Finite Group Databasebeta

← C13×#15398 #15701737

Subgroups — C13×#15398 #15701737

Order 3328.

1586 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C211yesmaximal, characteristic
2C2×C13×#389C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic
5C2×C13×#385C211yesmaximal, characteristic
6C2×C13×#381C211yesmaximal, characteristic
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1444C211yesmaximal, characteristic, complemented
9C13×#1443C211yesmaximal, characteristic, complemented
10C13×#1442C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×#1441C211yesmaximal, characteristic, complemented
13C13×#1440C211yesmaximal, characteristic
14C13×#1439C211yesmaximal, characteristic
15C13×#1436C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C13×#397—24no—
32C13×#389—24no—
33C13×#388—24no—
34C13×#385—24no—
35C13×#385—24no—
36C13×#381—24no—
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—41no—
64C23×C4×C13—41no—
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—41no—
96C2×C13×C4⋊C4—41no—
97C2×C13×C4⋊C4—41no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—41no—
115C2×C13×C22⋊C4—41no—
116C2×C13×C22⋊C4D414yes—
117C2×C13×C22⋊C4D414yes—
118C2×C42×C13—22no—
119C2×C42×C13—22no—
120C2×C42×C13—41no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—22no—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—41no—
139C13×#95—41no—
140C13×#95D414yes—
141#15398C1311yesmaximal, characteristic, direct product factor, Sylow
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13C2×D412yes—
155C24×C13C2×D412yes—
156C24×C13#4112yes—
157C24×C13C2411yescharacteristic
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—28no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—44no—
246C22×C4×C13—44no—
247C22×C4×C13—44no—
248C22×C4×C13—44no—
249C22×C4×C13—44no—
250C22×C4×C13—44no—
251C22×C4×C13C2×D412yes—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×D412yes—
254C22×C4×C13C2×D412yes—
255C22×C4×C13C2×D412yes—
256C22×C4×C13C2×D412yes—
257C22×C4×C13C2×D412yes—
258C22×C4×C13#4112yes—
259C22×C4×C13#4112yes—
260C22×C4×C13#4112yes—
261C22×C4×C13#4112yes—
262C22×C4×C13#4112yes—
263C13×C4⋊C4—28no—
264C13×C4⋊C4—44no—
265C13×C4⋊C4—44no—
266C13×C4⋊C4—44no—
267C13×C4⋊C4—44no—
268C13×C4⋊C4—44no—
269C13×C4⋊C4—44no—
270C13×C22⋊C4—28no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—28no—
273C13×C22⋊C4—44no—
274C13×C22⋊C4—44no—
275C13×C22⋊C4—44no—
276C42×C13—44no—
277C2×#397C2×C1311yescharacteristic
278C2×#389C2×C1311yescharacteristic, complemented
279C2×#388C2×C1311yescharacteristic
280C2×#385C2×C1311yescharacteristic
281C2×#385C2×C1311yescharacteristic
282C2×#381C2×C1311yescharacteristic
283#1445C2×C1311yescharacteristic, complemented
284#1444C2×C1311yescharacteristic, complemented
285#1443C2×C1311yescharacteristic, complemented
286#1442C2×C1311yescharacteristic, complemented
287#1441C2×C1311yescharacteristic, complemented
288#1441C2×C1311yescharacteristic, complemented
289#1440C2×C1311yescharacteristic
290#1439C2×C1311yescharacteristic
291#1436C2×C1311yescharacteristic, complemented
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13#12114yes—
327C23×C13C22×D411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C22×D411yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C132−1+411yescharacteristic
339C23×C132−1+411yescharacteristic
340C23×C132−1+411yescharacteristic
341C23×C132−1+411yescharacteristic
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—416no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13#12314yes—
441C24×C4C22×C1311yescharacteristic
442C22×C4⋊C4C22×C1311yescharacteristic
443C22×C4⋊C4C22×C1311yescharacteristic
444C22×C4⋊C4C22×C1311yescharacteristic
445C22×C4⋊C4C22×C1311yescharacteristic
446C22×C4⋊C4C22×C1311yescharacteristic
447C22×C4⋊C4C22×C1311yescharacteristic
448C22×C4⋊C4C22×C1311yescharacteristic
449C22×C22⋊C4C22×C1311yescharacteristic
450C22×C22⋊C4C22×C1311yescharacteristic
451C22×C22⋊C4C22×C1311yescharacteristic
452C22×C22⋊C4C22×C1311yescharacteristic
453C22×C22⋊C4C22×C1311yescharacteristic
454C22×C22⋊C4C22×C1311yescharacteristic
455C22×C42C22×C1311yescharacteristic
456#397—24no—
457#389—24no—
458#388—24no—
459#385—24no—
460#385—24no—
461#381—24no—
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
464C2×#95C22×C1311yescharacteristic
465C2×#95C22×C1311yescharacteristic
466C2×#95C22×C1311yescharacteristic
467C2×#95C22×C1311yescharacteristic
468C2×#95C22×C1311yescharacteristic
469C2×#95C22×C1311yescharacteristic
470C2×#95C22×C1311yescharacteristic
471C2×#95C22×C1311yescharacteristic
472C2×#95C22×C1311yescharacteristic
473C2×#95C22×C1311yescharacteristic
474C2×#95C22×C1311yescharacteristic
475C2×#95C22×C1311yescharacteristic
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C2×#95C22×C1311yescharacteristic
481C2×#95C22×C1311yescharacteristic
482C22×C13—24no—
483C22×C13—24no—
484C22×C13—24no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13C2×#12111yescharacteristic
498C22×C13C2×#12311yescharacteristic
499C22×C13#52511yescharacteristic
500C22×C13#52511yescharacteristic
501C22×C13#52511yescharacteristic
502C22×C13#52911yescharacteristic
503C22×C13#53611yescharacteristic
504C22×C13#53611yescharacteristic
505C22×C13#53611yescharacteristic
506C22×C13#53811yescharacteristic
507C22×C13#53911yescharacteristic
508C22×C13#53911yescharacteristic
509C22×C13#53911yescharacteristic
510C22×C13#54111yescharacteristic
511C22×C13#54211yescharacteristic
512C22×C13D4211yescharacteristic
513C22×C13D4211yescharacteristic
514C22×C13#54611yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54711yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54711yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#54711yescharacteristic
521C22×C13#54811yescharacteristic
522C22×C13#55211yescharacteristic
523C22×C13#55211yescharacteristic
524C22×C13#55211yescharacteristic
525C22×C13#55211yescharacteristic
526C22×C13#55311yescharacteristic
527C22×C13#55611yescharacteristic
528C22×C13#55611yescharacteristic
529C22×C13#55911yescharacteristic
530C22×C13#56311yescharacteristic
531C22×C13#56311yescharacteristic
532C4×C13—24no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—81no—
543C4×C13—81no—
544C4×C13—81no—
545C4×C13—81no—
546C25C23×C1311yescharacteristic
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—22no—
551C23×C4—22no—
552C23×C4—41no—
553C23×C4—41no—
554C23×C4C23×C1311yescharacteristic
555C23×C4C23×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557C23×C4C23×C1311yescharacteristic
558C23×C4C23×C1311yescharacteristic
559C23×C4C23×C1311yescharacteristic
560C23×C4C23×C1311yescharacteristic
561C23×C4C23×C1311yescharacteristic
562C23×C4C23×C1311yescharacteristic
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1311yescharacteristic
565C23×C4C23×C1311yescharacteristic
566C23×C4C23×C1311yescharacteristic
567C23×C4C23×C1311yescharacteristic
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4D4×C1314yes—
606C2×C22⋊C4D4×C1314yes—
607C2×C42—22no—
608C2×C42—22no—
609C2×C42—41no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—41no—
628#95—41no—
629#95D4×C1314yes—
630C2×C13—44no—
631C2×C13#241311yescharacteristic
632C2×C13#242411yescharacteristic
633C2×C13#244311yescharacteristic
634C2×C13#244711yescharacteristic
635C2×C13#245511yescharacteristic
636C2×C13#246611yescharacteristic
637C2×C13#247511yescharacteristic
638C2×C13#248611yescharacteristic
639C2×C13#259911yescharacteristic
640C2×C13#267411yescharacteristic
641C2×C13#268011yescharacteristic
642C2×C13#268911yescharacteristic
643C2×C13#268911yescharacteristic
644C2×C13#276511yescharacteristic
645C2×C13#277111yescharacteristic
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24C2×D4×C1312yes—
659C24C2×D4×C1312yes—
660C24C13×#4112yes—
661C24C24×C1311yescharacteristic
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—28no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4C2×D4×C1312yes—
756C22×C4C2×D4×C1312yes—
757C22×C4C2×D4×C1312yes—
758C22×C4C2×D4×C1312yes—
759C22×C4C2×D4×C1312yes—
760C22×C4C2×D4×C1312yes—
761C22×C4C2×D4×C1312yes—
762C22×C4C13×#4112yes—
763C22×C4C13×#4112yes—
764C22×C4C13×#4112yes—
765C22×C4C13×#4112yes—
766C22×C4C13×#4112yes—
767C4⋊C4—28no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C22⋊C4—28no—
775C22⋊C4—28no—
776C22⋊C4—28no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C42—44no—
781C13#1539811yescharacteristic, direct product factor, Sylow
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23C13×#12114yes—
817C23C22×D4×C1311yescharacteristic
818C23C22×D4×C1311yescharacteristic
819C23C22×D4×C1311yescharacteristic
820C23C2×C13×#4111yescharacteristic
821C23C2×C13×#4111yescharacteristic
822C23C2×C13×#4111yescharacteristic
823C23C2×C13×#4111yescharacteristic
824C23C2×C13×#4111yescharacteristic
825C23C2×C13×#4111yescharacteristic
826C23C13×H(5,𝔽2)11yescharacteristic
827C23C13×H(5,𝔽2)11yescharacteristic
828C23C13×2−1+411yescharacteristic
829C23C13×2−1+411yescharacteristic
830C23C13×2−1+411yescharacteristic
831C23C13×2−1+411yescharacteristic
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
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—22no—
864C2×C4—22no—
865C2×C4—416no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4C13×#12314yes—
931C22—24no—
932C22—24no—
933C22—24no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22C2×C13×#12111yescharacteristic
947C22C2×C13×#12311yescharacteristic
948C22C13×#52511yescharacteristic
949C22C13×#52511yescharacteristic
950C22C13×#52511yescharacteristic
951C22C13×#52911yescharacteristic
952C22C13×#53611yescharacteristic
953C22C13×#53611yescharacteristic
954C22C13×#53611yescharacteristic
955C22C13×#53811yescharacteristic
956C22C13×#53911yescharacteristic
957C22C13×#53911yescharacteristic
958C22C13×#53911yescharacteristic
959C22C13×#54111yescharacteristic
960C22C13×#54211yescharacteristic
961C22D42×C1311yescharacteristic
962C22D42×C1311yescharacteristic
963C22C13×#54611yescharacteristic
964C22C13×#54611yescharacteristic
965C22C13×#54711yescharacteristic
966C22C13×#54711yescharacteristic
967C22C13×#54711yescharacteristic
968C22C13×#54711yescharacteristic
969C22C13×#54711yescharacteristic
970C22C13×#54811yescharacteristic
971C22C13×#55211yescharacteristic
972C22C13×#55211yescharacteristic
973C22C13×#55211yescharacteristic
974C22C13×#55211yescharacteristic
975C22C13×#55311yescharacteristic
976C22C13×#55611yescharacteristic
977C22C13×#55611yescharacteristic
978C22C13×#55911yescharacteristic
979C22C13×#56311yescharacteristic
980C22C13×#56311yescharacteristic
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C4—81no—
994C4—81no—
995C2—44no—
996C2C13×#241311yescharacteristic
997C2C13×#242411yescharacteristic
998C2C13×#244311yescharacteristic
999C2C13×#244711yescharacteristic
1000C2C13×#245511yescharacteristic
1001C2C13×#246611yescharacteristic
1002C2C13×#247511yescharacteristic
1003C2C13×#248611yescharacteristic
1004C2C13×#259911yescharacteristic
1005C2C13×#267411yescharacteristic
1006C2C13×#268011yescharacteristic
1007C2C13×#268911yescharacteristic
1008C2C13×#268911yescharacteristic
1009C2C13×#276511yescharacteristic
1010C2C13×#277111yescharacteristic
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×#389C2semidirect
7. C13×#1445C2semidirect
8. C13×#1444C2semidirect
9. C13×#1443C2semidirect
10. C13×#1442C2semidirect
11. C13×#1441C2semidirect
12. C13×#1441C2semidirect
15. C13×#1436C2semidirect
141. #15398C13direct (N × H)
278. C2×#389C2×C13semidirect
283. #1445C2×C13semidirect
284. #1444C2×C13semidirect
285. #1443C2×C13semidirect
286. #1442C2×C13semidirect
287. #1441C2×C13semidirect
288. #1441C2×C13semidirect
291. #1436C2×C13semidirect
781. C13#15398direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3892
C2×C13×#3882
C2×C13×#3852
C2×C13×#3812
C13×#14452
C13×#14442
C13×#14432
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14362
#1539813