Finite Group Databasebeta

← C13×#24097 #15710436

Subgroups — C13×#24097 #15710436

Order 3328.

1138 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#554C211yesmaximal, characteristic
2C2×C13×#483C211yesmaximal, characteristic, complemented
3C22×C13×#106C211yesmaximal, characteristic, complemented
4C13×#2486C211yesmaximal, characteristic
5C13×#2058C212yesmaximal, complemented
6C13×#2035C212yesmaximal, complemented
7C13×#1892C211yesmaximal, characteristic, complemented
8C13×#1869C211yesmaximal, characteristic
9C13×#1865C212yesmaximal, complemented
10C13×#1853C212yesmaximal, complemented
11C13×#1824C211yesmaximal, characteristic, complemented
12C23×C8×C13C2211yescharacteristic
13C13×#554—24no—
14C13×#554—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#125—21no—
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8—21no—
20C2×C13×C22⋊Q8C2211yescharacteristic
21C2×C13×C22⋊Q8C2211yescharacteristic
22C2×C4×Q8×C13C2211yescharacteristic
23C2×C4×D4×C13—21no—
24C2×C4×D4×C13C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C13×#483—24no—
29C2×C13×#106—24no—
30C2×C13×#106C2212yes—
31C2×C13×#106C2212yes—
32C2×C13×#106C2212yes—
33C2×C13×#103C2212yes—
34C2×C13×#103C2212yes—
35C2×C13×C22⋊C8C2212yes—
36C2×C13×C22⋊C8C2211yescharacteristic
37C13×#398—21no—
38C13×#397—21no—
39C13×#389C2212yes—
40C13×#381—21no—
41C13×#380C2212yes—
42C13×#380C2211yescharacteristic
43C13×#340C2212yes—
44C13×#340C2212yes—
45C13×#340C2212yes—
46C13×#336C2212yes—
47C22×Q8×C13—21no—
48C22×Q8×C13C2311yescharacteristic
49C22×D4×C13D411yescharacteristic
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13—21no—
53C23×C4×C13C2311yescharacteristic
54C23×C4×C13C2311yescharacteristic
55C22×C8×C13—22no—
56C22×C8×C13—24no—
57C22×C8×C13C2312yes—
58C22×C8×C13C2312yes—
59C13×C4⋊Q8—22no—
60C13×C4⋊Q8—22no—
61C13×#125—28no—
62C13×#123—44no—
63C13×C22⋊Q8—28no—
64C13×C22⋊Q8—28no—
65C13×C22⋊Q8—22no—
66C13×C22⋊Q8—22no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8D414yes—
69C4×Q8×C13—22no—
70C4×Q8×C13—22no—
71C4×D4×C13—28no—
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—21no—
87C2×C13×C4⋊C4D411yescharacteristic
88C2×C13×C4⋊C4D414yes—
89C2×C13×C4⋊C4C2312yes—
90C2×C13×C4⋊C4C2312yes—
91C2×C13×C4⋊C4C2311yescharacteristic
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C13×C22⋊C4D411yescharacteristic
100C2×C42×C13—21no—
101C2×C42×C13C2311yescharacteristic
102C13×#106—24no—
103C13×#106—24no—
104C13×#106—24no—
105C13×#103—24no—
106C13×#103—24no—
107C13×C22⋊C8—22no—
108C13×C22⋊C8—24no—
109C13×#95—22no—
110C13×#95—21no—
111C13×#95—22no—
112#24097C1311yesmaximal, characteristic, direct product factor, Sylow
113C24×C13C2×D411yescharacteristic
114C24×C13C2×D411yescharacteristic
115C2×Q8×C13—24no—
116C2×Q8×C13—21no—
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—82no—
120C2×Q8×C13C2×D412yes—
121C2×D4×C13—22no—
122C2×D4×C13—22no—
123C2×D4×C13SD1614yes—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—24no—
131C22×C4×C13—24no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—42no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13—82no—
142C22×C4×C13—82no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2411yescharacteristic
150C2×C8×C13—28no—
151C2×C8×C13—22no—
152C2×C8×C13—22no—
153C2×C8×C13—22no—
154C2×C8×C13—22no—
155C2×C8×C13—22no—
156C2×C8×C13#4114yes—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—22no—
171C13×C4⋊C4—42no—
172C13×C4⋊C4—44no—
173C13×C4⋊C4C2×D412yes—
174C13×C4⋊C4C2×D412yes—
175C13×C4⋊C4C2×D412yes—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—24no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—42no—
181C13×C22⋊C4—44no—
182C42×C13—24no—
183C42×C13—21no—
184C42×C13—21no—
185C2×#554C2×C1311yescharacteristic
186C2×#483C2×C1311yescharacteristic, complemented
187C22×#106C2×C1311yescharacteristic, complemented
188#2486C2×C1311yescharacteristic
189#2058C2×C1312yescomplemented
190#2035C2×C1312yescomplemented
191#1892C2×C1311yescharacteristic, complemented
192#1869C2×C1311yescharacteristic
193#1865C2×C1312yescomplemented
194#1853C2×C1312yescomplemented
195#1824C2×C1311yescharacteristic, complemented
196C23×C13—22no—
197C23×C13—22no—
198C23×C13—21no—
199C23×C13—22no—
200C23×C13—21no—
201C23×C13—22no—
202C23×C13#12012yes—
203C23×C13C2×SD1612yes—
204C23×C13C2×SD1612yes—
205C23×C13#13712yes—
206C23×C13C22×D411yescharacteristic
207Q8×C13—24no—
208Q8×C13—41no—
209Q8×C13—41no—
210Q8×C13—84no—
211D4×C13—28no—
212C2×C4×C13—21no—
213C2×C4×C13—22no—
214C2×C4×C13—21no—
215C2×C4×C13—22no—
216C2×C4×C13—22no—
217C2×C4×C13—24no—
218C2×C4×C13—22no—
219C2×C4×C13—21no—
220C2×C4×C13—22no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—42no—
227C2×C4×C13—42no—
228C2×C4×C13—42no—
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—84no—
241C2×C4×C13—84no—
242C2×C4×C13#12012yes—
243C2×C4×C13C2×SD1612yes—
244C2×C4×C13C22×D411yescharacteristic
245C2×C4×C13C22×D411yescharacteristic
246C2×C4×C13C2×#4112yes—
247C2×C4×C132−1+412yes—
248C8×C13—24no—
249C8×C13—42no—
250C23×C8C22×C1311yescharacteristic
251#554—24no—
252#554—24no—
253C2×C4⋊Q8C22×C1311yescharacteristic
254C2×#125—21no—
255C2×#123—21no—
256C2×C22⋊Q8—21no—
257C2×C22⋊Q8—21no—
258C2×C22⋊Q8C22×C1311yescharacteristic
259C2×C22⋊Q8C22×C1311yescharacteristic
260C2×C4×Q8C22×C1311yescharacteristic
261C2×C4×D4—21no—
262C2×C4×D4C22×C1311yescharacteristic
263C22×C4⋊C4C22×C1311yescharacteristic
264C22×C4⋊C4C22×C1311yescharacteristic
265C22×C4⋊C4C22×C1311yescharacteristic
266#483—24no—
267C2×#106—24no—
268C2×#106C22×C1312yes—
269C2×#106C22×C1312yes—
270C2×#106C22×C1312yes—
271C2×#103C22×C1312yes—
272C2×#103C22×C1312yes—
273C2×C22⋊C8C22×C1311yescharacteristic
274C2×C22⋊C8C22×C1312yes—
275#398—21no—
276#397—21no—
277#389C22×C1312yes—
278#381—21no—
279#380C22×C1311yescharacteristic
280#380C22×C1312yes—
281#340C22×C1312yes—
282#340C22×C1312yes—
283#340C22×C1312yes—
284#336C22×C1312yes—
285C22×C13—24no—
286C22×C13—24no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—24no—
290C22×C13—22no—
291C22×C13—42no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13#44814yes—
295C22×C13C2×#12011yescharacteristic
296C22×C13#54712yes—
297C22×C13C22×SD1611yescharacteristic
298C22×C13C2×#13711yescharacteristic
299C22×C13#57712yes—
300C4×C13—22no—
301C4×C13—22no—
302C4×C13—41no—
303C4×C13—42no—
304C4×C13—41no—
305C4×C13—42no—
306C4×C13—42no—
307C4×C13—42no—
308C4×C13—82no—
309C4×C13—82no—
310C4×C13#52511yescharacteristic
311C4×C13#53611yescharacteristic
312C4×C13#54712yes—
313C22×Q8—21no—
314C22×Q8C23×C1311yescharacteristic
315C22×D4D4×C1311yescharacteristic
316C23×C4—21no—
317C23×C4—21no—
318C23×C4—21no—
319C23×C4C23×C1311yescharacteristic
320C23×C4C23×C1311yescharacteristic
321C22×C8—22no—
322C22×C8—24no—
323C22×C8C23×C1312yes—
324C22×C8C23×C1312yes—
325C4⋊Q8—22no—
326C4⋊Q8—22no—
327#125—28no—
328#123—44no—
329C22⋊Q8—28no—
330C22⋊Q8—28no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—22no—
334C22⋊Q8D4×C1314yes—
335C4×Q8—22no—
336C4×Q8—22no—
337C4×D4—28no—
338C4×D4—22no—
339C4×D4—22no—
340C2×C4⋊C4—21no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—22no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4D4×C1311yescharacteristic
354C2×C4⋊C4D4×C1314yes—
355C2×C4⋊C4C23×C1312yes—
356C2×C4⋊C4C23×C1312yes—
357C2×C4⋊C4C23×C1311yescharacteristic
358C2×C4⋊C4C23×C1311yescharacteristic
359C2×C4⋊C4C23×C1311yescharacteristic
360C2×C22⋊C4—21no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—22no—
364C2×C22⋊C4D4×C1311yescharacteristic
365C2×C22⋊C4D4×C1311yescharacteristic
366C2×C42—21no—
367C2×C42C23×C1311yescharacteristic
368#106—24no—
369#106—24no—
370#106—24no—
371#103—24no—
372#103—24no—
373C22⋊C8—22no—
374C22⋊C8—24no—
375#95—22no—
376#95—21no—
377#95—22no—
378C2×C13—24no—
379C2×C13—42no—
380C2×C13#240611yescharacteristic
381C2×C13C2×#44811yescharacteristic
382C2×C13#300911yescharacteristic
383C2×C13#333512yes—
384C2×C13#334412yes—
385C24C2×D4×C1311yescharacteristic
386C24C2×D4×C1311yescharacteristic
387C2×Q8—24no—
388C2×Q8—21no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—82no—
392C2×Q8C2×D4×C1312yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4C13×SD1614yes—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—42no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—82no—
414C22×C4—82no—
415C22×C4C2×D4×C1311yescharacteristic
416C22×C4C2×D4×C1311yescharacteristic
417C22×C4C2×D4×C1311yescharacteristic
418C22×C4C2×D4×C1312yes—
419C22×C4C2×D4×C1312yes—
420C22×C4C2×D4×C1311yescharacteristic
421C22×C4C24×C1311yescharacteristic
422C2×C8—28no—
423C2×C8—22no—
424C2×C8—22no—
425C2×C8—22no—
426C2×C8—22no—
427C2×C8—22no—
428C2×C8C13×#4114yes—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—24no—
435C4⋊C4—22no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—22no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—42no—
444C4⋊C4—44no—
445C4⋊C4C2×D4×C1312yes—
446C4⋊C4C2×D4×C1312yes—
447C4⋊C4C2×D4×C1312yes—
448C22⋊C4—24no—
449C22⋊C4—24no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—42no—
453C22⋊C4—44no—
454C42—24no—
455C42—21no—
456C42—21no—
457C13#2409711yescharacteristic, direct product factor, Sylow
458C23—22no—
459C23—22no—
460C23—21no—
461C23—22no—
462C23—21no—
463C23—22no—
464C23C13×#12012yes—
465C23C2×C13×SD1612yes—
466C23C2×C13×SD1612yes—
467C23C13×#13712yes—
468C23C22×D4×C1311yescharacteristic
469Q8—24no—
470Q8—41no—
471Q8—41no—
472Q8—84no—
473D4—28no—
474C2×C4—21no—
475C2×C4—22no—
476C2×C4—21no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—84no—
502C2×C4—84no—
503C2×C4—84no—
504C2×C4C13×#12012yes—
505C2×C4C2×C13×SD1612yes—
506C2×C4C22×D4×C1311yescharacteristic
507C2×C4C22×D4×C1311yescharacteristic
508C2×C4C2×C13×#4112yes—
509C2×C4C13×2−1+412yes—
510C8—24no—
511C8—42no—
512C22—22no—
513C22—24no—
514C22—24no—
515C22—22no—
516C22—24no—
517C22—22no—
518C22—41no—
519C22—42no—
520C22—41no—
521C22C13×#44814yes—
522C22C2×C13×#12011yescharacteristic
523C22C13×#54712yes—
524C22C22×C13×SD1611yescharacteristic
525C22C2×C13×#13711yescharacteristic
526C22C13×#57712yes—
527C4—22no—
528C4—22no—
529C4—41no—
530C4—42no—
531C4—42no—
532C4—42no—
533C4—41no—
534C4—42no—
535C4—82no—
536C4—82no—
537C4C13×#52511yescharacteristic
538C4C13×#53611yescharacteristic
539C4C13×#54712yes—
540C2—24no—
541C2—42no—
542C2C13×#240611yescharacteristic
543C2C2×C13×#44811yescharacteristic
544C2C13×#300911yescharacteristic
545C2C13×#333512yes—
546C2C13×#334412yes—
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. C22×C13×#106C2semidirect
5. C13×#2058C2semidirect
6. C13×#2035C2semidirect
7. C13×#1892C2semidirect
9. C13×#1865C2semidirect
10. C13×#1853C2semidirect
11. C13×#1824C2semidirect
112. #24097C13direct (N × H)
186. C2×#483C2×C13semidirect
187. C22×#106C2×C13semidirect
189. #2058C2×C13semidirect
190. #2035C2×C13semidirect
191. #1892C2×C13semidirect
193. #1865C2×C13semidirect
194. #1853C2×C13semidirect
195. #1824C2×C13semidirect
457. C13#24097direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5542
C2×C13×#4832
C22×C13×#1062
C13×#24862
C13×#20582
C13×#20352
C13×#18922
C13×#18692
C13×#18652
C13×#18532
C13×#18242
#2409713