Subgroups — D₁₆₀₇₅ #44565366

Order 32150.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₆₄₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₂₁₅	—	5	1	no	maximal
3	C₅×C₆₄₃	D₅	1	1	yes	characteristic
4	D₆₄₃	—	25	1	no	Hall
5	C₆₄₃	D₂₅	1	1	yes	characteristic, complemented, Sylow
6	D₂₅	—	643	1	no	maximal, Hall
7	C₂₅	D₆₄₃	1	1	yes	characteristic, complemented, Sylow
8	D₅	—	3215	1	no	—
9	C₅	D₃₂₁₅	1	1	yes	characteristic
10	C₂	—	16075	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅×C₆₄₃	C₂
Frattini	C₅	D₃₂₁₅
socle	C₅×C₆₄₃	D₅
LCS	G ▷ C₂₅×C₆₄₃
UCS	C₁

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.