Subgroups — #27273882

Order 13568.

634 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20283347	C₂	1	1	yes	maximal, characteristic
2	#20283343	C₂	1	1	yes	maximal, characteristic
3	#382×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20272575	C₂	1	1	yes	maximal, characteristic, complemented
5	#20272574	C₂	1	1	yes	maximal, characteristic, complemented
6	#20272573	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅₃×#1286	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄⋊C₄×D₅₃	—	2	1	no	—
9	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic
10	#16810679	—	2	1	no	—
11	#16810679	—	2	1	no	—
12	#16810679	C₄	1	2	yes	complemented
13	#16810677	—	2	1	no	—
14	#16810676	C₂²	1	1	yes	characteristic
15	#16810675	—	2	1	no	—
16	#16810675	C₄	1	2	yes	complemented
17	#16810674	C₄	1	2	yes	complemented
18	#16810647	C₂²	1	1	yes	characteristic
19	#16810645	—	2	1	no	—
20	#16810586	—	2	1	no	—
21	#16810585	—	2	1	no	—
22	M₁₆×Dic₅₃	—	2	1	no	—
23	C₄×#11719912	C₄	1	2	yes	complemented
24	#16810489	C₂²	1	1	yes	characteristic
25	#16810488	—	2	1	no	—
26	#16810487	—	2	1	no	—
27	#16810487	C₄	1	2	yes	—
28	#95×D₅₃	—	2	1	no	—
29	#95×D₅₃	C₄	1	2	yes	—
30	C₅₃×#431	C₂²	1	1	yes	characteristic
31	C₅₃×#423	C₂²	1	1	yes	characteristic
32	C₅₃×#382	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₅₃	—	2	2	no	—
34	C₂²×C₄×D₅₃	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₅₃	D₄	1	1	yes	characteristic
37	C₂×#11719917	—	2	1	no	—
38	C₂×#11719912	—	2	2	no	—
39	C₂×C₄⋊Dic₅₃	—	2	1	no	—
40	C₂×#11719919	—	2	2	no	—
41	C₄⋊C₄×D₅₃	—	4	2	no	—
42	C₄⋊C₄×D₅₃	—	4	2	no	—
43	C₂×C₄×Dic₅₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₅₃	D₄	1	1	yes	characteristic
46	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₅₃	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₅₃	D₄	1	1	yes	characteristic
51	C₄²×D₅₃	D₄	1	1	yes	characteristic
52	C₄²×D₅₃	Q₈	1	1	yes	characteristic
53	C₄²×D₅₃	Q₈	1	1	yes	characteristic
54	C₄⋊#88322	—	2	1	no	—
55	C₄⋊#88322	—	2	1	no	—
56	C₄⋊#88322	C₂×C₄	1	2	yes	complemented
57	#13133146	—	2	2	no	—
58	C₂²⋊#88322	—	2	1	no	—
59	#13133129	—	2	2	no	—
60	#13133129	—	2	2	no	—
61	#13133129	—	2	2	no	—
62	#13133127	—	2	2	no	—
63	#13133127	—	2	2	no	—
64	C₄×#88322	C₂×C₄	1	2	yes	complemented
65	C₈×Dic₅₃	—	2	2	no	—
66	#13133124	—	2	1	no	—
67	#13133124	—	2	2	no	—
68	#13133124	—	2	2	no	—
69	#13133124	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₅₃	—	2	1	no	—
71	C₂×C₄⋊C₄×C₅₃	—	2	1	no	—
72	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic
73	C₄⋊C₈×C₅₃	—	2	1	no	—
74	C₄⋊C₈×C₅₃	—	2	1	no	—
75	C₄⋊C₈×C₅₃	C₂×C₄	1	2	yes	complemented
76	C₂²⋊C₈×C₅₃	—	2	1	no	—
77	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
78	#95×C₅₃	—	2	1	no	—
79	#95×C₅₃	C₂×C₄	1	2	yes	—
80	C₂³×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₅₃	—	2	2	no	—
82	C₂²×C₄×C₅₃	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₅₃	—	2	2	no	—
86	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₅₃	—	2	1	no	—
90	C₂×C₄×D₅₃	—	2	1	no	—
91	C₂×C₄×D₅₃	—	2	1	no	—
92	C₂×C₄×D₅₃	—	2	1	no	—
93	C₂×C₄×D₅₃	—	4	2	no	—
94	C₂×C₄×D₅₃	—	4	2	no	—
95	C₂×C₄×D₅₃	—	4	4	no	—
96	C₂×C₄×D₅₃	—	4	4	no	—
97	C₂×C₄×D₅₃	—	4	4	no	—
98	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
99	C₂×C₄×D₅₃	C₄²	1	1	yes	characteristic
100	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₅₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₅₃	C₄⋊C₄	1	1	yes	characteristic
110	M₁₆×C₅₃	—	4	1	no	—
111	M₁₆×C₅₃	—	4	1	no	—
112	C₂×C₈×C₅₃	—	2	2	no	—
113	C₂×C₈×C₅₃	—	2	2	no	—
114	C₄⋊C₄×C₅₃	—	4	1	no	—
115	C₄⋊C₄×C₅₃	—	4	1	no	—
116	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₅₃	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₅₃	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₅₃	C₂×Q₈	1	1	yes	characteristic
120	C₄⋊Dic₅₃	—	4	1	no	—
121	C₄⋊Dic₅₃	—	4	1	no	—
122	#11719919	—	4	4	no	—
123	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
124	C₄×Dic₅₃	C₄²	1	1	yes	characteristic
125	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
127	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
128	C₄×Dic₅₃	C₂²⋊C₄	1	1	yes	characteristic
129	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₅₃	C₄⋊C₄	1	1	yes	characteristic
135	#11719917	—	4	1	no	—
136	#11719917	—	4	1	no	—
137	C₂×#88322	—	2	2	no	—
138	C₂×#88322	—	2	2	no	—
139	#11719912	—	4	4	no	—
140	C₂³×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂²×D₅₃	—	2	1	no	—
142	C₂²×D₅₃	—	2	1	no	—
143	C₂²×D₅₃	—	2	2	no	—
144	C₂²×D₅₃	—	2	2	no	—
145	C₂²×D₅₃	#95	1	1	yes	characteristic
146	C₂²×D₅₃	#95	1	1	yes	characteristic
147	C₂×C₄×C₅₃	—	4	1	no	—
148	C₂×C₄×C₅₃	—	4	1	no	—
149	C₂×C₄×C₅₃	—	4	2	no	—
150	C₂×C₄×C₅₃	—	4	2	no	—
151	C₂×C₄×C₅₃	—	4	2	no	—
152	C₂×C₄×C₅₃	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₅₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₅₃	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
161	C₂×C₄×C₅₃	#137	1	1	yes	characteristic
162	C₂×Dic₅₃	—	2	1	no	—
163	C₂×Dic₅₃	—	2	1	no	—
164	C₂×Dic₅₃	—	4	1	no	—
165	C₂×Dic₅₃	—	4	1	no	—
166	C₂×Dic₅₃	—	4	2	no	—
167	C₂×Dic₅₃	—	4	2	no	—
168	C₂×Dic₅₃	—	4	2	no	—
169	C₂×Dic₅₃	#95	1	1	yes	characteristic
170	C₂×Dic₅₃	#95	1	1	yes	characteristic
171	C₂×Dic₅₃	#95	1	1	yes	characteristic
172	C₂×Dic₅₃	#95	1	1	yes	characteristic
173	C₂×Dic₅₃	#95	1	1	yes	characteristic
174	C₂×Dic₅₃	#95	1	1	yes	characteristic
175	C₄×D₅₃	—	2	2	no	—
176	C₄×D₅₃	—	2	2	no	—
177	C₄×D₅₃	—	2	2	no	—
178	C₄×D₅₃	—	2	2	no	—
179	C₄×D₅₃	—	2	1	no	—
180	C₄×D₅₃	—	2	1	no	—
181	C₄×D₅₃	—	2	1	no	—
182	C₄×D₅₃	—	2	1	no	—
183	C₄×D₅₃	—	2	1	no	—
184	C₄×D₅₃	—	2	1	no	—
185	C₄×D₅₃	—	2	1	no	—
186	C₄×D₅₃	—	2	1	no	—
187	C₄×D₅₃	—	4	1	no	—
188	C₄×D₅₃	—	4	1	no	—
189	C₄×D₅₃	—	4	1	no	—
190	C₄×D₅₃	—	4	1	no	—
191	C₄×D₅₃	—	8	8	no	—
192	C₈×C₅₃	—	4	2	no	—
193	C₈×C₅₃	—	4	2	no	—
194	#88322	—	4	2	no	—
195	#88322	—	4	2	no	—
196	#7959	—	53	1	no	maximal, Sylow
197	C₂²×C₅₃	—	2	1	no	—
198	C₂²×C₅₃	—	2	1	no	—
199	C₂²×C₅₃	C₂×#95	1	1	yes	characteristic
200	C₂²×C₅₃	#418	1	1	yes	characteristic
201	C₂²×C₅₃	#419	1	1	yes	characteristic
202	C₂×D₅₃	—	2	4	no	—
203	C₂×D₅₃	—	2	4	no	—
204	C₂×D₅₃	—	2	1	no	—
205	C₂×D₅₃	—	2	1	no	—
206	C₂×D₅₃	—	2	1	no	—
207	C₂×D₅₃	—	2	1	no	—
208	C₂×D₅₃	H(3,ℤ/4)	1	2	yes	—
209	C₂×D₅₃	#344	1	2	yes	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	2	1	no	—
212	C₄×C₅₃	—	2	1	no	—
213	C₄×C₅₃	—	2	1	no	—
214	C₄×C₅₃	—	8	2	no	—
215	C₄×C₅₃	#417	1	1	yes	characteristic
216	C₄×C₅₃	#417	1	1	yes	characteristic
217	C₄×C₅₃	#428	1	1	yes	characteristic
218	C₄×C₅₃	#428	1	1	yes	characteristic
219	Dic₅₃	—	2	1	no	—
220	Dic₅₃	—	2	1	no	—
221	Dic₅₃	—	2	1	no	—
222	Dic₅₃	—	2	1	no	—
223	Dic₅₃	—	2	1	no	—
224	Dic₅₃	—	2	1	no	—
225	Dic₅₃	—	8	2	no	—
226	#2920	—	53	1	no	—
227	#2920	—	53	1	no	—
228	C₂×#382	—	53	1	no	—
229	#1286	—	53	1	no	—
230	#1286	—	53	1	no	—
231	#1286	—	53	1	no	—
232	#1286	D₅₃	1	1	yes	characteristic, complemented
233	C₂×C₅₃	—	2	1	no	—
234	C₂×C₅₃	—	2	1	no	—
235	C₂×C₅₃	C₂×H(3,ℤ/4)	1	1	yes	characteristic
236	C₂×C₅₃	#1736	1	1	yes	characteristic
237	C₂×C₅₃	C₂×#344	1	1	yes	characteristic
238	D₅₃	—	2	2	no	—
239	D₅₃	—	2	2	no	—
240	C₂²×C₄⋊C₄	—	106	1	no	—
241	C₂²×C₄²	—	53	1	no	—
242	#432	—	53	2	no	—
243	#432	—	106	1	no	—
244	#432	—	106	1	no	—
245	#432	—	106	1	no	—
246	#431	—	53	1	no	—
247	#431	—	53	2	no	—
248	#431	—	53	2	no	—
249	#431	—	106	1	no	—
250	#431	C₂×D₅₃	1	1	yes	characteristic
251	#423	—	53	1	no	—
252	#423	—	106	1	no	—
253	#423	C₂×D₅₃	1	1	yes	characteristic
254	#407	—	106	1	no	—
255	#407	—	106	1	no	—
256	C₄×M₁₆	—	53	2	no	—
257	C₄×M₁₆	—	106	1	no	—
258	#382	—	53	1	no	—
259	#382	—	53	2	no	—
260	#382	—	106	1	no	—
261	#382	—	106	1	no	—
262	#382	C₂×D₅₃	1	1	yes	characteristic
263	C₂×#95	—	53	2	no	—
264	C₂×#95	—	106	1	no	—
265	C₅₃	#7959	1	1	yes	characteristic, complemented, Sylow
266	C₂³×C₄	—	53	1	no	—
267	C₂³×C₄	—	53	1	no	—
268	C₂³×C₄	—	53	1	no	—
269	C₂³×C₄	—	106	2	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	106	2	no	—
272	C₂×M₁₆	—	106	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	106	2	no	—
275	C₂×C₄⋊C₄	—	106	1	no	—
276	C₂×C₄⋊C₄	—	212	2	no	—
277	C₂×C₄⋊C₄	—	212	2	no	—
278	C₂×C₄²	—	53	1	no	—
279	C₂×C₄²	—	53	1	no	—
280	C₂×C₄²	—	53	1	no	—
281	C₂×C₄²	—	53	1	no	—
282	C₂×C₄²	—	53	1	no	—
283	C₂×C₄²	—	53	1	no	—
284	C₂×C₄²	—	53	1	no	—
285	C₂×C₄²	—	53	1	no	—
286	C₂×C₄²	—	53	1	no	—
287	C₂×C₄²	—	53	1	no	—
288	C₂×C₄²	—	53	1	no	—
289	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	53	2	no	—
293	C₄⋊C₈	—	106	2	no	—
294	C₄⋊C₈	—	106	1	no	—
295	C₄⋊C₈	—	106	1	no	—
296	C₄⋊C₈	C₄×D₅₃	1	2	yes	complemented
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	106	2	no	—
299	C₂²⋊C₈	—	106	2	no	—
300	C₂²⋊C₈	—	106	2	no	—
301	C₂²⋊C₈	—	106	1	no	—
302	#97	—	106	2	no	—
303	#97	—	106	2	no	—
304	C₄×C₈	—	53	2	no	—
305	C₄×C₈	—	106	2	no	—
306	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
307	#95	—	2	1	no	—
308	#95	—	53	2	no	—
309	#95	—	106	2	no	—
310	#95	—	106	2	no	—
311	#95	—	106	1	no	—
312	#95	C₄×D₅₃	1	2	yes	—
313	C₂⁴	—	53	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	53	1	no	—
316	C₂²×C₄	—	53	1	no	—
317	C₂²×C₄	—	53	1	no	—
318	C₂²×C₄	—	53	1	no	—
319	C₂²×C₄	—	53	1	no	—
320	C₂²×C₄	—	53	1	no	—
321	C₂²×C₄	—	53	1	no	—
322	C₂²×C₄	—	53	1	no	—
323	C₂²×C₄	—	53	1	no	—
324	C₂²×C₄	—	53	1	no	—
325	C₂²×C₄	—	53	1	no	—
326	C₂²×C₄	—	53	1	no	—
327	C₂²×C₄	—	53	1	no	—
328	C₂²×C₄	—	53	1	no	—
329	C₂²×C₄	—	53	1	no	—
330	C₂²×C₄	—	106	1	no	—
331	C₂²×C₄	—	106	1	no	—
332	C₂²×C₄	—	106	1	no	—
333	C₂²×C₄	—	106	1	no	—
334	C₂²×C₄	—	106	2	no	—
335	C₂²×C₄	—	212	2	no	—
336	C₂²×C₄	—	212	2	no	—
337	C₂²×C₄	—	212	4	no	—
338	C₂²×C₄	—	212	4	no	—
339	C₂²×C₄	—	212	4	no	—
340	C₂²×C₄	C₂×C₄×D₅₃	1	1	yes	characteristic
341	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
342	C₂²×C₄	D₄×D₅₃	1	1	yes	characteristic
343	M₁₆	—	4	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	212	4	no	—
346	M₁₆	—	212	1	no	—
347	M₁₆	—	212	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	106	2	no	—
351	C₂×C₈	—	106	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	212	4	no	—
355	C₄⋊C₄	—	212	1	no	—
356	C₄⋊C₄	—	212	1	no	—
357	C₄²	—	53	1	no	—
358	C₄²	—	53	1	no	—
359	C₄²	—	53	1	no	—
360	C₄²	—	53	1	no	—
361	C₄²	—	53	1	no	—
362	C₄²	—	53	1	no	—
363	C₄²	—	53	1	no	—
364	C₄²	—	53	1	no	—
365	C₄²	—	53	1	no	—
366	C₄²	—	53	1	no	—
367	C₄²	—	53	1	no	—
368	C₄²	—	53	1	no	—
369	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
370	C₄²	C₂×C₄×D₅₃	1	1	yes	characteristic
371	C₄²	D₄×D₅₃	1	1	yes	characteristic
372	C₄²	Q₈×D₅₃	1	1	yes	characteristic
373	C₂³	—	53	1	no	—
374	C₂³	—	53	1	no	—
375	C₂³	—	106	2	no	—
376	C₂³	—	106	2	no	—
377	C₂³	—	106	1	no	—
378	C₂³	—	106	1	no	—
379	C₂³	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	53	1	no	—
386	C₂×C₄	—	53	1	no	—
387	C₂×C₄	—	53	1	no	—
388	C₂×C₄	—	53	1	no	—
389	C₂×C₄	—	53	1	no	—
390	C₂×C₄	—	53	1	no	—
391	C₂×C₄	—	106	2	no	—
392	C₂×C₄	—	106	2	no	—
393	C₂×C₄	—	106	2	no	—
394	C₂×C₄	—	106	2	no	—
395	C₂×C₄	—	106	1	no	—
396	C₂×C₄	—	106	1	no	—
397	C₂×C₄	—	106	1	no	—
398	C₂×C₄	—	106	1	no	—
399	C₂×C₄	—	106	1	no	—
400	C₂×C₄	—	106	1	no	—
401	C₂×C₄	—	106	1	no	—
402	C₂×C₄	—	106	1	no	—
403	C₂×C₄	—	106	1	no	—
404	C₂×C₄	—	106	1	no	—
405	C₂×C₄	—	424	8	no	—
406	C₂×C₄	—	212	1	no	—
407	C₂×C₄	—	212	1	no	—
408	C₂×C₄	—	212	1	no	—
409	C₂×C₄	—	212	1	no	—
410	C₂×C₄	—	212	1	no	—
411	C₂×C₄	—	212	1	no	—
412	C₂×C₄	—	212	2	no	—
413	C₂×C₄	—	212	2	no	—
414	C₂×C₄	—	212	2	no	—
415	C₂×C₄	C₄²×D₅₃	1	1	yes	characteristic
416	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
417	C₂×C₄	C₂²⋊C₄×D₅₃	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
420	C₂×C₄	C₄⋊C₄×D₅₃	1	1	yes	characteristic
421	C₂×C₄	#13133241	1	1	yes	characteristic
422	C₂×C₄	#13133244	1	1	yes	characteristic
423	C₂×C₄	#13133246	1	1	yes	characteristic
424	C₂×C₄	#13133249	1	1	yes	characteristic
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₈	—	212	2	no	—
428	C₈	—	212	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	53	2	no	—
432	C₂²	—	53	2	no	—
433	C₂²	—	106	4	no	—
434	C₂²	—	106	4	no	—
435	C₂²	—	106	1	no	—
436	C₂²	—	106	1	no	—
437	C₂²	—	106	1	no	—
438	C₂²	—	106	1	no	—
439	C₂²	#95×D₅₃	1	1	yes	characteristic
440	C₂²	#16810626	1	1	yes	characteristic
441	C₂²	#16810630	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	8	2	no	—
447	C₄	—	106	1	no	—
448	C₄	—	106	1	no	—
449	C₄	—	106	1	no	—
450	C₄	—	106	1	no	—
451	C₄	—	106	1	no	—
452	C₄	—	106	1	no	—
453	C₄	—	424	2	no	—
454	C₄	#16810621	1	1	yes	characteristic
455	C₄	#16810623	1	1	yes	characteristic
456	C₄	#16810662	1	1	yes	characteristic
457	C₄	#16810664	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	106	2	no	—
461	C₂	—	106	2	no	—
462	C₂	H(3,ℤ/4)×D₅₃	1	1	yes	characteristic
463	C₂	#20274433	1	1	yes	characteristic
464	C₂	#344×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#95×D₅₃
commutator	C₂×C₄×C₅₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₅₃
Fitting	C₅₃×#1286	C₂
socle	C₂²×C₅₃	C₂×#95
prime radical	C₂³×D₅₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₅₃	C₂³
hypercenter	#1286	D₅₃
hypocenter	C₅₃	#7959
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1286

Complements

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

N	H ≅ G/N	type
4. #20272575	C₂	semidirect
5. #20272574	C₂	semidirect
6. #20272573	C₂	semidirect
7. C₅₃×#1286	C₂	semidirect
12. #16810679	C₄	semidirect
16. #16810675	C₄	semidirect
17. #16810674	C₄	semidirect
23. C₄×#11719912	C₄	semidirect
56. C₄⋊#88322	C₂×C₄	semidirect
64. C₄×#88322	C₂×C₄	semidirect
75. C₄⋊C₈×C₅₃	C₂×C₄	semidirect
77. C₄×C₈×C₅₃	C₂×C₄	semidirect
232. #1286	D₅₃	semidirect
265. C₅₃	#7959	semidirect
296. C₄⋊C₈	C₄×D₅₃	semidirect
306. C₄×C₈	C₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
#20283347	2
#20283343	2
#382×D₅₃	2
#20272575	2
#20272574	2
#20272573	2
C₅₃×#1286	2
#7959	53