Subgroups — C₂×C₃²×D₅ #4387

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	C₃²×D₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×D₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₃²	—	5	1	no	maximal, Hall
6	C₂×C₃×C₅	C₂×C₃	1	4	yes	complemented
7	C₃×D₅	C₂×C₃	1	8	yes	direct product factor
8	C₂×D₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃²	—	5	2	no	—
10	C₂×C₃²	D₅	1	1	yes	characteristic, direct product factor
11	C₃×C₅	C₂²×C₃	1	4	yes	complemented
12	C₂²×C₃	—	5	4	no	—
13	C₂×C₅	C₂×C₃²	1	1	yes	characteristic, complemented
14	D₅	C₂×C₃²	1	2	yes	direct product factor
15	C₃²	C₂×D₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃	—	5	8	no	—
17	C₂×C₃	C₃×D₅	1	4	yes	direct product factor
18	C₅	C₂²×C₃²	1	1	yes	characteristic, complemented, Sylow
19	C₂²	—	5	1	no	Sylow
20	C₃	C₂×C₃×D₅	1	4	yes	direct product factor
21	C₂	—	5	2	no	—
22	C₂	C₃²×D₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₅
commutator, cosocle, hypocenter	C₅	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²

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.