Finite Group Databasebeta

← C13×#15257 #15701596

Subgroups — C13×#15257 #15701596

Order 3328.

4462 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic, complemented
2C22×C13×#120C211yesmaximal, characteristic, complemented
3C22×C13×#120C211yesmaximal, characteristic, complemented
4C2×C13×#392C212yesmaximal, complemented
5C2×C13×#386C212yesmaximal, complemented
6C2×C13×#379C211yesmaximal, characteristic, complemented
7C13×#1440C211yesmaximal, characteristic, complemented
8C13×#1439C212yesmaximal, complemented
9C13×#1438C212yesmaximal, complemented
10C13×#1438C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic, complemented
12C26×C13C2211yescharacteristic
13C23×D4×C13C2212yes—
14C23×D4×C13C2212yes—
15C23×D4×C13C2211yescharacteristic
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic, complemented
18C24×C4×C13C2211yescharacteristic, complemented
19C2×C13×#121—24no—
20C2×C13×#121—24no—
21C2×C13×#121—24no—
22C2×C13×#120—28no—
23C2×C13×#120—24no—
24C2×C13×#120—24no—
25C2×C13×#120—28no—
26C22×C13×C4⋊C4C2211yescharacteristic, complemented
27C22×C13×C22⋊C4C2212yes—
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2212yes—
31C22×C13×C22⋊C4C2212yes—
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2212yes—
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic, complemented
36C22×C13×C22⋊C4C2212yescomplemented
37C22×C13×C22⋊C4C2212yescomplemented
38C13×#392—28no—
39C13×#386—28no—
40C13×#379—24no—
41C2×C13×#95C2212yescomplemented
42C2×C13×#95C2212yescomplemented
43C2×C13×#95C2212yescomplemented
44C2×C13×#95C2212yescomplemented
45C25×C13—22no—
46C25×C13—22no—
47C25×C13—22no—
48C25×C13—24no—
49C25×C13—24no—
50C25×C13—24no—
51C25×C13—42no—
52C25×C13—42no—
53C25×C13—42no—
54C25×C13C2311yescharacteristic
55C25×C13C2311yescharacteristic
56C25×C13C2311yescharacteristic
57C25×C13C2312yes—
58C22×D4×C13—24no—
59C22×D4×C13—24no—
60C22×D4×C13—24no—
61C22×D4×C13—24no—
62C22×D4×C13—24no—
63C22×D4×C13—24no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—24no—
71C22×D4×C13—24no—
72C22×D4×C13—24no—
73C22×D4×C13—24no—
74C22×D4×C13—24no—
75C22×D4×C13—24no—
76C22×D4×C13—22no—
77C22×D4×C13—42no—
78C22×D4×C13—42no—
79C22×D4×C13—42no—
80C22×D4×C13—42no—
81C22×D4×C13—42no—
82C22×D4×C13—42no—
83C22×D4×C13—42no—
84C22×D4×C13D418yescomplemented
85C22×D4×C13D414yescomplemented
86C22×D4×C13D414yescomplemented
87C23×C4×C13—22no—
88C23×C4×C13—22no—
89C23×C4×C13—22no—
90C23×C4×C13—24no—
91C23×C4×C13—42no—
92C23×C4×C13C2312yes—
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2312yes—
97C23×C4×C13C2312yes—
98C23×C4×C13C2311yescharacteristic
99C13×#121—232no—
100C13×#120—232no—
101C13×#120—232no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—24no—
112C2×C13×C22⋊C4—24no—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4—24no—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—24no—
121C2×C13×C22⋊C4—24no—
122C2×C13×C22⋊C4—24no—
123C2×C13×C22⋊C4—24no—
124C2×C13×C22⋊C4—24no—
125C2×C13×C22⋊C4—24no—
126C2×C13×C22⋊C4—24no—
127C2×C13×C22⋊C4—42no—
128C2×C13×C22⋊C4—42no—
129C2×C13×C22⋊C4—42no—
130C2×C13×C22⋊C4—42no—
131C2×C13×C22⋊C4—42no—
132C2×C13×C22⋊C4—42no—
133C2×C13×C22⋊C4D414yescomplemented
134C2×C13×C22⋊C4D418yescomplemented
135C13×#95—24no—
136C13×#95—24no—
137C13×#95—24no—
138C13×#95—42no—
139#15257C1311yesmaximal, characteristic, direct product factor, Sylow
140C24×C13—22no—
141C24×C13—22no—
142C24×C13—22no—
143C24×C13—22no—
144C24×C13—22no—
145C24×C13—22no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—22no—
151C24×C13—22no—
152C24×C13—22no—
153C24×C13—22no—
154C24×C13—22no—
155C24×C13—22no—
156C24×C13—22no—
157C24×C13—22no—
158C24×C13—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—28no—
166C24×C13—28no—
167C24×C13—28no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—22no—
171C24×C13—22no—
172C24×C13—22no—
173C24×C13—22no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—48no—
177C24×C13—48no—
178C24×C13—48no—
179C24×C13—48no—
180C24×C13—48no—
181C24×C13—48no—
182C24×C13—48no—
183C24×C13—48no—
184C24×C13—48no—
185C24×C13—44no—
186C24×C13—44no—
187C24×C13—48no—
188C24×C13—44no—
189C24×C13—48no—
190C24×C13—48no—
191C24×C13—48no—
192C24×C13—44no—
193C24×C13—48no—
194C24×C13C2×D412yes—
195C24×C13C2×D412yes—
196C24×C13C2×D412yes—
197C24×C13C2×D412yes—
198C24×C13C2×D414yes—
199C24×C13C2×D412yes—
200C24×C13C2×D414yes—
201C24×C13C2×D414yes—
202C24×C13#4114yes—
203C24×C13C2411yescharacteristic
204C2×D4×C13—216no—
205C2×D4×C13—28no—
206C2×D4×C13—28no—
207C2×D4×C13—28no—
208C2×D4×C13—216no—
209C2×D4×C13—28no—
210C2×D4×C13—216no—
211C2×D4×C13—28no—
212C2×D4×C13—44no—
213C2×D4×C13—48no—
214C2×D4×C13—44no—
215C2×D4×C13—48no—
216C2×D4×C13—48no—
217C2×D4×C13—48no—
218C2×D4×C13—48no—
219C2×D4×C13—48no—
220C2×D4×C13—48no—
221C2×D4×C13—48no—
222C2×D4×C13—48no—
223C2×D4×C13—48no—
224C2×D4×C13—48no—
225C2×D4×C13—48no—
226C2×D4×C13—48no—
227C2×D4×C13—48no—
228C2×D4×C13—48no—
229C2×D4×C13—44no—
230C2×D4×C13—48no—
231C2×D4×C13—44no—
232C2×D4×C13—48no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—22no—
236C22×C4×C13—28no—
237C22×C4×C13—22no—
238C22×C4×C13—22no—
239C22×C4×C13—22no—
240C22×C4×C13—22no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—22no—
244C22×C4×C13—22no—
245C22×C4×C13—22no—
246C22×C4×C13—22no—
247C22×C4×C13—22no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—22no—
253C22×C4×C13—22no—
254C22×C4×C13—22no—
255C22×C4×C13—22no—
256C22×C4×C13—22no—
257C22×C4×C13—22no—
258C22×C4×C13—22no—
259C22×C4×C13—22no—
260C22×C4×C13—22no—
261C22×C4×C13—22no—
262C22×C4×C13—22no—
263C22×C4×C13—22no—
264C22×C4×C13—22no—
265C22×C4×C13—22no—
266C22×C4×C13—22no—
267C22×C4×C13—22no—
268C22×C4×C13—48no—
269C22×C4×C13—48no—
270C22×C4×C13—44no—
271C22×C4×C13—44no—
272C22×C4×C13C2×D414yes—
273C22×C4×C13C2×D414yes—
274C22×C4×C13C2×D412yes—
275C22×C4×C13C2×D412yes—
276C22×C4×C13C2×D412yes—
277C22×C4×C13C2×D414yes—
278C22×C4×C13C2×D412yes—
279C13×C4⋊C4—28no—
280C13×C22⋊C4—216no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—28no—
283C13×C22⋊C4—28no—
284C13×C22⋊C4—28no—
285C13×C22⋊C4—216no—
286C13×C22⋊C4—48no—
287C13×C22⋊C4—48no—
288C13×C22⋊C4—48no—
289C13×C22⋊C4—48no—
290C13×C22⋊C4—44no—
291C22×#121C2×C1311yescharacteristic, complemented
292C22×#120C2×C1311yescharacteristic, complemented
293C22×#120C2×C1311yescharacteristic, complemented
294C2×#392C2×C1312yescomplemented
295C2×#386C2×C1312yescomplemented
296C2×#379C2×C1311yescharacteristic, complemented
297#1440C2×C1311yescharacteristic, complemented
298#1439C2×C1312yescomplemented
299#1438C2×C1312yescomplemented
300#1438C2×C1311yescharacteristic, complemented
301#1438C2×C1311yescharacteristic, complemented
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—24no—
305C23×C13—24no—
306C23×C13—22no—
307C23×C13—24no—
308C23×C13—22no—
309C23×C13—24no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—24no—
314C23×C13—24no—
315C23×C13—22no—
316C23×C13—24no—
317C23×C13—24no—
318C23×C13—24no—
319C23×C13—24no—
320C23×C13—24no—
321C23×C13—24no—
322C23×C13—24no—
323C23×C13—24no—
324C23×C13—24no—
325C23×C13—24no—
326C23×C13—24no—
327C23×C13—24no—
328C23×C13—24no—
329C23×C13—24no—
330C23×C13—24no—
331C23×C13—24no—
332C23×C13—24no—
333C23×C13—24no—
334C23×C13—24no—
335C23×C13—24no—
336C23×C13—24no—
337C23×C13—24no—
338C23×C13—24no—
339C23×C13—24no—
340C23×C13—24no—
341C23×C13—24no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—24no—
346C23×C13—24no—
347C23×C13—416no—
348C23×C13—416no—
349C23×C13—416no—
350C23×C13—432no—
351C23×C13—432no—
352C23×C13—432no—
353C23×C13—432no—
354C23×C13—432no—
355C23×C13—432no—
356C23×C13—41no—
357C23×C13—42no—
358C23×C13—42no—
359C23×C13—42no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—42no—
363C23×C13—42no—
364C23×C13—42no—
365C23×C13—42no—
366C23×C13—41no—
367C23×C13—42no—
368C23×C13—42no—
369C23×C13—42no—
370C23×C13—42no—
371C23×C13—42no—
372C23×C13—42no—
373C23×C13—42no—
374C23×C13—42no—
375C23×C13—42no—
376C23×C13—42no—
377C23×C13—42no—
378C23×C13—42no—
379C23×C13—42no—
380C23×C13—42no—
381C23×C13—42no—
382C23×C13—42no—
383C23×C13—42no—
384C23×C13—42no—
385C23×C13—42no—
386C23×C13—42no—
387C23×C13—42no—
388C23×C13—42no—
389C23×C13—42no—
390C23×C13—41no—
391C23×C13—42no—
392C23×C13—41no—
393C23×C13—42no—
394C23×C13—41no—
395C23×C13—42no—
396C23×C13—41no—
397C23×C13—42no—
398C23×C13—42no—
399C23×C13—42no—
400C23×C13—42no—
401C23×C13—42no—
402C23×C13—42no—
403C23×C13—42no—
404C23×C13—42no—
405C23×C13—42no—
406C23×C13#12014yes—
407C23×C13#12014yescomplemented
408C23×C13#12118yescomplemented
409C23×C13C22×D411yescharacteristic
410C23×C13C22×D411yescharacteristic
411C23×C13C22×D412yes—
412C23×C13C22×D412yes—
413C23×C13C22×D411yescharacteristic
414C23×C13C2×#4112yes—
415C23×C13H(5,𝔽2)12yes—
416C23×C13H(5,𝔽2)12yes—
417C23×C13H(5,𝔽2)12yes—
418D4×C13—416no—
419D4×C13—416no—
420D4×C13—432no—
421D4×C13—416no—
422D4×C13—432no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—24no—
426C2×C4×C13—24no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—24no—
430C2×C4×C13—24no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—24no—
434C2×C4×C13—24no—
435C2×C4×C13—22no—
436C2×C4×C13—24no—
437C2×C4×C13—24no—
438C2×C4×C13—24no—
439C2×C4×C13—24no—
440C2×C4×C13—416no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—42no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—42no—
447C2×C4×C13—42no—
448C2×C4×C13—42no—
449C2×C4×C13—42no—
450C2×C4×C13—42no—
451C2×C4×C13—42no—
452C2×C4×C13—42no—
453C2×C4×C13—42no—
454C2×C4×C13—42no—
455C2×C4×C13—42no—
456C2×C4×C13—42no—
457C2×C4×C13—42no—
458C2×C4×C13—42no—
459C2×C4×C13—42no—
460C2×C4×C13—42no—
461C2×C4×C13—42no—
462C2×C4×C13—42no—
463C2×C4×C13—42no—
464C2×C4×C13#12014yescomplemented
465C26C22×C1311yescharacteristic
466C23×D4C22×C1312yes—
467C23×D4C22×C1312yes—
468C23×D4C22×C1311yescharacteristic
469C23×D4C22×C1311yescharacteristic
470C23×D4C22×C1311yescharacteristic, complemented
471C24×C4C22×C1311yescharacteristic, complemented
472C2×#121—24no—
473C2×#121—24no—
474C2×#121—24no—
475C2×#120—24no—
476C2×#120—24no—
477C2×#120—28no—
478C2×#120—28no—
479C22×C4⋊C4C22×C1311yescharacteristic, complemented
480C22×C22⋊C4C22×C1312yes—
481C22×C22⋊C4C22×C1311yescharacteristic
482C22×C22⋊C4C22×C1311yescharacteristic
483C22×C22⋊C4C22×C1312yes—
484C22×C22⋊C4C22×C1312yes—
485C22×C22⋊C4C22×C1312yes—
486C22×C22⋊C4C22×C1311yescharacteristic
487C22×C22⋊C4C22×C1311yescharacteristic
488C22×C22⋊C4C22×C1311yescharacteristic, complemented
489C22×C22⋊C4C22×C1312yescomplemented
490C22×C22⋊C4C22×C1312yescomplemented
491#392—28no—
492#386—28no—
493#379—24no—
494C2×#95C22×C1312yescomplemented
495C2×#95C22×C1312yescomplemented
496C2×#95C22×C1312yescomplemented
497C2×#95C22×C1312yescomplemented
498C22×C13—24no—
499C22×C13—24no—
500C22×C13—24no—
501C22×C13—24no—
502C22×C13—28no—
503C22×C13—28no—
504C22×C13—28no—
505C22×C13—28no—
506C22×C13—464no—
507C22×C13—42no—
508C22×C13—44no—
509C22×C13—44no—
510C22×C13—42no—
511C22×C13—44no—
512C22×C13—44no—
513C22×C13—44no—
514C22×C13—44no—
515C22×C13—44no—
516C22×C13—44no—
517C22×C13—44no—
518C22×C13—44no—
519C22×C13—44no—
520C22×C13—44no—
521C22×C13—44no—
522C22×C13—44no—
523C22×C13—44no—
524C22×C13—44no—
525C22×C13—44no—
526C22×C13—44no—
527C22×C13—44no—
528C22×C13—44no—
529C22×C13—44no—
530C22×C13—44no—
531C22×C13—44no—
532C22×C13—42no—
533C22×C13—42no—
534C22×C13—42no—
535C22×C13—44no—
536C22×C13—44no—
537C22×C13—82no—
538C22×C13—82no—
539C22×C13—82no—
540C22×C13—82no—
541C22×C13C2×#12011yescharacteristic
542C22×C13C2×#12011yescharacteristic
543C22×C13C2×#12011yescharacteristic
544C22×C13C2×#12112yes—
545C22×C13#52511yescharacteristic
546C22×C13#53411yescharacteristic
547C22×C13#53411yescharacteristic
548C22×C13#53412yes—
549C22×C13#53511yescharacteristic
550C22×C13#53512yes—
551C22×C13#53812yes—
552C22×C13D4212yes—
553C22×C13D4212yes—
554C22×C13D4212yes—
555C22×C13D4212yes—
556C22×C13D4212yes—
557C22×C13#54612yes—
558C22×C13#54612yes—
559C22×C13#54612yes—
560C22×C13#54612yes—
561C22×C13#56012yes—
562C4×C13—24no—
563C4×C13—42no—
564C4×C13—42no—
565C4×C13—42no—
566C4×C13—44no—
567C4×C13—44no—
568C4×C13—82no—
569C25—22no—
570C25—22no—
571C25—24no—
572C25—24no—
573C25—22no—
574C25—24no—
575C25—42no—
576C25—42no—
577C25—42no—
578C25C23×C1311yescharacteristic
579C25C23×C1311yescharacteristic
580C25C23×C1311yescharacteristic
581C25C23×C1312yes—
582C22×D4—24no—
583C22×D4—24no—
584C22×D4—24no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—24no—
594C22×D4—24no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—22no—
601C22×D4—42no—
602C22×D4—42no—
603C22×D4—42no—
604C22×D4—42no—
605C22×D4—42no—
606C22×D4—42no—
607C22×D4—42no—
608C22×D4D4×C1314yescomplemented
609C22×D4D4×C1314yescomplemented
610C22×D4D4×C1318yescomplemented
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—24no—
615C23×C4—42no—
616C23×C4C23×C1312yes—
617C23×C4C23×C1311yescharacteristic
618C23×C4C23×C1311yescharacteristic
619C23×C4C23×C1311yescharacteristic
620C23×C4C23×C1312yes—
621C23×C4C23×C1312yes—
622C23×C4C23×C1311yescharacteristic
623#121—232no—
624#120—232no—
625#120—232no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—24no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—24no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—22no—
642C2×C22⋊C4—22no—
643C2×C22⋊C4—22no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—24no—
647C2×C22⋊C4—24no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—42no—
652C2×C22⋊C4—42no—
653C2×C22⋊C4—42no—
654C2×C22⋊C4—42no—
655C2×C22⋊C4—42no—
656C2×C22⋊C4—42no—
657C2×C22⋊C4D4×C1318yescomplemented
658C2×C22⋊C4D4×C1314yescomplemented
659#95—24no—
660#95—24no—
661#95—24no—
662#95—42no—
663C2×C13—44no—
664C2×C13—44no—
665C2×C13—48no—
666C2×C13—82no—
667C2×C13#240311yescharacteristic
668C2×C13#240311yescharacteristic
669C2×C13#240411yescharacteristic
670C2×C13#240812yes—
671C2×C13#241012yes—
672C2×C13#242412yes—
673C2×C13#266812yes—
674C2×C13#266912yes—
675C2×C13#267812yes—
676C24—22no—
677C24—22no—
678C24—22no—
679C24—22no—
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—22no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—28no—
704C24—21no—
705C24—21no—
706C24—22no—
707C24—22no—
708C24—22no—
709C24—22no—
710C24—22no—
711C24—22no—
712C24—48no—
713C24—48no—
714C24—48no—
715C24—48no—
716C24—48no—
717C24—48no—
718C24—48no—
719C24—48no—
720C24—48no—
721C24—44no—
722C24—44no—
723C24—48no—
724C24—44no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—44no—
729C24—48no—
730C24C2×D4×C1312yes—
731C24C2×D4×C1312yes—
732C24C2×D4×C1312yes—
733C24C2×D4×C1312yes—
734C24C2×D4×C1314yes—
735C24C2×D4×C1312yes—
736C24C2×D4×C1314yes—
737C24C2×D4×C1314yes—
738C24C13×#4114yes—
739C24C24×C1311yescharacteristic
740C2×D4—216no—
741C2×D4—28no—
742C2×D4—28no—
743C2×D4—28no—
744C2×D4—28no—
745C2×D4—216no—
746C2×D4—216no—
747C2×D4—28no—
748C2×D4—44no—
749C2×D4—48no—
750C2×D4—44no—
751C2×D4—48no—
752C2×D4—48no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—48no—
758C2×D4—48no—
759C2×D4—48no—
760C2×D4—48no—
761C2×D4—48no—
762C2×D4—48no—
763C2×D4—48no—
764C2×D4—48no—
765C2×D4—44no—
766C2×D4—48no—
767C2×D4—44no—
768C2×D4—48no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—28no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—22no—
789C22×C4—22no—
790C22×C4—22no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—22no—
794C22×C4—22no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—22no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—22no—
804C22×C4—48no—
805C22×C4—48no—
806C22×C4—44no—
807C22×C4—44no—
808C22×C4C2×D4×C1314yes—
809C22×C4C2×D4×C1314yes—
810C22×C4C2×D4×C1312yes—
811C22×C4C2×D4×C1312yes—
812C22×C4C2×D4×C1312yes—
813C22×C4C2×D4×C1314yes—
814C22×C4C2×D4×C1312yes—
815C4⋊C4—28no—
816C22⋊C4—216no—
817C22⋊C4—28no—
818C22⋊C4—28no—
819C22⋊C4—28no—
820C22⋊C4—28no—
821C22⋊C4—216no—
822C22⋊C4—48no—
823C22⋊C4—48no—
824C22⋊C4—48no—
825C22⋊C4—48no—
826C22⋊C4—44no—
827C13#1525711yescharacteristic, direct product factor, Sylow
828C23—22no—
829C23—22no—
830C23—24no—
831C23—24no—
832C23—22no—
833C23—24no—
834C23—22no—
835C23—24no—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—24no—
851C23—24no—
852C23—24no—
853C23—24no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—22no—
869C23—22no—
870C23—22no—
871C23—24no—
872C23—24no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—432no—
879C23—432no—
880C23—432no—
881C23—432no—
882C23—41no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—41no—
887C23—41no—
888C23—42no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—41no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—42no—
905C23—42no—
906C23—42no—
907C23—42no—
908C23—42no—
909C23—42no—
910C23—42no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—42no—
918C23—41no—
919C23—42no—
920C23—41no—
921C23—42no—
922C23—41no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23—42no—
928C23—42no—
929C23—42no—
930C23—42no—
931C23—42no—
932C23C13×#12014yes—
933C23C13×#12014yescomplemented
934C23C13×#12118yescomplemented
935C23C22×D4×C1311yescharacteristic
936C23C22×D4×C1311yescharacteristic
937C23C22×D4×C1312yes—
938C23C22×D4×C1312yes—
939C23C22×D4×C1311yescharacteristic
940C23C2×C13×#4112yes—
941C23C13×H(5,𝔽2)12yes—
942C23C13×H(5,𝔽2)12yes—
943C23C13×H(5,𝔽2)12yes—
944D4—416no—
945D4—416no—
946D4—432no—
947D4—416no—
948D4—432no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—24no—
952C2×C4—24no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—24no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—22no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—42no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—42no—
981C2×C4—42no—
982C2×C4—42no—
983C2×C4—42no—
984C2×C4—42no—
985C2×C4—42no—
986C2×C4—42no—
987C2×C4—42no—
988C2×C4—42no—
989C2×C4—42no—
990C2×C4C13×#12014yescomplemented
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—28no—
996C22—28no—
997C22—28no—
998C22—28no—
999C22—464no—
1000C22—42no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—44no—
1007C22—44no—
1008C22—44no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22—44no—
1016C22—44no—
1017C22—44no—
1018C22—44no—
1019C22—44no—
1020C22—44no—
1021C22—44no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—42no—
1026C22—42no—
1027C22—42no—
1028C22—44no—
1029C22—44no—
1030C22—82no—
1031C22—82no—
1032C22—82no—
1033C22—82no—
1034C22C2×C13×#12011yescharacteristic
1035C22C2×C13×#12011yescharacteristic
1036C22C2×C13×#12011yescharacteristic
1037C22C2×C13×#12112yes—
1038C22C13×#52511yescharacteristic
1039C22C13×#53411yescharacteristic
1040C22C13×#53411yescharacteristic
1041C22C13×#53412yes—
1042C22C13×#53511yescharacteristic
1043C22C13×#53512yes—
1044C22C13×#53812yes—
1045C22D42×C1312yes—
1046C22D42×C1312yes—
1047C22D42×C1312yes—
1048C22D42×C1312yes—
1049C22D42×C1312yes—
1050C22C13×#54612yes—
1051C22C13×#54612yes—
1052C22C13×#54612yes—
1053C22C13×#54612yes—
1054C22C13×#56012yes—
1055C4—24no—
1056C4—42no—
1057C4—42no—
1058C4—42no—
1059C4—44no—
1060C4—44no—
1061C4—82no—
1062C2—44no—
1063C2—48no—
1064C2—44no—
1065C2—82no—
1066C2C13×#240311yescharacteristic
1067C2C13×#240311yescharacteristic
1068C2C13×#240411yescharacteristic
1069C2C13×#240812yes—
1070C2C13×#241012yes—
1071C2C13×#242412yes—
1072C2C13×#266812yes—
1073C2C13×#266912yes—
1074C2C13×#267812yes—
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×#121C2semidirect
2. C22×C13×#120C2semidirect
3. C22×C13×#120C2semidirect
4. C2×C13×#392C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#379C2semidirect
7. C13×#1440C2semidirect
8. C13×#1439C2semidirect
9. C13×#1438C2semidirect
10. C13×#1438C2semidirect
11. C13×#1438C2semidirect
17. C23×D4×C13C22semidirect
18. C24×C4×C13C22semidirect
26. C22×C13×C4⋊C4C22semidirect
35. C22×C13×C22⋊C4C22semidirect
36. C22×C13×C22⋊C4C22semidirect
37. C22×C13×C22⋊C4C22semidirect
41. C2×C13×#95C22semidirect
42. C2×C13×#95C22semidirect
43. C2×C13×#95C22semidirect
44. C2×C13×#95C22semidirect
84. C22×D4×C13D4semidirect
85. C22×D4×C13D4semidirect
86. C22×D4×C13D4semidirect
133. C2×C13×C22⋊C4D4semidirect
134. C2×C13×C22⋊C4D4semidirect
139. #15257C13direct (N × H)
291. C22×#121C2×C13semidirect
292. C22×#120C2×C13semidirect
293. C22×#120C2×C13semidirect
294. C2×#392C2×C13semidirect
295. C2×#386C2×C13semidirect
296. C2×#379C2×C13semidirect
297. #1440C2×C13semidirect
298. #1439C2×C13semidirect
299. #1438C2×C13semidirect
300. #1438C2×C13semidirect
301. #1438C2×C13semidirect
407. C23×C13#120semidirect
408. C23×C13#121semidirect
464. C2×C4×C13#120semidirect
470. C23×D4C22×C13semidirect
471. C24×C4C22×C13semidirect
479. C22×C4⋊C4C22×C13semidirect
488. C22×C22⋊C4C22×C13semidirect
489. C22×C22⋊C4C22×C13semidirect
490. C22×C22⋊C4C22×C13semidirect
494. C2×#95C22×C13semidirect
495. C2×#95C22×C13semidirect
496. C2×#95C22×C13semidirect
497. C2×#95C22×C13semidirect
608. C22×D4D4×C13semidirect
609. C22×D4D4×C13semidirect
610. C22×D4D4×C13semidirect
657. C2×C22⋊C4D4×C13semidirect
658. C2×C22⋊C4D4×C13semidirect
827. C13#15257direct (N × H)
933. C23C13×#120semidirect
934. C23C13×#121semidirect
990. C2×C4C13×#120semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C22×C13×#1202
C2×C13×#3922
C2×C13×#3862
C2×C13×#3792
C13×#14402
C13×#14392
C13×#14382
#1525713