Finite Group Databasebeta

← #91821

Subgroups — #91821

Order 480.

136 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 47 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×D4C211yesmaximal, characteristic, complemented
2#6817C211yesmaximal, characteristic, complemented
3#6716C212yesmaximal, complemented
4#6715C212yesmaximal, complemented
5#6710C211yesmaximal, characteristic, complemented
6#4078—31nomaximal, Hall
7C23×C3×C5—21no—
8C3×C5×D4—21no—
9C3×C5×D4C2212yes—
10C2×C3×C4×C5C2211yescharacteristic
11#1220—21no—
12D60C2211yescharacteristic, complemented
13C4×D15—21no—
14Dic30C2211yescharacteristic, complemented
15C3⋊#168C2212yescomplemented
16#932—51nomaximal, Hall
17C2×C5×D4D311yescharacteristic, complemented
18#709—31no—
19#687—32no—
20#686—32no—
21#681—31no—
22C22×C3×C5—22no—
23C22×C3×C5—42no—
24C22×C3×C5D411yescharacteristic
25C2×D15—21no—
26C3×C4×C5D411yescharacteristic
27C3×C4×C5C2311yescharacteristic
28Dic15—21no—
29C2×C3×D4D511yescharacteristic, complemented
30#235—51no—
31#214—52no—
32#213—52no—
33#208—51no—
34C23×C5—21no—
35C5×D4—21no—
36C5×D4C2×D312yes—
37C2×C4×C5C2×D311yescharacteristic
38C22⋊D5—61no—
39D20—31no—
40C4×D5—61no—
41Dic10—31no—
42#168—32no—
43AGL(1,ℤ/8)—151noSylow
44C2×C3×C5—21no—
45C2×C3×C5—42no—
46C2×C3×C5C2×D411yescharacteristic
47D15—41no—
48C23×C3—21no—
49C3×D4—21no—
50C3×D4C2×D512yes—
51C2×C3×C4C2×D511yescharacteristic
52#67—101no—
53D12—51no—
54C4×D3—101no—
55Dic6—51no—
56C3⋊C8—52no—
57C22×C5—22no—
58C22×C5—42no—
59C22×C5#6711yescharacteristic
60C2×D5—61no—
61C4×C5#6711yescharacteristic
62C4×C5C22×D311yescharacteristic
63Dic5—61no—
64#41—151no—
65C2×D4D1511yescharacteristic, complemented
66SD16—152no—
67D8—152no—
68M16—151no—
69C3×C5AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
70C22×C3—22no—
71C22×C3—42no—
72C22×C3C22⋊D511yescharacteristic
73C2×D3—101no—
74C3×C4C22⋊D511yescharacteristic
75C3×C4C22×D511yescharacteristic
76Dic3—101no—
77C2×C5—21no—
78C2×C5—42no—
79C2×C5C2×#6711yescharacteristic
80D5—121no—
81C23—21no—
82Q8—151no—
83D4—21no—
84D4—151no—
85D4—301no—
86D4C2×D1512yes—
87C2×C4—301no—
88C2×C4C2×D1511yescharacteristic
89C8—152no—
90C2×C3—21no—
91C2×C3—42no—
92C2×C3C2×C22⋊D511yescharacteristic
93D3—201no—
94C5#93211yescharacteristic, complemented, Sylow
95C22—22no—
96C22—42no—
97C22—301no—
98C22#122011yescharacteristic
99C4—301no—
100C4#122011yescharacteristic
101C4C22×D1511yescharacteristic
102C3#407811yescharacteristic, complemented, Sylow
103C2—21no—
104C2—42no—
105C2—601no—
106C2C2×#122011yescharacteristic
subgroupG/H
centerC2C2×#1220
commutator, cosocleC3×C4×C5C23
FrattiniC4C22×D15
FittingC2×C3×C5×D4C2
socleC2×C3×C5C2×D4
hypercenterC2×D4D15
hypocenterC3×C5AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×D4C2semidirect
2. #6817C2semidirect
3. #6716C2semidirect
4. #6715C2semidirect
5. #6710C2semidirect
12. D60C22semidirect
14. Dic30C22semidirect
15. C3⋊#168C22semidirect
17. C2×C5×D4D3semidirect
29. C2×C3×D4D5semidirect
65. C2×D4D15semidirect
69. C3×C5AGL(1,ℤ/8)semidirect
94. C5#932semidirect
102. C3#4078semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×D42
#68172
#67162
#67152
#67102
#40783
#9325