Finite Group Databasebeta

← C3×C7×(C11⋊C5)⋊Dic5 #37528340

Subgroups — C3×C7×(C11⋊C5)⋊Dic5 #37528340

Order 23100.

128 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 128 conjugacy classes of subgroups — too many to draw. Only its 56 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×C3×C5×C7×C11⋊C5C211yesmaximal, characteristic
2C7×(C11⋊C5)⋊Dic5C311yesmaximal, characteristic, direct product factor, Hall
3C3×C5×C7×C11⋊C5C411yescharacteristic, complemented, Hall
4C3×C7×Dic11⋊C5—51nomaximal
5C3×C7×Dic55C511yesmaximal, characteristic, complemented
6C2×C5×C7×C11⋊C5C2×C311yescharacteristic
7C3×(C11⋊C5)⋊Dic5C711yesmaximal, characteristic, direct product factor, Hall
8C2×C3×C7×C11⋊C5—22no—
9C2×C3×C7×C11⋊C5D511yescharacteristic
10C2×C3×C5×C7×C11C2×C511yescharacteristic
11C3×C5×C7×Dic5—111nomaximal, Hall
12C5×C7×C11⋊C5C3×C411yescharacteristic, complemented, Hall
13C2×C3×C5×C11⋊C5C2×C711yescharacteristic
14C7×Dic55C3×C511yescharacteristic, complemented
15C7×Dic11⋊C5—51no—
16C3×C5×C7×C11C4×C511yescharacteristic, complemented
17C3×C7×C11⋊C5—22no—
18C3×C7×C11⋊C5Dic511yescharacteristic, complemented
19(C11⋊C5)⋊Dic5C3×C711yescharacteristic, direct product factor, Hall
20C2×C3×C52×C7—111no—
21C3×C7×Dic11—51noHall
22C3×C5×C11⋊C5C4×C711yescharacteristic, complemented, Hall
23C2×C5×C7×C11C2×C3×C511yescharacteristic
24C2×C7×C11⋊C5—22no—
25C2×C7×C11⋊C5C3×D511yescharacteristic
26C5×C7×Dic5—111noHall
27C3×Dic55C5×C711yescharacteristic, complemented
28C3×Dic11⋊C5—51no—
29C2×C5×C11⋊C5C2×C3×C711yescharacteristic
30C3×C52×C7—111noHall
31C2×C3×C7×C11C5×D511yescharacteristic
32C3×C4×C5×C7—551no—
33C3×C7×Dic5—111no—
34C5×C7×C11C3×C4×C511yescharacteristic, complemented
35C7×C11⋊C5—22no—
36C7×C11⋊C5C3×Dic511yescharacteristic, complemented
37C2×C52×C7—111no—
38C2×C3×C5×C11C2×C5×C711yescharacteristic
39C2×C3×C11⋊C5—22no—
40C2×C3×C11⋊C5C7×D511yescharacteristic
41C7×Dic11—51noHall
42C3×C5×Dic5—111noHall
43C5×C11⋊C5C3×C4×C711yescharacteristic, complemented, Hall
44C3×C7×C11C5×Dic511yescharacteristic, complemented, Hall
45Dic55C3×C5×C711yescharacteristic, complemented
46Dic11⋊C5—51no—
47C2×C3×C5×C7—111no—
48C2×C3×C5×C7—222no—
49C2×C3×C5×C7AGL(1,𝔽11)11yescharacteristic
50C52×C7—111noHall
51C3×C5×C11C4×C5×C711yescharacteristic, complemented
52C3×C11⋊C5—22no—
53C3×C11⋊C5C7×Dic511yescharacteristic, complemented
54C2×C7×C11C3×C5×D511yescharacteristic
55C2×C3×C52—111no—
56C4×C5×C7—551no—
57C7×Dic5—111no—
58C3×Dic11—51noHall
59C2×C5×C11C2×C3×C5×C711yescharacteristic
60C2×C11⋊C5—22no—
61C2×C11⋊C5C3×C7×D511yescharacteristic
62C3×C5×C7—111no—
63C3×C5×C7—222no—
64C3×C5×C7Dic11⋊C511yescharacteristic, complemented
65C5×Dic5—111noHall
66C3×C4×C7—551noHall
67C7×C11C3×C5×Dic511yescharacteristic, complemented, Hall
68C3×C52—111noHall
69C2×C5×C7—111no—
70C2×C5×C7—222no—
71C2×C5×C7C3×AGL(1,𝔽11)11yescharacteristic
72C2×C3×C11C5×C7×D511yescharacteristic
73C3×C4×C5—551no—
74C3×Dic5—111no—
75C5×C11C3×C4×C5×C711yescharacteristic, complemented
76C11⋊C5—22no—
77C11⋊C5C3×C7×Dic511yescharacteristic, complemented
78C2×C52—111no—
79Dic11—51noHall
80C2×C3×C7C5⋊AGL(1,𝔽11)11yescharacteristic
81C5×C7—111no—
82C5×C7—222no—
83C5×C7C3×Dic11⋊C511yescharacteristic, complemented
84C3×C11C5×C7×Dic511yescharacteristic, complemented, Hall
85C2×C3×C5—111no—
86C2×C3×C5—222no—
87C2×C3×C5C7×AGL(1,𝔽11)11yescharacteristic
88C4×C7—551noHall
89C52—111noSylow
90C2×C11C3×C5×C7×D511yescharacteristic
91C3×C7(C11⋊C5)⋊Dic511yescharacteristic, direct product factor, Hall
92C4×C5—551no—
93Dic5—111no—
94C3×C5—111no—
95C3×C5—222no—
96C3×C5C7×Dic11⋊C511yescharacteristic, complemented
97C2×C7C3×C5⋊AGL(1,𝔽11)11yescharacteristic
98C3×C4—551noHall
99C11C3×C5×C7×Dic511yescharacteristic, complemented, Sylow
100C2×C5—111no—
101C2×C5—222no—
102C2×C5C3×C7×AGL(1,𝔽11)11yescharacteristic
103C7C3×(C11⋊C5)⋊Dic511yescharacteristic, direct product factor, Sylow
104C2×C3C7×C5⋊AGL(1,𝔽11)11yescharacteristic
105C5—111no—
106C5—222no—
107C5C3×C7×Dic11⋊C511yescharacteristic, complemented
108C4—551noSylow
109C3C7×(C11⋊C5)⋊Dic511yescharacteristic, direct product factor, Sylow
110C2C3×C7×C5⋊AGL(1,𝔽11)11yescharacteristic
subgroupG/H
center, hypercenterC2×C3×C7C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C3×C4×C5×C7
FrattiniC2C3×C7×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C5×C11C2×C3×C5×C7
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3×C7

Complements

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

NH ≅ G/Ntype
2. C7×(C11⋊C5)⋊Dic5C3direct (N × H)
3. C3×C5×C7×C11⋊C5C4semidirect
5. C3×C7×Dic55C5semidirect
7. C3×(C11⋊C5)⋊Dic5C7direct (N × H)
12. C5×C7×C11⋊C5C3×C4semidirect
14. C7×Dic55C3×C5semidirect
16. C3×C5×C7×C11C4×C5semidirect
18. C3×C7×C11⋊C5Dic5semidirect
19. (C11⋊C5)⋊Dic5C3×C7direct (N × H)
22. C3×C5×C11⋊C5C4×C7semidirect
27. C3×Dic55C5×C7semidirect
34. C5×C7×C11C3×C4×C5semidirect
36. C7×C11⋊C5C3×Dic5semidirect
43. C5×C11⋊C5C3×C4×C7semidirect
44. C3×C7×C11C5×Dic5semidirect
45. Dic55C3×C5×C7semidirect
51. C3×C5×C11C4×C5×C7semidirect
53. C3×C11⋊C5C7×Dic5semidirect
64. C3×C5×C7Dic11⋊C5semidirect
67. C7×C11C3×C5×Dic5semidirect
75. C5×C11C3×C4×C5×C7semidirect
77. C11⋊C5C3×C7×Dic5semidirect
83. C5×C7C3×Dic11⋊C5semidirect
84. C3×C11C5×C7×Dic5semidirect
91. C3×C7(C11⋊C5)⋊Dic5direct (N × H)
96. C3×C5C7×Dic11⋊C5semidirect
99. C11C3×C5×C7×Dic5semidirect
103. C7C3×(C11⋊C5)⋊Dic5direct (N × H)
107. C5C3×C7×Dic11⋊C5semidirect
109. C3C7×(C11⋊C5)⋊Dic5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×C7×C11⋊C52
C7×(C11⋊C5)⋊Dic53
C3×C7×Dic11⋊C55
C3×C7×Dic555
C3×(C11⋊C5)⋊Dic57
C3×C5×C7×Dic511