Subgroups — C₅×D₃×C₁₆ #91040

Order 480.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₁₆	—	3	1	no	maximal, Hall
5	C₄×C₅×D₃	C₄	1	1	yes	characteristic
6	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
7	C₅×C₃⋊C₈	C₄	1	1	yes	characteristic
8	D₃×C₁₆	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₅×C₈	—	3	1	no	—
10	C₅×C₁₆	—	3	1	no	—
11	C₅×C₁₆	D₃	1	1	yes	characteristic, direct product factor
12	C₂×C₅×D₃	C₈	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
14	C₅×Dic₃	C₈	1	1	yes	characteristic
15	D₃×C₈	C₂×C₅	1	1	yes	characteristic
16	C₃×C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
18	C₂×C₄×C₅	—	3	1	no	—
19	C₅×C₈	—	3	1	no	—
20	C₅×C₈	C₂×D₃	1	1	yes	characteristic
21	C₂×C₁₆	—	3	1	no	Sylow
22	C₂×C₃×C₅	C₂×C₈	1	1	yes	characteristic
23	C₅×D₃	C₁₆	1	2	yes	direct product factor
24	C₄×D₃	C₄×C₅	1	1	yes	characteristic
25	C₃×C₈	C₂²×C₅	1	1	yes	characteristic
26	C₃⋊C₈	C₄×C₅	1	1	yes	characteristic
27	C₂²×C₅	—	3	1	no	—
28	C₄×C₅	—	3	1	no	—
29	C₄×C₅	C₄×D₃	1	1	yes	characteristic
30	C₂×C₈	—	3	1	no	—
31	C₁₆	—	3	1	no	—
32	C₁₆	C₅×D₃	1	1	yes	characteristic, direct product factor
33	C₃×C₅	C₂×C₁₆	1	1	yes	characteristic, complemented, Hall
34	C₂×D₃	C₅×C₈	1	1	yes	characteristic
35	C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
36	Dic₃	C₅×C₈	1	1	yes	characteristic
37	C₂×C₅	—	3	2	no	—
38	C₂×C₅	D₃×C₈	1	1	yes	characteristic
39	C₂×C₄	—	3	1	no	—
40	C₈	—	3	1	no	—
41	C₈	C₂×C₅×D₃	1	1	yes	characteristic
42	C₂×C₃	C₂×C₅×C₈	1	1	yes	characteristic
43	D₃	C₅×C₁₆	1	2	yes	direct product factor
44	C₅	D₃×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
45	C₂²	—	3	1	no	—
46	C₄	—	3	1	no	—
47	C₄	C₄×C₅×D₃	1	1	yes	characteristic
48	C₃	C₂×C₅×C₁₆	1	1	yes	characteristic, complemented, Sylow
49	C₂	—	3	2	no	—
50	C₂	C₅×D₃×C₈	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₅×C₁₆	D₃
commutator, hypocenter	C₃	C₂×C₅×C₁₆
Frattini	C₈	C₂×C₅×D₃
Fitting	C₃×C₅×C₁₆	C₂
socle	C₂×C₃×C₅	C₂×C₈
prime radical	C₂×C₅×D₃	C₈
cosocle	C₃×C₈	C₂²×C₅
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×C₁₆	C₂	semidirect
3. C₅×C₃⋊C₁₆	C₂	semidirect
8. D₃×C₁₆	C₅	direct (N × H)
11. C₅×C₁₆	D₃	direct (N × H)
16. C₃×C₁₆	C₂×C₅	semidirect
17. C₃⋊C₁₆	C₂×C₅	semidirect
23. C₅×D₃	C₁₆	direct (N × H)
32. C₁₆	C₅×D₃	direct (N × H)
33. C₃×C₅	C₂×C₁₆	semidirect
43. D₃	C₅×C₁₆	direct (N × H)
44. C₅	D₃×C₁₆	direct (N × H)
48. C₃	C₂×C₅×C₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×C₈	2
C₃×C₅×C₁₆	2
C₅×C₃⋊C₁₆	2
C₂×C₅×C₁₆	3
D₃×C₁₆	5

Subgroups — C5×D3×C16 #91040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₃×C₁₆ #91040