Subgroups — C₂×D₄₅ #4366

Order 180.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₅	—	3	1	no	maximal
4	C₅×C₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₉	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅	D₃	1	1	yes	characteristic
7	D₁₅	—	3	2	no	—
8	C₂×D₅	—	9	1	no	Hall
9	C₂×C₉	D₅	1	1	yes	characteristic, complemented
10	D₉	—	5	2	no	—
11	C₃×C₅	C₂×D₃	1	1	yes	characteristic
12	C₂×D₃	—	15	1	no	—
13	C₂×C₅	D₉	1	1	yes	characteristic, complemented
14	D₅	—	9	2	no	—
15	C₉	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₃	D₁₅	1	1	yes	characteristic
17	D₃	—	15	2	no	—
18	C₅	C₂×D₉	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	45	1	no	Sylow
20	C₃	C₂×D₁₅	1	1	yes	characteristic
21	C₂	—	45	2	no	—
22	C₂	D₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂²
Frattini	C₃	C₂×D₁₅
Fitting	C₂×C₅×C₉	C₂
socle	C₂×C₃×C₅	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂

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.