Finite Group Databasebeta

← D5×D11×C49⋊C3 #44568360

Subgroups — D5×D11×C49⋊C3 #44568360

Order 32340.

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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
1D55×C49⋊C3C211yesmaximal, characteristic, complemented
2D5×C11×C49⋊C3C211yesmaximal, characteristic, complemented
3C5×D11×C49⋊C3C211yesmaximal, characteristic, complemented
4D5×D11×C49C311yesmaximal, characteristic, complemented, Hall
5C5×C11×C49⋊C3C2211yescharacteristic, complemented, Hall
6C2×D11×C49⋊C3—51nomaximal, Hall
7C49×D55C2×C311yescharacteristic, complemented
8D5×C11×C49C2×C311yescharacteristic, complemented
9C5×D11×C49C2×C311yescharacteristic, complemented
10D5×ΓL(1,𝔽8)×D11—71nomaximal
11C2×C11×C49⋊C3—51no—
12D11×C49⋊C3—51no—
13D11×C49⋊C3D511yescharacteristic, direct product factor
14C2×D5×C49⋊C3—111nomaximal, Hall
15C5×C11×C49C22×C311yescharacteristic, complemented, Hall
16ΓL(1,𝔽8)×D55—71no—
17D5×C11×ΓL(1,𝔽8)—71no—
18C5×ΓL(1,𝔽8)×D11—71no—
19C2×D11×C49—51noHall
20C11×C49⋊C3C2×D511yescharacteristic, complemented, Hall
21C7×D5×D11ΓL(1,𝔽8)11yescharacteristic
22C2×C5×C49⋊C3—111no—
23D5×C49⋊C3—111no—
24D5×C49⋊C3D1111yescharacteristic, direct product factor
25C5×C11×ΓL(1,𝔽8)—71no—
26C2×C11×C49—51no—
27D11×C49—51no—
28D11×C49C3×D511yescharacteristic, complemented
29C2×D5×C49—111noHall
30C2×ΓL(1,𝔽8)×D11—351no—
31C7×D55C2×ΓL(1,𝔽8)11yescharacteristic
32C7×D5×C11C2×ΓL(1,𝔽8)11yescharacteristic
33C5×C7×D11C2×ΓL(1,𝔽8)11yescharacteristic
34C5×C49⋊C3C2×D1111yescharacteristic, complemented, Hall
35C3×D5×D11—491noHall
36C22×C49⋊C3—551noHall
37C11×C49C2×C3×D511yescharacteristic, complemented, Hall
38C2×C5×C49—111no—
39D5×C49—111no—
40D5×C49C3×D1111yescharacteristic, complemented
41C2×C11×ΓL(1,𝔽8)—351no—
42ΓL(1,𝔽8)×D11—71no—
43ΓL(1,𝔽8)×D11—351no—
44C2×D5×ΓL(1,𝔽8)—771no—
45C5×C7×C11C22×ΓL(1,𝔽8)11yescharacteristic
46C3×D55—491no—
47C3×D5×C11—491no—
48C3×C5×D11—491no—
49C2×C7×D11—51no—
50C2×C49⋊C3—51no—
51C2×C49⋊C3—111no—
52C2×C49⋊C3—551no—
53C5×C49C2×C3×D1111yescharacteristic, complemented, Hall
54C11×ΓL(1,𝔽8)—71no—
55D5×D11C49⋊C311yescharacteristic, direct product factor, Hall
56C2×C5×ΓL(1,𝔽8)—771no—
57D5×ΓL(1,𝔽8)—71no—
58D5×ΓL(1,𝔽8)—771no—
59C22×C49—551noHall
60C3×C5×C11—491noHall
61C2×C7×C11—51no—
62C7×D11—51no—
63C7×D11D5×ΓL(1,𝔽8)11yescharacteristic
64C49⋊C3D5×D1111yescharacteristic, direct product factor, Hall
65C2×C7×D5—111no—
66C2×C3×D11—2451noHall
67D55C2×C49⋊C311yescharacteristic, complemented
68C5×D11C2×C49⋊C311yescharacteristic, complemented
69D5×C11C2×C49⋊C311yescharacteristic, complemented
70C5×ΓL(1,𝔽8)—71no—
71C2×C49—51no—
72C2×C49—111no—
73C2×C49—551no—
74C22×ΓL(1,𝔽8)—3851no—
75C7×C11C2×D5×ΓL(1,𝔽8)11yescharacteristic
76C2×C5×C7—111no—
77C7×D5—111no—
78C7×D5ΓL(1,𝔽8)×D1111yescharacteristic
79C2×C3×C11—2451no—
80C3×D11—491no—
81C3×D11—2451no—
82C2×C3×D5—5391noHall
83C5×C11C22×C49⋊C311yescharacteristic, complemented, Hall
84C49C3×D5×D1111yescharacteristic, complemented, Sylow
85C2×D11—51noHall
86C2×ΓL(1,𝔽8)—351no—
87C2×ΓL(1,𝔽8)—771no—
88C2×ΓL(1,𝔽8)—3851no—
89C5×C7C2×ΓL(1,𝔽8)×D1111yescharacteristic
90C3×C11—491noHall
91C2×C3×C5—5391no—
92C3×D5—5391no—
93C3×D5—491no—
94C22×C7—551no—
95C2×C11—51no—
96D11—51no—
97D11D5×C49⋊C311yescharacteristic, direct product factor
98ΓL(1,𝔽8)—71no—
99C2×D5—111noHall
100C3×C5—491noHall
101C2×C7—51no—
102C2×C7—111no—
103C2×C7—551no—
104C22×C3—26951noHall
105C11C2×D5×C49⋊C311yescharacteristic, complemented, Sylow
106C2×C5—111no—
107D5—111no—
108D5D11×C49⋊C311yescharacteristic, direct product factor
109C7D5×ΓL(1,𝔽8)×D1111yescharacteristic
110C2×C3—5391no—
111C2×C3—26951no—
112C2×C3—2451no—
113C5C2×D11×C49⋊C311yescharacteristic, complemented, Sylow
114C22—551noSylow
115C3—491noSylow
116C2—51no—
117C2—111no—
118C2—551no—
subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C11×C49C22×C3
FrattiniC7D5×ΓL(1,𝔽8)×D11
socleC5×C7×C11C22×ΓL(1,𝔽8)
LCSG ▷ C5×C11×C49
UCSC1

Complements

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

NH ≅ G/Ntype
1. D55×C49⋊C3C2semidirect
2. D5×C11×C49⋊C3C2semidirect
3. C5×D11×C49⋊C3C2semidirect
4. D5×D11×C49C3semidirect
5. C5×C11×C49⋊C3C22semidirect
7. C49×D55C2×C3semidirect
8. D5×C11×C49C2×C3semidirect
9. C5×D11×C49C2×C3semidirect
13. D11×C49⋊C3D5direct (N × H)
15. C5×C11×C49C22×C3semidirect
20. C11×C49⋊C3C2×D5semidirect
24. D5×C49⋊C3D11direct (N × H)
28. D11×C49C3×D5semidirect
34. C5×C49⋊C3C2×D11semidirect
37. C11×C49C2×C3×D5semidirect
40. D5×C49C3×D11semidirect
53. C5×C49C2×C3×D11semidirect
55. D5×D11C49⋊C3direct (N × H)
64. C49⋊C3D5×D11direct (N × H)
67. D55C2×C49⋊C3semidirect
68. C5×D11C2×C49⋊C3semidirect
69. D5×C11C2×C49⋊C3semidirect
83. C5×C11C22×C49⋊C3semidirect
84. C49C3×D5×D11semidirect
97. D11D5×C49⋊C3direct (N × H)
105. C11C2×D5×C49⋊C3semidirect
108. D5D11×C49⋊C3direct (N × H)
113. C5C2×D11×C49⋊C3semidirect

Maximal subgroups

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

subgroupindex
D55×C49⋊C32
D5×C11×C49⋊C32
C5×D11×C49⋊C32
D5×D11×C493
C2×D11×C49⋊C35
D5×ΓL(1,𝔽8)×D117
C2×D5×C49⋊C311