Subgroups — C₂×C₁₂₄₉⋊C₁₃ #44570331

Order 32474.

8 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₂₄₉⋊C₁₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₂₄₉	C₁₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₂₄₉	C₂×C₁₃	1	1	yes	characteristic, complemented, Sylow
4	C₂×C₁₃	—	1249	1	no	maximal, Hall
5	C₁₃	—	1249	1	no	Sylow
6	C₂	C₁₂₄₉⋊C₁₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂	C₁₂₄₉⋊C₁₃
commutator, cosocle, hypocenter	C₁₂₄₉	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₂₄₉	C₁₃
LCS	G ▷ C₁₂₄₉
UCS	C₁ ◁ C₂

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.