Finite Group Databasebeta

← C5×#1009 #92085

Subgroups — C5×#1009 #92085

Order 480.

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×C5×#41C211yesmaximal, characteristic, complemented
2C5×#239C212yesmaximal, complemented
3C5×D3×D4C216yesmaximal, complemented
4C5×#235C213yesmaximal, complemented
5C2×C5×D12C213yesmaximal, complemented
6C5×H(5,𝔽2)—31nomaximal, Hall
7C22×C5×D3C2216yescomplemented
8C3×C5×Q8C2211yescharacteristic, complemented
9C3×C5×D4C2213yescomplemented
10C2×C3×C4×C5C2213yescomplemented
11C5×#67C2216yescomplemented
12C5×D12C2213yescomplemented
13C5×D12C2216yescomplemented
14C4×C5×D3C2216yescomplemented
15C5×Dic6C2211yescharacteristic, complemented
16#1009C511yesmaximal, characteristic, direct product factor, Hall
17C5×#41—32no—
18C5×#41—33no—
19C5×#41D311yescharacteristic, complemented
20C2×C5×D4—36no—
21C2×C5×D4—33no—
22C22×C3×C5C2313yes—
23C2×C5×D3—46no—
24C2×C5×D3C2316yes—
25C3×C4×C5C2311yescharacteristic
26C3×C4×C5C2313yes—
27C5×Dic3C2312yes—
28C3×#41C2×C511yescharacteristic, complemented
29#239C2×C512yescomplemented
30D3×D4C2×C516yescomplemented
31#235C2×C513yescomplemented
32C2×D12C2×C513yescomplemented
33C23×C5—36no—
34C5×Q8—31no—
35C5×Q8C2×D311yescharacteristic, complemented
36C5×D4—36no—
37C5×D4—36no—
38C5×D4—33no—
39C5×D4C2×D313yescomplemented
40C2×C4×C5—36no—
41C2×C4×C5C2×D313yescomplemented
42H(5,𝔽2)—31noSylow
43C2×C3×C5—23no—
44C2×C3×C5C2411yescharacteristic
45C5×D3—26no—
46C22×D3C22×C516yescomplemented
47C3×Q8C22×C511yescharacteristic, complemented
48C3×D4C22×C513yescomplemented
49C2×C3×C4C22×C513yescomplemented
50#67C22×C516yescomplemented
51D12C22×C513yescomplemented
52D12C22×C516yescomplemented
53C4×D3C22×C516yescomplemented
54Dic6C22×C511yescharacteristic, complemented
55C22×C5—36no—
56C22×C5—126no—
57C22×C5C22×D313yes—
58C4×C5—32no—
59C4×C5C22×D313yes—
60C4×C5C22×D311yescharacteristic
61#41—32no—
62#41—33no—
63#41C5×D311yescharacteristic, complemented
64C2×D4—36no—
65C2×D4—33no—
66C3×C5H(5,𝔽2)11yescharacteristic, complemented, Hall
67C22×C3C23×C513yes—
68C2×D3—46no—
69C2×D3C23×C516yes—
70C3×C4C23×C511yescharacteristic
71C3×C4C23×C513yes—
72Dic3C23×C512yes—
73C2×C5—23no—
74C2×C5—66no—
75C2×C5C23×D311yescharacteristic
76C23—36no—
77Q8—31no—
78Q8C2×C5×D311yescharacteristic, complemented
79D4—36no—
80D4—36no—
81D4—33no—
82D4C2×C5×D313yescomplemented
83C2×C4—36no—
84C2×C4C2×C5×D313yescomplemented
85C2×C3—23no—
86C2×C3C24×C511yescharacteristic
87D3—26no—
88C5#100911yescharacteristic, direct product factor, Sylow
89C22—36no—
90C22—126no—
91C22C22×C5×D313yes—
92C4—32no—
93C4C22×C5×D313yes—
94C4C22×C5×D311yescharacteristic
95C3C5×H(5,𝔽2)11yescharacteristic, complemented, Sylow
96C2—23no—
97C2—66no—
98C2C23×C5×D311yescharacteristic
subgroupG/H
centerC2×C5C23×D3
commutator, cosocleC2×C3C24×C5
FrattiniC2C23×C5×D3
FittingC3×C5×#41C2
socleC2×C3×C5C24
hypercenterC5×#41D3
hypocenterC3C5×H(5,𝔽2)
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C5×#41

Complements

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

NH ≅ G/Ntype
1. C3×C5×#41C2semidirect
2. C5×#239C2semidirect
3. C5×D3×D4C2semidirect
4. C5×#235C2semidirect
5. C2×C5×D12C2semidirect
7. C22×C5×D3C22semidirect
8. C3×C5×Q8C22semidirect
9. C3×C5×D4C22semidirect
10. C2×C3×C4×C5C22semidirect
11. C5×#67C22semidirect
12. C5×D12C22semidirect
13. C5×D12C22semidirect
14. C4×C5×D3C22semidirect
15. C5×Dic6C22semidirect
16. #1009C5direct (N × H)
19. C5×#41D3semidirect
28. C3×#41C2×C5semidirect
29. #239C2×C5semidirect
30. D3×D4C2×C5semidirect
31. #235C2×C5semidirect
32. C2×D12C2×C5semidirect
35. C5×Q8C2×D3semidirect
39. C5×D4C2×D3semidirect
41. C2×C4×C5C2×D3semidirect
46. C22×D3C22×C5semidirect
47. C3×Q8C22×C5semidirect
48. C3×D4C22×C5semidirect
49. C2×C3×C4C22×C5semidirect
50. #67C22×C5semidirect
51. D12C22×C5semidirect
52. D12C22×C5semidirect
53. C4×D3C22×C5semidirect
54. Dic6C22×C5semidirect
63. #41C5×D3semidirect
66. C3×C5H(5,𝔽2)semidirect
78. Q8C2×C5×D3semidirect
82. D4C2×C5×D3semidirect
84. C2×C4C2×C5×D3semidirect
88. C5#1009direct (N × H)
95. C3C5×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×C5×#412
C5×#2392
C5×D3×D42
C5×#2352
C2×C5×D122
C5×H(5,𝔽2)3
#10095