Finite Group Databasebeta

← D3×D15×C121 #36344751

Subgroups — D3×D15×C121 #36344751

Order 21780.

132 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C3⋊D15×C121C211yesmaximal, characteristic, complemented
2C3×D15×C121C211yesmaximal, characteristic, complemented
3C3×C5×D3×C121C211yesmaximal, characteristic, complemented
4C2×D15×C121—31nomaximal
5D3×D5×C121—31nomaximal
6C32×C5×C121C2211yescharacteristic, complemented, Hall
7D32×C121—51nomaximal, Hall
8D15×C121—31no—
9D15×C121—31no—
10D15×C121—61no—
11D15×C121D311yescharacteristic, direct product factor
12C5×D3×C121D311yescharacteristic, complemented
13C3×D5×C121—31no—
14C2×C3×C5×C121—31no—
15C2×D5×C121—91noHall
16C3⋊D3×C121—51no—
17C3×D3×C121—51no—
18C3×D3×C121D511yescharacteristic, complemented
19D3×C11×D15C1111yesmaximal, characteristic
20C3×C5×C121—21no—
21C3×C5×C121C2×D311yescharacteristic, complemented
22C3×C5×C121C2×D311yescharacteristic, complemented
23C2×D3×C121—151no—
24C2×D3×C121—151no—
25C2×C5×C121—31no—
26D5×C121—31no—
27D5×C121—91no—
28C32×C121C2×D511yescharacteristic, complemented, Hall
29C11×C3⋊D15C2×C1111yescharacteristic
30C3×C11×D15C2×C1111yescharacteristic
31C3×C5×D3×C11C2×C1111yescharacteristic
32C2×C3×C121—31no—
33C2×C3×C121—151no—
34D3×C121—51no—
35D3×C121—151no—
36D3×C121—151no—
37D3×C121—301no—
38D3×C121D1511yescharacteristic, direct product factor
39C2×C11×D15—31no—
40D3×D5×C11—31no—
41C5×C121D3211yescharacteristic, complemented, Hall
42C32×C5×C11C22×C1111yescharacteristic
43C22×C121—451noHall
44D32×C11—51no—
45C3×C121—21no—
46C3×C121D3×D511yescharacteristic, complemented
47C3×C121C2×D1511yescharacteristic, complemented
48C2×C3×C5×C11—31no—
49C11×D15—31no—
50C11×D15—31no—
51C11×D15—61no—
52C11×D15D3×C1111yescharacteristic
53C5×D3×C11D3×C1111yescharacteristic
54C3×D5×C11—31no—
55C2×C121—31no—
56C2×C121—151no—
57C2×C121—451no—
58C2×D5×C11—91no—
59C11×C3⋊D3—51no—
60C3×D3×C11—51no—
61C3×D3×C11D5×C1111yescharacteristic
62D3×D15C12111yescharacteristic, direct product factor, Hall
63C3×C5×C11—21no—
64C3×C5×C11C2×D3×C1111yescharacteristic
65C3×C5×C11C2×D3×C1111yescharacteristic
66C2×D3×C11—151no—
67C2×D3×C11—151no—
68C121D3×D1511yescharacteristic, direct product factor, Sylow
69C2×C5×C11—31no—
70D5×C11—31no—
71D5×C11—91no—
72C32×C11C2×D5×C1111yescharacteristic
73C3⋊D15C2×C12111yescharacteristic, complemented
74C3×D15C2×C12111yescharacteristic, complemented
75C3×C5×D3C2×C12111yescharacteristic, complemented
76C2×C3×C11—31no—
77C2×C3×C11—151no—
78D3×C11—51no—
79D3×C11—151no—
80D3×C11—151no—
81D3×C11—301no—
82D3×C11C11×D1511yescharacteristic
83C2×D15—31no—
84D3×D5—31no—
85C5×C11D32×C1111yescharacteristic
86C32×C5C22×C12111yescharacteristic, complemented, Hall
87C22×C11—451no—
88D32—51noHall
89C3×C11—21no—
90C3×C11D3×D5×C1111yescharacteristic
91C3×C11C2×C11×D1511yescharacteristic
92C2×C3×C5—31no—
93D15—31no—
94D15—31no—
95D15—61no—
96D15D3×C12111yescharacteristic, direct product factor
97C3×D5—31no—
98C5×D3D3×C12111yescharacteristic, complemented
99C2×C11—31no—
100C2×C11—151no—
101C2×C11—451no—
102C2×D5—91noHall
103C3⋊D3—51no—
104C3×D3—51no—
105C3×D3D5×C12111yescharacteristic, complemented
106C3×C5—21no—
107C3×C5C2×D3×C12111yescharacteristic, complemented
108C3×C5C2×D3×C12111yescharacteristic, complemented
109C2×D3—151no—
110C2×D3—151no—
111C11D3×C11×D1511yescharacteristic
112C2×C5—31no—
113D5—31no—
114D5—91no—
115C32C2×D5×C12111yescharacteristic, complemented, Sylow
116C2×C3—31no—
117C2×C3—151no—
118D3—51no—
119D3—151no—
120D3—151no—
121D3—301no—
122D3D15×C12111yescharacteristic, direct product factor
123C5D32×C12111yescharacteristic, complemented, Sylow
124C22—451noSylow
125C3—21no—
126C3D3×D5×C12111yescharacteristic, complemented
127C3C2×D15×C12111yescharacteristic, complemented
128C2—31no—
129C2—151no—
130C2—451no—
subgroupG/H
center, hypercenterC121D3×D15
commutator, hypocenterC32×C5C22×C121
FrattiniC11D3×C11×D15
FittingC32×C5×C121C22
socle, cosocleC32×C5×C11C22×C11
prime radicalD3×C11×D15C11
LCSG ▷ C32×C5
UCSC1 ◁ C121

Complements

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

NH ≅ G/Ntype
1. C3⋊D15×C121C2semidirect
2. C3×D15×C121C2semidirect
3. C3×C5×D3×C121C2semidirect
6. C32×C5×C121C22semidirect
11. D15×C121D3direct (N × H)
12. C5×D3×C121D3semidirect
18. C3×D3×C121D5semidirect
21. C3×C5×C121C2×D3semidirect
22. C3×C5×C121C2×D3semidirect
28. C32×C121C2×D5semidirect
38. D3×C121D15direct (N × H)
41. C5×C121D32semidirect
46. C3×C121D3×D5semidirect
47. C3×C121C2×D15semidirect
62. D3×D15C121direct (N × H)
68. C121D3×D15direct (N × H)
73. C3⋊D15C2×C121semidirect
74. C3×D15C2×C121semidirect
75. C3×C5×D3C2×C121semidirect
86. C32×C5C22×C121semidirect
96. D15D3×C121direct (N × H)
98. C5×D3D3×C121semidirect
105. C3×D3D5×C121semidirect
107. C3×C5C2×D3×C121semidirect
108. C3×C5C2×D3×C121semidirect
115. C32C2×D5×C121semidirect
122. D3D15×C121direct (N × H)
123. C5D32×C121semidirect
126. C3D3×D5×C121semidirect
127. C3C2×D15×C121semidirect

Maximal subgroups

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

subgroupindex
C3⋊D15×C1212
C3×D15×C1212
C3×C5×D3×C1212
C2×D15×C1213
D3×D5×C1213
D32×C1215
D3×C11×D1511