Finite Group Databasebeta

← C13×#25566 #15711905

Subgroups — C13×#25566 #15711905

Order 3328.

1122 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic
2C13×#2484C211yesmaximal, characteristic, complemented
3C13×#2413C212yesmaximal, complemented
4C13×#2062C211yesmaximal, characteristic, complemented
5C13×#2044C211yesmaximal, characteristic
6C13×#2030C211yesmaximal, characteristic, complemented
7C13×#2022C211yesmaximal, characteristic
8C13×#1899C212yesmaximal, complemented
9C13×#1890C212yesmaximal, complemented
10C13×#1867C212yesmaximal, complemented
11C13×#1740C211yesmaximal, characteristic, complemented
12C13×#552—22no—
13C13×#552—22no—
14C13×#551—22no—
15C13×#551—22no—
16C13×#543C2211yescharacteristic
17C13×#539—21no—
18C13×#539—21no—
19C13×#534C2211yescharacteristic
20C13×#529—21no—
21C13×#529—21no—
22C2×C13×#123C2212yes—
23C2×C13×#123C2212yes—
24C13×#518C2212yes—
25C2×C13×#117C2212yes—
26C2×C13×#117C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C2×C13×#99C2212yes—
29C2×C13×#99C2212yes—
30C13×#400—21no—
31C13×#398—22no—
32C13×#398—21no—
33C13×#396—22no—
34C13×#389—22no—
35C13×#388—22no—
36C13×#387—21no—
37C13×#387—21no—
38C13×#386C2212yes—
39C13×#385C2211yescharacteristic
40C13×#385C2212yes—
41C13×#385C2211yescharacteristic
42C13×#381C2211yescharacteristic
43C13×#381C2212yes—
44C13×#381C2211yescharacteristic
45C13×#381C2211yescharacteristic
46C13×#342C2211yescharacteristic
47C13×#342C2211yescharacteristic
48C13×#342C2212yes—
49C13×#342C2212yes—
50C13×#342C2212yes—
51C22×D4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C13×#126—22no—
56C13×#126—22no—
57C13×#126—22no—
58C13×#126—22no—
59C13×#125—21no—
60C13×#125—21no—
61C13×#125—22no—
62C13×#125—22no—
63C13×#124—21no—
64C13×#124—21no—
65C13×#123—22no—
66C13×#123—22no—
67C13×#123—22no—
68C13×#123—22no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—24no—
73C13×#123—42no—
74C13×C22⋊Q8—22no—
75C13×C22⋊Q8—22no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—21no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—22no—
80C13×#121—21no—
81C13×#121—21no—
82C13×#120—22no—
83C4×Q8×C13—21no—
84C4×Q8×C13—21no—
85C4×D4×C13—21no—
86C4×D4×C13—21no—
87C4×D4×C13—22no—
88C4×D4×C13—22no—
89C4×D4×C13—22no—
90C4×D4×C13—22no—
91C13×#117—22no—
92C13×#117—22no—
93C13×#117—22no—
94C13×#117—22no—
95C13×#117—22no—
96C13×#117—24no—
97C13×#117—42no—
98C2×C13×C4⋊C4—21no—
99C2×C13×C4⋊C4—21no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—21no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—21no—
107C2×C13×C4⋊C4D412yes—
108C2×C13×C4⋊C4D411yescharacteristic
109C2×C13×C4⋊C4D412yes—
110C2×C13×C4⋊C4D411yescharacteristic
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4D412yes—
115C2×C13×C22⋊C4D412yes—
116C2×C13×C22⋊C4C2311yescharacteristic
117C2×C13×C22⋊C4C2311yescharacteristic
118C2×C13×C22⋊C4C2312yes—
119C2×C13×C22⋊C4C2311yescharacteristic
120C2×C13×C22⋊C4C2311yescharacteristic
121C2×C13×C22⋊C4C2312yes—
122C2×C13×C22⋊C4C2312yes—
123C2×C42×C13—22no—
124C2×C42×C13D411yescharacteristic
125C2×C42×C13D411yescharacteristic
126C13×#99—24no—
127C13×#99—42no—
128C13×#95—21no—
129C13×#95—21no—
130C13×#95—21no—
131C13×#95—21no—
132C13×#95—21no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—21no—
136C13×#95—21no—
137C13×#95—21no—
138C13×#95—22no—
139C13×#95—22no—
140#25566C1311yesmaximal, characteristic, direct product factor, Sylow
141C24×C13C2×D412yes—
142C24×C13C2411yescharacteristic
143C2×Q8×C13—21no—
144C2×Q8×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—22no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—21no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—22no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—42no—
170C22×C4×C13C2×D412yes—
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D412yes—
174C22×C4×C13C2×D412yes—
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D412yes—
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D412yes—
181C13×C4⋊C4—22no—
182C13×C4⋊C4—22no—
183C13×C4⋊C4—22no—
184C13×C4⋊C4—22no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—21no—
188C13×C4⋊C4—21no—
189C13×C4⋊C4—22no—
190C13×C4⋊C4—22no—
191C13×C4⋊C4—22no—
192C13×C4⋊C4—22no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—44no—
196C13×C4⋊C4—44no—
197C13×C4⋊C4—44no—
198C13×C4⋊C4—42no—
199C13×C4⋊C4—42no—
200C13×C4⋊C4—41no—
201C13×C4⋊C4—41no—
202C13×C4⋊C4—42no—
203C13×C22⋊C4—22no—
204C13×C22⋊C4—22no—
205C13×C22⋊C4—22no—
206C13×C22⋊C4—22no—
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—22no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—22no—
213C13×C22⋊C4—22no—
214C13×C22⋊C4—22no—
215C13×C22⋊C4—22no—
216C13×C22⋊C4—22no—
217C13×C22⋊C4—22no—
218C13×C22⋊C4—21no—
219C13×C22⋊C4—22no—
220C13×C22⋊C4—21no—
221C13×C22⋊C4—44no—
222C13×C22⋊C4—44no—
223C13×C22⋊C4#4114yes—
224C42×C13—22no—
225C42×C13—22no—
226C42×C13—21no—
227C42×C13—21no—
228C42×C13—21no—
229C42×C13—21no—
230C42×C13—44no—
231#3491C2×C1311yescharacteristic
232#2484C2×C1311yescharacteristic, complemented
233#2413C2×C1312yescomplemented
234#2062C2×C1311yescharacteristic, complemented
235#2044C2×C1311yescharacteristic
236#2030C2×C1311yescharacteristic, complemented
237#2022C2×C1311yescharacteristic
238#1899C2×C1312yescomplemented
239#1890C2×C1312yescomplemented
240#1867C2×C1312yescomplemented
241#1740C2×C1311yescharacteristic, complemented
242C23×C13—22no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—42no—
248C23×C13—42no—
249C23×C13C22×D411yescharacteristic
250C23×C13C22×D412yes—
251C23×C13C2×#4112yes—
252C23×C13H(5,𝔽2)11yescharacteristic
253C23×C132−1+411yescharacteristic
254Q8×C13—81no—
255Q8×C13—81no—
256D4×C13—42no—
257D4×C13—42no—
258D4×C13—42no—
259D4×C13—42no—
260D4×C13—81no—
261D4×C13—81no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—21no—
265C2×C4×C13—21no—
266C2×C4×C13—22no—
267C2×C4×C13—22no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—24no—
271C2×C4×C13—22no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—24no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—41no—
285C2×C4×C13—42no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—42no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—42no—
292C2×C4×C13—41no—
293C2×C4×C13—42no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—82no—
308C2×C4×C13—82no—
309C2×C4×C13#12011yescharacteristic
310C2×C4×C13#12011yescharacteristic
311C2×C4×C13#12012yes—
312#552—22no—
313#552—22no—
314#551—22no—
315#551—22no—
316#543C22×C1311yescharacteristic
317#539—21no—
318#539—21no—
319#534C22×C1311yescharacteristic
320#529—21no—
321#529—21no—
322C2×#123C22×C1312yes—
323C2×#123C22×C1312yes—
324#518C22×C1312yes—
325C2×#117C22×C1312yes—
326C2×#117C22×C1311yescharacteristic
327C22×C4⋊C4C22×C1311yescharacteristic
328C2×#99C22×C1312yes—
329C2×#99C22×C1312yes—
330#400—21no—
331#398—22no—
332#398—21no—
333#396—22no—
334#389—22no—
335#388—22no—
336#387—21no—
337#387—21no—
338#386C22×C1312yes—
339#385C22×C1312yes—
340#385C22×C1311yescharacteristic
341#385C22×C1311yescharacteristic
342#381C22×C1311yescharacteristic
343#381C22×C1312yes—
344#381C22×C1311yescharacteristic
345#381C22×C1311yescharacteristic
346#342C22×C1312yes—
347#342C22×C1311yescharacteristic
348#342C22×C1312yes—
349#342C22×C1312yes—
350#342C22×C1311yescharacteristic
351C22×C13—21no—
352C22×C13—22no—
353C22×C13—21no—
354C22×C13—22no—
355C22×C13—42no—
356C22×C13—41no—
357C22×C13—41no—
358C22×C13—42no—
359C22×C13—42no—
360C22×C13—42no—
361C22×C13—82no—
362C22×C13—82no—
363C22×C13C2×#12011yescharacteristic
364C22×C13#53211yescharacteristic
365C22×C13#53711yescharacteristic
366C22×C13#54612yes—
367C22×C13#54712yes—
368C4×C13—21no—
369C4×C13—22no—
370C4×C13—21no—
371C4×C13—44no—
372C4×C13—42no—
373C4×C13—42no—
374C4×C13—41no—
375C4×C13—42no—
376C4×C13—41no—
377C4×C13—41no—
378C4×C13—42no—
379C4×C13—41no—
380C4×C13—82no—
381C4×C13—81no—
382C4×C13—81no—
383C4×C13—81no—
384C22×D4C23×C1312yes—
385C23×C4C23×C1311yescharacteristic
386C23×C4C23×C1311yescharacteristic
387C23×C4C23×C1311yescharacteristic
388#126—22no—
389#126—22no—
390#126—22no—
391#126—22no—
392#125—21no—
393#125—21no—
394#125—22no—
395#125—22no—
396#124—21no—
397#124—21no—
398#123—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—22no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—42no—
407C22⋊Q8—22no—
408C22⋊Q8—22no—
409C22⋊Q8—21no—
410C22⋊Q8—21no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413#121—21no—
414#121—21no—
415#120—22no—
416C4×Q8—21no—
417C4×Q8—21no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423C4×D4—22no—
424#117—22no—
425#117—22no—
426#117—22no—
427#117—22no—
428#117—22no—
429#117—24no—
430#117—42no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—22no—
436C2×C4⋊C4—22no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—22no—
440C2×C4⋊C4D4×C1311yescharacteristic
441C2×C4⋊C4D4×C1311yescharacteristic
442C2×C4⋊C4D4×C1312yes—
443C2×C4⋊C4D4×C1312yes—
444C2×C22⋊C4—22no—
445C2×C22⋊C4—22no—
446C2×C22⋊C4—22no—
447C2×C22⋊C4D4×C1312yes—
448C2×C22⋊C4D4×C1312yes—
449C2×C22⋊C4C23×C1312yes—
450C2×C22⋊C4C23×C1311yescharacteristic
451C2×C22⋊C4C23×C1311yescharacteristic
452C2×C22⋊C4C23×C1311yescharacteristic
453C2×C22⋊C4C23×C1311yescharacteristic
454C2×C22⋊C4C23×C1312yes—
455C2×C22⋊C4C23×C1312yes—
456C2×C42—22no—
457C2×C42D4×C1311yescharacteristic
458C2×C42D4×C1311yescharacteristic
459#99—24no—
460#99—42no—
461#95—21no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—22no—
467#95—22no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—22no—
472#95—22no—
473C2×C13—22no—
474C2×C13—21no—
475C2×C13—21no—
476C2×C13—22no—
477C2×C13—82no—
478C2×C13#243011yescharacteristic
479C2×C13#302511yescharacteristic
480C2×C13#302811yescharacteristic
481C24C2×D4×C1312yes—
482C24C24×C1311yescharacteristic
483C2×Q8—21no—
484C2×Q8—21no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—22no—
490C2×D4—22no—
491C2×D4—21no—
492C2×D4—21no—
493C22×C4—22no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—42no—
510C22×C4C2×D4×C1312yes—
511C22×C4C2×D4×C1311yescharacteristic
512C22×C4C2×D4×C1311yescharacteristic
513C22×C4C2×D4×C1312yes—
514C22×C4C2×D4×C1312yes—
515C22×C4C2×D4×C1311yescharacteristic
516C22×C4C2×D4×C1311yescharacteristic
517C22×C4C2×D4×C1312yes—
518C22×C4C2×D4×C1311yescharacteristic
519C22×C4C2×D4×C1311yescharacteristic
520C22×C4C2×D4×C1312yes—
521C4⋊C4—22no—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—22no—
530C4⋊C4—22no—
531C4⋊C4—22no—
532C4⋊C4—22no—
533C4⋊C4—22no—
534C4⋊C4—22no—
535C4⋊C4—44no—
536C4⋊C4—44no—
537C4⋊C4—44no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—41no—
541C4⋊C4—41no—
542C4⋊C4—42no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—22no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—22no—
555C22⋊C4—22no—
556C22⋊C4—22no—
557C22⋊C4—22no—
558C22⋊C4—21no—
559C22⋊C4—22no—
560C22⋊C4—21no—
561C22⋊C4—44no—
562C22⋊C4—44no—
563C22⋊C4C13×#4114yes—
564C42—22no—
565C42—22no—
566C42—21no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—44no—
571C13#2556611yescharacteristic, direct product factor, Sylow
572C23—22no—
573C23—22no—
574C23—22no—
575C23—41no—
576C23—41no—
577C23—42no—
578C23—42no—
579C23C22×D4×C1311yescharacteristic
580C23C22×D4×C1312yes—
581C23C2×C13×#4112yes—
582C23C13×H(5,𝔽2)11yescharacteristic
583C23C13×2−1+411yescharacteristic
584Q8—81no—
585Q8—81no—
586D4—42no—
587D4—42no—
588D4—42no—
589D4—42no—
590D4—81no—
591D4—81no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—42no—
613C2×C4—41no—
614C2×C4—42no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—42no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—41no—
623C2×C4—42no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—42no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—82no—
638C2×C4—82no—
639C2×C4C13×#12011yescharacteristic
640C2×C4C13×#12011yescharacteristic
641C2×C4C13×#12012yes—
642C22—21no—
643C22—22no—
644C22—21no—
645C22—22no—
646C22—42no—
647C22—41no—
648C22—41no—
649C22—42no—
650C22—42no—
651C22—42no—
652C22—82no—
653C22—82no—
654C22C2×C13×#12011yescharacteristic
655C22C13×#53211yescharacteristic
656C22C13×#53711yescharacteristic
657C22C13×#54612yes—
658C22C13×#54712yes—
659C4—21no—
660C4—22no—
661C4—21no—
662C4—44no—
663C4—42no—
664C4—41no—
665C4—42no—
666C4—41no—
667C4—41no—
668C4—42no—
669C4—41no—
670C4—42no—
671C4—82no—
672C4—81no—
673C4—81no—
674C4—81no—
675C2—22no—
676C2—21no—
677C2—21no—
678C2—22no—
679C2—82no—
680C2C13×#243011yescharacteristic
681C2C13×#302511yescharacteristic
682C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#534C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2484C2semidirect
3. C13×#2413C2semidirect
4. C13×#2062C2semidirect
6. C13×#2030C2semidirect
8. C13×#1899C2semidirect
9. C13×#1890C2semidirect
10. C13×#1867C2semidirect
11. C13×#1740C2semidirect
140. #25566C13direct (N × H)
232. #2484C2×C13semidirect
233. #2413C2×C13semidirect
234. #2062C2×C13semidirect
236. #2030C2×C13semidirect
238. #1899C2×C13semidirect
239. #1890C2×C13semidirect
240. #1867C2×C13semidirect
241. #1740C2×C13semidirect
571. C13#25566direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34912
C13×#24842
C13×#24132
C13×#20622
C13×#20442
C13×#20302
C13×#20222
C13×#18992
C13×#18902
C13×#18672
C13×#17402
#2556613