Finite Group Databasebeta

← C13×#13084 #15699423

Subgroups — C13×#13084 #15699423

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#99C211yesmaximal, characteristic
2C13×#2405C211yesmaximal, characteristic
3C2×C13×#352C212yesmaximal, complemented
4C13×#1783C211yesmaximal, characteristic
5C13×#1390C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#123C411yescharacteristic, complemented
8C2×C13×#123C2211yescharacteristic
9C22×C13×C22⋊C4—21no—
10C22×C13×C22⋊C4C411yescharacteristic, complemented
11C2×C13×#100—21no—
12C2×C13×#100C2212yes—
13C2×C13×#99—21no—
14C2×C13×#99—24no—
15C2×C13×#99C2212yes—
16C13×#407—21no—
17C13×#394—21no—
18C13×#394—21no—
19C13×#386C411yescharacteristic, complemented
20C13×#386C2211yescharacteristic
21C13×#385—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—41no—
30C22×D4×C13—41no—
31C22×D4×C13—42no—
32C22×D4×C13C2×C411yescharacteristic
33C22×D4×C13D411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C22×D4×C13C2311yescharacteristic
36C23×C4×C13—41no—
37C23×C4×C13C2×C411yescharacteristic, complemented
38C23×C4×C13C2×C411yescharacteristic, complemented
39C23×C4×C13D411yescharacteristic
40C2×C13×M16—22no—
41C13×#123—22no—
42C13×#123—22no—
43C13×#123—42no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4—21no—
46C2×C13×C22⋊C4—24no—
47C2×C13×C22⋊C4—22no—
48C2×C13×C22⋊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—21no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—41no—
57C2×C13×C22⋊C4—42no—
58C2×C13×C22⋊C4—41no—
59C2×C13×C22⋊C4—41no—
60C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
61C2×C13×C22⋊C4C2×C411yescharacteristic, complemented
62C13×#100—22no—
63C13×#100—22no—
64C13×#100—42no—
65C13×#99—24no—
66C13×#99—22no—
67C13×#99D414yes—
68C13×C22⋊C8—41no—
69C13×C22⋊C8—41no—
70C13×#95—21no—
71C13×#95—21no—
72#13084C1311yesmaximal, characteristic, direct product factor, Sylow
73C24×C13—21no—
74C24×C13—22no—
75C24×C13—21no—
76C24×C13—21no—
77C24×C13—21no—
78C24×C13—21no—
79C24×C13—21no—
80C24×C13—22no—
81C24×C13—41no—
82C24×C13—42no—
83C24×C13—42no—
84C24×C13—81no—
85C24×C13—81no—
86C24×C13C22⋊C411yescharacteristic
87C24×C13C22⋊C411yescharacteristic
88C24×C13C22⋊C411yescharacteristic
89C24×C13C22×C411yescharacteristic
90C24×C13C2×D411yescharacteristic
91C2×D4×C13—22no—
92C2×D4×C13—22no—
93C2×D4×C13—22no—
94C2×D4×C13—21no—
95C2×D4×C13—21no—
96C2×D4×C13—22no—
97C2×D4×C13—41no—
98C2×D4×C13—41no—
99C2×D4×C13—41no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—44no—
104C2×D4×C13—44no—
105C2×D4×C13—44no—
106C2×D4×C13—44no—
107C2×D4×C13C2×D412yes—
108C2×D4×C13#4112yes—
109C22×C4×C13—21no—
110C22×C4×C13—21no—
111C22×C4×C13—22no—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—21no—
115C22×C4×C13—21no—
116C22×C4×C13—22no—
117C22×C4×C13—41no—
118C22×C4×C13—44no—
119C22×C4×C13—42no—
120C22×C4×C13—41no—
121C22×C4×C13—41no—
122C22×C4×C13—41no—
123C22×C4×C13—81no—
124C22×C4×C13—82no—
125C22×C4×C13—82no—
126C22×C4×C13C22⋊C411yescharacteristic
127C22×C4×C13C2×D411yescharacteristic
128C13×M16—42no—
129C13×M16—42no—
130C2×C8×C13—42no—
131C13×C4⋊C4—42no—
132C13×C4⋊C4—42no—
133C13×C22⋊C4—22no—
134C13×C22⋊C4—24no—
135C13×C22⋊C4—42no—
136C13×C22⋊C4—44no—
137C13×C22⋊C4—42no—
138C13×C22⋊C4—42no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—41no—
141C13×C22⋊C4—42no—
142C13×C22⋊C4—41no—
143C13×C22⋊C4—41no—
144C13×C22⋊C4—41no—
145C13×C22⋊C4—81no—
146C13×C22⋊C4—81no—
147C13×C22⋊C4—81no—
148C22×#99C2×C1311yescharacteristic
149#2405C2×C1311yescharacteristic
150C2×#352C2×C1312yescomplemented
151#1783C2×C1311yescharacteristic
152#1390C2×C1312yescomplemented
153C23×C13—22no—
154C23×C13—22no—
155C23×C13—22no—
156C23×C13—22no—
157C23×C13—22no—
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—21no—
167C23×C13—21no—
168C23×C13—21no—
169C23×C13—41no—
170C23×C13—42no—
171C23×C13—42no—
172C23×C13—42no—
173C23×C13—41no—
174C23×C13—41no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—42no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—42no—
183C23×C13—42no—
184C23×C13—81no—
185C23×C13—81no—
186C23×C13—81no—
187C23×C13—81no—
188C23×C13—84no—
189C23×C13—82no—
190C23×C13—82no—
191C23×C13—84no—
192C23×C13—84no—
193C23×C13#9911yescharacteristic
194C23×C13#9911yescharacteristic
195C23×C13#9912yes—
196C23×C13C2×C22⋊C411yescharacteristic
197C23×C13C4×D412yes—
198C23×C13#12011yescharacteristic
199C23×C13#12311yescharacteristic
200D4×C13—42no—
201D4×C13—42no—
202D4×C13—44no—
203D4×C13—44no—
204D4×C13—42no—
205D4×C13—42no—
206C2×C4×C13—21no—
207C2×C4×C13—21no—
208C2×C4×C13—21no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—42no—
212C2×C4×C13—42no—
213C2×C4×C13—44no—
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—41no—
223C2×C4×C13—41no—
224C2×C4×C13—41no—
225C2×C4×C13—41no—
226C2×C4×C13—88no—
227C2×C4×C13—82no—
228C2×C4×C13—82no—
229C2×C4×C13—82no—
230C2×C4×C13—82no—
231C2×C4×C13#12112yes—
232C8×C13—82no—
233C23×D4C22×C1311yescharacteristic
234C2×#123C4×C1311yescharacteristic, complemented
235C2×#123C22×C1311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4C4×C1311yescharacteristic, complemented
238C2×#100—21no—
239C2×#100C22×C1312yes—
240C2×#99—21no—
241C2×#99—24no—
242C2×#99C22×C1312yes—
243#407—21no—
244#394—21no—
245#394—21no—
246#386C4×C1311yescharacteristic, complemented
247#386C22×C1311yescharacteristic
248#385—21no—
249#379—21no—
250#379C4×C1311yescharacteristic, complemented
251#352—24no—
252C22×C13—21no—
253C22×C13—21no—
254C22×C13—21no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—22no—
261C22×C13—22no—
262C22×C13—21no—
263C22×C13—42no—
264C22×C13—42no—
265C22×C13—42no—
266C22×C13—42no—
267C22×C13—41no—
268C22×C13—41no—
269C22×C13—44no—
270C22×C13—42no—
271C22×C13—44no—
272C22×C13—41no—
273C22×C13—41no—
274C22×C13—41no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—81no—
282C22×C13—81no—
283C22×C13—84no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—82no—
287C22×C13—82no—
288C22×C13—84no—
289C22×C13#35212yescomplemented
290C22×C13#38611yescharacteristic
291C22×C13C2×#9911yescharacteristic
292C22×C13C2×#9911yescharacteristic
293C4×C13—22no—
294C4×C13—41no—
295C4×C13—81no—
296C4×C13—81no—
297C4×C13—84no—
298C4×C13—81no—
299C4×C13—81no—
300C25C2×C4×C1311yescharacteristic
301C25D4×C1311yescharacteristic
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—41no—
305C22×D4—41no—
306C22×D4—42no—
307C22×D4C2×C4×C1311yescharacteristic
308C22×D4D4×C1311yescharacteristic
309C22×D4D4×C1311yescharacteristic
310C22×D4C23×C1311yescharacteristic
311C23×C4—41no—
312C23×C4C2×C4×C1311yescharacteristic, complemented
313C23×C4C2×C4×C1311yescharacteristic, complemented
314C23×C4D4×C1311yescharacteristic
315C2×M16—22no—
316#123—22no—
317#123—22no—
318#123—42no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C22⋊C4—24no—
322C2×C22⋊C4—22no—
323C2×C22⋊C4—21no—
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—41no—
332C2×C22⋊C4—42no—
333C2×C22⋊C4—41no—
334C2×C22⋊C4—41no—
335C2×C22⋊C4C2×C4×C1311yescharacteristic, complemented
336C2×C22⋊C4C2×C4×C1311yescharacteristic, complemented
337#100—22no—
338#100—22no—
339#100—42no—
340#99—24no—
341#99—22no—
342#99D4×C1314yes—
343C22⋊C8—41no—
344C22⋊C8—41no—
345#95—21no—
346#95—21no—
347C2×C13—21no—
348C2×C13—21no—
349C2×C13—22no—
350C2×C13—41no—
351C2×C13—41no—
352C2×C13—42no—
353C2×C13—41no—
354C2×C13—42no—
355C2×C13—81no—
356C2×C13#189811yescharacteristic
357C2×C13C2×#35211yescharacteristic
358C2×C13#212111yescharacteristic
359C24—21no—
360C24—22no—
361C24—21no—
362C24—21no—
363C24—21no—
364C24—21no—
365C24—21no—
366C24—22no—
367C24—41no—
368C24—42no—
369C24—42no—
370C24—81no—
371C24—81no—
372C24C13×C22⋊C411yescharacteristic
373C24C13×C22⋊C411yescharacteristic
374C24C13×C22⋊C411yescharacteristic
375C24C22×C4×C1311yescharacteristic
376C24C2×D4×C1311yescharacteristic
377C2×D4—22no—
378C2×D4—22no—
379C2×D4—22no—
380C2×D4—21no—
381C2×D4—21no—
382C2×D4—22no—
383C2×D4—41no—
384C2×D4—41no—
385C2×D4—41no—
386C2×D4—41no—
387C2×D4—41no—
388C2×D4—41no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—44no—
393C2×D4C2×D4×C1312yes—
394C2×D4C13×#4112yes—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—22no—
403C22×C4—41no—
404C22×C4—44no—
405C22×C4—42no—
406C22×C4—41no—
407C22×C4—41no—
408C22×C4—41no—
409C22×C4—81no—
410C22×C4—82no—
411C22×C4—82no—
412C22×C4C13×C22⋊C411yescharacteristic
413C22×C4C2×D4×C1311yescharacteristic
414M16—42no—
415M16—42no—
416C2×C8—42no—
417C4⋊C4—42no—
418C4⋊C4—42no—
419C22⋊C4—22no—
420C22⋊C4—24no—
421C22⋊C4—44no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—42no—
425C22⋊C4—41no—
426C22⋊C4—41no—
427C22⋊C4—42no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C22⋊C4—41no—
431C22⋊C4—81no—
432C22⋊C4—81no—
433C22⋊C4—81no—
434C13#1308411yescharacteristic, direct product factor, Sylow
435C23—22no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—22no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—41no—
452C23—42no—
453C23—42no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—42no—
462C23—41no—
463C23—41no—
464C23—42no—
465C23—42no—
466C23—81no—
467C23—81no—
468C23—81no—
469C23—81no—
470C23—84no—
471C23—82no—
472C23—82no—
473C23—84no—
474C23—84no—
475C23C13×#9911yescharacteristic
476C23C13×#9911yescharacteristic
477C23C13×#9912yes—
478C23C2×C13×C22⋊C411yescharacteristic
479C23C4×D4×C1312yes—
480C23C13×#12011yescharacteristic
481C23C13×#12311yescharacteristic
482D4—42no—
483D4—42no—
484D4—44no—
485D4—44no—
486D4—42no—
487D4—42no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—44no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—88no—
509C2×C4—82no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4C13×#12112yes—
514C8—82no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—22no—
524C22—22no—
525C22—21no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—41no—
531C22—41no—
532C22—44no—
533C22—42no—
534C22—44no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—81no—
545C22—81no—
546C22—84no—
547C22—81no—
548C22—81no—
549C22—82no—
550C22—82no—
551C22—84no—
552C22C13×#35212yescomplemented
553C22C13×#38611yescharacteristic
554C22C2×C13×#9911yescharacteristic
555C22C2×C13×#9911yescharacteristic
556C4—22no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—84no—
561C4—81no—
562C4—81no—
563C2—21no—
564C2—21no—
565C2—22no—
566C2—41no—
567C2—41no—
568C2—42no—
569C2—41no—
570C2—42no—
571C2—81no—
572C2C13×#189811yescharacteristic
573C2C2×C13×#35211yescharacteristic
574C2C13×#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
7. C2×C13×#123C4semidirect
10. C22×C13×C22⋊C4C4semidirect
19. C13×#386C4semidirect
23. C13×#379C4semidirect
37. C23×C4×C13C2×C4semidirect
38. C23×C4×C13C2×C4semidirect
60. C2×C13×C22⋊C4C2×C4semidirect
61. C2×C13×C22⋊C4C2×C4semidirect
72. #13084C13direct (N × H)
150. C2×#352C2×C13semidirect
152. #1390C2×C13semidirect
234. C2×#123C4×C13semidirect
237. C22×C22⋊C4C4×C13semidirect
246. #386C4×C13semidirect
250. #379C4×C13semidirect
289. C22×C13#352semidirect
312. C23×C4C2×C4×C13semidirect
313. C23×C4C2×C4×C13semidirect
335. C2×C22⋊C4C2×C4×C13semidirect
336. C2×C22⋊C4C2×C4×C13semidirect
434. C13#13084direct (N × H)
552. C22C13×#352semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#992
C13×#24052
C2×C13×#3522
C13×#17832
C13×#13902
#1308413