Finite Group Databasebeta

← D5×#120 #65922

Subgroups — D5×#120 #65922

Order 320.

662 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 131 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×D5C211yesmaximal, characteristic, complemented
2C2×D4×D5C213yesmaximal, complemented
3C5×#120C211yesmaximal, characteristic, complemented
4#4099C211yesmaximal, characteristic, complemented
5#4083C213yesmaximal, complemented
6#4028C213yesmaximal, complemented
7D5×C22⋊C4C213yesmaximal, complemented
8C24×C5C2211yescharacteristic, complemented
9C23×D5—212no—
10C23×D5C2213yes—
11C23×D5C2213yescomplemented
12C23×D5C2211yescharacteristic, complemented
13C2×C5×D4C2213yescomplemented
14C2×C22⋊D5C2213yescomplemented
15C2×C22⋊D5C2213yescomplemented
16D4×D5—212no—
17C2×D20C2213yescomplemented
18C2×C4×D5C2213yescomplemented
19C5×C22⋊C4C2213yescomplemented
20C22⋊Dic5C2213yescomplemented
21#685C2216yescomplemented
22C2×#120—51nomaximal, Sylow
23C23×C5—26no—
24C23×C5C2313yes—
25C23×C5C2311yescharacteristic, complemented
26C22×D5—232no—
27C22×D5—26no—
28C22×D5—212no—
29C22×D5—212no—
30C22×D5—26no—
31C22×D5D4112yescomplemented
32C22×D5C2313yes—
33C22×D5C2311yescharacteristic
34C22×D5C2311yescharacteristic, complemented
35C5×D4—26no—
36C2×C4×C5C2313yescomplemented
37C22⋊D5—26no—
38C22⋊D5—26no—
39C2×Dic5C2313yescomplemented
40D20—26no—
41C4×D5—26no—
42C25—51no—
43C22×D4—53no—
44#120—51no—
45#120—53no—
46#120—53no—
47#120D511yescharacteristic, direct product factor
48C2×C22⋊C4—53no—
49C22×C5—28no—
50C22×C5—26no—
51C22×C5—23no—
52C22×C5C2×D416yescomplemented
53C22×C5C2411yescharacteristic
54C2×D5—224no—
55C2×D5—26no—
56C2×D5—224no—
57C2×D5—23no—
58C2×D5—44no—
59C2×D5C2×D416yes—
60C2×D5C2×D416yescomplemented
61C4×C5—23no—
62Dic5—23no—
63C24—53no—
64C24—53no—
65C24—51no—
66C24—1012no—
67C24C2×D511yescharacteristic, complemented
68C2×D4—53no—
69C2×D4—53no—
70C2×D4—53no—
71C2×D4—1012no—
72C2×D4C2×D513yescomplemented
73C22×C4—53no—
74C22⋊C4—53no—
75C22⋊C4—56no—
76C22⋊C4C2×D513yescomplemented
77C2×C5—26no—
78C2×C5—41no—
79C2×C5C22×D413yes—
80D5—26no—
81D5—41no—
82D5#12014yesdirect product factor
83C23—26no—
84C23—51no—
85C23—512no—
86C23—53no—
87C23—51no—
88C23—1012no—
89C23—1012no—
90C23—106no—
91C23—1032no—
92C23—106no—
93C23C22×D513yes—
94C23C22×D511yescharacteristic, complemented
95D4—26no—
96D4—106no—
97D4—106no—
98D4—106no—
99C2×C4—53no—
100C2×C4—106no—
101C2×C4C22×D513yescomplemented
102C5C2×#12011yescharacteristic, complemented, Sylow
103C22—28no—
104C22—26no—
105C22—23no—
106C22—56no—
107C22—56no—
108C22—1024no—
109C22—1024no—
110C22—106no—
111C22—103no—
112C22—204no—
113C22D4×D516yescomplemented
114C22C23×D511yescharacteristic
115C4—23no—
116C4—103no—
117C2—26no—
118C2—41no—
119C2—54no—
120C2—106no—
121C2—201no—
122C2C2×D4×D513yes—
subgroupG/H
center, FrattiniC22C23×D5
commutator, socle, cosocleC22×C5C24
FittingC5×#120C2
hypercenter#120D5
hypocenterC5C2×#120
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #120

Complements

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

NH ≅ G/Ntype
1. C24×D5C2semidirect
2. C2×D4×D5C2semidirect
3. C5×#120C2semidirect
4. #4099C2semidirect
5. #4083C2semidirect
6. #4028C2semidirect
7. D5×C22⋊C4C2semidirect
8. C24×C5C22semidirect
11. C23×D5C22semidirect
12. C23×D5C22semidirect
13. C2×C5×D4C22semidirect
14. C2×C22⋊D5C22semidirect
15. C2×C22⋊D5C22semidirect
17. C2×D20C22semidirect
18. C2×C4×D5C22semidirect
19. C5×C22⋊C4C22semidirect
20. C22⋊Dic5C22semidirect
21. #685C22semidirect
25. C23×C5C23semidirect
31. C22×D5D4semidirect
34. C22×D5C23semidirect
36. C2×C4×C5C23semidirect
39. C2×Dic5C23semidirect
47. #120D5direct (N × H)
52. C22×C5C2×D4semidirect
60. C2×D5C2×D4semidirect
67. C24C2×D5semidirect
72. C2×D4C2×D5semidirect
76. C22⋊C4C2×D5semidirect
82. D5#120direct (N × H)
94. C23C22×D5semidirect
101. C2×C4C22×D5semidirect
102. C5C2×#120semidirect
113. C22D4×D5semidirect

Maximal subgroups

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

subgroupindex
C24×D52
C2×D4×D52
C5×#1202
#40992
#40832
#40282
D5×C22⋊C42
C2×#1205