Subgroups — D₅₃×#2221 #27538645

Order 13568.

678 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#504×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#472×D₅₃	C₂	1	2	yes	maximal, complemented
4	#20276836	C₂	1	1	yes	maximal, characteristic, complemented
5	#20276835	C₂	1	1	yes	maximal, characteristic, complemented
6	#20276834	C₂	1	2	yes	maximal, complemented
7	#20276833	C₂	1	2	yes	maximal, complemented
8	#20276832	C₂	1	1	yes	maximal, characteristic, complemented
9	#368×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#361×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#2221	C₂	1	1	yes	maximal, characteristic, complemented
12	AGL(1,ℤ/8)×D₅₃	—	2	2	no	—
13	C₂×D₈×D₅₃	C₂²	1	2	yes	—
14	#131×D₅₃	C₂²	1	1	yes	characteristic
15	C₂×D₈₄₈	C₂²	1	1	yes	characteristic, complemented
16	C₂×#13133158	C₂²	1	2	yes	complemented
17	D₁₆×D₅₃	—	2	1	no	—
18	D₁₆×D₅₃	—	2	1	no	—
19	D₁₆×D₅₃	—	2	1	no	—
20	D₁₆×D₅₃	—	2	1	no	—
21	#16811041	—	2	1	no	—
22	#16811041	C₂²	1	1	yes	characteristic, complemented
23	#16811040	C₂²	1	1	yes	characteristic, complemented
24	#16811039	—	2	1	no	—
25	#16811039	C₂²	1	1	yes	characteristic, complemented
26	M₃₂×D₅₃	—	2	1	no	—
27	M₃₂×D₅₃	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₅₃	—	2	1	no	—
29	C₂×C₁₆×D₅₃	C₂²	1	1	yes	characteristic
30	#16810894	C₂²	1	2	yes	complemented
31	#16810893	C₂²	1	2	yes	complemented
32	#16810892	—	2	2	no	—
33	#16810891	—	2	2	no	—
34	#16810890	C₂²	1	2	yes	complemented
35	#108×D₅₃	C₂²	1	2	yes	—
36	#100×D₅₃	—	2	2	no	—
37	#16810453	C₂²	1	1	yes	characteristic, complemented
38	#16810452	C₂²	1	2	yes	complemented
39	#16810437	C₂²	1	2	yes	complemented
40	#16810436	C₂²	1	2	yes	complemented
41	#16810435	C₂²	1	2	yes	complemented
42	C₂×D₁₆×C₅₃	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#504	C₂²	1	1	yes	characteristic, complemented
44	C₅₃×#472	C₂²	1	2	yes	complemented
45	C₅₃×#368	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#361	C₂²	1	2	yes	complemented
47	#41×D₅₃	D₄	1	1	yes	characteristic
48	C₂×D₄×D₅₃	—	2	2	no	—
49	#13133245	—	2	2	no	—
50	#13133244	—	4	2	no	—
51	#13133243	—	2	2	no	—
52	#13133242	—	2	2	no	—
53	#13133241	—	4	2	no	—
54	SD₁₆×D₅₃	—	4	2	no	—
55	C₂×D₄₂₄	C₂³	1	2	yes	—
56	C₂×#11719922	—	2	2	no	—
57	D₈×D₅₃	—	2	2	no	—
58	D₈×D₅₃	—	2	2	no	—
59	D₈×D₅₃	—	2	2	no	—
60	D₈×D₅₃	—	2	2	no	—
61	D₈×D₅₃	—	4	2	no	—
62	#13133225	—	2	1	no	—
63	#13133225	D₄	1	1	yes	characteristic
64	#13133224	D₄	1	1	yes	characteristic
65	#13133223	—	2	1	no	—
66	#13133223	C₂³	1	1	yes	characteristic
67	M₁₆×D₅₃	—	2	1	no	—
68	M₁₆×D₅₃	—	2	2	no	—
69	M₁₆×D₅₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	—	2	1	no	—
71	C₂×C₈×D₅₃	C₂³	1	1	yes	characteristic
72	D₈₄₈	—	2	1	no	—
73	D₈₄₈	—	2	1	no	—
74	#13133158	—	2	2	no	—
75	#13133158	—	2	2	no	—
76	#13133157	—	2	1	no	—
77	#13133157	C₂³	1	1	yes	characteristic
78	#13133156	—	2	1	no	—
79	#13133156	—	2	1	no	—
80	#13133156	—	2	1	no	—
81	C₂×#11719908	—	2	1	no	—
82	C₂×#11719908	C₂³	1	1	yes	characteristic
83	C₁₆×D₅₃	—	2	1	no	—
84	C₁₆×D₅₃	—	2	1	no	—
85	C₁₆×D₅₃	—	2	1	no	—
86	C₁₆×D₅₃	D₄	1	1	yes	characteristic
87	C₁₆×D₅₃	D₄	1	1	yes	characteristic
88	C₁₆×D₅₃	D₄	1	1	yes	characteristic
89	C₁₆×D₅₃	D₄	1	1	yes	characteristic
90	#13133153	C₂³	1	2	yes	—
91	#13133152	—	2	2	no	—
92	#13133134	—	2	2	no	—
93	#13133133	—	2	2	no	—
94	#13133133	—	2	2	no	—
95	AGL(1,ℤ/8)×C₅₃	—	2	2	no	—
96	C₂×D₈×C₅₃	C₂³	1	2	yes	—
97	#131×C₅₃	C₂³	1	1	yes	characteristic
98	D₁₆×C₅₃	—	2	1	no	—
99	D₁₆×C₅₃	—	2	1	no	—
100	M₃₂×C₅₃	—	2	1	no	—
101	M₃₂×C₅₃	C₂³	1	1	yes	characteristic
102	C₂×C₁₆×C₅₃	—	2	1	no	—
103	C₂×C₁₆×C₅₃	C₂³	1	1	yes	characteristic
104	#108×C₅₃	C₂³	1	2	yes	—
105	#100×C₅₃	—	2	2	no	—
106	C₂³×D₅₃	—	4	2	no	—
107	#41×C₅₃	C₂×D₄	1	1	yes	characteristic
108	C₂×D₄×C₅₃	—	2	2	no	—
109	C₂×C₂²⋊D₅₃	—	4	2	no	—
110	#11719949	D₈	1	1	yes	characteristic
111	Q₈×D₅₃	D₈	1	1	yes	characteristic
112	#11719947	—	2	1	no	—
113	#11719947	D₈	1	1	yes	characteristic
114	D₄×D₅₃	—	2	1	no	—
115	D₄×D₅₃	—	4	2	no	—
116	D₄×D₅₃	—	4	2	no	—
117	D₄×D₅₃	—	4	2	no	—
118	D₄×D₅₃	—	4	2	no	—
119	D₄×D₅₃	D₈	1	1	yes	characteristic
120	#11719945	—	2	1	no	—
121	#11719945	C₂×D₄	1	1	yes	characteristic
122	C₂×D₂₁₂	—	2	2	no	—
123	C₂×C₄×D₅₃	—	2	1	no	—
124	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₅₃	—	4	2	no	—
126	D₈×C₅₃	—	2	2	no	—
127	D₈×C₅₃	—	2	2	no	—
128	D₈×C₅₃	—	4	2	no	—
129	M₁₆×C₅₃	—	2	1	no	—
130	M₁₆×C₅₃	—	2	2	no	—
131	M₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₅₃	—	2	1	no	—
133	C₂×C₈×C₅₃	C₂⁴	1	1	yes	characteristic
134	#11719924	—	4	2	no	—
135	#11719923	—	4	2	no	—
136	#11719922	—	4	2	no	—
137	#11719922	—	4	2	no	—
138	#11719922	—	4	2	no	—
139	#11719922	—	4	2	no	—
140	#11719917	—	2	1	no	—
141	#11719917	—	2	2	no	—
142	#11719917	C₂×D₄	1	1	yes	characteristic
143	C₂×#88322	—	2	1	no	—
144	C₂×#88322	C₂×D₄	1	1	yes	characteristic
145	D₄₂₄	—	2	2	no	—
146	D₄₂₄	—	2	2	no	—
147	D₄₂₄	—	4	2	no	—
148	#11719913	—	4	2	no	—
149	#11719912	—	2	1	no	—
150	#11719912	—	2	1	no	—
151	#11719912	—	2	1	no	—
152	#11719912	—	4	2	no	—
153	C₈×D₅₃	—	2	1	no	—
154	C₈×D₅₃	—	2	1	no	—
155	C₈×D₅₃	—	2	1	no	—
156	C₈×D₅₃	—	4	2	no	—
157	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
158	C₈×D₅₃	C₂×D₄	1	1	yes	characteristic
159	C₈×D₅₃	#41	1	1	yes	characteristic
160	C₈×D₅₃	#41	1	1	yes	characteristic
161	C₁₆×C₅₃	—	2	1	no	—
162	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
163	C₁₆×C₅₃	C₂×D₄	1	1	yes	characteristic
164	#11719908	—	2	1	no	—
165	#11719908	C₂×D₄	1	1	yes	characteristic
166	#11719908	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₅₃	—	4	2	no	—
168	C₂²×D₅₃	—	2	1	no	—
169	C₂²×D₅₃	—	4	2	no	—
170	C₂²×D₅₃	—	8	2	no	—
171	C₂²×D₅₃	—	8	2	no	—
172	C₂²×D₅₃	—	16	4	no	—
173	C₂²×D₅₃	#135	1	1	yes	characteristic
174	Q₈×C₅₃	C₂×D₈	1	1	yes	characteristic
175	D₄×C₅₃	—	2	1	no	—
176	D₄×C₅₃	—	4	2	no	—
177	D₄×C₅₃	—	4	2	no	—
178	D₄×C₅₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₅₃	—	2	1	no	—
180	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
181	C₂²⋊D₅₃	—	2	1	no	—
182	C₂²⋊D₅₃	—	2	1	no	—
183	C₂²⋊D₅₃	—	2	1	no	—
184	C₂²⋊D₅₃	—	8	2	no	—
185	C₂²⋊D₅₃	—	8	2	no	—
186	C₂×Dic₅₃	—	2	1	no	—
187	C₂×Dic₅₃	#135	1	1	yes	characteristic
188	D₂₁₂	—	2	1	no	—
189	D₂₁₂	—	4	2	no	—
190	D₂₁₂	—	4	2	no	—
191	D₂₁₂	C₂×D₈	1	1	yes	characteristic
192	C₄×D₅₃	—	2	1	no	—
193	C₄×D₅₃	—	2	1	no	—
194	C₄×D₅₃	—	2	1	no	—
195	C₄×D₅₃	#121	1	1	yes	characteristic
196	C₄×D₅₃	#121	1	1	yes	characteristic
197	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
198	C₄×D₅₃	C₂×D₈	1	1	yes	characteristic
199	Dic₁₀₆	—	2	1	no	—
200	Dic₁₀₆	C₂×D₈	1	1	yes	characteristic
201	C₈×C₅₃	—	2	1	no	—
202	C₈×C₅₃	—	4	2	no	—
203	C₈×C₅₃	C₂²×D₄	1	1	yes	characteristic
204	C₈×C₅₃	C₂×#41	1	1	yes	characteristic
205	#88322	—	2	1	no	—
206	#88322	—	4	2	no	—
207	#88322	#121	1	1	yes	characteristic
208	#88322	#121	1	1	yes	characteristic
209	C₂×#2221	—	53	1	no	maximal, Sylow
210	C₂²×C₅₃	—	2	1	no	—
211	C₂²×C₅₃	—	8	2	no	—
212	C₂²×C₅₃	—	16	2	no	—
213	C₂²×C₅₃	C₂×#135	1	1	yes	characteristic
214	C₂×D₅₃	—	2	2	no	—
215	C₂×D₅₃	—	2	1	no	—
216	C₂×D₅₃	—	4	2	no	—
217	C₂×D₅₃	—	8	2	no	—
218	C₂×D₅₃	—	16	4	no	—
219	C₂×D₅₃	—	16	4	no	—
220	C₂×D₅₃	—	16	2	no	—
221	C₂×D₅₃	#466	1	1	yes	characteristic
222	C₂×D₅₃	#466	1	1	yes	characteristic
223	C₄×C₅₃	—	2	1	no	—
224	C₄×C₅₃	C₂×#121	1	1	yes	characteristic
225	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
226	Dic₅₃	—	2	1	no	—
227	Dic₅₃	#466	1	1	yes	characteristic
228	Dic₅₃	#466	1	1	yes	characteristic
229	C₂²×D₁₆	—	53	1	no	—
230	C₂×#504	—	53	1	no	—
231	C₂×#472	—	53	2	no	—
232	#2221	—	53	1	no	—
233	#2221	—	53	1	no	—
234	#2221	—	53	2	no	—
235	#2221	—	53	1	no	—
236	#2221	—	53	2	no	—
237	#2221	D₅₃	1	1	yes	characteristic, direct product factor
238	C₂×#368	—	53	1	no	—
239	C₂×#361	—	53	2	no	—
240	C₂×C₅₃	—	2	1	no	—
241	C₂×C₅₃	—	4	1	no	—
242	C₂×C₅₃	—	16	2	no	—
243	C₂×C₅₃	C₂×#466	1	1	yes	characteristic
244	D₅₃	—	2	1	no	—
245	D₅₃	—	4	1	no	—
246	D₅₃	—	16	2	no	—
247	D₅₃	#2221	1	2	yes	direct product factor
248	C₂×AGL(1,ℤ/8)	—	106	2	no	—
249	C₂²×D₈	—	53	2	no	—
250	C₂×#131	—	53	1	no	—
251	C₂×D₁₆	—	53	2	no	—
252	C₂×D₁₆	—	53	1	no	—
253	C₂×D₁₆	—	106	1	no	—
254	C₂×D₁₆	—	106	1	no	—
255	C₂×D₁₆	—	106	1	no	—
256	C₂×D₁₆	—	106	1	no	—
257	C₂×D₁₆	C₂×D₅₃	1	1	yes	characteristic, complemented
258	#504	—	53	1	no	—
259	#504	—	53	1	no	—
260	#504	—	53	1	no	—
261	#504	—	106	1	no	—
262	#504	—	106	1	no	—
263	#504	C₂×D₅₃	1	1	yes	characteristic, complemented
264	C₂×M₃₂	—	53	1	no	—
265	C₂×M₃₂	—	106	1	no	—
266	C₂²×C₁₆	—	53	1	no	—
267	C₂²×C₁₆	—	106	1	no	—
268	#472	—	53	2	no	—
269	#472	—	53	2	no	—
270	#472	—	53	2	no	—
271	#472	—	106	2	no	—
272	#472	—	106	2	no	—
273	#472	C₂×D₅₃	1	2	yes	complemented
274	C₂×#108	—	53	2	no	—
275	C₂×#100	—	106	2	no	—
276	#368	—	53	1	no	—
277	#368	—	53	2	no	—
278	#368	C₂×D₅₃	1	1	yes	characteristic, complemented
279	#361	—	53	2	no	—
280	#361	—	53	2	no	—
281	#361	—	53	2	no	—
282	#361	C₂×D₅₃	1	2	yes	complemented
283	C₅₃	C₂×#2221	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	53	1	no	—
285	C₂²×D₄	—	106	2	no	—
286	AGL(1,ℤ/8)	—	2	2	no	—
287	AGL(1,ℤ/8)	—	106	2	no	—
288	AGL(1,ℤ/8)	—	106	2	no	—
289	AGL(1,ℤ/8)	—	106	2	no	—
290	AGL(1,ℤ/8)	—	212	2	no	—
291	AGL(1,ℤ/8)	—	212	2	no	—
292	C₂×SD₁₆	—	212	2	no	—
293	C₂×D₈	—	53	2	no	—
294	C₂×D₈	—	106	2	no	—
295	C₂×D₈	—	106	2	no	—
296	C₂×D₈	—	106	2	no	—
297	C₂×D₈	—	106	2	no	—
298	C₂×D₈	—	106	2	no	—
299	C₂×D₈	—	212	2	no	—
300	C₂×D₈	C₂²×D₅₃	1	2	yes	—
301	#131	—	53	1	no	—
302	#131	—	53	1	no	—
303	#131	—	53	1	no	—
304	#131	—	106	1	no	—
305	#131	—	106	1	no	—
306	#131	C₂²×D₅₃	1	1	yes	characteristic
307	C₂×M₁₆	—	53	1	no	—
308	C₂×M₁₆	—	106	1	no	—
309	C₂×M₁₆	—	106	2	no	—
310	C₂²×C₈	—	53	1	no	—
311	C₂²×C₈	—	106	1	no	—
312	D₁₆	—	2	1	no	—
313	D₁₆	—	2	1	no	—
314	D₁₆	—	106	2	no	—
315	D₁₆	—	106	2	no	—
316	D₁₆	—	106	1	no	—
317	D₁₆	—	106	1	no	—
318	M₃₂	—	2	1	no	—
319	M₃₂	—	53	1	no	—
320	M₃₂	—	106	1	no	—
321	M₃₂	—	106	1	no	—
322	M₃₂	—	106	1	no	—
323	M₃₂	—	106	1	no	—
324	M₃₂	C₂²×D₅₃	1	1	yes	characteristic
325	C₂×C₁₆	—	2	1	no	—
326	C₂×C₁₆	—	53	1	no	—
327	C₂×C₁₆	—	53	1	no	—
328	C₂×C₁₆	—	53	1	no	—
329	C₂×C₁₆	—	53	1	no	—
330	C₂×C₁₆	—	53	1	no	—
331	C₂×C₁₆	—	106	1	no	—
332	C₂×C₁₆	—	106	1	no	—
333	C₂×C₁₆	—	106	1	no	—
334	C₂×C₁₆	—	106	1	no	—
335	C₂×C₁₆	C₂²×D₅₃	1	1	yes	characteristic
336	#108	—	53	2	no	—
337	#108	—	106	2	no	—
338	#108	C₂²×D₅₃	1	2	yes	—
339	#100	—	2	2	no	—
340	#100	—	106	2	no	—
341	#100	—	106	2	no	—
342	#100	—	106	2	no	—
343	C₂⁴	—	212	2	no	—
344	#41	—	53	1	no	—
345	#41	—	53	1	no	—
346	#41	—	53	1	no	—
347	#41	—	106	1	no	—
348	#41	—	106	1	no	—
349	#41	D₄×D₅₃	1	1	yes	characteristic
350	C₂×Q₈	—	53	1	no	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	53	1	no	—
353	C₂×D₄	—	106	1	no	—
354	C₂×D₄	—	106	2	no	—
355	C₂×D₄	—	212	2	no	—
356	C₂×D₄	—	212	2	no	—
357	C₂×D₄	—	212	2	no	—
358	C₂×D₄	—	212	2	no	—
359	C₂×D₄	—	212	2	no	—
360	C₂²×C₄	—	53	1	no	—
361	C₂²×C₄	—	106	1	no	—
362	SD₁₆	—	4	2	no	—
363	SD₁₆	—	212	2	no	—
364	SD₁₆	—	212	2	no	—
365	SD₁₆	—	212	2	no	—
366	D₈	—	2	2	no	—
367	D₈	—	2	2	no	—
368	D₈	—	4	2	no	—
369	D₈	—	106	2	no	—
370	D₈	—	106	2	no	—
371	D₈	—	212	2	no	—
372	D₈	—	212	2	no	—
373	D₈	—	212	2	no	—
374	D₈	—	212	2	no	—
375	D₈	—	212	2	no	—
376	M₁₆	—	2	1	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	53	1	no	—
379	M₁₆	—	106	1	no	—
380	M₁₆	—	106	1	no	—
381	M₁₆	—	106	1	no	—
382	M₁₆	—	106	1	no	—
383	M₁₆	—	106	2	no	—
384	M₁₆	—	212	2	no	—
385	M₁₆	D₄×D₅₃	1	1	yes	characteristic
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	53	1	no	—
388	C₂×C₈	—	53	1	no	—
389	C₂×C₈	—	53	1	no	—
390	C₂×C₈	—	53	1	no	—
391	C₂×C₈	—	53	1	no	—
392	C₂×C₈	—	106	1	no	—
393	C₂×C₈	—	106	1	no	—
394	C₂×C₈	—	106	1	no	—
395	C₂×C₈	—	106	1	no	—
396	C₂×C₈	—	212	2	no	—
397	C₂×C₈	C₂³×D₅₃	1	1	yes	characteristic
398	C₁₆	—	2	1	no	—
399	C₁₆	—	53	1	no	—
400	C₁₆	—	53	1	no	—
401	C₁₆	—	106	1	no	—
402	C₁₆	D₄×D₅₃	1	1	yes	characteristic
403	C₁₆	D₄×D₅₃	1	1	yes	characteristic
404	C₂³	—	4	2	no	—
405	C₂³	—	53	1	no	—
406	C₂³	—	848	4	no	—
407	C₂³	—	106	1	no	—
408	C₂³	—	424	2	no	—
409	C₂³	—	424	2	no	—
410	C₂³	—	212	2	no	—
411	Q₈	—	53	1	no	—
412	Q₈	—	106	1	no	—
413	Q₈	D₈×D₅₃	1	1	yes	characteristic
414	D₄	—	2	1	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	53	1	no	—
418	D₄	—	106	1	no	—
419	D₄	—	106	1	no	—
420	D₄	—	106	1	no	—
421	D₄	—	106	1	no	—
422	D₄	—	424	2	no	—
423	D₄	—	424	2	no	—
424	D₄	—	212	2	no	—
425	D₄	—	212	2	no	—
426	D₄	D₈×D₅₃	1	1	yes	characteristic
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	53	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	1	no	—
432	C₂×C₄	—	53	1	no	—
433	C₂×C₄	—	106	1	no	—
434	C₂×C₄	—	106	1	no	—
435	C₂×C₄	—	106	1	no	—
436	C₂×C₄	—	106	1	no	—
437	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
438	C₈	—	2	1	no	—
439	C₈	—	4	2	no	—
440	C₈	—	53	1	no	—
441	C₈	—	53	1	no	—
442	C₈	—	106	1	no	—
443	C₈	—	212	2	no	—
444	C₈	C₂×D₄×D₅₃	1	1	yes	characteristic
445	C₈	#41×D₅₃	1	1	yes	characteristic
446	C₂²	—	2	1	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	16	2	no	—
449	C₂²	—	53	1	no	—
450	C₂²	—	53	1	no	—
451	C₂²	—	848	2	no	—
452	C₂²	—	848	4	no	—
453	C₂²	—	848	4	no	—
454	C₂²	—	106	2	no	—
455	C₂²	—	106	1	no	—
456	C₂²	—	424	2	no	—
457	C₂²	—	212	2	no	—
458	C₂²	#135×D₅₃	1	1	yes	characteristic
459	C₄	—	2	1	no	—
460	C₄	—	53	1	no	—
461	C₄	—	53	1	no	—
462	C₄	—	106	1	no	—
463	C₄	#121×D₅₃	1	1	yes	characteristic
464	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
465	C₂	—	2	1	no	—
466	C₂	—	4	1	no	—
467	C₂	—	16	2	no	—
468	C₂	—	53	2	no	—
469	C₂	—	848	2	no	—
470	C₂	—	106	1	no	—
471	C₂	—	212	1	no	—
472	C₂	#466×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#466×D₅₃
commutator, cosocle	C₂×C₈×C₅₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₅₃
Fitting	C₅₃×#2221	C₂
socle	C₂×C₅₃	C₂×#466
hypercenter	#2221	D₅₃
hypocenter	C₅₃	C₂×#2221
LCS	G ▷ C₂×C₈×C₅₃ ▷ C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #2221

Complements

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

N	H ≅ G/N	type
1. C₂×D₁₆×D₅₃	C₂	semidirect
2. #504×D₅₃	C₂	semidirect
3. #472×D₅₃	C₂	semidirect
4. #20276836	C₂	semidirect
5. #20276835	C₂	semidirect
6. #20276834	C₂	semidirect
7. #20276833	C₂	semidirect
8. #20276832	C₂	semidirect
9. #368×D₅₃	C₂	semidirect
10. #361×D₅₃	C₂	semidirect
11. C₅₃×#2221	C₂	semidirect
15. C₂×D₈₄₈	C₂²	semidirect
16. C₂×#13133158	C₂²	semidirect
22. #16811041	C₂²	semidirect
23. #16811040	C₂²	semidirect
25. #16811039	C₂²	semidirect
30. #16810894	C₂²	semidirect
31. #16810893	C₂²	semidirect
34. #16810890	C₂²	semidirect
37. #16810453	C₂²	semidirect
38. #16810452	C₂²	semidirect
39. #16810437	C₂²	semidirect
40. #16810436	C₂²	semidirect
41. #16810435	C₂²	semidirect
42. C₂×D₁₆×C₅₃	C₂²	semidirect
43. C₅₃×#504	C₂²	semidirect
44. C₅₃×#472	C₂²	semidirect
45. C₅₃×#368	C₂²	semidirect
46. C₅₃×#361	C₂²	semidirect
237. #2221	D₅₃	direct (N × H)
247. D₅₃	#2221	direct (N × H)
257. C₂×D₁₆	C₂×D₅₃	semidirect
263. #504	C₂×D₅₃	semidirect
273. #472	C₂×D₅₃	semidirect
278. #368	C₂×D₅₃	semidirect
282. #361	C₂×D₅₃	semidirect
283. C₅₃	C₂×#2221	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₅₃	2
#504×D₅₃	2
#472×D₅₃	2
#20276836	2
#20276835	2
#20276834	2
#20276833	2
#20276832	2
#368×D₅₃	2
#361×D₅₃	2
C₅₃×#2221	2
C₂×#2221	53

Subgroups — D53×#2221 #27538645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#2221 #27538645