Finite Group Databasebeta

← C23×C3×C4×C5 #92104

Subgroups — C23×C3×C4×C5 #92104

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C3×C5C211yesmaximal, characteristic
2C22×C3×C4×C5C2114yesmaximal, direct product factor
3C23×C4×C5C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C5C418yesdirect product factor
5C23×C3×C5C2217yes—
6C2×C3×C4×C5C22128yesdirect product factor
7C23×C3×C4C511yesmaximal, characteristic, direct product factor, Hall
8C24×C5C2×C311yescharacteristic
9C22×C4×C5C2×C3114yesdirect product factor
10C22×C3×C5C2×C4128yesdirect product factor
11C22×C3×C5C2317yes—
12C3×C4×C5C2318yesdirect product factor
13C24×C3C2×C511yescharacteristic
14C22×C3×C4C2×C5114yesdirect product factor
15C23×C5C3×C418yesdirect product factor
16C23×C5C22×C317yes—
17C2×C4×C5C22×C3128yesdirect product factor
18C23×C4C3×C511yescharacteristic, direct product factor, Sylow
19C2×C3×C5C22×C4114yesdirect product factor
20C2×C3×C5C2411yescharacteristic
21C23×C3C4×C518yesdirect product factor
22C23×C3C22×C517yes—
23C2×C3×C4C22×C5128yesdirect product factor
24C22×C5C2×C3×C4128yesdirect product factor
25C22×C5C23×C317yes—
26C4×C5C23×C318yesdirect product factor
27C24C2×C3×C511yescharacteristic
28C22×C4C2×C3×C5114yesdirect product factor
29C3×C5C23×C411yescharacteristic, direct product factor, Hall
30C22×C3C2×C4×C5128yesdirect product factor
31C22×C3C23×C517yes—
32C3×C4C23×C518yesdirect product factor
33C2×C5C22×C3×C4114yesdirect product factor
34C2×C5C24×C311yescharacteristic
35C23C3×C4×C518yesdirect product factor
36C23C22×C3×C517yes—
37C2×C4C22×C3×C5128yesdirect product factor
38C2×C3C22×C4×C5114yesdirect product factor
39C2×C3C24×C511yescharacteristic
40C5C23×C3×C411yescharacteristic, direct product factor, Sylow
41C22C2×C3×C4×C5128yesdirect product factor
42C22C23×C3×C517yes—
43C4C23×C3×C518yesdirect product factor
44C3C23×C4×C511yescharacteristic, direct product factor, Sylow
45C2C22×C3×C4×C5114yesdirect product factor
46C2C24×C3×C511yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C5
socle, prime radicalC24×C3×C5C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×C5C2direct (N × H)
3. C23×C4×C5C3direct (N × H)
4. C23×C3×C5C4direct (N × H)
6. C2×C3×C4×C5C22direct (N × H)
7. C23×C3×C4C5direct (N × H)
9. C22×C4×C5C2×C3direct (N × H)
10. C22×C3×C5C2×C4direct (N × H)
12. C3×C4×C5C23direct (N × H)
14. C22×C3×C4C2×C5direct (N × H)
15. C23×C5C3×C4direct (N × H)
17. C2×C4×C5C22×C3direct (N × H)
18. C23×C4C3×C5direct (N × H)
19. C2×C3×C5C22×C4direct (N × H)
21. C23×C3C4×C5direct (N × H)
23. C2×C3×C4C22×C5direct (N × H)
24. C22×C5C2×C3×C4direct (N × H)
26. C4×C5C23×C3direct (N × H)
28. C22×C4C2×C3×C5direct (N × H)
29. C3×C5C23×C4direct (N × H)
30. C22×C3C2×C4×C5direct (N × H)
32. C3×C4C23×C5direct (N × H)
33. C2×C5C22×C3×C4direct (N × H)
35. C23C3×C4×C5direct (N × H)
37. C2×C4C22×C3×C5direct (N × H)
38. C2×C3C22×C4×C5direct (N × H)
40. C5C23×C3×C4direct (N × H)
41. C22C2×C3×C4×C5direct (N × H)
43. C4C23×C3×C5direct (N × H)
44. C3C23×C4×C5direct (N × H)
45. C2C22×C3×C4×C5direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C3×C52
C22×C3×C4×C52
C23×C4×C53
C23×C3×C45