Subgroups — D₂₇₅₇₅ #72290902

Order 55150.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₅×C₁₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₅₅₁₅	—	5	1	no	maximal
3	C₅×C₁₁₀₃	D₅	1	1	yes	characteristic
4	D₁₁₀₃	—	25	1	no	Hall
5	C₁₁₀₃	D₂₅	1	1	yes	characteristic, complemented, Sylow
6	D₂₅	—	1103	1	no	maximal, Hall
7	C₂₅	D₁₁₀₃	1	1	yes	characteristic, complemented, Sylow
8	D₅	—	5515	1	no	—
9	C₅	D₅₅₁₅	1	1	yes	characteristic
10	C₂	—	27575	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₂₅×C₁₁₀₃	C₂
Frattini	C₅	D₅₅₁₅
socle	C₅×C₁₁₀₃	D₅
LCS	G ▷ C₂₅×C₁₁₀₃
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.