Finite Group Databasebeta

← C13×#15390 #15701729

Subgroups — C13×#15390 #15701729

Order 3328.

1946 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#397C211yesmaximal, characteristic, complemented
2C2×C13×#394C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#386C211yesmaximal, characteristic
5C2×C13×#385C211yesmaximal, characteristic, complemented
6C2×C13×#380C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1443C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1441C211yesmaximal, characteristic, complemented
11C13×#1440C211yesmaximal, characteristic, complemented
12C13×#1440C211yesmaximal, characteristic, complemented
13C13×#1439C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊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
33C13×#397—24no—
34C13×#394—24no—
35C13×#386—24no—
36C13×#386—24no—
37C13×#385—24no—
38C13×#380—24no—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C25×C13C2311yescharacteristic
59C22×D4×C13—22no—
60C22×D4×C13—22no—
61C22×D4×C13—22no—
62C22×D4×C13—22no—
63C22×D4×C13—41no—
64C22×D4×C13—41no—
65C22×D4×C13D414yes—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
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—41no—
75C23×C4×C13—41no—
76C23×C4×C13—41no—
77C23×C4×C13—41no—
78C23×C4×C13—41no—
79C23×C4×C13—41no—
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
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
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4—41no—
104C2×C13×C4⋊C4D414yescomplemented
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
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—41no—
129C2×C13×C22⋊C4—41no—
130C2×C13×C22⋊C4—41no—
131C2×C13×C22⋊C4—41no—
132C2×C13×C22⋊C4—41no—
133C2×C13×C22⋊C4—41no—
134C2×C13×C22⋊C4D414yes—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—22no—
147C13×#95—22no—
148C13×#95—41no—
149C13×#95—41no—
150C13×#95—41no—
151C13×#95—41no—
152C13×#95—41no—
153#15390C1311yesmaximal, characteristic, direct product factor, Sylow
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13—21no—
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×C13C2×D412yes—
179C24×C13C2×D412yes—
180C24×C13C2×D412yes—
181C24×C13#4112yes—
182C24×C13#4112yes—
183C24×C13#4112yes—
184C24×C13C2411yescharacteristic
185C2×D4×C13—28no—
186C2×D4×C13—28no—
187C2×D4×C13—44no—
188C2×D4×C13—44no—
189C2×D4×C13—44no—
190C2×D4×C13—44no—
191C2×D4×C13—44no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—28no—
197C22×C4×C13—21no—
198C22×C4×C13—21no—
199C22×C4×C13—21no—
200C22×C4×C13—21no—
201C22×C4×C13—21no—
202C22×C4×C13—21no—
203C22×C4×C13—21no—
204C22×C4×C13—21no—
205C22×C4×C13—21no—
206C22×C4×C13—21no—
207C22×C4×C13—21no—
208C22×C4×C13—21no—
209C22×C4×C13—21no—
210C22×C4×C13—21no—
211C22×C4×C13—21no—
212C22×C4×C13—21no—
213C22×C4×C13—21no—
214C22×C4×C13—21no—
215C22×C4×C13—21no—
216C22×C4×C13—21no—
217C22×C4×C13—21no—
218C22×C4×C13—21no—
219C22×C4×C13—21no—
220C22×C4×C13—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—44no—
276C22×C4×C13—44no—
277C22×C4×C13—44no—
278C22×C4×C13—44no—
279C22×C4×C13—44no—
280C22×C4×C13—44no—
281C22×C4×C13—44no—
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×C13C2×D412yes—
289C22×C4×C13C2×D412yes—
290C22×C4×C13C2×D412yes—
291C22×C4×C13C2×D412yes—
292C22×C4×C13C2×D412yes—
293C22×C4×C13C2×D412yes—
294C22×C4×C13#4112yes—
295C22×C4×C13#4112yes—
296C22×C4×C13#4112yes—
297C13×C4⋊C4—44no—
298C13×C4⋊C4—44no—
299C13×C4⋊C4—44no—
300C13×C4⋊C4—44no—
301C13×C22⋊C4—28no—
302C13×C22⋊C4—44no—
303C13×C22⋊C4—44no—
304C13×C22⋊C4—44no—
305C13×C22⋊C4—44no—
306C13×C22⋊C4—44no—
307C13×C22⋊C4—44no—
308C13×C22⋊C4—44no—
309C13×C22⋊C4—44no—
310C13×C22⋊C4—44no—
311C2×#397C2×C1311yescharacteristic, complemented
312C2×#394C2×C1311yescharacteristic
313C2×#386C2×C1311yescharacteristic
314C2×#386C2×C1311yescharacteristic
315C2×#385C2×C1311yescharacteristic, complemented
316C2×#380C2×C1311yescharacteristic, complemented
317#1445C2×C1311yescharacteristic, complemented
318#1443C2×C1311yescharacteristic, complemented
319#1441C2×C1311yescharacteristic, complemented
320#1441C2×C1311yescharacteristic, complemented
321#1440C2×C1311yescharacteristic, complemented
322#1440C2×C1311yescharacteristic, complemented
323#1439C2×C1311yescharacteristic, complemented
324C22⋊#95C2×C1311yescharacteristic, complemented
325C22⋊#95C2×C1311yescharacteristic, complemented
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—22no—
329C23×C13—22no—
330C23×C13—22no—
331C23×C13—22no—
332C23×C13—22no—
333C23×C13—22no—
334C23×C13—22no—
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—22no—
361C23×C13—22no—
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#12114yes—
395C23×C13#12314yes—
396C23×C13C22×D411yescharacteristic
397C23×C13C22×D411yescharacteristic
398C23×C13C22×D411yescharacteristic
399C23×C13C2×#4111yescharacteristic
400C23×C13C2×#4111yescharacteristic
401C23×C13C2×#4111yescharacteristic
402C23×C13C2×#4111yescharacteristic
403C23×C13C2×#4111yescharacteristic
404C23×C13C2×#4111yescharacteristic
405C23×C13H(5,𝔽2)11yescharacteristic
406C23×C13H(5,𝔽2)11yescharacteristic
407C23×C13H(5,𝔽2)11yescharacteristic
408C23×C13H(5,𝔽2)11yescharacteristic
409C23×C132−1+411yescharacteristic
410C23×C132−1+411yescharacteristic
411D4×C13—416no—
412C2×C4×C13—22no—
413C2×C4×C13—22no—
414C2×C4×C13—22no—
415C2×C4×C13—22no—
416C2×C4×C13—22no—
417C2×C4×C13—22no—
418C2×C4×C13—22no—
419C2×C4×C13—22no—
420C2×C4×C13—22no—
421C2×C4×C13—22no—
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—416no—
437C2×C4×C13—416no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13—41no—
455C2×C4×C13—41no—
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#12114yes—
505C23×D4C22×C1311yescharacteristic
506C24×C4C22×C1311yescharacteristic
507C24×C4C22×C1311yescharacteristic
508C22×C4⋊C4C22×C1311yescharacteristic
509C22×C4⋊C4C22×C1311yescharacteristic
510C22×C4⋊C4C22×C1311yescharacteristic
511C22×C4⋊C4C22×C1311yescharacteristic
512C22×C22⋊C4C22×C1311yescharacteristic
513C22×C22⋊C4C22×C1311yescharacteristic
514C22×C22⋊C4C22×C1311yescharacteristic
515C22×C22⋊C4C22×C1311yescharacteristic
516C22×C22⋊C4C22×C1311yescharacteristic
517C22×C22⋊C4C22×C1311yescharacteristic
518C22×C22⋊C4C22×C1311yescharacteristic
519C22×C22⋊C4C22×C1311yescharacteristic
520C22×C22⋊C4C22×C1311yescharacteristic
521C22×C22⋊C4C22×C1311yescharacteristic
522#397—24no—
523#394—24no—
524#386—24no—
525#386—24no—
526#385—24no—
527#380—24no—
528C2×#95C22×C1311yescharacteristic
529C2×#95C22×C1311yescharacteristic
530C2×#95C22×C1311yescharacteristic
531C2×#95C22×C1311yescharacteristic
532C2×#95C22×C1311yescharacteristic
533C2×#95C22×C1311yescharacteristic
534C2×#95C22×C1311yescharacteristic
535C2×#95C22×C1311yescharacteristic
536C2×#95C22×C1311yescharacteristic
537C2×#95C22×C1311yescharacteristic
538C2×#95C22×C1311yescharacteristic
539C2×#95C22×C1311yescharacteristic
540C2×#95C22×C1311yescharacteristic
541C2×#95C22×C1311yescharacteristic
542C2×#95C22×C1311yescharacteristic
543C2×#95C22×C1311yescharacteristic
544C2×#95C22×C1311yescharacteristic
545C2×#95C22×C1311yescharacteristic
546C22×C13—24no—
547C22×C13—24no—
548C22×C13—24no—
549C22×C13—24no—
550C22×C13—24no—
551C22×C13—24no—
552C22×C13—42no—
553C22×C13—42no—
554C22×C13—42no—
555C22×C13—42no—
556C22×C13—42no—
557C22×C13—42no—
558C22×C13—42no—
559C22×C13—42no—
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×C13C2×#12111yescharacteristic
577C22×C13C2×#12111yescharacteristic
578C22×C13C2×#12311yescharacteristic
579C22×C13#52511yescharacteristic
580C22×C13#52911yescharacteristic
581C22×C13#52911yescharacteristic
582C22×C13#53411yescharacteristic
583C22×C13#53411yescharacteristic
584C22×C13#53711yescharacteristic
585C22×C13#53811yescharacteristic
586C22×C13#53911yescharacteristic
587C22×C13#53911yescharacteristic
588C22×C13#53911yescharacteristic
589C22×C13#54211yescharacteristic
590C22×C13#54211yescharacteristic
591C22×C13D4211yescharacteristic
592C22×C13#54611yescharacteristic
593C22×C13#54611yescharacteristic
594C22×C13#54611yescharacteristic
595C22×C13#54611yescharacteristic
596C22×C13#54611yescharacteristic
597C22×C13#54711yescharacteristic
598C22×C13#54711yescharacteristic
599C22×C13#54711yescharacteristic
600C22×C13#54811yescharacteristic
601C22×C13#54811yescharacteristic
602C22×C13#55111yescharacteristic
603C22×C13#55111yescharacteristic
604C22×C13#55111yescharacteristic
605C22×C13#55111yescharacteristic
606C22×C13#55211yescharacteristic
607C22×C13#55311yescharacteristic
608C22×C13#55311yescharacteristic
609C22×C13#56011yescharacteristic
610C22×C13#56311yescharacteristic
611C4×C13—24no—
612C4×C13—42no—
613C4×C13—42no—
614C4×C13—42no—
615C4×C13—42no—
616C4×C13—42no—
617C4×C13—42no—
618C4×C13—81no—
619C4×C13—81no—
620C4×C13—81no—
621C4×C13—81no—
622C4×C13—81no—
623C4×C13—81no—
624C25C23×C1311yescharacteristic
625C25C23×C1311yescharacteristic
626C22×D4—22no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—22no—
630C22×D4—41no—
631C22×D4—41no—
632C22×D4D4×C1314yes—
633C23×C4—22no—
634C23×C4—22no—
635C23×C4—22no—
636C23×C4—22no—
637C23×C4—22no—
638C23×C4—22no—
639C23×C4—22no—
640C23×C4—22no—
641C23×C4—41no—
642C23×C4—41no—
643C23×C4—41no—
644C23×C4—41no—
645C23×C4—41no—
646C23×C4—41no—
647C23×C4C23×C1311yescharacteristic
648C23×C4C23×C1311yescharacteristic
649C23×C4C23×C1311yescharacteristic
650C23×C4C23×C1311yescharacteristic
651C23×C4C23×C1311yescharacteristic
652C23×C4C23×C1311yescharacteristic
653C23×C4C23×C1311yescharacteristic
654C23×C4C23×C1311yescharacteristic
655C23×C4C23×C1311yescharacteristic
656C23×C4C23×C1311yescharacteristic
657C23×C4C23×C1311yescharacteristic
658C23×C4C23×C1311yescharacteristic
659C23×C4C23×C1311yescharacteristic
660C2×C4⋊C4—22no—
661C2×C4⋊C4—22no—
662C2×C4⋊C4—22no—
663C2×C4⋊C4—22no—
664C2×C4⋊C4—22no—
665C2×C4⋊C4—22no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4—41no—
668C2×C4⋊C4—41no—
669C2×C4⋊C4—41no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4D4×C1314yescomplemented
672C2×C22⋊C4—22no—
673C2×C22⋊C4—22no—
674C2×C22⋊C4—22no—
675C2×C22⋊C4—22no—
676C2×C22⋊C4—22no—
677C2×C22⋊C4—22no—
678C2×C22⋊C4—22no—
679C2×C22⋊C4—22no—
680C2×C22⋊C4—22no—
681C2×C22⋊C4—22no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
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—41no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—41no—
701C2×C22⋊C4D4×C1314yes—
702#95—22no—
703#95—22no—
704#95—22no—
705#95—22no—
706#95—22no—
707#95—22no—
708#95—22no—
709#95—22no—
710#95—22no—
711#95—22no—
712#95—22no—
713#95—22no—
714#95—22no—
715#95—41no—
716#95—41no—
717#95—41no—
718#95—41no—
719#95—41no—
720C2×C13—44no—
721C2×C13—44no—
722C2×C13#241211yescharacteristic
723C2×C13#241611yescharacteristic
724C2×C13#241911yescharacteristic
725C2×C13#242511yescharacteristic
726C2×C13#242711yescharacteristic
727C2×C13#244311yescharacteristic
728C2×C13#247711yescharacteristic
729C2×C13#253411yescharacteristic
730C2×C13#257811yescharacteristic
731C2×C13#266811yescharacteristic
732C2×C13#269111yescharacteristic
733C2×C13#269511yescharacteristic
734C2×C13#271711yescharacteristic
735C2×C13#272811yescharacteristic
736C2×C13#274611yescharacteristic
737C24—21no—
738C24—21no—
739C24—21no—
740C24—21no—
741C24—21no—
742C24—21no—
743C24—21no—
744C24—21no—
745C24—21no—
746C24—21no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24C2×D4×C1312yes—
762C24C2×D4×C1312yes—
763C24C2×D4×C1312yes—
764C24C13×#4112yes—
765C24C13×#4112yes—
766C24C13×#4112yes—
767C24C24×C1311yescharacteristic
768C2×D4—28no—
769C2×D4—28no—
770C2×D4—44no—
771C2×D4—44no—
772C2×D4—44no—
773C2×D4—44no—
774C2×D4—44no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—28no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
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—21no—
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—44no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4—44no—
865C22×C4—44no—
866C22×C4—44no—
867C22×C4—44no—
868C22×C4—44no—
869C22×C4—44no—
870C22×C4—44no—
871C22×C4C2×D4×C1312yes—
872C22×C4C2×D4×C1312yes—
873C22×C4C2×D4×C1312yes—
874C22×C4C2×D4×C1312yes—
875C22×C4C2×D4×C1312yes—
876C22×C4C2×D4×C1312yes—
877C22×C4C13×#4112yes—
878C22×C4C13×#4112yes—
879C22×C4C13×#4112yes—
880C4⋊C4—44no—
881C4⋊C4—44no—
882C4⋊C4—44no—
883C4⋊C4—44no—
884C22⋊C4—28no—
885C22⋊C4—44no—
886C22⋊C4—44no—
887C22⋊C4—44no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—44no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C13#1539011yescharacteristic, direct product factor, Sylow
895C23—22no—
896C23—22no—
897C23—22no—
898C23—22no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
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—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
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—
963C23C13×#12114yes—
964C23C13×#12314yes—
965C23C22×D4×C1311yescharacteristic
966C23C22×D4×C1311yescharacteristic
967C23C22×D4×C1311yescharacteristic
968C23C2×C13×#4111yescharacteristic
969C23C2×C13×#4111yescharacteristic
970C23C2×C13×#4111yescharacteristic
971C23C2×C13×#4111yescharacteristic
972C23C2×C13×#4111yescharacteristic
973C23C2×C13×#4111yescharacteristic
974C23C13×H(5,𝔽2)11yescharacteristic
975C23C13×H(5,𝔽2)11yescharacteristic
976C23C13×H(5,𝔽2)11yescharacteristic
977C23C13×H(5,𝔽2)11yescharacteristic
978C23C13×2−1+411yescharacteristic
979C23C13×2−1+411yescharacteristic
980D4—416no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—22no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—416no—
1006C2×C4—416no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
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×C4C13×#12114yes—
1074C22—24no—
1075C22—24no—
1076C22—24no—
1077C22—24no—
1078C22—24no—
1079C22—24no—
1080C22—42no—
1081C22—42no—
1082C22—42no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—42no—
1103C22—42no—
1104C22C2×C13×#12111yescharacteristic
1105C22C2×C13×#12111yescharacteristic
1106C22C2×C13×#12311yescharacteristic
1107C22C13×#52511yescharacteristic
1108C22C13×#52911yescharacteristic
1109C22C13×#52911yescharacteristic
1110C22C13×#53411yescharacteristic
1111C22C13×#53411yescharacteristic
1112C22C13×#53711yescharacteristic
1113C22C13×#53811yescharacteristic
1114C22C13×#53911yescharacteristic
1115C22C13×#53911yescharacteristic
1116C22C13×#53911yescharacteristic
1117C22C13×#54211yescharacteristic
1118C22C13×#54211yescharacteristic
1119C22D42×C1311yescharacteristic
1120C22C13×#54611yescharacteristic
1121C22C13×#54611yescharacteristic
1122C22C13×#54611yescharacteristic
1123C22C13×#54611yescharacteristic
1124C22C13×#54611yescharacteristic
1125C22C13×#54711yescharacteristic
1126C22C13×#54711yescharacteristic
1127C22C13×#54711yescharacteristic
1128C22C13×#54811yescharacteristic
1129C22C13×#54811yescharacteristic
1130C22C13×#55111yescharacteristic
1131C22C13×#55111yescharacteristic
1132C22C13×#55111yescharacteristic
1133C22C13×#55111yescharacteristic
1134C22C13×#55211yescharacteristic
1135C22C13×#55311yescharacteristic
1136C22C13×#55311yescharacteristic
1137C22C13×#56011yescharacteristic
1138C22C13×#56311yescharacteristic
1139C4—24no—
1140C4—42no—
1141C4—42no—
1142C4—42no—
1143C4—42no—
1144C4—42no—
1145C4—42no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C2—44no—
1153C2—44no—
1154C2C13×#241211yescharacteristic
1155C2C13×#241611yescharacteristic
1156C2C13×#241911yescharacteristic
1157C2C13×#242511yescharacteristic
1158C2C13×#242711yescharacteristic
1159C2C13×#244311yescharacteristic
1160C2C13×#247711yescharacteristic
1161C2C13×#253411yescharacteristic
1162C2C13×#257811yescharacteristic
1163C2C13×#266811yescharacteristic
1164C2C13×#269111yescharacteristic
1165C2C13×#269511yescharacteristic
1166C2C13×#271711yescharacteristic
1167C2C13×#272811yescharacteristic
1168C2C13×#274611yescharacteristic
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. C2×C13×#397C2semidirect
5. C2×C13×#385C2semidirect
6. C2×C13×#380C2semidirect
7. C13×#1445C2semidirect
8. C13×#1443C2semidirect
9. C13×#1441C2semidirect
10. C13×#1441C2semidirect
11. C13×#1440C2semidirect
12. C13×#1440C2semidirect
13. C13×#1439C2semidirect
14. C13×C22⋊#95C2semidirect
15. C13×C22⋊#95C2semidirect
104. C2×C13×C4⋊C4D4semidirect
153. #15390C13direct (N × H)
311. C2×#397C2×C13semidirect
315. C2×#385C2×C13semidirect
316. C2×#380C2×C13semidirect
317. #1445C2×C13semidirect
318. #1443C2×C13semidirect
319. #1441C2×C13semidirect
320. #1441C2×C13semidirect
321. #1440C2×C13semidirect
322. #1440C2×C13semidirect
323. #1439C2×C13semidirect
324. C22⋊#95C2×C13semidirect
325. C22⋊#95C2×C13semidirect
671. C2×C4⋊C4D4×C13semidirect
894. C13#15390direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3972
C2×C13×#3942
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C13×#14452
C13×#14432
C13×#14412
C13×#14402
C13×#14392
C13×C22⋊#952
#1539013