Finite Group Databasebeta

← C13×#19031 #15705370

Subgroups — C13×#19031 #15705370

Order 3328.

834 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3563C211yesmaximal, characteristic, complemented
2C13×#3235C211yesmaximal, characteristic, complemented
3C13×#3171C211yesmaximal, characteristic
4C13×#3142C211yesmaximal, characteristic, complemented
5C13×#1664C212yesmaximal, complemented
6C13×#1663C212yesmaximal, complemented
7C13×#1658C212yesmaximal, complemented
8C13×#1657C212yesmaximal, complemented
9C13×#1529C211yesmaximal, characteristic, complemented
10C13×#1528C211yesmaximal, characteristic, complemented
11C13×#1526C211yesmaximal, characteristic, complemented
12C13×#564C2212yes—
13C13×#563C2212yes—
14C13×#557—21no—
15C13×#554—21no—
16C13×#552—21no—
17C13×#552—22no—
18C13×#552—21no—
19C13×#544—21no—
20C13×#544—21no—
21C13×#541—21no—
22C13×#541—22no—
23C13×#539—21no—
24C13×#533C2211yescharacteristic
25C13×#532C2211yescharacteristic
26C13×#529C2211yescharacteristic
27C2×C13×#125C2211yescharacteristic
28C13×#501C2211yescharacteristic
29C13×#501C2212yes—
30C13×#496C2211yescharacteristic
31C13×#491C2212yes—
32C13×#490C2212yes—
33C13×#490C2211yescharacteristic
34C13×#490C2212yes—
35C13×#489C2211yescharacteristic
36C13×#488—22no—
37C13×#482—22no—
38C13×#476—21no—
39C13×#474—21no—
40C13×#469—21no—
41C13×#468—21no—
42C4×C13×SD16—21no—
43C4×C13×D8—21no—
44C13×#432C2211yescharacteristic
45C13×#417—21no—
46C13×#417—21no—
47C4×C13×M16C2211yescharacteristic
48C4×C13×M16C2211yescharacteristic
49C13×#330C2212yes—
50C13×#330C2212yes—
51C13×#330C2212yes—
52C13×#330C2212yes—
53C13×#330C2212yes—
54C13×#329C2212yes—
55C2×C13×#41—21no—
56C2×C13×SD16—21no—
57C2×C13×D8—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8—22no—
63C13×C4⋊Q8D411yescharacteristic
64C13×C4⋊Q8D411yescharacteristic
65C13×C4⋊Q8C2311yescharacteristic
66C13×#127C2311yescharacteristic
67C13×#126—22no—
68C13×#126—22no—
69C13×#126—22no—
70C13×#126—22no—
71C13×#126—21no—
72C13×#125—22no—
73C13×#125—22no—
74C13×#125—21no—
75C13×#125—22no—
76C13×#125—22no—
77C13×#125—22no—
78C13×#125—22no—
79C13×#125—22no—
80C13×#125—22no—
81C13×#125—21no—
82C13×#125—21no—
83C13×#125D412yes—
84C13×#125C2312yes—
85C13×#125C2311yescharacteristic
86C13×#125C2312yes—
87C13×#124—21no—
88C13×#124C2311yescharacteristic
89C13×#123—22no—
90C13×#123—22no—
91C13×#123—21no—
92C13×C22⋊Q8—22no—
93C13×C22⋊Q8—21no—
94C13×C22⋊Q8—21no—
95C13×C22⋊Q8—22no—
96C13×C22⋊Q8—21no—
97C13×C22⋊Q8—21no—
98C13×C22⋊Q8—22no—
99C13×C22⋊Q8—22no—
100C13×C22⋊Q8D411yescharacteristic
101C13×#121—21no—
102C13×#121—21no—
103C13×#121D411yescharacteristic
104C4×Q8×C13—21no—
105C4×Q8×C13—22no—
106C4×Q8×C13—21no—
107C4×Q8×C13—21no—
108C4×Q8×C13—21no—
109C4×Q8×C13D411yescharacteristic
110C4×D4×C13—22no—
111C4×D4×C13—21no—
112C4×D4×C13—21no—
113C4×D4×C13—21no—
114C4×D4×C13D411yescharacteristic
115C13×#117—22no—
116C13×#117—21no—
117C13×#117—22no—
118C13×#117—21no—
119C13×#117D412yes—
120C2×C13×C4⋊C4—21no—
121C2×C13×C4⋊C4—21no—
122C2×C13×C4⋊C4—21no—
123C2×C13×C4⋊C4D411yescharacteristic
124C2×C13×C4⋊C4D411yescharacteristic
125C2×C42×C13C2311yescharacteristic
126C13×#107—21no—
127C13×#107—22no—
128C13×#106—21no—
129C13×#106—22no—
130C13×C4⋊C8—21no—
131C13×#103—21no—
132C13×#103—22no—
133C13×#103—22no—
134C13×#102—21no—
135C13×#102—22no—
136C13×#102—22no—
137C13×#102—21no—
138C13×#102—21no—
139C13×#102—22no—
140C13×#102—22no—
141C13×C22⋊C8—21no—
142C13×#97C2312yes—
143C13×#97C2312yes—
144C13×#97C2311yescharacteristic
145C13×#97C2311yescharacteristic
146C4×C8×C13—21no—
147C4×C8×C13—21no—
148#19031C1311yesmaximal, characteristic, direct product factor, Sylow
149C13×#41—44no—
150C2×Q8×C13—22no—
151C2×Q8×C13—21no—
152C2×Q8×C13—21no—
153C2×Q8×C13—21no—
154C2×Q8×C13C2×D411yescharacteristic
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—41no—
160C2×D4×C13C2×D411yescharacteristic
161C22×C4×C13—21no—
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—41no—
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D411yescharacteristic
168C22×C4×C13C2×D411yescharacteristic
169C13×SD16—42no—
170C13×D8—42no—
171C13×M16—42no—
172C13×M16—42no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—22no—
176C2×C8×C13—22no—
177C13×C4⋊C4—22no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—22no—
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—22no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C4⋊C4—22no—
194C13×C4⋊C4—22no—
195C13×C4⋊C4—21no—
196C13×C4⋊C4—21no—
197C13×C4⋊C4—22no—
198C13×C4⋊C4—22no—
199C13×C4⋊C4—21no—
200C13×C4⋊C4—21no—
201C13×C4⋊C4C2×D412yes—
202C13×C4⋊C4C2×D412yes—
203C13×C4⋊C4C2×D412yes—
204C13×C4⋊C4C2×D411yescharacteristic
205C13×C4⋊C4C2×D412yes—
206C13×C4⋊C4C2×D411yescharacteristic
207C13×C22⋊C4—22no—
208C13×C22⋊C4—22no—
209C13×C22⋊C4—22no—
210C13×C22⋊C4—21no—
211C13×C22⋊C4—22no—
212C13×C22⋊C4—21no—
213C13×C22⋊C4—21no—
214C13×C22⋊C4—21no—
215C13×C22⋊C4—21no—
216C13×C22⋊C4—41no—
217C13×C22⋊C4—41no—
218C42×C13—22no—
219C42×C13—22no—
220C42×C13—22no—
221C42×C13—22no—
222C42×C13—21no—
223C42×C13C2×D411yescharacteristic
224C42×C13C2×D411yescharacteristic
225C42×C13C2×D411yescharacteristic
226C42×C13C2411yescharacteristic
227#3563C2×C1311yescharacteristic, complemented
228#3235C2×C1311yescharacteristic, complemented
229#3171C2×C1311yescharacteristic
230#3142C2×C1311yescharacteristic, complemented
231#1664C2×C1312yescomplemented
232#1663C2×C1312yescomplemented
233#1658C2×C1312yescomplemented
234#1657C2×C1312yescomplemented
235#1529C2×C1311yescharacteristic, complemented
236#1528C2×C1311yescharacteristic, complemented
237#1526C2×C1311yescharacteristic, complemented
238C23×C13—21no—
239C23×C13—41no—
240C23×C13#12011yescharacteristic
241Q8×C13—41no—
242Q8×C13—42no—
243Q8×C13—42no—
244Q8×C13—81no—
245Q8×C13—82no—
246D4×C13—41no—
247D4×C13—41no—
248D4×C13—41no—
249D4×C13—42no—
250D4×C13—42no—
251D4×C13—42no—
252D4×C13—82no—
253C2×C4×C13—22no—
254C2×C4×C13—22no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—22no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—42no—
264C2×C4×C13—42no—
265C2×C4×C13—41no—
266C2×C4×C13—81no—
267C2×C4×C13—82no—
268C2×C4×C13—82no—
269C2×C4×C13#12011yescharacteristic
270C2×C4×C13#12011yescharacteristic
271C2×C4×C13#12011yescharacteristic
272C2×C4×C13C22×D411yescharacteristic
273C2×C4×C13C22×D411yescharacteristic
274C2×C4×C13C22×D411yescharacteristic
275C8×C13—22no—
276C8×C13—42no—
277C8×C13—42no—
278C8×C13—41no—
279#564C22×C1312yes—
280#563C22×C1312yes—
281#557—21no—
282#554—21no—
283#552—21no—
284#552—22no—
285#552—21no—
286#544—21no—
287#544—21no—
288#541—21no—
289#541—22no—
290#539—21no—
291#533C22×C1311yescharacteristic
292#532C22×C1311yescharacteristic
293#529C22×C1311yescharacteristic
294C2×#125C22×C1311yescharacteristic
295#501C22×C1311yescharacteristic
296#501C22×C1312yes—
297#496C22×C1311yescharacteristic
298#491C22×C1312yes—
299#490C22×C1312yes—
300#490C22×C1311yescharacteristic
301#490C22×C1312yes—
302#489C22×C1311yescharacteristic
303#488—22no—
304#482—22no—
305#476—21no—
306#474—21no—
307#469—21no—
308#468—21no—
309C4×SD16—21no—
310C4×D8—21no—
311#432C22×C1311yescharacteristic
312#417—21no—
313#417—21no—
314C4×M16C22×C1311yescharacteristic
315C4×M16C22×C1311yescharacteristic
316#330C22×C1312yes—
317#330C22×C1312yes—
318#330C22×C1312yes—
319#330C22×C1312yes—
320#330C22×C1312yes—
321#329C22×C1312yes—
322C22×C13—21no—
323C22×C13—21no—
324C22×C13—21no—
325C22×C13—41no—
326C22×C13—41no—
327C22×C13—41no—
328C22×C13—81no—
329C22×C13—81no—
330C22×C13—81no—
331C22×C13C2×#12011yescharacteristic
332C4×C13—21no—
333C4×C13—21no—
334C4×C13—21no—
335C4×C13—21no—
336C4×C13—21no—
337C4×C13—41no—
338C4×C13—42no—
339C4×C13—42no—
340C4×C13—42no—
341C4×C13—41no—
342C4×C13—42no—
343C4×C13—41no—
344C4×C13—81no—
345C4×C13#45412yes—
346C2×#41—21no—
347C2×SD16—21no—
348C2×D8—21no—
349C2×M16—21no—
350C2×M16—21no—
351C4⋊Q8—22no—
352C4⋊Q8—21no—
353C4⋊Q8—22no—
354C4⋊Q8D4×C1311yescharacteristic
355C4⋊Q8D4×C1311yescharacteristic
356C4⋊Q8C23×C1311yescharacteristic
357#127C23×C1311yescharacteristic
358#126—22no—
359#126—22no—
360#126—22no—
361#126—22no—
362#126—21no—
363#125—22no—
364#125—22no—
365#125—21no—
366#125—22no—
367#125—22no—
368#125—22no—
369#125—22no—
370#125—22no—
371#125—22no—
372#125—21no—
373#125—21no—
374#125D4×C1312yes—
375#125C23×C1312yes—
376#125C23×C1311yescharacteristic
377#125C23×C1312yes—
378#124—21no—
379#124C23×C1311yescharacteristic
380#123—22no—
381#123—22no—
382#123—21no—
383C22⋊Q8—22no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—22no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—22no—
390C22⋊Q8—22no—
391C22⋊Q8D4×C1311yescharacteristic
392#121—21no—
393#121—21no—
394#121D4×C1311yescharacteristic
395C4×Q8—21no—
396C4×Q8—22no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—21no—
400C4×Q8D4×C1311yescharacteristic
401C4×D4—22no—
402C4×D4—21no—
403C4×D4—21no—
404C4×D4—21no—
405C4×D4D4×C1311yescharacteristic
406#117—22no—
407#117—21no—
408#117—22no—
409#117—21no—
410#117D4×C1312yes—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4D4×C1311yescharacteristic
415C2×C4⋊C4D4×C1311yescharacteristic
416C2×C42C23×C1311yescharacteristic
417#107—21no—
418#107—22no—
419#106—21no—
420#106—22no—
421C4⋊C8—21no—
422#103—21no—
423#103—22no—
424#103—22no—
425#102—21no—
426#102—22no—
427#102—22no—
428#102—21no—
429#102—21no—
430#102—22no—
431#102—22no—
432C22⋊C8—21no—
433#97C23×C1312yes—
434#97C23×C1312yes—
435#97C23×C1311yescharacteristic
436#97C23×C1311yescharacteristic
437C4×C8—21no—
438C4×C8—21no—
439C2×C13—41no—
440C2×C13—81no—
441C2×C13—161no—
442C2×C13C2×#45411yescharacteristic
443C2×C13#301811yescharacteristic
444C2×C13#302011yescharacteristic
445#41—44no—
446C2×Q8—22no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C1311yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—41no—
456C2×D4C2×D4×C1311yescharacteristic
457C22×C4—21no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—41no—
462C22×C4C2×D4×C1311yescharacteristic
463C22×C4C2×D4×C1311yescharacteristic
464C22×C4C2×D4×C1311yescharacteristic
465SD16—42no—
466D8—42no—
467M16—42no—
468M16—42no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—22no—
472C2×C8—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—22no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—22no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—22no—
490C4⋊C4—22no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4C2×D4×C1312yes—
498C4⋊C4C2×D4×C1312yes—
499C4⋊C4C2×D4×C1312yes—
500C4⋊C4C2×D4×C1311yescharacteristic
501C4⋊C4C2×D4×C1312yes—
502C4⋊C4C2×D4×C1311yescharacteristic
503C22⋊C4—22no—
504C22⋊C4—22no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—21no—
511C22⋊C4—21no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—22no—
515C42—22no—
516C42—22no—
517C42—22no—
518C42—21no—
519C42C2×D4×C1311yescharacteristic
520C42C2×D4×C1311yescharacteristic
521C42C2×D4×C1311yescharacteristic
522C42C24×C1311yescharacteristic
523C13#1903111yescharacteristic, direct product factor, Sylow
524C23—21no—
525C23—41no—
526C23C13×#12011yescharacteristic
527Q8—41no—
528Q8—42no—
529Q8—42no—
530Q8—81no—
531Q8—82no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—42no—
536D4—42no—
537D4—42no—
538D4—82no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—22no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C13×#12011yescharacteristic
556C2×C4C13×#12011yescharacteristic
557C2×C4C13×#12011yescharacteristic
558C2×C4C22×D4×C1311yescharacteristic
559C2×C4C22×D4×C1311yescharacteristic
560C2×C4C22×D4×C1311yescharacteristic
561C8—22no—
562C8—42no—
563C8—42no—
564C8—41no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22C2×C13×#12011yescharacteristic
575C4—21no—
576C4—21no—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—41no—
581C4—42no—
582C4—42no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—81no—
588C4C13×#45412yes—
589C2—41no—
590C2—81no—
591C2—161no—
592C2C2×C13×#45411yescharacteristic
593C2C13×#301811yescharacteristic
594C2C13×#302011yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#3171C2
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
1. C13×#3563C2semidirect
2. C13×#3235C2semidirect
4. C13×#3142C2semidirect
5. C13×#1664C2semidirect
6. C13×#1663C2semidirect
7. C13×#1658C2semidirect
8. C13×#1657C2semidirect
9. C13×#1529C2semidirect
10. C13×#1528C2semidirect
11. C13×#1526C2semidirect
148. #19031C13direct (N × H)
227. #3563C2×C13semidirect
228. #3235C2×C13semidirect
230. #3142C2×C13semidirect
231. #1664C2×C13semidirect
232. #1663C2×C13semidirect
233. #1658C2×C13semidirect
234. #1657C2×C13semidirect
235. #1529C2×C13semidirect
236. #1528C2×C13semidirect
237. #1526C2×C13semidirect
523. C13#19031direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35632
C13×#32352
C13×#31712
C13×#31422
C13×#16642
C13×#16632
C13×#16582
C13×#16572
C13×#15292
C13×#15282
C13×#15262
#1903113