Finite Group Databasebeta

← #66085⋊C3 #11752178

Subgroups — #66085⋊C3 #11752178

Order 960.

146 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 29 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#4150⋊C3C211yesmaximal, characteristic, complemented
2C5⋊#994C211yesmaximal, characteristic, complemented
3C5×#131⋊C3C211yesmaximal, characteristic, complemented
4#66085C311yesmaximal, characteristic, complemented, Hall
5C5×#41⋊C3C2211yescharacteristic
6D5×SL(2,𝔽3)—21no—
7C5⋊(#41⋊C3)—21no—
8C3×#677—41nomaximal
9#577⋊C3—51nomaximal, Hall
10#4150C2×C311yescharacteristic
11#4149C2×C311yescharacteristic, complemented
12C5×#131C2×C311yescharacteristic, complemented
13#4055—31no—
14#4054—31no—
15#4050—31no—
16C2×#677—31no—
17C3×D20—41no—
18C3×Dic10—41no—
19C5×SL(2,𝔽3)D411yescharacteristic
20C3×C5×C8—41no—
212−1+4⋊C3—51no—
22#994—51no—
23#131⋊C3D511yescharacteristic, complemented
24C5×#41C22×C311yescharacteristic
25#713—21no—
26Q8×D5—21no—
27#711—61no—
28D4×D5—61no—
29#709—31no—
30#709—31no—
31C2×D20—31no—
32C2×Dic10—31no—
33C5×M16—31no—
34C2×C5×C8—31no—
35Dic20—31no—
36D40—31no—
37#677—32no—
38#677—31no—
39#677A411yescharacteristic
40#577—51noSylow
41C2×C3×D5—81no—
42C3×C4×C5—41no—
43C3×Dic5—81no—
44#41⋊C3—101no—
45#41⋊C3C2×D511yescharacteristic
46C2×SL(2,𝔽3)—101no—
47C3×SD16—201no—
48C22×D5—61no—
49C5×Q8C3×D411yescharacteristic
50C5×D4—31no—
51C2×C4×C5—31no—
52C22⋊D5—61no—
53C22⋊D5—61no—
54C2×Dic5—61no—
55D20—31no—
56D20—61no—
57D20C2×A411yescharacteristic
58C4×D5—61no—
59C4×D5—61no—
60Dic10—31no—
61Dic10—61no—
62Dic10C2×A411yescharacteristic
63C5×C8—31no—
64C5×C8C2×A411yescharacteristic
652−1+4—51no—
66H(5,𝔽2)—51no—
67#137—151no—
68AGL(1,ℤ/8)—151no—
69#135—151no—
70C2×SD16—151no—
71#131C3×D511yescharacteristic, complemented
72C2×C3×C5—41no—
73C3×D5—161no—
74C3×Q8—201no—
75C3×D4—201no—
76SL(2,𝔽3)D2011yescharacteristic
77C3×C8—41no—
78C22×C5—31no—
79C2×D5—21no—
80C2×D5—61no—
81C2×D5—241no—
82C4×C5—31no—
83C4×C5C22×A411yescharacteristic
84Dic5—21no—
85Dic5—61no—
86#41—101no—
87#41—151no—
88#41—151no—
89#41—301no—
90#41C2×C3×D511yescharacteristic
91C2×Q8—101no—
92C2×Q8—151no—
93C2×D4—151no—
94C2×D4—301no—
95Q16—151no—
96SD16—51no—
97SD16—152no—
98SD16—151no—
99D8—151no—
100M16—31no—
101C2×C8—31no—
102C3×C5—41noHall
103C22×C3—401no—
104C3×C4—41no—
105C3×C4—401no—
106C2×C5—61no—
107C2×C5D4×A411yescharacteristic
108D5—41no—
109D5—121no—
110C23—301no—
111Q8—51no—
112Q8—151no—
113Q8—301no—
114Q8C3×D2011yescharacteristic
115D4—31no—
116D4—51no—
117D4—151no—
118D4—301no—
119D4—301no—
120D4—301no—
121C2×C4—31no—
122C2×C4—301no—
123C2×C4—301no—
124C2×C4—301no—
125C8—31no—
126C8D5×A411yescharacteristic
127C2×C3—41no—
128C2×C3—801no—
129C5#577⋊C311yescharacteristic, complemented, Sylow
130C22—31no—
131C22—101no—
132C22—301no—
133C22—1201no—
134C4—31no—
135C4—101no—
136C4—301no—
137C4C2×D5×A411yescharacteristic
138C3—41noSylow
139C2—61no—
140C2—201no—
141C2—601no—
142C2A4×D2011yescharacteristic
subgroupG/H
centerC2A4×D20
commutator, cosocleC5×#41C22×C3
FrattiniC4C2×D5×A4
FittingC5×#131C2×C3
socleC2×C5D4×A4
hypercenterC8D5×A4
hypocenterC5×Q8C3×D4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C2 ◁ C4 ◁ C8

Complements

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

NH ≅ G/Ntype
1. #4150⋊C3C2semidirect
2. C5⋊#994C2semidirect
3. C5×#131⋊C3C2semidirect
4. #66085C3semidirect
11. #4149C2×C3semidirect
12. C5×#131C2×C3semidirect
23. #131⋊C3D5semidirect
71. #131C3×D5semidirect
129. C5#577⋊C3semidirect

Maximal subgroups

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

subgroupindex
#4150⋊C32
C5⋊#9942
C5×#131⋊C32
#660853
C3×#6774
#577⋊C35