Subgroups — #462×D₅₃ #20284149

Order 6784.

480 conjugacy classes of subgroups.

The subgroup lattice has 284 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×D₅₃	C₂	1	2	yes	maximal
2	C₄⋊Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×D₅₃	C₂	1	1	yes	maximal, characteristic
4	#16810834	C₂	1	1	yes	maximal, characteristic, complemented
5	#16810833	C₂	1	1	yes	maximal, characteristic, complemented
6	#16810832	C₂	1	2	yes	maximal, complemented
7	#16810831	C₂	1	2	yes	maximal, complemented
8	#16810830	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₈×D₅₃	C₂	1	1	yes	maximal, characteristic
10	#103×D₅₃	C₂	1	2	yes	maximal
11	C₅₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₈×D₅₃	C₂²	1	2	yes	—
13	C₂×Q₈×D₅₃	C₂²	1	1	yes	characteristic
14	C₂×Dic₂₁₂	C₂²	1	2	yes	—
15	C₂×#11719925	C₂²	1	2	yes	—
16	C₂×#11719925	C₂²	1	2	yes	—
17	Q₁₆×D₅₃	—	2	8	no	—
18	C₂×C₈×D₅₃	C₂²	1	2	yes	—
19	#13133217	C₂²	1	1	yes	characteristic
20	#13133216	—	2	1	no	—
21	#13133216	—	2	1	no	—
22	#13133215	C₂²	1	2	yes	—
23	Q₈×Dic₅₃	C₂²	1	1	yes	characteristic
24	C₄×Dic₁₀₆	—	2	1	no	—
25	C₄×Dic₁₀₆	C₂²	1	1	yes	characteristic
26	#13133182	—	2	1	no	—
27	#13133182	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×D₅₃	—	2	1	no	—
29	C₄⋊C₄×D₅₃	—	2	1	no	—
30	C₄⋊C₄×D₅₃	—	2	1	no	—
31	C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic
32	C₄²×D₅₃	—	2	1	no	—
33	C₄²×D₅₃	C₂²	1	1	yes	characteristic
34	C₄⋊#88322	C₂²	1	1	yes	characteristic
35	#13133146	C₂²	1	2	yes	—
36	#13133142	C₂²	1	2	yes	—
37	#13133141	C₂²	1	2	yes	—
38	#13133140	C₂²	1	2	yes	—
39	C₂×Q₁₆×C₅₃	C₂²	1	2	yes	—
40	C₄⋊Q₈×C₅₃	C₂²	1	1	yes	characteristic
41	C₄×Q₈×C₅₃	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×C₅₃	C₂²	1	1	yes	characteristic
43	#103×C₅₃	C₂²	1	2	yes	—
44	C₂×Q₈×C₅₃	C₂³	1	2	yes	—
45	C₂×Q₈×C₅₃	C₂³	1	1	yes	characteristic
46	Q₈×D₅₃	—	2	2	no	—
47	Q₈×D₅₃	—	2	4	no	—
48	Q₈×D₅₃	—	2	4	no	—
49	Q₈×D₅₃	D₄	1	4	yes	—
50	C₂×C₄×D₅₃	—	2	1	no	—
51	C₂×C₄×D₅₃	—	2	1	no	—
52	C₂×C₄×D₅₃	—	2	2	no	—
53	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
54	C₂×C₄×D₅₃	D₄	1	1	yes	characteristic
55	C₂×C₄×D₅₃	C₂³	1	1	yes	characteristic
56	C₂×Dic₁₀₆	—	2	1	no	—
57	C₂×Dic₁₀₆	—	2	2	no	—
58	C₂×Dic₁₀₆	C₂³	1	2	yes	—
59	C₂×Dic₁₀₆	C₂³	1	1	yes	characteristic
60	Q₁₆×C₅₃	—	2	4	no	—
61	C₂×C₈×C₅₃	C₂³	1	2	yes	—
62	C₄⋊C₄×C₅₃	—	2	1	no	—
63	C₄⋊C₄×C₅₃	—	2	1	no	—
64	C₄⋊C₄×C₅₃	—	2	1	no	—
65	C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic
66	C₄²×C₅₃	—	2	1	no	—
67	C₄²×C₅₃	C₂³	1	1	yes	characteristic
68	#11719925	—	2	4	no	—
69	#11719925	—	2	4	no	—
70	C₄⋊Dic₅₃	—	2	1	no	—
71	C₄⋊Dic₅₃	—	2	1	no	—
72	C₄⋊Dic₅₃	—	2	1	no	—
73	C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic
74	#11719919	—	2	1	no	—
75	#11719919	—	2	1	no	—
76	#11719919	—	2	2	no	—
77	#11719919	—	2	2	no	—
78	#11719919	—	2	1	no	—
79	C₄×Dic₅₃	—	2	1	no	—
80	C₄×Dic₅₃	—	2	1	no	—
81	C₄×Dic₅₃	—	2	1	no	—
82	C₄×Dic₅₃	D₄	1	1	yes	characteristic
83	C₄×Dic₅₃	D₄	1	1	yes	characteristic
84	C₄×Dic₅₃	C₂³	1	1	yes	characteristic
85	C₂×#88322	C₂³	1	2	yes	—
86	Dic₂₁₂	—	2	4	no	—
87	C₈×D₅₃	—	2	4	no	—
88	C₂²×D₅₃	C₂×D₄	1	1	yes	characteristic
89	Q₈×C₅₃	—	2	1	no	—
90	Q₈×C₅₃	—	2	2	no	—
91	Q₈×C₅₃	—	2	2	no	—
92	Q₈×C₅₃	C₂×D₄	1	2	yes	—
93	C₂×C₄×C₅₃	—	2	1	no	—
94	C₂×C₄×C₅₃	—	2	2	no	—
95	C₂×C₄×C₅₃	—	2	1	no	—
96	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×C₅₃	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
99	C₂×Dic₅₃	—	2	1	no	—
100	C₂×Dic₅₃	—	2	2	no	—
101	C₂×Dic₅₃	—	2	1	no	—
102	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
103	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
104	C₂×Dic₅₃	C₂×D₄	1	1	yes	characteristic
105	C₄×D₅₃	—	2	4	no	—
106	C₄×D₅₃	—	2	2	no	—
107	C₄×D₅₃	—	4	4	no	—
108	C₄×D₅₃	—	4	2	no	—
109	C₄×D₅₃	Q₁₆	1	4	yes	complemented
110	C₄×D₅₃	C₂×D₄	1	2	yes	—
111	C₄×D₅₃	#41	1	2	yes	—
112	Dic₁₀₆	—	2	1	no	—
113	Dic₁₀₆	—	2	4	no	—
114	Dic₁₀₆	—	2	2	no	—
115	Dic₁₀₆	—	2	2	no	—
116	Dic₁₀₆	—	4	4	no	—
117	Dic₁₀₆	C₂×D₄	1	2	yes	—
118	C₈×C₅₃	—	2	2	no	—
119	#88322	—	2	2	no	—
120	C₂²×C₅₃	C₂²×D₄	1	1	yes	characteristic
121	C₂×D₅₃	#121	1	2	yes	—
122	C₂×D₅₃	C₂×Q₁₆	1	2	yes	—
123	C₂×D₅₃	#137	1	2	yes	—
124	C₄×C₅₃	—	2	2	no	—
125	C₄×C₅₃	—	2	1	no	—
126	C₄×C₅₃	—	4	2	no	—
127	C₄×C₅₃	—	4	1	no	—
128	C₄×C₅₃	C₂×Q₁₆	1	2	yes	complemented
129	C₄×C₅₃	C₂²×D₄	1	1	yes	characteristic
130	C₄×C₅₃	C₂×#41	1	1	yes	characteristic
131	Dic₅₃	—	2	2	no	—
132	Dic₅₃	—	2	1	no	—
133	Dic₅₃	—	4	2	no	—
134	Dic₅₃	—	4	1	no	—
135	Dic₅₃	#121	1	2	yes	—
136	Dic₅₃	C₂×Q₁₆	1	2	yes	complemented
137	C₂×#462	—	53	1	no	maximal, Sylow
138	C₂×C₅₃	C₂×#121	1	1	yes	characteristic
139	C₂×C₅₃	C₂²×Q₁₆	1	1	yes	characteristic
140	C₂×C₅₃	C₂×#137	1	1	yes	characteristic
141	D₅₃	#462	1	4	yes	direct product factor
142	C₂²×Q₁₆	—	53	2	no	—
143	C₂×C₄⋊Q₈	—	53	1	no	—
144	C₂×C₄×Q₈	—	53	1	no	—
145	#462	—	53	2	no	—
146	#462	—	53	1	no	—
147	#462	—	53	1	no	—
148	#462	—	53	1	no	—
149	#462	—	53	2	no	—
150	#462	D₅₃	1	1	yes	characteristic, direct product factor
151	C₂×C₄⋊C₈	—	53	1	no	—
152	C₂×#103	—	53	2	no	—
153	C₅₃	C₂×#462	1	1	yes	characteristic, complemented, Sylow
154	C₂²×Q₈	—	53	1	no	—
155	C₂²×Q₈	—	53	2	no	—
156	C₂×Q₁₆	—	53	2	no	—
157	C₂×Q₁₆	—	53	2	no	—
158	C₂×Q₁₆	—	53	2	no	—
159	C₂×Q₁₆	—	106	8	no	—
160	C₂×Q₁₆	C₂×D₅₃	1	2	yes	—
161	C₂²×C₈	—	53	2	no	—
162	C₄⋊Q₈	—	53	2	no	—
163	C₄⋊Q₈	—	53	1	no	—
164	C₄⋊Q₈	—	106	1	no	—
165	C₄⋊Q₈	—	106	1	no	—
166	C₄⋊Q₈	C₂×D₅₃	1	1	yes	characteristic
167	C₄×Q₈	—	53	1	no	—
168	C₄×Q₈	—	53	1	no	—
169	C₄×Q₈	—	53	1	no	—
170	C₄×Q₈	—	106	1	no	—
171	C₄×Q₈	—	106	1	no	—
172	C₄×Q₈	C₂×D₅₃	1	1	yes	characteristic
173	C₂×C₄⋊C₄	—	53	1	no	—
174	C₂×C₄⋊C₄	—	106	1	no	—
175	C₂×C₄⋊C₄	—	106	1	no	—
176	C₂×C₄⋊C₄	—	106	1	no	—
177	C₂×C₄²	—	53	1	no	—
178	C₂×C₄²	—	106	1	no	—
179	C₄⋊C₈	—	53	2	no	—
180	C₄⋊C₈	—	53	1	no	—
181	C₄⋊C₈	C₂×D₅₃	1	1	yes	characteristic
182	#103	—	53	2	no	—
183	#103	—	53	2	no	—
184	#103	—	53	2	no	—
185	#103	C₂×D₅₃	1	2	yes	—
186	C₂×Q₈	—	53	4	no	—
187	C₂×Q₈	—	53	1	no	—
188	C₂×Q₈	—	53	2	no	—
189	C₂×Q₈	—	106	1	no	—
190	C₂×Q₈	—	106	2	no	—
191	C₂×Q₈	—	106	2	no	—
192	C₂×Q₈	—	106	4	no	—
193	C₂×Q₈	—	106	4	no	—
194	C₂×Q₈	C₂²×D₅₃	1	2	yes	—
195	C₂×Q₈	C₂²×D₅₃	1	1	yes	characteristic
196	C₂²×C₄	—	53	1	no	—
197	C₂²×C₄	—	53	1	no	—
198	C₂²×C₄	—	53	1	no	—
199	C₂²×C₄	—	106	1	no	—
200	C₂²×C₄	—	106	1	no	—
201	C₂²×C₄	—	106	2	no	—
202	Q₁₆	—	2	4	no	—
203	Q₁₆	—	106	4	no	—
204	Q₁₆	—	106	4	no	—
205	Q₁₆	—	106	4	no	—
206	C₂×C₈	—	53	2	no	—
207	C₂×C₈	—	106	4	no	—
208	C₂×C₈	C₂²×D₅₃	1	2	yes	—
209	C₄⋊C₄	—	2	1	no	—
210	C₄⋊C₄	—	2	1	no	—
211	C₄⋊C₄	—	2	1	no	—
212	C₄⋊C₄	—	53	1	no	—
213	C₄⋊C₄	—	106	1	no	—
214	C₄⋊C₄	—	106	1	no	—
215	C₄⋊C₄	—	106	1	no	—
216	C₄⋊C₄	—	106	2	no	—
217	C₄⋊C₄	—	106	2	no	—
218	C₄⋊C₄	—	106	1	no	—
219	C₄⋊C₄	—	106	1	no	—
220	C₄⋊C₄	—	106	1	no	—
221	C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic
222	C₄²	—	2	1	no	—
223	C₄²	—	53	1	no	—
224	C₄²	—	53	1	no	—
225	C₄²	—	53	1	no	—
226	C₄²	—	106	1	no	—
227	C₄²	—	106	1	no	—
228	C₄²	—	106	1	no	—
229	C₄²	C₂²×D₅₃	1	1	yes	characteristic
230	C₂³	—	53	1	no	—
231	Q₈	—	2	1	no	—
232	Q₈	—	2	2	no	—
233	Q₈	—	2	2	no	—
234	Q₈	—	53	2	no	—
235	Q₈	—	106	4	no	—
236	Q₈	—	106	1	no	—
237	Q₈	—	106	2	no	—
238	Q₈	—	106	2	no	—
239	Q₈	—	212	4	no	—
240	Q₈	D₄×D₅₃	1	2	yes	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	2	no	—
244	C₂×C₄	—	53	1	no	—
245	C₂×C₄	—	53	1	no	—
246	C₂×C₄	—	53	4	no	—
247	C₂×C₄	—	53	2	no	—
248	C₂×C₄	—	53	2	no	—
249	C₂×C₄	—	53	1	no	—
250	C₂×C₄	—	106	2	no	—
251	C₂×C₄	—	106	4	no	—
252	C₂×C₄	—	106	1	no	—
253	C₂×C₄	—	106	1	no	—
254	C₂×C₄	—	106	2	no	—
255	C₂×C₄	—	212	2	no	—
256	C₂×C₄	—	212	4	no	—
257	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
258	C₂×C₄	D₄×D₅₃	1	1	yes	characteristic
259	C₂×C₄	C₂³×D₅₃	1	1	yes	characteristic
260	C₈	—	2	2	no	—
261	C₈	—	106	2	no	—
262	C₂²	—	53	2	no	—
263	C₂²	—	53	2	no	—
264	C₂²	—	53	2	no	—
265	C₂²	C₂×D₄×D₅₃	1	1	yes	characteristic
266	C₄	—	2	2	no	—
267	C₄	—	2	1	no	—
268	C₄	—	4	2	no	—
269	C₄	—	4	1	no	—
270	C₄	—	53	2	no	—
271	C₄	—	53	2	no	—
272	C₄	—	106	2	no	—
273	C₄	—	106	1	no	—
274	C₄	—	212	2	no	—
275	C₄	—	212	1	no	—
276	C₄	Q₁₆×D₅₃	1	2	yes	complemented
277	C₄	C₂×D₄×D₅₃	1	1	yes	characteristic
278	C₄	#41×D₅₃	1	1	yes	characteristic
279	C₂	—	53	4	no	—
280	C₂	#121×D₅₃	1	1	yes	characteristic
281	C₂	C₂×Q₁₆×D₅₃	1	1	yes	characteristic
282	C₂	#137×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₃
commutator	C₂×C₄×C₅₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₃
Fitting	C₅₃×#462	C₂
socle	C₂²×C₅₃	C₂²×D₄
hypercenter	#462	D₅₃
hypocenter	C₅₃	C₂×#462
LCS	G ▷ C₂×C₄×C₅₃ ▷ C₂×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #462

Complements

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

N	H ≅ G/N	type
4. #16810834	C₂	semidirect
5. #16810833	C₂	semidirect
6. #16810832	C₂	semidirect
7. #16810831	C₂	semidirect
8. #16810830	C₂	semidirect
11. C₅₃×#462	C₂	semidirect
109. C₄×D₅₃	Q₁₆	semidirect
128. C₄×C₅₃	C₂×Q₁₆	semidirect
136. Dic₅₃	C₂×Q₁₆	semidirect
141. D₅₃	#462	direct (N × H)
150. #462	D₅₃	direct (N × H)
153. C₅₃	C₂×#462	semidirect
276. C₄	Q₁₆×D₅₃	semidirect

Subgroups — #462×D53 #20284149

Conjugacy classes of subgroups

Complements

Subgroups — #462×D₅₃ #20284149