Finite Group Databasebeta

← D15⋊D539 #44568418

Subgroups — D15⋊D539 #44568418

Order 32340.

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

normal subgroups only

This group has 120 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
1C11×D15×C49C211yesmaximal, characteristic, complemented
2C5×D1617C211yesmaximal, characteristic, complemented
3C3×D2695C211yesmaximal, characteristic, complemented
4D5×D539—31nomaximal, Hall
5C3×C5×C11×C49C2211yescharacteristic, complemented, Hall
6D3×D539—51nomaximal, Hall
7D2695D311yescharacteristic, complemented
8D5×C11×C49—31no—
9C5×D539—31no—
10D15⋊D77—71nomaximal
11D1617D511yescharacteristic, complemented
12D3×C11×C49—51no—
13C3×D539—51no—
14D15⋊D49—111nomaximal, Hall
15C5×C11×C49C2×D311yescharacteristic, complemented, Hall
16C7×C11×D15D711yescharacteristic
17C5×D231—71no—
18C3×D385—71no—
19C2×D539—151noHall
20C3×C11×C49C2×D511yescharacteristic, complemented, Hall
21D5×D77—211no—
22D15×C49D1111yescharacteristic, complemented
23C5×D147—111no—
24C3×D245—111no—
25C3×C5×C7×C11C2×D711yescharacteristic
26C2×C11×C49—151no—
27D539—31no—
28D539—51no—
29D5×D49—331noHall
30D3×D77—351no—
31D385—71no—
32C7×D5×C11—31no—
33C5×D77—211no—
34C3×C5×C49C2×D1111yescharacteristic, complemented, Hall
35D15⋊D11—491noHall
36D3×D49—551noHall
37C11×C49D3×D511yescharacteristic, complemented, Hall
38D245—111no—
39C5×D49—331no—
40D5×C49—31no—
41D231—71no—
42D3×C7×C11—51no—
43C3×D77—351no—
44D15⋊D7—771no—
45C5×C7×C11D3×D711yescharacteristic
46C11×D15D4911yescharacteristic, complemented
47C5×D33—491no—
48C3×D55—491no—
49C2×D77—1051no—
50D147—111no—
51C3×D49—551no—
52D3×C49—51no—
53C5×C49D3×D1111yescharacteristic, complemented, Hall
54C3×C7×C11D5×D711yescharacteristic
55D5×D11—1471noHall
56C7×D15D7711yescharacteristic
57C5×D21—771no—
58C3×D35—771no—
59C2×D49—1651noHall
60C3×C5×C11C2×D4911yescharacteristic, complemented, Hall
61C2×C7×C11—151no—
62D77—211no—
63D77—351no—
64C3×C49D5×D1111yescharacteristic, complemented, Hall
65D5×D7—2311no—
66D3×D11—2451noHall
67D55—491no—
68C5×D11—1471no—
69D5×C11—31no—
70C3×C5×C7C2×D7711yescharacteristic
71C2×C49—151no—
72D49—331no—
73D49—551no—
74D3×D7—3851no—
75C7×C11D15⋊D711yescharacteristic
76D35—771no—
77C5×D7—2311no—
78C7×D5—31no—
79D33—491no—
80C3×D11—2451no—
81D3×C11—51no—
82D3×D5—5391noHall
83C5×C11D3×D4911yescharacteristic, complemented, Hall
84C49D15⋊D1111yescharacteristic, complemented, Sylow
85C2×D11—7351noHall
86D21—771no—
87C3×D7—3851no—
88D3×C7—51no—
89C5×C7D3×D7711yescharacteristic
90C3×C11D5×D4911yescharacteristic, complemented, Hall
91D15D53911yescharacteristic, complemented
92C3×D5—5391no—
93C5×D3—5391no—
94C2×D7—11551no—
95C2×C11—151no—
96D11—1471no—
97D11—2451no—
98C3×C7D5×D7711yescharacteristic
99C2×D5—16171noHall
100C3×C5C2×D53911yescharacteristic, complemented, Hall
101C2×C7—151no—
102D7—3851no—
103D7—2311no—
104C2×D3—26951noHall
105C11D15⋊D4911yescharacteristic, complemented, Sylow
106C2×C5—16171no—
107D5—31no—
108D5—5391no—
109C7D15⋊D7711yescharacteristic
110C2×C3—26951no—
111D3—51no—
112D3—5391no—
113C5D3×D53911yescharacteristic, complemented, Sylow
114C22—80851noSylow
115C3D5×D53911yescharacteristic, complemented, Sylow
116C2—151no—
117C2—16171no—
118C2—26951no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C5×C11×C49C22
FrattiniC7D15⋊D77
socleC3×C5×C7×C11C2×D7
LCSG ▷ C3×C5×C11×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11×D15×C49C2semidirect
2. C5×D1617C2semidirect
3. C3×D2695C2semidirect
5. C3×C5×C11×C49C22semidirect
7. D2695D3semidirect
11. D1617D5semidirect
15. C5×C11×C49C2×D3semidirect
20. C3×C11×C49C2×D5semidirect
22. D15×C49D11semidirect
34. C3×C5×C49C2×D11semidirect
37. C11×C49D3×D5semidirect
46. C11×D15D49semidirect
53. C5×C49D3×D11semidirect
60. C3×C5×C11C2×D49semidirect
64. C3×C49D5×D11semidirect
83. C5×C11D3×D49semidirect
84. C49D15⋊D11semidirect
90. C3×C11D5×D49semidirect
91. D15D539semidirect
100. C3×C5C2×D539semidirect
105. C11D15⋊D49semidirect
113. C5D3×D539semidirect
115. C3D5×D539semidirect

Maximal subgroups

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

subgroupindex
C11×D15×C492
C5×D16172
C3×D26952
D5×D5393
D3×D5395
D15⋊D777
D15⋊D4911