Subgroups — H(3,𝔽₁₃)⋊C₁₃ #43270033

Order 28561.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃³	C₁₃	1	1	yes	maximal, characteristic, complemented
2	H(3,𝔽₁₃)	C₁₃	1	13	yes	maximal, complemented
3	C₁₃²	—	13	13	no	—
4	C₁₃²	—	13	1	no	—
5	C₁₃²	—	13	13	no	—
6	C₁₃²	C₁₃²	1	1	yes	characteristic
7	C₁₃	—	13	13	no	—
8	C₁₃	—	13	1	no	—
9	C₁₃	—	169	13	no	—
10	C₁₃	H(3,𝔽₁₃)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₁₃	H(3,𝔽₁₃)
commutator, Frattini, cosocle	C₁₃²	C₁₃²
LCS	G ▷ C₁₃² ▷ C₁₃ ▷ C₁
UCS	C₁ ◁ C₁₃ ◁ C₁₃² ◁ G
LECS	G ▷ C₁₃² ▷ C₁₃ ▷ C₁

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

N	H ≅ G/N	type
1. C₁₃³	C₁₃	semidirect
2. H(3,𝔽₁₃)	C₁₃	semidirect

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

subgroup	index
C₁₃³	13
H(3,𝔽₁₃)	13