Finite Group Databasebeta

← C2×C32×C5×D95 #30685979

Subgroups — C2×C32×C5×D95 #30685979

Order 17100.

288 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 132 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
1C32×C5×D95C212yesmaximal, direct product factor
2C2×C32×C52×C19C211yesmaximal, characteristic, complemented
3C2×C3×C5×D95C314yesmaximal, direct product factor
4C32×C52×C19C2211yescharacteristic, complemented, Hall
5C2×C32×C5×D19—51nomaximal
6C2×C32×D95C511yesmaximal, characteristic, direct product factor
7C3×C5×D95C2×C318yesdirect product factor
8C2×C3×C52×C19C2×C314yescomplemented
9C2×C5×D95C3211yescharacteristic, direct product factor, Hall
10C2×C32×C5×C19—22no—
11C2×C32×C5×C19D511yescharacteristic, complemented
12C2×C32×C5×C19C2×C511yescharacteristic, complemented
13C32×D95C2×C512yesdirect product factor
14C32×C5×D19—52no—
15C3×C52×C19C22×C314yescomplemented
16C2×C3×D95C3×C514yesdirect product factor
17C2×C3×C5×D19—54no—
18C2×C52×C19C2×C3211yescharacteristic, complemented
19C5×D95C2×C3212yesdirect product factor
20C2×C32×C5×D5—191nomaximal, Hall
21C32×C5×C19—22no—
22C32×C5×C19C2×D511yescharacteristic, complemented
23C32×C5×C19C22×C511yescharacteristic, complemented
24C2×C32×D19—51noHall
25C2×C3×C5×C19—28no—
26C2×C3×C5×C19C3×D514yescomplemented
27C2×C3×C5×C19C2×C3×C514yescomplemented
28C3×D95C2×C3×C518yesdirect product factor
29C3×C5×D19—58no—
30C52×C19C22×C3211yescharacteristic, complemented, Hall
31C2×C32×C52D1911yescharacteristic, complemented
32C32×C5×D5—192no—
33C2×D95C32×C511yescharacteristic, direct product factor
34C2×C5×D19—51no—
35C2×C32×C19C5×D511yescharacteristic, complemented
36C32×D19—52no—
37C2×C3×C5×D5—194no—
38C3×C5×C19—28no—
39C3×C5×C19C2×C3×D514yescomplemented
40C3×C5×C19C22×C3×C514yescomplemented
41C2×C3×D19—54no—
42C32×C52C2×D1911yescharacteristic, complemented, Hall
43C2×C5×C19—22no—
44C2×C5×C19C32×D511yescharacteristic, complemented
45C2×C5×C19C2×C32×C511yescharacteristic, complemented
46D95C2×C32×C512yesdirect product factor
47C5×D19—52no—
48C22×C32×C5—951no—
49C2×C32×D5—191no—
50C32×C19C2×C5×D511yescharacteristic, complemented, Hall
51C2×C3×C52C3×D1914yescomplemented
52C3×C5×D5—198no—
53C2×C3×C19C3×C5×D514yescomplemented
54C3×D19—58no—
55C2×C5×D5—191noHall
56C5×C19—22no—
57C5×C19C2×C32×D511yescharacteristic, complemented
58C5×C19C22×C32×C511yescharacteristic, complemented
59C2×C32×C5—22no—
60C2×C32×C5—952no—
61C2×C32×C5C5×D1911yescharacteristic, complemented
62C2×C32×C5D9511yescharacteristic, direct product factor
63C32×D5—192no—
64C2×D19—51noHall
65C3×C52C2×C3×D1914yescomplemented
66C22×C3×C5—954no—
67C2×C3×D5—194no—
68C3×C19C2×C3×C5×D514yescomplemented
69C2×C52C32×D1911yescharacteristic, complemented
70C5×D5—192no—
71C32×C5—22no—
72C32×C5C2×C5×D1911yescharacteristic, complemented
73C32×C5C2×D9511yescharacteristic, direct product factor
74C2×C19C32×C5×D511yescharacteristic, complemented
75D19—52no—
76C22×C32—951noHall
77C2×C3×C5—28no—
78C2×C3×C5—958no—
79C2×C3×C5C3×C5×D1914yescomplemented
80C2×C3×C5C3×D9514yesdirect product factor
81C3×D5—198no—
82C52C2×C32×D1911yescharacteristic, complemented, Sylow
83C22×C5—951no—
84C2×D5—191no—
85C19C2×C32×C5×D511yescharacteristic, complemented, Sylow
86C2×C32—952no—
87C2×C32C5×D9511yescharacteristic, direct product factor
88C3×C5—28no—
89C3×C5C2×C3×C5×D1914yescomplemented
90C3×C5C2×C3×D9514yesdirect product factor
91C22×C3—954no—
92C2×C5—22no—
93C2×C5—952no—
94C2×C5C32×C5×D1911yescharacteristic, complemented
95C2×C5C32×D9511yescharacteristic, direct product factor
96D5—192no—
97C32C2×C5×D9511yescharacteristic, direct product factor, Sylow
98C2×C3—958no—
99C2×C3C3×C5×D9514yesdirect product factor
100C5—22no—
101C5C2×C32×D9511yescharacteristic, direct product factor
102C5C2×C32×C5×D1911yescharacteristic, complemented
103C22—951noSylow
104C3C2×C3×C5×D9514yesdirect product factor
105C2—952no—
106C2C32×C5×D9511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C32×C5D95
commutator, cosocle, hypocenterC5×C19C22×C32×C5
FrattiniC1G
Fitting, socleC2×C32×C52×C19C2
LCSG ▷ C5×C19
UCSC1 ◁ C2×C32×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D95C2direct (N × H)
2. C2×C32×C52×C19C2semidirect
3. C2×C3×C5×D95C3direct (N × H)
4. C32×C52×C19C22semidirect
6. C2×C32×D95C5direct (N × H)
7. C3×C5×D95C2×C3direct (N × H)
8. C2×C3×C52×C19C2×C3semidirect
9. C2×C5×D95C32direct (N × H)
11. C2×C32×C5×C19D5semidirect
12. C2×C32×C5×C19C2×C5semidirect
13. C32×D95C2×C5direct (N × H)
15. C3×C52×C19C22×C3semidirect
16. C2×C3×D95C3×C5direct (N × H)
18. C2×C52×C19C2×C32semidirect
19. C5×D95C2×C32direct (N × H)
22. C32×C5×C19C2×D5semidirect
23. C32×C5×C19C22×C5semidirect
26. C2×C3×C5×C19C3×D5semidirect
27. C2×C3×C5×C19C2×C3×C5semidirect
28. C3×D95C2×C3×C5direct (N × H)
30. C52×C19C22×C32semidirect
31. C2×C32×C52D19semidirect
33. C2×D95C32×C5direct (N × H)
35. C2×C32×C19C5×D5semidirect
39. C3×C5×C19C2×C3×D5semidirect
40. C3×C5×C19C22×C3×C5semidirect
42. C32×C52C2×D19semidirect
44. C2×C5×C19C32×D5semidirect
45. C2×C5×C19C2×C32×C5semidirect
46. D95C2×C32×C5direct (N × H)
50. C32×C19C2×C5×D5semidirect
51. C2×C3×C52C3×D19semidirect
53. C2×C3×C19C3×C5×D5semidirect
57. C5×C19C2×C32×D5semidirect
58. C5×C19C22×C32×C5semidirect
61. C2×C32×C5C5×D19semidirect
62. C2×C32×C5D95direct (N × H)
65. C3×C52C2×C3×D19semidirect
68. C3×C19C2×C3×C5×D5semidirect
69. C2×C52C32×D19semidirect
72. C32×C5C2×C5×D19semidirect
73. C32×C5C2×D95direct (N × H)
74. C2×C19C32×C5×D5semidirect
79. C2×C3×C5C3×C5×D19semidirect
80. C2×C3×C5C3×D95direct (N × H)
82. C52C2×C32×D19semidirect
85. C19C2×C32×C5×D5semidirect
87. C2×C32C5×D95direct (N × H)
89. C3×C5C2×C3×C5×D19semidirect
90. C3×C5C2×C3×D95direct (N × H)
94. C2×C5C32×C5×D19semidirect
95. C2×C5C32×D95direct (N × H)
97. C32C2×C5×D95direct (N × H)
99. C2×C3C3×C5×D95direct (N × H)
101. C5C2×C32×D95direct (N × H)
102. C5C2×C32×C5×D19semidirect
104. C3C2×C3×C5×D95direct (N × H)
106. C2C32×C5×D95direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D952
C2×C32×C52×C192
C2×C3×C5×D953
C2×C32×C5×D195
C2×C32×D955
C2×C32×C5×D519