Subgroups — D₁₃₉₁₉ #42123770

Order 27838.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×C₄₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₄₄₉	—	31	1	no	maximal, Hall
3	C₄₄₉	D₃₁	1	1	yes	characteristic, complemented, Sylow
4	D₃₁	—	449	1	no	maximal, Hall
5	C₃₁	D₄₄₉	1	1	yes	characteristic, complemented, Sylow
6	C₂	—	13919	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃₁×C₄₄₉	C₂
LCS	G ▷ C₃₁×C₄₄₉
UCS	C₁

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.