Finite Group Databasebeta

← C13×#12860 #15699199

Subgroups — C13×#12860 #15699199

Order 3328.

638 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 126 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
1C2×C13×#391C211yesmaximal, characteristic
2C13×#1784C212yesmaximal
3C13×#1394C214yesmaximal, complemented
4C23×Q8×C13C2211yescharacteristic
5C22×C13×C4⋊C4C411yescharacteristic
6C22×C42×C13C411yescharacteristic
7C2×C13×#101—22no—
8C2×C13×#101C2214yes—
9C13×#407—22no—
10C13×#391—22no—
11C13×#391C412yes—
12C13×#391C2212yes—
13C2×C13×#95—22no—
14C22×Q8×C13—24no—
15C22×Q8×C13—41no—
16C22×Q8×C13—41no—
17C22×Q8×C13—42no—
18C22×Q8×C13C2×C411yescharacteristic
19C22×Q8×C13D412yes—
20C22×Q8×C13C2311yescharacteristic
21C23×C4×C13—21no—
22C23×C4×C13—21no—
23C23×C4×C13C2×C411yescharacteristic
24C23×C4×C13D412yes—
25C2×C13×M16—24no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4—41no—
28C2×C13×C4⋊C4—41no—
29C2×C13×C4⋊C4C2×C412yes—
30C2×C42×C13—21no—
31C2×C42×C13—42no—
32C2×C42×C13C2×C412yes—
33C13×#101—28no—
34C13×#101—44no—
35C13×C22⋊C8—42no—
36C13×C22⋊C8—42no—
37C13×#95—24no—
38C13×#95—24no—
39#12860C1311yesmaximal, characteristic, direct product factor, Sylow
40C24×C13C22⋊C411yescharacteristic
41C2×Q8×C13—24no—
42C2×Q8×C13—22no—
43C2×Q8×C13—24no—
44C2×Q8×C13—41no—
45C2×Q8×C13—41no—
46C2×Q8×C13—42no—
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×Q8×C13—48no—
50C2×Q8×C13—48no—
51C2×Q8×C13#4114yes—
52C22×C4×C13—21no—
53C22×C4×C13—21no—
54C22×C4×C13—22no—
55C22×C4×C13—22no—
56C22×C4×C13—24no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—24no—
61C22×C4×C13—22no—
62C22×C4×C13—42no—
63C22×C4×C13—42no—
64C22×C4×C13—42no—
65C22×C4×C13—44no—
66C22×C4×C13—41no—
67C22×C4×C13—41no—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13C22⋊C411yescharacteristic
70C22×C4×C13C22×C411yescharacteristic
71C22×C4×C13C2×D412yes—
72C13×M16—44no—
73C13×M16—44no—
74C2×C8×C13—44no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C42×C13—42no—
78C42×C13—42no—
79C2×#391C2×C1311yescharacteristic
80#1784C2×C1312yes—
81#1394C2×C1314yescomplemented
82C23×C13—22no—
83C23×C13—22no—
84C23×C13—21no—
85C23×C13—21no—
86C23×C13#9911yescharacteristic
87C23×C13#9911yescharacteristic
88C23×C13C2×C22⋊C411yescharacteristic
89Q8×C13—44no—
90Q8×C13—48no—
91Q8×C13—44no—
92C2×C4×C13—24no—
93C2×C4×C13—24no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13—22no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—22no—
100C2×C4×C13—24no—
101C2×C4×C13—22no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—44no—
105C2×C4×C13—44no—
106C2×C4×C13—48no—
107C2×C4×C13—42no—
108C2×C4×C13—42no—
109C2×C4×C13—44no—
110C2×C4×C13—42no—
111C2×C4×C13—82no—
112C2×C4×C13—82no—
113C2×C4×C13#9912yes—
114C2×C4×C13#11712yes—
115C2×C4×C13#12314yes—
116C8×C13—84no—
117C23×Q8C22×C1311yescharacteristic
118C22×C4⋊C4C4×C1311yescharacteristic
119C22×C42C4×C1311yescharacteristic
120C2×#101—22no—
121C2×#101C22×C1314yes—
122#407—22no—
123#391—22no—
124#391C4×C1312yes—
125#391C22×C1312yes—
126C2×#95—22no—
127C22×C13—24no—
128C22×C13—24no—
129C22×C13—21no—
130C22×C13—21no—
131C22×C13—21no—
132C22×C13—21no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13#35512yes—
136C22×C13#35612yes—
137C22×C13#38111yescharacteristic
138C22×C13C2×#9911yescharacteristic
139C22×C13C2×#9911yescharacteristic
140C4×C13—24no—
141C4×C13—22no—
142C4×C13—22no—
143C4×C13—44no—
144C4×C13—42no—
145C4×C13—82no—
146C22×Q8—24no—
147C22×Q8—41no—
148C22×Q8—41no—
149C22×Q8—42no—
150C22×Q8C2×C4×C1311yescharacteristic
151C22×Q8D4×C1312yes—
152C22×Q8C23×C1311yescharacteristic
153C23×C4—21no—
154C23×C4—21no—
155C23×C4C2×C4×C1311yescharacteristic
156C23×C4D4×C1312yes—
157C2×M16—24no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—41no—
161C2×C4⋊C4C2×C4×C1312yes—
162C2×C42—21no—
163C2×C42—42no—
164C2×C42C2×C4×C1312yes—
165#101—28no—
166#101—44no—
167C22⋊C8—42no—
168C22⋊C8—42no—
169#95—24no—
170#95—24no—
171C2×C13—21no—
172C2×C13—22no—
173C2×C13—22no—
174C2×C13—21no—
175C2×C13#181911yescharacteristic
176C2×C13C2×#35511yescharacteristic
177C2×C13C2×#35611yescharacteristic
178C24C13×C22⋊C411yescharacteristic
179C2×Q8—24no—
180C2×Q8—22no—
181C2×Q8—24no—
182C2×Q8—41no—
183C2×Q8—41no—
184C2×Q8—42no—
185C2×Q8—41no—
186C2×Q8—41no—
187C2×Q8—48no—
188C2×Q8—48no—
189C2×Q8C13×#4114yes—
190C22×C4—21no—
191C22×C4—21no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—24no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—22no—
198C22×C4—24no—
199C22×C4—22no—
200C22×C4—42no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—44no—
204C22×C4—41no—
205C22×C4—41no—
206C22×C4C13×C22⋊C412yes—
207C22×C4C13×C22⋊C411yescharacteristic
208C22×C4C22×C4×C1311yescharacteristic
209C22×C4C2×D4×C1312yes—
210M16—44no—
211M16—44no—
212C2×C8—44no—
213C4⋊C4—42no—
214C4⋊C4—42no—
215C42—42no—
216C42—42no—
217C13#1286011yescharacteristic, direct product factor, Sylow
218C23—21no—
219C23—21no—
220C23—22no—
221C23—22no—
222C23C13×#9911yescharacteristic
223C23C13×#9911yescharacteristic
224C23C2×C13×C22⋊C411yescharacteristic
225Q8—44no—
226Q8—48no—
227Q8—44no—
228C2×C4—24no—
229C2×C4—24no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—24no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—22no—
240C2×C4—44no—
241C2×C4—44no—
242C2×C4—48no—
243C2×C4—42no—
244C2×C4—42no—
245C2×C4—44no—
246C2×C4—42no—
247C2×C4—82no—
248C2×C4—82no—
249C2×C4C13×#9912yes—
250C2×C4C13×#11712yes—
251C2×C4C13×#12314yes—
252C8—84no—
253C22—24no—
254C22—24no—
255C22—21no—
256C22—21no—
257C22—21no—
258C22—21no—
259C22—21no—
260C22—21no—
261C22C13×#35512yes—
262C22C13×#35612yes—
263C22C13×#38111yescharacteristic
264C22C2×C13×#9911yescharacteristic
265C22C2×C13×#9911yescharacteristic
266C4—24no—
267C4—22no—
268C4—22no—
269C4—44no—
270C4—42no—
271C4—82no—
272C2—21no—
273C2—21no—
274C2—22no—
275C2—22no—
276C2C13×#181911yescharacteristic
277C2C2×C13×#35511yescharacteristic
278C2C2×C13×#35611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×Q8C23×C13
prime radicalC24×C13C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C23×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#1394C2semidirect
39. #12860C13direct (N × H)
81. #1394C2×C13semidirect
217. C13#12860direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3912
C13×#17842
C13×#13942
#1286013