Finite Group Databasebeta

← C13×#13087 #15699426

Subgroups — C13×#13087 #15699426

Order 3328.

820 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#410C211yesmaximal, characteristic, complemented
2C13×#2404C211yesmaximal, characteristic
3C2×C13×AΣL(1,𝔽16)C212yesmaximal, complemented
4C13×#1785C211yesmaximal, characteristic, complemented
5C13×#1390C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C2×C13×#120C411yescharacteristic, complemented
8C2×C13×#120C2211yescharacteristic
9C2×C13×#117—21no—
10C22×C13×C22⋊C4C411yescharacteristic, complemented
11C2×C13×#101—21no—
12C2×C13×#100C2212yes—
13C13×#410—24no—
14C2×C13×#99—21no—
15C2×C13×#99C2212yes—
16C13×#407—21no—
17C13×#393—21no—
18C13×#392—21no—
19C13×#386—21no—
20C13×#386—21no—
21C13×#386C411yescharacteristic, complemented
22C13×#386C2211yescharacteristic
23C13×#381C411yescharacteristic, complemented
24C13×AΣL(1,𝔽16)—24no—
25C25×C13C2×C411yescharacteristic
26C2×C13×#41—22no—
27C2×C13×#41—22no—
28C2×C13×#41—41no—
29C2×C13×#41—41no—
30C2×C13×#41—42no—
31C22×Q8×C13D411yescharacteristic
32C22×D4×C13—21no—
33C22×D4×C13—21no—
34C22×D4×C13C2×C411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C22×D4×C13C2311yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13C2×C411yescharacteristic
39C23×C4×C13D411yescharacteristic
40C23×C4×C13D411yescharacteristic
41C2×C13×M16—22no—
42C13×#120—22no—
43C13×#120—22no—
44C13×#120—42no—
45C13×#117—24no—
46C13×#117—42no—
47C2×C13×C4⋊C4—41no—
48C2×C13×C22⋊C4—22no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—21no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—41no—
56C2×C13×C22⋊C4—41no—
57C2×C13×C22⋊C4C2×C411yescharacteristic
58C2×C13×C22⋊C4C2×C411yescharacteristic
59C2×C42×C13—41no—
60C13×#101—42no—
61C13×#100—22no—
62C13×#100—22no—
63C13×#99—24no—
64C13×#99—22no—
65C13×#99D414yescomplemented
66C13×C22⋊C8—41no—
67C13×C22⋊C8—41no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—21no—
71C13×#95—21no—
72#13087C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13—21no—
74C24×C13—22no—
75C24×C13—41no—
76C24×C13—42no—
77C24×C13—41no—
78C24×C13—81no—
79C24×C13C22⋊C411yescharacteristic
80C24×C13C22×C411yescharacteristic
81C24×C13C2×D411yescharacteristic
82C13×#41—44no—
83C13×#41—44no—
84C13×#41—44no—
85C13×#41—44no—
86C2×Q8×C13—22no—
87C2×Q8×C13—22no—
88C2×Q8×C13—41no—
89C2×D4×C13—22no—
90C2×D4×C13—21no—
91C2×D4×C13—21no—
92C2×D4×C13—22no—
93C2×D4×C13—41no—
94C2×D4×C13—41no—
95C2×D4×C13—41no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—42no—
99C2×D4×C13—42no—
100C2×D4×C13—42no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—81no—
104C2×D4×C13—81no—
105C2×D4×C13C2×D412yes—
106C2×D4×C13#4112yes—
107C22×C4×C13—21no—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—22no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—42no—
124C22×C4×C13—41no—
125C22×C4×C13—81no—
126C22×C4×C13C22⋊C411yescharacteristic
127C22×C4×C13C22⋊C411yescharacteristic
128C22×C4×C13C22⋊C411yescharacteristic
129C22×C4×C13C2×D411yescharacteristic
130C13×M16—42no—
131C13×M16—42no—
132C2×C8×C13—42no—
133C13×C4⋊C4—44no—
134C13×C22⋊C4—22no—
135C13×C22⋊C4—24no—
136C13×C22⋊C4—42no—
137C13×C22⋊C4—42no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—42no—
141C13×C22⋊C4—42no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—81no—
144C13×C22⋊C4—81no—
145C42×C13—44no—
146C2×#410C2×C1311yescharacteristic, complemented
147#2404C2×C1311yescharacteristic
148C2×AΣL(1,𝔽16)C2×C1312yescomplemented
149#1785C2×C1311yescharacteristic, complemented
150#1390C2×C1312yescomplemented
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—21no—
155C23×C13—22no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—41no—
160C23×C13—41no—
161C23×C13—41no—
162C23×C13—41no—
163C23×C13—41no—
164C23×C13—41no—
165C23×C13—41no—
166C23×C13—41no—
167C23×C13—41no—
168C23×C13—42no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—41no—
172C23×C13—42no—
173C23×C13—82no—
174C23×C13—84no—
175C23×C13—84no—
176C23×C13—82no—
177C23×C13C2×C22⋊C411yescharacteristic
178C23×C13C4×D412yes—
179C23×C13#12011yescharacteristic
180C23×C13#12311yescharacteristic
181Q8×C13—44no—
182D4×C13—42no—
183D4×C13—42no—
184D4×C13—44no—
185D4×C13—42no—
186D4×C13—42no—
187D4×C13—82no—
188D4×C13—82no—
189D4×C13—84no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—22no—
193C2×C4×C13—22no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—21no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—44no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13—41no—
212C2×C4×C13—41no—
213C2×C4×C13—41no—
214C2×C4×C13—41no—
215C2×C4×C13—41no—
216C2×C4×C13—41no—
217C2×C4×C13—82no—
218C2×C4×C13—82no—
219C2×C4×C13—82no—
220C2×C4×C13#9912yes—
221C2×C4×C13#9911yescharacteristic
222C2×C4×C13#9911yescharacteristic
223C2×C4×C13#12112yes—
224C8×C13—82no—
225C22×#41C22×C1311yescharacteristic
226C2×#120C4×C1311yescharacteristic, complemented
227C2×#120C22×C1311yescharacteristic
228C2×#117—21no—
229C22×C22⋊C4C4×C1311yescharacteristic, complemented
230C2×#101—21no—
231C2×#100C22×C1312yes—
232#410—24no—
233C2×#99—21no—
234C2×#99C22×C1312yes—
235#407—21no—
236#393—21no—
237#392—21no—
238#386—21no—
239#386—21no—
240#386C4×C1311yescharacteristic, complemented
241#386C22×C1311yescharacteristic
242#381C4×C1311yescharacteristic, complemented
243AΣL(1,𝔽16)—24no—
244C22×C13—21no—
245C22×C13—21no—
246C22×C13—21no—
247C22×C13—21no—
248C22×C13—22no—
249C22×C13—41no—
250C22×C13—41no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13—42no—
255C22×C13—42no—
256C22×C13—41no—
257C22×C13—41no—
258C22×C13—41no—
259C22×C13—41no—
260C22×C13—41no—
261C22×C13—42no—
262C22×C13—41no—
263C22×C13—41no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13—81no—
267C22×C13—81no—
268C22×C13—84no—
269C22×C13—84no—
270C22×C13—81no—
271C22×C13—81no—
272C22×C13#38611yescharacteristic
273C22×C13C2×#9911yescharacteristic
274C22×C13C2×#9911yescharacteristic
275C4×C13—22no—
276C4×C13—21no—
277C4×C13—21no—
278C4×C13—22no—
279C4×C13—41no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13—84no—
283C4×C13—81no—
284C25C2×C4×C1311yescharacteristic
285C2×#41—22no—
286C2×#41—22no—
287C2×#41—41no—
288C2×#41—41no—
289C2×#41—42no—
290C22×Q8D4×C1311yescharacteristic
291C22×D4—21no—
292C22×D4—21no—
293C22×D4C2×C4×C1311yescharacteristic
294C22×D4D4×C1311yescharacteristic
295C22×D4C23×C1311yescharacteristic
296C23×C4C2×C4×C1311yescharacteristic
297C23×C4C2×C4×C1311yescharacteristic
298C23×C4D4×C1311yescharacteristic
299C23×C4D4×C1311yescharacteristic
300C2×M16—22no—
301#120—22no—
302#120—22no—
303#120—42no—
304#117—24no—
305#117—42no—
306C2×C4⋊C4—41no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4—41no—
316C2×C22⋊C4C2×C4×C1311yescharacteristic
317C2×C22⋊C4C2×C4×C1311yescharacteristic
318C2×C42—41no—
319#101—42no—
320#100—22no—
321#100—22no—
322#99—24no—
323#99—22no—
324#99D4×C1314yescomplemented
325C22⋊C8—41no—
326C22⋊C8—41no—
327#95—21no—
328#95—21no—
329#95—21no—
330#95—21no—
331C2×C13—21no—
332C2×C13—21no—
333C2×C13—41no—
334C2×C13—42no—
335C2×C13—41no—
336C2×C13—81no—
337C2×C13—82no—
338C2×C13#189811yescharacteristic
339C2×C13#212011yescharacteristic
340C2×C13#212211yescharacteristic
341C24—21no—
342C24—22no—
343C24—41no—
344C24—42no—
345C24—41no—
346C24—81no—
347C24C13×C22⋊C411yescharacteristic
348C24C22×C4×C1311yescharacteristic
349C24C2×D4×C1311yescharacteristic
350#41—44no—
351#41—44no—
352#41—44no—
353#41—44no—
354C2×Q8—22no—
355C2×Q8—22no—
356C2×Q8—41no—
357C2×D4—22no—
358C2×D4—21no—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—41no—
364C2×D4—41no—
365C2×D4—41no—
366C2×D4—42no—
367C2×D4—42no—
368C2×D4—42no—
369C2×D4—41no—
370C2×D4—41no—
371C2×D4—81no—
372C2×D4—81no—
373C2×D4C2×D4×C1312yes—
374C2×D4C13×#4112yes—
375C22×C4—21no—
376C22×C4—21no—
377C22×C4—21no—
378C22×C4—21no—
379C22×C4—22no—
380C22×C4—22no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—21no—
388C22×C4—21no—
389C22×C4—41no—
390C22×C4—41no—
391C22×C4—42no—
392C22×C4—41no—
393C22×C4—81no—
394C22×C4C13×C22⋊C411yescharacteristic
395C22×C4C13×C22⋊C411yescharacteristic
396C22×C4C13×C22⋊C411yescharacteristic
397C22×C4C2×D4×C1311yescharacteristic
398M16—42no—
399M16—42no—
400C2×C8—42no—
401C4⋊C4—44no—
402C22⋊C4—22no—
403C22⋊C4—24no—
404C22⋊C4—42no—
405C22⋊C4—42no—
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—41no—
411C22⋊C4—81no—
412C22⋊C4—81no—
413C42—44no—
414C13#1308711yescharacteristic, direct product factor, Sylow
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—22no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—41no—
429C23—41no—
430C23—41no—
431C23—41no—
432C23—42no—
433C23—42no—
434C23—41no—
435C23—41no—
436C23—41no—
437C23—82no—
438C23—84no—
439C23—84no—
440C23—82no—
441C23C2×C13×C22⋊C411yescharacteristic
442C23C4×D4×C1312yes—
443C23C13×#12011yescharacteristic
444C23C13×#12311yescharacteristic
445Q8—44no—
446D4—42no—
447D4—42no—
448D4—44no—
449D4—42no—
450D4—42no—
451D4—82no—
452D4—82no—
453D4—84no—
454C2×C4—22no—
455C2×C4—22no—
456C2×C4—22no—
457C2×C4—22no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—42no—
471C2×C4—44no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—41no—
478C2×C4—41no—
479C2×C4—41no—
480C2×C4—41no—
481C2×C4—82no—
482C2×C4—82no—
483C2×C4—82no—
484C2×C4C13×#9911yescharacteristic
485C2×C4C13×#9911yescharacteristic
486C2×C4C13×#9912yes—
487C2×C4C13×#12112yes—
488C8—82no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—22no—
494C22—41no—
495C22—41no—
496C22—42no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—42no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—42no—
507C22—41no—
508C22—41no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—84no—
514C22—84no—
515C22—81no—
516C22—81no—
517C22C13×#38611yescharacteristic
518C22C2×C13×#9911yescharacteristic
519C22C2×C13×#9911yescharacteristic
520C4—22no—
521C4—21no—
522C4—21no—
523C4—22no—
524C4—41no—
525C4—81no—
526C4—81no—
527C4—84no—
528C4—81no—
529C2—21no—
530C2—21no—
531C2—41no—
532C2—42no—
533C2—41no—
534C2—81no—
535C2—82no—
536C2C13×#189811yescharacteristic
537C2C13×#212011yescharacteristic
538C2C13×#212211yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC13×#2404C2
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×#41 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C13×#410C2semidirect
3. C2×C13×AΣL(1,𝔽16)C2semidirect
4. C13×#1785C2semidirect
5. C13×#1390C2semidirect
7. C2×C13×#120C4semidirect
10. C22×C13×C22⋊C4C4semidirect
21. C13×#386C4semidirect
23. C13×#381C4semidirect
65. C13×#99D4semidirect
72. #13087C13direct (N × H)
146. C2×#410C2×C13semidirect
148. C2×AΣL(1,𝔽16)C2×C13semidirect
149. #1785C2×C13semidirect
150. #1390C2×C13semidirect
226. C2×#120C4×C13semidirect
229. C22×C22⋊C4C4×C13semidirect
240. #386C4×C13semidirect
242. #381C4×C13semidirect
324. #99D4×C13semidirect
414. C13#13087direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4102
C13×#24042
C2×C13×AΣL(1,𝔽16)2
C13×#17852
C13×#13902
#1308713