Finite Group Databasebeta

← C13×#9408 #15695747

Subgroups — C13×#9408 #15695747

Order 3328.

618 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 130 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×#2583C211yesmaximal, characteristic
2C13×#2274C211yesmaximal, characteristic
3C13×#1508C212yesmaximal
4C13×#1463C211yesmaximal, characteristic
5C13×#1297C212yesmaximal
6C2×C13×C22⋊Q8C2211yescharacteristic
7C2×C13×#117—21no—
8C22×C13×C4⋊C4C2211yescharacteristic
9C13×#407C2212yes—
10C13×#398C412yescomplemented
11C13×#395C412yescomplemented
12C13×#389—22no—
13C13×#385—21no—
14C13×#385—21no—
15C4×C13×C4⋊C4—24no—
16C4×C13×C22⋊C4—21no—
17C4×C13×C22⋊C4C2211yescharacteristic
18C4×C13×C22⋊C4C2212yes—
19C13×#328—24no—
20C13×#324—22no—
21C22×Q8×C13C2×C411yescharacteristic
22C23×C4×C13D411yescharacteristic
23C23×C4×C13D411yescharacteristic
24C23×C4×C13C2311yescharacteristic
25C2×C13×M16—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C13×#117—28no—
29C2×C13×C4⋊C4—22no—
30C2×C13×C4⋊C4—22no—
31C2×C13×C4⋊C4—22no—
32C2×C13×C4⋊C4—22no—
33C2×C13×C4⋊C4—21no—
34C2×C13×C4⋊C4—22no—
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C412yes—
37C2×C13×C4⋊C4D412yes—
38C2×C13×C22⋊C4—22no—
39C2×C13×C22⋊C4—21no—
40C2×C13×C22⋊C4—21no—
41C2×C42×C13—22no—
42C2×C42×C13—22no—
43C2×C42×C13—22no—
44C2×C42×C13—21no—
45C13×C22⋊C8—22no—
46C13×C22⋊C8—22no—
47C13×#95—22no—
48C13×#95—22no—
49C13×#95—22no—
50C13×#95C2×C412yes—
51C13×#95D414yes—
52#9408C1311yesmaximal, characteristic, direct product factor, Sylow
53C24×C13C2×D411yescharacteristic
54C2×Q8×C13—22no—
55C2×Q8×C13—81no—
56C22×C4×C13—21no—
57C22×C4×C13—21no—
58C22×C4×C13—24no—
59C22×C4×C13—22no—
60C22×C4×C13—21no—
61C22×C4×C13—24no—
62C22×C4×C13—21no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—81no—
66C22×C4×C13—81no—
67C22×C4×C13C22⋊C412yes—
68C22×C4×C13C22⋊C412yes—
69C22×C4×C13C22×C411yescharacteristic
70C22×C4×C13C2×D412yes—
71C22×C4×C13C2×D411yescharacteristic
72C22×C4×C13#4112yes—
73C13×M16—82no—
74C2×C8×C13—42no—
75C13×C4⋊C4—28no—
76C13×C4⋊C4—24no—
77C13×C4⋊C4—24no—
78C13×C4⋊C4—22no—
79C13×C4⋊C4—44no—
80C13×C4⋊C4—42no—
81C13×C4⋊C4—82no—
82C13×C22⋊C4—24no—
83C13×C22⋊C4—28no—
84C13×C22⋊C4—41no—
85C13×C22⋊C4—41no—
86C42×C13—28no—
87C42×C13—82no—
88C42×C13—81no—
89C42×C13—82no—
90#2583C2×C1311yescharacteristic
91#2274C2×C1311yescharacteristic
92#1508C2×C1312yes—
93#1463C2×C1311yescharacteristic
94#1297C2×C1312yes—
95C23×C13—22no—
96C23×C13—22no—
97C23×C13—41no—
98C23×C13C2×C22⋊C411yescharacteristic
99C23×C13#12011yescharacteristic
100C23×C13#12311yescharacteristic
101Q8×C13—82no—
102C2×C4×C13—22no—
103C2×C4×C13—22no—
104C2×C4×C13—24no—
105C2×C4×C13—22no—
106C2×C4×C13—22no—
107C2×C4×C13—28no—
108C2×C4×C13—24no—
109C2×C4×C13—22no—
110C2×C4×C13—41no—
111C2×C4×C13—42no—
112C2×C4×C13—42no—
113C2×C4×C13—41no—
114C2×C4×C13—44no—
115C2×C4×C13—42no—
116C2×C4×C13—42no—
117C2×C4×C13—42no—
118C2×C4×C13—44no—
119C2×C4×C13—42no—
120C2×C4×C13—42no—
121C2×C4×C13—41no—
122C2×C4×C13—41no—
123C2×C4×C13—42no—
124C2×C4×C13—81no—
125C2×C4×C13#10414yes—
126C2×C4×C13C4×D412yes—
127C2×C4×C13#12112yes—
128C8×C13—82no—
129C2×C22⋊Q8C22×C1311yescharacteristic
130C2×#117—21no—
131C22×C4⋊C4C22×C1311yescharacteristic
132#407C22×C1312yes—
133#398C4×C1312yescomplemented
134#395C4×C1312yescomplemented
135#389—22no—
136#385—21no—
137#385—21no—
138C4×C4⋊C4—24no—
139C4×C22⋊C4—21no—
140C4×C22⋊C4C22×C1311yescharacteristic
141C4×C22⋊C4C22×C1312yes—
142#328—24no—
143#324—22no—
144C22×C13—21no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—21no—
148C22×C13—21no—
149C22×C13—21no—
150C22×C13—21no—
151C22×C13—44no—
152C22×C13#38611yescharacteristic
153C22×C13C2×#10412yes—
154C22×C13#45612yes—
155C4×C13—24no—
156C4×C13—22no—
157C4×C13—22no—
158C4×C13—48no—
159C4×C13—44no—
160C4×C13—42no—
161C4×C13—81no—
162C4×C13—81no—
163C22×Q8C2×C4×C1311yescharacteristic
164C23×C4D4×C1311yescharacteristic
165C23×C4D4×C1311yescharacteristic
166C23×C4C23×C1311yescharacteristic
167C2×M16—22no—
168C22⋊Q8—22no—
169C22⋊Q8—22no—
170#117—28no—
171C2×C4⋊C4—22no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—22no—
177C2×C4⋊C4C2×C4×C1311yescharacteristic
178C2×C4⋊C4C2×C4×C1312yes—
179C2×C4⋊C4D4×C1312yes—
180C2×C22⋊C4—22no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C42—22no—
184C2×C42—22no—
185C2×C42—22no—
186C2×C42—21no—
187C22⋊C8—22no—
188C22⋊C8—22no—
189#95—22no—
190#95—22no—
191#95—22no—
192#95C2×C4×C1312yes—
193#95D4×C1314yes—
194C2×C13—22no—
195C2×C13—22no—
196C2×C13—41no—
197C2×C13#188611yescharacteristic
198C2×C13#189611yescharacteristic
199C2×C13#191311yescharacteristic
200C24C2×D4×C1311yescharacteristic
201C2×Q8—22no—
202C2×Q8—81no—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—24no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—24no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—81no—
213C22×C4—81no—
214C22×C4C13×C22⋊C412yes—
215C22×C4C13×C22⋊C412yes—
216C22×C4C22×C4×C1311yescharacteristic
217C22×C4C2×D4×C1312yes—
218C22×C4C2×D4×C1311yescharacteristic
219C22×C4C13×#4112yes—
220M16—82no—
221C2×C8—42no—
222C4⋊C4—28no—
223C4⋊C4—24no—
224C4⋊C4—24no—
225C4⋊C4—22no—
226C4⋊C4—44no—
227C4⋊C4—42no—
228C4⋊C4—82no—
229C22⋊C4—28no—
230C22⋊C4—24no—
231C22⋊C4—41no—
232C22⋊C4—41no—
233C42—28no—
234C42—82no—
235C42—81no—
236C42—82no—
237C13#940811yescharacteristic, direct product factor, Sylow
238C23—22no—
239C23—22no—
240C23—41no—
241C23C2×C13×C22⋊C411yescharacteristic
242C23C13×#12011yescharacteristic
243C23C13×#12311yescharacteristic
244Q8—82no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—24no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—28no—
251C2×C4—24no—
252C2×C4—22no—
253C2×C4—41no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—44no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—44no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—81no—
268C2×C4C13×#10414yes—
269C2×C4C4×D4×C1312yes—
270C2×C4C13×#12112yes—
271C8—82no—
272C22—21no—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—44no—
280C22C13×#38611yescharacteristic
281C22C2×C13×#10412yes—
282C22C13×#45612yes—
283C4—24no—
284C4—22no—
285C4—22no—
286C4—48no—
287C4—44no—
288C4—42no—
289C4—81no—
290C4—81no—
291C2—22no—
292C2—22no—
293C2—41no—
294C2C13×#188611yescharacteristic
295C2C13×#189611yescharacteristic
296C2C13×#191311yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
10. C13×#398C4semidirect
11. C13×#395C4semidirect
52. #9408C13direct (N × H)
133. #398C4×C13semidirect
134. #395C4×C13semidirect
237. C13#9408direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#25832
C13×#22742
C13×#15082
C13×#14632
C13×#12972
#940813