Subgroups — D₅₃×#1594 #27353858

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#436×D₅₃	C₂	1	2	yes	maximal, complemented
3	#20273630	C₂	1	1	yes	maximal, characteristic, complemented
4	#20273629	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273628	C₂	1	1	yes	maximal, characteristic, complemented
6	#20273627	C₂	1	2	yes	maximal, complemented
7	#20273626	C₂	1	2	yes	maximal, complemented
8	#334×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄⋊C₈×D₅₃	C₂	1	2	yes	maximal, complemented
10	#322×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	C₄	1	1	yes	characteristic
13	C₂×M₁₆×D₅₃	—	2	2	no	—
14	C₄×D₄×D₅₃	C₂²	1	2	yes	—
15	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
16	D₈×Dic₅₃	C₄	1	1	yes	characteristic
17	#16810705	C₄	1	1	yes	characteristic
18	C₄×#11719922	C₂²	1	2	yes	—
19	#16810703	C₄	1	2	yes	—
20	#16810702	C₂²	1	2	yes	complemented
21	#16810701	C₂²	1	2	yes	complemented
22	#16810700	C₂²	1	2	yes	complemented
23	#16810699	—	2	2	no	—
24	#16810698	—	2	2	no	—
25	#107×D₅₃	C₄	1	1	yes	characteristic
26	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
27	#102×D₅₃	C₄	1	2	yes	—
28	C₂²⋊C₈×D₅₃	—	2	2	no	—
29	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810374	C₂²	1	1	yes	characteristic, complemented
33	#16810373	C₂²	1	2	yes	complemented
34	#16810352	C₂²	1	2	yes	complemented
35	D₄⋊#88322	C₂²	1	2	yes	complemented
36	#16810350	C₂²	1	2	yes	complemented
37	#16810345	C₂²	1	1	yes	characteristic, complemented
38	#16810345	C₂²	1	1	yes	characteristic, complemented
39	#16810344	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₅₃×#436	C₂²	1	2	yes	complemented
42	C₅₃×#334	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₅₃×#322	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₅₃	—	2	2	no	—
47	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719922	C₂×C₄	1	2	yes	—
49	D₈×D₅₃	—	2	4	no	—
50	C₂×#11719917	—	2	2	no	—
51	C₂×#11719912	—	2	2	no	—
52	C₂×#11719912	—	2	2	no	—
53	M₁₆×D₅₃	—	4	8	no	—
54	C₂×C₈×D₅₃	—	2	2	no	—
55	C₂×C₈×D₅₃	—	2	1	no	—
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	2	yes	—
59	C₄×D₂₁₂	C₂³	1	2	yes	—
60	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
61	#13133179	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₅₃	—	2	2	no	—
63	#13133177	—	2	2	no	—
64	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₅₃	—	2	2	no	—
66	C₄²×D₅₃	C₂³	1	1	yes	characteristic
67	#13133151	C₂×C₄	1	1	yes	characteristic
68	#13133150	C₂×C₄	1	2	yes	—
69	C₄⋊#88322	C₂³	1	2	yes	—
70	#13133146	—	2	2	no	—
71	#13133139	C₂×C₄	1	2	yes	—
72	#13133138	C₂×C₄	1	2	yes	—
73	#13133137	C₂×C₄	1	2	yes	—
74	C₂²⋊#88322	—	2	2	no	—
75	#13133129	—	2	2	no	—
76	#13133129	—	2	2	no	—
77	C₄×#88322	C₂³	1	1	yes	characteristic
78	C₄×#88322	C₂³	1	1	yes	characteristic
79	C₄×#88322	C₂³	1	1	yes	characteristic
80	C₈×Dic₅₃	—	2	1	no	—
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	D₄	1	2	yes	—
84	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
85	C₂×M₁₆×C₅₃	—	2	2	no	—
86	C₄×D₄×C₅₃	C₂³	1	2	yes	—
87	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
89	#102×C₅₃	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₅₃	—	2	2	no	—
91	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₂³×D₅₃	—	2	2	no	—
95	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₅₃	—	2	2	no	—
97	C₂×C₂²⋊D₅₃	—	2	2	no	—
98	C₂²×Dic₅₃	—	2	2	no	—
99	D₄×D₅₃	—	2	4	no	—
100	D₄×D₅₃	—	2	4	no	—
101	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
102	C₂×C₄×D₅₃	—	2	2	no	—
103	C₂×C₄×D₅₃	—	2	2	no	—
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×C₄×D₅₃	—	4	4	no	—
106	C₂×C₄×D₅₃	—	4	4	no	—
107	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
110	D₈×C₅₃	—	2	2	no	—
111	M₁₆×C₅₃	—	4	4	no	—
112	C₂×C₈×C₅₃	—	2	2	no	—
113	C₂×C₈×C₅₃	—	2	1	no	—
114	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₅₃	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₅₃	—	2	2	no	—
119	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₅₃	—	2	2	no	—
121	#11719922	—	2	4	no	—
122	#11719921	—	2	2	no	—
123	#11719921	—	2	2	no	—
124	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
125	#11719919	—	2	2	no	—
126	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₅₃	#41	1	1	yes	characteristic
129	#11719917	—	4	4	no	—
130	C₂×#88322	—	2	2	no	—
131	C₂×#88322	—	2	1	no	—
132	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
133	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
134	C₂×#88322	C₂×D₄	1	2	yes	—
135	D₄₂₄	—	2	2	no	—
136	#11719912	—	4	4	no	—
137	#11719912	—	4	4	no	—
138	C₈×D₅₃	—	2	2	no	—
139	C₈×D₅₃	—	2	4	no	—
140	C₈×D₅₃	—	4	2	no	—
141	C₈×D₅₃	—	4	4	no	—
142	C₈×D₅₃	M₁₆	1	4	yes	complemented
143	C₂³×C₅₃	—	2	2	no	—
144	C₂²×D₅₃	—	2	2	no	—
145	C₂²×D₅₃	—	4	4	no	—
146	C₂²×D₅₃	—	4	4	no	—
147	C₂²×D₅₃	—	4	4	no	—
148	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
149	D₄×C₅₃	—	2	2	no	—
150	D₄×C₅₃	—	2	2	no	—
151	C₂×C₄×C₅₃	—	2	2	no	—
152	C₂×C₄×C₅₃	—	4	2	no	—
153	C₂×C₄×C₅₃	—	4	2	no	—
154	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
157	C₂²⋊D₅₃	—	4	4	no	—
158	C₂×Dic₅₃	—	2	2	no	—
159	C₂×Dic₅₃	—	4	4	no	—
160	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
163	D₂₁₂	—	2	2	no	—
164	D₂₁₂	—	2	2	no	—
165	C₄×D₅₃	—	2	2	no	—
166	C₄×D₅₃	—	4	4	no	—
167	C₄×D₅₃	—	4	2	no	—
168	C₄×D₅₃	—	4	2	no	—
169	C₄×D₅₃	—	4	4	no	—
170	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
171	C₄×D₅₃	#131	1	2	yes	—
172	C₄×D₅₃	AGL(1,ℤ/8)	1	4	yes	—
173	C₈×C₅₃	—	2	1	no	—
174	C₈×C₅₃	—	2	2	no	—
175	C₈×C₅₃	—	4	1	no	—
176	C₈×C₅₃	—	4	2	no	—
177	C₈×C₅₃	C₂×M₁₆	1	2	yes	complemented
178	#88322	—	2	1	no	—
179	#88322	—	2	2	no	—
180	#88322	—	4	1	no	—
181	#88322	—	4	2	no	—
182	#88322	C₂×M₁₆	1	2	yes	complemented
183	C₂×#1594	—	53	1	no	maximal, Sylow
184	C₂²×C₅₃	—	4	2	no	—
185	C₂²×C₅₃	—	4	2	no	—
186	C₂²×C₅₃	—	4	2	no	—
187	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂×D₅₃	—	4	2	no	—
189	C₂×D₅₃	—	4	2	no	—
190	C₂×D₅₃	—	4	2	no	—
191	C₂×D₅₃	—	8	8	no	—
192	C₂×D₅₃	#436	1	2	yes	—
193	C₂×D₅₃	#442	1	2	yes	—
194	C₂×D₅₃	#444	1	2	yes	—
195	C₄×C₅₃	—	2	1	no	—
196	C₄×C₅₃	—	4	2	no	—
197	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
198	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
199	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	Dic₅₃	—	2	1	no	—
201	Dic₅₃	—	4	2	no	—
202	Dic₅₃	#436	1	2	yes	—
203	Dic₅₃	#442	1	2	yes	—
204	C₂×C₄×D₈	—	53	1	no	—
205	C₂×#436	—	53	2	no	—
206	#1594	—	53	1	no	—
207	#1594	—	53	2	no	—
208	#1594	—	53	1	no	—
209	#1594	—	53	2	no	—
210	#1594	—	53	1	no	—
211	#1594	D₅₃	1	1	yes	characteristic, direct product factor
212	C₂×#334	—	53	1	no	—
213	C₂×D₄⋊C₈	—	53	2	no	—
214	C₂×#322	—	53	1	no	—
215	C₂×C₅₃	—	8	2	no	—
216	C₂×C₅₃	C₂×#436	1	1	yes	characteristic
217	C₂×C₅₃	C₂×#442	1	1	yes	characteristic
218	C₂×C₅₃	C₂×#444	1	1	yes	characteristic
219	D₅₃	—	8	2	no	—
220	D₅₃	#1594	1	4	yes	direct product factor
221	C₂²×D₈	—	53	1	no	—
222	C₂²×M₁₆	—	106	2	no	—
223	C₂×C₄×D₄	—	53	2	no	—
224	C₄×D₈	—	53	1	no	—
225	C₄×D₈	—	53	2	no	—
226	C₄×D₈	—	53	1	no	—
227	C₄×D₈	—	53	2	no	—
228	C₄×D₈	—	53	1	no	—
229	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
230	#436	—	53	2	no	—
231	#436	—	53	2	no	—
232	#436	—	53	2	no	—
233	#436	—	106	2	no	—
234	#436	—	106	2	no	—
235	#436	C₂×D₅₃	1	2	yes	complemented
236	C₂×#107	—	53	1	no	—
237	C₂×C₄⋊C₈	—	53	2	no	—
238	C₂×#102	—	53	2	no	—
239	C₂×C₂²⋊C₈	—	106	2	no	—
240	C₂×C₄×C₈	—	53	1	no	—
241	C₂×C₄×C₈	—	53	1	no	—
242	C₂×C₄×C₈	—	53	1	no	—
243	#334	—	53	2	no	—
244	#334	—	53	1	no	—
245	#334	C₂×D₅₃	1	1	yes	characteristic, complemented
246	D₄⋊C₈	—	53	2	no	—
247	D₄⋊C₈	—	53	2	no	—
248	D₄⋊C₈	—	53	2	no	—
249	D₄⋊C₈	C₂×D₅₃	1	2	yes	complemented
250	#322	—	53	1	no	—
251	#322	—	53	1	no	—
252	#322	—	53	1	no	—
253	#322	C₂×D₅₃	1	1	yes	characteristic, complemented
254	C₅₃	C₂×#1594	1	1	yes	characteristic, complemented, Sylow
255	C₂²×D₄	—	53	2	no	—
256	C₂³×C₄	—	106	2	no	—
257	C₂×D₈	—	53	2	no	—
258	C₂×D₈	—	53	1	no	—
259	C₂×D₈	—	106	4	no	—
260	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	106	2	no	—
263	C₂×M₁₆	—	106	2	no	—
264	C₂×M₁₆	—	106	2	no	—
265	C₂×M₁₆	—	212	8	no	—
266	C₂²×C₈	—	53	1	no	—
267	C₂²×C₈	—	53	1	no	—
268	C₂²×C₈	—	53	2	no	—
269	C₂²×C₈	—	106	2	no	—
270	C₂²×C₈	—	106	1	no	—
271	C₄×D₄	—	53	2	no	—
272	C₄×D₄	—	53	2	no	—
273	C₄×D₄	—	53	2	no	—
274	C₄×D₄	—	106	2	no	—
275	C₄×D₄	—	106	2	no	—
276	C₄×D₄	C₂²×D₅₃	1	2	yes	—
277	C₂×C₄⋊C₄	—	53	2	no	—
278	C₂×C₂²⋊C₄	—	106	2	no	—
279	C₂×C₄²	—	53	1	no	—
280	#107	—	53	1	no	—
281	#107	—	53	2	no	—
282	#107	C₄×D₅₃	1	1	yes	characteristic
283	C₄⋊C₈	—	53	2	no	—
284	C₄⋊C₈	—	106	2	no	—
285	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
286	#102	—	53	2	no	—
287	#102	—	53	2	no	—
288	#102	—	53	2	no	—
289	#102	C₄×D₅₃	1	2	yes	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	106	2	no	—
292	C₂²⋊C₈	—	106	2	no	—
293	C₂²⋊C₈	—	106	2	no	—
294	C₄×C₈	—	53	1	no	—
295	C₄×C₈	—	53	1	no	—
296	C₄×C₈	—	53	2	no	—
297	C₄×C₈	—	53	1	no	—
298	C₄×C₈	—	53	1	no	—
299	C₄×C₈	—	53	1	no	—
300	C₄×C₈	—	106	1	no	—
301	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
304	C₂⁴	—	106	2	no	—
305	C₂×D₄	—	53	2	no	—
306	C₂×D₄	—	106	4	no	—
307	C₂×D₄	—	106	4	no	—
308	C₂×D₄	—	106	2	no	—
309	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	53	1	no	—
312	C₂²×C₄	—	53	1	no	—
313	C₂²×C₄	—	53	1	no	—
314	C₂²×C₄	—	106	2	no	—
315	C₂²×C₄	—	106	2	no	—
316	C₂²×C₄	—	106	2	no	—
317	C₂²×C₄	—	106	2	no	—
318	C₂²×C₄	—	212	4	no	—
319	C₂²×C₄	—	212	4	no	—
320	D₈	—	2	2	no	—
321	D₈	—	106	4	no	—
322	D₈	—	106	2	no	—
323	M₁₆	—	4	4	no	—
324	M₁₆	—	212	4	no	—
325	M₁₆	—	212	4	no	—
326	M₁₆	—	212	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	53	1	no	—
330	C₂×C₈	—	53	4	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	53	2	no	—
333	C₂×C₈	—	106	4	no	—
334	C₂×C₈	—	106	2	no	—
335	C₂×C₈	—	106	2	no	—
336	C₂×C₈	—	106	1	no	—
337	C₂×C₈	—	212	4	no	—
338	C₂×C₈	—	212	2	no	—
339	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
341	C₂×C₈	D₄×D₅₃	1	2	yes	—
342	C₄⋊C₄	—	53	2	no	—
343	C₄⋊C₄	—	106	2	no	—
344	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	106	2	no	—
347	C₂²⋊C₄	—	106	2	no	—
348	C₂²⋊C₄	—	106	2	no	—
349	C₄²	—	53	1	no	—
350	C₄²	—	53	1	no	—
351	C₄²	—	53	1	no	—
352	C₄²	C₂³×D₅₃	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	53	1	no	—
355	C₂³	—	106	2	no	—
356	C₂³	—	212	4	no	—
357	C₂³	—	212	4	no	—
358	C₂³	—	212	4	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	2	no	—
361	D₄	—	106	2	no	—
362	D₄	—	106	2	no	—
363	D₄	—	212	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	53	1	no	—
368	C₂×C₄	—	53	1	no	—
369	C₂×C₄	—	53	2	no	—
370	C₂×C₄	—	53	2	no	—
371	C₂×C₄	—	53	4	no	—
372	C₂×C₄	—	53	1	no	—
373	C₂×C₄	—	106	2	no	—
374	C₂×C₄	—	106	2	no	—
375	C₂×C₄	—	212	4	no	—
376	C₂×C₄	—	212	4	no	—
377	C₂×C₄	—	212	4	no	—
378	C₂×C₄	—	212	2	no	—
379	C₂×C₄	—	212	2	no	—
380	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
382	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	53	2	no	—
388	C₈	—	106	1	no	—
389	C₈	—	106	2	no	—
390	C₈	—	212	1	no	—
391	C₈	—	212	2	no	—
392	C₈	M₁₆×D₅₃	1	2	yes	complemented
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	53	2	no	—
397	C₂²	—	53	2	no	—
398	C₂²	—	53	2	no	—
399	C₂²	—	424	8	no	—
400	C₂²	—	212	2	no	—
401	C₂²	—	212	2	no	—
402	C₂²	—	212	2	no	—
403	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	53	2	no	—
407	C₄	—	53	2	no	—
408	C₄	—	106	1	no	—
409	C₄	—	212	2	no	—
410	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
411	C₄	#131×D₅₃	1	1	yes	characteristic
412	C₄	AGL(1,ℤ/8)×D₅₃	1	2	yes	—
413	C₂	—	8	2	no	—
414	C₂	—	53	4	no	—
415	C₂	—	424	2	no	—
416	C₂	#436×D₅₃	1	1	yes	characteristic
417	C₂	#442×D₅₃	1	1	yes	characteristic
418	C₂	#444×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1594	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₅₃	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	#1594	D₅₃
hypocenter	C₅₃	C₂×#1594
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1594

Complements

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

N	H ≅ G/N	type
2. #436×D₅₃	C₂	semidirect
3. #20273630	C₂	semidirect
4. #20273629	C₂	semidirect
5. #20273628	C₂	semidirect
6. #20273627	C₂	semidirect
7. #20273626	C₂	semidirect
8. #334×D₅₃	C₂	semidirect
9. D₄⋊C₈×D₅₃	C₂	semidirect
10. #322×D₅₃	C₂	semidirect
11. C₅₃×#1594	C₂	semidirect
20. #16810702	C₂²	semidirect
21. #16810701	C₂²	semidirect
22. #16810700	C₂²	semidirect
32. #16810374	C₂²	semidirect
33. #16810373	C₂²	semidirect
34. #16810352	C₂²	semidirect
35. D₄⋊#88322	C₂²	semidirect
36. #16810350	C₂²	semidirect
37. #16810345	C₂²	semidirect
38. #16810345	C₂²	semidirect
39. #16810344	C₂²	semidirect
41. C₅₃×#436	C₂²	semidirect
42. C₅₃×#334	C₂²	semidirect
43. C₅₃×D₄⋊C₈	C₂²	semidirect
44. C₅₃×#322	C₂²	semidirect
142. C₈×D₅₃	M₁₆	semidirect
177. C₈×C₅₃	C₂×M₁₆	semidirect
182. #88322	C₂×M₁₆	semidirect
211. #1594	D₅₃	direct (N × H)
220. D₅₃	#1594	direct (N × H)
235. #436	C₂×D₅₃	semidirect
245. #334	C₂×D₅₃	semidirect
249. D₄⋊C₈	C₂×D₅₃	semidirect
253. #322	C₂×D₅₃	semidirect
254. C₅₃	C₂×#1594	semidirect
392. C₈	M₁₆×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₅₃	2
#436×D₅₃	2
#20273630	2
#20273629	2
#20273628	2
#20273627	2
#20273626	2
#334×D₅₃	2
D₄⋊C₈×D₅₃	2
#322×D₅₃	2
C₅₃×#1594	2
C₂×#1594	53

Subgroups — D53×#1594 #27353858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1594 #27353858