Finite Group Databasebeta

← C5×#468 #65631

Subgroups — C5×#468 #65631

Order 320.

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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
1C2×C5×SD16C211yesmaximal, characteristic, complemented
2C2×C5×M16C211yesmaximal, characteristic, complemented
3C5×C22⋊Q8C211yesmaximal, characteristic, complemented
4C5×#121C211yesmaximal, characteristic
5C5×#107C211yesmaximal, characteristic, complemented
6C5×#103C211yesmaximal, characteristic, complemented
7C5×#102C211yesmaximal, characteristic, complemented
8C2×C5×Q8C2211yescharacteristic
9C2×C5×D4—21no—
10C2×C5×D4C2211yescharacteristic
11C22×C4×C5C2211yescharacteristic
12C5×SD16—22no—
13C5×M16—22no—
14C2×C5×C8C2211yescharacteristic
15C2×C5×C8C2211yescharacteristic
16C5×C4⋊C4—21no—
17C5×C4⋊C4C2211yescharacteristic
18C5×C4⋊C4C2211yescharacteristic
19C5×C22⋊C4—21no—
20C5×C22⋊C4—21no—
21#468C511yesmaximal, characteristic, direct product factor, Sylow
22C23×C5—21no—
23C23×C5D411yescharacteristic
24C5×Q8—21no—
25C5×Q8—21no—
26C5×D4—21no—
27C5×D4—21no—
28C5×D4—42no—
29C2×C4×C5—21no—
30C2×C4×C5—21no—
31C2×C4×C5—21no—
32C2×C4×C5—21no—
33C2×C4×C5—21no—
34C2×C4×C5D411yescharacteristic
35C2×C4×C5C2311yescharacteristic
36C5×C8—21no—
37C5×C8D412yescomplemented
38C2×SD16C2×C511yescharacteristic, complemented
39C2×M16C2×C511yescharacteristic, complemented
40C22⋊Q8C2×C511yescharacteristic, complemented
41#121C2×C511yescharacteristic
42#107C2×C511yescharacteristic, complemented
43#103C2×C511yescharacteristic, complemented
44#102C2×C511yescharacteristic, complemented
45C22×C5—21no—
46C22×C5—21no—
47C22×C5—21no—
48C22×C5—41no—
49C22×C5—41no—
50C22×C5—41no—
51C22×C5C2×D411yescharacteristic
52C4×C5—21no—
53C4×C5—41no—
54C4×C5—41no—
55C4×C5—41no—
56C4×C5C2×D411yescharacteristic
57C4×C5#4111yescharacteristic
58C2×Q8C22×C511yescharacteristic
59C2×D4—21no—
60C2×D4C22×C511yescharacteristic
61C22×C4C22×C511yescharacteristic
62SD16—22no—
63M16—22no—
64C2×C8C22×C511yescharacteristic
65C2×C8C22×C511yescharacteristic
66C4⋊C4—21no—
67C4⋊C4C22×C511yescharacteristic
68C4⋊C4C22×C511yescharacteristic
69C22⋊C4—21no—
70C22⋊C4—21no—
71C2×C5—41no—
72C2×C5—81no—
73C2×C5#12111yescharacteristic
74C2×C5AGL(1,ℤ/8)11yescharacteristic
75C2×C5#13711yescharacteristic
76C23—21no—
77C23C5×D411yescharacteristic
78Q8—21no—
79Q8—21no—
80D4—21no—
81D4—21no—
82D4—42no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—21no—
87C2×C4—21no—
88C2×C4C5×D411yescharacteristic
89C2×C4C23×C511yescharacteristic
90C8—21no—
91C8C5×D412yescomplemented
92C5#46811yescharacteristic, direct product factor, Sylow
93C22—21no—
94C22—21no—
95C22—21no—
96C22—41no—
97C22—41no—
98C22—41no—
99C22C2×C5×D411yescharacteristic
100C4—21no—
101C4—41no—
102C4—41no—
103C4—41no—
104C4C2×C5×D411yescharacteristic
105C4C5×#4111yescharacteristic
106C2—41no—
107C2—81no—
108C2C5×#12111yescharacteristic
109C2C5×AGL(1,ℤ/8)11yescharacteristic
110C2C5×#13711yescharacteristic
subgroupG/H
center, socleC22×C5C2×D4
commutator, Frattini, cosocleC2×C4C23×C5
prime radicalC5×#121C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×SD16C2semidirect
2. C2×C5×M16C2semidirect
3. C5×C22⋊Q8C2semidirect
5. C5×#107C2semidirect
6. C5×#103C2semidirect
7. C5×#102C2semidirect
21. #468C5direct (N × H)
37. C5×C8D4semidirect
38. C2×SD16C2×C5semidirect
39. C2×M16C2×C5semidirect
40. C22⋊Q8C2×C5semidirect
42. #107C2×C5semidirect
43. #103C2×C5semidirect
44. #102C2×C5semidirect
91. C8C5×D4semidirect
92. C5#468direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×SD162
C2×C5×M162
C5×C22⋊Q82
C5×#1212
C5×#1072
C5×#1032
C5×#1022
#4685