Finite Group Databasebeta

← C13×#14043 #15700382

Subgroups — C13×#14043 #15700382

Order 3328.

2366 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C13×C4⋊C4C211yesmaximal, characteristic
2C2×C13×#389C212yesmaximal, complemented
3C2×C13×#385C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic
5C2×C13×#385C211yesmaximal, characteristic
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
7C13×#1444C212yesmaximal, complemented
8C13×#1441C212yesmaximal, complemented
9C13×#1436C212yesmaximal, complemented
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
27C22×C42×C13C2212yes—
28C13×#389—28no—
29C13×#385—24no—
30C13×#385—24no—
31C13×#385C418yescomplemented
32C4×C13×C22⋊C4—24no—
33C2×C13×#95C2212yes—
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2212yes—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2212yes—
38C2×C13×#95C2212yes—
39C2×C13×#95C2212yes—
40C2×C13×#95C2212yes—
41C2×C13×#95C2212yes—
42C25×C13C2311yescharacteristic
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—24no—
46C23×C4×C13—24no—
47C23×C4×C13—22no—
48C23×C4×C13—22no—
49C23×C4×C13—22no—
50C23×C4×C13—24no—
51C23×C4×C13—24no—
52C23×C4×C13—22no—
53C23×C4×C13—22no—
54C23×C4×C13—42no—
55C23×C4×C13—42no—
56C23×C4×C13C2×C414yes—
57C23×C4×C13D414yes—
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2312yes—
64C23×C4×C13C2312yes—
65C23×C4×C13C2312yes—
66C23×C4×C13C2312yes—
67C23×C4×C13C2311yescharacteristic
68C2×C13×C4⋊C4—232no—
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—24no—
76C2×C13×C4⋊C4—24no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—24no—
80C2×C13×C4⋊C4—24no—
81C2×C13×C4⋊C4—42no—
82C2×C13×C4⋊C4—42no—
83C2×C13×C4⋊C4C2×C418yescomplemented
84C2×C13×C4⋊C4D418yes—
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⋊C4C2×C414yes—
93C2×C13×C22⋊C4C2×C414yes—
94C2×C13×C22⋊C4D414yes—
95C2×C13×C22⋊C4Q814yes—
96C2×C13×C22⋊C4Q814yes—
97C2×C42×C13—24no—
98C2×C42×C13—24no—
99C2×C42×C13—42no—
100C13×#95—24no—
101C13×#95—22no—
102C13×#95—22no—
103C13×#95—24no—
104C13×#95—24no—
105C13×#95—24no—
106C13×#95—24no—
107C13×#95—42no—
108C13×#95C2×C418yescomplemented
109#14043C1311yesmaximal, characteristic, direct product factor, Sylow
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13C22×C412yes—
115C24×C13C2×D412yes—
116C24×C13C2×D412yes—
117C24×C13C2×Q812yes—
118C24×C13C2×Q812yes—
119C24×C13#4112yes—
120C24×C13#4112yes—
121C24×C13C2411yescharacteristic
122C22×C4×C13—28no—
123C22×C4×C13—216no—
124C22×C4×C13—28no—
125C22×C4×C13—28no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—216no—
138C22×C4×C13—28no—
139C22×C4×C13—28no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—22no—
154C22×C4×C13—22no—
155C22×C4×C13—21no—
156C22×C4×C13—22no—
157C22×C4×C13—22no—
158C22×C4×C13—22no—
159C22×C4×C13—22no—
160C22×C4×C13—22no—
161C22×C4×C13—22no—
162C22×C4×C13—22no—
163C22×C4×C13—22no—
164C22×C4×C13—28no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—22no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—22no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
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×C13C22×C412yes—
183C22×C4×C13C22×C412yes—
184C22×C4×C13C22×C414yes—
185C22×C4×C13C22×C414yes—
186C22×C4×C13C2×D412yes—
187C22×C4×C13C2×D414yes—
188C22×C4×C13C2×D414yes—
189C22×C4×C13C2×D414yes—
190C22×C4×C13C2×D412yes—
191C22×C4×C13C2×D414yes—
192C22×C4×C13C2×Q814yes—
193C22×C4×C13C2×Q814yes—
194C22×C4×C13#4114yes—
195C13×C4⋊C4—216no—
196C13×C4⋊C4—216no—
197C13×C4⋊C4—216no—
198C13×C4⋊C4—48no—
199C13×C4⋊C4—44no—
200C13×C4⋊C4—44no—
201C13×C22⋊C4—28no—
202C13×C22⋊C4—28no—
203C13×C22⋊C4—44no—
204C13×C22⋊C4C4⋊C4116yescomplemented
205C42×C13—48no—
206C23×C4⋊C4C2×C1311yescharacteristic
207C2×#389C2×C1312yescomplemented
208C2×#385C2×C1311yescharacteristic
209C2×#385C2×C1311yescharacteristic
210C2×#385C2×C1311yescharacteristic
211C2×C4×C22⋊C4C2×C1311yescharacteristic
212#1444C2×C1312yescomplemented
213#1441C2×C1312yescomplemented
214#1436C2×C1312yescomplemented
215C22⋊#95C2×C1311yescharacteristic
216C22⋊#95C2×C1311yescharacteristic
217C23×C13—24no—
218C23×C13—24no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—24no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—24no—
225C23×C13—24no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—24no—
232C23×C13—24no—
233C23×C13C2×C4⋊C414yes—
234C23×C13C4×D414yes—
235C23×C13C4×Q814yes—
236C23×C13#12114yes—
237C23×C13C22⋊Q814yes—
238C23×C13#12514yes—
239C23×C13C4⋊Q814yes—
240C23×C13C23×C411yescharacteristic
241C23×C13C22×D411yescharacteristic
242C23×C13C22×D411yescharacteristic
243C23×C13C22×D412yes—
244C23×C13C22×Q811yescharacteristic
245C23×C13C22×Q811yescharacteristic
246C23×C13C2×#4111yescharacteristic
247C23×C13C2×#4112yes—
248C23×C13C2×#4111yescharacteristic
249C23×C13H(5,𝔽2)12yes—
250C23×C132−1+412yes—
251C2×C4×C13—232no—
252C2×C4×C13—24no—
253C2×C4×C13—24no—
254C2×C4×C13—24no—
255C2×C4×C13—24no—
256C2×C4×C13—24no—
257C2×C4×C13—22no—
258C2×C4×C13—24no—
259C2×C4×C13—24no—
260C2×C4×C13—24no—
261C2×C4×C13—22no—
262C2×C4×C13—24no—
263C2×C4×C13—24no—
264C2×C4×C13—24no—
265C2×C4×C13—24no—
266C2×C4×C13—24no—
267C2×C4×C13—24no—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—24no—
271C2×C4×C13—24no—
272C2×C4×C13—22no—
273C2×C4×C13—24no—
274C2×C4×C13—22no—
275C2×C4×C13—24no—
276C2×C4×C13—22no—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—416no—
282C2×C4×C13—416no—
283C2×C4×C13—41no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—41no—
287C2×C4×C13—42no—
288C2×C4×C13—41no—
289C2×C4×C13—42no—
290C2×C4×C13—41no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13C2×C4⋊C418yescomplemented
310C2×C4×C13C4×D418yes—
311C2×C4×C13#12014yes—
312C24×C4C22×C1311yescharacteristic
313C24×C4C22×C1311yescharacteristic
314C24×C4C22×C1311yescharacteristic
315C22×C4⋊C4—24no—
316C22×C4⋊C4—28no—
317C22×C4⋊C4C22×C1312yes—
318C22×C4⋊C4C22×C1311yescharacteristic
319C22×C4⋊C4C22×C1312yes—
320C22×C4⋊C4C22×C1312yes—
321C22×C4⋊C4C22×C1312yes—
322C22×C4⋊C4C22×C1311yescharacteristic
323C22×C22⋊C4C22×C1311yescharacteristic
324C22×C22⋊C4C22×C1311yescharacteristic
325C22×C22⋊C4C22×C1311yescharacteristic
326C22×C22⋊C4C22×C1311yescharacteristic
327C22×C42C22×C1312yes—
328#389—28no—
329#385—24no—
330#385—24no—
331#385C4×C1318yescomplemented
332C4×C22⋊C4—24no—
333C2×#95C22×C1312yes—
334C2×#95C22×C1312yes—
335C2×#95C22×C1312yes—
336C2×#95C22×C1311yescharacteristic
337C2×#95C22×C1312yes—
338C2×#95C22×C1311yescharacteristic
339C2×#95C22×C1312yes—
340C2×#95C22×C1312yes—
341C2×#95C22×C1312yes—
342C22×C13—24no—
343C22×C13—24no—
344C22×C13—28no—
345C22×C13—28no—
346C22×C13—24no—
347C22×C13—24no—
348C22×C13—24no—
349C22×C13—28no—
350C22×C13—28no—
351C22×C13—24no—
352C22×C13#38918yescomplemented
353C22×C13C22×C4⋊C411yescharacteristic
354C22×C13C2×C4×D411yescharacteristic
355C22×C13C2×C4×D412yes—
356C22×C13C2×C4×Q811yescharacteristic
357C22×C13#52012yes—
358C22×C13C2×#12011yescharacteristic
359C22×C13C2×#12111yescharacteristic
360C22×C13C2×C22⋊Q811yescharacteristic
361C22×C13#52511yescharacteristic
362C22×C13#52512yes—
363C22×C13C2×#12511yescharacteristic
364C22×C13C2×C4⋊Q811yescharacteristic
365C22×C13#53411yescharacteristic
366C22×C13#53611yescharacteristic
367C22×C13#53912yes—
368C22×C13D4212yes—
369C22×C13#54612yes—
370C22×C13#54712yes—
371C22×C13D4×Q812yes—
372C22×C13D4×Q812yes—
373C22×C13#55212yes—
374C22×C13#55412yes—
375C22×C13#55412yes—
376C4×C13—28no—
377C4×C13—24no—
378C4×C13—28no—
379C4×C13—42no—
380C4×C13—42no—
381C4×C13—44no—
382C4×C13—44no—
383C4×C13—42no—
384C4×C13—81no—
385C4×C13—81no—
386C25C23×C1311yescharacteristic
387C23×C4—22no—
388C23×C4—22no—
389C23×C4—24no—
390C23×C4—24no—
391C23×C4—22no—
392C23×C4—22no—
393C23×C4—22no—
394C23×C4—24no—
395C23×C4—24no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—42no—
399C23×C4—42no—
400C23×C4C2×C4×C1314yes—
401C23×C4D4×C1314yes—
402C23×C4C23×C1311yescharacteristic
403C23×C4C23×C1311yescharacteristic
404C23×C4C23×C1311yescharacteristic
405C23×C4C23×C1311yescharacteristic
406C23×C4C23×C1311yescharacteristic
407C23×C4C23×C1312yes—
408C23×C4C23×C1312yes—
409C23×C4C23×C1312yes—
410C23×C4C23×C1312yes—
411C23×C4C23×C1311yescharacteristic
412C2×C4⋊C4—232no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4—24no—
415C2×C4⋊C4—24no—
416C2×C4⋊C4—24no—
417C2×C4⋊C4—24no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—24no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—42no—
426C2×C4⋊C4—42no—
427C2×C4⋊C4C2×C4×C1318yescomplemented
428C2×C4⋊C4D4×C1318yes—
429C2×C22⋊C4—22no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—22no—
434C2×C22⋊C4—22no—
435C2×C22⋊C4—22no—
436C2×C22⋊C4C2×C4×C1314yes—
437C2×C22⋊C4C2×C4×C1314yes—
438C2×C22⋊C4D4×C1314yes—
439C2×C22⋊C4Q8×C1314yes—
440C2×C22⋊C4Q8×C1314yes—
441C2×C42—24no—
442C2×C42—24no—
443C2×C42—42no—
444#95—24no—
445#95—22no—
446#95—22no—
447#95—24no—
448#95—24no—
449#95—24no—
450#95—24no—
451#95—42no—
452#95C2×C4×C1318yescomplemented
453C2×C13—28no—
454C2×C13C2×#38911yescharacteristic
455C2×C13C4×#12011yescharacteristic
456C2×C13#232211yescharacteristic
457C2×C13D4×C4⋊C412yes—
458C2×C13#236012yes—
459C2×C13#241011yescharacteristic
460C2×C13#241311yescharacteristic
461C2×C13#243411yescharacteristic
462C2×C13#244912yes—
463C2×C13#247312yes—
464C2×C13#258311yescharacteristic
465C24—22no—
466C24—22no—
467C24—22no—
468C24—22no—
469C24C22×C4×C1312yes—
470C24C2×D4×C1312yes—
471C24C2×D4×C1312yes—
472C24C2×Q8×C1312yes—
473C24C2×Q8×C1312yes—
474C24C13×#4112yes—
475C24C13×#4112yes—
476C24C24×C1311yescharacteristic
477C22×C4—28no—
478C22×C4—216no—
479C22×C4—28no—
480C22×C4—28no—
481C22×C4—21no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—216no—
493C22×C4—28no—
494C22×C4—28no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—22no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—21no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—28no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—44no—
531C22×C4—48no—
532C22×C4—48no—
533C22×C4—48no—
534C22×C4—48no—
535C22×C4—44no—
536C22×C4—44no—
537C22×C4C22×C4×C1312yes—
538C22×C4C22×C4×C1312yes—
539C22×C4C22×C4×C1314yes—
540C22×C4C22×C4×C1314yes—
541C22×C4C2×D4×C1312yes—
542C22×C4C2×D4×C1314yes—
543C22×C4C2×D4×C1314yes—
544C22×C4C2×D4×C1314yes—
545C22×C4C2×D4×C1312yes—
546C22×C4C2×D4×C1314yes—
547C22×C4C2×Q8×C1314yes—
548C22×C4C2×Q8×C1314yes—
549C22×C4C13×#4114yes—
550C4⋊C4—216no—
551C4⋊C4—216no—
552C4⋊C4—216no—
553C4⋊C4—48no—
554C4⋊C4—44no—
555C4⋊C4—44no—
556C22⋊C4—28no—
557C22⋊C4—28no—
558C22⋊C4—44no—
559C22⋊C4C13×C4⋊C4116yescomplemented
560C42—48no—
561C13#1404311yescharacteristic, direct product factor, Sylow
562C23—24no—
563C23—24no—
564C23—22no—
565C23—22no—
566C23—24no—
567C23—22no—
568C23—22no—
569C23—24no—
570C23—24no—
571C23—24no—
572C23—24no—
573C23—24no—
574C23—24no—
575C23—24no—
576C23—24no—
577C23—24no—
578C23C2×C13×C4⋊C414yes—
579C23C4×D4×C1314yes—
580C23C4×Q8×C1314yes—
581C23C13×#12114yes—
582C23C13×C22⋊Q814yes—
583C23C13×#12514yes—
584C23C13×C4⋊Q814yes—
585C23C23×C4×C1311yescharacteristic
586C23C22×D4×C1311yescharacteristic
587C23C22×D4×C1311yescharacteristic
588C23C22×D4×C1312yes—
589C23C22×Q8×C1311yescharacteristic
590C23C22×Q8×C1311yescharacteristic
591C23C2×C13×#4111yescharacteristic
592C23C2×C13×#4112yes—
593C23C2×C13×#4111yescharacteristic
594C23C13×H(5,𝔽2)12yes—
595C23C13×2−1+412yes—
596C2×C4—232no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—22no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—22no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—22no—
618C2×C4—24no—
619C2×C4—22no—
620C2×C4—24no—
621C2×C4—22no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—24no—
626C2×C4—416no—
627C2×C4—416no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—42no—
651C2×C4—42no—
652C2×C4—42no—
653C2×C4—42no—
654C2×C4C2×C13×C4⋊C418yescomplemented
655C2×C4C4×D4×C1318yes—
656C2×C4C13×#12014yes—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—28no—
661C22—28no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—28no—
666C22—28no—
667C22C13×#38918yescomplemented
668C22C22×C13×C4⋊C411yescharacteristic
669C22C2×C4×D4×C1311yescharacteristic
670C22C2×C4×D4×C1312yes—
671C22C2×C4×Q8×C1311yescharacteristic
672C22C13×#52012yes—
673C22C2×C13×#12011yescharacteristic
674C22C2×C13×#12111yescharacteristic
675C22C2×C13×C22⋊Q811yescharacteristic
676C22C13×#52511yescharacteristic
677C22C13×#52512yes—
678C22C2×C13×#12511yescharacteristic
679C22C2×C13×C4⋊Q811yescharacteristic
680C22C13×#53411yescharacteristic
681C22C13×#53611yescharacteristic
682C22C13×#53912yes—
683C22D42×C1312yes—
684C22C13×#54612yes—
685C22C13×#54712yes—
686C22D4×Q8×C1312yes—
687C22D4×Q8×C1312yes—
688C22C13×#55212yes—
689C22C13×#55412yes—
690C22C13×#55412yes—
691C4—28no—
692C4—28no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—44no—
698C4—44no—
699C4—81no—
700C4—81no—
701C2—28no—
702C2C2×C13×#38911yescharacteristic
703C2C4×C13×#12011yescharacteristic
704C2C13×#232211yescharacteristic
705C2D4×C13×C4⋊C412yes—
706C2C13×#236012yes—
707C2C13×#241011yescharacteristic
708C2C13×#241311yescharacteristic
709C2C13×#243411yescharacteristic
710C2C13×#244912yes—
711C2C13×#247312yes—
712C2C13×#258311yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#389C2semidirect
7. C13×#1444C2semidirect
8. C13×#1441C2semidirect
9. C13×#1436C2semidirect
31. C13×#385C4semidirect
83. C2×C13×C4⋊C4C2×C4semidirect
108. C13×#95C2×C4semidirect
109. #14043C13direct (N × H)
204. C13×C22⋊C4C4⋊C4semidirect
207. C2×#389C2×C13semidirect
212. #1444C2×C13semidirect
213. #1441C2×C13semidirect
214. #1436C2×C13semidirect
309. C2×C4×C13C2×C4⋊C4semidirect
331. #385C4×C13semidirect
352. C22×C13#389semidirect
427. C2×C4⋊C4C2×C4×C13semidirect
452. #95C2×C4×C13semidirect
559. C22⋊C4C13×C4⋊C4semidirect
561. C13#14043direct (N × H)
654. C2×C4C2×C13×C4⋊C4semidirect
667. C22C13×#389semidirect

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×#3892
C2×C13×#3852
C2×C4×C13×C22⋊C42
C13×#14442
C13×#14412
C13×#14362
C13×C22⋊#952
#1404313