Subgroups — D₅₃×#2164 #27537163

Order 13568.

610 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#20276523	C₂	1	1	yes	maximal, characteristic, complemented
3	#20276522	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276521	C₂	1	2	yes	maximal, complemented
5	#20276520	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276519	C₂	1	2	yes	maximal, complemented
7	C₄⋊C₁₆×D₅₃	C₂	1	2	yes	maximal, complemented
8	C₂²⋊C₁₆×D₅₃	C₂	1	2	yes	maximal
9	#346×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
14	#117×D₅₃	C₄	1	1	yes	characteristic
15	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
16	C₂×C₁₆×D₅₃	C₂²	1	2	yes	—
17	#16810581	C₄	1	1	yes	characteristic
18	#16810580	C₄	1	1	yes	characteristic
19	#16810580	C₄	1	1	yes	characteristic
20	#16810579	C₄	1	1	yes	characteristic
21	#16810578	C₂²	1	1	yes	characteristic
22	#16810577	C₂²	1	1	yes	characteristic
23	#16810577	C₂²	1	1	yes	characteristic
24	#97×D₅₃	C₄	1	1	yes	characteristic
25	#97×D₅₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
27	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
28	C₄⋊#11719908	C₂²	1	2	yes	complemented
29	#16810441	C₂²	1	2	yes	complemented
30	#16810441	C₂²	1	2	yes	complemented
31	C₂²⋊#11719908	C₂²	1	2	yes	—
32	#16810402	C₂²	1	2	yes	—
33	#16810402	C₂²	1	2	yes	—
34	#16810399	C₂²	1	1	yes	characteristic, complemented
35	#16810398	C₂²	1	2	yes	complemented
36	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
37	C₁₆×Dic₅₃	C₂²	1	2	yes	complemented
38	C₅₃×#405	C₂²	1	1	yes	characteristic
39	C₅₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
40	C₅₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
41	C₅₃×#346	C₂²	1	1	yes	characteristic, complemented
42	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×#11719917	C₂×C₄	1	1	yes	characteristic
45	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
46	C₂×#11719912	C₂×C₄	1	1	yes	characteristic
47	M₁₆×D₅₃	—	2	4	no	—
48	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₅₃	—	2	4	no	—
50	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
56	#13133176	C₂×C₄	1	1	yes	characteristic
57	#13133175	C₈	1	2	yes	—
58	#13133174	C₂×C₄	1	1	yes	characteristic
59	#13133174	C₂×C₄	1	1	yes	characteristic
60	#13133173	C₈	1	2	yes	—
61	C₄⋊C₄×D₅₃	C₈	1	2	yes	—
62	C₂²⋊C₄×D₅₃	C₈	1	2	yes	—
63	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×#11719908	C₂³	1	2	yes	—
66	C₂×#11719908	C₂³	1	2	yes	—
67	C₁₆×D₅₃	—	2	4	no	—
68	C₁₆×D₅₃	—	2	4	no	—
69	#13133128	C₂×C₄	1	1	yes	characteristic
70	#13133128	C₂×C₄	1	1	yes	characteristic
71	#13133127	C₂×C₄	1	1	yes	characteristic
72	#13133127	C₂×C₄	1	1	yes	characteristic
73	#13133127	C₂×C₄	1	1	yes	characteristic
74	#13133127	C₂×C₄	1	1	yes	characteristic
75	C₄×#88322	C₂×C₄	1	1	yes	characteristic
76	C₄×#88322	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
80	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
83	#117×C₅₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
85	C₂×C₁₆×C₅₃	C₂³	1	2	yes	—
86	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
87	#97×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
90	C₂³×D₅₃	C₂×C₈	1	1	yes	characteristic
91	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
92	C₂²×Dic₅₃	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₅₃	—	2	2	no	—
94	C₂×C₄×D₅₃	—	2	2	no	—
95	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
96	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
97	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
98	C₂×C₄×D₅₃	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
101	M₁₆×C₅₃	—	2	2	no	—
102	C₂×C₈×C₅₃	—	2	2	no	—
103	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
107	C₄⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
108	C₂²⋊C₄×C₅₃	C₂×C₈	1	2	yes	—
109	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²⋊Dic₅₃	C₂×C₈	1	2	yes	—
112	#11719921	C₂×C₈	1	2	yes	—
113	#11719921	C₂×C₈	1	2	yes	—
114	C₄⋊Dic₅₃	C₂×C₈	1	2	yes	—
115	#11719919	C₂×C₈	1	2	yes	—
116	#11719919	C₂×C₈	1	2	yes	—
117	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
118	C₄×Dic₅₃	C₂×C₈	1	2	yes	—
119	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
121	#11719917	—	2	2	no	—
122	C₂×#88322	—	2	2	no	—
123	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
124	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
125	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
126	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
127	#11719912	—	2	2	no	—
128	#11719912	—	2	2	no	—
129	C₈×D₅₃	—	2	2	no	—
130	C₈×D₅₃	—	2	2	no	—
131	C₈×D₅₃	—	2	2	no	—
132	C₈×D₅₃	—	2	2	no	—
133	C₈×D₅₃	M₁₆	1	4	yes	—
134	C₈×D₅₃	#41	1	4	yes	—
135	C₁₆×C₅₃	—	2	2	no	—
136	C₁₆×C₅₃	—	2	2	no	—
137	#11719908	—	2	2	no	—
138	#11719908	—	2	2	no	—
139	C₂³×C₅₃	C₂²×C₈	1	1	yes	characteristic
140	C₂²×D₅₃	—	2	2	no	—
141	C₂²×D₅₃	—	2	4	no	—
142	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
143	C₂²×D₅₃	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₅₃	—	2	1	no	—
145	C₂×C₄×C₅₃	—	2	1	no	—
146	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
148	C₂×C₄×C₅₃	C₂²×C₈	1	2	yes	—
149	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
150	C₂×Dic₅₃	—	2	2	no	—
151	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
152	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
153	C₂×Dic₅₃	C₂²×C₈	1	2	yes	—
154	C₂×Dic₅₃	C₂²×C₈	1	1	yes	characteristic
155	C₄×D₅₃	—	2	2	no	—
156	C₄×D₅₃	—	2	4	no	—
157	C₄×D₅₃	—	2	4	no	—
158	C₄×D₅₃	—	2	1	no	—
159	C₄×D₅₃	—	2	1	no	—
160	C₄×D₅₃	—	2	2	no	—
161	C₄×D₅₃	#117	1	2	yes	—
162	C₄×D₅₃	C₂×M₁₆	1	2	yes	—
163	C₈×C₅₃	—	2	1	no	—
164	C₈×C₅₃	—	2	1	no	—
165	C₈×C₅₃	C₂×M₁₆	1	2	yes	—
166	C₈×C₅₃	C₂×#41	1	2	yes	—
167	#88322	—	2	1	no	—
168	#88322	—	2	1	no	—
169	#88322	#117	1	2	yes	—
170	#88322	C₂×M₁₆	1	2	yes	—
171	C₂×#2164	—	53	1	no	maximal, Sylow
172	C₂²×C₅₃	—	2	2	no	—
173	C₂²×C₅₃	—	2	1	no	—
174	C₂²×C₅₃	C₂³×C₈	1	1	yes	characteristic
175	C₂×D₅₃	—	2	2	no	—
176	C₂×D₅₃	—	2	1	no	—
177	C₂×D₅₃	—	4	4	no	—
178	C₂×D₅₃	#431	1	2	yes	—
179	C₂×D₅₃	#504	1	4	yes	—
180	C₄×C₅₃	—	2	2	no	—
181	C₄×C₅₃	—	2	2	no	—
182	C₄×C₅₃	—	2	1	no	—
183	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
184	C₄×C₅₃	C₂²×M₁₆	1	1	yes	characteristic
185	Dic₅₃	—	2	2	no	—
186	Dic₅₃	—	2	2	no	—
187	Dic₅₃	—	2	1	no	—
188	Dic₅₃	#431	1	2	yes	—
189	C₂×#405	—	53	1	no	—
190	#2164	—	53	1	no	—
191	#2164	—	53	2	no	—
192	#2164	—	53	2	no	—
193	#2164	—	53	1	no	—
194	#2164	—	53	1	no	—
195	#2164	D₅₃	1	1	yes	characteristic, direct product factor
196	C₂×C₄⋊C₁₆	—	53	2	no	—
197	C₂×C₂²⋊C₁₆	—	53	2	no	—
198	C₂×#346	—	53	1	no	—
199	C₂×C₄×C₁₆	—	53	1	no	—
200	C₂×C₅₃	—	4	1	no	—
201	C₂×C₅₃	C₂×#431	1	1	yes	characteristic
202	C₂×C₅₃	C₂×#504	1	2	yes	—
203	D₅₃	—	4	1	no	—
204	D₅₃	#2164	1	4	yes	direct product factor
205	C₂²×M₁₆	—	53	1	no	—
206	C₂³×C₈	—	53	1	no	—
207	C₂×#117	—	53	1	no	—
208	C₂²×C₁₆	—	53	2	no	—
209	C₂²×C₁₆	—	53	2	no	—
210	#405	—	53	1	no	—
211	#405	—	53	1	no	—
212	#405	—	53	1	no	—
213	#405	—	53	1	no	—
214	#405	—	53	1	no	—
215	#405	—	53	1	no	—
216	#405	—	53	1	no	—
217	#405	C₂×D₅₃	1	1	yes	characteristic
218	C₂×#97	—	53	1	no	—
219	C₂×#97	—	53	1	no	—
220	C₂×C₄×C₈	—	53	1	no	—
221	C₂×C₄×C₈	—	53	1	no	—
222	C₄⋊C₁₆	—	53	2	no	—
223	C₄⋊C₁₆	—	53	2	no	—
224	C₄⋊C₁₆	—	53	2	no	—
225	C₄⋊C₁₆	C₂×D₅₃	1	2	yes	complemented
226	C₂²⋊C₁₆	—	53	2	no	—
227	C₂²⋊C₁₆	—	53	2	no	—
228	C₂²⋊C₁₆	—	53	2	no	—
229	C₂²⋊C₁₆	C₂×D₅₃	1	2	yes	—
230	#346	—	53	2	no	—
231	#346	—	53	1	no	—
232	#346	C₂×D₅₃	1	1	yes	characteristic, complemented
233	C₄×C₁₆	—	53	2	no	—
234	C₄×C₁₆	—	53	1	no	—
235	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
236	C₅₃	C₂×#2164	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	—	53	1	no	—
238	C₂×M₁₆	—	53	1	no	—
239	C₂×M₁₆	—	53	1	no	—
240	C₂×M₁₆	—	53	1	no	—
241	C₂×M₁₆	—	106	4	no	—
242	C₂×M₁₆	C₄×D₅₃	1	1	yes	characteristic
243	C₂²×C₈	—	53	1	no	—
244	C₂²×C₈	—	53	1	no	—
245	C₂²×C₈	—	53	1	no	—
246	C₂²×C₈	—	53	1	no	—
247	C₂²×C₈	—	53	1	no	—
248	C₂²×C₈	—	53	1	no	—
249	C₂²×C₈	—	53	1	no	—
250	C₂²×C₈	—	106	4	no	—
251	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
252	#117	—	53	1	no	—
253	#117	—	53	2	no	—
254	#117	—	53	2	no	—
255	#117	—	53	1	no	—
256	#117	—	53	1	no	—
257	#117	C₄×D₅₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	53	2	no	—
259	C₂×C₂²⋊C₄	—	53	2	no	—
260	C₂×C₄²	—	53	1	no	—
261	C₂×C₄²	—	53	1	no	—
262	C₂×C₁₆	—	53	2	no	—
263	C₂×C₁₆	—	53	2	no	—
264	C₂×C₁₆	—	106	4	no	—
265	C₂×C₁₆	—	106	4	no	—
266	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
267	C₂×C₁₆	C₂²×D₅₃	1	2	yes	—
268	#97	—	53	1	no	—
269	#97	—	53	1	no	—
270	#97	—	53	1	no	—
271	#97	—	53	1	no	—
272	#97	—	53	1	no	—
273	#97	—	53	1	no	—
274	#97	C₄×D₅₃	1	1	yes	characteristic
275	#97	C₄×D₅₃	1	1	yes	characteristic
276	C₄×C₈	—	53	1	no	—
277	C₄×C₈	—	53	1	no	—
278	C₄×C₈	—	53	1	no	—
279	C₄×C₈	—	53	1	no	—
280	C₄×C₈	—	53	1	no	—
281	C₄×C₈	—	53	1	no	—
282	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
284	C₂⁴	—	53	1	no	—
285	C₂²×C₄	—	53	1	no	—
286	C₂²×C₄	—	53	1	no	—
287	C₂²×C₄	—	53	2	no	—
288	C₂²×C₄	—	53	2	no	—
289	C₂²×C₄	—	53	1	no	—
290	C₂²×C₄	—	53	1	no	—
291	C₂²×C₄	—	53	1	no	—
292	C₂²×C₄	—	106	2	no	—
293	C₂²×C₄	—	106	2	no	—
294	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	106	2	no	—
297	M₁₆	—	106	2	no	—
298	M₁₆	—	106	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	53	1	no	—
301	C₂×C₈	—	53	1	no	—
302	C₂×C₈	—	53	4	no	—
303	C₂×C₈	—	53	4	no	—
304	C₂×C₈	—	53	1	no	—
305	C₂×C₈	—	53	1	no	—
306	C₂×C₈	—	106	2	no	—
307	C₂×C₈	—	106	2	no	—
308	C₂×C₈	—	106	2	no	—
309	C₂×C₈	—	106	2	no	—
310	C₂×C₈	—	106	2	no	—
311	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
313	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
314	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
315	C₄⋊C₄	—	53	2	no	—
316	C₄⋊C₄	—	53	2	no	—
317	C₄⋊C₄	—	53	2	no	—
318	C₄⋊C₄	C₈×D₅₃	1	2	yes	—
319	C₂²⋊C₄	—	53	2	no	—
320	C₂²⋊C₄	—	53	2	no	—
321	C₂²⋊C₄	—	53	2	no	—
322	C₂²⋊C₄	C₈×D₅₃	1	2	yes	—
323	C₄²	—	53	2	no	—
324	C₄²	—	53	2	no	—
325	C₄²	—	53	1	no	—
326	C₄²	—	53	1	no	—
327	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
328	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
329	C₁₆	—	2	2	no	—
330	C₁₆	—	2	2	no	—
331	C₁₆	—	106	2	no	—
332	C₁₆	—	106	2	no	—
333	C₂³	—	53	1	no	—
334	C₂³	—	53	1	no	—
335	C₂³	—	106	2	no	—
336	C₂³	—	106	4	no	—
337	C₂³	C₂×C₈×D₅₃	1	1	yes	characteristic
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	53	1	no	—
341	C₂×C₄	—	53	2	no	—
342	C₂×C₄	—	53	2	no	—
343	C₂×C₄	—	53	2	no	—
344	C₂×C₄	—	53	2	no	—
345	C₂×C₄	—	53	1	no	—
346	C₂×C₄	—	106	2	no	—
347	C₂×C₄	—	106	4	no	—
348	C₂×C₄	—	106	4	no	—
349	C₂×C₄	—	106	2	no	—
350	C₂×C₄	—	106	2	no	—
351	C₂×C₄	—	106	1	no	—
352	C₂×C₄	—	106	1	no	—
353	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
354	C₂×C₄	C₂×C₈×D₅₃	1	2	yes	—
355	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
356	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
357	C₈	—	2	1	no	—
358	C₈	—	2	1	no	—
359	C₈	—	53	2	no	—
360	C₈	—	53	2	no	—
361	C₈	—	106	1	no	—
362	C₈	—	106	1	no	—
363	C₈	M₁₆×D₅₃	1	2	yes	—
364	C₈	#41×D₅₃	1	2	yes	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	53	4	no	—
368	C₂²	—	53	2	no	—
369	C₂²	—	106	2	no	—
370	C₂²	—	106	1	no	—
371	C₂²	—	212	4	no	—
372	C₂²	C₂²×C₈×D₅₃	1	1	yes	characteristic
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	1	no	—
376	C₄	—	53	2	no	—
377	C₄	—	106	2	no	—
378	C₄	—	106	2	no	—
379	C₄	—	106	1	no	—
380	C₄	#117×D₅₃	1	1	yes	characteristic
381	C₄	C₂×M₁₆×D₅₃	1	1	yes	characteristic
382	C₂	—	4	1	no	—
383	C₂	—	53	4	no	—
384	C₂	—	212	1	no	—
385	C₂	#431×D₅₃	1	1	yes	characteristic
386	C₂	#504×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₅₃
commutator, socle	C₂²×C₅₃	C₂³×C₈
Fitting	C₅₃×#2164	C₂
prime radical	C₂³×D₅₃	C₂×C₈
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2164	D₅₃
hypocenter	C₅₃	C₂×#2164
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ #2164

Complements

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

N	H ≅ G/N	type
2. #20276523	C₂	semidirect
3. #20276522	C₂	semidirect
4. #20276521	C₂	semidirect
5. #20276520	C₂	semidirect
6. #20276519	C₂	semidirect
7. C₄⋊C₁₆×D₅₃	C₂	semidirect
9. #346×D₅₃	C₂	semidirect
10. C₄×C₁₆×D₅₃	C₂	semidirect
11. C₅₃×#2164	C₂	semidirect
28. C₄⋊#11719908	C₂²	semidirect
29. #16810441	C₂²	semidirect
30. #16810441	C₂²	semidirect
34. #16810399	C₂²	semidirect
35. #16810398	C₂²	semidirect
36. C₄×#11719908	C₂²	semidirect
37. C₁₆×Dic₅₃	C₂²	semidirect
39. C₅₃×C₄⋊C₁₆	C₂²	semidirect
41. C₅₃×#346	C₂²	semidirect
42. C₄×C₁₆×C₅₃	C₂²	semidirect
195. #2164	D₅₃	direct (N × H)
204. D₅₃	#2164	direct (N × H)
225. C₄⋊C₁₆	C₂×D₅₃	semidirect
232. #346	C₂×D₅₃	semidirect
235. C₄×C₁₆	C₂×D₅₃	semidirect
236. C₅₃	C₂×#2164	semidirect

Maximal subgroups

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

subgroup	index
#405×D₅₃	2
#20276523	2
#20276522	2
#20276521	2
#20276520	2
#20276519	2
C₄⋊C₁₆×D₅₃	2
C₂²⋊C₁₆×D₅₃	2
#346×D₅₃	2
C₄×C₁₆×D₅₃	2
C₅₃×#2164	2
C₂×#2164	53

Subgroups — D53×#2164 #27537163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2164 #27537163