Finite Group Databasebeta

← C5×C7×D373 #39908306

Subgroups — C5×C7×D373 #39908306

Order 26110.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C7×C373C211yesmaximal, characteristic, complemented, Hall
2C7×D373C511yesmaximal, characteristic, direct product factor, Hall
3C5×D373C711yesmaximal, characteristic, direct product factor, Hall
4C7×C373C2×C511yescharacteristic, complemented, Hall
5C5×C373C2×C711yescharacteristic, complemented, Hall
6D373C5×C711yescharacteristic, direct product factor, Hall
7C373C2×C5×C711yescharacteristic, complemented, Sylow
8C2×C5×C7—3731nomaximal, Hall
9C5×C7D37311yescharacteristic, direct product factor, Hall
10C2×C7—3731noHall
11C2×C5—3731noHall
12C7C5×D37311yescharacteristic, direct product factor, Sylow
13C5C7×D37311yescharacteristic, direct product factor, Sylow
14C2—3731noSylow
subgroupG/H
center, hypercenterC5×C7D373
commutator, cosocle, hypocenterC373C2×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C373C2
LCSG ▷ C373
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C5×C7×C373C2semidirect
2. C7×D373C5direct (N × H)
3. C5×D373C7direct (N × H)
4. C7×C373C2×C5semidirect
5. C5×C373C2×C7semidirect
6. D373C5×C7direct (N × H)
7. C373C2×C5×C7semidirect
9. C5×C7D373direct (N × H)
12. C7C5×D373direct (N × H)
13. C5C7×D373direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×C3732
C7×D3735
C5×D3737
C2×C5×C7373