Subgroups — C₂⁴×C₃×D₅ #92134

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

	subgroup	G/H
center, hypercenter	C₂⁴×C₃	D₅
commutator, cosocle, hypocenter	C₅	C₂⁵×C₃
Frattini	C₁	G
Fitting, socle	C₂⁴×C₃×C₅	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₅	C₂	semidirect
2. C₂³×C₃×D₅	C₂	direct (N × H)
3. C₂⁴×D₅	C₃	direct (N × H)
4. C₂³×C₃×C₅	C₂²	semidirect
5. C₂²×C₃×D₅	C₂²	direct (N × H)
7. C₂⁴×C₅	C₂×C₃	semidirect
8. C₂³×D₅	C₂×C₃	direct (N × H)
9. C₂²×C₃×C₅	C₂³	semidirect
10. C₂×C₃×D₅	C₂³	direct (N × H)
12. C₂⁴×C₃	D₅	direct (N × H)
13. C₂³×C₅	C₂²×C₃	semidirect
14. C₂²×D₅	C₂²×C₃	direct (N × H)
16. C₂×C₃×C₅	C₂⁴	semidirect
17. C₃×D₅	C₂⁴	direct (N × H)
19. C₂³×C₃	C₂×D₅	direct (N × H)
20. C₂²×C₅	C₂³×C₃	semidirect
21. C₂×D₅	C₂³×C₃	direct (N × H)
23. C₂⁴	C₃×D₅	direct (N × H)
24. C₃×C₅	C₂⁵	semidirect
26. C₂²×C₃	C₂²×D₅	direct (N × H)
27. C₂×C₅	C₂⁴×C₃	semidirect
28. D₅	C₂⁴×C₃	direct (N × H)
30. C₂³	C₂×C₃×D₅	direct (N × H)
32. C₂×C₃	C₂³×D₅	direct (N × H)
33. C₅	C₂⁵×C₃	semidirect
35. C₂²	C₂²×C₃×D₅	direct (N × H)
36. C₃	C₂⁴×D₅	direct (N × H)
38. C₂	C₂³×C₃×D₅	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×C₃×D₅	2
C₂⁴×D₅	3
C₂⁵×C₃	5

Subgroups — C24×C3×D5 #92134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₃×D₅ #92134