Subgroups — C₂²×AGL(1,𝔽₅) #721

Order 80.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×AGL(1,𝔽₅)	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅	C₄	1	1	yes	characteristic, complemented
4	C₂×D₅	C₄	1	3	yes	complemented
5	C₂×D₅	C₂²	1	3	yes	—
6	AGL(1,𝔽₅)	C₂²	1	4	yes	direct product factor
7	C₂²×C₄	—	5	1	no	maximal, Sylow
8	C₂×C₅	C₂×C₄	1	3	yes	complemented
9	D₅	C₂×C₄	1	3	yes	complemented
10	D₅	C₂³	1	1	yes	characteristic
11	C₂³	—	5	1	no	—
12	C₂×C₄	—	5	6	no	—
13	C₅	C₂²×C₄	1	1	yes	characteristic, complemented, Sylow
14	C₂²	—	5	3	no	—
15	C₂²	—	5	3	no	—
16	C₂²	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor
17	C₄	—	5	4	no	—
18	C₂	—	5	1	no	—
19	C₂	—	5	3	no	—
20	C₂	C₂×AGL(1,𝔽₅)	1	3	yes	direct product factor

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.