Subgroups — #20286208

Order 6784.

546 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	C₂×#13133243	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×SD₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811283	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811009	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810871	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810858	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810840	C₂	1	1	yes	maximal, characteristic, complemented
9	#16810822	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810770	C₂	1	1	yes	maximal, characteristic, complemented
11	#16810760	C₂	1	1	yes	maximal, characteristic, complemented
12	#16810758	C₂	1	1	yes	maximal, characteristic, complemented
13	#16810720	C₂	1	1	yes	maximal, characteristic, complemented
14	#16810697	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#450	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719945	C₂²	1	1	yes	characteristic, complemented
17	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
18	C₂²×C₂²⋊D₅₃	—	2	1	no	—
19	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
20	#13133243	—	2	4	no	—
21	C₂×#11719913	C₂²	1	1	yes	characteristic, complemented
22	C₂×#11719923	C₂²	1	1	yes	characteristic
23	C₂×#11719923	C₂²	1	1	yes	characteristic, complemented
24	C₂×#11719924	C₂²	1	1	yes	characteristic, complemented
25	SD₁₆×D₅₃	—	2	4	no	—
26	C₂×D₄₂₄	C₂²	1	1	yes	characteristic, complemented
27	C₂×#11719922	C₂²	1	1	yes	characteristic
28	C₂×#11719922	C₂²	1	1	yes	characteristic, complemented
29	C₂×#11719917	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
31	#13133213	C₂²	1	1	yes	characteristic
32	#13133206	C₂²	1	1	yes	characteristic, complemented
33	#13133203	—	2	1	no	—
34	#13133195	—	2	1	no	—
35	#13133192	C₂²	1	1	yes	characteristic, complemented
36	#13133191	C₂²	1	1	yes	characteristic
37	#13133190	—	2	1	no	—
38	#13133189	—	2	1	no	—
39	#13133188	C₂²	1	1	yes	characteristic
40	#13133186	—	2	1	no	—
41	#13133185	—	2	1	no	—
42	#13133182	C₂²	1	1	yes	characteristic, complemented
43	D₄×Dic₅₃	C₂²	1	1	yes	characteristic
44	#13133179	—	2	1	no	—
45	C₄×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
46	#13133150	C₂²	1	1	yes	characteristic, complemented
47	#13133146	C₂²	1	1	yes	characteristic, complemented
48	#13133142	C₂²	1	1	yes	characteristic, complemented
49	#13133141	C₂²	1	1	yes	characteristic, complemented
50	#13133139	C₂²	1	1	yes	characteristic, complemented
51	#13133137	C₂²	1	1	yes	characteristic, complemented
52	#13133129	C₂²	1	1	yes	characteristic, complemented
53	#13133127	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₅₃	C₂²	1	1	yes	characteristic
55	C₂×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic
56	C₂×SD₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₂²⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	#102×C₅₃	C₂²	1	1	yes	characteristic
59	#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	C₂²⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₅₃	—	2	1	no	—
62	C₂³×D₅₃	—	2	1	no	—
63	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₅₃	—	2	2	no	—
65	C₂×D₄×C₅₃	—	2	1	no	—
66	C₂×D₄×C₅₃	—	4	1	no	—
67	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₅₃	—	2	1	no	—
71	C₂×C₂²⋊D₅₃	—	2	1	no	—
72	C₂×C₂²⋊D₅₃	—	2	1	no	—
73	C₂×C₂²⋊D₅₃	—	2	1	no	—
74	C₂×C₂²⋊D₅₃	—	2	1	no	—
75	C₂×C₂²⋊D₅₃	—	2	1	no	—
76	C₂×C₂²⋊D₅₃	—	4	4	no	—
77	C₂×C₂²⋊D₅₃	D₄	1	1	yes	characteristic
78	C₂²×Dic₅₃	—	2	1	no	—
79	Q₈×D₅₃	—	2	2	no	—
80	Q₈×D₅₃	—	4	1	no	—
81	D₄×D₅₃	—	2	2	no	—
82	D₄×D₅₃	—	4	1	no	—
83	#11719945	—	2	2	no	—
84	#11719945	—	4	1	no	—
85	C₂×D₂₁₂	—	2	1	no	—
86	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
87	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₅₃	—	2	1	no	—
89	C₂×C₄×D₅₃	—	2	1	no	—
90	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
91	C₂×Dic₁₀₆	—	2	1	no	—
92	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
93	SD₁₆×C₅₃	—	2	2	no	—
94	SD₁₆×C₅₃	—	4	1	no	—
95	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₅₃	—	2	1	no	—
98	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂²⋊C₄×C₅₃	—	2	1	no	—
100	C₂²⋊Dic₅₃	—	2	1	no	—
101	C₂²⋊Dic₅₃	—	2	1	no	—
102	C₂²⋊Dic₅₃	D₄	1	1	yes	characteristic
103	#11719924	—	2	2	no	—
104	#11719923	—	2	2	no	—
105	#11719923	D₄	1	4	yes	complemented
106	#11719922	—	2	2	no	—
107	#11719922	—	2	2	no	—
108	#11719921	—	2	1	no	—
109	#11719921	—	2	1	no	—
110	#11719921	—	2	1	no	—
111	#11719921	—	2	1	no	—
112	#11719921	D₄	1	1	yes	characteristic
113	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
114	#11719919	—	2	1	no	—
115	#11719919	D₄	1	1	yes	characteristic
116	C₄×Dic₅₃	—	2	1	no	—
117	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
118	#11719917	—	2	2	no	—
119	C₂×#88322	C₂³	1	1	yes	characteristic
120	C₂×#88322	C₂³	1	1	yes	characteristic
121	D₄₂₄	—	4	1	no	—
122	#11719913	—	2	2	no	—
123	C₈×D₅₃	—	2	2	no	—
124	C₂³×C₅₃	—	2	1	no	—
125	C₂³×C₅₃	—	2	1	no	—
126	C₂³×C₅₃	—	4	2	no	—
127	C₂³×C₅₃	—	4	2	no	—
128	C₂³×C₅₃	—	8	1	no	—
129	C₂³×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₅₃	—	2	1	no	—
131	C₂²×D₅₃	—	2	1	no	—
132	C₂²×D₅₃	—	4	2	no	—
133	C₂²×D₅₃	—	4	2	no	—
134	C₂²×D₅₃	—	8	1	no	—
135	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₅₃	—	2	1	no	—
137	Q₈×C₅₃	—	2	1	no	—
138	D₄×C₅₃	—	2	1	no	—
139	D₄×C₅₃	—	2	1	no	—
140	D₄×C₅₃	—	2	1	no	—
141	D₄×C₅₃	—	4	2	no	—
142	D₄×C₅₃	C₂×D₄	1	2	yes	—
143	C₂×C₄×C₅₃	—	2	1	no	—
144	C₂×C₄×C₅₃	—	2	1	no	—
145	C₂×C₄×C₅₃	—	2	1	no	—
146	C₂×C₄×C₅₃	—	2	1	no	—
147	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₅₃	—	2	2	no	—
150	C₂²⋊D₅₃	—	4	2	no	—
151	C₂²⋊D₅₃	—	4	2	no	—
152	C₂²⋊D₅₃	—	4	2	no	—
153	C₂²⋊D₅₃	—	4	2	no	—
154	C₂²⋊D₅₃	—	4	2	no	—
155	C₂²⋊D₅₃	—	8	1	no	—
156	C₂×Dic₅₃	—	2	1	no	—
157	C₂×Dic₅₃	—	2	1	no	—
158	C₂×Dic₅₃	—	4	2	no	—
159	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
160	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
162	D₂₁₂	—	2	1	no	—
163	D₂₁₂	—	2	1	no	—
164	D₂₁₂	—	2	1	no	—
165	D₂₁₂	—	2	1	no	—
166	D₂₁₂	—	4	2	no	—
167	C₄×D₅₃	—	2	1	no	—
168	C₄×D₅₃	—	2	1	no	—
169	C₄×D₅₃	—	4	2	no	—
170	C₄×D₅₃	—	4	2	no	—
171	Dic₁₀₆	—	2	1	no	—
172	Dic₁₀₆	—	4	2	no	—
173	Dic₁₀₆	C₂×D₄	1	2	yes	complemented
174	C₈×C₅₃	—	2	1	no	—
175	C₈×C₅₃	—	2	1	no	—
176	#88322	—	2	1	no	—
177	#88322	C₂×D₄	1	2	yes	complemented
178	C₂²×C₅₃	—	2	1	no	—
179	C₂²×C₅₃	—	2	2	no	—
180	C₂²×C₅₃	—	2	1	no	—
181	C₂²×C₅₃	—	2	1	no	—
182	C₂²×C₅₃	—	4	1	no	—
183	C₂²×C₅₃	—	4	1	no	—
184	C₂²×C₅₃	—	4	1	no	—
185	C₂²×C₅₃	—	4	1	no	—
186	C₂²×C₅₃	—	4	1	no	—
187	C₂²×C₅₃	—	8	4	no	—
188	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×D₅₃	—	2	1	no	—
190	C₂×D₅₃	—	2	1	no	—
191	C₂×D₅₃	—	4	1	no	—
192	C₂×D₅₃	—	4	1	no	—
193	C₂×D₅₃	—	4	1	no	—
194	C₂×D₅₃	—	4	1	no	—
195	C₂×D₅₃	—	4	1	no	—
196	C₂×D₅₃	—	4	1	no	—
197	C₂×D₅₃	—	8	4	no	—
198	C₂×D₅₃	AGL(1,ℤ/8)	1	2	yes	complemented
199	C₄×C₅₃	—	2	1	no	—
200	C₄×C₅₃	—	4	1	no	—
201	C₄×C₅₃	—	4	1	no	—
202	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
203	C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
204	Dic₅₃	—	2	2	no	—
205	Dic₅₃	—	2	1	no	—
206	Dic₅₃	—	2	1	no	—
207	Dic₅₃	—	2	1	no	—
208	Dic₅₃	—	4	1	no	—
209	#3265	—	53	1	no	maximal, Sylow
210	C₂×C₅₃	—	4	2	no	—
211	C₂×C₅₃	—	4	1	no	—
212	C₂×C₅₃	—	8	1	no	—
213	C₂×C₅₃	D₄²	1	1	yes	characteristic
214	C₂×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
215	C₂×C₅₃	#577	1	1	yes	characteristic
216	D₅₃	—	2	2	no	—
217	D₅₃	—	8	1	no	—
218	D₅₃	—	8	1	no	—
219	C₂×AGL(1,ℤ/8)	—	53	1	no	—
220	C₂²×SD₁₆	—	53	1	no	—
221	#548	—	53	1	no	—
222	D₄²	—	53	1	no	—
223	#496	—	53	1	no	—
224	#468	—	53	1	no	—
225	#466	—	53	1	no	—
226	#463	—	53	1	no	—
227	#460	—	53	1	no	—
228	#450	D₅₃	1	1	yes	characteristic, complemented
229	#449	—	53	1	no	—
230	#448	—	53	1	no	—
231	#447	—	53	1	no	—
232	#440	—	53	1	no	—
233	#435	—	53	1	no	—
234	C₅₃	#3265	1	1	yes	characteristic, complemented, Sylow
235	C₂×#41	—	53	1	no	—
236	C₂²×Q₈	—	53	1	no	—
237	C₂²×D₄	—	53	1	no	—
238	C₂²×D₄	—	106	1	no	—
239	C₂²×D₄	C₂×D₅₃	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	106	4	no	—
241	C₂×SD₁₆	—	53	1	no	—
242	C₂×SD₁₆	—	53	1	no	—
243	C₂×SD₁₆	—	53	1	no	—
244	C₂×SD₁₆	—	53	1	no	—
245	C₂×SD₁₆	—	106	4	no	—
246	C₂×SD₁₆	C₂×D₅₃	1	1	yes	characteristic
247	C₂×SD₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
248	C₂×D₈	—	53	1	no	—
249	C₂×D₈	—	53	1	no	—
250	C₂×D₈	—	53	1	no	—
251	C₂×M₁₆	—	53	1	no	—
252	C₂²×C₈	—	53	1	no	—
253	#127	—	53	1	no	—
254	#124	—	53	1	no	—
255	#124	—	106	1	no	—
256	C₂²⋊Q₈	—	106	1	no	—
257	C₂²⋊Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
258	#121	—	53	1	no	—
259	#121	—	53	1	no	—
260	#121	—	53	1	no	—
261	#121	—	106	1	no	—
262	#121	—	106	1	no	—
263	#120	—	106	1	no	—
264	#120	—	106	1	no	—
265	C₄×Q₈	—	53	1	no	—
266	C₄×D₄	—	53	1	no	—
267	C₄×D₄	—	53	1	no	—
268	C₄×D₄	—	106	1	no	—
269	#107	—	53	1	no	—
270	C₄⋊C₈	—	53	1	no	—
271	#103	—	53	1	no	—
272	#103	—	53	1	no	—
273	#102	—	53	1	no	—
274	#102	—	53	1	no	—
275	#102	C₂×D₅₃	1	1	yes	characteristic
276	#102	C₂×D₅₃	1	1	yes	characteristic, complemented
277	C₂²⋊C₈	—	53	1	no	—
278	C₂²⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
279	#97	—	53	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	106	1	no	—
282	#41	—	106	2	no	—
283	#41	—	212	1	no	—
284	C₂×Q₈	—	53	1	no	—
285	C₂×Q₈	—	106	1	no	—
286	C₂×Q₈	—	106	2	no	—
287	C₂×Q₈	—	212	1	no	—
288	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	53	1	no	—
293	C₂×D₄	—	53	1	no	—
294	C₂×D₄	—	53	1	no	—
295	C₂×D₄	—	106	1	no	—
296	C₂×D₄	—	106	1	no	—
297	C₂×D₄	—	106	1	no	—
298	C₂×D₄	—	106	1	no	—
299	C₂×D₄	—	106	2	no	—
300	C₂×D₄	—	106	1	no	—
301	C₂×D₄	—	106	1	no	—
302	C₂×D₄	—	106	1	no	—
303	C₂×D₄	—	212	1	no	—
304	C₂×D₄	—	212	4	no	—
305	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
307	C₂²×C₄	—	53	1	no	—
308	C₂²×C₄	—	106	1	no	—
309	C₂²×C₄	—	106	1	no	—
310	C₂²×C₄	—	106	1	no	—
311	C₂²×C₄	C₂²×D₅₃	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	4	1	no	—
314	SD₁₆	—	53	4	no	—
315	SD₁₆	—	106	2	no	—
316	SD₁₆	—	106	2	no	—
317	SD₁₆	—	106	2	no	—
318	D₈	—	106	2	no	—
319	D₈	—	106	2	no	—
320	D₈	—	212	1	no	—
321	M₁₆	—	106	2	no	—
322	C₂×C₈	—	53	1	no	—
323	C₂×C₈	—	53	1	no	—
324	C₂×C₈	—	106	2	no	—
325	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	53	1	no	—
329	C₄⋊C₄	—	53	1	no	—
330	C₄⋊C₄	—	106	1	no	—
331	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	53	1	no	—
334	C₂²⋊C₄	—	53	1	no	—
335	C₂²⋊C₄	—	106	1	no	—
336	C₂²⋊C₄	—	106	1	no	—
337	C₂²⋊C₄	—	106	1	no	—
338	C₂²⋊C₄	—	106	1	no	—
339	C₂²⋊C₄	—	106	1	no	—
340	C₂²⋊C₄	—	106	1	no	—
341	C₄²	—	53	1	no	—
342	C₄²	—	106	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	53	1	no	—
349	C₂³	—	106	1	no	—
350	C₂³	—	106	1	no	—
351	C₂³	—	424	1	no	—
352	C₂³	—	212	2	no	—
353	C₂³	—	212	2	no	—
354	C₂³	D₄×D₅₃	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	53	2	no	—
358	Q₈	—	106	1	no	—
359	Q₈	—	212	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	106	2	no	—
365	D₄	—	106	1	no	—
366	D₄	—	106	1	no	—
367	D₄	—	106	1	no	—
368	D₄	—	106	1	no	—
369	D₄	—	424	1	no	—
370	D₄	—	212	2	no	—
371	D₄	—	212	2	no	—
372	D₄	—	212	2	no	—
373	D₄	—	212	2	no	—
374	D₄	—	212	2	no	—
375	D₄	—	212	2	no	—
376	D₄	D₄×D₅₃	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	53	1	no	—
382	C₂×C₄	—	53	1	no	—
383	C₂×C₄	—	53	1	no	—
384	C₂×C₄	—	106	1	no	—
385	C₂×C₄	—	106	1	no	—
386	C₂×C₄	—	106	1	no	—
387	C₂×C₄	—	106	1	no	—
388	C₂×C₄	—	212	2	no	—
389	C₂×C₄	—	212	2	no	—
390	C₂×C₄	—	212	2	no	—
391	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	53	2	no	—
396	C₈	—	106	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	8	4	no	—
407	C₂²	—	53	2	no	—
408	C₂²	—	106	1	no	—
409	C₂²	—	106	1	no	—
410	C₂²	—	424	4	no	—
411	C₂²	—	212	1	no	—
412	C₂²	—	212	1	no	—
413	C₂²	—	212	1	no	—
414	C₂²	—	212	1	no	—
415	C₂²	—	212	1	no	—
416	C₂²	—	212	1	no	—
417	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	106	1	no	—
422	C₄	—	106	1	no	—
423	C₄	—	106	1	no	—
424	C₄	—	106	2	no	—
425	C₄	—	212	1	no	—
426	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
427	C₄	#13133262	1	1	yes	characteristic
428	C₂	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	106	2	no	—
432	C₂	—	424	1	no	—
433	C₂	—	424	1	no	—
434	C₂	#16811255	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
436	C₂	#16811429	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#450	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#450	D₅₃
hypocenter	C₅₃	#3265
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #450

Complements

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

N	H ≅ G/N	type
1. C₂×#13133243	C₂	semidirect
2. C₂×SD₁₆×D₅₃	C₂	semidirect
3. #16811283	C₂	semidirect
4. D₄×C₂²⋊D₅₃	C₂	semidirect
5. #16811009	C₂	semidirect
6. #16810871	C₂	semidirect
7. #16810858	C₂	semidirect
8. #16810840	C₂	semidirect
9. #16810822	C₂	semidirect
10. #16810770	C₂	semidirect
11. #16810760	C₂	semidirect
12. #16810758	C₂	semidirect
13. #16810720	C₂	semidirect
14. #16810697	C₂	semidirect
15. C₅₃×#450	C₂	semidirect
16. C₂×#11719945	C₂²	semidirect
17. C₂×Q₈×D₅₃	C₂²	semidirect
21. C₂×#11719913	C₂²	semidirect
23. C₂×#11719923	C₂²	semidirect
24. C₂×#11719924	C₂²	semidirect
26. C₂×D₄₂₄	C₂²	semidirect
28. C₂×#11719922	C₂²	semidirect
29. C₂×#11719917	C₂²	semidirect
30. C₂×C₈×D₅₃	C₂²	semidirect
32. #13133206	C₂²	semidirect
35. #13133192	C₂²	semidirect
42. #13133182	C₂²	semidirect
46. #13133150	C₂²	semidirect
47. #13133146	C₂²	semidirect
48. #13133142	C₂²	semidirect
49. #13133141	C₂²	semidirect
50. #13133139	C₂²	semidirect
51. #13133137	C₂²	semidirect
52. #13133129	C₂²	semidirect
53. #13133127	C₂²	semidirect
56. C₂×SD₁₆×C₅₃	C₂²	semidirect
57. C₂²⋊Q₈×C₅₃	C₂²	semidirect
59. #102×C₅₃	C₂²	semidirect
60. C₂²⋊C₈×C₅₃	C₂²	semidirect
105. #11719923	D₄	semidirect
173. Dic₁₀₆	C₂×D₄	semidirect
177. #88322	C₂×D₄	semidirect
198. C₂×D₅₃	AGL(1,ℤ/8)	semidirect
228. #450	D₅₃	semidirect
234. C₅₃	#3265	semidirect
247. C₂×SD₁₆	C₂×D₅₃	semidirect
257. C₂²⋊Q₈	C₂×D₅₃	semidirect
276. #102	C₂×D₅₃	semidirect
278. C₂²⋊C₈	C₂×D₅₃	semidirect