Finite Group Databasebeta

← C13×#14729 #15701068

Subgroups — C13×#14729 #15701068

Order 3328.

2506 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C13×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C13×#396C212yesmaximal, complemented
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#386C211yesmaximal, characteristic
5C2×C13×#386C211yesmaximal, characteristic
6C2×C13×#385C211yesmaximal, characteristic, complemented
7C2×C13×#380C211yesmaximal, characteristic, complemented
8C13×#1441C212yesmaximal, complemented
9C13×#1441C212yesmaximal, complemented
10C13×#1439C212yesmaximal, complemented
11C13×C22⋊#95C211yesmaximal, characteristic, complemented
12C23×D4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C24×C4×C13C2211yescharacteristic
16C22×C13×C4⋊C4—24no—
17C22×C13×C4⋊C4—28no—
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C4⋊C4C2212yes—
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2212yes—
26C22×C13×C22⋊C4C2212yes—
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C13×#396—28no—
30C13×#386—24no—
31C13×#386—24no—
32C13×#386—24no—
33C13×#385—24no—
34C13×#380—24no—
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2212yes—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2212yes—
41C2×C13×#95C2212yes—
42C2×C13×#95C2212yes—
43C25×C13C2311yescharacteristic
44C25×C13C2311yescharacteristic
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13—22no—
50C22×D4×C13—22no—
51C22×D4×C13Q814yes—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—24no—
55C23×C4×C13—24no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—24no—
60C23×C4×C13—24no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—42no—
64C23×C4×C13—42no—
65C23×C4×C13D414yes—
66C23×C4×C13D414yes—
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2312yes—
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2312yes—
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2312yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2312yes—
76C2×C13×C4⋊C4—232no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4—24no—
80C2×C13×C4⋊C4—24no—
81C2×C13×C4⋊C4—24no—
82C2×C13×C4⋊C4—24no—
83C2×C13×C4⋊C4—24no—
84C2×C13×C4⋊C4—24no—
85C2×C13×C4⋊C4—24no—
86C2×C13×C4⋊C4—24no—
87C2×C13×C4⋊C4—42no—
88C2×C13×C4⋊C4D418yescomplemented
89C2×C13×C22⋊C4—22no—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—24no—
98C2×C13×C22⋊C4—22no—
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—42no—
106C2×C13×C22⋊C4—42no—
107C2×C13×C22⋊C4D414yes—
108C13×#95—24no—
109C13×#95—24no—
110C13×#95—24no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—24no—
114C13×#95—24no—
115C13×#95—42no—
116#14729C1311yesmaximal, characteristic, direct product factor, Sylow
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13—22no—
122C24×C13—21no—
123C24×C13—21no—
124C24×C13—21no—
125C24×C13—22no—
126C24×C13—21no—
127C24×C13—21no—
128C24×C13—21no—
129C24×C13—22no—
130C24×C13—22no—
131C24×C13C2×D412yes—
132C24×C13C2×D412yes—
133C24×C13C2×D412yes—
134C24×C13C2×Q812yes—
135C24×C13C2×Q812yes—
136C24×C13#4112yes—
137C24×C13#4112yes—
138C24×C13#4112yes—
139C24×C13C2411yescharacteristic
140C2×D4×C13—28no—
141C2×D4×C13—28no—
142C2×D4×C13—28no—
143C2×D4×C13—44no—
144C2×D4×C13—44no—
145C2×D4×C13—44no—
146C2×D4×C13—44no—
147C22×C4×C13—28no—
148C22×C4×C13—216no—
149C22×C4×C13—28no—
150C22×C4×C13—28no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—21no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—21no—
157C22×C4×C13—22no—
158C22×C4×C13—216no—
159C22×C4×C13—28no—
160C22×C4×C13—28no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—21no—
174C22×C4×C13—22no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—22no—
179C22×C4×C13—22no—
180C22×C4×C13—22no—
181C22×C4×C13—22no—
182C22×C4×C13—22no—
183C22×C4×C13—28no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—22no—
187C22×C4×C13—21no—
188C22×C4×C13—22no—
189C22×C4×C13—22no—
190C22×C4×C13—22no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—22no—
195C22×C4×C13—22no—
196C22×C4×C13—22no—
197C22×C4×C13—22no—
198C22×C4×C13—22no—
199C22×C4×C13—22no—
200C22×C4×C13—22no—
201C22×C4×C13—44no—
202C22×C4×C13—48no—
203C22×C4×C13—48no—
204C22×C4×C13—48no—
205C22×C4×C13—48no—
206C22×C4×C13—44no—
207C22×C4×C13—44no—
208C22×C4×C13C2×D414yes—
209C22×C4×C13C2×D412yes—
210C22×C4×C13C2×D414yes—
211C22×C4×C13C2×D412yes—
212C22×C4×C13C2×D414yes—
213C22×C4×C13C2×D414yes—
214C22×C4×C13C2×D414yes—
215C22×C4×C13C2×Q812yes—
216C22×C4×C13#4114yes—
217C13×C4⋊C4—216no—
218C13×C4⋊C4—216no—
219C13×C4⋊C4—48no—
220C13×C4⋊C4—48no—
221C13×C22⋊C4—28no—
222C13×C22⋊C4—48no—
223C13×C22⋊C4—44no—
224C13×C22⋊C4—44no—
225C13×C22⋊C4—44no—
226C13×C22⋊C4—44no—
227C13×C22⋊C4—48no—
228C23×C4⋊C4C2×C1311yescharacteristic, complemented
229C2×#396C2×C1312yescomplemented
230C2×#386C2×C1311yescharacteristic
231C2×#386C2×C1311yescharacteristic
232C2×#386C2×C1311yescharacteristic
233C2×#385C2×C1311yescharacteristic, complemented
234C2×#380C2×C1311yescharacteristic, complemented
235#1441C2×C1312yescomplemented
236#1441C2×C1312yescomplemented
237#1439C2×C1312yescomplemented
238C22⋊#95C2×C1311yescharacteristic, complemented
239C23×C13—22no—
240C23×C13—24no—
241C23×C13—22no—
242C23×C13—24no—
243C23×C13—22no—
244C23×C13—22no—
245C23×C13—24no—
246C23×C13—24no—
247C23×C13—24no—
248C23×C13—24no—
249C23×C13—24no—
250C23×C13—24no—
251C23×C13—24no—
252C23×C13—24no—
253C23×C13—24no—
254C23×C13—24no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—24no—
259C23×C13—24no—
260C23×C13—41no—
261C23×C13—42no—
262C23×C13—41no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—42no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—42no—
271C23×C13—42no—
272C23×C13—42no—
273C23×C13—42no—
274C23×C13—42no—
275C23×C13—42no—
276C23×C13—42no—
277C23×C13—42no—
278C23×C13#12114yes—
279C23×C13#12114yes—
280C23×C13#12114yes—
281C23×C13C22⋊Q814yes—
282C23×C13C22⋊Q814yes—
283C23×C13C22⋊Q814yes—
284C23×C13#12614yes—
285C23×C13C22×D411yescharacteristic
286C23×C13C22×D412yes—
287C23×C13C22×D411yescharacteristic
288C23×C13C22×D411yescharacteristic
289C23×C13C22×Q811yescharacteristic
290C23×C13C2×#4111yescharacteristic
291C23×C13C2×#4111yescharacteristic
292C23×C13C2×#4111yescharacteristic
293C23×C13C2×#4112yes—
294C23×C13H(5,𝔽2)12yes—
295C23×C132−1+412yes—
296D4×C13—416no—
297C2×C4×C13—232no—
298C2×C4×C13—24no—
299C2×C4×C13—24no—
300C2×C4×C13—24no—
301C2×C4×C13—22no—
302C2×C4×C13—24no—
303C2×C4×C13—24no—
304C2×C4×C13—24no—
305C2×C4×C13—22no—
306C2×C4×C13—24no—
307C2×C4×C13—24no—
308C2×C4×C13—22no—
309C2×C4×C13—24no—
310C2×C4×C13—24no—
311C2×C4×C13—22no—
312C2×C4×C13—22no—
313C2×C4×C13—22no—
314C2×C4×C13—22no—
315C2×C4×C13—22no—
316C2×C4×C13—24no—
317C2×C4×C13—24no—
318C2×C4×C13—24no—
319C2×C4×C13—24no—
320C2×C4×C13—416no—
321C2×C4×C13—416no—
322C2×C4×C13—42no—
323C2×C4×C13—42no—
324C2×C4×C13—41no—
325C2×C4×C13—41no—
326C2×C4×C13—41no—
327C2×C4×C13—41no—
328C2×C4×C13—42no—
329C2×C4×C13—42no—
330C2×C4×C13—42no—
331C2×C4×C13—42no—
332C2×C4×C13—42no—
333C2×C4×C13—42no—
334C2×C4×C13—42no—
335C2×C4×C13—42no—
336C2×C4×C13—41no—
337C2×C4×C13—41no—
338C2×C4×C13—41no—
339C2×C4×C13—42no—
340C2×C4×C13—42no—
341C2×C4×C13—42no—
342C2×C4×C13—41no—
343C2×C4×C13—42no—
344C2×C4×C13—41no—
345C2×C4×C13—41no—
346C2×C4×C13—42no—
347C2×C4×C13—42no—
348C2×C4×C13—42no—
349C2×C4×C13—42no—
350C2×C4×C13—42no—
351C2×C4×C13—42no—
352C2×C4×C13—42no—
353C2×C4×C13#12014yes—
354C2×C4×C13#12118yes—
355C23×D4C22×C1311yescharacteristic
356C24×C4C22×C1311yescharacteristic
357C24×C4C22×C1311yescharacteristic
358C24×C4C22×C1311yescharacteristic
359C22×C4⋊C4—24no—
360C22×C4⋊C4—28no—
361C22×C4⋊C4C22×C1312yes—
362C22×C4⋊C4C22×C1312yes—
363C22×C4⋊C4C22×C1312yes—
364C22×C4⋊C4C22×C1312yes—
365C22×C22⋊C4C22×C1311yescharacteristic
366C22×C22⋊C4C22×C1312yes—
367C22×C22⋊C4C22×C1311yescharacteristic
368C22×C22⋊C4C22×C1311yescharacteristic
369C22×C22⋊C4C22×C1312yes—
370C22×C22⋊C4C22×C1311yescharacteristic
371C22×C22⋊C4C22×C1311yescharacteristic
372#396—28no—
373#386—24no—
374#386—24no—
375#386—24no—
376#385—24no—
377#380—24no—
378C2×#95C22×C1312yes—
379C2×#95C22×C1312yes—
380C2×#95C22×C1312yes—
381C2×#95C22×C1311yescharacteristic
382C2×#95C22×C1312yes—
383C2×#95C22×C1311yescharacteristic
384C2×#95C22×C1312yes—
385C2×#95C22×C1312yes—
386C22×C13—24no—
387C22×C13—24no—
388C22×C13—24no—
389C22×C13—24no—
390C22×C13—24no—
391C22×C13—24no—
392C22×C13—28no—
393C22×C13—28no—
394C22×C13—28no—
395C22×C13—28no—
396C22×C13—42no—
397C22×C13—42no—
398C22×C13—42no—
399C22×C13—44no—
400C22×C13—44no—
401C22×C13—81no—
402C22×C13—81no—
403C22×C13—81no—
404C22×C13—81no—
405C22×C13—82no—
406C22×C13—82no—
407C22×C13#39618yescomplemented
408C22×C13C2×#12011yescharacteristic
409C22×C13C2×#12111yescharacteristic
410C22×C13C2×#12112yes—
411C22×C13C2×#12111yescharacteristic
412C22×C13C2×#12111yescharacteristic
413C22×C13C2×C22⋊Q811yescharacteristic
414C22×C13C2×C22⋊Q811yescharacteristic
415C22×C13C2×C22⋊Q811yescharacteristic
416C22×C13#52511yescharacteristic
417C22×C13#52512yes—
418C22×C13C2×#12611yescharacteristic
419C22×C13#53411yescharacteristic
420C22×C13#53611yescharacteristic
421C22×C13#53712yes—
422C22×C13#53912yes—
423C22×C13D4212yes—
424C22×C13#54612yes—
425C22×C13#54712yes—
426C22×C13#54812yes—
427C22×C13D4×Q812yes—
428C22×C13#55212yes—
429C22×C13#55312yes—
430C22×C13#55412yes—
431C4×C13—28no—
432C4×C13—24no—
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—44no—
436C4×C13—44no—
437C4×C13—81no—
438C4×C13—81no—
439C4×C13—82no—
440C25C23×C1311yescharacteristic
441C25C23×C1311yescharacteristic
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4Q8×C1314yes—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—24no—
452C23×C4—24no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—24no—
457C23×C4—24no—
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4D4×C1314yes—
463C23×C4D4×C1314yes—
464C23×C4C23×C1311yescharacteristic
465C23×C4C23×C1312yes—
466C23×C4C23×C1311yescharacteristic
467C23×C4C23×C1312yes—
468C23×C4C23×C1311yescharacteristic
469C23×C4C23×C1312yes—
470C23×C4C23×C1311yescharacteristic
471C23×C4C23×C1311yescharacteristic
472C23×C4C23×C1312yes—
473C2×C4⋊C4—232no—
474C2×C4⋊C4—24no—
475C2×C4⋊C4—24no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—24no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—42no—
485C2×C4⋊C4D4×C1318yescomplemented
486C2×C22⋊C4—22no—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—24no—
495C2×C22⋊C4—22no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—24no—
501C2×C22⋊C4—24no—
502C2×C22⋊C4—42no—
503C2×C22⋊C4—42no—
504C2×C22⋊C4D4×C1314yes—
505#95—24no—
506#95—24no—
507#95—24no—
508#95—22no—
509#95—22no—
510#95—24no—
511#95—24no—
512#95—42no—
513C2×C13—28no—
514C2×C13—82no—
515C2×C13C2×#39611yescharacteristic
516C2×C13#240911yescharacteristic
517C2×C13#241011yescharacteristic
518C2×C13#241311yescharacteristic
519C2×C13#241612yes—
520C2×C13#241712yes—
521C2×C13#244912yes—
522C2×C13#248112yes—
523C2×C13#257911yescharacteristic
524C2×C13#261811yescharacteristic
525C2×C13#284711yescharacteristic
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—22no—
535C24—21no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—22no—
540C24C2×D4×C1312yes—
541C24C2×D4×C1312yes—
542C24C2×D4×C1312yes—
543C24C2×Q8×C1312yes—
544C24C2×Q8×C1312yes—
545C24C13×#4112yes—
546C24C13×#4112yes—
547C24C13×#4112yes—
548C24C24×C1311yescharacteristic
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C22×C4—28no—
557C22×C4—216no—
558C22×C4—28no—
559C22×C4—28no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—216no—
568C22×C4—28no—
569C22×C4—28no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—28no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—22no—
596C22×C4—21no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—44no—
611C22×C4—48no—
612C22×C4—48no—
613C22×C4—48no—
614C22×C4—48no—
615C22×C4—44no—
616C22×C4—44no—
617C22×C4C2×D4×C1314yes—
618C22×C4C2×D4×C1312yes—
619C22×C4C2×D4×C1314yes—
620C22×C4C2×D4×C1312yes—
621C22×C4C2×D4×C1314yes—
622C22×C4C2×D4×C1314yes—
623C22×C4C2×D4×C1314yes—
624C22×C4C2×Q8×C1312yes—
625C22×C4C13×#4114yes—
626C4⋊C4—216no—
627C4⋊C4—216no—
628C4⋊C4—48no—
629C4⋊C4—48no—
630C22⋊C4—28no—
631C22⋊C4—48no—
632C22⋊C4—44no—
633C22⋊C4—44no—
634C22⋊C4—44no—
635C22⋊C4—44no—
636C22⋊C4—48no—
637C13#1472911yescharacteristic, direct product factor, Sylow
638C23—22no—
639C23—24no—
640C23—22no—
641C23—24no—
642C23—22no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—24no—
658C23—24no—
659C23—41no—
660C23—42no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—42no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23C13×#12114yes—
678C23C13×#12114yes—
679C23C13×#12114yes—
680C23C13×C22⋊Q814yes—
681C23C13×C22⋊Q814yes—
682C23C13×C22⋊Q814yes—
683C23C13×#12614yes—
684C23C22×D4×C1311yescharacteristic
685C23C22×D4×C1312yes—
686C23C22×D4×C1311yescharacteristic
687C23C22×D4×C1311yescharacteristic
688C23C22×Q8×C1311yescharacteristic
689C23C2×C13×#4111yescharacteristic
690C23C2×C13×#4111yescharacteristic
691C23C2×C13×#4111yescharacteristic
692C23C2×C13×#4112yes—
693C23C13×H(5,𝔽2)12yes—
694C23C13×2−1+412yes—
695D4—416no—
696C2×C4—232no—
697C2×C4—24no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—22no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—24no—
718C2×C4—24no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—41no—
742C2×C4—42no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4C13×#12014yes—
753C2×C4C13×#12118yes—
754C22—24no—
755C22—24no—
756C22—24no—
757C22—24no—
758C22—24no—
759C22—24no—
760C22—28no—
761C22—28no—
762C22—28no—
763C22—28no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—44no—
768C22—44no—
769C22—81no—
770C22—81no—
771C22—81no—
772C22—81no—
773C22—82no—
774C22—82no—
775C22C13×#39618yescomplemented
776C22C2×C13×#12011yescharacteristic
777C22C2×C13×#12111yescharacteristic
778C22C2×C13×#12112yes—
779C22C2×C13×#12111yescharacteristic
780C22C2×C13×#12111yescharacteristic
781C22C2×C13×C22⋊Q811yescharacteristic
782C22C2×C13×C22⋊Q811yescharacteristic
783C22C2×C13×C22⋊Q811yescharacteristic
784C22C13×#52511yescharacteristic
785C22C13×#52512yes—
786C22C2×C13×#12611yescharacteristic
787C22C13×#53411yescharacteristic
788C22C13×#53611yescharacteristic
789C22C13×#53712yes—
790C22C13×#53912yes—
791C22D42×C1312yes—
792C22C13×#54612yes—
793C22C13×#54712yes—
794C22C13×#54812yes—
795C22D4×Q8×C1312yes—
796C22C13×#55212yes—
797C22C13×#55312yes—
798C22C13×#55412yes—
799C4—28no—
800C4—24no—
801C4—42no—
802C4—42no—
803C4—44no—
804C4—44no—
805C4—81no—
806C4—81no—
807C4—82no—
808C2—28no—
809C2—82no—
810C2C2×C13×#39611yescharacteristic
811C2C13×#240911yescharacteristic
812C2C13×#241011yescharacteristic
813C2C13×#241311yescharacteristic
814C2C13×#241612yes—
815C2C13×#241712yes—
816C2C13×#244912yes—
817C2C13×#248112yes—
818C2C13×#257911yescharacteristic
819C2C13×#261811yescharacteristic
820C2C13×#284711yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C23×C13×C4⋊C4C2semidirect
2. C2×C13×#396C2semidirect
6. C2×C13×#385C2semidirect
7. C2×C13×#380C2semidirect
8. C13×#1441C2semidirect
9. C13×#1441C2semidirect
10. C13×#1439C2semidirect
11. C13×C22⋊#95C2semidirect
88. C2×C13×C4⋊C4D4semidirect
116. #14729C13direct (N × H)
228. C23×C4⋊C4C2×C13semidirect
229. C2×#396C2×C13semidirect
233. C2×#385C2×C13semidirect
234. C2×#380C2×C13semidirect
235. #1441C2×C13semidirect
236. #1441C2×C13semidirect
237. #1439C2×C13semidirect
238. C22⋊#95C2×C13semidirect
407. C22×C13#396semidirect
485. C2×C4⋊C4D4×C13semidirect
637. C13#14729direct (N × H)
775. C22C13×#396semidirect

Maximal subgroups

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

subgroupindex
C23×C13×C4⋊C42
C2×C13×#3962
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C13×#14412
C13×#14392
C13×C22⋊#952
#1472913