Finite Group Databasebeta

← C11⋊C5×#1020 #72222580

Subgroups — C11⋊C5×#1020 #72222580

Order 5280.

224 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 21 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
1C22⋊A4×C11⋊C5C211yesmaximal, characteristic, complemented
2#120×C11⋊C5—31nomaximal, Hall
3S4×C11⋊C5—43nomaximal
4C11×#1020C511yesmaximal, characteristic, complemented, Hall
5C24×C11⋊C5D311yescharacteristic, complemented
6C2×D4×C11⋊C5—33no—
7C22⋊C4×C11⋊C5—33no—
8A4×C11⋊C5—43no—
9A4×C11⋊C5—81no—
10C11×C22⋊A4C2×C511yescharacteristic, complemented
11C5×#1020—111nomaximal, Hall
12C23×C11⋊C5—33no—
13C23×C11⋊C5—31no—
14C23×C11⋊C5—61no—
15D4×C11⋊C5—63no—
16D4×C11⋊C5—63no—
17C2×C4×C11⋊C5—33no—
18C11×#120—31noHall
19D3×C11⋊C5—161no—
20C11×S4—43no—
21C5×C22⋊A4—111no—
22C22×C11⋊C5—21no—
23C22×C11⋊C5—31no—
24C22×C11⋊C5—33no—
25C22×C11⋊C5—63no—
26C22×C11⋊C5—63no—
27C22×C11⋊C5S413yescomplemented
28C4×C11⋊C5—63no—
29C24×C11C5×D311yescharacteristic, complemented
30C2×D4×C11—33no—
31C11×C22⋊C4—33no—
32C3×C11⋊C5—161noHall
33C5×#120—331noHall
34C11×A4—43no—
35C11×A4—81no—
36C5×S4—443no—
37C2×C11⋊C5—33no—
38C2×C11⋊C5—61no—
39C2×C11⋊C5—121no—
40#1020C11⋊C511yescharacteristic, direct product factor, Hall
41C23×C11—33no—
42C23×C11—31no—
43C23×C11—61no—
44D4×C11—63no—
45D4×C11—63no—
46C2×C4×C11—33no—
47C24×C5—111no—
48C2×C5×D4—333no—
49C5×C22⋊C4—333no—
50D3×C11—161no—
51C5×A4—443no—
52C5×A4—881no—
53C11⋊C5#102011yescharacteristic, direct product factor, Hall
54C22⋊A4C2×C11⋊C511yescharacteristic, complemented
55C22×C11—21no—
56C22×C11—31no—
57C22×C11—33no—
58C22×C11—63no—
59C22×C11—63no—
60C22×C11C5×S413yescomplemented
61C4×C11—63no—
62C23×C5—333no—
63C23×C5—331no—
64C23×C5—661no—
65C5×D4—663no—
66C5×D4—663no—
67C2×C4×C5—333no—
68C3×C11—161noHall
69#120—31noSylow
70C5×D3—1761no—
71S4—43no—
72C2×C11—33no—
73C2×C11—61no—
74C2×C11—121no—
75C22×C5—113no—
76C22×C5—221no—
77C22×C5—331no—
78C22×C5—333no—
79C22×C5—663no—
80C22×C5—663no—
81C4×C5—663no—
82C24D3×C11⋊C511yescharacteristic, complemented
83C2×D4—33no—
84C22⋊C4—33no—
85C3×C5—1761noHall
86A4—43no—
87A4—81no—
88C11C5×#102011yescharacteristic, complemented, Sylow
89C2×C5—333no—
90C2×C5—661no—
91C2×C5—1321no—
92C23—33no—
93C23—31no—
94C23—61no—
95D4—63no—
96D4—63no—
97C2×C4—33no—
98D3—161no—
99C5—111noSylow
100C22—21no—
101C22—31no—
102C22—33no—
103C22—63no—
104C22—63no—
105C22S4×C11⋊C513yescomplemented
106C4—63no—
107C3—161noSylow
108C2—33no—
109C2—61no—
110C2—121no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocle, hypocenterC11×C22⋊A4C2×C5
Fitting, socleC24×C11C5×D3
LCSG ▷ C11×C22⋊A4
UCSC1

Complements

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

NH ≅ G/Ntype
1. C22⋊A4×C11⋊C5C2semidirect
4. C11×#1020C5semidirect
5. C24×C11⋊C5D3semidirect
10. C11×C22⋊A4C2×C5semidirect
27. C22×C11⋊C5S4semidirect
29. C24×C11C5×D3semidirect
40. #1020C11⋊C5direct (N × H)
53. C11⋊C5#1020direct (N × H)
54. C22⋊A4C2×C11⋊C5semidirect
60. C22×C11C5×S4semidirect
82. C24D3×C11⋊C5semidirect
88. C11C5×#1020semidirect
105. C22S4×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C22⋊A4×C11⋊C52
#120×C11⋊C53
S4×C11⋊C54
C11×#10205
C5×#102011