Finite Group Databasebeta

← C2×C17×(C61⋊C3)⋊C5 #44527431

Subgroups — C2×C17×(C61⋊C3)⋊C5 #44527431

Order 31110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×(C61⋊C3)⋊C5C211yesmaximal, characteristic, direct product factor, Hall
2C2×C17×C61⋊C5C311yesmaximal, characteristic, complemented, Hall
3C2×C17×C61⋊C3C511yesmaximal, characteristic, complemented, Hall
4C17×C61⋊C5C2×C311yescharacteristic, complemented, Hall
5C17×C61⋊C3C2×C511yescharacteristic, complemented, Hall
6C2×C17×C61C3×C511yescharacteristic, complemented, Hall
7C2×(C61⋊C3)⋊C5C1711yesmaximal, characteristic, direct product factor, Hall
8C17×C61C2×C3×C511yescharacteristic, complemented, Hall
9(C61⋊C3)⋊C5C2×C1711yescharacteristic, direct product factor, Hall
10C2×C61⋊C5C3×C1711yescharacteristic, complemented, Hall
11C2×C3×C5×C17—611nomaximal, Hall
12C2×C61⋊C3C5×C1711yescharacteristic, complemented, Hall
13C61⋊C5C2×C3×C1711yescharacteristic, complemented, Hall
14C3×C5×C17—611noHall
15C61⋊C3C2×C5×C1711yescharacteristic, complemented, Hall
16C2×C5×C17—611noHall
17C2×C61C3×C5×C1711yescharacteristic, complemented, Hall
18C2×C3×C17—611noHall
19C5×C17—611noHall
20C61C2×C3×C5×C1711yescharacteristic, complemented, Sylow
21C3×C17—611noHall
22C2×C17(C61⋊C3)⋊C511yescharacteristic, direct product factor, Hall
23C2×C3×C5—611noHall
24C17C2×(C61⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
25C3×C5—611noHall
26C2×C5—611noHall
27C2×C3—611noHall
28C5—611noSylow
29C3—611noSylow
30C2C17×(C61⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
subgroupG/H
center, hypercenterC2×C17(C61⋊C3)⋊C5
commutator, cosocle, hypocenterC61C2×C3×C5×C17
FrattiniC1G
Fitting, socleC2×C17×C61C3×C5
LCSG ▷ C61
UCSC1 ◁ C2×C17

Complements

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

NH ≅ G/Ntype
1. C17×(C61⋊C3)⋊C5C2direct (N × H)
2. C2×C17×C61⋊C5C3semidirect
3. C2×C17×C61⋊C3C5semidirect
4. C17×C61⋊C5C2×C3semidirect
5. C17×C61⋊C3C2×C5semidirect
6. C2×C17×C61C3×C5semidirect
7. C2×(C61⋊C3)⋊C5C17direct (N × H)
8. C17×C61C2×C3×C5semidirect
9. (C61⋊C3)⋊C5C2×C17direct (N × H)
10. C2×C61⋊C5C3×C17semidirect
12. C2×C61⋊C3C5×C17semidirect
13. C61⋊C5C2×C3×C17semidirect
15. C61⋊C3C2×C5×C17semidirect
17. C2×C61C3×C5×C17semidirect
20. C61C2×C3×C5×C17semidirect
22. C2×C17(C61⋊C3)⋊C5direct (N × H)
24. C17C2×(C61⋊C3)⋊C5direct (N × H)
30. C2C17×(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
C17×(C61⋊C3)⋊C52
C2×C17×C61⋊C53
C2×C17×C61⋊C35
C2×(C61⋊C3)⋊C517
C2×C3×C5×C1761