Finite Group Databasebeta

← C13×#15280 #15701619

Subgroups — C13×#15280 #15701619

Order 3328.

2142 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×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C13×#396C211yesmaximal, characteristic, complemented
3C2×C13×#393C211yesmaximal, characteristic, complemented
4C2×C13×#391C211yesmaximal, characteristic, complemented
5C2×C13×#390C211yesmaximal, characteristic
6C2×C13×#386C211yesmaximal, characteristic
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1439C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C2×C13×C22⋊Q8—24no—
20C2×C13×C22⋊Q8—24no—
21C2×C13×C22⋊Q8—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×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
38C22×C13×C22⋊C4C2211yescharacteristic
39C22×C42×C13C2211yescharacteristic
40C13×#396—24no—
41C13×#393—24no—
42C13×#391—24no—
43C13×#390—24no—
44C13×#386—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×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—41no—
66C22×Q8×C13—41no—
67C22×Q8×C13D414yescomplemented
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—41no—
81C23×C4×C13—41no—
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
95C13×C22⋊Q8—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—41no—
110C2×C13×C4⋊C4—41no—
111C2×C13×C4⋊C4—41no—
112C2×C13×C4⋊C4—41no—
113C2×C13×C4⋊C4D414yescomplemented
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
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—41no—
137C2×C13×C22⋊C4—41no—
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—41no—
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—41no—
161C13×#95—41no—
162C13×#95—41no—
163C13×#95D414yes—
164#15280C1311yesmaximal, 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×C13—21no—
190C24×C13—21no—
191C24×C13C2×D412yes—
192C24×C13C2×Q812yes—
193C24×C13C2×Q812yes—
194C24×C13#4112yes—
195C24×C13C2411yescharacteristic
196C2×Q8×C13—28no—
197C2×Q8×C13—28no—
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—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—28no—
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—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×D412yes—
304C22×C4×C13C2×Q812yes—
305C22×C4×C13#4112yes—
306C22×C4×C13#4112yes—
307C22×C4×C13#4112yes—
308C13×C4⋊C4—28no—
309C13×C4⋊C4—28no—
310C13×C4⋊C4—28no—
311C13×C4⋊C4—44no—
312C13×C4⋊C4—44no—
313C13×C4⋊C4—44no—
314C13×C22⋊C4—28no—
315C13×C22⋊C4—28no—
316C13×C22⋊C4—44no—
317C13×C22⋊C4—44no—
318C13×C22⋊C4—44no—
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—44no—
326C22×C22⋊Q8C2×C1311yescharacteristic, complemented
327C2×#396C2×C1311yescharacteristic, complemented
328C2×#393C2×C1311yescharacteristic, complemented
329C2×#391C2×C1311yescharacteristic, complemented
330C2×#390C2×C1311yescharacteristic
331C2×#386C2×C1311yescharacteristic
332#1444C2×C1311yescharacteristic, complemented
333#1441C2×C1311yescharacteristic, complemented
334#1439C2×C1311yescharacteristic, complemented
335#1439C2×C1311yescharacteristic, complemented
336#1439C2×C1311yescharacteristic, complemented
337#1439C2×C1311yescharacteristic, complemented
338#1438C2×C1311yescharacteristic
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—41no—
367C23×C13—41no—
368C23×C13—41no—
369C23×C13—41no—
370C23×C13—41no—
371C23×C13—41no—
372C23×C13—41no—
373C23×C13—41no—
374C23×C13—41no—
375C23×C13—41no—
376C23×C13—41no—
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×C13—41no—
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×C13H(5,𝔽2)11yescharacteristic
421C23×C13H(5,𝔽2)11yescharacteristic
422C23×C13H(5,𝔽2)11yescharacteristic
423C23×C13H(5,𝔽2)11yescharacteristic
424C23×C132−1+411yescharacteristic
425C23×C132−1+411yescharacteristic
426Q8×C13—416no—
427D4×C13—416no—
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—22no—
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⋊Q814yescomplemented
520C23×Q8C22×C1311yescharacteristic
521C23×D4C22×C1311yescharacteristic
522C24×C4C22×C1311yescharacteristic
523C2×C22⋊Q8—24no—
524C2×C22⋊Q8—24no—
525C2×C22⋊Q8—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×C22⋊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#396—24no—
545#393—24no—
546#391—24no—
547#390—24no—
548#386—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—42no—
567C22×C13—42no—
568C22×C13—42no—
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—81no—
586C22×C13—81no—
587C22×C13—81no—
588C22×C13—81no—
589C22×C13—81no—
590C22×C13—81no—
591C22×C13—81no—
592C22×C13—81no—
593C22×C13C2×#12011yescharacteristic
594C22×C13C2×#12111yescharacteristic
595C22×C13C2×C22⋊Q811yescharacteristic
596C22×C13C2×C22⋊Q811yescharacteristic
597C22×C13#52911yescharacteristic
598C22×C13#53211yescharacteristic
599C22×C13#53411yescharacteristic
600C22×C13#53511yescharacteristic
601C22×C13#53611yescharacteristic
602C22×C13#53711yescharacteristic
603C22×C13#53811yescharacteristic
604C22×C13#53911yescharacteristic
605C22×C13#54211yescharacteristic
606C22×C13#54211yescharacteristic
607C22×C13#54311yescharacteristic
608C22×C13D4211yescharacteristic
609C22×C13D4211yescharacteristic
610C22×C13#54611yescharacteristic
611C22×C13#54611yescharacteristic
612C22×C13#54611yescharacteristic
613C22×C13#54611yescharacteristic
614C22×C13#54611yescharacteristic
615C22×C13#54811yescharacteristic
616C22×C13#54811yescharacteristic
617C22×C13#54811yescharacteristic
618C22×C13D4×Q811yescharacteristic
619C22×C13D4×Q811yescharacteristic
620C22×C13#55011yescharacteristic
621C22×C13#55011yescharacteristic
622C22×C13#55111yescharacteristic
623C22×C13#55411yescharacteristic
624C22×C13#55411yescharacteristic
625C22×C13#55611yescharacteristic
626C22×C13#56211yescharacteristic
627C22×C13#56211yescharacteristic
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×Q8—22no—
644C22×Q8—22no—
645C22×Q8—22no—
646C22×Q8—22no—
647C22×Q8—41no—
648C22×Q8—41no—
649C22×Q8D4×C1314yescomplemented
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—22no—
653C22×D4—22no—
654C22×D4—41no—
655C22×D4—41no—
656C22×D4Q8×C1314yescomplemented
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—22no—
660C23×C4—22no—
661C23×C4—22no—
662C23×C4—41no—
663C23×C4—41no—
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
677C22⋊Q8—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—41no—
692C2×C4⋊C4—41no—
693C2×C4⋊C4—41no—
694C2×C4⋊C4—41no—
695C2×C4⋊C4D4×C1314yescomplemented
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
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—41no—
719C2×C22⋊C4—41no—
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—41no—
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—41no—
743#95—41no—
744#95—41no—
745#95D4×C1314yes—
746C2×C13—44no—
747C2×C13—82no—
748C2×C13#240911yescharacteristic
749C2×C13#241011yescharacteristic
750C2×C13#242611yescharacteristic
751C2×C13#243111yescharacteristic
752C2×C13#243711yescharacteristic
753C2×C13#245011yescharacteristic
754C2×C13#245211yescharacteristic
755C2×C13#253811yescharacteristic
756C2×C13#256011yescharacteristic
757C2×C13#267611yescharacteristic
758C2×C13#268111yescharacteristic
759C2×C13#269211yescharacteristic
760C2×C13#270011yescharacteristic
761C2×C13#273011yescharacteristic
762C2×C13#273211yescharacteristic
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—
787C24—21no—
788C24—21no—
789C24C2×D4×C1312yes—
790C24C2×Q8×C1312yes—
791C24C2×Q8×C1312yes—
792C24C13×#4112yes—
793C24C24×C1311yescharacteristic
794C2×Q8—28no—
795C2×Q8—28no—
796C2×Q8—44no—
797C2×Q8—44no—
798C2×Q8—44no—
799C2×Q8—44no—
800C2×Q8—44no—
801C2×D4—28no—
802C2×D4—28no—
803C2×D4—44no—
804C2×D4—44no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—44no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—28no—
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—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—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×D4×C1312yes—
902C22×C4C2×Q8×C1312yes—
903C22×C4C13×#4112yes—
904C22×C4C13×#4112yes—
905C22×C4C13×#4112yes—
906C4⋊C4—28no—
907C4⋊C4—28no—
908C4⋊C4—28no—
909C4⋊C4—44no—
910C4⋊C4—44no—
911C4⋊C4—44no—
912C22⋊C4—28no—
913C22⋊C4—28no—
914C22⋊C4—44no—
915C22⋊C4—44no—
916C22⋊C4—44no—
917C22⋊C4—44no—
918C22⋊C4—44no—
919C22⋊C4—44no—
920C22⋊C4—44no—
921C22⋊C4—44no—
922C22⋊C4—44no—
923C42—44no—
924C13#1528011yescharacteristic, 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—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
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—
993C23—41no—
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
1004C23C13×H(5,𝔽2)11yescharacteristic
1005C23C13×H(5,𝔽2)11yescharacteristic
1006C23C13×H(5,𝔽2)11yescharacteristic
1007C23C13×H(5,𝔽2)11yescharacteristic
1008C23C13×2−1+411yescharacteristic
1009C23C13×2−1+411yescharacteristic
1010Q8—416no—
1011D4—416no—
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—22no—
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⋊Q814yescomplemented
1104C22—24no—
1105C22—24no—
1106C22—24no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
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—81no—
1127C22—81no—
1128C22—81no—
1129C22—81no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22C2×C13×#12011yescharacteristic
1135C22C2×C13×#12111yescharacteristic
1136C22C2×C13×C22⋊Q811yescharacteristic
1137C22C2×C13×C22⋊Q811yescharacteristic
1138C22C13×#52911yescharacteristic
1139C22C13×#53211yescharacteristic
1140C22C13×#53411yescharacteristic
1141C22C13×#53511yescharacteristic
1142C22C13×#53611yescharacteristic
1143C22C13×#53711yescharacteristic
1144C22C13×#53811yescharacteristic
1145C22C13×#53911yescharacteristic
1146C22C13×#54211yescharacteristic
1147C22C13×#54211yescharacteristic
1148C22C13×#54311yescharacteristic
1149C22D42×C1311yescharacteristic
1150C22D42×C1311yescharacteristic
1151C22C13×#54611yescharacteristic
1152C22C13×#54611yescharacteristic
1153C22C13×#54611yescharacteristic
1154C22C13×#54611yescharacteristic
1155C22C13×#54611yescharacteristic
1156C22C13×#54811yescharacteristic
1157C22C13×#54811yescharacteristic
1158C22C13×#54811yescharacteristic
1159C22D4×Q8×C1311yescharacteristic
1160C22D4×Q8×C1311yescharacteristic
1161C22C13×#55011yescharacteristic
1162C22C13×#55011yescharacteristic
1163C22C13×#55111yescharacteristic
1164C22C13×#55411yescharacteristic
1165C22C13×#55411yescharacteristic
1166C22C13×#55611yescharacteristic
1167C22C13×#56211yescharacteristic
1168C22C13×#56211yescharacteristic
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—82no—
1184C2C13×#240911yescharacteristic
1185C2C13×#241011yescharacteristic
1186C2C13×#242611yescharacteristic
1187C2C13×#243111yescharacteristic
1188C2C13×#243711yescharacteristic
1189C2C13×#245011yescharacteristic
1190C2C13×#245211yescharacteristic
1191C2C13×#253811yescharacteristic
1192C2C13×#256011yescharacteristic
1193C2C13×#267611yescharacteristic
1194C2C13×#268111yescharacteristic
1195C2C13×#269211yescharacteristic
1196C2C13×#270011yescharacteristic
1197C2C13×#273011yescharacteristic
1198C2C13×#273211yescharacteristic
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×#396C2semidirect
3. C2×C13×#393C2semidirect
4. C2×C13×#391C2semidirect
7. C13×#1444C2semidirect
8. C13×#1441C2semidirect
9. C13×#1439C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
14. C13×#1436C2semidirect
15. C13×C22⋊#95C2semidirect
67. C22×Q8×C13D4semidirect
74. C22×D4×C13Q8semidirect
113. C2×C13×C4⋊C4D4semidirect
164. #15280C13direct (N × H)
326. C22×C22⋊Q8C2×C13semidirect
327. C2×#396C2×C13semidirect
328. C2×#393C2×C13semidirect
329. C2×#391C2×C13semidirect
332. #1444C2×C13semidirect
333. #1441C2×C13semidirect
334. #1439C2×C13semidirect
335. #1439C2×C13semidirect
336. #1439C2×C13semidirect
337. #1439C2×C13semidirect
339. #1436C2×C13semidirect
340. C22⋊#95C2×C13semidirect
519. C2×C4×C13C22⋊Q8semidirect
649. C22×Q8D4×C13semidirect
656. C22×D4Q8×C13semidirect
695. C2×C4⋊C4D4×C13semidirect
924. C13#15280direct (N × H)
1103. C2×C4C13×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×#3962
C2×C13×#3932
C2×C13×#3912
C2×C13×#3902
C2×C13×#3862
C13×#14442
C13×#14412
C13×#14392
C13×#14382
C13×#14362
C13×C22⋊#952
#1528013