Subgroups — AGL(1,𝔽₅)² #87911

Order 400.

63 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅⋊AGL(1,𝔽₅)	C₂	1	1	yes	maximal, characteristic
2	D₅×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
3	D₅²	C₂²	1	1	yes	characteristic
4	#1044	C₄	1	1	yes	characteristic, complemented
5	#1043	C₄	1	1	yes	characteristic, complemented
6	#1042	C₄	1	2	yes	complemented
7	C₅×AGL(1,𝔽₅)	C₄	1	2	yes	complemented
8	C₄×AGL(1,𝔽₅)	—	5	2	no	maximal
9	C₅⋊D₅	C₂×C₄	1	1	yes	characteristic
10	C₅×D₅	C₂×C₄	1	2	yes	—
11	C₂×AGL(1,𝔽₅)	—	5	2	no	—
12	C₂×AGL(1,𝔽₅)	—	5	2	no	—
13	C₄×D₅	—	5	2	no	—
14	C₅²	C₄²	1	1	yes	characteristic, complemented, Sylow
15	C₂×D₅	—	5	2	no	—
16	AGL(1,𝔽₅)	—	5	2	no	—
17	AGL(1,𝔽₅)	—	5	2	no	—
18	AGL(1,𝔽₅)	—	5	2	no	—
19	AGL(1,𝔽₅)	—	20	1	no	—
20	AGL(1,𝔽₅)	AGL(1,𝔽₅)	1	2	yes	direct product factor
21	C₄×C₅	—	5	2	no	—
22	Dic₅	—	5	2	no	—
23	C₄²	—	25	1	no	Sylow
24	C₂×C₅	—	5	2	no	—
25	D₅	—	5	2	no	—
26	D₅	—	20	1	no	—
27	D₅	C₂×AGL(1,𝔽₅)	1	2	yes	—
28	C₂×C₄	—	25	2	no	—
29	C₂×C₄	—	25	1	no	—
30	C₅	—	4	1	no	—
31	C₅	C₄×AGL(1,𝔽₅)	1	2	yes	complemented
32	C₂²	—	25	1	no	—
33	C₄	—	5	2	no	—
34	C₄	—	25	2	no	—
35	C₄	—	25	1	no	—
36	C₄	—	25	1	no	—
37	C₂	—	5	2	no	—
38	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²	C₄²
prime radical, cosocle	D₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁

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

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