Finite Group Databasebeta

← C13×#24115 #15710454

Subgroups — C13×#24115 #15710454

Order 3328.

1078 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3491C211yesmaximal, characteristic
2C13×#2623C212yesmaximal, complemented
3C13×#2317C211yesmaximal, characteristic, complemented
4C13×#2062C212yesmaximal, complemented
5C13×#2044C212yesmaximal
6C13×#1899C212yesmaximal, complemented
7C13×#1867C214yesmaximal, complemented
8C13×#1820C211yesmaximal, characteristic, complemented
9C13×#552—22no—
10C13×#552—22no—
11C13×#551—22no—
12C13×#551—22no—
13C13×#543C2211yescharacteristic
14C13×#539—21no—
15C13×#539—21no—
16C13×#534C2211yescharacteristic
17C13×#529—21no—
18C13×#529—21no—
19C2×C13×#123C2212yes—
20C13×#518C2212yes—
21C2×C13×#117C2211yescharacteristic
22C2×C13×#117C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C2×C13×#99C2214yes—
25C13×#400—22no—
26C13×#399—22no—
27C13×#398—22no—
28C13×#397—22no—
29C13×#389—21no—
30C13×#389—21no—
31C13×#386C2214yes—
32C13×#385C2212yes—
33C13×#385C2212yes—
34C13×#385C2214yes—
35C13×#384—21no—
36C13×#382—21no—
37C13×#381C2212yes—
38C13×#342C2212yes—
39C13×#342C2214yes—
40C13×#342C2212yes—
41C22×D4×C13C2312yes—
42C23×C4×C13C2312yes—
43C23×C4×C13C2311yescharacteristic
44C13×#126—22no—
45C13×#126—22no—
46C13×#126—22no—
47C13×#126—22no—
48C13×#125—21no—
49C13×#125—21no—
50C13×#125—22no—
51C13×#125—22no—
52C13×#124—21no—
53C13×#124—21no—
54C13×#123—22no—
55C13×#123—22no—
56C13×#123—22no—
57C13×#123—22no—
58C13×#123—22no—
59C13×#123—22no—
60C13×#123—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—21no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×#121—21no—
68C13×#121—21no—
69C13×#120—22no—
70C4×Q8×C13—21no—
71C4×Q8×C13—21no—
72C4×D4×C13—21no—
73C4×D4×C13—21no—
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C13×#117—22no—
79C13×#117—22no—
80C13×#117—22no—
81C13×#117—22no—
82C13×#117—22no—
83C13×#117—24no—
84C2×C13×C4⋊C4—21no—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—24no—
92C2×C13×C4⋊C4D411yescharacteristic
93C2×C13×C4⋊C4D411yescharacteristic
94C2×C13×C4⋊C4D412yes—
95C2×C13×C4⋊C4D412yes—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—24no—
98C2×C13×C22⋊C4D412yes—
99C2×C13×C22⋊C4D412yes—
100C2×C13×C22⋊C4C2314yes—
101C2×C13×C22⋊C4C2311yescharacteristic
102C2×C13×C22⋊C4C2311yescharacteristic
103C2×C13×C22⋊C4C2312yes—
104C2×C13×C22⋊C4C2312yes—
105C2×C42×C13—21no—
106C2×C42×C13D411yescharacteristic
107C2×C42×C13D411yescharacteristic
108C13×#99—28no—
109C13×#95—22no—
110C13×#95—22no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—24no—
114C13×#95—24no—
115#24115C1311yesmaximal, characteristic, direct product factor, Sylow
116C24×C13C2×D412yes—
117C24×C13C2411yescharacteristic
118C2×Q8×C13—21no—
119C2×Q8×C13—21no—
120C2×D4×C13—22no—
121C2×D4×C13—22no—
122C2×D4×C13—24no—
123C2×D4×C13—24no—
124C2×D4×C13—21no—
125C2×D4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13—24no—
133C22×C4×C13—22no—
134C22×C4×C13—82no—
135C22×C4×C13C2×D412yes—
136C22×C4×C13C2×D412yes—
137C22×C4×C13C2×D412yes—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D412yes—
146C13×C4⋊C4—24no—
147C13×C4⋊C4—22no—
148C13×C4⋊C4—22no—
149C13×C4⋊C4—22no—
150C13×C4⋊C4—22no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C4⋊C4—21no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—41no—
162C13×C4⋊C4—41no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—82no—
165C13×C4⋊C4—82no—
166C13×C4⋊C4—84no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—24no—
181C13×C22⋊C4—24no—
182C13×C22⋊C4—84no—
183C13×C22⋊C4#4114yes—
184C42×C13—24no—
185C42×C13—22no—
186C42×C13—22no—
187C42×C13—21no—
188C42×C13—21no—
189C42×C13—21no—
190C42×C13—21no—
191#3491C2×C1311yescharacteristic
192#2623C2×C1312yescomplemented
193#2317C2×C1311yescharacteristic, complemented
194#2062C2×C1312yescomplemented
195#2044C2×C1312yes—
196#1899C2×C1312yescomplemented
197#1867C2×C1314yescomplemented
198#1820C2×C1311yescharacteristic, complemented
199C23×C13—22no—
200C23×C13—24no—
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—42no—
204C23×C13—42no—
205C23×C13C22×D411yescharacteristic
206C23×C13C22×D412yes—
207C23×C13C2×#4112yes—
208C23×C132−1+412yes—
209Q8×C13—81no—
210Q8×C13—81no—
211D4×C13—42no—
212D4×C13—42no—
213D4×C13—44no—
214D4×C13—81no—
215D4×C13—81no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—21no—
219C2×C4×C13—21no—
220C2×C4×C13—24no—
221C2×C4×C13—24no—
222C2×C4×C13—21no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—24no—
231C2×C4×C13—42no—
232C2×C4×C13—42no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—41no—
239C2×C4×C13—44no—
240C2×C4×C13—44no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—44no—
244C2×C4×C13—44no—
245C2×C4×C13—42no—
246C2×C4×C13—44no—
247C2×C4×C13—82no—
248C2×C4×C13—82no—
249C2×C4×C13#12011yescharacteristic
250C2×C4×C13#12011yescharacteristic
251C2×C4×C13#12012yes—
252#552—22no—
253#552—22no—
254#551—22no—
255#551—22no—
256#543C22×C1311yescharacteristic
257#539—21no—
258#539—21no—
259#534C22×C1311yescharacteristic
260#529—21no—
261#529—21no—
262C2×#123C22×C1312yes—
263#518C22×C1312yes—
264C2×#117C22×C1311yescharacteristic
265C2×#117C22×C1311yescharacteristic
266C22×C4⋊C4C22×C1311yescharacteristic
267C2×#99C22×C1314yes—
268#400—22no—
269#399—22no—
270#398—22no—
271#397—22no—
272#389—21no—
273#389—21no—
274#386C22×C1314yes—
275#385C22×C1312yes—
276#385C22×C1312yes—
277#385C22×C1314yes—
278#384—21no—
279#382—21no—
280#381C22×C1312yes—
281#342C22×C1312yes—
282#342C22×C1314yes—
283#342C22×C1312yes—
284C22×C13—21no—
285C22×C13—22no—
286C22×C13—21no—
287C22×C13—22no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—84no—
294C22×C13C2×#12011yescharacteristic
295C22×C13#52511yescharacteristic
296C22×C13#53611yescharacteristic
297C22×C13#54714yes—
298C4×C13—22no—
299C4×C13—21no—
300C4×C13—21no—
301C4×C13—44no—
302C4×C13—42no—
303C4×C13—41no—
304C4×C13—42no—
305C4×C13—41no—
306C4×C13—41no—
307C4×C13—42no—
308C4×C13—41no—
309C4×C13—84no—
310C4×C13—82no—
311C22×D4C23×C1312yes—
312C23×C4C23×C1311yescharacteristic
313C23×C4C23×C1312yes—
314#126—22no—
315#126—22no—
316#126—22no—
317#126—22no—
318#125—21no—
319#125—21no—
320#125—22no—
321#125—22no—
322#124—21no—
323#124—21no—
324#123—22no—
325#123—22no—
326#123—22no—
327#123—22no—
328#123—22no—
329#123—22no—
330#123—22no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—21no—
334C22⋊Q8—21no—
335C22⋊Q8—22no—
336C22⋊Q8—22no—
337#121—21no—
338#121—21no—
339#120—22no—
340C4×Q8—21no—
341C4×Q8—21no—
342C4×D4—21no—
343C4×D4—21no—
344C4×D4—22no—
345C4×D4—22no—
346C4×D4—22no—
347C4×D4—22no—
348#117—22no—
349#117—22no—
350#117—22no—
351#117—22no—
352#117—22no—
353#117—24no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—22no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4D4×C1311yescharacteristic
363C2×C4⋊C4D4×C1311yescharacteristic
364C2×C4⋊C4D4×C1312yes—
365C2×C4⋊C4D4×C1312yes—
366C2×C22⋊C4—22no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4D4×C1312yes—
369C2×C22⋊C4D4×C1312yes—
370C2×C22⋊C4C23×C1314yes—
371C2×C22⋊C4C23×C1311yescharacteristic
372C2×C22⋊C4C23×C1311yescharacteristic
373C2×C22⋊C4C23×C1312yes—
374C2×C22⋊C4C23×C1312yes—
375C2×C42—21no—
376C2×C42D4×C1311yescharacteristic
377C2×C42D4×C1311yescharacteristic
378#99—28no—
379#95—22no—
380#95—22no—
381#95—22no—
382#95—22no—
383#95—24no—
384#95—24no—
385C2×C13—21no—
386C2×C13—24no—
387C2×C13—21no—
388C2×C13—82no—
389C2×C13#240611yescharacteristic
390C2×C13#302711yescharacteristic
391C2×C13#302811yescharacteristic
392C24C2×D4×C1312yes—
393C24C24×C1311yescharacteristic
394C2×Q8—21no—
395C2×Q8—21no—
396C2×D4—22no—
397C2×D4—22no—
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—21no—
401C2×D4—21no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—82no—
411C22×C4C2×D4×C1312yes—
412C22×C4C2×D4×C1312yes—
413C22×C4C2×D4×C1312yes—
414C22×C4C2×D4×C1311yescharacteristic
415C22×C4C2×D4×C1311yescharacteristic
416C22×C4C2×D4×C1311yescharacteristic
417C22×C4C2×D4×C1311yescharacteristic
418C22×C4C2×D4×C1312yes—
419C22×C4C2×D4×C1311yescharacteristic
420C22×C4C2×D4×C1311yescharacteristic
421C22×C4C2×D4×C1312yes—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—21no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—42no—
440C4⋊C4—82no—
441C4⋊C4—82no—
442C4⋊C4—84no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—24no—
458C22⋊C4—84no—
459C22⋊C4C13×#4114yes—
460C42—24no—
461C42—22no—
462C42—22no—
463C42—21no—
464C42—21no—
465C42—21no—
466C42—21no—
467C13#2411511yescharacteristic, direct product factor, Sylow
468C23—22no—
469C23—24no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23C22×D4×C1311yescharacteristic
475C23C22×D4×C1312yes—
476C23C2×C13×#4112yes—
477C23C13×2−1+412yes—
478Q8—81no—
479Q8—81no—
480D4—42no—
481D4—42no—
482D4—44no—
483D4—81no—
484D4—81no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—41no—
508C2×C4—44no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—44no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4C13×#12011yescharacteristic
519C2×C4C13×#12011yescharacteristic
520C2×C4C13×#12012yes—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—22no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22—84no—
531C22C2×C13×#12011yescharacteristic
532C22C13×#52511yescharacteristic
533C22C13×#53611yescharacteristic
534C22C13×#54714yes—
535C4—22no—
536C4—21no—
537C4—21no—
538C4—44no—
539C4—41no—
540C4—42no—
541C4—41no—
542C4—41no—
543C4—42no—
544C4—41no—
545C4—42no—
546C4—84no—
547C4—82no—
548C2—21no—
549C2—24no—
550C2—21no—
551C2—82no—
552C2C13×#240611yescharacteristic
553C2C13×#302711yescharacteristic
554C2C13×#302811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#534C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2623C2semidirect
3. C13×#2317C2semidirect
4. C13×#2062C2semidirect
6. C13×#1899C2semidirect
7. C13×#1867C2semidirect
8. C13×#1820C2semidirect
115. #24115C13direct (N × H)
192. #2623C2×C13semidirect
193. #2317C2×C13semidirect
194. #2062C2×C13semidirect
196. #1899C2×C13semidirect
197. #1867C2×C13semidirect
198. #1820C2×C13semidirect
467. C13#24115direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34912
C13×#26232
C13×#23172
C13×#20622
C13×#20442
C13×#18992
C13×#18672
C13×#18202
#2411513