Subgroups — 31₋¹⁺² #44446943

Order 29791.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁²	C₃₁	1	1	yes	maximal, characteristic
2	C₉₆₁	C₃₁	1	31	yes	maximal, complemented
3	C₃₁	—	31	1	no	—
4	C₃₁	C₃₁²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃₁	C₃₁²
prime radical	C₃₁²	C₃₁
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
2. C₉₆₁	C₃₁	semidirect

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

subgroup	index
C₃₁²	31
C₉₆₁	31