Finite Group Databasebeta

← D13×#2057 #15890936

Subgroups — D13×#2057 #15890936

Order 3328.

1454 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2C2×D13×#107C212yesmaximal
3D13×#389C211yesmaximal, characteristic
4#13116165C211yesmaximal, characteristic, complemented
5#13116164C211yesmaximal, characteristic, complemented
6#13116163C212yesmaximal, complemented
7#13116162C212yesmaximal, complemented
8#13116161C211yesmaximal, characteristic, complemented
9D13×#340C212yesmaximal
10D13×#336C211yesmaximal, characteristic
11C13×#2057C211yesmaximal, characteristic, complemented
12C22×Q8×D13—21no—
13C2×C13×C4⋊Q8C2211yescharacteristic
14C2×#88198—21no—
15C22×C8×D13C2212yes—
16D13×C4⋊Q8—28no—
17C2×C4⋊C4×D13—21no—
18C2×C4⋊C4×D13—21no—
19C2×C4⋊C4×D13C2211yescharacteristic
20C2×C4⋊C4×D13C2212yes—
21C2×C4⋊C4×D13C2211yescharacteristic
22C2×#88142—21no—
23C2×#88142C2212yes—
24C2×C42×D13C2211yescharacteristic
25C2×#88123C2211yescharacteristic
26C2×C13×#107C2212yes—
27C13×#389C2211yescharacteristic
28C2×#88058C2212yes—
29#11718646C2211yescharacteristic
30#11718634C2211yescharacteristic
31#11718633—21no—
32C2×#88047C2212yes—
33C2×#88047C2212yes—
34#11718589C2211yescharacteristic
35D13×#107—28no—
36D13×#95—21no—
37#11718308—21no—
38C13×#340C2212yes—
39C13×#336C2211yescharacteristic
40#11718143C2212yes—
41#11718142C2212yes—
42#11718121C2212yes—
43#11718121C2212yes—
44#11718116C2211yescharacteristic
45C22×Q8×C13—21no—
46C2×Q8×D13—28no—
47C2×Q8×D13—44no—
48C2×Q8×D13—44no—
49C22×C4×D13—21no—
50C22×C4×D13—22no—
51C22×C4×D13—21no—
52C22×C4×D13D411yescharacteristic
53C22×C4×D13D411yescharacteristic
54C22×C4×D13C2311yescharacteristic
55C22×Dic26—21no—
56C22×Dic26—22no—
57C22×C8×C13C2312yes—
58C13×C4⋊Q8—24no—
59C2×C13×C4⋊C4—21no—
60C2×C13×C4⋊C4—21no—
61C2×C13×C4⋊C4C2311yescharacteristic
62C2×C13×C4⋊C4C2312yes—
63C2×C13×C4⋊C4C2311yescharacteristic
64C2×C42×C13C2311yescharacteristic
65#88198—28no—
66C2×C4⋊Dic13—21no—
67C2×C4⋊Dic13—21no—
68C2×C4⋊Dic13C2311yescharacteristic
69C2×C4⋊Dic13C2312yes—
70C2×C4⋊Dic13C2311yescharacteristic
71C2×#6101—22no—
72C2×#6101—22no—
73C2×#6101—21no—
74C2×#6101—21no—
75C2×#6101—21no—
76C2×#6101—21no—
77C2×C4×Dic13D411yescharacteristic
78C2×C4×Dic13D411yescharacteristic
79C2×C4×Dic13C2311yescharacteristic
80C22×#1055C2312yes—
81C2×C8×D13—24no—
82C2×C8×D13—24no—
83C2×C8×D13Q818yescomplemented
84C4⋊C4×D13—28no—
85C4⋊C4×D13—24no—
86C4⋊C4×D13—22no—
87C4⋊C4×D13—24no—
88C4⋊C4×D13—44no—
89C4⋊C4×D13D418yes—
90C4⋊C4×D13Q814yescomplemented
91#88142—28no—
92#88142—24no—
93#88142—24no—
94C42×D13—24no—
95#88123—24no—
96C13×#107—24no—
97C13×#95—21no—
98#88071—21no—
99#88071—21no—
100#88071—21no—
101#88058—24no—
102#88047—24no—
103#88047—24no—
104C2×#2057—131nomaximal, Sylow
105C23×D13C2×D411yescharacteristic
106C2×Q8×C13—24no—
107C2×Q8×C13—42no—
108C2×Q8×C13—42no—
109C22×C4×C13—21no—
110C22×C4×C13—22no—
111C22×C4×C13—21no—
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2411yescharacteristic
115C22×Dic13—21no—
116C22×Dic13—22no—
117C22×Dic13—21no—
118C22×Dic13C2×D411yescharacteristic
119C22×Dic13C2×D411yescharacteristic
120C22×Dic13C2×D411yescharacteristic
121Q8×D13—432no—
122C2×C4×D13—22no—
123C2×C4×D13—22no—
124C2×C4×D13—22no—
125C2×C4×D13—22no—
126C2×C4×D13—28no—
127C2×C4×D13—24no—
128C2×C4×D13—42no—
129C2×C4×D13—44no—
130C2×C4×D13—44no—
131C2×C4×D13—42no—
132C2×C4×D13—42no—
133C2×C4×D13—42no—
134C2×C4×D13—42no—
135C2×C4×D13D814yes—
136C2×C4×D13Q1614yes—
137C2×C4×D13C2×D414yes—
138C2×C4×D13C2×Q814yes—
139C2×C4×D13C2×Q812yes—
140C2×C4×D13#4112yes—
141C2×Dic26—24no—
142C2×Dic26—28no—
143C2×Dic26—44no—
144C2×Dic26—42no—
145C2×Dic26—42no—
146C2×Dic26—44no—
147C2×C8×C13—22no—
148C2×C8×C13—22no—
149C2×C8×C13C2×Q814yescomplemented
150C13×C4⋊C4—24no—
151C13×C4⋊C4—22no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—22no—
154C13×C4⋊C4—42no—
155C13×C4⋊C4C2×D414yes—
156C13×C4⋊C4C2×Q812yescomplemented
157C42×C13—22no—
158C4⋊Dic13—24no—
159C4⋊Dic13—22no—
160C4⋊Dic13—21no—
161C4⋊Dic13—22no—
162C4⋊Dic13—42no—
163C4⋊Dic13C2×D414yes—
164C4⋊Dic13C2×Q812yescomplemented
165#6101—28no—
166#6101—28no—
167#6101—24no—
168#6101—42no—
169#6101—42no—
170#6101—42no—
171C4×Dic13—22no—
172C4×Dic13—22no—
173C4×Dic13—22no—
174C2×#1055—22no—
175C2×#1055—22no—
176C2×#1055C2×Q814yescomplemented
177C8×D13—216no—
178C22×C4⋊Q8—131no—
179C22×#107—132no—
180C2×#389—131no—
181#2057—132no—
182#2057—131no—
183#2057—132no—
184#2057—131no—
185#2057—131no—
186#2057D1311yescharacteristic, direct product factor
187C2×#340—132no—
188C2×#336—131no—
189C23×C13C22×D411yescharacteristic
190C22×D13#12012yes—
191C22×D13C22⋊Q812yes—
192C22×D13C4⋊Q812yes—
193C22×D13C2×D812yes—
194C22×D13C2×Q1612yes—
195C22×D13AGL(1,ℤ/8)12yes—
196C22×D13#13712yes—
197Q8×C13—48no—
198C2×C4×C13—21no—
199C2×C4×C13—21no—
200C2×C4×C13—21no—
201C2×C4×C13—21no—
202C2×C4×C13—24no—
203C2×C4×C13—22no—
204C2×C4×C13—41no—
205C2×C4×C13—42no—
206C2×C4×C13—42no—
207C2×C4×C13—41no—
208C2×C4×C13—41no—
209C2×C4×C13—41no—
210C2×C4×C13—41no—
211C2×C4×C13C2×D812yes—
212C2×C4×C13C2×Q1612yes—
213C2×C4×C13C22×D412yes—
214C2×C4×C13C22×Q812yes—
215C2×C4×C13C22×Q811yescharacteristic
216C2×C4×C13C2×#4111yescharacteristic
217C2×Dic13—21no—
218C2×Dic13—21no—
219C2×Dic13—21no—
220C2×Dic13—21no—
221C2×Dic13—24no—
222C2×Dic13—22no—
223C2×Dic13—41no—
224C2×Dic13—42no—
225C2×Dic13—42no—
226C2×Dic13—41no—
227C2×Dic13—41no—
228C2×Dic13—41no—
229C2×Dic13—41no—
230C2×Dic13#12012yes—
231C2×Dic13C22⋊Q812yes—
232C2×Dic13C4⋊Q812yes—
233C2×Dic13C2×D812yes—
234C2×Dic13C2×Q1612yes—
235C4×D13—28no—
236C4×D13—28no—
237C4×D13—416no—
238C4×D13—48no—
239C4×D13—84no—
240C4×D13C22⋊Q818yes—
241C4×D13C4⋊Q818yes—
242Dic26—416no—
243Dic26—48no—
244C8×C13—24no—
245#1055—24no—
246C23×Q8—261no—
247C23×C8—132no—
248C2×C4⋊Q8—132no—
249C2×C4⋊Q8—131no—
250C2×C4⋊Q8—261no—
251C2×C4⋊Q8—261no—
252C2×C4⋊Q8—268no—
253C2×C4⋊Q8C2×D1311yescharacteristic
254C22×C4⋊C4—132no—
255C22×C4⋊C4—131no—
256C22×C4⋊C4—131no—
257C22×C4⋊C4—261no—
258C22×C4⋊C4—261no—
259C22×C42—131no—
260C2×#107—132no—
261C2×#107—132no—
262C2×#107—132no—
263C2×#107—268no—
264C2×#107C2×D1312yes—
265#389—131no—
266#389—131no—
267#389—131no—
268#389—261no—
269#389—261no—
270#389C2×D1311yescharacteristic
271C2×#95—261no—
272#340—132no—
273#340—132no—
274#340—132no—
275#340C2×D1312yes—
276#336—132no—
277#336—131no—
278#336C2×D1311yescharacteristic
279C22×C13C2×#12011yescharacteristic
280C22×C13C2×C22⋊Q811yescharacteristic
281C22×C13C2×C4⋊Q811yescharacteristic
282C22×C13C22×D811yescharacteristic
283C22×C13C22×Q1611yescharacteristic
284C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
285C22×C13C2×#13711yescharacteristic
286C2×D13#39514yes—
287C2×D13#44714yes—
288C2×D13#45114yes—
289C2×D13#47414yes—
290C2×D13#47714yes—
291C2×D13#50014yes—
292C2×D13#50114yes—
293C4×C13—22no—
294C4×C13—22no—
295C4×C13—44no—
296C4×C13—42no—
297C4×C13—81no—
298C4×C13C2×C22⋊Q812yes—
299C4×C13C2×C4⋊Q812yes—
300Dic13—22no—
301Dic13—22no—
302Dic13—44no—
303Dic13—42no—
304Dic13—81no—
305Dic13#39514yes—
306C22×Q8—21no—
307C22×Q8—262no—
308C22×Q8—268no—
309C22×Q8—261no—
310C22×Q8—524no—
311C22×Q8—524no—
312C23×C4—131no—
313C23×C4—131no—
314C23×C4—131no—
315C23×C4—262no—
316C23×C4—261no—
317C23×C4—261no—
318C22×C8—132no—
319C22×C8—138no—
320C22×C8—264no—
321C22×C8—264no—
322C22×C8C22×D1312yes—
323C4⋊Q8—24no—
324C4⋊Q8—264no—
325C4⋊Q8—264no—
326C4⋊Q8—268no—
327C4⋊Q8—268no—
328C4⋊Q8—264no—
329C2×C4⋊C4—21no—
330C2×C4⋊C4—21no—
331C2×C4⋊C4—132no—
332C2×C4⋊C4—131no—
333C2×C4⋊C4—138no—
334C2×C4⋊C4—134no—
335C2×C4⋊C4—131no—
336C2×C4⋊C4—264no—
337C2×C4⋊C4—262no—
338C2×C4⋊C4—268no—
339C2×C4⋊C4—264no—
340C2×C4⋊C4—262no—
341C2×C4⋊C4—261no—
342C2×C4⋊C4—262no—
343C2×C4⋊C4—261no—
344C2×C4⋊C4—261no—
345C2×C4⋊C4—261no—
346C2×C4⋊C4—261no—
347C2×C4⋊C4—261no—
348C2×C4⋊C4—524no—
349C2×C4⋊C4C22×D1311yescharacteristic
350C2×C4⋊C4C22×D1312yes—
351C2×C4⋊C4C22×D1311yescharacteristic
352C2×C42—131no—
353C2×C42—131no—
354C2×C42—131no—
355C2×C42—264no—
356C2×C42C22×D1311yescharacteristic
357#107—24no—
358#107—264no—
359#107—264no—
360#107—264no—
361#95—21no—
362#95—261no—
363#95—261no—
364#95—261no—
365C2×C13C2×#39511yescharacteristic
366C2×C13C2×#44711yescharacteristic
367C2×C13C2×#45111yescharacteristic
368C2×C13C2×#47411yescharacteristic
369C2×C13C2×#47711yescharacteristic
370C2×C13C2×#50011yescharacteristic
371C2×C13C2×#50111yescharacteristic
372D13#205718yesdirect product factor
373C24—131no—
374C2×Q8—24no—
375C2×Q8—42no—
376C2×Q8—42no—
377C2×Q8—264no—
378C2×Q8—268no—
379C2×Q8—522no—
380C2×Q8—524no—
381C2×Q8—524no—
382C2×Q8—5232no—
383C2×Q8—522no—
384C22×C4—21no—
385C22×C4—22no—
386C22×C4—21no—
387C22×C4—131no—
388C22×C4—134no—
389C22×C4—132no—
390C22×C4—134no—
391C22×C4—132no—
392C22×C4—131no—
393C22×C4—131no—
394C22×C4—134no—
395C22×C4—134no—
396C22×C4—262no—
397C22×C4—262no—
398C22×C4—262no—
399C22×C4—262no—
400C22×C4—268no—
401C22×C4—264no—
402C22×C4—261no—
403C22×C4—262no—
404C22×C4—261no—
405C22×C4—522no—
406C22×C4—524no—
407C22×C4—524no—
408C22×C4—522no—
409C22×C4—522no—
410C22×C4—522no—
411C22×C4—522no—
412C22×C4D4×D1311yescharacteristic
413C22×C4D4×D1311yescharacteristic
414C22×C4C23×D1311yescharacteristic
415C2×C8—22no—
416C2×C8—22no—
417C2×C8—134no—
418C2×C8—2616no—
419C2×C8—262no—
420C2×C8—262no—
421C2×C8Q8×D1314yescomplemented
422C4⋊C4—24no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—22no—
426C4⋊C4—42no—
427C4⋊C4—134no—
428C4⋊C4—132no—
429C4⋊C4—268no—
430C4⋊C4—264no—
431C4⋊C4—268no—
432C4⋊C4—264no—
433C4⋊C4—262no—
434C4⋊C4—261no—
435C4⋊C4—262no—
436C4⋊C4—522no—
437C4⋊C4—522no—
438C4⋊C4—522no—
439C4⋊C4—522no—
440C4⋊C4D4×D1314yes—
441C4⋊C4Q8×D1312yescomplemented
442C42—22no—
443C42—262no—
444C42—262no—
445C42—262no—
446C13C2×#205711yescharacteristic, complemented, Sylow
447C23—132no—
448C23—132no—
449C23—132no—
450C23—132no—
451C23—132no—
452C23—132no—
453C23—132no—
454C23C2×D4×D1311yescharacteristic
455Q8—48no—
456Q8—528no—
457Q8—5216no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—24no—
463C2×C4—22no—
464C2×C4—41no—
465C2×C4—42no—
466C2×C4—42no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—132no—
472C2×C4—132no—
473C2×C4—132no—
474C2×C4—138no—
475C2×C4—138no—
476C2×C4—132no—
477C2×C4—132no—
478C2×C4—268no—
479C2×C4—268no—
480C2×C4—261no—
481C2×C4—261no—
482C2×C4—261no—
483C2×C4—261no—
484C2×C4—264no—
485C2×C4—262no—
486C2×C4—528no—
487C2×C4—5216no—
488C2×C4—521no—
489C2×C4—522no—
490C2×C4—522no—
491C2×C4—521no—
492C2×C4—521no—
493C2×C4—521no—
494C2×C4—521no—
495C2×C4—1044no—
496C2×C4D8×D1312yes—
497C2×C4Q16×D1312yes—
498C2×C4C2×D4×D1312yes—
499C2×C4C2×Q8×D1311yescharacteristic
500C2×C4C2×Q8×D1312yes—
501C2×C4#41×D1311yescharacteristic
502C8—24no—
503C8—264no—
504C22—134no—
505C22—134no—
506C22—134no—
507C22—134no—
508C22—134no—
509C22—134no—
510C22—134no—
511C22D13×#12011yescharacteristic
512C22D13×C22⋊Q811yescharacteristic
513C22D13×C4⋊Q811yescharacteristic
514C22C2×D8×D1311yescharacteristic
515C22C2×Q16×D1311yescharacteristic
516C22D13×AGL(1,ℤ/8)11yescharacteristic
517C22D13×#13711yescharacteristic
518C4—22no—
519C4—22no—
520C4—44no—
521C4—42no—
522C4—81no—
523C4—134no—
524C4—262no—
525C4—262no—
526C4—524no—
527C4—522no—
528C4—1041no—
529C4D13×C22⋊Q812yes—
530C4D13×C4⋊Q812yes—
531C2—138no—
532C2D13×#39511yescharacteristic
533C2D13×#44711yescharacteristic
534C2D13×#45111yescharacteristic
535C2D13×#47411yescharacteristic
536C2D13×#47711yescharacteristic
537C2D13×#50011yescharacteristic
538C2D13×#50111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2057C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
hypercenter#2057D13
hypocenterC13C2×#2057
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2057

Complements

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

NH ≅ G/Ntype
4. #13116165C2semidirect
5. #13116164C2semidirect
6. #13116163C2semidirect
7. #13116162C2semidirect
8. #13116161C2semidirect
11. C13×#2057C2semidirect
83. C2×C8×D13Q8semidirect
90. C4⋊C4×D13Q8semidirect
149. C2×C8×C13C2×Q8semidirect
156. C13×C4⋊C4C2×Q8semidirect
164. C4⋊Dic13C2×Q8semidirect
176. C2×#1055C2×Q8semidirect
186. #2057D13direct (N × H)
372. D13#2057direct (N × H)
421. C2×C8Q8×D13semidirect
441. C4⋊C4Q8×D13semidirect
446. C13C2×#2057semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
C2×D13×#1072
D13×#3892
#131161652
#131161642
#131161632
#131161622
#131161612
D13×#3402
D13×#3362
C13×#20572
C2×#205713