Subgroups — C₅₃×#62238 #27269750

Order 13568.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3389	C₂	1	2	yes	maximal, complemented
4	C₅₃×#3372	C₂	1	2	yes	maximal, complemented
5	C₅₃×#3351	C₂	1	2	yes	maximal, complemented
6	C₅₃×#3346	C₂	1	2	yes	maximal, complemented
7	C₅₃×#3343	C₂	1	2	yes	maximal, complemented
8	C₅₃×#3330	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
10	C₅₃×#3307	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3260	C₂	1	2	yes	maximal, complemented
12	C₅₃×#3254	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3242	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#3119	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3115	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3083	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3080	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#2995	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#563	—	2	1	no	—
21	C₅₃×#562	—	2	1	no	—
22	C₅₃×#557	C₂²	1	1	yes	characteristic
23	C₅₃×#554	C₂²	1	1	yes	characteristic
24	C₅₃×#554	C₂²	1	2	yes	—
25	C₅₃×#554	C₂²	1	1	yes	characteristic
26	C₅₃×#553	—	2	1	no	—
27	C₅₃×#553	C₂²	1	2	yes	—
28	C₅₃×#553	C₂²	1	2	yes	—
29	C₅₃×#552	—	2	2	no	—
30	C₅₃×#552	—	2	1	no	—
31	C₅₃×#552	C₂²	1	2	yes	—
32	C₅₃×#547	—	2	2	no	—
33	C₅₃×#547	C₂²	1	1	yes	characteristic
34	C₅₃×#547	C₂²	1	2	yes	—
35	C₅₃×#547	C₂²	1	2	yes	—
36	C₅₃×#544	C₂²	1	2	yes	—
37	C₅₃×#541	C₂²	1	2	yes	—
38	C₅₃×#540	C₂²	1	2	yes	—
39	C₅₃×#539	—	2	2	no	—
40	C₅₃×#539	—	2	2	no	—
41	C₅₃×#539	—	2	1	no	—
42	C₅₃×#537	—	2	1	no	—
43	C₅₃×#533	C₂²	1	1	yes	characteristic
44	C₅₃×#532	C₂²	1	1	yes	characteristic
45	C₅₃×#529	—	2	1	no	—
46	C₅₃×#529	C₂²	1	1	yes	characteristic
47	C₂×#125×C₅₃	—	2	1	no	—
48	C₂×#125×C₅₃	C₂²	1	1	yes	characteristic
49	C₅₃×#520	C₂²	1	2	yes	—
50	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
51	C₅₃×#501	C₂²	1	2	yes	—
52	C₅₃×#501	C₂²	1	2	yes	—
53	C₅₃×#499	C₂²	1	2	yes	—
54	C₅₃×#491	C₂²	1	2	yes	—
55	C₅₃×#491	C₂²	1	2	yes	—
56	C₅₃×#487	C₂²	1	2	yes	—
57	C₅₃×#485	C₂²	1	2	yes	—
58	C₅₃×#485	C₂²	1	2	yes	—
59	C₅₃×#484	C₂²	1	2	yes	—
60	C₅₃×#484	C₂²	1	2	yes	—
61	C₅₃×#483	C₂²	1	2	yes	—
62	C₅₃×#483	C₂²	1	2	yes	—
63	C₅₃×#482	C₂²	1	2	yes	—
64	C₅₃×#481	C₂²	1	2	yes	—
65	C₅₃×#480	C₂²	1	2	yes	—
66	C₅₃×#479	C₂²	1	2	yes	—
67	C₅₃×#479	C₂²	1	2	yes	—
68	C₅₃×#479	C₂²	1	2	yes	—
69	C₅₃×#479	C₂²	1	2	yes	—
70	C₅₃×#479	C₂²	1	2	yes	—
71	C₅₃×#478	C₂²	1	2	yes	—
72	C₅₃×#478	C₂²	1	2	yes	—
73	C₅₃×#478	C₂²	1	2	yes	—
74	C₅₃×#478	C₂²	1	2	yes	—
75	C₅₃×#478	C₂²	1	2	yes	—
76	C₅₃×#477	C₂²	1	2	yes	—
77	C₅₃×#477	C₂²	1	2	yes	—
78	C₅₃×#475	C₂²	1	1	yes	characteristic
79	C₅₃×#474	C₂²	1	2	yes	—
80	C₅₃×#474	C₂²	1	2	yes	—
81	C₅₃×#474	C₂²	1	1	yes	characteristic
82	C₅₃×#468	C₂²	1	2	yes	—
83	C₅₃×#468	C₂²	1	2	yes	—
84	C₅₃×#468	C₂²	1	2	yes	—
85	C₅₃×#468	C₂²	1	2	yes	—
86	C₅₃×#465	C₂²	1	2	yes	—
87	C₅₃×#465	C₂²	1	2	yes	—
88	C₅₃×#461	C₂²	1	2	yes	—
89	C₅₃×#461	C₂²	1	2	yes	—
90	C₅₃×#461	C₂²	1	2	yes	—
91	C₅₃×#460	C₂²	1	2	yes	—
92	C₅₃×#460	C₂²	1	1	yes	characteristic
93	C₅₃×#459	C₂²	1	1	yes	characteristic
94	C₅₃×#449	C₂²	1	2	yes	—
95	C₅₃×#449	C₂²	1	2	yes	—
96	C₅₃×#449	C₂²	1	2	yes	—
97	C₅₃×#446	C₂²	1	2	yes	—
98	C₅₃×#442	C₂²	1	2	yes	—
99	C₅₃×#442	C₂²	1	2	yes	—
100	C₅₃×#440	C₂²	1	2	yes	—
101	C₅₃×#440	C₂²	1	2	yes	—
102	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
103	C₄×D₈×C₅₃	C₂²	1	2	yes	—
104	C₅₃×#436	C₂²	1	2	yes	—
105	C₅₃×#435	C₂²	1	2	yes	—
106	C₅₃×#435	C₂²	1	2	yes	—
107	C₅₃×#433	C₂²	1	2	yes	—
108	C₅₃×#432	C₂²	1	1	yes	characteristic
109	C₅₃×#428	C₂²	1	1	yes	characteristic
110	C₅₃×#428	C₂²	1	1	yes	characteristic
111	C₅₃×#428	C₂²	1	2	yes	—
112	C₂×#107×C₅₃	C₂²	1	2	yes	—
113	C₅₃×#424	C₂²	1	2	yes	—
114	C₅₃×#423	C₂²	1	1	yes	characteristic
115	C₅₃×#417	C₂²	1	1	yes	characteristic
116	C₅₃×#417	C₂²	1	2	yes	—
117	C₅₃×#417	C₂²	1	1	yes	characteristic
118	C₅₃×#416	C₂²	1	2	yes	—
119	C₂×#41×C₅₃	—	2	2	no	—
120	C₂×#41×C₅₃	—	2	1	no	—
121	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
122	C₂×#41×C₅₃	C₂³	1	2	yes	—
123	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
124	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
125	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
126	C₂×D₈×C₅₃	C₂³	1	2	yes	—
127	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
128	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
129	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
130	C₂²×C₈×C₅₃	C₂³	1	2	yes	—
131	C₄⋊Q₈×C₅₃	—	2	2	no	—
132	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
133	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
134	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
135	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
137	#127×C₅₃	C₂³	1	1	yes	characteristic
138	#126×C₅₃	—	2	2	no	—
139	#126×C₅₃	—	2	2	no	—
140	#126×C₅₃	—	2	2	no	—
141	#126×C₅₃	—	2	2	no	—
142	#126×C₅₃	—	2	2	no	—
143	#126×C₅₃	D₄	1	2	yes	—
144	#125×C₅₃	—	2	2	no	—
145	#125×C₅₃	—	2	2	no	—
146	#125×C₅₃	—	2	1	no	—
147	#125×C₅₃	—	2	1	no	—
148	#125×C₅₃	—	2	2	no	—
149	#125×C₅₃	—	2	2	no	—
150	#125×C₅₃	—	2	2	no	—
151	#125×C₅₃	—	2	1	no	—
152	#125×C₅₃	—	2	1	no	—
153	#125×C₅₃	—	2	1	no	—
154	#125×C₅₃	D₄	1	1	yes	characteristic
155	#125×C₅₃	C₂³	1	2	yes	—
156	#125×C₅₃	C₂³	1	2	yes	—
157	#125×C₅₃	C₂³	1	2	yes	—
158	#125×C₅₃	C₂³	1	2	yes	—
159	#124×C₅₃	—	2	1	no	—
160	#124×C₅₃	D₄	1	1	yes	characteristic
161	#123×C₅₃	—	2	2	no	—
162	#123×C₅₃	—	2	2	no	—
163	#123×C₅₃	—	2	2	no	—
164	#123×C₅₃	—	2	2	no	—
165	#123×C₅₃	—	2	2	no	—
166	#123×C₅₃	—	2	2	no	—
167	#123×C₅₃	—	2	2	no	—
168	#123×C₅₃	—	2	2	no	—
169	#123×C₅₃	—	2	2	no	—
170	#123×C₅₃	—	2	2	no	—
171	#123×C₅₃	D₄	1	2	yes	—
172	C₂²⋊Q₈×C₅₃	—	2	2	no	—
173	C₂²⋊Q₈×C₅₃	—	2	2	no	—
174	C₂²⋊Q₈×C₅₃	—	2	2	no	—
175	C₂²⋊Q₈×C₅₃	—	2	2	no	—
176	C₂²⋊Q₈×C₅₃	—	2	2	no	—
177	C₂²⋊Q₈×C₅₃	—	2	2	no	—
178	C₂²⋊Q₈×C₅₃	—	2	2	no	—
179	C₂²⋊Q₈×C₅₃	—	2	1	no	—
180	C₂²⋊Q₈×C₅₃	—	2	2	no	—
181	C₂²⋊Q₈×C₅₃	—	2	1	no	—
182	C₂²⋊Q₈×C₅₃	D₄	1	1	yes	characteristic
183	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
184	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
185	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
186	#121×C₅₃	—	2	2	no	—
187	#121×C₅₃	—	2	2	no	—
188	#121×C₅₃	—	2	1	no	—
189	#121×C₅₃	—	2	2	no	—
190	#121×C₅₃	—	2	2	no	—
191	#121×C₅₃	—	2	2	no	—
192	#121×C₅₃	—	2	1	no	—
193	#121×C₅₃	D₄	1	1	yes	characteristic
194	#121×C₅₃	C₂³	1	2	yes	—
195	#121×C₅₃	C₂³	1	2	yes	—
196	#121×C₅₃	C₂³	1	2	yes	—
197	C₄×Q₈×C₅₃	—	2	1	no	—
198	C₄×Q₈×C₅₃	—	2	1	no	—
199	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
200	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
201	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
202	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
204	C₄×D₄×C₅₃	—	2	2	no	—
205	C₄×D₄×C₅₃	—	2	2	no	—
206	C₄×D₄×C₅₃	—	2	2	no	—
207	C₄×D₄×C₅₃	—	2	2	no	—
208	C₄×D₄×C₅₃	—	2	1	no	—
209	C₄×D₄×C₅₃	—	2	1	no	—
210	C₄×D₄×C₅₃	—	2	1	no	—
211	C₄×D₄×C₅₃	—	2	1	no	—
212	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₅₃	C₂³	1	2	yes	—
215	C₄×D₄×C₅₃	C₂³	1	2	yes	—
216	C₄×D₄×C₅₃	C₂³	1	2	yes	—
217	C₄×D₄×C₅₃	C₂³	1	2	yes	—
218	C₄×D₄×C₅₃	C₂³	1	2	yes	—
219	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
220	#117×C₅₃	—	2	2	no	—
221	#117×C₅₃	—	2	2	no	—
222	#117×C₅₃	—	2	1	no	—
223	#117×C₅₃	—	2	1	no	—
224	#117×C₅₃	C₂³	1	2	yes	—
225	#117×C₅₃	C₂³	1	1	yes	characteristic
226	#117×C₅₃	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
228	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
229	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
230	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
232	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
233	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
234	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
235	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
238	C₂×C₄²×C₅₃	—	2	1	no	—
239	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
240	#107×C₅₃	C₂³	1	2	yes	—
241	#107×C₅₃	C₂³	1	2	yes	—
242	#107×C₅₃	C₂³	1	2	yes	—
243	#107×C₅₃	C₂³	1	2	yes	—
244	#107×C₅₃	C₂³	1	2	yes	—
245	#107×C₅₃	C₂³	1	2	yes	—
246	#107×C₅₃	C₂³	1	2	yes	—
247	#106×C₅₃	C₂³	1	2	yes	—
248	#106×C₅₃	C₂³	1	2	yes	—
249	#106×C₅₃	C₂³	1	2	yes	—
250	#106×C₅₃	C₂³	1	2	yes	—
251	#106×C₅₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
254	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
256	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
258	#103×C₅₃	C₂³	1	2	yes	—
259	#103×C₅₃	C₂³	1	2	yes	—
260	#103×C₅₃	C₂³	1	2	yes	—
261	#103×C₅₃	C₂³	1	2	yes	—
262	#103×C₅₃	C₂³	1	2	yes	—
263	#103×C₅₃	C₂³	1	2	yes	—
264	#103×C₅₃	C₂³	1	2	yes	—
265	#103×C₅₃	C₂³	1	2	yes	—
266	#103×C₅₃	C₂³	1	2	yes	—
267	#102×C₅₃	C₂³	1	2	yes	—
268	#102×C₅₃	C₂³	1	2	yes	—
269	#102×C₅₃	C₂³	1	2	yes	—
270	#102×C₅₃	C₂³	1	2	yes	—
271	#102×C₅₃	C₂³	1	2	yes	—
272	#102×C₅₃	C₂³	1	2	yes	—
273	#102×C₅₃	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
277	#97×C₅₃	C₂³	1	2	yes	—
278	#97×C₅₃	C₂³	1	2	yes	—
279	C₄×C₈×C₅₃	C₂³	1	2	yes	—
280	#41×C₅₃	—	2	2	no	—
281	#41×C₅₃	—	2	4	no	—
282	#41×C₅₃	—	4	2	no	—
283	#41×C₅₃	—	4	1	no	—
284	#41×C₅₃	—	8	2	no	—
285	#41×C₅₃	—	8	4	no	—
286	C₂×Q₈×C₅₃	—	2	1	no	—
287	C₂×Q₈×C₅₃	—	2	2	no	—
288	C₂×Q₈×C₅₃	—	2	1	no	—
289	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
290	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
291	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	—
292	C₂×D₄×C₅₃	—	2	1	no	—
293	C₂×D₄×C₅₃	—	2	2	no	—
294	C₂×D₄×C₅₃	—	2	2	no	—
295	C₂×D₄×C₅₃	—	2	2	no	—
296	C₂×D₄×C₅₃	—	2	2	no	—
297	C₂×D₄×C₅₃	—	2	1	no	—
298	C₂×D₄×C₅₃	—	2	1	no	—
299	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
301	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
302	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄×C₅₃	—	2	1	no	—
304	C₂²×C₄×C₅₃	—	2	1	no	—
305	C₂²×C₄×C₅₃	—	2	2	no	—
306	C₂²×C₄×C₅₃	—	2	2	no	—
307	C₂²×C₄×C₅₃	—	2	1	no	—
308	C₂²×C₄×C₅₃	—	2	1	no	—
309	C₂²×C₄×C₅₃	—	2	2	no	—
310	C₂²×C₄×C₅₃	—	2	1	no	—
311	C₂²×C₄×C₅₃	—	2	2	no	—
312	C₂²×C₄×C₅₃	—	2	2	no	—
313	C₂²×C₄×C₅₃	—	2	2	no	—
314	C₂²×C₄×C₅₃	—	2	2	no	—
315	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
319	SD₁₆×C₅₃	—	4	2	no	—
320	SD₁₆×C₅₃	—	4	2	no	—
321	SD₁₆×C₅₃	—	4	2	no	—
322	D₈×C₅₃	—	2	4	no	—
323	M₁₆×C₅₃	—	4	1	no	—
324	M₁₆×C₅₃	—	4	2	no	—
325	M₁₆×C₅₃	—	4	1	no	—
326	C₂×C₈×C₅₃	—	4	2	no	—
327	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
328	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
329	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
330	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
331	C₄⋊C₄×C₅₃	—	2	2	no	—
332	C₄⋊C₄×C₅₃	—	2	2	no	—
333	C₄⋊C₄×C₅₃	—	2	1	no	—
334	C₄⋊C₄×C₅₃	—	2	1	no	—
335	C₄⋊C₄×C₅₃	—	2	2	no	—
336	C₄⋊C₄×C₅₃	—	2	2	no	—
337	C₄⋊C₄×C₅₃	—	2	2	no	—
338	C₄⋊C₄×C₅₃	—	2	2	no	—
339	C₄⋊C₄×C₅₃	—	2	2	no	—
340	C₄⋊C₄×C₅₃	—	2	2	no	—
341	C₄⋊C₄×C₅₃	—	2	2	no	—
342	C₄⋊C₄×C₅₃	—	2	2	no	—
343	C₄⋊C₄×C₅₃	—	2	2	no	—
344	C₄⋊C₄×C₅₃	—	2	2	no	—
345	C₄⋊C₄×C₅₃	—	2	2	no	—
346	C₄⋊C₄×C₅₃	—	2	2	no	—
347	C₄⋊C₄×C₅₃	—	2	1	no	—
348	C₄⋊C₄×C₅₃	—	2	2	no	—
349	C₄⋊C₄×C₅₃	—	2	1	no	—
350	C₄⋊C₄×C₅₃	—	2	1	no	—
351	C₄⋊C₄×C₅₃	—	2	1	no	—
352	C₄⋊C₄×C₅₃	—	2	2	no	—
353	C₄⋊C₄×C₅₃	—	2	1	no	—
354	C₄⋊C₄×C₅₃	—	2	2	no	—
355	C₄⋊C₄×C₅₃	—	2	1	no	—
356	C₄⋊C₄×C₅₃	—	2	2	no	—
357	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
358	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
359	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
362	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
369	C₂²⋊C₄×C₅₃	—	2	2	no	—
370	C₂²⋊C₄×C₅₃	—	2	2	no	—
371	C₂²⋊C₄×C₅₃	—	2	1	no	—
372	C₂²⋊C₄×C₅₃	—	2	2	no	—
373	C₂²⋊C₄×C₅₃	—	2	2	no	—
374	C₂²⋊C₄×C₅₃	—	2	1	no	—
375	C₂²⋊C₄×C₅₃	—	2	2	no	—
376	C₂²⋊C₄×C₅₃	—	2	1	no	—
377	C₂²⋊C₄×C₅₃	—	2	2	no	—
378	C₂²⋊C₄×C₅₃	—	2	2	no	—
379	C₂²⋊C₄×C₅₃	—	2	2	no	—
380	C₂²⋊C₄×C₅₃	—	2	2	no	—
381	C₂²⋊C₄×C₅₃	—	2	2	no	—
382	C₂²⋊C₄×C₅₃	—	2	2	no	—
383	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
384	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
385	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
386	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
388	C₄²×C₅₃	—	2	1	no	—
389	C₄²×C₅₃	—	2	1	no	—
390	C₄²×C₅₃	—	2	1	no	—
391	C₄²×C₅₃	—	2	2	no	—
392	C₄²×C₅₃	—	2	2	no	—
393	C₄²×C₅₃	—	2	2	no	—
394	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₄²×C₅₃	C₂⁴	1	2	yes	—
397	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
398	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₂³×C₅₃	—	2	1	no	—
400	C₂³×C₅₃	—	2	2	no	—
401	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
402	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
403	Q₈×C₅₃	—	2	1	no	—
404	Q₈×C₅₃	—	2	2	no	—
405	Q₈×C₅₃	—	2	1	no	—
406	Q₈×C₅₃	—	2	2	no	—
407	Q₈×C₅₃	—	4	1	no	—
408	Q₈×C₅₃	—	8	1	no	—
409	Q₈×C₅₃	—	8	1	no	—
410	Q₈×C₅₃	—	8	2	no	—
411	D₄×C₅₃	—	2	2	no	—
412	D₄×C₅₃	—	2	1	no	—
413	D₄×C₅₃	—	2	2	no	—
414	D₄×C₅₃	—	4	1	no	—
415	D₄×C₅₃	—	4	2	no	—
416	D₄×C₅₃	—	4	4	no	—
417	D₄×C₅₃	—	4	2	no	—
418	D₄×C₅₃	—	4	4	no	—
419	D₄×C₅₃	—	8	1	no	—
420	D₄×C₅₃	—	8	1	no	—
421	D₄×C₅₃	—	8	2	no	—
422	D₄×C₅₃	—	8	2	no	—
423	D₄×C₅₃	2₋¹⁺⁴	1	2	yes	—
424	C₂×C₄×C₅₃	—	2	1	no	—
425	C₂×C₄×C₅₃	—	2	2	no	—
426	C₂×C₄×C₅₃	—	2	2	no	—
427	C₂×C₄×C₅₃	—	2	1	no	—
428	C₂×C₄×C₅₃	—	2	2	no	—
429	C₂×C₄×C₅₃	—	2	1	no	—
430	C₂×C₄×C₅₃	—	2	2	no	—
431	C₂×C₄×C₅₃	—	2	2	no	—
432	C₂×C₄×C₅₃	—	2	2	no	—
433	C₂×C₄×C₅₃	—	2	1	no	—
434	C₂×C₄×C₅₃	—	2	2	no	—
435	C₂×C₄×C₅₃	—	2	1	no	—
436	C₂×C₄×C₅₃	—	4	1	no	—
437	C₂×C₄×C₅₃	—	4	1	no	—
438	C₂×C₄×C₅₃	—	4	2	no	—
439	C₂×C₄×C₅₃	—	4	4	no	—
440	C₂×C₄×C₅₃	—	4	2	no	—
441	C₂×C₄×C₅₃	—	4	2	no	—
442	C₂×C₄×C₅₃	—	8	1	no	—
443	C₂×C₄×C₅₃	—	8	2	no	—
444	C₂×C₄×C₅₃	—	8	2	no	—
445	C₂×C₄×C₅₃	—	8	2	no	—
446	C₂×C₄×C₅₃	—	8	2	no	—
447	C₂×C₄×C₅₃	—	8	2	no	—
448	C₂×C₄×C₅₃	—	8	1	no	—
449	C₂×C₄×C₅₃	—	8	2	no	—
450	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
459	C₈×C₅₃	—	2	2	no	—
460	C₈×C₅₃	—	2	2	no	—
461	C₈×C₅₃	—	2	2	no	—
462	C₈×C₅₃	—	2	2	no	—
463	#62238	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
464	C₂²×C₅₃	—	2	1	no	—
465	C₂²×C₅₃	—	2	2	no	—
466	C₂²×C₅₃	—	2	1	no	—
467	C₂²×C₅₃	—	2	2	no	—
468	C₂²×C₅₃	—	2	2	no	—
469	C₂²×C₅₃	—	2	1	no	—
470	C₂²×C₅₃	—	2	2	no	—
471	C₂²×C₅₃	—	4	1	no	—
472	C₂²×C₅₃	—	4	1	no	—
473	C₂²×C₅₃	—	4	2	no	—
474	C₂²×C₅₃	—	4	2	no	—
475	C₂²×C₅₃	—	4	2	no	—
476	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
477	C₄×C₅₃	—	2	1	no	—
478	C₄×C₅₃	—	2	1	no	—
479	C₄×C₅₃	—	2	2	no	—
480	C₄×C₅₃	—	2	1	no	—
481	C₄×C₅₃	—	2	1	no	—
482	C₄×C₅₃	—	2	2	no	—
483	C₄×C₅₃	—	2	2	no	—
484	C₄×C₅₃	—	2	1	no	—
485	C₄×C₅₃	—	4	2	no	—
486	C₄×C₅₃	—	4	1	no	—
487	C₄×C₅₃	—	4	2	no	—
488	C₄×C₅₃	—	4	2	no	—
489	C₄×C₅₃	—	4	1	no	—
490	C₄×C₅₃	—	4	2	no	—
491	C₄×C₅₃	—	4	1	no	—
492	C₄×C₅₃	—	4	2	no	—
493	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
494	C₄×C₅₃	#585	1	1	yes	characteristic
495	#3559	C₂×C₅₃	1	1	yes	characteristic, complemented
496	#3515	C₂×C₅₃	1	1	yes	characteristic, complemented
497	#3389	C₂×C₅₃	1	2	yes	complemented
498	#3372	C₂×C₅₃	1	2	yes	complemented
499	#3351	C₂×C₅₃	1	2	yes	complemented
500	#3346	C₂×C₅₃	1	2	yes	complemented
501	#3343	C₂×C₅₃	1	2	yes	complemented
502	#3330	C₂×C₅₃	1	2	yes	complemented
503	#3307	C₂×C₅₃	1	2	yes	complemented
504	#3307	C₂×C₅₃	1	2	yes	complemented
505	#3260	C₂×C₅₃	1	2	yes	complemented
506	#3254	C₂×C₅₃	1	1	yes	characteristic, complemented
507	#3242	C₂×C₅₃	1	2	yes	complemented
508	#3236	C₂×C₅₃	1	1	yes	characteristic, complemented
509	#3119	C₂×C₅₃	1	2	yes	complemented
510	#3115	C₂×C₅₃	1	1	yes	characteristic, complemented
511	#3083	C₂×C₅₃	1	2	yes	complemented
512	#3080	C₂×C₅₃	1	1	yes	characteristic, complemented
513	#2995	C₂×C₅₃	1	1	yes	characteristic, complemented
514	C₂×C₅₃	—	4	1	no	—
515	C₂×C₅₃	—	4	2	no	—
516	C₂×C₅₃	—	4	2	no	—
517	C₂×C₅₃	—	8	2	no	—
518	C₂×C₅₃	#3489	1	1	yes	characteristic
519	C₂×C₅₃	#3585	1	1	yes	characteristic
520	C₂×C₅₃	#3586	1	1	yes	characteristic
521	#563	—	2	1	no	—
522	#562	—	2	1	no	—
523	#557	C₂²×C₅₃	1	1	yes	characteristic
524	#554	C₂²×C₅₃	1	2	yes	—
525	#554	C₂²×C₅₃	1	1	yes	characteristic
526	#554	C₂²×C₅₃	1	1	yes	characteristic
527	#553	—	2	1	no	—
528	#553	C₂²×C₅₃	1	2	yes	—
529	#553	C₂²×C₅₃	1	2	yes	—
530	#552	—	2	2	no	—
531	#552	—	2	1	no	—
532	#552	C₂²×C₅₃	1	2	yes	—
533	#547	—	2	2	no	—
534	#547	C₂²×C₅₃	1	2	yes	—
535	#547	C₂²×C₅₃	1	1	yes	characteristic
536	#547	C₂²×C₅₃	1	2	yes	—
537	#544	C₂²×C₅₃	1	2	yes	—
538	#541	C₂²×C₅₃	1	2	yes	—
539	#540	C₂²×C₅₃	1	2	yes	—
540	#539	—	2	2	no	—
541	#539	—	2	2	no	—
542	#539	—	2	1	no	—
543	#537	—	2	1	no	—
544	#533	C₂²×C₅₃	1	1	yes	characteristic
545	#532	C₂²×C₅₃	1	1	yes	characteristic
546	#529	—	2	1	no	—
547	#529	C₂²×C₅₃	1	1	yes	characteristic
548	C₂×#125	—	2	1	no	—
549	C₂×#125	C₂²×C₅₃	1	1	yes	characteristic
550	#520	C₂²×C₅₃	1	2	yes	—
551	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
552	#501	C₂²×C₅₃	1	2	yes	—
553	#501	C₂²×C₅₃	1	2	yes	—
554	#499	C₂²×C₅₃	1	2	yes	—
555	#491	C₂²×C₅₃	1	2	yes	—
556	#491	C₂²×C₅₃	1	2	yes	—
557	#487	C₂²×C₅₃	1	2	yes	—
558	#485	C₂²×C₅₃	1	2	yes	—
559	#485	C₂²×C₅₃	1	2	yes	—
560	#484	C₂²×C₅₃	1	2	yes	—
561	#484	C₂²×C₅₃	1	2	yes	—
562	#483	C₂²×C₅₃	1	2	yes	—
563	#483	C₂²×C₅₃	1	2	yes	—
564	#482	C₂²×C₅₃	1	2	yes	—
565	#481	C₂²×C₅₃	1	2	yes	—
566	#480	C₂²×C₅₃	1	2	yes	—
567	#479	C₂²×C₅₃	1	2	yes	—
568	#479	C₂²×C₅₃	1	2	yes	—
569	#479	C₂²×C₅₃	1	2	yes	—
570	#479	C₂²×C₅₃	1	2	yes	—
571	#479	C₂²×C₅₃	1	2	yes	—
572	#478	C₂²×C₅₃	1	2	yes	—
573	#478	C₂²×C₅₃	1	2	yes	—
574	#478	C₂²×C₅₃	1	2	yes	—
575	#478	C₂²×C₅₃	1	2	yes	—
576	#478	C₂²×C₅₃	1	2	yes	—
577	#477	C₂²×C₅₃	1	2	yes	—
578	#477	C₂²×C₅₃	1	2	yes	—
579	#475	C₂²×C₅₃	1	1	yes	characteristic
580	#474	C₂²×C₅₃	1	2	yes	—
581	#474	C₂²×C₅₃	1	1	yes	characteristic
582	#474	C₂²×C₅₃	1	2	yes	—
583	#468	C₂²×C₅₃	1	2	yes	—
584	#468	C₂²×C₅₃	1	2	yes	—
585	#468	C₂²×C₅₃	1	2	yes	—
586	#468	C₂²×C₅₃	1	2	yes	—
587	#465	C₂²×C₅₃	1	2	yes	—
588	#465	C₂²×C₅₃	1	2	yes	—
589	#461	C₂²×C₅₃	1	2	yes	—
590	#461	C₂²×C₅₃	1	2	yes	—
591	#461	C₂²×C₅₃	1	2	yes	—
592	#460	C₂²×C₅₃	1	1	yes	characteristic
593	#460	C₂²×C₅₃	1	2	yes	—
594	#459	C₂²×C₅₃	1	1	yes	characteristic
595	#449	C₂²×C₅₃	1	2	yes	—
596	#449	C₂²×C₅₃	1	2	yes	—
597	#449	C₂²×C₅₃	1	2	yes	—
598	#446	C₂²×C₅₃	1	2	yes	—
599	#442	C₂²×C₅₃	1	2	yes	—
600	#442	C₂²×C₅₃	1	2	yes	—
601	#440	C₂²×C₅₃	1	2	yes	—
602	#440	C₂²×C₅₃	1	2	yes	—
603	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
604	C₄×D₈	C₂²×C₅₃	1	2	yes	—
605	#436	C₂²×C₅₃	1	2	yes	—
606	#435	C₂²×C₅₃	1	2	yes	—
607	#435	C₂²×C₅₃	1	2	yes	—
608	#433	C₂²×C₅₃	1	2	yes	—
609	#432	C₂²×C₅₃	1	1	yes	characteristic
610	#428	C₂²×C₅₃	1	1	yes	characteristic
611	#428	C₂²×C₅₃	1	1	yes	characteristic
612	#428	C₂²×C₅₃	1	2	yes	—
613	C₂×#107	C₂²×C₅₃	1	2	yes	—
614	#424	C₂²×C₅₃	1	2	yes	—
615	#423	C₂²×C₅₃	1	1	yes	characteristic
616	#417	C₂²×C₅₃	1	1	yes	characteristic
617	#417	C₂²×C₅₃	1	2	yes	—
618	#417	C₂²×C₅₃	1	1	yes	characteristic
619	#416	C₂²×C₅₃	1	2	yes	—
620	C₅₃	#62238	1	1	yes	characteristic, direct product factor, Sylow
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	C₂³×C₅₃	1	1	yes	characteristic
624	C₂×#41	C₂³×C₅₃	1	2	yes	—
625	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
626	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
627	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
628	C₂×D₈	C₂³×C₅₃	1	2	yes	—
629	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
630	C₂×M₁₆	C₂³×C₅₃	1	1	yes	characteristic
631	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
632	C₂²×C₈	C₂³×C₅₃	1	2	yes	—
633	C₄⋊Q₈	—	2	2	no	—
634	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
635	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
636	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
637	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
638	C₄⋊Q₈	C₂³×C₅₃	1	2	yes	—
639	#127	C₂³×C₅₃	1	1	yes	characteristic
640	#126	—	2	2	no	—
641	#126	—	2	2	no	—
642	#126	—	2	2	no	—
643	#126	—	2	2	no	—
644	#126	—	2	2	no	—
645	#126	D₄×C₅₃	1	2	yes	—
646	#125	—	2	2	no	—
647	#125	—	2	2	no	—
648	#125	—	2	1	no	—
649	#125	—	2	1	no	—
650	#125	—	2	2	no	—
651	#125	—	2	2	no	—
652	#125	—	2	2	no	—
653	#125	—	2	1	no	—
654	#125	—	2	1	no	—
655	#125	—	2	1	no	—
656	#125	D₄×C₅₃	1	1	yes	characteristic
657	#125	C₂³×C₅₃	1	2	yes	—
658	#125	C₂³×C₅₃	1	2	yes	—
659	#125	C₂³×C₅₃	1	2	yes	—
660	#125	C₂³×C₅₃	1	2	yes	—
661	#124	—	2	1	no	—
662	#124	D₄×C₅₃	1	1	yes	characteristic
663	#123	—	2	2	no	—
664	#123	—	2	2	no	—
665	#123	—	2	2	no	—
666	#123	—	2	2	no	—
667	#123	—	2	2	no	—
668	#123	—	2	2	no	—
669	#123	—	2	2	no	—
670	#123	—	2	2	no	—
671	#123	—	2	2	no	—
672	#123	—	2	2	no	—
673	#123	D₄×C₅₃	1	2	yes	—
674	C₂²⋊Q₈	—	2	1	no	—
675	C₂²⋊Q₈	—	2	2	no	—
676	C₂²⋊Q₈	—	2	1	no	—
677	C₂²⋊Q₈	—	2	2	no	—
678	C₂²⋊Q₈	—	2	2	no	—
679	C₂²⋊Q₈	—	2	2	no	—
680	C₂²⋊Q₈	—	2	2	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	D₄×C₅₃	1	1	yes	characteristic
685	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
686	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
687	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
688	#121	—	2	1	no	—
689	#121	—	2	2	no	—
690	#121	—	2	2	no	—
691	#121	—	2	2	no	—
692	#121	—	2	1	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	D₄×C₅₃	1	1	yes	characteristic
696	#121	C₂³×C₅₃	1	2	yes	—
697	#121	C₂³×C₅₃	1	2	yes	—
698	#121	C₂³×C₅₃	1	2	yes	—
699	C₄×Q₈	—	2	1	no	—
700	C₄×Q₈	—	2	1	no	—
701	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
702	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
703	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
704	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
705	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
706	C₄×D₄	—	2	1	no	—
707	C₄×D₄	—	2	1	no	—
708	C₄×D₄	—	2	1	no	—
709	C₄×D₄	—	2	2	no	—
710	C₄×D₄	—	2	2	no	—
711	C₄×D₄	—	2	2	no	—
712	C₄×D₄	—	2	2	no	—
713	C₄×D₄	—	2	1	no	—
714	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
715	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
716	C₄×D₄	C₂³×C₅₃	1	2	yes	—
717	C₄×D₄	C₂³×C₅₃	1	2	yes	—
718	C₄×D₄	C₂³×C₅₃	1	2	yes	—
719	C₄×D₄	C₂³×C₅₃	1	2	yes	—
720	C₄×D₄	C₂³×C₅₃	1	2	yes	—
721	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
722	#117	—	2	1	no	—
723	#117	—	2	2	no	—
724	#117	—	2	2	no	—
725	#117	—	2	1	no	—
726	#117	C₂³×C₅₃	1	1	yes	characteristic
727	#117	C₂³×C₅₃	1	2	yes	—
728	#117	C₂³×C₅₃	1	2	yes	—
729	C₂×C₄⋊C₄	—	2	1	no	—
730	C₂×C₄⋊C₄	—	2	1	no	—
731	C₂×C₄⋊C₄	—	2	2	no	—
732	C₂×C₄⋊C₄	—	2	1	no	—
733	C₂×C₄⋊C₄	—	2	2	no	—
734	C₂×C₄⋊C₄	—	2	1	no	—
735	C₂×C₄⋊C₄	—	2	2	no	—
736	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
740	C₂×C₄²	—	2	1	no	—
741	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
742	#107	C₂³×C₅₃	1	2	yes	—
743	#107	C₂³×C₅₃	1	2	yes	—
744	#107	C₂³×C₅₃	1	2	yes	—
745	#107	C₂³×C₅₃	1	2	yes	—
746	#107	C₂³×C₅₃	1	2	yes	—
747	#107	C₂³×C₅₃	1	2	yes	—
748	#107	C₂³×C₅₃	1	2	yes	—
749	#106	C₂³×C₅₃	1	2	yes	—
750	#106	C₂³×C₅₃	1	2	yes	—
751	#106	C₂³×C₅₃	1	2	yes	—
752	#106	C₂³×C₅₃	1	2	yes	—
753	#106	C₂³×C₅₃	1	2	yes	—
754	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
755	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
756	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
757	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
758	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
759	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
760	#103	C₂³×C₅₃	1	2	yes	—
761	#103	C₂³×C₅₃	1	2	yes	—
762	#103	C₂³×C₅₃	1	2	yes	—
763	#103	C₂³×C₅₃	1	2	yes	—
764	#103	C₂³×C₅₃	1	2	yes	—
765	#103	C₂³×C₅₃	1	2	yes	—
766	#103	C₂³×C₅₃	1	2	yes	—
767	#103	C₂³×C₅₃	1	2	yes	—
768	#103	C₂³×C₅₃	1	2	yes	—
769	#102	C₂³×C₅₃	1	2	yes	—
770	#102	C₂³×C₅₃	1	2	yes	—
771	#102	C₂³×C₅₃	1	2	yes	—
772	#102	C₂³×C₅₃	1	2	yes	—
773	#102	C₂³×C₅₃	1	2	yes	—
774	#102	C₂³×C₅₃	1	2	yes	—
775	#102	C₂³×C₅₃	1	2	yes	—
776	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
777	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
778	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
779	#97	C₂³×C₅₃	1	2	yes	—
780	#97	C₂³×C₅₃	1	2	yes	—
781	C₄×C₈	C₂³×C₅₃	1	2	yes	—
782	#41	—	2	2	no	—
783	#41	—	2	4	no	—
784	#41	—	4	2	no	—
785	#41	—	4	1	no	—
786	#41	—	8	2	no	—
787	#41	—	8	4	no	—
788	C₂×Q₈	—	2	1	no	—
789	C₂×Q₈	—	2	2	no	—
790	C₂×Q₈	—	2	1	no	—
791	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
792	C₂×Q₈	C₂⁴×C₅₃	1	2	yes	—
793	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
794	C₂×D₄	—	2	2	no	—
795	C₂×D₄	—	2	1	no	—
796	C₂×D₄	—	2	2	no	—
797	C₂×D₄	—	2	2	no	—
798	C₂×D₄	—	2	2	no	—
799	C₂×D₄	—	2	1	no	—
800	C₂×D₄	—	2	1	no	—
801	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
802	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
803	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
804	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
805	C₂²×C₄	—	2	1	no	—
806	C₂²×C₄	—	2	1	no	—
807	C₂²×C₄	—	2	2	no	—
808	C₂²×C₄	—	2	2	no	—
809	C₂²×C₄	—	2	1	no	—
810	C₂²×C₄	—	2	1	no	—
811	C₂²×C₄	—	2	2	no	—
812	C₂²×C₄	—	2	1	no	—
813	C₂²×C₄	—	2	2	no	—
814	C₂²×C₄	—	2	2	no	—
815	C₂²×C₄	—	2	2	no	—
816	C₂²×C₄	—	2	2	no	—
817	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
818	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
819	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
820	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
821	SD₁₆	—	4	2	no	—
822	SD₁₆	—	4	2	no	—
823	SD₁₆	—	4	2	no	—
824	D₈	—	2	4	no	—
825	M₁₆	—	4	1	no	—
826	M₁₆	—	4	2	no	—
827	M₁₆	—	4	1	no	—
828	C₂×C₈	—	4	2	no	—
829	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
830	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
831	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
832	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
833	C₄⋊C₄	—	2	2	no	—
834	C₄⋊C₄	—	2	2	no	—
835	C₄⋊C₄	—	2	1	no	—
836	C₄⋊C₄	—	2	1	no	—
837	C₄⋊C₄	—	2	2	no	—
838	C₄⋊C₄	—	2	2	no	—
839	C₄⋊C₄	—	2	2	no	—
840	C₄⋊C₄	—	2	2	no	—
841	C₄⋊C₄	—	2	2	no	—
842	C₄⋊C₄	—	2	2	no	—
843	C₄⋊C₄	—	2	2	no	—
844	C₄⋊C₄	—	2	2	no	—
845	C₄⋊C₄	—	2	2	no	—
846	C₄⋊C₄	—	2	2	no	—
847	C₄⋊C₄	—	2	2	no	—
848	C₄⋊C₄	—	2	2	no	—
849	C₄⋊C₄	—	2	1	no	—
850	C₄⋊C₄	—	2	2	no	—
851	C₄⋊C₄	—	2	1	no	—
852	C₄⋊C₄	—	2	1	no	—
853	C₄⋊C₄	—	2	1	no	—
854	C₄⋊C₄	—	2	2	no	—
855	C₄⋊C₄	—	2	1	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
860	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
861	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
862	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
863	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
864	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
865	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
866	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
867	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
868	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
870	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
871	C₂²⋊C₄	—	2	2	no	—
872	C₂²⋊C₄	—	2	2	no	—
873	C₂²⋊C₄	—	2	1	no	—
874	C₂²⋊C₄	—	2	2	no	—
875	C₂²⋊C₄	—	2	2	no	—
876	C₂²⋊C₄	—	2	1	no	—
877	C₂²⋊C₄	—	2	1	no	—
878	C₂²⋊C₄	—	2	2	no	—
879	C₂²⋊C₄	—	2	2	no	—
880	C₂²⋊C₄	—	2	2	no	—
881	C₂²⋊C₄	—	2	2	no	—
882	C₂²⋊C₄	—	2	2	no	—
883	C₂²⋊C₄	—	2	2	no	—
884	C₂²⋊C₄	—	2	2	no	—
885	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
886	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
887	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
888	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
889	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
890	C₄²	—	2	1	no	—
891	C₄²	—	2	1	no	—
892	C₄²	—	2	1	no	—
893	C₄²	—	2	2	no	—
894	C₄²	—	2	2	no	—
895	C₄²	—	2	2	no	—
896	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
897	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
898	C₄²	C₂⁴×C₅₃	1	2	yes	—
899	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
900	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
901	C₂³	—	2	1	no	—
902	C₂³	—	2	2	no	—
903	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
904	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
905	Q₈	—	2	2	no	—
906	Q₈	—	2	1	no	—
907	Q₈	—	2	1	no	—
908	Q₈	—	2	2	no	—
909	Q₈	—	4	1	no	—
910	Q₈	—	8	1	no	—
911	Q₈	—	8	1	no	—
912	Q₈	—	8	2	no	—
913	D₄	—	2	2	no	—
914	D₄	—	2	1	no	—
915	D₄	—	2	2	no	—
916	D₄	—	4	1	no	—
917	D₄	—	4	2	no	—
918	D₄	—	4	4	no	—
919	D₄	—	4	2	no	—
920	D₄	—	4	4	no	—
921	D₄	—	8	1	no	—
922	D₄	—	8	1	no	—
923	D₄	—	8	2	no	—
924	D₄	—	8	2	no	—
925	D₄	2₋¹⁺⁴×C₅₃	1	2	yes	—
926	C₂×C₄	—	2	1	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	2	2	no	—
929	C₂×C₄	—	2	1	no	—
930	C₂×C₄	—	2	1	no	—
931	C₂×C₄	—	2	1	no	—
932	C₂×C₄	—	2	1	no	—
933	C₂×C₄	—	2	2	no	—
934	C₂×C₄	—	2	2	no	—
935	C₂×C₄	—	2	2	no	—
936	C₂×C₄	—	2	2	no	—
937	C₂×C₄	—	2	2	no	—
938	C₂×C₄	—	4	1	no	—
939	C₂×C₄	—	4	1	no	—
940	C₂×C₄	—	4	2	no	—
941	C₂×C₄	—	4	4	no	—
942	C₂×C₄	—	4	2	no	—
943	C₂×C₄	—	4	2	no	—
944	C₂×C₄	—	8	1	no	—
945	C₂×C₄	—	8	2	no	—
946	C₂×C₄	—	8	2	no	—
947	C₂×C₄	—	8	2	no	—
948	C₂×C₄	—	8	2	no	—
949	C₂×C₄	—	8	2	no	—
950	C₂×C₄	—	8	1	no	—
951	C₂×C₄	—	8	2	no	—
952	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
953	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
954	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
955	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
956	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
957	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
958	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
959	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
960	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
961	C₈	—	2	2	no	—
962	C₈	—	2	2	no	—
963	C₈	—	2	2	no	—
964	C₈	—	2	2	no	—
965	C₂²	—	2	2	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	2	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	2	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	2	no	—
972	C₂²	—	4	1	no	—
973	C₂²	—	4	1	no	—
974	C₂²	—	4	2	no	—
975	C₂²	—	4	2	no	—
976	C₂²	—	4	2	no	—
977	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
978	C₄	—	2	2	no	—
979	C₄	—	2	1	no	—
980	C₄	—	2	1	no	—
981	C₄	—	2	1	no	—
982	C₄	—	2	2	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	2	no	—
986	C₄	—	4	1	no	—
987	C₄	—	4	2	no	—
988	C₄	—	4	2	no	—
989	C₄	—	4	1	no	—
990	C₄	—	4	2	no	—
991	C₄	—	4	2	no	—
992	C₄	—	4	1	no	—
993	C₄	—	4	2	no	—
994	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
995	C₄	C₅₃×#585	1	1	yes	characteristic
996	C₂	—	4	1	no	—
997	C₂	—	4	2	no	—
998	C₂	—	4	2	no	—
999	C₂	—	8	2	no	—
1000	C₂	C₅₃×#3489	1	1	yes	characteristic
1001	C₂	C₅₃×#3585	1	1	yes	characteristic
1002	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×#3559	C₂	semidirect
2. C₅₃×#3515	C₂	semidirect
3. C₅₃×#3389	C₂	semidirect
4. C₅₃×#3372	C₂	semidirect
5. C₅₃×#3351	C₂	semidirect
6. C₅₃×#3346	C₂	semidirect
7. C₅₃×#3343	C₂	semidirect
8. C₅₃×#3330	C₂	semidirect
9. C₅₃×#3307	C₂	semidirect
10. C₅₃×#3307	C₂	semidirect
11. C₅₃×#3260	C₂	semidirect
12. C₅₃×#3254	C₂	semidirect
13. C₅₃×#3242	C₂	semidirect
14. C₅₃×#3236	C₂	semidirect
15. C₅₃×#3119	C₂	semidirect
16. C₅₃×#3115	C₂	semidirect
17. C₅₃×#3083	C₂	semidirect
18. C₅₃×#3080	C₂	semidirect
19. C₅₃×#2995	C₂	semidirect
463. #62238	C₅₃	direct (N × H)
495. #3559	C₂×C₅₃	semidirect
496. #3515	C₂×C₅₃	semidirect
497. #3389	C₂×C₅₃	semidirect
498. #3372	C₂×C₅₃	semidirect
499. #3351	C₂×C₅₃	semidirect
500. #3346	C₂×C₅₃	semidirect
501. #3343	C₂×C₅₃	semidirect
502. #3330	C₂×C₅₃	semidirect
503. #3307	C₂×C₅₃	semidirect
504. #3307	C₂×C₅₃	semidirect
505. #3260	C₂×C₅₃	semidirect
506. #3254	C₂×C₅₃	semidirect
507. #3242	C₂×C₅₃	semidirect
508. #3236	C₂×C₅₃	semidirect
509. #3119	C₂×C₅₃	semidirect
510. #3115	C₂×C₅₃	semidirect
511. #3083	C₂×C₅₃	semidirect
512. #3080	C₂×C₅₃	semidirect
513. #2995	C₂×C₅₃	semidirect
620. C₅₃	#62238	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×#3559	2
C₅₃×#3515	2
C₅₃×#3389	2
C₅₃×#3372	2
C₅₃×#3351	2
C₅₃×#3346	2
C₅₃×#3343	2
C₅₃×#3330	2
C₅₃×#3307	2
C₅₃×#3260	2
C₅₃×#3254	2
C₅₃×#3242	2
C₅₃×#3236	2
C₅₃×#3119	2
C₅₃×#3115	2
C₅₃×#3083	2
C₅₃×#3080	2
C₅₃×#2995	2
#62238	53

Subgroups — C53×#62238 #27269750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62238 #27269750