Finite Group Databasebeta

← C2×C3×#711 #92064

Subgroups — C2×C3×#711 #92064

Order 480.

328 conjugacy classes of subgroups; only the 178 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 178 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×C3×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×C22⋊D5C212yesmaximal, complemented
3C22×C3×Dic5C212yesmaximal, complemented
4C3×#711C218yesmaximal, direct product factor
5C2×C3×C4×D5C211yesmaximal, characteristic, complemented
6C2×C3×Dic10C211yesmaximal, characteristic, complemented
7C2×#711C311yesmaximal, characteristic, direct product factor, Hall
8C23×C3×C5C2212yes—
9C22×C3×D5C2211yescharacteristic
10C3×C5×D4C2214yescomplemented
11C2×C3×C4×C5C2211yescharacteristic
12C3×C22⋊D5C2218yescomplemented
13C2×C3×Dic5C2212yes—
14C2×C3×Dic5C2211yescharacteristic
15C2×C3×Dic5C2218yescomplemented
16C3×C4×D5C2214yescomplemented
17C3×Dic10C2214yescomplemented
18C2×C3×#41—51nomaximal, Hall
19C2×C5×D4C2×C311yescharacteristic, complemented
20C2×C22⋊D5C2×C312yescomplemented
21C22×Dic5C2×C312yescomplemented
22#711C2×C318yesdirect product factor
23C2×C4×D5C2×C311yescharacteristic, complemented
24C2×Dic10C2×C311yescharacteristic, complemented
25C22×C3×C5—24no—
26C22×C3×C5C2314yes—
27C22×C3×C5C2311yescharacteristic
28C2×C3×D5—22no—
29C2×C3×D5C2312yes—
30C3×C4×C5C2312yes—
31C3×Dic5C2314yes—
32C3×Dic5C2312yes—
33C3×#41—58no—
34C2×C3×Q8—51no—
35C2×C3×D4—52no—
36C2×C3×D4D511yescharacteristic, complemented
37C22×C3×C4—52no—
38C22×C3×C4—51no—
39C23×C5C22×C312yes—
40C22×D5C22×C311yescharacteristic
41C5×D4C22×C314yescomplemented
42C2×C4×C5C22×C311yescharacteristic
43C22⋊D5C22×C318yescomplemented
44C2×Dic5C22×C312yes—
45C2×Dic5C22×C311yescharacteristic
46C2×Dic5C22×C318yescomplemented
47C4×D5C22×C314yescomplemented
48Dic10C22×C314yescomplemented
49C2×#41—51noSylow
50C2×C3×C5—24no—
51C2×C3×C5#4112yescomplemented
52C2×C3×C5C2411yescharacteristic
53C3×D5—22no—
54C23×C3—51no—
55C23×C3C2×D512yes—
56C3×Q8—54no—
57C3×D4—58no—
58C3×D4C2×D514yescomplemented
59C2×C3×C4—58no—
60C2×C3×C4—51no—
61C2×C3×C4—52no—
62C2×C3×C4—54no—
63C2×C3×C4C2×D511yescharacteristic
64C22×C5—24no—
65C22×C5C23×C314yes—
66C22×C5C23×C311yescharacteristic
67C2×D5—22no—
68C2×D5C23×C312yes—
69C4×C5C23×C312yes—
70Dic5C23×C314yes—
71Dic5C23×C312yes—
72#41—58no—
73C2×Q8—51no—
74C2×D4—52no—
75C2×D4C3×D511yescharacteristic, complemented
76C22×C4—52no—
77C22×C4—51no—
78C3×C5C2×#4111yescharacteristic, complemented, Hall
79C22×C3—24no—
80C22×C3—52no—
81C22×C3—102no—
82C22×C3C22×D514yes—
83C22×C3C22×D511yescharacteristic
84C3×C4—52no—
85C3×C4—54no—
86C3×C4C22×D512yes—
87C2×C5—24no—
88C2×C5C3×#4112yescomplemented
89C2×C5C24×C311yescharacteristic
90D5—22no—
91C23—51no—
92C23C2×C3×D512yes—
93Q8—54no—
94D4—58no—
95D4C2×C3×D514yescomplemented
96C2×C4—51no—
97C2×C4—52no—
98C2×C4—58no—
99C2×C4—54no—
100C2×C4C2×C3×D511yescharacteristic
101C2×C3—24no—
102C2×C3—102no—
103C2×C3#71112yesdirect product factor
104C2×C3C23×D511yescharacteristic
105C5C2×C3×#4111yescharacteristic, complemented, Sylow
106C22—24no—
107C22—52no—
108C22—102no—
109C22C22×C3×D514yes—
110C22C22×C3×D511yescharacteristic
111C4—52no—
112C4—54no—
113C4C22×C3×D512yes—
114C3C2×#71111yescharacteristic, direct product factor, Sylow
115C2—24no—
116C2—102no—
117C2C3×#71112yesdirect product factor
118C2C23×C3×D511yescharacteristic
subgroupG/H
centerC22×C3C22×D5
commutator, cosocleC2×C5C24×C3
FrattiniC2C23×C3×D5
FittingC2×C3×C5×D4C2
socleC22×C3×C5C23
hypercenterC2×C3×D4D5
hypocenterC5C2×C3×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×D4C2semidirect
2. C2×C3×C22⋊D5C2semidirect
3. C22×C3×Dic5C2semidirect
4. C3×#711C2direct (N × H)
5. C2×C3×C4×D5C2semidirect
6. C2×C3×Dic10C2semidirect
7. C2×#711C3direct (N × H)
10. C3×C5×D4C22semidirect
12. C3×C22⋊D5C22semidirect
15. C2×C3×Dic5C22semidirect
16. C3×C4×D5C22semidirect
17. C3×Dic10C22semidirect
19. C2×C5×D4C2×C3semidirect
20. C2×C22⋊D5C2×C3semidirect
21. C22×Dic5C2×C3semidirect
22. #711C2×C3direct (N × H)
23. C2×C4×D5C2×C3semidirect
24. C2×Dic10C2×C3semidirect
36. C2×C3×D4D5semidirect
41. C5×D4C22×C3semidirect
43. C22⋊D5C22×C3semidirect
46. C2×Dic5C22×C3semidirect
47. C4×D5C22×C3semidirect
48. Dic10C22×C3semidirect
51. C2×C3×C5#41semidirect
58. C3×D4C2×D5semidirect
75. C2×D4C3×D5semidirect
78. C3×C5C2×#41semidirect
88. C2×C5C3×#41semidirect
95. D4C2×C3×D5semidirect
103. C2×C3#711direct (N × H)
105. C5C2×C3×#41semidirect
114. C3C2×#711direct (N × H)
117. C2C3×#711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×D42
C2×C3×C22⋊D52
C22×C3×Dic52
C3×#7112
C2×C3×C4×D52
C2×C3×Dic102
C2×#7113
C2×C3×#415