Finite Group Databasebeta

← C₁₉×C₂₉×C₁₉⋊C₃ #44536094

Subgroups — C₁₉×C₂₉×C₁₉⋊C₃ #44536094

Order 31407.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉²×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃×C₁₉×C₂₉	—	19	1	no	maximal
3	C₂₉×C₁₉⋊C₃	C₁₉	1	1	yes	maximal, characteristic, direct product factor
4	C₁₉×C₁₉⋊C₃	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₁₉×C₂₉	—	3	6	no	—
6	C₁₉×C₂₉	C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
7	C₁₉×C₂₉	C₃×C₁₉	1	1	yes	characteristic, complemented
8	C₁₉²	C₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
9	C₃×C₂₉	—	19	1	no	Hall
10	C₃×C₁₉	—	19	1	no	—
11	C₁₉⋊C₃	C₁₉×C₂₉	1	1	yes	characteristic, direct product factor
12	C₂₉	C₁₉×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₉	—	3	6	no	—
14	C₁₉	C₂₉×C₁₉⋊C₃	1	1	yes	characteristic, direct product factor
15	C₁₉	C₃×C₁₉×C₂₉	1	1	yes	characteristic, complemented
16	C₃	—	19	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₉×C₂₉	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₃×C₁₉×C₂₉
Frattini	C₁	G
Fitting, socle	C₁₉²×C₂₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₁₉×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₉²×C₂₉	C₃	semidirect
3. C₂₉×C₁₉⋊C₃	C₁₉	direct (N × H)
4. C₁₉×C₁₉⋊C₃	C₂₉	direct (N × H)
6. C₁₉×C₂₉	C₁₉⋊C₃	direct (N × H)
7. C₁₉×C₂₉	C₃×C₁₉	semidirect
8. C₁₉²	C₃×C₂₉	semidirect
11. C₁₉⋊C₃	C₁₉×C₂₉	direct (N × H)
12. C₂₉	C₁₉×C₁₉⋊C₃	direct (N × H)
14. C₁₉	C₂₉×C₁₉⋊C₃	direct (N × H)
15. C₁₉	C₃×C₁₉×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉²×C₂₉	3
C₃×C₁₉×C₂₉	19
C₂₉×C₁₉⋊C₃	19
C₁₉×C₁₉⋊C₃	29