Finite Group Databasebeta

← C13×#14733 #15701072

Subgroups — C13×#14733 #15701072

Order 3328.

2298 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C13C211yesmaximal, characteristic
2C2×C13×#398C211yesmaximal, characteristic, complemented
3C2×C13×#396C211yesmaximal, characteristic, complemented
4C2×C13×#385C211yesmaximal, characteristic, complemented
5C2×C13×#385C211yesmaximal, characteristic, complemented
6C2×C13×#380C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1438C211yesmaximal, characteristic
12C13×#1438C211yesmaximal, characteristic
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C2×C4×D4×C13—24no—
20C2×C4×D4×C13—24no—
21C2×C4×D4×C13—24no—
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C13×C22⋊C4C2211yescharacteristic
34C22×C13×C22⋊C4C2211yescharacteristic
35C22×C13×C22⋊C4C2211yescharacteristic
36C22×C13×C22⋊C4C2211yescharacteristic
37C22×C13×C22⋊C4C2211yescharacteristic
38C22×C13×C22⋊C4C2211yescharacteristic
39C22×C42×C13C2211yescharacteristic
40C13×#398—24no—
41C13×#396—24no—
42C13×#385—24no—
43C13×#385—24no—
44C13×#380—24no—
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
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C25×C13C2311yescharacteristic
60C25×C13C2311yescharacteristic
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13Q814yes—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—22no—
73C23×C4×C13—22no—
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—41no—
78C23×C4×C13—41no—
79C23×C4×C13—41no—
80C23×C4×C13—41no—
81C23×C4×C13D414yes—
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
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C4×D4×C13—232no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—22no—
100C2×C13×C4⋊C4—22no—
101C2×C13×C4⋊C4—22no—
102C2×C13×C4⋊C4—22no—
103C2×C13×C4⋊C4—22no—
104C2×C13×C4⋊C4—22no—
105C2×C13×C4⋊C4—22no—
106C2×C13×C4⋊C4—22no—
107C2×C13×C4⋊C4—22no—
108C2×C13×C4⋊C4—22no—
109C2×C13×C4⋊C4—22no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—41no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4—41no—
115C2×C13×C4⋊C4—41no—
116C2×C13×C4⋊C4D414yes—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—22no—
120C2×C13×C22⋊C4—22no—
121C2×C13×C22⋊C4—22no—
122C2×C13×C22⋊C4—22no—
123C2×C13×C22⋊C4—22no—
124C2×C13×C22⋊C4—22no—
125C2×C13×C22⋊C4—22no—
126C2×C13×C22⋊C4—22no—
127C2×C13×C22⋊C4—22no—
128C2×C13×C22⋊C4—22no—
129C2×C13×C22⋊C4—22no—
130C2×C13×C22⋊C4—22no—
131C2×C13×C22⋊C4—22no—
132C2×C13×C22⋊C4—22no—
133C2×C13×C22⋊C4—22no—
134C2×C13×C22⋊C4—22no—
135C2×C13×C22⋊C4—22no—
136C2×C13×C22⋊C4—22no—
137C2×C13×C22⋊C4—22no—
138C2×C13×C22⋊C4—41no—
139C2×C13×C22⋊C4—41no—
140C2×C13×C22⋊C4—41no—
141C2×C13×C22⋊C4—41no—
142C2×C13×C22⋊C4—41no—
143C2×C13×C22⋊C4—41no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4D414yes—
147C2×C42×C13—22no—
148C2×C42×C13—22no—
149C2×C42×C13—22no—
150C13×#95—22no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—22no—
161C13×#95—41no—
162C13×#95—41no—
163C13×#95D414yescomplemented
164#14733C1311yesmaximal, characteristic, direct product factor, Sylow
165C24×C13—21no—
166C24×C13—21no—
167C24×C13—21no—
168C24×C13—21no—
169C24×C13—21no—
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13C2×D412yes—
190C24×C13C2×D412yes—
191C24×C13C2×Q812yes—
192C24×C13C2×Q812yes—
193C24×C13#4112yes—
194C24×C13#4112yes—
195C24×C13C2411yescharacteristic
196C2×D4×C13—28no—
197C2×D4×C13—28no—
198C2×D4×C13—28no—
199C2×D4×C13—28no—
200C2×D4×C13—28no—
201C2×D4×C13—28no—
202C2×D4×C13—28no—
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—28no—
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—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—28no—
253C22×C4×C13—28no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—44no—
283C22×C4×C13—44no—
284C22×C4×C13—44no—
285C22×C4×C13—44no—
286C22×C4×C13—44no—
287C22×C4×C13—44no—
288C22×C4×C13—44no—
289C22×C4×C13—44no—
290C22×C4×C13—44no—
291C22×C4×C13—44no—
292C22×C4×C13—44no—
293C22×C4×C13C2×D412yes—
294C22×C4×C13C2×D412yes—
295C22×C4×C13C2×D412yes—
296C22×C4×C13C2×D412yes—
297C22×C4×C13C2×D412yes—
298C22×C4×C13C2×D412yes—
299C22×C4×C13C2×D412yes—
300C22×C4×C13C2×D412yes—
301C22×C4×C13C2×D412yes—
302C22×C4×C13C2×D412yes—
303C22×C4×C13C2×Q812yes—
304C22×C4×C13#4112yes—
305C22×C4×C13#4112yes—
306C22×C4×C13#4112yes—
307C22×C4×C13#4112yes—
308C13×C4⋊C4—28no—
309C13×C4⋊C4—44no—
310C13×C4⋊C4—44no—
311C13×C4⋊C4—44no—
312C13×C4⋊C4—44no—
313C13×C4⋊C4—44no—
314C13×C4⋊C4—44no—
315C13×C22⋊C4—28no—
316C13×C22⋊C4—28no—
317C13×C22⋊C4—28no—
318C13×C22⋊C4—28no—
319C13×C22⋊C4—44no—
320C13×C22⋊C4—44no—
321C13×C22⋊C4—44no—
322C13×C22⋊C4—44no—
323C13×C22⋊C4—44no—
324C13×C22⋊C4—44no—
325C42×C13—28no—
326C22×C4×D4C2×C1311yescharacteristic
327C2×#398C2×C1311yescharacteristic, complemented
328C2×#396C2×C1311yescharacteristic, complemented
329C2×#385C2×C1311yescharacteristic, complemented
330C2×#385C2×C1311yescharacteristic, complemented
331C2×#380C2×C1311yescharacteristic, complemented
332#1441C2×C1311yescharacteristic, complemented
333#1439C2×C1311yescharacteristic, complemented
334#1439C2×C1311yescharacteristic, complemented
335#1439C2×C1311yescharacteristic, complemented
336#1438C2×C1311yescharacteristic
337#1438C2×C1311yescharacteristic
338#1436C2×C1311yescharacteristic, complemented
339#1436C2×C1311yescharacteristic, complemented
340C22⋊#95C2×C1311yescharacteristic, complemented
341C23×C13—22no—
342C23×C13—22no—
343C23×C13—22no—
344C23×C13—22no—
345C23×C13—22no—
346C23×C13—22no—
347C23×C13—22no—
348C23×C13—22no—
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
355C23×C13—22no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—22no—
375C23×C13—22no—
376C23×C13—22no—
377C23×C13—41no—
378C23×C13—41no—
379C23×C13—41no—
380C23×C13—41no—
381C23×C13—41no—
382C23×C13—41no—
383C23×C13—41no—
384C23×C13—41no—
385C23×C13—41no—
386C23×C13—41no—
387C23×C13—41no—
388C23×C13—41no—
389C23×C13—41no—
390C23×C13—41no—
391C23×C13—41no—
392C23×C13—41no—
393C23×C13—41no—
394C23×C13—41no—
395C23×C13—41no—
396C23×C13—41no—
397C23×C13—41no—
398C23×C13—41no—
399C23×C13—41no—
400C23×C13—41no—
401C23×C13—41no—
402C23×C13—41no—
403C23×C13—41no—
404C23×C13—41no—
405C23×C13—41no—
406C23×C13—41no—
407C23×C13—41no—
408C23×C13—41no—
409C23×C13C22⋊Q814yes—
410C23×C13C22⋊Q814yes—
411C23×C13C22×D411yescharacteristic
412C23×C13C22×D411yescharacteristic
413C23×C13C22×D411yescharacteristic
414C23×C13C22×D411yescharacteristic
415C23×C13C22×Q811yescharacteristic
416C23×C13C2×#4111yescharacteristic
417C23×C13C2×#4111yescharacteristic
418C23×C13C2×#4111yescharacteristic
419C23×C13C2×#4111yescharacteristic
420C23×C13C2×#4111yescharacteristic
421C23×C13C2×#4111yescharacteristic
422C23×C13H(5,𝔽2)11yescharacteristic
423C23×C13H(5,𝔽2)11yescharacteristic
424C23×C13H(5,𝔽2)11yescharacteristic
425C23×C132−1+411yescharacteristic
426D4×C13—232no—
427C2×C4×C13—22no—
428C2×C4×C13—22no—
429C2×C4×C13—22no—
430C2×C4×C13—22no—
431C2×C4×C13—22no—
432C2×C4×C13—22no—
433C2×C4×C13—22no—
434C2×C4×C13—22no—
435C2×C4×C13—22no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—22no—
457C2×C4×C13—22no—
458C2×C4×C13—22no—
459C2×C4×C13—22no—
460C2×C4×C13—22no—
461C2×C4×C13—22no—
462C2×C4×C13—22no—
463C2×C4×C13—416no—
464C2×C4×C13—416no—
465C2×C4×C13—41no—
466C2×C4×C13—41no—
467C2×C4×C13—41no—
468C2×C4×C13—41no—
469C2×C4×C13—41no—
470C2×C4×C13—41no—
471C2×C4×C13—41no—
472C2×C4×C13—41no—
473C2×C4×C13—41no—
474C2×C4×C13—41no—
475C2×C4×C13—41no—
476C2×C4×C13—41no—
477C2×C4×C13—41no—
478C2×C4×C13—41no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13—41no—
492C2×C4×C13—41no—
493C2×C4×C13—41no—
494C2×C4×C13—41no—
495C2×C4×C13—41no—
496C2×C4×C13—41no—
497C2×C4×C13—41no—
498C2×C4×C13—41no—
499C2×C4×C13—41no—
500C2×C4×C13—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C2×C4×C13—41no—
504C2×C4×C13—41no—
505C2×C4×C13—41no—
506C2×C4×C13—41no—
507C2×C4×C13—41no—
508C2×C4×C13—41no—
509C2×C4×C13—41no—
510C2×C4×C13—41no—
511C2×C4×C13—41no—
512C2×C4×C13—41no—
513C2×C4×C13—41no—
514C2×C4×C13—41no—
515C2×C4×C13—41no—
516C2×C4×C13—41no—
517C2×C4×C13#12014yes—
518C2×C4×C13#12114yes—
519C2×C4×C13C22⋊Q814yes—
520C23×D4C22×C1311yescharacteristic
521C24×C4C22×C1311yescharacteristic
522C24×C4C22×C1311yescharacteristic
523C2×C4×D4—24no—
524C2×C4×D4—24no—
525C2×C4×D4—24no—
526C22×C4⋊C4C22×C1311yescharacteristic
527C22×C4⋊C4C22×C1311yescharacteristic
528C22×C4⋊C4C22×C1311yescharacteristic
529C22×C4⋊C4C22×C1311yescharacteristic
530C22×C4⋊C4C22×C1311yescharacteristic
531C22×C4⋊C4C22×C1311yescharacteristic
532C22×C4⋊C4C22×C1311yescharacteristic
533C22×C22⋊C4C22×C1311yescharacteristic
534C22×C22⋊C4C22×C1311yescharacteristic
535C22×C22⋊C4C22×C1311yescharacteristic
536C22×C22⋊C4C22×C1311yescharacteristic
537C22×C22⋊C4C22×C1311yescharacteristic
538C22×C22⋊C4C22×C1311yescharacteristic
539C22×C22⋊C4C22×C1311yescharacteristic
540C22×C22⋊C4C22×C1311yescharacteristic
541C22×C22⋊C4C22×C1311yescharacteristic
542C22×C22⋊C4C22×C1311yescharacteristic
543C22×C42C22×C1311yescharacteristic
544#398—24no—
545#396—24no—
546#385—24no—
547#385—24no—
548#380—24no—
549C2×#95C22×C1311yescharacteristic
550C2×#95C22×C1311yescharacteristic
551C2×#95C22×C1311yescharacteristic
552C2×#95C22×C1311yescharacteristic
553C2×#95C22×C1311yescharacteristic
554C2×#95C22×C1311yescharacteristic
555C2×#95C22×C1311yescharacteristic
556C2×#95C22×C1311yescharacteristic
557C2×#95C22×C1311yescharacteristic
558C2×#95C22×C1311yescharacteristic
559C2×#95C22×C1311yescharacteristic
560C2×#95C22×C1311yescharacteristic
561C2×#95C22×C1311yescharacteristic
562C2×#95C22×C1311yescharacteristic
563C22×C13—24no—
564C22×C13—24no—
565C22×C13—24no—
566C22×C13—24no—
567C22×C13—24no—
568C22×C13—24no—
569C22×C13—42no—
570C22×C13—42no—
571C22×C13—42no—
572C22×C13—42no—
573C22×C13—42no—
574C22×C13—42no—
575C22×C13—42no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—42no—
585C22×C13—42no—
586C22×C13—42no—
587C22×C13—42no—
588C22×C13—42no—
589C22×C13—42no—
590C22×C13—42no—
591C22×C13—42no—
592C22×C13—42no—
593C22×C13C2×#12011yescharacteristic
594C22×C13C2×#12111yescharacteristic
595C22×C13C2×C22⋊Q811yescharacteristic
596C22×C13C2×C22⋊Q811yescharacteristic
597C22×C13C2×C22⋊Q811yescharacteristic
598C22×C13#52511yescharacteristic
599C22×C13#52511yescharacteristic
600C22×C13#52511yescharacteristic
601C22×C13#52511yescharacteristic
602C22×C13#52511yescharacteristic
603C22×C13#52911yescharacteristic
604C22×C13#52911yescharacteristic
605C22×C13#53211yescharacteristic
606C22×C13#53411yescharacteristic
607C22×C13#53711yescharacteristic
608C22×C13#53811yescharacteristic
609C22×C13#53911yescharacteristic
610C22×C13#54011yescharacteristic
611C22×C13#54211yescharacteristic
612C22×C13D4211yescharacteristic
613C22×C13D4211yescharacteristic
614C22×C13#54611yescharacteristic
615C22×C13#54611yescharacteristic
616C22×C13#54611yescharacteristic
617C22×C13#54611yescharacteristic
618C22×C13#54711yescharacteristic
619C22×C13#54811yescharacteristic
620C22×C13D4×Q811yescharacteristic
621C22×C13#55011yescharacteristic
622C22×C13#55211yescharacteristic
623C22×C13#55311yescharacteristic
624C22×C13#55311yescharacteristic
625C22×C13#55411yescharacteristic
626C22×C13#55411yescharacteristic
627C22×C13#55411yescharacteristic
628C4×C13—24no—
629C4×C13—24no—
630C4×C13—24no—
631C4×C13—42no—
632C4×C13—42no—
633C4×C13—42no—
634C4×C13—42no—
635C4×C13—42no—
636C4×C13—42no—
637C4×C13—81no—
638C4×C13—81no—
639C4×C13—81no—
640C4×C13—81no—
641C25C23×C1311yescharacteristic
642C25C23×C1311yescharacteristic
643C22×D4—22no—
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4Q8×C1314yes—
650C23×C4—22no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4—41no—
662C23×C4—41no—
663C23×C4D4×C1314yes—
664C23×C4C23×C1311yescharacteristic
665C23×C4C23×C1311yescharacteristic
666C23×C4C23×C1311yescharacteristic
667C23×C4C23×C1311yescharacteristic
668C23×C4C23×C1311yescharacteristic
669C23×C4C23×C1311yescharacteristic
670C23×C4C23×C1311yescharacteristic
671C23×C4C23×C1311yescharacteristic
672C23×C4C23×C1311yescharacteristic
673C23×C4C23×C1311yescharacteristic
674C23×C4C23×C1311yescharacteristic
675C23×C4C23×C1311yescharacteristic
676C23×C4C23×C1311yescharacteristic
677C4×D4—232no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—22no—
684C2×C4⋊C4—22no—
685C2×C4⋊C4—22no—
686C2×C4⋊C4—22no—
687C2×C4⋊C4—22no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4—41no—
696C2×C4⋊C4—41no—
697C2×C4⋊C4—41no—
698C2×C4⋊C4D4×C1314yes—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—22no—
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—41no—
721C2×C22⋊C4—41no—
722C2×C22⋊C4—41no—
723C2×C22⋊C4—41no—
724C2×C22⋊C4—41no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4D4×C1314yes—
729C2×C42—22no—
730C2×C42—22no—
731C2×C42—22no—
732#95—22no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95D4×C1314yescomplemented
746C2×C13—44no—
747C2×C13—44no—
748C2×C13#239211yescharacteristic
749C2×C13#240711yescharacteristic
750C2×C13#241011yescharacteristic
751C2×C13#241711yescharacteristic
752C2×C13#244911yescharacteristic
753C2×C13#245011yescharacteristic
754C2×C13#245211yescharacteristic
755C2×C13#245411yescharacteristic
756C2×C13#245611yescharacteristic
757C2×C13#246011yescharacteristic
758C2×C13#246411yescharacteristic
759C2×C13#246811yescharacteristic
760C2×C13#257911yescharacteristic
761C2×C13#263011yescharacteristic
762C2×C13#284811yescharacteristic
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24—21no—
774C24—21no—
775C24—21no—
776C24—21no—
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24C2×D4×C1312yes—
788C24C2×D4×C1312yes—
789C24C2×Q8×C1312yes—
790C24C2×Q8×C1312yes—
791C24C13×#4112yes—
792C24C13×#4112yes—
793C24C24×C1311yescharacteristic
794C2×D4—28no—
795C2×D4—28no—
796C2×D4—28no—
797C2×D4—28no—
798C2×D4—28no—
799C2×D4—28no—
800C2×D4—28no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—28no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—28no—
851C22×C4—28no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4—44no—
884C22×C4—44no—
885C22×C4—44no—
886C22×C4—44no—
887C22×C4—44no—
888C22×C4—44no—
889C22×C4—44no—
890C22×C4—44no—
891C22×C4C2×D4×C1312yes—
892C22×C4C2×D4×C1312yes—
893C22×C4C2×D4×C1312yes—
894C22×C4C2×D4×C1312yes—
895C22×C4C2×D4×C1312yes—
896C22×C4C2×D4×C1312yes—
897C22×C4C2×D4×C1312yes—
898C22×C4C2×D4×C1312yes—
899C22×C4C2×D4×C1312yes—
900C22×C4C2×D4×C1312yes—
901C22×C4C2×Q8×C1312yes—
902C22×C4C13×#4112yes—
903C22×C4C13×#4112yes—
904C22×C4C13×#4112yes—
905C22×C4C13×#4112yes—
906C4⋊C4—28no—
907C4⋊C4—44no—
908C4⋊C4—44no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C4⋊C4—44no—
913C22⋊C4—28no—
914C22⋊C4—28no—
915C22⋊C4—28no—
916C22⋊C4—28no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C42—28no—
924C13#1473311yescharacteristic, direct product factor, Sylow
925C23—22no—
926C23—22no—
927C23—22no—
928C23—22no—
929C23—22no—
930C23—22no—
931C23—22no—
932C23—22no—
933C23—22no—
934C23—22no—
935C23—22no—
936C23—22no—
937C23—22no—
938C23—22no—
939C23—22no—
940C23—22no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23C13×C22⋊Q814yes—
994C23C13×C22⋊Q814yes—
995C23C22×D4×C1311yescharacteristic
996C23C22×D4×C1311yescharacteristic
997C23C22×D4×C1311yescharacteristic
998C23C22×D4×C1311yescharacteristic
999C23C22×Q8×C1311yescharacteristic
1000C23C2×C13×#4111yescharacteristic
1001C23C2×C13×#4111yescharacteristic
1002C23C2×C13×#4111yescharacteristic
1003C23C2×C13×#4111yescharacteristic
1004C23C2×C13×#4111yescharacteristic
1005C23C2×C13×#4111yescharacteristic
1006C23C13×H(5,𝔽2)11yescharacteristic
1007C23C13×H(5,𝔽2)11yescharacteristic
1008C23C13×H(5,𝔽2)11yescharacteristic
1009C23C13×2−1+411yescharacteristic
1010D4—232no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—416no—
1048C2×C4—416no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4C13×#12014yes—
1102C2×C4C13×#12114yes—
1103C2×C4C13×C22⋊Q814yes—
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—24no—
1108C22—24no—
1109C22—24no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—42no—
1115C22—42no—
1116C22—42no—
1117C22—42no—
1118C22—42no—
1119C22—42no—
1120C22—42no—
1121C22—42no—
1122C22—42no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22C2×C13×#12011yescharacteristic
1135C22C2×C13×#12111yescharacteristic
1136C22C2×C13×C22⋊Q811yescharacteristic
1137C22C2×C13×C22⋊Q811yescharacteristic
1138C22C2×C13×C22⋊Q811yescharacteristic
1139C22C13×#52511yescharacteristic
1140C22C13×#52511yescharacteristic
1141C22C13×#52511yescharacteristic
1142C22C13×#52511yescharacteristic
1143C22C13×#52511yescharacteristic
1144C22C13×#52911yescharacteristic
1145C22C13×#52911yescharacteristic
1146C22C13×#53211yescharacteristic
1147C22C13×#53411yescharacteristic
1148C22C13×#53711yescharacteristic
1149C22C13×#53811yescharacteristic
1150C22C13×#53911yescharacteristic
1151C22C13×#54011yescharacteristic
1152C22C13×#54211yescharacteristic
1153C22D42×C1311yescharacteristic
1154C22D42×C1311yescharacteristic
1155C22C13×#54611yescharacteristic
1156C22C13×#54611yescharacteristic
1157C22C13×#54611yescharacteristic
1158C22C13×#54611yescharacteristic
1159C22C13×#54711yescharacteristic
1160C22C13×#54811yescharacteristic
1161C22D4×Q8×C1311yescharacteristic
1162C22C13×#55011yescharacteristic
1163C22C13×#55211yescharacteristic
1164C22C13×#55311yescharacteristic
1165C22C13×#55311yescharacteristic
1166C22C13×#55411yescharacteristic
1167C22C13×#55411yescharacteristic
1168C22C13×#55411yescharacteristic
1169C4—24no—
1170C4—24no—
1171C4—24no—
1172C4—42no—
1173C4—42no—
1174C4—42no—
1175C4—42no—
1176C4—42no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C2—44no—
1183C2—44no—
1184C2C13×#239211yescharacteristic
1185C2C13×#240711yescharacteristic
1186C2C13×#241011yescharacteristic
1187C2C13×#241711yescharacteristic
1188C2C13×#244911yescharacteristic
1189C2C13×#245011yescharacteristic
1190C2C13×#245211yescharacteristic
1191C2C13×#245411yescharacteristic
1192C2C13×#245611yescharacteristic
1193C2C13×#246011yescharacteristic
1194C2C13×#246411yescharacteristic
1195C2C13×#246811yescharacteristic
1196C2C13×#257911yescharacteristic
1197C2C13×#263011yescharacteristic
1198C2C13×#284811yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C13×#398C2semidirect
3. C2×C13×#396C2semidirect
4. C2×C13×#385C2semidirect
5. C2×C13×#385C2semidirect
6. C2×C13×#380C2semidirect
7. C13×#1441C2semidirect
8. C13×#1439C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
15. C13×C22⋊#95C2semidirect
163. C13×#95D4semidirect
164. #14733C13direct (N × H)
327. C2×#398C2×C13semidirect
328. C2×#396C2×C13semidirect
329. C2×#385C2×C13semidirect
330. C2×#385C2×C13semidirect
331. C2×#380C2×C13semidirect
332. #1441C2×C13semidirect
333. #1439C2×C13semidirect
334. #1439C2×C13semidirect
335. #1439C2×C13semidirect
338. #1436C2×C13semidirect
339. #1436C2×C13semidirect
340. C22⋊#95C2×C13semidirect
745. #95D4×C13semidirect
924. C13#14733direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D4×C132
C2×C13×#3982
C2×C13×#3962
C2×C13×#3852
C2×C13×#3802
C13×#14412
C13×#14392
C13×#14382
C13×#14362
C13×C22⋊#952
#1473313