Subgroups — D₅₃×#1693 #27366617

Order 13568.

758 conjugacy classes of subgroups.

The subgroup lattice has 470 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	#461×D₅₃	C₂	1	2	yes	maximal
3	#436×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20274229	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274228	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274227	C₂	1	2	yes	maximal, complemented
7	#20274226	C₂	1	2	yes	maximal, complemented
8	#20274225	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#332×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1693	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₅₃	—	2	2	no	—
13	C₂×M₁₆×D₅₃	—	2	1	no	—
14	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	—
15	C₄×D₄×D₅₃	C₂²	1	1	yes	characteristic
16	#16811028	C₂²	1	1	yes	characteristic, complemented
17	#16811027	—	2	1	no	—
18	#16811027	—	2	1	no	—
19	#16811026	C₂²	1	2	yes	complemented
20	#16810829	C₂²	1	2	yes	—
21	#16810828	C₂²	1	2	yes	—
22	#16810827	—	2	2	no	—
23	#16810826	—	2	2	no	—
24	#16810825	C₂²	1	2	yes	—
25	#16810702	C₂²	1	1	yes	characteristic
26	#16810701	C₂²	1	1	yes	characteristic
27	#16810700	C₂²	1	1	yes	characteristic
28	#16810699	—	2	1	no	—
29	#16810698	—	2	1	no	—
30	#107×D₅₃	—	2	1	no	—
31	#107×D₅₃	—	2	1	no	—
32	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
34	#103×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	#16810370	C₂²	1	2	yes	complemented
40	#16810369	C₂²	1	2	yes	complemented
41	#16810368	C₂²	1	2	yes	complemented
42	C₅₃×#500	C₂²	1	1	yes	characteristic, complemented
43	C₅₃×#461	C₂²	1	2	yes	—
44	C₅₃×#436	C₂²	1	1	yes	characteristic
45	C₅₃×#334	C₂²	1	1	yes	characteristic, complemented
46	C₅₃×#332	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×#11719913	—	2	2	no	—
51	C₂×#11719923	—	2	2	no	—
52	C₂×#11719924	—	2	2	no	—
53	SD₁₆×D₅₃	—	4	8	no	—
54	C₂×#11719917	—	2	1	no	—
55	C₂×#11719912	—	2	1	no	—
56	C₂×#11719912	—	2	1	no	—
57	M₁₆×D₅₃	—	4	4	no	—
58	C₂×C₈×D₅₃	—	2	1	no	—
59	C₂×C₈×D₅₃	—	2	2	no	—
60	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
62	#13133217	C₂³	1	2	yes	—
63	#13133216	—	2	2	no	—
64	#13133216	—	2	2	no	—
65	#13133215	—	2	2	no	—
66	C₄×D₂₁₂	C₂³	1	1	yes	characteristic
67	D₄×Dic₅₃	D₄	1	1	yes	characteristic
68	#13133179	D₄	1	1	yes	characteristic
69	C₄×C₂²⋊D₅₃	—	2	1	no	—
70	#13133177	—	2	1	no	—
71	C₄⋊C₄×D₅₃	—	2	2	no	—
72	C₄⋊C₄×D₅₃	—	2	2	no	—
73	C₄⋊C₄×D₅₃	D₄	1	1	yes	characteristic
74	C₂²⋊C₄×D₅₃	—	2	1	no	—
75	C₄²×D₅₃	C₂³	1	1	yes	characteristic
76	#13133151	—	2	1	no	—
77	#13133151	—	2	1	no	—
78	#13133150	—	2	2	no	—
79	#13133150	—	2	2	no	—
80	C₄⋊#88322	C₂³	1	2	yes	—
81	C₄⋊#88322	C₂³	1	1	yes	characteristic
82	#13133146	—	2	2	no	—
83	#13133146	—	2	1	no	—
84	#13133142	—	2	2	no	—
85	#13133141	—	2	2	no	—
86	#13133140	—	2	2	no	—
87	C₂²⋊#88322	—	2	1	no	—
88	#13133129	—	2	1	no	—
89	#13133129	—	2	1	no	—
90	C₄×#88322	C₂³	1	1	yes	characteristic
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×M₁₆×C₅₃	—	2	1	no	—
95	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	—
96	C₄×D₄×C₅₃	C₂³	1	1	yes	characteristic
97	#107×C₅₃	—	2	1	no	—
98	#107×C₅₃	—	2	1	no	—
99	C₄⋊C₈×C₅₃	C₂³	1	2	yes	—
100	C₄⋊C₈×C₅₃	C₂³	1	1	yes	characteristic
101	#103×C₅₃	—	2	2	no	—
102	C₂²⋊C₈×C₅₃	—	2	1	no	—
103	C₄×C₈×C₅₃	C₂³	1	1	yes	characteristic
104	C₂³×D₅₃	—	2	1	no	—
105	C₂×Q₈×C₅₃	—	2	2	no	—
106	C₂×D₄×C₅₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₅₃	—	2	1	no	—
108	C₂×C₂²⋊D₅₃	—	2	1	no	—
109	C₂²×Dic₅₃	—	2	1	no	—
110	Q₈×D₅₃	—	4	4	no	—
111	Q₈×D₅₃	—	4	4	no	—
112	D₄×D₅₃	—	2	4	no	—
113	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₅₃	—	2	1	no	—
115	C₂×C₄×D₅₃	—	2	1	no	—
116	C₂×C₄×D₅₃	—	2	1	no	—
117	C₂×C₄×D₅₃	—	4	2	no	—
118	C₂×C₄×D₅₃	—	4	2	no	—
119	C₂×C₄×D₅₃	—	4	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	2	no	—
124	C₂×Dic₁₀₆	—	4	2	no	—
125	SD₁₆×C₅₃	—	4	4	no	—
126	M₁₆×C₅₃	—	4	2	no	—
127	C₂×C₈×C₅₃	—	2	1	no	—
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
131	C₄⋊C₄×C₅₃	—	2	2	no	—
132	C₄⋊C₄×C₅₃	—	2	2	no	—
133	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
134	C₂²⋊C₄×C₅₃	—	2	1	no	—
135	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
136	C₂²⋊Dic₅₃	—	2	1	no	—
137	#11719924	—	4	4	no	—
138	#11719923	—	4	4	no	—
139	#11719921	—	2	1	no	—
140	#11719921	—	2	1	no	—
141	C₄⋊Dic₅₃	—	2	2	no	—
142	C₄⋊Dic₅₃	—	2	2	no	—
143	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
144	#11719919	—	2	1	no	—
145	#11719919	—	4	2	no	—
146	#11719919	—	4	2	no	—
147	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₅₃	#41	1	1	yes	characteristic
150	#11719917	—	4	2	no	—
151	C₂×#88322	—	2	1	no	—
152	C₂×#88322	—	2	2	no	—
153	C₂×#88322	C₂×D₄	1	1	yes	characteristic
154	C₂×#88322	C₂×D₄	1	1	yes	characteristic
155	#11719913	—	4	4	no	—
156	#11719912	—	4	2	no	—
157	#11719912	—	4	2	no	—
158	C₈×D₅₃	—	2	2	no	—
159	C₈×D₅₃	—	4	2	no	—
160	C₈×D₅₃	—	4	4	no	—
161	C₈×D₅₃	SD₁₆	1	4	yes	complemented
162	C₂³×C₅₃	—	2	1	no	—
163	C₂²×D₅₃	—	2	1	no	—
164	C₂²×D₅₃	—	4	2	no	—
165	C₂²×D₅₃	—	4	2	no	—
166	C₂²×D₅₃	—	4	2	no	—
167	C₂²×D₅₃	#121	1	1	yes	characteristic
168	Q₈×C₅₃	—	4	2	no	—
169	Q₈×C₅₃	—	4	2	no	—
170	D₄×C₅₃	—	2	2	no	—
171	C₂×C₄×C₅₃	—	2	1	no	—
172	C₂×C₄×C₅₃	—	4	1	no	—
173	C₂×C₄×C₅₃	—	4	1	no	—
174	C₂×C₄×C₅₃	—	4	2	no	—
175	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
178	C₂²⋊D₅₃	—	4	2	no	—
179	C₂×Dic₅₃	—	2	1	no	—
180	C₂×Dic₅₃	—	4	2	no	—
181	C₂×Dic₅₃	—	4	2	no	—
182	C₂×Dic₅₃	#121	1	1	yes	characteristic
183	C₂×Dic₅₃	#121	1	1	yes	characteristic
184	C₂×Dic₅₃	#121	1	1	yes	characteristic
185	D₂₁₂	—	2	2	no	—
186	C₄×D₅₃	—	2	2	no	—
187	C₄×D₅₃	—	4	2	no	—
188	C₄×D₅₃	—	4	1	no	—
189	C₄×D₅₃	—	4	1	no	—
190	C₄×D₅₃	—	4	2	no	—
191	C₄×D₅₃	—	8	4	no	—
192	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
193	C₄×D₅₃	AGL(1,ℤ/8)	1	4	yes	—
194	C₄×D₅₃	#137	1	2	yes	—
195	Dic₁₀₆	—	4	2	no	—
196	Dic₁₀₆	—	4	2	no	—
197	Dic₁₀₆	—	8	4	no	—
198	C₈×C₅₃	—	2	1	no	—
199	C₈×C₅₃	—	4	1	no	—
200	C₈×C₅₃	—	4	2	no	—
201	C₈×C₅₃	C₂×SD₁₆	1	2	yes	complemented
202	#88322	—	2	1	no	—
203	#88322	—	4	1	no	—
204	#88322	—	4	2	no	—
205	#88322	C₂×SD₁₆	1	2	yes	complemented
206	C₂×#1693	—	53	1	no	maximal, Sylow
207	C₂²×C₅₃	—	4	1	no	—
208	C₂²×C₅₃	—	4	1	no	—
209	C₂²×C₅₃	—	4	1	no	—
210	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
211	C₂×D₅₃	—	4	1	no	—
212	C₂×D₅₃	—	4	1	no	—
213	C₂×D₅₃	—	4	1	no	—
214	C₂×D₅₃	—	8	4	no	—
215	C₂×D₅₃	#461	1	2	yes	—
216	C₂×D₅₃	#469	1	2	yes	—
217	C₂×D₅₃	#473	1	2	yes	—
218	C₄×C₅₃	—	2	1	no	—
219	C₄×C₅₃	—	4	1	no	—
220	C₄×C₅₃	—	8	2	no	—
221	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
222	C₄×C₅₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
223	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
224	Dic₅₃	—	2	1	no	—
225	Dic₅₃	—	4	1	no	—
226	Dic₅₃	—	8	2	no	—
227	Dic₅₃	#461	1	2	yes	—
228	Dic₅₃	#469	1	2	yes	—
229	C₂×#500	—	53	1	no	—
230	C₂×#461	—	53	2	no	—
231	C₂×#436	—	53	1	no	—
232	#1693	—	53	1	no	—
233	#1693	—	53	2	no	—
234	#1693	—	53	1	no	—
235	#1693	—	53	1	no	—
236	#1693	—	53	2	no	—
237	#1693	D₅₃	1	1	yes	characteristic, direct product factor
238	C₂×#334	—	53	1	no	—
239	C₂×#332	—	53	2	no	—
240	C₂×C₅₃	—	8	1	no	—
241	C₂×C₅₃	C₂×#461	1	1	yes	characteristic
242	C₂×C₅₃	C₂×#469	1	1	yes	characteristic
243	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
244	D₅₃	—	8	1	no	—
245	D₅₃	#1693	1	4	yes	direct product factor
246	C₂²×SD₁₆	—	106	2	no	—
247	C₂²×M₁₆	—	106	1	no	—
248	C₂×C₄⋊Q₈	—	53	2	no	—
249	C₂×C₄×D₄	—	53	1	no	—
250	#500	—	53	2	no	—
251	#500	—	53	1	no	—
252	#500	—	106	1	no	—
253	#500	—	106	1	no	—
254	#500	C₂×D₅₃	1	1	yes	characteristic, complemented
255	#461	—	53	2	no	—
256	#461	—	53	2	no	—
257	#461	—	53	2	no	—
258	#461	—	106	2	no	—
259	#461	—	106	2	no	—
260	#461	C₂×D₅₃	1	2	yes	—
261	#436	—	53	1	no	—
262	#436	—	53	1	no	—
263	#436	—	53	1	no	—
264	#436	—	106	1	no	—
265	#436	—	106	1	no	—
266	#436	C₂×D₅₃	1	1	yes	characteristic
267	C₂×#107	—	106	1	no	—
268	C₂×#107	—	106	1	no	—
269	C₂×C₄⋊C₈	—	53	1	no	—
270	C₂×C₄⋊C₈	—	53	2	no	—
271	C₂×#103	—	106	2	no	—
272	C₂×C₂²⋊C₈	—	106	1	no	—
273	C₂×C₄×C₈	—	53	1	no	—
274	#334	—	53	2	no	—
275	#334	—	53	1	no	—
276	#334	C₂×D₅₃	1	1	yes	characteristic, complemented
277	#332	—	53	2	no	—
278	#332	—	53	2	no	—
279	#332	—	53	2	no	—
280	#332	C₂×D₅₃	1	2	yes	complemented
281	C₅₃	C₂×#1693	1	1	yes	characteristic, complemented, Sylow
282	C₂²×Q₈	—	106	2	no	—
283	C₂²×D₄	—	53	1	no	—
284	C₂³×C₄	—	106	1	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	106	2	no	—
287	C₂×SD₁₆	—	106	2	no	—
288	C₂×SD₁₆	—	106	2	no	—
289	C₂×SD₁₆	—	212	8	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₂×M₁₆	—	106	1	no	—
292	C₂×M₁₆	—	106	1	no	—
293	C₂×M₁₆	—	106	1	no	—
294	C₂×M₁₆	—	212	4	no	—
295	C₂²×C₈	—	53	1	no	—
296	C₂²×C₈	—	53	1	no	—
297	C₂²×C₈	—	106	1	no	—
298	C₂²×C₈	—	106	2	no	—
299	C₄⋊Q₈	—	53	2	no	—
300	C₄⋊Q₈	—	106	2	no	—
301	C₄⋊Q₈	—	106	2	no	—
302	C₄⋊Q₈	—	106	2	no	—
303	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
304	C₄×D₄	—	53	1	no	—
305	C₄×D₄	—	53	1	no	—
306	C₄×D₄	—	53	1	no	—
307	C₄×D₄	—	106	1	no	—
308	C₄×D₄	—	106	1	no	—
309	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	53	1	no	—
311	C₂×C₄⋊C₄	—	106	2	no	—
312	C₂×C₄⋊C₄	—	106	2	no	—
313	C₂×C₂²⋊C₄	—	106	1	no	—
314	C₂×C₄²	—	53	1	no	—
315	#107	—	2	1	no	—
316	#107	—	2	1	no	—
317	#107	—	106	2	no	—
318	#107	—	106	2	no	—
319	#107	—	106	1	no	—
320	#107	—	106	1	no	—
321	C₄⋊C₈	—	53	1	no	—
322	C₄⋊C₈	—	53	2	no	—
323	C₄⋊C₈	—	106	1	no	—
324	C₄⋊C₈	—	106	2	no	—
325	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
326	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
327	#103	—	2	2	no	—
328	#103	—	106	2	no	—
329	#103	—	106	2	no	—
330	#103	—	106	2	no	—
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	106	1	no	—
333	C₂²⋊C₈	—	106	1	no	—
334	C₂²⋊C₈	—	106	1	no	—
335	C₄×C₈	—	53	1	no	—
336	C₄×C₈	—	53	1	no	—
337	C₄×C₈	—	53	1	no	—
338	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
339	C₂⁴	—	106	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	106	2	no	—
342	C₂×Q₈	—	212	2	no	—
343	C₂×Q₈	—	212	4	no	—
344	C₂×Q₈	—	212	4	no	—
345	C₂×D₄	—	53	1	no	—
346	C₂×D₄	—	106	4	no	—
347	C₂×D₄	—	106	1	no	—
348	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	53	1	no	—
351	C₂²×C₄	—	53	1	no	—
352	C₂²×C₄	—	53	1	no	—
353	C₂²×C₄	—	106	1	no	—
354	C₂²×C₄	—	106	1	no	—
355	C₂²×C₄	—	106	1	no	—
356	C₂²×C₄	—	106	1	no	—
357	C₂²×C₄	—	212	2	no	—
358	C₂²×C₄	—	212	2	no	—
359	C₂²×C₄	—	212	2	no	—
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	212	4	no	—
362	SD₁₆	—	212	4	no	—
363	SD₁₆	—	212	4	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	—	212	2	no	—
366	M₁₆	—	212	2	no	—
367	M₁₆	—	212	2	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	53	1	no	—
371	C₂×C₈	—	53	4	no	—
372	C₂×C₈	—	53	1	no	—
373	C₂×C₈	—	106	2	no	—
374	C₂×C₈	—	106	1	no	—
375	C₂×C₈	—	106	2	no	—
376	C₂×C₈	—	212	2	no	—
377	C₂×C₈	—	212	4	no	—
378	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
379	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	53	1	no	—
383	C₄⋊C₄	—	106	1	no	—
384	C₄⋊C₄	—	106	2	no	—
385	C₄⋊C₄	—	106	2	no	—
386	C₄⋊C₄	—	212	2	no	—
387	C₄⋊C₄	—	212	2	no	—
388	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	106	1	no	—
391	C₂²⋊C₄	—	106	1	no	—
392	C₂²⋊C₄	—	106	1	no	—
393	C₄²	—	53	1	no	—
394	C₄²	—	53	1	no	—
395	C₄²	—	53	1	no	—
396	C₄²	C₂³×D₅₃	1	1	yes	characteristic
397	C₂³	—	2	1	no	—
398	C₂³	—	53	1	no	—
399	C₂³	—	106	1	no	—
400	C₂³	—	212	2	no	—
401	C₂³	—	212	2	no	—
402	C₂³	—	212	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	424	4	no	—
406	Q₈	—	212	2	no	—
407	Q₈	—	212	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	106	2	no	—
410	D₄	—	212	2	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	53	1	no	—
416	C₂×C₄	—	53	1	no	—
417	C₂×C₄	—	53	2	no	—
418	C₂×C₄	—	53	4	no	—
419	C₂×C₄	—	53	2	no	—
420	C₂×C₄	—	53	1	no	—
421	C₂×C₄	—	106	2	no	—
422	C₂×C₄	—	106	1	no	—
423	C₂×C₄	—	424	4	no	—
424	C₂×C₄	—	212	2	no	—
425	C₂×C₄	—	212	2	no	—
426	C₂×C₄	—	212	2	no	—
427	C₂×C₄	—	212	2	no	—
428	C₂×C₄	—	212	1	no	—
429	C₂×C₄	—	212	1	no	—
430	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
432	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	2	no	—
436	C₈	—	53	2	no	—
437	C₈	—	106	1	no	—
438	C₈	—	212	1	no	—
439	C₈	—	212	2	no	—
440	C₈	SD₁₆×D₅₃	1	2	yes	complemented
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	53	2	no	—
445	C₂²	—	53	2	no	—
446	C₂²	—	53	2	no	—
447	C₂²	—	424	4	no	—
448	C₂²	—	212	1	no	—
449	C₂²	—	212	1	no	—
450	C₂²	—	212	1	no	—
451	C₂²	#121×D₅₃	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	4	1	no	—
454	C₄	—	8	2	no	—
455	C₄	—	53	2	no	—
456	C₄	—	53	2	no	—
457	C₄	—	106	1	no	—
458	C₄	—	424	2	no	—
459	C₄	—	212	1	no	—
460	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
461	C₄	AGL(1,ℤ/8)×D₅₃	1	2	yes	—
462	C₄	#137×D₅₃	1	1	yes	characteristic
463	C₂	—	8	1	no	—
464	C₂	—	53	4	no	—
465	C₂	—	424	1	no	—
466	C₂	#461×D₅₃	1	1	yes	characteristic
467	C₂	#469×D₅₃	1	1	yes	characteristic
468	C₂	#473×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₅₃
commutator, cosocle	C₄²×C₅₃	C₂⁴
Frattini	C₄²	C₂³×D₅₃
Fitting	C₅₃×#1693	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×D₄×D₅₃	D₄
hypercenter	#1693	D₅₃
hypocenter	C₅₃	C₂×#1693
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1693

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
4. #20274229	C₂	semidirect
5. #20274228	C₂	semidirect
6. #20274227	C₂	semidirect
7. #20274226	C₂	semidirect
8. #20274225	C₂	semidirect
9. #334×D₅₃	C₂	semidirect
10. #332×D₅₃	C₂	semidirect
11. C₅₃×#1693	C₂	semidirect
16. #16811028	C₂²	semidirect
19. #16811026	C₂²	semidirect
37. #16810374	C₂²	semidirect
38. #16810373	C₂²	semidirect
39. #16810370	C₂²	semidirect
40. #16810369	C₂²	semidirect
41. #16810368	C₂²	semidirect
42. C₅₃×#500	C₂²	semidirect
45. C₅₃×#334	C₂²	semidirect
46. C₅₃×#332	C₂²	semidirect
161. C₈×D₅₃	SD₁₆	semidirect
201. C₈×C₅₃	C₂×SD₁₆	semidirect
205. #88322	C₂×SD₁₆	semidirect
237. #1693	D₅₃	direct (N × H)
245. D₅₃	#1693	direct (N × H)
254. #500	C₂×D₅₃	semidirect
276. #334	C₂×D₅₃	semidirect
280. #332	C₂×D₅₃	semidirect
281. C₅₃	C₂×#1693	semidirect
440. C₈	SD₁₆×D₅₃	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
#461×D₅₃	2
#436×D₅₃	2
#20274229	2
#20274228	2
#20274227	2
#20274226	2
#20274225	2
#334×D₅₃	2
#332×D₅₃	2
C₅₃×#1693	2
C₂×#1693	53

Subgroups — D53×#1693 #27366617

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1693 #27366617