Subgroups — D₅₃×#1673 #27366345

Order 13568.

790 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	#500×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#461×D₅₃	C₂	1	2	yes	maximal
3	C₈×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20274105	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274104	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274103	C₂	1	2	yes	maximal, complemented
7	#20274102	C₂	1	2	yes	maximal, complemented
8	#20274101	C₂	1	1	yes	maximal, characteristic, complemented
9	#335×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#332×D₅₃	C₂	1	2	yes	maximal, complemented
11	C₅₃×#1673	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₅₃	—	2	2	no	—
13	C₂²×C₈×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	C₈×D₂₁₂	C₂²	1	1	yes	characteristic
26	D₄×#88322	C₂²	1	1	yes	characteristic
27	#16810688	C₂²	1	1	yes	characteristic
28	C₈×C₂²⋊D₅₃	—	2	1	no	—
29	#16810686	—	2	1	no	—
30	#107×D₅₃	—	2	1	no	—
31	#107×D₅₃	—	2	1	no	—
32	C₄⋊C₈×D₅₃	C₂²	1	2	yes	—
33	C₄⋊C₈×D₅₃	C₂²	1	1	yes	characteristic
34	#103×D₅₃	—	2	2	no	—
35	C₂²⋊C₈×D₅₃	—	2	1	no	—
36	C₄×C₈×D₅₃	C₂²	1	1	yes	characteristic
37	#16810376	C₂²	1	1	yes	characteristic, complemented
38	#16810375	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	C₈×D₄×C₅₃	C₂²	1	1	yes	characteristic
45	C₅₃×#335	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	C₂²×#88322	—	2	1	no	—
55	C₂×C₈×D₅₃	—	2	1	no	—
56	C₂×C₈×D₅₃	—	2	1	no	—
57	C₂×C₈×D₅₃	—	2	1	no	—
58	C₂×C₈×D₅₃	—	2	2	no	—
59	C₂×C₈×D₅₃	—	4	4	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	C₂²×C₈×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	2	no	—
113	D₄×D₅₃	D₈	1	4	yes	—
114	C₂×D₂₁₂	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₅₃	—	2	1	no	—
116	C₂×C₄×D₅₃	—	2	1	no	—
117	C₂×C₄×D₅₃	—	2	1	no	—
118	C₂×C₄×D₅₃	—	4	2	no	—
119	C₂×C₄×D₅₃	—	4	2	no	—
120	C₂×C₄×D₅₃	—	4	2	no	—
121	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
124	C₂×Dic₁₀₆	—	2	2	no	—
125	C₂×Dic₁₀₆	—	4	2	no	—
126	SD₁₆×C₅₃	—	4	4	no	—
127	C₂×C₈×C₅₃	—	2	1	no	—
128	C₂×C₈×C₅₃	—	2	2	no	—
129	C₂×C₈×C₅₃	—	4	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	2	no	—
133	C₄⋊C₄×C₅₃	—	2	2	no	—
134	C₄⋊C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
135	C₂²⋊C₄×C₅₃	—	2	1	no	—
136	C₄²×C₅₃	C₂⁴	1	1	yes	characteristic
137	C₂²⋊Dic₅₃	—	2	1	no	—
138	#11719924	—	4	4	no	—
139	#11719923	—	4	4	no	—
140	#11719921	—	2	1	no	—
141	#11719921	—	2	1	no	—
142	C₄⋊Dic₅₃	—	2	2	no	—
143	C₄⋊Dic₅₃	—	2	2	no	—
144	C₄⋊Dic₅₃	C₂×D₄	1	1	yes	characteristic
145	#11719919	—	2	1	no	—
146	#11719919	—	4	2	no	—
147	#11719919	—	4	2	no	—
148	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₅₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₅₃	#41	1	1	yes	characteristic
151	C₂×#88322	—	2	1	no	—
152	C₂×#88322	—	2	2	no	—
153	C₂×#88322	—	4	2	no	—
154	C₂×#88322	C₂×D₄	1	1	yes	characteristic
155	C₂×#88322	C₂×D₄	1	1	yes	characteristic
156	#11719913	—	4	4	no	—
157	C₈×D₅₃	—	2	2	no	—
158	C₈×D₅₃	—	4	4	no	—
159	C₈×D₅₃	—	4	2	no	—
160	C₈×D₅₃	—	4	2	no	—
161	C₈×D₅₃	—	4	2	no	—
162	C₈×D₅₃	SD₁₆	1	4	yes	complemented
163	C₂³×C₅₃	—	2	1	no	—
164	C₂²×D₅₃	—	2	1	no	—
165	C₂²×D₅₃	—	2	4	no	—
166	C₂²×D₅₃	—	4	2	no	—
167	C₂²×D₅₃	—	4	2	no	—
168	C₂²×D₅₃	#121	1	1	yes	characteristic
169	Q₈×C₅₃	—	4	2	no	—
170	Q₈×C₅₃	—	4	2	no	—
171	D₄×C₅₃	—	2	1	no	—
172	D₄×C₅₃	C₂×D₈	1	2	yes	—
173	C₂×C₄×C₅₃	—	2	1	no	—
174	C₂×C₄×C₅₃	—	4	1	no	—
175	C₂×C₄×C₅₃	—	4	1	no	—
176	C₂×C₄×C₅₃	—	4	2	no	—
177	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₅₃	—	2	4	no	—
181	C₂×Dic₅₃	—	2	1	no	—
182	C₂×Dic₅₃	—	4	2	no	—
183	C₂×Dic₅₃	—	4	2	no	—
184	C₂×Dic₅₃	#121	1	1	yes	characteristic
185	C₂×Dic₅₃	#121	1	1	yes	characteristic
186	C₂×Dic₅₃	#121	1	1	yes	characteristic
187	D₂₁₂	—	2	1	no	—
188	D₂₁₂	C₂×D₈	1	2	yes	—
189	C₄×D₅₃	—	2	2	no	—
190	C₄×D₅₃	—	4	2	no	—
191	C₄×D₅₃	—	4	1	no	—
192	C₄×D₅₃	—	4	1	no	—
193	C₄×D₅₃	—	4	2	no	—
194	C₄×D₅₃	—	8	4	no	—
195	C₄×D₅₃	C₂×D₈	1	2	yes	—
196	C₄×D₅₃	C₂×SD₁₆	1	2	yes	—
197	C₄×D₅₃	#135	1	2	yes	—
198	C₄×D₅₃	#137	1	2	yes	—
199	Dic₁₀₆	—	4	2	no	—
200	Dic₁₀₆	—	4	2	no	—
201	Dic₁₀₆	—	8	4	no	—
202	C₈×C₅₃	—	2	1	no	—
203	C₈×C₅₃	—	4	2	no	—
204	C₈×C₅₃	—	4	1	no	—
205	C₈×C₅₃	C₂×SD₁₆	1	2	yes	complemented
206	#88322	—	2	1	no	—
207	#88322	—	4	2	no	—
208	#88322	—	4	1	no	—
209	#88322	C₂×SD₁₆	1	2	yes	complemented
210	C₂×#1673	—	53	1	no	maximal, Sylow
211	C₂²×C₅₃	—	2	2	no	—
212	C₂²×C₅₃	—	4	1	no	—
213	C₂²×C₅₃	—	4	1	no	—
214	C₂²×C₅₃	C₂×#121	1	1	yes	characteristic
215	C₂×D₅₃	—	2	2	no	—
216	C₂×D₅₃	—	4	1	no	—
217	C₂×D₅₃	—	4	1	no	—
218	C₂×D₅₃	—	4	8	no	—
219	C₂×D₅₃	#461	1	2	yes	—
220	C₂×D₅₃	#466	1	2	yes	—
221	C₂×D₅₃	#473	1	2	yes	—
222	C₄×C₅₃	—	2	1	no	—
223	C₄×C₅₃	—	4	1	no	—
224	C₄×C₅₃	—	8	2	no	—
225	C₄×C₅₃	C₂²×D₈	1	1	yes	characteristic
226	C₄×C₅₃	C₂²×SD₁₆	1	1	yes	characteristic
227	C₄×C₅₃	C₂×#135	1	1	yes	characteristic
228	C₄×C₅₃	C₂×#137	1	1	yes	characteristic
229	Dic₅₃	—	2	1	no	—
230	Dic₅₃	—	4	1	no	—
231	Dic₅₃	—	8	2	no	—
232	Dic₅₃	#461	1	2	yes	—
233	Dic₅₃	#466	1	2	yes	—
234	C₂×#500	—	53	1	no	—
235	C₂×#461	—	53	2	no	—
236	C₂×C₈×D₄	—	53	1	no	—
237	#1673	—	53	1	no	—
238	#1673	—	53	2	no	—
239	#1673	—	53	1	no	—
240	#1673	—	53	1	no	—
241	#1673	—	53	2	no	—
242	#1673	D₅₃	1	1	yes	characteristic, direct product factor
243	C₂×#335	—	53	1	no	—
244	C₂×#332	—	53	2	no	—
245	C₂×C₅₃	—	4	2	no	—
246	C₂×C₅₃	C₂×#461	1	1	yes	characteristic
247	C₂×C₅₃	C₂×#466	1	1	yes	characteristic
248	C₂×C₅₃	C₂×#473	1	1	yes	characteristic
249	D₅₃	—	4	2	no	—
250	D₅₃	#1673	1	4	yes	direct product factor
251	C₂²×SD₁₆	—	106	2	no	—
252	C₂³×C₈	—	106	1	no	—
253	C₂×C₄⋊Q₈	—	53	2	no	—
254	C₂×C₄×D₄	—	53	1	no	—
255	#500	—	53	2	no	—
256	#500	—	53	1	no	—
257	#500	—	106	1	no	—
258	#500	—	106	1	no	—
259	#500	C₂×D₅₃	1	1	yes	characteristic, complemented
260	#461	—	53	2	no	—
261	#461	—	53	2	no	—
262	#461	—	53	2	no	—
263	#461	—	106	2	no	—
264	#461	—	106	2	no	—
265	#461	C₂×D₅₃	1	2	yes	—
266	C₈×D₄	—	53	1	no	—
267	C₈×D₄	—	53	1	no	—
268	C₈×D₄	—	53	1	no	—
269	C₈×D₄	—	106	1	no	—
270	C₈×D₄	—	106	1	no	—
271	C₈×D₄	C₂×D₅₃	1	1	yes	characteristic
272	C₂×#107	—	106	1	no	—
273	C₂×#107	—	106	1	no	—
274	C₂×C₄⋊C₈	—	53	1	no	—
275	C₂×C₄⋊C₈	—	53	2	no	—
276	C₂×#103	—	106	2	no	—
277	C₂×C₂²⋊C₈	—	106	1	no	—
278	C₂×C₄×C₈	—	53	1	no	—
279	#335	—	53	2	no	—
280	#335	—	53	1	no	—
281	#335	C₂×D₅₃	1	1	yes	characteristic, complemented
282	#332	—	53	2	no	—
283	#332	—	53	2	no	—
284	#332	—	53	2	no	—
285	#332	C₂×D₅₃	1	2	yes	complemented
286	C₅₃	C₂×#1673	1	1	yes	characteristic, complemented, Sylow
287	C₂²×Q₈	—	106	2	no	—
288	C₂²×D₄	—	53	1	no	—
289	C₂³×C₄	—	106	1	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×SD₁₆	—	212	8	no	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	—	53	1	no	—
297	C₂²×C₈	—	53	1	no	—
298	C₂²×C₈	—	106	1	no	—
299	C₂²×C₈	—	106	1	no	—
300	C₂²×C₈	—	106	2	no	—
301	C₂²×C₈	—	106	1	no	—
302	C₂²×C₈	—	106	1	no	—
303	C₂²×C₈	—	212	4	no	—
304	C₄⋊Q₈	—	53	2	no	—
305	C₄⋊Q₈	—	106	2	no	—
306	C₄⋊Q₈	—	106	2	no	—
307	C₄⋊Q₈	—	106	2	no	—
308	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	—
309	C₄×D₄	—	53	1	no	—
310	C₄×D₄	—	53	1	no	—
311	C₄×D₄	—	53	1	no	—
312	C₄×D₄	—	106	1	no	—
313	C₄×D₄	—	106	1	no	—
314	C₄×D₄	C₂²×D₅₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	—	53	1	no	—
316	C₂×C₄⋊C₄	—	106	2	no	—
317	C₂×C₄⋊C₄	—	106	2	no	—
318	C₂×C₂²⋊C₄	—	106	1	no	—
319	C₂×C₄²	—	53	1	no	—
320	#107	—	2	1	no	—
321	#107	—	2	1	no	—
322	#107	—	106	2	no	—
323	#107	—	106	2	no	—
324	#107	—	106	1	no	—
325	#107	—	106	1	no	—
326	C₄⋊C₈	—	53	1	no	—
327	C₄⋊C₈	—	53	2	no	—
328	C₄⋊C₈	—	106	1	no	—
329	C₄⋊C₈	—	106	2	no	—
330	C₄⋊C₈	C₂²×D₅₃	1	1	yes	characteristic
331	C₄⋊C₈	C₂²×D₅₃	1	2	yes	—
332	#103	—	2	2	no	—
333	#103	—	106	2	no	—
334	#103	—	106	2	no	—
335	#103	—	106	2	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₂²⋊C₈	—	106	1	no	—
338	C₂²⋊C₈	—	106	1	no	—
339	C₂²⋊C₈	—	106	1	no	—
340	C₄×C₈	—	53	1	no	—
341	C₄×C₈	—	53	1	no	—
342	C₄×C₈	—	53	1	no	—
343	C₄×C₈	C₂²×D₅₃	1	1	yes	characteristic
344	C₂⁴	—	106	1	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	106	2	no	—
347	C₂×Q₈	—	212	2	no	—
348	C₂×Q₈	—	212	4	no	—
349	C₂×Q₈	—	212	4	no	—
350	C₂×D₄	—	53	4	no	—
351	C₂×D₄	—	53	1	no	—
352	C₂×D₄	—	106	2	no	—
353	C₂×D₄	—	106	1	no	—
354	C₂×D₄	D₄×D₅₃	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	53	1	no	—
357	C₂²×C₄	—	53	1	no	—
358	C₂²×C₄	—	53	1	no	—
359	C₂²×C₄	—	106	1	no	—
360	C₂²×C₄	—	106	1	no	—
361	C₂²×C₄	—	106	1	no	—
362	C₂²×C₄	—	106	1	no	—
363	C₂²×C₄	—	212	2	no	—
364	C₂²×C₄	—	212	2	no	—
365	C₂²×C₄	—	212	2	no	—
366	SD₁₆	—	4	4	no	—
367	SD₁₆	—	212	4	no	—
368	SD₁₆	—	212	4	no	—
369	SD₁₆	—	212	4	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	53	1	no	—
374	C₂×C₈	—	53	4	no	—
375	C₂×C₈	—	53	1	no	—
376	C₂×C₈	—	106	2	no	—
377	C₂×C₈	—	106	1	no	—
378	C₂×C₈	—	106	2	no	—
379	C₂×C₈	—	212	2	no	—
380	C₂×C₈	—	212	2	no	—
381	C₂×C₈	—	212	4	no	—
382	C₂×C₈	—	212	2	no	—
383	C₂×C₈	—	212	2	no	—
384	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	53	1	no	—
389	C₄⋊C₄	—	106	1	no	—
390	C₄⋊C₄	—	106	2	no	—
391	C₄⋊C₄	—	106	2	no	—
392	C₄⋊C₄	—	212	2	no	—
393	C₄⋊C₄	—	212	2	no	—
394	C₄⋊C₄	D₄×D₅₃	1	1	yes	characteristic
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	106	1	no	—
397	C₂²⋊C₄	—	106	1	no	—
398	C₂²⋊C₄	—	106	1	no	—
399	C₄²	—	53	1	no	—
400	C₄²	—	53	1	no	—
401	C₄²	—	53	1	no	—
402	C₄²	C₂³×D₅₃	1	1	yes	characteristic
403	C₂³	—	2	1	no	—
404	C₂³	—	53	1	no	—
405	C₂³	—	106	4	no	—
406	C₂³	—	106	1	no	—
407	C₂³	—	212	2	no	—
408	C₂³	—	212	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	424	4	no	—
412	Q₈	—	212	2	no	—
413	Q₈	—	212	2	no	—
414	D₄	—	2	1	no	—
415	D₄	—	53	2	no	—
416	D₄	—	106	4	no	—
417	D₄	—	106	1	no	—
418	D₄	D₈×D₅₃	1	2	yes	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	53	1	no	—
424	C₂×C₄	—	53	1	no	—
425	C₂×C₄	—	53	2	no	—
426	C₂×C₄	—	53	2	no	—
427	C₂×C₄	—	53	2	no	—
428	C₂×C₄	—	53	2	no	—
429	C₂×C₄	—	53	1	no	—
430	C₂×C₄	—	106	2	no	—
431	C₂×C₄	—	106	1	no	—
432	C₂×C₄	—	424	4	no	—
433	C₂×C₄	—	212	2	no	—
434	C₂×C₄	—	212	2	no	—
435	C₂×C₄	—	212	2	no	—
436	C₂×C₄	—	212	2	no	—
437	C₂×C₄	—	212	1	no	—
438	C₂×C₄	—	212	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	2	no	—
444	C₈	—	4	1	no	—
445	C₈	—	53	2	no	—
446	C₈	—	106	1	no	—
447	C₈	—	212	2	no	—
448	C₈	—	212	1	no	—
449	C₈	SD₁₆×D₅₃	1	2	yes	complemented
450	C₂²	—	2	2	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	53	2	no	—
454	C₂²	—	53	2	no	—
455	C₂²	—	53	2	no	—
456	C₂²	—	106	2	no	—
457	C₂²	—	212	8	no	—
458	C₂²	—	212	1	no	—
459	C₂²	—	212	1	no	—
460	C₂²	#121×D₅₃	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	8	2	no	—
464	C₄	—	53	2	no	—
465	C₄	—	53	2	no	—
466	C₄	—	106	1	no	—
467	C₄	—	424	2	no	—
468	C₄	—	212	1	no	—
469	C₄	C₂×D₈×D₅₃	1	1	yes	characteristic
470	C₄	C₂×SD₁₆×D₅₃	1	1	yes	characteristic
471	C₄	#135×D₅₃	1	1	yes	characteristic
472	C₄	#137×D₅₃	1	1	yes	characteristic
473	C₂	—	4	2	no	—
474	C₂	—	53	4	no	—
475	C₂	—	212	2	no	—
476	C₂	#461×D₅₃	1	1	yes	characteristic
477	C₂	#466×D₅₃	1	1	yes	characteristic
478	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×#1673	C₂
socle	C₂²×C₅₃	C₂×#121
prime radical	C₂×D₄×D₅₃	D₄
hypercenter	#1673	D₅₃
hypocenter	C₅₃	C₂×#1673
LCS	G ▷ C₄²×C₅₃ ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1673

Complements

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

N	H ≅ G/N	type
1. #500×D₅₃	C₂	semidirect
4. #20274105	C₂	semidirect
5. #20274104	C₂	semidirect
6. #20274103	C₂	semidirect
7. #20274102	C₂	semidirect
8. #20274101	C₂	semidirect
9. #335×D₅₃	C₂	semidirect
10. #332×D₅₃	C₂	semidirect
11. C₅₃×#1673	C₂	semidirect
16. #16811028	C₂²	semidirect
19. #16811026	C₂²	semidirect
37. #16810376	C₂²	semidirect
38. #16810375	C₂²	semidirect
39. #16810370	C₂²	semidirect
40. #16810369	C₂²	semidirect
41. #16810368	C₂²	semidirect
42. C₅₃×#500	C₂²	semidirect
45. C₅₃×#335	C₂²	semidirect
46. C₅₃×#332	C₂²	semidirect
162. C₈×D₅₃	SD₁₆	semidirect
205. C₈×C₅₃	C₂×SD₁₆	semidirect
209. #88322	C₂×SD₁₆	semidirect
242. #1673	D₅₃	direct (N × H)
250. D₅₃	#1673	direct (N × H)
259. #500	C₂×D₅₃	semidirect
281. #335	C₂×D₅₃	semidirect
285. #332	C₂×D₅₃	semidirect
286. C₅₃	C₂×#1673	semidirect
449. 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
C₈×D₄×D₅₃	2
#20274105	2
#20274104	2
#20274103	2
#20274102	2
#20274101	2
#335×D₅₃	2
#332×D₅₃	2
C₅₃×#1673	2
C₂×#1673	53

Subgroups — D53×#1673 #27366345

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1673 #27366345