Finite Group Databasebeta

← C13×#14768 #15701107

Subgroups — C13×#14768 #15701107

Order 3328.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1018 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#393C211yesmaximal, characteristic
2C2×C13×#391C211yesmaximal, characteristic, complemented
3C2×C13×#381C211yesmaximal, characteristic
4C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
5C13×#1446C211yesmaximal, characteristic, complemented
6C13×#1445C211yesmaximal, characteristic, complemented
7C13×#1443C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1439C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C13×#393—24no—
30C13×#391—24no—
31C13×#381—24no—
32C4×C13×C22⋊C4—24no—
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
56C22×Q8×C13—22no—
57C22×Q8×C13—22no—
58C22×Q8×C13—22no—
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—41no—
62C22×Q8×C13—41no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—41no—
68C23×C4×C13—41no—
69C23×C4×C13Q814yescomplemented
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—41no—
90C2×C13×C4⋊C4—41no—
91C2×C13×C4⋊C4—41no—
92C2×C13×C4⋊C4—41no—
93C2×C13×C22⋊C4—22no—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—41no—
107C2×C13×C22⋊C4—41no—
108C2×C13×C22⋊C4—41no—
109C2×C13×C22⋊C4—41no—
110C2×C13×C22⋊C4D414yes—
111C2×C42×C13—22no—
112C2×C42×C13—22no—
113C2×C42×C13—22no—
114C2×C42×C13—22no—
115C2×C42×C13—41no—
116C2×C42×C13—41no—
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—22no—
131C13×#95—22no—
132C13×#95—22no—
133C13×#95—22no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95D414yes—
139#14768C1311yesmaximal, 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×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13C2×D412yes—
153C24×C13C2×Q812yes—
154C24×C13#4112yes—
155C24×C13C2411yescharacteristic
156C2×Q8×C13—28no—
157C2×Q8×C13—44no—
158C2×Q8×C13—44no—
159C2×Q8×C13—44no—
160C2×Q8×C13—44no—
161C2×Q8×C13—44no—
162C2×Q8×C13—44no—
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—28no—
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—28no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—44no—
250C22×C4×C13—44no—
251C22×C4×C13—44no—
252C22×C4×C13—44no—
253C22×C4×C13—44no—
254C22×C4×C13C2×D412yes—
255C22×C4×C13C2×D412yes—
256C22×C4×C13C2×D412yes—
257C22×C4×C13C2×D412yes—
258C22×C4×C13C2×D412yes—
259C22×C4×C13C2×Q812yes—
260C22×C4×C13C2×Q812yes—
261C22×C4×C13#4112yes—
262C22×C4×C13#4112yes—
263C22×C4×C13#4112yes—
264C22×C4×C13#4112yes—
265C22×C4×C13#4112yes—
266C22×C4×C13#4112yes—
267C22×C4×C13#4112yes—
268C13×C4⋊C4—44no—
269C13×C4⋊C4—44no—
270C13×C4⋊C4—44no—
271C13×C22⋊C4—28no—
272C13×C22⋊C4—28no—
273C13×C22⋊C4—44no—
274C13×C22⋊C4—44no—
275C13×C22⋊C4—44no—
276C13×C22⋊C4—44no—
277C42×C13—44no—
278C42×C13—44no—
279C2×#393C2×C1311yescharacteristic
280C2×#391C2×C1311yescharacteristic, complemented
281C2×#381C2×C1311yescharacteristic
282C2×C4×C22⋊C4C2×C1311yescharacteristic
283#1446C2×C1311yescharacteristic, complemented
284#1445C2×C1311yescharacteristic, complemented
285#1443C2×C1311yescharacteristic, complemented
286#1441C2×C1311yescharacteristic, complemented
287#1439C2×C1311yescharacteristic
288#1439C2×C1311yescharacteristic
289#1439C2×C1311yescharacteristic
290#1436C2×C1311yescharacteristic, complemented
291#1436C2×C1311yescharacteristic, complemented
292#1434C2×C1311yescharacteristic, complemented
293C22⋊#95C2×C1311yescharacteristic
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
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—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13C22⋊Q814yes—
329C23×C13C22×D411yescharacteristic
330C23×C13C22×D411yescharacteristic
331C23×C13C22×Q811yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C13H(5,𝔽2)11yescharacteristic
342C23×C13H(5,𝔽2)11yescharacteristic
343C23×C132−1+411yescharacteristic
344Q8×C13—416no—
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—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—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—416no—
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×C13C22⋊Q814yes—
443C2×C4×C13#12314yes—
444C23×Q8C22×C1311yescharacteristic
445C24×C4C22×C1311yescharacteristic
446C22×C4⋊C4C22×C1311yescharacteristic
447C22×C4⋊C4C22×C1311yescharacteristic
448C22×C4⋊C4C22×C1311yescharacteristic
449C22×C22⋊C4C22×C1311yescharacteristic
450C22×C22⋊C4C22×C1311yescharacteristic
451C22×C22⋊C4C22×C1311yescharacteristic
452C22×C22⋊C4C22×C1311yescharacteristic
453C22×C22⋊C4C22×C1311yescharacteristic
454C22×C22⋊C4C22×C1311yescharacteristic
455C22×C42C22×C1311yescharacteristic
456C22×C42C22×C1311yescharacteristic
457#393—24no—
458#391—24no—
459#381—24no—
460C4×C22⋊C4—24no—
461C2×#95C22×C1311yescharacteristic
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
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
483C22×C13—24no—
484C22×C13—24no—
485C22×C13—24no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13C2×C22⋊Q811yescharacteristic
499C22×C13C2×C22⋊Q811yescharacteristic
500C22×C13C2×#12311yescharacteristic
501C22×C13#52511yescharacteristic
502C22×C13#52511yescharacteristic
503C22×C13#52911yescharacteristic
504C22×C13#52911yescharacteristic
505C22×C13#52911yescharacteristic
506C22×C13#52911yescharacteristic
507C22×C13#53211yescharacteristic
508C22×C13#53311yescharacteristic
509C22×C13#53311yescharacteristic
510C22×C13#53311yescharacteristic
511C22×C13#53811yescharacteristic
512C22×C13#53811yescharacteristic
513C22×C13#54211yescharacteristic
514C22×C13#54211yescharacteristic
515C22×C13#54311yescharacteristic
516C22×C13#54411yescharacteristic
517C22×C13D4211yescharacteristic
518C22×C13#54611yescharacteristic
519C22×C13#54611yescharacteristic
520C22×C13#54611yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54711yescharacteristic
523C22×C13#54811yescharacteristic
524C22×C13#55111yescharacteristic
525C22×C13#55111yescharacteristic
526C22×C13#55111yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55211yescharacteristic
529C22×C13#55511yescharacteristic
530C22×C13#55611yescharacteristic
531C22×C13#55911yescharacteristic
532C22×C13#55911yescharacteristic
533C4×C13—24no—
534C4×C13—24no—
535C4×C13—42no—
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543C4×C13—81no—
544C4×C13—81no—
545C4×C13—81no—
546C4×C13—81no—
547C25C23×C1311yescharacteristic
548C22×Q8—22no—
549C22×Q8—22no—
550C22×Q8—22no—
551C22×Q8—22no—
552C22×Q8—22no—
553C22×Q8—41no—
554C22×Q8—41no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—41no—
560C23×C4—41no—
561C23×C4Q8×C1314yescomplemented
562C23×C4C23×C1311yescharacteristic
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1311yescharacteristic
565C23×C4C23×C1311yescharacteristic
566C23×C4C23×C1311yescharacteristic
567C23×C4C23×C1311yescharacteristic
568C23×C4C23×C1311yescharacteristic
569C23×C4C23×C1311yescharacteristic
570C23×C4C23×C1311yescharacteristic
571C23×C4C23×C1311yescharacteristic
572C23×C4C23×C1311yescharacteristic
573C23×C4C23×C1311yescharacteristic
574C23×C4C23×C1311yescharacteristic
575C23×C4C23×C1311yescharacteristic
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—41no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4—41no—
600C2×C22⋊C4—41no—
601C2×C22⋊C4—41no—
602C2×C22⋊C4D4×C1314yes—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—41no—
608C2×C42—41no—
609#95—22no—
610#95—22no—
611#95—22no—
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—41no—
627#95—41no—
628#95—41no—
629#95—41no—
630#95D4×C1314yes—
631C2×C13—44no—
632C2×C13#239611yescharacteristic
633C2×C13#241811yescharacteristic
634C2×C13#243711yescharacteristic
635C2×C13#243811yescharacteristic
636C2×C13#243911yescharacteristic
637C2×C13#244711yescharacteristic
638C2×C13#245811yescharacteristic
639C2×C13#245911yescharacteristic
640C2×C13#246111yescharacteristic
641C2×C13#252711yescharacteristic
642C2×C13#255711yescharacteristic
643C2×C13#257211yescharacteristic
644C2×C13#260711yescharacteristic
645C2×C13#266511yescharacteristic
646C2×C13#285511yescharacteristic
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24C2×D4×C1312yes—
660C24C2×Q8×C1312yes—
661C24C13×#4112yes—
662C24C24×C1311yescharacteristic
663C2×Q8—28no—
664C2×Q8—44no—
665C2×Q8—44no—
666C2×Q8—44no—
667C2×Q8—44no—
668C2×Q8—44no—
669C2×Q8—44no—
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—28no—
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—28no—
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—44no—
757C22×C4—44no—
758C22×C4—44no—
759C22×C4—44no—
760C22×C4—44no—
761C22×C4C2×D4×C1312yes—
762C22×C4C2×D4×C1312yes—
763C22×C4C2×D4×C1312yes—
764C22×C4C2×D4×C1312yes—
765C22×C4C2×D4×C1312yes—
766C22×C4C2×Q8×C1312yes—
767C22×C4C2×Q8×C1312yes—
768C22×C4C13×#4112yes—
769C22×C4C13×#4112yes—
770C22×C4C13×#4112yes—
771C22×C4C13×#4112yes—
772C22×C4C13×#4112yes—
773C22×C4C13×#4112yes—
774C22×C4C13×#4112yes—
775C4⋊C4—44no—
776C4⋊C4—44no—
777C4⋊C4—44no—
778C22⋊C4—28no—
779C22⋊C4—28no—
780C22⋊C4—44no—
781C22⋊C4—44no—
782C22⋊C4—44no—
783C22⋊C4—44no—
784C42—44no—
785C42—44no—
786C13#1476811yescharacteristic, direct product factor, Sylow
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23C13×C22⋊Q814yes—
822C23C22×D4×C1311yescharacteristic
823C23C22×D4×C1311yescharacteristic
824C23C22×Q8×C1311yescharacteristic
825C23C2×C13×#4111yescharacteristic
826C23C2×C13×#4111yescharacteristic
827C23C2×C13×#4111yescharacteristic
828C23C2×C13×#4111yescharacteristic
829C23C2×C13×#4111yescharacteristic
830C23C2×C13×#4111yescharacteristic
831C23C2×C13×#4111yescharacteristic
832C23C2×C13×#4111yescharacteristic
833C23C13×H(5,𝔽2)11yescharacteristic
834C23C13×H(5,𝔽2)11yescharacteristic
835C23C13×H(5,𝔽2)11yescharacteristic
836C23C13×2−1+411yescharacteristic
837Q8—416no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
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—416no—
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—
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×C4C13×C22⋊Q814yes—
936C2×C4C13×#12314yes—
937C22—24no—
938C22—24no—
939C22—24no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22C2×C13×C22⋊Q811yescharacteristic
953C22C2×C13×C22⋊Q811yescharacteristic
954C22C2×C13×#12311yescharacteristic
955C22C13×#52511yescharacteristic
956C22C13×#52511yescharacteristic
957C22C13×#52911yescharacteristic
958C22C13×#52911yescharacteristic
959C22C13×#52911yescharacteristic
960C22C13×#52911yescharacteristic
961C22C13×#53211yescharacteristic
962C22C13×#53311yescharacteristic
963C22C13×#53311yescharacteristic
964C22C13×#53311yescharacteristic
965C22C13×#53811yescharacteristic
966C22C13×#53811yescharacteristic
967C22C13×#54211yescharacteristic
968C22C13×#54211yescharacteristic
969C22C13×#54311yescharacteristic
970C22C13×#54411yescharacteristic
971C22D42×C1311yescharacteristic
972C22C13×#54611yescharacteristic
973C22C13×#54611yescharacteristic
974C22C13×#54611yescharacteristic
975C22C13×#54611yescharacteristic
976C22C13×#54711yescharacteristic
977C22C13×#54811yescharacteristic
978C22C13×#55111yescharacteristic
979C22C13×#55111yescharacteristic
980C22C13×#55111yescharacteristic
981C22C13×#55111yescharacteristic
982C22C13×#55211yescharacteristic
983C22C13×#55511yescharacteristic
984C22C13×#55611yescharacteristic
985C22C13×#55911yescharacteristic
986C22C13×#55911yescharacteristic
987C4—24no—
988C4—24no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—42no—
996C4—42no—
997C4—81no—
998C4—81no—
999C4—81no—
1000C4—81no—
1001C2—44no—
1002C2C13×#239611yescharacteristic
1003C2C13×#241811yescharacteristic
1004C2C13×#243711yescharacteristic
1005C2C13×#243811yescharacteristic
1006C2C13×#243911yescharacteristic
1007C2C13×#244711yescharacteristic
1008C2C13×#245811yescharacteristic
1009C2C13×#245911yescharacteristic
1010C2C13×#246111yescharacteristic
1011C2C13×#252711yescharacteristic
1012C2C13×#255711yescharacteristic
1013C2C13×#257211yescharacteristic
1014C2C13×#260711yescharacteristic
1015C2C13×#266511yescharacteristic
1016C2C13×#285511yescharacteristic
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
2. C2×C13×#391C2semidirect
5. C13×#1446C2semidirect
6. C13×#1445C2semidirect
7. C13×#1443C2semidirect
8. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1434C2semidirect
69. C23×C4×C13Q8semidirect
139. #14768C13direct (N × H)
280. C2×#391C2×C13semidirect
283. #1446C2×C13semidirect
284. #1445C2×C13semidirect
285. #1443C2×C13semidirect
286. #1441C2×C13semidirect
290. #1436C2×C13semidirect
291. #1436C2×C13semidirect
292. #1434C2×C13semidirect
561. C23×C4Q8×C13semidirect
786. C13#14768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3932
C2×C13×#3912
C2×C13×#3812
C2×C4×C13×C22⋊C42
C13×#14462
C13×#14452
C13×#14432
C13×#14412
C13×#14392
C13×#14362
C13×#14342
C13×C22⋊#952
#1476813