Subgroups — C₄×D₁₆×D₅₃ #27537349

Order 13568.

806 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₄×D₈×D₅₃	C₂	1	2	yes	maximal, complemented
3	C₄×D₈₄₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₆×Dic₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276561	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#13133158	C₂	1	2	yes	maximal, complemented
7	#20276559	C₂	1	2	yes	maximal, complemented
8	#366×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#357×D₅₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	C₂²	1	2	yes	—
13	C₄×D₄×D₅₃	—	2	2	no	—
14	C₂×D₈₄₈	C₂²	1	1	yes	characteristic
15	C₂×#13133158	C₂²	1	2	yes	—
16	D₁₆×D₅₃	C₄	1	8	yes	direct product factor
17	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
19	C₄×D₄₂₄	C₂²	1	2	yes	complemented
20	D₈×Dic₅₃	C₂²	1	2	yes	complemented
21	#16810705	C₂²	1	2	yes	complemented
22	C₄×#11719922	—	2	2	no	—
23	#16810703	—	2	2	no	—
24	#107×D₅₃	C₂²	1	2	yes	—
25	#102×D₅₃	—	2	2	no	—
26	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	#16810449	C₂²	1	1	yes	characteristic, complemented
28	#16810448	C₂²	1	2	yes	complemented
29	#16810425	C₂²	1	2	yes	complemented
30	#16810424	C₂²	1	2	yes	complemented
31	#16810423	C₂²	1	2	yes	complemented
32	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
33	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₁₆×C₅₃	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₅₃	C₂²	1	2	yes	complemented
37	C₅₃×#366	C₂²	1	1	yes	characteristic, complemented
38	C₅₃×#357	C₂²	1	2	yes	complemented
39	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₅₃	—	2	2	no	—
41	C₂²×C₄×D₅₃	—	4	2	no	—
42	C₂×D₄₂₄	C₂³	1	2	yes	—
43	C₂×#11719922	—	2	2	no	—
44	D₈×D₅₃	—	2	4	no	—
45	D₈×D₅₃	C₂×C₄	1	8	yes	complemented
46	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
47	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
48	C₄×D₂₁₂	—	2	2	no	—
49	D₄×Dic₅₃	—	2	2	no	—
50	#13133179	—	2	2	no	—
51	C₄×C₂²⋊D₅₃	—	4	2	no	—
52	#13133177	—	4	2	no	—
53	C₄⋊C₄×D₅₃	—	2	2	no	—
54	C₂²⋊C₄×D₅₃	—	4	2	no	—
55	C₄²×D₅₃	D₄	1	1	yes	characteristic
56	D₈₄₈	C₂×C₄	1	4	yes	complemented
57	#13133158	C₂×C₄	1	8	yes	complemented
58	C₂×#11719908	C₂³	1	1	yes	characteristic
59	C₂×#11719908	C₂³	1	1	yes	characteristic
60	C₁₆×D₅₃	—	2	2	no	—
61	C₁₆×D₅₃	C₂×C₄	1	4	yes	complemented
62	#13133151	C₂³	1	2	yes	—
63	#13133150	—	2	2	no	—
64	#13133139	—	2	2	no	—
65	#13133138	—	2	2	no	—
66	#13133137	—	2	2	no	—
67	C₄×#88322	D₄	1	1	yes	characteristic
68	C₈×Dic₅₃	D₄	1	1	yes	characteristic
69	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
70	C₂×D₈×C₅₃	C₂³	1	2	yes	—
71	C₄×D₄×C₅₃	—	2	2	no	—
72	D₁₆×C₅₃	C₂×C₄	1	4	yes	complemented
73	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
75	#107×C₅₃	C₂³	1	2	yes	—
76	#102×C₅₃	—	2	2	no	—
77	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
78	C₂³×D₅₃	—	4	2	no	—
79	C₂×D₄×C₅₃	—	2	2	no	—
80	C₂²×C₄×C₅₃	—	4	2	no	—
81	C₂×C₂²⋊D₅₃	—	4	2	no	—
82	C₂²×Dic₅₃	—	4	2	no	—
83	D₄×D₅₃	—	2	8	no	—
84	D₄×D₅₃	—	4	4	no	—
85	C₂×D₂₁₂	—	2	2	no	—
86	C₂×C₄×D₅₃	—	4	2	no	—
87	C₂×C₄×D₅₃	—	4	2	no	—
88	C₂×C₄×D₅₃	—	4	2	no	—
89	C₂×C₄×D₅₃	—	8	8	no	—
90	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
91	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
93	D₈×C₅₃	—	2	2	no	—
94	D₈×C₅₃	C₂²×C₄	1	4	yes	complemented
95	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
97	C₄⋊C₄×C₅₃	—	2	2	no	—
98	C₂²⋊C₄×C₅₃	—	4	2	no	—
99	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
100	C₂²⋊Dic₅₃	—	4	2	no	—
101	#11719922	—	2	8	no	—
102	#11719921	—	4	2	no	—
103	#11719921	—	4	2	no	—
104	C₄⋊Dic₅₃	—	2	2	no	—
105	#11719919	—	4	2	no	—
106	C₄×Dic₅₃	D₈	1	1	yes	characteristic
107	C₄×Dic₅₃	D₈	1	1	yes	characteristic
108	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
109	C₂×#88322	C₂×D₄	1	1	yes	characteristic
110	C₂×#88322	C₂×D₄	1	1	yes	characteristic
111	D₄₂₄	—	2	2	no	—
112	D₄₂₄	C₂²×C₄	1	4	yes	complemented
113	C₈×D₅₃	—	2	2	no	—
114	C₈×D₅₃	C₂²×C₄	1	2	yes	—
115	C₈×D₅₃	#41	1	2	yes	—
116	C₁₆×C₅₃	—	2	1	no	—
117	C₁₆×C₅₃	C₂²×C₄	1	2	yes	complemented
118	#11719908	—	2	1	no	—
119	#11719908	C₂²×C₄	1	2	yes	complemented
120	C₂³×C₅₃	—	4	2	no	—
121	C₂²×D₅₃	—	4	2	no	—
122	C₂²×D₅₃	—	4	8	no	—
123	C₂²×D₅₃	—	8	4	no	—
124	C₂²×D₅₃	—	8	4	no	—
125	C₂²×D₅₃	C₂×D₈	1	1	yes	characteristic
126	D₄×C₅₃	—	2	4	no	—
127	D₄×C₅₃	—	4	2	no	—
128	C₂×C₄×C₅₃	—	4	2	no	—
129	C₂×C₄×C₅₃	—	8	4	no	—
130	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
132	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
133	C₂²⋊D₅₃	—	4	8	no	—
134	C₂×Dic₅₃	—	4	2	no	—
135	C₂×Dic₅₃	—	8	4	no	—
136	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
137	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
138	C₂×Dic₅₃	C₂×D₈	1	1	yes	characteristic
139	D₂₁₂	—	2	4	no	—
140	D₂₁₂	—	4	2	no	—
141	C₄×D₅₃	—	2	2	no	—
142	C₄×D₅₃	—	8	4	no	—
143	C₄×D₅₃	—	8	4	no	—
144	C₄×D₅₃	—	8	4	no	—
145	C₄×D₅₃	D₁₆	1	4	yes	direct product factor
146	C₄×D₅₃	C₄×D₄	1	2	yes	—
147	C₄×D₅₃	#135	1	2	yes	—
148	C₈×C₅₃	—	2	1	no	—
149	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
150	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
151	#88322	—	2	1	no	—
152	#88322	C₄×D₄	1	2	yes	—
153	C₂×C₄×D₁₆	—	53	1	no	maximal, Sylow
154	C₂²×C₅₃	—	4	4	no	—
155	C₂²×C₅₃	—	8	2	no	—
156	C₂²×C₅₃	—	8	2	no	—
157	C₂²×C₅₃	C₂²×D₈	1	1	yes	characteristic
158	C₂×D₅₃	—	4	4	no	—
159	C₂×D₅₃	—	8	2	no	—
160	C₂×D₅₃	—	8	2	no	—
161	C₂×D₅₃	—	8	16	no	—
162	C₂×D₅₃	C₄×D₈	1	2	yes	—
163	C₂×D₅₃	C₂×D₁₆	1	2	yes	—
164	C₂×D₅₃	#508	1	2	yes	—
165	C₄×C₅₃	—	2	1	no	—
166	C₄×C₅₃	—	8	2	no	—
167	C₄×C₅₃	C₂×D₁₆	1	2	yes	complemented
168	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
170	Dic₅₃	—	2	1	no	—
171	Dic₅₃	—	8	2	no	—
172	Dic₅₃	C₄×D₈	1	2	yes	—
173	Dic₅₃	C₂×D₁₆	1	2	yes	complemented
174	C₂²×D₁₆	—	53	1	no	—
175	C₂×C₄×D₈	—	53	2	no	—
176	C₄×D₁₆	—	53	1	no	—
177	C₄×D₁₆	—	53	2	no	—
178	C₄×D₁₆	—	53	1	no	—
179	C₄×D₁₆	—	53	2	no	—
180	C₄×D₁₆	—	53	1	no	—
181	C₄×D₁₆	D₅₃	1	1	yes	characteristic, direct product factor
182	C₂×#366	—	53	1	no	—
183	C₂×#357	—	53	2	no	—
184	C₂×C₄×C₁₆	—	53	1	no	—
185	C₂×C₅₃	—	8	4	no	—
186	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
187	C₂×C₅₃	C₂²×D₁₆	1	1	yes	characteristic
188	C₂×C₅₃	C₂×#508	1	1	yes	characteristic
189	D₅₃	—	8	4	no	—
190	D₅₃	C₄×D₁₆	1	4	yes	direct product factor
191	C₂²×D₈	—	53	2	no	—
192	C₂×C₄×D₄	—	106	2	no	—
193	C₂×D₁₆	—	53	2	no	—
194	C₂×D₁₆	—	53	8	no	—
195	C₂×D₁₆	—	53	1	no	—
196	C₂×D₁₆	C₂×D₅₃	1	1	yes	characteristic
197	C₂²×C₁₆	—	53	1	no	—
198	C₂²×C₁₆	—	53	1	no	—
199	C₄×D₈	—	53	2	no	—
200	C₄×D₈	—	53	2	no	—
201	C₄×D₈	—	53	2	no	—
202	C₄×D₈	—	106	2	no	—
203	C₄×D₈	—	106	2	no	—
204	C₄×D₈	C₂×D₅₃	1	2	yes	complemented
205	C₂×#107	—	53	2	no	—
206	C₂×#102	—	106	2	no	—
207	C₂×C₄×C₈	—	53	1	no	—
208	#366	—	53	1	no	—
209	#366	—	53	2	no	—
210	#366	C₂×D₅₃	1	1	yes	characteristic, complemented
211	#357	—	53	2	no	—
212	#357	—	53	2	no	—
213	#357	—	53	2	no	—
214	#357	C₂×D₅₃	1	2	yes	complemented
215	C₄×C₁₆	—	53	1	no	—
216	C₄×C₁₆	—	53	1	no	—
217	C₄×C₁₆	—	53	1	no	—
218	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
219	C₅₃	C₂×C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
220	C₂²×D₄	—	106	2	no	—
221	C₂³×C₄	—	212	2	no	—
222	C₂×D₈	—	53	8	no	—
223	C₂×D₈	—	53	2	no	—
224	C₂×D₈	—	106	4	no	—
225	C₂×D₈	—	106	2	no	—
226	C₂×D₈	C₂²×D₅₃	1	2	yes	—
227	C₂²×C₈	—	53	1	no	—
228	C₂²×C₈	—	53	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	106	2	no	—
231	C₄×D₄	—	106	2	no	—
232	C₄×D₄	—	106	2	no	—
233	C₄×D₄	—	212	2	no	—
234	C₄×D₄	—	212	2	no	—
235	C₂×C₄⋊C₄	—	106	2	no	—
236	C₂×C₂²⋊C₄	—	212	2	no	—
237	C₂×C₄²	—	53	1	no	—
238	D₁₆	—	53	8	no	—
239	D₁₆	—	53	4	no	—
240	D₁₆	C₄×D₅₃	1	4	yes	direct product factor
241	C₂×C₁₆	—	53	1	no	—
242	C₂×C₁₆	—	53	4	no	—
243	C₂×C₁₆	—	53	1	no	—
244	C₂×C₁₆	—	106	2	no	—
245	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
246	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
247	#107	—	53	2	no	—
248	#107	—	106	2	no	—
249	#107	C₂²×D₅₃	1	2	yes	—
250	#102	—	2	2	no	—
251	#102	—	106	2	no	—
252	#102	—	106	2	no	—
253	#102	—	106	2	no	—
254	C₄×C₈	—	53	1	no	—
255	C₄×C₈	—	53	1	no	—
256	C₄×C₈	—	53	1	no	—
257	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
258	C₂⁴	—	212	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	106	8	no	—
261	C₂×D₄	—	106	2	no	—
262	C₂×D₄	—	212	4	no	—
263	C₂×D₄	—	212	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	53	1	no	—
266	C₂²×C₄	—	53	1	no	—
267	C₂²×C₄	—	53	1	no	—
268	C₂²×C₄	—	424	8	no	—
269	C₂²×C₄	—	212	2	no	—
270	C₂²×C₄	—	212	2	no	—
271	C₂²×C₄	—	212	2	no	—
272	C₂²×C₄	—	212	2	no	—
273	D₈	—	2	2	no	—
274	D₈	—	53	4	no	—
275	D₈	—	106	8	no	—
276	D₈	—	106	2	no	—
277	D₈	C₂×C₄×D₅₃	1	4	yes	complemented
278	C₂×C₈	—	53	1	no	—
279	C₂×C₈	—	53	2	no	—
280	C₂×C₈	—	53	2	no	—
281	C₂×C₈	—	53	1	no	—
282	C₂×C₈	—	106	2	no	—
283	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
284	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	106	2	no	—
287	C₄⋊C₄	—	212	2	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	212	2	no	—
290	C₂²⋊C₄	—	212	2	no	—
291	C₂²⋊C₄	—	212	2	no	—
292	C₄²	—	53	1	no	—
293	C₄²	—	53	1	no	—
294	C₄²	—	53	1	no	—
295	C₄²	D₄×D₅₃	1	1	yes	characteristic
296	C₁₆	—	2	1	no	—
297	C₁₆	—	53	2	no	—
298	C₁₆	—	106	1	no	—
299	C₁₆	C₂×C₄×D₅₃	1	2	yes	complemented
300	C₂³	—	4	2	no	—
301	C₂³	—	53	1	no	—
302	C₂³	—	424	4	no	—
303	C₂³	—	424	4	no	—
304	C₂³	—	212	8	no	—
305	C₂³	—	212	2	no	—
306	D₄	—	2	4	no	—
307	D₄	—	4	2	no	—
308	D₄	—	106	4	no	—
309	D₄	—	212	8	no	—
310	D₄	—	212	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	—	53	1	no	—
314	C₂×C₄	—	53	1	no	—
315	C₂×C₄	—	53	4	no	—
316	C₂×C₄	—	53	2	no	—
317	C₂×C₄	—	53	2	no	—
318	C₂×C₄	—	53	1	no	—
319	C₂×C₄	—	106	2	no	—
320	C₂×C₄	—	424	4	no	—
321	C₂×C₄	—	424	4	no	—
322	C₂×C₄	—	424	4	no	—
323	C₂×C₄	—	424	4	no	—
324	C₂×C₄	—	212	2	no	—
325	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
326	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
328	C₈	—	2	1	no	—
329	C₈	—	53	2	no	—
330	C₈	—	106	1	no	—
331	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
332	C₈	#41×D₅₃	1	1	yes	characteristic
333	C₂²	—	4	4	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	53	2	no	—
337	C₂²	—	53	2	no	—
338	C₂²	—	53	2	no	—
339	C₂²	—	424	16	no	—
340	C₂²	—	424	2	no	—
341	C₂²	—	424	2	no	—
342	C₂²	—	212	4	no	—
343	C₂²	C₂×D₈×D₅₃	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	8	2	no	—
346	C₄	—	53	2	no	—
347	C₄	—	53	2	no	—
348	C₄	—	106	1	no	—
349	C₄	—	424	2	no	—
350	C₄	D₁₆×D₅₃	1	2	yes	direct product factor
351	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
352	C₄	#135×D₅₃	1	1	yes	characteristic
353	C₂	—	8	4	no	—
354	C₂	—	53	4	no	—
355	C₂	—	424	4	no	—
356	C₂	C₄×D₈×D₅₃	1	1	yes	characteristic
357	C₂	C₂×D₁₆×D₅₃	1	1	yes	characteristic
358	C₂	#508×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₄×D₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂²×D₈
prime radical	C₂×D₁₆×D₅₃	C₂
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	C₄×D₁₆	D₅₃
hypocenter	C₅₃	C₂×C₄×D₁₆
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×D₈×D₅₃	C₂	semidirect
3. C₄×D₈₄₈	C₂	semidirect
4. D₁₆×Dic₅₃	C₂	semidirect
5. #20276561	C₂	semidirect
6. C₄×#13133158	C₂	semidirect
7. #20276559	C₂	semidirect
8. #366×D₅₃	C₂	semidirect
9. #357×D₅₃	C₂	semidirect
10. C₄×C₁₆×D₅₃	C₂	semidirect
11. C₄×D₁₆×C₅₃	C₂	semidirect
16. D₁₆×D₅₃	C₄	direct (N × H)
19. C₄×D₄₂₄	C₂²	semidirect
20. D₈×Dic₅₃	C₂²	semidirect
21. #16810705	C₂²	semidirect
27. #16810449	C₂²	semidirect
28. #16810448	C₂²	semidirect
29. #16810425	C₂²	semidirect
30. #16810424	C₂²	semidirect
31. #16810423	C₂²	semidirect
32. C₄×#11719908	C₂²	semidirect
33. C₁₆×Dic₅₃	C₂²	semidirect
34. C₁₆×Dic₅₃	C₂²	semidirect
36. C₄×D₈×C₅₃	C₂²	semidirect
37. C₅₃×#366	C₂²	semidirect
38. C₅₃×#357	C₂²	semidirect
39. C₄×C₁₆×C₅₃	C₂²	semidirect
45. D₈×D₅₃	C₂×C₄	semidirect
56. D₈₄₈	C₂×C₄	semidirect
57. #13133158	C₂×C₄	semidirect
61. C₁₆×D₅₃	C₂×C₄	semidirect
72. D₁₆×C₅₃	C₂×C₄	semidirect
94. D₈×C₅₃	C₂²×C₄	semidirect
112. D₄₂₄	C₂²×C₄	semidirect
117. C₁₆×C₅₃	C₂²×C₄	semidirect
119. #11719908	C₂²×C₄	semidirect
145. C₄×D₅₃	D₁₆	direct (N × H)
167. C₄×C₅₃	C₂×D₁₆	semidirect
173. Dic₅₃	C₂×D₁₆	semidirect
181. C₄×D₁₆	D₅₃	direct (N × H)
190. D₅₃	C₄×D₁₆	direct (N × H)
204. C₄×D₈	C₂×D₅₃	semidirect
210. #366	C₂×D₅₃	semidirect
214. #357	C₂×D₅₃	semidirect
218. C₄×C₁₆	C₂×D₅₃	semidirect
219. C₅₃	C₂×C₄×D₁₆	semidirect
240. D₁₆	C₄×D₅₃	direct (N × H)
277. D₈	C₂×C₄×D₅₃	semidirect
299. C₁₆	C₂×C₄×D₅₃	semidirect
350. C₄	D₁₆×D₅₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₅₃	2
C₄×D₈×D₅₃	2
C₄×D₈₄₈	2
D₁₆×Dic₅₃	2
#20276561	2
C₄×#13133158	2
#20276559	2
#366×D₅₃	2
#357×D₅₃	2
C₄×C₁₆×D₅₃	2
C₄×D₁₆×C₅₃	2
C₂×C₄×D₁₆	53

Subgroups — C4×D16×D53 #27537349

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₆×D₅₃ #27537349