Finite Group Databasebeta

← C24×C5×C307 #72201803

Subgroups — C24×C5×C307 #72201803

Order 24560.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C5×C307C2115yesmaximal, direct product factor
2C22×C5×C307C22135yesdirect product factor
3C24×C307C511yesmaximal, characteristic, direct product factor, Hall
4C2×C5×C307C23115yesdirect product factor
5C23×C307C2×C5115yesdirect product factor
6C5×C307C2411yescharacteristic, direct product factor, Hall
7C22×C307C22×C5135yesdirect product factor
8C2×C307C23×C5115yesdirect product factor
9C307C24×C511yescharacteristic, direct product factor, Sylow
10C24×C5C30711yesmaximal, characteristic, direct product factor, Hall
11C23×C5C2×C307115yesdirect product factor
12C22×C5C22×C307135yesdirect product factor
13C24C5×C30711yescharacteristic, direct product factor, Sylow
14C2×C5C23×C307115yesdirect product factor
15C23C2×C5×C307115yesdirect product factor
16C5C24×C30711yescharacteristic, direct product factor, Sylow
17C22C22×C5×C307135yesdirect product factor
18C2C23×C5×C307115yesdirect 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. C23×C5×C307C2direct (N × H)
2. C22×C5×C307C22direct (N × H)
3. C24×C307C5direct (N × H)
4. C2×C5×C307C23direct (N × H)
5. C23×C307C2×C5direct (N × H)
6. C5×C307C24direct (N × H)
7. C22×C307C22×C5direct (N × H)
8. C2×C307C23×C5direct (N × H)
9. C307C24×C5direct (N × H)
10. C24×C5C307direct (N × H)
11. C23×C5C2×C307direct (N × H)
12. C22×C5C22×C307direct (N × H)
13. C24C5×C307direct (N × H)
14. C2×C5C23×C307direct (N × H)
15. C23C2×C5×C307direct (N × H)
16. C5C24×C307direct (N × H)
17. C22C22×C5×C307direct (N × H)
18. C2C23×C5×C307direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C3072
C24×C3075
C24×C5307