Finite Group Databasebeta

← C₃×C₁₃×D₄₀₉ #44542136

Subgroups — C₃×C₁₃×D₄₀₉ #44542136

Order 31902.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₄₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₄₀₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃×C₄₀₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₄₀₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₄₀₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
6	D₄₀₉	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
7	C₄₀₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₃×C₁₃	—	409	1	no	maximal, Hall
9	C₃×C₁₃	D₄₀₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₃	—	409	1	no	Hall
11	C₁₃	C₃×D₄₀₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	409	1	no	Hall
13	C₃	C₁₃×D₄₀₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	409	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₁₃	D₄₀₉
commutator, cosocle, hypocenter	C₄₀₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₄₀₉	C₂
LCS	G ▷ C₄₀₉
UCS	C₁ ◁ C₃×C₁₃

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₃×C₄₀₉	C₂	semidirect
2. C₁₃×D₄₀₉	C₃	direct (N × H)
3. C₁₃×C₄₀₉	C₂×C₃	semidirect
4. C₃×D₄₀₉	C₁₃	direct (N × H)
5. C₃×C₄₀₉	C₂×C₁₃	semidirect
6. D₄₀₉	C₃×C₁₃	direct (N × H)
7. C₄₀₉	C₂×C₃×C₁₃	semidirect
9. C₃×C₁₃	D₄₀₉	direct (N × H)
11. C₁₃	C₃×D₄₀₉	direct (N × H)
13. C₃	C₁₃×D₄₀₉	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×C₁₃×C₄₀₉	2
C₁₃×D₄₀₉	3
C₃×D₄₀₉	13
C₂×C₃×C₁₃	409