Subgroups — C₅₃×#62223 #27269735

Order 13568.

1762 conjugacy classes of subgroups.

The subgroup lattice has 1700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3565	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3389	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3388	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3355	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3351	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3350	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3348	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3347	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3324	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3318	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3310	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3257	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3257	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#3241	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3241	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#3235	C₂	1	1	yes	maximal, characteristic, complemented
25	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
26	C₅₃×#3118	C₂	1	1	yes	maximal, characteristic, complemented
27	C₅₃×#3114	C₂	1	1	yes	maximal, characteristic, complemented
28	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
29	C₅₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
30	C₅₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
31	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
32	C₅₃×#563	—	2	1	no	—
33	C₅₃×#562	—	2	1	no	—
34	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
35	C₅₃×#556	—	2	1	no	—
36	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#555	C₂²	1	1	yes	characteristic
38	C₅₃×#555	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#554	C₂²	1	1	yes	characteristic
40	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
41	C₅₃×#553	—	2	1	no	—
42	C₅₃×#553	C₂²	1	1	yes	characteristic
43	C₅₃×#553	C₂²	1	1	yes	characteristic
44	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#553	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#552	—	2	1	no	—
47	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
48	C₅₃×#552	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#550	C₂²	1	1	yes	characteristic
50	C₅₃×#546	—	2	1	no	—
51	C₅₃×#546	—	2	1	no	—
52	C₅₃×#546	—	2	1	no	—
53	D₄²×C₅₃	C₂²	1	1	yes	characteristic
54	D₄²×C₅₃	C₂²	1	1	yes	characteristic
55	D₄²×C₅₃	C₂²	1	1	yes	characteristic
56	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
57	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
58	C₅₃×#542	—	2	1	no	—
59	C₅₃×#542	—	2	1	no	—
60	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
61	C₅₃×#542	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#541	—	2	1	no	—
63	C₅₃×#540	C₂²	1	1	yes	characteristic
64	C₅₃×#540	C₂²	1	1	yes	characteristic
65	C₅₃×#539	—	2	1	no	—
66	C₅₃×#538	—	2	1	no	—
67	C₅₃×#538	—	2	1	no	—
68	C₅₃×#533	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#532	C₂²	1	1	yes	characteristic
70	C₅₃×#529	C₂²	1	1	yes	characteristic
71	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#525	—	2	1	no	—
73	C₂×#121×C₅₃	—	2	1	no	—
74	C₅₃×#518	C₂²	1	1	yes	characteristic
75	C₅₃×#518	C₂²	1	1	yes	characteristic
76	C₂×C₄×D₄×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×#499	C₂²	1	1	yes	characteristic, complemented
82	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
83	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#490	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
90	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#483	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
98	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
102	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#481	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
106	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
107	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
108	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
109	C₅₃×#478	C₂²	1	1	yes	characteristic
110	C₅₃×#478	C₂²	1	1	yes	characteristic
111	C₅₃×#478	C₂²	1	1	yes	characteristic
112	C₅₃×#478	C₂²	1	1	yes	characteristic
113	C₅₃×#478	C₂²	1	1	yes	characteristic
114	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
117	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
118	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
119	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
121	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
122	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
123	C₅₃×#476	C₂²	1	1	yes	characteristic
124	C₅₃×#476	C₂²	1	1	yes	characteristic
125	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
127	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
129	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#474	C₂²	1	1	yes	characteristic
131	C₅₃×#474	C₂²	1	1	yes	characteristic
132	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
133	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
135	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
136	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
137	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
138	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
139	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
140	C₅₃×#469	C₂²	1	1	yes	characteristic, complemented
141	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
142	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
143	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
144	C₅₃×#468	C₂²	1	1	yes	characteristic, complemented
145	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
146	C₅₃×#466	C₂²	1	1	yes	characteristic, complemented
147	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
148	C₅₃×#465	C₂²	1	1	yes	characteristic, complemented
149	C₅₃×#463	C₂²	1	1	yes	characteristic
150	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
151	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
152	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
153	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
154	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
155	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
156	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
157	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
158	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
159	C₅₃×#450	C₂²	1	1	yes	characteristic
160	C₅₃×#450	C₂²	1	1	yes	characteristic
161	C₅₃×#450	C₂²	1	1	yes	characteristic
162	C₅₃×#447	C₂²	1	1	yes	characteristic
163	C₅₃×#447	C₂²	1	1	yes	characteristic
164	C₅₃×#447	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×#442	C₂²	1	1	yes	characteristic
168	C₅₃×#442	C₂²	1	1	yes	characteristic
169	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
170	C₅₃×#442	C₂²	1	1	yes	characteristic, complemented
171	C₅₃×#440	C₂²	1	1	yes	characteristic
172	C₅₃×#440	C₂²	1	1	yes	characteristic
173	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
174	C₅₃×#440	C₂²	1	1	yes	characteristic, complemented
175	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
176	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
177	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
178	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
179	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
180	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
181	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
182	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
183	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
184	C₅₃×#435	C₂²	1	1	yes	characteristic, complemented
185	C₅₃×#433	C₂²	1	1	yes	characteristic, complemented
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, complemented
189	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
190	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
191	C₅₃×#428	C₂²	1	1	yes	characteristic, complemented
192	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
193	C₅₃×#427	C₂²	1	1	yes	characteristic, complemented
194	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
195	C₅₃×#424	C₂²	1	1	yes	characteristic, complemented
196	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
197	C₅₃×#418	C₂²	1	1	yes	characteristic
198	C₅₃×#418	C₂²	1	1	yes	characteristic
199	C₅₃×#418	C₂²	1	1	yes	characteristic
200	C₅₃×#418	C₂²	1	1	yes	characteristic
201	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
202	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
203	C₂×#41×C₅₃	—	2	1	no	—
204	C₂×#41×C₅₃	—	2	1	no	—
205	C₂²×D₄×C₅₃	—	2	1	no	—
206	C₂²×D₄×C₅₃	—	2	1	no	—
207	C₂²×D₄×C₅₃	—	2	1	no	—
208	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
209	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
210	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
211	C₂³×C₄×C₅₃	—	2	1	no	—
212	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
213	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
214	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
215	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
216	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
221	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
222	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
223	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
224	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
225	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄⋊Q₈×C₅₃	—	2	1	no	—
227	C₄⋊Q₈×C₅₃	—	2	1	no	—
228	C₄⋊Q₈×C₅₃	—	2	1	no	—
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	#127×C₅₃	C₂³	1	1	yes	characteristic
235	#127×C₅₃	C₂³	1	1	yes	characteristic
236	#127×C₅₃	C₂³	1	1	yes	characteristic
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	D₄	1	1	yes	characteristic
249	#126×C₅₃	D₄	1	1	yes	characteristic
250	#125×C₅₃	—	2	1	no	—
251	#125×C₅₃	—	2	1	no	—
252	#125×C₅₃	—	2	1	no	—
253	#125×C₅₃	—	2	1	no	—
254	#125×C₅₃	—	2	1	no	—
255	#125×C₅₃	—	2	1	no	—
256	#125×C₅₃	D₄	1	1	yes	characteristic
257	#125×C₅₃	C₂³	1	1	yes	characteristic
258	#125×C₅₃	C₂³	1	1	yes	characteristic
259	#125×C₅₃	C₂³	1	1	yes	characteristic
260	#125×C₅₃	C₂³	1	1	yes	characteristic
261	#125×C₅₃	C₂³	1	1	yes	characteristic
262	#125×C₅₃	C₂³	1	1	yes	characteristic
263	#125×C₅₃	C₂³	1	1	yes	characteristic
264	#124×C₅₃	—	2	1	no	—
265	#124×C₅₃	—	2	1	no	—
266	#124×C₅₃	—	2	1	no	—
267	#124×C₅₃	—	2	1	no	—
268	#124×C₅₃	—	2	1	no	—
269	#124×C₅₃	—	2	1	no	—
270	#124×C₅₃	—	2	1	no	—
271	#124×C₅₃	—	2	1	no	—
272	#124×C₅₃	D₄	1	1	yes	characteristic
273	#124×C₅₃	C₂³	1	1	yes	characteristic
274	#123×C₅₃	—	2	1	no	—
275	#123×C₅₃	—	2	1	no	—
276	#123×C₅₃	—	2	1	no	—
277	#123×C₅₃	—	2	1	no	—
278	#123×C₅₃	—	2	1	no	—
279	#123×C₅₃	—	2	1	no	—
280	#123×C₅₃	—	2	1	no	—
281	#123×C₅₃	—	2	1	no	—
282	#123×C₅₃	—	2	1	no	—
283	#123×C₅₃	—	2	1	no	—
284	#123×C₅₃	—	2	1	no	—
285	#123×C₅₃	—	2	1	no	—
286	#123×C₅₃	—	2	1	no	—
287	#123×C₅₃	D₄	1	1	yes	characteristic
288	#123×C₅₃	D₄	1	1	yes	characteristic
289	C₂²⋊Q₈×C₅₃	—	2	1	no	—
290	C₂²⋊Q₈×C₅₃	—	2	1	no	—
291	C₂²⋊Q₈×C₅₃	—	2	1	no	—
292	C₂²⋊Q₈×C₅₃	—	2	1	no	—
293	C₂²⋊Q₈×C₅₃	—	2	1	no	—
294	C₂²⋊Q₈×C₅₃	—	2	1	no	—
295	C₂²⋊Q₈×C₅₃	—	2	1	no	—
296	C₂²⋊Q₈×C₅₃	—	2	1	no	—
297	C₂²⋊Q₈×C₅₃	—	2	1	no	—
298	C₂²⋊Q₈×C₅₃	—	2	1	no	—
299	C₂²⋊Q₈×C₅₃	—	2	1	no	—
300	C₂²⋊Q₈×C₅₃	—	2	1	no	—
301	C₂²⋊Q₈×C₅₃	—	2	1	no	—
302	C₂²⋊Q₈×C₅₃	—	2	1	no	—
303	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
304	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
307	#121×C₅₃	—	2	1	no	—
308	#121×C₅₃	—	2	1	no	—
309	#121×C₅₃	—	2	1	no	—
310	#121×C₅₃	—	2	1	no	—
311	#121×C₅₃	—	2	1	no	—
312	#121×C₅₃	—	2	1	no	—
313	#121×C₅₃	—	2	1	no	—
314	#121×C₅₃	—	2	1	no	—
315	#121×C₅₃	—	2	1	no	—
316	#121×C₅₃	—	2	1	no	—
317	#121×C₅₃	—	2	1	no	—
318	#121×C₅₃	—	2	1	no	—
319	#121×C₅₃	—	2	1	no	—
320	#121×C₅₃	—	2	1	no	—
321	#121×C₅₃	—	2	1	no	—
322	#121×C₅₃	—	2	1	no	—
323	#121×C₅₃	—	2	1	no	—
324	#121×C₅₃	D₄	1	1	yes	characteristic
325	#121×C₅₃	C₂³	1	1	yes	characteristic
326	#121×C₅₃	C₂³	1	1	yes	characteristic
327	#121×C₅₃	C₂³	1	1	yes	characteristic
328	#121×C₅₃	C₂³	1	1	yes	characteristic
329	#121×C₅₃	C₂³	1	1	yes	characteristic
330	#121×C₅₃	C₂³	1	1	yes	characteristic
331	#121×C₅₃	C₂³	1	1	yes	characteristic
332	#121×C₅₃	C₂³	1	1	yes	characteristic
333	#121×C₅₃	C₂³	1	1	yes	characteristic
334	#120×C₅₃	—	2	1	no	—
335	#120×C₅₃	—	2	1	no	—
336	#120×C₅₃	—	2	1	no	—
337	#120×C₅₃	—	2	1	no	—
338	#120×C₅₃	—	2	1	no	—
339	#120×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	—	2	1	no	—
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×D₄×C₅₃	—	2	1	no	—
349	C₄×D₄×C₅₃	—	2	1	no	—
350	C₄×D₄×C₅₃	—	2	1	no	—
351	C₄×D₄×C₅₃	—	2	1	no	—
352	C₄×D₄×C₅₃	—	2	1	no	—
353	C₄×D₄×C₅₃	—	2	1	no	—
354	C₄×D₄×C₅₃	—	2	1	no	—
355	C₄×D₄×C₅₃	—	2	1	no	—
356	C₄×D₄×C₅₃	—	2	1	no	—
357	C₄×D₄×C₅₃	—	2	1	no	—
358	C₄×D₄×C₅₃	—	2	1	no	—
359	C₄×D₄×C₅₃	—	2	1	no	—
360	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
361	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
362	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
363	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
364	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
365	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
366	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
367	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
368	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
369	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
370	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
371	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
372	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
373	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
374	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
375	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
376	#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	—	2	1	no	—
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	#117×C₅₃	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×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	#102×C₅₃	C₂³	1	1	yes	characteristic
439	#102×C₅₃	C₂³	1	1	yes	characteristic
440	#102×C₅₃	C₂³	1	1	yes	characteristic
441	#102×C₅₃	C₂³	1	1	yes	characteristic
442	#102×C₅₃	C₂³	1	1	yes	characteristic
443	#102×C₅₃	C₂³	1	1	yes	characteristic
444	#102×C₅₃	C₂³	1	1	yes	characteristic
445	#102×C₅₃	C₂³	1	1	yes	characteristic
446	#102×C₅₃	C₂³	1	1	yes	characteristic
447	#102×C₅₃	C₂³	1	1	yes	characteristic
448	#102×C₅₃	C₂³	1	1	yes	characteristic
449	#102×C₅₃	C₂³	1	1	yes	characteristic
450	#102×C₅₃	C₂³	1	1	yes	characteristic
451	#102×C₅₃	C₂³	1	1	yes	characteristic
452	#102×C₅₃	C₂³	1	1	yes	characteristic
453	#102×C₅₃	C₂³	1	1	yes	characteristic
454	#102×C₅₃	C₂³	1	1	yes	characteristic
455	#102×C₅₃	C₂³	1	1	yes	characteristic
456	#102×C₅₃	C₂³	1	1	yes	characteristic
457	#102×C₅₃	C₂³	1	1	yes	characteristic
458	#102×C₅₃	C₂³	1	1	yes	characteristic
459	#102×C₅₃	C₂³	1	1	yes	characteristic
460	#102×C₅₃	C₂³	1	1	yes	characteristic
461	#102×C₅₃	C₂³	1	1	yes	characteristic
462	#102×C₅₃	C₂³	1	1	yes	characteristic
463	#102×C₅₃	C₂³	1	1	yes	characteristic
464	#102×C₅₃	C₂³	1	1	yes	characteristic
465	#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	C₂⁴×C₅₃	—	2	1	no	—
480	C₂⁴×C₅₃	—	2	1	no	—
481	#41×C₅₃	—	8	2	no	—
482	#41×C₅₃	—	8	2	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	C₂×D₄	1	1	yes	characteristic
489	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
490	C₂×D₄×C₅₃	—	2	2	no	—
491	C₂×D₄×C₅₃	—	2	2	no	—
492	C₂×D₄×C₅₃	—	2	2	no	—
493	C₂×D₄×C₅₃	—	2	1	no	—
494	C₂×D₄×C₅₃	—	2	1	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	—	2	1	no	—
501	C₂×D₄×C₅₃	—	2	1	no	—
502	C₂×D₄×C₅₃	—	2	1	no	—
503	C₂×D₄×C₅₃	—	2	1	no	—
504	C₂×D₄×C₅₃	—	2	1	no	—
505	C₂×D₄×C₅₃	—	2	1	no	—
506	C₂×D₄×C₅₃	—	2	1	no	—
507	C₂×D₄×C₅₃	—	2	1	no	—
508	C₂×D₄×C₅₃	—	2	1	no	—
509	C₂×D₄×C₅₃	—	2	1	no	—
510	C₂×D₄×C₅₃	—	2	1	no	—
511	C₂×D₄×C₅₃	—	4	1	no	—
512	C₂×D₄×C₅₃	—	4	1	no	—
513	C₂×D₄×C₅₃	—	4	1	no	—
514	C₂×D₄×C₅₃	—	8	2	no	—
515	C₂×D₄×C₅₃	—	8	2	no	—
516	C₂×D₄×C₅₃	—	8	2	no	—
517	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
518	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
519	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
520	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
521	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
522	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
523	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
524	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
525	C₂²×C₄×C₅₃	—	2	1	no	—
526	C₂²×C₄×C₅₃	—	2	1	no	—
527	C₂²×C₄×C₅₃	—	2	1	no	—
528	C₂²×C₄×C₅₃	—	2	1	no	—
529	C₂²×C₄×C₅₃	—	2	1	no	—
530	C₂²×C₄×C₅₃	—	2	1	no	—
531	C₂²×C₄×C₅₃	—	2	1	no	—
532	C₂²×C₄×C₅₃	—	2	1	no	—
533	C₂²×C₄×C₅₃	—	2	1	no	—
534	C₂²×C₄×C₅₃	—	2	1	no	—
535	C₂²×C₄×C₅₃	—	2	1	no	—
536	C₂²×C₄×C₅₃	—	2	1	no	—
537	C₂²×C₄×C₅₃	—	2	1	no	—
538	C₂²×C₄×C₅₃	—	2	1	no	—
539	C₂²×C₄×C₅₃	—	2	1	no	—
540	C₂²×C₄×C₅₃	—	2	1	no	—
541	C₂²×C₄×C₅₃	—	8	2	no	—
542	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
543	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
544	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
545	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
546	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
547	SD₁₆×C₅₃	—	2	2	no	—
548	SD₁₆×C₅₃	—	4	1	no	—
549	SD₁₆×C₅₃	—	4	1	no	—
550	SD₁₆×C₅₃	—	4	1	no	—
551	D₈×C₅₃	—	2	2	no	—
552	D₈×C₅₃	—	4	1	no	—
553	D₈×C₅₃	—	4	1	no	—
554	D₈×C₅₃	—	4	1	no	—
555	M₁₆×C₅₃	—	4	1	no	—
556	M₁₆×C₅₃	—	4	1	no	—
557	M₁₆×C₅₃	—	4	1	no	—
558	M₁₆×C₅₃	—	4	1	no	—
559	C₂×C₈×C₅₃	—	4	1	no	—
560	C₂×C₈×C₅₃	—	4	1	no	—
561	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
562	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
563	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
564	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
565	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
566	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
567	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
568	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
590	C₄⋊C₄×C₅₃	—	2	1	no	—
591	C₄⋊C₄×C₅₃	—	2	1	no	—
592	C₄⋊C₄×C₅₃	—	2	1	no	—
593	C₄⋊C₄×C₅₃	—	2	1	no	—
594	C₄⋊C₄×C₅₃	—	2	1	no	—
595	C₄⋊C₄×C₅₃	—	2	1	no	—
596	C₄⋊C₄×C₅₃	—	2	1	no	—
597	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
598	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
599	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
600	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
601	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
602	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
603	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
604	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
605	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
606	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
607	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
608	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
609	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
610	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
611	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
612	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
613	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
614	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
615	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
616	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
638	C₂²⋊C₄×C₅₃	—	2	1	no	—
639	C₂²⋊C₄×C₅₃	—	2	1	no	—
640	C₂²⋊C₄×C₅₃	—	2	1	no	—
641	C₂²⋊C₄×C₅₃	—	2	1	no	—
642	C₂²⋊C₄×C₅₃	—	2	1	no	—
643	C₂²⋊C₄×C₅₃	—	2	1	no	—
644	C₂²⋊C₄×C₅₃	—	2	1	no	—
645	C₂²⋊C₄×C₅₃	—	2	1	no	—
646	C₂²⋊C₄×C₅₃	—	2	1	no	—
647	C₂²⋊C₄×C₅₃	—	2	1	no	—
648	C₂²⋊C₄×C₅₃	—	2	1	no	—
649	C₂²⋊C₄×C₅₃	—	2	1	no	—
650	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
651	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
652	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
653	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
654	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
655	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
656	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
657	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
658	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
659	C₂²⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
660	C₄²×C₅₃	—	2	1	no	—
661	C₄²×C₅₃	—	2	1	no	—
662	C₄²×C₅₃	—	2	1	no	—
663	C₄²×C₅₃	—	2	1	no	—
664	C₄²×C₅₃	—	2	1	no	—
665	C₄²×C₅₃	—	2	1	no	—
666	C₄²×C₅₃	—	2	1	no	—
667	C₄²×C₅₃	—	2	1	no	—
668	C₄²×C₅₃	—	2	1	no	—
669	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
670	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
671	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
672	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
673	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
674	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
675	C₂³×C₅₃	—	2	1	no	—
676	C₂³×C₅₃	—	2	1	no	—
677	C₂³×C₅₃	—	2	1	no	—
678	C₂³×C₅₃	—	2	1	no	—
679	C₂³×C₅₃	—	2	1	no	—
680	C₂³×C₅₃	—	4	2	no	—
681	C₂³×C₅₃	—	4	2	no	—
682	C₂³×C₅₃	—	4	2	no	—
683	C₂³×C₅₃	—	4	2	no	—
684	C₂³×C₅₃	—	8	1	no	—
685	C₂³×C₅₃	—	8	1	no	—
686	C₂³×C₅₃	—	8	1	no	—
687	C₂³×C₅₃	—	8	1	no	—
688	C₂³×C₅₃	—	8	1	no	—
689	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
690	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
691	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
692	Q₈×C₅₃	—	2	1	no	—
693	Q₈×C₅₃	—	2	1	no	—
694	Q₈×C₅₃	—	4	1	no	—
695	Q₈×C₅₃	—	8	1	no	—
696	Q₈×C₅₃	—	8	1	no	—
697	Q₈×C₅₃	—	8	1	no	—
698	Q₈×C₅₃	—	8	1	no	—
699	Q₈×C₅₃	—	8	1	no	—
700	D₄×C₅₃	—	2	1	no	—
701	D₄×C₅₃	—	2	1	no	—
702	D₄×C₅₃	—	2	1	no	—
703	D₄×C₅₃	—	2	1	no	—
704	D₄×C₅₃	—	2	1	no	—
705	D₄×C₅₃	—	2	1	no	—
706	D₄×C₅₃	—	2	1	no	—
707	D₄×C₅₃	—	2	1	no	—
708	D₄×C₅₃	—	2	1	no	—
709	D₄×C₅₃	—	4	1	no	—
710	D₄×C₅₃	—	4	1	no	—
711	D₄×C₅₃	—	4	1	no	—
712	D₄×C₅₃	—	4	2	no	—
713	D₄×C₅₃	—	4	2	no	—
714	D₄×C₅₃	—	4	2	no	—
715	D₄×C₅₃	—	4	2	no	—
716	D₄×C₅₃	—	4	2	no	—
717	D₄×C₅₃	—	4	2	no	—
718	D₄×C₅₃	—	8	1	no	—
719	D₄×C₅₃	—	8	1	no	—
720	D₄×C₅₃	—	8	1	no	—
721	D₄×C₅₃	—	8	1	no	—
722	D₄×C₅₃	—	8	1	no	—
723	D₄×C₅₃	—	8	1	no	—
724	D₄×C₅₃	—	8	1	no	—
725	D₄×C₅₃	—	8	1	no	—
726	D₄×C₅₃	—	8	1	no	—
727	D₄×C₅₃	—	8	1	no	—
728	D₄×C₅₃	—	8	1	no	—
729	D₄×C₅₃	—	8	1	no	—
730	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
731	C₂×C₄×C₅₃	—	2	1	no	—
732	C₂×C₄×C₅₃	—	2	1	no	—
733	C₂×C₄×C₅₃	—	2	1	no	—
734	C₂×C₄×C₅₃	—	2	1	no	—
735	C₂×C₄×C₅₃	—	2	1	no	—
736	C₂×C₄×C₅₃	—	2	1	no	—
737	C₂×C₄×C₅₃	—	2	1	no	—
738	C₂×C₄×C₅₃	—	2	1	no	—
739	C₂×C₄×C₅₃	—	2	1	no	—
740	C₂×C₄×C₅₃	—	2	1	no	—
741	C₂×C₄×C₅₃	—	2	1	no	—
742	C₂×C₄×C₅₃	—	2	1	no	—
743	C₂×C₄×C₅₃	—	2	1	no	—
744	C₂×C₄×C₅₃	—	2	1	no	—
745	C₂×C₄×C₅₃	—	2	1	no	—
746	C₂×C₄×C₅₃	—	2	1	no	—
747	C₂×C₄×C₅₃	—	2	1	no	—
748	C₂×C₄×C₅₃	—	4	1	no	—
749	C₂×C₄×C₅₃	—	4	1	no	—
750	C₂×C₄×C₅₃	—	4	2	no	—
751	C₂×C₄×C₅₃	—	4	2	no	—
752	C₂×C₄×C₅₃	—	8	1	no	—
753	C₂×C₄×C₅₃	—	8	1	no	—
754	C₂×C₄×C₅₃	—	8	1	no	—
755	C₂×C₄×C₅₃	—	8	1	no	—
756	C₂×C₄×C₅₃	—	8	1	no	—
757	C₂×C₄×C₅₃	—	8	1	no	—
758	C₂×C₄×C₅₃	—	8	1	no	—
759	C₂×C₄×C₅₃	—	8	1	no	—
760	C₂×C₄×C₅₃	—	8	1	no	—
761	C₂×C₄×C₅₃	—	8	1	no	—
762	C₂×C₄×C₅₃	—	8	1	no	—
763	C₂×C₄×C₅₃	—	8	1	no	—
764	C₂×C₄×C₅₃	—	8	1	no	—
765	C₂×C₄×C₅₃	—	8	1	no	—
766	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
767	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
768	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
769	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
770	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
771	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
772	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
773	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
774	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
775	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
776	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
777	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
778	C₈×C₅₃	—	2	1	no	—
779	C₈×C₅₃	—	2	1	no	—
780	C₈×C₅₃	—	2	1	no	—
781	C₈×C₅₃	—	2	1	no	—
782	C₈×C₅₃	—	2	1	no	—
783	C₈×C₅₃	—	2	1	no	—
784	C₈×C₅₃	—	2	1	no	—
785	C₈×C₅₃	—	2	1	no	—
786	#62223	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
787	C₂²×C₅₃	—	2	1	no	—
788	C₂²×C₅₃	—	2	1	no	—
789	C₂²×C₅₃	—	2	1	no	—
790	C₂²×C₅₃	—	2	1	no	—
791	C₂²×C₅₃	—	2	1	no	—
792	C₂²×C₅₃	—	2	1	no	—
793	C₂²×C₅₃	—	2	1	no	—
794	C₂²×C₅₃	—	2	1	no	—
795	C₂²×C₅₃	—	2	1	no	—
796	C₂²×C₅₃	—	2	2	no	—
797	C₂²×C₅₃	—	4	1	no	—
798	C₂²×C₅₃	—	4	1	no	—
799	C₂²×C₅₃	—	4	1	no	—
800	C₂²×C₅₃	—	4	1	no	—
801	C₂²×C₅₃	—	4	1	no	—
802	C₂²×C₅₃	—	4	1	no	—
803	C₂²×C₅₃	—	4	1	no	—
804	C₂²×C₅₃	—	4	1	no	—
805	C₂²×C₅₃	—	4	1	no	—
806	C₂²×C₅₃	—	4	1	no	—
807	C₂²×C₅₃	—	4	1	no	—
808	C₂²×C₅₃	—	4	1	no	—
809	C₂²×C₅₃	—	4	1	no	—
810	C₂²×C₅₃	—	4	1	no	—
811	C₂²×C₅₃	—	8	4	no	—
812	C₂²×C₅₃	—	16	2	no	—
813	C₂²×C₅₃	—	16	2	no	—
814	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
815	C₄×C₅₃	—	2	1	no	—
816	C₄×C₅₃	—	2	1	no	—
817	C₄×C₅₃	—	2	1	no	—
818	C₄×C₅₃	—	2	1	no	—
819	C₄×C₅₃	—	2	1	no	—
820	C₄×C₅₃	—	2	1	no	—
821	C₄×C₅₃	—	2	1	no	—
822	C₄×C₅₃	—	2	1	no	—
823	C₄×C₅₃	—	2	1	no	—
824	C₄×C₅₃	—	2	1	no	—
825	C₄×C₅₃	—	2	1	no	—
826	C₄×C₅₃	—	4	1	no	—
827	C₄×C₅₃	—	4	1	no	—
828	C₄×C₅₃	—	4	1	no	—
829	C₄×C₅₃	—	4	1	no	—
830	C₄×C₅₃	—	4	1	no	—
831	C₄×C₅₃	—	4	1	no	—
832	C₄×C₅₃	—	4	1	no	—
833	C₄×C₅₃	—	4	1	no	—
834	C₄×C₅₃	—	4	1	no	—
835	C₄×C₅₃	—	4	1	no	—
836	C₄×C₅₃	—	4	1	no	—
837	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
838	C₄×C₅₃	#585	1	1	yes	characteristic
839	#3565	C₂×C₅₃	1	1	yes	characteristic, complemented
840	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
841	#3389	C₂×C₅₃	1	1	yes	characteristic, complemented
842	#3388	C₂×C₅₃	1	1	yes	characteristic, complemented
843	#3368	C₂×C₅₃	1	1	yes	characteristic, complemented
844	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
845	#3355	C₂×C₅₃	1	1	yes	characteristic, complemented
846	#3351	C₂×C₅₃	1	1	yes	characteristic, complemented
847	#3350	C₂×C₅₃	1	1	yes	characteristic, complemented
848	#3348	C₂×C₅₃	1	1	yes	characteristic, complemented
849	#3347	C₂×C₅₃	1	1	yes	characteristic, complemented
850	#3347	C₂×C₅₃	1	1	yes	characteristic, complemented
851	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
852	#3324	C₂×C₅₃	1	1	yes	characteristic, complemented
853	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
854	#3318	C₂×C₅₃	1	1	yes	characteristic, complemented
855	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
856	#3310	C₂×C₅₃	1	1	yes	characteristic, complemented
857	#3257	C₂×C₅₃	1	1	yes	characteristic, complemented
858	#3257	C₂×C₅₃	1	1	yes	characteristic, complemented
859	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
860	#3241	C₂×C₅₃	1	1	yes	characteristic, complemented
861	#3241	C₂×C₅₃	1	1	yes	characteristic, complemented
862	#3235	C₂×C₅₃	1	1	yes	characteristic, complemented
863	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
864	#3118	C₂×C₅₃	1	1	yes	characteristic, complemented
865	#3114	C₂×C₅₃	1	1	yes	characteristic, complemented
866	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
867	#3081	C₂×C₅₃	1	1	yes	characteristic, complemented
868	#3077	C₂×C₅₃	1	1	yes	characteristic, complemented
869	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
870	C₂×C₅₃	—	4	1	no	—
871	C₂×C₅₃	—	4	1	no	—
872	C₂×C₅₃	—	4	1	no	—
873	C₂×C₅₃	—	4	2	no	—
874	C₂×C₅₃	—	8	1	no	—
875	C₂×C₅₃	—	8	1	no	—
876	C₂×C₅₃	—	8	1	no	—
877	C₂×C₅₃	—	8	1	no	—
878	C₂×C₅₃	#3489	1	1	yes	characteristic
879	C₂×C₅₃	#3585	1	1	yes	characteristic
880	C₂×C₅₃	#3585	1	1	yes	characteristic
881	#563	—	2	1	no	—
882	#562	—	2	1	no	—
883	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
884	#556	—	2	1	no	—
885	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
886	#555	C₂²×C₅₃	1	1	yes	characteristic
887	#555	C₂²×C₅₃	1	1	yes	characteristic, complemented
888	#554	C₂²×C₅₃	1	1	yes	characteristic
889	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
890	#553	—	2	1	no	—
891	#553	C₂²×C₅₃	1	1	yes	characteristic
892	#553	C₂²×C₅₃	1	1	yes	characteristic
893	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
894	#553	C₂²×C₅₃	1	1	yes	characteristic, complemented
895	#552	—	2	1	no	—
896	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
897	#552	C₂²×C₅₃	1	1	yes	characteristic, complemented
898	#550	C₂²×C₅₃	1	1	yes	characteristic
899	#546	—	2	1	no	—
900	#546	—	2	1	no	—
901	#546	—	2	1	no	—
902	D₄²	C₂²×C₅₃	1	1	yes	characteristic
903	D₄²	C₂²×C₅₃	1	1	yes	characteristic
904	D₄²	C₂²×C₅₃	1	1	yes	characteristic
905	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
906	#544	C₂²×C₅₃	1	1	yes	characteristic, complemented
907	#542	—	2	1	no	—
908	#542	—	2	1	no	—
909	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
910	#542	C₂²×C₅₃	1	1	yes	characteristic, complemented
911	#541	—	2	1	no	—
912	#540	C₂²×C₅₃	1	1	yes	characteristic
913	#540	C₂²×C₅₃	1	1	yes	characteristic
914	#539	—	2	1	no	—
915	#538	—	2	1	no	—
916	#538	—	2	1	no	—
917	#533	C₂²×C₅₃	1	1	yes	characteristic, complemented
918	#532	C₂²×C₅₃	1	1	yes	characteristic
919	#529	C₂²×C₅₃	1	1	yes	characteristic
920	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
921	#525	—	2	1	no	—
922	C₂×#121	—	2	1	no	—
923	#518	C₂²×C₅₃	1	1	yes	characteristic
924	#518	C₂²×C₅₃	1	1	yes	characteristic
925	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
926	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
927	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
928	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
929	#501	C₂²×C₅₃	1	1	yes	characteristic, complemented
930	#499	C₂²×C₅₃	1	1	yes	characteristic, complemented
931	#499	C₂²×C₅₃	1	1	yes	characteristic, complemented
932	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
933	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
934	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
935	#490	C₂²×C₅₃	1	1	yes	characteristic, complemented
936	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
937	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
938	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
939	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
940	#483	C₂²×C₅₃	1	1	yes	characteristic, complemented
941	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
942	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
943	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
944	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
945	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
946	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
947	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
948	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
949	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
950	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
951	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
952	#481	C₂²×C₅₃	1	1	yes	characteristic, complemented
953	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
954	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
955	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
956	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
957	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
958	#478	C₂²×C₅₃	1	1	yes	characteristic
959	#478	C₂²×C₅₃	1	1	yes	characteristic
960	#478	C₂²×C₅₃	1	1	yes	characteristic
961	#478	C₂²×C₅₃	1	1	yes	characteristic
962	#478	C₂²×C₅₃	1	1	yes	characteristic
963	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
964	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
965	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
966	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
967	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
968	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
969	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
970	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
971	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
972	#476	C₂²×C₅₃	1	1	yes	characteristic
973	#476	C₂²×C₅₃	1	1	yes	characteristic
974	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
975	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
976	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
977	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
978	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
979	#474	C₂²×C₅₃	1	1	yes	characteristic
980	#474	C₂²×C₅₃	1	1	yes	characteristic
981	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
982	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
983	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
984	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
985	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
986	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
987	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
988	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
989	#469	C₂²×C₅₃	1	1	yes	characteristic, complemented
990	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
991	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
992	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
993	#468	C₂²×C₅₃	1	1	yes	characteristic, complemented
994	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
995	#466	C₂²×C₅₃	1	1	yes	characteristic, complemented
996	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
997	#465	C₂²×C₅₃	1	1	yes	characteristic, complemented
998	#463	C₂²×C₅₃	1	1	yes	characteristic
999	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1000	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1001	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
1002	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1003	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1004	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
1005	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1006	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1007	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
1008	#450	C₂²×C₅₃	1	1	yes	characteristic
1009	#450	C₂²×C₅₃	1	1	yes	characteristic
1010	#450	C₂²×C₅₃	1	1	yes	characteristic
1011	#447	C₂²×C₅₃	1	1	yes	characteristic
1012	#447	C₂²×C₅₃	1	1	yes	characteristic
1013	#447	C₂²×C₅₃	1	1	yes	characteristic
1014	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1015	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
1016	#442	C₂²×C₅₃	1	1	yes	characteristic
1017	#442	C₂²×C₅₃	1	1	yes	characteristic
1018	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1019	#442	C₂²×C₅₃	1	1	yes	characteristic, complemented
1020	#440	C₂²×C₅₃	1	1	yes	characteristic
1021	#440	C₂²×C₅₃	1	1	yes	characteristic
1022	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1023	#440	C₂²×C₅₃	1	1	yes	characteristic, complemented
1024	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
1025	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
1026	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
1027	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
1028	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1029	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
1030	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1031	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1032	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1033	#435	C₂²×C₅₃	1	1	yes	characteristic, complemented
1034	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1035	#433	C₂²×C₅₃	1	1	yes	characteristic, complemented
1036	#432	C₂²×C₅₃	1	1	yes	characteristic, complemented
1037	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1038	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1039	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1040	#428	C₂²×C₅₃	1	1	yes	characteristic, complemented
1041	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1042	#427	C₂²×C₅₃	1	1	yes	characteristic, complemented
1043	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1044	#424	C₂²×C₅₃	1	1	yes	characteristic, complemented
1045	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
1046	#418	C₂²×C₅₃	1	1	yes	characteristic
1047	#418	C₂²×C₅₃	1	1	yes	characteristic
1048	#418	C₂²×C₅₃	1	1	yes	characteristic
1049	#418	C₂²×C₅₃	1	1	yes	characteristic
1050	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1051	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
1052	C₅₃	#62223	1	1	yes	characteristic, direct product factor, Sylow
1053	C₂×#41	—	2	1	no	—
1054	C₂×#41	—	2	1	no	—
1055	C₂²×D₄	—	2	1	no	—
1056	C₂²×D₄	—	2	1	no	—
1057	C₂²×D₄	—	2	1	no	—
1058	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1059	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1060	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
1061	C₂³×C₄	—	2	1	no	—
1062	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1063	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1064	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1065	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
1066	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1067	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1068	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1069	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
1070	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1071	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1072	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1073	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
1074	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1075	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
1076	C₄⋊Q₈	—	2	1	no	—
1077	C₄⋊Q₈	—	2	1	no	—
1078	C₄⋊Q₈	—	2	1	no	—
1079	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1080	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1081	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1082	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1083	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1084	#127	C₂³×C₅₃	1	1	yes	characteristic
1085	#127	C₂³×C₅₃	1	1	yes	characteristic
1086	#127	C₂³×C₅₃	1	1	yes	characteristic
1087	#126	—	2	1	no	—
1088	#126	—	2	1	no	—
1089	#126	—	2	1	no	—
1090	#126	—	2	1	no	—
1091	#126	—	2	1	no	—
1092	#126	—	2	1	no	—
1093	#126	—	2	1	no	—
1094	#126	—	2	1	no	—
1095	#126	—	2	1	no	—
1096	#126	—	2	1	no	—
1097	#126	—	2	1	no	—
1098	#126	D₄×C₅₃	1	1	yes	characteristic
1099	#126	D₄×C₅₃	1	1	yes	characteristic
1100	#125	—	2	1	no	—
1101	#125	—	2	1	no	—
1102	#125	—	2	1	no	—
1103	#125	—	2	1	no	—
1104	#125	—	2	1	no	—
1105	#125	—	2	1	no	—
1106	#125	D₄×C₅₃	1	1	yes	characteristic
1107	#125	C₂³×C₅₃	1	1	yes	characteristic
1108	#125	C₂³×C₅₃	1	1	yes	characteristic
1109	#125	C₂³×C₅₃	1	1	yes	characteristic
1110	#125	C₂³×C₅₃	1	1	yes	characteristic
1111	#125	C₂³×C₅₃	1	1	yes	characteristic
1112	#125	C₂³×C₅₃	1	1	yes	characteristic
1113	#125	C₂³×C₅₃	1	1	yes	characteristic
1114	#124	—	2	1	no	—
1115	#124	—	2	1	no	—
1116	#124	—	2	1	no	—
1117	#124	—	2	1	no	—
1118	#124	—	2	1	no	—
1119	#124	—	2	1	no	—
1120	#124	—	2	1	no	—
1121	#124	—	2	1	no	—
1122	#124	D₄×C₅₃	1	1	yes	characteristic
1123	#124	C₂³×C₅₃	1	1	yes	characteristic
1124	#123	—	2	1	no	—
1125	#123	—	2	1	no	—
1126	#123	—	2	1	no	—
1127	#123	—	2	1	no	—
1128	#123	—	2	1	no	—
1129	#123	—	2	1	no	—
1130	#123	—	2	1	no	—
1131	#123	—	2	1	no	—
1132	#123	—	2	1	no	—
1133	#123	—	2	1	no	—
1134	#123	—	2	1	no	—
1135	#123	—	2	1	no	—
1136	#123	—	2	1	no	—
1137	#123	D₄×C₅₃	1	1	yes	characteristic
1138	#123	D₄×C₅₃	1	1	yes	characteristic
1139	C₂²⋊Q₈	—	2	1	no	—
1140	C₂²⋊Q₈	—	2	1	no	—
1141	C₂²⋊Q₈	—	2	1	no	—
1142	C₂²⋊Q₈	—	2	1	no	—
1143	C₂²⋊Q₈	—	2	1	no	—
1144	C₂²⋊Q₈	—	2	1	no	—
1145	C₂²⋊Q₈	—	2	1	no	—
1146	C₂²⋊Q₈	—	2	1	no	—
1147	C₂²⋊Q₈	—	2	1	no	—
1148	C₂²⋊Q₈	—	2	1	no	—
1149	C₂²⋊Q₈	—	2	1	no	—
1150	C₂²⋊Q₈	—	2	1	no	—
1151	C₂²⋊Q₈	—	2	1	no	—
1152	C₂²⋊Q₈	—	2	1	no	—
1153	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
1154	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1155	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1156	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
1157	#121	—	2	1	no	—
1158	#121	—	2	1	no	—
1159	#121	—	2	1	no	—
1160	#121	—	2	1	no	—
1161	#121	—	2	1	no	—
1162	#121	—	2	1	no	—
1163	#121	—	2	1	no	—
1164	#121	—	2	1	no	—
1165	#121	—	2	1	no	—
1166	#121	—	2	1	no	—
1167	#121	—	2	1	no	—
1168	#121	—	2	1	no	—
1169	#121	—	2	1	no	—
1170	#121	—	2	1	no	—
1171	#121	—	2	1	no	—
1172	#121	—	2	1	no	—
1173	#121	—	2	1	no	—
1174	#121	D₄×C₅₃	1	1	yes	characteristic
1175	#121	C₂³×C₅₃	1	1	yes	characteristic
1176	#121	C₂³×C₅₃	1	1	yes	characteristic
1177	#121	C₂³×C₅₃	1	1	yes	characteristic
1178	#121	C₂³×C₅₃	1	1	yes	characteristic
1179	#121	C₂³×C₅₃	1	1	yes	characteristic
1180	#121	C₂³×C₅₃	1	1	yes	characteristic
1181	#121	C₂³×C₅₃	1	1	yes	characteristic
1182	#121	C₂³×C₅₃	1	1	yes	characteristic
1183	#121	C₂³×C₅₃	1	1	yes	characteristic
1184	#120	—	2	1	no	—
1185	#120	—	2	1	no	—
1186	#120	—	2	1	no	—
1187	#120	—	2	1	no	—
1188	#120	—	2	1	no	—
1189	#120	—	2	1	no	—
1190	C₄×Q₈	—	2	1	no	—
1191	C₄×Q₈	—	2	1	no	—
1192	C₄×Q₈	—	2	1	no	—
1193	C₄×Q₈	—	2	1	no	—
1194	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1195	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1196	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1197	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
1198	C₄×D₄	—	2	1	no	—
1199	C₄×D₄	—	2	1	no	—
1200	C₄×D₄	—	2	1	no	—
1201	C₄×D₄	—	2	1	no	—
1202	C₄×D₄	—	2	1	no	—
1203	C₄×D₄	—	2	1	no	—
1204	C₄×D₄	—	2	1	no	—
1205	C₄×D₄	—	2	1	no	—
1206	C₄×D₄	—	2	1	no	—
1207	C₄×D₄	—	2	1	no	—
1208	C₄×D₄	—	2	1	no	—
1209	C₄×D₄	—	2	1	no	—
1210	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1211	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1212	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1213	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1214	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1215	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1216	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1217	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1218	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1219	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1220	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1221	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1222	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1223	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1224	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1225	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
1226	#117	—	2	1	no	—
1227	#117	—	2	1	no	—
1228	#117	—	2	1	no	—
1229	#117	—	2	1	no	—
1230	#117	—	2	1	no	—
1231	#117	C₂³×C₅₃	1	1	yes	characteristic
1232	#117	C₂³×C₅₃	1	1	yes	characteristic
1233	#117	C₂³×C₅₃	1	1	yes	characteristic
1234	#117	C₂³×C₅₃	1	1	yes	characteristic
1235	#117	C₂³×C₅₃	1	1	yes	characteristic
1236	#117	C₂³×C₅₃	1	1	yes	characteristic
1237	#117	C₂³×C₅₃	1	1	yes	characteristic
1238	#117	C₂³×C₅₃	1	1	yes	characteristic
1239	C₂×C₄⋊C₄	—	2	1	no	—
1240	C₂×C₄⋊C₄	—	2	1	no	—
1241	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1242	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1243	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
1244	C₂×C₂²⋊C₄	—	2	1	no	—
1245	C₂×C₂²⋊C₄	—	2	1	no	—
1246	C₂×C₂²⋊C₄	—	2	1	no	—
1247	C₂×C₂²⋊C₄	—	2	1	no	—
1248	C₂×C₂²⋊C₄	—	2	1	no	—
1249	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
1250	#107	C₂³×C₅₃	1	1	yes	characteristic
1251	#107	C₂³×C₅₃	1	1	yes	characteristic
1252	#107	C₂³×C₅₃	1	1	yes	characteristic
1253	#107	C₂³×C₅₃	1	1	yes	characteristic
1254	#107	C₂³×C₅₃	1	1	yes	characteristic
1255	#107	C₂³×C₅₃	1	1	yes	characteristic
1256	#107	C₂³×C₅₃	1	1	yes	characteristic
1257	#107	C₂³×C₅₃	1	1	yes	characteristic
1258	#107	C₂³×C₅₃	1	1	yes	characteristic
1259	#107	C₂³×C₅₃	1	1	yes	characteristic
1260	#107	C₂³×C₅₃	1	1	yes	characteristic
1261	#107	C₂³×C₅₃	1	1	yes	characteristic
1262	#106	C₂³×C₅₃	1	1	yes	characteristic
1263	#106	C₂³×C₅₃	1	1	yes	characteristic
1264	#106	C₂³×C₅₃	1	1	yes	characteristic
1265	#106	C₂³×C₅₃	1	1	yes	characteristic
1266	#106	C₂³×C₅₃	1	1	yes	characteristic
1267	#106	C₂³×C₅₃	1	1	yes	characteristic
1268	#106	C₂³×C₅₃	1	1	yes	characteristic
1269	#106	C₂³×C₅₃	1	1	yes	characteristic
1270	#106	C₂³×C₅₃	1	1	yes	characteristic
1271	#106	C₂³×C₅₃	1	1	yes	characteristic
1272	#106	C₂³×C₅₃	1	1	yes	characteristic
1273	#106	C₂³×C₅₃	1	1	yes	characteristic
1274	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1275	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1276	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1277	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1278	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1279	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1280	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1281	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1282	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1283	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1284	#103	C₂³×C₅₃	1	1	yes	characteristic
1285	#103	C₂³×C₅₃	1	1	yes	characteristic
1286	#103	C₂³×C₅₃	1	1	yes	characteristic
1287	#103	C₂³×C₅₃	1	1	yes	characteristic
1288	#102	C₂³×C₅₃	1	1	yes	characteristic
1289	#102	C₂³×C₅₃	1	1	yes	characteristic
1290	#102	C₂³×C₅₃	1	1	yes	characteristic
1291	#102	C₂³×C₅₃	1	1	yes	characteristic
1292	#102	C₂³×C₅₃	1	1	yes	characteristic
1293	#102	C₂³×C₅₃	1	1	yes	characteristic
1294	#102	C₂³×C₅₃	1	1	yes	characteristic
1295	#102	C₂³×C₅₃	1	1	yes	characteristic
1296	#102	C₂³×C₅₃	1	1	yes	characteristic
1297	#102	C₂³×C₅₃	1	1	yes	characteristic
1298	#102	C₂³×C₅₃	1	1	yes	characteristic
1299	#102	C₂³×C₅₃	1	1	yes	characteristic
1300	#102	C₂³×C₅₃	1	1	yes	characteristic
1301	#102	C₂³×C₅₃	1	1	yes	characteristic
1302	#102	C₂³×C₅₃	1	1	yes	characteristic
1303	#102	C₂³×C₅₃	1	1	yes	characteristic
1304	#102	C₂³×C₅₃	1	1	yes	characteristic
1305	#102	C₂³×C₅₃	1	1	yes	characteristic
1306	#102	C₂³×C₅₃	1	1	yes	characteristic
1307	#102	C₂³×C₅₃	1	1	yes	characteristic
1308	#102	C₂³×C₅₃	1	1	yes	characteristic
1309	#102	C₂³×C₅₃	1	1	yes	characteristic
1310	#102	C₂³×C₅₃	1	1	yes	characteristic
1311	#102	C₂³×C₅₃	1	1	yes	characteristic
1312	#102	C₂³×C₅₃	1	1	yes	characteristic
1313	#102	C₂³×C₅₃	1	1	yes	characteristic
1314	#102	C₂³×C₅₃	1	1	yes	characteristic
1315	#102	C₂³×C₅₃	1	1	yes	characteristic
1316	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1317	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1318	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1319	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1320	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1321	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
1322	#97	C₂³×C₅₃	1	1	yes	characteristic
1323	#97	C₂³×C₅₃	1	1	yes	characteristic
1324	#97	C₂³×C₅₃	1	1	yes	characteristic
1325	#97	C₂³×C₅₃	1	1	yes	characteristic
1326	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1327	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
1328	C₂⁴	—	2	1	no	—
1329	C₂⁴	—	2	1	no	—
1330	C₂⁴	—	2	1	no	—
1331	#41	—	8	2	no	—
1332	#41	—	8	2	no	—
1333	C₂×Q₈	—	2	1	no	—
1334	C₂×Q₈	—	2	1	no	—
1335	C₂×Q₈	—	2	1	no	—
1336	C₂×Q₈	—	2	1	no	—
1337	C₂×Q₈	—	2	1	no	—
1338	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
1339	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
1340	C₂×D₄	—	2	2	no	—
1341	C₂×D₄	—	2	2	no	—
1342	C₂×D₄	—	2	2	no	—
1343	C₂×D₄	—	2	1	no	—
1344	C₂×D₄	—	2	1	no	—
1345	C₂×D₄	—	2	1	no	—
1346	C₂×D₄	—	2	1	no	—
1347	C₂×D₄	—	2	1	no	—
1348	C₂×D₄	—	2	1	no	—
1349	C₂×D₄	—	2	1	no	—
1350	C₂×D₄	—	2	1	no	—
1351	C₂×D₄	—	2	1	no	—
1352	C₂×D₄	—	2	1	no	—
1353	C₂×D₄	—	2	1	no	—
1354	C₂×D₄	—	2	1	no	—
1355	C₂×D₄	—	2	1	no	—
1356	C₂×D₄	—	2	1	no	—
1357	C₂×D₄	—	2	1	no	—
1358	C₂×D₄	—	2	1	no	—
1359	C₂×D₄	—	2	1	no	—
1360	C₂×D₄	—	2	1	no	—
1361	C₂×D₄	—	4	1	no	—
1362	C₂×D₄	—	4	1	no	—
1363	C₂×D₄	—	4	1	no	—
1364	C₂×D₄	—	8	2	no	—
1365	C₂×D₄	—	8	2	no	—
1366	C₂×D₄	—	8	2	no	—
1367	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1368	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1369	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1370	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1371	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1372	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1373	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1374	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
1375	C₂²×C₄	—	2	1	no	—
1376	C₂²×C₄	—	2	1	no	—
1377	C₂²×C₄	—	2	1	no	—
1378	C₂²×C₄	—	2	1	no	—
1379	C₂²×C₄	—	2	1	no	—
1380	C₂²×C₄	—	2	1	no	—
1381	C₂²×C₄	—	2	1	no	—
1382	C₂²×C₄	—	2	1	no	—
1383	C₂²×C₄	—	2	1	no	—
1384	C₂²×C₄	—	2	1	no	—
1385	C₂²×C₄	—	2	1	no	—
1386	C₂²×C₄	—	2	1	no	—
1387	C₂²×C₄	—	2	1	no	—
1388	C₂²×C₄	—	2	1	no	—
1389	C₂²×C₄	—	2	1	no	—
1390	C₂²×C₄	—	2	1	no	—
1391	C₂²×C₄	—	8	2	no	—
1392	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1393	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1394	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1395	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1396	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1397	SD₁₆	—	2	2	no	—
1398	SD₁₆	—	4	1	no	—
1399	SD₁₆	—	4	1	no	—
1400	SD₁₆	—	4	1	no	—
1401	D₈	—	2	2	no	—
1402	D₈	—	4	1	no	—
1403	D₈	—	4	1	no	—
1404	D₈	—	4	1	no	—
1405	M₁₆	—	4	1	no	—
1406	M₁₆	—	4	1	no	—
1407	M₁₆	—	4	1	no	—
1408	M₁₆	—	4	1	no	—
1409	C₂×C₈	—	4	1	no	—
1410	C₂×C₈	—	4	1	no	—
1411	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1412	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1413	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1414	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1415	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1416	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1417	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1418	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1419	C₄⋊C₄	—	2	1	no	—
1420	C₄⋊C₄	—	2	1	no	—
1421	C₄⋊C₄	—	2	1	no	—
1422	C₄⋊C₄	—	2	1	no	—
1423	C₄⋊C₄	—	2	1	no	—
1424	C₄⋊C₄	—	2	1	no	—
1425	C₄⋊C₄	—	2	1	no	—
1426	C₄⋊C₄	—	2	1	no	—
1427	C₄⋊C₄	—	2	1	no	—
1428	C₄⋊C₄	—	2	1	no	—
1429	C₄⋊C₄	—	2	1	no	—
1430	C₄⋊C₄	—	2	1	no	—
1431	C₄⋊C₄	—	2	1	no	—
1432	C₄⋊C₄	—	2	1	no	—
1433	C₄⋊C₄	—	2	1	no	—
1434	C₄⋊C₄	—	2	1	no	—
1435	C₄⋊C₄	—	2	1	no	—
1436	C₄⋊C₄	—	2	1	no	—
1437	C₄⋊C₄	—	2	1	no	—
1438	C₄⋊C₄	—	2	1	no	—
1439	C₄⋊C₄	—	2	1	no	—
1440	C₄⋊C₄	—	2	1	no	—
1441	C₄⋊C₄	—	2	1	no	—
1442	C₄⋊C₄	—	2	1	no	—
1443	C₄⋊C₄	—	2	1	no	—
1444	C₄⋊C₄	—	2	1	no	—
1445	C₄⋊C₄	—	2	1	no	—
1446	C₄⋊C₄	—	2	1	no	—
1447	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1448	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1449	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1450	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1451	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1452	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1453	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1454	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1455	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1456	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1457	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1458	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1459	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1460	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1461	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1462	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1463	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1464	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1465	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1466	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1467	C₂²⋊C₄	—	2	1	no	—
1468	C₂²⋊C₄	—	2	1	no	—
1469	C₂²⋊C₄	—	2	1	no	—
1470	C₂²⋊C₄	—	2	1	no	—
1471	C₂²⋊C₄	—	2	1	no	—
1472	C₂²⋊C₄	—	2	1	no	—
1473	C₂²⋊C₄	—	2	1	no	—
1474	C₂²⋊C₄	—	2	1	no	—
1475	C₂²⋊C₄	—	2	1	no	—
1476	C₂²⋊C₄	—	2	1	no	—
1477	C₂²⋊C₄	—	2	1	no	—
1478	C₂²⋊C₄	—	2	1	no	—
1479	C₂²⋊C₄	—	2	1	no	—
1480	C₂²⋊C₄	—	2	1	no	—
1481	C₂²⋊C₄	—	2	1	no	—
1482	C₂²⋊C₄	—	2	1	no	—
1483	C₂²⋊C₄	—	2	1	no	—
1484	C₂²⋊C₄	—	2	1	no	—
1485	C₂²⋊C₄	—	2	1	no	—
1486	C₂²⋊C₄	—	2	1	no	—
1487	C₂²⋊C₄	—	2	1	no	—
1488	C₂²⋊C₄	—	2	1	no	—
1489	C₂²⋊C₄	—	2	1	no	—
1490	C₂²⋊C₄	—	2	1	no	—
1491	C₂²⋊C₄	—	2	1	no	—
1492	C₂²⋊C₄	—	2	1	no	—
1493	C₂²⋊C₄	—	2	1	no	—
1494	C₂²⋊C₄	—	2	1	no	—
1495	C₂²⋊C₄	—	2	1	no	—
1496	C₂²⋊C₄	—	2	1	no	—
1497	C₂²⋊C₄	—	2	1	no	—
1498	C₂²⋊C₄	—	2	1	no	—
1499	C₂²⋊C₄	—	2	1	no	—
1500	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1501	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1502	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1503	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1504	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1505	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1506	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1507	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1508	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1509	C₂²⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1510	C₄²	—	2	1	no	—
1511	C₄²	—	2	1	no	—
1512	C₄²	—	2	1	no	—
1513	C₄²	—	2	1	no	—
1514	C₄²	—	2	1	no	—
1515	C₄²	—	2	1	no	—
1516	C₄²	—	2	1	no	—
1517	C₄²	—	2	1	no	—
1518	C₄²	—	2	1	no	—
1519	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1520	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1521	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1522	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1523	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1524	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1525	C₂³	—	2	1	no	—
1526	C₂³	—	2	1	no	—
1527	C₂³	—	2	1	no	—
1528	C₂³	—	2	1	no	—
1529	C₂³	—	2	1	no	—
1530	C₂³	—	4	2	no	—
1531	C₂³	—	4	2	no	—
1532	C₂³	—	4	2	no	—
1533	C₂³	—	4	2	no	—
1534	C₂³	—	8	1	no	—
1535	C₂³	—	8	1	no	—
1536	C₂³	—	8	1	no	—
1537	C₂³	—	8	1	no	—
1538	C₂³	—	8	1	no	—
1539	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1540	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1541	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1542	Q₈	—	2	1	no	—
1543	Q₈	—	2	1	no	—
1544	Q₈	—	4	1	no	—
1545	Q₈	—	8	1	no	—
1546	Q₈	—	8	1	no	—
1547	Q₈	—	8	1	no	—
1548	Q₈	—	8	1	no	—
1549	Q₈	—	8	1	no	—
1550	D₄	—	2	1	no	—
1551	D₄	—	2	1	no	—
1552	D₄	—	2	1	no	—
1553	D₄	—	2	1	no	—
1554	D₄	—	2	1	no	—
1555	D₄	—	2	1	no	—
1556	D₄	—	2	1	no	—
1557	D₄	—	2	1	no	—
1558	D₄	—	2	1	no	—
1559	D₄	—	4	1	no	—
1560	D₄	—	4	1	no	—
1561	D₄	—	4	1	no	—
1562	D₄	—	4	2	no	—
1563	D₄	—	4	2	no	—
1564	D₄	—	4	2	no	—
1565	D₄	—	4	2	no	—
1566	D₄	—	4	2	no	—
1567	D₄	—	4	2	no	—
1568	D₄	—	8	1	no	—
1569	D₄	—	8	1	no	—
1570	D₄	—	8	1	no	—
1571	D₄	—	8	1	no	—
1572	D₄	—	8	1	no	—
1573	D₄	—	8	1	no	—
1574	D₄	—	8	1	no	—
1575	D₄	—	8	1	no	—
1576	D₄	—	8	1	no	—
1577	D₄	—	8	1	no	—
1578	D₄	—	8	1	no	—
1579	D₄	—	8	1	no	—
1580	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
1581	C₂×C₄	—	2	1	no	—
1582	C₂×C₄	—	2	1	no	—
1583	C₂×C₄	—	2	1	no	—
1584	C₂×C₄	—	2	1	no	—
1585	C₂×C₄	—	2	1	no	—
1586	C₂×C₄	—	2	1	no	—
1587	C₂×C₄	—	2	1	no	—
1588	C₂×C₄	—	2	1	no	—
1589	C₂×C₄	—	2	1	no	—
1590	C₂×C₄	—	2	1	no	—
1591	C₂×C₄	—	2	1	no	—
1592	C₂×C₄	—	2	1	no	—
1593	C₂×C₄	—	2	1	no	—
1594	C₂×C₄	—	2	1	no	—
1595	C₂×C₄	—	2	1	no	—
1596	C₂×C₄	—	2	1	no	—
1597	C₂×C₄	—	2	1	no	—
1598	C₂×C₄	—	4	1	no	—
1599	C₂×C₄	—	4	1	no	—
1600	C₂×C₄	—	4	2	no	—
1601	C₂×C₄	—	4	2	no	—
1602	C₂×C₄	—	8	1	no	—
1603	C₂×C₄	—	8	1	no	—
1604	C₂×C₄	—	8	1	no	—
1605	C₂×C₄	—	8	1	no	—
1606	C₂×C₄	—	8	1	no	—
1607	C₂×C₄	—	8	1	no	—
1608	C₂×C₄	—	8	1	no	—
1609	C₂×C₄	—	8	1	no	—
1610	C₂×C₄	—	8	1	no	—
1611	C₂×C₄	—	8	1	no	—
1612	C₂×C₄	—	8	1	no	—
1613	C₂×C₄	—	8	1	no	—
1614	C₂×C₄	—	8	1	no	—
1615	C₂×C₄	—	8	1	no	—
1616	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1617	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1618	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1619	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1620	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1621	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1622	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1623	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1624	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1625	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1626	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1627	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1628	C₈	—	2	1	no	—
1629	C₈	—	2	1	no	—
1630	C₈	—	2	1	no	—
1631	C₈	—	2	1	no	—
1632	C₈	—	2	1	no	—
1633	C₈	—	2	1	no	—
1634	C₈	—	2	1	no	—
1635	C₈	—	2	1	no	—
1636	C₂²	—	2	1	no	—
1637	C₂²	—	2	1	no	—
1638	C₂²	—	2	1	no	—
1639	C₂²	—	2	2	no	—
1640	C₂²	—	2	1	no	—
1641	C₂²	—	2	1	no	—
1642	C₂²	—	2	1	no	—
1643	C₂²	—	2	1	no	—
1644	C₂²	—	2	1	no	—
1645	C₂²	—	2	1	no	—
1646	C₂²	—	4	1	no	—
1647	C₂²	—	4	1	no	—
1648	C₂²	—	4	1	no	—
1649	C₂²	—	4	1	no	—
1650	C₂²	—	4	1	no	—
1651	C₂²	—	4	1	no	—
1652	C₂²	—	4	1	no	—
1653	C₂²	—	4	1	no	—
1654	C₂²	—	4	1	no	—
1655	C₂²	—	4	1	no	—
1656	C₂²	—	4	1	no	—
1657	C₂²	—	4	1	no	—
1658	C₂²	—	4	1	no	—
1659	C₂²	—	4	1	no	—
1660	C₂²	—	8	4	no	—
1661	C₂²	—	16	2	no	—
1662	C₂²	—	16	2	no	—
1663	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1664	C₄	—	2	1	no	—
1665	C₄	—	2	1	no	—
1666	C₄	—	2	1	no	—
1667	C₄	—	2	1	no	—
1668	C₄	—	2	1	no	—
1669	C₄	—	2	1	no	—
1670	C₄	—	2	1	no	—
1671	C₄	—	2	1	no	—
1672	C₄	—	2	1	no	—
1673	C₄	—	2	1	no	—
1674	C₄	—	2	1	no	—
1675	C₄	—	4	1	no	—
1676	C₄	—	4	1	no	—
1677	C₄	—	4	1	no	—
1678	C₄	—	4	1	no	—
1679	C₄	—	4	1	no	—
1680	C₄	—	4	1	no	—
1681	C₄	—	4	1	no	—
1682	C₄	—	4	1	no	—
1683	C₄	—	4	1	no	—
1684	C₄	—	4	1	no	—
1685	C₄	—	4	1	no	—
1686	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1687	C₄	C₅₃×#585	1	1	yes	characteristic
1688	C₂	—	4	1	no	—
1689	C₂	—	4	1	no	—
1690	C₂	—	4	1	no	—
1691	C₂	—	4	2	no	—
1692	C₂	—	8	1	no	—
1693	C₂	—	8	1	no	—
1694	C₂	—	8	1	no	—
1695	C₂	—	8	1	no	—
1696	C₂	C₅₃×#3489	1	1	yes	characteristic
1697	C₂	C₅₃×#3585	1	1	yes	characteristic
1698	C₂	C₅₃×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3565	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3388	C₂	semidirect
5. C₅₃×#3368	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3355	C₂	semidirect
8. C₅₃×#3351	C₂	semidirect
9. C₅₃×#3350	C₂	semidirect
10. C₅₃×#3348	C₂	semidirect
11. C₅₃×#3347	C₂	semidirect
12. C₅₃×#3347	C₂	semidirect
13. C₅₃×#3325	C₂	semidirect
14. C₅₃×#3324	C₂	semidirect
15. C₅₃×#3318	C₂	semidirect
16. C₅₃×#3318	C₂	semidirect
17. C₅₃×#3310	C₂	semidirect
18. C₅₃×#3310	C₂	semidirect
19. C₅₃×#3257	C₂	semidirect
20. C₅₃×#3257	C₂	semidirect
21. C₅₃×#3251	C₂	semidirect
22. C₅₃×#3241	C₂	semidirect
23. C₅₃×#3241	C₂	semidirect
24. C₅₃×#3235	C₂	semidirect
25. C₅₃×#3118	C₂	semidirect
26. C₅₃×#3118	C₂	semidirect
27. C₅₃×#3114	C₂	semidirect
28. C₅₃×#3081	C₂	semidirect
29. C₅₃×#3081	C₂	semidirect
30. C₅₃×#3077	C₂	semidirect
31. C₅₃×#2995	C₂	semidirect
34. C₅₃×#557	C₂²	semidirect
36. C₅₃×#556	C₂²	semidirect
38. C₅₃×#555	C₂²	semidirect
40. C₅₃×#554	C₂²	semidirect
44. C₅₃×#553	C₂²	semidirect
45. C₅₃×#553	C₂²	semidirect
47. C₅₃×#552	C₂²	semidirect
48. C₅₃×#552	C₂²	semidirect
56. C₅₃×#544	C₂²	semidirect
57. C₅₃×#544	C₂²	semidirect
60. C₅₃×#542	C₂²	semidirect
61. C₅₃×#542	C₂²	semidirect
68. C₅₃×#533	C₂²	semidirect
71. C₅₃×#529	C₂²	semidirect
77. C₅₃×#501	C₂²	semidirect
78. C₅₃×#501	C₂²	semidirect
79. C₅₃×#501	C₂²	semidirect
80. C₅₃×#501	C₂²	semidirect
81. C₅₃×#499	C₂²	semidirect
82. C₅₃×#499	C₂²	semidirect
83. C₅₃×#490	C₂²	semidirect
84. C₅₃×#490	C₂²	semidirect
85. C₅₃×#490	C₂²	semidirect
86. C₅₃×#490	C₂²	semidirect
87. C₅₃×#486	C₂²	semidirect
88. C₅₃×#486	C₂²	semidirect
89. C₅₃×#485	C₂²	semidirect
90. C₅₃×#485	C₂²	semidirect
91. C₅₃×#483	C₂²	semidirect
92. C₅₃×#482	C₂²	semidirect
93. C₅₃×#482	C₂²	semidirect
94. C₅₃×#482	C₂²	semidirect
95. C₅₃×#482	C₂²	semidirect
96. C₅₃×#482	C₂²	semidirect
97. C₅₃×#482	C₂²	semidirect
98. C₅₃×#482	C₂²	semidirect
99. C₅₃×#482	C₂²	semidirect
100. C₅₃×#482	C₂²	semidirect
101. C₅₃×#482	C₂²	semidirect
102. C₅₃×#481	C₂²	semidirect
103. C₅₃×#481	C₂²	semidirect
104. C₅₃×#480	C₂²	semidirect
105. C₅₃×#480	C₂²	semidirect
106. C₅₃×#480	C₂²	semidirect
107. C₅₃×#479	C₂²	semidirect
108. C₅₃×#479	C₂²	semidirect
114. C₅₃×#478	C₂²	semidirect
115. C₅₃×#478	C₂²	semidirect
116. C₅₃×#478	C₂²	semidirect
117. C₅₃×#478	C₂²	semidirect
118. C₅₃×#478	C₂²	semidirect
119. C₅₃×#478	C₂²	semidirect
120. C₅₃×#478	C₂²	semidirect
121. C₅₃×#478	C₂²	semidirect
122. C₅₃×#478	C₂²	semidirect
125. C₅₃×#476	C₂²	semidirect
126. C₅₃×#476	C₂²	semidirect
127. C₅₃×#476	C₂²	semidirect
128. C₅₃×#476	C₂²	semidirect
129. C₅₃×#475	C₂²	semidirect
132. C₅₃×#474	C₂²	semidirect
133. C₅₃×#474	C₂²	semidirect
134. C₅₃×#474	C₂²	semidirect
135. C₅₃×#474	C₂²	semidirect
136. C₅₃×#474	C₂²	semidirect
137. C₅₃×#469	C₂²	semidirect
138. C₅₃×#469	C₂²	semidirect
139. C₅₃×#469	C₂²	semidirect
140. C₅₃×#469	C₂²	semidirect
141. C₅₃×#468	C₂²	semidirect
142. C₅₃×#468	C₂²	semidirect
143. C₅₃×#468	C₂²	semidirect
144. C₅₃×#468	C₂²	semidirect
145. C₅₃×#466	C₂²	semidirect
146. C₅₃×#466	C₂²	semidirect
147. C₅₃×#465	C₂²	semidirect
148. C₅₃×#465	C₂²	semidirect
150. C₅₃×#463	C₂²	semidirect
151. C₅₃×#463	C₂²	semidirect
152. C₅₃×#463	C₂²	semidirect
153. C₅₃×#460	C₂²	semidirect
154. C₅₃×#460	C₂²	semidirect
155. C₅₃×#460	C₂²	semidirect
156. C₅₃×#459	C₂²	semidirect
157. C₅₃×#459	C₂²	semidirect
158. C₅₃×#459	C₂²	semidirect
165. C₅₃×#446	C₂²	semidirect
166. C₅₃×#446	C₂²	semidirect
169. C₅₃×#442	C₂²	semidirect
170. C₅₃×#442	C₂²	semidirect
173. C₅₃×#440	C₂²	semidirect
174. C₅₃×#440	C₂²	semidirect
176. C₄×SD₁₆×C₅₃	C₂²	semidirect
178. C₄×D₈×C₅₃	C₂²	semidirect
179. C₅₃×#436	C₂²	semidirect
180. C₅₃×#436	C₂²	semidirect
181. C₅₃×#435	C₂²	semidirect
182. C₅₃×#435	C₂²	semidirect
183. C₅₃×#435	C₂²	semidirect
184. C₅₃×#435	C₂²	semidirect
185. C₅₃×#433	C₂²	semidirect
186. C₅₃×#433	C₂²	semidirect
187. C₅₃×#432	C₂²	semidirect
188. C₅₃×#428	C₂²	semidirect
189. C₅₃×#428	C₂²	semidirect
190. C₅₃×#428	C₂²	semidirect
191. C₅₃×#428	C₂²	semidirect
192. C₅₃×#427	C₂²	semidirect
193. C₅₃×#427	C₂²	semidirect
194. C₅₃×#424	C₂²	semidirect
195. C₅₃×#424	C₂²	semidirect
196. C₅₃×#423	C₂²	semidirect
786. #62223	C₅₃	direct (N × H)
839. #3565	C₂×C₅₃	semidirect
840. #3519	C₂×C₅₃	semidirect
841. #3389	C₂×C₅₃	semidirect
842. #3388	C₂×C₅₃	semidirect
843. #3368	C₂×C₅₃	semidirect
844. #3366	C₂×C₅₃	semidirect
845. #3355	C₂×C₅₃	semidirect
846. #3351	C₂×C₅₃	semidirect
847. #3350	C₂×C₅₃	semidirect
848. #3348	C₂×C₅₃	semidirect
849. #3347	C₂×C₅₃	semidirect
850. #3347	C₂×C₅₃	semidirect
851. #3325	C₂×C₅₃	semidirect
852. #3324	C₂×C₅₃	semidirect
853. #3318	C₂×C₅₃	semidirect
854. #3318	C₂×C₅₃	semidirect
855. #3310	C₂×C₅₃	semidirect
856. #3310	C₂×C₅₃	semidirect
857. #3257	C₂×C₅₃	semidirect
858. #3257	C₂×C₅₃	semidirect
859. #3251	C₂×C₅₃	semidirect
860. #3241	C₂×C₅₃	semidirect
861. #3241	C₂×C₅₃	semidirect
862. #3235	C₂×C₅₃	semidirect
863. #3118	C₂×C₅₃	semidirect
864. #3118	C₂×C₅₃	semidirect
865. #3114	C₂×C₅₃	semidirect
866. #3081	C₂×C₅₃	semidirect
867. #3081	C₂×C₅₃	semidirect
868. #3077	C₂×C₅₃	semidirect
869. #2995	C₂×C₅₃	semidirect
883. #557	C₂²×C₅₃	semidirect
885. #556	C₂²×C₅₃	semidirect
887. #555	C₂²×C₅₃	semidirect
889. #554	C₂²×C₅₃	semidirect
893. #553	C₂²×C₅₃	semidirect
894. #553	C₂²×C₅₃	semidirect
896. #552	C₂²×C₅₃	semidirect
897. #552	C₂²×C₅₃	semidirect
905. #544	C₂²×C₅₃	semidirect
906. #544	C₂²×C₅₃	semidirect
909. #542	C₂²×C₅₃	semidirect
910. #542	C₂²×C₅₃	semidirect
917. #533	C₂²×C₅₃	semidirect
920. #529	C₂²×C₅₃	semidirect
926. #501	C₂²×C₅₃	semidirect
927. #501	C₂²×C₅₃	semidirect
928. #501	C₂²×C₅₃	semidirect
929. #501	C₂²×C₅₃	semidirect
930. #499	C₂²×C₅₃	semidirect
931. #499	C₂²×C₅₃	semidirect
932. #490	C₂²×C₅₃	semidirect
933. #490	C₂²×C₅₃	semidirect
934. #490	C₂²×C₅₃	semidirect
935. #490	C₂²×C₅₃	semidirect
936. #486	C₂²×C₅₃	semidirect
937. #486	C₂²×C₅₃	semidirect
938. #485	C₂²×C₅₃	semidirect
939. #485	C₂²×C₅₃	semidirect
940. #483	C₂²×C₅₃	semidirect
941. #482	C₂²×C₅₃	semidirect
942. #482	C₂²×C₅₃	semidirect
943. #482	C₂²×C₅₃	semidirect
944. #482	C₂²×C₅₃	semidirect
945. #482	C₂²×C₅₃	semidirect
946. #482	C₂²×C₅₃	semidirect
947. #482	C₂²×C₅₃	semidirect
948. #482	C₂²×C₅₃	semidirect
949. #482	C₂²×C₅₃	semidirect
950. #482	C₂²×C₅₃	semidirect
951. #481	C₂²×C₅₃	semidirect
952. #481	C₂²×C₅₃	semidirect
953. #480	C₂²×C₅₃	semidirect
954. #480	C₂²×C₅₃	semidirect
955. #480	C₂²×C₅₃	semidirect
956. #479	C₂²×C₅₃	semidirect
957. #479	C₂²×C₅₃	semidirect
963. #478	C₂²×C₅₃	semidirect
964. #478	C₂²×C₅₃	semidirect
965. #478	C₂²×C₅₃	semidirect
966. #478	C₂²×C₅₃	semidirect
967. #478	C₂²×C₅₃	semidirect
968. #478	C₂²×C₅₃	semidirect
969. #478	C₂²×C₅₃	semidirect
970. #478	C₂²×C₅₃	semidirect
971. #478	C₂²×C₅₃	semidirect
974. #476	C₂²×C₅₃	semidirect
975. #476	C₂²×C₅₃	semidirect
976. #476	C₂²×C₅₃	semidirect
977. #476	C₂²×C₅₃	semidirect
978. #475	C₂²×C₅₃	semidirect
981. #474	C₂²×C₅₃	semidirect
982. #474	C₂²×C₅₃	semidirect
983. #474	C₂²×C₅₃	semidirect
984. #474	C₂²×C₅₃	semidirect
985. #474	C₂²×C₅₃	semidirect
986. #469	C₂²×C₅₃	semidirect
987. #469	C₂²×C₅₃	semidirect
988. #469	C₂²×C₅₃	semidirect
989. #469	C₂²×C₅₃	semidirect
990. #468	C₂²×C₅₃	semidirect
991. #468	C₂²×C₅₃	semidirect
992. #468	C₂²×C₅₃	semidirect
993. #468	C₂²×C₅₃	semidirect
994. #466	C₂²×C₅₃	semidirect
995. #466	C₂²×C₅₃	semidirect
996. #465	C₂²×C₅₃	semidirect
997. #465	C₂²×C₅₃	semidirect
999. #463	C₂²×C₅₃	semidirect
1000. #463	C₂²×C₅₃	semidirect
1001. #463	C₂²×C₅₃	semidirect
1002. #460	C₂²×C₅₃	semidirect
1003. #460	C₂²×C₅₃	semidirect
1004. #460	C₂²×C₅₃	semidirect
1005. #459	C₂²×C₅₃	semidirect
1006. #459	C₂²×C₅₃	semidirect
1007. #459	C₂²×C₅₃	semidirect
1014. #446	C₂²×C₅₃	semidirect
1015. #446	C₂²×C₅₃	semidirect
1018. #442	C₂²×C₅₃	semidirect
1019. #442	C₂²×C₅₃	semidirect
1022. #440	C₂²×C₅₃	semidirect
1023. #440	C₂²×C₅₃	semidirect
1025. C₄×SD₁₆	C₂²×C₅₃	semidirect
1027. C₄×D₈	C₂²×C₅₃	semidirect
1028. #436	C₂²×C₅₃	semidirect
1029. #436	C₂²×C₅₃	semidirect
1030. #435	C₂²×C₅₃	semidirect
1031. #435	C₂²×C₅₃	semidirect
1032. #435	C₂²×C₅₃	semidirect
1033. #435	C₂²×C₅₃	semidirect
1034. #433	C₂²×C₅₃	semidirect
1035. #433	C₂²×C₅₃	semidirect
1036. #432	C₂²×C₅₃	semidirect
1037. #428	C₂²×C₅₃	semidirect
1038. #428	C₂²×C₅₃	semidirect
1039. #428	C₂²×C₅₃	semidirect
1040. #428	C₂²×C₅₃	semidirect
1041. #427	C₂²×C₅₃	semidirect
1042. #427	C₂²×C₅₃	semidirect
1043. #424	C₂²×C₅₃	semidirect
1044. #424	C₂²×C₅₃	semidirect
1045. #423	C₂²×C₅₃	semidirect
1052. C₅₃	#62223	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×#3565	2
C₅₃×#3519	2
C₅₃×#3389	2
C₅₃×#3388	2
C₅₃×#3368	2
C₅₃×#3366	2
C₅₃×#3355	2
C₅₃×#3351	2
C₅₃×#3350	2
C₅₃×#3348	2
C₅₃×#3347	2
C₅₃×#3325	2
C₅₃×#3324	2
C₅₃×#3318	2
C₅₃×#3310	2
C₅₃×#3257	2
C₅₃×#3251	2
C₅₃×#3241	2
C₅₃×#3235	2
C₅₃×#3118	2
C₅₃×#3114	2
C₅₃×#3081	2
C₅₃×#3077	2
C₅₃×#2995	2
#62223	53

Subgroups — C53×#62223 #27269735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62223 #27269735