Finite Group Databasebeta

← C3×Dic5×D15 #14268234

Subgroups — C3×Dic5×D15 #14268234

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
2C3×C3⋊#1039C211yesmaximal, characteristic, complemented
3C32×C5×Dic5C211yesmaximal, characteristic, complemented
4Dic5×D15C311yesmaximal, characteristic, direct product factor
5C3×D5×Dic5—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C3×C5×D15C412yescomplemented
8C3×C4×D15—51nomaximal
9C3×D3×Dic5—51nomaximal
10C2×C5×D15C2×C311yescharacteristic
11C2×C3×C5×D5—31no—
12C3⋊#1039C2×C311yescharacteristic, complemented
13C3×#1039—31no—
14C3×C5×Dic5—21no—
15C3×C5×Dic5D311yescharacteristic, complemented
16C3×C5×Dic5C2×C311yescharacteristic, complemented
17C32×C52C2×C411yescharacteristic, complemented, Hall
18D5×Dic5—31noHall
19C2×C3×D15D511yescharacteristic
20C2×C3×C5×D3—51no—
21C32×C4×C5—51no—
22C3×Dic15—51no—
23C3×Dic15—51no—
24C3×Dic15—102no—
25C32×Dic5D511yescharacteristic, complemented
26C2×C3×C52—21no—
27C2×C3×C52C2×D311yescharacteristic
28C2×C3×C52C22×C311yescharacteristic
29C5×D15C3×C412yescomplemented
30C3×C5×D5—32no—
31C4×D15—51no—
32C2×C3×Dic5—151no—
33C3×C4×D5—151no—
34D3×Dic5—51no—
35C2×C5×D5—31no—
36#1039—31no—
37C5×Dic5C3×D311yescharacteristic, complemented
38C2×C32×C5—22no—
39C2×C32×C5C2×D511yescharacteristic
40C2×C32×C5C2×D511yescharacteristic
41C3×D15Dic512yesdirect product factor
42C3×C5×D3—52no—
43C3×C52—21no—
44C3×C52C4×D311yescharacteristic, complemented
45C3×C52C2×C3×C411yescharacteristic, complemented
46C3×C4×D3—251noHall
47C22×C3×C5—151no—
48C2×D15C3×D511yescharacteristic
49C2×C5×D3—51no—
50C2×C3×D5—31no—
51C3×C4×C5—51no—
52C3×C4×C5—51no—
53C3×C4×C5—101no—
54Dic15—51no—
55Dic15—51no—
56Dic15—102no—
57C3×Dic5—21no—
58C3×Dic5—151no—
59C3×Dic5—151no—
60C3×Dic5—302no—
61C3×Dic5C3×D511yescharacteristic, complemented
62C3×Dic5D1511yescharacteristic, direct product factor
63C2×C52C2×C3×D311yescharacteristic
64C5×D5—32no—
65C32×C5—22no—
66C32×C5C4×D511yescharacteristic, complemented
67C32×C5C2×Dic511yescharacteristic, complemented
68C2×Dic5—151no—
69C4×D5—151no—
70C2×C3×D3—51no—
71C32×C4—51no—
72C3×Dic3—251no—
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×C3×D511yescharacteristic
81C2×C3×C5C2×C3×D511yescharacteristic
82C2×C3×C5C2×D1511yescharacteristic
83D15C3×Dic512yesdirect product factor
84C3×D5—32no—
85C5×D3—52no—
86C52C3×C4×D311yescharacteristic, complemented, Sylow
87C2×C3×C4—751no—
88C4×D3—251no—
89C22×C5—151no—
90C2×D5—31no—
91C4×C5—51no—
92Dic5—151no—
93Dic5—151no—
94Dic5—302no—
95Dic5C3×D1511yescharacteristic, direct product factor
96C2×C32D5211yescharacteristic
97C3×D3—52no—
98C3×C5—21no—
99C3×C5—21no—
100C3×C5—22no—
101C3×C5—22no—
102C3×C5—42no—
103C3×C5D3×Dic511yescharacteristic, complemented
104C3×C5C3×C4×D511yescharacteristic, complemented
105C3×C5C2×C3×Dic511yescharacteristic, complemented
106C3×C5C4×D1511yescharacteristic, complemented
107C22×C3—151no—
108C2×D3—51no—
109C3×C4—51no—
110C3×C4—51no—
111C3×C4—101no—
112C3×C4—751no—
113Dic3—251no—
114C2×C5—22no—
115C2×C5—152no—
116C2×C5C3×D3×D511yescharacteristic
117C2×C5C2×C3×D1511yescharacteristic
118D5—32no—
119C32D5×Dic511yescharacteristic, complemented, Sylow
120C2×C4—751noSylow
121C2×C3—21no—
122C2×C3—152no—
123C2×C3C3×D5211yescharacteristic
124C2×C3D5×D1511yescharacteristic
125D3—52no—
126C5—22no—
127C5C3×D3×Dic511yescharacteristic, complemented
128C5C3×C4×D1511yescharacteristic, complemented
129C22—151no—
130C4—51no—
131C4—751no—
132C3—21no—
133C3C3×D5×Dic511yescharacteristic, complemented
134C3Dic5×D1511yescharacteristic, direct product factor
135C2—152no—
136C2C3×D5×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C3D5×D15
commutator, hypocenterC3×C52C2×C3×C4
FrattiniC2C3×D5×D15
Fitting, socleC2×C32×C52C22
prime radicalC2×C3×C5×D15C2
cosocleC2×C3×C52C22×C3
LCSG ▷ C3×C52
UCSC1 ◁ C2×C3

Complements

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

NH ≅ G/Ntype
2. C3×C3⋊#1039C2semidirect
3. C32×C5×Dic5C2semidirect
4. Dic5×D15C3direct (N × H)
7. C3×C5×D15C4semidirect
12. C3⋊#1039C2×C3semidirect
15. C3×C5×Dic5D3semidirect
16. C3×C5×Dic5C2×C3semidirect
17. C32×C52C2×C4semidirect
25. C32×Dic5D5semidirect
29. C5×D15C3×C4semidirect
37. C5×Dic5C3×D3semidirect
41. C3×D15Dic5direct (N × H)
44. C3×C52C4×D3semidirect
45. C3×C52C2×C3×C4semidirect
61. C3×Dic5C3×D5semidirect
62. C3×Dic5D15direct (N × H)
66. C32×C5C4×D5semidirect
67. C32×C5C2×Dic5semidirect
83. D15C3×Dic5direct (N × H)
86. C52C3×C4×D3semidirect
95. Dic5C3×D15direct (N × H)
103. C3×C5D3×Dic5semidirect
104. C3×C5C3×C4×D5semidirect
105. C3×C5C2×C3×Dic5semidirect
106. C3×C5C4×D15semidirect
119. C32D5×Dic5semidirect
127. C5C3×D3×Dic5semidirect
128. C5C3×C4×D15semidirect
133. C3C3×D5×Dic5semidirect
134. C3Dic5×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×D152
C3×C3⋊#10392
C32×C5×Dic52
Dic5×D153
C3×D5×Dic53
C3×C4×D155
C3×D3×Dic55