Finite Group Databasebeta

← #13129646

Subgroups — #13129646

Order 1664.

5992 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.

normal subgroups only

This group has 5992 conjugacy classes of subgroups — too many to draw. Only its 3201 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×C13×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2#11719650C2116yesmaximal, complemented
3D13×H(5,𝔽2)C2116yesmaximal, complemented
4#11719648C2112yesmaximal, complemented
5C2×#88251C2118yesmaximal, complemented
6C13×H(5,𝔽2)C22116yescomplemented
7C2×C13×#41C2216yescomplemented
8C22×D4×C13C2219yescomplemented
9C22×C22⋊D13C22124yescomplemented
10#88257C22148yescomplemented
11#88256C22148yescomplemented
12#41×D13C22196yescomplemented
13#88254C2218yescomplemented
14#88251C22172yescomplemented
15#88251C221144yescomplemented
16C2×#6129C22172yescomplemented
17C2×D4×D13C22172yescomplemented
18C2×#6127C22136yescomplemented
19C24×C13C2316yescomplemented
20C23×D13C23124yescomplemented
21C13×#41C23148yescomplemented
22C2×Q8×C13C2312yescomplemented
23C2×D4×C13C23172yescomplemented
24C2×D4×C13C23118yescomplemented
25C22×C4×C13C2319yescomplemented
26C2×C22⋊D13C23172yescomplemented
27C2×C22⋊D13C231144yescomplemented
28C22×Dic13C23124yescomplemented
29#6131C23132yescomplemented
30Q8×D13C23132yescomplemented
31#6129C231288yescomplemented
32D4×D13C231288yescomplemented
33#6127C23148yescomplemented
34#6127C231144yescomplemented
35C2×D52C23136yescomplemented
36C2×C4×D13C23172yescomplemented
37C2×Dic26C23136yescomplemented
38H(7,𝔽2)—131nomaximal, Sylow
39C23×C13—86no—
40C23×C13C24124yes—
41C23×C13C2419yes—
42C22×D13—824no—
43C22×D13C24172yes—
44Q8×C13C2418yes—
45D4×C13C24172yes—
46C2×C4×C13C24136yes—
47C2×C4×C13C2416yes—
48C22⋊D13C24116yes—
49C22⋊D13C241144yes—
50C2×Dic13C24172yes—
51D52C24148yes—
52C4×D13C24196yes—
53Dic26C24148yes—
54#585—1316no—
55#585—1312no—
56C2×H(5,𝔽2)—1316no—
57C2×H(5,𝔽2)—1318no—
58C2×H(5,𝔽2)D1311yescharacteristic, complemented
59C22×C13—424no—
60C22×C13—49no—
61C22×C13C25118yes—
62C22×C13C2511yescharacteristic
63C2×D13—472no—
64C2×D13C25116yes—
65C4×C13C25112yes—
66Dic13C25116yes—
672−1+4—1348no—
682−1+4—138no—
69H(5,𝔽2)—1348no—
70H(5,𝔽2)—13144no—
71H(5,𝔽2)—1372no—
72H(5,𝔽2)C2×D13116yescomplemented
73C2×#41—1396no—
74C2×#41—1372no—
75C2×#41—1336no—
76C2×#41C2×D1316yescomplemented
77C22×D4—1324no—
78C22×D4—1372no—
79C22×D4C2×D1319yescomplemented
80C2×C13—218no—
81C2×C13—21no—
82C2×C13C2611yescharacteristic
83D13—216no—
84C24—1324no—
85C24C22×D1316yescomplemented
86#41—1332no—
87#41—13288no—
88#41—13144no—
89#41—1348no—
90#41C22×D13148yescomplemented
91C2×Q8—1332no—
92C2×Q8—1336no—
93C2×Q8C22×D1312yescomplemented
94C2×D4—13144no—
95C2×D4—1372no—
96C2×D4—13288no—
97C2×D4—1336no—
98C2×D4C22×D13172yescomplemented
99C2×D4C22×D13118yescomplemented
100C22×C4—1324no—
101C22×C4—1372no—
102C22×C4C22×D1319yescomplemented
103C13H(7,𝔽2)11yescharacteristic, complemented, Sylow
104C23—86no—
105C23—1372no—
106C23—10424no—
107C23C23×D13124yes—
108C23C23×D1319yes—
109Q8—1348no—
110Q8C23×D1318yes—
111D4—13144no—
112D4—1316no—
113D4—1348no—
114D4C23×D13172yes—
115C2×C4—1372no—
116C2×C4—1396no—
117C2×C4C23×D13136yes—
118C2×C4C23×D1316yes—
119C22—49no—
120C22—424no—
121C22—1316no—
122C22—5272no—
123C22C24×D13118yes—
124C22C24×D1311yescharacteristic
125C4—1316no—
126C4C24×D13112yes—
127C2—21no—
128C2—218no—
129C2—2616no—
130C2C25×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C25×D13
commutator, socle, cosocleC2×C13C26
FittingC2×C13×H(5,𝔽2)C2
hypercenterC2×H(5,𝔽2)D13
hypocenterC13H(7,𝔽2)
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C13×H(5,𝔽2)C2semidirect
2. #11719650C2semidirect
3. D13×H(5,𝔽2)C2semidirect
4. #11719648C2semidirect
5. C2×#88251C2semidirect
6. C13×H(5,𝔽2)C22semidirect
7. C2×C13×#41C22semidirect
8. C22×D4×C13C22semidirect
9. C22×C22⋊D13C22semidirect
10. #88257C22semidirect
11. #88256C22semidirect
12. #41×D13C22semidirect
13. #88254C22semidirect
14. #88251C22semidirect
15. #88251C22semidirect
16. C2×#6129C22semidirect
17. C2×D4×D13C22semidirect
18. C2×#6127C22semidirect
19. C24×C13C23semidirect
20. C23×D13C23semidirect
21. C13×#41C23semidirect
22. C2×Q8×C13C23semidirect
23. C2×D4×C13C23semidirect
24. C2×D4×C13C23semidirect
25. C22×C4×C13C23semidirect
26. C2×C22⋊D13C23semidirect
27. C2×C22⋊D13C23semidirect
28. C22×Dic13C23semidirect
29. #6131C23semidirect
30. Q8×D13C23semidirect
31. #6129C23semidirect
32. D4×D13C23semidirect
33. #6127C23semidirect
34. #6127C23semidirect
35. C2×D52C23semidirect
36. C2×C4×D13C23semidirect
37. C2×Dic26C23semidirect
58. C2×H(5,𝔽2)D13semidirect
72. H(5,𝔽2)C2×D13semidirect
76. C2×#41C2×D13semidirect
79. C22×D4C2×D13semidirect
85. C24C22×D13semidirect
90. #41C22×D13semidirect
93. C2×Q8C22×D13semidirect
98. C2×D4C22×D13semidirect
99. C2×D4C22×D13semidirect
102. C22×C4C22×D13semidirect
103. C13H(7,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C2×C13×H(5,𝔽2)2
#117196502
D13×H(5,𝔽2)2
#117196482
C2×#882512
H(7,𝔽2)13