Finite Group Databasebeta

← #66170⋊C3 #11752201

Subgroups — #66170⋊C3 #11752201

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×#994C211yesmaximal, characteristic, complemented
2#4150⋊C3C211yesmaximal, characteristic, complemented
3#4094⋊C3C211yesmaximal, characteristic, complemented
4#66170C311yesmaximal, characteristic, complemented, Hall
5C5×#41⋊C3—21no—
6C5×#41⋊C3C2211yescharacteristic
7D5×SL(2,𝔽3)—21no—
8C3×#688—41nomaximal
9#577⋊C3—51nomaximal, Hall
10C5×H(5,𝔽2)C2×C311yescharacteristic, complemented
11#4150C2×C311yescharacteristic
12#4097—31no—
13#4096—31no—
14#4094C2×C311yescharacteristic, complemented
15C2×#687—31no—
16#4078—31no—
17C3×C5×Q8—41no—
18C3×D20—41no—
19C5×SL(2,𝔽3)D411yescharacteristic
20C3×#168—41no—
212−1+4⋊C3—51no—
22#994D511yescharacteristic, complemented
23#131⋊C3—51no—
24C5×#41—21no—
25C5×#41—31no—
26C5×#41C22×C311yescharacteristic
27C2×C5×D4—31no—
28C2×C5×D4—61no—
29Q8×D5—21no—
30#711—61no—
31#709—31no—
32C2×Dic10—31no—
33#689—31no—
34#688A411yescharacteristic
35#687—32no—
36#687—31no—
37#686—31no—
38#681—31no—
39C2×#168—31no—
40#577—51noSylow
41C2×C3×D5—81no—
42C3×C4×C5—41no—
43C3×C4×C5—81no—
44#41⋊C3—21no—
45#41⋊C3C2×D511yescharacteristic
46C2×SL(2,𝔽3)—101no—
47C3×SD16—201no—
48C23×C5—61no—
49C5×Q8C3×D411yescharacteristic
50C5×Q8C2×A411yescharacteristic
51C5×D4—31no—
52C5×D4—31no—
53C5×D4—61no—
54C5×D4—61no—
55C2×C4×C5—31no—
56C2×C4×C5—61no—
57C22⋊D5—61no—
58C2×Dic5—61no—
59D20C2×A411yescharacteristic
60C4×D5—61no—
61Dic10—31no—
62Dic10—61no—
63#168—31no—
64#168C2×A411yescharacteristic
652−1+4—51no—
66H(5,𝔽2)C3×D511yescharacteristic, complemented
67#137—151no—
68AGL(1,ℤ/8)—151no—
69#135—151no—
70C2×SD16—151no—
71#131—51no—
72C2×C3×C5—41no—
73C3×D5—161no—
74C3×Q8—41no—
75C3×D4—201no—
76SL(2,𝔽3)C22⋊D511yescharacteristic
77C3×C8—201no—
78C22×C5—31no—
79C22×C5—61no—
80C22×C5—241no—
81C2×D5—21no—
82C4×C5—21no—
83C4×C5—31no—
84C4×C5C22×A411yescharacteristic
85Dic5—61no—
86#41—21no—
87#41—31no—
88#41—151no—
89#41—301no—
90#41C2×C3×D511yescharacteristic
91C2×Q8—101no—
92C2×Q8—151no—
93C2×D4—31no—
94C2×D4—61no—
95Q16—151no—
96SD16—51no—
97SD16—151no—
98SD16—152no—
99D8—151no—
100M16—151no—
101C2×C8—151no—
102C3×C5—41noHall
103C22×C3—401no—
104C3×C4—41no—
105C3×C4—81no—
106C2×C5—61no—
107C2×C5—121no—
108C2×C5D4×A411yescharacteristic
109D5—41no—
110C23—61no—
111Q8—151no—
112Q8—301no—
113Q8C3×C22⋊D511yescharacteristic
114Q8D5×A411yescharacteristic
115D4—31no—
116D4—31no—
117D4—51no—
118D4—61no—
119D4—61no—
120D4—301no—
121C2×C4—31no—
122C2×C4—61no—
123C2×C4—301no—
124C2×C4—301no—
125C8—51no—
126C8—151no—
127C2×C3—41no—
128C2×C3—801no—
129C5#577⋊C311yescharacteristic, complemented, Sylow
130C22—31no—
131C22—61no—
132C22—101no—
133C22—241no—
134C4—21no—
135C4—31no—
136C4—301no—
137C4C2×D5×A411yescharacteristic
138C3—41noSylow
139C2—61no—
140C2—121no—
141C2—201no—
142C2A4×C22⋊D511yescharacteristic
subgroupG/H
centerC2A4×C22⋊D5
commutator, cosocleC5×#41C22×C3
FrattiniC4C2×D5×A4
FittingC5×H(5,𝔽2)C2×C3
socleC2×C5D4×A4
hypercenterQ8D5×A4
hypocenterC5×Q8C3×D4
LCSG ▷ C5×#41 ▷ C5×Q8
UCSC1 ◁ C2 ◁ C4 ◁ Q8

Complements

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

NH ≅ G/Ntype
1. C5×#994C2semidirect
2. #4150⋊C3C2semidirect
3. #4094⋊C3C2semidirect
4. #66170C3semidirect
10. C5×H(5,𝔽2)C2×C3semidirect
14. #4094C2×C3semidirect
22. #994D5semidirect
66. H(5,𝔽2)C3×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
C5×#9942
#4150⋊C32
#4094⋊C32
#661703
C3×#6884
#577⋊C35