Subgroups — D₅₃×#2263 #27542222

Order 13568.

502 conjugacy classes of subgroups.

The subgroup lattice has 394 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, complemented
2	C₂×D₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20277030	C₂	1	1	yes	maximal, characteristic, complemented
4	#20277029	C₂	1	2	yes	maximal, complemented
5	#20277028	C₂	1	1	yes	maximal, characteristic, complemented
6	#20277027	C₂	1	1	yes	maximal, characteristic, complemented
7	#20277026	C₂	1	2	yes	maximal, complemented
8	SD₆₄×D₅₃	C₂	1	2	yes	maximal, complemented
9	D₃₂×D₅₃	C₂	1	2	yes	maximal, complemented
10	M₆₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅₃×#2263	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₅₃	—	2	1	no	—
13	C₂×D₈×D₅₃	—	2	1	no	—
14	#16811056	C₂²	1	1	yes	characteristic, complemented
15	#16811055	C₂²	1	1	yes	characteristic, complemented
16	#16811054	—	2	1	no	—
17	#16811053	—	2	1	no	—
18	#16811052	C₂²	1	1	yes	characteristic, complemented
19	Q₃₂×D₅₃	C₂²	1	1	yes	characteristic, complemented
20	SD₃₂×D₅₃	—	2	1	no	—
21	C₂×D₈₄₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13133158	—	2	1	no	—
23	D₁₆×D₅₃	—	2	1	no	—
24	D₁₆×D₅₃	—	2	1	no	—
25	D₁₆×D₅₃	C₂²	1	2	yes	—
26	D₁₆×D₅₃	C₂²	1	2	yes	complemented
27	D₁₆×D₅₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
29	#16810462	C₂²	1	2	yes	complemented
30	#16810461	C₂²	1	2	yes	complemented
31	#16810460	C₂²	1	2	yes	complemented
32	D₁₆₉₆	C₂²	1	2	yes	complemented
33	#16810458	C₂²	1	2	yes	complemented
34	#16810458	C₂²	1	2	yes	complemented
35	#16810457	C₂²	1	1	yes	characteristic, complemented
36	#16810456	C₂²	1	2	yes	complemented
37	C₃₂×D₅₃	C₂²	1	2	yes	complemented
38	C₅₃×#508	C₂²	1	1	yes	characteristic, complemented
39	C₂×D₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
40	C₅₃×SD₆₄	C₂²	1	2	yes	complemented
41	C₅₃×D₃₂	C₂²	1	2	yes	complemented
42	C₅₃×M₆₄	C₂²	1	1	yes	characteristic, complemented
43	#41×D₅₃	—	4	1	no	—
44	C₂×D₄×D₅₃	—	4	1	no	—
45	#13133240	—	2	1	no	—
46	#13133239	—	2	1	no	—
47	#13133238	—	4	1	no	—
48	#13133237	—	4	1	no	—
49	#13133236	—	2	1	no	—
50	Q₁₆×D₅₃	—	2	1	no	—
51	SD₁₆×D₅₃	—	4	1	no	—
52	C₂×D₄₂₄	—	2	1	no	—
53	C₂×#11719922	—	4	1	no	—
54	D₈×D₅₃	—	2	2	no	—
55	D₈×D₅₃	—	2	2	no	—
56	D₈×D₅₃	—	2	1	no	—
57	D₈×D₅₃	—	4	1	no	—
58	D₈×D₅₃	—	4	1	no	—
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	Dic₄₂₄	C₂³	1	1	yes	characteristic, complemented
61	#13133163	—	2	1	no	—
62	#13133162	—	2	1	no	—
63	#13133161	—	2	1	no	—
64	#13133160	—	2	1	no	—
65	D₈₄₈	—	2	1	no	—
66	D₈₄₈	C₂³	1	2	yes	—
67	D₈₄₈	C₂³	1	1	yes	characteristic, complemented
68	#13133158	—	2	2	no	—
69	#13133158	—	2	2	no	—
70	#13133158	—	2	1	no	—
71	C₂×#11719908	D₄	1	1	yes	characteristic
72	C₁₆×D₅₃	D₄	1	1	yes	characteristic
73	C₁₆×D₅₃	D₄	1	1	yes	characteristic
74	C₁₆×D₅₃	C₂³	1	1	yes	characteristic
75	C₁₆×D₅₃	C₂³	1	1	yes	characteristic
76	#13133123	C₂³	1	2	yes	complemented
77	#135×C₅₃	—	2	1	no	—
78	C₂×D₈×C₅₃	—	2	1	no	—
79	Q₃₂×C₅₃	C₂³	1	1	yes	characteristic, complemented
80	SD₃₂×C₅₃	—	2	1	no	—
81	D₁₆×C₅₃	—	2	1	no	—
82	D₁₆×C₅₃	C₂³	1	2	yes	—
83	D₁₆×C₅₃	C₂³	1	1	yes	characteristic, complemented
84	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
85	C₃₂×C₅₃	C₂³	1	2	yes	complemented
86	C₂³×D₅₃	—	8	1	no	—
87	#41×C₅₃	—	4	1	no	—
88	C₂×D₄×C₅₃	—	4	1	no	—
89	C₂×C₂²⋊D₅₃	—	8	1	no	—
90	#11719949	—	4	1	no	—
91	Q₈×D₅₃	—	4	1	no	—
92	#11719947	—	4	1	no	—
93	#11719947	—	8	1	no	—
94	D₄×D₅₃	—	4	2	no	—
95	D₄×D₅₃	—	4	2	no	—
96	D₄×D₅₃	—	4	1	no	—
97	D₄×D₅₃	—	8	1	no	—
98	D₄×D₅₃	—	8	1	no	—
99	D₄×D₅₃	—	8	1	no	—
100	#11719945	—	4	1	no	—
101	#11719945	—	8	1	no	—
102	C₂×D₂₁₂	—	4	1	no	—
103	C₂×C₄×D₅₃	—	8	1	no	—
104	C₂×C₄×D₅₃	D₈	1	1	yes	characteristic
105	Q₁₆×C₅₃	—	2	1	no	—
106	SD₁₆×C₅₃	—	4	1	no	—
107	D₈×C₅₃	—	2	2	no	—
108	D₈×C₅₃	—	2	1	no	—
109	D₈×C₅₃	—	4	1	no	—
110	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
111	#11719925	—	4	1	no	—
112	#11719924	—	4	1	no	—
113	#11719923	—	4	1	no	—
114	#11719922	—	4	2	no	—
115	#11719922	—	4	2	no	—
116	#11719922	—	4	1	no	—
117	C₂×#88322	D₈	1	1	yes	characteristic
118	Dic₂₁₂	—	2	1	no	—
119	D₄₂₄	—	2	2	no	—
120	D₄₂₄	—	2	1	no	—
121	D₄₂₄	—	4	1	no	—
122	#11719913	—	4	1	no	—
123	C₈×D₅₃	D₈	1	1	yes	characteristic
124	C₈×D₅₃	D₈	1	1	yes	characteristic
125	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
126	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
127	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₁₆×C₅₃	C₂⁴	1	1	yes	characteristic
129	#11719908	C₂×D₄	1	1	yes	characteristic
130	#11719908	C₂×D₄	1	1	yes	characteristic
131	C₂³×C₅₃	—	8	1	no	—
132	C₂²×D₅₃	—	8	1	no	—
133	C₂²×D₅₃	—	8	1	no	—
134	C₂²×D₅₃	—	8	2	no	—
135	C₂²×D₅₃	—	8	2	no	—
136	C₂²×D₅₃	—	16	4	no	—
137	C₂²×D₅₃	D₁₆	1	1	yes	characteristic
138	Q₈×C₅₃	—	4	1	no	—
139	D₄×C₅₃	—	4	2	no	—
140	D₄×C₅₃	—	4	1	no	—
141	D₄×C₅₃	—	8	1	no	—
142	D₄×C₅₃	—	8	1	no	—
143	C₂×C₄×C₅₃	—	8	1	no	—
144	C₂×C₄×C₅₃	C₂×D₈	1	1	yes	characteristic
145	C₂²⋊D₅₃	—	8	1	no	—
146	C₂²⋊D₅₃	—	8	1	no	—
147	C₂²⋊D₅₃	—	8	1	no	—
148	C₂²⋊D₅₃	—	8	2	no	—
149	C₂²⋊D₅₃	—	8	2	no	—
150	C₂×Dic₅₃	—	8	1	no	—
151	C₂×Dic₅₃	D₁₆	1	1	yes	characteristic
152	D₂₁₂	—	4	2	no	—
153	D₂₁₂	—	4	1	no	—
154	D₂₁₂	—	8	1	no	—
155	D₂₁₂	—	8	1	no	—
156	C₄×D₅₃	—	8	1	no	—
157	C₄×D₅₃	—	8	1	no	—
158	C₄×D₅₃	—	8	1	no	—
159	C₄×D₅₃	D₁₆	1	1	yes	characteristic
160	C₄×D₅₃	D₁₆	1	1	yes	characteristic
161	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
162	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
163	Dic₁₀₆	—	4	1	no	—
164	Dic₁₀₆	—	8	1	no	—
165	C₈×C₅₃	C₂×D₈	1	1	yes	characteristic
166	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
167	#88322	C₂×D₈	1	1	yes	characteristic
168	#88322	C₂×D₈	1	1	yes	characteristic
169	C₂×#2263	—	53	1	no	maximal, Sylow
170	C₂²×C₅₃	—	8	1	no	—
171	C₂²×C₅₃	—	8	2	no	—
172	C₂²×C₅₃	—	16	2	no	—
173	C₂²×C₅₃	C₂×D₁₆	1	1	yes	characteristic
174	C₂×D₅₃	—	2	2	no	—
175	C₂×D₅₃	—	8	1	no	—
176	C₂×D₅₃	—	8	2	no	—
177	C₂×D₅₃	—	16	4	no	—
178	C₂×D₅₃	—	16	2	no	—
179	C₂×D₅₃	—	16	2	no	—
180	C₂×D₅₃	—	16	4	no	—
181	C₂×D₅₃	C₂×D₁₆	1	1	yes	characteristic
182	C₂×D₅₃	C₂×D₁₆	1	1	yes	characteristic
183	C₄×C₅₃	—	8	1	no	—
184	C₄×C₅₃	C₂×D₁₆	1	1	yes	characteristic
185	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
186	Dic₅₃	—	8	1	no	—
187	Dic₅₃	C₂×D₁₆	1	1	yes	characteristic
188	Dic₅₃	C₂×D₁₆	1	1	yes	characteristic
189	C₂×#508	—	53	1	no	—
190	C₂²×D₁₆	—	53	1	no	—
191	#2263	—	53	1	no	—
192	#2263	—	53	1	no	—
193	#2263	—	53	2	no	—
194	#2263	—	53	2	no	—
195	#2263	—	53	1	no	—
196	#2263	D₅₃	1	1	yes	characteristic, direct product factor
197	C₂×SD₆₄	—	53	2	no	—
198	C₂×D₃₂	—	53	2	no	—
199	C₂×M₆₄	—	53	1	no	—
200	C₂×C₅₃	—	2	1	no	—
201	C₂×C₅₃	—	16	2	no	—
202	C₂×C₅₃	—	16	1	no	—
203	C₂×C₅₃	C₂²×D₁₆	1	1	yes	characteristic
204	D₅₃	—	2	1	no	—
205	D₅₃	—	16	1	no	—
206	D₅₃	—	16	2	no	—
207	D₅₃	#2263	1	2	yes	direct product factor
208	C₂×#135	—	106	1	no	—
209	C₂²×D₈	—	106	1	no	—
210	#508	—	53	1	no	—
211	#508	—	53	1	no	—
212	#508	—	53	1	no	—
213	#508	—	106	1	no	—
214	#508	—	106	1	no	—
215	#508	C₂×D₅₃	1	1	yes	characteristic, complemented
216	C₂×Q₃₂	—	53	1	no	—
217	C₂×SD₃₂	—	106	1	no	—
218	C₂×D₁₆	—	53	2	no	—
219	C₂×D₁₆	—	53	2	no	—
220	C₂×D₁₆	—	53	1	no	—
221	C₂×D₁₆	—	53	1	no	—
222	C₂×D₁₆	—	106	1	no	—
223	C₂×D₁₆	—	106	1	no	—
224	C₂×D₁₆	—	106	1	no	—
225	C₂×D₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
226	C₂²×C₁₆	—	53	1	no	—
227	SD₆₄	—	53	2	no	—
228	SD₆₄	—	53	2	no	—
229	SD₆₄	—	53	2	no	—
230	SD₆₄	C₂×D₅₃	1	2	yes	complemented
231	D₃₂	—	53	2	no	—
232	D₃₂	—	53	2	no	—
233	D₃₂	—	53	2	no	—
234	D₃₂	C₂×D₅₃	1	2	yes	complemented
235	M₆₄	—	53	1	no	—
236	M₆₄	—	53	2	no	—
237	M₆₄	C₂×D₅₃	1	1	yes	characteristic, complemented
238	C₂×C₃₂	—	53	2	no	—
239	C₅₃	C₂×#2263	1	1	yes	characteristic, complemented, Sylow
240	C₂×#41	—	212	1	no	—
241	C₂²×D₄	—	212	1	no	—
242	#135	—	2	1	no	—
243	#135	—	106	1	no	—
244	#135	—	106	1	no	—
245	#135	—	106	1	no	—
246	#135	—	212	1	no	—
247	#135	—	212	1	no	—
248	C₂×Q₁₆	—	106	1	no	—
249	C₂×SD₁₆	—	212	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×D₈	—	106	2	no	—
252	C₂×D₈	—	106	2	no	—
253	C₂×D₈	—	106	1	no	—
254	C₂×D₈	—	106	1	no	—
255	C₂×D₈	—	212	1	no	—
256	C₂×D₈	—	212	1	no	—
257	C₂×D₈	—	212	1	no	—
258	C₂²×C₈	—	53	1	no	—
259	Q₃₂	—	53	1	no	—
260	Q₃₂	—	106	1	no	—
261	Q₃₂	C₂²×D₅₃	1	1	yes	characteristic, complemented
262	SD₃₂	—	2	1	no	—
263	SD₃₂	—	106	1	no	—
264	SD₃₂	—	106	1	no	—
265	SD₃₂	—	106	1	no	—
266	D₁₆	—	2	1	no	—
267	D₁₆	—	53	2	no	—
268	D₁₆	—	53	1	no	—
269	D₁₆	—	106	2	no	—
270	D₁₆	—	106	2	no	—
271	D₁₆	—	106	1	no	—
272	D₁₆	—	106	1	no	—
273	D₁₆	C₂²×D₅₃	1	2	yes	—
274	D₁₆	C₂²×D₅₃	1	1	yes	characteristic, complemented
275	C₂×C₁₆	—	53	1	no	—
276	C₂×C₁₆	—	53	1	no	—
277	C₂×C₁₆	—	53	1	no	—
278	C₂×C₁₆	—	53	1	no	—
279	C₂×C₁₆	—	53	1	no	—
280	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
281	C₃₂	—	53	2	no	—
282	C₃₂	C₂²×D₅₃	1	2	yes	complemented
283	C₂⁴	—	424	1	no	—
284	#41	—	4	1	no	—
285	#41	—	424	1	no	—
286	#41	—	424	1	no	—
287	#41	—	212	1	no	—
288	#41	—	212	1	no	—
289	#41	—	212	1	no	—
290	C₂×Q₈	—	212	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	424	1	no	—
293	C₂×D₄	—	424	1	no	—
294	C₂×D₄	—	424	1	no	—
295	C₂×D₄	—	424	1	no	—
296	C₂×D₄	—	212	2	no	—
297	C₂×D₄	—	212	2	no	—
298	C₂×D₄	—	212	1	no	—
299	C₂×D₄	—	212	1	no	—
300	C₂²×C₄	—	53	1	no	—
301	C₂²×C₄	—	424	1	no	—
302	Q₁₆	—	2	1	no	—
303	Q₁₆	—	106	1	no	—
304	Q₁₆	—	212	1	no	—
305	SD₁₆	—	4	1	no	—
306	SD₁₆	—	212	1	no	—
307	SD₁₆	—	212	1	no	—
308	SD₁₆	—	212	1	no	—
309	D₈	—	2	2	no	—
310	D₈	—	2	1	no	—
311	D₈	—	4	1	no	—
312	D₈	—	106	2	no	—
313	D₈	—	106	1	no	—
314	D₈	—	212	2	no	—
315	D₈	—	212	2	no	—
316	D₈	—	212	1	no	—
317	D₈	—	212	1	no	—
318	C₂×C₈	—	53	1	no	—
319	C₂×C₈	—	53	1	no	—
320	C₂×C₈	—	53	1	no	—
321	C₂×C₈	—	53	1	no	—
322	C₂×C₈	—	53	1	no	—
323	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
324	C₁₆	—	53	1	no	—
325	C₁₆	—	53	1	no	—
326	C₁₆	D₄×D₅₃	1	1	yes	characteristic
327	C₁₆	C₂³×D₅₃	1	1	yes	characteristic
328	C₂³	—	8	1	no	—
329	C₂³	—	53	1	no	—
330	C₂³	—	848	4	no	—
331	C₂³	—	424	1	no	—
332	C₂³	—	424	2	no	—
333	C₂³	—	424	2	no	—
334	C₂³	—	424	1	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	424	1	no	—
337	Q₈	—	212	1	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	1	no	—
340	D₄	—	8	1	no	—
341	D₄	—	8	1	no	—
342	D₄	—	424	1	no	—
343	D₄	—	424	2	no	—
344	D₄	—	424	2	no	—
345	D₄	—	424	1	no	—
346	D₄	—	424	1	no	—
347	D₄	—	424	1	no	—
348	D₄	—	424	1	no	—
349	D₄	—	212	2	no	—
350	D₄	—	212	1	no	—
351	C₂×C₄	—	8	1	no	—
352	C₂×C₄	—	53	1	no	—
353	C₂×C₄	—	53	1	no	—
354	C₂×C₄	—	53	1	no	—
355	C₂×C₄	—	53	1	no	—
356	C₂×C₄	—	53	1	no	—
357	C₂×C₄	—	424	1	no	—
358	C₂×C₄	—	424	1	no	—
359	C₂×C₄	—	424	1	no	—
360	C₂×C₄	—	424	1	no	—
361	C₂×C₄	D₈×D₅₃	1	1	yes	characteristic
362	C₈	—	53	1	no	—
363	C₈	—	53	1	no	—
364	C₈	D₈×D₅₃	1	1	yes	characteristic
365	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
366	C₂²	—	8	1	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	2	no	—
369	C₂²	—	53	1	no	—
370	C₂²	—	53	1	no	—
371	C₂²	—	848	2	no	—
372	C₂²	—	848	4	no	—
373	C₂²	—	848	2	no	—
374	C₂²	—	848	4	no	—
375	C₂²	—	106	2	no	—
376	C₂²	—	424	1	no	—
377	C₂²	—	424	2	no	—
378	C₂²	D₁₆×D₅₃	1	1	yes	characteristic
379	C₄	—	8	1	no	—
380	C₄	—	53	1	no	—
381	C₄	—	53	1	no	—
382	C₄	—	424	1	no	—
383	C₄	D₁₆×D₅₃	1	1	yes	characteristic
384	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	16	2	no	—
387	C₂	—	16	1	no	—
388	C₂	—	53	2	no	—
389	C₂	—	848	2	no	—
390	C₂	—	848	1	no	—
391	C₂	—	106	1	no	—
392	C₂	C₂×D₁₆×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₆×D₅₃
commutator, cosocle	C₁₆×C₅₃	C₂⁴
Frattini	C₁₆	C₂³×D₅₃
Fitting	C₅₃×#2263	C₂
socle	C₂×C₅₃	C₂²×D₁₆
hypercenter	#2263	D₅₃
hypocenter	C₅₃	C₂×#2263
LCS	G ▷ C₁₆×C₅₃ ▷ C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #2263

Complements

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

N	H ≅ G/N	type
1. #508×D₅₃	C₂	semidirect
2. C₂×D₁₆×D₅₃	C₂	semidirect
3. #20277030	C₂	semidirect
4. #20277029	C₂	semidirect
5. #20277028	C₂	semidirect
6. #20277027	C₂	semidirect
7. #20277026	C₂	semidirect
8. SD₆₄×D₅₃	C₂	semidirect
9. D₃₂×D₅₃	C₂	semidirect
10. M₆₄×D₅₃	C₂	semidirect
11. C₅₃×#2263	C₂	semidirect
14. #16811056	C₂²	semidirect
15. #16811055	C₂²	semidirect
18. #16811052	C₂²	semidirect
19. Q₃₂×D₅₃	C₂²	semidirect
21. C₂×D₈₄₈	C₂²	semidirect
26. D₁₆×D₅₃	C₂²	semidirect
27. D₁₆×D₅₃	C₂²	semidirect
29. #16810462	C₂²	semidirect
30. #16810461	C₂²	semidirect
31. #16810460	C₂²	semidirect
32. D₁₆₉₆	C₂²	semidirect
33. #16810458	C₂²	semidirect
34. #16810458	C₂²	semidirect
35. #16810457	C₂²	semidirect
36. #16810456	C₂²	semidirect
37. C₃₂×D₅₃	C₂²	semidirect
38. C₅₃×#508	C₂²	semidirect
39. C₂×D₁₆×C₅₃	C₂²	semidirect
40. C₅₃×SD₆₄	C₂²	semidirect
41. C₅₃×D₃₂	C₂²	semidirect
42. C₅₃×M₆₄	C₂²	semidirect
60. Dic₄₂₄	C₂³	semidirect
67. D₈₄₈	C₂³	semidirect
76. #13133123	C₂³	semidirect
79. Q₃₂×C₅₃	C₂³	semidirect
83. D₁₆×C₅₃	C₂³	semidirect
85. C₃₂×C₅₃	C₂³	semidirect
196. #2263	D₅₃	direct (N × H)
207. D₅₃	#2263	direct (N × H)
215. #508	C₂×D₅₃	semidirect
225. C₂×D₁₆	C₂×D₅₃	semidirect
230. SD₆₄	C₂×D₅₃	semidirect
234. D₃₂	C₂×D₅₃	semidirect
237. M₆₄	C₂×D₅₃	semidirect
239. C₅₃	C₂×#2263	semidirect
261. Q₃₂	C₂²×D₅₃	semidirect
274. D₁₆	C₂²×D₅₃	semidirect
282. C₃₂	C₂²×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
C₂×D₁₆×D₅₃	2
#20277030	2
#20277029	2
#20277028	2
#20277027	2
#20277026	2
SD₆₄×D₅₃	2
D₃₂×D₅₃	2
M₆₄×D₅₃	2
C₅₃×#2263	2
C₂×#2263	53

Subgroups — D53×#2263 #27542222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2263 #27542222