Subgroups — C₅×C₁₃₆₉⋊C₃ #35206607

Order 20535.

12 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₃₆₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃₆₉⋊C₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₁₃₆₉	C₃×C₅	1	1	yes	characteristic, complemented, Sylow
4	C₅×C₃₇⋊C₃	—	37	1	no	maximal
5	C₅×C₃₇	C₃₇⋊C₃	1	1	yes	characteristic
6	C₃₇⋊C₃	—	37	1	no	—
7	C₃₇	C₅×C₃₇⋊C₃	1	1	yes	characteristic
8	C₃×C₅	—	1369	1	no	Hall
9	C₅	C₁₃₆₉⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
10	C₃	—	1369	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₁₃₆₉⋊C₃
commutator, cosocle, hypocenter	C₁₃₆₉	C₃×C₅
Frattini	C₃₇	C₅×C₃₇⋊C₃
Fitting	C₅×C₁₃₆₉	C₃
socle	C₅×C₃₇	C₃₇⋊C₃
LCS	G ▷ C₁₃₆₉
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.