Subgroups — C₅₃×#62154 #27269666

Order 13568.

1720 conjugacy classes of subgroups.

The subgroup lattice has 1104 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₃×#3515	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₃×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₃×#3381	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅₃×#3365	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅₃×#3361	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅₃×#3355	C₂	1	2	yes	maximal, complemented
9	C₅₃×#3353	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅₃×#3351	C₂	1	2	yes	maximal, complemented
11	C₅₃×#3333	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅₃×#3332	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅₃×#3327	C₂	1	2	yes	maximal, complemented
14	C₅₃×#3326	C₂	1	2	yes	maximal, complemented
15	C₅₃×#3256	C₂	1	2	yes	maximal, complemented
16	C₅₃×#3251	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3232	C₂	1	2	yes	maximal, complemented
18	C₅₃×#3228	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅₃×#3102	C₂	1	2	yes	maximal, complemented
21	C₅₃×#3080	C₂	1	2	yes	maximal, complemented
22	C₅₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#2991	C₂	1	1	yes	maximal, characteristic, complemented
24	C₅₃×#559	—	2	1	no	—
25	C₅₃×#559	C₂²	1	1	yes	characteristic
26	C₅₃×#557	C₂²	1	1	yes	characteristic
27	C₅₃×#557	C₂²	1	1	yes	characteristic
28	C₅₃×#556	—	2	1	no	—
29	C₅₃×#556	C₂²	1	1	yes	characteristic
30	C₅₃×#554	C₂²	1	1	yes	characteristic
31	C₅₃×#554	C₂²	1	1	yes	characteristic
32	C₅₃×#553	—	2	2	no	—
33	C₅₃×#553	C₂²	1	2	yes	—
34	C₅₃×#553	C₂²	1	2	yes	—
35	C₅₃×#552	—	2	1	no	—
36	C₅₃×#552	—	2	2	no	—
37	C₅₃×#552	C₂²	1	2	yes	—
38	C₅₃×#550	C₂²	1	1	yes	characteristic
39	C₅₃×#548	C₂²	1	2	yes	—
40	C₅₃×#547	—	2	1	no	—
41	C₅₃×#547	C₂²	1	1	yes	characteristic
42	C₅₃×#541	—	2	1	no	—
43	C₅₃×#539	—	2	2	no	—
44	C₅₃×#533	C₂²	1	1	yes	characteristic
45	C₅₃×#532	—	2	1	no	—
46	C₅₃×#532	C₂²	1	1	yes	characteristic
47	C₅₃×#529	—	2	2	no	—
48	C₅₃×#529	C₂²	1	2	yes	—
49	C₅₃×#529	C₂²	1	1	yes	characteristic
50	C₅₃×#529	C₂²	1	2	yes	—
51	C₂×#125×C₅₃	C₂²	1	2	yes	—
52	C₅₃×#520	—	2	1	no	—
53	C₄×#41×C₅₃	—	2	1	no	—
54	C₄×#41×C₅₃	C₂²	1	2	yes	—
55	C₄×#41×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
57	C₅₃×#500	C₂²	1	1	yes	characteristic
58	C₅₃×#499	C₂²	1	2	yes	—
59	C₅₃×#499	C₂²	1	2	yes	—
60	C₅₃×#498	C₂²	1	1	yes	characteristic
61	C₅₃×#488	C₂²	1	2	yes	—
62	C₅₃×#488	C₂²	1	2	yes	—
63	C₅₃×#486	C₂²	1	1	yes	characteristic
64	C₅₃×#486	C₂²	1	1	yes	characteristic
65	C₅₃×#485	C₂²	1	2	yes	—
66	C₅₃×#484	C₂²	1	2	yes	—
67	C₅₃×#483	C₂²	1	2	yes	—
68	C₅₃×#483	C₂²	1	1	yes	characteristic
69	C₅₃×#482	C₂²	1	2	yes	—
70	C₅₃×#482	C₂²	1	2	yes	—
71	C₅₃×#482	C₂²	1	2	yes	—
72	C₅₃×#481	C₂²	1	2	yes	—
73	C₅₃×#480	C₂²	1	2	yes	—
74	C₅₃×#480	C₂²	1	1	yes	characteristic
75	C₅₃×#479	C₂²	1	1	yes	characteristic
76	C₅₃×#479	C₂²	1	2	yes	—
77	C₅₃×#479	C₂²	1	2	yes	—
78	C₅₃×#479	C₂²	1	2	yes	—
79	C₅₃×#479	C₂²	1	2	yes	—
80	C₅₃×#479	C₂²	1	2	yes	—
81	C₅₃×#479	C₂²	1	1	yes	characteristic
82	C₅₃×#478	C₂²	1	2	yes	—
83	C₅₃×#478	C₂²	1	2	yes	—
84	C₅₃×#478	C₂²	1	2	yes	—
85	C₅₃×#478	C₂²	1	2	yes	—
86	C₅₃×#478	C₂²	1	2	yes	—
87	C₅₃×#478	C₂²	1	2	yes	—
88	C₅₃×#477	C₂²	1	1	yes	characteristic
89	C₅₃×#477	C₂²	1	1	yes	characteristic
90	C₅₃×#475	C₂²	1	1	yes	characteristic
91	C₅₃×#475	C₂²	1	1	yes	characteristic
92	C₅₃×#475	C₂²	1	1	yes	characteristic
93	C₅₃×#474	C₂²	1	1	yes	characteristic
94	C₅₃×#470	C₂²	1	2	yes	—
95	C₅₃×#469	C₂²	1	2	yes	—
96	C₅₃×#469	C₂²	1	2	yes	—
97	C₅₃×#468	C₂²	1	2	yes	—
98	C₅₃×#468	C₂²	1	2	yes	—
99	C₅₃×#468	C₂²	1	2	yes	—
100	C₅₃×#464	C₂²	1	1	yes	characteristic
101	C₅₃×#464	C₂²	1	2	yes	—
102	C₅₃×#464	C₂²	1	1	yes	characteristic
103	C₅₃×#463	C₂²	1	2	yes	—
104	C₅₃×#463	C₂²	1	2	yes	—
105	C₅₃×#460	C₂²	1	1	yes	characteristic
106	C₅₃×#459	C₂²	1	1	yes	characteristic
107	C₅₃×#452	C₂²	1	2	yes	—
108	C₅₃×#451	C₂²	1	1	yes	characteristic
109	C₅₃×#449	C₂²	1	2	yes	—
110	C₅₃×#448	C₂²	1	1	yes	characteristic
111	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
112	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic
113	C₄×Q₁₆×C₅₃	C₂²	1	2	yes	—
114	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
115	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
116	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
117	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
118	C₄×SD₁₆×C₅₃	C₂²	1	2	yes	—
119	C₄×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
120	C₄×D₈×C₅₃	C₂²	1	2	yes	—
121	C₅₃×#436	C₂²	1	2	yes	—
122	C₅₃×#436	C₂²	1	2	yes	—
123	C₅₃×#436	C₂²	1	1	yes	characteristic
124	C₅₃×#436	C₂²	1	1	yes	characteristic
125	C₅₃×#431	C₂²	1	1	yes	characteristic
126	C₅₃×#431	C₂²	1	2	yes	—
127	C₅₃×#428	C₂²	1	2	yes	—
128	C₅₃×#428	C₂²	1	2	yes	—
129	C₅₃×#428	C₂²	1	2	yes	—
130	C₅₃×#423	C₂²	1	1	yes	characteristic
131	C₅₃×#423	C₂²	1	2	yes	—
132	C₅₃×#419	C₂²	1	2	yes	—
133	C₅₃×#417	C₂²	1	2	yes	—
134	C₅₃×#417	C₂²	1	2	yes	—
135	C₂×#41×C₅₃	—	2	1	no	—
136	C₂×#41×C₅₃	—	2	1	no	—
137	C₂×#41×C₅₃	D₄	1	1	yes	characteristic
138	C₂×#41×C₅₃	C₂³	1	2	yes	—
139	C₂²×Q₈×C₅₃	C₂³	1	1	yes	characteristic
140	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
141	C₂×Q₁₆×C₅₃	C₂³	1	1	yes	characteristic
142	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
143	C₂×SD₁₆×C₅₃	C₂³	1	1	yes	characteristic
144	C₂×SD₁₆×C₅₃	C₂³	1	2	yes	—
145	C₂×D₈×C₅₃	C₂³	1	2	yes	—
146	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
147	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
148	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
149	C₄⋊Q₈×C₅₃	—	2	1	no	—
150	C₄⋊Q₈×C₅₃	—	2	1	no	—
151	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
152	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
153	C₄⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
154	#127×C₅₃	—	2	1	no	—
155	#127×C₅₃	C₂³	1	1	yes	characteristic
156	#126×C₅₃	—	2	2	no	—
157	#126×C₅₃	—	2	2	no	—
158	#126×C₅₃	—	2	2	no	—
159	#126×C₅₃	—	2	2	no	—
160	#126×C₅₃	—	2	2	no	—
161	#126×C₅₃	—	2	1	no	—
162	#126×C₅₃	—	2	2	no	—
163	#125×C₅₃	—	2	2	no	—
164	#125×C₅₃	—	2	2	no	—
165	#125×C₅₃	—	2	2	no	—
166	#125×C₅₃	—	2	1	no	—
167	#125×C₅₃	—	2	2	no	—
168	#125×C₅₃	—	2	2	no	—
169	#125×C₅₃	C₂³	1	2	yes	—
170	#125×C₅₃	C₂³	1	2	yes	—
171	#125×C₅₃	C₂³	1	2	yes	—
172	#125×C₅₃	C₂³	1	1	yes	characteristic
173	#125×C₅₃	C₂³	1	2	yes	—
174	#124×C₅₃	—	2	2	no	—
175	#124×C₅₃	—	2	1	no	—
176	#124×C₅₃	—	2	1	no	—
177	#124×C₅₃	—	2	1	no	—
178	#124×C₅₃	C₂³	1	2	yes	—
179	#124×C₅₃	C₂³	1	1	yes	characteristic
180	#123×C₅₃	—	2	2	no	—
181	#123×C₅₃	—	2	2	no	—
182	#123×C₅₃	—	2	2	no	—
183	#123×C₅₃	—	2	2	no	—
184	#123×C₅₃	—	2	2	no	—
185	#123×C₅₃	—	2	1	no	—
186	#123×C₅₃	—	2	2	no	—
187	#123×C₅₃	—	2	2	no	—
188	C₂²⋊Q₈×C₅₃	—	2	2	no	—
189	C₂²⋊Q₈×C₅₃	—	2	2	no	—
190	C₂²⋊Q₈×C₅₃	—	2	1	no	—
191	C₂²⋊Q₈×C₅₃	—	2	2	no	—
192	C₂²⋊Q₈×C₅₃	—	2	1	no	—
193	C₂²⋊Q₈×C₅₃	—	2	1	no	—
194	C₂²⋊Q₈×C₅₃	—	2	1	no	—
195	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₅₃	C₂³	1	2	yes	—
197	C₂²⋊Q₈×C₅₃	C₂³	1	1	yes	characteristic
198	#121×C₅₃	—	2	2	no	—
199	#121×C₅₃	—	2	2	no	—
200	#121×C₅₃	—	2	2	no	—
201	#121×C₅₃	—	2	2	no	—
202	#121×C₅₃	—	2	1	no	—
203	#121×C₅₃	C₂³	1	2	yes	—
204	#121×C₅₃	C₂³	1	2	yes	—
205	#121×C₅₃	C₂³	1	1	yes	characteristic
206	#121×C₅₃	C₂³	1	2	yes	—
207	C₄×Q₈×C₅₃	—	2	1	no	—
208	C₄×Q₈×C₅₃	—	2	1	no	—
209	C₄×Q₈×C₅₃	—	2	1	no	—
210	C₄×Q₈×C₅₃	—	2	1	no	—
211	C₄×Q₈×C₅₃	—	2	1	no	—
212	C₄×Q₈×C₅₃	—	2	1	no	—
213	C₄×Q₈×C₅₃	—	2	1	no	—
214	C₄×Q₈×C₅₃	D₄	1	1	yes	characteristic
215	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
216	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
217	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
218	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
219	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
220	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
221	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
222	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
223	C₄×D₄×C₅₃	—	2	1	no	—
224	C₄×D₄×C₅₃	—	2	1	no	—
225	C₄×D₄×C₅₃	—	2	2	no	—
226	C₄×D₄×C₅₃	—	2	2	no	—
227	C₄×D₄×C₅₃	—	2	2	no	—
228	C₄×D₄×C₅₃	—	2	1	no	—
229	C₄×D₄×C₅₃	—	2	1	no	—
230	C₄×D₄×C₅₃	—	2	2	no	—
231	C₄×D₄×C₅₃	—	2	2	no	—
232	C₄×D₄×C₅₃	—	2	2	no	—
233	C₄×D₄×C₅₃	—	2	2	no	—
234	C₄×D₄×C₅₃	—	2	1	no	—
235	C₄×D₄×C₅₃	D₄	1	1	yes	characteristic
236	C₄×D₄×C₅₃	D₄	1	2	yes	—
237	C₄×D₄×C₅₃	C₂³	1	2	yes	—
238	C₄×D₄×C₅₃	C₂³	1	2	yes	—
239	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₅₃	C₂³	1	2	yes	—
241	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
242	C₄×D₄×C₅₃	C₂³	1	2	yes	—
243	#117×C₅₃	—	2	2	no	—
244	#117×C₅₃	—	2	2	no	—
245	#117×C₅₃	—	2	2	no	—
246	#117×C₅₃	—	2	1	no	—
247	#117×C₅₃	—	2	2	no	—
248	#117×C₅₃	D₄	1	1	yes	characteristic
249	#117×C₅₃	D₄	1	2	yes	—
250	#117×C₅₃	C₂³	1	2	yes	—
251	#117×C₅₃	C₂³	1	2	yes	—
252	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
253	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
254	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
255	C₂×C₄⋊C₄×C₅₃	—	2	2	no	—
256	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
257	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₅₃	C₂³	1	2	yes	—
259	C₂×C₄²×C₅₃	—	2	2	no	—
260	C₂×C₄²×C₅₃	—	2	1	no	—
261	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
262	C₂×C₄²×C₅₃	C₂³	1	2	yes	—
263	#107×C₅₃	C₂³	1	2	yes	—
264	#107×C₅₃	C₂³	1	1	yes	characteristic
265	#107×C₅₃	C₂³	1	2	yes	—
266	#107×C₅₃	C₂³	1	2	yes	—
267	#107×C₅₃	C₂³	1	2	yes	—
268	#107×C₅₃	C₂³	1	2	yes	—
269	#107×C₅₃	C₂³	1	1	yes	characteristic
270	#106×C₅₃	C₂³	1	2	yes	—
271	#106×C₅₃	C₂³	1	2	yes	—
272	#106×C₅₃	C₂³	1	1	yes	characteristic
273	#106×C₅₃	C₂³	1	2	yes	—
274	#106×C₅₃	C₂³	1	2	yes	—
275	#106×C₅₃	C₂³	1	2	yes	—
276	#106×C₅₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
278	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
281	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
282	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
283	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
284	#103×C₅₃	C₂³	1	1	yes	characteristic
285	#103×C₅₃	C₂³	1	2	yes	—
286	#103×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	1	yes	characteristic
291	#103×C₅₃	C₂³	1	1	yes	characteristic
292	#103×C₅₃	C₂³	1	2	yes	—
293	#103×C₅₃	C₂³	1	2	yes	—
294	#103×C₅₃	C₂³	1	1	yes	characteristic
295	#102×C₅₃	C₂³	1	2	yes	—
296	#102×C₅₃	C₂³	1	2	yes	—
297	#102×C₅₃	C₂³	1	2	yes	—
298	#102×C₅₃	C₂³	1	2	yes	—
299	#102×C₅₃	C₂³	1	2	yes	—
300	#102×C₅₃	C₂³	1	2	yes	—
301	#102×C₅₃	C₂³	1	1	yes	characteristic
302	#102×C₅₃	C₂³	1	2	yes	—
303	#102×C₅₃	C₂³	1	1	yes	characteristic
304	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
305	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
306	C₂²⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
307	C₂²⋊C₈×C₅₃	C₂³	1	2	yes	—
308	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
309	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₅₃	C₂³	1	2	yes	—
311	C₄×C₈×C₅₃	C₂³	1	2	yes	—
312	#41×C₅₃	—	2	4	no	—
313	#41×C₅₃	—	4	2	no	—
314	#41×C₅₃	—	4	2	no	—
315	#41×C₅₃	—	4	4	no	—
316	#41×C₅₃	—	4	4	no	—
317	C₂×Q₈×C₅₃	—	2	1	no	—
318	C₂×Q₈×C₅₃	—	2	1	no	—
319	C₂×Q₈×C₅₃	—	2	1	no	—
320	C₂×Q₈×C₅₃	—	2	1	no	—
321	C₂×Q₈×C₅₃	—	2	2	no	—
322	C₂×Q₈×C₅₃	—	4	1	no	—
323	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₅₃	—	2	2	no	—
328	C₂×D₄×C₅₃	—	2	2	no	—
329	C₂×D₄×C₅₃	—	2	2	no	—
330	C₂×D₄×C₅₃	—	2	1	no	—
331	C₂×D₄×C₅₃	—	2	2	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	1	no	—
334	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
335	C₂×D₄×C₅₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
337	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₅₃	—	2	1	no	—
339	C₂²×C₄×C₅₃	—	2	2	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	—	2	2	no	—
342	C₂²×C₄×C₅₃	—	2	2	no	—
343	C₂²×C₄×C₅₃	—	2	2	no	—
344	C₂²×C₄×C₅₃	—	2	1	no	—
345	C₂²×C₄×C₅₃	—	2	2	no	—
346	C₂²×C₄×C₅₃	—	2	2	no	—
347	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
348	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
349	C₂²×C₄×C₅₃	C₂×D₄	1	2	yes	—
350	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
352	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
353	Q₁₆×C₅₃	—	2	2	no	—
354	Q₁₆×C₅₃	—	4	1	no	—
355	SD₁₆×C₅₃	—	2	2	no	—
356	SD₁₆×C₅₃	—	4	2	no	—
357	SD₁₆×C₅₃	—	4	1	no	—
358	D₈×C₅₃	—	4	2	no	—
359	M₁₆×C₅₃	—	4	2	no	—
360	M₁₆×C₅₃	—	4	2	no	—
361	M₁₆×C₅₃	—	4	2	no	—
362	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
367	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₅₃	—	2	2	no	—
369	C₄⋊C₄×C₅₃	—	2	1	no	—
370	C₄⋊C₄×C₅₃	—	2	1	no	—
371	C₄⋊C₄×C₅₃	—	2	1	no	—
372	C₄⋊C₄×C₅₃	—	2	2	no	—
373	C₄⋊C₄×C₅₃	—	2	1	no	—
374	C₄⋊C₄×C₅₃	—	2	2	no	—
375	C₄⋊C₄×C₅₃	—	2	2	no	—
376	C₄⋊C₄×C₅₃	—	2	1	no	—
377	C₄⋊C₄×C₅₃	—	2	1	no	—
378	C₄⋊C₄×C₅₃	—	2	1	no	—
379	C₄⋊C₄×C₅₃	—	2	2	no	—
380	C₄⋊C₄×C₅₃	—	2	2	no	—
381	C₄⋊C₄×C₅₃	—	2	1	no	—
382	C₄⋊C₄×C₅₃	—	2	2	no	—
383	C₄⋊C₄×C₅₃	—	2	2	no	—
384	C₄⋊C₄×C₅₃	—	2	1	no	—
385	C₄⋊C₄×C₅₃	—	2	2	no	—
386	C₄⋊C₄×C₅₃	—	2	2	no	—
387	C₄⋊C₄×C₅₃	—	2	2	no	—
388	C₄⋊C₄×C₅₃	—	2	2	no	—
389	C₄⋊C₄×C₅₃	—	2	1	no	—
390	C₄⋊C₄×C₅₃	—	2	2	no	—
391	C₄⋊C₄×C₅₃	—	2	1	no	—
392	C₄⋊C₄×C₅₃	—	2	1	no	—
393	C₄⋊C₄×C₅₃	—	2	2	no	—
394	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
398	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
400	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
401	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
402	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
405	C₂²⋊C₄×C₅₃	—	2	2	no	—
406	C₂²⋊C₄×C₅₃	—	2	2	no	—
407	C₂²⋊C₄×C₅₃	—	2	2	no	—
408	C₂²⋊C₄×C₅₃	—	2	2	no	—
409	C₂²⋊C₄×C₅₃	—	2	1	no	—
410	C₂²⋊C₄×C₅₃	—	2	1	no	—
411	C₂²⋊C₄×C₅₃	—	2	2	no	—
412	C₂²⋊C₄×C₅₃	—	2	1	no	—
413	C₂²⋊C₄×C₅₃	—	2	2	no	—
414	C₂²⋊C₄×C₅₃	—	2	1	no	—
415	C₂²⋊C₄×C₅₃	—	2	2	no	—
416	C₂²⋊C₄×C₅₃	—	2	2	no	—
417	C₂²⋊C₄×C₅₃	—	2	2	no	—
418	C₂²⋊C₄×C₅₃	—	2	2	no	—
419	C₂²⋊C₄×C₅₃	—	2	2	no	—
420	C₂²⋊C₄×C₅₃	—	2	2	no	—
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	—	2	1	no	—
427	C₄²×C₅₃	—	2	2	no	—
428	C₄²×C₅₃	—	2	2	no	—
429	C₄²×C₅₃	—	2	1	no	—
430	C₄²×C₅₃	—	2	1	no	—
431	C₄²×C₅₃	—	2	2	no	—
432	C₄²×C₅₃	—	2	2	no	—
433	C₄²×C₅₃	—	2	1	no	—
434	C₄²×C₅₃	C₂×D₄	1	2	yes	—
435	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₅₃	C₂×D₄	1	2	yes	—
437	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₅₃	C₂⁴	1	2	yes	—
439	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
440	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
441	C₂³×C₅₃	—	2	2	no	—
442	C₂³×C₅₃	—	2	1	no	—
443	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
444	C₂³×C₅₃	C₂²×D₄	1	2	yes	—
445	Q₈×C₅₃	—	2	2	no	—
446	Q₈×C₅₃	—	2	1	no	—
447	Q₈×C₅₃	—	2	1	no	—
448	Q₈×C₅₃	—	2	1	no	—
449	Q₈×C₅₃	—	2	1	no	—
450	Q₈×C₅₃	—	2	1	no	—
451	Q₈×C₅₃	—	4	2	no	—
452	Q₈×C₅₃	—	4	2	no	—
453	Q₈×C₅₃	—	4	2	no	—
454	Q₈×C₅₃	—	8	1	no	—
455	Q₈×C₅₃	2₋¹⁺⁴	1	2	yes	—
456	D₄×C₅₃	—	2	2	no	—
457	D₄×C₅₃	—	2	2	no	—
458	D₄×C₅₃	—	2	1	no	—
459	D₄×C₅₃	—	2	2	no	—
460	D₄×C₅₃	—	2	1	no	—
461	D₄×C₅₃	—	4	2	no	—
462	D₄×C₅₃	—	4	4	no	—
463	D₄×C₅₃	—	4	4	no	—
464	D₄×C₅₃	—	4	4	no	—
465	D₄×C₅₃	—	4	2	no	—
466	D₄×C₅₃	—	8	1	no	—
467	D₄×C₅₃	—	8	1	no	—
468	D₄×C₅₃	—	8	2	no	—
469	C₂×C₄×C₅₃	—	2	1	no	—
470	C₂×C₄×C₅₃	—	2	2	no	—
471	C₂×C₄×C₅₃	—	2	1	no	—
472	C₂×C₄×C₅₃	—	2	2	no	—
473	C₂×C₄×C₅₃	—	2	1	no	—
474	C₂×C₄×C₅₃	—	2	2	no	—
475	C₂×C₄×C₅₃	—	2	1	no	—
476	C₂×C₄×C₅₃	—	2	1	no	—
477	C₂×C₄×C₅₃	—	2	1	no	—
478	C₂×C₄×C₅₃	—	2	2	no	—
479	C₂×C₄×C₅₃	—	2	1	no	—
480	C₂×C₄×C₅₃	—	2	2	no	—
481	C₂×C₄×C₅₃	—	2	2	no	—
482	C₂×C₄×C₅₃	—	2	1	no	—
483	C₂×C₄×C₅₃	—	2	1	no	—
484	C₂×C₄×C₅₃	—	4	2	no	—
485	C₂×C₄×C₅₃	—	4	1	no	—
486	C₂×C₄×C₅₃	—	4	2	no	—
487	C₂×C₄×C₅₃	—	4	4	no	—
488	C₂×C₄×C₅₃	—	4	2	no	—
489	C₂×C₄×C₅₃	—	4	4	no	—
490	C₂×C₄×C₅₃	—	4	4	no	—
491	C₂×C₄×C₅₃	—	4	2	no	—
492	C₂×C₄×C₅₃	—	8	2	no	—
493	C₂×C₄×C₅₃	—	8	2	no	—
494	C₂×C₄×C₅₃	—	8	1	no	—
495	C₂×C₄×C₅₃	—	8	2	no	—
496	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
499	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
502	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
503	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
505	C₈×C₅₃	—	2	1	no	—
506	C₈×C₅₃	—	2	1	no	—
507	C₈×C₅₃	—	2	2	no	—
508	C₈×C₅₃	—	2	1	no	—
509	C₈×C₅₃	—	2	2	no	—
510	C₈×C₅₃	—	2	1	no	—
511	#62154	C₅₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
512	C₂²×C₅₃	—	2	1	no	—
513	C₂²×C₅₃	—	2	2	no	—
514	C₂²×C₅₃	—	2	1	no	—
515	C₂²×C₅₃	—	2	2	no	—
516	C₂²×C₅₃	—	2	1	no	—
517	C₂²×C₅₃	—	2	2	no	—
518	C₂²×C₅₃	—	4	1	no	—
519	C₂²×C₅₃	—	4	2	no	—
520	C₂²×C₅₃	—	4	2	no	—
521	C₂²×C₅₃	—	4	1	no	—
522	C₂²×C₅₃	—	4	2	no	—
523	C₂²×C₅₃	—	4	1	no	—
524	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
525	C₄×C₅₃	—	2	1	no	—
526	C₄×C₅₃	—	2	2	no	—
527	C₄×C₅₃	—	2	1	no	—
528	C₄×C₅₃	—	2	2	no	—
529	C₄×C₅₃	—	2	1	no	—
530	C₄×C₅₃	—	2	2	no	—
531	C₄×C₅₃	—	2	1	no	—
532	C₄×C₅₃	—	2	2	no	—
533	C₄×C₅₃	—	4	1	no	—
534	C₄×C₅₃	—	4	1	no	—
535	C₄×C₅₃	—	4	2	no	—
536	C₄×C₅₃	—	4	1	no	—
537	C₄×C₅₃	—	4	1	no	—
538	C₄×C₅₃	—	4	1	no	—
539	C₄×C₅₃	—	4	1	no	—
540	C₄×C₅₃	—	4	2	no	—
541	C₄×C₅₃	—	4	2	no	—
542	C₄×C₅₃	#575	1	2	yes	—
543	C₄×C₅₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
544	C₄×C₅₃	#585	1	1	yes	characteristic
545	#3515	C₂×C₅₃	1	1	yes	characteristic, complemented
546	#3480	C₂×C₅₃	1	1	yes	characteristic, complemented
547	#3383	C₂×C₅₃	1	1	yes	characteristic, complemented
548	#3381	C₂×C₅₃	1	1	yes	characteristic, complemented
549	#3365	C₂×C₅₃	1	1	yes	characteristic, complemented
550	#3361	C₂×C₅₃	1	1	yes	characteristic, complemented
551	#3356	C₂×C₅₃	1	1	yes	characteristic, complemented
552	#3355	C₂×C₅₃	1	2	yes	complemented
553	#3353	C₂×C₅₃	1	1	yes	characteristic, complemented
554	#3351	C₂×C₅₃	1	2	yes	complemented
555	#3333	C₂×C₅₃	1	1	yes	characteristic, complemented
556	#3332	C₂×C₅₃	1	1	yes	characteristic, complemented
557	#3327	C₂×C₅₃	1	2	yes	complemented
558	#3326	C₂×C₅₃	1	2	yes	complemented
559	#3256	C₂×C₅₃	1	2	yes	complemented
560	#3251	C₂×C₅₃	1	1	yes	characteristic, complemented
561	#3232	C₂×C₅₃	1	2	yes	complemented
562	#3228	C₂×C₅₃	1	1	yes	characteristic, complemented
563	#3108	C₂×C₅₃	1	1	yes	characteristic, complemented
564	#3102	C₂×C₅₃	1	2	yes	complemented
565	#3080	C₂×C₅₃	1	2	yes	complemented
566	#3078	C₂×C₅₃	1	1	yes	characteristic, complemented
567	#2991	C₂×C₅₃	1	1	yes	characteristic, complemented
568	C₂×C₅₃	—	4	1	no	—
569	C₂×C₅₃	—	4	2	no	—
570	C₂×C₅₃	—	8	1	no	—
571	C₂×C₅₃	—	8	2	no	—
572	C₂×C₅₃	#3489	1	1	yes	characteristic
573	C₂×C₅₃	C₂×#575	1	1	yes	characteristic
574	C₂×C₅₃	#3584	1	1	yes	characteristic
575	#559	—	2	1	no	—
576	#559	C₂²×C₅₃	1	1	yes	characteristic
577	#557	C₂²×C₅₃	1	1	yes	characteristic
578	#557	C₂²×C₅₃	1	1	yes	characteristic
579	#556	—	2	1	no	—
580	#556	C₂²×C₅₃	1	1	yes	characteristic
581	#554	C₂²×C₅₃	1	1	yes	characteristic
582	#554	C₂²×C₅₃	1	1	yes	characteristic
583	#553	—	2	2	no	—
584	#553	C₂²×C₅₃	1	2	yes	—
585	#553	C₂²×C₅₃	1	2	yes	—
586	#552	—	2	2	no	—
587	#552	—	2	1	no	—
588	#552	C₂²×C₅₃	1	2	yes	—
589	#550	C₂²×C₅₃	1	1	yes	characteristic
590	#548	C₂²×C₅₃	1	2	yes	—
591	#547	—	2	1	no	—
592	#547	C₂²×C₅₃	1	1	yes	characteristic
593	#541	—	2	1	no	—
594	#539	—	2	2	no	—
595	#533	C₂²×C₅₃	1	1	yes	characteristic
596	#532	—	2	1	no	—
597	#532	C₂²×C₅₃	1	1	yes	characteristic
598	#529	—	2	2	no	—
599	#529	C₂²×C₅₃	1	2	yes	—
600	#529	C₂²×C₅₃	1	1	yes	characteristic
601	#529	C₂²×C₅₃	1	2	yes	—
602	C₂×#125	C₂²×C₅₃	1	2	yes	—
603	#520	—	2	1	no	—
604	C₄×#41	—	2	1	no	—
605	C₄×#41	C₂²×C₅₃	1	2	yes	—
606	C₄×#41	C₂²×C₅₃	1	1	yes	characteristic
607	C₂×C₄×Q₈	C₂²×C₅₃	1	1	yes	characteristic
608	#500	C₂²×C₅₃	1	1	yes	characteristic
609	#499	C₂²×C₅₃	1	2	yes	—
610	#499	C₂²×C₅₃	1	2	yes	—
611	#498	C₂²×C₅₃	1	1	yes	characteristic
612	#488	C₂²×C₅₃	1	2	yes	—
613	#488	C₂²×C₅₃	1	2	yes	—
614	#486	C₂²×C₅₃	1	1	yes	characteristic
615	#486	C₂²×C₅₃	1	1	yes	characteristic
616	#485	C₂²×C₅₃	1	2	yes	—
617	#484	C₂²×C₅₃	1	2	yes	—
618	#483	C₂²×C₅₃	1	1	yes	characteristic
619	#483	C₂²×C₅₃	1	2	yes	—
620	#482	C₂²×C₅₃	1	2	yes	—
621	#482	C₂²×C₅₃	1	2	yes	—
622	#482	C₂²×C₅₃	1	2	yes	—
623	#481	C₂²×C₅₃	1	2	yes	—
624	#480	C₂²×C₅₃	1	2	yes	—
625	#480	C₂²×C₅₃	1	1	yes	characteristic
626	#479	C₂²×C₅₃	1	2	yes	—
627	#479	C₂²×C₅₃	1	2	yes	—
628	#479	C₂²×C₅₃	1	1	yes	characteristic
629	#479	C₂²×C₅₃	1	2	yes	—
630	#479	C₂²×C₅₃	1	2	yes	—
631	#479	C₂²×C₅₃	1	2	yes	—
632	#479	C₂²×C₅₃	1	1	yes	characteristic
633	#478	C₂²×C₅₃	1	2	yes	—
634	#478	C₂²×C₅₃	1	2	yes	—
635	#478	C₂²×C₅₃	1	2	yes	—
636	#478	C₂²×C₅₃	1	2	yes	—
637	#478	C₂²×C₅₃	1	2	yes	—
638	#478	C₂²×C₅₃	1	2	yes	—
639	#477	C₂²×C₅₃	1	1	yes	characteristic
640	#477	C₂²×C₅₃	1	1	yes	characteristic
641	#475	C₂²×C₅₃	1	1	yes	characteristic
642	#475	C₂²×C₅₃	1	1	yes	characteristic
643	#475	C₂²×C₅₃	1	1	yes	characteristic
644	#474	C₂²×C₅₃	1	1	yes	characteristic
645	#470	C₂²×C₅₃	1	2	yes	—
646	#469	C₂²×C₅₃	1	2	yes	—
647	#469	C₂²×C₅₃	1	2	yes	—
648	#468	C₂²×C₅₃	1	2	yes	—
649	#468	C₂²×C₅₃	1	2	yes	—
650	#468	C₂²×C₅₃	1	2	yes	—
651	#464	C₂²×C₅₃	1	1	yes	characteristic
652	#464	C₂²×C₅₃	1	1	yes	characteristic
653	#464	C₂²×C₅₃	1	2	yes	—
654	#463	C₂²×C₅₃	1	2	yes	—
655	#463	C₂²×C₅₃	1	2	yes	—
656	#460	C₂²×C₅₃	1	1	yes	characteristic
657	#459	C₂²×C₅₃	1	1	yes	characteristic
658	#452	C₂²×C₅₃	1	2	yes	—
659	#451	C₂²×C₅₃	1	1	yes	characteristic
660	#449	C₂²×C₅₃	1	2	yes	—
661	#448	C₂²×C₅₃	1	1	yes	characteristic
662	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
663	C₈×Q₈	C₂²×C₅₃	1	1	yes	characteristic
664	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
665	C₄×Q₁₆	C₂²×C₅₃	1	1	yes	characteristic
666	C₄×Q₁₆	C₂²×C₅₃	1	2	yes	—
667	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
668	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
669	C₄×SD₁₆	C₂²×C₅₃	1	1	yes	characteristic
670	C₄×SD₁₆	C₂²×C₅₃	1	2	yes	—
671	C₄×D₈	C₂²×C₅₃	1	2	yes	—
672	#436	C₂²×C₅₃	1	1	yes	characteristic
673	#436	C₂²×C₅₃	1	1	yes	characteristic
674	#436	C₂²×C₅₃	1	2	yes	—
675	#436	C₂²×C₅₃	1	2	yes	—
676	#431	C₂²×C₅₃	1	2	yes	—
677	#431	C₂²×C₅₃	1	1	yes	characteristic
678	#428	C₂²×C₅₃	1	2	yes	—
679	#428	C₂²×C₅₃	1	2	yes	—
680	#428	C₂²×C₅₃	1	2	yes	—
681	#423	C₂²×C₅₃	1	1	yes	characteristic
682	#423	C₂²×C₅₃	1	2	yes	—
683	#419	C₂²×C₅₃	1	2	yes	—
684	#417	C₂²×C₅₃	1	2	yes	—
685	#417	C₂²×C₅₃	1	2	yes	—
686	C₅₃	#62154	1	1	yes	characteristic, direct product factor, Sylow
687	C₂×#41	—	2	1	no	—
688	C₂×#41	—	2	1	no	—
689	C₂×#41	D₄×C₅₃	1	1	yes	characteristic
690	C₂×#41	C₂³×C₅₃	1	2	yes	—
691	C₂²×Q₈	C₂³×C₅₃	1	1	yes	characteristic
692	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
693	C₂×Q₁₆	C₂³×C₅₃	1	1	yes	characteristic
694	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
695	C₂×SD₁₆	C₂³×C₅₃	1	1	yes	characteristic
696	C₂×SD₁₆	C₂³×C₅₃	1	2	yes	—
697	C₂×D₈	C₂³×C₅₃	1	2	yes	—
698	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
699	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
700	C₂×M₁₆	C₂³×C₅₃	1	2	yes	—
701	C₄⋊Q₈	—	2	1	no	—
702	C₄⋊Q₈	—	2	1	no	—
703	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
705	C₄⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
706	#127	—	2	1	no	—
707	#127	C₂³×C₅₃	1	1	yes	characteristic
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	1	no	—
714	#126	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	—	2	2	no	—
720	#125	—	2	2	no	—
721	#125	C₂³×C₅₃	1	1	yes	characteristic
722	#125	C₂³×C₅₃	1	2	yes	—
723	#125	C₂³×C₅₃	1	2	yes	—
724	#125	C₂³×C₅₃	1	2	yes	—
725	#125	C₂³×C₅₃	1	2	yes	—
726	#124	—	2	1	no	—
727	#124	—	2	1	no	—
728	#124	—	2	2	no	—
729	#124	—	2	1	no	—
730	#124	C₂³×C₅₃	1	1	yes	characteristic
731	#124	C₂³×C₅₃	1	2	yes	—
732	#123	—	2	2	no	—
733	#123	—	2	1	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	—	2	2	no	—
738	#123	—	2	2	no	—
739	#123	—	2	2	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	1	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	1	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
748	C₂²⋊Q₈	C₂³×C₅₃	1	1	yes	characteristic
749	C₂²⋊Q₈	C₂³×C₅₃	1	2	yes	—
750	#121	—	2	2	no	—
751	#121	—	2	2	no	—
752	#121	—	2	2	no	—
753	#121	—	2	1	no	—
754	#121	—	2	2	no	—
755	#121	C₂³×C₅₃	1	2	yes	—
756	#121	C₂³×C₅₃	1	2	yes	—
757	#121	C₂³×C₅₃	1	1	yes	characteristic
758	#121	C₂³×C₅₃	1	2	yes	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	D₄×C₅₃	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
772	C₄×Q₈	C₂³×C₅₃	1	2	yes	—
773	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₅₃	1	1	yes	characteristic
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	2	no	—
779	C₄×D₄	—	2	2	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	D₄×C₅₃	1	1	yes	characteristic
788	C₄×D₄	D₄×C₅₃	1	2	yes	—
789	C₄×D₄	C₂³×C₅₃	1	2	yes	—
790	C₄×D₄	C₂³×C₅₃	1	2	yes	—
791	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
792	C₄×D₄	C₂³×C₅₃	1	2	yes	—
793	C₄×D₄	C₂³×C₅₃	1	1	yes	characteristic
794	C₄×D₄	C₂³×C₅₃	1	2	yes	—
795	#117	—	2	2	no	—
796	#117	—	2	2	no	—
797	#117	—	2	2	no	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	D₄×C₅₃	1	1	yes	characteristic
801	#117	D₄×C₅₃	1	2	yes	—
802	#117	C₂³×C₅₃	1	2	yes	—
803	#117	C₂³×C₅₃	1	2	yes	—
804	C₂×C₄⋊C₄	—	2	1	no	—
805	C₂×C₄⋊C₄	—	2	2	no	—
806	C₂×C₄⋊C₄	—	2	2	no	—
807	C₂×C₄⋊C₄	—	2	1	no	—
808	C₂×C₄⋊C₄	C₂³×C₅₃	1	1	yes	characteristic
809	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₅₃	1	2	yes	—
811	C₂×C₄²	—	2	1	no	—
812	C₂×C₄²	—	2	2	no	—
813	C₂×C₄²	C₂³×C₅₃	1	1	yes	characteristic
814	C₂×C₄²	C₂³×C₅₃	1	2	yes	—
815	#107	C₂³×C₅₃	1	2	yes	—
816	#107	C₂³×C₅₃	1	1	yes	characteristic
817	#107	C₂³×C₅₃	1	2	yes	—
818	#107	C₂³×C₅₃	1	2	yes	—
819	#107	C₂³×C₅₃	1	2	yes	—
820	#107	C₂³×C₅₃	1	2	yes	—
821	#107	C₂³×C₅₃	1	1	yes	characteristic
822	#106	C₂³×C₅₃	1	2	yes	—
823	#106	C₂³×C₅₃	1	1	yes	characteristic
824	#106	C₂³×C₅₃	1	2	yes	—
825	#106	C₂³×C₅₃	1	2	yes	—
826	#106	C₂³×C₅₃	1	2	yes	—
827	#106	C₂³×C₅₃	1	2	yes	—
828	#106	C₂³×C₅₃	1	1	yes	characteristic
829	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
830	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
831	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
832	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
833	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
834	C₄⋊C₈	C₂³×C₅₃	1	2	yes	—
835	C₄⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
836	#103	C₂³×C₅₃	1	1	yes	characteristic
837	#103	C₂³×C₅₃	1	1	yes	characteristic
838	#103	C₂³×C₅₃	1	2	yes	—
839	#103	C₂³×C₅₃	1	2	yes	—
840	#103	C₂³×C₅₃	1	2	yes	—
841	#103	C₂³×C₅₃	1	2	yes	—
842	#103	C₂³×C₅₃	1	1	yes	characteristic
843	#103	C₂³×C₅₃	1	1	yes	characteristic
844	#103	C₂³×C₅₃	1	1	yes	characteristic
845	#103	C₂³×C₅₃	1	2	yes	—
846	#103	C₂³×C₅₃	1	1	yes	characteristic
847	#102	C₂³×C₅₃	1	2	yes	—
848	#102	C₂³×C₅₃	1	2	yes	—
849	#102	C₂³×C₅₃	1	2	yes	—
850	#102	C₂³×C₅₃	1	2	yes	—
851	#102	C₂³×C₅₃	1	1	yes	characteristic
852	#102	C₂³×C₅₃	1	2	yes	—
853	#102	C₂³×C₅₃	1	2	yes	—
854	#102	C₂³×C₅₃	1	2	yes	—
855	#102	C₂³×C₅₃	1	1	yes	characteristic
856	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
857	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
858	C₂²⋊C₈	C₂³×C₅₃	1	1	yes	characteristic
859	C₂²⋊C₈	C₂³×C₅₃	1	2	yes	—
860	C₄×C₈	C₂³×C₅₃	1	2	yes	—
861	C₄×C₈	C₂³×C₅₃	1	2	yes	—
862	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
863	C₄×C₈	C₂³×C₅₃	1	1	yes	characteristic
864	#41	—	2	4	no	—
865	#41	—	4	2	no	—
866	#41	—	4	2	no	—
867	#41	—	4	4	no	—
868	#41	—	4	4	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	1	no	—
873	C₂×Q₈	—	2	2	no	—
874	C₂×Q₈	—	4	1	no	—
875	C₂×Q₈	C₂×D₄×C₅₃	1	1	yes	characteristic
876	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
877	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
878	C₂×Q₈	C₂⁴×C₅₃	1	1	yes	characteristic
879	C₂×D₄	—	2	2	no	—
880	C₂×D₄	—	2	2	no	—
881	C₂×D₄	—	2	2	no	—
882	C₂×D₄	—	2	1	no	—
883	C₂×D₄	—	2	2	no	—
884	C₂×D₄	—	2	1	no	—
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	C₂×D₄×C₅₃	1	1	yes	characteristic
887	C₂×D₄	C₂×D₄×C₅₃	1	2	yes	—
888	C₂×D₄	C₂⁴×C₅₃	1	2	yes	—
889	C₂×D₄	C₂⁴×C₅₃	1	1	yes	characteristic
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	2	2	no	—
892	C₂²×C₄	—	2	1	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	2	2	no	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	2	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
900	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
901	C₂²×C₄	C₂×D₄×C₅₃	1	2	yes	—
902	C₂²×C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
903	C₂²×C₄	C₂⁴×C₅₃	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₅₃	1	1	yes	characteristic
905	Q₁₆	—	2	2	no	—
906	Q₁₆	—	4	1	no	—
907	SD₁₆	—	2	2	no	—
908	SD₁₆	—	4	1	no	—
909	SD₁₆	—	4	2	no	—
910	D₈	—	4	2	no	—
911	M₁₆	—	4	2	no	—
912	M₁₆	—	4	2	no	—
913	M₁₆	—	4	2	no	—
914	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
915	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
916	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
917	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
918	C₂×C₈	C₂⁴×C₅₃	1	1	yes	characteristic
919	C₂×C₈	C₂⁴×C₅₃	1	2	yes	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂×D₄×C₅₃	1	1	yes	characteristic
948	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
949	C₄⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
950	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
953	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
954	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
955	C₄⋊C₄	C₂⁴×C₅₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂⁴×C₅₃	1	2	yes	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	1	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	2	2	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
975	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
976	C₂²⋊C₄	C₂×D₄×C₅₃	1	2	yes	—
977	C₄²	—	2	1	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	1	no	—
982	C₄²	—	2	1	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	2	no	—
985	C₄²	—	2	1	no	—
986	C₄²	C₂×D₄×C₅₃	1	2	yes	—
987	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
988	C₄²	C₂×D₄×C₅₃	1	2	yes	—
989	C₄²	C₂×D₄×C₅₃	1	1	yes	characteristic
990	C₄²	C₂⁴×C₅₃	1	2	yes	—
991	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
992	C₄²	C₂⁴×C₅₃	1	1	yes	characteristic
993	C₂³	—	2	1	no	—
994	C₂³	—	2	2	no	—
995	C₂³	C₂²×D₄×C₅₃	1	1	yes	characteristic
996	C₂³	C₂²×D₄×C₅₃	1	2	yes	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	1	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	1	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	4	2	no	—
1006	Q₈	—	8	1	no	—
1007	Q₈	2₋¹⁺⁴×C₅₃	1	2	yes	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	2	1	no	—
1012	D₄	—	2	2	no	—
1013	D₄	—	4	2	no	—
1014	D₄	—	4	4	no	—
1015	D₄	—	4	4	no	—
1016	D₄	—	4	4	no	—
1017	D₄	—	4	2	no	—
1018	D₄	—	8	1	no	—
1019	D₄	—	8	1	no	—
1020	D₄	—	8	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	1	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	4	no	—
1040	C₂×C₄	—	4	2	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	8	2	no	—
1045	C₂×C₄	—	8	2	no	—
1046	C₂×C₄	—	8	1	no	—
1047	C₂×C₄	—	8	2	no	—
1048	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1051	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1052	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₄×C₅₃	1	2	yes	—
1054	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1055	C₂×C₄	C₂²×D₄×C₅₃	1	1	yes	characteristic
1056	C₂×C₄	C₂⁵×C₅₃	1	1	yes	characteristic
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	2	no	—
1060	C₈	—	2	2	no	—
1061	C₈	—	2	1	no	—
1062	C₈	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	1	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	1	no	—
1073	C₂²	—	4	1	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	C₂³×D₄×C₅₃	1	1	yes	characteristic
1076	C₄	—	2	2	no	—
1077	C₄	—	2	1	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	2	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	2	2	no	—
1083	C₄	—	2	1	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	1	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	2	no	—
1088	C₄	—	4	2	no	—
1089	C₄	—	4	1	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	4	1	no	—
1093	C₄	C₅₃×#575	1	2	yes	—
1094	C₄	C₂×2₋¹⁺⁴×C₅₃	1	1	yes	characteristic
1095	C₄	C₅₃×#585	1	1	yes	characteristic
1096	C₂	—	4	1	no	—
1097	C₂	—	4	2	no	—
1098	C₂	—	8	2	no	—
1099	C₂	—	8	1	no	—
1100	C₂	C₅₃×#3489	1	1	yes	characteristic
1101	C₂	C₂×C₅₃×#575	1	1	yes	characteristic
1102	C₂	C₅₃×#3584	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 ◁ C₄×#41×C₅₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅₃×#3515	C₂	semidirect
2. C₅₃×#3480	C₂	semidirect
3. C₅₃×#3383	C₂	semidirect
4. C₅₃×#3381	C₂	semidirect
5. C₅₃×#3365	C₂	semidirect
6. C₅₃×#3361	C₂	semidirect
7. C₅₃×#3356	C₂	semidirect
8. C₅₃×#3355	C₂	semidirect
9. C₅₃×#3353	C₂	semidirect
10. C₅₃×#3351	C₂	semidirect
11. C₅₃×#3333	C₂	semidirect
12. C₅₃×#3332	C₂	semidirect
13. C₅₃×#3327	C₂	semidirect
14. C₅₃×#3326	C₂	semidirect
15. C₅₃×#3256	C₂	semidirect
16. C₅₃×#3251	C₂	semidirect
17. C₅₃×#3232	C₂	semidirect
18. C₅₃×#3228	C₂	semidirect
19. C₅₃×#3108	C₂	semidirect
20. C₅₃×#3102	C₂	semidirect
21. C₅₃×#3080	C₂	semidirect
22. C₅₃×#3078	C₂	semidirect
23. C₅₃×#2991	C₂	semidirect
511. #62154	C₅₃	direct (N × H)
545. #3515	C₂×C₅₃	semidirect
546. #3480	C₂×C₅₃	semidirect
547. #3383	C₂×C₅₃	semidirect
548. #3381	C₂×C₅₃	semidirect
549. #3365	C₂×C₅₃	semidirect
550. #3361	C₂×C₅₃	semidirect
551. #3356	C₂×C₅₃	semidirect
552. #3355	C₂×C₅₃	semidirect
553. #3353	C₂×C₅₃	semidirect
554. #3351	C₂×C₅₃	semidirect
555. #3333	C₂×C₅₃	semidirect
556. #3332	C₂×C₅₃	semidirect
557. #3327	C₂×C₅₃	semidirect
558. #3326	C₂×C₅₃	semidirect
559. #3256	C₂×C₅₃	semidirect
560. #3251	C₂×C₅₃	semidirect
561. #3232	C₂×C₅₃	semidirect
562. #3228	C₂×C₅₃	semidirect
563. #3108	C₂×C₅₃	semidirect
564. #3102	C₂×C₅₃	semidirect
565. #3080	C₂×C₅₃	semidirect
566. #3078	C₂×C₅₃	semidirect
567. #2991	C₂×C₅₃	semidirect
686. C₅₃	#62154	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×#3515	2
C₅₃×#3480	2
C₅₃×#3383	2
C₅₃×#3381	2
C₅₃×#3365	2
C₅₃×#3361	2
C₅₃×#3356	2
C₅₃×#3355	2
C₅₃×#3353	2
C₅₃×#3351	2
C₅₃×#3333	2
C₅₃×#3332	2
C₅₃×#3327	2
C₅₃×#3326	2
C₅₃×#3256	2
C₅₃×#3251	2
C₅₃×#3232	2
C₅₃×#3228	2
C₅₃×#3108	2
C₅₃×#3102	2
C₅₃×#3080	2
C₅₃×#3078	2
C₅₃×#2991	2
#62154	53

Subgroups — C53×#62154 #27269666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₃×#62154 #27269666