Finite Group Databasebeta

← C₃²×C₅₄₁⋊C₅ #37566713

Subgroups — C₃²×C₅₄₁⋊C₅ #37566713

Order 24345.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅₄₁⋊C₅	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₅₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅₄₁⋊C₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₅₄₁	C₃×C₅	1	4	yes	complemented
5	C₅₄₁	C₃²×C₅	1	1	yes	characteristic, complemented, Sylow
6	C₃²×C₅	—	541	1	no	maximal, Hall
7	C₃×C₅	—	541	4	no	—
8	C₃²	C₅₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
9	C₅	—	541	1	no	Sylow
10	C₃	C₃×C₅₄₁⋊C₅	1	4	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₃²	C₅₄₁⋊C₅
commutator, cosocle, hypocenter	C₅₄₁	C₃²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅₄₁	C₅
LCS	G ▷ C₅₄₁
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅₄₁⋊C₅	C₃	direct (N × H)
2. C₃²×C₅₄₁	C₅	semidirect
3. C₅₄₁⋊C₅	C₃²	direct (N × H)
4. C₃×C₅₄₁	C₃×C₅	semidirect
5. C₅₄₁	C₃²×C₅	semidirect
8. C₃²	C₅₄₁⋊C₅	direct (N × H)
10. C₃	C₃×C₅₄₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅₄₁⋊C₅	3
C₃²×C₅₄₁	5
C₃²×C₅	541