Finite Group Databasebeta

← C5×Dic15×C31⋊C3 #42124635

Subgroups — C5×Dic15×C31⋊C3 #42124635

Order 27900.

160 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 54 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×C31⋊C3C211yesmaximal, characteristic
2C5×C31×Dic15C311yesmaximal, characteristic, complemented
3C5×Dic5×C31⋊C3—31nomaximal
4C3×C52×C31⋊C3C411yescharacteristic, complemented, Hall
5Dic15×C31⋊C3C511yesmaximal, characteristic, direct product factor
6C5×Dic3×C31⋊C3—51nomaximal
7C2×C52×C31⋊C3—21no—
8C2×C52×C31⋊C3D311yescharacteristic
9C2×C3×C52×C31C2×C311yescharacteristic
10C5×Dic5×C31—31noHall
11C2×C3×C5×C31⋊C3—22no—
12C2×C3×C5×C31⋊C3D511yescharacteristic
13C2×C3×C5×C31⋊C3C2×C511yescharacteristic
14C52×C31⋊C3—21no—
15C52×C31⋊C3Dic311yescharacteristic, complemented
16C3×C52×C31C3×C411yescharacteristic, complemented
17C31×Dic15C3×C511yescharacteristic, complemented
18C5×Dic3×C31—51no—
19C4×C5×C31⋊C3—151no—
20Dic5×C31⋊C3—31no—
21C2×C52×C31C3×D311yescharacteristic
22C3×C5×C31⋊C3—22no—
23C3×C5×C31⋊C3Dic511yescharacteristic, complemented
24C3×C5×C31⋊C3C4×C511yescharacteristic, complemented
25Dic3×C31⋊C3—51noHall
26C2×C3×C5×C31—22no—
27C2×C3×C5×C31C3×D511yescharacteristic
28C2×C3×C5×C31C2×C3×C511yescharacteristic
29C2×C5×C31⋊C3—24no—
30C2×C5×C31⋊C3—21no—
31C2×C5×C31⋊C3—21no—
32C2×C5×C31⋊C3—22no—
33C2×C5×C31⋊C3C5×D311yescharacteristic
34C2×C5×C31⋊C3D1511yescharacteristic
35C3×C5×Dic15—311nomaximal, Hall
36C52×C31C3×Dic311yescharacteristic, complemented, Hall
37C4×C5×C31—151no—
38Dic5×C31—31no—
39C2×C3×C31⋊C3C5×D511yescharacteristic
40C3×C5×C31—22no—
41C3×C5×C31C3×Dic511yescharacteristic, complemented
42C3×C5×C31C3×C4×C511yescharacteristic, complemented
43C5×C31⋊C3—24no—
44C5×C31⋊C3—21no—
45C5×C31⋊C3—21no—
46C5×C31⋊C3—22no—
47C5×C31⋊C3C5×Dic311yescharacteristic, complemented
48C5×C31⋊C3Dic1511yescharacteristic, direct product factor
49C2×C32×C52—311no—
50Dic3×C31—51no—
51C4×C31⋊C3—151no—
52C2×C5×C31—22no—
53C2×C5×C31C3×C5×D311yescharacteristic
54C2×C5×C31C3×D1511yescharacteristic
55C5×Dic15C31⋊C311yescharacteristic, direct product factor
56C3×C5×Dic5—931no—
57C3×C31⋊C3C5×Dic511yescharacteristic, complemented, Hall
58C32×C52—311noHall
59C2×C3×C31C3×C5×D511yescharacteristic
60C2×C31⋊C3—21no—
61C2×C31⋊C3C5×D1511yescharacteristic
62C3×Dic15—311no—
63C3×C5×Dic3—1551no—
64C5×C31—22no—
65C5×C31C3×C5×Dic311yescharacteristic, complemented
66C5×C31C3×Dic1511yescharacteristic, complemented
67C2×C3×C52—311no—
68C2×C3×C52—621no—
69C2×C3×C52C2×C31⋊C311yescharacteristic
70C4×C31—151noHall
71C5×Dic5—31noHall
72C3×C31C3×C5×Dic511yescharacteristic, complemented
73C31⋊C3—21no—
74C31⋊C3C5×Dic1511yescharacteristic, direct product factor
75C2×C32×C5—311no—
76C2×C32×C5—311no—
77C2×C32×C5—622no—
78C3×C52—311no—
79C3×C52—621no—
80C3×C52C4×C31⋊C311yescharacteristic, complemented
81C2×C31C3×C5×D1511yescharacteristic
82C3×C4×C5—4651no—
83Dic15C5×C31⋊C311yescharacteristic, direct product factor
84C3×Dic5—931no—
85C5×Dic3—51no—
86C2×C52D3×C31⋊C311yescharacteristic
87C32×C5—311no—
88C32×C5—311no—
89C32×C5—622no—
90C3×Dic3—1551noHall
91C31C3×C5×Dic1511yescharacteristic, complemented, Sylow
92C2×C3×C5—22no—
93C2×C3×C5—311no—
94C2×C3×C5—311no—
95C2×C3×C5—622no—
96C2×C3×C5—624no—
97C2×C3×C5—621no—
98C2×C3×C5—621no—
99C2×C3×C5D5×C31⋊C311yescharacteristic
100C2×C3×C5C2×C5×C31⋊C311yescharacteristic
101C52Dic3×C31⋊C311yescharacteristic, complemented, Sylow
102C4×C5—151no—
103Dic5—31no—
104C2×C32—311no—
105C3×C5—22no—
106C3×C5—311no—
107C3×C5—311no—
108C3×C5—622no—
109C3×C5—624no—
110C3×C5—621no—
111C3×C5—621no—
112C3×C5Dic5×C31⋊C311yescharacteristic, complemented
113C3×C5C4×C5×C31⋊C311yescharacteristic, complemented
114C3×C4—4651no—
115Dic3—51no—
116C2×C5—22no—
117C2×C5C5×D3×C31⋊C311yescharacteristic
118C2×C5D15×C31⋊C311yescharacteristic
119C32—311noSylow
120C2×C3—311no—
121C2×C3—621no—
122C2×C3C5×D5×C31⋊C311yescharacteristic
123C5—22no—
124C5C5×Dic3×C31⋊C311yescharacteristic, complemented
125C5Dic15×C31⋊C311yescharacteristic, direct product factor
126C4—151noSylow
127C3—311no—
128C3—621no—
129C3C5×Dic5×C31⋊C311yescharacteristic, complemented
130C2C5×D15×C31⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C5D15×C31⋊C3
commutator, hypocenterC3×C5×C31C3×C4×C5
FrattiniC2C5×D15×C31⋊C3
Fitting, socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C52×C31⋊C3C2
cosocleC2×C3×C5×C31C2×C3×C5
LCSG ▷ C3×C5×C31
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×C31×Dic15C3semidirect
4. C3×C52×C31⋊C3C4semidirect
5. Dic15×C31⋊C3C5direct (N × H)
15. C52×C31⋊C3Dic3semidirect
16. C3×C52×C31C3×C4semidirect
17. C31×Dic15C3×C5semidirect
23. C3×C5×C31⋊C3Dic5semidirect
24. C3×C5×C31⋊C3C4×C5semidirect
36. C52×C31C3×Dic3semidirect
41. C3×C5×C31C3×Dic5semidirect
42. C3×C5×C31C3×C4×C5semidirect
47. C5×C31⋊C3C5×Dic3semidirect
48. C5×C31⋊C3Dic15direct (N × H)
55. C5×Dic15C31⋊C3direct (N × H)
57. C3×C31⋊C3C5×Dic5semidirect
65. C5×C31C3×C5×Dic3semidirect
66. C5×C31C3×Dic15semidirect
72. C3×C31C3×C5×Dic5semidirect
74. C31⋊C3C5×Dic15direct (N × H)
80. C3×C52C4×C31⋊C3semidirect
83. Dic15C5×C31⋊C3direct (N × H)
91. C31C3×C5×Dic15semidirect
101. C52Dic3×C31⋊C3semidirect
112. C3×C5Dic5×C31⋊C3semidirect
113. C3×C5C4×C5×C31⋊C3semidirect
124. C5C5×Dic3×C31⋊C3semidirect
125. C5Dic15×C31⋊C3direct (N × H)
129. C3C5×Dic5×C31⋊C3semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C52×C31⋊C32
C5×C31×Dic153
C5×Dic5×C31⋊C33
Dic15×C31⋊C35
C5×Dic3×C31⋊C35
C3×C5×Dic1531