Subgroups — C₃×D₃×D₅ #4381

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

	subgroup	G/H
center, hypercenter	C₃	D₃×D₅
commutator, cosocle, hypocenter	C₃×C₅	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅	C₂²
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×D₁₅	C₂	semidirect
2. C₃×C₅×D₃	C₂	semidirect
3. C₃²×D₅	C₂	semidirect
5. D₃×D₅	C₃	direct (N × H)
6. C₃²×C₅	C₂²	semidirect
9. D₁₅	C₂×C₃	semidirect
12. C₃×D₅	D₃	direct (N × H)
13. C₃×D₅	C₂×C₃	semidirect
14. C₅×D₃	C₂×C₃	semidirect
18. C₃×D₃	D₅	direct (N × H)
20. C₃×C₅	C₂×D₃	semidirect
21. C₃×C₅	C₂²×C₃	semidirect
26. D₅	C₃×D₃	direct (N × H)
27. C₃²	C₂×D₅	semidirect
34. D₃	C₃×D₅	direct (N × H)
35. C₅	C₂×C₃×D₃	semidirect
38. C₃	D₃×D₅	direct (N × H)
39. C₃	C₂×C₃×D₅	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×D₁₅	2
C₃×C₅×D₃	2
C₃²×D₅	2
C₂×C₃×D₅	3
D₃×D₅	3
C₂×C₃×D₃	5

Subgroups — C3×D3×D5 #4381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×D₅ #4381