Finite Group Databasebeta

← #11752124

Subgroups — #11752124

Order 960.

124 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 25 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#91955C211yesmaximal, characteristic
2C5×#131⋊C3C211yesmaximal, characteristic, complemented
3#91185C211yesmaximal, characteristic, complemented
4#65434—31nomaximal, Hall
5C5×#41⋊C3C2211yescharacteristic
6C5⋊GL(2,𝔽3)C411yescharacteristic, complemented
7C5⋊#226C411yescharacteristic, complemented
8#6705—41nomaximal
9#5405—51nomaximal, Hall
10C5×#131D311yescharacteristic, complemented
11#4096—31no—
12#4047—31no—
13#3969—31no—
14#3957—31no—
15#3954—31no—
16#3947—31no—
17C4×D15—41no—
18C5×SL(2,𝔽3)C2×C411yescharacteristic
19C3×C5×C8—41no—
20C3⋊#168—41no—
21#985—51no—
22#131⋊C3D511yescharacteristic, complemented
23GU(2,𝔽3)—51no—
24C5×#41C2×D311yescharacteristic
25#709—31no—
26C5×M16—31no—
27C2×C5×C8—31no—
28#689—31no—
29#688—31no—
30#687—31no—
31#686—31no—
32C4×Dic5—31no—
33#681—31no—
34C2×#168—31no—
35#676—61no—
36C8×D5—61no—
37#444—151noSylow
38C2×D15—41no—
39C3×C4×C5—41no—
40Dic15—41no—
41#41⋊C3C2×D511yescharacteristic
42GL(2,𝔽3)—51no—
43#226—51no—
44ΓL(1,𝔽25)—201no—
45C5×Q8C4×D311yescharacteristic
46C5×D4—31no—
47C2×C4×C5—31no—
48C22⋊D5—61no—
49C2×Dic5—61no—
50D20—31no—
51C4×D5—61no—
52Dic10—31no—
53C5×C8—31no—
54C5×C8S411yescharacteristic
55#168—31no—
56#168—31no—
57#168—61no—
58#135—151no—
59#131—151no—
60#131D1511yescharacteristic, complemented
61#108—151no—
62#104—151no—
63#104—151no—
64#97—151no—
65C2×C3×C5—41no—
66D15—81no—
67C4×D3—201no—
68SL(2,𝔽3)C4×D511yescharacteristic
69C3×C8—41no—
70C3⋊C8—201no—
71C22×C5—31no—
72C2×D5—61no—
73C4×C5—31no—
74C4×C5C2×S411yescharacteristic
75Dic5—61no—
76Dic5—121no—
77#41—151no—
78#41C2×D1511yescharacteristic
79Q16—151no—
80SD16—151no—
81SD16—151no—
82D8—151no—
83M16—31no—
84M16—151no—
85M16—301no—
86C2×C8—31no—
87C2×C8—151no—
88C2×C8—301no—
89C42—151no—
90C3×C5—41noHall
91C2×D3—201no—
92C3×C4—41no—
93Dic3—201no—
94C2×C5—61no—
95C2×C5C4×S411yescharacteristic
96D5—121no—
97Q8—151no—
98Q8C4×D1511yescharacteristic
99D4—31no—
100D4—151no—
101D4—301no—
102C2×C4—31no—
103C2×C4—301no—
104C2×C4—301no—
105C8—31no—
106C8—151no—
107C8—151no—
108C8—301no—
109C8C5⋊S411yescharacteristic
110C2×C3—41no—
111D3—401no—
112C5#540511yescharacteristic, complemented, Sylow
113C22—31no—
114C22—301no—
115C4—31no—
116C4—301no—
117C4—601no—
118C4C2×C5⋊S411yescharacteristic
119C3—41noSylow
120C2—61no—
121C2—601no—
122C2C4×C5⋊S411yescharacteristic
subgroupG/H
center, FrattiniC4C2×C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C2×C4
FittingC5×#131D3
socleC2×C5C4×S4
prime radical#91955C2
cosocleC5×#41⋊C3C22
hypercenterC8C5⋊S4
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
2. C5×#131⋊C3C2semidirect
3. #91185C2semidirect
6. C5⋊GL(2,𝔽3)C4semidirect
7. C5⋊#226C4semidirect
10. C5×#131D3semidirect
22. #131⋊C3D5semidirect
60. #131D15semidirect
112. C5#5405semidirect

Maximal subgroups

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

subgroupindex
#919552
C5×#131⋊C32
#911852
#654343
#67054
#54055