Finite Group Databasebeta

← C13×#24352 #15710691

Subgroups — C13×#24352 #15710691

Order 3328.

1198 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3501C211yesmaximal, characteristic, complemented
2C13×#2626C212yesmaximal, complemented
3C13×#2321C211yesmaximal, characteristic
4C13×#2062C212yesmaximal, complemented
5C13×#2029C212yesmaximal, complemented
6C13×#1996C212yesmaximal, complemented
7C13×#1889C212yesmaximal
8C13×#1867C212yesmaximal, complemented
9C13×#1799C211yesmaximal, 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×C22⋊Q8—21no—
18C2×C13×C22⋊Q8C2212yes—
19C2×C13×#120C2211yescharacteristic
20C13×#518C2212yes—
21C2×C4×D4×C13C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C2×C13×#99C2212yes—
24C13×#399—22no—
25C13×#396—24no—
26C13×#393—22no—
27C13×#390—21no—
28C13×#388—21no—
29C13×#388—21no—
30C13×#386—21no—
31C13×#386C2211yescharacteristic
32C13×#385C2211yescharacteristic
33C13×#385C2214yes—
34C13×#380C2212yes—
35C13×#379C2211yescharacteristic
36C13×#379C2214yes—
37C4×C13×C22⋊C4C2211yescharacteristic
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×C22⋊Q8—22no—
55C13×C22⋊Q8—22no—
56C13×C22⋊Q8—24no—
57C13×C22⋊Q8—24no—
58C13×C22⋊Q8—22no—
59C13×C22⋊Q8—22no—
60C13×C22⋊Q8—22no—
61C13×C22⋊Q8—22no—
62C13×C22⋊Q8—22no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—24no—
65C13×C22⋊Q8—24no—
66C13×#120—22no—
67C13×#120Q814yescomplemented
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—22no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—24no—
80C2×C13×C4⋊C4D411yescharacteristic
81C2×C13×C4⋊C4D414yescomplemented
82C2×C13×C4⋊C4D412yescomplemented
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—21no—
90C2×C13×C22⋊C4—21no—
91C2×C13×C22⋊C4—21no—
92C2×C13×C22⋊C4—24no—
93C2×C13×C22⋊C4—24no—
94C2×C13×C22⋊C4D411yescharacteristic
95C2×C13×C22⋊C4C2311yescharacteristic
96C2×C13×C22⋊C4C2314yes—
97C2×C13×C22⋊C4C2311yescharacteristic
98C2×C13×C22⋊C4C2314yes—
99C2×C13×C22⋊C4C2311yescharacteristic
100C2×C42×C13—21no—
101C2×C42×C13D411yescharacteristic
102C13×#99—24no—
103C13×#95—21no—
104C13×#95—22no—
105C13×#95—21no—
106C13×#95—24no—
107C13×#95—21no—
108#24352C1311yesmaximal, characteristic, direct product factor, Sylow
109C24×C13—22no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—22no—
113C24×C13—81no—
114C24×C13—81no—
115C24×C13C2×D411yescharacteristic
116C24×C13C2×Q812yescomplemented
117C24×C13C2411yescharacteristic
118C2×Q8×C13—22no—
119C2×Q8×C13—22no—
120C2×Q8×C13—22no—
121C2×Q8×C13—22no—
122C2×Q8×C13—82no—
123C2×Q8×C13—82no—
124C2×D4×C13—22no—
125C2×D4×C13—22no—
126C2×D4×C13—24no—
127C2×D4×C13—81no—
128C2×D4×C13—81no—
129C2×D4×C13C2×Q812yes—
130C2×D4×C13#4112yes—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—24no—
139C22×C4×C13—22no—
140C22×C4×C13—81no—
141C22×C4×C13—81no—
142C22×C4×C13—81no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D414yes—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D414yes—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D412yes—
152C13×C4⋊C4—22no—
153C13×C4⋊C4—24no—
154C13×C4⋊C4—22no—
155C13×C4⋊C4—22no—
156C13×C4⋊C4—24no—
157C13×C4⋊C4—22no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—22no—
162C13×C4⋊C4—24no—
163C13×C4⋊C4—82no—
164C13×C4⋊C4—81no—
165C13×C4⋊C4—84no—
166C13×C22⋊C4—24no—
167C13×C22⋊C4—24no—
168C13×C22⋊C4—22no—
169C13×C22⋊C4—24no—
170C13×C22⋊C4—21no—
171C13×C22⋊C4—22no—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—22no—
175C13×C22⋊C4—24no—
176C13×C22⋊C4—41no—
177C13×C22⋊C4—41no—
178C13×C22⋊C4—42no—
179C13×C22⋊C4—81no—
180C13×C22⋊C4—84no—
181C13×C22⋊C4—81no—
182C13×C22⋊C4—84no—
183C13×C22⋊C4—81no—
184C13×C22⋊C4C2×Q812yescomplemented
185C42×C13—24no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—81no—
189#3501C2×C1311yescharacteristic, complemented
190#2626C2×C1312yescomplemented
191#2321C2×C1311yescharacteristic
192#2062C2×C1312yescomplemented
193#2029C2×C1312yescomplemented
194#1996C2×C1312yescomplemented
195#1889C2×C1312yes—
196#1867C2×C1312yescomplemented
197#1799C2×C1311yescharacteristic, complemented
198C23×C13—21no—
199C23×C13—21no—
200C23×C13—22no—
201C23×C13—24no—
202C23×C13—41no—
203C23×C13—41no—
204C23×C13—41no—
205C23×C13—41no—
206C23×C13—44no—
207C23×C13—41no—
208C23×C13—44no—
209C23×C13—41no—
210C23×C13—41no—
211C23×C13—41no—
212C23×C13—41no—
213C23×C13—41no—
214C23×C13—42no—
215C23×C13—82no—
216C23×C13—82no—
217C23×C13—84no—
218C23×C13C22⋊Q812yes—
219C23×C13C22×D411yescharacteristic
220C23×C13C22×D412yes—
221C23×C13C22×Q811yescharacteristic
222C23×C13C2×#4111yescharacteristic
223C23×C132−1+412yes—
224Q8×C13—44no—
225Q8×C13—82no—
226Q8×C13—82no—
227Q8×C13—82no—
228D4×C13—24no—
229D4×C13—24no—
230D4×C13—84no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—24no—
235C2×C4×C13—24no—
236C2×C4×C13—21no—
237C2×C4×C13—22no—
238C2×C4×C13—41no—
239C2×C4×C13—42no—
240C2×C4×C13—41no—
241C2×C4×C13—42no—
242C2×C4×C13—42no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—44no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—44no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—44no—
252C2×C4×C13—44no—
253C2×C4×C13—41no—
254C2×C4×C13—44no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—44no—
259C2×C4×C13—81no—
260C2×C4×C13—82no—
261C2×C4×C13—82no—
262C2×C4×C13#12011yescharacteristic
263C2×C4×C13#12011yescharacteristic
264C2×C4×C13#12012yes—
265C2×C4×C13C22⋊Q812yes—
266#554—24no—
267#554—22no—
268D4×Q8—22no—
269#544—21no—
270#543—21no—
271#543C22×C1312yes—
272#533—21no—
273C2×C22⋊Q8—21no—
274C2×C22⋊Q8C22×C1312yes—
275C2×#120C22×C1311yescharacteristic
276#518C22×C1312yes—
277C2×C4×D4C22×C1311yescharacteristic
278C22×C22⋊C4C22×C1311yescharacteristic
279C2×#99C22×C1312yes—
280#399—22no—
281#396—24no—
282#393—22no—
283#390—21no—
284#388—21no—
285#388—21no—
286#386—21no—
287#386C22×C1311yescharacteristic
288#385C22×C1311yescharacteristic
289#385C22×C1314yes—
290#380C22×C1312yes—
291#379C22×C1311yescharacteristic
292#379C22×C1314yes—
293C4×C22⋊C4C22×C1311yescharacteristic
294#342C22×C1312yes—
295#342C22×C1314yes—
296#342C22×C1314yes—
297C22×C13—22no—
298C22×C13—21no—
299C22×C13—22no—
300C22×C13—21no—
301C22×C13—22no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—42no—
305C22×C13—42no—
306C22×C13—42no—
307C22×C13—42no—
308C22×C13—48no—
309C22×C13—41no—
310C22×C13—41no—
311C22×C13—42no—
312C22×C13—81no—
313C22×C13—84no—
314C22×C13—81no—
315C22×C13—81no—
316C22×C13—81no—
317C22×C13—81no—
318C22×C13C2×#12011yescharacteristic
319C22×C13C2×C22⋊Q811yescharacteristic
320C22×C13#53611yescharacteristic
321C22×C13#54812yes—
322C22×C13D4×Q812yes—
323C4×C13—22no—
324C4×C13—21no—
325C4×C13—21no—
326C4×C13—22no—
327C4×C13—42no—
328C4×C13—41no—
329C4×C13—44no—
330C4×C13—44no—
331C4×C13—41no—
332C4×C13—84no—
333C4×C13—81no—
334C4×C13—81no—
335C25C23×C1311yescharacteristic
336C22×Q8—21no—
337C22×Q8D4×C1312yescomplemented
338C22×D4—21no—
339C22×D4C23×C1311yescharacteristic
340C23×C4D4×C1311yescharacteristic
341C23×C4C23×C1311yescharacteristic
342C23×C4C23×C1311yescharacteristic
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—24no—
346#125—22no—
347#125—24no—
348C22⋊Q8—22no—
349C22⋊Q8—22no—
350C22⋊Q8—24no—
351C22⋊Q8—24no—
352C22⋊Q8—22no—
353C22⋊Q8—22no—
354C22⋊Q8—22no—
355C22⋊Q8—22no—
356C22⋊Q8—22no—
357C22⋊Q8—22no—
358C22⋊Q8—24no—
359C22⋊Q8—24no—
360#120—22no—
361#120Q8×C1314yescomplemented
362C4×Q8—22no—
363C4×Q8—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—24no—
367C4×D4—24no—
368#117—22no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—22no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—24no—
374C2×C4⋊C4D4×C1311yescharacteristic
375C2×C4⋊C4D4×C1314yescomplemented
376C2×C4⋊C4D4×C1312yescomplemented
377C2×C22⋊C4—22no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—22no—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—24no—
387C2×C22⋊C4—24no—
388C2×C22⋊C4D4×C1311yescharacteristic
389C2×C22⋊C4C23×C1311yescharacteristic
390C2×C22⋊C4C23×C1314yes—
391C2×C22⋊C4C23×C1311yescharacteristic
392C2×C22⋊C4C23×C1314yes—
393C2×C22⋊C4C23×C1311yescharacteristic
394C2×C42—21no—
395C2×C42D4×C1311yescharacteristic
396#99—24no—
397#95—21no—
398#95—22no—
399#95—21no—
400#95—24no—
401#95—21no—
402C2×C13—21no—
403C2×C13—22no—
404C2×C13—21no—
405C2×C13—22no—
406C2×C13—42no—
407C2×C13—82no—
408C2×C13#240911yescharacteristic
409C2×C13#302611yescharacteristic
410C2×C13#302711yescharacteristic
411C24—22no—
412C24—21no—
413C24—21no—
414C24—22no—
415C24—81no—
416C24—81no—
417C24C2×D4×C1311yescharacteristic
418C24C2×Q8×C1312yescomplemented
419C24C24×C1311yescharacteristic
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8—22no—
423C2×Q8—22no—
424C2×Q8—82no—
425C2×Q8—82no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—24no—
429C2×D4—81no—
430C2×D4—81no—
431C2×D4C2×Q8×C1312yes—
432C2×D4C13×#4112yes—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—81no—
443C22×C4—81no—
444C22×C4—81no—
445C22×C4C2×D4×C1311yescharacteristic
446C22×C4C2×D4×C1311yescharacteristic
447C22×C4C2×D4×C1314yes—
448C22×C4C2×D4×C1311yescharacteristic
449C22×C4C2×D4×C1314yes—
450C22×C4C2×D4×C1311yescharacteristic
451C22×C4C2×D4×C1312yes—
452C22×C4C2×D4×C1311yescharacteristic
453C22×C4C2×D4×C1312yes—
454C4⋊C4—22no—
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—24no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—22no—
464C4⋊C4—24no—
465C4⋊C4—82no—
466C4⋊C4—81no—
467C4⋊C4—84no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—22no—
471C22⋊C4—24no—
472C22⋊C4—21no—
473C22⋊C4—22no—
474C22⋊C4—24no—
475C22⋊C4—24no—
476C22⋊C4—22no—
477C22⋊C4—24no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—42no—
481C22⋊C4—81no—
482C22⋊C4—84no—
483C22⋊C4—81no—
484C22⋊C4—84no—
485C22⋊C4—81no—
486C22⋊C4C2×Q8×C1312yescomplemented
487C42—24no—
488C42—21no—
489C42—21no—
490C42—81no—
491C13#2435211yescharacteristic, direct product factor, Sylow
492C23—21no—
493C23—21no—
494C23—22no—
495C23—24no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—44no—
501C23—41no—
502C23—44no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—42no—
509C23—82no—
510C23—82no—
511C23—84no—
512C23C13×C22⋊Q812yes—
513C23C22×D4×C1311yescharacteristic
514C23C22×D4×C1312yes—
515C23C22×Q8×C1311yescharacteristic
516C23C2×C13×#4111yescharacteristic
517C23C13×2−1+412yes—
518Q8—44no—
519Q8—82no—
520Q8—82no—
521Q8—82no—
522D4—24no—
523D4—24no—
524D4—84no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—21no—
531C2×C4—22no—
532C2×C4—41no—
533C2×C4—42no—
534C2×C4—41no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—44no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—44no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—44no—
546C2×C4—44no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—44no—
553C2×C4—81no—
554C2×C4—82no—
555C2×C4—82no—
556C2×C4C13×#12011yescharacteristic
557C2×C4C13×#12011yescharacteristic
558C2×C4C13×#12012yes—
559C2×C4C13×C22⋊Q812yes—
560C22—22no—
561C22—21no—
562C22—22no—
563C22—21no—
564C22—22no—
565C22—41no—
566C22—41no—
567C22—42no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—48no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—81no—
576C22—84no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22C2×C13×#12011yescharacteristic
582C22C2×C13×C22⋊Q811yescharacteristic
583C22C13×#53611yescharacteristic
584C22C13×#54812yes—
585C22D4×Q8×C1312yes—
586C4—21no—
587C4—21no—
588C4—22no—
589C4—22no—
590C4—42no—
591C4—41no—
592C4—44no—
593C4—44no—
594C4—41no—
595C4—84no—
596C4—81no—
597C4—81no—
598C2—21no—
599C2—22no—
600C2—21no—
601C2—22no—
602C2—42no—
603C2—82no—
604C2C13×#240911yescharacteristic
605C2C13×#302611yescharacteristic
606C2C13×#302711yescharacteristic
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×#2626C2semidirect
4. C13×#2062C2semidirect
5. C13×#2029C2semidirect
6. C13×#1996C2semidirect
8. C13×#1867C2semidirect
9. C13×#1799C2semidirect
43. C22×Q8×C13D4semidirect
67. C13×#120Q8semidirect
81. C2×C13×C4⋊C4D4semidirect
82. C2×C13×C4⋊C4D4semidirect
108. #24352C13direct (N × H)
116. C24×C13C2×Q8semidirect
184. C13×C22⋊C4C2×Q8semidirect
189. #3501C2×C13semidirect
190. #2626C2×C13semidirect
192. #2062C2×C13semidirect
193. #2029C2×C13semidirect
194. #1996C2×C13semidirect
196. #1867C2×C13semidirect
197. #1799C2×C13semidirect
337. C22×Q8D4×C13semidirect
361. #120Q8×C13semidirect
375. C2×C4⋊C4D4×C13semidirect
376. C2×C4⋊C4D4×C13semidirect
418. C24C2×Q8×C13semidirect
486. C22⋊C4C2×Q8×C13semidirect
491. C13#24352direct (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×#26262
C13×#23212
C13×#20622
C13×#20292
C13×#19962
C13×#18892
C13×#18672
C13×#17992
#2435213