Subgroups — D₅₃×#1669 #27366323

Order 13568.

790 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#474×D₅₃	C₂	1	2	yes	maximal
3	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20274081	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274080	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274079	C₂	1	2	yes	maximal, complemented
7	#20274078	C₂	1	2	yes	maximal, complemented
8	#20274077	C₂	1	1	yes	maximal, characteristic, complemented
9	#335×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#332×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1669	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₃	—	2	1	no	—
13	C₂×Q₁₆×D₅₃	—	2	1	no	—
14	C₂²×C₈×D₅₃	—	2	1	no	—
15	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
16	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
17	#16811003	C₂²	1	1	yes	characteristic, complemented
18	#16811002	C₂²	1	2	yes	complemented
19	#16811001	—	2	1	no	—
20	#16811001	—	2	1	no	—
21	#16810904	C₂²	1	2	yes	—
22	#16810903	C₂²	1	2	yes	—
23	#16810902	—	2	2	no	—
24	#16810901	—	2	2	no	—
25	#16810900	C₂²	1	2	yes	—
26	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
27	D₄×#88322	C₂²	1	1	yes	characteristic
28	#16810688	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₅₃	—	2	1	no	—
30	#16810686	—	2	1	no	—
31	#107×D₅₃	—	2	2	no	—
32	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
33	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
34	#102×D₅₃	—	2	2	no	—
35	C₂²⋊C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic, complemented
38	#16810375	C₂²	1	2	yes	complemented
39	#16810370	C₂²	1	2	yes	complemented
40	#16810369	C₂²	1	2	yes	complemented
41	#16810368	C₂²	1	2	yes	complemented
42	C₅₃×#494	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#474	C₂²	1	2	yes	—
44	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#332	C₂²	1	2	yes	complemented
47	C₂×Q₈×D₅₃	—	2	2	no	—
48	C₂×D₄×D₅₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₅₃	—	2	1	no	—
50	C₂×Dic₂₁₂	—	2	1	no	—
51	C₂×Dic₂₁₂	—	2	1	no	—
52	C₂×#11719925	—	2	2	no	—
53	C₂×#11719925	—	2	2	no	—
54	Q₁₆×D₅₃	—	4	4	no	—
55	Q₁₆×D₅₃	—	4	4	no	—
56	C₂²×#88322	—	2	1	no	—
57	C₂×C₈×D₅₃	—	2	1	no	—
58	C₂×C₈×D₅₃	—	2	1	no	—
59	C₂×C₈×D₅₃	—	2	1	no	—
60	C₂×C₈×D₅₃	—	2	2	no	—
61	C₂×C₈×D₅₃	—	4	4	no	—
62	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
64	#13133217	C₂³	1	2	yes	—
65	#13133216	—	2	2	no	—
66	#13133216	—	2	2	no	—
67	#13133215	—	2	2	no	—
68	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
69	D₄×Dic₅₃	D₄	1	1	yes	characteristic
70	#13133179	D₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₅₃	—	2	1	no	—
72	#13133177	—	2	1	no	—
73	C₄⋊C₄×D₅₃	—	2	2	no	—
74	C₄⋊C₄×D₅₃	—	2	2	no	—
75	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
76	C₂²⋊C₄×D₅₃	—	2	1	no	—
77	C₄²×D₅₃	C₂³	1	1	yes	characteristic
78	#13133151	—	2	2	no	—
79	#13133150	—	2	2	no	—
80	#13133150	—	2	2	no	—
81	C₄⋊#88322	C₂³	1	1	yes	characteristic
82	C₄⋊#88322	C₂³	1	2	yes	—
83	#13133146	—	2	2	no	—
84	#13133146	—	2	1	no	—
85	#13133139	—	2	2	no	—
86	#13133138	—	2	2	no	—
87	#13133137	—	2	2	no	—
88	C₂²⋊#88322	—	2	1	no	—
89	#13133129	—	2	1	no	—
90	#13133129	—	2	1	no	—
91	C₄×#88322	C₂³	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₈×Dic₅₃	D₄	1	1	yes	characteristic
94	C₂×Q₁₆×C₅₃	—	2	1	no	—
95	C₂×Q₁₆×C₅₃	—	2	1	no	—
96	C₂²×C₈×C₅₃	—	2	1	no	—
97	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
98	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
99	#107×C₅₃	—	2	2	no	—
100	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
102	#102×C₅₃	—	2	2	no	—
103	C₂²⋊C₈×C₅₃	—	2	1	no	—
104	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
105	C₂³×D₅₃	—	2	1	no	—
106	C₂×Q₈×C₅₃	—	2	2	no	—
107	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅₃	—	2	1	no	—
109	C₂×C₂²⋊D₅₃	—	2	1	no	—
110	C₂²×Dic₅₃	—	2	1	no	—
111	Q₈×D₅₃	—	4	4	no	—
112	Q₈×D₅₃	—	4	4	no	—
113	D₄×D₅₃	—	2	2	no	—
114	D₄×D₅₃	Q₁₆	1	4	yes	complemented
115	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₅₃	—	2	1	no	—
117	C₂×C₄×D₅₃	—	2	1	no	—
118	C₂×C₄×D₅₃	—	2	1	no	—
119	C₂×C₄×D₅₃	—	4	2	no	—
120	C₂×C₄×D₅₃	—	4	2	no	—
121	C₂×C₄×D₅₃	—	4	2	no	—
122	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
125	C₂×Dic₁₀₆	—	2	2	no	—
126	C₂×Dic₁₀₆	—	4	2	no	—
127	Q₁₆×C₅₃	—	4	2	no	—
128	Q₁₆×C₅₃	—	4	2	no	—
129	C₂×C₈×C₅₃	—	2	1	no	—
130	C₂×C₈×C₅₃	—	2	2	no	—
131	C₂×C₈×C₅₃	—	4	2	no	—
132	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₄⋊C₄×C₅₃	—	2	2	no	—
135	C₄⋊C₄×C₅₃	—	2	2	no	—
136	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
137	C₂²⋊C₄×C₅₃	—	2	1	no	—
138	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
139	C₂²⋊Dic₅₃	—	2	1	no	—
140	#11719925	—	4	4	no	—
141	#11719925	—	4	4	no	—
142	#11719921	—	2	1	no	—
143	#11719921	—	2	1	no	—
144	C₄⋊Dic₅₃	—	2	2	no	—
145	C₄⋊Dic₅₃	—	2	2	no	—
146	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
147	#11719919	—	2	1	no	—
148	#11719919	—	4	2	no	—
149	#11719919	—	4	2	no	—
150	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₅₃	#41	1	1	yes	characteristic
153	C₂×#88322	—	2	1	no	—
154	C₂×#88322	—	2	2	no	—
155	C₂×#88322	—	4	2	no	—
156	C₂×#88322	C₂×D₄	1	1	yes	characteristic
157	C₂×#88322	C₂×D₄	1	1	yes	characteristic
158	Dic₂₁₂	—	4	2	no	—
159	Dic₂₁₂	—	4	2	no	—
160	C₈×D₅₃	—	2	2	no	—
161	C₈×D₅₃	—	4	2	no	—
162	C₈×D₅₃	—	4	4	no	—
163	C₈×D₅₃	—	4	2	no	—
164	C₈×D₅₃	—	4	2	no	—
165	C₈×D₅₃	D₈	1	4	yes	—
166	C₂³×C₅₃	—	2	1	no	—
167	C₂²×D₅₃	—	2	1	no	—
168	C₂²×D₅₃	—	2	4	no	—
169	C₂²×D₅₃	—	4	2	no	—
170	C₂²×D₅₃	—	4	2	no	—
171	C₂²×D₅₃	#121	1	1	yes	characteristic
172	Q₈×C₅₃	—	4	2	no	—
173	Q₈×C₅₃	—	4	2	no	—
174	D₄×C₅₃	—	2	1	no	—
175	D₄×C₅₃	C₂×Q₁₆	1	2	yes	complemented
176	C₂×C₄×C₅₃	—	2	1	no	—
177	C₂×C₄×C₅₃	—	4	1	no	—
178	C₂×C₄×C₅₃	—	4	1	no	—
179	C₂×C₄×C₅₃	—	4	2	no	—
180	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
183	C₂²⋊D₅₃	—	2	4	no	—
184	C₂×Dic₅₃	—	2	1	no	—
185	C₂×Dic₅₃	—	4	2	no	—
186	C₂×Dic₅₃	—	4	2	no	—
187	C₂×Dic₅₃	#121	1	1	yes	characteristic
188	C₂×Dic₅₃	#121	1	1	yes	characteristic
189	C₂×Dic₅₃	#121	1	1	yes	characteristic
190	D₂₁₂	—	2	1	no	—
191	D₂₁₂	C₂×Q₁₆	1	2	yes	complemented
192	C₄×D₅₃	—	2	2	no	—
193	C₄×D₅₃	—	4	2	no	—
194	C₄×D₅₃	—	4	1	no	—
195	C₄×D₅₃	—	4	1	no	—
196	C₄×D₅₃	—	4	2	no	—
197	C₄×D₅₃	—	8	4	no	—
198	C₄×D₅₃	C₂×D₈	1	2	yes	—
199	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
200	C₄×D₅₃	#135	1	2	yes	—
201	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
202	Dic₁₀₆	—	4	2	no	—
203	Dic₁₀₆	—	4	2	no	—
204	Dic₁₀₆	—	8	4	no	—
205	C₈×C₅₃	—	2	1	no	—
206	C₈×C₅₃	—	4	1	no	—
207	C₈×C₅₃	—	4	2	no	—
208	C₈×C₅₃	C₂×D₈	1	2	yes	—
209	#88322	—	2	1	no	—
210	#88322	—	4	1	no	—
211	#88322	—	4	2	no	—
212	#88322	C₂×D₈	1	2	yes	—
213	C₂×#1669	—	53	1	no	maximal, Sylow
214	C₂²×C₅₃	—	2	2	no	—
215	C₂²×C₅₃	—	4	1	no	—
216	C₂²×C₅₃	—	4	1	no	—
217	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
218	C₂×D₅₃	—	2	2	no	—
219	C₂×D₅₃	—	4	1	no	—
220	C₂×D₅₃	—	4	1	no	—
221	C₂×D₅₃	—	4	8	no	—
222	C₂×D₅₃	#459	1	2	yes	—
223	C₂×D₅₃	#467	1	2	yes	—
224	C₂×D₅₃	#473	1	2	yes	—
225	C₄×C₅₃	—	2	1	no	—
226	C₄×C₅₃	—	4	1	no	—
227	C₄×C₅₃	—	8	2	no	—
228	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
229	C₄×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
230	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
231	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	Dic₅₃	—	2	1	no	—
233	Dic₅₃	—	4	1	no	—
234	Dic₅₃	—	8	2	no	—
235	Dic₅₃	#459	1	2	yes	—
236	Dic₅₃	#467	1	2	yes	—
237	C₂×#494	—	53	1	no	—
238	C₂×#474	—	53	2	no	—
239	C₂×C₈×D₄	—	53	1	no	—
240	#1669	—	53	1	no	—
241	#1669	—	53	2	no	—
242	#1669	—	53	1	no	—
243	#1669	—	53	1	no	—
244	#1669	—	53	2	no	—
245	#1669	D₅₃	1	1	yes	characteristic, direct product factor
246	C₂×#335	—	53	1	no	—
247	C₂×#332	—	53	2	no	—
248	C₂×C₅₃	—	4	2	no	—
249	C₂×C₅₃	C₂×#459	1	1	yes	characteristic
250	C₂×C₅₃	C₂×#467	1	1	yes	characteristic
251	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
252	D₅₃	—	4	2	no	—
253	D₅₃	#1669	1	4	yes	direct product factor
254	C₂²×Q₁₆	—	106	1	no	—
255	C₂²×Q₁₆	—	106	1	no	—
256	C₂³×C₈	—	106	1	no	—
257	C₂×C₄⋊Q₈	—	53	2	no	—
258	C₂×C₄×D₄	—	53	1	no	—
259	#494	—	53	2	no	—
260	#494	—	53	1	no	—
261	#494	—	106	1	no	—
262	#494	—	106	1	no	—
263	#494	C₂×D₅₃	1	1	yes	characteristic, complemented
264	#474	—	53	2	no	—
265	#474	—	53	2	no	—
266	#474	—	53	2	no	—
267	#474	—	106	2	no	—
268	#474	—	106	2	no	—
269	#474	C₂×D₅₃	1	2	yes	—
270	C₈×D₄	—	53	1	no	—
271	C₈×D₄	—	53	1	no	—
272	C₈×D₄	—	53	1	no	—
273	C₈×D₄	—	106	1	no	—
274	C₈×D₄	—	106	1	no	—
275	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
276	C₂×#107	—	106	2	no	—
277	C₂×C₄⋊C₈	—	53	1	no	—
278	C₂×C₄⋊C₈	—	53	2	no	—
279	C₂×#102	—	106	2	no	—
280	C₂×C₂²⋊C₈	—	106	1	no	—
281	C₂×C₄×C₈	—	53	1	no	—
282	#335	—	53	2	no	—
283	#335	—	53	1	no	—
284	#335	C₂×D₅₃	1	1	yes	characteristic, complemented
285	#332	—	53	2	no	—
286	#332	—	53	2	no	—
287	#332	—	53	2	no	—
288	#332	C₂×D₅₃	1	2	yes	complemented
289	C₅₃	C₂×#1669	1	1	yes	characteristic, complemented, Sylow
290	C₂²×Q₈	—	106	2	no	—
291	C₂²×D₄	—	53	1	no	—
292	C₂³×C₄	—	106	1	no	—
293	C₂×Q₁₆	—	2	1	no	—
294	C₂×Q₁₆	—	2	1	no	—
295	C₂×Q₁₆	—	106	2	no	—
296	C₂×Q₁₆	—	106	2	no	—
297	C₂×Q₁₆	—	106	1	no	—
298	C₂×Q₁₆	—	106	1	no	—
299	C₂×Q₁₆	—	212	4	no	—
300	C₂×Q₁₆	—	212	4	no	—
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	53	1	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	106	1	no	—
305	C₂²×C₈	—	106	1	no	—
306	C₂²×C₈	—	106	2	no	—
307	C₂²×C₈	—	106	1	no	—
308	C₂²×C₈	—	106	1	no	—
309	C₂²×C₈	—	212	4	no	—
310	C₄⋊Q₈	—	53	2	no	—
311	C₄⋊Q₈	—	106	2	no	—
312	C₄⋊Q₈	—	106	2	no	—
313	C₄⋊Q₈	—	106	2	no	—
314	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
315	C₄×D₄	—	53	1	no	—
316	C₄×D₄	—	53	1	no	—
317	C₄×D₄	—	53	1	no	—
318	C₄×D₄	—	106	1	no	—
319	C₄×D₄	—	106	1	no	—
320	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	—	53	1	no	—
322	C₂×C₄⋊C₄	—	106	2	no	—
323	C₂×C₄⋊C₄	—	106	2	no	—
324	C₂×C₂²⋊C₄	—	106	1	no	—
325	C₂×C₄²	—	53	1	no	—
326	#107	—	2	2	no	—
327	#107	—	106	2	no	—
328	#107	—	106	2	no	—
329	#107	—	106	2	no	—
330	C₄⋊C₈	—	53	1	no	—
331	C₄⋊C₈	—	53	2	no	—
332	C₄⋊C₈	—	106	1	no	—
333	C₄⋊C₈	—	106	2	no	—
334	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
335	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
336	#102	—	2	2	no	—
337	#102	—	106	2	no	—
338	#102	—	106	2	no	—
339	#102	—	106	2	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	106	1	no	—
342	C₂²⋊C₈	—	106	1	no	—
343	C₂²⋊C₈	—	106	1	no	—
344	C₄×C₈	—	53	1	no	—
345	C₄×C₈	—	53	1	no	—
346	C₄×C₈	—	53	1	no	—
347	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
348	C₂⁴	—	106	1	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	106	2	no	—
351	C₂×Q₈	—	212	2	no	—
352	C₂×Q₈	—	212	4	no	—
353	C₂×Q₈	—	212	4	no	—
354	C₂×D₄	—	53	4	no	—
355	C₂×D₄	—	53	1	no	—
356	C₂×D₄	—	106	2	no	—
357	C₂×D₄	—	106	1	no	—
358	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	53	1	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	106	1	no	—
364	C₂²×C₄	—	106	1	no	—
365	C₂²×C₄	—	106	1	no	—
366	C₂²×C₄	—	106	1	no	—
367	C₂²×C₄	—	212	2	no	—
368	C₂²×C₄	—	212	2	no	—
369	C₂²×C₄	—	212	2	no	—
370	Q₁₆	—	4	2	no	—
371	Q₁₆	—	4	2	no	—
372	Q₁₆	—	212	2	no	—
373	Q₁₆	—	212	4	no	—
374	Q₁₆	—	212	4	no	—
375	Q₁₆	—	212	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	53	1	no	—
380	C₂×C₈	—	53	4	no	—
381	C₂×C₈	—	53	1	no	—
382	C₂×C₈	—	106	2	no	—
383	C₂×C₈	—	106	1	no	—
384	C₂×C₈	—	106	2	no	—
385	C₂×C₈	—	212	2	no	—
386	C₂×C₈	—	212	2	no	—
387	C₂×C₈	—	212	4	no	—
388	C₂×C₈	—	212	2	no	—
389	C₂×C₈	—	212	2	no	—
390	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
391	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	53	1	no	—
395	C₄⋊C₄	—	106	1	no	—
396	C₄⋊C₄	—	106	2	no	—
397	C₄⋊C₄	—	106	2	no	—
398	C₄⋊C₄	—	212	2	no	—
399	C₄⋊C₄	—	212	2	no	—
400	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
401	C₂²⋊C₄	—	2	1	no	—
402	C₂²⋊C₄	—	106	1	no	—
403	C₂²⋊C₄	—	106	1	no	—
404	C₂²⋊C₄	—	106	1	no	—
405	C₄²	—	53	1	no	—
406	C₄²	—	53	1	no	—
407	C₄²	—	53	1	no	—
408	C₄²	C₂³×D₅₃	1	1	yes	characteristic
409	C₂³	—	2	1	no	—
410	C₂³	—	53	1	no	—
411	C₂³	—	106	4	no	—
412	C₂³	—	106	1	no	—
413	C₂³	—	212	2	no	—
414	C₂³	—	212	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	424	4	no	—
418	Q₈	—	212	2	no	—
419	Q₈	—	212	2	no	—
420	D₄	—	2	1	no	—
421	D₄	—	53	2	no	—
422	D₄	—	106	4	no	—
423	D₄	—	106	1	no	—
424	D₄	Q₁₆×D₅₃	1	2	yes	complemented
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	2	no	—
432	C₂×C₄	—	53	2	no	—
433	C₂×C₄	—	53	2	no	—
434	C₂×C₄	—	53	2	no	—
435	C₂×C₄	—	53	1	no	—
436	C₂×C₄	—	106	2	no	—
437	C₂×C₄	—	106	1	no	—
438	C₂×C₄	—	424	4	no	—
439	C₂×C₄	—	212	2	no	—
440	C₂×C₄	—	212	2	no	—
441	C₂×C₄	—	212	2	no	—
442	C₂×C₄	—	212	2	no	—
443	C₂×C₄	—	212	1	no	—
444	C₂×C₄	—	212	1	no	—
445	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
446	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
447	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
448	C₈	—	2	1	no	—
449	C₈	—	4	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	53	2	no	—
452	C₈	—	106	1	no	—
453	C₈	—	212	1	no	—
454	C₈	—	212	2	no	—
455	C₈	D₈×D₅₃	1	2	yes	—
456	C₂²	—	2	2	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	4	1	no	—
459	C₂²	—	53	2	no	—
460	C₂²	—	53	2	no	—
461	C₂²	—	53	2	no	—
462	C₂²	—	106	2	no	—
463	C₂²	—	212	8	no	—
464	C₂²	—	212	1	no	—
465	C₂²	—	212	1	no	—
466	C₂²	#121×D₅₃	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	8	2	no	—
470	C₄	—	53	2	no	—
471	C₄	—	53	2	no	—
472	C₄	—	106	1	no	—
473	C₄	—	424	2	no	—
474	C₄	—	212	1	no	—
475	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
476	C₄	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
477	C₄	#135×D₅₃	1	1	yes	characteristic
478	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
479	C₂	—	4	2	no	—
480	C₂	—	53	4	no	—
481	C₂	—	212	2	no	—
482	C₂	#459×D₅₃	1	1	yes	characteristic
483	C₂	#467×D₅₃	1	1	yes	characteristic
484	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1669	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×D₄×D₅₃	D₄
hypercenter	#1669	D₅₃
hypocenter	C₅₃	C₂×#1669
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1669

Complements

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

N	H ≅ G/N	type
1. #494×D₅₃	C₂	semidirect
4. #20274081	C₂	semidirect
5. #20274080	C₂	semidirect
6. #20274079	C₂	semidirect
7. #20274078	C₂	semidirect
8. #20274077	C₂	semidirect
9. #335×D₅₃	C₂	semidirect
10. #332×D₅₃	C₂	semidirect
11. C₅₃×#1669	C₂	semidirect
17. #16811003	C₂²	semidirect
18. #16811002	C₂²	semidirect
37. #16810376	C₂²	semidirect
38. #16810375	C₂²	semidirect
39. #16810370	C₂²	semidirect
40. #16810369	C₂²	semidirect
41. #16810368	C₂²	semidirect
42. C₅₃×#494	C₂²	semidirect
45. C₅₃×#335	C₂²	semidirect
46. C₅₃×#332	C₂²	semidirect
114. D₄×D₅₃	Q₁₆	semidirect
175. D₄×C₅₃	C₂×Q₁₆	semidirect
191. D₂₁₂	C₂×Q₁₆	semidirect
245. #1669	D₅₃	direct (N × H)
253. D₅₃	#1669	direct (N × H)
263. #494	C₂×D₅₃	semidirect
284. #335	C₂×D₅₃	semidirect
288. #332	C₂×D₅₃	semidirect
289. C₅₃	C₂×#1669	semidirect
424. D₄	Q₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#494×D₅₃	2
#474×D₅₃	2
C₈×D₄×D₅₃	2
#20274081	2
#20274080	2
#20274079	2
#20274078	2
#20274077	2
#335×D₅₃	2
#332×D₅₃	2
C₅₃×#1669	2
C₂×#1669	53

Subgroups — D53×#1669 #27366323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1669 #27366323