Finite Group Databasebeta

← C5×Dic3×D15 #14268277

Subgroups — C5×Dic3×D15 #14268277

Order 1800.

168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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×C5×D15C211yesmaximal, characteristic
2C5×C3⋊Dic15C211yesmaximal, characteristic, complemented
3C3×C52×Dic3C211yesmaximal, characteristic, complemented
4C4×C5×D15—31nomaximal
5C5×D5×Dic3—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C3×C5×D15C412yescomplemented
8Dic3×D15C511yesmaximal, characteristic, direct product factor
9C5×D3×Dic3—51nomaximal
10C2×C5×D15D311yescharacteristic
11C2×C3×C5×D5—31no—
12C3×C4×C52—31no—
13C5×Dic15—31no—
14C5×Dic15—31no—
15C5×Dic15—61no—
16C52×Dic3D311yescharacteristic, complemented
17C32×C52C2×C411yescharacteristic, complemented, Hall
18C4×C5×D5—91noHall
19C2×C3×D15C2×C511yescharacteristic
20C2×C3×C5×D3—51no—
21C3⋊Dic15C2×C511yescharacteristic, complemented
22C5×C3⋊Dic3—51no—
23C3×C5×Dic3—22no—
24C3×C5×Dic3D511yescharacteristic, complemented
25C3×C5×Dic3C2×C511yescharacteristic, complemented
26C2×C3×C52—21no—
27C2×C3×C52C2×D311yescharacteristic
28C2×C3×C52C2×D311yescharacteristic
29C5×D15Dic312yesdirect product factor
30C3×C5×D5—32no—
31C4×D15—31no—
32C2×C5×Dic3—151no—
33C4×C5×D3—151no—
34D5×Dic3—31no—
35C2×C5×D5—31no—
36C4×C52—31no—
37C5×Dic5—91no—
38C2×C32×C5—22no—
39C2×C32×C5C2×D511yescharacteristic
40C2×C32×C5C22×C511yescharacteristic
41C3×D15C4×C512yescomplemented
42C3×C5×D3—52no—
43C3×C52—21no—
44C3×C52C4×D311yescharacteristic, complemented
45C3×C52C2×Dic311yescharacteristic, complemented
46D3×Dic3—51noHall
47C22×C3×C5—151no—
48C2×D15C5×D311yescharacteristic
49C2×C5×D3—51no—
50C2×C3×D5—31no—
51C3×C4×C5—31no—
52C3×C4×C5—31no—
53C3×C4×C5—62no—
54Dic15—31no—
55Dic15—31no—
56Dic15—61no—
57C5×Dic3—22no—
58C5×Dic3—151no—
59C5×Dic3—151no—
60C5×Dic3—301no—
61C5×Dic3C5×D311yescharacteristic, complemented
62C5×Dic3D1511yescharacteristic, direct product factor
63C2×C52D3211yescharacteristic
64C5×D5—32no—
65C32×C5—22no—
66C32×C5C4×D511yescharacteristic, complemented
67C32×C5C2×C4×C511yescharacteristic, complemented
68C2×C4×C5—451no—
69C4×D5—91no—
70C2×C3×D3—51no—
71C3⋊Dic3—51no—
72C3×Dic3C5×D511yescharacteristic, complemented
73C2×C3×C5—21no—
74C2×C3×C5—21no—
75C2×C3×C5—22no—
76C2×C3×C5—22no—
77C2×C3×C5—42no—
78C2×C3×C5—152no—
79C2×C3×C5D3×D511yescharacteristic
80C2×C3×C5C2×C5×D311yescharacteristic
81C2×C3×C5C2×C5×D311yescharacteristic
82C2×C3×C5C2×D1511yescharacteristic
83D15C5×Dic312yesdirect product factor
84C3×D5—32no—
85C5×D3—52no—
86C52D3×Dic311yescharacteristic, complemented, Sylow
87C2×Dic3—151no—
88C4×D3—151no—
89C22×C5—151no—
90C2×D5—31no—
91C4×C5—31no—
92C4×C5—31no—
93C4×C5—62no—
94C4×C5—451no—
95Dic5—91no—
96C2×C32C2×C5×D511yescharacteristic
97C3×D3—52no—
98C3×C5—21no—
99C3×C5—21no—
100C3×C5—22no—
101C3×C5—22no—
102C3×C5—42no—
103C3×C5D5×Dic311yescharacteristic, complemented
104C3×C5C4×C5×D311yescharacteristic, complemented
105C3×C5C2×C5×Dic311yescharacteristic, complemented
106C3×C5C4×D1511yescharacteristic, complemented
107C22×C3—151no—
108C2×D3—51no—
109C3×C4—31no—
110Dic3—151no—
111Dic3—151no—
112Dic3—301no—
113Dic3C5×D1511yescharacteristic, direct product factor
114C2×C5—22no—
115C2×C5—152no—
116C2×C5C5×D3211yescharacteristic
117C2×C5D3×D1511yescharacteristic
118D5—32no—
119C32C4×C5×D511yescharacteristic, complemented, Sylow
120C2×C4—451noSylow
121C2×C3—21no—
122C2×C3—152no—
123C2×C3C5×D3×D511yescharacteristic
124C2×C3C2×C5×D1511yescharacteristic
125D3—52no—
126C5—22no—
127C5C5×D3×Dic311yescharacteristic, complemented
128C5Dic3×D1511yescharacteristic, direct product factor
129C22—151no—
130C4—31no—
131C4—451no—
132C3—21no—
133C3C5×D5×Dic311yescharacteristic, complemented
134C3C4×C5×D1511yescharacteristic, complemented
135C2—152no—
136C2C5×D3×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C5D3×D15
commutator, hypocenterC32×C5C2×C4×C5
FrattiniC2C5×D3×D15
Fitting, socleC2×C32×C52C22
prime radicalC2×C3×C5×D15C2
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×C52×Dic3C2semidirect
7. C3×C5×D15C4semidirect
8. Dic3×D15C5direct (N × H)
16. C52×Dic3D3semidirect
17. C32×C52C2×C4semidirect
21. C3⋊Dic15C2×C5semidirect
24. C3×C5×Dic3D5semidirect
25. C3×C5×Dic3C2×C5semidirect
29. C5×D15Dic3direct (N × H)
41. C3×D15C4×C5semidirect
44. C3×C52C4×D3semidirect
45. C3×C52C2×Dic3semidirect
61. C5×Dic3C5×D3semidirect
62. C5×Dic3D15direct (N × H)
66. C32×C5C4×D5semidirect
67. C32×C5C2×C4×C5semidirect
72. C3×Dic3C5×D5semidirect
83. D15C5×Dic3direct (N × H)
86. C52D3×Dic3semidirect
103. C3×C5D5×Dic3semidirect
104. C3×C5C4×C5×D3semidirect
105. C3×C5C2×C5×Dic3semidirect
106. C3×C5C4×D15semidirect
113. Dic3C5×D15direct (N × H)
119. C32C4×C5×D5semidirect
127. C5C5×D3×Dic3semidirect
128. C5Dic3×D15direct (N × H)
133. C3C5×D5×Dic3semidirect
134. C3C4×C5×D15semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×D152
C5×C3⋊Dic152
C3×C52×Dic32
C4×C5×D153
C5×D5×Dic33
Dic3×D155
C5×D3×Dic35