Finite Group Databasebeta

← C13×#23901 #15710240

Subgroups — C13×#23901 #15710240

Order 3328.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3484C211yesmaximal, characteristic
2C22×C13×#123C211yesmaximal, characteristic, complemented
3C2×C13×#458C212yesmaximal, complemented
4C13×#2849C212yesmaximal, complemented
5C13×#2022C214yesmaximal, complemented
6C13×#1898C212yesmaximal, complemented
7C13×#1890C212yesmaximal, complemented
8C13×#1781C211yesmaximal, characteristic, complemented
9C2×C13×H(5,𝔽2)C2211yescharacteristic
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic, complemented
12C13×#546—24no—
13D42×C13—24no—
14C13×#535—21no—
15C13×#534—21no—
16C13×#534C2212yes—
17C13×#525—21no—
18C2×C13×#123—21no—
19C2×C13×#123—21no—
20C2×C13×#123—28no—
21C2×C13×#123C2212yes—
22C2×C13×#123C2212yescomplemented
23C2×C13×#123C2214yescomplemented
24C2×C13×#120—21no—
25C2×C13×#120C2212yes—
26C13×#518C2211yescharacteristic
27C22×C13×C4⋊C4—21no—
28C22×C13×C22⋊C4—21no—
29C22×C13×C22⋊C4C2211yescharacteristic, complemented
30C13×#458—28no—
31C2×C13×#99C2212yes—
32C2×C13×#99C2214yescomplemented
33C2×C13×#99C2212yescomplemented
34C13×#386—24no—
35C13×#385—24no—
36C13×#381C2214yescomplemented
37C13×#379C2212yescomplemented
38C13×#342C2214yescomplemented
39C25×C13D411yescharacteristic
40C25×C13C2311yescharacteristic
41C13×H(5,𝔽2)—24no—
42C13×H(5,𝔽2)—42no—
43C2×C13×#41—21no—
44C2×C13×#41—22no—
45C22×D4×C13—21no—
46C22×D4×C13—22no—
47C22×D4×C13—24no—
48C22×D4×C13—22no—
49C22×D4×C13—24no—
50C22×D4×C13—42no—
51C22×D4×C13D411yescharacteristic
52C22×D4×C13D411yescharacteristic
53C22×D4×C13D414yes—
54C22×D4×C13C2312yes—
55C22×D4×C13C2311yescharacteristic
56C22×D4×C13C2311yescharacteristic
57C23×C4×C13—21no—
58C23×C4×C13—21no—
59C23×C4×C13—21no—
60C23×C4×C13—24no—
61C23×C4×C13—24no—
62C23×C4×C13—42no—
63C23×C4×C13D411yescharacteristic
64C23×C4×C13C2312yes—
65C13×#127—22no—
66C13×#124—22no—
67C13×#123—28no—
68C13×#123—28no—
69C13×#123—22no—
70C13×#123—24no—
71C13×#123—22no—
72C13×#123—22no—
73C13×#123—24no—
74C13×#123—24no—
75C13×#123—28no—
76C13×#123—44no—
77C13×#123D418yescomplemented
78C13×C22⋊Q8—22no—
79C13×#121—22no—
80C13×#121—24no—
81C13×#121—24no—
82C13×#121—24no—
83C13×#120—24no—
84C13×#120—22no—
85C13×#120—22no—
86C13×#120—22no—
87C13×#120—22no—
88C13×#120—24no—
89C13×#120—22no—
90C4×D4×C13—24no—
91C4×D4×C13—24no—
92C13×#117—21no—
93C2×C13×C4⋊C4—28no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—24no—
97C2×C13×C22⋊C4—28no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—21no—
102C2×C13×C22⋊C4—21no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4D414yes—
107C2×C13×C22⋊C4C2314yes—
108C2×C13×C22⋊C4C2312yes—
109C2×C13×C22⋊C4C2312yes—
110C13×#99—24no—
111C13×#99—28no—
112C13×#99—42no—
113C13×#95—28no—
114#23901C1311yesmaximal, characteristic, direct product factor, Sylow
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—21no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—44no—
121C24×C13—41no—
122C24×C13—44no—
123C24×C13C2×D411yescharacteristic
124C24×C13C2×D414yes—
125C24×C13C2×D411yescharacteristic
126C24×C13C2×D412yes—
127C24×C13C2×D411yescharacteristic
128C24×C13C2×D411yescharacteristic
129C24×C13C2411yescharacteristic
130C13×#41—48no—
131C13×#41—42no—
132C13×#41—42no—
133C2×Q8×C13—21no—
134C2×D4×C13—22no—
135C2×D4×C13—22no—
136C2×D4×C13—22no—
137C2×D4×C13—21no—
138C2×D4×C13—24no—
139C2×D4×C13—22no—
140C2×D4×C13—22no—
141C2×D4×C13—22no—
142C2×D4×C13—24no—
143C2×D4×C13—22no—
144C2×D4×C13—22no—
145C2×D4×C13—22no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—24no—
149C2×D4×C13—24no—
150C2×D4×C13—24no—
151C2×D4×C13—22no—
152C2×D4×C13—41no—
153C2×D4×C13—41no—
154C2×D4×C13—416no—
155C2×D4×C13—48no—
156C2×D4×C13—42no—
157C2×D4×C13—42no—
158C2×D4×C13—48no—
159C2×D4×C13—84no—
160C2×D4×C13C2×D414yes—
161C22×C4×C13—24no—
162C22×C4×C13—24no—
163C22×C4×C13—21no—
164C22×C4×C13—22no—
165C22×C4×C13—24no—
166C22×C4×C13—22no—
167C22×C4×C13—24no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—24no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—24no—
175C22×C4×C13—41no—
176C22×C4×C13—416no—
177C22×C4×C13—44no—
178C22×C4×C13—42no—
179C22×C4×C13—42no—
180C22×C4×C13—42no—
181C22×C4×C13—42no—
182C22×C4×C13C2×D412yes—
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D414yes—
186C22×C4×C13C2×D414yescomplemented
187C13×C4⋊C4—28no—
188C13×C4⋊C4—22no—
189C13×C4⋊C4—24no—
190C13×C4⋊C4—28no—
191C13×C4⋊C4—48no—
192C13×C22⋊C4—24no—
193C13×C22⋊C4—28no—
194C13×C22⋊C4—22no—
195C13×C22⋊C4—24no—
196C13×C22⋊C4—24no—
197C13×C22⋊C4—28no—
198C13×C22⋊C4—24no—
199C13×C22⋊C4—24no—
200C13×C22⋊C4—22no—
201C13×C22⋊C4—22no—
202C13×C22⋊C4—22no—
203C13×C22⋊C4—24no—
204C13×C22⋊C4—24no—
205C13×C22⋊C4—48no—
206C13×C22⋊C4—48no—
207C13×C22⋊C4C2×D414yescomplemented
208C42×C13—22no—
209#3484C2×C1311yescharacteristic
210C22×#123C2×C1311yescharacteristic, complemented
211C2×#458C2×C1312yescomplemented
212#2849C2×C1312yescomplemented
213#2022C2×C1314yescomplemented
214#1898C2×C1312yescomplemented
215#1890C2×C1312yescomplemented
216#1781C2×C1311yescharacteristic, complemented
217C23×C13—21no—
218C23×C13—21no—
219C23×C13—24no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—28no—
224C23×C13—28no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—22no—
229C23×C13—21no—
230C23×C13—24no—
231C23×C13—44no—
232C23×C13—42no—
233C23×C13—42no—
234C23×C13—44no—
235C23×C13—48no—
236C23×C13—48no—
237C23×C13—42no—
238C23×C13—42no—
239C23×C13—48no—
240C23×C13—42no—
241C23×C13—44no—
242C23×C13—44no—
243C23×C13—82no—
244C23×C13—84no—
245C23×C13—82no—
246C23×C13#12012yes—
247C23×C13#12012yes—
248C23×C13#12012yes—
249C23×C13C22×D411yescharacteristic
250C23×C13C22×D412yes—
251C23×C13C22×D412yes—
252C23×C13H(5,𝔽2)12yes—
253Q8×C13—42no—
254D4×C13—28no—
255D4×C13—44no—
256D4×C13—42no—
257D4×C13—44no—
258D4×C13—44no—
259D4×C13—42no—
260D4×C13—42no—
261D4×C13—44no—
262D4×C13—44no—
263D4×C13—48no—
264D4×C13—84no—
265D4×C13—84no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—24no—
269C2×C4×C13—24no—
270C2×C4×C13—21no—
271C2×C4×C13—24no—
272C2×C4×C13—22no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—28no—
276C2×C4×C13—24no—
277C2×C4×C13—44no—
278C2×C4×C13—44no—
279C2×C4×C13—48no—
280C2×C4×C13—44no—
281C2×C4×C13—48no—
282C2×C4×C13—48no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—44no—
287C2×C4×C13—44no—
288C2×C4×C13—48no—
289C2×C4×C13—44no—
290C2×C4×C13—82no—
291C2×C4×C13#12012yes—
292C2×H(5,𝔽2)C22×C1311yescharacteristic
293C23×D4C22×C1311yescharacteristic
294C24×C4C22×C1311yescharacteristic, complemented
295#546—24no—
296D42—24no—
297#535—21no—
298#534—21no—
299#534C22×C1312yes—
300#525—21no—
301C2×#123—21no—
302C2×#123—21no—
303C2×#123—28no—
304C2×#123C22×C1312yes—
305C2×#123C22×C1312yescomplemented
306C2×#123C22×C1314yescomplemented
307C2×#120—21no—
308C2×#120C22×C1312yes—
309#518C22×C1311yescharacteristic
310C22×C4⋊C4—21no—
311C22×C22⋊C4—21no—
312C22×C22⋊C4C22×C1311yescharacteristic, complemented
313#458—28no—
314C2×#99C22×C1312yes—
315C2×#99C22×C1314yescomplemented
316C2×#99C22×C1312yescomplemented
317#386—24no—
318#385—24no—
319#381C22×C1314yescomplemented
320#379C22×C1312yescomplemented
321#342C22×C1314yescomplemented
322C22×C13—24no—
323C22×C13—24no—
324C22×C13—22no—
325C22×C13—24no—
326C22×C13—22no—
327C22×C13—22no—
328C22×C13—22no—
329C22×C13—22no—
330C22×C13—24no—
331C22×C13—42no—
332C22×C13—42no—
333C22×C13—416no—
334C22×C13—42no—
335C22×C13—42no—
336C22×C13—42no—
337C22×C13—42no—
338C22×C13—42no—
339C22×C13—42no—
340C22×C13—41no—
341C22×C13—44no—
342C22×C13—42no—
343C22×C13—81no—
344C22×C13—88no—
345C22×C13—84no—
346C22×C13—81no—
347C22×C13—162no—
348C22×C13#45814yescomplemented
349C22×C13C2×#12011yescharacteristic
350C22×C13C2×#12011yescharacteristic
351C22×C13#53411yescharacteristic
352C22×C13D4214yes—
353C4×C13—22no—
354C4×C13—44no—
355C4×C13—44no—
356C4×C13—41no—
357C4×C13—42no—
358C4×C13—44no—
359C4×C13—84no—
360C25D4×C1311yescharacteristic
361C25C23×C1311yescharacteristic
362H(5,𝔽2)—24no—
363H(5,𝔽2)—42no—
364C2×#41—21no—
365C2×#41—22no—
366C22×D4—21no—
367C22×D4—22no—
368C22×D4—24no—
369C22×D4—22no—
370C22×D4—24no—
371C22×D4—42no—
372C22×D4D4×C1311yescharacteristic
373C22×D4D4×C1311yescharacteristic
374C22×D4D4×C1314yes—
375C22×D4C23×C1312yes—
376C22×D4C23×C1311yescharacteristic
377C22×D4C23×C1311yescharacteristic
378C23×C4—21no—
379C23×C4—21no—
380C23×C4—21no—
381C23×C4—24no—
382C23×C4—24no—
383C23×C4—42no—
384C23×C4D4×C1311yescharacteristic
385C23×C4C23×C1312yes—
386#127—22no—
387#124—22no—
388#123—28no—
389#123—28no—
390#123—22no—
391#123—24no—
392#123—22no—
393#123—22no—
394#123—24no—
395#123—24no—
396#123—28no—
397#123—44no—
398#123D4×C1318yescomplemented
399C22⋊Q8—22no—
400#121—22no—
401#121—24no—
402#121—24no—
403#121—24no—
404#120—24no—
405#120—22no—
406#120—22no—
407#120—22no—
408#120—22no—
409#120—24no—
410#120—22no—
411C4×D4—24no—
412C4×D4—24no—
413#117—21no—
414C2×C4⋊C4—28no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C22⋊C4—28no—
419C2×C22⋊C4—22no—
420C2×C22⋊C4—22no—
421C2×C22⋊C4—22no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—24no—
426C2×C22⋊C4—24no—
427C2×C22⋊C4D4×C1314yes—
428C2×C22⋊C4C23×C1314yes—
429C2×C22⋊C4C23×C1312yes—
430C2×C22⋊C4C23×C1312yes—
431#99—24no—
432#99—28no—
433#99—42no—
434#95—28no—
435C2×C13—21no—
436C2×C13—24no—
437C2×C13—21no—
438C2×C13—24no—
439C2×C13—42no—
440C2×C13—42no—
441C2×C13—81no—
442C2×C13—82no—
443C2×C13#240311yescharacteristic
444C2×C13C2×#45812yes—
445C24—22no—
446C24—22no—
447C24—21no—
448C24—22no—
449C24—22no—
450C24—44no—
451C24—41no—
452C24—44no—
453C24C2×D4×C1311yescharacteristic
454C24C2×D4×C1314yes—
455C24C2×D4×C1311yescharacteristic
456C24C2×D4×C1312yes—
457C24C2×D4×C1311yescharacteristic
458C24C2×D4×C1311yescharacteristic
459C24C24×C1311yescharacteristic
460#41—48no—
461#41—42no—
462#41—42no—
463C2×Q8—21no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—21no—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—24no—
473C2×D4—22no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—24no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—22no—
482C2×D4—41no—
483C2×D4—41no—
484C2×D4—416no—
485C2×D4—48no—
486C2×D4—42no—
487C2×D4—42no—
488C2×D4—48no—
489C2×D4—84no—
490C2×D4C2×D4×C1314yes—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—24no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—24no—
505C22×C4—41no—
506C22×C4—416no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—44no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4C2×D4×C1312yes—
513C22×C4C2×D4×C1311yescharacteristic
514C22×C4C2×D4×C1311yescharacteristic
515C22×C4C2×D4×C1314yes—
516C22×C4C2×D4×C1314yescomplemented
517C4⋊C4—28no—
518C4⋊C4—22no—
519C4⋊C4—24no—
520C4⋊C4—28no—
521C4⋊C4—48no—
522C22⋊C4—24no—
523C22⋊C4—28no—
524C22⋊C4—22no—
525C22⋊C4—24no—
526C22⋊C4—24no—
527C22⋊C4—28no—
528C22⋊C4—24no—
529C22⋊C4—24no—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—24no—
534C22⋊C4—24no—
535C22⋊C4—48no—
536C22⋊C4—48no—
537C22⋊C4C2×D4×C1314yescomplemented
538C42—22no—
539C13#2390111yescharacteristic, direct product factor, Sylow
540C23—24no—
541C23—21no—
542C23—21no—
543C23—28no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23C13×#12012yes—
570C23C13×#12012yes—
571C23C13×#12012yes—
572C23C22×D4×C1311yescharacteristic
573C23C22×D4×C1312yes—
574C23C22×D4×C1312yes—
575C23C13×H(5,𝔽2)12yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—48no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—44no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4C13×#12012yes—
615C22—24no—
616C22—24no—
617C22—24no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—24no—
622C22—22no—
623C22—22no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—44no—
633C22—42no—
634C22—42no—
635C22—41no—
636C22—81no—
637C22—88no—
638C22—84no—
639C22—81no—
640C22—162no—
641C22C13×#45814yescomplemented
642C22C2×C13×#12011yescharacteristic
643C22C2×C13×#12011yescharacteristic
644C22C13×#53411yescharacteristic
645C22D42×C1314yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—44no—
650C4—41no—
651C4—42no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—24no—
656C2—21no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C13×#240311yescharacteristic
662C2C2×C13×#45812yes—
subgroupG/H
center, socleC22×C13C2×#120
commutator, Frattini, cosocleC24C24×C13
prime radicalC13×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C13 ◁ C25×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×C13×#123C2semidirect
3. C2×C13×#458C2semidirect
4. C13×#2849C2semidirect
5. C13×#2022C2semidirect
6. C13×#1898C2semidirect
7. C13×#1890C2semidirect
8. C13×#1781C2semidirect
11. C24×C4×C13C22semidirect
22. C2×C13×#123C22semidirect
23. C2×C13×#123C22semidirect
29. C22×C13×C22⋊C4C22semidirect
32. C2×C13×#99C22semidirect
33. C2×C13×#99C22semidirect
36. C13×#381C22semidirect
37. C13×#379C22semidirect
38. C13×#342C22semidirect
77. C13×#123D4semidirect
114. #23901C13direct (N × H)
186. C22×C4×C13C2×D4semidirect
207. C13×C22⋊C4C2×D4semidirect
210. C22×#123C2×C13semidirect
211. C2×#458C2×C13semidirect
212. #2849C2×C13semidirect
213. #2022C2×C13semidirect
214. #1898C2×C13semidirect
215. #1890C2×C13semidirect
216. #1781C2×C13semidirect
294. C24×C4C22×C13semidirect
305. C2×#123C22×C13semidirect
306. C2×#123C22×C13semidirect
312. C22×C22⋊C4C22×C13semidirect
315. C2×#99C22×C13semidirect
316. C2×#99C22×C13semidirect
319. #381C22×C13semidirect
320. #379C22×C13semidirect
321. #342C22×C13semidirect
348. C22×C13#458semidirect
398. #123D4×C13semidirect
516. C22×C4C2×D4×C13semidirect
537. C22⋊C4C2×D4×C13semidirect
539. C13#23901direct (N × H)
641. C22C13×#458semidirect

Maximal subgroups

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

subgroupindex
C13×#34842
C22×C13×#1232
C2×C13×#4582
C13×#28492
C13×#20222
C13×#18982
C13×#18902
C13×#17812
#2390113