Finite Group Databasebeta

← C13×#2613 #13111671

Subgroups — C13×#2613 #13111671

Order 1664.

1134 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 1134 conjugacy classes of subgroups — too many to draw. Only its 232 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
1C23×D4×C13C211yesmaximal, characteristic, complemented
2C2×C13×#123C211yesmaximal, characteristic, complemented
3C2×C13×#120C212yesmaximal, complemented
4C13×#394C214yesmaximal, complemented
5C13×#392C214yesmaximal, complemented
6C13×#381C211yesmaximal, characteristic, complemented
7C13×#379C212yesmaximal, complemented
8C25×C13C2212yes—
9C22×D4×C13—28no—
10C22×D4×C13—24no—
11C22×D4×C13C2214yes—
12C22×D4×C13C2211yescharacteristic
13C22×D4×C13C2214yescomplemented
14C23×C4×C13C2211yescharacteristic
15C13×#123—24no—
16C13×#120—28no—
17C2×C13×C4⋊C4C2212yescomplemented
18C2×C13×C22⋊C4C2211yescharacteristic
19C2×C13×C22⋊C4C2212yes—
20C2×C13×C22⋊C4C2212yescomplemented
21C2×C13×C22⋊C4C2214yescomplemented
22C2×C13×C22⋊C4C2218yescomplemented
23C13×#95C2214yescomplemented
24C24×C13—24no—
25C24×C13—24no—
26C24×C13—48no—
27C24×C13D418yescomplemented
28C24×C13C2311yescharacteristic
29C24×C13C2314yes—
30C24×C13C2311yescharacteristic
31C2×D4×C13—232no—
32C2×D4×C13—216no—
33C2×D4×C13—24no—
34C2×D4×C13—28no—
35C2×D4×C13—22no—
36C2×D4×C13—28no—
37C2×D4×C13—48no—
38C22×C4×C13—24no—
39C22×C4×C13D414yescomplemented
40C22×C4×C13C2314yes—
41C22×C4×C13C2312yes—
42C22×C4×C13C2311yescharacteristic
43C22×C4×C13C2312yes—
44C13×C4⋊C4—24no—
45C13×C22⋊C4—24no—
46C13×C22⋊C4—22no—
47C13×C22⋊C4—28no—
48C13×C22⋊C4—24no—
49C13×C22⋊C4—48no—
50#2613C1311yesmaximal, characteristic, direct product factor, Sylow
51C23×C13—24no—
52C23×C13—216no—
53C23×C13—24no—
54C23×C13—24no—
55C23×C13—28no—
56C23×C13—28no—
57C23×C13—21no—
58C23×C13—22no—
59C23×C13—24no—
60C23×C13—416no—
61C23×C13—416no—
62C23×C13—416no—
63C23×C13C2×D418yes—
64C23×C13C2×D414yes—
65C23×C13C2×D412yes—
66C23×C13C2411yescharacteristic
67D4×C13—232no—
68D4×C13—416no—
69D4×C13—44no—
70C2×C4×C13—28no—
71C2×C4×C13—24no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—24no—
75C2×C4×C13—21no—
76C2×C4×C13—24no—
77C2×C4×C13—28no—
78C2×C4×C13C2×D414yes—
79C23×D4C2×C1311yescharacteristic, complemented
80C2×#123C2×C1311yescharacteristic, complemented
81C2×#120C2×C1312yescomplemented
82#394C2×C1314yescomplemented
83#392C2×C1314yescomplemented
84#381C2×C1311yescharacteristic, complemented
85#379C2×C1312yescomplemented
86C22×C13—28no—
87C22×C13—24no—
88C22×C13—28no—
89C22×C13—28no—
90C22×C13—28no—
91C22×C13—432no—
92C22×C13—48no—
93C22×C13—48no—
94C22×C13—41no—
95C22×C13—44no—
96C22×C13—42no—
97C22×C13#12014yes—
98C22×C13C22×D412yes—
99C22×C13C22×D411yescharacteristic
100C22×C13H(5,𝔽2)14yes—
101C4×C13—24no—
102C4×C13—41no—
103C4×C13—44no—
104C4×C13—42no—
105C25C22×C1312yes—
106C22×D4—28no—
107C22×D4—24no—
108C22×D4C22×C1311yescharacteristic
109C22×D4C22×C1314yes—
110C22×D4C22×C1314yescomplemented
111C23×C4C22×C1311yescharacteristic
112#123—24no—
113#120—28no—
114C2×C4⋊C4C22×C1312yescomplemented
115C2×C22⋊C4C22×C1312yes—
116C2×C22⋊C4C22×C1311yescharacteristic
117C2×C22⋊C4C22×C1314yescomplemented
118C2×C22⋊C4C22×C1312yescomplemented
119C2×C22⋊C4C22×C1318yescomplemented
120#95C22×C1314yescomplemented
121C2×C13—24no—
122C2×C13—48no—
123C2×C13—81no—
124C2×C13C2×#12011yescharacteristic
125C2×C13#53414yes—
126C2×C13#53512yes—
127C24—24no—
128C24—24no—
129C24—48no—
130C24D4×C1318yescomplemented
131C24C23×C1311yescharacteristic
132C24C23×C1314yes—
133C24C23×C1311yescharacteristic
134C2×D4—232no—
135C2×D4—216no—
136C2×D4—24no—
137C2×D4—28no—
138C2×D4—22no—
139C2×D4—28no—
140C2×D4—48no—
141C22×C4—24no—
142C22×C4D4×C1314yescomplemented
143C22×C4C23×C1314yes—
144C22×C4C23×C1312yes—
145C22×C4C23×C1311yescharacteristic
146C22×C4C23×C1312yes—
147C4⋊C4—24no—
148C22⋊C4—24no—
149C22⋊C4—22no—
150C22⋊C4—28no—
151C22⋊C4—24no—
152C22⋊C4—48no—
153C13#261311yescharacteristic, direct product factor, Sylow
154C23—24no—
155C23—216no—
156C23—24no—
157C23—24no—
158C23—28no—
159C23—28no—
160C23—21no—
161C23—22no—
162C23—24no—
163C23—416no—
164C23—416no—
165C23—416no—
166C23C2×D4×C1318yes—
167C23C2×D4×C1314yes—
168C23C2×D4×C1312yes—
169C23C24×C1311yescharacteristic
170D4—232no—
171D4—416no—
172D4—44no—
173C2×C4—28no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—24no—
178C2×C4—21no—
179C2×C4—24no—
180C2×C4—28no—
181C2×C4C2×D4×C1314yes—
182C22—28no—
183C22—24no—
184C22—28no—
185C22—28no—
186C22—28no—
187C22—432no—
188C22—48no—
189C22—48no—
190C22—41no—
191C22—44no—
192C22—42no—
193C22C13×#12014yes—
194C22C22×D4×C1312yes—
195C22C22×D4×C1311yescharacteristic
196C22C13×H(5,𝔽2)14yes—
197C4—24no—
198C4—41no—
199C4—44no—
200C4—42no—
201C2—24no—
202C2—48no—
203C2—81no—
204C2C2×C13×#12011yescharacteristic
205C2C13×#53414yes—
206C2C13×#53512yes—
subgroupG/H
center, socleC23×C13C24
commutator, Frattini, cosocleC23C24×C13
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×D4×C13C2semidirect
2. C2×C13×#123C2semidirect
3. C2×C13×#120C2semidirect
4. C13×#394C2semidirect
5. C13×#392C2semidirect
6. C13×#381C2semidirect
7. C13×#379C2semidirect
13. C22×D4×C13C22semidirect
17. C2×C13×C4⋊C4C22semidirect
20. C2×C13×C22⋊C4C22semidirect
21. C2×C13×C22⋊C4C22semidirect
22. C2×C13×C22⋊C4C22semidirect
23. C13×#95C22semidirect
27. C24×C13D4semidirect
39. C22×C4×C13D4semidirect
50. #2613C13direct (N × H)
79. C23×D4C2×C13semidirect
80. C2×#123C2×C13semidirect
81. C2×#120C2×C13semidirect
82. #394C2×C13semidirect
83. #392C2×C13semidirect
84. #381C2×C13semidirect
85. #379C2×C13semidirect
110. C22×D4C22×C13semidirect
114. C2×C4⋊C4C22×C13semidirect
117. C2×C22⋊C4C22×C13semidirect
118. C2×C22⋊C4C22×C13semidirect
119. C2×C22⋊C4C22×C13semidirect
120. #95C22×C13semidirect
130. C24D4×C13semidirect
142. C22×C4D4×C13semidirect
153. C13#2613direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D4×C132
C2×C13×#1232
C2×C13×#1202
C13×#3942
C13×#3922
C13×#3812
C13×#3792
#261313