Finite Group Databasebeta

← C13×#15492 #15701831

Subgroups — C13×#15492 #15701831

Order 3328.

1386 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#401C211yesmaximal, characteristic, complemented
2C2×C13×#380C211yesmaximal, characteristic
3C13×#1443C211yesmaximal, characteristic, complemented
4C13×#1443C211yesmaximal, characteristic, complemented
5C13×#1442C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic
9C13×#1440C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, 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×C22⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C42×C13C2211yescharacteristic
27C13×#401—24no—
28C13×#380—24no—
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
52C2×C13×#95C2211yescharacteristic
53C25×C13C2311yescharacteristic
54C23×C4×C13—22no—
55C23×C4×C13—22no—
56C23×C4×C13—22no—
57C23×C4×C13—22no—
58C23×C4×C13—22no—
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—41no—
81C2×C13×C4⋊C4—41no—
82C2×C13×C4⋊C4—41no—
83C2×C13×C4⋊C4—41no—
84C2×C13×C22⋊C4—22no—
85C2×C13×C22⋊C4—22no—
86C2×C13×C22⋊C4—22no—
87C2×C13×C22⋊C4—22no—
88C2×C13×C22⋊C4—22no—
89C2×C13×C22⋊C4—22no—
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—41no—
97C2×C13×C22⋊C4—41no—
98C2×C13×C22⋊C4—41no—
99C2×C13×C22⋊C4—41no—
100C2×C13×C22⋊C4—41no—
101C2×C13×C22⋊C4—41no—
102C2×C42×C13—41no—
103C2×C42×C13—41no—
104C2×C42×C13—41no—
105C13×#95—22no—
106C13×#95—22no—
107C13×#95—22no—
108C13×#95—22no—
109C13×#95—22no—
110C13×#95—22no—
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—41no—
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×#95D414yes—
129#15492C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
142C24×C13#4112yes—
143C24×C13#4112yes—
144C24×C13#4112yes—
145C24×C13C2411yescharacteristic
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—21no—
150C22×C4×C13—28no—
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—44no—
238C22×C4×C13—44no—
239C22×C4×C13—44no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13—44no—
243C22×C4×C13C2×D412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13#4112yes—
247C22×C4×C13#4112yes—
248C22×C4×C13#4112yes—
249C22×C4×C13#4112yes—
250C22×C4×C13#4112yes—
251C13×C4⋊C4—44no—
252C13×C4⋊C4—44no—
253C13×C4⋊C4—44no—
254C13×C22⋊C4—44no—
255C13×C22⋊C4—44no—
256C13×C22⋊C4—44no—
257C13×C22⋊C4—44no—
258C13×C22⋊C4—44no—
259C13×C22⋊C4—44no—
260C42×C13—44no—
261C2×#401C2×C1311yescharacteristic, complemented
262C2×#380C2×C1311yescharacteristic
263#1443C2×C1311yescharacteristic, complemented
264#1443C2×C1311yescharacteristic, complemented
265#1442C2×C1311yescharacteristic, complemented
266#1442C2×C1311yescharacteristic, complemented
267#1441C2×C1311yescharacteristic, complemented
268#1440C2×C1311yescharacteristic
269#1440C2×C1311yescharacteristic
270#1439C2×C1311yescharacteristic
271#1437C2×C1311yescharacteristic
272#1436C2×C1311yescharacteristic, complemented
273#1436C2×C1311yescharacteristic, complemented
274C22⋊#95C2×C1311yescharacteristic
275C22⋊#95C2×C1311yescharacteristic
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—22no—
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—41no—
310C23×C13#12614yes—
311C23×C13C22×D411yescharacteristic
312C23×C13C2×#4111yescharacteristic
313C23×C13C2×#4111yescharacteristic
314C23×C13C2×#4111yescharacteristic
315C23×C13C2×#4111yescharacteristic
316C23×C13C2×#4111yescharacteristic
317C23×C13C2×#4111yescharacteristic
318C23×C13C2×#4111yescharacteristic
319C23×C13C2×#4111yescharacteristic
320C23×C13H(5,𝔽2)11yescharacteristic
321C23×C13H(5,𝔽2)11yescharacteristic
322C23×C13H(5,𝔽2)11yescharacteristic
323C23×C13H(5,𝔽2)11yescharacteristic
324C23×C132−1+411yescharacteristic
325C23×C132−1+411yescharacteristic
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—416no—
348C2×C4×C13—41no—
349C2×C4×C13—41no—
350C2×C4×C13—41no—
351C2×C4×C13—41no—
352C2×C4×C13—41no—
353C2×C4×C13—41no—
354C2×C4×C13—41no—
355C2×C4×C13—41no—
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—
424C2×C4×C13#12614yes—
425C24×C4C22×C1311yescharacteristic
426C22×C4⋊C4C22×C1311yescharacteristic
427C22×C4⋊C4C22×C1311yescharacteristic
428C22×C4⋊C4C22×C1311yescharacteristic
429C22×C22⋊C4C22×C1311yescharacteristic
430C22×C22⋊C4C22×C1311yescharacteristic
431C22×C22⋊C4C22×C1311yescharacteristic
432C22×C22⋊C4C22×C1311yescharacteristic
433C22×C22⋊C4C22×C1311yescharacteristic
434C22×C22⋊C4C22×C1311yescharacteristic
435C22×C42C22×C1311yescharacteristic
436#401—24no—
437#380—24no—
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
460C2×#95C22×C1311yescharacteristic
461C2×#95C22×C1311yescharacteristic
462C22×C13—24no—
463C22×C13—24no—
464C22×C13—24no—
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×C13—42no—
476C22×C13—42no—
477C22×C13#52511yescharacteristic
478C22×C13C2×#12611yescharacteristic
479C22×C13C2×#12611yescharacteristic
480C22×C13#52911yescharacteristic
481C22×C13#52911yescharacteristic
482C22×C13#53211yescharacteristic
483C22×C13#53711yescharacteristic
484C22×C13#53811yescharacteristic
485C22×C13#53811yescharacteristic
486C22×C13#53811yescharacteristic
487C22×C13#53911yescharacteristic
488C22×C13#53911yescharacteristic
489C22×C13#53911yescharacteristic
490C22×C13#54211yescharacteristic
491C22×C13#54211yescharacteristic
492C22×C13#54611yescharacteristic
493C22×C13#54611yescharacteristic
494C22×C13#54611yescharacteristic
495C22×C13#54811yescharacteristic
496C22×C13#55111yescharacteristic
497C22×C13#55111yescharacteristic
498C22×C13#55111yescharacteristic
499C22×C13#55111yescharacteristic
500C22×C13#55211yescharacteristic
501C22×C13#55211yescharacteristic
502C22×C13#55211yescharacteristic
503C22×C13#55311yescharacteristic
504C22×C13#55311yescharacteristic
505C22×C13#55311yescharacteristic
506C22×C13#55311yescharacteristic
507C22×C13#55311yescharacteristic
508C22×C13#55611yescharacteristic
509C22×C13#55611yescharacteristic
510C22×C13#56011yescharacteristic
511C22×C13#56311yescharacteristic
512C4×C13—24no—
513C4×C13—42no—
514C4×C13—42no—
515C4×C13—42no—
516C4×C13—42no—
517C4×C13—42no—
518C4×C13—81no—
519C4×C13—81no—
520C4×C13—81no—
521C4×C13—81no—
522C4×C13—81no—
523C4×C13—81no—
524C4×C13—81no—
525C4×C13—81no—
526C25C23×C1311yescharacteristic
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—22no—
530C23×C4—22no—
531C23×C4—22no—
532C23×C4—41no—
533C23×C4—41no—
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
546C23×C4C23×C1311yescharacteristic
547C23×C4C23×C1311yescharacteristic
548C2×C4⋊C4—22no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—22no—
553C2×C4⋊C4—41no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4—41no—
557C2×C22⋊C4—22no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—22no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—22no—
565C2×C22⋊C4—22no—
566C2×C22⋊C4—22no—
567C2×C22⋊C4—22no—
568C2×C22⋊C4—22no—
569C2×C22⋊C4—41no—
570C2×C22⋊C4—41no—
571C2×C22⋊C4—41no—
572C2×C22⋊C4—41no—
573C2×C22⋊C4—41no—
574C2×C22⋊C4—41no—
575C2×C42—41no—
576C2×C42—41no—
577C2×C42—41no—
578#95—22no—
579#95—22no—
580#95—22no—
581#95—22no—
582#95—22no—
583#95—22no—
584#95—22no—
585#95—22no—
586#95—22no—
587#95—22no—
588#95—22no—
589#95—22no—
590#95—22no—
591#95—22no—
592#95—41no—
593#95—41no—
594#95—41no—
595#95—41no—
596#95—41no—
597#95—41no—
598#95—41no—
599#95—41no—
600#95—41no—
601#95D4×C1314yes—
602C2×C13—44no—
603C2×C13#248011yescharacteristic
604C2×C13#248111yescharacteristic
605C2×C13#249311yescharacteristic
606C2×C13#249411yescharacteristic
607C2×C13#249411yescharacteristic
608C2×C13#251011yescharacteristic
609C2×C13#255911yescharacteristic
610C2×C13#256011yescharacteristic
611C2×C13#260111yescharacteristic
612C2×C13#269111yescharacteristic
613C2×C13#270211yescharacteristic
614C2×C13#274511yescharacteristic
615C2×C13#274611yescharacteristic
616C2×C13#277811yescharacteristic
617C2×C13#278711yescharacteristic
618C24—21no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—21no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—21no—
628C24—21no—
629C24—21no—
630C24C13×#4112yes—
631C24C13×#4112yes—
632C24C13×#4112yes—
633C24C24×C1311yescharacteristic
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—28no—
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—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—44no—
728C22×C4—44no—
729C22×C4—44no—
730C22×C4—44no—
731C22×C4C2×D4×C1312yes—
732C22×C4C2×D4×C1312yes—
733C22×C4C2×D4×C1312yes—
734C22×C4C13×#4112yes—
735C22×C4C13×#4112yes—
736C22×C4C13×#4112yes—
737C22×C4C13×#4112yes—
738C22×C4C13×#4112yes—
739C4⋊C4—44no—
740C4⋊C4—44no—
741C4⋊C4—44no—
742C22⋊C4—44no—
743C22⋊C4—44no—
744C22⋊C4—44no—
745C22⋊C4—44no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C42—44no—
749C13#1549211yescharacteristic, direct product factor, Sylow
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—22no—
767C23—22no—
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—
782C23—41no—
783C23—41no—
784C23C13×#12614yes—
785C23C22×D4×C1311yescharacteristic
786C23C2×C13×#4111yescharacteristic
787C23C2×C13×#4111yescharacteristic
788C23C2×C13×#4111yescharacteristic
789C23C2×C13×#4111yescharacteristic
790C23C2×C13×#4111yescharacteristic
791C23C2×C13×#4111yescharacteristic
792C23C2×C13×#4111yescharacteristic
793C23C2×C13×#4111yescharacteristic
794C23C13×H(5,𝔽2)11yescharacteristic
795C23C13×H(5,𝔽2)11yescharacteristic
796C23C13×H(5,𝔽2)11yescharacteristic
797C23C13×H(5,𝔽2)11yescharacteristic
798C23C13×2−1+411yescharacteristic
799C23C13×2−1+411yescharacteristic
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—416no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
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—
897C2×C4—41no—
898C2×C4C13×#12614yes—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22C13×#52511yescharacteristic
915C22C2×C13×#12611yescharacteristic
916C22C2×C13×#12611yescharacteristic
917C22C13×#52911yescharacteristic
918C22C13×#52911yescharacteristic
919C22C13×#53211yescharacteristic
920C22C13×#53711yescharacteristic
921C22C13×#53811yescharacteristic
922C22C13×#53811yescharacteristic
923C22C13×#53811yescharacteristic
924C22C13×#53911yescharacteristic
925C22C13×#53911yescharacteristic
926C22C13×#53911yescharacteristic
927C22C13×#54211yescharacteristic
928C22C13×#54211yescharacteristic
929C22C13×#54611yescharacteristic
930C22C13×#54611yescharacteristic
931C22C13×#54611yescharacteristic
932C22C13×#54811yescharacteristic
933C22C13×#55111yescharacteristic
934C22C13×#55111yescharacteristic
935C22C13×#55111yescharacteristic
936C22C13×#55111yescharacteristic
937C22C13×#55211yescharacteristic
938C22C13×#55211yescharacteristic
939C22C13×#55211yescharacteristic
940C22C13×#55311yescharacteristic
941C22C13×#55311yescharacteristic
942C22C13×#55311yescharacteristic
943C22C13×#55311yescharacteristic
944C22C13×#55311yescharacteristic
945C22C13×#55611yescharacteristic
946C22C13×#55611yescharacteristic
947C22C13×#56011yescharacteristic
948C22C13×#56311yescharacteristic
949C4—24no—
950C4—42no—
951C4—42no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—81no—
956C4—81no—
957C4—81no—
958C4—81no—
959C4—81no—
960C4—81no—
961C4—81no—
962C4—81no—
963C2—44no—
964C2C13×#248011yescharacteristic
965C2C13×#248111yescharacteristic
966C2C13×#249311yescharacteristic
967C2C13×#249411yescharacteristic
968C2C13×#249411yescharacteristic
969C2C13×#251011yescharacteristic
970C2C13×#255911yescharacteristic
971C2C13×#256011yescharacteristic
972C2C13×#260111yescharacteristic
973C2C13×#269111yescharacteristic
974C2C13×#270211yescharacteristic
975C2C13×#274511yescharacteristic
976C2C13×#274611yescharacteristic
977C2C13×#277811yescharacteristic
978C2C13×#278711yescharacteristic
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×#401C2semidirect
3. C13×#1443C2semidirect
4. C13×#1443C2semidirect
5. C13×#1442C2semidirect
6. C13×#1442C2semidirect
7. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
129. #15492C13direct (N × H)
261. C2×#401C2×C13semidirect
263. #1443C2×C13semidirect
264. #1443C2×C13semidirect
265. #1442C2×C13semidirect
266. #1442C2×C13semidirect
267. #1441C2×C13semidirect
272. #1436C2×C13semidirect
273. #1436C2×C13semidirect
749. C13#15492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#4012
C2×C13×#3802
C13×#14432
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×C22⋊#952
#1549213