Finite Group Databasebeta

Subgroups — #46777433

Order 33620.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30681146	C₂	1	1	yes	maximal, characteristic
2	#22554263	C₄	1	1	yes	characteristic, complemented, Hall
3	#20269609	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₁⋊D₄₁	C₂×C₅	1	1	yes	characteristic
5	C₄₁²	C₄×C₅	1	1	yes	characteristic, complemented, Sylow
6	#4223⋊C₅	—	41	2	no	maximal
7	D₄₁⋊C₅	—	41	2	no	—
8	C₄₁⋊C₅	—	41	2	no	—
9	#4223	—	41	2	no	—
10	D₄₁	—	41	2	no	—
11	D₄₁	—	410	4	no	—
12	C₄₁	—	10	4	no	—
13	C₄₁	#4223⋊C₅	1	2	yes	complemented
14	C₄×C₅	—	1681	1	no	Hall
15	C₂×C₅	—	1681	1	no	—
16	C₅	—	1681	1	no	Sylow
17	C₄	—	1681	1	no	Sylow
18	C₂	—	1681	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₄₁²	C₄×C₅
prime radical	#30681146	C₂
cosocle	C₄₁⋊D₄₁	C₂×C₅
LCS	G ▷ C₄₁²
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. #22554263	C₄	semidirect
3. #20269609	C₅	semidirect
5. C₄₁²	C₄×C₅	semidirect
13. C₄₁	#4223⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
#30681146	2
#20269609	5
#4223⋊C₅	41