Finite Group Databasebeta

← C5×D11×#64424 #44568633

Subgroups — C5×D11×#64424 #44568633

Order 32340.

400 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C5×D11×#3861C211yesmaximal, characteristic, complemented
2C5×C11⋊#64424C211yesmaximal, characteristic, complemented
3C5×C11×#64424C211yesmaximal, characteristic, complemented
4C5×D11×C7⋊D7C311yesmaximal, characteristic, complemented, Hall
5C5×C11×#3861C2211yescharacteristic, complemented, Hall
6D11×#64424C511yesmaximal, characteristic, direct product factor, Hall
7C5×C7⋊D77C2×C311yescharacteristic, complemented
8C5×C11×C7⋊D7C2×C311yescharacteristic, complemented
9C5×C72×D11C2×C311yescharacteristic, complemented
10C5×D11×AGL(1,𝔽7)—78nomaximal
11D11×#3861C2×C511yescharacteristic, complemented
12C11⋊#64424C2×C511yescharacteristic, complemented
13C11×#64424C2×C511yescharacteristic, complemented
14C2×C5×#64424—111nomaximal, Hall
15C5×C72×C11C22×C311yescharacteristic, complemented, Hall
16C5×C11⋊AGL(1,𝔽7)—78no—
17C5×C11×AGL(1,𝔽7)—78no—
18C5×ΓL(1,𝔽8)×D11—78no—
19D11×C7⋊D7C3×C511yescharacteristic, complemented, Hall
20C11×#3861C22×C511yescharacteristic, complemented, Hall
21C5×D7×D11—78no—
22C2×C5×#3861—111no—
23C5×#64424—111no—
24C5×#64424D1111yescharacteristic, direct product factor
25C5×C11×ΓL(1,𝔽8)—78no—
26C7⋊D77C2×C3×C511yescharacteristic, complemented
27C11×C7⋊D7C2×C3×C511yescharacteristic, complemented
28C72×D11C2×C3×C511yescharacteristic, complemented
29C2×C5×C7⋊D7—111noHall
30D11×AGL(1,𝔽7)—78no—
31C5×D77—78no—
32C5×C11×D7—78no—
33C5×C7×D11AGL(1,𝔽7)18yescomplemented
34C5×#3861C2×D1111yescharacteristic, complemented, Hall
35C2×C3×C5×D11—491noHall
36C2×#64424—111noHall
37C72×C11C22×C3×C511yescharacteristic, complemented, Hall
38C2×C5×C72—111no—
39C5×C7⋊D7—111no—
40C5×C7⋊D7C3×D1111yescharacteristic, complemented
41C11⋊AGL(1,𝔽7)—78no—
42C11×AGL(1,𝔽7)—78no—
43ΓL(1,𝔽8)×D11—78no—
44C2×C5×AGL(1,𝔽7)—778no—
45C5×C7×C11C2×AGL(1,𝔽7)18yescomplemented
46C2×C3×C5×C11—491no—
47C3×C5×D11—491no—
48C3×C5×D11—491no—
49D7×D11—78no—
50C2×#3861—111no—
51#64424—111no—
52#64424C5×D1111yescharacteristic, direct product factor
53C5×C72C2×C3×D1111yescharacteristic, complemented, Hall
54C11×ΓL(1,𝔽8)—78no—
55C2×C5×D11—491noHall
56C2×C5×ΓL(1,𝔽8)—778no—
57C5×AGL(1,𝔽7)—78no—
58C5×AGL(1,𝔽7)—778no—
59C2×C7⋊D7—111noHall
60C3×C5×C11—491noHall
61D77—78no—
62C7×D11C5×AGL(1,𝔽7)18yescomplemented
63C11×D7—78no—
64#3861C2×C5×D1111yescharacteristic, complemented, Hall
65C2×C5×D7—778no—
66C2×C3×D11—491noHall
67C2×C5×C11—491no—
68C5×D11—491no—
69C5×D11#6442411yescharacteristic, direct product factor
70C5×ΓL(1,𝔽8)—78no—
71C2×C72—111no—
72C7⋊D7—111no—
73C7⋊D7C3×C5×D1111yescharacteristic, complemented
74C2×AGL(1,𝔽7)—778no—
75C7×C11C2×C5×AGL(1,𝔽7)18yescomplemented
76C2×C5×C7—118no—
77C5×D7—78no—
78C5×D7—778no—
79C2×C3×C11—491no—
80C3×D11—491no—
81C3×D11—491no—
82C22×C3×C5—5391noHall
83C5×C11C2×#6442411yescharacteristic, complemented, Hall
84C72C2×C3×C5×D1111yescharacteristic, complemented, Sylow
85C2×D11—491noHall
86C2×ΓL(1,𝔽8)—778no—
87AGL(1,𝔽7)—78no—
88AGL(1,𝔽7)—778no—
89C5×C7D11×AGL(1,𝔽7)18yescomplemented
90C3×C11—491noHall
91C2×C3×C5—5391no—
92C2×C3×C5—5391no—
93C2×C3×C5—491no—
94C2×D7—778no—
95C2×C11—491no—
96D11—491no—
97D11C5×#6442411yescharacteristic, direct product factor
98ΓL(1,𝔽8)—78no—
99C22×C5—5391noHall
100C3×C5—491noHall
101C2×C7—118no—
102D7—78no—
103D7—778no—
104C22×C3—5391noHall
105C11C2×C5×#6442411yescharacteristic, complemented, Sylow
106C2×C5—111no—
107C2×C5—5391no—
108C2×C5—491no—
109C7C5×D11×AGL(1,𝔽7)18yescomplemented
110C2×C3—5391no—
111C2×C3—5391no—
112C2×C3—491no—
113C5D11×#6442411yescharacteristic, direct product factor, Sylow
114C22—5391noSylow
115C3—491noSylow
116C2—111no—
117C2—5391no—
118C2—491no—
subgroupG/H
center, hypercenterC5D11×#64424
commutator, cosocle, hypocenterC72×C11C22×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C11C22×C3
LCSG ▷ C72×C11
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×D11×#3861C2semidirect
2. C5×C11⋊#64424C2semidirect
3. C5×C11×#64424C2semidirect
4. C5×D11×C7⋊D7C3semidirect
5. C5×C11×#3861C22semidirect
6. D11×#64424C5direct (N × H)
7. C5×C7⋊D77C2×C3semidirect
8. C5×C11×C7⋊D7C2×C3semidirect
9. C5×C72×D11C2×C3semidirect
11. D11×#3861C2×C5semidirect
12. C11⋊#64424C2×C5semidirect
13. C11×#64424C2×C5semidirect
15. C5×C72×C11C22×C3semidirect
19. D11×C7⋊D7C3×C5semidirect
20. C11×#3861C22×C5semidirect
24. C5×#64424D11direct (N × H)
26. C7⋊D77C2×C3×C5semidirect
27. C11×C7⋊D7C2×C3×C5semidirect
28. C72×D11C2×C3×C5semidirect
33. C5×C7×D11AGL(1,𝔽7)semidirect
34. C5×#3861C2×D11semidirect
37. C72×C11C22×C3×C5semidirect
40. C5×C7⋊D7C3×D11semidirect
45. C5×C7×C11C2×AGL(1,𝔽7)semidirect
52. #64424C5×D11direct (N × H)
53. C5×C72C2×C3×D11semidirect
62. C7×D11C5×AGL(1,𝔽7)semidirect
64. #3861C2×C5×D11semidirect
69. C5×D11#64424direct (N × H)
73. C7⋊D7C3×C5×D11semidirect
75. C7×C11C2×C5×AGL(1,𝔽7)semidirect
83. C5×C11C2×#64424semidirect
84. C72C2×C3×C5×D11semidirect
89. C5×C7D11×AGL(1,𝔽7)semidirect
97. D11C5×#64424direct (N × H)
105. C11C2×C5×#64424semidirect
109. C7C5×D11×AGL(1,𝔽7)semidirect
113. C5D11×#64424direct (N × H)

Maximal subgroups

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

subgroupindex
C5×D11×#38612
C5×C11⋊#644242
C5×C11×#644242
C5×D11×C7⋊D73
D11×#644245
C5×D11×AGL(1,𝔽7)7
C2×C5×#6442411