Finite Group Databasebeta

← C13×(D61⋊C3)⋊C5 #37558216

Subgroups — C13×(D61⋊C3)⋊C5 #37558216

Order 23790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×(C61⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2C13×D61⋊C5C311yesmaximal, characteristic, complemented, Hall
3C13×D61⋊C3C511yesmaximal, characteristic, complemented, Hall
4C13×C61⋊C5C2×C311yescharacteristic, complemented, Hall
5C13×C61⋊C3C2×C511yescharacteristic, complemented, Hall
6(D61⋊C3)⋊C5C1311yesmaximal, characteristic, direct product factor, Hall
7C13×D61C3×C511yescharacteristic, complemented, Hall
8(C61⋊C3)⋊C5C2×C1311yescharacteristic, complemented, Hall
9C13×C61C2×C3×C511yescharacteristic, complemented, Hall
10D61⋊C5C3×C1311yescharacteristic, complemented, Hall
11C2×C3×C5×C13—611nomaximal, Hall
12D61⋊C3C5×C1311yescharacteristic, complemented, Hall
13C61⋊C5C2×C3×C1311yescharacteristic, complemented, Hall
14C3×C5×C13—611noHall
15C61⋊C3C2×C5×C1311yescharacteristic, complemented, Hall
16C2×C5×C13—611noHall
17D61C3×C5×C1311yescharacteristic, complemented, Hall
18C2×C3×C13—611noHall
19C5×C13—611noHall
20C61C2×C3×C5×C1311yescharacteristic, complemented, Sylow
21C3×C13—611noHall
22C2×C3×C5—611noHall
23C2×C13—611noHall
24C3×C5—611noHall
25C13(D61⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
26C2×C5—611noHall
27C2×C3—611noHall
28C5—611noSylow
29C3—611noSylow
30C2—611noSylow
subgroupG/H
center, hypercenterC13(D61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C2×C3×C5×C13
FrattiniC1G
Fitting, socleC13×C61C2×C3×C5
LCSG ▷ C61
UCSC1 ◁ C13

Complements

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

NH ≅ G/Ntype
1. C13×(C61⋊C3)⋊C5C2semidirect
2. C13×D61⋊C5C3semidirect
3. C13×D61⋊C3C5semidirect
4. C13×C61⋊C5C2×C3semidirect
5. C13×C61⋊C3C2×C5semidirect
6. (D61⋊C3)⋊C5C13direct (N × H)
7. C13×D61C3×C5semidirect
8. (C61⋊C3)⋊C5C2×C13semidirect
9. C13×C61C2×C3×C5semidirect
10. D61⋊C5C3×C13semidirect
12. D61⋊C3C5×C13semidirect
13. C61⋊C5C2×C3×C13semidirect
15. C61⋊C3C2×C5×C13semidirect
17. D61C3×C5×C13semidirect
20. C61C2×C3×C5×C13semidirect
25. C13(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
C13×(C61⋊C3)⋊C52
C13×D61⋊C53
C13×D61⋊C35
(D61⋊C3)⋊C513
C2×C3×C5×C1361