Subgroups — D₅₃×#2178 #27537488

Order 13568.

662 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#508×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#443×D₅₃	C₂	1	2	yes	maximal, complemented
3	#20276597	C₂	1	1	yes	maximal, characteristic, complemented
4	#20276596	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276595	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276594	C₂	1	2	yes	maximal, complemented
7	#20276593	C₂	1	2	yes	maximal, complemented
8	#368×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#359×D₅₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2178	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₃	C₂²	1	2	yes	—
13	#131×D₅₃	—	2	2	no	—
14	#16811056	C₄	1	1	yes	characteristic, complemented
15	#16811055	C₂²	1	1	yes	characteristic
16	#16811054	C₄	1	2	yes	complemented
17	#16811053	C₂²	1	2	yes	—
18	#16811052	C₄	1	1	yes	characteristic, complemented
19	Q₃₂×D₅₃	C₄	1	1	yes	characteristic, complemented
20	SD₃₂×D₅₃	C₄	1	2	yes	complemented
21	D₁₆×D₅₃	C₄	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
24	#16810741	C₂²	1	2	yes	complemented
25	#16810740	C₂²	1	2	yes	complemented
26	#16810739	C₂²	1	2	yes	complemented
27	#16810738	—	2	2	no	—
28	#16810737	—	2	2	no	—
29	#108×D₅₃	C₂²	1	2	yes	—
30	#104×D₅₃	—	2	2	no	—
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810453	C₂²	1	1	yes	characteristic, complemented
33	#16810452	C₂²	1	2	yes	complemented
34	#16810431	C₂²	1	2	yes	complemented
35	#16810430	C₂²	1	2	yes	complemented
36	#16810429	C₂²	1	2	yes	complemented
37	C₄×#11719908	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×#508	C₂²	1	1	yes	characteristic
41	C₅₃×#443	C₂²	1	2	yes	complemented
42	C₅₃×#368	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#359	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	#41×D₅₃	—	2	2	no	—
46	#13133240	C₂×C₄	1	2	yes	—
47	#13133239	C₂³	1	2	yes	—
48	#13133238	—	2	2	no	—
49	#13133237	—	2	2	no	—
50	#13133236	C₂×C₄	1	2	yes	—
51	Q₁₆×D₅₃	C₂×C₄	1	2	yes	—
52	SD₁₆×D₅₃	—	2	2	no	—
53	D₈×D₅₃	C₂×C₄	1	2	yes	—
54	#13133225	—	2	2	no	—
55	#13133225	—	4	2	no	—
56	#13133224	—	2	2	no	—
57	#13133223	—	2	2	no	—
58	#13133223	—	4	2	no	—
59	M₁₆×D₅₃	—	2	2	no	—
60	M₁₆×D₅₃	—	4	2	no	—
61	C₂×C₈×D₅₃	—	4	2	no	—
62	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
64	C₄²×D₅₃	D₄	1	1	yes	characteristic
65	Dic₄₂₄	C₂×C₄	1	1	yes	characteristic, complemented
66	#13133163	C₂×C₄	1	2	yes	complemented
67	#13133162	C₂×C₄	1	2	yes	complemented
68	#13133161	C₂×C₄	1	2	yes	complemented
69	#13133160	C₂×C₄	1	2	yes	complemented
70	D₈₄₈	C₂×C₄	1	1	yes	characteristic, complemented
71	#13133158	C₂×C₄	1	2	yes	complemented
72	C₂×#11719908	C₂³	1	1	yes	characteristic
73	C₂×#11719908	C₂³	1	1	yes	characteristic
74	C₁₆×D₅₃	—	2	1	no	—
75	C₁₆×D₅₃	—	2	1	no	—
76	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
77	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
78	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
79	C₁₆×D₅₃	C₂×C₄	1	1	yes	characteristic
80	#13133153	C₂³	1	2	yes	—
81	#13133152	—	2	2	no	—
82	#13133145	—	2	2	no	—
83	#13133144	—	2	2	no	—
84	#13133143	—	2	2	no	—
85	C₄×#88322	D₄	1	1	yes	characteristic
86	C₈×Dic₅₃	D₄	1	1	yes	characteristic
87	C₈×Dic₅₃	C₂³	1	1	yes	characteristic
88	#135×C₅₃	C₂³	1	2	yes	—
89	#131×C₅₃	—	2	2	no	—
90	Q₃₂×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
91	SD₃₂×C₅₃	C₂×C₄	1	2	yes	complemented
92	D₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic, complemented
93	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
95	#108×C₅₃	C₂³	1	2	yes	—
96	#104×C₅₃	—	2	2	no	—
97	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
98	#41×C₅₃	—	2	2	no	—
99	#11719949	—	2	2	no	—
100	Q₈×D₅₃	—	2	2	no	—
101	#11719947	—	2	2	no	—
102	#11719947	—	4	2	no	—
103	D₄×D₅₃	—	2	2	no	—
104	D₄×D₅₃	—	4	2	no	—
105	#11719945	—	2	2	no	—
106	#11719945	—	4	2	no	—
107	C₂×C₄×D₅₃	—	2	1	no	—
108	C₂×C₄×D₅₃	—	4	2	no	—
109	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₅₃	C₂²×C₄	1	2	yes	—
111	SD₁₆×C₅₃	—	2	2	no	—
112	D₈×C₅₃	C₂²×C₄	1	2	yes	—
113	M₁₆×C₅₃	—	2	2	no	—
114	M₁₆×C₅₃	—	4	2	no	—
115	C₂×C₈×C₅₃	—	4	2	no	—
116	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
118	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
119	#11719925	—	2	2	no	—
120	#11719924	—	2	2	no	—
121	#11719923	—	2	2	no	—
122	#11719922	—	2	2	no	—
123	C₄×Dic₅₃	—	2	1	no	—
124	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
125	#11719917	—	2	2	no	—
126	#11719917	—	4	2	no	—
127	C₂×#88322	—	4	2	no	—
128	C₂×#88322	C₂×D₄	1	1	yes	characteristic
129	C₂×#88322	C₂×D₄	1	1	yes	characteristic
130	Dic₂₁₂	C₂²×C₄	1	2	yes	—
131	D₄₂₄	C₂²×C₄	1	2	yes	—
132	#11719913	—	2	2	no	—
133	#11719912	—	4	2	no	—
134	#11719912	—	4	2	no	—
135	#11719912	—	4	2	no	—
136	C₈×D₅₃	—	4	2	no	—
137	C₈×D₅₃	—	4	2	no	—
138	C₈×D₅₃	—	4	2	no	—
139	C₈×D₅₃	D₈	1	1	yes	characteristic
140	C₈×D₅₃	D₈	1	1	yes	characteristic
141	C₈×D₅₃	D₈	1	1	yes	characteristic
142	C₈×D₅₃	D₈	1	1	yes	characteristic
143	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
144	C₈×D₅₃	C₂²×C₄	1	1	yes	characteristic
145	C₈×D₅₃	#41	1	1	yes	characteristic
146	C₈×D₅₃	#41	1	1	yes	characteristic
147	C₁₆×C₅₃	—	2	1	no	—
148	C₁₆×C₅₃	C₂²×C₄	1	1	yes	characteristic
149	C₁₆×C₅₃	C₂²×C₄	1	1	yes	characteristic
150	#11719908	—	2	1	no	—
151	#11719908	C₂²×C₄	1	1	yes	characteristic
152	#11719908	C₂²×C₄	1	1	yes	characteristic
153	C₂²×D₅₃	—	4	2	no	—
154	C₂²×D₅₃	#135	1	1	yes	characteristic
155	Q₈×C₅₃	—	2	2	no	—
156	D₄×C₅₃	—	2	2	no	—
157	D₄×C₅₃	—	4	2	no	—
158	C₂×C₄×C₅₃	—	2	1	no	—
159	C₂×C₄×C₅₃	—	4	2	no	—
160	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
161	C₂²⋊D₅₃	—	4	2	no	—
162	C₂²⋊D₅₃	—	4	2	no	—
163	C₂²⋊D₅₃	—	4	2	no	—
164	C₂×Dic₅₃	—	2	1	no	—
165	C₂×Dic₅₃	—	4	2	no	—
166	C₂×Dic₅₃	#135	1	1	yes	characteristic
167	D₂₁₂	—	2	2	no	—
168	D₂₁₂	—	4	2	no	—
169	C₄×D₅₃	—	2	4	no	—
170	C₄×D₅₃	—	4	2	no	—
171	C₄×D₅₃	—	4	2	no	—
172	C₄×D₅₃	—	4	2	no	—
173	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
174	C₄×D₅₃	C₄×D₄	1	1	yes	characteristic
175	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
176	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
177	Dic₁₀₆	—	2	2	no	—
178	Dic₁₀₆	—	4	2	no	—
179	C₈×C₅₃	—	4	2	no	—
180	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
181	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
182	C₈×C₅₃	C₂³×C₄	1	1	yes	characteristic
183	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
184	#88322	—	4	2	no	—
185	#88322	C₄×D₄	1	1	yes	characteristic
186	#88322	C₄×D₄	1	1	yes	characteristic
187	#88322	C₂×D₈	1	1	yes	characteristic
188	#88322	C₂×D₈	1	1	yes	characteristic
189	C₂×#2178	—	53	1	no	maximal, Sylow
190	C₂²×C₅₃	—	4	2	no	—
191	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
192	C₂×D₅₃	—	2	2	no	—
193	C₂×D₅₃	—	4	2	no	—
194	C₂×D₅₃	—	8	4	no	—
195	C₂×D₅₃	C₄×D₈	1	1	yes	characteristic
196	C₂×D₅₃	C₄×D₈	1	1	yes	characteristic
197	C₄×C₅₃	—	2	2	no	—
198	C₄×C₅₃	—	4	2	no	—
199	C₄×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
200	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
201	Dic₅₃	—	2	2	no	—
202	Dic₅₃	—	4	2	no	—
203	Dic₅₃	C₄×D₈	1	1	yes	characteristic
204	Dic₅₃	C₄×D₈	1	1	yes	characteristic
205	C₂×#508	—	53	1	no	—
206	C₂×#443	—	53	2	no	—
207	#2178	—	53	1	no	—
208	#2178	—	53	2	no	—
209	#2178	—	53	1	no	—
210	#2178	—	53	2	no	—
211	#2178	—	53	1	no	—
212	#2178	D₅₃	1	1	yes	characteristic, direct product factor
213	C₂×#368	—	53	1	no	—
214	C₂×#359	—	53	2	no	—
215	C₂×C₄×C₁₆	—	53	1	no	—
216	C₂×C₅₃	—	2	1	no	—
217	C₂×C₅₃	—	8	2	no	—
218	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
219	D₅₃	—	2	1	no	—
220	D₅₃	—	8	2	no	—
221	D₅₃	#2178	1	2	yes	direct product factor
222	C₂×#135	—	53	2	no	—
223	C₂×#131	—	106	2	no	—
224	#508	—	53	2	no	—
225	#508	—	53	1	no	—
226	#508	—	53	2	no	—
227	#508	—	53	1	no	—
228	#508	—	53	1	no	—
229	#508	C₂×D₅₃	1	1	yes	characteristic
230	C₂×Q₃₂	—	53	1	no	—
231	C₂×SD₃₂	—	53	2	no	—
232	C₂×D₁₆	—	53	1	no	—
233	C₂²×C₁₆	—	53	1	no	—
234	C₂²×C₁₆	—	53	1	no	—
235	#443	—	53	2	no	—
236	#443	—	53	2	no	—
237	#443	—	53	2	no	—
238	#443	—	106	2	no	—
239	#443	—	106	2	no	—
240	#443	C₂×D₅₃	1	2	yes	complemented
241	C₂×#108	—	53	2	no	—
242	C₂×#104	—	106	2	no	—
243	C₂×C₄×C₈	—	53	1	no	—
244	#368	—	53	1	no	—
245	#368	—	53	2	no	—
246	#368	C₂×D₅₃	1	1	yes	characteristic, complemented
247	#359	—	53	2	no	—
248	#359	—	53	2	no	—
249	#359	—	53	2	no	—
250	#359	C₂×D₅₃	1	2	yes	complemented
251	C₄×C₁₆	—	53	1	no	—
252	C₄×C₁₆	—	53	1	no	—
253	C₄×C₁₆	—	53	1	no	—
254	C₄×C₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
255	C₅₃	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
256	C₂×#41	—	106	2	no	—
257	#135	—	53	2	no	—
258	#135	—	53	2	no	—
259	#135	—	53	2	no	—
260	#135	—	106	2	no	—
261	#135	—	106	2	no	—
262	#135	C₂²×D₅₃	1	2	yes	—
263	C₂×Q₁₆	—	53	2	no	—
264	C₂×SD₁₆	—	106	2	no	—
265	C₂×D₈	—	53	2	no	—
266	#131	—	2	2	no	—
267	#131	—	106	2	no	—
268	#131	—	106	2	no	—
269	#131	—	106	2	no	—
270	#131	—	212	2	no	—
271	#131	—	212	2	no	—
272	C₂×M₁₆	—	106	2	no	—
273	C₂×M₁₆	—	212	2	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	53	1	no	—
276	C₂²×C₈	—	212	2	no	—
277	C₂×C₄²	—	53	1	no	—
278	Q₃₂	—	53	2	no	—
279	Q₃₂	—	53	1	no	—
280	Q₃₂	C₄×D₅₃	1	1	yes	characteristic, complemented
281	SD₃₂	—	53	2	no	—
282	SD₃₂	—	53	2	no	—
283	SD₃₂	—	53	2	no	—
284	SD₃₂	C₄×D₅₃	1	2	yes	complemented
285	D₁₆	—	53	2	no	—
286	D₁₆	—	53	1	no	—
287	D₁₆	C₄×D₅₃	1	1	yes	characteristic, complemented
288	C₂×C₁₆	—	53	1	no	—
289	C₂×C₁₆	—	53	1	no	—
290	C₂×C₁₆	—	53	1	no	—
291	C₂×C₁₆	—	53	1	no	—
292	C₂×C₁₆	—	53	1	no	—
293	C₂×C₁₆	—	53	1	no	—
294	C₂×C₁₆	—	106	1	no	—
295	C₂×C₁₆	—	106	1	no	—
296	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
298	#108	—	53	2	no	—
299	#108	—	106	2	no	—
300	#108	C₂²×D₅₃	1	2	yes	—
301	#104	—	2	2	no	—
302	#104	—	106	2	no	—
303	#104	—	106	2	no	—
304	#104	—	106	2	no	—
305	C₄×C₈	—	53	1	no	—
306	C₄×C₈	—	53	1	no	—
307	C₄×C₈	—	53	1	no	—
308	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
309	#41	—	2	2	no	—
310	#41	—	106	2	no	—
311	#41	—	106	2	no	—
312	#41	—	106	2	no	—
313	#41	—	212	2	no	—
314	#41	—	212	2	no	—
315	C₂×Q₈	—	106	2	no	—
316	C₂×D₄	—	106	2	no	—
317	C₂×D₄	—	212	2	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	106	1	no	—
320	C₂²×C₄	—	212	2	no	—
321	Q₁₆	—	53	2	no	—
322	Q₁₆	—	106	2	no	—
323	Q₁₆	C₂×C₄×D₅₃	1	2	yes	—
324	SD₁₆	—	2	2	no	—
325	SD₁₆	—	106	2	no	—
326	SD₁₆	—	106	2	no	—
327	SD₁₆	—	106	2	no	—
328	D₈	—	53	2	no	—
329	D₈	—	106	2	no	—
330	D₈	C₂×C₄×D₅₃	1	2	yes	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	2	no	—
333	M₁₆	—	106	2	no	—
334	M₁₆	—	212	2	no	—
335	M₁₆	—	212	2	no	—
336	M₁₆	—	212	2	no	—
337	M₁₆	—	212	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	—	53	1	no	—
340	C₂×C₈	—	53	1	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	53	1	no	—
344	C₂×C₈	—	53	1	no	—
345	C₂×C₈	—	53	1	no	—
346	C₂×C₈	—	53	1	no	—
347	C₂×C₈	—	53	1	no	—
348	C₂×C₈	—	53	1	no	—
349	C₂×C₈	—	212	2	no	—
350	C₂×C₈	—	212	2	no	—
351	C₂×C₈	—	212	2	no	—
352	C₂×C₈	—	212	2	no	—
353	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
355	C₄²	—	53	1	no	—
356	C₄²	—	106	1	no	—
357	C₄²	D₄×D₅₃	1	1	yes	characteristic
358	C₁₆	—	2	1	no	—
359	C₁₆	—	53	1	no	—
360	C₁₆	—	53	1	no	—
361	C₁₆	—	106	1	no	—
362	C₁₆	C₂×C₄×D₅₃	1	1	yes	characteristic
363	C₁₆	C₂×C₄×D₅₃	1	1	yes	characteristic
364	C₂³	—	53	1	no	—
365	C₂³	—	212	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	106	2	no	—
368	Q₈	—	212	2	no	—
369	D₄	—	2	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	106	2	no	—
372	D₄	—	212	2	no	—
373	D₄	—	212	2	no	—
374	D₄	—	212	2	no	—
375	D₄	—	212	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	53	1	no	—
379	C₂×C₄	—	53	1	no	—
380	C₂×C₄	—	53	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	106	4	no	—
384	C₂×C₄	—	106	1	no	—
385	C₂×C₄	—	212	2	no	—
386	C₂×C₄	—	212	2	no	—
387	C₂×C₄	—	212	2	no	—
388	C₂×C₄	—	212	2	no	—
389	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
390	C₈	—	4	2	no	—
391	C₈	—	53	1	no	—
392	C₈	—	53	1	no	—
393	C₈	—	53	1	no	—
394	C₈	—	53	1	no	—
395	C₈	—	212	2	no	—
396	C₈	D₈×D₅₃	1	1	yes	characteristic
397	C₈	D₈×D₅₃	1	1	yes	characteristic
398	C₈	C₂²×C₄×D₅₃	1	1	yes	characteristic
399	C₈	#41×D₅₃	1	1	yes	characteristic
400	C₂²	—	4	2	no	—
401	C₂²	—	53	1	no	—
402	C₂²	—	53	1	no	—
403	C₂²	—	106	2	no	—
404	C₂²	—	424	4	no	—
405	C₂²	—	212	2	no	—
406	C₂²	#135×D₅₃	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	53	1	no	—
410	C₄	—	53	1	no	—
411	C₄	—	106	2	no	—
412	C₄	—	212	2	no	—
413	C₄	C₄×D₄×D₅₃	1	1	yes	characteristic
414	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	8	2	no	—
417	C₂	—	53	2	no	—
418	C₂	—	106	1	no	—
419	C₂	—	424	2	no	—
420	C₂	C₄×D₈×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₈×D₅₃
commutator	C₈×C₅₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2178	C₂
socle	C₂×C₅₃	C₂×C₄×D₈
prime radical	#508×D₅₃	C₂
cosocle	C₂×C₈×C₅₃	C₂⁴
hypercenter	#2178	D₅₃
hypocenter	C₅₃	C₂×#2178
LCS	G ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #2178

Complements

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

N	H ≅ G/N	type
2. #443×D₅₃	C₂	semidirect
3. #20276597	C₂	semidirect
4. #20276596	C₂	semidirect
5. #20276595	C₂	semidirect
6. #20276594	C₂	semidirect
7. #20276593	C₂	semidirect
8. #368×D₅₃	C₂	semidirect
9. #359×D₅₃	C₂	semidirect
10. C₄×C₁₆×D₅₃	C₂	semidirect
11. C₅₃×#2178	C₂	semidirect
14. #16811056	C₄	semidirect
16. #16811054	C₄	semidirect
18. #16811052	C₄	semidirect
19. Q₃₂×D₅₃	C₄	semidirect
20. SD₃₂×D₅₃	C₄	semidirect
21. D₁₆×D₅₃	C₄	semidirect
24. #16810741	C₂²	semidirect
25. #16810740	C₂²	semidirect
26. #16810739	C₂²	semidirect
32. #16810453	C₂²	semidirect
33. #16810452	C₂²	semidirect
34. #16810431	C₂²	semidirect
35. #16810430	C₂²	semidirect
36. #16810429	C₂²	semidirect
37. C₄×#11719908	C₂²	semidirect
38. C₁₆×Dic₅₃	C₂²	semidirect
39. C₁₆×Dic₅₃	C₂²	semidirect
41. C₅₃×#443	C₂²	semidirect
42. C₅₃×#368	C₂²	semidirect
43. C₅₃×#359	C₂²	semidirect
44. C₄×C₁₆×C₅₃	C₂²	semidirect
65. Dic₄₂₄	C₂×C₄	semidirect
66. #13133163	C₂×C₄	semidirect
67. #13133162	C₂×C₄	semidirect
68. #13133161	C₂×C₄	semidirect
69. #13133160	C₂×C₄	semidirect
70. D₈₄₈	C₂×C₄	semidirect
71. #13133158	C₂×C₄	semidirect
90. Q₃₂×C₅₃	C₂×C₄	semidirect
91. SD₃₂×C₅₃	C₂×C₄	semidirect
92. D₁₆×C₅₃	C₂×C₄	semidirect
212. #2178	D₅₃	direct (N × H)
221. D₅₃	#2178	direct (N × H)
240. #443	C₂×D₅₃	semidirect
246. #368	C₂×D₅₃	semidirect
250. #359	C₂×D₅₃	semidirect
254. C₄×C₁₆	C₂×D₅₃	semidirect
255. C₅₃	C₂×#2178	semidirect
280. Q₃₂	C₄×D₅₃	semidirect
284. SD₃₂	C₄×D₅₃	semidirect
287. D₁₆	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#508×D₅₃	2
#443×D₅₃	2
#20276597	2
#20276596	2
#20276595	2
#20276594	2
#20276593	2
#368×D₅₃	2
#359×D₅₃	2
C₄×C₁₆×D₅₃	2
C₅₃×#2178	2
C₂×#2178	53

Subgroups — D53×#2178 #27537488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2178 #27537488