Finite Group Databasebeta

← D13×#2583 #16033143

Subgroups — D13×#2583 #16033143

Order 3328.

3094 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D13×C22⋊Q8C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3#13120217C211yesmaximal, characteristic, complemented
4#13120216C211yesmaximal, characteristic, complemented
5#13120215C212yesmaximal, complemented
6#13120214C214yesmaximal, complemented
7#13120213C212yesmaximal, complemented
8#13120212C212yesmaximal, complemented
9#13120211C211yesmaximal, characteristic, complemented
10#13120210C212yesmaximal, complemented
11D13×#398C212yesmaximal, complemented
12D13×#395C212yesmaximal, complemented
13D13×#389C214yesmaximal, complemented
14D13×#385C212yesmaximal
15D13×#385C212yesmaximal
16C4×C22⋊C4×D13C211yesmaximal, characteristic
17C13×#2583C211yesmaximal, characteristic, complemented
18C22×Q8×D13C2211yescharacteristic
19C23×C4×D13C2211yescharacteristic
20C23×C4×D13C2211yescharacteristic
21C23×C4×D13C2211yescharacteristic
22C2×C13×C22⋊Q8C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C2×#88200C2211yescharacteristic
25C22×C4⋊Dic13C2211yescharacteristic
26C2×#88178C2211yescharacteristic
27C22×#6101C2211yescharacteristic
28C22×#6101C2211yescharacteristic
29D13×C22⋊Q8—28no—
30C2×#88151C2211yescharacteristic
31C2×#88150C2212yes—
32C2×C4⋊C4×D13—28no—
33C2×C4⋊C4×D13C2212yes—
34C2×C4⋊C4×D13C2212yes—
35C2×C4⋊C4×D13C2212yes—
36C2×C4⋊C4×D13C2212yes—
37C2×C4⋊C4×D13C2214yes—
38C2×C4⋊C4×D13C2212yes—
39C2×C4⋊C4×D13C2211yescharacteristic
40C2×C4⋊C4×D13C2214yes—
41C2×C22⋊C4×D13C2212yes—
42C2×C22⋊C4×D13C2212yes—
43C2×#88132C2212yes—
44C2×C42×D13C2212yes—
45C13×#398C2212yescomplemented
46C13×#395C2212yescomplemented
47C13×#389C2214yescomplemented
48C13×#385C2212yes—
49C13×#385C2212yes—
50C4×C13×C22⋊C4C2211yescharacteristic
51#11718890C2212yescomplemented
52#11718871C2212yes—
53#11718871C2212yes—
54C4×C22⋊Dic13C2211yescharacteristic
55#11718650C2214yes—
56#11718650C2214yes—
57#11718646C2214yescomplemented
58#11718645C2214yescomplemented
59#11718644C2212yescomplemented
60#11718641C2212yescomplemented
61#11718640C2212yescomplemented
62#11718640C2214yescomplemented
63#11718634C2214yescomplemented
64#11718633C2214yescomplemented
65#11718633C2214yescomplemented
66#11718611C2212yes—
67#11718611C2212yes—
68#11718607C2212yes—
69#11718607C2212yes—
70C22⋊C4×Dic13C2212yes—
71C4×#6103C2212yes—
72#11718589C2214yescomplemented
73#11718329C2214yes—
74#11718329C2214yes—
75#11718327C2212yes—
76D13×#95C2214yes—
77D13×#95C2214yes—
78D13×#95C2212yes—
79#11718322C2212yescomplemented
80#11718318C2214yescomplemented
81#11718317C2212yescomplemented
82#11718317C2214yescomplemented
83#11718308C2214yescomplemented
84#11718308C2214yescomplemented
85C24×D13C2311yescharacteristic
86C22×Q8×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×Dic13C2311yescharacteristic
91C23×Dic13C2311yescharacteristic
92C23×Dic13C2311yescharacteristic
93C2×Q8×D13—24no—
94C2×Q8×D13—44no—
95C22×C4×D13—24no—
96C22×C4×D13—28no—
97C22×C4×D13—24no—
98C22×C4×D13—44no—
99C22×C4×D13—44no—
100C22×C4×D13D418yes—
101C22×C4×D13C2312yes—
102C22×C4×D13C2312yes—
103C22×C4×D13C2312yes—
104C22×C4×D13C2312yes—
105C22×C4×D13C2311yescharacteristic
106C22×C4×D13C2311yescharacteristic
107C22×C4×D13C2314yes—
108C22×C4×D13C2312yes—
109C22×C4×D13C2312yes—
110C22×C4×D13C2311yescharacteristic
111C22×C4×D13C2311yescharacteristic
112C22×Dic26C2312yes—
113C22×Dic26C2311yescharacteristic
114C13×C22⋊Q8—24no—
115C2×C13×C4⋊C4—24no—
116C2×C13×C4⋊C4C2314yes—
117C2×C13×C4⋊C4C2312yes—
118C2×C13×C4⋊C4C2312yes—
119C2×C13×C4⋊C4C2312yes—
120C2×C13×C4⋊C4C2311yescharacteristic
121C2×C13×C4⋊C4C2314yes—
122C2×C13×C22⋊C4C2312yes—
123C2×C13×C22⋊C4C2312yes—
124C2×C42×C13C2312yes—
125C2×C22⋊Dic13C2312yes—
126C2×C22⋊Dic13C2312yes—
127#88200—24no—
128C2×#6103C2312yes—
129C2×#6103C2312yes—
130C2×#6103C2314yes—
131C2×C4⋊Dic13—24no—
132C2×C4⋊Dic13C2312yes—
133C2×C4⋊Dic13C2312yes—
134C2×C4⋊Dic13C2312yes—
135C2×C4⋊Dic13C2311yescharacteristic
136C2×C4⋊Dic13C2314yes—
137C2×C4⋊Dic13C2314yes—
138#88178—24no—
139C2×#6101—24no—
140C2×#6101—24no—
141C2×#6101C2312yes—
142C2×#6101C2312yes—
143C2×#6101C2312yes—
144C2×#6101C2312yes—
145C2×#6101C2312yes—
146C2×#6101C2312yes—
147C2×#6101C2312yes—
148C2×#6101C2314yes—
149C2×#6101C2314yes—
150C2×#6101C2314yes—
151C2×#6101C2314yes—
152C2×C4×Dic13C2314yes—
153C2×C4×Dic13C2312yes—
154#88151—24no—
155#88150—28no—
156C4⋊C4×D13—28no—
157C4⋊C4×D13—28no—
158C4⋊C4×D13—28no—
159C4⋊C4×D13—28no—
160C4⋊C4×D13—28no—
161C4⋊C4×D13—24no—
162C4⋊C4×D13—216no—
163C4⋊C4×D13—48no—
164C22⋊C4×D13—28no—
165C22⋊C4×D13Q8116yescomplemented
166#88132—28no—
167C42×D13—44no—
168C13×#95C2312yes—
169C13×#95C2314yes—
170C13×#95C2314yes—
171#88071C2314yes—
172#88071C2314yes—
173#88071C2314yes—
174#88071C2314yes—
175#88071C2314yes—
176#88071C2312yes—
177#88071C2314yes—
178#88071C2314yes—
179C2×#2583—131nomaximal, Sylow
180C24×C13C2411yescharacteristic
181C23×D13—24no—
182C23×D13—24no—
183C23×D13C2×D414yes—
184C23×D13C2×Q818yes—
185C23×D13C2411yescharacteristic
186C23×D13C2411yescharacteristic
187C2×Q8×C13—22no—
188C2×Q8×C13—42no—
189C22×C4×C13—22no—
190C22×C4×C13—24no—
191C22×C4×C13—22no—
192C22×C4×C13—42no—
193C22×C4×C13—42no—
194C22×C4×C13C2×D414yes—
195C22×C4×C13C2412yes—
196C22×C4×C13C2412yes—
197C22×C4×C13C2412yes—
198C22×C4×C13C2411yescharacteristic
199C22×C4×C13C2411yescharacteristic
200C22×C4×C13C2414yes—
201C22×C4×C13C2412yes—
202C22×Dic13—22no—
203C22×Dic13—24no—
204C22×Dic13—22no—
205C22×Dic13—42no—
206C22×Dic13—42no—
207C22×Dic13C2×D414yes—
208C22×Dic13C2412yes—
209C22×Dic13C2412yes—
210C22×Dic13C2412yes—
211C22×Dic13C2411yescharacteristic
212C22×Dic13C2411yescharacteristic
213C22×Dic13C2414yes—
214C22×Dic13C2412yes—
215Q8×D13—416no—
216C2×C4×D13—232no—
217C2×C4×D13—24no—
218C2×C4×D13—24no—
219C2×C4×D13—28no—
220C2×C4×D13—24no—
221C2×C4×D13—28no—
222C2×C4×D13—24no—
223C2×C4×D13—24no—
224C2×C4×D13—24no—
225C2×C4×D13—24no—
226C2×C4×D13—24no—
227C2×C4×D13—24no—
228C2×C4×D13—24no—
229C2×C4×D13—24no—
230C2×C4×D13—28no—
231C2×C4×D13—28no—
232C2×C4×D13—28no—
233C2×C4×D13—416no—
234C2×C4×D13—42no—
235C2×C4×D13—42no—
236C2×C4×D13—44no—
237C2×C4×D13—416no—
238C2×C4×D13C2×D414yes—
239C2×C4×D13C2×D414yes—
240C2×C4×D13C2×D414yes—
241C2×C4×D13C2×D414yes—
242C2×C4×D13C2×Q8116yes—
243C2×C4×D13#4118yes—
244C2×Dic26—22no—
245C2×Dic26—24no—
246C2×Dic26—44no—
247C2×Dic26—42no—
248C13×C4⋊C4—24no—
249C13×C4⋊C4—24no—
250C13×C4⋊C4—24no—
251C13×C4⋊C4—22no—
252C13×C4⋊C4—28no—
253C13×C4⋊C4—44no—
254C13×C22⋊C4—24no—
255C13×C22⋊C4C2×Q818yescomplemented
256C42×C13—42no—
257C22⋊Dic13—24no—
258C22⋊Dic13C2×Q818yescomplemented
259#6103—24no—
260#6103—24no—
261#6103C2×Q8116yescomplemented
262C4⋊Dic13—22no—
263C4⋊Dic13—24no—
264C4⋊Dic13—24no—
265C4⋊Dic13—24no—
266C4⋊Dic13—28no—
267C4⋊Dic13—44no—
268#6101—24no—
269#6101—24no—
270#6101—24no—
271#6101—28no—
272#6101—24no—
273#6101—24no—
274#6101—24no—
275#6101—24no—
276#6101—28no—
277#6101—44no—
278#6101—44no—
279C4×Dic13—42no—
280C4×Dic13—44no—
281C22×C22⋊Q8—131no—
282C23×C4⋊C4—131no—
283#2583—132no—
284#2583—132no—
285#2583—134no—
286#2583—132no—
287#2583—132no—
288#2583—131no—
289#2583—131no—
290#2583—131no—
291#2583D1311yescharacteristic, direct product factor
292C2×#398—132no—
293C2×#395—132no—
294C2×#389—134no—
295C2×#385—132no—
296C2×#385—132no—
297C2×C4×C22⋊C4—131no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13C22×D412yes—
301C23×C13C22×Q814yes—
302C23×C13C2511yescharacteristic
303C22×D13—22no—
304C22×D13—22no—
305C22×D13—28no—
306C22×D13—28no—
307C22×D13—232no—
308C22×D13C4⋊Q8116yes—
309C22×D13C22×D412yes—
310C22×D13C22×D412yes—
311C22×D13C22×Q814yes—
312C22×D13C22×Q814yes—
313C22×D13C2×#4114yes—
314C22×D13H(5,𝔽2)14yes—
315Q8×C13—44no—
316C2×C4×C13—28no—
317C2×C4×C13—22no—
318C2×C4×C13—24no—
319C2×C4×C13—22no—
320C2×C4×C13—24no—
321C2×C4×C13—22no—
322C2×C4×C13—22no—
323C2×C4×C13—22no—
324C2×C4×C13—22no—
325C2×C4×C13—22no—
326C2×C4×C13—24no—
327C2×C4×C13—24no—
328C2×C4×C13—24no—
329C2×C4×C13—44no—
330C2×C4×C13—44no—
331C2×C4×C13C22×D412yes—
332C2×C4×C13C22×D412yes—
333C2×C4×C13C22×Q818yes—
334C2×C4×C13C2×#4114yes—
335C2×Dic13—28no—
336C2×Dic13—22no—
337C2×Dic13—24no—
338C2×Dic13—22no—
339C2×Dic13—24no—
340C2×Dic13—22no—
341C2×Dic13—22no—
342C2×Dic13—22no—
343C2×Dic13—22no—
344C2×Dic13—22no—
345C2×Dic13—24no—
346C2×Dic13—24no—
347C2×Dic13—24no—
348C2×Dic13—44no—
349C2×Dic13—44no—
350C2×Dic13C22×D412yes—
351C2×Dic13C22×D412yes—
352C2×Dic13C22×Q818yes—
353C2×Dic13C2×#4114yes—
354C4×D13—216no—
355C4×D13—216no—
356C4×D13—28no—
357C4×D13—28no—
358C4×D13—232no—
359C4×D13—44no—
360C4×D13—44no—
361C4×D13—48no—
362C4×D13—48no—
363C4×D13—48no—
364C4×D13—48no—
365Dic26—48no—
366Dic26—44no—
367C23×Q8—131no—
368C24×C4—131no—
369C24×C4—131no—
370C24×C4—131no—
371C2×C22⋊Q8—131no—
372C2×C22⋊Q8—131no—
373C2×C22⋊Q8—132no—
374C2×C22⋊Q8—131no—
375C2×C22⋊Q8—132no—
376C2×C22⋊Q8—268no—
377C2×C22⋊Q8C2×D1311yescharacteristic
378C22×C4⋊C4—131no—
379C22×C4⋊C4—131no—
380C22×C4⋊C4—131no—
381C22×C4⋊C4—132no—
382C22×C4⋊C4—132no—
383C22×C4⋊C4—132no—
384C22×C4⋊C4—131no—
385C22×C4⋊C4—134no—
386C22×C4⋊C4—132no—
387C22×C4⋊C4—132no—
388C22×C4⋊C4—134no—
389C22×C4⋊C4—268no—
390C22×C4⋊C4C2×D1311yescharacteristic
391C22×C22⋊C4—132no—
392C22×C22⋊C4—132no—
393C22×C42—132no—
394#398—132no—
395#398—132no—
396#398—134no—
397#398—134no—
398#398—132no—
399#398C2×D1312yescomplemented
400#395—132no—
401#395—134no—
402#395—132no—
403#395—134no—
404#395—132no—
405#395C2×D1312yescomplemented
406#389—134no—
407#389—134no—
408#389—134no—
409#389—134no—
410#389—134no—
411#389—134no—
412#389—134no—
413#389C2×D1314yescomplemented
414#385—132no—
415#385—132no—
416#385—134no—
417#385—134no—
418#385—132no—
419#385—132no—
420#385—132no—
421#385—132no—
422#385—134no—
423#385—134no—
424#385C2×D1312yes—
425#385C2×D1312yes—
426C4×C22⋊C4—131no—
427C4×C22⋊C4—132no—
428C4×C22⋊C4—132no—
429C4×C22⋊C4—132no—
430C4×C22⋊C4C2×D1311yescharacteristic
431C2×#95—132no—
432C2×#95—134no—
433C2×#95—134no—
434C22×C13—22no—
435C22×C13—22no—
436C22×C13—28no—
437C22×C13C2×C4⋊Q814yes—
438C22×C13C23×D411yescharacteristic
439C22×C13C23×Q812yes—
440C22×C13C22×#4112yes—
441C22×C13C2×H(5,𝔽2)12yes—
442C2×D13—22no—
443C2×D13—22no—
444C2×D13—28no—
445C2×D13—232no—
446C2×D13#52514yes—
447C2×D13C2×C4⋊Q814yes—
448C2×D13C2×C4⋊Q814yes—
449C2×D13#53414yes—
450C2×D13#554116yes—
451C4×C13—24no—
452C4×C13—22no—
453C4×C13—22no—
454C4×C13—28no—
455C4×C13—42no—
456C4×C13—42no—
457C4×C13—42no—
458Dic13—24no—
459Dic13—22no—
460Dic13—22no—
461Dic13—28no—
462Dic13—42no—
463Dic13—42no—
464Dic13—42no—
465C25—131no—
466C22×Q8—132no—
467C22×Q8—131no—
468C22×Q8—264no—
469C22×Q8—524no—
470C22×Q8C22×D1311yescharacteristic
471C23×C4—131no—
472C23×C4—134no—
473C23×C4—132no—
474C23×C4—131no—
475C23×C4—131no—
476C23×C4—138no—
477C23×C4—131no—
478C23×C4—131no—
479C23×C4—131no—
480C23×C4—131no—
481C23×C4—132no—
482C23×C4—132no—
483C23×C4—132no—
484C23×C4—132no—
485C23×C4—132no—
486C23×C4—268no—
487C23×C4—264no—
488C23×C4—264no—
489C23×C4—524no—
490C23×C4—524no—
491C23×C4C22×D1311yescharacteristic
492C23×C4C22×D1311yescharacteristic
493C23×C4C22×D1311yescharacteristic
494C22⋊Q8—24no—
495C22⋊Q8—268no—
496C22⋊Q8—268no—
497C22⋊Q8—264no—
498C22⋊Q8—264no—
499C22⋊Q8—264no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—132no—
502C2×C4⋊C4—132no—
503C2×C4⋊C4—132no—
504C2×C4⋊C4—132no—
505C2×C4⋊C4—132no—
506C2×C4⋊C4—132no—
507C2×C4⋊C4—132no—
508C2×C4⋊C4—132no—
509C2×C4⋊C4—132no—
510C2×C4⋊C4—132no—
511C2×C4⋊C4—131no—
512C2×C4⋊C4—134no—
513C2×C4⋊C4—134no—
514C2×C4⋊C4—134no—
515C2×C4⋊C4—134no—
516C2×C4⋊C4—134no—
517C2×C4⋊C4—134no—
518C2×C4⋊C4—268no—
519C2×C4⋊C4—268no—
520C2×C4⋊C4—268no—
521C2×C4⋊C4—268no—
522C2×C4⋊C4—264no—
523C2×C4⋊C4—268no—
524C2×C4⋊C4—2616no—
525C2×C4⋊C4—264no—
526C2×C4⋊C4—264no—
527C2×C4⋊C4—264no—
528C2×C4⋊C4—528no—
529C2×C4⋊C4C22×D1312yes—
530C2×C4⋊C4C22×D1312yes—
531C2×C4⋊C4C22×D1312yes—
532C2×C4⋊C4C22×D1311yescharacteristic
533C2×C4⋊C4C22×D1314yes—
534C2×C4⋊C4C22×D1314yes—
535C2×C22⋊C4—132no—
536C2×C22⋊C4—134no—
537C2×C22⋊C4—1316no—
538C2×C22⋊C4—132no—
539C2×C22⋊C4—132no—
540C2×C22⋊C4—132no—
541C2×C22⋊C4—268no—
542C2×C22⋊C4C22×D1312yes—
543C2×C22⋊C4C22×D1312yes—
544C2×C42—132no—
545C2×C42—134no—
546C2×C42—524no—
547C2×C42C22×D1312yes—
548#95—132no—
549#95—134no—
550#95—134no—
551#95—134no—
552#95—134no—
553#95—134no—
554#95—134no—
555#95—134no—
556#95C22×D1312yes—
557#95C22×D1314yes—
558#95C22×D1314yes—
559C2×C13—24no—
560C2×C13C2×#52511yescharacteristic
561C2×C13C22×C4⋊Q811yescharacteristic
562C2×C13C2×#53411yescharacteristic
563C2×C13C2×#55414yes—
564D13—24no—
565D13#258318yesdirect product factor
566C24—131no—
567C24—134no—
568C24—138no—
569C24—131no—
570C24—264no—
571C24—264no—
572C24C23×D1311yescharacteristic
573C2×Q8—22no—
574C2×Q8—42no—
575C2×Q8—264no—
576C2×Q8—262no—
577C2×Q8—522no—
578C2×Q8—524no—
579C2×Q8—5216no—
580C22×C4—22no—
581C22×C4—24no—
582C22×C4—22no—
583C22×C4—42no—
584C22×C4—42no—
585C22×C4—134no—
586C22×C4—132no—
587C22×C4—131no—
588C22×C4—131no—
589C22×C4—134no—
590C22×C4—134no—
591C22×C4—134no—
592C22×C4—1316no—
593C22×C4—138no—
594C22×C4—134no—
595C22×C4—134no—
596C22×C4—132no—
597C22×C4—132no—
598C22×C4—132no—
599C22×C4—264no—
600C22×C4—268no—
601C22×C4—264no—
602C22×C4—264no—
603C22×C4—264no—
604C22×C4—268no—
605C22×C4—264no—
606C22×C4—264no—
607C22×C4—2632no—
608C22×C4—264no—
609C22×C4—264no—
610C22×C4—264no—
611C22×C4—264no—
612C22×C4—268no—
613C22×C4—268no—
614C22×C4—268no—
615C22×C4—264no—
616C22×C4—262no—
617C22×C4—264no—
618C22×C4—262no—
619C22×C4—522no—
620C22×C4—522no—
621C22×C4—524no—
622C22×C4—5216no—
623C22×C4—5216no—
624C22×C4—522no—
625C22×C4—522no—
626C22×C4D4×D1314yes—
627C22×C4C23×D1312yes—
628C22×C4C23×D1312yes—
629C22×C4C23×D1312yes—
630C22×C4C23×D1311yescharacteristic
631C22×C4C23×D1311yescharacteristic
632C22×C4C23×D1314yes—
633C22×C4C23×D1312yes—
634C4⋊C4—24no—
635C4⋊C4—24no—
636C4⋊C4—22no—
637C4⋊C4—24no—
638C4⋊C4—28no—
639C4⋊C4—44no—
640C4⋊C4—264no—
641C4⋊C4—264no—
642C4⋊C4—264no—
643C4⋊C4—264no—
644C4⋊C4—264no—
645C4⋊C4—264no—
646C4⋊C4—264no—
647C4⋊C4—268no—
648C4⋊C4—268no—
649C4⋊C4—264no—
650C4⋊C4—264no—
651C4⋊C4—264no—
652C4⋊C4—262no—
653C4⋊C4—268no—
654C4⋊C4—524no—
655C4⋊C4—524no—
656C4⋊C4—524no—
657C22⋊C4—24no—
658C22⋊C4—138no—
659C22⋊C4—1316no—
660C22⋊C4—264no—
661C22⋊C4—264no—
662C22⋊C4—264no—
663C22⋊C4Q8×D1318yescomplemented
664C42—42no—
665C42—524no—
666C42—522no—
667C13C2×#258311yescharacteristic, complemented, Sylow
668C23—22no—
669C23—22no—
670C23—132no—
671C23—134no—
672C23—134no—
673C23—134no—
674C23—1316no—
675C23—132no—
676C23—134no—
677C23—268no—
678C23—268no—
679C23—2632no—
680C23—262no—
681C23—262no—
682C23C2×D4×D1312yes—
683C23C2×Q8×D1314yes—
684C23C24×D1311yescharacteristic
685Q8—44no—
686Q8—524no—
687Q8—528no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—24no—
701C2×C4—44no—
702C2×C4—44no—
703C2×C4—132no—
704C2×C4—132no—
705C2×C4—138no—
706C2×C4—134no—
707C2×C4—2632no—
708C2×C4—2616no—
709C2×C4—268no—
710C2×C4—268no—
711C2×C4—2616no—
712C2×C4—268no—
713C2×C4—262no—
714C2×C4—264no—
715C2×C4—262no—
716C2×C4—264no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—264no—
723C2×C4—264no—
724C2×C4—264no—
725C2×C4—524no—
726C2×C4—524no—
727C2×C4—528no—
728C2×C4—528no—
729C2×C4—528no—
730C2×C4—528no—
731C2×C4—524no—
732C2×C4—524no—
733C2×C4C2×D4×D1312yes—
734C2×C4C2×D4×D1312yes—
735C2×C4C2×Q8×D1318yes—
736C2×C4#41×D1314yes—
737C22—22no—
738C22—28no—
739C22—22no—
740C22—134no—
741C22—1316no—
742C22—134no—
743C22—134no—
744C22—134no—
745C22—2632no—
746C22—262no—
747C22—268no—
748C22—262no—
749C22D13×C4⋊Q814yes—
750C22C22×D4×D1311yescharacteristic
751C22C22×Q8×D1312yes—
752C22C2×#41×D1312yes—
753C22D13×H(5,𝔽2)12yes—
754C4—24no—
755C4—28no—
756C4—22no—
757C4—22no—
758C4—42no—
759C4—42no—
760C4—42no—
761C4—264no—
762C4—268no—
763C4—262no—
764C4—262no—
765C4—522no—
766C4—522no—
767C4—522no—
768C2—24no—
769C2—138no—
770C2—264no—
771C2D13×#52511yescharacteristic
772C2C2×D13×C4⋊Q811yescharacteristic
773C2D13×#53411yescharacteristic
774C2D13×#55414yes—
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2583C2
prime radicalC24×D13C23
hypercenter#2583D13
hypocenterC13C2×#2583
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2583

Complements

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

NH ≅ G/Ntype
3. #13120217C2semidirect
4. #13120216C2semidirect
5. #13120215C2semidirect
6. #13120214C2semidirect
7. #13120213C2semidirect
8. #13120212C2semidirect
9. #13120211C2semidirect
10. #13120210C2semidirect
11. D13×#398C2semidirect
12. D13×#395C2semidirect
13. D13×#389C2semidirect
17. C13×#2583C2semidirect
45. C13×#398C22semidirect
46. C13×#395C22semidirect
47. C13×#389C22semidirect
51. #11718890C22semidirect
57. #11718646C22semidirect
58. #11718645C22semidirect
59. #11718644C22semidirect
60. #11718641C22semidirect
61. #11718640C22semidirect
62. #11718640C22semidirect
63. #11718634C22semidirect
64. #11718633C22semidirect
65. #11718633C22semidirect
72. #11718589C22semidirect
79. #11718322C22semidirect
80. #11718318C22semidirect
81. #11718317C22semidirect
82. #11718317C22semidirect
83. #11718308C22semidirect
84. #11718308C22semidirect
165. C22⋊C4×D13Q8semidirect
255. C13×C22⋊C4C2×Q8semidirect
258. C22⋊Dic13C2×Q8semidirect
261. #6103C2×Q8semidirect
291. #2583D13direct (N × H)
399. #398C2×D13semidirect
405. #395C2×D13semidirect
413. #389C2×D13semidirect
565. D13#2583direct (N × H)
663. C22⋊C4Q8×D13semidirect
667. C13C2×#2583semidirect

Maximal subgroups

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

subgroupindex
C2×D13×C22⋊Q82
C22×C4⋊C4×D132
#131202172
#131202162
#131202152
#131202142
#131202132
#131202122
#131202112
#131202102
D13×#3982
D13×#3952
D13×#3892
D13×#3852
C4×C22⋊C4×D132
C13×#25832
C2×#258313