Finite Group Databasebeta

← C13×#15275 #15701614

Subgroups — C13×#15275 #15701614

Order 3328.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C13×#394C211yesmaximal, characteristic
3C2×C13×#393C211yesmaximal, characteristic, complemented
4C2×C13×#391C211yesmaximal, characteristic, complemented
5C2×C13×#388C211yesmaximal, characteristic, complemented
6C2×C13×#386C211yesmaximal, characteristic
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1440C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic
14C13×#1437C211yesmaximal, 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×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊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×C42×C13C2211yescharacteristic
38C13×#394—24no—
39C13×#393—24no—
40C13×#391—24no—
41C13×#388—24no—
42C13×#386—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—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—22no—
73C22×D4×C13—41no—
74C22×D4×C13—41no—
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—41no—
107C2×C13×C4⋊C4D414yescomplemented
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
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—41no—
135C2×C13×C22⋊C4—41no—
136C2×C13×C22⋊C4—41no—
137C2×C13×C22⋊C4—41no—
138C2×C13×C22⋊C4—41no—
139C2×C13×C22⋊C4—41no—
140C2×C13×C22⋊C4D414yes—
141C2×C42×C13—22no—
142C2×C42×C13—22no—
143C2×C42×C13—41no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95—22no—
148C13×#95—22no—
149C13×#95—22no—
150C13×#95—22no—
151C13×#95—22no—
152C13×#95—22no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—41no—
156C13×#95—41no—
157C13×#95—41no—
158C13×#95—41no—
159C13×#95D414yes—
160#15275C1311yesmaximal, characteristic, direct product factor, Sylow
161C24×C13—21no—
162C24×C13—21no—
163C24×C13—21no—
164C24×C13—21no—
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×C13C2×D412yes—
188C24×C13#4112yes—
189C24×C13#4112yes—
190C24×C13#4112yes—
191C24×C13C2411yescharacteristic
192C2×Q8×C13—28no—
193C2×Q8×C13—28no—
194C2×Q8×C13—44no—
195C2×Q8×C13—44no—
196C2×Q8×C13—44no—
197C2×Q8×C13—44no—
198C2×Q8×C13—44no—
199C2×D4×C13—28no—
200C2×D4×C13—44no—
201C2×D4×C13—44no—
202C2×D4×C13—44no—
203C2×D4×C13—44no—
204C2×D4×C13—44no—
205C2×D4×C13—44no—
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—28no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—21no—
221C22×C4×C13—21no—
222C22×C4×C13—21no—
223C22×C4×C13—21no—
224C22×C4×C13—21no—
225C22×C4×C13—21no—
226C22×C4×C13—21no—
227C22×C4×C13—21no—
228C22×C4×C13—21no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—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—44no—
286C22×C4×C13—44no—
287C22×C4×C13—44no—
288C22×C4×C13—44no—
289C22×C4×C13—44no—
290C22×C4×C13—44no—
291C22×C4×C13C2×D412yes—
292C22×C4×C13C2×D412yes—
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×C13#4112yes—
303C22×C4×C13#4112yes—
304C13×C4⋊C4—28no—
305C13×C4⋊C4—28no—
306C13×C4⋊C4—28no—
307C13×C4⋊C4—44no—
308C13×C22⋊C4—28no—
309C13×C22⋊C4—28no—
310C13×C22⋊C4—28no—
311C13×C22⋊C4—44no—
312C13×C22⋊C4—44no—
313C13×C22⋊C4—44no—
314C13×C22⋊C4—44no—
315C13×C22⋊C4—44no—
316C13×C22⋊C4—44no—
317C13×C22⋊C4—44no—
318C13×C22⋊C4—44no—
319C42×C13—44no—
320C22×C22⋊Q8C2×C1311yescharacteristic, complemented
321C2×#394C2×C1311yescharacteristic
322C2×#393C2×C1311yescharacteristic, complemented
323C2×#391C2×C1311yescharacteristic, complemented
324C2×#388C2×C1311yescharacteristic, complemented
325C2×#386C2×C1311yescharacteristic
326#1442C2×C1311yescharacteristic, complemented
327#1442C2×C1311yescharacteristic, complemented
328#1441C2×C1311yescharacteristic, complemented
329#1440C2×C1311yescharacteristic, complemented
330#1439C2×C1311yescharacteristic, complemented
331#1439C2×C1311yescharacteristic, complemented
332#1438C2×C1311yescharacteristic
333#1437C2×C1311yescharacteristic, complemented
334C22⋊#95C2×C1311yescharacteristic, complemented
335C23×C13—22no—
336C23×C13—22no—
337C23×C13—22no—
338C23×C13—22no—
339C23×C13—22no—
340C23×C13—22no—
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—41no—
361C23×C13—41no—
362C23×C13—41no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13—41no—
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#12414yes—
405C23×C13C22×D411yescharacteristic
406C23×C13C22×D411yescharacteristic
407C23×C13C22×D411yescharacteristic
408C23×C13C22×D411yescharacteristic
409C23×C13C2×#4111yescharacteristic
410C23×C13C2×#4111yescharacteristic
411C23×C13C2×#4111yescharacteristic
412C23×C13C2×#4111yescharacteristic
413C23×C13C2×#4111yescharacteristic
414C23×C13H(5,𝔽2)11yescharacteristic
415C23×C13H(5,𝔽2)11yescharacteristic
416C23×C13H(5,𝔽2)11yescharacteristic
417C23×C132−1+411yescharacteristic
418C23×C132−1+411yescharacteristic
419C23×C132−1+411yescharacteristic
420Q8×C13—416no—
421D4×C13—416no—
422C2×C4×C13—22no—
423C2×C4×C13—22no—
424C2×C4×C13—22no—
425C2×C4×C13—22no—
426C2×C4×C13—22no—
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—416no—
456C2×C4×C13—41no—
457C2×C4×C13—41no—
458C2×C4×C13—41no—
459C2×C4×C13—41no—
460C2×C4×C13—41no—
461C2×C4×C13—41no—
462C2×C4×C13—41no—
463C2×C4×C13—41no—
464C2×C4×C13—41no—
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#12014yes—
513C2×C4×C13#12114yes—
514C23×Q8C22×C1311yescharacteristic
515C23×D4C22×C1311yescharacteristic
516C24×C4C22×C1311yescharacteristic
517C2×C22⋊Q8—24no—
518C2×C22⋊Q8—24no—
519C2×C22⋊Q8—24no—
520C22×C4⋊C4C22×C1311yescharacteristic
521C22×C4⋊C4C22×C1311yescharacteristic
522C22×C4⋊C4C22×C1311yescharacteristic
523C22×C4⋊C4C22×C1311yescharacteristic
524C22×C22⋊C4C22×C1311yescharacteristic
525C22×C22⋊C4C22×C1311yescharacteristic
526C22×C22⋊C4C22×C1311yescharacteristic
527C22×C22⋊C4C22×C1311yescharacteristic
528C22×C22⋊C4C22×C1311yescharacteristic
529C22×C22⋊C4C22×C1311yescharacteristic
530C22×C22⋊C4C22×C1311yescharacteristic
531C22×C22⋊C4C22×C1311yescharacteristic
532C22×C22⋊C4C22×C1311yescharacteristic
533C22×C22⋊C4C22×C1311yescharacteristic
534C22×C22⋊C4C22×C1311yescharacteristic
535C22×C42C22×C1311yescharacteristic
536#394—24no—
537#393—24no—
538#391—24no—
539#388—24no—
540#386—24no—
541C2×#95C22×C1311yescharacteristic
542C2×#95C22×C1311yescharacteristic
543C2×#95C22×C1311yescharacteristic
544C2×#95C22×C1311yescharacteristic
545C2×#95C22×C1311yescharacteristic
546C2×#95C22×C1311yescharacteristic
547C2×#95C22×C1311yescharacteristic
548C2×#95C22×C1311yescharacteristic
549C2×#95C22×C1311yescharacteristic
550C2×#95C22×C1311yescharacteristic
551C2×#95C22×C1311yescharacteristic
552C2×#95C22×C1311yescharacteristic
553C2×#95C22×C1311yescharacteristic
554C2×#95C22×C1311yescharacteristic
555C2×#95C22×C1311yescharacteristic
556C2×#95C22×C1311yescharacteristic
557C22×C13—24no—
558C22×C13—24no—
559C22×C13—24no—
560C22×C13—42no—
561C22×C13—42no—
562C22×C13—42no—
563C22×C13—42no—
564C22×C13—42no—
565C22×C13—42no—
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—81no—
580C22×C13—81no—
581C22×C13—81no—
582C22×C13—81no—
583C22×C13—81no—
584C22×C13—81no—
585C22×C13—81no—
586C22×C13—81no—
587C22×C13C2×#12011yescharacteristic
588C22×C13C2×#12111yescharacteristic
589C22×C13#52511yescharacteristic
590C22×C13#52511yescharacteristic
591C22×C13C2×#12411yescharacteristic
592C22×C13#52911yescharacteristic
593C22×C13#53411yescharacteristic
594C22×C13#53611yescharacteristic
595C22×C13#53611yescharacteristic
596C22×C13#53711yescharacteristic
597C22×C13#53811yescharacteristic
598C22×C13#53911yescharacteristic
599C22×C13#53911yescharacteristic
600C22×C13#54211yescharacteristic
601C22×C13#54211yescharacteristic
602C22×C13D4211yescharacteristic
603C22×C13D4211yescharacteristic
604C22×C13#54611yescharacteristic
605C22×C13#54611yescharacteristic
606C22×C13#54611yescharacteristic
607C22×C13#54611yescharacteristic
608C22×C13#54711yescharacteristic
609C22×C13#54811yescharacteristic
610C22×C13#54811yescharacteristic
611C22×C13#54811yescharacteristic
612C22×C13#54811yescharacteristic
613C22×C13#54811yescharacteristic
614C22×C13#54811yescharacteristic
615C22×C13#55011yescharacteristic
616C22×C13#55111yescharacteristic
617C22×C13#55111yescharacteristic
618C22×C13#55211yescharacteristic
619C22×C13#55211yescharacteristic
620C22×C13#56211yescharacteristic
621C22×C13#56311yescharacteristic
622C4×C13—24no—
623C4×C13—24no—
624C4×C13—42no—
625C4×C13—42no—
626C4×C13—42no—
627C4×C13—42no—
628C4×C13—42no—
629C4×C13—42no—
630C4×C13—42no—
631C4×C13—81no—
632C4×C13—81no—
633C4×C13—81no—
634C4×C13—81no—
635C25C23×C1311yescharacteristic
636C25C23×C1311yescharacteristic
637C22×Q8—22no—
638C22×Q8—22no—
639C22×Q8—22no—
640C22×Q8—22no—
641C22×Q8—41no—
642C22×Q8—41no—
643C22×Q8D4×C1314yescomplemented
644C22×D4—22no—
645C22×D4—22no—
646C22×D4—22no—
647C22×D4—22no—
648C22×D4—22no—
649C22×D4—41no—
650C22×D4—41no—
651C23×C4—22no—
652C23×C4—22no—
653C23×C4—22no—
654C23×C4—22no—
655C23×C4—22no—
656C23×C4—41no—
657C23×C4—41no—
658C23×C4C23×C1311yescharacteristic
659C23×C4C23×C1311yescharacteristic
660C23×C4C23×C1311yescharacteristic
661C23×C4C23×C1311yescharacteristic
662C23×C4C23×C1311yescharacteristic
663C23×C4C23×C1311yescharacteristic
664C23×C4C23×C1311yescharacteristic
665C23×C4C23×C1311yescharacteristic
666C23×C4C23×C1311yescharacteristic
667C23×C4C23×C1311yescharacteristic
668C23×C4C23×C1311yescharacteristic
669C23×C4C23×C1311yescharacteristic
670C23×C4C23×C1311yescharacteristic
671C22⋊Q8—232no—
672C2×C4⋊C4—22no—
673C2×C4⋊C4—22no—
674C2×C4⋊C4—22no—
675C2×C4⋊C4—22no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—41no—
683C2×C4⋊C4D4×C1314yescomplemented
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
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—41no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4D4×C1314yes—
717C2×C42—22no—
718C2×C42—22no—
719C2×C42—41no—
720#95—22no—
721#95—22no—
722#95—22no—
723#95—22no—
724#95—22no—
725#95—22no—
726#95—22no—
727#95—22no—
728#95—22no—
729#95—22no—
730#95—22no—
731#95—41no—
732#95—41no—
733#95—41no—
734#95—41no—
735#95D4×C1314yes—
736C2×C13—44no—
737C2×C13—82no—
738C2×C13#240711yescharacteristic
739C2×C13#241011yescharacteristic
740C2×C13#242611yescharacteristic
741C2×C13#243611yescharacteristic
742C2×C13#246311yescharacteristic
743C2×C13#247211yescharacteristic
744C2×C13#247711yescharacteristic
745C2×C13#248811yescharacteristic
746C2×C13#253611yescharacteristic
747C2×C13#267411yescharacteristic
748C2×C13#268111yescharacteristic
749C2×C13#268711yescharacteristic
750C2×C13#270211yescharacteristic
751C2×C13#272811yescharacteristic
752C2×C13#273011yescharacteristic
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
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—
779C24C2×D4×C1312yes—
780C24C13×#4112yes—
781C24C13×#4112yes—
782C24C13×#4112yes—
783C24C24×C1311yescharacteristic
784C2×Q8—28no—
785C2×Q8—28no—
786C2×Q8—44no—
787C2×Q8—44no—
788C2×Q8—44no—
789C2×Q8—44no—
790C2×Q8—44no—
791C2×D4—28no—
792C2×D4—44no—
793C2×D4—44no—
794C2×D4—44no—
795C2×D4—44no—
796C2×D4—44no—
797C2×D4—44no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—28no—
807C22×C4—21no—
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—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—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—44no—
878C22×C4—44no—
879C22×C4—44no—
880C22×C4—44no—
881C22×C4—44no—
882C22×C4—44no—
883C22×C4C2×D4×C1312yes—
884C22×C4C2×D4×C1312yes—
885C22×C4C2×D4×C1312yes—
886C22×C4C2×D4×C1312yes—
887C22×C4C2×D4×C1312yes—
888C22×C4C2×D4×C1312yes—
889C22×C4C2×D4×C1312yes—
890C22×C4C2×D4×C1312yes—
891C22×C4C2×D4×C1312yes—
892C22×C4C2×D4×C1312yes—
893C22×C4C2×D4×C1312yes—
894C22×C4C13×#4112yes—
895C22×C4C13×#4112yes—
896C4⋊C4—28no—
897C4⋊C4—28no—
898C4⋊C4—28no—
899C4⋊C4—44no—
900C22⋊C4—28no—
901C22⋊C4—28no—
902C22⋊C4—28no—
903C22⋊C4—44no—
904C22⋊C4—44no—
905C22⋊C4—44no—
906C22⋊C4—44no—
907C22⋊C4—44no—
908C22⋊C4—44no—
909C22⋊C4—44no—
910C22⋊C4—44no—
911C42—44no—
912C13#1527511yescharacteristic, direct product factor, Sylow
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
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—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
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—
982C23C13×#12414yes—
983C23C22×D4×C1311yescharacteristic
984C23C22×D4×C1311yescharacteristic
985C23C22×D4×C1311yescharacteristic
986C23C22×D4×C1311yescharacteristic
987C23C2×C13×#4111yescharacteristic
988C23C2×C13×#4111yescharacteristic
989C23C2×C13×#4111yescharacteristic
990C23C2×C13×#4111yescharacteristic
991C23C2×C13×#4111yescharacteristic
992C23C13×H(5,𝔽2)11yescharacteristic
993C23C13×H(5,𝔽2)11yescharacteristic
994C23C13×H(5,𝔽2)11yescharacteristic
995C23C13×2−1+411yescharacteristic
996C23C13×2−1+411yescharacteristic
997C23C13×2−1+411yescharacteristic
998Q8—416no—
999D4—416no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
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—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
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×C4C13×#12014yes—
1091C2×C4C13×#12114yes—
1092C22—24no—
1093C22—24no—
1094C22—24no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—42no—
1108C22—42no—
1109C22—42no—
1110C22—42no—
1111C22—42no—
1112C22—42no—
1113C22—42no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×C13×#12011yescharacteristic
1123C22C2×C13×#12111yescharacteristic
1124C22C13×#52511yescharacteristic
1125C22C13×#52511yescharacteristic
1126C22C2×C13×#12411yescharacteristic
1127C22C13×#52911yescharacteristic
1128C22C13×#53411yescharacteristic
1129C22C13×#53611yescharacteristic
1130C22C13×#53611yescharacteristic
1131C22C13×#53711yescharacteristic
1132C22C13×#53811yescharacteristic
1133C22C13×#53911yescharacteristic
1134C22C13×#53911yescharacteristic
1135C22C13×#54211yescharacteristic
1136C22C13×#54211yescharacteristic
1137C22D42×C1311yescharacteristic
1138C22D42×C1311yescharacteristic
1139C22C13×#54611yescharacteristic
1140C22C13×#54611yescharacteristic
1141C22C13×#54611yescharacteristic
1142C22C13×#54611yescharacteristic
1143C22C13×#54711yescharacteristic
1144C22C13×#54811yescharacteristic
1145C22C13×#54811yescharacteristic
1146C22C13×#54811yescharacteristic
1147C22C13×#54811yescharacteristic
1148C22C13×#54811yescharacteristic
1149C22C13×#54811yescharacteristic
1150C22C13×#55011yescharacteristic
1151C22C13×#55111yescharacteristic
1152C22C13×#55111yescharacteristic
1153C22C13×#55211yescharacteristic
1154C22C13×#55211yescharacteristic
1155C22C13×#56211yescharacteristic
1156C22C13×#56311yescharacteristic
1157C4—24no—
1158C4—24no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—42no—
1163C4—42no—
1164C4—42no—
1165C4—42no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C2—44no—
1171C2—82no—
1172C2C13×#240711yescharacteristic
1173C2C13×#241011yescharacteristic
1174C2C13×#242611yescharacteristic
1175C2C13×#243611yescharacteristic
1176C2C13×#246311yescharacteristic
1177C2C13×#247211yescharacteristic
1178C2C13×#247711yescharacteristic
1179C2C13×#248811yescharacteristic
1180C2C13×#253611yescharacteristic
1181C2C13×#267411yescharacteristic
1182C2C13×#268111yescharacteristic
1183C2C13×#268711yescharacteristic
1184C2C13×#270211yescharacteristic
1185C2C13×#272811yescharacteristic
1186C2C13×#273011yescharacteristic
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
3. C2×C13×#393C2semidirect
4. C2×C13×#391C2semidirect
5. C2×C13×#388C2semidirect
7. C13×#1442C2semidirect
8. C13×#1442C2semidirect
9. C13×#1441C2semidirect
10. C13×#1440C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
14. C13×#1437C2semidirect
15. C13×C22⋊#95C2semidirect
67. C22×Q8×C13D4semidirect
107. C2×C13×C4⋊C4D4semidirect
160. #15275C13direct (N × H)
320. C22×C22⋊Q8C2×C13semidirect
322. C2×#393C2×C13semidirect
323. C2×#391C2×C13semidirect
324. C2×#388C2×C13semidirect
326. #1442C2×C13semidirect
327. #1442C2×C13semidirect
328. #1441C2×C13semidirect
329. #1440C2×C13semidirect
330. #1439C2×C13semidirect
331. #1439C2×C13semidirect
333. #1437C2×C13semidirect
334. C22⋊#95C2×C13semidirect
643. C22×Q8D4×C13semidirect
683. C2×C4⋊C4D4×C13semidirect
912. C13#15275direct (N × H)

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×#3942
C2×C13×#3932
C2×C13×#3912
C2×C13×#3882
C2×C13×#3862
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14382
C13×#14372
C13×C22⋊#952
#1527513