Subgroups — C₂×C₃×D₁₅ #4389

Order 180.

44 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	C₃×D₁₅	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₅	—	3	1	no	maximal
5	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃	—	5	1	no	maximal, Hall
7	C₂×C₃×C₅	—	2	1	no	—
8	C₂×C₃×C₅	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅	C₂×C₃	1	1	yes	characteristic, complemented
10	D₁₅	C₂×C₃	1	2	yes	direct product factor
11	C₃×D₅	—	3	2	no	—
12	C₂×D₅	—	3	1	no	Hall
13	C₂×C₃²	D₅	1	1	yes	characteristic, complemented
14	C₃×D₃	—	5	2	no	—
15	C₃×C₅	—	2	1	no	—
16	C₃×C₅	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃	—	15	1	no	—
19	C₂×D₃	—	5	1	no	—
20	C₂×C₅	C₃×D₃	1	1	yes	characteristic, complemented
21	D₅	—	3	2	no	—
22	C₃²	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₃	—	2	1	no	—
24	C₂×C₃	—	15	2	no	—
25	C₂×C₃	C₃×D₅	1	1	yes	characteristic, complemented
26	C₂×C₃	D₁₅	1	1	yes	characteristic, direct product factor
27	D₃	—	5	2	no	—
28	C₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Sylow
29	C₂²	—	15	1	no	Sylow
30	C₃	—	2	1	no	—
31	C₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented
32	C₃	C₂×D₁₅	1	1	yes	characteristic, direct product factor
33	C₂	—	15	2	no	—
34	C₂	C₃×D₁₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₃

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.