Subgroups — C₅×C₇⋊C₉ #64649

Order 315.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇	C₃	1	1	yes	maximal, characteristic
2	C₇⋊C₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₉	—	7	1	no	maximal, Hall
4	C₅×C₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃×C₇	C₃×C₅	1	1	yes	characteristic
6	C₃×C₅	ΓL(1,𝔽₈)	1	1	yes	characteristic
7	C₉	—	7	1	no	Sylow
8	C₇	C₅×C₉	1	1	yes	characteristic, complemented, Sylow
9	C₅	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	C₅×ΓL(1,𝔽₈)	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.