Finite Group Databasebeta

← C13×#13083 #15699422

Subgroups — C13×#13083 #15699422

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#413C211yesmaximal, characteristic, complemented
2C13×#2404C211yesmaximal, characteristic
3C2×C13×AΣL(1,𝔽16)C212yesmaximal, complemented
4C13×#1782C211yesmaximal, characteristic, complemented
5C13×#1390C212yesmaximal, complemented
6C22×C13×#41C2211yescharacteristic
7C22×C13×M16—21no—
8C2×C13×#120C411yescharacteristic, complemented
9C2×C13×#120C2211yescharacteristic
10C22×C13×C22⋊C4C411yescharacteristic, complemented
11C13×#413—24no—
12C2×C13×#101—21no—
13C2×C13×#100C2212yes—
14C2×C13×#99—21no—
15C2×C13×#99C2212yes—
16C13×#393—21no—
17C13×#392—21no—
18C13×#386—21no—
19C13×#386—21no—
20C13×#386C411yescharacteristic, complemented
21C13×#386C2211yescharacteristic
22C13×#381—21no—
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—24no—
42C2×C13×M16—22no—
43C2×C13×M16—42no—
44C2×C13×M16—41no—
45C22×C8×C13—41no—
46C13×#120—22no—
47C13×#120—22no—
48C13×#120—42no—
49C2×C13×C22⋊C4—21no—
50C2×C13×C22⋊C4—21no—
51C2×C13×C22⋊C4—21no—
52C2×C13×C22⋊C4—21no—
53C2×C13×C22⋊C4—22no—
54C2×C13×C22⋊C4—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—41no—
57C2×C13×C22⋊C4—41no—
58C2×C13×C22⋊C4C2×C411yescharacteristic
59C2×C13×C22⋊C4C2×C411yescharacteristic
60C13×#101—24no—
61C13×#100—22no—
62C13×#100D414yescomplemented
63C13×#99—22no—
64C13×#99—22no—
65C13×#99—42no—
66C13×#95—21no—
67C13×#95—21no—
68C13×#95—21no—
69C13×#95—21no—
70C13×#95—41no—
71C13×#95—41no—
72#13083C1311yesmaximal, 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—21no—
87C2×Q8×C13—21no—
88C2×Q8×C13—41no—
89C2×Q8×C13—41no—
90C2×D4×C13—22no—
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
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—42no—
102C2×D4×C13—81no—
103C2×D4×C13—81no—
104C2×D4×C13C2×D412yes—
105C2×D4×C13#4112yes—
106C22×C4×C13—22no—
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—21no—
118C22×C4×C13—21no—
119C22×C4×C13—21no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—42no—
124C22×C4×C13—81no—
125C22×C4×C13C22⋊C411yescharacteristic
126C22×C4×C13C22⋊C411yescharacteristic
127C22×C4×C13C22⋊C411yescharacteristic
128C22×C4×C13C2×D411yescharacteristic
129C13×M16—24no—
130C13×M16—44no—
131C13×M16—42no—
132C2×C8×C13—44no—
133C2×C8×C13—42no—
134C13×C22⋊C4—22no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—42no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—41no—
142C13×C22⋊C4—42no—
143C13×C22⋊C4—42no—
144C13×C22⋊C4—81no—
145C13×C22⋊C4—81no—
146C2×#413C2×C1311yescharacteristic, complemented
147#2404C2×C1311yescharacteristic
148C2×AΣL(1,𝔽16)C2×C1312yescomplemented
149#1782C2×C1311yescharacteristic, complemented
150#1390C2×C1312yescomplemented
151C23×C13—21no—
152C23×C13—21no—
153C23×C13—21no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—22no—
158C23×C13—41no—
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—42no—
168C23×C13—41no—
169C23×C13—41no—
170C23×C13—41no—
171C23×C13—42no—
172C23×C13—82no—
173C23×C13—84no—
174C23×C13—84no—
175C23×C13—82no—
176C23×C13#9912yes—
177C23×C13C2×C22⋊C411yescharacteristic
178C23×C13C4×D412yes—
179C23×C13#12112yes—
180Q8×C13—42no—
181Q8×C13—42no—
182D4×C13—42no—
183D4×C13—42no—
184D4×C13—44no—
185D4×C13—44no—
186D4×C13—84no—
187D4×C13—84no—
188C2×C4×C13—22no—
189C2×C4×C13—22no—
190C2×C4×C13—22no—
191C2×C4×C13—22no—
192C2×C4×C13—21no—
193C2×C4×C13—21no—
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—42no—
203C2×C4×C13—42no—
204C2×C4×C13—42no—
205C2×C4×C13—42no—
206C2×C4×C13—41no—
207C2×C4×C13—41no—
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—82no—
216C2×C4×C13—82no—
217C2×C4×C13—82no—
218C2×C4×C13—82no—
219C2×C4×C13#9911yescharacteristic
220C2×C4×C13#9911yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12311yescharacteristic
223C8×C13—44no—
224C22×#41C22×C1311yescharacteristic
225C22×M16—21no—
226C2×#120C4×C1311yescharacteristic, complemented
227C2×#120C22×C1311yescharacteristic
228C22×C22⋊C4C4×C1311yescharacteristic, complemented
229#413—24no—
230C2×#101—21no—
231C2×#100C22×C1312yes—
232C2×#99—21no—
233C2×#99C22×C1312yes—
234#393—21no—
235#392—21no—
236#386—21no—
237#386—21no—
238#386C4×C1311yescharacteristic, complemented
239#386C22×C1311yescharacteristic
240#381—21no—
241#381C4×C1311yescharacteristic, complemented
242AΣL(1,𝔽16)—24no—
243C22×C13—21no—
244C22×C13—21no—
245C22×C13—22no—
246C22×C13—22no—
247C22×C13—22no—
248C22×C13—42no—
249C22×C13—42no—
250C22×C13—42no—
251C22×C13—42no—
252C22×C13—42no—
253C22×C13—42no—
254C22×C13—41no—
255C22×C13—41no—
256C22×C13—41no—
257C22×C13—41no—
258C22×C13—41no—
259C22×C13—41no—
260C22×C13—42no—
261C22×C13—81no—
262C22×C13—81no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—84no—
266C22×C13—84no—
267C22×C13—81no—
268C22×C13—81no—
269C22×C13#38611yescharacteristic
270C22×C13C2×#9911yescharacteristic
271C22×C13C2×#9911yescharacteristic
272C4×C13—21no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—21no—
276C4×C13—41no—
277C4×C13—41no—
278C4×C13—81no—
279C4×C13—81no—
280C4×C13—81no—
281C4×C13—162no—
282C25C2×C4×C1311yescharacteristic
283C2×#41—22no—
284C2×#41—22no—
285C2×#41—41no—
286C2×#41—41no—
287C2×#41—42no—
288C22×Q8D4×C1311yescharacteristic
289C22×D4—21no—
290C22×D4—21no—
291C22×D4C2×C4×C1311yescharacteristic
292C22×D4D4×C1311yescharacteristic
293C22×D4C23×C1311yescharacteristic
294C23×C4C2×C4×C1311yescharacteristic
295C23×C4C2×C4×C1311yescharacteristic
296C23×C4D4×C1311yescharacteristic
297C23×C4D4×C1311yescharacteristic
298C2×M16—24no—
299C2×M16—22no—
300C2×M16—42no—
301C2×M16—41no—
302C22×C8—41no—
303#120—22no—
304#120—22no—
305#120—42no—
306C2×C22⋊C4—21no—
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—41no—
314C2×C22⋊C4—41no—
315C2×C22⋊C4C2×C4×C1311yescharacteristic
316C2×C22⋊C4C2×C4×C1311yescharacteristic
317#101—24no—
318#100—22no—
319#100D4×C1314yescomplemented
320#99—22no—
321#99—22no—
322#99—42no—
323#95—21no—
324#95—21no—
325#95—21no—
326#95—21no—
327#95—41no—
328#95—41no—
329C2×C13—21no—
330C2×C13—21no—
331C2×C13—42no—
332C2×C13—42no—
333C2×C13—42no—
334C2×C13—82no—
335C2×C13#189811yescharacteristic
336C2×C13#212011yescharacteristic
337C2×C13#212211yescharacteristic
338C24—21no—
339C24—22no—
340C24—41no—
341C24—42no—
342C24—41no—
343C24—81no—
344C24C13×C22⋊C411yescharacteristic
345C24C22×C4×C1311yescharacteristic
346C24C2×D4×C1311yescharacteristic
347#41—44no—
348#41—44no—
349#41—44no—
350#41—44no—
351C2×Q8—21no—
352C2×Q8—21no—
353C2×Q8—41no—
354C2×Q8—41no—
355C2×D4—22no—
356C2×D4—22no—
357C2×D4—22no—
358C2×D4—22no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—41no—
363C2×D4—42no—
364C2×D4—42no—
365C2×D4—42no—
366C2×D4—42no—
367C2×D4—81no—
368C2×D4—81no—
369C2×D4C2×D4×C1312yes—
370C2×D4C13×#4112yes—
371C22×C4—22no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—22no—
378C22×C4—21no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—21no—
382C22×C4—21no—
383C22×C4—21no—
384C22×C4—21no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—42no—
389C22×C4—81no—
390C22×C4C13×C22⋊C411yescharacteristic
391C22×C4C13×C22⋊C411yescharacteristic
392C22×C4C13×C22⋊C411yescharacteristic
393C22×C4C2×D4×C1311yescharacteristic
394M16—24no—
395M16—44no—
396M16—42no—
397C2×C8—44no—
398C2×C8—42no—
399C22⋊C4—22no—
400C22⋊C4—42no—
401C22⋊C4—42no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—41no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—81no—
410C22⋊C4—81no—
411C13#1308311yescharacteristic, direct product factor, Sylow
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—22no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—41no—
425C23—41no—
426C23—41no—
427C23—41no—
428C23—42no—
429C23—42no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—82no—
434C23—84no—
435C23—84no—
436C23—82no—
437C23C13×#9912yes—
438C23C2×C13×C22⋊C411yescharacteristic
439C23C4×D4×C1312yes—
440C23C13×#12112yes—
441Q8—42no—
442Q8—42no—
443D4—42no—
444D4—42no—
445D4—44no—
446D4—44no—
447D4—84no—
448D4—84no—
449C2×C4—22no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—22no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—82no—
477C2×C4—82no—
478C2×C4—82no—
479C2×C4—82no—
480C2×C4C13×#9911yescharacteristic
481C2×C4C13×#9911yescharacteristic
482C2×C4C13×#12011yescharacteristic
483C2×C4C13×#12311yescharacteristic
484C8—44no—
485C22—21no—
486C22—21no—
487C22—22no—
488C22—22no—
489C22—22no—
490C22—42no—
491C22—42no—
492C22—42no—
493C22—42no—
494C22—42no—
495C22—42no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—42no—
503C22—81no—
504C22—81no—
505C22—81no—
506C22—81no—
507C22—84no—
508C22—84no—
509C22—81no—
510C22—81no—
511C22C13×#38611yescharacteristic
512C22C2×C13×#9911yescharacteristic
513C22C2×C13×#9911yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—41no—
519C4—41no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—162no—
524C2—21no—
525C2—21no—
526C2—42no—
527C2—42no—
528C2—42no—
529C2—82no—
530C2C13×#189811yescharacteristic
531C2C13×#212011yescharacteristic
532C2C13×#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×#413C2semidirect
3. C2×C13×AΣL(1,𝔽16)C2semidirect
4. C13×#1782C2semidirect
5. C13×#1390C2semidirect
8. C2×C13×#120C4semidirect
10. C22×C13×C22⋊C4C4semidirect
20. C13×#386C4semidirect
23. C13×#381C4semidirect
62. C13×#100D4semidirect
72. #13083C13direct (N × H)
146. C2×#413C2×C13semidirect
148. C2×AΣL(1,𝔽16)C2×C13semidirect
149. #1782C2×C13semidirect
150. #1390C2×C13semidirect
226. C2×#120C4×C13semidirect
228. C22×C22⋊C4C4×C13semidirect
238. #386C4×C13semidirect
241. #381C4×C13semidirect
319. #100D4×C13semidirect
411. C13#13083direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4132
C13×#24042
C2×C13×AΣL(1,𝔽16)2
C13×#17822
C13×#13902
#1308313