Subgroups — D₅₃×#1833 #27384261

Order 13568.

786 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₅₃	C₂	1	1	yes	maximal, characteristic
2	#427×D₅₃	C₂	1	1	yes	maximal, characteristic
3	#405×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#20274840	C₂	1	1	yes	maximal, characteristic, complemented
5	#20274839	C₂	1	1	yes	maximal, characteristic, complemented
6	#20274838	C₂	1	1	yes	maximal, characteristic, complemented
7	#20274837	C₂	1	2	yes	maximal, complemented
8	#20274836	C₂	1	2	yes	maximal, complemented
9	#344×D₅₃	C₂	1	2	yes	maximal
10	H(3,ℤ/4)×D₅₃	C₂	1	2	yes	maximal
11	C₅₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₅₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₅₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₅₃	C₂²	1	1	yes	characteristic
15	#117×D₅₃	C₂²	1	2	yes	—
16	#117×D₅₃	C₂²	1	1	yes	characteristic
17	C₂×#13133153	C₂²	1	1	yes	characteristic
18	C₂×#13133152	C₂²	1	2	yes	—
19	#108×D₅₃	—	2	1	no	—
20	#108×D₅₃	—	2	1	no	—
21	#108×D₅₃	—	2	1	no	—
22	#108×D₅₃	—	2	1	no	—
23	#16810661	C₂²	1	1	yes	characteristic
24	#16810660	—	2	1	no	—
25	#16810659	C₂²	1	2	yes	—
26	#16810658	—	2	1	no	—
27	#107×D₅₃	—	2	1	no	—
28	#106×D₅₃	—	2	1	no	—
29	#16810581	C₂²	1	1	yes	characteristic
30	#16810580	C₄	1	2	yes	complemented
31	#16810579	C₂²	1	1	yes	characteristic
32	#16810578	C₂²	1	1	yes	characteristic
33	#16810577	C₄	1	2	yes	complemented
34	#97×D₅₃	C₄	1	2	yes	complemented
35	C₄×C₈×D₅₃	C₄	1	2	yes	complemented
36	#16810395	C₂²	1	2	yes	—
37	#16810394	C₂²	1	2	yes	—
38	#16810393	C₂²	1	2	yes	—
39	#16810380	C₂²	1	2	yes	—
40	#16810379	C₂²	1	2	yes	—
41	#16810379	C₂²	1	2	yes	—
42	C₂×#108×C₅₃	C₂²	1	1	yes	characteristic
43	C₅₃×#427	C₂²	1	1	yes	characteristic
44	C₅₃×#405	C₂²	1	1	yes	characteristic
45	C₅₃×#344	C₂²	1	2	yes	—
46	C₅₃×H(3,ℤ/4)	C₂²	1	2	yes	—
47	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
48	C₂×#11719917	C₂³	1	2	yes	—
49	C₂×#11719917	C₂³	1	1	yes	characteristic
50	C₂×#11719912	—	2	2	no	—
51	C₂×#11719912	C₂×C₄	1	2	yes	—
52	M₁₆×D₅₃	—	2	2	no	—
53	M₁₆×D₅₃	—	2	2	no	—
54	M₁₆×D₅₃	—	2	1	no	—
55	M₁₆×D₅₃	—	2	1	no	—
56	M₁₆×D₅₃	—	2	1	no	—
57	M₁₆×D₅₃	—	2	1	no	—
58	M₁₆×D₅₃	—	2	2	no	—
59	M₁₆×D₅₃	—	2	2	no	—
60	C₂²×#88322	C₂³	1	1	yes	characteristic
61	C₂×C₈×D₅₃	—	2	2	no	—
62	C₂×C₈×D₅₃	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₅₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
68	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
69	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
70	C₂×C₈×D₅₃	D₄	1	1	yes	characteristic
71	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
72	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
73	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
74	C₂×C₈×D₅₃	Q₈	1	1	yes	characteristic
75	#13133176	C₂³	1	2	yes	—
76	#13133176	C₂³	1	1	yes	characteristic
77	#13133175	—	2	2	no	—
78	#13133175	—	2	1	no	—
79	#13133174	—	2	2	no	—
80	#13133174	C₂×C₄	1	2	yes	—
81	#13133173	—	2	1	no	—
82	#13133173	—	2	2	no	—
83	C₄⋊C₄×D₅₃	—	2	1	no	—
84	C₄⋊C₄×D₅₃	—	2	2	no	—
85	C₂²⋊C₄×D₅₃	—	2	1	no	—
86	C₂²⋊C₄×D₅₃	—	2	2	no	—
87	C₄²×D₅₃	—	2	2	no	—
88	C₄²×D₅₃	C₂×C₄	1	2	yes	—
89	#13133153	—	2	1	no	—
90	#13133153	—	2	1	no	—
91	#13133152	—	2	2	no	—
92	#13133152	—	2	2	no	—
93	#13133151	—	2	1	no	—
94	#13133150	—	2	2	no	—
95	#13133149	—	2	1	no	—
96	#13133148	—	2	2	no	—
97	#13133128	C₂×C₄	1	2	yes	complemented
98	#13133127	C₂×C₄	1	2	yes	complemented
99	#13133127	C₂×C₄	1	2	yes	complemented
100	C₄×#88322	C₂×C₄	1	2	yes	complemented
101	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
102	C₈×Dic₅₃	C₂×C₄	1	2	yes	complemented
103	C₂×M₁₆×C₅₃	C₂³	1	2	yes	—
104	C₂×M₁₆×C₅₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₅₃	C₂³	1	1	yes	characteristic
106	#117×C₅₃	C₂³	1	2	yes	—
107	#117×C₅₃	C₂³	1	1	yes	characteristic
108	#108×C₅₃	—	2	1	no	—
109	#108×C₅₃	—	2	1	no	—
110	#107×C₅₃	—	2	1	no	—
111	#106×C₅₃	—	2	1	no	—
112	#97×C₅₃	C₂×C₄	1	2	yes	complemented
113	C₄×C₈×C₅₃	C₂×C₄	1	2	yes	complemented
114	C₂³×D₅₃	#41	1	1	yes	characteristic
115	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
116	C₂²×Dic₅₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₅₃	—	2	2	no	—
118	C₂×C₄×D₅₃	—	4	2	no	—
119	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₄×D₅₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₅₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
124	C₂×C₄×D₅₃	C₂×Q₈	1	1	yes	characteristic
125	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
126	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
127	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
128	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
129	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
130	C₂×C₄×D₅₃	#41	1	1	yes	characteristic
131	M₁₆×C₅₃	—	2	1	no	—
132	M₁₆×C₅₃	—	2	1	no	—
133	M₁₆×C₅₃	—	2	2	no	—
134	M₁₆×C₅₃	—	2	2	no	—
135	C₂×C₈×C₅₃	—	2	2	no	—
136	C₂×C₈×C₅₃	C₂²×C₄	1	2	yes	—
137	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₅₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₅₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
142	C₂×C₈×C₅₃	C₂×Q₈	1	1	yes	characteristic
143	C₄⋊C₄×C₅₃	—	2	1	no	—
144	C₄⋊C₄×C₅₃	—	2	2	no	—
145	C₂²⋊C₄×C₅₃	—	2	1	no	—
146	C₂²⋊C₄×C₅₃	—	2	2	no	—
147	C₄²×C₅₃	—	2	2	no	—
148	C₄²×C₅₃	C₂²×C₄	1	2	yes	—
149	C₂²⋊Dic₅₃	—	2	1	no	—
150	C₂²⋊Dic₅₃	—	2	2	no	—
151	#11719921	—	2	2	no	—
152	#11719921	—	4	2	no	—
153	C₄⋊Dic₅₃	—	2	1	no	—
154	C₄⋊Dic₅₃	—	2	2	no	—
155	#11719919	—	2	2	no	—
156	#11719919	—	4	2	no	—
157	C₄×Dic₅₃	—	2	2	no	—
158	C₄×Dic₅₃	—	2	2	no	—
159	C₄×Dic₅₃	—	4	2	no	—
160	C₄×Dic₅₃	C₂²×C₄	1	2	yes	—
161	#11719917	—	2	1	no	—
162	#11719917	—	2	1	no	—
163	#11719917	—	2	2	no	—
164	#11719917	—	2	2	no	—
165	C₂×#88322	—	2	2	no	—
166	C₂×#88322	C₂²×C₄	1	2	yes	—
167	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
168	C₂×#88322	C₂²×C₄	1	1	yes	characteristic
169	C₂×#88322	C₂×D₄	1	1	yes	characteristic
170	C₂×#88322	C₂×D₄	1	1	yes	characteristic
171	C₂×#88322	C₂×Q₈	1	1	yes	characteristic
172	C₂×#88322	C₂×Q₈	1	1	yes	characteristic
173	#11719912	—	2	2	no	—
174	#11719912	—	2	2	no	—
175	#11719912	—	4	2	no	—
176	#11719912	—	4	2	no	—
177	C₈×D₅₃	—	2	2	no	—
178	C₈×D₅₃	—	2	2	no	—
179	C₈×D₅₃	—	4	2	no	—
180	C₈×D₅₃	—	4	2	no	—
181	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
182	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
183	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
184	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
185	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
186	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
187	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
188	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
189	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
190	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
191	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
192	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
193	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
194	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
195	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
196	C₈×D₅₃	C₄⋊C₄	1	1	yes	characteristic
197	C₂³×C₅₃	C₂×#41	1	1	yes	characteristic
198	C₂²×D₅₃	—	4	2	no	—
199	C₂²×D₅₃	#117	1	1	yes	characteristic
200	C₂²×D₅₃	#117	1	1	yes	characteristic
201	C₂²×D₅₃	#124	1	1	yes	characteristic
202	C₂²×D₅₃	#124	1	1	yes	characteristic
203	C₂²×D₅₃	#125	1	1	yes	characteristic
204	C₂²×D₅₃	#125	1	1	yes	characteristic
205	C₂×C₄×C₅₃	—	2	2	no	—
206	C₂×C₄×C₅₃	—	4	2	no	—
207	C₂×C₄×C₅₃	C₂³×C₄	1	1	yes	characteristic
208	C₂×C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₅₃	C₂²×Q₈	1	1	yes	characteristic
210	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅₃	C₂×#41	1	1	yes	characteristic
213	C₂×Dic₅₃	—	2	2	no	—
214	C₂×Dic₅₃	—	4	2	no	—
215	C₂×Dic₅₃	#117	1	1	yes	characteristic
216	C₂×Dic₅₃	#117	1	1	yes	characteristic
217	C₂×Dic₅₃	#124	1	1	yes	characteristic
218	C₂×Dic₅₃	#124	1	1	yes	characteristic
219	C₂×Dic₅₃	#125	1	1	yes	characteristic
220	C₂×Dic₅₃	#125	1	1	yes	characteristic
221	C₄×D₅₃	—	4	4	no	—
222	C₄×D₅₃	—	8	4	no	—
223	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
224	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
225	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
226	C₄×D₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
227	C₄×D₅₃	#117	1	1	yes	characteristic
228	C₄×D₅₃	#117	1	1	yes	characteristic
229	C₄×D₅₃	#117	1	1	yes	characteristic
230	C₄×D₅₃	#117	1	1	yes	characteristic
231	C₄×D₅₃	#124	1	1	yes	characteristic
232	C₄×D₅₃	#124	1	1	yes	characteristic
233	C₄×D₅₃	#124	1	1	yes	characteristic
234	C₄×D₅₃	#124	1	1	yes	characteristic
235	C₄×D₅₃	#125	1	1	yes	characteristic
236	C₄×D₅₃	#125	1	1	yes	characteristic
237	C₄×D₅₃	#125	1	1	yes	characteristic
238	C₄×D₅₃	#125	1	1	yes	characteristic
239	C₈×C₅₃	—	2	2	no	—
240	C₈×C₅₃	—	4	2	no	—
241	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
242	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
243	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
244	C₈×C₅₃	C₂×C₄⋊C₄	1	1	yes	characteristic
245	#88322	—	2	2	no	—
246	#88322	—	4	2	no	—
247	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
248	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
249	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
250	#88322	C₂×C₄⋊C₄	1	1	yes	characteristic
251	C₂×#1833	—	53	1	no	maximal, Sylow
252	C₂²×C₅₃	—	4	1	no	—
253	C₂²×C₅₃	C₂×#117	1	1	yes	characteristic
254	C₂²×C₅₃	C₂×#124	1	1	yes	characteristic
255	C₂²×C₅₃	C₂×#125	1	1	yes	characteristic
256	C₂×D₅₃	—	2	2	no	—
257	C₂×D₅₃	—	2	2	no	—
258	C₂×D₅₃	—	2	2	no	—
259	C₂×D₅₃	—	4	1	no	—
260	C₂×D₅₃	—	4	1	no	—
261	C₂×D₅₃	—	4	1	no	—
262	C₂×D₅₃	#382	1	1	yes	characteristic
263	C₂×D₅₃	#382	1	1	yes	characteristic
264	C₂×D₅₃	#382	1	1	yes	characteristic
265	C₂×D₅₃	#382	1	1	yes	characteristic
266	C₄×C₅₃	—	4	2	no	—
267	C₄×C₅₃	—	8	2	no	—
268	C₄×C₅₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₄×C₅₃	C₂×#117	1	1	yes	characteristic
270	C₄×C₅₃	C₂×#124	1	1	yes	characteristic
271	C₄×C₅₃	C₂×#125	1	1	yes	characteristic
272	Dic₅₃	—	4	2	no	—
273	Dic₅₃	—	8	2	no	—
274	Dic₅₃	#382	1	1	yes	characteristic
275	Dic₅₃	#382	1	1	yes	characteristic
276	Dic₅₃	#382	1	1	yes	characteristic
277	Dic₅₃	#382	1	1	yes	characteristic
278	C₂²×#108	—	53	1	no	—
279	C₂×#427	—	53	1	no	—
280	C₂×#405	—	53	1	no	—
281	#1833	—	53	1	no	—
282	#1833	—	53	1	no	—
283	#1833	—	53	1	no	—
284	#1833	—	53	2	no	—
285	#1833	—	53	2	no	—
286	#1833	D₅₃	1	1	yes	characteristic, direct product factor
287	C₂×#344	—	53	2	no	—
288	C₂×H(3,ℤ/4)	—	53	2	no	—
289	C₂×C₅₃	—	2	1	no	—
290	C₂×C₅₃	—	2	1	no	—
291	C₂×C₅₃	—	2	1	no	—
292	C₂×C₅₃	C₂×#382	1	1	yes	characteristic
293	D₅₃	—	2	1	no	—
294	D₅₃	—	2	1	no	—
295	D₅₃	—	2	1	no	—
296	D₅₃	#1833	1	2	yes	direct product factor
297	C₂²×M₁₆	—	53	1	no	—
298	C₂²×M₁₆	—	53	2	no	—
299	C₂³×C₈	—	53	1	no	—
300	C₂×#117	—	53	1	no	—
301	C₂×#117	—	53	2	no	—
302	C₂×#108	—	53	2	no	—
303	C₂×#108	—	53	1	no	—
304	C₂×#108	—	106	1	no	—
305	C₂×#108	—	106	1	no	—
306	C₂×#108	—	106	1	no	—
307	C₂×#108	—	106	1	no	—
308	C₂×#108	C₂×D₅₃	1	1	yes	characteristic
309	#427	—	53	1	no	—
310	#427	—	53	2	no	—
311	#427	—	106	1	no	—
312	#427	—	106	1	no	—
313	#427	C₂×D₅₃	1	1	yes	characteristic
314	C₂×#107	—	106	1	no	—
315	C₂×#106	—	106	1	no	—
316	#405	—	53	1	no	—
317	#405	—	53	1	no	—
318	#405	—	53	1	no	—
319	#405	—	53	2	no	—
320	#405	—	53	2	no	—
321	#405	C₂×D₅₃	1	1	yes	characteristic
322	C₂×#97	—	53	2	no	—
323	C₂×C₄×C₈	—	53	2	no	—
324	#344	—	53	2	no	—
325	#344	—	53	2	no	—
326	#344	—	53	2	no	—
327	#344	C₂×D₅₃	1	2	yes	—
328	H(3,ℤ/4)	—	53	2	no	—
329	H(3,ℤ/4)	—	53	2	no	—
330	H(3,ℤ/4)	—	53	2	no	—
331	H(3,ℤ/4)	C₂×D₅₃	1	2	yes	—
332	C₅₃	C₂×#1833	1	1	yes	characteristic, complemented, Sylow
333	C₂³×C₄	—	53	1	no	—
334	C₂×M₁₆	—	53	1	no	—
335	C₂×M₁₆	—	53	2	no	—
336	C₂×M₁₆	—	53	2	no	—
337	C₂×M₁₆	—	106	2	no	—
338	C₂×M₁₆	—	106	1	no	—
339	C₂×M₁₆	—	106	1	no	—
340	C₂×M₁₆	—	106	1	no	—
341	C₂×M₁₆	—	106	1	no	—
342	C₂×M₁₆	—	106	2	no	—
343	C₂×M₁₆	—	106	2	no	—
344	C₂×M₁₆	—	106	2	no	—
345	C₂×M₁₆	—	106	2	no	—
346	C₂×M₁₆	C₂²×D₅₃	1	2	yes	—
347	C₂×M₁₆	C₂²×D₅₃	1	1	yes	characteristic
348	C₂²×C₈	—	53	1	no	—
349	C₂²×C₈	—	53	1	no	—
350	C₂²×C₈	—	53	1	no	—
351	C₂²×C₈	—	53	1	no	—
352	C₂²×C₈	—	53	1	no	—
353	C₂²×C₈	—	53	1	no	—
354	C₂²×C₈	—	53	1	no	—
355	C₂²×C₈	—	53	1	no	—
356	C₂²×C₈	—	53	1	no	—
357	C₂²×C₈	—	53	1	no	—
358	C₂²×C₈	—	53	1	no	—
359	C₂²×C₈	—	53	1	no	—
360	C₂²×C₈	—	53	1	no	—
361	C₂²×C₈	—	53	2	no	—
362	C₂²×C₈	—	106	2	no	—
363	C₂²×C₈	C₂²×D₅₃	1	1	yes	characteristic
364	#117	—	53	1	no	—
365	#117	—	53	2	no	—
366	#117	—	53	2	no	—
367	#117	—	106	2	no	—
368	#117	—	106	1	no	—
369	#117	—	106	1	no	—
370	#117	—	106	2	no	—
371	#117	—	106	2	no	—
372	#117	C₂²×D₅₃	1	2	yes	—
373	#117	C₂²×D₅₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	—	106	1	no	—
375	C₂×C₄⋊C₄	—	106	2	no	—
376	C₂×C₂²⋊C₄	—	106	1	no	—
377	C₂×C₂²⋊C₄	—	106	2	no	—
378	C₂×C₄²	—	53	2	no	—
379	C₂×C₄²	—	106	2	no	—
380	#108	—	2	1	no	—
381	#108	—	2	1	no	—
382	#108	—	106	2	no	—
383	#108	—	106	2	no	—
384	#108	—	106	1	no	—
385	#108	—	106	1	no	—
386	#107	—	2	1	no	—
387	#107	—	106	2	no	—
388	#107	—	106	1	no	—
389	#106	—	2	1	no	—
390	#106	—	106	2	no	—
391	#106	—	106	1	no	—
392	#97	—	53	2	no	—
393	#97	—	53	2	no	—
394	#97	—	53	2	no	—
395	#97	C₄×D₅₃	1	2	yes	complemented
396	C₄×C₈	—	53	2	no	—
397	C₄×C₈	—	53	2	no	—
398	C₄×C₈	—	53	2	no	—
399	C₄×C₈	C₄×D₅₃	1	2	yes	complemented
400	C₂⁴	—	53	1	no	—
401	C₂²×C₄	—	53	1	no	—
402	C₂²×C₄	—	53	1	no	—
403	C₂²×C₄	—	53	1	no	—
404	C₂²×C₄	—	53	1	no	—
405	C₂²×C₄	—	53	1	no	—
406	C₂²×C₄	—	53	1	no	—
407	C₂²×C₄	—	53	1	no	—
408	C₂²×C₄	—	53	1	no	—
409	C₂²×C₄	—	53	1	no	—
410	C₂²×C₄	—	53	1	no	—
411	C₂²×C₄	—	53	1	no	—
412	C₂²×C₄	—	53	1	no	—
413	C₂²×C₄	—	53	1	no	—
414	C₂²×C₄	—	106	2	no	—
415	C₂²×C₄	—	212	2	no	—
416	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	2	no	—
420	M₁₆	—	2	2	no	—
421	M₁₆	—	106	2	no	—
422	M₁₆	—	106	2	no	—
423	M₁₆	—	106	1	no	—
424	M₁₆	—	106	1	no	—
425	M₁₆	—	106	2	no	—
426	M₁₆	—	106	2	no	—
427	M₁₆	—	212	2	no	—
428	M₁₆	—	212	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	53	1	no	—
431	C₂×C₈	—	53	1	no	—
432	C₂×C₈	—	53	1	no	—
433	C₂×C₈	—	53	1	no	—
434	C₂×C₈	—	53	1	no	—
435	C₂×C₈	—	53	1	no	—
436	C₂×C₈	—	53	1	no	—
437	C₂×C₈	—	53	1	no	—
438	C₂×C₈	—	53	1	no	—
439	C₂×C₈	—	53	1	no	—
440	C₂×C₈	—	53	1	no	—
441	C₂×C₈	—	53	1	no	—
442	C₂×C₈	—	53	1	no	—
443	C₂×C₈	—	53	1	no	—
444	C₂×C₈	—	53	1	no	—
445	C₂×C₈	—	53	1	no	—
446	C₂×C₈	—	53	1	no	—
447	C₂×C₈	—	53	1	no	—
448	C₂×C₈	—	53	1	no	—
449	C₂×C₈	—	53	1	no	—
450	C₂×C₈	—	53	1	no	—
451	C₂×C₈	—	53	1	no	—
452	C₂×C₈	—	53	2	no	—
453	C₂×C₈	—	106	2	no	—
454	C₂×C₈	—	106	2	no	—
455	C₂×C₈	—	106	2	no	—
456	C₂×C₈	—	212	2	no	—
457	C₂×C₈	—	212	2	no	—
458	C₂×C₈	C₂×C₄×D₅₃	1	2	yes	—
459	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
460	C₂×C₈	C₂×C₄×D₅₃	1	1	yes	characteristic
461	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
462	C₂×C₈	D₄×D₅₃	1	1	yes	characteristic
463	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
464	C₂×C₈	Q₈×D₅₃	1	1	yes	characteristic
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	106	2	no	—
468	C₄⋊C₄	—	106	1	no	—
469	C₄⋊C₄	—	106	2	no	—
470	C₄⋊C₄	—	212	2	no	—
471	C₂²⋊C₄	—	2	1	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	106	2	no	—
474	C₂²⋊C₄	—	106	1	no	—
475	C₂²⋊C₄	—	106	2	no	—
476	C₂²⋊C₄	—	212	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	53	2	no	—
479	C₄²	—	106	2	no	—
480	C₄²	—	106	2	no	—
481	C₄²	—	212	2	no	—
482	C₄²	C₂×C₄×D₅₃	1	2	yes	—
483	C₂³	—	53	1	no	—
484	C₂³	—	53	1	no	—
485	C₂³	—	53	1	no	—
486	C₂³	—	53	1	no	—
487	C₂³	—	53	1	no	—
488	C₂³	—	53	1	no	—
489	C₂³	—	212	2	no	—
490	C₂³	#41×D₅₃	1	1	yes	characteristic
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	53	1	no	—
494	C₂×C₄	—	53	1	no	—
495	C₂×C₄	—	53	1	no	—
496	C₂×C₄	—	53	1	no	—
497	C₂×C₄	—	53	1	no	—
498	C₂×C₄	—	53	1	no	—
499	C₂×C₄	—	53	1	no	—
500	C₂×C₄	—	53	1	no	—
501	C₂×C₄	—	53	1	no	—
502	C₂×C₄	—	53	1	no	—
503	C₂×C₄	—	53	1	no	—
504	C₂×C₄	—	53	1	no	—
505	C₂×C₄	—	53	1	no	—
506	C₂×C₄	—	53	1	no	—
507	C₂×C₄	—	53	1	no	—
508	C₂×C₄	—	53	1	no	—
509	C₂×C₄	—	53	1	no	—
510	C₂×C₄	—	53	1	no	—
511	C₂×C₄	—	53	1	no	—
512	C₂×C₄	—	53	1	no	—
513	C₂×C₄	—	53	1	no	—
514	C₂×C₄	—	53	1	no	—
515	C₂×C₄	—	106	2	no	—
516	C₂×C₄	—	424	4	no	—
517	C₂×C₄	—	212	4	no	—
518	C₂×C₄	—	212	2	no	—
519	C₂×C₄	C₂²×C₄×D₅₃	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
521	C₂×C₄	C₂×Q₈×D₅₃	1	1	yes	characteristic
522	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
523	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
524	C₂×C₄	#41×D₅₃	1	1	yes	characteristic
525	C₈	—	2	2	no	—
526	C₈	—	4	2	no	—
527	C₈	—	53	1	no	—
528	C₈	—	53	1	no	—
529	C₈	—	53	1	no	—
530	C₈	—	53	1	no	—
531	C₈	—	106	2	no	—
532	C₈	—	212	2	no	—
533	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
534	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
535	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
536	C₈	C₄⋊C₄×D₅₃	1	1	yes	characteristic
537	C₂²	—	4	1	no	—
538	C₂²	—	53	1	no	—
539	C₂²	—	53	1	no	—
540	C₂²	—	53	1	no	—
541	C₂²	—	53	1	no	—
542	C₂²	—	106	2	no	—
543	C₂²	—	106	2	no	—
544	C₂²	—	106	2	no	—
545	C₂²	—	212	1	no	—
546	C₂²	—	212	1	no	—
547	C₂²	—	212	1	no	—
548	C₂²	#117×D₅₃	1	1	yes	characteristic
549	C₂²	#124×D₅₃	1	1	yes	characteristic
550	C₂²	#125×D₅₃	1	1	yes	characteristic
551	C₄	—	4	2	no	—
552	C₄	—	8	2	no	—
553	C₄	—	53	1	no	—
554	C₄	—	53	1	no	—
555	C₄	—	53	1	no	—
556	C₄	—	53	1	no	—
557	C₄	—	424	2	no	—
558	C₄	—	212	2	no	—
559	C₄	C₂×C₄⋊C₄×D₅₃	1	1	yes	characteristic
560	C₄	#117×D₅₃	1	1	yes	characteristic
561	C₄	#124×D₅₃	1	1	yes	characteristic
562	C₄	#125×D₅₃	1	1	yes	characteristic
563	C₂	—	2	1	no	—
564	C₂	—	2	1	no	—
565	C₂	—	2	1	no	—
566	C₂	—	53	2	no	—
567	C₂	—	106	1	no	—
568	C₂	—	106	1	no	—
569	C₂	—	106	1	no	—
570	C₂	#382×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₅₃
commutator	C₂×C₄×C₅₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₅₃
Fitting	C₅₃×#1833	C₂
socle	C₂×C₅₃	C₂×#382
prime radical	C₂³×D₅₃	#41
cosocle	C₂²×C₄×C₅₃	C₂⁴
hypercenter	#1833	D₅₃
hypocenter	C₅₃	C₂×#1833
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₄ ◁ #117 ◁ #1833

Complements

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

N	H ≅ G/N	type
4. #20274840	C₂	semidirect
5. #20274839	C₂	semidirect
6. #20274838	C₂	semidirect
7. #20274837	C₂	semidirect
8. #20274836	C₂	semidirect
11. C₅₃×#1833	C₂	semidirect
30. #16810580	C₄	semidirect
33. #16810577	C₄	semidirect
34. #97×D₅₃	C₄	semidirect
35. C₄×C₈×D₅₃	C₄	semidirect
97. #13133128	C₂×C₄	semidirect
98. #13133127	C₂×C₄	semidirect
99. #13133127	C₂×C₄	semidirect
100. C₄×#88322	C₂×C₄	semidirect
101. C₈×Dic₅₃	C₂×C₄	semidirect
102. C₈×Dic₅₃	C₂×C₄	semidirect
112. #97×C₅₃	C₂×C₄	semidirect
113. C₄×C₈×C₅₃	C₂×C₄	semidirect
286. #1833	D₅₃	direct (N × H)
296. D₅₃	#1833	direct (N × H)
332. C₅₃	C₂×#1833	semidirect
395. #97	C₄×D₅₃	semidirect
399. 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
C₂×#108×D₅₃	2
#427×D₅₃	2
#405×D₅₃	2
#20274840	2
#20274839	2
#20274838	2
#20274837	2
#20274836	2
#344×D₅₃	2
H(3,ℤ/4)×D₅₃	2
C₅₃×#1833	2
C₂×#1833	53

Subgroups — D53×#1833 #27384261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#1833 #27384261