Subgroups — C₄₁×#29110 #23805311

Order 10496.

1078 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#2851	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₁×#390	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#2073	C₂	1	2	yes	maximal, complemented
4	C₄₁×#2025	C₂	1	2	yes	maximal, complemented
5	C₄₁×#1936	C₂	1	4	yes	maximal, complemented
6	C₄₁×#1823	C₂	1	2	yes	maximal, complemented
7	C₄₁×#1786	C₂	1	2	yes	maximal
8	C₄₁×#1749	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×#125×C₄₁	C₂²	1	1	yes	characteristic, complemented
11	C₂²×C₄⋊C₄×C₄₁	C₂²	1	1	yes	characteristic
12	C₂²×C₂²⋊C₄×C₄₁	—	2	2	no	—
13	C₂²×C₄²×C₄₁	C₂²	1	1	yes	characteristic
14	C₂×#102×C₄₁	C₂²	1	4	yes	—
15	C₂×#102×C₄₁	C₂²	1	4	yes	—
16	C₂×C₂²⋊C₈×C₄₁	C₂²	1	2	yes	—
17	C₂×#97×C₄₁	C₂²	1	2	yes	complemented
18	C₄₁×#390	—	2	2	no	—
19	C₄₁×#390	C₂²	1	2	yes	—
20	C₄₁×#390	C₂²	1	2	yes	—
21	C₄₁×#389	C₂²	1	2	yes	complemented
22	C₄₁×#387	—	2	2	no	—
23	C₄₁×#385	—	2	2	no	—
24	C₄₁×#382	C₂²	1	1	yes	characteristic, complemented
25	C₄₁×#380	C₂²	1	2	yes	—
26	C₄₁×#340	C₂²	1	4	yes	complemented
27	C₄₁×#340	C₂²	1	4	yes	complemented
28	C₄₁×#336	C₂²	1	2	yes	complemented
29	C₂⁵×C₄₁	—	2	1	no	—
30	C₂²×D₄×C₄₁	—	2	4	no	—
31	C₂²×D₄×C₄₁	—	2	1	no	—
32	C₂²×D₄×C₄₁	—	2	4	no	—
33	C₂²×D₄×C₄₁	—	4	2	no	—
34	C₂²×D₄×C₄₁	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₁	—	2	1	no	—
36	C₂³×C₄×C₄₁	D₄	1	2	yes	—
37	C₂³×C₄×C₄₁	C₂³	1	1	yes	characteristic
38	C₂²×C₈×C₄₁	C₂³	1	4	yes	—
39	#125×C₄₁	—	4	2	no	—
40	C₂×C₄⋊C₄×C₄₁	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₁	—	2	1	no	—
42	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
45	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
46	C₂×C₄⋊C₄×C₄₁	C₂³	1	2	yes	—
47	C₂×C₂²⋊C₄×C₄₁	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
49	C₂×C₂²⋊C₄×C₄₁	—	2	4	no	—
50	C₂×C₂²⋊C₄×C₄₁	—	4	8	no	—
51	C₂×C₄²×C₄₁	—	4	2	no	—
52	C₂×C₄²×C₄₁	D₄	1	2	yes	—
53	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
54	C₂×C₄²×C₄₁	C₂³	1	1	yes	characteristic
55	#102×C₄₁	—	2	8	no	—
56	#102×C₄₁	—	4	4	no	—
57	C₂²⋊C₈×C₄₁	—	2	4	no	—
58	#97×C₄₁	—	4	2	no	—
59	#95×C₄₁	—	2	2	no	—
60	#95×C₄₁	—	2	2	no	—
61	#95×C₄₁	—	2	2	no	—
62	C₂⁴×C₄₁	—	2	4	no	—
63	C₂⁴×C₄₁	—	2	2	no	—
64	C₂⁴×C₄₁	—	4	2	no	—
65	C₂⁴×C₄₁	—	4	4	no	—
66	C₂⁴×C₄₁	—	4	2	no	—
67	C₂⁴×C₄₁	—	4	4	no	—
68	C₂⁴×C₄₁	C₂×D₄	1	1	yes	characteristic
69	C₂×D₄×C₄₁	—	2	4	no	—
70	C₂×D₄×C₄₁	—	2	4	no	—
71	C₂×D₄×C₄₁	—	2	2	no	—
72	C₂×D₄×C₄₁	—	2	4	no	—
73	C₂×D₄×C₄₁	—	4	16	no	—
74	C₂×D₄×C₄₁	—	4	2	no	—
75	C₂×D₄×C₄₁	—	4	2	no	—
76	C₂×D₄×C₄₁	#41	1	4	yes	—
77	C₂²×C₄×C₄₁	—	2	2	no	—
78	C₂²×C₄×C₄₁	—	2	2	no	—
79	C₂²×C₄×C₄₁	—	2	4	no	—
80	C₂²×C₄×C₄₁	—	2	2	no	—
81	C₂²×C₄×C₄₁	—	2	2	no	—
82	C₂²×C₄×C₄₁	—	2	2	no	—
83	C₂²×C₄×C₄₁	—	4	2	no	—
84	C₂²×C₄×C₄₁	—	4	2	no	—
85	C₂²×C₄×C₄₁	—	4	2	no	—
86	C₂²×C₄×C₄₁	—	4	4	no	—
87	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₁	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₁	#41	1	4	yes	—
91	C₂²×C₄×C₄₁	C₂⁴	1	1	yes	characteristic
92	C₂×C₈×C₄₁	—	2	4	no	—
93	C₂×C₈×C₄₁	—	2	4	no	—
94	C₂×C₈×C₄₁	—	2	4	no	—
95	C₄⋊C₄×C₄₁	—	2	4	no	—
96	C₄⋊C₄×C₄₁	—	2	4	no	—
97	C₄⋊C₄×C₄₁	—	2	4	no	—
98	C₄⋊C₄×C₄₁	—	4	4	no	—
99	C₄⋊C₄×C₄₁	—	4	4	no	—
100	C₄⋊C₄×C₄₁	—	4	2	no	—
101	C₂²⋊C₄×C₄₁	—	4	8	no	—
102	C₂²⋊C₄×C₄₁	—	4	8	no	—
103	C₂²⋊C₄×C₄₁	—	4	4	no	—
104	C₄²×C₄₁	—	2	2	no	—
105	C₄²×C₄₁	—	2	2	no	—
106	C₄²×C₄₁	—	4	2	no	—
107	C₂³×C₄₁	—	2	1	no	—
108	C₂³×C₄₁	—	2	1	no	—
109	C₂³×C₄₁	—	2	2	no	—
110	C₂³×C₄₁	—	2	4	no	—
111	C₂³×C₄₁	—	4	8	no	—
112	C₂³×C₄₁	—	4	16	no	—
113	C₂³×C₄₁	—	4	2	no	—
114	C₂³×C₄₁	—	4	2	no	—
115	C₂³×C₄₁	—	4	4	no	—
116	C₂³×C₄₁	—	4	4	no	—
117	C₂³×C₄₁	—	8	4	no	—
118	C₂³×C₄₁	—	8	8	no	—
119	C₂³×C₄₁	—	8	4	no	—
120	C₂³×C₄₁	#124	1	2	yes	—
121	C₂³×C₄₁	AGL(1,ℤ/8)	1	4	yes	—
122	C₂³×C₄₁	C₂²×D₄	1	1	yes	characteristic
123	D₄×C₄₁	—	2	8	no	—
124	D₄×C₄₁	—	4	8	no	—
125	D₄×C₄₁	—	4	4	no	—
126	C₂×C₄×C₄₁	—	2	1	no	—
127	C₂×C₄×C₄₁	—	2	1	no	—
128	C₂×C₄×C₄₁	—	2	8	no	—
129	C₂×C₄×C₄₁	—	2	2	no	—
130	C₂×C₄×C₄₁	—	2	2	no	—
131	C₂×C₄×C₄₁	—	2	2	no	—
132	C₂×C₄×C₄₁	—	2	2	no	—
133	C₂×C₄×C₄₁	—	2	2	no	—
134	C₂×C₄×C₄₁	—	2	2	no	—
135	C₂×C₄×C₄₁	—	4	8	no	—
136	C₂×C₄×C₄₁	—	4	2	no	—
137	C₂×C₄×C₄₁	—	4	2	no	—
138	C₂×C₄×C₄₁	—	4	2	no	—
139	C₂×C₄×C₄₁	—	4	4	no	—
140	C₂×C₄×C₄₁	—	4	2	no	—
141	C₂×C₄×C₄₁	—	4	2	no	—
142	C₂×C₄×C₄₁	—	4	2	no	—
143	C₂×C₄×C₄₁	—	4	2	no	—
144	C₂×C₄×C₄₁	—	8	4	no	—
145	C₂×C₄×C₄₁	#124	1	2	yes	—
146	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
147	C₂×C₄×C₄₁	C₂×#41	1	2	yes	—
148	C₂×C₄×C₄₁	H(5,𝔽₂)	1	2	yes	—
149	C₈×C₄₁	—	4	4	no	—
150	#29110	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂²×C₄₁	—	2	2	no	—
152	C₂²×C₄₁	—	2	4	no	—
153	C₂²×C₄₁	—	2	2	no	—
154	C₂²×C₄₁	—	2	4	no	—
155	C₂²×C₄₁	—	4	4	no	—
156	C₂²×C₄₁	—	4	8	no	—
157	C₂²×C₄₁	—	8	16	no	—
158	C₂²×C₄₁	—	8	2	no	—
159	C₂²×C₄₁	—	8	2	no	—
160	C₂²×C₄₁	—	8	4	no	—
161	C₂²×C₄₁	#490	1	4	yes	—
162	C₂²×C₄₁	#525	1	1	yes	characteristic
163	C₂²×C₄₁	C₂×#124	1	1	yes	characteristic
164	C₂²×C₄₁	#534	1	1	yes	characteristic
165	C₂²×C₄₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
166	C₂²×C₄₁	#575	1	2	yes	—
167	C₄×C₄₁	—	2	2	no	—
168	C₄×C₄₁	—	4	2	no	—
169	C₄×C₄₁	—	4	2	no	—
170	C₄×C₄₁	—	8	2	no	—
171	C₄×C₄₁	—	8	2	no	—
172	C₄×C₄₁	—	8	2	no	—
173	C₄×C₄₁	#551	1	4	yes	—
174	#2851	C₂×C₄₁	1	1	yes	characteristic, complemented
175	C₂×#390	C₂×C₄₁	1	1	yes	characteristic
176	#2073	C₂×C₄₁	1	2	yes	complemented
177	#2025	C₂×C₄₁	1	2	yes	complemented
178	#1936	C₂×C₄₁	1	4	yes	complemented
179	#1823	C₂×C₄₁	1	2	yes	complemented
180	#1786	C₂×C₄₁	1	2	yes	—
181	#1749	C₂×C₄₁	1	1	yes	characteristic, complemented
182	C₂×C₄₁	—	2	4	no	—
183	C₂×C₄₁	—	8	4	no	—
184	C₂×C₄₁	#2561	1	1	yes	characteristic
185	C₂×C₄₁	#3114	1	2	yes	—
186	C₂×C₄₁	C₂×#490	1	1	yes	characteristic
187	C₂×C₄₁	#3140	1	1	yes	characteristic
188	C₂×C₄₁	#3194	1	2	yes	—
189	C₂³×D₄	C₂²×C₄₁	1	1	yes	characteristic
190	C₂×#125	C₂²×C₄₁	1	1	yes	characteristic, complemented
191	C₂²×C₄⋊C₄	C₂²×C₄₁	1	1	yes	characteristic
192	C₂²×C₂²⋊C₄	—	2	2	no	—
193	C₂²×C₄²	C₂²×C₄₁	1	1	yes	characteristic
194	C₂×#102	C₂²×C₄₁	1	4	yes	—
195	C₂×#102	C₂²×C₄₁	1	4	yes	—
196	C₂×C₂²⋊C₈	C₂²×C₄₁	1	2	yes	—
197	C₂×#97	C₂²×C₄₁	1	2	yes	complemented
198	#390	—	2	2	no	—
199	#390	C₂²×C₄₁	1	2	yes	—
200	#390	C₂²×C₄₁	1	2	yes	—
201	#389	C₂²×C₄₁	1	2	yes	complemented
202	#387	—	2	2	no	—
203	#385	—	2	2	no	—
204	#382	C₂²×C₄₁	1	1	yes	characteristic, complemented
205	#380	C₂²×C₄₁	1	2	yes	—
206	#340	C₂²×C₄₁	1	4	yes	complemented
207	#340	C₂²×C₄₁	1	4	yes	complemented
208	#336	C₂²×C₄₁	1	2	yes	complemented
209	C₄₁	#29110	1	1	yes	characteristic, direct product factor, Sylow
210	C₂⁵	—	2	1	no	—
211	C₂²×D₄	—	2	4	no	—
212	C₂²×D₄	—	2	1	no	—
213	C₂²×D₄	—	2	4	no	—
214	C₂²×D₄	—	4	2	no	—
215	C₂²×D₄	C₂³×C₄₁	1	2	yes	—
216	C₂³×C₄	—	2	1	no	—
217	C₂³×C₄	D₄×C₄₁	1	2	yes	—
218	C₂³×C₄	C₂³×C₄₁	1	1	yes	characteristic
219	C₂²×C₈	C₂³×C₄₁	1	4	yes	—
220	#125	—	4	2	no	—
221	C₂×C₄⋊C₄	—	2	4	no	—
222	C₂×C₄⋊C₄	—	2	1	no	—
223	C₂×C₄⋊C₄	—	2	2	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
226	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
227	C₂×C₄⋊C₄	C₂³×C₄₁	1	2	yes	—
228	C₂×C₂²⋊C₄	—	2	2	no	—
229	C₂×C₂²⋊C₄	—	2	4	no	—
230	C₂×C₂²⋊C₄	—	2	4	no	—
231	C₂×C₂²⋊C₄	—	4	8	no	—
232	C₂×C₄²	—	4	2	no	—
233	C₂×C₄²	D₄×C₄₁	1	2	yes	—
234	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
235	C₂×C₄²	C₂³×C₄₁	1	1	yes	characteristic
236	#102	—	2	8	no	—
237	#102	—	4	4	no	—
238	C₂²⋊C₈	—	2	4	no	—
239	#97	—	4	2	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	#95	—	2	2	no	—
243	C₂⁴	—	2	4	no	—
244	C₂⁴	—	2	2	no	—
245	C₂⁴	—	4	2	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	—	4	2	no	—
248	C₂⁴	—	4	4	no	—
249	C₂⁴	C₂×D₄×C₄₁	1	1	yes	characteristic
250	C₂×D₄	—	2	4	no	—
251	C₂×D₄	—	2	4	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	4	no	—
254	C₂×D₄	—	4	16	no	—
255	C₂×D₄	—	4	2	no	—
256	C₂×D₄	—	4	2	no	—
257	C₂×D₄	#41×C₄₁	1	4	yes	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	4	2	no	—
266	C₂²×C₄	—	4	2	no	—
267	C₂²×C₄	—	4	4	no	—
268	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
269	C₂²×C₄	C₂×D₄×C₄₁	1	2	yes	—
270	C₂²×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
271	C₂²×C₄	#41×C₄₁	1	4	yes	—
272	C₂²×C₄	C₂⁴×C₄₁	1	1	yes	characteristic
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	—	2	4	no	—
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	4	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	—	4	4	no	—
280	C₄⋊C₄	—	4	4	no	—
281	C₄⋊C₄	—	4	2	no	—
282	C₂²⋊C₄	—	4	8	no	—
283	C₂²⋊C₄	—	4	8	no	—
284	C₂²⋊C₄	—	4	4	no	—
285	C₄²	—	2	2	no	—
286	C₄²	—	2	2	no	—
287	C₄²	—	4	2	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	1	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	2	4	no	—
292	C₂³	—	4	8	no	—
293	C₂³	—	4	16	no	—
294	C₂³	—	4	2	no	—
295	C₂³	—	4	2	no	—
296	C₂³	—	4	4	no	—
297	C₂³	—	4	4	no	—
298	C₂³	—	8	4	no	—
299	C₂³	—	8	8	no	—
300	C₂³	—	8	4	no	—
301	C₂³	#124×C₄₁	1	2	yes	—
302	C₂³	AGL(1,ℤ/8)×C₄₁	1	4	yes	—
303	C₂³	C₂²×D₄×C₄₁	1	1	yes	characteristic
304	D₄	—	2	8	no	—
305	D₄	—	4	8	no	—
306	D₄	—	4	4	no	—
307	C₂×C₄	—	2	1	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	8	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	8	no	—
317	C₂×C₄	—	4	2	no	—
318	C₂×C₄	—	4	2	no	—
319	C₂×C₄	—	4	2	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	2	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	8	4	no	—
326	C₂×C₄	#124×C₄₁	1	2	yes	—
327	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
328	C₂×C₄	C₂×#41×C₄₁	1	2	yes	—
329	C₂×C₄	H(5,𝔽₂)×C₄₁	1	2	yes	—
330	C₈	—	4	4	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	4	no	—
335	C₂²	—	4	4	no	—
336	C₂²	—	4	8	no	—
337	C₂²	—	8	16	no	—
338	C₂²	—	8	2	no	—
339	C₂²	—	8	2	no	—
340	C₂²	—	8	4	no	—
341	C₂²	C₄₁×#490	1	4	yes	—
342	C₂²	C₄₁×#525	1	1	yes	characteristic
343	C₂²	C₂×#124×C₄₁	1	1	yes	characteristic
344	C₂²	C₄₁×#534	1	1	yes	characteristic
345	C₂²	C₂×AGL(1,ℤ/8)×C₄₁	1	2	yes	—
346	C₂²	C₄₁×#575	1	2	yes	—
347	C₄	—	2	2	no	—
348	C₄	—	4	2	no	—
349	C₄	—	4	2	no	—
350	C₄	—	8	2	no	—
351	C₄	—	8	2	no	—
352	C₄	—	8	2	no	—
353	C₄	C₄₁×#551	1	4	yes	—
354	C₂	—	2	4	no	—
355	C₂	—	8	4	no	—
356	C₂	C₄₁×#2561	1	1	yes	characteristic
357	C₂	C₄₁×#3114	1	2	yes	—
358	C₂	C₂×C₄₁×#490	1	1	yes	characteristic
359	C₂	C₄₁×#3140	1	1	yes	characteristic
360	C₂	C₄₁×#3194	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₁
prime radical	C₂³×D₄×C₄₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂²×C₄²×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#2851	C₂	semidirect
3. C₄₁×#2073	C₂	semidirect
4. C₄₁×#2025	C₂	semidirect
5. C₄₁×#1936	C₂	semidirect
6. C₄₁×#1823	C₂	semidirect
8. C₄₁×#1749	C₂	semidirect
10. C₂×#125×C₄₁	C₂²	semidirect
17. C₂×#97×C₄₁	C₂²	semidirect
21. C₄₁×#389	C₂²	semidirect
24. C₄₁×#382	C₂²	semidirect
26. C₄₁×#340	C₂²	semidirect
27. C₄₁×#340	C₂²	semidirect
28. C₄₁×#336	C₂²	semidirect
150. #29110	C₄₁	direct (N × H)
174. #2851	C₂×C₄₁	semidirect
176. #2073	C₂×C₄₁	semidirect
177. #2025	C₂×C₄₁	semidirect
178. #1936	C₂×C₄₁	semidirect
179. #1823	C₂×C₄₁	semidirect
181. #1749	C₂×C₄₁	semidirect
190. C₂×#125	C₂²×C₄₁	semidirect
197. C₂×#97	C₂²×C₄₁	semidirect
201. #389	C₂²×C₄₁	semidirect
204. #382	C₂²×C₄₁	semidirect
206. #340	C₂²×C₄₁	semidirect
207. #340	C₂²×C₄₁	semidirect
208. #336	C₂²×C₄₁	semidirect
209. C₄₁	#29110	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#2851	2
C₂×C₄₁×#390	2
C₄₁×#2073	2
C₄₁×#2025	2
C₄₁×#1936	2
C₄₁×#1823	2
C₄₁×#1786	2
C₄₁×#1749	2
#29110	41

Subgroups — C41×#29110 #23805311

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#29110 #23805311