Subgroups — C₈₉×D₁₅₁ #41001855

Order 26878.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×C₁₅₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₁₅₁	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₈₉	—	151	1	no	maximal, Hall
4	C₁₅₁	C₂×C₈₉	1	1	yes	characteristic, complemented, Sylow
5	C₈₉	D₁₅₁	1	1	yes	characteristic, direct product factor, Sylow
6	C₂	—	151	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₈₉	D₁₅₁
commutator, cosocle, hypocenter	C₁₅₁	C₂×C₈₉
Frattini	C₁	G
Fitting, socle	C₈₉×C₁₅₁	C₂
LCS	G ▷ C₁₅₁
UCS	C₁ ◁ C₈₉

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.