Subgroups — D₅₃⋊#1566 #28316100

Order 13568.

854 conjugacy classes of subgroups.

The subgroup lattice has 380 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	#20290271	C₂	1	2	yes	maximal, complemented
3	#20290270	C₂	1	2	yes	maximal, complemented
4	#20290269	C₂	1	4	yes	maximal, complemented
5	D₅₃⋊#334	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	#16811485	C₂²	1	8	yes	complemented
15	#16811484	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	SD₁₆	1	8	yes	—
83	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
85	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
88	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
89	#11719940	—	4	8	no	—
90	C₂×#88324	—	2	8	no	—
91	#11719936	—	4	8	no	—
92	D₅₃⋊C₈	—	4	8	no	—
93	C₂×C₈×C₅₃	—	2	4	no	—
94	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
96	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
97	C₄²×C₅₃	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
99	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₄×Dic₅₃	C₄⋊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	C₂²×C₄	1	1	yes	characteristic
105	C₄×Dic₅₃	C₂×D₄	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×Q₈	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	C₂⁴	1	1	yes	characteristic
112	C₂×#88322	—	2	4	no	—
113	C₂×#88322	C₂²×C₄	1	2	yes	—
114	C₂×#88322	C₂²×C₄	1	2	yes	—
115	C₈×D₅₃	—	2	4	no	—
116	C₈×D₅₃	—	2	4	no	—
117	C₈×D₅₃	—	2	4	no	—
118	C₈×D₅₃	M₁₆	1	8	yes	complemented
119	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂²×D₅₃	—	2	2	no	—
121	C₂²×D₅₃	—	2	2	no	—
122	C₂²×D₅₃	#106	1	4	yes	—
123	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂²×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×C₅₃	—	2	2	no	—
126	C₂×C₄×C₅₃	—	2	2	no	—
127	C₂×C₄×C₅₃	#106	1	4	yes	—
128	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	C₂³×C₄	1	1	yes	characteristic
134	C₂×Dic₅₃	—	2	2	no	—
135	C₂×Dic₅₃	—	2	2	no	—
136	C₂×Dic₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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×SD₁₆	1	4	yes	—
141	C₂×Dic₅₃	C₂²×D₄	1	1	yes	characteristic
142	C₂×Dic₅₃	C₂²×Q₈	1	1	yes	characteristic
143	C₄×D₅₃	—	2	2	no	—
144	C₄×D₅₃	—	2	2	no	—
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	#106	1	4	yes	—
150	C₄×D₅₃	#106	1	4	yes	—
151	C₄×D₅₃	#108	1	4	yes	—
152	C₄×D₅₃	C₂×M₁₆	1	4	yes	—
153	C₄×D₅₃	C₂×SD₁₆	1	4	yes	—
154	C₄×D₅₃	C₂×SD₁₆	1	4	yes	—
155	#88324	—	4	8	no	—
156	C₈×C₅₃	—	2	2	no	—
157	C₈×C₅₃	C₂×M₁₆	1	4	yes	complemented
158	#88322	—	2	2	no	—
159	#88322	C₂×M₁₆	1	4	yes	complemented
160	C₂×#1566	—	53	1	no	maximal, Sylow
161	C₂²×C₅₃	—	2	1	no	—
162	C₂²×C₅₃	—	2	1	no	—
163	C₂²×C₅₃	C₂×#106	1	2	yes	—
164	C₂²×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
165	C₂×D₅₃	—	2	1	no	—
166	C₂×D₅₃	—	2	1	no	—
167	C₂×D₅₃	—	2	8	no	—
168	C₂×D₅₃	#423	1	2	yes	—
169	C₂×D₅₃	C₂×#106	1	2	yes	—
170	C₂×D₅₃	C₂×#106	1	2	yes	—
171	C₂×D₅₃	C₂×#108	1	2	yes	—
172	C₄×C₅₃	—	2	1	no	—
173	C₄×C₅₃	—	2	1	no	—
174	C₄×C₅₃	C₂×#106	1	2	yes	—
175	C₄×C₅₃	C₂×#106	1	2	yes	—
176	C₄×C₅₃	C₂×#108	1	2	yes	—
177	C₄×C₅₃	C₂²×M₁₆	1	2	yes	—
178	Dic₅₃	—	2	1	no	—
179	Dic₅₃	—	2	1	no	—
180	Dic₅₃	#423	1	2	yes	—
181	Dic₅₃	C₂×#106	1	2	yes	—
182	Dic₅₃	C₂×#108	1	2	yes	—
183	Dic₅₃	C₂²×SD₁₆	1	2	yes	—
184	C₂×#423	—	53	2	no	—
185	C₂²×C₄×C₈	—	53	1	no	—
186	#1566	—	53	4	no	—
187	#1566	—	53	2	no	—
188	#1566	—	53	2	no	—
189	C₂×#334	—	53	4	no	—
190	C₂×C₅₃	—	2	2	no	—
191	C₂×C₅₃	C₂×#423	1	1	yes	characteristic
192	C₂×C₅₃	C₂²×#106	1	1	yes	characteristic
193	C₂×C₅₃	C₂²×#108	1	1	yes	characteristic
194	D₅₃	—	2	2	no	—
195	D₅₃	#1566	1	4	yes	complemented
196	C₂²×M₁₆	—	106	2	no	—
197	C₂³×C₈	—	53	2	no	—
198	C₂²×C₄²	—	53	1	no	—
199	#423	—	53	4	no	—
200	#423	—	53	4	no	—
201	#423	—	106	2	no	—
202	#423	—	106	2	no	—
203	C₂×C₄⋊C₈	—	53	4	no	—
204	C₂×C₄⋊C₈	—	106	2	no	—
205	C₂×C₄×C₈	—	53	2	no	—
206	C₂×C₄×C₈	—	53	1	no	—
207	C₂×C₄×C₈	—	53	2	no	—
208	C₂×C₄×C₈	—	53	1	no	—
209	C₂×C₄×C₈	—	53	1	no	—
210	C₂×C₄×C₈	—	53	1	no	—
211	C₂×C₄×C₈	—	53	2	no	—
212	C₂×C₄×C₈	—	53	1	no	—
213	C₂×C₄×C₈	#6157	1	1	yes	characteristic
214	#334	—	53	8	no	—
215	#334	—	53	8	no	—
216	C₅₃	C₂×#1566	1	1	yes	characteristic, complemented, Sylow
217	C₂³×C₄	—	53	1	no	—
218	C₂³×C₄	—	53	1	no	—
219	C₂³×C₄	—	53	1	no	—
220	C₂×M₁₆	—	106	4	no	—
221	C₂×M₁₆	—	106	4	no	—
222	C₂×M₁₆	—	212	8	no	—
223	C₂²×C₈	—	53	2	no	—
224	C₂²×C₈	—	53	2	no	—
225	C₂²×C₈	—	53	2	no	—
226	C₂²×C₈	—	53	2	no	—
227	C₂²×C₈	—	53	2	no	—
228	C₂²×C₈	—	106	8	no	—
229	C₂²×C₈	—	106	4	no	—
230	C₂²×C₈	C₂×#6157	1	2	yes	—
231	C₂×C₄²	—	53	1	no	—
232	C₂×C₄²	—	53	1	no	—
233	C₂×C₄²	—	53	1	no	—
234	C₂×C₄²	—	53	1	no	—
235	C₂×C₄²	—	53	1	no	—
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	C₂×#6157	1	1	yes	characteristic
243	C₄⋊C₈	—	53	8	no	—
244	C₄⋊C₈	—	106	4	no	—
245	C₄⋊C₈	—	106	4	no	—
246	C₄⋊C₈	—	106	4	no	—
247	C₄×C₈	—	53	2	no	—
248	C₄×C₈	—	53	2	no	—
249	C₄×C₈	—	53	2	no	—
250	C₄×C₈	—	53	2	no	—
251	C₄×C₈	—	53	1	no	—
252	C₄×C₈	—	53	1	no	—
253	C₄×C₈	—	53	2	no	—
254	C₄×C₈	C₂×#6157	1	1	yes	characteristic
255	C₄×C₈	C₂×#6157	1	1	yes	characteristic
256	C₄×C₈	C₂×#6157	1	2	yes	—
257	C₂⁴	—	53	1	no	—
258	C₂²×C₄	—	53	1	no	—
259	C₂²×C₄	—	53	8	no	—
260	C₂²×C₄	—	53	1	no	—
261	C₂²×C₄	—	53	1	no	—
262	C₂²×C₄	—	53	1	no	—
263	C₂²×C₄	—	53	1	no	—
264	C₂²×C₄	—	53	1	no	—
265	C₂²×C₄	—	53	1	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	—	106	4	no	—
275	C₂²×C₄	—	106	4	no	—
276	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
277	C₂²×C₄	C₄⋊#6157	1	1	yes	characteristic
278	C₂²×C₄	C₂²×#6157	1	1	yes	characteristic
279	M₁₆	—	212	8	no	—
280	M₁₆	—	212	8	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	53	2	no	—
283	C₂×C₈	—	53	8	no	—
284	C₂×C₈	—	53	2	no	—
285	C₂×C₈	—	106	4	no	—
286	C₂×C₈	—	106	4	no	—
287	C₂×C₈	—	106	4	no	—
288	C₂×C₈	—	106	4	no	—
289	C₂×C₈	—	106	8	no	—
290	C₂×C₈	—	212	8	no	—
291	C₂×C₈	C₂²×#6157	1	2	yes	—
292	C₂×C₈	C₂²×#6157	1	2	yes	—
293	C₄²	—	53	1	no	—
294	C₄²	—	53	1	no	—
295	C₄²	—	53	1	no	—
296	C₄²	—	53	1	no	—
297	C₄²	—	53	1	no	—
298	C₄²	—	53	1	no	—
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	C₄⋊#6157	1	1	yes	characteristic
306	C₄²	C₄⋊#6157	1	1	yes	characteristic
307	C₄²	C₂²×#6157	1	1	yes	characteristic
308	C₄²	C₂²×#6157	1	1	yes	characteristic
309	C₂³	—	53	1	no	—
310	C₂³	—	53	4	no	—
311	C₂³	—	53	1	no	—
312	C₂³	—	106	2	no	—
313	C₂³	—	106	2	no	—
314	C₂³	C₂×C₄⋊#6157	1	1	yes	characteristic
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	53	4	no	—
318	C₂×C₄	—	53	1	no	—
319	C₂×C₄	—	53	1	no	—
320	C₂×C₄	—	53	1	no	—
321	C₂×C₄	—	53	1	no	—
322	C₂×C₄	—	53	4	no	—
323	C₂×C₄	—	53	4	no	—
324	C₂×C₄	—	53	4	no	—
325	C₂×C₄	—	53	4	no	—
326	C₂×C₄	—	53	4	no	—
327	C₂×C₄	—	53	4	no	—
328	C₂×C₄	—	53	1	no	—
329	C₂×C₄	—	53	1	no	—
330	C₂×C₄	—	106	2	no	—
331	C₂×C₄	—	106	2	no	—
332	C₂×C₄	—	106	2	no	—
333	C₂×C₄	—	106	2	no	—
334	C₂×C₄	—	106	2	no	—
335	C₂×C₄	—	106	2	no	—
336	C₂×C₄	—	106	2	no	—
337	C₂×C₄	—	106	2	no	—
338	C₂×C₄	#13133285	1	4	yes	—
339	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
340	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
341	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
342	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊#6157	1	1	yes	characteristic
344	C₂×C₄	C₂³×#6157	1	1	yes	characteristic
345	C₈	—	2	2	no	—
346	C₈	—	53	4	no	—
347	C₈	—	106	2	no	—
348	C₈	—	212	8	no	—
349	C₈	D₅₃⋊M₁₆	1	4	yes	complemented
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	53	2	no	—
353	C₂²	—	53	2	no	—
354	C₂²	—	53	2	no	—
355	C₂²	—	53	2	no	—
356	C₂²	—	106	8	no	—
357	C₂²	—	106	1	no	—
358	C₂²	—	106	1	no	—
359	C₂²	C₂×#13133285	1	2	yes	—
360	C₂²	C₂²×C₄⋊#6157	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	53	2	no	—
364	C₄	—	53	2	no	—
365	C₄	—	53	2	no	—
366	C₄	—	53	2	no	—
367	C₄	—	106	1	no	—
368	C₄	—	106	1	no	—
369	C₄	C₂×#13133285	1	2	yes	—
370	C₄	C₂×#13133285	1	2	yes	—
371	C₄	D₅₃⋊#108	1	2	yes	—
372	C₄	C₂×D₅₃⋊M₁₆	1	2	yes	—
373	C₂	—	2	2	no	—
374	C₂	—	53	4	no	—
375	C₂	—	106	2	no	—
376	C₂	D₅₃⋊#423	1	1	yes	characteristic
377	C₂	C₂²×#13133285	1	1	yes	characteristic
378	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×#1566
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. #20290271	C₂	semidirect
3. #20290270	C₂	semidirect
4. #20290269	C₂	semidirect
5. D₅₃⋊#334	C₂	semidirect
14. #16811485	C₂²	semidirect
15. #16811484	C₂²	semidirect
118. C₈×D₅₃	M₁₆	semidirect
157. C₈×C₅₃	C₂×M₁₆	semidirect
159. #88322	C₂×M₁₆	semidirect
195. D₅₃	#1566	semidirect
216. C₅₃	C₂×#1566	semidirect
349. 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
#20290271	2
#20290270	2
#20290269	2
D₅₃⋊#334	2
C₂×C₄×C₈×D₅₃	2
C₂×#1566	53

Subgroups — D53⋊#1566 #28316100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃⋊#1566 #28316100