Finite Group Databasebeta

← C13×#24078 #15710417

Subgroups — C13×#24078 #15710417

Order 3328.

1038 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
1C13×#3493C211yesmaximal, characteristic
2C13×#3093C212yesmaximal, complemented
3C13×#2285C211yesmaximal, characteristic, complemented
4C13×#2061C211yesmaximal, characteristic, complemented
5C13×#2060C211yesmaximal, characteristic, complemented
6C13×#2040C211yesmaximal, characteristic, complemented
7C13×#2039C211yesmaximal, characteristic, complemented
8C13×#1896C212yesmaximal, complemented
9C13×#1860C212yesmaximal, complemented
10C13×#1859C212yesmaximal, complemented
11C13×#1822C211yesmaximal, characteristic, complemented
12C13×#556—22no—
13C13×#555—22no—
14C13×#553—22no—
15C13×#552—22no—
16C13×#544C2211yescharacteristic
17C13×#538—22no—
18C13×#537C2211yescharacteristic
19C13×#529—22no—
20C13×#525C2212yes—
21C13×#520C2212yes—
22C2×C13×#117C2211yescharacteristic
23C2×C13×#117C2211yescharacteristic
24C22×C42×C13C2211yescharacteristic
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×#384C2211yescharacteristic
37C13×#384C2211yescharacteristic
38C13×#382C2211yescharacteristic
39C13×#382C2211yescharacteristic
40C13×#380—22no—
41C4×C13×C4⋊C4—22no—
42C13×#343C2211yescharacteristic
43C13×#343C2211yescharacteristic
44C13×#343C2212yes—
45C13×#339C2212yes—
46C13×#339C2212yes—
47C2×C13×#41C2312yes—
48C23×C4×C13—21no—
49C23×C4×C13C2311yescharacteristic
50C2×C13×M16C2312yes—
51C2×C13×M16C2312yes—
52C13×C4⋊Q8—22no—
53C13×#126—24no—
54C13×#126—24no—
55C13×#125—22no—
56C13×#125—22no—
57C13×#124—22no—
58C13×#124—24no—
59C13×#123—24no—
60C13×#123—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8D412yes—
64C13×C22⋊Q8D412yes—
65C13×#121—24no—
66C13×#121—22no—
67C13×#121—22no—
68C13×#121D412yes—
69C13×#121D412yes—
70C13×#120—22no—
71C4×Q8×C13—22no—
72C4×Q8×C13—22no—
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C4×D4×C13—24no—
76C4×D4×C13—22no—
77C4×D4×C13—22no—
78C13×#117—24no—
79C13×#117—22no—
80C13×#117—22no—
81C13×#117—22no—
82C13×#117—22no—
83C13×#117—22no—
84C13×#117C2312yes—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C4⋊C4C2311yescharacteristic
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C22⋊C4—21no—
93C2×C13×C22⋊C4D412yes—
94C2×C42×C13—21no—
95C2×C42×C13—22no—
96C2×C42×C13—22no—
97C2×C42×C13—21no—
98C2×C42×C13D412yes—
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#24078C1311yesmaximal, characteristic, direct product factor, Sylow
116C24×C13C2×D411yescharacteristic
117C13×#41—22no—
118C13×#41—22no—
119C13×#41—22no—
120C13×#41—22no—
121C2×Q8×C13—22no—
122C2×Q8×C13C2×D412yes—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13C2×D412yes—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—24no—
133C22×C4×C13—21no—
134C22×C4×C13—24no—
135C22×C4×C13—22no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2×D412yes—
142C22×C4×C13C2×D412yes—
143C22×C4×C13C2×D412yes—
144C22×C4×C13C2×D412yes—
145C22×C4×C13C2411yescharacteristic
146C13×M16—22no—
147C13×M16—22no—
148C13×M16—22no—
149C13×M16—22no—
150C2×C8×C13—22no—
151C2×C8×C13—22no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—22no—
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—22no—
162C13×C4⋊C4—44no—
163C13×C4⋊C4—44no—
164C13×C4⋊C4C2×D412yes—
165C13×C4⋊C4C2×D412yes—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—22no—
174C13×C22⋊C4—42no—
175C42×C13—24no—
176C42×C13—24no—
177C42×C13—22no—
178C42×C13—22no—
179C42×C13—22no—
180C42×C13—21no—
181C42×C13—21no—
182C42×C13—41no—
183C42×C13—41no—
184C42×C13#4112yes—
185C42×C13#4112yes—
186#3493C2×C1311yescharacteristic
187#3093C2×C1312yescomplemented
188#2285C2×C1311yescharacteristic, complemented
189#2061C2×C1311yescharacteristic, complemented
190#2060C2×C1311yescharacteristic, complemented
191#2040C2×C1311yescharacteristic, complemented
192#2039C2×C1311yescharacteristic, complemented
193#1896C2×C1312yescomplemented
194#1860C2×C1312yescomplemented
195#1859C2×C1312yescomplemented
196#1822C2×C1311yescharacteristic, complemented
197C23×C13—21no—
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—41no—
201C23×C13—41no—
202C23×C13#12012yes—
203C23×C13C22×D411yescharacteristic
204Q8×C13—22no—
205Q8×C13—22no—
206Q8×C13—82no—
207D4×C13—22no—
208D4×C13—22no—
209D4×C13—42no—
210D4×C13—42no—
211D4×C13—82no—
212D4×C13—82no—
213D4×C13—82no—
214C2×C4×C13—22no—
215C2×C4×C13—22no—
216C2×C4×C13—21no—
217C2×C4×C13—22no—
218C2×C4×C13—21no—
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—22no—
229C2×C4×C13—48no—
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—41no—
239C2×C4×C13—41no—
240C2×C4×C13—84no—
241C2×C4×C13#12011yescharacteristic
242C2×C4×C13#12011yescharacteristic
243C2×C4×C13C22×D412yes—
244C2×C4×C13C2×#4111yescharacteristic
245C2×C4×C13C2×#4111yescharacteristic
246C2×C4×C132−1+412yes—
247C8×C13—42no—
248C8×C13—42no—
249#556—22no—
250#555—22no—
251#553—22no—
252#552—22no—
253#544C22×C1311yescharacteristic
254#538—22no—
255#537C22×C1311yescharacteristic
256#529—22no—
257#525C22×C1312yes—
258#520C22×C1312yes—
259C2×#117C22×C1311yescharacteristic
260C2×#117C22×C1311yescharacteristic
261C22×C42C22×C1311yescharacteristic
262#485—22no—
263#485—22no—
264#482—22no—
265#482—22no—
266#428C22×C1312yes—
267#428C22×C1312yes—
268C2×#104C22×C1312yes—
269C2×#104C22×C1312yes—
270#417C22×C1312yes—
271#417C22×C1312yes—
272#407C22×C1312yes—
273#384C22×C1311yescharacteristic
274#384C22×C1311yescharacteristic
275#382C22×C1311yescharacteristic
276#382C22×C1311yescharacteristic
277#380—22no—
278C4×C4⋊C4—22no—
279#343C22×C1311yescharacteristic
280#343C22×C1311yescharacteristic
281#343C22×C1312yes—
282#339C22×C1312yes—
283#339C22×C1312yes—
284C22×C13—21no—
285C22×C13—21no—
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×C13C2×#12011yescharacteristic
295C22×C13#52511yescharacteristic
296C22×C13#53611yescharacteristic
297C4×C13—24no—
298C4×C13—21no—
299C4×C13—21no—
300C4×C13—42no—
301C4×C13—42no—
302C4×C13—42no—
303C4×C13—42no—
304C4×C13—42no—
305C4×C13—42no—
306C4×C13—81no—
307C4×C13—81no—
308C4×C13#54712yes—
309C4×C13#54712yes—
310C2×#41C23×C1312yes—
311C23×C4—21no—
312C23×C4C23×C1311yescharacteristic
313C2×M16C23×C1312yes—
314C2×M16C23×C1312yes—
315C4⋊Q8—22no—
316#126—24no—
317#126—24no—
318#125—22no—
319#125—22no—
320#124—22no—
321#124—24no—
322#123—24no—
323#123—22no—
324C22⋊Q8—22no—
325C22⋊Q8—22no—
326C22⋊Q8D4×C1312yes—
327C22⋊Q8D4×C1312yes—
328#121—24no—
329#121—22no—
330#121—22no—
331#121D4×C1312yes—
332#121D4×C1312yes—
333#120—22no—
334C4×Q8—22no—
335C4×Q8—22no—
336C4×D4—22no—
337C4×D4—22no—
338C4×D4—24no—
339C4×D4—22no—
340C4×D4—22no—
341#117—24no—
342#117—22no—
343#117—22no—
344#117—22no—
345#117—22no—
346#117—22no—
347#117C23×C1312yes—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4C23×C1311yescharacteristic
352C2×C4⋊C4C23×C1311yescharacteristic
353C2×C4⋊C4C23×C1311yescharacteristic
354C2×C4⋊C4C23×C1311yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4D4×C1312yes—
357C2×C42—21no—
358C2×C42—22no—
359C2×C42—22no—
360C2×C42—21no—
361C2×C42D4×C1312yes—
362C2×C42C23×C1311yescharacteristic
363C2×C42C23×C1311yescharacteristic
364#107—22no—
365#107—22no—
366#106—22no—
367#106—22no—
368#104—24no—
369#104—24no—
370#103—22no—
371#103—22no—
372#102—22no—
373#102—22no—
374C22⋊C8—22no—
375C22⋊C8—22no—
376#95—22no—
377#95—22no—
378C2×C13—21no—
379C2×C13—21no—
380C2×C13—42no—
381C2×C13—82no—
382C2×C13#240611yescharacteristic
383C2×C13#301811yescharacteristic
384C2×C13#301811yescharacteristic
385C24C2×D4×C1311yescharacteristic
386#41—22no—
387#41—22no—
388#41—22no—
389#41—22no—
390C2×Q8—22no—
391C2×Q8C2×D4×C1312yes—
392C2×D4—22no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—22no—
396C2×D4C2×D4×C1312yes—
397C22×C4—21no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—21no—
403C22×C4—24no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—42no—
408C22×C4—42no—
409C22×C4C2×D4×C1311yescharacteristic
410C22×C4C2×D4×C1312yes—
411C22×C4C2×D4×C1312yes—
412C22×C4C2×D4×C1312yes—
413C22×C4C2×D4×C1312yes—
414C22×C4C24×C1311yescharacteristic
415M16—22no—
416M16—22no—
417M16—22no—
418M16—22no—
419C2×C8—22no—
420C2×C8—22no—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—22no—
426C4⋊C4—22no—
427C4⋊C4—22no—
428C4⋊C4—22no—
429C4⋊C4—22no—
430C4⋊C4—22no—
431C4⋊C4—44no—
432C4⋊C4—44no—
433C4⋊C4C2×D4×C1312yes—
434C4⋊C4C2×D4×C1312yes—
435C22⋊C4—24no—
436C22⋊C4—24no—
437C22⋊C4—24no—
438C22⋊C4—22no—
439C22⋊C4—22no—
440C22⋊C4—22no—
441C22⋊C4—22no—
442C22⋊C4—22no—
443C22⋊C4—42no—
444C42—24no—
445C42—24no—
446C42—22no—
447C42—22no—
448C42—22no—
449C42—21no—
450C42—21no—
451C42—41no—
452C42—41no—
453C42C13×#4112yes—
454C42C13×#4112yes—
455C13#2407811yescharacteristic, direct product factor, Sylow
456C23—21no—
457C23—21no—
458C23—22no—
459C23—41no—
460C23—41no—
461C23C13×#12012yes—
462C23C22×D4×C1311yescharacteristic
463Q8—22no—
464Q8—22no—
465Q8—82no—
466D4—22no—
467D4—22no—
468D4—42no—
469D4—42no—
470D4—82no—
471D4—82no—
472D4—82no—
473C2×C4—22no—
474C2×C4—22no—
475C2×C4—21no—
476C2×C4—22no—
477C2×C4—21no—
478C2×C4—22no—
479C2×C4—22no—
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—48no—
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—41no—
498C2×C4—41no—
499C2×C4—84no—
500C2×C4C13×#12011yescharacteristic
501C2×C4C13×#12011yescharacteristic
502C2×C4C22×D4×C1312yes—
503C2×C4C2×C13×#4111yescharacteristic
504C2×C4C2×C13×#4111yescharacteristic
505C2×C4C13×2−1+412yes—
506C8—42no—
507C8—42no—
508C22—21no—
509C22—21no—
510C22—22no—
511C22—22no—
512C22—22no—
513C22—42no—
514C22—42no—
515C22—42no—
516C22—42no—
517C22—42no—
518C22C2×C13×#12011yescharacteristic
519C22C13×#52511yescharacteristic
520C22C13×#53611yescharacteristic
521C4—24no—
522C4—21no—
523C4—21no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—42no—
528C4—42no—
529C4—42no—
530C4—81no—
531C4—81no—
532C4C13×#54712yes—
533C4C13×#54712yes—
534C2—21no—
535C2—21no—
536C2—42no—
537C2—82no—
538C2C13×#240611yescharacteristic
539C2C13×#301811yescharacteristic
540C2C13×#301811yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3493C2
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×#2285C2semidirect
4. C13×#2061C2semidirect
5. C13×#2060C2semidirect
6. C13×#2040C2semidirect
7. C13×#2039C2semidirect
8. C13×#1896C2semidirect
9. C13×#1860C2semidirect
10. C13×#1859C2semidirect
11. C13×#1822C2semidirect
115. #24078C13direct (N × H)
187. #3093C2×C13semidirect
188. #2285C2×C13semidirect
189. #2061C2×C13semidirect
190. #2060C2×C13semidirect
191. #2040C2×C13semidirect
192. #2039C2×C13semidirect
193. #1896C2×C13semidirect
194. #1860C2×C13semidirect
195. #1859C2×C13semidirect
196. #1822C2×C13semidirect
455. C13#24078direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#34932
C13×#30932
C13×#22852
C13×#20612
C13×#20602
C13×#20402
C13×#20392
C13×#18962
C13×#18602
C13×#18592
C13×#18222
#2407813