Finite Group Databasebeta

← C₁₃×D₁₉×C₅₉ #44415313

Subgroups — C₁₃×D₁₉×C₅₉ #44415313

Order 29146.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₉×C₅₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₁₃×C₅₉	—	19	1	no	maximal, Hall
4	C₁₉×C₅₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Hall
5	C₁₃×C₅₉	D₁₉	1	1	yes	characteristic, direct product factor, Hall
6	C₁₃×D₁₉	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₃×C₁₉	C₂×C₅₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅₉	—	19	1	no	Hall
9	C₅₉	C₁₃×D₁₉	1	1	yes	characteristic, direct product factor, Sylow
10	D₁₉	C₁₃×C₅₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₃	—	19	1	no	Hall
12	C₁₉	C₂×C₁₃×C₅₉	1	1	yes	characteristic, complemented, Sylow
13	C₁₃	D₁₉×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃×C₅₉	D₁₉
commutator, cosocle, hypocenter	C₁₉	C₂×C₁₃×C₅₉
Frattini	C₁	G
Fitting, socle	C₁₃×C₁₉×C₅₉	C₂
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₁₃×C₅₉

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₅₉	C₂	semidirect
2. D₁₉×C₅₉	C₁₃	direct (N × H)
4. C₁₉×C₅₉	C₂×C₁₃	semidirect
5. C₁₃×C₅₉	D₁₉	direct (N × H)
6. C₁₃×D₁₉	C₅₉	direct (N × H)
7. C₁₃×C₁₉	C₂×C₅₉	semidirect
9. C₅₉	C₁₃×D₁₉	direct (N × H)
10. D₁₉	C₁₃×C₅₉	direct (N × H)
12. C₁₉	C₂×C₁₃×C₅₉	semidirect
13. C₁₃	D₁₉×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₅₉	2
D₁₉×C₅₉	13
C₂×C₁₃×C₅₉	19
C₁₃×D₁₉	59