Finite Group Databasebeta

← C2×C3×C42×C5×C37 #72195608

Subgroups — C2×C3×C42×C5×C37 #72195608

Order 17760.

432 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×C5×C37C213yesmaximal
2C3×C42×C5×C37C214yesmaximal, direct product factor
3C2×C42×C5×C37C311yesmaximal, characteristic, direct product factor, Hall
4C23×C3×C5×C37C2211yescharacteristic
5C2×C3×C4×C5×C37C4112yesdirect product factor
6C2×C3×C4×C5×C37C2216yes—
7C2×C3×C42×C37C511yesmaximal, characteristic, direct product factor, Hall
8C22×C4×C5×C37C2×C313yes—
9C42×C5×C37C2×C314yesdirect product factor
10C22×C3×C5×C37C2×C416yes—
11C22×C3×C5×C37C2311yescharacteristic
12C3×C4×C5×C37C2×C4112yesdirect product factor
13C22×C3×C4×C37C2×C513yes—
14C3×C42×C37C2×C514yesdirect product factor
15C23×C5×C37C22×C311yescharacteristic
16C2×C4×C5×C37C3×C4112yesdirect product factor
17C2×C4×C5×C37C22×C316yes—
18C2×C42×C37C3×C511yescharacteristic, direct product factor, Hall
19C2×C3×C5×C37C4214yesdirect product factor
20C2×C3×C5×C37C22×C413yes—
21C23×C3×C37C22×C511yescharacteristic
22C2×C3×C4×C37C4×C5112yesdirect product factor
23C2×C3×C4×C37C22×C516yes—
24C22×C5×C37C2×C3×C416yes—
25C22×C5×C37C23×C311yescharacteristic
26C4×C5×C37C2×C3×C4112yesdirect product factor
27C22×C4×C37C2×C3×C513yes—
28C42×C37C2×C3×C514yesdirect product factor
29C3×C5×C37C2×C4211yescharacteristic, direct product factor, Hall
30C2×C3×C42×C5C3711yesmaximal, characteristic, direct product factor, Hall
31C22×C3×C37C2×C4×C516yes—
32C22×C3×C37C23×C511yescharacteristic
33C3×C4×C37C2×C4×C5112yesdirect product factor
34C2×C5×C37C3×C4214yesdirect product factor
35C2×C5×C37C22×C3×C413yes—
36C23×C37C22×C3×C511yescharacteristic
37C2×C4×C37C3×C4×C5112yesdirect product factor
38C2×C4×C37C22×C3×C516yes—
39C22×C3×C4×C5C2×C3713yes—
40C3×C42×C5C2×C3714yesdirect product factor
41C2×C3×C37C42×C514yesdirect product factor
42C2×C3×C37C22×C4×C513yes—
43C5×C37C2×C3×C4211yescharacteristic, direct product factor, Hall
44C2×C42×C5C3×C3711yescharacteristic, direct product factor, Hall
45C22×C37C2×C3×C4×C516yes—
46C22×C37C23×C3×C511yescharacteristic
47C4×C37C2×C3×C4×C5112yesdirect product factor
48C23×C3×C5C22×C3711yescharacteristic
49C2×C3×C4×C5C4×C37112yesdirect product factor
50C2×C3×C4×C5C22×C3716yes—
51C3×C37C2×C42×C511yescharacteristic, direct product factor, Hall
52C2×C3×C42C5×C3711yescharacteristic, direct product factor, Hall
53C22×C4×C5C2×C3×C3713yes—
54C42×C5C2×C3×C3714yesdirect product factor
55C2×C37C3×C42×C514yesdirect product factor
56C2×C37C22×C3×C4×C513yes—
57C22×C3×C5C2×C4×C3716yes—
58C22×C3×C5C23×C3711yescharacteristic
59C3×C4×C5C2×C4×C37112yesdirect product factor
60C22×C3×C4C2×C5×C3713yes—
61C3×C42C2×C5×C3714yesdirect product factor
62C23×C5C22×C3×C3711yescharacteristic
63C2×C4×C5C3×C4×C37112yesdirect product factor
64C2×C4×C5C22×C3×C3716yes—
65C37C2×C3×C42×C511yescharacteristic, direct product factor, Sylow
66C2×C42C3×C5×C3711yescharacteristic, direct product factor, Sylow
67C2×C3×C5C42×C3714yesdirect product factor
68C2×C3×C5C22×C4×C3713yes—
69C23×C3C22×C5×C3711yescharacteristic
70C2×C3×C4C4×C5×C37112yesdirect product factor
71C2×C3×C4C22×C5×C3716yes—
72C22×C5C2×C3×C4×C3716yes—
73C22×C5C23×C3×C3711yescharacteristic
74C4×C5C2×C3×C4×C37112yesdirect product factor
75C22×C4C2×C3×C5×C3713yes—
76C42C2×C3×C5×C3714yesdirect product factor
77C3×C5C2×C42×C3711yescharacteristic, direct product factor, Hall
78C22×C3C2×C4×C5×C3716yes—
79C22×C3C23×C5×C3711yescharacteristic
80C3×C4C2×C4×C5×C37112yesdirect product factor
81C2×C5C3×C42×C3714yesdirect product factor
82C2×C5C22×C3×C4×C3713yes—
83C23C22×C3×C5×C3711yescharacteristic
84C2×C4C3×C4×C5×C37112yesdirect product factor
85C2×C4C22×C3×C5×C3716yes—
86C2×C3C42×C5×C3714yesdirect product factor
87C2×C3C22×C4×C5×C3713yes—
88C5C2×C3×C42×C3711yescharacteristic, direct product factor, Sylow
89C22C2×C3×C4×C5×C3716yes—
90C22C23×C3×C5×C3711yescharacteristic
91C4C2×C3×C4×C5×C37112yesdirect product factor
92C3C2×C42×C5×C3711yescharacteristic, direct product factor, Sylow
93C2C3×C42×C5×C3714yesdirect product factor
94C2C22×C3×C4×C5×C3713yes—
subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C5×C37
socle, prime radicalC23×C3×C5×C37C22
LCSG ▷ C1
UCSC1 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×C42×C5×C37C2direct (N × H)
3. C2×C42×C5×C37C3direct (N × H)
5. C2×C3×C4×C5×C37C4direct (N × H)
7. C2×C3×C42×C37C5direct (N × H)
9. C42×C5×C37C2×C3direct (N × H)
12. C3×C4×C5×C37C2×C4direct (N × H)
14. C3×C42×C37C2×C5direct (N × H)
16. C2×C4×C5×C37C3×C4direct (N × H)
18. C2×C42×C37C3×C5direct (N × H)
19. C2×C3×C5×C37C42direct (N × H)
22. C2×C3×C4×C37C4×C5direct (N × H)
26. C4×C5×C37C2×C3×C4direct (N × H)
28. C42×C37C2×C3×C5direct (N × H)
29. C3×C5×C37C2×C42direct (N × H)
30. C2×C3×C42×C5C37direct (N × H)
33. C3×C4×C37C2×C4×C5direct (N × H)
34. C2×C5×C37C3×C42direct (N × H)
37. C2×C4×C37C3×C4×C5direct (N × H)
40. C3×C42×C5C2×C37direct (N × H)
41. C2×C3×C37C42×C5direct (N × H)
43. C5×C37C2×C3×C42direct (N × H)
44. C2×C42×C5C3×C37direct (N × H)
47. C4×C37C2×C3×C4×C5direct (N × H)
49. C2×C3×C4×C5C4×C37direct (N × H)
51. C3×C37C2×C42×C5direct (N × H)
52. C2×C3×C42C5×C37direct (N × H)
54. C42×C5C2×C3×C37direct (N × H)
55. C2×C37C3×C42×C5direct (N × H)
59. C3×C4×C5C2×C4×C37direct (N × H)
61. C3×C42C2×C5×C37direct (N × H)
63. C2×C4×C5C3×C4×C37direct (N × H)
65. C37C2×C3×C42×C5direct (N × H)
66. C2×C42C3×C5×C37direct (N × H)
67. C2×C3×C5C42×C37direct (N × H)
70. C2×C3×C4C4×C5×C37direct (N × H)
74. C4×C5C2×C3×C4×C37direct (N × H)
76. C42C2×C3×C5×C37direct (N × H)
77. C3×C5C2×C42×C37direct (N × H)
80. C3×C4C2×C4×C5×C37direct (N × H)
81. C2×C5C3×C42×C37direct (N × H)
84. C2×C4C3×C4×C5×C37direct (N × H)
86. C2×C3C42×C5×C37direct (N × H)
88. C5C2×C3×C42×C37direct (N × H)
91. C4C2×C3×C4×C5×C37direct (N × H)
92. C3C2×C42×C5×C37direct (N × H)
93. C2C3×C42×C5×C37direct (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×C372
C3×C42×C5×C372
C2×C42×C5×C373
C2×C3×C42×C375
C2×C3×C42×C537