Finite Group Databasebeta

← C3⋊Dic3×A5 #72228163

Subgroups — C3⋊Dic3×A5 #72228163

Order 2160.

250 conjugacy classes of subgroups; only the 26 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 26 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×A5C211yesmaximal, characteristic
2Dic3×A5—34nomaximal
3C32×A5C411yescharacteristic, complemented
4A4×C3⋊Dic3—51nomaximal, Hall
5C2×C3×A5D314yes—
6D5×C3⋊Dic3—61nomaximal
7C4×A5—91no—
8C2×C32×A4—51no—
9D3×C3⋊Dic3—101nomaximal
10C2×C32×D5—61no—
11C3×A5Dic314yescomplemented
12C3⋊Dic15—61no—
13C5×C3⋊Dic3—61no—
14C22×C3⋊Dic3—51no—
15Dic3×A4—154no—
16C2×A5C3⋊D311yescharacteristic
17D5×Dic3—184no—
18C2×C32×D3—101no—
19C32×A4—51no—
20C3⋊(C3⋊Dic3)—101no—
21C3×C3⋊Dic3—101no—
22C2×C32×C5—61no—
23C32×D5—61no—
24C32×D5—61no—
25C23×C32—51no—
26C2×C3×A4—54no—
27C2×C3×A4—104no—
28C2×C3⋊Dic3—151no—
29C2×C3⋊Dic3—151no—
30D3×Dic3—304no—
31C2×C3×D5—64no—
32A5C3⋊Dic311yescharacteristic, direct product factor
33Dic15—184no—
34C5×Dic3—184no—
35C2×C33—101no—
36C32×D3—101no—
37C32×D3—101no—
38C22×Dic3—154no—
39C4×A4—451no—
40C32×C5—61no—
41C4×D5—541no—
42C22×C32—51no—
43C22×C32—151no—
44C22×C32—151no—
45C2×C3×D3—104no—
46C3×A4—54no—
47C3×A4—104no—
48C3⋊Dic3—151no—
49C3⋊Dic3—304no—
50C3⋊Dic3—604no—
51C3⋊Dic3A511yesmaximal normal, characteristic, direct product factor
52C3×Dic3—304no—
53C2×C3×C5—64no—
54C3×D5—64no—
55C3×D5—64no—
56C33—101noSylow
57C23×C3—54no—
58C2×A4—51no—
59C2×A4—104no—
60C2×Dic3—454no—
61C2×Dic3—454no—
62C4×D3—901no—
63C2×D5—61no—
64C4×C5—541no—
65Dic5—541no—
66C2×C32—104no—
67C2×C32—151no—
68C2×C32—151no—
69C2×C32—204no—
70C2×C32C2×A511yescharacteristic
71C3×D3—104no—
72C3×D3—104no—
73C22×C4—451noSylow
74C3×C5—64no—
75C22×C3—54no—
76C22×C3—154no—
77C22×C3—154no—
78C2×D3—101no—
79A4—51no—
80A4—104no—
81C3×C4—901no—
82Dic3—34no—
83Dic3—454no—
84Dic3—901no—
85Dic3—1804no—
86C2×C5—61no—
87D5—61no—
88D5—61no—
89C32—104no—
90C32—204no—
91C32C4×A511yescharacteristic, complemented
92C23—51no—
93C2×C4—1351no—
94C2×C4—1351no—
95C2×C3—101no—
96C2×C3—154no—
97C2×C3—154no—
98C2×C3—204no—
99C2×C3D3×A514yes—
100D3—101no—
101D3—101no—
102C5—61noSylow
103C22—51no—
104C22—151no—
105C22—151no—
106C4—91no—
107C4—1351no—
108C3—101no—
109C3—204no—
110C3Dic3×A514yescomplemented
111C2—151no—
112C2—151no—
113C2C3⋊D3×A511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2C3⋊D3×A5
commutator, hypocenterC32×A5C4
Fitting, cosocleC2×C32C2×A5
socle, prime radicalC2×C32×A5C2
LCSG ▷ C32×A5
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
3. C32×A5C4semidirect
11. C3×A5Dic3semidirect
32. A5C3⋊Dic3direct (N × H)
51. C3⋊Dic3A5direct (N × H)
91. C32C4×A5semidirect
110. C3Dic3×A5semidirect

Maximal subgroups

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

subgroupindex
C2×C32×A52
Dic3×A53
A4×C3⋊Dic35
D5×C3⋊Dic36
D3×C3⋊Dic310