Subgroups — C₅×D₃² #4383

Order 180.

44 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, complemented
2	C₃×C₅×D₃	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×D₃	—	3	2	no	maximal
4	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₃²	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅	—	3	2	no	—
7	C₅×D₃	—	3	2	no	—
8	C₅×D₃	—	6	1	no	—
9	C₅×D₃	D₃	1	2	yes	direct product factor
10	C₂²×C₅	—	9	1	no	Hall
11	C₃⋊D₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×D₃	C₂×C₅	1	2	yes	complemented
13	C₃×C₅	—	2	1	no	—
14	C₃×C₅	C₂×D₃	1	2	yes	complemented
15	C₂×D₃	—	3	2	no	—
16	C₂×C₅	—	3	2	no	—
17	C₂×C₅	—	9	1	no	—
18	C₃²	C₂²×C₅	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	3	2	no	—
20	D₃	—	3	2	no	—
21	D₃	—	6	1	no	—
22	D₃	C₅×D₃	1	2	yes	direct product factor
23	C₅	D₃²	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²	—	9	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	C₂×C₅×D₃	1	2	yes	complemented
27	C₂	—	3	2	no	—
28	C₂	—	9	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₃²
commutator, cosocle, hypocenter	C₃²	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅	C₂²
LCS	G ▷ C₃²
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.