Finite Group Databasebeta

← C9×D5×C11×D13 #38787873

Subgroups — C9×D5×C11×D13 #38787873

Order 25740.

120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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
1C9×C11×D65C211yesmaximal, characteristic, complemented
2C9×D5×C11×C13C211yesmaximal, characteristic, complemented
3C5×C9×C11×D13C211yesmaximal, characteristic, complemented
4C3×D5×C11×D13C311yesmaximal, characteristic
5C5×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C9×C11×D13—51nomaximal, Hall
7C3×C11×D65C2×C311yescharacteristic
8C3×D5×C11×C13C2×C311yescharacteristic
9C3×C5×C11×D13C2×C311yescharacteristic
10D5×C11×D13C911yescharacteristic, direct product factor, Hall
11C9×C11×D13—51no—
12C9×C11×D13D511yescharacteristic, direct product factor
13C2×C9×C11×C13—51no—
14C9×D5×D13C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C22×C311yescharacteristic
16C2×C9×D5×C11—131nomaximal, Hall
17C2×C3×C11×D13—51no—
18C11×D65C2×C911yescharacteristic, complemented
19D5×C11×C13C2×C911yescharacteristic, complemented
20C5×C11×D13C2×C911yescharacteristic, complemented
21C9×C11×C13C2×D511yescharacteristic, complemented, Hall
22C9×D65C2×C1111yescharacteristic, complemented
23C9×D5×C13C2×C1111yescharacteristic, complemented
24C5×C9×D13C2×C1111yescharacteristic, complemented
25C2×C5×C9×C11—131no—
26C9×D5×C11—131no—
27C9×D5×C11D1311yescharacteristic, direct product factor
28C2×C3×C11×C13—51no—
29C3×C11×D13—51no—
30C3×C11×D13C3×D511yescharacteristic
31C3×D5×D13C3×C1111yescharacteristic
32C5×C11×C13C22×C911yescharacteristic, complemented, Hall
33C2×C3×D5×C11—131no—
34C5×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C2×C11×D13—51noHall
36C5×C9×C11C2×D1311yescharacteristic, complemented, Hall
37C2×C9×D13—51noHall
38C3×C11×C13C2×C3×D511yescharacteristic
39C22×C9×C11—651noHall
40C3×D65C2×C3×C1111yescharacteristic
41C3×D5×C13C2×C3×C1111yescharacteristic
42C3×C5×D13C2×C3×C1111yescharacteristic
43C2×C3×C5×C11—131no—
44C3×D5×C11—131no—
45C3×D5×C11C3×D1311yescharacteristic
46C2×C11×C13—51no—
47C11×D13—51no—
48C11×D13C9×D511yescharacteristic, direct product factor
49D5×D13C9×C1111yescharacteristic, direct product factor, Hall
50C2×C9×C13—51no—
51C9×D13—51no—
52C9×D13D5×C1111yescharacteristic, direct product factor
53C2×D5×C11—131noHall
54C2×C9×C11—51no—
55C2×C9×C11—131no—
56C2×C9×C11—651no—
57C3×C5×C13C22×C3×C1111yescharacteristic
58C2×C9×D5—131noHall
59C3×C5×C11C2×C3×D1311yescharacteristic
60C2×C3×D13—51no—
61C11×C13C2×C9×D511yescharacteristic, complemented, Hall
62C22×C3×C11—651no—
63D65C2×C9×C1111yescharacteristic, complemented
64C5×D13C2×C9×C1111yescharacteristic, complemented
65D5×C13C2×C9×C1111yescharacteristic, complemented
66C9×C13C2×D5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—131no—
68D5×C11—131no—
69D5×C11C9×D1311yescharacteristic, direct product factor
70C9×C11D5×D1311yescharacteristic, direct product factor, Hall
71C2×C5×C9—131no—
72C9×D5—131no—
73C9×D5C11×D1311yescharacteristic, direct product factor
74C2×C3×C13—51no—
75C3×D13—51no—
76C3×D13C3×D5×C1111yescharacteristic
77C2×C3×C11—51no—
78C2×C3×C11—131no—
79C2×C3×C11—651no—
80C5×C13C22×C9×C1111yescharacteristic, complemented, Hall
81C2×C3×D5—131no—
82C5×C11C2×C9×D1311yescharacteristic, complemented, Hall
83C2×D13—51noHall
84C5×C9C2×C11×D1311yescharacteristic, complemented, Hall
85C22×C11—651noHall
86C3×C13C2×C3×D5×C1111yescharacteristic
87C22×C9—651noHall
88C3×C11C3×D5×D1311yescharacteristic
89C2×C3×C5—131no—
90C3×D5—131no—
91C3×D5C3×C11×D1311yescharacteristic
92C2×C13—51no—
93D13—51no—
94D13C9×D5×C1111yescharacteristic, direct product factor
95C2×C11—51no—
96C2×C11—131no—
97C2×C11—651no—
98C2×D5—131noHall
99C2×C9—51no—
100C2×C9—131no—
101C2×C9—651no—
102C3×C5C2×C3×C11×D1311yescharacteristic
103C13C2×C9×D5×C1111yescharacteristic, complemented, Sylow
104C22×C3—651no—
105C11C9×D5×D1311yescharacteristic, direct product factor, Sylow
106C2×C5—131no—
107D5—131no—
108D5C9×C11×D1311yescharacteristic, direct product factor
109C9D5×C11×D1311yescharacteristic, direct product factor, Sylow
110C2×C3—51no—
111C2×C3—131no—
112C2×C3—651no—
113C5C2×C9×C11×D1311yescharacteristic, complemented, Sylow
114C22—651noSylow
115C3C3×D5×C11×D1311yescharacteristic
116C2—51no—
117C2—131no—
118C2—651no—
subgroupG/H
center, hypercenterC9×C11D5×D13
commutator, hypocenterC5×C13C22×C9×C11
FrattiniC3C3×D5×C11×D13
FittingC5×C9×C11×C13C22
socleC3×C5×C11×C13C22×C3
prime radicalC3×D5×C11×D13C3
cosocleC3×C5×C13C22×C3×C11
LCSG ▷ C5×C13
UCSC1 ◁ C9×C11

Complements

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

NH ≅ G/Ntype
1. C9×C11×D65C2semidirect
2. C9×D5×C11×C13C2semidirect
3. C5×C9×C11×D13C2semidirect
5. C5×C9×C11×C13C22semidirect
10. D5×C11×D13C9direct (N × H)
12. C9×C11×D13D5direct (N × H)
14. C9×D5×D13C11direct (N × H)
18. C11×D65C2×C9semidirect
19. D5×C11×C13C2×C9semidirect
20. C5×C11×D13C2×C9semidirect
21. C9×C11×C13C2×D5semidirect
22. C9×D65C2×C11semidirect
23. C9×D5×C13C2×C11semidirect
24. C5×C9×D13C2×C11semidirect
27. C9×D5×C11D13direct (N × H)
32. C5×C11×C13C22×C9semidirect
34. C5×C9×C13C22×C11semidirect
36. C5×C9×C11C2×D13semidirect
48. C11×D13C9×D5direct (N × H)
49. D5×D13C9×C11direct (N × H)
52. C9×D13D5×C11direct (N × H)
61. C11×C13C2×C9×D5semidirect
63. D65C2×C9×C11semidirect
64. C5×D13C2×C9×C11semidirect
65. D5×C13C2×C9×C11semidirect
66. C9×C13C2×D5×C11semidirect
69. D5×C11C9×D13direct (N × H)
70. C9×C11D5×D13direct (N × H)
73. C9×D5C11×D13direct (N × H)
80. C5×C13C22×C9×C11semidirect
82. C5×C11C2×C9×D13semidirect
84. C5×C9C2×C11×D13semidirect
94. D13C9×D5×C11direct (N × H)
103. C13C2×C9×D5×C11semidirect
105. C11C9×D5×D13direct (N × H)
108. D5C9×C11×D13direct (N × H)
109. C9D5×C11×D13direct (N × H)
113. C5C2×C9×C11×D13semidirect

Maximal subgroups

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

subgroupindex
C9×C11×D652
C9×D5×C11×C132
C5×C9×C11×D132
C3×D5×C11×D133
C2×C9×C11×D135
C9×D5×D1311
C2×C9×D5×C1113