Finite Group Databasebeta

← C3×D37×(C5⋊D5)⋊C3 #45686205

Subgroups — C3×D37×(C5⋊D5)⋊C3 #45686205

Order 33300.

160 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C3×D37×C52⋊C3C211yesmaximal, characteristic, complemented
2C3×#19149853C211yesmaximal, characteristic, complemented
3C3×C37×(C5⋊D5)⋊C3C211yesmaximal, characteristic, complemented
4C3×C5⋊D5×D37C311yesmaximal, characteristic, complemented
5D37×(C5⋊D5)⋊C3C313yesmaximal, direct product factor
6C3×C37×C52⋊C3C2211yescharacteristic, complemented, Hall
7C3×C5⋊D185C2×C311yescharacteristic, complemented
8C3×C37×C5⋊D5C2×C311yescharacteristic, complemented
9C3×C52×D37C2×C311yescharacteristic, complemented
10D37×C52⋊C3C2×C313yescomplemented
11#19149853C2×C313yescomplemented
12C37×(C5⋊D5)⋊C3C2×C313yescomplemented
13C5⋊D5×D37C3211yescharacteristic, complemented, Hall
14C37×C52⋊C3C22×C313yescomplemented
15C3×C52×C37C22×C311yescharacteristic, complemented
16C3×D5×D37—152no—
17C5⋊D185C2×C3211yescharacteristic, complemented
18C37×C5⋊D5C2×C3211yescharacteristic, complemented
19C52×D37C2×C3211yescharacteristic, complemented
20C2×C32×D37—251nomaximal, Hall
21C3×D185—152no—
22C3×D5×C37—152no—
23C3×C5×D37—32no—
24C52×C37C22×C3211yescharacteristic, complemented, Hall
25C2×C3×(C5⋊D5)⋊C3—371nomaximal, Hall
26D5×D37—152no—
27C2×C32×C37—251no—
28C32×D37—251no—
29C32×D37—251no—
30C3×C5×C37—32no—
31C2×C3×C52⋊C3—371no—
32C3×(C5⋊D5)⋊C3—371no—
33C3×(C5⋊D5)⋊C3D3711yescharacteristic, direct product factor
34C2×C3×D37—253no—
35C2×C3×D37—251no—
36D185—152no—
37C5×D37—32no—
38D5×C37—152no—
39C32×C37—251noHall
40C2×C3×C5⋊D5—371no—
41C2×(C5⋊D5)⋊C3—373no—
42C3×C52⋊C3C2×D3711yescharacteristic, complemented, Hall
43C2×C3×C37—253no—
44C2×C3×C37—251no—
45C3×D37—253no—
46C3×D37—253no—
47C3×D37—251no—
48C3×D37(C5⋊D5)⋊C311yescharacteristic, direct product factor
49C5×C37—32no—
50C2×C3×C52—371no—
51C3×C5⋊D5—371no—
52C3×C5⋊D5C3×D3711yescharacteristic, complemented
53C2×C52⋊C3—373no—
54(C5⋊D5)⋊C3—373no—
55(C5⋊D5)⋊C3C3×D3713yesdirect product factor
56C2×D37—251noHall
57C3×C37—253no—
58C3×C37C2×(C5⋊D5)⋊C311yescharacteristic, complemented
59C2×C5⋊D5—371noHall
60C3×C52C2×C3×D3711yescharacteristic, complemented
61C52⋊C3C2×C3×D3713yescomplemented
62C2×C37—251no—
63D37—251no—
64D37C3×(C5⋊D5)⋊C311yescharacteristic, direct product factor
65C2×C3×D5—5552no—
66C2×C52—371no—
67C5⋊D5—371no—
68C5⋊D5C32×D3711yescharacteristic, complemented
69C37C2×C3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
70C22×C32—9251noHall
71C2×C3×C5—1112no—
72C3×D5—152no—
73C3×D5—5552no—
74C52C2×C32×D3711yescharacteristic, complemented, Sylow
75C2×D5—5552no—
76C2×C32—251no—
77C2×C32—9251no—
78C2×C32—9251no—
79C3×C5—32no—
80C22×C3—9251no—
81C22×C3—9253no—
82C2×C5—1112no—
83D5—152no—
84D5—5552no—
85C32—251noSylow
86C2×C3—253no—
87C2×C3—251no—
88C2×C3—371no—
89C2×C3—9253no—
90C2×C3—9253no—
91C2×C3—9251no—
92C5—32no—
93C22—9251noSylow
94C3—253no—
95C3D37×(C5⋊D5)⋊C311yescharacteristic, direct product factor
96C2—251no—
97C2—371no—
98C2—9251no—
subgroupG/H
center, hypercenterC3D37×(C5⋊D5)⋊C3
commutator, cosocle, hypocenterC52×C37C22×C32
FrattiniC1G
Fitting, socleC3×C52×C37C22×C3
LCSG ▷ C52×C37
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C3×D37×C52⋊C3C2semidirect
2. C3×#19149853C2semidirect
3. C3×C37×(C5⋊D5)⋊C3C2semidirect
4. C3×C5⋊D5×D37C3semidirect
5. D37×(C5⋊D5)⋊C3C3direct (N × H)
6. C3×C37×C52⋊C3C22semidirect
7. C3×C5⋊D185C2×C3semidirect
8. C3×C37×C5⋊D5C2×C3semidirect
9. C3×C52×D37C2×C3semidirect
10. D37×C52⋊C3C2×C3semidirect
11. #19149853C2×C3semidirect
12. C37×(C5⋊D5)⋊C3C2×C3semidirect
13. C5⋊D5×D37C32semidirect
14. C37×C52⋊C3C22×C3semidirect
15. C3×C52×C37C22×C3semidirect
17. C5⋊D185C2×C32semidirect
18. C37×C5⋊D5C2×C32semidirect
19. C52×D37C2×C32semidirect
24. C52×C37C22×C32semidirect
33. C3×(C5⋊D5)⋊C3D37direct (N × H)
42. C3×C52⋊C3C2×D37semidirect
48. C3×D37(C5⋊D5)⋊C3direct (N × H)
52. C3×C5⋊D5C3×D37semidirect
55. (C5⋊D5)⋊C3C3×D37direct (N × H)
58. C3×C37C2×(C5⋊D5)⋊C3semidirect
60. C3×C52C2×C3×D37semidirect
61. C52⋊C3C2×C3×D37semidirect
64. D37C3×(C5⋊D5)⋊C3direct (N × H)
68. C5⋊D5C32×D37semidirect
69. C37C2×C3×(C5⋊D5)⋊C3semidirect
74. C52C2×C32×D37semidirect
95. C3D37×(C5⋊D5)⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C3×D37×C52⋊C32
C3×#191498532
C3×C37×(C5⋊D5)⋊C32
C3×C5⋊D5×D373
D37×(C5⋊D5)⋊C33
C2×C32×D3725
C2×C3×(C5⋊D5)⋊C337