Subgroups — C₅₃×#61423 #27268935

Order 13568.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1190 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×#3507	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×#3400	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3398	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3394	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3393	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3156	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×#3044	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3042	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₅₃×#464	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×#137×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×#137×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×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
32	C₂²×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
33	C₅₃×#559	C₂²	1	2	yes	—
34	C₅₃×#559	C₂²	1	2	yes	—
35	C₅₃×#559	C₂²	1	2	yes	complemented
36	C₅₃×#557	C₂²	1	2	yes	complemented
37	C₅₃×#556	—	2	1	no	—
38	C₅₃×#556	C₂²	1	2	yes	—
39	C₅₃×#556	C₂²	1	2	yes	—
40	C₅₃×#556	C₂²	1	2	yes	complemented
41	C₅₃×#556	C₂²	1	2	yes	complemented
42	C₅₃×#554	—	2	1	no	—
43	C₅₃×#552	—	2	1	no	—
44	C₅₃×#552	—	2	1	no	—
45	C₅₃×#551	—	2	2	no	—
46	C₅₃×#551	—	2	2	no	—
47	C₅₃×#542	—	2	1	no	—
48	C₅₃×#542	—	2	1	no	—
49	C₅₃×#539	—	2	2	no	—
50	C₅₃×#536	C₂²	1	1	yes	characteristic
51	C₅₃×#536	C₂²	1	1	yes	characteristic
52	C₅₃×#536	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	C₅₃×#529	—	2	2	no	—
59	C₂×#124×C₅₃	C₂²	1	1	yes	characteristic
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×Q₈×C₅₃	C₂²	1	1	yes	characteristic
66	C₅₃×#497	C₂²	1	2	yes	—
67	C₅₃×#497	C₂²	1	2	yes	—
68	C₅₃×#497	C₂²	1	2	yes	complemented
69	C₅₃×#497	C₂²	1	2	yes	complemented
70	C₅₃×#496	C₂²	1	2	yes	—
71	C₅₃×#496	C₂²	1	2	yes	—
72	C₅₃×#495	C₂²	1	2	yes	—
73	C₅₃×#495	C₂²	1	2	yes	—
74	C₅₃×#495	C₂²	1	2	yes	—
75	C₅₃×#495	C₂²	1	2	yes	complemented
76	C₅₃×#494	C₂²	1	2	yes	complemented
77	C₅₃×#492	C₂²	1	2	yes	—
78	C₅₃×#464	C₂²	1	2	yes	—
79	C₅₃×#464	C₂²	1	2	yes	—
80	C₅₃×#464	C₂²	1	2	yes	—
81	C₅₃×#464	C₂²	1	2	yes	—
82	C₅₃×#464	C₂²	1	2	yes	—
83	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
84	C₅₃×#464	C₂²	1	1	yes	characteristic, complemented
85	C₅₃×#464	C₂²	1	2	yes	complemented
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#463	C₂²	1	2	yes	—
89	C₅₃×#463	C₂²	1	2	yes	—
90	C₅₃×#463	C₂²	1	2	yes	—
91	C₅₃×#463	C₂²	1	1	yes	characteristic, complemented
92	C₅₃×#463	C₂²	1	1	yes	characteristic, 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×#462	C₂²	1	2	yes	complemented
97	C₅₃×#462	C₂²	1	2	yes	complemented
98	C₅₃×#461	C₂²	1	2	yes	—
99	C₅₃×#461	C₂²	1	2	yes	—
100	C₅₃×#461	C₂²	1	1	yes	characteristic, complemented
101	C₅₃×#461	C₂²	1	2	yes	complemented
102	C₅₃×#460	C₂²	1	2	yes	—
103	C₅₃×#460	C₂²	1	1	yes	characteristic, complemented
104	C₅₃×#459	C₂²	1	2	yes	—
105	C₅₃×#459	C₂²	1	1	yes	characteristic, 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	—
111	C₅₃×#441	C₂²	1	2	yes	complemented
112	C₅₃×#441	C₂²	1	2	yes	complemented
113	C₅₃×#440	C₂²	1	2	yes	—
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×Q₁₆×C₅₃	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
120	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
121	C₄×D₈×C₅₃	C₂²	1	2	yes	—
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×#419	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	C₂³	1	1	yes	characteristic
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
138	C₂²×Q₈×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	#137×C₅₃	—	2	4	no	—
142	#137×C₅₃	—	2	4	no	—
143	#137×C₅₃	—	4	2	no	—
144	AGL(1,ℤ/8)×C₅₃	—	2	4	no	—
145	AGL(1,ℤ/8)×C₅₃	—	4	2	no	—
146	#135×C₅₃	—	4	2	no	—
147	#135×C₅₃	—	4	2	no	—
148	C₂×Q₁₆×C₅₃	—	4	2	no	—
149	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
154	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
155	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	—	4	2	no	—
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
163	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
164	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
165	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
166	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
167	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
168	C₂×D₈×C₅₃	C₂³	1	2	yes	—
169	C₂×D₈×C₅₃	C₂³	1	2	yes	—
170	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
171	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
172	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
175	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
176	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
177	C₄⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
178	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
179	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
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	1	yes	characteristic
184	#126×C₅₃	—	2	2	no	—
185	#126×C₅₃	—	2	2	no	—
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	—	2	2	no	—
193	#125×C₅₃	—	2	2	no	—
194	#125×C₅₃	—	2	2	no	—
195	#125×C₅₃	D₄	1	1	yes	characteristic
196	#125×C₅₃	D₄	1	1	yes	characteristic
197	#124×C₅₃	—	2	1	no	—
198	#124×C₅₃	—	2	1	no	—
199	#124×C₅₃	—	2	2	no	—
200	#124×C₅₃	—	2	2	no	—
201	#124×C₅₃	—	2	2	no	—
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	#124×C₅₃	C₂³	1	2	yes	—
209	#124×C₅₃	C₂³	1	2	yes	—
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	#123×C₅₃	—	2	2	no	—
218	#123×C₅₃	—	2	2	no	—
219	C₂²⋊Q₈×C₅₃	—	2	1	no	—
220	C₂²⋊Q₈×C₅₃	—	2	1	no	—
221	C₂²⋊Q₈×C₅₃	—	2	1	no	—
222	C₂²⋊Q₈×C₅₃	—	2	1	no	—
223	C₂²⋊Q₈×C₅₃	—	2	1	no	—
224	C₂²⋊Q₈×C₅₃	—	2	1	no	—
225	C₂²⋊Q₈×C₅₃	—	2	2	no	—
226	C₂²⋊Q₈×C₅₃	—	2	2	no	—
227	C₂²⋊Q₈×C₅₃	—	2	2	no	—
228	C₂²⋊Q₈×C₅₃	—	2	2	no	—
229	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
230	C₂²⋊Q₈×C₅₃	D₄	1	2	yes	—
231	#121×C₅₃	—	2	1	no	—
232	#121×C₅₃	—	2	1	no	—
233	#121×C₅₃	—	2	1	no	—
234	#121×C₅₃	—	2	1	no	—
235	#120×C₅₃	—	2	2	no	—
236	C₄×Q₈×C₅₃	—	2	1	no	—
237	C₄×Q₈×C₅₃	—	2	1	no	—
238	C₄×Q₈×C₅₃	—	2	1	no	—
239	C₄×Q₈×C₅₃	—	2	1	no	—
240	C₄×Q₈×C₅₃	—	2	2	no	—
241	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
242	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
243	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
244	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
245	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
246	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
247	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
248	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
249	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
250	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
251	C₄×D₄×C₅₃	—	2	1	no	—
252	C₄×D₄×C₅₃	—	2	1	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	2	no	—
257	C₄×D₄×C₅₃	—	2	2	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	1	yes	characteristic
263	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
264	C₄×D₄×C₅₃	C₂³	1	2	yes	—
265	C₄×D₄×C₅₃	C₂³	1	2	yes	—
266	C₄×D₄×C₅₃	C₂³	1	2	yes	—
267	C₄×D₄×C₅₃	C₂³	1	2	yes	—
268	#117×C₅₃	—	2	1	no	—
269	#117×C₅₃	—	2	1	no	—
270	#117×C₅₃	—	2	2	no	—
271	#117×C₅₃	—	2	2	no	—
272	#117×C₅₃	—	2	2	no	—
273	#117×C₅₃	—	2	2	no	—
274	#117×C₅₃	—	2	2	no	—
275	#117×C₅₃	—	2	1	no	—
276	#117×C₅₃	C₂³	1	1	yes	characteristic
277	#117×C₅₃	C₂³	1	1	yes	characteristic
278	#117×C₅₃	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
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×C₄²×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	#103×C₅₃	C₂³	1	2	yes	—
307	#103×C₅₃	C₂³	1	2	yes	—
308	#102×C₅₃	C₂³	1	2	yes	—
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	1	yes	characteristic
311	#102×C₅₃	C₂³	1	1	yes	characteristic
312	#102×C₅₃	C₂³	1	1	yes	characteristic
313	#102×C₅₃	C₂³	1	1	yes	characteristic
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	#41×C₅₃	—	2	2	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	C₂×Q₈×C₅₃	—	2	1	no	—
329	C₂×Q₈×C₅₃	—	2	1	no	—
330	C₂×Q₈×C₅₃	—	2	2	no	—
331	C₂×Q₈×C₅₃	—	2	2	no	—
332	C₂×Q₈×C₅₃	—	2	2	no	—
333	C₂×Q₈×C₅₃	—	2	2	no	—
334	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
335	C₂×Q₈×C₅₃	C₂×D₄	1	2	yes	—
336	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
337	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
338	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
340	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
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	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	2	no	—
350	C₂×D₄×C₅₃	—	2	2	no	—
351	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	1	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	1	no	—
359	C₂²×C₄×C₅₃	—	2	1	no	—
360	C₂²×C₄×C₅₃	—	2	1	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	2	1	no	—
363	C₂²×C₄×C₅₃	—	2	2	no	—
364	C₂²×C₄×C₅₃	—	2	2	no	—
365	C₂²×C₄×C₅₃	—	2	2	no	—
366	C₂²×C₄×C₅₃	—	2	2	no	—
367	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
368	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
369	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
370	Q₁₆×C₅₃	—	2	4	no	—
371	Q₁₆×C₅₃	—	2	4	no	—
372	Q₁₆×C₅₃	—	4	2	no	—
373	Q₁₆×C₅₃	—	4	2	no	—
374	Q₁₆×C₅₃	—	4	1	no	—
375	Q₁₆×C₅₃	—	4	1	no	—
376	Q₁₆×C₅₃	—	4	2	no	—
377	SD₁₆×C₅₃	—	2	4	no	—
378	SD₁₆×C₅₃	—	2	4	no	—
379	SD₁₆×C₅₃	—	2	4	no	—
380	SD₁₆×C₅₃	—	4	2	no	—
381	SD₁₆×C₅₃	—	4	2	no	—
382	SD₁₆×C₅₃	—	4	1	no	—
383	SD₁₆×C₅₃	—	4	1	no	—
384	SD₁₆×C₅₃	—	4	1	no	—
385	SD₁₆×C₅₃	—	4	1	no	—
386	SD₁₆×C₅₃	—	4	2	no	—
387	SD₁₆×C₅₃	—	4	2	no	—
388	D₈×C₅₃	—	2	4	no	—
389	D₈×C₅₃	—	4	1	no	—
390	D₈×C₅₃	—	4	1	no	—
391	D₈×C₅₃	—	4	2	no	—
392	M₁₆×C₅₃	—	2	2	no	—
393	M₁₆×C₅₃	#41	1	4	yes	—
394	C₂×C₈×C₅₃	—	2	2	no	—
395	C₂×C₈×C₅₃	—	2	2	no	—
396	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
399	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₄⋊C₄×C₅₃	—	2	2	no	—
404	C₄⋊C₄×C₅₃	—	2	2	no	—
405	C₄⋊C₄×C₅₃	—	2	2	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	1	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	2	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	2	no	—
413	C₄⋊C₄×C₅₃	—	2	2	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	—	2	2	no	—
419	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
424	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₂⁴	1	2	yes	—
430	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
432	C₂²⋊C₄×C₅₃	—	2	1	no	—
433	C₂²⋊C₄×C₅₃	—	2	2	no	—
434	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
440	C₂²⋊C₄×C₅₃	—	2	1	no	—
441	C₂²⋊C₄×C₅₃	—	2	1	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	2	no	—
449	C₂²⋊C₄×C₅₃	—	2	1	no	—
450	C₂²⋊C₄×C₅₃	—	2	1	no	—
451	C₂²⋊C₄×C₅₃	—	2	2	no	—
452	C₂²⋊C₄×C₅₃	—	2	2	no	—
453	C₂²⋊C₄×C₅₃	—	2	2	no	—
454	C₂²⋊C₄×C₅₃	—	2	2	no	—
455	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
456	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
457	C₄²×C₅₃	—	2	1	no	—
458	C₄²×C₅₃	—	2	1	no	—
459	C₄²×C₅₃	—	2	2	no	—
460	C₄²×C₅₃	—	2	1	no	—
461	C₄²×C₅₃	—	2	2	no	—
462	C₄²×C₅₃	—	2	2	no	—
463	C₄²×C₅₃	—	2	2	no	—
464	C₄²×C₅₃	—	2	2	no	—
465	C₄²×C₅₃	—	2	2	no	—
466	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
467	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
468	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
469	C₄²×C₅₃	C₂⁴	1	2	yes	—
470	C₄²×C₅₃	C₂⁴	1	2	yes	—
471	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
472	C₂³×C₅₃	—	2	1	no	—
473	C₂³×C₅₃	—	2	1	no	—
474	C₂³×C₅₃	—	2	1	no	—
475	C₂³×C₅₃	—	2	2	no	—
476	C₂³×C₅₃	—	4	2	no	—
477	C₂³×C₅₃	—	8	1	no	—
478	C₂³×C₅₃	—	8	1	no	—
479	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
480	Q₈×C₅₃	—	2	2	no	—
481	Q₈×C₅₃	—	2	2	no	—
482	Q₈×C₅₃	—	2	1	no	—
483	Q₈×C₅₃	—	2	1	no	—
484	Q₈×C₅₃	—	2	1	no	—
485	Q₈×C₅₃	—	2	2	no	—
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	—	4	2	no	—
491	Q₈×C₅₃	—	4	2	no	—
492	Q₈×C₅₃	—	4	2	no	—
493	Q₈×C₅₃	—	4	2	no	—
494	D₄×C₅₃	—	2	2	no	—
495	D₄×C₅₃	—	2	1	no	—
496	D₄×C₅₃	—	2	1	no	—
497	D₄×C₅₃	—	2	1	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	—	4	2	no	—
503	D₄×C₅₃	—	4	2	no	—
504	D₄×C₅₃	—	4	2	no	—
505	D₄×C₅₃	—	4	2	no	—
506	D₄×C₅₃	—	4	2	no	—
507	D₄×C₅₃	—	8	1	no	—
508	D₄×C₅₃	—	8	2	no	—
509	D₄×C₅₃	—	8	2	no	—
510	C₂×C₄×C₅₃	—	2	1	no	—
511	C₂×C₄×C₅₃	—	2	1	no	—
512	C₂×C₄×C₅₃	—	2	2	no	—
513	C₂×C₄×C₅₃	—	2	1	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	2	no	—
517	C₂×C₄×C₅₃	—	2	2	no	—
518	C₂×C₄×C₅₃	—	4	1	no	—
519	C₂×C₄×C₅₃	—	4	1	no	—
520	C₂×C₄×C₅₃	—	4	2	no	—
521	C₂×C₄×C₅₃	—	4	2	no	—
522	C₂×C₄×C₅₃	—	4	2	no	—
523	C₂×C₄×C₅₃	—	4	2	no	—
524	C₂×C₄×C₅₃	—	4	2	no	—
525	C₂×C₄×C₅₃	—	8	1	no	—
526	C₂×C₄×C₅₃	—	8	2	no	—
527	C₂×C₄×C₅₃	—	8	2	no	—
528	C₂×C₄×C₅₃	—	8	2	no	—
529	C₂×C₄×C₅₃	—	8	1	no	—
530	C₂×C₄×C₅₃	—	8	2	no	—
531	C₂×C₄×C₅₃	—	8	1	no	—
532	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
534	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
537	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
538	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
539	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
540	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
541	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
542	C₂×C₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
543	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
544	C₈×C₅₃	—	2	1	no	—
545	C₈×C₅₃	—	2	1	no	—
546	C₈×C₅₃	—	2	1	no	—
547	C₈×C₅₃	—	2	1	no	—
548	C₈×C₅₃	—	2	2	no	—
549	C₈×C₅₃	C₂×#41	1	4	yes	—
550	#61423	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
551	C₂²×C₅₃	—	2	1	no	—
552	C₂²×C₅₃	—	2	1	no	—
553	C₂²×C₅₃	—	4	1	no	—
554	C₂²×C₅₃	—	4	1	no	—
555	C₂²×C₅₃	—	4	1	no	—
556	C₂²×C₅₃	—	4	2	no	—
557	C₂²×C₅₃	—	4	1	no	—
558	C₂²×C₅₃	—	4	2	no	—
559	C₂²×C₅₃	—	4	1	no	—
560	C₂²×C₅₃	—	4	1	no	—
561	C₂²×C₅₃	—	4	1	no	—
562	C₂²×C₅₃	—	4	1	no	—
563	C₂²×C₅₃	—	4	1	no	—
564	C₂²×C₅₃	—	4	2	no	—
565	C₂²×C₅₃	—	16	2	no	—
566	C₂²×C₅₃	#550	1	2	yes	—
567	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
568	C₄×C₅₃	—	2	1	no	—
569	C₄×C₅₃	—	2	1	no	—
570	C₄×C₅₃	—	2	2	no	—
571	C₄×C₅₃	—	2	2	no	—
572	C₄×C₅₃	—	2	1	no	—
573	C₄×C₅₃	—	2	1	no	—
574	C₄×C₅₃	—	2	2	no	—
575	C₄×C₅₃	—	2	2	no	—
576	C₄×C₅₃	—	4	1	no	—
577	C₄×C₅₃	—	4	2	no	—
578	C₄×C₅₃	—	4	1	no	—
579	C₄×C₅₃	—	4	1	no	—
580	C₄×C₅₃	—	4	1	no	—
581	C₄×C₅₃	—	4	1	no	—
582	C₄×C₅₃	—	4	2	no	—
583	C₄×C₅₃	—	4	2	no	—
584	C₄×C₅₃	#550	1	2	yes	—
585	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
586	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
587	#3510	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3507	C₂×C₅₃	1	1	yes	characteristic, complemented
589	#3403	C₂×C₅₃	1	2	yes	complemented
590	#3402	C₂×C₅₃	1	2	yes	complemented
591	#3401	C₂×C₅₃	1	2	yes	complemented
592	#3401	C₂×C₅₃	1	2	yes	complemented
593	#3400	C₂×C₅₃	1	2	yes	complemented
594	#3398	C₂×C₅₃	1	2	yes	complemented
595	#3394	C₂×C₅₃	1	2	yes	complemented
596	#3393	C₂×C₅₃	1	2	yes	complemented
597	#3156	C₂×C₅₃	1	1	yes	characteristic, complemented
598	#3154	C₂×C₅₃	1	1	yes	characteristic, complemented
599	#3153	C₂×C₅₃	1	1	yes	characteristic, complemented
600	#3046	C₂×C₅₃	1	1	yes	characteristic, complemented
601	#3045	C₂×C₅₃	1	1	yes	characteristic, complemented
602	#3044	C₂×C₅₃	1	1	yes	characteristic, complemented
603	#3042	C₂×C₅₃	1	1	yes	characteristic, complemented
604	#3035	C₂×C₅₃	1	1	yes	characteristic, complemented
605	C₂×#464	C₂×C₅₃	1	1	yes	characteristic, complemented
606	#2962	C₂×C₅₃	1	1	yes	characteristic, complemented
607	#2947	C₂×C₅₃	1	1	yes	characteristic, complemented
608	#2946	C₂×C₅₃	1	1	yes	characteristic, complemented
609	C₄×#137	C₂×C₅₃	1	1	yes	characteristic, complemented
610	C₂×C₅₃	—	2	2	no	—
611	C₂×C₅₃	—	8	1	no	—
612	C₂×C₅₃	—	8	1	no	—
613	C₂×C₅₃	—	8	1	no	—
614	C₂×C₅₃	—	8	2	no	—
615	C₂×C₅₃	C₂×#550	1	1	yes	characteristic
616	C₂×C₅₃	#3584	1	1	yes	characteristic
617	C₂×C₅₃	#3586	1	1	yes	characteristic
618	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
619	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
620	C₂×#137	C₂²×C₅₃	1	1	yes	characteristic
621	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
622	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	1	yes	characteristic
623	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
624	C₂×#135	C₂²×C₅₃	1	1	yes	characteristic
625	C₂²×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
626	C₂²×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
627	#559	C₂²×C₅₃	1	2	yes	—
628	#559	C₂²×C₅₃	1	2	yes	—
629	#559	C₂²×C₅₃	1	2	yes	complemented
630	#557	C₂²×C₅₃	1	2	yes	complemented
631	#556	—	2	1	no	—
632	#556	C₂²×C₅₃	1	2	yes	—
633	#556	C₂²×C₅₃	1	2	yes	—
634	#556	C₂²×C₅₃	1	2	yes	complemented
635	#556	C₂²×C₅₃	1	2	yes	complemented
636	#554	—	2	1	no	—
637	#552	—	2	1	no	—
638	#552	—	2	1	no	—
639	#551	—	2	2	no	—
640	#551	—	2	2	no	—
641	#542	—	2	1	no	—
642	#542	—	2	1	no	—
643	#539	—	2	2	no	—
644	#536	C₂²×C₅₃	1	1	yes	characteristic
645	#536	C₂²×C₅₃	1	1	yes	characteristic
646	#536	C₂²×C₅₃	1	1	yes	characteristic
647	#535	C₂²×C₅₃	1	1	yes	characteristic
648	#533	C₂²×C₅₃	1	1	yes	characteristic
649	#532	C₂²×C₅₃	1	1	yes	characteristic
650	#529	—	2	1	no	—
651	#529	—	2	1	no	—
652	#529	—	2	2	no	—
653	C₂×#124	C₂²×C₅₃	1	1	yes	characteristic
654	#520	C₂²×C₅₃	1	1	yes	characteristic
655	#520	C₂²×C₅₃	1	1	yes	characteristic
656	#519	C₂²×C₅₃	1	1	yes	characteristic
657	#518	C₂²×C₅₃	1	1	yes	characteristic
658	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
659	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
660	#497	C₂²×C₅₃	1	2	yes	—
661	#497	C₂²×C₅₃	1	2	yes	—
662	#497	C₂²×C₅₃	1	2	yes	complemented
663	#497	C₂²×C₅₃	1	2	yes	complemented
664	#496	C₂²×C₅₃	1	2	yes	—
665	#496	C₂²×C₅₃	1	2	yes	—
666	#495	C₂²×C₅₃	1	2	yes	—
667	#495	C₂²×C₅₃	1	2	yes	—
668	#495	C₂²×C₅₃	1	2	yes	—
669	#495	C₂²×C₅₃	1	2	yes	complemented
670	#494	C₂²×C₅₃	1	2	yes	complemented
671	#492	C₂²×C₅₃	1	2	yes	—
672	#464	C₂²×C₅₃	1	2	yes	—
673	#464	C₂²×C₅₃	1	2	yes	—
674	#464	C₂²×C₅₃	1	2	yes	—
675	#464	C₂²×C₅₃	1	2	yes	—
676	#464	C₂²×C₅₃	1	2	yes	—
677	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
678	#464	C₂²×C₅₃	1	2	yes	complemented
679	#464	C₂²×C₅₃	1	2	yes	complemented
680	#464	C₂²×C₅₃	1	2	yes	complemented
681	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
682	#463	C₂²×C₅₃	1	2	yes	—
683	#463	C₂²×C₅₃	1	2	yes	—
684	#463	C₂²×C₅₃	1	2	yes	—
685	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
686	#463	C₂²×C₅₃	1	1	yes	characteristic, complemented
687	#463	C₂²×C₅₃	1	2	yes	complemented
688	#462	C₂²×C₅₃	1	2	yes	complemented
689	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
690	#462	C₂²×C₅₃	1	2	yes	complemented
691	#462	C₂²×C₅₃	1	2	yes	complemented
692	#461	C₂²×C₅₃	1	2	yes	—
693	#461	C₂²×C₅₃	1	2	yes	—
694	#461	C₂²×C₅₃	1	2	yes	complemented
695	#461	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	#460	C₂²×C₅₃	1	2	yes	—
697	#460	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	#459	C₂²×C₅₃	1	2	yes	—
699	#459	C₂²×C₅₃	1	1	yes	characteristic, complemented
700	#446	C₂²×C₅₃	1	2	yes	complemented
701	#446	C₂²×C₅₃	1	2	yes	complemented
702	#446	C₂²×C₅₃	1	2	yes	complemented
703	C₈×Q₈	C₂²×C₅₃	1	2	yes	complemented
704	#442	C₂²×C₅₃	1	2	yes	—
705	#441	C₂²×C₅₃	1	2	yes	complemented
706	#441	C₂²×C₅₃	1	2	yes	complemented
707	#440	C₂²×C₅₃	1	2	yes	—
708	#440	C₂²×C₅₃	1	2	yes	complemented
709	#440	C₂²×C₅₃	1	2	yes	complemented
710	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
711	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	complemented
712	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
713	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
714	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
715	C₄×D₈	C₂²×C₅₃	1	2	yes	—
716	#428	C₂²×C₅₃	1	1	yes	characteristic
717	#424	C₂²×C₅₃	1	1	yes	characteristic
718	#424	C₂²×C₅₃	1	1	yes	characteristic
719	C₂×C₄⋊C₈	C₂²×C₅₃	1	1	yes	characteristic
720	#419	C₂²×C₅₃	1	1	yes	characteristic
721	#417	C₂²×C₅₃	1	1	yes	characteristic
722	#416	C₂²×C₅₃	1	1	yes	characteristic
723	#416	C₂²×C₅₃	1	1	yes	characteristic
724	C₂×#103	C₂²×C₅₃	1	1	yes	characteristic
725	C₂×#102	C₂²×C₅₃	1	1	yes	characteristic
726	#405	C₂²×C₅₃	1	1	yes	characteristic
727	#405	C₂²×C₅₃	1	1	yes	characteristic
728	C₄×M₁₆	C₂²×C₅₃	1	1	yes	characteristic
729	C₅₃	#61423	1	1	yes	characteristic, direct product factor, Sylow
730	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
731	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
732	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
733	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
734	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
735	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
736	#137	—	2	4	no	—
737	#137	—	2	4	no	—
738	#137	—	4	2	no	—
739	AGL(1,ℤ/8)	—	2	4	no	—
740	AGL(1,ℤ/8)	—	4	2	no	—
741	#135	—	4	2	no	—
742	#135	—	4	2	no	—
743	C₂×Q₁₆	—	4	2	no	—
744	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
745	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
746	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
747	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
748	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
749	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
750	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
751	C₂×SD₁₆	—	4	2	no	—
752	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
753	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
754	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
755	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
757	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
758	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
759	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
762	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
763	C₂×D₈	C₂³×C₅₃	1	2	yes	—
764	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
765	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
766	C₂×D₈	C₂³×C₅₃	1	2	yes	—
767	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
768	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
769	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
770	C₂²×C₈	C₂³×C₅₃	1	1	yes	characteristic
771	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
772	C₄⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
773	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
775	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
776	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
777	#127	C₂³×C₅₃	1	1	yes	characteristic
778	#127	C₂³×C₅₃	1	2	yes	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#126	—	2	2	no	—
784	#126	—	2	2	no	—
785	#126	—	2	2	no	—
786	#126	—	2	2	no	—
787	#125	—	2	2	no	—
788	#125	—	2	2	no	—
789	#125	—	2	2	no	—
790	#125	D₄×C₅₃	1	1	yes	characteristic
791	#125	D₄×C₅₃	1	1	yes	characteristic
792	#124	—	2	2	no	—
793	#124	—	2	2	no	—
794	#124	—	2	2	no	—
795	#124	—	2	1	no	—
796	#124	—	2	1	no	—
797	#124	C₂³×C₅₃	1	2	yes	—
798	#124	C₂³×C₅₃	1	2	yes	—
799	#124	C₂³×C₅₃	1	1	yes	characteristic
800	#124	C₂³×C₅₃	1	1	yes	characteristic
801	#124	C₂³×C₅₃	1	2	yes	—
802	#124	C₂³×C₅₃	1	2	yes	—
803	#124	C₂³×C₅₃	1	2	yes	—
804	#124	C₂³×C₅₃	1	2	yes	—
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	—	2	2	no	—
811	#123	—	2	2	no	—
812	#123	—	2	2	no	—
813	#123	—	2	2	no	—
814	C₂²⋊Q₈	—	2	2	no	—
815	C₂²⋊Q₈	—	2	2	no	—
816	C₂²⋊Q₈	—	2	2	no	—
817	C₂²⋊Q₈	—	2	2	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	—	2	1	no	—
820	C₂²⋊Q₈	—	2	1	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	1	no	—
824	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
825	C₂²⋊Q₈	D₄×C₅₃	1	2	yes	—
826	#121	—	2	1	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#120	—	2	2	no	—
831	C₄×Q₈	—	2	2	no	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	—	2	1	no	—
834	C₄×Q₈	—	2	1	no	—
835	C₄×Q₈	—	2	1	no	—
836	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
837	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
838	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
839	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
840	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
841	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
842	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
843	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
844	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
845	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	2	no	—
851	C₄×D₄	—	2	2	no	—
852	C₄×D₄	—	2	2	no	—
853	C₄×D₄	—	2	2	no	—
854	C₄×D₄	—	2	2	no	—
855	C₄×D₄	—	2	1	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₅₃	1	2	yes	—
860	C₄×D₄	C₂³×C₅₃	1	2	yes	—
861	C₄×D₄	C₂³×C₅₃	1	2	yes	—
862	C₄×D₄	C₂³×C₅₃	1	2	yes	—
863	#117	—	2	1	no	—
864	#117	—	2	1	no	—
865	#117	—	2	2	no	—
866	#117	—	2	2	no	—
867	#117	—	2	2	no	—
868	#117	—	2	2	no	—
869	#117	—	2	2	no	—
870	#117	—	2	1	no	—
871	#117	C₂³×C₅₃	1	1	yes	characteristic
872	#117	C₂³×C₅₃	1	1	yes	characteristic
873	#117	C₂³×C₅₃	1	1	yes	characteristic
874	C₂×C₄⋊C₄	—	2	1	no	—
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
878	C₂×C₂²⋊C₄	—	2	1	no	—
879	C₂×C₂²⋊C₄	—	2	1	no	—
880	C₂×C₂²⋊C₄	—	2	2	no	—
881	C₂×C₄²	—	2	1	no	—
882	C₂×C₄²	—	2	1	no	—
883	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
884	#107	C₂³×C₅₃	1	2	yes	—
885	#106	C₂³×C₅₃	1	2	yes	—
886	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
887	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
888	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
891	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
892	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
893	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
894	#103	C₂³×C₅₃	1	2	yes	—
895	#103	C₂³×C₅₃	1	2	yes	—
896	#103	C₂³×C₅₃	1	1	yes	characteristic
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	#103	C₂³×C₅₃	1	2	yes	—
901	#103	C₂³×C₅₃	1	2	yes	—
902	#103	C₂³×C₅₃	1	2	yes	—
903	#102	C₂³×C₅₃	1	2	yes	—
904	#102	C₂³×C₅₃	1	2	yes	—
905	#102	C₂³×C₅₃	1	1	yes	characteristic
906	#102	C₂³×C₅₃	1	1	yes	characteristic
907	#102	C₂³×C₅₃	1	1	yes	characteristic
908	#102	C₂³×C₅₃	1	1	yes	characteristic
909	#102	C₂³×C₅₃	1	2	yes	—
910	#97	C₂³×C₅₃	1	2	yes	—
911	#97	C₂³×C₅₃	1	2	yes	—
912	#97	C₂³×C₅₃	1	2	yes	—
913	C₄×C₈	C₂³×C₅₃	1	2	yes	—
914	C₄×C₈	C₂³×C₅₃	1	2	yes	—
915	C₄×C₈	C₂³×C₅₃	1	2	yes	—
916	C₂⁴	—	2	1	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	—	2	2	no	—
921	#41	—	2	2	no	—
922	#41	—	2	2	no	—
923	C₂×Q₈	—	2	1	no	—
924	C₂×Q₈	—	2	1	no	—
925	C₂×Q₈	—	2	2	no	—
926	C₂×Q₈	—	2	2	no	—
927	C₂×Q₈	—	2	2	no	—
928	C₂×Q₈	—	2	2	no	—
929	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
930	C₂×Q₈	C₂×D₄×C₅₃	1	2	yes	—
931	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
932	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
933	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
934	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
935	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
936	C₂×D₄	—	2	1	no	—
937	C₂×D₄	—	2	1	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	1	no	—
940	C₂×D₄	—	2	1	no	—
941	C₂×D₄	—	2	2	no	—
942	C₂×D₄	—	2	2	no	—
943	C₂×D₄	—	2	1	no	—
944	C₂×D₄	—	2	2	no	—
945	C₂×D₄	—	2	2	no	—
946	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
947	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
949	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
950	C₂²×C₄	—	2	1	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	1	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	1	no	—
958	C₂²×C₄	—	2	2	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
963	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
964	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
965	Q₁₆	—	2	4	no	—
966	Q₁₆	—	2	4	no	—
967	Q₁₆	—	4	2	no	—
968	Q₁₆	—	4	2	no	—
969	Q₁₆	—	4	1	no	—
970	Q₁₆	—	4	1	no	—
971	Q₁₆	—	4	2	no	—
972	SD₁₆	—	2	4	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	SD₁₆	—	4	2	no	—
976	SD₁₆	—	4	2	no	—
977	SD₁₆	—	4	1	no	—
978	SD₁₆	—	4	1	no	—
979	SD₁₆	—	4	1	no	—
980	SD₁₆	—	4	1	no	—
981	SD₁₆	—	4	2	no	—
982	SD₁₆	—	4	2	no	—
983	D₈	—	2	4	no	—
984	D₈	—	4	1	no	—
985	D₈	—	4	1	no	—
986	D₈	—	4	2	no	—
987	M₁₆	—	2	2	no	—
988	M₁₆	#41×C₅₃	1	4	yes	—
989	C₂×C₈	—	2	2	no	—
990	C₂×C₈	—	2	2	no	—
991	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
993	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
994	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
995	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	2	no	—
999	C₄⋊C₄	—	2	2	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	1	no	—
1003	C₄⋊C₄	—	2	1	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	—	2	2	no	—
1009	C₄⋊C₄	—	2	2	no	—
1010	C₄⋊C₄	—	2	1	no	—
1011	C₄⋊C₄	—	2	1	no	—
1012	C₄⋊C₄	—	2	2	no	—
1013	C₄⋊C₄	—	2	2	no	—
1014	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1015	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1017	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1018	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1019	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1020	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1021	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1022	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1023	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1024	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1025	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1026	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	2	no	—
1032	C₂²⋊C₄	—	2	2	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	1	no	—
1035	C₂²⋊C₄	—	2	1	no	—
1036	C₂²⋊C₄	—	2	1	no	—
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	2	no	—
1039	C₂²⋊C₄	—	2	2	no	—
1040	C₂²⋊C₄	—	2	2	no	—
1041	C₂²⋊C₄	—	2	2	no	—
1042	C₂²⋊C₄	—	2	2	no	—
1043	C₂²⋊C₄	—	2	2	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	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	C₂×D₄×C₅₃	1	2	yes	—
1051	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1052	C₄²	—	2	1	no	—
1053	C₄²	—	2	1	no	—
1054	C₄²	—	2	2	no	—
1055	C₄²	—	2	1	no	—
1056	C₄²	—	2	2	no	—
1057	C₄²	—	2	2	no	—
1058	C₄²	—	2	2	no	—
1059	C₄²	—	2	2	no	—
1060	C₄²	—	2	2	no	—
1061	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1062	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1063	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1064	C₄²	C₂⁴×C₅₃	1	2	yes	—
1065	C₄²	C₂⁴×C₅₃	1	2	yes	—
1066	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1067	C₂³	—	2	1	no	—
1068	C₂³	—	2	1	no	—
1069	C₂³	—	2	2	no	—
1070	C₂³	—	2	1	no	—
1071	C₂³	—	4	2	no	—
1072	C₂³	—	8	1	no	—
1073	C₂³	—	8	1	no	—
1074	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1075	Q₈	—	2	1	no	—
1076	Q₈	—	2	2	no	—
1077	Q₈	—	2	2	no	—
1078	Q₈	—	2	1	no	—
1079	Q₈	—	2	1	no	—
1080	Q₈	—	2	1	no	—
1081	Q₈	—	2	2	no	—
1082	Q₈	—	2	1	no	—
1083	Q₈	—	2	2	no	—
1084	Q₈	—	2	1	no	—
1085	Q₈	—	4	2	no	—
1086	Q₈	—	4	2	no	—
1087	Q₈	—	4	2	no	—
1088	Q₈	—	4	2	no	—
1089	D₄	—	2	1	no	—
1090	D₄	—	2	2	no	—
1091	D₄	—	2	1	no	—
1092	D₄	—	2	1	no	—
1093	D₄	—	2	1	no	—
1094	D₄	—	2	1	no	—
1095	D₄	—	2	2	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	4	2	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	4	2	no	—
1100	D₄	—	4	2	no	—
1101	D₄	—	4	2	no	—
1102	D₄	—	8	1	no	—
1103	D₄	—	8	2	no	—
1104	D₄	—	8	2	no	—
1105	C₂×C₄	—	2	1	no	—
1106	C₂×C₄	—	2	1	no	—
1107	C₂×C₄	—	2	2	no	—
1108	C₂×C₄	—	2	2	no	—
1109	C₂×C₄	—	2	1	no	—
1110	C₂×C₄	—	2	2	no	—
1111	C₂×C₄	—	2	1	no	—
1112	C₂×C₄	—	2	1	no	—
1113	C₂×C₄	—	4	1	no	—
1114	C₂×C₄	—	4	1	no	—
1115	C₂×C₄	—	4	2	no	—
1116	C₂×C₄	—	4	2	no	—
1117	C₂×C₄	—	4	2	no	—
1118	C₂×C₄	—	4	2	no	—
1119	C₂×C₄	—	4	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	—	8	2	no	—
1122	C₂×C₄	—	8	2	no	—
1123	C₂×C₄	—	8	2	no	—
1124	C₂×C₄	—	8	1	no	—
1125	C₂×C₄	—	8	2	no	—
1126	C₂×C₄	—	8	1	no	—
1127	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1128	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1129	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1130	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1131	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1132	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1133	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1134	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1135	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1136	C₂×C₄	C₂×#41×C₅₃	1	2	yes	—
1137	C₂×C₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1138	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1139	C₈	—	2	1	no	—
1140	C₈	—	2	1	no	—
1141	C₈	—	2	1	no	—
1142	C₈	—	2	1	no	—
1143	C₈	—	2	2	no	—
1144	C₈	C₂×#41×C₅₃	1	4	yes	—
1145	C₂²	—	2	1	no	—
1146	C₂²	—	2	1	no	—
1147	C₂²	—	4	1	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	2	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	4	1	no	—
1153	C₂²	—	4	1	no	—
1154	C₂²	—	4	2	no	—
1155	C₂²	—	4	1	no	—
1156	C₂²	—	4	2	no	—
1157	C₂²	—	4	1	no	—
1158	C₂²	—	4	1	no	—
1159	C₂²	—	16	2	no	—
1160	C₂²	C₅₃×#550	1	2	yes	—
1161	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1162	C₄	—	2	1	no	—
1163	C₄	—	2	1	no	—
1164	C₄	—	2	2	no	—
1165	C₄	—	2	2	no	—
1166	C₄	—	2	1	no	—
1167	C₄	—	2	1	no	—
1168	C₄	—	2	2	no	—
1169	C₄	—	2	2	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	1	no	—
1172	C₄	—	4	1	no	—
1173	C₄	—	4	2	no	—
1174	C₄	—	4	2	no	—
1175	C₄	—	4	1	no	—
1176	C₄	—	4	2	no	—
1177	C₄	—	4	1	no	—
1178	C₄	C₅₃×#550	1	2	yes	—
1179	C₄	C₂²×#41×C₅₃	1	1	yes	characteristic
1180	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1181	C₂	—	2	2	no	—
1182	C₂	—	8	2	no	—
1183	C₂	—	8	1	no	—
1184	C₂	—	8	1	no	—
1185	C₂	—	8	1	no	—
1186	C₂	C₂×C₅₃×#550	1	1	yes	characteristic
1187	C₂	C₅₃×#3584	1	1	yes	characteristic
1188	C₂	C₅₃×#3586	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×#3507	C₂	semidirect
3. C₅₃×#3403	C₂	semidirect
4. C₅₃×#3402	C₂	semidirect
5. C₅₃×#3401	C₂	semidirect
6. C₅₃×#3401	C₂	semidirect
7. C₅₃×#3400	C₂	semidirect
8. C₅₃×#3398	C₂	semidirect
9. C₅₃×#3394	C₂	semidirect
10. C₅₃×#3393	C₂	semidirect
11. C₅₃×#3156	C₂	semidirect
12. C₅₃×#3154	C₂	semidirect
13. C₅₃×#3153	C₂	semidirect
14. C₅₃×#3046	C₂	semidirect
15. C₅₃×#3045	C₂	semidirect
16. C₅₃×#3044	C₂	semidirect
17. C₅₃×#3042	C₂	semidirect
18. C₅₃×#3035	C₂	semidirect
19. C₂×C₅₃×#464	C₂	semidirect
20. C₅₃×#2962	C₂	semidirect
21. C₅₃×#2947	C₂	semidirect
22. C₅₃×#2946	C₂	semidirect
23. C₄×#137×C₅₃	C₂	semidirect
35. C₅₃×#559	C₂²	semidirect
36. C₅₃×#557	C₂²	semidirect
40. C₅₃×#556	C₂²	semidirect
41. C₅₃×#556	C₂²	semidirect
68. C₅₃×#497	C₂²	semidirect
69. C₅₃×#497	C₂²	semidirect
75. C₅₃×#495	C₂²	semidirect
76. C₅₃×#494	C₂²	semidirect
83. C₅₃×#464	C₂²	semidirect
84. C₅₃×#464	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	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×#462	C₂²	semidirect
97. C₅₃×#462	C₂²	semidirect
100. C₅₃×#461	C₂²	semidirect
101. C₅₃×#461	C₂²	semidirect
103. C₅₃×#460	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
111. C₅₃×#441	C₂²	semidirect
112. C₅₃×#441	C₂²	semidirect
114. C₅₃×#440	C₂²	semidirect
115. C₅₃×#440	C₂²	semidirect
116. C₄×Q₁₆×C₅₃	C₂²	semidirect
117. C₄×Q₁₆×C₅₃	C₂²	semidirect
119. C₄×SD₁₆×C₅₃	C₂²	semidirect
120. C₄×SD₁₆×C₅₃	C₂²	semidirect
550. #61423	C₅₃	direct (N × H)
587. #3510	C₂×C₅₃	semidirect
588. #3507	C₂×C₅₃	semidirect
589. #3403	C₂×C₅₃	semidirect
590. #3402	C₂×C₅₃	semidirect
591. #3401	C₂×C₅₃	semidirect
592. #3401	C₂×C₅₃	semidirect
593. #3400	C₂×C₅₃	semidirect
594. #3398	C₂×C₅₃	semidirect
595. #3394	C₂×C₅₃	semidirect
596. #3393	C₂×C₅₃	semidirect
597. #3156	C₂×C₅₃	semidirect
598. #3154	C₂×C₅₃	semidirect
599. #3153	C₂×C₅₃	semidirect
600. #3046	C₂×C₅₃	semidirect
601. #3045	C₂×C₅₃	semidirect
602. #3044	C₂×C₅₃	semidirect
603. #3042	C₂×C₅₃	semidirect
604. #3035	C₂×C₅₃	semidirect
605. C₂×#464	C₂×C₅₃	semidirect
606. #2962	C₂×C₅₃	semidirect
607. #2947	C₂×C₅₃	semidirect
608. #2946	C₂×C₅₃	semidirect
609. C₄×#137	C₂×C₅₃	semidirect
629. #559	C₂²×C₅₃	semidirect
630. #557	C₂²×C₅₃	semidirect
634. #556	C₂²×C₅₃	semidirect
635. #556	C₂²×C₅₃	semidirect
662. #497	C₂²×C₅₃	semidirect
663. #497	C₂²×C₅₃	semidirect
669. #495	C₂²×C₅₃	semidirect
670. #494	C₂²×C₅₃	semidirect
677. #464	C₂²×C₅₃	semidirect
678. #464	C₂²×C₅₃	semidirect
679. #464	C₂²×C₅₃	semidirect
680. #464	C₂²×C₅₃	semidirect
681. #464	C₂²×C₅₃	semidirect
685. #463	C₂²×C₅₃	semidirect
686. #463	C₂²×C₅₃	semidirect
687. #463	C₂²×C₅₃	semidirect
688. #462	C₂²×C₅₃	semidirect
689. #462	C₂²×C₅₃	semidirect
690. #462	C₂²×C₅₃	semidirect
691. #462	C₂²×C₅₃	semidirect
694. #461	C₂²×C₅₃	semidirect
695. #461	C₂²×C₅₃	semidirect
697. #460	C₂²×C₅₃	semidirect
699. #459	C₂²×C₅₃	semidirect
700. #446	C₂²×C₅₃	semidirect
701. #446	C₂²×C₅₃	semidirect
702. #446	C₂²×C₅₃	semidirect
703. C₈×Q₈	C₂²×C₅₃	semidirect
705. #441	C₂²×C₅₃	semidirect
706. #441	C₂²×C₅₃	semidirect
708. #440	C₂²×C₅₃	semidirect
709. #440	C₂²×C₅₃	semidirect
710. C₄×Q₁₆	C₂²×C₅₃	semidirect
711. C₄×Q₁₆	C₂²×C₅₃	semidirect
713. C₄×SD₁₆	C₂²×C₅₃	semidirect
714. C₄×SD₁₆	C₂²×C₅₃	semidirect
729. C₅₃	#61423	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×#3510	2
C₅₃×#3507	2
C₅₃×#3403	2
C₅₃×#3402	2
C₅₃×#3401	2
C₅₃×#3400	2
C₅₃×#3398	2
C₅₃×#3394	2
C₅₃×#3393	2
C₅₃×#3156	2
C₅₃×#3154	2
C₅₃×#3153	2
C₅₃×#3046	2
C₅₃×#3045	2
C₅₃×#3044	2
C₅₃×#3042	2
C₅₃×#3035	2
C₂×C₅₃×#464	2
C₅₃×#2962	2
C₅₃×#2947	2
C₅₃×#2946	2
C₄×#137×C₅₃	2
#61423	53

Subgroups — C53×#61423 #27268935

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#61423 #27268935