Subgroups — C₅×C₉ #194

Order 45.

6 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅	C₃	1	1	yes	maximal, characteristic
2	C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
3	C₅	C₉	1	1	yes	characteristic, direct product factor, Sylow
4	C₃	C₃×C₅	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₉	C₅	direct (N × H)
3. C₅	C₉	direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅	3
C₉	5