Finite Group Databasebeta

← C13×#14739 #15701078

Subgroups — C13×#14739 #15701078

Order 3328.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#394C211yesmaximal, characteristic
2C2×C13×#388C211yesmaximal, characteristic, complemented
3C2×C13×#386C211yesmaximal, characteristic
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
5C13×#1445C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1440C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic, complemented
9C13×#1440C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic
12C13×#1437C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊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×C13×C22⋊C4C2211yescharacteristic
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C13×#394—24no—
34C13×#388—24no—
35C13×#386—24no—
36C4×C13×C22⋊C4—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
55C25×C13C2311yescharacteristic
56C25×C13C2311yescharacteristic
57C22×D4×C13—22no—
58C22×D4×C13—22no—
59C22×D4×C13—22no—
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—41no—
63C22×D4×C13—41no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—41no—
70C23×C4×C13—41no—
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—41no—
89C2×C13×C4⋊C4—41no—
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—22no—
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—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—41no—
112C2×C13×C22⋊C4—41no—
113C2×C13×C22⋊C4—41no—
114C2×C13×C22⋊C4—41no—
115C2×C13×C22⋊C4—41no—
116C2×C13×C22⋊C4—41no—
117C2×C13×C22⋊C4—41no—
118C2×C13×C22⋊C4—41no—
119C2×C13×C22⋊C4—41no—
120C2×C13×C22⋊C4—41no—
121C2×C13×C22⋊C4D414yes—
122C2×C13×C22⋊C4D414yes—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C2×C42×C13—22no—
126C2×C42×C13—22no—
127C2×C42×C13—41no—
128C2×C42×C13—41no—
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—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—41no—
142C13×#95—41no—
143C13×#95—41no—
144C13×#95—41no—
145C13×#95—41no—
146C13×#95—41no—
147#14739C1311yesmaximal, characteristic, direct product factor, Sylow
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13C2×D412yes—
175C24×C13C2×D412yes—
176C24×C13#4112yes—
177C24×C13#4112yes—
178C24×C13C2411yescharacteristic
179C2×D4×C13—28no—
180C2×D4×C13—44no—
181C2×D4×C13—44no—
182C2×D4×C13—44no—
183C2×D4×C13—44no—
184C2×D4×C13—44no—
185C2×D4×C13—44no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—28no—
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—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—44no—
268C22×C4×C13—44no—
269C22×C4×C13—44no—
270C22×C4×C13—44no—
271C22×C4×C13—44no—
272C22×C4×C13—44no—
273C22×C4×C13C2×D412yes—
274C22×C4×C13C2×D412yes—
275C22×C4×C13C2×D412yes—
276C22×C4×C13C2×D412yes—
277C22×C4×C13#4112yes—
278C22×C4×C13#4112yes—
279C22×C4×C13#4112yes—
280C22×C4×C13#4112yes—
281C22×C4×C13#4112yes—
282C22×C4×C13#4112yes—
283C22×C4×C13#4112yes—
284C13×C4⋊C4—44no—
285C13×C4⋊C4—44no—
286C13×C22⋊C4—28no—
287C13×C22⋊C4—28no—
288C13×C22⋊C4—28no—
289C13×C22⋊C4—44no—
290C13×C22⋊C4—44no—
291C13×C22⋊C4—44no—
292C13×C22⋊C4—44no—
293C13×C22⋊C4—44no—
294C13×C22⋊C4—44no—
295C13×C22⋊C4—44no—
296C13×C22⋊C4—44no—
297C42×C13—44no—
298C42×C13—44no—
299C2×#394C2×C1311yescharacteristic
300C2×#388C2×C1311yescharacteristic, complemented
301C2×#386C2×C1311yescharacteristic
302C2×C4×C22⋊C4C2×C1311yescharacteristic, complemented
303#1445C2×C1311yescharacteristic, complemented
304#1442C2×C1311yescharacteristic, complemented
305#1440C2×C1311yescharacteristic, complemented
306#1440C2×C1311yescharacteristic, complemented
307#1440C2×C1311yescharacteristic, complemented
308#1439C2×C1311yescharacteristic, complemented
309#1438C2×C1311yescharacteristic
310#1437C2×C1311yescharacteristic, complemented
311#1436C2×C1311yescharacteristic, complemented
312#1434C2×C1311yescharacteristic, complemented
313C22⋊#95C2×C1311yescharacteristic, complemented
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13—41no—
345C23×C13—41no—
346C23×C13—41no—
347C23×C13—41no—
348C23×C13—41no—
349C23×C13—41no—
350C23×C13—41no—
351C23×C13—41no—
352C23×C13—41no—
353C23×C13—41no—
354C23×C13—41no—
355C23×C13—41no—
356C23×C13—41no—
357C23×C13—41no—
358C23×C13—41no—
359C23×C13—41no—
360C23×C13—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13#12314yes—
384C23×C13C22×D411yescharacteristic
385C23×C13C22×D411yescharacteristic
386C23×C13C2×#4111yescharacteristic
387C23×C13C2×#4111yescharacteristic
388C23×C13C2×#4111yescharacteristic
389C23×C13C2×#4111yescharacteristic
390C23×C13C2×#4111yescharacteristic
391C23×C13C2×#4111yescharacteristic
392C23×C13C2×#4111yescharacteristic
393C23×C13C2×#4111yescharacteristic
394C23×C13C2×#4111yescharacteristic
395C23×C13H(5,𝔽2)11yescharacteristic
396C23×C13H(5,𝔽2)11yescharacteristic
397C23×C13H(5,𝔽2)11yescharacteristic
398C23×C13H(5,𝔽2)11yescharacteristic
399D4×C13—416no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—22no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—416no—
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—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13#12314yes—
492C23×D4C22×C1311yescharacteristic
493C24×C4C22×C1311yescharacteristic
494C22×C4⋊C4C22×C1311yescharacteristic
495C22×C4⋊C4C22×C1311yescharacteristic
496C22×C22⋊C4C22×C1311yescharacteristic
497C22×C22⋊C4C22×C1311yescharacteristic
498C22×C22⋊C4C22×C1311yescharacteristic
499C22×C22⋊C4C22×C1311yescharacteristic
500C22×C22⋊C4C22×C1311yescharacteristic
501C22×C22⋊C4C22×C1311yescharacteristic
502C22×C22⋊C4C22×C1311yescharacteristic
503C22×C22⋊C4C22×C1311yescharacteristic
504C22×C22⋊C4C22×C1311yescharacteristic
505C22×C22⋊C4C22×C1311yescharacteristic
506C22×C22⋊C4C22×C1311yescharacteristic
507C22×C42C22×C1311yescharacteristic
508C22×C42C22×C1311yescharacteristic
509#394—24no—
510#388—24no—
511#386—24no—
512C4×C22⋊C4—24no—
513C2×#95C22×C1311yescharacteristic
514C2×#95C22×C1311yescharacteristic
515C2×#95C22×C1311yescharacteristic
516C2×#95C22×C1311yescharacteristic
517C2×#95C22×C1311yescharacteristic
518C2×#95C22×C1311yescharacteristic
519C2×#95C22×C1311yescharacteristic
520C2×#95C22×C1311yescharacteristic
521C2×#95C22×C1311yescharacteristic
522C2×#95C22×C1311yescharacteristic
523C2×#95C22×C1311yescharacteristic
524C2×#95C22×C1311yescharacteristic
525C2×#95C22×C1311yescharacteristic
526C2×#95C22×C1311yescharacteristic
527C2×#95C22×C1311yescharacteristic
528C2×#95C22×C1311yescharacteristic
529C2×#95C22×C1311yescharacteristic
530C2×#95C22×C1311yescharacteristic
531C22×C13—24no—
532C22×C13—24no—
533C22×C13—24no—
534C22×C13—42no—
535C22×C13—42no—
536C22×C13—42no—
537C22×C13—42no—
538C22×C13—42no—
539C22×C13—42no—
540C22×C13—42no—
541C22×C13—42no—
542C22×C13—42no—
543C22×C13—42no—
544C22×C13—42no—
545C22×C13—42no—
546C22×C13—42no—
547C22×C13—42no—
548C22×C13—42no—
549C22×C13—42no—
550C22×C13—42no—
551C22×C13—42no—
552C22×C13—42no—
553C22×C13—81no—
554C22×C13—81no—
555C22×C13—81no—
556C22×C13—81no—
557C22×C13—81no—
558C22×C13—81no—
559C22×C13—81no—
560C22×C13—81no—
561C22×C13C2×#12311yescharacteristic
562C22×C13C2×#12311yescharacteristic
563C22×C13#52511yescharacteristic
564C22×C13#52511yescharacteristic
565C22×C13#52511yescharacteristic
566C22×C13#52911yescharacteristic
567C22×C13#52911yescharacteristic
568C22×C13#52911yescharacteristic
569C22×C13#52911yescharacteristic
570C22×C13#52911yescharacteristic
571C22×C13#52911yescharacteristic
572C22×C13#52911yescharacteristic
573C22×C13#53211yescharacteristic
574C22×C13#53811yescharacteristic
575C22×C13#53811yescharacteristic
576C22×C13#53811yescharacteristic
577C22×C13#53811yescharacteristic
578C22×C13#54011yescharacteristic
579C22×C13#54011yescharacteristic
580C22×C13D4211yescharacteristic
581C22×C13#54611yescharacteristic
582C22×C13#54611yescharacteristic
583C22×C13#54611yescharacteristic
584C22×C13#54611yescharacteristic
585C22×C13#54611yescharacteristic
586C22×C13#54611yescharacteristic
587C22×C13#55111yescharacteristic
588C22×C13#55111yescharacteristic
589C22×C13#55311yescharacteristic
590C22×C13#55311yescharacteristic
591C22×C13#55311yescharacteristic
592C22×C13#55311yescharacteristic
593C22×C13#55511yescharacteristic
594C22×C13#55511yescharacteristic
595C22×C13#55911yescharacteristic
596C4×C13—24no—
597C4×C13—42no—
598C4×C13—42no—
599C4×C13—42no—
600C4×C13—42no—
601C4×C13—42no—
602C4×C13—42no—
603C4×C13—42no—
604C4×C13—42no—
605C4×C13—81no—
606C4×C13—81no—
607C4×C13—81no—
608C4×C13—81no—
609C25C23×C1311yescharacteristic
610C25C23×C1311yescharacteristic
611C22×D4—22no—
612C22×D4—22no—
613C22×D4—22no—
614C22×D4—22no—
615C22×D4—22no—
616C22×D4—41no—
617C22×D4—41no—
618C23×C4—22no—
619C23×C4—22no—
620C23×C4—22no—
621C23×C4—22no—
622C23×C4—22no—
623C23×C4—41no—
624C23×C4—41no—
625C23×C4C23×C1311yescharacteristic
626C23×C4C23×C1311yescharacteristic
627C23×C4C23×C1311yescharacteristic
628C23×C4C23×C1311yescharacteristic
629C23×C4C23×C1311yescharacteristic
630C23×C4C23×C1311yescharacteristic
631C23×C4C23×C1311yescharacteristic
632C23×C4C23×C1311yescharacteristic
633C23×C4C23×C1311yescharacteristic
634C23×C4C23×C1311yescharacteristic
635C23×C4C23×C1311yescharacteristic
636C23×C4C23×C1311yescharacteristic
637C23×C4C23×C1311yescharacteristic
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—41no—
643C2×C4⋊C4—41no—
644C2×C22⋊C4—22no—
645C2×C22⋊C4—22no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—22no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—22no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—22no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—22no—
664C2×C22⋊C4—22no—
665C2×C22⋊C4—41no—
666C2×C22⋊C4—41no—
667C2×C22⋊C4—41no—
668C2×C22⋊C4—41no—
669C2×C22⋊C4—41no—
670C2×C22⋊C4—41no—
671C2×C22⋊C4—41no—
672C2×C22⋊C4—41no—
673C2×C22⋊C4—41no—
674C2×C22⋊C4—41no—
675C2×C22⋊C4D4×C1314yes—
676C2×C22⋊C4D4×C1314yes—
677C2×C42—22no—
678C2×C42—22no—
679C2×C42—22no—
680C2×C42—22no—
681C2×C42—41no—
682C2×C42—41no—
683#95—22no—
684#95—22no—
685#95—22no—
686#95—22no—
687#95—22no—
688#95—22no—
689#95—22no—
690#95—22no—
691#95—22no—
692#95—22no—
693#95—22no—
694#95—22no—
695#95—41no—
696#95—41no—
697#95—41no—
698#95—41no—
699#95—41no—
700#95—41no—
701C2×C13—44no—
702C2×C13—82no—
703C2×C13#239511yescharacteristic
704C2×C13#241811yescharacteristic
705C2×C13#241811yescharacteristic
706C2×C13#242011yescharacteristic
707C2×C13#244411yescharacteristic
708C2×C13#245911yescharacteristic
709C2×C13#245911yescharacteristic
710C2×C13#246411yescharacteristic
711C2×C13#247611yescharacteristic
712C2×C13#251811yescharacteristic
713C2×C13#253111yescharacteristic
714C2×C13#255911yescharacteristic
715C2×C13#259511yescharacteristic
716C2×C13#264811yescharacteristic
717C2×C13#285311yescharacteristic
718C24—21no—
719C24—21no—
720C24—21no—
721C24—21no—
722C24—21no—
723C24—21no—
724C24—21no—
725C24—21no—
726C24—21no—
727C24—21no—
728C24—21no—
729C24—21no—
730C24—21no—
731C24—21no—
732C24—21no—
733C24—21no—
734C24—21no—
735C24—21no—
736C24—21no—
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24C2×D4×C1312yes—
745C24C2×D4×C1312yes—
746C24C13×#4112yes—
747C24C13×#4112yes—
748C24C24×C1311yescharacteristic
749C2×D4—28no—
750C2×D4—44no—
751C2×D4—44no—
752C2×D4—44no—
753C2×D4—44no—
754C2×D4—44no—
755C2×D4—44no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—28no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—44no—
838C22×C4—44no—
839C22×C4—44no—
840C22×C4—44no—
841C22×C4—44no—
842C22×C4—44no—
843C22×C4C2×D4×C1312yes—
844C22×C4C2×D4×C1312yes—
845C22×C4C2×D4×C1312yes—
846C22×C4C2×D4×C1312yes—
847C22×C4C13×#4112yes—
848C22×C4C13×#4112yes—
849C22×C4C13×#4112yes—
850C22×C4C13×#4112yes—
851C22×C4C13×#4112yes—
852C22×C4C13×#4112yes—
853C22×C4C13×#4112yes—
854C4⋊C4—44no—
855C4⋊C4—44no—
856C22⋊C4—28no—
857C22⋊C4—28no—
858C22⋊C4—28no—
859C22⋊C4—44no—
860C22⋊C4—44no—
861C22⋊C4—44no—
862C22⋊C4—44no—
863C22⋊C4—44no—
864C22⋊C4—44no—
865C22⋊C4—44no—
866C22⋊C4—44no—
867C42—44no—
868C42—44no—
869C13#1473911yescharacteristic, direct product factor, Sylow
870C23—22no—
871C23—22no—
872C23—22no—
873C23—22no—
874C23—22no—
875C23—22no—
876C23—22no—
877C23—22no—
878C23—22no—
879C23—22no—
880C23—22no—
881C23—22no—
882C23—22no—
883C23—22no—
884C23—22no—
885C23—22no—
886C23—22no—
887C23—22no—
888C23—22no—
889C23—22no—
890C23—22no—
891C23—22no—
892C23—22no—
893C23—22no—
894C23—22no—
895C23—41no—
896C23—41no—
897C23—41no—
898C23—41no—
899C23—41no—
900C23—41no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—41no—
911C23—41no—
912C23—41no—
913C23—41no—
914C23—41no—
915C23—41no—
916C23—41no—
917C23—41no—
918C23—41no—
919C23—41no—
920C23—41no—
921C23—41no—
922C23—41no—
923C23—41no—
924C23—41no—
925C23—41no—
926C23—41no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23C13×#12314yes—
940C23C22×D4×C1311yescharacteristic
941C23C22×D4×C1311yescharacteristic
942C23C2×C13×#4111yescharacteristic
943C23C2×C13×#4111yescharacteristic
944C23C2×C13×#4111yescharacteristic
945C23C2×C13×#4111yescharacteristic
946C23C2×C13×#4111yescharacteristic
947C23C2×C13×#4111yescharacteristic
948C23C2×C13×#4111yescharacteristic
949C23C2×C13×#4111yescharacteristic
950C23C2×C13×#4111yescharacteristic
951C23C13×H(5,𝔽2)11yescharacteristic
952C23C13×H(5,𝔽2)11yescharacteristic
953C23C13×H(5,𝔽2)11yescharacteristic
954C23C13×H(5,𝔽2)11yescharacteristic
955D4—416no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—22no—
960C2×C4—22no—
961C2×C4—22no—
962C2×C4—22no—
963C2×C4—22no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—22no—
969C2×C4—22no—
970C2×C4—22no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—22no—
976C2×C4—22no—
977C2×C4—22no—
978C2×C4—22no—
979C2×C4—22no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—416no—
987C2×C4—41no—
988C2×C4—41no—
989C2×C4—41no—
990C2×C4—41no—
991C2×C4—41no—
992C2×C4—41no—
993C2×C4—41no—
994C2×C4—41no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4C13×#12314yes—
1048C22—24no—
1049C22—24no—
1050C22—24no—
1051C22—42no—
1052C22—42no—
1053C22—42no—
1054C22—42no—
1055C22—42no—
1056C22—42no—
1057C22—42no—
1058C22—42no—
1059C22—42no—
1060C22—42no—
1061C22—42no—
1062C22—42no—
1063C22—42no—
1064C22—42no—
1065C22—42no—
1066C22—42no—
1067C22—42no—
1068C22—42no—
1069C22—42no—
1070C22—81no—
1071C22—81no—
1072C22—81no—
1073C22—81no—
1074C22—81no—
1075C22—81no—
1076C22—81no—
1077C22—81no—
1078C22C2×C13×#12311yescharacteristic
1079C22C2×C13×#12311yescharacteristic
1080C22C13×#52511yescharacteristic
1081C22C13×#52511yescharacteristic
1082C22C13×#52511yescharacteristic
1083C22C13×#52911yescharacteristic
1084C22C13×#52911yescharacteristic
1085C22C13×#52911yescharacteristic
1086C22C13×#52911yescharacteristic
1087C22C13×#52911yescharacteristic
1088C22C13×#52911yescharacteristic
1089C22C13×#52911yescharacteristic
1090C22C13×#53211yescharacteristic
1091C22C13×#53811yescharacteristic
1092C22C13×#53811yescharacteristic
1093C22C13×#53811yescharacteristic
1094C22C13×#53811yescharacteristic
1095C22C13×#54011yescharacteristic
1096C22C13×#54011yescharacteristic
1097C22D42×C1311yescharacteristic
1098C22C13×#54611yescharacteristic
1099C22C13×#54611yescharacteristic
1100C22C13×#54611yescharacteristic
1101C22C13×#54611yescharacteristic
1102C22C13×#54611yescharacteristic
1103C22C13×#54611yescharacteristic
1104C22C13×#55111yescharacteristic
1105C22C13×#55111yescharacteristic
1106C22C13×#55311yescharacteristic
1107C22C13×#55311yescharacteristic
1108C22C13×#55311yescharacteristic
1109C22C13×#55311yescharacteristic
1110C22C13×#55511yescharacteristic
1111C22C13×#55511yescharacteristic
1112C22C13×#55911yescharacteristic
1113C4—24no—
1114C4—42no—
1115C4—42no—
1116C4—42no—
1117C4—42no—
1118C4—42no—
1119C4—42no—
1120C4—42no—
1121C4—42no—
1122C4—81no—
1123C4—81no—
1124C4—81no—
1125C4—81no—
1126C2—44no—
1127C2—82no—
1128C2C13×#239511yescharacteristic
1129C2C13×#241811yescharacteristic
1130C2C13×#241811yescharacteristic
1131C2C13×#242011yescharacteristic
1132C2C13×#244411yescharacteristic
1133C2C13×#245911yescharacteristic
1134C2C13×#245911yescharacteristic
1135C2C13×#246411yescharacteristic
1136C2C13×#247611yescharacteristic
1137C2C13×#251811yescharacteristic
1138C2C13×#253111yescharacteristic
1139C2C13×#255911yescharacteristic
1140C2C13×#259511yescharacteristic
1141C2C13×#264811yescharacteristic
1142C2C13×#285311yescharacteristic
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
2. C2×C13×#388C2semidirect
4. C2×C4×C13×C22⋊C4C2semidirect
5. C13×#1445C2semidirect
6. C13×#1442C2semidirect
7. C13×#1440C2semidirect
8. C13×#1440C2semidirect
9. C13×#1440C2semidirect
10. C13×#1439C2semidirect
12. C13×#1437C2semidirect
13. C13×#1436C2semidirect
14. C13×#1434C2semidirect
15. C13×C22⋊#95C2semidirect
147. #14739C13direct (N × H)
300. C2×#388C2×C13semidirect
302. C2×C4×C22⋊C4C2×C13semidirect
303. #1445C2×C13semidirect
304. #1442C2×C13semidirect
305. #1440C2×C13semidirect
306. #1440C2×C13semidirect
307. #1440C2×C13semidirect
308. #1439C2×C13semidirect
310. #1437C2×C13semidirect
311. #1436C2×C13semidirect
312. #1434C2×C13semidirect
313. C22⋊#95C2×C13semidirect
869. C13#14739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3942
C2×C13×#3882
C2×C13×#3862
C2×C4×C13×C22⋊C42
C13×#14452
C13×#14422
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×#14362
C13×#14342
C13×C22⋊#952
#1473913