Subgroups — D₃×D₁₅ #4384

Order 180.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₅	—	3	1	no	maximal
5	D₃×D₅	—	3	1	no	maximal
6	C₃²×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃²	—	5	1	no	maximal, Hall
8	C₂×C₃×C₅	—	3	1	no	—
9	D₁₅	—	3	1	no	—
10	D₁₅	—	3	1	no	—
11	D₁₅	—	6	1	no	—
12	D₁₅	D₃	1	1	yes	characteristic, direct product factor
13	C₃×D₅	—	3	1	no	—
14	C₅×D₃	D₃	1	1	yes	characteristic, complemented
15	C₂×D₅	—	9	1	no	Hall
16	C₃⋊D₃	—	5	1	no	—
17	C₃×D₃	—	5	1	no	—
18	C₃×D₃	D₅	1	1	yes	characteristic, complemented
19	C₃×C₅	—	2	1	no	—
20	C₃×C₅	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₃	—	15	1	no	—
23	C₂×D₃	—	15	1	no	—
24	C₂×C₅	—	3	1	no	—
25	D₅	—	3	1	no	—
26	D₅	—	9	1	no	—
27	C₃²	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
28	C₂×C₃	—	3	1	no	—
29	C₂×C₃	—	15	1	no	—
30	D₃	—	5	1	no	—
31	D₃	—	15	1	no	—
32	D₃	—	15	1	no	—
33	D₃	—	30	1	no	—
34	D₃	D₁₅	1	1	yes	characteristic, direct product factor
35	C₅	D₃²	1	1	yes	characteristic, complemented, Sylow
36	C₂²	—	45	1	no	Sylow
37	C₃	—	2	1	no	—
38	C₃	D₃×D₅	1	1	yes	characteristic, complemented
39	C₃	C₂×D₁₅	1	1	yes	characteristic, complemented
40	C₂	—	3	1	no	—
41	C₂	—	15	1	no	—
42	C₂	—	45	1	no	—

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

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.