Finite Group Databasebeta

← C5×C11⋊#10596872 #44568481

Subgroups — C5×C11⋊#10596872 #44568481

Order 32340.

104 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 46 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
1C2×C5×C11×#3862C211yesmaximal, characteristic
2C5×C7×Dic77C311yesmaximal, characteristic, complemented, Hall
3C5×C11×#3862C411yescharacteristic, complemented, Hall
4C11⋊#10596872C511yesmaximal, characteristic, direct product factor, Hall
5C2×C5×C72×C11C2×C311yescharacteristic
6C5×C11⋊(ΓL(1,𝔽8)⋊C4)—71nomaximal
7C5×ΓL(1,𝔽8)×Dic11—71nomaximal
8C2×C11×#3862C2×C511yescharacteristic
9C5×#10596872—111nomaximal, Hall
10C5×C72×C11C3×C411yescharacteristic, complemented, Hall
11C2×C5×C11×ΓL(1,𝔽8)—71no—
12C2×C5×C11×ΓL(1,𝔽8)—71no—
13C7×Dic77C3×C511yescharacteristic, complemented, Hall
14C11×#3862C4×C511yescharacteristic, complemented, Hall
15C5×Dic77ΓL(1,𝔽8)11yescharacteristic, complemented
16C5×C7×Dic11—71no—
17C2×C5×#3862D1111yescharacteristic
18C5×C11×ΓL(1,𝔽8)—71no—
19C5×C11×ΓL(1,𝔽8)—71no—
20C2×C72×C11C2×C3×C511yescharacteristic
21C5×C7×Dic7—111noHall
22C11⋊(ΓL(1,𝔽8)⋊C4)—71no—
23ΓL(1,𝔽8)×Dic11—71no—
24C2×C5×C7×C11—61no—
25C2×C5×C7×C11AGL(1,𝔽7)11yescharacteristic
26C2×C5×C7×C11C2×ΓL(1,𝔽8)11yescharacteristic
27C5×#3862Dic1111yescharacteristic, complemented, Hall
28C3×C5×Dic11—491noHall
29#10596872—111noHall
30C72×C11C3×C4×C511yescharacteristic, complemented, Hall
31C2×C5×C72C3×D1111yescharacteristic
32C2×C11×ΓL(1,𝔽8)—71no—
33C2×C11×ΓL(1,𝔽8)—71no—
34C4×C5×ΓL(1,𝔽8)—771no—
35C5×ΓL(1,𝔽8)⋊C4—771no—
36C5×C7×C11—61no—
37C5×C7×C11ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
38C5×C7×C11C4×ΓL(1,𝔽8)11yescharacteristic, complemented
39C2×C3×C5×C11—491no—
40Dic77C5×ΓL(1,𝔽8)11yescharacteristic, complemented
41C7×Dic11—71no—
42C2×#3862C5×D1111yescharacteristic
43C5×C72C3×Dic1111yescharacteristic, complemented, Hall
44C11×ΓL(1,𝔽8)—71no—
45C11×ΓL(1,𝔽8)—71no—
46C5×Dic11—71noHall
47C2×C5×ΓL(1,𝔽8)—71no—
48C2×C5×ΓL(1,𝔽8)—71no—
49C7×Dic7—111noHall
50C3×C5×C11—491noHall
51C2×C7×C11—61no—
52C2×C7×C11C5×AGL(1,𝔽7)11yescharacteristic
53C2×C7×C11C2×C5×ΓL(1,𝔽8)11yescharacteristic
54#3862C5×Dic1111yescharacteristic, complemented, Hall
55C4×C5×C7—771no—
56C5×Dic7—111no—
57C3×Dic11—491noHall
58C2×C5×C11#6442211yescharacteristic
59C5×ΓL(1,𝔽8)—71no—
60C5×ΓL(1,𝔽8)—71no—
61C2×C72C3×C5×D1111yescharacteristic
62C4×ΓL(1,𝔽8)—771no—
63ΓL(1,𝔽8)⋊C4—771no—
64C7×C11—61no—
65C7×C11C5×ΓL(1,𝔽8)⋊C411yescharacteristic, complemented
66C7×C11C4×C5×ΓL(1,𝔽8)11yescharacteristic, complemented
67C2×C5×C7—61no—
68C2×C5×C7ΓL(1,𝔽8)×D1111yescharacteristic
69C2×C5×C7C11⋊AGL(1,𝔽7)11yescharacteristic
70C2×C3×C11—491no—
71C3×C4×C5—5391noHall
72C5×C11#1059687211yescharacteristic, complemented, Hall
73C72C3×C5×Dic1111yescharacteristic, complemented, Sylow
74Dic11—71noHall
75C2×ΓL(1,𝔽8)—71no—
76C2×ΓL(1,𝔽8)—71no—
77C5×C7—61no—
78C5×C7ΓL(1,𝔽8)×Dic1111yescharacteristic, complemented
79C5×C7C11⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented
80C3×C11—491noHall
81C2×C3×C5—491no—
82C4×C7—771no—
83Dic7—111no—
84C2×C11C5×#6442211yescharacteristic
85ΓL(1,𝔽8)—71no—
86ΓL(1,𝔽8)—71no—
87C4×C5—771noHall
88C3×C5—491noHall
89C2×C7—61no—
90C2×C7C5×ΓL(1,𝔽8)×D1111yescharacteristic
91C2×C7C5×C11⋊AGL(1,𝔽7)11yescharacteristic
92C3×C4—5391noHall
93C11C5×#1059687211yescharacteristic, complemented, Sylow
94C2×C5C11⋊#6442211yescharacteristic
95C7—61no—
96C7C5×ΓL(1,𝔽8)×Dic1111yescharacteristic, complemented
97C7C5×C11⋊(ΓL(1,𝔽8)⋊C4)11yescharacteristic, complemented
98C2×C3—491no—
99C5C11⋊#1059687211yescharacteristic, direct product factor, Sylow
100C4—771noSylow
101C3—491noSylow
102C2C5×C11⋊#6442211yescharacteristic
subgroupG/H
center, hypercenterC2×C5C11⋊#64422
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C5×C11⋊#64422
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C11×#3862C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

Complements

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

NH ≅ G/Ntype
2. C5×C7×Dic77C3semidirect
3. C5×C11×#3862C4semidirect
4. C11⋊#10596872C5direct (N × H)
10. C5×C72×C11C3×C4semidirect
13. C7×Dic77C3×C5semidirect
14. C11×#3862C4×C5semidirect
15. C5×Dic77ΓL(1,𝔽8)semidirect
27. C5×#3862Dic11semidirect
30. C72×C11C3×C4×C5semidirect
37. C5×C7×C11ΓL(1,𝔽8)⋊C4semidirect
38. C5×C7×C11C4×ΓL(1,𝔽8)semidirect
40. Dic77C5×ΓL(1,𝔽8)semidirect
43. C5×C72C3×Dic11semidirect
54. #3862C5×Dic11semidirect
65. C7×C11C5×ΓL(1,𝔽8)⋊C4semidirect
66. C7×C11C4×C5×ΓL(1,𝔽8)semidirect
72. C5×C11#10596872semidirect
73. C72C3×C5×Dic11semidirect
78. C5×C7ΓL(1,𝔽8)×Dic11semidirect
79. C5×C7C11⋊(ΓL(1,𝔽8)⋊C4)semidirect
93. C11C5×#10596872semidirect
96. C7C5×ΓL(1,𝔽8)×Dic11semidirect
97. C7C5×C11⋊(ΓL(1,𝔽8)⋊C4)semidirect
99. C5C11⋊#10596872direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×C11×#38622
C5×C7×Dic773
C11⋊#105968725
C5×C11⋊(ΓL(1,𝔽8)⋊C4)7
C5×ΓL(1,𝔽8)×Dic117
C5×#1059687211