Subgroups — C₅²×D₆₃₁ #44538793

Order 31550.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₆₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₆₃₁	C₅	1	6	yes	maximal, direct product factor
3	C₅×C₆₃₁	C₂×C₅	1	6	yes	complemented
4	D₆₃₁	C₅²	1	1	yes	characteristic, direct product factor, Hall
5	C₆₃₁	C₂×C₅²	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₅²	—	631	1	no	maximal, Hall
7	C₅²	D₆₃₁	1	1	yes	characteristic, direct product factor, Sylow
8	C₂×C₅	—	631	6	no	—
9	C₅	C₅×D₆₃₁	1	6	yes	direct product factor
10	C₂	—	631	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₆₃₁
commutator, cosocle, hypocenter	C₆₃₁	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₅²×C₆₃₁	C₂
LCS	G ▷ C₆₃₁
UCS	C₁ ◁ C₅²

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.