Finite Group Databasebeta

← #11751490

Subgroups — #11751490

Order 960.

114 conjugacy classes of subgroups; only the 12 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 12 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
1#91870C211yesmaximal, characteristic
2#91145C211yesmaximal, characteristic, complemented
3GL(2,𝔽5)C211yesmaximal, characteristic, complemented
4#6732C2211yescharacteristic
5#6729C411yescharacteristic, complemented
6#6728C411yescharacteristic, complemented
7#5404—51nomaximal, Hall
8C8×AGL(1,𝔽5)—61nomaximal
9SL(2,𝔽5)C2×C411yescharacteristic
10#985—51no—
11#901—101nomaximal
12#131⋊C3—51no—
13GU(2,𝔽3)—51no—
14C4×AGL(1,𝔽5)—61no—
15D5⋊C8—61no—
16C8×D5—61no—
17#443—151noSylow
18#235—101no—
19#41⋊C3—51no—
20GL(2,𝔽3)—51no—
21#226—51no—
22C2×C3×C8—101no—
23#208—101no—
24ΓL(1,𝔽25)—101no—
25ΓL(1,𝔽25)—101no—
26D3×C8—101no—
27D3×C8—101no—
28C2×AGL(1,𝔽5)—62no—
29C4×D5—61no—
30#170—61no—
31#170—61no—
32C5×C8—61no—
33#168—61no—
34#135—151no—
35#131—51no—
36#131—151no—
37#108—151no—
38#104—151no—
39#104—151no—
40C4×C8—151no—
41C2×C3×C4—101no—
42#67—101no—
43#67—101no—
44D12—101no—
45C4×D3—101no—
46C4×D3—101no—
47Dic6—101no—
48SL(2,𝔽3)—51no—
49C3×C8—101no—
50C3×C8—101no—
51C3⋊C8—101no—
52C3⋊C8—101no—
53C2×D5—61no—
54AGL(1,𝔽5)—64no—
55C4×C5—61no—
56Dic5—61no—
57#41—51no—
58#41—151no—
59Q16—151no—
60SD16—151no—
61SD16—151no—
62D8—151no—
63M16—151no—
64M16—151no—
65M16—301no—
66C2×C8—101no—
67C2×C8—151no—
68C2×C8—151no—
69C42—151no—
70C22×C3—101no—
71C2×D3—101no—
72C2×D3—101no—
73C3×C4—101no—
74C3×C4—101no—
75Dic3—101no—
76Dic3—101no—
77C2×C5—61no—
78D5—62no—
79Q8—51no—
80Q8—151no—
81D4—151no—
82D4—151no—
83D4—301no—
84C2×C4—101no—
85C2×C4—151no—
86C2×C4—301no—
87C8—101no—
88C8—151no—
89C8—151no—
90C8—151no—
91C8S511yescharacteristic
92C2×C3—101no—
93C2×C3—201no—
94D3—201no—
95D3—201no—
96C5—61noSylow
97C22—101no—
98C22—151no—
99C4—101no—
100C4—151no—
101C4—302no—
102C4C2×S511yescharacteristic
103C3—101noSylow
104C2—201no—
105C2—301no—
106C2C4×S511yescharacteristic
subgroupG/H
center, Fitting, hypercenterC8S5
commutator, hypocenterSL(2,𝔽5)C2×C4
FrattiniC4C2×S5
socleC2C4×S5
prime radical#91870C2
cosocle#6732C22
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C8

Complements

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

NH ≅ G/Ntype
2. #91145C2semidirect
3. GL(2,𝔽5)C2semidirect
5. #6729C4semidirect
6. #6728C4semidirect

Maximal subgroups

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

subgroupindex
#918702
#911452
GL(2,𝔽5)2
#54045
C8×AGL(1,𝔽5)6
#90110