Finite Group Databasebeta

← C22×C3×C4×C5 #6824

Subgroups — C22×C3×C4×C5 #6824

Order 240.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C5C211yesmaximal, characteristic
2C2×C3×C4×C5C216yesmaximal, direct product factor
3C22×C4×C5C311yesmaximal, characteristic, direct product factor, Hall
4C22×C3×C5C414yesdirect product factor
5C22×C3×C5C2213yes—
6C3×C4×C5C2214yesdirect product factor
7C22×C3×C4C511yesmaximal, characteristic, direct product factor, Hall
8C23×C5C2×C311yescharacteristic
9C2×C4×C5C2×C316yesdirect product factor
10C2×C3×C5C2×C416yesdirect product factor
11C2×C3×C5C2311yescharacteristic
12C23×C3C2×C511yescharacteristic
13C2×C3×C4C2×C516yesdirect product factor
14C22×C5C3×C414yesdirect product factor
15C22×C5C22×C313yes—
16C4×C5C22×C314yesdirect product factor
17C22×C4C3×C511yescharacteristic, direct product factor, Sylow
18C3×C5C22×C411yescharacteristic, direct product factor, Hall
19C22×C3C4×C514yesdirect product factor
20C22×C3C22×C513yes—
21C3×C4C22×C514yesdirect product factor
22C2×C5C2×C3×C416yesdirect product factor
23C2×C5C23×C311yescharacteristic
24C23C2×C3×C511yescharacteristic
25C2×C4C2×C3×C516yesdirect product factor
26C2×C3C2×C4×C516yesdirect product factor
27C2×C3C23×C511yescharacteristic
28C5C22×C3×C411yescharacteristic, direct product factor, Sylow
29C22C3×C4×C514yesdirect product factor
30C22C22×C3×C513yes—
31C4C22×C3×C514yesdirect product factor
32C3C22×C4×C511yescharacteristic, direct product factor, Sylow
33C2C2×C3×C4×C516yesdirect product factor
34C2C23×C3×C511yescharacteristic
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C5
socle, prime radicalC23×C3×C5C2
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C5C2direct (N × H)
3. C22×C4×C5C3direct (N × H)
4. C22×C3×C5C4direct (N × H)
6. C3×C4×C5C22direct (N × H)
7. C22×C3×C4C5direct (N × H)
9. C2×C4×C5C2×C3direct (N × H)
10. C2×C3×C5C2×C4direct (N × H)
13. C2×C3×C4C2×C5direct (N × H)
14. C22×C5C3×C4direct (N × H)
16. C4×C5C22×C3direct (N × H)
17. C22×C4C3×C5direct (N × H)
18. C3×C5C22×C4direct (N × H)
19. C22×C3C4×C5direct (N × H)
21. C3×C4C22×C5direct (N × H)
22. C2×C5C2×C3×C4direct (N × H)
25. C2×C4C2×C3×C5direct (N × H)
26. C2×C3C2×C4×C5direct (N × H)
28. C5C22×C3×C4direct (N × H)
29. C22C3×C4×C5direct (N × H)
31. C4C22×C3×C5direct (N × H)
32. C3C22×C4×C5direct (N × H)
33. C2C2×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
C23×C3×C52
C2×C3×C4×C52
C22×C4×C53
C22×C3×C45