Finite Group Databasebeta

← C5×#67037 #13183416

Subgroups — C5×#67037 #13183416

Order 1760.

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
1C2×C5×D4×C11C211yesmaximal, characteristic, complemented
2C2×C5×C22⋊D11C214yesmaximal, complemented
3C5×#4341C214yesmaximal, complemented
4C5×D4×D11C214yesmaximal, complemented
5C5×#4339C212yesmaximal, complemented
6C23×C5×C11C2212yescomplemented
7C22×C5×D11C2214yescomplemented
8C5×D4×C11C2214yescomplemented
9C2×C4×C5×C11C2211yescharacteristic, complemented
10C5×C22⋊D11C2214yescomplemented
11C5×C22⋊D11C2218yescomplemented
12C2×C5×Dic11C2214yescomplemented
13C5×D44C2212yescomplemented
14C4×C5×D11C2214yescomplemented
15C5×Dic22C2212yescomplemented
16#67037C511yesmaximal, characteristic, direct product factor, Hall
17C22×C5×C11—42no—
18C22×C5×C11C2314yes—
19C22×C5×C11C2311yescharacteristic
20C2×C5×D11—44no—
21C2×C5×D11C2314yes—
22C4×C5×C11C2312yes—
23C5×Dic11C2314yes—
24C2×D4×C11C2×C511yescharacteristic, complemented
25C2×C22⋊D11C2×C514yescomplemented
26#4341C2×C514yescomplemented
27D4×D11C2×C514yescomplemented
28#4339C2×C512yescomplemented
29C5×H(5,𝔽2)—111nomaximal, Hall
30C2×C5×C11—24no—
31C2×C5×C11—21no—
32C2×C5×C11C2411yescharacteristic
33C5×D11—24no—
34C23×C11C22×C512yescomplemented
35C22×D11C22×C514yescomplemented
36D4×C11C22×C514yescomplemented
37C2×C4×C11C22×C511yescharacteristic, complemented
38C22⋊D11C22×C514yescomplemented
39C22⋊D11C22×C518yescomplemented
40C2×Dic11C22×C514yescomplemented
41D44C22×C512yescomplemented
42C4×D11C22×C514yescomplemented
43Dic22C22×C512yescomplemented
44C5×#41—114no—
45C5×#41—112no—
46C2×C5×D4—114no—
47C2×C5×D4—114no—
48C2×C5×D4D1111yescharacteristic, complemented
49C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
50C22×C11—42no—
51C22×C11C23×C511yescharacteristic
52C22×C11C23×C514yes—
53C2×D11—44no—
54C2×D11C23×C514yes—
55C4×C11C23×C512yes—
56Dic11C23×C514yes—
57C23×C5—114no—
58C23×C5C2×D1112yescomplemented
59C5×Q8—112no—
60C5×D4—118no—
61C5×D4—114no—
62C5×D4—112no—
63C5×D4C2×D1114yescomplemented
64C2×C4×C5—114no—
65C2×C4×C5—114no—
66C2×C4×C5C2×D1111yescharacteristic, complemented
67H(5,𝔽2)—111noSylow
68C2×C11—24no—
69C2×C11—21no—
70C2×C11C24×C511yescharacteristic
71D11—24no—
72C22×C5—42no—
73C22×C5—114no—
74C22×C5—444no—
75C22×C5C22×D1114yes—
76C22×C5C22×D1111yescharacteristic
77C4×C5—114no—
78C4×C5C22×D1112yes—
79#41—114no—
80#41—112no—
81C2×D4—114no—
82C2×D4—114no—
83C2×D4C5×D1111yescharacteristic, complemented
84C11C5×H(5,𝔽2)11yescharacteristic, complemented, Sylow
85C2×C5—21no—
86C2×C5—24no—
87C2×C5—224no—
88C2×C5C23×D1111yescharacteristic
89C23—114no—
90C23C2×C5×D1112yescomplemented
91Q8—112no—
92D4—118no—
93D4—114no—
94D4—112no—
95D4C2×C5×D1114yescomplemented
96C2×C4—114no—
97C2×C4—114no—
98C2×C4C2×C5×D1111yescharacteristic, complemented
99C5#6703711yescharacteristic, direct product factor, Sylow
100C22—42no—
101C22—114no—
102C22—444no—
103C22C22×C5×D1114yes—
104C22C22×C5×D1111yescharacteristic
105C4—114no—
106C4C22×C5×D1112yes—
107C2—21no—
108C2—24no—
109C2—224no—
110C2C23×C5×D1111yescharacteristic
subgroupG/H
centerC2×C5C23×D11
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×C5×D11
FittingC2×C5×D4×C11C2
socleC2×C5×C11C24
hypercenterC2×C5×D4D11
hypocenterC11C5×H(5,𝔽2)
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×D4×C11C2semidirect
2. C2×C5×C22⋊D11C2semidirect
3. C5×#4341C2semidirect
4. C5×D4×D11C2semidirect
5. C5×#4339C2semidirect
6. C23×C5×C11C22semidirect
7. C22×C5×D11C22semidirect
8. C5×D4×C11C22semidirect
9. C2×C4×C5×C11C22semidirect
10. C5×C22⋊D11C22semidirect
11. C5×C22⋊D11C22semidirect
12. C2×C5×Dic11C22semidirect
13. C5×D44C22semidirect
14. C4×C5×D11C22semidirect
15. C5×Dic22C22semidirect
16. #67037C5direct (N × H)
24. C2×D4×C11C2×C5semidirect
25. C2×C22⋊D11C2×C5semidirect
26. #4341C2×C5semidirect
27. D4×D11C2×C5semidirect
28. #4339C2×C5semidirect
34. C23×C11C22×C5semidirect
35. C22×D11C22×C5semidirect
36. D4×C11C22×C5semidirect
37. C2×C4×C11C22×C5semidirect
38. C22⋊D11C22×C5semidirect
39. C22⋊D11C22×C5semidirect
40. C2×Dic11C22×C5semidirect
41. D44C22×C5semidirect
42. C4×D11C22×C5semidirect
43. Dic22C22×C5semidirect
48. C2×C5×D4D11semidirect
49. C5×C11H(5,𝔽2)semidirect
58. C23×C5C2×D11semidirect
63. C5×D4C2×D11semidirect
66. C2×C4×C5C2×D11semidirect
83. C2×D4C5×D11semidirect
84. C11C5×H(5,𝔽2)semidirect
90. C23C2×C5×D11semidirect
95. D4C2×C5×D11semidirect
98. C2×C4C2×C5×D11semidirect
99. C5#67037direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×D4×C112
C2×C5×C22⋊D112
C5×#43412
C5×D4×D112
C5×#43392
#670375
C5×H(5,𝔽2)11