Subgroups — AGL(1,𝔽₅)×C₁₅₄₉ #44526431

Order 30980.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₅×C₁₅₄₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₅₄₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₄×C₁₅₄₉	—	5	1	no	maximal, Hall
4	C₂×C₁₅₄₉	—	5	1	no	—
5	C₁₅₄₉	AGL(1,𝔽₅)	1	1	yes	characteristic, direct product factor, Sylow
6	AGL(1,𝔽₅)	C₁₅₄₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	D₅	C₂×C₁₅₄₉	1	1	yes	characteristic
8	C₅	C₄×C₁₅₄₉	1	1	yes	characteristic, complemented, Sylow
9	C₄	—	5	1	no	Sylow
10	C₂	—	5	1	no	—

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.