Finite Group Databasebeta

← C2×C3×D4×D5 #92063

Subgroups — C2×C3×D4×D5 #92063

Order 480.

472 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 194 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×C3×D5C212yesmaximal, complemented
2C2×C3×C5×D4C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊D5C212yesmaximal, complemented
4C3×D4×D5C218yesmaximal, direct product factor
5C2×C3×D20C211yesmaximal, characteristic, complemented
6C2×C3×C4×D5C211yesmaximal, characteristic, complemented
7C2×D4×D5C311yesmaximal, characteristic, direct product factor, Hall
8C23×C3×C5C2212yescomplemented
9C22×C3×D5—28no—
10C22×C3×D5C2211yescharacteristic
11C22×C3×D5C2218yescomplemented
12C22×C3×D5C2212yescomplemented
13C3×C5×D4C2214yescomplemented
14C2×C3×C4×C5C2211yescharacteristic, complemented
15C3×C22⋊D5C2218yescomplemented
16C2×C3×Dic5C2211yescharacteristic, complemented
17C3×D20C2214yescomplemented
18C3×C4×D5C2214yescomplemented
19C22×C3×D4—51nomaximal, Hall
20C23×D5C2×C312yescomplemented
21C2×C5×D4C2×C311yescharacteristic, complemented
22C2×C22⋊D5C2×C312yescomplemented
23D4×D5C2×C318yesdirect product factor
24C2×D20C2×C311yescharacteristic, complemented
25C2×C4×D5C2×C311yescharacteristic, complemented
26C22×C3×C5—24no—
27C22×C3×C5C2311yescharacteristic
28C22×C3×C5C2314yescomplemented
29C2×C3×D5—24no—
30C2×C3×D5—216no—
31C2×C3×D5D414yesdirect product factor
32C2×C3×D5C2312yes—
33C2×C3×D5C2314yescomplemented
34C3×C4×C5C2312yescomplemented
35C3×Dic5C2312yescomplemented
36C24×C3—52no—
37C2×C3×D4—52no—
38C2×C3×D4—58no—
39C2×C3×D4—51no—
40C2×C3×D4D511yescharacteristic, direct product factor
41C22×C3×C4—51no—
42C23×C5C22×C312yescomplemented
43C22×D5—28no—
44C22×D5C22×C311yescharacteristic
45C22×D5C22×C318yescomplemented
46C22×D5C22×C312yescomplemented
47C5×D4C22×C314yescomplemented
48C2×C4×C5C22×C311yescharacteristic, complemented
49C22⋊D5C22×C318yescomplemented
50C2×Dic5C22×C311yescharacteristic, complemented
51D20C22×C314yescomplemented
52C4×D5C22×C314yescomplemented
53C22×D4—51noSylow
54C2×C3×C5—24no—
55C2×C3×C5C2×D412yescomplemented
56C2×C3×C5C2411yescharacteristic
57C3×D5—24no—
58C3×D5C2×D414yesdirect product factor
59C23×C3—51no—
60C23×C3—52no—
61C23×C3—58no—
62C23×C3—108no—
63C23×C3C2×D512yescomplemented
64C3×D4—58no—
65C3×D4—54no—
66C3×D4C2×D514yesdirect product factor
67C2×C3×C4—51no—
68C2×C3×C4—54no—
69C2×C3×C4C2×D511yescharacteristic, complemented
70C22×C5—24no—
71C22×C5C23×C311yescharacteristic
72C22×C5C23×C314yescomplemented
73C2×D5—24no—
74C2×D5—216no—
75C2×D5C3×D414yesdirect product factor
76C2×D5C23×C312yes—
77C2×D5C23×C314yescomplemented
78C4×C5C23×C312yescomplemented
79Dic5C23×C312yescomplemented
80C24—52no—
81C2×D4—52no—
82C2×D4—58no—
83C2×D4—51no—
84C2×D4C3×D511yescharacteristic, direct product factor
85C22×C4—51no—
86C3×C5C22×D411yescharacteristic, complemented, Hall
87C22×C3—24no—
88C22×C3—54no—
89C22×C3—52no—
90C22×C3—54no—
91C22×C3—1016no—
92C22×C3—104no—
93C22×C3C22×D511yescharacteristic
94C22×C3C22×D514yescomplemented
95C3×C4—52no—
96C3×C4C22×D512yescomplemented
97C2×C5—24no—
98C2×C5C2×C3×D412yescomplemented
99C2×C5C24×C311yescharacteristic
100D5—24no—
101D5C2×C3×D414yesdirect product factor
102C23—51no—
103C23—52no—
104C23—58no—
105C23—108no—
106C23C2×C3×D512yescomplemented
107D4—58no—
108D4—54no—
109D4C2×C3×D514yesdirect product factor
110C2×C4—51no—
111C2×C4—54no—
112C2×C4C2×C3×D511yescharacteristic, complemented
113C2×C3—24no—
114C2×C3—54no—
115C2×C3—104no—
116C2×C3D4×D512yesdirect product factor
117C2×C3C23×D511yescharacteristic
118C5C22×C3×D411yescharacteristic, complemented, Sylow
119C22—24no—
120C22—54no—
121C22—52no—
122C22—54no—
123C22—1016no—
124C22—104no—
125C22C22×C3×D511yescharacteristic
126C22C22×C3×D514yescomplemented
127C4—52no—
128C4C22×C3×D512yescomplemented
129C3C2×D4×D511yescharacteristic, direct product factor, Sylow
130C2—24no—
131C2—54no—
132C2—104no—
133C2C3×D4×D512yesdirect product factor
134C2C23×C3×D511yescharacteristic
subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC2×C5C24×C3
FrattiniC2C23×C3×D5
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×C3×D4D5
hypocenterC5C22×C3×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C23×C3×D5C2semidirect
2. C2×C3×C5×D4C2semidirect
3. C2×C3×C22⋊D5C2semidirect
4. C3×D4×D5C2direct (N × H)
5. C2×C3×D20C2semidirect
6. C2×C3×C4×D5C2semidirect
7. C2×D4×D5C3direct (N × H)
8. C23×C3×C5C22semidirect
11. C22×C3×D5C22semidirect
12. C22×C3×D5C22semidirect
13. C3×C5×D4C22semidirect
14. C2×C3×C4×C5C22semidirect
15. C3×C22⋊D5C22semidirect
16. C2×C3×Dic5C22semidirect
17. C3×D20C22semidirect
18. C3×C4×D5C22semidirect
20. C23×D5C2×C3semidirect
21. C2×C5×D4C2×C3semidirect
22. C2×C22⋊D5C2×C3semidirect
23. D4×D5C2×C3direct (N × H)
24. C2×D20C2×C3semidirect
25. C2×C4×D5C2×C3semidirect
28. C22×C3×C5C23semidirect
31. C2×C3×D5D4direct (N × H)
33. C2×C3×D5C23semidirect
34. C3×C4×C5C23semidirect
35. C3×Dic5C23semidirect
40. C2×C3×D4D5direct (N × H)
42. C23×C5C22×C3semidirect
45. C22×D5C22×C3semidirect
46. C22×D5C22×C3semidirect
47. C5×D4C22×C3semidirect
48. C2×C4×C5C22×C3semidirect
49. C22⋊D5C22×C3semidirect
50. C2×Dic5C22×C3semidirect
51. D20C22×C3semidirect
52. C4×D5C22×C3semidirect
55. C2×C3×C5C2×D4semidirect
58. C3×D5C2×D4direct (N × H)
63. C23×C3C2×D5semidirect
66. C3×D4C2×D5direct (N × H)
69. C2×C3×C4C2×D5semidirect
72. C22×C5C23×C3semidirect
75. C2×D5C3×D4direct (N × H)
77. C2×D5C23×C3semidirect
78. C4×C5C23×C3semidirect
79. Dic5C23×C3semidirect
84. C2×D4C3×D5direct (N × H)
86. C3×C5C22×D4semidirect
94. C22×C3C22×D5semidirect
96. C3×C4C22×D5semidirect
98. C2×C5C2×C3×D4semidirect
101. D5C2×C3×D4direct (N × H)
106. C23C2×C3×D5semidirect
109. D4C2×C3×D5direct (N × H)
112. C2×C4C2×C3×D5semidirect
116. C2×C3D4×D5direct (N × H)
118. C5C22×C3×D4semidirect
126. C22C22×C3×D5semidirect
128. C4C22×C3×D5semidirect
129. C3C2×D4×D5direct (N × H)
133. C2C3×D4×D5direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×D52
C2×C3×C5×D42
C2×C3×C22⋊D52
C3×D4×D52
C2×C3×D202
C2×C3×C4×D52
C2×D4×D53
C22×C3×D45