Finite Group Databasebeta

← C13×#3549 #13112607

Subgroups — C13×#3549 #13112607

Order 1664.

1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 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×H(3,𝔽4)C214yesmaximal, complemented
2C13×#555C216yesmaximal, complemented
3D42×C13C216yesmaximal, complemented
4C13×#535C2112yesmaximal, complemented
5C13×#532C213yesmaximal, complemented
6C2×C13×#41C2216yescomplemented
7C22×D4×C13C22112yescomplemented
8C13×C4⋊Q8C2213yescomplemented
9C13×#127C2213yes—
10C13×#127C2218yescomplemented
11C13×#124C2216yescomplemented
12C13×#124C22124yescomplemented
13C13×#121C22112yescomplemented
14C13×#121C22124yescomplemented
15C13×#120C2218yescomplemented
16C13×#120C22124yescomplemented
17C4×D4×C13C22112yescomplemented
18C13×#117C22112yescomplemented
19C2×C42×C13C2211yescharacteristic, complemented
20C24×C13C2318yes—
21C13×#41—412no—
22C2×Q8×C13C2316yes—
23C2×D4×C13—424no—
24C2×D4×C13C23112yes—
25C2×D4×C13C2316yes—
26C2×D4×C13C23124yes—
27C2×D4×C13C23112yes—
28C22×C4×C13C2313yes—
29C22×C4×C13C23112yes—
30C13×C4⋊C4C23112yes—
31C13×C22⋊C4C23124yes—
32C13×C22⋊C4C23124yes—
33C42×C13C2313yes—
34C42×C13C2311yescharacteristic
35C42×C13C2318yes—
36#3549C1311yesmaximal, characteristic, direct product factor, Sylow
37C23×C13—424no—
38C23×C13C24112yes—
39C23×C13C2411yescharacteristic
40Q8×C13—46no—
41D4×C13—224no—
42D4×C13—424no—
43D4×C13—412no—
44D4×C13—46no—
45C2×C4×C13—224no—
46C2×C4×C13—26no—
47C2×C4×C13C2413yes—
48C2×C4×C13C24112yes—
49C2×C4×C13C2413yes—
50H(3,𝔽4)C2×C1314yescomplemented
51#555C2×C1316yescomplemented
52D42C2×C1316yescomplemented
53#535C2×C13112yescomplemented
54#532C2×C1313yescomplemented
55C22×C13—23no—
56C22×C13—212no—
57C22×C13—224no—
58C22×C13—816no—
59C22×C13C2511yescharacteristic
60C4×C13—212no—
61C4×C13—23no—
62C4×C13H(5,𝔽2)16yes—
63C2×#41C22×C1316yescomplemented
64C22×D4C22×C13112yescomplemented
65C4⋊Q8C22×C1313yescomplemented
66#127C22×C1313yes—
67#127C22×C1318yescomplemented
68#124C22×C1316yescomplemented
69#124C22×C13124yescomplemented
70#121C22×C13112yescomplemented
71#121C22×C13124yescomplemented
72#120C22×C1318yescomplemented
73#120C22×C13124yescomplemented
74C4×D4C22×C13112yescomplemented
75#117C22×C13112yescomplemented
76C2×C42C22×C1311yescharacteristic, complemented
77C2×C13—41no—
78C2×C13—412no—
79C2×C13C2×H(5,𝔽2)13yes—
80C24C23×C1318yes—
81#41—412no—
82C2×Q8C23×C1316yes—
83C2×D4—424no—
84C2×D4C23×C13112yes—
85C2×D4C23×C1316yes—
86C2×D4C23×C13124yes—
87C2×D4C23×C13112yes—
88C22×C4C23×C1313yes—
89C22×C4C23×C13112yes—
90C4⋊C4C23×C13112yes—
91C22⋊C4C23×C13124yes—
92C22⋊C4C23×C13124yes—
93C42C23×C1313yes—
94C42C23×C1311yescharacteristic
95C42C23×C1318yes—
96C13#354911yescharacteristic, direct product factor, Sylow
97C23—424no—
98C23C24×C13112yes—
99C23C24×C1311yescharacteristic
100Q8—46no—
101D4—224no—
102D4—424no—
103D4—412no—
104D4—46no—
105C2×C4—224no—
106C2×C4—26no—
107C2×C4C24×C1313yes—
108C2×C4C24×C13112yes—
109C2×C4C24×C1313yes—
110C22—23no—
111C22—212no—
112C22—224no—
113C22—816no—
114C22C25×C1311yescharacteristic
115C4—212no—
116C4—23no—
117C4C13×H(5,𝔽2)16yes—
118C2—412no—
119C2—41no—
120C2C2×C13×H(5,𝔽2)13yes—
subgroupG/H
center, socleC22×C13C25
commutator, Frattini, cosocleC22C25×C13
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×H(3,𝔽4)C2semidirect
2. C13×#555C2semidirect
3. D42×C13C2semidirect
4. C13×#535C2semidirect
5. C13×#532C2semidirect
6. C2×C13×#41C22semidirect
7. C22×D4×C13C22semidirect
8. C13×C4⋊Q8C22semidirect
10. C13×#127C22semidirect
11. C13×#124C22semidirect
12. C13×#124C22semidirect
13. C13×#121C22semidirect
14. C13×#121C22semidirect
15. C13×#120C22semidirect
16. C13×#120C22semidirect
17. C4×D4×C13C22semidirect
18. C13×#117C22semidirect
19. C2×C42×C13C22semidirect
36. #3549C13direct (N × H)
50. H(3,𝔽4)C2×C13semidirect
51. #555C2×C13semidirect
52. D42C2×C13semidirect
53. #535C2×C13semidirect
54. #532C2×C13semidirect
63. C2×#41C22×C13semidirect
64. C22×D4C22×C13semidirect
65. C4⋊Q8C22×C13semidirect
67. #127C22×C13semidirect
68. #124C22×C13semidirect
69. #124C22×C13semidirect
70. #121C22×C13semidirect
71. #121C22×C13semidirect
72. #120C22×C13semidirect
73. #120C22×C13semidirect
74. C4×D4C22×C13semidirect
75. #117C22×C13semidirect
76. C2×C42C22×C13semidirect
96. C13#3549direct (N × H)

Maximal subgroups

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

subgroupindex
C13×H(3,𝔽4)2
C13×#5552
D42×C132
C13×#5352
C13×#5322
#354913