Finite Group Databasebeta

← C5×#575 #66239

Subgroups — C5×#575 #66239

Order 320.

262 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 158 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×#41C212yesmaximal, complemented
2C5×#137C214yesmaximal, complemented
3C5×AGL(1,ℤ/8)C214yesmaximal, complemented
4C5×#135C214yesmaximal, complemented
5C2×C5×M16C211yesmaximal, characteristic, complemented
6C5×#41—22no—
7C5×#41—22no—
8C5×#41C2214yes—
9C5×#41C2214yescomplemented
10C2×C5×Q8C2212yescomplemented
11C2×C5×D4—22no—
12C2×C5×D4C2212yescomplemented
13C22×C4×C5—22no—
14C22×C4×C5C2211yescharacteristic
15C5×Q16C2214yescomplemented
16C5×SD16C2218yescomplemented
17C5×D8C2214yescomplemented
18C5×M16C2214yescomplemented
19C2×C5×C8C2212yescomplemented
20#575C511yesmaximal, characteristic, direct product factor, Sylow
21C23×C5—22no—
22C23×C5D411yescharacteristic
23C5×Q8—22no—
24C5×Q8C2314yes—
25C5×D4—24no—
26C5×D4—24no—
27C5×D4—22no—
28C5×D4C2314yes—
29C2×C4×C5—22no—
30C2×C4×C5—24no—
31C2×C4×C5—24no—
32C2×C4×C5D411yescharacteristic
33C2×C4×C5D412yes—
34C2×C4×C5C2312yes—
35C2×C4×C5C2311yescharacteristic
36C5×C8C2314yes—
37C2×#41C2×C512yescomplemented
38#137C2×C514yescomplemented
39AGL(1,ℤ/8)C2×C514yescomplemented
40#135C2×C514yescomplemented
41C2×M16C2×C511yescharacteristic, complemented
42C22×C5—24no—
43C22×C5—41no—
44C22×C5—44no—
45C22×C5C2×D412yes—
46C22×C5C2×D411yescharacteristic
47C4×C5—24no—
48C4×C5C2×D412yes—
49C4×C5C2×D411yescharacteristic
50C4×C5C2411yescharacteristic
51#41—22no—
52#41—22no—
53#41C22×C514yes—
54#41C22×C514yescomplemented
55C2×Q8C22×C512yescomplemented
56C2×D4—22no—
57C2×D4C22×C512yescomplemented
58C22×C4—22no—
59C22×C4C22×C511yescharacteristic
60Q16C22×C514yescomplemented
61SD16C22×C518yescomplemented
62D8C22×C514yescomplemented
63M16C22×C514yescomplemented
64C2×C8C22×C512yescomplemented
65C2×C5—22no—
66C2×C5—21no—
67C2×C5—44no—
68C2×C5C22×D411yescharacteristic
69C23—22no—
70C23C5×D411yescharacteristic
71Q8—22no—
72Q8C23×C514yes—
73D4—24no—
74D4—24no—
75D4—22no—
76D4C23×C514yes—
77C2×C4—22no—
78C2×C4—24no—
79C2×C4—24no—
80C2×C4C5×D412yes—
81C2×C4C5×D411yescharacteristic
82C2×C4C23×C511yescharacteristic
83C2×C4C23×C512yes—
84C8C23×C514yes—
85C5#57511yescharacteristic, direct product factor, Sylow
86C22—24no—
87C22—41no—
88C22—44no—
89C22C2×C5×D412yes—
90C22C2×C5×D411yescharacteristic
91C4—24no—
92C4C2×C5×D411yescharacteristic
93C4C2×C5×D412yes—
94C4C24×C511yescharacteristic
95C2—22no—
96C2—21no—
97C2—44no—
98C2C22×C5×D411yescharacteristic
subgroupG/H
centerC4×C5C2×D4
commutator, Frattini, cosocleC4C24×C5
socleC2×C5C22×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#41C2semidirect
2. C5×#137C2semidirect
3. C5×AGL(1,ℤ/8)C2semidirect
4. C5×#135C2semidirect
5. C2×C5×M16C2semidirect
9. C5×#41C22semidirect
10. C2×C5×Q8C22semidirect
12. C2×C5×D4C22semidirect
15. C5×Q16C22semidirect
16. C5×SD16C22semidirect
17. C5×D8C22semidirect
18. C5×M16C22semidirect
19. C2×C5×C8C22semidirect
20. #575C5direct (N × H)
37. C2×#41C2×C5semidirect
38. #137C2×C5semidirect
39. AGL(1,ℤ/8)C2×C5semidirect
40. #135C2×C5semidirect
41. C2×M16C2×C5semidirect
54. #41C22×C5semidirect
55. C2×Q8C22×C5semidirect
57. C2×D4C22×C5semidirect
60. Q16C22×C5semidirect
61. SD16C22×C5semidirect
62. D8C22×C5semidirect
63. M16C22×C5semidirect
64. C2×C8C22×C5semidirect
85. C5#575direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#412
C5×#1372
C5×AGL(1,ℤ/8)2
C5×#1352
C2×C5×M162
#5755