Finite Group Databasebeta

← C13×#11514 #15697853

Subgroups — C13×#11514 #15697853

Order 3328.

434 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 110 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×#2317C211yesmaximal, characteristic
2C13×#1463C212yesmaximal
3C13×#1325C212yesmaximal, complemented
4C13×#1324C212yesmaximal, complemented
5C2×C13×#117C411yescharacteristic
6C2×C13×#117C411yescharacteristic
7C22×C13×C4⋊C4C2211yescharacteristic
8C13×#407—22no—
9C13×#389—22no—
10C13×#385—22no—
11C13×#384C411yescharacteristic
12C13×#384C2211yescharacteristic
13C13×#382C411yescharacteristic
14C13×#382C2211yescharacteristic
15C13×#324—22no—
16C13×#324C2214yes—
17C23×C4×C13C2×C411yescharacteristic
18C23×C4×C13D412yes—
19C2×C13×M16—42no—
20C13×#117—22no—
21C13×#117—22no—
22C13×#117—42no—
23C2×C13×C4⋊C4—21no—
24C2×C13×C4⋊C4—22no—
25C2×C13×C4⋊C4—22no—
26C2×C13×C4⋊C4—42no—
27C2×C13×C4⋊C4C2×C411yescharacteristic
28C2×C13×C4⋊C4C2×C411yescharacteristic
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4D412yes—
31C2×C13×C4⋊C4C2311yescharacteristic
32C2×C13×C22⋊C4—21no—
33C2×C13×C22⋊C4—21no—
34C2×C42×C13—21no—
35C2×C42×C13C2×C411yescharacteristic
36C2×C42×C13C2×C411yescharacteristic
37C13×C22⋊C8—24no—
38C13×C22⋊C8—42no—
39C13×#95—22no—
40C13×#95—22no—
41#11514C1311yesmaximal, characteristic, direct product factor, Sylow
42C24×C13C22⋊C411yescharacteristic
43C22×C4×C13—22no—
44C22×C4×C13—22no—
45C22×C4×C13—21no—
46C22×C4×C13—21no—
47C22×C4×C13—22no—
48C22×C4×C13—21no—
49C22×C4×C13—21no—
50C22×C4×C13—22no—
51C22×C4×C13—21no—
52C22×C4×C13—21no—
53C22×C4×C13—82no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×C4×C13C22⋊C412yes—
56C22×C4×C13C22×C411yescharacteristic
57C22×C4×C13C2×D412yes—
58C13×M16—84no—
59C2×C8×C13—44no—
60C13×C4⋊C4—24no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—42no—
63C13×C4⋊C4—41no—
64C13×C4⋊C4—41no—
65C13×C4⋊C4—41no—
66C13×C4⋊C4—82no—
67C13×C4⋊C4—82no—
68C13×C22⋊C4—24no—
69C13×C22⋊C4—42no—
70C42×C13—21no—
71C42×C13—21no—
72C42×C13—42no—
73C42×C13M1612yescomplemented
74C42×C13M1612yescomplemented
75#2317C2×C1311yescharacteristic
76#1463C2×C1312yes—
77#1325C2×C1312yescomplemented
78#1324C2×C1312yescomplemented
79C23×C13—21no—
80C23×C13—21no—
81C23×C13—41no—
82C23×C13—41no—
83C23×C13#9912yes—
84C23×C13C2×C22⋊C411yescharacteristic
85C2×C4×C13—24no—
86C2×C4×C13—24no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—22no—
92C2×C4×C13—22no—
93C2×C4×C13—22no—
94C2×C4×C13—22no—
95C2×C4×C13—41no—
96C2×C4×C13—41no—
97C2×C4×C13—44no—
98C2×C4×C13—41no—
99C2×C4×C13—41no—
100C2×C4×C13—42no—
101C2×C4×C13—42no—
102C2×C4×C13—42no—
103C2×C4×C13—42no—
104C2×C4×C13—41no—
105C2×C4×C13—41no—
106C2×C4×C13—82no—
107C2×C4×C13#10112yes—
108C2×C4×C13C2×M1611yescharacteristic
109C2×C4×C13C2×M1611yescharacteristic
110C8×C13—84no—
111C2×#117C4×C1311yescharacteristic
112C2×#117C4×C1311yescharacteristic
113C22×C4⋊C4C22×C1311yescharacteristic
114#407—22no—
115#389—22no—
116#385—22no—
117#384C4×C1311yescharacteristic
118#384C22×C1311yescharacteristic
119#382C4×C1311yescharacteristic
120#382C22×C1311yescharacteristic
121#324—22no—
122#324C22×C1314yes—
123C22×C13—21no—
124C22×C13—21no—
125C22×C13—22no—
126C22×C13—22no—
127C22×C13—22no—
128C22×C13—42no—
129C22×C13—42no—
130C22×C13#40711yescharacteristic
131C22×C13C2×#9911yescharacteristic
132C22×C13C2×#10111yescharacteristic
133C4×C13—22no—
134C4×C13—21no—
135C4×C13—21no—
136C4×C13—42no—
137C4×C13—42no—
138C4×C13—42no—
139C4×C13—42no—
140C4×C13—81no—
141C4×C13—81no—
142C23×C4C2×C4×C1311yescharacteristic
143C23×C4D4×C1312yes—
144C2×M16—42no—
145#117—22no—
146#117—22no—
147#117—42no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4—42no—
152C2×C4⋊C4C2×C4×C1311yescharacteristic
153C2×C4⋊C4C2×C4×C1311yescharacteristic
154C2×C4⋊C4C2×C4×C1311yescharacteristic
155C2×C4⋊C4D4×C1312yes—
156C2×C4⋊C4C23×C1311yescharacteristic
157C2×C22⋊C4—21no—
158C2×C22⋊C4—21no—
159C2×C42—21no—
160C2×C42C2×C4×C1311yescharacteristic
161C2×C42C2×C4×C1311yescharacteristic
162C22⋊C8—24no—
163C22⋊C8—42no—
164#95—22no—
165#95—22no—
166C2×C13—21no—
167C2×C13—21no—
168C2×C13—42no—
169C2×C13#146311yescharacteristic
170C2×C13#212711yescharacteristic
171C2×C13#213311yescharacteristic
172C24C13×C22⋊C411yescharacteristic
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—22no—
178C22×C4—21no—
179C22×C4—21no—
180C22×C4—22no—
181C22×C4—21no—
182C22×C4—21no—
183C22×C4—82no—
184C22×C4C13×C22⋊C411yescharacteristic
185C22×C4C13×C22⋊C412yes—
186C22×C4C22×C4×C1311yescharacteristic
187C22×C4C2×D4×C1312yes—
188M16—84no—
189C2×C8—44no—
190C4⋊C4—24no—
191C4⋊C4—41no—
192C4⋊C4—42no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—82no—
197C4⋊C4—82no—
198C22⋊C4—24no—
199C22⋊C4—42no—
200C42—21no—
201C42—21no—
202C42—42no—
203C42C13×M1612yescomplemented
204C42C13×M1612yescomplemented
205C13#1151411yescharacteristic, direct product factor, Sylow
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23C13×#9912yes—
211C23C2×C13×C22⋊C411yescharacteristic
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4C13×#10112yes—
235C2×C4C2×C13×M1611yescharacteristic
236C2×C4C2×C13×M1611yescharacteristic
237C8—84no—
238C22—21no—
239C22—21no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—42no—
244C22—42no—
245C22C13×#40711yescharacteristic
246C22C2×C13×#9911yescharacteristic
247C22C2×C13×#10111yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—42no—
260C2C13×#146311yescharacteristic
261C2C13×#212711yescharacteristic
262C2C13×#213311yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC2×C4⋊C4C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C22×C13×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1325C2semidirect
4. C13×#1324C2semidirect
41. #11514C13direct (N × H)
73. C42×C13M16semidirect
74. C42×C13M16semidirect
77. #1325C2×C13semidirect
78. #1324C2×C13semidirect
203. C42C13×M16semidirect
204. C42C13×M16semidirect
205. C13#11514direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#23172
C13×#14632
C13×#13252
C13×#13242
#1151413