Finite Group Databasebeta

← C13×#19021 #15705360

Subgroups — C13×#19021 #15705360

Order 3328.

1012 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C211yesmaximal, characteristic
2C13×#3239C211yesmaximal, characteristic, complemented
3C2×C13×#497C211yesmaximal, characteristic, complemented
4C13×#3141C211yesmaximal, characteristic, complemented
5C13×#1661C214yesmaximal, complemented
6C13×#1659C214yesmaximal, complemented
7C13×#1530C211yesmaximal, characteristic, complemented
8C13×#1527C211yesmaximal, characteristic, complemented
9C13×#1524C211yesmaximal, characteristic, complemented
10C22×C13×Q16—21no—
11C22×C13×SD16—21no—
12C13×#562C2212yes—
13C13×H(3,𝔽4)C2212yes—
14C13×#559—21no—
15C13×#548—21no—
16C13×#546—22no—
17C13×#546—21no—
18D42×C13—21no—
19C13×#542—21no—
20C13×#538—22no—
21C13×#538—21no—
22C13×#535—21no—
23C13×#534—21no—
24C13×#532C2211yescharacteristic
25C2×C13×C4⋊Q8C2211yescharacteristic, complemented
26C13×#529C2211yescharacteristic
27C2×C13×#124C2211yescharacteristic
28C13×#501C2212yescomplemented
29C13×#497—22no—
30C13×#497C2214yescomplemented
31C13×#489C2214yescomplemented
32C13×#489C2212yescomplemented
33C13×#487—21no—
34C13×#486—21no—
35C13×#484—21no—
36C13×#481—21no—
37C13×#475—21no—
38C13×#474—21no—
39C13×#432C2211yescharacteristic, complemented
40C13×#417—22no—
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—24no—
55C2×C13×Q16—44no—
56C2×C13×SD16—24no—
57C2×C13×SD16—44no—
58C2×C13×M16—21no—
59C22×C8×C13—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—21no—
63C13×C4⋊Q8D411yescharacteristic
64C13×C4⋊Q8C2312yes—
65C13×#127—21no—
66C13×#127D411yescharacteristic
67C13×#126—22no—
68C13×#126—21no—
69C13×#125C2311yescharacteristic
70C13×#124—21no—
71C13×#124—22no—
72C13×#124—22no—
73C13×#124—22no—
74C13×#124—21no—
75C13×#124—21no—
76C13×#124D412yes—
77C13×#124C2311yescharacteristic
78C13×#124C2312yes—
79C13×#124C2312yes—
80C13×#123—22no—
81C13×#123—22no—
82C13×#123—21no—
83C13×#123—22no—
84C13×#123—22no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—22no—
88C13×C22⋊Q8D411yescharacteristic
89C13×#121—22no—
90C13×#121—22no—
91C13×#121—22no—
92C13×#121—21no—
93C13×#121—22no—
94C13×#121—22no—
95C13×#121—21no—
96C13×#121—21no—
97C13×#121D411yescharacteristic
98C13×#120—22no—
99C13×#120—22no—
100C13×#120—22no—
101C13×#120—22no—
102C13×#120—22no—
103C4×Q8×C13—21no—
104C4×Q8×C13D411yescharacteristic
105C4×D4×C13—22no—
106C4×D4×C13—22no—
107C4×D4×C13—21no—
108C4×D4×C13—21no—
109C4×D4×C13—21no—
110C4×D4×C13—21no—
111C4×D4×C13D411yescharacteristic
112C13×#117—21no—
113C2×C13×C4⋊C4—21no—
114C2×C13×C4⋊C4—21no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C42×C13C2311yescharacteristic
119C13×#107—22no—
120C13×#106—22no—
121C13×C4⋊C8—21no—
122C13×#103—24no—
123C13×#103—22no—
124C13×#102—24no—
125C13×#102—22no—
126C13×C22⋊C8—21no—
127C13×#97—21no—
128C13×#97C2312yes—
129C13×#97C2312yes—
130C13×#97C2312yes—
131C4×C8×C13—21no—
132#19021C1311yesmaximal, characteristic, direct product factor, Sylow
133C24×C13—22no—
134C24×C13—21no—
135C13×#41—44no—
136C13×#41—82no—
137C2×Q8×C13—21no—
138C2×Q8×C13—22no—
139C2×Q8×C13—42no—
140C2×Q8×C13—42no—
141C2×Q8×C13—42no—
142C2×Q8×C13—41no—
143C2×Q8×C13C2×D411yescharacteristic
144C2×Q8×C13C2×D412yes—
145C2×Q8×C13C2×D412yes—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—22no—
151C2×D4×C13—22no—
152C2×D4×C13—22no—
153C2×D4×C13—21no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—42no—
157C2×D4×C13—82no—
158C2×D4×C13—84no—
159C2×D4×C13C2×D411yescharacteristic
160C2×D4×C13C2×D412yes—
161C2×D4×C13C2×D412yes—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—22no—
167C22×C4×C13—41no—
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C13×Q16—48no—
172C13×SD16—48no—
173C13×M16—42no—
174C2×C8×C13—24no—
175C2×C8×C13—22no—
176C2×C8×C13—22no—
177C2×C8×C13—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—22no—
187C13×C4⋊C4—22no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4C2×D411yescharacteristic
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—22no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—21no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—21no—
205C13×C22⋊C4—21no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C42×C13—22no—
209C42×C13—21no—
210C42×C13C2×D411yescharacteristic
211C42×C13C2×D411yescharacteristic
212C42×C13C2×D411yescharacteristic
213C42×C13C2411yescharacteristic
214#3558C2×C1311yescharacteristic
215#3239C2×C1311yescharacteristic, complemented
216C2×#497C2×C1311yescharacteristic, complemented
217#3141C2×C1311yescharacteristic, complemented
218#1661C2×C1314yescomplemented
219#1659C2×C1314yescomplemented
220#1530C2×C1311yescharacteristic, complemented
221#1527C2×C1311yescharacteristic, complemented
222#1524C2×C1311yescharacteristic, complemented
223C23×C13—21no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—42no—
227C23×C13—81no—
228C23×C13—81no—
229C23×C13—82no—
230C23×C13—82no—
231C23×C13—82no—
232C23×C13#12011yescharacteristic
233Q8×C13—42no—
234Q8×C13—41no—
235Q8×C13—42no—
236Q8×C13—42no—
237Q8×C13—42no—
238Q8×C13—42no—
239Q8×C13—82no—
240D4×C13—42no—
241D4×C13—41no—
242D4×C13—42no—
243D4×C13—42no—
244D4×C13—44no—
245D4×C13—42no—
246D4×C13—42no—
247D4×C13—81no—
248D4×C13—82no—
249D4×C13—82no—
250D4×C13—82no—
251D4×C13—82no—
252D4×C13—82no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—41no—
261C2×C4×C13—42no—
262C2×C4×C13—42no—
263C2×C4×C13—82no—
264C2×C4×C13—81no—
265C2×C4×C13—82no—
266C2×C4×C13—82no—
267C2×C4×C13—82no—
268C2×C4×C13#12011yescharacteristic
269C2×C4×C13#12011yescharacteristic
270C2×C4×C13#12011yescharacteristic
271C2×C4×C13C22×D411yescharacteristic
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C8×C13—24no—
275C8×C13—42no—
276C8×C13—42no—
277C22×Q16—21no—
278C22×SD16—21no—
279#562C22×C1312yes—
280H(3,𝔽4)C22×C1312yes—
281#559—21no—
282#548—21no—
283#546—22no—
284#546—21no—
285D42—21no—
286#542—21no—
287#538—22no—
288#538—21no—
289#535—21no—
290#534—21no—
291#532C22×C1311yescharacteristic
292C2×C4⋊Q8C22×C1311yescharacteristic, complemented
293#529C22×C1311yescharacteristic
294C2×#124C22×C1311yescharacteristic
295#501C22×C1312yescomplemented
296#497—22no—
297#497C22×C1314yescomplemented
298#489C22×C1314yescomplemented
299#489C22×C1312yescomplemented
300#487—21no—
301#486—21no—
302#484—21no—
303#481—21no—
304#475—21no—
305#474—21no—
306#432C22×C1311yescharacteristic, complemented
307#417—22no—
308C4×M16C22×C1311yescharacteristic, complemented
309C2×#97C22×C1311yescharacteristic, complemented
310#330C22×C1312yescomplemented
311#329C22×C1312yescomplemented
312#329C22×C1314yescomplemented
313#329C22×C1314yescomplemented
314C22×C13—21no—
315C22×C13—21no—
316C22×C13—41no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—42no—
320C22×C13—42no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—42no—
324C22×C13—42no—
325C22×C13—162no—
326C22×C13—164no—
327C22×C13#45512yes—
328C22×C13C2×#12011yescharacteristic
329C4×C13—21no—
330C4×C13—21no—
331C4×C13—21no—
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—41no—
335C4×C13—42no—
336C4×C13—41no—
337C4×C13—42no—
338C4×C13—41no—
339C4×C13—82no—
340C4×C13#45312yes—
341C2×#41—21no—
342C2×#41D4×C1312yes—
343C22×Q8—21no—
344C22×Q8D4×C1311yescharacteristic
345C22×D4—22no—
346C22×D4—21no—
347C22×D4D4×C1311yescharacteristic
348C2×Q16—24no—
349C2×Q16—44no—
350C2×SD16—24no—
351C2×SD16—44no—
352C2×M16—21no—
353C22×C8—21no—
354C4⋊Q8—21no—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8D4×C1311yescharacteristic
358C4⋊Q8C23×C1312yes—
359#127—21no—
360#127D4×C1311yescharacteristic
361#126—22no—
362#126—21no—
363#125C23×C1311yescharacteristic
364#124—21no—
365#124—22no—
366#124—22no—
367#124—22no—
368#124—21no—
369#124—21no—
370#124D4×C1312yes—
371#124C23×C1312yes—
372#124C23×C1311yescharacteristic
373#124C23×C1312yes—
374#123—22no—
375#123—22no—
376#123—21no—
377#123—22no—
378#123—22no—
379C22⋊Q8—21no—
380C22⋊Q8—22no—
381C22⋊Q8—22no—
382C22⋊Q8D4×C1311yescharacteristic
383#121—22no—
384#121—22no—
385#121—22no—
386#121—21no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121D4×C1311yescharacteristic
392#120—22no—
393#120—22no—
394#120—22no—
395#120—22no—
396#120—22no—
397C4×Q8—21no—
398C4×Q8D4×C1311yescharacteristic
399C4×D4—22no—
400C4×D4—22no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4D4×C1311yescharacteristic
406#117—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C22⋊C4—22no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C42C23×C1311yescharacteristic
413#107—22no—
414#106—22no—
415C4⋊C8—21no—
416#103—24no—
417#103—22no—
418#102—24no—
419#102—22no—
420C22⋊C8—21no—
421#97—21no—
422#97C23×C1312yes—
423#97C23×C1312yes—
424#97C23×C1312yes—
425C4×C8—21no—
426C2×C13—22no—
427C2×C13—82no—
428C2×C13—81no—
429C2×C13—82no—
430C2×C13C2×#45311yescharacteristic
431C2×C13C2×#45511yescharacteristic
432C2×C13#302211yescharacteristic
433C24—22no—
434C24—21no—
435#41—44no—
436#41—82no—
437C2×Q8—21no—
438C2×Q8—22no—
439C2×Q8—42no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—41no—
443C2×Q8C2×D4×C1311yescharacteristic
444C2×Q8C2×D4×C1312yes—
445C2×Q8C2×D4×C1312yes—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—42no—
457C2×D4—82no—
458C2×D4—84no—
459C2×D4C2×D4×C1311yescharacteristic
460C2×D4C2×D4×C1312yes—
461C2×D4C2×D4×C1312yes—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—22no—
467C22×C4—41no—
468C22×C4C2×D4×C1311yescharacteristic
469C22×C4C2×D4×C1311yescharacteristic
470C22×C4C2×D4×C1311yescharacteristic
471Q16—48no—
472SD16—48no—
473M16—42no—
474C2×C8—24no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C1311yescharacteristic
491C4⋊C4C2×D4×C1311yescharacteristic
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—22no—
497C22⋊C4—21no—
498C22⋊C4—22no—
499C22⋊C4—21no—
500C22⋊C4—22no—
501C22⋊C4—21no—
502C22⋊C4—22no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—22no—
507C22⋊C4—22no—
508C42—22no—
509C42—21no—
510C42C2×D4×C1311yescharacteristic
511C42C2×D4×C1311yescharacteristic
512C42C2×D4×C1311yescharacteristic
513C42C24×C1311yescharacteristic
514C13#1902111yescharacteristic, direct product factor, Sylow
515C23—21no—
516C23—22no—
517C23—22no—
518C23—42no—
519C23—81no—
520C23—81no—
521C23—82no—
522C23—82no—
523C23—82no—
524C23C13×#12011yescharacteristic
525Q8—42no—
526Q8—42no—
527Q8—41no—
528Q8—42no—
529Q8—42no—
530Q8—42no—
531Q8—82no—
532D4—42no—
533D4—41no—
534D4—42no—
535D4—42no—
536D4—44no—
537D4—42no—
538D4—42no—
539D4—81no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—82no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—82no—
556C2×C4—81no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4C13×#12011yescharacteristic
561C2×C4C13×#12011yescharacteristic
562C2×C4C13×#12011yescharacteristic
563C2×C4C22×D4×C1311yescharacteristic
564C2×C4C22×D4×C1311yescharacteristic
565C2×C4C22×D4×C1311yescharacteristic
566C8—24no—
567C8—42no—
568C8—42no—
569C22—21no—
570C22—21no—
571C22—41no—
572C22—42no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—41no—
577C22—41no—
578C22—42no—
579C22—42no—
580C22—162no—
581C22—164no—
582C22C13×#45512yes—
583C22C2×C13×#12011yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—42no—
591C4—41no—
592C4—42no—
593C4—41no—
594C4—82no—
595C4C13×#45312yes—
596C2—22no—
597C2—81no—
598C2—82no—
599C2—82no—
600C2C2×C13×#45311yescharacteristic
601C2C2×C13×#45511yescharacteristic
602C2C13×#302211yescharacteristic
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×#3239C2semidirect
3. C2×C13×#497C2semidirect
4. C13×#3141C2semidirect
5. C13×#1661C2semidirect
6. C13×#1659C2semidirect
7. C13×#1530C2semidirect
8. C13×#1527C2semidirect
9. C13×#1524C2semidirect
25. C2×C13×C4⋊Q8C22semidirect
28. C13×#501C22semidirect
30. C13×#497C22semidirect
31. C13×#489C22semidirect
32. C13×#489C22semidirect
39. C13×#432C22semidirect
41. C4×C13×M16C22semidirect
42. C2×C13×#97C22semidirect
43. C13×#330C22semidirect
44. C13×#329C22semidirect
45. C13×#329C22semidirect
46. C13×#329C22semidirect
132. #19021C13direct (N × H)
215. #3239C2×C13semidirect
216. C2×#497C2×C13semidirect
217. #3141C2×C13semidirect
218. #1661C2×C13semidirect
219. #1659C2×C13semidirect
220. #1530C2×C13semidirect
221. #1527C2×C13semidirect
222. #1524C2×C13semidirect
292. C2×C4⋊Q8C22×C13semidirect
295. #501C22×C13semidirect
297. #497C22×C13semidirect
298. #489C22×C13semidirect
299. #489C22×C13semidirect
306. #432C22×C13semidirect
308. C4×M16C22×C13semidirect
309. C2×#97C22×C13semidirect
310. #330C22×C13semidirect
311. #329C22×C13semidirect
312. #329C22×C13semidirect
313. #329C22×C13semidirect
514. C13#19021direct (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×#32392
C2×C13×#4972
C13×#31412
C13×#16612
C13×#16592
C13×#15302
C13×#15272
C13×#15242
#1902113