Finite Group Databasebeta

← #39908206

Subgroups — #39908206

Order 26100.

288 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C32×C5⋊D145C211yesmaximal, characteristic, complemented
2C5×C29×C3⋊D15C211yesmaximal, characteristic, complemented
3C5×C3⋊D435C211yesmaximal, characteristic, complemented
4D15⋊D145—34nomaximal
5C32×C52×C29C2211yescharacteristic, complemented, Hall
6D145⋊(C3⋊D3)—51nomaximal
7C3⋊D3×D145—51nomaximal
8C5×D435—34no—
9C5×C29×D15—34no—
10C3×C5⋊D145D314yescomplemented
11D5×D145—91noHall
12C3⋊D435D511yescharacteristic, complemented
13C29×C3⋊D15D511yescharacteristic, complemented
14C5×C3⋊D87—51no—
15C5×C3⋊D3×C29—51no—
16C32×D145—51no—
17C32×D145—51no—
18C32×D145—102no—
19C3×C52×C29C2×D314yescomplemented
20D15⋊D29—154no—
21D3×D145—154no—
22C5⋊D145C3⋊D311yescharacteristic, complemented
23C5×D145—91no—
24C5×D5×C29—91no—
25C32×C5×C29—22no—
26C32×C5×C29C2×D511yescharacteristic, complemented
27C32×C5×C29C2×D511yescharacteristic, complemented
28C3⋊D3×D29—251noHall
29#11744719—291nomaximal, Hall
30D435—34no—
31C29×D15—34no—
32C5×D87—154no—
33C5×D3×C29—154no—
34C3×D145—54no—
35C3×D145—54no—
36C3×D145—108no—
37C52×C29C2×C3⋊D311yescharacteristic, complemented, Hall
38C2×D145—451no—
39D5×D29—451no—
40C3⋊D87—51no—
41C3⋊D3×C29—51no—
42C32×D29—251no—
43C5×C3⋊D15—291no—
44C5×C3⋊D15D2911yescharacteristic, complemented
45C32×C5⋊D5—291no—
46C3×C5×C29—28no—
47C3×C5×C29D3×D514yescomplemented
48C3×C5×C29D3×D514yescomplemented
49D3×D29—754no—
50D15⋊D5—874no—
51C2×C5×C29—451no—
52D145—51no—
53D145—51no—
54D145—91no—
55D145—102no—
56C5×D29—451no—
57D5×C29—91no—
58C32×C29D5211yescharacteristic, complemented, Hall
59C32×C52C2×D2911yescharacteristic, complemented, Hall
60D5×C3⋊D3—1451no—
61D5×C3⋊D3—1451no—
62D87—154no—
63C3×D29—254no—
64D3×C29—154no—
65C5×D15—34no—
66C5×D15—874no—
67C3×C5⋊D5—294no—
68C5×C29—22no—
69C5×C29D5×C3⋊D311yescharacteristic, complemented
70C5×C29D5×C3⋊D311yescharacteristic, complemented
71C2×D29—2251noHall
72D52—2611noHall
73C3⋊D15—291no—
74C3⋊D15D14511yescharacteristic, complemented
75C5×C3⋊D3—51no—
76C5×C3⋊D3—1451no—
77C32×D5—2902no—
78C32×D5—1451no—
79C32×D5—1451no—
80C3×C29D15⋊D514yescomplemented
81C3×C52D3×D2914yescomplemented
82D3×D5—4354no—
83D3×D5—4354no—
84C2×C29—451no—
85D29—251no—
86D29—451no—
87C5⋊D5—291no—
88C5×D5—2611no—
89C5×D5—91no—
90C32×C5—22no—
91C32×C5D5×D2911yescharacteristic, complemented
92C32×C5C2×D14511yescharacteristic, complemented
93C2×C3⋊D3—7251noHall
94D15—34no—
95D15—874no—
96C3×D5—2908no—
97C3×D5—1454no—
98C3×D5—1454no—
99C5×D3—154no—
100C5×D3—4354no—
101C29#1174471911yescharacteristic, complemented, Sylow
102C52C3⋊D3×D2911yescharacteristic, complemented, Sylow
103C2×D5—13051no—
104C2×D5—13051no—
105C2×C32—7251no—
106C3⋊D3—51no—
107C3⋊D3—1451no—
108C3×C5—28no—
109C3×C5D3×D14514yescomplemented
110C3×C5D15⋊D2914yescomplemented
111C2×D3—21754no—
112C2×C5—13051no—
113C2×C5—451no—
114D5—2611no—
115D5—91no—
116D5—2902no—
117D5—1451no—
118D5—1451no—
119C32D5×D14511yescharacteristic, complemented, Sylow
120C2×C3—7254no—
121D3—154no—
122D3—4354no—
123C5—22no—
124C5C3⋊D3×D14511yescharacteristic, complemented
125C5D145⋊(C3⋊D3)11yescharacteristic, complemented
126C22—65251noSylow
127C3D15⋊D14514yescomplemented
128C2—13051no—
129C2—451no—
130C2—7251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C29C22
LCSG ▷ C32×C52×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C32×C5⋊D145C2semidirect
2. C5×C29×C3⋊D15C2semidirect
3. C5×C3⋊D435C2semidirect
5. C32×C52×C29C22semidirect
10. C3×C5⋊D145D3semidirect
12. C3⋊D435D5semidirect
13. C29×C3⋊D15D5semidirect
19. C3×C52×C29C2×D3semidirect
22. C5⋊D145C3⋊D3semidirect
26. C32×C5×C29C2×D5semidirect
27. C32×C5×C29C2×D5semidirect
37. C52×C29C2×C3⋊D3semidirect
44. C5×C3⋊D15D29semidirect
47. C3×C5×C29D3×D5semidirect
48. C3×C5×C29D3×D5semidirect
58. C32×C29D52semidirect
59. C32×C52C2×D29semidirect
69. C5×C29D5×C3⋊D3semidirect
70. C5×C29D5×C3⋊D3semidirect
74. C3⋊D15D145semidirect
80. C3×C29D15⋊D5semidirect
81. C3×C52D3×D29semidirect
91. C32×C5D5×D29semidirect
92. C32×C5C2×D145semidirect
101. C29#11744719semidirect
102. C52C3⋊D3×D29semidirect
109. C3×C5D3×D145semidirect
110. C3×C5D15⋊D29semidirect
119. C32D5×D145semidirect
124. C5C3⋊D3×D145semidirect
125. C5D145⋊(C3⋊D3)semidirect
127. C3D15⋊D145semidirect

Maximal subgroups

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

subgroupindex
C32×C5⋊D1452
C5×C29×C3⋊D152
C5×C3⋊D4352
D15⋊D1453
D145⋊(C3⋊D3)5
C3⋊D3×D1455
#1174471929