Finite Group Databasebeta

← D145⋊D45 #39907973

Subgroups — D145⋊D45 #39907973

Order 26100.

144 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 35 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
1C29×C5⋊D45C211yesmaximal, characteristic, complemented
2C5×D1305C211yesmaximal, characteristic, complemented
3C5×C9×D145C211yesmaximal, characteristic, complemented
4D145⋊D15—31nomaximal
5C52×C9×C29C2211yescharacteristic, complemented, Hall
6D45⋊D29—51nomaximal
7D29×D45—51nomaximal
8C29×C3⋊(C5⋊D5)—31no—
9C5×D435—31no—
10C3×C5×D145D311yescharacteristic
11(C5⋊D5)⋊D29—91noHall
12D1305D511yescharacteristic, complemented
13C29×D45—51no—
14C29×D45—51no—
15C29×D45—102no—
16C5×D261—51no—
17C9×D145D511yescharacteristic, complemented
18C5×C9×D29—51no—
19C3×C52×C29C2×D311yescharacteristic
20D15⋊D29—151no—
21D15×D29—151no—
22C29×C5⋊D5—91no—
23C5×D145—91no—
24C5×D145D911yescharacteristic, complemented
25C5×C9×C29—22no—
26C5×C9×C29C2×D511yescharacteristic, complemented
27C5×C9×C29C2×D511yescharacteristic, complemented
28D9×D29—251noHall
29D5×D45—291nomaximal, Hall
30D435—31no—
31C29×D15—151no—
32C29×D15—151no—
33C29×D15—302no—
34C5×D87—151no—
35C3×D145D1511yescharacteristic
36C3×C5×D29—51no—
37C52×C29C2×D911yescharacteristic, complemented, Hall
38D5×D29—451no—
39D5×D29—451no—
40D261—51no—
41C9×D29—51no—
42D9×C29—251no—
43C5⋊D45D2911yescharacteristic, complemented
44C5×D45—291no—
45C5×C9×D5—291no—
46C3×C5×C29—22no—
47C3×C5×C29D3×D511yescharacteristic
48C3×C5×C29C2×D1511yescharacteristic
49D3×D29—751no—
50D5×D15—871no—
51D145—91no—
52D145D4511yescharacteristic, complemented
53C5×D29—51no—
54C5×D29—451no—
55D5×C29—451no—
56D5×C29—451no—
57D5×C29—902no—
58C9×C29D5211yescharacteristic, complemented, Hall
59C52×C9C2×D2911yescharacteristic, complemented, Hall
60C2×D45—1451no—
61D5×D9—1451no—
62D87—151no—
63C3×D29—51no—
64D3×C29—751no—
65C3⋊(C5⋊D5)—31no—
66C5×D15—871no—
67C3×C5×D5—291no—
68C5×C29—22no—
69C5×C29D5×D911yescharacteristic, complemented
70C5×C29C2×D4511yescharacteristic, complemented
71C2×D29—2251noHall
72D52—2611noHall
73C2×C5×C9—1451no—
74D45—51no—
75D45—51no—
76D45—102no—
77D45—291no—
78C9×D5—291no—
79C5×D9—1451no—
80C3×C29D5×D1511yescharacteristic
81C3×C52D3×D2911yescharacteristic
82C2×D15—4351no—
83D3×D5—4351no—
84C2×C29—2251no—
85D29—51no—
86D29—451no—
87C5⋊D5—91no—
88C5×D5—2611no—
89C5×D5—291no—
90C5×C9—22no—
91C5×C9D5×D2911yescharacteristic, complemented
92C5×C9D5×D2911yescharacteristic, complemented
93C2×D9—7251noHall
94C2×C3×C5—1451no—
95D15—151no—
96D15—151no—
97D15—302no—
98D15—871no—
99C3×D5—291no—
100C5×D3—4351no—
101C29D5×D4511yescharacteristic, complemented, Sylow
102C52D9×D2911yescharacteristic, complemented, Sylow
103C2×D5—13051no—
104C2×D5—13051no—
105C2×C9—1451no—
106D9—251no—
107D9—1451no—
108C3×C5—22no—
109C3×C5D15×D2911yescharacteristic
110C3×C5D15⋊D2911yescharacteristic
111C2×D3—21751no—
112C2×C5—13051no—
113C2×C5—1451no—
114D5—2611no—
115D5—291no—
116D5—451no—
117D5—451no—
118D5—902no—
119C9(C5⋊D5)⋊D2911yescharacteristic, complemented, Sylow
120C2×C3—1451no—
121D3—751no—
122D3—4351no—
123C5—22no—
124C5D29×D4511yescharacteristic, complemented
125C5D45⋊D2911yescharacteristic, complemented
126C22—65251noSylow
127C3D145⋊D1511yescharacteristic
128C2—13051no—
129C2—1451no—
130C2—2251no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC52×C9×C29C22
FrattiniC3D145⋊D15
socleC3×C52×C29C2×D3
LCSG ▷ C52×C9×C29
UCSC1

Complements

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

NH ≅ G/Ntype
1. C29×C5⋊D45C2semidirect
2. C5×D1305C2semidirect
3. C5×C9×D145C2semidirect
5. C52×C9×C29C22semidirect
12. D1305D5semidirect
17. C9×D145D5semidirect
24. C5×D145D9semidirect
26. C5×C9×C29C2×D5semidirect
27. C5×C9×C29C2×D5semidirect
37. C52×C29C2×D9semidirect
43. C5⋊D45D29semidirect
52. D145D45semidirect
58. C9×C29D52semidirect
59. C52×C9C2×D29semidirect
69. C5×C29D5×D9semidirect
70. C5×C29C2×D45semidirect
91. C5×C9D5×D29semidirect
92. C5×C9D5×D29semidirect
101. C29D5×D45semidirect
102. C52D9×D29semidirect
119. C9(C5⋊D5)⋊D29semidirect
124. C5D29×D45semidirect
125. C5D45⋊D29semidirect

Maximal subgroups

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

subgroupindex
C29×C5⋊D452
C5×D13052
C5×C9×D1452
D145⋊D153
D45⋊D295
D29×D455
D5×D4529