Finite Group Databasebeta

← C13×#13090 #15699429

Subgroups — C13×#13090 #15699429

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#99C211yesmaximal, characteristic
2C13×#2435C211yesmaximal, characteristic
3C2×C13×#354C212yesmaximal, complemented
4C13×#1781C211yesmaximal, characteristic
5C13×#1393C212yesmaximal, complemented
6C23×D4×C13C2211yescharacteristic
7C2×C13×#124C411yescharacteristic, complemented
8C2×C13×#124C2211yescharacteristic
9C2×C13×C22⋊Q8C411yescharacteristic, complemented
10C22×C13×C22⋊C4—21no—
11C2×C13×#99—21no—
12C2×C13×#99—24no—
13C2×C13×#99—21no—
14C2×C13×#99C2212yes—
15C2×C13×#99C2212yes—
16C13×#394—21no—
17C13×#394—21no—
18C13×#390C411yescharacteristic, complemented
19C13×#390C2211yescharacteristic
20C13×#379—21no—
21C13×#379—21no—
22C13×#379—21no—
23C4×C13×C22⋊C4C411yescharacteristic, complemented
24C13×#354—24no—
25C25×C13D411yescharacteristic
26C25×C13D411yescharacteristic
27C22×Q8×C13C2×C411yescharacteristic, complemented
28C22×D4×C13—22no—
29C22×D4×C13—22no—
30C22×D4×C13—41no—
31C22×D4×C13—41no—
32C22×D4×C13—42no—
33C22×D4×C13C2×C411yescharacteristic
34C22×D4×C13D411yescharacteristic
35C22×D4×C13D411yescharacteristic
36C22×D4×C13C2311yescharacteristic
37C23×C4×C13—41no—
38C23×C4×C13C2×C411yescharacteristic
39C13×#124—22no—
40C13×#124—22no—
41C13×#124—42no—
42C13×C22⋊Q8—41no—
43C13×C22⋊Q8—41no—
44C2×C13×C4⋊C4—21no—
45C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
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—22no—
55C2×C13×C22⋊C4—21no—
56C2×C13×C22⋊C4—21no—
57C2×C13×C22⋊C4—21no—
58C2×C13×C22⋊C4—21no—
59C2×C13×C22⋊C4—41no—
60C2×C13×C22⋊C4—42no—
61C2×C13×C22⋊C4—41no—
62C2×C13×C22⋊C4—41no—
63C2×C42×C13C2×C411yescharacteristic, complemented
64C2×C42×C13C2×C411yescharacteristic, complemented
65C13×#99—24no—
66C13×#99—22no—
67C13×#99—22no—
68C13×#99—22no—
69C13×#99—42no—
70C13×#99D414yes—
71C13×#95—21no—
72#13090C1311yesmaximal, 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×C13C2×D411yescharacteristic
90C24×C13C2×D411yescharacteristic
91C2×Q8×C13—22no—
92C2×Q8×C13—41no—
93C2×Q8×C13—41no—
94C2×D4×C13—22no—
95C2×D4×C13—22no—
96C2×D4×C13—21no—
97C2×D4×C13—22no—
98C2×D4×C13—21no—
99C2×D4×C13—22no—
100C2×D4×C13—41no—
101C2×D4×C13—41no—
102C2×D4×C13—41no—
103C2×D4×C13—41no—
104C2×D4×C13—41no—
105C2×D4×C13—41no—
106C2×D4×C13—44no—
107C2×D4×C13—44no—
108C2×D4×C13—44no—
109C2×D4×C13—44no—
110C2×D4×C13C2×D412yes—
111C2×D4×C13#4112yes—
112C22×C4×C13—21no—
113C22×C4×C13—21no—
114C22×C4×C13—22no—
115C22×C4×C13—21no—
116C22×C4×C13—21no—
117C22×C4×C13—21no—
118C22×C4×C13—21no—
119C22×C4×C13—41no—
120C22×C4×C13—44no—
121C22×C4×C13—42no—
122C22×C4×C13—42no—
123C22×C4×C13—82no—
124C22×C4×C13—82no—
125C22×C4×C13C22⋊C411yescharacteristic
126C22×C4×C13C22×C411yescharacteristic
127C13×C4⋊C4—41no—
128C13×C4⋊C4—42no—
129C13×C22⋊C4—24no—
130C13×C22⋊C4—42no—
131C13×C22⋊C4—44no—
132C13×C22⋊C4—42no—
133C13×C22⋊C4—42no—
134C13×C22⋊C4—41no—
135C13×C22⋊C4—41no—
136C13×C22⋊C4—42no—
137C13×C22⋊C4—41no—
138C13×C22⋊C4—42no—
139C13×C22⋊C4—41no—
140C13×C22⋊C4—42no—
141C13×C22⋊C4—42no—
142C13×C22⋊C4—81no—
143C13×C22⋊C4—81no—
144C13×C22⋊C4—81no—
145C13×C22⋊C4—81no—
146C13×C22⋊C4—82no—
147C13×C22⋊C4—82no—
148C42×C13—22no—
149C42×C13—41no—
150C22×#99C2×C1311yescharacteristic
151#2435C2×C1311yescharacteristic
152C2×#354C2×C1312yescomplemented
153#1781C2×C1311yescharacteristic
154#1393C2×C1312yescomplemented
155C23×C13—22no—
156C23×C13—22no—
157C23×C13—22no—
158C23×C13—22no—
159C23×C13—22no—
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—21no—
170C23×C13—21no—
171C23×C13—41no—
172C23×C13—42no—
173C23×C13—42no—
174C23×C13—42no—
175C23×C13—41no—
176C23×C13—41no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13—41no—
180C23×C13—41no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13—42no—
184C23×C13—42no—
185C23×C13—42no—
186C23×C13—81no—
187C23×C13—81no—
188C23×C13—81no—
189C23×C13—81no—
190C23×C13—84no—
191C23×C13—82no—
192C23×C13—82no—
193C23×C13—84no—
194C23×C13—84no—
195C23×C13#9911yescharacteristic
196C23×C13#9911yescharacteristic
197C23×C13#9912yes—
198C23×C13C2×C22⋊C411yescharacteristic
199C23×C13#12011yescharacteristic
200C23×C13#12112yes—
201C23×C13#12311yescharacteristic
202Q8×C13—82no—
203D4×C13—42no—
204D4×C13—42no—
205D4×C13—44no—
206D4×C13—44no—
207D4×C13—42no—
208D4×C13—42no—
209C2×C4×C13—21no—
210C2×C4×C13—21no—
211C2×C4×C13—21no—
212C2×C4×C13—21no—
213C2×C4×C13—21no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—44no—
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—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—88no—
230C2×C4×C13—82no—
231C2×C4×C13—82no—
232C2×C4×C13—82no—
233C2×C4×C13—82no—
234C2×C4×C13—82no—
235C2×C4×C13C4×D412yes—
236C23×D4C22×C1311yescharacteristic
237C2×#124C4×C1311yescharacteristic, complemented
238C2×#124C22×C1311yescharacteristic
239C2×C22⋊Q8C4×C1311yescharacteristic, complemented
240C22×C22⋊C4—21no—
241C2×#99—21no—
242C2×#99—24no—
243C2×#99—21no—
244C2×#99C22×C1312yes—
245C2×#99C22×C1312yes—
246#394—21no—
247#394—21no—
248#390C4×C1311yescharacteristic, complemented
249#390C22×C1311yescharacteristic
250#379—21no—
251#379—21no—
252#379—21no—
253C4×C22⋊C4C4×C1311yescharacteristic, complemented
254#354—24no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—21no—
263C22×C13—22no—
264C22×C13—22no—
265C22×C13—21no—
266C22×C13—42no—
267C22×C13—42no—
268C22×C13—42no—
269C22×C13—41no—
270C22×C13—42no—
271C22×C13—41no—
272C22×C13—44no—
273C22×C13—44no—
274C22×C13—42no—
275C22×C13—41no—
276C22×C13—41no—
277C22×C13—41no—
278C22×C13—41no—
279C22×C13—41no—
280C22×C13—41no—
281C22×C13—41no—
282C22×C13—41no—
283C22×C13—41no—
284C22×C13—81no—
285C22×C13—81no—
286C22×C13—81no—
287C22×C13—84no—
288C22×C13—81no—
289C22×C13—82no—
290C22×C13—82no—
291C22×C13—84no—
292C22×C13#35412yescomplemented
293C22×C13#38611yescharacteristic
294C22×C13C2×#9911yescharacteristic
295C22×C13C2×#9911yescharacteristic
296C4×C13—22no—
297C4×C13—41no—
298C4×C13—81no—
299C4×C13—81no—
300C4×C13—84no—
301C4×C13—81no—
302C4×C13—81no—
303C4×C13—162no—
304C25D4×C1311yescharacteristic
305C25D4×C1311yescharacteristic
306C22×Q8C2×C4×C1311yescharacteristic, complemented
307C22×D4—22no—
308C22×D4—22no—
309C22×D4—41no—
310C22×D4—41no—
311C22×D4—42no—
312C22×D4C2×C4×C1311yescharacteristic
313C22×D4D4×C1311yescharacteristic
314C22×D4D4×C1311yescharacteristic
315C22×D4C23×C1311yescharacteristic
316C23×C4—41no—
317C23×C4C2×C4×C1311yescharacteristic
318#124—22no—
319#124—22no—
320#124—42no—
321C22⋊Q8—41no—
322C22⋊Q8—41no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
325C2×C22⋊C4—24no—
326C2×C22⋊C4—22no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—21no—
332C2×C22⋊C4—21no—
333C2×C22⋊C4—22no—
334C2×C22⋊C4—21no—
335C2×C22⋊C4—21no—
336C2×C22⋊C4—21no—
337C2×C22⋊C4—21no—
338C2×C22⋊C4—41no—
339C2×C22⋊C4—42no—
340C2×C22⋊C4—41no—
341C2×C22⋊C4—41no—
342C2×C42C2×C4×C1311yescharacteristic, complemented
343C2×C42C2×C4×C1311yescharacteristic, complemented
344#99—24no—
345#99—22no—
346#99—22no—
347#99—22no—
348#99—42no—
349#99D4×C1314yes—
350#95—21no—
351C2×C13—21no—
352C2×C13—21no—
353C2×C13—22no—
354C2×C13—41no—
355C2×C13—42no—
356C2×C13—41no—
357C2×C13—42no—
358C2×C13—41no—
359C2×C13—81no—
360C2×C13#189811yescharacteristic
361C2×C13C2×#35411yescharacteristic
362C2×C13#212711yescharacteristic
363C24—21no—
364C24—22no—
365C24—21no—
366C24—21no—
367C24—21no—
368C24—21no—
369C24—21no—
370C24—22no—
371C24—41no—
372C24—42no—
373C24—42no—
374C24—81no—
375C24—81no—
376C24C13×C22⋊C411yescharacteristic
377C24C13×C22⋊C411yescharacteristic
378C24C13×C22⋊C411yescharacteristic
379C24C2×D4×C1311yescharacteristic
380C24C2×D4×C1311yescharacteristic
381C2×Q8—22no—
382C2×Q8—41no—
383C2×Q8—41no—
384C2×D4—22no—
385C2×D4—22no—
386C2×D4—21no—
387C2×D4—22no—
388C2×D4—21no—
389C2×D4—22no—
390C2×D4—41no—
391C2×D4—41no—
392C2×D4—41no—
393C2×D4—41no—
394C2×D4—41no—
395C2×D4—41no—
396C2×D4—44no—
397C2×D4—44no—
398C2×D4—44no—
399C2×D4—44no—
400C2×D4C2×D4×C1312yes—
401C2×D4C13×#4112yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—41no—
410C22×C4—44no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4C13×C22⋊C411yescharacteristic
416C22×C4C22×C4×C1311yescharacteristic
417C4⋊C4—41no—
418C4⋊C4—42no—
419C22⋊C4—24no—
420C22⋊C4—44no—
421C22⋊C4—42no—
422C22⋊C4—42no—
423C22⋊C4—42no—
424C22⋊C4—41no—
425C22⋊C4—41no—
426C22⋊C4—42no—
427C22⋊C4—41no—
428C22⋊C4—42no—
429C22⋊C4—41no—
430C22⋊C4—42no—
431C22⋊C4—42no—
432C22⋊C4—81no—
433C22⋊C4—81no—
434C22⋊C4—81no—
435C22⋊C4—81no—
436C22⋊C4—82no—
437C22⋊C4—82no—
438C42—22no—
439C42—41no—
440C13#1309011yescharacteristic, direct product factor, Sylow
441C23—22no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—22no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—41no—
458C23—42no—
459C23—42no—
460C23—42no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—41no—
468C23—41no—
469C23—42no—
470C23—42no—
471C23—42no—
472C23—81no—
473C23—81no—
474C23—81no—
475C23—81no—
476C23—84no—
477C23—82no—
478C23—82no—
479C23—84no—
480C23—84no—
481C23C13×#9911yescharacteristic
482C23C13×#9911yescharacteristic
483C23C13×#9912yes—
484C23C2×C13×C22⋊C411yescharacteristic
485C23C13×#12011yescharacteristic
486C23C13×#12112yes—
487C23C13×#12311yescharacteristic
488Q8—82no—
489D4—42no—
490D4—42no—
491D4—44no—
492D4—44no—
493D4—42no—
494D4—42no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—44no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—88no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—82no—
519C2×C4—82no—
520C2×C4—82no—
521C2×C4C4×D4×C1312yes—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—21no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—22no—
532C22—21no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—41no—
537C22—42no—
538C22—41no—
539C22—44no—
540C22—44no—
541C22—42no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—84no—
555C22—81no—
556C22—82no—
557C22—82no—
558C22—84no—
559C22C13×#35412yescomplemented
560C22C13×#38611yescharacteristic
561C22C2×C13×#9911yescharacteristic
562C22C2×C13×#9911yescharacteristic
563C4—22no—
564C4—41no—
565C4—81no—
566C4—81no—
567C4—84no—
568C4—81no—
569C4—81no—
570C4—162no—
571C2—21no—
572C2—21no—
573C2—22no—
574C2—41no—
575C2—42no—
576C2—41no—
577C2—42no—
578C2—41no—
579C2—81no—
580C2C13×#189811yescharacteristic
581C2C2×C13×#35411yescharacteristic
582C2C13×#212711yescharacteristic
subgroupG/H
center, socleC22×C13C2×#99
commutatorC22×C4C22×C4×C13
Frattini, cosocleC22×D4C23×C13
prime radicalC23×D4×C13C22
LCSG ▷ C22×C4 ▷ 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×#354C2semidirect
5. C13×#1393C2semidirect
7. C2×C13×#124C4semidirect
9. C2×C13×C22⋊Q8C4semidirect
18. C13×#390C4semidirect
23. C4×C13×C22⋊C4C4semidirect
27. C22×Q8×C13C2×C4semidirect
45. C2×C13×C4⋊C4C2×C4semidirect
63. C2×C42×C13C2×C4semidirect
64. C2×C42×C13C2×C4semidirect
72. #13090C13direct (N × H)
152. C2×#354C2×C13semidirect
154. #1393C2×C13semidirect
237. C2×#124C4×C13semidirect
239. C2×C22⋊Q8C4×C13semidirect
248. #390C4×C13semidirect
253. C4×C22⋊C4C4×C13semidirect
292. C22×C13#354semidirect
306. C22×Q8C2×C4×C13semidirect
324. C2×C4⋊C4C2×C4×C13semidirect
342. C2×C42C2×C4×C13semidirect
343. C2×C42C2×C4×C13semidirect
440. C13#13090direct (N × H)
559. C22C13×#354semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#992
C13×#24352
C2×C13×#3542
C13×#17812
C13×#13932
#1309013