Subgroups — C₈×Q₁₆×D₅₃ #27353459

Order 13568.

734 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	C₈×Q₈×D₅₃	C₂	1	2	yes	maximal
2	C₄×Q₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₈×Dic₂₁₂	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₁₆×#88322	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273521	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#11719925	C₂	1	2	yes	maximal, complemented
7	#20273519	C₂	1	2	yes	maximal, complemented
8	#335×D₅₃	C₂	1	1	yes	maximal, characteristic
9	Q₈⋊C₈×D₅₃	C₂	1	2	yes	maximal
10	C₈²×D₅₃	C₂	1	1	yes	maximal, characteristic
11	C₈×Q₁₆×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₅₃	C₄	1	1	yes	characteristic
13	C₄×Q₈×D₅₃	C₂²	1	2	yes	—
14	Q₈×#88322	C₂²	1	2	yes	—
15	C₈×Dic₁₀₆	—	2	2	no	—
16	C₈×Dic₁₀₆	C₂²	1	2	yes	—
17	#16810747	—	2	2	no	—
18	#16810747	C₂²	1	2	yes	—
19	C₄×Dic₂₁₂	C₂²	1	1	yes	characteristic
20	Q₁₆×Dic₅₃	C₄	1	1	yes	characteristic
21	#16810717	C₄	1	1	yes	characteristic
22	C₄×#11719925	C₂²	1	2	yes	—
23	#16810715	C₄	1	2	yes	—
24	#107×D₅₃	C₄	1	1	yes	characteristic
25	C₄⋊C₈×D₅₃	—	2	2	no	—
26	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
27	#103×D₅₃	C₄	1	2	yes	—
28	C₄×C₈×D₅₃	—	2	2	no	—
29	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
32	#16810376	C₂²	1	1	yes	characteristic
33	#16810375	C₂²	1	2	yes	—
34	#16810355	C₂²	1	2	yes	—
35	Q₈⋊#88322	C₂²	1	2	yes	—
36	#16810353	C₂²	1	2	yes	—
37	C₈×#88322	C₂²	1	1	yes	characteristic
38	C₈×#88322	C₂²	1	1	yes	characteristic
39	C₈×#88322	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₅₃	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₅₃	C₂²	1	1	yes	characteristic
42	C₅₃×#335	C₂²	1	1	yes	characteristic
43	C₅₃×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic
45	C₂×Q₈×D₅₃	C₂×C₄	1	2	yes	—
46	C₂×Dic₂₁₂	C₂×C₄	1	1	yes	characteristic
47	C₂×#11719925	C₂×C₄	1	2	yes	—
48	Q₁₆×D₅₃	C₈	1	8	yes	direct product factor
49	C₂×C₈×D₅₃	—	2	2	no	—
50	C₂×C₈×D₅₃	—	2	1	no	—
51	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
54	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
55	Q₈×Dic₅₃	C₂×C₄	1	2	yes	—
56	C₄×Dic₁₀₆	—	2	2	no	—
57	C₄×Dic₁₀₆	C₂³	1	2	yes	—
58	#13133182	—	2	2	no	—
59	#13133182	C₂×C₄	1	2	yes	—
60	C₄⋊C₄×D₅₃	—	2	2	no	—
61	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
62	C₄²×D₅₃	—	2	2	no	—
63	C₄²×D₅₃	C₂³	1	1	yes	characteristic
64	#13133151	C₂×C₄	1	1	yes	characteristic
65	#13133150	C₂×C₄	1	2	yes	—
66	C₄⋊#88322	—	2	2	no	—
67	C₄⋊#88322	C₂³	1	2	yes	—
68	#13133146	—	2	2	no	—
69	#13133146	—	2	2	no	—
70	#13133146	—	2	2	no	—
71	#13133142	C₂×C₄	1	2	yes	—
72	#13133141	C₂×C₄	1	2	yes	—
73	#13133140	C₂×C₄	1	2	yes	—
74	C₄×#88322	—	2	2	no	—
75	C₄×#88322	C₂³	1	1	yes	characteristic
76	C₄×#88322	C₂³	1	1	yes	characteristic
77	C₄×#88322	C₂³	1	1	yes	characteristic
78	C₈×Dic₅₃	—	2	2	no	—
79	C₈×Dic₅₃	—	2	1	no	—
80	C₈×Dic₅₃	—	2	2	no	—
81	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	D₄	1	1	yes	characteristic
84	C₈×Dic₅₃	D₄	1	1	yes	characteristic
85	C₂×Q₁₆×C₅₃	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₅₃	C₂³	1	2	yes	—
87	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₅₃	—	2	2	no	—
89	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
90	#103×C₅₃	C₂×C₄	1	2	yes	—
91	C₄×C₈×C₅₃	—	2	2	no	—
92	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₂×Q₈×C₅₃	C₂²×C₄	1	2	yes	—
96	Q₈×D₅₃	—	2	4	no	—
97	Q₈×D₅₃	C₂×C₈	1	8	yes	—
98	C₂×C₄×D₅₃	—	2	2	no	—
99	C₂×C₄×D₅₃	—	2	2	no	—
100	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
103	C₂×Dic₁₀₆	—	2	2	no	—
104	C₂×Dic₁₀₆	C₂²×C₄	1	2	yes	—
105	Q₁₆×C₅₃	C₂×C₈	1	4	yes	complemented
106	C₂×C₈×C₅₃	—	2	1	no	—
107	C₂×C₈×C₅₃	—	2	2	no	—
108	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
112	C₄⋊C₄×C₅₃	—	2	2	no	—
113	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
114	C₄²×C₅₃	—	2	2	no	—
115	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
116	#11719925	C₂×C₈	1	8	yes	complemented
117	C₄⋊Dic₅₃	—	2	2	no	—
118	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
119	#11719919	—	2	2	no	—
120	#11719919	—	2	2	no	—
121	#11719919	—	2	2	no	—
122	C₄×Dic₅₃	—	2	2	no	—
123	C₄×Dic₅₃	—	2	2	no	—
124	C₄×Dic₅₃	—	2	2	no	—
125	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₅₃	#41	1	1	yes	characteristic
128	C₂×#88322	—	2	1	no	—
129	C₂×#88322	—	2	2	no	—
130	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
131	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
132	C₂×#88322	C₂×D₄	1	1	yes	characteristic
133	C₂×#88322	C₂×D₄	1	1	yes	characteristic
134	Dic₂₁₂	C₂×C₈	1	4	yes	complemented
135	C₈×D₅₃	—	2	4	no	—
136	C₈×D₅₃	—	2	2	no	—
137	C₈×D₅₃	—	2	2	no	—
138	C₈×D₅₃	—	4	4	no	—
139	C₈×D₅₃	C₂×C₈	1	4	yes	—
140	C₈×D₅₃	Q₁₆	1	4	yes	direct product factor
141	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
142	Q₈×C₅₃	—	2	2	no	—
143	Q₈×C₅₃	C₂²×C₈	1	4	yes	—
144	C₂×C₄×C₅₃	—	2	2	no	—
145	C₂×C₄×C₅₃	—	2	2	no	—
146	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₅₃	—	2	2	no	—
150	C₂×Dic₅₃	—	2	2	no	—
151	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
152	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
154	C₄×D₅₃	—	2	8	no	—
155	C₄×D₅₃	—	2	2	no	—
156	C₄×D₅₃	—	4	4	no	—
157	C₄×D₅₃	C₂²×C₈	1	2	yes	—
158	C₄×D₅₃	#131	1	2	yes	—
159	C₄×D₅₃	C₂×Q₁₆	1	2	yes	—
160	C₄×D₅₃	#135	1	2	yes	—
161	Dic₁₀₆	—	2	2	no	—
162	Dic₁₀₆	—	2	8	no	—
163	Dic₁₀₆	C₂²×C₈	1	4	yes	—
164	C₈×C₅₃	—	2	2	no	—
165	C₈×C₅₃	—	2	1	no	—
166	C₈×C₅₃	—	2	1	no	—
167	C₈×C₅₃	—	4	2	no	—
168	C₈×C₅₃	C₂²×C₈	1	2	yes	—
169	C₈×C₅₃	C₂×Q₁₆	1	2	yes	complemented
170	#88322	—	2	2	no	—
171	#88322	—	2	1	no	—
172	#88322	—	2	1	no	—
173	#88322	—	4	2	no	—
174	#88322	C₂²×C₈	1	2	yes	—
175	#88322	C₂×Q₁₆	1	2	yes	complemented
176	C₂×C₈×Q₁₆	—	53	1	no	maximal, Sylow
177	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂×D₅₃	C₈×D₄	1	2	yes	—
179	C₂×D₅₃	C₄×Q₁₆	1	2	yes	—
180	C₂×D₅₃	#443	1	2	yes	—
181	C₄×C₅₃	—	2	4	no	—
182	C₄×C₅₃	—	2	1	no	—
183	C₄×C₅₃	—	4	2	no	—
184	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
185	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
186	C₄×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
187	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
188	Dic₅₃	—	2	4	no	—
189	Dic₅₃	—	2	1	no	—
190	Dic₅₃	—	4	2	no	—
191	Dic₅₃	C₈×D₄	1	2	yes	—
192	Dic₅₃	C₄×Q₁₆	1	2	yes	—
193	C₂×C₈×Q₈	—	53	2	no	—
194	C₂×C₄×Q₁₆	—	53	1	no	—
195	C₈×Q₁₆	—	53	2	no	—
196	C₈×Q₁₆	—	53	1	no	—
197	C₈×Q₁₆	—	53	1	no	—
198	C₈×Q₁₆	—	53	2	no	—
199	C₈×Q₁₆	—	53	1	no	—
200	C₈×Q₁₆	D₅₃	1	1	yes	characteristic, direct product factor
201	C₂×#335	—	53	1	no	—
202	C₂×Q₈⋊C₈	—	53	2	no	—
203	C₂×C₈²	—	53	1	no	—
204	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
205	C₂×C₅₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
206	C₂×C₅₃	C₂×#443	1	1	yes	characteristic
207	D₅₃	C₈×Q₁₆	1	4	yes	direct product factor
208	C₂²×Q₁₆	—	53	1	no	—
209	C₂×C₄×Q₈	—	53	2	no	—
210	C₈×Q₈	—	53	2	no	—
211	C₈×Q₈	—	53	2	no	—
212	C₈×Q₈	—	53	2	no	—
213	C₈×Q₈	—	106	2	no	—
214	C₈×Q₈	—	106	2	no	—
215	C₈×Q₈	C₂×D₅₃	1	2	yes	—
216	C₄×Q₁₆	—	53	1	no	—
217	C₄×Q₁₆	—	53	2	no	—
218	C₄×Q₁₆	—	53	1	no	—
219	C₄×Q₁₆	—	53	2	no	—
220	C₄×Q₁₆	—	53	1	no	—
221	C₄×Q₁₆	C₂×D₅₃	1	1	yes	characteristic
222	C₂×#107	—	53	1	no	—
223	C₂×C₄⋊C₈	—	53	2	no	—
224	C₂×C₄⋊C₈	—	106	2	no	—
225	C₂×#103	—	53	2	no	—
226	C₂×C₄×C₈	—	53	1	no	—
227	C₂×C₄×C₈	—	53	1	no	—
228	C₂×C₄×C₈	—	53	1	no	—
229	C₂×C₄×C₈	—	106	2	no	—
230	#335	—	53	2	no	—
231	#335	—	53	1	no	—
232	#335	C₂×D₅₃	1	1	yes	characteristic
233	Q₈⋊C₈	—	53	2	no	—
234	Q₈⋊C₈	—	53	2	no	—
235	Q₈⋊C₈	—	53	2	no	—
236	Q₈⋊C₈	C₂×D₅₃	1	2	yes	—
237	C₈²	—	53	1	no	—
238	C₈²	—	53	1	no	—
239	C₈²	—	53	1	no	—
240	C₈²	C₂×D₅₃	1	1	yes	characteristic
241	C₅₃	C₂×C₈×Q₁₆	1	1	yes	characteristic, complemented, Sylow
242	C₂²×Q₈	—	53	2	no	—
243	C₂×Q₁₆	—	53	2	no	—
244	C₂×Q₁₆	—	53	8	no	—
245	C₂×Q₁₆	—	53	1	no	—
246	C₂×Q₁₆	C₄×D₅₃	1	1	yes	characteristic
247	C₂²×C₈	—	53	1	no	—
248	C₂²×C₈	—	53	1	no	—
249	C₂²×C₈	—	53	1	no	—
250	C₂²×C₈	—	53	1	no	—
251	C₂²×C₈	—	106	1	no	—
252	C₂²×C₈	—	106	2	no	—
253	C₄×Q₈	—	53	2	no	—
254	C₄×Q₈	—	53	2	no	—
255	C₄×Q₈	—	53	2	no	—
256	C₄×Q₈	—	106	2	no	—
257	C₄×Q₈	—	106	2	no	—
258	C₄×Q₈	C₂²×D₅₃	1	2	yes	—
259	C₂×C₄⋊C₄	—	53	2	no	—
260	C₂×C₄⋊C₄	—	106	2	no	—
261	C₂×C₄²	—	53	1	no	—
262	C₂×C₄²	—	106	2	no	—
263	#107	—	53	1	no	—
264	#107	—	53	2	no	—
265	#107	C₄×D₅₃	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	53	2	no	—
268	C₄⋊C₈	—	106	2	no	—
269	C₄⋊C₈	—	106	2	no	—
270	C₄⋊C₈	—	106	2	no	—
271	C₄⋊C₈	—	106	2	no	—
272	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
273	#103	—	53	2	no	—
274	#103	—	53	2	no	—
275	#103	—	53	2	no	—
276	#103	C₄×D₅₃	1	2	yes	—
277	C₄×C₈	—	2	2	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	—	53	1	no	—
283	C₄×C₈	—	53	1	no	—
284	C₄×C₈	—	53	1	no	—
285	C₄×C₈	—	106	2	no	—
286	C₄×C₈	—	106	1	no	—
287	C₄×C₈	—	106	2	no	—
288	C₄×C₈	—	106	2	no	—
289	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
292	C₂×Q₈	—	53	8	no	—
293	C₂×Q₈	—	53	2	no	—
294	C₂×Q₈	—	106	2	no	—
295	C₂×Q₈	—	106	4	no	—
296	C₂×Q₈	C₂×C₄×D₅₃	1	2	yes	—
297	C₂²×C₄	—	53	1	no	—
298	C₂²×C₄	—	53	1	no	—
299	C₂²×C₄	—	53	1	no	—
300	C₂²×C₄	—	106	2	no	—
301	C₂²×C₄	—	106	2	no	—
302	Q₁₆	—	53	8	no	—
303	Q₁₆	—	53	4	no	—
304	Q₁₆	C₈×D₅₃	1	4	yes	direct product factor
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	53	1	no	—
308	C₂×C₈	—	53	1	no	—
309	C₂×C₈	—	53	4	no	—
310	C₂×C₈	—	53	4	no	—
311	C₂×C₈	—	53	1	no	—
312	C₂×C₈	—	53	1	no	—
313	C₂×C₈	—	106	2	no	—
314	C₂×C₈	—	106	2	no	—
315	C₂×C₈	—	106	4	no	—
316	C₂×C₈	—	106	1	no	—
317	C₂×C₈	—	106	2	no	—
318	C₂×C₈	—	212	4	no	—
319	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
320	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
321	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
322	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	53	2	no	—
325	C₄⋊C₄	—	106	2	no	—
326	C₄⋊C₄	—	106	2	no	—
327	C₄⋊C₄	—	106	2	no	—
328	C₄⋊C₄	—	106	2	no	—
329	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
330	C₄²	—	2	2	no	—
331	C₄²	—	53	1	no	—
332	C₄²	—	53	1	no	—
333	C₄²	—	53	1	no	—
334	C₄²	—	106	2	no	—
335	C₄²	—	106	2	no	—
336	C₄²	—	106	2	no	—
337	C₄²	C₂³×D₅₃	1	1	yes	characteristic
338	C₂³	—	53	1	no	—
339	Q₈	—	2	2	no	—
340	Q₈	—	53	4	no	—
341	Q₈	—	106	8	no	—
342	Q₈	—	106	2	no	—
343	Q₈	C₂×C₈×D₅₃	1	4	yes	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	53	1	no	—
347	C₂×C₄	—	53	1	no	—
348	C₂×C₄	—	53	2	no	—
349	C₂×C₄	—	53	2	no	—
350	C₂×C₄	—	53	2	no	—
351	C₂×C₄	—	53	2	no	—
352	C₂×C₄	—	53	1	no	—
353	C₂×C₄	—	106	2	no	—
354	C₂×C₄	—	106	8	no	—
355	C₂×C₄	—	106	2	no	—
356	C₂×C₄	—	106	2	no	—
357	C₂×C₄	—	212	4	no	—
358	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
360	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
361	C₈	—	2	2	no	—
362	C₈	—	2	1	no	—
363	C₈	—	2	1	no	—
364	C₈	—	4	2	no	—
365	C₈	—	53	2	no	—
366	C₈	—	53	2	no	—
367	C₈	—	106	2	no	—
368	C₈	—	106	1	no	—
369	C₈	—	106	1	no	—
370	C₈	—	212	2	no	—
371	C₈	C₂×C₈×D₅₃	1	2	yes	—
372	C₈	Q₁₆×D₅₃	1	2	yes	direct product factor
373	C₂²	—	53	2	no	—
374	C₂²	—	53	2	no	—
375	C₂²	—	53	2	no	—
376	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	53	2	no	—
381	C₄	—	53	2	no	—
382	C₄	—	106	1	no	—
383	C₄	—	106	4	no	—
384	C₄	—	212	2	no	—
385	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
386	C₄	#131×D₅₃	1	1	yes	characteristic
387	C₄	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
388	C₄	#135×D₅₃	1	1	yes	characteristic
389	C₂	—	53	4	no	—
390	C₂	C₈×D₄×D₅₃	1	1	yes	characteristic
391	C₂	C₄×Q₁₆×D₅₃	1	1	yes	characteristic
392	C₂	#443×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₅₃
commutator	C₄×C₅₃	C₂³×C₈
Frattini	C₄²	C₂³×D₅₃
Fitting	C₈×Q₁₆×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂²×D₅₃	C₄×D₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	C₈×Q₁₆	D₅₃
hypocenter	C₅₃	C₂×C₈×Q₁₆
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
3. C₈×Dic₂₁₂	C₂	semidirect
4. Q₁₆×#88322	C₂	semidirect
5. #20273521	C₂	semidirect
6. C₈×#11719925	C₂	semidirect
7. #20273519	C₂	semidirect
11. C₈×Q₁₆×C₅₃	C₂	semidirect
48. Q₁₆×D₅₃	C₈	direct (N × H)
105. Q₁₆×C₅₃	C₂×C₈	semidirect
116. #11719925	C₂×C₈	semidirect
134. Dic₂₁₂	C₂×C₈	semidirect
140. C₈×D₅₃	Q₁₆	direct (N × H)
169. C₈×C₅₃	C₂×Q₁₆	semidirect
175. #88322	C₂×Q₁₆	semidirect
200. C₈×Q₁₆	D₅₃	direct (N × H)
207. D₅₃	C₈×Q₁₆	direct (N × H)
241. C₅₃	C₂×C₈×Q₁₆	semidirect
304. Q₁₆	C₈×D₅₃	direct (N × H)
372. C₈	Q₁₆×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
C₈×Q₈×D₅₃	2
C₄×Q₁₆×D₅₃	2
C₈×Dic₂₁₂	2
Q₁₆×#88322	2
#20273521	2
C₈×#11719925	2
#20273519	2
#335×D₅₃	2
Q₈⋊C₈×D₅₃	2
C₈²×D₅₃	2
C₈×Q₁₆×C₅₃	2
C₂×C₈×Q₁₆	53

Subgroups — C8×Q16×D53 #27353459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×Q₁₆×D₅₃ #27353459