Finite Group Databasebeta

← C13×#18431 #15704770

Subgroups — C13×#18431 #15704770

Order 3328.

928 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3559C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3206C211yesmaximal, characteristic, complemented
4C13×#2660C211yesmaximal, characteristic, complemented
5C13×#1604C214yesmaximal, complemented
6C13×#1603C214yesmaximal, complemented
7C13×#1505C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1470C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#554—21no—
13C13×#553—21no—
14C13×#553—21no—
15C13×#547—22no—
16C13×#547—21no—
17C13×#544—21no—
18C13×#540—21no—
19C13×#539—22no—
20C13×#539C2212yes—
21C13×#537C2212yes—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#125C2211yescharacteristic
26C13×#497—21no—
27C13×#492—21no—
28C13×#491—21no—
29C13×#487—21no—
30C13×#462—21no—
31C13×#461—22no—
32C13×#461—21no—
33C13×#451C2212yes—
34C13×#448C2214yes—
35C13×#448C2212yes—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#398—22no—
39C13×#395C2214yes—
40C13×#384—21no—
41C13×#382—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#327C2212yes—
45C13×#327C2214yes—
46C13×#324C2214yes—
47C2×C13×#41—21no—
48C2×C13×#41—22no—
49C22×Q8×C13C2312yes—
50C2×C13×Q16—22no—
51C2×C13×SD16—24no—
52C2×C13×SD16—22no—
53C13×C4⋊Q8—21no—
54C13×C4⋊Q8—22no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8D411yescharacteristic
60C13×#127D411yescharacteristic
61C13×#126—22no—
62C13×#126—22no—
63C13×#126—21no—
64C13×#125—21no—
65C13×#125—22no—
66C13×#125—21no—
67C13×#125—21no—
68C13×#125—21no—
69C13×#125—21no—
70C13×#125D411yescharacteristic
71C13×#124—21no—
72C13×#124D411yescharacteristic
73C13×#123—22no—
74C13×#123—22no—
75C13×#123—22no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—21no—
79C13×#123—22no—
80C13×C22⋊Q8—22no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—22no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8C2311yescharacteristic
87C13×#121—21no—
88C13×#121—22no—
89C13×#121—21no—
90C13×#121—22no—
91C13×#121—22no—
92C13×#121—21no—
93C13×#121—22no—
94C13×#121C2311yescharacteristic
95C13×#121C2312yes—
96C4×Q8×C13D411yescharacteristic
97C4×D4×C13—22no—
98C4×D4×C13—21no—
99C4×D4×C13—21no—
100C4×D4×C13—21no—
101C4×D4×C13—22no—
102C4×D4×C13—21no—
103C4×D4×C13D411yescharacteristic
104C4×D4×C13D412yes—
105C13×#117—21no—
106C13×#117—21no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—21no—
109C2×C13×C4⋊C4—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—24no—
112C2×C13×C4⋊C4D411yescharacteristic
113C2×C13×C4⋊C4D411yescharacteristic
114C2×C13×C4⋊C4D412yes—
115C2×C13×C4⋊C4C2312yes—
116C2×C42×C13—21no—
117C2×C42×C13C2311yescharacteristic
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—24no—
121C13×#103—22no—
122C13×#103—22no—
123C13×C22⋊C8C2312yes—
124C13×C22⋊C8C2312yes—
125C13×#97—21no—
126C4×C8×C13—21no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18431C1311yesmaximal, characteristic, direct product factor, Sylow
131C13×#41—82no—
132C13×#41—84no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—22no—
136C2×Q8×C13—22no—
137C2×Q8×C13—82no—
138C2×Q8×C13C2×D411yescharacteristic
139C2×D4×C13—21no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—22no—
143C2×D4×C13—21no—
144C2×D4×C13—21no—
145C2×D4×C13C2×D411yescharacteristic
146C2×D4×C13C2×D412yes—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2411yescharacteristic
159C13×Q16—82no—
160C13×SD16—84no—
161C13×SD16—82no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—22no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—41no—
184C13×C4⋊C4—41no—
185C13×C4⋊C4—84no—
186C13×C4⋊C4C2×D412yes—
187C13×C4⋊C4C2×D411yescharacteristic
188C13×C4⋊C4C2×D411yescharacteristic
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—22no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—22no—
201C42×C13—24no—
202C42×C13—22no—
203C42×C13—21no—
204C42×C13C2×D411yescharacteristic
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208#3559C2×C1311yescharacteristic
209#3218C2×C1311yescharacteristic, complemented
210#3206C2×C1311yescharacteristic, complemented
211#2660C2×C1311yescharacteristic, complemented
212#1604C2×C1314yescomplemented
213#1603C2×C1314yescomplemented
214#1505C2×C1311yescharacteristic, complemented
215#1500C2×C1311yescharacteristic, complemented
216#1470C2×C1311yescharacteristic, complemented
217C23×C13—21no—
218C23×C13—22no—
219C23×C13C22×D411yescharacteristic
220Q8×C13—41no—
221Q8×C13—44no—
222Q8×C13—42no—
223Q8×C13—42no—
224Q8×C13—81no—
225Q8×C13—82no—
226D4×C13—42no—
227D4×C13—41no—
228D4×C13—44no—
229D4×C13—42no—
230D4×C13—42no—
231D4×C13—81no—
232D4×C13—82no—
233D4×C13—82no—
234C2×C4×C13—22no—
235C2×C4×C13—22no—
236C2×C4×C13—24no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—24no—
244C2×C4×C13—41no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—44no—
250C2×C4×C13—42no—
251C2×C4×C13—82no—
252C2×C4×C13—82no—
253C2×C4×C13—82no—
254C2×C4×C13—82no—
255C2×C4×C13#12011yescharacteristic
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12011yescharacteristic
258C2×C4×C13#12011yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C22×D411yescharacteristic
261C8×C13—42no—
262C8×C13—42no—
263#563—21no—
264#562—21no—
265#554—21no—
266#553—21no—
267#553—21no—
268#547—22no—
269#547—21no—
270#544—21no—
271#540—21no—
272#539—22no—
273#539C22×C1312yes—
274#537C22×C1312yes—
275#532C22×C1311yescharacteristic
276C2×C4⋊Q8C22×C1311yescharacteristic
277#529C22×C1311yescharacteristic
278C2×#125C22×C1311yescharacteristic
279#497—21no—
280#492—21no—
281#491—21no—
282#487—21no—
283#462—21no—
284#461—22no—
285#461—21no—
286#451C22×C1312yes—
287#448C22×C1314yes—
288#448C22×C1312yes—
289#432C22×C1311yescharacteristic
290#431C22×C1311yescharacteristic
291#398—22no—
292#395C22×C1314yes—
293#384—21no—
294#382—21no—
295#376C22×C1311yescharacteristic
296#328C22×C1312yes—
297#327C22×C1314yes—
298#327C22×C1312yes—
299#324C22×C1314yes—
300C22×C13—21no—
301C22×C13—21no—
302C22×C13—42no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—41no—
308C22×C13C2×#12011yescharacteristic
309C22×C13#57712yes—
310C4×C13—21no—
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—21no—
315C4×C13—44no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13—41no—
319C4×C13—41no—
320C4×C13—42no—
321C4×C13—41no—
322C4×C13—82no—
323C4×C13#45612yes—
324C2×#41—21no—
325C2×#41—22no—
326C22×Q8C23×C1312yes—
327C2×Q16—22no—
328C2×SD16—24no—
329C2×SD16—22no—
330C4⋊Q8—21no—
331C4⋊Q8—22no—
332C4⋊Q8—21no—
333C4⋊Q8—21no—
334C4⋊Q8—21no—
335C4⋊Q8—21no—
336C4⋊Q8D4×C1311yescharacteristic
337#127D4×C1311yescharacteristic
338#126—22no—
339#126—22no—
340#126—21no—
341#125—21no—
342#125—22no—
343#125—21no—
344#125—21no—
345#125—21no—
346#125—21no—
347#125D4×C1311yescharacteristic
348#124—21no—
349#124D4×C1311yescharacteristic
350#123—22no—
351#123—22no—
352#123—22no—
353#123—22no—
354#123—22no—
355#123—21no—
356#123—22no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8—22no—
360C22⋊Q8—22no—
361C22⋊Q8—22no—
362C22⋊Q8—22no—
363C22⋊Q8C23×C1311yescharacteristic
364#121—21no—
365#121—22no—
366#121—21no—
367#121—22no—
368#121—22no—
369#121—21no—
370#121—22no—
371#121C23×C1311yescharacteristic
372#121C23×C1312yes—
373C4×Q8D4×C1311yescharacteristic
374C4×D4—22no—
375C4×D4—21no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4D4×C1311yescharacteristic
381C4×D4D4×C1312yes—
382#117—21no—
383#117—21no—
384C2×C4⋊C4—22no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—24no—
389C2×C4⋊C4D4×C1311yescharacteristic
390C2×C4⋊C4D4×C1312yes—
391C2×C4⋊C4D4×C1311yescharacteristic
392C2×C4⋊C4C23×C1312yes—
393C2×C42—21no—
394C2×C42C23×C1311yescharacteristic
395C4⋊C8—21no—
396C4⋊C8—21no—
397#103—24no—
398#103—22no—
399#103—22no—
400C22⋊C8C23×C1312yes—
401C22⋊C8C23×C1312yes—
402#97—21no—
403C4×C8—21no—
404#95—21no—
405#95—24no—
406#95C23×C1312yes—
407C2×C13—22no—
408C2×C13—81no—
409C2×C13—82no—
410C2×C13#300911yescharacteristic
411C2×C13C2×#45611yescharacteristic
412C2×C13#302711yescharacteristic
413#41—82no—
414#41—84no—
415C2×Q8—22no—
416C2×Q8—21no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—82no—
420C2×Q8C2×D4×C1311yescharacteristic
421C2×D4—21no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4C2×D4×C1311yescharacteristic
428C2×D4C2×D4×C1312yes—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4C2×D4×C1312yes—
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1311yescharacteristic
439C22×C4C2×D4×C1312yes—
440C22×C4C24×C1311yescharacteristic
441Q16—82no—
442SD16—84no—
443SD16—82no—
444C2×C8—22no—
445C2×C8—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—22no—
461C4⋊C4—22no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—84no—
468C4⋊C4C2×D4×C1312yes—
469C4⋊C4C2×D4×C1311yescharacteristic
470C4⋊C4C2×D4×C1311yescharacteristic
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—22no—
481C22⋊C4—21no—
482C22⋊C4—22no—
483C42—24no—
484C42—22no—
485C42—21no—
486C42C2×D4×C1311yescharacteristic
487C42C2×D4×C1311yescharacteristic
488C42C2×D4×C1311yescharacteristic
489C42C2×D4×C1311yescharacteristic
490C13#1843111yescharacteristic, direct product factor, Sylow
491C23—21no—
492C23—22no—
493C23C22×D4×C1311yescharacteristic
494Q8—41no—
495Q8—44no—
496Q8—42no—
497Q8—42no—
498Q8—81no—
499Q8—82no—
500D4—42no—
501D4—41no—
502D4—44no—
503D4—42no—
504D4—42no—
505D4—81no—
506D4—82no—
507D4—82no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—24no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—44no—
524C2×C4—42no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—82no—
529C2×C4C13×#12011yescharacteristic
530C2×C4C13×#12011yescharacteristic
531C2×C4C13×#12011yescharacteristic
532C2×C4C13×#12011yescharacteristic
533C2×C4C22×D4×C1311yescharacteristic
534C2×C4C22×D4×C1311yescharacteristic
535C8—42no—
536C8—42no—
537C22—21no—
538C22—21no—
539C22—42no—
540C22—41no—
541C22—41no—
542C22—42no—
543C22—42no—
544C22—41no—
545C22C2×C13×#12011yescharacteristic
546C22C13×#57712yes—
547C4—21no—
548C4—21no—
549C4—21no—
550C4—21no—
551C4—21no—
552C4—44no—
553C4—42no—
554C4—42no—
555C4—41no—
556C4—41no—
557C4—42no—
558C4—41no—
559C4—82no—
560C4C13×#45612yes—
561C2—22no—
562C2—81no—
563C2—82no—
564C2C13×#300911yescharacteristic
565C2C2×C13×#45611yescharacteristic
566C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3559C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#3218C2semidirect
3. C13×#3206C2semidirect
4. C13×#2660C2semidirect
5. C13×#1604C2semidirect
6. C13×#1603C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1470C2semidirect
130. #18431C13direct (N × H)
209. #3218C2×C13semidirect
210. #3206C2×C13semidirect
211. #2660C2×C13semidirect
212. #1604C2×C13semidirect
213. #1603C2×C13semidirect
214. #1505C2×C13semidirect
215. #1500C2×C13semidirect
216. #1470C2×C13semidirect
490. C13#18431direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35592
C13×#32182
C13×#32062
C13×#26602
C13×#16042
C13×#16032
C13×#15052
C13×#15002
C13×#14702
#1843113