Finite Group Databasebeta

← D13×#1441 #15784588

Subgroups — D13×#1441 #15784588

Order 3328.

3246 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D13C211yesmaximal, characteristic
2C22×C4⋊C4×D13C211yesmaximal, characteristic
3C2×D13×#95C212yesmaximal
4C2×D13×#95C212yesmaximal
5C2×D13×#95C211yesmaximal, characteristic
6#13113090C211yesmaximal, characteristic, complemented
7#13113089C211yesmaximal, characteristic, complemented
8#13113088C212yesmaximal, complemented
9#13113087C212yesmaximal, complemented
10#13113086C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C23×C4×D13C2212yes—
14C23×C4×D13C2212yes—
15C23×C4×D13C2211yescharacteristic
16C23×C4×D13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×#6101C2211yescharacteristic
23C22×#6101C2211yescharacteristic
24C2×C4⋊C4×D13—28no—
25C2×C4⋊C4×D13—24no—
26C2×C4⋊C4×D13—24no—
27C2×C4⋊C4×D13—24no—
28C2×C4⋊C4×D13C418yescomplemented
29C2×C13×#95C2212yes—
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39C2×#88071C2212yes—
40D13×#95—28no—
41D13×#95—24no—
42D13×#95—28no—
43C24×D13C2311yescharacteristic
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×C4×C13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2312yes—
52C23×Dic13C2311yescharacteristic
53C23×Dic13C2311yescharacteristic
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—24no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13—24no—
60C22×C4×D13—22no—
61C22×C4×D13—22no—
62C22×C4×D13—24no—
63C22×C4×D13—24no—
64C22×C4×D13—24no—
65C22×C4×D13—24no—
66C22×C4×D13—24no—
67C22×C4×D13—24no—
68C22×C4×D13—24no—
69C22×C4×D13—24no—
70C22×C4×D13—24no—
71C22×C4×D13—24no—
72C22×C4×D13—24no—
73C22×C4×D13—24no—
74C22×C4×D13—24no—
75C22×C4×D13—24no—
76C22×C4×D13C2×C414yes—
77C22×C4×D13C2×C414yes—
78C22×C4×D13C2×C414yes—
79C22×C4×D13D418yes—
80C22×C4×D13D414yes—
81C22×C4×D13D414yes—
82C22×C4×D13D414yes—
83C22×C4×D13Q818yes—
84C22×C4×D13Q814yes—
85C2×C13×C4⋊C4—24no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4C2×C414yescomplemented
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—24no—
92C2×C4⋊Dic13—22no—
93C2×C4⋊Dic13—22no—
94C2×C4⋊Dic13C2×C414yescomplemented
95C2×#6101—24no—
96C2×#6101—22no—
97C2×#6101—22no—
98C2×#6101—24no—
99C2×#6101—24no—
100C2×#6101—22no—
101C2×#6101—22no—
102C2×#6101C2×C414yescomplemented
103C2×#6101C2×C414yescomplemented
104C4⋊C4×D13—232no—
105C4⋊C4×D13—232no—
106C13×#95—24no—
107C13×#95—22no—
108C13×#95—24no—
109#88071—24no—
110#88071—22no—
111#88071—24no—
112#88071—24no—
113#88071—24no—
114#88071—24no—
115#88071—24no—
116#88071—24no—
117C2×#1441—131nomaximal, Sylow
118C24×C13C2411yescharacteristic
119C23×D13C22×C412yes—
120C23×D13C2×D412yes—
121C23×D13C2×D412yes—
122C23×D13C2×D412yes—
123C23×D13C2×D414yes—
124C23×D13C2×Q812yes—
125C23×D13C2×Q814yes—
126C23×D13#4112yes—
127C23×D13#4112yes—
128C23×D13#4114yes—
129C23×D13#4114yes—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13C22×C412yes—
153C22×C4×C13C22×C412yes—
154C22×C4×C13C22×C412yes—
155C22×C4×C13C2×D414yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D412yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×Q814yes—
160C22×C4×C13C2×Q812yes—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—22no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—22no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13C22×C412yes—
184C22×Dic13C22×C412yes—
185C22×Dic13C22×C412yes—
186C22×Dic13C2×D414yes—
187C22×Dic13C2×D412yes—
188C22×Dic13C2×D412yes—
189C22×Dic13C2×D412yes—
190C22×Dic13C2×Q814yes—
191C22×Dic13C2×Q812yes—
192C2×C4×D13—28no—
193C2×C4×D13—28no—
194C2×C4×D13—216no—
195C2×C4×D13—28no—
196C2×C4×D13—28no—
197C2×C4×D13—28no—
198C2×C4×D13—216no—
199C2×C4×D13—28no—
200C2×C4×D13—28no—
201C2×C4×D13—28no—
202C2×C4×D13—28no—
203C2×C4×D13—216no—
204C2×C4×D13—216no—
205C2×C4×D13—216no—
206C2×C4×D13—216no—
207C2×C4×D13—216no—
208C2×C4×D13—216no—
209C2×C4×D13—216no—
210C2×C4×D13—44no—
211C2×C4×D13—48no—
212C2×C4×D13—48no—
213C2×C4×D13—48no—
214C2×C4×D13—48no—
215C2×C4×D13—48no—
216C2×C4×D13—48no—
217C2×C4×D13—44no—
218C2×C4×D13—48no—
219C2×C4×D13—48no—
220C2×C4×D13—48no—
221C2×C4×D13C22⋊C4116yes—
222C2×C4×D13C4⋊C4116yescomplemented
223C13×C4⋊C4—28no—
224C13×C4⋊C4—28no—
225C4⋊Dic13—28no—
226C4⋊Dic13—28no—
227#6101—216no—
228#6101—28no—
229#6101—28no—
230C23×C4⋊C4—131no—
231C23×C4⋊C4—131no—
232C22×#95—131no—
233C22×#95—132no—
234C22×#95—132no—
235#1441—132no—
236#1441—131no—
237#1441—132no—
238#1441—131no—
239#1441—131no—
240#1441D1311yescharacteristic, direct product factor
241C23×C13C23×C411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×D411yescharacteristic
244C23×C13C22×D411yescharacteristic
245C23×C13C22×D412yes—
246C23×C13C22×Q811yescharacteristic
247C23×C13C22×Q812yes—
248C23×C13C2×#4111yescharacteristic
249C23×C13C2×#4111yescharacteristic
250C23×C13C2×#4112yes—
251C23×C13C2×#4112yes—
252C22×D13C2×C22⋊C414yes—
253C22×D13C2×C4⋊C414yes—
254C22×D13#11714yes—
255C22×D13C4×D418yes—
256C22×D13C4×Q818yes—
257C22×D13#12014yes—
258C22×D13#12114yes—
259C22×D13#12114yes—
260C22×D13#12118yes—
261C22×D13#12118yes—
262C22×D13C22⋊Q814yes—
263C22×D13C22⋊Q814yes—
264C22×D13C22⋊Q818yes—
265C22×D13C22⋊Q818yes—
266C22×D13C22⋊Q818yes—
267C22×D13#12314yes—
268C22×D13#12318yes—
269C22×D13#12414yes—
270C22×D13#12518yes—
271C22×D13#12518yes—
272C22×D13#12618yes—
273C22×D13C4⋊Q818yes—
274C22×D13C4⋊Q814yes—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—24no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—24no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—24no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13C2×C22⋊C414yes—
305C2×C4×C13C2×C4⋊C414yescomplemented
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—24no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—24no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—24no—
318C2×Dic13—24no—
319C2×Dic13—24no—
320C2×Dic13—24no—
321C2×Dic13—24no—
322C2×Dic13—24no—
323C2×Dic13—24no—
324C2×Dic13—41no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13C2×C22⋊C414yes—
336C2×Dic13C2×C4⋊C414yescomplemented
337C4×D13—232no—
338C4×D13—232no—
339C4×D13—416no—
340C4×D13—432no—
341C4×D13—432no—
342C24×C4—131no—
343C24×C4—131no—
344C24×C4—131no—
345C24×C4—132no—
346C24×C4—132no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4—131no—
350C22×C4⋊C4—138no—
351C22×C4⋊C4—132no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—264no—
354C22×C4⋊C4—264no—
355C22×C4⋊C4—264no—
356C22×C4⋊C4—268no—
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C4⋊C4C2×D1311yescharacteristic
359C2×#95—132no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95—131no—
367C2×#95—264no—
368C2×#95—268no—
369C2×#95—268no—
370C2×#95C2×D1312yes—
371C2×#95C2×D1312yes—
372C2×#95C2×D1311yescharacteristic
373C22×C13C22×C22⋊C411yescharacteristic
374C22×C13C22×C4⋊C411yescharacteristic
375C22×C13C2×#11711yescharacteristic
376C22×C13C2×C4×D412yes—
377C22×C13C2×C4×Q812yes—
378C22×C13C2×#12011yescharacteristic
379C22×C13C2×#12112yes—
380C22×C13C2×#12111yescharacteristic
381C22×C13C2×#12111yescharacteristic
382C22×C13C2×#12112yes—
383C22×C13C2×C22⋊Q812yes—
384C22×C13C2×C22⋊Q811yescharacteristic
385C22×C13C2×C22⋊Q812yes—
386C22×C13C2×C22⋊Q812yes—
387C22×C13C2×C22⋊Q811yescharacteristic
388C22×C13C2×#12312yes—
389C22×C13C2×#12311yescharacteristic
390C22×C13C2×#12411yescharacteristic
391C22×C13C2×#12512yes—
392C22×C13C2×#12512yes—
393C22×C13C2×#12612yes—
394C22×C13C2×C4⋊Q812yes—
395C22×C13C2×C4⋊Q811yescharacteristic
396C2×D13#38018yes—
397C2×D13#38618yes—
398C2×D13#387116yes—
399C2×D13#389116yes—
400C2×D13#39118yes—
401C2×D13#39418yes—
402C2×D13#39518yes—
403C2×D13#396116yes—
404C2×D13#39818yes—
405C2×D13#398116yes—
406C2×D13#40018yes—
407C4×C13—24no—
408C4×C13—24no—
409C4×C13—44no—
410C4×C13—44no—
411C4×C13—42no—
412Dic13—24no—
413Dic13—24no—
414Dic13—44no—
415Dic13—44no—
416Dic13—42no—
417C25—131no—
418C23×C4—131no—
419C23×C4—131no—
420C23×C4—134no—
421C23×C4—134no—
422C23×C4—134no—
423C23×C4—134no—
424C23×C4—134no—
425C23×C4—134no—
426C23×C4—131no—
427C23×C4—132no—
428C23×C4—132no—
429C23×C4—134no—
430C23×C4—138no—
431C23×C4—138no—
432C23×C4—264no—
433C23×C4—262no—
434C23×C4—262no—
435C23×C4—264no—
436C23×C4—262no—
437C23×C4—262no—
438C23×C4—262no—
439C23×C4—262no—
440C23×C4—264no—
441C23×C4—264no—
442C23×C4—264no—
443C23×C4—264no—
444C23×C4—264no—
445C23×C4—264no—
446C23×C4—264no—
447C23×C4—264no—
448C23×C4—264no—
449C23×C4—264no—
450C23×C4—264no—
451C23×C4—264no—
452C23×C4—264no—
453C23×C4—264no—
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1312yes—
456C23×C4C22×D1312yes—
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C2×C4⋊C4—24no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—134no—
466C2×C4⋊C4—2632no—
467C2×C4⋊C4—2632no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—264no—
471C2×C4⋊C4—264no—
472C2×C4⋊C4—262no—
473C2×C4⋊C4—262no—
474C2×C4⋊C4—264no—
475C2×C4⋊C4—264no—
476C2×C4⋊C4—262no—
477C2×C4⋊C4—262no—
478C2×C4⋊C4—262no—
479C2×C4⋊C4C4×D1314yescomplemented
480#95—24no—
481#95—22no—
482#95—24no—
483#95—264no—
484#95—264no—
485#95—264no—
486#95—264no—
487#95—264no—
488#95—264no—
489#95—262no—
490#95—264no—
491C2×C13C2×#38011yescharacteristic
492C2×C13C2×#38611yescharacteristic
493C2×C13C2×#38712yes—
494C2×C13C2×#38912yes—
495C2×C13C2×#39111yescharacteristic
496C2×C13C2×#39411yescharacteristic
497C2×C13C2×#39511yescharacteristic
498C2×C13C2×#39612yes—
499C2×C13C2×#39811yescharacteristic
500C2×C13C2×#39812yes—
501C2×C13C2×#40011yescharacteristic
502D13#1441116yesdirect product factor
503C24—132no—
504C24—132no—
505C24—134no—
506C24—132no—
507C24—132no—
508C24—132no—
509C24—134no—
510C24—132no—
511C24—132no—
512C24—134no—
513C24—134no—
514C24C23×D1311yescharacteristic
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—132no—
542C22×C4—132no—
543C22×C4—1316no—
544C22×C4—1316no—
545C22×C4—132no—
546C22×C4—134no—
547C22×C4—134no—
548C22×C4—268no—
549C22×C4—268no—
550C22×C4—268no—
551C22×C4—2616no—
552C22×C4—2616no—
553C22×C4—268no—
554C22×C4—268no—
555C22×C4—268no—
556C22×C4—268no—
557C22×C4—268no—
558C22×C4—268no—
559C22×C4—2616no—
560C22×C4—2616no—
561C22×C4—2616no—
562C22×C4—2616no—
563C22×C4—2616no—
564C22×C4—2616no—
565C22×C4—2616no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—262no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—524no—
589C22×C4—528no—
590C22×C4—528no—
591C22×C4—528no—
592C22×C4—528no—
593C22×C4—528no—
594C22×C4—528no—
595C22×C4—524no—
596C22×C4—528no—
597C22×C4—528no—
598C22×C4—528no—
599C22×C4C2×C4×D1312yes—
600C22×C4C2×C4×D1312yes—
601C22×C4C2×C4×D1312yes—
602C22×C4D4×D1314yes—
603C22×C4D4×D1312yes—
604C22×C4D4×D1312yes—
605C22×C4D4×D1312yes—
606C22×C4Q8×D1314yes—
607C22×C4Q8×D1312yes—
608C4⋊C4—28no—
609C4⋊C4—28no—
610C4⋊C4—268no—
611C4⋊C4—268no—
612C4⋊C4—2616no—
613C4⋊C4—268no—
614C4⋊C4—268no—
615C13C2×#144111yescharacteristic, complemented, Sylow
616C23—138no—
617C23—134no—
618C23—134no—
619C23—134no—
620C23—134no—
621C23—138no—
622C23—138no—
623C23—134no—
624C23—134no—
625C23—134no—
626C23—138no—
627C23—138no—
628C23—134no—
629C23—134no—
630C23—138no—
631C23—138no—
632C23—138no—
633C23—134no—
634C23—138no—
635C23—134no—
636C23—138no—
637C23—138no—
638C23—138no—
639C23C22×C4×D1311yescharacteristic
640C23C2×D4×D1311yescharacteristic
641C23C2×D4×D1312yes—
642C23C2×D4×D1311yescharacteristic
643C23C2×D4×D1311yescharacteristic
644C23C2×Q8×D1311yescharacteristic
645C23C2×Q8×D1312yes—
646C23#41×D1311yescharacteristic
647C23#41×D1311yescharacteristic
648C23#41×D1312yes—
649C23#41×D1312yes—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—24no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—41no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—41no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—134no—
680C2×C4—134no—
681C2×C4—2632no—
682C2×C4—2632no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—264no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—264no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—264no—
695C2×C4—264no—
696C2×C4—264no—
697C2×C4—264no—
698C2×C4—264no—
699C2×C4—264no—
700C2×C4—264no—
701C2×C4—5216no—
702C2×C4—5232no—
703C2×C4—5232no—
704C2×C4—521no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—522no—
708C2×C4—522no—
709C2×C4—522no—
710C2×C4—522no—
711C2×C4—521no—
712C2×C4—522no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4C22⋊C4×D1314yes—
716C2×C4C4⋊C4×D1314yescomplemented
717C22—138no—
718C22—138no—
719C22—1316no—
720C22—138no—
721C22—138no—
722C22—1316no—
723C22—1316no—
724C22—1316no—
725C22—138no—
726C22—138no—
727C22—138no—
728C22C2×C22⋊C4×D1311yescharacteristic
729C22C2×C4⋊C4×D1311yescharacteristic
730C22D13×#11711yescharacteristic
731C22C4×D4×D1312yes—
732C22C4×Q8×D1312yes—
733C22D13×#12011yescharacteristic
734C22D13×#12111yescharacteristic
735C22D13×#12111yescharacteristic
736C22D13×#12112yes—
737C22D13×#12112yes—
738C22D13×C22⋊Q811yescharacteristic
739C22D13×C22⋊Q811yescharacteristic
740C22D13×C22⋊Q812yes—
741C22D13×C22⋊Q812yes—
742C22D13×C22⋊Q812yes—
743C22D13×#12311yescharacteristic
744C22D13×#12312yes—
745C22D13×#12411yescharacteristic
746C22D13×#12512yes—
747C22D13×#12512yes—
748C22D13×#12612yes—
749C22D13×C4⋊Q812yes—
750C22D13×C4⋊Q811yescharacteristic
751C4—24no—
752C4—24no—
753C4—42no—
754C4—44no—
755C4—44no—
756C4—264no—
757C4—264no—
758C4—522no—
759C4—524no—
760C4—524no—
761C2—1316no—
762C2D13×#38011yescharacteristic
763C2D13×#38611yescharacteristic
764C2D13×#38712yes—
765C2D13×#38912yes—
766C2D13×#39111yescharacteristic
767C2D13×#39411yescharacteristic
768C2D13×#39511yescharacteristic
769C2D13×#39612yes—
770C2D13×#39812yes—
771C2D13×#39811yescharacteristic
772C2D13×#40011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×#1441C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenter#1441D13
hypocenterC13C2×#1441
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ #1441

Complements

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

NH ≅ G/Ntype
6. #13113090C2semidirect
7. #13113089C2semidirect
8. #13113088C2semidirect
9. #13113087C2semidirect
10. #13113086C2semidirect
11. C13×#1441C2semidirect
28. C2×C4⋊C4×D13C4semidirect
89. C2×C13×C4⋊C4C2×C4semidirect
94. C2×C4⋊Dic13C2×C4semidirect
102. C2×#6101C2×C4semidirect
103. C2×#6101C2×C4semidirect
222. C2×C4×D13C4⋊C4semidirect
240. #1441D13direct (N × H)
305. C2×C4×C13C2×C4⋊C4semidirect
336. C2×Dic13C2×C4⋊C4semidirect
479. C2×C4⋊C4C4×D13semidirect
502. D13#1441direct (N × H)
615. C13C2×#1441semidirect
716. C2×C4C4⋊C4×D13semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D132
C2×D13×#952
#131130902
#131130892
#131130882
#131130872
#131130862
C13×#14412
C2×#144113