₂²	semidirect
110. C₅₃×#479	C₂²	semidirect
111. C₅₃×#479	C₂²	semidirect
112. C₅₃×#479	C₂²	semidirect
113. C₅₃×#479	C₂²	semidirect
114. C₅₃×#479	C₂²	semidirect
115. C₅₃×#479	C₂²	semidirect
123. C₅₃×#477	C₂²	semidirect
124. C₅₃×#477	C₂²	semidirect
125. C₅₃×#477	C₂²	semidirect
130. C₅₃×#475	C₂²	semidirect
131. C₅₃×#475	C₂²	semidirect
132. C₅₃×#475	C₂²	semidirect
133. C₅₃×#475	C₂²	semidirect
139. C₅₃×#470	C₂²	semidirect
143. C₅₃×#467	C₂²	semidirect
144. C₅₃×#467	C₂²	semidirect
145. C₅₃×#467	C₂²	semidirect
153. C₅₃×#462	C₂²	semidirect
154. C₅₃×#462	C₂²	semidirect
155. C₅₃×#462	C₂²	semidirect
156. C₅₃×#462	C₂²	semidirect
165. C₅₃×#446	C₂²	semidirect
166. C₅₃×#446	C₂²	semidirect
167. C₅₃×#441	C₂²	semidirect
168. C₅₃×#441	C₂²	semidirect
169. C₅₃×#441	C₂²	semidirect
175. C₄×Q₁₆×C₅₃	C₂²	semidirect
182. C₅₃×#435	C₂²	semidirect
184. C₈×D₄×C₅₃	C₂²	semidirect
186. C₅₃×#433	C₂²	semidirect
187. C₅₃×#432	C₂²	semidirect
189. C₅₃×#428	C₂²	semidirect
191. C₅₃×#427	C₂²	semidirect
192. C₅₃×#427	C₂²	semidirect
193. C₂×#106×C₅₃	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
757. #62172	C₅₃	direct (N × H)
802. #3555	C₂×C₅₃	semidirect
804. #3388	C₂×C₅₃	semidirect
805. #3385	C₂×C₅₃	semidirect
806. #3377	C₂×C₅₃	semidirect
807. #3369	C₂×C₅₃	semidirect
808. #3350	C₂×C₅₃	semidirect
809. #3349	C₂×C₅₃	semidirect
810. #3349	C₂×C₅₃	semidirect
811. #3344	C₂×C₅₃	semidirect
812. #3342	C₂×C₅₃	semidirect
813. #3337	C₂×C₅₃	semidirect
814. #3315	C₂×C₅₃	semidirect
815. #3314	C₂×C₅₃	semidirect
816. #3311	C₂×C₅₃	semidirect
817. #3311	C₂×C₅₃	semidirect
818. #3302	C₂×C₅₃	semidirect
819. #3296	C₂×C₅₃	semidirect
820. #3261	C₂×C₅₃	semidirect
821. #3258	C₂×C₅₃	semidirect
822. #3248	C₂×C₅₃	semidirect
823. #3243	C₂×C₅₃	semidirect
824. #3242	C₂×C₅₃	semidirect
825. #3240	C₂×C₅₃	semidirect
826. #3123	C₂×C₅₃	semidirect
827. #3120	C₂×C₅₃	semidirect
828. #3116	C₂×C₅₃	semidirect
829. #3084	C₂×C₅₃	semidirect
830. #3081	C₂×C₅₃	semidirect
831. #3076	C₂×C₅₃	semidirect
832. #2992	C₂×C₅₃	semidirect
843. Q₈²	C₂²×C₅₃	semidirect
845. #557	C₂²×C₅₃	semidirect
851. #556	C₂²×C₅₃	semidirect
859. #552	C₂²×C₅₃	semidirect
866. #544	C₂²×C₅₃	semidirect
874. #541	C₂²×C₅₃	semidirect
877. #533	C₂²×C₅₃	semidirect
878. #533	C₂²×C₅₃	semidirect
886. #501	C₂²×C₅₃	semidirect
887. #501	C₂²×C₅₃	semidirect
888. #501	C₂²×C₅₃	semidirect
889. #501	C₂²×C₅₃	semidirect
890. #500	C₂²×C₅₃	semidirect
891. #499	C₂²×C₅₃	semidirect
892. #491	C₂²×C₅₃	semidirect
897. #487	C₂²×C₅₃	semidirect
902. #485	C₂²×C₅₃	semidirect
903. #485	C₂²×C₅₃	semidirect
904. #485	C₂²×C₅₃	semidirect
905. #485	C₂²×C₅₃	semidirect
906. #485	C₂²×C₅₃	semidirect
908. #484	C₂²×C₅₃	semidirect
909. #484	C₂²×C₅₃	semidirect
911. #483	C₂²×C₅₃	semidirect
916. #479	C₂²×C₅₃	semidirect
917. #479	C₂²×C₅₃	semidirect
918. #479	C₂²×C₅₃	semidirect
919. #479	C₂²×C₅₃	semidirect
920. #479	C₂²×C₅₃	semidirect
921. #479	C₂²×C₅₃	semidirect
922. #479	C₂²×C₅₃	semidirect
923. #479	C₂²×C₅₃	semidirect
924. #479	C₂²×C₅₃	semidirect
932. #477	C₂²×C₅₃	semidirect
933. #477	C₂²×C₅₃	semidirect
934. #477	C₂²×C₅₃	semidirect
939. #475	C₂²×C₅₃	semidirect
940. #475	C₂²×C₅₃	semidirect
941. #475	C₂²×C₅₃	semidirect
942. #475	C₂²×C₅₃	semidirect
948. #470	C₂²×C₅₃	semidirect
952. #467	C₂²×C₅₃	semidirect
953. #467	C₂²×C₅₃	semidirect
954. #467	C₂²×C₅₃	semidirect
962. #462	C₂²×C₅₃	semidirect
963. #462	C₂²×C₅₃	semidirect
964. #462	C₂²×C₅₃	semidirect
965. #462	C₂²×C₅₃	semidirect
974. #446	C₂²×C₅₃	semidirect
975. #446	C₂²×C₅₃	semidirect
976. #441	C₂²×C₅₃	semidirect
977. #441	C₂²×C₅₃	semidirect
978. #441	C₂²×C₅₃	semidirect
984. C₄×Q₁₆	C₂²×C₅₃	semidirect
991. #435	C₂²×C₅₃	semidirect
993. C₈×D₄	C₂²×C₅₃	semidirect
995. #433	C₂²×C₅₃	semidirect
996. #432	C₂²×C₅₃	semidirect
998. #428	C₂²×C₅₃	semidirect
1000. #427	C₂²×C₅₃	semidirect
1001. #427	C₂²×C₅₃	semidirect
1002. C₂×#106	C₂²×C₅₃	semidirect
1004. #424	C₂²×C₅₃	semidirect
1005. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
1012. C₅₃	#62172	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×#3555	2
C₅₃×#3521	2
C₅₃×#3388	2
C₅₃×#3385	2
C₅₃×#3377	2
C₅₃×#3369	2
C₅₃×#3350	2
C₅₃×#3349	2
C₅₃×#3344	2
C₅₃×#3342	2
C₅₃×#3337	2
C₅₃×#3315	2
C₅₃×#3314	2
C₅₃×#3311	2
C₅₃×#3302	2
C₅₃×#3296	2
C₅₃×#3261	2
C₅₃×#3258	2
C₅₃×#3248	2
C₅₃×#3243	2
C₅₃×#3242	2
C₅₃×#3240	2
C₅₃×#3123	2
C₅₃×#3120	2
C₅₃×#3116	2
C₅₃×#3084	2
C₅₃×#3081	2
C₅₃×#3076	2
C₅₃×#2992	2
#62172	53

Subgroups — C53×#62172 #27269684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62172 #27269684