Finite Group Databasebeta

← C2×C3×C29×#3874 #39908067

Subgroups — C2×C3×C29×#3874 #39908067

Order 26100.

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×C29×C52⋊C3C211yesmaximal, characteristic, complemented
2C3×C29×#3874C212yesmaximal, direct product factor
3C2×C3×C5×D5×C29—31nomaximal
4C2×C29×#3874C311yesmaximal, characteristic, direct product factor
5C3×C29×C52⋊C3C2211yescharacteristic, complemented, Hall
6C3×C5×D5×C29—32no—
7C2×C29×C52⋊C3—21no—
8C2×C29×C52⋊C3C2×C311yescharacteristic, complemented
9C29×#3874C2×C312yesdirect product factor
10C2×C3×C52×C29D311yescharacteristic, complemented
11C2×C5×D5×C29—31noHall
12C29×C52⋊C3—21no—
13C29×C52⋊C3C22×C311yescharacteristic, complemented
14C3×C52×C29C2×D311yescharacteristic, complemented
15C22×C3×C5×C29—151no—
16C2×C3×D5×C29—31no—
17C2×C52×C29C3×D311yescharacteristic, complemented
18C5×D5×C29—32no—
19C2×C3×D3×C29—251nomaximal, Hall
20C2×C3×#3874C2911yesmaximal, characteristic, direct product factor, Hall
21C2×C3×C5×C29—31no—
22C2×C3×C5×C29—31no—
23C2×C3×C5×C29—152no—
24C3×D5×C29—32no—
25C52×C29C2×C3×D311yescharacteristic, complemented, Hall
26C22×C5×C29—151no—
27C2×D5×C29—31no—
28C2×C32×C29—251no—
29C3×D3×C29—252no—
30C2×C3×C52⋊C3C2×C2911yescharacteristic, complemented
31C3×#3874C2×C2912yesdirect product factor
32C3×C5×C29—31no—
33C3×C5×C29—31no—
34C22×C3×C29—151no—
35C2×D3×C29—251no—
36C2×C3×C5×D5—31no—
37C2×#3874C3×C2911yescharacteristic, direct product factor
38C2×C5×C29—31no—
39C2×C5×C29—31no—
40C2×C5×C29—152no—
41D5×C29—32no—
42C32×C29—251noHall
43C3×C52⋊C3C22×C2911yescharacteristic, complemented, Hall
44C2×C3×C29—152no—
45C2×C3×C29—251no—
46C2×C3×C29—501no—
47C2×C3×C29#387411yescharacteristic, direct product factor
48D3×C29—252no—
49C2×C3×C52D3×C2911yescharacteristic, complemented
50C3×C5×D5—32no—
51C2×C52⋊C3—21no—
52C2×C52⋊C3C2×C3×C2911yescharacteristic, complemented
53#3874C2×C3×C2912yesdirect product factor
54C5×C29—31no—
55C5×C29—31no—
56C22×C29—151noHall
57C2×C5×D5—31noHall
58C3×C29—251no—
59C3×C29—501no—
60C3×C29C2×#387411yescharacteristic, direct product factor
61C3×C52C2×D3×C2911yescharacteristic, complemented
62C52⋊C3—21no—
63C52⋊C3C22×C3×C2911yescharacteristic, complemented
64C22×C3×C5—151no—
65C2×C3×D5—31no—
66C2×C29—152no—
67C2×C29C3×#387411yescharacteristic, direct product factor
68C2×C52C3×D3×C2911yescharacteristic, complemented
69C5×D5—32no—
70C2×C3×D3—251noHall
71C2×C3×C5—31no—
72C2×C3×C5—31no—
73C2×C3×C5—152no—
74C3×D5—32no—
75C29C2×C3×#387411yescharacteristic, direct product factor, Sylow
76C52C2×C3×D3×C2911yescharacteristic, complemented, Sylow
77C22×C5—151no—
78C2×D5—31no—
79C2×C32—251no—
80C3×D3—252no—
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×C3C29×#387411yescharacteristic, direct product factor
94D3—252no—
95C5—31no—
96C5—31no—
97C22—151noSylow
98C3—251no—
99C3—501no—
100C3C2×C29×#387411yescharacteristic, direct product factor
101C2—152no—
102C2C3×C29×#387411yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C29#3874
commutator, cosocle, hypocenterC52⋊C3C22×C3×C29
FrattiniC1G
Fitting, socleC2×C3×C52×C29D3
LCSG ▷ C52⋊C3
UCSC1 ◁ C2×C3×C29

Complements

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

NH ≅ G/Ntype
1. C2×C3×C29×C52⋊C3C2semidirect
2. C3×C29×#3874C2direct (N × H)
4. C2×C29×#3874C3direct (N × H)
5. C3×C29×C52⋊C3C22semidirect
8. C2×C29×C52⋊C3C2×C3semidirect
9. C29×#3874C2×C3direct (N × H)
10. C2×C3×C52×C29D3semidirect
13. C29×C52⋊C3C22×C3semidirect
14. C3×C52×C29C2×D3semidirect
17. C2×C52×C29C3×D3semidirect
20. C2×C3×#3874C29direct (N × H)
25. C52×C29C2×C3×D3semidirect
30. C2×C3×C52⋊C3C2×C29semidirect
31. C3×#3874C2×C29direct (N × H)
37. C2×#3874C3×C29direct (N × H)
43. C3×C52⋊C3C22×C29semidirect
47. C2×C3×C29#3874direct (N × H)
49. C2×C3×C52D3×C29semidirect
52. C2×C52⋊C3C2×C3×C29semidirect
53. #3874C2×C3×C29direct (N × H)
60. C3×C29C2×#3874direct (N × H)
61. C3×C52C2×D3×C29semidirect
63. C52⋊C3C22×C3×C29semidirect
67. C2×C29C3×#3874direct (N × H)
68. C2×C52C3×D3×C29semidirect
75. C29C2×C3×#3874direct (N × H)
76. C52C2×C3×D3×C29semidirect
93. C2×C3C29×#3874direct (N × H)
100. C3C2×C29×#3874direct (N × H)
102. C2C3×C29×#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×C29×C52⋊C32
C3×C29×#38742
C2×C3×C5×D5×C293
C2×C29×#38743
C2×C3×D3×C2925
C2×C3×#387429