Finite Group Databasebeta

← D5×C11×C13×D9 #38787904

Subgroups — D5×C11×C13×D9 #38787904

Order 25740.

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C11×C13×D45C211yesmaximal, characteristic, complemented
2C5×C11×C13×D9C211yesmaximal, characteristic, complemented
3C9×D5×C11×C13C211yesmaximal, characteristic, complemented
4D3×D5×C11×C13—31nomaximal
5C5×C9×C11×C13C2211yescharacteristic, complemented, Hall
6C2×C11×C13×D9—51nomaximal, Hall
7C11×C13×D15—31no—
8C5×D3×C11×C13—31no—
9C3×D5×C11×C13D311yescharacteristic
10C2×D5×C11×C13—91noHall
11C11×C13×D9—51no—
12C11×C13×D9D511yescharacteristic, direct product factor
13C2×C9×C11×C13—51no—
14D5×C13×D9C1111yesmaximal, characteristic, direct product factor, Hall
15C3×C5×C11×C13C2×D311yescharacteristic
16D5×C11×D9C1311yesmaximal, characteristic, direct product factor, Hall
17C2×D3×C11×C13—151no—
18C2×C5×C11×C13—91no—
19D5×C11×C13—91no—
20D5×C11×C13D911yescharacteristic, direct product factor
21C9×C11×C13C2×D511yescharacteristic, complemented, Hall
22C13×D45C2×C1111yescharacteristic, complemented
23C5×C13×D9C2×C1111yescharacteristic, complemented
24C9×D5×C13C2×C1111yescharacteristic, complemented
25C11×D45C2×C1311yescharacteristic, complemented
26C5×C11×D9C2×C1311yescharacteristic, complemented
27C9×D5×C11C2×C1311yescharacteristic, complemented
28C2×C3×C11×C13—51no—
29D3×C11×C13—31no—
30D3×C11×C13—151no—
31D3×D5×C13—31no—
32C5×C11×C13C2×D911yescharacteristic, complemented, Hall
33D3×D5×C11—31no—
34C5×C9×C13C22×C1111yescharacteristic, complemented, Hall
35C22×C11×C13—451noHall
36C5×C9×C11C22×C1311yescharacteristic, complemented, Hall
37C2×C13×D9—51noHall
38C3×C11×C13D3×D511yescharacteristic
39C2×C11×D9—51noHall
40C13×D15—31no—
41C5×D3×C13—31no—
42C3×D5×C13D3×C1111yescharacteristic
43C11×D15—31no—
44C5×D3×C11—31no—
45C3×D5×C11D3×C1311yescharacteristic
46C2×C11×C13—51no—
47C2×C11×C13—91no—
48C2×C11×C13—451no—
49C2×D5×C13—91noHall
50C2×C9×C13—51no—
51C13×D9—51no—
52C13×D9D5×C1111yescharacteristic, direct product factor
53C2×D5×C11—91noHall
54C2×C9×C11—51no—
55C11×D9—51no—
56C11×D9D5×C1311yescharacteristic, direct product factor
57C3×C5×C13C2×D3×C1111yescharacteristic
58D5×D9C11×C1311yescharacteristic, direct product factor, Hall
59C3×C5×C11C2×D3×C1311yescharacteristic
60C2×D3×C13—151no—
61C11×C13D5×D911yescharacteristic, direct product factor, Hall
62C2×D3×C11—151no—
63C2×C5×C13—91no—
64D5×C13—91no—
65D5×C13C11×D911yescharacteristic, direct product factor
66C9×C13C2×D5×C1111yescharacteristic, complemented, Hall
67C2×C5×C11—91no—
68D5×C11—91no—
69D5×C11C13×D911yescharacteristic, direct product factor
70C9×C11C2×D5×C1311yescharacteristic, complemented, Hall
71D45C2×C11×C1311yescharacteristic, complemented
72C9×D5C2×C11×C1311yescharacteristic, complemented
73C5×D9C2×C11×C1311yescharacteristic, complemented
74C2×C3×C13—51no—
75D3×C13—31no—
76D3×C13—151no—
77C2×C3×C11—51no—
78D3×C11—31no—
79D3×C11—151no—
80C5×C13C2×C11×D911yescharacteristic, complemented, Hall
81D3×D5—31no—
82C5×C11C2×C13×D911yescharacteristic, complemented, Hall
83C22×C13—451noHall
84C5×C9C22×C11×C1311yescharacteristic, complemented, Hall
85C22×C11—451noHall
86C3×C13D3×D5×C1111yescharacteristic
87C2×D9—51noHall
88C3×C11D3×D5×C1311yescharacteristic
89D15—31no—
90C3×D5D3×C11×C1311yescharacteristic
91C5×D3—31no—
92C2×C13—51no—
93C2×C13—91no—
94C2×C13—451no—
95C2×C11—51no—
96C2×C11—91no—
97C2×C11—451no—
98C2×D5—91noHall
99C2×C9—51no—
100D9—51no—
101D9D5×C11×C1311yescharacteristic, direct product factor
102C3×C5C2×D3×C11×C1311yescharacteristic
103C13D5×C11×D911yescharacteristic, direct product factor, Sylow
104C2×D3—151no—
105C11D5×C13×D911yescharacteristic, direct product factor, Sylow
106C2×C5—91no—
107D5—91no—
108D5C11×C13×D911yescharacteristic, direct product factor
109C9C2×D5×C11×C1311yescharacteristic, complemented, Sylow
110C2×C3—51no—
111D3—31no—
112D3—151no—
113C5C2×C11×C13×D911yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×D5×C11×C1311yescharacteristic
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC11×C13D5×D9
commutator, cosocle, hypocenterC5×C9C22×C11×C13
FrattiniC3D3×D5×C11×C13
FittingC5×C9×C11×C13C22
socleC3×C5×C11×C13C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C11×C13

Complements

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

NH ≅ G/Ntype
1. C11×C13×D45C2semidirect
2. C5×C11×C13×D9C2semidirect
3. C9×D5×C11×C13C2semidirect
5. C5×C9×C11×C13C22semidirect
12. C11×C13×D9D5direct (N × H)
14. D5×C13×D9C11direct (N × H)
16. D5×C11×D9C13direct (N × H)
20. D5×C11×C13D9direct (N × H)
21. C9×C11×C13C2×D5semidirect
22. C13×D45C2×C11semidirect
23. C5×C13×D9C2×C11semidirect
24. C9×D5×C13C2×C11semidirect
25. C11×D45C2×C13semidirect
26. C5×C11×D9C2×C13semidirect
27. C9×D5×C11C2×C13semidirect
32. C5×C11×C13C2×D9semidirect
34. C5×C9×C13C22×C11semidirect
36. C5×C9×C11C22×C13semidirect
52. C13×D9D5×C11direct (N × H)
56. C11×D9D5×C13direct (N × H)
58. D5×D9C11×C13direct (N × H)
61. C11×C13D5×D9direct (N × H)
65. D5×C13C11×D9direct (N × H)
66. C9×C13C2×D5×C11semidirect
69. D5×C11C13×D9direct (N × H)
70. C9×C11C2×D5×C13semidirect
71. D45C2×C11×C13semidirect
72. C9×D5C2×C11×C13semidirect
73. C5×D9C2×C11×C13semidirect
80. C5×C13C2×C11×D9semidirect
82. C5×C11C2×C13×D9semidirect
84. C5×C9C22×C11×C13semidirect
101. D9D5×C11×C13direct (N × H)
103. C13D5×C11×D9direct (N × H)
105. C11D5×C13×D9direct (N × H)
108. D5C11×C13×D9direct (N × H)
109. C9C2×D5×C11×C13semidirect
113. C5C2×C11×C13×D9semidirect

Maximal subgroups

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

subgroupindex
C11×C13×D452
C5×C11×C13×D92
C9×D5×C11×C132
D3×D5×C11×C133
C2×C11×C13×D95
D5×C13×D911
D5×C11×D913