Subgroups — D₅₃×#3136 #28253322

Order 13568.

2262 conjugacy classes of subgroups.

The subgroup lattice has 1274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#544×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#535×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20285074	C₂	1	1	yes	maximal, characteristic, complemented
4	#20285073	C₂	1	1	yes	maximal, characteristic, complemented
5	#20285072	C₂	1	1	yes	maximal, characteristic, complemented
6	#20285071	C₂	1	1	yes	maximal, characteristic, complemented
7	#20285070	C₂	1	2	yes	maximal, complemented
8	#20285069	C₂	1	1	yes	maximal, characteristic, complemented
9	#20285068	C₂	1	2	yes	maximal, complemented
10	#20285067	C₂	1	1	yes	maximal, characteristic, complemented
11	#20285066	C₂	1	2	yes	maximal, complemented
12	#20285065	C₂	1	1	yes	maximal, characteristic, complemented
13	#20285064	C₂	1	2	yes	maximal, complemented
14	#490×D₅₃	C₂	1	2	yes	maximal, complemented
15	#489×D₅₃	C₂	1	2	yes	maximal, complemented
16	#488×D₅₃	C₂	1	2	yes	maximal, complemented
17	#486×D₅₃	C₂	1	2	yes	maximal, complemented
18	#417×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#418×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#416×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#102×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#405×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₅₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×D₅₃	C₂²	1	1	yes	characteristic
25	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
26	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	#16811254	C₂²	1	1	yes	characteristic, complemented
29	#16811253	—	2	1	no	—
30	#16811253	C₂²	1	2	yes	complemented
31	#16811252	—	2	2	no	—
32	#16811251	C₂²	1	1	yes	characteristic, complemented
33	#16811251	C₂²	1	1	yes	characteristic, complemented
34	#16811250	—	2	1	no	—
35	#16811250	C₂²	1	2	yes	complemented
36	#16811192	C₂²	1	1	yes	characteristic
37	#16811191	C₂²	1	2	yes	—
38	#16811190	C₂²	1	1	yes	characteristic
39	#16811189	—	2	1	no	—
40	#16811189	—	2	1	no	—
41	#16811188	—	2	2	no	—
42	#16811187	C₂²	1	1	yes	characteristic
43	#16811186	C₂²	1	2	yes	—
44	C₄⋊Q₈×D₅₃	—	2	1	no	—
45	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
46	#127×D₅₃	C₂²	1	2	yes	—
47	#125×D₅₃	—	2	1	no	—
48	#125×D₅₃	C₂²	1	2	yes	complemented
49	#124×D₅₃	C₂²	1	2	yes	—
50	C₂²⋊Q₈×D₅₃	—	2	2	no	—
51	#121×D₅₃	—	2	1	no	—
52	#121×D₅₃	—	2	1	no	—
53	#120×D₅₃	—	2	2	no	—
54	#117×D₅₃	C₂²	1	1	yes	characteristic
55	#117×D₅₃	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
57	#16810989	C₂²	1	2	yes	complemented
58	#16810988	C₂²	1	2	yes	complemented
59	#16810987	C₂²	1	2	yes	complemented
60	#16810986	C₂²	1	2	yes	complemented
61	#16810986	C₂²	1	2	yes	complemented
62	#16810986	C₂²	1	2	yes	complemented
63	#16810986	C₂²	1	2	yes	complemented
64	#16810985	C₂²	1	2	yes	complemented
65	#16810984	C₂²	1	2	yes	complemented
66	#16810984	C₂²	1	2	yes	complemented
67	#16810983	C₂²	1	2	yes	complemented
68	#16810982	C₂²	1	2	yes	complemented
69	#16810981	C₂²	1	2	yes	complemented
70	#16810981	C₂²	1	2	yes	complemented
71	#16810980	C₂²	1	2	yes	complemented
72	#16810979	C₂²	1	2	yes	complemented
73	#16810979	C₂²	1	2	yes	complemented
74	#16810978	C₂²	1	2	yes	complemented
75	#16810977	C₂²	1	2	yes	complemented
76	#16810976	C₂²	1	2	yes	complemented
77	#16810976	C₂²	1	2	yes	complemented
78	#16810971	C₂²	1	2	yes	complemented
79	#16810970	C₂²	1	2	yes	complemented
80	#16810969	C₂²	1	2	yes	complemented
81	#16810968	C₂²	1	2	yes	complemented
82	#16810968	C₂²	1	2	yes	complemented
83	#16810968	C₂²	1	2	yes	complemented
84	#16810968	C₂²	1	2	yes	complemented
85	#16810629	C₂²	1	1	yes	characteristic, complemented
86	#16810628	C₂²	1	1	yes	characteristic, complemented
87	#16810627	C₂²	1	1	yes	characteristic, complemented
88	#16810626	C₂²	1	2	yes	complemented
89	#16810626	C₂²	1	2	yes	complemented
90	#16810625	C₂²	1	1	yes	characteristic, complemented
91	#16810624	C₂²	1	1	yes	characteristic, complemented
92	#16810623	C₂²	1	2	yes	complemented
93	#16810622	C₂²	1	1	yes	characteristic, complemented
94	#16810621	C₂²	1	2	yes	complemented
95	#16810620	C₂²	1	1	yes	characteristic, complemented
96	#16810619	C₂²	1	1	yes	characteristic, complemented
97	#16810618	C₂²	1	1	yes	characteristic, complemented
98	#16810618	C₂²	1	1	yes	characteristic, complemented
99	#16810617	C₂²	1	1	yes	characteristic, complemented
100	#16810616	C₂²	1	1	yes	characteristic, complemented
101	#16810616	C₂²	1	1	yes	characteristic, complemented
102	#103×D₅₃	C₂²	1	1	yes	characteristic, complemented
103	#103×D₅₃	C₂²	1	1	yes	characteristic, complemented
104	#103×D₅₃	C₂²	1	2	yes	complemented
105	C₂×#13133139	C₂²	1	1	yes	characteristic, complemented
106	C₂×#13133138	C₂²	1	1	yes	characteristic, complemented
107	C₂×#13133137	C₂²	1	1	yes	characteristic, complemented
108	#102×D₅₃	C₂²	1	2	yes	—
109	#102×D₅₃	C₂²	1	2	yes	—
110	#102×D₅₃	C₂²	1	2	yes	—
111	#102×D₅₃	C₂²	1	2	yes	—
112	#102×D₅₃	C₂²	1	2	yes	complemented
113	#102×D₅₃	C₂²	1	2	yes	complemented
114	#102×D₅₃	C₂²	1	1	yes	characteristic, complemented
115	#102×D₅₃	C₂²	1	1	yes	characteristic, complemented
116	#102×D₅₃	C₂²	1	2	yes	complemented
117	#16810581	C₂²	1	1	yes	characteristic, complemented
118	#16810580	C₂²	1	2	yes	complemented
119	#16810579	C₂²	1	1	yes	characteristic, complemented
120	#16810578	C₂²	1	1	yes	characteristic, complemented
121	#16810577	C₂²	1	2	yes	complemented
122	#97×D₅₃	C₂²	1	2	yes	complemented
123	C₄×C₈×D₅₃	C₂²	1	2	yes	complemented
124	C₅₃×#544	C₂²	1	1	yes	characteristic, complemented
125	C₅₃×#535	C₂²	1	1	yes	characteristic
126	C₅₃×#490	C₂²	1	2	yes	complemented
127	C₅₃×#489	C₂²	1	2	yes	complemented
128	C₅₃×#488	C₂²	1	2	yes	complemented
129	C₅₃×#486	C₂²	1	2	yes	complemented
130	C₅₃×#418	C₂²	1	1	yes	characteristic, complemented
131	C₅₃×#417	C₂²	1	1	yes	characteristic, complemented
132	C₅₃×#416	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
134	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
135	C₂⁴×D₅₃	—	2	1	no	—
136	C₂×#11719949	C₂³	1	1	yes	characteristic
137	C₂×#11719945	—	2	1	no	—
138	C₂×#11719945	C₂³	1	1	yes	characteristic
139	C₂×#11719947	—	2	1	no	—
140	C₂×#11719947	C₂³	1	1	yes	characteristic
141	#41×D₅₃	—	2	4	no	—
142	#41×D₅₃	—	2	4	no	—
143	C₂×Q₈×D₅₃	—	2	2	no	—
144	C₂×Q₈×D₅₃	C₂³	1	1	yes	characteristic
145	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
146	C₂²×C₂²⋊D₅₃	—	2	1	no	—
147	C₂×D₄×D₅₃	—	2	1	no	—
148	C₂×D₄×D₅₃	—	2	1	no	—
149	C₂×D₄×D₅₃	—	2	1	no	—
150	C₂×D₄×D₅₃	—	2	2	no	—
151	C₂×D₄×D₅₃	—	2	2	no	—
152	C₂×D₄×D₅₃	—	2	4	no	—
153	C₂×D₄×D₅₃	—	2	4	no	—
154	C₂×D₄×D₅₃	C₂³	1	2	yes	—
155	C₂×D₄×D₅₃	C₂³	1	1	yes	characteristic
156	C₂×D₄×D₅₃	C₂³	1	2	yes	—
157	C₂²×C₄×D₅₃	—	2	1	no	—
158	C₂²×C₄×D₅₃	—	2	1	no	—
159	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
160	C₂×#11719917	C₂³	1	1	yes	characteristic
161	C₂×#11719912	C₂³	1	2	yes	—
162	M₁₆×D₅₃	—	2	4	no	—
163	C₂²×#88322	C₂³	1	1	yes	characteristic
164	C₂×C₈×D₅₃	—	2	4	no	—
165	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
166	C₂×C₈×D₅₃	C₂³	1	2	yes	—
167	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
168	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
169	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
170	#13133217	—	2	1	no	—
171	#13133217	C₂³	1	2	yes	complemented
172	#13133216	—	2	1	no	—
173	#13133216	—	2	1	no	—
174	#13133216	—	2	2	no	—
175	#13133216	—	2	2	no	—
176	#13133216	C₂³	1	2	yes	complemented
177	#13133216	C₂³	1	2	yes	complemented
178	#13133215	—	2	2	no	—
179	#13133215	—	2	2	no	—
180	#13133214	C₂³	1	2	yes	—
181	#13133213	—	2	2	no	—
182	#13133213	—	2	2	no	—
183	#13133213	C₂³	1	2	yes	—
184	#13133213	C₂³	1	2	yes	—
185	#13133209	—	2	1	no	—
186	#13133209	C₂³	1	2	yes	complemented
187	#13133208	—	2	1	no	—
188	#13133208	—	2	1	no	—
189	#13133208	C₂³	1	2	yes	complemented
190	#13133208	C₂³	1	2	yes	complemented
191	#13133207	—	2	2	no	—
192	#13133207	—	2	2	no	—
193	#13133207	—	2	2	no	—
194	#13133207	—	2	2	no	—
195	#13133206	C₂³	1	2	yes	—
196	#13133205	C₂³	1	2	yes	—
197	#13133204	C₂³	1	2	yes	—
198	#13133203	—	2	2	no	—
199	#13133203	—	2	2	no	—
200	#13133197	—	2	2	no	—
201	#13133196	—	2	2	no	—
202	#13133195	—	2	2	no	—
203	#13133195	—	2	2	no	—
204	#13133194	—	2	2	no	—
205	#13133194	—	2	2	no	—
206	#13133193	—	2	2	no	—
207	#13133192	—	2	1	no	—
208	#13133192	—	2	1	no	—
209	#13133191	—	2	1	no	—
210	#13133191	—	2	1	no	—
211	#13133190	—	2	2	no	—
212	#13133190	—	2	2	no	—
213	#13133189	—	2	2	no	—
214	#13133189	—	2	2	no	—
215	#13133188	—	2	1	no	—
216	#13133188	—	2	1	no	—
217	#13133187	—	2	2	no	—
218	#13133187	—	2	2	no	—
219	#13133187	—	2	2	no	—
220	#13133186	—	2	2	no	—
221	#13133185	—	2	2	no	—
222	#13133185	—	2	2	no	—
223	#13133185	—	2	2	no	—
224	#13133176	C₂³	1	1	yes	characteristic
225	#13133176	C₂³	1	1	yes	characteristic
226	#13133175	D₄	1	1	yes	characteristic
227	#13133175	D₄	1	1	yes	characteristic
228	#13133175	C₂³	1	1	yes	characteristic
229	#13133175	C₂³	1	1	yes	characteristic
230	#13133174	—	2	1	no	—
231	#13133174	C₂³	1	2	yes	—
232	#13133173	—	2	1	no	—
233	#13133173	D₄	1	2	yes	—
234	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
235	C₂×#11719919	—	2	1	no	—
236	C₄⋊C₄×D₅₃	—	2	1	no	—
237	C₄⋊C₄×D₅₃	—	2	1	no	—
238	C₄⋊C₄×D₅₃	—	2	2	no	—
239	C₄⋊C₄×D₅₃	—	2	2	no	—
240	C₄⋊C₄×D₅₃	—	2	2	no	—
241	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
242	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
243	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
244	C₄⋊C₄×D₅₃	C₂³	1	2	yes	—
245	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×D₅₃	C₂³	1	1	yes	characteristic
247	C₂²⋊C₄×D₅₃	—	2	1	no	—
248	C₂²⋊C₄×D₅₃	—	2	2	no	—
249	C₂²⋊C₄×D₅₃	—	2	2	no	—
250	C₂²⋊C₄×D₅₃	D₄	1	2	yes	—
251	C₄²×D₅₃	—	2	1	no	—
252	C₄²×D₅₃	C₂³	1	2	yes	—
253	#13133142	C₂³	1	1	yes	characteristic, complemented
254	#13133142	C₂³	1	1	yes	characteristic, complemented
255	#13133142	C₂³	1	2	yes	complemented
256	#13133141	C₂³	1	1	yes	characteristic, complemented
257	#13133141	C₂³	1	1	yes	characteristic, complemented
258	#13133141	C₂³	1	2	yes	complemented
259	#13133140	C₂³	1	1	yes	characteristic, complemented
260	#13133140	C₂³	1	1	yes	characteristic, complemented
261	#13133140	C₂³	1	2	yes	complemented
262	#13133139	C₂³	1	2	yes	—
263	#13133139	C₂³	1	2	yes	—
264	#13133139	C₂³	1	2	yes	—
265	#13133139	C₂³	1	2	yes	—
266	#13133139	C₂³	1	1	yes	characteristic, complemented
267	#13133139	C₂³	1	1	yes	characteristic, complemented
268	#13133139	C₂³	1	2	yes	complemented
269	#13133138	C₂³	1	2	yes	—
270	#13133138	C₂³	1	2	yes	—
271	#13133138	C₂³	1	2	yes	—
272	#13133138	C₂³	1	2	yes	—
273	#13133138	C₂³	1	1	yes	characteristic, complemented
274	#13133138	C₂³	1	1	yes	characteristic, complemented
275	#13133138	C₂³	1	2	yes	complemented
276	#13133137	C₂³	1	2	yes	—
277	#13133137	C₂³	1	2	yes	—
278	#13133137	C₂³	1	2	yes	—
279	#13133137	C₂³	1	2	yes	—
280	#13133137	C₂³	1	1	yes	characteristic, complemented
281	#13133137	C₂³	1	1	yes	characteristic, complemented
282	#13133137	C₂³	1	2	yes	complemented
283	#13133128	C₂³	1	2	yes	complemented
284	#13133127	C₂³	1	2	yes	complemented
285	#13133127	C₂³	1	2	yes	complemented
286	C₄×#88322	C₂³	1	2	yes	complemented
287	C₈×Dic₅₃	C₂³	1	2	yes	complemented
288	C₈×Dic₅₃	C₂³	1	2	yes	complemented
289	C₂×#41×C₅₃	C₂³	1	1	yes	characteristic
290	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
291	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
292	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
293	C₄⋊Q₈×C₅₃	—	2	1	no	—
294	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
295	#127×C₅₃	C₂³	1	2	yes	—
296	#125×C₅₃	—	2	1	no	—
297	#125×C₅₃	C₂³	1	2	yes	complemented
298	#124×C₅₃	C₂³	1	2	yes	—
299	C₂²⋊Q₈×C₅₃	—	2	2	no	—
300	#121×C₅₃	—	2	1	no	—
301	#121×C₅₃	—	2	1	no	—
302	#120×C₅₃	—	2	2	no	—
303	#117×C₅₃	C₂³	1	1	yes	characteristic
304	#117×C₅₃	C₂³	1	1	yes	characteristic
305	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
306	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
307	#103×C₅₃	C₂³	1	2	yes	complemented
308	#103×C₅₃	C₂³	1	1	yes	characteristic, complemented
309	#102×C₅₃	C₂³	1	2	yes	—
310	#102×C₅₃	C₂³	1	2	yes	—
311	#102×C₅₃	C₂³	1	2	yes	—
312	#102×C₅₃	C₂³	1	2	yes	—
313	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
314	#102×C₅₃	C₂³	1	2	yes	complemented
315	#102×C₅₃	C₂³	1	1	yes	characteristic, complemented
316	#97×C₅₃	C₂³	1	2	yes	complemented
317	C₄×C₈×C₅₃	C₂³	1	2	yes	complemented
318	C₂⁴×C₅₃	—	2	1	no	—
319	C₂³×D₅₃	—	2	1	no	—
320	C₂³×D₅₃	—	2	2	no	—
321	C₂³×D₅₃	—	2	1	no	—
322	C₂³×D₅₃	—	2	2	no	—
323	C₂³×D₅₃	—	4	4	no	—
324	C₂³×D₅₃	—	8	2	no	—
325	C₂³×D₅₃	—	8	2	no	—
326	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
327	#41×C₅₃	—	2	2	no	—
328	#41×C₅₃	—	2	2	no	—
329	C₂×Q₈×C₅₃	—	2	2	no	—
330	C₂×Q₈×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₅₃	—	2	1	no	—
332	C₂×D₄×C₅₃	—	2	1	no	—
333	C₂×D₄×C₅₃	—	2	2	no	—
334	C₂×D₄×C₅₃	—	2	2	no	—
335	C₂×D₄×C₅₃	—	2	2	no	—
336	C₂×D₄×C₅₃	—	2	2	no	—
337	C₂×D₄×C₅₃	C₂⁴	1	2	yes	—
338	C₂×D₄×C₅₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₅₃	—	2	1	no	—
340	C₂²×C₄×C₅₃	—	2	1	no	—
341	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₂²⋊D₅₃	—	2	1	no	—
343	C₂×C₂²⋊D₅₃	—	2	1	no	—
344	C₂×C₂²⋊D₅₃	—	2	2	no	—
345	C₂×C₂²⋊D₅₃	—	2	2	no	—
346	C₂×C₂²⋊D₅₃	—	2	1	no	—
347	C₂×C₂²⋊D₅₃	—	2	2	no	—
348	C₂×C₂²⋊D₅₃	—	2	2	no	—
349	C₂×C₂²⋊D₅₃	—	2	2	no	—
350	C₂×C₂²⋊D₅₃	—	2	2	no	—
351	C₂×C₂²⋊D₅₃	—	4	4	no	—
352	C₂²×Dic₅₃	—	2	1	no	—
353	C₂²×Dic₅₃	—	2	1	no	—
354	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
355	#11719949	—	2	2	no	—
356	#11719949	—	2	2	no	—
357	Q₈×D₅₃	—	2	2	no	—
358	Q₈×D₅₃	—	2	2	no	—
359	Q₈×D₅₃	—	8	4	no	—
360	#11719947	—	2	2	no	—
361	#11719947	—	2	2	no	—
362	#11719947	—	4	4	no	—
363	D₄×D₅₃	—	2	4	no	—
364	D₄×D₅₃	—	2	4	no	—
365	D₄×D₅₃	—	2	4	no	—
366	D₄×D₅₃	—	2	4	no	—
367	D₄×D₅₃	—	2	2	no	—
368	D₄×D₅₃	—	2	2	no	—
369	D₄×D₅₃	—	4	4	no	—
370	D₄×D₅₃	—	4	4	no	—
371	D₄×D₅₃	—	4	4	no	—
372	D₄×D₅₃	—	8	4	no	—
373	D₄×D₅₃	—	8	4	no	—
374	#11719945	—	2	2	no	—
375	#11719945	—	2	2	no	—
376	#11719945	—	4	4	no	—
377	C₂×D₂₁₂	—	2	2	no	—
378	C₂×D₂₁₂	—	2	2	no	—
379	C₂×D₂₁₂	—	2	1	no	—
380	C₂×D₂₁₂	—	2	1	no	—
381	C₂×D₂₁₂	—	2	2	no	—
382	C₂×D₂₁₂	—	2	2	no	—
383	C₂×D₂₁₂	C₂⁴	1	2	yes	—
384	C₂×D₂₁₂	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×D₅₃	—	2	1	no	—
386	C₂×C₄×D₅₃	—	2	1	no	—
387	C₂×C₄×D₅₃	—	2	1	no	—
388	C₂×C₄×D₅₃	—	2	2	no	—
389	C₂×C₄×D₅₃	—	2	1	no	—
390	C₂×C₄×D₅₃	—	2	1	no	—
391	C₂×C₄×D₅₃	—	2	2	no	—
392	C₂×C₄×D₅₃	—	4	4	no	—
393	C₂×C₄×D₅₃	—	8	2	no	—
394	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
395	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
396	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
397	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
398	C₂×C₄×D₅₃	#41	1	4	yes	—
399	C₂×C₄×D₅₃	#41	1	4	yes	—
400	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₀₆	—	2	1	no	—
403	C₂×Dic₁₀₆	—	2	2	no	—
404	C₂×Dic₁₀₆	—	2	2	no	—
405	C₂×Dic₁₀₆	—	2	2	no	—
406	C₂×Dic₁₀₆	C₂⁴	1	1	yes	characteristic
407	M₁₆×C₅₃	—	2	2	no	—
408	C₂×C₈×C₅₃	—	2	2	no	—
409	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
410	C₂×C₈×C₅₃	C₂⁴	1	2	yes	—
411	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₅₃	—	2	1	no	—
413	C₄⋊C₄×C₅₃	—	2	2	no	—
414	C₄⋊C₄×C₅₃	—	2	2	no	—
415	C₄⋊C₄×C₅₃	—	2	2	no	—
416	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
417	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₅₃	C₂⁴	1	2	yes	—
419	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₅₃	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₅₃	—	2	1	no	—
422	C₂²⋊C₄×C₅₃	—	2	2	no	—
423	C₂²⋊C₄×C₅₃	—	2	2	no	—
424	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
425	C₄²×C₅₃	—	2	1	no	—
426	C₄²×C₅₃	C₂⁴	1	2	yes	—
427	C₂²⋊Dic₅₃	—	2	1	no	—
428	C₂²⋊Dic₅₃	—	2	2	no	—
429	C₂²⋊Dic₅₃	—	2	2	no	—
430	C₂²⋊Dic₅₃	C₂×D₄	1	2	yes	—
431	#11719921	—	2	1	no	—
432	#11719921	—	2	1	no	—
433	#11719921	—	2	2	no	—
434	#11719921	—	2	2	no	—
435	#11719921	—	2	2	no	—
436	#11719921	—	2	2	no	—
437	#11719921	C₂×D₄	1	2	yes	—
438	#11719921	C₂×D₄	1	2	yes	—
439	C₄⋊Dic₅₃	—	2	1	no	—
440	C₄⋊Dic₅₃	—	2	2	no	—
441	C₄⋊Dic₅₃	—	2	2	no	—
442	C₄⋊Dic₅₃	—	2	2	no	—
443	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
445	C₄⋊Dic₅₃	C₂⁴	1	2	yes	—
446	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊Dic₅₃	C₂⁴	1	1	yes	characteristic
448	#11719919	—	2	2	no	—
449	#11719919	—	2	2	no	—
450	#11719919	—	2	2	no	—
451	#11719919	—	2	2	no	—
452	#11719919	—	2	2	no	—
453	#11719919	—	2	2	no	—
454	#11719919	—	2	2	no	—
455	#11719919	—	2	2	no	—
456	#11719919	—	2	1	no	—
457	#11719919	—	2	1	no	—
458	#11719919	C₂×D₄	1	2	yes	—
459	#11719919	C₂×D₄	1	2	yes	—
460	C₄×Dic₅₃	—	2	1	no	—
461	C₄×Dic₅₃	—	2	1	no	—
462	C₄×Dic₅₃	—	2	1	no	—
463	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
464	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
465	C₄×Dic₅₃	C₂⁴	1	2	yes	—
466	#11719917	—	2	2	no	—
467	C₂×#88322	—	2	2	no	—
468	C₂×#88322	C₂⁴	1	1	yes	characteristic
469	C₂×#88322	C₂⁴	1	2	yes	—
470	C₂×#88322	C₂⁴	1	1	yes	characteristic
471	#11719912	—	2	4	no	—
472	C₈×D₅₃	—	2	2	no	—
473	C₈×D₅₃	—	2	2	no	—
474	C₈×D₅₃	—	2	2	no	—
475	C₈×D₅₃	—	2	2	no	—
476	C₈×D₅₃	—	2	4	no	—
477	C₂³×C₅₃	—	2	1	no	—
478	C₂³×C₅₃	—	2	2	no	—
479	C₂³×C₅₃	—	4	2	no	—
480	C₂³×C₅₃	—	8	1	no	—
481	C₂³×C₅₃	—	8	1	no	—
482	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
483	C₂²×D₅₃	—	2	2	no	—
484	C₂²×D₅₃	—	2	2	no	—
485	C₂²×D₅₃	—	2	1	no	—
486	C₂²×D₅₃	—	2	2	no	—
487	C₂²×D₅₃	—	4	2	no	—
488	C₂²×D₅₃	—	4	2	no	—
489	C₂²×D₅₃	—	4	4	no	—
490	C₂²×D₅₃	—	4	4	no	—
491	C₂²×D₅₃	—	4	2	no	—
492	C₂²×D₅₃	—	4	4	no	—
493	C₂²×D₅₃	—	4	2	no	—
494	C₂²×D₅₃	—	4	4	no	—
495	C₂²×D₅₃	—	8	2	no	—
496	C₂²×D₅₃	—	8	2	no	—
497	C₂²×D₅₃	—	8	16	no	—
498	C₂²×D₅₃	—	8	1	no	—
499	C₂²×D₅₃	—	8	1	no	—
500	C₂²×D₅₃	#124	1	4	yes	—
501	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
502	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
503	Q₈×C₅₃	—	2	1	no	—
504	Q₈×C₅₃	—	2	1	no	—
505	Q₈×C₅₃	—	8	2	no	—
506	D₄×C₅₃	—	2	2	no	—
507	D₄×C₅₃	—	2	2	no	—
508	D₄×C₅₃	—	2	1	no	—
509	D₄×C₅₃	—	2	1	no	—
510	D₄×C₅₃	—	4	2	no	—
511	D₄×C₅₃	—	4	2	no	—
512	D₄×C₅₃	—	8	2	no	—
513	D₄×C₅₃	—	8	2	no	—
514	C₂×C₄×C₅₃	—	2	1	no	—
515	C₂×C₄×C₅₃	—	2	1	no	—
516	C₂×C₄×C₅₃	—	2	2	no	—
517	C₂×C₄×C₅₃	—	2	1	no	—
518	C₂×C₄×C₅₃	—	4	2	no	—
519	C₂×C₄×C₅₃	—	8	1	no	—
520	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
524	C₂×C₄×C₅₃	C₂×#41	1	2	yes	—
525	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
526	C₂²⋊D₅₃	—	4	2	no	—
527	C₂²⋊D₅₃	—	4	2	no	—
528	C₂²⋊D₅₃	—	4	2	no	—
529	C₂²⋊D₅₃	—	4	4	no	—
530	C₂²⋊D₅₃	—	4	4	no	—
531	C₂²⋊D₅₃	—	8	2	no	—
532	C₂²⋊D₅₃	—	8	2	no	—
533	C₂²⋊D₅₃	—	8	2	no	—
534	C₂²⋊D₅₃	—	8	2	no	—
535	C₂×Dic₅₃	—	2	1	no	—
536	C₂×Dic₅₃	—	2	2	no	—
537	C₂×Dic₅₃	—	2	1	no	—
538	C₂×Dic₅₃	—	2	1	no	—
539	C₂×Dic₅₃	—	4	2	no	—
540	C₂×Dic₅₃	—	8	1	no	—
541	C₂×Dic₅₃	#124	1	4	yes	—
542	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
543	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
544	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
545	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
546	D₂₁₂	—	2	2	no	—
547	D₂₁₂	—	2	2	no	—
548	D₂₁₂	—	2	1	no	—
549	D₂₁₂	—	2	1	no	—
550	D₂₁₂	—	4	2	no	—
551	D₂₁₂	—	4	2	no	—
552	D₂₁₂	—	8	2	no	—
553	D₂₁₂	—	8	2	no	—
554	C₄×D₅₃	—	2	4	no	—
555	C₄×D₅₃	—	2	4	no	—
556	C₄×D₅₃	—	4	2	no	—
557	C₄×D₅₃	—	4	4	no	—
558	C₄×D₅₃	—	4	2	no	—
559	C₄×D₅₃	—	4	2	no	—
560	C₄×D₅₃	—	4	2	no	—
561	C₄×D₅₃	—	4	2	no	—
562	C₄×D₅₃	—	8	2	no	—
563	C₄×D₅₃	#124	1	4	yes	—
564	C₄×D₅₃	#124	1	4	yes	—
565	C₄×D₅₃	C₂×#41	1	2	yes	—
566	C₄×D₅₃	C₂×#41	1	2	yes	—
567	C₄×D₅₃	C₂×#41	1	2	yes	—
568	C₄×D₅₃	C₂×#41	1	2	yes	—
569	Dic₁₀₆	—	2	1	no	—
570	Dic₁₀₆	—	2	1	no	—
571	Dic₁₀₆	—	4	2	no	—
572	Dic₁₀₆	—	8	2	no	—
573	Dic₁₀₆	—	8	2	no	—
574	Dic₁₀₆	—	8	2	no	—
575	C₈×C₅₃	—	2	1	no	—
576	C₈×C₅₃	—	2	1	no	—
577	C₈×C₅₃	—	2	2	no	—
578	#88322	—	2	1	no	—
579	#88322	—	2	1	no	—
580	#88322	—	2	2	no	—
581	C₂×#3136	—	53	1	no	maximal, Sylow
582	C₂²×C₅₃	—	2	1	no	—
583	C₂²×C₅₃	—	2	1	no	—
584	C₂²×C₅₃	—	4	1	no	—
585	C₂²×C₅₃	—	4	2	no	—
586	C₂²×C₅₃	—	4	1	no	—
587	C₂²×C₅₃	—	4	2	no	—
588	C₂²×C₅₃	—	4	1	no	—
589	C₂²×C₅₃	—	4	2	no	—
590	C₂²×C₅₃	—	8	4	no	—
591	C₂²×C₅₃	C₂×#124	1	2	yes	—
592	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
593	C₂×D₅₃	—	2	1	no	—
594	C₂×D₅₃	—	2	1	no	—
595	C₂×D₅₃	—	2	8	no	—
596	C₂×D₅₃	—	4	1	no	—
597	C₂×D₅₃	—	4	2	no	—
598	C₂×D₅₃	—	4	1	no	—
599	C₂×D₅₃	—	4	2	no	—
600	C₂×D₅₃	—	4	1	no	—
601	C₂×D₅₃	—	4	2	no	—
602	C₂×D₅₃	—	8	8	no	—
603	C₂×D₅₃	—	8	4	no	—
604	C₂×D₅₃	—	8	4	no	—
605	C₂×D₅₃	—	8	8	no	—
606	C₂×D₅₃	C₂×#124	1	2	yes	—
607	C₂×D₅₃	C₂×#124	1	2	yes	—
608	C₂×D₅₃	#576	1	2	yes	—
609	C₂×D₅₃	#577	1	2	yes	—
610	C₄×C₅₃	—	2	2	no	—
611	C₄×C₅₃	—	2	2	no	—
612	C₄×C₅₃	—	4	1	no	—
613	C₄×C₅₃	—	4	1	no	—
614	C₄×C₅₃	—	4	2	no	—
615	C₄×C₅₃	—	4	1	no	—
616	C₄×C₅₃	C₂×#124	1	2	yes	—
617	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
618	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
619	Dic₅₃	—	2	2	no	—
620	Dic₅₃	—	2	2	no	—
621	Dic₅₃	—	4	1	no	—
622	Dic₅₃	—	4	1	no	—
623	Dic₅₃	—	4	2	no	—
624	Dic₅₃	—	4	1	no	—
625	Dic₅₃	C₂×#124	1	2	yes	—
626	Dic₅₃	C₂×#124	1	2	yes	—
627	C₂×#544	—	53	1	no	—
628	C₂×#535	—	53	1	no	—
629	#3136	—	53	2	no	—
630	#3136	—	53	2	no	—
631	#3136	—	53	2	no	—
632	#3136	—	53	2	no	—
633	#3136	—	53	1	no	—
634	#3136	—	53	1	no	—
635	#3136	—	53	1	no	—
636	#3136	—	53	1	no	—
637	#3136	—	53	1	no	—
638	#3136	—	53	1	no	—
639	#3136	—	53	1	no	—
640	#3136	D₅₃	1	1	yes	characteristic, direct product factor
641	C₂×#490	—	53	2	no	—
642	C₂×#489	—	53	2	no	—
643	C₂×#488	—	53	2	no	—
644	C₂×#486	—	53	2	no	—
645	C₂×#417	—	53	1	no	—
646	C₂×#418	—	53	1	no	—
647	C₂×#416	—	53	1	no	—
648	C₂²×#102	—	53	1	no	—
649	C₂×#405	—	53	1	no	—
650	C₂×C₅₃	—	2	2	no	—
651	C₂×C₅₃	—	8	2	no	—
652	C₂×C₅₃	—	8	1	no	—
653	C₂×C₅₃	C₂²×#124	1	1	yes	characteristic
654	C₂×C₅₃	C₂×#576	1	1	yes	characteristic
655	C₂×C₅₃	C₂×#577	1	1	yes	characteristic
656	D₅₃	—	2	2	no	—
657	D₅₃	—	8	1	no	—
658	D₅₃	—	8	2	no	—
659	D₅₃	#3136	1	4	yes	direct product factor
660	C₂²×#41	—	53	1	no	—
661	C₂³×D₄	—	53	1	no	—
662	C₂²×M₁₆	—	53	1	no	—
663	C₂³×C₈	—	53	1	no	—
664	#544	—	53	2	no	—
665	#544	—	53	2	no	—
666	#544	—	53	1	no	—
667	#544	—	53	1	no	—
668	#544	—	53	1	no	—
669	#544	—	106	2	no	—
670	#544	—	106	1	no	—
671	#544	—	106	1	no	—
672	#544	C₂×D₅₃	1	1	yes	characteristic, complemented
673	#535	—	53	1	no	—
674	#535	—	53	1	no	—
675	#535	—	53	2	no	—
676	#535	—	53	2	no	—
677	#535	—	53	1	no	—
678	#535	—	106	2	no	—
679	#535	—	106	1	no	—
680	#535	—	106	1	no	—
681	#535	C₂×D₅₃	1	1	yes	characteristic
682	C₂×C₄⋊Q₈	—	53	2	no	—
683	C₂×C₄⋊Q₈	—	106	1	no	—
684	C₂×#127	—	53	2	no	—
685	C₂×#125	—	53	2	no	—
686	C₂×#125	—	106	1	no	—
687	C₂×#124	—	53	2	no	—
688	C₂×C₂²⋊Q₈	—	106	2	no	—
689	C₂×#121	—	106	1	no	—
690	C₂×#121	—	106	1	no	—
691	C₂×#120	—	106	2	no	—
692	C₂×#117	—	53	1	no	—
693	C₂×#117	—	53	1	no	—
694	C₂²×C₄⋊C₄	—	53	1	no	—
695	#490	—	53	2	no	—
696	#490	—	53	2	no	—
697	#490	—	53	2	no	—
698	#490	—	53	2	no	—
699	#490	—	53	2	no	—
700	#490	—	53	2	no	—
701	#490	—	53	2	no	—
702	#490	C₂×D₅₃	1	2	yes	complemented
703	#489	—	53	2	no	—
704	#489	—	53	2	no	—
705	#489	—	53	2	no	—
706	#489	—	53	2	no	—
707	#489	—	53	2	no	—
708	#489	—	53	2	no	—
709	#489	—	53	2	no	—
710	#489	C₂×D₅₃	1	2	yes	complemented
711	#488	—	53	2	no	—
712	#488	—	53	2	no	—
713	#488	—	53	2	no	—
714	#488	—	53	2	no	—
715	#488	—	53	2	no	—
716	#488	—	53	2	no	—
717	#488	—	53	2	no	—
718	#488	C₂×D₅₃	1	2	yes	complemented
719	#486	—	53	2	no	—
720	#486	—	53	2	no	—
721	#486	—	53	2	no	—
722	#486	—	53	2	no	—
723	#486	—	53	2	no	—
724	#486	—	53	2	no	—
725	#486	—	53	2	no	—
726	#486	C₂×D₅₃	1	2	yes	complemented
727	#418	—	53	1	no	—
728	#418	—	53	1	no	—
729	#418	—	53	1	no	—
730	#418	—	53	2	no	—
731	#418	—	53	2	no	—
732	#418	C₂×D₅₃	1	1	yes	characteristic, complemented
733	#417	—	53	1	no	—
734	#417	—	53	1	no	—
735	#417	—	53	1	no	—
736	#417	—	53	2	no	—
737	#417	—	53	2	no	—
738	#417	C₂×D₅₃	1	1	yes	characteristic, complemented
739	#416	—	53	1	no	—
740	#416	—	53	1	no	—
741	#416	—	53	1	no	—
742	#416	—	53	1	no	—
743	#416	—	53	1	no	—
744	#416	—	53	1	no	—
745	#416	—	53	1	no	—
746	#416	C₂×D₅₃	1	1	yes	characteristic, complemented
747	C₂×#103	—	53	1	no	—
748	C₂×#103	—	53	2	no	—
749	C₂×#103	—	53	1	no	—
750	C₂×#102	—	53	1	no	—
751	C₂×#102	—	53	1	no	—
752	C₂×#102	—	53	1	no	—
753	C₂×#102	—	53	2	no	—
754	C₂×#102	—	53	2	no	—
755	C₂×#102	—	53	2	no	—
756	C₂×#102	—	53	2	no	—
757	C₂×#102	—	53	2	no	—
758	C₂×#102	—	53	2	no	—
759	C₂×#102	—	53	1	no	—
760	C₂×#102	—	53	2	no	—
761	C₂×#102	—	53	1	no	—
762	C₂×#102	C₂×D₅₃	1	1	yes	characteristic, complemented
763	#405	—	53	1	no	—
764	#405	—	53	1	no	—
765	#405	—	53	1	no	—
766	#405	—	53	2	no	—
767	#405	—	53	2	no	—
768	#405	C₂×D₅₃	1	1	yes	characteristic, complemented
769	C₂×#97	—	53	2	no	—
770	C₂×C₄×C₈	—	53	2	no	—
771	C₅₃	C₂×#3136	1	1	yes	characteristic, complemented, Sylow
772	C₂⁵	—	106	1	no	—
773	C₂×#41	—	53	1	no	—
774	C₂×#41	—	53	1	no	—
775	C₂×#41	—	53	1	no	—
776	C₂×#41	—	106	1	no	—
777	C₂×#41	—	106	1	no	—
778	C₂×#41	—	106	4	no	—
779	C₂×#41	—	106	4	no	—
780	C₂×#41	C₂²×D₅₃	1	1	yes	characteristic
781	C₂²×Q₈	—	53	1	no	—
782	C₂²×Q₈	—	106	2	no	—
783	C₂²×D₄	—	53	2	no	—
784	C₂²×D₄	—	53	1	no	—
785	C₂²×D₄	—	53	2	no	—
786	C₂²×D₄	—	53	1	no	—
787	C₂²×D₄	—	106	4	no	—
788	C₂²×D₄	—	106	4	no	—
789	C₂²×D₄	—	106	2	no	—
790	C₂²×D₄	—	106	2	no	—
791	C₂²×D₄	—	106	1	no	—
792	C₂²×D₄	—	106	1	no	—
793	C₂²×D₄	—	106	1	no	—
794	C₂²×D₄	—	106	1	no	—
795	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
796	C₂³×C₄	—	53	1	no	—
797	C₂³×C₄	—	106	1	no	—
798	C₂³×C₄	—	106	1	no	—
799	C₂×M₁₆	—	53	1	no	—
800	C₂×M₁₆	—	53	2	no	—
801	C₂×M₁₆	—	106	4	no	—
802	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
803	C₂²×C₈	—	53	1	no	—
804	C₂²×C₈	—	53	1	no	—
805	C₂²×C₈	—	53	1	no	—
806	C₂²×C₈	—	53	1	no	—
807	C₂²×C₈	—	53	1	no	—
808	C₂²×C₈	—	53	2	no	—
809	C₂²×C₈	—	106	4	no	—
810	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
811	C₄⋊Q₈	—	2	1	no	—
812	C₄⋊Q₈	—	53	2	no	—
813	C₄⋊Q₈	—	53	2	no	—
814	C₄⋊Q₈	—	53	2	no	—
815	C₄⋊Q₈	—	106	1	no	—
816	C₄⋊Q₈	—	106	2	no	—
817	C₄⋊Q₈	—	106	2	no	—
818	C₄⋊Q₈	—	106	2	no	—
819	C₄⋊Q₈	—	106	1	no	—
820	C₄⋊Q₈	—	106	2	no	—
821	C₄⋊Q₈	—	106	1	no	—
822	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
823	#127	—	53	2	no	—
824	#127	—	53	2	no	—
825	#127	—	53	2	no	—
826	#127	—	106	2	no	—
827	#127	—	106	2	no	—
828	#127	C₂²×D₅₃	1	2	yes	—
829	#125	—	2	1	no	—
830	#125	—	53	2	no	—
831	#125	—	53	2	no	—
832	#125	—	53	2	no	—
833	#125	—	106	1	no	—
834	#125	—	106	2	no	—
835	#125	—	106	2	no	—
836	#125	—	106	2	no	—
837	#125	—	106	2	no	—
838	#125	—	106	1	no	—
839	#125	—	106	1	no	—
840	#125	C₂²×D₅₃	1	2	yes	complemented
841	#124	—	53	2	no	—
842	#124	—	53	2	no	—
843	#124	—	53	2	no	—
844	#124	—	106	2	no	—
845	#124	—	106	2	no	—
846	#124	C₂²×D₅₃	1	2	yes	—
847	C₂²⋊Q₈	—	2	2	no	—
848	C₂²⋊Q₈	—	106	2	no	—
849	C₂²⋊Q₈	—	106	2	no	—
850	C₂²⋊Q₈	—	106	2	no	—
851	C₂²⋊Q₈	—	106	2	no	—
852	C₂²⋊Q₈	—	106	2	no	—
853	C₂²⋊Q₈	—	106	2	no	—
854	C₂²⋊Q₈	—	106	2	no	—
855	#121	—	2	1	no	—
856	#121	—	2	1	no	—
857	#121	—	106	2	no	—
858	#121	—	106	2	no	—
859	#121	—	106	1	no	—
860	#121	—	106	1	no	—
861	#121	—	106	1	no	—
862	#121	—	106	1	no	—
863	#121	—	106	2	no	—
864	#121	—	106	2	no	—
865	#121	—	106	1	no	—
866	#121	—	106	1	no	—
867	#120	—	2	2	no	—
868	#120	—	106	2	no	—
869	#120	—	106	2	no	—
870	#120	—	106	2	no	—
871	#120	—	106	2	no	—
872	#120	—	106	2	no	—
873	#120	—	106	2	no	—
874	#120	—	106	2	no	—
875	#117	—	53	1	no	—
876	#117	—	53	1	no	—
877	#117	—	53	1	no	—
878	#117	—	53	2	no	—
879	#117	—	53	2	no	—
880	#117	—	53	1	no	—
881	#117	—	53	1	no	—
882	#117	—	53	1	no	—
883	#117	—	106	1	no	—
884	#117	—	106	1	no	—
885	#117	C₂²×D₅₃	1	1	yes	characteristic
886	#117	C₂²×D₅₃	1	1	yes	characteristic
887	C₂×C₄⋊C₄	—	53	1	no	—
888	C₂×C₄⋊C₄	—	53	1	no	—
889	C₂×C₄⋊C₄	—	53	1	no	—
890	C₂×C₄⋊C₄	—	53	2	no	—
891	C₂×C₄⋊C₄	—	53	2	no	—
892	C₂×C₄⋊C₄	—	53	1	no	—
893	C₂×C₄⋊C₄	—	53	1	no	—
894	C₂×C₄⋊C₄	—	106	1	no	—
895	C₂×C₄⋊C₄	—	106	1	no	—
896	C₂×C₄⋊C₄	—	106	2	no	—
897	C₂×C₄⋊C₄	—	106	2	no	—
898	C₂×C₄⋊C₄	—	106	2	no	—
899	C₂×C₄⋊C₄	—	106	1	no	—
900	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
901	C₂×C₂²⋊C₄	—	53	2	no	—
902	C₂×C₂²⋊C₄	—	106	2	no	—
903	C₂×C₂²⋊C₄	—	106	2	no	—
904	C₂×C₂²⋊C₄	—	106	1	no	—
905	C₂×C₄²	—	53	2	no	—
906	C₂×C₄²	—	106	1	no	—
907	#103	—	53	1	no	—
908	#103	—	53	1	no	—
909	#103	—	53	2	no	—
910	#103	—	53	1	no	—
911	#103	—	53	1	no	—
912	#103	—	53	2	no	—
913	#103	—	53	1	no	—
914	#103	—	53	1	no	—
915	#103	—	53	2	no	—
916	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
917	#103	C₂²×D₅₃	1	1	yes	characteristic, complemented
918	#103	C₂²×D₅₃	1	2	yes	complemented
919	#102	—	53	2	no	—
920	#102	—	53	2	no	—
921	#102	—	53	2	no	—
922	#102	—	53	2	no	—
923	#102	—	53	1	no	—
924	#102	—	53	1	no	—
925	#102	—	53	2	no	—
926	#102	—	53	2	no	—
927	#102	—	53	2	no	—
928	#102	—	53	2	no	—
929	#102	—	53	2	no	—
930	#102	—	53	1	no	—
931	#102	—	53	1	no	—
932	#102	—	53	2	no	—
933	#102	—	53	2	no	—
934	#102	—	53	2	no	—
935	#102	—	53	2	no	—
936	#102	—	53	2	no	—
937	#102	—	53	1	no	—
938	#102	—	53	1	no	—
939	#102	—	53	2	no	—
940	#102	C₂²×D₅₃	1	2	yes	—
941	#102	C₂²×D₅₃	1	2	yes	—
942	#102	C₂²×D₅₃	1	2	yes	—
943	#102	C₂²×D₅₃	1	2	yes	—
944	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
945	#102	C₂²×D₅₃	1	1	yes	characteristic, complemented
946	#102	C₂²×D₅₃	1	2	yes	complemented
947	#97	—	53	2	no	—
948	#97	—	53	2	no	—
949	#97	—	53	2	no	—
950	#97	C₂²×D₅₃	1	2	yes	complemented
951	C₄×C₈	—	53	2	no	—
952	C₄×C₈	—	53	2	no	—
953	C₄×C₈	—	53	2	no	—
954	C₄×C₈	C₂²×D₅₃	1	2	yes	complemented
955	C₂⁴	—	2	1	no	—
956	C₂⁴	—	53	1	no	—
957	C₂⁴	—	106	2	no	—
958	C₂⁴	—	106	2	no	—
959	C₂⁴	—	106	1	no	—
960	C₂⁴	—	106	1	no	—
961	C₂⁴	—	424	2	no	—
962	C₂⁴	—	424	2	no	—
963	C₂⁴	—	212	4	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	106	2	no	—
967	#41	—	106	2	no	—
968	#41	—	106	2	no	—
969	#41	—	106	2	no	—
970	#41	—	106	2	no	—
971	#41	—	106	2	no	—
972	#41	—	212	4	no	—
973	#41	—	212	4	no	—
974	C₂×Q₈	—	2	2	no	—
975	C₂×Q₈	—	53	1	no	—
976	C₂×Q₈	—	106	2	no	—
977	C₂×Q₈	—	106	2	no	—
978	C₂×Q₈	—	106	1	no	—
979	C₂×Q₈	—	106	2	no	—
980	C₂×Q₈	—	106	2	no	—
981	C₂×Q₈	—	106	2	no	—
982	C₂×Q₈	—	424	4	no	—
983	C₂×Q₈	C₂³×D₅₃	1	1	yes	characteristic
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	53	2	no	—
991	C₂×D₄	—	53	1	no	—
992	C₂×D₄	—	106	1	no	—
993	C₂×D₄	—	106	4	no	—
994	C₂×D₄	—	106	4	no	—
995	C₂×D₄	—	106	4	no	—
996	C₂×D₄	—	106	4	no	—
997	C₂×D₄	—	106	2	no	—
998	C₂×D₄	—	106	2	no	—
999	C₂×D₄	—	106	2	no	—
1000	C₂×D₄	—	106	2	no	—
1001	C₂×D₄	—	106	2	no	—
1002	C₂×D₄	—	106	2	no	—
1003	C₂×D₄	—	106	2	no	—
1004	C₂×D₄	—	106	2	no	—
1005	C₂×D₄	—	106	1	no	—
1006	C₂×D₄	—	106	1	no	—
1007	C₂×D₄	—	106	1	no	—
1008	C₂×D₄	—	106	2	no	—
1009	C₂×D₄	—	106	2	no	—
1010	C₂×D₄	—	106	1	no	—
1011	C₂×D₄	—	106	2	no	—
1012	C₂×D₄	—	106	2	no	—
1013	C₂×D₄	—	424	4	no	—
1014	C₂×D₄	—	424	4	no	—
1015	C₂×D₄	—	212	4	no	—
1016	C₂×D₄	—	212	4	no	—
1017	C₂×D₄	—	212	4	no	—
1018	C₂×D₄	—	212	4	no	—
1019	C₂×D₄	C₂³×D₅₃	1	2	yes	—
1020	C₂×D₄	C₂³×D₅₃	1	1	yes	characteristic
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	1	no	—
1023	C₂²×C₄	—	53	1	no	—
1024	C₂²×C₄	—	53	1	no	—
1025	C₂²×C₄	—	53	1	no	—
1026	C₂²×C₄	—	53	4	no	—
1027	C₂²×C₄	—	53	4	no	—
1028	C₂²×C₄	—	53	1	no	—
1029	C₂²×C₄	—	53	1	no	—
1030	C₂²×C₄	—	53	2	no	—
1031	C₂²×C₄	—	53	2	no	—
1032	C₂²×C₄	—	106	1	no	—
1033	C₂²×C₄	—	106	2	no	—
1034	C₂²×C₄	—	106	1	no	—
1035	C₂²×C₄	—	106	1	no	—
1036	C₂²×C₄	—	106	1	no	—
1037	C₂²×C₄	—	106	2	no	—
1038	C₂²×C₄	—	106	1	no	—
1039	C₂²×C₄	—	106	1	no	—
1040	C₂²×C₄	—	106	1	no	—
1041	C₂²×C₄	—	424	2	no	—
1042	C₂²×C₄	—	212	4	no	—
1043	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1044	M₁₆	—	2	2	no	—
1045	M₁₆	—	106	4	no	—
1046	M₁₆	—	106	2	no	—
1047	C₂×C₈	—	2	2	no	—
1048	C₂×C₈	—	53	1	no	—
1049	C₂×C₈	—	53	2	no	—
1050	C₂×C₈	—	53	1	no	—
1051	C₂×C₈	—	106	2	no	—
1052	C₂×C₈	—	106	2	no	—
1053	C₂×C₈	—	106	2	no	—
1054	C₂×C₈	—	106	2	no	—
1055	C₂×C₈	—	106	4	no	—
1056	C₂×C₈	—	106	2	no	—
1057	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1058	C₂×C₈	C₂³×D₅₃	1	2	yes	—
1059	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	2	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	53	2	no	—
1065	C₄⋊C₄	—	53	1	no	—
1066	C₄⋊C₄	—	53	2	no	—
1067	C₄⋊C₄	—	53	1	no	—
1068	C₄⋊C₄	—	53	2	no	—
1069	C₄⋊C₄	—	53	1	no	—
1070	C₄⋊C₄	—	53	1	no	—
1071	C₄⋊C₄	—	106	2	no	—
1072	C₄⋊C₄	—	106	2	no	—
1073	C₄⋊C₄	—	106	1	no	—
1074	C₄⋊C₄	—	106	1	no	—
1075	C₄⋊C₄	—	106	2	no	—
1076	C₄⋊C₄	—	106	2	no	—
1077	C₄⋊C₄	—	106	2	no	—
1078	C₄⋊C₄	—	106	2	no	—
1079	C₄⋊C₄	—	106	2	no	—
1080	C₄⋊C₄	—	106	2	no	—
1081	C₄⋊C₄	—	106	1	no	—
1082	C₄⋊C₄	—	106	2	no	—
1083	C₄⋊C₄	—	106	2	no	—
1084	C₄⋊C₄	—	106	2	no	—
1085	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1086	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
1087	C₄⋊C₄	C₂³×D₅₃	1	2	yes	—
1088	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1089	C₄⋊C₄	C₂³×D₅₃	1	1	yes	characteristic
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	2	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	53	2	no	—
1094	C₂²⋊C₄	—	53	2	no	—
1095	C₂²⋊C₄	—	53	2	no	—
1096	C₂²⋊C₄	—	106	2	no	—
1097	C₂²⋊C₄	—	106	2	no	—
1098	C₂²⋊C₄	—	106	1	no	—
1099	C₂²⋊C₄	—	106	1	no	—
1100	C₂²⋊C₄	—	106	2	no	—
1101	C₂²⋊C₄	—	106	2	no	—
1102	C₂²⋊C₄	—	106	1	no	—
1103	C₂²⋊C₄	—	106	2	no	—
1104	C₂²⋊C₄	—	106	2	no	—
1105	C₂²⋊C₄	D₄×D₅₃	1	2	yes	—
1106	C₄²	—	2	1	no	—
1107	C₄²	—	53	2	no	—
1108	C₄²	—	53	2	no	—
1109	C₄²	—	53	2	no	—
1110	C₄²	—	106	1	no	—
1111	C₄²	—	106	1	no	—
1112	C₄²	—	106	1	no	—
1113	C₄²	C₂³×D₅₃	1	2	yes	—
1114	C₂³	—	2	2	no	—
1115	C₂³	—	2	1	no	—
1116	C₂³	—	4	2	no	—
1117	C₂³	—	8	1	no	—
1118	C₂³	—	8	1	no	—
1119	C₂³	—	53	1	no	—
1120	C₂³	—	53	4	no	—
1121	C₂³	—	53	1	no	—
1122	C₂³	—	106	2	no	—
1123	C₂³	—	106	2	no	—
1124	C₂³	—	106	2	no	—
1125	C₂³	—	106	1	no	—
1126	C₂³	—	424	1	no	—
1127	C₂³	—	424	1	no	—
1128	C₂³	—	424	2	no	—
1129	C₂³	—	424	2	no	—
1130	C₂³	—	424	16	no	—
1131	C₂³	—	212	2	no	—
1132	C₂³	—	212	4	no	—
1133	C₂³	—	212	4	no	—
1134	C₂³	—	212	2	no	—
1135	C₂³	—	212	2	no	—
1136	C₂³	—	212	4	no	—
1137	C₂³	—	212	4	no	—
1138	C₂³	—	212	2	no	—
1139	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
1140	Q₈	—	2	1	no	—
1141	Q₈	—	2	1	no	—
1142	Q₈	—	8	2	no	—
1143	Q₈	—	106	1	no	—
1144	Q₈	—	106	1	no	—
1145	Q₈	—	424	2	no	—
1146	Q₈	—	424	2	no	—
1147	Q₈	—	424	2	no	—
1148	Q₈	—	212	2	no	—
1149	D₄	—	2	2	no	—
1150	D₄	—	2	2	no	—
1151	D₄	—	2	1	no	—
1152	D₄	—	2	1	no	—
1153	D₄	—	4	2	no	—
1154	D₄	—	4	2	no	—
1155	D₄	—	8	2	no	—
1156	D₄	—	8	2	no	—
1157	D₄	—	106	2	no	—
1158	D₄	—	106	2	no	—
1159	D₄	—	106	1	no	—
1160	D₄	—	106	1	no	—
1161	D₄	—	424	2	no	—
1162	D₄	—	424	2	no	—
1163	D₄	—	424	2	no	—
1164	D₄	—	424	2	no	—
1165	D₄	—	424	2	no	—
1166	D₄	—	424	2	no	—
1167	D₄	—	212	2	no	—
1168	D₄	—	212	4	no	—
1169	D₄	—	212	4	no	—
1170	D₄	—	212	2	no	—
1171	D₄	—	212	2	no	—
1172	D₄	—	212	2	no	—
1173	D₄	—	212	2	no	—
1174	C₂×C₄	—	2	1	no	—
1175	C₂×C₄	—	2	1	no	—
1176	C₂×C₄	—	2	1	no	—
1177	C₂×C₄	—	2	2	no	—
1178	C₂×C₄	—	4	2	no	—
1179	C₂×C₄	—	8	1	no	—
1180	C₂×C₄	—	53	4	no	—
1181	C₂×C₄	—	53	1	no	—
1182	C₂×C₄	—	53	1	no	—
1183	C₂×C₄	—	53	4	no	—
1184	C₂×C₄	—	53	4	no	—
1185	C₂×C₄	—	53	2	no	—
1186	C₂×C₄	—	53	2	no	—
1187	C₂×C₄	—	53	2	no	—
1188	C₂×C₄	—	53	2	no	—
1189	C₂×C₄	—	53	2	no	—
1190	C₂×C₄	—	53	2	no	—
1191	C₂×C₄	—	106	4	no	—
1192	C₂×C₄	—	106	4	no	—
1193	C₂×C₄	—	106	1	no	—
1194	C₂×C₄	—	106	1	no	—
1195	C₂×C₄	—	106	1	no	—
1196	C₂×C₄	—	106	2	no	—
1197	C₂×C₄	—	424	2	no	—
1198	C₂×C₄	—	424	1	no	—
1199	C₂×C₄	—	212	2	no	—
1200	C₂×C₄	—	212	2	no	—
1201	C₂×C₄	—	212	4	no	—
1202	C₂×C₄	—	212	2	no	—
1203	C₂×C₄	—	212	2	no	—
1204	C₂×C₄	—	212	2	no	—
1205	C₂×C₄	—	212	2	no	—
1206	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1207	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
1208	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
1209	C₂×C₄	#41×D₅₃	1	2	yes	—
1210	C₂×C₄	#41×D₅₃	1	2	yes	—
1211	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1212	C₈	—	2	1	no	—
1213	C₈	—	2	1	no	—
1214	C₈	—	2	2	no	—
1215	C₈	—	106	1	no	—
1216	C₈	—	106	1	no	—
1217	C₈	—	106	2	no	—
1218	C₂²	—	2	1	no	—
1219	C₂²	—	2	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	2	no	—
1226	C₂²	—	8	4	no	—
1227	C₂²	—	53	2	no	—
1228	C₂²	—	53	2	no	—
1229	C₂²	—	53	2	no	—
1230	C₂²	—	53	2	no	—
1231	C₂²	—	106	8	no	—
1232	C₂²	—	106	1	no	—
1233	C₂²	—	106	1	no	—
1234	C₂²	—	424	4	no	—
1235	C₂²	—	424	8	no	—
1236	C₂²	—	424	4	no	—
1237	C₂²	—	424	8	no	—
1238	C₂²	—	212	1	no	—
1239	C₂²	—	212	2	no	—
1240	C₂²	—	212	1	no	—
1241	C₂²	—	212	2	no	—
1242	C₂²	—	212	1	no	—
1243	C₂²	—	212	2	no	—
1244	C₂²	#124×D₅₃	1	2	yes	—
1245	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
1246	C₄	—	2	2	no	—
1247	C₄	—	2	2	no	—
1248	C₄	—	4	2	no	—
1249	C₄	—	4	1	no	—
1250	C₄	—	4	1	no	—
1251	C₄	—	4	1	no	—
1252	C₄	—	53	2	no	—
1253	C₄	—	53	2	no	—
1254	C₄	—	106	2	no	—
1255	C₄	—	106	2	no	—
1256	C₄	—	212	2	no	—
1257	C₄	—	212	1	no	—
1258	C₄	—	212	1	no	—
1259	C₄	—	212	1	no	—
1260	C₄	#124×D₅₃	1	2	yes	—
1261	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1262	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
1263	C₂	—	2	2	no	—
1264	C₂	—	8	2	no	—
1265	C₂	—	8	1	no	—
1266	C₂	—	53	4	no	—
1267	C₂	—	106	2	no	—
1268	C₂	—	424	2	no	—
1269	C₂	—	424	1	no	—
1270	C₂	C₂×#124×D₅₃	1	1	yes	characteristic
1271	C₂	#576×D₅₃	1	1	yes	characteristic
1272	C₂	#577×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3136	C₂
socle	C₂²×C₅₃	C₂³×D₄
prime radical	#535×D₅₃	C₂
hypercenter	#3136	D₅₃
hypocenter	C₅₃	C₂×#3136
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3136

Complements

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

N	H ≅ G/N	type
1. #544×D₅₃	C₂	semidirect
3. #20285074	C₂	semidirect
4. #20285073	C₂	semidirect
5. #20285072	C₂	semidirect
6. #20285071	C₂	semidirect
7. #20285070	C₂	semidirect
8. #20285069	C₂	semidirect
9. #20285068	C₂	semidirect
10. #20285067	C₂	semidirect
11. #20285066	C₂	semidirect
12. #20285065	C₂	semidirect
13. #20285064	C₂	semidirect
14. #490×D₅₃	C₂	semidirect
15. #489×D₅₃	C₂	semidirect
16. #488×D₅₃	C₂	semidirect
17. #486×D₅₃	C₂	semidirect
18. #417×D₅₃	C₂	semidirect
19. #418×D₅₃	C₂	semidirect
20. #416×D₅₃	C₂	semidirect
21. C₂×#102×D₅₃	C₂	semidirect
22. #405×D₅₃	C₂	semidirect
23. C₅₃×#3136	C₂	semidirect
28. #16811254	C₂²	semidirect
30. #16811253	C₂²	semidirect
32. #16811251	C₂²	semidirect
33. #16811251	C₂²	semidirect
35. #16811250	C₂²	semidirect
45. C₄⋊Q₈×D₅₃	C₂²	semidirect
48. #125×D₅₃	C₂²	semidirect
57. #16810989	C₂²	semidirect
58. #16810988	C₂²	semidirect
59. #16810987	C₂²	semidirect
60. #16810986	C₂²	semidirect
61. #16810986	C₂²	semidirect
62. #16810986	C₂²	semidirect
63. #16810986	C₂²	semidirect
64. #16810985	C₂²	semidirect
65. #16810984	C₂²	semidirect
66. #16810984	C₂²	semidirect
67. #16810983	C₂²	semidirect
68. #16810982	C₂²	semidirect
69. #16810981	C₂²	semidirect
70. #16810981	C₂²	semidirect
71. #16810980	C₂²	semidirect
72. #16810979	C₂²	semidirect
73. #16810979	C₂²	semidirect
74. #16810978	C₂²	semidirect
75. #16810977	C₂²	semidirect
76. #16810976	C₂²	semidirect
77. #16810976	C₂²	semidirect
78. #16810971	C₂²	semidirect
79. #16810970	C₂²	semidirect
80. #16810969	C₂²	semidirect
81. #16810968	C₂²	semidirect
82. #16810968	C₂²	semidirect
83. #16810968	C₂²	semidirect
84. #16810968	C₂²	semidirect
85. #16810629	C₂²	semidirect
86. #16810628	C₂²	semidirect
87. #16810627	C₂²	semidirect
88. #16810626	C₂²	semidirect
89. #16810626	C₂²	semidirect
90. #16810625	C₂²	semidirect
91. #16810624	C₂²	semidirect
92. #16810623	C₂²	semidirect
93. #16810622	C₂²	semidirect
94. #16810621	C₂²	semidirect
95. #16810620	C₂²	semidirect
96. #16810619	C₂²	semidirect
97. #16810618	C₂²	semidirect
98. #16810618	C₂²	semidirect
99. #16810617	C₂²	semidirect
100. #16810616	C₂²	semidirect
101. #16810616	C₂²	semidirect
102. #103×D₅₃	C₂²	semidirect
103. #103×D₅₃	C₂²	semidirect
104. #103×D₅₃	C₂²	semidirect
105. C₂×#13133139	C₂²	semidirect
106. C₂×#13133138	C₂²	semidirect
107. C₂×#13133137	C₂²	semidirect
112. #102×D₅₃	C₂²	semidirect
113. #102×D₅₃	C₂²	semidirect
114. #102×D₅₃	C₂²	semidirect
115. #102×D₅₃	C₂²	semidirect
116. #102×D₅₃	C₂²	semidirect
117. #16810581	C₂²	semidirect
118. #16810580	C₂²	semidirect
119. #16810579	C₂²	semidirect
120. #16810578	C₂²	semidirect
121. #16810577	C₂²	semidirect
122. #97×D₅₃	C₂²	semidirect
123. C₄×C₈×D₅₃	C₂²	semidirect
124. C₅₃×#544	C₂²	semidirect
126. C₅₃×#490	C₂²	semidirect
127. C₅₃×#489	C₂²	semidirect
128. C₅₃×#488	C₂²	semidirect
129. C₅₃×#486	C₂²	semidirect
130. C₅₃×#418	C₂²	semidirect
131. C₅₃×#417	C₂²	semidirect
132. C₅₃×#416	C₂²	semidirect
133. C₂×#102×C₅₃	C₂²	semidirect
134. C₅₃×#405	C₂²	semidirect
171. #13133217	C₂³	semidirect
176. #13133216	C₂³	semidirect
177. #13133216	C₂³	semidirect
186. #13133209	C₂³	semidirect
189. #13133208	C₂³	semidirect
190. #13133208	C₂³	semidirect
253. #13133142	C₂³	semidirect
254. #13133142	C₂³	semidirect
255. #13133142	C₂³	semidirect
256. #13133141	C₂³	semidirect
257. #13133141	C₂³	semidirect
258. #13133141	C₂³	semidirect
259. #13133140	C₂³	semidirect
260. #13133140	C₂³	semidirect
261. #13133140	C₂³	semidirect
266. #13133139	C₂³	semidirect
267. #13133139	C₂³	semidirect
268. #13133139	C₂³	semidirect
273. #13133138	C₂³	semidirect
274. #13133138	C₂³	semidirect
275. #13133138	C₂³	semidirect
280. #13133137	C₂³	semidirect
281. #13133137	C₂³	semidirect
282. #13133137	C₂³	semidirect
283. #13133128	C₂³	semidirect
284. #13133127	C₂³	semidirect
285. #13133127	C₂³	semidirect
286. C₄×#88322	C₂³	semidirect
287. C₈×Dic₅₃	C₂³	semidirect
288. C₈×Dic₅₃	C₂³	semidirect
294. C₄⋊Q₈×C₅₃	C₂³	semidirect
297. #125×C₅₃	C₂³	semidirect
306. #103×C₅₃	C₂³	semidirect
307. #103×C₅₃	C₂³	semidirect
308. #103×C₅₃	C₂³	semidirect
313. #102×C₅₃	C₂³	semidirect
314. #102×C₅₃	C₂³	semidirect
315. #102×C₅₃	C₂³	semidirect
316. #97×C₅₃	C₂³	semidirect
317. C₄×C₈×C₅₃	C₂³	semidirect
640. #3136	D₅₃	direct (N × H)
659. D₅₃	#3136	direct (N × H)
672. #544	C₂×D₅₃	semidirect
702. #490	C₂×D₅₃	semidirect
710. #489	C₂×D₅₃	semidirect
718. #488	C₂×D₅₃	semidirect
726. #486	C₂×D₅₃	semidirect
732. #418	C₂×D₅₃	semidirect
738. #417	C₂×D₅₃	semidirect
746. #416	C₂×D₅₃	semidirect
762. C₂×#102	C₂×D₅₃	semidirect
768. #405	C₂×D₅₃	semidirect
771. C₅₃	C₂×#3136	semidirect
822. C₄⋊Q₈	C₂²×D₅₃	semidirect
840. #125	C₂²×D₅₃	semidirect
916. #103	C₂²×D₅₃	semidirect
917. #103	C₂²×D₅₃	semidirect
918. #103	C₂²×D₅₃	semidirect
944. #102	C₂²×D₅₃	semidirect
945. #102	C₂²×D₅₃	semidirect
946. #102	C₂²×D₅₃	semidirect
950. #97	C₂²×D₅₃	semidirect
954. C₄×C₈	C₂²×D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#544×D₅₃	2
#535×D₅₃	2
#20285074	2
#20285073	2
#20285072	2
#20285071	2
#20285070	2
#20285069	2
#20285068	2
#20285067	2
#20285066	2
#20285065	2
#20285064	2
#490×D₅₃	2
#489×D₅₃	2
#488×D₅₃	2
#486×D₅₃	2
#417×D₅₃	2
#418×D₅₃	2
#416×D₅₃	2
C₂×#102×D₅₃	2
#405×D₅₃	2
C₅₃×#3136	2
C₂×#3136	53

Subgroups — D53×#3136 #28253322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3136 #28253322