Finite Group Databasebeta

← C5×(Dic61⋊C3)⋊C5 #32912949

Subgroups — C5×(Dic61⋊C3)⋊C5 #32912949

Order 18300.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×(C61⋊C3)⋊C5C211yesmaximal, characteristic
2C5×Dic61⋊C5C311yesmaximal, characteristic, complemented, Hall
3C5×(C61⋊C3)⋊C5C411yescharacteristic, complemented, Hall
4C5×Dic61⋊C3C511yesmaximal, characteristic, complemented
5(Dic61⋊C3)⋊C5C515yesmaximal, direct product factor
6C2×C5×C61⋊C5C2×C311yescharacteristic
7C2×C5×C61⋊C3C2×C511yescharacteristic
8C2×(C61⋊C3)⋊C5C2×C515yes—
9C5×C61⋊C5C3×C411yescharacteristic, complemented, Hall
10C5×Dic61C3×C511yescharacteristic, complemented
11Dic61⋊C5C3×C515yescomplemented
12C5×C61⋊C3C4×C511yescharacteristic, complemented
13(C61⋊C3)⋊C5C4×C515yescomplemented
14Dic61⋊C3C5211yescharacteristic, complemented, Hall
15C2×C5×C61C2×C3×C511yescharacteristic
16C2×C61⋊C5C2×C3×C515yes—
17C2×C61⋊C3C2×C5211yescharacteristic
18C5×C61C3×C4×C511yescharacteristic, complemented
19C61⋊C5C3×C4×C515yescomplemented
20C3×C4×C52—611nomaximal, Hall
21Dic61C3×C5211yescharacteristic, complemented, Hall
22C61⋊C3C4×C5211yescharacteristic, complemented, Hall
23C2×C3×C52—611no—
24C2×C61C2×C3×C5211yescharacteristic
25C4×C52—611noHall
26C3×C52—611noHall
27C61C3×C4×C5211yescharacteristic, complemented, Sylow
28C3×C4×C5—3051no—
29C3×C4×C5—615no—
30C2×C52—611no—
31C2×C3×C5—3051no—
32C2×C3×C5—615no—
33C52—611noSylow
34C4×C5—3051no—
35C4×C5—615no—
36C3×C5—3051no—
37C3×C5—615no—
38C3×C4—3051noHall
39C2×C5—615no—
40C2×C5(D61⋊C3)⋊C511yescharacteristic
41C2×C3—3051no—
42C5—615no—
43C5(Dic61⋊C3)⋊C511yescharacteristic, direct product factor
44C4—3051noSylow
45C3—3051noSylow
46C2C5×(D61⋊C3)⋊C511yescharacteristic
subgroupG/H
center, hypercenterC2×C5(D61⋊C3)⋊C5
commutator, hypocenterC61C3×C4×C52
FrattiniC2C5×(D61⋊C3)⋊C5
Fitting, socleC2×C5×C61C2×C3×C5
prime radicalC2×C5×(C61⋊C3)⋊C5C2
cosocleC2×C61C2×C3×C52
LCSG ▷ C61
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×Dic61⋊C5C3semidirect
3. C5×(C61⋊C3)⋊C5C4semidirect
4. C5×Dic61⋊C3C5semidirect
5. (Dic61⋊C3)⋊C5C5direct (N × H)
9. C5×C61⋊C5C3×C4semidirect
10. C5×Dic61C3×C5semidirect
11. Dic61⋊C5C3×C5semidirect
12. C5×C61⋊C3C4×C5semidirect
13. (C61⋊C3)⋊C5C4×C5semidirect
14. Dic61⋊C3C52semidirect
18. C5×C61C3×C4×C5semidirect
19. C61⋊C5C3×C4×C5semidirect
21. Dic61C3×C52semidirect
22. C61⋊C3C4×C52semidirect
27. C61C3×C4×C52semidirect
43. C5(Dic61⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×(C61⋊C3)⋊C52
C5×Dic61⋊C53
C5×Dic61⋊C35
(Dic61⋊C3)⋊C55
C3×C4×C5261