Finite Group Databasebeta

← D5×C3⋊#157 #11762167

Subgroups — D5×C3⋊#157 #11762167

Order 1080.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D5×C3⋊D3C211yesmaximal, characteristic
2C3⋊#4379C211yesmaximal, characteristic, complemented
3C5×C3⋊#157C211yesmaximal, characteristic, complemented
4D5×#157—31nomaximal
5C3×C3⋊D15C411yescharacteristic, complemented
6C3×C5×C3⋊D3C2211yescharacteristic
7C33×D5C411yescharacteristic, complemented
8C2×C3⋊#157—51nomaximal, Hall
9D5×C3⋊D3D311yescharacteristic
10C3×D3×D5—62no—
11#4379—31no—
12C5×#157—31no—
13C33×C5C2×C411yescharacteristic, complemented, Hall
14D5×Dic3—91nomaximal
15C2×C3×C3⋊D3—51no—
16C3⋊#157—51no—
17C3⋊#157D511yescharacteristic, direct product factor
18C3⋊D15Dic311yescharacteristic, complemented
19C5×C3⋊D3C2×D311yescharacteristic
20C3×D15—62no—
21C3×C5×D3—62no—
22C32×D5—22no—
23C32×D5—42no—
24C32×D5Dic311yescharacteristic, complemented
25C2×#157—151no—
26C2×C3×D5—91no—
27D3×D5—62no—
28Dic15—91no—
29C5×Dic3—91no—
30C2×C33—51no—
31C3×C3⋊D3—51no—
32C3×C3⋊D3C2×D511yescharacteristic
33C32×C5—22no—
34C32×C5—42no—
35C32×C5C2×Dic311yescharacteristic, complemented
36C4×D5—271noHall
37C2×C3⋊D3—51no—
38C2×C3×D3—302no—
39#157—31no—
40#157—151no—
41C2×C3×C5—91no—
42D15—62no—
43C3×D5—22no—
44C3×D5—42no—
45C3×D5—91no—
46C3×D5#15711yescharacteristic, complemented
47C5×D3—62no—
48C33C4×D511yescharacteristic, complemented, Sylow
49C2×Dic3—451no—
50C2×D5—91no—
51C4×C5—271no—
52Dic5—271no—
53C2×C32—51no—
54C2×C32—102no—
55C2×C32—202no—
56C3⋊D3—51no—
57C3⋊D3D3×D511yescharacteristic
58C3×D3—62no—
59C3×D3—302no—
60C3×C5—22no—
61C3×C5—42no—
62C3×C5C2×#15711yescharacteristic, complemented
63C22×C3—451no—
64C2×D3—302no—
65Dic3—91no—
66Dic3—451no—
67C2×C5—91no—
68D5—91no—
69D5C3⋊#15711yescharacteristic, direct product factor
70C32—22no—
71C32—42no—
72C32D5×Dic311yescharacteristic, complemented
73C2×C4—1351noSylow
74C2×C3—51no—
75C2×C3—91no—
76C2×C3—102no—
77C2×C3—202no—
78C2×C3—451no—
79D3—62no—
80D3—302no—
81C5C2×C3⋊#15711yescharacteristic, complemented, Sylow
82C22—451no—
83C4—271no—
84C4—1351no—
85C3—22no—
86C3—42no—
87C3D5×#15711yescharacteristic, complemented
88C2—51no—
89C2—91no—
90C2—451no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC33×C5C2×C4
prime radicalC3×D5×C3⋊D3C2
cosocleC3×C5×C3⋊D3C22
LCSG ▷ C33×C5
UCSC1

Complements

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

NH ≅ G/Ntype
2. C3⋊#4379C2semidirect
3. C5×C3⋊#157C2semidirect
5. C3×C3⋊D15C4semidirect
7. C33×D5C4semidirect
13. C33×C5C2×C4semidirect
17. C3⋊#157D5direct (N × H)
18. C3⋊D15Dic3semidirect
24. C32×D5Dic3semidirect
35. C32×C5C2×Dic3semidirect
46. C3×D5#157semidirect
48. C33C4×D5semidirect
62. C3×C5C2×#157semidirect
69. D5C3⋊#157direct (N × H)
72. C32D5×Dic3semidirect
81. C5C2×C3⋊#157semidirect
87. C3D5×#157semidirect

Maximal subgroups

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

subgroupindex
C3×D5×C3⋊D32
C3⋊#43792
C5×C3⋊#1572
D5×#1573
C2×C3⋊#1575
D5×Dic39