Finite Group Databasebeta

← C13×#1004 #11929291

Subgroups — C13×#1004 #11929291

Order 1248.

332 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 170 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
1C2×C3×D4×C13C211yesmaximal, characteristic, complemented
2C2×C13×#67C214yesmaximal, complemented
3C13×#237C214yesmaximal, complemented
4D3×D4×C13C214yesmaximal, complemented
5C13×#235C212yesmaximal, complemented
6C13×H(5,𝔽2)—31nomaximal, Hall
7C23×C3×C13C2212yescomplemented
8C22×D3×C13C2214yescomplemented
9C3×D4×C13C2214yescomplemented
10C2×C3×C4×C13C2211yescharacteristic, complemented
11C13×#67C2214yescomplemented
12C13×#67C2218yescomplemented
13C2×Dic3×C13C2214yescomplemented
14C13×D12C2212yescomplemented
15C4×D3×C13C2214yescomplemented
16C13×Dic6C2212yescomplemented
17C13×#41—34no—
18C13×#41—32no—
19C2×D4×C13—34no—
20C2×D4×C13—34no—
21C2×D4×C13D311yescharacteristic, complemented
22C22×C3×C13—42no—
23C22×C3×C13C2314yes—
24C22×C3×C13C2311yescharacteristic
25C2×D3×C13—44no—
26C2×D3×C13C2314yes—
27C3×C4×C13C2312yes—
28Dic3×C13C2314yes—
29C23×C13—34no—
30C23×C13C2×D312yescomplemented
31Q8×C13—32no—
32D4×C13—38no—
33D4×C13—34no—
34D4×C13—32no—
35D4×C13C2×D314yescomplemented
36C2×C4×C13—34no—
37C2×C4×C13—34no—
38C2×C4×C13C2×D311yescharacteristic, complemented
39#1004C1311yesmaximal, characteristic, direct product factor, Hall
40C2×C3×C13—24no—
41C2×C3×C13—21no—
42C2×C3×C13C2411yescharacteristic
43D3×C13—24no—
44C22×C13—34no—
45C22×C13—42no—
46C22×C13—124no—
47C22×C13C22×D314yes—
48C22×C13C22×D311yescharacteristic
49C4×C13—34no—
50C4×C13C22×D312yes—
51C2×C3×D4C2×C1311yescharacteristic, complemented
52C2×#67C2×C1314yescomplemented
53#237C2×C1314yescomplemented
54D3×D4C2×C1314yescomplemented
55#235C2×C1312yescomplemented
56C3×C13H(5,𝔽2)11yescharacteristic, complemented, Hall
57H(5,𝔽2)—31noSylow
58C2×C13—21no—
59C2×C13—24no—
60C2×C13—64no—
61C2×C13C23×D311yescharacteristic
62C23×C3C22×C1312yescomplemented
63C22×D3C22×C1314yescomplemented
64C3×D4C22×C1314yescomplemented
65C2×C3×C4C22×C1311yescharacteristic, complemented
66#67C22×C1314yescomplemented
67#67C22×C1318yescomplemented
68C2×Dic3C22×C1314yescomplemented
69D12C22×C1312yescomplemented
70C4×D3C22×C1314yescomplemented
71Dic6C22×C1312yescomplemented
72#41—34no—
73#41—32no—
74C2×D4—34no—
75C2×D4—34no—
76C2×D4D3×C1311yescharacteristic, complemented
77C13#100411yescharacteristic, direct product factor, Sylow
78C22×C3—42no—
79C22×C3C23×C1314yes—
80C22×C3C23×C1311yescharacteristic
81C2×D3—44no—
82C2×D3C23×C1314yes—
83C3×C4C23×C1312yes—
84Dic3C23×C1314yes—
85C23—34no—
86C23C2×D3×C1312yescomplemented
87Q8—32no—
88D4—38no—
89D4—34no—
90D4—32no—
91D4C2×D3×C1314yescomplemented
92C2×C4—34no—
93C2×C4—34no—
94C2×C4C2×D3×C1311yescharacteristic, complemented
95C2×C3—24no—
96C2×C3—21no—
97C2×C3C24×C1311yescharacteristic
98D3—24no—
99C22—34no—
100C22—42no—
101C22—124no—
102C22C22×D3×C1314yes—
103C22C22×D3×C1311yescharacteristic
104C4—34no—
105C4C22×D3×C1312yes—
106C3C13×H(5,𝔽2)11yescharacteristic, complemented, Sylow
107C2—21no—
108C2—24no—
109C2—64no—
110C2C23×D3×C1311yescharacteristic
subgroupG/H
centerC2×C13C23×D3
commutator, cosocleC2×C3C24×C13
FrattiniC2C23×D3×C13
FittingC2×C3×D4×C13C2
socleC2×C3×C13C24
hypercenterC2×D4×C13D3
hypocenterC3C13×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C2×D4×C13

Complements

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

NH ≅ G/Ntype
1. C2×C3×D4×C13C2semidirect
2. C2×C13×#67C2semidirect
3. C13×#237C2semidirect
4. D3×D4×C13C2semidirect
5. C13×#235C2semidirect
7. C23×C3×C13C22semidirect
8. C22×D3×C13C22semidirect
9. C3×D4×C13C22semidirect
10. C2×C3×C4×C13C22semidirect
11. C13×#67C22semidirect
12. C13×#67C22semidirect
13. C2×Dic3×C13C22semidirect
14. C13×D12C22semidirect
15. C4×D3×C13C22semidirect
16. C13×Dic6C22semidirect
21. C2×D4×C13D3semidirect
30. C23×C13C2×D3semidirect
35. D4×C13C2×D3semidirect
38. C2×C4×C13C2×D3semidirect
39. #1004C13direct (N × H)
51. C2×C3×D4C2×C13semidirect
52. C2×#67C2×C13semidirect
53. #237C2×C13semidirect
54. D3×D4C2×C13semidirect
55. #235C2×C13semidirect
56. C3×C13H(5,𝔽2)semidirect
62. C23×C3C22×C13semidirect
63. C22×D3C22×C13semidirect
64. C3×D4C22×C13semidirect
65. C2×C3×C4C22×C13semidirect
66. #67C22×C13semidirect
67. #67C22×C13semidirect
68. C2×Dic3C22×C13semidirect
69. D12C22×C13semidirect
70. C4×D3C22×C13semidirect
71. Dic6C22×C13semidirect
76. C2×D4D3×C13semidirect
77. C13#1004direct (N × H)
86. C23C2×D3×C13semidirect
91. D4C2×D3×C13semidirect
94. C2×C4C2×D3×C13semidirect
106. C3C13×H(5,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D4×C132
C2×C13×#672
C13×#2372
D3×D4×C132
C13×#2352
C13×H(5,𝔽2)3
#100413