Subgroups — D₅₃×#1695 #27366623

Order 13568.

694 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#476×D₅₃	C₂	1	2	yes	maximal
3	#436×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20274239	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274238	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274237	C₂	1	2	yes	maximal, complemented
7	#20274236	C₂	1	2	yes	maximal, complemented
8	#20274235	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#333×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1695	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	—	2	1	no	—
13	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
14	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
15	#16811028	C₂²	1	1	yes	characteristic, complemented
16	#16811027	—	2	1	no	—
17	#16811027	—	2	1	no	—
18	#16811026	C₂²	1	2	yes	complemented
19	#16810914	C₂²	1	2	yes	—
20	#16810913	C₂²	1	2	yes	—
21	#16810912	—	2	2	no	—
22	#16810911	—	2	2	no	—
23	#16810910	C₂²	1	2	yes	—
24	#16810702	C₂²	1	1	yes	characteristic
25	#16810701	C₂²	1	1	yes	characteristic
26	#16810700	C₂²	1	1	yes	characteristic
27	#16810699	—	2	1	no	—
28	#16810698	—	2	1	no	—
29	#107×D₅₃	—	2	1	no	—
30	#107×D₅₃	—	2	1	no	—
31	#106×D₅₃	—	2	2	no	—
32	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
34	#102×D₅₃	—	2	2	no	—
35	C₂²⋊C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810374	C₂²	1	1	yes	characteristic, complemented
38	#16810373	C₂²	1	2	yes	complemented
39	#16810372	C₂²	1	2	yes	complemented
40	#16810371	C₂²	1	2	yes	complemented
41	#16810371	C₂²	1	2	yes	complemented
42	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#476	C₂²	1	2	yes	—
44	C₅₃×#436	C₂²	1	1	yes	characteristic
45	C₅₃×#334	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#333	C₂²	1	2	yes	complemented
47	C₂×Q₈×D₅₃	—	2	2	no	—
48	C₂×D₄×D₅₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₅₃	—	2	1	no	—
50	C₂×#11719917	—	2	1	no	—
51	C₂×#11719912	—	2	1	no	—
52	C₂×#11719912	—	2	1	no	—
53	M₁₆×D₅₃	—	4	4	no	—
54	C₂×C₈×D₅₃	—	2	1	no	—
55	C₂×C₈×D₅₃	—	2	2	no	—
56	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
58	#13133217	C₂³	1	2	yes	—
59	#13133216	—	2	2	no	—
60	#13133216	—	2	2	no	—
61	#13133215	—	2	2	no	—
62	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
63	D₄×Dic₅₃	D₄	1	1	yes	characteristic
64	#13133179	D₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₅₃	—	2	1	no	—
66	#13133177	—	2	1	no	—
67	C₄⋊C₄×D₅₃	—	2	2	no	—
68	C₄⋊C₄×D₅₃	—	2	2	no	—
69	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
70	C₂²⋊C₄×D₅₃	—	2	1	no	—
71	C₄²×D₅₃	C₂³	1	1	yes	characteristic
72	#13133151	—	2	1	no	—
73	#13133151	—	2	1	no	—
74	#13133150	—	2	2	no	—
75	#13133150	—	2	2	no	—
76	#13133149	—	2	2	no	—
77	#13133148	—	2	2	no	—
78	#13133148	—	2	2	no	—
79	C₄⋊#88322	C₂³	1	1	yes	characteristic
80	C₄⋊#88322	C₂³	1	2	yes	—
81	#13133146	—	2	2	no	—
82	#13133146	—	2	1	no	—
83	#13133139	—	2	2	no	—
84	#13133138	—	2	2	no	—
85	#13133137	—	2	2	no	—
86	C₂²⋊#88322	—	2	1	no	—
87	#13133129	—	2	1	no	—
88	#13133129	—	2	1	no	—
89	C₄×#88322	C₂³	1	1	yes	characteristic
90	C₈×Dic₅₃	D₄	1	1	yes	characteristic
91	C₈×Dic₅₃	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₅₃	—	2	1	no	—
93	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
94	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
95	#107×C₅₃	—	2	1	no	—
96	#107×C₅₃	—	2	1	no	—
97	#106×C₅₃	—	2	2	no	—
98	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
100	#102×C₅₃	—	2	2	no	—
101	C₂²⋊C₈×C₅₃	—	2	1	no	—
102	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
103	C₂³×D₅₃	—	2	1	no	—
104	C₂×Q₈×C₅₃	—	2	2	no	—
105	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₅₃	—	2	1	no	—
107	C₂×C₂²⋊D₅₃	—	2	1	no	—
108	C₂²×Dic₅₃	—	2	1	no	—
109	Q₈×D₅₃	—	8	4	no	—
110	D₄×D₅₃	—	2	4	no	—
111	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₅₃	—	2	1	no	—
113	C₂×C₄×D₅₃	—	2	1	no	—
114	C₂×C₄×D₅₃	—	2	1	no	—
115	C₂×C₄×D₅₃	—	4	2	no	—
116	C₂×C₄×D₅₃	—	4	2	no	—
117	C₂×C₄×D₅₃	—	4	2	no	—
118	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
121	C₂×Dic₁₀₆	—	2	2	no	—
122	C₂×Dic₁₀₆	—	4	2	no	—
123	M₁₆×C₅₃	—	4	2	no	—
124	C₂×C₈×C₅₃	—	2	1	no	—
125	C₂×C₈×C₅₃	—	2	2	no	—
126	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₅₃	—	2	2	no	—
129	C₄⋊C₄×C₅₃	—	2	2	no	—
130	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₂²⋊C₄×C₅₃	—	2	1	no	—
132	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₅₃	—	2	1	no	—
134	#11719921	—	2	1	no	—
135	#11719921	—	2	1	no	—
136	C₄⋊Dic₅₃	—	2	2	no	—
137	C₄⋊Dic₅₃	—	2	2	no	—
138	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
139	#11719919	—	2	1	no	—
140	#11719919	—	4	2	no	—
141	#11719919	—	4	2	no	—
142	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₅₃	#41	1	1	yes	characteristic
145	#11719917	—	4	2	no	—
146	C₂×#88322	—	2	1	no	—
147	C₂×#88322	—	2	2	no	—
148	C₂×#88322	C₂×D₄	1	1	yes	characteristic
149	C₂×#88322	C₂×D₄	1	1	yes	characteristic
150	#11719912	—	4	2	no	—
151	#11719912	—	4	2	no	—
152	C₈×D₅₃	—	2	2	no	—
153	C₈×D₅₃	—	4	2	no	—
154	C₈×D₅₃	—	4	4	no	—
155	C₈×D₅₃	SD₁₆	1	4	yes	—
156	C₂³×C₅₃	—	2	1	no	—
157	C₂²×D₅₃	—	2	1	no	—
158	C₂²×D₅₃	—	4	2	no	—
159	C₂²×D₅₃	—	4	2	no	—
160	C₂²×D₅₃	—	4	2	no	—
161	C₂²×D₅₃	#121	1	1	yes	characteristic
162	Q₈×C₅₃	—	8	2	no	—
163	D₄×C₅₃	—	2	2	no	—
164	C₂×C₄×C₅₃	—	2	1	no	—
165	C₂×C₄×C₅₃	—	4	1	no	—
166	C₂×C₄×C₅₃	—	4	1	no	—
167	C₂×C₄×C₅₃	—	4	2	no	—
168	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₅₃	—	4	2	no	—
172	C₂×Dic₅₃	—	2	1	no	—
173	C₂×Dic₅₃	—	4	2	no	—
174	C₂×Dic₅₃	—	4	2	no	—
175	C₂×Dic₅₃	#121	1	1	yes	characteristic
176	C₂×Dic₅₃	#121	1	1	yes	characteristic
177	C₂×Dic₅₃	#121	1	1	yes	characteristic
178	D₂₁₂	—	2	2	no	—
179	C₄×D₅₃	—	2	2	no	—
180	C₄×D₅₃	—	4	2	no	—
181	C₄×D₅₃	—	4	1	no	—
182	C₄×D₅₃	—	4	1	no	—
183	C₄×D₅₃	—	4	2	no	—
184	C₄×D₅₃	—	8	4	no	—
185	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
186	C₄×D₅₃	#137	1	2	yes	—
187	C₄×D₅₃	#137	1	4	yes	—
188	Dic₁₀₆	—	8	4	no	—
189	Dic₁₀₆	—	8	2	no	—
190	C₈×C₅₃	—	2	1	no	—
191	C₈×C₅₃	—	4	1	no	—
192	C₈×C₅₃	—	4	2	no	—
193	C₈×C₅₃	C₂×SD₁₆	1	2	yes	—
194	#88322	—	2	1	no	—
195	#88322	—	4	1	no	—
196	#88322	—	4	2	no	—
197	#88322	C₂×SD₁₆	1	2	yes	—
198	C₂×#1695	—	53	1	no	maximal, Sylow
199	C₂²×C₅₃	—	4	1	no	—
200	C₂²×C₅₃	—	4	1	no	—
201	C₂²×C₅₃	—	4	1	no	—
202	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
203	C₂×D₅₃	—	4	1	no	—
204	C₂×D₅₃	—	4	1	no	—
205	C₂×D₅₃	—	4	1	no	—
206	C₂×D₅₃	—	8	4	no	—
207	C₂×D₅₃	#461	1	2	yes	—
208	C₂×D₅₃	#470	1	2	yes	—
209	C₂×D₅₃	#472	1	2	yes	—
210	C₄×C₅₃	—	2	1	no	—
211	C₄×C₅₃	—	4	1	no	—
212	C₄×C₅₃	—	8	2	no	—
213	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
214	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
215	C₄×C₅₃	C₂×#137	1	2	yes	—
216	Dic₅₃	—	2	1	no	—
217	Dic₅₃	—	4	1	no	—
218	Dic₅₃	—	8	2	no	—
219	Dic₅₃	#461	1	2	yes	—
220	Dic₅₃	#470	1	2	yes	—
221	C₂×#500	—	53	1	no	—
222	C₂×#476	—	53	2	no	—
223	C₂×#436	—	53	1	no	—
224	#1695	—	53	1	no	—
225	#1695	—	53	2	no	—
226	#1695	—	53	1	no	—
227	#1695	—	53	1	no	—
228	#1695	—	53	2	no	—
229	#1695	D₅₃	1	1	yes	characteristic, direct product factor
230	C₂×#334	—	53	1	no	—
231	C₂×#333	—	53	2	no	—
232	C₂×C₅₃	—	8	1	no	—
233	C₂×C₅₃	C₂×#461	1	1	yes	characteristic
234	C₂×C₅₃	C₂×#470	1	1	yes	characteristic
235	C₂×C₅₃	C₂×#472	1	1	yes	characteristic
236	D₅₃	—	8	1	no	—
237	D₅₃	#1695	1	4	yes	direct product factor
238	C₂²×M₁₆	—	106	1	no	—
239	C₂×C₄⋊Q₈	—	53	2	no	—
240	C₂×C₄×D₄	—	53	1	no	—
241	#500	—	53	2	no	—
242	#500	—	53	1	no	—
243	#500	—	106	1	no	—
244	#500	—	106	1	no	—
245	#500	C₂×D₅₃	1	1	yes	characteristic, complemented
246	#476	—	53	2	no	—
247	#476	—	53	2	no	—
248	#476	—	53	2	no	—
249	#476	—	106	2	no	—
250	#476	—	106	2	no	—
251	#476	C₂×D₅₃	1	2	yes	—
252	#436	—	53	1	no	—
253	#436	—	53	1	no	—
254	#436	—	53	1	no	—
255	#436	—	106	1	no	—
256	#436	—	106	1	no	—
257	#436	C₂×D₅₃	1	1	yes	characteristic
258	C₂×#107	—	106	1	no	—
259	C₂×#107	—	106	1	no	—
260	C₂×#106	—	106	2	no	—
261	C₂×C₄⋊C₈	—	53	1	no	—
262	C₂×C₄⋊C₈	—	53	2	no	—
263	C₂×#102	—	106	2	no	—
264	C₂×C₂²⋊C₈	—	106	1	no	—
265	C₂×C₄×C₈	—	53	1	no	—
266	#334	—	53	2	no	—
267	#334	—	53	1	no	—
268	#334	C₂×D₅₃	1	1	yes	characteristic, complemented
269	#333	—	53	2	no	—
270	#333	—	53	2	no	—
271	#333	—	53	2	no	—
272	#333	C₂×D₅₃	1	2	yes	complemented
273	C₅₃	C₂×#1695	1	1	yes	characteristic, complemented, Sylow
274	C₂²×Q₈	—	106	2	no	—
275	C₂²×D₄	—	53	1	no	—
276	C₂³×C₄	—	106	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	106	1	no	—
279	C₂×M₁₆	—	106	1	no	—
280	C₂×M₁₆	—	106	1	no	—
281	C₂×M₁₆	—	212	4	no	—
282	C₂²×C₈	—	53	1	no	—
283	C₂²×C₈	—	53	1	no	—
284	C₂²×C₈	—	106	1	no	—
285	C₂²×C₈	—	106	2	no	—
286	C₄⋊Q₈	—	53	2	no	—
287	C₄⋊Q₈	—	106	2	no	—
288	C₄⋊Q₈	—	106	2	no	—
289	C₄⋊Q₈	—	106	2	no	—
290	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
291	C₄×D₄	—	53	1	no	—
292	C₄×D₄	—	53	1	no	—
293	C₄×D₄	—	53	1	no	—
294	C₄×D₄	—	106	1	no	—
295	C₄×D₄	—	106	1	no	—
296	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	53	1	no	—
298	C₂×C₄⋊C₄	—	106	2	no	—
299	C₂×C₄⋊C₄	—	106	2	no	—
300	C₂×C₂²⋊C₄	—	106	1	no	—
301	C₂×C₄²	—	53	1	no	—
302	#107	—	2	1	no	—
303	#107	—	2	1	no	—
304	#107	—	106	2	no	—
305	#107	—	106	2	no	—
306	#107	—	106	1	no	—
307	#107	—	106	1	no	—
308	#106	—	2	2	no	—
309	#106	—	106	2	no	—
310	#106	—	106	2	no	—
311	#106	—	106	2	no	—
312	C₄⋊C₈	—	53	1	no	—
313	C₄⋊C₈	—	53	2	no	—
314	C₄⋊C₈	—	106	1	no	—
315	C₄⋊C₈	—	106	2	no	—
316	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
318	#102	—	2	2	no	—
319	#102	—	106	2	no	—
320	#102	—	106	2	no	—
321	#102	—	106	2	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	106	1	no	—
324	C₂²⋊C₈	—	106	1	no	—
325	C₂²⋊C₈	—	106	1	no	—
326	C₄×C₈	—	53	1	no	—
327	C₄×C₈	—	53	1	no	—
328	C₄×C₈	—	53	1	no	—
329	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
330	C₂⁴	—	106	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	106	2	no	—
333	C₂×Q₈	—	424	4	no	—
334	C₂×Q₈	—	212	2	no	—
335	C₂×D₄	—	53	1	no	—
336	C₂×D₄	—	106	4	no	—
337	C₂×D₄	—	106	1	no	—
338	C₂×D₄	D₄×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	—	53	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	—	212	2	no	—
348	C₂²×C₄	—	212	2	no	—
349	C₂²×C₄	—	212	2	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	212	2	no	—
352	M₁₆	—	212	2	no	—
353	M₁₆	—	212	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	53	1	no	—
357	C₂×C₈	—	53	4	no	—
358	C₂×C₈	—	53	1	no	—
359	C₂×C₈	—	106	2	no	—
360	C₂×C₈	—	106	1	no	—
361	C₂×C₈	—	106	2	no	—
362	C₂×C₈	—	212	2	no	—
363	C₂×C₈	—	212	4	no	—
364	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
365	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	53	1	no	—
369	C₄⋊C₄	—	106	1	no	—
370	C₄⋊C₄	—	106	2	no	—
371	C₄⋊C₄	—	106	2	no	—
372	C₄⋊C₄	—	212	2	no	—
373	C₄⋊C₄	—	212	2	no	—
374	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	106	1	no	—
377	C₂²⋊C₄	—	106	1	no	—
378	C₂²⋊C₄	—	106	1	no	—
379	C₄²	—	53	1	no	—
380	C₄²	—	53	1	no	—
381	C₄²	—	53	1	no	—
382	C₄²	C₂³×D₅₃	1	1	yes	characteristic
383	C₂³	—	2	1	no	—
384	C₂³	—	53	1	no	—
385	C₂³	—	106	1	no	—
386	C₂³	—	212	2	no	—
387	C₂³	—	212	2	no	—
388	C₂³	—	212	2	no	—
389	Q₈	—	8	2	no	—
390	Q₈	—	424	2	no	—
391	Q₈	—	424	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	106	2	no	—
394	D₄	—	212	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	53	1	no	—
400	C₂×C₄	—	53	1	no	—
401	C₂×C₄	—	53	2	no	—
402	C₂×C₄	—	53	2	no	—
403	C₂×C₄	—	53	4	no	—
404	C₂×C₄	—	53	1	no	—
405	C₂×C₄	—	106	2	no	—
406	C₂×C₄	—	106	1	no	—
407	C₂×C₄	—	424	4	no	—
408	C₂×C₄	—	212	2	no	—
409	C₂×C₄	—	212	2	no	—
410	C₂×C₄	—	212	2	no	—
411	C₂×C₄	—	212	2	no	—
412	C₂×C₄	—	212	1	no	—
413	C₂×C₄	—	212	1	no	—
414	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
416	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
417	C₈	—	2	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	53	2	no	—
421	C₈	—	106	1	no	—
422	C₈	—	212	1	no	—
423	C₈	—	212	2	no	—
424	C₈	SD₁₆×D₅₃	1	2	yes	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	53	2	no	—
429	C₂²	—	53	2	no	—
430	C₂²	—	53	2	no	—
431	C₂²	—	424	4	no	—
432	C₂²	—	212	1	no	—
433	C₂²	—	212	1	no	—
434	C₂²	—	212	1	no	—
435	C₂²	#121×D₅₃	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	53	2	no	—
440	C₄	—	53	2	no	—
441	C₄	—	106	1	no	—
442	C₄	—	424	2	no	—
443	C₄	—	212	1	no	—
444	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
445	C₄	#137×D₅₃	1	2	yes	—
446	C₄	#137×D₅₃	1	1	yes	characteristic
447	C₂	—	8	1	no	—
448	C₂	—	53	4	no	—
449	C₂	—	424	1	no	—
450	C₂	#461×D₅₃	1	1	yes	characteristic
451	C₂	#470×D₅₃	1	1	yes	characteristic
452	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×#1695	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×D₄×D₅₃	D₄
hypercenter	#1695	D₅₃
hypocenter	C₅₃	C₂×#1695
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1695

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
4. #20274239	C₂	semidirect
5. #20274238	C₂	semidirect
6. #20274237	C₂	semidirect
7. #20274236	C₂	semidirect
8. #20274235	C₂	semidirect
9. #334×D₅₃	C₂	semidirect
10. #333×D₅₃	C₂	semidirect
11. C₅₃×#1695	C₂	semidirect
15. #16811028	C₂²	semidirect
18. #16811026	C₂²	semidirect
37. #16810374	C₂²	semidirect
38. #16810373	C₂²	semidirect
39. #16810372	C₂²	semidirect
40. #16810371	C₂²	semidirect
41. #16810371	C₂²	semidirect
42. C₅₃×#500	C₂²	semidirect
45. C₅₃×#334	C₂²	semidirect
46. C₅₃×#333	C₂²	semidirect
229. #1695	D₅₃	direct (N × H)
237. D₅₃	#1695	direct (N × H)
245. #500	C₂×D₅₃	semidirect
268. #334	C₂×D₅₃	semidirect
272. #333	C₂×D₅₃	semidirect
273. C₅₃	C₂×#1695	semidirect

Maximal subgroups

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

subgroup	index
#500×D₅₃	2
#476×D₅₃	2
#436×D₅₃	2
#20274239	2
#20274238	2
#20274237	2
#20274236	2
#20274235	2
#334×D₅₃	2
#333×D₅₃	2
C₅₃×#1695	2
C₂×#1695	53

Subgroups — D53×#1695 #27366623

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1695 #27366623