Finite Group Databasebeta

← C13×#24069 #15710408

Subgroups — C13×#24069 #15710408

Order 3328.

1130 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#540C211yesmaximal, characteristic
2C2×C13×#481C211yesmaximal, characteristic, complemented
3C2×C13×#480C211yesmaximal, characteristic, complemented
4C13×#2317C211yesmaximal, characteristic, complemented
5C13×#2059C212yesmaximal, complemented
6C13×#2041C212yesmaximal, complemented
7C13×#1875C211yesmaximal, characteristic, complemented
8C13×#1875C211yesmaximal, characteristic, complemented
9C13×#1864C212yesmaximal, complemented
10C13×#1862C212yesmaximal, complemented
11C13×#1818C211yesmaximal, characteristic, complemented
12C13×#540—24no—
13C13×#540—24no—
14C2×C13×#127C2211yescharacteristic
15C2×C13×#125C2211yescharacteristic
16C2×C13×#123—21no—
17C2×C13×#123—21no—
18C2×C13×#121—21no—
19C2×C13×#121—21no—
20C2×C13×#121C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117C2211yescharacteristic
25C2×C13×#117C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C13×#481—24no—
28C13×#480—24no—
29C2×C13×#107C2212yes—
30C2×C13×#106C2212yes—
31C2×C13×#102C2212yes—
32C2×C13×#102C2212yes—
33C2×C13×#102C2212yes—
34C2×C13×#102C2212yes—
35C2×C13×C22⋊C8C2211yescharacteristic
36C2×C13×C22⋊C8C2211yescharacteristic
37C13×#389C2212yes—
38C13×#389C2212yes—
39C13×#385—21no—
40C13×#385—21no—
41C13×#384—21no—
42C13×#382—21no—
43C13×#340C2212yes—
44C13×#340C2212yes—
45C13×#336C2212yes—
46C13×#336C2212yes—
47C22×D4×C13—21no—
48C22×D4×C13—21no—
49C22×D4×C13—21no—
50C22×D4×C13—21no—
51C22×D4×C13C2311yescharacteristic
52C22×D4×C13C2311yescharacteristic
53C23×C4×C13—21no—
54C23×C4×C13—21no—
55C23×C4×C13—21no—
56C23×C4×C13C2311yescharacteristic
57C22×C8×C13C2312yes—
58C22×C8×C13C2312yes—
59C13×#127—22no—
60C13×#127—22no—
61C13×#125—22no—
62C13×#125—22no—
63C13×#123—28no—
64C13×#123—28no—
65C13×#121—28no—
66C13×#121—28no—
67C13×#121—22no—
68C13×#121—22no—
69C13×#121D414yes—
70C13×#121D414yes—
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C13×#117—22no—
76C13×#117—22no—
77C13×#117—24no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—21no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4D411yescharacteristic
86C2×C13×C4⋊C4D411yescharacteristic
87C2×C13×C4⋊C4C2312yes—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2312yes—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4—21no—
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4D411yescharacteristic
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C42×C13—21no—
99C2×C42×C13C2311yescharacteristic
100C2×C42×C13C2311yescharacteristic
101C13×#107—24no—
102C13×#106—24no—
103C13×#102—24no—
104C13×#102—24no—
105C13×#102—24no—
106C13×#102—24no—
107C13×C22⋊C8—22no—
108C13×C22⋊C8—22no—
109C13×#95—22no—
110C13×#95—22no—
111#24069C1311yesmaximal, characteristic, direct product factor, Sylow
112C24×C13—21no—
113C24×C13—21no—
114C24×C13C2×D411yescharacteristic
115C2×D4×C13—24no—
116C2×D4×C13—24no—
117C2×D4×C13—24no—
118C2×D4×C13—24no—
119C2×D4×C13—21no—
120C2×D4×C13—21no—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—82no—
126C2×D4×C13—82no—
127C2×D4×C13—82no—
128C2×D4×C13—82no—
129C2×D4×C13C2×D412yes—
130C2×D4×C13C2×D412yes—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—24no—
137C22×C4×C13—24no—
138C22×C4×C13—22no—
139C22×C4×C13—42no—
140C22×C4×C13—82no—
141C22×C4×C13—82no—
142C22×C4×C13—82no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2411yescharacteristic
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C2×C8×C13—22no—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—82no—
168C13×C4⋊C4—82no—
169C13×C4⋊C4C2×D412yes—
170C13×C4⋊C4C2×D412yes—
171C13×C4⋊C4#4114yes—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—24no—
178C13×C22⋊C4—24no—
179C42×C13—24no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C2×#540C2×C1311yescharacteristic
185C2×#481C2×C1311yescharacteristic, complemented
186C2×#480C2×C1311yescharacteristic, complemented
187#2317C2×C1311yescharacteristic, complemented
188#2059C2×C1312yescomplemented
189#2041C2×C1312yescomplemented
190#1875C2×C1311yescharacteristic, complemented
191#1875C2×C1311yescharacteristic, complemented
192#1864C2×C1312yescomplemented
193#1862C2×C1312yescomplemented
194#1818C2×C1311yescharacteristic, complemented
195C23×C13—21no—
196C23×C13—21no—
197C23×C13—22no—
198C23×C13—22no—
199C23×C13—22no—
200C23×C13—22no—
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13#12012yes—
210C23×C13C22×D411yescharacteristic
211D4×C13—24no—
212D4×C13—24no—
213D4×C13—42no—
214D4×C13—42no—
215D4×C13—84no—
216D4×C13—84no—
217D4×C13—84no—
218D4×C13—84no—
219C2×C4×C13—21no—
220C2×C4×C13—21no—
221C2×C4×C13—24no—
222C2×C4×C13—24no—
223C2×C4×C13—21no—
224C2×C4×C13—21no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—24no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—84no—
242C2×C4×C13—84no—
243C2×C4×C13—84no—
244C2×C4×C13#12012yes—
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C2×#4112yes—
248C2×C4×C132−1+412yes—
249C8×C13—42no—
250C8×C13—42no—
251#540—24no—
252#540—24no—
253C2×#127C22×C1311yescharacteristic
254C2×#125C22×C1311yescharacteristic
255C2×#123—21no—
256C2×#123—21no—
257C2×#121—21no—
258C2×#121—21no—
259C2×#121C22×C1311yescharacteristic
260C2×#121C22×C1311yescharacteristic
261C2×C4×D4C22×C1311yescharacteristic
262C2×C4×D4C22×C1311yescharacteristic
263C2×#117C22×C1311yescharacteristic
264C2×#117C22×C1311yescharacteristic
265C22×C4⋊C4C22×C1311yescharacteristic
266#481—24no—
267#480—24no—
268C2×#107C22×C1312yes—
269C2×#106C22×C1312yes—
270C2×#102C22×C1312yes—
271C2×#102C22×C1312yes—
272C2×#102C22×C1312yes—
273C2×#102C22×C1312yes—
274C2×C22⋊C8C22×C1311yescharacteristic
275C2×C22⋊C8C22×C1311yescharacteristic
276#389C22×C1312yes—
277#389C22×C1312yes—
278#385—21no—
279#385—21no—
280#384—21no—
281#382—21no—
282#340C22×C1312yes—
283#340C22×C1312yes—
284#336C22×C1312yes—
285#336C22×C1312yes—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—42no—
290C22×C13—42no—
291C22×C13—42no—
292C22×C13—42no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—82no—
298C22×C13—82no—
299C22×C13—82no—
300C22×C13—82no—
301C22×C13C2×#12011yescharacteristic
302C22×C13#52511yescharacteristic
303C22×C13#53611yescharacteristic
304C22×C13#57612yes—
305C22×C13#57712yes—
306C4×C13—22no—
307C4×C13—44no—
308C4×C13—41no—
309C4×C13—41no—
310C4×C13—42no—
311C4×C13—41no—
312C4×C13—41no—
313C4×C13—42no—
314C4×C13—82no—
315C4×C13#54712yes—
316C4×C13#54712yes—
317C22×D4—21no—
318C22×D4—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4C23×C1311yescharacteristic
322C22×D4C23×C1311yescharacteristic
323C23×C4—21no—
324C23×C4—21no—
325C23×C4—21no—
326C23×C4C23×C1311yescharacteristic
327C22×C8C23×C1312yes—
328C22×C8C23×C1312yes—
329#127—22no—
330#127—22no—
331#125—22no—
332#125—22no—
333#123—28no—
334#123—28no—
335#121—28no—
336#121—28no—
337#121—22no—
338#121—22no—
339#121D4×C1314yes—
340#121D4×C1314yes—
341C4×D4—22no—
342C4×D4—22no—
343C4×D4—22no—
344C4×D4—22no—
345#117—22no—
346#117—22no—
347#117—24no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4D4×C1311yescharacteristic
356C2×C4⋊C4D4×C1311yescharacteristic
357C2×C4⋊C4C23×C1312yes—
358C2×C4⋊C4C23×C1311yescharacteristic
359C2×C4⋊C4C23×C1311yescharacteristic
360C2×C4⋊C4C23×C1312yes—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4D4×C1311yescharacteristic
367C2×C22⋊C4D4×C1311yescharacteristic
368C2×C42—21no—
369C2×C42C23×C1311yescharacteristic
370C2×C42C23×C1311yescharacteristic
371#107—24no—
372#106—24no—
373#102—24no—
374#102—24no—
375#102—24no—
376#102—24no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379#95—22no—
380#95—22no—
381C2×C13—42no—
382C2×C13—82no—
383C2×C13—82no—
384C2×C13#240611yescharacteristic
385C2×C13#300811yescharacteristic
386C2×C13#300911yescharacteristic
387C2×C13#311912yes—
388C2×C13#324112yes—
389C24—21no—
390C24—21no—
391C24C2×D4×C1311yescharacteristic
392C2×D4—24no—
393C2×D4—24no—
394C2×D4—24no—
395C2×D4—24no—
396C2×D4—21no—
397C2×D4—21no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4—22no—
402C2×D4—82no—
403C2×D4—82no—
404C2×D4—82no—
405C2×D4—82no—
406C2×D4C2×D4×C1312yes—
407C2×D4C2×D4×C1312yes—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—42no—
417C22×C4—82no—
418C22×C4—82no—
419C22×C4—82no—
420C22×C4C2×D4×C1311yescharacteristic
421C22×C4C2×D4×C1311yescharacteristic
422C22×C4C2×D4×C1311yescharacteristic
423C22×C4C2×D4×C1311yescharacteristic
424C22×C4C2×D4×C1311yescharacteristic
425C22×C4C2×D4×C1312yes—
426C22×C4C2×D4×C1312yes—
427C22×C4C24×C1311yescharacteristic
428C2×C8—22no—
429C2×C8—22no—
430C2×C8—22no—
431C2×C8—22no—
432C2×C8—22no—
433C2×C8—22no—
434C4⋊C4—24no—
435C4⋊C4—24no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—82no—
445C4⋊C4—82no—
446C4⋊C4C2×D4×C1312yes—
447C4⋊C4C2×D4×C1312yes—
448C4⋊C4C13×#4114yes—
449C22⋊C4—24no—
450C22⋊C4—24no—
451C22⋊C4—24no—
452C22⋊C4—22no—
453C22⋊C4—22no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C42—24no—
457C42—21no—
458C42—21no—
459C42—21no—
460C42—21no—
461C13#2406911yescharacteristic, direct product factor, Sylow
462C23—21no—
463C23—21no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—41no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—42no—
473C23—42no—
474C23—42no—
475C23—42no—
476C23C13×#12012yes—
477C23C22×D4×C1311yescharacteristic
478D4—24no—
479D4—24no—
480D4—42no—
481D4—42no—
482D4—84no—
483D4—84no—
484D4—84no—
485D4—84no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—84no—
509C2×C4—84no—
510C2×C4—84no—
511C2×C4C13×#12012yes—
512C2×C4C22×D4×C1311yescharacteristic
513C2×C4C22×D4×C1311yescharacteristic
514C2×C4C2×C13×#4112yes—
515C2×C4C13×2−1+412yes—
516C8—42no—
517C8—42no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—82no—
530C22—82no—
531C22—82no—
532C22—82no—
533C22C2×C13×#12011yescharacteristic
534C22C13×#52511yescharacteristic
535C22C13×#53611yescharacteristic
536C22C13×#57612yes—
537C22C13×#57712yes—
538C4—22no—
539C4—41no—
540C4—41no—
541C4—42no—
542C4—41no—
543C4—41no—
544C4—42no—
545C4—44no—
546C4—82no—
547C4C13×#54712yes—
548C4C13×#54712yes—
549C2—42no—
550C2—82no—
551C2—82no—
552C2C13×#240611yescharacteristic
553C2C13×#300811yescharacteristic
554C2C13×#300911yescharacteristic
555C2C13×#311912yes—
556C2C13×#324112yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#540C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C2×C13×#117 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#481C2semidirect
3. C2×C13×#480C2semidirect
4. C13×#2317C2semidirect
5. C13×#2059C2semidirect
6. C13×#2041C2semidirect
7. C13×#1875C2semidirect
8. C13×#1875C2semidirect
9. C13×#1864C2semidirect
10. C13×#1862C2semidirect
11. C13×#1818C2semidirect
111. #24069C13direct (N × H)
185. C2×#481C2×C13semidirect
186. C2×#480C2×C13semidirect
187. #2317C2×C13semidirect
188. #2059C2×C13semidirect
189. #2041C2×C13semidirect
190. #1875C2×C13semidirect
191. #1875C2×C13semidirect
192. #1864C2×C13semidirect
193. #1862C2×C13semidirect
194. #1818C2×C13semidirect
461. C13#24069direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5402
C2×C13×#4812
C2×C13×#4802
C13×#23172
C13×#20592
C13×#20412
C13×#18752
C13×#18642
C13×#18622
C13×#18182
#2406913