Subgroups — C₂×C₅×C₃⋊D₃ #4390

Order 180.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×C₃⋊D₃	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅×D₃	—	3	4	no	maximal
4	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊D₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅	D₃	1	4	yes	complemented
7	C₅×D₃	—	3	8	no	—
8	C₂²×C₅	—	9	1	no	Hall
9	C₂×C₃²	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃⋊D₃	C₂×C₅	1	2	yes	direct product factor
11	C₃×C₅	C₂×D₃	1	4	yes	complemented
12	C₂×D₃	—	3	4	no	—
13	C₂×C₅	—	9	2	no	—
14	C₂×C₅	C₃⋊D₃	1	1	yes	characteristic, direct product factor
15	C₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃	C₅×D₃	1	4	yes	complemented
17	D₃	—	3	8	no	—
18	C₅	C₂×C₃⋊D₃	1	1	yes	characteristic, direct product factor, Sylow
19	C₂²	—	9	1	no	Sylow
20	C₃	C₂×C₅×D₃	1	4	yes	complemented
21	C₂	—	9	2	no	—
22	C₂	C₅×C₃⋊D₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×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.