Subgroups — C₂×C₄×D₅×AGL(1,𝔽₅) #13107611

Order 1600.

1023 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₂×C₄×D₅²	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#1042	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₅×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Dic₅×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
6	C₄×D₅×AGL(1,𝔽₅)	C₂	1	8	yes	maximal, direct product factor
7	C₂²×D₅²	C₂²	1	1	yes	characteristic
8	C₂²×#1042	C₂²	1	2	yes	—
9	C₂²×C₅×AGL(1,𝔽₅)	C₂²	1	2	yes	—
10	C₂×D₅×AGL(1,𝔽₅)	C₄	1	16	yes	direct product factor
11	C₂×D₅×AGL(1,𝔽₅)	C₂²	1	8	yes	—
12	C₂×C₄×C₅⋊D₅	C₄	1	1	yes	characteristic, complemented
13	C₂×C₄×C₅×D₅	C₄	1	1	yes	characteristic, complemented
14	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
15	C₂×#6036	C₄	1	1	yes	characteristic, complemented
16	C₂×D₅×Dic₅	C₄	1	1	yes	characteristic, complemented
17	C₂×D₅×Dic₅	C₂²	1	1	yes	characteristic
18	C₄×D₅²	C₄	1	4	yes	complemented
19	C₄×D₅²	C₂²	1	4	yes	—
20	C₄×#1042	C₂²	1	4	yes	complemented
21	C₄×C₅×AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
22	Dic₅×AGL(1,𝔽₅)	C₂²	1	8	yes	complemented
23	C₂²×C₄×AGL(1,𝔽₅)	—	5	1	no	maximal
24	C₂×C₄²×D₅	—	5	1	no	maximal
25	C₂²×C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₅×D₅	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
28	C₂×D₅²	C₂×C₄	1	2	yes	—
29	C₂×D₅²	C₂×C₄	1	8	yes	—
30	C₂×D₅²	C₂³	1	2	yes	—
31	C₂×#1042	C₂×C₄	1	8	yes	complemented
32	C₂×#1042	C₂³	1	4	yes	—
33	C₂×C₅×AGL(1,𝔽₅)	C₂×C₄	1	8	yes	complemented
34	C₂×C₅×AGL(1,𝔽₅)	C₂³	1	4	yes	—
35	D₅×AGL(1,𝔽₅)	C₂×C₄	1	32	yes	direct product factor
36	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic, complemented
37	C₂×#1039	C₂×C₄	1	1	yes	characteristic, complemented
38	C₄×C₅⋊D₅	C₂×C₄	1	4	yes	complemented
39	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
40	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
41	C₄×C₅×D₅	C₂×C₄	1	2	yes	complemented
42	C₄×C₅×D₅	C₂×C₄	1	4	yes	complemented
43	C₄×C₅×D₅	C₂³	1	2	yes	—
44	#6036	C₂×C₄	1	4	yes	complemented
45	D₅×Dic₅	C₂×C₄	1	2	yes	complemented
46	D₅×Dic₅	C₂×C₄	1	4	yes	complemented
47	D₅×Dic₅	C₂³	1	2	yes	—
48	C₂³×AGL(1,𝔽₅)	—	5	2	no	—
49	C₂²×C₄×D₅	—	5	2	no	—
50	C₂²×C₄×D₅	—	5	1	no	—
51	C₂²×C₄×D₅	—	5	1	no	—
52	C₂×C₄×AGL(1,𝔽₅)	—	5	2	no	—
53	C₂×C₄×AGL(1,𝔽₅)	—	5	1	no	—
54	C₂×C₄×AGL(1,𝔽₅)	—	5	8	no	—
55	C₂×C₄×AGL(1,𝔽₅)	D₅	1	1	yes	characteristic, direct product factor
56	C₂×C₄²×C₅	—	5	1	no	—
57	C₂×C₄×Dic₅	—	5	1	no	—
58	C₂×C₄×Dic₅	—	5	2	no	—
59	C₄²×D₅	—	5	8	no	—
60	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₅⋊D₅	C₄²	1	4	yes	complemented
62	C₂×C₅⋊D₅	C₂²×C₄	1	2	yes	—
63	C₂×C₅×D₅	C₄²	1	4	yes	complemented
64	C₂×C₅×D₅	C₂²×C₄	1	4	yes	—
65	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₅×D₅	C₂²×C₄	1	2	yes	—
67	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
68	D₅²	C₄²	1	8	yes	complemented
69	D₅²	C₂²×C₄	1	8	yes	—
70	#1042	C₂²×C₄	1	8	yes	complemented
71	C₅×AGL(1,𝔽₅)	C₂²×C₄	1	8	yes	complemented
72	C₄×C₅²	C₂²×C₄	1	2	yes	complemented
73	#1039	C₂²×C₄	1	2	yes	complemented
74	C₅×Dic₅	C₂²×C₄	1	2	yes	complemented
75	C₅×Dic₅	C₂²×C₄	1	2	yes	complemented
76	C₂³×D₅	—	5	1	no	—
77	C₂³×D₅	—	5	1	no	—
78	C₂²×AGL(1,𝔽₅)	—	5	2	no	—
79	C₂²×AGL(1,𝔽₅)	—	5	16	no	—
80	C₂²×AGL(1,𝔽₅)	—	5	8	no	—
81	C₂²×AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
82	C₂²×C₄×C₅	—	5	2	no	—
83	C₂²×C₄×C₅	—	5	1	no	—
84	C₂²×C₄×C₅	—	5	1	no	—
85	C₂²×Dic₅	—	5	2	no	—
86	C₂²×Dic₅	—	5	1	no	—
87	C₂²×Dic₅	—	5	1	no	—
88	C₂×C₄×D₅	—	5	16	no	—
89	C₂×C₄×D₅	—	5	8	no	—
90	C₂×C₄×D₅	—	5	1	no	—
91	C₂×C₄×D₅	—	5	1	no	—
92	C₂×C₄×D₅	—	5	1	no	—
93	C₂×C₄×D₅	—	5	1	no	—
94	C₂×C₄×D₅	—	5	1	no	—
95	C₂×C₄×D₅	—	5	1	no	—
96	C₂×C₄×D₅	—	5	4	no	—
97	C₂×C₄×D₅	—	5	4	no	—
98	C₂×C₄×D₅	—	5	4	no	—
99	C₂×C₄×D₅	—	5	4	no	—
100	C₂×C₄×D₅	—	20	1	no	—
101	C₂×C₄×D₅	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
102	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
103	C₄×AGL(1,𝔽₅)	—	5	8	no	—
104	C₄×AGL(1,𝔽₅)	—	5	4	no	—
105	C₄×AGL(1,𝔽₅)	C₂×D₅	1	4	yes	direct product factor
106	C₄²×C₅	—	5	4	no	—
107	C₄×Dic₅	—	5	8	no	—
108	C₄×Dic₅	—	5	4	no	—
109	C₂²×C₄²	—	25	1	no	Sylow
110	C₂×C₅²	C₂×C₄²	1	2	yes	complemented
111	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
112	C₅⋊D₅	C₂×C₄²	1	4	yes	complemented
113	C₅×D₅	C₂×C₄²	1	4	yes	complemented
114	C₅×D₅	C₂×C₄²	1	2	yes	complemented
115	C₅×D₅	C₂³×C₄	1	2	yes	—
116	C₂³×C₅	—	5	1	no	—
117	C₂³×C₅	—	5	1	no	—
118	C₂²×D₅	—	5	1	no	—
119	C₂²×D₅	—	5	1	no	—
120	C₂²×D₅	—	5	8	no	—
121	C₂²×D₅	—	5	2	no	—
122	C₂²×D₅	—	5	8	no	—
123	C₂²×D₅	—	5	2	no	—
124	C₂²×D₅	—	5	2	no	—
125	C₂²×D₅	—	5	2	no	—
126	C₂²×D₅	—	20	1	no	—
127	C₂²×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
128	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
129	C₂×AGL(1,𝔽₅)	—	5	8	no	—
130	C₂×AGL(1,𝔽₅)	—	5	4	no	—
131	C₂×AGL(1,𝔽₅)	—	5	32	no	—
132	C₂×AGL(1,𝔽₅)	C₄×D₅	1	8	yes	direct product factor
133	C₂×AGL(1,𝔽₅)	C₂²×D₅	1	4	yes	—
134	C₂×C₄×C₅	—	4	1	no	—
135	C₂×C₄×C₅	—	5	4	no	—
136	C₂×C₄×C₅	—	5	8	no	—
137	C₂×C₄×C₅	—	5	1	no	—
138	C₂×C₄×C₅	—	5	1	no	—
139	C₂×C₄×C₅	—	5	4	no	—
140	C₂×C₄×C₅	—	5	2	no	—
141	C₂×C₄×C₅	—	5	2	no	—
142	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic, complemented
143	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
144	C₂×Dic₅	—	5	4	no	—
145	C₂×Dic₅	—	5	8	no	—
146	C₂×Dic₅	—	5	1	no	—
147	C₂×Dic₅	—	5	1	no	—
148	C₂×Dic₅	—	5	4	no	—
149	C₂×Dic₅	—	5	2	no	—
150	C₂×Dic₅	—	5	2	no	—
151	C₂×Dic₅	—	20	1	no	—
152	C₂×Dic₅	C₄×D₅	1	1	yes	characteristic, complemented
153	C₂×Dic₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
154	C₄×D₅	—	5	32	no	—
155	C₄×D₅	—	5	2	no	—
156	C₄×D₅	—	5	4	no	—
157	C₄×D₅	—	5	2	no	—
158	C₄×D₅	—	5	4	no	—
159	C₄×D₅	—	5	4	no	—
160	C₄×D₅	—	5	4	no	—
161	C₄×D₅	—	5	4	no	—
162	C₄×D₅	—	20	4	no	—
163	C₄×D₅	C₄×D₅	1	2	yes	complemented
164	C₄×D₅	C₂×AGL(1,𝔽₅)	1	4	yes	direct product factor
165	C₄×D₅	C₂²×D₅	1	2	yes	—
166	C₂³×C₄	—	25	1	no	—
167	C₂³×C₄	—	25	2	no	—
168	C₂×C₄²	—	5	1	no	—
169	C₂×C₄²	—	25	8	no	—
170	C₂×C₄²	—	25	2	no	—
171	C₂×C₄²	—	25	1	no	—
172	C₅²	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
173	C₂²×C₅	—	4	1	no	—
174	C₂²×C₅	—	5	4	no	—
175	C₂²×C₅	—	5	2	no	—
176	C₂²×C₅	—	5	1	no	—
177	C₂²×C₅	—	5	1	no	—
178	C₂²×C₅	—	5	4	no	—
179	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
180	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
181	C₂×D₅	—	5	4	no	—
182	C₂×D₅	—	5	2	no	—
183	C₂×D₅	—	5	2	no	—
184	C₂×D₅	—	5	4	no	—
185	C₂×D₅	—	5	8	no	—
186	C₂×D₅	—	5	8	no	—
187	C₂×D₅	—	5	8	no	—
188	C₂×D₅	—	5	8	no	—
189	C₂×D₅	—	20	4	no	—
190	C₂×D₅	—	20	2	no	—
191	C₂×D₅	C₄×AGL(1,𝔽₅)	1	4	yes	direct product factor
192	C₂×D₅	C₂×C₄×D₅	1	4	yes	—
193	C₂×D₅	C₂×C₄×D₅	1	1	yes	characteristic
194	C₂×D₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
195	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
196	AGL(1,𝔽₅)	—	5	8	no	—
197	AGL(1,𝔽₅)	C₂×C₄×D₅	1	8	yes	direct product factor
198	C₄×C₅	—	4	2	no	—
199	C₄×C₅	—	5	8	no	—
200	C₄×C₅	—	5	2	no	—
201	C₄×C₅	—	5	2	no	—
202	C₄×C₅	C₂×C₄×D₅	1	2	yes	complemented
203	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
204	Dic₅	—	5	8	no	—
205	Dic₅	—	5	2	no	—
206	Dic₅	—	5	2	no	—
207	Dic₅	—	20	2	no	—
208	Dic₅	C₂×C₄×D₅	1	2	yes	complemented
209	Dic₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
210	C₂⁴	—	25	1	no	—
211	C₂²×C₄	—	5	2	no	—
212	C₂²×C₄	—	5	1	no	—
213	C₂²×C₄	—	5	1	no	—
214	C₂²×C₄	—	25	4	no	—
215	C₂²×C₄	—	25	1	no	—
216	C₂²×C₄	—	25	4	no	—
217	C₂²×C₄	—	25	1	no	—
218	C₂²×C₄	—	25	1	no	—
219	C₂²×C₄	—	25	8	no	—
220	C₂²×C₄	—	25	16	no	—
221	C₂²×C₄	—	25	2	no	—
222	C₂²×C₄	—	25	1	no	—
223	C₄²	—	5	4	no	—
224	C₄²	—	25	8	no	—
225	C₄²	—	25	4	no	—
226	C₂×C₅	—	4	1	no	—
227	C₂×C₅	—	4	2	no	—
228	C₂×C₅	—	5	4	no	—
229	C₂×C₅	—	5	2	no	—
230	C₂×C₅	—	5	2	no	—
231	C₂×C₅	C₄²×D₅	1	2	yes	complemented
232	C₂×C₅	C₂×C₄×AGL(1,𝔽₅)	1	2	yes	complemented
233	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
234	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
235	D₅	—	5	4	no	—
236	D₅	—	5	4	no	—
237	D₅	—	20	4	no	—
238	D₅	C₄²×D₅	1	2	yes	complemented
239	D₅	C₂×C₄×AGL(1,𝔽₅)	1	4	yes	direct product factor
240	D₅	C₂²×C₄×D₅	1	2	yes	—
241	C₂³	—	5	1	no	—
242	C₂³	—	5	1	no	—
243	C₂³	—	25	2	no	—
244	C₂³	—	25	2	no	—
245	C₂³	—	25	8	no	—
246	C₂³	—	25	1	no	—
247	C₂×C₄	—	5	4	no	—
248	C₂×C₄	—	5	8	no	—
249	C₂×C₄	—	5	1	no	—
250	C₂×C₄	—	5	1	no	—
251	C₂×C₄	—	5	2	no	—
252	C₂×C₄	—	5	2	no	—
253	C₂×C₄	—	5	4	no	—
254	C₂×C₄	—	25	4	no	—
255	C₂×C₄	—	25	2	no	—
256	C₂×C₄	—	25	4	no	—
257	C₂×C₄	—	25	2	no	—
258	C₂×C₄	—	25	32	no	—
259	C₂×C₄	—	25	4	no	—
260	C₂×C₄	—	25	8	no	—
261	C₂×C₄	—	25	1	no	—
262	C₂×C₄	—	25	4	no	—
263	C₂×C₄	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
264	C₅	—	4	1	no	—
265	C₅	C₂×C₄²×D₅	1	1	yes	characteristic, complemented
266	C₅	C₂²×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
267	C₂²	—	5	1	no	—
268	C₂²	—	5	1	no	—
269	C₂²	—	5	2	no	—
270	C₂²	—	5	4	no	—
271	C₂²	—	5	4	no	—
272	C₂²	—	25	8	no	—
273	C₂²	—	25	8	no	—
274	C₂²	—	25	2	no	—
275	C₂²	—	25	4	no	—
276	C₂²	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
277	C₄	—	5	8	no	—
278	C₄	—	5	2	no	—
279	C₄	—	5	2	no	—
280	C₄	—	25	8	no	—
281	C₄	—	25	2	no	—
282	C₄	C₂×D₅×AGL(1,𝔽₅)	1	2	yes	direct product factor
283	C₂	—	5	2	no	—
284	C₂	—	5	4	no	—
285	C₂	—	5	2	no	—
286	C₂	—	25	4	no	—
287	C₂	C₄×D₅×AGL(1,𝔽₅)	1	2	yes	direct product factor
288	C₂	C₂²×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
commutator, hypocenter	C₅²	C₂²×C₄²
Frattini	C₂	C₂²×D₅×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅²	C₂×C₄
socle	C₂²×C₅²	C₂²×C₄
prime radical	C₂²×D₅²	C₂²
cosocle	C₂×C₅×D₅	C₂⁴
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#1042	C₂	semidirect
4. C₂×C₄×C₅×AGL(1,𝔽₅)	C₂	semidirect
5. C₂×Dic₅×AGL(1,𝔽₅)	C₂	semidirect
6. C₄×D₅×AGL(1,𝔽₅)	C₂	direct (N × H)
10. C₂×D₅×AGL(1,𝔽₅)	C₄	direct (N × H)
12. C₂×C₄×C₅⋊D₅	C₄	semidirect
13. C₂×C₄×C₅×D₅	C₄	semidirect
15. C₂×#6036	C₄	semidirect
16. C₂×D₅×Dic₅	C₄	semidirect
18. C₄×D₅²	C₄	semidirect
20. C₄×#1042	C₂²	semidirect
21. C₄×C₅×AGL(1,𝔽₅)	C₂²	semidirect
22. Dic₅×AGL(1,𝔽₅)	C₂²	semidirect
31. C₂×#1042	C₂×C₄	semidirect
33. C₂×C₅×AGL(1,𝔽₅)	C₂×C₄	semidirect
35. D₅×AGL(1,𝔽₅)	C₂×C₄	direct (N × H)
36. C₂×C₄×C₅²	C₂×C₄	semidirect
37. C₂×#1039	C₂×C₄	semidirect
38. C₄×C₅⋊D₅	C₂×C₄	semidirect
39. C₂×C₅×Dic₅	C₂×C₄	semidirect
40. C₂×C₅×Dic₅	C₂×C₄	semidirect
41. C₄×C₅×D₅	C₂×C₄	semidirect
42. C₄×C₅×D₅	C₂×C₄	semidirect
44. #6036	C₂×C₄	semidirect
45. D₅×Dic₅	C₂×C₄	semidirect
46. D₅×Dic₅	C₂×C₄	semidirect
55. C₂×C₄×AGL(1,𝔽₅)	D₅	direct (N × H)
61. C₂×C₅⋊D₅	C₄²	semidirect
63. C₂×C₅×D₅	C₄²	semidirect
68. D₅²	C₄²	semidirect
70. #1042	C₂²×C₄	semidirect
71. C₅×AGL(1,𝔽₅)	C₂²×C₄	semidirect
72. C₄×C₅²	C₂²×C₄	semidirect
73. #1039	C₂²×C₄	semidirect
74. C₅×Dic₅	C₂²×C₄	semidirect
75. C₅×Dic₅	C₂²×C₄	semidirect
101. C₂×C₄×D₅	AGL(1,𝔽₅)	direct (N × H)
105. C₄×AGL(1,𝔽₅)	C₂×D₅	direct (N × H)
110. C₂×C₅²	C₂×C₄²	semidirect
112. C₅⋊D₅	C₂×C₄²	semidirect
113. C₅×D₅	C₂×C₄²	semidirect
114. C₅×D₅	C₂×C₄²	semidirect
132. C₂×AGL(1,𝔽₅)	C₄×D₅	direct (N × H)
142. C₂×C₄×C₅	C₄×D₅	semidirect
143. C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
152. C₂×Dic₅	C₄×D₅	semidirect
153. C₂×Dic₅	C₂×AGL(1,𝔽₅)	semidirect
163. C₄×D₅	C₄×D₅	semidirect
164. C₄×D₅	C₂×AGL(1,𝔽₅)	direct (N × H)
172. C₅²	C₂²×C₄²	semidirect
191. C₂×D₅	C₄×AGL(1,𝔽₅)	direct (N × H)
197. AGL(1,𝔽₅)	C₂×C₄×D₅	direct (N × H)
202. C₄×C₅	C₂×C₄×D₅	semidirect
203. C₄×C₅	C₂²×AGL(1,𝔽₅)	semidirect
208. Dic₅	C₂×C₄×D₅	semidirect
209. Dic₅	C₂²×AGL(1,𝔽₅)	semidirect
231. C₂×C₅	C₄²×D₅	semidirect
232. C₂×C₅	C₂×C₄×AGL(1,𝔽₅)	semidirect
238. D₅	C₄²×D₅	semidirect
239. D₅	C₂×C₄×AGL(1,𝔽₅)	direct (N × H)
263. C₂×C₄	D₅×AGL(1,𝔽₅)	direct (N × H)
265. C₅	C₂×C₄²×D₅	semidirect
266. C₅	C₂²×C₄×AGL(1,𝔽₅)	semidirect
282. C₄	C₂×D₅×AGL(1,𝔽₅)	direct (N × H)
287. C₂	C₄×D₅×AGL(1,𝔽₅)	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×D₅×AGL(1,𝔽₅)	2
C₂×C₄×D₅²	2
C₂×C₄×#1042	2
C₂×C₄×C₅×AGL(1,𝔽₅)	2
C₂×Dic₅×AGL(1,𝔽₅)	2
C₄×D₅×AGL(1,𝔽₅)	2
C₂²×C₄×AGL(1,𝔽₅)	5
C₂×C₄²×D₅	5

Subgroups — C2×C4×D5×AGL(1,𝔽5) #13107611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₅×AGL(1,𝔽₅) #13107611