Subgroups — #20286190

Order 6784.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13133241	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₈×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#16811268	C₂	1	1	yes	maximal, characteristic, complemented
4	#16811258	C₂	1	1	yes	maximal, characteristic, complemented
5	#16811010	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810875	C₂	1	1	yes	maximal, characteristic, complemented
7	#16810851	C₂	1	1	yes	maximal, characteristic, complemented
8	#16810839	C₂	1	1	yes	maximal, characteristic, complemented
9	#16810775	C₂	1	1	yes	maximal, characteristic, complemented
10	#16810765	C₂	1	1	yes	maximal, characteristic, complemented
11	#16810758	C₂	1	1	yes	maximal, characteristic, complemented
12	#16810755	C₂	1	1	yes	maximal, characteristic, complemented
13	#16810733	C₂	1	1	yes	maximal, characteristic, complemented
14	#16810693	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11719947	C₂²	1	1	yes	characteristic, complemented
17	C₂×D₄×D₅₃	—	2	1	no	—
18	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
21	#13133241	—	2	4	no	—
22	C₂×#11719913	C₂²	1	1	yes	characteristic, complemented
23	C₂×#11719923	C₂²	1	1	yes	characteristic, complemented
24	C₂×#11719923	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄₂₄	C₂²	1	1	yes	characteristic
26	C₂×#11719922	C₂²	1	1	yes	characteristic
27	C₂×#11719922	C₂²	1	1	yes	characteristic, complemented
28	C₂×#11719922	C₂²	1	1	yes	characteristic, complemented
29	D₈×D₅₃	—	2	4	no	—
30	C₂×#11719912	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₈×D₅₃	C₂²	1	1	yes	characteristic, complemented
32	#13133205	C₂²	1	1	yes	characteristic, complemented
33	#13133201	—	2	1	no	—
34	#13133197	C₂²	1	1	yes	characteristic, complemented
35	#13133192	C₂²	1	1	yes	characteristic, complemented
36	#13133191	—	2	1	no	—
37	#13133188	—	2	1	no	—
38	#13133188	C₂²	1	1	yes	characteristic
39	#13133188	C₂²	1	1	yes	characteristic, complemented
40	#13133187	—	2	1	no	—
41	#13133185	—	2	1	no	—
42	#13133185	—	2	1	no	—
43	C₄×D₂₁₂	C₂²	1	1	yes	characteristic
44	C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
45	C₂×#11719921	—	2	1	no	—
46	#13133148	C₂²	1	1	yes	characteristic, complemented
47	#13133142	C₂²	1	1	yes	characteristic, complemented
48	#13133139	C₂²	1	1	yes	characteristic, complemented
49	#13133138	C₂²	1	1	yes	characteristic, complemented
50	#13133137	C₂²	1	1	yes	characteristic, complemented
51	#13133129	C₂²	1	1	yes	characteristic, complemented
52	#13133129	C₂²	1	1	yes	characteristic, complemented
53	#13133128	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×D₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
56	#127×C₅₃	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
59	#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
60	#102×C₅₃	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₅₃	—	2	1	no	—
62	C₂³×D₅₃	—	2	1	no	—
63	C₂³×D₅₃	—	2	1	no	—
64	C₂×D₄×C₅₃	—	2	1	no	—
65	C₂×D₄×C₅₃	—	2	1	no	—
66	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₅₃	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₅₃	—	2	1	no	—
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	C₂²×Dic₅₃	—	2	1	no	—
77	#11719947	—	2	2	no	—
78	#11719947	—	4	1	no	—
79	D₄×D₅₃	—	2	2	no	—
80	D₄×D₅₃	—	2	2	no	—
81	D₄×D₅₃	—	2	2	no	—
82	D₄×D₅₃	—	4	1	no	—
83	D₄×D₅₃	—	4	1	no	—
84	D₄×D₅₃	—	4	1	no	—
85	D₄×D₅₃	—	4	4	no	—
86	C₂×D₂₁₂	—	2	1	no	—
87	C₂×D₂₁₂	D₄	1	1	yes	characteristic
88	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
89	C₂×D₂₁₂	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₅₃	—	2	1	no	—
91	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
93	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
94	D₈×C₅₃	—	2	2	no	—
95	D₈×C₅₃	—	2	2	no	—
96	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
97	C₂×C₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
99	C₂²⋊C₄×C₅₃	—	2	1	no	—
100	C₄²×C₅₃	C₂³	1	1	yes	characteristic
101	C₂²⋊Dic₅₃	—	2	1	no	—
102	C₂²⋊Dic₅₃	—	2	1	no	—
103	#11719923	—	2	2	no	—
104	#11719923	—	4	1	no	—
105	#11719922	—	2	2	no	—
106	#11719922	—	4	1	no	—
107	#11719922	D₄	1	4	yes	complemented
108	#11719921	—	2	1	no	—
109	#11719921	—	2	1	no	—
110	#11719921	—	2	1	no	—
111	#11719921	—	2	1	no	—
112	#11719921	—	2	1	no	—
113	#11719921	D₄	1	1	yes	characteristic
114	#11719921	D₄	1	1	yes	characteristic
115	C₄⋊Dic₅₃	—	2	1	no	—
116	C₄⋊Dic₅₃	D₄	1	1	yes	characteristic
117	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
118	C₂×#88322	C₂³	1	1	yes	characteristic
119	C₂×#88322	C₂³	1	1	yes	characteristic
120	D₄₂₄	—	2	2	no	—
121	#11719913	—	2	2	no	—
122	#11719912	—	2	2	no	—
123	C₈×D₅₃	—	2	2	no	—
124	C₂³×C₅₃	—	2	1	no	—
125	C₂³×C₅₃	—	2	1	no	—
126	C₂³×C₅₃	—	2	1	no	—
127	C₂²×D₅₃	—	2	1	no	—
128	C₂²×D₅₃	—	2	1	no	—
129	C₂²×D₅₃	—	4	2	no	—
130	C₂²×D₅₃	—	4	2	no	—
131	C₂²×D₅₃	—	4	2	no	—
132	C₂²×D₅₃	—	4	2	no	—
133	C₂²×D₅₃	—	4	2	no	—
134	C₂²×D₅₃	—	4	2	no	—
135	C₂²×D₅₃	—	8	1	no	—
136	C₂²×D₅₃	—	8	1	no	—
137	C₂²×D₅₃	—	8	1	no	—
138	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
140	D₄×C₅₃	—	2	1	no	—
141	D₄×C₅₃	—	2	1	no	—
142	D₄×C₅₃	—	2	1	no	—
143	D₄×C₅₃	—	2	1	no	—
144	D₄×C₅₃	—	2	1	no	—
145	D₄×C₅₃	—	4	2	no	—
146	D₄×C₅₃	—	8	1	no	—
147	D₄×C₅₃	C₂×D₄	1	2	yes	complemented
148	C₂×C₄×C₅₃	—	2	1	no	—
149	C₂×C₄×C₅₃	—	8	1	no	—
150	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
153	C₂²⋊D₅₃	—	4	2	no	—
154	C₂²⋊D₅₃	—	4	2	no	—
155	C₂²⋊D₅₃	—	4	2	no	—
156	C₂²⋊D₅₃	—	4	2	no	—
157	C₂²⋊D₅₃	—	4	2	no	—
158	C₂²⋊D₅₃	—	4	2	no	—
159	C₂×Dic₅₃	—	2	1	no	—
160	C₂×Dic₅₃	—	2	1	no	—
161	C₂×Dic₅₃	—	4	2	no	—
162	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
164	D₂₁₂	—	2	2	no	—
165	D₂₁₂	—	2	1	no	—
166	D₂₁₂	—	2	1	no	—
167	D₂₁₂	—	2	1	no	—
168	D₂₁₂	—	8	1	no	—
169	D₂₁₂	C₂×D₄	1	2	yes	—
170	C₄×D₅₃	—	2	1	no	—
171	C₄×D₅₃	—	2	1	no	—
172	C₄×D₅₃	—	2	1	no	—
173	C₄×D₅₃	—	2	1	no	—
174	C₄×D₅₃	—	4	2	no	—
175	Dic₁₀₆	—	2	1	no	—
176	Dic₁₀₆	—	2	1	no	—
177	C₈×C₅₃	—	2	1	no	—
178	C₈×C₅₃	—	2	1	no	—
179	#88322	—	2	1	no	—
180	#88322	C₂×D₄	1	2	yes	complemented
181	C₂²×C₅₃	—	2	2	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	—	4	1	no	—
188	C₂²×C₅₃	—	4	1	no	—
189	C₂²×C₅₃	—	4	1	no	—
190	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×D₅₃	—	2	1	no	—
192	C₂×D₅₃	—	2	1	no	—
193	C₂×D₅₃	—	2	1	no	—
194	C₂×D₅₃	—	2	2	no	—
195	C₂×D₅₃	—	2	1	no	—
196	C₂×D₅₃	—	2	1	no	—
197	C₂×D₅₃	—	4	1	no	—
198	C₂×D₅₃	—	4	1	no	—
199	C₂×D₅₃	—	4	1	no	—
200	C₂×D₅₃	—	4	1	no	—
201	C₂×D₅₃	—	4	1	no	—
202	C₂×D₅₃	—	8	4	no	—
203	C₂×D₅₃	—	8	4	no	—
204	C₂×D₅₃	—	8	4	no	—
205	C₂×D₅₃	AGL(1,ℤ/8)	1	2	yes	complemented
206	C₄×C₅₃	—	2	1	no	—
207	C₄×C₅₃	—	2	1	no	—
208	C₄×C₅₃	—	4	1	no	—
209	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
210	C₄×C₅₃	H(5,𝔽₂)	1	1	yes	characteristic
211	Dic₅₃	—	2	1	no	—
212	Dic₅₃	—	2	1	no	—
213	Dic₅₃	—	4	1	no	—
214	Dic₅₃	—	4	1	no	—
215	#3264	—	53	1	no	maximal, Sylow
216	C₂×C₅₃	—	4	2	no	—
217	C₂×C₅₃	—	8	1	no	—
218	C₂×C₅₃	—	8	1	no	—
219	C₂×C₅₃	D₄²	1	1	yes	characteristic
220	C₂×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂×C₅₃	#576	1	1	yes	characteristic
222	D₅₃	—	2	2	no	—
223	D₅₃	—	4	1	no	—
224	D₅₃	—	4	2	no	—
225	D₅₃	—	8	1	no	—
226	C₂×AGL(1,ℤ/8)	—	53	1	no	—
227	C₂²×D₈	—	53	1	no	—
228	#546	—	53	1	no	—
229	D₄²	—	53	1	no	—
230	#496	—	53	1	no	—
231	#469	—	53	1	no	—
232	#465	—	53	1	no	—
233	#463	—	53	1	no	—
234	#459	D₅₃	1	1	yes	characteristic, complemented
235	#450	—	53	1	no	—
236	#449	—	53	1	no	—
237	#447	—	53	1	no	—
238	#447	—	53	1	no	—
239	#442	—	53	1	no	—
240	#435	—	53	1	no	—
241	C₅₃	#3264	1	1	yes	characteristic, complemented, Sylow
242	C₂×#41	—	53	1	no	—
243	C₂²×D₄	—	53	1	no	—
244	C₂²×D₄	—	53	1	no	—
245	C₂²×D₄	—	53	1	no	—
246	C₂²×D₄	—	106	1	no	—
247	AGL(1,ℤ/8)	—	106	4	no	—
248	C₂×SD₁₆	—	53	1	no	—
249	C₂×SD₁₆	—	53	1	no	—
250	C₂×SD₁₆	—	53	1	no	—
251	C₂×D₈	—	53	1	no	—
252	C₂×D₈	—	53	1	no	—
253	C₂×D₈	—	53	1	no	—
254	C₂×D₈	—	53	1	no	—
255	C₂×D₈	—	106	4	no	—
256	C₂×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
257	C₂×D₈	C₂×D₅₃	1	1	yes	characteristic, complemented
258	C₂×M₁₆	—	53	1	no	—
259	C₂²×C₈	—	53	1	no	—
260	#127	C₂×D₅₃	1	1	yes	characteristic, complemented
261	#124	—	53	1	no	—
262	#123	—	106	1	no	—
263	C₂²⋊Q₈	—	53	1	no	—
264	#121	—	53	1	no	—
265	#121	—	53	1	no	—
266	#121	—	53	1	no	—
267	#121	—	106	1	no	—
268	#121	—	106	1	no	—
269	#120	—	106	1	no	—
270	#120	—	106	1	no	—
271	#120	—	106	1	no	—
272	C₄×D₄	—	53	1	no	—
273	C₄×D₄	—	53	1	no	—
274	C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
275	C₂×C₂²⋊C₄	—	106	1	no	—
276	#106	—	53	1	no	—
277	C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic, complemented
278	#103	—	53	1	no	—
279	#102	—	53	1	no	—
280	#102	—	53	1	no	—
281	#102	—	53	1	no	—
282	#102	C₂×D₅₃	1	1	yes	characteristic, complemented
283	#102	C₂×D₅₃	1	1	yes	characteristic, complemented
284	C₂²⋊C₈	—	53	1	no	—
285	C₂²⋊C₈	—	53	1	no	—
286	#97	—	53	1	no	—
287	C₂⁴	—	106	1	no	—
288	C₂⁴	—	106	1	no	—
289	C₂⁴	—	106	1	no	—
290	#41	—	106	2	no	—
291	#41	—	212	1	no	—
292	C₂×Q₈	—	53	1	no	—
293	C₂×D₄	—	2	1	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	53	1	no	—
296	C₂×D₄	—	53	1	no	—
297	C₂×D₄	—	53	1	no	—
298	C₂×D₄	—	106	1	no	—
299	C₂×D₄	—	106	1	no	—
300	C₂×D₄	—	106	1	no	—
301	C₂×D₄	—	106	1	no	—
302	C₂×D₄	—	106	2	no	—
303	C₂×D₄	—	106	2	no	—
304	C₂×D₄	—	106	2	no	—
305	C₂×D₄	—	106	1	no	—
306	C₂×D₄	—	106	1	no	—
307	C₂×D₄	—	106	1	no	—
308	C₂×D₄	—	212	1	no	—
309	C₂×D₄	—	212	1	no	—
310	C₂×D₄	—	212	1	no	—
311	C₂×D₄	—	212	4	no	—
312	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
313	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₅₃	1	1	yes	characteristic
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	106	1	no	—
319	C₂²×C₄	—	106	1	no	—
320	SD₁₆	—	106	2	no	—
321	SD₁₆	—	106	2	no	—
322	SD₁₆	—	212	1	no	—
323	D₈	—	2	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	53	4	no	—
326	D₈	—	106	2	no	—
327	D₈	—	106	2	no	—
328	D₈	—	212	1	no	—
329	M₁₆	—	106	2	no	—
330	C₂×C₈	—	53	1	no	—
331	C₂×C₈	—	53	1	no	—
332	C₂×C₈	—	106	2	no	—
333	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
334	C₂×C₈	C₂²×D₅₃	1	1	yes	characteristic
335	C₄⋊C₄	—	53	1	no	—
336	C₄⋊C₄	—	53	1	no	—
337	C₄⋊C₄	—	106	1	no	—
338	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
339	C₂²⋊C₄	—	2	1	no	—
340	C₂²⋊C₄	—	53	1	no	—
341	C₂²⋊C₄	—	53	1	no	—
342	C₂²⋊C₄	—	106	1	no	—
343	C₂²⋊C₄	—	106	1	no	—
344	C₂²⋊C₄	—	106	1	no	—
345	C₂²⋊C₄	—	106	1	no	—
346	C₂²⋊C₄	—	106	1	no	—
347	C₂²⋊C₄	—	106	1	no	—
348	C₂²⋊C₄	—	106	1	no	—
349	C₄²	C₂²×D₅₃	1	1	yes	characteristic
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	1	no	—
353	C₂³	—	53	1	no	—
354	C₂³	—	53	1	no	—
355	C₂³	—	106	1	no	—
356	C₂³	—	106	1	no	—
357	C₂³	—	424	1	no	—
358	C₂³	—	424	1	no	—
359	C₂³	—	424	1	no	—
360	C₂³	—	212	2	no	—
361	C₂³	—	212	2	no	—
362	C₂³	—	212	2	no	—
363	C₂³	—	212	2	no	—
364	C₂³	—	212	2	no	—
365	C₂³	—	212	2	no	—
366	Q₈	—	106	1	no	—
367	Q₈	—	106	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	2	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	2	1	no	—
373	D₄	—	4	2	no	—
374	D₄	—	8	1	no	—
375	D₄	—	53	2	no	—
376	D₄	—	106	2	no	—
377	D₄	—	106	1	no	—
378	D₄	—	106	1	no	—
379	D₄	—	106	1	no	—
380	D₄	—	424	1	no	—
381	D₄	—	212	2	no	—
382	D₄	—	212	2	no	—
383	D₄	—	212	2	no	—
384	D₄	—	212	2	no	—
385	D₄	—	212	2	no	—
386	D₄	—	212	2	no	—
387	D₄	D₄×D₅₃	1	2	yes	complemented
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	8	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	53	1	no	—
392	C₂×C₄	—	106	1	no	—
393	C₂×C₄	—	106	1	no	—
394	C₂×C₄	—	106	1	no	—
395	C₂×C₄	—	106	1	no	—
396	C₂×C₄	—	106	1	no	—
397	C₂×C₄	—	106	1	no	—
398	C₂×C₄	—	212	2	no	—
399	C₂×C₄	—	212	2	no	—
400	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
401	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	53	2	no	—
406	C₈	—	106	1	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	53	2	no	—
417	C₂²	—	106	1	no	—
418	C₂²	—	106	1	no	—
419	C₂²	—	106	1	no	—
420	C₂²	—	106	1	no	—
421	C₂²	—	106	1	no	—
422	C₂²	—	106	2	no	—
423	C₂²	—	424	4	no	—
424	C₂²	—	424	4	no	—
425	C₂²	—	424	4	no	—
426	C₂²	—	212	1	no	—
427	C₂²	—	212	1	no	—
428	C₂²	—	212	1	no	—
429	C₂²	—	212	1	no	—
430	C₂²	—	212	1	no	—
431	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	4	1	no	—
435	C₄	—	106	1	no	—
436	C₄	—	106	1	no	—
437	C₄	—	212	1	no	—
438	C₄	—	212	1	no	—
439	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
440	C₄	#13133263	1	1	yes	characteristic
441	C₂	—	4	2	no	—
442	C₂	—	8	1	no	—
443	C₂	—	8	1	no	—
444	C₂	—	106	2	no	—
445	C₂	—	424	1	no	—
446	C₂	—	212	1	no	—
447	C₂	—	212	2	no	—
448	C₂	#16811257	1	1	yes	characteristic
449	C₂	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
450	C₂	#16811424	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#459	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#459	D₅₃
hypocenter	C₅₃	#3264
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #459

Complements

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

N	H ≅ G/N	type
1. C₂×#13133241	C₂	semidirect
2. C₂×D₈×D₅₃	C₂	semidirect
3. #16811268	C₂	semidirect
4. #16811258	C₂	semidirect
5. #16811010	C₂	semidirect
6. #16810875	C₂	semidirect
7. #16810851	C₂	semidirect
8. #16810839	C₂	semidirect
9. #16810775	C₂	semidirect
10. #16810765	C₂	semidirect
11. #16810758	C₂	semidirect
12. #16810755	C₂	semidirect
13. #16810733	C₂	semidirect
14. #16810693	C₂	semidirect
15. C₅₃×#459	C₂	semidirect
16. C₂×#11719947	C₂²	semidirect
19. C₂×D₄×D₅₃	C₂²	semidirect
20. C₂×D₄×D₅₃	C₂²	semidirect
22. C₂×#11719913	C₂²	semidirect
23. C₂×#11719923	C₂²	semidirect
24. C₂×#11719923	C₂²	semidirect
27. C₂×#11719922	C₂²	semidirect
28. C₂×#11719922	C₂²	semidirect
30. C₂×#11719912	C₂²	semidirect
31. C₂×C₈×D₅₃	C₂²	semidirect
32. #13133205	C₂²	semidirect
34. #13133197	C₂²	semidirect
35. #13133192	C₂²	semidirect
39. #13133188	C₂²	semidirect
44. C₄×D₂₁₂	C₂²	semidirect
46. #13133148	C₂²	semidirect
47. #13133142	C₂²	semidirect
48. #13133139	C₂²	semidirect
49. #13133138	C₂²	semidirect
50. #13133137	C₂²	semidirect
51. #13133129	C₂²	semidirect
52. #13133129	C₂²	semidirect
53. #13133128	C₂²	semidirect
54. C₂×D₈×C₅₃	C₂²	semidirect
55. C₂×D₈×C₅₃	C₂²	semidirect
56. #127×C₅₃	C₂²	semidirect
57. C₄×D₄×C₅₃	C₂²	semidirect
58. C₄⋊C₈×C₅₃	C₂²	semidirect
59. #102×C₅₃	C₂²	semidirect
60. #102×C₅₃	C₂²	semidirect
107. #11719922	D₄	semidirect
147. D₄×C₅₃	C₂×D₄	semidirect
180. #88322	C₂×D₄	semidirect
205. C₂×D₅₃	AGL(1,ℤ/8)	semidirect
234. #459	D₅₃	semidirect
241. C₅₃	#3264	semidirect
256. C₂×D₈	C₂×D₅₃	semidirect
257. C₂×D₈	C₂×D₅₃	semidirect
260. #127	C₂×D₅₃	semidirect
274. C₄×D₄	C₂×D₅₃	semidirect
277. C₄⋊C₈	C₂×D₅₃	semidirect
282. #102	C₂×D₅₃	semidirect
283. #102	C₂×D₅₃	semidirect
387. D₄	D₄×D₅₃	semidirect