Finite Group Databasebeta

← C3×C5×C7×C11⋊AGL(1,𝔽5) #37528607

Subgroups — C3×C5×C7×C11⋊AGL(1,𝔽5) #37528607

Order 23100.

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

normal subgroups only

This group has 104 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
1C3×C5×C7×D5×C11C211yesmaximal, characteristic
2C5×C7×C11⋊AGL(1,𝔽5)C311yesmaximal, characteristic, direct product factor, Hall
3C3×C52×C7×C11C411yescharacteristic, complemented, Hall
4C3×C7×C11⋊AGL(1,𝔽5)C511yesmaximal, characteristic, direct product factor
5C3×C5×C7×Dic11—51nomaximal
6C5×C7×D5×C11C2×C311yescharacteristic
7C3×C5×C11⋊AGL(1,𝔽5)C711yesmaximal, characteristic, direct product factor, Hall
8C3×C7×D5×C11C2×C511yescharacteristic
9C2×C3×C5×C7×C11—51no—
10C3×C5×C7×AGL(1,𝔽5)—111nomaximal, Hall
11C52×C7×C11C3×C411yescharacteristic, complemented, Hall
12C3×C5×D5×C11C2×C711yescharacteristic
13C7×C11⋊AGL(1,𝔽5)C3×C511yescharacteristic, direct product factor
14C5×C7×Dic11—51no—
15C3×C5×C7×C11—41no—
16C3×C5×C7×C11C4×C511yescharacteristic, complemented
17C3×C5×C7×C11AGL(1,𝔽5)11yescharacteristic, complemented
18C5×C11⋊AGL(1,𝔽5)C3×C711yescharacteristic, direct product factor, Hall
19C3×C5×C7×D5D1111yescharacteristic
20C3×C7×Dic11—51noHall
21C3×C52×C11C4×C711yescharacteristic, complemented, Hall
22C2×C5×C7×C11—51no—
23C7×D5×C11C2×C3×C511yescharacteristic
24C5×C7×AGL(1,𝔽5)—111noHall
25C3×C11⋊AGL(1,𝔽5)C5×C711yescharacteristic, direct product factor
26C3×C5×Dic11—51no—
27C5×D5×C11C2×C3×C711yescharacteristic
28C3×C52×C7Dic1111yescharacteristic, complemented, Hall
29C2×C3×C7×C11—51no—
30C3×C7×AGL(1,𝔽5)—111no—
31C3×C4×C5×C7—551no—
32C5×C7×C11—41no—
33C5×C7×C11C3×C4×C511yescharacteristic, complemented
34C5×C7×C11C3×AGL(1,𝔽5)11yescharacteristic, complemented
35C5×C7×D5C3×D1111yescharacteristic
36C2×C3×C5×C11—51no—
37C3×D5×C11C2×C5×C711yescharacteristic
38C7×Dic11—51noHall
39C3×C5×AGL(1,𝔽5)—111noHall
40C52×C11C3×C4×C711yescharacteristic, complemented, Hall
41C3×C7×C11C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
42C11⋊AGL(1,𝔽5)C3×C5×C711yescharacteristic, direct product factor
43C5×Dic11—51no—
44C2×C3×C5×C7—51no—
45C3×C7×D5C5×D1111yescharacteristic
46C52×C7C3×Dic1111yescharacteristic, complemented, Hall
47C3×C5×C11—41no—
48C3×C5×C11C4×C5×C711yescharacteristic, complemented
49C3×C5×C11C7×AGL(1,𝔽5)11yescharacteristic, complemented
50C2×C7×C11—51no—
51C3×C5×D5C7×D1111yescharacteristic
52C7×AGL(1,𝔽5)—111no—
53C4×C5×C7—551no—
54C3×Dic11—51noHall
55C2×C5×C11—51no—
56D5×C11C2×C3×C5×C711yescharacteristic
57C3×C5×C7—41no—
58C3×C5×C7C5×Dic1111yescharacteristic, complemented
59C3×C5×C7C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
60C5×AGL(1,𝔽5)—111noHall
61C3×C4×C7—551noHall
62C7×C11C3×C5×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
63C3×C52C7×Dic1111yescharacteristic, complemented, Hall
64C2×C5×C7—51no—
65C7×D5C3×C5×D1111yescharacteristic
66C2×C3×C11—51no—
67C3×AGL(1,𝔽5)—111no—
68C3×C4×C5—551no—
69C5×C11—41no—
70C5×C11C3×C4×C5×C711yescharacteristic, complemented
71C5×C11C3×C7×AGL(1,𝔽5)11yescharacteristic, complemented
72C5×D5C3×C7×D1111yescharacteristic
73Dic11—51noHall
74C2×C3×C7—51no—
75C5×C7—41no—
76C5×C7C3×C5×Dic1111yescharacteristic, complemented
77C5×C7C3×C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
78C3×C11C5×C7×AGL(1,𝔽5)11yescharacteristic, complemented, Hall
79C2×C3×C5—51no—
80C3×D5C5×C7×D1111yescharacteristic
81C4×C7—551noHall
82C52C3×C7×Dic1111yescharacteristic, complemented, Sylow
83C2×C11—51no—
84C3×C7C5×C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Hall
85AGL(1,𝔽5)—111no—
86C4×C5—551no—
87C3×C5—41no—
88C3×C5C5×C7×Dic1111yescharacteristic, complemented
89C3×C5C7×C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
90C2×C7—51no—
91C3×C4—551noHall
92C11C3×C5×C7×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
93C2×C5—51no—
94D5C3×C5×C7×D1111yescharacteristic
95C7C3×C5×C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
96C2×C3—51no—
97C5—41no—
98C5C3×C5×C7×Dic1111yescharacteristic, complemented
99C5C3×C7×C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor
100C4—551noSylow
101C3C5×C7×C11⋊AGL(1,𝔽5)11yescharacteristic, direct product factor, Sylow
102C2—51no—
subgroupG/H
center, hypercenterC3×C5×C7C11⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C5×C7
FrattiniC1G
Fitting, socleC3×C52×C7×C11C4
prime radicalC3×C5×C7×D5×C11C2
cosocleD5×C11C2×C3×C5×C7
LCSG ▷ C5×C11
UCSC1 ◁ C3×C5×C7

Complements

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

NH ≅ G/Ntype
2. C5×C7×C11⋊AGL(1,𝔽5)C3direct (N × H)
3. C3×C52×C7×C11C4semidirect
4. C3×C7×C11⋊AGL(1,𝔽5)C5direct (N × H)
7. C3×C5×C11⋊AGL(1,𝔽5)C7direct (N × H)
11. C52×C7×C11C3×C4semidirect
13. C7×C11⋊AGL(1,𝔽5)C3×C5direct (N × H)
16. C3×C5×C7×C11C4×C5semidirect
17. C3×C5×C7×C11AGL(1,𝔽5)semidirect
18. C5×C11⋊AGL(1,𝔽5)C3×C7direct (N × H)
21. C3×C52×C11C4×C7semidirect
25. C3×C11⋊AGL(1,𝔽5)C5×C7direct (N × H)
28. C3×C52×C7Dic11semidirect
33. C5×C7×C11C3×C4×C5semidirect
34. C5×C7×C11C3×AGL(1,𝔽5)semidirect
40. C52×C11C3×C4×C7semidirect
41. C3×C7×C11C5×AGL(1,𝔽5)semidirect
42. C11⋊AGL(1,𝔽5)C3×C5×C7direct (N × H)
46. C52×C7C3×Dic11semidirect
48. C3×C5×C11C4×C5×C7semidirect
49. C3×C5×C11C7×AGL(1,𝔽5)semidirect
58. C3×C5×C7C5×Dic11semidirect
59. C3×C5×C7C11⋊AGL(1,𝔽5)direct (N × H)
62. C7×C11C3×C5×AGL(1,𝔽5)semidirect
63. C3×C52C7×Dic11semidirect
70. C5×C11C3×C4×C5×C7semidirect
71. C5×C11C3×C7×AGL(1,𝔽5)semidirect
76. C5×C7C3×C5×Dic11semidirect
77. C5×C7C3×C11⋊AGL(1,𝔽5)direct (N × H)
78. C3×C11C5×C7×AGL(1,𝔽5)semidirect
82. C52C3×C7×Dic11semidirect
84. C3×C7C5×C11⋊AGL(1,𝔽5)direct (N × H)
88. C3×C5C5×C7×Dic11semidirect
89. C3×C5C7×C11⋊AGL(1,𝔽5)direct (N × H)
92. C11C3×C5×C7×AGL(1,𝔽5)semidirect
95. C7C3×C5×C11⋊AGL(1,𝔽5)direct (N × H)
98. C5C3×C5×C7×Dic11semidirect
99. C5C3×C7×C11⋊AGL(1,𝔽5)direct (N × H)
101. C3C5×C7×C11⋊AGL(1,𝔽5)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C5×C7×D5×C112
C5×C7×C11⋊AGL(1,𝔽5)3
C3×C7×C11⋊AGL(1,𝔽5)5
C3×C5×C7×Dic115
C3×C5×C11⋊AGL(1,𝔽5)7
C3×C5×C7×AGL(1,𝔽5)11