Finite Group Databasebeta

← C13×#15514 #15701853

Subgroups — C13×#15514 #15701853

Order 3328.

1430 conjugacy classes of subgroups.

The subgroup lattice has 992 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
3C13×#1445C211yesmaximal, characteristic, complemented
4C13×#1445C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1441C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1434C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic
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×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C13×#400—24no—
30C13×#385—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
53C25×C13C2311yescharacteristic
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—41no—
58C23×C4×C13—41no—
59C23×C4×C13—41no—
60C23×C4×C13—41no—
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
74C23×C4×C13C2311yescharacteristic
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
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—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
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—41no—
102C2×C13×C22⋊C4—41no—
103C2×C13×C22⋊C4—41no—
104C2×C13×C22⋊C4—41no—
105C2×C13×C22⋊C4—41no—
106C2×C13×C22⋊C4—41no—
107C2×C13×C22⋊C4Q814yes—
108C2×C42×C13—22no—
109C2×C42×C13—41no—
110C2×C42×C13—41no—
111C13×#95—22no—
112C13×#95—22no—
113C13×#95—22no—
114C13×#95—22no—
115C13×#95—22no—
116C13×#95—22no—
117C13×#95—22no—
118C13×#95—22no—
119C13×#95—22no—
120C13×#95—41no—
121C13×#95—41no—
122C13×#95—41no—
123C13×#95—41no—
124C13×#95—41no—
125C13×#95—41no—
126C13×#95—41no—
127C13×#95—41no—
128C13×#95—41no—
129C13×#95—41no—
130C13×#95—41no—
131C13×#95—41no—
132C13×#95D414yes—
133#15514C1311yesmaximal, characteristic, direct product factor, Sylow
134C24×C13—21no—
135C24×C13—21no—
136C24×C13—21no—
137C24×C13—21no—
138C24×C13—21no—
139C24×C13—21no—
140C24×C13—21no—
141C24×C13—21no—
142C24×C13—21no—
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13C2×Q812yes—
147C24×C13#4112yes—
148C24×C13#4112yes—
149C24×C13C2411yescharacteristic
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—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—44no—
239C22×C4×C13—44no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13—44no—
243C22×C4×C13—44no—
244C22×C4×C13—44no—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×Q812yes—
249C22×C4×C13C2×Q812yes—
250C22×C4×C13#4112yes—
251C22×C4×C13#4112yes—
252C22×C4×C13#4112yes—
253C22×C4×C13#4112yes—
254C22×C4×C13#4112yes—
255C13×C4⋊C4—44no—
256C13×C4⋊C4—44no—
257C13×C4⋊C4—44no—
258C13×C4⋊C4—44no—
259C13×C4⋊C4—44no—
260C13×C22⋊C4—28no—
261C13×C22⋊C4—44no—
262C13×C22⋊C4—44no—
263C13×C22⋊C4—44no—
264C13×C22⋊C4—44no—
265C13×C22⋊C4—44no—
266C42×C13—44no—
267C2×#400C2×C1311yescharacteristic, complemented
268C2×#385C2×C1311yescharacteristic
269#1445C2×C1311yescharacteristic, complemented
270#1445C2×C1311yescharacteristic, complemented
271#1442C2×C1311yescharacteristic, complemented
272#1441C2×C1311yescharacteristic, complemented
273#1441C2×C1311yescharacteristic, complemented
274#1439C2×C1311yescharacteristic
275#1439C2×C1311yescharacteristic
276#1439C2×C1311yescharacteristic
277#1437C2×C1311yescharacteristic
278#1436C2×C1311yescharacteristic, complemented
279#1434C2×C1311yescharacteristic, complemented
280C22⋊#95C2×C1311yescharacteristic
281C22⋊#95C2×C1311yescharacteristic
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—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
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—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13#12514yes—
317C23×C13C22×D411yescharacteristic
318C23×C13C22×Q811yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13C2×#4111yescharacteristic
321C23×C13C2×#4111yescharacteristic
322C23×C13C2×#4111yescharacteristic
323C23×C13C2×#4111yescharacteristic
324C23×C13C2×#4111yescharacteristic
325C23×C13C2×#4111yescharacteristic
326C23×C13H(5,𝔽2)11yescharacteristic
327C23×C13H(5,𝔽2)11yescharacteristic
328C23×C13H(5,𝔽2)11yescharacteristic
329C23×C13H(5,𝔽2)11yescharacteristic
330C23×C13H(5,𝔽2)11yescharacteristic
331C23×C132−1+411yescharacteristic
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—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—416no—
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—
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—
431C24×C4C22×C1311yescharacteristic
432C22×C4⋊C4C22×C1311yescharacteristic
433C22×C4⋊C4C22×C1311yescharacteristic
434C22×C4⋊C4C22×C1311yescharacteristic
435C22×C4⋊C4C22×C1311yescharacteristic
436C22×C4⋊C4C22×C1311yescharacteristic
437C22×C22⋊C4C22×C1311yescharacteristic
438C22×C22⋊C4C22×C1311yescharacteristic
439C22×C22⋊C4C22×C1311yescharacteristic
440C22×C22⋊C4C22×C1311yescharacteristic
441C22×C22⋊C4C22×C1311yescharacteristic
442C22×C22⋊C4C22×C1311yescharacteristic
443C22×C42C22×C1311yescharacteristic
444#400—24no—
445#385—24no—
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
460C2×#95C22×C1311yescharacteristic
461C2×#95C22×C1311yescharacteristic
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
464C2×#95C22×C1311yescharacteristic
465C2×#95C22×C1311yescharacteristic
466C2×#95C22×C1311yescharacteristic
467C2×#95C22×C1311yescharacteristic
468C22×C13—24no—
469C22×C13—24no—
470C22×C13—24no—
471C22×C13—42no—
472C22×C13—42no—
473C22×C13—42no—
474C22×C13—42no—
475C22×C13—42no—
476C22×C13—42no—
477C22×C13—42no—
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13#52511yescharacteristic
484C22×C13C2×#12511yescharacteristic
485C22×C13#52911yescharacteristic
486C22×C13#52911yescharacteristic
487C22×C13#53211yescharacteristic
488C22×C13#53311yescharacteristic
489C22×C13#53511yescharacteristic
490C22×C13#53811yescharacteristic
491C22×C13#53811yescharacteristic
492C22×C13#53811yescharacteristic
493C22×C13#53911yescharacteristic
494C22×C13#53911yescharacteristic
495C22×C13#54011yescharacteristic
496C22×C13#54211yescharacteristic
497C22×C13#54311yescharacteristic
498C22×C13#54611yescharacteristic
499C22×C13#54611yescharacteristic
500C22×C13#54611yescharacteristic
501C22×C13D4×Q811yescharacteristic
502C22×C13#55111yescharacteristic
503C22×C13#55111yescharacteristic
504C22×C13#55111yescharacteristic
505C22×C13#55111yescharacteristic
506C22×C13#55111yescharacteristic
507C22×C13#55211yescharacteristic
508C22×C13#55211yescharacteristic
509C22×C13#55311yescharacteristic
510C22×C13#55311yescharacteristic
511C22×C13#55311yescharacteristic
512C22×C13#55411yescharacteristic
513C22×C13#55411yescharacteristic
514C22×C13#55411yescharacteristic
515C22×C13#55911yescharacteristic
516C22×C13#56011yescharacteristic
517C22×C13#56211yescharacteristic
518C4×C13—42no—
519C4×C13—42no—
520C4×C13—42no—
521C4×C13—42no—
522C4×C13—42no—
523C4×C13—42no—
524C4×C13—42no—
525C4×C13—42no—
526C4×C13—42no—
527C4×C13—42no—
528C4×C13—81no—
529C4×C13—81no—
530C4×C13—81no—
531C4×C13—81no—
532C25C23×C1311yescharacteristic
533C23×C4—22no—
534C23×C4—22no—
535C23×C4—22no—
536C23×C4—41no—
537C23×C4—41no—
538C23×C4—41no—
539C23×C4—41no—
540C23×C4C23×C1311yescharacteristic
541C23×C4C23×C1311yescharacteristic
542C23×C4C23×C1311yescharacteristic
543C23×C4C23×C1311yescharacteristic
544C23×C4C23×C1311yescharacteristic
545C23×C4C23×C1311yescharacteristic
546C23×C4C23×C1311yescharacteristic
547C23×C4C23×C1311yescharacteristic
548C23×C4C23×C1311yescharacteristic
549C23×C4C23×C1311yescharacteristic
550C23×C4C23×C1311yescharacteristic
551C23×C4C23×C1311yescharacteristic
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4—41no—
565C2×C4⋊C4—41no—
566C2×C4⋊C4—41no—
567C2×C4⋊C4—41no—
568C2×C4⋊C4—41no—
569C2×C22⋊C4—22no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—22no—
572C2×C22⋊C4—22no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4—22no—
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—41no—
581C2×C22⋊C4—41no—
582C2×C22⋊C4—41no—
583C2×C22⋊C4—41no—
584C2×C22⋊C4—41no—
585C2×C22⋊C4—41no—
586C2×C22⋊C4Q8×C1314yes—
587C2×C42—22no—
588C2×C42—41no—
589C2×C42—41no—
590#95—22no—
591#95—22no—
592#95—22no—
593#95—22no—
594#95—22no—
595#95—22no—
596#95—22no—
597#95—22no—
598#95—22no—
599#95—41no—
600#95—41no—
601#95—41no—
602#95—41no—
603#95—41no—
604#95—41no—
605#95—41no—
606#95—41no—
607#95—41no—
608#95—41no—
609#95—41no—
610#95—41no—
611#95D4×C1314yes—
612C2×C13—44no—
613C2×C13#245711yescharacteristic
614C2×C13#247311yescharacteristic
615C2×C13#250511yescharacteristic
616C2×C13#251511yescharacteristic
617C2×C13#255611yescharacteristic
618C2×C13#255711yescharacteristic
619C2×C13#256911yescharacteristic
620C2×C13#258911yescharacteristic
621C2×C13#260311yescharacteristic
622C2×C13#268511yescharacteristic
623C2×C13#269211yescharacteristic
624C2×C13#274311yescharacteristic
625C2×C13#275011yescharacteristic
626C2×C13#278011yescharacteristic
627C2×C13#279611yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24C2×Q8×C1312yes—
641C24C13×#4112yes—
642C24C13×#4112yes—
643C24C24×C1311yescharacteristic
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—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—44no—
733C22×C4—44no—
734C22×C4—44no—
735C22×C4—44no—
736C22×C4—44no—
737C22×C4—44no—
738C22×C4—44no—
739C22×C4C2×D4×C1312yes—
740C22×C4C2×D4×C1312yes—
741C22×C4C2×D4×C1312yes—
742C22×C4C2×Q8×C1312yes—
743C22×C4C2×Q8×C1312yes—
744C22×C4C13×#4112yes—
745C22×C4C13×#4112yes—
746C22×C4C13×#4112yes—
747C22×C4C13×#4112yes—
748C22×C4C13×#4112yes—
749C4⋊C4—44no—
750C4⋊C4—44no—
751C4⋊C4—44no—
752C4⋊C4—44no—
753C4⋊C4—44no—
754C22⋊C4—28no—
755C22⋊C4—44no—
756C22⋊C4—44no—
757C22⋊C4—44no—
758C22⋊C4—44no—
759C22⋊C4—44no—
760C42—44no—
761C13#1551411yescharacteristic, direct product factor, Sylow
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C13×#12514yes—
797C23C22×D4×C1311yescharacteristic
798C23C22×Q8×C1311yescharacteristic
799C23C2×C13×#4111yescharacteristic
800C23C2×C13×#4111yescharacteristic
801C23C2×C13×#4111yescharacteristic
802C23C2×C13×#4111yescharacteristic
803C23C2×C13×#4111yescharacteristic
804C23C2×C13×#4111yescharacteristic
805C23C2×C13×#4111yescharacteristic
806C23C13×H(5,𝔽2)11yescharacteristic
807C23C13×H(5,𝔽2)11yescharacteristic
808C23C13×H(5,𝔽2)11yescharacteristic
809C23C13×H(5,𝔽2)11yescharacteristic
810C23C13×H(5,𝔽2)11yescharacteristic
811C23C13×2−1+411yescharacteristic
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—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
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—416no—
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—
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—
911C22—24no—
912C22—24no—
913C22—24no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—42no—
926C22C13×#52511yescharacteristic
927C22C2×C13×#12511yescharacteristic
928C22C13×#52911yescharacteristic
929C22C13×#52911yescharacteristic
930C22C13×#53211yescharacteristic
931C22C13×#53311yescharacteristic
932C22C13×#53511yescharacteristic
933C22C13×#53811yescharacteristic
934C22C13×#53811yescharacteristic
935C22C13×#53811yescharacteristic
936C22C13×#53911yescharacteristic
937C22C13×#53911yescharacteristic
938C22C13×#54011yescharacteristic
939C22C13×#54211yescharacteristic
940C22C13×#54311yescharacteristic
941C22C13×#54611yescharacteristic
942C22C13×#54611yescharacteristic
943C22C13×#54611yescharacteristic
944C22D4×Q8×C1311yescharacteristic
945C22C13×#55111yescharacteristic
946C22C13×#55111yescharacteristic
947C22C13×#55111yescharacteristic
948C22C13×#55111yescharacteristic
949C22C13×#55111yescharacteristic
950C22C13×#55211yescharacteristic
951C22C13×#55211yescharacteristic
952C22C13×#55311yescharacteristic
953C22C13×#55311yescharacteristic
954C22C13×#55311yescharacteristic
955C22C13×#55411yescharacteristic
956C22C13×#55411yescharacteristic
957C22C13×#55411yescharacteristic
958C22C13×#55911yescharacteristic
959C22C13×#56011yescharacteristic
960C22C13×#56211yescharacteristic
961C4—42no—
962C4—42no—
963C4—42no—
964C4—42no—
965C4—42no—
966C4—42no—
967C4—42no—
968C4—42no—
969C4—42no—
970C4—42no—
971C4—81no—
972C4—81no—
973C4—81no—
974C4—81no—
975C2—44no—
976C2C13×#245711yescharacteristic
977C2C13×#247311yescharacteristic
978C2C13×#250511yescharacteristic
979C2C13×#251511yescharacteristic
980C2C13×#255611yescharacteristic
981C2C13×#255711yescharacteristic
982C2C13×#256911yescharacteristic
983C2C13×#258911yescharacteristic
984C2C13×#260311yescharacteristic
985C2C13×#268511yescharacteristic
986C2C13×#269211yescharacteristic
987C2C13×#274311yescharacteristic
988C2C13×#275011yescharacteristic
989C2C13×#278011yescharacteristic
990C2C13×#279611yescharacteristic
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
3. C13×#1445C2semidirect
4. C13×#1445C2semidirect
5. C13×#1442C2semidirect
6. C13×#1441C2semidirect
7. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1434C2semidirect
133. #15514C13direct (N × H)
267. C2×#400C2×C13semidirect
269. #1445C2×C13semidirect
270. #1445C2×C13semidirect
271. #1442C2×C13semidirect
272. #1441C2×C13semidirect
273. #1441C2×C13semidirect
278. #1436C2×C13semidirect
279. #1434C2×C13semidirect
761. C13#15514direct (N × H)

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
C13×#14452
C13×#14422
C13×#14412
C13×#14392
C13×#14372
C13×#14362
C13×#14342
C13×C22⋊#952
#1551413