Subgroups — D₁₃×C₃₁² #38735901

Order 24986.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₃₁²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₃₁²	—	13	1	no	maximal, Hall
3	C₃₁²	D₁₃	1	1	yes	characteristic, direct product factor, Sylow
4	D₁₃×C₃₁	C₃₁	1	32	yes	maximal, direct product factor
5	C₁₃×C₃₁	C₂×C₃₁	1	32	yes	complemented
6	C₂×C₃₁	—	13	32	no	—
7	C₃₁	D₁₃×C₃₁	1	32	yes	direct product factor
8	D₁₃	C₃₁²	1	1	yes	characteristic, direct product factor, Hall
9	C₁₃	C₂×C₃₁²	1	1	yes	characteristic, complemented, Sylow
10	C₂	—	13	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₁²	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃₁²
Frattini	C₁	G
Fitting, socle	C₁₃×C₃₁²	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃₁²

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.