Finite Group Databasebeta

← (C5⋊D5)⋊C3×D123 #49147017

Subgroups — (C5⋊D5)⋊C3×D123 #49147017

Order 36900.

128 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 27 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
1C52⋊C3×D123C211yesmaximal, characteristic, complemented
2C3⋊(C41⋊((C5⋊D5)⋊C3))C211yesmaximal, characteristic, complemented
3C3×C41×(C5⋊D5)⋊C3C211yesmaximal, characteristic, complemented
4C5⋊D5×D123C311yesmaximal, characteristic, complemented
5D41×(C5⋊D5)⋊C3—31nomaximal
6C3×C41×C52⋊C3C2211yescharacteristic, complemented, Hall
7C3⋊(C5⋊D205)C2×C311yescharacteristic, complemented
8C52×D123C2×C311yescharacteristic, complemented
9C3×C41×C5⋊D5C2×C311yescharacteristic, complemented
10C52⋊C3×D41—31no—
11C41⋊((C5⋊D5)⋊C3)—31no—
12C41×(C5⋊D5)⋊C3—21no—
13C41×(C5⋊D5)⋊C3D311yescharacteristic, complemented
14C5⋊D5×D41—31noHall
15C41×C52⋊C3—21no—
16C41×C52⋊C3C2×D311yescharacteristic, complemented
17C3×C52×C41C22×C311yescharacteristic, complemented
18D5×D123—152no—
19C5⋊D205—31no—
20C41×C5⋊D5C3×D311yescharacteristic, complemented
21C52×D41—31no—
22C2×C3×D123—251nomaximal, Hall
23D615—152no—
24C5×D123—32no—
25C3×D5×C41—152no—
26C52×C41C2×C3×D311yescharacteristic, complemented, Hall
27D3×(C5⋊D5)⋊C3—411nomaximal, Hall
28D5×D41—452no—
29C2×C32×C41—251no—
30C3×D123—251no—
31C3×D123—251no—
32C3×C5×C41—32no—
33C2×D123—251no—
34C2×C3×D41—751no—
35C3⋊((C5⋊D5)⋊C3)—411no—
36D3×C52⋊C3—411no—
37C3×(C5⋊D5)⋊C3D4111yescharacteristic, complemented
38D205—452no—
39C5×D41—92no—
40D5×C41—152no—
41C32×C41—251noHall
42D3×C5⋊D5—411no—
43C2×(C5⋊D5)⋊C3—1231no—
44C2×C3×C41—251no—
45C2×C3×C41—251no—
46C2×C3×C41—501no—
47D123—251no—
48D123(C5⋊D5)⋊C311yescharacteristic, direct product factor
49C3×D41—751no—
50C3×D41—751no—
51C3×C52⋊C3C2×D4111yescharacteristic, complemented, Hall
52C5×C41—32no—
53C2×D41—751noHall
54C3⋊(C5⋊D5)—411no—
55C52×D3—411no—
56C3×C5⋊D5C3×D4111yescharacteristic, complemented
57C2×C52⋊C3—1231no—
58(C5⋊D5)⋊C3—21no—
59(C5⋊D5)⋊C3—1231no—
60(C5⋊D5)⋊C3D12311yescharacteristic, direct product factor
61C3×C41—251no—
62C3×C41—501no—
63C3×C41C2×(C5⋊D5)⋊C311yescharacteristic, complemented
64C2×C5⋊D5—1231noHall
65C2×C41—251no—
66D41—31no—
67D41—751no—
68C3×C52C2×C3×D4111yescharacteristic, complemented
69C52⋊C3—21no—
70C52⋊C3C2×D12311yescharacteristic, complemented
71D3×D5—6152no—
72C2×C52—1231no—
73C5⋊D5—1231no—
74C5⋊D5C3×D12311yescharacteristic, complemented
75C41D3×(C5⋊D5)⋊C311yescharacteristic, complemented, Sylow
76C2×C3×D3—10251noHall
77D15—6152no—
78C3×D5—152no—
79C5×D3—1232no—
80C52C2×C3×D12311yescharacteristic, complemented, Sylow
81C2×D5—18452no—
82C2×C32—251no—
83C3×D3—10251no—
84C3×D3—10251no—
85C3×C5—32no—
86C22×C3—30751no—
87C2×D3—10251no—
88C2×C5—3692no—
89D5—152no—
90D5—18452no—
91C32—251noSylow
92C2×C3—30751no—
93C2×C3—30751no—
94C2×C3—251no—
95C2×C3—251no—
96C2×C3—501no—
97D3—10251no—
98D3—411no—
99C5—32no—
100C22—30751noSylow
101C3—251no—
102C3—501no—
103C3D41×(C5⋊D5)⋊C311yescharacteristic, complemented
104C2—30751no—
105C2—251no—
106C2—1231no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C41C22×C3
LCSG ▷ C3×C52×C41
UCSC1

Complements

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

NH ≅ G/Ntype
1. C52⋊C3×D123C2semidirect
2. C3⋊(C41⋊((C5⋊D5)⋊C3))C2semidirect
3. C3×C41×(C5⋊D5)⋊C3C2semidirect
4. C5⋊D5×D123C3semidirect
6. C3×C41×C52⋊C3C22semidirect
7. C3⋊(C5⋊D205)C2×C3semidirect
8. C52×D123C2×C3semidirect
9. C3×C41×C5⋊D5C2×C3semidirect
13. C41×(C5⋊D5)⋊C3D3semidirect
16. C41×C52⋊C3C2×D3semidirect
17. C3×C52×C41C22×C3semidirect
20. C41×C5⋊D5C3×D3semidirect
26. C52×C41C2×C3×D3semidirect
37. C3×(C5⋊D5)⋊C3D41semidirect
48. D123(C5⋊D5)⋊C3direct (N × H)
51. C3×C52⋊C3C2×D41semidirect
56. C3×C5⋊D5C3×D41semidirect
60. (C5⋊D5)⋊C3D123direct (N × H)
63. C3×C41C2×(C5⋊D5)⋊C3semidirect
68. C3×C52C2×C3×D41semidirect
70. C52⋊C3C2×D123semidirect
74. C5⋊D5C3×D123semidirect
75. C41D3×(C5⋊D5)⋊C3semidirect
80. C52C2×C3×D123semidirect
103. C3D41×(C5⋊D5)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C52⋊C3×D1232
C3⋊(C41⋊((C5⋊D5)⋊C3))2
C3×C41×(C5⋊D5)⋊C32
C5⋊D5×D1233
D41×(C5⋊D5)⋊C33
C2×C3×D12325
D3×(C5⋊D5)⋊C341