Finite Group Databasebeta

← C5×#67042 #13183421

Subgroups — C5×#67042 #13183421

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
1C5×C11×#41C211yesmaximal, characteristic, complemented
2C5×#4343C212yesmaximal, complemented
3C5×D4×D11C216yesmaximal, complemented
4C5×#4339C213yesmaximal, complemented
5C2×C5×D44C213yesmaximal, complemented
6C22×C5×D11C2216yescomplemented
7C5×Q8×C11C2211yescharacteristic, complemented
8C5×D4×C11C2213yescomplemented
9C2×C4×C5×C11C2213yescomplemented
10C5×C22⋊D11C2216yescomplemented
11C5×D44C2213yescomplemented
12C5×D44C2216yescomplemented
13C4×C5×D11C2216yescomplemented
14C5×Dic22C2211yescharacteristic, complemented
15#67042C511yesmaximal, characteristic, direct product factor, Hall
16C22×C5×C11C2313yes—
17C2×C5×D11—46no—
18C2×C5×D11C2316yes—
19C4×C5×C11C2311yescharacteristic
20C4×C5×C11C2313yes—
21C5×Dic11C2312yes—
22C11×#41C2×C511yescharacteristic, complemented
23#4343C2×C512yescomplemented
24D4×D11C2×C516yescomplemented
25#4339C2×C513yescomplemented
26C2×D44C2×C513yescomplemented
27C5×H(5,𝔽2)—111nomaximal, Hall
28C2×C5×C11—23no—
29C2×C5×C11C2411yescharacteristic
30C5×D11—26no—
31C22×D11C22×C516yescomplemented
32Q8×C11C22×C511yescharacteristic, complemented
33D4×C11C22×C513yescomplemented
34C2×C4×C11C22×C513yescomplemented
35C22⋊D11C22×C516yescomplemented
36D44C22×C513yescomplemented
37D44C22×C516yescomplemented
38C4×D11C22×C516yescomplemented
39Dic22C22×C511yescharacteristic, complemented
40C5×#41—112no—
41C5×#41—113no—
42C5×#41D1111yescharacteristic, complemented
43C2×C5×D4—116no—
44C2×C5×D4—113no—
45C5×C11H(5,𝔽2)11yescharacteristic, complemented, Hall
46C22×C11C23×C513yes—
47C2×D11—46no—
48C2×D11C23×C516yes—
49C4×C11C23×C511yescharacteristic
50C4×C11C23×C513yes—
51Dic11C23×C512yes—
52C23×C5—116no—
53C5×Q8—111no—
54C5×Q8C2×D1111yescharacteristic, complemented
55C5×D4—116no—
56C5×D4—116no—
57C5×D4—113no—
58C5×D4C2×D1113yescomplemented
59C2×C4×C5—116no—
60C2×C4×C5C2×D1113yescomplemented
61H(5,𝔽2)—111noSylow
62C2×C11—23no—
63C2×C11C24×C511yescharacteristic
64D11—26no—
65C22×C5—116no—
66C22×C5—446no—
67C22×C5C22×D1113yes—
68C4×C5—112no—
69C4×C5C22×D1113yes—
70C4×C5C22×D1111yescharacteristic
71#41—112no—
72#41—113no—
73#41C5×D1111yescharacteristic, complemented
74C2×D4—116no—
75C2×D4—113no—
76C11C5×H(5,𝔽2)11yescharacteristic, complemented, Sylow
77C2×C5—23no—
78C2×C5—226no—
79C2×C5C23×D1111yescharacteristic
80C23—116no—
81Q8—111no—
82Q8C2×C5×D1111yescharacteristic, complemented
83D4—116no—
84D4—116no—
85D4—113no—
86D4C2×C5×D1113yescomplemented
87C2×C4—116no—
88C2×C4C2×C5×D1113yescomplemented
89C5#6704211yescharacteristic, direct product factor, Sylow
90C22—116no—
91C22—446no—
92C22C22×C5×D1113yes—
93C4—112no—
94C4C22×C5×D1113yes—
95C4C22×C5×D1111yescharacteristic
96C2—23no—
97C2—226no—
98C2C23×C5×D1111yescharacteristic
subgroupG/H
centerC2×C5C23×D11
commutator, cosocleC2×C11C24×C5
FrattiniC2C23×C5×D11
FittingC5×C11×#41C2
socleC2×C5×C11C24
hypercenterC5×#41D11
hypocenterC11C5×H(5,𝔽2)
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C5 ◁ C5×#41

Complements

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

NH ≅ G/Ntype
1. C5×C11×#41C2semidirect
2. C5×#4343C2semidirect
3. C5×D4×D11C2semidirect
4. C5×#4339C2semidirect
5. C2×C5×D44C2semidirect
6. C22×C5×D11C22semidirect
7. C5×Q8×C11C22semidirect
8. C5×D4×C11C22semidirect
9. C2×C4×C5×C11C22semidirect
10. C5×C22⋊D11C22semidirect
11. C5×D44C22semidirect
12. C5×D44C22semidirect
13. C4×C5×D11C22semidirect
14. C5×Dic22C22semidirect
15. #67042C5direct (N × H)
22. C11×#41C2×C5semidirect
23. #4343C2×C5semidirect
24. D4×D11C2×C5semidirect
25. #4339C2×C5semidirect
26. C2×D44C2×C5semidirect
31. C22×D11C22×C5semidirect
32. Q8×C11C22×C5semidirect
33. D4×C11C22×C5semidirect
34. C2×C4×C11C22×C5semidirect
35. C22⋊D11C22×C5semidirect
36. D44C22×C5semidirect
37. D44C22×C5semidirect
38. C4×D11C22×C5semidirect
39. Dic22C22×C5semidirect
42. C5×#41D11semidirect
45. C5×C11H(5,𝔽2)semidirect
54. C5×Q8C2×D11semidirect
58. C5×D4C2×D11semidirect
60. C2×C4×C5C2×D11semidirect
73. #41C5×D11semidirect
76. C11C5×H(5,𝔽2)semidirect
82. Q8C2×C5×D11semidirect
86. D4C2×C5×D11semidirect
88. C2×C4C2×C5×D11semidirect
89. C5#67042direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×#412
C5×#43432
C5×D4×D112
C5×#43392
C2×C5×D442
#670425
C5×H(5,𝔽2)11