Subgroups — C₁₃×#21966 #15708305

Order 3328.

754 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#424	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2314	C₂	1	2	yes	maximal
3	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1949	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1948	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1947	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1809	C₂	1	2	yes	maximal
8	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1807	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#107	C₂²	1	2	yes	—
14	C₂×C₁₃×#107	C₂²	1	2	yes	—
15	C₂×C₁₃×#106	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	2	yes	—
17	C₁₃×#424	C₄	1	8	yes	complemented
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₁₃×#388	—	2	2	no	—
21	C₁₃×#388	—	2	2	no	—
22	C₁₃×#387	—	2	2	no	—
23	C₁₃×#387	—	2	2	no	—
24	C₁₃×#384	C₂²	1	2	yes	—
25	C₁₃×#382	C₂²	1	2	yes	—
26	C₁₃×#380	C₂²	1	2	yes	—
27	C₁₃×#380	C₂²	1	2	yes	—
28	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
29	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
30	C₁₃×#340	C₂²	1	1	yes	characteristic
31	C₁₃×#340	C₂²	1	1	yes	characteristic
32	C₁₃×#340	C₂²	1	1	yes	characteristic
33	C₁₃×#340	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₁₃×M₁₆	—	4	2	no	—
38	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₁₃	—	4	2	no	—
40	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₁₃×#117	C₂×C₄	1	4	yes	—
45	C₁₃×#117	Q₈	1	4	yes	—
46	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
49	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
50	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
51	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
52	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
53	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
54	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
57	C₂×C₄²×C₁₃	—	2	2	no	—
58	C₂×C₄²×C₁₃	—	2	2	no	—
59	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
60	C₁₃×#107	—	4	2	no	—
61	C₁₃×#107	—	4	2	no	—
62	C₁₃×#106	—	4	2	no	—
63	C₁₃×#106	—	4	2	no	—
64	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
65	C₁₃×C₄⋊C₈	C₂×C₄	1	8	yes	—
66	C₁₃×#95	—	2	2	no	—
67	C₁₃×#95	—	2	2	no	—
68	C₁₃×#95	—	2	2	no	—
69	C₁₃×#95	—	2	2	no	—
70	C₁₃×#95	—	2	2	no	—
71	C₁₃×#95	—	2	2	no	—
72	#21966	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
73	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	—	2	2	no	—
75	C₂²×C₄×C₁₃	—	2	2	no	—
76	C₂²×C₄×C₁₃	—	2	2	no	—
77	C₂²×C₄×C₁₃	—	2	2	no	—
78	C₂²×C₄×C₁₃	—	2	2	no	—
79	C₂²×C₄×C₁₃	—	2	2	no	—
80	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
86	C₁₃×M₁₆	—	4	4	no	—
87	C₂×C₈×C₁₃	—	2	2	no	—
88	C₂×C₈×C₁₃	—	2	2	no	—
89	C₂×C₈×C₁₃	—	2	2	no	—
90	C₂×C₈×C₁₃	—	2	2	no	—
91	C₂×C₈×C₁₃	—	4	4	no	—
92	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
95	C₁₃×C₄⋊C₄	—	2	2	no	—
96	C₁₃×C₄⋊C₄	—	2	2	no	—
97	C₁₃×C₄⋊C₄	—	2	2	no	—
98	C₁₃×C₄⋊C₄	—	2	2	no	—
99	C₁₃×C₄⋊C₄	—	2	2	no	—
100	C₁₃×C₄⋊C₄	—	2	2	no	—
101	C₁₃×C₄⋊C₄	—	2	2	no	—
102	C₁₃×C₄⋊C₄	—	2	2	no	—
103	C₁₃×C₄⋊C₄	—	8	2	no	—
104	C₁₃×C₄⋊C₄	—	8	2	no	—
105	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
106	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
107	C₁₃×C₂²⋊C₄	—	8	2	no	—
108	C₁₃×C₂²⋊C₄	—	8	2	no	—
109	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
110	C₄²×C₁₃	—	8	2	no	—
111	C₄²×C₁₃	—	8	2	no	—
112	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
113	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
114	C₂×#424	C₂×C₁₃	1	1	yes	characteristic
115	#2314	C₂×C₁₃	1	2	yes	—
116	#1949	C₂×C₁₃	1	2	yes	complemented
117	#1949	C₂×C₁₃	1	2	yes	complemented
118	#1948	C₂×C₁₃	1	2	yes	complemented
119	#1947	C₂×C₁₃	1	2	yes	complemented
120	#1809	C₂×C₁₃	1	2	yes	—
121	#1808	C₂×C₁₃	1	1	yes	characteristic
122	#1807	C₂×C₁₃	1	1	yes	characteristic
123	C₂³×C₁₃	—	2	2	no	—
124	C₂³×C₁₃	—	2	1	no	—
125	C₂³×C₁₃	—	2	2	no	—
126	C₂³×C₁₃	—	2	1	no	—
127	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₃	—	2	2	no	—
130	C₂×C₄×C₁₃	—	2	2	no	—
131	C₂×C₄×C₁₃	—	2	2	no	—
132	C₂×C₄×C₁₃	—	2	2	no	—
133	C₂×C₄×C₁₃	—	2	2	no	—
134	C₂×C₄×C₁₃	—	2	2	no	—
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	—	2	4	no	—
137	C₂×C₄×C₁₃	—	4	2	no	—
138	C₂×C₄×C₁₃	—	4	2	no	—
139	C₂×C₄×C₁₃	—	4	2	no	—
140	C₂×C₄×C₁₃	—	4	2	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	2	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	4	2	no	—
146	C₂×C₄×C₁₃	—	4	2	no	—
147	C₂×C₄×C₁₃	—	4	2	no	—
148	C₂×C₄×C₁₃	—	4	2	no	—
149	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
152	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
155	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
156	C₈×C₁₃	—	2	2	no	—
157	C₈×C₁₃	—	2	2	no	—
158	C₈×C₁₃	—	2	4	no	—
159	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
160	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
161	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
162	C₂×#107	C₂²×C₁₃	1	2	yes	—
163	C₂×#107	C₂²×C₁₃	1	2	yes	—
164	C₂×#106	C₂²×C₁₃	1	2	yes	—
165	C₂×#106	C₂²×C₁₃	1	2	yes	—
166	#424	C₄×C₁₃	1	8	yes	complemented
167	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
168	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
169	#388	—	2	2	no	—
170	#388	—	2	2	no	—
171	#387	—	2	2	no	—
172	#387	—	2	2	no	—
173	#384	C₂²×C₁₃	1	2	yes	—
174	#382	C₂²×C₁₃	1	2	yes	—
175	#380	C₂²×C₁₃	1	2	yes	—
176	#380	C₂²×C₁₃	1	2	yes	—
177	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
178	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
179	#340	C₂²×C₁₃	1	1	yes	characteristic
180	#340	C₂²×C₁₃	1	1	yes	characteristic
181	#340	C₂²×C₁₃	1	1	yes	characteristic
182	#340	C₂²×C₁₃	1	1	yes	characteristic
183	#340	C₂²×C₁₃	1	2	yes	—
184	#340	C₂²×C₁₃	1	2	yes	—
185	C₂²×C₁₃	—	2	2	no	—
186	C₂²×C₁₃	—	2	2	no	—
187	C₂²×C₁₃	—	2	2	no	—
188	C₂²×C₁₃	—	4	2	no	—
189	C₂²×C₁₃	—	4	2	no	—
190	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
191	C₂²×C₁₃	#537	1	2	yes	—
192	C₂²×C₁₃	#576	1	1	yes	characteristic
193	C₂²×C₁₃	#577	1	2	yes	—
194	C₂²×C₁₃	#578	1	1	yes	characteristic
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	4	no	—
197	C₄×C₁₃	—	2	4	no	—
198	C₄×C₁₃	—	8	2	no	—
199	C₄×C₁₃	—	8	2	no	—
200	C₄×C₁₃	—	8	2	no	—
201	C₄×C₁₃	—	8	2	no	—
202	C₄×C₁₃	#518	1	1	yes	characteristic
203	C₄×C₁₃	#519	1	1	yes	characteristic
204	C₄×C₁₃	#544	1	2	yes	—
205	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
206	C₂×M₁₆	—	4	2	no	—
207	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
208	C₂²×C₈	—	4	2	no	—
209	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
210	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
211	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
212	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
213	#117	C₂×C₄×C₁₃	1	4	yes	—
214	#117	Q₈×C₁₃	1	4	yes	—
215	C₂×C₄⋊C₄	—	2	2	no	—
216	C₂×C₄⋊C₄	—	2	2	no	—
217	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
218	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
219	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
220	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
221	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
222	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
223	C₂×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
226	C₂×C₄²	—	2	2	no	—
227	C₂×C₄²	—	2	2	no	—
228	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
229	#107	—	4	2	no	—
230	#107	—	4	2	no	—
231	#106	—	4	2	no	—
232	#106	—	4	2	no	—
233	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
234	C₄⋊C₈	C₂×C₄×C₁₃	1	8	yes	—
235	#95	—	2	2	no	—
236	#95	—	2	2	no	—
237	#95	—	2	2	no	—
238	#95	—	2	2	no	—
239	#95	—	2	2	no	—
240	#95	—	2	2	no	—
241	C₂×C₁₃	—	4	2	no	—
242	C₂×C₁₃	#2316	1	1	yes	characteristic
243	C₂×C₁₃	#2912	1	1	yes	characteristic
244	C₂×C₁₃	#2913	1	1	yes	characteristic
245	C₂×C₁₃	#3257	1	2	yes	—
246	C₂×C₁₃	#3258	1	2	yes	—
247	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	—	2	2	no	—
250	C₂²×C₄	—	2	2	no	—
251	C₂²×C₄	—	2	2	no	—
252	C₂²×C₄	—	2	2	no	—
253	C₂²×C₄	—	2	2	no	—
254	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
255	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
257	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
258	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
259	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
260	M₁₆	—	4	4	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	4	4	no	—
266	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
267	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
268	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
269	C₄⋊C₄	—	2	2	no	—
270	C₄⋊C₄	—	2	2	no	—
271	C₄⋊C₄	—	2	2	no	—
272	C₄⋊C₄	—	2	2	no	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	8	2	no	—
278	C₄⋊C₄	—	8	2	no	—
279	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
280	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
281	C₂²⋊C₄	—	8	2	no	—
282	C₂²⋊C₄	—	8	2	no	—
283	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
284	C₄²	—	8	2	no	—
285	C₄²	—	8	2	no	—
286	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
287	C₄²	C₂×Q₈×C₁₃	1	4	yes	—
288	C₁₃	#21966	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³	—	2	2	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	1	no	—
293	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
294	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	4	2	no	—
307	C₂×C₄	—	4	2	no	—
308	C₂×C₄	—	4	2	no	—
309	C₂×C₄	—	4	2	no	—
310	C₂×C₄	—	4	2	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
316	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
317	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
318	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
320	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
321	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
322	C₈	—	2	2	no	—
323	C₈	—	2	2	no	—
324	C₈	—	2	4	no	—
325	C₂²	—	2	2	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	4	2	no	—
329	C₂²	—	4	2	no	—
330	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
331	C₂²	C₁₃×#537	1	2	yes	—
332	C₂²	C₁₃×#576	1	1	yes	characteristic
333	C₂²	C₁₃×#577	1	2	yes	—
334	C₂²	C₁₃×#578	1	1	yes	characteristic
335	C₄	—	2	2	no	—
336	C₄	—	2	4	no	—
337	C₄	—	2	4	no	—
338	C₄	—	8	2	no	—
339	C₄	—	8	2	no	—
340	C₄	—	8	2	no	—
341	C₄	—	8	2	no	—
342	C₄	C₁₃×#518	1	1	yes	characteristic
343	C₄	C₁₃×#519	1	1	yes	characteristic
344	C₄	C₁₃×#544	1	2	yes	—
345	C₂	—	4	2	no	—
346	C₂	C₁₃×#2316	1	1	yes	characteristic
347	C₂	C₁₃×#2912	1	1	yes	characteristic
348	C₂	C₁₃×#2913	1	1	yes	characteristic
349	C₂	C₁₃×#3257	1	2	yes	—
350	C₂	C₁₃×#3258	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1949	C₂	semidirect
4. C₁₃×#1949	C₂	semidirect
5. C₁₃×#1948	C₂	semidirect
6. C₁₃×#1947	C₂	semidirect
17. C₁₃×#424	C₄	semidirect
72. #21966	C₁₃	direct (N × H)
116. #1949	C₂×C₁₃	semidirect
117. #1949	C₂×C₁₃	semidirect
118. #1948	C₂×C₁₃	semidirect
119. #1947	C₂×C₁₃	semidirect
166. #424	C₄×C₁₃	semidirect
288. C₁₃	#21966	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#424	2
C₁₃×#2314	2
C₁₃×#1949	2
C₁₃×#1948	2
C₁₃×#1947	2
C₁₃×#1809	2
C₁₃×#1808	2
C₁₃×#1807	2
#21966	13

Subgroups — C13×#21966 #15708305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21966 #15708305