Finite Group Databasebeta

← C13×#18439 #15704778

Subgroups — C13×#18439 #15704778

Order 3328.

964 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C13×#3230C211yesmaximal, characteristic, complemented
4C13×#2658C211yesmaximal, characteristic, complemented
5C13×#1618C214yesmaximal, complemented
6C13×#1614C214yesmaximal, complemented
7C13×#1506C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#556—21no—
13C13×#551—22no—
14D4×Q8×C13—21no—
15C13×#548—21no—
16C13×#546—21no—
17C13×#543C2212yes—
18C13×#542—21no—
19C13×#542—22no—
20C13×#538C2212yes—
21C13×#536—21no—
22C13×#533C2211yescharacteristic
23C2×C13×C4⋊Q8—21no—
24C2×C13×C4⋊Q8C2211yescharacteristic
25C13×#529C2211yescharacteristic
26C2×C13×#124—21no—
27C2×C13×#124C2211yescharacteristic
28C13×#501—21no—
29C13×#500—21no—
30C13×#489—21no—
31C13×#487—21no—
32C13×#484C2212yes—
33C13×#484C2214yes—
34C13×#481C2212yes—
35C13×#477—22no—
36C13×#475—21no—
37C13×#474—21no—
38C13×#432C2211yescharacteristic
39C13×#431C2211yescharacteristic
40C13×#399—22no—
41C13×#399C2214yes—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#323C2214yes—
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13D411yescharacteristic
52C13×C4⋊Q8—21no—
53C13×C4⋊Q8—22no—
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—44no—
59C13×C4⋊Q8D411yescharacteristic
60C13×C4⋊Q8D411yescharacteristic
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—22no—
64C13×#126—21no—
65C13×#125—21no—
66C13×#125D411yescharacteristic
67C13×#124—21no—
68C13×#124—22no—
69C13×#124—22no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124—21no—
74C13×#124—44no—
75C13×#124D411yescharacteristic
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—21no—
80C13×#123—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—21no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8C2311yescharacteristic
91C13×C22⋊Q8C2312yes—
92C13×#121—21no—
93C13×#121—22no—
94C13×#121—22no—
95C13×#121C2311yescharacteristic
96C13×#120—22no—
97C4×Q8×C13—21no—
98C4×Q8×C13—21no—
99C4×Q8×C13D411yescharacteristic
100C4×Q8×C13D412yes—
101C4×D4×C13—21no—
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13—22no—
105C4×D4×C13D411yescharacteristic
106C13×#117—22no—
107C13×#117—21no—
108C13×#117—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—24no—
111C2×C13×C4⋊C4C2312yes—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4D412yes—
115C2×C13×C22⋊C4C2312yes—
116C2×C42×C13—21no—
117C2×C42×C13C2311yescharacteristic
118C13×#107—22no—
119C13×#107—24no—
120C13×#106—22no—
121C13×C4⋊C8—21no—
122C13×C4⋊C8—21no—
123C13×#103—22no—
124C13×#103—24no—
125C13×#102—22no—
126C13×C22⋊C8C2312yes—
127C13×C22⋊C8C2312yes—
128C13×#97—21no—
129C4×C8×C13—21no—
130C13×#95—21no—
131C13×#95C2312yes—
132#18439C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13C2×D412yes—
134C13×#41—82no—
135C2×Q8×C13—22no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—21no—
139C2×Q8×C13—42no—
140C2×Q8×C13—42no—
141C2×Q8×C13—42no—
142C2×Q8×C13—41no—
143C2×Q8×C13—41no—
144C2×Q8×C13—82no—
145C2×Q8×C13C2×D411yescharacteristic
146C2×Q8×C13C2×D412yes—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—42no—
153C2×D4×C13C2×D411yescharacteristic
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—22no—
160C22×C4×C13C2×D411yescharacteristic
161C22×C4×C13C2×D411yescharacteristic
162C22×C4×C13C2×D412yes—
163C22×C4×C13C2411yescharacteristic
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
181C13×C4⋊C4—48no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—41no—
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C4⋊C4C2×D411yescharacteristic
186C13×C4⋊C4C2×D412yes—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—21no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—48no—
203C42×C13—24no—
204C42×C13—22no—
205C42×C13—22no—
206C42×C13—21no—
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2×D411yescharacteristic
211#3561C2×C1311yescharacteristic
212#3239C2×C1311yescharacteristic, complemented
213#3230C2×C1311yescharacteristic, complemented
214#2658C2×C1311yescharacteristic, complemented
215#1618C2×C1314yescomplemented
216#1614C2×C1314yescomplemented
217#1506C2×C1311yescharacteristic, complemented
218#1500C2×C1311yescharacteristic, complemented
219#1469C2×C1311yescharacteristic, complemented
220C23×C13—22no—
221C23×C13—21no—
222C23×C13—24no—
223C23×C13—42no—
224C23×C13—42no—
225C23×C13C22×D411yescharacteristic
226Q8×C13—41no—
227Q8×C13—42no—
228Q8×C13—42no—
229Q8×C13—42no—
230Q8×C13—81no—
231Q8×C13—82no—
232Q8×C13—82no—
233Q8×C13—82no—
234D4×C13—41no—
235D4×C13—42no—
236D4×C13—42no—
237D4×C13—81no—
238D4×C13—82no—
239D4×C13—82no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—24no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—22no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—42no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—82no—
258C2×C4×C13—82no—
259C2×C4×C13—82no—
260C2×C4×C13#12011yescharacteristic
261C2×C4×C13#12011yescharacteristic
262C2×C4×C13#12011yescharacteristic
263C2×C4×C13#12011yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C2×C4×C13C22×D411yescharacteristic
266C8×C13—42no—
267C8×C13—42no—
268#563—21no—
269#562—21no—
270#556—21no—
271#551—22no—
272D4×Q8—21no—
273#548—21no—
274#546—21no—
275#543C22×C1312yes—
276#542—21no—
277#542—22no—
278#538C22×C1312yes—
279#536—21no—
280#533C22×C1311yescharacteristic
281C2×C4⋊Q8—21no—
282C2×C4⋊Q8C22×C1311yescharacteristic
283#529C22×C1311yescharacteristic
284C2×#124—21no—
285C2×#124C22×C1311yescharacteristic
286#501—21no—
287#500—21no—
288#489—21no—
289#487—21no—
290#484C22×C1312yes—
291#484C22×C1314yes—
292#481C22×C1312yes—
293#477—22no—
294#475—21no—
295#474—21no—
296#432C22×C1311yescharacteristic
297#431C22×C1311yescharacteristic
298#399—22no—
299#399C22×C1314yes—
300#376C22×C1311yescharacteristic
301#328C22×C1312yes—
302#328C22×C1314yes—
303#327C22×C1312yes—
304#323C22×C1314yes—
305C22×C13—21no—
306C22×C13—21no—
307C22×C13—41no—
308C22×C13—42no—
309C22×C13—41no—
310C22×C13—42no—
311C22×C13—42no—
312C22×C13—41no—
313C22×C13—84no—
314C22×C13C2×#12011yescharacteristic
315C22×C13#57812yes—
316C4×C13—21no—
317C4×C13—21no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—21no—
321C4×C13—44no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—42no—
325C4×C13—42no—
326C4×C13—41no—
327C4×C13—42no—
328C4×C13—82no—
329C4×C13#45312yes—
330C2×#41—21no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8D4×C1311yescharacteristic
334C22×D4D4×C1311yescharacteristic
335C4⋊Q8—21no—
336C4⋊Q8—22no—
337C4⋊Q8—21no—
338C4⋊Q8—21no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—44no—
342C4⋊Q8D4×C1311yescharacteristic
343C4⋊Q8D4×C1311yescharacteristic
344#126—22no—
345#126—22no—
346#126—22no—
347#126—21no—
348#125—21no—
349#125D4×C1311yescharacteristic
350#124—21no—
351#124—22no—
352#124—22no—
353#124—21no—
354#124—21no—
355#124—21no—
356#124—21no—
357#124—44no—
358#124D4×C1311yescharacteristic
359#123—22no—
360#123—22no—
361#123—22no—
362#123—21no—
363#123—22no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8C23×C1311yescharacteristic
374C22⋊Q8C23×C1312yes—
375#121—21no—
376#121—22no—
377#121—22no—
378#121C23×C1311yescharacteristic
379#120—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8D4×C1311yescharacteristic
383C4×Q8D4×C1312yes—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4D4×C1311yescharacteristic
389#117—22no—
390#117—21no—
391#117—21no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4C23×C1312yes—
395C2×C22⋊C4—22no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4D4×C1312yes—
398C2×C22⋊C4C23×C1312yes—
399C2×C42—21no—
400C2×C42C23×C1311yescharacteristic
401#107—22no—
402#107—24no—
403#106—22no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406#103—22no—
407#103—24no—
408#102—22no—
409C22⋊C8C23×C1312yes—
410C22⋊C8C23×C1312yes—
411#97—21no—
412C4×C8—21no—
413#95—21no—
414#95C23×C1312yes—
415C2×C13—22no—
416C2×C13—81no—
417C2×C13—82no—
418C2×C13#301111yescharacteristic
419C2×C13C2×#45311yescharacteristic
420C2×C13#302811yescharacteristic
421C24C2×D4×C1312yes—
422#41—82no—
423C2×Q8—22no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—42no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8—41no—
431C2×Q8—41no—
432C2×Q8—82no—
433C2×Q8C2×D4×C1311yescharacteristic
434C2×Q8C2×D4×C1312yes—
435C2×D4—21no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—42no—
441C2×D4C2×D4×C1311yescharacteristic
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4C2×D4×C1311yescharacteristic
449C22×C4C2×D4×C1311yescharacteristic
450C22×C4C2×D4×C1312yes—
451C22×C4C24×C1311yescharacteristic
452C2×C8—22no—
453C2×C8—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—22no—
465C4⋊C4—21no—
466C4⋊C4—22no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—48no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C1311yescharacteristic
473C4⋊C4C2×D4×C1311yescharacteristic
474C4⋊C4C2×D4×C1312yes—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—22no—
479C22⋊C4—22no—
480C22⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—21no—
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—21no—
490C22⋊C4—48no—
491C42—24no—
492C42—22no—
493C42—22no—
494C42—21no—
495C42C2×D4×C1311yescharacteristic
496C42C2×D4×C1311yescharacteristic
497C42C2×D4×C1311yescharacteristic
498C42C2×D4×C1311yescharacteristic
499C13#1843911yescharacteristic, direct product factor, Sylow
500C23—22no—
501C23—21no—
502C23—24no—
503C23—42no—
504C23—42no—
505C23C22×D4×C1311yescharacteristic
506Q8—41no—
507Q8—42no—
508Q8—42no—
509Q8—42no—
510Q8—81no—
511Q8—82no—
512Q8—82no—
513Q8—82no—
514D4—41no—
515D4—42no—
516D4—42no—
517D4—81no—
518D4—82no—
519D4—82no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—82no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4C13×#12011yescharacteristic
541C2×C4C13×#12011yescharacteristic
542C2×C4C13×#12011yescharacteristic
543C2×C4C13×#12011yescharacteristic
544C2×C4C22×D4×C1311yescharacteristic
545C2×C4C22×D4×C1311yescharacteristic
546C8—42no—
547C8—42no—
548C22—21no—
549C22—21no—
550C22—41no—
551C22—42no—
552C22—41no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—84no—
557C22C2×C13×#12011yescharacteristic
558C22C13×#57812yes—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—41no—
566C4—41no—
567C4—42no—
568C4—42no—
569C4—41no—
570C4—42no—
571C4—82no—
572C4C13×#45312yes—
573C2—22no—
574C2—82no—
575C2—81no—
576C2C13×#301111yescharacteristic
577C2C2×C13×#45311yescharacteristic
578C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3561C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3239C2semidirect
3. C13×#3230C2semidirect
4. C13×#2658C2semidirect
5. C13×#1618C2semidirect
6. C13×#1614C2semidirect
7. C13×#1506C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
132. #18439C13direct (N × H)
212. #3239C2×C13semidirect
213. #3230C2×C13semidirect
214. #2658C2×C13semidirect
215. #1618C2×C13semidirect
216. #1614C2×C13semidirect
217. #1506C2×C13semidirect
218. #1500C2×C13semidirect
219. #1469C2×C13semidirect
499. C13#18439direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#32392
C13×#32302
C13×#26582
C13×#16182
C13×#16142
C13×#15062
C13×#15002
C13×#14692
#1843913