Finite Group Databasebeta

← C3×C42×D15 #13087968

Subgroups — C3×C42×D15 #13087968

Order 1440.

462 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 198 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×D15C213yesmaximal
2C32×C42×C5C211yesmaximal, characteristic, complemented
3C3×C4×Dic15C213yesmaximal, complemented
4C42×D15C311yesmaximal, characteristic, direct product factor
5C3×C42×D5—31nomaximal
6C22×C3×D15C2211yescharacteristic
7C2×C32×C4×C5C2213yes—
8C2×C3×Dic15C2213yes—
9C3×C4×D15C4112yesdirect product factor
10C3×C42×D3—51nomaximal, Hall
11C2×C4×D15C2×C313yes—
12C2×C3×C4×D5—33no—
13C3×C42×C5—21no—
14C3×C42×C5D311yescharacteristic, complemented
15C3×C42×C5C2×C311yescharacteristic, complemented
16C4×Dic15C2×C313yescomplemented
17C3×C4×Dic5—33no—
18C22×C32×C5C2311yescharacteristic
19C2×C3×D15C2×C416yes—
20C32×C4×C5C2×C416yescomplemented
21C3×Dic15C2×C416yescomplemented
22C42×D5—31noHall
23C2×C3×C4×D3—53no—
24C32×C42D511yescharacteristic, complemented
25C3×C4×Dic3—53no—
26C22×D15C22×C311yescharacteristic
27C22×C3×D5—31no—
28C2×C3×C4×C5—23no—
29C2×C3×C4×C5C2×D313yes—
30C2×C3×C4×C5C22×C313yes—
31C2×Dic15C22×C313yes—
32C4×D15C3×C4112yesdirect product factor
33C2×C3×Dic5—33no—
34C3×C4×D5—312no—
35C2×C3×C42—151no—
36C42×D3—51no—
37C2×C32×C5C22×C413yes—
38C3×D15C4214yesdirect product factor
39C2×C4×D5—33no—
40C42×C5C3×D311yescharacteristic, complemented
41C4×Dic5—33no—
42C22×C3×D3—51no—
43C2×C32×C4C2×D513yes—
44C2×C3×Dic3—53no—
45C3×C4×D3—512no—
46C22×C3×C5—21no—
47C22×C3×C5C22×D311yescharacteristic
48C22×C3×C5C23×C311yescharacteristic
49C2×D15C2×C3×C416yes—
50C2×C3×D5—36no—
51C3×C4×C5—26no—
52C3×C4×C5C4×D316yescomplemented
53C3×C4×C5C2×C3×C416yescomplemented
54Dic15C2×C3×C416yescomplemented
55C3×Dic5—36no—
56C22×C3×C4—153no—
57C2×C4×D3—53no—
58C3×C42—21no—
59C3×C42—153no—
60C3×C42C3×D511yescharacteristic, complemented
61C3×C42D1511yescharacteristic, direct product factor
62C4×Dic3—53no—
63C32×C5C2×C4211yescharacteristic, complemented, Hall
64C22×D5—31no—
65C2×C4×C5C2×C3×D313yes—
66C2×Dic5—33no—
67C4×D5—312no—
68C22×C32C22×D511yescharacteristic
69C2×C3×D3—56no—
70C32×C4C4×D516yescomplemented
71C3×Dic3—56no—
72C2×C42—151noSylow
73C2×C3×C5—23no—
74C2×C3×C5C2×C4×D313yes—
75C2×C3×C5C22×C3×C413yes—
76D15C3×C4214yesdirect product factor
77C3×D5—34no—
78C23×C3—151no—
79C22×D3—51no—
80C2×C3×C4—23no—
81C2×C3×C4—153no—
82C2×C3×C4—1512no—
83C2×C3×C4C2×C3×D513yes—
84C2×C3×C4C2×D1513yes—
85C2×Dic3—53no—
86C4×D3—512no—
87C22×C5C22×C3×D311yescharacteristic
88C2×D5—36no—
89C4×C5C3×C4×D316yescomplemented
90Dic5—36no—
91C2×C32C2×C4×D513yes—
92C3×D3—54no—
93C22×C4—153no—
94C42—153no—
95C42C3×D1511yescharacteristic, direct product factor
96C3×C5—21no—
97C3×C5C42×D311yescharacteristic, complemented
98C3×C5C2×C3×C4211yescharacteristic, complemented
99C22×C3—21no—
100C22×C3—156no—
101C22×C3C22×C3×D511yescharacteristic
102C22×C3C22×D1511yescharacteristic
103C2×D3—56no—
104C3×C4—26no—
105C3×C4—156no—
106C3×C4C3×C4×D516yescomplemented
107C3×C4C4×D1516yesdirect product factor
108Dic3—56no—
109C2×C5C2×C3×C4×D313yes—
110D5—34no—
111C32C42×D511yescharacteristic, complemented, Sylow
112C23—151no—
113C2×C4—153no—
114C2×C4—1512no—
115C2×C4C2×C3×D1513yes—
116C2×C3—23no—
117C2×C3—154no—
118C2×C3C2×C3×C4×D513yes—
119C2×C3C2×C4×D1513yes—
120D3—54no—
121C5C3×C42×D311yescharacteristic, complemented, Sylow
122C22—156no—
123C22C22×C3×D1511yescharacteristic
124C4—156no—
125C4C3×C4×D1516yesdirect product factor
126C3—21no—
127C3C3×C42×D511yescharacteristic, complemented
128C3C42×D1511yescharacteristic, direct product factor
129C2—154no—
130C2C2×C3×C4×D1513yes—
subgroupG/H
center, hypercenterC3×C42D15
commutator, hypocenterC3×C5C2×C3×C42
FrattiniC22C22×C3×D15
FittingC32×C42×C5C2
socleC22×C32×C5C23
prime radicalC22×C3×D15C22
cosocleC22×C3×C5C23×C3
LCSG ▷ C3×C5
UCSC1 ◁ C3×C42

Complements

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

NH ≅ G/Ntype
2. C32×C42×C5C2semidirect
3. C3×C4×Dic15C2semidirect
4. C42×D15C3direct (N × H)
9. C3×C4×D15C4direct (N × H)
14. C3×C42×C5D3semidirect
15. C3×C42×C5C2×C3semidirect
16. C4×Dic15C2×C3semidirect
20. C32×C4×C5C2×C4semidirect
21. C3×Dic15C2×C4semidirect
24. C32×C42D5semidirect
32. C4×D15C3×C4direct (N × H)
38. C3×D15C42direct (N × H)
40. C42×C5C3×D3semidirect
52. C3×C4×C5C4×D3semidirect
53. C3×C4×C5C2×C3×C4semidirect
54. Dic15C2×C3×C4semidirect
60. C3×C42C3×D5semidirect
61. C3×C42D15direct (N × H)
63. C32×C5C2×C42semidirect
70. C32×C4C4×D5semidirect
76. D15C3×C42direct (N × H)
89. C4×C5C3×C4×D3semidirect
95. C42C3×D15direct (N × H)
97. C3×C5C42×D3semidirect
98. C3×C5C2×C3×C42semidirect
106. C3×C4C3×C4×D5semidirect
107. C3×C4C4×D15direct (N × H)
111. C32C42×D5semidirect
121. C5C3×C42×D3semidirect
125. C4C3×C4×D15direct (N × H)
127. C3C3×C42×D5semidirect
128. C3C42×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×D152
C32×C42×C52
C3×C4×Dic152
C42×D153
C3×C42×D53
C3×C42×D35