Finite Group Databasebeta

← C13×#10624889 #23745040

Subgroups — C13×#10624889 #23745040

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×#6897C3118yesmaximal, complemented
2C13×#6896C319yesmaximal, 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⋊C9C32112yes—
21C92×C13C3219yescomplemented
22#10624889C1311yesmaximal, characteristic, direct product factor, Sylow
23C33×C13—33no—
24C33×C13—91no—
25C33×C13—92no—
26C33×C13C3312yes—
27C33×C13C3311yescharacteristic
28C33×C13C3311yescharacteristic
29C13×3−1+2—39no—
30C13×3−1+2—96no—
31C3×C9×C13—91no—
32C3×C9×C13—92no—
33C3×C9×C13C3313yes—
34C3×C9×C13C3319yes—
35C3×C9×C13C33118yes—
36C3×C9×C13C3316yes—
37#6897C3×C13118yescomplemented
38#6896C3×C1319yescomplemented
39#6894C3×C1316yescomplemented
40#6891C3×C1312yes—
41#6891C3×C1311yescharacteristic
42C9×3−1+2C3×C1313yescomplemented
43C3×C32⋊C9C3×C1311yescharacteristic
44C32×C13—31no—
45C32×C13—32no—
46C32×C13—32no—
47C32×C13—31no—
48C32×C13—32no—
49C32×C13—32no—
50C32×C13—34no—
51C32×C13—31no—
52C32×C13—99no—
53C32×C13#73713yes—
54C32×C13C3411yescharacteristic
55C9×C13—39no—
56C9×C13—33no—
57C9×C13—36no—
58C9×C13—318no—
59C34C32×C1311yescharacteristic
60C3×3−1+2C32×C1313yes—
61C3×3−1+2C32×C1316yes—
62C32×C9C32×C1311yescharacteristic
63C32×C9C32×C1312yes—
64C9⋊C9C32×C13118yescomplemented
65C9⋊C9C32×C13154yescomplemented
66C32⋊C9C32×C1313yes—
67C32⋊C9C32×C1316yes—
68C32⋊C9C32×C1316yes—
69C32⋊C9C32×C1313yes—
70C32⋊C9C32×C1316yes—
71C32⋊C9C32×C13112yes—
72C92C32×C1319yescomplemented
73C3×C13—33no—
74C3×C13—91no—
75C3×C13—92no—
76C3×C13C3×#73711yescharacteristic
77C3×C133−1+411yescharacteristic
78C3×C133−1+412yes—
79C33—33no—
80C33—91no—
81C33—92no—
82C33C33×C1312yes—
83C33C33×C1311yescharacteristic
84C33C33×C1311yescharacteristic
853−1+2—39no—
863−1+2—96no—
87C3×C9—91no—
88C3×C9—92no—
89C3×C9C33×C1313yes—
90C3×C9C33×C1319yes—
91C3×C9C33×C13118yes—
92C3×C9C33×C1316yes—
93C13#1062488911yescharacteristic, direct product factor, Sylow
94C32—31no—
95C32—32no—
96C32—32no—
97C32—31no—
98C32—32no—
99C32—32no—
100C32—34no—
101C32—31no—
102C32—99no—
103C32C13×#73713yes—
104C32C34×C1311yescharacteristic
105C9—39no—
106C9—33no—
107C9—36no—
108C9—318no—
109C3—33no—
110C3—91no—
111C3—92no—
112C3C3×C13×#73711yescharacteristic
113C3C13×3−1+411yescharacteristic
114C3C13×3−1+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×#6897C3semidirect
2. C13×#6896C3semidirect
3. C13×#6894C3semidirect
6. C9×C13×3−1+2C3semidirect
13. C13×C9⋊C9C32semidirect
14. C13×C9⋊C9C32semidirect
21. C92×C13C32semidirect
22. #10624889C13direct (N × H)
37. #6897C3×C13semidirect
38. #6896C3×C13semidirect
39. #6894C3×C13semidirect
42. C9×3−1+2C3×C13semidirect
64. C9⋊C9C32×C13semidirect
65. C9⋊C9C32×C13semidirect
72. C92C32×C13semidirect
93. C13#10624889direct (N × H)