Finite Group Databasebeta

← C5×D3×Dic15 #14268278

Subgroups — C5×D3×Dic15 #14268278

Order 1800.

184 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 64 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×C52×D3C211yesmaximal, characteristic
2C5×C3⋊Dic15C211yesmaximal, characteristic, complemented
3C3×C5×Dic15C211yesmaximal, characteristic, complemented
4C2×C5×Dic15—31nomaximal
5C5×D3×Dic5—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C3×C52×D3C412yescomplemented
8D3×Dic15C511yesmaximal, characteristic, direct product factor
9C5×D3×Dic3—51nomaximal
10C22×C3×C52—31no—
11C2×C52×D3D311yescharacteristic
12C5×Dic15—31no—
13C5×Dic15—31no—
14C5×Dic15—61no—
15C5×Dic15D311yescharacteristic, direct product factor
16C3×C5×Dic5—31no—
17C32×C52C2×C411yescharacteristic, complemented, Hall
18C2×C5×Dic5—91noHall
19C2×C3×C5×D3—22no—
20C2×C3×C5×D3D511yescharacteristic
21C2×C3×C5×D3C2×C511yescharacteristic
22C3⋊Dic15C2×C511yescharacteristic, complemented
23C5×C3⋊Dic3—51no—
24C3×Dic15C2×C511yescharacteristic, complemented
25C3×C5×Dic3—51no—
26C2×C3×C52—21no—
27C2×C3×C52—32no—
28C2×C3×C52C2×D311yescharacteristic
29C2×C3×C52C2×D311yescharacteristic
30C52×D3Dic312yescomplemented
31C2×Dic15—31no—
32C2×C5×Dic3—151no—
33C4×C5×D3—151no—
34D3×Dic5—31no—
35C22×C52—31no—
36C5×Dic5—31no—
37C5×Dic5—91no—
38C2×C32×C5—22no—
39C2×C32×C5C2×D511yescharacteristic
40C2×C32×C5C22×C511yescharacteristic
41C3×C5×D3—24no—
42C3×C5×D3Dic512yescomplemented
43C3×C5×D3C4×C512yescomplemented
44C3×C52—21no—
45C3×C52C4×D311yescharacteristic, complemented
46C3×C52C2×Dic311yescharacteristic, complemented
47D3×Dic3—51noHall
48C22×C3×C5—31no—
49C22×C3×C5—31no—
50C22×C3×C5—62no—
51C2×C5×D3—22no—
52C2×C5×D3C5×D311yescharacteristic
53C2×C5×D3D1511yescharacteristic
54C3×C4×C5—151no—
55Dic15—31no—
56Dic15—31no—
57Dic15—61no—
58Dic15C5×D311yescharacteristic, direct product factor
59C3×Dic5—31no—
60C5×Dic3—51no—
61C5×Dic3—151no—
62C5×Dic3—151no—
63C5×Dic3—301no—
64C2×C52—32no—
65C2×C52D3211yescharacteristic
66C32×C5—22no—
67C32×C5C2×Dic511yescharacteristic, complemented
68C32×C5C2×C4×C511yescharacteristic, complemented
69C2×C4×C5—451no—
70C2×Dic5—91no—
71C2×C3×D3C5×D511yescharacteristic
72C3⋊Dic3—51no—
73C3×Dic3—51no—
74C2×C3×C5—21no—
75C2×C3×C5—21no—
76C2×C3×C5—22no—
77C2×C3×C5—22no—
78C2×C3×C5—32no—
79C2×C3×C5—32no—
80C2×C3×C5—42no—
81C2×C3×C5—64no—
82C2×C3×C5D3×D511yescharacteristic
83C2×C3×C5C2×C5×D311yescharacteristic
84C2×C3×C5C2×C5×D311yescharacteristic
85C2×C3×C5C2×D1511yescharacteristic
86C5×D3—24no—
87C5×D3C5×Dic312yescomplemented
88C5×D3Dic1512yesdirect product factor
89C52D3×Dic311yescharacteristic, complemented, Sylow
90C2×Dic3—151no—
91C4×D3—151no—
92C22×C5—31no—
93C22×C5—31no—
94C22×C5—62no—
95C4×C5—151no—
96C4×C5—451no—
97Dic5—31no—
98Dic5—91no—
99C2×C32C2×C5×D511yescharacteristic
100C3×D3C5×Dic512yescomplemented
101C3×C5—21no—
102C3×C5—21no—
103C3×C5—22no—
104C3×C5—22no—
105C3×C5—42no—
106C3×C5D3×Dic511yescharacteristic, complemented
107C3×C5C4×C5×D311yescharacteristic, complemented
108C3×C5C2×C5×Dic311yescharacteristic, complemented
109C3×C5C2×Dic1511yescharacteristic, complemented
110C22×C3—31no—
111C2×D3C5×D1511yescharacteristic
112C3×C4—151no—
113Dic3—51no—
114Dic3—151no—
115Dic3—151no—
116Dic3—301no—
117C2×C5—22no—
118C2×C5—32no—
119C2×C5—32no—
120C2×C5—64no—
121C2×C5C5×D3211yescharacteristic
122C2×C5D3×D1511yescharacteristic
123C32C2×C5×Dic511yescharacteristic, complemented, Sylow
124C2×C4—451noSylow
125C2×C3—21no—
126C2×C3—32no—
127C2×C3C5×D3×D511yescharacteristic
128C2×C3C2×C5×D1511yescharacteristic
129D3C5×Dic1512yesdirect product factor
130C5—22no—
131C5C5×D3×Dic311yescharacteristic, complemented
132C5D3×Dic1511yescharacteristic, direct product factor
133C22—31no—
134C4—151no—
135C4—451no—
136C3—21no—
137C3C5×D3×Dic511yescharacteristic, complemented
138C3C2×C5×Dic1511yescharacteristic, complemented
139C2—32no—
140C2C5×D3×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C5D3×D15
commutator, hypocenterC32×C5C2×C4×C5
FrattiniC2C5×D3×D15
Fitting, socleC2×C32×C52C22
prime radicalC2×C3×C52×D3C2
cosocleC2×C32×C5C22×C5
LCSG ▷ C32×C5
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×C3⋊Dic15C2semidirect
3. C3×C5×Dic15C2semidirect
7. C3×C52×D3C4semidirect
8. D3×Dic15C5direct (N × H)
15. C5×Dic15D3direct (N × H)
17. C32×C52C2×C4semidirect
22. C3⋊Dic15C2×C5semidirect
24. C3×Dic15C2×C5semidirect
30. C52×D3Dic3semidirect
42. C3×C5×D3Dic5semidirect
43. C3×C5×D3C4×C5semidirect
45. C3×C52C4×D3semidirect
46. C3×C52C2×Dic3semidirect
58. Dic15C5×D3direct (N × H)
67. C32×C5C2×Dic5semidirect
68. C32×C5C2×C4×C5semidirect
87. C5×D3C5×Dic3semidirect
88. C5×D3Dic15direct (N × H)
89. C52D3×Dic3semidirect
100. C3×D3C5×Dic5semidirect
106. C3×C5D3×Dic5semidirect
107. C3×C5C4×C5×D3semidirect
108. C3×C5C2×C5×Dic3semidirect
109. C3×C5C2×Dic15semidirect
123. C32C2×C5×Dic5semidirect
129. D3C5×Dic15direct (N × H)
131. C5C5×D3×Dic3semidirect
132. C5D3×Dic15direct (N × H)
137. C3C5×D3×Dic5semidirect
138. C3C2×C5×Dic15semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C52×D32
C5×C3⋊Dic152
C3×C5×Dic152
C2×C5×Dic153
C5×D3×Dic53
D3×Dic155
C5×D3×Dic35