Finite Group Databasebeta

← C13×#24079 #15710418

Subgroups — C13×#24079 #15710418

Order 3328.

1030 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3492C211yesmaximal, characteristic
2C13×#3093C212yesmaximal, complemented
3C13×#2317C211yesmaximal, characteristic, complemented
4C13×#2061C211yesmaximal, characteristic, complemented
5C13×#2060C211yesmaximal, characteristic, complemented
6C13×#2040C211yesmaximal, characteristic, complemented
7C13×#2039C211yesmaximal, characteristic, complemented
8C13×#1897C212yesmaximal, complemented
9C13×#1860C212yesmaximal, complemented
10C13×#1859C212yesmaximal, complemented
11C13×#1821C211yesmaximal, characteristic, complemented
12C13×#554—22no—
13C13×#553—22no—
14C13×#552—22no—
15C13×#547—22no—
16C13×#544C2211yescharacteristic
17C13×#539—22no—
18C13×#537C2211yescharacteristic
19C13×#525—22no—
20C13×#525C2212yes—
21C13×#520C2212yes—
22C2×C13×#117C2211yescharacteristic
23C2×C13×#117C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C13×#485—22no—
26C13×#485—22no—
27C13×#482—22no—
28C13×#482—22no—
29C13×#428C2212yes—
30C13×#428C2212yes—
31C2×C13×#104C2212yes—
32C2×C13×#104C2212yes—
33C13×#417C2212yes—
34C13×#417C2212yes—
35C13×#407C2212yes—
36C13×#389—22no—
37C13×#385—22no—
38C13×#384C2211yescharacteristic
39C13×#384C2211yescharacteristic
40C13×#382C2211yescharacteristic
41C13×#382C2211yescharacteristic
42C13×#343C2211yescharacteristic
43C13×#343C2211yescharacteristic
44C13×#343C2212yes—
45C13×#339C2212yes—
46C13×#339C2212yes—
47C2×C13×#41—22no—
48C2×C13×#41C2312yes—
49C23×C4×C13D412yes—
50C23×C4×C13C2311yescharacteristic
51C2×C13×M16C2312yes—
52C2×C13×M16C2312yes—
53C13×C4⋊Q8—22no—
54C13×#126—24no—
55C13×#125—24no—
56C13×#125—22no—
57C13×#123—24no—
58C13×#123—24no—
59C13×#123—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8D412yes—
65C13×C22⋊Q8D412yes—
66C13×#121—22no—
67C13×#121—22no—
68C13×#121—22no—
69C13×#121D412yes—
70C13×#121D412yes—
71C13×#120—22no—
72C4×Q8×C13—22no—
73C4×D4×C13—24no—
74C4×D4×C13—22no—
75C4×D4×C13—24no—
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—22no—
84C13×#117C2312yes—
85C2×C13×C4⋊C4—21no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4D412yes—
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C4⋊C4C2311yescharacteristic
95C2×C13×C4⋊C4C2311yescharacteristic
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C42×C13—21no—
99C2×C42×C13C2311yescharacteristic
100C2×C42×C13C2311yescharacteristic
101C13×#107—22no—
102C13×#107—22no—
103C13×#106—22no—
104C13×#106—22no—
105C13×#104—24no—
106C13×#104—24no—
107C13×#103—22no—
108C13×#103—22no—
109C13×#102—22no—
110C13×#102—22no—
111C13×C22⋊C8—22no—
112C13×C22⋊C8—22no—
113C13×#95—22no—
114C13×#95—22no—
115#24079C1311yesmaximal, characteristic, direct product factor, Sylow
116C24×C13C2×D411yescharacteristic
117C13×#41—22no—
118C13×#41—22no—
119C13×#41—22no—
120C13×#41—22no—
121C13×#41—84no—
122C2×Q8×C13—22no—
123C2×Q8×C13C2×D412yes—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—22no—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—24no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—82no—
141C22×C4×C13C2×D411yescharacteristic
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2411yescharacteristic
147C13×M16—22no—
148C13×M16—22no—
149C13×M16—22no—
150C13×M16—22no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—24no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—82no—
166C13×C4⋊C4—82no—
167C13×C4⋊C4C2×D412yes—
168C13×C4⋊C4C2×D412yes—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—24no—
171C13×C22⋊C4—24no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—41no—
179C42×C13—24no—
180C42×C13—22no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—42no—
184C42×C13#4112yescomplemented
185C42×C13#4112yescomplemented
186#3492C2×C1311yescharacteristic
187#3093C2×C1312yescomplemented
188#2317C2×C1311yescharacteristic, complemented
189#2061C2×C1311yescharacteristic, complemented
190#2060C2×C1311yescharacteristic, complemented
191#2040C2×C1311yescharacteristic, complemented
192#2039C2×C1311yescharacteristic, complemented
193#1897C2×C1312yescomplemented
194#1860C2×C1312yescomplemented
195#1859C2×C1312yescomplemented
196#1821C2×C1311yescharacteristic, complemented
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—41no—
201C23×C13—41no—
202C23×C13#12011yescharacteristic
203C23×C13#12011yescharacteristic
204C23×C13C22×D411yescharacteristic
205Q8×C13—22no—
206Q8×C13—22no—
207Q8×C13—82no—
208D4×C13—22no—
209D4×C13—22no—
210D4×C13—44no—
211D4×C13—44no—
212D4×C13—42no—
213D4×C13—42no—
214D4×C13—82no—
215C2×C4×C13—21no—
216C2×C4×C13—21no—
217C2×C4×C13—22no—
218C2×C4×C13—22no—
219C2×C4×C13—22no—
220C2×C4×C13—22no—
221C2×C4×C13—22no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—41no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—44no—
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—41no—
240C2×C4×C13—41no—
241C2×C4×C13—82no—
242C2×C4×C13—84no—
243C2×C4×C13#12012yes—
244C2×C4×C13C22×D412yes—
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C13C2×#4111yescharacteristic
247C2×C4×C132−1+412yes—
248C8×C13—42no—
249C8×C13—42no—
250#554—22no—
251#553—22no—
252#552—22no—
253#547—22no—
254#544C22×C1311yescharacteristic
255#539—22no—
256#537C22×C1311yescharacteristic
257#525—22no—
258#525C22×C1312yes—
259#520C22×C1312yes—
260C2×#117C22×C1311yescharacteristic
261C2×#117C22×C1311yescharacteristic
262C22×C4⋊C4C22×C1311yescharacteristic
263#485—22no—
264#485—22no—
265#482—22no—
266#482—22no—
267#428C22×C1312yes—
268#428C22×C1312yes—
269C2×#104C22×C1312yes—
270C2×#104C22×C1312yes—
271#417C22×C1312yes—
272#417C22×C1312yes—
273#407C22×C1312yes—
274#389—22no—
275#385—22no—
276#384C22×C1311yescharacteristic
277#384C22×C1311yescharacteristic
278#382C22×C1311yescharacteristic
279#382C22×C1311yescharacteristic
280#343C22×C1311yescharacteristic
281#343C22×C1311yescharacteristic
282#343C22×C1312yes—
283#339C22×C1312yes—
284#339C22×C1312yes—
285C22×C13—21no—
286C22×C13—21no—
287C22×C13—21no—
288C22×C13—21no—
289C22×C13—21no—
290C22×C13—21no—
291C22×C13—21no—
292C22×C13—21no—
293C22×C13—42no—
294C22×C13—42no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13C2×#12011yescharacteristic
299C22×C13#52511yescharacteristic
300C22×C13#53611yescharacteristic
301C4×C13—22no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—42no—
306C4×C13—42no—
307C4×C13—42no—
308C4×C13—42no—
309C4×C13—81no—
310C4×C13—81no—
311C4×C13#54712yes—
312C4×C13#54712yes—
313C2×#41—22no—
314C2×#41C23×C1312yes—
315C23×C4D4×C1312yes—
316C23×C4C23×C1311yescharacteristic
317C2×M16C23×C1312yes—
318C2×M16C23×C1312yes—
319C4⋊Q8—22no—
320#126—24no—
321#125—24no—
322#125—22no—
323#123—24no—
324#123—24no—
325#123—22no—
326C22⋊Q8—22no—
327C22⋊Q8—24no—
328C22⋊Q8—22no—
329C22⋊Q8—22no—
330C22⋊Q8D4×C1312yes—
331C22⋊Q8D4×C1312yes—
332#121—22no—
333#121—22no—
334#121—22no—
335#121D4×C1312yes—
336#121D4×C1312yes—
337#120—22no—
338C4×Q8—22no—
339C4×D4—24no—
340C4×D4—22no—
341C4×D4—24no—
342C4×D4—22no—
343C4×D4—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117—22no—
348#117—22no—
349#117—22no—
350#117C23×C1312yes—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4D4×C1312yes—
358C2×C4⋊C4C23×C1311yescharacteristic
359C2×C4⋊C4C23×C1311yescharacteristic
360C2×C4⋊C4C23×C1311yescharacteristic
361C2×C4⋊C4C23×C1311yescharacteristic
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C42—21no—
365C2×C42C23×C1311yescharacteristic
366C2×C42C23×C1311yescharacteristic
367#107—22no—
368#107—22no—
369#106—22no—
370#106—22no—
371#104—24no—
372#104—24no—
373#103—22no—
374#103—22no—
375#102—22no—
376#102—22no—
377C22⋊C8—22no—
378C22⋊C8—22no—
379#95—22no—
380#95—22no—
381C2×C13—21no—
382C2×C13—21no—
383C2×C13—41no—
384C2×C13—41no—
385C2×C13—82no—
386C2×C13#240611yescharacteristic
387C2×C13#301911yescharacteristic
388C2×C13#302011yescharacteristic
389C24C2×D4×C1311yescharacteristic
390#41—22no—
391#41—22no—
392#41—22no—
393#41—22no—
394#41—84no—
395C2×Q8—22no—
396C2×Q8C2×D4×C1312yes—
397C2×D4—22no—
398C2×D4—22no—
399C2×D4—22no—
400C2×D4—22no—
401C2×D4C2×D4×C1312yes—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—21no—
413C22×C4—82no—
414C22×C4C2×D4×C1311yescharacteristic
415C22×C4C2×D4×C1312yes—
416C22×C4C2×D4×C1312yes—
417C22×C4C2×D4×C1312yes—
418C22×C4C2×D4×C1312yes—
419C22×C4C24×C1311yescharacteristic
420M16—22no—
421M16—22no—
422M16—22no—
423M16—22no—
424C2×C8—22no—
425C2×C8—22no—
426C4⋊C4—24no—
427C4⋊C4—24no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—22no—
433C4⋊C4—22no—
434C4⋊C4—22no—
435C4⋊C4—22no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—82no—
439C4⋊C4—82no—
440C4⋊C4C2×D4×C1312yes—
441C4⋊C4C2×D4×C1312yes—
442C22⋊C4—24no—
443C22⋊C4—24no—
444C22⋊C4—24no—
445C22⋊C4—22no—
446C22⋊C4—22no—
447C22⋊C4—22no—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C42—24no—
453C42—22no—
454C42—21no—
455C42—21no—
456C42—42no—
457C42C13×#4112yescomplemented
458C42C13×#4112yescomplemented
459C13#2407911yescharacteristic, direct product factor, Sylow
460C23—21no—
461C23—21no—
462C23—22no—
463C23—41no—
464C23—41no—
465C23C13×#12011yescharacteristic
466C23C13×#12011yescharacteristic
467C23C22×D4×C1311yescharacteristic
468Q8—22no—
469Q8—22no—
470Q8—82no—
471D4—22no—
472D4—22no—
473D4—44no—
474D4—44no—
475D4—42no—
476D4—42no—
477D4—82no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—44no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—82no—
505C2×C4—84no—
506C2×C4C13×#12012yes—
507C2×C4C22×D4×C1312yes—
508C2×C4C2×C13×#4111yescharacteristic
509C2×C4C2×C13×#4111yescharacteristic
510C2×C4C13×2−1+412yes—
511C8—42no—
512C8—42no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—21no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—42no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22C2×C13×#12011yescharacteristic
527C22C13×#52511yescharacteristic
528C22C13×#53611yescharacteristic
529C4—22no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—81no—
538C4—81no—
539C4C13×#54712yes—
540C4C13×#54712yes—
541C2—21no—
542C2—21no—
543C2—41no—
544C2—41no—
545C2—82no—
546C2C13×#240611yescharacteristic
547C2C13×#301911yescharacteristic
548C2C13×#302011yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3492C2
LCSG ▷ C22×C4 ▷ 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×#3093C2semidirect
3. C13×#2317C2semidirect
4. C13×#2061C2semidirect
5. C13×#2060C2semidirect
6. C13×#2040C2semidirect
7. C13×#2039C2semidirect
8. C13×#1897C2semidirect
9. C13×#1860C2semidirect
10. C13×#1859C2semidirect
11. C13×#1821C2semidirect
115. #24079C13direct (N × H)
184. C42×C13#41semidirect
185. C42×C13#41semidirect
187. #3093C2×C13semidirect
188. #2317C2×C13semidirect
189. #2061C2×C13semidirect
190. #2060C2×C13semidirect
191. #2040C2×C13semidirect
192. #2039C2×C13semidirect
193. #1897C2×C13semidirect
194. #1860C2×C13semidirect
195. #1859C2×C13semidirect
196. #1821C2×C13semidirect
457. C42C13×#41semidirect
458. C42C13×#41semidirect
459. C13#24079direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34922
C13×#30932
C13×#23172
C13×#20612
C13×#20602
C13×#20402
C13×#20392
C13×#18972
C13×#18602
C13×#18592
C13×#18212
#2407913