Subgroups — H(3,𝔽₃₁) #44446942

Order 29791.

67 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁²	C₃₁	1	32	yes	maximal, complemented
2	C₃₁	—	31	32	no	—
3	C₃₁	C₃₁²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃₁	C₃₁²
LCS	G ▷ C₃₁ ▷ C₁
UCS	C₁ ◁ C₃₁ ◁ G
LECS	G ▷ C₃₁ ▷ C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃₁²	C₃₁	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃₁²	31