Finite Group Databasebeta

← #65031

Subgroups — #65031

Order 320.

160 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 39 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#4144C211yesmaximal, characteristic
2#4081C211yesmaximal, characteristic, complemented
3#4032C212yesmaximal, complemented
4C5×#99C211yesmaximal, characteristic, complemented
5#3938C212yesmaximal, complemented
6C2×C5×D4C2211yescharacteristic
7C2×C22⋊D5—21no—
8C2×C22⋊D5C2212yes—
9C22×Dic5C2211yescharacteristic, complemented
10#711—22no—
11D4×D5—22no—
12#709—21no—
13C5×C22⋊C4C2212yescomplemented
14C22⋊Dic5—21no—
15C22⋊Dic5C2211yescharacteristic, complemented
16#685—22no—
17C4⋊Dic5—22no—
18#683—21no—
19#458—51nomaximal, Sylow
20C23×C5D411yescharacteristic
21C23×C5C2311yescharacteristic
22C22×D5—21no—
23C22×D5D412yes—
24C5×D4—22no—
25C2×C4×C5—22no—
26C2×C4×C5D411yescharacteristic
27C22⋊D5—22no—
28C22⋊D5—22no—
29C22⋊D5—22no—
30C2×Dic5—21no—
31C2×Dic5—21no—
32C2×Dic5—21no—
33C2×Dic5—22no—
34C2×Dic5D412yes—
35D20—21no—
36C4×D5—22no—
37Dic10—21no—
38H(5,𝔽2)—51no—
39#123—51no—
40#123—52no—
41#99—52no—
42#99D511yescharacteristic, complemented
43C22×C5—21no—
44C22×C5—41no—
45C22×C5—41no—
46C22×C5C2×D411yescharacteristic
47C22×C5C2×D412yes—
48C2×D5—22no—
49C2×D5—42no—
50C2×D5—81no—
51C4×C5—21no—
52C4×C5—42no—
53Dic5—22no—
54Dic5—41no—
55Dic5—41no—
56#41—102no—
57#41—101no—
58C2×D4—52no—
59C2×D4—102no—
60C2×D4—101no—
61C2×D4C2×D511yescharacteristic
62C22×C4—51no—
63C4⋊C4—102no—
64C4⋊C4—101no—
65C22⋊C4—51no—
66C22⋊C4—102no—
67C22⋊C4—101no—
68C22⋊C4C2×D512yescomplemented
69C2×C5—21no—
70C2×C5—22no—
71C2×C5—41no—
72C2×C5#12011yescharacteristic
73D5—42no—
74C23—52no—
75C23—101no—
76C23D2011yescharacteristic
77C23C22×D511yescharacteristic
78Q8—101no—
79D4—22no—
80D4—101no—
81D4—102no—
82D4—102no—
83D4—102no—
84C2×C4—22no—
85C2×C4—52no—
86C2×C4—102no—
87C2×C4—101no—
88C2×C4—101no—
89C2×C4—101no—
90C2×C4—102no—
91C2×C4D2011yescharacteristic
92C5#45811yescharacteristic, complemented, Sylow
93C22—21no—
94C22—41no—
95C22—41no—
96C22—102no—
97C22—202no—
98C22—401no—
99C22C2×D2011yescharacteristic
100C22D4×D512yes—
101C4—21no—
102C4—42no—
103C4—102no—
104C4—201no—
105C4—201no—
106C2—22no—
107C2—21no—
108C2—41no—
109C2—202no—
110C2#402811yescharacteristic
subgroupG/H
centerC2#4028
commutator, cosocleC23×C5C23
FrattiniC23C22×D5
FittingC5×#99C2
socleC2×C5#120
prime radical#4144C2
hypercenter#99D5
hypocenterC5#458
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2 ◁ C23 ◁ #99

Complements

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

NH ≅ G/Ntype
2. #4081C2semidirect
3. #4032C2semidirect
4. C5×#99C2semidirect
5. #3938C2semidirect
9. C22×Dic5C22semidirect
13. C5×C22⋊C4C22semidirect
15. C22⋊Dic5C22semidirect
42. #99D5semidirect
68. C22⋊C4C2×D5semidirect
92. C5#458semidirect

Maximal subgroups

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

subgroupindex
#41442
#40812
#40322
C5×#992
#39382
#4585