Subgroups — #27277930

Order 13568.

500 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16810675	C₂	1	1	yes	maximal, characteristic
2	#20274692	C₂	1	1	yes	maximal, characteristic
3	C₄×#13133129	C₂	1	1	yes	maximal, characteristic
4	C₂×#16810375	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272550	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272549	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅₃×#334	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
9	#16810675	—	2	2	no	—
10	#16810675	—	2	2	no	—
11	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊#88322	C₂²	1	1	yes	characteristic
13	C₂×#13133129	—	2	1	no	—
14	C₂×#13133129	—	2	1	no	—
15	C₂×#13133129	C₄	1	1	yes	characteristic
16	C₂×#13133129	C₄	1	1	yes	characteristic
17	C₂×C₄×#88322	C₂²	1	1	yes	characteristic
18	C₂×C₈×Dic₅₃	—	2	1	no	—
19	#16810377	—	2	1	no	—
20	#16810377	C₄	1	1	yes	characteristic
21	#16810377	C₄	1	1	yes	characteristic
22	#16810375	—	2	2	no	—
23	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₅₃	C₂²	1	1	yes	characteristic
26	C₅₃×#334	—	2	2	no	—
27	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₅₃	Q₈	1	1	yes	characteristic
30	C₂²×#88322	—	2	1	no	—
31	C₂²×#88322	—	2	1	no	—
32	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
33	C₂²×#88322	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
36	C₂×C₄×Dic₅₃	Q₈	1	1	yes	characteristic
37	C₄²×D₅₃	—	2	1	no	—
38	C₄²×D₅₃	—	2	1	no	—
39	C₄²×D₅₃	—	2	1	no	—
40	C₄²×D₅₃	—	2	1	no	—
41	C₄⋊#88322	—	2	1	no	—
42	C₄⋊#88322	—	2	1	no	—
43	C₄⋊#88322	—	2	1	no	—
44	C₄⋊#88322	D₄	1	2	yes	—
45	#13133129	—	2	4	no	—
46	#13133129	—	2	2	no	—
47	#13133129	—	4	2	no	—
48	#13133129	C₈	1	4	yes	complemented
49	C₄×#88322	—	2	1	no	—
50	C₄×#88322	—	2	1	no	—
51	C₈×Dic₅₃	—	2	4	no	—
52	C₂²×C₈×C₅₃	—	2	1	no	—
53	C₂²×C₈×C₅₃	—	2	1	no	—
54	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₈×C₅₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₅₃	—	2	1	no	—
58	C₄⋊C₈×C₅₃	—	2	1	no	—
59	C₄⋊C₈×C₅₃	—	2	1	no	—
60	C₄⋊C₈×C₅₃	D₄	1	2	yes	—
61	C₄×C₈×C₅₃	—	2	1	no	—
62	C₄×C₈×C₅₃	—	2	1	no	—
63	C₂³×D₅₃	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₅₃	C₂×Q₈	1	1	yes	characteristic
67	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
69	C₂²×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₄×D₅₃	—	2	1	no	—
71	C₂×C₄×D₅₃	—	2	1	no	—
72	C₂×C₄×D₅₃	—	2	1	no	—
73	C₂×C₄×D₅₃	—	2	1	no	—
74	C₂×C₄×D₅₃	—	2	1	no	—
75	C₂×C₄×D₅₃	—	2	1	no	—
76	C₂×C₄×D₅₃	—	2	1	no	—
77	C₂×C₄×D₅₃	—	2	1	no	—
78	C₂×C₄×D₅₃	—	2	1	no	—
79	C₂×C₄×D₅₃	—	2	1	no	—
80	C₂×C₄×D₅₃	—	2	1	no	—
81	C₂×C₄×D₅₃	—	2	1	no	—
82	C₂×C₄×D₅₃	—	2	2	no	—
83	C₂×C₄×D₅₃	—	4	1	no	—
84	C₂×C₄×D₅₃	C₂×C₈	1	2	yes	—
85	C₂×C₄×D₅₃	M₁₆	1	2	yes	—
86	C₂×C₈×C₅₃	—	2	1	no	—
87	C₂×C₈×C₅₃	—	2	1	no	—
88	C₂×C₈×C₅₃	—	2	1	no	—
89	C₂×C₈×C₅₃	—	2	2	no	—
90	C₂×C₈×C₅₃	—	2	1	no	—
91	C₂×C₈×C₅₃	—	2	1	no	—
92	C₂×C₈×C₅₃	—	4	1	no	—
93	C₂×C₈×C₅₃	—	4	1	no	—
94	C₂×C₈×C₅₃	—	4	1	no	—
95	C₂×C₈×C₅₃	—	4	1	no	—
96	C₂×C₈×C₅₃	—	4	1	no	—
97	C₂×C₈×C₅₃	C₂×C₈	1	2	yes	—
98	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
99	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
100	C₄²×C₅₃	#41	1	1	yes	characteristic
101	C₄²×C₅₃	#41	1	1	yes	characteristic
102	C₄×Dic₅₃	—	2	1	no	—
103	C₄×Dic₅₃	—	2	1	no	—
104	C₄×Dic₅₃	—	2	1	no	—
105	C₄×Dic₅₃	—	2	1	no	—
106	C₄×Dic₅₃	—	2	1	no	—
107	C₄×Dic₅₃	—	2	1	no	—
108	C₂×#88322	—	2	1	no	—
109	C₂×#88322	—	2	1	no	—
110	C₂×#88322	—	2	1	no	—
111	C₂×#88322	—	2	2	no	—
112	C₂×#88322	—	2	1	no	—
113	C₂×#88322	—	2	1	no	—
114	C₂×#88322	—	4	1	no	—
115	C₂×#88322	—	4	1	no	—
116	C₂×#88322	—	4	1	no	—
117	C₂×#88322	—	4	1	no	—
118	C₂×#88322	—	4	1	no	—
119	C₂×#88322	C₂×C₈	1	2	yes	—
120	C₂³×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂²×D₅₃	—	2	1	no	—
122	C₂²×D₅₃	—	2	1	no	—
123	C₂²×D₅₃	—	2	1	no	—
124	C₂²×D₅₃	—	2	1	no	—
125	C₂²×D₅₃	—	2	1	no	—
126	C₂²×D₅₃	—	2	1	no	—
127	C₂²×D₅₃	C₄⋊C₈	1	2	yes	—
128	C₂×C₄×C₅₃	—	2	1	no	—
129	C₂×C₄×C₅₃	—	2	1	no	—
130	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
131	C₂×C₄×C₅₃	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₅₃	#120	1	1	yes	characteristic
133	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₅₃	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₅₃	#123	1	1	yes	characteristic
136	C₂×C₄×C₅₃	C₂²×C₈	1	1	yes	characteristic
137	C₂×C₄×C₅₃	C₂×M₁₆	1	1	yes	characteristic
138	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
139	C₂×C₄×C₅₃	#131	1	1	yes	characteristic
140	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
141	C₂×C₄×C₅₃	#135	1	1	yes	characteristic
142	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
143	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
144	C₂×Dic₅₃	—	2	1	no	—
145	C₂×Dic₅₃	—	2	1	no	—
146	C₂×Dic₅₃	—	2	1	no	—
147	C₂×Dic₅₃	—	2	1	no	—
148	C₂×Dic₅₃	—	2	1	no	—
149	C₂×Dic₅₃	—	2	1	no	—
150	C₂×Dic₅₃	—	2	1	no	—
151	C₂×Dic₅₃	C₄⋊C₈	1	2	yes	—
152	C₂×Dic₅₃	#108	1	2	yes	—
153	C₄×D₅₃	—	2	2	no	—
154	C₄×D₅₃	—	2	2	no	—
155	C₄×D₅₃	—	2	2	no	—
156	C₄×D₅₃	—	2	2	no	—
157	C₄×D₅₃	—	4	2	no	—
158	C₄×D₅₃	—	4	2	no	—
159	C₄×D₅₃	—	4	1	no	—
160	C₄×D₅₃	—	4	1	no	—
161	C₄×D₅₃	—	4	1	no	—
162	C₄×D₅₃	—	4	1	no	—
163	C₈×C₅₃	—	2	2	no	—
164	C₈×C₅₃	—	4	1	no	—
165	C₈×C₅₃	—	4	2	no	—
166	C₈×C₅₃	—	8	1	no	—
167	#88322	—	2	2	no	—
168	#88322	—	4	1	no	—
169	#88322	—	4	2	no	—
170	#88322	—	8	1	no	—
171	#8831	—	53	1	no	maximal, Sylow
172	C₂²×C₅₃	#385	1	1	yes	characteristic
173	C₂²×C₅₃	C₂×C₄⋊C₈	1	1	yes	characteristic
174	C₂²×C₅₃	#424	1	1	yes	characteristic
175	C₂²×C₅₃	#427	1	1	yes	characteristic
176	C₂²×C₅₃	#428	1	1	yes	characteristic
177	C₂²×C₅₃	C₂×#108	1	1	yes	characteristic
178	C₂²×C₅₃	#430	1	1	yes	characteristic
179	C₂×D₅₃	—	2	2	no	—
180	C₂×D₅₃	—	2	2	no	—
181	C₂×D₅₃	—	2	2	no	—
182	C₂×D₅₃	—	4	1	no	—
183	C₂×D₅₃	—	4	1	no	—
184	C₂×D₅₃	—	4	1	no	—
185	C₂×D₅₃	—	4	1	no	—
186	C₄×C₅₃	—	2	1	no	—
187	C₄×C₅₃	—	2	1	no	—
188	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
189	C₄×C₅₃	C₈×D₄	1	1	yes	characteristic
190	C₄×C₅₃	#435	1	1	yes	characteristic
191	C₄×C₅₃	#435	1	1	yes	characteristic
192	C₄×C₅₃	#449	1	1	yes	characteristic
193	C₄×C₅₃	#452	1	1	yes	characteristic
194	C₄×C₅₃	#482	1	1	yes	characteristic
195	C₄×C₅₃	#485	1	1	yes	characteristic
196	Dic₅₃	—	2	2	no	—
197	Dic₅₃	—	2	2	no	—
198	Dic₅₃	—	4	1	no	—
199	C₂×#431	—	53	1	no	—
200	#1797	—	53	1	no	—
201	C₄×C₂²⋊C₈	—	53	1	no	—
202	C₂×#335	—	53	1	no	—
203	C₂×#334	D₅₃	1	1	yes	characteristic, complemented
204	#1277	—	53	1	no	—
205	#1277	—	53	1	no	—
206	C₂×C₅₃	#1564	1	1	yes	characteristic
207	C₂×C₅₃	#1565	1	1	yes	characteristic
208	C₂×C₅₃	#1572	1	1	yes	characteristic
209	C₂×C₅₃	#1574	1	1	yes	characteristic
210	C₂×C₅₃	#1850	1	1	yes	characteristic
211	C₂×C₅₃	#1854	1	1	yes	characteristic
212	C₂×C₅₃	#1855	1	1	yes	characteristic
213	D₅₃	—	4	2	no	—
214	C₂²×C₄²	—	53	1	no	—
215	#431	—	106	2	no	—
216	#431	—	106	2	no	—
217	C₂×C₄⋊C₈	—	53	1	no	—
218	C₂×C₄⋊C₈	—	53	1	no	—
219	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	—	53	1	no	—
222	C₂×C₂²⋊C₈	—	53	1	no	—
223	C₂×C₂²⋊C₈	—	106	1	no	—
224	C₂×C₂²⋊C₈	—	106	1	no	—
225	C₂×C₄×C₈	—	53	1	no	—
226	C₂×C₄×C₈	—	106	1	no	—
227	C₂×C₄×C₈	C₂×D₅₃	1	1	yes	characteristic
228	#336	—	53	1	no	—
229	#336	—	53	1	no	—
230	#336	—	106	1	no	—
231	#335	—	106	2	no	—
232	#334	—	2	2	no	—
233	C₅₃	#8831	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₄	—	53	1	no	—
235	C₂³×C₄	—	53	1	no	—
236	C₂³×C₄	—	53	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	53	1	no	—
240	C₂²×C₈	—	53	1	no	—
241	C₂²×C₈	—	106	1	no	—
242	C₂²×C₈	—	106	1	no	—
243	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
244	C₂²×C₈	C₄×D₅₃	1	1	yes	characteristic
245	C₂×C₄²	—	53	1	no	—
246	C₂×C₄²	—	53	1	no	—
247	C₂×C₄²	—	53	1	no	—
248	C₂×C₄²	—	106	1	no	—
249	C₂×C₄²	—	106	1	no	—
250	C₂×C₄²	—	106	1	no	—
251	C₂×C₄²	—	106	1	no	—
252	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	2	1	no	—
255	C₄⋊C₈	—	2	1	no	—
256	C₄⋊C₈	—	53	2	no	—
257	C₄⋊C₈	—	106	1	no	—
258	C₄⋊C₈	—	106	1	no	—
259	C₄⋊C₈	—	106	1	no	—
260	C₄⋊C₈	C₂²⋊D₅₃	1	2	yes	—
261	C₂²⋊C₈	—	53	4	no	—
262	C₂²⋊C₈	—	106	2	no	—
263	C₂²⋊C₈	—	106	4	no	—
264	C₂²⋊C₈	—	212	2	no	—
265	C₄×C₈	—	2	1	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	106	4	no	—
268	C₄×C₈	—	106	1	no	—
269	C₄×C₈	—	106	1	no	—
270	C₂⁴	—	53	1	no	—
271	C₂²×C₄	—	53	1	no	—
272	C₂²×C₄	—	53	1	no	—
273	C₂²×C₄	—	53	2	no	—
274	C₂²×C₄	—	53	2	no	—
275	C₂²×C₄	—	53	1	no	—
276	C₂²×C₄	—	106	2	no	—
277	C₂²×C₄	—	106	1	no	—
278	C₂²×C₄	—	106	1	no	—
279	C₂²×C₄	—	106	1	no	—
280	C₂²×C₄	—	106	1	no	—
281	C₂²×C₄	—	106	1	no	—
282	C₂²×C₄	—	106	1	no	—
283	C₂²×C₄	—	106	1	no	—
284	C₂²×C₄	—	106	1	no	—
285	C₂²×C₄	—	106	1	no	—
286	C₂²×C₄	—	106	1	no	—
287	C₂²×C₄	—	106	1	no	—
288	C₂²×C₄	—	106	1	no	—
289	C₂²×C₄	—	212	1	no	—
290	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
292	C₂²×C₄	Q₈×D₅₃	1	1	yes	characteristic
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	53	2	no	—
305	C₂×C₈	—	106	1	no	—
306	C₂×C₈	—	106	1	no	—
307	C₂×C₈	—	106	1	no	—
308	C₂×C₈	—	106	2	no	—
309	C₂×C₈	—	106	1	no	—
310	C₂×C₈	—	106	1	no	—
311	C₂×C₈	—	212	1	no	—
312	C₂×C₈	—	212	1	no	—
313	C₂×C₈	—	212	1	no	—
314	C₂×C₈	—	212	1	no	—
315	C₂×C₈	—	212	1	no	—
316	C₂×C₈	C₈×D₅₃	1	2	yes	—
317	C₄²	—	106	1	no	—
318	C₄²	—	106	1	no	—
319	C₄²	—	106	1	no	—
320	C₄²	—	106	1	no	—
321	C₄²	—	106	1	no	—
322	C₄²	—	106	1	no	—
323	C₄²	#11719945	1	1	yes	characteristic
324	C₄²	D₄×D₅₃	1	1	yes	characteristic
325	C₄²	#11719949	1	1	yes	characteristic
326	C₄²	C₂×C₂²⋊D₅₃	1	1	yes	characteristic
327	C₂³	—	53	2	no	—
328	C₂³	—	106	1	no	—
329	C₂³	—	106	1	no	—
330	C₂³	—	106	1	no	—
331	C₂³	—	106	1	no	—
332	C₂³	—	106	1	no	—
333	C₂³	—	106	1	no	—
334	C₂³	C₄⋊C₄×D₅₃	1	1	yes	characteristic
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	53	2	no	—
338	C₂×C₄	—	53	2	no	—
339	C₂×C₄	—	106	1	no	—
340	C₂×C₄	—	106	1	no	—
341	C₂×C₄	—	106	1	no	—
342	C₂×C₄	—	106	1	no	—
343	C₂×C₄	—	106	2	no	—
344	C₂×C₄	—	106	2	no	—
345	C₂×C₄	—	106	2	no	—
346	C₂×C₄	—	106	2	no	—
347	C₂×C₄	—	106	1	no	—
348	C₂×C₄	—	106	1	no	—
349	C₂×C₄	—	106	1	no	—
350	C₂×C₄	—	212	2	no	—
351	C₂×C₄	—	212	2	no	—
352	C₂×C₄	—	212	1	no	—
353	C₂×C₄	—	212	1	no	—
354	C₂×C₄	—	212	1	no	—
355	C₂×C₄	—	212	1	no	—
356	C₂×C₄	C₄×C₂²⋊D₅₃	1	1	yes	characteristic
357	C₂×C₄	#13133179	1	1	yes	characteristic
358	C₂×C₄	#13133185	1	1	yes	characteristic
359	C₂×C₄	#13133193	1	1	yes	characteristic
360	C₂×C₄	#13133195	1	1	yes	characteristic
361	C₂×C₄	#13133202	1	1	yes	characteristic
362	C₂×C₄	C₂×C₈×D₅₃	1	1	yes	characteristic
363	C₂×C₄	M₁₆×D₅₃	1	1	yes	characteristic
364	C₂×C₄	#13133223	1	1	yes	characteristic
365	C₂×C₄	#13133225	1	1	yes	characteristic
366	C₂×C₄	#13133238	1	1	yes	characteristic
367	C₂×C₄	#13133238	1	1	yes	characteristic
368	C₂×C₄	#13133244	1	1	yes	characteristic
369	C₂×C₄	#13133246	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	8	1	no	—
374	C₈	—	106	2	no	—
375	C₈	—	424	1	no	—
376	C₈	—	212	2	no	—
377	C₈	—	212	1	no	—
378	C₂²	—	106	2	no	—
379	C₂²	—	106	2	no	—
380	C₂²	—	106	2	no	—
381	C₂²	—	212	1	no	—
382	C₂²	—	212	1	no	—
383	C₂²	—	212	1	no	—
384	C₂²	—	212	1	no	—
385	C₂²	#16810494	1	1	yes	characteristic
386	C₂²	C₄⋊C₈×D₅₃	1	1	yes	characteristic
387	C₂²	#16810648	1	1	yes	characteristic
388	C₂²	#16810658	1	1	yes	characteristic
389	C₂²	#16810662	1	1	yes	characteristic
390	C₂²	#108×D₅₃	1	1	yes	characteristic
391	C₂²	#16810670	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	106	2	no	—
395	C₄	—	106	2	no	—
396	C₄	—	212	1	no	—
397	C₄	C₈×C₂²⋊D₅₃	1	1	yes	characteristic
398	C₄	#16810688	1	1	yes	characteristic
399	C₄	#16810692	1	1	yes	characteristic
400	C₄	#16810693	1	1	yes	characteristic
401	C₄	#16810767	1	1	yes	characteristic
402	C₄	#16810782	1	1	yes	characteristic
403	C₄	#16810949	1	1	yes	characteristic
404	C₄	#16810967	1	1	yes	characteristic
405	C₂	—	212	2	no	—
406	C₂	#20273460	1	1	yes	characteristic
407	C₂	#20273464	1	1	yes	characteristic
408	C₂	#20273492	1	1	yes	characteristic
409	C₂	#20273502	1	1	yes	characteristic
410	C₂	#20274891	1	1	yes	characteristic
411	C₂	#20274913	1	1	yes	characteristic
412	C₂	#20274918	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₂×C₅₃×#334	C₂
socle	C₂³×C₅₃	C₂×C₄⋊C₄
prime radical	C₂³×D₅₃	C₄⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	C₂×#334	D₅₃
hypocenter	C₅₃	#8831
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
4. C₂×#16810375	C₂	semidirect
5. #20272550	C₂	semidirect
6. #20272549	C₂	semidirect
7. C₂×C₅₃×#334	C₂	semidirect
48. #13133129	C₈	semidirect
203. C₂×#334	D₅₃	semidirect
233. C₅₃	#8831	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16810675	2
#20274692	2
C₄×#13133129	2
C₂×#16810375	2
#20272550	2
#20272549	2
C₂×C₅₃×#334	2
#8831	53