Finite Group Databasebeta

← C22×C3×C5×C449 #41002255

Subgroups — C22×C3×C5×C449 #41002255

Order 26940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C449C213yesmaximal, direct product factor
2C22×C5×C449C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C449C2211yescharacteristic, direct product factor, Hall
4C22×C3×C449C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C449C2×C313yesdirect product factor
6C2×C3×C449C2×C513yesdirect product factor
7C5×C449C22×C311yescharacteristic, direct product factor, Hall
8C22×C449C3×C511yescharacteristic, direct product factor, Hall
9C3×C449C22×C511yescharacteristic, direct product factor, Hall
10C2×C449C2×C3×C513yesdirect product factor
11C449C22×C3×C511yescharacteristic, direct product factor, Sylow
12C22×C3×C5C44911yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5C2×C44913yesdirect product factor
14C22×C5C3×C44911yescharacteristic, direct product factor, Hall
15C3×C5C22×C44911yescharacteristic, direct product factor, Hall
16C22×C3C5×C44911yescharacteristic, direct product factor, Hall
17C2×C5C2×C3×C44913yesdirect product factor
18C2×C3C2×C5×C44913yesdirect product factor
19C5C22×C3×C44911yescharacteristic, direct product factor, Sylow
20C22C3×C5×C44911yescharacteristic, direct product factor, Sylow
21C3C22×C5×C44911yescharacteristic, direct product factor, Sylow
22C2C2×C3×C5×C44913yesdirect product factor
subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C449C2direct (N × H)
2. C22×C5×C449C3direct (N × H)
3. C3×C5×C449C22direct (N × H)
4. C22×C3×C449C5direct (N × H)
5. C2×C5×C449C2×C3direct (N × H)
6. C2×C3×C449C2×C5direct (N × H)
7. C5×C449C22×C3direct (N × H)
8. C22×C449C3×C5direct (N × H)
9. C3×C449C22×C5direct (N × H)
10. C2×C449C2×C3×C5direct (N × H)
11. C449C22×C3×C5direct (N × H)
12. C22×C3×C5C449direct (N × H)
13. C2×C3×C5C2×C449direct (N × H)
14. C22×C5C3×C449direct (N × H)
15. C3×C5C22×C449direct (N × H)
16. C22×C3C5×C449direct (N × H)
17. C2×C5C2×C3×C449direct (N × H)
18. C2×C3C2×C5×C449direct (N × H)
19. C5C22×C3×C449direct (N × H)
20. C22C3×C5×C449direct (N × H)
21. C3C22×C5×C449direct (N × H)
22. C2C2×C3×C5×C449direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C4492
C22×C5×C4493
C22×C3×C4495
C22×C3×C5449