Finite Group Databasebeta

← C13×#14738 #15701077

Subgroups — C13×#14738 #15701077

Order 3328.

1794 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#400C211yesmaximal, characteristic, complemented
2C2×C13×#385C211yesmaximal, characteristic
3C2×C13×#385C211yesmaximal, characteristic
4C22×C13×#95C211yesmaximal, characteristic
5C13×#1445C211yesmaximal, characteristic, complemented
6C13×#1443C211yesmaximal, characteristic, complemented
7C13×#1443C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1442C211yesmaximal, characteristic, complemented
10C13×#1442C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×C22⋊#95C211yesmaximal, characteristic
13C13×C22⋊#95C211yesmaximal, characteristic
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C13×#400—24no—
28C13×#385—24no—
29C13×#385—24no—
30C2×C13×#95—24no—
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
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C25×C13C2311yescharacteristic
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—41no—
72C23×C4×C13—41no—
73C23×C4×C13—41no—
74C23×C4×C13—41no—
75C23×C4×C13—41no—
76C23×C4×C13—41no—
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C23×C4×C13C2311yescharacteristic
88C23×C4×C13C2311yescharacteristic
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
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⋊C4D414yes—
114C2×C13×C22⋊C4Q814yes—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—22no—
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—41no—
131C13×#95—41no—
132C13×#95—41no—
133C13×#95—41no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95D414yes—
139#14738C1311yesmaximal, characteristic, direct product factor, Sylow
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13C2×D412yes—
149C24×C13C2×Q812yes—
150C24×C13#4112yes—
151C24×C13#4112yes—
152C24×C13#4112yes—
153C24×C13#4112yes—
154C24×C13#4112yes—
155C24×C13C2411yescharacteristic
156C22×C4×C13—28no—
157C22×C4×C13—28no—
158C22×C4×C13—28no—
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—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—44no—
248C22×C4×C13—44no—
249C22×C4×C13—44no—
250C22×C4×C13—44no—
251C22×C4×C13—44no—
252C22×C4×C13—44no—
253C22×C4×C13—44no—
254C22×C4×C13—44no—
255C22×C4×C13—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13—44no—
259C22×C4×C13—44no—
260C22×C4×C13—44no—
261C22×C4×C13—44no—
262C22×C4×C13—44no—
263C22×C4×C13—44no—
264C22×C4×C13—44no—
265C22×C4×C13C2×D412yes—
266C22×C4×C13C2×D412yes—
267C22×C4×C13C2×D412yes—
268C22×C4×C13C2×D412yes—
269C22×C4×C13C2×D412yes—
270C22×C4×C13C2×Q812yes—
271C22×C4×C13C2×Q812yes—
272C22×C4×C13#4112yes—
273C22×C4×C13#4112yes—
274C22×C4×C13#4112yes—
275C13×C4⋊C4—44no—
276C13×C4⋊C4—44no—
277C13×C4⋊C4—44no—
278C13×C4⋊C4—44no—
279C13×C22⋊C4—28no—
280C13×C22⋊C4—28no—
281C13×C22⋊C4—44no—
282C13×C22⋊C4—44no—
283C2×#400C2×C1311yescharacteristic, complemented
284C2×#385C2×C1311yescharacteristic
285C2×#385C2×C1311yescharacteristic
286C22×#95C2×C1311yescharacteristic
287#1445C2×C1311yescharacteristic, complemented
288#1443C2×C1311yescharacteristic, complemented
289#1443C2×C1311yescharacteristic, complemented
290#1442C2×C1311yescharacteristic, complemented
291#1442C2×C1311yescharacteristic, complemented
292#1442C2×C1311yescharacteristic, complemented
293#1441C2×C1311yescharacteristic, complemented
294C22⋊#95C2×C1311yescharacteristic
295C22⋊#95C2×C1311yescharacteristic
296C22⋊#95C2×C1311yescharacteristic
297C22⋊#95C2×C1311yescharacteristic
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—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
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×C13C22⋊Q814yes—
327C23×C13#12314yes—
328C23×C13#12414yes—
329C23×C13#12514yes—
330C23×C13#12514yes—
331C23×C13#12614yes—
332C23×C13#12614yes—
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×Q811yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13C2×#4111yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C132−1+411yescharacteristic
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—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—416no—
379C2×C4×C13—416no—
380C2×C4×C13—416no—
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—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—
449C24×C4C22×C1311yescharacteristic
450C24×C4C22×C1311yescharacteristic
451C24×C4C22×C1311yescharacteristic
452C22×C4⋊C4C22×C1311yescharacteristic
453C22×C4⋊C4C22×C1311yescharacteristic
454C22×C4⋊C4C22×C1311yescharacteristic
455C22×C4⋊C4C22×C1311yescharacteristic
456C22×C22⋊C4C22×C1311yescharacteristic
457C22×C22⋊C4C22×C1311yescharacteristic
458C22×C22⋊C4C22×C1311yescharacteristic
459C22×C22⋊C4C22×C1311yescharacteristic
460#400—24no—
461#385—24no—
462#385—24no—
463C2×#95—24no—
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
482C2×#95C22×C1311yescharacteristic
483C2×#95C22×C1311yescharacteristic
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C22×C13—24no—
489C22×C13—24no—
490C22×C13—24no—
491C22×C13—24no—
492C22×C13—24no—
493C22×C13—24no—
494C22×C13—24no—
495C22×C13—24no—
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—24no—
500C22×C13—24no—
501C22×C13—24no—
502C22×C13#40018yescomplemented
503C22×C13C2×C22⋊Q811yescharacteristic
504C22×C13C2×#12311yescharacteristic
505C22×C13#52511yescharacteristic
506C22×C13#52511yescharacteristic
507C22×C13#52511yescharacteristic
508C22×C13C2×#12411yescharacteristic
509C22×C13C2×#12511yescharacteristic
510C22×C13C2×#12511yescharacteristic
511C22×C13C2×#12611yescharacteristic
512C22×C13C2×#12611yescharacteristic
513C22×C13#52911yescharacteristic
514C22×C13#52911yescharacteristic
515C22×C13#52911yescharacteristic
516C22×C13#53811yescharacteristic
517C22×C13#53811yescharacteristic
518C22×C13#53811yescharacteristic
519C22×C13#53911yescharacteristic
520C22×C13#53911yescharacteristic
521C22×C13#53911yescharacteristic
522C22×C13D4211yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54611yescharacteristic
525C22×C13#54611yescharacteristic
526C22×C13#54611yescharacteristic
527C22×C13#54711yescharacteristic
528C22×C13D4×Q811yescharacteristic
529C22×C13#55111yescharacteristic
530C22×C13#55111yescharacteristic
531C22×C13#55111yescharacteristic
532C22×C13#55111yescharacteristic
533C22×C13#55211yescharacteristic
534C22×C13#55211yescharacteristic
535C22×C13#55411yescharacteristic
536C22×C13#55411yescharacteristic
537C22×C13#55411yescharacteristic
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—42no—
548C4×C13—81no—
549C4×C13—81no—
550C4×C13—81no—
551C4×C13—81no—
552C25C23×C1311yescharacteristic
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—22no—
565C23×C4—22no—
566C23×C4—22no—
567C23×C4—22no—
568C23×C4—41no—
569C23×C4—41no—
570C23×C4—41no—
571C23×C4—41no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C23×C1311yescharacteristic
575C23×C4C23×C1311yescharacteristic
576C23×C4C23×C1311yescharacteristic
577C23×C4C23×C1311yescharacteristic
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
580C23×C4C23×C1311yescharacteristic
581C23×C4C23×C1311yescharacteristic
582C23×C4C23×C1311yescharacteristic
583C23×C4C23×C1311yescharacteristic
584C23×C4C23×C1311yescharacteristic
585C23×C4C23×C1311yescharacteristic
586C23×C4C23×C1311yescharacteristic
587C23×C4C23×C1311yescharacteristic
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
599C2×C4⋊C4—41no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4D4×C1314yes—
611C2×C22⋊C4Q8×C1314yes—
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#95—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95—41no—
635#95D4×C1314yes—
636C2×C13—28no—
637C2×C13C2×#40011yescharacteristic
638C2×C13#241811yescharacteristic
639C2×C13#241911yescharacteristic
640C2×C13#244911yescharacteristic
641C2×C13#245011yescharacteristic
642C2×C13#247211yescharacteristic
643C2×C13#247311yescharacteristic
644C2×C13#247311yescharacteristic
645C2×C13#248011yescharacteristic
646C2×C13#248811yescharacteristic
647C2×C13#249311yescharacteristic
648C2×C13#250511yescharacteristic
649C2×C13#250511yescharacteristic
650C2×C13#264311yescharacteristic
651C2×C13#285211yescharacteristic
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24C2×D4×C1312yes—
661C24C2×Q8×C1312yes—
662C24C13×#4112yes—
663C24C13×#4112yes—
664C24C13×#4112yes—
665C24C13×#4112yes—
666C24C13×#4112yes—
667C24C24×C1311yescharacteristic
668C22×C4—28no—
669C22×C4—28no—
670C22×C4—28no—
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—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4—44no—
762C22×C4—44no—
763C22×C4—44no—
764C22×C4—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4—44no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C2×D4×C1312yes—
778C22×C4C2×D4×C1312yes—
779C22×C4C2×D4×C1312yes—
780C22×C4C2×D4×C1312yes—
781C22×C4C2×D4×C1312yes—
782C22×C4C2×Q8×C1312yes—
783C22×C4C2×Q8×C1312yes—
784C22×C4C13×#4112yes—
785C22×C4C13×#4112yes—
786C22×C4C13×#4112yes—
787C4⋊C4—44no—
788C4⋊C4—44no—
789C4⋊C4—44no—
790C4⋊C4—44no—
791C22⋊C4—28no—
792C22⋊C4—28no—
793C22⋊C4—44no—
794C22⋊C4—44no—
795C13#1473811yescharacteristic, direct product factor, Sylow
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23C13×C22⋊Q814yes—
825C23C13×#12314yes—
826C23C13×#12414yes—
827C23C13×#12514yes—
828C23C13×#12514yes—
829C23C13×#12614yes—
830C23C13×#12614yes—
831C23C22×D4×C1311yescharacteristic
832C23C22×D4×C1311yescharacteristic
833C23C22×Q8×C1311yescharacteristic
834C23C2×C13×#4111yescharacteristic
835C23C2×C13×#4111yescharacteristic
836C23C2×C13×#4111yescharacteristic
837C23C2×C13×#4111yescharacteristic
838C23C2×C13×#4111yescharacteristic
839C23C2×C13×#4111yescharacteristic
840C23C2×C13×#4111yescharacteristic
841C23C2×C13×#4111yescharacteristic
842C23C13×H(5,𝔽2)11yescharacteristic
843C23C13×H(5,𝔽2)11yescharacteristic
844C23C13×H(5,𝔽2)11yescharacteristic
845C23C13×2−1+411yescharacteristic
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—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—416no—
877C2×C4—416no—
878C2×C4—416no—
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×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—24no—
951C22—24no—
952C22—24no—
953C22—24no—
954C22—24no—
955C22—24no—
956C22—24no—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—24no—
961C22C13×#40018yescomplemented
962C22C2×C13×C22⋊Q811yescharacteristic
963C22C2×C13×#12311yescharacteristic
964C22C13×#52511yescharacteristic
965C22C13×#52511yescharacteristic
966C22C13×#52511yescharacteristic
967C22C2×C13×#12411yescharacteristic
968C22C2×C13×#12511yescharacteristic
969C22C2×C13×#12511yescharacteristic
970C22C2×C13×#12611yescharacteristic
971C22C2×C13×#12611yescharacteristic
972C22C13×#52911yescharacteristic
973C22C13×#52911yescharacteristic
974C22C13×#52911yescharacteristic
975C22C13×#53811yescharacteristic
976C22C13×#53811yescharacteristic
977C22C13×#53811yescharacteristic
978C22C13×#53911yescharacteristic
979C22C13×#53911yescharacteristic
980C22C13×#53911yescharacteristic
981C22D42×C1311yescharacteristic
982C22C13×#54611yescharacteristic
983C22C13×#54611yescharacteristic
984C22C13×#54611yescharacteristic
985C22C13×#54611yescharacteristic
986C22C13×#54711yescharacteristic
987C22D4×Q8×C1311yescharacteristic
988C22C13×#55111yescharacteristic
989C22C13×#55111yescharacteristic
990C22C13×#55111yescharacteristic
991C22C13×#55111yescharacteristic
992C22C13×#55211yescharacteristic
993C22C13×#55211yescharacteristic
994C22C13×#55411yescharacteristic
995C22C13×#55411yescharacteristic
996C22C13×#55411yescharacteristic
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—81no—
1008C4—81no—
1009C4—81no—
1010C4—81no—
1011C2—28no—
1012C2C2×C13×#40011yescharacteristic
1013C2C13×#241811yescharacteristic
1014C2C13×#241911yescharacteristic
1015C2C13×#244911yescharacteristic
1016C2C13×#245011yescharacteristic
1017C2C13×#247211yescharacteristic
1018C2C13×#247311yescharacteristic
1019C2C13×#247311yescharacteristic
1020C2C13×#248011yescharacteristic
1021C2C13×#248811yescharacteristic
1022C2C13×#249311yescharacteristic
1023C2C13×#250511yescharacteristic
1024C2C13×#250511yescharacteristic
1025C2C13×#264311yescharacteristic
1026C2C13×#285211yescharacteristic
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
1. C2×C13×#400C2semidirect
5. C13×#1445C2semidirect
6. C13×#1443C2semidirect
7. C13×#1443C2semidirect
8. C13×#1442C2semidirect
9. C13×#1442C2semidirect
10. C13×#1442C2semidirect
11. C13×#1441C2semidirect
139. #14738C13direct (N × H)
283. C2×#400C2×C13semidirect
287. #1445C2×C13semidirect
288. #1443C2×C13semidirect
289. #1443C2×C13semidirect
290. #1442C2×C13semidirect
291. #1442C2×C13semidirect
292. #1442C2×C13semidirect
293. #1441C2×C13semidirect
502. C22×C13#400semidirect
795. C13#14738direct (N × H)
961. C22C13×#400semidirect

Maximal subgroups

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

subgroupindex
C2×C13×#4002
C2×C13×#3852
C22×C13×#952
C13×#14452
C13×#14432
C13×#14422
C13×#14412
C13×C22⋊#952
#1473813