Finite Group Databasebeta

← C₅²×C₁₃₉⋊C₉ #44530801

Subgroups — C₅²×C₁₃₉⋊C₉ #44530801

Order 31275.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₁₃₉	C₃	1	1	yes	maximal, characteristic
2	C₅×C₁₃₉⋊C₉	C₅	1	6	yes	maximal, direct product factor
3	C₅²×C₁₃₉	C₉	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₁₃₉	C₃×C₅	1	6	yes	—
5	C₁₃₉⋊C₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
6	C₅×C₁₃₉	C₅×C₉	1	6	yes	complemented
7	C₃×C₁₃₉	C₃×C₅²	1	1	yes	characteristic
8	C₅²×C₉	—	139	1	no	maximal, Hall
9	C₁₃₉	C₅²×C₉	1	1	yes	characteristic, complemented, Sylow
10	C₃×C₅²	C₁₃₉⋊C₃	1	1	yes	characteristic
11	C₅×C₉	—	139	6	no	—
12	C₅²	C₁₃₉⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
13	C₃×C₅	C₅×C₁₃₉⋊C₃	1	6	yes	—
14	C₉	—	139	1	no	Sylow
15	C₅	C₅×C₁₃₉⋊C₉	1	6	yes	direct product factor
16	C₃	C₅²×C₁₃₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₅²	C₁₃₉⋊C₃
commutator, hypocenter	C₁₃₉	C₅²×C₉
Frattini	C₃	C₅²×C₁₃₉⋊C₃
Fitting, socle, prime radical	C₃×C₅²×C₁₃₉	C₃
cosocle	C₃×C₁₃₉	C₃×C₅²
LCS	G ▷ C₁₃₉
UCS	C₁ ◁ C₃×C₅²

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₃₉⋊C₉	C₅	direct (N × H)
3. C₅²×C₁₃₉	C₉	semidirect
5. C₁₃₉⋊C₉	C₅²	direct (N × H)
6. C₅×C₁₃₉	C₅×C₉	semidirect
9. C₁₃₉	C₅²×C₉	semidirect
12. C₅²	C₁₃₉⋊C₉	direct (N × H)
15. C₅	C₅×C₁₃₉⋊C₉	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×C₅²×C₁₃₉	3
C₅×C₁₃₉⋊C₉	5
C₅²×C₉	139