Subgroups — C₅⋊D₁₆₅₅ #30658482

Order 16550.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₆₅₅	—	5	6	no	maximal
3	C₅×C₃₃₁	D₅	1	6	yes	complemented
4	D₃₃₁	—	25	1	no	Hall
5	C₃₃₁	C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
6	C₅⋊D₅	—	331	1	no	maximal, Hall
7	C₅²	D₃₃₁	1	1	yes	characteristic, complemented, Sylow
8	D₅	—	1655	6	no	—
9	C₅	D₁₆₅₅	1	6	yes	complemented
10	C₂	—	8275	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₃₃₁	C₂
LCS	G ▷ C₅²×C₃₃₁
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.