Finite Group Databasebeta

← C13×#18348 #15704687

Subgroups — C13×#18348 #15704687

Order 3328.

1016 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3492C211yesmaximal, characteristic, complemented
2C13×#3194C212yesmaximal, complemented
3C13×#2618C211yesmaximal, characteristic, complemented
4C13×#1611C211yesmaximal, characteristic, complemented
5C13×#1610C211yesmaximal, characteristic, complemented
6C13×#1609C212yesmaximal, complemented
7C13×#1599C211yesmaximal, characteristic, complemented
8C13×#1598C211yesmaximal, characteristic, complemented
9C13×#1597C212yesmaximal, complemented
10C13×#1513C212yesmaximal, complemented
11C13×#1463C211yesmaximal, characteristic, complemented
12C13×#554—22no—
13C13×#553—22no—
14C13×#552—22no—
15C13×#547—22no—
16C13×#544C2211yescharacteristic
17C13×#539—21no—
18C13×#539C2212yes—
19C13×#537C2211yescharacteristic
20C13×#525—21no—
21C13×#525—21no—
22C13×#525C2212yes—
23C2×C13×#123—21no—
24C2×C13×#121C2211yescharacteristic
25C13×#520—21no—
26C22×C13×C4⋊C4C2211yescharacteristic
27C13×#483C2212yes—
28C13×#482—22no—
29C13×#480C2212yes—
30C13×#469—22no—
31C13×#468—22no—
32C13×#450C2212yes—
33C13×#449—22no—
34C13×#447C2212yes—
35C13×#407C2212yes—
36C13×#398C2211yescharacteristic
37C13×#398C2211yescharacteristic
38C13×#396—21no—
39C13×#396—21no—
40C13×#394C2211yescharacteristic
41C13×#394C2211yescharacteristic
42C13×#386—21no—
43C13×#380C2211yescharacteristic
44C13×#328C2212yes—
45C13×#328C2212yes—
46C13×#327C2212yes—
47C13×#327C2212yes—
48C13×#324C2212yes—
49C13×#324C2211yescharacteristic
50C13×#324C2211yescharacteristic
51C2×C13×#41—21no—
52C2×C13×#41—21no—
53C2×C13×#41D412yes—
54C22×D4×C13—21no—
55C22×D4×C13C2311yescharacteristic
56C23×C4×C13D411yescharacteristic
57C23×C4×C13D411yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C2×C13×SD16—22no—
60C2×C13×D8—22no—
61C2×C13×M16—22no—
62C13×C4⋊Q8—22no—
63C13×#126—22no—
64C13×#126—22no—
65C13×#125—22no—
66C13×#125—22no—
67C13×#125—22no—
68C13×#123—22no—
69C13×#123—22no—
70C13×#123—22no—
71C13×#123—22no—
72C13×#123—22no—
73C13×#123—44no—
74C13×C22⋊Q8—21no—
75C13×C22⋊Q8—21no—
76C13×C22⋊Q8—21no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—21no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8D412yes—
82C13×C22⋊Q8C2312yes—
83C13×#121—21no—
84C13×#121—21no—
85C13×#121—21no—
86C13×#121—22no—
87C13×#121—21no—
88C13×#121—22no—
89C13×#121—22no—
90C13×#121D412yes—
91C13×#121C2312yes—
92C13×#120—22no—
93C4×Q8×C13—22no—
94C4×D4×C13—22no—
95C4×D4×C13—22no—
96C4×D4×C13—22no—
97C4×D4×C13—22no—
98C4×D4×C13—22no—
99C4×D4×C13—22no—
100C4×D4×C13—22no—
101C13×#117—22no—
102C13×#117—21no—
103C13×#117—21no—
104C13×#117D412yes—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4D411yescharacteristic
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4C2311yescharacteristic
114C2×C13×C4⋊C4C2311yescharacteristic
115C2×C13×C4⋊C4C2311yescharacteristic
116C2×C13×C22⋊C4—21no—
117C2×C13×C22⋊C4—21no—
118C2×C13×C22⋊C4—21no—
119C2×C13×C22⋊C4—21no—
120C2×C13×C22⋊C4—21no—
121C2×C13×C22⋊C4—21no—
122C13×#107—22no—
123C13×#106—22no—
124C13×#103—22no—
125C13×#102—22no—
126C13×#102—22no—
127C13×#102—22no—
128C13×C22⋊C8—22no—
129C13×C22⋊C8C2312yes—
130C13×C22⋊C8C2312yes—
131C13×#95—21no—
132C13×#95—21no—
133C13×#95C2311yescharacteristic
134C13×#95C2311yescharacteristic
135#18348C1311yesmaximal, characteristic, direct product factor, Sylow
136C24×C13—21no—
137C24×C13C2×D411yescharacteristic
138C13×#41—42no—
139C13×#41—42no—
140C13×#41—82no—
141C13×#41—82no—
142C2×Q8×C13—21no—
143C2×Q8×C13—21no—
144C2×Q8×C13C2×D412yes—
145C2×D4×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—21no—
150C2×D4×C13—22no—
151C2×D4×C13—42no—
152C2×D4×C13—42no—
153C2×D4×C13—41no—
154C2×D4×C13—41no—
155C2×D4×C13—81no—
156C2×D4×C13C2×D412yes—
157C22×C4×C13—22no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—22no—
162C22×C4×C13—21no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—41no—
169C22×C4×C13—81no—
170C22×C4×C13—81no—
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×D411yescharacteristic
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D412yes—
177C22×C4×C13C2×D412yes—
178C22×C4×C13C2411yescharacteristic
179C13×SD16—82no—
180C13×D8—82no—
181C13×M16—82no—
182C2×C8×C13—22no—
183C2×C8×C13—22no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—22no—
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—22no—
196C13×C4⋊C4—22no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—42no—
200C13×C4⋊C4—42no—
201C13×C4⋊C4—81no—
202C13×C4⋊C4C2×D412yes—
203C13×C4⋊C4C2×D412yes—
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—42no—
214C13×C22⋊C4—42no—
215C13×C22⋊C4—42no—
216C13×C22⋊C4—42no—
217C13×C22⋊C4—81no—
218C13×C22⋊C4—81no—
219C42×C13—22no—
220C42×C13—22no—
221C42×C13—22no—
222#3492C2×C1311yescharacteristic, complemented
223#3194C2×C1312yescomplemented
224#2618C2×C1311yescharacteristic, complemented
225#1611C2×C1311yescharacteristic, complemented
226#1610C2×C1311yescharacteristic, complemented
227#1609C2×C1312yescomplemented
228#1599C2×C1311yescharacteristic, complemented
229#1598C2×C1311yescharacteristic, complemented
230#1597C2×C1312yescomplemented
231#1513C2×C1312yescomplemented
232#1463C2×C1311yescharacteristic, complemented
233C23×C13—21no—
234C23×C13—21no—
235C23×C13—22no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13#12011yescharacteristic
246C23×C13#12011yescharacteristic
247C23×C13C22×D411yescharacteristic
248Q8×C13—42no—
249Q8×C13—42no—
250Q8×C13—81no—
251D4×C13—42no—
252D4×C13—42no—
253D4×C13—42no—
254D4×C13—42no—
255D4×C13—44no—
256D4×C13—44no—
257D4×C13—42no—
258D4×C13—42no—
259D4×C13—81no—
260D4×C13—82no—
261D4×C13—82no—
262C2×C4×C13—21no—
263C2×C4×C13—21no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—21no—
267C2×C4×C13—22no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—41no—
273C2×C4×C13—42no—
274C2×C4×C13—42no—
275C2×C4×C13—41no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—44no—
279C2×C4×C13—42no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—82no—
292C2×C4×C13—81no—
293C2×C4×C13—82no—
294C2×C4×C13#12012yes—
295C2×C4×C13AGL(1,ℤ/8)12yes—
296C2×C4×C13C22×D412yes—
297C8×C13—42no—
298C8×C13—42no—
299#554—22no—
300#553—22no—
301#552—22no—
302#547—22no—
303#544C22×C1311yescharacteristic
304#539—21no—
305#539C22×C1312yes—
306#537C22×C1311yescharacteristic
307#525—21no—
308#525—21no—
309#525C22×C1312yes—
310C2×#123—21no—
311C2×#121C22×C1311yescharacteristic
312#520—21no—
313C22×C4⋊C4C22×C1311yescharacteristic
314#483C22×C1312yes—
315#482—22no—
316#480C22×C1312yes—
317#469—22no—
318#468—22no—
319#450C22×C1312yes—
320#449—22no—
321#447C22×C1312yes—
322#407C22×C1312yes—
323#398C22×C1311yescharacteristic
324#398C22×C1311yescharacteristic
325#396—21no—
326#396—21no—
327#394C22×C1311yescharacteristic
328#394C22×C1311yescharacteristic
329#386—21no—
330#380C22×C1311yescharacteristic
331#328C22×C1312yes—
332#328C22×C1312yes—
333#327C22×C1312yes—
334#327C22×C1312yes—
335#324C22×C1312yes—
336#324C22×C1311yescharacteristic
337#324C22×C1311yescharacteristic
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—21no—
341C22×C13—21no—
342C22×C13—21no—
343C22×C13—21no—
344C22×C13—21no—
345C22×C13—21no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13—42no—
350C22×C13—42no—
351C22×C13—81no—
352C22×C13—81no—
353C22×C13—81no—
354C22×C13—81no—
355C22×C13—81no—
356C22×C13—81no—
357C22×C13—81no—
358C22×C13C2×#12011yescharacteristic
359C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
360C22×C13#57511yescharacteristic
361C4×C13—22no—
362C4×C13—22no—
363C4×C13—22no—
364C4×C13—41no—
365C4×C13—42no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—41no—
369C4×C13—42no—
370C4×C13—81no—
371C4×C13—81no—
372C4×C13—81no—
373C2×#41—21no—
374C2×#41—21no—
375C2×#41D4×C1312yes—
376C22×D4—21no—
377C22×D4C23×C1311yescharacteristic
378C23×C4D4×C1311yescharacteristic
379C23×C4D4×C1311yescharacteristic
380C23×C4C23×C1311yescharacteristic
381C2×SD16—22no—
382C2×D8—22no—
383C2×M16—22no—
384C4⋊Q8—22no—
385#126—22no—
386#126—22no—
387#125—22no—
388#125—22no—
389#125—22no—
390#123—22no—
391#123—22no—
392#123—22no—
393#123—22no—
394#123—22no—
395#123—44no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—22no—
403C22⋊Q8D4×C1312yes—
404C22⋊Q8C23×C1312yes—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—22no—
409#121—21no—
410#121—22no—
411#121—22no—
412#121D4×C1312yes—
413#121C23×C1312yes—
414#120—22no—
415C4×Q8—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—22no—
421C4×D4—22no—
422C4×D4—22no—
423#117—22no—
424#117—21no—
425#117—21no—
426#117D4×C1312yes—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—22no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C1311yescharacteristic
434C2×C4⋊C4D4×C1311yescharacteristic
435C2×C4⋊C4C23×C1311yescharacteristic
436C2×C4⋊C4C23×C1311yescharacteristic
437C2×C4⋊C4C23×C1311yescharacteristic
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444#107—22no—
445#106—22no—
446#103—22no—
447#102—22no—
448#102—22no—
449#102—22no—
450C22⋊C8—22no—
451C22⋊C8C23×C1312yes—
452C22⋊C8C23×C1312yes—
453#95—21no—
454#95—21no—
455#95C23×C1311yescharacteristic
456#95C23×C1311yescharacteristic
457C2×C13—21no—
458C2×C13—21no—
459C2×C13—41no—
460C2×C13—41no—
461C2×C13—82no—
462C2×C13—161no—
463C2×C13#300611yescharacteristic
464C2×C13#302011yescharacteristic
465C2×C13#302611yescharacteristic
466C24—21no—
467C24C2×D4×C1311yescharacteristic
468#41—42no—
469#41—42no—
470#41—82no—
471#41—82no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8C2×D4×C1312yes—
475C2×D4—21no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—21no—
480C2×D4—22no—
481C2×D4—42no—
482C2×D4—42no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—81no—
486C2×D4C2×D4×C1312yes—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—41no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4C2×D4×C1311yescharacteristic
502C22×C4C2×D4×C1311yescharacteristic
503C22×C4C2×D4×C1311yescharacteristic
504C22×C4C2×D4×C1311yescharacteristic
505C22×C4C2×D4×C1311yescharacteristic
506C22×C4C2×D4×C1312yes—
507C22×C4C2×D4×C1312yes—
508C22×C4C24×C1311yescharacteristic
509SD16—82no—
510D8—82no—
511M16—82no—
512C2×C8—22no—
513C2×C8—22no—
514C4⋊C4—21no—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—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—42no—
530C4⋊C4—42no—
531C4⋊C4—81no—
532C4⋊C4C2×D4×C1312yes—
533C4⋊C4C2×D4×C1312yes—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—22no—
542C22⋊C4—22no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C42—22no—
550C42—22no—
551C42—22no—
552C13#1834811yescharacteristic, direct product factor, Sylow
553C23—21no—
554C23—21no—
555C23—22no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23C13×#12011yescharacteristic
566C23C13×#12011yescharacteristic
567C23C22×D4×C1311yescharacteristic
568Q8—42no—
569Q8—42no—
570Q8—81no—
571D4—42no—
572D4—42no—
573D4—42no—
574D4—42no—
575D4—44no—
576D4—44no—
577D4—42no—
578D4—42no—
579D4—81no—
580D4—82no—
581D4—82no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—41no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—44no—
599C2×C4—42no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—82no—
612C2×C4—81no—
613C2×C4—82no—
614C2×C4C13×#12012yes—
615C2×C4C13×AGL(1,ℤ/8)12yes—
616C2×C4C22×D4×C1312yes—
617C8—42no—
618C8—42no—
619C22—21no—
620C22—21no—
621C22—21no—
622C22—21no—
623C22—21no—
624C22—21no—
625C22—21no—
626C22—21no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—81no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22C2×C13×#12011yescharacteristic
640C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
641C22C13×#57511yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—41no—
646C4—42no—
647C4—42no—
648C4—41no—
649C4—41no—
650C4—42no—
651C4—81no—
652C4—81no—
653C4—81no—
654C2—21no—
655C2—21no—
656C2—41no—
657C2—41no—
658C2—82no—
659C2—161no—
660C2C13×#300611yescharacteristic
661C2C13×#302011yescharacteristic
662C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3492C2semidirect
2. C13×#3194C2semidirect
3. C13×#2618C2semidirect
4. C13×#1611C2semidirect
5. C13×#1610C2semidirect
6. C13×#1609C2semidirect
7. C13×#1599C2semidirect
8. C13×#1598C2semidirect
9. C13×#1597C2semidirect
10. C13×#1513C2semidirect
11. C13×#1463C2semidirect
135. #18348C13direct (N × H)
222. #3492C2×C13semidirect
223. #3194C2×C13semidirect
224. #2618C2×C13semidirect
225. #1611C2×C13semidirect
226. #1610C2×C13semidirect
227. #1609C2×C13semidirect
228. #1599C2×C13semidirect
229. #1598C2×C13semidirect
230. #1597C2×C13semidirect
231. #1513C2×C13semidirect
232. #1463C2×C13semidirect
552. C13#18348direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34922
C13×#31942
C13×#26182
C13×#16112
C13×#16102
C13×#16092
C13×#15992
C13×#15982
C13×#15972
C13×#15132
C13×#14632
#1834813