Finite Group Databasebeta

← C13×#15368 #15701707

Subgroups — C13×#15368 #15701707

Order 3328.

2474 conjugacy classes of subgroups.

The subgroup lattice has 1346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#123C211yesmaximal, characteristic, complemented
2C2×C13×#392C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic, complemented
4C2×C13×#386C211yesmaximal, characteristic, complemented
5C2×C13×#386C211yesmaximal, characteristic, complemented
6C2×C13×#380C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1440C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic, complemented
14C13×#1438C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C23×D4×C13C2211yescharacteristic
18C23×D4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C2×C13×#123—24no—
22C2×C13×#123—24no—
23C2×C13×#123—24no—
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊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×C13×C22⋊C4C2211yescharacteristic
38C22×C13×C22⋊C4C2211yescharacteristic
39C22×C13×C22⋊C4C2211yescharacteristic
40C13×#392—24no—
41C13×#386—24no—
42C13×#386—24no—
43C13×#386—24no—
44C13×#380—24no—
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C2×C13×#95C2211yescharacteristic
59C25×C13C2311yescharacteristic
60C25×C13C2311yescharacteristic
61C25×C13C2311yescharacteristic
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13—22no—
67C22×D4×C13—22no—
68C22×D4×C13—22no—
69C22×D4×C13—22no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—22no—
75C22×D4×C13—22no—
76C22×D4×C13—41no—
77C22×D4×C13—41no—
78C22×D4×C13—41no—
79C22×D4×C13—41no—
80C22×D4×C13—41no—
81C22×D4×C13—41no—
82C22×D4×C13D414yes—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—22no—
88C23×C4×C13—22no—
89C23×C4×C13—22no—
90C23×C4×C13—22no—
91C23×C4×C13—22no—
92C23×C4×C13—22no—
93C23×C4×C13—41no—
94C23×C4×C13—41no—
95C23×C4×C13—41no—
96C23×C4×C13—41no—
97C23×C4×C13C2311yescharacteristic
98C23×C4×C13C2311yescharacteristic
99C23×C4×C13C2311yescharacteristic
100C23×C4×C13C2311yescharacteristic
101C23×C4×C13C2311yescharacteristic
102C23×C4×C13C2311yescharacteristic
103C23×C4×C13C2311yescharacteristic
104C23×C4×C13C2311yescharacteristic
105C23×C4×C13C2311yescharacteristic
106C23×C4×C13C2311yescharacteristic
107C23×C4×C13C2311yescharacteristic
108C23×C4×C13C2311yescharacteristic
109C13×#123—232no—
110C2×C13×C4⋊C4—22no—
111C2×C13×C4⋊C4—22no—
112C2×C13×C4⋊C4—22no—
113C2×C13×C4⋊C4—22no—
114C2×C13×C4⋊C4—22no—
115C2×C13×C4⋊C4—22no—
116C2×C13×C4⋊C4—41no—
117C2×C13×C4⋊C4—41no—
118C2×C13×C4⋊C4D414yescomplemented
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—22no—
139C2×C13×C22⋊C4—22no—
140C2×C13×C22⋊C4—22no—
141C2×C13×C22⋊C4—22no—
142C2×C13×C22⋊C4—41no—
143C2×C13×C22⋊C4—41no—
144C2×C13×C22⋊C4—41no—
145C2×C13×C22⋊C4—41no—
146C2×C13×C22⋊C4—41no—
147C2×C13×C22⋊C4—41no—
148C2×C13×C22⋊C4—41no—
149C2×C13×C22⋊C4—41no—
150C2×C13×C22⋊C4—41no—
151C2×C13×C22⋊C4—41no—
152C2×C13×C22⋊C4—41no—
153C2×C13×C22⋊C4—41no—
154C2×C13×C22⋊C4—41no—
155C2×C13×C22⋊C4—41no—
156C2×C13×C22⋊C4D414yescomplemented
157C2×C13×C22⋊C4D414yescomplemented
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—22no—
161C13×#95—22no—
162C13×#95—22no—
163C13×#95—22no—
164C13×#95—22no—
165C13×#95—22no—
166C13×#95—22no—
167C13×#95—22no—
168C13×#95—41no—
169C13×#95—41no—
170C13×#95—41no—
171C13×#95—41no—
172#15368C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13—21no—
198C24×C13—21no—
199C24×C13—21no—
200C24×C13—21no—
201C24×C13—21no—
202C24×C13—21no—
203C24×C13—21no—
204C24×C13—21no—
205C24×C13—21no—
206C24×C13—21no—
207C24×C13—21no—
208C24×C13—21no—
209C24×C13—21no—
210C24×C13—21no—
211C24×C13C2×D412yes—
212C24×C13C2×D412yes—
213C24×C13C2×D412yes—
214C24×C13C2×D412yes—
215C24×C13#4112yes—
216C24×C13#4112yes—
217C24×C13#4112yes—
218C24×C13C2411yescharacteristic
219C2×D4×C13—28no—
220C2×D4×C13—28no—
221C2×D4×C13—28no—
222C2×D4×C13—28no—
223C2×D4×C13—44no—
224C2×D4×C13—44no—
225C2×D4×C13—44no—
226C2×D4×C13—44no—
227C2×D4×C13—44no—
228C2×D4×C13—44no—
229C2×D4×C13—44no—
230C2×D4×C13—44no—
231C2×D4×C13—44no—
232C2×D4×C13—44no—
233C2×D4×C13—44no—
234C2×D4×C13—44no—
235C2×D4×C13—44no—
236C2×D4×C13—44no—
237C2×D4×C13—44no—
238C2×D4×C13—44no—
239C2×D4×C13—44no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—28no—
245C22×C4×C13—28no—
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—21no—
291C22×C4×C13—21no—
292C22×C4×C13—21no—
293C22×C4×C13—21no—
294C22×C4×C13—21no—
295C22×C4×C13—21no—
296C22×C4×C13—21no—
297C22×C4×C13—21no—
298C22×C4×C13—21no—
299C22×C4×C13—21no—
300C22×C4×C13—21no—
301C22×C4×C13—21no—
302C22×C4×C13—21no—
303C22×C4×C13—21no—
304C22×C4×C13—21no—
305C22×C4×C13—21no—
306C22×C4×C13—21no—
307C22×C4×C13—21no—
308C22×C4×C13—21no—
309C22×C4×C13—21no—
310C22×C4×C13—21no—
311C22×C4×C13—21no—
312C22×C4×C13—21no—
313C22×C4×C13—21no—
314C22×C4×C13—21no—
315C22×C4×C13—21no—
316C22×C4×C13—44no—
317C22×C4×C13—44no—
318C22×C4×C13—44no—
319C22×C4×C13—44no—
320C22×C4×C13—44no—
321C22×C4×C13—44no—
322C22×C4×C13—44no—
323C22×C4×C13—44no—
324C22×C4×C13—44no—
325C22×C4×C13—44no—
326C22×C4×C13—44no—
327C22×C4×C13—44no—
328C22×C4×C13C2×D412yes—
329C22×C4×C13C2×D412yes—
330C22×C4×C13C2×D412yes—
331C22×C4×C13C2×D412yes—
332C22×C4×C13C2×D412yes—
333C22×C4×C13C2×D412yes—
334C22×C4×C13C2×D412yes—
335C22×C4×C13C2×D412yes—
336C22×C4×C13#4112yes—
337C22×C4×C13#4112yes—
338C13×C4⋊C4—28no—
339C13×C4⋊C4—28no—
340C13×C4⋊C4—44no—
341C13×C22⋊C4—28no—
342C13×C22⋊C4—28no—
343C13×C22⋊C4—28no—
344C13×C22⋊C4—44no—
345C13×C22⋊C4—44no—
346C13×C22⋊C4—44no—
347C13×C22⋊C4—44no—
348C13×C22⋊C4—44no—
349C13×C22⋊C4—44no—
350C13×C22⋊C4—44no—
351C13×C22⋊C4—44no—
352C13×C22⋊C4—44no—
353C13×C22⋊C4—44no—
354C22×#123C2×C1311yescharacteristic, complemented
355C2×#392C2×C1311yescharacteristic
356C2×#386C2×C1311yescharacteristic, complemented
357C2×#386C2×C1311yescharacteristic, complemented
358C2×#386C2×C1311yescharacteristic, complemented
359C2×#380C2×C1311yescharacteristic, complemented
360#1445C2×C1311yescharacteristic, complemented
361#1442C2×C1311yescharacteristic, complemented
362#1440C2×C1311yescharacteristic, complemented
363#1439C2×C1311yescharacteristic, complemented
364#1439C2×C1311yescharacteristic, complemented
365#1439C2×C1311yescharacteristic, complemented
366#1438C2×C1311yescharacteristic, complemented
367#1438C2×C1311yescharacteristic, complemented
368C22⋊#95C2×C1311yescharacteristic, complemented
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—22no—
382C23×C13—22no—
383C23×C13—22no—
384C23×C13—22no—
385C23×C13—22no—
386C23×C13—22no—
387C23×C13—22no—
388C23×C13—22no—
389C23×C13—22no—
390C23×C13—22no—
391C23×C13—22no—
392C23×C13—22no—
393C23×C13—22no—
394C23×C13—22no—
395C23×C13—22no—
396C23×C13—22no—
397C23×C13—22no—
398C23×C13—22no—
399C23×C13—22no—
400C23×C13—22no—
401C23×C13—22no—
402C23×C13—22no—
403C23×C13—22no—
404C23×C13—22no—
405C23×C13—22no—
406C23×C13—22no—
407C23×C13—22no—
408C23×C13—22no—
409C23×C13—22no—
410C23×C13—22no—
411C23×C13—22no—
412C23×C13—41no—
413C23×C13—41no—
414C23×C13—41no—
415C23×C13—41no—
416C23×C13—41no—
417C23×C13—41no—
418C23×C13—41no—
419C23×C13—41no—
420C23×C13—41no—
421C23×C13—41no—
422C23×C13—41no—
423C23×C13—41no—
424C23×C13—41no—
425C23×C13—41no—
426C23×C13—41no—
427C23×C13—41no—
428C23×C13—41no—
429C23×C13—41no—
430C23×C13—41no—
431C23×C13—41no—
432C23×C13—41no—
433C23×C13—41no—
434C23×C13—41no—
435C23×C13—41no—
436C23×C13—41no—
437C23×C13—41no—
438C23×C13—41no—
439C23×C13—41no—
440C23×C13—41no—
441C23×C13—41no—
442C23×C13—41no—
443C23×C13—41no—
444C23×C13—41no—
445C23×C13—41no—
446C23×C13—41no—
447C23×C13—41no—
448C23×C13—41no—
449C23×C13—41no—
450C23×C13—41no—
451C23×C13—41no—
452C23×C13—41no—
453C23×C13—41no—
454C23×C13—41no—
455C23×C13—41no—
456C23×C13—41no—
457C23×C13—41no—
458C23×C13—41no—
459C23×C13—41no—
460C23×C13—41no—
461C23×C13—41no—
462C23×C13—41no—
463C23×C13—41no—
464C23×C13—41no—
465C23×C13—41no—
466C23×C13—41no—
467C23×C13—41no—
468C23×C13—41no—
469C23×C13—41no—
470C23×C13—41no—
471C23×C13—41no—
472C23×C13#12114yes—
473C23×C13#12314yescomplemented
474C23×C13C22×D411yescharacteristic
475C23×C13C22×D411yescharacteristic
476C23×C13C22×D411yescharacteristic
477C23×C13C22×D411yescharacteristic
478C23×C13C2×#4111yescharacteristic
479C23×C13C2×#4111yescharacteristic
480C23×C13C2×#4111yescharacteristic
481C23×C13C2×#4111yescharacteristic
482C23×C13C2×#4111yescharacteristic
483C23×C13H(5,𝔽2)11yescharacteristic
484C23×C13H(5,𝔽2)11yescharacteristic
485C23×C13H(5,𝔽2)11yescharacteristic
486C23×C13H(5,𝔽2)11yescharacteristic
487C23×C13H(5,𝔽2)11yescharacteristic
488C23×C132−1+411yescharacteristic
489D4×C13—416no—
490D4×C13—416no—
491D4×C13—416no—
492C2×C4×C13—22no—
493C2×C4×C13—22no—
494C2×C4×C13—22no—
495C2×C4×C13—22no—
496C2×C4×C13—22no—
497C2×C4×C13—22no—
498C2×C4×C13—22no—
499C2×C4×C13—22no—
500C2×C4×C13—22no—
501C2×C4×C13—22no—
502C2×C4×C13—22no—
503C2×C4×C13—22no—
504C2×C4×C13—22no—
505C2×C4×C13—22no—
506C2×C4×C13—22no—
507C2×C4×C13—22no—
508C2×C4×C13—22no—
509C2×C4×C13—22no—
510C2×C4×C13—22no—
511C2×C4×C13—22no—
512C2×C4×C13—22no—
513C2×C4×C13—22no—
514C2×C4×C13—22no—
515C2×C4×C13—22no—
516C2×C4×C13—22no—
517C2×C4×C13—22no—
518C2×C4×C13—22no—
519C2×C4×C13—416no—
520C2×C4×C13—416no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13—41no—
524C2×C4×C13—41no—
525C2×C4×C13—41no—
526C2×C4×C13—41no—
527C2×C4×C13—41no—
528C2×C4×C13—41no—
529C2×C4×C13—41no—
530C2×C4×C13—41no—
531C2×C4×C13—41no—
532C2×C4×C13—41no—
533C2×C4×C13—41no—
534C2×C4×C13—41no—
535C2×C4×C13—41no—
536C2×C4×C13—41no—
537C2×C4×C13—41no—
538C2×C4×C13—41no—
539C2×C4×C13—41no—
540C2×C4×C13—41no—
541C2×C4×C13—41no—
542C2×C4×C13—41no—
543C2×C4×C13—41no—
544C2×C4×C13—41no—
545C2×C4×C13—41no—
546C2×C4×C13—41no—
547C2×C4×C13—41no—
548C2×C4×C13—41no—
549C2×C4×C13—41no—
550C2×C4×C13—41no—
551C2×C4×C13—41no—
552C2×C4×C13—41no—
553C2×C4×C13—41no—
554C2×C4×C13—41no—
555C2×C4×C13—41no—
556C2×C4×C13—41no—
557C2×C4×C13—41no—
558C2×C4×C13—41no—
559C2×C4×C13—41no—
560C2×C4×C13—41no—
561C2×C4×C13—41no—
562C2×C4×C13—41no—
563C2×C4×C13—41no—
564C2×C4×C13—41no—
565C2×C4×C13—41no—
566C2×C4×C13—41no—
567C2×C4×C13—41no—
568C2×C4×C13—41no—
569C2×C4×C13—41no—
570C2×C4×C13—41no—
571C2×C4×C13—41no—
572C2×C4×C13—41no—
573C2×C4×C13—41no—
574C2×C4×C13—41no—
575C2×C4×C13—41no—
576C2×C4×C13—41no—
577C2×C4×C13#12014yes—
578C23×D4C22×C1311yescharacteristic
579C23×D4C22×C1311yescharacteristic
580C23×D4C22×C1311yescharacteristic
581C24×C4C22×C1311yescharacteristic
582C24×C4C22×C1311yescharacteristic
583C2×#123—24no—
584C2×#123—24no—
585C2×#123—24no—
586C22×C4⋊C4C22×C1311yescharacteristic
587C22×C4⋊C4C22×C1311yescharacteristic
588C22×C4⋊C4C22×C1311yescharacteristic
589C22×C22⋊C4C22×C1311yescharacteristic
590C22×C22⋊C4C22×C1311yescharacteristic
591C22×C22⋊C4C22×C1311yescharacteristic
592C22×C22⋊C4C22×C1311yescharacteristic
593C22×C22⋊C4C22×C1311yescharacteristic
594C22×C22⋊C4C22×C1311yescharacteristic
595C22×C22⋊C4C22×C1311yescharacteristic
596C22×C22⋊C4C22×C1311yescharacteristic
597C22×C22⋊C4C22×C1311yescharacteristic
598C22×C22⋊C4C22×C1311yescharacteristic
599C22×C22⋊C4C22×C1311yescharacteristic
600C22×C22⋊C4C22×C1311yescharacteristic
601C22×C22⋊C4C22×C1311yescharacteristic
602#392—24no—
603#386—24no—
604#386—24no—
605#386—24no—
606#380—24no—
607C2×#95C22×C1311yescharacteristic
608C2×#95C22×C1311yescharacteristic
609C2×#95C22×C1311yescharacteristic
610C2×#95C22×C1311yescharacteristic
611C2×#95C22×C1311yescharacteristic
612C2×#95C22×C1311yescharacteristic
613C2×#95C22×C1311yescharacteristic
614C2×#95C22×C1311yescharacteristic
615C2×#95C22×C1311yescharacteristic
616C2×#95C22×C1311yescharacteristic
617C2×#95C22×C1311yescharacteristic
618C2×#95C22×C1311yescharacteristic
619C2×#95C22×C1311yescharacteristic
620C2×#95C22×C1311yescharacteristic
621C22×C13—24no—
622C22×C13—24no—
623C22×C13—24no—
624C22×C13—24no—
625C22×C13—24no—
626C22×C13—24no—
627C22×C13—42no—
628C22×C13—42no—
629C22×C13—42no—
630C22×C13—42no—
631C22×C13—42no—
632C22×C13—42no—
633C22×C13—42no—
634C22×C13—42no—
635C22×C13—42no—
636C22×C13—42no—
637C22×C13—42no—
638C22×C13—42no—
639C22×C13—42no—
640C22×C13—42no—
641C22×C13—42no—
642C22×C13—42no—
643C22×C13—42no—
644C22×C13—42no—
645C22×C13—42no—
646C22×C13—42no—
647C22×C13—42no—
648C22×C13—42no—
649C22×C13—42no—
650C22×C13—42no—
651C22×C13—42no—
652C22×C13—42no—
653C22×C13—42no—
654C22×C13—42no—
655C22×C13—42no—
656C22×C13—42no—
657C22×C13—42no—
658C22×C13—81no—
659C22×C13—81no—
660C22×C13—81no—
661C22×C13—81no—
662C22×C13—81no—
663C22×C13—81no—
664C22×C13—81no—
665C22×C13—81no—
666C22×C13C2×#12011yescharacteristic
667C22×C13C2×#12111yescharacteristic
668C22×C13C2×#12311yescharacteristic
669C22×C13#52511yescharacteristic
670C22×C13#52511yescharacteristic
671C22×C13#52911yescharacteristic
672C22×C13#53411yescharacteristic
673C22×C13#53511yescharacteristic
674C22×C13#53511yescharacteristic
675C22×C13#53711yescharacteristic
676C22×C13#53811yescharacteristic
677C22×C13#53911yescharacteristic
678C22×C13#53911yescharacteristic
679C22×C13#54011yescharacteristic
680C22×C13#54011yescharacteristic
681C22×C13D4211yescharacteristic
682C22×C13D4211yescharacteristic
683C22×C13#54611yescharacteristic
684C22×C13#54611yescharacteristic
685C22×C13#54611yescharacteristic
686C22×C13#54611yescharacteristic
687C22×C13#54611yescharacteristic
688C22×C13#54611yescharacteristic
689C22×C13#54611yescharacteristic
690C22×C13#54611yescharacteristic
691C22×C13#54711yescharacteristic
692C22×C13#54711yescharacteristic
693C22×C13#54811yescharacteristic
694C22×C13#55011yescharacteristic
695C22×C13#55111yescharacteristic
696C22×C13#55111yescharacteristic
697C22×C13#55111yescharacteristic
698C22×C13#55311yescharacteristic
699C22×C13#56011yescharacteristic
700C22×C13#56211yescharacteristic
701C4×C13—24no—
702C4×C13—42no—
703C4×C13—42no—
704C4×C13—42no—
705C4×C13—42no—
706C4×C13—42no—
707C4×C13—42no—
708C4×C13—42no—
709C4×C13—81no—
710C4×C13—81no—
711C4×C13—81no—
712C4×C13—81no—
713C25C23×C1311yescharacteristic
714C25C23×C1311yescharacteristic
715C25C23×C1311yescharacteristic
716C22×D4—22no—
717C22×D4—22no—
718C22×D4—22no—
719C22×D4—22no—
720C22×D4—22no—
721C22×D4—22no—
722C22×D4—22no—
723C22×D4—22no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—22no—
727C22×D4—22no—
728C22×D4—22no—
729C22×D4—22no—
730C22×D4—41no—
731C22×D4—41no—
732C22×D4—41no—
733C22×D4—41no—
734C22×D4—41no—
735C22×D4—41no—
736C22×D4D4×C1314yes—
737C23×C4—22no—
738C23×C4—22no—
739C23×C4—22no—
740C23×C4—22no—
741C23×C4—22no—
742C23×C4—22no—
743C23×C4—22no—
744C23×C4—22no—
745C23×C4—22no—
746C23×C4—22no—
747C23×C4—41no—
748C23×C4—41no—
749C23×C4—41no—
750C23×C4—41no—
751C23×C4C23×C1311yescharacteristic
752C23×C4C23×C1311yescharacteristic
753C23×C4C23×C1311yescharacteristic
754C23×C4C23×C1311yescharacteristic
755C23×C4C23×C1311yescharacteristic
756C23×C4C23×C1311yescharacteristic
757C23×C4C23×C1311yescharacteristic
758C23×C4C23×C1311yescharacteristic
759C23×C4C23×C1311yescharacteristic
760C23×C4C23×C1311yescharacteristic
761C23×C4C23×C1311yescharacteristic
762C23×C4C23×C1311yescharacteristic
763#123—232no—
764C2×C4⋊C4—22no—
765C2×C4⋊C4—22no—
766C2×C4⋊C4—22no—
767C2×C4⋊C4—22no—
768C2×C4⋊C4—22no—
769C2×C4⋊C4—22no—
770C2×C4⋊C4—41no—
771C2×C4⋊C4—41no—
772C2×C4⋊C4D4×C1314yescomplemented
773C2×C22⋊C4—22no—
774C2×C22⋊C4—22no—
775C2×C22⋊C4—22no—
776C2×C22⋊C4—22no—
777C2×C22⋊C4—22no—
778C2×C22⋊C4—22no—
779C2×C22⋊C4—22no—
780C2×C22⋊C4—22no—
781C2×C22⋊C4—22no—
782C2×C22⋊C4—22no—
783C2×C22⋊C4—22no—
784C2×C22⋊C4—22no—
785C2×C22⋊C4—22no—
786C2×C22⋊C4—22no—
787C2×C22⋊C4—22no—
788C2×C22⋊C4—22no—
789C2×C22⋊C4—22no—
790C2×C22⋊C4—22no—
791C2×C22⋊C4—22no—
792C2×C22⋊C4—22no—
793C2×C22⋊C4—22no—
794C2×C22⋊C4—22no—
795C2×C22⋊C4—22no—
796C2×C22⋊C4—41no—
797C2×C22⋊C4—41no—
798C2×C22⋊C4—41no—
799C2×C22⋊C4—41no—
800C2×C22⋊C4—41no—
801C2×C22⋊C4—41no—
802C2×C22⋊C4—41no—
803C2×C22⋊C4—41no—
804C2×C22⋊C4—41no—
805C2×C22⋊C4—41no—
806C2×C22⋊C4—41no—
807C2×C22⋊C4—41no—
808C2×C22⋊C4—41no—
809C2×C22⋊C4—41no—
810C2×C22⋊C4D4×C1314yescomplemented
811C2×C22⋊C4D4×C1314yescomplemented
812#95—22no—
813#95—22no—
814#95—22no—
815#95—22no—
816#95—22no—
817#95—22no—
818#95—22no—
819#95—22no—
820#95—22no—
821#95—22no—
822#95—41no—
823#95—41no—
824#95—41no—
825#95—41no—
826C2×C13—44no—
827C2×C13—44no—
828C2×C13—82no—
829C2×C13#240411yescharacteristic
830C2×C13#240711yescharacteristic
831C2×C13#240811yescharacteristic
832C2×C13#241211yescharacteristic
833C2×C13#241811yescharacteristic
834C2×C13#242511yescharacteristic
835C2×C13#244311yescharacteristic
836C2×C13#245711yescharacteristic
837C2×C13#247111yescharacteristic
838C2×C13#267111yescharacteristic
839C2×C13#267311yescharacteristic
840C2×C13#269311yescharacteristic
841C2×C13#269611yescharacteristic
842C2×C13#270311yescharacteristic
843C2×C13#270611yescharacteristic
844C24—21no—
845C24—21no—
846C24—21no—
847C24—21no—
848C24—21no—
849C24—21no—
850C24—21no—
851C24—21no—
852C24—21no—
853C24—21no—
854C24—21no—
855C24—21no—
856C24—21no—
857C24—21no—
858C24—21no—
859C24—21no—
860C24—21no—
861C24—21no—
862C24—21no—
863C24—21no—
864C24—21no—
865C24—21no—
866C24—21no—
867C24—21no—
868C24—21no—
869C24—21no—
870C24—21no—
871C24—21no—
872C24—21no—
873C24—21no—
874C24—21no—
875C24—21no—
876C24—21no—
877C24—21no—
878C24—21no—
879C24—21no—
880C24—21no—
881C24—21no—
882C24C2×D4×C1312yes—
883C24C2×D4×C1312yes—
884C24C2×D4×C1312yes—
885C24C2×D4×C1312yes—
886C24C13×#4112yes—
887C24C13×#4112yes—
888C24C13×#4112yes—
889C24C24×C1311yescharacteristic
890C2×D4—28no—
891C2×D4—28no—
892C2×D4—28no—
893C2×D4—28no—
894C2×D4—44no—
895C2×D4—44no—
896C2×D4—44no—
897C2×D4—44no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—44no—
901C2×D4—44no—
902C2×D4—44no—
903C2×D4—44no—
904C2×D4—44no—
905C2×D4—44no—
906C2×D4—44no—
907C2×D4—44no—
908C2×D4—44no—
909C2×D4—44no—
910C2×D4—44no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—28no—
916C22×C4—28no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—21no—
975C22×C4—21no—
976C22×C4—21no—
977C22×C4—21no—
978C22×C4—21no—
979C22×C4—21no—
980C22×C4—21no—
981C22×C4—21no—
982C22×C4—21no—
983C22×C4—21no—
984C22×C4—21no—
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—44no—
988C22×C4—44no—
989C22×C4—44no—
990C22×C4—44no—
991C22×C4—44no—
992C22×C4—44no—
993C22×C4—44no—
994C22×C4—44no—
995C22×C4—44no—
996C22×C4—44no—
997C22×C4—44no—
998C22×C4—44no—
999C22×C4C2×D4×C1312yes—
1000C22×C4C2×D4×C1312yes—
1001C22×C4C2×D4×C1312yes—
1002C22×C4C2×D4×C1312yes—
1003C22×C4C2×D4×C1312yes—
1004C22×C4C2×D4×C1312yes—
1005C22×C4C2×D4×C1312yes—
1006C22×C4C2×D4×C1312yes—
1007C22×C4C13×#4112yes—
1008C22×C4C13×#4112yes—
1009C4⋊C4—28no—
1010C4⋊C4—28no—
1011C4⋊C4—44no—
1012C22⋊C4—28no—
1013C22⋊C4—28no—
1014C22⋊C4—28no—
1015C22⋊C4—44no—
1016C22⋊C4—44no—
1017C22⋊C4—44no—
1018C22⋊C4—44no—
1019C22⋊C4—44no—
1020C22⋊C4—44no—
1021C22⋊C4—44no—
1022C22⋊C4—44no—
1023C22⋊C4—44no—
1024C22⋊C4—44no—
1025C13#1536811yescharacteristic, direct product factor, Sylow
1026C23—22no—
1027C23—22no—
1028C23—22no—
1029C23—22no—
1030C23—22no—
1031C23—22no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—22no—
1037C23—22no—
1038C23—22no—
1039C23—22no—
1040C23—22no—
1041C23—22no—
1042C23—22no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—22no—
1048C23—22no—
1049C23—22no—
1050C23—22no—
1051C23—22no—
1052C23—22no—
1053C23—22no—
1054C23—22no—
1055C23—22no—
1056C23—22no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—22no—
1061C23—22no—
1062C23—22no—
1063C23—22no—
1064C23—22no—
1065C23—22no—
1066C23—22no—
1067C23—22no—
1068C23—22no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—41no—
1090C23—41no—
1091C23—41no—
1092C23—41no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23C13×#12114yes—
1130C23C13×#12314yescomplemented
1131C23C22×D4×C1311yescharacteristic
1132C23C22×D4×C1311yescharacteristic
1133C23C22×D4×C1311yescharacteristic
1134C23C22×D4×C1311yescharacteristic
1135C23C2×C13×#4111yescharacteristic
1136C23C2×C13×#4111yescharacteristic
1137C23C2×C13×#4111yescharacteristic
1138C23C2×C13×#4111yescharacteristic
1139C23C2×C13×#4111yescharacteristic
1140C23C13×H(5,𝔽2)11yescharacteristic
1141C23C13×H(5,𝔽2)11yescharacteristic
1142C23C13×H(5,𝔽2)11yescharacteristic
1143C23C13×H(5,𝔽2)11yescharacteristic
1144C23C13×H(5,𝔽2)11yescharacteristic
1145C23C13×2−1+411yescharacteristic
1146D4—416no—
1147D4—416no—
1148D4—416no—
1149C2×C4—22no—
1150C2×C4—22no—
1151C2×C4—22no—
1152C2×C4—22no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—22no—
1167C2×C4—22no—
1168C2×C4—22no—
1169C2×C4—22no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—22no—
1173C2×C4—22no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—416no—
1177C2×C4—416no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4C13×#12014yes—
1235C22—24no—
1236C22—24no—
1237C22—24no—
1238C22—24no—
1239C22—24no—
1240C22—24no—
1241C22—42no—
1242C22—42no—
1243C22—42no—
1244C22—42no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—42no—
1249C22—42no—
1250C22—42no—
1251C22—42no—
1252C22—42no—
1253C22—42no—
1254C22—42no—
1255C22—42no—
1256C22—42no—
1257C22—42no—
1258C22—42no—
1259C22—42no—
1260C22—42no—
1261C22—42no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—42no—
1266C22—42no—
1267C22—42no—
1268C22—42no—
1269C22—42no—
1270C22—42no—
1271C22—42no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22C2×C13×#12011yescharacteristic
1281C22C2×C13×#12111yescharacteristic
1282C22C2×C13×#12311yescharacteristic
1283C22C13×#52511yescharacteristic
1284C22C13×#52511yescharacteristic
1285C22C13×#52911yescharacteristic
1286C22C13×#53411yescharacteristic
1287C22C13×#53511yescharacteristic
1288C22C13×#53511yescharacteristic
1289C22C13×#53711yescharacteristic
1290C22C13×#53811yescharacteristic
1291C22C13×#53911yescharacteristic
1292C22C13×#53911yescharacteristic
1293C22C13×#54011yescharacteristic
1294C22C13×#54011yescharacteristic
1295C22D42×C1311yescharacteristic
1296C22D42×C1311yescharacteristic
1297C22C13×#54611yescharacteristic
1298C22C13×#54611yescharacteristic
1299C22C13×#54611yescharacteristic
1300C22C13×#54611yescharacteristic
1301C22C13×#54611yescharacteristic
1302C22C13×#54611yescharacteristic
1303C22C13×#54611yescharacteristic
1304C22C13×#54611yescharacteristic
1305C22C13×#54711yescharacteristic
1306C22C13×#54711yescharacteristic
1307C22C13×#54811yescharacteristic
1308C22C13×#55011yescharacteristic
1309C22C13×#55111yescharacteristic
1310C22C13×#55111yescharacteristic
1311C22C13×#55111yescharacteristic
1312C22C13×#55311yescharacteristic
1313C22C13×#56011yescharacteristic
1314C22C13×#56211yescharacteristic
1315C4—24no—
1316C4—42no—
1317C4—42no—
1318C4—42no—
1319C4—42no—
1320C4—42no—
1321C4—42no—
1322C4—42no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C2—44no—
1328C2—44no—
1329C2—82no—
1330C2C13×#240411yescharacteristic
1331C2C13×#240711yescharacteristic
1332C2C13×#240811yescharacteristic
1333C2C13×#241211yescharacteristic
1334C2C13×#241811yescharacteristic
1335C2C13×#242511yescharacteristic
1336C2C13×#244311yescharacteristic
1337C2C13×#245711yescharacteristic
1338C2C13×#247111yescharacteristic
1339C2C13×#267111yescharacteristic
1340C2C13×#267311yescharacteristic
1341C2C13×#269311yescharacteristic
1342C2C13×#269611yescharacteristic
1343C2C13×#270311yescharacteristic
1344C2C13×#270611yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC2×C13×#392C2
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C13×#123C2semidirect
3. C2×C13×#386C2semidirect
4. C2×C13×#386C2semidirect
5. C2×C13×#386C2semidirect
6. C2×C13×#380C2semidirect
7. C13×#1445C2semidirect
8. C13×#1442C2semidirect
9. C13×#1440C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
13. C13×#1438C2semidirect
14. C13×#1438C2semidirect
15. C13×C22⋊#95C2semidirect
118. C2×C13×C4⋊C4D4semidirect
156. C2×C13×C22⋊C4D4semidirect
157. C2×C13×C22⋊C4D4semidirect
172. #15368C13direct (N × H)
354. C22×#123C2×C13semidirect
356. C2×#386C2×C13semidirect
357. C2×#386C2×C13semidirect
358. C2×#386C2×C13semidirect
359. C2×#380C2×C13semidirect
360. #1445C2×C13semidirect
361. #1442C2×C13semidirect
362. #1440C2×C13semidirect
363. #1439C2×C13semidirect
364. #1439C2×C13semidirect
365. #1439C2×C13semidirect
366. #1438C2×C13semidirect
367. #1438C2×C13semidirect
368. C22⋊#95C2×C13semidirect
473. C23×C13#123semidirect
772. C2×C4⋊C4D4×C13semidirect
810. C2×C22⋊C4D4×C13semidirect
811. C2×C22⋊C4D4×C13semidirect
1025. C13#15368direct (N × H)
1130. C23C13×#123semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1232
C2×C13×#3922
C2×C13×#3862
C2×C13×#3802
C13×#14452
C13×#14422
C13×#14402
C13×#14392
C13×#14382
C13×C22⋊#952
#1536813