Finite Group Databasebeta

← #1043×AGL(1,𝔽13) #72246825

Subgroups — #1043×AGL(1,𝔽13) #72246825

Order 15600.

480 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 82 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
1#72246824C211yesmaximal, characteristic
2C5⋊D5×AGL(1,𝔽13)C211yesmaximal, characteristic
3D13⋊C3×#1043C211yesmaximal, characteristic
4#261×#1043C311yesmaximal, characteristic, complemented, Hall
5#72246794C2×C311yescharacteristic
6C5⋊D5×#261C2×C311yescharacteristic
7D13×#1043C2×C311yescharacteristic
8AGL(1,𝔽5)×AGL(1,𝔽13)—56nomaximal
9C5⋊D5×D13⋊C3C2211yescharacteristic
10#16839092C411yescharacteristic, complemented
11C13⋊C3×#1043C411yescharacteristic, complemented
12#16839083C411yescharacteristic, complemented
13#16839082C411yescharacteristic, complemented
14#16839081C411yescharacteristic, complemented
15C52×AGL(1,𝔽13)C411yescharacteristic, complemented
16C5⋊(C5⋊(D13⋊C3))C2×C411yescharacteristic
17C13⋊C3×C5⋊D5C2×C411yescharacteristic
18C52×D13⋊C3C2×C411yescharacteristic
19D5×AGL(1,𝔽13)—56no—
20AGL(1,𝔽5)×D13⋊C3—56no—
21D5⋊AGL(1,𝔽13)—56no—
22D13×C5⋊D5C22×C311yescharacteristic
23#13049937C3×C411yescharacteristic, complemented
24#13049929C3×C411yescharacteristic, complemented
25#13049928C3×C411yescharacteristic, complemented
26#13049927C3×C411yescharacteristic, complemented
27C13×#1043C3×C411yescharacteristic, complemented
28C52×#261C3×C411yescharacteristic, complemented
29C3×C4×#1043—131nomaximal, Hall
30AGL(1,𝔽5)×#261—56no—
31C52×C13⋊C3C4211yescharacteristic, complemented, Hall
32D5×D13⋊C3—56no—
33#63118⋊C3—56no—
34#63120⋊C3—56no—
35#63121⋊C3—56no—
36#63122⋊C3—56no—
37AGL(1,𝔽5)×C13⋊C3—56no—
38C5×AGL(1,𝔽13)AGL(1,𝔽5)16yescomplemented
39C5⋊D65C2×C3×C411yescharacteristic
40C13×C5⋊D5C2×C3×C411yescharacteristic
41C52×D13C2×C3×C411yescharacteristic
42C4×AGL(1,𝔽13)—251noHall
43C2×C3×#1043—131no—
44C2×C3×#1043—131no—
45C3×C4×C5⋊D5—131no—
46D5×#261—56no—
47AGL(1,𝔽5)×D13—56no—
48D5⋊#261—56no—
49C4×#1043—131noHall
50C5⋊(D13⋊C3)—56no—
51D5×C13⋊C3—56no—
52C5×D13⋊C3C2×AGL(1,𝔽5)16yes—
53C52×C13C3×C4211yescharacteristic, complemented, Hall
54C2×AGL(1,𝔽13)—251no—
55C2×AGL(1,𝔽13)—251no—
56C4×D13⋊C3—251no—
57C2×C3×C5⋊D5—131no—
58C3×#1043—131no—
59C3×#1043—131no—
60C3×#1043—131no—
61C3×#1043—521no—
62C3×C4×C52—131no—
63C3×#1039—131no—
64D5×D13—56no—
65#63122—56no—
66#63121—56no—
67#63120—56no—
68C13×AGL(1,𝔽5)—56no—
69#63118—56no—
70C5×#261C3×AGL(1,𝔽5)16yescomplemented
71C3×C4×AGL(1,𝔽5)—656no—
72C4×#261—251noHall
73C2×#1043—131no—
74C2×#1043—131no—
75C4×C5⋊D5—131no—
76C5×C13⋊C3C4×AGL(1,𝔽5)16yescomplemented
77C2×D13⋊C3—251no—
78AGL(1,𝔽13)—251no—
79AGL(1,𝔽13)—251no—
80AGL(1,𝔽13)—251no—
81AGL(1,𝔽13)#104311yescharacteristic, direct product factor
82C4×C13⋊C3—251no—
83Dic13⋊C3—251no—
84C2×C3×C52—131no—
85C3×C5⋊D5—131no—
86C3×C5⋊D5—521no—
87D65—56no—
88C5×D13C2×C3×AGL(1,𝔽5)16yes—
89D5×C13—56no—
90C2×C3×AGL(1,𝔽5)—656no—
91C2×C3×AGL(1,𝔽5)—656no—
92C3×C4×D5—656no—
93C2×#261—251no—
94C2×#261—251no—
95C4×D13—251no—
96C2×C5⋊D5—131no—
97#1043—131no—
98#1043—131no—
99#1043—131no—
100#1043AGL(1,𝔽13)11yescharacteristic, direct product factor
101C4×C52—131no—
102#1039—131no—
103C4×AGL(1,𝔽5)—656no—
104C2×C13⋊C3—251no—
105D13⋊C3—251no—
106D13⋊C3C2×#104311yescharacteristic
107C3×C52—521noHall
108C5×C13C3×C4×AGL(1,𝔽5)16yescomplemented
109C2×C3×D5—656no—
110C3×AGL(1,𝔽5)—2606no—
111C3×AGL(1,𝔽5)—656no—
112C3×AGL(1,𝔽5)—656no—
113C3×AGL(1,𝔽5)—656no—
114C3×C4×C5—136no—
115C3×Dic5—656no—
116C2×D13—251no—
117#261—251no—
118#261—251no—
119#261—251no—
120#261C3×#104311yescharacteristic, complemented
121C4×C13—251no—
122Dic13—251no—
123C2×C52—131no—
124C5⋊D5—131no—
125C5⋊D5C2×AGL(1,𝔽13)11yescharacteristic
126C3×C42—3251noHall
127C2×AGL(1,𝔽5)—656no—
128C2×AGL(1,𝔽5)—656no—
129C4×D5—656no—
130C13⋊C3C4×#104311yescharacteristic, complemented, Hall
131C2×C3×C5—136no—
132C3×D5—2606no—
133C3×D5—656no—
134C2×C13—251no—
135D13—251no—
136D13C2×C3×#104311yescharacteristic
137C52C4×AGL(1,𝔽13)11yescharacteristic, complemented, Sylow
138C2×C3×C4—3251no—
139C2×C3×C4—3251no—
140C2×C3×C4—3251no—
141C2×D5—656no—
142AGL(1,𝔽5)—56no—
143AGL(1,𝔽5)—656no—
144AGL(1,𝔽5)—656no—
145AGL(1,𝔽5)—656no—
146C4×C5—136no—
147Dic5—656no—
148C42—3251noSylow
149C3×C5—526no—
150C13C3×C4×#104311yescharacteristic, complemented, Sylow
151C22×C3—3251no—
152C3×C4—131no—
153C3×C4—13001no—
154C3×C4—3251no—
155C3×C4—3251no—
156C3×C4—3251no—
157C3×C4—3251no—
158C2×C5—136no—
159D5—56no—
160D5—656no—
161C2×C4—3251no—
162C2×C4—3251no—
163C2×C4—3251no—
164C2×C3—131no—
165C2×C3—13001no—
166C2×C3—3251no—
167C5AGL(1,𝔽5)×AGL(1,𝔽13)16yescomplemented
168C22—3251no—
169C4—131no—
170C4—251no—
171C4—3251no—
172C4—3251no—
173C4—3251no—
174C4—3251no—
175C3—521noSylow
176C2—131no—
177C2—251no—
178C2—3251no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC52×C13C3×C42
prime radicalC5⋊D5×D13⋊C3C22
cosocleD13×C5⋊D5C22×C3
LCSG ▷ C52×C13
UCSC1

Complements

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

NH ≅ G/Ntype
4. #261×#1043C3semidirect
10. #16839092C4semidirect
11. C13⋊C3×#1043C4semidirect
12. #16839083C4semidirect
13. #16839082C4semidirect
14. #16839081C4semidirect
15. C52×AGL(1,𝔽13)C4semidirect
23. #13049937C3×C4semidirect
24. #13049929C3×C4semidirect
25. #13049928C3×C4semidirect
26. #13049927C3×C4semidirect
27. C13×#1043C3×C4semidirect
28. C52×#261C3×C4semidirect
31. C52×C13⋊C3C42semidirect
38. C5×AGL(1,𝔽13)AGL(1,𝔽5)semidirect
53. C52×C13C3×C42semidirect
70. C5×#261C3×AGL(1,𝔽5)semidirect
76. C5×C13⋊C3C4×AGL(1,𝔽5)semidirect
81. AGL(1,𝔽13)#1043direct (N × H)
100. #1043AGL(1,𝔽13)direct (N × H)
108. C5×C13C3×C4×AGL(1,𝔽5)semidirect
120. #261C3×#1043semidirect
130. C13⋊C3C4×#1043semidirect
137. C52C4×AGL(1,𝔽13)semidirect
150. C13C3×C4×#1043semidirect
167. C5AGL(1,𝔽5)×AGL(1,𝔽13)semidirect

Maximal subgroups

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

subgroupindex
#722468242
C5⋊D5×AGL(1,𝔽13)2
D13⋊C3×#10432
#261×#10433
AGL(1,𝔽5)×AGL(1,𝔽13)5
C3×C4×#104313