Finite Group Databasebeta

← C3⋊(#585⋊C5) #11756806

Subgroups — C3⋊(#585⋊C5) #11756806

Order 960.

180 conjugacy classes of subgroups; only the 11 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 11 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
1C3×2−1+4⋊C5C211yesmaximal, characteristic, complemented
2#585⋊C5—31nomaximal, Hall
3#5968C511yesmaximal, characteristic, complemented, Hall
42−1+4⋊C5D311yescharacteristic, complemented
5C3×2−1+4C2×C511yescharacteristic
6#1009—52no—
7D3×#41—52no—
8#1007—51no—
9C2×#239—51no—
10#585—31noSylow
11C5×Dic3—161nomaximal
12C3×#41—52no—
13C2×C3×Q8—51no—
14#239—54no—
15#239—52no—
16D3×Q8—52no—
17#237—52no—
18D3×D4—52no—
19D3×D4—54no—
20#235—52no—
21#235—54no—
22C2×D12—51no—
23C2×D12—52no—
24C2×C4×D3—51no—
25C2×C4×D3—52no—
262−1+4—151no—
272−1+4C5×D311yescharacteristic
28H(5,𝔽2)—152no—
29C2×#41—151no—
30C2×#41—152no—
31C2×C3×C5—161no—
32C22×D3—51no—
33C22×D3—52no—
34C3×Q8—52no—
35C3×D4—52no—
36C2×C3×C4—51no—
37C2×C3×C4—52no—
38#67—54no—
39C2×Dic3—51no—
40D12—52no—
41D12—54no—
42C4×D3—52no—
43C4×D3—54no—
44C4×D3—52no—
45Dic6—52no—
46C4×C5—481no—
47#41—52no—
48#41—152no—
49#41—154no—
50#41—154no—
51#41—152no—
52#41—152no—
53C2×Q8—51no—
54C2×Q8—152no—
55C2×D4—151no—
56C2×D4—152no—
57C2×D4—152no—
58C2×D4—154no—
59C22×C4—151no—
60C22×C4—152no—
61C3×C5—161noHall
62C22×C3—51no—
63C2×D3—52no—
64C2×D3—201no—
65C2×D3—202no—
66C3×C4—52no—
67Dic3—51no—
68Dic3C24⋊C511yescharacteristic
69C2×C5—161no—
70C23—151no—
71C23—152no—
72Q8—52no—
73Q8—152no—
74D4—52no—
75D4—152no—
76D4—154no—
77D4—154no—
78C2×C4—51no—
79C2×C4—52no—
80C2×C4—152no—
81C2×C4—151no—
82C2×C4—152no—
83C2×C4—154no—
84C2×C3—101no—
85C2×C3C2×C24⋊C511yescharacteristic
86D3—102no—
87C5—161noSylow
88C22—51no—
89C22—152no—
90C22—602no—
91C22—601no—
92C4—31no—
93C4—52no—
94C4—151no—
95C3#585⋊C511yescharacteristic, complemented, Sylow
96C2—101no—
97C2—302no—
98C2D3×C24⋊C511yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D3×C24⋊C5
commutator, Fitting, cosocle, hypocenterC3×2−1+4C2×C5
socleC2×C3C2×C24⋊C5
LCSG ▷ C3×2−1+4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C3×2−1+4⋊C5C2semidirect
3. #5968C5semidirect
4. 2−1+4⋊C5D3semidirect
95. C3#585⋊C5semidirect

Maximal subgroups

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

subgroupindex
C3×2−1+4⋊C52
#585⋊C53
#59685
C5×Dic316