Finite Group Databasebeta

← C5×C7×(C61⋊C3)⋊C5 #44545056

Subgroups — C5×C7×(C61⋊C3)⋊C5 #44545056

Order 32025.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C7×C61⋊C5C311yesmaximal, characteristic, complemented, Hall
2C7×(C61⋊C3)⋊C5C515yesmaximal, direct product factor
3C5×C7×C61⋊C3C511yesmaximal, characteristic, complemented
4C5×(C61⋊C3)⋊C5C711yesmaximal, characteristic, direct product factor, Hall
5C5×C7×C61C3×C511yescharacteristic, complemented
6C7×C61⋊C5C3×C515yescomplemented
7C5×C61⋊C5C3×C711yescharacteristic, complemented, Hall
8C7×C61⋊C3C5211yescharacteristic, complemented, Hall
9C5×C61⋊C3C5×C711yescharacteristic, complemented
10(C61⋊C3)⋊C5C5×C715yesdirect product factor
11C3×C52×C7—611nomaximal, Hall
12C7×C61C3×C5211yescharacteristic, complemented, Hall
13C5×C61C3×C5×C711yescharacteristic, complemented
14C61⋊C5C3×C5×C715yescomplemented
15C61⋊C3C52×C711yescharacteristic, complemented, Hall
16C52×C7—611noHall
17C3×C5×C7—615no—
18C3×C5×C7—611no—
19C3×C52—611noHall
20C61C3×C52×C711yescharacteristic, complemented, Sylow
21C5×C7—615no—
22C5×C7(C61⋊C3)⋊C511yescharacteristic, direct product factor
23C52—611noSylow
24C3×C7—611noHall
25C3×C5—615no—
26C3×C5—611no—
27C7C5×(C61⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
28C5—615no—
29C5C7×(C61⋊C3)⋊C511yescharacteristic, direct product factor
30C3—611noSylow
subgroupG/H
center, hypercenterC5×C7(C61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C3×C52×C7
FrattiniC1G
Fitting, socleC5×C7×C61C3×C5
LCSG ▷ C61
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C5×C7×C61⋊C5C3semidirect
2. C7×(C61⋊C3)⋊C5C5direct (N × H)
3. C5×C7×C61⋊C3C5semidirect
4. C5×(C61⋊C3)⋊C5C7direct (N × H)
5. C5×C7×C61C3×C5semidirect
6. C7×C61⋊C5C3×C5semidirect
7. C5×C61⋊C5C3×C7semidirect
8. C7×C61⋊C3C52semidirect
9. C5×C61⋊C3C5×C7semidirect
10. (C61⋊C3)⋊C5C5×C7direct (N × H)
12. C7×C61C3×C52semidirect
13. C5×C61C3×C5×C7semidirect
14. C61⋊C5C3×C5×C7semidirect
15. C61⋊C3C52×C7semidirect
20. C61C3×C52×C7semidirect
22. C5×C7(C61⋊C3)⋊C5direct (N × H)
27. C7C5×(C61⋊C3)⋊C5direct (N × H)
29. C5C7×(C61⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C7×C61⋊C53
C7×(C61⋊C3)⋊C55
C5×C7×C61⋊C35
C5×(C61⋊C3)⋊C57
C3×C52×C761