Finite Group Databasebeta

← C17×D152 #29506037

Subgroups — C17×D152 #29506037

Order 15300.

224 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 52 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×C3⋊(C3⋊(C5⋊D5))C211yesmaximal, characteristic, complemented
2C3×C5×C17×D15C212yesmaximal, complemented
3D5×C17×D15—32nomaximal
4C32×C52×C17C2211yescharacteristic, complemented, Hall
5D3×C17×D15—52nomaximal
6C17×C3⋊(C5⋊D5)—32no—
7C17×C3⋊(C5⋊D5)—61no—
8C5×C17×D15D312yescomplemented
9C3×C5×D5×C17—32no—
10D52×C17—91noHall
11C17×C3⋊D15—52no—
12C17×C3⋊D15—102no—
13C3×C17×D15D512yescomplemented
14C3×C5×D3×C17—52no—
15C3×C52×C17—21no—
16C3×C52×C17C2×D312yescomplemented
17C2×C17×D15—152no—
18D3×D5×C17—152no—
19D152C1711yesmaximal, characteristic, direct product factor, Hall
20C17×C5⋊D5—91no—
21C5×D5×C17—32no—
22C32×C5×C17—22no—
23C32×C5×C17C2×D512yescomplemented
24D32×C17—251noHall
25C2×C3×C5×C17—152no—
26C17×D15—152no—
27C17×D15—152no—
28C17×D15—304no—
29C17×D15—302no—
30C17×D15—304no—
31C17×D15D1512yesdirect product factor
32C5×D3×C17—52no—
33C3×D5×C17—32no—
34C3⋊(C3⋊(C5⋊D5))C2×C1711yescharacteristic, complemented
35C3×C5×D15C2×C1712yescomplemented
36C52×C17D3211yescharacteristic, complemented, Hall
37C2×D5×C17—452no—
38C17×C3⋊D3—251no—
39C3×D3×C17—52no—
40D5×D15—32no—
41C3×C5×C17—24no—
42C3×C5×C17—22no—
43C3×C5×C17—24no—
44C3×C5×C17D3×D512yescomplemented
45C3×C5×C17C2×D1512yescomplemented
46C32×C52C22×C1711yescharacteristic, complemented, Hall
47C2×D3×C17—752no—
48D3×D15—52no—
49C2×C5×C17—152no—
50D5×C17—32no—
51D5×C17—452no—
52D5×C17—902no—
53C32×C17D5211yescharacteristic, complemented, Hall
54C3⋊(C5⋊D5)—32no—
55C3⋊(C5⋊D5)—61no—
56C5×D15D3×C1712yescomplemented
57C3×C5×D5—32no—
58C2×C3×C17—152no—
59D3×C17—52no—
60D3×C17—752no—
61D3×C17—1501no—
62D52—91noHall
63C3⋊D15—52no—
64C3⋊D15—102no—
65C3×D15D5×C1712yescomplemented
66C3×C5×D3—52no—
67C5×C17—22no—
68C5×C17D3×D1512yescomplemented
69C3×C52—21no—
70C3×C52C2×D3×C1712yescomplemented
71C22×C17—2251noHall
72C2×D15—152no—
73D3×D5—152no—
74C3×C17—21no—
75C3×C17D5×D1512yescomplemented
76C5⋊D5—91no—
77C5×D5—32no—
78C32×C5—22no—
79C32×C5C2×D5×C1712yescomplemented
80D32—251noHall
81C2×C17—152no—
82C2×C17—2251no—
83C2×C3×C5—152no—
84D15—152no—
85D15—152no—
86D15—304no—
87D15—302no—
88D15—304no—
89D15C17×D1512yesdirect product factor
90C3×D5—32no—
91C5×D3—52no—
92C52D32×C1711yescharacteristic, complemented, Sylow
93C2×D5—452no—
94C3⋊D3—251no—
95C3×D3—52no—
96C17D15211yescharacteristic, direct product factor, Sylow
97C3×C5—24no—
98C3×C5—22no—
99C3×C5—24no—
100C3×C5D3×D5×C1712yescomplemented
101C3×C5C2×C17×D1512yescomplemented
102C2×D3—752no—
103C2×C5—152no—
104D5—32no—
105D5—452no—
106D5—902no—
107C32D52×C1711yescharacteristic, complemented, Sylow
108C2×C3—152no—
109D3—52no—
110D3—752no—
111D3—1501no—
112C5—22no—
113C5D3×C17×D1512yescomplemented
114C22—2251noSylow
115C3—21no—
116C3D5×C17×D1512yescomplemented
117C2—152no—
118C2—2251no—
subgroupG/H
center, hypercenterC17D152
commutator, cosocle, hypocenterC32×C52C22×C17
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C32×C52
UCSC1 ◁ C17

Complements

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

NH ≅ G/Ntype
1. C17×C3⋊(C3⋊(C5⋊D5))C2semidirect
2. C3×C5×C17×D15C2semidirect
4. C32×C52×C17C22semidirect
8. C5×C17×D15D3semidirect
13. C3×C17×D15D5semidirect
16. C3×C52×C17C2×D3semidirect
19. D152C17direct (N × H)
23. C32×C5×C17C2×D5semidirect
31. C17×D15D15direct (N × H)
34. C3⋊(C3⋊(C5⋊D5))C2×C17semidirect
35. C3×C5×D15C2×C17semidirect
36. C52×C17D32semidirect
44. C3×C5×C17D3×D5semidirect
45. C3×C5×C17C2×D15semidirect
46. C32×C52C22×C17semidirect
53. C32×C17D52semidirect
56. C5×D15D3×C17semidirect
65. C3×D15D5×C17semidirect
68. C5×C17D3×D15semidirect
70. C3×C52C2×D3×C17semidirect
75. C3×C17D5×D15semidirect
79. C32×C5C2×D5×C17semidirect
89. D15C17×D15direct (N × H)
92. C52D32×C17semidirect
96. C17D152direct (N × H)
100. C3×C5D3×D5×C17semidirect
101. C3×C5C2×C17×D15semidirect
107. C32D52×C17semidirect
113. C5D3×C17×D15semidirect
116. C3D5×C17×D15semidirect

Maximal subgroups

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

subgroupindex
C17×C3⋊(C3⋊(C5⋊D5))2
C3×C5×C17×D152
D5×C17×D153
D3×C17×D155
D15217