Finite Group Databasebeta

← C13×#9886 #15696225

Subgroups — C13×#9886 #15696225

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2851C211yesmaximal, characteristic
2C4×C13×C22⋊C8C211yesmaximal, characteristic
3C13×#1434C211yesmaximal, characteristic
4C13×#1294C212yesmaximal
5C13×#1294C212yesmaximal
6C2×C13×#125C411yescharacteristic, complemented
7C22×C42×C13C2211yescharacteristic
8C2×C13×C22⋊C8C2212yes—
9C2×C4×C8×C13—21no—
10C13×#389C411yescharacteristic, complemented
11C13×#389C411yescharacteristic, complemented
12C13×#387—21no—
13C13×#387—21no—
14C13×#385—21no—
15C13×#385—21no—
16C13×#382C411yescharacteristic, complemented
17C13×#380C2211yescharacteristic
18C13×#380C2211yescharacteristic
19C2×C13×#95—21no—
20C2×C13×#95—21no—
21C2×C13×#95C2212yes—
22C13×#336—21no—
23C23×C4×C13—22no—
24C23×C4×C13D411yescharacteristic
25C23×C4×C13D411yescharacteristic
26C23×C4×C13C2311yescharacteristic
27C22×C8×C13—22no—
28C13×#125—42no—
29C2×C13×C4⋊C4—21no—
30C2×C13×C4⋊C4—21no—
31C2×C13×C4⋊C4—21no—
32C2×C13×C4⋊C4—21no—
33C2×C13×C4⋊C4C2×C411yescharacteristic
34C2×C13×C4⋊C4C2×C411yescharacteristic
35C2×C13×C4⋊C4C2×C411yescharacteristic
36C2×C13×C4⋊C4C2×C411yescharacteristic
37C2×C13×C22⋊C4—21no—
38C2×C13×C22⋊C4—21no—
39C2×C42×C13—42no—
40C2×C42×C13C2×C411yescharacteristic
41C2×C42×C13C2×C411yescharacteristic
42C2×C42×C13D411yescharacteristic
43C2×C42×C13D411yescharacteristic
44C13×C22⋊C8—22no—
45C13×C22⋊C8Q814yes—
46C4×C8×C13—42no—
47C13×#95—24no—
48C13×#95—21no—
49C13×#95—21no—
50C13×#95—21no—
51C13×#95—21no—
52C13×#95—21no—
53C13×#95—21no—
54C13×#95—24no—
55C13×#95—42no—
56#9886C1311yesmaximal, characteristic, direct product factor, Sylow
57C24×C13C2×D411yescharacteristic
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—24no—
63C22×C4×C13—21no—
64C22×C4×C13—21no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13—41no—
68C22×C4×C13—41no—
69C22×C4×C13—41no—
70C22×C4×C13—41no—
71C22×C4×C13—42no—
72C22×C4×C13—42no—
73C22×C4×C13—42no—
74C22×C4×C13—42no—
75C22×C4×C13—42no—
76C22×C4×C13—42no—
77C22×C4×C13C22⋊C411yescharacteristic
78C22×C4×C13C22⋊C411yescharacteristic
79C22×C4×C13C22⋊C411yescharacteristic
80C22×C4×C13C22⋊C411yescharacteristic
81C22×C4×C13C22×C411yescharacteristic
82C22×C4×C13C2×D411yescharacteristic
83C22×C4×C13C2×Q812yes—
84C22×C4×C13#4112yes—
85C2×C8×C13—24no—
86C2×C8×C13—42no—
87C2×C8×C13—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—41no—
91C13×C4⋊C4—41no—
92C13×C4⋊C4—42no—
93C13×C4⋊C4—42no—
94C13×C4⋊C4—42no—
95C13×C4⋊C4—42no—
96C13×C22⋊C4—42no—
97C13×C22⋊C4—42no—
98C42×C13—22no—
99C42×C13—22no—
100C42×C13—41no—
101C42×C13—41no—
102#2851C2×C1311yescharacteristic
103C4×C22⋊C8C2×C1311yescharacteristic
104#1434C2×C1311yescharacteristic
105#1294C2×C1312yes—
106#1294C2×C1312yes—
107C23×C13—21no—
108C23×C13—21no—
109C23×C13—21no—
110C23×C13—21no—
111C23×C13C2×C22⋊C411yescharacteristic
112C23×C13#12411yescharacteristic
113C23×C13C4⋊Q811yescharacteristic
114C23×C13#13512yes—
115C23×C13#13512yes—
116C2×C4×C13—21no—
117C2×C4×C13—21no—
118C2×C4×C13—21no—
119C2×C4×C13—21no—
120C2×C4×C13—21no—
121C2×C4×C13—21no—
122C2×C4×C13—21no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—42no—
131C2×C4×C13—42no—
132C2×C4×C13—44no—
133C2×C4×C13—44no—
134C2×C4×C13—44no—
135C2×C4×C13—44no—
136C2×C4×C13—44no—
137C2×C4×C13—41no—
138C2×C4×C13—41no—
139C2×C4×C13—41no—
140C2×C4×C13—41no—
141C2×C4×C13—41no—
142C2×C4×C13—41no—
143C2×C4×C13—41no—
144C2×C4×C13—41no—
145C2×C4×C13—41no—
146C2×C4×C13—41no—
147C2×C4×C13—41no—
148C2×C4×C13—41no—
149C2×C4×C13—82no—
150C2×C4×C13—82no—
151C2×C4×C13—82no—
152C2×C4×C13—82no—
153C2×C4×C13#9912yes—
154C2×C4×C13#10412yes—
155C2×C4×C13C4×Q812yes—
156C2×C4×C13C22⋊Q812yes—
157C8×C13—44no—
158C2×#125C4×C1311yescharacteristic, complemented
159C22×C42C22×C1311yescharacteristic
160C2×C22⋊C8C22×C1312yes—
161C2×C4×C8—21no—
162#389C4×C1311yescharacteristic, complemented
163#389C4×C1311yescharacteristic, complemented
164#387—21no—
165#387—21no—
166#385—21no—
167#385—21no—
168#382C4×C1311yescharacteristic, complemented
169#380C22×C1311yescharacteristic
170#380C22×C1311yescharacteristic
171C2×#95—21no—
172C2×#95—21no—
173C2×#95C22×C1312yes—
174#336—21no—
175C22×C13—21no—
176C22×C13—21no—
177C22×C13—21no—
178C22×C13—21no—
179C22×C13—22no—
180C22×C13—22no—
181C22×C13—22no—
182C22×C13—22no—
183C22×C13#39111yescharacteristic
184C22×C13C2×#9911yescharacteristic
185C22×C13#41011yescharacteristic
186C22×C13#41611yescharacteristic
187C22×C13#41611yescharacteristic
188C22×C13C2×#10411yescharacteristic
189C22×C13#42111yescharacteristic
190C22×C13#48812yes—
191C22×C13#49912yes—
192C4×C13—22no—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—22no—
196C4×C13—41no—
197C4×C13—41no—
198C4×C13—84no—
199C4×C13—81no—
200C4×C13—81no—
201C4×C13—81no—
202C4×C13—81no—
203C23×C4—22no—
204C23×C4D4×C1311yescharacteristic
205C23×C4D4×C1311yescharacteristic
206C23×C4C23×C1311yescharacteristic
207C22×C8—22no—
208#125—42no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C1311yescharacteristic
214C2×C4⋊C4C2×C4×C1311yescharacteristic
215C2×C4⋊C4C2×C4×C1311yescharacteristic
216C2×C4⋊C4C2×C4×C1311yescharacteristic
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C42—42no—
220C2×C42C2×C4×C1311yescharacteristic
221C2×C42C2×C4×C1311yescharacteristic
222C2×C42D4×C1311yescharacteristic
223C2×C42D4×C1311yescharacteristic
224C22⋊C8—22no—
225C22⋊C8Q8×C1314yes—
226C4×C8—42no—
227#95—24no—
228#95—21no—
229#95—21no—
230#95—21no—
231#95—21no—
232#95—21no—
233#95—21no—
234#95—24no—
235#95—42no—
236C2×C13—22no—
237C2×C13—22no—
238C2×C13#150011yescharacteristic
239C2×C13#150111yescharacteristic
240C2×C13#151611yescharacteristic
241C2×C13#152111yescharacteristic
242C2×C13#198611yescharacteristic
243C2×C13#199111yescharacteristic
244C2×C13#199611yescharacteristic
245C24C2×D4×C1311yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—24no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—41no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4—42no—
260C22×C4—42no—
261C22×C4—42no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—42no—
265C22×C4C13×C22⋊C411yescharacteristic
266C22×C4C13×C22⋊C411yescharacteristic
267C22×C4C13×C22⋊C411yescharacteristic
268C22×C4C13×C22⋊C411yescharacteristic
269C22×C4C22×C4×C1311yescharacteristic
270C22×C4C2×D4×C1311yescharacteristic
271C22×C4C2×Q8×C1312yes—
272C22×C4C13×#4112yes—
273C2×C8—24no—
274C2×C8—42no—
275C2×C8—42no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—41no—
280C4⋊C4—42no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—42no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C42—22no—
287C42—22no—
288C42—41no—
289C42—41no—
290C13#988611yescharacteristic, direct product factor, Sylow
291C23—21no—
292C23—21no—
293C23—21no—
294C23—21no—
295C23C2×C13×C22⋊C411yescharacteristic
296C23C13×#12411yescharacteristic
297C23C13×C4⋊Q811yescharacteristic
298C23C13×#13512yes—
299C23C13×#13512yes—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4—44no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—82no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4C13×#9912yes—
338C2×C4C13×#10412yes—
339C2×C4C4×Q8×C1312yes—
340C2×C4C13×C22⋊Q812yes—
341C8—44no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—22no—
349C22—22no—
350C22C13×#39111yescharacteristic
351C22C2×C13×#9911yescharacteristic
352C22C13×#41011yescharacteristic
353C22C13×#41611yescharacteristic
354C22C13×#41611yescharacteristic
355C22C2×C13×#10411yescharacteristic
356C22C13×#42111yescharacteristic
357C22C13×#48812yes—
358C22C13×#49912yes—
359C4—22no—
360C4—22no—
361C4—22no—
362C4—22no—
363C4—41no—
364C4—41no—
365C4—84no—
366C4—81no—
367C4—81no—
368C4—81no—
369C4—81no—
370C2—22no—
371C2—22no—
372C2C13×#150011yescharacteristic
373C2C13×#150111yescharacteristic
374C2C13×#151611yescharacteristic
375C2C13×#152111yescharacteristic
376C2C13×#198611yescharacteristic
377C2C13×#199111yescharacteristic
378C2C13×#199611yescharacteristic
subgroupG/H
center, socleC23×C13C2×C22⋊C4
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC24×C13C2×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C13 ◁ C22×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
6. C2×C13×#125C4semidirect
10. C13×#389C4semidirect
11. C13×#389C4semidirect
16. C13×#382C4semidirect
56. #9886C13direct (N × H)
158. C2×#125C4×C13semidirect
162. #389C4×C13semidirect
163. #389C4×C13semidirect
168. #382C4×C13semidirect
290. C13#9886direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28512
C4×C13×C22⋊C82
C13×#14342
C13×#12942
#988613