Finite Group Databasebeta

← C13×#25949 #15712288

Subgroups — C13×#25949 #15712288

Order 3328.

1202 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic, complemented
2C13×#2561C212yesmaximal, complemented
3C13×#2534C211yesmaximal, characteristic
4C13×#2030C212yesmaximal, complemented
5C13×#2029C212yesmaximal, complemented
6C13×#1996C212yesmaximal, complemented
7C13×#1890C212yesmaximal, complemented
8C13×#1889C212yesmaximal
9C4×C13×#99C211yesmaximal, characteristic, complemented
10C13×#554—24no—
11C13×#554—22no—
12D4×Q8×C13—22no—
13C13×#544—21no—
14C13×#543—21no—
15C13×#543C2212yes—
16C13×#533—21no—
17C2×C13×#123C2211yescharacteristic
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8C2212yes—
20C2×C13×#120C2211yescharacteristic
21C13×#518C2212yes—
22C2×C4×D4×C13C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C2×C13×#99C2212yes—
25C13×#397—22no—
26C13×#396—21no—
27C13×#394—21no—
28C13×#393—22no—
29C13×#388—24no—
30C13×#388—21no—
31C13×#386—21no—
32C13×#381C2211yescharacteristic
33C13×#381C2214yes—
34C13×#380C2211yescharacteristic
35C13×#379C2211yescharacteristic
36C13×#379C2214yes—
37C4×C13×C22⋊C4C2212yes—
38C13×#342C2214yes—
39C13×#342C2214yes—
40C13×#342C2212yes—
41C25×C13C2311yescharacteristic
42C22×Q8×C13—21no—
43C22×Q8×C13D412yescomplemented
44C22×D4×C13—21no—
45C22×D4×C13C2311yescharacteristic
46C23×C4×C13D411yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C13×C4⋊Q8—21no—
50C13×C4⋊Q8—21no—
51C13×C4⋊Q8—24no—
52C13×#125—22no—
53C13×#125—24no—
54C13×#123—24no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—22no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—24no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C13×C22⋊Q8—24no—
66C13×C22⋊Q8—24no—
67C13×#120—24no—
68C4×Q8×C13—22no—
69C4×Q8×C13—22no—
70C4×D4×C13—22no—
71C4×D4×C13—22no—
72C4×D4×C13—24no—
73C4×D4×C13—24no—
74C13×#117—22no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4D411yescharacteristic
80C2×C13×C4⋊C4D414yescomplemented
81C2×C13×C4⋊C4D412yescomplemented
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—24no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—24no—
93C2×C13×C22⋊C4D411yescharacteristic
94C2×C13×C22⋊C4C2314yes—
95C2×C13×C22⋊C4C2311yescharacteristic
96C2×C13×C22⋊C4C2311yescharacteristic
97C2×C13×C22⋊C4C2311yescharacteristic
98C2×C13×C22⋊C4C2314yes—
99C2×C42×C13—22no—
100C2×C42×C13D411yescharacteristic
101C13×#99—24no—
102C13×#95—22no—
103C13×#95—21no—
104C13×#95—21no—
105C13×#95—24no—
106C13×#95—21no—
107C13×#95—24no—
108#25949C1311yesmaximal, characteristic, direct product factor, Sylow
109C24×C13—22no—
110C24×C13—21no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—42no—
114C24×C13—81no—
115C24×C13C2×D411yescharacteristic
116C24×C13C2411yescharacteristic
117C2×Q8×C13—22no—
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—82no—
122C2×Q8×C13—82no—
123C2×D4×C13—22no—
124C2×D4×C13—22no—
125C2×D4×C13—42no—
126C2×D4×C13—42no—
127C2×D4×C13—81no—
128C2×D4×C13#4114yes—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—22no—
134C22×C4×C13—24no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—81no—
141C22×C4×C13—81no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D414yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D412yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D411yescharacteristic
151C13×C4⋊C4—22no—
152C13×C4⋊C4—24no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—24no—
156C13×C4⋊C4—22no—
157C13×C4⋊C4—24no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—42no—
163C13×C4⋊C4—81no—
164C13×C22⋊C4—24no—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—22no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—48no—
174C13×C22⋊C4—42no—
175C13×C22⋊C4—42no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—81no—
181C13×C22⋊C4—84no—
182C42×C13—24no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—82no—
186#3501C2×C1311yescharacteristic, complemented
187#2561C2×C1312yescomplemented
188#2534C2×C1311yescharacteristic
189#2030C2×C1312yescomplemented
190#2029C2×C1312yescomplemented
191#1996C2×C1312yescomplemented
192#1890C2×C1312yescomplemented
193#1889C2×C1312yes—
194C4×#99C2×C1311yescharacteristic, complemented
195C23×C13—21no—
196C23×C13—21no—
197C23×C13—24no—
198C23×C13—22no—
199C23×C13—41no—
200C23×C13—41no—
201C23×C13—41no—
202C23×C13—41no—
203C23×C13—44no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—42no—
207C23×C13—41no—
208C23×C13—41no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—44no—
212C23×C13—84no—
213C23×C13—84no—
214C23×C13#12412yes—
215C23×C13C22×D411yescharacteristic
216C23×C13C22×D412yes—
217C23×C13C2×#4112yes—
218C23×C132−1+412yes—
219Q8×C13—44no—
220Q8×C13—82no—
221Q8×C13—82no—
222Q8×C13—82no—
223D4×C13—28no—
224D4×C13—84no—
225C2×C4×C13—21no—
226C2×C4×C13—21no—
227C2×C4×C13—21no—
228C2×C4×C13—24no—
229C2×C4×C13—24no—
230C2×C4×C13—21no—
231C2×C4×C13—42no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—42no—
235C2×C4×C13—42no—
236C2×C4×C13—44no—
237C2×C4×C13—41no—
238C2×C4×C13—41no—
239C2×C4×C13—44no—
240C2×C4×C13—44no—
241C2×C4×C13—44no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—44no—
252C2×C4×C13—44no—
253C2×C4×C13—81no—
254C2×C4×C13—82no—
255C2×C4×C13—82no—
256C2×C4×C13#12011yescharacteristic
257C2×C4×C13#12011yescharacteristic
258C2×C4×C13#12012yes—
259C2×C4×C13#12412yes—
260#554—24no—
261#554—22no—
262D4×Q8—22no—
263#544—21no—
264#543—21no—
265#543C22×C1312yes—
266#533—21no—
267C2×#123C22×C1311yescharacteristic
268C2×C22⋊Q8—21no—
269C2×C22⋊Q8C22×C1312yes—
270C2×#120C22×C1311yescharacteristic
271#518C22×C1312yes—
272C2×C4×D4C22×C1311yescharacteristic
273C22×C22⋊C4C22×C1311yescharacteristic
274C2×#99C22×C1312yes—
275#397—22no—
276#396—21no—
277#394—21no—
278#393—22no—
279#388—24no—
280#388—21no—
281#386—21no—
282#381C22×C1314yes—
283#381C22×C1311yescharacteristic
284#380C22×C1311yescharacteristic
285#379C22×C1314yes—
286#379C22×C1311yescharacteristic
287C4×C22⋊C4C22×C1312yes—
288#342C22×C1314yes—
289#342C22×C1314yes—
290#342C22×C1312yes—
291C22×C13—22no—
292C22×C13—21no—
293C22×C13—22no—
294C22×C13—21no—
295C22×C13—22no—
296C22×C13—42no—
297C22×C13—42no—
298C22×C13—42no—
299C22×C13—42no—
300C22×C13—48no—
301C22×C13—42no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—42no—
305C22×C13—81no—
306C22×C13—81no—
307C22×C13—84no—
308C22×C13—81no—
309C22×C13—81no—
310C22×C13—81no—
311C22×C13C2×#12011yescharacteristic
312C22×C13C2×#12411yescharacteristic
313C22×C13#53611yescharacteristic
314C22×C13#54814yes—
315C4×C13—22no—
316C4×C13—21no—
317C4×C13—21no—
318C4×C13—22no—
319C4×C13—44no—
320C4×C13—41no—
321C4×C13—41no—
322C4×C13—44no—
323C4×C13—81no—
324C4×C13—84no—
325C4×C13—81no—
326C4×C13—81no—
327C25C23×C1311yescharacteristic
328C22×Q8—21no—
329C22×Q8D4×C1312yescomplemented
330C22×D4—21no—
331C22×D4C23×C1311yescharacteristic
332C23×C4D4×C1311yescharacteristic
333C23×C4C23×C1311yescharacteristic
334C23×C4C23×C1311yescharacteristic
335C4⋊Q8—21no—
336C4⋊Q8—21no—
337C4⋊Q8—24no—
338#125—22no—
339#125—24no—
340#123—24no—
341C22⋊Q8—22no—
342C22⋊Q8—22no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—22no—
346C22⋊Q8—22no—
347C22⋊Q8—22no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—24no—
352C22⋊Q8—24no—
353#120—24no—
354C4×Q8—22no—
355C4×Q8—22no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—24no—
359C4×D4—24no—
360#117—22no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—22no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4D4×C1311yescharacteristic
366C2×C4⋊C4D4×C1314yescomplemented
367C2×C4⋊C4D4×C1312yescomplemented
368C2×C22⋊C4—22no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4D4×C1311yescharacteristic
380C2×C22⋊C4C23×C1311yescharacteristic
381C2×C22⋊C4C23×C1311yescharacteristic
382C2×C22⋊C4C23×C1314yes—
383C2×C22⋊C4C23×C1311yescharacteristic
384C2×C22⋊C4C23×C1314yes—
385C2×C42—22no—
386C2×C42D4×C1311yescharacteristic
387#99—24no—
388#95—22no—
389#95—21no—
390#95—21no—
391#95—24no—
392#95—21no—
393#95—24no—
394C2×C13—21no—
395C2×C13—24no—
396C2×C13—21no—
397C2×C13—42no—
398C2×C13—82no—
399C2×C13#243611yescharacteristic
400C2×C13#302511yescharacteristic
401C2×C13#302611yescharacteristic
402C24—22no—
403C24—21no—
404C24—22no—
405C24—22no—
406C24—42no—
407C24—81no—
408C24C2×D4×C1311yescharacteristic
409C24C24×C1311yescharacteristic
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—22no—
414C2×Q8—82no—
415C2×Q8—82no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—42no—
419C2×D4—42no—
420C2×D4—81no—
421C2×D4C13×#4114yes—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—81no—
434C22×C4—81no—
435C22×C4C2×D4×C1311yescharacteristic
436C22×C4C2×D4×C1311yescharacteristic
437C22×C4C2×D4×C1311yescharacteristic
438C22×C4C2×D4×C1314yes—
439C22×C4C2×D4×C1314yes—
440C22×C4C2×D4×C1311yescharacteristic
441C22×C4C2×D4×C1312yes—
442C22×C4C2×D4×C1312yes—
443C22×C4C2×D4×C1311yescharacteristic
444C4⋊C4—22no—
445C4⋊C4—24no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—24no—
449C4⋊C4—22no—
450C4⋊C4—24no—
451C4⋊C4—22no—
452C4⋊C4—22no—
453C4⋊C4—22no—
454C4⋊C4—24no—
455C4⋊C4—42no—
456C4⋊C4—81no—
457C22⋊C4—24no—
458C22⋊C4—24no—
459C22⋊C4—22no—
460C22⋊C4—24no—
461C22⋊C4—22no—
462C22⋊C4—24no—
463C22⋊C4—22no—
464C22⋊C4—22no—
465C22⋊C4—24no—
466C22⋊C4—48no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—42no—
472C22⋊C4—42no—
473C22⋊C4—81no—
474C22⋊C4—84no—
475C42—24no—
476C42—21no—
477C42—21no—
478C42—82no—
479C13#2594911yescharacteristic, direct product factor, Sylow
480C23—21no—
481C23—21no—
482C23—24no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—44no—
489C23—41no—
490C23—41no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—44no—
497C23—84no—
498C23—84no—
499C23C13×#12412yes—
500C23C22×D4×C1311yescharacteristic
501C23C22×D4×C1312yes—
502C23C2×C13×#4112yes—
503C23C13×2−1+412yes—
504Q8—44no—
505Q8—82no—
506Q8—82no—
507Q8—82no—
508D4—28no—
509D4—84no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—42no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—44no—
525C2×C4—44no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—81no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4C13×#12011yescharacteristic
542C2×C4C13×#12011yescharacteristic
543C2×C4C13×#12012yes—
544C2×C4C13×#12412yes—
545C22—22no—
546C22—21no—
547C22—22no—
548C22—21no—
549C22—22no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—48no—
555C22—42no—
556C22—41no—
557C22—41no—
558C22—42no—
559C22—81no—
560C22—81no—
561C22—84no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22C2×C13×#12011yescharacteristic
566C22C2×C13×#12411yescharacteristic
567C22C13×#53611yescharacteristic
568C22C13×#54814yes—
569C4—21no—
570C4—21no—
571C4—22no—
572C4—22no—
573C4—44no—
574C4—41no—
575C4—41no—
576C4—44no—
577C4—81no—
578C4—84no—
579C4—81no—
580C4—81no—
581C2—21no—
582C2—24no—
583C2—21no—
584C2—42no—
585C2—82no—
586C2C13×#243611yescharacteristic
587C2C13×#302511yescharacteristic
588C2C13×#302611yescharacteristic
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#120C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C13×#3501C2semidirect
2. C13×#2561C2semidirect
4. C13×#2030C2semidirect
5. C13×#2029C2semidirect
6. C13×#1996C2semidirect
7. C13×#1890C2semidirect
9. C4×C13×#99C2semidirect
43. C22×Q8×C13D4semidirect
80. C2×C13×C4⋊C4D4semidirect
81. C2×C13×C4⋊C4D4semidirect
108. #25949C13direct (N × H)
186. #3501C2×C13semidirect
187. #2561C2×C13semidirect
189. #2030C2×C13semidirect
190. #2029C2×C13semidirect
191. #1996C2×C13semidirect
192. #1890C2×C13semidirect
194. C4×#99C2×C13semidirect
329. C22×Q8D4×C13semidirect
366. C2×C4⋊C4D4×C13semidirect
367. C2×C4⋊C4D4×C13semidirect
479. C13#25949direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35012
C13×#25612
C13×#25342
C13×#20302
C13×#20292
C13×#19962
C13×#18902
C13×#18892
C4×C13×#992
#2594913