Finite Group Databasebeta

← C13×#15323 #15701662

Subgroups — C13×#15323 #15701662

Order 3328.

2258 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C13×#393C211yesmaximal, characteristic, complemented
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#386C211yesmaximal, characteristic
5C2×C13×#385C211yesmaximal, characteristic, complemented
6C2×C13×#380C211yesmaximal, characteristic, complemented
7C13×#1446C211yesmaximal, characteristic, complemented
8C13×#1445C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1441C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1439C211yesmaximal, characteristic, complemented
14C13×#1438C211yesmaximal, characteristic
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C2×C13×C22⋊Q8—24no—
21C2×C13×C22⋊Q8—24no—
22C2×C13×C22⋊Q8—24no—
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C22⋊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
38C13×#393—24no—
39C13×#386—24no—
40C13×#386—24no—
41C13×#385—24no—
42C13×#380—24no—
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
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C25×C13C2311yescharacteristic
60C25×C13C2311yescharacteristic
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—41no—
67C22×Q8×C13—41no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—41no—
73C22×D4×C13—41no—
74C22×D4×C13Q814yescomplemented
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—22no—
78C23×C4×C13—22no—
79C23×C4×C13—22no—
80C23×C4×C13—22no—
81C23×C4×C13—22no—
82C23×C4×C13—22no—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—41no—
86C23×C4×C13—41no—
87C23×C4×C13—41no—
88C23×C4×C13—41no—
89C23×C4×C13C2311yescharacteristic
90C23×C4×C13C2311yescharacteristic
91C23×C4×C13C2311yescharacteristic
92C23×C4×C13C2311yescharacteristic
93C23×C4×C13C2311yescharacteristic
94C23×C4×C13C2311yescharacteristic
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C13×C22⋊Q8—232no—
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—22no—
113C2×C13×C4⋊C4—41no—
114C2×C13×C4⋊C4—41no—
115C2×C13×C4⋊C4—41no—
116C2×C13×C4⋊C4D414yescomplemented
117C2×C13×C4⋊C4D414yescomplemented
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×C13×C22⋊C4D414yes—
148C13×#95—22no—
149C13×#95—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—41no—
160C13×#95—41no—
161C13×#95—41no—
162C13×#95—41no—
163C13×#95—41no—
164#15323C1311yesmaximal, 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×Q8×C13—28no—
197C2×Q8×C13—44no—
198C2×Q8×C13—44no—
199C2×Q8×C13—44no—
200C2×Q8×C13—44no—
201C2×Q8×C13—44no—
202C2×Q8×C13—44no—
203C2×D4×C13—28no—
204C2×D4×C13—28no—
205C2×D4×C13—44no—
206C2×D4×C13—44no—
207C2×D4×C13—44no—
208C2×D4×C13—44no—
209C2×D4×C13—44no—
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—28no—
219C22×C4×C13—28no—
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—21no—
253C22×C4×C13—21no—
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—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—44no—
291C22×C4×C13—44no—
292C22×C4×C13—44no—
293C22×C4×C13—44no—
294C22×C4×C13—44no—
295C22×C4×C13—44no—
296C22×C4×C13—44no—
297C22×C4×C13—44no—
298C22×C4×C13—44no—
299C22×C4×C13—44no—
300C22×C4×C13—44no—
301C22×C4×C13—44no—
302C22×C4×C13C2×D412yes—
303C22×C4×C13C2×D412yes—
304C22×C4×C13C2×D412yes—
305C22×C4×C13C2×D412yes—
306C22×C4×C13C2×D412yes—
307C22×C4×C13C2×D412yes—
308C22×C4×C13C2×D412yes—
309C22×C4×C13C2×D412yes—
310C22×C4×C13C2×D412yes—
311C22×C4×C13C2×D412yes—
312C22×C4×C13C2×Q812yes—
313C22×C4×C13#4112yes—
314C22×C4×C13#4112yes—
315C13×C4⋊C4—28no—
316C13×C4⋊C4—28no—
317C13×C4⋊C4—28no—
318C13×C4⋊C4—44no—
319C13×C4⋊C4—44no—
320C13×C22⋊C4—28no—
321C13×C22⋊C4—28no—
322C13×C22⋊C4—28no—
323C13×C22⋊C4—44no—
324C13×C22⋊C4—44no—
325C13×C22⋊C4—44no—
326C13×C22⋊C4—44no—
327C13×C22⋊C4—44no—
328C13×C22⋊C4—44no—
329C13×C22⋊C4—44no—
330C22×C22⋊Q8C2×C1311yescharacteristic, complemented
331C2×#393C2×C1311yescharacteristic, complemented
332C2×#386C2×C1311yescharacteristic
333C2×#386C2×C1311yescharacteristic
334C2×#385C2×C1311yescharacteristic, complemented
335C2×#380C2×C1311yescharacteristic, complemented
336#1446C2×C1311yescharacteristic, complemented
337#1445C2×C1311yescharacteristic, complemented
338#1441C2×C1311yescharacteristic, complemented
339#1441C2×C1311yescharacteristic, complemented
340#1439C2×C1311yescharacteristic, complemented
341#1439C2×C1311yescharacteristic, complemented
342#1439C2×C1311yescharacteristic, complemented
343#1438C2×C1311yescharacteristic
344C22⋊#95C2×C1311yescharacteristic, complemented
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—22no—
378C23×C13—22no—
379C23×C13—22no—
380C23×C13—22no—
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×C13—41no—
410C23×C13—41no—
411C23×C13—41no—
412C23×C13—41no—
413C23×C13C22⋊Q814yes—
414C23×C13C22⋊Q814yescomplemented
415C23×C13C22×D411yescharacteristic
416C23×C13C22×D411yescharacteristic
417C23×C13C22×D411yescharacteristic
418C23×C13C22×D411yescharacteristic
419C23×C13C22×Q811yescharacteristic
420C23×C13C2×#4111yescharacteristic
421C23×C13C2×#4111yescharacteristic
422C23×C13C2×#4111yescharacteristic
423C23×C13C2×#4111yescharacteristic
424C23×C13H(5,𝔽2)11yescharacteristic
425C23×C13H(5,𝔽2)11yescharacteristic
426C23×C13H(5,𝔽2)11yescharacteristic
427C23×C13H(5,𝔽2)11yescharacteristic
428C23×C132−1+411yescharacteristic
429C23×C132−1+411yescharacteristic
430Q8×C13—416no—
431D4×C13—416no—
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—22no—
464C2×C4×C13—22no—
465C2×C4×C13—416no—
466C2×C4×C13—416no—
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—41no—
518C2×C4×C13—41no—
519C2×C4×C13—41no—
520C2×C4×C13—41no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13#12014yes—
524C2×C4×C13#12114yes—
525C23×Q8C22×C1311yescharacteristic
526C23×D4C22×C1311yescharacteristic
527C24×C4C22×C1311yescharacteristic
528C24×C4C22×C1311yescharacteristic
529C2×C22⋊Q8—24no—
530C2×C22⋊Q8—24no—
531C2×C22⋊Q8—24no—
532C22×C4⋊C4C22×C1311yescharacteristic
533C22×C4⋊C4C22×C1311yescharacteristic
534C22×C4⋊C4C22×C1311yescharacteristic
535C22×C4⋊C4C22×C1311yescharacteristic
536C22×C4⋊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×C22⋊C4C22×C1311yescharacteristic
544C22×C22⋊C4C22×C1311yescharacteristic
545C22×C22⋊C4C22×C1311yescharacteristic
546C22×C22⋊C4C22×C1311yescharacteristic
547#393—24no—
548#386—24no—
549#386—24no—
550#385—24no—
551#380—24no—
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
563C2×#95C22×C1311yescharacteristic
564C2×#95C22×C1311yescharacteristic
565C2×#95C22×C1311yescharacteristic
566C2×#95C22×C1311yescharacteristic
567C2×#95C22×C1311yescharacteristic
568C22×C13—24no—
569C22×C13—24no—
570C22×C13—24no—
571C22×C13—24no—
572C22×C13—24no—
573C22×C13—24no—
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×C13—42no—
594C22×C13—42no—
595C22×C13—42no—
596C22×C13—42no—
597C22×C13—42no—
598C22×C13C2×#12011yescharacteristic
599C22×C13C2×#12111yescharacteristic
600C22×C13C2×C22⋊Q811yescharacteristic
601C22×C13C2×C22⋊Q811yescharacteristic
602C22×C13#52511yescharacteristic
603C22×C13#52911yescharacteristic
604C22×C13#53511yescharacteristic
605C22×C13#53511yescharacteristic
606C22×C13#53611yescharacteristic
607C22×C13#53711yescharacteristic
608C22×C13#53811yescharacteristic
609C22×C13#53911yescharacteristic
610C22×C13#54211yescharacteristic
611C22×C13#54211yescharacteristic
612C22×C13#54311yescharacteristic
613C22×C13D4211yescharacteristic
614C22×C13D4211yescharacteristic
615C22×C13#54611yescharacteristic
616C22×C13#54611yescharacteristic
617C22×C13#54611yescharacteristic
618C22×C13#54611yescharacteristic
619C22×C13#54611yescharacteristic
620C22×C13#54611yescharacteristic
621C22×C13#54611yescharacteristic
622C22×C13#54711yescharacteristic
623C22×C13#54811yescharacteristic
624C22×C13#54811yescharacteristic
625C22×C13D4×Q811yescharacteristic
626C22×C13D4×Q811yescharacteristic
627C22×C13#55111yescharacteristic
628C22×C13#55211yescharacteristic
629C22×C13#55411yescharacteristic
630C22×C13#55411yescharacteristic
631C22×C13#56211yescharacteristic
632C22×C13#56211yescharacteristic
633C4×C13—24no—
634C4×C13—24no—
635C4×C13—42no—
636C4×C13—42no—
637C4×C13—42no—
638C4×C13—42no—
639C4×C13—42no—
640C4×C13—42no—
641C4×C13—42no—
642C4×C13—81no—
643C4×C13—81no—
644C4×C13—81no—
645C4×C13—81no—
646C25C23×C1311yescharacteristic
647C25C23×C1311yescharacteristic
648C22×Q8—22no—
649C22×Q8—22no—
650C22×Q8—22no—
651C22×Q8—22no—
652C22×Q8—22no—
653C22×Q8—41no—
654C22×Q8—41no—
655C22×D4—22no—
656C22×D4—22no—
657C22×D4—22no—
658C22×D4—22no—
659C22×D4—41no—
660C22×D4—41no—
661C22×D4Q8×C1314yescomplemented
662C23×C4—22no—
663C23×C4—22no—
664C23×C4—22no—
665C23×C4—22no—
666C23×C4—22no—
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4—41no—
675C23×C4—41no—
676C23×C4C23×C1311yescharacteristic
677C23×C4C23×C1311yescharacteristic
678C23×C4C23×C1311yescharacteristic
679C23×C4C23×C1311yescharacteristic
680C23×C4C23×C1311yescharacteristic
681C23×C4C23×C1311yescharacteristic
682C23×C4C23×C1311yescharacteristic
683C23×C4C23×C1311yescharacteristic
684C23×C4C23×C1311yescharacteristic
685C23×C4C23×C1311yescharacteristic
686C23×C4C23×C1311yescharacteristic
687C23×C4C23×C1311yescharacteristic
688C23×C4C23×C1311yescharacteristic
689C22⋊Q8—232no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—41no—
701C2×C4⋊C4—41no—
702C2×C4⋊C4—41no—
703C2×C4⋊C4D4×C1314yescomplemented
704C2×C4⋊C4D4×C1314yescomplemented
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—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—41no—
726C2×C22⋊C4—41no—
727C2×C22⋊C4—41no—
728C2×C22⋊C4—41no—
729C2×C22⋊C4—41no—
730C2×C22⋊C4—41no—
731C2×C22⋊C4—41no—
732C2×C22⋊C4—41no—
733C2×C22⋊C4D4×C1314yes—
734C2×C22⋊C4D4×C1314yes—
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—22no—
744#95—22no—
745#95—22no—
746#95—41no—
747#95—41no—
748#95—41no—
749#95—41no—
750#95—41no—
751C2×C13—44no—
752C2×C13—44no—
753C2×C13#240411yescharacteristic
754C2×C13#240811yescharacteristic
755C2×C13#240911yescharacteristic
756C2×C13#241711yescharacteristic
757C2×C13#242711yescharacteristic
758C2×C13#243711yescharacteristic
759C2×C13#244911yescharacteristic
760C2×C13#245011yescharacteristic
761C2×C13#247711yescharacteristic
762C2×C13#267211yescharacteristic
763C2×C13#267611yescharacteristic
764C2×C13#268711yescharacteristic
765C2×C13#269211yescharacteristic
766C2×C13#269211yescharacteristic
767C2×C13#269611yescharacteristic
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—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24C2×D4×C1312yes—
793C24C2×D4×C1312yes—
794C24C2×Q8×C1312yes—
795C24C2×Q8×C1312yes—
796C24C13×#4112yes—
797C24C13×#4112yes—
798C24C24×C1311yescharacteristic
799C2×Q8—28no—
800C2×Q8—44no—
801C2×Q8—44no—
802C2×Q8—44no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—44no—
806C2×D4—28no—
807C2×D4—28no—
808C2×D4—44no—
809C2×D4—44no—
810C2×D4—44no—
811C2×D4—44no—
812C2×D4—44no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—28no—
822C22×C4—28no—
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—21no—
851C22×C4—21no—
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—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—44no—
894C22×C4—44no—
895C22×C4—44no—
896C22×C4—44no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4C2×D4×C1312yes—
906C22×C4C2×D4×C1312yes—
907C22×C4C2×D4×C1312yes—
908C22×C4C2×D4×C1312yes—
909C22×C4C2×D4×C1312yes—
910C22×C4C2×D4×C1312yes—
911C22×C4C2×D4×C1312yes—
912C22×C4C2×D4×C1312yes—
913C22×C4C2×D4×C1312yes—
914C22×C4C2×D4×C1312yes—
915C22×C4C2×Q8×C1312yes—
916C22×C4C13×#4112yes—
917C22×C4C13×#4112yes—
918C4⋊C4—28no—
919C4⋊C4—28no—
920C4⋊C4—28no—
921C4⋊C4—44no—
922C4⋊C4—44no—
923C22⋊C4—28no—
924C22⋊C4—28no—
925C22⋊C4—28no—
926C22⋊C4—44no—
927C22⋊C4—44no—
928C22⋊C4—44no—
929C22⋊C4—44no—
930C22⋊C4—44no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C13#1532311yescharacteristic, direct product factor, Sylow
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—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
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—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23C13×C22⋊Q814yes—
1003C23C13×C22⋊Q814yescomplemented
1004C23C22×D4×C1311yescharacteristic
1005C23C22×D4×C1311yescharacteristic
1006C23C22×D4×C1311yescharacteristic
1007C23C22×D4×C1311yescharacteristic
1008C23C22×Q8×C1311yescharacteristic
1009C23C2×C13×#4111yescharacteristic
1010C23C2×C13×#4111yescharacteristic
1011C23C2×C13×#4111yescharacteristic
1012C23C2×C13×#4111yescharacteristic
1013C23C13×H(5,𝔽2)11yescharacteristic
1014C23C13×H(5,𝔽2)11yescharacteristic
1015C23C13×H(5,𝔽2)11yescharacteristic
1016C23C13×H(5,𝔽2)11yescharacteristic
1017C23C13×2−1+411yescharacteristic
1018C23C13×2−1+411yescharacteristic
1019Q8—416no—
1020D4—416no—
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—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—416no—
1055C2×C4—416no—
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×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4C13×#12014yes—
1113C2×C4C13×#12114yes—
1114C22—24no—
1115C22—24no—
1116C22—24no—
1117C22—24no—
1118C22—24no—
1119C22—24no—
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—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—42no—
1143C22—42no—
1144C22C2×C13×#12011yescharacteristic
1145C22C2×C13×#12111yescharacteristic
1146C22C2×C13×C22⋊Q811yescharacteristic
1147C22C2×C13×C22⋊Q811yescharacteristic
1148C22C13×#52511yescharacteristic
1149C22C13×#52911yescharacteristic
1150C22C13×#53511yescharacteristic
1151C22C13×#53511yescharacteristic
1152C22C13×#53611yescharacteristic
1153C22C13×#53711yescharacteristic
1154C22C13×#53811yescharacteristic
1155C22C13×#53911yescharacteristic
1156C22C13×#54211yescharacteristic
1157C22C13×#54211yescharacteristic
1158C22C13×#54311yescharacteristic
1159C22D42×C1311yescharacteristic
1160C22D42×C1311yescharacteristic
1161C22C13×#54611yescharacteristic
1162C22C13×#54611yescharacteristic
1163C22C13×#54611yescharacteristic
1164C22C13×#54611yescharacteristic
1165C22C13×#54611yescharacteristic
1166C22C13×#54611yescharacteristic
1167C22C13×#54611yescharacteristic
1168C22C13×#54711yescharacteristic
1169C22C13×#54811yescharacteristic
1170C22C13×#54811yescharacteristic
1171C22D4×Q8×C1311yescharacteristic
1172C22D4×Q8×C1311yescharacteristic
1173C22C13×#55111yescharacteristic
1174C22C13×#55211yescharacteristic
1175C22C13×#55411yescharacteristic
1176C22C13×#55411yescharacteristic
1177C22C13×#56211yescharacteristic
1178C22C13×#56211yescharacteristic
1179C4—24no—
1180C4—24no—
1181C4—42no—
1182C4—42no—
1183C4—42no—
1184C4—42no—
1185C4—42no—
1186C4—42no—
1187C4—42no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C2—44no—
1193C2—44no—
1194C2C13×#240411yescharacteristic
1195C2C13×#240811yescharacteristic
1196C2C13×#240911yescharacteristic
1197C2C13×#241711yescharacteristic
1198C2C13×#242711yescharacteristic
1199C2C13×#243711yescharacteristic
1200C2C13×#244911yescharacteristic
1201C2C13×#245011yescharacteristic
1202C2C13×#247711yescharacteristic
1203C2C13×#267211yescharacteristic
1204C2C13×#267611yescharacteristic
1205C2C13×#268711yescharacteristic
1206C2C13×#269211yescharacteristic
1207C2C13×#269211yescharacteristic
1208C2C13×#269611yescharacteristic
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
1. C22×C13×C22⋊Q8C2semidirect
2. C2×C13×#393C2semidirect
5. C2×C13×#385C2semidirect
6. C2×C13×#380C2semidirect
7. C13×#1446C2semidirect
8. C13×#1445C2semidirect
9. C13×#1441C2semidirect
10. C13×#1441C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1439C2semidirect
15. C13×C22⋊#95C2semidirect
74. C22×D4×C13Q8semidirect
116. C2×C13×C4⋊C4D4semidirect
117. C2×C13×C4⋊C4D4semidirect
164. #15323C13direct (N × H)
330. C22×C22⋊Q8C2×C13semidirect
331. C2×#393C2×C13semidirect
334. C2×#385C2×C13semidirect
335. C2×#380C2×C13semidirect
336. #1446C2×C13semidirect
337. #1445C2×C13semidirect
338. #1441C2×C13semidirect
339. #1441C2×C13semidirect
340. #1439C2×C13semidirect
341. #1439C2×C13semidirect
342. #1439C2×C13semidirect
344. C22⋊#95C2×C13semidirect
414. C23×C13C22⋊Q8semidirect
661. C22×D4Q8×C13semidirect
703. C2×C4⋊C4D4×C13semidirect
704. C2×C4⋊C4D4×C13semidirect
933. C13#15323direct (N × H)
1003. C23C13×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#3932
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C13×#14462
C13×#14452
C13×#14412
C13×#14392
C13×#14382
C13×C22⋊#952
#1532313