Subgroups — C₂₅×D₃₄₇ #31774792

Order 17350.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₃₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₃₄₇	C₅	1	1	yes	maximal, characteristic
3	C₅×C₃₄₇	C₂×C₅	1	1	yes	characteristic
4	D₃₄₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
5	C₃₄₇	C₂×C₂₅	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₂₅	—	347	1	no	maximal, Hall
7	C₂₅	D₃₄₇	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₅	—	347	1	no	—
9	C₅	C₅×D₃₄₇	1	1	yes	characteristic
10	C₂	—	347	1	no	Sylow

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.