Subgroups — D₅⋊AGL(1,𝔽₅) #6055

Order 200.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅²	C₂	1	1	yes	maximal, characteristic
2	#1044	C₂	1	1	yes	maximal, characteristic, complemented
3	#1043	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅⋊D₅	C₂²	1	1	yes	characteristic
5	C₅×D₅	C₄	1	2	yes	complemented
6	C₂×AGL(1,𝔽₅)	—	5	2	no	maximal
7	C₅²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₅	—	5	2	no	—
9	AGL(1,𝔽₅)	—	5	2	no	—
10	AGL(1,𝔽₅)	—	5	2	no	—
11	AGL(1,𝔽₅)	—	10	2	no	—
12	C₂×C₅	—	5	2	no	—
13	D₅	—	5	2	no	—
14	D₅	—	10	2	no	—
15	D₅	AGL(1,𝔽₅)	1	2	yes	complemented
16	C₂×C₄	—	25	1	no	Sylow
17	C₅	—	2	2	no	—
18	C₅	C₂×AGL(1,𝔽₅)	1	2	yes	complemented
19	C₂²	—	25	1	no	—
20	C₄	—	25	1	no	—
21	C₄	—	25	1	no	—
22	C₂	—	5	2	no	—
23	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²	C₂×C₄
prime radical	D₅²	C₂
cosocle	C₅⋊D₅	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.