Subgroups — #88036

Order 416.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6090	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	—	13	1	no	—
7	C₁₃	C₃₂	1	1	yes	characteristic, complemented, Sylow
8	C₈	#261	1	1	yes	characteristic
9	C₄	#1057	1	1	yes	characteristic
10	C₂	#6092	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₈	#261
commutator, hypocenter	C₁₃	C₃₂
Fitting	C₈×C₁₃	C₄
socle, prime radical	C₂×C₁₃	C₁₆
cosocle	#6090	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₈

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
#6090	2
C₃₂	13