Finite Group Databasebeta

← C13×#10624890 #23745041

Subgroups — C13×#10624890 #23745041

Order 9477.

620 conjugacy classes of subgroups; only the 440 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 440 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
1C13×#6899C3118yesmaximal, complemented
2C13×#6898C319yesmaximal, complemented
3C13×#6894C316yesmaximal, complemented
4C13×#6891C312yesmaximal
5C13×#6891C311yesmaximal, characteristic
6C9×C13×3−1+2C313yesmaximal, complemented
7C3×C13×C32⋊C9C311yesmaximal, characteristic
8C34×C13C3211yescharacteristic
9C3×C13×3−1+2C3213yes—
10C3×C13×3−1+2C3216yes—
11C32×C9×C13C3211yescharacteristic
12C32×C9×C13C3212yes—
13C13×C9⋊C9C32118yescomplemented
14C13×C9⋊C9C32154yescomplemented
15C13×C32⋊C9C3213yes—
16C13×C32⋊C9C3216yes—
17C13×C32⋊C9C3216yes—
18C13×C32⋊C9C3213yes—
19C13×C32⋊C9C3216yes—
20C13×C32⋊C9C3216yes—
21C13×C32⋊C9C3216yes—
22C92×C13C3219yescomplemented
23#10624890C1311yesmaximal, characteristic, direct product factor, Sylow
24C33×C13—33no—
25C33×C13—91no—
26C33×C13—92no—
27C33×C13C3311yescharacteristic
28C33×C13C3312yes—
29C33×C13C3311yescharacteristic
30C13×3−1+2—39no—
31C13×3−1+2—96no—
32C3×C9×C13—91no—
33C3×C9×C13—92no—
34C3×C9×C13C3313yes—
35C3×C9×C13C3319yes—
36C3×C9×C13C33118yes—
37C3×C9×C13C3316yes—
38#6899C3×C13118yescomplemented
39#6898C3×C1319yescomplemented
40#6894C3×C1316yescomplemented
41#6891C3×C1312yes—
42#6891C3×C1311yescharacteristic
43C9×3−1+2C3×C1313yescomplemented
44C3×C32⋊C9C3×C1311yescharacteristic
45C32×C13—31no—
46C32×C13—32no—
47C32×C13—31no—
48C32×C13—32no—
49C32×C13—32no—
50C32×C13—31no—
51C32×C13—32no—
52C32×C13—32no—
53C32×C13—32no—
54C32×C13—99no—
55C32×C13#73713yes—
56C32×C13C3411yescharacteristic
57C9×C13—39no—
58C9×C13—33no—
59C9×C13—36no—
60C9×C13—318no—
61C34C32×C1311yescharacteristic
62C3×3−1+2C32×C1313yes—
63C3×3−1+2C32×C1316yes—
64C32×C9C32×C1311yescharacteristic
65C32×C9C32×C1312yes—
66C9⋊C9C32×C13118yescomplemented
67C9⋊C9C32×C13154yescomplemented
68C32⋊C9C32×C1313yes—
69C32⋊C9C32×C1316yes—
70C32⋊C9C32×C1316yes—
71C32⋊C9C32×C1313yes—
72C32⋊C9C32×C1316yes—
73C32⋊C9C32×C1316yes—
74C32⋊C9C32×C1316yes—
75C92C32×C1319yescomplemented
76C3×C13—33no—
77C3×C13—92no—
78C3×C13—91no—
79C3×C13C3×#73711yescharacteristic
80C3×C133−1+411yescharacteristic
81C3×C133−1+412yes—
82C33—33no—
83C33—91no—
84C33—92no—
85C33C33×C1311yescharacteristic
86C33C33×C1312yes—
87C33C33×C1311yescharacteristic
883−1+2—39no—
893−1+2—96no—
90C3×C9—91no—
91C3×C9—92no—
92C3×C9C33×C1313yes—
93C3×C9C33×C1319yes—
94C3×C9C33×C13118yes—
95C3×C9C33×C1316yes—
96C13#1062489011yescharacteristic, direct product factor, Sylow
97C32—31no—
98C32—32no—
99C32—31no—
100C32—32no—
101C32—32no—
102C32—31no—
103C32—32no—
104C32—32no—
105C32—32no—
106C32—99no—
107C32C13×#73713yes—
108C32C34×C1311yescharacteristic
109C9—39no—
110C9—33no—
111C9—36no—
112C9—318no—
113C3—33no—
114C3—92no—
115C3—91no—
116C3C3×C13×#73711yescharacteristic
117C3C13×3−1+411yescharacteristic
118C3C13×3−1+412yes—
subgroupG/H
center, socleC32×C13C34
commutator, Frattini, cosocleC32C34×C13
prime radicalC34×C13C32
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#6899C3semidirect
2. C13×#6898C3semidirect
3. C13×#6894C3semidirect
6. C9×C13×3−1+2C3semidirect
13. C13×C9⋊C9C32semidirect
14. C13×C9⋊C9C32semidirect
22. C92×C13C32semidirect
23. #10624890C13direct (N × H)
38. #6899C3×C13semidirect
39. #6898C3×C13semidirect
40. #6894C3×C13semidirect
43. C9×3−1+2C3×C13semidirect
66. C9⋊C9C32×C13semidirect
67. C9⋊C9C32×C13semidirect
75. C92C32×C13semidirect
96. C13#10624890direct (N × H)