Subgroups — C₄×AGL(1,𝔽₅) #701

Order 80.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×AGL(1,𝔽₅)	C₂	1	2	yes	maximal
2	C₄×D₅	C₂	1	1	yes	maximal, characteristic
3	C₂×D₅	C₂²	1	1	yes	characteristic
4	AGL(1,𝔽₅)	C₄	1	4	yes	direct product factor
5	C₄×C₅	C₄	1	1	yes	characteristic, complemented
6	Dic₅	C₄	1	1	yes	characteristic, complemented
7	C₄²	—	5	1	no	maximal, Sylow
8	C₂×C₅	C₂×C₄	1	1	yes	characteristic
9	D₅	C₂×C₄	1	2	yes	—
10	C₂×C₄	—	5	2	no	—
11	C₂×C₄	—	5	1	no	—
12	C₅	C₄²	1	1	yes	characteristic, complemented, Sylow
13	C₂²	—	5	1	no	—
14	C₄	—	5	4	no	—
15	C₄	—	5	1	no	—
16	C₄	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
17	C₂	—	5	2	no	—
18	C₂	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic

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.