Finite Group Databasebeta

← C₃×C₂₉×D₁₃₉ #37564038

Subgroups — C₃×C₂₉×D₁₃₉ #37564038

Order 24186.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₂₉×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₁₃₉	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂₉×C₁₃₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×D₁₃₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₃₉	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
6	D₁₃₉	C₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₃×C₂₉	—	139	1	no	maximal, Hall
8	C₁₃₉	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₂₉	D₁₃₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₂₉	—	139	1	no	Hall
11	C₂₉	C₃×D₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₃	—	139	1	no	Hall
13	C₃	C₂₉×D₁₃₉	1	1	yes	characteristic, direct product factor, Sylow
14	C₂	—	139	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₂₉	D₁₃₉
commutator, cosocle, hypocenter	C₁₃₉	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₂₉×C₁₃₉	C₂
LCS	G ▷ C₁₃₉
UCS	C₁ ◁ C₃×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₂₉×C₁₃₉	C₂	semidirect
2. C₂₉×D₁₃₉	C₃	direct (N × H)
3. C₂₉×C₁₃₉	C₂×C₃	semidirect
4. C₃×D₁₃₉	C₂₉	direct (N × H)
5. C₃×C₁₃₉	C₂×C₂₉	semidirect
6. D₁₃₉	C₃×C₂₉	direct (N × H)
8. C₁₃₉	C₂×C₃×C₂₉	semidirect
9. C₃×C₂₉	D₁₃₉	direct (N × H)
11. C₂₉	C₃×D₁₃₉	direct (N × H)
13. C₃	C₂₉×D₁₃₉	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×C₂₉×C₁₃₉	2
C₂₉×D₁₃₉	3
C₃×D₁₃₉	29
C₂×C₃×C₂₉	139