Subgroups — C₅₃×#62032 #27269544

Order 13568.

1832 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3514	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3367	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3329	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅₃×#3321	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3302	C₂	1	1	yes	maximal, characteristic, complemented
11	D₄×SD₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3275	C₂	1	2	yes	maximal, complemented
13	C₅₃×#3272	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅₃×#3266	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3258	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3225	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3123	C₂	1	2	yes	maximal, complemented
20	C₅₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
21	C₅₃×#3042	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3039	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	C₂²×SD₁₆×C₅₃	C₂²	1	2	yes	—
27	C₅₃×#563	—	2	2	no	—
28	C₅₃×#559	C₂²	1	1	yes	characteristic
29	C₅₃×#557	C₂²	1	1	yes	characteristic, complemented
30	C₅₃×#556	C₂²	1	1	yes	characteristic
31	C₅₃×#556	C₂²	1	1	yes	characteristic, complemented
32	C₅₃×#555	C₂²	1	2	yes	—
33	C₅₃×#554	—	2	1	no	—
34	C₅₃×#553	—	2	1	no	—
35	C₅₃×#551	—	2	2	no	—
36	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
37	D₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₅₃	C₂²	1	2	yes	complemented
39	C₅₃×#548	—	2	1	no	—
40	C₅₃×#548	C₂²	1	2	yes	complemented
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#546	—	2	1	no	—
43	C₅₃×#546	C₂²	1	2	yes	—
44	D₄²×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#544	—	2	1	no	—
46	C₅₃×#542	—	2	1	no	—
47	C₅₃×#542	C₂²	1	2	yes	—
48	C₅₃×#541	C₂²	1	2	yes	complemented
49	C₅₃×#539	—	2	2	no	—
50	C₅₃×#538	—	2	2	no	—
51	C₅₃×#536	C₂²	1	2	yes	complemented
52	C₅₃×#532	C₂²	1	1	yes	characteristic
53	C₂×C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
54	C₅₃×#529	—	2	1	no	—
55	C₅₃×#529	C₂²	1	1	yes	characteristic
56	C₅₃×#529	C₂²	1	1	yes	characteristic, complemented
57	C₂×#124×C₅₃	—	2	1	no	—
58	C₅₃×#518	C₂²	1	2	yes	—
59	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
60	C₅₃×#497	C₂²	1	2	yes	complemented
61	C₅₃×#495	C₂²	1	2	yes	complemented
62	C₅₃×#492	C₂²	1	1	yes	characteristic
63	C₅₃×#492	C₂²	1	1	yes	characteristic
64	C₅₃×#489	C₂²	1	2	yes	complemented
65	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
66	C₅₃×#487	C₂²	1	1	yes	characteristic, complemented
67	C₅₃×#487	C₂²	1	2	yes	complemented
68	C₅₃×#485	C₂²	1	2	yes	complemented
69	C₅₃×#485	C₂²	1	2	yes	complemented
70	C₅₃×#485	C₂²	1	1	yes	characteristic, complemented
71	C₅₃×#482	C₂²	1	1	yes	characteristic, complemented
72	C₅₃×#479	C₂²	1	1	yes	characteristic, complemented
73	C₅₃×#478	C₂²	1	1	yes	characteristic
74	C₅₃×#478	C₂²	1	2	yes	complemented
75	C₅₃×#477	C₂²	1	2	yes	complemented
76	C₅₃×#475	C₂²	1	1	yes	characteristic, complemented
77	C₅₃×#475	C₂²	1	2	yes	complemented
78	C₅₃×#474	C₂²	1	1	yes	characteristic, complemented
79	C₅₃×#470	C₂²	1	2	yes	complemented
80	C₅₃×#469	C₂²	1	2	yes	complemented
81	C₅₃×#468	C₂²	1	2	yes	—
82	C₅₃×#468	C₂²	1	2	yes	complemented
83	C₅₃×#467	C₂²	1	2	yes	complemented
84	C₅₃×#465	C₂²	1	2	yes	—
85	C₅₃×#464	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic
90	C₅₃×#463	C₂²	1	2	yes	complemented
91	C₅₃×#463	C₂²	1	2	yes	complemented
92	C₅₃×#462	C₂²	1	2	yes	complemented
93	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
94	C₅₃×#462	C₂²	1	1	yes	characteristic, complemented
95	C₅₃×#461	C₂²	1	2	yes	—
96	C₅₃×#461	C₂²	1	1	yes	characteristic
97	C₅₃×#461	C₂²	1	1	yes	characteristic
98	C₅₃×#461	C₂²	1	2	yes	—
99	C₅₃×#461	C₂²	1	2	yes	complemented
100	C₅₃×#461	C₂²	1	2	yes	complemented
101	C₅₃×#461	C₂²	1	2	yes	complemented
102	C₅₃×#460	C₂²	1	1	yes	characteristic
103	C₅₃×#459	C₂²	1	1	yes	characteristic
104	C₅₃×#452	C₂²	1	1	yes	characteristic
105	C₅₃×#452	C₂²	1	2	yes	complemented
106	C₅₃×#451	C₂²	1	2	yes	complemented
107	C₅₃×#450	C₂²	1	2	yes	—
108	C₅₃×#450	C₂²	1	2	yes	—
109	C₅₃×#449	C₂²	1	2	yes	—
110	C₅₃×#449	C₂²	1	1	yes	characteristic
111	C₅₃×#448	C₂²	1	2	yes	—
112	C₅₃×#448	C₂²	1	2	yes	complemented
113	C₅₃×#448	C₂²	1	2	yes	complemented
114	C₅₃×#446	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
116	C₅₃×#440	C₂²	1	2	yes	—
117	C₅₃×#440	C₂²	1	2	yes	complemented
118	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
120	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
121	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
122	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	complemented
123	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
124	C₅₃×#436	C₂²	1	1	yes	characteristic
125	C₅₃×#436	C₂²	1	2	yes	complemented
126	C₅₃×#435	C₂²	1	2	yes	complemented
127	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
128	C₅₃×#433	C₂²	1	2	yes	complemented
129	C₅₃×#431	C₂²	1	1	yes	characteristic, complemented
130	C₅₃×#424	C₂²	1	2	yes	complemented
131	C₅₃×#423	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#419	C₂²	1	2	yes	complemented
133	C₅₃×#419	C₂²	1	2	yes	complemented
134	C₅₃×#416	C₂²	1	2	yes	complemented
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
137	C₂×#41×C₅₃	C₂³	1	2	yes	—
138	C₂²×Q₈×C₅₃	—	2	1	no	—
139	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
140	C₂²×Q₈×C₅₃	C₂³	1	2	yes	—
141	C₂²×D₄×C₅₃	—	2	1	no	—
142	C₂²×D₄×C₅₃	C₂³	1	2	yes	—
143	#137×C₅₃	—	4	4	no	—
144	AGL(1,ℤ/8)×C₅₃	—	4	4	no	—
145	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
146	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
147	C₂×Q₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₅₃	—	4	4	no	—
149	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
150	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
151	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
152	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
158	C₂×D₈×C₅₃	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
165	C₄⋊Q₈×C₅₃	—	2	1	no	—
166	C₄⋊Q₈×C₅₃	—	2	1	no	—
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	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
172	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
173	#127×C₅₃	C₂³	1	1	yes	characteristic
174	#126×C₅₃	—	2	2	no	—
175	#126×C₅₃	—	2	2	no	—
176	#126×C₅₃	—	2	2	no	—
177	#126×C₅₃	—	2	2	no	—
178	#126×C₅₃	—	2	2	no	—
179	#126×C₅₃	—	2	1	no	—
180	#126×C₅₃	D₄	1	2	yes	—
181	#125×C₅₃	—	2	2	no	—
182	#125×C₅₃	—	2	2	no	—
183	#125×C₅₃	—	2	2	no	—
184	#125×C₅₃	—	2	1	no	—
185	#125×C₅₃	D₄	1	1	yes	characteristic
186	#125×C₅₃	C₂³	1	1	yes	characteristic
187	#124×C₅₃	—	2	2	no	—
188	#124×C₅₃	—	2	2	no	—
189	#124×C₅₃	—	2	2	no	—
190	#124×C₅₃	—	2	2	no	—
191	#124×C₅₃	—	2	1	no	—
192	#124×C₅₃	—	2	1	no	—
193	#124×C₅₃	—	2	1	no	—
194	#124×C₅₃	D₄	1	1	yes	characteristic
195	#124×C₅₃	C₂³	1	2	yes	—
196	#124×C₅₃	C₂³	1	2	yes	—
197	#124×C₅₃	C₂³	1	1	yes	characteristic
198	#123×C₅₃	—	2	2	no	—
199	#123×C₅₃	—	2	2	no	—
200	#123×C₅₃	—	2	2	no	—
201	#123×C₅₃	—	2	2	no	—
202	#123×C₅₃	—	2	2	no	—
203	#123×C₅₃	—	2	2	no	—
204	#123×C₅₃	—	2	1	no	—
205	#123×C₅₃	D₄	1	2	yes	—
206	C₂²⋊Q₈×C₅₃	—	2	1	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	2	no	—
214	C₂²⋊Q₈×C₅₃	—	2	2	no	—
215	C₂²⋊Q₈×C₅₃	—	2	1	no	—
216	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
217	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
219	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
220	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
221	#121×C₅₃	—	2	1	no	—
222	#121×C₅₃	—	2	2	no	—
223	#121×C₅₃	—	2	2	no	—
224	#121×C₅₃	—	2	2	no	—
225	#121×C₅₃	—	2	1	no	—
226	#121×C₅₃	—	2	1	no	—
227	#121×C₅₃	D₄	1	1	yes	characteristic
228	#121×C₅₃	C₂³	1	1	yes	characteristic
229	#121×C₅₃	C₂³	1	2	yes	—
230	#121×C₅₃	C₂³	1	2	yes	—
231	#120×C₅₃	—	2	2	no	—
232	#120×C₅₃	—	2	2	no	—
233	C₄×Q₈×C₅₃	—	2	1	no	—
234	C₄×Q₈×C₅₃	—	2	1	no	—
235	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
240	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	—	2	2	no	—
242	C₄×D₄×C₅₃	—	2	2	no	—
243	C₄×D₄×C₅₃	—	2	1	no	—
244	C₄×D₄×C₅₃	—	2	2	no	—
245	C₄×D₄×C₅₃	—	2	1	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	C₂³	1	1	yes	characteristic
252	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₅₃	C₂³	1	2	yes	—
254	C₄×D₄×C₅₃	C₂³	1	2	yes	—
255	C₄×D₄×C₅₃	C₂³	1	2	yes	—
256	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
258	C₄×D₄×C₅₃	C₂³	1	2	yes	—
259	#117×C₅₃	—	2	2	no	—
260	#117×C₅₃	—	2	1	no	—
261	#117×C₅₃	—	2	1	no	—
262	#117×C₅₃	—	2	1	no	—
263	#117×C₅₃	C₂³	1	2	yes	—
264	#117×C₅₃	C₂³	1	1	yes	characteristic
265	#117×C₅₃	C₂³	1	2	yes	—
266	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
267	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
268	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
269	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
270	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
271	C₂×C₂²⋊C₄×C₅₃	—	2	2	no	—
272	C₂×C₄²×C₅₃	—	2	1	no	—
273	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
274	#107×C₅₃	C₂³	1	1	yes	characteristic
275	#107×C₅₃	C₂³	1	1	yes	characteristic
276	#107×C₅₃	C₂³	1	2	yes	—
277	#106×C₅₃	C₂³	1	1	yes	characteristic
278	#106×C₅₃	C₂³	1	2	yes	—
279	#106×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
281	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
282	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
285	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
287	#103×C₅₃	C₂³	1	1	yes	characteristic
288	#103×C₅₃	C₂³	1	2	yes	—
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	2	yes	—
295	#103×C₅₃	C₂³	1	2	yes	—
296	#103×C₅₃	C₂³	1	2	yes	—
297	#103×C₅₃	C₂³	1	2	yes	—
298	#103×C₅₃	C₂³	1	1	yes	characteristic
299	#103×C₅₃	C₂³	1	1	yes	characteristic
300	#102×C₅₃	C₂³	1	1	yes	characteristic
301	#102×C₅₃	C₂³	1	2	yes	—
302	#102×C₅₃	C₂³	1	1	yes	characteristic
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	#102×C₅₃	C₂³	1	1	yes	characteristic
305	#102×C₅₃	C₂³	1	2	yes	—
306	#102×C₅₃	C₂³	1	2	yes	—
307	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
311	#97×C₅₃	C₂³	1	2	yes	—
312	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₅₃	C₂³	1	2	yes	—
315	C₂⁴×C₅₃	—	2	2	no	—
316	#41×C₅₃	—	2	2	no	—
317	#41×C₅₃	—	4	1	no	—
318	#41×C₅₃	—	4	2	no	—
319	#41×C₅₃	—	4	2	no	—
320	#41×C₅₃	—	8	2	no	—
321	C₂×Q₈×C₅₃	—	2	1	no	—
322	C₂×Q₈×C₅₃	—	2	2	no	—
323	C₂×Q₈×C₅₃	—	2	2	no	—
324	C₂×Q₈×C₅₃	—	2	2	no	—
325	C₂×Q₈×C₅₃	—	4	2	no	—
326	C₂×Q₈×C₅₃	—	4	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	2	yes	—
334	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×D₄×C₅₃	—	2	4	no	—
336	C₂×D₄×C₅₃	—	2	1	no	—
337	C₂×D₄×C₅₃	—	2	1	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	2	no	—
342	C₂×D₄×C₅₃	—	2	1	no	—
343	C₂×D₄×C₅₃	—	2	1	no	—
344	C₂×D₄×C₅₃	—	4	2	no	—
345	C₂×D₄×C₅₃	—	8	2	no	—
346	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
347	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
348	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
349	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
350	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	—	2	2	no	—
352	C₂²×C₄×C₅₃	—	2	2	no	—
353	C₂²×C₄×C₅₃	—	2	1	no	—
354	C₂²×C₄×C₅₃	—	2	1	no	—
355	C₂²×C₄×C₅₃	—	2	1	no	—
356	C₂²×C₄×C₅₃	—	2	1	no	—
357	C₂²×C₄×C₅₃	—	2	2	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	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
363	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
365	Q₁₆×C₅₃	—	4	1	no	—
366	Q₁₆×C₅₃	—	4	2	no	—
367	Q₁₆×C₅₃	—	4	2	no	—
368	SD₁₆×C₅₃	—	2	2	no	—
369	SD₁₆×C₅₃	—	2	4	no	—
370	SD₁₆×C₅₃	—	2	4	no	—
371	SD₁₆×C₅₃	—	4	2	no	—
372	SD₁₆×C₅₃	—	4	2	no	—
373	SD₁₆×C₅₃	—	4	2	no	—
374	SD₁₆×C₅₃	—	4	1	no	—
375	SD₁₆×C₅₃	—	4	2	no	—
376	SD₁₆×C₅₃	—	4	2	no	—
377	D₈×C₅₃	—	2	2	no	—
378	D₈×C₅₃	—	4	2	no	—
379	M₁₆×C₅₃	—	4	2	no	—
380	M₁₆×C₅₃	—	4	2	no	—
381	C₂×C₈×C₅₃	—	4	2	no	—
382	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
383	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
384	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
385	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
386	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
387	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
388	C₄⋊C₄×C₅₃	—	2	1	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	1	no	—
391	C₄⋊C₄×C₅₃	—	2	2	no	—
392	C₄⋊C₄×C₅₃	—	2	2	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	—	2	1	no	—
395	C₄⋊C₄×C₅₃	—	2	1	no	—
396	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
402	C₄⋊C₄×C₅₃	—	2	2	no	—
403	C₄⋊C₄×C₅₃	—	2	1	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	2	no	—
408	C₄⋊C₄×C₅₃	—	2	1	no	—
409	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
412	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
413	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
414	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
415	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	2	no	—
422	C₂²⋊C₄×C₅₃	—	2	1	no	—
423	C₂²⋊C₄×C₅₃	—	2	1	no	—
424	C₂²⋊C₄×C₅₃	—	2	2	no	—
425	C₂²⋊C₄×C₅₃	—	2	2	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	2	no	—
430	C₂²⋊C₄×C₅₃	—	2	2	no	—
431	C₂²⋊C₄×C₅₃	—	2	2	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	1	no	—
436	C₂²⋊C₄×C₅₃	—	2	1	no	—
437	C₂²⋊C₄×C₅₃	—	2	2	no	—
438	C₂²⋊C₄×C₅₃	—	2	1	no	—
439	C₂²⋊C₄×C₅₃	—	2	2	no	—
440	C₂²⋊C₄×C₅₃	—	2	1	no	—
441	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
442	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
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	C₄²×C₅₃	—	2	1	no	—
447	C₄²×C₅₃	—	2	1	no	—
448	C₄²×C₅₃	—	2	1	no	—
449	C₄²×C₅₃	—	2	2	no	—
450	C₄²×C₅₃	—	2	1	no	—
451	C₄²×C₅₃	—	2	2	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	1	no	—
460	C₂³×C₅₃	—	2	2	no	—
461	C₂³×C₅₃	—	4	4	no	—
462	C₂³×C₅₃	—	8	2	no	—
463	C₂³×C₅₃	—	8	2	no	—
464	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
465	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
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	2	no	—
472	Q₈×C₅₃	—	2	1	no	—
473	Q₈×C₅₃	—	2	2	no	—
474	Q₈×C₅₃	—	2	1	no	—
475	Q₈×C₅₃	—	4	2	no	—
476	Q₈×C₅₃	—	8	2	no	—
477	Q₈×C₅₃	—	8	2	no	—
478	Q₈×C₅₃	—	8	2	no	—
479	D₄×C₅₃	—	2	2	no	—
480	D₄×C₅₃	—	2	2	no	—
481	D₄×C₅₃	—	2	1	no	—
482	D₄×C₅₃	—	2	1	no	—
483	D₄×C₅₃	—	2	2	no	—
484	D₄×C₅₃	—	2	1	no	—
485	D₄×C₅₃	—	4	2	no	—
486	D₄×C₅₃	—	4	4	no	—
487	D₄×C₅₃	—	4	2	no	—
488	D₄×C₅₃	—	4	2	no	—
489	D₄×C₅₃	—	4	2	no	—
490	D₄×C₅₃	—	8	1	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	2	no	—
497	C₂×C₄×C₅₃	—	2	1	no	—
498	C₂×C₄×C₅₃	—	2	2	no	—
499	C₂×C₄×C₅₃	—	2	1	no	—
500	C₂×C₄×C₅₃	—	2	1	no	—
501	C₂×C₄×C₅₃	—	2	2	no	—
502	C₂×C₄×C₅₃	—	2	2	no	—
503	C₂×C₄×C₅₃	—	2	2	no	—
504	C₂×C₄×C₅₃	—	2	1	no	—
505	C₂×C₄×C₅₃	—	2	1	no	—
506	C₂×C₄×C₅₃	—	2	1	no	—
507	C₂×C₄×C₅₃	—	2	1	no	—
508	C₂×C₄×C₅₃	—	2	1	no	—
509	C₂×C₄×C₅₃	—	4	1	no	—
510	C₂×C₄×C₅₃	—	4	2	no	—
511	C₂×C₄×C₅₃	—	4	2	no	—
512	C₂×C₄×C₅₃	—	4	2	no	—
513	C₂×C₄×C₅₃	—	8	1	no	—
514	C₂×C₄×C₅₃	—	8	2	no	—
515	C₂×C₄×C₅₃	—	8	2	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	2	no	—
520	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
521	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
522	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
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	1	yes	characteristic
527	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
528	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
529	C₈×C₅₃	—	2	1	no	—
530	C₈×C₅₃	—	2	2	no	—
531	C₈×C₅₃	—	2	1	no	—
532	C₈×C₅₃	—	2	2	no	—
533	C₈×C₅₃	—	2	1	no	—
534	C₈×C₅₃	—	2	1	no	—
535	#62032	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
536	C₂²×C₅₃	—	2	1	no	—
537	C₂²×C₅₃	—	2	2	no	—
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	—	4	1	no	—
544	C₂²×C₅₃	—	4	1	no	—
545	C₂²×C₅₃	—	4	2	no	—
546	C₂²×C₅₃	—	4	1	no	—
547	C₂²×C₅₃	—	4	1	no	—
548	C₂²×C₅₃	—	4	2	no	—
549	C₂²×C₅₃	—	4	1	no	—
550	C₂²×C₅₃	—	4	2	no	—
551	C₂²×C₅₃	—	16	4	no	—
552	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
553	C₄×C₅₃	—	2	1	no	—
554	C₄×C₅₃	—	2	1	no	—
555	C₄×C₅₃	—	2	2	no	—
556	C₄×C₅₃	—	2	1	no	—
557	C₄×C₅₃	—	2	2	no	—
558	C₄×C₅₃	—	2	1	no	—
559	C₄×C₅₃	—	2	2	no	—
560	C₄×C₅₃	—	4	1	no	—
561	C₄×C₅₃	—	4	1	no	—
562	C₄×C₅₃	—	4	1	no	—
563	C₄×C₅₃	—	4	2	no	—
564	C₄×C₅₃	—	4	1	no	—
565	C₄×C₅₃	—	4	2	no	—
566	C₄×C₅₃	—	4	1	no	—
567	C₄×C₅₃	—	4	1	no	—
568	C₄×C₅₃	—	4	2	no	—
569	C₄×C₅₃	#577	1	2	yes	—
570	C₄×C₅₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
571	C₄×C₅₃	#585	1	1	yes	characteristic
572	#3552	C₂×C₅₃	1	1	yes	characteristic, complemented
573	#3514	C₂×C₅₃	1	1	yes	characteristic, complemented
574	#3400	C₂×C₅₃	1	1	yes	characteristic, complemented
575	#3394	C₂×C₅₃	1	1	yes	characteristic, complemented
576	#3367	C₂×C₅₃	1	1	yes	characteristic, complemented
577	#3359	C₂×C₅₃	1	1	yes	characteristic, complemented
578	#3329	C₂×C₅₃	1	2	yes	complemented
579	#3328	C₂×C₅₃	1	1	yes	characteristic, complemented
580	#3321	C₂×C₅₃	1	2	yes	complemented
581	#3302	C₂×C₅₃	1	1	yes	characteristic, complemented
582	D₄×SD₁₆	C₂×C₅₃	1	1	yes	characteristic, complemented
583	#3275	C₂×C₅₃	1	2	yes	complemented
584	#3272	C₂×C₅₃	1	1	yes	characteristic, complemented
585	#3266	C₂×C₅₃	1	2	yes	complemented
586	#3258	C₂×C₅₃	1	2	yes	complemented
587	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
588	#3225	C₂×C₅₃	1	2	yes	complemented
589	#3206	C₂×C₅₃	1	1	yes	characteristic, complemented
590	#3123	C₂×C₅₃	1	2	yes	complemented
591	#3102	C₂×C₅₃	1	1	yes	characteristic, complemented
592	#3042	C₂×C₅₃	1	2	yes	complemented
593	#3039	C₂×C₅₃	1	1	yes	characteristic, complemented
594	#2993	C₂×C₅₃	1	1	yes	characteristic, complemented
595	C₂×C₅₃	—	4	1	no	—
596	C₂×C₅₃	—	4	2	no	—
597	C₂×C₅₃	—	4	2	no	—
598	C₂×C₅₃	—	8	1	no	—
599	C₂×C₅₃	—	8	2	no	—
600	C₂×C₅₃	#3488	1	1	yes	characteristic
601	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
602	C₂×C₅₃	#3586	1	1	yes	characteristic
603	C₂×#137	C₂²×C₅₃	1	2	yes	—
604	C₂×AGL(1,ℤ/8)	C₂²×C₅₃	1	2	yes	—
605	C₂²×SD₁₆	C₂²×C₅₃	1	2	yes	—
606	#563	—	2	2	no	—
607	#559	C₂²×C₅₃	1	1	yes	characteristic
608	#557	C₂²×C₅₃	1	1	yes	characteristic, complemented
609	#556	C₂²×C₅₃	1	1	yes	characteristic
610	#556	C₂²×C₅₃	1	1	yes	characteristic, complemented
611	#555	C₂²×C₅₃	1	2	yes	—
612	#554	—	2	1	no	—
613	#553	—	2	1	no	—
614	#551	—	2	2	no	—
615	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
616	D₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
617	D₄×Q₈	C₂²×C₅₃	1	2	yes	complemented
618	#548	—	2	1	no	—
619	#548	C₂²×C₅₃	1	2	yes	complemented
620	#547	C₂²×C₅₃	1	1	yes	characteristic
621	#546	—	2	1	no	—
622	#546	C₂²×C₅₃	1	2	yes	—
623	D₄²	C₂²×C₅₃	1	1	yes	characteristic
624	#544	—	2	1	no	—
625	#542	—	2	1	no	—
626	#542	C₂²×C₅₃	1	2	yes	—
627	#541	C₂²×C₅₃	1	2	yes	complemented
628	#539	—	2	2	no	—
629	#538	—	2	2	no	—
630	#536	C₂²×C₅₃	1	2	yes	complemented
631	#532	C₂²×C₅₃	1	1	yes	characteristic
632	C₂×C₄⋊Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
633	#529	—	2	1	no	—
634	#529	C₂²×C₅₃	1	1	yes	characteristic
635	#529	C₂²×C₅₃	1	1	yes	characteristic, complemented
636	C₂×#124	—	2	1	no	—
637	#518	C₂²×C₅₃	1	2	yes	—
638	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
639	#497	C₂²×C₅₃	1	2	yes	complemented
640	#495	C₂²×C₅₃	1	2	yes	complemented
641	#492	C₂²×C₅₃	1	1	yes	characteristic
642	#492	C₂²×C₅₃	1	1	yes	characteristic
643	#489	C₂²×C₅₃	1	2	yes	complemented
644	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
645	#487	C₂²×C₅₃	1	2	yes	complemented
646	#487	C₂²×C₅₃	1	1	yes	characteristic, complemented
647	#485	C₂²×C₅₃	1	2	yes	complemented
648	#485	C₂²×C₅₃	1	1	yes	characteristic, complemented
649	#485	C₂²×C₅₃	1	2	yes	complemented
650	#482	C₂²×C₅₃	1	1	yes	characteristic, complemented
651	#479	C₂²×C₅₃	1	1	yes	characteristic, complemented
652	#478	C₂²×C₅₃	1	1	yes	characteristic
653	#478	C₂²×C₅₃	1	2	yes	complemented
654	#477	C₂²×C₅₃	1	2	yes	complemented
655	#475	C₂²×C₅₃	1	1	yes	characteristic, complemented
656	#475	C₂²×C₅₃	1	2	yes	complemented
657	#474	C₂²×C₅₃	1	1	yes	characteristic, complemented
658	#470	C₂²×C₅₃	1	2	yes	complemented
659	#469	C₂²×C₅₃	1	2	yes	complemented
660	#468	C₂²×C₅₃	1	2	yes	—
661	#468	C₂²×C₅₃	1	2	yes	complemented
662	#467	C₂²×C₅₃	1	2	yes	complemented
663	#465	C₂²×C₅₃	1	2	yes	—
664	#464	C₂²×C₅₃	1	1	yes	characteristic, complemented
665	#464	C₂²×C₅₃	1	2	yes	complemented
666	#464	C₂²×C₅₃	1	2	yes	complemented
667	#463	C₂²×C₅₃	1	1	yes	characteristic
668	#463	C₂²×C₅₃	1	2	yes	—
669	#463	C₂²×C₅₃	1	2	yes	complemented
670	#463	C₂²×C₅₃	1	2	yes	complemented
671	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
672	#462	C₂²×C₅₃	1	1	yes	characteristic, complemented
673	#462	C₂²×C₅₃	1	2	yes	complemented
674	#461	C₂²×C₅₃	1	2	yes	—
675	#461	C₂²×C₅₃	1	1	yes	characteristic
676	#461	C₂²×C₅₃	1	1	yes	characteristic
677	#461	C₂²×C₅₃	1	2	yes	—
678	#461	C₂²×C₅₃	1	2	yes	complemented
679	#461	C₂²×C₅₃	1	2	yes	complemented
680	#461	C₂²×C₅₃	1	2	yes	complemented
681	#460	C₂²×C₅₃	1	1	yes	characteristic
682	#459	C₂²×C₅₃	1	1	yes	characteristic
683	#452	C₂²×C₅₃	1	1	yes	characteristic
684	#452	C₂²×C₅₃	1	2	yes	complemented
685	#451	C₂²×C₅₃	1	2	yes	complemented
686	#450	C₂²×C₅₃	1	2	yes	—
687	#450	C₂²×C₅₃	1	2	yes	—
688	#449	C₂²×C₅₃	1	1	yes	characteristic
689	#449	C₂²×C₅₃	1	2	yes	—
690	#448	C₂²×C₅₃	1	2	yes	—
691	#448	C₂²×C₅₃	1	2	yes	complemented
692	#448	C₂²×C₅₃	1	2	yes	complemented
693	#446	C₂²×C₅₃	1	1	yes	characteristic, complemented
694	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic, complemented
695	#440	C₂²×C₅₃	1	2	yes	—
696	#440	C₂²×C₅₃	1	2	yes	complemented
697	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
699	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
700	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	complemented
701	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic, complemented
702	C₄×D₈	C₂²×C₅₃	1	1	yes	characteristic
703	#436	C₂²×C₅₃	1	1	yes	characteristic
704	#436	C₂²×C₅₃	1	2	yes	complemented
705	#435	C₂²×C₅₃	1	2	yes	complemented
706	C₈×D₄	C₂²×C₅₃	1	1	yes	characteristic
707	#433	C₂²×C₅₃	1	2	yes	complemented
708	#431	C₂²×C₅₃	1	1	yes	characteristic, complemented
709	#424	C₂²×C₅₃	1	2	yes	complemented
710	#423	C₂²×C₅₃	1	1	yes	characteristic, complemented
711	#419	C₂²×C₅₃	1	2	yes	complemented
712	#419	C₂²×C₅₃	1	2	yes	complemented
713	#416	C₂²×C₅₃	1	2	yes	complemented
714	C₅₃	#62032	1	1	yes	characteristic, direct product factor, Sylow
715	C₂×#41	—	2	1	no	—
716	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
717	C₂×#41	C₂³×C₅₃	1	2	yes	—
718	C₂²×Q₈	—	2	1	no	—
719	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
720	C₂²×Q₈	C₂³×C₅₃	1	2	yes	—
721	C₂²×D₄	—	2	1	no	—
722	C₂²×D₄	C₂³×C₅₃	1	2	yes	—
723	#137	—	4	4	no	—
724	AGL(1,ℤ/8)	—	4	4	no	—
725	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₅₃	1	2	yes	—
727	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
728	C₂×SD₁₆	—	4	4	no	—
729	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
730	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
731	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
732	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
733	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
734	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
735	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
736	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
737	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
738	C₂×D₈	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×D₈	C₂³×C₅₃	1	2	yes	—
740	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
741	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
742	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
743	C₄⋊Q₈	—	2	1	no	—
744	C₄⋊Q₈	—	2	2	no	—
745	C₄⋊Q₈	—	2	1	no	—
746	C₄⋊Q₈	—	2	1	no	—
747	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
748	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
749	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
750	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
751	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
752	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
753	#127	C₂³×C₅₃	1	1	yes	characteristic
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	1	no	—
760	#126	D₄×C₅₃	1	2	yes	—
761	#125	—	2	2	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	D₄×C₅₃	1	1	yes	characteristic
766	#125	C₂³×C₅₃	1	1	yes	characteristic
767	#124	—	2	1	no	—
768	#124	—	2	1	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	2	no	—
772	#124	—	2	2	no	—
773	#124	—	2	1	no	—
774	#124	D₄×C₅₃	1	1	yes	characteristic
775	#124	C₂³×C₅₃	1	1	yes	characteristic
776	#124	C₂³×C₅₃	1	2	yes	—
777	#124	C₂³×C₅₃	1	2	yes	—
778	#123	—	2	1	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	#123	—	2	2	no	—
784	#123	—	2	2	no	—
785	#123	D₄×C₅₃	1	2	yes	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	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	D₄×C₅₃	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
799	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	2	no	—
807	#121	D₄×C₅₃	1	1	yes	characteristic
808	#121	C₂³×C₅₃	1	1	yes	characteristic
809	#121	C₂³×C₅₃	1	2	yes	—
810	#121	C₂³×C₅₃	1	2	yes	—
811	#120	—	2	2	no	—
812	#120	—	2	2	no	—
813	C₄×Q₈	—	2	1	no	—
814	C₄×Q₈	—	2	1	no	—
815	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
816	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
817	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
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×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	1	no	—
824	C₄×D₄	—	2	1	no	—
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	2	no	—
827	C₄×D₄	—	2	2	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	2	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
832	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
833	C₄×D₄	C₂³×C₅₃	1	2	yes	—
834	C₄×D₄	C₂³×C₅₃	1	2	yes	—
835	C₄×D₄	C₂³×C₅₃	1	2	yes	—
836	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
837	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₅₃	1	2	yes	—
839	#117	—	2	2	no	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	C₂³×C₅₃	1	1	yes	characteristic
844	#117	C₂³×C₅₃	1	2	yes	—
845	#117	C₂³×C₅₃	1	2	yes	—
846	C₂×C₄⋊C₄	—	2	1	no	—
847	C₂×C₄⋊C₄	—	2	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₂²⋊C₄	—	2	2	no	—
850	C₂×C₂²⋊C₄	—	2	2	no	—
851	C₂×C₂²⋊C₄	—	2	2	no	—
852	C₂×C₄²	—	2	1	no	—
853	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
854	#107	C₂³×C₅₃	1	1	yes	characteristic
855	#107	C₂³×C₅₃	1	1	yes	characteristic
856	#107	C₂³×C₅₃	1	2	yes	—
857	#106	C₂³×C₅₃	1	1	yes	characteristic
858	#106	C₂³×C₅₃	1	2	yes	—
859	#106	C₂³×C₅₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
861	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
863	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
864	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
865	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
866	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
867	#103	C₂³×C₅₃	1	2	yes	—
868	#103	C₂³×C₅₃	1	2	yes	—
869	#103	C₂³×C₅₃	1	2	yes	—
870	#103	C₂³×C₅₃	1	1	yes	characteristic
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	2	yes	—
875	#103	C₂³×C₅₃	1	1	yes	characteristic
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	#102	C₂³×C₅₃	1	1	yes	characteristic
881	#102	C₂³×C₅₃	1	2	yes	—
882	#102	C₂³×C₅₃	1	1	yes	characteristic
883	#102	C₂³×C₅₃	1	1	yes	characteristic
884	#102	C₂³×C₅₃	1	1	yes	characteristic
885	#102	C₂³×C₅₃	1	2	yes	—
886	#102	C₂³×C₅₃	1	2	yes	—
887	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
888	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
889	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
890	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
891	#97	C₂³×C₅₃	1	2	yes	—
892	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
893	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
894	C₄×C₈	C₂³×C₅₃	1	2	yes	—
895	C₂⁴	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	4	1	no	—
898	#41	—	4	2	no	—
899	#41	—	4	2	no	—
900	#41	—	8	2	no	—
901	C₂×Q₈	—	2	1	no	—
902	C₂×Q₈	—	2	2	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	2	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	4	2	no	—
907	C₂×Q₈	—	4	2	no	—
908	C₂×Q₈	—	4	2	no	—
909	C₂×Q₈	—	8	2	no	—
910	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
911	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
912	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
913	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
914	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
915	C₂×D₄	—	2	4	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	1	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	1	no	—
923	C₂×D₄	—	2	1	no	—
924	C₂×D₄	—	4	2	no	—
925	C₂×D₄	—	8	2	no	—
926	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
927	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
928	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
929	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
930	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
931	C₂²×C₄	—	2	2	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	2	no	—
938	C₂²×C₄	—	2	2	no	—
939	C₂²×C₄	—	2	2	no	—
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
942	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
943	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
944	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
945	Q₁₆	—	4	2	no	—
946	Q₁₆	—	4	2	no	—
947	Q₁₆	—	4	1	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	2	4	no	—
950	SD₁₆	—	2	4	no	—
951	SD₁₆	—	4	2	no	—
952	SD₁₆	—	4	2	no	—
953	SD₁₆	—	4	2	no	—
954	SD₁₆	—	4	2	no	—
955	SD₁₆	—	4	1	no	—
956	SD₁₆	—	4	2	no	—
957	D₈	—	2	2	no	—
958	D₈	—	4	2	no	—
959	M₁₆	—	4	2	no	—
960	M₁₆	—	4	2	no	—
961	C₂×C₈	—	4	2	no	—
962	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
963	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
964	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
965	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
966	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
967	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	1	no	—
984	C₄⋊C₄	—	2	2	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
991	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
992	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
993	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
994	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
995	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
996	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
999	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	2	no	—
1005	C₂²⋊C₄	—	2	2	no	—
1006	C₂²⋊C₄	—	2	1	no	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	2	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	1	no	—
1013	C₂²⋊C₄	—	2	2	no	—
1014	C₂²⋊C₄	—	2	2	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	1	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	1	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	1	no	—
1021	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1022	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1023	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1024	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1025	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	2	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	2	2	no	—
1032	C₄²	—	2	2	no	—
1033	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1034	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
1035	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1036	C₄²	C₂⁴×C₅₃	1	2	yes	—
1037	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
1038	C₂³	—	2	1	no	—
1039	C₂³	—	2	1	no	—
1040	C₂³	—	2	2	no	—
1041	C₂³	—	4	4	no	—
1042	C₂³	—	8	2	no	—
1043	C₂³	—	8	2	no	—
1044	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
1045	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
1046	Q₈	—	2	2	no	—
1047	Q₈	—	2	1	no	—
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	—	4	2	no	—
1056	Q₈	—	8	2	no	—
1057	Q₈	—	8	2	no	—
1058	Q₈	—	8	2	no	—
1059	D₄	—	2	2	no	—
1060	D₄	—	2	1	no	—
1061	D₄	—	2	2	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	2	2	no	—
1064	D₄	—	2	1	no	—
1065	D₄	—	4	2	no	—
1066	D₄	—	4	4	no	—
1067	D₄	—	4	2	no	—
1068	D₄	—	4	2	no	—
1069	D₄	—	4	2	no	—
1070	D₄	—	8	1	no	—
1071	D₄	—	8	2	no	—
1072	D₄	—	8	2	no	—
1073	D₄	—	8	2	no	—
1074	D₄	H(5,𝔽₂)×C₅₃	1	2	yes	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	2	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	2	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	4	2	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	8	2	no	—
1095	C₂×C₄	—	8	2	no	—
1096	C₂×C₄	—	8	2	no	—
1097	C₂×C₄	—	8	2	no	—
1098	C₂×C₄	—	8	2	no	—
1099	C₂×C₄	—	8	2	no	—
1100	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1101	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1102	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1103	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1104	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1105	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1106	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1107	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	2	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	2	2	no	—
1113	C₈	—	2	1	no	—
1114	C₈	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	2	no	—
1120	C₂²	—	2	1	no	—
1121	C₂²	—	2	2	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	4	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	2	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	4	2	no	—
1128	C₂²	—	4	2	no	—
1129	C₂²	—	4	1	no	—
1130	C₂²	—	16	4	no	—
1131	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	2	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	2	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	C₅₃×#577	1	2	yes	—
1149	C₄	C₂×H(5,𝔽₂)×C₅₃	1	1	yes	characteristic
1150	C₄	C₅₃×#585	1	1	yes	characteristic
1151	C₂	—	4	2	no	—
1152	C₂	—	4	1	no	—
1153	C₂	—	4	2	no	—
1154	C₂	—	8	2	no	—
1155	C₂	—	8	1	no	—
1156	C₂	C₅₃×#3488	1	1	yes	characteristic
1157	C₂	C₂×C₅₃×#577	1	1	yes	characteristic
1158	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×#3552	C₂	semidirect
2. C₅₃×#3514	C₂	semidirect
3. C₅₃×#3400	C₂	semidirect
4. C₅₃×#3394	C₂	semidirect
5. C₅₃×#3367	C₂	semidirect
6. C₅₃×#3359	C₂	semidirect
7. C₅₃×#3329	C₂	semidirect
8. C₅₃×#3328	C₂	semidirect
9. C₅₃×#3321	C₂	semidirect
10. C₅₃×#3302	C₂	semidirect
11. D₄×SD₁₆×C₅₃	C₂	semidirect
12. C₅₃×#3275	C₂	semidirect
13. C₅₃×#3272	C₂	semidirect
14. C₅₃×#3266	C₂	semidirect
15. C₅₃×#3258	C₂	semidirect
16. C₅₃×#3251	C₂	semidirect
17. C₅₃×#3225	C₂	semidirect
18. C₅₃×#3206	C₂	semidirect
19. C₅₃×#3123	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3042	C₂	semidirect
22. C₅₃×#3039	C₂	semidirect
23. C₅₃×#2993	C₂	semidirect
29. C₅₃×#557	C₂²	semidirect
31. C₅₃×#556	C₂²	semidirect
38. D₄×Q₈×C₅₃	C₂²	semidirect
40. C₅₃×#548	C₂²	semidirect
48. C₅₃×#541	C₂²	semidirect
51. C₅₃×#536	C₂²	semidirect
53. C₂×C₄⋊Q₈×C₅₃	C₂²	semidirect
56. C₅₃×#529	C₂²	semidirect
60. C₅₃×#497	C₂²	semidirect
61. C₅₃×#495	C₂²	semidirect
64. C₅₃×#489	C₂²	semidirect
65. C₅₃×#487	C₂²	semidirect
66. C₅₃×#487	C₂²	semidirect
67. C₅₃×#487	C₂²	semidirect
68. C₅₃×#485	C₂²	semidirect
69. C₅₃×#485	C₂²	semidirect
70. C₅₃×#485	C₂²	semidirect
71. C₅₃×#482	C₂²	semidirect
72. C₅₃×#479	C₂²	semidirect
74. C₅₃×#478	C₂²	semidirect
75. C₅₃×#477	C₂²	semidirect
76. C₅₃×#475	C₂²	semidirect
77. C₅₃×#475	C₂²	semidirect
78. C₅₃×#474	C₂²	semidirect
79. C₅₃×#470	C₂²	semidirect
80. C₅₃×#469	C₂²	semidirect
82. C₅₃×#468	C₂²	semidirect
83. C₅₃×#467	C₂²	semidirect
85. C₅₃×#464	C₂²	semidirect
86. C₅₃×#464	C₂²	semidirect
87. C₅₃×#464	C₂²	semidirect
90. C₅₃×#463	C₂²	semidirect
91. C₅₃×#463	C₂²	semidirect
92. C₅₃×#462	C₂²	semidirect
93. C₅₃×#462	C₂²	semidirect
94. C₅₃×#462	C₂²	semidirect
99. C₅₃×#461	C₂²	semidirect
100. C₅₃×#461	C₂²	semidirect
101. C₅₃×#461	C₂²	semidirect
105. C₅₃×#452	C₂²	semidirect
106. C₅₃×#451	C₂²	semidirect
112. C₅₃×#448	C₂²	semidirect
113. C₅₃×#448	C₂²	semidirect
114. C₅₃×#446	C₂²	semidirect
115. C₈×Q₈×C₅₃	C₂²	semidirect
117. C₅₃×#440	C₂²	semidirect
118. C₄×Q₁₆×C₅₃	C₂²	semidirect
121. C₄×SD₁₆×C₅₃	C₂²	semidirect
122. C₄×SD₁₆×C₅₃	C₂²	semidirect
125. C₅₃×#436	C₂²	semidirect
126. C₅₃×#435	C₂²	semidirect
128. C₅₃×#433	C₂²	semidirect
129. C₅₃×#431	C₂²	semidirect
130. C₅₃×#424	C₂²	semidirect
131. C₅₃×#423	C₂²	semidirect
132. C₅₃×#419	C₂²	semidirect
133. C₅₃×#419	C₂²	semidirect
134. C₅₃×#416	C₂²	semidirect
535. #62032	C₅₃	direct (N × H)
572. #3552	C₂×C₅₃	semidirect
573. #3514	C₂×C₅₃	semidirect
574. #3400	C₂×C₅₃	semidirect
575. #3394	C₂×C₅₃	semidirect
576. #3367	C₂×C₅₃	semidirect
577. #3359	C₂×C₅₃	semidirect
578. #3329	C₂×C₅₃	semidirect
579. #3328	C₂×C₅₃	semidirect
580. #3321	C₂×C₅₃	semidirect
581. #3302	C₂×C₅₃	semidirect
582. D₄×SD₁₆	C₂×C₅₃	semidirect
583. #3275	C₂×C₅₃	semidirect
584. #3272	C₂×C₅₃	semidirect
585. #3266	C₂×C₅₃	semidirect
586. #3258	C₂×C₅₃	semidirect
587. #3251	C₂×C₅₃	semidirect
588. #3225	C₂×C₅₃	semidirect
589. #3206	C₂×C₅₃	semidirect
590. #3123	C₂×C₅₃	semidirect
591. #3102	C₂×C₅₃	semidirect
592. #3042	C₂×C₅₃	semidirect
593. #3039	C₂×C₅₃	semidirect
594. #2993	C₂×C₅₃	semidirect
608. #557	C₂²×C₅₃	semidirect
610. #556	C₂²×C₅₃	semidirect
617. D₄×Q₈	C₂²×C₅₃	semidirect
619. #548	C₂²×C₅₃	semidirect
627. #541	C₂²×C₅₃	semidirect
630. #536	C₂²×C₅₃	semidirect
632. C₂×C₄⋊Q₈	C₂²×C₅₃	semidirect
635. #529	C₂²×C₅₃	semidirect
639. #497	C₂²×C₅₃	semidirect
640. #495	C₂²×C₅₃	semidirect
643. #489	C₂²×C₅₃	semidirect
644. #487	C₂²×C₅₃	semidirect
645. #487	C₂²×C₅₃	semidirect
646. #487	C₂²×C₅₃	semidirect
647. #485	C₂²×C₅₃	semidirect
648. #485	C₂²×C₅₃	semidirect
649. #485	C₂²×C₅₃	semidirect
650. #482	C₂²×C₅₃	semidirect
651. #479	C₂²×C₅₃	semidirect
653. #478	C₂²×C₅₃	semidirect
654. #477	C₂²×C₅₃	semidirect
655. #475	C₂²×C₅₃	semidirect
656. #475	C₂²×C₅₃	semidirect
657. #474	C₂²×C₅₃	semidirect
658. #470	C₂²×C₅₃	semidirect
659. #469	C₂²×C₅₃	semidirect
661. #468	C₂²×C₅₃	semidirect
662. #467	C₂²×C₅₃	semidirect
664. #464	C₂²×C₅₃	semidirect
665. #464	C₂²×C₅₃	semidirect
666. #464	C₂²×C₅₃	semidirect
669. #463	C₂²×C₅₃	semidirect
670. #463	C₂²×C₅₃	semidirect
671. #462	C₂²×C₅₃	semidirect
672. #462	C₂²×C₅₃	semidirect
673. #462	C₂²×C₅₃	semidirect
678. #461	C₂²×C₅₃	semidirect
679. #461	C₂²×C₅₃	semidirect
680. #461	C₂²×C₅₃	semidirect
684. #452	C₂²×C₅₃	semidirect
685. #451	C₂²×C₅₃	semidirect
691. #448	C₂²×C₅₃	semidirect
692. #448	C₂²×C₅₃	semidirect
693. #446	C₂²×C₅₃	semidirect
694. C₈×Q₈	C₂²×C₅₃	semidirect
696. #440	C₂²×C₅₃	semidirect
697. C₄×Q₁₆	C₂²×C₅₃	semidirect
700. C₄×SD₁₆	C₂²×C₅₃	semidirect
701. C₄×SD₁₆	C₂²×C₅₃	semidirect
704. #436	C₂²×C₅₃	semidirect
705. #435	C₂²×C₅₃	semidirect
707. #433	C₂²×C₅₃	semidirect
708. #431	C₂²×C₅₃	semidirect
709. #424	C₂²×C₅₃	semidirect
710. #423	C₂²×C₅₃	semidirect
711. #419	C₂²×C₅₃	semidirect
712. #419	C₂²×C₅₃	semidirect
713. #416	C₂²×C₅₃	semidirect
714. C₅₃	#62032	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×#3552	2
C₅₃×#3514	2
C₅₃×#3400	2
C₅₃×#3394	2
C₅₃×#3367	2
C₅₃×#3359	2
C₅₃×#3329	2
C₅₃×#3328	2
C₅₃×#3321	2
C₅₃×#3302	2
D₄×SD₁₆×C₅₃	2
C₅₃×#3275	2
C₅₃×#3272	2
C₅₃×#3266	2
C₅₃×#3258	2
C₅₃×#3251	2
C₅₃×#3225	2
C₅₃×#3206	2
C₅₃×#3123	2
C₅₃×#3102	2
C₅₃×#3042	2
C₅₃×#3039	2
C₅₃×#2993	2
#62032	53

Subgroups — C53×#62032 #27269544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62032 #27269544