Finite Group Databasebeta

← C7×(D61⋊C3)⋊C5 #27165490

Subgroups — C7×(D61⋊C3)⋊C5 #27165490

Order 12810.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C7×(C61⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2C7×D61⋊C5C311yesmaximal, characteristic, complemented, Hall
3C7×D61⋊C3C511yesmaximal, characteristic, complemented, Hall
4C7×C61⋊C5C2×C311yescharacteristic, complemented, Hall
5(D61⋊C3)⋊C5C711yesmaximal, characteristic, direct product factor, Hall
6C7×C61⋊C3C2×C511yescharacteristic, complemented, Hall
7(C61⋊C3)⋊C5C2×C711yescharacteristic, complemented, Hall
8C7×D61C3×C511yescharacteristic, complemented, Hall
9D61⋊C5C3×C711yescharacteristic, complemented, Hall
10C7×C61C2×C3×C511yescharacteristic, complemented, Hall
11D61⋊C3C5×C711yescharacteristic, complemented, Hall
12C61⋊C5C2×C3×C711yescharacteristic, complemented, Hall
13C2×C3×C5×C7—611nomaximal, Hall
14C61⋊C3C2×C5×C711yescharacteristic, complemented, Hall
15D61C3×C5×C711yescharacteristic, complemented, Hall
16C3×C5×C7—611noHall
17C2×C5×C7—611noHall
18C61C2×C3×C5×C711yescharacteristic, complemented, Sylow
19C2×C3×C7—611noHall
20C5×C7—611noHall
21C2×C3×C5—611noHall
22C3×C7—611noHall
23C3×C5—611noHall
24C2×C7—611noHall
25C2×C5—611noHall
26C7(D61⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
27C2×C3—611noHall
28C5—611noSylow
29C3—611noSylow
30C2—611noSylow
subgroupG/H
center, hypercenterC7(D61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C2×C3×C5×C7
FrattiniC1G
Fitting, socleC7×C61C2×C3×C5
LCSG ▷ C61
UCSC1 ◁ C7

Complements

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

NH ≅ G/Ntype
1. C7×(C61⋊C3)⋊C5C2semidirect
2. C7×D61⋊C5C3semidirect
3. C7×D61⋊C3C5semidirect
4. C7×C61⋊C5C2×C3semidirect
5. (D61⋊C3)⋊C5C7direct (N × H)
6. C7×C61⋊C3C2×C5semidirect
7. (C61⋊C3)⋊C5C2×C7semidirect
8. C7×D61C3×C5semidirect
9. D61⋊C5C3×C7semidirect
10. C7×C61C2×C3×C5semidirect
11. D61⋊C3C5×C7semidirect
12. C61⋊C5C2×C3×C7semidirect
14. C61⋊C3C2×C5×C7semidirect
15. D61C3×C5×C7semidirect
18. C61C2×C3×C5×C7semidirect
26. C7(D61⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C7×(C61⋊C3)⋊C52
C7×D61⋊C53
C7×D61⋊C35
(D61⋊C3)⋊C57
C2×C3×C5×C761