Finite Group Databasebeta

← C13×#24002 #15710341

Subgroups — C13×#24002 #15710341

Order 3328.

1844 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic
2C2×C13×#480C212yesmaximal, complemented
3C2×C13×#380C211yesmaximal, characteristic, complemented
4C13×#2033C214yesmaximal, complemented
5C13×#1874C212yesmaximal, complemented
6C13×#1852C212yesmaximal, complemented
7C13×#1786C212yesmaximal, complemented
8C13×#1779C211yesmaximal, characteristic, complemented
9C23×D4×C13—21no—
10C23×D4×C13C2211yescharacteristic
11C24×C4×C13C2211yescharacteristic
12C2×C13×#121—21no—
13C2×C13×#121—21no—
14C2×C13×#121—28no—
15C2×C13×#121C2212yes—
16C2×C13×#121C2212yes—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic, complemented
19C22×C13×C4⋊C4C2211yescharacteristic, complemented
20C22×C13×C22⋊C4—21no—
21C22×C13×C22⋊C4—21no—
22C13×#480—28no—
23C2×C13×#107C2214yescomplemented
24C2×C13×#102C2214yescomplemented
25C2×C13×#102C2214yescomplemented
26C2×C13×C22⋊C8C2212yes—
27C2×C13×C22⋊C8C2212yescomplemented
28C2×C13×C22⋊C8C2212yescomplemented
29C13×#380—21no—
30C13×#380—21no—
31C13×#380C2212yes—
32C13×#380C2212yescomplemented
33C2×C13×#95—21no—
34C13×#340C2214yescomplemented
35C25×C13—21no—
36C25×C13D411yescharacteristic
37C22×D4×C13—28no—
38C22×D4×C13—22no—
39C22×D4×C13—22no—
40C22×D4×C13—24no—
41C22×D4×C13—21no—
42C22×D4×C13—24no—
43C22×D4×C13—42no—
44C22×D4×C13—44no—
45C22×D4×C13—44no—
46C22×D4×C13C2312yes—
47C23×C4×C13—21no—
48C23×C4×C13—24no—
49C23×C4×C13—24no—
50C23×C4×C13—21no—
51C23×C4×C13—21no—
52C23×C4×C13—42no—
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×C8×C13C2314yes—
60C13×#121—28no—
61C13×#121—28no—
62C13×#121—24no—
63C13×#121—24no—
64C13×#121—24no—
65C13×#121D418yes—
66C2×C13×C4⋊C4—21no—
67C2×C13×C4⋊C4—24no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—42no—
72C2×C13×C4⋊C4C2312yes—
73C2×C13×C4⋊C4C2312yes—
74C2×C13×C4⋊C4C2312yes—
75C2×C13×C22⋊C4—28no—
76C2×C13×C22⋊C4—22no—
77C2×C13×C22⋊C4—22no—
78C2×C13×C22⋊C4—22no—
79C2×C13×C22⋊C4—22no—
80C2×C13×C22⋊C4—44no—
81C13×#107—28no—
82C13×#102—28no—
83C13×#102—44no—
84C13×C22⋊C8—24no—
85C13×C22⋊C8—24no—
86C13×C22⋊C8—42no—
87C13×#95—22no—
88C13×#95—22no—
89#24002C1311yesmaximal, characteristic, direct product factor, Sylow
90C24×C13—22no—
91C24×C13—22no—
92C24×C13—22no—
93C24×C13—22no—
94C24×C13—24no—
95C24×C13—22no—
96C24×C13—41no—
97C24×C13—41no—
98C24×C13—42no—
99C24×C13—42no—
100C24×C13—42no—
101C24×C13—42no—
102C24×C13—42no—
103C24×C13—42no—
104C24×C13D814yes—
105C24×C13C2×D411yescharacteristic
106C24×C13C2×D411yescharacteristic
107C24×C13C2×D411yescharacteristic
108C2×D4×C13—24no—
109C2×D4×C13—28no—
110C2×D4×C13—28no—
111C2×D4×C13—22no—
112C2×D4×C13—24no—
113C2×D4×C13—24no—
114C2×D4×C13—416no—
115C2×D4×C13—42no—
116C2×D4×C13—432no—
117C2×D4×C13—44no—
118C2×D4×C13—44no—
119C2×D4×C13—44no—
120C2×D4×C13—44no—
121C2×D4×C13—42no—
122C2×D4×C13C2×D414yes—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—24no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—41no—
141C22×C4×C13—41no—
142C22×C4×C13—41no—
143C22×C4×C13—416no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D414yes—
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13#4114yes—
157C22×C4×C13C2411yescharacteristic
158C2×C8×C13—24no—
159C2×C8×C13—24no—
160C2×C8×C13—24no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—24no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4C2×D414yes—
168C13×C22⋊C4—28no—
169C13×C22⋊C4—28no—
170C13×C22⋊C4—44no—
171C13×C22⋊C4—44no—
172C22×#121C2×C1311yescharacteristic
173C2×#480C2×C1312yescomplemented
174C2×#380C2×C1311yescharacteristic, complemented
175#2033C2×C1314yescomplemented
176#1874C2×C1312yescomplemented
177#1852C2×C1312yescomplemented
178#1786C2×C1312yescomplemented
179#1779C2×C1311yescharacteristic, complemented
180C23×C13—21no—
181C23×C13—21no—
182C23×C13—21no—
183C23×C13—21no—
184C23×C13—21no—
185C23×C13—21no—
186C23×C13—21no—
187C23×C13—21no—
188C23×C13—21no—
189C23×C13—21no—
190C23×C13—21no—
191C23×C13—21no—
192C23×C13—21no—
193C23×C13—21no—
194C23×C13—28no—
195C23×C13—28no—
196C23×C13—24no—
197C23×C13—44no—
198C23×C13—44no—
199C23×C13—44no—
200C23×C13—44no—
201C23×C13—44no—
202C23×C13—48no—
203C23×C13—48no—
204C23×C13—48no—
205C23×C13—42no—
206C23×C13—42no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13—42no—
211C23×C13—84no—
212C23×C13—84no—
213C23×C13—84no—
214C23×C13—84no—
215C23×C13#12012yes—
216C23×C13#12312yes—
217C23×C13C2×D812yes—
218C23×C13C2×D812yes—
219C23×C13C2×D812yes—
220C23×C13AGL(1,ℤ/8)12yes—
221C23×C13#13712yes—
222C23×C13C22×D411yescharacteristic
223D4×C13—28no—
224D4×C13—48no—
225D4×C13—416no—
226D4×C13—416no—
227D4×C13—44no—
228C2×C4×C13—21no—
229C2×C4×C13—21no—
230C2×C4×C13—21no—
231C2×C4×C13—21no—
232C2×C4×C13—28no—
233C2×C4×C13—28no—
234C2×C4×C13—21no—
235C2×C4×C13—24no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—44no—
239C2×C4×C13—44no—
240C2×C4×C13—44no—
241C2×C4×C13—48no—
242C2×C4×C13—42no—
243C2×C4×C13—42no—
244C2×C4×C13—44no—
245C2×C4×C13—42no—
246C2×C4×C13—42no—
247C2×C4×C13—42no—
248C2×C4×C13—42no—
249C2×C4×C13—42no—
250C2×C4×C13—42no—
251C2×C4×C13—84no—
252C2×C4×C13—84no—
253C2×C4×C13#12012yes—
254C2×C4×C13#12312yes—
255C2×C4×C13C22×D412yes—
256C2×C4×C13C2×#4112yes—
257C2×C4×C13H(5,𝔽2)12yes—
258C8×C13—44no—
259C23×D4—21no—
260C23×D4C22×C1311yescharacteristic
261C24×C4C22×C1311yescharacteristic
262C2×#121—21no—
263C2×#121—21no—
264C2×#121—28no—
265C2×#121C22×C1312yes—
266C2×#121C22×C1312yes—
267C22×C4⋊C4C22×C1311yescharacteristic
268C22×C4⋊C4C22×C1311yescharacteristic, complemented
269C22×C4⋊C4C22×C1311yescharacteristic, complemented
270C22×C22⋊C4—21no—
271C22×C22⋊C4—21no—
272#480—28no—
273C2×#107C22×C1314yescomplemented
274C2×#102C22×C1314yescomplemented
275C2×#102C22×C1314yescomplemented
276C2×C22⋊C8C22×C1312yes—
277C2×C22⋊C8C22×C1312yescomplemented
278C2×C22⋊C8C22×C1312yescomplemented
279#380—21no—
280#380—21no—
281#380C22×C1312yes—
282#380C22×C1312yescomplemented
283C2×#95—21no—
284#340C22×C1314yescomplemented
285C22×C13—22no—
286C22×C13—22no—
287C22×C13—22no—
288C22×C13—22no—
289C22×C13—22no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13—22no—
294C22×C13—22no—
295C22×C13—22no—
296C22×C13—22no—
297C22×C13—22no—
298C22×C13—22no—
299C22×C13—22no—
300C22×C13—416no—
301C22×C13—41no—
302C22×C13—41no—
303C22×C13—41no—
304C22×C13—41no—
305C22×C13—44no—
306C22×C13—44no—
307C22×C13—44no—
308C22×C13—816no—
309C22×C13—82no—
310C22×C13—82no—
311C22×C13—82no—
312C22×C13—82no—
313C22×C13#44714yes—
314C22×C13#48014yescomplemented
315C22×C13C2×#12011yescharacteristic
316C22×C13C2×#12311yescharacteristic
317C22×C13#53411yescharacteristic
318C22×C13C22×D811yescharacteristic
319C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
320C22×C13C2×#13711yescharacteristic
321C22×C13#57511yescharacteristic
322C4×C13—22no—
323C4×C13—22no—
324C4×C13—41no—
325C4×C13—44no—
326C4×C13—82no—
327C4×C13—82no—
328C4×C13#54614yes—
329C25—21no—
330C25D4×C1311yescharacteristic
331C22×D4—28no—
332C22×D4—22no—
333C22×D4—22no—
334C22×D4—24no—
335C22×D4—21no—
336C22×D4—24no—
337C22×D4—42no—
338C22×D4—44no—
339C22×D4—44no—
340C22×D4C23×C1312yes—
341C23×C4—21no—
342C23×C4—24no—
343C23×C4—24no—
344C23×C4—21no—
345C23×C4—21no—
346C23×C4—42no—
347C23×C4D4×C1311yescharacteristic
348C23×C4D4×C1311yescharacteristic
349C23×C4D4×C1311yescharacteristic
350C23×C4C23×C1311yescharacteristic
351C23×C4C23×C1311yescharacteristic
352C23×C4C23×C1311yescharacteristic
353C22×C8C23×C1314yes—
354#121—28no—
355#121—28no—
356#121—24no—
357#121—24no—
358#121—24no—
359#121D4×C1318yes—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—24no—
362C2×C4⋊C4—24no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—42no—
366C2×C4⋊C4C23×C1312yes—
367C2×C4⋊C4C23×C1312yes—
368C2×C4⋊C4C23×C1312yes—
369C2×C22⋊C4—28no—
370C2×C22⋊C4—22no—
371C2×C22⋊C4—22no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—44no—
375#107—28no—
376#102—28no—
377#102—44no—
378C22⋊C8—24no—
379C22⋊C8—24no—
380C22⋊C8—42no—
381#95—22no—
382#95—22no—
383C2×C13—24no—
384C2×C13—24no—
385C2×C13—42no—
386C2×C13—84no—
387C2×C13#240511yescharacteristic
388C2×C13C2×#44711yescharacteristic
389C2×C13#300711yescharacteristic
390C2×C13C2×#48011yescharacteristic
391C2×C13#309411yescharacteristic
392C2×C13#318611yescharacteristic
393C2×C13#319311yescharacteristic
394C24—22no—
395C24—22no—
396C24—22no—
397C24—22no—
398C24—24no—
399C24—22no—
400C24—41no—
401C24—41no—
402C24—42no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24C13×D814yes—
409C24C2×D4×C1311yescharacteristic
410C24C2×D4×C1311yescharacteristic
411C24C2×D4×C1311yescharacteristic
412C2×D4—24no—
413C2×D4—28no—
414C2×D4—28no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—416no—
419C2×D4—42no—
420C2×D4—432no—
421C2×D4—44no—
422C2×D4—44no—
423C2×D4—44no—
424C2×D4—44no—
425C2×D4—42no—
426C2×D4C2×D4×C1314yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—24no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—416no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4C2×D4×C1311yescharacteristic
457C22×C4C2×D4×C1311yescharacteristic
458C22×C4C2×D4×C1314yes—
459C22×C4C2×D4×C1311yescharacteristic
460C22×C4C13×#4114yes—
461C22×C4C24×C1311yescharacteristic
462C2×C8—24no—
463C2×C8—24no—
464C2×C8—24no—
465C4⋊C4—24no—
466C4⋊C4—22no—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—42no—
470C4⋊C4—42no—
471C4⋊C4C2×D4×C1314yes—
472C22⋊C4—28no—
473C22⋊C4—28no—
474C22⋊C4—44no—
475C22⋊C4—44no—
476C13#2400211yescharacteristic, direct product factor, Sylow
477C23—21no—
478C23—21no—
479C23—21no—
480C23—21no—
481C23—21no—
482C23—21no—
483C23—21no—
484C23—21no—
485C23—28no—
486C23—28no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—24no—
494C23—44no—
495C23—44no—
496C23—44no—
497C23—44no—
498C23—44no—
499C23—48no—
500C23—48no—
501C23—48no—
502C23—42no—
503C23—42no—
504C23—42no—
505C23—42no—
506C23—42no—
507C23—42no—
508C23—84no—
509C23—84no—
510C23—84no—
511C23—84no—
512C23C13×#12012yes—
513C23C13×#12312yes—
514C23C2×C13×D812yes—
515C23C2×C13×D812yes—
516C23C2×C13×D812yes—
517C23C13×AGL(1,ℤ/8)12yes—
518C23C13×#13712yes—
519C23C22×D4×C1311yescharacteristic
520D4—28no—
521D4—48no—
522D4—416no—
523D4—416no—
524D4—44no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—28no—
530C2×C4—28no—
531C2×C4—21no—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—48no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—44no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—84no—
549C2×C4—84no—
550C2×C4C13×#12012yes—
551C2×C4C13×#12312yes—
552C2×C4C22×D4×C1312yes—
553C2×C4C2×C13×#4112yes—
554C2×C4C13×H(5,𝔽2)12yes—
555C8—44no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—22no—
571C22—416no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—44no—
577C22—44no—
578C22—44no—
579C22—816no—
580C22—82no—
581C22—82no—
582C22—82no—
583C22—82no—
584C22C13×#44714yes—
585C22C13×#48014yescomplemented
586C22C2×C13×#12011yescharacteristic
587C22C2×C13×#12311yescharacteristic
588C22C13×#53411yescharacteristic
589C22C22×C13×D811yescharacteristic
590C22C2×C13×AGL(1,ℤ/8)11yescharacteristic
591C22C2×C13×#13711yescharacteristic
592C22C13×#57511yescharacteristic
593C4—22no—
594C4—22no—
595C4—41no—
596C4—44no—
597C4—82no—
598C4—82no—
599C4C13×#54614yes—
600C2—24no—
601C2—24no—
602C2—42no—
603C2—84no—
604C2C13×#240511yescharacteristic
605C2C2×C13×#44711yescharacteristic
606C2C13×#300711yescharacteristic
607C2C2×C13×#48011yescharacteristic
608C2C13×#309411yescharacteristic
609C2C13×#318611yescharacteristic
610C2C13×#319311yescharacteristic
subgroupG/H
center, socleC23×C13C22×D4
commutator, Frattini, cosocleC22×C4C24×C13
prime radicalC22×C13×#121C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C13 ◁ C24×C4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#480C2semidirect
3. C2×C13×#380C2semidirect
4. C13×#2033C2semidirect
5. C13×#1874C2semidirect
6. C13×#1852C2semidirect
7. C13×#1786C2semidirect
8. C13×#1779C2semidirect
18. C22×C13×C4⋊C4C22semidirect
19. C22×C13×C4⋊C4C22semidirect
23. C2×C13×#107C22semidirect
24. C2×C13×#102C22semidirect
25. C2×C13×#102C22semidirect
27. C2×C13×C22⋊C8C22semidirect
28. C2×C13×C22⋊C8C22semidirect
32. C13×#380C22semidirect
34. C13×#340C22semidirect
89. #24002C13direct (N × H)
173. C2×#480C2×C13semidirect
174. C2×#380C2×C13semidirect
175. #2033C2×C13semidirect
176. #1874C2×C13semidirect
177. #1852C2×C13semidirect
178. #1786C2×C13semidirect
179. #1779C2×C13semidirect
268. C22×C4⋊C4C22×C13semidirect
269. C22×C4⋊C4C22×C13semidirect
273. C2×#107C22×C13semidirect
274. C2×#102C22×C13semidirect
275. C2×#102C22×C13semidirect
277. C2×C22⋊C8C22×C13semidirect
278. C2×C22⋊C8C22×C13semidirect
282. #380C22×C13semidirect
284. #340C22×C13semidirect
314. C22×C13#480semidirect
476. C13#24002direct (N × H)
585. C22C13×#480semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C2×C13×#4802
C2×C13×#3802
C13×#20332
C13×#18742
C13×#18522
C13×#17862
C13×#17792
#2400213