Finite Group Databasebeta

← C3×D5×Dic15 #14268235

Subgroups — C3×D5×Dic15 #14268235

Order 1800.

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

normal subgroups only

This group has 176 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×C32×C5×D5C211yesmaximal, characteristic
2C3×C3⋊#1039C211yesmaximal, characteristic, complemented
3C3×C5×Dic15C211yesmaximal, characteristic, complemented
4D5×Dic15C311yesmaximal, characteristic, direct product factor
5C3×D5×Dic5—31nomaximal
6C2×C32×C52C2211yescharacteristic
7C32×C5×D5C412yescomplemented
8C2×C3×Dic15—51nomaximal
9C3×D5×Dic3—51nomaximal
10C2×C3×C5×D5—21no—
11C2×C3×C5×D5D311yescharacteristic
12C2×C3×C5×D5C2×C311yescharacteristic
13C3⋊#1039C2×C311yescharacteristic, complemented
14C5×Dic15C2×C311yescharacteristic, complemented
15C3×#1039—31no—
16C3×C5×Dic5—31no—
17C32×C52C2×C411yescharacteristic, complemented, Hall
18D5×Dic5—31noHall
19C22×C32×C5—51no—
20C2×C32×D5D511yescharacteristic
21C3×Dic15—51no—
22C3×Dic15—51no—
23C3×Dic15—102no—
24C3×Dic15D511yescharacteristic, direct product factor
25C3×C5×Dic3—51no—
26C2×C3×C52—21no—
27C2×C3×C52C2×D311yescharacteristic
28C2×C3×C52C22×C311yescharacteristic
29C3×C5×D5—22no—
30C3×C5×D5Dic312yescomplemented
31C3×C5×D5C3×C412yescomplemented
32C2×Dic15—51no—
33C2×C3×Dic5—151no—
34C3×C4×D5—151no—
35D5×Dic3—51no—
36C2×C5×D5C3×D311yescharacteristic
37#1039—31no—
38C5×Dic5—31no—
39C2×C32×C5—22no—
40C2×C32×C5—52no—
41C2×C32×C5C2×D511yescharacteristic
42C2×C32×C5C2×D511yescharacteristic
43C32×D5Dic512yescomplemented
44C3×C52—21no—
45C3×C52C2×Dic311yescharacteristic, complemented
46C3×C52C2×C3×C411yescharacteristic, complemented
47C2×C3×Dic3—251noHall
48C22×C3×C5—51no—
49C22×C3×C5—51no—
50C22×C3×C5—101no—
51C2×C3×D5—21no—
52C2×C3×D5C3×D511yescharacteristic
53C2×C3×D5D1511yescharacteristic
54C3×C4×C5—151no—
55Dic15—51no—
56Dic15—51no—
57Dic15—102no—
58Dic15C3×D511yescharacteristic, direct product factor
59C3×Dic5—31no—
60C3×Dic5—151no—
61C3×Dic5—151no—
62C3×Dic5—302no—
63C5×Dic3—51no—
64C2×C52C2×C3×D311yescharacteristic
65C5×D5C3×Dic312yescomplemented
66C32×C5—22no—
67C32×C5C4×D511yescharacteristic, complemented
68C32×C5C2×Dic511yescharacteristic, complemented
69C2×Dic5—151no—
70C4×D5—151no—
71C22×C32—51no—
72C3×Dic3—51no—
73C3×Dic3—251no—
74C2×C3×C5—21no—
75C2×C3×C5—21no—
76C2×C3×C5—22no—
77C2×C3×C5—22no—
78C2×C3×C5—42no—
79C2×C3×C5—52no—
80C2×C3×C5—52no—
81C2×C3×C5—102no—
82C2×C3×C5D3×D511yescharacteristic
83C2×C3×C5C2×C3×D511yescharacteristic
84C2×C3×C5C2×C3×D511yescharacteristic
85C2×C3×C5C2×D1511yescharacteristic
86C3×D5—22no—
87C3×D5C3×Dic512yescomplemented
88C3×D5Dic1512yesdirect product factor
89C52C2×C3×Dic311yescharacteristic, complemented, Sylow
90C2×C3×C4—751no—
91C2×Dic3—251no—
92C22×C5—51no—
93C2×D5C3×D1511yescharacteristic
94C4×C5—151no—
95Dic5—31no—
96Dic5—151no—
97Dic5—151no—
98Dic5—302no—
99C2×C32—52no—
100C2×C32D5211yescharacteristic
101C3×C5—21no—
102C3×C5—21no—
103C3×C5—22no—
104C3×C5—22no—
105C3×C5—42no—
106C3×C5D5×Dic311yescharacteristic, complemented
107C3×C5C3×C4×D511yescharacteristic, complemented
108C3×C5C2×C3×Dic511yescharacteristic, complemented
109C3×C5C2×Dic1511yescharacteristic, complemented
110C22×C3—51no—
111C22×C3—51no—
112C22×C3—101no—
113C3×C4—151no—
114C3×C4—751no—
115Dic3—51no—
116Dic3—251no—
117C2×C5—22no—
118C2×C5—52no—
119C2×C5C3×D3×D511yescharacteristic
120C2×C5C2×C3×D1511yescharacteristic
121D5C3×Dic1512yesdirect product factor
122C32D5×Dic511yescharacteristic, complemented, Sylow
123C2×C4—751noSylow
124C2×C3—21no—
125C2×C3—52no—
126C2×C3—52no—
127C2×C3—102no—
128C2×C3C3×D5211yescharacteristic
129C2×C3D5×D1511yescharacteristic
130C5—22no—
131C5C3×D5×Dic311yescharacteristic, complemented
132C5C2×C3×Dic1511yescharacteristic, complemented
133C22—51no—
134C4—151no—
135C4—751no—
136C3—21no—
137C3C3×D5×Dic511yescharacteristic, complemented
138C3D5×Dic1511yescharacteristic, direct product factor
139C2—52no—
140C2C3×D5×D1511yescharacteristic
subgroupG/H
center, hypercenterC2×C3D5×D15
commutator, hypocenterC3×C52C2×C3×C4
FrattiniC2C3×D5×D15
Fitting, socleC2×C32×C52C22
prime radicalC2×C32×C5×D5C2
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. C3×C5×Dic15C2semidirect
4. D5×Dic15C3direct (N × H)
7. C32×C5×D5C4semidirect
13. C3⋊#1039C2×C3semidirect
14. C5×Dic15C2×C3semidirect
17. C32×C52C2×C4semidirect
24. C3×Dic15D5direct (N × H)
30. C3×C5×D5Dic3semidirect
31. C3×C5×D5C3×C4semidirect
43. C32×D5Dic5semidirect
45. C3×C52C2×Dic3semidirect
46. C3×C52C2×C3×C4semidirect
58. Dic15C3×D5direct (N × H)
65. C5×D5C3×Dic3semidirect
67. C32×C5C4×D5semidirect
68. C32×C5C2×Dic5semidirect
87. C3×D5C3×Dic5semidirect
88. C3×D5Dic15direct (N × H)
89. C52C2×C3×Dic3semidirect
106. C3×C5D5×Dic3semidirect
107. C3×C5C3×C4×D5semidirect
108. C3×C5C2×C3×Dic5semidirect
109. C3×C5C2×Dic15semidirect
121. D5C3×Dic15direct (N × H)
122. C32D5×Dic5semidirect
131. C5C3×D5×Dic3semidirect
132. C5C2×C3×Dic15semidirect
137. C3C3×D5×Dic5semidirect
138. C3D5×Dic15direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C5×D52
C3×C3⋊#10392
C3×C5×Dic152
D5×Dic153
C3×D5×Dic53
C2×C3×Dic155
C3×D5×Dic35