Finite Group Databasebeta

← C₃×C₁₉×C₁₅₁⋊C₃ #38788872

Subgroups — C₃×C₁₉×C₁₅₁⋊C₃ #38788872

Order 25821.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₉×C₁₅₁	C₃	1	1	yes	maximal, characteristic, complemented
2	C₁₉×C₁₅₁⋊C₃	C₃	1	3	yes	maximal, direct product factor
3	C₁₉×C₁₅₁	C₃²	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₅₁⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₁₅₁	C₃×C₁₉	1	1	yes	characteristic, complemented
6	C₁₅₁⋊C₃	C₃×C₁₉	1	3	yes	direct product factor
7	C₃²×C₁₉	—	151	1	no	maximal, Hall
8	C₁₅₁	C₃²×C₁₉	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₁₉	—	151	3	no	—
10	C₃×C₁₉	C₁₅₁⋊C₃	1	1	yes	characteristic, direct product factor
11	C₁₉	C₃×C₁₅₁⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₃²	—	151	1	no	Sylow
13	C₃	—	151	3	no	—
14	C₃	C₁₉×C₁₅₁⋊C₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₃×C₁₉	C₁₅₁⋊C₃
commutator, cosocle, hypocenter	C₁₅₁	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₁₉×C₁₅₁	C₃
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₃×C₁₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₁₉×C₁₅₁	C₃	semidirect
2. C₁₉×C₁₅₁⋊C₃	C₃	direct (N × H)
3. C₁₉×C₁₅₁	C₃²	semidirect
4. C₃×C₁₅₁⋊C₃	C₁₉	direct (N × H)
5. C₃×C₁₅₁	C₃×C₁₉	semidirect
6. C₁₅₁⋊C₃	C₃×C₁₉	direct (N × H)
8. C₁₅₁	C₃²×C₁₉	semidirect
10. C₃×C₁₉	C₁₅₁⋊C₃	direct (N × H)
11. C₁₉	C₃×C₁₅₁⋊C₃	direct (N × H)
14. C₃	C₁₉×C₁₅₁⋊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
C₃×C₁₉×C₁₅₁	3
C₁₉×C₁₅₁⋊C₃	3
C₃×C₁₅₁⋊C₃	19
C₃²×C₁₉	151