Subgroups — #88034

Order 416.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₈×C₁₃	C₄	1	1	yes	characteristic
3	C₄×C₁₃	C₈	1	1	yes	characteristic
4	C₃₂	—	13	1	no	maximal, Sylow
5	C₂×C₁₃	C₁₆	1	1	yes	characteristic
6	C₁₆	D₁₃	1	1	yes	characteristic
7	C₁₃	C₃₂	1	1	yes	characteristic, complemented, Sylow
8	C₈	Dic₁₃	1	1	yes	characteristic
9	C₄	#1055	1	1	yes	characteristic
10	C₂	#6090	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₁₆	D₁₃
commutator, hypocenter	C₁₃	C₃₂
Fitting, cosocle	C₁₃×C₁₆	C₂
socle, prime radical	C₂×C₁₃	C₁₆
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₁₆

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

N	H ≅ G/N	type
7. C₁₃	C₃₂	semidirect

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

subgroup	index
C₁₃×C₁₆	2
C₃₂	13