Subgroups — C₈×D₈×D₅₃ #27353445

Order 13568.

910 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic
2	C₈×D₄×D₅₃	C₂	1	2	yes	maximal, complemented
3	C₈×D₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₈×#88322	C₂	1	1	yes	maximal, characteristic, complemented
5	#20273509	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#11719922	C₂	1	2	yes	maximal, complemented
7	#20273507	C₂	1	2	yes	maximal, complemented
8	#335×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄⋊C₈×D₅₃	C₂	1	2	yes	maximal, complemented
10	C₈²×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₅₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₅₃	—	2	2	no	—
14	C₄×D₄×D₅₃	C₂²	1	2	yes	—
15	C₄×D₄₂₄	C₂²	1	1	yes	characteristic
16	D₈×Dic₅₃	C₄	1	1	yes	characteristic
17	#16810705	C₄	1	1	yes	characteristic
18	C₄×#11719922	C₂²	1	2	yes	—
19	#16810703	C₄	1	2	yes	—
20	C₈×D₂₁₂	C₂²	1	2	yes	complemented
21	D₄×#88322	C₂²	1	2	yes	complemented
22	#16810688	C₂²	1	2	yes	complemented
23	C₈×C₂²⋊D₅₃	—	2	2	no	—
24	#16810686	—	2	2	no	—
25	#107×D₅₃	C₄	1	1	yes	characteristic
26	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
27	#102×D₅₃	C₄	1	2	yes	—
28	C₂²⋊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, complemented
33	#16810375	C₂²	1	2	yes	complemented
34	#16810352	C₂²	1	2	yes	complemented
35	D₄⋊#88322	C₂²	1	2	yes	complemented
36	#16810350	C₂²	1	2	yes	complemented
37	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
38	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
39	C₈×#88322	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₅₃	C₂²	1	2	yes	complemented
42	C₅₃×#335	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₈²×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₅₃	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₅₃	—	2	2	no	—
47	C₂×D₄₂₄	C₂×C₄	1	1	yes	characteristic
48	C₂×#11719922	C₂×C₄	1	2	yes	—
49	D₈×D₅₃	C₈	1	8	yes	direct product factor
50	C₂²×#88322	—	2	2	no	—
51	C₂×C₈×D₅₃	—	2	2	no	—
52	C₂×C₈×D₅₃	—	2	2	no	—
53	C₂×C₈×D₅₃	—	2	2	no	—
54	C₂×C₈×D₅₃	—	2	1	no	—
55	C₂×C₈×D₅₃	—	4	8	no	—
56	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
60	C₄×D₂₁₂	C₂³	1	2	yes	—
61	D₄×Dic₅₃	C₂×C₄	1	2	yes	—
62	#13133179	C₂×C₄	1	2	yes	—
63	C₄×C₂²⋊D₅₃	—	2	2	no	—
64	#13133177	—	2	2	no	—
65	C₄⋊C₄×D₅₃	C₂×C₄	1	2	yes	—
66	C₂²⋊C₄×D₅₃	—	2	2	no	—
67	C₄²×D₅₃	C₂³	1	1	yes	characteristic
68	#13133151	C₂×C₄	1	1	yes	characteristic
69	#13133150	C₂×C₄	1	2	yes	—
70	C₄⋊#88322	C₂³	1	2	yes	—
71	#13133146	—	2	2	no	—
72	#13133139	C₂×C₄	1	2	yes	—
73	#13133138	C₂×C₄	1	2	yes	—
74	#13133137	C₂×C₄	1	2	yes	—
75	C₂²⋊#88322	—	2	2	no	—
76	#13133129	—	2	2	no	—
77	#13133129	—	2	2	no	—
78	C₄×#88322	C₂³	1	1	yes	characteristic
79	C₄×#88322	C₂³	1	1	yes	characteristic
80	C₄×#88322	C₂³	1	1	yes	characteristic
81	C₈×Dic₅₃	—	2	1	no	—
82	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₅₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₅₃	D₄	1	1	yes	characteristic
85	C₈×Dic₅₃	D₄	1	1	yes	characteristic
86	C₂×D₈×C₅₃	C₂×C₄	1	1	yes	characteristic
87	C₂²×C₈×C₅₃	—	2	2	no	—
88	C₄×D₄×C₅₃	C₂³	1	2	yes	—
89	#107×C₅₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
91	#102×C₅₃	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₅₃	—	2	2	no	—
93	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₂³×D₅₃	—	2	2	no	—
97	C₂×D₄×C₅₃	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₅₃	—	2	2	no	—
99	C₂×C₂²⋊D₅₃	—	2	2	no	—
100	C₂²×Dic₅₃	—	2	2	no	—
101	D₄×D₅₃	—	2	4	no	—
102	D₄×D₅₃	C₂×C₈	1	8	yes	complemented
103	C₂×D₂₁₂	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₅₃	—	2	2	no	—
105	C₂×C₄×D₅₃	—	2	2	no	—
106	C₂×C₄×D₅₃	—	2	2	no	—
107	C₂×C₄×D₅₃	—	4	4	no	—
108	C₂×C₄×D₅₃	—	4	4	no	—
109	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
112	D₈×C₅₃	C₂×C₈	1	4	yes	complemented
113	C₂×C₈×C₅₃	—	2	1	no	—
114	C₂×C₈×C₅₃	—	2	2	no	—
115	C₂×C₈×C₅₃	—	4	4	no	—
116	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
120	C₄⋊C₄×C₅₃	C₂²×C₄	1	2	yes	—
121	C₂²⋊C₄×C₅₃	—	2	2	no	—
122	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
123	C₂²⋊Dic₅₃	—	2	2	no	—
124	#11719922	C₂×C₈	1	8	yes	complemented
125	#11719921	—	2	2	no	—
126	#11719921	—	2	2	no	—
127	C₄⋊Dic₅₃	C₂²×C₄	1	2	yes	—
128	#11719919	—	2	2	no	—
129	C₄×Dic₅₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄×Dic₅₃	#41	1	1	yes	characteristic
132	C₂×#88322	—	2	1	no	—
133	C₂×#88322	—	2	2	no	—
134	C₂×#88322	—	4	4	no	—
135	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
136	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
137	C₂×#88322	C₂×D₄	1	1	yes	characteristic
138	C₂×#88322	C₂×D₄	1	1	yes	characteristic
139	D₄₂₄	C₂×C₈	1	4	yes	complemented
140	C₈×D₅₃	—	2	4	no	—
141	C₈×D₅₃	—	2	2	no	—
142	C₈×D₅₃	—	2	2	no	—
143	C₈×D₅₃	—	4	4	no	—
144	C₈×D₅₃	—	4	4	no	—
145	C₈×D₅₃	—	4	4	no	—
146	C₈×D₅₃	C₂×C₈	1	4	yes	complemented
147	C₈×D₅₃	D₈	1	4	yes	direct product factor
148	C₂³×C₅₃	—	2	2	no	—
149	C₂²×D₅₃	—	2	2	no	—
150	C₂²×D₅₃	—	2	8	no	—
151	C₂²×D₅₃	—	4	4	no	—
152	C₂²×D₅₃	—	4	4	no	—
153	C₂²×D₅₃	C₄×D₄	1	1	yes	characteristic
154	D₄×C₅₃	—	2	2	no	—
155	D₄×C₅₃	C₂²×C₈	1	4	yes	complemented
156	C₂×C₄×C₅₃	—	2	2	no	—
157	C₂×C₄×C₅₃	—	4	2	no	—
158	C₂×C₄×C₅₃	—	4	2	no	—
159	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₅₃	—	2	8	no	—
163	C₂×Dic₅₃	—	2	2	no	—
164	C₂×Dic₅₃	—	4	4	no	—
165	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
166	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
167	C₂×Dic₅₃	C₄×D₄	1	1	yes	characteristic
168	D₂₁₂	—	2	2	no	—
169	D₂₁₂	C₂²×C₈	1	4	yes	complemented
170	C₄×D₅₃	—	2	2	no	—
171	C₄×D₅₃	—	4	4	no	—
172	C₄×D₅₃	—	4	2	no	—
173	C₄×D₅₃	—	4	2	no	—
174	C₄×D₅₃	—	4	4	no	—
175	C₄×D₅₃	C₂²×C₈	1	2	yes	—
176	C₄×D₅₃	#131	1	2	yes	—
177	C₄×D₅₃	C₂×D₈	1	2	yes	—
178	C₄×D₅₃	#135	1	2	yes	—
179	C₈×C₅₃	—	2	2	no	—
180	C₈×C₅₃	—	2	1	no	—
181	C₈×C₅₃	—	2	1	no	—
182	C₈×C₅₃	—	4	2	no	—
183	C₈×C₅₃	C₂²×C₈	1	2	yes	complemented
184	C₈×C₅₃	C₂×D₈	1	2	yes	complemented
185	#88322	—	2	2	no	—
186	#88322	—	2	1	no	—
187	#88322	—	2	1	no	—
188	#88322	—	4	2	no	—
189	#88322	C₂²×C₈	1	2	yes	complemented
190	#88322	C₂×D₈	1	2	yes	complemented
191	C₂×C₈×D₈	—	53	1	no	maximal, Sylow
192	C₂²×C₅₃	—	2	4	no	—
193	C₂²×C₅₃	—	4	2	no	—
194	C₂²×C₅₃	—	4	2	no	—
195	C₂²×C₅₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂×D₅₃	—	2	4	no	—
197	C₂×D₅₃	—	4	2	no	—
198	C₂×D₅₃	—	4	2	no	—
199	C₂×D₅₃	—	4	16	no	—
200	C₂×D₅₃	C₈×D₄	1	2	yes	—
201	C₂×D₅₃	C₄×D₈	1	2	yes	—
202	C₂×D₅₃	#443	1	2	yes	—
203	C₄×C₅₃	—	2	1	no	—
204	C₄×C₅₃	—	4	2	no	—
205	C₄×C₅₃	C₂³×C₈	1	1	yes	characteristic
206	C₄×C₅₃	C₂×#131	1	1	yes	characteristic
207	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
208	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
209	Dic₅₃	—	2	1	no	—
210	Dic₅₃	—	4	2	no	—
211	Dic₅₃	C₈×D₄	1	2	yes	—
212	Dic₅₃	C₄×D₈	1	2	yes	—
213	C₂×C₄×D₈	—	53	1	no	—
214	C₂×C₈×D₄	—	53	2	no	—
215	C₈×D₈	—	53	1	no	—
216	C₈×D₈	—	53	2	no	—
217	C₈×D₈	—	53	1	no	—
218	C₈×D₈	—	53	2	no	—
219	C₈×D₈	—	53	1	no	—
220	C₈×D₈	D₅₃	1	1	yes	characteristic, direct product factor
221	C₂×#335	—	53	1	no	—
222	C₂×D₄⋊C₈	—	53	2	no	—
223	C₂×C₈²	—	53	1	no	—
224	C₂×C₅₃	—	4	4	no	—
225	C₂×C₅₃	C₂×C₈×D₄	1	1	yes	characteristic
226	C₂×C₅₃	C₂×C₄×D₈	1	1	yes	characteristic
227	C₂×C₅₃	C₂×#443	1	1	yes	characteristic
228	D₅₃	—	4	4	no	—
229	D₅₃	C₈×D₈	1	4	yes	direct product factor
230	C₂²×D₈	—	53	1	no	—
231	C₂³×C₈	—	106	2	no	—
232	C₂×C₄×D₄	—	53	2	no	—
233	C₄×D₈	—	53	1	no	—
234	C₄×D₈	—	53	2	no	—
235	C₄×D₈	—	53	1	no	—
236	C₄×D₈	—	53	2	no	—
237	C₄×D₈	—	53	1	no	—
238	C₄×D₈	C₂×D₅₃	1	1	yes	characteristic
239	C₈×D₄	—	53	2	no	—
240	C₈×D₄	—	53	2	no	—
241	C₈×D₄	—	53	2	no	—
242	C₈×D₄	—	106	2	no	—
243	C₈×D₄	—	106	2	no	—
244	C₈×D₄	C₂×D₅₃	1	2	yes	complemented
245	C₂×#107	—	53	1	no	—
246	C₂×C₄⋊C₈	—	53	2	no	—
247	C₂×#102	—	53	2	no	—
248	C₂×C₂²⋊C₈	—	106	2	no	—
249	C₂×C₄×C₈	—	53	1	no	—
250	C₂×C₄×C₈	—	53	1	no	—
251	C₂×C₄×C₈	—	53	1	no	—
252	#335	—	53	2	no	—
253	#335	—	53	1	no	—
254	#335	C₂×D₅₃	1	1	yes	characteristic, complemented
255	D₄⋊C₈	—	53	2	no	—
256	D₄⋊C₈	—	53	2	no	—
257	D₄⋊C₈	—	53	2	no	—
258	D₄⋊C₈	C₂×D₅₃	1	2	yes	complemented
259	C₈²	—	53	1	no	—
260	C₈²	—	53	1	no	—
261	C₈²	—	53	1	no	—
262	C₈²	C₂×D₅₃	1	1	yes	characteristic, complemented
263	C₅₃	C₂×C₈×D₈	1	1	yes	characteristic, complemented, Sylow
264	C₂²×D₄	—	53	2	no	—
265	C₂³×C₄	—	106	2	no	—
266	C₂×D₈	—	53	2	no	—
267	C₂×D₈	—	53	8	no	—
268	C₂×D₈	—	53	1	no	—
269	C₂×D₈	C₄×D₅₃	1	1	yes	characteristic
270	C₂²×C₈	—	2	2	no	—
271	C₂²×C₈	—	53	1	no	—
272	C₂²×C₈	—	53	1	no	—
273	C₂²×C₈	—	53	1	no	—
274	C₂²×C₈	—	53	1	no	—
275	C₂²×C₈	—	106	2	no	—
276	C₂²×C₈	—	106	1	no	—
277	C₂²×C₈	—	106	2	no	—
278	C₂²×C₈	—	106	2	no	—
279	C₂²×C₈	—	106	2	no	—
280	C₂²×C₈	—	212	8	no	—
281	C₄×D₄	—	53	2	no	—
282	C₄×D₄	—	53	2	no	—
283	C₄×D₄	—	53	2	no	—
284	C₄×D₄	—	106	2	no	—
285	C₄×D₄	—	106	2	no	—
286	C₄×D₄	C₂²×D₅₃	1	2	yes	—
287	C₂×C₄⋊C₄	—	53	2	no	—
288	C₂×C₂²⋊C₄	—	106	2	no	—
289	C₂×C₄²	—	53	1	no	—
290	#107	—	53	1	no	—
291	#107	—	53	2	no	—
292	#107	C₄×D₅₃	1	1	yes	characteristic
293	C₄⋊C₈	—	53	2	no	—
294	C₄⋊C₈	—	106	2	no	—
295	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
296	#102	—	53	2	no	—
297	#102	—	53	2	no	—
298	#102	—	53	2	no	—
299	#102	C₄×D₅₃	1	2	yes	—
300	C₂²⋊C₈	—	2	2	no	—
301	C₂²⋊C₈	—	106	2	no	—
302	C₂²⋊C₈	—	106	2	no	—
303	C₂²⋊C₈	—	106	2	no	—
304	C₄×C₈	—	53	1	no	—
305	C₄×C₈	—	53	1	no	—
306	C₄×C₈	—	53	1	no	—
307	C₄×C₈	—	53	1	no	—
308	C₄×C₈	—	53	1	no	—
309	C₄×C₈	—	53	1	no	—
310	C₄×C₈	—	53	1	no	—
311	C₄×C₈	—	106	1	no	—
312	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
315	C₂⁴	—	106	2	no	—
316	C₂×D₄	—	53	8	no	—
317	C₂×D₄	—	53	2	no	—
318	C₂×D₄	—	106	4	no	—
319	C₂×D₄	—	106	2	no	—
320	C₂×D₄	C₂×C₄×D₅₃	1	2	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	106	2	no	—
326	C₂²×C₄	—	106	2	no	—
327	C₂²×C₄	—	106	2	no	—
328	C₂²×C₄	—	106	2	no	—
329	C₂²×C₄	—	212	4	no	—
330	C₂²×C₄	—	212	4	no	—
331	D₈	—	53	8	no	—
332	D₈	—	53	4	no	—
333	D₈	C₈×D₅₃	1	4	yes	direct product factor
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	—	53	1	no	—
338	C₂×C₈	—	53	1	no	—
339	C₂×C₈	—	53	4	no	—
340	C₂×C₈	—	53	4	no	—
341	C₂×C₈	—	53	1	no	—
342	C₂×C₈	—	53	1	no	—
343	C₂×C₈	—	106	2	no	—
344	C₂×C₈	—	106	2	no	—
345	C₂×C₈	—	106	4	no	—
346	C₂×C₈	—	106	1	no	—
347	C₂×C₈	—	106	2	no	—
348	C₂×C₈	—	212	4	no	—
349	C₂×C₈	—	212	4	no	—
350	C₂×C₈	—	212	4	no	—
351	C₂×C₈	—	212	4	no	—
352	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
353	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
354	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
355	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
356	C₄⋊C₄	—	53	2	no	—
357	C₄⋊C₄	—	106	2	no	—
358	C₄⋊C₄	C₂×C₄×D₅₃	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	106	2	no	—
361	C₂²⋊C₄	—	106	2	no	—
362	C₂²⋊C₄	—	106	2	no	—
363	C₄²	—	53	1	no	—
364	C₄²	—	53	1	no	—
365	C₄²	—	53	1	no	—
366	C₄²	C₂³×D₅₃	1	1	yes	characteristic
367	C₂³	—	2	2	no	—
368	C₂³	—	53	1	no	—
369	C₂³	—	106	8	no	—
370	C₂³	—	106	2	no	—
371	C₂³	—	212	4	no	—
372	C₂³	—	212	4	no	—
373	D₄	—	2	2	no	—
374	D₄	—	53	4	no	—
375	D₄	—	106	8	no	—
376	D₄	—	106	2	no	—
377	D₄	C₂×C₈×D₅₃	1	4	yes	complemented
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	2	no	—
384	C₂×C₄	—	53	2	no	—
385	C₂×C₄	—	53	2	no	—
386	C₂×C₄	—	53	2	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	106	2	no	—
389	C₂×C₄	—	106	2	no	—
390	C₂×C₄	—	212	4	no	—
391	C₂×C₄	—	212	4	no	—
392	C₂×C₄	—	212	4	no	—
393	C₂×C₄	—	212	2	no	—
394	C₂×C₄	—	212	2	no	—
395	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
397	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	2	1	no	—
400	C₈	—	2	1	no	—
401	C₈	—	4	2	no	—
402	C₈	—	53	2	no	—
403	C₈	—	53	2	no	—
404	C₈	—	106	2	no	—
405	C₈	—	106	1	no	—
406	C₈	—	106	1	no	—
407	C₈	—	212	2	no	—
408	C₈	C₂×C₈×D₅₃	1	2	yes	complemented
409	C₈	D₈×D₅₃	1	2	yes	direct product factor
410	C₂²	—	2	4	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	53	2	no	—
414	C₂²	—	53	2	no	—
415	C₂²	—	53	2	no	—
416	C₂²	—	106	4	no	—
417	C₂²	—	212	16	no	—
418	C₂²	—	212	2	no	—
419	C₂²	—	212	2	no	—
420	C₂²	C₄×D₄×D₅₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	4	2	no	—
423	C₄	—	53	2	no	—
424	C₄	—	53	2	no	—
425	C₄	—	106	1	no	—
426	C₄	—	212	2	no	—
427	C₄	C₂²×C₈×D₅₃	1	1	yes	characteristic
428	C₄	#131×D₅₃	1	1	yes	characteristic
429	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
430	C₄	#135×D₅₃	1	1	yes	characteristic
431	C₂	—	4	4	no	—
432	C₂	—	53	4	no	—
433	C₂	—	212	4	no	—
434	C₂	C₈×D₄×D₅₃	1	1	yes	characteristic
435	C₂	C₄×D₈×D₅₃	1	1	yes	characteristic
436	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×D₈×C₅₃	C₂
socle	C₂²×C₅₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₅₃	C₄
cosocle	C₄²×C₅₃	C₂⁴
hypercenter	C₈×D₈	D₅₃
hypocenter	C₅₃	C₂×C₈×D₈
LCS	G ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
2. C₈×D₄×D₅₃	C₂	semidirect
3. C₈×D₄₂₄	C₂	semidirect
4. D₈×#88322	C₂	semidirect
5. #20273509	C₂	semidirect
6. C₈×#11719922	C₂	semidirect
7. #20273507	C₂	semidirect
8. #335×D₅₃	C₂	semidirect
9. D₄⋊C₈×D₅₃	C₂	semidirect
10. C₈²×D₅₃	C₂	semidirect
11. C₈×D₈×C₅₃	C₂	semidirect
20. C₈×D₂₁₂	C₂²	semidirect
21. D₄×#88322	C₂²	semidirect
22. #16810688	C₂²	semidirect
32. #16810376	C₂²	semidirect
33. #16810375	C₂²	semidirect
34. #16810352	C₂²	semidirect
35. D₄⋊#88322	C₂²	semidirect
36. #16810350	C₂²	semidirect
37. C₈×#88322	C₂²	semidirect
38. C₈×#88322	C₂²	semidirect
39. C₈×#88322	C₂²	semidirect
41. C₈×D₄×C₅₃	C₂²	semidirect
42. C₅₃×#335	C₂²	semidirect
43. C₅₃×D₄⋊C₈	C₂²	semidirect
44. C₈²×C₅₃	C₂²	semidirect
49. D₈×D₅₃	C₈	direct (N × H)
102. D₄×D₅₃	C₂×C₈	semidirect
112. D₈×C₅₃	C₂×C₈	semidirect
124. #11719922	C₂×C₈	semidirect
139. D₄₂₄	C₂×C₈	semidirect
146. C₈×D₅₃	C₂×C₈	semidirect
147. C₈×D₅₃	D₈	direct (N × H)
155. D₄×C₅₃	C₂²×C₈	semidirect
169. D₂₁₂	C₂²×C₈	semidirect
183. C₈×C₅₃	C₂²×C₈	semidirect
184. C₈×C₅₃	C₂×D₈	semidirect
189. #88322	C₂²×C₈	semidirect
190. #88322	C₂×D₈	semidirect
220. C₈×D₈	D₅₃	direct (N × H)
229. D₅₃	C₈×D₈	direct (N × H)
244. C₈×D₄	C₂×D₅₃	semidirect
254. #335	C₂×D₅₃	semidirect
258. D₄⋊C₈	C₂×D₅₃	semidirect
262. C₈²	C₂×D₅₃	semidirect
263. C₅₃	C₂×C₈×D₈	semidirect
333. D₈	C₈×D₅₃	direct (N × H)
377. D₄	C₂×C₈×D₅₃	semidirect
408. C₈	C₂×C₈×D₅₃	semidirect
409. C₈	D₈×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
C₄×D₈×D₅₃	2
C₈×D₄×D₅₃	2
C₈×D₄₂₄	2
D₈×#88322	2
#20273509	2
C₈×#11719922	2
#20273507	2
#335×D₅₃	2
D₄⋊C₈×D₅₃	2
C₈²×D₅₃	2
C₈×D₈×C₅₃	2
C₂×C₈×D₈	53

Subgroups — C8×D8×D53 #27353445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×D₈×D₅₃ #27353445