Finite Group Databasebeta

← C13×#14722 #15701061

Subgroups — C13×#14722 #15701061

Order 3328.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#121C211yesmaximal, characteristic, complemented
2C22×C4×D4×C13C211yesmaximal, characteristic, complemented
3C2×C13×#394C211yesmaximal, characteristic, complemented
4C2×C13×#392C212yesmaximal, complemented
5C2×C13×#392C211yesmaximal, characteristic, complemented
6C2×C13×#386C212yesmaximal, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic, complemented
9C13×#1438C212yesmaximal, complemented
10C13×#1437C212yesmaximal, complemented
11C13×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C13C2211yescharacteristic
13C23×D4×C13C2212yes—
14C23×D4×C13C2211yescharacteristic
15C23×D4×C13C2212yes—
16C24×C4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×#121—24no—
19C2×C13×#121—28no—
20C2×C4×D4×C13—24no—
21C2×C4×D4×C13—24no—
22C2×C4×D4×C13—24no—
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2212yes—
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2212yes—
28C22×C13×C22⋊C4C2212yes—
29C22×C13×C22⋊C4C2212yes—
30C22×C13×C22⋊C4C2212yes—
31C22×C13×C22⋊C4C2212yes—
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C13×#394—24no—
35C13×#392—28no—
36C13×#392—24no—
37C13×#386—28no—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2212yes—
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2212yes—
44C25×C13C2312yes—
45C25×C13C2311yescharacteristic
46C25×C13C2311yescharacteristic
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13—22no—
51C22×D4×C13—24no—
52C22×D4×C13—24no—
53C22×D4×C13—24no—
54C22×D4×C13—24no—
55C22×D4×C13—24no—
56C22×D4×C13—24no—
57C22×D4×C13—24no—
58C22×D4×C13—24no—
59C22×D4×C13—24no—
60C22×D4×C13—22no—
61C22×D4×C13—24no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—24no—
67C22×D4×C13—42no—
68C22×D4×C13—42no—
69C22×D4×C13—42no—
70C22×D4×C13—42no—
71C22×D4×C13—42no—
72C22×D4×C13D414yescomplemented
73C23×C4×C13—22no—
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—22no—
78C23×C4×C13—24no—
79C23×C4×C13—24no—
80C23×C4×C13—42no—
81C23×C4×C13—42no—
82C23×C4×C13D414yescomplemented
83C23×C4×C13C2312yes—
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2312yes—
87C23×C4×C13C2312yes—
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C13×#121—232no—
92C4×D4×C13—232no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—24no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4D414yescomplemented
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—24no—
104C2×C13×C22⋊C4—24no—
105C2×C13×C22⋊C4—24no—
106C2×C13×C22⋊C4—24no—
107C2×C13×C22⋊C4—24no—
108C2×C13×C22⋊C4—24no—
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—24no—
115C2×C13×C22⋊C4—24no—
116C2×C13×C22⋊C4—42no—
117C2×C13×C22⋊C4—42no—
118C2×C13×C22⋊C4—42no—
119C2×C13×C22⋊C4—42no—
120C2×C13×C22⋊C4D418yescomplemented
121C2×C13×C22⋊C4D414yescomplemented
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C13×#95—24no—
126C13×#95—24no—
127C13×#95—22no—
128C13×#95—24no—
129C13×#95—22no—
130C13×#95—42no—
131#14722C1311yesmaximal, characteristic, direct product factor, Sylow
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—22no—
137C24×C13—22no—
138C24×C13—22no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—22no—
144C24×C13—22no—
145C24×C13—22no—
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—22no—
159C24×C13—22no—
160C24×C13—22no—
161C24×C13—22no—
162C24×C13C2×D414yes—
163C24×C13C2×D412yes—
164C24×C13C2×D412yes—
165C24×C13C2×D412yes—
166C24×C13C2×D412yes—
167C24×C13#4112yes—
168C24×C13#4112yes—
169C24×C13C2411yescharacteristic
170C2×D4×C13—28no—
171C2×D4×C13—28no—
172C2×D4×C13—28no—
173C2×D4×C13—28no—
174C2×D4×C13—28no—
175C2×D4×C13—28no—
176C2×D4×C13—28no—
177C2×D4×C13—216no—
178C2×D4×C13—216no—
179C2×D4×C13—28no—
180C2×D4×C13—48no—
181C2×D4×C13—48no—
182C2×D4×C13—48no—
183C2×D4×C13—48no—
184C2×D4×C13—48no—
185C2×D4×C13—48no—
186C2×D4×C13—44no—
187C2×D4×C13—48no—
188C2×D4×C13—48no—
189C2×D4×C13—48no—
190C2×D4×C13—48no—
191C2×D4×C13—48no—
192C2×D4×C13—48no—
193C2×D4×C13—48no—
194C2×D4×C13—48no—
195C2×D4×C13—44no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—22no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—22no—
204C22×C4×C13—22no—
205C22×C4×C13—28no—
206C22×C4×C13—22no—
207C22×C4×C13—22no—
208C22×C4×C13—22no—
209C22×C4×C13—22no—
210C22×C4×C13—22no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—22no—
216C22×C4×C13—22no—
217C22×C4×C13—22no—
218C22×C4×C13—22no—
219C22×C4×C13—22no—
220C22×C4×C13—22no—
221C22×C4×C13—22no—
222C22×C4×C13—22no—
223C22×C4×C13—22no—
224C22×C4×C13—22no—
225C22×C4×C13—22no—
226C22×C4×C13—28no—
227C22×C4×C13—28no—
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—44no—
236C22×C4×C13—48no—
237C22×C4×C13—48no—
238C22×C4×C13—48no—
239C22×C4×C13—48no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13C2×D414yes—
243C22×C4×C13C2×D412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D414yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×D412yes—
249C22×C4×C13C2×D412yes—
250C22×C4×C13C2×D412yes—
251C22×C4×C13C2×D412yes—
252C22×C4×C13#4114yes—
253C22×C4×C13#4112yes—
254C13×C4⋊C4—28no—
255C13×C4⋊C4—28no—
256C13×C22⋊C4—28no—
257C13×C22⋊C4—28no—
258C13×C22⋊C4—216no—
259C13×C22⋊C4—48no—
260C13×C22⋊C4—48no—
261C13×C22⋊C4—48no—
262C13×C22⋊C4—48no—
263C13×C22⋊C4—48no—
264C42×C13—28no—
265C22×#121C2×C1311yescharacteristic, complemented
266C22×C4×D4C2×C1311yescharacteristic, complemented
267C2×#394C2×C1311yescharacteristic, complemented
268C2×#392C2×C1312yescomplemented
269C2×#392C2×C1311yescharacteristic, complemented
270C2×#386C2×C1312yescomplemented
271#1441C2×C1311yescharacteristic, complemented
272#1439C2×C1311yescharacteristic, complemented
273#1438C2×C1312yescomplemented
274#1437C2×C1312yescomplemented
275C22⋊#95C2×C1311yescharacteristic, complemented
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—24no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—24no—
294C23×C13—24no—
295C23×C13—24no—
296C23×C13—24no—
297C23×C13—24no—
298C23×C13—24no—
299C23×C13—24no—
300C23×C13—24no—
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—41no—
310C23×C13—42no—
311C23×C13—42no—
312C23×C13—42no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—42no—
317C23×C13—42no—
318C23×C13—42no—
319C23×C13—42no—
320C23×C13—42no—
321C23×C13—42no—
322C23×C13—42no—
323C23×C13—42no—
324C23×C13—42no—
325C23×C13—42no—
326C23×C13—42no—
327C23×C13—42no—
328C23×C13—42no—
329C23×C13—42no—
330C23×C13—42no—
331C23×C13—42no—
332C23×C13—42no—
333C23×C13—42no—
334C23×C13—42no—
335C23×C13—42no—
336C23×C13—42no—
337C23×C13—42no—
338C23×C13—42no—
339C23×C13—42no—
340C23×C13—42no—
341C23×C13—42no—
342C23×C13—42no—
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#12114yes—
356C23×C13#12114yescomplemented
357C23×C13C22×D411yescharacteristic
358C23×C13C22×D411yescharacteristic
359C23×C13C22×D411yescharacteristic
360C23×C13C22×D412yes—
361C23×C13C22×D411yescharacteristic
362C23×C13C2×#4111yescharacteristic
363C23×C13C2×#4111yescharacteristic
364C23×C13C2×#4111yescharacteristic
365C23×C13C2×#4112yes—
366C23×C13H(5,𝔽2)12yes—
367C23×C13H(5,𝔽2)12yes—
368D4×C13—232no—
369D4×C13—416no—
370D4×C13—432no—
371D4×C13—432no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—24no—
383C2×C4×C13—24no—
384C2×C4×C13—24no—
385C2×C4×C13—24no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—24no—
389C2×C4×C13—24no—
390C2×C4×C13—24no—
391C2×C4×C13—24no—
392C2×C4×C13—24no—
393C2×C4×C13—24no—
394C2×C4×C13—24no—
395C2×C4×C13—24no—
396C2×C4×C13—416no—
397C2×C4×C13—416no—
398C2×C4×C13—41no—
399C2×C4×C13—42no—
400C2×C4×C13—42no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—42no—
405C2×C4×C13—42no—
406C2×C4×C13—42no—
407C2×C4×C13—42no—
408C2×C4×C13—42no—
409C2×C4×C13—42no—
410C2×C4×C13—42no—
411C2×C4×C13—42no—
412C2×C4×C13—42no—
413C2×C4×C13—42no—
414C2×C4×C13—42no—
415C2×C4×C13—42no—
416C2×C4×C13—42no—
417C2×C4×C13—42no—
418C2×C4×C13—42no—
419C2×C4×C13#12014yes—
420C2×C4×C13#12014yes—
421C2×C4×C13#12114yescomplemented
422C23×D4C22×C1311yescharacteristic
423C23×D4C22×C1312yes—
424C23×D4C22×C1311yescharacteristic
425C23×D4C22×C1312yes—
426C24×C4C22×C1311yescharacteristic
427C24×C4C22×C1311yescharacteristic
428C2×#121—24no—
429C2×#121—28no—
430C2×C4×D4—24no—
431C2×C4×D4—24no—
432C2×C4×D4—24no—
433C22×C4⋊C4C22×C1311yescharacteristic
434C22×C4⋊C4C22×C1311yescharacteristic
435C22×C22⋊C4C22×C1312yes—
436C22×C22⋊C4C22×C1311yescharacteristic
437C22×C22⋊C4C22×C1312yes—
438C22×C22⋊C4C22×C1312yes—
439C22×C22⋊C4C22×C1312yes—
440C22×C22⋊C4C22×C1312yes—
441C22×C22⋊C4C22×C1311yescharacteristic
442C22×C22⋊C4C22×C1312yes—
443C22×C42C22×C1311yescharacteristic
444#394—24no—
445#392—28no—
446#392—24no—
447#386—28no—
448C2×#95C22×C1311yescharacteristic
449C2×#95C22×C1312yes—
450C2×#95C22×C1311yescharacteristic
451C2×#95C22×C1312yes—
452C2×#95C22×C1312yes—
453C2×#95C22×C1312yes—
454C22×C13—24no—
455C22×C13—24no—
456C22×C13—24no—
457C22×C13—28no—
458C22×C13—24no—
459C22×C13—42no—
460C22×C13—42no—
461C22×C13—42no—
462C22×C13—42no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—44no—
467C22×C13—44no—
468C22×C13—44no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—44no—
472C22×C13—44no—
473C22×C13—44no—
474C22×C13—44no—
475C22×C13—42no—
476C22×C13—44no—
477C22×C13—44no—
478C22×C13—44no—
479C22×C13—44no—
480C22×C13—44no—
481C22×C13—44no—
482C22×C13—44no—
483C22×C13—82no—
484C22×C13—82no—
485C22×C13—82no—
486C22×C13—82no—
487C22×C13—82no—
488C22×C13—82no—
489C22×C13—82no—
490C22×C13—82no—
491C22×C13C2×#12011yescharacteristic
492C22×C13C2×#12011yescharacteristic
493C22×C13C2×#12111yescharacteristic
494C22×C13C2×#12111yescharacteristic
495C22×C13C2×#12111yescharacteristic
496C22×C13#52511yescharacteristic
497C22×C13#52511yescharacteristic
498C22×C13#52511yescharacteristic
499C22×C13#52512yes—
500C22×C13#53212yes—
501C22×C13#53211yescharacteristic
502C22×C13#53411yescharacteristic
503C22×C13#53511yescharacteristic
504C22×C13#53812yes—
505C22×C13#54012yes—
506C22×C13D4212yes—
507C22×C13D4212yes—
508C22×C13D4212yes—
509C22×C13#54612yes—
510C22×C13#54612yes—
511C22×C13#54612yes—
512C22×C13#55012yes—
513C22×C13#55312yes—
514C4×C13—24no—
515C4×C13—24no—
516C4×C13—24no—
517C4×C13—42no—
518C4×C13—44no—
519C4×C13—44no—
520C4×C13—42no—
521C4×C13—82no—
522C25C23×C1312yes—
523C25C23×C1311yescharacteristic
524C25C23×C1311yescharacteristic
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—24no—
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—24no—
533C22×D4—24no—
534C22×D4—24no—
535C22×D4—24no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—22no—
539C22×D4—24no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—24no—
545C22×D4—42no—
546C22×D4—42no—
547C22×D4—42no—
548C22×D4—42no—
549C22×D4—42no—
550C22×D4D4×C1314yescomplemented
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—24no—
557C23×C4—24no—
558C23×C4—42no—
559C23×C4—42no—
560C23×C4D4×C1314yescomplemented
561C23×C4C23×C1312yes—
562C23×C4C23×C1311yescharacteristic
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1312yes—
565C23×C4C23×C1312yes—
566C23×C4C23×C1311yescharacteristic
567C23×C4C23×C1311yescharacteristic
568C23×C4C23×C1311yescharacteristic
569#121—232no—
570C4×D4—232no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—24no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4D4×C1314yescomplemented
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—24no—
582C2×C22⋊C4—24no—
583C2×C22⋊C4—24no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—24no—
589C2×C22⋊C4—24no—
590C2×C22⋊C4—24no—
591C2×C22⋊C4—24no—
592C2×C22⋊C4—24no—
593C2×C22⋊C4—24no—
594C2×C22⋊C4—42no—
595C2×C22⋊C4—42no—
596C2×C22⋊C4—42no—
597C2×C22⋊C4—42no—
598C2×C22⋊C4D4×C1314yescomplemented
599C2×C22⋊C4D4×C1318yescomplemented
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603#95—24no—
604#95—24no—
605#95—22no—
606#95—24no—
607#95—22no—
608#95—42no—
609C2×C13—44no—
610C2×C13—44no—
611C2×C13—84no—
612C2×C13#238811yescharacteristic
613C2×C13#240311yescharacteristic
614C2×C13#240811yescharacteristic
615C2×C13#242412yes—
616C2×C13#242812yes—
617C2×C13#243111yescharacteristic
618C2×C13#245612yes—
619C2×C13#246412yes—
620C2×C13#254311yescharacteristic
621C2×C13#263511yescharacteristic
622C2×C13#284711yescharacteristic
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24C2×D4×C1314yes—
654C24C2×D4×C1312yes—
655C24C2×D4×C1312yes—
656C24C2×D4×C1312yes—
657C24C2×D4×C1312yes—
658C24C13×#4112yes—
659C24C13×#4112yes—
660C24C24×C1311yescharacteristic
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—216no—
669C2×D4—216no—
670C2×D4—28no—
671C2×D4—48no—
672C2×D4—48no—
673C2×D4—48no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—44no—
678C2×D4—48no—
679C2×D4—48no—
680C2×D4—48no—
681C2×D4—48no—
682C2×D4—48no—
683C2×D4—48no—
684C2×D4—48no—
685C2×D4—48no—
686C2×D4—44no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—22no—
707C22×C4—22no—
708C22×C4—22no—
709C22×C4—22no—
710C22×C4—22no—
711C22×C4—22no—
712C22×C4—22no—
713C22×C4—22no—
714C22×C4—22no—
715C22×C4—22no—
716C22×C4—22no—
717C22×C4—28no—
718C22×C4—28no—
719C22×C4—22no—
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—22no—
723C22×C4—22no—
724C22×C4—22no—
725C22×C4—22no—
726C22×C4—44no—
727C22×C4—48no—
728C22×C4—48no—
729C22×C4—48no—
730C22×C4—48no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4C2×D4×C1314yes—
734C22×C4C2×D4×C1312yes—
735C22×C4C2×D4×C1312yes—
736C22×C4C2×D4×C1314yes—
737C22×C4C2×D4×C1312yes—
738C22×C4C2×D4×C1312yes—
739C22×C4C2×D4×C1312yes—
740C22×C4C2×D4×C1312yes—
741C22×C4C2×D4×C1312yes—
742C22×C4C2×D4×C1312yes—
743C22×C4C13×#4114yes—
744C22×C4C13×#4112yes—
745C4⋊C4—28no—
746C4⋊C4—28no—
747C22⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—216no—
750C22⋊C4—48no—
751C22⋊C4—48no—
752C22⋊C4—48no—
753C22⋊C4—48no—
754C22⋊C4—48no—
755C42—28no—
756C13#1472211yescharacteristic, direct product factor, Sylow
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—24no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—41no—
791C23—42no—
792C23—41no—
793C23—42no—
794C23—42no—
795C23—41no—
796C23—41no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23C13×#12114yes—
837C23C13×#12114yescomplemented
838C23C22×D4×C1311yescharacteristic
839C23C22×D4×C1311yescharacteristic
840C23C22×D4×C1311yescharacteristic
841C23C22×D4×C1312yes—
842C23C22×D4×C1311yescharacteristic
843C23C2×C13×#4111yescharacteristic
844C23C2×C13×#4111yescharacteristic
845C23C2×C13×#4111yescharacteristic
846C23C2×C13×#4112yes—
847C23C13×H(5,𝔽2)12yes—
848C23C13×H(5,𝔽2)12yes—
849D4—232no—
850D4—416no—
851D4—432no—
852D4—432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—24no—
866C2×C4—24no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—24no—
870C2×C4—24no—
871C2×C4—24no—
872C2×C4—24no—
873C2×C4—24no—
874C2×C4—24no—
875C2×C4—24no—
876C2×C4—24no—
877C2×C4—416no—
878C2×C4—416no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—42no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—42no—
885C2×C4—41no—
886C2×C4—42no—
887C2×C4—42no—
888C2×C4—42no—
889C2×C4—42no—
890C2×C4—42no—
891C2×C4—42no—
892C2×C4—42no—
893C2×C4—42no—
894C2×C4—42no—
895C2×C4—42no—
896C2×C4—42no—
897C2×C4—42no—
898C2×C4—42no—
899C2×C4—42no—
900C2×C4C13×#12014yes—
901C2×C4C13×#12014yes—
902C2×C4C13×#12114yescomplemented
903C22—24no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—28no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—44no—
917C22—44no—
918C22—44no—
919C22—42no—
920C22—42no—
921C22—44no—
922C22—44no—
923C22—44no—
924C22—44no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22C2×C13×#12011yescharacteristic
941C22C2×C13×#12011yescharacteristic
942C22C2×C13×#12111yescharacteristic
943C22C2×C13×#12111yescharacteristic
944C22C2×C13×#12111yescharacteristic
945C22C13×#52511yescharacteristic
946C22C13×#52511yescharacteristic
947C22C13×#52511yescharacteristic
948C22C13×#52512yes—
949C22C13×#53211yescharacteristic
950C22C13×#53212yes—
951C22C13×#53411yescharacteristic
952C22C13×#53511yescharacteristic
953C22C13×#53812yes—
954C22C13×#54012yes—
955C22D42×C1312yes—
956C22D42×C1312yes—
957C22D42×C1312yes—
958C22C13×#54612yes—
959C22C13×#54612yes—
960C22C13×#54612yes—
961C22C13×#55012yes—
962C22C13×#55312yes—
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—44no—
968C4—44no—
969C4—42no—
970C4—82no—
971C2—44no—
972C2—44no—
973C2—84no—
974C2C13×#238811yescharacteristic
975C2C13×#240311yescharacteristic
976C2C13×#240811yescharacteristic
977C2C13×#242412yes—
978C2C13×#242812yes—
979C2C13×#243111yescharacteristic
980C2C13×#245612yes—
981C2C13×#246412yes—
982C2C13×#254311yescharacteristic
983C2C13×#263511yescharacteristic
984C2C13×#284711yescharacteristic
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×C4×D4×C13C2semidirect
3. C2×C13×#394C2semidirect
4. C2×C13×#392C2semidirect
5. C2×C13×#392C2semidirect
6. C2×C13×#386C2semidirect
7. C13×#1441C2semidirect
8. C13×#1439C2semidirect
9. C13×#1438C2semidirect
10. C13×#1437C2semidirect
11. C13×C22⋊#95C2semidirect
72. C22×D4×C13D4semidirect
82. C23×C4×C13D4semidirect
97. C2×C13×C4⋊C4D4semidirect
120. C2×C13×C22⋊C4D4semidirect
121. C2×C13×C22⋊C4D4semidirect
131. #14722C13direct (N × H)
265. C22×#121C2×C13semidirect
266. C22×C4×D4C2×C13semidirect
267. C2×#394C2×C13semidirect
268. C2×#392C2×C13semidirect
269. C2×#392C2×C13semidirect
270. C2×#386C2×C13semidirect
271. #1441C2×C13semidirect
272. #1439C2×C13semidirect
273. #1438C2×C13semidirect
274. #1437C2×C13semidirect
275. C22⋊#95C2×C13semidirect
356. C23×C13#121semidirect
421. C2×C4×C13#121semidirect
550. C22×D4D4×C13semidirect
560. C23×C4D4×C13semidirect
575. C2×C4⋊C4D4×C13semidirect
598. C2×C22⋊C4D4×C13semidirect
599. C2×C22⋊C4D4×C13semidirect
756. C13#14722direct (N × H)
837. C23C13×#121semidirect
902. C2×C4C13×#121semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1212
C22×C4×D4×C132
C2×C13×#3942
C2×C13×#3922
C2×C13×#3862
C13×#14412
C13×#14392
C13×#14382
C13×#14372
C13×C22⋊#952
#1472213