Finite Group Databasebeta

← C13×#13080 #15699419

Subgroups — C13×#13080 #15699419

Order 3328.

864 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#100C211yesmaximal, characteristic
2C13×#2405C211yesmaximal, characteristic
3C2×C13×#352C212yesmaximal, complemented
4C13×#1781C211yesmaximal, characteristic
5C13×#1390C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C22×C13×M16—21no—
8C2×C13×#123C411yescharacteristic, complemented
9C2×C13×#123C2211yescharacteristic
10C22×C13×C22⋊C4C411yescharacteristic, complemented
11C2×C13×#100—21no—
12C2×C13×#100—24no—
13C2×C13×#100C2212yes—
14C2×C13×#99—21no—
15C2×C13×#99C2212yes—
16C13×#394—21no—
17C13×#394—21no—
18C13×#386C411yescharacteristic, complemented
19C13×#386C2211yescharacteristic
20C13×#385—21no—
21C13×#379—21no—
22C13×#379—21no—
23C13×#379C411yescharacteristic, complemented
24C13×#352—24no—
25C25×C13C2×C411yescharacteristic
26C25×C13D411yescharacteristic
27C22×D4×C13—22no—
28C22×D4×C13—22no—
29C22×D4×C13—42no—
30C22×D4×C13—41no—
31C22×D4×C13—41no—
32C22×D4×C13C2×C411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C22×D4×C13C2311yescharacteristic
36C23×C4×C13C2×C411yescharacteristic
37C23×C4×C13C2×C411yescharacteristic
38C23×C4×C13D411yescharacteristic
39C2×C13×M16—24no—
40C2×C13×M16—22no—
41C2×C13×M16—41no—
42C2×C13×M16—42no—
43C22×C8×C13—41no—
44C13×#123—22no—
45C13×#123—22no—
46C13×#123—42no—
47C2×C13×C4⋊C4—21no—
48C2×C13×C4⋊C4—21no—
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—22no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—41no—
59C2×C13×C22⋊C4—41no—
60C2×C13×C22⋊C4—41no—
61C2×C13×C22⋊C4—41no—
62C2×C13×C22⋊C4C2×C411yescharacteristic
63C2×C13×C22⋊C4C2×C411yescharacteristic
64C13×#100—24no—
65C13×#100—22no—
66C13×#100D414yes—
67C13×#99—22no—
68C13×#99—22no—
69C13×#99—42no—
70C13×#95—21no—
71C13×#95—21no—
72#13080C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13—21no—
74C24×C13—21no—
75C24×C13—21no—
76C24×C13—21no—
77C24×C13—22no—
78C24×C13—22no—
79C24×C13—41no—
80C24×C13—41no—
81C24×C13—42no—
82C24×C13—42no—
83C24×C13—81no—
84C24×C13—81no—
85C24×C13C22⋊C411yescharacteristic
86C24×C13C22⋊C411yescharacteristic
87C24×C13C22⋊C411yescharacteristic
88C24×C13C22×C411yescharacteristic
89C24×C13C2×D411yescharacteristic
90C2×D4×C13—22no—
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—41no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—44no—
103C2×D4×C13—44no—
104C2×D4×C13—44no—
105C2×D4×C13—44no—
106C2×D4×C13C2×D412yes—
107C2×D4×C13#4112yes—
108C22×C4×C13—21no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—22no—
118C22×C4×C13—41no—
119C22×C4×C13—41no—
120C22×C4×C13—41no—
121C22×C4×C13—42no—
122C22×C4×C13—81no—
123C22×C4×C13C22⋊C411yescharacteristic
124C22×C4×C13C2×D411yescharacteristic
125C13×M16—24no—
126C13×M16—44no—
127C13×M16—42no—
128C2×C8×C13—44no—
129C2×C8×C13—42no—
130C13×C4⋊C4—42no—
131C13×C4⋊C4—41no—
132C13×C4⋊C4—41no—
133C13×C22⋊C4—22no—
134C13×C22⋊C4—42no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—42no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—41no—
139C13×C22⋊C4—42no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—42no—
142C13×C22⋊C4—42no—
143C13×C22⋊C4—81no—
144C13×C22⋊C4—81no—
145C13×C22⋊C4—81no—
146C13×C22⋊C4—82no—
147C13×C22⋊C4—82no—
148C22×#100C2×C1311yescharacteristic
149#2405C2×C1311yescharacteristic
150C2×#352C2×C1312yescomplemented
151#1781C2×C1311yescharacteristic
152#1390C2×C1312yescomplemented
153C23×C13—22no—
154C23×C13—21no—
155C23×C13—21no—
156C23×C13—21no—
157C23×C13—21no—
158C23×C13—21no—
159C23×C13—21no—
160C23×C13—21no—
161C23×C13—21no—
162C23×C13—21no—
163C23×C13—21no—
164C23×C13—21no—
165C23×C13—21no—
166C23×C13—41no—
167C23×C13—42no—
168C23×C13—42no—
169C23×C13—42no—
170C23×C13—42no—
171C23×C13—41no—
172C23×C13—41no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—42no—
178C23×C13—42no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—42no—
182C23×C13—42no—
183C23×C13—81no—
184C23×C13—81no—
185C23×C13—81no—
186C23×C13—81no—
187C23×C13—84no—
188C23×C13—84no—
189C23×C13—84no—
190C23×C13—84no—
191C23×C13#9911yescharacteristic
192C23×C13#9911yescharacteristic
193C23×C13C2×C22⋊C411yescharacteristic
194C23×C13C4×D412yes—
195C23×C13#12112yes—
196D4×C13—42no—
197D4×C13—42no—
198D4×C13—44no—
199D4×C13—44no—
200D4×C13—42no—
201D4×C13—42no—
202C2×C4×C13—22no—
203C2×C4×C13—22no—
204C2×C4×C13—22no—
205C2×C4×C13—22no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
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—41no—
218C2×C4×C13—41no—
219C2×C4×C13—41no—
220C2×C4×C13—41no—
221C2×C4×C13—41no—
222C2×C4×C13—82no—
223C2×C4×C13—82no—
224C2×C4×C13—82no—
225C2×C4×C13—82no—
226C2×C4×C13—82no—
227C2×C4×C13#9912yes—
228C2×C4×C13#12011yescharacteristic
229C2×C4×C13#12311yescharacteristic
230C8×C13—44no—
231C23×D4C22×C1311yescharacteristic
232C22×M16—21no—
233C2×#123C4×C1311yescharacteristic, complemented
234C2×#123C22×C1311yescharacteristic
235C22×C22⋊C4C4×C1311yescharacteristic, complemented
236C2×#100—21no—
237C2×#100—24no—
238C2×#100C22×C1312yes—
239C2×#99—21no—
240C2×#99C22×C1312yes—
241#394—21no—
242#394—21no—
243#386C4×C1311yescharacteristic, complemented
244#386C22×C1311yescharacteristic
245#385—21no—
246#379—21no—
247#379—21no—
248#379C4×C1311yescharacteristic, complemented
249#352—24no—
250C22×C13—21no—
251C22×C13—21no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—22no—
258C22×C13—22no—
259C22×C13—42no—
260C22×C13—42no—
261C22×C13—42no—
262C22×C13—42no—
263C22×C13—42no—
264C22×C13—42no—
265C22×C13—41no—
266C22×C13—41no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13—41no—
270C22×C13—41no—
271C22×C13—41no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13—81no—
276C22×C13—84no—
277C22×C13—84no—
278C22×C13—81no—
279C22×C13—81no—
280C22×C13—81no—
281C22×C13—84no—
282C22×C13—84no—
283C22×C13#35212yescomplemented
284C22×C13#38611yescharacteristic
285C22×C13C2×#9911yescharacteristic
286C22×C13C2×#9911yescharacteristic
287C4×C13—21no—
288C4×C13—22no—
289C4×C13—21no—
290C4×C13—81no—
291C4×C13—81no—
292C4×C13—81no—
293C4×C13—81no—
294C4×C13—162no—
295C25C2×C4×C1311yescharacteristic
296C25D4×C1311yescharacteristic
297C22×D4—22no—
298C22×D4—22no—
299C22×D4—42no—
300C22×D4—41no—
301C22×D4—41no—
302C22×D4C2×C4×C1311yescharacteristic
303C22×D4D4×C1311yescharacteristic
304C22×D4D4×C1311yescharacteristic
305C22×D4C23×C1311yescharacteristic
306C23×C4C2×C4×C1311yescharacteristic
307C23×C4C2×C4×C1311yescharacteristic
308C23×C4D4×C1311yescharacteristic
309C2×M16—24no—
310C2×M16—22no—
311C2×M16—41no—
312C2×M16—42no—
313C22×C8—41no—
314#123—22no—
315#123—22no—
316#123—42no—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—22no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—41no—
329C2×C22⋊C4—41no—
330C2×C22⋊C4—41no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4C2×C4×C1311yescharacteristic
333C2×C22⋊C4C2×C4×C1311yescharacteristic
334#100—24no—
335#100—22no—
336#100D4×C1314yes—
337#99—22no—
338#99—22no—
339#99—42no—
340#95—21no—
341#95—21no—
342C2×C13—21no—
343C2×C13—21no—
344C2×C13—22no—
345C2×C13—42no—
346C2×C13—41no—
347C2×C13—42no—
348C2×C13—81no—
349C2×C13—81no—
350C2×C13#189811yescharacteristic
351C2×C13C2×#35211yescharacteristic
352C2×C13#212111yescharacteristic
353C24—21no—
354C24—21no—
355C24—21no—
356C24—21no—
357C24—22no—
358C24—22no—
359C24—41no—
360C24—41no—
361C24—42no—
362C24—42no—
363C24—81no—
364C24—81no—
365C24C13×C22⋊C411yescharacteristic
366C24C13×C22⋊C411yescharacteristic
367C24C13×C22⋊C411yescharacteristic
368C24C22×C4×C1311yescharacteristic
369C24C2×D4×C1311yescharacteristic
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—21no—
375C2×D4—21no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4—44no—
383C2×D4—44no—
384C2×D4—44no—
385C2×D4—44no—
386C2×D4C2×D4×C1312yes—
387C2×D4C13×#4112yes—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—22no—
391C22×C4—21no—
392C22×C4—21no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—41no—
399C22×C4—41no—
400C22×C4—41no—
401C22×C4—42no—
402C22×C4—81no—
403C22×C4C13×C22⋊C411yescharacteristic
404C22×C4C2×D4×C1311yescharacteristic
405M16—24no—
406M16—44no—
407M16—42no—
408C2×C8—44no—
409C2×C8—42no—
410C4⋊C4—42no—
411C4⋊C4—41no—
412C4⋊C4—41no—
413C22⋊C4—22no—
414C22⋊C4—42no—
415C22⋊C4—42no—
416C22⋊C4—42no—
417C22⋊C4—41no—
418C22⋊C4—41no—
419C22⋊C4—42no—
420C22⋊C4—41no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—81no—
424C22⋊C4—81no—
425C22⋊C4—81no—
426C22⋊C4—82no—
427C22⋊C4—82no—
428C13#1308011yescharacteristic, direct product factor, Sylow
429C23—21no—
430C23—21no—
431C23—21no—
432C23—21no—
433C23—21no—
434C23—22no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—41no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—41no—
448C23—41no—
449C23—41no—
450C23—41no—
451C23—41no—
452C23—41no—
453C23—42no—
454C23—42no—
455C23—41no—
456C23—41no—
457C23—42no—
458C23—42no—
459C23—81no—
460C23—81no—
461C23—81no—
462C23—81no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—84no—
467C23C13×#9911yescharacteristic
468C23C13×#9911yescharacteristic
469C23C2×C13×C22⋊C411yescharacteristic
470C23C4×D4×C1312yes—
471C23C13×#12112yes—
472D4—42no—
473D4—42no—
474D4—44no—
475D4—44no—
476D4—42no—
477D4—42no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—82no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4—82no—
503C2×C4C13×#9912yes—
504C2×C4C13×#12011yescharacteristic
505C2×C4C13×#12311yescharacteristic
506C8—44no—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—22no—
515C22—22no—
516C22—42no—
517C22—42no—
518C22—42no—
519C22—42no—
520C22—42no—
521C22—42no—
522C22—41no—
523C22—41no—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—84no—
534C22—84no—
535C22—81no—
536C22—81no—
537C22—81no—
538C22—84no—
539C22—84no—
540C22C13×#35212yescomplemented
541C22C13×#38611yescharacteristic
542C22C2×C13×#9911yescharacteristic
543C22C2×C13×#9911yescharacteristic
544C4—21no—
545C4—22no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—162no—
552C2—21no—
553C2—21no—
554C2—22no—
555C2—42no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—81no—
560C2C13×#189811yescharacteristic
561C2C2×C13×#35211yescharacteristic
562C2C13×#212111yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC24C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C24×C13 ◁ C23×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C13×#352C2semidirect
5. C13×#1390C2semidirect
8. C2×C13×#123C4semidirect
10. C22×C13×C22⋊C4C4semidirect
18. C13×#386C4semidirect
23. C13×#379C4semidirect
72. #13080C13direct (N × H)
150. C2×#352C2×C13semidirect
152. #1390C2×C13semidirect
233. C2×#123C4×C13semidirect
235. C22×C22⋊C4C4×C13semidirect
243. #386C4×C13semidirect
248. #379C4×C13semidirect
283. C22×C13#352semidirect
428. C13#13080direct (N × H)
540. C22C13×#352semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1002
C13×#24052
C2×C13×#3522
C13×#17812
C13×#13902
#1308013