Finite Group Databasebeta

← C13×#14509 #15700848

Subgroups — C13×#14509 #15700848

Order 3328.

1406 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#388C211yesmaximal, characteristic
2C13×#1445C211yesmaximal, characteristic, complemented
3C13×#1443C211yesmaximal, characteristic, complemented
4C13×#1443C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1440C211yesmaximal, characteristic
7C13×#1439C211yesmaximal, characteristic
8C13×#1437C211yesmaximal, characteristic
9C13×#1436C211yesmaximal, characteristic, complemented
10C13×#1436C211yesmaximal, characteristic, complemented
11C13×#1434C211yesmaximal, characteristic, complemented
12C13×#1434C211yesmaximal, characteristic, complemented
13C13×C22⋊#95C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C22⋊C4C2211yescharacteristic
20C22×C13×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C42×C13C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C13×#388C418yescomplemented
28C2×C13×#95C2211yescharacteristic
29C2×C13×#95C2211yescharacteristic
30C2×C13×#95C2211yescharacteristic
31C2×C13×#95C2211yescharacteristic
32C2×C13×#95C2211yescharacteristic
33C2×C13×#95C2211yescharacteristic
34C2×C13×#95C2211yescharacteristic
35C2×C13×#95C2211yescharacteristic
36C2×C13×#95C2211yescharacteristic
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
52C25×C13C2311yescharacteristic
53C23×C4×C13—22no—
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—41no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13—41no—
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
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
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4—41no—
77C2×C13×C4⋊C4—41no—
78C2×C13×C4⋊C4—41no—
79C2×C13×C4⋊C4C2×C414yescomplemented
80C2×C13×C22⋊C4—22no—
81C2×C13×C22⋊C4—22no—
82C2×C13×C22⋊C4—22no—
83C2×C13×C22⋊C4—22no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—41no—
88C2×C13×C22⋊C4—41no—
89C2×C13×C22⋊C4—41no—
90C2×C13×C22⋊C4—41no—
91C2×C13×C22⋊C4—41no—
92C2×C13×C22⋊C4—41no—
93C2×C13×C22⋊C4—41no—
94C2×C13×C22⋊C4—41no—
95C2×C13×C22⋊C4C2×C414yes—
96C2×C13×C22⋊C4C2×C414yes—
97C2×C13×C22⋊C4C2×C414yes—
98C2×C42×C13—41no—
99C2×C42×C13—41no—
100C2×C42×C13—41no—
101C2×C42×C13—41no—
102C2×C42×C13—41no—
103C2×C42×C13C2×C414yescomplemented
104C13×#95—22no—
105C13×#95—22no—
106C13×#95—22no—
107C13×#95—22no—
108C13×#95—22no—
109C13×#95—22no—
110C13×#95—22no—
111C13×#95—41no—
112C13×#95—41no—
113C13×#95—41no—
114C13×#95—41no—
115C13×#95—41no—
116C13×#95—41no—
117C13×#95—41no—
118C13×#95—41no—
119C13×#95—41no—
120C13×#95—41no—
121C13×#95—41no—
122C13×#95—41no—
123C13×#95—41no—
124C13×#95—41no—
125C13×#95—41no—
126C13×#95C2×C414yescomplemented
127C13×#95C2×C414yescomplemented
128#14509C1311yesmaximal, characteristic, direct product factor, Sylow
129C24×C13—21no—
130C24×C13—21no—
131C24×C13—21no—
132C24×C13—21no—
133C24×C13—21no—
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13C22×C412yes—
142C24×C13#4112yes—
143C24×C13#4112yes—
144C24×C13C2411yescharacteristic
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—21no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
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—44no—
234C22×C4×C13—44no—
235C22×C4×C13—44no—
236C22×C4×C13—44no—
237C22×C4×C13—44no—
238C22×C4×C13—44no—
239C22×C4×C13—44no—
240C22×C4×C13C22×C412yes—
241C22×C4×C13C22×C412yes—
242C22×C4×C13C22×C412yes—
243C22×C4×C13C22×C412yes—
244C22×C4×C13C22×C412yes—
245C22×C4×C13C22×C412yes—
246C22×C4×C13#4112yes—
247C22×C4×C13#4112yes—
248C22×C4×C13#4112yes—
249C22×C4×C13#4112yes—
250C13×C4⋊C4—44no—
251C13×C4⋊C4—44no—
252C13×C22⋊C4—28no—
253C13×C22⋊C4—44no—
254C13×C22⋊C4—44no—
255C13×C22⋊C4—44no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4—44no—
258C42×C13—44no—
259C42×C13—44no—
260C2×#388C2×C1311yescharacteristic
261#1445C2×C1311yescharacteristic, complemented
262#1443C2×C1311yescharacteristic, complemented
263#1443C2×C1311yescharacteristic, complemented
264#1442C2×C1311yescharacteristic, complemented
265#1440C2×C1311yescharacteristic
266#1439C2×C1311yescharacteristic
267#1437C2×C1311yescharacteristic
268#1436C2×C1311yescharacteristic, complemented
269#1436C2×C1311yescharacteristic, complemented
270#1434C2×C1311yescharacteristic, complemented
271#1434C2×C1311yescharacteristic, complemented
272C22⋊#95C2×C1311yescharacteristic
273C22⋊#95C2×C1311yescharacteristic
274C22⋊#95C2×C1311yescharacteristic
275C23×C13—22no—
276C23×C13—22no—
277C23×C13—22no—
278C23×C13—22no—
279C23×C13—22no—
280C23×C13—22no—
281C23×C13—22no—
282C23×C13—22no—
283C23×C13—22no—
284C23×C13—22no—
285C23×C13—22no—
286C23×C13—22no—
287C23×C13—22no—
288C23×C13—22no—
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—41no—
294C23×C13—41no—
295C23×C13—41no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13#11714yes—
310C23×C13C23×C411yescharacteristic
311C23×C13C2×#4111yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13H(5,𝔽2)11yescharacteristic
318C23×C13H(5,𝔽2)11yescharacteristic
319C23×C13H(5,𝔽2)11yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C132−1+411yescharacteristic
324C23×C132−1+411yescharacteristic
325C2×C4×C13—22no—
326C2×C4×C13—22no—
327C2×C4×C13—22no—
328C2×C4×C13—22no—
329C2×C4×C13—22no—
330C2×C4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—22no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—22no—
336C2×C4×C13—22no—
337C2×C4×C13—22no—
338C2×C4×C13—22no—
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
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—416no—
356C2×C4×C13—41no—
357C2×C4×C13—41no—
358C2×C4×C13—41no—
359C2×C4×C13—41no—
360C2×C4×C13—41no—
361C2×C4×C13—41no—
362C2×C4×C13—41no—
363C2×C4×C13—41no—
364C2×C4×C13—41no—
365C2×C4×C13—41no—
366C2×C4×C13—41no—
367C2×C4×C13—41no—
368C2×C4×C13—41no—
369C2×C4×C13—41no—
370C2×C4×C13—41no—
371C2×C4×C13—41no—
372C2×C4×C13—41no—
373C2×C4×C13—41no—
374C2×C4×C13—41no—
375C2×C4×C13—41no—
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—
424C24×C4C22×C1311yescharacteristic
425C22×C4⋊C4C22×C1311yescharacteristic
426C22×C4⋊C4C22×C1311yescharacteristic
427C22×C22⋊C4C22×C1311yescharacteristic
428C22×C22⋊C4C22×C1311yescharacteristic
429C22×C22⋊C4C22×C1311yescharacteristic
430C22×C22⋊C4C22×C1311yescharacteristic
431C22×C22⋊C4C22×C1311yescharacteristic
432C22×C22⋊C4C22×C1311yescharacteristic
433C22×C42C22×C1311yescharacteristic
434C22×C42C22×C1311yescharacteristic
435#388C4×C1318yescomplemented
436C2×#95C22×C1311yescharacteristic
437C2×#95C22×C1311yescharacteristic
438C2×#95C22×C1311yescharacteristic
439C2×#95C22×C1311yescharacteristic
440C2×#95C22×C1311yescharacteristic
441C2×#95C22×C1311yescharacteristic
442C2×#95C22×C1311yescharacteristic
443C2×#95C22×C1311yescharacteristic
444C2×#95C22×C1311yescharacteristic
445C2×#95C22×C1311yescharacteristic
446C2×#95C22×C1311yescharacteristic
447C2×#95C22×C1311yescharacteristic
448C2×#95C22×C1311yescharacteristic
449C2×#95C22×C1311yescharacteristic
450C2×#95C22×C1311yescharacteristic
451C2×#95C22×C1311yescharacteristic
452C2×#95C22×C1311yescharacteristic
453C2×#95C22×C1311yescharacteristic
454C2×#95C22×C1311yescharacteristic
455C2×#95C22×C1311yescharacteristic
456C2×#95C22×C1311yescharacteristic
457C2×#95C22×C1311yescharacteristic
458C2×#95C22×C1311yescharacteristic
459C2×#95C22×C1311yescharacteristic
460C22×C13—24no—
461C22×C13—24no—
462C22×C13—24no—
463C22×C13—42no—
464C22×C13—42no—
465C22×C13—42no—
466C22×C13—42no—
467C22×C13—42no—
468C22×C13—42no—
469C22×C13—42no—
470C22×C13—42no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13C2×#11711yescharacteristic
476C22×C13C4×#4111yescharacteristic
477C22×C13C4×#4111yescharacteristic
478C22×C13#51811yescharacteristic
479C22×C13#51811yescharacteristic
480C22×C13#52011yescharacteristic
481C22×C13#52011yescharacteristic
482C22×C13#53811yescharacteristic
483C22×C13#53811yescharacteristic
484C22×C13#53811yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53811yescharacteristic
487C22×C13#53911yescharacteristic
488C22×C13#53911yescharacteristic
489C22×C13#53911yescharacteristic
490C22×C13#54111yescharacteristic
491C22×C13#54211yescharacteristic
492C22×C13#54211yescharacteristic
493C22×C13#54211yescharacteristic
494C22×C13#55111yescharacteristic
495C22×C13#55111yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55111yescharacteristic
499C22×C13#55211yescharacteristic
500C22×C13#55211yescharacteristic
501C22×C13#55311yescharacteristic
502C22×C13#55311yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55911yescharacteristic
506C22×C13#56011yescharacteristic
507C22×C13#56011yescharacteristic
508C22×C13#56211yescharacteristic
509C22×C13#56211yescharacteristic
510C4×C13—42no—
511C4×C13—42no—
512C4×C13—42no—
513C4×C13—42no—
514C4×C13—42no—
515C4×C13—42no—
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—81no—
521C4×C13—81no—
522C4×C13—81no—
523C4×C13—81no—
524C25C23×C1311yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—41no—
529C23×C4—41no—
530C23×C4—41no—
531C23×C4—41no—
532C23×C4C23×C1311yescharacteristic
533C23×C4C23×C1311yescharacteristic
534C23×C4C23×C1311yescharacteristic
535C23×C4C23×C1311yescharacteristic
536C23×C4C23×C1311yescharacteristic
537C23×C4C23×C1311yescharacteristic
538C23×C4C23×C1311yescharacteristic
539C23×C4C23×C1311yescharacteristic
540C23×C4C23×C1311yescharacteristic
541C23×C4C23×C1311yescharacteristic
542C23×C4C23×C1311yescharacteristic
543C23×C4C23×C1311yescharacteristic
544C23×C4C23×C1311yescharacteristic
545C23×C4C23×C1311yescharacteristic
546C2×C4⋊C4—22no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—41no—
550C2×C4⋊C4—41no—
551C2×C4⋊C4C2×C4×C1314yescomplemented
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—41no—
560C2×C22⋊C4—41no—
561C2×C22⋊C4—41no—
562C2×C22⋊C4—41no—
563C2×C22⋊C4—41no—
564C2×C22⋊C4—41no—
565C2×C22⋊C4—41no—
566C2×C22⋊C4—41no—
567C2×C22⋊C4C2×C4×C1314yes—
568C2×C22⋊C4C2×C4×C1314yes—
569C2×C22⋊C4C2×C4×C1314yes—
570C2×C42—41no—
571C2×C42—41no—
572C2×C42—41no—
573C2×C42—41no—
574C2×C42—41no—
575C2×C42C2×C4×C1314yescomplemented
576#95—22no—
577#95—22no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—41no—
584#95—41no—
585#95—41no—
586#95—41no—
587#95—41no—
588#95—41no—
589#95—41no—
590#95—41no—
591#95—41no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95C2×C4×C1314yescomplemented
599#95C2×C4×C1314yescomplemented
600C2×C13—44no—
601C2×C13#231811yescharacteristic
602C2×C13#233411yescharacteristic
603C2×C13#233711yescharacteristic
604C2×C13#234311yescharacteristic
605C2×C13#235311yescharacteristic
606C2×C13#237411yescharacteristic
607C2×C13#237711yescharacteristic
608C2×C13#273511yescharacteristic
609C2×C13#273911yescharacteristic
610C2×C13#274611yescharacteristic
611C2×C13#274711yescharacteristic
612C2×C13#275111yescharacteristic
613C2×C13#277811yescharacteristic
614C2×C13#277911yescharacteristic
615C2×C13#279611yescharacteristic
616C24—21no—
617C24—21no—
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24C22×C4×C1312yes—
629C24C13×#4112yes—
630C24C13×#4112yes—
631C24C24×C1311yescharacteristic
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
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—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4C22×C4×C1312yes—
728C22×C4C22×C4×C1312yes—
729C22×C4C22×C4×C1312yes—
730C22×C4C22×C4×C1312yes—
731C22×C4C22×C4×C1312yes—
732C22×C4C22×C4×C1312yes—
733C22×C4C13×#4112yes—
734C22×C4C13×#4112yes—
735C22×C4C13×#4112yes—
736C22×C4C13×#4112yes—
737C4⋊C4—44no—
738C4⋊C4—44no—
739C22⋊C4—28no—
740C22⋊C4—44no—
741C22⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C42—44no—
746C42—44no—
747C13#1450911yescharacteristic, direct product factor, Sylow
748C23—22no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—22no—
753C23—22no—
754C23—22no—
755C23—22no—
756C23—22no—
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23C13×#11714yes—
783C23C23×C4×C1311yescharacteristic
784C23C2×C13×#4111yescharacteristic
785C23C2×C13×#4111yescharacteristic
786C23C2×C13×#4111yescharacteristic
787C23C2×C13×#4111yescharacteristic
788C23C2×C13×#4111yescharacteristic
789C23C2×C13×#4111yescharacteristic
790C23C13×H(5,𝔽2)11yescharacteristic
791C23C13×H(5,𝔽2)11yescharacteristic
792C23C13×H(5,𝔽2)11yescharacteristic
793C23C13×H(5,𝔽2)11yescharacteristic
794C23C13×H(5,𝔽2)11yescharacteristic
795C23C13×H(5,𝔽2)11yescharacteristic
796C23C13×2−1+411yescharacteristic
797C23C13×2−1+411yescharacteristic
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—416no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
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—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—42no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22C2×C13×#11711yescharacteristic
913C22C4×C13×#4111yescharacteristic
914C22C4×C13×#4111yescharacteristic
915C22C13×#51811yescharacteristic
916C22C13×#51811yescharacteristic
917C22C13×#52011yescharacteristic
918C22C13×#52011yescharacteristic
919C22C13×#53811yescharacteristic
920C22C13×#53811yescharacteristic
921C22C13×#53811yescharacteristic
922C22C13×#53811yescharacteristic
923C22C13×#53811yescharacteristic
924C22C13×#53911yescharacteristic
925C22C13×#53911yescharacteristic
926C22C13×#53911yescharacteristic
927C22C13×#54111yescharacteristic
928C22C13×#54211yescharacteristic
929C22C13×#54211yescharacteristic
930C22C13×#54211yescharacteristic
931C22C13×#55111yescharacteristic
932C22C13×#55111yescharacteristic
933C22C13×#55111yescharacteristic
934C22C13×#55111yescharacteristic
935C22C13×#55111yescharacteristic
936C22C13×#55211yescharacteristic
937C22C13×#55211yescharacteristic
938C22C13×#55311yescharacteristic
939C22C13×#55311yescharacteristic
940C22C13×#55311yescharacteristic
941C22C13×#55311yescharacteristic
942C22C13×#55911yescharacteristic
943C22C13×#56011yescharacteristic
944C22C13×#56011yescharacteristic
945C22C13×#56211yescharacteristic
946C22C13×#56211yescharacteristic
947C4—42no—
948C4—42no—
949C4—42no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—42no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—81no—
961C2—44no—
962C2C13×#231811yescharacteristic
963C2C13×#233411yescharacteristic
964C2C13×#233711yescharacteristic
965C2C13×#234311yescharacteristic
966C2C13×#235311yescharacteristic
967C2C13×#237411yescharacteristic
968C2C13×#237711yescharacteristic
969C2C13×#273511yescharacteristic
970C2C13×#273911yescharacteristic
971C2C13×#274611yescharacteristic
972C2C13×#274711yescharacteristic
973C2C13×#275111yescharacteristic
974C2C13×#277811yescharacteristic
975C2C13×#277911yescharacteristic
976C2C13×#279611yescharacteristic
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. C13×#1445C2semidirect
3. C13×#1443C2semidirect
4. C13×#1443C2semidirect
5. C13×#1442C2semidirect
9. C13×#1436C2semidirect
10. C13×#1436C2semidirect
11. C13×#1434C2semidirect
12. C13×#1434C2semidirect
27. C13×#388C4semidirect
79. C2×C13×C4⋊C4C2×C4semidirect
103. C2×C42×C13C2×C4semidirect
126. C13×#95C2×C4semidirect
127. C13×#95C2×C4semidirect
128. #14509C13direct (N × H)
261. #1445C2×C13semidirect
262. #1443C2×C13semidirect
263. #1443C2×C13semidirect
264. #1442C2×C13semidirect
268. #1436C2×C13semidirect
269. #1436C2×C13semidirect
270. #1434C2×C13semidirect
271. #1434C2×C13semidirect
435. #388C4×C13semidirect
551. C2×C4⋊C4C2×C4×C13semidirect
575. C2×C42C2×C4×C13semidirect
598. #95C2×C4×C13semidirect
599. #95C2×C4×C13semidirect
747. C13#14509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3882
C13×#14452
C13×#14432
C13×#14422
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×#14342
C13×C22⋊#952
#1450913