Subgroups — #27367294

Order 13568.

774 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20285655	C₂	1	2	yes	maximal, complemented
2	#493×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#20283644	C₂	1	1	yes	maximal, characteristic, complemented
4	#20274198	C₂	1	2	yes	maximal, complemented
5	#20274197	C₂	1	2	yes	maximal, complemented
6	#20274076	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274075	C₂	1	1	yes	maximal, characteristic, complemented
8	#20274072	C₂	1	1	yes	maximal, characteristic, complemented
9	#20273462	C₂	1	1	yes	maximal, characteristic, complemented
10	#20273381	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₅₃	—	2	1	no	—
13	C₂×D₈×D₅₃	—	2	1	no	—
14	#16811177	C₂²	1	1	yes	characteristic
15	#127×D₅₃	C₂²	1	2	yes	—
16	#16811000	C₂²	1	1	yes	characteristic
17	#16810999	C₂²	1	2	yes	—
18	#16810998	—	2	1	no	—
19	#16810998	—	2	1	no	—
20	#16810994	—	2	2	no	—
21	#16810968	—	2	2	no	—
22	#16810824	C₂²	1	2	yes	complemented
23	#16810823	C₂²	1	2	yes	complemented
24	#16810820	C₂²	1	2	yes	complemented
25	#16810775	—	2	2	no	—
26	#16810772	—	2	2	no	—
27	#16810754	C₂²	1	1	yes	characteristic, complemented
28	#16810752	—	2	1	no	—
29	#16810750	C₂²	1	1	yes	characteristic, complemented
30	C₈×Dic₁₀₆	—	2	1	no	—
31	C₈×Dic₁₀₆	C₂²	1	1	yes	characteristic, complemented
32	#16810675	C₂²	1	2	yes	—
33	#16810648	—	2	1	no	—
34	#16810645	C₂²	1	1	yes	characteristic
35	#16810577	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic, complemented
38	#16810373	C₂²	1	2	yes	complemented
39	#16810367	C₂²	1	2	yes	complemented
40	#16810366	C₂²	1	2	yes	complemented
41	#16810366	C₂²	1	2	yes	complemented
42	C₅₃×#493	C₂²	1	1	yes	characteristic
43	C₅₃×#460	C₂²	1	2	yes	complemented
44	C₈×Q₈×C₅₃	C₂²	1	1	yes	characteristic, complemented
45	C₅₃×#335	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#331	C₂²	1	2	yes	complemented
47	C₂×D₄×D₅₃	—	2	2	no	—
48	C₂×D₄×D₅₃	—	2	2	no	—
49	C₂×D₄×D₅₃	—	2	2	no	—
50	C₂×#11719913	—	2	2	no	—
51	C₂×#11719923	—	2	2	no	—
52	C₂×#11719924	—	2	2	no	—
53	C₂×D₄₂₄	—	2	1	no	—
54	C₂×D₄₂₄	—	2	1	no	—
55	C₂×#11719922	—	2	2	no	—
56	C₂×#11719922	—	2	2	no	—
57	D₈×D₅₃	—	4	4	no	—
58	D₈×D₅₃	—	4	4	no	—
59	C₂×#11719912	—	2	1	no	—
60	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
62	#13133216	D₄	1	1	yes	characteristic
63	#13133215	D₄	1	1	yes	characteristic
64	#13133214	C₂³	1	2	yes	—
65	#13133213	—	2	2	no	—
66	#13133213	—	2	2	no	—
67	#13133213	—	2	2	no	—
68	#13133207	—	2	1	no	—
69	#13133197	D₄	1	1	yes	characteristic
70	#13133195	—	2	1	no	—
71	#13133193	D₄	1	1	yes	characteristic
72	C₄×Dic₁₀₆	—	2	1	no	—
73	C₄×Dic₁₀₆	C₂³	1	1	yes	characteristic
74	#13133174	—	2	1	no	—
75	C₄²×D₅₃	C₂³	1	1	yes	characteristic
76	C₄⋊#88322	—	2	1	no	—
77	C₄⋊#88322	C₂³	1	1	yes	characteristic
78	C₄⋊#88322	C₂³	1	2	yes	—
79	#13133146	—	2	1	no	—
80	#13133146	—	2	1	no	—
81	#13133146	—	2	1	no	—
82	#13133139	—	2	2	no	—
83	#13133138	—	2	2	no	—
84	#13133137	—	2	2	no	—
85	#13133129	—	2	2	no	—
86	#13133128	—	2	1	no	—
87	#13133127	—	2	1	no	—
88	C₄×#88322	C₂³	1	1	yes	characteristic
89	C₈×Dic₅₃	—	2	1	no	—
90	C₈×Dic₅₃	—	2	2	no	—
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₈×Dic₅₃	D₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₅₃	—	2	2	no	—
94	C₂×D₈×C₅₃	—	2	1	no	—
95	C₂×D₈×C₅₃	—	2	1	no	—
96	#127×C₅₃	C₂³	1	2	yes	—
97	C₄×Q₈×C₅₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₅₃	—	2	1	no	—
99	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
100	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
101	#102×C₅₃	—	2	2	no	—
102	C₄×C₈×C₅₃	—	2	1	no	—
103	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂³×D₅₃	—	4	2	no	—
105	C₂×Q₈×C₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₅₃	—	2	2	no	—
107	C₂×D₄×C₅₃	—	2	2	no	—
108	C₂×D₄×C₅₃	—	2	2	no	—
109	C₂×C₂²⋊D₅₃	—	4	2	no	—
110	C₂×C₂²⋊D₅₃	—	4	2	no	—
111	C₂×C₂²⋊D₅₃	—	4	2	no	—
112	D₄×D₅₃	—	4	4	no	—
113	D₄×D₅₃	—	4	4	no	—
114	D₄×D₅₃	—	8	2	no	—
115	D₄×D₅₃	—	8	2	no	—
116	D₄×D₅₃	—	8	4	no	—
117	C₂×D₂₁₂	—	2	2	no	—
118	C₂×D₂₁₂	—	2	2	no	—
119	C₂×D₂₁₂	—	2	2	no	—
120	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
123	C₂×Dic₁₀₆	—	2	1	no	—
124	C₂×Dic₁₀₆	C₂×D₄	1	1	yes	characteristic
125	SD₁₆×C₅₃	—	8	2	no	—
126	D₈×C₅₃	—	4	2	no	—
127	D₈×C₅₃	—	4	2	no	—
128	C₂×C₈×C₅₃	—	2	1	no	—
129	C₂×C₈×C₅₃	—	2	2	no	—
130	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
132	C₄⋊C₄×C₅₃	—	2	1	no	—
133	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₅₃	—	2	1	no	—
135	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
136	#11719924	—	8	2	no	—
137	#11719923	—	8	2	no	—
138	#11719922	—	4	4	no	—
139	#11719922	—	4	4	no	—
140	#11719921	—	2	1	no	—
141	#11719921	—	2	1	no	—
142	C₄⋊Dic₅₃	—	2	1	no	—
143	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
144	#11719919	—	2	1	no	—
145	#11719919	—	2	1	no	—
146	#11719919	—	2	1	no	—
147	#11719919	—	2	1	no	—
148	#11719919	—	2	1	no	—
149	C₄×Dic₅₃	—	2	1	no	—
150	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₅₃	#41	1	1	yes	characteristic
153	C₂×#88322	—	2	1	no	—
154	C₂×#88322	—	2	2	no	—
155	C₂×#88322	C₂×D₄	1	1	yes	characteristic
156	C₂×#88322	C₂×D₄	1	1	yes	characteristic
157	D₄₂₄	—	4	2	no	—
158	D₄₂₄	—	4	2	no	—
159	#11719913	—	8	2	no	—
160	#11719912	—	4	2	no	—
161	C₈×D₅₃	—	2	2	no	—
162	C₈×D₅₃	SD₁₆	1	4	yes	complemented
163	C₂³×C₅₃	—	4	2	no	—
164	C₂²×D₅₃	—	4	2	no	—
165	C₂²×D₅₃	—	8	4	no	—
166	C₂²×D₅₃	—	8	4	no	—
167	C₂²×D₅₃	—	8	4	no	—
168	C₂²×D₅₃	#121	1	1	yes	characteristic
169	Q₈×C₅₃	—	2	1	no	—
170	Q₈×C₅₃	—	2	1	no	—
171	D₄×C₅₃	—	4	2	no	—
172	D₄×C₅₃	—	4	2	no	—
173	D₄×C₅₃	—	4	2	no	—
174	D₄×C₅₃	—	4	2	no	—
175	D₄×C₅₃	—	8	2	no	—
176	C₂×C₄×C₅₃	—	2	1	no	—
177	C₂×C₄×C₅₃	—	2	1	no	—
178	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₅₃	—	8	4	no	—
182	C₂²⋊D₅₃	—	8	4	no	—
183	C₂²⋊D₅₃	—	8	4	no	—
184	C₂×Dic₅₃	—	2	1	no	—
185	C₂×Dic₅₃	—	2	1	no	—
186	C₂×Dic₅₃	#121	1	1	yes	characteristic
187	C₂×Dic₅₃	#121	1	1	yes	characteristic
188	C₂×Dic₅₃	#121	1	1	yes	characteristic
189	D₂₁₂	—	4	2	no	—
190	D₂₁₂	—	4	2	no	—
191	D₂₁₂	—	4	2	no	—
192	D₂₁₂	—	4	2	no	—
193	D₂₁₂	—	8	2	no	—
194	C₄×D₅₃	—	2	1	no	—
195	C₄×D₅₃	—	2	1	no	—
196	C₄×D₅₃	—	2	2	no	—
197	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
198	C₄×D₅₃	AGL(1,ℤ/8)	1	2	yes	—
199	Dic₁₀₆	—	2	1	no	—
200	Dic₁₀₆	—	2	1	no	—
201	Dic₁₀₆	—	4	2	no	—
202	C₈×C₅₃	—	2	1	no	—
203	C₈×C₅₃	—	4	1	no	—
204	C₈×C₅₃	—	4	2	no	—
205	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
206	#88322	—	2	1	no	—
207	#88322	—	4	1	no	—
208	#88322	—	4	2	no	—
209	#88322	C₂×SD₁₆	1	2	yes	—
210	#19203	—	53	1	no	maximal, Sylow
211	C₂²×C₅₃	—	8	2	no	—
212	C₂²×C₅₃	—	8	2	no	—
213	C₂²×C₅₃	—	8	2	no	—
214	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
215	C₂×D₅₃	—	2	1	no	—
216	C₂×D₅₃	—	2	1	no	—
217	C₂×D₅₃	—	8	2	no	—
218	C₂×D₅₃	—	8	2	no	—
219	C₂×D₅₃	—	8	2	no	—
220	C₂×D₅₃	—	16	8	no	—
221	C₂×D₅₃	#460	1	2	yes	—
222	C₄×C₅₃	—	2	1	no	—
223	C₄×C₅₃	—	4	1	no	—
224	C₄×C₅₃	—	4	1	no	—
225	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
226	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₅₃	#576	1	1	yes	characteristic
228	C₄×C₅₃	#576	1	1	yes	characteristic
229	Dic₅₃	—	2	1	no	—
230	Dic₅₃	—	4	1	no	—
231	Dic₅₃	—	4	1	no	—
232	Dic₅₃	#460	1	2	yes	—
233	Dic₅₃	#472	1	2	yes	—
234	#3208	—	53	2	no	—
235	C₂×#493	—	53	1	no	—
236	#2960	—	53	1	no	—
237	#1688	—	53	2	no	—
238	#1688	—	53	2	no	—
239	#1668	—	53	1	no	—
240	#1668	—	53	1	no	—
241	#1668	—	53	1	no	—
242	#1668	D₅₃	1	1	yes	characteristic, complemented
243	#1564	—	53	1	no	—
244	#1545	—	53	2	no	—
245	C₂×C₅₃	—	16	2	no	—
246	C₂×C₅₃	C₂×#460	1	1	yes	characteristic
247	C₂×C₅₃	#3058	1	1	yes	characteristic
248	C₂×C₅₃	C₂×#472	1	1	yes	characteristic
249	D₅₃	—	2	2	no	—
250	D₅₃	—	16	2	no	—
251	C₂²×D₈	—	106	1	no	—
252	C₂²×D₈	—	106	1	no	—
253	#533	—	53	1	no	—
254	C₂×#127	—	53	2	no	—
255	#493	—	53	2	no	—
256	#493	—	53	1	no	—
257	#493	—	106	1	no	—
258	#493	—	106	1	no	—
259	#493	C₂×D₅₃	1	1	yes	characteristic
260	#492	—	106	2	no	—
261	#486	—	106	2	no	—
262	#460	—	53	2	no	—
263	#460	—	53	2	no	—
264	#460	—	53	2	no	—
265	#460	C₂×D₅₃	1	2	yes	complemented
266	#450	—	106	2	no	—
267	#450	—	106	2	no	—
268	#446	—	53	1	no	—
269	#446	—	53	1	no	—
270	#446	—	106	1	no	—
271	C₈×Q₈	—	53	1	no	—
272	C₈×Q₈	—	106	1	no	—
273	C₈×Q₈	C₂×D₅₃	1	1	yes	characteristic, complemented
274	#431	—	53	2	no	—
275	#424	—	106	1	no	—
276	#423	—	53	1	no	—
277	#405	—	106	1	no	—
278	C₂×C₄×C₈	—	53	1	no	—
279	#335	—	53	1	no	—
280	#335	C₂×D₅₃	1	1	yes	characteristic, complemented
281	#334	—	53	2	no	—
282	#331	—	53	2	no	—
283	#331	—	53	2	no	—
284	#331	—	53	2	no	—
285	#331	C₂×D₅₃	1	2	yes	complemented
286	C₅₃	#19203	1	1	yes	characteristic, complemented, Sylow
287	C₂²×D₄	—	106	2	no	—
288	C₂²×D₄	—	106	2	no	—
289	C₂²×D₄	—	106	2	no	—
290	C₂×SD₁₆	—	2	2	no	—
291	C₂×SD₁₆	—	106	2	no	—
292	C₂×SD₁₆	—	106	2	no	—
293	C₂×SD₁₆	—	106	2	no	—
294	C₂×D₈	—	2	1	no	—
295	C₂×D₈	—	2	1	no	—
296	C₂×D₈	—	106	2	no	—
297	C₂×D₈	—	106	2	no	—
298	C₂×D₈	—	106	1	no	—
299	C₂×D₈	—	106	1	no	—
300	C₂×D₈	—	212	4	no	—
301	C₂×D₈	—	212	4	no	—
302	C₂×M₁₆	—	106	1	no	—
303	C₂²×C₈	—	53	1	no	—
304	C₂²×C₈	—	53	1	no	—
305	C₄⋊Q₈	—	53	1	no	—
306	C₄⋊Q₈	—	53	1	no	—
307	#127	—	53	2	no	—
308	#127	—	106	2	no	—
309	#127	—	106	2	no	—
310	#127	—	106	2	no	—
311	#127	C₂²×D₅₃	1	2	yes	—
312	#125	—	106	1	no	—
313	C₂²⋊Q₈	—	53	1	no	—
314	C₂²⋊Q₈	—	53	1	no	—
315	C₂²⋊Q₈	—	106	1	no	—
316	C₄×Q₈	—	53	1	no	—
317	C₄×Q₈	—	106	1	no	—
318	C₄×Q₈	C₂²×D₅₃	1	1	yes	characteristic
319	#117	—	106	1	no	—
320	C₂×C₄²	—	53	1	no	—
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	53	1	no	—
323	C₄⋊C₈	—	53	2	no	—
324	C₄⋊C₈	—	106	1	no	—
325	C₄⋊C₈	—	106	1	no	—
326	C₄⋊C₈	—	106	1	no	—
327	C₄⋊C₈	—	106	1	no	—
328	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
329	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
330	#102	—	2	2	no	—
331	#102	—	106	2	no	—
332	#102	—	106	2	no	—
333	#102	—	106	2	no	—
334	C₂²⋊C₈	—	106	2	no	—
335	#97	—	106	1	no	—
336	#97	—	106	1	no	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	—	53	1	no	—
339	C₄×C₈	—	53	1	no	—
340	C₄×C₈	—	53	1	no	—
341	C₄×C₈	—	106	2	no	—
342	C₄×C₈	—	106	1	no	—
343	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
344	C₂⁴	—	212	2	no	—
345	C₂×Q₈	—	53	1	no	—
346	C₂×Q₈	—	106	1	no	—
347	C₂×Q₈	D₄×D₅₃	1	1	yes	characteristic
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	106	2	no	—
352	C₂×D₄	—	106	2	no	—
353	C₂×D₄	—	106	2	no	—
354	C₂×D₄	—	424	2	no	—
355	C₂×D₄	—	424	2	no	—
356	C₂×D₄	—	424	4	no	—
357	C₂×D₄	—	212	4	no	—
358	C₂×D₄	—	212	4	no	—
359	C₂×D₄	—	212	2	no	—
360	C₂×D₄	—	212	2	no	—
361	C₂×D₄	—	212	2	no	—
362	C₂²×C₄	—	53	1	no	—
363	C₂²×C₄	—	53	1	no	—
364	C₂²×C₄	—	53	1	no	—
365	SD₁₆	—	8	2	no	—
366	SD₁₆	—	424	2	no	—
367	SD₁₆	—	424	2	no	—
368	SD₁₆	—	424	2	no	—
369	D₈	—	4	2	no	—
370	D₈	—	4	2	no	—
371	D₈	—	212	2	no	—
372	D₈	—	212	4	no	—
373	D₈	—	212	4	no	—
374	D₈	—	212	2	no	—
375	M₁₆	—	212	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	53	1	no	—
379	C₂×C₈	—	53	4	no	—
380	C₂×C₈	—	53	1	no	—
381	C₂×C₈	—	106	2	no	—
382	C₂×C₈	—	106	1	no	—
383	C₂×C₈	—	106	2	no	—
384	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	53	1	no	—
388	C₄⋊C₄	—	106	1	no	—
389	C₄⋊C₄	—	106	1	no	—
390	C₄⋊C₄	—	106	1	no	—
391	C₄⋊C₄	—	106	1	no	—
392	C₄⋊C₄	—	106	1	no	—
393	C₄⋊C₄	—	106	1	no	—
394	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
395	C₂²⋊C₄	—	106	1	no	—
396	C₂²⋊C₄	—	106	1	no	—
397	C₄²	—	2	1	no	—
398	C₄²	—	53	1	no	—
399	C₄²	—	53	1	no	—
400	C₄²	—	53	1	no	—
401	C₄²	—	106	1	no	—
402	C₄²	C₂³×D₅₃	1	1	yes	characteristic
403	C₂³	—	4	2	no	—
404	C₂³	—	53	1	no	—
405	C₂³	—	424	4	no	—
406	C₂³	—	424	4	no	—
407	C₂³	—	424	4	no	—
408	C₂³	—	212	2	no	—
409	Q₈	—	2	1	no	—
410	Q₈	—	2	1	no	—
411	Q₈	—	106	1	no	—
412	Q₈	—	106	1	no	—
413	Q₈	—	212	2	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	8	2	no	—
419	D₄	—	424	2	no	—
420	D₄	—	424	4	no	—
421	D₄	—	424	4	no	—
422	D₄	—	424	4	no	—
423	D₄	—	212	2	no	—
424	D₄	—	212	2	no	—
425	D₄	—	212	2	no	—
426	D₄	—	212	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	53	1	no	—
431	C₂×C₄	—	53	2	no	—
432	C₂×C₄	—	53	2	no	—
433	C₂×C₄	—	53	1	no	—
434	C₂×C₄	—	106	2	no	—
435	C₂×C₄	—	106	1	no	—
436	C₂×C₄	—	106	1	no	—
437	C₂×C₄	—	106	1	no	—
438	C₂×C₄	—	106	1	no	—
439	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
440	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
441	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
442	C₈	—	2	1	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	2	no	—
445	C₈	—	53	2	no	—
446	C₈	—	106	1	no	—
447	C₈	—	212	1	no	—
448	C₈	—	212	2	no	—
449	C₈	SD₁₆×D₅₃	1	2	yes	—
450	C₂²	—	8	2	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	53	2	no	—
454	C₂²	—	848	8	no	—
455	C₂²	—	106	1	no	—
456	C₂²	—	106	1	no	—
457	C₂²	—	424	2	no	—
458	C₂²	—	424	2	no	—
459	C₂²	—	424	2	no	—
460	C₂²	#121×D₅₃	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	53	2	no	—
465	C₄	—	53	2	no	—
466	C₄	—	106	1	no	—
467	C₄	—	212	1	no	—
468	C₄	—	212	1	no	—
469	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
470	C₄	AGL(1,ℤ/8)×D₅₃	1	1	yes	characteristic
471	C₄	#16811424	1	1	yes	characteristic
472	C₄	#16811425	1	1	yes	characteristic
473	C₂	—	16	2	no	—
474	C₂	—	848	2	no	—
475	C₂	—	106	2	no	—
476	C₂	#460×D₅₃	1	1	yes	characteristic
477	C₂	#20284358	1	1	yes	characteristic
478	C₂	#472×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1668	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	#493×D₅₃	C₂
hypercenter	#1668	D₅₃
hypocenter	C₅₃	#19203
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1668

Complements

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

N	H ≅ G/N	type
1. #20285655	C₂	semidirect
3. #20283644	C₂	semidirect
4. #20274198	C₂	semidirect
5. #20274197	C₂	semidirect
6. #20274076	C₂	semidirect
7. #20274075	C₂	semidirect
8. #20274072	C₂	semidirect
9. #20273462	C₂	semidirect
10. #20273381	C₂	semidirect
11. C₅₃×#1668	C₂	semidirect
22. #16810824	C₂²	semidirect
23. #16810823	C₂²	semidirect
24. #16810820	C₂²	semidirect
27. #16810754	C₂²	semidirect
29. #16810750	C₂²	semidirect
31. C₈×Dic₁₀₆	C₂²	semidirect
37. #16810376	C₂²	semidirect
38. #16810373	C₂²	semidirect
39. #16810367	C₂²	semidirect
40. #16810366	C₂²	semidirect
41. #16810366	C₂²	semidirect
43. C₅₃×#460	C₂²	semidirect
44. C₈×Q₈×C₅₃	C₂²	semidirect
45. C₅₃×#335	C₂²	semidirect
46. C₅₃×#331	C₂²	semidirect
162. C₈×D₅₃	SD₁₆	semidirect
242. #1668	D₅₃	semidirect
265. #460	C₂×D₅₃	semidirect
273. C₈×Q₈	C₂×D₅₃	semidirect
280. #335	C₂×D₅₃	semidirect
285. #331	C₂×D₅₃	semidirect
286. C₅₃	#19203	semidirect

Maximal subgroups

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

subgroup	index
#20285655	2
#493×D₅₃	2
#20283644	2
#20274198	2
#20274197	2
#20274076	2
#20274075	2
#20274072	2
#20273462	2
#20273381	2
C₅₃×#1668	2
#19203	53