Finite Group Databasebeta

← (Dic305⋊C3)⋊C5 #32912950

Subgroups — (Dic305⋊C3)⋊C5 #32912950

Order 18300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×(C61⋊C3)⋊C5C211yesmaximal, characteristic
2Dic305⋊C5C311yesmaximal, characteristic, complemented, Hall
3C5×(C61⋊C3)⋊C5C411yescharacteristic, complemented, Hall
4Dic305⋊C3C511yesmaximal, characteristic, complemented
5(Dic61⋊C3)⋊C5—51nomaximal
6C2×C5×C61⋊C5C2×C311yescharacteristic
7C2×C5×C61⋊C3C2×C511yescharacteristic
8C2×(C61⋊C3)⋊C5—22no—
9C2×(C61⋊C3)⋊C5D511yescharacteristic
10C5×C61⋊C5C3×C411yescharacteristic, complemented, Hall
11Dic305C3×C511yescharacteristic, complemented
12Dic61⋊C5—51no—
13C5×C61⋊C3C4×C511yescharacteristic, complemented
14(C61⋊C3)⋊C5—22no—
15(C61⋊C3)⋊C5Dic511yescharacteristic, complemented
16Dic61⋊C3—51noHall
17C2×C5×C61C2×C3×C511yescharacteristic
18C2×C61⋊C5—22no—
19C2×C61⋊C5C3×D511yescharacteristic
20C2×C61⋊C3C5×D511yescharacteristic
21C5×C61C3×C4×C511yescharacteristic, complemented
22C61⋊C5—22no—
23C61⋊C5C3×Dic511yescharacteristic, complemented
24C3×C5×Dic5—611nomaximal, Hall
25Dic61—51noHall
26C61⋊C3C5×Dic511yescharacteristic, complemented, Hall
27C2×C3×C52—1221no—
28C2×C61C3×C5×D511yescharacteristic
29C5×Dic5—611noHall
30C3×C52—1221noHall
31C61C3×C5×Dic511yescharacteristic, complemented, Sylow
32C3×C4×C5—3051no—
33C3×Dic5—611no—
34C2×C52—1221no—
35C2×C3×C5—1221no—
36C2×C3×C5—1222no—
37C2×C3×C5—1221no—
38C52—1221noSylow
39C4×C5—3051no—
40Dic5—611no—
41C3×C5—1222no—
42C3×C5—1221no—
43C3×C5—1221no—
44C3×C4—3051noHall
45C2×C5—1221no—
46C2×C5—1222no—
47C2×C5(D61⋊C3)⋊C511yescharacteristic
48C2×C3—611no—
49C5—1222no—
50C5—1221no—
51C5(Dic61⋊C3)⋊C511yescharacteristic, complemented
52C4—3051noSylow
53C3—611noSylow
54C2C5⋊((D61⋊C3)⋊C5)11yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C5⋊((D61⋊C3)⋊C5)
commutator, hypocenterC5×C61C3×C4×C5
Fitting, socle, cosocleC2×C5×C61C2×C3×C5
prime radicalC2×C5×(C61⋊C3)⋊C5C2
LCSG ▷ C5×C61
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
2. Dic305⋊C5C3semidirect
3. C5×(C61⋊C3)⋊C5C4semidirect
4. Dic305⋊C3C5semidirect
10. C5×C61⋊C5C3×C4semidirect
11. Dic305C3×C5semidirect
13. C5×C61⋊C3C4×C5semidirect
15. (C61⋊C3)⋊C5Dic5semidirect
21. C5×C61C3×C4×C5semidirect
23. C61⋊C5C3×Dic5semidirect
26. C61⋊C3C5×Dic5semidirect
31. C61C3×C5×Dic5semidirect
51. C5(Dic61⋊C3)⋊C5semidirect

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
Dic305⋊C53
Dic305⋊C35
(Dic61⋊C3)⋊C55
C3×C5×Dic561