Subgroups — C₅₃×#62040 #27269552

Order 13568.

1960 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3546	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3397	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3360	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3325	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3322	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3309	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3303	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3274	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3264	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3257	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3253	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3220	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3207	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3118	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3041	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3036	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	C₂²×D₈×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#560	—	2	2	no	—
28	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
29	C₅₃×#555	C₂²	1	1	yes	characteristic
30	C₅₃×#554	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#553	—	2	1	no	—
32	C₅₃×#553	—	2	1	no	—
33	C₅₃×#553	C₂²	1	2	yes	complemented
34	C₅₃×#550	C₂²	1	2	yes	complemented
35	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
36	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
37	C₅₃×#547	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#546	—	2	1	no	—
39	C₅₃×#546	—	2	1	no	—
40	C₅₃×#546	—	2	2	no	—
41	C₅₃×#546	C₂²	1	2	yes	complemented
42	D₄²×C₅₃	C₂²	1	1	yes	characteristic
43	D₄²×C₅₃	C₂²	1	2	yes	complemented
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#542	C₂²	1	2	yes	complemented
46	C₅₃×#540	C₂²	1	2	yes	complemented
47	C₅₃×#538	—	2	2	no	—
48	C₅₃×#538	—	2	2	no	—
49	C₅₃×#537	—	2	1	no	—
50	C₅₃×#535	—	2	1	no	—
51	C₅₃×#535	C₂²	1	2	yes	complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
53	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#532	C₂²	1	1	yes	characteristic, complemented
55	C₅₃×#529	C₂²	1	1	yes	characteristic
56	C₅₃×#525	—	2	1	no	—
57	C₂×#121×C₅₃	—	2	1	no	—
58	C₅₃×#518	C₂²	1	2	yes	complemented
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₅₃×#496	C₂²	1	2	yes	complemented
61	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
62	C₅₃×#493	C₂²	1	2	yes	complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#490	C₂²	1	2	yes	complemented
65	C₅₃×#488	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	2	yes	complemented
69	C₅₃×#482	C₂²	1	2	yes	complemented
70	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#480	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#479	C₂²	1	2	yes	complemented
73	C₅₃×#478	C₂²	1	2	yes	complemented
74	C₅₃×#476	C₂²	1	2	yes	complemented
75	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
76	C₅₃×#476	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#469	C₂²	1	2	yes	complemented
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×#465	C₂²	1	2	yes	complemented
85	C₅₃×#463	C₂²	1	2	yes	—
86	C₅₃×#463	C₂²	1	2	yes	complemented
87	C₅₃×#463	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	complemented
90	C₅₃×#463	C₂²	1	2	yes	complemented
91	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
93	C₅₃×#460	C₂²	1	2	yes	complemented
94	C₅₃×#459	C₂²	1	1	yes	characteristic
95	C₅₃×#459	C₂²	1	1	yes	characteristic
96	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#459	C₂²	1	2	yes	complemented
98	C₅₃×#459	C₂²	1	1	yes	characteristic, 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×#450	C₂²	1	2	yes	complemented
105	C₅₃×#449	C₂²	1	2	yes	complemented
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×#447	C₂²	1	1	yes	characteristic
110	C₅₃×#447	C₂²	1	2	yes	—
111	C₅₃×#447	C₂²	1	2	yes	complemented
112	C₅₃×#447	C₂²	1	2	yes	complemented
113	C₅₃×#447	C₂²	1	1	yes	characteristic, 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×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
123	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
124	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#436	C₂²	1	2	yes	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	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	—	2	1	no	—
138	C₂×#41×C₅₃	—	2	1	no	—
139	C₂×#41×C₅₃	C₂³	1	2	yes	—
140	C₂×#41×C₅₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₃	—	2	1	no	—
142	C₂²×D₄×C₅₃	—	2	2	no	—
143	C₂²×D₄×C₅₃	—	2	1	no	—
144	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
145	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
146	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₅₃	—	2	1	no	—
148	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
149	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×D₈×C₅₃	—	4	4	no	—
155	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×D₈×C₅₃	C₂³	1	2	yes	—
157	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
169	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	#127×C₅₃	—	2	2	no	—
172	#127×C₅₃	C₂³	1	1	yes	characteristic
173	#127×C₅₃	C₂³	1	2	yes	—
174	#127×C₅₃	C₂³	1	1	yes	characteristic
175	#127×C₅₃	C₂³	1	2	yes	—
176	#127×C₅₃	C₂³	1	1	yes	characteristic
177	#126×C₅₃	—	2	2	no	—
178	#126×C₅₃	—	2	2	no	—
179	#126×C₅₃	—	2	2	no	—
180	#126×C₅₃	D₄	1	2	yes	—
181	#125×C₅₃	D₄	1	1	yes	characteristic
182	#125×C₅₃	C₂³	1	2	yes	—
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	1	no	—
186	#124×C₅₃	—	2	1	no	—
187	#124×C₅₃	D₄	1	1	yes	characteristic
188	#124×C₅₃	C₂³	1	2	yes	—
189	#124×C₅₃	C₂³	1	2	yes	—
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	2	no	—
196	#123×C₅₃	D₄	1	2	yes	—
197	C₂²⋊Q₈×C₅₃	—	2	2	no	—
198	C₂²⋊Q₈×C₅₃	—	2	2	no	—
199	C₂²⋊Q₈×C₅₃	—	2	1	no	—
200	C₂²⋊Q₈×C₅₃	—	2	1	no	—
201	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
202	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
203	#121×C₅₃	—	2	1	no	—
204	#121×C₅₃	—	2	1	no	—
205	#121×C₅₃	—	2	1	no	—
206	#121×C₅₃	—	2	2	no	—
207	#121×C₅₃	—	2	2	no	—
208	#121×C₅₃	—	2	1	no	—
209	#121×C₅₃	—	2	2	no	—
210	#121×C₅₃	—	2	2	no	—
211	#121×C₅₃	—	2	2	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	1	no	—
219	#121×C₅₃	—	2	1	no	—
220	#121×C₅₃	—	2	1	no	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	1	no	—
223	#121×C₅₃	—	2	1	no	—
224	#121×C₅₃	D₄	1	1	yes	characteristic
225	#121×C₅₃	C₂³	1	2	yes	—
226	#121×C₅₃	C₂³	1	1	yes	characteristic
227	#121×C₅₃	C₂³	1	1	yes	characteristic
228	#121×C₅₃	C₂³	1	2	yes	—
229	#121×C₅₃	C₂³	1	2	yes	—
230	#121×C₅₃	C₂³	1	2	yes	—
231	#120×C₅₃	—	2	2	no	—
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	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
240	C₄×D₄×C₅₃	—	2	2	no	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	2	no	—
244	C₄×D₄×C₅₃	—	2	1	no	—
245	C₄×D₄×C₅₃	—	2	1	no	—
246	C₄×D₄×C₅₃	—	2	1	no	—
247	C₄×D₄×C₅₃	—	2	1	no	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
251	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	C₂³	1	2	yes	—
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	C₄×D₄×C₅₃	C₂³	1	2	yes	—
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
259	C₄×D₄×C₅₃	C₂³	1	2	yes	—
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	C₄×D₄×C₅₃	C₂³	1	2	yes	—
262	#117×C₅₃	—	2	1	no	—
263	#117×C₅₃	—	2	1	no	—
264	#117×C₅₃	C₂³	1	2	yes	—
265	#117×C₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
267	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₂²⋊C₄×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	1	yes	characteristic
277	#107×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
288	#103×C₅₃	C₂³	1	2	yes	—
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#102×C₅₃	C₂³	1	2	yes	—
292	#102×C₅₃	C₂³	1	2	yes	—
293	#102×C₅₃	C₂³	1	1	yes	characteristic
294	#102×C₅₃	C₂³	1	2	yes	—
295	#102×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	1	yes	characteristic
301	#102×C₅₃	C₂³	1	1	yes	characteristic
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	2	yes	—
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
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	1	no	—
316	C₂⁴×C₅₃	—	2	2	no	—
317	C₂⁴×C₅₃	—	2	2	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	4	2	no	—
320	#41×C₅₃	—	4	2	no	—
321	#41×C₅₃	—	4	2	no	—
322	#41×C₅₃	—	8	2	no	—
323	#41×C₅₃	—	8	2	no	—
324	#41×C₅₃	—	8	2	no	—
325	#41×C₅₃	—	8	2	no	—
326	C₂×Q₈×C₅₃	—	2	1	no	—
327	C₂×Q₈×C₅₃	—	2	1	no	—
328	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
330	C₂×D₄×C₅₃	—	2	4	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	2	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	1	no	—
340	C₂×D₄×C₅₃	—	2	1	no	—
341	C₂×D₄×C₅₃	—	2	2	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	2	1	no	—
345	C₂×D₄×C₅₃	—	2	1	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	1	no	—
349	C₂×D₄×C₅₃	—	2	1	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	—	4	2	no	—
354	C₂×D₄×C₅₃	—	4	1	no	—
355	C₂×D₄×C₅₃	—	4	2	no	—
356	C₂×D₄×C₅₃	—	4	2	no	—
357	C₂×D₄×C₅₃	—	8	2	no	—
358	C₂×D₄×C₅₃	—	8	2	no	—
359	C₂×D₄×C₅₃	—	8	4	no	—
360	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
362	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
364	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
366	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
367	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	—	2	1	no	—
369	C₂²×C₄×C₅₃	—	2	1	no	—
370	C₂²×C₄×C₅₃	—	2	1	no	—
371	C₂²×C₄×C₅₃	—	2	1	no	—
372	C₂²×C₄×C₅₃	—	2	1	no	—
373	C₂²×C₄×C₅₃	—	2	1	no	—
374	C₂²×C₄×C₅₃	—	2	2	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	—	2	1	no	—
381	C₂²×C₄×C₅₃	—	8	2	no	—
382	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
383	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
386	SD₁₆×C₅₃	—	2	4	no	—
387	SD₁₆×C₅₃	—	4	2	no	—
388	SD₁₆×C₅₃	—	4	2	no	—
389	SD₁₆×C₅₃	—	4	2	no	—
390	D₈×C₅₃	—	2	2	no	—
391	D₈×C₅₃	—	2	4	no	—
392	D₈×C₅₃	—	2	2	no	—
393	D₈×C₅₃	—	4	2	no	—
394	D₈×C₅₃	—	4	2	no	—
395	D₈×C₅₃	—	4	2	no	—
396	D₈×C₅₃	—	4	1	no	—
397	D₈×C₅₃	—	4	1	no	—
398	D₈×C₅₃	—	4	2	no	—
399	D₈×C₅₃	—	4	2	no	—
400	M₁₆×C₅₃	—	4	2	no	—
401	M₁₆×C₅₃	—	4	2	no	—
402	C₂×C₈×C₅₃	—	4	2	no	—
403	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
407	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
409	C₄⋊C₄×C₅₃	—	2	1	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	1	no	—
414	C₄⋊C₄×C₅₃	—	2	2	no	—
415	C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₄⋊C₄×C₅₃	—	2	1	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
421	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
422	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
423	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
425	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
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	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	1	no	—
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	—	2	1	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	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	2	no	—
445	C₂²⋊C₄×C₅₃	—	2	2	no	—
446	C₂²⋊C₄×C₅₃	—	2	2	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	1	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	1	no	—
451	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
452	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
453	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
454	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
455	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
456	C₄²×C₅₃	—	2	2	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	1	no	—
465	C₂³×C₅₃	—	2	2	no	—
466	C₂³×C₅₃	—	2	1	no	—
467	C₂³×C₅₃	—	2	2	no	—
468	C₂³×C₅₃	—	2	1	no	—
469	C₂³×C₅₃	—	4	2	no	—
470	C₂³×C₅₃	—	4	4	no	—
471	C₂³×C₅₃	—	4	2	no	—
472	C₂³×C₅₃	—	8	1	no	—
473	C₂³×C₅₃	—	8	2	no	—
474	C₂³×C₅₃	—	8	2	no	—
475	C₂³×C₅₃	—	8	2	no	—
476	C₂³×C₅₃	—	8	2	no	—
477	C₂³×C₅₃	—	8	2	no	—
478	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
479	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
480	Q₈×C₅₃	—	2	2	no	—
481	Q₈×C₅₃	—	2	2	no	—
482	Q₈×C₅₃	—	2	2	no	—
483	Q₈×C₅₃	—	8	1	no	—
484	Q₈×C₅₃	—	8	1	no	—
485	D₄×C₅₃	—	2	2	no	—
486	D₄×C₅₃	—	2	2	no	—
487	D₄×C₅₃	—	2	1	no	—
488	D₄×C₅₃	—	2	1	no	—
489	D₄×C₅₃	—	2	2	no	—
490	D₄×C₅₃	—	2	1	no	—
491	D₄×C₅₃	—	2	1	no	—
492	D₄×C₅₃	—	2	1	no	—
493	D₄×C₅₃	—	2	2	no	—
494	D₄×C₅₃	—	2	1	no	—
495	D₄×C₅₃	—	2	2	no	—
496	D₄×C₅₃	—	2	1	no	—
497	D₄×C₅₃	—	4	2	no	—
498	D₄×C₅₃	—	4	2	no	—
499	D₄×C₅₃	—	4	4	no	—
500	D₄×C₅₃	—	4	4	no	—
501	D₄×C₅₃	—	4	2	no	—
502	D₄×C₅₃	—	4	2	no	—
503	D₄×C₅₃	—	8	1	no	—
504	D₄×C₅₃	—	8	1	no	—
505	D₄×C₅₃	—	8	2	no	—
506	D₄×C₅₃	—	8	2	no	—
507	D₄×C₅₃	—	8	2	no	—
508	D₄×C₅₃	—	8	1	no	—
509	D₄×C₅₃	—	8	1	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	D₄×C₅₃	—	8	1	no	—
518	D₄×C₅₃	—	8	1	no	—
519	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
520	C₂×C₄×C₅₃	—	2	2	no	—
521	C₂×C₄×C₅₃	—	2	2	no	—
522	C₂×C₄×C₅₃	—	2	1	no	—
523	C₂×C₄×C₅₃	—	2	2	no	—
524	C₂×C₄×C₅₃	—	2	1	no	—
525	C₂×C₄×C₅₃	—	2	1	no	—
526	C₂×C₄×C₅₃	—	2	1	no	—
527	C₂×C₄×C₅₃	—	2	1	no	—
528	C₂×C₄×C₅₃	—	2	2	no	—
529	C₂×C₄×C₅₃	—	2	2	no	—
530	C₂×C₄×C₅₃	—	2	1	no	—
531	C₂×C₄×C₅₃	—	4	1	no	—
532	C₂×C₄×C₅₃	—	4	2	no	—
533	C₂×C₄×C₅₃	—	4	2	no	—
534	C₂×C₄×C₅₃	—	4	2	no	—
535	C₂×C₄×C₅₃	—	4	2	no	—
536	C₂×C₄×C₅₃	—	8	1	no	—
537	C₂×C₄×C₅₃	—	8	1	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	—	8	2	no	—
542	C₂×C₄×C₅₃	—	8	2	no	—
543	C₂×C₄×C₅₃	—	8	2	no	—
544	C₂×C₄×C₅₃	—	8	1	no	—
545	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
546	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
547	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
548	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
549	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
551	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
552	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
553	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
554	C₈×C₅₃	—	2	1	no	—
555	C₈×C₅₃	—	2	2	no	—
556	C₈×C₅₃	—	2	1	no	—
557	C₈×C₅₃	—	2	2	no	—
558	C₈×C₅₃	—	2	1	no	—
559	C₈×C₅₃	—	2	1	no	—
560	#62040	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
561	C₂²×C₅₃	—	2	1	no	—
562	C₂²×C₅₃	—	2	2	no	—
563	C₂²×C₅₃	—	2	1	no	—
564	C₂²×C₅₃	—	2	2	no	—
565	C₂²×C₅₃	—	2	2	no	—
566	C₂²×C₅₃	—	2	1	no	—
567	C₂²×C₅₃	—	2	2	no	—
568	C₂²×C₅₃	—	4	1	no	—
569	C₂²×C₅₃	—	4	1	no	—
570	C₂²×C₅₃	—	4	2	no	—
571	C₂²×C₅₃	—	4	1	no	—
572	C₂²×C₅₃	—	4	1	no	—
573	C₂²×C₅₃	—	4	2	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	4	1	no	—
576	C₂²×C₅₃	—	4	2	no	—
577	C₂²×C₅₃	—	4	1	no	—
578	C₂²×C₅₃	—	4	2	no	—
579	C₂²×C₅₃	—	4	1	no	—
580	C₂²×C₅₃	—	4	1	no	—
581	C₂²×C₅₃	—	4	1	no	—
582	C₂²×C₅₃	—	4	1	no	—
583	C₂²×C₅₃	—	4	2	no	—
584	C₂²×C₅₃	—	4	2	no	—
585	C₂²×C₅₃	—	8	4	no	—
586	C₂²×C₅₃	—	16	4	no	—
587	C₂²×C₅₃	—	16	4	no	—
588	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
589	C₄×C₅₃	—	2	1	no	—
590	C₄×C₅₃	—	2	1	no	—
591	C₄×C₅₃	—	2	2	no	—
592	C₄×C₅₃	—	2	1	no	—
593	C₄×C₅₃	—	2	2	no	—
594	C₄×C₅₃	—	2	1	no	—
595	C₄×C₅₃	—	2	2	no	—
596	C₄×C₅₃	—	4	2	no	—
597	C₄×C₅₃	—	4	2	no	—
598	C₄×C₅₃	—	4	1	no	—
599	C₄×C₅₃	—	4	1	no	—
600	C₄×C₅₃	—	4	1	no	—
601	C₄×C₅₃	—	4	1	no	—
602	C₄×C₅₃	#576	1	2	yes	—
603	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	C₄×C₅₃	#585	1	1	yes	characteristic
605	#3546	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#3519	C₂×C₅₃	1	1	yes	characteristic, complemented
607	#3397	C₂×C₅₃	1	1	yes	characteristic, complemented
608	#3391	C₂×C₅₃	1	1	yes	characteristic, complemented
609	#3366	C₂×C₅₃	1	1	yes	characteristic, complemented
610	#3360	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3325	C₂×C₅₃	1	1	yes	characteristic, complemented
612	#3322	C₂×C₅₃	1	2	yes	complemented
613	#3309	C₂×C₅₃	1	2	yes	complemented
614	#3303	C₂×C₅₃	1	1	yes	characteristic, complemented
615	D₄×D₈	C₂×C₅₃	1	1	yes	characteristic, complemented
616	#3274	C₂×C₅₃	1	2	yes	complemented
617	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
618	#3264	C₂×C₅₃	1	2	yes	complemented
619	#3257	C₂×C₅₃	1	2	yes	complemented
620	#3253	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#3220	C₂×C₅₃	1	2	yes	complemented
622	#3207	C₂×C₅₃	1	1	yes	characteristic, complemented
623	#3118	C₂×C₅₃	1	2	yes	complemented
624	#3100	C₂×C₅₃	1	1	yes	characteristic, complemented
625	#3041	C₂×C₅₃	1	2	yes	complemented
626	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
627	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
628	C₂×C₅₃	—	4	1	no	—
629	C₂×C₅₃	—	4	2	no	—
630	C₂×C₅₃	—	4	2	no	—
631	C₂×C₅₃	—	8	1	no	—
632	C₂×C₅₃	—	8	1	no	—
633	C₂×C₅₃	—	8	2	no	—
634	C₂×C₅₃	—	8	2	no	—
635	C₂×C₅₃	—	8	1	no	—
636	C₂×C₅₃	#3488	1	1	yes	characteristic
637	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
638	C₂×C₅₃	#3585	1	1	yes	characteristic
639	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
640	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	complemented
641	C₂²×D₈	C₂²×C₅₃	1	2	yes	—
642	#560	—	2	2	no	—
643	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#555	C₂²×C₅₃	1	1	yes	characteristic
645	#554	C₂²×C₅₃	1	1	yes	characteristic, complemented
646	#553	—	2	1	no	—
647	#553	—	2	1	no	—
648	#553	C₂²×C₅₃	1	2	yes	complemented
649	#550	C₂²×C₅₃	1	2	yes	complemented
650	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#547	C₂²×C₅₃	1	1	yes	characteristic, complemented
653	#546	—	2	1	no	—
654	#546	—	2	1	no	—
655	#546	—	2	2	no	—
656	#546	C₂²×C₅₃	1	2	yes	complemented
657	D₄²	C₂²×C₅₃	1	1	yes	characteristic
658	D₄²	C₂²×C₅₃	1	2	yes	complemented
659	D₄²	C₂²×C₅₃	1	1	yes	characteristic, complemented
660	#542	C₂²×C₅₃	1	2	yes	complemented
661	#540	C₂²×C₅₃	1	2	yes	complemented
662	#538	—	2	2	no	—
663	#538	—	2	2	no	—
664	#537	—	2	1	no	—
665	#535	—	2	1	no	—
666	#535	C₂²×C₅₃	1	2	yes	complemented
667	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
668	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
669	#532	C₂²×C₅₃	1	1	yes	characteristic, complemented
670	#529	C₂²×C₅₃	1	1	yes	characteristic
671	#525	—	2	1	no	—
672	C₂×#121	—	2	1	no	—
673	#518	C₂²×C₅₃	1	2	yes	complemented
674	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
675	#496	C₂²×C₅₃	1	2	yes	complemented
676	#493	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#493	C₂²×C₅₃	1	2	yes	complemented
678	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
679	#490	C₂²×C₅₃	1	2	yes	complemented
680	#488	C₂²×C₅₃	1	2	yes	complemented
681	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
683	#485	C₂²×C₅₃	1	2	yes	complemented
684	#482	C₂²×C₅₃	1	2	yes	complemented
685	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#480	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#479	C₂²×C₅₃	1	2	yes	complemented
688	#478	C₂²×C₅₃	1	2	yes	complemented
689	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#476	C₂²×C₅₃	1	1	yes	characteristic, complemented
691	#476	C₂²×C₅₃	1	2	yes	complemented
692	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
693	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	#469	C₂²×C₅₃	1	2	yes	complemented
695	#469	C₂²×C₅₃	1	2	yes	complemented
696	#469	C₂²×C₅₃	1	2	yes	complemented
697	#468	C₂²×C₅₃	1	2	yes	complemented
698	#466	C₂²×C₅₃	1	2	yes	complemented
699	#465	C₂²×C₅₃	1	2	yes	complemented
700	#463	C₂²×C₅₃	1	2	yes	—
701	#463	C₂²×C₅₃	1	2	yes	complemented
702	#463	C₂²×C₅₃	1	2	yes	complemented
703	#463	C₂²×C₅₃	1	2	yes	complemented
704	#463	C₂²×C₅₃	1	2	yes	complemented
705	#463	C₂²×C₅₃	1	2	yes	complemented
706	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
708	#460	C₂²×C₅₃	1	2	yes	complemented
709	#459	C₂²×C₅₃	1	1	yes	characteristic
710	#459	C₂²×C₅₃	1	1	yes	characteristic
711	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
712	#459	C₂²×C₅₃	1	2	yes	complemented
713	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
714	#459	C₂²×C₅₃	1	2	yes	complemented
715	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
716	#459	C₂²×C₅₃	1	2	yes	complemented
717	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
718	#459	C₂²×C₅₃	1	2	yes	complemented
719	#450	C₂²×C₅₃	1	2	yes	complemented
720	#449	C₂²×C₅₃	1	2	yes	complemented
721	#449	C₂²×C₅₃	1	2	yes	complemented
722	#449	C₂²×C₅₃	1	2	yes	complemented
723	#449	C₂²×C₅₃	1	2	yes	complemented
724	#447	C₂²×C₅₃	1	1	yes	characteristic
725	#447	C₂²×C₅₃	1	2	yes	—
726	#447	C₂²×C₅₃	1	1	yes	characteristic, complemented
727	#447	C₂²×C₅₃	1	2	yes	complemented
728	#447	C₂²×C₅₃	1	2	yes	complemented
729	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
730	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
731	#442	C₂²×C₅₃	1	2	yes	complemented
732	#440	C₂²×C₅₃	1	2	yes	complemented
733	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
734	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
735	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
736	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
737	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
738	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
739	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
740	#436	C₂²×C₅₃	1	2	yes	complemented
741	#435	C₂²×C₅₃	1	2	yes	complemented
742	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
743	#433	C₂²×C₅₃	1	2	yes	complemented
744	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
745	#424	C₂²×C₅₃	1	2	yes	complemented
746	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
747	#418	C₂²×C₅₃	1	2	yes	complemented
748	#417	C₂²×C₅₃	1	2	yes	complemented
749	#416	C₂²×C₅₃	1	2	yes	complemented
750	C₅₃	#62040	1	1	yes	characteristic, direct product factor, Sylow
751	C₂×#41	—	2	1	no	—
752	C₂×#41	—	2	1	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	C₂³×C₅₃	1	2	yes	—
756	C₂×#41	C₂³×C₅₃	1	2	yes	—
757	C₂²×D₄	—	2	1	no	—
758	C₂²×D₄	—	2	2	no	—
759	C₂²×D₄	—	2	1	no	—
760	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
761	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
762	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
763	C₂³×C₄	—	2	1	no	—
764	AGL(1,ℤ/8)	—	4	4	no	—
765	AGL(1,ℤ/8)	—	4	4	no	—
766	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
767	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
768	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
769	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
770	C₂×D₈	—	4	4	no	—
771	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×D₈	C₂³×C₅₃	1	2	yes	—
773	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₂×D₈	C₂³×C₅₃	1	2	yes	—
775	C₂×D₈	C₂³×C₅₃	1	2	yes	—
776	C₂×D₈	C₂³×C₅₃	1	2	yes	—
777	C₂×D₈	C₂³×C₅₃	1	2	yes	—
778	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₅₃	1	2	yes	—
780	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
781	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
782	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
783	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
784	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
785	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
786	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
787	#127	—	2	2	no	—
788	#127	C₂³×C₅₃	1	1	yes	characteristic
789	#127	C₂³×C₅₃	1	1	yes	characteristic
790	#127	C₂³×C₅₃	1	1	yes	characteristic
791	#127	C₂³×C₅₃	1	2	yes	—
792	#127	C₂³×C₅₃	1	2	yes	—
793	#126	—	2	2	no	—
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	D₄×C₅₃	1	2	yes	—
797	#125	D₄×C₅₃	1	1	yes	characteristic
798	#125	C₂³×C₅₃	1	2	yes	—
799	#124	—	2	2	no	—
800	#124	—	2	2	no	—
801	#124	—	2	1	no	—
802	#124	—	2	1	no	—
803	#124	D₄×C₅₃	1	1	yes	characteristic
804	#124	C₂³×C₅₃	1	2	yes	—
805	#124	C₂³×C₅₃	1	2	yes	—
806	#123	—	2	2	no	—
807	#123	—	2	2	no	—
808	#123	—	2	2	no	—
809	#123	—	2	2	no	—
810	#123	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	D₄×C₅₃	1	2	yes	—
813	C₂²⋊Q₈	—	2	1	no	—
814	C₂²⋊Q₈	—	2	1	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
818	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
819	#121	—	2	2	no	—
820	#121	—	2	1	no	—
821	#121	—	2	1	no	—
822	#121	—	2	1	no	—
823	#121	—	2	1	no	—
824	#121	—	2	1	no	—
825	#121	—	2	1	no	—
826	#121	—	2	1	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	2	no	—
830	#121	—	2	2	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	—	2	2	no	—
840	#121	D₄×C₅₃	1	1	yes	characteristic
841	#121	C₂³×C₅₃	1	2	yes	—
842	#121	C₂³×C₅₃	1	1	yes	characteristic
843	#121	C₂³×C₅₃	1	1	yes	characteristic
844	#121	C₂³×C₅₃	1	2	yes	—
845	#121	C₂³×C₅₃	1	2	yes	—
846	#121	C₂³×C₅₃	1	2	yes	—
847	#120	—	2	2	no	—
848	#120	—	2	2	no	—
849	#120	—	2	2	no	—
850	#120	—	2	2	no	—
851	#120	—	2	2	no	—
852	#120	—	2	2	no	—
853	#120	—	2	2	no	—
854	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
855	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
856	C₄×D₄	—	2	2	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	2	no	—
859	C₄×D₄	—	2	2	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₅₃	1	2	yes	—
871	C₄×D₄	C₂³×C₅₃	1	2	yes	—
872	C₄×D₄	C₂³×C₅₃	1	2	yes	—
873	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₅₃	1	2	yes	—
876	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
877	C₄×D₄	C₂³×C₅₃	1	2	yes	—
878	#117	—	2	1	no	—
879	#117	—	2	1	no	—
880	#117	C₂³×C₅₃	1	2	yes	—
881	#117	C₂³×C₅₃	1	2	yes	—
882	C₂×C₄⋊C₄	—	2	1	no	—
883	C₂×C₄⋊C₄	—	2	1	no	—
884	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	2	no	—
887	C₂×C₂²⋊C₄	—	2	2	no	—
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
890	#107	C₂³×C₅₃	1	1	yes	characteristic
891	#107	C₂³×C₅₃	1	1	yes	characteristic
892	#107	C₂³×C₅₃	1	1	yes	characteristic
893	#107	C₂³×C₅₃	1	1	yes	characteristic
894	#106	C₂³×C₅₃	1	2	yes	—
895	#106	C₂³×C₅₃	1	2	yes	—
896	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
897	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
898	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
899	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
900	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
901	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
902	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
903	#103	C₂³×C₅₃	1	2	yes	—
904	#103	C₂³×C₅₃	1	2	yes	—
905	#103	C₂³×C₅₃	1	2	yes	—
906	#103	C₂³×C₅₃	1	2	yes	—
907	#102	C₂³×C₅₃	1	1	yes	characteristic
908	#102	C₂³×C₅₃	1	2	yes	—
909	#102	C₂³×C₅₃	1	2	yes	—
910	#102	C₂³×C₅₃	1	2	yes	—
911	#102	C₂³×C₅₃	1	1	yes	characteristic
912	#102	C₂³×C₅₃	1	2	yes	—
913	#102	C₂³×C₅₃	1	2	yes	—
914	#102	C₂³×C₅₃	1	1	yes	characteristic
915	#102	C₂³×C₅₃	1	1	yes	characteristic
916	#102	C₂³×C₅₃	1	1	yes	characteristic
917	#102	C₂³×C₅₃	1	1	yes	characteristic
918	#102	C₂³×C₅₃	1	1	yes	characteristic
919	#102	C₂³×C₅₃	1	1	yes	characteristic
920	#102	C₂³×C₅₃	1	2	yes	—
921	#102	C₂³×C₅₃	1	2	yes	—
922	#102	C₂³×C₅₃	1	2	yes	—
923	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
924	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
925	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
926	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
927	#97	C₂³×C₅₃	1	2	yes	—
928	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
929	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
930	C₄×C₈	C₂³×C₅₃	1	2	yes	—
931	C₂⁴	—	2	1	no	—
932	C₂⁴	—	2	2	no	—
933	C₂⁴	—	2	2	no	—
934	#41	—	4	2	no	—
935	#41	—	4	2	no	—
936	#41	—	4	2	no	—
937	#41	—	4	2	no	—
938	#41	—	8	2	no	—
939	#41	—	8	2	no	—
940	#41	—	8	2	no	—
941	#41	—	8	2	no	—
942	C₂×Q₈	—	2	1	no	—
943	C₂×Q₈	—	2	1	no	—
944	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
945	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
946	C₂×D₄	—	2	4	no	—
947	C₂×D₄	—	2	2	no	—
948	C₂×D₄	—	2	2	no	—
949	C₂×D₄	—	2	1	no	—
950	C₂×D₄	—	2	2	no	—
951	C₂×D₄	—	2	2	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	1	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	1	no	—
960	C₂×D₄	—	2	1	no	—
961	C₂×D₄	—	2	1	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	1	no	—
966	C₂×D₄	—	2	2	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	4	2	no	—
970	C₂×D₄	—	4	1	no	—
971	C₂×D₄	—	4	2	no	—
972	C₂×D₄	—	4	2	no	—
973	C₂×D₄	—	8	2	no	—
974	C₂×D₄	—	8	2	no	—
975	C₂×D₄	—	8	4	no	—
976	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
977	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
978	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
979	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
980	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
981	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
982	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
983	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	2	1	no	—
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	2	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	2	no	—
993	C₂²×C₄	—	2	2	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	8	2	no	—
998	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
999	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1000	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1001	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
1002	SD₁₆	—	2	4	no	—
1003	SD₁₆	—	4	2	no	—
1004	SD₁₆	—	4	2	no	—
1005	SD₁₆	—	4	2	no	—
1006	D₈	—	2	2	no	—
1007	D₈	—	2	4	no	—
1008	D₈	—	2	2	no	—
1009	D₈	—	4	2	no	—
1010	D₈	—	4	2	no	—
1011	D₈	—	4	2	no	—
1012	D₈	—	4	2	no	—
1013	D₈	—	4	1	no	—
1014	D₈	—	4	2	no	—
1015	D₈	—	4	1	no	—
1016	M₁₆	—	4	2	no	—
1017	M₁₆	—	4	2	no	—
1018	C₂×C₈	—	4	2	no	—
1019	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1020	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1021	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1022	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1023	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1024	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1025	C₄⋊C₄	—	2	1	no	—
1026	C₄⋊C₄	—	2	1	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1036	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1037	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1038	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1039	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1040	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1041	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1043	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1044	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	1	no	—
1048	C₂²⋊C₄	—	2	1	no	—
1049	C₂²⋊C₄	—	2	2	no	—
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	2	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	1	no	—
1067	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1068	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1069	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1070	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1071	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1072	C₄²	—	2	2	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1075	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1076	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1077	C₄²	C₂⁴×C₅₃	1	2	yes	—
1078	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1079	C₂³	—	2	1	no	—
1080	C₂³	—	2	1	no	—
1081	C₂³	—	2	2	no	—
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	2	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	4	2	no	—
1086	C₂³	—	4	4	no	—
1087	C₂³	—	4	2	no	—
1088	C₂³	—	8	1	no	—
1089	C₂³	—	8	2	no	—
1090	C₂³	—	8	2	no	—
1091	C₂³	—	8	2	no	—
1092	C₂³	—	8	2	no	—
1093	C₂³	—	8	2	no	—
1094	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1095	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1096	Q₈	—	2	2	no	—
1097	Q₈	—	2	2	no	—
1098	Q₈	—	2	2	no	—
1099	Q₈	—	8	1	no	—
1100	Q₈	—	8	1	no	—
1101	D₄	—	2	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	2	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	2	2	no	—
1106	D₄	—	2	1	no	—
1107	D₄	—	2	1	no	—
1108	D₄	—	2	1	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	4	2	no	—
1114	D₄	—	4	2	no	—
1115	D₄	—	4	4	no	—
1116	D₄	—	4	4	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	8	1	no	—
1120	D₄	—	8	1	no	—
1121	D₄	—	8	2	no	—
1122	D₄	—	8	2	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	1	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	1	no	—
1128	D₄	—	8	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	—	8	1	no	—
1134	D₄	—	8	1	no	—
1135	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	2	no	—
1144	C₂×C₄	—	2	2	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	4	1	no	—
1148	C₂×C₄	—	4	2	no	—
1149	C₂×C₄	—	4	2	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	8	1	no	—
1153	C₂×C₄	—	8	1	no	—
1154	C₂×C₄	—	8	2	no	—
1155	C₂×C₄	—	8	2	no	—
1156	C₂×C₄	—	8	2	no	—
1157	C₂×C₄	—	8	2	no	—
1158	C₂×C₄	—	8	2	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	1	no	—
1161	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1162	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1163	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1166	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1167	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1168	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1169	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1170	C₈	—	2	1	no	—
1171	C₈	—	2	2	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	2	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	2	no	—
1178	C₂²	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	2	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	2	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	4	2	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	2	no	—
1196	C₂²	—	4	1	no	—
1197	C₂²	—	4	1	no	—
1198	C₂²	—	4	2	no	—
1199	C₂²	—	4	1	no	—
1200	C₂²	—	8	4	no	—
1201	C₂²	—	16	4	no	—
1202	C₂²	—	16	4	no	—
1203	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1204	C₄	—	2	1	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	1	no	—
1207	C₄	—	2	2	no	—
1208	C₄	—	2	1	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	2	no	—
1211	C₄	—	4	2	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	2	no	—
1217	C₄	C₅₃×#576	1	2	yes	—
1218	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1219	C₄	C₅₃×#585	1	1	yes	characteristic
1220	C₂	—	4	1	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	4	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	—	8	1	no	—
1225	C₂	—	8	2	no	—
1226	C₂	—	8	2	no	—
1227	C₂	—	8	1	no	—
1228	C₂	C₅₃×#3488	1	1	yes	characteristic
1229	C₂	C₂×C₅₃×#576	1	1	yes	characteristic
1230	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×#3546	C₂	semidirect
2. C₅₃×#3519	C₂	semidirect
3. C₅₃×#3397	C₂	semidirect
4. C₅₃×#3391	C₂	semidirect
5. C₅₃×#3366	C₂	semidirect
6. C₅₃×#3360	C₂	semidirect
7. C₅₃×#3325	C₂	semidirect
8. C₅₃×#3322	C₂	semidirect
9. C₅₃×#3309	C₂	semidirect
10. C₅₃×#3303	C₂	semidirect
11. D₄×D₈×C₅₃	C₂	semidirect
12. C₅₃×#3274	C₂	semidirect
13. C₅₃×#3272	C₂	semidirect
14. C₅₃×#3264	C₂	semidirect
15. C₅₃×#3257	C₂	semidirect
16. C₅₃×#3253	C₂	semidirect
17. C₅₃×#3220	C₂	semidirect
18. C₅₃×#3207	C₂	semidirect
19. C₅₃×#3118	C₂	semidirect
20. C₅₃×#3100	C₂	semidirect
21. C₅₃×#3041	C₂	semidirect
22. C₅₃×#3036	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
28. C₅₃×#556	C₂²	semidirect
30. C₅₃×#554	C₂²	semidirect
33. C₅₃×#553	C₂²	semidirect
34. C₅₃×#550	C₂²	semidirect
35. C₅₃×#550	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
37. C₅₃×#547	C₂²	semidirect
41. C₅₃×#546	C₂²	semidirect
43. D₄²×C₅₃	C₂²	semidirect
44. D₄²×C₅₃	C₂²	semidirect
45. C₅₃×#542	C₂²	semidirect
46. C₅₃×#540	C₂²	semidirect
51. C₅₃×#535	C₂²	semidirect
52. C₅₃×#532	C₂²	semidirect
53. C₅₃×#532	C₂²	semidirect
54. C₅₃×#532	C₂²	semidirect
58. C₅₃×#518	C₂²	semidirect
59. C₂×C₄×D₄×C₅₃	C₂²	semidirect
60. C₅₃×#496	C₂²	semidirect
61. C₅₃×#493	C₂²	semidirect
62. C₅₃×#493	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#490	C₂²	semidirect
65. C₅₃×#488	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#482	C₂²	semidirect
70. C₅₃×#480	C₂²	semidirect
71. C₅₃×#480	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
73. C₅₃×#478	C₂²	semidirect
74. C₅₃×#476	C₂²	semidirect
75. C₅₃×#476	C₂²	semidirect
76. C₅₃×#476	C₂²	semidirect
77. C₅₃×#474	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
79. C₅₃×#469	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
81. C₅₃×#469	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
83. C₅₃×#466	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
86. C₅₃×#463	C₂²	semidirect
87. C₅₃×#463	C₂²	semidirect
88. C₅₃×#463	C₂²	semidirect
89. C₅₃×#463	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#461	C₂²	semidirect
92. C₅₃×#461	C₂²	semidirect
93. 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×#450	C₂²	semidirect
105. C₅₃×#449	C₂²	semidirect
106. C₅₃×#449	C₂²	semidirect
107. C₅₃×#449	C₂²	semidirect
108. C₅₃×#449	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×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₄×D₈×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. C₅₃×#416	C₂²	semidirect
560. #62040	C₅₃	direct (N × H)
605. #3546	C₂×C₅₃	semidirect
606. #3519	C₂×C₅₃	semidirect
607. #3397	C₂×C₅₃	semidirect
608. #3391	C₂×C₅₃	semidirect
609. #3366	C₂×C₅₃	semidirect
610. #3360	C₂×C₅₃	semidirect
611. #3325	C₂×C₅₃	semidirect
612. #3322	C₂×C₅₃	semidirect
613. #3309	C₂×C₅₃	semidirect
614. #3303	C₂×C₅₃	semidirect
615. D₄×D₈	C₂×C₅₃	semidirect
616. #3274	C₂×C₅₃	semidirect
617. #3272	C₂×C₅₃	semidirect
618. #3264	C₂×C₅₃	semidirect
619. #3257	C₂×C₅₃	semidirect
620. #3253	C₂×C₅₃	semidirect
621. #3220	C₂×C₅₃	semidirect
622. #3207	C₂×C₅₃	semidirect
623. #3118	C₂×C₅₃	semidirect
624. #3100	C₂×C₅₃	semidirect
625. #3041	C₂×C₅₃	semidirect
626. #3036	C₂×C₅₃	semidirect
627. #2993	C₂×C₅₃	semidirect
639. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
640. C₂×AGL(1,ℤ/8)	C₂²×C₅₃	semidirect
643. #556	C₂²×C₅₃	semidirect
645. #554	C₂²×C₅₃	semidirect
648. #553	C₂²×C₅₃	semidirect
649. #550	C₂²×C₅₃	semidirect
650. #550	C₂²×C₅₃	semidirect
651. #550	C₂²×C₅₃	semidirect
652. #547	C₂²×C₅₃	semidirect
656. #546	C₂²×C₅₃	semidirect
658. D₄²	C₂²×C₅₃	semidirect
659. D₄²	C₂²×C₅₃	semidirect
660. #542	C₂²×C₅₃	semidirect
661. #540	C₂²×C₅₃	semidirect
666. #535	C₂²×C₅₃	semidirect
667. #532	C₂²×C₅₃	semidirect
668. #532	C₂²×C₅₃	semidirect
669. #532	C₂²×C₅₃	semidirect
673. #518	C₂²×C₅₃	semidirect
674. C₂×C₄×D₄	C₂²×C₅₃	semidirect
675. #496	C₂²×C₅₃	semidirect
676. #493	C₂²×C₅₃	semidirect
677. #493	C₂²×C₅₃	semidirect
678. #492	C₂²×C₅₃	semidirect
679. #490	C₂²×C₅₃	semidirect
680. #488	C₂²×C₅₃	semidirect
681. #487	C₂²×C₅₃	semidirect
682. #486	C₂²×C₅₃	semidirect
683. #485	C₂²×C₅₃	semidirect
684. #482	C₂²×C₅₃	semidirect
685. #480	C₂²×C₅₃	semidirect
686. #480	C₂²×C₅₃	semidirect
687. #479	C₂²×C₅₃	semidirect
688. #478	C₂²×C₅₃	semidirect
689. #476	C₂²×C₅₃	semidirect
690. #476	C₂²×C₅₃	semidirect
691. #476	C₂²×C₅₃	semidirect
692. #474	C₂²×C₅₃	semidirect
693. #474	C₂²×C₅₃	semidirect
694. #469	C₂²×C₅₃	semidirect
695. #469	C₂²×C₅₃	semidirect
696. #469	C₂²×C₅₃	semidirect
697. #468	C₂²×C₅₃	semidirect
698. #466	C₂²×C₅₃	semidirect
699. #465	C₂²×C₅₃	semidirect
701. #463	C₂²×C₅₃	semidirect
702. #463	C₂²×C₅₃	semidirect
703. #463	C₂²×C₅₃	semidirect
704. #463	C₂²×C₅₃	semidirect
705. #463	C₂²×C₅₃	semidirect
706. #461	C₂²×C₅₃	semidirect
707. #461	C₂²×C₅₃	semidirect
708. #460	C₂²×C₅₃	semidirect
711. #459	C₂²×C₅₃	semidirect
712. #459	C₂²×C₅₃	semidirect
713. #459	C₂²×C₅₃	semidirect
714. #459	C₂²×C₅₃	semidirect
715. #459	C₂²×C₅₃	semidirect
716. #459	C₂²×C₅₃	semidirect
717. #459	C₂²×C₅₃	semidirect
718. #459	C₂²×C₅₃	semidirect
719. #450	C₂²×C₅₃	semidirect
720. #449	C₂²×C₅₃	semidirect
721. #449	C₂²×C₅₃	semidirect
722. #449	C₂²×C₅₃	semidirect
723. #449	C₂²×C₅₃	semidirect
726. #447	C₂²×C₅₃	semidirect
727. #447	C₂²×C₅₃	semidirect
728. #447	C₂²×C₅₃	semidirect
729. #446	C₂²×C₅₃	semidirect
730. C₈×Q₈	C₂²×C₅₃	semidirect
731. #442	C₂²×C₅₃	semidirect
732. #440	C₂²×C₅₃	semidirect
733. C₄×SD₁₆	C₂²×C₅₃	semidirect
735. C₄×D₈	C₂²×C₅₃	semidirect
736. C₄×D₈	C₂²×C₅₃	semidirect
737. C₄×D₈	C₂²×C₅₃	semidirect
738. C₄×D₈	C₂²×C₅₃	semidirect
739. #436	C₂²×C₅₃	semidirect
740. #436	C₂²×C₅₃	semidirect
741. #435	C₂²×C₅₃	semidirect
742. C₈×D₄	C₂²×C₅₃	semidirect
743. #433	C₂²×C₅₃	semidirect
744. #431	C₂²×C₅₃	semidirect
745. #424	C₂²×C₅₃	semidirect
746. #423	C₂²×C₅₃	semidirect
747. #418	C₂²×C₅₃	semidirect
748. #417	C₂²×C₅₃	semidirect
749. #416	C₂²×C₅₃	semidirect
750. C₅₃	#62040	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×#3546	2
C₅₃×#3519	2
C₅₃×#3397	2
C₅₃×#3391	2
C₅₃×#3366	2
C₅₃×#3360	2
C₅₃×#3325	2
C₅₃×#3322	2
C₅₃×#3309	2
C₅₃×#3303	2
D₄×D₈×C₅₃	2
C₅₃×#3274	2
C₅₃×#3272	2
C₅₃×#3264	2
C₅₃×#3257	2
C₅₃×#3253	2
C₅₃×#3220	2
C₅₃×#3207	2
C₅₃×#3118	2
C₅₃×#3100	2
C₅₃×#3041	2
C₅₃×#3036	2
C₅₃×#2993	2
#62040	53

Subgroups — C53×#62040 #27269552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62040 #27269552