Subgroups — 29₋¹⁺² #37567240

Order 24389.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉²	C₂₉	1	1	yes	maximal, characteristic
2	C₈₄₁	C₂₉	1	29	yes	maximal, complemented
3	C₂₉	—	29	1	no	—
4	C₂₉	C₂₉²	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂₉	C₂₉²
prime radical	C₂₉²	C₂₉
LCS	G ▷ C₂₉ ▷ C₁
UCS	C₁ ◁ C₂₉ ◁ G
LECS	G ▷ C₂₉ ▷ C₁

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

N	H ≅ G/N	type
2. C₈₄₁	C₂₉	semidirect

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

subgroup	index
C₂₉²	29
C₈₄₁	29