Finite Group Databasebeta

← C13×#10624897 #23745048

Subgroups — C13×#10624897 #23745048

Order 9477.

950 conjugacy classes of subgroups; only the 482 normal subgroups are shown.

normal subgroups only

This group has 950 conjugacy classes of subgroups — too many to draw. Only its 482 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
1C32×C13×H(3,𝔽3)C311yesmaximal, characteristic
2C13×C9⋊H(3,𝔽3)C3124yesmaximal, complemented
3C13×#6891C318yesmaximal, complemented
4C9×C13×H(3,𝔽3)C313yesmaximal, complemented
5C3×C13×C32⋊C9C314yesmaximal, complemented
6C34×C13C3214yes—
7C3×C13×3−1+2C32124yescomplemented
8C3×C13×H(3,𝔽3)—39no—
9C3×C13×H(3,𝔽3)C3218yes—
10C3×C13×H(3,𝔽3)C3211yescharacteristic
11C32×C9×C13C32112yescomplemented
12C13×C32⋊C9C3211yescharacteristic
13C13×C32⋊C9C3218yes—
14C13×C32⋊C9C32124yescomplemented
15C13×C32⋊C9C32124yescomplemented
16C13×C32⋊C9C32124yescomplemented
17#10624897C1311yesmaximal, characteristic, direct product factor, Sylow
18C33×C13—312no—
19C33×C13—312no—
20C33×C13—94no—
21C33×C13—94no—
22C33×C13C3318yes—
23C33×C13C3314yes—
24C33×C13C3311yescharacteristic
25C13×3−1+2—924no—
26C13×H(3,𝔽3)—324no—
27C13×H(3,𝔽3)3−1+219yescomplemented
28C3×C9×C13—912no—
29C3×C9×C13C3313yes—
30C3×C9×C13C33124yes—
31C32×H(3,𝔽3)C3×C1311yescharacteristic
32C9⋊H(3,𝔽3)C3×C13124yescomplemented
33#6891C3×C1318yescomplemented
34C9×H(3,𝔽3)C3×C1313yescomplemented
35C3×C32⋊C9C3×C1314yescomplemented
36C32×C13—31no—
37C32×C13—34no—
38C32×C13—34no—
39C32×C13—31no—
40C32×C13—31no—
41C32×C13—34no—
42C32×C13—38no—
43C32×C13—38no—
44C32×C13—38no—
45C32×C13—38no—
46C32×C13—936no—
47C32×C13C3×3−1+2112yes—
48C32×C13#73713yes—
49C32×C13C3411yescharacteristic
50C9×C13—33no—
51C9×C13—324no—
52C34C32×C1314yes—
53C3×3−1+2C32×C13124yescomplemented
54C3×H(3,𝔽3)—39no—
55C3×H(3,𝔽3)C32×C1318yes—
56C3×H(3,𝔽3)C32×C1311yescharacteristic
57C32×C9C32×C13112yescomplemented
58C32⋊C9C32×C1311yescharacteristic
59C32⋊C9C32×C1318yes—
60C32⋊C9C32×C13124yescomplemented
61C32⋊C9C32×C13124yescomplemented
62C32⋊C9C32×C13124yescomplemented
63C3×C13—33no—
64C3×C13—312no—
65C3×C13—98no—
66C3×C13C32×3−1+211yescharacteristic
67C3×C13C3×#73711yescharacteristic
68C3×C13H(5,𝔽3)11yescharacteristic
69C3×C133−1+411yescharacteristic
70C33—312no—
71C33—312no—
72C33—94no—
73C33—94no—
74C33C33×C1318yes—
75C33C33×C1314yes—
76C33C33×C1311yescharacteristic
773−1+2—924no—
78H(3,𝔽3)—324no—
79H(3,𝔽3)C13×3−1+219yescomplemented
80C3×C9—912no—
81C3×C9C33×C1313yes—
82C3×C9C33×C13124yes—
83C13#1062489711yescharacteristic, direct product factor, Sylow
84C32—31no—
85C32—34no—
86C32—34no—
87C32—31no—
88C32—31no—
89C32—34no—
90C32—38no—
91C32—38no—
92C32—38no—
93C32—38no—
94C32—936no—
95C32C3×C13×3−1+2112yes—
96C32C13×#73713yes—
97C32C34×C1311yescharacteristic
98C9—33no—
99C9—324no—
100C3—33no—
101C3—312no—
102C3—98no—
103C3C32×C13×3−1+211yescharacteristic
104C3C3×C13×#73711yescharacteristic
105C3C13×H(5,𝔽3)11yescharacteristic
106C3C13×3−1+411yescharacteristic
subgroupG/H
center, socleC32×C13C34
commutator, Frattini, cosocleC32C34×C13
prime radicalC32×C13×H(3,𝔽3)C3
LCSG ▷ C32 ▷ C1
UCSC1 ◁ C32×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×C9⋊H(3,𝔽3)C3semidirect
3. C13×#6891C3semidirect
4. C9×C13×H(3,𝔽3)C3semidirect
5. C3×C13×C32⋊C9C3semidirect
7. C3×C13×3−1+2C32semidirect
11. C32×C9×C13C32semidirect
14. C13×C32⋊C9C32semidirect
15. C13×C32⋊C9C32semidirect
16. C13×C32⋊C9C32semidirect
17. #10624897C13direct (N × H)
27. C13×H(3,𝔽3)3−1+2semidirect
32. C9⋊H(3,𝔽3)C3×C13semidirect
33. #6891C3×C13semidirect
34. C9×H(3,𝔽3)C3×C13semidirect
35. C3×C32⋊C9C3×C13semidirect
53. C3×3−1+2C32×C13semidirect
57. C32×C9C32×C13semidirect
60. C32⋊C9C32×C13semidirect
61. C32⋊C9C32×C13semidirect
62. C32⋊C9C32×C13semidirect
79. H(3,𝔽3)C13×3−1+2semidirect
83. C13#10624897direct (N × H)