Finite Group Databasebeta

← D5×C11×D49⋊C3 #44568356

Subgroups — D5×C11×D49⋊C3 #44568356

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
1C11×C5⋊(D49⋊C3)C211yesmaximal, characteristic, complemented
2D5×C11×C49⋊C3C211yesmaximal, characteristic, complemented
3C5×C11×D49⋊C3C211yesmaximal, characteristic, complemented
4D5×C11×D49C311yesmaximal, characteristic, complemented, Hall
5C5×C11×C49⋊C3C2211yescharacteristic, complemented, Hall
6C2×C11×D49⋊C3—51nomaximal, Hall
7C11×D245C2×C311yescharacteristic, complemented
8D5×C11×C49C2×C311yescharacteristic, complemented
9C5×C11×D49C2×C311yescharacteristic, complemented
10D5×C11×AGL(1,𝔽7)—71nomaximal
11C2×C11×C49⋊C3—51no—
12C11×D49⋊C3—51no—
13C11×D49⋊C3D511yescharacteristic, direct product factor
14D5×D49⋊C3C1111yesmaximal, characteristic, direct product factor, Hall
15C5×C11×C49C22×C311yescharacteristic, complemented, Hall
16C11×C5⋊AGL(1,𝔽7)—71no—
17D5×C11×ΓL(1,𝔽8)—71no—
18C5×C11×AGL(1,𝔽7)—71no—
19C2×C11×D49—51noHall
20C11×C49⋊C3C2×D511yescharacteristic, complemented, Hall
21D5×C11×D7—71no—
22C5⋊(D49⋊C3)C2×C1111yescharacteristic, complemented
23D5×C49⋊C3C2×C1111yescharacteristic, complemented
24C5×D49⋊C3C2×C1111yescharacteristic, complemented
25C5×C11×ΓL(1,𝔽8)—71no—
26C2×C11×C49—51no—
27C11×D49—51no—
28C11×D49C3×D511yescharacteristic, complemented
29D5×D49C3×C1111yescharacteristic, complemented, Hall
30C2×C11×AGL(1,𝔽7)—351no—
31C11×D35—71no—
32C7×D5×C11AGL(1,𝔽7)11yescharacteristic
33C5×C11×D7—71no—
34C5×C49⋊C3C22×C1111yescharacteristic, complemented, Hall
35C2×C3×D5×C11—491noHall
36C2×D49⋊C3—51noHall
37C11×C49C2×C3×D511yescharacteristic, complemented, Hall
38D245C2×C3×C1111yescharacteristic, complemented
39C5×D49C2×C3×C1111yescharacteristic, complemented
40D5×C49C2×C3×C1111yescharacteristic, complemented
41C2×C11×ΓL(1,𝔽8)—351no—
42C11×AGL(1,𝔽7)—71no—
43C11×AGL(1,𝔽7)—351no—
44D5×AGL(1,𝔽7)—71no—
45C5×C7×C11C2×AGL(1,𝔽7)11yescharacteristic
46C2×C3×C5×C11—491no—
47C3×D5×C11—491no—
48C3×D5×C11—491no—
49C2×C11×D7—351no—
50C2×C49⋊C3—51no—
51D49⋊C3—51no—
52D49⋊C3D5×C1111yescharacteristic, direct product factor
53C5×C49C22×C3×C1111yescharacteristic, complemented, Hall
54C11×ΓL(1,𝔽8)—71no—
55C2×D5×C11—491noHall
56C5⋊AGL(1,𝔽7)—71no—
57D5×ΓL(1,𝔽8)—71no—
58C5×AGL(1,𝔽7)—71no—
59C2×D49—51noHall
60C3×C5×C11—491noHall
61C2×C7×C11—51no—
62C11×D7—71no—
63C11×D7—351no—
64C49⋊C3C2×D5×C1111yescharacteristic, complemented, Hall
65D5×D7—71no—
66C22×C3×C11—2451noHall
67C2×C5×C11—491no—
68D5×C11—491no—
69D5×C11D49⋊C311yescharacteristic, direct product factor
70C5×ΓL(1,𝔽8)—71no—
71C2×C49—51no—
72D49—51no—
73D49C3×D5×C1111yescharacteristic, complemented
74C2×AGL(1,𝔽7)—351no—
75C7×C11D5×AGL(1,𝔽7)11yescharacteristic
76D35—71no—
77C5×D7—71no—
78C7×D5C11×AGL(1,𝔽7)11yescharacteristic
79C2×C3×C11—491no—
80C2×C3×C11—2451no—
81C2×C3×C11—2451no—
82C2×C3×D5—491noHall
83C5×C11C2×D49⋊C311yescharacteristic, complemented, Hall
84C49C2×C3×D5×C1111yescharacteristic, complemented, Sylow
85C22×C11—2451noHall
86C2×ΓL(1,𝔽8)—351no—
87AGL(1,𝔽7)—71no—
88AGL(1,𝔽7)—351no—
89C5×C7C2×C11×AGL(1,𝔽7)11yescharacteristic
90C3×C11—491noHall
91C2×C3×C5—491no—
92C3×D5—491no—
93C3×D5—491no—
94C2×D7—351no—
95C2×C11—51no—
96C2×C11—491no—
97C2×C11—2451no—
98ΓL(1,𝔽8)—71no—
99C2×D5—491noHall
100C3×C5—491noHall
101C2×C7—51no—
102D7—71no—
103D7—351no—
104C22×C3—2451noHall
105C11D5×D49⋊C311yescharacteristic, direct product factor, Sylow
106C2×C5—491no—
107D5—491no—
108D5C11×D49⋊C311yescharacteristic, direct product factor
109C7D5×C11×AGL(1,𝔽7)11yescharacteristic
110C2×C3—491no—
111C2×C3—2451no—
112C2×C3—2451no—
113C5C2×C11×D49⋊C311yescharacteristic, complemented, Sylow
114C22—2451noSylow
115C3—491noSylow
116C2—51no—
117C2—491no—
118C2—2451no—
subgroupG/H
center, hypercenterC11D5×D49⋊C3
commutator, cosocle, hypocenterC5×C49C22×C3×C11
FrattiniC7D5×C11×AGL(1,𝔽7)
FittingC5×C11×C49C22×C3
socleC5×C7×C11C2×AGL(1,𝔽7)
LCSG ▷ C5×C49
UCSC1 ◁ C11

Complements

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

NH ≅ G/Ntype
1. C11×C5⋊(D49⋊C3)C2semidirect
2. D5×C11×C49⋊C3C2semidirect
3. C5×C11×D49⋊C3C2semidirect
4. D5×C11×D49C3semidirect
5. C5×C11×C49⋊C3C22semidirect
7. C11×D245C2×C3semidirect
8. D5×C11×C49C2×C3semidirect
9. C5×C11×D49C2×C3semidirect
13. C11×D49⋊C3D5direct (N × H)
14. D5×D49⋊C3C11direct (N × H)
15. C5×C11×C49C22×C3semidirect
20. C11×C49⋊C3C2×D5semidirect
22. C5⋊(D49⋊C3)C2×C11semidirect
23. D5×C49⋊C3C2×C11semidirect
24. C5×D49⋊C3C2×C11semidirect
28. C11×D49C3×D5semidirect
29. D5×D49C3×C11semidirect
34. C5×C49⋊C3C22×C11semidirect
37. C11×C49C2×C3×D5semidirect
38. D245C2×C3×C11semidirect
39. C5×D49C2×C3×C11semidirect
40. D5×C49C2×C3×C11semidirect
52. D49⋊C3D5×C11direct (N × H)
53. C5×C49C22×C3×C11semidirect
64. C49⋊C3C2×D5×C11semidirect
69. D5×C11D49⋊C3direct (N × H)
73. D49C3×D5×C11semidirect
83. C5×C11C2×D49⋊C3semidirect
84. C49C2×C3×D5×C11semidirect
105. C11D5×D49⋊C3direct (N × H)
108. D5C11×D49⋊C3direct (N × H)
113. C5C2×C11×D49⋊C3semidirect

Maximal subgroups

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

subgroupindex
C11×C5⋊(D49⋊C3)2
D5×C11×C49⋊C32
C5×C11×D49⋊C32
D5×C11×D493
C2×C11×D49⋊C35
D5×C11×AGL(1,𝔽7)7
D5×D49⋊C311