Finite Group Databasebeta

← D75⋊D111 #45685911

Subgroups — D75⋊D111 #45685911

Order 33300.

132 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 34 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
1C25×C3⋊D111C211yesmaximal, characteristic, complemented
2C3×D2775C211yesmaximal, characteristic, complemented
3C3×C37×D75C211yesmaximal, characteristic, complemented
4D75⋊D37—31nomaximal
5D25×D111—31nomaximal
6C32×C25×C37C2211yescharacteristic, complemented, Hall
7D15⋊D111—51nomaximal
8D2775D311yescharacteristic, complemented
9C37×D75D311yescharacteristic, complemented
10C25×D111—31no—
11C25×D111—31no—
12C25×D111—61no—
13C3×D925—31no—
14C3×C37×D25—31no—
15D25×D37—91noHall
16C5×C3⋊D111D511yescharacteristic
17C3×D555—51no—
18C3×D15×C37—51no—
19C3×C25×C37—21no—
20C3×C25×C37C2×D311yescharacteristic, complemented
21C3×C25×C37C2×D311yescharacteristic, complemented
22D15⋊D37—151no—
23D5×D111—151no—
24D925—31no—
25C25×D37—91no—
26C37×D25—31no—
27C32×C5×C37C2×D511yescharacteristic
28D3×D111—251noHall
29D555—51no—
30D15×C37—51no—
31C5×D111—31no—
32C5×D111—31no—
33C5×D111—61no—
34C3×D185—151no—
35C3×D5×C37—151no—
36C25×C37D3211yescharacteristic, complemented, Hall
37(C3⋊D3)⋊D25—371nomaximal, Hall
38D5×D37—451no—
39C3⋊D111D2511yescharacteristic, complemented
40C3×D111—251no—
41C3×D3×C37—251no—
42C3×C5×C37—21no—
43C3×C5×C37D3×D511yescharacteristic
44C3×C5×C37D3×D511yescharacteristic
45C3⋊D3×C25—371no—
46C3×D75—371no—
47C3×D75D3711yescharacteristic, complemented
48C2×D111—751no—
49D3×D37—751no—
50D185—151no—
51C5×D37—91no—
52D5×C37—151no—
53C32×C37C2×D2511yescharacteristic, complemented, Hall
54D3×D25—1111no—
55D3×D25—1111no—
56C32×C25C2×D3711yescharacteristic, complemented, Hall
57C2×C3×C37—751no—
58D111—31no—
59D111—31no—
60D111—61no—
61D111—251no—
62C3×D37—751no—
63D3×C37—251no—
64C5×C37(C3⋊D3)⋊D511yescharacteristic
65(C3⋊D3)⋊D5—1851no—
66D75—371no—
67D75D11111yescharacteristic, complemented
68C3×D25—31no—
69C3×D25—1111no—
70D3×C25—1111no—
71D3×C25—1111no—
72D3×C25—2221no—
73C2×D37—2251noHall
74C3×C37—21no—
75C3×C37D3×D2511yescharacteristic, complemented
76C3×C37D3×D2511yescharacteristic, complemented
77C2×D25—3331noHall
78C5×C3⋊D3—371no—
79C3×D15—51no—
80C3×D15—1851no—
81C3×C25—21no—
82C3×C25D3×D3711yescharacteristic, complemented
83C3×C25C2×D11111yescharacteristic, complemented
84C2×C37—751no—
85D37—91no—
86D37—751no—
87D3×D5—5551no—
88D3×D5—5551no—
89C2×C25—3331no—
90D25—31no—
91D25—1111no—
92C32×C5D5×D3711yescharacteristic
93C37(C3⋊D3)⋊D2511yescharacteristic, complemented, Sylow
94D32—9251noHall
95D15—51no—
96D15—1851no—
97C3×D5—151no—
98C3×D5—5551no—
99C5×D3—1111no—
100C5×D3—1111no—
101C5×D3—2221no—
102C25D3×D11111yescharacteristic, complemented, Sylow
103C2×D5—16651no—
104C3⋊D3—371no—
105C3×D3—251no—
106C3×D3—9251no—
107C3×C5—21no—
108C3×C5D5×D11111yescharacteristic
109C3×C5D15⋊D3711yescharacteristic
110C2×D3—27751no—
111C2×D3—27751no—
112C2×C5—3331no—
113D5—151no—
114D5—5551no—
115C32D25×D3711yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—27751no—
118D3—251no—
119D3—1111no—
120D3—1111no—
121D3—9251no—
122D3—2221no—
123C5D15⋊D11111yescharacteristic
124C22—83251noSylow
125C3—21no—
126C3D25×D11111yescharacteristic, complemented
127C3D75⋊D3711yescharacteristic, complemented
128C2—751no—
129C2—3331no—
130C2—27751no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C25×C37C22
FrattiniC5D15⋊D111
socleC32×C5×C37C2×D5
LCSG ▷ C32×C25×C37
UCSC1

Complements

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

NH ≅ G/Ntype
1. C25×C3⋊D111C2semidirect
2. C3×D2775C2semidirect
3. C3×C37×D75C2semidirect
6. C32×C25×C37C22semidirect
8. D2775D3semidirect
9. C37×D75D3semidirect
20. C3×C25×C37C2×D3semidirect
21. C3×C25×C37C2×D3semidirect
36. C25×C37D32semidirect
39. C3⋊D111D25semidirect
47. C3×D75D37semidirect
53. C32×C37C2×D25semidirect
56. C32×C25C2×D37semidirect
67. D75D111semidirect
75. C3×C37D3×D25semidirect
76. C3×C37D3×D25semidirect
82. C3×C25D3×D37semidirect
83. C3×C25C2×D111semidirect
93. C37(C3⋊D3)⋊D25semidirect
102. C25D3×D111semidirect
115. C32D25×D37semidirect
126. C3D25×D111semidirect
127. C3D75⋊D37semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D1112
C3×D27752
C3×C37×D752
D75⋊D373
D25×D1113
D15⋊D1115
(C3⋊D3)⋊D2537