Subgroups — C₂²×#19099305 #35195141

Order 20224.

10246 conjugacy classes of subgroups.

The subgroup lattice has 306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19099305	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#14579150	C₂	1	2	yes	maximal, complemented
3	C₂²×#14579149	C₂	1	2	yes	maximal, complemented
4	C₂²×#14579147	C₂	1	4	yes	maximal, complemented
5	C₂²×#14579131	C₂	1	4	yes	maximal, complemented
6	C₂²×#14579129	C₂	1	2	yes	maximal, complemented
7	C₂²×#124×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂⁵×D₇₉	C₂²	1	2	yes	complemented
9	C₂³×Dic₁₅₈	C₂²	1	2	yes	complemented
10	C₂³×D₃₁₆	C₂²	1	2	yes	—
11	C₂³×D₃₁₆	C₂²	1	2	yes	—
12	C₂³×C₂²⋊D₇₉	C₂²	1	4	yes	—
13	#19099305	C₂²	1	256	yes	direct product factor
14	C₂×#14579150	C₂²	1	48	yes	complemented
15	C₂×#14579149	C₂²	1	48	yes	complemented
16	C₂×#14579147	C₂²	1	96	yes	complemented
17	C₂×#14579131	C₂²	1	96	yes	complemented
18	C₂×#14579129	C₂²	1	48	yes	complemented
19	C₂²×C₂²⋊Dic₇₉	C₂²	1	2	yes	complemented
20	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
21	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
22	C₂²×(C₂×D₇₉)⋊C₄	C₂²	1	4	yes	complemented
23	C₂²×C₄×Dic₇₉	C₂²	1	2	yes	complemented
24	C₂³×Q₈×C₇₉	C₂²	1	1	yes	characteristic, complemented
25	C₂³×D₄×C₇₉	C₂²	1	1	yes	characteristic
26	C₂×#124×C₇₉	C₂²	1	24	yes	complemented
27	C₂²×C₂²⋊C₄×C₇₉	C₂²	1	4	yes	complemented
28	C₂²×C₄²×C₇₉	C₂²	1	1	yes	characteristic, complemented
29	C₂⁴×D₇₉	—	4	16	no	—
30	C₂⁴×D₇₉	—	4	8	no	—
31	C₂⁴×D₇₉	C₂³	1	4	yes	—
32	C₂⁴×D₇₉	C₂³	1	24	yes	complemented
33	C₂²×Dic₁₅₈	—	4	8	no	—
34	C₂²×Dic₁₅₈	C₂³	1	24	yes	complemented
35	C₂²×D₃₁₆	—	4	8	no	—
36	C₂²×D₃₁₆	—	4	8	no	—
37	C₂²×D₃₁₆	C₂³	1	24	yes	—
38	C₂²×D₃₁₆	C₂³	1	24	yes	—
39	C₂²×C₂²⋊D₇₉	—	4	16	no	—
40	C₂²×C₂²⋊D₇₉	C₂³	1	48	yes	—
41	C₂³×Dic₇₉	C₂³	1	4	yes	—
42	#14579150	C₂³	1	128	yes	complemented
43	#14579149	C₂³	1	128	yes	complemented
44	#14579147	C₂³	1	256	yes	complemented
45	#14579131	C₂³	1	256	yes	complemented
46	#14579129	C₂³	1	128	yes	complemented
47	C₂×C₂²⋊Dic₇₉	C₂³	1	24	yes	complemented
48	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	48	yes	complemented
49	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	48	yes	complemented
50	C₂×(C₂×D₇₉)⋊C₄	C₂³	1	48	yes	complemented
51	C₂×C₄×Dic₇₉	C₂³	1	24	yes	complemented
52	C₂⁵×C₇₉	C₂³	1	2	yes	—
53	C₂²×Q₈×C₇₉	—	4	4	no	—
54	C₂²×Q₈×C₇₉	C₂³	1	12	yes	complemented
55	C₂²×D₄×C₇₉	—	4	4	no	—
56	C₂²×D₄×C₇₉	C₂³	1	12	yes	—
57	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₇₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₇₉	C₂³	1	2	yes	—
60	#124×C₇₉	C₂³	1	64	yes	complemented
61	C₂×C₂²⋊C₄×C₇₉	C₂³	1	48	yes	complemented
62	C₂×C₄²×C₇₉	C₂³	1	12	yes	complemented
63	C₂³×D₇₉	—	2	16	no	—
64	C₂³×D₇₉	—	2	16	no	—
65	C₂³×D₇₉	—	2	16	no	—
66	C₂³×D₇₉	—	4	96	no	—
67	C₂³×D₇₉	—	4	48	no	—
68	C₂³×D₇₉	—	4	128	no	—
69	C₂³×D₇₉	C₂⁴	1	24	yes	—
70	C₂³×D₇₉	C₂⁴	1	32	yes	complemented
71	C₂×Dic₁₅₈	—	4	48	no	—
72	C₂×Dic₁₅₈	C₂⁴	1	32	yes	complemented
73	C₂×D₃₁₆	—	4	48	no	—
74	C₂×D₃₁₆	—	4	48	no	—
75	C₂×D₃₁₆	C₂⁴	1	32	yes	—
76	C₂×D₃₁₆	C₂⁴	1	32	yes	—
77	C₂×C₂²⋊D₇₉	—	4	96	no	—
78	C₂×C₂²⋊D₇₉	C₂⁴	1	64	yes	—
79	C₂²×Dic₇₉	—	2	16	no	—
80	C₂²×Dic₇₉	C₂⁴	1	24	yes	—
81	C₂²⋊Dic₇₉	C₂⁴	1	32	yes	complemented
82	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	complemented
83	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	complemented
84	(C₂×D₇₉)⋊C₄	C₂⁴	1	64	yes	complemented
85	C₄×Dic₇₉	C₂⁴	1	32	yes	complemented
86	C₂⁴×C₇₉	—	2	8	no	—
87	C₂⁴×C₇₉	—	2	16	no	—
88	C₂⁴×C₇₉	C₂⁴	1	12	yes	—
89	C₂⁴×C₇₉	C₂⁴	1	1	yes	characteristic
90	C₂×Q₈×C₇₉	—	4	24	no	—
91	C₂×Q₈×C₇₉	C₂⁴	1	16	yes	complemented
92	C₂×D₄×C₇₉	—	4	24	no	—
93	C₂×D₄×C₇₉	C₂⁴	1	16	yes	—
94	C₂²×C₄×C₇₉	—	2	8	no	—
95	C₂²×C₄×C₇₉	—	2	4	no	—
96	C₂²×C₄×C₇₉	—	2	8	no	—
97	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
98	C₂²×C₄×C₇₉	C₂⁴	1	6	yes	—
99	C₂²×C₄×C₇₉	C₂⁴	1	12	yes	—
100	C₂²⋊C₄×C₇₉	C₂⁴	1	64	yes	complemented
101	C₄²×C₇₉	C₂⁴	1	16	yes	complemented
102	C₂³×C₇₉	—	2	48	no	—
103	C₂³×C₇₉	—	2	24	no	—
104	C₂³×C₇₉	—	4	32	no	—
105	C₂³×C₇₉	H(5,𝔽₂)	1	4	yes	—
106	C₂³×C₇₉	H(5,𝔽₂)	1	8	yes	—
107	C₂³×C₇₉	C₂⁵	1	8	yes	—
108	C₂³×C₇₉	C₂⁵	1	3	yes	—
109	C₂²×D₇₉	—	2	48	no	—
110	C₂²×D₇₉	—	2	48	no	—
111	C₂²×D₇₉	—	2	48	no	—
112	C₂²×D₇₉	—	4	64	no	—
113	C₂²×D₇₉	—	4	32	no	—
114	C₂²×D₇₉	—	4	384	no	—
115	C₂²×D₇₉	—	4	64	no	—
116	C₂²×D₇₉	C₂⁵	1	16	yes	—
117	Q₈×C₇₉	—	4	16	no	—
118	D₄×C₇₉	—	4	16	no	—
119	C₂×C₄×C₇₉	—	2	24	no	—
120	C₂×C₄×C₇₉	—	2	24	no	—
121	C₂×C₄×C₇₉	—	2	12	no	—
122	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
123	C₂×C₄×C₇₉	C₂⁵	1	4	yes	—
124	C₂×C₄×C₇₉	C₂⁵	1	8	yes	—
125	C₂²⋊D₇₉	—	4	64	no	—
126	C₂×Dic₇₉	—	2	48	no	—
127	C₂×Dic₇₉	C₂⁵	1	16	yes	—
128	D₃₁₆	—	4	32	no	—
129	D₃₁₆	—	4	32	no	—
130	Dic₁₅₈	—	4	32	no	—
131	C₂²×C₇₉	—	2	16	no	—
132	C₂²×C₇₉	—	2	8	no	—
133	C₂²×C₇₉	—	4	48	no	—
134	C₂²×C₇₉	H(3,𝔽₄)	1	16	yes	complemented
135	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	6	yes	—
136	C₂²×C₇₉	C₂×H(5,𝔽₂)	1	12	yes	—
137	C₂²×C₇₉	C₂⁶	1	1	yes	characteristic
138	C₂×D₇₉	—	2	16	no	—
139	C₂×D₇₉	—	2	16	no	—
140	C₂×D₇₉	—	2	16	no	—
141	C₂×D₇₉	—	4	128	no	—
142	C₂×D₇₉	—	4	96	no	—
143	C₄×C₇₉	—	2	4	no	—
144	C₄×C₇₉	—	2	8	no	—
145	C₄×C₇₉	—	2	8	no	—
146	Dic₇₉	—	2	16	no	—
147	C₂²×H(3,𝔽₄)	—	79	1	no	maximal, Sylow
148	C₂×C₇₉	—	4	8	no	—
149	C₂×C₇₉	C₂×H(3,𝔽₄)	1	12	yes	complemented
150	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₇₉	C₂²×H(5,𝔽₂)	1	2	yes	—
152	D₇₉	—	4	16	no	—
153	C₂×H(3,𝔽₄)	—	79	48	no	—
154	C₂²×#124	—	79	2	no	—
155	C₂²×#124	—	79	2	no	—
156	C₂²×#124	—	79	4	no	—
157	C₂²×#124	D₇₉	1	1	yes	characteristic, complemented
158	C₂²×#120	—	79	2	no	—
159	C₂²×#120	—	79	4	no	—
160	C₇₉	C₂²×H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
161	C₂⁶	—	79	2	no	—
162	C₂³×Q₈	—	79	2	no	—
163	C₂³×Q₈	C₂×D₇₉	1	1	yes	characteristic, complemented
164	C₂³×D₄	—	79	4	no	—
165	C₂³×D₄	—	79	2	no	—
166	C₂³×D₄	—	79	2	no	—
167	C₂³×D₄	C₂×D₇₉	1	1	yes	characteristic
168	H(3,𝔽₄)	—	79	256	no	—
169	C₂×#124	—	79	48	no	—
170	C₂×#124	—	79	96	no	—
171	C₂×#124	—	79	48	no	—
172	C₂×#124	C₂×D₇₉	1	24	yes	complemented
173	C₂×#120	—	79	48	no	—
174	C₂×#120	—	79	96	no	—
175	C₂²×C₂²⋊C₄	—	79	2	no	—
176	C₂²×C₂²⋊C₄	—	79	4	no	—
177	C₂²×C₂²⋊C₄	—	79	4	no	—
178	C₂²×C₂²⋊C₄	—	79	4	no	—
179	C₂²×C₂²⋊C₄	C₂×D₇₉	1	4	yes	complemented
180	C₂²×C₄²	—	79	2	no	—
181	C₂²×C₄²	C₂×D₇₉	1	1	yes	characteristic, complemented
182	C₂⁵	—	316	8	no	—
183	C₂⁵	—	316	16	no	—
184	C₂⁵	—	79	24	no	—
185	C₂⁵	—	79	4	no	—
186	C₂⁵	C₂²×D₇₉	1	2	yes	—
187	C₂²×Q₈	—	4	4	no	—
188	C₂²×Q₈	—	316	8	no	—
189	C₂²×Q₈	—	79	24	no	—
190	C₂²×Q₈	C₂²×D₇₉	1	12	yes	complemented
191	C₂²×D₄	—	4	4	no	—
192	C₂²×D₄	—	316	8	no	—
193	C₂²×D₄	—	316	8	no	—
194	C₂²×D₄	—	316	16	no	—
195	C₂²×D₄	—	79	48	no	—
196	C₂²×D₄	—	79	24	no	—
197	C₂²×D₄	—	79	24	no	—
198	C₂²×D₄	C₂²×D₇₉	1	12	yes	—
199	C₂³×C₄	—	79	4	no	—
200	C₂³×C₄	C₂²×D₇₉	1	1	yes	characteristic
201	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
202	C₂³×C₄	C₂²×D₇₉	1	2	yes	—
203	#124	—	79	128	no	—
204	#124	—	79	256	no	—
205	#124	—	79	128	no	—
206	#124	C₂²×D₇₉	1	64	yes	complemented
207	#120	—	79	128	no	—
208	#120	—	79	256	no	—
209	C₂×C₂²⋊C₄	—	79	24	no	—
210	C₂×C₂²⋊C₄	—	79	48	no	—
211	C₂×C₂²⋊C₄	—	79	48	no	—
212	C₂×C₂²⋊C₄	—	79	48	no	—
213	C₂×C₂²⋊C₄	C₂²×D₇₉	1	48	yes	complemented
214	C₂×C₄²	—	79	24	no	—
215	C₂×C₄²	C₂²×D₇₉	1	12	yes	complemented
216	C₂⁴	—	2	8	no	—
217	C₂⁴	—	2	16	no	—
218	C₂⁴	—	316	48	no	—
219	C₂⁴	—	316	96	no	—
220	C₂⁴	—	316	128	no	—
221	C₂⁴	—	79	32	no	—
222	C₂⁴	—	79	24	no	—
223	C₂⁴	—	158	16	no	—
224	C₂⁴	—	158	16	no	—
225	C₂⁴	—	158	16	no	—
226	C₂⁴	C₂³×D₇₉	1	12	yes	—
227	C₂⁴	C₂³×D₇₉	1	1	yes	characteristic
228	C₂×Q₈	—	4	24	no	—
229	C₂×Q₈	—	316	48	no	—
230	C₂×Q₈	—	79	32	no	—
231	C₂×Q₈	C₂³×D₇₉	1	16	yes	complemented
232	C₂×D₄	—	4	24	no	—
233	C₂×D₄	—	316	48	no	—
234	C₂×D₄	—	316	48	no	—
235	C₂×D₄	—	316	96	no	—
236	C₂×D₄	—	79	64	no	—
237	C₂×D₄	—	79	32	no	—
238	C₂×D₄	—	79	32	no	—
239	C₂×D₄	C₂³×D₇₉	1	16	yes	—
240	C₂²×C₄	—	2	4	no	—
241	C₂²×C₄	—	2	8	no	—
242	C₂²×C₄	—	2	8	no	—
243	C₂²×C₄	—	79	24	no	—
244	C₂²×C₄	—	158	16	no	—
245	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
246	C₂²×C₄	C₂³×D₇₉	1	6	yes	—
247	C₂²×C₄	C₂³×D₇₉	1	12	yes	—
248	C₂²⋊C₄	—	79	32	no	—
249	C₂²⋊C₄	—	79	64	no	—
250	C₂²⋊C₄	—	79	64	no	—
251	C₂²⋊C₄	—	79	64	no	—
252	C₂²⋊C₄	C₂³×D₇₉	1	64	yes	complemented
253	C₄²	—	79	32	no	—
254	C₄²	C₂³×D₇₉	1	16	yes	complemented
255	C₂³	—	2	24	no	—
256	C₂³	—	2	48	no	—
257	C₂³	—	4	32	no	—
258	C₂³	—	316	32	no	—
259	C₂³	—	316	64	no	—
260	C₂³	—	316	384	no	—
261	C₂³	—	316	64	no	—
262	C₂³	—	79	16	no	—
263	C₂³	—	158	48	no	—
264	C₂³	—	158	48	no	—
265	C₂³	—	158	48	no	—
266	C₂³	#14579206	1	4	yes	—
267	C₂³	#14579207	1	8	yes	—
268	C₂³	C₂⁴×D₇₉	1	8	yes	—
269	C₂³	C₂⁴×D₇₉	1	3	yes	—
270	Q₈	—	4	16	no	—
271	Q₈	—	316	32	no	—
272	D₄	—	4	16	no	—
273	D₄	—	316	32	no	—
274	D₄	—	316	32	no	—
275	D₄	—	316	64	no	—
276	C₂×C₄	—	2	12	no	—
277	C₂×C₄	—	2	24	no	—
278	C₂×C₄	—	2	24	no	—
279	C₂×C₄	—	79	16	no	—
280	C₂×C₄	—	158	48	no	—
281	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
282	C₂×C₄	C₂⁴×D₇₉	1	4	yes	—
283	C₂×C₄	C₂⁴×D₇₉	1	8	yes	—
284	C₂²	—	2	8	no	—
285	C₂²	—	2	16	no	—
286	C₂²	—	4	48	no	—
287	C₂²	—	316	128	no	—
288	C₂²	—	316	96	no	—
289	C₂²	—	158	16	no	—
290	C₂²	—	158	16	no	—
291	C₂²	—	158	16	no	—
292	C₂²	#19099305	1	16	yes	direct product factor
293	C₂²	C₂×#14579206	1	6	yes	—
294	C₂²	C₂×#14579207	1	12	yes	—
295	C₂²	C₂⁵×D₇₉	1	1	yes	characteristic
296	C₄	—	2	4	no	—
297	C₄	—	2	8	no	—
298	C₄	—	2	8	no	—
299	C₄	—	158	16	no	—
300	C₂	—	4	8	no	—
301	C₂	—	316	16	no	—
302	C₂	C₂×#19099305	1	12	yes	direct product factor
303	C₂	C₂²×#14579206	1	1	yes	characteristic
304	C₂	C₂²×#14579207	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂²×C₇₉	C₂⁶
Frattini	C₂²	C₂⁵×D₇₉
Fitting	C₂²×#124×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×#124	D₇₉
hypocenter	C₇₉	C₂²×H(3,𝔽₄)
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#124

Complements

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

N	H ≅ G/N	type
1. C₂×#19099305	C₂	direct (N × H)
2. C₂²×#14579150	C₂	semidirect
3. C₂²×#14579149	C₂	semidirect
4. C₂²×#14579147	C₂	semidirect
5. C₂²×#14579131	C₂	semidirect
6. C₂²×#14579129	C₂	semidirect
7. C₂²×#124×C₇₉	C₂	semidirect
8. C₂⁵×D₇₉	C₂²	semidirect
9. C₂³×Dic₁₅₈	C₂²	semidirect
13. #19099305	C₂²	direct (N × H)
14. C₂×#14579150	C₂²	semidirect
15. C₂×#14579149	C₂²	semidirect
16. C₂×#14579147	C₂²	semidirect
17. C₂×#14579131	C₂²	semidirect
18. C₂×#14579129	C₂²	semidirect
19. C₂²×C₂²⋊Dic₇₉	C₂²	semidirect
20. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
21. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
22. C₂²×(C₂×D₇₉)⋊C₄	C₂²	semidirect
23. C₂²×C₄×Dic₇₉	C₂²	semidirect
24. C₂³×Q₈×C₇₉	C₂²	semidirect
26. C₂×#124×C₇₉	C₂²	semidirect
27. C₂²×C₂²⋊C₄×C₇₉	C₂²	semidirect
28. C₂²×C₄²×C₇₉	C₂²	semidirect
32. C₂⁴×D₇₉	C₂³	semidirect
34. C₂²×Dic₁₅₈	C₂³	semidirect
42. #14579150	C₂³	semidirect
43. #14579149	C₂³	semidirect
44. #14579147	C₂³	semidirect
45. #14579131	C₂³	semidirect
46. #14579129	C₂³	semidirect
47. C₂×C₂²⋊Dic₇₉	C₂³	semidirect
48. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
49. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
50. C₂×(C₂×D₇₉)⋊C₄	C₂³	semidirect
51. C₂×C₄×Dic₇₉	C₂³	semidirect
54. C₂²×Q₈×C₇₉	C₂³	semidirect
60. #124×C₇₉	C₂³	semidirect
61. C₂×C₂²⋊C₄×C₇₉	C₂³	semidirect
62. C₂×C₄²×C₇₉	C₂³	semidirect
70. C₂³×D₇₉	C₂⁴	semidirect
72. C₂×Dic₁₅₈	C₂⁴	semidirect
81. C₂²⋊Dic₇₉	C₂⁴	semidirect
82. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
83. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
84. (C₂×D₇₉)⋊C₄	C₂⁴	semidirect
85. C₄×Dic₇₉	C₂⁴	semidirect
91. C₂×Q₈×C₇₉	C₂⁴	semidirect
100. C₂²⋊C₄×C₇₉	C₂⁴	semidirect
101. C₄²×C₇₉	C₂⁴	semidirect
134. C₂²×C₇₉	H(3,𝔽₄)	semidirect
149. C₂×C₇₉	C₂×H(3,𝔽₄)	semidirect
157. C₂²×#124	D₇₉	semidirect
160. C₇₉	C₂²×H(3,𝔽₄)	semidirect
163. C₂³×Q₈	C₂×D₇₉	semidirect
172. C₂×#124	C₂×D₇₉	semidirect
179. C₂²×C₂²⋊C₄	C₂×D₇₉	semidirect
181. C₂²×C₄²	C₂×D₇₉	semidirect
190. C₂²×Q₈	C₂²×D₇₉	semidirect
206. #124	C₂²×D₇₉	semidirect
213. C₂×C₂²⋊C₄	C₂²×D₇₉	semidirect
215. C₂×C₄²	C₂²×D₇₉	semidirect
231. C₂×Q₈	C₂³×D₇₉	semidirect
252. C₂²⋊C₄	C₂³×D₇₉	semidirect
254. C₄²	C₂³×D₇₉	semidirect
292. C₂²	#19099305	direct (N × H)
302. C₂	C₂×#19099305	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×#19099305	2
C₂²×#14579150	2
C₂²×#14579149	2
C₂²×#14579147	2
C₂²×#14579131	2
C₂²×#14579129	2
C₂²×#124×C₇₉	2
C₂²×H(3,𝔽₄)	79

Subgroups — C22×#19099305 #35195141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#19099305 #35195141