Subgroups — C₃₁×#21966 #21478725

Order 7936.

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×C₃₁×#424	C₂	1	1	yes	maximal, characteristic
2	C₃₁×#2314	C₂	1	2	yes	maximal
3	C₃₁×#1949	C₂	1	2	yes	maximal, complemented
4	C₃₁×#1949	C₂	1	2	yes	maximal, complemented
5	C₃₁×#1948	C₂	1	2	yes	maximal, complemented
6	C₃₁×#1947	C₂	1	2	yes	maximal, complemented
7	C₃₁×#1809	C₂	1	2	yes	maximal
8	C₃₁×#1808	C₂	1	1	yes	maximal, characteristic
9	C₃₁×#1807	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₃₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₃₁×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃₁×#107	C₂²	1	2	yes	—
14	C₂×C₃₁×#107	C₂²	1	2	yes	—
15	C₂×C₃₁×#106	C₂²	1	2	yes	—
16	C₂×C₃₁×#106	C₂²	1	2	yes	—
17	C₃₁×#424	C₄	1	8	yes	complemented
18	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₃₁×C₄⋊C₈	C₂²	1	2	yes	—
20	C₃₁×#388	—	2	2	no	—
21	C₃₁×#388	—	2	2	no	—
22	C₃₁×#387	—	2	2	no	—
23	C₃₁×#387	—	2	2	no	—
24	C₃₁×#384	C₂²	1	2	yes	—
25	C₃₁×#382	C₂²	1	2	yes	—
26	C₃₁×#380	C₂²	1	2	yes	—
27	C₃₁×#380	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
30	C₃₁×#340	C₂²	1	1	yes	characteristic
31	C₃₁×#340	C₂²	1	1	yes	characteristic
32	C₃₁×#340	C₂²	1	1	yes	characteristic
33	C₃₁×#340	C₂²	1	1	yes	characteristic
34	C₃₁×#340	C₂²	1	2	yes	—
35	C₃₁×#340	C₂²	1	2	yes	—
36	C₂³×C₄×C₃₁	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₃₁	—	4	2	no	—
38	C₂×M₁₆×C₃₁	C₂×C₄	1	4	yes	—
39	C₂²×C₈×C₃₁	—	4	2	no	—
40	C₂²×C₈×C₃₁	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₃₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₃₁	C₂³	1	1	yes	characteristic
44	C₃₁×#117	C₂×C₄	1	4	yes	—
45	C₃₁×#117	Q₈	1	4	yes	—
46	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
47	C₂×C₄⋊C₄×C₃₁	—	2	2	no	—
48	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
49	C₂×C₄⋊C₄×C₃₁	D₄	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
51	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₃₁	C₂³	1	2	yes	—
54	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₃₁	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₃₁	D₄	1	2	yes	—
57	C₂×C₄²×C₃₁	—	2	2	no	—
58	C₂×C₄²×C₃₁	—	2	2	no	—
59	C₂×C₄²×C₃₁	C₂³	1	2	yes	—
60	C₃₁×#107	—	4	2	no	—
61	C₃₁×#107	—	4	2	no	—
62	C₃₁×#106	—	4	2	no	—
63	C₃₁×#106	—	4	2	no	—
64	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
65	C₃₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
66	C₃₁×#95	—	2	2	no	—
67	C₃₁×#95	—	2	2	no	—
68	C₃₁×#95	—	2	2	no	—
69	C₃₁×#95	—	2	2	no	—
70	C₃₁×#95	—	2	2	no	—
71	C₃₁×#95	—	2	2	no	—
72	C₂⁴×C₃₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₃₁	—	2	2	no	—
74	C₂²×C₄×C₃₁	—	2	2	no	—
75	C₂²×C₄×C₃₁	—	2	2	no	—
76	C₂²×C₄×C₃₁	—	2	2	no	—
77	C₂²×C₄×C₃₁	—	2	2	no	—
78	C₂²×C₄×C₃₁	—	2	2	no	—
79	C₂²×C₄×C₃₁	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₃₁	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₃₁	C₂×D₄	1	2	yes	—
83	C₂²×C₄×C₃₁	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₃₁	C₂⁴	1	1	yes	characteristic
85	M₁₆×C₃₁	—	4	4	no	—
86	C₂×C₈×C₃₁	—	2	2	no	—
87	C₂×C₈×C₃₁	—	2	2	no	—
88	C₂×C₈×C₃₁	—	2	2	no	—
89	C₂×C₈×C₃₁	—	2	2	no	—
90	C₂×C₈×C₃₁	—	4	4	no	—
91	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
92	C₂×C₈×C₃₁	C₂²×C₄	1	2	yes	—
93	C₂×C₈×C₃₁	C₂²×C₄	1	4	yes	—
94	C₄⋊C₄×C₃₁	—	2	2	no	—
95	C₄⋊C₄×C₃₁	—	2	2	no	—
96	C₄⋊C₄×C₃₁	—	2	2	no	—
97	C₄⋊C₄×C₃₁	—	2	2	no	—
98	C₄⋊C₄×C₃₁	—	2	2	no	—
99	C₄⋊C₄×C₃₁	—	2	2	no	—
100	C₄⋊C₄×C₃₁	—	2	2	no	—
101	C₄⋊C₄×C₃₁	—	2	2	no	—
102	C₄⋊C₄×C₃₁	—	8	2	no	—
103	C₄⋊C₄×C₃₁	—	8	2	no	—
104	C₄⋊C₄×C₃₁	C₄⋊C₄	1	4	yes	—
105	C₄⋊C₄×C₃₁	C₄⋊C₄	1	4	yes	—
106	C₂²⋊C₄×C₃₁	—	8	2	no	—
107	C₂²⋊C₄×C₃₁	—	8	2	no	—
108	C₂²⋊C₄×C₃₁	C₄⋊C₄	1	8	yes	—
109	C₄²×C₃₁	—	8	2	no	—
110	C₄²×C₃₁	—	8	2	no	—
111	C₄²×C₃₁	C₂²×C₄	1	4	yes	—
112	C₄²×C₃₁	C₂×Q₈	1	4	yes	—
113	#21966	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂³×C₃₁	—	2	2	no	—
115	C₂³×C₃₁	—	2	1	no	—
116	C₂³×C₃₁	—	2	2	no	—
117	C₂³×C₃₁	—	2	1	no	—
118	C₂³×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
119	C₂³×C₃₁	C₂²×D₄	1	1	yes	characteristic
120	C₂×C₄×C₃₁	—	2	2	no	—
121	C₂×C₄×C₃₁	—	2	2	no	—
122	C₂×C₄×C₃₁	—	2	2	no	—
123	C₂×C₄×C₃₁	—	2	2	no	—
124	C₂×C₄×C₃₁	—	2	2	no	—
125	C₂×C₄×C₃₁	—	2	2	no	—
126	C₂×C₄×C₃₁	—	2	2	no	—
127	C₂×C₄×C₃₁	—	2	4	no	—
128	C₂×C₄×C₃₁	—	4	2	no	—
129	C₂×C₄×C₃₁	—	4	2	no	—
130	C₂×C₄×C₃₁	—	4	2	no	—
131	C₂×C₄×C₃₁	—	4	2	no	—
132	C₂×C₄×C₃₁	—	4	2	no	—
133	C₂×C₄×C₃₁	—	4	2	no	—
134	C₂×C₄×C₃₁	—	4	2	no	—
135	C₂×C₄×C₃₁	—	4	2	no	—
136	C₂×C₄×C₃₁	—	4	2	no	—
137	C₂×C₄×C₃₁	—	4	2	no	—
138	C₂×C₄×C₃₁	—	4	2	no	—
139	C₂×C₄×C₃₁	—	4	2	no	—
140	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
141	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	4	yes	—
142	C₂×C₄×C₃₁	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₃₁	C₂³×C₄	1	1	yes	characteristic
144	C₂×C₄×C₃₁	C₂²×Q₈	1	1	yes	characteristic
145	C₂×C₄×C₃₁	H(5,𝔽₂)	1	2	yes	—
146	C₂×C₄×C₃₁	2₋¹⁺⁴	1	2	yes	—
147	C₈×C₃₁	—	2	2	no	—
148	C₈×C₃₁	—	2	2	no	—
149	C₈×C₃₁	—	2	4	no	—
150	C₂×#424	C₂×C₃₁	1	1	yes	characteristic
151	#2314	C₂×C₃₁	1	2	yes	—
152	#1949	C₂×C₃₁	1	2	yes	complemented
153	#1949	C₂×C₃₁	1	2	yes	complemented
154	#1948	C₂×C₃₁	1	2	yes	complemented
155	#1947	C₂×C₃₁	1	2	yes	complemented
156	#1809	C₂×C₃₁	1	2	yes	—
157	#1808	C₂×C₃₁	1	1	yes	characteristic
158	#1807	C₂×C₃₁	1	1	yes	characteristic
159	C₂²×C₃₁	—	2	2	no	—
160	C₂²×C₃₁	—	2	2	no	—
161	C₂²×C₃₁	—	2	2	no	—
162	C₂²×C₃₁	—	4	2	no	—
163	C₂²×C₃₁	—	4	2	no	—
164	C₂²×C₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×C₃₁	#537	1	2	yes	—
166	C₂²×C₃₁	#576	1	1	yes	characteristic
167	C₂²×C₃₁	#577	1	2	yes	—
168	C₂²×C₃₁	#578	1	1	yes	characteristic
169	C₄×C₃₁	—	2	2	no	—
170	C₄×C₃₁	—	2	4	no	—
171	C₄×C₃₁	—	2	4	no	—
172	C₄×C₃₁	—	8	2	no	—
173	C₄×C₃₁	—	8	2	no	—
174	C₄×C₃₁	—	8	2	no	—
175	C₄×C₃₁	—	8	2	no	—
176	C₄×C₃₁	#518	1	1	yes	characteristic
177	C₄×C₃₁	#519	1	1	yes	characteristic
178	C₄×C₃₁	#544	1	2	yes	—
179	C₂²×M₁₆	C₂²×C₃₁	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₃₁	1	1	yes	characteristic
181	C₂×#117	C₂²×C₃₁	1	1	yes	characteristic
182	C₂×#107	C₂²×C₃₁	1	2	yes	—
183	C₂×#107	C₂²×C₃₁	1	2	yes	—
184	C₂×#106	C₂²×C₃₁	1	2	yes	—
185	C₂×#106	C₂²×C₃₁	1	2	yes	—
186	#424	C₄×C₃₁	1	8	yes	complemented
187	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
188	C₂×C₄⋊C₈	C₂²×C₃₁	1	2	yes	—
189	#388	—	2	2	no	—
190	#388	—	2	2	no	—
191	#387	—	2	2	no	—
192	#387	—	2	2	no	—
193	#384	C₂²×C₃₁	1	2	yes	—
194	#382	C₂²×C₃₁	1	2	yes	—
195	#380	C₂²×C₃₁	1	2	yes	—
196	#380	C₂²×C₃₁	1	2	yes	—
197	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
198	C₄×C₄⋊C₄	C₂²×C₃₁	1	2	yes	—
199	#340	C₂²×C₃₁	1	1	yes	characteristic
200	#340	C₂²×C₃₁	1	1	yes	characteristic
201	#340	C₂²×C₃₁	1	1	yes	characteristic
202	#340	C₂²×C₃₁	1	1	yes	characteristic
203	#340	C₂²×C₃₁	1	2	yes	—
204	#340	C₂²×C₃₁	1	2	yes	—
205	C₂×C₃₁	—	4	2	no	—
206	C₂×C₃₁	#2316	1	1	yes	characteristic
207	C₂×C₃₁	#2912	1	1	yes	characteristic
208	C₂×C₃₁	#2913	1	1	yes	characteristic
209	C₂×C₃₁	#3257	1	2	yes	—
210	C₂×C₃₁	#3258	1	2	yes	—
211	C₂³×C₄	C₂³×C₃₁	1	1	yes	characteristic
212	C₂×M₁₆	—	4	2	no	—
213	C₂×M₁₆	C₂×C₄×C₃₁	1	4	yes	—
214	C₂²×C₈	—	4	2	no	—
215	C₂²×C₈	C₂×C₄×C₃₁	1	4	yes	—
216	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
217	C₂²×C₈	C₂³×C₃₁	1	1	yes	characteristic
218	C₂²×C₈	C₂³×C₃₁	1	2	yes	—
219	#117	C₂×C₄×C₃₁	1	4	yes	—
220	#117	Q₈×C₃₁	1	4	yes	—
221	C₂×C₄⋊C₄	—	2	2	no	—
222	C₂×C₄⋊C₄	—	2	2	no	—
223	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
224	C₂×C₄⋊C₄	D₄×C₃₁	1	1	yes	characteristic
225	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
228	C₂×C₄⋊C₄	C₂³×C₃₁	1	2	yes	—
229	C₂×C₂²⋊C₄	—	2	2	no	—
230	C₂×C₂²⋊C₄	—	2	2	no	—
231	C₂×C₂²⋊C₄	D₄×C₃₁	1	2	yes	—
232	C₂×C₄²	—	2	2	no	—
233	C₂×C₄²	—	2	2	no	—
234	C₂×C₄²	C₂³×C₃₁	1	2	yes	—
235	#107	—	4	2	no	—
236	#107	—	4	2	no	—
237	#106	—	4	2	no	—
238	#106	—	4	2	no	—
239	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
240	C₄⋊C₈	C₂×C₄×C₃₁	1	8	yes	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	#95	—	2	2	no	—
244	#95	—	2	2	no	—
245	#95	—	2	2	no	—
246	#95	—	2	2	no	—
247	C₃₁	#21966	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁴	C₂×D₄×C₃₁	1	1	yes	characteristic
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	—	2	2	no	—
255	C₂²×C₄	C₂²×C₄×C₃₁	1	2	yes	—
256	C₂²×C₄	C₂×D₄×C₃₁	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
258	C₂²×C₄	C₂×D₄×C₃₁	1	2	yes	—
259	C₂²×C₄	C₂×Q₈×C₃₁	1	2	yes	—
260	C₂²×C₄	C₂⁴×C₃₁	1	1	yes	characteristic
261	M₁₆	—	4	4	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	2	no	—
265	C₂×C₈	—	2	2	no	—
266	C₂×C₈	—	4	4	no	—
267	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
268	C₂×C₈	C₂²×C₄×C₃₁	1	2	yes	—
269	C₂×C₈	C₂²×C₄×C₃₁	1	4	yes	—
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	—	2	2	no	—
278	C₄⋊C₄	—	8	2	no	—
279	C₄⋊C₄	—	8	2	no	—
280	C₄⋊C₄	C₄⋊C₄×C₃₁	1	4	yes	—
281	C₄⋊C₄	C₄⋊C₄×C₃₁	1	4	yes	—
282	C₂²⋊C₄	—	8	2	no	—
283	C₂²⋊C₄	—	8	2	no	—
284	C₂²⋊C₄	C₄⋊C₄×C₃₁	1	8	yes	—
285	C₄²	—	8	2	no	—
286	C₄²	—	8	2	no	—
287	C₄²	C₂²×C₄×C₃₁	1	4	yes	—
288	C₄²	C₂×Q₈×C₃₁	1	4	yes	—
289	C₂³	—	2	2	no	—
290	C₂³	—	2	1	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	1	no	—
293	C₂³	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
294	C₂³	C₂²×D₄×C₃₁	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×C₄⋊C₄×C₃₁	1	4	yes	—
316	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	4	yes	—
317	C₂×C₄	C₂×C₄⋊C₄×C₃₁	1	2	yes	—
318	C₂×C₄	C₂³×C₄×C₃₁	1	1	yes	characteristic
319	C₂×C₄	C₂²×Q₈×C₃₁	1	1	yes	characteristic
320	C₂×C₄	C₃₁×H(5,𝔽₂)	1	2	yes	—
321	C₂×C₄	C₃₁×2₋¹⁺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×C₄⋊C₄×C₃₁	1	1	yes	characteristic
331	C₂²	C₃₁×#537	1	2	yes	—
332	C₂²	C₃₁×#576	1	1	yes	characteristic
333	C₂²	C₃₁×#577	1	2	yes	—
334	C₂²	C₃₁×#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	C₃₁×#518	1	1	yes	characteristic
343	C₄	C₃₁×#519	1	1	yes	characteristic
344	C₄	C₃₁×#544	1	2	yes	—
345	C₂	—	4	2	no	—
346	C₂	C₃₁×#2316	1	1	yes	characteristic
347	C₂	C₃₁×#2912	1	1	yes	characteristic
348	C₂	C₃₁×#2913	1	1	yes	characteristic
349	C₂	C₃₁×#3257	1	2	yes	—
350	C₂	C₃₁×#3258	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₃₁
prime radical	C₂⁴×C₃₁	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃₁ ◁ C₂×C₃₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₃₁×#1949	C₂	semidirect
4. C₃₁×#1949	C₂	semidirect
5. C₃₁×#1948	C₂	semidirect
6. C₃₁×#1947	C₂	semidirect
17. C₃₁×#424	C₄	semidirect
113. #21966	C₃₁	direct (N × H)
152. #1949	C₂×C₃₁	semidirect
153. #1949	C₂×C₃₁	semidirect
154. #1948	C₂×C₃₁	semidirect
155. #1947	C₂×C₃₁	semidirect
186. #424	C₄×C₃₁	semidirect
247. C₃₁	#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×C₃₁×#424	2
C₃₁×#2314	2
C₃₁×#1949	2
C₃₁×#1948	2
C₃₁×#1947	2
C₃₁×#1809	2
C₃₁×#1808	2
C₃₁×#1807	2
#21966	31

Subgroups — C31×#21966 #21478725

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃₁×#21966 #21478725