Finite Group Databasebeta

← C₂₉×#11762246 #44536096

Subgroups — C₂₉×#11762246 #44536096

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	C₂₉×C₁₉⋊C₃	—	19	2	no	maximal
3	#11762246	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₁₉×C₂₉	—	3	6	no	—
5	C₁₉×C₂₉	C₁₉⋊C₃	1	2	yes	complemented
6	C₁₉²	C₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
7	C₃×C₂₉	—	361	1	no	Hall
8	C₁₉⋊C₃	—	19	2	no	—
9	C₂₉	#11762246	1	1	yes	characteristic, direct product factor, Sylow
10	C₁₉	—	3	6	no	—
11	C₁₉	C₂₉×C₁₉⋊C₃	1	2	yes	complemented
12	C₃	—	361	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	#11762246
commutator, cosocle, hypocenter	C₁₉²	C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₁₉²×C₂₉	C₃
LCS	G ▷ C₁₉²
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₁₉²×C₂₉	C₃	semidirect
3. #11762246	C₂₉	direct (N × H)
5. C₁₉×C₂₉	C₁₉⋊C₃	semidirect
6. C₁₉²	C₃×C₂₉	semidirect
9. C₂₉	#11762246	direct (N × H)
11. C₁₉	C₂₉×C₁₉⋊C₃	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
C₂₉×C₁₉⋊C₃	19
#11762246	29