Finite Group Databasebeta

← C2×D4×D15 #92093

Subgroups — C2×D4×D15 #92093

Order 480.

472 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 135 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×D15C212yesmaximal, complemented
2C2×C3×C5×D4C211yesmaximal, characteristic, complemented
3C2×#1220C212yesmaximal, complemented
4D4×D15C218yesmaximal, direct product factor
5C2×D60C211yesmaximal, characteristic, complemented
6C2×C4×D15C211yesmaximal, characteristic, complemented
7C2×D4×D5—31nomaximal, Hall
8C23×C3×C5C2212yescomplemented
9C22×D15—28no—
10C22×D15C2211yescharacteristic
11C22×D15C2218yescomplemented
12C22×D15C2212yescomplemented
13C3×C5×D4C2214yescomplemented
14C2×C3×C4×C5C2211yescharacteristic, complemented
15#1220C2218yescomplemented
16C2×Dic15C2211yescharacteristic, complemented
17D60C2214yescomplemented
18C4×D15C2214yescomplemented
19C2×D3×D4—51nomaximal, Hall
20C23×D5—32no—
21C2×C5×D4D311yescharacteristic, complemented
22C2×C22⋊D5—32no—
23D4×D5—38no—
24C2×D20—31no—
25C2×C4×D5—31no—
26C22×C3×C5—24no—
27C22×C3×C5C2311yescharacteristic
28C22×C3×C5C2314yescomplemented
29C2×D15—24no—
30C2×D15—216no—
31C2×D15D414yesdirect product factor
32C2×D15C2312yes—
33C2×D15C2314yescomplemented
34C3×C4×C5C2312yescomplemented
35Dic15C2312yescomplemented
36C23×D3—52no—
37C2×C3×D4D511yescharacteristic, complemented
38C2×#67—52no—
39D3×D4—58no—
40C2×D12—51no—
41C2×C4×D3—51no—
42C23×C5C2×D312yescomplemented
43C22×D5—31no—
44C22×D5—32no—
45C22×D5—38no—
46C22×D5—68no—
47C5×D4C2×D314yescomplemented
48C2×C4×C5C2×D311yescharacteristic, complemented
49C22⋊D5—38no—
50C2×Dic5—31no—
51D20—34no—
52C4×D5—34no—
53C22×D4—151noSylow
54C2×C3×C5—24no—
55C2×C3×C5C2×D412yescomplemented
56C2×C3×C5C2411yescharacteristic
57D15—24no—
58D15C2×D414yesdirect product factor
59C23×C3C2×D512yescomplemented
60C22×D3—51no—
61C22×D3—52no—
62C22×D3—58no—
63C22×D3—108no—
64C3×D4C2×D514yescomplemented
65C2×C3×C4C2×D511yescharacteristic, complemented
66#67—58no—
67C2×Dic3—51no—
68D12—54no—
69C4×D3—54no—
70C22×C5—24no—
71C22×C5C22×D311yescharacteristic
72C22×C5C22×D314yescomplemented
73C2×D5—34no—
74C2×D5—32no—
75C2×D5—34no—
76C2×D5—616no—
77C2×D5—64no—
78C4×C5C22×D312yescomplemented
79Dic5—32no—
80C24—152no—
81C2×D4—152no—
82C2×D4—158no—
83C2×D4—151no—
84C2×D4D1511yescharacteristic, direct product factor
85C22×C4—151no—
86C3×C5C22×D411yescharacteristic, complemented, Hall
87C22×C3—24no—
88C22×C3C22×D511yescharacteristic
89C22×C3C22×D514yescomplemented
90C2×D3—54no—
91C2×D3—52no—
92C2×D3—54no—
93C2×D3—1016no—
94C2×D3—104no—
95C3×C4C22×D512yescomplemented
96Dic3—52no—
97C2×C5—24no—
98C2×C5D3×D412yescomplemented
99C2×C5C23×D311yescharacteristic
100D5—34no—
101D5—64no—
102C23—151no—
103C23—152no—
104C23—158no—
105C23—308no—
106C23C2×D1512yescomplemented
107D4—158no—
108D4—154no—
109D4C2×D1514yesdirect product factor
110C2×C4—151no—
111C2×C4—154no—
112C2×C4C2×D1511yescharacteristic, complemented
113C2×C3—24no—
114C2×C3D4×D512yescomplemented
115C2×C3C23×D511yescharacteristic
116D3—54no—
117D3—104no—
118C5C2×D3×D411yescharacteristic, complemented, Sylow
119C22—24no—
120C22—154no—
121C22—152no—
122C22—154no—
123C22—3016no—
124C22—304no—
125C22C22×D1511yescharacteristic
126C22C22×D1514yescomplemented
127C4—152no—
128C4C22×D1512yescomplemented
129C3C2×D4×D511yescharacteristic, complemented, Sylow
130C2—24no—
131C2—154no—
132C2—304no—
133C2D4×D1512yesdirect product factor
134C2C23×D1511yescharacteristic
subgroupG/H
centerC22C22×D15
commutator, cosocleC2×C3×C5C24
FrattiniC2C23×D15
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×D4D15
hypocenterC3×C5C22×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C23×D15C2semidirect
2. C2×C3×C5×D4C2semidirect
3. C2×#1220C2semidirect
4. D4×D15C2direct (N × H)
5. C2×D60C2semidirect
6. C2×C4×D15C2semidirect
8. C23×C3×C5C22semidirect
11. C22×D15C22semidirect
12. C22×D15C22semidirect
13. C3×C5×D4C22semidirect
14. C2×C3×C4×C5C22semidirect
15. #1220C22semidirect
16. C2×Dic15C22semidirect
17. D60C22semidirect
18. C4×D15C22semidirect
21. C2×C5×D4D3semidirect
28. C22×C3×C5C23semidirect
31. C2×D15D4direct (N × H)
33. C2×D15C23semidirect
34. C3×C4×C5C23semidirect
35. Dic15C23semidirect
37. C2×C3×D4D5semidirect
42. C23×C5C2×D3semidirect
47. C5×D4C2×D3semidirect
48. C2×C4×C5C2×D3semidirect
55. C2×C3×C5C2×D4semidirect
58. D15C2×D4direct (N × H)
59. C23×C3C2×D5semidirect
64. C3×D4C2×D5semidirect
65. C2×C3×C4C2×D5semidirect
72. C22×C5C22×D3semidirect
78. C4×C5C22×D3semidirect
84. C2×D4D15direct (N × H)
86. C3×C5C22×D4semidirect
89. C22×C3C22×D5semidirect
95. C3×C4C22×D5semidirect
98. C2×C5D3×D4semidirect
106. C23C2×D15semidirect
109. D4C2×D15direct (N × H)
112. C2×C4C2×D15semidirect
114. C2×C3D4×D5semidirect
118. C5C2×D3×D4semidirect
126. C22C22×D15semidirect
128. C4C22×D15semidirect
129. C3C2×D4×D5semidirect
133. C2D4×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D152
C2×C3×C5×D42
C2×#12202
D4×D152
C2×D602
C2×C4×D152
C2×D4×D53
C2×D3×D45