Finite Group Databasebeta

← C2×C3⋊(C25⋊(D19⋊C3)) #30685482

Subgroups — C2×C3⋊(C25⋊(D19⋊C3)) #30685482

Order 17100.

132 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 42 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×C3×C25×C19⋊C3C211yesmaximal, characteristic, complemented
2C3⋊(C25⋊(D19⋊C3))C212yesmaximal, direct product factor
3C2×D1425C311yesmaximal, characteristic, complemented
4C2×C25⋊(D19⋊C3)—31nomaximal
5C3×C25×C19⋊C3C2211yescharacteristic, complemented, Hall
6C2×C3⋊(C5⋊(D19⋊C3))—51nomaximal
7D1425C2×C312yescomplemented
8C2×C25×C19⋊C3—21no—
9C2×C25×C19⋊C3D311yescharacteristic, complemented
10C25⋊(D19⋊C3)—32no—
11C2×C3×C19×C25C2×C311yescharacteristic, complemented
12C2×D475—31noHall
13C2×C3×C5×C19⋊C3D511yescharacteristic
14C3⋊(C5⋊(D19⋊C3))—52no—
15C3×C19×C25C22×C311yescharacteristic, complemented
16C25×C19⋊C3—21no—
17C25×C19⋊C3C2×D311yescharacteristic, complemented
18C2×D285—51no—
19C2×C5⋊(D19⋊C3)—151no—
20C2×C19×C25C3×D311yescharacteristic, complemented
21D475—32no—
22C2×C3×D75—191nomaximal, Hall
23C3×C5×C19⋊C3C2×D511yescharacteristic
24C2×C3⋊(D19⋊C3)—251noHall
25C2×C3×C5×C19C3×D511yescharacteristic
26D285—52no—
27C2×C5×C19⋊C3—21no—
28C2×C5×C19⋊C3D1511yescharacteristic
29C5⋊(D19⋊C3)—152no—
30C19×C25C2×C3×D311yescharacteristic, complemented, Hall
31C2×C32×C25—381no—
32C3×D75—192no—
33C2×D95—151no—
34C2×C3×C19⋊C3D2511yescharacteristic, complemented
35C3⋊(D19⋊C3)—252no—
36C2×D75—191no—
37C2×C3×D25—571no—
38C3×C5×C19C2×C3×D511yescharacteristic
39C5×C19⋊C3—21no—
40C5×C19⋊C3C2×D1511yescharacteristic
41C2×D57—251no—
42C2×D19⋊C3—751no—
43C32×C25—381noHall
44C2×C5×C19C3×D1511yescharacteristic
45D95—152no—
46C2×C3×D15—951no—
47C3×C19⋊C3C2×D2511yescharacteristic, complemented, Hall
48C2×C3×C25—381no—
49C2×C3×C25—381no—
50C2×C3×C25D19⋊C311yescharacteristic, complemented
51D75—192no—
52C3×D25—572no—
53C2×C3×C19C3×D2511yescharacteristic, complemented
54D57—252no—
55C2×C19⋊C3—21no—
56C2×C19⋊C3D7511yescharacteristic, complemented
57D19⋊C3—752no—
58C2×D25—571noHall
59C5×C19C2×C3×D1511yescharacteristic
60C2×C32×C5—381no—
61C3×D15—952no—
62C2×D19—751noHall
63C3×C25—381no—
64C3×C25—381no—
65C3×C25C2×D19⋊C311yescharacteristic, complemented
66C2×D15—951no—
67C2×C3×D5—2851no—
68C3×C19C2×C3×D2511yescharacteristic, complemented
69C19⋊C3—21no—
70C19⋊C3C2×D7511yescharacteristic, complemented
71C2×C25C3⋊(D19⋊C3)11yescharacteristic, complemented
72D25—572no—
73C32×C5—381no—
74C2×C19C3×D7511yescharacteristic, complemented
75D19—752no—
76C2×C3×D3—4751noHall
77C2×C3×C5—381no—
78C2×C3×C5—381no—
79C2×C3×C5C5⋊(D19⋊C3)11yescharacteristic
80D15—952no—
81C3×D5—2852no—
82C25C2×C3⋊(D19⋊C3)11yescharacteristic, complemented, Sylow
83C2×D5—2851no—
84C19C2×C3×D7511yescharacteristic, complemented, Sylow
85C2×C32—381no—
86C3×D3—4752no—
87C3×C5—381no—
88C3×C5—381no—
89C3×C5C2×C5⋊(D19⋊C3)11yescharacteristic
90C22×C3—14251no—
91C2×D3—4751no—
92C2×C5C3⋊(C5⋊(D19⋊C3))11yescharacteristic
93D5—2852no—
94C32—381noSylow
95C2×C3—381no—
96C2×C3—381no—
97C2×C3—14252no—
98C2×C3C25⋊(D19⋊C3)11yescharacteristic, complemented
99D3—4752no—
100C5C2×C3⋊(C5⋊(D19⋊C3))11yescharacteristic
101C22—14251noSylow
102C3—381no—
103C3—381no—
104C3C2×C25⋊(D19⋊C3)11yescharacteristic, complemented
105C2—14252no—
106C2C3⋊(C25⋊(D19⋊C3))11yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2C3⋊(C25⋊(D19⋊C3))
commutator, cosocle, hypocenterC3×C19×C25C22×C3
FrattiniC5C2×C3⋊(C5⋊(D19⋊C3))
FittingC2×C3×C19×C25C2×C3
socleC2×C3×C5×C19C3×D5
LCSG ▷ C3×C19×C25
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×C25×C19⋊C3C2semidirect
2. C3⋊(C25⋊(D19⋊C3))C2direct (N × H)
3. C2×D1425C3semidirect
5. C3×C25×C19⋊C3C22semidirect
7. D1425C2×C3semidirect
9. C2×C25×C19⋊C3D3semidirect
11. C2×C3×C19×C25C2×C3semidirect
15. C3×C19×C25C22×C3semidirect
17. C25×C19⋊C3C2×D3semidirect
20. C2×C19×C25C3×D3semidirect
30. C19×C25C2×C3×D3semidirect
34. C2×C3×C19⋊C3D25semidirect
47. C3×C19⋊C3C2×D25semidirect
50. C2×C3×C25D19⋊C3semidirect
53. C2×C3×C19C3×D25semidirect
56. C2×C19⋊C3D75semidirect
65. C3×C25C2×D19⋊C3semidirect
68. C3×C19C2×C3×D25semidirect
70. C19⋊C3C2×D75semidirect
71. C2×C25C3⋊(D19⋊C3)semidirect
74. C2×C19C3×D75semidirect
82. C25C2×C3⋊(D19⋊C3)semidirect
84. C19C2×C3×D75semidirect
98. C2×C3C25⋊(D19⋊C3)semidirect
104. C3C2×C25⋊(D19⋊C3)semidirect
106. C2C3⋊(C25⋊(D19⋊C3))direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C25×C19⋊C32
C3⋊(C25⋊(D19⋊C3))2
C2×D14253
C2×C25⋊(D19⋊C3)3
C2×C3⋊(C5⋊(D19⋊C3))5
C2×C3×D7519