Finite Group Databasebeta

← C13×#13975 #15700314

Subgroups — C13×#13975 #15700314

Order 3328.

2690 conjugacy classes of subgroups.

The subgroup lattice has 1234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D4×C13C211yesmaximal, characteristic
2C2×C13×#386C211yesmaximal, characteristic
3C2×C13×#386C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic, complemented
5C2×C13×#385C211yesmaximal, characteristic, complemented
6C2×C13×#380C211yesmaximal, characteristic, complemented
7C22×C13×#95C211yesmaximal, characteristic, complemented
8C13×#1444C211yesmaximal, characteristic, complemented
9C13×#1442C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic, complemented
11C13×#1439C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×C22⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C24×C4×C13C2211yescharacteristic
19C24×C4×C13C2211yescharacteristic
20C24×C4×C13C2211yescharacteristic
21C2×C4×D4×C13—24no—
22C2×C4×D4×C13—24no—
23C2×C4×D4×C13—24no—
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C4⋊C4C2211yescharacteristic
28C22×C13×C4⋊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×#386—24no—
39C13×#386C418yescomplemented
40C13×#385—24no—
41C13×#385—24no—
42C13×#380—24no—
43C2×C13×#95—24no—
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
59C2×C13×#95C2211yescharacteristic
60C25×C13C2311yescharacteristic
61C25×C13C2311yescharacteristic
62C22×D4×C13—22no—
63C22×D4×C13—22no—
64C22×D4×C13—22no—
65C22×D4×C13—22no—
66C22×D4×C13C2×C414yes—
67C22×D4×C13D414yes—
68C22×D4×C13Q814yes—
69C23×C4×C13—22no—
70C23×C4×C13—22no—
71C23×C4×C13—22no—
72C23×C4×C13—22no—
73C23×C4×C13—22no—
74C23×C4×C13—22no—
75C23×C4×C13—22no—
76C23×C4×C13—22no—
77C23×C4×C13—22no—
78C23×C4×C13—22no—
79C23×C4×C13—22no—
80C23×C4×C13—22no—
81C23×C4×C13—22no—
82C23×C4×C13—22no—
83C23×C4×C13—22no—
84C23×C4×C13—22no—
85C23×C4×C13—22no—
86C23×C4×C13—22no—
87C23×C4×C13—41no—
88C23×C4×C13—41no—
89C23×C4×C13—41no—
90C23×C4×C13—41no—
91C23×C4×C13—41no—
92C23×C4×C13—41no—
93C23×C4×C13—41no—
94C23×C4×C13—41no—
95C23×C4×C13C2×C414yescomplemented
96C23×C4×C13D414yes—
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
109C23×C4×C13C2311yescharacteristic
110C4×D4×C13—232no—
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—22no—
117C2×C13×C4⋊C4—22no—
118C2×C13×C4⋊C4—22no—
119C2×C13×C4⋊C4—22no—
120C2×C13×C4⋊C4—22no—
121C2×C13×C4⋊C4—22no—
122C2×C13×C4⋊C4—41no—
123C2×C13×C4⋊C4—41no—
124C2×C13×C4⋊C4—41no—
125C2×C13×C4⋊C4—41no—
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⋊C4C2×C414yescomplemented
147C2×C13×C22⋊C4C2×C414yescomplemented
148C2×C13×C22⋊C4C2×C414yescomplemented
149C2×C13×C22⋊C4D414yes—
150C2×C42×C13—22no—
151C2×C42×C13—22no—
152C2×C42×C13—22no—
153C13×#95—22no—
154C13×#95—22no—
155C13×#95—22no—
156C13×#95—22no—
157C13×#95—22no—
158C13×#95—22no—
159C13×#95—22no—
160C13×#95—22no—
161C13×#95—22no—
162C13×#95—22no—
163C13×#95—22no—
164C13×#95—41no—
165C13×#95—41no—
166C13×#95C2×C414yescomplemented
167C13×#95C2×C414yescomplemented
168C13×#95D414yescomplemented
169#13975C1311yesmaximal, characteristic, direct product factor, Sylow
170C24×C13—21no—
171C24×C13—21no—
172C24×C13—21no—
173C24×C13—21no—
174C24×C13—21no—
175C24×C13—21no—
176C24×C13—21no—
177C24×C13—21no—
178C24×C13—21no—
179C24×C13—21no—
180C24×C13—21no—
181C24×C13—21no—
182C24×C13—21no—
183C24×C13—21no—
184C24×C13—21no—
185C24×C13—21no—
186C24×C13—21no—
187C24×C13—21no—
188C24×C13—21no—
189C24×C13—21no—
190C24×C13C22×C412yes—
191C24×C13C22×C412yes—
192C24×C13C2×D412yes—
193C24×C13C2×D412yes—
194C24×C13C2×D412yes—
195C24×C13C2×D412yes—
196C24×C13C2×Q812yes—
197C24×C13C2×Q812yes—
198C24×C13#4112yes—
199C24×C13#4112yes—
200C24×C13C2411yescharacteristic
201C2×D4×C13—28no—
202C2×D4×C13—28no—
203C2×D4×C13—28no—
204C2×D4×C13—28no—
205C2×D4×C13—28no—
206C2×D4×C13—28no—
207C2×D4×C13C4⋊C4116yescomplemented
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—28no—
221C22×C4×C13—28no—
222C22×C4×C13—28no—
223C22×C4×C13—28no—
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—28no—
273C22×C4×C13—28no—
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—44no—
289C22×C4×C13—44no—
290C22×C4×C13—44no—
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×C13—44no—
298C22×C4×C13—44no—
299C22×C4×C13—44no—
300C22×C4×C13—44no—
301C22×C4×C13—44no—
302C22×C4×C13—44no—
303C22×C4×C13—44no—
304C22×C4×C13—44no—
305C22×C4×C13—44no—
306C22×C4×C13—44no—
307C22×C4×C13—44no—
308C22×C4×C13—44no—
309C22×C4×C13—44no—
310C22×C4×C13C22×C412yes—
311C22×C4×C13C22×C412yes—
312C22×C4×C13C22×C412yes—
313C22×C4×C13C22×C412yes—
314C22×C4×C13C22×C412yes—
315C22×C4×C13C2×D412yes—
316C22×C4×C13C2×D412yes—
317C22×C4×C13C2×D412yes—
318C22×C4×C13C2×D412yes—
319C22×C4×C13C2×D412yes—
320C22×C4×C13C2×D412yes—
321C22×C4×C13C2×D412yes—
322C22×C4×C13C2×D412yes—
323C22×C4×C13C2×Q812yes—
324C22×C4×C13#4112yes—
325C22×C4×C13#4112yes—
326C22×C4×C13#4112yes—
327C13×C4⋊C4—28no—
328C13×C4⋊C4—44no—
329C13×C4⋊C4—44no—
330C13×C4⋊C4—44no—
331C13×C4⋊C4—44no—
332C13×C22⋊C4—28no—
333C13×C22⋊C4—28no—
334C13×C22⋊C4—28no—
335C13×C22⋊C4—28no—
336C13×C22⋊C4—44no—
337C13×C22⋊C4—44no—
338C13×C22⋊C4—44no—
339C13×C22⋊C4—44no—
340C42×C13—28no—
341C22×C4×D4C2×C1311yescharacteristic
342C2×#386C2×C1311yescharacteristic
343C2×#386C2×C1311yescharacteristic
344C2×#385C2×C1311yescharacteristic, complemented
345C2×#385C2×C1311yescharacteristic, complemented
346C2×#380C2×C1311yescharacteristic, complemented
347C22×#95C2×C1311yescharacteristic, complemented
348#1444C2×C1311yescharacteristic, complemented
349#1442C2×C1311yescharacteristic, complemented
350#1439C2×C1311yescharacteristic, complemented
351#1439C2×C1311yescharacteristic, complemented
352#1436C2×C1311yescharacteristic, complemented
353#1436C2×C1311yescharacteristic, complemented
354C22⋊#95C2×C1311yescharacteristic, complemented
355C22⋊#95C2×C1311yescharacteristic, complemented
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—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—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×C13C2×C4⋊C414yes—
419C23×C13C2×C4⋊C414yes—
420C23×C13C4×D414yes—
421C23×C13C4×D414yes—
422C23×C13#12014yes—
423C23×C13C22⋊Q814yes—
424C23×C13C22⋊Q814yes—
425C23×C13#12314yes—
426C23×C13C23×C411yescharacteristic
427C23×C13C22×D411yescharacteristic
428C23×C13C22×D411yescharacteristic
429C23×C13C22×D411yescharacteristic
430C23×C13C22×D411yescharacteristic
431C23×C13C22×Q811yescharacteristic
432C23×C13C2×#4111yescharacteristic
433C23×C13C2×#4111yescharacteristic
434C23×C13C2×#4111yescharacteristic
435C23×C13C2×#4111yescharacteristic
436C23×C13C2×#4111yescharacteristic
437C23×C13H(5,𝔽2)11yescharacteristic
438C23×C13H(5,𝔽2)11yescharacteristic
439C23×C13H(5,𝔽2)11yescharacteristic
440C23×C132−1+411yescharacteristic
441D4×C13—232no—
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—22no—
479C2×C4×C13—22no—
480C2×C4×C13—22no—
481C2×C4×C13—22no—
482C2×C4×C13—22no—
483C2×C4×C13—22no—
484C2×C4×C13—416no—
485C2×C4×C13—416no—
486C2×C4×C13—416no—
487C2×C4×C13—416no—
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—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×C13C2×C4⋊C414yes—
535C2×C4×C13C4×D414yescomplemented
536C2×C4×C13#12114yes—
537C23×D4C22×C1311yescharacteristic
538C24×C4C22×C1311yescharacteristic
539C24×C4C22×C1311yescharacteristic
540C24×C4C22×C1311yescharacteristic
541C24×C4C22×C1311yescharacteristic
542C2×C4×D4—24no—
543C2×C4×D4—24no—
544C2×C4×D4—24no—
545C22×C4⋊C4C22×C1311yescharacteristic
546C22×C4⋊C4C22×C1311yescharacteristic
547C22×C4⋊C4C22×C1311yescharacteristic
548C22×C4⋊C4C22×C1311yescharacteristic
549C22×C4⋊C4C22×C1311yescharacteristic
550C22×C22⋊C4C22×C1311yescharacteristic
551C22×C22⋊C4C22×C1311yescharacteristic
552C22×C22⋊C4C22×C1311yescharacteristic
553C22×C22⋊C4C22×C1311yescharacteristic
554C22×C22⋊C4C22×C1311yescharacteristic
555C22×C22⋊C4C22×C1311yescharacteristic
556C22×C22⋊C4C22×C1311yescharacteristic
557C22×C22⋊C4C22×C1311yescharacteristic
558C22×C42C22×C1311yescharacteristic
559#386—24no—
560#386C4×C1318yescomplemented
561#385—24no—
562#385—24no—
563#380—24no—
564C2×#95—24no—
565C2×#95C22×C1311yescharacteristic
566C2×#95C22×C1311yescharacteristic
567C2×#95C22×C1311yescharacteristic
568C2×#95C22×C1311yescharacteristic
569C2×#95C22×C1311yescharacteristic
570C2×#95C22×C1311yescharacteristic
571C2×#95C22×C1311yescharacteristic
572C2×#95C22×C1311yescharacteristic
573C2×#95C22×C1311yescharacteristic
574C2×#95C22×C1311yescharacteristic
575C2×#95C22×C1311yescharacteristic
576C2×#95C22×C1311yescharacteristic
577C2×#95C22×C1311yescharacteristic
578C2×#95C22×C1311yescharacteristic
579C2×#95C22×C1311yescharacteristic
580C2×#95C22×C1311yescharacteristic
581C22×C13—24no—
582C22×C13—24no—
583C22×C13—24no—
584C22×C13—24no—
585C22×C13—24no—
586C22×C13—24no—
587C22×C13—24no—
588C22×C13—24no—
589C22×C13—24no—
590C22×C13—24no—
591C22×C13—24no—
592C22×C13—24no—
593C22×C13—24no—
594C22×C13—24no—
595C22×C13—24no—
596C22×C13—24no—
597C22×C13—24no—
598C22×C13—42no—
599C22×C13—42no—
600C22×C13—42no—
601C22×C13—42no—
602C22×C13—42no—
603C22×C13—42no—
604C22×C13—42no—
605C22×C13—42no—
606C22×C13—42no—
607C22×C13—42no—
608C22×C13—42no—
609C22×C13—42no—
610C22×C13#38518yescomplemented
611C22×C13C22×C4⋊C411yescharacteristic
612C22×C13C2×C4×D411yescharacteristic
613C22×C13C2×C4×D411yescharacteristic
614C22×C13C2×C4×D411yescharacteristic
615C22×C13C4×#4111yescharacteristic
616C22×C13#51811yescharacteristic
617C22×C13#52011yescharacteristic
618C22×C13C2×#12011yescharacteristic
619C22×C13C2×#12111yescharacteristic
620C22×C13C2×C22⋊Q811yescharacteristic
621C22×C13C2×C22⋊Q811yescharacteristic
622C22×C13C2×#12311yescharacteristic
623C22×C13#52511yescharacteristic
624C22×C13#52911yescharacteristic
625C22×C13#53211yescharacteristic
626C22×C13#53411yescharacteristic
627C22×C13#53711yescharacteristic
628C22×C13#53811yescharacteristic
629C22×C13#53911yescharacteristic
630C22×C13D4211yescharacteristic
631C22×C13D4211yescharacteristic
632C22×C13#54611yescharacteristic
633C22×C13#54611yescharacteristic
634C22×C13#54611yescharacteristic
635C22×C13#54611yescharacteristic
636C22×C13#54611yescharacteristic
637C22×C13#54711yescharacteristic
638C22×C13#54711yescharacteristic
639C22×C13D4×Q811yescharacteristic
640C22×C13#55111yescharacteristic
641C22×C13#55111yescharacteristic
642C22×C13#55211yescharacteristic
643C22×C13#55411yescharacteristic
644C22×C13#55411yescharacteristic
645C22×C13#55411yescharacteristic
646C4×C13—24no—
647C4×C13—24no—
648C4×C13—24no—
649C4×C13—42no—
650C4×C13—42no—
651C4×C13—42no—
652C4×C13—42no—
653C4×C13—42no—
654C4×C13—42no—
655C4×C13—42no—
656C4×C13—42no—
657C4×C13—81no—
658C4×C13—81no—
659C25C23×C1311yescharacteristic
660C25C23×C1311yescharacteristic
661C22×D4—22no—
662C22×D4—22no—
663C22×D4—22no—
664C22×D4—22no—
665C22×D4C2×C4×C1314yes—
666C22×D4D4×C1314yes—
667C22×D4Q8×C1314yes—
668C23×C4—22no—
669C23×C4—22no—
670C23×C4—22no—
671C23×C4—22no—
672C23×C4—22no—
673C23×C4—22no—
674C23×C4—22no—
675C23×C4—22no—
676C23×C4—22no—
677C23×C4—22no—
678C23×C4—22no—
679C23×C4—22no—
680C23×C4—22no—
681C23×C4—22no—
682C23×C4—22no—
683C23×C4—22no—
684C23×C4—22no—
685C23×C4—22no—
686C23×C4—41no—
687C23×C4—41no—
688C23×C4—41no—
689C23×C4—41no—
690C23×C4—41no—
691C23×C4—41no—
692C23×C4—41no—
693C23×C4—41no—
694C23×C4C2×C4×C1314yescomplemented
695C23×C4D4×C1314yes—
696C23×C4C23×C1311yescharacteristic
697C23×C4C23×C1311yescharacteristic
698C23×C4C23×C1311yescharacteristic
699C23×C4C23×C1311yescharacteristic
700C23×C4C23×C1311yescharacteristic
701C23×C4C23×C1311yescharacteristic
702C23×C4C23×C1311yescharacteristic
703C23×C4C23×C1311yescharacteristic
704C23×C4C23×C1311yescharacteristic
705C23×C4C23×C1311yescharacteristic
706C23×C4C23×C1311yescharacteristic
707C23×C4C23×C1311yescharacteristic
708C23×C4C23×C1311yescharacteristic
709C4×D4—232no—
710C2×C4⋊C4—22no—
711C2×C4⋊C4—22no—
712C2×C4⋊C4—22no—
713C2×C4⋊C4—22no—
714C2×C4⋊C4—22no—
715C2×C4⋊C4—22no—
716C2×C4⋊C4—22no—
717C2×C4⋊C4—22no—
718C2×C4⋊C4—22no—
719C2×C4⋊C4—22no—
720C2×C4⋊C4—22no—
721C2×C4⋊C4—41no—
722C2×C4⋊C4—41no—
723C2×C4⋊C4—41no—
724C2×C4⋊C4—41no—
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—22no—
739C2×C22⋊C4—22no—
740C2×C22⋊C4—22no—
741C2×C22⋊C4—41no—
742C2×C22⋊C4—41no—
743C2×C22⋊C4—41no—
744C2×C22⋊C4—41no—
745C2×C22⋊C4C2×C4×C1314yescomplemented
746C2×C22⋊C4C2×C4×C1314yescomplemented
747C2×C22⋊C4C2×C4×C1314yescomplemented
748C2×C22⋊C4D4×C1314yes—
749C2×C42—22no—
750C2×C42—22no—
751C2×C42—22no—
752#95—22no—
753#95—22no—
754#95—22no—
755#95—22no—
756#95—22no—
757#95—22no—
758#95—22no—
759#95—22no—
760#95—22no—
761#95—22no—
762#95—22no—
763#95—41no—
764#95—41no—
765#95C2×C4×C1314yescomplemented
766#95C2×C4×C1314yescomplemented
767#95D4×C1314yescomplemented
768C2×C13—28no—
769C2×C13—44no—
770C2×C13C2×#38511yescharacteristic
771C2×C13C4×#12111yescharacteristic
772C2×C13#232511yescharacteristic
773C2×C13D4×C4⋊C411yescharacteristic
774C2×C13#234911yescharacteristic
775C2×C13#235811yescharacteristic
776C2×C13#235911yescharacteristic
777C2×C13#241011yescharacteristic
778C2×C13#241711yescharacteristic
779C2×C13#241811yescharacteristic
780C2×C13#241911yescharacteristic
781C2×C13#243011yescharacteristic
782C2×C13#244911yescharacteristic
783C2×C13#245011yescharacteristic
784C2×C13#256411yescharacteristic
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—
803C24—21no—
804C24—21no—
805C24C22×C4×C1312yes—
806C24C22×C4×C1312yes—
807C24C2×D4×C1312yes—
808C24C2×D4×C1312yes—
809C24C2×D4×C1312yes—
810C24C2×D4×C1312yes—
811C24C2×Q8×C1312yes—
812C24C2×Q8×C1312yes—
813C24C13×#4112yes—
814C24C13×#4112yes—
815C24C24×C1311yescharacteristic
816C2×D4—28no—
817C2×D4—28no—
818C2×D4—28no—
819C2×D4—28no—
820C2×D4—28no—
821C2×D4—28no—
822C2×D4C13×C4⋊C4116yescomplemented
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—28no—
836C22×C4—28no—
837C22×C4—28no—
838C22×C4—28no—
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—28no—
888C22×C4—28no—
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—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—44no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—44no—
909C22×C4—44no—
910C22×C4—44no—
911C22×C4—44no—
912C22×C4—44no—
913C22×C4—44no—
914C22×C4—44no—
915C22×C4—44no—
916C22×C4—44no—
917C22×C4—44no—
918C22×C4—44no—
919C22×C4—44no—
920C22×C4—44no—
921C22×C4—44no—
922C22×C4—44no—
923C22×C4—44no—
924C22×C4—44no—
925C22×C4C22×C4×C1312yes—
926C22×C4C22×C4×C1312yes—
927C22×C4C22×C4×C1312yes—
928C22×C4C22×C4×C1312yes—
929C22×C4C22×C4×C1312yes—
930C22×C4C2×D4×C1312yes—
931C22×C4C2×D4×C1312yes—
932C22×C4C2×D4×C1312yes—
933C22×C4C2×D4×C1312yes—
934C22×C4C2×D4×C1312yes—
935C22×C4C2×D4×C1312yes—
936C22×C4C2×D4×C1312yes—
937C22×C4C2×D4×C1312yes—
938C22×C4C2×Q8×C1312yes—
939C22×C4C13×#4112yes—
940C22×C4C13×#4112yes—
941C22×C4C13×#4112yes—
942C4⋊C4—28no—
943C4⋊C4—44no—
944C4⋊C4—44no—
945C4⋊C4—44no—
946C4⋊C4—44no—
947C22⋊C4—28no—
948C22⋊C4—28no—
949C22⋊C4—28no—
950C22⋊C4—28no—
951C22⋊C4—44no—
952C22⋊C4—44no—
953C22⋊C4—44no—
954C22⋊C4—44no—
955C42—28no—
956C13#1397511yescharacteristic, direct product factor, Sylow
957C23—22no—
958C23—22no—
959C23—22no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—22no—
964C23—22no—
965C23—22no—
966C23—22no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—22no—
972C23—22no—
973C23—22no—
974C23—22no—
975C23—22no—
976C23—22no—
977C23—22no—
978C23—22no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—22no—
987C23—22no—
988C23—22no—
989C23—22no—
990C23—22no—
991C23—22no—
992C23—22no—
993C23—22no—
994C23—22no—
995C23—22no—
996C23—22no—
997C23—22no—
998C23—22no—
999C23—22no—
1000C23—22no—
1001C23—22no—
1002C23—22no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23C2×C13×C4⋊C414yes—
1020C23C2×C13×C4⋊C414yes—
1021C23C4×D4×C1314yes—
1022C23C4×D4×C1314yes—
1023C23C13×#12014yes—
1024C23C13×C22⋊Q814yes—
1025C23C13×C22⋊Q814yes—
1026C23C13×#12314yes—
1027C23C23×C4×C1311yescharacteristic
1028C23C22×D4×C1311yescharacteristic
1029C23C22×D4×C1311yescharacteristic
1030C23C22×D4×C1311yescharacteristic
1031C23C22×D4×C1311yescharacteristic
1032C23C22×Q8×C1311yescharacteristic
1033C23C2×C13×#4111yescharacteristic
1034C23C2×C13×#4111yescharacteristic
1035C23C2×C13×#4111yescharacteristic
1036C23C2×C13×#4111yescharacteristic
1037C23C2×C13×#4111yescharacteristic
1038C23C13×H(5,𝔽2)11yescharacteristic
1039C23C13×H(5,𝔽2)11yescharacteristic
1040C23C13×H(5,𝔽2)11yescharacteristic
1041C23C13×2−1+411yescharacteristic
1042D4—232no—
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—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—22no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—22no—
1080C2×C4—22no—
1081C2×C4—22no—
1082C2×C4—22no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—416no—
1086C2×C4—416no—
1087C2×C4—416no—
1088C2×C4—416no—
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×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4C2×C13×C4⋊C414yes—
1136C2×C4C4×D4×C1314yescomplemented
1137C2×C4C13×#12114yes—
1138C22—24no—
1139C22—24no—
1140C22—24no—
1141C22—24no—
1142C22—24no—
1143C22—24no—
1144C22—24no—
1145C22—24no—
1146C22—24no—
1147C22—24no—
1148C22—24no—
1149C22—24no—
1150C22—24no—
1151C22—24no—
1152C22—24no—
1153C22—24no—
1154C22—24no—
1155C22—42no—
1156C22—42no—
1157C22—42no—
1158C22—42no—
1159C22—42no—
1160C22—42no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22C13×#38518yescomplemented
1168C22C22×C13×C4⋊C411yescharacteristic
1169C22C2×C4×D4×C1311yescharacteristic
1170C22C2×C4×D4×C1311yescharacteristic
1171C22C2×C4×D4×C1311yescharacteristic
1172C22C4×C13×#4111yescharacteristic
1173C22C13×#51811yescharacteristic
1174C22C13×#52011yescharacteristic
1175C22C2×C13×#12011yescharacteristic
1176C22C2×C13×#12111yescharacteristic
1177C22C2×C13×C22⋊Q811yescharacteristic
1178C22C2×C13×C22⋊Q811yescharacteristic
1179C22C2×C13×#12311yescharacteristic
1180C22C13×#52511yescharacteristic
1181C22C13×#52911yescharacteristic
1182C22C13×#53211yescharacteristic
1183C22C13×#53411yescharacteristic
1184C22C13×#53711yescharacteristic
1185C22C13×#53811yescharacteristic
1186C22C13×#53911yescharacteristic
1187C22D42×C1311yescharacteristic
1188C22D42×C1311yescharacteristic
1189C22C13×#54611yescharacteristic
1190C22C13×#54611yescharacteristic
1191C22C13×#54611yescharacteristic
1192C22C13×#54611yescharacteristic
1193C22C13×#54611yescharacteristic
1194C22C13×#54711yescharacteristic
1195C22C13×#54711yescharacteristic
1196C22D4×Q8×C1311yescharacteristic
1197C22C13×#55111yescharacteristic
1198C22C13×#55111yescharacteristic
1199C22C13×#55211yescharacteristic
1200C22C13×#55411yescharacteristic
1201C22C13×#55411yescharacteristic
1202C22C13×#55411yescharacteristic
1203C4—24no—
1204C4—24no—
1205C4—24no—
1206C4—42no—
1207C4—42no—
1208C4—42no—
1209C4—42no—
1210C4—42no—
1211C4—42no—
1212C4—42no—
1213C4—42no—
1214C4—81no—
1215C4—81no—
1216C2—28no—
1217C2—44no—
1218C2C2×C13×#38511yescharacteristic
1219C2C4×C13×#12111yescharacteristic
1220C2C13×#232511yescharacteristic
1221C2D4×C13×C4⋊C411yescharacteristic
1222C2C13×#234911yescharacteristic
1223C2C13×#235811yescharacteristic
1224C2C13×#235911yescharacteristic
1225C2C13×#241011yescharacteristic
1226C2C13×#241711yescharacteristic
1227C2C13×#241811yescharacteristic
1228C2C13×#241911yescharacteristic
1229C2C13×#243011yescharacteristic
1230C2C13×#244911yescharacteristic
1231C2C13×#245011yescharacteristic
1232C2C13×#256411yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC23×D4×C13C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×C13×#385C2semidirect
5. C2×C13×#385C2semidirect
6. C2×C13×#380C2semidirect
7. C22×C13×#95C2semidirect
8. C13×#1444C2semidirect
9. C13×#1442C2semidirect
10. C13×#1439C2semidirect
11. C13×#1439C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×C22⋊#95C2semidirect
15. C13×C22⋊#95C2semidirect
39. C13×#386C4semidirect
95. C23×C4×C13C2×C4semidirect
146. C2×C13×C22⋊C4C2×C4semidirect
147. C2×C13×C22⋊C4C2×C4semidirect
148. C2×C13×C22⋊C4C2×C4semidirect
166. C13×#95C2×C4semidirect
167. C13×#95C2×C4semidirect
168. C13×#95D4semidirect
169. #13975C13direct (N × H)
207. C2×D4×C13C4⋊C4semidirect
344. C2×#385C2×C13semidirect
345. C2×#385C2×C13semidirect
346. C2×#380C2×C13semidirect
347. C22×#95C2×C13semidirect
348. #1444C2×C13semidirect
349. #1442C2×C13semidirect
350. #1439C2×C13semidirect
351. #1439C2×C13semidirect
352. #1436C2×C13semidirect
353. #1436C2×C13semidirect
354. C22⋊#95C2×C13semidirect
355. C22⋊#95C2×C13semidirect
535. C2×C4×C13C4×D4semidirect
560. #386C4×C13semidirect
610. C22×C13#385semidirect
694. C23×C4C2×C4×C13semidirect
745. C2×C22⋊C4C2×C4×C13semidirect
746. C2×C22⋊C4C2×C4×C13semidirect
747. C2×C22⋊C4C2×C4×C13semidirect
765. #95C2×C4×C13semidirect
766. #95C2×C4×C13semidirect
767. #95D4×C13semidirect
822. C2×D4C13×C4⋊C4semidirect
956. C13#13975direct (N × H)
1136. C2×C4C4×D4×C13semidirect
1167. C22C13×#385semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D4×C132
C2×C13×#3862
C2×C13×#3852
C2×C13×#3802
C22×C13×#952
C13×#14442
C13×#14422
C13×#14392
C13×#14362
C13×C22⋊#952
#1397513