Subgroups — D₅₃×#3176 #28253918

Order 13568.

2098 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#540×D₅₃	C₂	1	2	yes	maximal, complemented
2	#20285366	C₂	1	1	yes	maximal, characteristic, complemented
3	#20285365	C₂	1	1	yes	maximal, characteristic, complemented
4	#20285364	C₂	1	2	yes	maximal, complemented
5	#20285363	C₂	1	2	yes	maximal, complemented
6	#20285362	C₂	1	1	yes	maximal, characteristic, complemented
7	#20285361	C₂	1	2	yes	maximal, complemented
8	#20285360	C₂	1	2	yes	maximal, complemented
9	#20285359	C₂	1	2	yes	maximal, complemented
10	#20285358	C₂	1	2	yes	maximal, complemented
11	#499×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#493×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#490×D₅₃	C₂	1	2	yes	maximal, complemented
14	#469×D₅₃	C₂	1	2	yes	maximal, complemented
15	#466×D₅₃	C₂	1	2	yes	maximal, complemented
16	#442×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₄×D₈×D₅₃	C₂	1	2	yes	maximal, complemented
18	#405×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₈×D₅₃	C₂²	1	2	yes	—
21	C₂×D₈×D₅₃	C₂²	1	2	yes	—
22	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
24	#16811229	C₂²	1	2	yes	complemented
25	#16811228	C₂²	1	2	yes	complemented
26	#16811227	C₂²	1	2	yes	complemented
27	#16811226	C₂²	1	4	yes	complemented
28	#16811225	—	2	4	no	—
29	#16811224	C₂²	1	4	yes	complemented
30	#16811223	—	2	4	no	—
31	#127×D₅₃	C₂²	1	2	yes	—
32	#125×D₅₃	C₂²	1	2	yes	—
33	#123×D₅₃	—	2	4	no	—
34	#121×D₅₃	—	2	4	no	—
35	#121×D₅₃	C₂²	1	4	yes	—
36	C₄×D₄×D₅₃	C₂²	1	4	yes	—
37	#117×D₅₃	C₂²	1	1	yes	characteristic
38	#16811025	C₂²	1	1	yes	characteristic, complemented
39	#16811024	C₂²	1	2	yes	complemented
40	#16811023	C₂²	1	2	yes	complemented
41	#16811022	C₂²	1	2	yes	complemented
42	#16811000	C₂²	1	1	yes	characteristic, complemented
43	#16810999	C₂²	1	2	yes	complemented
44	#16810998	C₂²	1	2	yes	complemented
45	#16810998	C₂²	1	2	yes	complemented
46	#16810989	C₂²	1	2	yes	complemented
47	#16810988	C₂²	1	2	yes	complemented
48	#16810987	C₂²	1	2	yes	complemented
49	#16810986	C₂²	1	4	yes	complemented
50	#16810986	C₂²	1	4	yes	complemented
51	#16810877	C₂²	1	2	yes	complemented
52	#16810876	C₂²	1	2	yes	complemented
53	#16810875	C₂²	1	4	yes	complemented
54	#16810874	C₂²	1	4	yes	complemented
55	#16810873	C₂²	1	2	yes	complemented
56	#16810860	C₂²	1	2	yes	complemented
57	#16810859	C₂²	1	2	yes	complemented
58	#16810858	C₂²	1	4	yes	complemented
59	#16810857	C₂²	1	4	yes	complemented
60	#16810856	C₂²	1	2	yes	complemented
61	#16810736	C₂²	1	2	yes	complemented
62	#16810735	C₂²	1	2	yes	complemented
63	#16810734	C₂²	1	2	yes	complemented
64	#16810733	C₂²	1	4	yes	complemented
65	#16810732	C₂²	1	4	yes	complemented
66	C₄×D₄₂₄	C₂²	1	2	yes	complemented
67	D₈×Dic₅₃	C₂²	1	2	yes	complemented
68	#16810705	C₂²	1	2	yes	complemented
69	C₄×#11719922	C₂²	1	4	yes	complemented
70	#16810703	C₂²	1	4	yes	complemented
71	#107×D₅₃	C₂²	1	2	yes	—
72	#106×D₅₃	C₂²	1	2	yes	—
73	#102×D₅₃	C₂²	1	4	yes	—
74	#102×D₅₃	C₂²	1	4	yes	—
75	#16810581	C₂²	1	1	yes	characteristic, complemented
76	#16810580	C₂²	1	1	yes	characteristic, complemented
77	#16810580	C₂²	1	1	yes	characteristic, complemented
78	#16810579	C₂²	1	1	yes	characteristic, complemented
79	#16810578	C₂²	1	1	yes	characteristic, complemented
80	#16810577	C₂²	1	1	yes	characteristic, complemented
81	#16810577	C₂²	1	1	yes	characteristic, complemented
82	#97×D₅₃	C₂²	1	1	yes	characteristic
83	#97×D₅₃	C₂²	1	1	yes	characteristic
84	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
85	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
86	C₅₃×#540	C₂²	1	2	yes	complemented
87	C₅₃×#499	C₂²	1	1	yes	characteristic, complemented
88	C₅₃×#493	C₂²	1	1	yes	characteristic, complemented
89	C₅₃×#490	C₂²	1	2	yes	complemented
90	C₅₃×#469	C₂²	1	2	yes	complemented
91	C₅₃×#466	C₂²	1	2	yes	complemented
92	C₅₃×#442	C₂²	1	2	yes	complemented
93	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
94	C₅₃×#405	C₂²	1	1	yes	characteristic, complemented
95	C₂×D₄×D₅₃	—	2	4	no	—
96	C₂×D₄×D₅₃	—	2	4	no	—
97	C₂×D₄×D₅₃	C₂³	1	4	yes	—
98	C₂²×C₄×D₅₃	—	2	4	no	—
99	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
100	C₂×D₄₂₄	C₂³	1	2	yes	—
101	C₂×D₄₂₄	C₂³	1	2	yes	—
102	C₂×#11719922	C₂³	1	4	yes	—
103	C₂×#11719922	C₂³	1	4	yes	—
104	D₈×D₅₃	—	2	8	no	—
105	D₈×D₅₃	—	2	8	no	—
106	C₂×#11719917	C₂³	1	1	yes	characteristic
107	C₂×#11719912	C₂³	1	1	yes	characteristic
108	C₂×#11719912	C₂³	1	1	yes	characteristic
109	M₁₆×D₅₃	—	2	4	no	—
110	C₂²×#88322	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₅₃	—	2	4	no	—
112	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
113	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
116	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
117	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
118	#13133214	C₂³	1	2	yes	—
119	#13133213	—	2	4	no	—
120	#13133213	C₂³	1	4	yes	—
121	#13133209	C₂³	1	2	yes	—
122	#13133208	C₂³	1	4	yes	—
123	#13133207	—	2	4	no	—
124	#13133202	—	2	4	no	—
125	#13133202	—	2	4	no	—
126	#13133201	—	2	4	no	—
127	#13133200	—	2	4	no	—
128	#13133199	—	2	4	no	—
129	#13133199	—	2	4	no	—
130	#13133198	—	2	4	no	—
131	#13133192	—	2	4	no	—
132	#13133192	C₂³	1	4	yes	—
133	#13133191	—	2	4	no	—
134	#13133191	C₂³	1	4	yes	—
135	#13133190	—	2	4	no	—
136	#13133190	—	2	4	no	—
137	#13133190	—	2	4	no	—
138	#13133189	—	2	4	no	—
139	#13133189	—	2	4	no	—
140	#13133189	—	2	4	no	—
141	#13133188	—	2	4	no	—
142	#13133188	C₂³	1	4	yes	—
143	C₄×D₂₁₂	C₂³	1	4	yes	—
144	D₄×Dic₅₃	C₂³	1	4	yes	—
145	#13133179	C₂³	1	4	yes	—
146	C₄×C₂²⋊D₅₃	—	2	4	no	—
147	#13133177	—	2	4	no	—
148	#13133176	C₂³	1	1	yes	characteristic
149	#13133175	D₄	1	2	yes	—
150	#13133174	C₂³	1	1	yes	characteristic
151	#13133174	C₂³	1	1	yes	characteristic
152	#13133173	D₄	1	2	yes	—
153	C₄⋊C₄×D₅₃	—	2	4	no	—
154	C₄⋊C₄×D₅₃	D₄	1	2	yes	—
155	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
156	C₂²⋊C₄×D₅₃	—	2	4	no	—
157	C₂²⋊C₄×D₅₃	—	2	4	no	—
158	C₂²⋊C₄×D₅₃	D₄	1	2	yes	—
159	C₄²×D₅₃	C₂³	1	1	yes	characteristic
160	C₄²×D₅₃	C₂³	1	1	yes	characteristic
161	#13133151	C₂³	1	2	yes	—
162	#13133150	C₂³	1	4	yes	—
163	#13133149	C₂³	1	2	yes	—
164	#13133148	C₂³	1	4	yes	—
165	#13133139	C₂³	1	4	yes	—
166	#13133139	C₂³	1	4	yes	—
167	#13133138	C₂³	1	4	yes	—
168	#13133138	C₂³	1	4	yes	—
169	#13133137	C₂³	1	4	yes	—
170	#13133137	C₂³	1	4	yes	—
171	#13133128	C₂³	1	1	yes	characteristic
172	#13133128	C₂³	1	1	yes	characteristic
173	#13133127	C₂³	1	1	yes	characteristic
174	#13133127	C₂³	1	1	yes	characteristic
175	#13133127	C₂³	1	1	yes	characteristic
176	#13133127	C₂³	1	1	yes	characteristic
177	C₄×#88322	C₂³	1	1	yes	characteristic
178	C₄×#88322	C₂³	1	1	yes	characteristic
179	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
180	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
181	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
182	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
183	C₂×D₈×C₅₃	C₂³	1	2	yes	—
184	C₂×D₈×C₅₃	C₂³	1	2	yes	—
185	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
187	#127×C₅₃	C₂³	1	2	yes	—
188	#125×C₅₃	C₂³	1	2	yes	—
189	#123×C₅₃	—	2	4	no	—
190	#121×C₅₃	—	2	4	no	—
191	#121×C₅₃	C₂³	1	4	yes	—
192	C₄×D₄×C₅₃	C₂³	1	4	yes	—
193	#117×C₅₃	C₂³	1	1	yes	characteristic
194	#107×C₅₃	C₂³	1	2	yes	—
195	#106×C₅₃	C₂³	1	2	yes	—
196	#102×C₅₃	C₂³	1	4	yes	—
197	#102×C₅₃	C₂³	1	4	yes	—
198	#97×C₅₃	C₂³	1	1	yes	characteristic
199	#97×C₅₃	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
202	C₂³×D₅₃	—	2	4	no	—
203	C₂³×D₅₃	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₅₃	—	2	4	no	—
205	C₂×D₄×C₅₃	—	2	4	no	—
206	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₅₃	—	2	4	no	—
208	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₂²⋊D₅₃	—	2	4	no	—
210	C₂×C₂²⋊D₅₃	—	2	4	no	—
211	C₂×C₂²⋊D₅₃	—	2	4	no	—
212	C₂×C₂²⋊D₅₃	—	2	4	no	—
213	C₂×C₂²⋊D₅₃	—	2	4	no	—
214	C₂²×Dic₅₃	—	2	4	no	—
215	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
216	D₄×D₅₃	—	2	8	no	—
217	D₄×D₅₃	—	2	8	no	—
218	D₄×D₅₃	—	8	8	no	—
219	D₄×D₅₃	—	8	8	no	—
220	C₂×D₂₁₂	—	2	4	no	—
221	C₂×D₂₁₂	—	2	4	no	—
222	C₂×D₂₁₂	C₂⁴	1	4	yes	—
223	C₂×C₄×D₅₃	—	2	2	no	—
224	C₂×C₄×D₅₃	—	2	2	no	—
225	C₂×C₄×D₅₃	—	2	4	no	—
226	C₂×C₄×D₅₃	—	2	4	no	—
227	C₂×C₄×D₅₃	—	2	4	no	—
228	C₂×C₄×D₅₃	—	8	8	no	—
229	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
230	C₂×C₄×D₅₃	C₂×D₄	1	2	yes	—
231	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
232	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
233	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
235	D₈×C₅₃	—	2	4	no	—
236	D₈×C₅₃	—	2	4	no	—
237	M₁₆×C₅₃	—	2	2	no	—
238	C₂×C₈×C₅₃	—	2	2	no	—
239	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
243	C₄⋊C₄×C₅₃	—	2	4	no	—
244	C₄⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
246	C₂²⋊C₄×C₅₃	—	2	4	no	—
247	C₂²⋊C₄×C₅₃	—	2	4	no	—
248	C₂²⋊C₄×C₅₃	C₂×D₄	1	2	yes	—
249	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
250	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
251	C₂²⋊Dic₅₃	—	2	4	no	—
252	C₂²⋊Dic₅₃	—	2	4	no	—
253	C₂²⋊Dic₅₃	C₂×D₄	1	2	yes	—
254	#11719922	—	2	8	no	—
255	#11719922	—	2	8	no	—
256	#11719921	—	2	4	no	—
257	#11719921	—	2	4	no	—
258	#11719921	—	2	4	no	—
259	#11719921	—	2	4	no	—
260	#11719921	C₂×D₄	1	2	yes	—
261	#11719921	C₂×D₄	1	2	yes	—
262	C₄⋊Dic₅₃	—	2	4	no	—
263	C₄⋊Dic₅₃	C₂×D₄	1	2	yes	—
264	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
265	#11719919	—	2	4	no	—
266	#11719919	—	2	4	no	—
267	#11719919	—	2	4	no	—
268	#11719919	C₂×D₄	1	2	yes	—
269	#11719919	C₂×D₄	1	2	yes	—
270	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
271	C₄×Dic₅₃	C₂×D₄	1	2	yes	—
272	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
273	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
274	#11719917	—	2	2	no	—
275	C₂×#88322	—	2	2	no	—
276	C₂×#88322	C₂⁴	1	1	yes	characteristic
277	C₂×#88322	C₂⁴	1	1	yes	characteristic
278	C₂×#88322	C₂⁴	1	1	yes	characteristic
279	C₂×#88322	C₂⁴	1	1	yes	characteristic
280	D₄₂₄	—	2	4	no	—
281	D₄₂₄	—	2	4	no	—
282	#11719912	—	2	2	no	—
283	#11719912	—	2	2	no	—
284	C₈×D₅₃	—	2	2	no	—
285	C₈×D₅₃	—	2	2	no	—
286	C₈×D₅₃	—	2	2	no	—
287	C₈×D₅₃	—	2	2	no	—
288	C₈×D₅₃	#41	1	4	yes	—
289	C₈×D₅₃	#41	1	4	yes	—
290	C₂³×C₅₃	—	2	4	no	—
291	C₂³×C₅₃	C₂²×D₄	1	1	yes	characteristic
292	C₂²×D₅₃	—	2	2	no	—
293	C₂²×D₅₃	—	2	4	no	—
294	C₂²×D₅₃	—	2	4	no	—
295	C₂²×D₅₃	—	4	8	no	—
296	C₂²×D₅₃	—	4	8	no	—
297	C₂²×D₅₃	—	4	8	no	—
298	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
299	C₂²×D₅₃	C₂²×D₄	1	1	yes	characteristic
300	D₄×C₅₃	—	2	4	no	—
301	D₄×C₅₃	—	2	4	no	—
302	D₄×C₅₃	—	8	4	no	—
303	D₄×C₅₃	—	8	4	no	—
304	C₂×C₄×C₅₃	—	2	1	no	—
305	C₂×C₄×C₅₃	—	2	1	no	—
306	C₂×C₄×C₅₃	—	2	4	no	—
307	C₂×C₄×C₅₃	—	8	4	no	—
308	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅₃	C₂²×D₄	1	2	yes	—
311	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
312	C₂²⋊D₅₃	—	4	8	no	—
313	C₂²⋊D₅₃	—	8	4	no	—
314	C₂²⋊D₅₃	—	8	4	no	—
315	C₂²⋊D₅₃	—	8	4	no	—
316	C₂²⋊D₅₃	—	8	4	no	—
317	C₂×Dic₅₃	—	2	2	no	—
318	C₂×Dic₅₃	—	2	4	no	—
319	C₂×Dic₅₃	—	8	4	no	—
320	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
321	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
322	C₂×Dic₅₃	C₂²×D₄	1	2	yes	—
323	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
324	D₂₁₂	—	2	4	no	—
325	D₂₁₂	—	2	4	no	—
326	D₂₁₂	—	8	4	no	—
327	D₂₁₂	—	8	4	no	—
328	C₄×D₅₃	—	2	2	no	—
329	C₄×D₅₃	—	2	4	no	—
330	C₄×D₅₃	—	2	4	no	—
331	C₄×D₅₃	—	2	1	no	—
332	C₄×D₅₃	—	2	1	no	—
333	C₄×D₅₃	—	2	2	no	—
334	C₄×D₅₃	—	4	8	no	—
335	C₄×D₅₃	—	8	4	no	—
336	C₄×D₅₃	—	8	4	no	—
337	C₄×D₅₃	C₂×#41	1	2	yes	—
338	C₄×D₅₃	C₂×#41	1	2	yes	—
339	C₈×C₅₃	—	2	1	no	—
340	C₈×C₅₃	—	2	1	no	—
341	C₈×C₅₃	C₂×#41	1	2	yes	—
342	C₈×C₅₃	C₂×#41	1	2	yes	—
343	#88322	—	2	1	no	—
344	#88322	—	2	1	no	—
345	#88322	C₂×#41	1	2	yes	—
346	#88322	C₂×#41	1	2	yes	—
347	C₂×#3176	—	53	1	no	maximal, Sylow
348	C₂²×C₅₃	—	2	1	no	—
349	C₂²×C₅₃	—	2	2	no	—
350	C₂²×C₅₃	—	4	4	no	—
351	C₂²×C₅₃	—	4	4	no	—
352	C₂²×C₅₃	—	4	4	no	—
353	C₂²×C₅₃	C₂³×D₄	1	1	yes	characteristic
354	C₂×D₅₃	—	2	1	no	—
355	C₂×D₅₃	—	2	2	no	—
356	C₂×D₅₃	—	4	4	no	—
357	C₂×D₅₃	—	4	4	no	—
358	C₂×D₅₃	—	4	4	no	—
359	C₂×D₅₃	—	4	4	no	—
360	C₂×D₅₃	—	8	16	no	—
361	C₂×D₅₃	#532	1	2	yes	—
362	C₂×D₅₃	#576	1	4	yes	—
363	C₄×C₅₃	—	2	1	no	—
364	C₄×C₅₃	—	2	2	no	—
365	C₄×C₅₃	—	2	2	no	—
366	C₄×C₅₃	—	4	4	no	—
367	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
368	C₄×C₅₃	C₂²×#41	1	1	yes	characteristic
369	Dic₅₃	—	2	1	no	—
370	Dic₅₃	—	2	2	no	—
371	Dic₅₃	—	2	2	no	—
372	Dic₅₃	—	4	4	no	—
373	Dic₅₃	#532	1	2	yes	—
374	C₂×#540	—	53	2	no	—
375	#3176	—	53	1	no	—
376	#3176	—	53	1	no	—
377	#3176	—	53	2	no	—
378	#3176	—	53	2	no	—
379	#3176	—	53	2	no	—
380	#3176	—	53	2	no	—
381	#3176	—	53	2	no	—
382	#3176	—	53	1	no	—
383	#3176	—	53	2	no	—
384	#3176	D₅₃	1	1	yes	characteristic, direct product factor
385	C₂×#499	—	53	1	no	—
386	C₂×#493	—	53	1	no	—
387	C₂×#490	—	53	2	no	—
388	C₂×#469	—	53	2	no	—
389	C₂×#466	—	53	2	no	—
390	C₂×#442	—	53	2	no	—
391	C₂×C₄×D₈	—	53	2	no	—
392	C₂×#405	—	53	1	no	—
393	C₂×C₅₃	—	4	1	no	—
394	C₂×C₅₃	—	8	4	no	—
395	C₂×C₅₃	C₂×#532	1	1	yes	characteristic
396	C₂×C₅₃	C₂×#576	1	2	yes	—
397	D₅₃	—	4	1	no	—
398	D₅₃	—	8	4	no	—
399	D₅₃	#3176	1	4	yes	direct product factor
400	C₂²×D₈	—	53	2	no	—
401	C₂²×D₈	—	53	2	no	—
402	C₂²×M₁₆	—	53	1	no	—
403	C₂³×C₈	—	53	1	no	—
404	#540	—	53	2	no	—
405	#540	—	53	2	no	—
406	#540	—	53	4	no	—
407	#540	—	53	4	no	—
408	#540	—	53	2	no	—
409	#540	—	106	4	no	—
410	#540	—	106	4	no	—
411	#540	C₂×D₅₃	1	2	yes	complemented
412	C₂×#127	—	53	2	no	—
413	C₂×#125	—	53	2	no	—
414	C₂×#123	—	106	4	no	—
415	C₂×#121	—	53	4	no	—
416	C₂×#121	—	106	4	no	—
417	C₂×C₄×D₄	—	53	4	no	—
418	C₂×#117	—	53	1	no	—
419	#499	—	53	2	no	—
420	#499	—	53	2	no	—
421	#499	—	53	2	no	—
422	#499	—	53	1	no	—
423	#499	C₂×D₅₃	1	1	yes	characteristic, complemented
424	#493	—	53	2	no	—
425	#493	—	53	2	no	—
426	#493	—	53	2	no	—
427	#493	—	53	1	no	—
428	#493	C₂×D₅₃	1	1	yes	characteristic, complemented
429	#490	—	53	2	no	—
430	#490	—	53	2	no	—
431	#490	—	53	4	no	—
432	#490	—	53	4	no	—
433	#490	—	53	2	no	—
434	#490	C₂×D₅₃	1	2	yes	complemented
435	#469	—	53	2	no	—
436	#469	—	53	2	no	—
437	#469	—	53	4	no	—
438	#469	—	53	2	no	—
439	#469	—	53	4	no	—
440	#469	C₂×D₅₃	1	2	yes	complemented
441	#466	—	53	2	no	—
442	#466	—	53	2	no	—
443	#466	—	53	4	no	—
444	#466	—	53	2	no	—
445	#466	—	53	4	no	—
446	#466	C₂×D₅₃	1	2	yes	complemented
447	#442	—	53	2	no	—
448	#442	—	53	4	no	—
449	#442	—	53	2	no	—
450	#442	—	53	4	no	—
451	#442	—	53	2	no	—
452	#442	C₂×D₅₃	1	2	yes	complemented
453	C₄×D₈	—	53	2	no	—
454	C₄×D₈	—	53	4	no	—
455	C₄×D₈	—	53	2	no	—
456	C₄×D₈	—	53	4	no	—
457	C₄×D₈	—	53	2	no	—
458	C₄×D₈	C₂×D₅₃	1	2	yes	complemented
459	C₂×#107	—	53	2	no	—
460	C₂×#106	—	53	2	no	—
461	C₂×#102	—	53	4	no	—
462	C₂×#102	—	53	4	no	—
463	#405	—	53	1	no	—
464	#405	—	53	1	no	—
465	#405	—	53	1	no	—
466	#405	—	53	1	no	—
467	#405	—	53	1	no	—
468	#405	—	53	1	no	—
469	#405	—	53	1	no	—
470	#405	C₂×D₅₃	1	1	yes	characteristic, complemented
471	C₂×#97	—	53	1	no	—
472	C₂×#97	—	53	1	no	—
473	C₂×C₄×C₈	—	53	1	no	—
474	C₂×C₄×C₈	—	53	1	no	—
475	C₅₃	C₂×#3176	1	1	yes	characteristic, complemented, Sylow
476	C₂²×D₄	—	53	4	no	—
477	C₂²×D₄	—	106	4	no	—
478	C₂²×D₄	—	106	4	no	—
479	C₂³×C₄	—	53	1	no	—
480	C₂³×C₄	—	106	4	no	—
481	C₂×D₈	—	53	4	no	—
482	C₂×D₈	—	53	4	no	—
483	C₂×D₈	—	53	2	no	—
484	C₂×D₈	—	53	2	no	—
485	C₂×D₈	—	106	8	no	—
486	C₂×D₈	—	106	8	no	—
487	C₂×D₈	C₂²×D₅₃	1	2	yes	—
488	C₂×D₈	C₂²×D₅₃	1	2	yes	—
489	C₂×M₁₆	—	53	1	no	—
490	C₂×M₁₆	—	53	1	no	—
491	C₂×M₁₆	—	53	1	no	—
492	C₂×M₁₆	—	106	4	no	—
493	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
494	C₂²×C₈	—	53	1	no	—
495	C₂²×C₈	—	53	1	no	—
496	C₂²×C₈	—	53	1	no	—
497	C₂²×C₈	—	53	1	no	—
498	C₂²×C₈	—	53	1	no	—
499	C₂²×C₈	—	53	1	no	—
500	C₂²×C₈	—	53	1	no	—
501	C₂²×C₈	—	106	4	no	—
502	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
503	#127	—	53	4	no	—
504	#127	—	53	2	no	—
505	#127	—	106	4	no	—
506	#127	C₂²×D₅₃	1	2	yes	—
507	#125	—	53	4	no	—
508	#125	—	53	2	no	—
509	#125	—	106	4	no	—
510	#125	C₂²×D₅₃	1	2	yes	—
511	#123	—	2	4	no	—
512	#123	—	106	4	no	—
513	#123	—	106	4	no	—
514	#123	—	106	4	no	—
515	#123	—	106	4	no	—
516	#123	—	106	4	no	—
517	#123	—	106	4	no	—
518	#123	—	106	4	no	—
519	#121	—	2	4	no	—
520	#121	—	53	4	no	—
521	#121	—	53	4	no	—
522	#121	—	53	4	no	—
523	#121	—	106	4	no	—
524	#121	—	106	4	no	—
525	#121	—	106	4	no	—
526	#121	—	106	4	no	—
527	#121	—	106	4	no	—
528	#121	—	106	4	no	—
529	#121	—	106	4	no	—
530	#121	—	106	4	no	—
531	#121	—	106	4	no	—
532	#121	C₂²×D₅₃	1	4	yes	—
533	C₄×D₄	—	53	4	no	—
534	C₄×D₄	—	53	4	no	—
535	C₄×D₄	—	53	4	no	—
536	C₄×D₄	—	106	4	no	—
537	C₄×D₄	—	106	4	no	—
538	C₄×D₄	C₂²×D₅₃	1	4	yes	—
539	#117	—	53	1	no	—
540	#117	—	53	2	no	—
541	#117	—	53	2	no	—
542	#117	—	53	1	no	—
543	#117	—	53	1	no	—
544	#117	C₂²×D₅₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	—	53	2	no	—
546	C₂×C₄⋊C₄	—	53	4	no	—
547	C₂×C₄⋊C₄	—	106	4	no	—
548	C₂×C₂²⋊C₄	—	53	2	no	—
549	C₂×C₂²⋊C₄	—	106	4	no	—
550	C₂×C₂²⋊C₄	—	106	4	no	—
551	C₂×C₄²	—	53	1	no	—
552	C₂×C₄²	—	53	1	no	—
553	#107	—	53	2	no	—
554	#107	—	53	4	no	—
555	#107	C₂²×D₅₃	1	2	yes	—
556	#106	—	53	2	no	—
557	#106	—	53	4	no	—
558	#106	C₂²×D₅₃	1	2	yes	—
559	#102	—	53	4	no	—
560	#102	—	53	4	no	—
561	#102	—	53	4	no	—
562	#102	—	53	4	no	—
563	#102	—	53	4	no	—
564	#102	—	53	4	no	—
565	#102	C₂²×D₅₃	1	4	yes	—
566	#102	C₂²×D₅₃	1	4	yes	—
567	#97	—	53	1	no	—
568	#97	—	53	1	no	—
569	#97	—	53	1	no	—
570	#97	—	53	1	no	—
571	#97	—	53	1	no	—
572	#97	—	53	1	no	—
573	#97	C₂²×D₅₃	1	1	yes	characteristic
574	#97	C₂²×D₅₃	1	1	yes	characteristic
575	C₄×C₈	—	53	1	no	—
576	C₄×C₈	—	53	1	no	—
577	C₄×C₈	—	53	1	no	—
578	C₄×C₈	—	53	1	no	—
579	C₄×C₈	—	53	1	no	—
580	C₄×C₈	—	53	1	no	—
581	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
582	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
583	C₂⁴	—	53	1	no	—
584	C₂⁴	—	106	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	53	4	no	—
588	C₂×D₄	—	106	4	no	—
589	C₂×D₄	—	106	8	no	—
590	C₂×D₄	—	106	8	no	—
591	C₂×D₄	—	106	4	no	—
592	C₂×D₄	—	106	4	no	—
593	C₂×D₄	—	106	4	no	—
594	C₂×D₄	—	106	4	no	—
595	C₂×D₄	—	106	4	no	—
596	C₂×D₄	—	106	4	no	—
597	C₂×D₄	—	424	8	no	—
598	C₂×D₄	—	424	8	no	—
599	C₂×D₄	C₂³×D₅₃	1	4	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	53	1	no	—
602	C₂²×C₄	—	53	1	no	—
603	C₂²×C₄	—	53	2	no	—
604	C₂²×C₄	—	53	2	no	—
605	C₂²×C₄	—	53	1	no	—
606	C₂²×C₄	—	53	1	no	—
607	C₂²×C₄	—	53	1	no	—
608	C₂²×C₄	—	106	2	no	—
609	C₂²×C₄	—	106	2	no	—
610	C₂²×C₄	—	106	4	no	—
611	C₂²×C₄	—	106	4	no	—
612	C₂²×C₄	—	106	4	no	—
613	C₂²×C₄	—	106	4	no	—
614	C₂²×C₄	—	424	8	no	—
615	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
616	D₈	—	2	4	no	—
617	D₈	—	2	4	no	—
618	D₈	—	106	8	no	—
619	D₈	—	106	8	no	—
620	D₈	—	106	4	no	—
621	D₈	—	106	4	no	—
622	M₁₆	—	2	2	no	—
623	M₁₆	—	106	2	no	—
624	M₁₆	—	106	2	no	—
625	M₁₆	—	106	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	53	1	no	—
628	C₂×C₈	—	53	1	no	—
629	C₂×C₈	—	53	4	no	—
630	C₂×C₈	—	53	4	no	—
631	C₂×C₈	—	53	1	no	—
632	C₂×C₈	—	53	1	no	—
633	C₂×C₈	—	106	2	no	—
634	C₂×C₈	—	106	2	no	—
635	C₂×C₈	—	106	2	no	—
636	C₂×C₈	—	106	2	no	—
637	C₂×C₈	—	106	2	no	—
638	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
639	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
640	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
641	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	53	2	no	—
644	C₄⋊C₄	—	53	2	no	—
645	C₄⋊C₄	—	53	2	no	—
646	C₄⋊C₄	—	53	4	no	—
647	C₄⋊C₄	—	106	4	no	—
648	C₄⋊C₄	—	106	4	no	—
649	C₄⋊C₄	—	106	4	no	—
650	C₄⋊C₄	—	106	4	no	—
651	C₄⋊C₄	D₄×D₅₃	1	2	yes	—
652	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	53	2	no	—
656	C₂²⋊C₄	—	53	2	no	—
657	C₂²⋊C₄	—	53	2	no	—
658	C₂²⋊C₄	—	106	4	no	—
659	C₂²⋊C₄	—	106	4	no	—
660	C₂²⋊C₄	—	106	4	no	—
661	C₂²⋊C₄	—	106	4	no	—
662	C₂²⋊C₄	—	106	4	no	—
663	C₂²⋊C₄	—	106	4	no	—
664	C₂²⋊C₄	D₄×D₅₃	1	2	yes	—
665	C₄²	—	53	2	no	—
666	C₄²	—	53	2	no	—
667	C₄²	—	53	1	no	—
668	C₄²	—	53	1	no	—
669	C₄²	C₂³×D₅₃	1	1	yes	characteristic
670	C₄²	C₂³×D₅₃	1	1	yes	characteristic
671	C₂³	—	2	4	no	—
672	C₂³	—	53	1	no	—
673	C₂³	—	53	1	no	—
674	C₂³	—	106	2	no	—
675	C₂³	—	106	4	no	—
676	C₂³	—	106	4	no	—
677	C₂³	—	212	8	no	—
678	C₂³	—	212	8	no	—
679	C₂³	—	212	8	no	—
680	C₂³	C₂×D₄×D₅₃	1	1	yes	characteristic
681	D₄	—	2	4	no	—
682	D₄	—	2	4	no	—
683	D₄	—	8	4	no	—
684	D₄	—	8	4	no	—
685	D₄	—	106	4	no	—
686	D₄	—	106	4	no	—
687	D₄	—	424	4	no	—
688	D₄	—	424	4	no	—
689	D₄	—	424	4	no	—
690	D₄	—	424	4	no	—
691	D₄	—	424	4	no	—
692	D₄	—	424	4	no	—
693	D₄	—	212	8	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	8	4	no	—
698	C₂×C₄	—	53	1	no	—
699	C₂×C₄	—	53	2	no	—
700	C₂×C₄	—	53	2	no	—
701	C₂×C₄	—	53	2	no	—
702	C₂×C₄	—	53	2	no	—
703	C₂×C₄	—	53	1	no	—
704	C₂×C₄	—	106	2	no	—
705	C₂×C₄	—	106	2	no	—
706	C₂×C₄	—	106	4	no	—
707	C₂×C₄	—	106	4	no	—
708	C₂×C₄	—	106	2	no	—
709	C₂×C₄	—	106	1	no	—
710	C₂×C₄	—	106	1	no	—
711	C₂×C₄	—	106	4	no	—
712	C₂×C₄	—	424	4	no	—
713	C₂×C₄	—	424	4	no	—
714	C₂×C₄	—	424	4	no	—
715	C₂×C₄	—	212	8	no	—
716	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
717	C₂×C₄	C₂×D₄×D₅₃	1	2	yes	—
718	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
719	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
720	C₈	—	2	1	no	—
721	C₈	—	2	1	no	—
722	C₈	—	53	2	no	—
723	C₈	—	53	2	no	—
724	C₈	—	106	1	no	—
725	C₈	—	106	1	no	—
726	C₈	#41×D₅₃	1	2	yes	—
727	C₈	#41×D₅₃	1	2	yes	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	53	4	no	—
734	C₂²	—	53	2	no	—
735	C₂²	—	106	2	no	—
736	C₂²	—	106	1	no	—
737	C₂²	—	424	16	no	—
738	C₂²	—	212	4	no	—
739	C₂²	—	212	4	no	—
740	C₂²	—	212	4	no	—
741	C₂²	—	212	4	no	—
742	C₂²	C₂²×D₄×D₅₃	1	1	yes	characteristic
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	1	no	—
746	C₄	—	4	4	no	—
747	C₄	—	53	2	no	—
748	C₄	—	106	2	no	—
749	C₄	—	106	2	no	—
750	C₄	—	106	1	no	—
751	C₄	—	212	4	no	—
752	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
753	C₄	C₂×#41×D₅₃	1	1	yes	characteristic
754	C₂	—	4	1	no	—
755	C₂	—	8	4	no	—
756	C₂	—	53	4	no	—
757	C₂	—	424	4	no	—
758	C₂	—	212	1	no	—
759	C₂	#532×D₅₃	1	1	yes	characteristic
760	C₂	#576×D₅₃	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₅₃
commutator, cosocle	C₂×C₄×C₅₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₅₃
Fitting	C₅₃×#3176	C₂
socle	C₂²×C₅₃	C₂³×D₄
hypercenter	#3176	D₅₃
hypocenter	C₅₃	C₂×#3176
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #540×D₅₃	C₂	semidirect
2. #20285366	C₂	semidirect
3. #20285365	C₂	semidirect
4. #20285364	C₂	semidirect
5. #20285363	C₂	semidirect
6. #20285362	C₂	semidirect
7. #20285361	C₂	semidirect
8. #20285360	C₂	semidirect
9. #20285359	C₂	semidirect
10. #20285358	C₂	semidirect
11. #499×D₅₃	C₂	semidirect
12. #493×D₅₃	C₂	semidirect
13. #490×D₅₃	C₂	semidirect
14. #469×D₅₃	C₂	semidirect
15. #466×D₅₃	C₂	semidirect
16. #442×D₅₃	C₂	semidirect
17. C₄×D₈×D₅₃	C₂	semidirect
18. #405×D₅₃	C₂	semidirect
19. C₅₃×#3176	C₂	semidirect
24. #16811229	C₂²	semidirect
25. #16811228	C₂²	semidirect
26. #16811227	C₂²	semidirect
27. #16811226	C₂²	semidirect
29. #16811224	C₂²	semidirect
38. #16811025	C₂²	semidirect
39. #16811024	C₂²	semidirect
40. #16811023	C₂²	semidirect
41. #16811022	C₂²	semidirect
42. #16811000	C₂²	semidirect
43. #16810999	C₂²	semidirect
44. #16810998	C₂²	semidirect
45. #16810998	C₂²	semidirect
46. #16810989	C₂²	semidirect
47. #16810988	C₂²	semidirect
48. #16810987	C₂²	semidirect
49. #16810986	C₂²	semidirect
50. #16810986	C₂²	semidirect
51. #16810877	C₂²	semidirect
52. #16810876	C₂²	semidirect
53. #16810875	C₂²	semidirect
54. #16810874	C₂²	semidirect
55. #16810873	C₂²	semidirect
56. #16810860	C₂²	semidirect
57. #16810859	C₂²	semidirect
58. #16810858	C₂²	semidirect
59. #16810857	C₂²	semidirect
60. #16810856	C₂²	semidirect
61. #16810736	C₂²	semidirect
62. #16810735	C₂²	semidirect
63. #16810734	C₂²	semidirect
64. #16810733	C₂²	semidirect
65. #16810732	C₂²	semidirect
66. C₄×D₄₂₄	C₂²	semidirect
67. D₈×Dic₅₃	C₂²	semidirect
68. #16810705	C₂²	semidirect
69. C₄×#11719922	C₂²	semidirect
70. #16810703	C₂²	semidirect
75. #16810581	C₂²	semidirect
76. #16810580	C₂²	semidirect
77. #16810580	C₂²	semidirect
78. #16810579	C₂²	semidirect
79. #16810578	C₂²	semidirect
80. #16810577	C₂²	semidirect
81. #16810577	C₂²	semidirect
86. C₅₃×#540	C₂²	semidirect
87. C₅₃×#499	C₂²	semidirect
88. C₅₃×#493	C₂²	semidirect
89. C₅₃×#490	C₂²	semidirect
90. C₅₃×#469	C₂²	semidirect
91. C₅₃×#466	C₂²	semidirect
92. C₅₃×#442	C₂²	semidirect
93. C₄×D₈×C₅₃	C₂²	semidirect
94. C₅₃×#405	C₂²	semidirect
384. #3176	D₅₃	direct (N × H)
399. D₅₃	#3176	direct (N × H)
411. #540	C₂×D₅₃	semidirect
423. #499	C₂×D₅₃	semidirect
428. #493	C₂×D₅₃	semidirect
434. #490	C₂×D₅₃	semidirect
440. #469	C₂×D₅₃	semidirect
446. #466	C₂×D₅₃	semidirect
452. #442	C₂×D₅₃	semidirect
458. C₄×D₈	C₂×D₅₃	semidirect
470. #405	C₂×D₅₃	semidirect
475. C₅₃	C₂×#3176	semidirect

Maximal subgroups

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

subgroup	index
#540×D₅₃	2
#20285366	2
#20285365	2
#20285364	2
#20285363	2
#20285362	2
#20285361	2
#20285360	2
#20285359	2
#20285358	2
#499×D₅₃	2
#493×D₅₃	2
#490×D₅₃	2
#469×D₅₃	2
#466×D₅₃	2
#442×D₅₃	2
C₄×D₈×D₅₃	2
#405×D₅₃	2
C₅₃×#3176	2
C₂×#3176	53

Subgroups — D53×#3176 #28253918

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3176 #28253918