Subgroups — C₅₃×#62025 #27269537

Order 13568.

1786 conjugacy classes of subgroups.

The subgroup lattice has 1738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3524	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3403	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3374	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3371	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3321	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3320	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3315	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3309	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3300	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3271	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3271	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3270	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3269	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3263	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3248	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3225	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3221	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3219	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3124	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3121	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3116	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3044	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
33	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
34	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
35	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
36	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
37	C₂²×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
38	C₅₃×#562	—	2	1	no	—
39	C₅₃×#562	—	2	1	no	—
40	C₅₃×#559	—	2	1	no	—
41	C₅₃×#559	—	2	1	no	—
42	C₅₃×#559	C₂²	1	1	yes	characteristic
43	C₅₃×#559	C₂²	1	1	yes	characteristic
44	C₅₃×#557	C₂²	1	1	yes	characteristic
45	C₅₃×#557	C₂²	1	1	yes	characteristic
46	C₅₃×#555	—	2	1	no	—
47	C₅₃×#555	C₂²	1	1	yes	characteristic
48	C₅₃×#554	—	2	1	no	—
49	C₅₃×#553	—	2	1	no	—
50	C₅₃×#553	C₂²	1	1	yes	characteristic
51	C₅₃×#552	—	2	1	no	—
52	C₅₃×#552	C₂²	1	1	yes	characteristic
53	C₅₃×#550	C₂²	1	1	yes	characteristic
54	C₅₃×#550	C₂²	1	1	yes	characteristic
55	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
56	C₅₃×#548	C₂²	1	1	yes	characteristic
57	C₅₃×#548	C₂²	1	1	yes	characteristic
58	C₅₃×#548	C₂²	1	1	yes	characteristic
59	C₅₃×#548	C₂²	1	1	yes	characteristic
60	C₅₃×#547	C₂²	1	1	yes	characteristic
61	C₅₃×#547	C₂²	1	1	yes	characteristic
62	C₅₃×#542	—	2	1	no	—
63	C₅₃×#542	—	2	1	no	—
64	C₅₃×#542	C₂²	1	1	yes	characteristic
65	C₅₃×#542	C₂²	1	1	yes	characteristic
66	C₅₃×#542	C₂²	1	1	yes	characteristic
67	C₅₃×#540	—	2	1	no	—
68	C₅₃×#540	—	2	1	no	—
69	C₅₃×#540	C₂²	1	1	yes	characteristic
70	C₅₃×#539	—	2	1	no	—
71	C₅₃×#539	—	2	1	no	—
72	C₅₃×#536	C₂²	1	1	yes	characteristic
73	C₅₃×#536	C₂²	1	1	yes	characteristic
74	C₅₃×#533	C₂²	1	1	yes	characteristic
75	C₅₃×#532	C₂²	1	1	yes	characteristic
76	C₅₃×#529	—	2	1	no	—
77	C₅₃×#529	—	2	1	no	—
78	C₅₃×#529	C₂²	1	1	yes	characteristic
79	C₅₃×#529	C₂²	1	1	yes	characteristic
80	C₅₃×#520	C₂²	1	1	yes	characteristic
81	C₅₃×#519	C₂²	1	1	yes	characteristic
82	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
83	C₅₃×#497	C₂²	1	1	yes	characteristic
84	C₅₃×#497	C₂²	1	1	yes	characteristic
85	C₅₃×#496	C₂²	1	1	yes	characteristic
86	C₅₃×#496	C₂²	1	1	yes	characteristic
87	C₅₃×#495	C₂²	1	1	yes	characteristic
88	C₅₃×#492	C₂²	1	1	yes	characteristic
89	C₅₃×#491	C₂²	1	1	yes	characteristic
90	C₅₃×#491	C₂²	1	1	yes	characteristic
91	C₅₃×#490	C₂²	1	1	yes	characteristic
92	C₅₃×#489	C₂²	1	1	yes	characteristic
93	C₅₃×#488	C₂²	1	1	yes	characteristic
94	C₅₃×#487	C₂²	1	1	yes	characteristic
95	C₅₃×#485	C₂²	1	1	yes	characteristic
96	C₅₃×#485	C₂²	1	1	yes	characteristic
97	C₅₃×#485	C₂²	1	1	yes	characteristic
98	C₅₃×#484	C₂²	1	1	yes	characteristic
99	C₅₃×#482	C₂²	1	1	yes	characteristic
100	C₅₃×#480	C₂²	1	1	yes	characteristic
101	C₅₃×#479	C₂²	1	1	yes	characteristic
102	C₅₃×#479	C₂²	1	1	yes	characteristic
103	C₅₃×#479	C₂²	1	1	yes	characteristic
104	C₅₃×#478	C₂²	1	1	yes	characteristic
105	C₅₃×#477	C₂²	1	1	yes	characteristic
106	C₅₃×#476	C₂²	1	1	yes	characteristic
107	C₅₃×#476	C₂²	1	1	yes	characteristic
108	C₅₃×#475	C₂²	1	1	yes	characteristic
109	C₅₃×#475	C₂²	1	1	yes	characteristic
110	C₅₃×#474	C₂²	1	1	yes	characteristic
111	C₅₃×#470	C₂²	1	1	yes	characteristic
112	C₅₃×#469	C₂²	1	1	yes	characteristic
113	C₅₃×#469	C₂²	1	1	yes	characteristic
114	C₅₃×#468	C₂²	1	1	yes	characteristic
115	C₅₃×#467	C₂²	1	1	yes	characteristic
116	C₅₃×#467	C₂²	1	1	yes	characteristic
117	C₅₃×#466	C₂²	1	1	yes	characteristic
118	C₅₃×#465	C₂²	1	1	yes	characteristic
119	C₅₃×#465	C₂²	1	1	yes	characteristic
120	C₅₃×#465	C₂²	1	1	yes	characteristic
121	C₅₃×#465	C₂²	1	1	yes	characteristic
122	C₅₃×#465	C₂²	1	1	yes	characteristic
123	C₅₃×#464	C₂²	1	1	yes	characteristic
124	C₅₃×#464	C₂²	1	1	yes	characteristic
125	C₅₃×#464	C₂²	1	1	yes	characteristic
126	C₅₃×#464	C₂²	1	1	yes	characteristic
127	C₅₃×#464	C₂²	1	1	yes	characteristic
128	C₅₃×#464	C₂²	1	1	yes	characteristic
129	C₅₃×#464	C₂²	1	1	yes	characteristic
130	C₅₃×#464	C₂²	1	1	yes	characteristic
131	C₅₃×#464	C₂²	1	1	yes	characteristic
132	C₅₃×#464	C₂²	1	1	yes	characteristic
133	C₅₃×#463	C₂²	1	1	yes	characteristic
134	C₅₃×#463	C₂²	1	1	yes	characteristic
135	C₅₃×#463	C₂²	1	1	yes	characteristic
136	C₅₃×#463	C₂²	1	1	yes	characteristic
137	C₅₃×#463	C₂²	1	1	yes	characteristic
138	C₅₃×#463	C₂²	1	1	yes	characteristic
139	C₅₃×#462	C₂²	1	1	yes	characteristic
140	C₅₃×#462	C₂²	1	1	yes	characteristic
141	C₅₃×#462	C₂²	1	1	yes	characteristic
142	C₅₃×#462	C₂²	1	1	yes	characteristic
143	C₅₃×#462	C₂²	1	1	yes	characteristic
144	C₅₃×#462	C₂²	1	1	yes	characteristic
145	C₅₃×#461	C₂²	1	1	yes	characteristic
146	C₅₃×#461	C₂²	1	1	yes	characteristic
147	C₅₃×#461	C₂²	1	1	yes	characteristic
148	C₅₃×#461	C₂²	1	1	yes	characteristic
149	C₅₃×#460	C₂²	1	1	yes	characteristic
150	C₅₃×#460	C₂²	1	1	yes	characteristic
151	C₅₃×#459	C₂²	1	1	yes	characteristic
152	C₅₃×#459	C₂²	1	1	yes	characteristic
153	C₅₃×#452	C₂²	1	1	yes	characteristic
154	C₅₃×#452	C₂²	1	1	yes	characteristic
155	C₅₃×#452	C₂²	1	1	yes	characteristic
156	C₅₃×#452	C₂²	1	1	yes	characteristic
157	C₅₃×#452	C₂²	1	1	yes	characteristic
158	C₅₃×#452	C₂²	1	1	yes	characteristic
159	C₅₃×#451	C₂²	1	1	yes	characteristic
160	C₅₃×#451	C₂²	1	1	yes	characteristic
161	C₅₃×#449	C₂²	1	1	yes	characteristic
162	C₅₃×#449	C₂²	1	1	yes	characteristic
163	C₅₃×#449	C₂²	1	1	yes	characteristic
164	C₅₃×#449	C₂²	1	1	yes	characteristic
165	C₅₃×#449	C₂²	1	1	yes	characteristic
166	C₅₃×#449	C₂²	1	1	yes	characteristic
167	C₅₃×#448	C₂²	1	1	yes	characteristic
168	C₅₃×#448	C₂²	1	1	yes	characteristic
169	C₅₃×#448	C₂²	1	1	yes	characteristic
170	C₅₃×#448	C₂²	1	1	yes	characteristic
171	C₅₃×#446	C₂²	1	1	yes	characteristic
172	C₅₃×#446	C₂²	1	1	yes	characteristic
173	C₅₃×#441	C₂²	1	1	yes	characteristic
174	C₅₃×#441	C₂²	1	1	yes	characteristic
175	C₅₃×#441	C₂²	1	1	yes	characteristic
176	C₅₃×#440	C₂²	1	1	yes	characteristic
177	C₅₃×#440	C₂²	1	1	yes	characteristic
178	C₅₃×#440	C₂²	1	1	yes	characteristic
179	C₅₃×#440	C₂²	1	1	yes	characteristic
180	C₅₃×#440	C₂²	1	1	yes	characteristic
181	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
182	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
183	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
184	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
185	C₅₃×#435	C₂²	1	1	yes	characteristic
186	C₅₃×#435	C₂²	1	1	yes	characteristic
187	C₅₃×#435	C₂²	1	1	yes	characteristic
188	C₅₃×#435	C₂²	1	1	yes	characteristic
189	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
190	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
191	C₅₃×#433	C₂²	1	1	yes	characteristic
192	C₅₃×#433	C₂²	1	1	yes	characteristic
193	C₅₃×#432	C₂²	1	1	yes	characteristic
194	C₅₃×#424	C₂²	1	1	yes	characteristic
195	C₅₃×#424	C₂²	1	1	yes	characteristic
196	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
197	C₅₃×#419	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×#103×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	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
206	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
207	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
208	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
211	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
212	#137×C₅₃	—	4	2	no	—
213	#137×C₅₃	—	4	2	no	—
214	#135×C₅₃	—	4	2	no	—
215	#135×C₅₃	—	4	2	no	—
216	#135×C₅₃	—	4	2	no	—
217	C₂×Q₁₆×C₅₃	—	4	2	no	—
218	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
225	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
226	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
227	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
228	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
229	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
230	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
231	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
232	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
233	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
234	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
235	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
238	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
243	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
244	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
245	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
246	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
248	C₄⋊Q₈×C₅₃	—	2	1	no	—
249	C₄⋊Q₈×C₅₃	—	2	1	no	—
250	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
254	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
256	#127×C₅₃	—	2	1	no	—
257	#127×C₅₃	—	2	1	no	—
258	#127×C₅₃	C₂³	1	1	yes	characteristic
259	#127×C₅₃	C₂³	1	1	yes	characteristic
260	#126×C₅₃	—	2	1	no	—
261	#126×C₅₃	—	2	1	no	—
262	#126×C₅₃	—	2	1	no	—
263	#126×C₅₃	—	2	1	no	—
264	#126×C₅₃	—	2	1	no	—
265	#126×C₅₃	—	2	1	no	—
266	#126×C₅₃	D₄	1	1	yes	characteristic
267	#126×C₅₃	D₄	1	1	yes	characteristic
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	—	2	1	no	—
274	#125×C₅₃	—	2	1	no	—
275	#125×C₅₃	D₄	1	1	yes	characteristic
276	#125×C₅₃	C₂³	1	1	yes	characteristic
277	#125×C₅₃	C₂³	1	1	yes	characteristic
278	#124×C₅₃	—	2	1	no	—
279	#124×C₅₃	—	2	1	no	—
280	#124×C₅₃	—	2	1	no	—
281	#124×C₅₃	—	2	1	no	—
282	#124×C₅₃	—	2	1	no	—
283	#124×C₅₃	—	2	1	no	—
284	#124×C₅₃	—	2	1	no	—
285	#124×C₅₃	—	2	1	no	—
286	#124×C₅₃	—	2	1	no	—
287	#124×C₅₃	—	2	1	no	—
288	#124×C₅₃	—	2	1	no	—
289	#124×C₅₃	D₄	1	1	yes	characteristic
290	#124×C₅₃	C₂³	1	1	yes	characteristic
291	#124×C₅₃	C₂³	1	1	yes	characteristic
292	#124×C₅₃	C₂³	1	1	yes	characteristic
293	#124×C₅₃	C₂³	1	1	yes	characteristic
294	#124×C₅₃	C₂³	1	1	yes	characteristic
295	#124×C₅₃	C₂³	1	1	yes	characteristic
296	#123×C₅₃	—	2	1	no	—
297	#123×C₅₃	—	2	1	no	—
298	#123×C₅₃	—	2	1	no	—
299	#123×C₅₃	—	2	1	no	—
300	#123×C₅₃	—	2	1	no	—
301	#123×C₅₃	—	2	1	no	—
302	#123×C₅₃	—	2	1	no	—
303	#123×C₅₃	—	2	1	no	—
304	#123×C₅₃	—	2	1	no	—
305	#123×C₅₃	—	2	1	no	—
306	#123×C₅₃	—	2	1	no	—
307	#123×C₅₃	—	2	1	no	—
308	#123×C₅₃	—	2	1	no	—
309	#123×C₅₃	—	2	1	no	—
310	#123×C₅₃	—	2	1	no	—
311	#123×C₅₃	—	2	1	no	—
312	#123×C₅₃	—	2	1	no	—
313	#123×C₅₃	—	2	1	no	—
314	#123×C₅₃	—	2	1	no	—
315	#123×C₅₃	—	2	1	no	—
316	#123×C₅₃	D₄	1	1	yes	characteristic
317	#123×C₅₃	D₄	1	1	yes	characteristic
318	C₂²⋊Q₈×C₅₃	—	2	1	no	—
319	C₂²⋊Q₈×C₅₃	—	2	1	no	—
320	C₂²⋊Q₈×C₅₃	—	2	1	no	—
321	C₂²⋊Q₈×C₅₃	—	2	1	no	—
322	C₂²⋊Q₈×C₅₃	—	2	1	no	—
323	C₂²⋊Q₈×C₅₃	—	2	1	no	—
324	C₂²⋊Q₈×C₅₃	—	2	1	no	—
325	C₂²⋊Q₈×C₅₃	—	2	1	no	—
326	C₂²⋊Q₈×C₅₃	—	2	1	no	—
327	C₂²⋊Q₈×C₅₃	—	2	1	no	—
328	C₂²⋊Q₈×C₅₃	—	2	1	no	—
329	C₂²⋊Q₈×C₅₃	—	2	1	no	—
330	C₂²⋊Q₈×C₅₃	—	2	1	no	—
331	C₂²⋊Q₈×C₅₃	—	2	1	no	—
332	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
333	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
334	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
335	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
336	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
337	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
338	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
339	#121×C₅₃	—	2	1	no	—
340	#121×C₅₃	—	2	1	no	—
341	#121×C₅₃	—	2	1	no	—
342	#121×C₅₃	—	2	1	no	—
343	#121×C₅₃	—	2	1	no	—
344	#121×C₅₃	—	2	1	no	—
345	#121×C₅₃	—	2	1	no	—
346	#121×C₅₃	—	2	1	no	—
347	#121×C₅₃	—	2	1	no	—
348	#121×C₅₃	—	2	1	no	—
349	#121×C₅₃	—	2	1	no	—
350	#121×C₅₃	—	2	1	no	—
351	#121×C₅₃	—	2	1	no	—
352	#121×C₅₃	—	2	1	no	—
353	#121×C₅₃	—	2	1	no	—
354	#121×C₅₃	—	2	1	no	—
355	#121×C₅₃	D₄	1	1	yes	characteristic
356	#121×C₅₃	C₂³	1	1	yes	characteristic
357	#121×C₅₃	C₂³	1	1	yes	characteristic
358	#121×C₅₃	C₂³	1	1	yes	characteristic
359	#121×C₅₃	C₂³	1	1	yes	characteristic
360	#121×C₅₃	C₂³	1	1	yes	characteristic
361	#121×C₅₃	C₂³	1	1	yes	characteristic
362	C₄×Q₈×C₅₃	—	2	1	no	—
363	C₄×Q₈×C₅₃	—	2	1	no	—
364	C₄×Q₈×C₅₃	—	2	1	no	—
365	C₄×Q₈×C₅₃	—	2	1	no	—
366	C₄×Q₈×C₅₃	—	2	1	no	—
367	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
376	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
377	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
378	C₄×D₄×C₅₃	—	2	1	no	—
379	C₄×D₄×C₅₃	—	2	1	no	—
380	C₄×D₄×C₅₃	—	2	1	no	—
381	C₄×D₄×C₅₃	—	2	1	no	—
382	C₄×D₄×C₅₃	—	2	1	no	—
383	C₄×D₄×C₅₃	—	2	1	no	—
384	C₄×D₄×C₅₃	—	2	1	no	—
385	C₄×D₄×C₅₃	—	2	1	no	—
386	C₄×D₄×C₅₃	—	2	1	no	—
387	C₄×D₄×C₅₃	—	2	1	no	—
388	C₄×D₄×C₅₃	—	2	1	no	—
389	C₄×D₄×C₅₃	—	2	1	no	—
390	C₄×D₄×C₅₃	—	2	1	no	—
391	C₄×D₄×C₅₃	—	2	1	no	—
392	C₄×D₄×C₅₃	—	2	1	no	—
393	C₄×D₄×C₅₃	—	2	1	no	—
394	C₄×D₄×C₅₃	—	2	1	no	—
395	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
396	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
397	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
398	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
399	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
400	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
401	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
402	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
403	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
404	#117×C₅₃	—	2	1	no	—
405	#117×C₅₃	—	2	1	no	—
406	#117×C₅₃	—	2	1	no	—
407	#117×C₅₃	—	2	1	no	—
408	#117×C₅₃	—	2	1	no	—
409	#117×C₅₃	—	2	1	no	—
410	#117×C₅₃	—	2	1	no	—
411	#117×C₅₃	—	2	1	no	—
412	#117×C₅₃	C₂³	1	1	yes	characteristic
413	#117×C₅₃	C₂³	1	1	yes	characteristic
414	#117×C₅₃	C₂³	1	1	yes	characteristic
415	#117×C₅₃	C₂³	1	1	yes	characteristic
416	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
419	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
420	C₂×C₄²×C₅₃	—	2	1	no	—
421	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
422	#107×C₅₃	C₂³	1	1	yes	characteristic
423	#107×C₅₃	C₂³	1	1	yes	characteristic
424	#107×C₅₃	C₂³	1	1	yes	characteristic
425	#107×C₅₃	C₂³	1	1	yes	characteristic
426	#106×C₅₃	C₂³	1	1	yes	characteristic
427	#106×C₅₃	C₂³	1	1	yes	characteristic
428	#106×C₅₃	C₂³	1	1	yes	characteristic
429	#106×C₅₃	C₂³	1	1	yes	characteristic
430	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
431	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
432	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
433	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
434	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
435	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
436	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
437	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
438	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
439	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
440	#103×C₅₃	C₂³	1	1	yes	characteristic
441	#103×C₅₃	C₂³	1	1	yes	characteristic
442	#103×C₅₃	C₂³	1	1	yes	characteristic
443	#103×C₅₃	C₂³	1	1	yes	characteristic
444	#103×C₅₃	C₂³	1	1	yes	characteristic
445	#103×C₅₃	C₂³	1	1	yes	characteristic
446	#103×C₅₃	C₂³	1	1	yes	characteristic
447	#103×C₅₃	C₂³	1	1	yes	characteristic
448	#103×C₅₃	C₂³	1	1	yes	characteristic
449	#103×C₅₃	C₂³	1	1	yes	characteristic
450	#103×C₅₃	C₂³	1	1	yes	characteristic
451	#103×C₅₃	C₂³	1	1	yes	characteristic
452	#103×C₅₃	C₂³	1	1	yes	characteristic
453	#103×C₅₃	C₂³	1	1	yes	characteristic
454	#103×C₅₃	C₂³	1	1	yes	characteristic
455	#103×C₅₃	C₂³	1	1	yes	characteristic
456	#103×C₅₃	C₂³	1	1	yes	characteristic
457	#103×C₅₃	C₂³	1	1	yes	characteristic
458	#103×C₅₃	C₂³	1	1	yes	characteristic
459	#103×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#102×C₅₃	C₂³	1	1	yes	characteristic
466	#102×C₅₃	C₂³	1	1	yes	characteristic
467	#102×C₅₃	C₂³	1	1	yes	characteristic
468	#102×C₅₃	C₂³	1	1	yes	characteristic
469	#102×C₅₃	C₂³	1	1	yes	characteristic
470	#102×C₅₃	C₂³	1	1	yes	characteristic
471	#102×C₅₃	C₂³	1	1	yes	characteristic
472	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
473	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
474	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
475	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
476	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
477	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
478	#97×C₅₃	C₂³	1	1	yes	characteristic
479	#97×C₅₃	C₂³	1	1	yes	characteristic
480	#97×C₅₃	C₂³	1	1	yes	characteristic
481	#97×C₅₃	C₂³	1	1	yes	characteristic
482	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
483	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
484	#41×C₅₃	—	2	2	no	—
485	#41×C₅₃	—	2	2	no	—
486	#41×C₅₃	—	4	1	no	—
487	#41×C₅₃	—	4	1	no	—
488	#41×C₅₃	—	4	1	no	—
489	#41×C₅₃	—	4	1	no	—
490	#41×C₅₃	—	4	1	no	—
491	#41×C₅₃	—	4	1	no	—
492	#41×C₅₃	—	4	1	no	—
493	#41×C₅₃	—	4	1	no	—
494	#41×C₅₃	—	4	1	no	—
495	#41×C₅₃	—	4	1	no	—
496	C₂×Q₈×C₅₃	—	2	1	no	—
497	C₂×Q₈×C₅₃	—	2	1	no	—
498	C₂×Q₈×C₅₃	—	2	1	no	—
499	C₂×Q₈×C₅₃	—	2	1	no	—
500	C₂×Q₈×C₅₃	—	2	1	no	—
501	C₂×Q₈×C₅₃	—	2	2	no	—
502	C₂×Q₈×C₅₃	—	4	1	no	—
503	C₂×Q₈×C₅₃	—	4	1	no	—
504	C₂×Q₈×C₅₃	—	4	1	no	—
505	C₂×Q₈×C₅₃	—	4	1	no	—
506	C₂×Q₈×C₅₃	—	4	1	no	—
507	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
508	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
509	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
510	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
511	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
512	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
513	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
514	C₂×D₄×C₅₃	—	2	1	no	—
515	C₂×D₄×C₅₃	—	2	1	no	—
516	C₂×D₄×C₅₃	—	2	1	no	—
517	C₂×D₄×C₅₃	—	2	1	no	—
518	C₂×D₄×C₅₃	—	2	1	no	—
519	C₂×D₄×C₅₃	—	2	1	no	—
520	C₂×D₄×C₅₃	—	2	1	no	—
521	C₂×D₄×C₅₃	—	2	1	no	—
522	C₂×D₄×C₅₃	—	2	1	no	—
523	C₂×D₄×C₅₃	—	2	1	no	—
524	C₂×D₄×C₅₃	—	2	1	no	—
525	C₂×D₄×C₅₃	—	2	1	no	—
526	C₂×D₄×C₅₃	—	2	1	no	—
527	C₂×D₄×C₅₃	—	2	1	no	—
528	C₂×D₄×C₅₃	—	2	1	no	—
529	C₂×D₄×C₅₃	—	2	1	no	—
530	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
531	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
532	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
533	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
534	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
535	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
536	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
537	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	—	2	1	no	—
548	C₂²×C₄×C₅₃	—	2	1	no	—
549	C₂²×C₄×C₅₃	—	2	1	no	—
550	C₂²×C₄×C₅₃	—	2	1	no	—
551	C₂²×C₄×C₅₃	—	2	1	no	—
552	C₂²×C₄×C₅₃	—	2	1	no	—
553	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
554	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
555	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
556	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
557	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
558	Q₁₆×C₅₃	—	2	2	no	—
559	Q₁₆×C₅₃	—	2	2	no	—
560	Q₁₆×C₅₃	—	2	2	no	—
561	Q₁₆×C₅₃	—	2	2	no	—
562	Q₁₆×C₅₃	—	4	1	no	—
563	Q₁₆×C₅₃	—	4	1	no	—
564	Q₁₆×C₅₃	—	4	1	no	—
565	Q₁₆×C₅₃	—	4	1	no	—
566	SD₁₆×C₅₃	—	2	2	no	—
567	SD₁₆×C₅₃	—	2	2	no	—
568	SD₁₆×C₅₃	—	4	1	no	—
569	SD₁₆×C₅₃	—	4	1	no	—
570	SD₁₆×C₅₃	—	4	1	no	—
571	SD₁₆×C₅₃	—	4	1	no	—
572	SD₁₆×C₅₃	—	4	1	no	—
573	SD₁₆×C₅₃	—	4	1	no	—
574	SD₁₆×C₅₃	—	4	1	no	—
575	SD₁₆×C₅₃	—	4	1	no	—
576	SD₁₆×C₅₃	—	4	1	no	—
577	SD₁₆×C₅₃	—	4	1	no	—
578	D₈×C₅₃	—	4	1	no	—
579	D₈×C₅₃	—	4	1	no	—
580	D₈×C₅₃	—	4	1	no	—
581	D₈×C₅₃	—	4	1	no	—
582	M₁₆×C₅₃	—	4	1	no	—
583	M₁₆×C₅₃	—	4	1	no	—
584	C₂×C₈×C₅₃	—	4	1	no	—
585	C₂×C₈×C₅₃	—	4	1	no	—
586	C₂×C₈×C₅₃	—	4	1	no	—
587	C₂×C₈×C₅₃	—	4	1	no	—
588	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
589	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
590	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
591	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
592	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
593	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
594	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
595	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
606	C₄⋊C₄×C₅₃	—	2	1	no	—
607	C₄⋊C₄×C₅₃	—	2	1	no	—
608	C₄⋊C₄×C₅₃	—	2	1	no	—
609	C₄⋊C₄×C₅₃	—	2	1	no	—
610	C₄⋊C₄×C₅₃	—	2	1	no	—
611	C₄⋊C₄×C₅₃	—	2	1	no	—
612	C₄⋊C₄×C₅₃	—	2	1	no	—
613	C₄⋊C₄×C₅₃	—	2	1	no	—
614	C₄⋊C₄×C₅₃	—	2	1	no	—
615	C₄⋊C₄×C₅₃	—	2	1	no	—
616	C₄⋊C₄×C₅₃	—	2	1	no	—
617	C₄⋊C₄×C₅₃	—	2	1	no	—
618	C₄⋊C₄×C₅₃	—	2	1	no	—
619	C₄⋊C₄×C₅₃	—	2	1	no	—
620	C₄⋊C₄×C₅₃	—	2	1	no	—
621	C₄⋊C₄×C₅₃	—	2	1	no	—
622	C₄⋊C₄×C₅₃	—	2	1	no	—
623	C₄⋊C₄×C₅₃	—	2	1	no	—
624	C₄⋊C₄×C₅₃	—	2	1	no	—
625	C₄⋊C₄×C₅₃	—	2	1	no	—
626	C₄⋊C₄×C₅₃	—	2	1	no	—
627	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
628	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
629	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
630	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
631	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
632	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
633	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
634	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
635	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
636	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
637	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
638	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
639	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
640	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
641	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
642	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	—	2	1	no	—
651	C₂²⋊C₄×C₅₃	—	2	1	no	—
652	C₂²⋊C₄×C₅₃	—	2	1	no	—
653	C₂²⋊C₄×C₅₃	—	2	1	no	—
654	C₂²⋊C₄×C₅₃	—	2	1	no	—
655	C₂²⋊C₄×C₅₃	—	2	1	no	—
656	C₂²⋊C₄×C₅₃	—	2	1	no	—
657	C₂²⋊C₄×C₅₃	—	2	1	no	—
658	C₂²⋊C₄×C₅₃	—	2	1	no	—
659	C₂²⋊C₄×C₅₃	—	2	1	no	—
660	C₂²⋊C₄×C₅₃	—	2	1	no	—
661	C₂²⋊C₄×C₅₃	—	2	1	no	—
662	C₂²⋊C₄×C₅₃	—	2	1	no	—
663	C₂²⋊C₄×C₅₃	—	2	1	no	—
664	C₂²⋊C₄×C₅₃	—	2	1	no	—
665	C₂²⋊C₄×C₅₃	—	2	1	no	—
666	C₂²⋊C₄×C₅₃	—	2	1	no	—
667	C₂²⋊C₄×C₅₃	—	2	1	no	—
668	C₂²⋊C₄×C₅₃	—	2	1	no	—
669	C₂²⋊C₄×C₅₃	—	2	1	no	—
670	C₂²⋊C₄×C₅₃	—	2	1	no	—
671	C₂²⋊C₄×C₅₃	—	2	1	no	—
672	C₂²⋊C₄×C₅₃	—	2	1	no	—
673	C₂²⋊C₄×C₅₃	—	2	1	no	—
674	C₂²⋊C₄×C₅₃	—	2	1	no	—
675	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
676	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
677	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
678	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
679	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
680	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
681	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
682	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
683	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
684	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
685	C₄²×C₅₃	—	2	1	no	—
686	C₄²×C₅₃	—	2	1	no	—
687	C₄²×C₅₃	—	2	1	no	—
688	C₄²×C₅₃	—	2	1	no	—
689	C₄²×C₅₃	—	2	1	no	—
690	C₄²×C₅₃	—	2	1	no	—
691	C₄²×C₅₃	—	2	1	no	—
692	C₄²×C₅₃	—	2	1	no	—
693	C₄²×C₅₃	—	2	1	no	—
694	C₄²×C₅₃	—	2	1	no	—
695	C₄²×C₅₃	—	2	1	no	—
696	C₄²×C₅₃	—	2	1	no	—
697	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
698	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
699	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
700	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
701	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
702	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
703	C₂³×C₅₃	—	2	1	no	—
704	C₂³×C₅₃	—	2	1	no	—
705	C₂³×C₅₃	—	2	1	no	—
706	C₂³×C₅₃	—	2	1	no	—
707	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
708	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
709	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
710	Q₈×C₅₃	—	2	1	no	—
711	Q₈×C₅₃	—	2	1	no	—
712	Q₈×C₅₃	—	2	1	no	—
713	Q₈×C₅₃	—	2	1	no	—
714	Q₈×C₅₃	—	2	1	no	—
715	Q₈×C₅₃	—	2	1	no	—
716	Q₈×C₅₃	—	2	1	no	—
717	Q₈×C₅₃	—	2	1	no	—
718	Q₈×C₅₃	—	2	1	no	—
719	Q₈×C₅₃	—	2	1	no	—
720	Q₈×C₅₃	—	2	1	no	—
721	Q₈×C₅₃	—	4	1	no	—
722	Q₈×C₅₃	—	4	2	no	—
723	Q₈×C₅₃	—	8	1	no	—
724	Q₈×C₅₃	—	8	1	no	—
725	Q₈×C₅₃	—	8	1	no	—
726	Q₈×C₅₃	—	8	1	no	—
727	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
728	D₄×C₅₃	—	2	1	no	—
729	D₄×C₅₃	—	2	1	no	—
730	D₄×C₅₃	—	2	1	no	—
731	D₄×C₅₃	—	2	1	no	—
732	D₄×C₅₃	—	2	1	no	—
733	D₄×C₅₃	—	2	1	no	—
734	D₄×C₅₃	—	2	1	no	—
735	D₄×C₅₃	—	2	1	no	—
736	D₄×C₅₃	—	4	1	no	—
737	D₄×C₅₃	—	4	1	no	—
738	D₄×C₅₃	—	4	1	no	—
739	D₄×C₅₃	—	4	2	no	—
740	D₄×C₅₃	—	4	2	no	—
741	D₄×C₅₃	—	4	2	no	—
742	D₄×C₅₃	—	8	1	no	—
743	D₄×C₅₃	—	8	1	no	—
744	D₄×C₅₃	—	8	1	no	—
745	D₄×C₅₃	—	8	1	no	—
746	D₄×C₅₃	—	8	1	no	—
747	D₄×C₅₃	—	8	1	no	—
748	D₄×C₅₃	—	8	1	no	—
749	D₄×C₅₃	—	8	1	no	—
750	D₄×C₅₃	—	8	1	no	—
751	D₄×C₅₃	—	8	1	no	—
752	D₄×C₅₃	—	8	1	no	—
753	D₄×C₅₃	—	8	1	no	—
754	D₄×C₅₃	—	8	1	no	—
755	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	—	2	1	no	—
762	C₂×C₄×C₅₃	—	2	1	no	—
763	C₂×C₄×C₅₃	—	2	1	no	—
764	C₂×C₄×C₅₃	—	2	1	no	—
765	C₂×C₄×C₅₃	—	2	1	no	—
766	C₂×C₄×C₅₃	—	2	1	no	—
767	C₂×C₄×C₅₃	—	2	1	no	—
768	C₂×C₄×C₅₃	—	2	1	no	—
769	C₂×C₄×C₅₃	—	2	1	no	—
770	C₂×C₄×C₅₃	—	2	1	no	—
771	C₂×C₄×C₅₃	—	2	1	no	—
772	C₂×C₄×C₅₃	—	2	1	no	—
773	C₂×C₄×C₅₃	—	4	1	no	—
774	C₂×C₄×C₅₃	—	4	1	no	—
775	C₂×C₄×C₅₃	—	4	2	no	—
776	C₂×C₄×C₅₃	—	4	2	no	—
777	C₂×C₄×C₅₃	—	4	2	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	—	8	1	no	—
782	C₂×C₄×C₅₃	—	8	1	no	—
783	C₂×C₄×C₅₃	—	8	1	no	—
784	C₂×C₄×C₅₃	—	8	1	no	—
785	C₂×C₄×C₅₃	—	8	1	no	—
786	C₂×C₄×C₅₃	—	8	1	no	—
787	C₂×C₄×C₅₃	—	8	1	no	—
788	C₂×C₄×C₅₃	—	8	1	no	—
789	C₂×C₄×C₅₃	—	8	1	no	—
790	C₂×C₄×C₅₃	—	8	1	no	—
791	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
792	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
793	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
794	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
795	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
796	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
797	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
798	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
799	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
800	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
801	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
802	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
803	C₈×C₅₃	—	2	1	no	—
804	C₈×C₅₃	—	2	1	no	—
805	C₈×C₅₃	—	2	1	no	—
806	C₈×C₅₃	—	2	1	no	—
807	C₈×C₅₃	—	2	1	no	—
808	C₈×C₅₃	—	2	1	no	—
809	C₈×C₅₃	—	2	1	no	—
810	C₈×C₅₃	—	2	1	no	—
811	#62025	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
812	C₂²×C₅₃	—	2	1	no	—
813	C₂²×C₅₃	—	2	1	no	—
814	C₂²×C₅₃	—	2	1	no	—
815	C₂²×C₅₃	—	2	1	no	—
816	C₂²×C₅₃	—	2	1	no	—
817	C₂²×C₅₃	—	2	1	no	—
818	C₂²×C₅₃	—	2	1	no	—
819	C₂²×C₅₃	—	2	1	no	—
820	C₂²×C₅₃	—	2	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	—	4	1	no	—
827	C₂²×C₅₃	—	4	1	no	—
828	C₂²×C₅₃	—	4	1	no	—
829	C₂²×C₅₃	—	4	1	no	—
830	C₂²×C₅₃	—	4	1	no	—
831	C₂²×C₅₃	—	4	1	no	—
832	C₂²×C₅₃	—	4	1	no	—
833	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
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	—	2	1	no	—
842	C₄×C₅₃	—	2	1	no	—
843	C₄×C₅₃	—	2	1	no	—
844	C₄×C₅₃	—	2	1	no	—
845	C₄×C₅₃	—	2	2	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	—	4	1	no	—
853	C₄×C₅₃	—	4	1	no	—
854	C₄×C₅₃	—	4	1	no	—
855	C₄×C₅₃	—	4	1	no	—
856	C₄×C₅₃	—	4	1	no	—
857	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
858	C₄×C₅₃	#585	1	1	yes	characteristic
859	#3554	C₂×C₅₃	1	1	yes	characteristic, complemented
860	#3524	C₂×C₅₃	1	1	yes	characteristic, complemented
861	#3403	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#3400	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#3374	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#3371	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#3321	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#3320	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#3315	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#3309	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
870	#3300	C₂×C₅₃	1	1	yes	characteristic, complemented
871	#3285	C₂×C₅₃	1	1	yes	characteristic, complemented
872	#3284	C₂×C₅₃	1	1	yes	characteristic, complemented
873	#3271	C₂×C₅₃	1	1	yes	characteristic, complemented
874	#3271	C₂×C₅₃	1	1	yes	characteristic, complemented
875	#3270	C₂×C₅₃	1	1	yes	characteristic, complemented
876	#3269	C₂×C₅₃	1	1	yes	characteristic, complemented
877	#3263	C₂×C₅₃	1	1	yes	characteristic, complemented
878	#3257	C₂×C₅₃	1	1	yes	characteristic, complemented
879	#3248	C₂×C₅₃	1	1	yes	characteristic, complemented
880	#3225	C₂×C₅₃	1	1	yes	characteristic, complemented
881	#3221	C₂×C₅₃	1	1	yes	characteristic, complemented
882	#3219	C₂×C₅₃	1	1	yes	characteristic, complemented
883	#3124	C₂×C₅₃	1	1	yes	characteristic, complemented
884	#3121	C₂×C₅₃	1	1	yes	characteristic, complemented
885	#3116	C₂×C₅₃	1	1	yes	characteristic, complemented
886	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
887	#3044	C₂×C₅₃	1	1	yes	characteristic, complemented
888	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
889	#2992	C₂×C₅₃	1	1	yes	characteristic, complemented
890	C₂×C₅₃	—	4	1	no	—
891	C₂×C₅₃	—	4	1	no	—
892	C₂×C₅₃	—	4	1	no	—
893	C₂×C₅₃	—	8	1	no	—
894	C₂×C₅₃	—	8	1	no	—
895	C₂×C₅₃	—	8	1	no	—
896	C₂×C₅₃	—	8	1	no	—
897	C₂×C₅₃	#3488	1	1	yes	characteristic
898	C₂×C₅₃	#3584	1	1	yes	characteristic
899	C₂×C₅₃	#3586	1	1	yes	characteristic
900	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
901	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
902	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
903	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
904	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
905	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
906	#562	—	2	1	no	—
907	#562	—	2	1	no	—
908	#559	—	2	1	no	—
909	#559	—	2	1	no	—
910	#559	C₂²×C₅₃	1	1	yes	characteristic
911	#559	C₂²×C₅₃	1	1	yes	characteristic
912	#557	C₂²×C₅₃	1	1	yes	characteristic
913	#557	C₂²×C₅₃	1	1	yes	characteristic
914	#555	—	2	1	no	—
915	#555	C₂²×C₅₃	1	1	yes	characteristic
916	#554	—	2	1	no	—
917	#553	—	2	1	no	—
918	#553	C₂²×C₅₃	1	1	yes	characteristic
919	#552	—	2	1	no	—
920	#552	C₂²×C₅₃	1	1	yes	characteristic
921	#550	C₂²×C₅₃	1	1	yes	characteristic
922	#550	C₂²×C₅₃	1	1	yes	characteristic
923	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
924	#548	C₂²×C₅₃	1	1	yes	characteristic
925	#548	C₂²×C₅₃	1	1	yes	characteristic
926	#548	C₂²×C₅₃	1	1	yes	characteristic
927	#548	C₂²×C₅₃	1	1	yes	characteristic
928	#547	C₂²×C₅₃	1	1	yes	characteristic
929	#547	C₂²×C₅₃	1	1	yes	characteristic
930	#542	—	2	1	no	—
931	#542	—	2	1	no	—
932	#542	C₂²×C₅₃	1	1	yes	characteristic
933	#542	C₂²×C₅₃	1	1	yes	characteristic
934	#542	C₂²×C₅₃	1	1	yes	characteristic
935	#540	—	2	1	no	—
936	#540	—	2	1	no	—
937	#540	C₂²×C₅₃	1	1	yes	characteristic
938	#539	—	2	1	no	—
939	#539	—	2	1	no	—
940	#536	C₂²×C₅₃	1	1	yes	characteristic
941	#536	C₂²×C₅₃	1	1	yes	characteristic
942	#533	C₂²×C₅₃	1	1	yes	characteristic
943	#532	C₂²×C₅₃	1	1	yes	characteristic
944	#529	—	2	1	no	—
945	#529	—	2	1	no	—
946	#529	C₂²×C₅₃	1	1	yes	characteristic
947	#529	C₂²×C₅₃	1	1	yes	characteristic
948	#520	C₂²×C₅₃	1	1	yes	characteristic
949	#519	C₂²×C₅₃	1	1	yes	characteristic
950	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
951	#497	C₂²×C₅₃	1	1	yes	characteristic
952	#497	C₂²×C₅₃	1	1	yes	characteristic
953	#496	C₂²×C₅₃	1	1	yes	characteristic
954	#496	C₂²×C₅₃	1	1	yes	characteristic
955	#495	C₂²×C₅₃	1	1	yes	characteristic
956	#492	C₂²×C₅₃	1	1	yes	characteristic
957	#491	C₂²×C₅₃	1	1	yes	characteristic
958	#491	C₂²×C₅₃	1	1	yes	characteristic
959	#490	C₂²×C₅₃	1	1	yes	characteristic
960	#489	C₂²×C₅₃	1	1	yes	characteristic
961	#488	C₂²×C₅₃	1	1	yes	characteristic
962	#487	C₂²×C₅₃	1	1	yes	characteristic
963	#485	C₂²×C₅₃	1	1	yes	characteristic
964	#485	C₂²×C₅₃	1	1	yes	characteristic
965	#485	C₂²×C₅₃	1	1	yes	characteristic
966	#484	C₂²×C₅₃	1	1	yes	characteristic
967	#482	C₂²×C₅₃	1	1	yes	characteristic
968	#480	C₂²×C₅₃	1	1	yes	characteristic
969	#479	C₂²×C₅₃	1	1	yes	characteristic
970	#479	C₂²×C₅₃	1	1	yes	characteristic
971	#479	C₂²×C₅₃	1	1	yes	characteristic
972	#478	C₂²×C₅₃	1	1	yes	characteristic
973	#477	C₂²×C₅₃	1	1	yes	characteristic
974	#476	C₂²×C₅₃	1	1	yes	characteristic
975	#476	C₂²×C₅₃	1	1	yes	characteristic
976	#475	C₂²×C₅₃	1	1	yes	characteristic
977	#475	C₂²×C₅₃	1	1	yes	characteristic
978	#474	C₂²×C₅₃	1	1	yes	characteristic
979	#470	C₂²×C₅₃	1	1	yes	characteristic
980	#469	C₂²×C₅₃	1	1	yes	characteristic
981	#469	C₂²×C₅₃	1	1	yes	characteristic
982	#468	C₂²×C₅₃	1	1	yes	characteristic
983	#467	C₂²×C₅₃	1	1	yes	characteristic
984	#467	C₂²×C₅₃	1	1	yes	characteristic
985	#466	C₂²×C₅₃	1	1	yes	characteristic
986	#465	C₂²×C₅₃	1	1	yes	characteristic
987	#465	C₂²×C₅₃	1	1	yes	characteristic
988	#465	C₂²×C₅₃	1	1	yes	characteristic
989	#465	C₂²×C₅₃	1	1	yes	characteristic
990	#465	C₂²×C₅₃	1	1	yes	characteristic
991	#464	C₂²×C₅₃	1	1	yes	characteristic
992	#464	C₂²×C₅₃	1	1	yes	characteristic
993	#464	C₂²×C₅₃	1	1	yes	characteristic
994	#464	C₂²×C₅₃	1	1	yes	characteristic
995	#464	C₂²×C₅₃	1	1	yes	characteristic
996	#464	C₂²×C₅₃	1	1	yes	characteristic
997	#464	C₂²×C₅₃	1	1	yes	characteristic
998	#464	C₂²×C₅₃	1	1	yes	characteristic
999	#464	C₂²×C₅₃	1	1	yes	characteristic
1000	#464	C₂²×C₅₃	1	1	yes	characteristic
1001	#463	C₂²×C₅₃	1	1	yes	characteristic
1002	#463	C₂²×C₅₃	1	1	yes	characteristic
1003	#463	C₂²×C₅₃	1	1	yes	characteristic
1004	#463	C₂²×C₅₃	1	1	yes	characteristic
1005	#463	C₂²×C₅₃	1	1	yes	characteristic
1006	#463	C₂²×C₅₃	1	1	yes	characteristic
1007	#462	C₂²×C₅₃	1	1	yes	characteristic
1008	#462	C₂²×C₅₃	1	1	yes	characteristic
1009	#462	C₂²×C₅₃	1	1	yes	characteristic
1010	#462	C₂²×C₅₃	1	1	yes	characteristic
1011	#462	C₂²×C₅₃	1	1	yes	characteristic
1012	#462	C₂²×C₅₃	1	1	yes	characteristic
1013	#461	C₂²×C₅₃	1	1	yes	characteristic
1014	#461	C₂²×C₅₃	1	1	yes	characteristic
1015	#461	C₂²×C₅₃	1	1	yes	characteristic
1016	#461	C₂²×C₅₃	1	1	yes	characteristic
1017	#460	C₂²×C₅₃	1	1	yes	characteristic
1018	#460	C₂²×C₅₃	1	1	yes	characteristic
1019	#459	C₂²×C₅₃	1	1	yes	characteristic
1020	#459	C₂²×C₅₃	1	1	yes	characteristic
1021	#452	C₂²×C₅₃	1	1	yes	characteristic
1022	#452	C₂²×C₅₃	1	1	yes	characteristic
1023	#452	C₂²×C₅₃	1	1	yes	characteristic
1024	#452	C₂²×C₅₃	1	1	yes	characteristic
1025	#452	C₂²×C₅₃	1	1	yes	characteristic
1026	#452	C₂²×C₅₃	1	1	yes	characteristic
1027	#451	C₂²×C₅₃	1	1	yes	characteristic
1028	#451	C₂²×C₅₃	1	1	yes	characteristic
1029	#449	C₂²×C₅₃	1	1	yes	characteristic
1030	#449	C₂²×C₅₃	1	1	yes	characteristic
1031	#449	C₂²×C₅₃	1	1	yes	characteristic
1032	#449	C₂²×C₅₃	1	1	yes	characteristic
1033	#449	C₂²×C₅₃	1	1	yes	characteristic
1034	#449	C₂²×C₅₃	1	1	yes	characteristic
1035	#448	C₂²×C₅₃	1	1	yes	characteristic
1036	#448	C₂²×C₅₃	1	1	yes	characteristic
1037	#448	C₂²×C₅₃	1	1	yes	characteristic
1038	#448	C₂²×C₅₃	1	1	yes	characteristic
1039	#446	C₂²×C₅₃	1	1	yes	characteristic
1040	#446	C₂²×C₅₃	1	1	yes	characteristic
1041	#441	C₂²×C₅₃	1	1	yes	characteristic
1042	#441	C₂²×C₅₃	1	1	yes	characteristic
1043	#441	C₂²×C₅₃	1	1	yes	characteristic
1044	#440	C₂²×C₅₃	1	1	yes	characteristic
1045	#440	C₂²×C₅₃	1	1	yes	characteristic
1046	#440	C₂²×C₅₃	1	1	yes	characteristic
1047	#440	C₂²×C₅₃	1	1	yes	characteristic
1048	#440	C₂²×C₅₃	1	1	yes	characteristic
1049	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
1050	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
1051	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
1052	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1053	#435	C₂²×C₅₃	1	1	yes	characteristic
1054	#435	C₂²×C₅₃	1	1	yes	characteristic
1055	#435	C₂²×C₅₃	1	1	yes	characteristic
1056	#435	C₂²×C₅₃	1	1	yes	characteristic
1057	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1058	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
1059	#433	C₂²×C₅₃	1	1	yes	characteristic
1060	#433	C₂²×C₅₃	1	1	yes	characteristic
1061	#432	C₂²×C₅₃	1	1	yes	characteristic
1062	#424	C₂²×C₅₃	1	1	yes	characteristic
1063	#424	C₂²×C₅₃	1	1	yes	characteristic
1064	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
1065	#419	C₂²×C₅₃	1	1	yes	characteristic
1066	#417	C₂²×C₅₃	1	1	yes	characteristic
1067	#416	C₂²×C₅₃	1	1	yes	characteristic
1068	#416	C₂²×C₅₃	1	1	yes	characteristic
1069	#416	C₂²×C₅₃	1	1	yes	characteristic
1070	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
1071	C₅₃	#62025	1	1	yes	characteristic, direct product factor, Sylow
1072	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1076	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1077	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
1078	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1079	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1080	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1081	#137	—	4	2	no	—
1082	#137	—	4	2	no	—
1083	#135	—	4	2	no	—
1084	#135	—	4	2	no	—
1085	#135	—	4	2	no	—
1086	C₂×Q₁₆	—	4	2	no	—
1087	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1088	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1089	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1090	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1091	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1092	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1093	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1094	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
1095	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1096	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1097	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1098	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1099	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1100	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1101	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1102	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1103	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1104	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1105	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1106	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1107	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1108	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1109	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1110	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1111	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1112	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1113	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1114	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1115	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1116	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1117	C₄⋊Q₈	—	2	1	no	—
1118	C₄⋊Q₈	—	2	1	no	—
1119	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1120	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1121	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1122	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1123	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1124	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1125	#127	—	2	1	no	—
1126	#127	—	2	1	no	—
1127	#127	C₂³×C₅₃	1	1	yes	characteristic
1128	#127	C₂³×C₅₃	1	1	yes	characteristic
1129	#126	—	2	1	no	—
1130	#126	—	2	1	no	—
1131	#126	—	2	1	no	—
1132	#126	—	2	1	no	—
1133	#126	—	2	1	no	—
1134	#126	—	2	1	no	—
1135	#126	D₄×C₅₃	1	1	yes	characteristic
1136	#126	D₄×C₅₃	1	1	yes	characteristic
1137	#125	—	2	1	no	—
1138	#125	—	2	1	no	—
1139	#125	—	2	1	no	—
1140	#125	—	2	1	no	—
1141	#125	—	2	1	no	—
1142	#125	—	2	1	no	—
1143	#125	—	2	1	no	—
1144	#125	D₄×C₅₃	1	1	yes	characteristic
1145	#125	C₂³×C₅₃	1	1	yes	characteristic
1146	#125	C₂³×C₅₃	1	1	yes	characteristic
1147	#124	—	2	1	no	—
1148	#124	—	2	1	no	—
1149	#124	—	2	1	no	—
1150	#124	—	2	1	no	—
1151	#124	—	2	1	no	—
1152	#124	—	2	1	no	—
1153	#124	—	2	1	no	—
1154	#124	—	2	1	no	—
1155	#124	—	2	1	no	—
1156	#124	—	2	1	no	—
1157	#124	—	2	1	no	—
1158	#124	D₄×C₅₃	1	1	yes	characteristic
1159	#124	C₂³×C₅₃	1	1	yes	characteristic
1160	#124	C₂³×C₅₃	1	1	yes	characteristic
1161	#124	C₂³×C₅₃	1	1	yes	characteristic
1162	#124	C₂³×C₅₃	1	1	yes	characteristic
1163	#124	C₂³×C₅₃	1	1	yes	characteristic
1164	#124	C₂³×C₅₃	1	1	yes	characteristic
1165	#123	—	2	1	no	—
1166	#123	—	2	1	no	—
1167	#123	—	2	1	no	—
1168	#123	—	2	1	no	—
1169	#123	—	2	1	no	—
1170	#123	—	2	1	no	—
1171	#123	—	2	1	no	—
1172	#123	—	2	1	no	—
1173	#123	—	2	1	no	—
1174	#123	—	2	1	no	—
1175	#123	—	2	1	no	—
1176	#123	—	2	1	no	—
1177	#123	—	2	1	no	—
1178	#123	—	2	1	no	—
1179	#123	—	2	1	no	—
1180	#123	—	2	1	no	—
1181	#123	—	2	1	no	—
1182	#123	—	2	1	no	—
1183	#123	—	2	1	no	—
1184	#123	—	2	1	no	—
1185	#123	D₄×C₅₃	1	1	yes	characteristic
1186	#123	D₄×C₅₃	1	1	yes	characteristic
1187	C₂²⋊Q₈	—	2	1	no	—
1188	C₂²⋊Q₈	—	2	1	no	—
1189	C₂²⋊Q₈	—	2	1	no	—
1190	C₂²⋊Q₈	—	2	1	no	—
1191	C₂²⋊Q₈	—	2	1	no	—
1192	C₂²⋊Q₈	—	2	1	no	—
1193	C₂²⋊Q₈	—	2	1	no	—
1194	C₂²⋊Q₈	—	2	1	no	—
1195	C₂²⋊Q₈	—	2	1	no	—
1196	C₂²⋊Q₈	—	2	1	no	—
1197	C₂²⋊Q₈	—	2	1	no	—
1198	C₂²⋊Q₈	—	2	1	no	—
1199	C₂²⋊Q₈	—	2	1	no	—
1200	C₂²⋊Q₈	—	2	1	no	—
1201	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1202	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1203	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1204	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1205	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1206	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1207	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1208	#121	—	2	1	no	—
1209	#121	—	2	1	no	—
1210	#121	—	2	1	no	—
1211	#121	—	2	1	no	—
1212	#121	—	2	1	no	—
1213	#121	—	2	1	no	—
1214	#121	—	2	1	no	—
1215	#121	—	2	1	no	—
1216	#121	—	2	1	no	—
1217	#121	—	2	1	no	—
1218	#121	—	2	1	no	—
1219	#121	—	2	1	no	—
1220	#121	—	2	1	no	—
1221	#121	—	2	1	no	—
1222	#121	—	2	1	no	—
1223	#121	—	2	1	no	—
1224	#121	D₄×C₅₃	1	1	yes	characteristic
1225	#121	C₂³×C₅₃	1	1	yes	characteristic
1226	#121	C₂³×C₅₃	1	1	yes	characteristic
1227	#121	C₂³×C₅₃	1	1	yes	characteristic
1228	#121	C₂³×C₅₃	1	1	yes	characteristic
1229	#121	C₂³×C₅₃	1	1	yes	characteristic
1230	#121	C₂³×C₅₃	1	1	yes	characteristic
1231	C₄×Q₈	—	2	1	no	—
1232	C₄×Q₈	—	2	1	no	—
1233	C₄×Q₈	—	2	1	no	—
1234	C₄×Q₈	—	2	1	no	—
1235	C₄×Q₈	—	2	1	no	—
1236	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1237	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1238	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1239	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1240	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1241	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1242	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1243	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1244	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1245	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1246	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1247	C₄×D₄	—	2	1	no	—
1248	C₄×D₄	—	2	1	no	—
1249	C₄×D₄	—	2	1	no	—
1250	C₄×D₄	—	2	1	no	—
1251	C₄×D₄	—	2	1	no	—
1252	C₄×D₄	—	2	1	no	—
1253	C₄×D₄	—	2	1	no	—
1254	C₄×D₄	—	2	1	no	—
1255	C₄×D₄	—	2	1	no	—
1256	C₄×D₄	—	2	1	no	—
1257	C₄×D₄	—	2	1	no	—
1258	C₄×D₄	—	2	1	no	—
1259	C₄×D₄	—	2	1	no	—
1260	C₄×D₄	—	2	1	no	—
1261	C₄×D₄	—	2	1	no	—
1262	C₄×D₄	—	2	1	no	—
1263	C₄×D₄	—	2	1	no	—
1264	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1265	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1266	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1267	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1268	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1269	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1270	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1271	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1272	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1273	#117	—	2	1	no	—
1274	#117	—	2	1	no	—
1275	#117	—	2	1	no	—
1276	#117	—	2	1	no	—
1277	#117	—	2	1	no	—
1278	#117	—	2	1	no	—
1279	#117	—	2	1	no	—
1280	#117	—	2	1	no	—
1281	#117	C₂³×C₅₃	1	1	yes	characteristic
1282	#117	C₂³×C₅₃	1	1	yes	characteristic
1283	#117	C₂³×C₅₃	1	1	yes	characteristic
1284	#117	C₂³×C₅₃	1	1	yes	characteristic
1285	C₂×C₄⋊C₄	—	2	1	no	—
1286	C₂×C₄⋊C₄	—	2	1	no	—
1287	C₂×C₄⋊C₄	—	2	1	no	—
1288	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1289	C₂×C₄²	—	2	1	no	—
1290	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1291	#107	C₂³×C₅₃	1	1	yes	characteristic
1292	#107	C₂³×C₅₃	1	1	yes	characteristic
1293	#107	C₂³×C₅₃	1	1	yes	characteristic
1294	#107	C₂³×C₅₃	1	1	yes	characteristic
1295	#106	C₂³×C₅₃	1	1	yes	characteristic
1296	#106	C₂³×C₅₃	1	1	yes	characteristic
1297	#106	C₂³×C₅₃	1	1	yes	characteristic
1298	#106	C₂³×C₅₃	1	1	yes	characteristic
1299	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1300	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1301	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1302	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1303	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1304	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1305	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1306	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1307	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1308	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1309	#103	C₂³×C₅₃	1	1	yes	characteristic
1310	#103	C₂³×C₅₃	1	1	yes	characteristic
1311	#103	C₂³×C₅₃	1	1	yes	characteristic
1312	#103	C₂³×C₅₃	1	1	yes	characteristic
1313	#103	C₂³×C₅₃	1	1	yes	characteristic
1314	#103	C₂³×C₅₃	1	1	yes	characteristic
1315	#103	C₂³×C₅₃	1	1	yes	characteristic
1316	#103	C₂³×C₅₃	1	1	yes	characteristic
1317	#103	C₂³×C₅₃	1	1	yes	characteristic
1318	#103	C₂³×C₅₃	1	1	yes	characteristic
1319	#103	C₂³×C₅₃	1	1	yes	characteristic
1320	#103	C₂³×C₅₃	1	1	yes	characteristic
1321	#103	C₂³×C₅₃	1	1	yes	characteristic
1322	#103	C₂³×C₅₃	1	1	yes	characteristic
1323	#103	C₂³×C₅₃	1	1	yes	characteristic
1324	#103	C₂³×C₅₃	1	1	yes	characteristic
1325	#103	C₂³×C₅₃	1	1	yes	characteristic
1326	#103	C₂³×C₅₃	1	1	yes	characteristic
1327	#103	C₂³×C₅₃	1	1	yes	characteristic
1328	#103	C₂³×C₅₃	1	1	yes	characteristic
1329	#102	C₂³×C₅₃	1	1	yes	characteristic
1330	#102	C₂³×C₅₃	1	1	yes	characteristic
1331	#102	C₂³×C₅₃	1	1	yes	characteristic
1332	#102	C₂³×C₅₃	1	1	yes	characteristic
1333	#102	C₂³×C₅₃	1	1	yes	characteristic
1334	#102	C₂³×C₅₃	1	1	yes	characteristic
1335	#102	C₂³×C₅₃	1	1	yes	characteristic
1336	#102	C₂³×C₅₃	1	1	yes	characteristic
1337	#102	C₂³×C₅₃	1	1	yes	characteristic
1338	#102	C₂³×C₅₃	1	1	yes	characteristic
1339	#102	C₂³×C₅₃	1	1	yes	characteristic
1340	#102	C₂³×C₅₃	1	1	yes	characteristic
1341	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1342	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1343	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1344	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1345	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1346	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1347	#97	C₂³×C₅₃	1	1	yes	characteristic
1348	#97	C₂³×C₅₃	1	1	yes	characteristic
1349	#97	C₂³×C₅₃	1	1	yes	characteristic
1350	#97	C₂³×C₅₃	1	1	yes	characteristic
1351	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1352	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1353	#41	—	2	2	no	—
1354	#41	—	2	2	no	—
1355	#41	—	4	1	no	—
1356	#41	—	4	1	no	—
1357	#41	—	4	1	no	—
1358	#41	—	4	1	no	—
1359	#41	—	4	1	no	—
1360	#41	—	4	1	no	—
1361	#41	—	4	1	no	—
1362	#41	—	4	1	no	—
1363	#41	—	4	1	no	—
1364	#41	—	4	1	no	—
1365	C₂×Q₈	—	2	1	no	—
1366	C₂×Q₈	—	2	1	no	—
1367	C₂×Q₈	—	2	1	no	—
1368	C₂×Q₈	—	2	1	no	—
1369	C₂×Q₈	—	2	1	no	—
1370	C₂×Q₈	—	2	2	no	—
1371	C₂×Q₈	—	4	1	no	—
1372	C₂×Q₈	—	4	1	no	—
1373	C₂×Q₈	—	4	1	no	—
1374	C₂×Q₈	—	4	1	no	—
1375	C₂×Q₈	—	4	1	no	—
1376	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1377	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1378	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1379	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1380	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1381	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1382	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1383	C₂×D₄	—	2	1	no	—
1384	C₂×D₄	—	2	1	no	—
1385	C₂×D₄	—	2	1	no	—
1386	C₂×D₄	—	2	1	no	—
1387	C₂×D₄	—	2	1	no	—
1388	C₂×D₄	—	2	1	no	—
1389	C₂×D₄	—	2	1	no	—
1390	C₂×D₄	—	2	1	no	—
1391	C₂×D₄	—	2	1	no	—
1392	C₂×D₄	—	2	1	no	—
1393	C₂×D₄	—	2	1	no	—
1394	C₂×D₄	—	2	1	no	—
1395	C₂×D₄	—	2	1	no	—
1396	C₂×D₄	—	2	1	no	—
1397	C₂×D₄	—	2	1	no	—
1398	C₂×D₄	—	2	1	no	—
1399	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1400	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1401	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1402	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1403	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1404	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1405	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1413	C₂²×C₄	—	2	1	no	—
1414	C₂²×C₄	—	2	1	no	—
1415	C₂²×C₄	—	2	1	no	—
1416	C₂²×C₄	—	2	1	no	—
1417	C₂²×C₄	—	2	1	no	—
1418	C₂²×C₄	—	2	1	no	—
1419	C₂²×C₄	—	2	1	no	—
1420	C₂²×C₄	—	2	1	no	—
1421	C₂²×C₄	—	2	1	no	—
1422	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1423	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1424	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1425	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1426	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1427	Q₁₆	—	2	2	no	—
1428	Q₁₆	—	2	2	no	—
1429	Q₁₆	—	2	2	no	—
1430	Q₁₆	—	2	2	no	—
1431	Q₁₆	—	4	1	no	—
1432	Q₁₆	—	4	1	no	—
1433	Q₁₆	—	4	1	no	—
1434	Q₁₆	—	4	1	no	—
1435	SD₁₆	—	2	2	no	—
1436	SD₁₆	—	2	2	no	—
1437	SD₁₆	—	4	1	no	—
1438	SD₁₆	—	4	1	no	—
1439	SD₁₆	—	4	1	no	—
1440	SD₁₆	—	4	1	no	—
1441	SD₁₆	—	4	1	no	—
1442	SD₁₆	—	4	1	no	—
1443	SD₁₆	—	4	1	no	—
1444	SD₁₆	—	4	1	no	—
1445	SD₁₆	—	4	1	no	—
1446	SD₁₆	—	4	1	no	—
1447	D₈	—	4	1	no	—
1448	D₈	—	4	1	no	—
1449	D₈	—	4	1	no	—
1450	D₈	—	4	1	no	—
1451	M₁₆	—	4	1	no	—
1452	M₁₆	—	4	1	no	—
1453	C₂×C₈	—	4	1	no	—
1454	C₂×C₈	—	4	1	no	—
1455	C₂×C₈	—	4	1	no	—
1456	C₂×C₈	—	4	1	no	—
1457	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1458	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1459	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1460	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1461	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1462	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1463	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1464	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1471	C₄⋊C₄	—	2	1	no	—
1472	C₄⋊C₄	—	2	1	no	—
1473	C₄⋊C₄	—	2	1	no	—
1474	C₄⋊C₄	—	2	1	no	—
1475	C₄⋊C₄	—	2	1	no	—
1476	C₄⋊C₄	—	2	1	no	—
1477	C₄⋊C₄	—	2	1	no	—
1478	C₄⋊C₄	—	2	1	no	—
1479	C₄⋊C₄	—	2	1	no	—
1480	C₄⋊C₄	—	2	1	no	—
1481	C₄⋊C₄	—	2	1	no	—
1482	C₄⋊C₄	—	2	1	no	—
1483	C₄⋊C₄	—	2	1	no	—
1484	C₄⋊C₄	—	2	1	no	—
1485	C₄⋊C₄	—	2	1	no	—
1486	C₄⋊C₄	—	2	1	no	—
1487	C₄⋊C₄	—	2	1	no	—
1488	C₄⋊C₄	—	2	1	no	—
1489	C₄⋊C₄	—	2	1	no	—
1490	C₄⋊C₄	—	2	1	no	—
1491	C₄⋊C₄	—	2	1	no	—
1492	C₄⋊C₄	—	2	1	no	—
1493	C₄⋊C₄	—	2	1	no	—
1494	C₄⋊C₄	—	2	1	no	—
1495	C₄⋊C₄	—	2	1	no	—
1496	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1497	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1498	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1499	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1500	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1501	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1502	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1503	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1504	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1505	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1506	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1507	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1508	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1509	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1510	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1511	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
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	—	2	1	no	—
1528	C₂²⋊C₄	—	2	1	no	—
1529	C₂²⋊C₄	—	2	1	no	—
1530	C₂²⋊C₄	—	2	1	no	—
1531	C₂²⋊C₄	—	2	1	no	—
1532	C₂²⋊C₄	—	2	1	no	—
1533	C₂²⋊C₄	—	2	1	no	—
1534	C₂²⋊C₄	—	2	1	no	—
1535	C₂²⋊C₄	—	2	1	no	—
1536	C₂²⋊C₄	—	2	1	no	—
1537	C₂²⋊C₄	—	2	1	no	—
1538	C₂²⋊C₄	—	2	1	no	—
1539	C₂²⋊C₄	—	2	1	no	—
1540	C₂²⋊C₄	—	2	1	no	—
1541	C₂²⋊C₄	—	2	1	no	—
1542	C₂²⋊C₄	—	2	1	no	—
1543	C₂²⋊C₄	—	2	1	no	—
1544	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1545	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1546	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1547	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1548	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1549	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1550	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1551	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1552	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1553	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1554	C₄²	—	2	1	no	—
1555	C₄²	—	2	1	no	—
1556	C₄²	—	2	1	no	—
1557	C₄²	—	2	1	no	—
1558	C₄²	—	2	1	no	—
1559	C₄²	—	2	1	no	—
1560	C₄²	—	2	1	no	—
1561	C₄²	—	2	1	no	—
1562	C₄²	—	2	1	no	—
1563	C₄²	—	2	1	no	—
1564	C₄²	—	2	1	no	—
1565	C₄²	—	2	1	no	—
1566	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1567	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1568	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1569	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1570	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1571	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1572	C₂³	—	2	1	no	—
1573	C₂³	—	2	1	no	—
1574	C₂³	—	2	1	no	—
1575	C₂³	—	2	1	no	—
1576	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1577	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1578	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1579	Q₈	—	2	1	no	—
1580	Q₈	—	2	1	no	—
1581	Q₈	—	2	1	no	—
1582	Q₈	—	2	1	no	—
1583	Q₈	—	2	1	no	—
1584	Q₈	—	2	1	no	—
1585	Q₈	—	2	1	no	—
1586	Q₈	—	2	1	no	—
1587	Q₈	—	2	1	no	—
1588	Q₈	—	2	1	no	—
1589	Q₈	—	2	1	no	—
1590	Q₈	—	4	1	no	—
1591	Q₈	—	4	2	no	—
1592	Q₈	—	8	1	no	—
1593	Q₈	—	8	1	no	—
1594	Q₈	—	8	1	no	—
1595	Q₈	—	8	1	no	—
1596	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1597	D₄	—	2	1	no	—
1598	D₄	—	2	1	no	—
1599	D₄	—	2	1	no	—
1600	D₄	—	2	1	no	—
1601	D₄	—	2	1	no	—
1602	D₄	—	2	1	no	—
1603	D₄	—	2	1	no	—
1604	D₄	—	2	1	no	—
1605	D₄	—	4	1	no	—
1606	D₄	—	4	1	no	—
1607	D₄	—	4	1	no	—
1608	D₄	—	4	2	no	—
1609	D₄	—	4	2	no	—
1610	D₄	—	4	2	no	—
1611	D₄	—	8	1	no	—
1612	D₄	—	8	1	no	—
1613	D₄	—	8	1	no	—
1614	D₄	—	8	1	no	—
1615	D₄	—	8	1	no	—
1616	D₄	—	8	1	no	—
1617	D₄	—	8	1	no	—
1618	D₄	—	8	1	no	—
1619	D₄	—	8	1	no	—
1620	D₄	—	8	1	no	—
1621	D₄	—	8	1	no	—
1622	D₄	—	8	1	no	—
1623	D₄	—	8	1	no	—
1624	C₂×C₄	—	2	1	no	—
1625	C₂×C₄	—	2	1	no	—
1626	C₂×C₄	—	2	1	no	—
1627	C₂×C₄	—	2	1	no	—
1628	C₂×C₄	—	2	1	no	—
1629	C₂×C₄	—	2	1	no	—
1630	C₂×C₄	—	2	1	no	—
1631	C₂×C₄	—	2	1	no	—
1632	C₂×C₄	—	2	1	no	—
1633	C₂×C₄	—	2	1	no	—
1634	C₂×C₄	—	2	1	no	—
1635	C₂×C₄	—	2	1	no	—
1636	C₂×C₄	—	2	1	no	—
1637	C₂×C₄	—	2	1	no	—
1638	C₂×C₄	—	2	1	no	—
1639	C₂×C₄	—	2	1	no	—
1640	C₂×C₄	—	2	1	no	—
1641	C₂×C₄	—	2	1	no	—
1642	C₂×C₄	—	4	1	no	—
1643	C₂×C₄	—	4	1	no	—
1644	C₂×C₄	—	4	2	no	—
1645	C₂×C₄	—	4	2	no	—
1646	C₂×C₄	—	4	2	no	—
1647	C₂×C₄	—	8	1	no	—
1648	C₂×C₄	—	8	1	no	—
1649	C₂×C₄	—	8	1	no	—
1650	C₂×C₄	—	8	1	no	—
1651	C₂×C₄	—	8	1	no	—
1652	C₂×C₄	—	8	1	no	—
1653	C₂×C₄	—	8	1	no	—
1654	C₂×C₄	—	8	1	no	—
1655	C₂×C₄	—	8	1	no	—
1656	C₂×C₄	—	8	1	no	—
1657	C₂×C₄	—	8	1	no	—
1658	C₂×C₄	—	8	1	no	—
1659	C₂×C₄	—	8	1	no	—
1660	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1661	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1662	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1663	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1664	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1665	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1666	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1667	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1668	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1669	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1670	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1671	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1672	C₈	—	2	1	no	—
1673	C₈	—	2	1	no	—
1674	C₈	—	2	1	no	—
1675	C₈	—	2	1	no	—
1676	C₈	—	2	1	no	—
1677	C₈	—	2	1	no	—
1678	C₈	—	2	1	no	—
1679	C₈	—	2	1	no	—
1680	C₂²	—	2	1	no	—
1681	C₂²	—	2	1	no	—
1682	C₂²	—	2	1	no	—
1683	C₂²	—	2	1	no	—
1684	C₂²	—	2	1	no	—
1685	C₂²	—	2	1	no	—
1686	C₂²	—	2	1	no	—
1687	C₂²	—	2	1	no	—
1688	C₂²	—	2	1	no	—
1689	C₂²	—	4	1	no	—
1690	C₂²	—	4	1	no	—
1691	C₂²	—	4	1	no	—
1692	C₂²	—	4	1	no	—
1693	C₂²	—	4	1	no	—
1694	C₂²	—	4	1	no	—
1695	C₂²	—	4	1	no	—
1696	C₂²	—	4	1	no	—
1697	C₂²	—	4	1	no	—
1698	C₂²	—	4	1	no	—
1699	C₂²	—	4	1	no	—
1700	C₂²	—	4	1	no	—
1701	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1702	C₄	—	2	1	no	—
1703	C₄	—	2	1	no	—
1704	C₄	—	2	1	no	—
1705	C₄	—	2	2	no	—
1706	C₄	—	2	1	no	—
1707	C₄	—	2	1	no	—
1708	C₄	—	2	1	no	—
1709	C₄	—	2	1	no	—
1710	C₄	—	2	1	no	—
1711	C₄	—	2	1	no	—
1712	C₄	—	2	1	no	—
1713	C₄	—	2	1	no	—
1714	C₄	—	4	1	no	—
1715	C₄	—	4	1	no	—
1716	C₄	—	4	1	no	—
1717	C₄	—	4	1	no	—
1718	C₄	—	4	1	no	—
1719	C₄	—	4	1	no	—
1720	C₄	—	4	1	no	—
1721	C₄	—	4	1	no	—
1722	C₄	—	4	1	no	—
1723	C₄	—	4	1	no	—
1724	C₄	—	4	1	no	—
1725	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1726	C₄	C₅₃×#585	1	1	yes	characteristic
1727	C₂	—	4	1	no	—
1728	C₂	—	4	1	no	—
1729	C₂	—	4	1	no	—
1730	C₂	—	8	1	no	—
1731	C₂	—	8	1	no	—
1732	C₂	—	8	1	no	—
1733	C₂	—	8	1	no	—
1734	C₂	C₅₃×#3488	1	1	yes	characteristic
1735	C₂	C₅₃×#3584	1	1	yes	characteristic
1736	C₂	C₅₃×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3554	C₂	semidirect
2. C₅₃×#3524	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3400	C₂	semidirect
5. C₅₃×#3374	C₂	semidirect
6. C₅₃×#3371	C₂	semidirect
7. C₅₃×#3321	C₂	semidirect
8. C₅₃×#3320	C₂	semidirect
9. C₅₃×#3315	C₂	semidirect
10. C₅₃×#3309	C₂	semidirect
11. C₅₃×#3303	C₂	semidirect
12. C₅₃×#3300	C₂	semidirect
13. C₅₃×#3285	C₂	semidirect
14. C₅₃×#3284	C₂	semidirect
15. C₅₃×#3271	C₂	semidirect
16. C₅₃×#3271	C₂	semidirect
17. C₅₃×#3270	C₂	semidirect
18. C₅₃×#3269	C₂	semidirect
19. C₅₃×#3263	C₂	semidirect
20. C₅₃×#3257	C₂	semidirect
21. C₅₃×#3248	C₂	semidirect
22. C₅₃×#3225	C₂	semidirect
23. C₅₃×#3221	C₂	semidirect
24. C₅₃×#3219	C₂	semidirect
25. C₅₃×#3124	C₂	semidirect
26. C₅₃×#3121	C₂	semidirect
27. C₅₃×#3116	C₂	semidirect
28. C₅₃×#3046	C₂	semidirect
29. C₅₃×#3044	C₂	semidirect
30. C₅₃×#3035	C₂	semidirect
31. C₅₃×#2992	C₂	semidirect
811. #62025	C₅₃	direct (N × H)
859. #3554	C₂×C₅₃	semidirect
860. #3524	C₂×C₅₃	semidirect
861. #3403	C₂×C₅₃	semidirect
862. #3400	C₂×C₅₃	semidirect
863. #3374	C₂×C₅₃	semidirect
864. #3371	C₂×C₅₃	semidirect
865. #3321	C₂×C₅₃	semidirect
866. #3320	C₂×C₅₃	semidirect
867. #3315	C₂×C₅₃	semidirect
868. #3309	C₂×C₅₃	semidirect
869. #3303	C₂×C₅₃	semidirect
870. #3300	C₂×C₅₃	semidirect
871. #3285	C₂×C₅₃	semidirect
872. #3284	C₂×C₅₃	semidirect
873. #3271	C₂×C₅₃	semidirect
874. #3271	C₂×C₅₃	semidirect
875. #3270	C₂×C₅₃	semidirect
876. #3269	C₂×C₅₃	semidirect
877. #3263	C₂×C₅₃	semidirect
878. #3257	C₂×C₅₃	semidirect
879. #3248	C₂×C₅₃	semidirect
880. #3225	C₂×C₅₃	semidirect
881. #3221	C₂×C₅₃	semidirect
882. #3219	C₂×C₅₃	semidirect
883. #3124	C₂×C₅₃	semidirect
884. #3121	C₂×C₅₃	semidirect
885. #3116	C₂×C₅₃	semidirect
886. #3046	C₂×C₅₃	semidirect
887. #3044	C₂×C₅₃	semidirect
888. #3035	C₂×C₅₃	semidirect
889. #2992	C₂×C₅₃	semidirect
1071. C₅₃	#62025	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×#3554	2
C₅₃×#3524	2
C₅₃×#3403	2
C₅₃×#3400	2
C₅₃×#3374	2
C₅₃×#3371	2
C₅₃×#3321	2
C₅₃×#3320	2
C₅₃×#3315	2
C₅₃×#3309	2
C₅₃×#3303	2
C₅₃×#3300	2
C₅₃×#3285	2
C₅₃×#3284	2
C₅₃×#3271	2
C₅₃×#3270	2
C₅₃×#3269	2
C₅₃×#3263	2
C₅₃×#3257	2
C₅₃×#3248	2
C₅₃×#3225	2
C₅₃×#3221	2
C₅₃×#3219	2
C₅₃×#3124	2
C₅₃×#3121	2
C₅₃×#3116	2
C₅₃×#3046	2
C₅₃×#3044	2
C₅₃×#3035	2
C₅₃×#2992	2
#62025	53

Subgroups — C53×#62025 #27269537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62025 #27269537