Finite Group Databasebeta

← C3×C42×C5×D3 #13087882

Subgroups — C3×C42×C5×D3 #13087882

Order 1440.

462 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 276 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×C3×C4×C5×D3C213yesmaximal
2C32×C42×C5C211yesmaximal, characteristic, complemented
3C3×C4×C5×Dic3C213yesmaximal, complemented
4C2×C3×C42×C5—31nomaximal
5C42×C5×D3C311yesmaximal, characteristic, direct product factor
6C22×C3×C5×D3C2211yescharacteristic
7C2×C32×C4×C5C2213yes—
8C2×C3×C5×Dic3C2213yes—
9C3×C4×C5×D3C4112yesdirect product factor
10C3×C42×D3C511yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C4×C5—33no—
12C2×C4×C5×D3C2×C313yes—
13C3×C42×C5—21no—
14C3×C42×C5—33no—
15C3×C42×C5D311yescharacteristic, direct product factor
16C3×C42×C5C2×C311yescharacteristic, complemented
17C4×C5×Dic3C2×C313yescomplemented
18C22×C32×C5C2311yescharacteristic
19C2×C3×C5×D3C2×C416yes—
20C32×C4×C5C2×C416yescomplemented
21C3×C5×Dic3C2×C416yescomplemented
22C2×C42×C5—31noHall
23C2×C3×C4×D3C2×C513yes—
24C32×C42C2×C511yescharacteristic, complemented
25C3×C4×Dic3C2×C513yescomplemented
26C23×C3×C5—31no—
27C22×C5×D3C22×C311yescharacteristic
28C2×C3×C4×C5—23no—
29C2×C3×C4×C5—33no—
30C2×C3×C4×C5—312no—
31C2×C3×C4×C5C2×D313yes—
32C2×C3×C4×C5C22×C313yes—
33C2×C5×Dic3C22×C313yes—
34C4×C5×D3C3×C4112yesdirect product factor
35C2×C3×C42—31no—
36C42×D3C3×C511yescharacteristic, direct product factor
37C2×C32×C5C22×C413yes—
38C3×C5×D3C4214yesdirect product factor
39C22×C4×C5—33no—
40C42×C5—33no—
41C42×C5C3×D311yescharacteristic, direct product factor
42C22×C3×D3C22×C511yescharacteristic
43C2×C32×C4C22×C513yes—
44C2×C3×Dic3C22×C513yes—
45C3×C4×D3C4×C5112yesdirect product factor
46C22×C3×C5—21no—
47C22×C3×C5—36no—
48C22×C3×C5C22×D311yescharacteristic
49C22×C3×C5C23×C311yescharacteristic
50C2×C5×D3C2×C3×C416yes—
51C3×C4×C5—26no—
52C3×C4×C5—36no—
53C3×C4×C5C4×D316yesdirect product factor
54C3×C4×C5C2×C3×C416yescomplemented
55C5×Dic3C2×C3×C416yescomplemented
56C22×C3×C4—33no—
57C2×C4×D3C2×C3×C513yes—
58C3×C42—21no—
59C3×C42—33no—
60C3×C42C5×D311yescharacteristic, direct product factor
61C3×C42C2×C3×C511yescharacteristic, complemented
62C4×Dic3C2×C3×C513yescomplemented
63C32×C5C2×C4211yescharacteristic, complemented, Hall
64C23×C5—31no—
65C2×C4×C5—33no—
66C2×C4×C5—312no—
67C2×C4×C5C2×C3×D313yes—
68C22×C32C23×C511yescharacteristic
69C2×C3×D3C2×C4×C516yes—
70C32×C4C2×C4×C516yescomplemented
71C3×Dic3C2×C4×C516yescomplemented
72C2×C42—31noSylow
73C2×C3×C5—23no—
74C2×C3×C5—34no—
75C2×C3×C5C2×C4×D313yes—
76C2×C3×C5C22×C3×C413yes—
77C5×D3C3×C4214yesdirect product factor
78C23×C3—31no—
79C22×D3C22×C3×C511yescharacteristic
80C2×C3×C4—23no—
81C2×C3×C4—33no—
82C2×C3×C4—312no—
83C2×C3×C4C2×C5×D313yes—
84C2×C3×C4C22×C3×C513yes—
85C2×Dic3C22×C3×C513yes—
86C4×D3C3×C4×C5112yesdirect product factor
87C22×C5—36no—
88C22×C5C22×C3×D311yescharacteristic
89C4×C5—36no—
90C4×C5C3×C4×D316yesdirect product factor
91C2×C32C22×C4×C513yes—
92C3×D3C42×C514yesdirect product factor
93C22×C4—33no—
94C42—33no—
95C42C3×C5×D311yescharacteristic, direct product factor
96C3×C5—21no—
97C3×C5C42×D311yescharacteristic, direct product factor
98C3×C5C2×C3×C4211yescharacteristic, complemented
99C22×C3—21no—
100C22×C3—36no—
101C22×C3C22×C5×D311yescharacteristic
102C22×C3C23×C3×C511yescharacteristic
103C2×D3C2×C3×C4×C516yes—
104C3×C4—26no—
105C3×C4—36no—
106C3×C4C4×C5×D316yesdirect product factor
107C3×C4C2×C3×C4×C516yescomplemented
108Dic3C2×C3×C4×C516yescomplemented
109C2×C5—34no—
110C2×C5C2×C3×C4×D313yes—
111C32C2×C42×C511yescharacteristic, complemented, Sylow
112C23—31no—
113C2×C4—33no—
114C2×C4—312no—
115C2×C4C2×C3×C5×D313yes—
116C2×C3—23no—
117C2×C3—34no—
118C2×C3C2×C4×C5×D313yes—
119C2×C3C22×C3×C4×C513yes—
120D3C3×C42×C514yesdirect product factor
121C5C3×C42×D311yescharacteristic, direct product factor, Sylow
122C22—36no—
123C22C22×C3×C5×D311yescharacteristic
124C4—36no—
125C4C3×C4×C5×D316yesdirect product factor
126C3—21no—
127C3C42×C5×D311yescharacteristic, direct product factor
128C3C2×C3×C42×C511yescharacteristic, complemented
129C2—34no—
130C2C2×C3×C4×C5×D313yes—
subgroupG/H
center, hypercenterC3×C42×C5D3
commutator, hypocenterC3C2×C3×C42×C5
FrattiniC22C22×C3×C5×D3
FittingC32×C42×C5C2
socleC22×C32×C5C23
prime radicalC22×C3×C5×D3C22
cosocleC22×C3C23×C3×C5
LCSG ▷ C3
UCSC1 ◁ C3×C42×C5

Complements

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

NH ≅ G/Ntype
2. C32×C42×C5C2semidirect
3. C3×C4×C5×Dic3C2semidirect
5. C42×C5×D3C3direct (N × H)
9. C3×C4×C5×D3C4direct (N × H)
10. C3×C42×D3C5direct (N × H)
15. C3×C42×C5D3direct (N × H)
16. C3×C42×C5C2×C3semidirect
17. C4×C5×Dic3C2×C3semidirect
20. C32×C4×C5C2×C4semidirect
21. C3×C5×Dic3C2×C4semidirect
24. C32×C42C2×C5semidirect
25. C3×C4×Dic3C2×C5semidirect
34. C4×C5×D3C3×C4direct (N × H)
36. C42×D3C3×C5direct (N × H)
38. C3×C5×D3C42direct (N × H)
41. C42×C5C3×D3direct (N × H)
45. C3×C4×D3C4×C5direct (N × H)
53. C3×C4×C5C4×D3direct (N × H)
54. C3×C4×C5C2×C3×C4semidirect
55. C5×Dic3C2×C3×C4semidirect
60. C3×C42C5×D3direct (N × H)
61. C3×C42C2×C3×C5semidirect
62. C4×Dic3C2×C3×C5semidirect
63. C32×C5C2×C42semidirect
70. C32×C4C2×C4×C5semidirect
71. C3×Dic3C2×C4×C5semidirect
77. C5×D3C3×C42direct (N × H)
86. C4×D3C3×C4×C5direct (N × H)
90. C4×C5C3×C4×D3direct (N × H)
92. C3×D3C42×C5direct (N × H)
95. C42C3×C5×D3direct (N × H)
97. C3×C5C42×D3direct (N × H)
98. C3×C5C2×C3×C42semidirect
106. C3×C4C4×C5×D3direct (N × H)
107. C3×C4C2×C3×C4×C5semidirect
108. Dic3C2×C3×C4×C5semidirect
111. C32C2×C42×C5semidirect
120. D3C3×C42×C5direct (N × H)
121. C5C3×C42×D3direct (N × H)
125. C4C3×C4×C5×D3direct (N × H)
127. C3C42×C5×D3direct (N × H)
128. C3C2×C3×C42×C5semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D32
C32×C42×C52
C3×C4×C5×Dic32
C2×C3×C42×C53
C42×C5×D33
C3×C42×D35