Subgroups — C₂×D₅×C₄⋊AGL(1,𝔽₅) #13107613

Order 1600.

863 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	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×C₅×C₄⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#87825	C₂	1	2	yes	maximal, complemented
6	D₅×C₄⋊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)	—	2	8	no	—
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	C₅×C₄⋊AGL(1,𝔽₅)	C₂²	1	4	yes	complemented
22	#87825	C₂²	1	8	yes	complemented
23	C₂²×C₄⋊AGL(1,𝔽₅)	—	5	1	no	maximal
24	C₂×D₅×C₄⋊C₄	—	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	D₄	1	4	yes	—
30	C₂×D₅²	Q₈	1	4	yes	—
31	C₂×D₅²	C₂³	1	2	yes	—
32	C₂×#1042	—	2	4	no	—
33	C₂×#1042	C₂³	1	4	yes	—
34	C₂×C₅×AGL(1,𝔽₅)	—	2	4	no	—
35	C₂×C₅×AGL(1,𝔽₅)	C₂³	1	4	yes	—
36	D₅×AGL(1,𝔽₅)	—	2	16	no	—
37	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic, complemented
38	C₂×#1039	C₂×C₄	1	1	yes	characteristic, complemented
39	C₄×C₅⋊D₅	C₂×C₄	1	4	yes	complemented
40	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
41	C₂×C₅×Dic₅	C₂×C₄	1	1	yes	characteristic, complemented
42	C₄×C₅×D₅	C₂×C₄	1	2	yes	complemented
43	C₄×C₅×D₅	C₂×C₄	1	4	yes	complemented
44	C₄×C₅×D₅	C₂³	1	2	yes	—
45	#6036	C₂×C₄	1	4	yes	complemented
46	D₅×Dic₅	C₂×C₄	1	2	yes	complemented
47	D₅×Dic₅	C₂×C₄	1	4	yes	complemented
48	D₅×Dic₅	C₂³	1	2	yes	—
49	C₂³×AGL(1,𝔽₅)	—	5	2	no	—
50	C₂²×C₄×D₅	—	5	1	no	—
51	C₂²×C₄×D₅	—	5	1	no	—
52	C₂²×C₄×D₅	—	5	2	no	—
53	C₂×C₄⋊AGL(1,𝔽₅)	—	5	2	no	—
54	C₂×C₄⋊AGL(1,𝔽₅)	—	5	1	no	—
55	C₂×C₄⋊AGL(1,𝔽₅)	—	5	8	no	—
56	C₂×C₄⋊AGL(1,𝔽₅)	D₅	1	1	yes	characteristic, direct product factor
57	C₂×C₅×C₄⋊C₄	—	5	1	no	—
58	C₂×C₄⋊Dic₅	—	5	1	no	—
59	C₂×#683	—	5	2	no	—
60	D₅×C₄⋊C₄	—	5	8	no	—
61	C₂²×C₅²	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₅⋊D₅	C₄⋊C₄	1	4	yes	complemented
63	C₂×C₅⋊D₅	C₂²×C₄	1	2	yes	—
64	C₂×C₅×D₅	C₄⋊C₄	1	4	yes	complemented
65	C₂×C₅×D₅	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₅×D₅	C₂²×C₄	1	2	yes	—
67	C₂×C₅×D₅	C₂×D₄	1	2	yes	—
68	C₂×C₅×D₅	C₂×Q₈	1	2	yes	—
69	C₂×C₅×D₅	C₂⁴	1	1	yes	characteristic
70	D₅²	C₄⋊C₄	1	8	yes	complemented
71	D₅²	C₂×D₄	1	4	yes	—
72	D₅²	C₂×Q₈	1	4	yes	—
73	#1042	—	2	4	no	—
74	C₅×AGL(1,𝔽₅)	—	2	4	no	—
75	C₄×C₅²	C₂²×C₄	1	2	yes	complemented
76	#1039	C₂²×C₄	1	2	yes	complemented
77	C₅×Dic₅	C₂²×C₄	1	2	yes	complemented
78	C₅×Dic₅	C₂²×C₄	1	2	yes	complemented
79	C₂³×D₅	—	5	1	no	—
80	C₂³×D₅	—	5	1	no	—
81	C₂²×AGL(1,𝔽₅)	—	5	2	no	—
82	C₂²×AGL(1,𝔽₅)	—	5	8	no	—
83	C₂²×AGL(1,𝔽₅)	—	10	8	no	—
84	C₂²×AGL(1,𝔽₅)	C₂×D₅	1	2	yes	—
85	C₂²×C₄×C₅	—	5	1	no	—
86	C₂²×C₄×C₅	—	5	1	no	—
87	C₂²×C₄×C₅	—	5	2	no	—
88	C₂²×Dic₅	—	5	1	no	—
89	C₂²×Dic₅	—	5	1	no	—
90	C₂²×Dic₅	—	5	2	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	1	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	—	5	4	no	—
101	C₂×C₄×D₅	—	5	8	no	—
102	C₂×C₄×D₅	—	10	8	no	—
103	C₂×C₄×D₅	—	20	1	no	—
104	C₂×C₄×D₅	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
105	C₂×C₄×D₅	C₂×D₅	1	1	yes	characteristic
106	C₄⋊AGL(1,𝔽₅)	—	5	8	no	—
107	C₄⋊AGL(1,𝔽₅)	—	5	4	no	—
108	C₄⋊AGL(1,𝔽₅)	C₂×D₅	1	4	yes	direct product factor
109	C₅×C₄⋊C₄	—	5	4	no	—
110	C₄⋊Dic₅	—	5	4	no	—
111	#683	—	5	8	no	—
112	C₂²×C₄⋊C₄	—	25	1	no	Sylow
113	C₂×C₅²	C₂×C₄⋊C₄	1	2	yes	complemented
114	C₂×C₅²	C₂³×C₄	1	1	yes	characteristic
115	C₅⋊D₅	C₂×C₄⋊C₄	1	4	yes	complemented
116	C₅×D₅	C₂×C₄⋊C₄	1	4	yes	complemented
117	C₅×D₅	C₂×C₄⋊C₄	1	2	yes	complemented
118	C₅×D₅	C₂²×D₄	1	1	yes	characteristic
119	C₅×D₅	C₂²×Q₈	1	1	yes	characteristic
120	C₂³×C₅	—	5	1	no	—
121	C₂³×C₅	—	5	1	no	—
122	C₂²×D₅	—	5	1	no	—
123	C₂²×D₅	—	5	1	no	—
124	C₂²×D₅	—	5	4	no	—
125	C₂²×D₅	—	5	4	no	—
126	C₂²×D₅	—	5	2	no	—
127	C₂²×D₅	—	5	4	no	—
128	C₂²×D₅	—	5	4	no	—
129	C₂²×D₅	—	5	2	no	—
130	C₂²×D₅	—	5	2	no	—
131	C₂²×D₅	—	5	2	no	—
132	C₂²×D₅	—	20	1	no	—
133	C₂²×D₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
134	C₂²×D₅	C₂²×D₅	1	1	yes	characteristic
135	C₂×AGL(1,𝔽₅)	—	2	4	no	—
136	C₂×AGL(1,𝔽₅)	—	5	4	no	—
137	C₂×AGL(1,𝔽₅)	—	10	16	no	—
138	C₂×AGL(1,𝔽₅)	—	10	4	no	—
139	C₂×AGL(1,𝔽₅)	C₂²×D₅	1	4	yes	—
140	C₂×C₄×C₅	—	4	1	no	—
141	C₂×C₄×C₅	—	5	1	no	—
142	C₂×C₄×C₅	—	5	1	no	—
143	C₂×C₄×C₅	—	5	4	no	—
144	C₂×C₄×C₅	—	5	2	no	—
145	C₂×C₄×C₅	—	5	2	no	—
146	C₂×C₄×C₅	—	5	4	no	—
147	C₂×C₄×C₅	—	10	4	no	—
148	C₂×C₄×C₅	C₄×D₅	1	1	yes	characteristic, complemented
149	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
150	C₂×Dic₅	—	5	1	no	—
151	C₂×Dic₅	—	5	1	no	—
152	C₂×Dic₅	—	5	4	no	—
153	C₂×Dic₅	—	5	2	no	—
154	C₂×Dic₅	—	5	2	no	—
155	C₂×Dic₅	—	5	4	no	—
156	C₂×Dic₅	—	10	4	no	—
157	C₂×Dic₅	—	20	1	no	—
158	C₂×Dic₅	C₄×D₅	1	1	yes	characteristic, complemented
159	C₂×Dic₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
160	C₄×D₅	—	5	2	no	—
161	C₄×D₅	—	5	4	no	—
162	C₄×D₅	—	5	2	no	—
163	C₄×D₅	—	5	4	no	—
164	C₄×D₅	—	5	4	no	—
165	C₄×D₅	—	5	4	no	—
166	C₄×D₅	—	5	4	no	—
167	C₄×D₅	—	10	16	no	—
168	C₄×D₅	—	20	4	no	—
169	C₄×D₅	C₄×D₅	1	2	yes	complemented
170	C₄×D₅	C₂×AGL(1,𝔽₅)	1	4	yes	complemented
171	C₄×D₅	C₂²×D₅	1	2	yes	—
172	C₂³×C₄	—	25	1	no	—
173	C₂³×C₄	—	25	2	no	—
174	C₂×C₄⋊C₄	—	5	1	no	—
175	C₂×C₄⋊C₄	—	25	8	no	—
176	C₂×C₄⋊C₄	—	25	2	no	—
177	C₂×C₄⋊C₄	—	25	1	no	—
178	C₅²	C₂²×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
179	C₂²×C₅	—	4	1	no	—
180	C₂²×C₅	—	5	2	no	—
181	C₂²×C₅	—	5	2	no	—
182	C₂²×C₅	—	5	2	no	—
183	C₂²×C₅	—	5	1	no	—
184	C₂²×C₅	—	5	1	no	—
185	C₂²×C₅	—	5	4	no	—
186	C₂²×C₅	C₂×C₄×D₅	1	1	yes	characteristic
187	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
188	C₂×D₅	—	5	4	no	—
189	C₂×D₅	—	5	2	no	—
190	C₂×D₅	—	5	2	no	—
191	C₂×D₅	—	5	4	no	—
192	C₂×D₅	—	5	8	no	—
193	C₂×D₅	—	5	4	no	—
194	C₂×D₅	—	5	4	no	—
195	C₂×D₅	—	5	4	no	—
196	C₂×D₅	—	5	4	no	—
197	C₂×D₅	—	5	8	no	—
198	C₂×D₅	—	20	4	no	—
199	C₂×D₅	—	20	2	no	—
200	C₂×D₅	C₄⋊AGL(1,𝔽₅)	1	4	yes	direct product factor
201	C₂×D₅	C₂×C₄×D₅	1	1	yes	characteristic
202	C₂×D₅	D₄×D₅	1	2	yes	—
203	C₂×D₅	Q₈×D₅	1	2	yes	—
204	C₂×D₅	C₂²×AGL(1,𝔽₅)	1	2	yes	—
205	C₂×D₅	C₂³×D₅	1	1	yes	characteristic
206	AGL(1,𝔽₅)	—	2	4	no	—
207	AGL(1,𝔽₅)	—	10	4	no	—
208	C₄×C₅	—	4	2	no	—
209	C₄×C₅	—	5	2	no	—
210	C₄×C₅	—	5	2	no	—
211	C₄×C₅	—	10	4	no	—
212	C₄×C₅	C₂×C₄×D₅	1	2	yes	complemented
213	C₄×C₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
214	Dic₅	—	5	2	no	—
215	Dic₅	—	5	2	no	—
216	Dic₅	—	10	4	no	—
217	Dic₅	—	20	2	no	—
218	Dic₅	C₂×C₄×D₅	1	2	yes	complemented
219	Dic₅	C₂²×AGL(1,𝔽₅)	1	2	yes	complemented
220	C₂⁴	—	25	1	no	—
221	C₂²×C₄	—	5	1	no	—
222	C₂²×C₄	—	5	1	no	—
223	C₂²×C₄	—	5	2	no	—
224	C₂²×C₄	—	25	4	no	—
225	C₂²×C₄	—	25	1	no	—
226	C₂²×C₄	—	25	4	no	—
227	C₂²×C₄	—	25	1	no	—
228	C₂²×C₄	—	25	1	no	—
229	C₂²×C₄	—	25	8	no	—
230	C₂²×C₄	—	25	1	no	—
231	C₂²×C₄	—	25	2	no	—
232	C₂²×C₄	—	50	8	no	—
233	C₄⋊C₄	—	5	4	no	—
234	C₄⋊C₄	—	25	8	no	—
235	C₄⋊C₄	—	25	4	no	—
236	C₂×C₅	—	4	1	no	—
237	C₂×C₅	—	4	2	no	—
238	C₂×C₅	—	5	4	no	—
239	C₂×C₅	—	5	1	no	—
240	C₂×C₅	—	5	2	no	—
241	C₂×C₅	—	5	1	no	—
242	C₂×C₅	D₅×C₄⋊C₄	1	2	yes	complemented
243	C₂×C₅	C₂×C₄⋊AGL(1,𝔽₅)	1	2	yes	complemented
244	C₂×C₅	C₂²×C₄×D₅	1	1	yes	characteristic
245	C₂×C₅	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
246	D₅	—	5	4	no	—
247	D₅	—	5	4	no	—
248	D₅	—	20	4	no	—
249	D₅	D₅×C₄⋊C₄	1	2	yes	complemented
250	D₅	C₂×C₄⋊AGL(1,𝔽₅)	1	4	yes	direct product factor
251	D₅	C₂×D₄×D₅	1	1	yes	characteristic
252	D₅	C₂×Q₈×D₅	1	1	yes	characteristic
253	C₂³	—	5	1	no	—
254	C₂³	—	5	1	no	—
255	C₂³	—	25	2	no	—
256	C₂³	—	25	2	no	—
257	C₂³	—	25	4	no	—
258	C₂³	—	25	4	no	—
259	C₂³	—	25	1	no	—
260	C₂×C₄	—	5	1	no	—
261	C₂×C₄	—	5	1	no	—
262	C₂×C₄	—	5	2	no	—
263	C₂×C₄	—	5	2	no	—
264	C₂×C₄	—	5	4	no	—
265	C₂×C₄	—	5	4	no	—
266	C₂×C₄	—	10	4	no	—
267	C₂×C₄	—	25	4	no	—
268	C₂×C₄	—	25	2	no	—
269	C₂×C₄	—	25	4	no	—
270	C₂×C₄	—	25	2	no	—
271	C₂×C₄	—	25	1	no	—
272	C₂×C₄	—	25	4	no	—
273	C₂×C₄	—	25	4	no	—
274	C₂×C₄	—	50	16	no	—
275	C₂×C₄	—	50	4	no	—
276	C₂×C₄	D₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
277	C₅	—	4	1	no	—
278	C₅	C₂×D₅×C₄⋊C₄	1	1	yes	characteristic, complemented
279	C₅	C₂²×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
280	C₂²	—	5	1	no	—
281	C₂²	—	5	1	no	—
282	C₂²	—	5	2	no	—
283	C₂²	—	5	2	no	—
284	C₂²	—	5	4	no	—
285	C₂²	—	5	2	no	—
286	C₂²	—	25	4	no	—
287	C₂²	—	25	4	no	—
288	C₂²	—	25	8	no	—
289	C₂²	—	25	2	no	—
290	C₂²	—	25	4	no	—
291	C₂²	C₂×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic
292	C₄	—	5	2	no	—
293	C₄	—	5	2	no	—
294	C₄	—	10	4	no	—
295	C₄	—	25	2	no	—
296	C₄	—	50	4	no	—
297	C₄	C₂×D₅×AGL(1,𝔽₅)	1	2	yes	complemented
298	C₂	—	5	1	no	—
299	C₂	—	5	4	no	—
300	C₂	—	5	1	no	—
301	C₂	—	5	2	no	—
302	C₂	—	25	4	no	—
303	C₂	D₅×C₄⋊AGL(1,𝔽₅)	1	2	yes	direct product factor
304	C₂	C₂²×D₅×AGL(1,𝔽₅)	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₅×AGL(1,𝔽₅)
commutator	C₂×C₅²	C₂³×C₄
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
hypercenter	C₂×C₄	D₅×AGL(1,𝔽₅)
hypocenter	C₅²	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ 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×C₅×C₄⋊AGL(1,𝔽₅)	C₂	semidirect
5. C₂×#87825	C₂	semidirect
6. D₅×C₄⋊AGL(1,𝔽₅)	C₂	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. C₅×C₄⋊AGL(1,𝔽₅)	C₂²	semidirect
22. #87825	C₂²	semidirect
37. C₂×C₄×C₅²	C₂×C₄	semidirect
38. C₂×#1039	C₂×C₄	semidirect
39. C₄×C₅⋊D₅	C₂×C₄	semidirect
40. C₂×C₅×Dic₅	C₂×C₄	semidirect
41. C₂×C₅×Dic₅	C₂×C₄	semidirect
42. C₄×C₅×D₅	C₂×C₄	semidirect
43. C₄×C₅×D₅	C₂×C₄	semidirect
45. #6036	C₂×C₄	semidirect
46. D₅×Dic₅	C₂×C₄	semidirect
47. D₅×Dic₅	C₂×C₄	semidirect
56. C₂×C₄⋊AGL(1,𝔽₅)	D₅	direct (N × H)
62. C₂×C₅⋊D₅	C₄⋊C₄	semidirect
64. C₂×C₅×D₅	C₄⋊C₄	semidirect
70. D₅²	C₄⋊C₄	semidirect
75. C₄×C₅²	C₂²×C₄	semidirect
76. #1039	C₂²×C₄	semidirect
77. C₅×Dic₅	C₂²×C₄	semidirect
78. C₅×Dic₅	C₂²×C₄	semidirect
104. C₂×C₄×D₅	AGL(1,𝔽₅)	semidirect
108. C₄⋊AGL(1,𝔽₅)	C₂×D₅	direct (N × H)
113. C₂×C₅²	C₂×C₄⋊C₄	semidirect
115. C₅⋊D₅	C₂×C₄⋊C₄	semidirect
116. C₅×D₅	C₂×C₄⋊C₄	semidirect
117. C₅×D₅	C₂×C₄⋊C₄	semidirect
148. C₂×C₄×C₅	C₄×D₅	semidirect
149. C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	semidirect
158. C₂×Dic₅	C₄×D₅	semidirect
159. C₂×Dic₅	C₂×AGL(1,𝔽₅)	semidirect
169. C₄×D₅	C₄×D₅	semidirect
170. C₄×D₅	C₂×AGL(1,𝔽₅)	semidirect
178. C₅²	C₂²×C₄⋊C₄	semidirect
200. C₂×D₅	C₄⋊AGL(1,𝔽₅)	direct (N × H)
212. C₄×C₅	C₂×C₄×D₅	semidirect
213. C₄×C₅	C₂²×AGL(1,𝔽₅)	semidirect
218. Dic₅	C₂×C₄×D₅	semidirect
219. Dic₅	C₂²×AGL(1,𝔽₅)	semidirect
242. C₂×C₅	D₅×C₄⋊C₄	semidirect
243. C₂×C₅	C₂×C₄⋊AGL(1,𝔽₅)	semidirect
249. D₅	D₅×C₄⋊C₄	semidirect
250. D₅	C₂×C₄⋊AGL(1,𝔽₅)	direct (N × H)
276. C₂×C₄	D₅×AGL(1,𝔽₅)	semidirect
278. C₅	C₂×D₅×C₄⋊C₄	semidirect
279. C₅	C₂²×C₄⋊AGL(1,𝔽₅)	semidirect
297. C₄	C₂×D₅×AGL(1,𝔽₅)	semidirect
303. C₂	D₅×C₄⋊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×C₅×C₄⋊AGL(1,𝔽₅)	2
C₂×#87825	2
D₅×C₄⋊AGL(1,𝔽₅)	2
C₂²×C₄⋊AGL(1,𝔽₅)	5
C₂×D₅×C₄⋊C₄	5

Subgroups — C2×D5×C4⋊AGL(1,𝔽5) #13107613

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₄⋊AGL(1,𝔽₅) #13107613