Finite Group Databasebeta

← C13×#24086 #15710425

Subgroups — C13×#24086 #15710425

Order 3328.

1014 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3495C211yesmaximal, characteristic
2C13×#3092C211yesmaximal, characteristic
3C2×C13×#428C211yesmaximal, characteristic, complemented
4C13×#2502C211yesmaximal, characteristic, complemented
5C13×#2060C212yesmaximal, complemented
6C13×#2038C212yesmaximal, complemented
7C13×#1901C211yesmaximal, characteristic, complemented
8C13×#1871C211yesmaximal, characteristic
9C13×#1859C212yesmaximal, complemented
10C13×#1857C212yesmaximal, complemented
11C13×#1826C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C13×#556—21no—
14C13×#554—21no—
15C13×#552—21no—
16C13×#552—22no—
17C13×#552—21no—
18C13×#551—22no—
19C13×#544C2211yescharacteristic
20C13×#542—21no—
21C13×#541—21no—
22C13×#536C2211yescharacteristic
23C13×#533—21no—
24C13×#529—21no—
25C13×#525C2211yescharacteristic
26C2×C13×C22⋊Q8C2211yescharacteristic
27C13×#520C2211yescharacteristic
28C13×#519C2211yescharacteristic
29C2×C13×#117C2211yescharacteristic
30C22×C13×C4⋊C4C2211yescharacteristic
31C13×#484—21no—
32C13×#483—21no—
33C13×#481—21no—
34C13×#480—21no—
35C13×#428—21no—
36C13×#428—21no—
37C13×#428C2212yes—
38C13×#428C2212yes—
39C13×#428C2212yes—
40C2×C13×#107—21no—
41C2×C13×#106—21no—
42C2×C13×#104C2212yes—
43C13×#417C2212yes—
44C2×C13×#101C2212yes—
45C13×#407C2211yescharacteristic
46C13×#398—22no—
47C13×#391C2212yes—
48C13×#385—22no—
49C13×#384C2212yes—
50C4×C13×C22⋊C4C2211yescharacteristic
51C13×#343C2212yes—
52C13×#339C2212yes—
53C13×#339C2212yes—
54C13×#339C2212yes—
55C2×C13×#41C2311yescharacteristic
56C22×Q8×C13C2311yescharacteristic
57C23×C4×C13—21no—
58C23×C4×C13C2311yescharacteristic
59C2×C13×M16—21no—
60C2×C13×M16—24no—
61C2×C13×M16C2312yes—
62C2×C13×M16C2312yes—
63C22×C8×C13—21no—
64C13×C4⋊Q8—21no—
65C13×C4⋊Q8—21no—
66C13×C4⋊Q8—21no—
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—22no—
70C13×#126—22no—
71C13×#125—22no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—21no—
76C13×#124—22no—
77C13×#124—21no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—21no—
81C13×#123—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—21no—
85C13×C22⋊Q8—21no—
86C13×C22⋊Q8—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8D411yescharacteristic
92C13×C22⋊Q8D411yescharacteristic
93C13×#121D411yescharacteristic
94C13×#121D411yescharacteristic
95C13×#120—21no—
96C4×Q8×C13—22no—
97C4×Q8×C13—21no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13—21no—
101C4×Q8×C13—21no—
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13—22no—
105C4×D4×C13—21no—
106C4×D4×C13—21no—
107C13×#117—22no—
108C13×#117—22no—
109C13×#117—21no—
110C13×#117—21no—
111C13×#117—22no—
112C13×#117—21no—
113C13×#117D411yescharacteristic
114C13×#117D411yescharacteristic
115C13×#117C2311yescharacteristic
116C13×#117C2311yescharacteristic
117C13×#117C2311yescharacteristic
118C2×C13×C4⋊C4—21no—
119C2×C13×C4⋊C4—21no—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4—21no—
124C2×C13×C4⋊C4—24no—
125C2×C13×C4⋊C4D412yes—
126C2×C13×C4⋊C4D411yescharacteristic
127C2×C13×C4⋊C4D411yescharacteristic
128C2×C13×C4⋊C4C2312yes—
129C2×C13×C4⋊C4C2311yescharacteristic
130C2×C13×C22⋊C4—21no—
131C2×C13×C22⋊C4—21no—
132C2×C13×C22⋊C4D412yes—
133C2×C42×C13—21no—
134C2×C42×C13C2312yes—
135C13×#107—22no—
136C13×#107—22no—
137C13×#107—22no—
138C13×#106—22no—
139C13×#106—22no—
140C13×#106—22no—
141C13×#104—24no—
142C13×#103—22no—
143C13×#102—22no—
144C13×#101—24no—
145C13×C22⋊C8—21no—
146C13×C22⋊C8—21no—
147C13×#95—21no—
148C13×#95—24no—
149#24086C1311yesmaximal, characteristic, direct product factor, Sylow
150C24×C13C2×D411yescharacteristic
151C13×#41—22no—
152C13×#41—22no—
153C2×Q8×C13—22no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13—22no—
157C2×Q8×C13—22no—
158C2×Q8×C13C2×D411yescharacteristic
159C2×D4×C13—21no—
160C2×D4×C13—21no—
161C2×D4×C13—21no—
162C2×D4×C13C2×D411yescharacteristic
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—22no—
171C22×C4×C13—41no—
172C22×C4×C13—41no—
173C22×C4×C13—82no—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D412yes—
181C22×C4×C13C2411yescharacteristic
182C13×M16—24no—
183C13×M16—22no—
184C13×M16—22no—
185C13×M16—22no—
186C13×M16#4114yes—
187C2×C8×C13—24no—
188C2×C8×C13—22no—
189C2×C8×C13—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—21no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—22no—
201C13×C4⋊C4—22no—
202C13×C4⋊C4—21no—
203C13×C4⋊C4—21no—
204C13×C4⋊C4—21no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—22no—
207C13×C4⋊C4—22no—
208C13×C4⋊C4—41no—
209C13×C4⋊C4—41no—
210C13×C4⋊C4—84no—
211C13×C4⋊C4C2×D411yescharacteristic
212C13×C4⋊C4C2×D411yescharacteristic
213C13×C4⋊C4C2×D411yescharacteristic
214C13×C4⋊C4C2×D411yescharacteristic
215C13×C4⋊C4C2×D411yescharacteristic
216C13×C4⋊C4C2×D411yescharacteristic
217C13×C22⋊C4—24no—
218C13×C22⋊C4—22no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—22no—
221C13×C22⋊C4—21no—
222C13×C22⋊C4—21no—
223C13×C22⋊C4—22no—
224C13×C22⋊C4—22no—
225C13×C22⋊C4—21no—
226C13×C22⋊C4—21no—
227C13×C22⋊C4—21no—
228C13×C22⋊C4—21no—
229C13×C22⋊C4—21no—
230C13×C22⋊C4—21no—
231C13×C22⋊C4—21no—
232C42×C13—22no—
233C42×C13—22no—
234C42×C13—22no—
235C42×C13—21no—
236C42×C13—21no—
237C42×C13—21no—
238C42×C13—21no—
239C42×C13—21no—
240C42×C13—22no—
241C42×C13—22no—
242#3495C2×C1311yescharacteristic
243#3092C2×C1311yescharacteristic
244C2×#428C2×C1311yescharacteristic, complemented
245#2502C2×C1311yescharacteristic, complemented
246#2060C2×C1312yescomplemented
247#2038C2×C1312yescomplemented
248#1901C2×C1311yescharacteristic, complemented
249#1871C2×C1311yescharacteristic
250#1859C2×C1312yescomplemented
251#1857C2×C1312yescomplemented
252#1826C2×C1311yescharacteristic, complemented
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—21no—
256C23×C13—41no—
257C23×C13#12011yescharacteristic
258C23×C13#12011yescharacteristic
259C23×C13C22×D411yescharacteristic
260Q8×C13—22no—
261Q8×C13—41no—
262Q8×C13—41no—
263Q8×C13—42no—
264Q8×C13—82no—
265D4×C13—22no—
266D4×C13—42no—
267D4×C13—42no—
268D4×C13—81no—
269C2×C4×C13—22no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—24no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—22no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—22no—
286C2×C4×C13—24no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—42no—
293C2×C4×C13—44no—
294C2×C4×C13—42no—
295C2×C4×C13—81no—
296C2×C4×C13—82no—
297C2×C4×C13—82no—
298C2×C4×C13—82no—
299C2×C4×C13#12011yescharacteristic
300C2×C4×C13#12011yescharacteristic
301C2×C4×C13C22×D411yescharacteristic
302C2×C4×C13C22×D411yescharacteristic
303C2×C4×C13C2×#4112yes—
304C2×C4×C132−1+412yes—
305C8×C13—24no—
306C8×C13—42no—
307C22×M16C22×C1311yescharacteristic
308#556—21no—
309#554—21no—
310#552—21no—
311#552—22no—
312#552—21no—
313#551—22no—
314#544C22×C1311yescharacteristic
315#542—21no—
316#541—21no—
317#536C22×C1311yescharacteristic
318#533—21no—
319#529—21no—
320#525C22×C1311yescharacteristic
321C2×C22⋊Q8C22×C1311yescharacteristic
322#520C22×C1311yescharacteristic
323#519C22×C1311yescharacteristic
324C2×#117C22×C1311yescharacteristic
325C22×C4⋊C4C22×C1311yescharacteristic
326#484—21no—
327#483—21no—
328#481—21no—
329#480—21no—
330#428—21no—
331#428—21no—
332#428C22×C1312yes—
333#428C22×C1312yes—
334#428C22×C1312yes—
335C2×#107—21no—
336C2×#106—21no—
337C2×#104C22×C1312yes—
338#417C22×C1312yes—
339C2×#101C22×C1312yes—
340#407C22×C1311yescharacteristic
341#398—22no—
342#391C22×C1312yes—
343#385—22no—
344#384C22×C1312yes—
345C4×C22⋊C4C22×C1311yescharacteristic
346#343C22×C1312yes—
347#339C22×C1312yes—
348#339C22×C1312yes—
349#339C22×C1312yes—
350C22×C13—21no—
351C22×C13—21no—
352C22×C13—21no—
353C22×C13—21no—
354C22×C13—21no—
355C22×C13—21no—
356C22×C13—21no—
357C22×C13—44no—
358C22×C13—41no—
359C22×C13—41no—
360C22×C13—41no—
361C22×C13#45612yes—
362C22×C13C2×#12011yescharacteristic
363C22×C13#54712yes—
364C4×C13—21no—
365C4×C13—21no—
366C4×C13—44no—
367C4×C13—42no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—82no—
377C4×C13#52511yescharacteristic
378C4×C13#53611yescharacteristic
379C4×C13#54712yes—
380C2×#41C23×C1311yescharacteristic
381C22×Q8C23×C1311yescharacteristic
382C23×C4—21no—
383C23×C4C23×C1311yescharacteristic
384C2×M16—21no—
385C2×M16—24no—
386C2×M16C23×C1312yes—
387C2×M16C23×C1312yes—
388C22×C8—21no—
389C4⋊Q8—21no—
390C4⋊Q8—21no—
391C4⋊Q8—21no—
392#126—22no—
393#126—22no—
394#126—22no—
395#126—22no—
396#125—22no—
397#125—22no—
398#125—22no—
399#125—21no—
400#125—21no—
401#124—22no—
402#124—21no—
403#123—22no—
404#123—22no—
405#123—21no—
406#123—22no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—21no—
412C22⋊Q8—21no—
413C22⋊Q8—22no—
414C22⋊Q8—21no—
415C22⋊Q8—21no—
416C22⋊Q8D4×C1311yescharacteristic
417C22⋊Q8D4×C1311yescharacteristic
418#121D4×C1311yescharacteristic
419#121D4×C1311yescharacteristic
420#120—21no—
421C4×Q8—22no—
422C4×Q8—21no—
423C4×Q8—21no—
424C4×Q8—21no—
425C4×Q8—21no—
426C4×Q8—21no—
427C4×D4—22no—
428C4×D4—21no—
429C4×D4—22no—
430C4×D4—21no—
431C4×D4—21no—
432#117—22no—
433#117—22no—
434#117—21no—
435#117—21no—
436#117—22no—
437#117—21no—
438#117D4×C1311yescharacteristic
439#117D4×C1311yescharacteristic
440#117C23×C1311yescharacteristic
441#117C23×C1311yescharacteristic
442#117C23×C1311yescharacteristic
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4—21no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—24no—
450C2×C4⋊C4D4×C1312yes—
451C2×C4⋊C4D4×C1311yescharacteristic
452C2×C4⋊C4D4×C1311yescharacteristic
453C2×C4⋊C4C23×C1312yes—
454C2×C4⋊C4C23×C1311yescharacteristic
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C1312yes—
458C2×C42—21no—
459C2×C42C23×C1312yes—
460#107—22no—
461#107—22no—
462#107—22no—
463#106—22no—
464#106—22no—
465#106—22no—
466#104—24no—
467#103—22no—
468#102—22no—
469#101—24no—
470C22⋊C8—21no—
471C22⋊C8—21no—
472#95—21no—
473#95—24no—
474C2×C13—22no—
475C2×C13—22no—
476C2×C13—41no—
477C2×C13—81no—
478C2×C13#240611yescharacteristic
479C2×C13C2×#45611yescharacteristic
480C2×C13#302111yescharacteristic
481C24C2×D4×C1311yescharacteristic
482#41—22no—
483#41—22no—
484C2×Q8—22no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8C2×D4×C1311yescharacteristic
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4C2×D4×C1311yescharacteristic
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—41no—
503C22×C4—41no—
504C22×C4—82no—
505C22×C4C2×D4×C1312yes—
506C22×C4C2×D4×C1311yescharacteristic
507C22×C4C2×D4×C1311yescharacteristic
508C22×C4C2×D4×C1311yescharacteristic
509C22×C4C2×D4×C1311yescharacteristic
510C22×C4C2×D4×C1311yescharacteristic
511C22×C4C2×D4×C1312yes—
512C22×C4C24×C1311yescharacteristic
513M16—24no—
514M16—22no—
515M16—22no—
516M16—22no—
517M16C13×#4114yes—
518C2×C8—24no—
519C2×C8—22no—
520C2×C8—22no—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—22no—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—22no—
538C4⋊C4—22no—
539C4⋊C4—41no—
540C4⋊C4—41no—
541C4⋊C4—84no—
542C4⋊C4C2×D4×C1311yescharacteristic
543C4⋊C4C2×D4×C1311yescharacteristic
544C4⋊C4C2×D4×C1311yescharacteristic
545C4⋊C4C2×D4×C1311yescharacteristic
546C4⋊C4C2×D4×C1311yescharacteristic
547C4⋊C4C2×D4×C1311yescharacteristic
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—21no—
553C22⋊C4—21no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—21no—
557C22⋊C4—21no—
558C22⋊C4—21no—
559C22⋊C4—21no—
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C42—22no—
564C42—22no—
565C42—22no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—22no—
572C42—22no—
573C13#2408611yescharacteristic, direct product factor, Sylow
574C23—22no—
575C23—22no—
576C23—21no—
577C23—41no—
578C23C13×#12011yescharacteristic
579C23C13×#12011yescharacteristic
580C23C22×D4×C1311yescharacteristic
581Q8—22no—
582Q8—41no—
583Q8—41no—
584Q8—42no—
585Q8—82no—
586D4—22no—
587D4—42no—
588D4—42no—
589D4—81no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—81no—
617C2×C4—82no—
618C2×C4—82no—
619C2×C4—82no—
620C2×C4C13×#12011yescharacteristic
621C2×C4C13×#12011yescharacteristic
622C2×C4C22×D4×C1311yescharacteristic
623C2×C4C22×D4×C1311yescharacteristic
624C2×C4C2×C13×#4112yes—
625C2×C4C13×2−1+412yes—
626C8—24no—
627C8—42no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—21no—
635C22—44no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22C13×#45612yes—
640C22C2×C13×#12011yescharacteristic
641C22C13×#54712yes—
642C4—21no—
643C4—21no—
644C4—44no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—41no—
652C4—42no—
653C4—41no—
654C4—82no—
655C4C13×#52511yescharacteristic
656C4C13×#53611yescharacteristic
657C4C13×#54712yes—
658C2—22no—
659C2—22no—
660C2—41no—
661C2—81no—
662C2C13×#240611yescharacteristic
663C2C2×C13×#45611yescharacteristic
664C2C13×#302111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#525C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#428C2semidirect
4. C13×#2502C2semidirect
5. C13×#2060C2semidirect
6. C13×#2038C2semidirect
7. C13×#1901C2semidirect
9. C13×#1859C2semidirect
10. C13×#1857C2semidirect
11. C13×#1826C2semidirect
149. #24086C13direct (N × H)
244. C2×#428C2×C13semidirect
245. #2502C2×C13semidirect
246. #2060C2×C13semidirect
247. #2038C2×C13semidirect
248. #1901C2×C13semidirect
250. #1859C2×C13semidirect
251. #1857C2×C13semidirect
252. #1826C2×C13semidirect
573. C13#24086direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34952
C13×#30922
C2×C13×#4282
C13×#25022
C13×#20602
C13×#20382
C13×#19012
C13×#18712
C13×#18592
C13×#18572
C13×#18262
#2408613