Finite Group Databasebeta

← #91902

Subgroups — #91902

Order 480.

112 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 112 conjugacy classes of subgroups — too many to draw. Only its 19 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×C5⋊S4C211yesmaximal, characteristic, complemented
2C2×C5×S4C211yesmaximal, characteristic, complemented
3A4×Dic5C211yesmaximal, characteristic, complemented
4#4085—31nomaximal, Hall
5C2×C5×A4C2211yescharacteristic
6C5⋊S4—21no—
7C5×S4—21no—
8#1203—41nomaximal
9C4⋊S4—51nomaximal, Hall
10C2×C5×D4—31no—
11C2×C22⋊D5—31no—
12C2×C22⋊D5—31no—
13C22×Dic5D311yescharacteristic, complemented
14C22⋊Dic5—31no—
15#685—31no—
16#683—31no—
17C2×D15—41no—
18C2×C5×D3—41no—
19C5×A4D411yescharacteristic, complemented
20C3×Dic5—41no—
21C2×S4—51no—
22C2×S4D511yescharacteristic, complemented
23C4×A4—51no—
24C23×C5—31no—
25C23×C5C2×D311yescharacteristic
26C22×D5—31no—
27C5×D4—61no—
28C5×D4—61no—
29C2×C4×C5—31no—
30C22⋊D5—61no—
31C22⋊D5—61no—
32C22⋊D5—61no—
33C22⋊D5—61no—
34C2×Dic5—31no—
35C2×Dic5—31no—
36C2×Dic5—31no—
37#121—151noSylow
38C2×C3×C5—41no—
39D15—81no—
40C5×D3—81no—
41C2×A4C2×D511yescharacteristic
42S4—21no—
43S4—101no—
44D12—201no—
45C22×C5—31no—
46C22×C5—31no—
47C22×C5—61no—
48C22×C5—61no—
49C22×C5—61no—
50C22×C5D1211yescharacteristic, complemented
51C2×D5—61no—
52C2×D5—61no—
53C2×D5—61no—
54C4×C5—61no—
55Dic5—31no—
56Dic5—61no—
57Dic5S411yescharacteristic, complemented
58C2×D4—31no—
59C2×D4—151no—
60C2×D4—151no—
61C22×C4—51no—
62C4⋊C4—151no—
63C22⋊C4—151no—
64C22⋊C4—151no—
65C3×C5—41noHall
66C2×D3—41no—
67C2×D3—201no—
68A4C22⋊D511yescharacteristic, complemented
69C3×C4—201no—
70C2×C5—31no—
71C2×C5—31no—
72C2×C5—121no—
73C2×C5C2×S411yescharacteristic
74D5—121no—
75C23—31no—
76C23—151no—
77C23D3×D511yescharacteristic
78D4—61no—
79D4—61no—
80D4—301no—
81D4—301no—
82D4—301no—
83D4—301no—
84C2×C4—31no—
85C2×C4—151no—
86C2×C4—151no—
87C2×C4—151no—
88C2×C3—41no—
89D3—81no—
90D3—401no—
91C5C4⋊S411yescharacteristic, complemented, Sylow
92C22—31no—
93C22—31no—
94C22—61no—
95C22—61no—
96C22—61no—
97C22—301no—
98C22—301no—
99C22—301no—
100C22#120311yescharacteristic, complemented
101C4—51no—
102C4—61no—
103C4—151no—
104C4—301no—
105C3—41noSylow
106C2—31no—
107C2—31no—
108C2—121no—
109C2—601no—
110C2D5×S411yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2D5×S4
commutator, cosocleC2×C5×A4C22
Fitting, socleC23×C5C2×D3
hypocenterC5×A4D4
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C5⋊S4C2semidirect
2. C2×C5×S4C2semidirect
3. A4×Dic5C2semidirect
13. C22×Dic5D3semidirect
19. C5×A4D4semidirect
22. C2×S4D5semidirect
50. C22×C5D12semidirect
57. Dic5S4semidirect
68. A4C22⋊D5semidirect
91. C5C4⋊S4semidirect
100. C22#1203semidirect

Maximal subgroups

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

subgroupindex
C2×C5⋊S42
C2×C5×S42
A4×Dic52
#40853
#12034
C4⋊S45