Finite Group Databasebeta

← C13×#1009 #11929296

Subgroups — C13×#1009 #11929296

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
1C3×C13×#41C211yesmaximal, characteristic, complemented
2C13×#239C212yesmaximal, complemented
3D3×D4×C13C216yesmaximal, complemented
4C13×#235C213yesmaximal, complemented
5C2×C13×D12C213yesmaximal, complemented
6C13×H(5,𝔽2)—31nomaximal, Hall
7C22×D3×C13C2216yescomplemented
8C3×Q8×C13C2211yescharacteristic, complemented
9C3×D4×C13C2213yescomplemented
10C2×C3×C4×C13C2213yescomplemented
11C13×#67C2216yescomplemented
12C13×D12C2213yescomplemented
13C13×D12C2216yescomplemented
14C4×D3×C13C2216yescomplemented
15C13×Dic6C2211yescharacteristic, complemented
16C13×#41—32no—
17C13×#41—33no—
18C13×#41D311yescharacteristic, complemented
19C2×D4×C13—36no—
20C2×D4×C13—33no—
21C22×C3×C13C2313yes—
22C2×D3×C13—46no—
23C2×D3×C13C2316yes—
24C3×C4×C13C2311yescharacteristic
25C3×C4×C13C2313yes—
26Dic3×C13C2312yes—
27C23×C13—36no—
28Q8×C13—31no—
29Q8×C13C2×D311yescharacteristic, complemented
30D4×C13—36no—
31D4×C13—36no—
32D4×C13—33no—
33D4×C13C2×D313yescomplemented
34C2×C4×C13—36no—
35C2×C4×C13C2×D313yescomplemented
36#1009C1311yesmaximal, characteristic, direct product factor, Hall
37C2×C3×C13—23no—
38C2×C3×C13C2411yescharacteristic
39D3×C13—26no—
40C22×C13—36no—
41C22×C13—126no—
42C22×C13C22×D313yes—
43C4×C13—32no—
44C4×C13C22×D313yes—
45C4×C13C22×D311yescharacteristic
46C3×#41C2×C1311yescharacteristic, complemented
47#239C2×C1312yescomplemented
48D3×D4C2×C1316yescomplemented
49#235C2×C1313yescomplemented
50C2×D12C2×C1313yescomplemented
51C3×C13H(5,𝔽2)11yescharacteristic, complemented, Hall
52H(5,𝔽2)—31noSylow
53C2×C13—23no—
54C2×C13—66no—
55C2×C13C23×D311yescharacteristic
56C22×D3C22×C1316yescomplemented
57C3×Q8C22×C1311yescharacteristic, complemented
58C3×D4C22×C1313yescomplemented
59C2×C3×C4C22×C1313yescomplemented
60#67C22×C1316yescomplemented
61D12C22×C1313yescomplemented
62D12C22×C1316yescomplemented
63C4×D3C22×C1316yescomplemented
64Dic6C22×C1311yescharacteristic, complemented
65#41—32no—
66#41—33no—
67#41D3×C1311yescharacteristic, complemented
68C2×D4—36no—
69C2×D4—33no—
70C13#100911yescharacteristic, direct product factor, Sylow
71C22×C3C23×C1313yes—
72C2×D3—46no—
73C2×D3C23×C1316yes—
74C3×C4C23×C1311yescharacteristic
75C3×C4C23×C1313yes—
76Dic3C23×C1312yes—
77C23—36no—
78Q8—31no—
79Q8C2×D3×C1311yescharacteristic, complemented
80D4—36no—
81D4—36no—
82D4—33no—
83D4C2×D3×C1313yescomplemented
84C2×C4—36no—
85C2×C4C2×D3×C1313yescomplemented
86C2×C3—23no—
87C2×C3C24×C1311yescharacteristic
88D3—26no—
89C22—36no—
90C22—126no—
91C22C22×D3×C1313yes—
92C4—32no—
93C4C22×D3×C1313yes—
94C4C22×D3×C1311yescharacteristic
95C3C13×H(5,𝔽2)11yescharacteristic, complemented, Sylow
96C2—23no—
97C2—66no—
98C2C23×D3×C1311yescharacteristic
subgroupG/H
centerC2×C13C23×D3
commutator, cosocleC2×C3C24×C13
FrattiniC2C23×D3×C13
FittingC3×C13×#41C2
socleC2×C3×C13C24
hypercenterC13×#41D3
hypocenterC3C13×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C13 ◁ C13×#41

Complements

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

NH ≅ G/Ntype
1. C3×C13×#41C2semidirect
2. C13×#239C2semidirect
3. D3×D4×C13C2semidirect
4. C13×#235C2semidirect
5. C2×C13×D12C2semidirect
7. C22×D3×C13C22semidirect
8. C3×Q8×C13C22semidirect
9. C3×D4×C13C22semidirect
10. C2×C3×C4×C13C22semidirect
11. C13×#67C22semidirect
12. C13×D12C22semidirect
13. C13×D12C22semidirect
14. C4×D3×C13C22semidirect
15. C13×Dic6C22semidirect
18. C13×#41D3semidirect
29. Q8×C13C2×D3semidirect
33. D4×C13C2×D3semidirect
35. C2×C4×C13C2×D3semidirect
36. #1009C13direct (N × H)
46. C3×#41C2×C13semidirect
47. #239C2×C13semidirect
48. D3×D4C2×C13semidirect
49. #235C2×C13semidirect
50. C2×D12C2×C13semidirect
51. C3×C13H(5,𝔽2)semidirect
56. C22×D3C22×C13semidirect
57. C3×Q8C22×C13semidirect
58. C3×D4C22×C13semidirect
59. C2×C3×C4C22×C13semidirect
60. #67C22×C13semidirect
61. D12C22×C13semidirect
62. D12C22×C13semidirect
63. C4×D3C22×C13semidirect
64. Dic6C22×C13semidirect
67. #41D3×C13semidirect
70. C13#1009direct (N × H)
79. Q8C2×D3×C13semidirect
83. D4C2×D3×C13semidirect
85. C2×C4C2×D3×C13semidirect
95. 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
C3×C13×#412
C13×#2392
D3×D4×C132
C13×#2352
C2×C13×D122
C13×H(5,𝔽2)3
#100913