Subgroups — C₅₃×#62042 #27269554

Order 13568.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3398	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3373	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3331	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3316	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3298	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#3284	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3276	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3267	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3263	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3255	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3125	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3046	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×#137×C₅₃	C₂²	1	2	yes	—
25	C₂×AGL(1,ℤ/8)×C₅₃	C₂²	1	2	yes	—
26	C₂×#135×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#562	—	2	2	no	—
28	C₅₃×#559	—	2	1	no	—
29	C₅₃×#559	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
31	C₅₃×#556	C₂²	1	1	yes	characteristic
32	C₅₃×#554	—	2	1	no	—
33	C₅₃×#554	C₂²	1	2	yes	—
34	C₅₃×#552	—	2	1	no	—
35	C₅₃×#551	—	2	2	no	—
36	C₅₃×#550	C₂²	1	1	yes	characteristic, complemented
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₅₃×#548	—	2	1	no	—
40	C₅₃×#548	C₂²	1	2	yes	—
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#547	C₂²	1	2	yes	—
43	C₅₃×#547	C₂²	1	1	yes	characteristic
44	C₅₃×#546	C₂²	1	2	yes	—
45	C₅₃×#542	—	2	1	no	—
46	C₅₃×#542	C₂²	1	2	yes	—
47	C₅₃×#542	C₂²	1	2	yes	complemented
48	C₅₃×#540	—	2	1	no	—
49	C₅₃×#539	—	2	2	no	—
50	C₅₃×#539	—	2	2	no	—
51	C₅₃×#536	C₂²	1	2	yes	complemented
52	C₅₃×#533	C₂²	1	1	yes	characteristic
53	C₅₃×#533	C₂²	1	1	yes	characteristic
54	C₅₃×#532	C₂²	1	1	yes	characteristic
55	C₅₃×#529	C₂²	1	1	yes	characteristic
56	C₅₃×#525	—	2	1	no	—
57	C₂×C₂²⋊Q₈×C₅₃	—	2	1	no	—
58	C₅₃×#520	C₂²	1	2	yes	—
59	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#497	C₂²	1	2	yes	—
61	C₅₃×#495	C₂²	1	2	yes	—
62	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
63	C₅₃×#492	C₂²	1	1	yes	characteristic, complemented
64	C₅₃×#489	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#487	C₂²	1	2	yes	complemented
67	C₅₃×#486	C₂²	1	1	yes	characteristic, complemented
68	C₅₃×#483	C₂²	1	1	yes	characteristic
69	C₅₃×#483	C₂²	1	1	yes	characteristic
70	C₅₃×#483	C₂²	1	2	yes	complemented
71	C₅₃×#481	C₂²	1	2	yes	complemented
72	C₅₃×#476	C₂²	1	1	yes	characteristic
73	C₅₃×#476	C₂²	1	1	yes	characteristic
74	C₅₃×#476	C₂²	1	2	yes	complemented
75	C₅₃×#475	C₂²	1	2	yes	complemented
76	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
78	C₅₃×#475	C₂²	1	2	yes	complemented
79	C₅₃×#470	C₂²	1	2	yes	—
80	C₅₃×#470	C₂²	1	2	yes	—
81	C₅₃×#470	C₂²	1	2	yes	complemented
82	C₅₃×#469	C₂²	1	2	yes	—
83	C₅₃×#465	C₂²	1	2	yes	—
84	C₅₃×#465	C₂²	1	2	yes	complemented
85	C₅₃×#464	C₂²	1	2	yes	—
86	C₅₃×#464	C₂²	1	2	yes	complemented
87	C₅₃×#464	C₂²	1	2	yes	complemented
88	C₅₃×#464	C₂²	1	2	yes	complemented
89	C₅₃×#463	C₂²	1	2	yes	—
90	C₅₃×#463	C₂²	1	2	yes	—
91	C₅₃×#463	C₂²	1	2	yes	—
92	C₅₃×#463	C₂²	1	2	yes	—
93	C₅₃×#462	C₂²	1	2	yes	complemented
94	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
96	C₅₃×#462	C₂²	1	2	yes	complemented
97	C₅₃×#461	C₂²	1	1	yes	characteristic
98	C₅₃×#461	C₂²	1	2	yes	—
99	C₅₃×#461	C₂²	1	1	yes	characteristic
100	C₅₃×#461	C₂²	1	1	yes	characteristic
101	C₅₃×#461	C₂²	1	1	yes	characteristic
102	C₅₃×#459	C₂²	1	1	yes	characteristic
103	C₅₃×#459	C₂²	1	1	yes	characteristic
104	C₅₃×#452	C₂²	1	2	yes	—
105	C₅₃×#452	C₂²	1	2	yes	—
106	C₅₃×#452	C₂²	1	2	yes	—
107	C₅₃×#452	C₂²	1	2	yes	complemented
108	C₅₃×#451	C₂²	1	2	yes	complemented
109	C₅₃×#450	C₂²	1	1	yes	characteristic
110	C₅₃×#450	C₂²	1	1	yes	characteristic
111	C₅₃×#449	C₂²	1	2	yes	—
112	C₅₃×#449	C₂²	1	2	yes	—
113	C₅₃×#448	C₂²	1	2	yes	—
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	—
117	C₅₃×#441	C₂²	1	2	yes	complemented
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
122	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
124	C₅₃×#436	C₂²	1	2	yes	—
125	C₅₃×#436	C₂²	1	1	yes	characteristic, complemented
126	C₅₃×#435	C₂²	1	2	yes	—
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
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₅₃×#423	C₂²	1	1	yes	characteristic
132	C₅₃×#417	C₂²	1	2	yes	—
133	C₅₃×#417	C₂²	1	2	yes	complemented
134	C₂×#103×C₅₃	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	C₂³	1	2	yes	—
137	C₂×#41×C₅₃	C₂³	1	2	yes	—
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₃	—	2	1	no	—
140	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
142	C₂³×C₄×C₅₃	—	2	1	no	—
143	#137×C₅₃	—	4	4	no	—
144	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
145	#135×C₅₃	—	4	4	no	—
146	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
149	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
150	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	2	yes	—
159	C₂×D₈×C₅₃	C₂³	1	2	yes	—
160	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
161	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
162	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
163	C₄⋊Q₈×C₅₃	—	2	1	no	—
164	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
165	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
166	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
168	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
169	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
170	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
171	#127×C₅₃	—	2	1	no	—
172	#127×C₅₃	C₂³	1	1	yes	characteristic
173	#126×C₅₃	—	2	2	no	—
174	#126×C₅₃	—	2	2	no	—
175	#126×C₅₃	—	2	2	no	—
176	#126×C₅₃	D₄	1	2	yes	—
177	#125×C₅₃	—	2	2	no	—
178	#125×C₅₃	—	2	2	no	—
179	#125×C₅₃	—	2	1	no	—
180	#125×C₅₃	—	2	1	no	—
181	#125×C₅₃	—	2	1	no	—
182	#125×C₅₃	D₄	1	1	yes	characteristic
183	#124×C₅₃	—	2	2	no	—
184	#124×C₅₃	—	2	2	no	—
185	#124×C₅₃	—	2	2	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	#124×C₅₃	C₂³	1	2	yes	—
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	—	2	2	no	—
197	#123×C₅₃	—	2	2	no	—
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	D₄	1	2	yes	—
202	C₂²⋊Q₈×C₅₃	—	2	2	no	—
203	C₂²⋊Q₈×C₅₃	—	2	1	no	—
204	C₂²⋊Q₈×C₅₃	—	2	1	no	—
205	C₂²⋊Q₈×C₅₃	—	2	2	no	—
206	C₂²⋊Q₈×C₅₃	—	2	2	no	—
207	C₂²⋊Q₈×C₅₃	—	2	2	no	—
208	C₂²⋊Q₈×C₅₃	—	2	2	no	—
209	C₂²⋊Q₈×C₅₃	—	2	2	no	—
210	C₂²⋊Q₈×C₅₃	—	2	2	no	—
211	C₂²⋊Q₈×C₅₃	—	2	2	no	—
212	C₂²⋊Q₈×C₅₃	—	2	2	no	—
213	C₂²⋊Q₈×C₅₃	—	2	1	no	—
214	C₂²⋊Q₈×C₅₃	—	2	1	no	—
215	C₂²⋊Q₈×C₅₃	—	2	1	no	—
216	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
217	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
218	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	1	no	—
225	#121×C₅₃	—	2	2	no	—
226	#121×C₅₃	—	2	2	no	—
227	#121×C₅₃	—	2	1	no	—
228	#121×C₅₃	—	2	1	no	—
229	#121×C₅₃	D₄	1	1	yes	characteristic
230	#121×C₅₃	C₂³	1	2	yes	—
231	#121×C₅₃	C₂³	1	2	yes	—
232	#120×C₅₃	—	2	2	no	—
233	C₄×Q₈×C₅₃	—	2	1	no	—
234	C₄×Q₈×C₅₃	—	2	1	no	—
235	C₄×Q₈×C₅₃	—	2	1	no	—
236	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
238	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
239	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
242	C₄×D₄×C₅₃	—	2	1	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	2	no	—
246	C₄×D₄×C₅₃	—	2	2	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	—	2	1	no	—
251	C₄×D₄×C₅₃	—	2	2	no	—
252	C₄×D₄×C₅₃	—	2	1	no	—
253	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₃	C₂³	1	2	yes	—
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	C₄×D₄×C₅₃	C₂³	1	2	yes	—
260	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
261	#117×C₅₃	—	2	2	no	—
262	#117×C₅₃	—	2	1	no	—
263	#117×C₅₃	—	2	1	no	—
264	#117×C₅₃	—	2	1	no	—
265	#117×C₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
267	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
269	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
270	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
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	#106×C₅₃	C₂³	1	1	yes	characteristic
275	#106×C₅₃	C₂³	1	1	yes	characteristic
276	#106×C₅₃	C₂³	1	1	yes	characteristic
277	#106×C₅₃	C₂³	1	2	yes	—
278	#106×C₅₃	C₂³	1	1	yes	characteristic
279	#106×C₅₃	C₂³	1	2	yes	—
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	2	yes	—
288	#103×C₅₃	C₂³	1	1	yes	characteristic
289	#103×C₅₃	C₂³	1	2	yes	—
290	#103×C₅₃	C₂³	1	2	yes	—
291	#103×C₅₃	C₂³	1	2	yes	—
292	#103×C₅₃	C₂³	1	1	yes	characteristic
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	1	yes	characteristic
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	1	yes	characteristic
306	#102×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
311	#97×C₅₃	C₂³	1	2	yes	—
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	1	no	—
316	#41×C₅₃	—	2	4	no	—
317	#41×C₅₃	—	4	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	C₂×Q₈×C₅₃	—	2	1	no	—
324	C₂×Q₈×C₅₃	—	2	1	no	—
325	C₂×Q₈×C₅₃	—	2	2	no	—
326	C₂×Q₈×C₅₃	—	2	2	no	—
327	C₂×Q₈×C₅₃	—	4	2	no	—
328	C₂×Q₈×C₅₃	—	4	2	no	—
329	C₂×Q₈×C₅₃	—	8	2	no	—
330	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
331	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
332	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
333	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
334	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	—	2	2	no	—
338	C₂×D₄×C₅₃	—	2	2	no	—
339	C₂×D₄×C₅₃	—	2	2	no	—
340	C₂×D₄×C₅₃	—	2	2	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	—	4	1	no	—
345	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
346	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
347	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
348	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
350	C₂²×C₄×C₅₃	—	2	1	no	—
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	2	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	2	no	—
357	C₂²×C₄×C₅₃	—	2	1	no	—
358	C₂²×C₄×C₅₃	—	2	2	no	—
359	C₂²×C₄×C₅₃	—	2	2	no	—
360	C₂²×C₄×C₅₃	—	2	2	no	—
361	C₂²×C₄×C₅₃	—	2	1	no	—
362	C₂²×C₄×C₅₃	—	8	2	no	—
363	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
367	Q₁₆×C₅₃	—	4	2	no	—
368	Q₁₆×C₅₃	—	4	2	no	—
369	Q₁₆×C₅₃	—	4	2	no	—
370	Q₁₆×C₅₃	—	4	2	no	—
371	SD₁₆×C₅₃	—	2	2	no	—
372	SD₁₆×C₅₃	—	2	4	no	—
373	SD₁₆×C₅₃	—	2	2	no	—
374	SD₁₆×C₅₃	—	4	1	no	—
375	SD₁₆×C₅₃	—	4	2	no	—
376	SD₁₆×C₅₃	—	4	1	no	—
377	SD₁₆×C₅₃	—	4	2	no	—
378	SD₁₆×C₅₃	—	4	2	no	—
379	D₈×C₅₃	—	2	4	no	—
380	D₈×C₅₃	—	4	2	no	—
381	M₁₆×C₅₃	—	4	2	no	—
382	M₁₆×C₅₃	—	4	2	no	—
383	C₂×C₈×C₅₃	—	4	2	no	—
384	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
386	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
389	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	2	no	—
395	C₄⋊C₄×C₅₃	—	2	2	no	—
396	C₄⋊C₄×C₅₃	—	2	2	no	—
397	C₄⋊C₄×C₅₃	—	2	2	no	—
398	C₄⋊C₄×C₅₃	—	2	1	no	—
399	C₄⋊C₄×C₅₃	—	2	1	no	—
400	C₄⋊C₄×C₅₃	—	2	1	no	—
401	C₄⋊C₄×C₅₃	—	2	1	no	—
402	C₄⋊C₄×C₅₃	—	2	1	no	—
403	C₄⋊C₄×C₅₃	—	2	1	no	—
404	C₄⋊C₄×C₅₃	—	2	1	no	—
405	C₄⋊C₄×C₅₃	—	2	1	no	—
406	C₄⋊C₄×C₅₃	—	2	2	no	—
407	C₄⋊C₄×C₅₃	—	2	2	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	—	2	2	no	—
410	C₄⋊C₄×C₅₃	—	2	1	no	—
411	C₄⋊C₄×C₅₃	—	2	2	no	—
412	C₄⋊C₄×C₅₃	—	2	1	no	—
413	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
415	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
416	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	1	no	—
426	C₂²⋊C₄×C₅₃	—	2	1	no	—
427	C₂²⋊C₄×C₅₃	—	2	2	no	—
428	C₂²⋊C₄×C₅₃	—	2	2	no	—
429	C₂²⋊C₄×C₅₃	—	2	1	no	—
430	C₂²⋊C₄×C₅₃	—	2	1	no	—
431	C₂²⋊C₄×C₅₃	—	2	1	no	—
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	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	C₂×D₄	1	2	yes	—
444	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
447	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
448	C₄²×C₅₃	—	2	2	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	1	no	—
451	C₄²×C₅₃	—	2	1	no	—
452	C₄²×C₅₃	—	2	2	no	—
453	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
454	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
456	C₄²×C₅₃	C₂⁴	1	2	yes	—
457	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
458	C₂³×C₅₃	—	2	1	no	—
459	C₂³×C₅₃	—	2	2	no	—
460	C₂³×C₅₃	—	2	1	no	—
461	C₂³×C₅₃	—	4	2	no	—
462	C₂³×C₅₃	—	4	2	no	—
463	C₂³×C₅₃	—	8	1	no	—
464	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
465	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
466	Q₈×C₅₃	—	2	2	no	—
467	Q₈×C₅₃	—	2	1	no	—
468	Q₈×C₅₃	—	2	2	no	—
469	Q₈×C₅₃	—	2	2	no	—
470	Q₈×C₅₃	—	2	1	no	—
471	Q₈×C₅₃	—	2	1	no	—
472	Q₈×C₅₃	—	2	2	no	—
473	Q₈×C₅₃	—	2	1	no	—
474	Q₈×C₅₃	—	2	2	no	—
475	Q₈×C₅₃	—	4	2	no	—
476	Q₈×C₅₃	—	8	1	no	—
477	Q₈×C₅₃	—	8	2	no	—
478	Q₈×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	2	1	no	—
481	D₄×C₅₃	—	2	2	no	—
482	D₄×C₅₃	—	2	1	no	—
483	D₄×C₅₃	—	2	1	no	—
484	D₄×C₅₃	—	2	2	no	—
485	D₄×C₅₃	—	4	2	no	—
486	D₄×C₅₃	—	4	2	no	—
487	D₄×C₅₃	—	4	4	no	—
488	D₄×C₅₃	—	4	2	no	—
489	D₄×C₅₃	—	8	1	no	—
490	D₄×C₅₃	—	8	2	no	—
491	D₄×C₅₃	—	8	2	no	—
492	D₄×C₅₃	—	8	2	no	—
493	D₄×C₅₃	—	8	2	no	—
494	D₄×C₅₃	H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄×C₅₃	—	2	2	no	—
496	C₂×C₄×C₅₃	—	2	1	no	—
497	C₂×C₄×C₅₃	—	2	2	no	—
498	C₂×C₄×C₅₃	—	2	1	no	—
499	C₂×C₄×C₅₃	—	2	2	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	1	no	—
502	C₂×C₄×C₅₃	—	2	1	no	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	2	2	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	2	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	4	1	no	—
510	C₂×C₄×C₅₃	—	4	4	no	—
511	C₂×C₄×C₅₃	—	4	2	no	—
512	C₂×C₄×C₅₃	—	4	2	no	—
513	C₂×C₄×C₅₃	—	8	2	no	—
514	C₂×C₄×C₅₃	—	8	1	no	—
515	C₂×C₄×C₅₃	—	8	1	no	—
516	C₂×C₄×C₅₃	—	8	2	no	—
517	C₂×C₄×C₅₃	—	8	2	no	—
518	C₂×C₄×C₅₃	—	8	2	no	—
519	C₂×C₄×C₅₃	—	8	1	no	—
520	C₂×C₄×C₅₃	—	8	2	no	—
521	C₂×C₄×C₅₃	—	8	2	no	—
522	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
525	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
526	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
527	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
529	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
531	C₈×C₅₃	—	2	1	no	—
532	C₈×C₅₃	—	2	2	no	—
533	C₈×C₅₃	—	2	2	no	—
534	C₈×C₅₃	—	2	1	no	—
535	C₈×C₅₃	—	2	1	no	—
536	C₈×C₅₃	—	2	1	no	—
537	#62042	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
538	C₂²×C₅₃	—	2	1	no	—
539	C₂²×C₅₃	—	2	2	no	—
540	C₂²×C₅₃	—	2	2	no	—
541	C₂²×C₅₃	—	2	1	no	—
542	C₂²×C₅₃	—	2	2	no	—
543	C₂²×C₅₃	—	2	1	no	—
544	C₂²×C₅₃	—	2	2	no	—
545	C₂²×C₅₃	—	4	1	no	—
546	C₂²×C₅₃	—	4	1	no	—
547	C₂²×C₅₃	—	4	2	no	—
548	C₂²×C₅₃	—	4	1	no	—
549	C₂²×C₅₃	—	4	2	no	—
550	C₂²×C₅₃	—	4	1	no	—
551	C₂²×C₅₃	—	4	1	no	—
552	C₂²×C₅₃	—	4	2	no	—
553	C₂²×C₅₃	—	8	4	no	—
554	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
555	C₄×C₅₃	—	2	1	no	—
556	C₄×C₅₃	—	2	1	no	—
557	C₄×C₅₃	—	2	2	no	—
558	C₄×C₅₃	—	2	2	no	—
559	C₄×C₅₃	—	2	1	no	—
560	C₄×C₅₃	—	2	1	no	—
561	C₄×C₅₃	—	2	2	no	—
562	C₄×C₅₃	—	4	1	no	—
563	C₄×C₅₃	—	4	1	no	—
564	C₄×C₅₃	—	4	2	no	—
565	C₄×C₅₃	—	4	1	no	—
566	C₄×C₅₃	—	4	2	no	—
567	C₄×C₅₃	—	4	1	no	—
568	C₄×C₅₃	—	4	1	no	—
569	C₄×C₅₃	—	4	1	no	—
570	C₄×C₅₃	—	4	2	no	—
571	C₄×C₅₃	#577	1	2	yes	—
572	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
573	C₄×C₅₃	#585	1	1	yes	characteristic
574	#3554	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#3520	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3398	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3394	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3373	C₂×C₅₃	1	1	yes	characteristic, complemented
579	#3359	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
581	#3331	C₂×C₅₃	1	2	yes	complemented
582	#3316	C₂×C₅₃	1	2	yes	complemented
583	#3298	C₂×C₅₃	1	1	yes	characteristic, complemented
584	#3284	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3276	C₂×C₅₃	1	1	yes	characteristic, complemented
586	#3275	C₂×C₅₃	1	2	yes	complemented
587	#3267	C₂×C₅₃	1	2	yes	complemented
588	#3263	C₂×C₅₃	1	2	yes	complemented
589	#3255	C₂×C₅₃	1	1	yes	characteristic, complemented
590	#3225	C₂×C₅₃	1	2	yes	complemented
591	#3210	C₂×C₅₃	1	1	yes	characteristic, complemented
592	#3125	C₂×C₅₃	1	2	yes	complemented
593	#3101	C₂×C₅₃	1	1	yes	characteristic, complemented
594	#3046	C₂×C₅₃	1	2	yes	complemented
595	#3036	C₂×C₅₃	1	1	yes	characteristic, complemented
596	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
597	C₂×C₅₃	—	4	2	no	—
598	C₂×C₅₃	—	4	1	no	—
599	C₂×C₅₃	—	4	2	no	—
600	C₂×C₅₃	—	8	2	no	—
601	C₂×C₅₃	—	8	1	no	—
602	C₂×C₅₃	#3488	1	1	yes	characteristic
603	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
604	C₂×C₅₃	#3586	1	1	yes	characteristic
605	C₂×#137	C₂²×C₅₃	1	2	yes	—
606	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
607	C₂×#135	C₂²×C₅₃	1	2	yes	—
608	#562	—	2	2	no	—
609	#559	—	2	1	no	—
610	#559	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
612	#556	C₂²×C₅₃	1	1	yes	characteristic
613	#554	—	2	1	no	—
614	#554	C₂²×C₅₃	1	2	yes	—
615	#552	—	2	1	no	—
616	#551	—	2	2	no	—
617	#550	C₂²×C₅₃	1	1	yes	characteristic, complemented
618	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
619	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
620	#548	—	2	1	no	—
621	#548	C₂²×C₅₃	1	2	yes	—
622	#547	C₂²×C₅₃	1	2	yes	—
623	#547	C₂²×C₅₃	1	1	yes	characteristic
624	#547	C₂²×C₅₃	1	1	yes	characteristic
625	#546	C₂²×C₅₃	1	2	yes	—
626	#542	—	2	1	no	—
627	#542	C₂²×C₅₃	1	2	yes	—
628	#542	C₂²×C₅₃	1	2	yes	complemented
629	#540	—	2	1	no	—
630	#539	—	2	2	no	—
631	#539	—	2	2	no	—
632	#536	C₂²×C₅₃	1	2	yes	complemented
633	#533	C₂²×C₅₃	1	1	yes	characteristic
634	#533	C₂²×C₅₃	1	1	yes	characteristic
635	#532	C₂²×C₅₃	1	1	yes	characteristic
636	#529	C₂²×C₅₃	1	1	yes	characteristic
637	#525	—	2	1	no	—
638	C₂×C₂²⋊Q₈	—	2	1	no	—
639	#520	C₂²×C₅₃	1	2	yes	—
640	C₂×C₄×D₄	C₂²×C₅₃	1	1	yes	characteristic
641	#497	C₂²×C₅₃	1	2	yes	—
642	#495	C₂²×C₅₃	1	2	yes	—
643	#494	C₂²×C₅₃	1	1	yes	characteristic, complemented
644	#492	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#489	C₂²×C₅₃	1	2	yes	complemented
646	#487	C₂²×C₅₃	1	2	yes	complemented
647	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
648	#486	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#483	C₂²×C₅₃	1	1	yes	characteristic
650	#483	C₂²×C₅₃	1	1	yes	characteristic
651	#483	C₂²×C₅₃	1	2	yes	complemented
652	#481	C₂²×C₅₃	1	2	yes	complemented
653	#476	C₂²×C₅₃	1	1	yes	characteristic
654	#476	C₂²×C₅₃	1	1	yes	characteristic
655	#476	C₂²×C₅₃	1	2	yes	complemented
656	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
657	#475	C₂²×C₅₃	1	2	yes	complemented
658	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
659	#475	C₂²×C₅₃	1	2	yes	complemented
660	#470	C₂²×C₅₃	1	2	yes	—
661	#470	C₂²×C₅₃	1	2	yes	—
662	#470	C₂²×C₅₃	1	2	yes	complemented
663	#469	C₂²×C₅₃	1	2	yes	—
664	#465	C₂²×C₅₃	1	2	yes	—
665	#465	C₂²×C₅₃	1	2	yes	complemented
666	#464	C₂²×C₅₃	1	2	yes	—
667	#464	C₂²×C₅₃	1	2	yes	complemented
668	#464	C₂²×C₅₃	1	2	yes	complemented
669	#464	C₂²×C₅₃	1	2	yes	complemented
670	#463	C₂²×C₅₃	1	2	yes	—
671	#463	C₂²×C₅₃	1	2	yes	—
672	#463	C₂²×C₅₃	1	2	yes	—
673	#463	C₂²×C₅₃	1	2	yes	—
674	#462	C₂²×C₅₃	1	2	yes	complemented
675	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
676	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
677	#462	C₂²×C₅₃	1	2	yes	complemented
678	#461	C₂²×C₅₃	1	1	yes	characteristic
679	#461	C₂²×C₅₃	1	1	yes	characteristic
680	#461	C₂²×C₅₃	1	2	yes	—
681	#461	C₂²×C₅₃	1	1	yes	characteristic
682	#461	C₂²×C₅₃	1	1	yes	characteristic
683	#459	C₂²×C₅₃	1	1	yes	characteristic
684	#459	C₂²×C₅₃	1	1	yes	characteristic
685	#452	C₂²×C₅₃	1	2	yes	—
686	#452	C₂²×C₅₃	1	2	yes	—
687	#452	C₂²×C₅₃	1	2	yes	—
688	#452	C₂²×C₅₃	1	2	yes	complemented
689	#451	C₂²×C₅₃	1	2	yes	complemented
690	#450	C₂²×C₅₃	1	1	yes	characteristic
691	#450	C₂²×C₅₃	1	1	yes	characteristic
692	#449	C₂²×C₅₃	1	2	yes	—
693	#449	C₂²×C₅₃	1	2	yes	—
694	#448	C₂²×C₅₃	1	2	yes	—
695	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
696	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
697	#442	C₂²×C₅₃	1	2	yes	—
698	#441	C₂²×C₅₃	1	2	yes	complemented
699	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
700	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
701	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
702	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
703	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
704	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
705	#436	C₂²×C₅₃	1	2	yes	—
706	#436	C₂²×C₅₃	1	1	yes	characteristic, complemented
707	#435	C₂²×C₅₃	1	2	yes	—
708	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#433	C₂²×C₅₃	1	2	yes	complemented
710	#431	C₂²×C₅₃	1	1	yes	characteristic
711	#424	C₂²×C₅₃	1	2	yes	complemented
712	#423	C₂²×C₅₃	1	1	yes	characteristic
713	#417	C₂²×C₅₃	1	2	yes	—
714	#417	C₂²×C₅₃	1	2	yes	complemented
715	C₂×#103	C₂²×C₅₃	1	2	yes	complemented
716	C₅₃	#62042	1	1	yes	characteristic, direct product factor, Sylow
717	C₂×#41	—	2	1	no	—
718	C₂×#41	C₂³×C₅₃	1	2	yes	—
719	C₂×#41	C₂³×C₅₃	1	2	yes	—
720	C₂×#41	C₂³×C₅₃	1	2	yes	—
721	C₂²×Q₈	—	2	1	no	—
722	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
723	C₂²×D₄	C₂³×C₅₃	1	1	yes	characteristic
724	C₂³×C₄	—	2	1	no	—
725	#137	—	4	4	no	—
726	AGL(1,ℤ/8)	—	4	4	no	—
727	#135	—	4	4	no	—
728	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
729	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
730	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
731	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
733	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
735	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
737	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
738	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
740	C₂×D₈	C₂³×C₅₃	1	2	yes	—
741	C₂×D₈	C₂³×C₅₃	1	2	yes	—
742	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
743	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
744	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
747	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
748	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
753	#127	—	2	1	no	—
754	#127	C₂³×C₅₃	1	1	yes	characteristic
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	D₄×C₅₃	1	2	yes	—
759	#125	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	—	2	1	no	—
763	#125	—	2	1	no	—
764	#125	D₄×C₅₃	1	1	yes	characteristic
765	#124	—	2	1	no	—
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	2	no	—
769	#124	D₄×C₅₃	1	1	yes	characteristic
770	#124	C₂³×C₅₃	1	2	yes	—
771	#124	C₂³×C₅₃	1	2	yes	—
772	#124	C₂³×C₅₃	1	2	yes	—
773	#123	—	2	2	no	—
774	#123	—	2	2	no	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	D₄×C₅₃	1	2	yes	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	2	no	—
788	C₂²⋊Q₈	—	2	1	no	—
789	C₂²⋊Q₈	—	2	1	no	—
790	C₂²⋊Q₈	—	2	2	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	—	2	2	no	—
793	C₂²⋊Q₈	—	2	2	no	—
794	C₂²⋊Q₈	—	2	2	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
799	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
801	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
802	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
804	#121	—	2	1	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	D₄×C₅₃	1	1	yes	characteristic
812	#121	C₂³×C₅₃	1	2	yes	—
813	#121	C₂³×C₅₃	1	2	yes	—
814	#120	—	2	2	no	—
815	C₄×Q₈	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
819	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
820	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
821	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
822	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
823	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
824	C₄×D₄	—	2	2	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	2	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	2	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₅₃	1	2	yes	—
840	C₄×D₄	C₂³×C₅₃	1	2	yes	—
841	C₄×D₄	C₂³×C₅₃	1	2	yes	—
842	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
843	#117	—	2	1	no	—
844	#117	—	2	1	no	—
845	#117	—	2	2	no	—
846	#117	—	2	1	no	—
847	#117	C₂³×C₅₃	1	2	yes	—
848	C₂×C₄⋊C₄	—	2	2	no	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	2	no	—
851	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
852	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	2	no	—
855	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
856	#106	C₂³×C₅₃	1	1	yes	characteristic
857	#106	C₂³×C₅₃	1	1	yes	characteristic
858	#106	C₂³×C₅₃	1	1	yes	characteristic
859	#106	C₂³×C₅₃	1	2	yes	—
860	#106	C₂³×C₅₃	1	1	yes	characteristic
861	#106	C₂³×C₅₃	1	2	yes	—
862	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
863	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
865	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
866	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
867	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
868	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
869	#103	C₂³×C₅₃	1	1	yes	characteristic
870	#103	C₂³×C₅₃	1	2	yes	—
871	#103	C₂³×C₅₃	1	2	yes	—
872	#103	C₂³×C₅₃	1	2	yes	—
873	#103	C₂³×C₅₃	1	2	yes	—
874	#103	C₂³×C₅₃	1	1	yes	characteristic
875	#103	C₂³×C₅₃	1	2	yes	—
876	#103	C₂³×C₅₃	1	2	yes	—
877	#103	C₂³×C₅₃	1	1	yes	characteristic
878	#103	C₂³×C₅₃	1	1	yes	characteristic
879	#103	C₂³×C₅₃	1	2	yes	—
880	#103	C₂³×C₅₃	1	2	yes	—
881	#102	C₂³×C₅₃	1	2	yes	—
882	#102	C₂³×C₅₃	1	2	yes	—
883	#102	C₂³×C₅₃	1	2	yes	—
884	#102	C₂³×C₅₃	1	1	yes	characteristic
885	#102	C₂³×C₅₃	1	1	yes	characteristic
886	#102	C₂³×C₅₃	1	1	yes	characteristic
887	#102	C₂³×C₅₃	1	1	yes	characteristic
888	#102	C₂³×C₅₃	1	2	yes	—
889	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
890	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
891	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
892	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
893	#97	C₂³×C₅₃	1	2	yes	—
894	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
895	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
896	C₄×C₈	C₂³×C₅₃	1	2	yes	—
897	C₂⁴	—	2	1	no	—
898	#41	—	2	4	no	—
899	#41	—	4	2	no	—
900	#41	—	4	2	no	—
901	#41	—	4	2	no	—
902	#41	—	4	2	no	—
903	#41	—	4	2	no	—
904	#41	—	8	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	1	no	—
907	C₂×Q₈	—	2	2	no	—
908	C₂×Q₈	—	2	2	no	—
909	C₂×Q₈	—	4	2	no	—
910	C₂×Q₈	—	4	2	no	—
911	C₂×Q₈	—	8	2	no	—
912	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
913	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
914	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
915	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	2	2	no	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	2	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	2	1	no	—
925	C₂×D₄	—	2	1	no	—
926	C₂×D₄	—	4	1	no	—
927	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
928	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
929	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
930	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	2	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	2	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	8	2	no	—
945	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
946	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
947	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
948	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
949	Q₁₆	—	4	2	no	—
950	Q₁₆	—	4	2	no	—
951	Q₁₆	—	4	2	no	—
952	Q₁₆	—	4	2	no	—
953	SD₁₆	—	2	2	no	—
954	SD₁₆	—	2	4	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	2	no	—
957	SD₁₆	—	4	2	no	—
958	SD₁₆	—	4	1	no	—
959	SD₁₆	—	4	2	no	—
960	SD₁₆	—	4	1	no	—
961	D₈	—	2	4	no	—
962	D₈	—	4	2	no	—
963	M₁₆	—	4	2	no	—
964	M₁₆	—	4	2	no	—
965	C₂×C₈	—	4	2	no	—
966	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
968	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
969	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
970	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
971	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	1	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	2	no	—
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	1	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
996	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
998	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
999	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
1000	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1001	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1002	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1003	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
1004	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1006	C₂²⋊C₄	—	2	2	no	—
1007	C₂²⋊C₄	—	2	1	no	—
1008	C₂²⋊C₄	—	2	1	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	1	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	2	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1027	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1028	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1029	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1030	C₄²	—	2	2	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	2	1	no	—
1034	C₄²	—	2	2	no	—
1035	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1036	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1037	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1038	C₄²	C₂⁴×C₅₃	1	2	yes	—
1039	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1040	C₂³	—	2	1	no	—
1041	C₂³	—	2	1	no	—
1042	C₂³	—	2	2	no	—
1043	C₂³	—	4	2	no	—
1044	C₂³	—	4	2	no	—
1045	C₂³	—	8	1	no	—
1046	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1047	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	2	no	—
1053	Q₈	—	2	2	no	—
1054	Q₈	—	2	1	no	—
1055	Q₈	—	2	1	no	—
1056	Q₈	—	2	2	no	—
1057	Q₈	—	4	2	no	—
1058	Q₈	—	8	1	no	—
1059	Q₈	—	8	2	no	—
1060	Q₈	—	8	2	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	2	no	—
1063	D₄	—	2	1	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	2	1	no	—
1066	D₄	—	2	2	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	4	no	—
1070	D₄	—	4	2	no	—
1071	D₄	—	8	1	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	—	8	2	no	—
1075	D₄	—	8	2	no	—
1076	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	4	1	no	—
1092	C₂×C₄	—	4	4	no	—
1093	C₂×C₄	—	4	2	no	—
1094	C₂×C₄	—	4	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	1	no	—
1097	C₂×C₄	—	8	1	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	—	8	2	no	—
1101	C₂×C₄	—	8	1	no	—
1102	C₂×C₄	—	8	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1105	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1106	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1107	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1108	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1109	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1110	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1111	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1112	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1113	C₈	—	2	1	no	—
1114	C₈	—	2	2	no	—
1115	C₈	—	2	2	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	2	no	—
1124	C₂²	—	2	1	no	—
1125	C₂²	—	2	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	1	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	4	1	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	4	2	no	—
1133	C₂²	—	4	1	no	—
1134	C₂²	—	8	4	no	—
1135	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	2	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	4	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	1	no	—
1152	C₄	C₅₃×#577	1	2	yes	—
1153	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1154	C₄	C₅₃×#585	1	1	yes	characteristic
1155	C₂	—	4	1	no	—
1156	C₂	—	4	2	no	—
1157	C₂	—	4	2	no	—
1158	C₂	—	8	1	no	—
1159	C₂	—	8	2	no	—
1160	C₂	C₅₃×#3488	1	1	yes	characteristic
1161	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1162	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×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3554	C₂	semidirect
2. C₅₃×#3520	C₂	semidirect
3. C₅₃×#3398	C₂	semidirect
4. C₅₃×#3394	C₂	semidirect
5. C₅₃×#3373	C₂	semidirect
6. C₅₃×#3359	C₂	semidirect
7. C₅₃×#3332	C₂	semidirect
8. C₅₃×#3331	C₂	semidirect
9. C₅₃×#3316	C₂	semidirect
10. C₅₃×#3298	C₂	semidirect
11. C₅₃×#3284	C₂	semidirect
12. C₅₃×#3276	C₂	semidirect
13. C₅₃×#3275	C₂	semidirect
14. C₅₃×#3267	C₂	semidirect
15. C₅₃×#3263	C₂	semidirect
16. C₅₃×#3255	C₂	semidirect
17. C₅₃×#3225	C₂	semidirect
18. C₅₃×#3210	C₂	semidirect
19. C₅₃×#3125	C₂	semidirect
20. C₅₃×#3101	C₂	semidirect
21. C₅₃×#3046	C₂	semidirect
22. C₅₃×#3036	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
29. C₅₃×#559	C₂²	semidirect
30. C₅₃×#557	C₂²	semidirect
36. C₅₃×#550	C₂²	semidirect
38. D₄×Q₈×C₅₃	C₂²	semidirect
47. C₅₃×#542	C₂²	semidirect
51. C₅₃×#536	C₂²	semidirect
62. C₅₃×#494	C₂²	semidirect
63. C₅₃×#492	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#486	C₂²	semidirect
70. C₅₃×#483	C₂²	semidirect
71. C₅₃×#481	C₂²	semidirect
74. C₅₃×#476	C₂²	semidirect
75. C₅₃×#475	C₂²	semidirect
76. C₅₃×#475	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#475	C₂²	semidirect
81. C₅₃×#470	C₂²	semidirect
84. C₅₃×#465	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
88. C₅₃×#464	C₂²	semidirect
93. C₅₃×#462	C₂²	semidirect
94. C₅₃×#462	C₂²	semidirect
95. C₅₃×#462	C₂²	semidirect
96. C₅₃×#462	C₂²	semidirect
107. C₅₃×#452	C₂²	semidirect
108. C₅₃×#451	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
117. C₅₃×#441	C₂²	semidirect
123. C₄×SD₁₆×C₅₃	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
127. C₈×D₄×C₅₃	C₂²	semidirect
128. C₅₃×#433	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
133. C₅₃×#417	C₂²	semidirect
134. C₂×#103×C₅₃	C₂²	semidirect
537. #62042	C₅₃	direct (N × H)
574. #3554	C₂×C₅₃	semidirect
575. #3520	C₂×C₅₃	semidirect
576. #3398	C₂×C₅₃	semidirect
577. #3394	C₂×C₅₃	semidirect
578. #3373	C₂×C₅₃	semidirect
579. #3359	C₂×C₅₃	semidirect
580. #3332	C₂×C₅₃	semidirect
581. #3331	C₂×C₅₃	semidirect
582. #3316	C₂×C₅₃	semidirect
583. #3298	C₂×C₅₃	semidirect
584. #3284	C₂×C₅₃	semidirect
585. #3276	C₂×C₅₃	semidirect
586. #3275	C₂×C₅₃	semidirect
587. #3267	C₂×C₅₃	semidirect
588. #3263	C₂×C₅₃	semidirect
589. #3255	C₂×C₅₃	semidirect
590. #3225	C₂×C₅₃	semidirect
591. #3210	C₂×C₅₃	semidirect
592. #3125	C₂×C₅₃	semidirect
593. #3101	C₂×C₅₃	semidirect
594. #3046	C₂×C₅₃	semidirect
595. #3036	C₂×C₅₃	semidirect
596. #2993	C₂×C₅₃	semidirect
610. #559	C₂²×C₅₃	semidirect
611. #557	C₂²×C₅₃	semidirect
617. #550	C₂²×C₅₃	semidirect
619. D₄×Q₈	C₂²×C₅₃	semidirect
628. #542	C₂²×C₅₃	semidirect
632. #536	C₂²×C₅₃	semidirect
643. #494	C₂²×C₅₃	semidirect
644. #492	C₂²×C₅₃	semidirect
645. #489	C₂²×C₅₃	semidirect
646. #487	C₂²×C₅₃	semidirect
647. #487	C₂²×C₅₃	semidirect
648. #486	C₂²×C₅₃	semidirect
651. #483	C₂²×C₅₃	semidirect
652. #481	C₂²×C₅₃	semidirect
655. #476	C₂²×C₅₃	semidirect
656. #475	C₂²×C₅₃	semidirect
657. #475	C₂²×C₅₃	semidirect
658. #475	C₂²×C₅₃	semidirect
659. #475	C₂²×C₅₃	semidirect
662. #470	C₂²×C₅₃	semidirect
665. #465	C₂²×C₅₃	semidirect
667. #464	C₂²×C₅₃	semidirect
668. #464	C₂²×C₅₃	semidirect
669. #464	C₂²×C₅₃	semidirect
674. #462	C₂²×C₅₃	semidirect
675. #462	C₂²×C₅₃	semidirect
676. #462	C₂²×C₅₃	semidirect
677. #462	C₂²×C₅₃	semidirect
688. #452	C₂²×C₅₃	semidirect
689. #451	C₂²×C₅₃	semidirect
695. #446	C₂²×C₅₃	semidirect
696. C₈×Q₈	C₂²×C₅₃	semidirect
698. #441	C₂²×C₅₃	semidirect
704. C₄×SD₁₆	C₂²×C₅₃	semidirect
706. #436	C₂²×C₅₃	semidirect
708. C₈×D₄	C₂²×C₅₃	semidirect
709. #433	C₂²×C₅₃	semidirect
711. #424	C₂²×C₅₃	semidirect
714. #417	C₂²×C₅₃	semidirect
715. C₂×#103	C₂²×C₅₃	semidirect
716. C₅₃	#62042	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×#3554	2
C₅₃×#3520	2
C₅₃×#3398	2
C₅₃×#3394	2
C₅₃×#3373	2
C₅₃×#3359	2
C₅₃×#3332	2
C₅₃×#3331	2
C₅₃×#3316	2
C₅₃×#3298	2
C₅₃×#3284	2
C₅₃×#3276	2
C₅₃×#3275	2
C₅₃×#3267	2
C₅₃×#3263	2
C₅₃×#3255	2
C₅₃×#3225	2
C₅₃×#3210	2
C₅₃×#3125	2
C₅₃×#3101	2
C₅₃×#3046	2
C₅₃×#3036	2
C₅₃×#2993	2
#62042	53

Subgroups — C53×#62042 #27269554

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62042 #27269554