Finite Group Databasebeta

← C13×#14718 #15701057

Subgroups — C13×#14718 #15701057

Order 3328.

4034 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#120C211yesmaximal, characteristic
2C23×C13×C22⋊C4C211yesmaximal, characteristic, complemented
3C2×C13×#394C212yesmaximal, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#385C211yesmaximal, characteristic, complemented
7C2×C13×#379C211yesmaximal, characteristic, complemented
8C13×#1440C212yesmaximal, complemented
9C13×#1439C212yesmaximal, complemented
10C13×#1438C212yesmaximal, complemented
11C13×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C13C2211yescharacteristic
13C23×D4×C13C2211yescharacteristic
14C23×D4×C13C2211yescharacteristic
15C23×D4×C13C2211yescharacteristic
16C24×C4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×#120—24no—
19C2×C13×#120—24no—
20C2×C13×#120—24no—
21C22×C13×C4⋊C4C2212yescomplemented
22C22×C13×C22⋊C4—24no—
23C22×C13×C22⋊C4—28no—
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2212yes—
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2212yes—
29C22×C13×C22⋊C4C2212yes—
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2212yes—
33C22×C13×C22⋊C4C2212yescomplemented
34C22×C13×C22⋊C4C2212yescomplemented
35C13×#394—28no—
36C13×#386—24no—
37C13×#386—24no—
38C13×#385—24no—
39C13×#379—24no—
40C2×C13×#95C2212yescomplemented
41C2×C13×#95C2212yescomplemented
42C2×C13×#95C2212yescomplemented
43C2×C13×#95C2212yescomplemented
44C2×C13×#95C2212yescomplemented
45C25×C13—24no—
46C25×C13—24no—
47C25×C13—22no—
48C25×C13—22no—
49C25×C13—22no—
50C25×C13—22no—
51C25×C13—22no—
52C25×C13—22no—
53C25×C13—42no—
54C25×C13—42no—
55C25×C13D414yes—
56C25×C13C2311yescharacteristic
57C25×C13C2311yescharacteristic
58C25×C13C2311yescharacteristic
59C25×C13C2311yescharacteristic
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
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—22no—
73C22×D4×C13—22no—
74C22×D4×C13—42no—
75C22×D4×C13—42no—
76C22×D4×C13D414yes—
77C23×C4×C13—22no—
78C23×C4×C13—22no—
79C23×C4×C13—24no—
80C23×C4×C13—24no—
81C23×C4×C13—22no—
82C23×C4×C13—22no—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—42no—
86C23×C4×C13—42no—
87C23×C4×C13C2312yes—
88C23×C4×C13C2312yes—
89C23×C4×C13C2312yes—
90C23×C4×C13C2312yes—
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C13×#120—232no—
95C2×C13×C4⋊C4—24no—
96C2×C13×C4⋊C4—24no—
97C2×C13×C4⋊C4—42no—
98C2×C13×C22⋊C4—232no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—24no—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4—24no—
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—42no—
126C2×C13×C22⋊C4—42no—
127C2×C13×C22⋊C4—42no—
128C2×C13×C22⋊C4—42no—
129C2×C13×C22⋊C4D414yes—
130C2×C13×C22⋊C4D414yescomplemented
131C2×C13×C22⋊C4D418yescomplemented
132C13×#95—24no—
133C13×#95—24no—
134C13×#95—24no—
135C13×#95—24no—
136C13×#95—42no—
137#14718C1311yesmaximal, characteristic, direct product factor, Sylow
138C24×C13—22no—
139C24×C13—22no—
140C24×C13—22no—
141C24×C13—22no—
142C24×C13—216no—
143C24×C13—216no—
144C24×C13—28no—
145C24×C13—28no—
146C24×C13—28no—
147C24×C13—22no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—22no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—22no—
162C24×C13—22no—
163C24×C13—22no—
164C24×C13—22no—
165C24×C13—28no—
166C24×C13—28no—
167C24×C13—21no—
168C24×C13—22no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—22no—
175C24×C13—22no—
176C24×C13—22no—
177C24×C13—44no—
178C24×C13—44no—
179C24×C13—48no—
180C24×C13—48no—
181C24×C13—48no—
182C24×C13—48no—
183C24×C13—48no—
184C24×C13—48no—
185C24×C13—48no—
186C24×C13—48no—
187C24×C13—48no—
188C24×C13—48no—
189C24×C13—44no—
190C24×C13—44no—
191C24×C13—44no—
192C24×C13—44no—
193C24×C13C2×D412yes—
194C24×C13C2×D412yes—
195C24×C13C2×D414yes—
196C24×C13C2×D412yes—
197C24×C13C2×D412yes—
198C24×C13C2×D412yes—
199C24×C13C2×D412yes—
200C24×C13C2×D412yes—
201C24×C13#4114yes—
202C24×C13#4112yes—
203C24×C13#4112yes—
204C24×C13#4112yes—
205C24×C13C2411yescharacteristic
206C2×D4×C13—28no—
207C2×D4×C13—28no—
208C2×D4×C13—28no—
209C2×D4×C13—28no—
210C2×D4×C13—28no—
211C2×D4×C13—48no—
212C2×D4×C13—48no—
213C2×D4×C13—48no—
214C2×D4×C13—48no—
215C2×D4×C13—44no—
216C2×D4×C13—44no—
217C2×D4×C13—44no—
218C2×D4×C13—44no—
219C2×D4×C13—44no—
220C2×D4×C13—44no—
221C2×D4×C13—44no—
222C2×D4×C13—44no—
223C22×C4×C13—28no—
224C22×C4×C13—28no—
225C22×C4×C13—21no—
226C22×C4×C13—22no—
227C22×C4×C13—22no—
228C22×C4×C13—22no—
229C22×C4×C13—22no—
230C22×C4×C13—22no—
231C22×C4×C13—22no—
232C22×C4×C13—22no—
233C22×C4×C13—22no—
234C22×C4×C13—22no—
235C22×C4×C13—22no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—22no—
243C22×C4×C13—22no—
244C22×C4×C13—22no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—22no—
249C22×C4×C13—22no—
250C22×C4×C13—22no—
251C22×C4×C13—22no—
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—48no—
265C22×C4×C13—48no—
266C22×C4×C13—48no—
267C22×C4×C13—48no—
268C22×C4×C13—44no—
269C22×C4×C13—44no—
270C22×C4×C13—44no—
271C22×C4×C13—44no—
272C22×C4×C13C2×D412yes—
273C22×C4×C13C2×D412yes—
274C22×C4×C13C2×D414yes—
275C22×C4×C13C2×D414yes—
276C22×C4×C13C2×D414yes—
277C22×C4×C13C2×D412yes—
278C13×C4⋊C4—48no—
279C13×C22⋊C4—216no—
280C13×C22⋊C4—28no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—216no—
283C13×C22⋊C4—28no—
284C13×C22⋊C4—28no—
285C13×C22⋊C4—48no—
286C13×C22⋊C4—48no—
287C13×C22⋊C4—48no—
288C13×C22⋊C4—48no—
289C13×C22⋊C4—44no—
290C22×#120C2×C1311yescharacteristic
291C23×C22⋊C4C2×C1311yescharacteristic, complemented
292C2×#394C2×C1312yescomplemented
293C2×#386C2×C1311yescharacteristic, complemented
294C2×#386C2×C1311yescharacteristic, complemented
295C2×#385C2×C1311yescharacteristic, complemented
296C2×#379C2×C1311yescharacteristic, complemented
297#1440C2×C1312yescomplemented
298#1439C2×C1312yescomplemented
299#1438C2×C1312yescomplemented
300C22⋊#95C2×C1311yescharacteristic, complemented
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—24no—
304C23×C13—24no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—24no—
308C23×C13—24no—
309C23×C13—24no—
310C23×C13—24no—
311C23×C13—24no—
312C23×C13—24no—
313C23×C13—24no—
314C23×C13—24no—
315C23×C13—24no—
316C23×C13—24no—
317C23×C13—232no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—24no—
327C23×C13—24no—
328C23×C13—24no—
329C23×C13—24no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
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—416no—
351C23×C13—416no—
352C23×C13—432no—
353C23×C13—432no—
354C23×C13—432no—
355C23×C13—432no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—42no—
365C23×C13—42no—
366C23×C13—42no—
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—416no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—42no—
383C23×C13—42no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—42no—
388C23×C13—42no—
389C23×C13—42no—
390C23×C13—42no—
391C23×C13—42no—
392C23×C13—42no—
393C23×C13—42no—
394C23×C13—42no—
395C23×C13#12014yes—
396C23×C13#12014yes—
397C23×C13#12114yes—
398C23×C13#12114yes—
399C23×C13#12114yes—
400C23×C13#12314yes—
401C23×C13#12314yes—
402C23×C13#12314yes—
403C23×C13#12414yes—
404C23×C13C22×D411yescharacteristic
405C23×C13C22×D411yescharacteristic
406C23×C13C22×D411yescharacteristic
407C23×C13C22×D412yes—
408C23×C13C22×D411yescharacteristic
409C23×C13C2×#4111yescharacteristic
410C23×C13C2×#4111yescharacteristic
411C23×C13C2×#4111yescharacteristic
412C23×C13C2×#4112yes—
413C23×C13H(5,𝔽2)12yes—
414C23×C13H(5,𝔽2)12yes—
415D4×C13—416no—
416D4×C13—416no—
417D4×C13—416no—
418C2×C4×C13—24no—
419C2×C4×C13—24no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—24no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—24no—
427C2×C4×C13—24no—
428C2×C4×C13—24no—
429C2×C4×C13—24no—
430C2×C4×C13—24no—
431C2×C4×C13—24no—
432C2×C4×C13—24no—
433C2×C4×C13—24no—
434C2×C4×C13—416no—
435C2×C4×C13—416no—
436C2×C4×C13—42no—
437C2×C4×C13—41no—
438C2×C4×C13—42no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—42no—
444C2×C4×C13—41no—
445C2×C4×C13—42no—
446C2×C4×C13—42no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
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—42no—
465C26C22×C1311yescharacteristic
466C23×D4C22×C1311yescharacteristic
467C23×D4C22×C1311yescharacteristic
468C23×D4C22×C1311yescharacteristic
469C24×C4C22×C1311yescharacteristic
470C24×C4C22×C1311yescharacteristic
471C2×#120—24no—
472C2×#120—24no—
473C2×#120—24no—
474C22×C4⋊C4C22×C1312yescomplemented
475C22×C22⋊C4—24no—
476C22×C22⋊C4—28no—
477C22×C22⋊C4C22×C1312yes—
478C22×C22⋊C4C22×C1311yescharacteristic
479C22×C22⋊C4C22×C1311yescharacteristic
480C22×C22⋊C4C22×C1311yescharacteristic
481C22×C22⋊C4C22×C1312yes—
482C22×C22⋊C4C22×C1312yes—
483C22×C22⋊C4C22×C1311yescharacteristic
484C22×C22⋊C4C22×C1312yes—
485C22×C22⋊C4C22×C1311yescharacteristic
486C22×C22⋊C4C22×C1312yescomplemented
487C22×C22⋊C4C22×C1312yescomplemented
488#394—28no—
489#386—24no—
490#386—24no—
491#385—24no—
492#379—24no—
493C2×#95C22×C1312yescomplemented
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—24no—
503C22×C13—24no—
504C22×C13—28no—
505C22×C13—28no—
506C22×C13—28no—
507C22×C13—28no—
508C22×C13—24no—
509C22×C13—24no—
510C22×C13—24no—
511C22×C13—24no—
512C22×C13—24no—
513C22×C13—24no—
514C22×C13—464no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13—42no—
518C22×C13—42no—
519C22×C13—42no—
520C22×C13—42no—
521C22×C13—42no—
522C22×C13—42no—
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—42no—
532C22×C13—42no—
533C22×C13—42no—
534C22×C13—44no—
535C22×C13—44no—
536C22×C13—81no—
537C22×C13—81no—
538C22×C13—81no—
539C22×C13—81no—
540C22×C13—82no—
541C22×C13—82no—
542C22×C13#39418yescomplemented
543C22×C13C2×#12011yescharacteristic
544C22×C13C2×#12011yescharacteristic
545C22×C13C2×#12111yescharacteristic
546C22×C13C2×#12111yescharacteristic
547C22×C13C2×#12111yescharacteristic
548C22×C13C2×#12311yescharacteristic
549C22×C13C2×#12311yescharacteristic
550C22×C13C2×#12311yescharacteristic
551C22×C13#52512yes—
552C22×C13#52512yes—
553C22×C13C2×#12411yescharacteristic
554C22×C13#53411yescharacteristic
555C22×C13#53411yescharacteristic
556C22×C13#53812yes—
557C22×C13#53812yes—
558C22×C13D4212yes—
559C22×C13D4212yes—
560C22×C13D4212yes—
561C22×C13#54612yes—
562C22×C13#54612yes—
563C22×C13#54612yes—
564C22×C13#54612yes—
565C22×C13#55112yes—
566C4×C13—42no—
567C4×C13—44no—
568C4×C13—42no—
569C4×C13—42no—
570C4×C13—44no—
571C4×C13—44no—
572C4×C13—82no—
573C25—24no—
574C25—24no—
575C25—22no—
576C25—22no—
577C25—22no—
578C25—22no—
579C25—22no—
580C25—22no—
581C25—42no—
582C25—42no—
583C25D4×C1314yes—
584C25C23×C1311yescharacteristic
585C25C23×C1311yescharacteristic
586C25C23×C1311yescharacteristic
587C25C23×C1311yescharacteristic
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—22no—
597C22×D4—22no—
598C22×D4—24no—
599C22×D4—24no—
600C22×D4—22no—
601C22×D4—22no—
602C22×D4—42no—
603C22×D4—42no—
604C22×D4D4×C1314yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—24no—
608C23×C4—24no—
609C23×C4—22no—
610C23×C4—22no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—42no—
614C23×C4—42no—
615C23×C4C23×C1312yes—
616C23×C4C23×C1312yes—
617C23×C4C23×C1312yes—
618C23×C4C23×C1312yes—
619C23×C4C23×C1311yescharacteristic
620C23×C4C23×C1311yescharacteristic
621C23×C4C23×C1311yescharacteristic
622#120—232no—
623C2×C4⋊C4—24no—
624C2×C4⋊C4—24no—
625C2×C4⋊C4—42no—
626C2×C22⋊C4—232no—
627C2×C22⋊C4—24no—
628C2×C22⋊C4—24no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—22no—
634C2×C22⋊C4—22no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—24no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—22no—
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—22no—
648C2×C22⋊C4—24no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—24no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—42no—
654C2×C22⋊C4—42no—
655C2×C22⋊C4—42no—
656C2×C22⋊C4—42no—
657C2×C22⋊C4D4×C1314yes—
658C2×C22⋊C4D4×C1318yescomplemented
659C2×C22⋊C4D4×C1314yescomplemented
660#95—24no—
661#95—24no—
662#95—24no—
663#95—24no—
664#95—42no—
665C2×C13—28no—
666C2×C13—44no—
667C2×C13—44no—
668C2×C13—82no—
669C2×C13C2×#39411yescharacteristic
670C2×C13#240311yescharacteristic
671C2×C13#240511yescharacteristic
672C2×C13#241011yescharacteristic
673C2×C13#241211yescharacteristic
674C2×C13#241812yes—
675C2×C13#242412yes—
676C2×C13#242412yes—
677C2×C13#247212yes—
678C2×C13#262211yescharacteristic
679C2×C13#284911yescharacteristic
680C24—22no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—216no—
685C24—216no—
686C24—28no—
687C24—28no—
688C24—28no—
689C24—22no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24—21no—
698C24—21no—
699C24—21no—
700C24—22no—
701C24—21no—
702C24—21no—
703C24—22no—
704C24—22no—
705C24—22no—
706C24—22no—
707C24—28no—
708C24—28no—
709C24—21no—
710C24—22no—
711C24—21no—
712C24—21no—
713C24—21no—
714C24—21no—
715C24—21no—
716C24—22no—
717C24—22no—
718C24—22no—
719C24—44no—
720C24—44no—
721C24—48no—
722C24—48no—
723C24—48no—
724C24—48no—
725C24—48no—
726C24—48no—
727C24—48no—
728C24—48no—
729C24—48no—
730C24—48no—
731C24—44no—
732C24—44no—
733C24—44no—
734C24—44no—
735C24C2×D4×C1312yes—
736C24C2×D4×C1312yes—
737C24C2×D4×C1314yes—
738C24C2×D4×C1312yes—
739C24C2×D4×C1312yes—
740C24C2×D4×C1312yes—
741C24C2×D4×C1312yes—
742C24C2×D4×C1312yes—
743C24C13×#4114yes—
744C24C13×#4112yes—
745C24C13×#4112yes—
746C24C13×#4112yes—
747C24C24×C1311yescharacteristic
748C2×D4—28no—
749C2×D4—28no—
750C2×D4—28no—
751C2×D4—28no—
752C2×D4—28no—
753C2×D4—48no—
754C2×D4—48no—
755C2×D4—48no—
756C2×D4—48no—
757C2×D4—44no—
758C2×D4—44no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—44no—
762C2×D4—44no—
763C2×D4—44no—
764C2×D4—44no—
765C22×C4—28no—
766C22×C4—28no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—22no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
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—22no—
805C22×C4—22no—
806C22×C4—48no—
807C22×C4—48no—
808C22×C4—48no—
809C22×C4—48no—
810C22×C4—44no—
811C22×C4—44no—
812C22×C4—44no—
813C22×C4—44no—
814C22×C4C2×D4×C1312yes—
815C22×C4C2×D4×C1312yes—
816C22×C4C2×D4×C1314yes—
817C22×C4C2×D4×C1314yes—
818C22×C4C2×D4×C1314yes—
819C22×C4C2×D4×C1312yes—
820C4⋊C4—48no—
821C22⋊C4—216no—
822C22⋊C4—28no—
823C22⋊C4—28no—
824C22⋊C4—216no—
825C22⋊C4—28no—
826C22⋊C4—28no—
827C22⋊C4—48no—
828C22⋊C4—48no—
829C22⋊C4—48no—
830C22⋊C4—48no—
831C22⋊C4—44no—
832C13#1471811yescharacteristic, direct product factor, Sylow
833C23—22no—
834C23—22no—
835C23—24no—
836C23—24no—
837C23—22no—
838C23—22no—
839C23—24no—
840C23—24no—
841C23—24no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—232no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—24no—
870C23—24no—
871C23—24no—
872C23—24no—
873C23—24no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—24no—
878C23—24no—
879C23—416no—
880C23—416no—
881C23—416no—
882C23—416no—
883C23—416no—
884C23—432no—
885C23—432no—
886C23—432no—
887C23—432no—
888C23—416no—
889C23—41no—
890C23—41no—
891C23—41no—
892C23—41no—
893C23—41no—
894C23—41no—
895C23—41no—
896C23—41no—
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—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—42no—
915C23—42no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—42no—
920C23—42no—
921C23—42no—
922C23—42no—
923C23—42no—
924C23—42no—
925C23—42no—
926C23—42no—
927C23C13×#12014yes—
928C23C13×#12014yes—
929C23C13×#12114yes—
930C23C13×#12114yes—
931C23C13×#12114yes—
932C23C13×#12314yes—
933C23C13×#12314yes—
934C23C13×#12314yes—
935C23C13×#12414yes—
936C23C22×D4×C1311yescharacteristic
937C23C22×D4×C1311yescharacteristic
938C23C22×D4×C1311yescharacteristic
939C23C22×D4×C1312yes—
940C23C22×D4×C1311yescharacteristic
941C23C2×C13×#4111yescharacteristic
942C23C2×C13×#4111yescharacteristic
943C23C2×C13×#4111yescharacteristic
944C23C2×C13×#4112yes—
945C23C13×H(5,𝔽2)12yes—
946C23C13×H(5,𝔽2)12yes—
947D4—416no—
948D4—416no—
949D4—416no—
950C2×C4—24no—
951C2×C4—24no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—24no—
959C2×C4—24no—
960C2×C4—24no—
961C2×C4—24no—
962C2×C4—24no—
963C2×C4—24no—
964C2×C4—24no—
965C2×C4—24no—
966C2×C4—416no—
967C2×C4—416no—
968C2×C4—42no—
969C2×C4—41no—
970C2×C4—42no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—42no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—41no—
980C2×C4—41no—
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×C4—42no—
991C2×C4—42no—
992C2×C4—42no—
993C2×C4—42no—
994C2×C4—42no—
995C2×C4—42no—
996C2×C4—42no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22—28no—
1004C22—28no—
1005C22—28no—
1006C22—28no—
1007C22—24no—
1008C22—24no—
1009C22—24no—
1010C22—24no—
1011C22—24no—
1012C22—24no—
1013C22—464no—
1014C22—42no—
1015C22—42no—
1016C22—42no—
1017C22—42no—
1018C22—42no—
1019C22—42no—
1020C22—42no—
1021C22—42no—
1022C22—44no—
1023C22—44no—
1024C22—44no—
1025C22—44no—
1026C22—44no—
1027C22—44no—
1028C22—44no—
1029C22—44no—
1030C22—42no—
1031C22—42no—
1032C22—42no—
1033C22—44no—
1034C22—44no—
1035C22—81no—
1036C22—81no—
1037C22—81no—
1038C22—81no—
1039C22—82no—
1040C22—82no—
1041C22C13×#39418yescomplemented
1042C22C2×C13×#12011yescharacteristic
1043C22C2×C13×#12011yescharacteristic
1044C22C2×C13×#12111yescharacteristic
1045C22C2×C13×#12111yescharacteristic
1046C22C2×C13×#12111yescharacteristic
1047C22C2×C13×#12311yescharacteristic
1048C22C2×C13×#12311yescharacteristic
1049C22C2×C13×#12311yescharacteristic
1050C22C13×#52512yes—
1051C22C13×#52512yes—
1052C22C2×C13×#12411yescharacteristic
1053C22C13×#53411yescharacteristic
1054C22C13×#53411yescharacteristic
1055C22C13×#53812yes—
1056C22C13×#53812yes—
1057C22D42×C1312yes—
1058C22D42×C1312yes—
1059C22D42×C1312yes—
1060C22C13×#54612yes—
1061C22C13×#54612yes—
1062C22C13×#54612yes—
1063C22C13×#54612yes—
1064C22C13×#55112yes—
1065C4—42no—
1066C4—44no—
1067C4—42no—
1068C4—42no—
1069C4—44no—
1070C4—44no—
1071C4—82no—
1072C2—28no—
1073C2—44no—
1074C2—44no—
1075C2—82no—
1076C2C2×C13×#39411yescharacteristic
1077C2C13×#240311yescharacteristic
1078C2C13×#240511yescharacteristic
1079C2C13×#241011yescharacteristic
1080C2C13×#241211yescharacteristic
1081C2C13×#241812yes—
1082C2C13×#242412yes—
1083C2C13×#242412yes—
1084C2C13×#247212yes—
1085C2C13×#262211yescharacteristic
1086C2C13×#284911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC22×C13×#120C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C13×C22⋊C4C2semidirect
3. C2×C13×#394C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#385C2semidirect
7. C2×C13×#379C2semidirect
8. C13×#1440C2semidirect
9. C13×#1439C2semidirect
10. C13×#1438C2semidirect
11. C13×C22⋊#95C2semidirect
21. C22×C13×C4⋊C4C22semidirect
33. C22×C13×C22⋊C4C22semidirect
34. C22×C13×C22⋊C4C22semidirect
40. C2×C13×#95C22semidirect
41. C2×C13×#95C22semidirect
42. C2×C13×#95C22semidirect
43. C2×C13×#95C22semidirect
44. C2×C13×#95C22semidirect
130. C2×C13×C22⋊C4D4semidirect
131. C2×C13×C22⋊C4D4semidirect
137. #14718C13direct (N × H)
291. C23×C22⋊C4C2×C13semidirect
292. C2×#394C2×C13semidirect
293. C2×#386C2×C13semidirect
294. C2×#386C2×C13semidirect
295. C2×#385C2×C13semidirect
296. C2×#379C2×C13semidirect
297. #1440C2×C13semidirect
298. #1439C2×C13semidirect
299. #1438C2×C13semidirect
300. C22⋊#95C2×C13semidirect
474. C22×C4⋊C4C22×C13semidirect
486. C22×C22⋊C4C22×C13semidirect
487. C22×C22⋊C4C22×C13semidirect
493. C2×#95C22×C13semidirect
494. C2×#95C22×C13semidirect
495. C2×#95C22×C13semidirect
496. C2×#95C22×C13semidirect
497. C2×#95C22×C13semidirect
542. C22×C13#394semidirect
658. C2×C22⋊C4D4×C13semidirect
659. C2×C22⋊C4D4×C13semidirect
832. C13#14718direct (N × H)
1041. C22C13×#394semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1202
C23×C13×C22⋊C42
C2×C13×#3942
C2×C13×#3862
C2×C13×#3852
C2×C13×#3792
C13×#14402
C13×#14392
C13×#14382
C13×C22⋊#952
#1471813