Subgroups — C₂₉×D₅₂₉ #44501596

Order 30682.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₅₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂₉×D₂₃	—	23	1	no	maximal
3	D₅₂₉	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂₃×C₂₉	D₂₃	1	1	yes	characteristic
5	C₅₂₉	C₂×C₂₉	1	1	yes	characteristic, complemented, Sylow
6	C₂×C₂₉	—	529	1	no	Hall
7	D₂₃	—	23	1	no	—
8	C₂₉	D₅₂₉	1	1	yes	characteristic, direct product factor, Sylow
9	C₂₃	C₂₉×D₂₃	1	1	yes	characteristic
10	C₂	—	529	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	D₅₂₉
commutator, cosocle, hypocenter	C₅₂₉	C₂×C₂₉
Frattini	C₂₃	C₂₉×D₂₃
Fitting	C₂₉×C₅₂₉	C₂
socle	C₂₃×C₂₉	D₂₃
LCS	G ▷ C₅₂₉
UCS	C₁ ◁ C₂₉

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

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