Finite Group Databasebeta

← C13×#18436 #15704775

Subgroups — C13×#18436 #15704775

Order 3328.

972 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3558C211yesmaximal, characteristic
2C13×#3238C211yesmaximal, characteristic, complemented
3C13×#3226C211yesmaximal, characteristic, complemented
4C13×#2640C211yesmaximal, characteristic, complemented
5C13×#1612C214yesmaximal, complemented
6C13×#1607C214yesmaximal, complemented
7C13×#1505C211yesmaximal, characteristic, complemented
8C13×#1500C211yesmaximal, characteristic, complemented
9C13×#1469C211yesmaximal, characteristic, complemented
10C13×#562—21no—
11C13×H(3,𝔽4)—21no—
12C13×#559—21no—
13C13×#548—21no—
14C13×#546—21no—
15C13×#546—22no—
16D42×C13—21no—
17C13×#542—21no—
18C13×#538—22no—
19C13×#538C2212yes—
20C13×#535—21no—
21C13×#534C2212yes—
22C13×#532C2211yescharacteristic
23C2×C13×C4⋊Q8C2211yescharacteristic, complemented
24C13×#529C2211yescharacteristic
25C2×C13×#124C2211yescharacteristic
26C13×#501—21no—
27C13×#500—21no—
28C13×#489—21no—
29C13×#486—21no—
30C13×#483C2212yescomplemented
31C13×#480C2212yes—
32C13×#480C2214yescomplemented
33C13×#477—21no—
34C13×#476—21no—
35C13×#474—22no—
36C13×#432C2211yescharacteristic, complemented
37C13×#431C2211yescharacteristic, complemented
38C13×#397C2214yescomplemented
39C13×#393—22no—
40C13×#391—21no—
41C13×#390—21no—
42C13×#376C2211yescharacteristic, complemented
43C13×#328C2212yescomplemented
44C13×#327C2212yes—
45C13×#327C2214yescomplemented
46C13×#323C2214yescomplemented
47C2×C13×#41—21no—
48C2×C13×#41—21no—
49C22×Q8×C13—21no—
50C22×Q8×C13D411yescharacteristic
51C22×D4×C13—21no—
52C22×D4×C13—22no—
53C22×D4×C13D411yescharacteristic
54C13×C4⋊Q8—21no—
55C13×C4⋊Q8—21no—
56C13×C4⋊Q8—21no—
57C13×C4⋊Q8—21no—
58C13×C4⋊Q8D411yescharacteristic
59C13×#127—21no—
60C13×#127D411yescharacteristic
61C13×#126—22no—
62C13×#126—21no—
63C13×#125D411yescharacteristic
64C13×#124—21no—
65C13×#124—22no—
66C13×#124—22no—
67C13×#124—22no—
68C13×#124—21no—
69C13×#124—21no—
70C13×#124—21no—
71C13×#124—21no—
72C13×#124—21no—
73C13×#124D411yescharacteristic
74C13×#123—22no—
75C13×#123—21no—
76C13×#123—22no—
77C13×#123—22no—
78C13×#123—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—21no—
81C13×C22⋊Q8—22no—
82C13×C22⋊Q8C2311yescharacteristic
83C13×#121—22no—
84C13×#121—22no—
85C13×#121—22no—
86C13×#121—21no—
87C13×#121—22no—
88C13×#121—21no—
89C13×#121—22no—
90C13×#121C2311yescharacteristic
91C13×#121C2312yes—
92C13×#120—22no—
93C13×#120—22no—
94C13×#120—22no—
95C13×#120—22no—
96C13×#120—22no—
97C4×Q8×C13—21no—
98C4×Q8×C13D411yescharacteristic
99C4×D4×C13—22no—
100C4×D4×C13—21no—
101C4×D4×C13—21no—
102C4×D4×C13—22no—
103C4×D4×C13—21no—
104C4×D4×C13D412yes—
105C4×D4×C13D411yescharacteristic
106C13×#117—21no—
107C2×C13×C4⋊C4—21no—
108C2×C13×C4⋊C4C2312yes—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4D412yes—
112C2×C13×C22⋊C4C2312yes—
113C2×C42×C13—21no—
114C2×C42×C13C2311yescharacteristic
115C13×#107—24no—
116C13×#107—22no—
117C13×#106—22no—
118C13×C4⋊C8—21no—
119C13×C4⋊C8—21no—
120C13×#103—22no—
121C13×#102—24no—
122C13×#102—22no—
123C13×C22⋊C8C2312yes—
124C13×C22⋊C8C2312yes—
125C13×#97—21no—
126C4×C8×C13—21no—
127C13×#95—24no—
128C13×#95—21no—
129C13×#95C2312yes—
130#18436C1311yesmaximal, characteristic, direct product factor, Sylow
131C24×C13—22no—
132C24×C13C2×D412yes—
133C13×#41—82no—
134C13×#41—82no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13—21no—
138C2×Q8×C13—42no—
139C2×Q8×C13—41no—
140C2×Q8×C13—41no—
141C2×Q8×C13—82no—
142C2×Q8×C13C2×D411yescharacteristic
143C2×D4×C13—22no—
144C2×D4×C13—21no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—22no—
149C2×D4×C13—22no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—21no—
154C2×D4×C13—42no—
155C2×D4×C13—82no—
156C2×D4×C13—84no—
157C2×D4×C13C2×D411yescharacteristic
158C2×D4×C13C2×D412yes—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—21no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—22no—
165C22×C4×C13C2×D411yescharacteristic
166C22×C4×C13C2×D411yescharacteristic
167C22×C4×C13C2×D412yes—
168C22×C4×C13C2411yescharacteristic
169C2×C8×C13—22no—
170C2×C8×C13—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—21no—
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—41no—
181C13×C4⋊C4—41no—
182C13×C4⋊C4C2×D411yescharacteristic
183C13×C4⋊C4C2×D412yes—
184C13×C4⋊C4C2×D411yescharacteristic
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—22no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—21no—
191C13×C22⋊C4—21no—
192C13×C22⋊C4—22no—
193C13×C22⋊C4—22no—
194C13×C22⋊C4—21no—
195C13×C22⋊C4—21no—
196C13×C22⋊C4—22no—
197C13×C22⋊C4—22no—
198C13×C22⋊C4—22no—
199C13×C22⋊C4—21no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—84no—
202C42×C13—22no—
203C42×C13—21no—
204C42×C13—42no—
205C42×C13C2×D411yescharacteristic
206C42×C13C2×D411yescharacteristic
207C42×C13C2×D411yescharacteristic
208C42×C13C2×D411yescharacteristic
209#3558C2×C1311yescharacteristic
210#3238C2×C1311yescharacteristic, complemented
211#3226C2×C1311yescharacteristic, complemented
212#2640C2×C1311yescharacteristic, complemented
213#1612C2×C1314yescomplemented
214#1607C2×C1314yescomplemented
215#1505C2×C1311yescharacteristic, complemented
216#1500C2×C1311yescharacteristic, complemented
217#1469C2×C1311yescharacteristic, complemented
218C23×C13—22no—
219C23×C13—21no—
220C23×C13—22no—
221C23×C13—24no—
222C23×C13—42no—
223C23×C13—42no—
224C23×C13—82no—
225C23×C13—82no—
226C23×C13—82no—
227C23×C13C22×D411yescharacteristic
228Q8×C13—41no—
229Q8×C13—42no—
230Q8×C13—81no—
231Q8×C13—81no—
232Q8×C13—82no—
233Q8×C13—82no—
234D4×C13—42no—
235D4×C13—41no—
236D4×C13—42no—
237D4×C13—44no—
238D4×C13—42no—
239D4×C13—42no—
240D4×C13—81no—
241D4×C13—81no—
242D4×C13—82no—
243D4×C13—82no—
244D4×C13—82no—
245D4×C13—82no—
246D4×C13—82no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—41no—
255C2×C4×C13—42no—
256C2×C4×C13—42no—
257C2×C4×C13—42no—
258C2×C4×C13—42no—
259C2×C4×C13—42no—
260C2×C4×C13—42no—
261C2×C4×C13—44no—
262C2×C4×C13—82no—
263C2×C4×C13—82no—
264C2×C4×C13—82no—
265C2×C4×C13#12011yescharacteristic
266C2×C4×C13#12011yescharacteristic
267C2×C4×C13#12011yescharacteristic
268C2×C4×C13#12011yescharacteristic
269C2×C4×C13C22×D411yescharacteristic
270C2×C4×C13C22×D411yescharacteristic
271C8×C13—42no—
272C8×C13—42no—
273#562—21no—
274H(3,𝔽4)—21no—
275#559—21no—
276#548—21no—
277#546—21no—
278#546—22no—
279D42—21no—
280#542—21no—
281#538—22no—
282#538C22×C1312yes—
283#535—21no—
284#534C22×C1312yes—
285#532C22×C1311yescharacteristic
286C2×C4⋊Q8C22×C1311yescharacteristic, complemented
287#529C22×C1311yescharacteristic
288C2×#124C22×C1311yescharacteristic
289#501—21no—
290#500—21no—
291#489—21no—
292#486—21no—
293#483C22×C1312yescomplemented
294#480C22×C1312yes—
295#480C22×C1314yescomplemented
296#477—21no—
297#476—21no—
298#474—22no—
299#432C22×C1311yescharacteristic, complemented
300#431C22×C1311yescharacteristic, complemented
301#397C22×C1314yescomplemented
302#393—22no—
303#391—21no—
304#390—21no—
305#376C22×C1311yescharacteristic, complemented
306#328C22×C1312yescomplemented
307#327C22×C1312yes—
308#327C22×C1314yescomplemented
309#323C22×C1314yescomplemented
310C22×C13—21no—
311C22×C13—21no—
312C22×C13—42no—
313C22×C13—42no—
314C22×C13—41no—
315C22×C13—41no—
316C22×C13—42no—
317C22×C13—42no—
318C22×C13—42no—
319C22×C13—41no—
320C22×C13—42no—
321C22×C13—84no—
322C22×C13—164no—
323C22×C13C2×#12011yescharacteristic
324C22×C13#57612yes—
325C4×C13—21no—
326C4×C13—21no—
327C4×C13—21no—
328C4×C13—21no—
329C4×C13—21no—
330C4×C13—41no—
331C4×C13—42no—
332C4×C13—41no—
333C4×C13—42no—
334C4×C13—41no—
335C4×C13—82no—
336C4×C13—82no—
337C4×C13#45512yes—
338C2×#41—21no—
339C2×#41—21no—
340C22×Q8—21no—
341C22×Q8D4×C1311yescharacteristic
342C22×D4—21no—
343C22×D4—22no—
344C22×D4D4×C1311yescharacteristic
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8D4×C1311yescharacteristic
350#127—21no—
351#127D4×C1311yescharacteristic
352#126—22no—
353#126—21no—
354#125D4×C1311yescharacteristic
355#124—21no—
356#124—22no—
357#124—22no—
358#124—22no—
359#124—21no—
360#124—21no—
361#124—21no—
362#124—21no—
363#124—21no—
364#124D4×C1311yescharacteristic
365#123—22no—
366#123—21no—
367#123—22no—
368#123—22no—
369#123—22no—
370C22⋊Q8—22no—
371C22⋊Q8—21no—
372C22⋊Q8—22no—
373C22⋊Q8C23×C1311yescharacteristic
374#121—22no—
375#121—22no—
376#121—22no—
377#121—21no—
378#121—22no—
379#121—21no—
380#121—22no—
381#121C23×C1311yescharacteristic
382#121C23×C1312yes—
383#120—22no—
384#120—22no—
385#120—22no—
386#120—22no—
387#120—22no—
388C4×Q8—21no—
389C4×Q8D4×C1311yescharacteristic
390C4×D4—22no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4—22no—
394C4×D4—21no—
395C4×D4D4×C1311yescharacteristic
396C4×D4D4×C1312yes—
397#117—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4C23×C1312yes—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—24no—
402C2×C22⋊C4D4×C1312yes—
403C2×C22⋊C4C23×C1312yes—
404C2×C42—21no—
405C2×C42C23×C1311yescharacteristic
406#107—24no—
407#107—22no—
408#106—22no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411#103—22no—
412#102—24no—
413#102—22no—
414C22⋊C8C23×C1312yes—
415C22⋊C8C23×C1312yes—
416#97—21no—
417C4×C8—21no—
418#95—21no—
419#95—24no—
420#95C23×C1312yes—
421C2×C13—22no—
422C2×C13—82no—
423C2×C13—82no—
424C2×C13—81no—
425C2×C13#300811yescharacteristic
426C2×C13C2×#45511yescharacteristic
427C2×C13#302811yescharacteristic
428C24—22no—
429C24C2×D4×C1312yes—
430#41—82no—
431#41—82no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8—41no—
437C2×Q8—41no—
438C2×Q8—82no—
439C2×Q8C2×D4×C1311yescharacteristic
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—22no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—82no—
453C2×D4—84no—
454C2×D4C2×D4×C1311yescharacteristic
455C2×D4C2×D4×C1312yes—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4C2×D4×C1311yescharacteristic
463C22×C4C2×D4×C1311yescharacteristic
464C22×C4C2×D4×C1312yes—
465C22×C4C24×C1311yescharacteristic
466C2×C8—22no—
467C2×C8—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4C2×D4×C1311yescharacteristic
480C4⋊C4C2×D4×C1312yes—
481C4⋊C4C2×D4×C1311yescharacteristic
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—22no—
494C22⋊C4—22no—
495C22⋊C4—22no—
496C22⋊C4—21no—
497C22⋊C4—22no—
498C22⋊C4—84no—
499C42—22no—
500C42—21no—
501C42—42no—
502C42C2×D4×C1311yescharacteristic
503C42C2×D4×C1311yescharacteristic
504C42C2×D4×C1311yescharacteristic
505C42C2×D4×C1311yescharacteristic
506C13#1843611yescharacteristic, direct product factor, Sylow
507C23—22no—
508C23—21no—
509C23—22no—
510C23—24no—
511C23—42no—
512C23—42no—
513C23—82no—
514C23—82no—
515C23—82no—
516C23C22×D4×C1311yescharacteristic
517Q8—41no—
518Q8—42no—
519Q8—81no—
520Q8—81no—
521Q8—82no—
522Q8—82no—
523D4—42no—
524D4—41no—
525D4—42no—
526D4—44no—
527D4—42no—
528D4—42no—
529D4—81no—
530D4—81no—
531D4—82no—
532D4—82no—
533D4—82no—
534D4—82no—
535D4—82no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—21no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—42no—
550C2×C4—44no—
551C2×C4—82no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4C13×#12011yescharacteristic
555C2×C4C13×#12011yescharacteristic
556C2×C4C13×#12011yescharacteristic
557C2×C4C13×#12011yescharacteristic
558C2×C4C22×D4×C1311yescharacteristic
559C2×C4C22×D4×C1311yescharacteristic
560C8—42no—
561C8—42no—
562C22—21no—
563C22—21no—
564C22—42no—
565C22—42no—
566C22—41no—
567C22—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—41no—
572C22—42no—
573C22—84no—
574C22—164no—
575C22C2×C13×#12011yescharacteristic
576C22C13×#57612yes—
577C4—21no—
578C4—21no—
579C4—21no—
580C4—21no—
581C4—21no—
582C4—41no—
583C4—42no—
584C4—41no—
585C4—42no—
586C4—41no—
587C4—82no—
588C4—82no—
589C4C13×#45512yes—
590C2—22no—
591C2—82no—
592C2—81no—
593C2—82no—
594C2C13×#300811yescharacteristic
595C2C2×C13×#45511yescharacteristic
596C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3558C2
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×#3238C2semidirect
3. C13×#3226C2semidirect
4. C13×#2640C2semidirect
5. C13×#1612C2semidirect
6. C13×#1607C2semidirect
7. C13×#1505C2semidirect
8. C13×#1500C2semidirect
9. C13×#1469C2semidirect
23. C2×C13×C4⋊Q8C22semidirect
30. C13×#483C22semidirect
32. C13×#480C22semidirect
36. C13×#432C22semidirect
37. C13×#431C22semidirect
38. C13×#397C22semidirect
42. C13×#376C22semidirect
43. C13×#328C22semidirect
45. C13×#327C22semidirect
46. C13×#323C22semidirect
130. #18436C13direct (N × H)
210. #3238C2×C13semidirect
211. #3226C2×C13semidirect
212. #2640C2×C13semidirect
213. #1612C2×C13semidirect
214. #1607C2×C13semidirect
215. #1505C2×C13semidirect
216. #1500C2×C13semidirect
217. #1469C2×C13semidirect
286. C2×C4⋊Q8C22×C13semidirect
293. #483C22×C13semidirect
295. #480C22×C13semidirect
299. #432C22×C13semidirect
300. #431C22×C13semidirect
301. #397C22×C13semidirect
305. #376C22×C13semidirect
306. #328C22×C13semidirect
308. #327C22×C13semidirect
309. #323C22×C13semidirect
506. C13#18436direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35582
C13×#32382
C13×#32262
C13×#26402
C13×#16122
C13×#16072
C13×#15052
C13×#15002
C13×#14692
#1843613