Subgroups — D₅₃⋊#1567 #28316104

Order 13568.

854 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅₃⋊#423	C₂	1	2	yes	maximal
2	#20290274	C₂	1	2	yes	maximal, complemented
3	#20290273	C₂	1	2	yes	maximal, complemented
4	#20290272	C₂	1	4	yes	maximal, complemented
5	D₅₃⋊#335	C₂	1	4	yes	maximal, complemented
6	C₂×C₄×C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
7	C₂×D₅₃⋊M₁₆	—	2	2	no	—
8	#16811628	—	2	2	no	—
9	#16811627	C₂²	1	4	yes	—
10	#16811626	—	2	2	no	—
11	#16811626	C₂²	1	4	yes	—
12	D₅₃⋊(C₄⋊C₈)	—	2	2	no	—
13	D₅₃⋊(C₄⋊C₈)	C₂²	1	4	yes	—
14	#16811487	C₂²	1	8	yes	complemented
15	#16811486	C₂²	1	8	yes	complemented
16	C₂²×C₈×D₅₃	C₄	1	2	yes	—
17	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×#88322	C₄	1	1	yes	characteristic
19	C₂×C₈×Dic₅₃	C₂²	1	2	yes	—
20	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
21	C₄×C₈×D₅₃	C₄	1	2	yes	—
22	C₄×C₈×D₅₃	C₄	1	1	yes	characteristic
23	C₄×C₈×D₅₃	C₂²	1	2	yes	—
24	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
25	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₅₃	C₄	1	1	yes	characteristic
27	C₂×#11719936	—	2	4	no	—
28	D₅₃⋊M₁₆	—	4	8	no	—
29	C₂×#11719940	—	2	4	no	—
30	C₂×D₅₃⋊C₈	—	2	4	no	—
31	#13133284	—	2	4	no	—
32	#13133284	—	2	4	no	—
33	C₄⋊#88324	—	2	4	no	—
34	C₄⋊#88324	C₂³	1	8	yes	—
35	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
38	C₂²×#88322	C₂×C₄	1	2	yes	—
39	C₂×C₈×D₅₃	—	2	8	no	—
40	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
41	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
42	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
46	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic
47	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₅₃	D₄	1	1	yes	characteristic
50	C₄²×D₅₃	D₄	1	1	yes	characteristic
51	C₄²×D₅₃	Q₈	1	1	yes	characteristic
52	C₄²×D₅₃	Q₈	1	1	yes	characteristic
53	C₄²×D₅₃	C₂³	1	1	yes	characteristic
54	C₄²×D₅₃	C₂³	1	1	yes	characteristic
55	C₄×#88322	C₂×C₄	1	1	yes	characteristic
56	C₄×#88322	C₂×C₄	1	2	yes	—
57	C₄×#88322	C₂×C₄	1	1	yes	characteristic
58	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
59	C₈×Dic₅₃	C₂×C₄	1	2	yes	—
60	C₈×Dic₅₃	C₂³	1	2	yes	—
61	C₈×Dic₅₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₅₃	C₂×C₄	1	2	yes	—
63	C₂×C₄²×C₅₃	C₂×C₄	1	1	yes	characteristic
64	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
65	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	—
66	C₄×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
71	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×Dic₅₃	C₂×D₄	1	1	yes	characteristic
73	C₂²×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
74	C₂×C₄×D₅₃	—	2	4	no	—
75	C₂×C₄×D₅₃	—	2	4	no	—
76	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₅₃	D₈	1	4	yes	—
83	C₂×C₄×D₅₃	Q₁₆	1	4	yes	—
84	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
90	#11719940	—	4	8	no	—
91	C₂×#88324	—	2	8	no	—
92	#11719936	—	4	8	no	—
93	D₅₃⋊C₈	—	4	8	no	—
94	C₂×C₈×C₅₃	—	2	4	no	—
95	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
96	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
97	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
102	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
103	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
104	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
105	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
107	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
108	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
109	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
110	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
111	C₄×Dic₅₃	C₂×Q₈	1	1	yes	characteristic
112	C₄×Dic₅₃	C₂⁴	1	1	yes	characteristic
113	C₂×#88322	—	2	4	no	—
114	C₂×#88322	C₂²×C₄	1	2	yes	—
115	C₂×#88322	C₂²×C₄	1	2	yes	—
116	C₈×D₅₃	—	2	4	no	—
117	C₈×D₅₃	—	2	4	no	—
118	C₈×D₅₃	—	2	4	no	—
119	C₈×D₅₃	M₁₆	1	8	yes	complemented
120	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂²×D₅₃	—	2	2	no	—
122	C₂²×D₅₃	—	2	2	no	—
123	C₂²×D₅₃	#107	1	4	yes	—
124	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₅₃	—	2	2	no	—
127	C₂×C₄×C₅₃	—	2	2	no	—
128	C₂×C₄×C₅₃	#107	1	4	yes	—
129	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
135	C₂×Dic₅₃	—	2	2	no	—
136	C₂×Dic₅₃	—	2	2	no	—
137	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×Dic₅₃	C₂×D₈	1	2	yes	—
142	C₂×Dic₅₃	C₂×Q₁₆	1	2	yes	—
143	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
144	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
145	C₄×D₅₃	—	2	2	no	—
146	C₄×D₅₃	—	2	2	no	—
147	C₄×D₅₃	—	2	2	no	—
148	C₄×D₅₃	—	2	2	no	—
149	C₄×D₅₃	—	2	2	no	—
150	C₄×D₅₃	—	2	2	no	—
151	C₄×D₅₃	#107	1	4	yes	—
152	C₄×D₅₃	#107	1	4	yes	—
153	C₄×D₅₃	#108	1	4	yes	—
154	C₄×D₅₃	C₂×M₁₆	1	4	yes	—
155	C₄×D₅₃	C₂×D₈	1	2	yes	—
156	C₄×D₅₃	C₂×D₈	1	2	yes	—
157	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
158	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
159	#88324	—	4	8	no	—
160	C₈×C₅₃	—	2	2	no	—
161	C₈×C₅₃	C₂×M₁₆	1	4	yes	complemented
162	#88322	—	2	2	no	—
163	#88322	C₂×M₁₆	1	4	yes	complemented
164	C₂×#1567	—	53	1	no	maximal, Sylow
165	C₂²×C₅₃	—	2	1	no	—
166	C₂²×C₅₃	—	2	1	no	—
167	C₂²×C₅₃	C₂×#107	1	2	yes	—
168	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
169	C₂×D₅₃	—	2	1	no	—
170	C₂×D₅₃	—	2	1	no	—
171	C₂×D₅₃	—	2	8	no	—
172	C₂×D₅₃	#423	1	2	yes	—
173	C₂×D₅₃	C₂×#107	1	2	yes	—
174	C₂×D₅₃	C₂×#107	1	2	yes	—
175	C₂×D₅₃	C₂×#108	1	2	yes	—
176	C₄×C₅₃	—	2	1	no	—
177	C₄×C₅₃	—	2	1	no	—
178	C₄×C₅₃	C₂×#107	1	2	yes	—
179	C₄×C₅₃	C₂×#107	1	2	yes	—
180	C₄×C₅₃	C₂×#108	1	2	yes	—
181	C₄×C₅₃	C₂²×M₁₆	1	2	yes	—
182	Dic₅₃	—	2	1	no	—
183	Dic₅₃	—	2	1	no	—
184	Dic₅₃	#423	1	2	yes	—
185	Dic₅₃	C₂×#107	1	2	yes	—
186	Dic₅₃	C₂×#108	1	2	yes	—
187	Dic₅₃	C₂²×D₈	1	1	yes	characteristic
188	Dic₅₃	C₂²×Q₁₆	1	1	yes	characteristic
189	C₂×#423	—	53	2	no	—
190	C₂²×C₄×C₈	—	53	1	no	—
191	#1567	—	53	4	no	—
192	#1567	—	53	2	no	—
193	#1567	—	53	2	no	—
194	C₂×#335	—	53	4	no	—
195	C₂×C₅₃	—	2	2	no	—
196	C₂×C₅₃	C₂×#423	1	1	yes	characteristic
197	C₂×C₅₃	C₂²×#107	1	1	yes	characteristic
198	C₂×C₅₃	C₂²×#108	1	1	yes	characteristic
199	D₅₃	—	2	2	no	—
200	D₅₃	#1567	1	4	yes	complemented
201	C₂²×M₁₆	—	106	2	no	—
202	C₂³×C₈	—	53	2	no	—
203	C₂²×C₄²	—	53	1	no	—
204	#423	—	53	4	no	—
205	#423	—	53	4	no	—
206	#423	—	106	2	no	—
207	#423	—	106	2	no	—
208	C₂×C₄⋊C₈	—	53	4	no	—
209	C₂×C₄⋊C₈	—	106	2	no	—
210	C₂×C₄×C₈	—	53	2	no	—
211	C₂×C₄×C₈	—	53	1	no	—
212	C₂×C₄×C₈	—	53	2	no	—
213	C₂×C₄×C₈	—	53	1	no	—
214	C₂×C₄×C₈	—	53	1	no	—
215	C₂×C₄×C₈	—	53	1	no	—
216	C₂×C₄×C₈	—	53	2	no	—
217	C₂×C₄×C₈	—	53	1	no	—
218	C₂×C₄×C₈	#6157	1	1	yes	characteristic
219	#335	—	53	8	no	—
220	#335	—	53	8	no	—
221	C₅₃	C₂×#1567	1	1	yes	characteristic, complemented, Sylow
222	C₂³×C₄	—	53	1	no	—
223	C₂³×C₄	—	53	1	no	—
224	C₂³×C₄	—	53	1	no	—
225	C₂×M₁₆	—	106	4	no	—
226	C₂×M₁₆	—	106	4	no	—
227	C₂×M₁₆	—	212	8	no	—
228	C₂²×C₈	—	53	2	no	—
229	C₂²×C₈	—	53	2	no	—
230	C₂²×C₈	—	53	2	no	—
231	C₂²×C₈	—	53	2	no	—
232	C₂²×C₈	—	53	2	no	—
233	C₂²×C₈	—	106	8	no	—
234	C₂²×C₈	—	106	4	no	—
235	C₂²×C₈	C₂×#6157	1	2	yes	—
236	C₂×C₄²	—	53	1	no	—
237	C₂×C₄²	—	53	1	no	—
238	C₂×C₄²	—	53	1	no	—
239	C₂×C₄²	—	53	1	no	—
240	C₂×C₄²	—	53	1	no	—
241	C₂×C₄²	—	53	1	no	—
242	C₂×C₄²	—	53	1	no	—
243	C₂×C₄²	—	53	1	no	—
244	C₂×C₄²	—	53	1	no	—
245	C₂×C₄²	—	53	1	no	—
246	C₂×C₄²	—	53	1	no	—
247	C₂×C₄²	C₂×#6157	1	1	yes	characteristic
248	C₄⋊C₈	—	53	8	no	—
249	C₄⋊C₈	—	106	4	no	—
250	C₄⋊C₈	—	106	4	no	—
251	C₄⋊C₈	—	106	4	no	—
252	C₄×C₈	—	53	2	no	—
253	C₄×C₈	—	53	2	no	—
254	C₄×C₈	—	53	2	no	—
255	C₄×C₈	—	53	2	no	—
256	C₄×C₈	—	53	1	no	—
257	C₄×C₈	—	53	1	no	—
258	C₄×C₈	—	53	2	no	—
259	C₄×C₈	C₂×#6157	1	1	yes	characteristic
260	C₄×C₈	C₂×#6157	1	1	yes	characteristic
261	C₄×C₈	C₂×#6157	1	2	yes	—
262	C₂⁴	—	53	1	no	—
263	C₂²×C₄	—	53	1	no	—
264	C₂²×C₄	—	53	4	no	—
265	C₂²×C₄	—	53	4	no	—
266	C₂²×C₄	—	53	1	no	—
267	C₂²×C₄	—	53	1	no	—
268	C₂²×C₄	—	53	1	no	—
269	C₂²×C₄	—	53	1	no	—
270	C₂²×C₄	—	53	1	no	—
271	C₂²×C₄	—	53	1	no	—
272	C₂²×C₄	—	53	1	no	—
273	C₂²×C₄	—	53	1	no	—
274	C₂²×C₄	—	53	1	no	—
275	C₂²×C₄	—	53	1	no	—
276	C₂²×C₄	—	53	1	no	—
277	C₂²×C₄	—	53	1	no	—
278	C₂²×C₄	—	53	1	no	—
279	C₂²×C₄	—	53	1	no	—
280	C₂²×C₄	—	106	4	no	—
281	C₂²×C₄	—	106	4	no	—
282	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
283	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
284	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
285	M₁₆	—	212	8	no	—
286	M₁₆	—	212	8	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	53	2	no	—
289	C₂×C₈	—	53	8	no	—
290	C₂×C₈	—	53	2	no	—
291	C₂×C₈	—	106	4	no	—
292	C₂×C₈	—	106	4	no	—
293	C₂×C₈	—	106	4	no	—
294	C₂×C₈	—	106	4	no	—
295	C₂×C₈	—	106	8	no	—
296	C₂×C₈	—	212	8	no	—
297	C₂×C₈	C₂²×#6157	1	2	yes	—
298	C₂×C₈	C₂²×#6157	1	2	yes	—
299	C₄²	—	53	1	no	—
300	C₄²	—	53	1	no	—
301	C₄²	—	53	1	no	—
302	C₄²	—	53	1	no	—
303	C₄²	—	53	1	no	—
304	C₄²	—	53	1	no	—
305	C₄²	—	53	1	no	—
306	C₄²	—	53	1	no	—
307	C₄²	—	53	1	no	—
308	C₄²	—	53	1	no	—
309	C₄²	—	53	1	no	—
310	C₄²	—	53	1	no	—
311	C₄²	C₄⋊#6157	1	1	yes	characteristic
312	C₄²	C₄⋊#6157	1	1	yes	characteristic
313	C₄²	C₂²×#6157	1	1	yes	characteristic
314	C₄²	C₂²×#6157	1	1	yes	characteristic
315	C₂³	—	53	1	no	—
316	C₂³	—	53	4	no	—
317	C₂³	—	53	1	no	—
318	C₂³	—	106	2	no	—
319	C₂³	—	106	2	no	—
320	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	53	2	no	—
324	C₂×C₄	—	53	2	no	—
325	C₂×C₄	—	53	1	no	—
326	C₂×C₄	—	53	1	no	—
327	C₂×C₄	—	53	1	no	—
328	C₂×C₄	—	53	1	no	—
329	C₂×C₄	—	53	4	no	—
330	C₂×C₄	—	53	4	no	—
331	C₂×C₄	—	53	2	no	—
332	C₂×C₄	—	53	2	no	—
333	C₂×C₄	—	53	2	no	—
334	C₂×C₄	—	53	2	no	—
335	C₂×C₄	—	53	4	no	—
336	C₂×C₄	—	53	4	no	—
337	C₂×C₄	—	53	1	no	—
338	C₂×C₄	—	53	1	no	—
339	C₂×C₄	—	106	2	no	—
340	C₂×C₄	—	106	2	no	—
341	C₂×C₄	—	106	2	no	—
342	C₂×C₄	—	106	2	no	—
343	C₂×C₄	—	106	2	no	—
344	C₂×C₄	—	106	2	no	—
345	C₂×C₄	—	106	2	no	—
346	C₂×C₄	—	106	2	no	—
347	C₂×C₄	#13133286	1	4	yes	—
348	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
349	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
351	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
352	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
353	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
354	C₈	—	2	2	no	—
355	C₈	—	53	4	no	—
356	C₈	—	106	2	no	—
357	C₈	—	212	8	no	—
358	C₈	D₅₃⋊M₁₆	1	4	yes	complemented
359	C₂²	—	2	1	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	53	2	no	—
362	C₂²	—	53	2	no	—
363	C₂²	—	53	2	no	—
364	C₂²	—	53	2	no	—
365	C₂²	—	106	8	no	—
366	C₂²	—	106	1	no	—
367	C₂²	—	106	1	no	—
368	C₂²	C₂×#13133286	1	2	yes	—
369	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	53	2	no	—
373	C₄	—	53	1	no	—
374	C₄	—	53	1	no	—
375	C₄	—	53	2	no	—
376	C₄	—	53	2	no	—
377	C₄	—	106	1	no	—
378	C₄	—	106	1	no	—
379	C₄	C₂×#13133286	1	2	yes	—
380	C₄	C₂×#13133286	1	2	yes	—
381	C₄	D₅₃⋊#108	1	2	yes	—
382	C₄	C₂×D₅₃⋊M₁₆	1	2	yes	—
383	C₂	—	2	2	no	—
384	C₂	—	53	4	no	—
385	C₂	—	106	2	no	—
386	C₂	D₅₃⋊#423	1	1	yes	characteristic
387	C₂	C₂²×#13133286	1	1	yes	characteristic
388	C₂	C₂×D₅₃⋊#108	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#6157
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#6157
Fitting	C₂×C₄×C₈×C₅₃	C₄
socle	C₂²×C₅₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₄×Dic₅₃	C₂⁴
hypercenter	C₂×C₄×C₈	#6157
hypocenter	C₅₃	C₂×#1567
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #20290274	C₂	semidirect
3. #20290273	C₂	semidirect
4. #20290272	C₂	semidirect
5. D₅₃⋊#335	C₂	semidirect
14. #16811487	C₂²	semidirect
15. #16811486	C₂²	semidirect
119. C₈×D₅₃	M₁₆	semidirect
161. C₈×C₅₃	C₂×M₁₆	semidirect
163. #88322	C₂×M₁₆	semidirect
200. D₅₃	#1567	semidirect
221. C₅₃	C₂×#1567	semidirect
358. C₈	D₅₃⋊M₁₆	semidirect

Maximal subgroups

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

subgroup	index
D₅₃⋊#423	2
#20290274	2
#20290273	2
#20290272	2
D₅₃⋊#335	2
C₂×C₄×C₈×D₅₃	2
C₂×#1567	53

Subgroups — D53⋊#1567 #28316104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#1567 #28316104