Finite Group Databasebeta

← C13×#19857 #15706196

Subgroups — C13×#19857 #15706196

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3400C211yesmaximal, characteristic, complemented
2C13×#3381C211yesmaximal, characteristic, complemented
3C13×#3361C211yesmaximal, characteristic
4C13×#3338C211yesmaximal, characteristic, complemented
5C13×#1714C211yesmaximal, characteristic, complemented
6C13×#1696C211yesmaximal, characteristic, complemented
7C13×#1678C211yesmaximal, characteristic, complemented
8C13×#1672C211yesmaximal, characteristic, complemented
9C13×#1665C211yesmaximal, characteristic
10C13×#1644C211yesmaximal, characteristic, complemented
11C13×#1636C211yesmaximal, characteristic, complemented
12C13×#1630C211yesmaximal, characteristic, complemented
13C13×#1622C211yesmaximal, characteristic
14C13×#1582C211yesmaximal, characteristic, complemented
15C13×#1579C211yesmaximal, characteristic, complemented
16C13×#559C2211yescharacteristic
17C13×#557C2211yescharacteristic
18C13×#554C2211yescharacteristic
19C13×#554C2211yescharacteristic
20C13×#500C2211yescharacteristic
21C13×#499—21no—
22C13×#498C2211yescharacteristic
23C13×#497—21no—
24C13×#492C2211yescharacteristic
25C13×#492C2211yescharacteristic
26C13×#488—21no—
27C13×#487C2211yescharacteristic
28C13×#486C2211yescharacteristic
29C13×#484—21no—
30C13×#484—21no—
31C13×#479—21no—
32C13×#478—21no—
33C13×#478—21no—
34C13×#477C2211yescharacteristic
35C13×#477C2211yescharacteristic
36C13×#477C2211yescharacteristic
37C13×#477C2211yescharacteristic
38C13×#474C2211yescharacteristic
39C13×#467—21no—
40C13×#464—21no—
41C13×#463—21no—
42C13×#462C2211yescharacteristic
43C13×#461—21no—
44C13×#460C2211yescharacteristic
45C13×#459C2211yescharacteristic
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C8×Q8×C13C2211yescharacteristic
49C13×#440—21no—
50C4×C13×Q16C2211yescharacteristic
51C4×C13×SD16—21no—
52C4×C13×SD16C2211yescharacteristic
53C4×C13×D8—21no—
54C8×D4×C13C2211yescharacteristic
55C2×C13×#107—21no—
56C13×#334C2211yescharacteristic
57C13×#334C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#333C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#331C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×Q8⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C2×C13×Q16—21no—
68C2×C13×Q16D411yescharacteristic
69C2×C13×SD16—21no—
70C2×C13×SD16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16—41no—
73C2×C13×SD16D411yescharacteristic
74C2×C13×D8—21no—
75C22×C8×C13—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×#127C2311yescharacteristic
81C13×#125—21no—
82C13×#125—21no—
83C13×#125—21no—
84C13×#125—41no—
85C13×#124—21no—
86C13×#124—21no—
87C13×#123—41no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—41no—
91C13×C22⋊Q8—41no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13C2311yescharacteristic
95C4×Q8×C13C2311yescharacteristic
96C4×Q8×C13C2311yescharacteristic
97C4×D4×C13—21no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13C2311yescharacteristic
102C2×C13×C4⋊C4—21no—
103C2×C13×C4⋊C4—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107—21no—
107C13×#107—21no—
108C13×#107—21no—
109C13×#107—21no—
110C13×#107—21no—
111C13×#107D411yescharacteristic
112C13×#106—21no—
113C13×#106—21no—
114C13×#106D411yescharacteristic
115C13×C4⋊C8—21no—
116C13×C4⋊C8—21no—
117C13×C4⋊C8—21no—
118C13×C4⋊C8C2311yescharacteristic
119C13×C4⋊C8C2311yescharacteristic
120C13×C4⋊C8C2311yescharacteristic
121C13×C4⋊C8C2311yescharacteristic
122C13×#103—21no—
123C13×#103—21no—
124C13×#103—21no—
125C13×#103—21no—
126C13×#103—21no—
127C13×#103—41no—
128C13×#103D411yescharacteristic
129C13×#103D411yescharacteristic
130C13×#103D411yescharacteristic
131C13×#102—21no—
132C13×#102—21no—
133C13×#102—21no—
134C13×#102—21no—
135C13×#102—21no—
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×#97—21no—
139C4×C8×C13—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19857C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13C2×D411yescharacteristic
149C2×Q8×C13C2×D411yescharacteristic
150C2×Q8×C13C2×D411yescharacteristic
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13C2×D411yescharacteristic
155C22×C4×C13—21no—
156C22×C4×C13—41no—
157C22×C4×C13—41no—
158C22×C4×C13—41no—
159C13×Q16—22no—
160C13×Q16—81no—
161C13×SD16—22no—
162C13×SD16—42no—
163C13×SD16—81no—
164C13×SD16—81no—
165C13×SD16—82no—
166C13×D8—42no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13—21no—
172C2×C8×C13—42no—
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C2×C8×C13C2×D411yescharacteristic
176C2×C8×C13C2×D411yescharacteristic
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4—41no—
191C13×C4⋊C4—41no—
192C13×C4⋊C4—41no—
193C13×C4⋊C4C2×D411yescharacteristic
194C13×C4⋊C4C2×D411yescharacteristic
195C13×C4⋊C4C2×D411yescharacteristic
196C13×C4⋊C4C2×D411yescharacteristic
197C13×C22⋊C4—21no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4—41no—
200C13×C22⋊C4—41no—
201C13×C22⋊C4—41no—
202C13×C22⋊C4—41no—
203C42×C13—21no—
204C42×C13—21no—
205C42×C13—21no—
206C42×C13—41no—
207C42×C13C2411yescharacteristic
208#3400C2×C1311yescharacteristic, complemented
209#3381C2×C1311yescharacteristic, complemented
210#3361C2×C1311yescharacteristic
211#3338C2×C1311yescharacteristic, complemented
212#1714C2×C1311yescharacteristic, complemented
213#1696C2×C1311yescharacteristic, complemented
214#1678C2×C1311yescharacteristic, complemented
215#1672C2×C1311yescharacteristic, complemented
216#1665C2×C1311yescharacteristic
217#1644C2×C1311yescharacteristic, complemented
218#1636C2×C1311yescharacteristic, complemented
219#1630C2×C1311yescharacteristic, complemented
220#1622C2×C1311yescharacteristic
221#1582C2×C1311yescharacteristic, complemented
222#1579C2×C1311yescharacteristic, complemented
223C23×C13—21no—
224C23×C13—41no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—21no—
230Q8×C13—21no—
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—81no—
234Q8×C13—81no—
235D4×C13—21no—
236D4×C13—41no—
237D4×C13—41no—
238D4×C13—41no—
239D4×C13—41no—
240D4×C13—81no—
241D4×C13#13712yes—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—161no—
255C2×C4×C13—161no—
256C2×C4×C13—161no—
257C2×C4×C13C22×D411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13H(5,𝔽2)11yescharacteristic
260C8×C13—21no—
261C8×C13—21no—
262C8×C13—21no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13—41no—
267C8×C13—41no—
268C8×C13#13512yes—
269#559C22×C1311yescharacteristic
270#557C22×C1311yescharacteristic
271#554C22×C1311yescharacteristic
272#554C22×C1311yescharacteristic
273#500C22×C1311yescharacteristic
274#499—21no—
275#498C22×C1311yescharacteristic
276#497—21no—
277#492C22×C1311yescharacteristic
278#492C22×C1311yescharacteristic
279#488—21no—
280#487C22×C1311yescharacteristic
281#486C22×C1311yescharacteristic
282#484—21no—
283#484—21no—
284#479—21no—
285#478—21no—
286#478—21no—
287#477C22×C1311yescharacteristic
288#477C22×C1311yescharacteristic
289#477C22×C1311yescharacteristic
290#477C22×C1311yescharacteristic
291#474C22×C1311yescharacteristic
292#467—21no—
293#464—21no—
294#463—21no—
295#462C22×C1311yescharacteristic
296#461—21no—
297#460C22×C1311yescharacteristic
298#459C22×C1311yescharacteristic
299#446C22×C1311yescharacteristic
300C8×Q8C22×C1311yescharacteristic
301C8×Q8C22×C1311yescharacteristic
302#440—21no—
303C4×Q16C22×C1311yescharacteristic
304C4×SD16—21no—
305C4×SD16C22×C1311yescharacteristic
306C4×D8—21no—
307C8×D4C22×C1311yescharacteristic
308C2×#107—21no—
309#334C22×C1311yescharacteristic
310#334C22×C1311yescharacteristic
311#333C22×C1311yescharacteristic
312#333C22×C1311yescharacteristic
313#332C22×C1311yescharacteristic
314#331C22×C1311yescharacteristic
315Q8⋊C8C22×C1311yescharacteristic
316Q8⋊C8C22×C1311yescharacteristic
317Q8⋊C8C22×C1311yescharacteristic
318D4⋊C8C22×C1311yescharacteristic
319#322C22×C1311yescharacteristic
320C22×C13—22no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—81no—
324C22×C13—81no—
325C22×C13—81no—
326C22×C13D4211yescharacteristic
327C4×C13—21no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—41no—
333C4×C13—41no—
334C4×C13—41no—
335C4×C13—81no—
336C4×C13—81no—
337C4×C13—81no—
338C4×C13C2×#13511yescharacteristic
339C4×C13C2×#13711yescharacteristic
340C4×C13#57711yescharacteristic
341C4×C13#57811yescharacteristic
342C2×Q16—21no—
343C2×Q16D4×C1311yescharacteristic
344C2×SD16—21no—
345C2×SD16—21no—
346C2×SD16—21no—
347C2×SD16—41no—
348C2×SD16D4×C1311yescharacteristic
349C2×D8—21no—
350C22×C8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C23×C1311yescharacteristic
353C4⋊Q8C23×C1311yescharacteristic
354C4⋊Q8C23×C1311yescharacteristic
355#127C23×C1311yescharacteristic
356#125—21no—
357#125—21no—
358#125—21no—
359#125—41no—
360#124—21no—
361#124—21no—
362#123—41no—
363C22⋊Q8—21no—
364C22⋊Q8—21no—
365C22⋊Q8—41no—
366C22⋊Q8—41no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C1311yescharacteristic
370C4×Q8C23×C1311yescharacteristic
371C4×Q8C23×C1311yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C4×D4C23×C1311yescharacteristic
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#107—21no—
386#107D4×C1311yescharacteristic
387#106—21no—
388#106—21no—
389#106D4×C1311yescharacteristic
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8C23×C1311yescharacteristic
394C4⋊C8C23×C1311yescharacteristic
395C4⋊C8C23×C1311yescharacteristic
396C4⋊C8C23×C1311yescharacteristic
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—41no—
403#103D4×C1311yescharacteristic
404#103D4×C1311yescharacteristic
405#103D4×C1311yescharacteristic
406#102—21no—
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102D4×C1311yescharacteristic
412C22⋊C8—21no—
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C1311yescharacteristic
417C4×C8C23×C1311yescharacteristic
418C4×C8C23×C1311yescharacteristic
419C2×C13—42no—
420C2×C13—161no—
421C2×C13#327011yescharacteristic
422C2×C13#328411yescharacteristic
423C2×C13#328811yescharacteristic
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8C2×D4×C1311yescharacteristic
428C2×Q8C2×D4×C1311yescharacteristic
429C2×Q8C2×D4×C1311yescharacteristic
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4C2×D4×C1311yescharacteristic
434C22×C4—21no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438Q16—22no—
439Q16—81no—
440SD16—22no—
441SD16—42no—
442SD16—81no—
443SD16—81no—
444SD16—82no—
445D8—42no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—42no—
452C2×C8C2×D4×C1311yescharacteristic
453C2×C8C2×D4×C1311yescharacteristic
454C2×C8C2×D4×C1311yescharacteristic
455C2×C8C2×D4×C1311yescharacteristic
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C1311yescharacteristic
473C4⋊C4C2×D4×C1311yescharacteristic
474C4⋊C4C2×D4×C1311yescharacteristic
475C4⋊C4C2×D4×C1311yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—41no—
486C42C24×C1311yescharacteristic
487C13#1985711yescharacteristic, direct product factor, Sylow
488C23—21no—
489C23—41no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—81no—
500D4—21no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—81no—
506D4C13×#13712yes—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—161no—
520C2×C4—161no—
521C2×C4—161no—
522C2×C4C22×D4×C1311yescharacteristic
523C2×C4C22×D4×C1311yescharacteristic
524C2×C4C13×H(5,𝔽2)11yescharacteristic
525C8—21no—
526C8—21no—
527C8—21no—
528C8—41no—
529C8—41no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8C13×#13512yes—
534C22—22no—
535C22—41no—
536C22—41no—
537C22—81no—
538C22—81no—
539C22—81no—
540C22D42×C1311yescharacteristic
541C4—21no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4C2×C13×#13511yescharacteristic
553C4C2×C13×#13711yescharacteristic
554C4C13×#57711yescharacteristic
555C4C13×#57811yescharacteristic
556C2—42no—
557C2—161no—
558C2C13×#327011yescharacteristic
559C2C13×#328411yescharacteristic
560C2C13×#328811yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#459C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3400C2semidirect
2. C13×#3381C2semidirect
4. C13×#3338C2semidirect
5. C13×#1714C2semidirect
6. C13×#1696C2semidirect
7. C13×#1678C2semidirect
8. C13×#1672C2semidirect
10. C13×#1644C2semidirect
11. C13×#1636C2semidirect
12. C13×#1630C2semidirect
14. C13×#1582C2semidirect
15. C13×#1579C2semidirect
144. #19857C13direct (N × H)
208. #3400C2×C13semidirect
209. #3381C2×C13semidirect
211. #3338C2×C13semidirect
212. #1714C2×C13semidirect
213. #1696C2×C13semidirect
214. #1678C2×C13semidirect
215. #1672C2×C13semidirect
217. #1644C2×C13semidirect
218. #1636C2×C13semidirect
219. #1630C2×C13semidirect
221. #1582C2×C13semidirect
222. #1579C2×C13semidirect
487. C13#19857direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34002
C13×#33812
C13×#33612
C13×#33382
C13×#17142
C13×#16962
C13×#16782
C13×#16722
C13×#16652
C13×#16442
C13×#16362
C13×#16302
C13×#16222
C13×#15822
C13×#15792
#1985713