Finite Group Databasebeta

← C22×C4×C5×C3⋊D3 #13089489

Subgroups — C22×C4×C5×C3⋊D3 #13089489

Order 1440.

1416 conjugacy classes of subgroups; only the 506 normal subgroups are shown.

normal subgroups only

This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 506 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
1C23×C5×C3⋊D3C211yesmaximal, characteristic
2C22×C32×C4×C5C211yesmaximal, characteristic, complemented
3C22×C5×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×C4×C5×C3⋊D3C2112yesmaximal, direct product factor
5C22×C4×C5×D3—34nomaximal
6C23×C32×C5C2211yescharacteristic
7C22×C5×C3⋊D3C418yesdirect product factor
8C22×C5×C3⋊D3C2216yes—
9C2×C32×C4×C5C2216yescomplemented
10C2×C5×C3⋊Dic3C2216yescomplemented
11C4×C5×C3⋊D3C22116yesdirect product factor
12C22×C4×C3⋊D3C511yesmaximal, characteristic, direct product factor, Hall
13C23×C5×D3—34no—
14C22×C3×C4×C5D314yescomplemented
15C22×C5×Dic3—34no—
16C2×C4×C5×D3—348no—
17C22×C32×C5C2×C414yescomplemented
18C22×C32×C5C2313yes—
19C2×C5×C3⋊D3C2×C4124yesdirect product factor
20C2×C5×C3⋊D3C2314yes—
21C32×C4×C5C2314yescomplemented
22C5×C3⋊Dic3C2314yescomplemented
23C23×C4×C5—91noHall
24C23×C3⋊D3C2×C511yescharacteristic
25C22×C32×C4C2×C511yescharacteristic, complemented
26C22×C3⋊Dic3C2×C511yescharacteristic, complemented
27C2×C4×C3⋊D3C2×C5112yesdirect product factor
28C23×C3×C5C2×D314yes—
29C22×C5×D3—332no—
30C22×C5×D3—324no—
31C2×C3×C4×C5C2×D3124yescomplemented
32C2×C5×Dic3—324no—
33C4×C5×D3—364no—
34C22×C4×D3—34no—
35C2×C32×C5C22×C416yescomplemented
36C2×C32×C5C2411yescharacteristic
37C5×C3⋊D3C22×C418yesdirect product factor
38C24×C5—91no—
39C22×C4×C5—91no—
40C22×C4×C5—912no—
41C22×C4×C5C3⋊D311yescharacteristic, direct product factor
42C23×C32C22×C511yescharacteristic
43C22×C3⋊D3C4×C518yesdirect product factor
44C22×C3⋊D3C22×C516yes—
45C2×C32×C4C22×C516yescomplemented
46C2×C3⋊Dic3C22×C516yescomplemented
47C4×C3⋊D3C22×C5116yesdirect product factor
48C22×C3×C5C4×D3116yescomplemented
49C22×C3×C5C22×D3112yes—
50C2×C5×D3—396no—
51C2×C5×D3—316no—
52C3×C4×C5C22×D3116yescomplemented
53C5×Dic3—316no—
54C23×D3—34no—
55C22×C3×C4C5×D314yescomplemented
56C22×Dic3—34no—
57C2×C4×D3—348no—
58C32×C5C23×C411yescharacteristic, complemented, Hall
59C23×C5—98no—
60C23×C5—96no—
61C23×C5C2×C3⋊D311yescharacteristic
62C2×C4×C5—96no—
63C2×C4×C5—916no—
64C2×C4×C5C2×C3⋊D316yesdirect product factor
65C22×C32C2×C4×C514yescomplemented
66C22×C32C23×C513yes—
67C2×C3⋊D3C2×C4×C5124yesdirect product factor
68C2×C3⋊D3C23×C514yes—
69C32×C4C23×C514yescomplemented
70C3⋊Dic3C23×C514yescomplemented
71C23×C4—91noSylow
72C2×C3×C5C2×C4×D3124yescomplemented
73C2×C3×C5C23×D314yes—
74C5×D3—332no—
75C23×C3C2×C5×D314yes—
76C22×D3—332no—
77C22×D3—324no—
78C2×C3×C4C2×C5×D3124yescomplemented
79C2×Dic3—324no—
80C4×D3—364no—
81C22×C5—94no—
82C22×C5—924no—
83C22×C5C4×C3⋊D314yesdirect product factor
84C22×C5C22×C3⋊D313yes—
85C4×C5—94no—
86C4×C5C22×C3⋊D314yesdirect product factor
87C2×C32C22×C4×C516yescomplemented
88C2×C32C24×C511yescharacteristic
89C3⋊D3C22×C4×C518yesdirect product factor
90C24—91no—
91C22×C4—91no—
92C22×C4—912no—
93C22×C4C5×C3⋊D311yescharacteristic, direct product factor
94C3×C5C22×C4×D314yescomplemented
95C22×C3C4×C5×D3116yescomplemented
96C22×C3C22×C5×D3112yes—
97C2×D3—396no—
98C2×D3—316no—
99C3×C4C22×C5×D3116yescomplemented
100Dic3—316no—
101C2×C5—98no—
102C2×C5C2×C4×C3⋊D316yesdirect product factor
103C2×C5C23×C3⋊D311yescharacteristic
104C32C23×C4×C511yescharacteristic, complemented, Sylow
105C23—98no—
106C23—96no—
107C23C2×C5×C3⋊D311yescharacteristic
108C2×C4—96no—
109C2×C4—916no—
110C2×C4C2×C5×C3⋊D316yesdirect product factor
111C2×C3C2×C4×C5×D3124yescomplemented
112C2×C3C23×C5×D314yes—
113D3—332no—
114C5C22×C4×C3⋊D311yescharacteristic, direct product factor, Sylow
115C22—924no—
116C22—94no—
117C22C4×C5×C3⋊D314yesdirect product factor
118C22C22×C5×C3⋊D313yes—
119C4—94no—
120C4C22×C5×C3⋊D314yesdirect product factor
121C3C22×C4×C5×D314yescomplemented
122C2—98no—
123C2C2×C4×C5×C3⋊D316yesdirect product factor
124C2C23×C5×C3⋊D311yescharacteristic
subgroupG/H
center, hypercenterC22×C4×C5C3⋊D3
commutator, hypocenterC32C23×C4×C5
FrattiniC2C23×C5×C3⋊D3
FittingC22×C32×C4×C5C2
socleC23×C32×C5C22
prime radicalC23×C5×C3⋊D3C2
cosocleC2×C32C24×C5
LCSG ▷ C32
UCSC1 ◁ C22×C4×C5

Complements

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

NH ≅ G/Ntype
2. C22×C32×C4×C5C2semidirect
3. C22×C5×C3⋊Dic3C2semidirect
4. C2×C4×C5×C3⋊D3C2direct (N × H)
7. C22×C5×C3⋊D3C4direct (N × H)
9. C2×C32×C4×C5C22semidirect
10. C2×C5×C3⋊Dic3C22semidirect
11. C4×C5×C3⋊D3C22direct (N × H)
12. C22×C4×C3⋊D3C5direct (N × H)
14. C22×C3×C4×C5D3semidirect
17. C22×C32×C5C2×C4semidirect
19. C2×C5×C3⋊D3C2×C4direct (N × H)
21. C32×C4×C5C23semidirect
22. C5×C3⋊Dic3C23semidirect
25. C22×C32×C4C2×C5semidirect
26. C22×C3⋊Dic3C2×C5semidirect
27. C2×C4×C3⋊D3C2×C5direct (N × H)
31. C2×C3×C4×C5C2×D3semidirect
35. C2×C32×C5C22×C4semidirect
37. C5×C3⋊D3C22×C4direct (N × H)
41. C22×C4×C5C3⋊D3direct (N × H)
43. C22×C3⋊D3C4×C5direct (N × H)
45. C2×C32×C4C22×C5semidirect
46. C2×C3⋊Dic3C22×C5semidirect
47. C4×C3⋊D3C22×C5direct (N × H)
48. C22×C3×C5C4×D3semidirect
52. C3×C4×C5C22×D3semidirect
55. C22×C3×C4C5×D3semidirect
58. C32×C5C23×C4semidirect
64. C2×C4×C5C2×C3⋊D3direct (N × H)
65. C22×C32C2×C4×C5semidirect
67. C2×C3⋊D3C2×C4×C5direct (N × H)
69. C32×C4C23×C5semidirect
70. C3⋊Dic3C23×C5semidirect
72. C2×C3×C5C2×C4×D3semidirect
78. C2×C3×C4C2×C5×D3semidirect
83. C22×C5C4×C3⋊D3direct (N × H)
86. C4×C5C22×C3⋊D3direct (N × H)
87. C2×C32C22×C4×C5semidirect
89. C3⋊D3C22×C4×C5direct (N × H)
93. C22×C4C5×C3⋊D3direct (N × H)
94. C3×C5C22×C4×D3semidirect
95. C22×C3C4×C5×D3semidirect
99. C3×C4C22×C5×D3semidirect
102. C2×C5C2×C4×C3⋊D3direct (N × H)
104. C32C23×C4×C5semidirect
110. C2×C4C2×C5×C3⋊D3direct (N × H)
111. C2×C3C2×C4×C5×D3semidirect
114. C5C22×C4×C3⋊D3direct (N × H)
117. C22C4×C5×C3⋊D3direct (N × H)
120. C4C22×C5×C3⋊D3direct (N × H)
121. C3C22×C4×C5×D3semidirect
123. C2C2×C4×C5×C3⋊D3direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C5×C3⋊D32
C22×C32×C4×C52
C22×C5×C3⋊Dic32
C2×C4×C5×C3⋊D32
C22×C4×C5×D33
C22×C4×C3⋊D35