Finite Group Databasebeta

← C3×#3969 #91039

Subgroups — C3×#3969 #91039

Order 480.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#41C211yesmaximal, characteristic
2C3×C4×Dic5C211yesmaximal, characteristic, complemented
3C3×#681C211yesmaximal, characteristic, complemented
4#3969C311yesmaximal, characteristic, direct product factor, Hall
5C3×C5×Q8C411yescharacteristic, complemented
6C3×C5×D4—21no—
7C3×C5×D4C411yescharacteristic, complemented
8C2×C3×C4×C5—21no—
9C2×C3×C4×C5C2211yescharacteristic
10C2×C3×Dic5—21no—
11C3×#168—21no—
12C3×#104—51nomaximal, Hall
13C5×#41C2×C311yescharacteristic
14C4×Dic5C2×C311yescharacteristic, complemented
15#681C2×C311yescharacteristic, complemented
16C22×C3×C5—21no—
17C22×C3×C5D411yescharacteristic
18C3×C4×C5—21no—
19C3×C4×C5C2×C411yescharacteristic
20C3×C4×C5D411yescharacteristic
21C3×Dic5—22no—
22C3×#41D511yescharacteristic
23C3×M16—51no—
24C3×C42—51no—
25C5×Q8C3×C411yescharacteristic, complemented
26C5×D4—21no—
27C5×D4C3×C411yescharacteristic, complemented
28C2×C4×C5—21no—
29C2×C4×C5C22×C311yescharacteristic
30C2×Dic5—21no—
31#168—21no—
32#104—51noSylow
33C2×C3×C5—21no—
34C2×C3×C5—41no—
35C2×C3×C5C22⋊C411yescharacteristic
36C3×Q8Dic511yescharacteristic, complemented
37C3×D4—21no—
38C3×D4Dic511yescharacteristic, complemented
39C2×C3×C4—21no—
40C2×C3×C4—101no—
41C2×C3×C4C2×D511yescharacteristic
42C3×C8—101no—
43C22×C5—21no—
44C22×C5C3×D411yescharacteristic
45C4×C5—21no—
46C4×C5C2×C3×C411yescharacteristic
47C4×C5C3×D411yescharacteristic
48Dic5—22no—
49#41C3×D511yescharacteristic
50M16—51no—
51C42—51no—
52C3×C5#10411yescharacteristic, complemented, Hall
53C22×C3—21no—
54C22×C3C22⋊D511yescharacteristic
55C3×C4—21no—
56C3×C4—102no—
57C3×C4C2×Dic511yescharacteristic
58C3×C4C22⋊D511yescharacteristic
59C2×C5—21no—
60C2×C5—41no—
61C2×C5C3×C22⋊C411yescharacteristic
62Q8C3×Dic511yescharacteristic, complemented
63D4—21no—
64D4C3×Dic511yescharacteristic, complemented
65C2×C4—21no—
66C2×C4—101no—
67C2×C4C2×C3×D511yescharacteristic
68C8—101no—
69C2×C3—21no—
70C2×C3—41no—
71C2×C3C22⋊Dic511yescharacteristic
72C5C3×#10411yescharacteristic, complemented, Sylow
73C22—21no—
74C22C3×C22⋊D511yescharacteristic
75C4—21no—
76C4—102no—
77C4C2×C3×Dic511yescharacteristic
78C4C3×C22⋊D511yescharacteristic
79C3#396911yescharacteristic, direct product factor, Sylow
80C2—21no—
81C2—41no—
82C2C3×C22⋊Dic511yescharacteristic
subgroupG/H
centerC3×C4C22⋊D5
commutatorC4×C5C2×C3×C4
FrattiniC2×C4C2×C3×D5
Fitting, prime radicalC3×C5×#41C2
socleC2×C3×C5C22⋊C4
cosocleC2×C4×C5C22×C3
hypercenterC3×#41D5
hypocenterC5C3×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C3×C4 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C3×C4×Dic5C2semidirect
3. C3×#681C2semidirect
4. #3969C3direct (N × H)
5. C3×C5×Q8C4semidirect
7. C3×C5×D4C4semidirect
14. C4×Dic5C2×C3semidirect
15. #681C2×C3semidirect
25. C5×Q8C3×C4semidirect
27. C5×D4C3×C4semidirect
36. C3×Q8Dic5semidirect
38. C3×D4Dic5semidirect
52. C3×C5#104semidirect
62. Q8C3×Dic5semidirect
64. D4C3×Dic5semidirect
72. C5C3×#104semidirect
79. C3#3969direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×#412
C3×C4×Dic52
C3×#6812
#39693
C3×#1045