Subgroups — AGL(1,𝔽₅)×#401 #13028093

Order 1280.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×#401	C₂	1	1	yes	maximal, characteristic
2	#10603803	C₂	1	7	yes	maximal
3	AGL(1,𝔽₅)×#95	C₂	1	7	yes	maximal
4	C₂²×C₄×AGL(1,𝔽₅)	C₂²	1	7	yes	—
5	C₂×(C₂×AGL(1,𝔽₅))⋊C₄	C₂²	1	21	yes	—
6	C₅×#401	C₄	1	1	yes	characteristic, complemented
7	D₅×#95	C₂²	1	7	yes	—
8	C₅⋊#401	C₄	1	7	yes	complemented
9	C₄×#401	—	5	1	no	maximal, Sylow
10	C₂³×AGL(1,𝔽₅)	C₂³	1	7	yes	—
11	C₂³×AGL(1,𝔽₅)	C₂³	1	1	yes	characteristic
12	C₂²×C₄×D₅	C₂³	1	7	yes	—
13	C₂×C₄×AGL(1,𝔽₅)	—	2	42	no	—
14	(C₂×AGL(1,𝔽₅))⋊C₄	—	2	42	no	—
15	C₅×#95	C₂×C₄	1	7	yes	—
16	#3963	C₂×C₄	1	21	yes	—
17	C₂×#401	—	5	1	no	—
18	#1443	—	5	7	no	—
19	C₄×#95	—	5	7	no	—
20	C₂³×D₅	C₂⁴	1	1	yes	characteristic
21	C₂²×AGL(1,𝔽₅)	—	2	21	no	—
22	C₂²×AGL(1,𝔽₅)	—	2	21	no	—
23	C₂²×AGL(1,𝔽₅)	#41	1	14	yes	—
24	C₂²×AGL(1,𝔽₅)	#41	1	14	yes	—
25	C₂²×C₄×C₅	C₂²×C₄	1	7	yes	—
26	C₂²×Dic₅	C₂²×C₄	1	7	yes	—
27	C₂×C₄×D₅	—	2	21	no	—
28	C₂×C₄×D₅	—	2	21	no	—
29	C₄×AGL(1,𝔽₅)	—	4	28	no	—
30	C₂²×C₄²	—	5	7	no	—
31	#401	—	5	7	no	—
32	#401	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
33	C₂×#95	—	5	7	no	—
34	C₂×#95	—	5	21	no	—
35	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
36	C₂²×D₅	C₂×#41	1	7	yes	—
37	C₂²×D₅	C₂×#41	1	7	yes	—
38	C₂×AGL(1,𝔽₅)	—	2	42	no	—
39	C₂×AGL(1,𝔽₅)	—	4	7	no	—
40	C₂×AGL(1,𝔽₅)	—	4	21	no	—
41	C₂×AGL(1,𝔽₅)	#126	1	28	yes	—
42	C₂×C₄×C₅	—	2	21	no	—
43	C₂×Dic₅	—	2	21	no	—
44	C₄×D₅	—	4	7	no	—
45	C₄×D₅	—	4	21	no	—
46	C₂³×C₄	—	5	1	no	—
47	C₂³×C₄	—	5	7	no	—
48	C₂³×C₄	—	5	7	no	—
49	C₂×C₄²	—	10	42	no	—
50	#95	—	5	21	no	—
51	#95	—	10	42	no	—
52	#95	C₂×AGL(1,𝔽₅)	1	7	yes	—
53	C₂²×C₅	C₄×#41	1	7	yes	—
54	C₂×D₅	C₂×#126	1	7	yes	—
55	C₂×D₅	#529	1	21	yes	—
56	AGL(1,𝔽₅)	—	4	14	no	—
57	AGL(1,𝔽₅)	#401	1	8	yes	direct product factor
58	C₄×C₅	—	4	7	no	—
59	Dic₅	—	4	7	no	—
60	C₂⁴	—	5	1	no	—
61	C₂²×C₄	—	5	14	no	—
62	C₂²×C₄	—	5	14	no	—
63	C₂²×C₄	—	5	7	no	—
64	C₂²×C₄	—	10	21	no	—
65	C₂²×C₄	—	10	21	no	—
66	C₂²×C₄	—	10	21	no	—
67	C₂²×C₄	—	10	21	no	—
68	C₂²×C₄	C₂²×AGL(1,𝔽₅)	1	7	yes	—
69	C₄²	—	20	28	no	—
70	C₂×C₅	C₄×#126	1	7	yes	—
71	D₅	C₂×#401	1	1	yes	characteristic
72	D₅	#2401	1	7	yes	—
73	C₂³	—	5	7	no	—
74	C₂³	—	5	7	no	—
75	C₂³	C₂³×AGL(1,𝔽₅)	1	1	yes	characteristic
76	C₂×C₄	—	2	21	no	—
77	C₂×C₄	—	5	28	no	—
78	C₂×C₄	—	10	42	no	—
79	C₂×C₄	—	10	21	no	—
80	C₂×C₄	—	20	7	no	—
81	C₂×C₄	—	20	21	no	—
82	C₂×C₄	—	20	7	no	—
83	C₂×C₄	—	20	21	no	—
84	C₅	C₄×#401	1	1	yes	characteristic, complemented, Sylow
85	C₂²	—	5	7	no	—
86	C₂²	—	5	21	no	—
87	C₂²	#41×AGL(1,𝔽₅)	1	7	yes	—
88	C₄	—	4	7	no	—
89	C₄	—	5	8	no	—
90	C₄	—	20	14	no	—
91	C₄	—	20	7	no	—
92	C₂	—	5	1	no	—
93	C₂	—	5	7	no	—
94	C₂	AGL(1,𝔽₅)×#126	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×AGL(1,𝔽₅)
commutator, socle	C₂³×C₅	C₂³×C₄
Fitting	C₅×#401	C₄
prime radical, cosocle	C₂³×D₅	C₂⁴
hypercenter	#401	AGL(1,𝔽₅)
hypocenter	C₅	C₄×#401
LCS	G ▷ C₂³×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ #401

Complements

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

N	H ≅ G/N	type
6. C₅×#401	C₄	semidirect
8. C₅⋊#401	C₄	semidirect
32. #401	AGL(1,𝔽₅)	direct (N × H)
57. AGL(1,𝔽₅)	#401	direct (N × H)
84. C₅	C₄×#401	semidirect

Maximal subgroups

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

subgroup	index
D₅×#401	2
#10603803	2
AGL(1,𝔽₅)×#95	2
C₄×#401	5

Subgroups — AGL(1,𝔽5)×#401 #13028093

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — AGL(1,𝔽₅)×#401 #13028093