Subgroups — C₃×C₅×D₁₆ #91138

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₈	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₆	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₃×C₅×D₄	—	2	2	no	—
5	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	C₃×D₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×D₈	C₂×C₃	1	2	yes	complemented
8	C₅×C₁₆	C₂×C₃	1	1	yes	characteristic, complemented
9	C₂²×C₃×C₅	—	4	2	no	—
10	C₃×C₄×C₅	D₄	1	1	yes	characteristic
11	C₃×D₈	C₂×C₅	1	2	yes	complemented
12	C₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
13	C₅×D₄	—	2	2	no	—
14	C₅×C₈	C₂²×C₃	1	1	yes	characteristic
15	D₁₆	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₃×C₅	—	8	2	no	—
17	C₂×C₃×C₅	D₈	1	1	yes	characteristic
18	C₃×D₄	—	2	2	no	—
19	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
20	C₂²×C₅	—	4	2	no	—
21	C₄×C₅	C₃×D₄	1	1	yes	characteristic
22	D₈	C₂×C₃×C₅	1	2	yes	complemented
23	C₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
24	C₃×C₅	D₁₆	1	1	yes	characteristic, direct product factor, Hall
25	C₂²×C₃	—	4	2	no	—
26	C₃×C₄	C₅×D₄	1	1	yes	characteristic
27	C₂×C₅	—	8	2	no	—
28	C₂×C₅	C₃×D₈	1	1	yes	characteristic
29	D₄	—	2	2	no	—
30	C₈	C₂²×C₃×C₅	1	1	yes	characteristic
31	C₂×C₃	—	8	2	no	—
32	C₂×C₃	C₅×D₈	1	1	yes	characteristic
33	C₅	C₃×D₁₆	1	1	yes	characteristic, direct product factor, Sylow
34	C₂²	—	4	2	no	—
35	C₄	C₃×C₅×D₄	1	1	yes	characteristic
36	C₃	C₅×D₁₆	1	1	yes	characteristic, direct product factor, Sylow
37	C₂	—	8	2	no	—
38	C₂	C₃×C₅×D₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₃×C₅
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₃×C₄×C₅ ◁ C₃×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₈	C₂	semidirect
2. C₃×C₅×C₁₆	C₂	semidirect
3. C₅×D₁₆	C₃	direct (N × H)
6. C₃×D₁₆	C₅	direct (N × H)
7. C₅×D₈	C₂×C₃	semidirect
8. C₅×C₁₆	C₂×C₃	semidirect
11. C₃×D₈	C₂×C₅	semidirect
12. C₃×C₁₆	C₂×C₅	semidirect
15. D₁₆	C₃×C₅	direct (N × H)
22. D₈	C₂×C₃×C₅	semidirect
23. C₁₆	C₂×C₃×C₅	semidirect
24. C₃×C₅	D₁₆	direct (N × H)
33. C₅	C₃×D₁₆	direct (N × H)
36. C₃	C₅×D₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×D₈	2
C₃×C₅×C₁₆	2
C₅×D₁₆	3
C₃×D₁₆	5

Subgroups — C3×C5×D16 #91138

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₁₆ #91138