Finite Group Databasebeta

← C13×#9520 #15695859

Subgroups — C13×#9520 #15695859

Order 3328.

772 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3003C211yesmaximal, characteristic
2C13×#2976C211yesmaximal, characteristic, complemented
3C13×#1786C211yesmaximal, characteristic, complemented
4C13×#1783C211yesmaximal, characteristic, complemented
5C13×#1513C211yesmaximal, characteristic, complemented
6C13×#1305C211yesmaximal, characteristic, complemented
7C13×#1293C211yesmaximal, characteristic, complemented
8C23×D4×C13C2211yescharacteristic
9C2×C13×AGL(1,ℤ/8)—21no—
10C13×#525C2211yescharacteristic
11C13×#450—21no—
12C13×#450C412yescomplemented
13C13×#447—21no—
14C13×#447C412yescomplemented
15C13×#436—21no—
16C13×#435—21no—
17C13×#435—21no—
18C8×D4×C13—21no—
19C13×#433—21no—
20C13×#418—21no—
21C2×C13×#102—21no—
22C2×C13×#102—21no—
23C2×C13×#100—21no—
24C2×C13×#100—21no—
25C13×#408—21no—
26C13×#407C2211yescharacteristic
27C13×#407C2211yescharacteristic
28C13×#407C2211yescharacteristic
29C2×C13×C22⋊C8C2211yescharacteristic
30C13×#380C2211yescharacteristic
31C13×#328—21no—
32C13×#327—21no—
33C25×C13—21no—
34C2×C13×#41D411yescharacteristic
35C22×D4×C13—21no—
36C22×D4×C13—21no—
37C22×D4×C13—21no—
38C22×D4×C13—21no—
39C22×D4×C13—21no—
40C22×D4×C13—42no—
41C22×D4×C13—42no—
42C22×D4×C13C2×C412yes—
43C23×C4×C13C2311yescharacteristic
44C13×AGL(1,ℤ/8)—42no—
45C13×AGL(1,ℤ/8)—42no—
46C2×C13×SD16—22no—
47C2×C13×D8—22no—
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16D411yescharacteristic
52C2×C13×M16D411yescharacteristic
53C22×C8×C13—21no—
54C22×C8×C13D411yescharacteristic
55C22×C8×C13D411yescharacteristic
56C13×#123—21no—
57C13×C22⋊Q8C2×C411yescharacteristic
58C13×C22⋊Q8D411yescharacteristic
59C13×#121C2×C411yescharacteristic
60C13×#121D411yescharacteristic
61C13×#120—21no—
62C4×D4×C13—21no—
63C4×D4×C13—21no—
64C13×#117D411yescharacteristic
65C2×C13×C4⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C13×C4⋊C8—21no—
68C13×C4⋊C8—21no—
69C13×#102—22no—
70C13×#102—22no—
71C13×#102—42no—
72C13×#102—42no—
73C13×#100—42no—
74C13×#100—42no—
75C13×C22⋊C8—21no—
76C13×C22⋊C8—21no—
77C13×C22⋊C8—21no—
78C13×C22⋊C8—21no—
79C13×C22⋊C8—21no—
80C13×C22⋊C8—21no—
81C13×C22⋊C8—21no—
82C13×C22⋊C8—21no—
83C13×C22⋊C8—21no—
84C13×C22⋊C8C2×C412yes—
85C13×#97—21no—
86C4×C8×C13—21no—
87C13×#95—21no—
88#9520C1311yesmaximal, characteristic, direct product factor, Sylow
89C24×C13—22no—
90C24×C13—44no—
91C24×C13—41no—
92C24×C13—41no—
93C24×C13—81no—
94C24×C13—81no—
95C24×C13—82no—
96C24×C13#4111yescharacteristic
97C13×#41—41no—
98C13×#41—41no—
99C2×Q8×C13C22⋊C411yescharacteristic
100C2×D4×C13—22no—
101C2×D4×C13—22no—
102C2×D4×C13—22no—
103C2×D4×C13—22no—
104C2×D4×C13—22no—
105C2×D4×C13—22no—
106C2×D4×C13—21no—
107C2×D4×C13—21no—
108C2×D4×C13—21no—
109C2×D4×C13—22no—
110C2×D4×C13—22no—
111C2×D4×C13—41no—
112C2×D4×C13—41no—
113C2×D4×C13—41no—
114C2×D4×C13—41no—
115C2×D4×C13—41no—
116C2×D4×C13—41no—
117C2×D4×C13—44no—
118C2×D4×C13—44no—
119C2×D4×C13—44no—
120C2×D4×C13—41no—
121C2×D4×C13—41no—
122C2×D4×C13C22⋊C411yescharacteristic
123C22×C4×C13—21no—
124C22×C4×C13—41no—
125C22×C4×C13—41no—
126C22×C4×C13—41no—
127C22×C4×C13C22×C411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C22×C4×C13C2×D411yescharacteristic
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13#4111yescharacteristic
133C13×SD16—44no—
134C13×D8—44no—
135C13×M16—41no—
136C13×M16—41no—
137C13×M16—41no—
138C13×M16—41no—
139C13×M16—41no—
140C13×M16—41no—
141C13×M16—81no—
142C2×C8×C13—22no—
143C2×C8×C13—21no—
144C2×C8×C13—21no—
145C2×C8×C13—21no—
146C2×C8×C13—21no—
147C2×C8×C13—41no—
148C2×C8×C13—41no—
149C2×C8×C13—41no—
150C2×C8×C13—81no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—41no—
154C13×C4⋊C4—41no—
155C13×C4⋊C4C22⋊C411yescharacteristic
156C13×C4⋊C4C22⋊C411yescharacteristic
157C13×C22⋊C4—21no—
158C13×C22⋊C4—21no—
159C13×C22⋊C4—21no—
160C13×C22⋊C4—21no—
161C13×C22⋊C4—21no—
162C13×C22⋊C4—81no—
163C42×C13—21no—
164#3003C2×C1311yescharacteristic
165#2976C2×C1311yescharacteristic, complemented
166#1786C2×C1311yescharacteristic, complemented
167#1783C2×C1311yescharacteristic, complemented
168#1513C2×C1311yescharacteristic, complemented
169#1305C2×C1311yescharacteristic, complemented
170#1293C2×C1311yescharacteristic, complemented
171C23×C13—21no—
172C23×C13—21no—
173C23×C13—24no—
174C23×C13—21no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—42no—
178C23×C13—42no—
179C23×C13—42no—
180C23×C13—42no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—82no—
184C23×C13—81no—
185C23×C13—81no—
186C23×C13—82no—
187C23×C13—82no—
188C23×C13—82no—
189C23×C13—88no—
190C23×C13—88no—
191C23×C13—81no—
192C23×C13—81no—
193C23×C13C4×D411yescharacteristic
194C23×C13#12111yescharacteristic
195C23×C13#12311yescharacteristic
196Q8×C13—41no—
197D4×C13—24no—
198D4×C13—24no—
199D4×C13—42no—
200D4×C13—42no—
201D4×C13—42no—
202D4×C13—42no—
203D4×C13—41no—
204D4×C13—41no—
205D4×C13—41no—
206D4×C13—42no—
207D4×C13—42no—
208D4×C13—81no—
209D4×C13—81no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—21no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—41no—
223C2×C4×C13—41no—
224C2×C4×C13—81no—
225C2×C4×C13—81no—
226C2×C4×C13—81no—
227C2×C4×C13C2×C22⋊C411yescharacteristic
228C2×C4×C13C4×D411yescharacteristic
229C2×C4×C13#12011yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C8×C13—42no—
232C8×C13—41no—
233C8×C13—41no—
234C8×C13—41no—
235C8×C13—41no—
236C8×C13—81no—
237C23×D4C22×C1311yescharacteristic
238C2×AGL(1,ℤ/8)—21no—
239#525C22×C1311yescharacteristic
240#450—21no—
241#450C4×C1312yescomplemented
242#447—21no—
243#447C4×C1312yescomplemented
244#436—21no—
245#435—21no—
246#435—21no—
247C8×D4—21no—
248#433—21no—
249#418—21no—
250C2×#102—21no—
251C2×#102—21no—
252C2×#100—21no—
253C2×#100—21no—
254#408—21no—
255#407C22×C1311yescharacteristic
256#407C22×C1311yescharacteristic
257#407C22×C1311yescharacteristic
258C2×C22⋊C8C22×C1311yescharacteristic
259#380C22×C1311yescharacteristic
260#328—21no—
261#327—21no—
262C22×C13—21no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—21no—
270C22×C13—42no—
271C22×C13—42no—
272C22×C13—41no—
273C22×C13—44no—
274C22×C13—41no—
275C22×C13—41no—
276C22×C13—82no—
277C22×C13—82no—
278C22×C13—82no—
279C22×C13—82no—
280C22×C13—84no—
281C22×C13—84no—
282C22×C13—84no—
283C22×C13—84no—
284C22×C13—82no—
285C22×C13—82no—
286C22×C13#38611yescharacteristic
287C22×C13#47111yescharacteristic
288C22×C13#47211yescharacteristic
289C4×C13—21no—
290C4×C13—21no—
291C4×C13—21no—
292C4×C13—41no—
293C4×C13—41no—
294C4×C13—41no—
295C4×C13—161no—
296C4×C13B(4,𝔽2)11yescharacteristic
297C4×C13B(4,𝔽2)11yescharacteristic
298C25—21no—
299C2×#41D4×C1311yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—42no—
306C22×D4—42no—
307C22×D4C2×C4×C1312yes—
308C23×C4C23×C1311yescharacteristic
309AGL(1,ℤ/8)—42no—
310AGL(1,ℤ/8)—42no—
311C2×SD16—22no—
312C2×D8—22no—
313C2×M16—21no—
314C2×M16—21no—
315C2×M16—21no—
316C2×M16D4×C1311yescharacteristic
317C2×M16D4×C1311yescharacteristic
318C22×C8—21no—
319C22×C8D4×C1311yescharacteristic
320C22×C8D4×C1311yescharacteristic
321#123—21no—
322C22⋊Q8C2×C4×C1311yescharacteristic
323C22⋊Q8D4×C1311yescharacteristic
324#121C2×C4×C1311yescharacteristic
325#121D4×C1311yescharacteristic
326#120—21no—
327C4×D4—21no—
328C4×D4—21no—
329#117D4×C1311yescharacteristic
330C2×C4⋊C4—21no—
331C2×C22⋊C4—21no—
332C4⋊C8—21no—
333C4⋊C8—21no—
334#102—22no—
335#102—22no—
336#102—42no—
337#102—42no—
338#100—42no—
339#100—42no—
340C22⋊C8—21no—
341C22⋊C8—21no—
342C22⋊C8—21no—
343C22⋊C8—21no—
344C22⋊C8—21no—
345C22⋊C8—21no—
346C22⋊C8—21no—
347C22⋊C8—21no—
348C22⋊C8—21no—
349C22⋊C8C2×C4×C1312yes—
350#97—21no—
351C4×C8—21no—
352#95—21no—
353C2×C13—21no—
354C2×C13—21no—
355C2×C13—41no—
356C2×C13—41no—
357C2×C13—81no—
358C2×C13—84no—
359C2×C13#188911yescharacteristic
360C2×C13#190311yescharacteristic
361C2×C13#190711yescharacteristic
362C24—22no—
363C24—44no—
364C24—41no—
365C24—41no—
366C24—81no—
367C24—81no—
368C24—82no—
369C24C13×#4111yescharacteristic
370#41—41no—
371#41—41no—
372C2×Q8C13×C22⋊C411yescharacteristic
373C2×D4—22no—
374C2×D4—22no—
375C2×D4—22no—
376C2×D4—22no—
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—21no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—41no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4C13×C22⋊C411yescharacteristic
396C22×C4—21no—
397C22×C4—41no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4C22×C4×C1311yescharacteristic
401C22×C4C2×D4×C1311yescharacteristic
402C22×C4C2×D4×C1311yescharacteristic
403C22×C4C2×D4×C1311yescharacteristic
404C22×C4C2×D4×C1311yescharacteristic
405C22×C4C13×#4111yescharacteristic
406SD16—44no—
407D8—44no—
408M16—41no—
409M16—41no—
410M16—41no—
411M16—41no—
412M16—41no—
413M16—41no—
414M16—81no—
415C2×C8—22no—
416C2×C8—21no—
417C2×C8—21no—
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—41no—
421C2×C8—41no—
422C2×C8—41no—
423C2×C8—81no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—41no—
427C4⋊C4—41no—
428C4⋊C4C13×C22⋊C411yescharacteristic
429C4⋊C4C13×C22⋊C411yescharacteristic
430C22⋊C4—21no—
431C22⋊C4—21no—
432C22⋊C4—21no—
433C22⋊C4—21no—
434C22⋊C4—21no—
435C22⋊C4—81no—
436C42—21no—
437C13#952011yescharacteristic, direct product factor, Sylow
438C23—21no—
439C23—21no—
440C23—24no—
441C23—21no—
442C23—41no—
443C23—41no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—42no—
449C23—42no—
450C23—82no—
451C23—82no—
452C23—81no—
453C23—81no—
454C23—82no—
455C23—82no—
456C23—88no—
457C23—88no—
458C23—81no—
459C23—81no—
460C23C4×D4×C1311yescharacteristic
461C23C13×#12111yescharacteristic
462C23C13×#12311yescharacteristic
463Q8—41no—
464D4—24no—
465D4—24no—
466D4—41no—
467D4—42no—
468D4—42no—
469D4—42no—
470D4—42no—
471D4—41no—
472D4—41no—
473D4—42no—
474D4—42no—
475D4—81no—
476D4—81no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—81no—
492C2×C4—81no—
493C2×C4—81no—
494C2×C4C2×C13×C22⋊C411yescharacteristic
495C2×C4C4×D4×C1311yescharacteristic
496C2×C4C13×#12011yescharacteristic
497C2×C4C13×#12111yescharacteristic
498C8—42no—
499C8—41no—
500C8—41no—
501C8—41no—
502C8—41no—
503C8—81no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—42no—
513C22—42no—
514C22—41no—
515C22—44no—
516C22—41no—
517C22—41no—
518C22—82no—
519C22—82no—
520C22—82no—
521C22—82no—
522C22—84no—
523C22—84no—
524C22—84no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22C13×#38611yescharacteristic
529C22C13×#47111yescharacteristic
530C22C13×#47211yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—161no—
538C4C13×B(4,𝔽2)11yescharacteristic
539C4C13×B(4,𝔽2)11yescharacteristic
540C2—21no—
541C2—21no—
542C2—41no—
543C2—41no—
544C2—81no—
545C2—84no—
546C2C13×#188911yescharacteristic
547C2C13×#190311yescharacteristic
548C2C13×#190711yescharacteristic
subgroupG/H
center, socleC22×C13#386
commutatorC22×C4C22×C4×C13
Frattini, cosocleC23×C4C23×C13
prime radicalC13×#3003C2
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
2. C13×#2976C2semidirect
3. C13×#1786C2semidirect
4. C13×#1783C2semidirect
5. C13×#1513C2semidirect
6. C13×#1305C2semidirect
7. C13×#1293C2semidirect
12. C13×#450C4semidirect
14. C13×#447C4semidirect
88. #9520C13direct (N × H)
165. #2976C2×C13semidirect
166. #1786C2×C13semidirect
167. #1783C2×C13semidirect
168. #1513C2×C13semidirect
169. #1305C2×C13semidirect
170. #1293C2×C13semidirect
241. #450C4×C13semidirect
243. #447C4×C13semidirect
437. C13#9520direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#30032
C13×#29762
C13×#17862
C13×#17832
C13×#15132
C13×#13052
C13×#12932
#952013