Finite Group Databasebeta

← C5×C7×C11×C49 #72196608

Subgroups — C5×C7×C11×C49 #72196608

Order 18865.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×C11×C49C511yesmaximal, characteristic, direct product factor, Hall
2C5×C72×C11C711yesmaximal, characteristic
3C5×C11×C49C717yesmaximal, direct product factor
4C5×C7×C49C1111yesmaximal, characteristic, direct product factor, Hall
5C72×C11C5×C711yescharacteristic
6C11×C49C5×C717yesdirect product factor
7C5×C7×C11C4917yesdirect product factor
8C5×C7×C11C7211yescharacteristic
9C7×C49C5×C1111yescharacteristic, direct product factor, Sylow
10C5×C72C7×C1111yescharacteristic
11C5×C49C7×C1117yesdirect product factor
12C7×C11C5×C4917yesdirect product factor
13C7×C11C5×C7211yescharacteristic
14C5×C11C7×C4911yescharacteristic, direct product factor, Hall
15C72C5×C7×C1111yescharacteristic
16C49C5×C7×C1117yesdirect product factor
17C5×C7C11×C4917yesdirect product factor
18C5×C7C72×C1111yescharacteristic
19C11C5×C7×C4911yescharacteristic, direct product factor, Sylow
20C7C5×C11×C4917yesdirect product factor
21C7C5×C72×C1111yescharacteristic
22C5C7×C11×C4911yescharacteristic, direct product factor, Sylow
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC7C5×C72×C11
socle, prime radicalC5×C72×C11C7
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
1. C7×C11×C49C5direct (N × H)
3. C5×C11×C49C7direct (N × H)
4. C5×C7×C49C11direct (N × H)
6. C11×C49C5×C7direct (N × H)
7. C5×C7×C11C49direct (N × H)
9. C7×C49C5×C11direct (N × H)
11. C5×C49C7×C11direct (N × H)
12. C7×C11C5×C49direct (N × H)
14. C5×C11C7×C49direct (N × H)
16. C49C5×C7×C11direct (N × H)
17. C5×C7C11×C49direct (N × H)
19. C11C5×C7×C49direct (N × H)
20. C7C5×C11×C49direct (N × H)
22. C5C7×C11×C49direct (N × H)

Maximal subgroups

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

subgroupindex
C7×C11×C495
C5×C72×C117
C5×C11×C497
C5×C7×C4911