Finite Group Databasebeta

← C13×#18429 #15704768

Subgroups — C13×#18429 #15704768

Order 3328.

932 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3561C211yesmaximal, characteristic
2C13×#3218C211yesmaximal, characteristic, complemented
3C13×#3209C211yesmaximal, characteristic, complemented
4C13×#2640C211yesmaximal, characteristic, complemented
5C13×#1606C214yesmaximal, complemented
6C13×#1602C214yesmaximal, complemented
7C13×#1506C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#563—21no—
11C13×#562—21no—
12C13×#556—21no—
13C13×#551—22no—
14D4×Q8×C13—21no—
15C13×#548—21no—
16C13×#546—21no—
17C13×#543C2212yes—
18C13×#542—21no—
19C13×#542—22no—
20C13×#538C2212yes—
21C13×#536—21no—
22C13×#533C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic
24C13×#529C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C13×#497—21no—
27C13×#494—21no—
28C13×#491—21no—
29C13×#487—21no—
30C13×#462—22no—
31C13×#462—21no—
32C13×#461—21no—
33C13×#451C2212yes—
34C13×#451C2214yes—
35C13×#448C2212yes—
36C13×#432C2211yescharacteristic
37C13×#431C2211yescharacteristic
38C13×#397—22no—
39C13×#393C2214yes—
40C13×#391—21no—
41C13×#390—21no—
42C13×#376C2211yescharacteristic
43C13×#328C2212yes—
44C13×#328C2214yes—
45C13×#327C2212yes—
46C13×#323C2214yes—
47C2×C13×#41—21no—
48C22×Q8×C13—21no—
49C22×Q8×C13D411yescharacteristic
50C22×Q8×C13C2312yes—
51C22×D4×C13D411yescharacteristic
52C2×C13×Q16—24no—
53C2×C13×Q16—22no—
54C2×C13×SD16—22no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—22no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8—21no—
59C13×C4⋊Q8—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8D411yescharacteristic
62C13×C4⋊Q8D411yescharacteristic
63C13×#126—22no—
64C13×#126—22no—
65C13×#126—22no—
66C13×#126—21no—
67C13×#125—21no—
68C13×#125D411yescharacteristic
69C13×#124—21no—
70C13×#124—22no—
71C13×#124—22no—
72C13×#124—21no—
73C13×#124—21no—
74C13×#124—21no—
75C13×#124—21no—
76C13×#124D411yescharacteristic
77C13×#123—22no—
78C13×#123—22no—
79C13×#123—22no—
80C13×#123—21no—
81C13×#123—22no—
82C13×C22⋊Q8—22no—
83C13×C22⋊Q8—21no—
84C13×C22⋊Q8—22no—
85C13×C22⋊Q8—22no—
86C13×C22⋊Q8—22no—
87C13×C22⋊Q8—21no—
88C13×C22⋊Q8—22no—
89C13×C22⋊Q8—22no—
90C13×C22⋊Q8—22no—
91C13×C22⋊Q8C2311yescharacteristic
92C13×C22⋊Q8C2312yes—
93C13×#121—21no—
94C13×#121—22no—
95C13×#121—22no—
96C13×#121C2311yescharacteristic
97C13×#120—22no—
98C4×Q8×C13—21no—
99C4×Q8×C13—21no—
100C4×Q8×C13D411yescharacteristic
101C4×Q8×C13D412yes—
102C4×D4×C13—21no—
103C4×D4×C13—22no—
104C4×D4×C13—21no—
105C4×D4×C13—22no—
106C4×D4×C13D411yescharacteristic
107C13×#117—22no—
108C13×#117—21no—
109C13×#117—21no—
110C2×C13×C4⋊C4—21no—
111C2×C13×C4⋊C4—21no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4D412yes—
115C2×C13×C22⋊C4C2312yes—
116C2×C42×C13—21no—
117C2×C42×C13C2311yescharacteristic
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—22no—
121C13×#103—22no—
122C13×#103—24no—
123C13×C22⋊C8C2312yes—
124C13×C22⋊C8C2312yes—
125C13×#97—21no—
126C4×C8×C13—21no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18429C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13C2×D412yes—
132C13×#41—82no—
133C2×Q8×C13—22no—
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—22no—
138C2×Q8×C13—22no—
139C2×Q8×C13—42no—
140C2×Q8×C13—82no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×Q8×C13C2×D412yes—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—21no—
149C2×D4×C13—42no—
150C2×D4×C13C2×D411yescharacteristic
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—21no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13C2×D411yescharacteristic
158C22×C4×C13C2×D411yescharacteristic
159C22×C4×C13C2×D412yes—
160C22×C4×C13C2411yescharacteristic
161C13×Q16—82no—
162C13×Q16—84no—
163C13×SD16—82no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—41no—
180C13×C4⋊C4—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4—41no—
183C13×C4⋊C4C2×D411yescharacteristic
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C4⋊C4C2×D412yes—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—21no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—21no—
197C13×C22⋊C4—21no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—22no—
200C13×C22⋊C4—21no—
201C13×C22⋊C4—84no—
202C42×C13—22no—
203C42×C13—22no—
204C42×C13—21no—
205C42×C13—42no—
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209C42×C13C2×D411yescharacteristic
210#3561C2×C1311yescharacteristic
211#3218C2×C1311yescharacteristic, complemented
212#3209C2×C1311yescharacteristic, complemented
213#2640C2×C1311yescharacteristic, complemented
214#1606C2×C1314yescomplemented
215#1602C2×C1314yescomplemented
216#1506C2×C1311yescharacteristic, complemented
217#1500C2×C1311yescharacteristic, complemented
218#1469C2×C1311yescharacteristic, complemented
219C23×C13—22no—
220C23×C13—21no—
221C23×C13—24no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13C22×D411yescharacteristic
225Q8×C13—41no—
226Q8×C13—42no—
227Q8×C13—42no—
228Q8×C13—42no—
229Q8×C13—44no—
230Q8×C13—42no—
231Q8×C13—42no—
232Q8×C13—81no—
233Q8×C13—82no—
234D4×C13—41no—
235D4×C13—42no—
236D4×C13—42no—
237D4×C13—81no—
238D4×C13—82no—
239D4×C13—82no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—22no—
244C2×C4×C13—21no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—42no—
252C2×C4×C13—42no—
253C2×C4×C13—44no—
254C2×C4×C13—42no—
255C2×C4×C13—42no—
256C2×C4×C13—82no—
257C2×C4×C13—82no—
258C2×C4×C13—82no—
259C2×C4×C13#12011yescharacteristic
260C2×C4×C13#12011yescharacteristic
261C2×C4×C13#12011yescharacteristic
262C2×C4×C13#12011yescharacteristic
263C2×C4×C13C22×D411yescharacteristic
264C2×C4×C13C22×D411yescharacteristic
265C8×C13—42no—
266C8×C13—42no—
267#563—21no—
268#562—21no—
269#556—21no—
270#551—22no—
271D4×Q8—21no—
272#548—21no—
273#546—21no—
274#543C22×C1312yes—
275#542—21no—
276#542—22no—
277#538C22×C1312yes—
278#536—21no—
279#533C22×C1311yescharacteristic
280C2×C4⋊Q8C22×C1311yescharacteristic
281#529C22×C1311yescharacteristic
282C2×#124C22×C1311yescharacteristic
283#497—21no—
284#494—21no—
285#491—21no—
286#487—21no—
287#462—22no—
288#462—21no—
289#461—21no—
290#451C22×C1312yes—
291#451C22×C1314yes—
292#448C22×C1312yes—
293#432C22×C1311yescharacteristic
294#431C22×C1311yescharacteristic
295#397—22no—
296#393C22×C1314yes—
297#391—21no—
298#390—21no—
299#376C22×C1311yescharacteristic
300#328C22×C1312yes—
301#328C22×C1314yes—
302#327C22×C1312yes—
303#323C22×C1314yes—
304C22×C13—21no—
305C22×C13—21no—
306C22×C13—41no—
307C22×C13—42no—
308C22×C13—41no—
309C22×C13—42no—
310C22×C13—42no—
311C22×C13—41no—
312C22×C13—84no—
313C22×C13C2×#12011yescharacteristic
314C22×C13#57812yes—
315C4×C13—21no—
316C4×C13—21no—
317C4×C13—21no—
318C4×C13—21no—
319C4×C13—21no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—42no—
323C4×C13—42no—
324C4×C13—41no—
325C4×C13—42no—
326C4×C13—82no—
327C4×C13—82no—
328C4×C13#45512yes—
329C2×#41—21no—
330C22×Q8—21no—
331C22×Q8D4×C1311yescharacteristic
332C22×Q8C23×C1312yes—
333C22×D4D4×C1311yescharacteristic
334C2×Q16—24no—
335C2×Q16—22no—
336C2×SD16—22no—
337C4⋊Q8—21no—
338C4⋊Q8—22no—
339C4⋊Q8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342C4⋊Q8—21no—
343C4⋊Q8D4×C1311yescharacteristic
344C4⋊Q8D4×C1311yescharacteristic
345#126—22no—
346#126—22no—
347#126—22no—
348#126—21no—
349#125—21no—
350#125D4×C1311yescharacteristic
351#124—21no—
352#124—22no—
353#124—22no—
354#124—21no—
355#124—21no—
356#124—21no—
357#124—21no—
358#124D4×C1311yescharacteristic
359#123—22no—
360#123—22no—
361#123—22no—
362#123—21no—
363#123—22no—
364C22⋊Q8—22no—
365C22⋊Q8—21no—
366C22⋊Q8—22no—
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—21no—
370C22⋊Q8—22no—
371C22⋊Q8—22no—
372C22⋊Q8—22no—
373C22⋊Q8C23×C1311yescharacteristic
374C22⋊Q8C23×C1312yes—
375#121—21no—
376#121—22no—
377#121—22no—
378#121C23×C1311yescharacteristic
379#120—22no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8D4×C1311yescharacteristic
383C4×Q8D4×C1312yes—
384C4×D4—21no—
385C4×D4—22no—
386C4×D4—21no—
387C4×D4—22no—
388C4×D4D4×C1311yescharacteristic
389#117—22no—
390#117—21no—
391#117—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C22⋊C4—22no—
395C2×C22⋊C4—24no—
396C2×C22⋊C4D4×C1312yes—
397C2×C22⋊C4C23×C1312yes—
398C2×C42—21no—
399C2×C42C23×C1311yescharacteristic
400C4⋊C8—21no—
401C4⋊C8—21no—
402#103—22no—
403#103—22no—
404#103—24no—
405C22⋊C8C23×C1312yes—
406C22⋊C8C23×C1312yes—
407#97—21no—
408C4×C8—21no—
409#95—21no—
410#95—24no—
411#95C23×C1312yes—
412C2×C13—22no—
413C2×C13—81no—
414C2×C13—82no—
415C2×C13#301111yescharacteristic
416C2×C13C2×#45511yescharacteristic
417C2×C13#302711yescharacteristic
418C24C2×D4×C1312yes—
419#41—82no—
420C2×Q8—22no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—42no—
427C2×Q8—82no—
428C2×Q8—82no—
429C2×Q8C2×D4×C1311yescharacteristic
430C2×Q8C2×D4×C1312yes—
431C2×D4—21no—
432C2×D4—22no—
433C2×D4—22no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—42no—
437C2×D4C2×D4×C1311yescharacteristic
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4C2×D4×C1311yescharacteristic
445C22×C4C2×D4×C1311yescharacteristic
446C22×C4C2×D4×C1312yes—
447C22×C4C24×C1311yescharacteristic
448Q16—82no—
449Q16—84no—
450SD16—82no—
451C2×C8—22no—
452C2×C8—22no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—22no—
464C4⋊C4—21no—
465C4⋊C4—22no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4C2×D4×C1311yescharacteristic
471C4⋊C4C2×D4×C1311yescharacteristic
472C4⋊C4C2×D4×C1312yes—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—22no—
477C22⋊C4—22no—
478C22⋊C4—21no—
479C22⋊C4—22no—
480C22⋊C4—22no—
481C22⋊C4—22no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—21no—
488C22⋊C4—84no—
489C42—22no—
490C42—22no—
491C42—21no—
492C42—42no—
493C42C2×D4×C1311yescharacteristic
494C42C2×D4×C1311yescharacteristic
495C42C2×D4×C1311yescharacteristic
496C42C2×D4×C1311yescharacteristic
497C13#1842911yescharacteristic, direct product factor, Sylow
498C23—22no—
499C23—21no—
500C23—24no—
501C23—42no—
502C23—42no—
503C23C22×D4×C1311yescharacteristic
504Q8—41no—
505Q8—42no—
506Q8—42no—
507Q8—42no—
508Q8—44no—
509Q8—42no—
510Q8—42no—
511Q8—81no—
512Q8—82no—
513D4—41no—
514D4—42no—
515D4—42no—
516D4—81no—
517D4—82no—
518D4—82no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—21no—
527C2×C4—41no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4C13×#12011yescharacteristic
539C2×C4C13×#12011yescharacteristic
540C2×C4C13×#12011yescharacteristic
541C2×C4C13×#12011yescharacteristic
542C2×C4C22×D4×C1311yescharacteristic
543C2×C4C22×D4×C1311yescharacteristic
544C8—42no—
545C8—42no—
546C22—21no—
547C22—21no—
548C22—41no—
549C22—42no—
550C22—41no—
551C22—42no—
552C22—42no—
553C22—41no—
554C22—84no—
555C22C2×C13×#12011yescharacteristic
556C22C13×#57812yes—
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—21no—
562C4—41no—
563C4—41no—
564C4—42no—
565C4—42no—
566C4—41no—
567C4—42no—
568C4—82no—
569C4—82no—
570C4C13×#45512yes—
571C2—22no—
572C2—82no—
573C2—81no—
574C2C13×#301111yescharacteristic
575C2C2×C13×#45511yescharacteristic
576C2C13×#302711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3561C2
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×#3209C2semidirect
4. C13×#2640C2semidirect
5. C13×#1606C2semidirect
6. C13×#1602C2semidirect
7. C13×#1506C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
130. #18429C13direct (N × H)
211. #3218C2×C13semidirect
212. #3209C2×C13semidirect
213. #2640C2×C13semidirect
214. #1606C2×C13semidirect
215. #1602C2×C13semidirect
216. #1506C2×C13semidirect
217. #1500C2×C13semidirect
218. #1469C2×C13semidirect
497. C13#18429direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35612
C13×#32182
C13×#32092
C13×#26402
C13×#16062
C13×#16022
C13×#15062
C13×#15002
C13×#14692
#1842913