Finite Group Databasebeta

← C13×#19846 #15706185

Subgroups — C13×#19846 #15706185

Order 3328.

566 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×C13×Q16C211yesmaximal, characteristic, complemented
2C13×#3375C211yesmaximal, characteristic
3C13×#3365C211yesmaximal, characteristic
4C13×#3363C211yesmaximal, characteristic, complemented
5C13×#1719C211yesmaximal, characteristic
6C13×#1704C211yesmaximal, characteristic, complemented
7C13×#1682C211yesmaximal, characteristic
8C13×#1678C211yesmaximal, characteristic
9C13×#1676C211yesmaximal, characteristic, complemented
10C13×#1645C211yesmaximal, characteristic, complemented
11C13×#1636C211yesmaximal, characteristic, complemented
12C13×#1630C211yesmaximal, characteristic
13C13×#1623C211yesmaximal, characteristic
14C13×#1584C211yesmaximal, characteristic, complemented
15C13×#1579C211yesmaximal, characteristic, complemented
16C13×#559C2211yescharacteristic
17Q82×C13C2211yescharacteristic
18Q82×C13C2211yescharacteristic
19C13×#557C2211yescharacteristic
20C13×#500—21no—
21C13×#500C2211yescharacteristic
22C13×#492C2211yescharacteristic
23C13×#489—21no—
24C13×#488—21no—
25C13×#487—21no—
26C13×#487C2211yescharacteristic
27C13×#487C2211yescharacteristic
28C13×#486C2211yescharacteristic
29C13×#486C2211yescharacteristic
30C13×#478—21no—
31C13×#477—21no—
32C13×#477—21no—
33C13×#477—21no—
34C13×#477C2211yescharacteristic
35C13×#477C2211yescharacteristic
36C13×#477C2211yescharacteristic
37C13×#477C2211yescharacteristic
38C13×#475C2211yescharacteristic
39C13×#474—21no—
40C13×#464—21no—
41C13×#464—21no—
42C13×#462—21no—
43C13×#462C2211yescharacteristic
44C13×#460C2211yescharacteristic
45C13×#460C2211yescharacteristic
46C13×#446C2211yescharacteristic
47C8×Q8×C13C2211yescharacteristic
48C8×Q8×C13C2211yescharacteristic
49C8×Q8×C13C2211yescharacteristic
50C13×#440—21no—
51C4×C13×Q16—21no—
52C4×C13×Q16—21no—
53C4×C13×Q16C2211yescharacteristic
54C4×C13×Q16C2211yescharacteristic
55C4×C13×SD16—21no—
56C13×#335C2211yescharacteristic
57C13×#334C2211yescharacteristic
58C13×#333C2211yescharacteristic
59C13×#333C2211yescharacteristic
60C13×#332C2211yescharacteristic
61C13×#331C2211yescharacteristic
62C13×Q8⋊C8C2211yescharacteristic
63C13×Q8⋊C8C2211yescharacteristic
64C13×Q8⋊C8C2211yescharacteristic
65C13×Q8⋊C8C2211yescharacteristic
66C13×#322C2211yescharacteristic
67C2×C13×Q16—21no—
68C2×C13×Q16D411yescharacteristic
69C2×C13×Q16D411yescharacteristic
70C2×C13×SD16—21no—
71C2×C13×SD16—21no—
72C2×C13×SD16—41no—
73C13×C4⋊Q8—21no—
74C13×C4⋊Q8—21no—
75C13×C4⋊Q8—21no—
76C13×C4⋊Q8—21no—
77C13×C4⋊Q8—21no—
78C13×C4⋊Q8—41no—
79C13×C4⋊Q8—41no—
80C13×C4⋊Q8C2311yescharacteristic
81C13×C4⋊Q8C2311yescharacteristic
82C13×C4⋊Q8C2311yescharacteristic
83C13×#127C2311yescharacteristic
84C13×#125—21no—
85C13×#125—41no—
86C13×#124—21no—
87C13×#124—21no—
88C13×#123—41no—
89C4×Q8×C13—21no—
90C4×Q8×C13—21no—
91C4×Q8×C13—21no—
92C4×Q8×C13—21no—
93C4×Q8×C13—21no—
94C4×Q8×C13—21no—
95C4×Q8×C13C2311yescharacteristic
96C4×Q8×C13C2311yescharacteristic
97C4×Q8×C13C2311yescharacteristic
98C4×Q8×C13C2311yescharacteristic
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C13×#107—21no—
102C13×#107—21no—
103C13×#107—21no—
104C13×#107—21no—
105C13×#107—21no—
106C13×#107—21no—
107C13×#107D411yescharacteristic
108C13×#107D411yescharacteristic
109C13×#106—21no—
110C13×C4⋊C8—21no—
111C13×C4⋊C8—21no—
112C13×C4⋊C8—21no—
113C13×C4⋊C8—21no—
114C13×C4⋊C8C2311yescharacteristic
115C13×C4⋊C8C2311yescharacteristic
116C13×C4⋊C8C2311yescharacteristic
117C13×C4⋊C8C2311yescharacteristic
118C13×#103—21no—
119C13×#103—21no—
120C13×#103—21no—
121C13×#103—21no—
122C13×#103—21no—
123C13×#103—21no—
124C13×#103—21no—
125C13×#103—21no—
126C13×#103—41no—
127C13×#103D411yescharacteristic
128C13×#103D411yescharacteristic
129C13×#103D411yescharacteristic
130C13×#103D411yescharacteristic
131C13×#102—21no—
132C13×#102—21no—
133C13×#102—21no—
134C13×#102—21no—
135C13×#102—21no—
136C13×#102—21no—
137C13×#97—21no—
138C4×C8×C13—21no—
139C4×C8×C13—21no—
140C4×C8×C13—21no—
141C4×C8×C13C2311yescharacteristic
142C4×C8×C13C2311yescharacteristic
143C4×C8×C13C2311yescharacteristic
144#19846C1311yesmaximal, characteristic, direct product factor, Sylow
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—41no—
149C2×Q8×C13—41no—
150C2×Q8×C13C2×D411yescharacteristic
151C2×Q8×C13C2×D411yescharacteristic
152C2×Q8×C13C2×D411yescharacteristic
153C2×Q8×C13C2×D411yescharacteristic
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C22×C4×C13—41no—
158C13×Q16—22no—
159C13×Q16—22no—
160C13×Q16—42no—
161C13×SD16—42no—
162C13×SD16—42no—
163C13×SD16—82no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13C2×D411yescharacteristic
170C2×C8×C13C2×D411yescharacteristic
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C13×C4⋊C4—21no—
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—41no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4—41no—
186C13×C4⋊C4—41no—
187C13×C4⋊C4—41no—
188C13×C4⋊C4—41no—
189C13×C4⋊C4—41no—
190C13×C4⋊C4C2×D411yescharacteristic
191C13×C4⋊C4C2×D411yescharacteristic
192C13×C4⋊C4C2×D411yescharacteristic
193C13×C4⋊C4C2×D411yescharacteristic
194C13×C22⋊C4—41no—
195C13×C22⋊C4—41no—
196C13×C22⋊C4—41no—
197C42×C13—21no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—41no—
202C42×C13—41no—
203C42×C13—41no—
204C42×C13C2411yescharacteristic
205Q8×Q16C2×C1311yescharacteristic, complemented
206#3375C2×C1311yescharacteristic
207#3365C2×C1311yescharacteristic
208#3363C2×C1311yescharacteristic, complemented
209#1719C2×C1311yescharacteristic
210#1704C2×C1311yescharacteristic, complemented
211#1682C2×C1311yescharacteristic
212#1678C2×C1311yescharacteristic
213#1676C2×C1311yescharacteristic, complemented
214#1645C2×C1311yescharacteristic, complemented
215#1636C2×C1311yescharacteristic, complemented
216#1630C2×C1311yescharacteristic
217#1623C2×C1311yescharacteristic
218#1584C2×C1311yescharacteristic, complemented
219#1579C2×C1311yescharacteristic, complemented
220C23×C13—41no—
221Q8×C13—21no—
222Q8×C13—21no—
223Q8×C13—21no—
224Q8×C13—21no—
225Q8×C13—21no—
226Q8×C13—21no—
227Q8×C13—41no—
228Q8×C13—41no—
229Q8×C13—81no—
230Q8×C13—81no—
231Q8×C13—161no—
232Q8×C13—161no—
233Q8×C13#13512yes—
234Q8×C13#13712yes—
235D4×C13—41no—
236D4×C13—41no—
237D4×C13—41no—
238D4×C13—41no—
239D4×C13—81no—
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—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—161no—
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C22×D411yescharacteristic
254C2×C4×C13H(5,𝔽2)11yescharacteristic
255C8×C13—21no—
256C8×C13—21no—
257C8×C13—21no—
258C8×C13—21no—
259C8×C13—41no—
260C8×C13—41no—
261C8×C13—41no—
262C8×C13—41no—
263C8×C13—41no—
264#559C22×C1311yescharacteristic
265Q82C22×C1311yescharacteristic
266Q82C22×C1311yescharacteristic
267#557C22×C1311yescharacteristic
268#500—21no—
269#500C22×C1311yescharacteristic
270#492C22×C1311yescharacteristic
271#489—21no—
272#488—21no—
273#487—21no—
274#487C22×C1311yescharacteristic
275#487C22×C1311yescharacteristic
276#486C22×C1311yescharacteristic
277#486C22×C1311yescharacteristic
278#478—21no—
279#477—21no—
280#477—21no—
281#477—21no—
282#477C22×C1311yescharacteristic
283#477C22×C1311yescharacteristic
284#477C22×C1311yescharacteristic
285#477C22×C1311yescharacteristic
286#475C22×C1311yescharacteristic
287#474—21no—
288#464—21no—
289#464—21no—
290#462—21no—
291#462C22×C1311yescharacteristic
292#460C22×C1311yescharacteristic
293#460C22×C1311yescharacteristic
294#446C22×C1311yescharacteristic
295C8×Q8C22×C1311yescharacteristic
296C8×Q8C22×C1311yescharacteristic
297C8×Q8C22×C1311yescharacteristic
298#440—21no—
299C4×Q16—21no—
300C4×Q16—21no—
301C4×Q16C22×C1311yescharacteristic
302C4×Q16C22×C1311yescharacteristic
303C4×SD16—21no—
304#335C22×C1311yescharacteristic
305#334C22×C1311yescharacteristic
306#333C22×C1311yescharacteristic
307#333C22×C1311yescharacteristic
308#332C22×C1311yescharacteristic
309#331C22×C1311yescharacteristic
310Q8⋊C8C22×C1311yescharacteristic
311Q8⋊C8C22×C1311yescharacteristic
312Q8⋊C8C22×C1311yescharacteristic
313Q8⋊C8C22×C1311yescharacteristic
314#322C22×C1311yescharacteristic
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13D4211yescharacteristic
319C4×C13—22no—
320C4×C13—22no—
321C4×C13—21no—
322C4×C13—41no—
323C4×C13—41no—
324C4×C13—41no—
325C4×C13—41no—
326C4×C13—41no—
327C4×C13—41no—
328C4×C13—81no—
329C4×C13—81no—
330C4×C13—81no—
331C4×C13C2×#13511yescharacteristic
332C4×C13C2×#13711yescharacteristic
333C4×C13#57811yescharacteristic
334C4×C13#57811yescharacteristic
335C2×Q16—21no—
336C2×Q16D4×C1311yescharacteristic
337C2×Q16D4×C1311yescharacteristic
338C2×SD16—21no—
339C2×SD16—21no—
340C2×SD16—41no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—41no—
347C4⋊Q8—41no—
348C4⋊Q8C23×C1311yescharacteristic
349C4⋊Q8C23×C1311yescharacteristic
350C4⋊Q8C23×C1311yescharacteristic
351#127C23×C1311yescharacteristic
352#125—21no—
353#125—41no—
354#124—21no—
355#124—21no—
356#123—41no—
357C4×Q8—21no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8C23×C1311yescharacteristic
364C4×Q8C23×C1311yescharacteristic
365C4×Q8C23×C1311yescharacteristic
366C4×Q8C23×C1311yescharacteristic
367C4×D4—21no—
368C4×D4—21no—
369#107—21no—
370#107—21no—
371#107—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107D4×C1311yescharacteristic
376#107D4×C1311yescharacteristic
377#106—21no—
378C4⋊C8—21no—
379C4⋊C8—21no—
380C4⋊C8—21no—
381C4⋊C8—21no—
382C4⋊C8C23×C1311yescharacteristic
383C4⋊C8C23×C1311yescharacteristic
384C4⋊C8C23×C1311yescharacteristic
385C4⋊C8C23×C1311yescharacteristic
386#103—21no—
387#103—21no—
388#103—21no—
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—41no—
395#103D4×C1311yescharacteristic
396#103D4×C1311yescharacteristic
397#103D4×C1311yescharacteristic
398#103D4×C1311yescharacteristic
399#102—21no—
400#102—21no—
401#102—21no—
402#102—21no—
403#102—21no—
404#102—21no—
405#97—21no—
406C4×C8—21no—
407C4×C8—21no—
408C4×C8—21no—
409C4×C8C23×C1311yescharacteristic
410C4×C8C23×C1311yescharacteristic
411C4×C8C23×C1311yescharacteristic
412C2×C13—161no—
413C2×C13#327011yescharacteristic
414C2×C13#328511yescharacteristic
415C2×C13#328811yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8—41no—
421C2×Q8C2×D4×C1311yescharacteristic
422C2×Q8C2×D4×C1311yescharacteristic
423C2×Q8C2×D4×C1311yescharacteristic
424C2×Q8C2×D4×C1311yescharacteristic
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C22×C4—41no—
429Q16—22no—
430Q16—22no—
431Q16—42no—
432SD16—42no—
433SD16—42no—
434SD16—82no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8C2×D4×C1311yescharacteristic
441C2×C8C2×D4×C1311yescharacteristic
442C2×C8C2×D4×C1311yescharacteristic
443C2×C8C2×D4×C1311yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4C2×D4×C1311yescharacteristic
462C4⋊C4C2×D4×C1311yescharacteristic
463C4⋊C4C2×D4×C1311yescharacteristic
464C4⋊C4C2×D4×C1311yescharacteristic
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—41no—
473C42—41no—
474C42—41no—
475C42C24×C1311yescharacteristic
476C13#1984611yescharacteristic, direct product factor, Sylow
477C23—41no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—81no—
487Q8—81no—
488Q8—161no—
489Q8—161no—
490Q8C13×#13512yes—
491Q8C13×#13712yes—
492D4—41no—
493D4—41no—
494D4—41no—
495D4—41no—
496D4—81no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4C22×D4×C1311yescharacteristic
510C2×C4C22×D4×C1311yescharacteristic
511C2×C4C13×H(5,𝔽2)11yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8—41no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22D42×C1311yescharacteristic
525C4—22no—
526C4—22no—
527C4—21no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×C13×#13511yescharacteristic
538C4C2×C13×#13711yescharacteristic
539C4C13×#57811yescharacteristic
540C4C13×#57811yescharacteristic
541C2—161no—
542C2C13×#327011yescharacteristic
543C2C13×#328511yescharacteristic
544C2C13×#328811yescharacteristic
subgroupG/H
center, socleC22×C13D42
commutator, Frattini, cosocleC42C24×C13
prime radicalC13×#127C23
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. Q8×C13×Q16C2semidirect
4. C13×#3363C2semidirect
6. C13×#1704C2semidirect
9. C13×#1676C2semidirect
10. C13×#1645C2semidirect
11. C13×#1636C2semidirect
14. C13×#1584C2semidirect
15. C13×#1579C2semidirect
144. #19846C13direct (N × H)
205. Q8×Q16C2×C13semidirect
208. #3363C2×C13semidirect
210. #1704C2×C13semidirect
213. #1676C2×C13semidirect
214. #1645C2×C13semidirect
215. #1636C2×C13semidirect
218. #1584C2×C13semidirect
219. #1579C2×C13semidirect
476. C13#19846direct (N × H)

Maximal subgroups

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

subgroupindex
Q8×C13×Q162
C13×#33752
C13×#33652
C13×#33632
C13×#17192
C13×#17042
C13×#16822
C13×#16782
C13×#16762
C13×#16452
C13×#16362
C13×#16302
C13×#16232
C13×#15842
C13×#15792
#1984613