Finite Group Databasebeta

← D13×#1919 #15865059

Subgroups — D13×#1919 #15865059

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×#106C211yesmaximal, characteristic
2D13×#389C211yesmaximal, characteristic
3C4×C4⋊C4×D13C211yesmaximal, characteristic
4#13115417C211yesmaximal, characteristic, complemented
5#13115416C211yesmaximal, characteristic, complemented
6#13115415C211yesmaximal, characteristic, complemented
7#13115414C211yesmaximal, characteristic, complemented
8#13115413C211yesmaximal, characteristic, complemented
9#13115412C211yesmaximal, characteristic, complemented
10#13115411C211yesmaximal, characteristic, complemented
11D13×#340C211yesmaximal, characteristic
12D13×#340C211yesmaximal, characteristic
13D13×#340C211yesmaximal, characteristic
14D13×#336C211yesmaximal, characteristic
15C13×#1919C211yesmaximal, characteristic, complemented
16C22×C8×D13C2211yescharacteristic
17C22×C8×D13C2211yescharacteristic
18C2×C4⋊C4×D13—21no—
19C2×C4⋊C4×D13C2211yescharacteristic
20C2×C4⋊C4×D13C2211yescharacteristic
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×C4⋊C4×D13C2211yescharacteristic
23C2×C42×D13—21no—
24C2×C42×D13C2211yescharacteristic
25C2×C13×#106C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C4×C13×C4⋊C4C2211yescharacteristic
28C2×#88057C2211yescharacteristic
29#11718646C2211yescharacteristic
30C4⋊C4×Dic13C2211yescharacteristic
31C4⋊C4×Dic13C2211yescharacteristic
32#11718634C2211yescharacteristic
33#11718633—21no—
34C2×#88048C2211yescharacteristic
35C2×#88048C2211yescharacteristic
36C4×C4⋊Dic13C2211yescharacteristic
37C4×#6101—21no—
38#11718589C2211yescharacteristic
39D13×#106C418yescomplemented
40D13×#95—21no—
41D13×#95—21no—
42#11718310—21no—
43#11718308—21no—
44C13×#340C2211yescharacteristic
45C13×#340C2211yescharacteristic
46C13×#340C2211yescharacteristic
47C13×#336C2211yescharacteristic
48#11718143C2211yescharacteristic
49#11718143C2211yescharacteristic
50#11718143C2211yescharacteristic
51#11718142C2211yescharacteristic
52#11718142C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60C22×C4×D13—21no—
61C22×C4×D13—21no—
62C22×C4×D13—21no—
63C22×C4×D13—21no—
64C22×C4×D13D411yescharacteristic
65C22×C4×D13D411yescharacteristic
66C22×C4×D13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C42×C13—21no—
75C2×C42×C13C2311yescharacteristic
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2311yescharacteristic
78C2×C4⋊Dic13C2311yescharacteristic
79C2×C4⋊Dic13C2311yescharacteristic
80C2×C4⋊Dic13C2311yescharacteristic
81C2×#6101—21no—
82C2×#6101—21no—
83C2×#6101—21no—
84C2×#6101—21no—
85C2×#6101—21no—
86C2×#6101—21no—
87C2×C4×Dic13—21no—
88C2×C4×Dic13—21no—
89C2×C4×Dic13—21no—
90C2×C4×Dic13D411yescharacteristic
91C2×C4×Dic13D411yescharacteristic
92C2×C4×Dic13C2311yescharacteristic
93C22×#1055C2311yescharacteristic
94C22×#1055C2311yescharacteristic
95C2×C8×D13—22no—
96C2×C8×D13—22no—
97C2×C8×D13—22no—
98C2×C8×D13—22no—
99C2×C8×D13—22no—
100C2×C8×D13C2×C414yes—
101C4⋊C4×D13—22no—
102C4⋊C4×D13—22no—
103C4⋊C4×D13—22no—
104C4⋊C4×D13—22no—
105C4⋊C4×D13—22no—
106C4⋊C4×D13—44no—
107C4⋊C4×D13C2×C414yes—
108C4⋊C4×D13C2×C414yes—
109C4⋊C4×D13Q814yes—
110C42×D13—22no—
111C42×D13—22no—
112C42×D13—44no—
113C13×#106C2×C414yescomplemented
114C13×#95—21no—
115C13×#95—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88057C2×C414yescomplemented
123#88048C2×C414yescomplemented
124#88048C2×C414yescomplemented
125C2×#1919—131nomaximal, Sylow
126C23×D13C2×D411yescharacteristic
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13C2×D411yescharacteristic
132C22×C4×C13C2×D411yescharacteristic
133C22×C4×C13C2411yescharacteristic
134C22×Dic13—21no—
135C22×Dic13—21no—
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13C2×D411yescharacteristic
139C22×Dic13C2×D411yescharacteristic
140C22×Dic13C2×D411yescharacteristic
141C2×C4×D13—22no—
142C2×C4×D13—22no—
143C2×C4×D13—24no—
144C2×C4×D13—24no—
145C2×C4×D13—24no—
146C2×C4×D13—22no—
147C2×C4×D13—22no—
148C2×C4×D13—22no—
149C2×C4×D13—42no—
150C2×C4×D13—42no—
151C2×C4×D13—42no—
152C2×C4×D13—42no—
153C2×C4×D13—42no—
154C2×C4×D13—42no—
155C2×C4×D13—42no—
156C2×C4×D13—42no—
157C2×C4×D13—42no—
158C2×C4×D13SD1614yes—
159C2×C4×D13C22×C412yes—
160C2×C4×D13C2×Q812yes—
161C2×C4×D13#4112yes—
162C2×C4×D13#4112yes—
163C2×C4×D13#4112yes—
164C2×C4×D13#4112yes—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C22×C412yes—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4C22×C412yes—
178C13×C4⋊C4C22×C412yes—
179C13×C4⋊C4C2×Q812yes—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—42no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—42no—
189C4⋊Dic13C22×C412yes—
190C4⋊Dic13C22×C412yes—
191C4⋊Dic13C2×Q812yes—
192#6101—24no—
193#6101—24no—
194#6101—24no—
195#6101—42no—
196#6101—42no—
197#6101—42no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—22no—
201C4×Dic13—22no—
202C4×Dic13—42no—
203C4×Dic13—42no—
204C4×Dic13—42no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055C22×C412yes—
211C8×D13—28no—
212C8×D13—44no—
213C22×#106—131no—
214C2×#389—131no—
215C2×C4×C4⋊C4—131no—
216#1919—131no—
217#1919—131no—
218#1919—131no—
219#1919—131no—
220#1919—131no—
221#1919—131no—
222#1919—131no—
223#1919D1311yescharacteristic, direct product factor
224C2×#340—131no—
225C2×#340—131no—
226C2×#340—131no—
227C2×#336—131no—
228C23×C13C22×D411yescharacteristic
229C22×D13C4×D412yes—
230C22×D13C22⋊Q812yes—
231C22×D13#12312yes—
232C22×D13C2×SD1612yes—
233C22×D13#13512yes—
234C22×D13AGL(1,ℤ/8)12yes—
235C22×D13#13712yes—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13C2×SD1612yes—
254C2×C4×C13C23×C411yescharacteristic
255C2×C4×C13C22×Q811yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—41no—
269C2×Dic13—41no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13C4×D412yes—
278C2×Dic13C22⋊Q812yes—
279C2×Dic13#12312yes—
280C2×Dic13C2×SD1612yes—
281C4×D13—28no—
282C4×D13—48no—
283C4×D13—48no—
284C4×D13—48no—
285C4×D13—44no—
286C4×D13—84no—
287C4×D13#11714yes—
288C4×D13C4×Q814yes—
289C4×D13#12514yes—
290C4×D13#12614yes—
291C8×C13—22no—
292C8×C13—41no—
293#1055—22no—
294#1055—41no—
295C23×C8—131no—
296C23×C8—131no—
297C22×C4⋊C4—131no—
298C22×C4⋊C4—131no—
299C22×C4⋊C4—131no—
300C22×C4⋊C4—131no—
301C22×C4⋊C4—261no—
302C22×C42—131no—
303C22×C42—261no—
304C2×#106—131no—
305C2×#106—131no—
306C2×#106—131no—
307C2×#106—138no—
308C2×#106C2×D1311yescharacteristic
309#389—131no—
310#389—131no—
311#389—131no—
312#389—261no—
313#389—261no—
314#389C2×D1311yescharacteristic
315C4×C4⋊C4—131no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—261no—
319C4×C4⋊C4—261no—
320C4×C4⋊C4C2×D1311yescharacteristic
321C2×#95—261no—
322C2×#95—261no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340C2×D1311yescharacteristic
333#340C2×D1311yescharacteristic
334#340C2×D1311yescharacteristic
335#336—131no—
336#336—131no—
337#336—131no—
338#336C2×D1311yescharacteristic
339C22×C13C2×C4×D411yescharacteristic
340C22×C13C2×C22⋊Q811yescharacteristic
341C22×C13C2×#12311yescharacteristic
342C22×C13C22×SD1611yescharacteristic
343C22×C13C2×#13511yescharacteristic
344C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
345C22×C13C2×#13711yescharacteristic
346C2×D13#38714yes—
347C2×D13C4×SD1614yes—
348C2×D13#44014yes—
349C2×D13#47514yes—
350C2×D13#47814yes—
351C2×D13#48114yes—
352C2×D13#48514yes—
353C4×C13—22no—
354C4×C13—42no—
355C4×C13—41no—
356C4×C13—42no—
357C4×C13—42no—
358C4×C13—81no—
359C4×C13C2×#11711yescharacteristic
360C4×C13C2×C4×Q811yescharacteristic
361C4×C13C2×#12511yescharacteristic
362C4×C13C2×#12611yescharacteristic
363Dic13—22no—
364Dic13—42no—
365Dic13—41no—
366Dic13—42no—
367Dic13—42no—
368Dic13—81no—
369Dic13#38714yes—
370C23×C4—131no—
371C23×C4—131no—
372C23×C4—131no—
373C23×C4—261no—
374C23×C4—261no—
375C23×C4—261no—
376C23×C4—261no—
377C22×C8—131no—
378C22×C8—134no—
379C22×C8—131no—
380C22×C8—262no—
381C22×C8—262no—
382C22×C8—262no—
383C22×C8—262no—
384C22×C8—262no—
385C22×C8C22×D1311yescharacteristic
386C22×C8C22×D1311yescharacteristic
387C2×C4⋊C4—21no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—134no—
392C2×C4⋊C4—134no—
393C2×C4⋊C4—134no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—262no—
396C2×C4⋊C4—262no—
397C2×C4⋊C4—262no—
398C2×C4⋊C4—262no—
399C2×C4⋊C4—262no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—524no—
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C4⋊C4C22×D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C42—21no—
413C2×C42—131no—
414C2×C42—131no—
415C2×C42—131no—
416C2×C42—262no—
417C2×C42—262no—
418C2×C42—261no—
419C2×C42—261no—
420C2×C42—261no—
421C2×C42—524no—
422C2×C42C22×D1311yescharacteristic
423#106—134no—
424#106—134no—
425#106—134no—
426#106C4×D1314yescomplemented
427#95—21no—
428#95—21no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434#95—261no—
435C2×C13C2×#38711yescharacteristic
436C2×C13C2×C4×SD1611yescharacteristic
437C2×C13C2×#44011yescharacteristic
438C2×C13C2×#47811yescharacteristic
439C2×C13C2×#47511yescharacteristic
440C2×C13C2×#48511yescharacteristic
441C2×C13C2×#48111yescharacteristic
442D13#191918yesdirect product factor
443C24—131no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—131no—
449C22×C4—132no—
450C22×C4—132no—
451C22×C4—132no—
452C22×C4—132no—
453C22×C4—132no—
454C22×C4—132no—
455C22×C4—131no—
456C22×C4—134no—
457C22×C4—131no—
458C22×C4—262no—
459C22×C4—262no—
460C22×C4—262no—
461C22×C4—264no—
462C22×C4—264no—
463C22×C4—264no—
464C22×C4—262no—
465C22×C4—262no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—522no—
471C22×C4—522no—
472C22×C4—522no—
473C22×C4—522no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4—522no—
477C22×C4—522no—
478C22×C4—522no—
479C22×C4D4×D1311yescharacteristic
480C22×C4D4×D1311yescharacteristic
481C22×C4C23×D1311yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—132no—
488C2×C8—268no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—524no—
495C2×C8C2×C4×D1312yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—132no—
503C4⋊C4—132no—
504C4⋊C4—132no—
505C4⋊C4—264no—
506C4⋊C4—264no—
507C4⋊C4—264no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—522no—
514C4⋊C4—522no—
515C4⋊C4—522no—
516C4⋊C4—522no—
517C4⋊C4C2×C4×D1312yes—
518C4⋊C4C2×C4×D1312yes—
519C4⋊C4Q8×D1312yes—
520C42—21no—
521C42—21no—
522C42—42no—
523C42—262no—
524C42—262no—
525C42—261no—
526C42—261no—
527C42—522no—
528C42—522no—
529C42—522no—
530C13C2×#191911yescharacteristic, complemented, Sylow
531C23—132no—
532C23—132no—
533C23—132no—
534C23—132no—
535C23—132no—
536C23—132no—
537C23—132no—
538C23C2×D4×D1311yescharacteristic
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—134no—
560C2×C4—134no—
561C2×C4—134no—
562C2×C4—134no—
563C2×C4—132no—
564C2×C4—268no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—262no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—261no—
573C2×C4—524no—
574C2×C4—528no—
575C2×C4—528no—
576C2×C4—528no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—1044no—
587C2×C4SD16×D1312yes—
588C2×C4C22×C4×D1311yescharacteristic
589C2×C4C2×Q8×D1311yescharacteristic
590C2×C4#41×D1311yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C8—22no—
595C8—41no—
596C8—262no—
597C8—521no—
598C22—134no—
599C22—134no—
600C22—134no—
601C22—134no—
602C22—134no—
603C22—134no—
604C22—134no—
605C22C4×D4×D1311yescharacteristic
606C22D13×C22⋊Q811yescharacteristic
607C22D13×#12311yescharacteristic
608C22C2×SD16×D1311yescharacteristic
609C22D13×#13511yescharacteristic
610C22D13×AGL(1,ℤ/8)11yescharacteristic
611C22D13×#13711yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—41no—
616C4—42no—
617C4—81no—
618C4—134no—
619C4—262no—
620C4—522no—
621C4—522no—
622C4—521no—
623C4—522no—
624C4—1041no—
625C4D13×#11711yescharacteristic
626C4C4×Q8×D1311yescharacteristic
627C4D13×#12511yescharacteristic
628C4D13×#12611yescharacteristic
629C2—138no—
630C2D13×#38711yescharacteristic
631C2C4×SD16×D1311yescharacteristic
632C2D13×#44011yescharacteristic
633C2D13×#47811yescharacteristic
634C2D13×#47511yescharacteristic
635C2D13×#48511yescharacteristic
636C2D13×#48111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1919C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1919D13
hypocenterC13C2×#1919
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
4. #13115417C2semidirect
5. #13115416C2semidirect
6. #13115415C2semidirect
7. #13115414C2semidirect
8. #13115413C2semidirect
9. #13115412C2semidirect
10. #13115411C2semidirect
15. C13×#1919C2semidirect
39. D13×#106C4semidirect
113. C13×#106C2×C4semidirect
122. #88057C2×C4semidirect
123. #88048C2×C4semidirect
124. #88048C2×C4semidirect
223. #1919D13direct (N × H)
426. #106C4×D13semidirect
442. D13#1919direct (N × H)
530. C13C2×#1919semidirect

Maximal subgroups

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

subgroupindex
C2×D13×#1062
D13×#3892
C4×C4⋊C4×D132
#131154172
#131154162
#131154152
#131154142
#131154132
#131154122
#131154112
D13×#3402
D13×#3362
C13×#19192
C2×#191913