Finite Group Databasebeta

← C13×#15325 #15701664

Subgroups — C13×#15325 #15701664

Order 3328.

2226 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C13×#399C211yesmaximal, characteristic, complemented
3C2×C13×#396C211yesmaximal, characteristic, complemented
4C2×C13×#395C211yesmaximal, characteristic, complemented
5C2×C13×#393C211yesmaximal, characteristic, complemented
6C2×C13×#390C211yesmaximal, characteristic
7C2×C13×#386C211yesmaximal, characteristic
8C2×C13×#385C211yesmaximal, characteristic, complemented
9C13×#1444C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic, complemented
13C13×#1438C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C4⋊#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×C4⋊C4C2211yescharacteristic
29C22×C13×C4⋊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
40C22×C13×C22⋊C4C2211yescharacteristic
41C22×C42×C13C2211yescharacteristic
42C13×#399—24no—
43C13×#396—24no—
44C13×#395—24no—
45C13×#393—24no—
46C13×#390—24no—
47C13×#386—24no—
48C13×#385—24no—
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
59C2×C13×#95C2211yescharacteristic
60C2×C13×#95C2211yescharacteristic
61C25×C13C2311yescharacteristic
62C25×C13C2311yescharacteristic
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—22no—
66C22×Q8×C13—22no—
67C22×Q8×C13—22no—
68C22×Q8×C13—41no—
69C22×Q8×C13—41no—
70C22×D4×C13—22no—
71C22×D4×C13—22no—
72C22×D4×C13—22no—
73C22×D4×C13—22no—
74C22×D4×C13—41no—
75C22×D4×C13—41no—
76C22×D4×C13Q814yescomplemented
77C23×C4×C13—22no—
78C23×C4×C13—22no—
79C23×C4×C13—22no—
80C23×C4×C13—22no—
81C23×C4×C13—22no—
82C23×C4×C13—41no—
83C23×C4×C13—41no—
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
95C23×C4×C13C2311yescharacteristic
96C23×C4×C13C2311yescharacteristic
97C13×C22⋊Q8—232no—
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—22no—
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⋊C4—41no—
119C2×C13×C4⋊C4—41no—
120C2×C13×C4⋊C4D414yescomplemented
121C2×C13×C4⋊C4D414yescomplemented
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—22no—
143C2×C13×C22⋊C4—22no—
144C2×C13×C22⋊C4—22no—
145C2×C13×C22⋊C4—22no—
146C2×C13×C22⋊C4—22no—
147C2×C13×C22⋊C4—22no—
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⋊C4D414yes—
155C2×C42×C13—22no—
156C2×C42×C13—22no—
157C2×C42×C13—41no—
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—41no—
168C13×#95D414yes—
169C13×#95D414yescomplemented
170#15325C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
192C24×C13—21no—
193C24×C13—21no—
194C24×C13—21no—
195C24×C13—21no—
196C24×C13—21no—
197C24×C13C2×D412yes—
198C24×C13C2×Q812yes—
199C24×C13C2×Q812yes—
200C24×C13#4112yes—
201C24×C13C2411yescharacteristic
202C2×Q8×C13—28no—
203C2×Q8×C13—44no—
204C2×Q8×C13—44no—
205C2×Q8×C13—44no—
206C2×Q8×C13—44no—
207C2×Q8×C13—44no—
208C2×Q8×C13—44no—
209C2×D4×C13—28no—
210C2×D4×C13—28no—
211C2×D4×C13—44no—
212C2×D4×C13—44no—
213C2×D4×C13—44no—
214C2×D4×C13—44no—
215C2×D4×C13—44no—
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—28no—
229C22×C4×C13—21no—
230C22×C4×C13—21no—
231C22×C4×C13—21no—
232C22×C4×C13—21no—
233C22×C4×C13—21no—
234C22×C4×C13—21no—
235C22×C4×C13—21no—
236C22×C4×C13—21no—
237C22×C4×C13—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—21no—
259C22×C4×C13—21no—
260C22×C4×C13—21no—
261C22×C4×C13—21no—
262C22×C4×C13—21no—
263C22×C4×C13—21no—
264C22×C4×C13—21no—
265C22×C4×C13—21no—
266C22×C4×C13—21no—
267C22×C4×C13—21no—
268C22×C4×C13—21no—
269C22×C4×C13—21no—
270C22×C4×C13—21no—
271C22×C4×C13—21no—
272C22×C4×C13—21no—
273C22×C4×C13—21no—
274C22×C4×C13—21no—
275C22×C4×C13—21no—
276C22×C4×C13—21no—
277C22×C4×C13—21no—
278C22×C4×C13—21no—
279C22×C4×C13—21no—
280C22×C4×C13—21no—
281C22×C4×C13—21no—
282C22×C4×C13—21no—
283C22×C4×C13—21no—
284C22×C4×C13—21no—
285C22×C4×C13—21no—
286C22×C4×C13—21no—
287C22×C4×C13—21no—
288C22×C4×C13—21no—
289C22×C4×C13—21no—
290C22×C4×C13—21no—
291C22×C4×C13—44no—
292C22×C4×C13—44no—
293C22×C4×C13—44no—
294C22×C4×C13—44no—
295C22×C4×C13—44no—
296C22×C4×C13—44no—
297C22×C4×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×D412yes—
305C22×C4×C13C2×D412yes—
306C22×C4×C13C2×D412yes—
307C22×C4×C13C2×D412yes—
308C22×C4×C13C2×D412yes—
309C22×C4×C13C2×D412yes—
310C22×C4×C13C2×D412yes—
311C22×C4×C13C2×Q812yes—
312C22×C4×C13#4112yes—
313C22×C4×C13#4112yes—
314C13×C4⋊C4—28no—
315C13×C4⋊C4—28no—
316C13×C4⋊C4—28no—
317C13×C4⋊C4—44no—
318C13×C4⋊C4—44no—
319C13×C4⋊C4—44no—
320C13×C4⋊C4—44no—
321C13×C4⋊C4—44no—
322C13×C22⋊C4—28no—
323C13×C22⋊C4—28no—
324C13×C22⋊C4—28no—
325C13×C22⋊C4—44no—
326C13×C22⋊C4—44no—
327C13×C22⋊C4—44no—
328C13×C22⋊C4—44no—
329C13×C22⋊C4—44no—
330C13×C22⋊C4—44no—
331C13×C22⋊C4—44no—
332C13×C22⋊C4—44no—
333C42×C13—44no—
334C22×C22⋊Q8C2×C1311yescharacteristic, complemented
335C2×#399C2×C1311yescharacteristic, complemented
336C2×#396C2×C1311yescharacteristic, complemented
337C2×#395C2×C1311yescharacteristic, complemented
338C2×#393C2×C1311yescharacteristic, complemented
339C2×#390C2×C1311yescharacteristic
340C2×#386C2×C1311yescharacteristic
341C2×#385C2×C1311yescharacteristic, complemented
342#1444C2×C1311yescharacteristic, complemented
343#1439C2×C1311yescharacteristic, complemented
344#1439C2×C1311yescharacteristic, complemented
345#1439C2×C1311yescharacteristic, complemented
346#1438C2×C1311yescharacteristic
347#1436C2×C1311yescharacteristic, complemented
348C4⋊#95C2×C1311yescharacteristic, complemented
349C23×C13—22no—
350C23×C13—22no—
351C23×C13—22no—
352C23×C13—22no—
353C23×C13—22no—
354C23×C13—22no—
355C23×C13—22no—
356C23×C13—22no—
357C23×C13—22no—
358C23×C13—22no—
359C23×C13—22no—
360C23×C13—22no—
361C23×C13—22no—
362C23×C13—22no—
363C23×C13—22no—
364C23×C13—22no—
365C23×C13—22no—
366C23×C13—22no—
367C23×C13—22no—
368C23×C13—22no—
369C23×C13—22no—
370C23×C13—22no—
371C23×C13—22no—
372C23×C13—22no—
373C23×C13—22no—
374C23×C13—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×C13—41no—
411C23×C13—41no—
412C23×C13—41no—
413C23×C13—41no—
414C23×C13—41no—
415C23×C13—41no—
416C23×C13—41no—
417C23×C13—41no—
418C23×C13C22⋊Q814yes—
419C23×C13C22×D411yescharacteristic
420C23×C13C22×D411yescharacteristic
421C23×C13C22×D411yescharacteristic
422C23×C13C22×D411yescharacteristic
423C23×C13C22×D411yescharacteristic
424C23×C13C22×Q811yescharacteristic
425C23×C13C2×#4111yescharacteristic
426C23×C13C2×#4111yescharacteristic
427C23×C13C2×#4111yescharacteristic
428C23×C13H(5,𝔽2)11yescharacteristic
429C23×C13H(5,𝔽2)11yescharacteristic
430C23×C13H(5,𝔽2)11yescharacteristic
431C23×C132−1+411yescharacteristic
432C23×C132−1+411yescharacteristic
433C23×C132−1+411yescharacteristic
434Q8×C13—416no—
435D4×C13—416no—
436C2×C4×C13—22no—
437C2×C4×C13—22no—
438C2×C4×C13—22no—
439C2×C4×C13—22no—
440C2×C4×C13—22no—
441C2×C4×C13—22no—
442C2×C4×C13—22no—
443C2×C4×C13—22no—
444C2×C4×C13—22no—
445C2×C4×C13—22no—
446C2×C4×C13—22no—
447C2×C4×C13—22no—
448C2×C4×C13—22no—
449C2×C4×C13—22no—
450C2×C4×C13—22no—
451C2×C4×C13—22no—
452C2×C4×C13—22no—
453C2×C4×C13—22no—
454C2×C4×C13—22no—
455C2×C4×C13—22no—
456C2×C4×C13—22no—
457C2×C4×C13—22no—
458C2×C4×C13—22no—
459C2×C4×C13—22no—
460C2×C4×C13—22no—
461C2×C4×C13—22no—
462C2×C4×C13—22no—
463C2×C4×C13—22no—
464C2×C4×C13—22no—
465C2×C4×C13—22no—
466C2×C4×C13—22no—
467C2×C4×C13—22no—
468C2×C4×C13—22no—
469C2×C4×C13—22no—
470C2×C4×C13—22no—
471C2×C4×C13—22no—
472C2×C4×C13—22no—
473C2×C4×C13—22no—
474C2×C4×C13—22no—
475C2×C4×C13—22no—
476C2×C4×C13—22no—
477C2×C4×C13—22no—
478C2×C4×C13—416no—
479C2×C4×C13—41no—
480C2×C4×C13—41no—
481C2×C4×C13—41no—
482C2×C4×C13—41no—
483C2×C4×C13—41no—
484C2×C4×C13—41no—
485C2×C4×C13—41no—
486C2×C4×C13—41no—
487C2×C4×C13—41no—
488C2×C4×C13—41no—
489C2×C4×C13—41no—
490C2×C4×C13—41no—
491C2×C4×C13—41no—
492C2×C4×C13—41no—
493C2×C4×C13—41no—
494C2×C4×C13—41no—
495C2×C4×C13—41no—
496C2×C4×C13—41no—
497C2×C4×C13—41no—
498C2×C4×C13—41no—
499C2×C4×C13—41no—
500C2×C4×C13—41no—
501C2×C4×C13—41no—
502C2×C4×C13—41no—
503C2×C4×C13—41no—
504C2×C4×C13—41no—
505C2×C4×C13—41no—
506C2×C4×C13—41no—
507C2×C4×C13—41no—
508C2×C4×C13—41no—
509C2×C4×C13—41no—
510C2×C4×C13—41no—
511C2×C4×C13—41no—
512C2×C4×C13—41no—
513C2×C4×C13—41no—
514C2×C4×C13—41no—
515C2×C4×C13—41no—
516C2×C4×C13—41no—
517C2×C4×C13—41no—
518C2×C4×C13—41no—
519C2×C4×C13—41no—
520C2×C4×C13—41no—
521C2×C4×C13—41no—
522C2×C4×C13—41no—
523C2×C4×C13—41no—
524C2×C4×C13—41no—
525C2×C4×C13#12014yes—
526C2×C4×C13C22⋊Q814yescomplemented
527C2×C4×C13#12714yes—
528C23×Q8C22×C1311yescharacteristic
529C23×D4C22×C1311yescharacteristic
530C24×C4C22×C1311yescharacteristic
531C2×C22⋊Q8—24no—
532C2×C22⋊Q8—24no—
533C2×C22⋊Q8—24no—
534C22×C4⋊C4C22×C1311yescharacteristic
535C22×C4⋊C4C22×C1311yescharacteristic
536C22×C4⋊C4C22×C1311yescharacteristic
537C22×C4⋊C4C22×C1311yescharacteristic
538C22×C4⋊C4C22×C1311yescharacteristic
539C22×C4⋊C4C22×C1311yescharacteristic
540C22×C4⋊C4C22×C1311yescharacteristic
541C22×C4⋊C4C22×C1311yescharacteristic
542C22×C22⋊C4C22×C1311yescharacteristic
543C22×C22⋊C4C22×C1311yescharacteristic
544C22×C22⋊C4C22×C1311yescharacteristic
545C22×C22⋊C4C22×C1311yescharacteristic
546C22×C22⋊C4C22×C1311yescharacteristic
547C22×C22⋊C4C22×C1311yescharacteristic
548C22×C22⋊C4C22×C1311yescharacteristic
549C22×C22⋊C4C22×C1311yescharacteristic
550C22×C22⋊C4C22×C1311yescharacteristic
551C22×C22⋊C4C22×C1311yescharacteristic
552C22×C22⋊C4C22×C1311yescharacteristic
553C22×C42C22×C1311yescharacteristic
554#399—24no—
555#396—24no—
556#395—24no—
557#393—24no—
558#390—24no—
559#386—24no—
560#385—24no—
561C2×#95C22×C1311yescharacteristic
562C2×#95C22×C1311yescharacteristic
563C2×#95C22×C1311yescharacteristic
564C2×#95C22×C1311yescharacteristic
565C2×#95C22×C1311yescharacteristic
566C2×#95C22×C1311yescharacteristic
567C2×#95C22×C1311yescharacteristic
568C2×#95C22×C1311yescharacteristic
569C2×#95C22×C1311yescharacteristic
570C2×#95C22×C1311yescharacteristic
571C2×#95C22×C1311yescharacteristic
572C2×#95C22×C1311yescharacteristic
573C22×C13—24no—
574C22×C13—24no—
575C22×C13—24no—
576C22×C13—42no—
577C22×C13—42no—
578C22×C13—42no—
579C22×C13—42no—
580C22×C13—42no—
581C22×C13—42no—
582C22×C13—42no—
583C22×C13—42no—
584C22×C13—42no—
585C22×C13—42no—
586C22×C13—42no—
587C22×C13—42no—
588C22×C13—42no—
589C22×C13—42no—
590C22×C13—42no—
591C22×C13—42no—
592C22×C13—42no—
593C22×C13—42no—
594C22×C13—42no—
595C22×C13—81no—
596C22×C13—81no—
597C22×C13—81no—
598C22×C13—81no—
599C22×C13—81no—
600C22×C13—81no—
601C22×C13—81no—
602C22×C13—81no—
603C22×C13C2×#12011yescharacteristic
604C22×C13C2×C22⋊Q811yescharacteristic
605C22×C13C2×C22⋊Q811yescharacteristic
606C22×C13#52511yescharacteristic
607C22×C13C2×#12711yescharacteristic
608C22×C13#53211yescharacteristic
609C22×C13#53511yescharacteristic
610C22×C13#53611yescharacteristic
611C22×C13#53611yescharacteristic
612C22×C13#53711yescharacteristic
613C22×C13#53711yescharacteristic
614C22×C13#53911yescharacteristic
615C22×C13#54211yescharacteristic
616C22×C13#54211yescharacteristic
617C22×C13#54311yescharacteristic
618C22×C13D4211yescharacteristic
619C22×C13D4211yescharacteristic
620C22×C13D4211yescharacteristic
621C22×C13D4211yescharacteristic
622C22×C13#54611yescharacteristic
623C22×C13#54611yescharacteristic
624C22×C13#54611yescharacteristic
625C22×C13#54711yescharacteristic
626C22×C13#54711yescharacteristic
627C22×C13#54711yescharacteristic
628C22×C13#54811yescharacteristic
629C22×C13#54811yescharacteristic
630C22×C13#54811yescharacteristic
631C22×C13D4×Q811yescharacteristic
632C22×C13D4×Q811yescharacteristic
633C22×C13D4×Q811yescharacteristic
634C22×C13#55111yescharacteristic
635C22×C13#55411yescharacteristic
636C22×C13#56211yescharacteristic
637C22×C13#56311yescharacteristic
638C4×C13—24no—
639C4×C13—24no—
640C4×C13—24no—
641C4×C13—42no—
642C4×C13—42no—
643C4×C13—42no—
644C4×C13—42no—
645C4×C13—42no—
646C4×C13—42no—
647C4×C13—42no—
648C4×C13—42no—
649C4×C13—81no—
650C4×C13—81no—
651C25C23×C1311yescharacteristic
652C25C23×C1311yescharacteristic
653C22×Q8—22no—
654C22×Q8—22no—
655C22×Q8—22no—
656C22×Q8—22no—
657C22×Q8—22no—
658C22×Q8—41no—
659C22×Q8—41no—
660C22×D4—22no—
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—41no—
665C22×D4—41no—
666C22×D4Q8×C1314yescomplemented
667C23×C4—22no—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—41no—
673C23×C4—41no—
674C23×C4C23×C1311yescharacteristic
675C23×C4C23×C1311yescharacteristic
676C23×C4C23×C1311yescharacteristic
677C23×C4C23×C1311yescharacteristic
678C23×C4C23×C1311yescharacteristic
679C23×C4C23×C1311yescharacteristic
680C23×C4C23×C1311yescharacteristic
681C23×C4C23×C1311yescharacteristic
682C23×C4C23×C1311yescharacteristic
683C23×C4C23×C1311yescharacteristic
684C23×C4C23×C1311yescharacteristic
685C23×C4C23×C1311yescharacteristic
686C23×C4C23×C1311yescharacteristic
687C22⋊Q8—232no—
688C2×C4⋊C4—22no—
689C2×C4⋊C4—22no—
690C2×C4⋊C4—22no—
691C2×C4⋊C4—22no—
692C2×C4⋊C4—22no—
693C2×C4⋊C4—22no—
694C2×C4⋊C4—22no—
695C2×C4⋊C4—22no—
696C2×C4⋊C4—22no—
697C2×C4⋊C4—22no—
698C2×C4⋊C4—22no—
699C2×C4⋊C4—22no—
700C2×C4⋊C4—22no—
701C2×C4⋊C4—22no—
702C2×C4⋊C4—22no—
703C2×C4⋊C4—22no—
704C2×C4⋊C4—22no—
705C2×C4⋊C4—22no—
706C2×C4⋊C4—41no—
707C2×C4⋊C4—41no—
708C2×C4⋊C4—41no—
709C2×C4⋊C4—41no—
710C2×C4⋊C4D4×C1314yescomplemented
711C2×C4⋊C4D4×C1314yescomplemented
712C2×C22⋊C4—22no—
713C2×C22⋊C4—22no—
714C2×C22⋊C4—22no—
715C2×C22⋊C4—22no—
716C2×C22⋊C4—22no—
717C2×C22⋊C4—22no—
718C2×C22⋊C4—22no—
719C2×C22⋊C4—22no—
720C2×C22⋊C4—22no—
721C2×C22⋊C4—22no—
722C2×C22⋊C4—22no—
723C2×C22⋊C4—22no—
724C2×C22⋊C4—22no—
725C2×C22⋊C4—22no—
726C2×C22⋊C4—22no—
727C2×C22⋊C4—22no—
728C2×C22⋊C4—22no—
729C2×C22⋊C4—22no—
730C2×C22⋊C4—22no—
731C2×C22⋊C4—22no—
732C2×C22⋊C4—22no—
733C2×C22⋊C4—22no—
734C2×C22⋊C4—22no—
735C2×C22⋊C4—22no—
736C2×C22⋊C4—22no—
737C2×C22⋊C4—22no—
738C2×C22⋊C4—41no—
739C2×C22⋊C4—41no—
740C2×C22⋊C4—41no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4D4×C1314yes—
745C2×C42—22no—
746C2×C42—22no—
747C2×C42—41no—
748#95—22no—
749#95—22no—
750#95—22no—
751#95—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—41no—
758#95D4×C1314yes—
759#95D4×C1314yescomplemented
760C2×C13—44no—
761C2×C13—82no—
762C2×C13#240911yescharacteristic
763C2×C13#243011yescharacteristic
764C2×C13#243311yescharacteristic
765C2×C13#243711yescharacteristic
766C2×C13#244911yescharacteristic
767C2×C13#245211yescharacteristic
768C2×C13#246111yescharacteristic
769C2×C13#254011yescharacteristic
770C2×C13#254211yescharacteristic
771C2×C13#267211yescharacteristic
772C2×C13#267411yescharacteristic
773C2×C13#268111yescharacteristic
774C2×C13#268311yescharacteristic
775C2×C13#269211yescharacteristic
776C2×C13#272311yescharacteristic
777C24—21no—
778C24—21no—
779C24—21no—
780C24—21no—
781C24—21no—
782C24—21no—
783C24—21no—
784C24—21no—
785C24—21no—
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—21no—
791C24—21no—
792C24—21no—
793C24—21no—
794C24—21no—
795C24—21no—
796C24—21no—
797C24—21no—
798C24—21no—
799C24—21no—
800C24—21no—
801C24—21no—
802C24—21no—
803C24C2×D4×C1312yes—
804C24C2×Q8×C1312yes—
805C24C2×Q8×C1312yes—
806C24C13×#4112yes—
807C24C24×C1311yescharacteristic
808C2×Q8—28no—
809C2×Q8—44no—
810C2×Q8—44no—
811C2×Q8—44no—
812C2×Q8—44no—
813C2×Q8—44no—
814C2×Q8—44no—
815C2×D4—28no—
816C2×D4—28no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—44no—
820C2×D4—44no—
821C2×D4—44no—
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—28no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—44no—
898C22×C4—44no—
899C22×C4—44no—
900C22×C4—44no—
901C22×C4—44no—
902C22×C4—44no—
903C22×C4C2×D4×C1312yes—
904C22×C4C2×D4×C1312yes—
905C22×C4C2×D4×C1312yes—
906C22×C4C2×D4×C1312yes—
907C22×C4C2×D4×C1312yes—
908C22×C4C2×D4×C1312yes—
909C22×C4C2×D4×C1312yes—
910C22×C4C2×D4×C1312yes—
911C22×C4C2×D4×C1312yes—
912C22×C4C2×D4×C1312yes—
913C22×C4C2×D4×C1312yes—
914C22×C4C2×D4×C1312yes—
915C22×C4C2×D4×C1312yes—
916C22×C4C2×D4×C1312yes—
917C22×C4C2×Q8×C1312yes—
918C22×C4C13×#4112yes—
919C22×C4C13×#4112yes—
920C4⋊C4—28no—
921C4⋊C4—28no—
922C4⋊C4—28no—
923C4⋊C4—44no—
924C4⋊C4—44no—
925C4⋊C4—44no—
926C4⋊C4—44no—
927C4⋊C4—44no—
928C22⋊C4—28no—
929C22⋊C4—28no—
930C22⋊C4—28no—
931C22⋊C4—44no—
932C22⋊C4—44no—
933C22⋊C4—44no—
934C22⋊C4—44no—
935C22⋊C4—44no—
936C22⋊C4—44no—
937C22⋊C4—44no—
938C22⋊C4—44no—
939C42—44no—
940C13#1532511yescharacteristic, direct product factor, Sylow
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—22no—
946C23—22no—
947C23—22no—
948C23—22no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—22no—
956C23—22no—
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—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—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23C13×C22⋊Q814yes—
1011C23C22×D4×C1311yescharacteristic
1012C23C22×D4×C1311yescharacteristic
1013C23C22×D4×C1311yescharacteristic
1014C23C22×D4×C1311yescharacteristic
1015C23C22×D4×C1311yescharacteristic
1016C23C22×Q8×C1311yescharacteristic
1017C23C2×C13×#4111yescharacteristic
1018C23C2×C13×#4111yescharacteristic
1019C23C2×C13×#4111yescharacteristic
1020C23C13×H(5,𝔽2)11yescharacteristic
1021C23C13×H(5,𝔽2)11yescharacteristic
1022C23C13×H(5,𝔽2)11yescharacteristic
1023C23C13×2−1+411yescharacteristic
1024C23C13×2−1+411yescharacteristic
1025C23C13×2−1+411yescharacteristic
1026Q8—416no—
1027D4—416no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
1035C2×C4—22no—
1036C2×C4—22no—
1037C2×C4—22no—
1038C2×C4—22no—
1039C2×C4—22no—
1040C2×C4—22no—
1041C2×C4—22no—
1042C2×C4—22no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—22no—
1049C2×C4—22no—
1050C2×C4—22no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
1068C2×C4—22no—
1069C2×C4—22no—
1070C2×C4—416no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4C13×#12014yes—
1118C2×C4C13×C22⋊Q814yescomplemented
1119C2×C4C13×#12714yes—
1120C22—24no—
1121C22—24no—
1122C22—24no—
1123C22—42no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22C2×C13×#12011yescharacteristic
1151C22C2×C13×C22⋊Q811yescharacteristic
1152C22C2×C13×C22⋊Q811yescharacteristic
1153C22C13×#52511yescharacteristic
1154C22C2×C13×#12711yescharacteristic
1155C22C13×#53211yescharacteristic
1156C22C13×#53511yescharacteristic
1157C22C13×#53611yescharacteristic
1158C22C13×#53611yescharacteristic
1159C22C13×#53711yescharacteristic
1160C22C13×#53711yescharacteristic
1161C22C13×#53911yescharacteristic
1162C22C13×#54211yescharacteristic
1163C22C13×#54211yescharacteristic
1164C22C13×#54311yescharacteristic
1165C22D42×C1311yescharacteristic
1166C22D42×C1311yescharacteristic
1167C22D42×C1311yescharacteristic
1168C22D42×C1311yescharacteristic
1169C22C13×#54611yescharacteristic
1170C22C13×#54611yescharacteristic
1171C22C13×#54611yescharacteristic
1172C22C13×#54711yescharacteristic
1173C22C13×#54711yescharacteristic
1174C22C13×#54711yescharacteristic
1175C22C13×#54811yescharacteristic
1176C22C13×#54811yescharacteristic
1177C22C13×#54811yescharacteristic
1178C22D4×Q8×C1311yescharacteristic
1179C22D4×Q8×C1311yescharacteristic
1180C22D4×Q8×C1311yescharacteristic
1181C22C13×#55111yescharacteristic
1182C22C13×#55411yescharacteristic
1183C22C13×#56211yescharacteristic
1184C22C13×#56311yescharacteristic
1185C4—24no—
1186C4—24no—
1187C4—24no—
1188C4—42no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—42no—
1193C4—42no—
1194C4—42no—
1195C4—42no—
1196C4—81no—
1197C4—81no—
1198C2—44no—
1199C2—82no—
1200C2C13×#240911yescharacteristic
1201C2C13×#243011yescharacteristic
1202C2C13×#243311yescharacteristic
1203C2C13×#243711yescharacteristic
1204C2C13×#244911yescharacteristic
1205C2C13×#245211yescharacteristic
1206C2C13×#246111yescharacteristic
1207C2C13×#254011yescharacteristic
1208C2C13×#254211yescharacteristic
1209C2C13×#267211yescharacteristic
1210C2C13×#267411yescharacteristic
1211C2C13×#268111yescharacteristic
1212C2C13×#268311yescharacteristic
1213C2C13×#269211yescharacteristic
1214C2C13×#272311yescharacteristic
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×#399C2semidirect
3. C2×C13×#396C2semidirect
4. C2×C13×#395C2semidirect
5. C2×C13×#393C2semidirect
8. C2×C13×#385C2semidirect
9. C13×#1444C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1439C2semidirect
14. C13×#1436C2semidirect
15. C13×C4⋊#95C2semidirect
76. C22×D4×C13Q8semidirect
120. C2×C13×C4⋊C4D4semidirect
121. C2×C13×C4⋊C4D4semidirect
169. C13×#95D4semidirect
170. #15325C13direct (N × H)
334. C22×C22⋊Q8C2×C13semidirect
335. C2×#399C2×C13semidirect
336. C2×#396C2×C13semidirect
337. C2×#395C2×C13semidirect
338. C2×#393C2×C13semidirect
341. C2×#385C2×C13semidirect
342. #1444C2×C13semidirect
343. #1439C2×C13semidirect
344. #1439C2×C13semidirect
345. #1439C2×C13semidirect
347. #1436C2×C13semidirect
348. C4⋊#95C2×C13semidirect
526. C2×C4×C13C22⋊Q8semidirect
666. C22×D4Q8×C13semidirect
710. C2×C4⋊C4D4×C13semidirect
711. C2×C4⋊C4D4×C13semidirect
759. #95D4×C13semidirect
940. C13#15325direct (N × H)
1118. 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×#3992
C2×C13×#3962
C2×C13×#3952
C2×C13×#3932
C2×C13×#3902
C2×C13×#3862
C2×C13×#3852
C13×#14442
C13×#14392
C13×#14382
C13×#14362
C13×C4⋊#952
#1532513