Finite Group Databasebeta

← D5×C17×D45 #29505818

Subgroups — D5×C17×D45 #29505818

Order 15300.

144 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 44 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
1C17×C5⋊D45C211yesmaximal, characteristic, complemented
2C5×C17×D45C211yesmaximal, characteristic, complemented
3C5×C9×D5×C17C211yesmaximal, characteristic, complemented
4D5×C17×D15—31nomaximal
5C52×C9×C17C2211yescharacteristic, complemented, Hall
6C2×C17×D45—51nomaximal
7D5×C17×D9—51nomaximal
8C17×C3⋊(C5⋊D5)—31no—
9C5×C17×D15—31no—
10C3×C5×D5×C17D311yescharacteristic
11D52×C17—91noHall
12C2×C5×C9×C17—51no—
13C17×D45—51no—
14C17×D45—51no—
15C17×D45—102no—
16C17×D45D511yescharacteristic, direct product factor
17C5×C17×D9—51no—
18C9×D5×C17D511yescharacteristic, complemented
19C3×C52×C17C2×D311yescharacteristic
20C2×C17×D15—151no—
21D3×D5×C17—151no—
22D5×D45C1711yesmaximal, characteristic, direct product factor, Hall
23C17×C5⋊D5—91no—
24C5×D5×C17—91no—
25C5×D5×C17D911yescharacteristic, complemented
26C5×C9×C17—22no—
27C5×C9×C17C2×D511yescharacteristic, complemented
28C5×C9×C17C2×D511yescharacteristic, complemented
29C2×C17×D9—251noHall
30C2×C3×C5×C17—51no—
31C17×D15—31no—
32C17×D15—151no—
33C17×D15—151no—
34C17×D15—302no—
35C5×D3×C17—151no—
36C3×D5×C17D1511yescharacteristic
37C5⋊D45C2×C1711yescharacteristic, complemented
38C5×D45C2×C1711yescharacteristic, complemented
39C5×C9×D5C2×C1711yescharacteristic, complemented
40C52×C17C2×D911yescharacteristic, complemented, Hall
41C2×D5×C17—451no—
42C2×D5×C17—451no—
43C2×C9×C17—51no—
44C17×D9—51no—
45C17×D9—251no—
46D5×D15—31no—
47C3×C5×C17—22no—
48C3×C5×C17D3×D511yescharacteristic
49C3×C5×C17C2×D1511yescharacteristic
50C52×C9C22×C1711yescharacteristic, complemented, Hall
51C2×D3×C17—751no—
52C2×D45—51no—
53D5×D9—51no—
54C2×C5×C17—51no—
55C2×C5×C17—451no—
56D5×C17—91no—
57D5×C17—451no—
58D5×C17—451no—
59D5×C17—902no—
60D5×C17D4511yescharacteristic, direct product factor
61C9×C17D5211yescharacteristic, complemented, Hall
62C3⋊(C5⋊D5)—31no—
63C5×D15—31no—
64C3×C5×D5D3×C1711yescharacteristic
65C2×C3×C17—51no—
66D3×C17—151no—
67D3×C17—751no—
68D52—91noHall
69C2×C5×C9—51no—
70D45—51no—
71D45—51no—
72D45—102no—
73D45D5×C1711yescharacteristic, direct product factor
74C9×D5D5×C1711yescharacteristic, complemented
75C5×D9—51no—
76C5×C17—22no—
77C5×C17D5×D911yescharacteristic, complemented
78C5×C17C2×D4511yescharacteristic, complemented
79C3×C52C2×D3×C1711yescharacteristic
80C22×C17—2251noHall
81C2×D15—151no—
82D3×D5—151no—
83C3×C17D5×D1511yescharacteristic
84C5⋊D5—91no—
85C5×D5—91no—
86C5×D5C17×D911yescharacteristic, complemented
87C5×C9—22no—
88C5×C9C2×D5×C1711yescharacteristic, complemented
89C5×C9C2×D5×C1711yescharacteristic, complemented
90C2×D9—251noHall
91C2×C17—51no—
92C2×C17—451no—
93C2×C17—2251no—
94C2×C3×C5—51no—
95D15—31no—
96D15—151no—
97D15—151no—
98D15—302no—
99C3×D5C17×D1511yescharacteristic
100C5×D3—151no—
101C52C2×C17×D911yescharacteristic, complemented, Sylow
102C2×D5—451no—
103C2×D5—451no—
104C2×C9—51no—
105D9—51no—
106D9—251no—
107C17D5×D4511yescharacteristic, direct product factor, Sylow
108C3×C5—22no—
109C3×C5D3×D5×C1711yescharacteristic
110C3×C5C2×C17×D1511yescharacteristic
111C2×D3—751no—
112C2×C5—51no—
113C2×C5—451no—
114D5—91no—
115D5—451no—
116D5—451no—
117D5—902no—
118D5C17×D4511yescharacteristic, direct product factor
119C9D52×C1711yescharacteristic, complemented, Sylow
120C2×C3—51no—
121D3—151no—
122D3—751no—
123C5—22no—
124C5D5×C17×D911yescharacteristic, complemented
125C5C2×C17×D4511yescharacteristic, complemented
126C22—2251noSylow
127C3D5×C17×D1511yescharacteristic
128C2—51no—
129C2—451no—
130C2—2251no—
subgroupG/H
center, hypercenterC17D5×D45
commutator, cosocle, hypocenterC52×C9C22×C17
FrattiniC3D5×C17×D15
FittingC52×C9×C17C22
socleC3×C52×C17C2×D3
LCSG ▷ C52×C9
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C17×C5⋊D45C2semidirect
2. C5×C17×D45C2semidirect
3. C5×C9×D5×C17C2semidirect
5. C52×C9×C17C22semidirect
16. C17×D45D5direct (N × H)
18. C9×D5×C17D5semidirect
22. D5×D45C17direct (N × H)
25. C5×D5×C17D9semidirect
27. C5×C9×C17C2×D5semidirect
28. C5×C9×C17C2×D5semidirect
37. C5⋊D45C2×C17semidirect
38. C5×D45C2×C17semidirect
39. C5×C9×D5C2×C17semidirect
40. C52×C17C2×D9semidirect
50. C52×C9C22×C17semidirect
60. D5×C17D45direct (N × H)
61. C9×C17D52semidirect
73. D45D5×C17direct (N × H)
74. C9×D5D5×C17semidirect
77. C5×C17D5×D9semidirect
78. C5×C17C2×D45semidirect
86. C5×D5C17×D9semidirect
88. C5×C9C2×D5×C17semidirect
89. C5×C9C2×D5×C17semidirect
101. C52C2×C17×D9semidirect
107. C17D5×D45direct (N × H)
118. D5C17×D45direct (N × H)
119. C9D52×C17semidirect
124. C5D5×C17×D9semidirect
125. C5C2×C17×D45semidirect

Maximal subgroups

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

subgroupindex
C17×C5⋊D452
C5×C17×D452
C5×C9×D5×C172
D5×C17×D153
C2×C17×D455
D5×C17×D95
D5×D4517