Finite Group Databasebeta

← C13×#10624750 #23744901

Subgroups — C13×#10624750 #23744901

Order 9477.

414 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C13×3−1+4C311yesmaximal, characteristic, complemented
2C13×#6912C311yesmaximal, characteristic, complemented
3C13×#6912C311yesmaximal, characteristic, complemented
4C13×#6912C311yesmaximal, characteristic, complemented
5C13×#6910C311yesmaximal, characteristic, complemented
6C13×#6910C311yesmaximal, characteristic, complemented
7C13×#6909C311yesmaximal, characteristic, complemented
8C13×#6909C311yesmaximal, characteristic, complemented
9C13×#6909C311yesmaximal, characteristic, complemented
10C3×C13×#733C311yesmaximal, characteristic, complemented
11C3×C13×#731C311yesmaximal, characteristic, complemented
12C13×#6893C311yesmaximal, characteristic, complemented
13C13×#6893C311yesmaximal, characteristic, complemented
14C13×#737—33no—
15C13×#737—33no—
16C13×#737—33no—
17C3×C13×3−1+2—33no—
18C3×C13×3−1+2C3211yescharacteristic
19C3×C13×3−1+2C3211yescharacteristic
20C3×C13×3−1+2C3211yescharacteristic
21C3×C13×3−1+2C3211yescharacteristic
22C3×C13×3−1+2C3211yescharacteristic
23C3×C13×3−1+2C3211yescharacteristic
24C3×C13×3−1+2C3211yescharacteristic
25C3×C13×3−1+2C3211yescharacteristic
26C3×C13×3−1+2C3211yescharacteristic
27C3×C13×H(3,𝔽3)C3211yescharacteristic
28C3×C13×H(3,𝔽3)C3211yescharacteristic
29C3×C13×H(3,𝔽3)C3211yescharacteristic
30C32×C9×C13C3211yescharacteristic
31C13×#733—33no—
32C13×#733—33no—
33C13×#733—33no—
34C13×#733—33no—
35C13×#731—33no—
36C13×#731—33no—
37C13×#731—33no—
38C13×AΣL(1,𝔽27)—33no—
39C13×AΣL(1,𝔽27)—33no—
40C13×AΣL(1,𝔽27)—33no—
41C13×C32⋊C9—33no—
42C13×C32⋊C9—33no—
43#10624750C1311yesmaximal, characteristic, direct product factor, Sylow
44C33×C13—31no—
45C33×C13—31no—
46C33×C13H(3,𝔽3)13yes—
47C33×C13C3311yescharacteristic
48C13×3−1+2—318no—
49C13×3−1+2—31no—
50C13×3−1+2—31no—
51C13×3−1+2—31no—
52C13×3−1+2—31no—
53C13×3−1+2—31no—
54C13×3−1+2—31no—
55C13×3−1+2—31no—
56C13×3−1+2—31no—
57C13×3−1+2—31no—
58C13×3−1+2—31no—
59C13×3−1+2—31no—
60C13×3−1+2—31no—
61C13×3−1+2—31no—
62C13×3−1+2—31no—
63C13×3−1+2—31no—
64C13×3−1+2—31no—
65C13×3−1+2—31no—
66C13×3−1+2—31no—
67C13×3−1+2—31no—
68C13×3−1+2—31no—
69C13×3−1+2—31no—
70C13×3−1+2—31no—
71C13×3−1+2—31no—
72C13×3−1+2—31no—
73C13×3−1+2—31no—
74C13×3−1+2H(3,𝔽3)13yes—
75C13×3−1+2H(3,𝔽3)13yes—
76C13×H(3,𝔽3)—31no—
77C13×H(3,𝔽3)—31no—
78C13×H(3,𝔽3)—31no—
79C13×H(3,𝔽3)—31no—
80C13×H(3,𝔽3)—31no—
81C13×H(3,𝔽3)—31no—
82C13×H(3,𝔽3)—31no—
83C13×H(3,𝔽3)—31no—
84C13×H(3,𝔽3)—31no—
85C3×C9×C13—39no—
86C3×C9×C13—31no—
87C3×C9×C13—31no—
88C3×C9×C13—31no—
89C3×C9×C13—31no—
90C3×C9×C13—31no—
91C3×C9×C13—31no—
92C3×C9×C13—31no—
93C3×C9×C13—31no—
94C3×C9×C13—31no—
95C3×C9×C13—31no—
96C3×C9×C13—31no—
97C3×C9×C13—31no—
98C3×C9×C13H(3,𝔽3)13yes—
993−1+4C3×C1311yescharacteristic, complemented
100#6912C3×C1311yescharacteristic, complemented
101#6912C3×C1311yescharacteristic, complemented
102#6912C3×C1311yescharacteristic, complemented
103#6910C3×C1311yescharacteristic, complemented
104#6910C3×C1311yescharacteristic, complemented
105#6909C3×C1311yescharacteristic, complemented
106#6909C3×C1311yescharacteristic, complemented
107#6909C3×C1311yescharacteristic, complemented
108C3×#733C3×C1311yescharacteristic, complemented
109C3×#731C3×C1311yescharacteristic, complemented
110#6893C3×C1311yescharacteristic, complemented
111#6893C3×C1311yescharacteristic, complemented
112C32×C13—33no—
113C32×C13—91no—
114C32×C13—93no—
115C32×C13—93no—
116C32×C13—91no—
117C32×C13—91no—
118C32×C13—271no—
119C32×C13C3×H(3,𝔽3)11yescharacteristic
120C32×C13C3×H(3,𝔽3)11yescharacteristic
121C32×C13C3×H(3,𝔽3)11yescharacteristic
122C32×C13C3×H(3,𝔽3)11yescharacteristic
123C9×C13—33no—
124C9×C13—33no—
125C9×C13—33no—
126C9×C13—91no—
127C9×C13—91no—
128C9×C13—91no—
129C9×C13—91no—
130C9×C13—91no—
131C9×C13—91no—
132C9×C13—91no—
133#737—33no—
134#737—33no—
135#737—33no—
136C3×3−1+2—33no—
137C3×3−1+2C32×C1311yescharacteristic
138C3×3−1+2C32×C1311yescharacteristic
139C3×3−1+2C32×C1311yescharacteristic
140C3×3−1+2C32×C1311yescharacteristic
141C3×3−1+2C32×C1311yescharacteristic
142C3×3−1+2C32×C1311yescharacteristic
143C3×3−1+2C32×C1311yescharacteristic
144C3×3−1+2C32×C1311yescharacteristic
145C3×3−1+2C32×C1311yescharacteristic
146C3×H(3,𝔽3)C32×C1311yescharacteristic
147C3×H(3,𝔽3)C32×C1311yescharacteristic
148C3×H(3,𝔽3)C32×C1311yescharacteristic
149C32×C9C32×C1311yescharacteristic
150#733—33no—
151#733—33no—
152#733—33no—
153#733—33no—
154#731—33no—
155#731—33no—
156#731—33no—
157AΣL(1,𝔽27)—33no—
158AΣL(1,𝔽27)—33no—
159AΣL(1,𝔽27)—33no—
160C32⋊C9—33no—
161C32⋊C9—33no—
162C3×C13—31no—
163C3×C13—31no—
164C3×C13—31no—
165C3×C13—31no—
166C3×C13—93no—
167C3×C13—271no—
168C3×C13—271no—
169C3×C13C32⋊H(3,𝔽3)11yescharacteristic
170C33—31no—
171C33—31no—
172C33C13×H(3,𝔽3)13yes—
173C33C33×C1311yescharacteristic
1743−1+2—318no—
1753−1+2—31no—
1763−1+2—31no—
1773−1+2—31no—
1783−1+2—31no—
1793−1+2—31no—
1803−1+2—31no—
1813−1+2—31no—
1823−1+2—31no—
1833−1+2—31no—
1843−1+2—31no—
1853−1+2—31no—
1863−1+2—31no—
1873−1+2—31no—
1883−1+2—31no—
1893−1+2—31no—
1903−1+2—31no—
1913−1+2—31no—
1923−1+2—31no—
1933−1+2—31no—
1943−1+2—31no—
1953−1+2—31no—
1963−1+2—31no—
1973−1+2—31no—
1983−1+2—31no—
1993−1+2—31no—
2003−1+2C13×H(3,𝔽3)13yes—
2013−1+2C13×H(3,𝔽3)13yes—
202H(3,𝔽3)—31no—
203H(3,𝔽3)—31no—
204H(3,𝔽3)—31no—
205H(3,𝔽3)—31no—
206H(3,𝔽3)—31no—
207H(3,𝔽3)—31no—
208H(3,𝔽3)—31no—
209H(3,𝔽3)—31no—
210H(3,𝔽3)—31no—
211C3×C9—39no—
212C3×C9—31no—
213C3×C9—31no—
214C3×C9—31no—
215C3×C9—31no—
216C3×C9—31no—
217C3×C9—31no—
218C3×C9—31no—
219C3×C9—31no—
220C3×C9—31no—
221C3×C9—31no—
222C3×C9—31no—
223C3×C9—31no—
224C3×C9C13×H(3,𝔽3)13yes—
225C13#1062475011yescharacteristic, direct product factor, Sylow
226C32—33no—
227C32—91no—
228C32—93no—
229C32—93no—
230C32—91no—
231C32—91no—
232C32—271no—
233C32C3×C13×H(3,𝔽3)11yescharacteristic
234C32C3×C13×H(3,𝔽3)11yescharacteristic
235C32C3×C13×H(3,𝔽3)11yescharacteristic
236C32C3×C13×H(3,𝔽3)11yescharacteristic
237C9—33no—
238C9—33no—
239C9—33no—
240C9—91no—
241C9—91no—
242C9—91no—
243C9—91no—
244C9—91no—
245C9—91no—
246C9—91no—
247C3—31no—
248C3—31no—
249C3—31no—
250C3—31no—
251C3—93no—
252C3—271no—
253C3—271no—
254C3C13×C32⋊H(3,𝔽3)11yescharacteristic
subgroupG/H
center, socleC3×C13C32⋊H(3,𝔽3)
commutator, Frattini, cosocleC33C33×C13
LCSG ▷ C33 ▷ C3 ▷ C1
UCSC1 ◁ C3×C13 ◁ C33×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×3−1+4C3semidirect
2. C13×#6912C3semidirect
3. C13×#6912C3semidirect
4. C13×#6912C3semidirect
5. C13×#6910C3semidirect
6. C13×#6910C3semidirect
7. C13×#6909C3semidirect
8. C13×#6909C3semidirect
9. C13×#6909C3semidirect
10. C3×C13×#733C3semidirect
11. C3×C13×#731C3semidirect
12. C13×#6893C3semidirect
13. C13×#6893C3semidirect
43. #10624750C13direct (N × H)
99. 3−1+4C3×C13semidirect
100. #6912C3×C13semidirect
101. #6912C3×C13semidirect
102. #6912C3×C13semidirect
103. #6910C3×C13semidirect
104. #6910C3×C13semidirect
105. #6909C3×C13semidirect
106. #6909C3×C13semidirect
107. #6909C3×C13semidirect
108. C3×#733C3×C13semidirect
109. C3×#731C3×C13semidirect
110. #6893C3×C13semidirect
111. #6893C3×C13semidirect
225. C13#10624750direct (N × H)