Finite Group Databasebeta

← D13×#1549 #15831262

Subgroups — D13×#1549 #15831262

Order 3328.

1246 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C4⋊Q8C211yesmaximal, characteristic
2D13×#431C211yesmaximal, characteristic
3D13×#423C211yesmaximal, characteristic
4#13113522C211yesmaximal, characteristic, complemented
5#13113521C211yesmaximal, characteristic, complemented
6#13113520C211yesmaximal, characteristic, complemented
7#13113519C214yesmaximal, complemented
8D13×#332C214yesmaximal, complemented
9C13×#1549C211yesmaximal, characteristic, complemented
10C22×Q8×D13—21no—
11C2×C13×C4⋊Q8C2211yescharacteristic
12C2×#88198—21no—
13C2×M16×D13—21no—
14D13×C4⋊Q8—21no—
15D13×C4⋊Q8—21no—
16D13×C4⋊Q8—21no—
17D13×C4⋊Q8—21no—
18D13×C4⋊Q8C412yes—
19D13×C4⋊Q8C412yes—
20D13×C4⋊Q8C2212yes—
21D13×C4⋊Q8C2212yes—
22C2×C4⋊C4×D13—21no—
23C2×C4⋊C4×D13C412yes—
24C2×#88142—21no—
25C2×#88142C412yes—
26C2×C42×D13C2211yescharacteristic
27C2×#88123C2211yescharacteristic
28C13×#431C2211yescharacteristic
29C13×#423C2211yescharacteristic
30#11718779—21no—
31#11718586C2211yescharacteristic
32#11718585C2211yescharacteristic
33#11718498—21no—
34#11718498C2212yes—
35#11718494C2212yes—
36D13×C4⋊C8—21no—
37D13×C4⋊C8C2212yes—
38D13×C4⋊C8C2212yes—
39D13×C22⋊C8—21no—
40#11718379—21no—
41#11718346—21no—
42C4×C8×D13—21no—
43C13×#332C2214yescomplemented
44#11718139C2214yescomplemented
45#11718078C2214yescomplemented
46#11718074C2214yescomplemented
47C22×Q8×C13—21no—
48C2×Q8×D13—22no—
49C2×Q8×D13—22no—
50C2×Q8×D13—22no—
51C2×Q8×D13—22no—
52C2×Q8×D13—48no—
53C22×C4×D13—22no—
54C22×C4×D13C2×C411yescharacteristic
55C22×C4×D13D411yescharacteristic
56C22×C4×D13D411yescharacteristic
57C22×Dic26—21no—
58C22×Dic26—22no—
59C2×C13×M16—21no—
60C13×C4⋊Q8—21no—
61C13×C4⋊Q8—21no—
62C13×C4⋊Q8C2×C412yes—
63C13×C4⋊Q8C2312yes—
64C2×C13×C4⋊C4—21no—
65C2×C13×C4⋊C4C2×C412yes—
66C2×C42×C13C2311yescharacteristic
67#88198—22no—
68#88198—22no—
69#88198—22no—
70#88198—22no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13C2×C412yes—
73C2×#6101—22no—
74C2×#6101—22no—
75C2×C4×Dic13C2×C411yescharacteristic
76C2×C4×Dic13D411yescharacteristic
77C2×C4×Dic13D411yescharacteristic
78C2×#6099—21no—
79M16×D13—44no—
80C2×#6094—22no—
81C2×C8×D13—22no—
82C2×C8×D13—22no—
83C4⋊C4×D13—22no—
84C4⋊C4×D13—22no—
85C4⋊C4×D13—22no—
86C4⋊C4×D13—22no—
87C4⋊C4×D13—22no—
88C4⋊C4×D13—22no—
89C4⋊C4×D13C2×C414yes—
90C4⋊C4×D13C2×C414yes—
91#88142—22no—
92#88142—22no—
93#88142—22no—
94#88142—22no—
95#88142—22no—
96#88142—22no—
97#88142C2×C414yes—
98#88142C2×C414yes—
99C42×D13C2×C411yescharacteristic
100C42×D13C2×C411yescharacteristic
101C42×D13D411yescharacteristic
102C42×D13D411yescharacteristic
103C42×D13D411yescharacteristic
104C42×D13D411yescharacteristic
105C42×D13C2311yescharacteristic
106C42×D13C2311yescharacteristic
107#88123—21no—
108#88123—21no—
109#88123C2×C412yes—
110#88123C2312yes—
111C13×C4⋊C8—21no—
112C13×C4⋊C8C2312yes—
113C13×C4⋊C8C2312yes—
114C13×C22⋊C8—21no—
115C4×C8×C13—21no—
116C22⋊#1055—21no—
117#88060—22no—
118#88054—22no—
119#88054—22no—
120#88054—22no—
121C8×Dic13—22no—
122C4⋊#1055—21no—
123C4⋊#1055C2312yes—
124C4⋊#1055C2312yes—
125C4×#1055—21no—
126C2×#1549—131nomaximal, Sylow
127C23×D13C22⋊C411yescharacteristic
128C2×Q8×C13—22no—
129C2×Q8×C13—22no—
130C2×Q8×C13—44no—
131C22×C4×C13—22no—
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C2×D411yescharacteristic
134C22×C4×C13C2×D411yescharacteristic
135C22×Dic13—22no—
136C22×Dic13C22⋊C411yescharacteristic
137C22×Dic13C22⋊C411yescharacteristic
138C22×Dic13C22⋊C411yescharacteristic
139Q8×D13—48no—
140Q8×D13—48no—
141Q8×D13—48no—
142Q8×D13—48no—
143C2×C4×D13—24no—
144C2×C4×D13—24no—
145C2×C4×D13—24no—
146C2×C4×D13—24no—
147C2×C4×D13—48no—
148C2×C4×D13C22⋊C411yescharacteristic
149C2×C4×D13C22⋊C411yescharacteristic
150C2×C4×D13C22⋊C411yescharacteristic
151C2×C4×D13C22⋊C411yescharacteristic
152C2×C4×D13C22⋊C411yescharacteristic
153C2×C4×D13C22⋊C411yescharacteristic
154C2×C4×D13SD1614yes—
155C2×C4×D13Q1614yes—
156C2×C4×D13C22×C411yescharacteristic
157C2×C4×D13C22×C411yescharacteristic
158C2×C4×D13C2×D411yescharacteristic
159C2×C4×D13C2×D411yescharacteristic
160C2×C4×D13C2×D411yescharacteristic
161C2×C4×D13C2×D411yescharacteristic
162C2×Dic26—22no—
163C2×Dic26—22no—
164C2×Dic26—24no—
165C2×Dic26—24no—
166C2×Dic26—48no—
167C2×Dic26—44no—
168C13×M16—42no—
169C2×C8×C13—22no—
170C2×C8×C13—22no—
171C13×C4⋊C4—22no—
172C13×C4⋊C4—22no—
173C13×C4⋊C4—22no—
174C13×C4⋊C4C22×C414yes—
175C42×C13C22×C411yescharacteristic
176C42×C13C2×D411yescharacteristic
177C42×C13C2×D411yescharacteristic
178C42×C13C2411yescharacteristic
179C4⋊Dic13—22no—
180C4⋊Dic13—22no—
181C4⋊Dic13—22no—
182C4⋊Dic13C22×C414yes—
183#6101—24no—
184#6101—24no—
185#6101—24no—
186#6101—24no—
187C4×Dic13C22⋊C411yescharacteristic
188C4×Dic13C22⋊C411yescharacteristic
189C4×Dic13C22⋊C411yescharacteristic
190C4×Dic13C22⋊C411yescharacteristic
191C4×Dic13C22⋊C411yescharacteristic
192C4×Dic13C22⋊C411yescharacteristic
193C4×Dic13C22×C411yescharacteristic
194C4×Dic13C22×C411yescharacteristic
195C4×Dic13C2×D411yescharacteristic
196C4×Dic13C2×D411yescharacteristic
197C4×Dic13C2×D411yescharacteristic
198C4×Dic13C2×D411yescharacteristic
199#6099—42no—
200C2×#1055—22no—
201C2×#1055—22no—
202#6094—44no—
203C8×D13—44no—
204C8×D13—44no—
205C22×C4⋊Q8—131no—
206C2×#431—131no—
207C2×#423—131no—
208#1549—131no—
209#1549—131no—
210#1549—134no—
211#1549—131no—
212#1549D1311yescharacteristic, direct product factor
213C2×#332—134no—
214C23×C13C2×C22⋊C411yescharacteristic
215C22×D13—22no—
216C22×D13—22no—
217C22×D13#10314yes—
218C22×D13C2×C22⋊C411yescharacteristic
219C22×D13C2×C22⋊C411yescharacteristic
220Q8×C13—44no—
221Q8×C13—44no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—24no—
225C2×C4×C13—44no—
226C2×C4×C13C2×C22⋊C411yescharacteristic
227C2×C4×C13C2×C22⋊C411yescharacteristic
228C2×C4×C13C2×C22⋊C411yescharacteristic
229C2×C4×C13C2×SD1612yes—
230C2×C4×C13C2×Q1612yes—
231C2×C4×C13C23×C411yescharacteristic
232C2×C4×C13C22×D411yescharacteristic
233C2×C4×C13C22×D411yescharacteristic
234C2×Dic13—22no—
235C2×Dic13—22no—
236C2×Dic13—24no—
237C2×Dic13—44no—
238C2×Dic13#10314yes—
239C2×Dic13C2×C22⋊C411yescharacteristic
240C2×Dic13C2×C22⋊C411yescharacteristic
241C2×Dic13C2×C22⋊C411yescharacteristic
242C2×Dic13C2×C22⋊C411yescharacteristic
243C2×Dic13C2×C22⋊C411yescharacteristic
244C2×Dic13C2×C22⋊C411yescharacteristic
245C4×D13—22no—
246C4×D13—22no—
247C4×D13—22no—
248C4×D13—22no—
249C4×D13—22no—
250C4×D13—22no—
251C4×D13—48no—
252C4×D13—48no—
253C4×D13#10114yes—
254C4×D13#10314yes—
255C4×D13#10314yes—
256C4×D13C2×SD1612yes—
257C4×D13C2×SD1612yes—
258C4×D13C2×Q1612yes—
259C4×D13C2×Q1612yes—
260C4×D13AGL(1,ℤ/8)14yes—
261Dic26—48no—
262Dic26—44no—
263Dic26—44no—
264Dic26—48no—
265C8×C13—42no—
266C8×C13—42no—
267#1055—42no—
268#1055—42no—
269C23×Q8—261no—
270C22×M16—261no—
271C2×C4⋊Q8—132no—
272C2×C4⋊Q8—132no—
273C2×C4⋊Q8—132no—
274C2×C4⋊Q8—132no—
275C2×C4⋊Q8—132no—
276C2×C4⋊Q8—131no—
277C2×C4⋊Q8—261no—
278C2×C4⋊Q8—261no—
279C2×C4⋊Q8—261no—
280C2×C4⋊Q8—261no—
281C2×C4⋊Q8—261no—
282C2×C4⋊Q8—261no—
283C2×C4⋊Q8C2×D1311yescharacteristic
284C22×C4⋊C4—132no—
285C22×C4⋊C4—261no—
286C22×C42—131no—
287#431—131no—
288#431—132no—
289#431—261no—
290#431—261no—
291#431C2×D1311yescharacteristic
292#423—131no—
293#423—132no—
294#423—261no—
295#423—261no—
296#423C2×D1311yescharacteristic
297C2×C4⋊C8—132no—
298C2×C4⋊C8—132no—
299C2×C4⋊C8—261no—
300C2×C22⋊C8—261no—
301C2×C4×C8—261no—
302#332—134no—
303#332—134no—
304#332—134no—
305#332C2×D1314yescomplemented
306C22×C13—21no—
307C22×C13—21no—
308C22×C13C2×#10312yes—
309C22×C13C22×C22⋊C411yescharacteristic
310C2×D13—21no—
311C2×D13—21no—
312C2×D13—28no—
313C2×D13C2×#10112yes—
314C2×D13C2×#10312yes—
315C2×D13C2×#10312yes—
316C2×D13#41812yes—
317C4×C13—21no—
318C4×C13—21no—
319C4×C13—44no—
320C4×C13C2×#10112yes—
321C4×C13C2×#10312yes—
322C4×C13C22×SD1611yescharacteristic
323C4×C13C22×Q1611yescharacteristic
324C4×C13C2×AGL(1,ℤ/8)12yes—
325Dic13—21no—
326Dic13—21no—
327Dic13—44no—
328Dic13C2×#10112yes—
329Dic13C2×#10312yes—
330Dic13C2×#10312yes—
331Dic13#41812yes—
332C22×Q8—21no—
333C22×Q8—262no—
334C22×Q8—262no—
335C22×Q8—262no—
336C22×Q8—262no—
337C22×Q8—262no—
338C22×Q8—261no—
339C22×Q8—528no—
340C23×C4—131no—
341C23×C4—131no—
342C23×C4—131no—
343C23×C4—262no—
344C2×M16—21no—
345C2×M16—262no—
346C2×M16—261no—
347C2×M16—524no—
348C22×C8—262no—
349C22×C8—262no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—134no—
353C4⋊Q8—134no—
354C4⋊Q8—132no—
355C4⋊Q8—132no—
356C4⋊Q8—262no—
357C4⋊Q8—262no—
358C4⋊Q8—262no—
359C4⋊Q8—262no—
360C4⋊Q8—262no—
361C4⋊Q8—262no—
362C4⋊Q8—262no—
363C4⋊Q8—262no—
364C4⋊Q8—262no—
365C4⋊Q8—262no—
366C4⋊Q8—261no—
367C4⋊Q8—261no—
368C4⋊Q8C4×D1312yes—
369C4⋊Q8C22×D1312yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—132no—
372C2×C4⋊C4—134no—
373C2×C4⋊C4—134no—
374C2×C4⋊C4—262no—
375C2×C4⋊C4—262no—
376C2×C4⋊C4—262no—
377C2×C4⋊C4—262no—
378C2×C4⋊C4—262no—
379C2×C4⋊C4—262no—
380C2×C4⋊C4—262no—
381C2×C4⋊C4—262no—
382C2×C4⋊C4—261no—
383C2×C4⋊C4C4×D1312yes—
384C2×C42—131no—
385C2×C42—131no—
386C2×C42—131no—
387C2×C42—131no—
388C2×C42—131no—
389C2×C42—131no—
390C2×C42—131no—
391C2×C42—131no—
392C2×C42—131no—
393C2×C42—131no—
394C2×C42—131no—
395C2×C42C22×D1311yescharacteristic
396C4⋊C8—21no—
397C4⋊C8—132no—
398C4⋊C8—132no—
399C4⋊C8—262no—
400C4⋊C8—262no—
401C4⋊C8—262no—
402C4⋊C8—261no—
403C4⋊C8C22×D1312yes—
404C4⋊C8C22×D1312yes—
405C22⋊C8—21no—
406C22⋊C8—262no—
407C22⋊C8—261no—
408C4×C8—21no—
409C4×C8—262no—
410C4×C8—261no—
411C2×C13—22no—
412C2×C13C22×#10111yescharacteristic
413C2×C13C22×#10311yescharacteristic
414C2×C13C2×#41811yescharacteristic
415D13—22no—
416D13#154914yesdirect product factor
417C24—131no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—44no—
421C2×Q8—264no—
422C2×Q8—264no—
423C2×Q8—262no—
424C2×Q8—262no—
425C2×Q8—524no—
426C2×Q8—528no—
427C2×Q8—528no—
428C2×Q8—528no—
429C2×Q8—528no—
430C2×Q8—528no—
431C22×C4—22no—
432C22×C4—131no—
433C22×C4—131no—
434C22×C4—131no—
435C22×C4—131no—
436C22×C4—134no—
437C22×C4—134no—
438C22×C4—131no—
439C22×C4—131no—
440C22×C4—131no—
441C22×C4—131no—
442C22×C4—131no—
443C22×C4—131no—
444C22×C4—131no—
445C22×C4—131no—
446C22×C4—131no—
447C22×C4—131no—
448C22×C4—131no—
449C22×C4—264no—
450C22×C4—264no—
451C22×C4—264no—
452C22×C4—264no—
453C22×C4—262no—
454C22×C4—528no—
455C22×C4C2×C4×D1311yescharacteristic
456C22×C4D4×D1311yescharacteristic
457C22×C4D4×D1311yescharacteristic
458M16—42no—
459M16—524no—
460M16—522no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—262no—
464C2×C8—262no—
465C2×C8—524no—
466C2×C8—524no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—134no—
471C4⋊C4—264no—
472C4⋊C4—264no—
473C4⋊C4—264no—
474C4⋊C4—264no—
475C4⋊C4—262no—
476C4⋊C4—262no—
477C4⋊C4—262no—
478C4⋊C4C2×C4×D1314yes—
479C42—131no—
480C42—131no—
481C42—131no—
482C42—131no—
483C42—131no—
484C42—131no—
485C42—131no—
486C42—131no—
487C42—131no—
488C42—131no—
489C42—131no—
490C42—131no—
491C42C2×C4×D1311yescharacteristic
492C42D4×D1311yescharacteristic
493C42D4×D1311yescharacteristic
494C42C23×D1311yescharacteristic
495C13C2×#154911yescharacteristic, complemented, Sylow
496C23—131no—
497C23—131no—
498C23—134no—
499C23—262no—
500C23—262no—
501C23C22⋊C4×D1311yescharacteristic
502Q8—44no—
503Q8—44no—
504Q8—524no—
505Q8—528no—
506Q8—528no—
507Q8—524no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—131no—
513C2×C4—131no—
514C2×C4—131no—
515C2×C4—131no—
516C2×C4—134no—
517C2×C4—134no—
518C2×C4—132no—
519C2×C4—132no—
520C2×C4—132no—
521C2×C4—132no—
522C2×C4—134no—
523C2×C4—134no—
524C2×C4—134no—
525C2×C4—131no—
526C2×C4—131no—
527C2×C4—262no—
528C2×C4—262no—
529C2×C4—262no—
530C2×C4—262no—
531C2×C4—262no—
532C2×C4—262no—
533C2×C4—262no—
534C2×C4—262no—
535C2×C4—264no—
536C2×C4—528no—
537C2×C4—528no—
538C2×C4—524no—
539C2×C4C22⋊C4×D1311yescharacteristic
540C2×C4C22⋊C4×D1311yescharacteristic
541C2×C4C22⋊C4×D1311yescharacteristic
542C2×C4SD16×D1312yes—
543C2×C4Q16×D1312yes—
544C2×C4C22×C4×D1311yescharacteristic
545C2×C4C2×D4×D1311yescharacteristic
546C2×C4C2×D4×D1311yescharacteristic
547C8—42no—
548C8—42no—
549C8—522no—
550C8—522no—
551C22—21no—
552C22—21no—
553C22—132no—
554C22—132no—
555C22—132no—
556C22—132no—
557C22—268no—
558C22—261no—
559C22—261no—
560C22D13×#10312yes—
561C22C2×C22⋊C4×D1311yescharacteristic
562C4—21no—
563C4—21no—
564C4—44no—
565C4—132no—
566C4—132no—
567C4—132no—
568C4—132no—
569C4—261no—
570C4—261no—
571C4—524no—
572C4D13×#10112yes—
573C4D13×#10312yes—
574C4C2×SD16×D1311yescharacteristic
575C4C2×Q16×D1311yescharacteristic
576C4D13×AGL(1,ℤ/8)12yes—
577C2—22no—
578C2—134no—
579C2—262no—
580C2C2×D13×#10111yescharacteristic
581C2C2×D13×#10311yescharacteristic
582C2D13×#41811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1549C2
socleC22×C13C22×C22⋊C4
prime radicalC23×D13C22⋊C4
cosocleC42×C13C24
hypercenter#1549D13
hypocenterC13C2×#1549
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1549

Complements

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

NH ≅ G/Ntype
4. #13113522C2semidirect
5. #13113521C2semidirect
6. #13113520C2semidirect
7. #13113519C2semidirect
8. D13×#332C2semidirect
9. C13×#1549C2semidirect
43. C13×#332C22semidirect
44. #11718139C22semidirect
45. #11718078C22semidirect
46. #11718074C22semidirect
212. #1549D13direct (N × H)
305. #332C2×D13semidirect
416. D13#1549direct (N × H)
495. C13C2×#1549semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C4⋊Q82
D13×#4312
D13×#4232
#131135222
#131135212
#131135202
#131135192
D13×#3322
C13×#15492
C2×#154913