Finite Group Databasebeta

← C2×C3×C42×C5×C59 #72205305

Subgroups — C2×C3×C42×C5×C59 #72205305

Order 28320.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C5×C59C213yesmaximal
2C3×C42×C5×C59C214yesmaximal, direct product factor
3C2×C42×C5×C59C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C5×C59C2211yescharacteristic
5C2×C3×C4×C5×C59C4112yesdirect product factor
6C2×C3×C4×C5×C59C2216yes—
7C2×C3×C42×C59C511yesmaximal, characteristic, direct product factor, Hall
8C22×C4×C5×C59C2×C313yes—
9C42×C5×C59C2×C314yesdirect product factor
10C22×C3×C4×C59C2×C513yes—
11C3×C42×C59C2×C514yesdirect product factor
12C23×C5×C59C22×C311yescharacteristic
13C2×C4×C5×C59C3×C4112yesdirect product factor
14C2×C4×C5×C59C22×C316yes—
15C22×C3×C5×C59C2×C416yes—
16C22×C3×C5×C59C2311yescharacteristic
17C3×C4×C5×C59C2×C4112yesdirect product factor
18C2×C42×C59C3×C511yescharacteristic, direct product factor, Hall
19C2×C3×C5×C59C4214yesdirect product factor
20C2×C3×C5×C59C22×C413yes—
21C23×C3×C59C22×C511yescharacteristic
22C2×C3×C4×C59C4×C5112yesdirect product factor
23C2×C3×C4×C59C22×C516yes—
24C22×C5×C59C2×C3×C416yes—
25C22×C5×C59C23×C311yescharacteristic
26C4×C5×C59C2×C3×C4112yesdirect product factor
27C22×C4×C59C2×C3×C513yes—
28C42×C59C2×C3×C514yesdirect product factor
29C3×C5×C59C2×C4211yescharacteristic, direct product factor, Hall
30C22×C3×C59C2×C4×C516yes—
31C22×C3×C59C23×C511yescharacteristic
32C3×C4×C59C2×C4×C5112yesdirect product factor
33C2×C5×C59C3×C4214yesdirect product factor
34C2×C5×C59C22×C3×C413yes—
35C2×C3×C42×C5C5911yesmaximal, characteristic, direct product factor, Hall
36C23×C59C22×C3×C511yescharacteristic
37C2×C4×C59C3×C4×C5112yesdirect product factor
38C2×C4×C59C22×C3×C516yes—
39C2×C3×C59C42×C514yesdirect product factor
40C2×C3×C59C22×C4×C513yes—
41C5×C59C2×C3×C4211yescharacteristic, direct product factor, Hall
42C22×C3×C4×C5C2×C5913yes—
43C3×C42×C5C2×C5914yesdirect product factor
44C22×C59C2×C3×C4×C516yes—
45C22×C59C23×C3×C511yescharacteristic
46C4×C59C2×C3×C4×C5112yesdirect product factor
47C3×C59C2×C42×C511yescharacteristic, direct product factor, Hall
48C2×C42×C5C3×C5911yescharacteristic, direct product factor, Hall
49C23×C3×C5C22×C5911yescharacteristic
50C2×C3×C4×C5C4×C59112yesdirect product factor
51C2×C3×C4×C5C22×C5916yes—
52C2×C59C3×C42×C514yesdirect product factor
53C2×C59C22×C3×C4×C513yes—
54C2×C3×C42C5×C5911yescharacteristic, direct product factor, Hall
55C22×C4×C5C2×C3×C5913yes—
56C42×C5C2×C3×C5914yesdirect product factor
57C22×C3×C5C2×C4×C5916yes—
58C22×C3×C5C23×C5911yescharacteristic
59C3×C4×C5C2×C4×C59112yesdirect product factor
60C59C2×C3×C42×C511yescharacteristic, direct product factor, Sylow
61C22×C3×C4C2×C5×C5913yes—
62C3×C42C2×C5×C5914yesdirect product factor
63C23×C5C22×C3×C5911yescharacteristic
64C2×C4×C5C3×C4×C59112yesdirect product factor
65C2×C4×C5C22×C3×C5916yes—
66C2×C42C3×C5×C5911yescharacteristic, direct product factor, Sylow
67C2×C3×C5C42×C5914yesdirect product factor
68C2×C3×C5C22×C4×C5913yes—
69C23×C3C22×C5×C5911yescharacteristic
70C2×C3×C4C4×C5×C59112yesdirect product factor
71C2×C3×C4C22×C5×C5916yes—
72C22×C5C2×C3×C4×C5916yes—
73C22×C5C23×C3×C5911yescharacteristic
74C4×C5C2×C3×C4×C59112yesdirect product factor
75C22×C4C2×C3×C5×C5913yes—
76C42C2×C3×C5×C5914yesdirect product factor
77C3×C5C2×C42×C5911yescharacteristic, direct product factor, Hall
78C22×C3C2×C4×C5×C5916yes—
79C22×C3C23×C5×C5911yescharacteristic
80C3×C4C2×C4×C5×C59112yesdirect product factor
81C2×C5C3×C42×C5914yesdirect product factor
82C2×C5C22×C3×C4×C5913yes—
83C23C22×C3×C5×C5911yescharacteristic
84C2×C4C3×C4×C5×C59112yesdirect product factor
85C2×C4C22×C3×C5×C5916yes—
86C2×C3C42×C5×C5914yesdirect product factor
87C2×C3C22×C4×C5×C5913yes—
88C5C2×C3×C42×C5911yescharacteristic, direct product factor, Sylow
89C22C2×C3×C4×C5×C5916yes—
90C22C23×C3×C5×C5911yescharacteristic
91C4C2×C3×C4×C5×C59112yesdirect product factor
92C3C2×C42×C5×C5911yescharacteristic, direct product factor, Sylow
93C2C3×C42×C5×C5914yesdirect product factor
94C2C22×C3×C4×C5×C5913yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C5×C59
socle, prime radicalC23×C3×C5×C59C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C42×C5×C59C2direct (N × H)
3. C2×C42×C5×C59C3direct (N × H)
5. C2×C3×C4×C5×C59C4direct (N × H)
7. C2×C3×C42×C59C5direct (N × H)
9. C42×C5×C59C2×C3direct (N × H)
11. C3×C42×C59C2×C5direct (N × H)
13. C2×C4×C5×C59C3×C4direct (N × H)
17. C3×C4×C5×C59C2×C4direct (N × H)
18. C2×C42×C59C3×C5direct (N × H)
19. C2×C3×C5×C59C42direct (N × H)
22. C2×C3×C4×C59C4×C5direct (N × H)
26. C4×C5×C59C2×C3×C4direct (N × H)
28. C42×C59C2×C3×C5direct (N × H)
29. C3×C5×C59C2×C42direct (N × H)
32. C3×C4×C59C2×C4×C5direct (N × H)
33. C2×C5×C59C3×C42direct (N × H)
35. C2×C3×C42×C5C59direct (N × H)
37. C2×C4×C59C3×C4×C5direct (N × H)
39. C2×C3×C59C42×C5direct (N × H)
41. C5×C59C2×C3×C42direct (N × H)
43. C3×C42×C5C2×C59direct (N × H)
46. C4×C59C2×C3×C4×C5direct (N × H)
47. C3×C59C2×C42×C5direct (N × H)
48. C2×C42×C5C3×C59direct (N × H)
50. C2×C3×C4×C5C4×C59direct (N × H)
52. C2×C59C3×C42×C5direct (N × H)
54. C2×C3×C42C5×C59direct (N × H)
56. C42×C5C2×C3×C59direct (N × H)
59. C3×C4×C5C2×C4×C59direct (N × H)
60. C59C2×C3×C42×C5direct (N × H)
62. C3×C42C2×C5×C59direct (N × H)
64. C2×C4×C5C3×C4×C59direct (N × H)
66. C2×C42C3×C5×C59direct (N × H)
67. C2×C3×C5C42×C59direct (N × H)
70. C2×C3×C4C4×C5×C59direct (N × H)
74. C4×C5C2×C3×C4×C59direct (N × H)
76. C42C2×C3×C5×C59direct (N × H)
77. C3×C5C2×C42×C59direct (N × H)
80. C3×C4C2×C4×C5×C59direct (N × H)
81. C2×C5C3×C42×C59direct (N × H)
84. C2×C4C3×C4×C5×C59direct (N × H)
86. C2×C3C42×C5×C59direct (N × H)
88. C5C2×C3×C42×C59direct (N × H)
91. C4C2×C3×C4×C5×C59direct (N × H)
92. C3C2×C42×C5×C59direct (N × H)
93. C2C3×C42×C5×C59direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×C5×C592
C3×C42×C5×C592
C2×C42×C5×C593
C2×C3×C42×C595
C2×C3×C42×C559