Subgroups — C₂²⋊AGL(1,𝔽₅) #705

Order 80.

34 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	2	yes	maximal, complemented
3	C₂²×C₅	C₄	1	1	yes	characteristic, complemented
4	C₂×D₅	—	2	2	no	—
5	C₂×D₅	C₄	1	1	yes	characteristic, complemented
6	C₂×D₅	C₂²	1	1	yes	characteristic
7	AGL(1,𝔽₅)	—	2	2	no	—
8	C₂²⋊C₄	—	5	1	no	maximal, Sylow
9	C₂×C₅	—	2	1	no	—
10	C₂×C₅	C₂×C₄	1	1	yes	characteristic
11	D₅	—	2	1	no	—
12	D₅	D₄	1	2	yes	—
13	C₂³	—	5	1	no	—
14	C₂×C₄	—	5	2	no	—
15	C₅	C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
16	C₂²	—	5	1	no	—
17	C₂²	—	5	1	no	—
18	C₂²	—	10	2	no	—
19	C₂²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
20	C₄	—	10	2	no	—
21	C₂	—	2	1	no	—
22	C₂	—	5	2	no	—
23	C₂	—	10	1	no	—
24	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.