Finite Group Databasebeta

Subgroups — #46777461

Order 33620.

264 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(C₄₁⋊D₄₁)	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄₁²	C₄	1	1	yes	characteristic, complemented, Hall
3	#20269608	—	5	1	no	maximal, Hall
4	C₄₁⋊D₄₁	—	5	1	no	—
5	C₄₁²	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
6	#11717961	—	41	42	no	maximal
7	D₂₀₅	—	41	42	no	—
8	C₅×C₄₁	#4223	1	42	yes	complemented
9	#4223	—	205	42	no	—
10	D₄₁	—	205	42	no	—
11	C₄₁	#11717961	1	42	yes	complemented
12	AGL(1,𝔽₅)	—	1681	1	no	Hall
13	D₅	—	1681	1	no	—
14	C₅	#20269608	1	1	yes	characteristic, complemented, Sylow
15	C₄	—	8405	1	no	Sylow
16	C₂	—	8405	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₄₁²	C₄
prime radical, cosocle	C₅⋊(C₄₁⋊D₄₁)	C₂
LCS	G ▷ C₅×C₄₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₅×C₄₁²	C₄	semidirect
5. C₄₁²	AGL(1,𝔽₅)	semidirect
8. C₅×C₄₁	#4223	semidirect
11. C₄₁	#11717961	semidirect
14. C₅	#20269608	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊(C₄₁⋊D₄₁)	2
#20269608	5
#11717961	41