Finite Group Databasebeta

← C5×C11×#64422⋊C2 #44568639

Subgroups — C5×C11×#64422⋊C2 #44568639

Order 32340.

168 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 60 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×C11×#64422C212yesmaximal, complemented
2C5×C11×#64425C211yesmaximal, characteristic, complemented
3C5×C11×D72C311yesmaximal, characteristic, complemented, Hall
4C5×C11×#3862C2211yescharacteristic, complemented, Hall
5C11×#64422⋊C2C511yesmaximal, characteristic, direct product factor, Hall
6C5×C11×C7⋊D7C2×C311yescharacteristic, complemented
7C5×C7×C11×D7C2×C312yescomplemented
8C2×C5×C11×AGL(1,𝔽7)—72nomaximal
9C11×#64422C2×C512yescomplemented
10C11×#64425C2×C511yescharacteristic, complemented
11C5×#64422⋊C2C1111yesmaximal, characteristic, direct product factor, Hall
12C5×C72×C11C22×C311yescharacteristic, complemented, Hall
13C5×C11×AGL(1,𝔽7)—72no—
14C5×C11×AGL(1,𝔽7)—72no—
15C2×C5×C11×ΓL(1,𝔽8)—72no—
16C11×D72C3×C511yescharacteristic, complemented, Hall
17C11×#3862C22×C511yescharacteristic, complemented, Hall
18C2×C5×C11×D7—72no—
19C5×#64422C2×C1112yescomplemented
20C5×#64425C2×C1111yescharacteristic, complemented
21C5×C11×ΓL(1,𝔽8)—72no—
22C11×C7⋊D7C2×C3×C511yescharacteristic, complemented
23C7×C11×D7C2×C3×C512yescomplemented
24C5×D72C3×C1111yescharacteristic, complemented, Hall
25C2×C11×AGL(1,𝔽7)—72no—
26C2×C5×C7×C11—72no—
27C5×C11×D7—72no—
28C5×C11×D7—421no—
29C5×C11×D7AGL(1,𝔽7)12yescomplemented
30C5×#3862C22×C1111yescharacteristic, complemented, Hall
31C22×C3×C5×C11—491noHall
32#64422⋊C2C5×C1111yescharacteristic, direct product factor, Hall
33C72×C11C22×C3×C511yescharacteristic, complemented, Hall
34C5×C7⋊D7C2×C3×C1111yescharacteristic, complemented
35C5×C7×D7C2×C3×C1112yescomplemented
36C2×C11×ΓL(1,𝔽8)—72no—
37C11×AGL(1,𝔽7)—72no—
38C11×AGL(1,𝔽7)—72no—
39C2×C5×AGL(1,𝔽7)—72no—
40C5×C7×C11—61no—
41C5×C7×C11C2×AGL(1,𝔽7)12yescomplemented
42C2×C3×C5×C11—492no—
43C2×C3×C5×C11—491no—
44C2×C11×D7—72no—
45#64425C2×C5×C1111yescharacteristic, complemented
46#64422C2×C5×C1112yescomplemented
47C5×C72C22×C3×C1111yescharacteristic, complemented, Hall
48C11×ΓL(1,𝔽8)—72no—
49C22×C5×C11—491noHall
50C2×C5×ΓL(1,𝔽8)—72no—
51C5×AGL(1,𝔽7)—72no—
52C5×AGL(1,𝔽7)—72no—
53D72C3×C5×C1111yescharacteristic, complemented, Hall
54C3×C5×C11—491noHall
55C2×C7×C11—72no—
56C11×D7—72no—
57C11×D7—421no—
58C11×D7C5×AGL(1,𝔽7)12yescomplemented
59#3862C22×C5×C1111yescharacteristic, complemented, Hall
60C2×C5×D7—72no—
61C22×C3×C11—491noHall
62C2×C5×C11—72no—
63C2×C5×C11—491no—
64C5×ΓL(1,𝔽8)—72no—
65C7⋊D7C2×C3×C5×C1111yescharacteristic, complemented
66C7×D7C2×C3×C5×C1112yescomplemented
67C2×AGL(1,𝔽7)—72no—
68C7×C11—61no—
69C7×C11C2×C5×AGL(1,𝔽7)12yescomplemented
70C2×C5×C7—72no—
71C5×D7—72no—
72C5×D7—421no—
73C5×D7C11×AGL(1,𝔽7)12yescomplemented
74C2×C3×C11—492no—
75C2×C3×C11—491no—
76C22×C3×C5—491noHall
77C5×C11#64422⋊C211yescharacteristic, direct product factor, Hall
78C72C22×C3×C5×C1111yescharacteristic, complemented, Sylow
79C22×C11—491noHall
80C2×ΓL(1,𝔽8)—72no—
81AGL(1,𝔽7)—72no—
82AGL(1,𝔽7)—72no—
83C5×C7—61no—
84C5×C7C2×C11×AGL(1,𝔽7)12yescomplemented
85C3×C11—491noHall
86C2×C3×C5—492no—
87C2×C3×C5—491no—
88C2×D7—72no—
89C2×C11—72no—
90C2×C11—491no—
91ΓL(1,𝔽8)—72no—
92C22×C5—491noHall
93C3×C5—491noHall
94C2×C7—72no—
95D7—72no—
96D7—421no—
97D7C5×C11×AGL(1,𝔽7)12yescomplemented
98C22×C3—491noHall
99C11C5×#64422⋊C211yescharacteristic, direct product factor, Sylow
100C2×C5—72no—
101C2×C5—491no—
102C7—61no—
103C7C2×C5×C11×AGL(1,𝔽7)12yescomplemented
104C2×C3—492no—
105C2×C3—491no—
106C5C11×#64422⋊C211yescharacteristic, direct product factor, Sylow
107C22—491noSylow
108C3—491noSylow
109C2—72no—
110C2—491no—
subgroupG/H
center, hypercenterC5×C11#64422⋊C2
commutator, cosocle, hypocenterC72C22×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C22×C3
LCSG ▷ C72
UCSC1 ◁ C5×C11

Complements

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

NH ≅ G/Ntype
1. C5×C11×#64422C2semidirect
2. C5×C11×#64425C2semidirect
3. C5×C11×D72C3semidirect
4. C5×C11×#3862C22semidirect
5. C11×#64422⋊C2C5direct (N × H)
6. C5×C11×C7⋊D7C2×C3semidirect
7. C5×C7×C11×D7C2×C3semidirect
9. C11×#64422C2×C5semidirect
10. C11×#64425C2×C5semidirect
11. C5×#64422⋊C2C11direct (N × H)
12. C5×C72×C11C22×C3semidirect
16. C11×D72C3×C5semidirect
17. C11×#3862C22×C5semidirect
19. C5×#64422C2×C11semidirect
20. C5×#64425C2×C11semidirect
22. C11×C7⋊D7C2×C3×C5semidirect
23. C7×C11×D7C2×C3×C5semidirect
24. C5×D72C3×C11semidirect
29. C5×C11×D7AGL(1,𝔽7)semidirect
30. C5×#3862C22×C11semidirect
32. #64422⋊C2C5×C11direct (N × H)
33. C72×C11C22×C3×C5semidirect
34. C5×C7⋊D7C2×C3×C11semidirect
35. C5×C7×D7C2×C3×C11semidirect
41. C5×C7×C11C2×AGL(1,𝔽7)semidirect
45. #64425C2×C5×C11semidirect
46. #64422C2×C5×C11semidirect
47. C5×C72C22×C3×C11semidirect
53. D72C3×C5×C11semidirect
58. C11×D7C5×AGL(1,𝔽7)semidirect
59. #3862C22×C5×C11semidirect
65. C7⋊D7C2×C3×C5×C11semidirect
66. C7×D7C2×C3×C5×C11semidirect
69. C7×C11C2×C5×AGL(1,𝔽7)semidirect
73. C5×D7C11×AGL(1,𝔽7)semidirect
77. C5×C11#64422⋊C2direct (N × H)
78. C72C22×C3×C5×C11semidirect
84. C5×C7C2×C11×AGL(1,𝔽7)semidirect
97. D7C5×C11×AGL(1,𝔽7)semidirect
99. C11C5×#64422⋊C2direct (N × H)
103. C7C2×C5×C11×AGL(1,𝔽7)semidirect
106. C5C11×#64422⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C11×#644222
C5×C11×#644252
C5×C11×D723
C11×#64422⋊C25
C2×C5×C11×AGL(1,𝔽7)7
C5×#64422⋊C211