Subgroups — C₃×C₅×D₁₅ #90664

Order 450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₁₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₅×D₅	—	3	1	no	maximal
4	C₃×D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₃×C₅×D₃	—	5	1	no	maximal
6	C₃×C₅²	—	2	1	no	—
7	C₃×C₅²	D₃	1	1	yes	characteristic, complemented
8	C₃×C₅²	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₅	—	3	1	no	Hall
10	C₃²×C₅	—	2	2	no	—
11	C₃²×C₅	D₅	1	1	yes	characteristic, complemented
12	C₃²×C₅	C₂×C₅	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅	—	15	1	no	—
14	D₁₅	C₃×C₅	1	1	yes	characteristic, direct product factor
15	C₃×D₅	—	3	1	no	—
16	C₅×D₃	—	5	1	no	—
17	C₅²	C₃×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×D₃	—	5	1	no	Hall
19	C₃×C₅	—	2	4	no	—
20	C₃×C₅	—	2	1	no	—
21	C₃×C₅	—	2	1	no	—
22	C₃×C₅	—	2	2	no	—
23	C₃×C₅	—	2	2	no	—
24	C₃×C₅	C₅×D₃	1	1	yes	characteristic, complemented
25	C₃×C₅	C₃×D₅	1	1	yes	characteristic, complemented
26	C₃×C₅	D₁₅	1	1	yes	characteristic, direct product factor
27	C₃×C₅	C₂×C₃×C₅	1	1	yes	characteristic, complemented
28	C₂×C₅	—	15	1	no	—
29	D₅	—	3	1	no	—
30	C₃²	C₅×D₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	—	15	1	no	—
32	D₃	—	5	1	no	—
33	C₅	—	2	2	no	—
34	C₅	C₃×C₅×D₃	1	1	yes	characteristic, complemented
35	C₅	C₃×D₁₅	1	1	yes	characteristic, direct product factor
36	C₃	—	2	1	no	—
37	C₃	C₃×C₅×D₅	1	1	yes	characteristic, complemented
38	C₃	C₅×D₁₅	1	1	yes	characteristic, direct product factor
39	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃×C₅	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₃²×C₅²	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₃×C₅

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²	C₂	semidirect
2. C₅×D₁₅	C₃	direct (N × H)
4. C₃×D₁₅	C₅	direct (N × H)
7. C₃×C₅²	D₃	semidirect
8. C₃×C₅²	C₂×C₃	semidirect
11. C₃²×C₅	D₅	semidirect
12. C₃²×C₅	C₂×C₅	semidirect
14. D₁₅	C₃×C₅	direct (N × H)
17. C₅²	C₃×D₃	semidirect
24. C₃×C₅	C₅×D₃	semidirect
25. C₃×C₅	C₃×D₅	semidirect
26. C₃×C₅	D₁₅	direct (N × H)
27. C₃×C₅	C₂×C₃×C₅	semidirect
30. C₃²	C₅×D₅	semidirect
34. C₅	C₃×C₅×D₃	semidirect
35. C₅	C₃×D₁₅	direct (N × H)
37. C₃	C₃×C₅×D₅	semidirect
38. C₃	C₅×D₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₅²	2
C₅×D₁₅	3
C₃×C₅×D₅	3
C₃×D₁₅	5
C₃×C₅×D₃	5

Subgroups — C3×C5×D15 #90664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₅ #90664