Finite Group Databasebeta

← D17×(C61⋊C3)⋊C5 #44527462

Subgroups — D17×(C61⋊C3)⋊C5 #44527462

Order 31110.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C17×(C61⋊C3)⋊C5C211yesmaximal, characteristic, complemented, Hall
2D17×C61⋊C5C311yesmaximal, characteristic, complemented, Hall
3D17×C61⋊C3C511yesmaximal, characteristic, complemented, Hall
4C17×C61⋊C5C2×C311yescharacteristic, complemented, Hall
5C17×C61⋊C3C2×C511yescharacteristic, complemented, Hall
6D17×C61C3×C511yescharacteristic, complemented, Hall
7C2×(C61⋊C3)⋊C5—171nomaximal, Hall
8C17×C61C2×C3×C511yescharacteristic, complemented, Hall
9(C61⋊C3)⋊C5D1711yescharacteristic, direct product factor, Hall
10C2×C61⋊C5—171noHall
11C3×C5×D17—611nomaximal, Hall
12C2×C61⋊C3—171noHall
13C61⋊C5C3×D1711yescharacteristic, complemented, Hall
14C3×C5×C17—611noHall
15C61⋊C3C5×D1711yescharacteristic, complemented, Hall
16C5×D17—611noHall
17C2×C61—171noHall
18C3×D17—611noHall
19C5×C17—611noHall
20C61C3×C5×D1711yescharacteristic, complemented, Sylow
21C3×C17—611noHall
22D17(C61⋊C3)⋊C511yescharacteristic, direct product factor, Hall
23C2×C3×C5—10371noHall
24C17C2×(C61⋊C3)⋊C511yescharacteristic, complemented, Sylow
25C3×C5—611noHall
26C2×C5—10371noHall
27C2×C3—10371noHall
28C5—611noSylow
29C3—611noSylow
30C2—171noSylow
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC17×C61C2×C3×C5
LCSG ▷ C17×C61
UCSC1

Complements

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

NH ≅ G/Ntype
1. C17×(C61⋊C3)⋊C5C2semidirect
2. D17×C61⋊C5C3semidirect
3. D17×C61⋊C3C5semidirect
4. C17×C61⋊C5C2×C3semidirect
5. C17×C61⋊C3C2×C5semidirect
6. D17×C61C3×C5semidirect
8. C17×C61C2×C3×C5semidirect
9. (C61⋊C3)⋊C5D17direct (N × H)
13. C61⋊C5C3×D17semidirect
15. C61⋊C3C5×D17semidirect
20. C61C3×C5×D17semidirect
22. D17(C61⋊C3)⋊C5direct (N × H)
24. C17C2×(C61⋊C3)⋊C5semidirect

Maximal subgroups

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

subgroupindex
C17×(C61⋊C3)⋊C52
D17×C61⋊C53
D17×C61⋊C35
C2×(C61⋊C3)⋊C517
C3×C5×D1761