Subgroups — C₁₀₉×D₁₀₉ #37557701

Order 23762.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉²	C₂	1	1	yes	maximal, characteristic, complemented, Sylow
2	C₂×C₁₀₉	—	109	1	no	maximal
3	D₁₀₉	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor
4	C₁₀₉	—	2	54	no	—
5	C₁₀₉	D₁₀₉	1	1	yes	characteristic, direct product factor
6	C₁₀₉	C₂×C₁₀₉	1	1	yes	characteristic, complemented
7	C₂	—	109	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₀₉	D₁₀₉
commutator, cosocle, hypocenter	C₁₀₉	C₂×C₁₀₉
Frattini	C₁	G
Fitting, socle	C₁₀₉²	C₂
LCS	G ▷ C₁₀₉
UCS	C₁ ◁ C₁₀₉

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.