Finite Group Databasebeta

← C₃×C₅²⋊(C₁₃₉⋊C₃) #44530805

Subgroups — C₃×C₅²⋊(C₁₃₉⋊C₃) #44530805

Order 31275.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²⋊(C₁₃₉⋊C₃)	C₃	1	3	yes	maximal, direct product factor
2	C₃×C₅²×C₁₃₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₅²×C₁₃₉	C₃²	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅×C₁₃₉	—	3	2	no	—
5	C₃×C₁₃₉⋊C₃	—	25	1	no	maximal, Hall
6	C₅×C₁₃₉	—	3	2	no	—
7	C₃×C₁₃₉	C₅²⋊C₃	1	1	yes	characteristic, complemented
8	C₁₃₉⋊C₃	—	25	3	no	—
9	C₃×C₅²⋊C₃	—	139	1	no	maximal, Hall
10	C₁₃₉	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
11	C₃×C₅²	C₁₃₉⋊C₃	1	1	yes	characteristic, complemented
12	C₅²⋊C₃	—	139	3	no	—
13	C₅²	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×C₅	—	3	2	no	—
15	C₃²	—	3475	1	no	Sylow
16	C₅	—	3	2	no	—
17	C₃	—	3475	3	no	—
18	C₃	C₅²⋊(C₁₃₉⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃	C₅²⋊(C₁₃₉⋊C₃)
commutator, cosocle, hypocenter	C₅²×C₁₃₉	C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃₉	C₃
LCS	G ▷ C₅²×C₁₃₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₅²⋊(C₁₃₉⋊C₃)	C₃	direct (N × H)
2. C₃×C₅²×C₁₃₉	C₃	semidirect
3. C₅²×C₁₃₉	C₃²	semidirect
7. C₃×C₁₃₉	C₅²⋊C₃	semidirect
10. C₁₃₉	C₃×C₅²⋊C₃	semidirect
11. C₃×C₅²	C₁₃₉⋊C₃	semidirect
13. C₅²	C₃×C₁₃₉⋊C₃	semidirect
18. C₃	C₅²⋊(C₁₃₉⋊C₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²⋊(C₁₃₉⋊C₃)	3
C₃×C₅²×C₁₃₉	3
C₃×C₁₃₉⋊C₃	25
C₃×C₅²⋊C₃	139