Finite Group Databasebeta

← C13×#13995 #15700334

Subgroups — C13×#13995 #15700334

Order 3328.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 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×#390C212yesmaximal, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#385C211yesmaximal, characteristic, complemented
7C2×C13×#379C211yesmaximal, characteristic, complemented
8C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
9C13×#1439C212yesmaximal, complemented
10C13×#1438C212yesmaximal, complemented
11C13×#1437C212yesmaximal, complemented
12C26×C13C2211yescharacteristic
13C23×D4×C13C2211yescharacteristic
14C23×D4×C13C2212yes—
15C24×C4×C13C2211yescharacteristic
16C24×C4×C13C2211yescharacteristic
17C2×C13×#120—24no—
18C2×C13×#120—24no—
19C2×C13×#120C418yescomplemented
20C22×C13×C4⋊C4C2212yescomplemented
21C22×C13×C22⋊C4—24no—
22C22×C13×C22⋊C4—28no—
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2212yes—
25C22×C13×C22⋊C4C2212yes—
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2212yes—
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2212yes—
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic, complemented
32C22×C13×C22⋊C4C2212yescomplemented
33C22×C13×C22⋊C4C2211yescharacteristic, complemented
34C22×C42×C13C2212yescomplemented
35C13×#390—28no—
36C13×#386—24no—
37C13×#386—24no—
38C13×#385—24no—
39C13×#379—24no—
40C4×C13×C22⋊C4—24no—
41C2×C13×#95C2212yescomplemented
42C2×C13×#95C2212yescomplemented
43C2×C13×#95C2211yescharacteristic, complemented
44C2×C13×#95C2212yescomplemented
45C2×C13×#95C2211yescharacteristic, complemented
46C25×C13—24no—
47C25×C13—22no—
48C25×C13—24no—
49C25×C13—22no—
50C25×C13—22no—
51C25×C13—22no—
52C25×C13—22no—
53C25×C13—22no—
54C25×C13—42no—
55C25×C13—42no—
56C25×C13C2×C414yes—
57C25×C13C2311yescharacteristic
58C25×C13C2312yes—
59C25×C13C2311yescharacteristic
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—24no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—24no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—24no—
69C22×D4×C13—24no—
70C22×D4×C13—42no—
71C22×D4×C13—42no—
72C22×D4×C13C2×C414yes—
73C22×D4×C13C2×C418yescomplemented
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—24no—
78C23×C4×C13—24no—
79C23×C4×C13—22no—
80C23×C4×C13—22no—
81C23×C4×C13—42no—
82C23×C4×C13—42no—
83C23×C4×C13D414yescomplemented
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2312yes—
88C23×C4×C13C2312yes—
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2312yes—
91C23×C4×C13C2311yescharacteristic
92C13×#120—232no—
93C2×C13×C4⋊C4—24no—
94C2×C13×C4⋊C4—24no—
95C2×C13×C4⋊C4—42no—
96C2×C13×C22⋊C4—232no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—24no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—24no—
101C2×C13×C22⋊C4—24no—
102C2×C13×C22⋊C4—24no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—24no—
110C2×C13×C22⋊C4—24no—
111C2×C13×C22⋊C4—24no—
112C2×C13×C22⋊C4—24no—
113C2×C13×C22⋊C4—24no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—24no—
117C2×C13×C22⋊C4—24no—
118C2×C13×C22⋊C4—42no—
119C2×C13×C22⋊C4—42no—
120C2×C13×C22⋊C4—42no—
121C2×C13×C22⋊C4—42no—
122C2×C13×C22⋊C4C2×C414yes—
123C2×C13×C22⋊C4C2×C418yescomplemented
124C2×C13×C22⋊C4D414yes—
125C2×C13×C22⋊C4D414yes—
126C2×C13×C22⋊C4D414yescomplemented
127C2×C13×C22⋊C4D418yescomplemented
128C2×C42×C13—24no—
129C2×C42×C13—24no—
130C2×C42×C13—42no—
131C13×#95—24no—
132C13×#95—24no—
133C13×#95—24no—
134C13×#95—22no—
135C13×#95—22no—
136#13995C1311yesmaximal, characteristic, direct product factor, Sylow
137C24×C13—22no—
138C24×C13—22no—
139C24×C13—22no—
140C24×C13—22no—
141C24×C13—28no—
142C24×C13—28no—
143C24×C13—216no—
144C24×C13—216no—
145C24×C13—28no—
146C24×C13—22no—
147C24×C13—22no—
148C24×C13—22no—
149C24×C13—22no—
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—28no—
159C24×C13—28no—
160C24×C13—21no—
161C24×C13—22no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—22no—
168C24×C13—22no—
169C24×C13—22no—
170C24×C13—48no—
171C24×C13—48no—
172C24×C13—48no—
173C24×C13—48no—
174C24×C13—48no—
175C24×C13—48no—
176C24×C13—48no—
177C24×C13—48no—
178C24×C13—48no—
179C24×C13—44no—
180C24×C13—44no—
181C24×C13—48no—
182C24×C13—44no—
183C24×C13—44no—
184C24×C13—44no—
185C24×C13—44no—
186C24×C13C22×C412yes—
187C24×C13C22×C414yes—
188C24×C13C22×C412yes—
189C24×C13C2×D414yes—
190C24×C13C2×D412yes—
191C24×C13C2×D412yes—
192C24×C13C2×D412yes—
193C24×C13C2×D412yes—
194C24×C13#4114yes—
195C24×C13#4112yes—
196C24×C13#4112yes—
197C24×C13C2411yescharacteristic
198C2×D4×C13—28no—
199C2×D4×C13—28no—
200C2×D4×C13—28no—
201C2×D4×C13—216no—
202C2×D4×C13—216no—
203C2×D4×C13—48no—
204C2×D4×C13—48no—
205C2×D4×C13—48no—
206C2×D4×C13—48no—
207C2×D4×C13—48no—
208C2×D4×C13—44no—
209C2×D4×C13—44no—
210C2×D4×C13—44no—
211C2×D4×C13—44no—
212C22×C4×C13—21no—
213C22×C4×C13—22no—
214C22×C4×C13—21no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—28no—
220C22×C4×C13—28no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—22no—
227C22×C4×C13—22no—
228C22×C4×C13—22no—
229C22×C4×C13—22no—
230C22×C4×C13—22no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—22no—
234C22×C4×C13—22no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—22no—
239C22×C4×C13—22no—
240C22×C4×C13—22no—
241C22×C4×C13—22no—
242C22×C4×C13—22no—
243C22×C4×C13—28no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—22no—
250C22×C4×C13—21no—
251C22×C4×C13—22no—
252C22×C4×C13—22no—
253C22×C4×C13—22no—
254C22×C4×C13—44no—
255C22×C4×C13—48no—
256C22×C4×C13—48no—
257C22×C4×C13—48no—
258C22×C4×C13—48no—
259C22×C4×C13—44no—
260C22×C4×C13—44no—
261C22×C4×C13C22×C412yes—
262C22×C4×C13C22×C414yes—
263C22×C4×C13C2×D414yes—
264C22×C4×C13C2×D412yes—
265C22×C4×C13C2×D414yes—
266C22×C4×C13C2×D414yes—
267C22×C4×C13C2×D414yes—
268C22×C4×C13C2×D412yes—
269C22×C4×C13C2×D414yes—
270C13×C4⋊C4—48no—
271C13×C22⋊C4—216no—
272C13×C22⋊C4—28no—
273C13×C22⋊C4—216no—
274C13×C22⋊C4—216no—
275C13×C22⋊C4—48no—
276C13×C22⋊C4—48no—
277C13×C22⋊C4—48no—
278C13×C22⋊C4—44no—
279C13×C22⋊C4—44no—
280C13×C22⋊C4—44no—
281C13×C22⋊C4C22⋊C4116yescomplemented
282C42×C13—48no—
283C22×#120C2×C1311yescharacteristic
284C23×C22⋊C4C2×C1311yescharacteristic, complemented
285C2×#390C2×C1312yescomplemented
286C2×#386C2×C1311yescharacteristic, complemented
287C2×#386C2×C1311yescharacteristic, complemented
288C2×#385C2×C1311yescharacteristic, complemented
289C2×#379C2×C1311yescharacteristic, complemented
290C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
291#1439C2×C1312yescomplemented
292#1438C2×C1312yescomplemented
293#1437C2×C1312yescomplemented
294C23×C13—24no—
295C23×C13—24no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—24no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—24no—
302C23×C13—24no—
303C23×C13—24no—
304C23×C13—24no—
305C23×C13—24no—
306C23×C13—24no—
307C23×C13—24no—
308C23×C13—24no—
309C23×C13—24no—
310C23×C13—232no—
311C23×C13—24no—
312C23×C13—24no—
313C23×C13—24no—
314C23×C13—24no—
315C23×C13—24no—
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—22no—
330C23×C13—22no—
331C23×C13—24no—
332C23×C13—22no—
333C23×C13—24no—
334C23×C13—432no—
335C23×C13—432no—
336C23×C13—416no—
337C23×C13—416no—
338C23×C13—416no—
339C23×C13—432no—
340C23×C13—416no—
341C23×C13—432no—
342C23×C13—416no—
343C23×C13—42no—
344C23×C13—42no—
345C23×C13—42no—
346C23×C13—42no—
347C23×C13—42no—
348C23×C13—42no—
349C23×C13—42no—
350C23×C13—42no—
351C23×C13—42no—
352C23×C13—42no—
353C23×C13—42no—
354C23×C13—42no—
355C23×C13—42no—
356C23×C13—42no—
357C23×C13—42no—
358C23×C13—42no—
359C23×C13—416no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—42no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
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×C13C2×C22⋊C414yes—
379C23×C13C4×D418yes—
380C23×C13C4×D414yes—
381C23×C13C4×D414yes—
382C23×C13#12114yes—
383C23×C13#12114yes—
384C23×C13#12414yes—
385C23×C13#12714yes—
386C23×C13C23×C411yescharacteristic
387C23×C13C22×D411yescharacteristic
388C23×C13C22×D411yescharacteristic
389C23×C13C22×D411yescharacteristic
390C23×C13C22×D412yes—
391C23×C13C22×D411yescharacteristic
392C23×C13C2×#4111yescharacteristic
393C23×C13C2×#4111yescharacteristic
394C23×C13C2×#4112yes—
395C23×C13H(5,𝔽2)12yes—
396C23×C13H(5,𝔽2)12yes—
397D4×C13—432no—
398D4×C13—416no—
399C2×C4×C13—24no—
400C2×C4×C13—24no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—24no—
404C2×C4×C13—24no—
405C2×C4×C13—24no—
406C2×C4×C13—24no—
407C2×C4×C13—24no—
408C2×C4×C13—24no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—24no—
414C2×C4×C13—24no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—24no—
418C2×C4×C13—24no—
419C2×C4×C13—24no—
420C2×C4×C13—24no—
421C2×C4×C13—416no—
422C2×C4×C13—416no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—42no—
426C2×C4×C13—41no—
427C2×C4×C13—42no—
428C2×C4×C13—41no—
429C2×C4×C13—42no—
430C2×C4×C13—42no—
431C2×C4×C13—42no—
432C2×C4×C13—42no—
433C2×C4×C13—42no—
434C2×C4×C13—42no—
435C2×C4×C13—42no—
436C2×C4×C13—42no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—42no—
444C2×C4×C13—42no—
445C2×C4×C13—42no—
446C2×C4×C13—42no—
447C2×C4×C13C2×C22⋊C418yescomplemented
448C2×C4×C13#12014yescomplemented
449C26C22×C1311yescharacteristic
450C23×D4C22×C1311yescharacteristic
451C23×D4C22×C1312yes—
452C24×C4C22×C1311yescharacteristic
453C24×C4C22×C1311yescharacteristic
454C2×#120—24no—
455C2×#120—24no—
456C2×#120C4×C1318yescomplemented
457C22×C4⋊C4C22×C1312yescomplemented
458C22×C22⋊C4—24no—
459C22×C22⋊C4—28no—
460C22×C22⋊C4C22×C1312yes—
461C22×C22⋊C4C22×C1311yescharacteristic
462C22×C22⋊C4C22×C1312yes—
463C22×C22⋊C4C22×C1312yes—
464C22×C22⋊C4C22×C1312yes—
465C22×C22⋊C4C22×C1312yes—
466C22×C22⋊C4C22×C1311yescharacteristic
467C22×C22⋊C4C22×C1311yescharacteristic
468C22×C22⋊C4C22×C1311yescharacteristic, complemented
469C22×C22⋊C4C22×C1312yescomplemented
470C22×C22⋊C4C22×C1311yescharacteristic, complemented
471C22×C42C22×C1312yescomplemented
472#390—28no—
473#386—24no—
474#386—24no—
475#385—24no—
476#379—24no—
477C4×C22⋊C4—24no—
478C2×#95C22×C1311yescharacteristic, complemented
479C2×#95C22×C1312yescomplemented
480C2×#95C22×C1312yescomplemented
481C2×#95C22×C1312yescomplemented
482C2×#95C22×C1311yescharacteristic, complemented
483C22×C13—24no—
484C22×C13—28no—
485C22×C13—28no—
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—28no—
489C22×C13—24no—
490C22×C13—28no—
491C22×C13—24no—
492C22×C13—24no—
493C22×C13—28no—
494C22×C13—28no—
495C22×C13—28no—
496C22×C13—464no—
497C22×C13—44no—
498C22×C13—44no—
499C22×C13—44no—
500C22×C13—44no—
501C22×C13—44no—
502C22×C13—44no—
503C22×C13—44no—
504C22×C13—44no—
505C22×C13—44no—
506C22×C13—44no—
507C22×C13—44no—
508C22×C13—44no—
509C22×C13—42no—
510C22×C13—44no—
511C22×C13—44no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13—81no—
515C22×C13—81no—
516C22×C13—82no—
517C22×C13—81no—
518C22×C13—82no—
519C22×C13—81no—
520C22×C13#39018yescomplemented
521C22×C13C22×C22⋊C411yescharacteristic
522C22×C13C2×C4×D411yescharacteristic
523C22×C13C2×C4×D412yes—
524C22×C13C2×C4×D411yescharacteristic
525C22×C13#51812yes—
526C22×C13C2×#12011yescharacteristic
527C22×C13C2×#12111yescharacteristic
528C22×C13C2×#12111yescharacteristic
529C22×C13#52511yescharacteristic
530C22×C13#52512yes—
531C22×C13C2×#12411yescharacteristic
532C22×C13C2×#12711yescharacteristic
533C22×C13#53411yescharacteristic
534C22×C13#53511yescharacteristic
535C22×C13#53812yes—
536C22×C13D4212yes—
537C22×C13D4212yes—
538C22×C13D4212yes—
539C22×C13#54612yes—
540C22×C13#54612yes—
541C22×C13#54612yes—
542C22×C13#54612yes—
543C22×C13#55112yes—
544C4×C13—28no—
545C4×C13—24no—
546C4×C13—42no—
547C4×C13—44no—
548C4×C13—44no—
549C4×C13—42no—
550C4×C13—81no—
551C4×C13—81no—
552C25—24no—
553C25—22no—
554C25—24no—
555C25—22no—
556C25—22no—
557C25—22no—
558C25—22no—
559C25—22no—
560C25—42no—
561C25—42no—
562C25C2×C4×C1314yes—
563C25C23×C1311yescharacteristic
564C25C23×C1312yes—
565C25C23×C1311yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—22no—
569C22×D4—22no—
570C22×D4—24no—
571C22×D4—24no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—24no—
575C22×D4—24no—
576C22×D4—42no—
577C22×D4—42no—
578C22×D4C2×C4×C1314yes—
579C22×D4C2×C4×C1318yescomplemented
580C23×C4—22no—
581C23×C4—22no—
582C23×C4—22no—
583C23×C4—24no—
584C23×C4—24no—
585C23×C4—22no—
586C23×C4—22no—
587C23×C4—42no—
588C23×C4—42no—
589C23×C4D4×C1314yescomplemented
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1312yes—
594C23×C4C23×C1312yes—
595C23×C4C23×C1311yescharacteristic
596C23×C4C23×C1312yes—
597C23×C4C23×C1311yescharacteristic
598#120—232no—
599C2×C4⋊C4—24no—
600C2×C4⋊C4—24no—
601C2×C4⋊C4—42no—
602C2×C22⋊C4—232no—
603C2×C22⋊C4—24no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—24no—
607C2×C22⋊C4—24no—
608C2×C22⋊C4—24no—
609C2×C22⋊C4—24no—
610C2×C22⋊C4—24no—
611C2×C22⋊C4—24no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—24no—
616C2×C22⋊C4—24no—
617C2×C22⋊C4—24no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—24no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—42no—
625C2×C22⋊C4—42no—
626C2×C22⋊C4—42no—
627C2×C22⋊C4—42no—
628C2×C22⋊C4C2×C4×C1314yes—
629C2×C22⋊C4C2×C4×C1318yescomplemented
630C2×C22⋊C4D4×C1314yes—
631C2×C22⋊C4D4×C1314yes—
632C2×C22⋊C4D4×C1318yescomplemented
633C2×C22⋊C4D4×C1314yescomplemented
634C2×C42—24no—
635C2×C42—24no—
636C2×C42—42no—
637#95—24no—
638#95—24no—
639#95—24no—
640#95—22no—
641#95—22no—
642C2×C13—28no—
643C2×C13—48no—
644C2×C13—82no—
645C2×C13C2×#39011yescharacteristic
646C2×C13C4×#12011yescharacteristic
647C2×C13#232111yescharacteristic
648C2×C13D4×C22⋊C412yes—
649C2×C13#235812yes—
650C2×C13#241011yescharacteristic
651C2×C13#241111yescharacteristic
652C2×C13#242412yes—
653C2×C13#243311yescharacteristic
654C2×C13#247212yes—
655C2×C13#253911yescharacteristic
656C24—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—28no—
661C24—28no—
662C24—216no—
663C24—216no—
664C24—28no—
665C24—22no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—28no—
678C24—28no—
679C24—21no—
680C24—22no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—48no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—44no—
699C24—44no—
700C24—48no—
701C24—44no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24C22×C4×C1312yes—
706C24C22×C4×C1314yes—
707C24C22×C4×C1312yes—
708C24C2×D4×C1314yes—
709C24C2×D4×C1312yes—
710C24C2×D4×C1312yes—
711C24C2×D4×C1312yes—
712C24C2×D4×C1312yes—
713C24C13×#4114yes—
714C24C13×#4112yes—
715C24C13×#4112yes—
716C24C24×C1311yescharacteristic
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—216no—
721C2×D4—216no—
722C2×D4—48no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—44no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C22×C4—21no—
732C22×C4—22no—
733C22×C4—21no—
734C22×C4—22no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—28no—
739C22×C4—28no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—22no—
753C22×C4—22no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—28no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—44no—
774C22×C4—48no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4C22×C4×C1312yes—
781C22×C4C22×C4×C1314yes—
782C22×C4C2×D4×C1314yes—
783C22×C4C2×D4×C1312yes—
784C22×C4C2×D4×C1314yes—
785C22×C4C2×D4×C1314yes—
786C22×C4C2×D4×C1314yes—
787C22×C4C2×D4×C1312yes—
788C22×C4C2×D4×C1314yes—
789C4⋊C4—48no—
790C22⋊C4—216no—
791C22⋊C4—28no—
792C22⋊C4—216no—
793C22⋊C4—216no—
794C22⋊C4—48no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—44no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4C13×C22⋊C4116yescomplemented
801C42—48no—
802C13#1399511yescharacteristic, direct product factor, Sylow
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—416no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C13×C22⋊C414yes—
888C23C4×D4×C1318yes—
889C23C4×D4×C1314yes—
890C23C4×D4×C1314yes—
891C23C13×#12114yes—
892C23C13×#12114yes—
893C23C13×#12414yes—
894C23C13×#12714yes—
895C23C23×C4×C1311yescharacteristic
896C23C22×D4×C1311yescharacteristic
897C23C22×D4×C1311yescharacteristic
898C23C22×D4×C1311yescharacteristic
899C23C22×D4×C1312yes—
900C23C22×D4×C1311yescharacteristic
901C23C2×C13×#4111yescharacteristic
902C23C2×C13×#4111yescharacteristic
903C23C2×C13×#4112yes—
904C23C13×H(5,𝔽2)12yes—
905C23C13×H(5,𝔽2)12yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C13×C22⋊C418yescomplemented
957C2×C4C13×#12014yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22C13×#39018yescomplemented
996C22C22×C13×C22⋊C411yescharacteristic
997C22C2×C4×D4×C1311yescharacteristic
998C22C2×C4×D4×C1311yescharacteristic
999C22C2×C4×D4×C1312yes—
1000C22C13×#51812yes—
1001C22C2×C13×#12011yescharacteristic
1002C22C2×C13×#12111yescharacteristic
1003C22C2×C13×#12111yescharacteristic
1004C22C13×#52511yescharacteristic
1005C22C13×#52512yes—
1006C22C2×C13×#12411yescharacteristic
1007C22C2×C13×#12711yescharacteristic
1008C22C13×#53411yescharacteristic
1009C22C13×#53511yescharacteristic
1010C22C13×#53812yes—
1011C22D42×C1312yes—
1012C22D42×C1312yes—
1013C22D42×C1312yes—
1014C22C13×#54612yes—
1015C22C13×#54612yes—
1016C22C13×#54612yes—
1017C22C13×#54612yes—
1018C22C13×#55112yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×C13×#39011yescharacteristic
1031C2C4×C13×#12011yescharacteristic
1032C2C13×#232111yescharacteristic
1033C2D4×C13×C22⋊C412yes—
1034C2C13×#235812yes—
1035C2C13×#241011yescharacteristic
1036C2C13×#241111yescharacteristic
1037C2C13×#242412yes—
1038C2C13×#243311yescharacteristic
1039C2C13×#247212yes—
1040C2C13×#253911yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC22×C13×#120C2
LCSG ▷ C23 ▷ 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×#390C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#385C2semidirect
7. C2×C13×#379C2semidirect
8. C2×C4×C13×C22⋊C4C2semidirect
9. C13×#1439C2semidirect
10. C13×#1438C2semidirect
11. C13×#1437C2semidirect
19. C2×C13×#120C4semidirect
20. C22×C13×C4⋊C4C22semidirect
31. C22×C13×C22⋊C4C22semidirect
32. C22×C13×C22⋊C4C22semidirect
33. C22×C13×C22⋊C4C22semidirect
34. C22×C42×C13C22semidirect
41. C2×C13×#95C22semidirect
42. C2×C13×#95C22semidirect
43. C2×C13×#95C22semidirect
44. C2×C13×#95C22semidirect
45. C2×C13×#95C22semidirect
73. C22×D4×C13C2×C4semidirect
83. C23×C4×C13D4semidirect
123. C2×C13×C22⋊C4C2×C4semidirect
126. C2×C13×C22⋊C4D4semidirect
127. C2×C13×C22⋊C4D4semidirect
136. #13995C13direct (N × H)
281. C13×C22⋊C4C22⋊C4semidirect
284. C23×C22⋊C4C2×C13semidirect
285. C2×#390C2×C13semidirect
286. C2×#386C2×C13semidirect
287. C2×#386C2×C13semidirect
288. C2×#385C2×C13semidirect
289. C2×#379C2×C13semidirect
290. C2×C4×C22⋊C4C2×C13semidirect
291. #1439C2×C13semidirect
292. #1438C2×C13semidirect
293. #1437C2×C13semidirect
447. C2×C4×C13C2×C22⋊C4semidirect
448. C2×C4×C13#120semidirect
456. C2×#120C4×C13semidirect
457. C22×C4⋊C4C22×C13semidirect
468. C22×C22⋊C4C22×C13semidirect
469. C22×C22⋊C4C22×C13semidirect
470. C22×C22⋊C4C22×C13semidirect
471. C22×C42C22×C13semidirect
478. C2×#95C22×C13semidirect
479. C2×#95C22×C13semidirect
480. C2×#95C22×C13semidirect
481. C2×#95C22×C13semidirect
482. C2×#95C22×C13semidirect
520. C22×C13#390semidirect
579. C22×D4C2×C4×C13semidirect
589. C23×C4D4×C13semidirect
629. C2×C22⋊C4C2×C4×C13semidirect
632. C2×C22⋊C4D4×C13semidirect
633. C2×C22⋊C4D4×C13semidirect
800. C22⋊C4C13×C22⋊C4semidirect
802. C13#13995direct (N × H)
956. C2×C4C2×C13×C22⋊C4semidirect
957. C2×C4C13×#120semidirect
995. C22C13×#390semidirect

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×#3902
C2×C13×#3862
C2×C13×#3852
C2×C13×#3792
C2×C4×C13×C22⋊C42
C13×#14392
C13×#14382
C13×#14372
#1399513