Finite Group Databasebeta

← C13×#19020 #15705359

Subgroups — C13×#19020 #15705359

Order 3328.

960 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3141C211yesmaximal, characteristic, complemented
4C2×C13×#489C211yesmaximal, characteristic, complemented
5C13×#1662C214yesmaximal, complemented
6C13×#1659C214yesmaximal, complemented
7C13×#1530C211yesmaximal, characteristic, complemented
8C13×#1527C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C13×#562C2212yes—
11C13×H(3,𝔽4)C2212yes—
12C13×#559—21no—
13C13×#548—21no—
14C13×#546—22no—
15C13×#546—21no—
16D42×C13—21no—
17C13×#542—21no—
18C13×#538—22no—
19C13×#538—21no—
20C13×#535—21no—
21C13×#534—21no—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic, complemented
24C13×#529C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C13×#497C2212yescomplemented
27C13×#491C2212yescomplemented
28C13×#489—22no—
29C13×#489C2214yescomplemented
30C13×#489C2214yescomplemented
31C13×#487—21no—
32C13×#486—21no—
33C13×#462—21no—
34C13×#461—21no—
35C13×#451—21no—
36C13×#448—21no—
37C13×#432C2211yescharacteristic, complemented
38C13×#417—22no—
39C2×C13×#103—21no—
40C2×C13×#102—21no—
41C4×C13×M16C2211yescharacteristic, complemented
42C2×C13×#97C2211yescharacteristic, complemented
43C13×#330C2212yescomplemented
44C13×#329C2212yescomplemented
45C13×#329C2214yescomplemented
46C13×#329C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41D412yes—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13—22no—
52C22×D4×C13—21no—
53C22×D4×C13D411yescharacteristic
54C2×C13×Q16—22no—
55C2×C13×SD16—22no—
56C2×C13×M16—21no—
57C22×C8×C13—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8D411yescharacteristic
62C13×C4⋊Q8C2312yes—
63C13×#127—21no—
64C13×#127D411yescharacteristic
65C13×#126—22no—
66C13×#126—21no—
67C13×#125C2311yescharacteristic
68C13×#124—21no—
69C13×#124—22no—
70C13×#124—22no—
71C13×#124—22no—
72C13×#124—21no—
73C13×#124—21no—
74C13×#124D412yes—
75C13×#124C2312yes—
76C13×#124C2312yes—
77C13×#124C2311yescharacteristic
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—21no—
81C13×#123—22no—
82C13×#123—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8D411yescharacteristic
87C13×#121—22no—
88C13×#121—22no—
89C13×#121—22no—
90C13×#121—21no—
91C13×#121—22no—
92C13×#121—22no—
93C13×#121—21no—
94C13×#121—21no—
95C13×#121D411yescharacteristic
96C13×#120—22no—
97C13×#120—22no—
98C13×#120—22no—
99C13×#120—22no—
100C13×#120—22no—
101C4×Q8×C13—21no—
102C4×Q8×C13D411yescharacteristic
103C4×D4×C13—22no—
104C4×D4×C13—22no—
105C4×D4×C13—21no—
106C4×D4×C13—21no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C4×D4×C13D411yescharacteristic
110C13×#117—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C4⋊C4—21no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—21no—
115C2×C13×C22⋊C4—21no—
116C2×C42×C13C2311yescharacteristic
117C13×C4⋊C8—21no—
118C13×#103—24no—
119C13×#103—24no—
120C13×#103—22no—
121C13×#103—22no—
122C13×#102—24no—
123C13×#102—24no—
124C13×C22⋊C8—21no—
125C13×#97—21no—
126C13×#97C2312yes—
127C13×#97C2312yes—
128C13×#97C2312yes—
129C4×C8×C13—21no—
130#19020C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—22no—
132C24×C13—21no—
133C13×#41—44no—
134C13×#41—82no—
135C2×Q8×C13—21no—
136C2×Q8×C13—22no—
137C2×Q8×C13—42no—
138C2×Q8×C13—41no—
139C2×Q8×C13—82no—
140C2×Q8×C13C2×D412yes—
141C2×Q8×C13C2×D412yes—
142C2×Q8×C13C2×D411yescharacteristic
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—42no—
154C2×D4×C13—82no—
155C2×D4×C13—84no—
156C2×D4×C13C2×D412yes—
157C2×D4×C13C2×D412yes—
158C2×D4×C13C2×D411yescharacteristic
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—22no—
164C22×C4×C13—41no—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C13×Q16—82no—
169C13×SD16—82no—
170C13×M16—42no—
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—22no—
174C2×C8×C13—42no—
175C13×C4⋊C4—22no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C4⋊C4C2×D411yescharacteristic
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—21no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—21no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C42×C13—22no—
206C42×C13—21no—
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210C42×C13C2411yescharacteristic
211#3558C2×C1311yescharacteristic
212#3218C2×C1311yescharacteristic, complemented
213#3141C2×C1311yescharacteristic, complemented
214C2×#489C2×C1311yescharacteristic, complemented
215#1662C2×C1314yescomplemented
216#1659C2×C1314yescomplemented
217#1530C2×C1311yescharacteristic, complemented
218#1527C2×C1311yescharacteristic, complemented
219#1524C2×C1311yescharacteristic, complemented
220C23×C13—21no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—42no—
224C23×C13—81no—
225C23×C13—81no—
226C23×C13—82no—
227C23×C13—82no—
228C23×C13—82no—
229C23×C13#12011yescharacteristic
230Q8×C13—41no—
231Q8×C13—42no—
232Q8×C13—42no—
233Q8×C13—42no—
234Q8×C13—42no—
235Q8×C13—42no—
236Q8×C13—82no—
237D4×C13—41no—
238D4×C13—42no—
239D4×C13—42no—
240D4×C13—42no—
241D4×C13—44no—
242D4×C13—42no—
243D4×C13—42no—
244D4×C13—81no—
245D4×C13—82no—
246D4×C13—82no—
247D4×C13—82no—
248D4×C13—82no—
249D4×C13—82no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—41no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—82no—
261C2×C4×C13—81no—
262C2×C4×C13—82no—
263C2×C4×C13—82no—
264C2×C4×C13—82no—
265C2×C4×C13#12011yescharacteristic
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13C22×D411yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×D411yescharacteristic
271C8×C13—42no—
272C8×C13—42no—
273C8×C13—42no—
274#562C22×C1312yes—
275H(3,𝔽4)C22×C1312yes—
276#559—21no—
277#548—21no—
278#546—22no—
279#546—21no—
280D42—21no—
281#542—21no—
282#538—22no—
283#538—21no—
284#535—21no—
285#534—21no—
286#532C22×C1311yescharacteristic
287C2×C4⋊Q8C22×C1311yescharacteristic, complemented
288#529C22×C1311yescharacteristic
289C2×#124C22×C1311yescharacteristic
290#497C22×C1312yescomplemented
291#491C22×C1312yescomplemented
292#489—22no—
293#489C22×C1314yescomplemented
294#489C22×C1314yescomplemented
295#487—21no—
296#486—21no—
297#462—21no—
298#461—21no—
299#451—21no—
300#448—21no—
301#432C22×C1311yescharacteristic, complemented
302#417—22no—
303C2×#103—21no—
304C2×#102—21no—
305C4×M16C22×C1311yescharacteristic, complemented
306C2×#97C22×C1311yescharacteristic, complemented
307#330C22×C1312yescomplemented
308#329C22×C1312yescomplemented
309#329C22×C1314yescomplemented
310#329C22×C1314yescomplemented
311C22×C13—21no—
312C22×C13—21no—
313C22×C13—41no—
314C22×C13—42no—
315C22×C13—42no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—42no—
321C22×C13—42no—
322C22×C13—162no—
323C22×C13—164no—
324C22×C13#45512yes—
325C22×C13C2×#12011yescharacteristic
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—42no—
335C4×C13—41no—
336C4×C13—82no—
337C4×C13#45512yes—
338C2×#41—21no—
339C2×#41D4×C1312yes—
340C22×Q8—21no—
341C22×Q8D4×C1311yescharacteristic
342C22×D4—22no—
343C22×D4—21no—
344C22×D4D4×C1311yescharacteristic
345C2×Q16—22no—
346C2×SD16—22no—
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8D4×C1311yescharacteristic
353C4⋊Q8C23×C1312yes—
354#127—21no—
355#127D4×C1311yescharacteristic
356#126—22no—
357#126—21no—
358#125C23×C1311yescharacteristic
359#124—21no—
360#124—22no—
361#124—22no—
362#124—22no—
363#124—21no—
364#124—21no—
365#124D4×C1312yes—
366#124C23×C1312yes—
367#124C23×C1311yescharacteristic
368#124C23×C1312yes—
369#123—22no—
370#123—22no—
371#123—21no—
372#123—22no—
373#123—22no—
374C22⋊Q8—21no—
375C22⋊Q8—22no—
376C22⋊Q8—22no—
377C22⋊Q8D4×C1311yescharacteristic
378#121—22no—
379#121—22no—
380#121—22no—
381#121—21no—
382#121—22no—
383#121—22no—
384#121—21no—
385#121—21no—
386#121D4×C1311yescharacteristic
387#120—22no—
388#120—22no—
389#120—22no—
390#120—22no—
391#120—22no—
392C4×Q8—21no—
393C4×Q8D4×C1311yescharacteristic
394C4×D4—22no—
395C4×D4—22no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—21no—
399C4×D4—21no—
400C4×D4D4×C1311yescharacteristic
401#117—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C22⋊C4—22no—
405C2×C22⋊C4—21no—
406C2×C22⋊C4—21no—
407C2×C42C23×C1311yescharacteristic
408C4⋊C8—21no—
409#103—24no—
410#103—24no—
411#103—22no—
412#103—22no—
413#102—24no—
414#102—24no—
415C22⋊C8—21no—
416#97—21no—
417#97C23×C1312yes—
418#97C23×C1312yes—
419#97C23×C1312yes—
420C4×C8—21no—
421C2×C13—22no—
422C2×C13—82no—
423C2×C13—81no—
424C2×C13—82no—
425C2×C13C2×#45511yescharacteristic
426C2×C13C2×#45511yescharacteristic
427C2×C13#302111yescharacteristic
428C24—22no—
429C24—21no—
430#41—44no—
431#41—82no—
432C2×Q8—21no—
433C2×Q8—22no—
434C2×Q8—42no—
435C2×Q8—41no—
436C2×Q8—82no—
437C2×Q8C2×D4×C1312yes—
438C2×Q8C2×D4×C1312yes—
439C2×Q8C2×D4×C1311yescharacteristic
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—42no—
451C2×D4—82no—
452C2×D4—84no—
453C2×D4C2×D4×C1312yes—
454C2×D4C2×D4×C1312yes—
455C2×D4C2×D4×C1311yescharacteristic
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—22no—
461C22×C4—41no—
462C22×C4C2×D4×C1311yescharacteristic
463C22×C4C2×D4×C1311yescharacteristic
464C22×C4C2×D4×C1311yescharacteristic
465Q16—82no—
466SD16—82no—
467M16—42no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—42no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—22no—
481C4⋊C4—22no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4C2×D4×C1311yescharacteristic
485C4⋊C4C2×D4×C1311yescharacteristic
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—22no—
493C22⋊C4—21no—
494C22⋊C4—22no—
495C22⋊C4—21no—
496C22⋊C4—22no—
497C22⋊C4—22no—
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—22no—
502C42—22no—
503C42—21no—
504C42C2×D4×C1311yescharacteristic
505C42C2×D4×C1311yescharacteristic
506C42C2×D4×C1311yescharacteristic
507C42C24×C1311yescharacteristic
508C13#1902011yescharacteristic, direct product factor, Sylow
509C23—21no—
510C23—22no—
511C23—22no—
512C23—42no—
513C23—81no—
514C23—81no—
515C23—82no—
516C23—82no—
517C23—82no—
518C23C13×#12011yescharacteristic
519Q8—41no—
520Q8—42no—
521Q8—42no—
522Q8—42no—
523Q8—42no—
524Q8—42no—
525Q8—82no—
526D4—41no—
527D4—42no—
528D4—42no—
529D4—42no—
530D4—44no—
531D4—42no—
532D4—42no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—82no—
537D4—82no—
538D4—82no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—82no—
550C2×C4—81no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4C13×#12011yescharacteristic
555C2×C4C13×#12011yescharacteristic
556C2×C4C13×#12011yescharacteristic
557C2×C4C22×D4×C1311yescharacteristic
558C2×C4C22×D4×C1311yescharacteristic
559C2×C4C22×D4×C1311yescharacteristic
560C8—42no—
561C8—42no—
562C8—42no—
563C22—21no—
564C22—21no—
565C22—41no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—41no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—162no—
575C22—164no—
576C22C13×#45512yes—
577C22C2×C13×#12011yescharacteristic
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—42no—
586C4—42no—
587C4—41no—
588C4—82no—
589C4C13×#45512yes—
590C2—22no—
591C2—81no—
592C2—82no—
593C2—82no—
594C2C2×C13×#45511yescharacteristic
595C2C2×C13×#45511yescharacteristic
596C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3558C2
LCSG ▷ C42 ▷ 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×#3218C2semidirect
3. C13×#3141C2semidirect
4. C2×C13×#489C2semidirect
5. C13×#1662C2semidirect
6. C13×#1659C2semidirect
7. C13×#1530C2semidirect
8. C13×#1527C2semidirect
9. C13×#1524C2semidirect
23. C2×C13×C4⋊Q8C22semidirect
26. C13×#497C22semidirect
27. C13×#491C22semidirect
29. C13×#489C22semidirect
30. C13×#489C22semidirect
37. C13×#432C22semidirect
41. C4×C13×M16C22semidirect
42. C2×C13×#97C22semidirect
43. C13×#330C22semidirect
44. C13×#329C22semidirect
45. C13×#329C22semidirect
46. C13×#329C22semidirect
130. #19020C13direct (N × H)
212. #3218C2×C13semidirect
213. #3141C2×C13semidirect
214. C2×#489C2×C13semidirect
215. #1662C2×C13semidirect
216. #1659C2×C13semidirect
217. #1530C2×C13semidirect
218. #1527C2×C13semidirect
219. #1524C2×C13semidirect
287. C2×C4⋊Q8C22×C13semidirect
290. #497C22×C13semidirect
291. #491C22×C13semidirect
293. #489C22×C13semidirect
294. #489C22×C13semidirect
301. #432C22×C13semidirect
305. C4×M16C22×C13semidirect
306. C2×#97C22×C13semidirect
307. #330C22×C13semidirect
308. #329C22×C13semidirect
309. #329C22×C13semidirect
310. #329C22×C13semidirect
508. C13#19020direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35582
C13×#32182
C13×#31412
C2×C13×#4892
C13×#16622
C13×#16592
C13×#15302
C13×#15272
C13×#15242
#1902013