Finite Group Databasebeta

← C13×#9443 #15695782

Subgroups — C13×#9443 #15695782

Order 3328.

712 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#2879C211yesmaximal, characteristic
2C13×#2432C211yesmaximal, characteristic
3C13×#1782C211yesmaximal, characteristic
4C13×#1511C212yesmaximal, complemented
5C13×#1284C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C22×C13×M16—21no—
8C2×C13×C4⋊Q8C411yescharacteristic, complemented
9C2×C13×#124C411yescharacteristic, complemented
10C2×C13×C22⋊Q8C2211yescharacteristic
11C2×C13×#99—21no—
12C2×C13×#99—21no—
13C13×#408—24no—
14C13×#407—21no—
15C13×#407C2212yes—
16C13×#394—21no—
17C13×#394—21no—
18C13×#391C411yescharacteristic, complemented
19C13×#390C411yescharacteristic, complemented
20C13×#385—21no—
21C13×#385—21no—
22C13×#381C2212yes—
23C4×C13×C22⋊C4C2211yescharacteristic
24C13×#328—24no—
25C2×C13×#41—22no—
26C2×C13×#41—22no—
27C2×C13×#41—42no—
28C2×C13×#41—42no—
29C22×Q8×C13C2×C411yescharacteristic
30C22×Q8×C13C2×C411yescharacteristic
31C22×D4×C13C2×C411yescharacteristic
32C22×D4×C13D411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C23×C4×C13D411yescharacteristic
35C23×C4×C13D411yescharacteristic
36C23×C4×C13C2311yescharacteristic
37C2×C13×M16—22no—
38C2×C13×M16—22no—
39C2×C13×M16—42no—
40C2×C13×M16—42no—
41C22×C8×C13—22no—
42C13×C4⋊Q8—42no—
43C13×#124—42no—
44C13×C22⋊Q8—22no—
45C13×C22⋊Q8—22no—
46C2×C13×C4⋊C4—21no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
49C2×C13×C4⋊C4C2×C411yescharacteristic
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—22no—
57C2×C42×C13C2×C411yescharacteristic
58C2×C42×C13C2×C411yescharacteristic
59C13×#99—42no—
60C13×#99—42no—
61C13×C22⋊C8—24no—
62C13×C22⋊C8—22no—
63C13×C22⋊C8D414yes—
64C13×#95—21no—
65C13×#95—21no—
66C13×#95—21no—
67C13×#95—22no—
68C13×#95—22no—
69#9443C1311yesmaximal, characteristic, direct product factor, Sylow
70C24×C13C22⋊C411yescharacteristic
71C24×C13C22⋊C411yescharacteristic
72C24×C13C2×D411yescharacteristic
73C13×#41—44no—
74C13×#41—44no—
75C13×#41—48no—
76C2×Q8×C13—22no—
77C2×Q8×C13—22no—
78C2×Q8×C13—22no—
79C2×Q8×C13—41no—
80C2×Q8×C13—41no—
81C2×Q8×C13—41no—
82C2×D4×C13—22no—
83C2×D4×C13—22no—
84C2×D4×C13—22no—
85C2×D4×C13—22no—
86C2×D4×C13—22no—
87C2×D4×C13—22no—
88C2×D4×C13—41no—
89C2×D4×C13—41no—
90C2×D4×C13—41no—
91C22×C4×C13—22no—
92C22×C4×C13—22no—
93C22×C4×C13—21no—
94C22×C4×C13—21no—
95C22×C4×C13—21no—
96C22×C4×C13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13—21no—
100C22×C4×C13—21no—
101C22×C4×C13—41no—
102C22×C4×C13—41no—
103C22×C4×C13—41no—
104C22×C4×C13—41no—
105C22×C4×C13—42no—
106C22×C4×C13C22⋊C411yescharacteristic
107C22×C4×C13C22⋊C411yescharacteristic
108C22×C4×C13C22×C411yescharacteristic
109C22×C4×C13C2×D411yescharacteristic
110C22×C4×C13C2×D412yes—
111C22×C4×C13#4112yes—
112C13×M16—44no—
113C13×M16—42no—
114C13×M16—42no—
115C2×C8×C13—24no—
116C2×C8×C13—44no—
117C13×C4⋊C4—22no—
118C13×C4⋊C4—42no—
119C13×C4⋊C4—42no—
120C13×C4⋊C4—41no—
121C13×C4⋊C4—41no—
122C13×C22⋊C4—42no—
123C13×C22⋊C4—42no—
124C13×C22⋊C4—42no—
125C13×C22⋊C4—42no—
126C13×C22⋊C4—42no—
127C13×C22⋊C4—42no—
128C13×C22⋊C4—42no—
129C13×C22⋊C4—42no—
130C42×C13—41no—
131C42×C13—41no—
132#2879C2×C1311yescharacteristic
133#2432C2×C1311yescharacteristic
134#1782C2×C1311yescharacteristic
135#1511C2×C1312yescomplemented
136#1284C2×C1312yescomplemented
137C23×C13—21no—
138C23×C13—21no—
139C23×C13—21no—
140C23×C13—21no—
141C23×C13—21no—
142C23×C13—21no—
143C23×C13—21no—
144C23×C13—41no—
145C23×C13—41no—
146C23×C13—41no—
147C23×C13—41no—
148C23×C13—41no—
149C23×C13—41no—
150C23×C13#9912yes—
151C23×C13C2×C22⋊C411yescharacteristic
152C23×C13#12112yes—
153Q8×C13—44no—
154Q8×C13—82no—
155D4×C13—44no—
156D4×C13—44no—
157D4×C13—44no—
158C2×C4×C13—22no—
159C2×C4×C13—22no—
160C2×C4×C13—24no—
161C2×C4×C13—21no—
162C2×C4×C13—21no—
163C2×C4×C13—21no—
164C2×C4×C13—21no—
165C2×C4×C13—21no—
166C2×C4×C13—21no—
167C2×C4×C13—22no—
168C2×C4×C13—21no—
169C2×C4×C13—21no—
170C2×C4×C13—21no—
171C2×C4×C13—42no—
172C2×C4×C13—42no—
173C2×C4×C13—42no—
174C2×C4×C13—42no—
175C2×C4×C13—41no—
176C2×C4×C13—41no—
177C2×C4×C13—41no—
178C2×C4×C13—41no—
179C2×C4×C13—41no—
180C2×C4×C13—41no—
181C2×C4×C13—41no—
182C2×C4×C13—41no—
183C2×C4×C13—41no—
184C2×C4×C13—41no—
185C2×C4×C13—41no—
186C2×C4×C13—82no—
187C2×C4×C13—82no—
188C2×C4×C13—82no—
189C2×C4×C13#9912yes—
190C2×C4×C13C4×D412yes—
191C2×C4×C13#12011yescharacteristic
192C2×C4×C13#12311yescharacteristic
193C8×C13—44no—
194C22×#41C22×C1311yescharacteristic
195C22×M16—21no—
196C2×C4⋊Q8C4×C1311yescharacteristic, complemented
197C2×#124C4×C1311yescharacteristic, complemented
198C2×C22⋊Q8C22×C1311yescharacteristic
199C2×#99—21no—
200C2×#99—21no—
201#408—24no—
202#407—21no—
203#407C22×C1312yes—
204#394—21no—
205#394—21no—
206#391C4×C1311yescharacteristic, complemented
207#390C4×C1311yescharacteristic, complemented
208#385—21no—
209#385—21no—
210#381C22×C1312yes—
211C4×C22⋊C4C22×C1311yescharacteristic
212#328—24no—
213C22×C13—21no—
214C22×C13—21no—
215C22×C13—22no—
216C22×C13—22no—
217C22×C13—22no—
218C22×C13—22no—
219C22×C13—42no—
220C22×C13—42no—
221C22×C13—41no—
222C22×C13—41no—
223C22×C13—41no—
224C22×C13—41no—
225C22×C13—41no—
226C22×C13—81no—
227C22×C13—81no—
228C22×C13—81no—
229C22×C13—81no—
230C22×C13#38611yescharacteristic
231C22×C13C2×#9911yescharacteristic
232C22×C13C2×#9911yescharacteristic
233C4×C13—21no—
234C4×C13—21no—
235C4×C13—22no—
236C4×C13—22no—
237C4×C13—42no—
238C4×C13—41no—
239C4×C13—81no—
240C4×C13—81no—
241C4×C13—81no—
242C4×C13—162no—
243C2×#41—22no—
244C2×#41—22no—
245C2×#41—42no—
246C2×#41—42no—
247C22×Q8C2×C4×C1311yescharacteristic
248C22×Q8C2×C4×C1311yescharacteristic
249C22×D4C2×C4×C1311yescharacteristic
250C22×D4D4×C1311yescharacteristic
251C22×D4D4×C1311yescharacteristic
252C23×C4D4×C1311yescharacteristic
253C23×C4D4×C1311yescharacteristic
254C23×C4C23×C1311yescharacteristic
255C2×M16—22no—
256C2×M16—22no—
257C2×M16—42no—
258C2×M16—42no—
259C22×C8—22no—
260C4⋊Q8—42no—
261#124—42no—
262C22⋊Q8—22no—
263C22⋊Q8—22no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4C2×C4×C1311yescharacteristic
268C2×C22⋊C4—21no—
269C2×C22⋊C4—21no—
270C2×C22⋊C4—21no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—21no—
274C2×C22⋊C4—22no—
275C2×C42C2×C4×C1311yescharacteristic
276C2×C42C2×C4×C1311yescharacteristic
277#99—42no—
278#99—42no—
279C22⋊C8—24no—
280C22⋊C8—22no—
281C22⋊C8D4×C1314yes—
282#95—21no—
283#95—21no—
284#95—21no—
285#95—22no—
286#95—22no—
287C2×C13—21no—
288C2×C13—21no—
289C2×C13—42no—
290C2×C13—42no—
291C2×C13—81no—
292C2×C13#188411yescharacteristic
293C2×C13#189811yescharacteristic
294C2×C13#190911yescharacteristic
295C24C13×C22⋊C411yescharacteristic
296C24C13×C22⋊C411yescharacteristic
297C24C2×D4×C1311yescharacteristic
298#41—44no—
299#41—44no—
300#41—48no—
301C2×Q8—22no—
302C2×Q8—22no—
303C2×Q8—22no—
304C2×Q8—41no—
305C2×Q8—41no—
306C2×Q8—41no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—22no—
312C2×D4—22no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—21no—
319C22×C4—21no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—21no—
323C22×C4—21no—
324C22×C4—21no—
325C22×C4—21no—
326C22×C4—41no—
327C22×C4—41no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—42no—
331C22×C4C13×C22⋊C411yescharacteristic
332C22×C4C13×C22⋊C411yescharacteristic
333C22×C4C22×C4×C1311yescharacteristic
334C22×C4C2×D4×C1311yescharacteristic
335C22×C4C2×D4×C1312yes—
336C22×C4C13×#4112yes—
337M16—44no—
338M16—42no—
339M16—42no—
340C2×C8—24no—
341C2×C8—44no—
342C4⋊C4—22no—
343C4⋊C4—42no—
344C4⋊C4—42no—
345C4⋊C4—41no—
346C4⋊C4—41no—
347C22⋊C4—42no—
348C22⋊C4—42no—
349C22⋊C4—42no—
350C22⋊C4—42no—
351C22⋊C4—42no—
352C22⋊C4—42no—
353C22⋊C4—42no—
354C22⋊C4—42no—
355C42—41no—
356C42—41no—
357C13#944311yescharacteristic, direct product factor, Sylow
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—41no—
366C23—41no—
367C23—41no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23C13×#9912yes—
372C23C2×C13×C22⋊C411yescharacteristic
373C23C13×#12112yes—
374Q8—44no—
375Q8—82no—
376D4—44no—
377D4—44no—
378D4—44no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—24no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—22no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—42no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—41no—
397C2×C4—41no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—41no—
402C2×C4—41no—
403C2×C4—41no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—82no—
408C2×C4—82no—
409C2×C4—82no—
410C2×C4C13×#9912yes—
411C2×C4C4×D4×C1312yes—
412C2×C4C13×#12011yescharacteristic
413C2×C4C13×#12311yescharacteristic
414C8—44no—
415C22—21no—
416C22—21no—
417C22—22no—
418C22—22no—
419C22—22no—
420C22—22no—
421C22—42no—
422C22—42no—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22—81no—
432C22C13×#38611yescharacteristic
433C22C2×C13×#9911yescharacteristic
434C22C2×C13×#9911yescharacteristic
435C4—21no—
436C4—21no—
437C4—22no—
438C4—22no—
439C4—42no—
440C4—41no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—162no—
445C2—21no—
446C2—21no—
447C2—42no—
448C2—42no—
449C2—81no—
450C2C13×#188411yescharacteristic
451C2C13×#189811yescharacteristic
452C2C13×#190911yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC22×C13×#41C22
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
4. C13×#1511C2semidirect
5. C13×#1284C2semidirect
8. C2×C13×C4⋊Q8C4semidirect
9. C2×C13×#124C4semidirect
18. C13×#391C4semidirect
19. C13×#390C4semidirect
69. #9443C13direct (N × H)
135. #1511C2×C13semidirect
136. #1284C2×C13semidirect
196. C2×C4⋊Q8C4×C13semidirect
197. C2×#124C4×C13semidirect
206. #391C4×C13semidirect
207. #390C4×C13semidirect
357. C13#9443direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#28792
C13×#24322
C13×#17822
C13×#15112
C13×#12842
#944313