Subgroups — (C₄₂₁⋊C₃)⋊C₂₅ #44539028

Order 31575.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₂₁⋊C₂₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₄₂₁⋊C₃	C₅	1	1	yes	maximal, characteristic
3	C₅×C₄₂₁	C₃×C₅	1	1	yes	characteristic
4	C₄₂₁⋊C₃	C₂₅	1	1	yes	characteristic, complemented, Hall
5	C₄₂₁	C₃×C₂₅	1	1	yes	characteristic, complemented, Sylow
6	C₃×C₂₅	—	421	1	no	maximal, Hall
7	C₂₅	—	421	1	no	Sylow
8	C₃×C₅	—	421	1	no	—
9	C₅	(C₄₂₁⋊C₃)⋊C₅	1	1	yes	characteristic
10	C₃	—	421	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₅	(C₄₂₁⋊C₃)⋊C₅
commutator, hypocenter	C₄₂₁	C₃×C₂₅
Fitting, socle, cosocle	C₅×C₄₂₁	C₃×C₅
prime radical	C₅×C₄₂₁⋊C₃	C₅
LCS	G ▷ C₄₂₁
UCS	C₁ ◁ C₅

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.