Finite Group Databasebeta

← C24×#713 #13013184

Subgroups — C24×#713 #13013184

Order 1280.

65470 conjugacy classes of subgroups; only the 32651 normal subgroups are shown.

normal subgroups only

This group has 65470 conjugacy classes of subgroups — too many to draw. Only its 32651 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
1C24×C5×Q8C211yesmaximal, characteristic, complemented
2C23×#713C21120yesmaximal, direct product factor
3C24×D20C213yesmaximal, complemented
4C24×C4×D5C213yesmaximal, complemented
5C25×D5C2213yes—
6C23×C5×Q8C22160yescomplemented
7C24×C4×C5C2213yes—
8C24×Dic5C2211yescharacteristic
9C22×#713C2212240yesdirect product factor
10C23×D20C221180yescomplemented
11C23×C4×D5C221180yescomplemented
12C24×#41—51nomaximal, Sylow
13C25×C5C2311yescharacteristic
14C24×D5—248no—
15C24×D5C23190yes—
16C22×C5×Q8C231560yescomplemented
17C23×C4×C5C23190yes—
18C23×Dic5C23130yes—
19C2×#713C2317680yesdirect product factor
20C22×D20C2311680yescomplemented
21C22×C4×D5C2311680yescomplemented
22C23×#41—5120no—
23C24×Q8D511yescharacteristic, complemented
24C24×D4—53no—
25C25×C4—53no—
26C24×C5#41116yescomplemented
27C24×C5C24115yes—
28C23×D5—2720no—
29C23×D5C241420yes—
30C2×C5×Q8C241960yescomplemented
31C22×C4×C5C241420yes—
32C22×Dic5C241140yes—
33#713C2414096yesdirect product factor
34C2×D20C2412880yescomplemented
35C2×C4×D5C2412880yescomplemented
36C26—53no—
37C22×#41—52240no—
38C23×Q8C2×D5160yescomplemented
39C23×D4—5180no—
40C24×C4—51no—
41C24×C4—5180no—
42C24×C4C2×D513yes—
43C23×C5C2×#411120yescomplemented
44C23×C5C25135yes—
45C22×D5—21680no—
46C22×D5C251360yes—
47C5×Q8C251256yescomplemented
48C2×C4×C5C251360yes—
49C2×Dic5C251120yes—
50D20C251768yescomplemented
51C4×D5C251768yescomplemented
52C25—590no—
53C25—1048no—
54C25C22×D511yescharacteristic
55C2×#41—57680no—
56C22×Q8C22×D51560yescomplemented
57C22×D4—51680no—
58C23×C4—530no—
59C23×C4—51680no—
60C23×C4C22×D5190yes—
61C22×C5C22×#411140yescomplemented
62C22×C5C26115yes—
63C2×D5—2720no—
64C2×D5C26148yes—
65C4×C5C26148yes—
66Dic5C26116yes—
67C24—5420no—
68C24—10720no—
69C24#713116yesdirect product factor
70C24C23×D5115yes—
71#41—54096no—
72C2×Q8C23×D51960yescomplemented
73C2×D4—52880no—
74C22×C4—5140no—
75C22×C4—52880no—
76C22×C4C23×D51420yes—
77C2×C5C23×#41130yescomplemented
78C2×C5C2711yescharacteristic
79D5—248no—
80C23—5360no—
81C23—101680no—
82C23C2×#7131120yesdirect product factor
83C23C24×D5135yes—
84Q8C24×D51256yescomplemented
85D4—5768no—
86C2×C4—5120no—
87C2×C4—5768no—
88C2×C4C24×D51360yes—
89C5C24×#4111yescharacteristic, complemented, Sylow
90C22—548no—
91C22—10720no—
92C22C22×#7131140yesdirect product factor
93C22C25×D5115yes—
94C4—516no—
95C4C25×D5148yes—
96C2—1048no—
97C2C23×#713130yesdirect product factor
98C2C26×D511yescharacteristic
subgroupG/H
centerC25C22×D5
commutator, cosocleC2×C5C27
FrattiniC2C26×D5
FittingC24×C5×Q8C2
socleC25×C5C23
hypercenterC24×Q8D5
hypocenterC5C24×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C25 ◁ C24×Q8

Complements

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

NH ≅ G/Ntype
1. C24×C5×Q8C2semidirect
2. C23×#713C2direct (N × H)
3. C24×D20C2semidirect
4. C24×C4×D5C2semidirect
6. C23×C5×Q8C22semidirect
9. C22×#713C22direct (N × H)
10. C23×D20C22semidirect
11. C23×C4×D5C22semidirect
16. C22×C5×Q8C23semidirect
19. C2×#713C23direct (N × H)
20. C22×D20C23semidirect
21. C22×C4×D5C23semidirect
23. C24×Q8D5semidirect
26. C24×C5#41semidirect
30. C2×C5×Q8C24semidirect
33. #713C24direct (N × H)
34. C2×D20C24semidirect
35. C2×C4×D5C24semidirect
38. C23×Q8C2×D5semidirect
43. C23×C5C2×#41semidirect
47. C5×Q8C25semidirect
50. D20C25semidirect
51. C4×D5C25semidirect
56. C22×Q8C22×D5semidirect
61. C22×C5C22×#41semidirect
69. C24#713direct (N × H)
72. C2×Q8C23×D5semidirect
77. C2×C5C23×#41semidirect
82. C23C2×#713direct (N × H)
84. Q8C24×D5semidirect
89. C5C24×#41semidirect
92. C22C22×#713direct (N × H)
97. C2C23×#713direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C5×Q82
C23×#7132
C24×D202
C24×C4×D52
C24×#415