Subgroups — C₂×C₁₃×#2211 #15719917

Order 3328.

722 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×SD₃₂	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2211	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#358	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#357	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×SD₁₆	—	2	1	no	—
12	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#124	—	2	1	no	—
14	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
15	C₂×C₁₃×Q₃₂	—	2	4	no	—
16	C₂×C₁₃×Q₃₂	C₂²	1	4	yes	complemented
17	C₂×C₁₃×SD₃₂	—	2	4	no	—
18	C₂×C₁₃×SD₃₂	C₂²	1	4	yes	—
19	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
21	C₁₃×#495	—	2	2	no	—
22	C₁₃×#495	C₂²	1	4	yes	—
23	C₄×C₁₃×Q₁₆	—	2	2	no	—
24	C₄×C₁₃×Q₁₆	C₂²	1	4	yes	complemented
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	—	2	1	no	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×C₄⋊C₁₆	C₂²	1	4	yes	complemented
29	C₁₃×#358	C₂²	1	4	yes	complemented
30	C₁₃×#357	C₂²	1	4	yes	—
31	C₂²×Q₈×C₁₃	—	2	1	no	—
32	C₂²×Q₈×C₁₃	—	2	1	no	—
33	C₂²×D₄×C₁₃	—	2	1	no	—
34	C₂×C₁₃×Q₁₆	—	2	1	no	—
35	C₂×C₁₃×Q₁₆	—	2	2	no	—
36	C₂×C₁₃×Q₁₆	—	2	1	no	—
37	C₂×C₁₃×Q₁₆	—	2	2	no	—
38	C₂×C₁₃×Q₁₆	—	2	2	no	—
39	C₂×C₁₃×Q₁₆	D₄	1	4	yes	—
40	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
41	C₂×C₁₃×Q₁₆	C₂³	1	2	yes	—
42	C₂×C₁₃×SD₁₆	—	2	4	no	—
43	C₂×C₁₃×SD₁₆	—	4	4	no	—
44	C₂×C₁₃×D₈	—	2	2	no	—
45	C₂×C₁₃×D₈	—	2	1	no	—
46	C₂×C₁₃×D₈	—	2	2	no	—
47	C₂×C₁₃×D₈	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₁₃×#124	—	2	4	no	—
51	C₁₃×#124	—	4	2	no	—
52	C₄×Q₈×C₁₃	—	2	4	no	—
53	C₄×Q₈×C₁₃	—	4	2	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
56	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
57	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
58	C₂×C₄²×C₁₃	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	C₁₃×Q₃₂	—	2	8	no	—
61	C₁₃×SD₃₂	—	2	8	no	—
62	C₂×C₁₃×C₁₆	—	2	2	no	—
63	C₂×C₁₃×C₁₆	—	2	2	no	—
64	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
65	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
66	C₁₃×#107	—	2	1	no	—
67	C₁₃×#107	C₂³	1	2	yes	—
68	C₁₃×#103	—	2	4	no	—
69	C₄×C₈×C₁₃	D₄	1	2	yes	—
70	C₄×C₈×C₁₃	C₂³	1	2	yes	—
71	C₂×#2211	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂⁴×C₁₃	—	4	1	no	—
73	C₂×Q₈×C₁₃	—	2	4	no	—
74	C₂×Q₈×C₁₃	—	2	2	no	—
75	C₂×Q₈×C₁₃	—	2	2	no	—
76	C₂×Q₈×C₁₃	—	4	1	no	—
77	C₂×Q₈×C₁₃	—	4	1	no	—
78	C₂×Q₈×C₁₃	—	4	2	no	—
79	C₂×Q₈×C₁₃	—	4	2	no	—
80	C₂×Q₈×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	—	2	2	no	—
82	C₂×D₄×C₁₃	—	4	2	no	—
83	C₂×D₄×C₁₃	—	4	1	no	—
84	C₂×D₄×C₁₃	—	4	2	no	—
85	C₂²×C₄×C₁₃	—	4	1	no	—
86	C₂²×C₄×C₁₃	—	4	1	no	—
87	C₂²×C₄×C₁₃	—	4	1	no	—
88	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
91	C₁₃×Q₁₆	—	2	4	no	—
92	C₁₃×Q₁₆	—	2	2	no	—
93	C₁₃×Q₁₆	—	2	2	no	—
94	C₁₃×Q₁₆	—	2	2	no	—
95	C₁₃×Q₁₆	—	4	2	no	—
96	C₁₃×Q₁₆	C₂×D₄	1	4	yes	—
97	C₁₃×SD₁₆	—	4	8	no	—
98	C₁₃×D₈	—	2	2	no	—
99	C₁₃×D₈	—	2	2	no	—
100	C₁₃×D₈	—	4	2	no	—
101	C₂×C₈×C₁₃	—	2	2	no	—
102	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
105	C₂×C₈×C₁₃	#41	1	2	yes	—
106	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
107	C₁₃×C₄⋊C₄	—	2	2	no	—
108	C₁₃×C₄⋊C₄	—	4	1	no	—
109	C₁₃×C₄⋊C₄	—	4	4	no	—
110	C₁₃×C₂²⋊C₄	—	4	4	no	—
111	C₁₃×C₂²⋊C₄	—	4	4	no	—
112	C₄²×C₁₃	—	4	4	no	—
113	C₄²×C₁₃	D₈	1	2	yes	—
114	C₄²×C₁₃	C₂×D₄	1	2	yes	—
115	C₁₃×C₁₆	—	2	2	no	—
116	C₁₃×C₁₆	—	2	2	no	—
117	C₂²×Q₃₂	C₂×C₁₃	1	1	yes	characteristic, complemented
118	C₂²×SD₃₂	C₂×C₁₃	1	1	yes	characteristic
119	C₂×#495	C₂×C₁₃	1	1	yes	characteristic
120	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
121	#2211	C₂×C₁₃	1	8	yes	direct product factor
122	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
123	C₂×#358	C₂×C₁₃	1	1	yes	characteristic, complemented
124	C₂×#357	C₂×C₁₃	1	1	yes	characteristic
125	C₂³×C₁₃	—	4	2	no	—
126	C₂³×C₁₃	—	8	2	no	—
127	C₂³×C₁₃	—	8	2	no	—
128	C₂³×C₁₃	—	8	2	no	—
129	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
130	Q₈×C₁₃	—	2	4	no	—
131	Q₈×C₁₃	—	4	2	no	—
132	Q₈×C₁₃	—	4	4	no	—
133	Q₈×C₁₃	—	4	2	no	—
134	Q₈×C₁₃	—	4	2	no	—
135	Q₈×C₁₃	—	8	2	no	—
136	D₄×C₁₃	—	4	2	no	—
137	D₄×C₁₃	—	4	2	no	—
138	D₄×C₁₃	—	8	2	no	—
139	C₂×C₄×C₁₃	—	2	2	no	—
140	C₂×C₄×C₁₃	—	2	2	no	—
141	C₂×C₄×C₁₃	—	4	2	no	—
142	C₂×C₄×C₁₃	—	4	4	no	—
143	C₂×C₄×C₁₃	—	4	2	no	—
144	C₂×C₄×C₁₃	—	4	2	no	—
145	C₂×C₄×C₁₃	—	8	2	no	—
146	C₂×C₄×C₁₃	—	8	2	no	—
147	C₂×C₄×C₁₃	#121	1	2	yes	—
148	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
150	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
151	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
152	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
153	C₈×C₁₃	—	2	2	no	—
154	C₈×C₁₃	#121	1	2	yes	—
155	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
156	C₈×C₁₃	C₂×#41	1	1	yes	characteristic
157	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
158	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
159	C₂²×SD₁₆	—	2	1	no	—
160	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
161	C₂×#124	—	2	1	no	—
162	C₂×C₄×Q₈	—	2	1	no	—
163	C₂×Q₃₂	—	2	4	no	—
164	C₂×Q₃₂	C₂²×C₁₃	1	4	yes	complemented
165	C₂×SD₃₂	—	2	4	no	—
166	C₂×SD₃₂	C₂²×C₁₃	1	4	yes	—
167	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
168	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
169	#495	—	2	2	no	—
170	#495	C₂²×C₁₃	1	4	yes	—
171	C₄×Q₁₆	—	2	2	no	—
172	C₄×Q₁₆	C₂²×C₁₃	1	4	yes	complemented
173	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
174	C₂×#103	—	2	1	no	—
175	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
176	C₄⋊C₁₆	C₂²×C₁₃	1	4	yes	complemented
177	#358	C₂²×C₁₃	1	4	yes	complemented
178	#357	C₂²×C₁₃	1	4	yes	—
179	C₂²×C₁₃	—	8	2	no	—
180	C₂²×C₁₃	—	8	2	no	—
181	C₂²×C₁₃	—	8	2	no	—
182	C₂²×C₁₃	—	16	4	no	—
183	C₂²×C₁₃	#459	1	2	yes	—
184	C₂²×C₁₃	#508	1	2	yes	—
185	C₂²×C₁₃	#510	1	2	yes	—
186	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
187	C₄×C₁₃	—	2	2	no	—
188	C₄×C₁₃	—	2	2	no	—
189	C₄×C₁₃	—	4	4	no	—
190	C₄×C₁₃	—	8	2	no	—
191	C₄×C₁₃	—	8	2	no	—
192	C₄×C₁₃	#459	1	2	yes	—
193	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
194	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×Q₈	—	2	1	no	—
196	C₂²×Q₈	—	2	1	no	—
197	C₂²×D₄	—	2	1	no	—
198	C₂×Q₁₆	—	2	1	no	—
199	C₂×Q₁₆	—	2	2	no	—
200	C₂×Q₁₆	—	2	1	no	—
201	C₂×Q₁₆	—	2	2	no	—
202	C₂×Q₁₆	—	2	2	no	—
203	C₂×Q₁₆	D₄×C₁₃	1	4	yes	—
204	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
205	C₂×Q₁₆	C₂³×C₁₃	1	2	yes	—
206	C₂×SD₁₆	—	2	4	no	—
207	C₂×SD₁₆	—	4	4	no	—
208	C₂×D₈	—	2	2	no	—
209	C₂×D₈	—	2	1	no	—
210	C₂×D₈	—	2	2	no	—
211	C₂×D₈	C₂³×C₁₃	1	2	yes	—
212	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
213	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
214	#124	—	2	4	no	—
215	#124	—	4	2	no	—
216	C₄×Q₈	—	2	4	no	—
217	C₄×Q₈	—	4	2	no	—
218	C₂×C₄⋊C₄	—	2	1	no	—
219	C₂×C₄⋊C₄	—	4	1	no	—
220	C₂×C₂²⋊C₄	—	4	1	no	—
221	C₂×C₂²⋊C₄	—	4	1	no	—
222	C₂×C₄²	—	4	1	no	—
223	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
224	Q₃₂	—	2	8	no	—
225	SD₃₂	—	2	8	no	—
226	C₂×C₁₆	—	2	2	no	—
227	C₂×C₁₆	—	2	2	no	—
228	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
229	C₂×C₁₆	C₂³×C₁₃	1	2	yes	—
230	#107	—	2	1	no	—
231	#107	C₂³×C₁₃	1	2	yes	—
232	#103	—	2	4	no	—
233	C₄×C₈	D₄×C₁₃	1	2	yes	—
234	C₄×C₈	C₂³×C₁₃	1	2	yes	—
235	C₂×C₁₃	—	16	2	no	—
236	C₂×C₁₃	#2211	1	4	yes	direct product factor
237	C₂×C₁₃	C₂×#459	1	1	yes	characteristic
238	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
239	C₂×C₁₃	C₂×#510	1	1	yes	characteristic
240	C₂⁴	—	4	1	no	—
241	C₂×Q₈	—	2	4	no	—
242	C₂×Q₈	—	2	2	no	—
243	C₂×Q₈	—	2	2	no	—
244	C₂×Q₈	—	4	1	no	—
245	C₂×Q₈	—	4	1	no	—
246	C₂×Q₈	—	4	2	no	—
247	C₂×Q₈	—	4	2	no	—
248	C₂×Q₈	—	4	2	no	—
249	C₂×D₄	—	2	2	no	—
250	C₂×D₄	—	4	2	no	—
251	C₂×D₄	—	4	1	no	—
252	C₂×D₄	—	4	2	no	—
253	C₂²×C₄	—	4	1	no	—
254	C₂²×C₄	—	4	1	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
257	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
259	Q₁₆	—	2	4	no	—
260	Q₁₆	—	2	2	no	—
261	Q₁₆	—	2	2	no	—
262	Q₁₆	—	2	2	no	—
263	Q₁₆	—	4	2	no	—
264	Q₁₆	C₂×D₄×C₁₃	1	4	yes	—
265	SD₁₆	—	4	8	no	—
266	D₈	—	2	2	no	—
267	D₈	—	2	2	no	—
268	D₈	—	4	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
271	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
272	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
273	C₂×C₈	C₁₃×#41	1	2	yes	—
274	C₂×C₈	C₂⁴×C₁₃	1	1	yes	characteristic
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	—	4	4	no	—
278	C₂²⋊C₄	—	4	4	no	—
279	C₂²⋊C₄	—	4	4	no	—
280	C₄²	—	4	4	no	—
281	C₄²	C₁₃×D₈	1	2	yes	—
282	C₄²	C₂×D₄×C₁₃	1	2	yes	—
283	C₁₆	—	2	2	no	—
284	C₁₆	—	2	2	no	—
285	C₁₃	C₂×#2211	1	1	yes	characteristic, direct product factor, Sylow
286	C₂³	—	4	2	no	—
287	C₂³	—	8	2	no	—
288	C₂³	—	8	2	no	—
289	C₂³	—	8	2	no	—
290	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
291	Q₈	—	2	4	no	—
292	Q₈	—	4	4	no	—
293	Q₈	—	4	2	no	—
294	Q₈	—	4	2	no	—
295	Q₈	—	4	2	no	—
296	Q₈	—	8	2	no	—
297	D₄	—	4	2	no	—
298	D₄	—	4	2	no	—
299	D₄	—	8	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	4	2	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	—	4	2	no	—
306	C₂×C₄	—	8	2	no	—
307	C₂×C₄	—	8	2	no	—
308	C₂×C₄	C₁₃×#121	1	2	yes	—
309	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
310	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
311	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
312	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
313	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
314	C₈	—	2	2	no	—
315	C₈	C₁₃×#121	1	2	yes	—
316	C₈	C₂²×D₄×C₁₃	1	1	yes	characteristic
317	C₈	C₂×C₁₃×#41	1	1	yes	characteristic
318	C₂²	—	8	2	no	—
319	C₂²	—	8	2	no	—
320	C₂²	—	8	2	no	—
321	C₂²	—	16	4	no	—
322	C₂²	C₁₃×#459	1	2	yes	—
323	C₂²	C₁₃×#508	1	2	yes	—
324	C₂²	C₁₃×#510	1	2	yes	—
325	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
326	C₄	—	2	2	no	—
327	C₄	—	2	2	no	—
328	C₄	—	4	4	no	—
329	C₄	—	8	2	no	—
330	C₄	—	8	2	no	—
331	C₄	C₁₃×#459	1	2	yes	—
332	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
333	C₄	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₂	—	16	2	no	—
335	C₂	C₁₃×#2211	1	4	yes	direct product factor
336	C₂	C₂×C₁₃×#459	1	1	yes	characteristic
337	C₂	C₂×C₁₃×#508	1	1	yes	characteristic
338	C₂	C₂×C₁₃×#510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₃×Q₃₂	C₂	semidirect
4. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#2211	C₂	direct (N × H)
6. C₂×C₁₃×C₄⋊C₁₆	C₂	semidirect
7. C₂×C₁₃×#358	C₂	semidirect
16. C₂×C₁₃×Q₃₂	C₂²	semidirect
24. C₄×C₁₃×Q₁₆	C₂²	semidirect
28. C₁₃×C₄⋊C₁₆	C₂²	semidirect
29. C₁₃×#358	C₂²	semidirect
71. C₂×#2211	C₁₃	direct (N × H)
117. C₂²×Q₃₂	C₂×C₁₃	semidirect
120. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
121. #2211	C₂×C₁₃	direct (N × H)
122. C₂×C₄⋊C₁₆	C₂×C₁₃	semidirect
123. C₂×#358	C₂×C₁₃	semidirect
164. C₂×Q₃₂	C₂²×C₁₃	semidirect
172. C₄×Q₁₆	C₂²×C₁₃	semidirect
176. C₄⋊C₁₆	C₂²×C₁₃	semidirect
177. #358	C₂²×C₁₃	semidirect
236. C₂×C₁₃	#2211	direct (N × H)
285. C₁₃	C₂×#2211	direct (N × H)
335. C₂	C₁₃×#2211	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×Q₃₂	2
C₂²×C₁₃×SD₃₂	2
C₂×C₁₃×#495	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2211	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×C₁₃×#358	2
C₂×C₁₃×#357	2
C₂×#2211	13

Subgroups — C2×C13×#2211 #15719917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2211 #15719917