Finite Group Databasebeta

← C2×C3×C17×#3874 #29505914

Subgroups — C2×C3×C17×#3874 #29505914

Order 15300.

128 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 36 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×C17×C52⋊C3C211yesmaximal, characteristic, complemented
2C3×C17×#3874C212yesmaximal, direct product factor
3C2×C3×C5×D5×C17—31nomaximal
4C2×C17×#3874C311yesmaximal, characteristic, direct product factor
5C3×C17×C52⋊C3C2211yescharacteristic, complemented, Hall
6C3×C5×D5×C17—32no—
7C2×C17×C52⋊C3—21no—
8C2×C17×C52⋊C3C2×C311yescharacteristic, complemented
9C17×#3874C2×C312yesdirect product factor
10C2×C3×C52×C17D311yescharacteristic, complemented
11C2×C5×D5×C17—31noHall
12C3×C52×C17C2×D311yescharacteristic, complemented
13C17×C52⋊C3—21no—
14C17×C52⋊C3C22×C311yescharacteristic, complemented
15C22×C3×C5×C17—151no—
16C2×C3×D5×C17—31no—
17C2×C3×#3874C1711yesmaximal, characteristic, direct product factor, Hall
18C2×C52×C17C3×D311yescharacteristic, complemented
19C5×D5×C17—32no—
20C2×C3×D3×C17—251nomaximal, Hall
21C2×C3×C5×C17—31no—
22C2×C3×C5×C17—31no—
23C2×C3×C5×C17—152no—
24C3×D5×C17—32no—
25C2×C3×C52⋊C3C2×C1711yescharacteristic, complemented
26C3×#3874C2×C1712yesdirect product factor
27C52×C17C2×C3×D311yescharacteristic, complemented, Hall
28C22×C5×C17—151no—
29C2×D5×C17—31no—
30C2×C32×C17—251no—
31C3×D3×C17—252no—
32C2×C3×C5×D5—31no—
33C2×#3874C3×C1711yescharacteristic, direct product factor
34C3×C5×C17—31no—
35C3×C5×C17—31no—
36C3×C52⋊C3C22×C1711yescharacteristic, complemented, Hall
37C22×C3×C17—151no—
38C2×D3×C17—251no—
39C2×C5×C17—31no—
40C2×C5×C17—31no—
41C2×C5×C17—152no—
42D5×C17—32no—
43C32×C17—251noHall
44C2×C3×C52D3×C1711yescharacteristic, complemented
45C3×C5×D5—32no—
46C2×C52⋊C3—21no—
47C2×C52⋊C3C2×C3×C1711yescharacteristic, complemented
48#3874C2×C3×C1712yesdirect product factor
49C2×C3×C17—152no—
50C2×C3×C17—251no—
51C2×C3×C17—501no—
52C2×C3×C17#387411yescharacteristic, direct product factor
53D3×C17—252no—
54C2×C5×D5—31noHall
55C5×C17—31no—
56C5×C17—31no—
57C3×C52C2×D3×C1711yescharacteristic, complemented
58C52⋊C3—21no—
59C52⋊C3C22×C3×C1711yescharacteristic, complemented
60C22×C17—151noHall
61C22×C3×C5—151no—
62C2×C3×D5—31no—
63C3×C17—251no—
64C3×C17—501no—
65C3×C17C2×#387411yescharacteristic, direct product factor
66C2×C52C3×D3×C1711yescharacteristic, complemented
67C5×D5—32no—
68C2×C3×D3—251noHall
69C2×C17—152no—
70C2×C17C3×#387411yescharacteristic, direct product factor
71C2×C3×C5—31no—
72C2×C3×C5—31no—
73C2×C3×C5—152no—
74C3×D5—32no—
75C52C2×C3×D3×C1711yescharacteristic, complemented, Sylow
76C22×C5—151no—
77C2×D5—31no—
78C2×C32—251no—
79C3×D3—252no—
80C17C2×C3×#387411yescharacteristic, direct product factor, Sylow
81C3×C5—31no—
82C3×C5—31no—
83C22×C3—151no—
84C2×D3—251no—
85C2×C5—31no—
86C2×C5—31no—
87C2×C5—152no—
88D5—32no—
89C32—251noSylow
90C2×C3—152no—
91C2×C3—251no—
92C2×C3—501no—
93C2×C3C17×#387411yescharacteristic, direct product factor
94D3—252no—
95C5—31no—
96C5—31no—
97C22—151noSylow
98C3—251no—
99C3—501no—
100C3C2×C17×#387411yescharacteristic, direct product factor
101C2—152no—
102C2C3×C17×#387411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C17#3874
commutator, cosocle, hypocenterC52⋊C3C22×C3×C17
FrattiniC1G
Fitting, socleC2×C3×C52×C17D3
LCSG ▷ C52⋊C3
UCSC1 ◁ C2×C3×C17

Complements

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

NH ≅ G/Ntype
1. C2×C3×C17×C52⋊C3C2semidirect
2. C3×C17×#3874C2direct (N × H)
4. C2×C17×#3874C3direct (N × H)
5. C3×C17×C52⋊C3C22semidirect
8. C2×C17×C52⋊C3C2×C3semidirect
9. C17×#3874C2×C3direct (N × H)
10. C2×C3×C52×C17D3semidirect
12. C3×C52×C17C2×D3semidirect
14. C17×C52⋊C3C22×C3semidirect
17. C2×C3×#3874C17direct (N × H)
18. C2×C52×C17C3×D3semidirect
25. C2×C3×C52⋊C3C2×C17semidirect
26. C3×#3874C2×C17direct (N × H)
27. C52×C17C2×C3×D3semidirect
33. C2×#3874C3×C17direct (N × H)
36. C3×C52⋊C3C22×C17semidirect
44. C2×C3×C52D3×C17semidirect
47. C2×C52⋊C3C2×C3×C17semidirect
48. #3874C2×C3×C17direct (N × H)
52. C2×C3×C17#3874direct (N × H)
57. C3×C52C2×D3×C17semidirect
59. C52⋊C3C22×C3×C17semidirect
65. C3×C17C2×#3874direct (N × H)
66. C2×C52C3×D3×C17semidirect
70. C2×C17C3×#3874direct (N × H)
75. C52C2×C3×D3×C17semidirect
80. C17C2×C3×#3874direct (N × H)
93. C2×C3C17×#3874direct (N × H)
100. C3C2×C17×#3874direct (N × H)
102. C2C3×C17×#3874direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C17×C52⋊C32
C3×C17×#38742
C2×C3×C5×D5×C173
C2×C17×#38743
C2×C3×#387417
C2×C3×D3×C1725