Finite Group Databasebeta

← C2×C13×#585 #13112651

Subgroups — C2×C13×#585 #13112651

Order 1664.

5956 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#585C2132yesmaximal, direct product factor
2C2×C13×2−1+4C216yesmaximal, complemented
3C2×C13×H(5,𝔽2)C2110yesmaximal, complemented
4C22×C13×#41C2115yesmaximal, complemented
5C13×2−1+4C22196yescomplemented
6C13×H(5,𝔽2)C221160yescomplemented
7C2×C13×#41C22120yescomplemented
8C2×C13×#41C22160yescomplemented
9C2×C13×#41C221240yescomplemented
10C22×Q8×C13C22115yescomplemented
11C22×D4×C13C22145yescomplemented
12C23×C4×C13C22115yescomplemented
13C24×C13C23115yes—
14C13×#41C231160yescomplemented
15C13×#41C231480yescomplemented
16C2×Q8×C13C23120yes—
17C2×Q8×C13C231120yescomplemented
18C2×D4×C13C23160yes—
19C2×D4×C13C231360yescomplemented
20C22×C4×C13C23145yes—
21C22×C4×C13C23115yes—
22C22×C4×C13C231120yescomplemented
23C2×#585C1311yesmaximal, characteristic, direct product factor, Sylow
24C23×C13—430no—
25C23×C13C24115yes—
26C23×C13C24160yes—
27Q8×C13C24180yes—
28D4×C13C241240yes—
29C2×C4×C13C24115yes—
30C2×C4×C13C24160yes—
31C2×C4×C13C241180yes—
32C2×C4×C13C2411yescharacteristic
33#585C2×C13132yesdirect product factor
34C2×2−1+4C2×C1316yescomplemented
35C2×H(5,𝔽2)C2×C13110yescomplemented
36C22×#41C2×C13115yescomplemented
37C22×C13—230no—
38C22×C13—460no—
39C22×C13C25130yes—
40C22×C13C2511yescharacteristic
41C4×C13C2512yes—
42C4×C13C25130yes—
432−1+4C22×C13196yescomplemented
44H(5,𝔽2)C22×C131160yescomplemented
45C2×#41C22×C13120yescomplemented
46C2×#41C22×C13160yescomplemented
47C2×#41C22×C131240yescomplemented
48C22×Q8C22×C13115yescomplemented
49C22×D4C22×C13145yescomplemented
50C23×C4C22×C13115yescomplemented
51C2×C13—230no—
52C2×C13#58512yesdirect product factor
53C2×C13C2611yescharacteristic
54C24C23×C13115yes—
55#41C23×C131160yescomplemented
56#41C23×C131480yescomplemented
57C2×Q8C23×C13120yes—
58C2×Q8C23×C131120yescomplemented
59C2×D4C23×C13160yes—
60C2×D4C23×C131360yescomplemented
61C22×C4C23×C13115yes—
62C22×C4C23×C13145yes—
63C22×C4C23×C131120yescomplemented
64C13C2×#58511yescharacteristic, direct product factor, Sylow
65C23—430no—
66C23C24×C13115yes—
67C23C24×C13160yes—
68Q8C24×C13180yes—
69D4C24×C131240yes—
70C2×C4C24×C1311yescharacteristic
71C2×C4C24×C13115yes—
72C2×C4C24×C13160yes—
73C2×C4C24×C131180yes—
74C22—230no—
75C22—460no—
76C22C25×C13130yes—
77C22C25×C1311yescharacteristic
78C4C25×C1312yes—
79C4C25×C13130yes—
80C2—230no—
81C2C13×#58512yesdirect product factor
82C2C26×C1311yescharacteristic
subgroupG/H
centerC2×C4×C13C24
commutator, Frattini, cosocleC2C26×C13
socleC22×C13C25
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#585C2direct (N × H)
2. C2×C13×2−1+4C2semidirect
3. C2×C13×H(5,𝔽2)C2semidirect
4. C22×C13×#41C2semidirect
5. C13×2−1+4C22semidirect
6. C13×H(5,𝔽2)C22semidirect
7. C2×C13×#41C22semidirect
8. C2×C13×#41C22semidirect
9. C2×C13×#41C22semidirect
10. C22×Q8×C13C22semidirect
11. C22×D4×C13C22semidirect
12. C23×C4×C13C22semidirect
14. C13×#41C23semidirect
15. C13×#41C23semidirect
17. C2×Q8×C13C23semidirect
19. C2×D4×C13C23semidirect
22. C22×C4×C13C23semidirect
23. C2×#585C13direct (N × H)
33. #585C2×C13direct (N × H)
34. C2×2−1+4C2×C13semidirect
35. C2×H(5,𝔽2)C2×C13semidirect
36. C22×#41C2×C13semidirect
43. 2−1+4C22×C13semidirect
44. H(5,𝔽2)C22×C13semidirect
45. C2×#41C22×C13semidirect
46. C2×#41C22×C13semidirect
47. C2×#41C22×C13semidirect
48. C22×Q8C22×C13semidirect
49. C22×D4C22×C13semidirect
50. C23×C4C22×C13semidirect
52. C2×C13#585direct (N × H)
55. #41C23×C13semidirect
56. #41C23×C13semidirect
58. C2×Q8C23×C13semidirect
60. C2×D4C23×C13semidirect
63. C22×C4C23×C13semidirect
64. C13C2×#585direct (N × H)
81. C2C13×#585direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#5852
C2×C13×2−1+42
C2×C13×H(5,𝔽2)2
C22×C13×#412
C2×#58513