Finite Group Databasebeta

← C5×C13⋊C3×AGL(1,𝔽13) #44477870

Subgroups — C5×C13⋊C3×AGL(1,𝔽13) #44477870

Order 30420.

148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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×C13⋊C3×D13⋊C3C211yesmaximal, characteristic
2C5×C13⋊C3×#261C311yesmaximal, characteristic, complemented
3C5×#14523153C311yesmaximal, characteristic, complemented
4C5×#14523152C311yesmaximal, characteristic, complemented
5C5×C13×AGL(1,𝔽13)C311yesmaximal, characteristic, complemented
6C5×C13⋊C32C411yescharacteristic, complemented, Hall
7C13⋊C3×AGL(1,𝔽13)C511yesmaximal, characteristic, direct product factor, Hall
8C5×D13×C13⋊C3C2×C311yescharacteristic
9C5×#11759818C2×C311yescharacteristic
10C5×#11759817C2×C311yescharacteristic
11C5×C13×D13⋊C3C2×C311yescharacteristic
12C5×C13×#261C3211yescharacteristic, complemented, Hall
13C13⋊C3×D13⋊C3C2×C511yescharacteristic
14C5×#92789C3×C411yescharacteristic, complemented
15C5×#92788C3×C411yescharacteristic, complemented
16C5×C13×C13⋊C3C3×C411yescharacteristic, complemented
17C5×C13×C13⋊C3C3×C411yescharacteristic, complemented
18C3×C5×AGL(1,𝔽13)—131nomaximal
19C3×C4×C5×C13⋊C3—131nomaximal
20C13⋊C3×#261C3×C511yescharacteristic, complemented
21#14523153C3×C511yescharacteristic, complemented
22#14523152C3×C511yescharacteristic, complemented
23C13×AGL(1,𝔽13)C3×C511yescharacteristic, complemented
24C5×C13×D13C2×C3211yescharacteristic
25C13⋊C32C4×C511yescharacteristic, complemented, Hall
26C2×C3×C5×C13⋊C3—131no—
27C3×C5×D13⋊C3—131no—
28D13×C13⋊C3C2×C3×C511yescharacteristic
29#11759818C2×C3×C511yescharacteristic
30#11759817C2×C3×C511yescharacteristic
31C13×D13⋊C3C2×C3×C511yescharacteristic
32C5×C132C32×C411yescharacteristic, complemented, Hall
33C3×C5×#261—131no—
34C5×AGL(1,𝔽13)—131no—
35C5×AGL(1,𝔽13)—131no—
36C5×AGL(1,𝔽13)C13⋊C311yescharacteristic, direct product factor
37C3×C4×C5×C13—131no—
38C4×C5×C13⋊C3—131no—
39C4×C5×C13⋊C3—131no—
40C4×C5×C13⋊C3—391no—
41C13×#261C32×C511yescharacteristic, complemented, Hall
42C3×C5×C13⋊C3—131no—
43C3×C5×C13⋊C3—131no—
44#92789C3×C4×C511yescharacteristic, complemented
45#92788C3×C4×C511yescharacteristic, complemented
46C13×C13⋊C3C3×C4×C511yescharacteristic, complemented
47C13×C13⋊C3C3×C4×C511yescharacteristic, complemented
48C3×AGL(1,𝔽13)—131no—
49C3×C4×C13⋊C3—131no—
50C2×C3×C5×C13—131no—
51C3×C5×D13—131no—
52C2×C5×C13⋊C3—131no—
53C2×C5×C13⋊C3—131no—
54C2×C5×C13⋊C3—391no—
55C5×D13⋊C3—131no—
56C5×D13⋊C3—131no—
57C5×D13⋊C3C2×C13⋊C311yescharacteristic
58C13×D13C2×C32×C511yescharacteristic
59C5×#261C3×C13⋊C311yescharacteristic, complemented
60C4×C5×C13—391no—
61C2×C3×C13⋊C3—131no—
62C3×D13⋊C3—131no—
63C3×C5×C13—131no—
64C3×C5×C13—131no—
65C5×C13⋊C3—131no—
66C5×C13⋊C3—131no—
67C5×C13⋊C3—131no—
68C5×C13⋊C3—131no—
69C5×C13⋊C3—1561no—
70C5×C13⋊C3C4×C13⋊C311yescharacteristic, complemented
71C5×C13⋊C3AGL(1,𝔽13)11yescharacteristic, direct product factor
72C32×C4×C5—1691noHall
73C132C32×C4×C511yescharacteristic, complemented, Sylow
74C3×#261—131no—
75AGL(1,𝔽13)—131no—
76AGL(1,𝔽13)—131no—
77AGL(1,𝔽13)C5×C13⋊C311yescharacteristic, direct product factor
78C3×C4×C13—131no—
79C4×C13⋊C3—131no—
80C4×C13⋊C3—131no—
81C4×C13⋊C3—391no—
82C2×C5×C13—391no—
83C5×D13C2×C3×C13⋊C311yescharacteristic
84C3×C13⋊C3—131no—
85C3×C13⋊C3—131no—
86C2×C32×C5—1691no—
87C2×C3×C13—131no—
88C3×D13—131no—
89C2×C13⋊C3—131no—
90C2×C13⋊C3—131no—
91C2×C13⋊C3—391no—
92D13⋊C3—131no—
93D13⋊C3—131no—
94D13⋊C3C2×C5×C13⋊C311yescharacteristic
95C5×C13—121no—
96C5×C13C3×C4×C13⋊C311yescharacteristic, complemented
97C5×C13C3×AGL(1,𝔽13)11yescharacteristic, complemented
98C3×C4×C5—131no—
99C3×C4×C5—1691no—
100C3×C4×C5—1691no—
101C3×C4×C5—1691no—
102#261C3×C5×C13⋊C311yescharacteristic, complemented
103C4×C13—391no—
104C32×C5—1691noHall
105C3×C13—131no—
106C3×C13—131no—
107C13⋊C3—131no—
108C13⋊C3—131no—
109C13⋊C3—131no—
110C13⋊C3—131no—
111C13⋊C3—1561no—
112C13⋊C3C4×C5×C13⋊C311yescharacteristic, complemented
113C13⋊C3C5×AGL(1,𝔽13)11yescharacteristic, direct product factor
114C32×C4—1691noHall
115C2×C3×C5—131no—
116C2×C3×C5—1691no—
117C2×C3×C5—1691no—
118C2×C3×C5—5071no—
119C2×C13—391no—
120D13C2×C3×C5×C13⋊C311yescharacteristic
121C4×C5—131noHall
122C2×C32—1691no—
123C3×C5—131no—
124C3×C5—131no—
125C3×C5—1691no—
126C3×C5—1691no—
127C13—121no—
128C13C3×C4×C5×C13⋊C311yescharacteristic, complemented
129C13C3×C5×AGL(1,𝔽13)11yescharacteristic, complemented
130C3×C4—131no—
131C3×C4—1691no—
132C3×C4—1691no—
133C3×C4—1691no—
134C2×C5—391no—
135C32—1691noSylow
136C2×C3—131no—
137C2×C3—1691no—
138C2×C3—1691no—
139C2×C3—5071no—
140C5C13⋊C3×AGL(1,𝔽13)11yescharacteristic, direct product factor, Sylow
141C4—131noSylow
142C3—131no—
143C3—131no—
144C3—1691no—
145C3—1691no—
146C2—391no—
subgroupG/H
center, hypercenterC5C13⋊C3×AGL(1,𝔽13)
commutator, hypocenterC132C32×C4×C5
FrattiniC1G
Fitting, socleC5×C132C32×C4
prime radicalC5×C13⋊C3×D13⋊C3C2
cosocleC13×D13C2×C32×C5
LCSG ▷ C132
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
2. C5×C13⋊C3×#261C3semidirect
3. C5×#14523153C3semidirect
4. C5×#14523152C3semidirect
5. C5×C13×AGL(1,𝔽13)C3semidirect
6. C5×C13⋊C32C4semidirect
7. C13⋊C3×AGL(1,𝔽13)C5direct (N × H)
12. C5×C13×#261C32semidirect
14. C5×#92789C3×C4semidirect
15. C5×#92788C3×C4semidirect
16. C5×C13×C13⋊C3C3×C4semidirect
17. C5×C13×C13⋊C3C3×C4semidirect
20. C13⋊C3×#261C3×C5semidirect
21. #14523153C3×C5semidirect
22. #14523152C3×C5semidirect
23. C13×AGL(1,𝔽13)C3×C5semidirect
25. C13⋊C32C4×C5semidirect
32. C5×C132C32×C4semidirect
36. C5×AGL(1,𝔽13)C13⋊C3direct (N × H)
41. C13×#261C32×C5semidirect
44. #92789C3×C4×C5semidirect
45. #92788C3×C4×C5semidirect
46. C13×C13⋊C3C3×C4×C5semidirect
47. C13×C13⋊C3C3×C4×C5semidirect
59. C5×#261C3×C13⋊C3semidirect
70. C5×C13⋊C3C4×C13⋊C3semidirect
71. C5×C13⋊C3AGL(1,𝔽13)direct (N × H)
73. C132C32×C4×C5semidirect
77. AGL(1,𝔽13)C5×C13⋊C3direct (N × H)
96. C5×C13C3×C4×C13⋊C3semidirect
97. C5×C13C3×AGL(1,𝔽13)semidirect
102. #261C3×C5×C13⋊C3semidirect
112. C13⋊C3C4×C5×C13⋊C3semidirect
113. C13⋊C3C5×AGL(1,𝔽13)direct (N × H)
128. C13C3×C4×C5×C13⋊C3semidirect
129. C13C3×C5×AGL(1,𝔽13)semidirect
140. C5C13⋊C3×AGL(1,𝔽13)direct (N × H)

Maximal subgroups

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

subgroupindex
C5×C13⋊C3×D13⋊C32
C5×C13⋊C3×#2613
C5×#145231533
C5×#145231523
C5×C13×AGL(1,𝔽13)3
C13⋊C3×AGL(1,𝔽13)5
C3×C5×AGL(1,𝔽13)13
C3×C4×C5×C13⋊C313