Finite Group Databasebeta

← C13×#33569 #15719908

Subgroups — C13×#33569 #15719908

Order 3328.

1082 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3544C211yesmaximal, characteristic, complemented
2C13×#3020C212yesmaximal, complemented
3C2×C13×#456C211yesmaximal, characteristic, complemented
4C13×#2205C212yesmaximal, complemented
5C13×#2204C212yesmaximal, complemented
6C13×#2203C214yesmaximal, complemented
7C13×#2133C212yesmaximal, complemented
8C2×C13×#356C211yesmaximal, characteristic, complemented
9C2×C13×2−1+4C2211yescharacteristic
10C13×#575—22no—
11C2×C13×#137—21no—
12C13×#563—21no—
13C13×#563C2212yescomplemented
14Q82×C13C2211yescharacteristic, complemented
15C13×#555C2211yescharacteristic, complemented
16C13×#554—21no—
17C13×#552—22no—
18C13×#547—22no—
19C13×#544—22no—
20C13×#542—22no—
21C13×#536—21no—
22C13×#536C2212yes—
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529—21no—
25C13×#456—21no—
26C13×#456—21no—
27C13×#456—22no—
28C13×#456C2212yes—
29C13×#456C2212yes—
30C13×#456C2214yes—
31C13×#454—22no—
32C13×#454C2214yes—
33C13×#421—22no—
34C2×C13×#104—21no—
35C2×C13×#101C2211yescharacteristic
36C2×C13×#101C2212yes—
37C13×#356C2212yescomplemented
38C13×#356C2212yescomplemented
39C13×#356C2214yescomplemented
40C13×#355C2214yescomplemented
41C13×2−1+4—22no—
42C13×2−1+4—21no—
43C13×2−1+4—42no—
44C13×2−1+4C2312yes—
45C2×C13×#41—21no—
46C2×C13×#41—21no—
47C2×C13×#41—22no—
48C2×C13×#41—41no—
49C2×C13×#41D412yes—
50C22×Q8×C13—41no—
51C22×Q8×C13D411yescharacteristic
52C22×Q8×C13C2311yescharacteristic
53C13×#137—22no—
54C13×#137—22no—
55C13×#137—24no—
56C13×#137—42no—
57C13×#137—42no—
58C13×AGL(1,ℤ/8)—24no—
59C13×AGL(1,ℤ/8)—42no—
60C13×#135—44no—
61C2×C13×Q16—41no—
62C2×C13×SD16—41no—
63C2×C13×M16—21no—
64C2×C13×M16—22no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—22no—
67C13×C4⋊Q8—21no—
68C13×C4⋊Q8—22no—
69C13×C4⋊Q8D411yescharacteristic
70C13×C4⋊Q8D411yescharacteristic
71C13×C4⋊Q8D412yes—
72C13×C4⋊Q8C2311yescharacteristic
73C13×C4⋊Q8C2311yescharacteristic
74C13×C4⋊Q8C2312yes—
75C13×#126—22no—
76C13×#126—22no—
77C13×#126—22no—
78C13×#125—21no—
79C13×#125—22no—
80C13×#125—22no—
81C13×#125—22no—
82C13×#124—21no—
83C13×#124—21no—
84C13×#124—21no—
85C13×#124D412yes—
86C13×#124C2312yes—
87C13×#123—22no—
88C13×#123—22no—
89C13×#123—22no—
90C13×#123—22no—
91C13×#123—22no—
92C13×C22⋊Q8—21no—
93C13×C22⋊Q8—22no—
94C13×C22⋊Q8—22no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—22no—
97C13×C22⋊Q8—22no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8—22no—
100C13×#121—21no—
101C13×#121—22no—
102C4×Q8×C13—21no—
103C4×Q8×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13—22no—
106C4×D4×C13—21no—
107C13×#117—22no—
108C13×#117—21no—
109C13×#117—22no—
110C13×#117D412yes—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C42×C13D411yescharacteristic
114C13×#104—22no—
115C13×#104—22no—
116C13×#104—24no—
117C13×#104—24no—
118C13×#101—22no—
119C13×#101—21no—
120C13×#101C2312yes—
121C13×#101C2314yes—
122#33569C1311yesmaximal, characteristic, direct product factor, Sylow
123C13×#41—24no—
124C13×#41—22no—
125C13×#41—24no—
126C13×#41—22no—
127C13×#41—42no—
128C13×#41—41no—
129C13×#41—42no—
130C13×#41—42no—
131C13×#41—42no—
132C13×#41—44no—
133C13×#41—42no—
134C13×#41—41no—
135C13×#41—42no—
136C13×#41—81no—
137C13×#41—81no—
138C2×Q8×C13—21no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—22no—
143C2×Q8×C13—41no—
144C2×Q8×C13—41no—
145C2×Q8×C13—41no—
146C2×Q8×C13—41no—
147C2×Q8×C13—42no—
148C2×Q8×C13—44no—
149C2×Q8×C13—42no—
150C2×Q8×C13C2×D411yescharacteristic
151C2×Q8×C13C2×D412yes—
152C2×Q8×C13C2×D411yescharacteristic
153C2×Q8×C13C2×D411yescharacteristic
154C2×Q8×C13C2×D412yes—
155C2×Q8×C13C2411yescharacteristic
156C2×D4×C13—21no—
157C2×D4×C13—22no—
158C2×D4×C13—21no—
159C2×D4×C13—22no—
160C2×D4×C13—21no—
161C2×D4×C13—41no—
162C2×D4×C13C2×D412yes—
163C22×C4×C13—22no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—41no—
169C22×C4×C13—42no—
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D412yes—
172C13×Q16—42no—
173C13×Q16—42no—
174C13×Q16—44no—
175C13×SD16—42no—
176C13×SD16—42no—
177C13×SD16—44no—
178C13×SD16—44no—
179C13×D8—44no—
180C13×M16—24no—
181C13×M16—22no—
182C13×M16—42no—
183C13×M16—41no—
184C2×C8×C13—41no—
185C2×C8×C13—42no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—22no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C42×C13—21no—
212C42×C13—22no—
213C42×C13—21no—
214C42×C13—21no—
215C42×C13C2×D411yescharacteristic
216C42×C13C2×D411yescharacteristic
217C42×C13C2×D412yes—
218C42×C13C2×D412yes—
219#3544C2×C1311yescharacteristic, complemented
220#3020C2×C1312yescomplemented
221C2×#456C2×C1311yescharacteristic, complemented
222#2205C2×C1312yescomplemented
223#2204C2×C1312yescomplemented
224#2203C2×C1314yescomplemented
225#2133C2×C1312yescomplemented
226C2×#356C2×C1311yescharacteristic, complemented
227C23×C13—22no—
228C23×C13—41no—
229C23×C13#12011yescharacteristic
230Q8×C13—24no—
231Q8×C13—22no—
232Q8×C13—42no—
233Q8×C13—41no—
234Q8×C13—41no—
235Q8×C13—42no—
236Q8×C13—42no—
237Q8×C13—41no—
238Q8×C13—41no—
239Q8×C13—41no—
240Q8×C13—42no—
241Q8×C13—81no—
242Q8×C13—81no—
243D4×C13—24no—
244D4×C13—22no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—41no—
248D4×C13—42no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—81no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—21no—
263C2×C4×C13—22no—
264C2×C4×C13—21no—
265C2×C4×C13—42no—
266C2×C4×C13—44no—
267C2×C4×C13—44no—
268C2×C4×C13—42no—
269C2×C4×C13—44no—
270C2×C4×C13—42no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—82no—
275C2×C4×C13—82no—
276C2×C4×C13#12011yescharacteristic
277C2×C4×C13#12012yes—
278C2×C4×C13C22×D411yescharacteristic
279C2×C4×C13C22×D412yes—
280C8×C13—44no—
281C8×C13—42no—
282C2×2−1+4C22×C1311yescharacteristic
283#575—22no—
284C2×#137—21no—
285#563—21no—
286#563C22×C1312yescomplemented
287Q82C22×C1311yescharacteristic, complemented
288#555C22×C1311yescharacteristic, complemented
289#554—21no—
290#552—22no—
291#547—22no—
292#544—22no—
293#542—22no—
294#536—21no—
295#536C22×C1312yes—
296C2×C4⋊Q8C22×C1311yescharacteristic
297#529—21no—
298#456—21no—
299#456—21no—
300#456—22no—
301#456C22×C1312yes—
302#456C22×C1314yes—
303#456C22×C1312yes—
304#454—22no—
305#454C22×C1314yes—
306#421—22no—
307C2×#104—21no—
308C2×#101C22×C1312yes—
309C2×#101C22×C1311yescharacteristic
310#356C22×C1312yescomplemented
311#356C22×C1312yescomplemented
312#356C22×C1314yescomplemented
313#355C22×C1314yescomplemented
314C22×C13—41no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—82no—
320C22×C13B(4,𝔽2)11yescharacteristic
321C22×C13B(4,𝔽2)11yescharacteristic
322C22×C13C2×#12011yescharacteristic
323C4×C13—22no—
324C4×C13—22no—
325C4×C13—21no—
326C4×C13—22no—
327C4×C13—21no—
328C4×C13—42no—
329C4×C13—41no—
330C4×C13—42no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—42no—
3352−1+4—22no—
3362−1+4—21no—
3372−1+4—42no—
3382−1+4C23×C1312yes—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—22no—
342C2×#41—41no—
343C2×#41D4×C1312yes—
344C22×Q8—41no—
345C22×Q8D4×C1311yescharacteristic
346C22×Q8C23×C1311yescharacteristic
347#137—22no—
348#137—22no—
349#137—24no—
350#137—42no—
351#137—42no—
352AGL(1,ℤ/8)—24no—
353AGL(1,ℤ/8)—42no—
354#135—44no—
355C2×Q16—41no—
356C2×SD16—41no—
357C2×M16—21no—
358C2×M16—22no—
359C4⋊Q8—21no—
360C4⋊Q8—22no—
361C4⋊Q8—21no—
362C4⋊Q8—22no—
363C4⋊Q8D4×C1311yescharacteristic
364C4⋊Q8D4×C1311yescharacteristic
365C4⋊Q8D4×C1312yes—
366C4⋊Q8C23×C1311yescharacteristic
367C4⋊Q8C23×C1311yescharacteristic
368C4⋊Q8C23×C1312yes—
369#126—22no—
370#126—22no—
371#126—22no—
372#125—21no—
373#125—22no—
374#125—22no—
375#125—22no—
376#124—21no—
377#124—21no—
378#124—21no—
379#124D4×C1312yes—
380#124C23×C1312yes—
381#123—22no—
382#123—22no—
383#123—22no—
384#123—22no—
385#123—22no—
386C22⋊Q8—21no—
387C22⋊Q8—22no—
388C22⋊Q8—22no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8—22no—
392C22⋊Q8—22no—
393C22⋊Q8—22no—
394#121—21no—
395#121—22no—
396C4×Q8—21no—
397C4×Q8—22no—
398C4×D4—22no—
399C4×D4—22no—
400C4×D4—21no—
401#117—22no—
402#117—21no—
403#117—22no—
404#117D4×C1312yes—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—22no—
407C2×C42D4×C1311yescharacteristic
408#104—22no—
409#104—22no—
410#104—24no—
411#104—24no—
412#101—22no—
413#101—21no—
414#101C23×C1312yes—
415#101C23×C1314yes—
416C2×C13—21no—
417C2×C13—21no—
418C2×C13—21no—
419C2×C13—82no—
420C2×C13—82no—
421C2×C13C2×B(4,𝔽2)11yescharacteristic
422#41—24no—
423#41—22no—
424#41—24no—
425#41—22no—
426#41—42no—
427#41—41no—
428#41—42no—
429#41—42no—
430#41—42no—
431#41—44no—
432#41—42no—
433#41—41no—
434#41—42no—
435#41—81no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—22no—
442C2×Q8—41no—
443C2×Q8—41no—
444C2×Q8—41no—
445C2×Q8—41no—
446C2×Q8—42no—
447C2×Q8—44no—
448C2×Q8—42no—
449C2×Q8C2×D4×C1311yescharacteristic
450C2×Q8C2×D4×C1312yes—
451C2×Q8C2×D4×C1311yescharacteristic
452C2×Q8C2×D4×C1311yescharacteristic
453C2×Q8C2×D4×C1312yes—
454C2×Q8C24×C1311yescharacteristic
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—21no—
458C2×D4—22no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4C2×D4×C1312yes—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4—42no—
469C22×C4C2×D4×C1311yescharacteristic
470C22×C4C2×D4×C1312yes—
471Q16—42no—
472Q16—42no—
473Q16—44no—
474SD16—42no—
475SD16—42no—
476SD16—44no—
477SD16—44no—
478D8—44no—
479M16—24no—
480M16—22no—
481M16—42no—
482M16—41no—
483C2×C8—41no—
484C2×C8—42no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C22⋊C4—22no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—22no—
510C42—21no—
511C42—22no—
512C42—21no—
513C42—21no—
514C42C2×D4×C1311yescharacteristic
515C42C2×D4×C1311yescharacteristic
516C42C2×D4×C1312yes—
517C42C2×D4×C1312yes—
518C13#3356911yescharacteristic, direct product factor, Sylow
519C23—22no—
520C23—41no—
521C23C13×#12011yescharacteristic
522Q8—24no—
523Q8—22no—
524Q8—42no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—42no—
530Q8—42no—
531Q8—41no—
532Q8—42no—
533Q8—81no—
534Q8—81no—
535D4—24no—
536D4—22no—
537D4—42no—
538D4—42no—
539D4—42no—
540D4—41no—
541D4—42no—
542D4—42no—
543D4—42no—
544D4—42no—
545D4—81no—
546C2×C4—21no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—22no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—44no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—82no—
567C2×C4—82no—
568C2×C4C13×#12011yescharacteristic
569C2×C4C13×#12012yes—
570C2×C4C22×D4×C1311yescharacteristic
571C2×C4C22×D4×C1312yes—
572C8—44no—
573C8—42no—
574C22—41no—
575C22—42no—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—82no—
580C22C13×B(4,𝔽2)11yescharacteristic
581C22C13×B(4,𝔽2)11yescharacteristic
582C22C2×C13×#12011yescharacteristic
583C4—22no—
584C4—22no—
585C4—21no—
586C4—22no—
587C4—21no—
588C4—42no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—41no—
593C4—42no—
594C4—42no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—82no—
599C2—82no—
600C2C2×C13×B(4,𝔽2)11yescharacteristic
subgroupG/H
center, socleC2×C13C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×Q8C24×C13
LCSG ▷ C2×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3544C2semidirect
2. C13×#3020C2semidirect
3. C2×C13×#456C2semidirect
4. C13×#2205C2semidirect
5. C13×#2204C2semidirect
6. C13×#2203C2semidirect
7. C13×#2133C2semidirect
8. C2×C13×#356C2semidirect
13. C13×#563C22semidirect
14. Q82×C13C22semidirect
15. C13×#555C22semidirect
37. C13×#356C22semidirect
38. C13×#356C22semidirect
39. C13×#356C22semidirect
40. C13×#355C22semidirect
122. #33569C13direct (N × H)
219. #3544C2×C13semidirect
220. #3020C2×C13semidirect
221. C2×#456C2×C13semidirect
222. #2205C2×C13semidirect
223. #2204C2×C13semidirect
224. #2203C2×C13semidirect
225. #2133C2×C13semidirect
226. C2×#356C2×C13semidirect
286. #563C22×C13semidirect
287. Q82C22×C13semidirect
288. #555C22×C13semidirect
310. #356C22×C13semidirect
311. #356C22×C13semidirect
312. #356C22×C13semidirect
313. #355C22×C13semidirect
518. C13#33569direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35442
C13×#30202
C2×C13×#4562
C13×#22052
C13×#22042
C13×#22032
C13×#21332
C2×C13×#3562
#3356913