Finite Group Databasebeta

← C13×#10624756 #23744907

Subgroups — C13×#10624756 #23744907

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
1C3×C13×#737C311yesmaximal, characteristic, complemented
2C13×#6912C312yesmaximal, complemented
3C13×#6911C311yesmaximal, characteristic, complemented
4C13×#6910C312yesmaximal, complemented
5C13×#6910C311yesmaximal, characteristic, complemented
6C13×#6909C312yesmaximal, complemented
7C13×#6909C311yesmaximal, characteristic, complemented
8C3×C13×#731C311yesmaximal, characteristic, complemented
9C3×C13×#731C312yesmaximal, complemented
10C13×#737—36no—
11C13×#737—33no—
12C3×C13×3−1+2—32no—
13C3×C13×3−1+2C3212yes—
14C3×C13×3−1+2C3212yes—
15C3×C13×3−1+2C3211yescharacteristic
16C3×C13×3−1+2C3211yescharacteristic
17C3×C13×3−1+2C3212yes—
18C3×C13×H(3,𝔽3)C3211yescharacteristic
19C3×C13×H(3,𝔽3)C3212yes—
20C3×C13×H(3,𝔽3)C3211yescharacteristic
21C32×C9×C13—31no—
22C32×C9×C13C3211yescharacteristic
23C13×#733—36no—
24C13×#732—33no—
25C13×#731—36no—
26C13×#731—33no—
27C13×#731—31no—
28C13×#731—32no—
29C13×#731—32no—
30C13×#731—34no—
31C13×AΣL(1,𝔽27)—36no—
32C13×AΣL(1,𝔽27)—33no—
33#10624756C1311yesmaximal, characteristic, direct product factor, Sylow
34C33×C13—31no—
35C33×C13—32no—
36C33×C13—31no—
37C33×C13C3311yescharacteristic
38C13×3−1+2—318no—
39C13×3−1+2—32no—
40C13×3−1+2—32no—
41C13×3−1+2—32no—
42C13×3−1+2—32no—
43C13×3−1+2—32no—
44C13×3−1+2—32no—
45C13×3−1+2—32no—
46C13×3−1+2—32no—
47C13×3−1+2—31no—
48C13×3−1+2—31no—
49C13×3−1+2—32no—
50C13×3−1+2—32no—
51C13×3−1+2H(3,𝔽3)16yes—
52C13×H(3,𝔽3)—32no—
53C13×H(3,𝔽3)—32no—
54C13×H(3,𝔽3)—32no—
55C13×H(3,𝔽3)—31no—
56C13×H(3,𝔽3)—32no—
57C13×H(3,𝔽3)—32no—
58C13×H(3,𝔽3)H(3,𝔽3)13yes—
59C3×C9×C13—39no—
60C3×C9×C13—32no—
61C3×C9×C13—32no—
62C3×C9×C13—31no—
63C3×C9×C13—32no—
64C3×C9×C13—31no—
65C3×C9×C13—31no—
66C3×C9×C13—32no—
67C3×C9×C13H(3,𝔽3)11yescharacteristic
68C3×C9×C13H(3,𝔽3)12yes—
69C3×#737C3×C1311yescharacteristic, complemented
70#6912C3×C1312yescomplemented
71#6911C3×C1311yescharacteristic, complemented
72#6910C3×C1312yescomplemented
73#6910C3×C1311yescharacteristic, complemented
74#6909C3×C1312yescomplemented
75#6909C3×C1311yescharacteristic, complemented
76C3×#731C3×C1311yescharacteristic, complemented
77C3×#731C3×C1312yescomplemented
78C32×C13—33no—
79C32×C13—91no—
80C32×C13—93no—
81C32×C13—91no—
82C32×C13—92no—
83C32×C13—272no—
84C32×C13—271no—
85C32×C13C3×H(3,𝔽3)12yes—
86C32×C13C3×H(3,𝔽3)11yescharacteristic
87C32×C13C3×H(3,𝔽3)11yescharacteristic
88C9×C13—31no—
89C9×C13—36no—
90C9×C13—32no—
91C9×C13—92no—
92C9×C13—91no—
93C9×C13—91no—
94C9×C13—92no—
95#737—36no—
96#737—33no—
97C3×3−1+2—32no—
98C3×3−1+2C32×C1311yescharacteristic
99C3×3−1+2C32×C1312yes—
100C3×3−1+2C32×C1312yes—
101C3×3−1+2C32×C1311yescharacteristic
102C3×3−1+2C32×C1312yes—
103C3×H(3,𝔽3)C32×C1311yescharacteristic
104C3×H(3,𝔽3)C32×C1312yes—
105C3×H(3,𝔽3)C32×C1311yescharacteristic
106C32×C9—31no—
107C32×C9C32×C1311yescharacteristic
108#733—36no—
109#732—33no—
110#731—36no—
111#731—33no—
112#731—31no—
113#731—32no—
114#731—32no—
115#731—34no—
116AΣL(1,𝔽27)—36no—
117AΣL(1,𝔽27)—33no—
118C3×C13—31no—
119C3×C13—32no—
120C3×C13—31no—
121C3×C13—93no—
122C3×C13—271no—
123C3×C13—272no—
124C3×C13C32⋊H(3,𝔽3)11yescharacteristic
125C33—31no—
126C33—32no—
127C33—31no—
128C33C33×C1311yescharacteristic
1293−1+2—318no—
1303−1+2—32no—
1313−1+2—32no—
1323−1+2—32no—
1333−1+2—32no—
1343−1+2—32no—
1353−1+2—32no—
1363−1+2—31no—
1373−1+2—32no—
1383−1+2—32no—
1393−1+2—31no—
1403−1+2—32no—
1413−1+2—32no—
1423−1+2C13×H(3,𝔽3)16yes—
143H(3,𝔽3)—32no—
144H(3,𝔽3)—32no—
145H(3,𝔽3)—32no—
146H(3,𝔽3)—31no—
147H(3,𝔽3)—32no—
148H(3,𝔽3)—32no—
149H(3,𝔽3)C13×H(3,𝔽3)13yes—
150C3×C9—39no—
151C3×C9—32no—
152C3×C9—32no—
153C3×C9—31no—
154C3×C9—32no—
155C3×C9—31no—
156C3×C9—31no—
157C3×C9—32no—
158C3×C9C13×H(3,𝔽3)11yescharacteristic
159C3×C9C13×H(3,𝔽3)12yes—
160C13#1062475611yescharacteristic, direct product factor, Sylow
161C32—33no—
162C32—91no—
163C32—93no—
164C32—91no—
165C32—92no—
166C32—272no—
167C32—271no—
168C32C3×C13×H(3,𝔽3)12yes—
169C32C3×C13×H(3,𝔽3)11yescharacteristic
170C32C3×C13×H(3,𝔽3)11yescharacteristic
171C9—31no—
172C9—36no—
173C9—32no—
174C9—92no—
175C9—91no—
176C9—91no—
177C9—92no—
178C3—31no—
179C3—32no—
180C3—31no—
181C3—93no—
182C3—271no—
183C3—272no—
184C3C13×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. C3×C13×#737C3semidirect
2. C13×#6912C3semidirect
3. C13×#6911C3semidirect
4. C13×#6910C3semidirect
5. C13×#6910C3semidirect
6. C13×#6909C3semidirect
7. C13×#6909C3semidirect
8. C3×C13×#731C3semidirect
9. C3×C13×#731C3semidirect
33. #10624756C13direct (N × H)
69. C3×#737C3×C13semidirect
70. #6912C3×C13semidirect
71. #6911C3×C13semidirect
72. #6910C3×C13semidirect
73. #6910C3×C13semidirect
74. #6909C3×C13semidirect
75. #6909C3×C13semidirect
76. C3×#731C3×C13semidirect
77. C3×#731C3×C13semidirect
160. C13#10624756direct (N × H)