Finite Group Databasebeta

← C13×#14728 #15701067

Subgroups — C13×#14728 #15701067

Order 3328.

2190 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C13×C4⋊C4C211yesmaximal, characteristic
2C2×C13×#398C212yesmaximal, complemented
3C2×C13×#385C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic
5C2×C13×#380C211yesmaximal, characteristic
6C13×#1444C212yesmaximal, complemented
7C13×#1442C212yesmaximal, complemented
8C13×#1441C212yesmaximal, complemented
9C13×C22⋊#95C211yesmaximal, characteristic
10C13×C22⋊#95C211yesmaximal, characteristic
11C13×C22⋊#95C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C24×C4×C13C2211yescharacteristic
15C22×C13×C4⋊C4—24no—
16C22×C13×C4⋊C4—28no—
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2212yes—
19C22×C13×C4⋊C4C2212yes—
20C22×C13×C4⋊C4C2212yes—
21C22×C13×C4⋊C4C2212yes—
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C13×#398—28no—
28C13×#385—24no—
29C13×#385—24no—
30C13×#380—24no—
31C2×C13×#95C2212yes—
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2212yes—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2212yes—
36C2×C13×#95C2212yes—
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—24no—
45C23×C4×C13—24no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—24no—
50C23×C4×C13—24no—
51C23×C4×C13—22no—
52C23×C4×C13—22no—
53C23×C4×C13—42no—
54C23×C4×C13—42no—
55C23×C4×C13D414yes—
56C23×C4×C13Q814yes—
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2312yes—
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2312yes—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2312yes—
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2312yes—
67C2×C13×C4⋊C4—232no—
68C2×C13×C4⋊C4—24no—
69C2×C13×C4⋊C4—24no—
70C2×C13×C4⋊C4—24no—
71C2×C13×C4⋊C4—24no—
72C2×C13×C4⋊C4—24no—
73C2×C13×C4⋊C4—24no—
74C2×C13×C4⋊C4—24no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—24no—
78C2×C13×C4⋊C4—24no—
79C2×C13×C4⋊C4—24no—
80C2×C13×C4⋊C4—42no—
81C2×C13×C4⋊C4—42no—
82C2×C13×C4⋊C4—42no—
83C2×C13×C4⋊C4D418yes—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
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⋊C4D414yes—
95C2×C13×C22⋊C4Q814yes—
96C13×#95—24no—
97C13×#95—22no—
98C13×#95—22no—
99C13×#95—24no—
100C13×#95—24no—
101C13×#95—24no—
102C13×#95—24no—
103C13×#95—24no—
104C13×#95—24no—
105C13×#95—42no—
106#14728C1311yesmaximal, characteristic, direct product factor, Sylow
107C24×C13—22no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13C2×D412yes—
112C24×C13C2×D412yes—
113C24×C13C2×Q812yes—
114C24×C13C2×Q812yes—
115C24×C13#4112yes—
116C24×C13#4112yes—
117C24×C13#4112yes—
118C24×C13C2411yescharacteristic
119C22×C4×C13—28no—
120C22×C4×C13—216no—
121C22×C4×C13—28no—
122C22×C4×C13—28no—
123C22×C4×C13—22no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—216no—
131C22×C4×C13—28no—
132C22×C4×C13—28no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13—22no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—22no—
156C22×C4×C13—22no—
157C22×C4×C13—28no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—22no—
166C22×C4×C13—22no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—22no—
170C22×C4×C13—22no—
171C22×C4×C13—22no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—22no—
175C22×C4×C13—44no—
176C22×C4×C13—48no—
177C22×C4×C13—48no—
178C22×C4×C13—48no—
179C22×C4×C13—48no—
180C22×C4×C13—44no—
181C22×C4×C13—44no—
182C22×C4×C13C2×D414yes—
183C22×C4×C13C2×D412yes—
184C22×C4×C13C2×D414yes—
185C22×C4×C13C2×D412yes—
186C22×C4×C13C2×D414yes—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×Q812yes—
189C22×C4×C13C2×Q812yes—
190C22×C4×C13C2×Q814yes—
191C22×C4×C13#4114yes—
192C13×C4⋊C4—216no—
193C13×C4⋊C4—216no—
194C13×C4⋊C4—48no—
195C13×C4⋊C4—48no—
196C13×C4⋊C4—44no—
197C13×C4⋊C4—44no—
198C13×C22⋊C4—28no—
199C13×C22⋊C4—28no—
200C13×C22⋊C4—44no—
201C13×C22⋊C4—44no—
202C23×C4⋊C4C2×C1311yescharacteristic
203C2×#398C2×C1312yescomplemented
204C2×#385C2×C1311yescharacteristic
205C2×#385C2×C1311yescharacteristic
206C2×#380C2×C1311yescharacteristic
207#1444C2×C1312yescomplemented
208#1442C2×C1312yescomplemented
209#1441C2×C1312yescomplemented
210C22⋊#95C2×C1311yescharacteristic
211C22⋊#95C2×C1311yescharacteristic
212C22⋊#95C2×C1311yescharacteristic
213C23×C13—22no—
214C23×C13—24no—
215C23×C13—22no—
216C23×C13—24no—
217C23×C13—22no—
218C23×C13—22no—
219C23×C13—24no—
220C23×C13—24no—
221C23×C13—24no—
222C23×C13—24no—
223C23×C13—24no—
224C23×C13—24no—
225C23×C13—24no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13#12114yes—
230C23×C13C22⋊Q814yes—
231C23×C13C22⋊Q814yes—
232C23×C13#12314yes—
233C23×C13#12514yes—
234C23×C13#12514yes—
235C23×C13C4⋊Q814yes—
236C23×C13C22×D411yescharacteristic
237C23×C13C22×D412yes—
238C23×C13C22×D411yescharacteristic
239C23×C13C22×Q811yescharacteristic
240C23×C13C22×Q811yescharacteristic
241C23×C13C2×#4111yescharacteristic
242C23×C13C2×#4111yescharacteristic
243C23×C13C2×#4111yescharacteristic
244C23×C13C2×#4112yes—
245C23×C13H(5,𝔽2)12yes—
246C23×C132−1+412yes—
247C2×C4×C13—232no—
248C2×C4×C13—24no—
249C2×C4×C13—22no—
250C2×C4×C13—24no—
251C2×C4×C13—24no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—22no—
256C2×C4×C13—24no—
257C2×C4×C13—24no—
258C2×C4×C13—22no—
259C2×C4×C13—24no—
260C2×C4×C13—22no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—24no—
264C2×C4×C13—22no—
265C2×C4×C13—24no—
266C2×C4×C13—24no—
267C2×C4×C13—24no—
268C2×C4×C13—24no—
269C2×C4×C13—24no—
270C2×C4×C13—24no—
271C2×C4×C13—416no—
272C2×C4×C13—416no—
273C2×C4×C13—41no—
274C2×C4×C13—42no—
275C2×C4×C13—41no—
276C2×C4×C13—42no—
277C2×C4×C13—41no—
278C2×C4×C13—42no—
279C2×C4×C13—41no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—42no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13#12014yes—
307C2×C4×C13C22⋊Q818yes—
308C24×C4C22×C1311yescharacteristic
309C24×C4C22×C1311yescharacteristic
310C24×C4C22×C1311yescharacteristic
311C22×C4⋊C4—24no—
312C22×C4⋊C4—28no—
313C22×C4⋊C4C22×C1311yescharacteristic
314C22×C4⋊C4C22×C1312yes—
315C22×C4⋊C4C22×C1312yes—
316C22×C4⋊C4C22×C1312yes—
317C22×C4⋊C4C22×C1312yes—
318C22×C4⋊C4C22×C1311yescharacteristic
319C22×C22⋊C4C22×C1311yescharacteristic
320C22×C22⋊C4C22×C1311yescharacteristic
321C22×C22⋊C4C22×C1311yescharacteristic
322C22×C22⋊C4C22×C1311yescharacteristic
323#398—28no—
324#385—24no—
325#385—24no—
326#380—24no—
327C2×#95C22×C1312yes—
328C2×#95C22×C1312yes—
329C2×#95C22×C1312yes—
330C2×#95C22×C1312yes—
331C2×#95C22×C1312yes—
332C2×#95C22×C1311yescharacteristic
333C2×#95C22×C1312yes—
334C2×#95C22×C1311yescharacteristic
335C2×#95C22×C1312yes—
336C2×#95C22×C1312yes—
337C22×C13—24no—
338C22×C13—24no—
339C22×C13—24no—
340C22×C13—24no—
341C22×C13—24no—
342C22×C13—24no—
343C22×C13—28no—
344C22×C13—28no—
345C22×C13—28no—
346C22×C13—28no—
347C22×C13#39818yescomplemented
348C22×C13C2×#12011yescharacteristic
349C22×C13C2×#12111yescharacteristic
350C22×C13C2×C22⋊Q811yescharacteristic
351C22×C13C2×C22⋊Q811yescharacteristic
352C22×C13C2×C22⋊Q812yes—
353C22×C13C2×#12311yescharacteristic
354C22×C13#52511yescharacteristic
355C22×C13#52512yes—
356C22×C13C2×#12511yescharacteristic
357C22×C13C2×#12511yescharacteristic
358C22×C13C2×C4⋊Q811yescharacteristic
359C22×C13#53411yescharacteristic
360C22×C13#53611yescharacteristic
361C22×C13#53912yes—
362C22×C13#54412yes—
363C22×C13D4212yes—
364C22×C13#54612yes—
365C22×C13#54712yes—
366C22×C13#54812yes—
367C22×C13D4×Q812yes—
368C22×C13#55212yes—
369C22×C13#55312yes—
370C22×C13#55412yes—
371C4×C13—28no—
372C4×C13—24no—
373C4×C13—42no—
374C4×C13—42no—
375C4×C13—42no—
376C4×C13—44no—
377C4×C13—44no—
378C4×C13—81no—
379C4×C13—81no—
380C4×C13—82no—
381C25C23×C1311yescharacteristic
382C23×C4—22no—
383C23×C4—22no—
384C23×C4—24no—
385C23×C4—24no—
386C23×C4—22no—
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—42no—
394C23×C4—42no—
395C23×C4D4×C1314yes—
396C23×C4Q8×C1314yes—
397C23×C4C23×C1311yescharacteristic
398C23×C4C23×C1312yes—
399C23×C4C23×C1311yescharacteristic
400C23×C4C23×C1312yes—
401C23×C4C23×C1311yescharacteristic
402C23×C4C23×C1312yes—
403C23×C4C23×C1311yescharacteristic
404C23×C4C23×C1311yescharacteristic
405C23×C4C23×C1311yescharacteristic
406C23×C4C23×C1312yes—
407C2×C4⋊C4—232no—
408C2×C4⋊C4—24no—
409C2×C4⋊C4—24no—
410C2×C4⋊C4—24no—
411C2×C4⋊C4—24no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—22no—
416C2×C4⋊C4—22no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—42no—
421C2×C4⋊C4—42no—
422C2×C4⋊C4—42no—
423C2×C4⋊C4D4×C1318yes—
424C2×C22⋊C4—22no—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—22no—
427C2×C22⋊C4—22no—
428C2×C22⋊C4—22no—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4D4×C1314yes—
435C2×C22⋊C4Q8×C1314yes—
436#95—24no—
437#95—22no—
438#95—22no—
439#95—24no—
440#95—24no—
441#95—24no—
442#95—24no—
443#95—24no—
444#95—24no—
445#95—42no—
446C2×C13—28no—
447C2×C13C2×#39811yescharacteristic
448C2×C13#240911yescharacteristic
449C2×C13#241011yescharacteristic
450C2×C13#241311yescharacteristic
451C2×C13#244012yes—
452C2×C13#244212yes—
453C2×C13#244312yes—
454C2×C13#247312yes—
455C2×C13#257911yescharacteristic
456C2×C13#262711yescharacteristic
457C2×C13#284811yescharacteristic
458C24—22no—
459C24—22no—
460C24—22no—
461C24—22no—
462C24C2×D4×C1312yes—
463C24C2×D4×C1312yes—
464C24C2×Q8×C1312yes—
465C24C2×Q8×C1312yes—
466C24C13×#4112yes—
467C24C13×#4112yes—
468C24C13×#4112yes—
469C24C24×C1311yescharacteristic
470C22×C4—28no—
471C22×C4—216no—
472C22×C4—28no—
473C22×C4—28no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—216no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—22no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—28no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—44no—
527C22×C4—48no—
528C22×C4—48no—
529C22×C4—48no—
530C22×C4—48no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4C2×D4×C1314yes—
534C22×C4C2×D4×C1312yes—
535C22×C4C2×D4×C1314yes—
536C22×C4C2×D4×C1312yes—
537C22×C4C2×D4×C1314yes—
538C22×C4C2×D4×C1314yes—
539C22×C4C2×Q8×C1312yes—
540C22×C4C2×Q8×C1312yes—
541C22×C4C2×Q8×C1314yes—
542C22×C4C13×#4114yes—
543C4⋊C4—216no—
544C4⋊C4—216no—
545C4⋊C4—48no—
546C4⋊C4—48no—
547C4⋊C4—44no—
548C4⋊C4—44no—
549C22⋊C4—28no—
550C22⋊C4—28no—
551C22⋊C4—44no—
552C22⋊C4—44no—
553C13#1472811yescharacteristic, direct product factor, Sylow
554C23—22no—
555C23—24no—
556C23—22no—
557C23—24no—
558C23—22no—
559C23—22no—
560C23—24no—
561C23—24no—
562C23—24no—
563C23—24no—
564C23—24no—
565C23—24no—
566C23—24no—
567C23—24no—
568C23—24no—
569C23—24no—
570C23C13×#12114yes—
571C23C13×C22⋊Q814yes—
572C23C13×C22⋊Q814yes—
573C23C13×#12314yes—
574C23C13×#12514yes—
575C23C13×#12514yes—
576C23C13×C4⋊Q814yes—
577C23C22×D4×C1311yescharacteristic
578C23C22×D4×C1312yes—
579C23C22×D4×C1311yescharacteristic
580C23C22×Q8×C1311yescharacteristic
581C23C22×Q8×C1311yescharacteristic
582C23C2×C13×#4111yescharacteristic
583C23C2×C13×#4111yescharacteristic
584C23C2×C13×#4111yescharacteristic
585C23C2×C13×#4112yes—
586C23C13×H(5,𝔽2)12yes—
587C23C13×2−1+412yes—
588C2×C4—232no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—22no—
600C2×C4—24no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—24no—
605C2×C4—22no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—416no—
613C2×C4—416no—
614C2×C4—41no—
615C2×C4—42no—
616C2×C4—41no—
617C2×C4—42no—
618C2×C4—41no—
619C2×C4—42no—
620C2×C4—41no—
621C2×C4—42no—
622C2×C4—42no—
623C2×C4—42no—
624C2×C4—42no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—42no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—42no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4C13×#12014yes—
648C2×C4C13×C22⋊Q818yes—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—24no—
653C22—24no—
654C22—24no—
655C22—28no—
656C22—28no—
657C22—28no—
658C22—28no—
659C22C13×#39818yescomplemented
660C22C2×C13×#12011yescharacteristic
661C22C2×C13×#12111yescharacteristic
662C22C2×C13×C22⋊Q811yescharacteristic
663C22C2×C13×C22⋊Q811yescharacteristic
664C22C2×C13×C22⋊Q812yes—
665C22C2×C13×#12311yescharacteristic
666C22C13×#52511yescharacteristic
667C22C13×#52512yes—
668C22C2×C13×#12511yescharacteristic
669C22C2×C13×#12511yescharacteristic
670C22C2×C13×C4⋊Q811yescharacteristic
671C22C13×#53411yescharacteristic
672C22C13×#53611yescharacteristic
673C22C13×#53912yes—
674C22C13×#54412yes—
675C22D42×C1312yes—
676C22C13×#54612yes—
677C22C13×#54712yes—
678C22C13×#54812yes—
679C22D4×Q8×C1312yes—
680C22C13×#55212yes—
681C22C13×#55312yes—
682C22C13×#55412yes—
683C4—28no—
684C4—24no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—44no—
689C4—44no—
690C4—81no—
691C4—81no—
692C4—82no—
693C2—28no—
694C2C2×C13×#39811yescharacteristic
695C2C13×#240911yescharacteristic
696C2C13×#241011yescharacteristic
697C2C13×#241311yescharacteristic
698C2C13×#244012yes—
699C2C13×#244212yes—
700C2C13×#244312yes—
701C2C13×#247312yes—
702C2C13×#257911yescharacteristic
703C2C13×#262711yescharacteristic
704C2C13×#284811yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#398C2semidirect
6. C13×#1444C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
106. #14728C13direct (N × H)
203. C2×#398C2×C13semidirect
207. #1444C2×C13semidirect
208. #1442C2×C13semidirect
209. #1441C2×C13semidirect
347. C22×C13#398semidirect
553. C13#14728direct (N × H)
659. C22C13×#398semidirect

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×#3982
C2×C13×#3852
C2×C13×#3802
C13×#14442
C13×#14422
C13×#14412
C13×C22⋊#952
#1472813