Finite Group Databasebeta

← D75⋊D57 #30685511

Subgroups — D75⋊D57 #30685511

Order 17100.

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⋊D57C211yesmaximal, characteristic, complemented
2C3×D1425C211yesmaximal, characteristic, complemented
3C3×C19×D75C211yesmaximal, characteristic, complemented
4D57⋊D25—31nomaximal
5D25×D57—31nomaximal
6C32×C19×C25C2211yescharacteristic, complemented, Hall
7D15⋊D57—51nomaximal
8D1425D311yescharacteristic, complemented
9C19×D75D311yescharacteristic, complemented
10C25×D57—31no—
11C25×D57—31no—
12C25×D57—61no—
13C3×D475—31no—
14C3×C19×D25—31no—
15D19×D25—91noHall
16C5×C3⋊D57D511yescharacteristic
17C3×D285—51no—
18C3×C19×D15—51no—
19C3×C19×C25—21no—
20C3×C19×C25C2×D311yescharacteristic, complemented
21C3×C19×C25C2×D311yescharacteristic, complemented
22D15⋊D19—151no—
23D5×D57—151no—
24D475—31no—
25C25×D19—91no—
26C19×D25—31no—
27(C3⋊D3)⋊D25—191nomaximal, Hall
28C32×C5×C19C2×D511yescharacteristic
29D3×D57—251noHall
30D285—51no—
31C19×D15—51no—
32C5×D57—31no—
33C5×D57—31no—
34C5×D57—61no—
35C3×D95—151no—
36C3×D5×C19—151no—
37C19×C25D3211yescharacteristic, complemented, Hall
38C3⋊D3×C25—191no—
39C3×D75—191no—
40C3×D75D1911yescharacteristic, complemented
41D5×D19—451no—
42C3⋊D57D2511yescharacteristic, complemented
43C3×D57—251no—
44C3×D3×C19—251no—
45D3×D25—571no—
46D3×D25—571no—
47C3×C5×C19—21no—
48C3×C5×C19D3×D511yescharacteristic
49C3×C5×C19D3×D511yescharacteristic
50C2×D57—751no—
51D3×D19—751no—
52C32×C25C2×D1911yescharacteristic, complemented, Hall
53D95—151no—
54C5×D19—91no—
55D5×C19—151no—
56(C3⋊D3)⋊D5—951no—
57C32×C19C2×D2511yescharacteristic, complemented, Hall
58D75—191no—
59D75D5711yescharacteristic, complemented
60C3×D25—31no—
61C3×D25—571no—
62D3×C25—571no—
63D3×C25—571no—
64D3×C25—1141no—
65C2×C3×C19—751no—
66D57—31no—
67D57—31no—
68D57—61no—
69D57—251no—
70C3×D19—751no—
71D3×C19—251no—
72C2×D25—1711noHall
73C5×C19(C3⋊D3)⋊D511yescharacteristic
74C5×C3⋊D3—191no—
75C3×D15—51no—
76C3×D15—951no—
77C2×D19—2251noHall
78C3×C25—21no—
79C3×C25D3×D1911yescharacteristic, complemented
80C3×C25C2×D5711yescharacteristic, complemented
81D3×D5—2851no—
82D3×D5—2851no—
83C3×C19—21no—
84C3×C19D3×D2511yescharacteristic, complemented
85C3×C19D3×D2511yescharacteristic, complemented
86C2×C25—1711no—
87D25—31no—
88D25—571no—
89C32×C5D5×D1911yescharacteristic
90C2×C19—751no—
91D19—91no—
92D19—751no—
93D32—4751noHall
94D15—51no—
95D15—951no—
96C3×D5—151no—
97C3×D5—2851no—
98C5×D3—571no—
99C5×D3—571no—
100C5×D3—1141no—
101C25D3×D5711yescharacteristic, complemented, Sylow
102C2×D5—8551no—
103C19(C3⋊D3)⋊D2511yescharacteristic, complemented, Sylow
104C3⋊D3—191no—
105C3×D3—251no—
106C3×D3—4751no—
107C3×C5—21no—
108C3×C5D5×D5711yescharacteristic
109C3×C5D15⋊D1911yescharacteristic
110C2×D3—14251no—
111C2×D3—14251no—
112C2×C5—1711no—
113D5—151no—
114D5—2851no—
115C32D19×D2511yescharacteristic, complemented, Sylow
116C2×C3—751no—
117C2×C3—14251no—
118D3—251no—
119D3—571no—
120D3—571no—
121D3—1141no—
122D3—4751no—
123C5D15⋊D5711yescharacteristic
124C22—42751noSylow
125C3—21no—
126C3D25×D5711yescharacteristic, complemented
127C3D57⋊D2511yescharacteristic, complemented
128C2—751no—
129C2—14251no—
130C2—1711no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC32×C19×C25C22
FrattiniC5D15⋊D57
socleC32×C5×C19C2×D5
LCSG ▷ C32×C19×C25
UCSC1

Complements

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

NH ≅ G/Ntype
1. C25×C3⋊D57C2semidirect
2. C3×D1425C2semidirect
3. C3×C19×D75C2semidirect
6. C32×C19×C25C22semidirect
8. D1425D3semidirect
9. C19×D75D3semidirect
20. C3×C19×C25C2×D3semidirect
21. C3×C19×C25C2×D3semidirect
37. C19×C25D32semidirect
40. C3×D75D19semidirect
42. C3⋊D57D25semidirect
52. C32×C25C2×D19semidirect
57. C32×C19C2×D25semidirect
59. D75D57semidirect
79. C3×C25D3×D19semidirect
80. C3×C25C2×D57semidirect
84. C3×C19D3×D25semidirect
85. C3×C19D3×D25semidirect
101. C25D3×D57semidirect
103. C19(C3⋊D3)⋊D25semidirect
115. C32D19×D25semidirect
126. C3D25×D57semidirect
127. C3D57⋊D25semidirect

Maximal subgroups

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

subgroupindex
C25×C3⋊D572
C3×D14252
C3×C19×D752
D57⋊D253
D25×D573
D15⋊D575
(C3⋊D3)⋊D2519