Subgroups — D₂₉×C₅₄₇ #44540589

Order 31726.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₅₄₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅₄₇	—	29	1	no	maximal, Hall
3	C₅₄₇	D₂₉	1	1	yes	characteristic, direct product factor, Sylow
4	D₂₉	C₅₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂₉	C₂×C₅₄₇	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	29	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅₄₇	D₂₉
commutator, cosocle, hypocenter	C₂₉	C₂×C₅₄₇
Frattini	C₁	G
Fitting, socle	C₂₉×C₅₄₇	C₂
LCS	G ▷ C₂₉
UCS	C₁ ◁ C₅₄₇

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.