Finite Group Databasebeta

← #66171⋊C3 #11752204

Subgroups — #66171⋊C3 #11752204

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
1C5×2−1+4⋊C3C211yesmaximal, characteristic, complemented
2C5⋊#994C211yesmaximal, characteristic, complemented
3#4094⋊C3C211yesmaximal, characteristic, complemented
4#66171C311yesmaximal, characteristic, complemented, Hall
5C5×#41⋊C3C2211yescharacteristic
6C2×C5×SL(2,𝔽3)—21no—
7C5⋊(#41⋊C3)—21no—
8C3×#687—41nomaximal
9#577⋊C3—51nomaximal, Hall
10C5×2−1+4C2×C311yescharacteristic
11#4149C2×C311yescharacteristic, complemented
12#4096—31no—
13#4095—31no—
14#4094C2×C311yescharacteristic, complemented
15#4088—31no—
16C2×#688—31no—
17C3×C5×D4—41no—
18C3×Dic10—41no—
19C5×SL(2,𝔽3)D411yescharacteristic
20C3×#168—41no—
212−1+4⋊C3D511yescharacteristic, complemented
22#994—51no—
23#131⋊C3—51no—
24C5×#41—31no—
25C5×#41—61no—
26C5×#41C22×C311yescharacteristic
27C2×C5×Q8—21no—
28C2×C5×Q8—31no—
29#713—21no—
30D4×D5—61no—
31#709—31no—
32C2×D20—31no—
33#689—31no—
34#688—32no—
35#688—31no—
36#687A411yescharacteristic
37#686—31no—
38#681—31no—
39C2×#168—31no—
40#577—51noSylow
41C22×C3×C5—81no—
42C3×C4×C5—41no—
43C3×Dic5—81no—
44#41⋊C3—101no—
45#41⋊C3C2×D511yescharacteristic
46C2×SL(2,𝔽3)—21no—
47C3×SD16—201no—
48C22×D5—61no—
49C5×Q8—31no—
50C5×Q8—61no—
51C5×Q8C3×D411yescharacteristic
52C5×D4—31no—
53C5×D4—61no—
54C5×D4C2×A411yescharacteristic
55C2×C4×C5—31no—
56C2×C4×C5—61no—
57C2×C4×C5—61no—
58C22⋊D5—61no—
59D20—31no—
60D20—61no—
61C4×D5—61no—
62Dic10C2×A411yescharacteristic
63#168—31no—
64#168C2×A411yescharacteristic
652−1+4C3×D511yescharacteristic
66H(5,𝔽2)—51no—
67#137—151no—
68AGL(1,ℤ/8)—151no—
69#135—151no—
70C2×SD16—151no—
71#131—51no—
72C2×C3×C5—41no—
73C2×C3×C5—161no—
74C3×Q8—201no—
75C3×D4—41no—
76SL(2,𝔽3)C22⋊D511yescharacteristic
77C3×C8—201no—
78C22×C5—21no—
79C22×C5—31no—
80C2×D5—61no—
81C2×D5—241no—
82C4×C5—31no—
83C4×C5—61no—
84C4×C5C22×A411yescharacteristic
85Dic5—21no—
86#41—31no—
87#41—61no—
88#41—101no—
89#41—151no—
90#41C2×C3×D511yescharacteristic
91C2×Q8—21no—
92C2×Q8—31no—
93C2×D4—151no—
94C2×D4—301no—
95Q16—151no—
96SD16—51no—
97SD16—151no—
98SD16—152no—
99D8—151no—
100M16—151no—
101C2×C8—151no—
102C3×C5—41noHall
103C22×C3—81no—
104C3×C4—41no—
105C3×C4—401no—
106C2×C5—41no—
107C2×C5—61no—
108C2×C5D4×A411yescharacteristic
109D5—121no—
110C23—301no—
111Q8—31no—
112Q8—51no—
113Q8—61no—
114Q8C3×C22⋊D511yescharacteristic
115D4—31no—
116D4—61no—
117D4—151no—
118D4—301no—
119D4—301no—
120D4D5×A411yescharacteristic
121C2×C4—31no—
122C2×C4—61no—
123C2×C4—61no—
124C2×C4—301no—
125C8—51no—
126C8—151no—
127C2×C3—41no—
128C2×C3—161no—
129C5#577⋊C311yescharacteristic, complemented, Sylow
130C22—21no—
131C22—31no—
132C22—301no—
133C22—1201no—
134C4—31no—
135C4—61no—
136C4—101no—
137C4C2×D5×A411yescharacteristic
138C3—41noSylow
139C2—41no—
140C2—61no—
141C2—601no—
142C2A4×C22⋊D511yescharacteristic
subgroupG/H
centerC2A4×C22⋊D5
commutator, cosocleC5×#41C22×C3
FrattiniC4C2×D5×A4
FittingC5×2−1+4C2×C3
socleC2×C5D4×A4
hypercenterD4D5×A4
hypocenterC5×Q8C3×D4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C2 ◁ C4 ◁ D4

Complements

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

NH ≅ G/Ntype
1. C5×2−1+4⋊C3C2semidirect
2. C5⋊#994C2semidirect
3. #4094⋊C3C2semidirect
4. #66171C3semidirect
11. #4149C2×C3semidirect
14. #4094C2×C3semidirect
21. 2−1+4⋊C3D5semidirect
129. C5#577⋊C3semidirect

Maximal subgroups

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

subgroupindex
C5×2−1+4⋊C32
C5⋊#9942
#4094⋊C32
#661713
C3×#6874
#577⋊C35