Subgroups — C₅₃×#62037 #27269549

Order 13568.

1950 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3517	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3399	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3368	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3318	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3294	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3287	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3274	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3268	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3259	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3220	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3205	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3119	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3045	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3038	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2993	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	complemented
26	C₂×#135×C₅₃	C₂²	1	2	yes	complemented
27	C₅₃×#560	—	2	2	no	—
28	C₅₃×#559	C₂²	1	1	yes	characteristic
29	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#553	—	2	2	no	—
31	C₅₃×#553	C₂²	1	2	yes	complemented
32	C₅₃×#550	—	2	1	no	—
33	C₅₃×#550	C₂²	1	1	yes	characteristic
34	C₅₃×#550	C₂²	1	1	yes	characteristic
35	C₅₃×#550	C₂²	1	2	yes	complemented
36	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#547	—	2	1	no	—
39	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#546	—	2	1	no	—
41	C₅₃×#546	C₂²	1	2	yes	—
42	D₄²×C₅₃	—	2	1	no	—
43	D₄²×C₅₃	C₂²	1	1	yes	characteristic
44	D₄²×C₅₃	C₂²	1	2	yes	—
45	C₅₃×#540	—	2	1	no	—
46	C₅₃×#540	—	2	2	no	—
47	C₅₃×#540	C₂²	1	2	yes	—
48	C₅₃×#540	C₂²	1	2	yes	complemented
49	C₅₃×#535	—	2	1	no	—
50	C₅₃×#535	C₂²	1	2	yes	—
51	C₅₃×#534	—	2	2	no	—
52	C₅₃×#532	—	2	1	no	—
53	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₂×#127×C₅₃	C₂²	1	1	yes	characteristic
55	C₅₃×#529	—	2	1	no	—
56	C₅₃×#529	C₂²	1	1	yes	characteristic
57	C₅₃×#529	C₂²	1	1	yes	characteristic
58	C₅₃×#520	C₂²	1	2	yes	complemented
59	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#496	C₂²	1	2	yes	complemented
61	C₅₃×#493	C₂²	1	1	yes	characteristic
62	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#493	C₂²	1	2	yes	complemented
64	C₅₃×#490	C₂²	1	2	yes	complemented
65	C₅₃×#488	C₂²	1	2	yes	complemented
66	C₅₃×#486	C₂²	1	1	yes	characteristic
67	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
69	C₅₃×#482	C₂²	1	1	yes	characteristic
70	C₅₃×#481	C₂²	1	2	yes	complemented
71	C₅₃×#480	C₂²	1	2	yes	complemented
72	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#478	C₂²	1	1	yes	characteristic, complemented
75	C₅₃×#478	C₂²	1	2	yes	complemented
76	C₅₃×#478	C₂²	1	2	yes	complemented
77	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#469	C₂²	1	2	yes	—
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#469	C₂²	1	2	yes	complemented
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#466	C₂²	1	2	yes	complemented
84	C₅₃×#466	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
87	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#460	C₂²	1	1	yes	characteristic
91	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#460	C₂²	1	2	yes	complemented
93	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#460	C₂²	1	2	yes	complemented
95	C₅₃×#459	C₂²	1	1	yes	characteristic
96	C₅₃×#459	C₂²	1	2	yes	complemented
97	C₅₃×#459	C₂²	1	2	yes	complemented
98	C₅₃×#459	C₂²	1	2	yes	complemented
99	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
100	C₅₃×#459	C₂²	1	2	yes	complemented
101	C₅₃×#459	C₂²	1	2	yes	complemented
102	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
103	C₅₃×#459	C₂²	1	2	yes	complemented
104	C₅₃×#452	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#449	C₂²	1	1	yes	characteristic
106	C₅₃×#449	C₂²	1	2	yes	complemented
107	C₅₃×#449	C₂²	1	2	yes	complemented
108	C₅₃×#449	C₂²	1	2	yes	complemented
109	C₅₃×#449	C₂²	1	2	yes	complemented
110	C₅₃×#447	C₂²	1	2	yes	complemented
111	C₅₃×#447	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	2	yes	complemented
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#442	C₂²	1	2	yes	complemented
117	C₅₃×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
124	C₅₃×#436	C₂²	1	2	yes	complemented
125	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
128	C₅₃×#433	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#418	C₂²	1	2	yes	complemented
133	C₅₃×#417	C₂²	1	2	yes	complemented
134	C₂×#102×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂×#41×C₅₃	C₂³	1	2	yes	—
142	C₂²×D₄×C₅₃	—	2	2	no	—
143	C₂²×D₄×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	—	2	1	no	—
145	C₂²×D₄×C₅₃	—	2	1	no	—
146	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
147	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
148	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
149	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
150	#135×C₅₃	—	4	4	no	—
151	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
160	C₂×D₈×C₅₃	C₂³	1	2	yes	—
161	C₂×D₈×C₅₃	C₂³	1	2	yes	—
162	C₂×D₈×C₅₃	C₂³	1	2	yes	—
163	C₂×D₈×C₅₃	C₂³	1	2	yes	—
164	C₂×D₈×C₅₃	C₂³	1	2	yes	—
165	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
167	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
168	C₄⋊Q₈×C₅₃	—	2	1	no	—
169	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	#127×C₅₃	—	2	1	no	—
171	#127×C₅₃	—	2	1	no	—
172	#127×C₅₃	—	2	1	no	—
173	#127×C₅₃	—	2	1	no	—
174	#127×C₅₃	—	2	2	no	—
175	#127×C₅₃	C₂³	1	1	yes	characteristic
176	#127×C₅₃	C₂³	1	1	yes	characteristic
177	#127×C₅₃	C₂³	1	2	yes	—
178	#127×C₅₃	C₂³	1	1	yes	characteristic
179	#127×C₅₃	C₂³	1	2	yes	—
180	#127×C₅₃	C₂³	1	2	yes	—
181	#126×C₅₃	—	2	2	no	—
182	#126×C₅₃	—	2	1	no	—
183	#126×C₅₃	D₄	1	2	yes	—
184	#125×C₅₃	—	2	2	no	—
185	#125×C₅₃	D₄	1	1	yes	characteristic
186	#125×C₅₃	C₂³	1	2	yes	—
187	#125×C₅₃	C₂³	1	1	yes	characteristic
188	#124×C₅₃	—	2	1	no	—
189	#124×C₅₃	—	2	1	no	—
190	#124×C₅₃	D₄	1	1	yes	characteristic
191	#124×C₅₃	C₂³	1	2	yes	—
192	#124×C₅₃	C₂³	1	1	yes	characteristic
193	#123×C₅₃	—	2	2	no	—
194	#123×C₅₃	—	2	2	no	—
195	#123×C₅₃	—	2	2	no	—
196	#123×C₅₃	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	1	no	—
202	#123×C₅₃	D₄	1	2	yes	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
205	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
206	#121×C₅₃	—	2	1	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	1	no	—
212	#121×C₅₃	—	2	2	no	—
213	#121×C₅₃	—	2	2	no	—
214	#121×C₅₃	—	2	2	no	—
215	#121×C₅₃	—	2	2	no	—
216	#121×C₅₃	—	2	2	no	—
217	#121×C₅₃	—	2	2	no	—
218	#121×C₅₃	—	2	2	no	—
219	#121×C₅₃	—	2	2	no	—
220	#121×C₅₃	—	2	2	no	—
221	#121×C₅₃	—	2	2	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	D₄	1	1	yes	characteristic
226	#121×C₅₃	C₂³	1	1	yes	characteristic
227	#121×C₅₃	C₂³	1	2	yes	—
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	2	yes	—
230	#121×C₅₃	C₂³	1	2	yes	—
231	#121×C₅₃	C₂³	1	2	yes	—
232	#120×C₅₃	—	2	2	no	—
233	#120×C₅₃	—	2	2	no	—
234	#120×C₅₃	—	2	2	no	—
235	#120×C₅₃	—	2	2	no	—
236	#120×C₅₃	—	2	2	no	—
237	#120×C₅₃	—	2	2	no	—
238	C₄×Q₈×C₅₃	—	2	1	no	—
239	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	2	no	—
246	C₄×D₄×C₅₃	—	2	1	no	—
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	2	no	—
249	C₄×D₄×C₅₃	—	2	2	no	—
250	C₄×D₄×C₅₃	—	2	2	no	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	—	2	1	no	—
254	C₄×D₄×C₅₃	—	2	1	no	—
255	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₃	C₂³	1	2	yes	—
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
260	C₄×D₄×C₅₃	C₂³	1	2	yes	—
261	C₄×D₄×C₅₃	C₂³	1	2	yes	—
262	C₄×D₄×C₅₃	C₂³	1	2	yes	—
263	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
264	#117×C₅₃	—	2	2	no	—
265	#117×C₅₃	—	2	1	no	—
266	#117×C₅₃	—	2	1	no	—
267	#117×C₅₃	C₂³	1	1	yes	characteristic
268	#117×C₅₃	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₄²×C₅₃	—	2	1	no	—
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	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	2	yes	—
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	1	yes	characteristic
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	2	yes	—
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
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	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	2	no	—
316	C₂⁴×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	2	4	no	—
318	#41×C₅₃	—	2	2	no	—
319	#41×C₅₃	—	4	1	no	—
320	#41×C₅₃	—	4	2	no	—
321	#41×C₅₃	—	4	2	no	—
322	#41×C₅₃	—	4	2	no	—
323	#41×C₅₃	—	8	2	no	—
324	#41×C₅₃	—	8	2	no	—
325	#41×C₅₃	—	8	2	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	1	yes	characteristic
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	1	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	2	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	1	no	—
341	C₂×D₄×C₅₃	—	2	1	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	2	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	1	no	—
348	C₂×D₄×C₅₃	—	2	2	no	—
349	C₂×D₄×C₅₃	—	2	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	—	2	2	no	—
352	C₂×D₄×C₅₃	—	2	2	no	—
353	C₂×D₄×C₅₃	—	2	1	no	—
354	C₂×D₄×C₅₃	—	4	2	no	—
355	C₂×D₄×C₅₃	—	4	2	no	—
356	C₂×D₄×C₅₃	—	4	2	no	—
357	C₂×D₄×C₅₃	—	4	2	no	—
358	C₂×D₄×C₅₃	—	8	2	no	—
359	C₂×D₄×C₅₃	—	8	2	no	—
360	C₂×D₄×C₅₃	—	8	2	no	—
361	C₂×D₄×C₅₃	—	8	4	no	—
362	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
364	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
365	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
367	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
369	C₂²×C₄×C₅₃	—	2	2	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	1	no	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	1	no	—
374	C₂²×C₄×C₅₃	—	2	1	no	—
375	C₂²×C₄×C₅₃	—	2	2	no	—
376	C₂²×C₄×C₅₃	—	2	2	no	—
377	C₂²×C₄×C₅₃	—	2	2	no	—
378	C₂²×C₄×C₅₃	—	2	2	no	—
379	C₂²×C₄×C₅₃	—	2	2	no	—
380	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
381	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
382	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
384	Q₁₆×C₅₃	—	2	2	no	—
385	SD₁₆×C₅₃	—	2	4	no	—
386	SD₁₆×C₅₃	—	2	2	no	—
387	SD₁₆×C₅₃	—	2	4	no	—
388	SD₁₆×C₅₃	—	4	1	no	—
389	SD₁₆×C₅₃	—	4	2	no	—
390	D₈×C₅₃	—	4	1	no	—
391	D₈×C₅₃	—	4	2	no	—
392	D₈×C₅₃	—	4	2	no	—
393	D₈×C₅₃	—	4	2	no	—
394	D₈×C₅₃	—	4	2	no	—
395	D₈×C₅₃	—	4	2	no	—
396	D₈×C₅₃	—	4	2	no	—
397	D₈×C₅₃	—	4	2	no	—
398	M₁₆×C₅₃	—	4	2	no	—
399	M₁₆×C₅₃	—	4	2	no	—
400	C₂×C₈×C₅₃	—	4	2	no	—
401	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
406	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
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	1	no	—
412	C₄⋊C₄×C₅₃	—	2	1	no	—
413	C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₄⋊C₄×C₅₃	—	2	1	no	—
415	C₄⋊C₄×C₅₃	—	2	2	no	—
416	C₄⋊C₄×C₅₃	—	2	2	no	—
417	C₄⋊C₄×C₅₃	—	2	1	no	—
418	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	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	1	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	1	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	1	no	—
441	C₂²⋊C₄×C₅₃	—	2	2	no	—
442	C₂²⋊C₄×C₅₃	—	2	2	no	—
443	C₂²⋊C₄×C₅₃	—	2	2	no	—
444	C₂²⋊C₄×C₅₃	—	2	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	1	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
449	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
450	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
451	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
453	C₄²×C₅₃	—	2	1	no	—
454	C₄²×C₅₃	—	2	1	no	—
455	C₄²×C₅₃	—	2	1	no	—
456	C₄²×C₅₃	—	2	1	no	—
457	C₄²×C₅₃	—	2	2	no	—
458	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
460	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
461	C₄²×C₅₃	C₂⁴	1	2	yes	—
462	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
463	C₂³×C₅₃	—	2	1	no	—
464	C₂³×C₅₃	—	2	2	no	—
465	C₂³×C₅₃	—	2	2	no	—
466	C₂³×C₅₃	—	2	2	no	—
467	C₂³×C₅₃	—	2	1	no	—
468	C₂³×C₅₃	—	4	4	no	—
469	C₂³×C₅₃	—	8	2	no	—
470	C₂³×C₅₃	—	8	2	no	—
471	C₂³×C₅₃	—	8	2	no	—
472	C₂³×C₅₃	—	8	2	no	—
473	C₂³×C₅₃	—	8	2	no	—
474	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
475	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
476	Q₈×C₅₃	—	2	2	no	—
477	Q₈×C₅₃	—	2	1	no	—
478	Q₈×C₅₃	—	2	1	no	—
479	Q₈×C₅₃	—	2	1	no	—
480	Q₈×C₅₃	—	4	2	no	—
481	Q₈×C₅₃	H(5,𝔽₂)	1	2	yes	—
482	D₄×C₅₃	—	2	2	no	—
483	D₄×C₅₃	—	2	2	no	—
484	D₄×C₅₃	—	2	1	no	—
485	D₄×C₅₃	—	2	2	no	—
486	D₄×C₅₃	—	2	1	no	—
487	D₄×C₅₃	—	2	2	no	—
488	D₄×C₅₃	—	2	2	no	—
489	D₄×C₅₃	—	2	1	no	—
490	D₄×C₅₃	—	2	2	no	—
491	D₄×C₅₃	—	2	2	no	—
492	D₄×C₅₃	—	2	1	no	—
493	D₄×C₅₃	—	4	2	no	—
494	D₄×C₅₃	—	4	4	no	—
495	D₄×C₅₃	—	4	2	no	—
496	D₄×C₅₃	—	4	2	no	—
497	D₄×C₅₃	—	4	2	no	—
498	D₄×C₅₃	—	4	2	no	—
499	D₄×C₅₃	—	4	2	no	—
500	D₄×C₅₃	—	8	1	no	—
501	D₄×C₅₃	—	8	2	no	—
502	D₄×C₅₃	—	8	2	no	—
503	D₄×C₅₃	—	8	2	no	—
504	D₄×C₅₃	—	8	2	no	—
505	D₄×C₅₃	—	8	1	no	—
506	D₄×C₅₃	—	8	1	no	—
507	D₄×C₅₃	—	8	2	no	—
508	D₄×C₅₃	—	8	2	no	—
509	D₄×C₅₃	—	8	2	no	—
510	D₄×C₅₃	—	8	2	no	—
511	D₄×C₅₃	—	8	2	no	—
512	D₄×C₅₃	—	8	2	no	—
513	D₄×C₅₃	—	8	2	no	—
514	D₄×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	8	2	no	—
516	D₄×C₅₃	—	8	2	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	2	2	no	—
519	C₂×C₄×C₅₃	—	2	1	no	—
520	C₂×C₄×C₅₃	—	2	2	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	2	no	—
523	C₂×C₄×C₅₃	—	2	1	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	2	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	1	no	—
529	C₂×C₄×C₅₃	—	4	1	no	—
530	C₂×C₄×C₅₃	—	4	4	no	—
531	C₂×C₄×C₅₃	—	4	2	no	—
532	C₂×C₄×C₅₃	—	4	2	no	—
533	C₂×C₄×C₅₃	—	4	2	no	—
534	C₂×C₄×C₅₃	—	8	1	no	—
535	C₂×C₄×C₅₃	—	8	2	no	—
536	C₂×C₄×C₅₃	—	8	2	no	—
537	C₂×C₄×C₅₃	—	8	2	no	—
538	C₂×C₄×C₅₃	—	8	2	no	—
539	C₂×C₄×C₅₃	—	8	2	no	—
540	C₂×C₄×C₅₃	—	8	2	no	—
541	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
542	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
543	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
544	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
547	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
550	C₈×C₅₃	—	2	1	no	—
551	C₈×C₅₃	—	2	2	no	—
552	C₈×C₅₃	—	2	1	no	—
553	C₈×C₅₃	—	2	2	no	—
554	C₈×C₅₃	—	2	1	no	—
555	C₈×C₅₃	—	2	1	no	—
556	#62037	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
557	C₂²×C₅₃	—	2	1	no	—
558	C₂²×C₅₃	—	2	2	no	—
559	C₂²×C₅₃	—	2	2	no	—
560	C₂²×C₅₃	—	2	1	no	—
561	C₂²×C₅₃	—	2	1	no	—
562	C₂²×C₅₃	—	2	2	no	—
563	C₂²×C₅₃	—	4	1	no	—
564	C₂²×C₅₃	—	4	2	no	—
565	C₂²×C₅₃	—	4	1	no	—
566	C₂²×C₅₃	—	4	2	no	—
567	C₂²×C₅₃	—	4	2	no	—
568	C₂²×C₅₃	—	4	1	no	—
569	C₂²×C₅₃	—	4	2	no	—
570	C₂²×C₅₃	—	4	2	no	—
571	C₂²×C₅₃	—	4	2	no	—
572	C₂²×C₅₃	—	4	1	no	—
573	C₂²×C₅₃	—	4	1	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	4	2	no	—
576	C₂²×C₅₃	—	4	2	no	—
577	C₂²×C₅₃	—	4	2	no	—
578	C₂²×C₅₃	—	16	4	no	—
579	C₂²×C₅₃	—	16	4	no	—
580	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
581	C₄×C₅₃	—	2	1	no	—
582	C₄×C₅₃	—	2	1	no	—
583	C₄×C₅₃	—	2	2	no	—
584	C₄×C₅₃	—	2	2	no	—
585	C₄×C₅₃	—	2	1	no	—
586	C₄×C₅₃	—	2	2	no	—
587	C₄×C₅₃	—	2	1	no	—
588	C₄×C₅₃	—	2	2	no	—
589	C₄×C₅₃	—	4	1	no	—
590	C₄×C₅₃	—	4	1	no	—
591	C₄×C₅₃	—	4	1	no	—
592	C₄×C₅₃	—	4	1	no	—
593	C₄×C₅₃	—	4	1	no	—
594	C₄×C₅₃	—	4	2	no	—
595	C₄×C₅₃	#576	1	2	yes	—
596	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
597	C₄×C₅₃	#585	1	1	yes	characteristic
598	#3543	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3517	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3399	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3391	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3368	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#3365	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
605	#3322	C₂×C₅₃	1	2	yes	complemented
606	#3318	C₂×C₅₃	1	2	yes	complemented
607	#3294	C₂×C₅₃	1	1	yes	characteristic, complemented
608	#3287	C₂×C₅₃	1	1	yes	characteristic, complemented
609	#3274	C₂×C₅₃	1	2	yes	complemented
610	#3274	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3268	C₂×C₅₃	1	2	yes	complemented
612	#3259	C₂×C₅₃	1	2	yes	complemented
613	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#3220	C₂×C₅₃	1	2	yes	complemented
615	#3205	C₂×C₅₃	1	1	yes	characteristic, complemented
616	#3119	C₂×C₅₃	1	2	yes	complemented
617	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#3045	C₂×C₅₃	1	2	yes	complemented
619	#3038	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
621	C₂×C₅₃	—	4	2	no	—
622	C₂×C₅₃	—	4	1	no	—
623	C₂×C₅₃	—	8	1	no	—
624	C₂×C₅₃	—	8	2	no	—
625	C₂×C₅₃	—	8	2	no	—
626	C₂×C₅₃	—	8	2	no	—
627	C₂×C₅₃	—	8	1	no	—
628	C₂×C₅₃	#3488	1	1	yes	characteristic
629	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
630	C₂×C₅₃	#3585	1	1	yes	characteristic
631	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
632	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
633	C₂×#135	C₂²×C₅₃	1	2	yes	complemented
634	#560	—	2	2	no	—
635	#559	C₂²×C₅₃	1	1	yes	characteristic
636	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
637	#553	—	2	2	no	—
638	#553	C₂²×C₅₃	1	2	yes	complemented
639	#550	—	2	1	no	—
640	#550	C₂²×C₅₃	1	1	yes	characteristic
641	#550	C₂²×C₅₃	1	1	yes	characteristic
642	#550	C₂²×C₅₃	1	2	yes	complemented
643	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#547	—	2	1	no	—
646	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#546	—	2	1	no	—
648	#546	C₂²×C₅₃	1	2	yes	—
649	D₄²	—	2	1	no	—
650	D₄²	C₂²×C₅₃	1	1	yes	characteristic
651	D₄²	C₂²×C₅₃	1	2	yes	—
652	#540	—	2	1	no	—
653	#540	—	2	2	no	—
654	#540	C₂²×C₅₃	1	2	yes	—
655	#540	C₂²×C₅₃	1	2	yes	complemented
656	#535	—	2	1	no	—
657	#535	C₂²×C₅₃	1	2	yes	—
658	#534	—	2	2	no	—
659	#532	—	2	1	no	—
660	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
661	C₂×#127	C₂²×C₅₃	1	1	yes	characteristic
662	#529	—	2	1	no	—
663	#529	C₂²×C₅₃	1	1	yes	characteristic
664	#529	C₂²×C₅₃	1	1	yes	characteristic
665	#520	C₂²×C₅₃	1	2	yes	complemented
666	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic, complemented
667	#496	C₂²×C₅₃	1	2	yes	complemented
668	#493	C₂²×C₅₃	1	1	yes	characteristic
669	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#493	C₂²×C₅₃	1	2	yes	complemented
671	#490	C₂²×C₅₃	1	2	yes	complemented
672	#488	C₂²×C₅₃	1	2	yes	complemented
673	#486	C₂²×C₅₃	1	1	yes	characteristic
674	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#482	C₂²×C₅₃	1	1	yes	characteristic
677	#481	C₂²×C₅₃	1	2	yes	complemented
678	#480	C₂²×C₅₃	1	2	yes	complemented
679	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
680	#478	C₂²×C₅₃	1	1	yes	characteristic, complemented
681	#478	C₂²×C₅₃	1	2	yes	complemented
682	#478	C₂²×C₅₃	1	2	yes	complemented
683	#478	C₂²×C₅₃	1	2	yes	complemented
684	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
685	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#469	C₂²×C₅₃	1	2	yes	—
687	#469	C₂²×C₅₃	1	2	yes	complemented
688	#469	C₂²×C₅₃	1	2	yes	complemented
689	#468	C₂²×C₅₃	1	2	yes	complemented
690	#466	C₂²×C₅₃	1	2	yes	complemented
691	#466	C₂²×C₅₃	1	2	yes	complemented
692	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#464	C₂²×C₅₃	1	2	yes	complemented
694	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#463	C₂²×C₅₃	1	2	yes	complemented
696	#463	C₂²×C₅₃	1	2	yes	complemented
697	#460	C₂²×C₅₃	1	1	yes	characteristic
698	#460	C₂²×C₅₃	1	2	yes	complemented
699	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#460	C₂²×C₅₃	1	2	yes	complemented
701	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#459	C₂²×C₅₃	1	1	yes	characteristic
703	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#459	C₂²×C₅₃	1	2	yes	complemented
705	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#459	C₂²×C₅₃	1	2	yes	complemented
707	#459	C₂²×C₅₃	1	2	yes	complemented
708	#459	C₂²×C₅₃	1	2	yes	complemented
709	#459	C₂²×C₅₃	1	2	yes	complemented
710	#459	C₂²×C₅₃	1	2	yes	complemented
711	#452	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#449	C₂²×C₅₃	1	1	yes	characteristic
713	#449	C₂²×C₅₃	1	2	yes	complemented
714	#449	C₂²×C₅₃	1	2	yes	complemented
715	#449	C₂²×C₅₃	1	2	yes	complemented
716	#449	C₂²×C₅₃	1	2	yes	complemented
717	#447	C₂²×C₅₃	1	2	yes	complemented
718	#447	C₂²×C₅₃	1	2	yes	complemented
719	#447	C₂²×C₅₃	1	2	yes	complemented
720	#447	C₂²×C₅₃	1	2	yes	complemented
721	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
722	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
723	#442	C₂²×C₅₃	1	2	yes	complemented
724	#440	C₂²×C₅₃	1	2	yes	complemented
725	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
726	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
728	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
729	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
731	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
732	#436	C₂²×C₅₃	1	2	yes	complemented
733	#435	C₂²×C₅₃	1	2	yes	complemented
734	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
735	#433	C₂²×C₅₃	1	2	yes	complemented
736	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	#424	C₂²×C₅₃	1	2	yes	complemented
738	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
739	#418	C₂²×C₅₃	1	2	yes	complemented
740	#417	C₂²×C₅₃	1	2	yes	complemented
741	C₂×#102	C₂²×C₅₃	1	2	yes	complemented
742	C₅₃	#62037	1	1	yes	characteristic, direct product factor, Sylow
743	C₂×#41	—	2	1	no	—
744	C₂×#41	—	2	1	no	—
745	C₂×#41	—	2	1	no	—
746	C₂×#41	—	2	1	no	—
747	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
748	C₂×#41	C₂³×C₅₃	1	2	yes	—
749	C₂×#41	C₂³×C₅₃	1	2	yes	—
750	C₂²×D₄	—	2	2	no	—
751	C₂²×D₄	—	2	1	no	—
752	C₂²×D₄	—	2	1	no	—
753	C₂²×D₄	—	2	1	no	—
754	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
755	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
756	AGL(1,ℤ/8)	—	4	4	no	—
757	AGL(1,ℤ/8)	—	4	4	no	—
758	#135	—	4	4	no	—
759	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
761	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
764	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
765	C₂×D₈	C₂³×C₅₃	1	2	yes	—
766	C₂×D₈	C₂³×C₅₃	1	2	yes	—
767	C₂×D₈	C₂³×C₅₃	1	2	yes	—
768	C₂×D₈	C₂³×C₅₃	1	2	yes	—
769	C₂×D₈	C₂³×C₅₃	1	2	yes	—
770	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×D₈	C₂³×C₅₃	1	2	yes	—
772	C₂×D₈	C₂³×C₅₃	1	2	yes	—
773	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
774	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
775	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
776	C₄⋊Q₈	—	2	1	no	—
777	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
778	#127	—	2	1	no	—
779	#127	—	2	1	no	—
780	#127	—	2	2	no	—
781	#127	—	2	1	no	—
782	#127	—	2	1	no	—
783	#127	C₂³×C₅₃	1	2	yes	—
784	#127	C₂³×C₅₃	1	1	yes	characteristic
785	#127	C₂³×C₅₃	1	1	yes	characteristic
786	#127	C₂³×C₅₃	1	1	yes	characteristic
787	#127	C₂³×C₅₃	1	2	yes	—
788	#127	C₂³×C₅₃	1	2	yes	—
789	#126	—	2	2	no	—
790	#126	—	2	1	no	—
791	#126	D₄×C₅₃	1	2	yes	—
792	#125	—	2	2	no	—
793	#125	D₄×C₅₃	1	1	yes	characteristic
794	#125	C₂³×C₅₃	1	1	yes	characteristic
795	#125	C₂³×C₅₃	1	2	yes	—
796	#124	—	2	1	no	—
797	#124	—	2	1	no	—
798	#124	D₄×C₅₃	1	1	yes	characteristic
799	#124	C₂³×C₅₃	1	1	yes	characteristic
800	#124	C₂³×C₅₃	1	2	yes	—
801	#123	—	2	1	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	2	no	—
805	#123	—	2	2	no	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	D₄×C₅₃	1	2	yes	—
811	C₂²⋊Q₈	—	2	1	no	—
812	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
813	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
814	#121	—	2	2	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	2	no	—
818	#121	—	2	2	no	—
819	#121	—	2	2	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	2	no	—
823	#121	—	2	2	no	—
824	#121	—	2	2	no	—
825	#121	—	2	2	no	—
826	#121	—	2	2	no	—
827	#121	—	2	2	no	—
828	#121	—	2	2	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	D₄×C₅₃	1	1	yes	characteristic
834	#121	C₂³×C₅₃	1	1	yes	characteristic
835	#121	C₂³×C₅₃	1	2	yes	—
836	#121	C₂³×C₅₃	1	2	yes	—
837	#121	C₂³×C₅₃	1	2	yes	—
838	#121	C₂³×C₅₃	1	2	yes	—
839	#121	C₂³×C₅₃	1	2	yes	—
840	#120	—	2	2	no	—
841	#120	—	2	2	no	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
848	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
849	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
850	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	2	1	no	—
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	2	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
864	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
865	C₄×D₄	C₂³×C₅₃	1	2	yes	—
866	C₄×D₄	C₂³×C₅₃	1	2	yes	—
867	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₅₃	1	2	yes	—
869	C₄×D₄	C₂³×C₅₃	1	2	yes	—
870	C₄×D₄	C₂³×C₅₃	1	2	yes	—
871	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
872	#117	—	2	2	no	—
873	#117	—	2	1	no	—
874	#117	—	2	1	no	—
875	#117	C₂³×C₅₃	1	1	yes	characteristic
876	#117	C₂³×C₅₃	1	2	yes	—
877	C₂×C₄⋊C₄	—	2	2	no	—
878	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
879	C₂×C₂²⋊C₄	—	2	2	no	—
880	C₂×C₄²	—	2	1	no	—
881	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
882	#107	C₂³×C₅₃	1	1	yes	characteristic
883	#107	C₂³×C₅₃	1	1	yes	characteristic
884	#107	C₂³×C₅₃	1	2	yes	—
885	#106	C₂³×C₅₃	1	1	yes	characteristic
886	#106	C₂³×C₅₃	1	2	yes	—
887	#106	C₂³×C₅₃	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
889	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
892	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
893	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
894	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
895	#103	C₂³×C₅₃	1	1	yes	characteristic
896	#103	C₂³×C₅₃	1	2	yes	—
897	#103	C₂³×C₅₃	1	1	yes	characteristic
898	#103	C₂³×C₅₃	1	1	yes	characteristic
899	#103	C₂³×C₅₃	1	1	yes	characteristic
900	#102	C₂³×C₅₃	1	1	yes	characteristic
901	#102	C₂³×C₅₃	1	2	yes	—
902	#102	C₂³×C₅₃	1	2	yes	—
903	#102	C₂³×C₅₃	1	2	yes	—
904	#102	C₂³×C₅₃	1	2	yes	—
905	#102	C₂³×C₅₃	1	2	yes	—
906	#102	C₂³×C₅₃	1	2	yes	—
907	#102	C₂³×C₅₃	1	2	yes	—
908	#102	C₂³×C₅₃	1	2	yes	—
909	#102	C₂³×C₅₃	1	1	yes	characteristic
910	#102	C₂³×C₅₃	1	2	yes	—
911	#102	C₂³×C₅₃	1	1	yes	characteristic
912	#102	C₂³×C₅₃	1	1	yes	characteristic
913	#102	C₂³×C₅₃	1	2	yes	—
914	#102	C₂³×C₅₃	1	2	yes	—
915	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
916	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
917	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
918	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
919	#97	C₂³×C₅₃	1	2	yes	—
920	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
921	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
922	C₄×C₈	C₂³×C₅₃	1	2	yes	—
923	C₂⁴	—	2	2	no	—
924	C₂⁴	—	2	2	no	—
925	#41	—	2	4	no	—
926	#41	—	2	2	no	—
927	#41	—	4	1	no	—
928	#41	—	4	2	no	—
929	#41	—	4	2	no	—
930	#41	—	4	2	no	—
931	#41	—	8	2	no	—
932	#41	—	8	2	no	—
933	#41	—	8	2	no	—
934	#41	—	8	2	no	—
935	C₂×Q₈	—	2	1	no	—
936	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
937	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
938	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	2	no	—
941	C₂×D₄	—	2	1	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	2	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	—	2	2	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	1	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	1	no	—
951	C₂×D₄	—	2	1	no	—
952	C₂×D₄	—	2	2	no	—
953	C₂×D₄	—	2	2	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	1	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	2	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	4	2	no	—
963	C₂×D₄	—	4	2	no	—
964	C₂×D₄	—	4	2	no	—
965	C₂×D₄	—	4	2	no	—
966	C₂×D₄	—	8	2	no	—
967	C₂×D₄	—	8	2	no	—
968	C₂×D₄	—	8	2	no	—
969	C₂×D₄	—	8	4	no	—
970	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
971	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
972	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
973	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
974	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
975	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
976	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
977	C₂²×C₄	—	2	2	no	—
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	1	no	—
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	2	no	—
984	C₂²×C₄	—	2	2	no	—
985	C₂²×C₄	—	2	2	no	—
986	C₂²×C₄	—	2	2	no	—
987	C₂²×C₄	—	2	2	no	—
988	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
989	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
990	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
991	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
992	Q₁₆	—	2	2	no	—
993	SD₁₆	—	2	4	no	—
994	SD₁₆	—	2	2	no	—
995	SD₁₆	—	2	4	no	—
996	SD₁₆	—	4	2	no	—
997	SD₁₆	—	4	1	no	—
998	D₈	—	4	2	no	—
999	D₈	—	4	2	no	—
1000	D₈	—	4	2	no	—
1001	D₈	—	4	2	no	—
1002	D₈	—	4	2	no	—
1003	D₈	—	4	2	no	—
1004	D₈	—	4	1	no	—
1005	D₈	—	4	2	no	—
1006	M₁₆	—	4	2	no	—
1007	M₁₆	—	4	2	no	—
1008	C₂×C₈	—	4	2	no	—
1009	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1010	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1011	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1012	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1013	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1014	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	2	no	—
1017	C₄⋊C₄	—	2	2	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	2	no	—
1024	C₄⋊C₄	—	2	2	no	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1029	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1030	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1032	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1034	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1036	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	2	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	2	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1057	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1058	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1059	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1060	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	—	2	2	no	—
1066	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1067	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1068	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1069	C₄²	C₂⁴×C₅₃	1	2	yes	—
1070	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1071	C₂³	—	2	1	no	—
1072	C₂³	—	2	2	no	—
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	2	no	—
1075	C₂³	—	2	2	no	—
1076	C₂³	—	4	4	no	—
1077	C₂³	—	8	2	no	—
1078	C₂³	—	8	2	no	—
1079	C₂³	—	8	2	no	—
1080	C₂³	—	8	2	no	—
1081	C₂³	—	8	2	no	—
1082	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1083	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1084	Q₈	—	2	2	no	—
1085	Q₈	—	2	1	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	4	2	no	—
1089	Q₈	H(5,𝔽₂)×C₅₃	1	2	yes	—
1090	D₄	—	2	2	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	2	no	—
1093	D₄	—	2	2	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	2	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	2	1	no	—
1099	D₄	—	2	2	no	—
1100	D₄	—	2	2	no	—
1101	D₄	—	4	2	no	—
1102	D₄	—	4	4	no	—
1103	D₄	—	4	2	no	—
1104	D₄	—	4	2	no	—
1105	D₄	—	4	2	no	—
1106	D₄	—	4	2	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	8	2	no	—
1110	D₄	—	8	2	no	—
1111	D₄	—	8	2	no	—
1112	D₄	—	8	2	no	—
1113	D₄	—	8	2	no	—
1114	D₄	—	8	1	no	—
1115	D₄	—	8	1	no	—
1116	D₄	—	8	2	no	—
1117	D₄	—	8	2	no	—
1118	D₄	—	8	2	no	—
1119	D₄	—	8	2	no	—
1120	D₄	—	8	2	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	2	no	—
1127	C₂×C₄	—	2	2	no	—
1128	C₂×C₄	—	2	1	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	2	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	4	1	no	—
1138	C₂×C₄	—	4	4	no	—
1139	C₂×C₄	—	4	2	no	—
1140	C₂×C₄	—	4	2	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	8	1	no	—
1143	C₂×C₄	—	8	2	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	2	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1150	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1151	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1152	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1153	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1154	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1155	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1156	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1157	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1158	C₈	—	2	1	no	—
1159	C₈	—	2	2	no	—
1160	C₈	—	2	1	no	—
1161	C₈	—	2	2	no	—
1162	C₈	—	2	1	no	—
1163	C₈	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	2	1	no	—
1166	C₂²	—	2	1	no	—
1167	C₂²	—	2	2	no	—
1168	C₂²	—	2	1	no	—
1169	C₂²	—	2	2	no	—
1170	C₂²	—	4	1	no	—
1171	C₂²	—	4	2	no	—
1172	C₂²	—	4	2	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	1	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	2	no	—
1179	C₂²	—	4	2	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	1	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	2	no	—
1184	C₂²	—	4	2	no	—
1185	C₂²	—	16	4	no	—
1186	C₂²	—	16	4	no	—
1187	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1188	C₄	—	2	2	no	—
1189	C₄	—	2	1	no	—
1190	C₄	—	2	2	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	1	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	2	no	—
1196	C₄	—	4	1	no	—
1197	C₄	—	4	1	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	2	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	1	no	—
1202	C₄	C₅₃×#576	1	2	yes	—
1203	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1204	C₄	C₅₃×#585	1	1	yes	characteristic
1205	C₂	—	4	1	no	—
1206	C₂	—	4	2	no	—
1207	C₂	—	8	1	no	—
1208	C₂	—	8	2	no	—
1209	C₂	—	8	2	no	—
1210	C₂	—	8	1	no	—
1211	C₂	—	8	2	no	—
1212	C₂	C₅₃×#3488	1	1	yes	characteristic
1213	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1214	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×#3543	C₂	semidirect
2. C₅₃×#3517	C₂	semidirect
3. C₅₃×#3399	C₂	semidirect
4. C₅₃×#3391	C₂	semidirect
5. C₅₃×#3368	C₂	semidirect
6. C₅₃×#3365	C₂	semidirect
7. C₅₃×#3332	C₂	semidirect
8. C₅₃×#3322	C₂	semidirect
9. C₅₃×#3318	C₂	semidirect
10. C₅₃×#3294	C₂	semidirect
11. C₅₃×#3287	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3274	C₂	semidirect
14. C₅₃×#3268	C₂	semidirect
15. C₅₃×#3259	C₂	semidirect
16. C₅₃×#3251	C₂	semidirect
17. C₅₃×#3220	C₂	semidirect
18. C₅₃×#3205	C₂	semidirect
19. C₅₃×#3119	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3045	C₂	semidirect
22. C₅₃×#3038	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
24. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
25. C₂×AGL(1,ℤ/8)×C₅₃	C₂²	semidirect
26. C₂×#135×C₅₃	C₂²	semidirect
29. C₅₃×#557	C₂²	semidirect
31. C₅₃×#553	C₂²	semidirect
35. C₅₃×#550	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
37. C₅₃×#550	C₂²	semidirect
39. C₅₃×#547	C₂²	semidirect
48. C₅₃×#540	C₂²	semidirect
53. C₅₃×#532	C₂²	semidirect
58. C₅₃×#520	C₂²	semidirect
59. C₄×#41×C₅₃	C₂²	semidirect
60. C₅₃×#496	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#493	C₂²	semidirect
64. C₅₃×#490	C₂²	semidirect
65. C₅₃×#488	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
70. C₅₃×#481	C₂²	semidirect
71. C₅₃×#480	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#478	C₂²	semidirect
76. C₅₃×#478	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#469	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#466	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
91. C₅₃×#460	C₂²	semidirect
92. C₅₃×#460	C₂²	semidirect
93. C₅₃×#460	C₂²	semidirect
94. C₅₃×#460	C₂²	semidirect
96. C₅₃×#459	C₂²	semidirect
97. C₅₃×#459	C₂²	semidirect
98. C₅₃×#459	C₂²	semidirect
99. C₅₃×#459	C₂²	semidirect
100. C₅₃×#459	C₂²	semidirect
101. C₅₃×#459	C₂²	semidirect
102. C₅₃×#459	C₂²	semidirect
103. C₅₃×#459	C₂²	semidirect
104. C₅₃×#452	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	C₂²	semidirect
109. C₅₃×#449	C₂²	semidirect
110. C₅₃×#447	C₂²	semidirect
111. C₅₃×#447	C₂²	semidirect
112. C₅₃×#447	C₂²	semidirect
113. C₅₃×#447	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
116. C₅₃×#442	C₂²	semidirect
117. C₅₃×#440	C₂²	semidirect
118. C₄×Q₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×SD₁₆×C₅₃	C₂²	semidirect
121. C₄×SD₁₆×C₅₃	C₂²	semidirect
122. C₄×D₈×C₅₃	C₂²	semidirect
123. C₄×D₈×C₅₃	C₂²	semidirect
124. C₅₃×#436	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
127. C₈×D₄×C₅₃	C₂²	semidirect
128. C₅₃×#433	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₅₃×#423	C₂²	semidirect
132. C₅₃×#418	C₂²	semidirect
133. C₅₃×#417	C₂²	semidirect
134. C₂×#102×C₅₃	C₂²	semidirect
556. #62037	C₅₃	direct (N × H)
598. #3543	C₂×C₅₃	semidirect
599. #3517	C₂×C₅₃	semidirect
600. #3399	C₂×C₅₃	semidirect
601. #3391	C₂×C₅₃	semidirect
602. #3368	C₂×C₅₃	semidirect
603. #3365	C₂×C₅₃	semidirect
604. #3332	C₂×C₅₃	semidirect
605. #3322	C₂×C₅₃	semidirect
606. #3318	C₂×C₅₃	semidirect
607. #3294	C₂×C₅₃	semidirect
608. #3287	C₂×C₅₃	semidirect
609. #3274	C₂×C₅₃	semidirect
610. #3274	C₂×C₅₃	semidirect
611. #3268	C₂×C₅₃	semidirect
612. #3259	C₂×C₅₃	semidirect
613. #3251	C₂×C₅₃	semidirect
614. #3220	C₂×C₅₃	semidirect
615. #3205	C₂×C₅₃	semidirect
616. #3119	C₂×C₅₃	semidirect
617. #3102	C₂×C₅₃	semidirect
618. #3045	C₂×C₅₃	semidirect
619. #3038	C₂×C₅₃	semidirect
620. #2993	C₂×C₅₃	semidirect
631. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
632. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
633. C₂×#135	C₂²×C₅₃	semidirect
636. #557	C₂²×C₅₃	semidirect
638. #553	C₂²×C₅₃	semidirect
642. #550	C₂²×C₅₃	semidirect
643. #550	C₂²×C₅₃	semidirect
644. #550	C₂²×C₅₃	semidirect
646. #547	C₂²×C₅₃	semidirect
655. #540	C₂²×C₅₃	semidirect
660. #532	C₂²×C₅₃	semidirect
665. #520	C₂²×C₅₃	semidirect
666. C₄×#41	C₂²×C₅₃	semidirect
667. #496	C₂²×C₅₃	semidirect
669. #493	C₂²×C₅₃	semidirect
670. #493	C₂²×C₅₃	semidirect
671. #490	C₂²×C₅₃	semidirect
672. #488	C₂²×C₅₃	semidirect
674. #486	C₂²×C₅₃	semidirect
675. #485	C₂²×C₅₃	semidirect
677. #481	C₂²×C₅₃	semidirect
678. #480	C₂²×C₅₃	semidirect
679. #479	C₂²×C₅₃	semidirect
680. #478	C₂²×C₅₃	semidirect
681. #478	C₂²×C₅₃	semidirect
682. #478	C₂²×C₅₃	semidirect
683. #478	C₂²×C₅₃	semidirect
684. #475	C₂²×C₅₃	semidirect
685. #474	C₂²×C₅₃	semidirect
687. #469	C₂²×C₅₃	semidirect
688. #469	C₂²×C₅₃	semidirect
689. #468	C₂²×C₅₃	semidirect
690. #466	C₂²×C₅₃	semidirect
691. #466	C₂²×C₅₃	semidirect
692. #464	C₂²×C₅₃	semidirect
693. #464	C₂²×C₅₃	semidirect
694. #463	C₂²×C₅₃	semidirect
695. #463	C₂²×C₅₃	semidirect
696. #463	C₂²×C₅₃	semidirect
698. #460	C₂²×C₅₃	semidirect
699. #460	C₂²×C₅₃	semidirect
700. #460	C₂²×C₅₃	semidirect
701. #460	C₂²×C₅₃	semidirect
703. #459	C₂²×C₅₃	semidirect
704. #459	C₂²×C₅₃	semidirect
705. #459	C₂²×C₅₃	semidirect
706. #459	C₂²×C₅₃	semidirect
707. #459	C₂²×C₅₃	semidirect
708. #459	C₂²×C₅₃	semidirect
709. #459	C₂²×C₅₃	semidirect
710. #459	C₂²×C₅₃	semidirect
711. #452	C₂²×C₅₃	semidirect
713. #449	C₂²×C₅₃	semidirect
714. #449	C₂²×C₅₃	semidirect
715. #449	C₂²×C₅₃	semidirect
716. #449	C₂²×C₅₃	semidirect
717. #447	C₂²×C₅₃	semidirect
718. #447	C₂²×C₅₃	semidirect
719. #447	C₂²×C₅₃	semidirect
720. #447	C₂²×C₅₃	semidirect
721. #446	C₂²×C₅₃	semidirect
722. C₈×Q₈	C₂²×C₅₃	semidirect
723. #442	C₂²×C₅₃	semidirect
724. #440	C₂²×C₅₃	semidirect
725. C₄×Q₁₆	C₂²×C₅₃	semidirect
726. C₄×SD₁₆	C₂²×C₅₃	semidirect
727. C₄×SD₁₆	C₂²×C₅₃	semidirect
728. C₄×SD₁₆	C₂²×C₅₃	semidirect
729. C₄×D₈	C₂²×C₅₃	semidirect
730. C₄×D₈	C₂²×C₅₃	semidirect
731. #436	C₂²×C₅₃	semidirect
732. #436	C₂²×C₅₃	semidirect
733. #435	C₂²×C₅₃	semidirect
734. C₈×D₄	C₂²×C₅₃	semidirect
735. #433	C₂²×C₅₃	semidirect
736. #431	C₂²×C₅₃	semidirect
737. #424	C₂²×C₅₃	semidirect
738. #423	C₂²×C₅₃	semidirect
739. #418	C₂²×C₅₃	semidirect
740. #417	C₂²×C₅₃	semidirect
741. C₂×#102	C₂²×C₅₃	semidirect
742. C₅₃	#62037	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×#3543	2
C₅₃×#3517	2
C₅₃×#3399	2
C₅₃×#3391	2
C₅₃×#3368	2
C₅₃×#3365	2
C₅₃×#3332	2
C₅₃×#3322	2
C₅₃×#3318	2
C₅₃×#3294	2
C₅₃×#3287	2
C₅₃×#3274	2
C₅₃×#3268	2
C₅₃×#3259	2
C₅₃×#3251	2
C₅₃×#3220	2
C₅₃×#3205	2
C₅₃×#3119	2
C₅₃×#3102	2
C₅₃×#3045	2
C₅₃×#3038	2
C₅₃×#2993	2
#62037	53

Subgroups — C53×#62037 #27269549

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62037 #27269549