Finite Group Databasebeta

← C5×C3⋊(C3⋊#11717961) #49147174

Subgroups — C5×C3⋊(C3⋊#11717961) #49147174

Order 36900.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C5×D205C211yesmaximal, characteristic
2C5×C3⋊#11717961—34nomaximal
3C32×C52×C41C411yescharacteristic, complemented, Hall
4C3⋊(C3⋊#11717961)C511yesmaximal, characteristic, direct product factor
5C5×C3⋊(C3⋊#4223)—51nomaximal
6C3×C5×D205D314yes—
7C5×#11717961—91noHall
8C32×D205C2×C511yescharacteristic
9C32×C5×D41—51no—
10C3×C52×C41Dic314yescomplemented
11C3⋊#11717961—34no—
12C5×C3⋊#4223—154no—
13C5×D205C3⋊D311yescharacteristic
14C32×C5×C41—41no—
15C32×C5×C41C4×C511yescharacteristic, complemented
16C32×C5×C41AGL(1,𝔽5)11yescharacteristic, complemented
17C3⋊(C3⋊#4223)—51noHall
18C3×D205C5×D314yes—
19C3×C5×D41—54no—
20C52×C41C3⋊Dic311yescharacteristic, complemented, Hall
21C5×C3⋊ΓL(1,𝔽16)—411nomaximal, Hall
22#11717961—91no—
23C5×#4223—451no—
24C32×D41—51no—
25C3×C5×C41—44no—
26C3×C5×C41C5×Dic314yescomplemented
27C3×C5×C41ΓL(1,𝔽16)14yescomplemented
28C3⋊#4223—154no—
29C32×C5×D5—411no—
30D205C5×C3⋊D311yescharacteristic
31C5×D41—51no—
32C32×C41C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
33C5×ΓL(1,𝔽16)—1234no—
34C3×D41—54no—
35C32×C52#422311yescharacteristic, complemented, Hall
36C5×C41—41no—
37C5×C41C5×C3⋊Dic311yescharacteristic, complemented
38C5×C41C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented
39C3⋊ΓL(1,𝔽16)—411no—
40C5×C3⋊Dic3—2051no—
41#4223—451noHall
42C3×C5×D5—414no—
43C3×C41C5×ΓL(1,𝔽16)14yescomplemented
44C5×AGL(1,𝔽5)—3691noHall
45C2×C32×C5—2051no—
46C32×D5—411no—
47D41—51no—
48C3×C52C3⋊#422314yescomplemented
49ΓL(1,𝔽16)—1234no—
50C5×Dic3—6154no—
51C5×D5—411no—
52C32×C5—41no—
53C32×C5C5×#422311yescharacteristic, complemented
54C32×C5#1171796111yescharacteristic, complemented
55C41C5×C3⋊ΓL(1,𝔽16)11yescharacteristic, complemented, Sylow
56C3⋊Dic3—2051noHall
57C2×C3×C5—2054no—
58C3×D5—414no—
59C52C3⋊(C3⋊#4223)11yescharacteristic, complemented, Sylow
60AGL(1,𝔽5)—3691no—
61C4×C5—18451no—
62C2×C32—2051no—
63C3×C5—44no—
64C3×C5C5×C3⋊#422314yescomplemented
65C3×C5C3⋊#1171796114yescomplemented
66Dic3—6154no—
67C2×C5—2051no—
68D5—411no—
69C32C5×#1171796111yescharacteristic, complemented, Sylow
70C2×C3—2054no—
71C5—41no—
72C5C5×C3⋊(C3⋊#4223)11yescharacteristic, complemented
73C5C3⋊(C3⋊#11717961)11yescharacteristic, direct product factor
74C4—18451noSylow
75C3C5×C3⋊#1171796114yescomplemented
76C2—2051no—
subgroupG/H
center, hypercenterC5C3⋊(C3⋊#11717961)
commutator, hypocenterC32×C5×C41C4×C5
FrattiniC1G
Fitting, socleC32×C52×C41C4
prime radicalC32×C5×D205C2
cosocleC32×D205C2×C5
LCSG ▷ C32×C5×C41
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
3. C32×C52×C41C4semidirect
4. C3⋊(C3⋊#11717961)C5direct (N × H)
10. C3×C52×C41Dic3semidirect
15. C32×C5×C41C4×C5semidirect
16. C32×C5×C41AGL(1,𝔽5)semidirect
20. C52×C41C3⋊Dic3semidirect
26. C3×C5×C41C5×Dic3semidirect
27. C3×C5×C41ΓL(1,𝔽16)semidirect
32. C32×C41C5×AGL(1,𝔽5)semidirect
35. C32×C52#4223semidirect
37. C5×C41C5×C3⋊Dic3semidirect
38. C5×C41C3⋊ΓL(1,𝔽16)semidirect
43. C3×C41C5×ΓL(1,𝔽16)semidirect
48. C3×C52C3⋊#4223semidirect
53. C32×C5C5×#4223semidirect
54. C32×C5#11717961semidirect
55. C41C5×C3⋊ΓL(1,𝔽16)semidirect
59. C52C3⋊(C3⋊#4223)semidirect
64. C3×C5C5×C3⋊#4223semidirect
65. C3×C5C3⋊#11717961semidirect
69. C32C5×#11717961semidirect
72. C5C5×C3⋊(C3⋊#4223)semidirect
73. C5C3⋊(C3⋊#11717961)direct (N × H)
75. C3C5×C3⋊#11717961semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D2052
C5×C3⋊#117179613
C3⋊(C3⋊#11717961)5
C5×C3⋊(C3⋊#4223)5
C5×C3⋊ΓL(1,𝔽16)41