Finite Group Databasebeta

← #13129647

Subgroups — #13129647

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
1C13×#585C211yesmaximal, characteristic, complemented
2#11719652C2112yesmaximal, complemented
3D13×H(5,𝔽2)C2120yesmaximal, complemented
4#11719648C2115yesmaximal, complemented
5C2×#88256C2115yesmaximal, complemented
6C13×2−1+4C2216yescomplemented
7C13×H(5,𝔽2)C22110yescomplemented
8C2×C13×#41C22115yescomplemented
9#88257C22120yescomplemented
10#88256C22160yescomplemented
11#88256C221120yescomplemented
12#41×D13C221120yescomplemented
13#88254C22130yescomplemented
14C2×#6131C22130yescomplemented
15#88251C22190yescomplemented
16C2×D4×D13C22190yescomplemented
17C2×#6127C22145yescomplemented
18C22×D52C22115yescomplemented
19C23×D13C23130yescomplemented
20C13×#41C23160yescomplemented
21C13×#41C23120yescomplemented
22C2×Q8×C13C23115yescomplemented
23C2×D4×C13C23145yescomplemented
24C22×C4×C13C23115yescomplemented
25C2×C22⋊D13C23190yescomplemented
26#6131C231120yescomplemented
27Q8×D13C23140yescomplemented
28#6129C231120yescomplemented
29D4×D13C231360yescomplemented
30#6127C23160yescomplemented
31#6127C231180yescomplemented
32C2×D52C23145yescomplemented
33C2×D52C23190yescomplemented
34C2×C4×D13C23190yescomplemented
35C2×Dic26C23115yescomplemented
36H(7,𝔽2)—131nomaximal, Sylow
37C23×C13C24115yes—
38C22×D13—830no—
39C22×D13C24190yes—
40Q8×C13C24120yes—
41D4×C13C24160yes—
42C2×C4×C13C24115yes—
43C2×C4×C13C24145yes—
44C22⋊D13C241120yes—
45C2×Dic13C24130yes—
46D52C24110yes—
47D52C24190yes—
48C4×D13C241120yes—
49Dic26C2416yes—
50Dic26C24130yes—
51#585—1312no—
52#585—1315no—
53#585D1311yescharacteristic, complemented
54C2×H(5,𝔽2)—1320no—
55C2×H(5,𝔽2)—1315no—
56C22×C13—415no—
57C22×C13C25115yes—
58C2×D13—490no—
59C2×D13C25120yes—
60C4×C13C2511yescharacteristic
61C4×C13C25115yes—
62Dic13C25112yes—
632−1+4—1320no—
642−1+4—1330no—
652−1+4C2×D1316yescomplemented
66H(5,𝔽2)—13120no—
67H(5,𝔽2)—1360no—
68H(5,𝔽2)—1390no—
69H(5,𝔽2)C2×D13110yescomplemented
70C2×#41—13120no—
71C2×#41—1330no—
72C2×#41—1345no—
73C2×#41C2×D13115yescomplemented
74C22×D4—1390no—
75C22×D4—1315no—
76C2×C13—215no—
77C2×C13C2611yescharacteristic
78D13—220no—
79C24—1330no—
80#41—13120no—
81#41—13120no—
82#41—13180no—
83#41—1360no—
84#41C22×D13160yescomplemented
85#41C22×D13120yescomplemented
86C2×Q8—1340no—
87C2×Q8—1315no—
88C2×Q8C22×D13115yescomplemented
89C2×D4—1390no—
90C2×D4—13360no—
91C2×D4—1390no—
92C2×D4—1345no—
93C2×D4C22×D13145yescomplemented
94C22×C4—1390no—
95C22×C4C22×D13115yescomplemented
96C13H(7,𝔽2)11yescharacteristic, complemented, Sylow
97C23—1390no—
98C23—10430no—
99C23C23×D13115yes—
100Q8—1330no—
101Q8—136no—
102Q8C23×D13120yes—
103D4—13120no—
104D4—1390no—
105D4—1310no—
106D4C23×D13160yes—
107C2×C4—1330no—
108C2×C4—13120no—
109C2×C4C23×D13145yes—
110C2×C4C23×D13115yes—
111C22—415no—
112C22—1320no—
113C22—5290no—
114C22C24×D13115yes—
115C4—1312no—
116C4C24×D13115yes—
117C4C24×D1311yescharacteristic
118C2—215no—
119C2—2620no—
120C2C25×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C25×D13
commutator, socle, cosocleC2×C13C26
FittingC13×#585C2
hypercenter#585D13
hypocenterC13H(7,𝔽2)
LCSG ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ #585

Complements

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

NH ≅ G/Ntype
1. C13×#585C2semidirect
2. #11719652C2semidirect
3. D13×H(5,𝔽2)C2semidirect
4. #11719648C2semidirect
5. C2×#88256C2semidirect
6. C13×2−1+4C22semidirect
7. C13×H(5,𝔽2)C22semidirect
8. C2×C13×#41C22semidirect
9. #88257C22semidirect
10. #88256C22semidirect
11. #88256C22semidirect
12. #41×D13C22semidirect
13. #88254C22semidirect
14. C2×#6131C22semidirect
15. #88251C22semidirect
16. C2×D4×D13C22semidirect
17. C2×#6127C22semidirect
18. C22×D52C22semidirect
19. C23×D13C23semidirect
20. C13×#41C23semidirect
21. C13×#41C23semidirect
22. C2×Q8×C13C23semidirect
23. C2×D4×C13C23semidirect
24. C22×C4×C13C23semidirect
25. C2×C22⋊D13C23semidirect
26. #6131C23semidirect
27. Q8×D13C23semidirect
28. #6129C23semidirect
29. D4×D13C23semidirect
30. #6127C23semidirect
31. #6127C23semidirect
32. C2×D52C23semidirect
33. C2×D52C23semidirect
34. C2×C4×D13C23semidirect
35. C2×Dic26C23semidirect
53. #585D13semidirect
65. 2−1+4C2×D13semidirect
69. H(5,𝔽2)C2×D13semidirect
73. C2×#41C2×D13semidirect
84. #41C22×D13semidirect
85. #41C22×D13semidirect
88. C2×Q8C22×D13semidirect
93. C2×D4C22×D13semidirect
95. C22×C4C22×D13semidirect
96. C13H(7,𝔽2)semidirect

Maximal subgroups

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

subgroupindex
C13×#5852
#117196522
D13×H(5,𝔽2)2
#117196482
C2×#882562
H(7,𝔽2)13