Subgroups — C₅₃×#61424 #27268936

Order 13568.

1932 conjugacy classes of subgroups.

The subgroup lattice has 1218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3506	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3403	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3402	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3401	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3401	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3399	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3397	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3396	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3394	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3155	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3154	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3153	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3046	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3045	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅₃×#3043	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#463	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#2947	C₂	1	1	yes	maximal, characteristic, complemented
22	C₅₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×AGL(1,ℤ/8)×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×#137×C₅₃	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
27	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
28	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	1	yes	characteristic
29	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
30	C₂×#135×C₅₃	C₂²	1	1	yes	characteristic
31	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×D₈×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#559	C₂²	1	2	yes	complemented
34	C₅₃×#559	C₂²	1	2	yes	complemented
35	C₅₃×#559	C₂²	1	2	yes	complemented
36	C₅₃×#559	C₂²	1	2	yes	complemented
37	C₅₃×#556	C₂²	1	2	yes	complemented
38	C₅₃×#556	C₂²	1	2	yes	complemented
39	C₅₃×#556	C₂²	1	2	yes	complemented
40	C₅₃×#555	—	2	1	no	—
41	C₅₃×#553	—	2	1	no	—
42	C₅₃×#553	—	2	1	no	—
43	C₅₃×#551	—	2	2	no	—
44	C₅₃×#551	—	2	2	no	—
45	C₅₃×#550	C₂²	1	2	yes	complemented
46	C₅₃×#547	—	2	1	no	—
47	C₅₃×#542	—	2	1	no	—
48	C₅₃×#542	—	2	1	no	—
49	C₅₃×#538	—	2	2	no	—
50	C₅₃×#536	C₂²	1	1	yes	characteristic
51	C₅₃×#535	C₂²	1	1	yes	characteristic
52	C₅₃×#535	C₂²	1	1	yes	characteristic
53	C₅₃×#535	C₂²	1	1	yes	characteristic
54	C₅₃×#533	C₂²	1	1	yes	characteristic
55	C₅₃×#532	C₂²	1	1	yes	characteristic
56	C₅₃×#529	—	2	1	no	—
57	C₅₃×#529	—	2	1	no	—
58	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
59	C₅₃×#525	—	2	2	no	—
60	C₅₃×#520	C₂²	1	1	yes	characteristic
61	C₅₃×#520	C₂²	1	1	yes	characteristic
62	C₅₃×#519	C₂²	1	1	yes	characteristic
63	C₅₃×#518	C₂²	1	1	yes	characteristic
64	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
65	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#497	C₂²	1	2	yes	complemented
67	C₅₃×#497	C₂²	1	2	yes	complemented
68	C₅₃×#496	C₂²	1	2	yes	—
69	C₅₃×#496	C₂²	1	2	yes	—
70	C₅₃×#496	C₂²	1	2	yes	complemented
71	C₅₃×#496	C₂²	1	2	yes	complemented
72	C₅₃×#495	C₂²	1	2	yes	—
73	C₅₃×#495	C₂²	1	2	yes	complemented
74	C₅₃×#495	C₂²	1	2	yes	complemented
75	C₅₃×#495	C₂²	1	2	yes	complemented
76	C₅₃×#493	C₂²	1	2	yes	—
77	C₅₃×#492	C₂²	1	2	yes	complemented
78	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
80	C₅₃×#464	C₂²	1	2	yes	complemented
81	C₅₃×#464	C₂²	1	2	yes	complemented
82	C₅₃×#464	C₂²	1	2	yes	complemented
83	C₅₃×#464	C₂²	1	2	yes	complemented
84	C₅₃×#463	C₂²	1	2	yes	—
85	C₅₃×#463	C₂²	1	2	yes	—
86	C₅₃×#463	C₂²	1	2	yes	—
87	C₅₃×#463	C₂²	1	2	yes	—
88	C₅₃×#463	C₂²	1	2	yes	—
89	C₅₃×#463	C₂²	1	2	yes	—
90	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
91	C₅₃×#463	C₂²	1	1	yes	characteristic, 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×#462	C₂²	1	2	yes	complemented
96	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
97	C₅₃×#461	C₂²	1	2	yes	complemented
98	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
99	C₅₃×#460	C₂²	1	2	yes	complemented
100	C₅₃×#460	C₂²	1	2	yes	complemented
101	C₅₃×#460	C₂²	1	2	yes	complemented
102	C₅₃×#459	C₂²	1	2	yes	—
103	C₅₃×#459	C₂²	1	2	yes	—
104	C₅₃×#459	C₂²	1	1	yes	characteristic, complemented
105	C₅₃×#459	C₂²	1	2	yes	complemented
106	C₅₃×#446	C₂²	1	2	yes	complemented
107	C₅₃×#446	C₂²	1	2	yes	complemented
108	C₅₃×#446	C₂²	1	2	yes	complemented
109	C₈×Q₈×C₅₃	C₂²	1	2	yes	complemented
110	C₅₃×#442	C₂²	1	2	yes	complemented
111	C₅₃×#442	C₂²	1	2	yes	complemented
112	C₅₃×#441	C₂²	1	2	yes	complemented
113	C₅₃×#440	C₂²	1	2	yes	complemented
114	C₅₃×#440	C₂²	1	2	yes	complemented
115	C₅₃×#440	C₂²	1	2	yes	complemented
116	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
117	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
119	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
120	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
121	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
122	C₅₃×#428	C₂²	1	1	yes	characteristic
123	C₅₃×#424	C₂²	1	1	yes	characteristic
124	C₅₃×#424	C₂²	1	1	yes	characteristic
125	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
126	C₅₃×#418	C₂²	1	1	yes	characteristic
127	C₅₃×#417	C₂²	1	1	yes	characteristic
128	C₅₃×#416	C₂²	1	1	yes	characteristic
129	C₅₃×#416	C₂²	1	1	yes	characteristic
130	C₂×#103×C₅₃	C₂²	1	1	yes	characteristic
131	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic
132	C₅₃×#405	C₂²	1	1	yes	characteristic
133	C₅₃×#405	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₅₃	C₂²	1	1	yes	characteristic
135	C₂×#41×C₅₃	—	2	2	no	—
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
139	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
140	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	—	2	1	no	—
143	#137×C₅₃	—	2	4	no	—
144	#137×C₅₃	—	4	2	no	—
145	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
146	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
147	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
148	#135×C₅₃	—	4	2	no	—
149	#135×C₅₃	—	4	2	no	—
150	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
152	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
154	C₂×SD₁₆×C₅₃	—	4	2	no	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
159	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
164	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×D₈×C₅₃	—	4	2	no	—
167	C₂×D₈×C₅₃	C₂³	1	2	yes	—
168	C₂×D₈×C₅₃	C₂³	1	2	yes	—
169	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₂×D₈×C₅₃	C₂³	1	2	yes	—
171	C₂×D₈×C₅₃	C₂³	1	2	yes	—
172	C₂×D₈×C₅₃	C₂³	1	2	yes	—
173	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
176	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
178	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
179	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
180	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
181	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
182	#127×C₅₃	C₂³	1	2	yes	—
183	#127×C₅₃	C₂³	1	2	yes	—
184	#127×C₅₃	C₂³	1	2	yes	—
185	#127×C₅₃	C₂³	1	1	yes	characteristic
186	#126×C₅₃	—	2	2	no	—
187	#126×C₅₃	—	2	2	no	—
188	#126×C₅₃	—	2	2	no	—
189	#126×C₅₃	—	2	2	no	—
190	#126×C₅₃	—	2	2	no	—
191	#126×C₅₃	—	2	2	no	—
192	#125×C₅₃	D₄	1	1	yes	characteristic
193	#125×C₅₃	D₄	1	1	yes	characteristic
194	#124×C₅₃	—	2	1	no	—
195	#124×C₅₃	—	2	1	no	—
196	#124×C₅₃	—	2	2	no	—
197	#124×C₅₃	—	2	2	no	—
198	#124×C₅₃	—	2	2	no	—
199	#124×C₅₃	—	2	2	no	—
200	#124×C₅₃	C₂³	1	2	yes	—
201	#124×C₅₃	C₂³	1	2	yes	—
202	#124×C₅₃	C₂³	1	2	yes	—
203	#124×C₅₃	C₂³	1	1	yes	characteristic
204	#124×C₅₃	C₂³	1	1	yes	characteristic
205	#124×C₅₃	C₂³	1	2	yes	—
206	#124×C₅₃	C₂³	1	2	yes	—
207	#124×C₅₃	C₂³	1	2	yes	—
208	#123×C₅₃	—	2	2	no	—
209	#123×C₅₃	—	2	2	no	—
210	#123×C₅₃	—	2	2	no	—
211	#123×C₅₃	—	2	2	no	—
212	#123×C₅₃	—	2	2	no	—
213	#123×C₅₃	—	2	2	no	—
214	#123×C₅₃	—	2	2	no	—
215	#123×C₅₃	—	2	2	no	—
216	#123×C₅₃	—	2	2	no	—
217	C₂²⋊Q₈×C₅₃	—	2	1	no	—
218	C₂²⋊Q₈×C₅₃	—	2	1	no	—
219	C₂²⋊Q₈×C₅₃	—	2	2	no	—
220	C₂²⋊Q₈×C₅₃	—	2	2	no	—
221	C₂²⋊Q₈×C₅₃	—	2	2	no	—
222	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
223	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	—	2	1	no	—
230	#121×C₅₃	—	2	1	no	—
231	#121×C₅₃	—	2	2	no	—
232	#121×C₅₃	—	2	2	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	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	—	2	1	no	—
240	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
241	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
243	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
244	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
246	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
247	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
248	C₄×D₄×C₅₃	—	2	1	no	—
249	C₄×D₄×C₅₃	—	2	1	no	—
250	C₄×D₄×C₅₃	—	2	2	no	—
251	C₄×D₄×C₅₃	—	2	2	no	—
252	C₄×D₄×C₅₃	—	2	2	no	—
253	C₄×D₄×C₅₃	—	2	2	no	—
254	C₄×D₄×C₅₃	—	2	2	no	—
255	C₄×D₄×C₅₃	—	2	2	no	—
256	C₄×D₄×C₅₃	—	2	1	no	—
257	C₄×D₄×C₅₃	—	2	1	no	—
258	C₄×D₄×C₅₃	—	2	1	no	—
259	C₄×D₄×C₅₃	—	2	1	no	—
260	C₄×D₄×C₅₃	—	2	1	no	—
261	C₄×D₄×C₅₃	—	2	1	no	—
262	C₄×D₄×C₅₃	C₂³	1	2	yes	—
263	C₄×D₄×C₅₃	C₂³	1	2	yes	—
264	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
265	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
266	C₄×D₄×C₅₃	C₂³	1	2	yes	—
267	C₄×D₄×C₅₃	C₂³	1	2	yes	—
268	C₄×D₄×C₅₃	C₂³	1	2	yes	—
269	C₄×D₄×C₅₃	C₂³	1	2	yes	—
270	#117×C₅₃	—	2	1	no	—
271	#117×C₅₃	—	2	1	no	—
272	#117×C₅₃	—	2	2	no	—
273	#117×C₅₃	—	2	2	no	—
274	#117×C₅₃	—	2	2	no	—
275	#117×C₅₃	—	2	2	no	—
276	#117×C₅₃	—	2	1	no	—
277	#117×C₅₃	C₂³	1	1	yes	characteristic
278	#117×C₅₃	C₂³	1	1	yes	characteristic
279	#117×C₅₃	C₂³	1	1	yes	characteristic
280	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
281	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
282	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
283	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
284	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
285	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
286	C₂×C₂²⋊C₄×C₅₃	—	2	1	no	—
287	C₂×C₄²×C₅₃	—	2	1	no	—
288	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
289	#107×C₅₃	C₂³	1	2	yes	—
290	#106×C₅₃	C₂³	1	2	yes	—
291	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
292	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
294	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
295	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
296	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
297	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
298	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
299	#103×C₅₃	C₂³	1	2	yes	—
300	#103×C₅₃	C₂³	1	2	yes	—
301	#103×C₅₃	C₂³	1	1	yes	characteristic
302	#103×C₅₃	C₂³	1	1	yes	characteristic
303	#103×C₅₃	C₂³	1	1	yes	characteristic
304	#103×C₅₃	C₂³	1	1	yes	characteristic
305	#103×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	#102×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	1	yes	characteristic
309	#102×C₅₃	C₂³	1	1	yes	characteristic
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	1	yes	characteristic
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	2	yes	—
314	#102×C₅₃	C₂³	1	2	yes	—
315	#97×C₅₃	C₂³	1	2	yes	—
316	#97×C₅₃	C₂³	1	2	yes	—
317	#97×C₅₃	C₂³	1	2	yes	—
318	C₄×C₈×C₅₃	C₂³	1	2	yes	—
319	C₄×C₈×C₅₃	C₂³	1	2	yes	—
320	C₄×C₈×C₅₃	C₂³	1	2	yes	—
321	C₂⁴×C₅₃	—	2	1	no	—
322	C₂⁴×C₅₃	—	2	1	no	—
323	#41×C₅₃	—	2	2	no	—
324	#41×C₅₃	—	2	2	no	—
325	#41×C₅₃	—	2	2	no	—
326	#41×C₅₃	—	2	2	no	—
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	#41×C₅₃	—	8	4	no	—
330	C₂×Q₈×C₅₃	—	2	1	no	—
331	C₂×Q₈×C₅₃	—	2	2	no	—
332	C₂×Q₈×C₅₃	—	2	2	no	—
333	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
334	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
336	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
337	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×D₄×C₅₃	—	2	1	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	1	no	—
345	C₂×D₄×C₅₃	—	2	2	no	—
346	C₂×D₄×C₅₃	—	2	2	no	—
347	C₂×D₄×C₅₃	—	2	2	no	—
348	C₂×D₄×C₅₃	—	2	2	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	—	2	2	no	—
354	C₂×D₄×C₅₃	—	2	2	no	—
355	C₂×D₄×C₅₃	—	2	2	no	—
356	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
357	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
358	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
359	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
360	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	1	no	—
363	C₂²×C₄×C₅₃	—	2	1	no	—
364	C₂²×C₄×C₅₃	—	2	1	no	—
365	C₂²×C₄×C₅₃	—	2	1	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	—	2	1	no	—
368	C₂²×C₄×C₅₃	—	2	1	no	—
369	C₂²×C₄×C₅₃	—	2	2	no	—
370	C₂²×C₄×C₅₃	—	2	2	no	—
371	C₂²×C₄×C₅₃	—	2	2	no	—
372	C₂²×C₄×C₅₃	—	2	2	no	—
373	C₂²×C₄×C₅₃	—	2	2	no	—
374	C₂²×C₄×C₅₃	—	8	2	no	—
375	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
376	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
377	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₅₃	—	2	4	no	—
379	Q₁₆×C₅₃	—	4	1	no	—
380	Q₁₆×C₅₃	—	4	1	no	—
381	Q₁₆×C₅₃	—	4	2	no	—
382	SD₁₆×C₅₃	—	2	4	no	—
383	SD₁₆×C₅₃	—	2	4	no	—
384	SD₁₆×C₅₃	—	2	4	no	—
385	SD₁₆×C₅₃	—	4	2	no	—
386	SD₁₆×C₅₃	—	4	2	no	—
387	SD₁₆×C₅₃	—	4	1	no	—
388	SD₁₆×C₅₃	—	4	1	no	—
389	SD₁₆×C₅₃	—	4	1	no	—
390	SD₁₆×C₅₃	—	4	1	no	—
391	SD₁₆×C₅₃	—	4	2	no	—
392	SD₁₆×C₅₃	—	4	2	no	—
393	D₈×C₅₃	—	2	4	no	—
394	D₈×C₅₃	—	2	4	no	—
395	D₈×C₅₃	—	4	2	no	—
396	D₈×C₅₃	—	4	2	no	—
397	D₈×C₅₃	—	4	1	no	—
398	D₈×C₅₃	—	4	1	no	—
399	D₈×C₅₃	—	4	2	no	—
400	M₁₆×C₅₃	—	2	2	no	—
401	M₁₆×C₅₃	#41	1	4	yes	complemented
402	C₂×C₈×C₅₃	—	2	2	no	—
403	C₂×C₈×C₅₃	—	2	2	no	—
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	1	yes	characteristic
409	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
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	1	no	—
415	C₄⋊C₄×C₅₃	—	2	1	no	—
416	C₄⋊C₄×C₅₃	—	2	2	no	—
417	C₄⋊C₄×C₅₃	—	2	2	no	—
418	C₄⋊C₄×C₅₃	—	2	2	no	—
419	C₄⋊C₄×C₅₃	—	2	2	no	—
420	C₄⋊C₄×C₅₃	—	2	1	no	—
421	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
422	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
423	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
426	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
427	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
428	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
429	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
430	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
434	C₂²⋊C₄×C₅₃	—	2	1	no	—
435	C₂²⋊C₄×C₅₃	—	2	2	no	—
436	C₂²⋊C₄×C₅₃	—	2	2	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	2	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	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	1	no	—
447	C₂²⋊C₄×C₅₃	—	2	2	no	—
448	C₂²⋊C₄×C₅₃	—	2	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	2	no	—
450	C₂²⋊C₄×C₅₃	—	2	2	no	—
451	C₂²⋊C₄×C₅₃	—	2	1	no	—
452	C₂²⋊C₄×C₅₃	—	2	1	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	—	2	1	no	—
456	C₂²⋊C₄×C₅₃	—	2	1	no	—
457	C₂²⋊C₄×C₅₃	—	2	2	no	—
458	C₂²⋊C₄×C₅₃	—	2	2	no	—
459	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
460	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
461	C₄²×C₅₃	—	2	1	no	—
462	C₄²×C₅₃	—	2	1	no	—
463	C₄²×C₅₃	—	2	1	no	—
464	C₄²×C₅₃	—	2	2	no	—
465	C₄²×C₅₃	—	2	2	no	—
466	C₄²×C₅₃	—	2	2	no	—
467	C₄²×C₅₃	—	2	2	no	—
468	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
470	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
471	C₄²×C₅₃	C₂⁴	1	2	yes	—
472	C₄²×C₅₃	C₂⁴	1	2	yes	—
473	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
474	C₂³×C₅₃	—	2	1	no	—
475	C₂³×C₅₃	—	2	1	no	—
476	C₂³×C₅₃	—	2	1	no	—
477	C₂³×C₅₃	—	2	2	no	—
478	C₂³×C₅₃	—	2	2	no	—
479	C₂³×C₅₃	—	4	2	no	—
480	C₂³×C₅₃	—	4	2	no	—
481	C₂³×C₅₃	—	8	1	no	—
482	C₂³×C₅₃	—	8	1	no	—
483	C₂³×C₅₃	—	8	1	no	—
484	C₂³×C₅₃	—	8	1	no	—
485	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
486	Q₈×C₅₃	—	2	2	no	—
487	Q₈×C₅₃	—	2	1	no	—
488	Q₈×C₅₃	—	2	1	no	—
489	Q₈×C₅₃	—	2	1	no	—
490	Q₈×C₅₃	—	2	2	no	—
491	Q₈×C₅₃	—	2	1	no	—
492	Q₈×C₅₃	—	2	1	no	—
493	Q₈×C₅₃	—	2	1	no	—
494	Q₈×C₅₃	—	4	2	no	—
495	Q₈×C₅₃	—	4	2	no	—
496	Q₈×C₅₃	—	4	2	no	—
497	D₄×C₅₃	—	2	2	no	—
498	D₄×C₅₃	—	2	2	no	—
499	D₄×C₅₃	—	2	1	no	—
500	D₄×C₅₃	—	2	1	no	—
501	D₄×C₅₃	—	2	1	no	—
502	D₄×C₅₃	—	2	2	no	—
503	D₄×C₅₃	—	2	2	no	—
504	D₄×C₅₃	—	2	1	no	—
505	D₄×C₅₃	—	2	1	no	—
506	D₄×C₅₃	—	2	1	no	—
507	D₄×C₅₃	—	4	2	no	—
508	D₄×C₅₃	—	4	2	no	—
509	D₄×C₅₃	—	4	2	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	4	2	no	—
512	D₄×C₅₃	—	4	2	no	—
513	D₄×C₅₃	—	8	1	no	—
514	D₄×C₅₃	—	8	2	no	—
515	D₄×C₅₃	—	8	2	no	—
516	D₄×C₅₃	—	8	2	no	—
517	D₄×C₅₃	—	8	2	no	—
518	D₄×C₅₃	—	8	2	no	—
519	D₄×C₅₃	—	8	2	no	—
520	C₂×C₄×C₅₃	—	2	2	no	—
521	C₂×C₄×C₅₃	—	2	1	no	—
522	C₂×C₄×C₅₃	—	2	1	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	—	4	1	no	—
528	C₂×C₄×C₅₃	—	4	1	no	—
529	C₂×C₄×C₅₃	—	4	4	no	—
530	C₂×C₄×C₅₃	—	4	2	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	1	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	—	8	1	no	—
542	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
543	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
544	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
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	2	yes	—
548	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
549	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
550	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
552	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
553	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
554	C₈×C₅₃	—	2	1	no	—
555	C₈×C₅₃	—	2	1	no	—
556	C₈×C₅₃	—	2	1	no	—
557	C₈×C₅₃	—	2	1	no	—
558	C₈×C₅₃	—	2	2	no	—
559	C₈×C₅₃	C₂×#41	1	4	yes	—
560	#61424	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
561	C₂²×C₅₃	—	2	1	no	—
562	C₂²×C₅₃	—	2	1	no	—
563	C₂²×C₅₃	—	4	1	no	—
564	C₂²×C₅₃	—	4	2	no	—
565	C₂²×C₅₃	—	4	1	no	—
566	C₂²×C₅₃	—	4	1	no	—
567	C₂²×C₅₃	—	4	2	no	—
568	C₂²×C₅₃	—	4	2	no	—
569	C₂²×C₅₃	—	4	1	no	—
570	C₂²×C₅₃	—	4	1	no	—
571	C₂²×C₅₃	—	4	1	no	—
572	C₂²×C₅₃	—	4	2	no	—
573	C₂²×C₅₃	—	4	1	no	—
574	C₂²×C₅₃	—	4	1	no	—
575	C₂²×C₅₃	—	4	1	no	—
576	C₂²×C₅₃	—	4	2	no	—
577	C₂²×C₅₃	—	4	2	no	—
578	C₂²×C₅₃	—	8	4	no	—
579	C₂²×C₅₃	—	16	2	no	—
580	C₂²×C₅₃	#550	1	2	yes	—
581	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
582	C₄×C₅₃	—	2	1	no	—
583	C₄×C₅₃	—	2	1	no	—
584	C₄×C₅₃	—	2	2	no	—
585	C₄×C₅₃	—	2	2	no	—
586	C₄×C₅₃	—	2	1	no	—
587	C₄×C₅₃	—	2	1	no	—
588	C₄×C₅₃	—	2	2	no	—
589	C₄×C₅₃	—	2	2	no	—
590	C₄×C₅₃	—	4	1	no	—
591	C₄×C₅₃	—	4	2	no	—
592	C₄×C₅₃	—	4	1	no	—
593	C₄×C₅₃	—	4	1	no	—
594	C₄×C₅₃	—	4	1	no	—
595	C₄×C₅₃	—	4	1	no	—
596	C₄×C₅₃	—	4	2	no	—
597	C₄×C₅₃	#550	1	2	yes	—
598	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
599	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
600	#3510	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3506	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3403	C₂×C₅₃	1	2	yes	complemented
603	#3402	C₂×C₅₃	1	2	yes	complemented
604	#3401	C₂×C₅₃	1	2	yes	complemented
605	#3401	C₂×C₅₃	1	2	yes	complemented
606	#3399	C₂×C₅₃	1	2	yes	complemented
607	#3397	C₂×C₅₃	1	2	yes	complemented
608	#3396	C₂×C₅₃	1	2	yes	complemented
609	#3394	C₂×C₅₃	1	2	yes	complemented
610	#3155	C₂×C₅₃	1	1	yes	characteristic, complemented
611	#3154	C₂×C₅₃	1	1	yes	characteristic, complemented
612	#3153	C₂×C₅₃	1	1	yes	characteristic, complemented
613	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
614	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
615	#3043	C₂×C₅₃	1	1	yes	characteristic, complemented
616	#3041	C₂×C₅₃	1	1	yes	characteristic, complemented
617	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
618	C₂×#463	C₂×C₅₃	1	1	yes	characteristic, complemented
619	#2962	C₂×C₅₃	1	1	yes	characteristic, complemented
620	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
621	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
622	C₄×AGL(1,ℤ/8)	C₂×C₅₃	1	1	yes	characteristic, complemented
623	C₂×C₅₃	—	2	2	no	—
624	C₂×C₅₃	—	8	1	no	—
625	C₂×C₅₃	—	8	1	no	—
626	C₂×C₅₃	—	8	1	no	—
627	C₂×C₅₃	—	8	2	no	—
628	C₂×C₅₃	—	8	2	no	—
629	C₂×C₅₃	C₂×#550	1	1	yes	characteristic
630	C₂×C₅₃	#3584	1	1	yes	characteristic
631	C₂×C₅₃	#3585	1	1	yes	characteristic
632	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
633	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
634	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
635	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
636	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
637	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
638	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
639	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
640	C₂²×D₈	C₂²×C₅₃	1	1	yes	characteristic
641	#559	C₂²×C₅₃	1	2	yes	complemented
642	#559	C₂²×C₅₃	1	2	yes	complemented
643	#559	C₂²×C₅₃	1	2	yes	complemented
644	#559	C₂²×C₅₃	1	2	yes	complemented
645	#556	C₂²×C₅₃	1	2	yes	complemented
646	#556	C₂²×C₅₃	1	2	yes	complemented
647	#556	C₂²×C₅₃	1	2	yes	complemented
648	#555	—	2	1	no	—
649	#553	—	2	1	no	—
650	#553	—	2	1	no	—
651	#551	—	2	2	no	—
652	#551	—	2	2	no	—
653	#550	C₂²×C₅₃	1	2	yes	complemented
654	#547	—	2	1	no	—
655	#542	—	2	1	no	—
656	#542	—	2	1	no	—
657	#538	—	2	2	no	—
658	#536	C₂²×C₅₃	1	1	yes	characteristic
659	#535	C₂²×C₅₃	1	1	yes	characteristic
660	#535	C₂²×C₅₃	1	1	yes	characteristic
661	#535	C₂²×C₅₃	1	1	yes	characteristic
662	#533	C₂²×C₅₃	1	1	yes	characteristic
663	#532	C₂²×C₅₃	1	1	yes	characteristic
664	#529	—	2	1	no	—
665	#529	—	2	1	no	—
666	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
667	#525	—	2	2	no	—
668	#520	C₂²×C₅₃	1	1	yes	characteristic
669	#520	C₂²×C₅₃	1	1	yes	characteristic
670	#519	C₂²×C₅₃	1	1	yes	characteristic
671	#518	C₂²×C₅₃	1	1	yes	characteristic
672	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
673	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
674	#497	C₂²×C₅₃	1	2	yes	complemented
675	#497	C₂²×C₅₃	1	2	yes	complemented
676	#496	C₂²×C₅₃	1	2	yes	—
677	#496	C₂²×C₅₃	1	2	yes	—
678	#496	C₂²×C₅₃	1	2	yes	complemented
679	#496	C₂²×C₅₃	1	2	yes	complemented
680	#495	C₂²×C₅₃	1	2	yes	—
681	#495	C₂²×C₅₃	1	2	yes	complemented
682	#495	C₂²×C₅₃	1	2	yes	complemented
683	#495	C₂²×C₅₃	1	2	yes	complemented
684	#493	C₂²×C₅₃	1	2	yes	—
685	#492	C₂²×C₅₃	1	2	yes	complemented
686	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#464	C₂²×C₅₃	1	2	yes	complemented
688	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
689	#464	C₂²×C₅₃	1	2	yes	complemented
690	#464	C₂²×C₅₃	1	2	yes	complemented
691	#464	C₂²×C₅₃	1	2	yes	complemented
692	#463	C₂²×C₅₃	1	2	yes	—
693	#463	C₂²×C₅₃	1	2	yes	—
694	#463	C₂²×C₅₃	1	2	yes	—
695	#463	C₂²×C₅₃	1	2	yes	—
696	#463	C₂²×C₅₃	1	2	yes	—
697	#463	C₂²×C₅₃	1	2	yes	—
698	#463	C₂²×C₅₃	1	2	yes	complemented
699	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#463	C₂²×C₅₃	1	2	yes	complemented
701	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	#462	C₂²×C₅₃	1	2	yes	complemented
703	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
704	#461	C₂²×C₅₃	1	2	yes	complemented
705	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
706	#460	C₂²×C₅₃	1	2	yes	complemented
707	#460	C₂²×C₅₃	1	2	yes	complemented
708	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#460	C₂²×C₅₃	1	2	yes	complemented
710	#459	C₂²×C₅₃	1	2	yes	—
711	#459	C₂²×C₅₃	1	2	yes	—
712	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
713	#459	C₂²×C₅₃	1	2	yes	complemented
714	#446	C₂²×C₅₃	1	2	yes	complemented
715	#446	C₂²×C₅₃	1	2	yes	complemented
716	#446	C₂²×C₅₃	1	2	yes	complemented
717	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
718	#442	C₂²×C₅₃	1	2	yes	complemented
719	#442	C₂²×C₅₃	1	2	yes	complemented
720	#441	C₂²×C₅₃	1	2	yes	complemented
721	#440	C₂²×C₅₃	1	2	yes	complemented
722	#440	C₂²×C₅₃	1	2	yes	complemented
723	#440	C₂²×C₅₃	1	2	yes	complemented
724	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
725	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
726	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
727	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
728	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
729	C₄×D₈	C₂²×C₅₃	1	2	yes	complemented
730	#428	C₂²×C₅₃	1	1	yes	characteristic
731	#424	C₂²×C₅₃	1	1	yes	characteristic
732	#424	C₂²×C₅₃	1	1	yes	characteristic
733	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
734	#418	C₂²×C₅₃	1	1	yes	characteristic
735	#417	C₂²×C₅₃	1	1	yes	characteristic
736	#416	C₂²×C₅₃	1	1	yes	characteristic
737	#416	C₂²×C₅₃	1	1	yes	characteristic
738	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
739	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
740	#405	C₂²×C₅₃	1	1	yes	characteristic
741	#405	C₂²×C₅₃	1	1	yes	characteristic
742	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
743	C₅₃	#61424	1	1	yes	characteristic, direct product factor, Sylow
744	C₂×#41	—	2	2	no	—
745	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
746	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
747	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
748	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
750	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
751	C₂³×C₄	—	2	1	no	—
752	#137	—	2	4	no	—
753	#137	—	4	2	no	—
754	AGL(1,ℤ/8)	—	2	4	no	—
755	AGL(1,ℤ/8)	—	2	4	no	—
756	AGL(1,ℤ/8)	—	4	2	no	—
757	#135	—	4	2	no	—
758	#135	—	4	2	no	—
759	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
760	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
762	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂×SD₁₆	—	4	2	no	—
764	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
765	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic
770	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
771	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
772	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
773	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
775	C₂×D₈	—	4	2	no	—
776	C₂×D₈	C₂³×C₅₃	1	2	yes	—
777	C₂×D₈	C₂³×C₅₃	1	2	yes	—
778	C₂×D₈	C₂³×C₅₃	1	2	yes	—
779	C₂×D₈	C₂³×C₅₃	1	2	yes	—
780	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
781	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
782	C₂×D₈	C₂³×C₅₃	1	2	yes	—
783	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
784	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
785	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
786	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
787	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
788	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
789	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
790	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
791	#127	C₂³×C₅₃	1	1	yes	characteristic
792	#127	C₂³×C₅₃	1	2	yes	—
793	#127	C₂³×C₅₃	1	2	yes	—
794	#127	C₂³×C₅₃	1	2	yes	—
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#126	—	2	2	no	—
798	#126	—	2	2	no	—
799	#126	—	2	2	no	—
800	#126	—	2	2	no	—
801	#125	D₄×C₅₃	1	1	yes	characteristic
802	#125	D₄×C₅₃	1	1	yes	characteristic
803	#124	—	2	2	no	—
804	#124	—	2	2	no	—
805	#124	—	2	2	no	—
806	#124	—	2	2	no	—
807	#124	—	2	1	no	—
808	#124	—	2	1	no	—
809	#124	C₂³×C₅₃	1	2	yes	—
810	#124	C₂³×C₅₃	1	2	yes	—
811	#124	C₂³×C₅₃	1	1	yes	characteristic
812	#124	C₂³×C₅₃	1	1	yes	characteristic
813	#124	C₂³×C₅₃	1	2	yes	—
814	#124	C₂³×C₅₃	1	2	yes	—
815	#124	C₂³×C₅₃	1	2	yes	—
816	#124	C₂³×C₅₃	1	2	yes	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	#123	—	2	2	no	—
822	#123	—	2	2	no	—
823	#123	—	2	2	no	—
824	#123	—	2	2	no	—
825	#123	—	2	2	no	—
826	C₂²⋊Q₈	—	2	2	no	—
827	C₂²⋊Q₈	—	2	2	no	—
828	C₂²⋊Q₈	—	2	2	no	—
829	C₂²⋊Q₈	—	2	1	no	—
830	C₂²⋊Q₈	—	2	1	no	—
831	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
832	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
833	#121	—	2	1	no	—
834	#121	—	2	1	no	—
835	#121	—	2	2	no	—
836	#121	—	2	1	no	—
837	#121	—	2	1	no	—
838	#121	—	2	1	no	—
839	#121	—	2	1	no	—
840	#121	—	2	1	no	—
841	#121	—	2	1	no	—
842	#121	—	2	2	no	—
843	#121	—	2	2	no	—
844	#120	—	2	2	no	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
850	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
852	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
853	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
854	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
855	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
856	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
857	C₄×D₄	—	2	1	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	2	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	—	2	2	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	2	1	no	—
869	C₄×D₄	—	2	1	no	—
870	C₄×D₄	—	2	1	no	—
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	2	yes	—
877	C₄×D₄	C₂³×C₅₃	1	2	yes	—
878	C₄×D₄	C₂³×C₅₃	1	2	yes	—
879	#117	—	2	1	no	—
880	#117	—	2	1	no	—
881	#117	—	2	2	no	—
882	#117	—	2	2	no	—
883	#117	—	2	2	no	—
884	#117	—	2	2	no	—
885	#117	—	2	1	no	—
886	#117	C₂³×C₅₃	1	1	yes	characteristic
887	#117	C₂³×C₅₃	1	1	yes	characteristic
888	#117	C₂³×C₅₃	1	1	yes	characteristic
889	C₂×C₄⋊C₄	—	2	1	no	—
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
892	C₂×C₂²⋊C₄	—	2	1	no	—
893	C₂×C₂²⋊C₄	—	2	1	no	—
894	C₂×C₂²⋊C₄	—	2	1	no	—
895	C₂×C₂²⋊C₄	—	2	2	no	—
896	C₂×C₄²	—	2	1	no	—
897	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
898	#107	C₂³×C₅₃	1	2	yes	—
899	#106	C₂³×C₅₃	1	2	yes	—
900	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
902	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
903	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
904	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
905	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
906	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
907	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
908	#103	C₂³×C₅₃	1	2	yes	—
909	#103	C₂³×C₅₃	1	2	yes	—
910	#103	C₂³×C₅₃	1	1	yes	characteristic
911	#103	C₂³×C₅₃	1	1	yes	characteristic
912	#103	C₂³×C₅₃	1	1	yes	characteristic
913	#103	C₂³×C₅₃	1	1	yes	characteristic
914	#103	C₂³×C₅₃	1	2	yes	—
915	#102	C₂³×C₅₃	1	2	yes	—
916	#102	C₂³×C₅₃	1	2	yes	—
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	1	yes	characteristic
921	#102	C₂³×C₅₃	1	2	yes	—
922	#102	C₂³×C₅₃	1	2	yes	—
923	#102	C₂³×C₅₃	1	2	yes	—
924	#97	C₂³×C₅₃	1	2	yes	—
925	#97	C₂³×C₅₃	1	2	yes	—
926	#97	C₂³×C₅₃	1	2	yes	—
927	C₄×C₈	C₂³×C₅₃	1	2	yes	—
928	C₄×C₈	C₂³×C₅₃	1	2	yes	—
929	C₄×C₈	C₂³×C₅₃	1	2	yes	—
930	C₂⁴	—	2	1	no	—
931	C₂⁴	—	2	1	no	—
932	#41	—	2	2	no	—
933	#41	—	2	2	no	—
934	#41	—	2	2	no	—
935	#41	—	2	2	no	—
936	#41	—	2	2	no	—
937	#41	—	2	2	no	—
938	#41	—	8	4	no	—
939	C₂×Q₈	—	2	1	no	—
940	C₂×Q₈	—	2	2	no	—
941	C₂×Q₈	—	2	2	no	—
942	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
943	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
944	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
945	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
946	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
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	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	2	2	no	—
955	C₂×D₄	—	2	2	no	—
956	C₂×D₄	—	2	2	no	—
957	C₂×D₄	—	2	2	no	—
958	C₂×D₄	—	2	1	no	—
959	C₂×D₄	—	2	2	no	—
960	C₂×D₄	—	2	2	no	—
961	C₂×D₄	—	2	2	no	—
962	C₂×D₄	—	2	2	no	—
963	C₂×D₄	—	2	2	no	—
964	C₂×D₄	—	2	2	no	—
965	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
966	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
968	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
969	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	2	1	no	—
975	C₂²×C₄	—	2	2	no	—
976	C₂²×C₄	—	2	1	no	—
977	C₂²×C₄	—	2	1	no	—
978	C₂²×C₄	—	2	2	no	—
979	C₂²×C₄	—	2	2	no	—
980	C₂²×C₄	—	2	2	no	—
981	C₂²×C₄	—	2	2	no	—
982	C₂²×C₄	—	2	2	no	—
983	C₂²×C₄	—	8	2	no	—
984	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
985	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
986	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
987	Q₁₆	—	2	4	no	—
988	Q₁₆	—	4	1	no	—
989	Q₁₆	—	4	1	no	—
990	Q₁₆	—	4	2	no	—
991	SD₁₆	—	2	4	no	—
992	SD₁₆	—	2	4	no	—
993	SD₁₆	—	2	4	no	—
994	SD₁₆	—	4	2	no	—
995	SD₁₆	—	4	2	no	—
996	SD₁₆	—	4	1	no	—
997	SD₁₆	—	4	1	no	—
998	SD₁₆	—	4	1	no	—
999	SD₁₆	—	4	1	no	—
1000	SD₁₆	—	4	2	no	—
1001	SD₁₆	—	4	2	no	—
1002	D₈	—	2	4	no	—
1003	D₈	—	2	4	no	—
1004	D₈	—	4	2	no	—
1005	D₈	—	4	2	no	—
1006	D₈	—	4	1	no	—
1007	D₈	—	4	1	no	—
1008	D₈	—	4	2	no	—
1009	M₁₆	—	2	2	no	—
1010	M₁₆	#41×C₅₃	1	4	yes	complemented
1011	C₂×C₈	—	2	2	no	—
1012	C₂×C₈	—	2	2	no	—
1013	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1014	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1015	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1016	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1017	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
1018	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	2	no	—
1021	C₄⋊C₄	—	2	2	no	—
1022	C₄⋊C₄	—	2	1	no	—
1023	C₄⋊C₄	—	2	1	no	—
1024	C₄⋊C₄	—	2	1	no	—
1025	C₄⋊C₄	—	2	2	no	—
1026	C₄⋊C₄	—	2	2	no	—
1027	C₄⋊C₄	—	2	2	no	—
1028	C₄⋊C₄	—	2	2	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1031	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1032	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1033	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1035	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
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	1	yes	characteristic
1041	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1042	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	2	no	—
1045	C₂²⋊C₄	—	2	2	no	—
1046	C₂²⋊C₄	—	2	2	no	—
1047	C₂²⋊C₄	—	2	2	no	—
1048	C₂²⋊C₄	—	2	2	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	2	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	2	no	—
1059	C₂²⋊C₄	—	2	2	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1069	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1070	C₄²	—	2	1	no	—
1071	C₄²	—	2	1	no	—
1072	C₄²	—	2	1	no	—
1073	C₄²	—	2	2	no	—
1074	C₄²	—	2	2	no	—
1075	C₄²	—	2	2	no	—
1076	C₄²	—	2	2	no	—
1077	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1078	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1079	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1080	C₄²	C₂⁴×C₅₃	1	2	yes	—
1081	C₄²	C₂⁴×C₅₃	1	2	yes	—
1082	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1083	C₂³	—	2	2	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	2	2	no	—
1086	C₂³	—	2	1	no	—
1087	C₂³	—	2	1	no	—
1088	C₂³	—	4	2	no	—
1089	C₂³	—	4	2	no	—
1090	C₂³	—	8	1	no	—
1091	C₂³	—	8	1	no	—
1092	C₂³	—	8	1	no	—
1093	C₂³	—	8	1	no	—
1094	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	1	no	—
1097	Q₈	—	2	2	no	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	2	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	2	1	no	—
1103	Q₈	—	4	2	no	—
1104	Q₈	—	4	2	no	—
1105	Q₈	—	4	2	no	—
1106	D₄	—	2	1	no	—
1107	D₄	—	2	1	no	—
1108	D₄	—	2	2	no	—
1109	D₄	—	2	2	no	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	2	no	—
1112	D₄	—	2	1	no	—
1113	D₄	—	2	2	no	—
1114	D₄	—	2	1	no	—
1115	D₄	—	2	1	no	—
1116	D₄	—	4	2	no	—
1117	D₄	—	4	2	no	—
1118	D₄	—	4	2	no	—
1119	D₄	—	4	2	no	—
1120	D₄	—	4	2	no	—
1121	D₄	—	4	2	no	—
1122	D₄	—	8	1	no	—
1123	D₄	—	8	2	no	—
1124	D₄	—	8	2	no	—
1125	D₄	—	8	2	no	—
1126	D₄	—	8	2	no	—
1127	D₄	—	8	2	no	—
1128	D₄	—	8	2	no	—
1129	C₂×C₄	—	2	1	no	—
1130	C₂×C₄	—	2	1	no	—
1131	C₂×C₄	—	2	1	no	—
1132	C₂×C₄	—	2	1	no	—
1133	C₂×C₄	—	2	2	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	2	no	—
1136	C₂×C₄	—	4	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	—	4	2	no	—
1143	C₂×C₄	—	8	1	no	—
1144	C₂×C₄	—	8	2	no	—
1145	C₂×C₄	—	8	1	no	—
1146	C₂×C₄	—	8	2	no	—
1147	C₂×C₄	—	8	2	no	—
1148	C₂×C₄	—	8	2	no	—
1149	C₂×C₄	—	8	2	no	—
1150	C₂×C₄	—	8	1	no	—
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	C₂²×D₄×C₅₃	1	1	yes	characteristic
1158	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1159	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1160	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1161	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1162	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1163	C₈	—	2	1	no	—
1164	C₈	—	2	1	no	—
1165	C₈	—	2	1	no	—
1166	C₈	—	2	1	no	—
1167	C₈	—	2	2	no	—
1168	C₈	C₂×#41×C₅₃	1	4	yes	—
1169	C₂²	—	2	1	no	—
1170	C₂²	—	2	1	no	—
1171	C₂²	—	4	1	no	—
1172	C₂²	—	4	1	no	—
1173	C₂²	—	4	1	no	—
1174	C₂²	—	4	2	no	—
1175	C₂²	—	4	2	no	—
1176	C₂²	—	4	1	no	—
1177	C₂²	—	4	2	no	—
1178	C₂²	—	4	1	no	—
1179	C₂²	—	4	1	no	—
1180	C₂²	—	4	2	no	—
1181	C₂²	—	4	2	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	2	no	—
1186	C₂²	—	8	4	no	—
1187	C₂²	—	16	2	no	—
1188	C₂²	C₅₃×#550	1	2	yes	—
1189	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1190	C₄	—	2	1	no	—
1191	C₄	—	2	1	no	—
1192	C₄	—	2	2	no	—
1193	C₄	—	2	2	no	—
1194	C₄	—	2	1	no	—
1195	C₄	—	2	1	no	—
1196	C₄	—	2	2	no	—
1197	C₄	—	2	2	no	—
1198	C₄	—	4	1	no	—
1199	C₄	—	4	1	no	—
1200	C₄	—	4	1	no	—
1201	C₄	—	4	2	no	—
1202	C₄	—	4	1	no	—
1203	C₄	—	4	2	no	—
1204	C₄	—	4	1	no	—
1205	C₄	C₅₃×#550	1	2	yes	—
1206	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1207	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1208	C₂	—	2	2	no	—
1209	C₂	—	8	2	no	—
1210	C₂	—	8	2	no	—
1211	C₂	—	8	1	no	—
1212	C₂	—	8	1	no	—
1213	C₂	—	8	1	no	—
1214	C₂	C₂×C₅₃×#550	1	1	yes	characteristic
1215	C₂	C₅₃×#3584	1	1	yes	characteristic
1216	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×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3510	C₂	semidirect
2. C₅₃×#3506	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3402	C₂	semidirect
5. C₅₃×#3401	C₂	semidirect
6. C₅₃×#3401	C₂	semidirect
7. C₅₃×#3399	C₂	semidirect
8. C₅₃×#3397	C₂	semidirect
9. C₅₃×#3396	C₂	semidirect
10. C₅₃×#3394	C₂	semidirect
11. C₅₃×#3155	C₂	semidirect
12. C₅₃×#3154	C₂	semidirect
13. C₅₃×#3153	C₂	semidirect
14. C₅₃×#3046	C₂	semidirect
15. C₅₃×#3045	C₂	semidirect
16. C₅₃×#3043	C₂	semidirect
17. C₅₃×#3041	C₂	semidirect
18. C₅₃×#3035	C₂	semidirect
19. C₂×C₅₃×#463	C₂	semidirect
20. C₅₃×#2962	C₂	semidirect
21. C₅₃×#2947	C₂	semidirect
22. C₅₃×#2946	C₂	semidirect
23. C₄×AGL(1,ℤ/8)×C₅₃	C₂	semidirect
33. C₅₃×#559	C₂²	semidirect
34. C₅₃×#559	C₂²	semidirect
35. C₅₃×#559	C₂²	semidirect
36. C₅₃×#559	C₂²	semidirect
37. C₅₃×#556	C₂²	semidirect
38. C₅₃×#556	C₂²	semidirect
39. C₅₃×#556	C₂²	semidirect
45. C₅₃×#550	C₂²	semidirect
66. C₅₃×#497	C₂²	semidirect
67. C₅₃×#497	C₂²	semidirect
70. C₅₃×#496	C₂²	semidirect
71. C₅₃×#496	C₂²	semidirect
73. C₅₃×#495	C₂²	semidirect
74. C₅₃×#495	C₂²	semidirect
75. C₅₃×#495	C₂²	semidirect
77. C₅₃×#492	C₂²	semidirect
78. C₅₃×#464	C₂²	semidirect
79. C₅₃×#464	C₂²	semidirect
80. C₅₃×#464	C₂²	semidirect
81. C₅₃×#464	C₂²	semidirect
82. C₅₃×#464	C₂²	semidirect
83. 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
95. C₅₃×#462	C₂²	semidirect
96. C₅₃×#461	C₂²	semidirect
97. C₅₃×#461	C₂²	semidirect
98. C₅₃×#460	C₂²	semidirect
99. C₅₃×#460	C₂²	semidirect
100. C₅₃×#460	C₂²	semidirect
101. C₅₃×#460	C₂²	semidirect
104. C₅₃×#459	C₂²	semidirect
105. C₅₃×#459	C₂²	semidirect
106. C₅₃×#446	C₂²	semidirect
107. C₅₃×#446	C₂²	semidirect
108. C₅₃×#446	C₂²	semidirect
109. C₈×Q₈×C₅₃	C₂²	semidirect
110. C₅₃×#442	C₂²	semidirect
111. C₅₃×#442	C₂²	semidirect
112. C₅₃×#441	C₂²	semidirect
113. C₅₃×#440	C₂²	semidirect
114. C₅₃×#440	C₂²	semidirect
115. C₅₃×#440	C₂²	semidirect
116. C₄×Q₁₆×C₅₃	C₂²	semidirect
117. C₄×SD₁₆×C₅₃	C₂²	semidirect
118. C₄×SD₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×D₈×C₅₃	C₂²	semidirect
121. C₄×D₈×C₅₃	C₂²	semidirect
401. M₁₆×C₅₃	#41	semidirect
560. #61424	C₅₃	direct (N × H)
600. #3510	C₂×C₅₃	semidirect
601. #3506	C₂×C₅₃	semidirect
602. #3403	C₂×C₅₃	semidirect
603. #3402	C₂×C₅₃	semidirect
604. #3401	C₂×C₅₃	semidirect
605. #3401	C₂×C₅₃	semidirect
606. #3399	C₂×C₅₃	semidirect
607. #3397	C₂×C₅₃	semidirect
608. #3396	C₂×C₅₃	semidirect
609. #3394	C₂×C₅₃	semidirect
610. #3155	C₂×C₅₃	semidirect
611. #3154	C₂×C₅₃	semidirect
612. #3153	C₂×C₅₃	semidirect
613. #3046	C₂×C₅₃	semidirect
614. #3045	C₂×C₅₃	semidirect
615. #3043	C₂×C₅₃	semidirect
616. #3041	C₂×C₅₃	semidirect
617. #3035	C₂×C₅₃	semidirect
618. C₂×#463	C₂×C₅₃	semidirect
619. #2962	C₂×C₅₃	semidirect
620. #2947	C₂×C₅₃	semidirect
621. #2946	C₂×C₅₃	semidirect
622. C₄×AGL(1,ℤ/8)	C₂×C₅₃	semidirect
641. #559	C₂²×C₅₃	semidirect
642. #559	C₂²×C₅₃	semidirect
643. #559	C₂²×C₅₃	semidirect
644. #559	C₂²×C₅₃	semidirect
645. #556	C₂²×C₅₃	semidirect
646. #556	C₂²×C₅₃	semidirect
647. #556	C₂²×C₅₃	semidirect
653. #550	C₂²×C₅₃	semidirect
674. #497	C₂²×C₅₃	semidirect
675. #497	C₂²×C₅₃	semidirect
678. #496	C₂²×C₅₃	semidirect
679. #496	C₂²×C₅₃	semidirect
681. #495	C₂²×C₅₃	semidirect
682. #495	C₂²×C₅₃	semidirect
683. #495	C₂²×C₅₃	semidirect
685. #492	C₂²×C₅₃	semidirect
686. #464	C₂²×C₅₃	semidirect
687. #464	C₂²×C₅₃	semidirect
688. #464	C₂²×C₅₃	semidirect
689. #464	C₂²×C₅₃	semidirect
690. #464	C₂²×C₅₃	semidirect
691. #464	C₂²×C₅₃	semidirect
698. #463	C₂²×C₅₃	semidirect
699. #463	C₂²×C₅₃	semidirect
700. #463	C₂²×C₅₃	semidirect
701. #463	C₂²×C₅₃	semidirect
702. #462	C₂²×C₅₃	semidirect
703. #462	C₂²×C₅₃	semidirect
704. #461	C₂²×C₅₃	semidirect
705. #461	C₂²×C₅₃	semidirect
706. #460	C₂²×C₅₃	semidirect
707. #460	C₂²×C₅₃	semidirect
708. #460	C₂²×C₅₃	semidirect
709. #460	C₂²×C₅₃	semidirect
712. #459	C₂²×C₅₃	semidirect
713. #459	C₂²×C₅₃	semidirect
714. #446	C₂²×C₅₃	semidirect
715. #446	C₂²×C₅₃	semidirect
716. #446	C₂²×C₅₃	semidirect
717. C₈×Q₈	C₂²×C₅₃	semidirect
718. #442	C₂²×C₅₃	semidirect
719. #442	C₂²×C₅₃	semidirect
720. #441	C₂²×C₅₃	semidirect
721. #440	C₂²×C₅₃	semidirect
722. #440	C₂²×C₅₃	semidirect
723. #440	C₂²×C₅₃	semidirect
724. C₄×Q₁₆	C₂²×C₅₃	semidirect
725. C₄×SD₁₆	C₂²×C₅₃	semidirect
726. C₄×SD₁₆	C₂²×C₅₃	semidirect
727. C₄×SD₁₆	C₂²×C₅₃	semidirect
728. C₄×D₈	C₂²×C₅₃	semidirect
729. C₄×D₈	C₂²×C₅₃	semidirect
743. C₅₃	#61424	direct (N × H)
1010. M₁₆	#41×C₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅₃×#3510	2
C₅₃×#3506	2
C₅₃×#3403	2
C₅₃×#3402	2
C₅₃×#3401	2
C₅₃×#3399	2
C₅₃×#3397	2
C₅₃×#3396	2
C₅₃×#3394	2
C₅₃×#3155	2
C₅₃×#3154	2
C₅₃×#3153	2
C₅₃×#3046	2
C₅₃×#3045	2
C₅₃×#3043	2
C₅₃×#3041	2
C₅₃×#3035	2
C₂×C₅₃×#463	2
C₅₃×#2962	2
C₅₃×#2947	2
C₅₃×#2946	2
C₄×AGL(1,ℤ/8)×C₅₃	2
#61424	53

Subgroups — C53×#61424 #27268936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61424 #27268936