Finite Group Databasebeta

← C3×C5×D3×C16 #13084957

Subgroups — C3×C5×D3×C16 #13084957

Order 1440.

122 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 122 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C3×C5×D3×C8C211yesmaximal, characteristic
2C32×C5×C16C211yesmaximal, characteristic, complemented
3C3×C5×C3⋊C16C211yesmaximal, characteristic, complemented
4C2×C3×C5×C16—31nomaximal
5C5×D3×C16C311yesmaximal, characteristic, direct product factor
6C3×C4×C5×D3C411yescharacteristic
7C32×C5×C8C2211yescharacteristic
8C3×C5×C3⋊C8C411yescharacteristic
9C3×D3×C16C511yesmaximal, characteristic, direct product factor, Hall
10C2×C3×C5×C8—31no—
11C5×D3×C8C2×C311yescharacteristic
12C3×C5×C16—21no—
13C3×C5×C16—31no—
14C3×C5×C16D311yescharacteristic, direct product factor
15C3×C5×C16C2×C311yescharacteristic, complemented
16C5×C3⋊C16C2×C311yescharacteristic, complemented
17C2×C3×C5×D3C811yescharacteristic
18C32×C4×C5C2×C411yescharacteristic
19C3×C5×Dic3C811yescharacteristic
20C2×C5×C16—31noHall
21C3×D3×C8C2×C511yescharacteristic
22C32×C16C2×C511yescharacteristic, complemented
23C3×C3⋊C16C2×C511yescharacteristic, complemented
24C2×C3×C4×C5—31no—
25C4×C5×D3C3×C411yescharacteristic
26C3×C5×C8—21no—
27C3×C5×C8—31no—
28C3×C5×C8C2×D311yescharacteristic
29C3×C5×C8C22×C311yescharacteristic
30C5×C3⋊C8C3×C411yescharacteristic
31C2×C3×C16—31no—
32D3×C16C3×C511yescharacteristic, direct product factor
33C2×C32×C5C2×C811yescharacteristic
34C3×C5×D3C1612yesdirect product factor
35C2×C5×C8—31no—
36C5×C16—31no—
37C5×C16C3×D311yescharacteristic, direct product factor
38C3×C4×D3C4×C511yescharacteristic
39C32×C8C22×C511yescharacteristic
40C3×C3⋊C8C4×C511yescharacteristic
41C22×C3×C5—31no—
42C2×C5×D3C3×C811yescharacteristic
43C3×C4×C5—21no—
44C3×C4×C5—31no—
45C3×C4×C5C4×D311yescharacteristic
46C3×C4×C5C2×C3×C411yescharacteristic
47C5×Dic3C3×C811yescharacteristic
48C2×C3×C8—31no—
49D3×C8C2×C3×C511yescharacteristic
50C3×C16—21no—
51C3×C16—31no—
52C3×C16C5×D311yescharacteristic, direct product factor
53C3×C16C2×C3×C511yescharacteristic, complemented
54C3⋊C16C2×C3×C511yescharacteristic, complemented
55C32×C5C2×C1611yescharacteristic, complemented, Hall
56C2×C4×C5—31no—
57C5×C8—31no—
58C5×C8C2×C3×D311yescharacteristic
59C2×C3×D3C5×C811yescharacteristic
60C32×C4C2×C4×C511yescharacteristic
61C3×Dic3C5×C811yescharacteristic
62C2×C16—31noSylow
63C2×C3×C5—21no—
64C2×C3×C5—32no—
65C2×C3×C5D3×C811yescharacteristic
66C2×C3×C5C2×C3×C811yescharacteristic
67C5×D3C3×C1612yesdirect product factor
68C2×C3×C4—31no—
69C4×D3C3×C4×C511yescharacteristic
70C3×C8—21no—
71C3×C8—31no—
72C3×C8C2×C5×D311yescharacteristic
73C3×C8C22×C3×C511yescharacteristic
74C3⋊C8C3×C4×C511yescharacteristic
75C22×C5—31no—
76C4×C5—31no—
77C4×C5C3×C4×D311yescharacteristic
78C2×C32C2×C5×C811yescharacteristic
79C3×D3C5×C1612yesdirect product factor
80C2×C8—31no—
81C16—31no—
82C16C3×C5×D311yescharacteristic, direct product factor
83C3×C5—21no—
84C3×C5D3×C1611yescharacteristic, direct product factor
85C3×C5C2×C3×C1611yescharacteristic, complemented
86C22×C3—31no—
87C2×D3C3×C5×C811yescharacteristic
88C3×C4—21no—
89C3×C4—31no—
90C3×C4C4×C5×D311yescharacteristic
91C3×C4C2×C3×C4×C511yescharacteristic
92Dic3C3×C5×C811yescharacteristic
93C2×C5—32no—
94C2×C5C3×D3×C811yescharacteristic
95C32C2×C5×C1611yescharacteristic, complemented, Sylow
96C2×C4—31no—
97C8—31no—
98C8C2×C3×C5×D311yescharacteristic
99C2×C3—21no—
100C2×C3—32no—
101C2×C3C5×D3×C811yescharacteristic
102C2×C3C2×C3×C5×C811yescharacteristic
103D3C3×C5×C1612yesdirect product factor
104C5C3×D3×C1611yescharacteristic, direct product factor, Sylow
105C22—31no—
106C4—31no—
107C4C3×C4×C5×D311yescharacteristic
108C3—21no—
109C3C5×D3×C1611yescharacteristic, direct product factor
110C3C2×C3×C5×C1611yescharacteristic, complemented
111C2—32no—
112C2C3×C5×D3×C811yescharacteristic
subgroupG/H
center, hypercenterC3×C5×C16D3
commutator, hypocenterC3C2×C3×C5×C16
FrattiniC8C2×C3×C5×D3
FittingC32×C5×C16C2
socleC2×C32×C5C2×C8
prime radicalC2×C3×C5×D3C8
cosocleC3×C8C22×C3×C5
LCSG ▷ C3
UCSC1 ◁ C3×C5×C16

Complements

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

NH ≅ G/Ntype
2. C32×C5×C16C2semidirect
3. C3×C5×C3⋊C16C2semidirect
5. C5×D3×C16C3direct (N × H)
9. C3×D3×C16C5direct (N × H)
14. C3×C5×C16D3direct (N × H)
15. C3×C5×C16C2×C3semidirect
16. C5×C3⋊C16C2×C3semidirect
22. C32×C16C2×C5semidirect
23. C3×C3⋊C16C2×C5semidirect
32. D3×C16C3×C5direct (N × H)
34. C3×C5×D3C16direct (N × H)
37. C5×C16C3×D3direct (N × H)
52. C3×C16C5×D3direct (N × H)
53. C3×C16C2×C3×C5semidirect
54. C3⋊C16C2×C3×C5semidirect
55. C32×C5C2×C16semidirect
67. C5×D3C3×C16direct (N × H)
79. C3×D3C5×C16direct (N × H)
82. C16C3×C5×D3direct (N × H)
84. C3×C5D3×C16direct (N × H)
85. C3×C5C2×C3×C16semidirect
95. C32C2×C5×C16semidirect
103. D3C3×C5×C16direct (N × H)
104. C5C3×D3×C16direct (N × H)
109. C3C5×D3×C16direct (N × H)
110. C3C2×C3×C5×C16semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D3×C82
C32×C5×C162
C3×C5×C3⋊C162
C2×C3×C5×C163
C5×D3×C163
C3×D3×C165