Subgroups — #4379

Order 180.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅	C₄	1	1	yes	characteristic, complemented, Hall
3	#157	—	5	1	no	maximal, Hall
4	C₅×D₃	—	6	2	no	—
5	Dic₅	—	9	1	no	maximal, Hall
6	C₃⋊D₃	D₅	1	1	yes	characteristic
7	C₃×C₅	—	2	2	no	—
8	C₂×C₅	—	9	1	no	—
9	C₃²	Dic₅	1	1	yes	characteristic, complemented, Sylow
10	D₃	—	6	2	no	—
11	C₅	#157	1	1	yes	characteristic, complemented, Sylow
12	C₄	—	45	1	no	Sylow
13	C₃	—	2	2	no	—
14	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅	C₄
prime radical, cosocle	C₅×C₃⋊D₃	C₂
LCS	G ▷ C₃²×C₅
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.