Finite Group Databasebeta

← C13×#24104 #15710443

Subgroups — C13×#24104 #15710443

Order 3328.

1146 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#555C211yesmaximal, characteristic
2C2×C13×#481C211yesmaximal, characteristic, complemented
3C2×C13×#428C211yesmaximal, characteristic, complemented
4C13×#2486C211yesmaximal, characteristic, complemented
5C13×#2058C212yesmaximal, complemented
6C13×#2034C212yesmaximal, complemented
7C13×#1895C211yesmaximal, characteristic, complemented
8C13×#1870C211yesmaximal, characteristic, complemented
9C13×#1862C212yesmaximal, complemented
10C13×#1854C212yesmaximal, complemented
11C13×#1825C211yesmaximal, characteristic, complemented
12C22×C13×M16C2211yescharacteristic
13C13×#555—24no—
14C13×#555—24no—
15C2×C13×C4⋊Q8C2211yescharacteristic
16C2×C13×#124—21no—
17C2×C13×#124—21no—
18C2×C13×#123—21no—
19C2×C13×#121—21no—
20C2×C13×#121C2211yescharacteristic
21C2×C13×#121C2211yescharacteristic
22C2×C4×D4×C13C2211yescharacteristic
23C2×C4×D4×C13C2211yescharacteristic
24C2×C13×#117—21no—
25C2×C13×#117C2211yescharacteristic
26C2×C13×#117C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C13×#481—24no—
29C13×#428—24no—
30C2×C13×#107C2212yes—
31C2×C13×#106C2212yes—
32C2×C13×#106C2212yes—
33C2×C13×#102C2212yes—
34C2×C13×#102C2212yes—
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×D4×C13—21no—
49C22×D4×C13—21no—
50C22×D4×C13D411yescharacteristic
51C22×D4×C13C2311yescharacteristic
52C23×C4×C13—21no—
53C23×C4×C13—21no—
54C23×C4×C13C2311yescharacteristic
55C23×C4×C13C2311yescharacteristic
56C2×C13×M16—22no—
57C2×C13×M16—24no—
58C22×C8×C13C2312yes—
59C22×C8×C13C2312yes—
60C13×C4⋊Q8—22no—
61C13×C4⋊Q8—22no—
62C13×#124—28no—
63C13×#124—28no—
64C13×#123—44no—
65C13×#121—28no—
66C13×#121—22no—
67C13×#121—22no—
68C13×#121—22no—
69C13×#121D414yes—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C13×#117—28no—
75C13×#117—22no—
76C13×#117—22no—
77C13×#117—22no—
78C13×#117D414yes—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—21no—
84C2×C13×C4⋊C4D411yescharacteristic
85C2×C13×C4⋊C4C2312yes—
86C2×C13×C4⋊C4C2312yes—
87C2×C13×C4⋊C4C2311yescharacteristic
88C2×C13×C4⋊C4C2311yescharacteristic
89C2×C13×C4⋊C4C2311yescharacteristic
90C2×C13×C22⋊C4—21no—
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⋊C4—22no—
97C2×C13×C22⋊C4D411yescharacteristic
98C2×C13×C22⋊C4D411yescharacteristic
99C2×C42×C13—21no—
100C2×C42×C13—21no—
101C2×C42×C13C2311yescharacteristic
102C13×#107—24no—
103C13×#106—24no—
104C13×#106—24no—
105C13×#102—24no—
106C13×#102—24no—
107C13×C22⋊C8—22no—
108C13×C22⋊C8—24no—
109C13×#95—22no—
110C13×#95—21no—
111C13×#95—22no—
112#24104C1311yesmaximal, characteristic, direct product factor, Sylow
113C24×C13—21no—
114C24×C13C2×D411yescharacteristic
115C24×C13C2×D411yescharacteristic
116C2×Q8×C13—24no—
117C2×Q8×C13—82no—
118C2×D4×C13—22no—
119C2×D4×C13—24no—
120C2×D4×C13—24no—
121C2×D4×C13—22no—
122C2×D4×C13—21no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—41no—
126C2×D4×C13—82no—
127C2×D4×C13—82no—
128C2×D4×C13C2×D412yes—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—24no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C13×M16—28no—
154C2×C8×C13—22no—
155C2×C8×C13—22no—
156C2×C8×C13—22no—
157C2×C8×C13—22no—
158C2×C8×C13—22no—
159C2×C8×C13#4114yes—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—22no—
166C13×C4⋊C4—22no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4—44no—
171C13×C4⋊C4C2×D412yes—
172C13×C4⋊C4C2×D412yes—
173C13×C4⋊C4C2×D412yes—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—24no—
176C13×C22⋊C4—24no—
177C13×C22⋊C4—24no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—24no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—42no—
182C13×C22⋊C4—44no—
183C42×C13—24no—
184C42×C13—24no—
185C42×C13—21no—
186C42×C13—21no—
187C2×#555C2×C1311yescharacteristic
188C2×#481C2×C1311yescharacteristic, complemented
189C2×#428C2×C1311yescharacteristic, complemented
190#2486C2×C1311yescharacteristic, complemented
191#2058C2×C1312yescomplemented
192#2034C2×C1312yescomplemented
193#1895C2×C1311yescharacteristic, complemented
194#1870C2×C1311yescharacteristic, complemented
195#1862C2×C1312yescomplemented
196#1854C2×C1312yescomplemented
197#1825C2×C1311yescharacteristic, complemented
198C23×C13—22no—
199C23×C13—21no—
200C23×C13—21no—
201C23×C13—22no—
202C23×C13—21no—
203C23×C13—22no—
204C23×C13—22no—
205C23×C13—21no—
206C23×C13—21no—
207C23×C13—22no—
208C23×C13—42no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—42no—
212C23×C13#12012yes—
213C23×C13C22×D411yescharacteristic
214Q8×C13—84no—
215D4×C13—24no—
216D4×C13—44no—
217D4×C13—41no—
218D4×C13—41no—
219D4×C13—84no—
220D4×C13—84no—
221C2×C4×C13—21no—
222C2×C4×C13—22no—
223C2×C4×C13—21no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—24no—
227C2×C4×C13—21no—
228C2×C4×C13—22no—
229C2×C4×C13—21no—
230C2×C4×C13—22no—
231C2×C4×C13—22no—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—48no—
235C2×C4×C13—41no—
236C2×C4×C13—41no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—41no—
240C2×C4×C13—41no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—42no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—84no—
249C2×C4×C13#12012yes—
250C2×C4×C13AGL(1,ℤ/8)12yes—
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C22×D411yescharacteristic
253C2×C4×C13C2×#4112yes—
254C2×C4×C132−1+412yes—
255C8×C13—24no—
256C8×C13—42no—
257C22×M16C22×C1311yescharacteristic
258#555—24no—
259#555—24no—
260C2×C4⋊Q8C22×C1311yescharacteristic
261C2×#124—21no—
262C2×#124—21no—
263C2×#123—21no—
264C2×#121—21no—
265C2×#121C22×C1311yescharacteristic
266C2×#121C22×C1311yescharacteristic
267C2×C4×D4C22×C1311yescharacteristic
268C2×C4×D4C22×C1311yescharacteristic
269C2×#117—21no—
270C2×#117C22×C1311yescharacteristic
271C2×#117C22×C1311yescharacteristic
272C22×C4⋊C4C22×C1311yescharacteristic
273#481—24no—
274#428—24no—
275C2×#107C22×C1312yes—
276C2×#106C22×C1312yes—
277C2×#106C22×C1312yes—
278C2×#102C22×C1312yes—
279C2×#102C22×C1312yes—
280C2×C22⋊C8C22×C1311yescharacteristic
281C2×C22⋊C8C22×C1312yes—
282#398—21no—
283#397—21no—
284#389C22×C1312yes—
285#381—21no—
286#380C22×C1311yescharacteristic
287#380C22×C1312yes—
288#340C22×C1312yes—
289#340C22×C1312yes—
290#340C22×C1312yes—
291#336C22×C1312yes—
292C22×C13—22no—
293C22×C13—22no—
294C22×C13—22no—
295C22×C13—42no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—41no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—42no—
305C22×C13—82no—
306C22×C13—82no—
307C22×C13C2×#12011yescharacteristic
308C22×C13#54712yes—
309C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
310C22×C13#57511yescharacteristic
311C22×C13#57712yes—
312C4×C13—22no—
313C4×C13—22no—
314C4×C13—41no—
315C4×C13—42no—
316C4×C13—41no—
317C4×C13—42no—
318C4×C13—42no—
319C4×C13—82no—
320C4×C13—82no—
321C4×C13#52511yescharacteristic
322C4×C13#53611yescharacteristic
323C4×C13#54712yes—
324C22×Q8—21no—
325C22×D4—21no—
326C22×D4—21no—
327C22×D4D4×C1311yescharacteristic
328C22×D4C23×C1311yescharacteristic
329C23×C4—21no—
330C23×C4—21no—
331C23×C4C23×C1311yescharacteristic
332C23×C4C23×C1311yescharacteristic
333C2×M16—22no—
334C2×M16—24no—
335C22×C8C23×C1312yes—
336C22×C8C23×C1312yes—
337C4⋊Q8—22no—
338C4⋊Q8—22no—
339#124—28no—
340#124—28no—
341#123—44no—
342#121—28no—
343#121—22no—
344#121—22no—
345#121—22no—
346#121D4×C1314yes—
347C4×D4—22no—
348C4×D4—22no—
349C4×D4—22no—
350C4×D4—22no—
351#117—28no—
352#117—22no—
353#117—22no—
354#117—22no—
355#117D4×C1314yes—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—22no—
361C2×C4⋊C4D4×C1311yescharacteristic
362C2×C4⋊C4C23×C1312yes—
363C2×C4⋊C4C23×C1312yes—
364C2×C4⋊C4C23×C1311yescharacteristic
365C2×C4⋊C4C23×C1311yescharacteristic
366C2×C4⋊C4C23×C1311yescharacteristic
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4D4×C1311yescharacteristic
375C2×C22⋊C4D4×C1311yescharacteristic
376C2×C42—21no—
377C2×C42—21no—
378C2×C42C23×C1311yescharacteristic
379#107—24no—
380#106—24no—
381#106—24no—
382#102—24no—
383#102—24no—
384C22⋊C8—22no—
385C22⋊C8—24no—
386#95—22no—
387#95—21no—
388#95—22no—
389C2×C13—42no—
390C2×C13—81no—
391C2×C13—82no—
392C2×C13#240611yescharacteristic
393C2×C13#300611yescharacteristic
394C2×C13#300911yescharacteristic
395C2×C13#334812yes—
396C2×C13#335412yes—
397C24—21no—
398C24C2×D4×C1311yescharacteristic
399C24C2×D4×C1311yescharacteristic
400C2×Q8—24no—
401C2×Q8—82no—
402C2×D4—22no—
403C2×D4—24no—
404C2×D4—24no—
405C2×D4—22no—
406C2×D4—21no—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—41no—
410C2×D4—82no—
411C2×D4—82no—
412C2×D4C2×D4×C1312yes—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—24no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—42no—
426C22×C4—42no—
427C22×C4—42no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4C2×D4×C1311yescharacteristic
431C22×C4C2×D4×C1311yescharacteristic
432C22×C4C2×D4×C1311yescharacteristic
433C22×C4C2×D4×C1312yes—
434C22×C4C2×D4×C1312yes—
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C24×C1311yescharacteristic
437M16—28no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8C13×#4114yes—
444C4⋊C4—24no—
445C4⋊C4—22no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—42no—
454C4⋊C4—44no—
455C4⋊C4C2×D4×C1312yes—
456C4⋊C4C2×D4×C1312yes—
457C4⋊C4C2×D4×C1312yes—
458C22⋊C4—24no—
459C22⋊C4—24no—
460C22⋊C4—24no—
461C22⋊C4—24no—
462C22⋊C4—22no—
463C22⋊C4—24no—
464C22⋊C4—22no—
465C22⋊C4—42no—
466C22⋊C4—44no—
467C42—24no—
468C42—24no—
469C42—21no—
470C42—21no—
471C13#2410411yescharacteristic, direct product factor, Sylow
472C23—22no—
473C23—21no—
474C23—21no—
475C23—22no—
476C23—21no—
477C23—22no—
478C23—22no—
479C23—21no—
480C23—21no—
481C23—22no—
482C23—42no—
483C23—41no—
484C23—41no—
485C23—42no—
486C23C13×#12012yes—
487C23C22×D4×C1311yescharacteristic
488Q8—84no—
489D4—24no—
490D4—44no—
491D4—41no—
492D4—41no—
493D4—84no—
494D4—84no—
495C2×C4—21no—
496C2×C4—22no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—21no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—48no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—84no—
523C2×C4C13×#12012yes—
524C2×C4C13×AGL(1,ℤ/8)12yes—
525C2×C4C22×D4×C1311yescharacteristic
526C2×C4C22×D4×C1311yescharacteristic
527C2×C4C2×C13×#4112yes—
528C2×C4C13×2−1+412yes—
529C8—24no—
530C8—42no—
531C22—22no—
532C22—22no—
533C22—22no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—41no—
538C22—41no—
539C22—42no—
540C22—42no—
541C22—42no—
542C22—41no—
543C22—42no—
544C22—82no—
545C22—82no—
546C22C2×C13×#12011yescharacteristic
547C22C13×#54712yes—
548C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
549C22C13×#57511yescharacteristic
550C22C13×#57712yes—
551C4—22no—
552C4—22no—
553C4—42no—
554C4—41no—
555C4—42no—
556C4—42no—
557C4—41no—
558C4—82no—
559C4—82no—
560C4C13×#52511yescharacteristic
561C4C13×#53611yescharacteristic
562C4C13×#54712yes—
563C2—42no—
564C2—81no—
565C2—82no—
566C2C13×#240611yescharacteristic
567C2C13×#300611yescharacteristic
568C2C13×#300911yescharacteristic
569C2C13×#334812yes—
570C2C13×#335412yes—
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC2×C13×#555C2
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×#481C2semidirect
3. C2×C13×#428C2semidirect
4. C13×#2486C2semidirect
5. C13×#2058C2semidirect
6. C13×#2034C2semidirect
7. C13×#1895C2semidirect
8. C13×#1870C2semidirect
9. C13×#1862C2semidirect
10. C13×#1854C2semidirect
11. C13×#1825C2semidirect
112. #24104C13direct (N × H)
188. C2×#481C2×C13semidirect
189. C2×#428C2×C13semidirect
190. #2486C2×C13semidirect
191. #2058C2×C13semidirect
192. #2034C2×C13semidirect
193. #1895C2×C13semidirect
194. #1870C2×C13semidirect
195. #1862C2×C13semidirect
196. #1854C2×C13semidirect
197. #1825C2×C13semidirect
471. C13#24104direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#5552
C2×C13×#4812
C2×C13×#4282
C13×#24862
C13×#20582
C13×#20342
C13×#18952
C13×#18702
C13×#18622
C13×#18542
C13×#18252
#2410413