Subgroups — C₅×C₄₃⋊D₄₃ #32914949

Order 18490.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄₃²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₄₃⋊D₄₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₄₃²	C₂×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₅×D₄₃	—	43	44	no	maximal
5	C₅×C₄₃	D₄₃	1	44	yes	complemented
6	D₄₃	—	43	44	no	—
7	C₄₃	C₅×D₄₃	1	44	yes	complemented
8	C₂×C₅	—	1849	1	no	Hall
9	C₅	C₄₃⋊D₄₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₂	—	1849	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₄₃⋊D₄₃
commutator, cosocle, hypocenter	C₄₃²	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₄₃²	C₂
LCS	G ▷ C₄₃²
UCS	C₁ ◁ C₅

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.