Finite Group Databasebeta

← C13×#24111 #15710450

Subgroups — C13×#24111 #15710450

Order 3328.

1068 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#552C211yesmaximal, characteristic
2C2×C13×#483C211yesmaximal, characteristic, complemented
3C2×C13×#428C211yesmaximal, characteristic, complemented
4C13×#2487C211yesmaximal, characteristic
5C13×#2059C212yesmaximal, complemented
6C13×#2036C212yesmaximal, complemented
7C13×#1894C211yesmaximal, characteristic, complemented
8C13×#1870C211yesmaximal, characteristic
9C13×#1865C212yesmaximal, complemented
10C13×#1853C212yesmaximal, complemented
11C13×#1825C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C13×#552—24no—
14C13×#552—24no—
15C2×C13×#126—21no—
16C2×C13×#125—21no—
17C2×C13×#125C2211yescharacteristic
18C2×C13×#123—21no—
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C4×Q8×C13C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C13×#117—21no—
24C2×C13×#117C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C13×#483—24no—
28C13×#428—24no—
29C2×C13×#107C2212yes—
30C2×C13×#106C2212yes—
31C2×C13×#106C2212yes—
32C2×C13×#103C2212yes—
33C2×C13×#103C2212yes—
34C2×C13×C22⋊C8C2212yes—
35C2×C13×C22⋊C8C2211yescharacteristic
36C13×#400—21no—
37C13×#399—21no—
38C13×#389C2212yes—
39C13×#386—21no—
40C13×#385—21no—
41C13×#380C2212yes—
42C13×#380C2211yescharacteristic
43C13×#340C2212yes—
44C13×#340C2212yes—
45C13×#340C2212yes—
46C13×#336C2212yes—
47C22×Q8×C13C2311yescharacteristic
48C22×D4×C13D411yescharacteristic
49C23×C4×C13—21no—
50C23×C4×C13—21no—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C2×C13×M16—22no—
54C2×C13×M16—24no—
55C22×C8×C13C2312yes—
56C22×C8×C13C2312yes—
57C13×#126—28no—
58C13×#125—28no—
59C13×#125—22no—
60C13×#125—22no—
61C13×#123—28no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8D414yes—
66C4×Q8×C13—22no—
67C4×Q8×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C13×#117—28no—
71C13×#117—22no—
72C13×#117D414yes—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4D411yescharacteristic
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4D411yescharacteristic
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C42×C13—21no—
99C2×C42×C13—21no—
100C2×C42×C13C2311yescharacteristic
101C13×#107—24no—
102C13×#106—24no—
103C13×#106—24no—
104C13×#103—24no—
105C13×#103—24no—
106C13×C22⋊C8—22no—
107C13×C22⋊C8—24no—
108C13×#95—22no—
109C13×#95—21no—
110C13×#95—22no—
111#24111C1311yesmaximal, characteristic, direct product factor, Sylow
112C24×C13C2×D411yescharacteristic
113C24×C13C2×D411yescharacteristic
114C2×Q8×C13—21no—
115C2×Q8×C13—22no—
116C2×Q8×C13—22no—
117C2×Q8×C13C2×D412yes—
118C2×D4×C13—22no—
119C2×D4×C13—22no—
120C2×D4×C13—41no—
121C22×C4×C13—22no—
122C22×C4×C13—22no—
123C22×C4×C13—24no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—42no—
135C22×C4×C13—42no—
136C22×C4×C13—42no—
137C22×C4×C13—82no—
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2411yescharacteristic
145C13×M16—28no—
146C2×C8×C13—22no—
147C2×C8×C13—22no—
148C2×C8×C13—22no—
149C2×C8×C13—22no—
150C2×C8×C13—22no—
151C2×C8×C13#4114yes—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—82no—
168C13×C4⋊C4C2×D412yes—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×D412yes—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—42no—
177C13×C22⋊C4—82no—
178C42×C13—24no—
179C42×C13—24no—
180C42×C13—21no—
181C42×C13—21no—
182C2×#552C2×C1311yescharacteristic
183C2×#483C2×C1311yescharacteristic, complemented
184C2×#428C2×C1311yescharacteristic, complemented
185#2487C2×C1311yescharacteristic
186#2059C2×C1312yescomplemented
187#2036C2×C1312yescomplemented
188#1894C2×C1311yescharacteristic, complemented
189#1870C2×C1311yescharacteristic
190#1865C2×C1312yescomplemented
191#1853C2×C1312yescomplemented
192#1825C2×C1311yescharacteristic, complemented
193C23×C13—21no—
194C23×C13—22no—
195C23×C13—22no—
196C23×C13—21no—
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13#12012yes—
202C23×C13#13712yes—
203C23×C13C22×D411yescharacteristic
204Q8×C13—24no—
205Q8×C13—41no—
206Q8×C13—41no—
207D4×C13—44no—
208C2×C4×C13—22no—
209C2×C4×C13—22no—
210C2×C4×C13—22no—
211C2×C4×C13—24no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—21no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—21no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—48no—
224C2×C4×C13—42no—
225C2×C4×C13—41no—
226C2×C4×C13—41no—
227C2×C4×C13—41no—
228C2×C4×C13—41no—
229C2×C4×C13—42no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—42no—
233C2×C4×C13—42no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—84no—
240C2×C4×C13#12012yes—
241C2×C4×C13C22×D411yescharacteristic
242C2×C4×C13C22×D411yescharacteristic
243C2×C4×C13C2×#4112yes—
244C2×C4×C132−1+412yes—
245C8×C13—24no—
246C8×C13—42no—
247C22×M16C22×C1311yescharacteristic
248#552—24no—
249#552—24no—
250C2×#126—21no—
251C2×#125—21no—
252C2×#125C22×C1311yescharacteristic
253C2×#123—21no—
254C2×C22⋊Q8C22×C1311yescharacteristic
255C2×C22⋊Q8C22×C1311yescharacteristic
256C2×C4×Q8C22×C1311yescharacteristic
257C2×C4×D4C22×C1311yescharacteristic
258C2×#117—21no—
259C2×#117C22×C1311yescharacteristic
260C22×C4⋊C4C22×C1311yescharacteristic
261C22×C4⋊C4C22×C1311yescharacteristic
262#483—24no—
263#428—24no—
264C2×#107C22×C1312yes—
265C2×#106C22×C1312yes—
266C2×#106C22×C1312yes—
267C2×#103C22×C1312yes—
268C2×#103C22×C1312yes—
269C2×C22⋊C8C22×C1311yescharacteristic
270C2×C22⋊C8C22×C1312yes—
271#400—21no—
272#399—21no—
273#389C22×C1312yes—
274#386—21no—
275#385—21no—
276#380C22×C1311yescharacteristic
277#380C22×C1312yes—
278#340C22×C1312yes—
279#340C22×C1312yes—
280#340C22×C1312yes—
281#336C22×C1312yes—
282C22×C13—24no—
283C22×C13—22no—
284C22×C13—22no—
285C22×C13—22no—
286C22×C13—22no—
287C22×C13—42no—
288C22×C13—42no—
289C22×C13—42no—
290C22×C13—41no—
291C22×C13—41no—
292C22×C13C2×#12011yescharacteristic
293C22×C13#54712yes—
294C22×C13C2×#13711yescharacteristic
295C22×C13#57511yescharacteristic
296C22×C13#57712yes—
297C4×C13—22no—
298C4×C13—41no—
299C4×C13—42no—
300C4×C13—41no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—41no—
304C4×C13—42no—
305C4×C13—82no—
306C4×C13—82no—
307C4×C13#52511yescharacteristic
308C4×C13#53611yescharacteristic
309C4×C13#54712yes—
310C22×Q8C23×C1311yescharacteristic
311C22×D4D4×C1311yescharacteristic
312C23×C4—21no—
313C23×C4—21no—
314C23×C4C23×C1311yescharacteristic
315C23×C4C23×C1311yescharacteristic
316C2×M16—22no—
317C2×M16—24no—
318C22×C8C23×C1312yes—
319C22×C8C23×C1312yes—
320#126—28no—
321#125—28no—
322#125—22no—
323#125—22no—
324#123—28no—
325C22⋊Q8—22no—
326C22⋊Q8—22no—
327C22⋊Q8—22no—
328C22⋊Q8D4×C1314yes—
329C4×Q8—22no—
330C4×Q8—22no—
331C4×D4—22no—
332C4×D4—22no—
333#117—28no—
334#117—22no—
335#117D4×C1314yes—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—21no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4D4×C1311yescharacteristic
349C2×C4⋊C4C23×C1312yes—
350C2×C4⋊C4C23×C1312yes—
351C2×C4⋊C4C23×C1311yescharacteristic
352C2×C4⋊C4C23×C1311yescharacteristic
353C2×C4⋊C4C23×C1311yescharacteristic
354C2×C22⋊C4—21no—
355C2×C22⋊C4—21no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4D4×C1311yescharacteristic
360C2×C22⋊C4D4×C1311yescharacteristic
361C2×C42—21no—
362C2×C42—21no—
363C2×C42C23×C1311yescharacteristic
364#107—24no—
365#106—24no—
366#106—24no—
367#103—24no—
368#103—24no—
369C22⋊C8—22no—
370C22⋊C8—24no—
371#95—22no—
372#95—21no—
373#95—22no—
374C2×C13—42no—
375C2×C13—42no—
376C2×C13#240611yescharacteristic
377C2×C13#300711yescharacteristic
378C2×C13#301011yescharacteristic
379C2×C13#334412yes—
380C2×C13#335112yes—
381C24C2×D4×C1311yescharacteristic
382C24C2×D4×C1311yescharacteristic
383C2×Q8—21no—
384C2×Q8—22no—
385C2×Q8—22no—
386C2×Q8C2×D4×C1312yes—
387C2×D4—22no—
388C2×D4—22no—
389C2×D4—41no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—21no—
394C22×C4—21no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—82no—
407C22×C4C2×D4×C1311yescharacteristic
408C22×C4C2×D4×C1311yescharacteristic
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1311yescharacteristic
411C22×C4C2×D4×C1312yes—
412C22×C4C2×D4×C1312yes—
413C22×C4C24×C1311yescharacteristic
414M16—28no—
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—22no—
420C2×C8C13×#4114yes—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—24no—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—21no—
430C4⋊C4—21no—
431C4⋊C4—22no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—42no—
436C4⋊C4—82no—
437C4⋊C4C2×D4×C1312yes—
438C4⋊C4C2×D4×C1312yes—
439C4⋊C4C2×D4×C1312yes—
440C22⋊C4—24no—
441C22⋊C4—24no—
442C22⋊C4—24no—
443C22⋊C4—22no—
444C22⋊C4—22no—
445C22⋊C4—42no—
446C22⋊C4—82no—
447C42—24no—
448C42—24no—
449C42—21no—
450C42—21no—
451C13#2411111yescharacteristic, direct product factor, Sylow
452C23—21no—
453C23—22no—
454C23—22no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—22no—
459C23—22no—
460C23C13×#12012yes—
461C23C13×#13712yes—
462C23C22×D4×C1311yescharacteristic
463Q8—24no—
464Q8—41no—
465Q8—41no—
466D4—44no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—24no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—22no—
482C2×C4—48no—
483C2×C4—42no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—84no—
499C2×C4C13×#12012yes—
500C2×C4C22×D4×C1311yescharacteristic
501C2×C4C22×D4×C1311yescharacteristic
502C2×C4C2×C13×#4112yes—
503C2×C4C13×2−1+412yes—
504C8—24no—
505C8—42no—
506C22—22no—
507C22—22no—
508C22—22no—
509C22—24no—
510C22—22no—
511C22—41no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—41no—
516C22C2×C13×#12011yescharacteristic
517C22C13×#54712yes—
518C22C2×C13×#13711yescharacteristic
519C22C13×#57511yescharacteristic
520C22C13×#57712yes—
521C4—22no—
522C4—41no—
523C4—42no—
524C4—42no—
525C4—41no—
526C4—42no—
527C4—41no—
528C4—42no—
529C4—82no—
530C4—82no—
531C4C13×#52511yescharacteristic
532C4C13×#53611yescharacteristic
533C4C13×#54712yes—
534C2—42no—
535C2—42no—
536C2C13×#240611yescharacteristic
537C2C13×#300711yescharacteristic
538C2C13×#301011yescharacteristic
539C2C13×#334412yes—
540C2C13×#335112yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×D4×C13D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#483C2semidirect
3. C2×C13×#428C2semidirect
5. C13×#2059C2semidirect
6. C13×#2036C2semidirect
7. C13×#1894C2semidirect
9. C13×#1865C2semidirect
10. C13×#1853C2semidirect
11. C13×#1825C2semidirect
111. #24111C13direct (N × H)
183. C2×#483C2×C13semidirect
184. C2×#428C2×C13semidirect
186. #2059C2×C13semidirect
187. #2036C2×C13semidirect
188. #1894C2×C13semidirect
190. #1865C2×C13semidirect
191. #1853C2×C13semidirect
192. #1825C2×C13semidirect
451. C13#24111direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5522
C2×C13×#4832
C2×C13×#4282
C13×#24872
C13×#20592
C13×#20362
C13×#18942
C13×#18702
C13×#18652
C13×#18532
C13×#18252
#2411113