Finite Group Databasebeta

← C2×#4149 #66281

Subgroups — C2×#4149 #66281

Order 320.

898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.

normal subgroups only

This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 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×C5×#41C211yesmaximal, characteristic, complemented
2#4149C2116yesmaximal, direct product factor
3C2×#713C212yesmaximal, complemented
4C2×D4×D5C216yesmaximal, complemented
5C2×#709C213yesmaximal, complemented
6C22×D20C213yesmaximal, complemented
7C23×D5C2216yescomplemented
8C5×#41C2218yescomplemented
9C2×C5×Q8C2211yescharacteristic, complemented
10C2×C5×D4C2213yescomplemented
11C22×C4×C5C2213yescomplemented
12C2×C22⋊D5C2216yescomplemented
13#713C22116yescomplemented
14D4×D5C22148yescomplemented
15#709C22124yescomplemented
16C2×D20C2213yescomplemented
17C2×D20C2216yescomplemented
18C2×D20C22124yescomplemented
19C2×C4×D5C2216yescomplemented
20C2×Dic10C2211yescharacteristic, complemented
21C2×H(5,𝔽2)—51nomaximal, Sylow
22C23×C5C2313yes—
23C22×D5—412no—
24C22×D5C2316yes—
25C22×D5C23124yescomplemented
26C5×Q8C2314yescomplemented
27C5×D4C23112yescomplemented
28C2×C4×C5C2311yescharacteristic
29C2×C4×C5C2313yes—
30C2×C4×C5C23112yescomplemented
31C22⋊D5C23124yescomplemented
32C2×Dic5C2312yes—
33D20C23112yescomplemented
34D20C23124yescomplemented
35C4×D5C23124yescomplemented
36Dic10C2314yescomplemented
37H(5,𝔽2)—516no—
38C2×#41—52no—
39C2×#41—53no—
40C2×#41D511yescharacteristic, complemented
41C22×D4—56no—
42C22×D4—53no—
43C22×C5—26no—
44C22×C5C2416yes—
45C22×C5C2411yescharacteristic
46C2×D5—212no—
47C2×D5—424no—
48C2×D5C24112yes—
49C4×C5C2412yes—
50C4×C5C2416yes—
51Dic5C2414yes—
52C24—56no—
53#41—516no—
54#41—524no—
55#41C2×D518yescomplemented
56C2×Q8—51no—
57C2×Q8C2×D511yescharacteristic, complemented
58C2×D4—56no—
59C2×D4—548no—
60C2×D4—56no—
61C2×D4—53no—
62C2×D4—524no—
63C2×D4C2×D513yescomplemented
64C22×C4—56no—
65C22×C4C2×D513yescomplemented
66C2×C5—26no—
67C2×C5H(5,𝔽2)12yescomplemented
68C2×C5C2511yescharacteristic
69D5—212no—
70C23—56no—
71C23—524no—
72C23—2012no—
73C23C22×D513yes—
74Q8—54no—
75Q8C22×D514yescomplemented
76D4—524no—
77D4—524no—
78D4—512no—
79D4C22×D5112yescomplemented
80C2×C4—52no—
81C2×C4—524no—
82C2×C4C22×D513yes—
83C2×C4C22×D511yescharacteristic
84C2×C4C22×D5112yescomplemented
85C5C2×H(5,𝔽2)11yescharacteristic, complemented, Sylow
86C22—26no—
87C22—512no—
88C22—1012no—
89C22—2024no—
90C22C23×D516yes—
91C22C23×D511yescharacteristic
92C4—54no—
93C4C23×D516yes—
94C4C23×D512yes—
95C2—26no—
96C2—1012no—
97C2#414912yesdirect product factor
98C2C24×D511yescharacteristic
subgroupG/H
centerC22C23×D5
commutator, cosocleC2×C5C25
FrattiniC2C24×D5
FittingC2×C5×#41C2
socleC22×C5C24
hypercenterC2×#41D5
hypocenterC5C2×H(5,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C5×#41C2semidirect
2. #4149C2direct (N × H)
3. C2×#713C2semidirect
4. C2×D4×D5C2semidirect
5. C2×#709C2semidirect
6. C22×D20C2semidirect
7. C23×D5C22semidirect
8. C5×#41C22semidirect
9. C2×C5×Q8C22semidirect
10. C2×C5×D4C22semidirect
11. C22×C4×C5C22semidirect
12. C2×C22⋊D5C22semidirect
13. #713C22semidirect
14. D4×D5C22semidirect
15. #709C22semidirect
16. C2×D20C22semidirect
17. C2×D20C22semidirect
18. C2×D20C22semidirect
19. C2×C4×D5C22semidirect
20. C2×Dic10C22semidirect
25. C22×D5C23semidirect
26. C5×Q8C23semidirect
27. C5×D4C23semidirect
30. C2×C4×C5C23semidirect
31. C22⋊D5C23semidirect
33. D20C23semidirect
34. D20C23semidirect
35. C4×D5C23semidirect
36. Dic10C23semidirect
40. C2×#41D5semidirect
55. #41C2×D5semidirect
57. C2×Q8C2×D5semidirect
63. C2×D4C2×D5semidirect
65. C22×C4C2×D5semidirect
67. C2×C5H(5,𝔽2)semidirect
75. Q8C22×D5semidirect
79. D4C22×D5semidirect
84. C2×C4C22×D5semidirect
85. C5C2×H(5,𝔽2)semidirect
97. C2#4149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#412
#41492
C2×#7132
C2×D4×D52
C2×#7092
C22×D202
C2×H(5,𝔽2)5