Finite Group Databasebeta

← C13×#19856 #15706195

Subgroups — C13×#19856 #15706195

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×#3398C211yesmaximal, characteristic, complemented
2C13×#3364C211yesmaximal, characteristic, complemented
3C13×#3340C211yesmaximal, characteristic
4C13×#3340C211yesmaximal, characteristic
5C13×#1716C211yesmaximal, characteristic, complemented
6C13×#1692C211yesmaximal, characteristic, complemented
7C13×#1679C211yesmaximal, characteristic, complemented
8C13×#1672C211yesmaximal, characteristic, complemented
9C13×#1669C211yesmaximal, characteristic, complemented
10C13×#1652C211yesmaximal, characteristic, complemented
11C13×#1652C211yesmaximal, characteristic, complemented
12C13×#1646C211yesmaximal, characteristic
13C13×#1636C211yesmaximal, characteristic, complemented
14C13×#1582C211yesmaximal, characteristic, complemented
15C13×SD16⋊C8C211yesmaximal, characteristic, complemented
16C13×#557C2211yescharacteristic
17C13×#556C2211yescharacteristic
18C13×#556C2211yescharacteristic
19C13×#555C2211yescharacteristic
20C13×#498C2211yescharacteristic
21C13×#498C2211yescharacteristic
22C13×#498C2211yescharacteristic
23C13×#497—21no—
24C13×#494C2211yescharacteristic
25C13×#488—21no—
26C13×#487C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#485—21no—
29C13×#485—21no—
30C13×#482—21no—
31C13×#482—21no—
32C13×#479—21no—
33C13×#477C2211yescharacteristic
34C13×#477C2211yescharacteristic
35C13×#474C2211yescharacteristic
36C13×#474C2211yescharacteristic
37C13×#474C2211yescharacteristic
38C13×#465—21no—
39C13×#465—21no—
40C13×#464—21no—
41C13×#464—21no—
42C13×#462—21no—
43C13×#462C2211yescharacteristic
44C13×#462C2211yescharacteristic
45C13×#461C2211yescharacteristic
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C13×#441—21no—
49C4×C13×Q16—21no—
50C4×C13×SD16C2211yescharacteristic
51C4×C13×SD16C2211yescharacteristic
52C8×D4×C13C2211yescharacteristic
53C8×D4×C13C2211yescharacteristic
54C13×#427—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×Q16—21no—
70C2×C13×Q16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16D411yescharacteristic
73C2×C13×SD16D411yescharacteristic
74C22×C8×C13—21no—
75C22×C8×C13—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8C2311yescharacteristic
78C13×C4⋊Q8C2311yescharacteristic
79C13×C4⋊Q8C2311yescharacteristic
80C13×C4⋊Q8C2311yescharacteristic
81C13×#126—41no—
82C13×#126—41no—
83C13×#125—21no—
84C13×#125—41no—
85C13×#124—21no—
86C13×#124—21no—
87C13×#124—41no—
88C13×C22⋊Q8—21no—
89C13×C22⋊Q8—21no—
90C13×#121—21no—
91C13×#121—21no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13—21no—
96C4×Q8×C13C2311yescharacteristic
97C4×Q8×C13C2311yescharacteristic
98C4×D4×C13C2311yescharacteristic
99C4×D4×C13C2311yescharacteristic
100C13×#117—21no—
101C13×#117—21no—
102C13×#117—21no—
103C13×#117—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107—21no—
107C13×#107—21no—
108C13×#107—21no—
109C13×#106—21no—
110C13×#106—21no—
111C13×#106—21no—
112C13×#106—21no—
113C13×#106—41no—
114C13×#106D411yescharacteristic
115C13×#106D411yescharacteristic
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—41no—
130C13×#103D411yescharacteristic
131C13×#103D411yescharacteristic
132C13×#102—21no—
133C13×#102—21no—
134C13×#102—21no—
135C13×#102D411yescharacteristic
136C13×#102D411yescharacteristic
137C13×C22⋊C8—21no—
138C13×C22⋊C8—21no—
139C13×#97—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19856C1311yesmaximal, 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×C13—41no—
152C2×D4×C13C2×D411yescharacteristic
153C2×D4×C13C2×D411yescharacteristic
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C13×Q16—42no—
157C13×Q16—42no—
158C13×Q16—81no—
159C13×Q16—81no—
160C13×SD16—22no—
161C13×SD16—41no—
162C13×SD16—81no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—42no—
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—
201C42×C13—21no—
202C42×C13—21no—
203C42×C13—41no—
204C42×C13—41no—
205C42×C13—41no—
206C42×C13—41no—
207C42×C13C2411yescharacteristic
208#3398C2×C1311yescharacteristic, complemented
209#3364C2×C1311yescharacteristic, complemented
210#3340C2×C1311yescharacteristic
211#3340C2×C1311yescharacteristic
212#1716C2×C1311yescharacteristic, complemented
213#1692C2×C1311yescharacteristic, complemented
214#1679C2×C1311yescharacteristic, complemented
215#1672C2×C1311yescharacteristic, complemented
216#1669C2×C1311yescharacteristic, complemented
217#1652C2×C1311yescharacteristic, complemented
218#1652C2×C1311yescharacteristic, complemented
219#1646C2×C1311yescharacteristic
220#1636C2×C1311yescharacteristic, complemented
221#1582C2×C1311yescharacteristic, complemented
222SD16⋊C8C2×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—
240D4×C13—161no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
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—41no—
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#557C22×C1311yescharacteristic
268#556C22×C1311yescharacteristic
269#556C22×C1311yescharacteristic
270#555C22×C1311yescharacteristic
271#498C22×C1311yescharacteristic
272#498C22×C1311yescharacteristic
273#498C22×C1311yescharacteristic
274#497—21no—
275#494C22×C1311yescharacteristic
276#488—21no—
277#487C22×C1311yescharacteristic
278#487C22×C1311yescharacteristic
279#485—21no—
280#485—21no—
281#482—21no—
282#482—21no—
283#479—21no—
284#477C22×C1311yescharacteristic
285#477C22×C1311yescharacteristic
286#474C22×C1311yescharacteristic
287#474C22×C1311yescharacteristic
288#474C22×C1311yescharacteristic
289#465—21no—
290#465—21no—
291#464—21no—
292#464—21no—
293#462—21no—
294#462C22×C1311yescharacteristic
295#462C22×C1311yescharacteristic
296#461C22×C1311yescharacteristic
297#446C22×C1311yescharacteristic
298C8×Q8C22×C1311yescharacteristic
299#441—21no—
300C4×Q16—21no—
301C4×SD16C22×C1311yescharacteristic
302C4×SD16C22×C1311yescharacteristic
303C8×D4C22×C1311yescharacteristic
304C8×D4C22×C1311yescharacteristic
305#427—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×Q16—21no—
343C2×Q16—21no—
344C2×SD16—21no—
345C2×SD16D4×C1311yescharacteristic
346C2×SD16D4×C1311yescharacteristic
347C22×C8—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C23×C1311yescharacteristic
351C4⋊Q8C23×C1311yescharacteristic
352C4⋊Q8C23×C1311yescharacteristic
353C4⋊Q8C23×C1311yescharacteristic
354#126—41no—
355#126—41no—
356#125—21no—
357#125—41no—
358#124—21no—
359#124—21no—
360#124—41no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363#121—21no—
364#121—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C1311yescharacteristic
370C4×Q8C23×C1311yescharacteristic
371C4×D4C23×C1311yescharacteristic
372C4×D4C23×C1311yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376#117—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—41no—
387#106D4×C1311yescharacteristic
388#106D4×C1311yescharacteristic
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—41no—
403#103D4×C1311yescharacteristic
404#103D4×C1311yescharacteristic
405#102—21no—
406#102—21no—
407#102—21no—
408#102D4×C1311yescharacteristic
409#102D4×C1311yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8C23×C1311yescharacteristic
415C4×C8C23×C1311yescharacteristic
416C4×C8C23×C1311yescharacteristic
417C2×C13—81no—
418C2×C13—81no—
419C2×C13#326911yescharacteristic
420C2×C13#328411yescharacteristic
421C2×C13#328911yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8C2×D4×C1311yescharacteristic
427C2×Q8C2×D4×C1311yescharacteristic
428C2×D4—41no—
429C2×D4C2×D4×C1311yescharacteristic
430C2×D4C2×D4×C1311yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433Q16—42no—
434Q16—42no—
435Q16—81no—
436Q16—81no—
437SD16—22no—
438SD16—41no—
439SD16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—42no—
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—
478C42—21no—
479C42—21no—
480C42—41no—
481C42—41no—
482C42—41no—
483C42—41no—
484C42C24×C1311yescharacteristic
485C13#1985611yescharacteristic, 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—
503D4—161no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
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×#326911yescharacteristic
555C2C13×#328411yescharacteristic
556C2C13×#328911yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#555C22
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×#3398C2semidirect
2. C13×#3364C2semidirect
5. C13×#1716C2semidirect
6. C13×#1692C2semidirect
7. C13×#1679C2semidirect
8. C13×#1672C2semidirect
9. C13×#1669C2semidirect
10. C13×#1652C2semidirect
11. C13×#1652C2semidirect
13. C13×#1636C2semidirect
14. C13×#1582C2semidirect
15. C13×SD16⋊C8C2semidirect
144. #19856C13direct (N × H)
208. #3398C2×C13semidirect
209. #3364C2×C13semidirect
212. #1716C2×C13semidirect
213. #1692C2×C13semidirect
214. #1679C2×C13semidirect
215. #1672C2×C13semidirect
216. #1669C2×C13semidirect
217. #1652C2×C13semidirect
218. #1652C2×C13semidirect
220. #1636C2×C13semidirect
221. #1582C2×C13semidirect
222. SD16⋊C8C2×C13semidirect
485. C13#19856direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#33982
C13×#33642
C13×#33402
C13×#17162
C13×#16922
C13×#16792
C13×#16722
C13×#16692
C13×#16522
C13×#16462
C13×#16362
C13×#15822
C13×SD16⋊C82
#1985613