Finite Group Databasebeta

← #42124945

Subgroups — #42124945

Order 27900.

352 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 79 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×C31×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D155)C211yesmaximal, characteristic, complemented
3C52×C3⋊D93C211yesmaximal, characteristic, complemented
4D93⋊(C5⋊D5)—31nomaximal
5C5⋊D5×D93—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7D15⋊D93—56nomaximal
8C3⋊(C5⋊D155)D311yescharacteristic, complemented
9C31×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C52×D93—31no—
11C52×D93—31no—
12C52×D93—61no—
13C3×C5⋊D155—31no—
14C3×C31×C5⋊D5—31no—
15C5⋊D5×D31—91noHall
16C5×C3⋊D93D516yescomplemented
17C3×D465—56no—
18C3×D15×C31—56no—
19C3×C52×C31—21no—
20C3×C52×C31C2×D311yescharacteristic, complemented
21C3×C52×C31C2×D311yescharacteristic, complemented
22D15⋊D31—156no—
23D5×D93—156no—
24C5⋊D155—31no—
25C31×C5⋊D5—31no—
26C52×D31—91no—
27C32×C5×C31C2×D516yescomplemented
28D3×D93—251noHall
29D465—56no—
30D15×C31—56no—
31C5×D93—36no—
32C5×D93—36no—
33C5×D93—66no—
34C3×D155—156no—
35C3×D5×C31—156no—
36(C3⋊D3)⋊(C5⋊D5)—311nomaximal, Hall
37C52×C31D3211yescharacteristic, complemented, Hall
38D5×D31—456no—
39C3⋊D93C5⋊D511yescharacteristic, complemented
40C3×D93—251no—
41C3×D3×C31—251no—
42C3×C5×C31—26no—
43C3×C5×C31D3×D516yescomplemented
44C3×C5×C31D3×D516yescomplemented
45C52×C3⋊D3—311no—
46C3×C3⋊(C5⋊D5)—311no—
47C3×C3⋊(C5⋊D5)D3111yescharacteristic, complemented
48C2×D93—751no—
49D3×D31—751no—
50D155—156no—
51C5×D31—96no—
52D5×C31—156no—
53D3×C5⋊D5—931no—
54D3×C5⋊D5—931no—
55C32×C31C2×C5⋊D511yescharacteristic, complemented, Hall
56C32×C52C2×D3111yescharacteristic, complemented, Hall
57C2×C3×C31—751no—
58D93—31no—
59D93—31no—
60D93—61no—
61D93—251no—
62C3×D31—751no—
63D3×C31—251no—
64(C3⋊D3)⋊D5—1556no—
65C5×C31(C3⋊D3)⋊D516yescomplemented
66C3⋊(C5⋊D5)—311no—
67C3⋊(C5⋊D5)D9311yescharacteristic, complemented
68C52×D3—931no—
69C52×D3—931no—
70C52×D3—1861no—
71C3×C5⋊D5—31no—
72C3×C5⋊D5—931no—
73C2×D31—2251noHall
74C2×C5⋊D5—2791noHall
75C3×C31—21no—
76C3×C31D3×C5⋊D511yescharacteristic, complemented
77C3×C31D3×C5⋊D511yescharacteristic, complemented
78C5×C3⋊D3—316no—
79C3×D15—56no—
80C3×D15—1556no—
81C3×C52—21no—
82C3×C52D3×D3111yescharacteristic, complemented
83C3×C52C2×D9311yescharacteristic, complemented
84C2×C31—751no—
85D31—91no—
86D31—751no—
87D3×D5—4656no—
88D3×D5—4656no—
89C2×C52—2791no—
90C5⋊D5—31no—
91C5⋊D5—931no—
92C32×C5D5×D3116yescomplemented
93D32—7751noHall
94C31(C3⋊D3)⋊(C5⋊D5)11yescharacteristic, complemented, Sylow
95D15—56no—
96D15—1556no—
97C3×D5—156no—
98C3×D5—4656no—
99C5×D3—936no—
100C5×D3—936no—
101C5×D3—1866no—
102C52D3×D9311yescharacteristic, complemented, Sylow
103C2×D5—13956no—
104C3⋊D3—311no—
105C3×D3—7751no—
106C3×D3—251no—
107C3×C5—26no—
108C3×C5D5×D9316yescomplemented
109C3×C5D15⋊D3116yescomplemented
110C2×D3—23251no—
111C2×D3—23251no—
112C2×C5—2796no—
113D5—156no—
114D5—4656no—
115C32C5⋊D5×D3111yescharacteristic, complemented, Sylow
116C2×C3—23251no—
117C2×C3—751no—
118D3—7751no—
119D3—251no—
120D3—931no—
121D3—931no—
122D3—1861no—
123C5D15⋊D9316yescomplemented
124C22—69751noSylow
125C3—21no—
126C3C5⋊D5×D9311yescharacteristic, complemented
127C3D93⋊(C5⋊D5)11yescharacteristic, complemented
128C2—23251no—
129C2—2791no—
130C2—751no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C31C22
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C31×C3⋊(C5⋊D5)C2semidirect
2. C3×C3⋊(C5⋊D155)C2semidirect
3. C52×C3⋊D93C2semidirect
6. C32×C52×C31C22semidirect
8. C3⋊(C5⋊D155)D3semidirect
9. C31×C3⋊(C5⋊D5)D3semidirect
16. C5×C3⋊D93D5semidirect
20. C3×C52×C31C2×D3semidirect
21. C3×C52×C31C2×D3semidirect
27. C32×C5×C31C2×D5semidirect
37. C52×C31D32semidirect
39. C3⋊D93C5⋊D5semidirect
43. C3×C5×C31D3×D5semidirect
44. C3×C5×C31D3×D5semidirect
47. C3×C3⋊(C5⋊D5)D31semidirect
55. C32×C31C2×C5⋊D5semidirect
56. C32×C52C2×D31semidirect
65. C5×C31(C3⋊D3)⋊D5semidirect
67. C3⋊(C5⋊D5)D93semidirect
76. C3×C31D3×C5⋊D5semidirect
77. C3×C31D3×C5⋊D5semidirect
82. C3×C52D3×D31semidirect
83. C3×C52C2×D93semidirect
92. C32×C5D5×D31semidirect
94. C31(C3⋊D3)⋊(C5⋊D5)semidirect
102. C52D3×D93semidirect
108. C3×C5D5×D93semidirect
109. C3×C5D15⋊D31semidirect
115. C32C5⋊D5×D31semidirect
123. C5D15⋊D93semidirect
126. C3C5⋊D5×D93semidirect
127. C3D93⋊(C5⋊D5)semidirect

Maximal subgroups

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

subgroupindex
C3×C31×C3⋊(C5⋊D5)2
C3×C3⋊(C5⋊D155)2
C52×C3⋊D932
D93⋊(C5⋊D5)3
C5⋊D5×D933
D15⋊D935
(C3⋊D3)⋊(C5⋊D5)31