Finite Group Databasebeta

← C13×#19866 #15706205

Subgroups — C13×#19866 #15706205

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3393C211yesmaximal, characteristic
2C13×#3360C211yesmaximal, characteristic
3C13×#3356C211yesmaximal, characteristic, complemented
4C13×#3342C211yesmaximal, characteristic, complemented
5C13×#1723C211yesmaximal, characteristic, complemented
6C13×#1693C211yesmaximal, characteristic, complemented
7C13×#1684C211yesmaximal, characteristic, complemented
8C13×#1671C211yesmaximal, characteristic, complemented
9C13×#1670C211yesmaximal, characteristic, complemented
10C13×#1650C211yesmaximal, characteristic, complemented
11C13×#1650C211yesmaximal, characteristic, complemented
12C13×#1643C211yesmaximal, characteristic, complemented
13C13×#1638C211yesmaximal, characteristic, complemented
14C13×#1581C211yesmaximal, characteristic
15C13×#1579C211yesmaximal, characteristic, complemented
16C13×#556C2211yescharacteristic
17C13×#556C2211yescharacteristic
18C13×#556C2211yescharacteristic
19C13×#554C2211yescharacteristic
20C13×#500C2211yescharacteristic
21C13×#500C2211yescharacteristic
22C13×#498C2211yescharacteristic
23C13×#495—21no—
24C13×#494C2211yescharacteristic
25C13×#488—21no—
26C13×#487C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#485—21no—
29C13×#485—21no—
30C13×#485—21no—
31C13×#483—21no—
32C13×#479—21no—
33C13×#477C2211yescharacteristic
34C13×#476C2211yescharacteristic
35C13×#475C2211yescharacteristic
36C13×#475C2211yescharacteristic
37C13×#475C2211yescharacteristic
38C13×#470—21no—
39C13×#467—21no—
40C13×#464—21no—
41C13×#464—21no—
42C13×#463—21no—
43C13×#461C2211yescharacteristic
44C13×#461C2211yescharacteristic
45C13×#461C2211yescharacteristic
46C8×Q8×C13C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C4×C13×Q16—21no—
49C4×C13×Q16C2211yescharacteristic
50C4×C13×SD16—21no—
51C4×C13×D8C2211yescharacteristic
52C13×#436C2211yescharacteristic
53C8×D4×C13C2211yescharacteristic
54C13×#428—21no—
55C13×#427—21no—
56C13×#335C2211yescharacteristic
57C13×#334C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#332C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#332C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×D4⋊C8C2211yescharacteristic
65C13×D4⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C2×C13×Q16—21no—
68C2×C13×Q16—21no—
69C2×C13×Q16D411yescharacteristic
70C2×C13×SD16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16—21no—
73C2×C13×D8D411yescharacteristic
74C2×C13×M16—21no—
75C22×C8×C13—21no—
76C13×C4⋊Q8C2311yescharacteristic
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×#126—41no—
81C13×#126—41no—
82C13×#126—41no—
83C13×#125—21no—
84C13×#124—21no—
85C13×#124—21no—
86C13×#124—21no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×C22⋊Q8—21no—
91C13×C22⋊Q8—41no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13C2311yescharacteristic
96C4×Q8×C13C2311yescharacteristic
97C4×D4×C13—21no—
98C4×D4×C13C2311yescharacteristic
99C4×D4×C13C2311yescharacteristic
100C13×#117—21no—
101C13×#117—21no—
102C13×#117—21no—
103C2×C13×C4⋊C4—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107—21no—
107C13×#107—41no—
108C13×#107D411yescharacteristic
109C13×#107D411yescharacteristic
110C13×#106—21no—
111C13×#106—21no—
112C13×#106—21no—
113C13×#106—21no—
114C13×#106—21no—
115C13×#106—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—21no—
128C13×#103—21no—
129C13×#103—21no—
130C13×#103—21no—
131C13×#103—41no—
132C13×#103D411yescharacteristic
133C13×#103D411yescharacteristic
134C13×#102—21no—
135C13×#102D411yescharacteristic
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×C22⋊C8—21no—
139C4×C8×C13—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19866C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13C2×D411yescharacteristic
150C2×Q8×C13C2×D411yescharacteristic
151C2×D4×C13C2×D411yescharacteristic
152C2×D4×C13C2×D411yescharacteristic
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—41no—
156C13×Q16—22no—
157C13×Q16—42no—
158C13×Q16—81no—
159C13×SD16—42no—
160C13×SD16—81no—
161C13×SD16—81no—
162C13×D8—41no—
163C13×M16—42no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—42no—
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
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—41no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4C2×D411yescharacteristic
190C13×C4⋊C4C2×D411yescharacteristic
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C22⋊C4—21no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—41no—
196C13×C22⋊C4—41no—
197C13×C22⋊C4—41no—
198C13×C22⋊C4—41no—
199C13×C22⋊C4—41no—
200C13×C22⋊C4—41no—
201C13×C22⋊C4—41no—
202C42×C13—21no—
203C42×C13—21no—
204C42×C13—41no—
205C42×C13—41no—
206C42×C13—41no—
207C42×C13C2411yescharacteristic
208#3393C2×C1311yescharacteristic
209#3360C2×C1311yescharacteristic
210#3356C2×C1311yescharacteristic, complemented
211#3342C2×C1311yescharacteristic, complemented
212#1723C2×C1311yescharacteristic, complemented
213#1693C2×C1311yescharacteristic, complemented
214#1684C2×C1311yescharacteristic, complemented
215#1671C2×C1311yescharacteristic, complemented
216#1670C2×C1311yescharacteristic, complemented
217#1650C2×C1311yescharacteristic, complemented
218#1650C2×C1311yescharacteristic, complemented
219#1643C2×C1311yescharacteristic, complemented
220#1638C2×C1311yescharacteristic, complemented
221#1581C2×C1311yescharacteristic
222#1579C2×C1311yescharacteristic, complemented
223C23×C13—21no—
224C23×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—21no—
228Q8×C13—21no—
229Q8×C13—41no—
230Q8×C13—41no—
231Q8×C13—41no—
232Q8×C13—41no—
233Q8×C13—41no—
234Q8×C13—41no—
235Q8×C13—81no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
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×C13C22×D411yescharacteristic
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13H(5,𝔽2)11yescharacteristic
258C8×C13—21no—
259C8×C13—21no—
260C8×C13—21no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264C8×C13—41no—
265C8×C13—41no—
266C8×C13#13512yes—
267#556C22×C1311yescharacteristic
268#556C22×C1311yescharacteristic
269#556C22×C1311yescharacteristic
270#554C22×C1311yescharacteristic
271#500C22×C1311yescharacteristic
272#500C22×C1311yescharacteristic
273#498C22×C1311yescharacteristic
274#495—21no—
275#494C22×C1311yescharacteristic
276#488—21no—
277#487C22×C1311yescharacteristic
278#487C22×C1311yescharacteristic
279#485—21no—
280#485—21no—
281#485—21no—
282#483—21no—
283#479—21no—
284#477C22×C1311yescharacteristic
285#476C22×C1311yescharacteristic
286#475C22×C1311yescharacteristic
287#475C22×C1311yescharacteristic
288#475C22×C1311yescharacteristic
289#470—21no—
290#467—21no—
291#464—21no—
292#464—21no—
293#463—21no—
294#461C22×C1311yescharacteristic
295#461C22×C1311yescharacteristic
296#461C22×C1311yescharacteristic
297C8×Q8C22×C1311yescharacteristic
298C8×Q8C22×C1311yescharacteristic
299C4×Q16—21no—
300C4×Q16C22×C1311yescharacteristic
301C4×SD16—21no—
302C4×D8C22×C1311yescharacteristic
303#436C22×C1311yescharacteristic
304C8×D4C22×C1311yescharacteristic
305#428—21no—
306#427—21no—
307#335C22×C1311yescharacteristic
308#334C22×C1311yescharacteristic
309#333C22×C1311yescharacteristic
310#332C22×C1311yescharacteristic
311#332C22×C1311yescharacteristic
312#332C22×C1311yescharacteristic
313Q8⋊C8C22×C1311yescharacteristic
314Q8⋊C8C22×C1311yescharacteristic
315D4⋊C8C22×C1311yescharacteristic
316D4⋊C8C22×C1311yescharacteristic
317#322C22×C1311yescharacteristic
318C22×C13—41no—
319C22×C13—41no—
320C22×C13—41no—
321C22×C13—41no—
322C22×C13—41no—
323C22×C13—41no—
324C22×C13D4211yescharacteristic
325C4×C13—21no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—41no—
329C4×C13—41no—
330C4×C13—41no—
331C4×C13—41no—
332C4×C13—81no—
333C4×C13—81no—
334C4×C13—81no—
335C4×C13—81no—
336C4×C13C2×#13511yescharacteristic
337C4×C13#57511yescharacteristic
338C4×C13#57711yescharacteristic
339C4×C13#57811yescharacteristic
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16D4×C1311yescharacteristic
343C2×SD16—21no—
344C2×SD16—21no—
345C2×SD16—21no—
346C2×D8D4×C1311yescharacteristic
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8C23×C1311yescharacteristic
350C4⋊Q8C23×C1311yescharacteristic
351C4⋊Q8C23×C1311yescharacteristic
352C4⋊Q8C23×C1311yescharacteristic
353#126—41no—
354#126—41no—
355#126—41no—
356#125—21no—
357#124—21no—
358#124—21no—
359#124—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—21no—
364C22⋊Q8—41no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C1311yescharacteristic
369C4×Q8C23×C1311yescharacteristic
370C4×D4—21no—
371C4×D4C23×C1311yescharacteristic
372C4×D4C23×C1311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376C2×C4⋊C4—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—41no—
381#107D4×C1311yescharacteristic
382#107D4×C1311yescharacteristic
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C1311yescharacteristic
392C4⋊C8C23×C1311yescharacteristic
393C4⋊C8C23×C1311yescharacteristic
394C4⋊C8C23×C1311yescharacteristic
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—41no—
405#103D4×C1311yescharacteristic
406#103D4×C1311yescharacteristic
407#102—21no—
408#102D4×C1311yescharacteristic
409#102D4×C1311yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—21no—
412C4×C8—21no—
413C4×C8—21no—
414C4×C8C23×C1311yescharacteristic
415C4×C8C23×C1311yescharacteristic
416C4×C8C23×C1311yescharacteristic
417C2×C13—81no—
418C2×C13—81no—
419C2×C13#327111yescharacteristic
420C2×C13#328311yescharacteristic
421C2×C13#328911yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C1311yescharacteristic
427C2×Q8C2×D4×C1311yescharacteristic
428C2×D4C2×D4×C1311yescharacteristic
429C2×D4C2×D4×C1311yescharacteristic
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—42no—
435Q16—81no—
436SD16—42no—
437SD16—81no—
438SD16—81no—
439D8—41no—
440M16—42no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8C2×D4×C1311yescharacteristic
448C2×C8C2×D4×C1311yescharacteristic
449C2×C8C2×D4×C1311yescharacteristic
450C2×C8C2×D4×C1311yescharacteristic
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4C2×D4×C1311yescharacteristic
467C4⋊C4C2×D4×C1311yescharacteristic
468C4⋊C4C2×D4×C1311yescharacteristic
469C4⋊C4C2×D4×C1311yescharacteristic
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42C24×C1311yescharacteristic
485C13#1986611yescharacteristic, direct product factor, Sylow
486C23—21no—
487C23—21no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499D4—21no—
500D4—21no—
501D4—21no—
502D4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—161no—
518C2×C4C22×D4×C1311yescharacteristic
519C2×C4C22×D4×C1311yescharacteristic
520C2×C4C13×H(5,𝔽2)11yescharacteristic
521C8—21no—
522C8—21no—
523C8—21no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8C13×#13512yes—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22D42×C1311yescharacteristic
537C4—21no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4C2×C13×#13511yescharacteristic
549C4C13×#57511yescharacteristic
550C4C13×#57711yescharacteristic
551C4C13×#57811yescharacteristic
552C2—81no—
553C2—81no—
554C2C13×#327111yescharacteristic
555C2C13×#328311yescharacteristic
556C2C13×#328911yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC2×C13×D8D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C13×#3356C2semidirect
4. C13×#3342C2semidirect
5. C13×#1723C2semidirect
6. C13×#1693C2semidirect
7. C13×#1684C2semidirect
8. C13×#1671C2semidirect
9. C13×#1670C2semidirect
10. C13×#1650C2semidirect
11. C13×#1650C2semidirect
12. C13×#1643C2semidirect
13. C13×#1638C2semidirect
15. C13×#1579C2semidirect
144. #19866C13direct (N × H)
210. #3356C2×C13semidirect
211. #3342C2×C13semidirect
212. #1723C2×C13semidirect
213. #1693C2×C13semidirect
214. #1684C2×C13semidirect
215. #1671C2×C13semidirect
216. #1670C2×C13semidirect
217. #1650C2×C13semidirect
218. #1650C2×C13semidirect
219. #1643C2×C13semidirect
220. #1638C2×C13semidirect
222. #1579C2×C13semidirect
485. C13#19866direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33932
C13×#33602
C13×#33562
C13×#33422
C13×#17232
C13×#16932
C13×#16842
C13×#16712
C13×#16702
C13×#16502
C13×#16432
C13×#16382
C13×#15812
C13×#15792
#1986613