Finite Group Databasebeta

← C3×D5×C3⋊Dic3 #11762035

Subgroups — C3×D5×C3⋊Dic3 #11762035

Order 1080.

272 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C33×D5C211yesmaximal, characteristic
2C3×C3⋊Dic15C211yesmaximal, characteristic, complemented
3C3×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
4D5×C3⋊Dic3C311yesmaximal, characteristic, direct product factor
5C3×D5×Dic3—34nomaximal
6C2×C33×C5C2211yescharacteristic
7C33×D5C412yescomplemented
8C2×C3×C3⋊Dic3—51nomaximal, Hall
9C2×C32×D5—24no—
10C2×C32×D5D314yes—
11C2×C32×D5C2×C311yescharacteristic
12C3⋊Dic15C2×C311yescharacteristic, complemented
13C5×C3⋊Dic3C2×C311yescharacteristic, complemented
14C3×Dic15—34no—
15C3×C5×Dic3—34no—
16C33×C5C2×C411yescharacteristic, complemented, Hall
17C3×C4×D5—91no—
18D5×Dic3—34no—
19C22×C33—51no—
20C3×C3⋊Dic3—51no—
21C3×C3⋊Dic3D511yescharacteristic, direct product factor
22C2×C32×C5—24no—
23C2×C32×C5C2×D314yes—
24C2×C32×C5C22×C311yescharacteristic
25C32×D5—28no—
26C32×D5Dic318yescomplemented
27C32×D5C3×C412yescomplemented
28C2×C3⋊Dic3—51no—
29C2×C3×Dic3—154no—
30C2×C3×D5—24no—
31C2×C3×D5C3×D314yes—
32C2×C3×D5C3⋊D311yescharacteristic
33C3×C4×C5—91no—
34Dic15—34no—
35C3×Dic5—91no—
36C5×Dic3—34no—
37C2×C33—52no—
38C2×C33C2×D511yescharacteristic
39C32×C5—24no—
40C32×C5C2×Dic314yescomplemented
41C32×C5C2×C3×C411yescharacteristic, complemented
42C4×D5—91noHall
43C22×C32—51no—
44C22×C32—54no—
45C22×C32—104no—
46C3⋊Dic3—51no—
47C3⋊Dic3C3×D511yescharacteristic, direct product factor
48C3×Dic3—34no—
49C3×Dic3—154no—
50C2×C3×C5—24no—
51C2×C3×C5C2×C3×D314yes—
52C2×C3×C5C2×C3⋊D311yescharacteristic
53C3×D5—28no—
54C3×D5C3×Dic318yescomplemented
55C3×D5C3⋊Dic312yesdirect product factor
56C33C4×D511yescharacteristic, complemented, Sylow
57C2×C3×C4—451no—
58C2×Dic3—154no—
59C2×D5C3×C3⋊D311yescharacteristic
60C4×C5—91no—
61Dic5—91no—
62C2×C32—24no—
63C2×C32—52no—
64C2×C32—58no—
65C2×C32—108no—
66C2×C32D3×D514yes—
67C2×C32C2×C3×D511yescharacteristic
68C3×C5—24no—
69C3×C5C2×C3×Dic314yescomplemented
70C3×C5C2×C3⋊Dic311yescharacteristic, complemented
71C22×C3—54no—
72C22×C3—51no—
73C22×C3—104no—
74C3×C4—91no—
75C3×C4—451no—
76Dic3—34no—
77Dic3—154no—
78C2×C5C2×C3×C3⋊D311yescharacteristic
79D5C3×C3⋊Dic312yesdirect product factor
80C32—24no—
81C32D5×Dic314yescomplemented
82C32C3×C4×D511yescharacteristic, complemented
83C2×C4—451noSylow
84C2×C3—24no—
85C2×C3—58no—
86C2×C3—52no—
87C2×C3—108no—
88C2×C3C3×D3×D514yes—
89C2×C3D5×C3⋊D311yescharacteristic
90C5C2×C3×C3⋊Dic311yescharacteristic, complemented, Sylow
91C22—51no—
92C4—91no—
93C4—451no—
94C3—24no—
95C3C3×D5×Dic314yescomplemented
96C3D5×C3⋊Dic311yescharacteristic, direct product factor
97C2—52no—
98C2C3×D5×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2×C3D5×C3⋊D3
commutator, hypocenterC32×C5C2×C3×C4
FrattiniC2C3×D5×C3⋊D3
Fitting, socleC2×C33×C5C22
prime radicalC2×C33×D5C2
cosocleC2×C32×C5C22×C3
LCSG ▷ C32×C5
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊Dic15C2semidirect
3. C3×C5×C3⋊Dic3C2semidirect
4. D5×C3⋊Dic3C3direct (N × H)
7. C33×D5C4semidirect
12. C3⋊Dic15C2×C3semidirect
13. C5×C3⋊Dic3C2×C3semidirect
16. C33×C5C2×C4semidirect
21. C3×C3⋊Dic3D5direct (N × H)
26. C32×D5Dic3semidirect
27. C32×D5C3×C4semidirect
40. C32×C5C2×Dic3semidirect
41. C32×C5C2×C3×C4semidirect
47. C3⋊Dic3C3×D5direct (N × H)
54. C3×D5C3×Dic3semidirect
55. C3×D5C3⋊Dic3direct (N × H)
56. C33C4×D5semidirect
69. C3×C5C2×C3×Dic3semidirect
70. C3×C5C2×C3⋊Dic3semidirect
79. D5C3×C3⋊Dic3direct (N × H)
81. C32D5×Dic3semidirect
82. C32C3×C4×D5semidirect
90. C5C2×C3×C3⋊Dic3semidirect
95. C3C3×D5×Dic3semidirect
96. C3D5×C3⋊Dic3direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C33×D52
C3×C3⋊Dic152
C3×C5×C3⋊Dic32
D5×C3⋊Dic33
C3×D5×Dic33
C2×C3×C3⋊Dic35