Subgroups — C₂⁴×D₁₅ #92136

Order 480.

1496 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₁₅	C₂	1	30	yes	maximal, direct product factor
3	C₂⁴×D₅	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₅	C₂²	1	15	yes	complemented
5	C₂²×D₁₅	C₂²	1	140	yes	direct product factor
6	C₂⁴×D₃	—	5	1	no	maximal, Hall
7	C₂⁴×C₅	D₃	1	1	yes	characteristic, complemented
8	C₂³×D₅	—	3	30	no	—
9	C₂²×C₃×C₅	C₂³	1	35	yes	complemented
10	C₂×D₁₅	C₂³	1	120	yes	direct product factor
11	C₂⁴×C₃	D₅	1	1	yes	characteristic, complemented
12	C₂³×D₃	—	5	30	no	—
13	C₂³×C₅	C₂×D₃	1	15	yes	complemented
14	C₂²×D₅	—	3	140	no	—
15	C₂⁵	—	15	1	no	Sylow
16	C₂×C₃×C₅	C₂⁴	1	15	yes	complemented
17	D₁₅	C₂⁴	1	16	yes	direct product factor
18	C₂³×C₃	C₂×D₅	1	15	yes	complemented
19	C₂²×D₃	—	5	140	no	—
20	C₂²×C₅	C₂²×D₃	1	35	yes	complemented
21	C₂×D₅	—	3	120	no	—
22	C₂⁴	—	15	30	no	—
23	C₂⁴	D₁₅	1	1	yes	characteristic, direct product factor
24	C₃×C₅	C₂⁵	1	1	yes	characteristic, complemented, Hall
25	C₂²×C₃	C₂²×D₅	1	35	yes	complemented
26	C₂×D₃	—	5	120	no	—
27	C₂×C₅	C₂³×D₃	1	15	yes	complemented
28	D₅	—	3	16	no	—
29	C₂³	—	15	140	no	—
30	C₂³	C₂×D₁₅	1	15	yes	direct product factor
31	C₂×C₃	C₂³×D₅	1	15	yes	complemented
32	D₃	—	5	16	no	—
33	C₅	C₂⁴×D₃	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	15	120	no	—
35	C₂²	C₂²×D₁₅	1	35	yes	direct product factor
36	C₃	C₂⁴×D₅	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	15	16	no	—
38	C₂	C₂³×D₁₅	1	15	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁴	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂⁵
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₅	C₂	semidirect
2. C₂³×D₁₅	C₂	direct (N × H)
4. C₂³×C₃×C₅	C₂²	semidirect
5. C₂²×D₁₅	C₂²	direct (N × H)
7. C₂⁴×C₅	D₃	semidirect
9. C₂²×C₃×C₅	C₂³	semidirect
10. C₂×D₁₅	C₂³	direct (N × H)
11. C₂⁴×C₃	D₅	semidirect
13. C₂³×C₅	C₂×D₃	semidirect
16. C₂×C₃×C₅	C₂⁴	semidirect
17. D₁₅	C₂⁴	direct (N × H)
18. C₂³×C₃	C₂×D₅	semidirect
20. C₂²×C₅	C₂²×D₃	semidirect
23. C₂⁴	D₁₅	direct (N × H)
24. C₃×C₅	C₂⁵	semidirect
25. C₂²×C₃	C₂²×D₅	semidirect
27. C₂×C₅	C₂³×D₃	semidirect
30. C₂³	C₂×D₁₅	direct (N × H)
31. C₂×C₃	C₂³×D₅	semidirect
33. C₅	C₂⁴×D₃	semidirect
35. C₂²	C₂²×D₁₅	direct (N × H)
36. C₃	C₂⁴×D₅	semidirect
38. C₂	C₂³×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
C₂⁴×C₃×C₅	2
C₂³×D₁₅	2
C₂⁴×D₅	3
C₂⁴×D₃	5

Subgroups — C24×D15 #92136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₁₅ #92136