Subgroups — C₅₃×#61974 #27269486

Order 13568.

1920 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3481	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3372	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3331	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3256	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3219	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3114	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3036	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2989	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
26	C₂×#135×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#559	C₂²	1	1	yes	characteristic
28	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#554	C₂²	1	1	yes	characteristic
30	C₅₃×#554	C₂²	1	1	yes	characteristic
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	—	2	2	no	—
34	C₅₃×#553	C₂²	1	2	yes	—
35	C₅₃×#551	—	2	2	no	—
36	C₅₃×#550	—	2	1	no	—
37	C₅₃×#550	C₂²	1	1	yes	characteristic
38	C₅₃×#550	C₂²	1	2	yes	complemented
39	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#547	C₂²	1	1	yes	characteristic
41	C₅₃×#547	C₂²	1	2	yes	complemented
42	C₅₃×#546	—	2	1	no	—
43	C₅₃×#546	C₂²	1	2	yes	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#540	—	2	1	no	—
46	C₅₃×#540	—	2	2	no	—
47	C₅₃×#532	C₂²	1	1	yes	characteristic
48	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
49	C₅₃×#532	C₂²	1	2	yes	complemented
50	C₅₃×#529	—	2	1	no	—
51	C₅₃×#529	C₂²	1	2	yes	—
52	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#529	C₂²	1	2	yes	complemented
54	C₅₃×#525	—	2	2	no	—
55	C₅₃×#520	—	2	1	no	—
56	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
57	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×D₄×C₅₃	—	2	1	no	—
59	C₂×C₄×D₄×C₅₃	C₂²	1	2	yes	—
60	C₅₃×#497	C₂²	1	2	yes	complemented
61	C₅₃×#496	C₂²	1	2	yes	complemented
62	C₅₃×#493	C₂²	1	1	yes	characteristic
63	C₅₃×#492	C₂²	1	1	yes	characteristic
64	C₅₃×#491	C₂²	1	2	yes	complemented
65	C₅₃×#490	C₂²	1	2	yes	complemented
66	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#483	C₂²	1	2	yes	complemented
70	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#480	C₂²	1	2	yes	complemented
72	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#479	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	complemented
77	C₅₃×#477	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#470	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	—
81	C₅₃×#468	C₂²	1	2	yes	—
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	—
89	C₅₃×#463	C₂²	1	1	yes	characteristic
90	C₅₃×#463	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#463	C₂²	1	2	yes	complemented
93	C₅₃×#463	C₂²	1	2	yes	complemented
94	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#461	C₂²	1	2	yes	—
96	C₅₃×#461	C₂²	1	1	yes	characteristic
97	C₅₃×#461	C₂²	1	2	yes	complemented
98	C₅₃×#460	C₂²	1	1	yes	characteristic
99	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#459	C₂²	1	1	yes	characteristic
101	C₅₃×#459	C₂²	1	2	yes	—
102	C₅₃×#459	C₂²	1	1	yes	characteristic
103	C₅₃×#459	C₂²	1	2	yes	complemented
104	C₅₃×#452	C₂²	1	1	yes	characteristic
105	C₅₃×#452	C₂²	1	2	yes	complemented
106	C₅₃×#452	C₂²	1	2	yes	complemented
107	C₅₃×#450	C₂²	1	2	yes	—
108	C₅₃×#449	C₂²	1	2	yes	—
109	C₅₃×#449	C₂²	1	2	yes	—
110	C₅₃×#449	C₂²	1	1	yes	characteristic
111	C₅₃×#449	C₂²	1	2	yes	complemented
112	C₅₃×#449	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	—
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#442	C₂²	1	2	yes	—
117	C₅₃×#442	C₂²	1	2	yes	complemented
118	C₅₃×#440	C₂²	1	2	yes	—
119	C₅₃×#440	C₂²	1	2	yes	complemented
120	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
124	C₅₃×#436	C₂²	1	1	yes	characteristic
125	C₅₃×#436	C₂²	1	1	yes	characteristic
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₅₃×#435	C₂²	1	2	yes	complemented
128	C₅₃×#432	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#423	C₂²	1	2	yes	complemented
131	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#417	C₂²	1	2	yes	complemented
133	C₅₃×#417	C₂²	1	2	yes	complemented
134	C₅₃×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
138	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
139	C₂×#41×C₅₃	C₂³	1	2	yes	—
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₅₃	—	2	1	no	—
143	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₅₃	—	2	2	no	—
145	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
146	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
147	#135×C₅₃	—	4	4	no	—
148	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
149	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×D₈×C₅₃	C₂³	1	2	yes	—
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
165	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
166	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
168	#127×C₅₃	—	2	1	no	—
169	#127×C₅₃	—	2	2	no	—
170	#127×C₅₃	C₂³	1	1	yes	characteristic
171	#127×C₅₃	C₂³	1	2	yes	—
172	#127×C₅₃	C₂³	1	1	yes	characteristic
173	#126×C₅₃	—	2	2	no	—
174	#126×C₅₃	—	2	2	no	—
175	#126×C₅₃	—	2	1	no	—
176	#126×C₅₃	—	2	2	no	—
177	#125×C₅₃	—	2	1	no	—
178	#125×C₅₃	—	2	1	no	—
179	#125×C₅₃	—	2	2	no	—
180	#125×C₅₃	C₂³	1	2	yes	—
181	#125×C₅₃	C₂³	1	1	yes	characteristic
182	#124×C₅₃	—	2	1	no	—
183	#124×C₅₃	—	2	1	no	—
184	#124×C₅₃	C₂³	1	2	yes	—
185	#124×C₅₃	C₂³	1	1	yes	characteristic
186	#124×C₅₃	C₂³	1	2	yes	—
187	#123×C₅₃	—	2	2	no	—
188	#123×C₅₃	—	2	2	no	—
189	#123×C₅₃	—	2	2	no	—
190	#123×C₅₃	—	2	2	no	—
191	#123×C₅₃	—	2	2	no	—
192	#123×C₅₃	—	2	2	no	—
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	1	no	—
196	C₂²⋊Q₈×C₅₃	—	2	2	no	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	1	no	—
199	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
201	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	—	2	2	no	—
205	#121×C₅₃	—	2	2	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	2	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	1	no	—
211	#121×C₅₃	—	2	2	no	—
212	#121×C₅₃	—	2	1	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	1	no	—
215	#121×C₅₃	—	2	1	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	C₂³	1	2	yes	—
218	#121×C₅₃	C₂³	1	2	yes	—
219	#121×C₅₃	C₂³	1	1	yes	characteristic
220	#121×C₅₃	C₂³	1	2	yes	—
221	#120×C₅₃	—	2	2	no	—
222	#120×C₅₃	—	2	2	no	—
223	C₄×Q₈×C₅₃	—	2	1	no	—
224	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
225	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
226	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
229	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
230	C₄×D₄×C₅₃	—	2	1	no	—
231	C₄×D₄×C₅₃	—	2	1	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	—	2	2	no	—
236	C₄×D₄×C₅₃	—	2	2	no	—
237	C₄×D₄×C₅₃	—	2	1	no	—
238	C₄×D₄×C₅₃	—	2	2	no	—
239	C₄×D₄×C₅₃	—	2	1	no	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	1	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	2	no	—
247	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
248	C₄×D₄×C₅₃	D₄	1	2	yes	—
249	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
250	C₄×D₄×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	C₂³	1	2	yes	—
252	C₄×D₄×C₅₃	C₂³	1	2	yes	—
253	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₃	C₂³	1	2	yes	—
258	#117×C₅₃	—	2	1	no	—
259	#117×C₅₃	—	2	1	no	—
260	#117×C₅₃	—	2	2	no	—
261	#117×C₅₃	—	2	2	no	—
262	#117×C₅₃	D₄	1	2	yes	—
263	#117×C₅₃	D₄	1	1	yes	characteristic
264	#117×C₅₃	C₂³	1	1	yes	characteristic
265	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
266	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
267	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₄²×C₅₃	—	2	1	no	—
272	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	1	yes	characteristic
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	1	yes	characteristic
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	#97×C₅₃	C₂³	1	2	yes	—
312	#97×C₅₃	C₂³	1	2	yes	—
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₅₃	—	2	2	no	—
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	4	2	no	—
318	#41×C₅₃	—	4	1	no	—
319	#41×C₅₃	—	4	2	no	—
320	#41×C₅₃	—	4	2	no	—
321	#41×C₅₃	—	4	2	no	—
322	#41×C₅₃	—	4	2	no	—
323	#41×C₅₃	—	4	2	no	—
324	#41×C₅₃	—	4	2	no	—
325	#41×C₅₃	—	4	4	no	—
326	#41×C₅₃	—	8	2	no	—
327	C₂×Q₈×C₅₃	—	2	1	no	—
328	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
331	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₅₃	—	2	4	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	2	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	2	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	1	no	—
347	C₂×D₄×C₅₃	—	2	1	no	—
348	C₂×D₄×C₅₃	—	4	2	no	—
349	C₂×D₄×C₅₃	—	4	4	no	—
350	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
352	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
355	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	2	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	2	2	no	—
368	C₂²×C₄×C₅₃	—	8	4	no	—
369	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
370	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
371	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
372	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
375	Q₁₆×C₅₃	—	4	1	no	—
376	Q₁₆×C₅₃	—	4	2	no	—
377	SD₁₆×C₅₃	—	2	4	no	—
378	SD₁₆×C₅₃	—	2	2	no	—
379	SD₁₆×C₅₃	—	4	1	no	—
380	SD₁₆×C₅₃	—	4	2	no	—
381	SD₁₆×C₅₃	—	4	2	no	—
382	SD₁₆×C₅₃	—	4	2	no	—
383	SD₁₆×C₅₃	—	4	2	no	—
384	D₈×C₅₃	—	2	4	no	—
385	D₈×C₅₃	—	2	2	no	—
386	D₈×C₅₃	—	4	2	no	—
387	D₈×C₅₃	—	4	2	no	—
388	D₈×C₅₃	—	4	2	no	—
389	M₁₆×C₅₃	—	4	2	no	—
390	M₁₆×C₅₃	—	4	2	no	—
391	C₂×C₈×C₅₃	—	4	2	no	—
392	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
397	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	2	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	—	2	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	1	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	1	no	—
407	C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₄⋊C₄×C₅₃	—	2	2	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	1	no	—
413	C₄⋊C₄×C₅₃	—	2	2	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
418	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	2	no	—
427	C₂²⋊C₄×C₅₃	—	2	1	no	—
428	C₂²⋊C₄×C₅₃	—	2	1	no	—
429	C₂²⋊C₄×C₅₃	—	2	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	no	—
432	C₂²⋊C₄×C₅₃	—	2	2	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	2	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	1	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	1	no	—
445	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
448	C₄²×C₅₃	—	2	1	no	—
449	C₄²×C₅₃	—	2	1	no	—
450	C₄²×C₅₃	—	2	1	no	—
451	C₄²×C₅₃	—	2	2	no	—
452	C₄²×C₅₃	—	2	1	no	—
453	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₃	C₂×D₄	1	2	yes	—
455	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
456	C₄²×C₅₃	C₂×D₄	1	2	yes	—
457	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₄²×C₅₃	C₂⁴	1	2	yes	—
459	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
460	C₂³×C₅₃	—	2	1	no	—
461	C₂³×C₅₃	—	2	1	no	—
462	C₂³×C₅₃	—	2	2	no	—
463	C₂³×C₅₃	—	2	2	no	—
464	C₂³×C₅₃	—	4	4	no	—
465	C₂³×C₅₃	—	4	4	no	—
466	C₂³×C₅₃	—	8	2	no	—
467	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
468	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
469	Q₈×C₅₃	—	2	2	no	—
470	Q₈×C₅₃	—	2	1	no	—
471	Q₈×C₅₃	—	2	1	no	—
472	Q₈×C₅₃	—	2	2	no	—
473	Q₈×C₅₃	—	2	2	no	—
474	Q₈×C₅₃	—	2	1	no	—
475	Q₈×C₅₃	—	2	1	no	—
476	Q₈×C₅₃	—	8	1	no	—
477	D₄×C₅₃	—	2	2	no	—
478	D₄×C₅₃	—	2	2	no	—
479	D₄×C₅₃	—	2	1	no	—
480	D₄×C₅₃	—	2	2	no	—
481	D₄×C₅₃	—	2	1	no	—
482	D₄×C₅₃	—	2	2	no	—
483	D₄×C₅₃	—	2	2	no	—
484	D₄×C₅₃	—	2	1	no	—
485	D₄×C₅₃	—	4	2	no	—
486	D₄×C₅₃	—	4	4	no	—
487	D₄×C₅₃	—	4	4	no	—
488	D₄×C₅₃	—	4	2	no	—
489	D₄×C₅₃	—	4	4	no	—
490	D₄×C₅₃	—	4	2	no	—
491	D₄×C₅₃	—	4	2	no	—
492	D₄×C₅₃	—	8	2	no	—
493	D₄×C₅₃	—	8	1	no	—
494	D₄×C₅₃	—	8	1	no	—
495	D₄×C₅₃	—	8	2	no	—
496	D₄×C₅₃	—	8	1	no	—
497	D₄×C₅₃	—	8	2	no	—
498	D₄×C₅₃	—	8	2	no	—
499	D₄×C₅₃	—	8	2	no	—
500	D₄×C₅₃	—	8	2	no	—
501	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
502	C₂×C₄×C₅₃	—	2	2	no	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	2	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	2	no	—
509	C₂×C₄×C₅₃	—	2	1	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	2	no	—
512	C₂×C₄×C₅₃	—	2	1	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	4	2	no	—
516	C₂×C₄×C₅₃	—	4	2	no	—
517	C₂×C₄×C₅₃	—	4	1	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	4	2	no	—
520	C₂×C₄×C₅₃	—	4	4	no	—
521	C₂×C₄×C₅₃	—	4	4	no	—
522	C₂×C₄×C₅₃	—	4	2	no	—
523	C₂×C₄×C₅₃	—	4	2	no	—
524	C₂×C₄×C₅₃	—	8	2	no	—
525	C₂×C₄×C₅₃	—	8	2	no	—
526	C₂×C₄×C₅₃	—	8	2	no	—
527	C₂×C₄×C₅₃	—	8	2	no	—
528	C₂×C₄×C₅₃	—	8	2	no	—
529	C₂×C₄×C₅₃	—	8	2	no	—
530	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
535	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
536	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
539	C₈×C₅₃	—	2	2	no	—
540	C₈×C₅₃	—	2	2	no	—
541	C₈×C₅₃	—	2	1	no	—
542	C₈×C₅₃	—	2	1	no	—
543	C₈×C₅₃	—	2	1	no	—
544	C₈×C₅₃	—	2	1	no	—
545	#61974	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
546	C₂²×C₅₃	—	2	2	no	—
547	C₂²×C₅₃	—	2	1	no	—
548	C₂²×C₅₃	—	2	1	no	—
549	C₂²×C₅₃	—	2	2	no	—
550	C₂²×C₅₃	—	2	2	no	—
551	C₂²×C₅₃	—	2	1	no	—
552	C₂²×C₅₃	—	2	2	no	—
553	C₂²×C₅₃	—	4	1	no	—
554	C₂²×C₅₃	—	4	1	no	—
555	C₂²×C₅₃	—	4	2	no	—
556	C₂²×C₅₃	—	4	1	no	—
557	C₂²×C₅₃	—	4	2	no	—
558	C₂²×C₅₃	—	4	1	no	—
559	C₂²×C₅₃	—	4	2	no	—
560	C₂²×C₅₃	—	4	2	no	—
561	C₂²×C₅₃	—	4	2	no	—
562	C₂²×C₅₃	—	4	1	no	—
563	C₂²×C₅₃	—	4	2	no	—
564	C₂²×C₅₃	—	8	8	no	—
565	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
566	C₄×C₅₃	—	2	1	no	—
567	C₄×C₅₃	—	2	2	no	—
568	C₄×C₅₃	—	2	1	no	—
569	C₄×C₅₃	—	2	1	no	—
570	C₄×C₅₃	—	2	2	no	—
571	C₄×C₅₃	—	2	1	no	—
572	C₄×C₅₃	—	2	2	no	—
573	C₄×C₅₃	—	4	1	no	—
574	C₄×C₅₃	—	4	2	no	—
575	C₄×C₅₃	—	4	1	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	—	4	1	no	—
578	C₄×C₅₃	—	4	2	no	—
579	C₄×C₅₃	—	4	1	no	—
580	C₄×C₅₃	—	4	1	no	—
581	C₄×C₅₃	#575	1	2	yes	—
582	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
583	C₄×C₅₃	#585	1	1	yes	characteristic
584	#3517	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3481	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3400	C₂×C₅₃	1	1	yes	characteristic, complemented
587	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3372	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
590	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
591	#3331	C₂×C₅₃	1	1	yes	characteristic, complemented
592	#3309	C₂×C₅₃	1	2	yes	complemented
593	#3307	C₂×C₅₃	1	2	yes	complemented
594	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
595	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#3268	C₂×C₅₃	1	2	yes	complemented
597	#3267	C₂×C₅₃	1	2	yes	complemented
598	#3256	C₂×C₅₃	1	2	yes	complemented
599	#3247	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3219	C₂×C₅₃	1	2	yes	complemented
601	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3114	C₂×C₅₃	1	2	yes	complemented
603	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3036	C₂×C₅₃	1	2	yes	complemented
605	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#2989	C₂×C₅₃	1	1	yes	characteristic, complemented
607	C₂×C₅₃	—	4	1	no	—
608	C₂×C₅₃	—	4	2	no	—
609	C₂×C₅₃	—	4	2	no	—
610	C₂×C₅₃	—	8	1	no	—
611	C₂×C₅₃	—	8	2	no	—
612	C₂×C₅₃	—	8	2	no	—
613	C₂×C₅₃	#3488	1	1	yes	characteristic
614	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
615	C₂×C₅₃	#3585	1	1	yes	characteristic
616	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
617	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
618	C₂×#135	C₂²×C₅₃	1	2	yes	—
619	#559	C₂²×C₅₃	1	1	yes	characteristic
620	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
621	#554	C₂²×C₅₃	1	1	yes	characteristic
622	#554	C₂²×C₅₃	1	1	yes	characteristic
623	#553	—	2	1	no	—
624	#553	—	2	1	no	—
625	#553	—	2	2	no	—
626	#553	C₂²×C₅₃	1	2	yes	—
627	#551	—	2	2	no	—
628	#550	—	2	1	no	—
629	#550	C₂²×C₅₃	1	1	yes	characteristic
630	#550	C₂²×C₅₃	1	2	yes	complemented
631	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
632	#547	C₂²×C₅₃	1	1	yes	characteristic
633	#547	C₂²×C₅₃	1	2	yes	complemented
634	#546	—	2	1	no	—
635	#546	C₂²×C₅₃	1	2	yes	—
636	D₄²	C₂²×C₅₃	1	1	yes	characteristic
637	#540	—	2	1	no	—
638	#540	—	2	2	no	—
639	#532	C₂²×C₅₃	1	1	yes	characteristic
640	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
641	#532	C₂²×C₅₃	1	2	yes	complemented
642	#529	—	2	1	no	—
643	#529	C₂²×C₅₃	1	2	yes	—
644	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#529	C₂²×C₅₃	1	2	yes	complemented
646	#525	—	2	2	no	—
647	#520	—	2	1	no	—
648	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
649	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
650	C₂×C₄×D₄	—	2	1	no	—
651	C₂×C₄×D₄	C₂²×C₅₃	1	2	yes	—
652	#497	C₂²×C₅₃	1	2	yes	complemented
653	#496	C₂²×C₅₃	1	2	yes	complemented
654	#493	C₂²×C₅₃	1	1	yes	characteristic
655	#492	C₂²×C₅₃	1	1	yes	characteristic
656	#491	C₂²×C₅₃	1	2	yes	complemented
657	#490	C₂²×C₅₃	1	2	yes	complemented
658	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	#483	C₂²×C₅₃	1	2	yes	complemented
662	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
663	#480	C₂²×C₅₃	1	2	yes	complemented
664	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#479	C₂²×C₅₃	1	2	yes	complemented
666	#478	C₂²×C₅₃	1	1	yes	characteristic
667	#478	C₂²×C₅₃	1	2	yes	complemented
668	#478	C₂²×C₅₃	1	2	yes	complemented
669	#477	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
671	#470	C₂²×C₅₃	1	2	yes	complemented
672	#469	C₂²×C₅₃	1	2	yes	—
673	#468	C₂²×C₅₃	1	2	yes	—
674	#468	C₂²×C₅₃	1	2	yes	complemented
675	#466	C₂²×C₅₃	1	2	yes	complemented
676	#465	C₂²×C₅₃	1	2	yes	complemented
677	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#464	C₂²×C₅₃	1	2	yes	complemented
679	#464	C₂²×C₅₃	1	2	yes	complemented
680	#463	C₂²×C₅₃	1	1	yes	characteristic
681	#463	C₂²×C₅₃	1	2	yes	—
682	#463	C₂²×C₅₃	1	2	yes	complemented
683	#463	C₂²×C₅₃	1	2	yes	complemented
684	#463	C₂²×C₅₃	1	2	yes	complemented
685	#463	C₂²×C₅₃	1	2	yes	complemented
686	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#461	C₂²×C₅₃	1	2	yes	—
688	#461	C₂²×C₅₃	1	1	yes	characteristic
689	#461	C₂²×C₅₃	1	2	yes	complemented
690	#460	C₂²×C₅₃	1	1	yes	characteristic
691	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
692	#459	C₂²×C₅₃	1	2	yes	—
693	#459	C₂²×C₅₃	1	1	yes	characteristic
694	#459	C₂²×C₅₃	1	1	yes	characteristic
695	#459	C₂²×C₅₃	1	2	yes	complemented
696	#452	C₂²×C₅₃	1	1	yes	characteristic
697	#452	C₂²×C₅₃	1	2	yes	complemented
698	#452	C₂²×C₅₃	1	2	yes	complemented
699	#450	C₂²×C₅₃	1	2	yes	—
700	#449	C₂²×C₅₃	1	1	yes	characteristic
701	#449	C₂²×C₅₃	1	2	yes	—
702	#449	C₂²×C₅₃	1	2	yes	—
703	#449	C₂²×C₅₃	1	2	yes	complemented
704	#449	C₂²×C₅₃	1	2	yes	complemented
705	#447	C₂²×C₅₃	1	2	yes	—
706	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#442	C₂²×C₅₃	1	2	yes	—
709	#442	C₂²×C₅₃	1	2	yes	complemented
710	#440	C₂²×C₅₃	1	2	yes	—
711	#440	C₂²×C₅₃	1	2	yes	complemented
712	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
714	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
715	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
716	#436	C₂²×C₅₃	1	1	yes	characteristic
717	#436	C₂²×C₅₃	1	1	yes	characteristic
718	#435	C₂²×C₅₃	1	2	yes	complemented
719	#435	C₂²×C₅₃	1	2	yes	complemented
720	#432	C₂²×C₅₃	1	2	yes	complemented
721	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	#423	C₂²×C₅₃	1	2	yes	complemented
723	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
724	#417	C₂²×C₅₃	1	2	yes	complemented
725	#417	C₂²×C₅₃	1	2	yes	complemented
726	#416	C₂²×C₅₃	1	2	yes	complemented
727	C₅₃	#61974	1	1	yes	characteristic, direct product factor, Sylow
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
731	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
732	C₂×#41	C₂³×C₅₃	1	2	yes	—
733	C₂×#41	C₂³×C₅₃	1	2	yes	—
734	C₂×#41	C₂³×C₅₃	1	2	yes	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
737	C₂³×C₄	—	2	2	no	—
738	AGL(1,ℤ/8)	—	4	4	no	—
739	AGL(1,ℤ/8)	—	4	4	no	—
740	#135	—	4	4	no	—
741	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
742	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
743	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
745	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
749	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
750	C₂×D₈	C₂³×C₅₃	1	2	yes	—
751	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
752	C₂×D₈	C₂³×C₅₃	1	2	yes	—
753	C₂×D₈	C₂³×C₅₃	1	2	yes	—
754	C₂×D₈	C₂³×C₅₃	1	2	yes	—
755	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
756	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
757	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
758	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
760	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
761	#127	—	2	1	no	—
762	#127	—	2	2	no	—
763	#127	C₂³×C₅₃	1	1	yes	characteristic
764	#127	C₂³×C₅₃	1	1	yes	characteristic
765	#127	C₂³×C₅₃	1	2	yes	—
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	1	no	—
769	#126	—	2	2	no	—
770	#125	—	2	1	no	—
771	#125	—	2	1	no	—
772	#125	—	2	2	no	—
773	#125	C₂³×C₅₃	1	2	yes	—
774	#125	C₂³×C₅₃	1	1	yes	characteristic
775	#124	—	2	1	no	—
776	#124	—	2	1	no	—
777	#124	C₂³×C₅₃	1	2	yes	—
778	#124	C₂³×C₅₃	1	1	yes	characteristic
779	#124	C₂³×C₅₃	1	2	yes	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	1	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	—	2	2	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
793	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
794	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
795	#121	—	2	2	no	—
796	#121	—	2	1	no	—
797	#121	—	2	2	no	—
798	#121	—	2	1	no	—
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	—	2	2	no	—
810	#121	C₂³×C₅₃	1	2	yes	—
811	#121	C₂³×C₅₃	1	2	yes	—
812	#121	C₂³×C₅₃	1	1	yes	characteristic
813	#121	C₂³×C₅₃	1	2	yes	—
814	#120	—	2	2	no	—
815	#120	—	2	2	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
818	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
819	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
820	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
822	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	2	no	—
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	2	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	2	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
841	C₄×D₄	D₄×C₅₃	1	2	yes	—
842	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₅₃	1	2	yes	—
844	C₄×D₄	C₂³×C₅₃	1	2	yes	—
845	C₄×D₄	C₂³×C₅₃	1	2	yes	—
846	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
847	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
848	C₄×D₄	C₂³×C₅₃	1	2	yes	—
849	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
850	C₄×D₄	C₂³×C₅₃	1	2	yes	—
851	#117	—	2	1	no	—
852	#117	—	2	1	no	—
853	#117	—	2	2	no	—
854	#117	—	2	2	no	—
855	#117	D₄×C₅₃	1	2	yes	—
856	#117	D₄×C₅₃	1	1	yes	characteristic
857	#117	C₂³×C₅₃	1	1	yes	characteristic
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	—	2	1	no	—
860	C₂×C₄⋊C₄	—	2	2	no	—
861	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
862	C₂×C₂²⋊C₄	—	2	2	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₄²	—	2	1	no	—
865	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
866	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
867	#107	C₂³×C₅₃	1	1	yes	characteristic
868	#107	C₂³×C₅₃	1	1	yes	characteristic
869	#107	C₂³×C₅₃	1	2	yes	—
870	#106	C₂³×C₅₃	1	1	yes	characteristic
871	#106	C₂³×C₅₃	1	1	yes	characteristic
872	#106	C₂³×C₅₃	1	2	yes	—
873	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
874	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
875	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
876	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
877	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
878	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
879	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
880	#103	C₂³×C₅₃	1	2	yes	—
881	#103	C₂³×C₅₃	1	2	yes	—
882	#103	C₂³×C₅₃	1	1	yes	characteristic
883	#103	C₂³×C₅₃	1	2	yes	—
884	#103	C₂³×C₅₃	1	2	yes	—
885	#103	C₂³×C₅₃	1	1	yes	characteristic
886	#103	C₂³×C₅₃	1	1	yes	characteristic
887	#103	C₂³×C₅₃	1	1	yes	characteristic
888	#103	C₂³×C₅₃	1	2	yes	—
889	#102	C₂³×C₅₃	1	2	yes	—
890	#102	C₂³×C₅₃	1	2	yes	—
891	#102	C₂³×C₅₃	1	1	yes	characteristic
892	#102	C₂³×C₅₃	1	2	yes	—
893	#102	C₂³×C₅₃	1	2	yes	—
894	#102	C₂³×C₅₃	1	1	yes	characteristic
895	#102	C₂³×C₅₃	1	1	yes	characteristic
896	#102	C₂³×C₅₃	1	1	yes	characteristic
897	#102	C₂³×C₅₃	1	2	yes	—
898	#102	C₂³×C₅₃	1	2	yes	—
899	#102	C₂³×C₅₃	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
904	#97	C₂³×C₅₃	1	2	yes	—
905	#97	C₂³×C₅₃	1	2	yes	—
906	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
907	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
908	C₂⁴	—	2	2	no	—
909	#41	—	2	2	no	—
910	#41	—	4	2	no	—
911	#41	—	4	1	no	—
912	#41	—	4	2	no	—
913	#41	—	4	2	no	—
914	#41	—	4	2	no	—
915	#41	—	4	2	no	—
916	#41	—	4	2	no	—
917	#41	—	4	2	no	—
918	#41	—	4	4	no	—
919	#41	—	8	2	no	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
922	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
923	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
924	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
925	C₂×D₄	—	2	4	no	—
926	C₂×D₄	—	2	1	no	—
927	C₂×D₄	—	2	2	no	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	1	no	—
930	C₂×D₄	—	2	2	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	2	2	no	—
934	C₂×D₄	—	2	2	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	2	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	4	2	no	—
942	C₂×D₄	—	4	4	no	—
943	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
944	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
945	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
947	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
948	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	2	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	2	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	8	4	no	—
962	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
964	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
965	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
966	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
967	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
968	Q₁₆	—	4	2	no	—
969	Q₁₆	—	4	1	no	—
970	SD₁₆	—	2	4	no	—
971	SD₁₆	—	2	2	no	—
972	SD₁₆	—	4	2	no	—
973	SD₁₆	—	4	2	no	—
974	SD₁₆	—	4	2	no	—
975	SD₁₆	—	4	1	no	—
976	SD₁₆	—	4	2	no	—
977	D₈	—	2	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	4	2	no	—
980	D₈	—	4	2	no	—
981	D₈	—	4	2	no	—
982	M₁₆	—	4	2	no	—
983	M₁₆	—	4	2	no	—
984	C₂×C₈	—	4	2	no	—
985	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
986	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
990	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
991	C₄⋊C₄	—	2	1	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	2	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	1	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	1	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	1	no	—
1008	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1011	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	—	2	1	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	1	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	—	2	2	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1039	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1040	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	2	1	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1047	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1048	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1049	C₄²	C₂×D₄×C₅₃	1	2	yes	—
1050	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1051	C₄²	C₂⁴×C₅₃	1	2	yes	—
1052	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1053	C₂³	—	2	1	no	—
1054	C₂³	—	2	2	no	—
1055	C₂³	—	2	1	no	—
1056	C₂³	—	2	2	no	—
1057	C₂³	—	4	4	no	—
1058	C₂³	—	4	4	no	—
1059	C₂³	—	8	2	no	—
1060	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1061	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1062	Q₈	—	2	2	no	—
1063	Q₈	—	2	1	no	—
1064	Q₈	—	2	2	no	—
1065	Q₈	—	2	1	no	—
1066	Q₈	—	2	1	no	—
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	8	1	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	2	2	no	—
1073	D₄	—	2	2	no	—
1074	D₄	—	2	1	no	—
1075	D₄	—	2	2	no	—
1076	D₄	—	2	2	no	—
1077	D₄	—	2	1	no	—
1078	D₄	—	4	2	no	—
1079	D₄	—	4	4	no	—
1080	D₄	—	4	4	no	—
1081	D₄	—	4	2	no	—
1082	D₄	—	4	4	no	—
1083	D₄	—	4	2	no	—
1084	D₄	—	4	2	no	—
1085	D₄	—	8	2	no	—
1086	D₄	—	8	1	no	—
1087	D₄	—	8	1	no	—
1088	D₄	—	8	2	no	—
1089	D₄	—	8	1	no	—
1090	D₄	—	8	2	no	—
1091	D₄	—	8	2	no	—
1092	D₄	—	8	2	no	—
1093	D₄	—	8	2	no	—
1094	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	2	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	1	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	1	no	—
1103	C₂×C₄	—	2	1	no	—
1104	C₂×C₄	—	2	1	no	—
1105	C₂×C₄	—	2	2	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	1	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	4	2	no	—
1113	C₂×C₄	—	4	4	no	—
1114	C₂×C₄	—	4	4	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	2	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	2	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1125	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1129	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1130	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1131	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1132	C₈	—	2	2	no	—
1133	C₈	—	2	2	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	1	no	—
1137	C₈	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	1	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	2	no	—
1144	C₂²	—	2	1	no	—
1145	C₂²	—	4	1	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	2	no	—
1149	C₂²	—	4	2	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	2	no	—
1153	C₂²	—	4	2	no	—
1154	C₂²	—	4	1	no	—
1155	C₂²	—	4	2	no	—
1156	C₂²	—	8	8	no	—
1157	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	2	1	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	2	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	—	4	1	no	—
1173	C₄	C₅₃×#575	1	2	yes	—
1174	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1175	C₄	C₅₃×#585	1	1	yes	characteristic
1176	C₂	—	4	2	no	—
1177	C₂	—	4	1	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	2	no	—
1180	C₂	—	8	1	no	—
1181	C₂	—	8	2	no	—
1182	C₂	C₅₃×#3488	1	1	yes	characteristic
1183	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1184	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3517	C₂	semidirect
2. C₅₃×#3481	C₂	semidirect
3. C₅₃×#3400	C₂	semidirect
4. C₅₃×#3399	C₂	semidirect
5. C₅₃×#3372	C₂	semidirect
6. C₅₃×#3366	C₂	semidirect
7. C₅₃×#3333	C₂	semidirect
8. C₅₃×#3331	C₂	semidirect
9. C₅₃×#3309	C₂	semidirect
10. C₅₃×#3307	C₂	semidirect
11. C₅₃×#3274	C₂	semidirect
12. C₅₃×#3272	C₂	semidirect
13. C₅₃×#3268	C₂	semidirect
14. C₅₃×#3267	C₂	semidirect
15. C₅₃×#3256	C₂	semidirect
16. C₅₃×#3247	C₂	semidirect
17. C₅₃×#3219	C₂	semidirect
18. C₅₃×#3207	C₂	semidirect
19. C₅₃×#3114	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3036	C₂	semidirect
22. C₅₃×#3035	C₂	semidirect
23. C₅₃×#2989	C₂	semidirect
28. C₅₃×#557	C₂²	semidirect
38. C₅₃×#550	C₂²	semidirect
39. C₅₃×#550	C₂²	semidirect
41. C₅₃×#547	C₂²	semidirect
48. C₅₃×#532	C₂²	semidirect
49. C₅₃×#532	C₂²	semidirect
52. C₅₃×#529	C₂²	semidirect
53. C₅₃×#529	C₂²	semidirect
60. C₅₃×#497	C₂²	semidirect
61. C₅₃×#496	C₂²	semidirect
64. C₅₃×#491	C₂²	semidirect
65. C₅₃×#490	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#483	C₂²	semidirect
70. C₅₃×#482	C₂²	semidirect
71. C₅₃×#480	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#479	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#478	C₂²	semidirect
77. C₅₃×#477	C₂²	semidirect
78. C₅₃×#476	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#463	C₂²	semidirect
93. C₅₃×#463	C₂²	semidirect
94. C₅₃×#462	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
99. C₅₃×#460	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#452	C₂²	semidirect
111. C₅₃×#449	C₂²	semidirect
112. C₅₃×#449	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₅₃×#446	C₂²	semidirect
117. C₅₃×#442	C₂²	semidirect
119. C₅₃×#440	C₂²	semidirect
120. C₄×Q₁₆×C₅₃	C₂²	semidirect
122. C₄×SD₁₆×C₅₃	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
127. C₅₃×#435	C₂²	semidirect
128. C₅₃×#432	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#423	C₂²	semidirect
131. C₂×C₄⋊C₈×C₅₃	C₂²	semidirect
132. C₅₃×#417	C₂²	semidirect
133. C₅₃×#417	C₂²	semidirect
134. C₅₃×#416	C₂²	semidirect
545. #61974	C₅₃	direct (N × H)
584. #3517	C₂×C₅₃	semidirect
585. #3481	C₂×C₅₃	semidirect
586. #3400	C₂×C₅₃	semidirect
587. #3399	C₂×C₅₃	semidirect
588. #3372	C₂×C₅₃	semidirect
589. #3366	C₂×C₅₃	semidirect
590. #3333	C₂×C₅₃	semidirect
591. #3331	C₂×C₅₃	semidirect
592. #3309	C₂×C₅₃	semidirect
593. #3307	C₂×C₅₃	semidirect
594. #3274	C₂×C₅₃	semidirect
595. #3272	C₂×C₅₃	semidirect
596. #3268	C₂×C₅₃	semidirect
597. #3267	C₂×C₅₃	semidirect
598. #3256	C₂×C₅₃	semidirect
599. #3247	C₂×C₅₃	semidirect
600. #3219	C₂×C₅₃	semidirect
601. #3207	C₂×C₅₃	semidirect
602. #3114	C₂×C₅₃	semidirect
603. #3102	C₂×C₅₃	semidirect
604. #3036	C₂×C₅₃	semidirect
605. #3035	C₂×C₅₃	semidirect
606. #2989	C₂×C₅₃	semidirect
620. #557	C₂²×C₅₃	semidirect
630. #550	C₂²×C₅₃	semidirect
631. #550	C₂²×C₅₃	semidirect
633. #547	C₂²×C₅₃	semidirect
640. #532	C₂²×C₅₃	semidirect
641. #532	C₂²×C₅₃	semidirect
644. #529	C₂²×C₅₃	semidirect
645. #529	C₂²×C₅₃	semidirect
652. #497	C₂²×C₅₃	semidirect
653. #496	C₂²×C₅₃	semidirect
656. #491	C₂²×C₅₃	semidirect
657. #490	C₂²×C₅₃	semidirect
658. #487	C₂²×C₅₃	semidirect
659. #486	C₂²×C₅₃	semidirect
660. #485	C₂²×C₅₃	semidirect
661. #483	C₂²×C₅₃	semidirect
662. #482	C₂²×C₅₃	semidirect
663. #480	C₂²×C₅₃	semidirect
664. #479	C₂²×C₅₃	semidirect
665. #479	C₂²×C₅₃	semidirect
667. #478	C₂²×C₅₃	semidirect
668. #478	C₂²×C₅₃	semidirect
669. #477	C₂²×C₅₃	semidirect
670. #476	C₂²×C₅₃	semidirect
671. #470	C₂²×C₅₃	semidirect
674. #468	C₂²×C₅₃	semidirect
675. #466	C₂²×C₅₃	semidirect
676. #465	C₂²×C₅₃	semidirect
677. #464	C₂²×C₅₃	semidirect
678. #464	C₂²×C₅₃	semidirect
679. #464	C₂²×C₅₃	semidirect
682. #463	C₂²×C₅₃	semidirect
683. #463	C₂²×C₅₃	semidirect
684. #463	C₂²×C₅₃	semidirect
685. #463	C₂²×C₅₃	semidirect
686. #462	C₂²×C₅₃	semidirect
689. #461	C₂²×C₅₃	semidirect
691. #460	C₂²×C₅₃	semidirect
695. #459	C₂²×C₅₃	semidirect
697. #452	C₂²×C₅₃	semidirect
698. #452	C₂²×C₅₃	semidirect
703. #449	C₂²×C₅₃	semidirect
704. #449	C₂²×C₅₃	semidirect
706. #446	C₂²×C₅₃	semidirect
707. #446	C₂²×C₅₃	semidirect
709. #442	C₂²×C₅₃	semidirect
711. #440	C₂²×C₅₃	semidirect
712. C₄×Q₁₆	C₂²×C₅₃	semidirect
714. C₄×SD₁₆	C₂²×C₅₃	semidirect
718. #435	C₂²×C₅₃	semidirect
719. #435	C₂²×C₅₃	semidirect
720. #432	C₂²×C₅₃	semidirect
721. #431	C₂²×C₅₃	semidirect
722. #423	C₂²×C₅₃	semidirect
723. C₂×C₄⋊C₈	C₂²×C₅₃	semidirect
724. #417	C₂²×C₅₃	semidirect
725. #417	C₂²×C₅₃	semidirect
726. #416	C₂²×C₅₃	semidirect
727. C₅₃	#61974	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×#3517	2
C₅₃×#3481	2
C₅₃×#3400	2
C₅₃×#3399	2
C₅₃×#3372	2
C₅₃×#3366	2
C₅₃×#3333	2
C₅₃×#3331	2
C₅₃×#3309	2
C₅₃×#3307	2
C₅₃×#3274	2
C₅₃×#3272	2
C₅₃×#3268	2
C₅₃×#3267	2
C₅₃×#3256	2
C₅₃×#3247	2
C₅₃×#3219	2
C₅₃×#3207	2
C₅₃×#3114	2
C₅₃×#3102	2
C₅₃×#3036	2
C₅₃×#3035	2
C₅₃×#2989	2
#61974	53

Subgroups — C53×#61974 #27269486

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61974 #27269486