Subgroups — AGL(1,𝔽₅)×#709 #13107615

Order 1600.

640 conjugacy classes of subgroups.

The subgroup lattice has 343 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#709	C₂	1	1	yes	maximal, characteristic
2	#11717425	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	AGL(1,𝔽₅)×C₂²⋊D₅	C₂	1	4	yes	maximal, complemented
5	AGL(1,𝔽₅)×D₂₀	C₂	1	2	yes	maximal, complemented
6	C₄×D₅×AGL(1,𝔽₅)	C₂	1	2	yes	maximal, complemented
7	#11717325	C₂	1	2	yes	maximal, complemented
8	AGL(1,𝔽₅)×Dic₁₀	C₂	1	2	yes	maximal, complemented
9	C₂²×C₅×AGL(1,𝔽₅)	C₂²	1	2	yes	—
10	C₂×D₅×AGL(1,𝔽₅)	C₂²	1	4	yes	—
11	#87900	C₄	1	1	yes	characteristic, complemented
12	C₅×#709	C₄	1	1	yes	characteristic, complemented
13	C₂×C₄×C₅×D₅	C₂²	1	1	yes	characteristic
14	D₅×C₂²⋊D₅	C₂²	1	2	yes	—
15	#87879	C₄	1	2	yes	complemented
16	D₅×D₂₀	C₂²	1	1	yes	characteristic
17	C₄×D₅²	C₂²	1	2	yes	—
18	#87874	C₄	1	1	yes	characteristic, complemented
19	#87873	C₄	1	2	yes	complemented
20	#87870	C₄	1	1	yes	characteristic, complemented
21	D₅×Dic₁₀	C₂²	1	1	yes	characteristic
22	C₂²⋊#1042	C₂²	1	2	yes	—
23	C₄⋊#1042	C₂²	1	2	yes	—
24	C₄×#1042	C₂²	1	2	yes	—
25	C₄×C₅×AGL(1,𝔽₅)	C₂²	1	2	yes	—
26	C₄×C₅×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
27	C₄×C₅×AGL(1,𝔽₅)	C₂²	1	1	yes	characteristic
28	#87825	C₂²	1	4	yes	—
29	(C₂×AGL(1,𝔽₅))⋊D₅	C₂²	1	4	yes	—
30	Dic₅×AGL(1,𝔽₅)	C₂²	1	4	yes	—
31	#41×AGL(1,𝔽₅)	—	5	1	no	maximal
32	C₄×#709	—	5	1	no	maximal
33	C₂²×C₅×D₅	C₂³	1	1	yes	characteristic
34	C₂×D₅²	C₂³	1	2	yes	—
35	C₂×#1042	C₂³	1	4	yes	—
36	C₂×C₅×AGL(1,𝔽₅)	—	2	4	no	—
37	C₂×C₅×AGL(1,𝔽₅)	C₂³	1	2	yes	—
38	C₂×C₅×AGL(1,𝔽₅)	C₂³	1	2	yes	—
39	D₅×AGL(1,𝔽₅)	—	2	8	no	—
40	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂²⋊(C₅⋊D₅)	C₂×C₄	1	2	yes	complemented
42	C₄⋊(C₅⋊D₅)	C₂×C₄	1	1	yes	characteristic, complemented
43	C₄×C₅⋊D₅	C₂×C₄	1	2	yes	complemented
44	#6045	C₂×C₄	1	1	yes	characteristic, complemented
45	C₅×C₂²⋊D₅	C₂×C₄	1	2	yes	complemented
46	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
47	C₅×D₂₀	C₂×C₄	1	1	yes	characteristic, complemented
48	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
49	C₄×C₅×D₅	C₂×C₄	1	1	yes	characteristic, complemented
50	C₄×C₅×D₅	C₂×C₄	1	2	yes	complemented
51	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
52	C₄×C₅×D₅	C₂³	1	1	yes	characteristic
53	C₅×Dic₁₀	C₂×C₄	1	1	yes	characteristic, complemented
54	#6039	C₂×C₄	1	2	yes	complemented
55	#6038	C₂×C₄	1	2	yes	complemented
56	#6038	C₂×C₄	1	2	yes	complemented
57	#6037	C₂×C₄	1	2	yes	complemented
58	#6036	C₂×C₄	1	2	yes	complemented
59	D₅×Dic₅	C₂×C₄	1	2	yes	complemented
60	D₅×Dic₅	C₂³	1	2	yes	—
61	D₅×#41	—	5	1	no	—
62	C₂×#709	—	5	1	no	—
63	Q₈×AGL(1,𝔽₅)	—	5	2	no	—
64	D₄×AGL(1,𝔽₅)	—	5	4	no	—
65	D₄×AGL(1,𝔽₅)	—	5	2	no	—
66	#4130	—	5	1	no	—
67	#4130	—	5	2	no	—
68	C₂×C₄×AGL(1,𝔽₅)	—	5	2	no	—
69	C₂×C₄×AGL(1,𝔽₅)	D₅	1	1	yes	characteristic, complemented
70	C₂×C₄²×C₅	—	5	1	no	—
71	C₄×C₂²⋊D₅	—	5	4	no	—
72	#4072	—	5	1	no	—
73	C₄×D₂₀	—	5	2	no	—
74	#4018	—	5	2	no	—
75	C₄²×D₅	—	5	2	no	—
76	C₄×Dic₁₀	—	5	2	no	—
77	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
78	C₂×C₅⋊D₅	C₂²×C₄	1	2	yes	—
79	C₂×C₅×D₅	—	2	2	no	—
80	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₅×D₅	C₂²×C₄	1	2	yes	—
82	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
83	D₅²	—	2	4	no	—
84	#1042	—	2	4	no	—
85	C₅×AGL(1,𝔽₅)	—	2	2	no	—
86	C₅×AGL(1,𝔽₅)	#41	1	4	yes	complemented
87	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
88	C₄×C₅²	C₂²×C₄	1	1	yes	characteristic
89	#1039	C₂²×C₄	1	2	yes	—
90	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
91	C₅×Dic₅	C₂²×C₄	1	1	yes	characteristic
92	C₅×Dic₅	C₂²×C₄	1	2	yes	—
93	C₂²×AGL(1,𝔽₅)	—	5	4	no	—
94	C₂²×AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
95	C₅×#41	—	5	1	no	—
96	C₂²×C₄×C₅	—	5	1	no	—
97	C₂²×C₄×C₅	—	5	2	no	—
98	C₂×C₂²⋊D₅	—	5	2	no	—
99	#713	—	5	1	no	—
100	Q₈×D₅	—	5	1	no	—
101	#711	—	5	2	no	—
102	#711	—	5	1	no	—
103	D₄×D₅	—	5	2	no	—
104	D₄×D₅	—	5	1	no	—
105	#709	—	5	1	no	—
106	#709	—	5	1	no	—
107	#709	—	5	2	no	—
108	#709	—	5	1	no	—
109	#709	—	5	2	no	—
110	#709	—	5	2	no	—
111	#709	—	5	1	no	—
112	#709	—	20	1	no	—
113	#709	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
114	C₂×D₂₀	—	5	1	no	—
115	C₂×C₄×D₅	—	5	2	no	—
116	C₂×C₄×D₅	—	5	2	no	—
117	C₂×C₄×D₅	—	5	4	no	—
118	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
119	C₂×Dic₁₀	—	5	1	no	—
120	C₂²⋊AGL(1,𝔽₅)	—	5	2	no	—
121	C₂²⋊AGL(1,𝔽₅)	—	5	4	no	—
122	C₄⋊AGL(1,𝔽₅)	—	5	4	no	—
123	C₄⋊AGL(1,𝔽₅)	—	5	2	no	—
124	C₄×AGL(1,𝔽₅)	—	5	4	no	—
125	C₄×AGL(1,𝔽₅)	—	5	2	no	—
126	C₄×AGL(1,𝔽₅)	C₂×D₅	1	1	yes	characteristic
127	C₄×AGL(1,𝔽₅)	C₂×D₅	1	1	yes	characteristic
128	C₄×AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
129	C₄²×C₅	—	5	2	no	—
130	C₄²×C₅	—	5	1	no	—
131	C₄²×C₅	—	5	1	no	—
132	C₂²⋊Dic₅	—	5	2	no	—
133	#685	—	5	4	no	—
134	C₄⋊Dic₅	—	5	2	no	—
135	#683	—	5	4	no	—
136	C₄×Dic₅	—	5	4	no	—
137	C₄×Dic₅	—	5	2	no	—
138	C₄×#41	—	25	1	no	Sylow
139	C₂×C₅²	—	2	1	no	—
140	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
141	C₅⋊D₅	—	2	2	no	—
142	C₅×D₅	—	2	2	no	—
143	C₅×D₅	—	2	1	no	—
144	C₅×D₅	C₂×#41	1	2	yes	—
145	C₂³×C₅	—	5	1	no	—
146	C₂²×D₅	—	5	2	no	—
147	C₂²×D₅	—	5	2	no	—
148	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
149	C₂×AGL(1,𝔽₅)	—	2	4	no	—
150	C₂×AGL(1,𝔽₅)	—	5	4	no	—
151	C₂×AGL(1,𝔽₅)	—	10	8	no	—
152	C₂×AGL(1,𝔽₅)	C₂²×D₅	1	2	yes	—
153	C₂×AGL(1,𝔽₅)	C₂²×D₅	1	2	yes	—
154	C₅×Q₈	—	5	1	no	—
155	C₅×D₄	—	5	2	no	—
156	C₅×D₄	—	5	1	no	—
157	C₂×C₄×C₅	—	4	1	no	—
158	C₂×C₄×C₅	—	5	2	no	—
159	C₂×C₄×C₅	—	5	1	no	—
160	C₂×C₄×C₅	—	5	2	no	—
161	C₂×C₄×C₅	—	5	1	no	—
162	C₂×C₄×C₅	—	5	1	no	—
163	C₂×C₄×C₅	—	5	1	no	—
164	C₂×C₄×C₅	—	5	1	no	—
165	C₂×C₄×C₅	—	5	2	no	—
166	C₂×C₄×C₅	—	10	4	no	—
167	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic, complemented
168	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
169	C₂²⋊D₅	—	5	2	no	—
170	C₂²⋊D₅	—	5	2	no	—
171	C₂²⋊D₅	—	5	2	no	—
172	C₂²⋊D₅	—	5	2	no	—
173	C₂²⋊D₅	—	5	2	no	—
174	C₂²⋊D₅	—	5	2	no	—
175	C₂²⋊D₅	—	20	2	no	—
176	C₂²⋊D₅	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
177	C₂×Dic₅	—	5	2	no	—
178	C₂×Dic₅	—	5	2	no	—
179	C₂×Dic₅	—	5	4	no	—
180	C₂×Dic₅	C₄×D₅	1	1	yes	characteristic, complemented
181	D₂₀	—	5	2	no	—
182	D₂₀	—	5	2	no	—
183	D₂₀	—	5	1	no	—
184	D₂₀	—	5	1	no	—
185	D₂₀	—	20	1	no	—
186	D₂₀	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
187	C₄×D₅	—	5	2	no	—
188	C₄×D₅	—	5	2	no	—
189	C₄×D₅	—	5	2	no	—
190	C₄×D₅	—	5	2	no	—
191	C₄×D₅	—	5	2	no	—
192	C₄×D₅	—	5	2	no	—
193	C₄×D₅	—	10	8	no	—
194	C₄×D₅	—	20	2	no	—
195	C₄×D₅	C₄×D₅	1	1	yes	characteristic, complemented
196	C₄×D₅	C₄×D₅	1	1	yes	characteristic, complemented
197	C₄×D₅	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
198	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
199	C₄×D₅	C₂²×D₅	1	1	yes	characteristic
200	Dic₁₀	—	5	1	no	—
201	Dic₁₀	—	5	1	no	—
202	Dic₁₀	—	5	2	no	—
203	Dic₁₀	—	5	2	no	—
204	Dic₁₀	—	20	1	no	—
205	Dic₁₀	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
206	C₂×#41	—	25	1	no	—
207	C₄×Q₈	—	25	2	no	—
208	C₄×D₄	—	25	2	no	—
209	C₄×D₄	—	25	4	no	—
210	#117	—	25	2	no	—
211	#117	—	25	1	no	—
212	C₂×C₄²	—	5	1	no	—
213	C₂×C₄²	—	25	2	no	—
214	C₅²	C₄×#41	1	1	yes	characteristic, complemented, Sylow
215	C₂²×C₅	—	4	1	no	—
216	C₂²×C₅	—	5	1	no	—
217	C₂²×C₅	—	5	2	no	—
218	C₂²×C₅	—	5	1	no	—
219	C₂²×C₅	—	10	2	no	—
220	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
221	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
222	C₂×D₅	—	2	2	no	—
223	C₂×D₅	—	5	2	no	—
224	C₂×D₅	—	5	2	no	—
225	C₂×D₅	—	10	4	no	—
226	C₂×D₅	—	10	4	no	—
227	C₂×D₅	—	20	2	no	—
228	C₂×D₅	C₂×C₄×D₅	1	1	yes	characteristic
229	C₂×D₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
230	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
231	AGL(1,𝔽₅)	—	2	2	no	—
232	AGL(1,𝔽₅)	—	10	4	no	—
233	AGL(1,𝔽₅)	#709	1	4	yes	direct product factor
234	C₄×C₅	—	4	1	no	—
235	C₄×C₅	—	4	1	no	—
236	C₄×C₅	—	5	4	no	—
237	C₄×C₅	—	5	2	no	—
238	C₄×C₅	—	5	1	no	—
239	C₄×C₅	—	5	1	no	—
240	C₄×C₅	—	10	2	no	—
241	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
242	C₄×C₅	C₂×C₄×D₅	1	1	yes	characteristic
243	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
244	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
245	Dic₅	—	5	2	no	—
246	Dic₅	—	5	2	no	—
247	Dic₅	—	10	4	no	—
248	Dic₅	—	20	2	no	—
249	Dic₅	C₂×C₄×D₅	1	1	yes	characteristic
250	Dic₅	C₂×C₄×D₅	1	1	yes	characteristic
251	Dic₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
252	#41	—	5	1	no	—
253	#41	—	25	2	no	—
254	#41	—	25	2	no	—
255	#41	—	25	1	no	—
256	#41	—	25	1	no	—
257	#41	—	25	1	no	—
258	C₂×Q₈	—	25	1	no	—
259	C₂×D₄	—	25	1	no	—
260	C₂×D₄	—	25	2	no	—
261	C₂²×C₄	—	5	1	no	—
262	C₂²×C₄	—	5	2	no	—
263	C₂²×C₄	—	25	2	no	—
264	C₂²×C₄	—	25	4	no	—
265	C₄⋊C₄	—	25	4	no	—
266	C₄⋊C₄	—	25	2	no	—
267	C₂²⋊C₄	—	25	4	no	—
268	C₂²⋊C₄	—	25	2	no	—
269	C₄²	—	5	1	no	—
270	C₄²	—	5	1	no	—
271	C₄²	—	5	2	no	—
272	C₄²	—	25	2	no	—
273	C₄²	—	25	4	no	—
274	C₂×C₅	—	2	1	no	—
275	C₂×C₅	—	2	1	no	—
276	C₂×C₅	—	4	1	no	—
277	C₂×C₅	—	5	2	no	—
278	C₂×C₅	—	8	1	no	—
279	C₂×C₅	—	10	2	no	—
280	C₂×C₅	—	10	1	no	—
281	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
282	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
283	D₅	—	2	1	no	—
284	D₅	—	2	2	no	—
285	D₅	—	10	2	no	—
286	D₅	—	10	2	no	—
287	D₅	—	40	2	no	—
288	D₅	C₂×#709	1	2	yes	—
289	C₂³	—	5	1	no	—
290	C₂³	—	25	2	no	—
291	Q₈	—	5	1	no	—
292	Q₈	—	25	2	no	—
293	Q₈	—	25	1	no	—
294	D₄	—	5	2	no	—
295	D₄	—	5	1	no	—
296	D₄	—	25	2	no	—
297	D₄	—	25	2	no	—
298	D₄	—	25	2	no	—
299	D₄	—	25	2	no	—
300	D₄	—	25	1	no	—
301	C₂×C₄	—	5	2	no	—
302	C₂×C₄	—	5	1	no	—
303	C₂×C₄	—	5	1	no	—
304	C₂×C₄	—	5	1	no	—
305	C₂×C₄	—	5	1	no	—
306	C₂×C₄	—	5	1	no	—
307	C₂×C₄	—	5	2	no	—
308	C₂×C₄	—	5	2	no	—
309	C₂×C₄	—	10	4	no	—
310	C₂×C₄	—	25	2	no	—
311	C₂×C₄	—	25	2	no	—
312	C₂×C₄	—	25	2	no	—
313	C₂×C₄	—	25	2	no	—
314	C₂×C₄	—	25	4	no	—
315	C₂×C₄	—	50	8	no	—
316	C₂×C₄	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
317	C₅	—	4	1	no	—
318	C₅	C₄×#709	1	1	yes	characteristic, complemented
319	C₅	#41×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
320	C₂²	—	5	1	no	—
321	C₂²	—	5	1	no	—
322	C₂²	—	5	2	no	—
323	C₂²	—	10	2	no	—
324	C₂²	—	25	2	no	—
325	C₂²	—	50	4	no	—
326	C₂²	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
327	C₄	—	5	4	no	—
328	C₄	—	5	1	no	—
329	C₄	—	5	1	no	—
330	C₄	—	5	2	no	—
331	C₄	—	10	2	no	—
332	C₄	—	25	2	no	—
333	C₄	—	50	4	no	—
334	C₄	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
335	C₄	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
336	C₂	—	2	1	no	—
337	C₂	—	5	2	no	—
338	C₂	—	10	1	no	—
339	C₂	—	10	2	no	—
340	C₂	—	50	2	no	—
341	C₂	C₂²×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₅×AGL(1,𝔽₅)
commutator, socle	C₂×C₅²	C₂³×C₄
Frattini	C₂	C₂²×D₅×AGL(1,𝔽₅)
Fitting	C₂×C₄×C₅²	C₂×C₄
prime radical	D₅×#709	C₂
cosocle	C₂×C₅×D₅	C₂⁴
hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
hypocenter	C₅²	C₄×#41
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
2. #11717425	C₂	semidirect
3. C₂×C₄×C₅×AGL(1,𝔽₅)	C₂	semidirect
4. AGL(1,𝔽₅)×C₂²⋊D₅	C₂	semidirect
5. AGL(1,𝔽₅)×D₂₀	C₂	semidirect
6. C₄×D₅×AGL(1,𝔽₅)	C₂	semidirect
7. #11717325	C₂	semidirect
8. AGL(1,𝔽₅)×Dic₁₀	C₂	semidirect
11. #87900	C₄	semidirect
12. C₅×#709	C₄	semidirect
15. #87879	C₄	semidirect
18. #87874	C₄	semidirect
19. #87873	C₄	semidirect
20. #87870	C₄	semidirect
40. C₂×C₄×C₅²	C₂×C₄	semidirect
41. C₂²⋊(C₅⋊D₅)	C₂×C₄	semidirect
42. C₄⋊(C₅⋊D₅)	C₂×C₄	semidirect
43. C₄×C₅⋊D₅	C₂×C₄	semidirect
44. #6045	C₂×C₄	semidirect
45. C₅×C₂²⋊D₅	C₂×C₄	semidirect
46. C₂×C₅×Dic₅	C₂×C₄	semidirect
47. C₅×D₂₀	C₂×C₄	semidirect
48. C₄×C₅×D₅	C₂×C₄	semidirect
49. C₄×C₅×D₅	C₂×C₄	semidirect
50. C₄×C₅×D₅	C₂×C₄	semidirect
53. C₅×Dic₁₀	C₂×C₄	semidirect
54. #6039	C₂×C₄	semidirect
55. #6038	C₂×C₄	semidirect
56. #6038	C₂×C₄	semidirect
57. #6037	C₂×C₄	semidirect
58. #6036	C₂×C₄	semidirect
59. D₅×Dic₅	C₂×C₄	semidirect
69. C₂×C₄×AGL(1,𝔽₅)	D₅	semidirect
86. C₅×AGL(1,𝔽₅)	#41	semidirect
113. #709	AGL(1,𝔽₅)	direct (N × H)
167. C₂×C₄×C₅	C₄×D₅	semidirect
168. C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
176. C₂²⋊D₅	C₂×AGL(1,𝔽₅)	semidirect
180. C₂×Dic₅	C₄×D₅	semidirect
186. D₂₀	C₂×AGL(1,𝔽₅)	semidirect
195. C₄×D₅	C₄×D₅	semidirect
196. C₄×D₅	C₄×D₅	semidirect
197. C₄×D₅	C₂×AGL(1,𝔽₅)	semidirect
205. Dic₁₀	C₂×AGL(1,𝔽₅)	semidirect
214. C₅²	C₄×#41	semidirect
233. AGL(1,𝔽₅)	#709	direct (N × H)
316. C₂×C₄	D₅×AGL(1,𝔽₅)	semidirect
318. C₅	C₄×#709	semidirect
319. C₅	#41×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
D₅×#709	2
#11717425	2
C₂×C₄×C₅×AGL(1,𝔽₅)	2
AGL(1,𝔽₅)×C₂²⋊D₅	2
AGL(1,𝔽₅)×D₂₀	2
C₄×D₅×AGL(1,𝔽₅)	2
#11717325	2
AGL(1,𝔽₅)×Dic₁₀	2
#41×AGL(1,𝔽₅)	5
C₄×#709	5

Subgroups — AGL(1,𝔽5)×#709 #13107615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#709 #13107615