Finite Group Databasebeta

← C13×#14099 #15700438

Subgroups — C13×#14099 #15700438

Order 3328.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1050 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#391C211yesmaximal, characteristic, complemented
3C2×C13×#387C211yesmaximal, characteristic, complemented
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
6C13×#1446C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×C22⋊Q8—24no—
19C2×C13×C22⋊Q8—24no—
20C2×C13×C22⋊Q8C418yescomplemented
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C22×C42×C13C2211yescharacteristic
36C13×#391—24no—
37C13×#387—24no—
38C4×C13×C4⋊C4—24no—
39C4×C13×C22⋊C4—24no—
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
57C2×C13×#95C2211yescharacteristic
58C25×C13C2311yescharacteristic
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—41no—
64C22×Q8×C13—41no—
65C22×Q8×C13C2×C414yes—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13C2×C414yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C13×C22⋊Q8—232no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—41no—
98C2×C13×C4⋊C4C2×C414yes—
99C2×C13×C4⋊C4C2×C414yes—
100C2×C13×C4⋊C4C2×C414yes—
101C2×C13×C4⋊C4D414yes—
102C2×C13×C4⋊C4D414yes—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
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—41no—
117C2×C13×C22⋊C4—41no—
118C2×C13×C22⋊C4C2×C414yes—
119C2×C13×C22⋊C4C2×C414yes—
120C2×C13×C22⋊C4Q814yescomplemented
121C2×C42×C13—22no—
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C2×C42×C13—22no—
126C2×C42×C13—22no—
127C2×C42×C13—22no—
128C2×C42×C13—22no—
129C2×C42×C13—22no—
130C2×C42×C13—41no—
131C2×C42×C13—41no—
132C2×C42×C13—41no—
133C13×#95—22no—
134C13×#95—22no—
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×#95D414yes—
151#14099C1311yesmaximal, characteristic, direct product factor, Sylow
152C24×C13—21no—
153C24×C13—21no—
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×C13C22×C412yes—
165C24×C13C2×Q812yes—
166C24×C13#4112yes—
167C24×C13C2411yescharacteristic
168C2×Q8×C13—28no—
169C2×Q8×C13—28no—
170C2×Q8×C13—44no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
173C2×Q8×C13—44no—
174C2×Q8×C13—44no—
175C22×C4×C13—21no—
176C22×C4×C13—21no—
177C22×C4×C13—21no—
178C22×C4×C13—21no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—21no—
192C22×C4×C13—21no—
193C22×C4×C13—21no—
194C22×C4×C13—21no—
195C22×C4×C13—21no—
196C22×C4×C13—21no—
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—28no—
238C22×C4×C13—28no—
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—44no—
254C22×C4×C13—44no—
255C22×C4×C13—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13C22×C412yes—
259C22×C4×C13C22×C412yes—
260C22×C4×C13C22×C412yes—
261C22×C4×C13C22×C412yes—
262C22×C4×C13C22×C412yes—
263C22×C4×C13C22×C412yes—
264C22×C4×C13C2×D412yes—
265C22×C4×C13C2×D412yes—
266C22×C4×C13C2×D412yes—
267C22×C4×C13C2×D412yes—
268C22×C4×C13C2×D412yes—
269C22×C4×C13C2×D412yes—
270C22×C4×C13C2×D412yes—
271C22×C4×C13C2×D412yes—
272C22×C4×C13C2×D412yes—
273C22×C4×C13C2×Q812yes—
274C22×C4×C13C2×Q812yes—
275C22×C4×C13#4112yes—
276C22×C4×C13#4112yes—
277C22×C4×C13#4112yes—
278C22×C4×C13#4112yes—
279C22×C4×C13#4112yes—
280C13×C4⋊C4—28no—
281C13×C4⋊C4—28no—
282C13×C4⋊C4—28no—
283C13×C4⋊C4—44no—
284C13×C4⋊C4C22⋊C4116yescomplemented
285C13×C22⋊C4—28no—
286C13×C22⋊C4—28no—
287C13×C22⋊C4—28no—
288C13×C22⋊C4—28no—
289C13×C22⋊C4—44no—
290C13×C22⋊C4—44no—
291C42×C13—28no—
292C42×C13—44no—
293C42×C13—44no—
294C42×C13—44no—
295C22×C22⋊Q8C2×C1311yescharacteristic
296C2×#391C2×C1311yescharacteristic, complemented
297C2×#387C2×C1311yescharacteristic, complemented
298C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
299C2×C4×C22⋊C4C2×C1311yescharacteristic
300#1446C2×C1311yescharacteristic, complemented
301#1441C2×C1311yescharacteristic, complemented
302#1439C2×C1311yescharacteristic
303#1439C2×C1311yescharacteristic
304#1437C2×C1311yescharacteristic
305#1437C2×C1311yescharacteristic
306#1436C2×C1311yescharacteristic, complemented
307#1436C2×C1311yescharacteristic, complemented
308#1436C2×C1311yescharacteristic, complemented
309C22⋊#95C2×C1311yescharacteristic
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—22no—
323C23×C13—22no—
324C23×C13—22no—
325C23×C13—22no—
326C23×C13—22no—
327C23×C13—22no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13—41no—
339C23×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13—41no—
343C23×C13—41no—
344C23×C13C4×Q814yes—
345C23×C13C23×C411yescharacteristic
346C23×C13C22×D411yescharacteristic
347C23×C13C22×D411yescharacteristic
348C23×C13C22×D411yescharacteristic
349C23×C13C22×Q811yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13C2×#4111yescharacteristic
355C23×C13C2×#4111yescharacteristic
356C23×C13H(5,𝔽2)11yescharacteristic
357C23×C13H(5,𝔽2)11yescharacteristic
358C23×C132−1+411yescharacteristic
359C23×C132−1+411yescharacteristic
360Q8×C13—416no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—22no—
398C2×C4×C13—22no—
399C2×C4×C13—22no—
400C2×C4×C13—22no—
401C2×C4×C13—22no—
402C2×C4×C13—22no—
403C2×C4×C13—22no—
404C2×C4×C13—22no—
405C2×C4×C13—22no—
406C2×C4×C13—22no—
407C2×C4×C13—22no—
408C2×C4×C13—22no—
409C2×C4×C13—22no—
410C2×C4×C13—22no—
411C2×C4×C13—22no—
412C2×C4×C13—416no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
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×C13C2×C22⋊C414yes—
456C2×C4×C13C2×C22⋊C414yes—
457C2×C4×C13C2×C22⋊C414yes—
458C2×C4×C13C4×D414yes—
459C2×C4×C13C22⋊Q814yescomplemented
460C23×Q8C22×C1311yescharacteristic
461C24×C4C22×C1311yescharacteristic
462C2×C22⋊Q8—24no—
463C2×C22⋊Q8—24no—
464C2×C22⋊Q8C4×C1318yescomplemented
465C22×C4⋊C4C22×C1311yescharacteristic
466C22×C4⋊C4C22×C1311yescharacteristic
467C22×C4⋊C4C22×C1311yescharacteristic
468C22×C4⋊C4C22×C1311yescharacteristic
469C22×C4⋊C4C22×C1311yescharacteristic
470C22×C22⋊C4C22×C1311yescharacteristic
471C22×C22⋊C4C22×C1311yescharacteristic
472C22×C22⋊C4C22×C1311yescharacteristic
473C22×C22⋊C4C22×C1311yescharacteristic
474C22×C22⋊C4C22×C1311yescharacteristic
475C22×C22⋊C4C22×C1311yescharacteristic
476C22×C42C22×C1311yescharacteristic
477C22×C42C22×C1311yescharacteristic
478C22×C42C22×C1311yescharacteristic
479C22×C42C22×C1311yescharacteristic
480#391—24no—
481#387—24no—
482C4×C4⋊C4—24no—
483C4×C22⋊C4—24no—
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C2×#95C22×C1311yescharacteristic
492C2×#95C22×C1311yescharacteristic
493C2×#95C22×C1311yescharacteristic
494C2×#95C22×C1311yescharacteristic
495C2×#95C22×C1311yescharacteristic
496C2×#95C22×C1311yescharacteristic
497C2×#95C22×C1311yescharacteristic
498C2×#95C22×C1311yescharacteristic
499C2×#95C22×C1311yescharacteristic
500C2×#95C22×C1311yescharacteristic
501C2×#95C22×C1311yescharacteristic
502C22×C13—24no—
503C22×C13—24no—
504C22×C13—24no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13—42no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13—42no—
515C22×C13—42no—
516C22×C13—42no—
517C22×C13C22×C22⋊C411yescharacteristic
518C22×C13C2×C4×D411yescharacteristic
519C22×C13C2×C4×Q811yescharacteristic
520C22×C13C4×#4111yescharacteristic
521C22×C13C4×#4111yescharacteristic
522C22×C13#51811yescharacteristic
523C22×C13#51911yescharacteristic
524C22×C13C2×C22⋊Q811yescharacteristic
525C22×C13#52511yescharacteristic
526C22×C13#52511yescharacteristic
527C22×C13#52511yescharacteristic
528C22×C13#52911yescharacteristic
529C22×C13#53211yescharacteristic
530C22×C13#53211yescharacteristic
531C22×C13#53311yescharacteristic
532C22×C13#53911yescharacteristic
533C22×C13#53911yescharacteristic
534C22×C13#54211yescharacteristic
535C22×C13#54211yescharacteristic
536C22×C13D4211yescharacteristic
537C22×C13D4211yescharacteristic
538C22×C13#54611yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54711yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13#54811yescharacteristic
543C22×C13#54811yescharacteristic
544C22×C13D4×Q811yescharacteristic
545C22×C13D4×Q811yescharacteristic
546C22×C13#55111yescharacteristic
547C22×C13#55111yescharacteristic
548C22×C13#55211yescharacteristic
549C22×C13#55411yescharacteristic
550C22×C13#55411yescharacteristic
551C22×C13#55611yescharacteristic
552C4×C13—24no—
553C4×C13—24no—
554C4×C13—24no—
555C4×C13—24no—
556C4×C13—24no—
557C4×C13—42no—
558C4×C13—42no—
559C4×C13—42no—
560C4×C13—42no—
561C4×C13—42no—
562C4×C13—42no—
563C4×C13—42no—
564C4×C13—81no—
565C4×C13—81no—
566C25C23×C1311yescharacteristic
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—22no—
570C22×Q8—22no—
571C22×Q8—41no—
572C22×Q8—41no—
573C22×Q8C2×C4×C1314yes—
574C23×C4—22no—
575C23×C4—22no—
576C23×C4—22no—
577C23×C4—22no—
578C23×C4—41no—
579C23×C4—41no—
580C23×C4C2×C4×C1314yes—
581C23×C4C23×C1311yescharacteristic
582C23×C4C23×C1311yescharacteristic
583C23×C4C23×C1311yescharacteristic
584C23×C4C23×C1311yescharacteristic
585C23×C4C23×C1311yescharacteristic
586C23×C4C23×C1311yescharacteristic
587C23×C4C23×C1311yescharacteristic
588C23×C4C23×C1311yescharacteristic
589C23×C4C23×C1311yescharacteristic
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C23×C4C23×C1311yescharacteristic
593C23×C4C23×C1311yescharacteristic
594C23×C4C23×C1311yescharacteristic
595C22⋊Q8—232no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4C2×C4×C1314yes—
607C2×C4⋊C4C2×C4×C1314yes—
608C2×C4⋊C4C2×C4×C1314yes—
609C2×C4⋊C4D4×C1314yes—
610C2×C4⋊C4D4×C1314yes—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4C2×C4×C1314yes—
627C2×C22⋊C4C2×C4×C1314yes—
628C2×C22⋊C4Q8×C1314yescomplemented
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—22no—
636C2×C42—22no—
637C2×C42—22no—
638C2×C42—41no—
639C2×C42—41no—
640C2×C42—41no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—22no—
653#95—22no—
654#95—22no—
655#95—22no—
656#95—41no—
657#95—41no—
658#95D4×C1314yes—
659C2×C13—44no—
660C2×C13#229711yescharacteristic
661C2×C13C4×C22⋊Q811yescharacteristic
662C2×C13#233211yescharacteristic
663C2×C13D4×C22⋊C411yescharacteristic
664C2×C13Q8×C22⋊C411yescharacteristic
665C2×C13#236211yescharacteristic
666C2×C13#236811yescharacteristic
667C2×C13#244911yescharacteristic
668C2×C13#245211yescharacteristic
669C2×C13#246111yescharacteristic
670C2×C13#246311yescharacteristic
671C2×C13#246511yescharacteristic
672C2×C13#247711yescharacteristic
673C2×C13#255611yescharacteristic
674C2×C13#256011yescharacteristic
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24C22×C4×C1312yes—
688C24C2×Q8×C1312yes—
689C24C13×#4112yes—
690C24C24×C1311yescharacteristic
691C2×Q8—28no—
692C2×Q8—28no—
693C2×Q8—44no—
694C2×Q8—44no—
695C2×Q8—44no—
696C2×Q8—44no—
697C2×Q8—44no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—28no—
761C22×C4—28no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C1312yes—
782C22×C4C22×C4×C1312yes—
783C22×C4C22×C4×C1312yes—
784C22×C4C22×C4×C1312yes—
785C22×C4C22×C4×C1312yes—
786C22×C4C22×C4×C1312yes—
787C22×C4C2×D4×C1312yes—
788C22×C4C2×D4×C1312yes—
789C22×C4C2×D4×C1312yes—
790C22×C4C2×D4×C1312yes—
791C22×C4C2×D4×C1312yes—
792C22×C4C2×D4×C1312yes—
793C22×C4C2×D4×C1312yes—
794C22×C4C2×D4×C1312yes—
795C22×C4C2×D4×C1312yes—
796C22×C4C2×Q8×C1312yes—
797C22×C4C2×Q8×C1312yes—
798C22×C4C13×#4112yes—
799C22×C4C13×#4112yes—
800C22×C4C13×#4112yes—
801C22×C4C13×#4112yes—
802C22×C4C13×#4112yes—
803C4⋊C4—28no—
804C4⋊C4—28no—
805C4⋊C4—28no—
806C4⋊C4—44no—
807C4⋊C4C13×C22⋊C4116yescomplemented
808C22⋊C4—28no—
809C22⋊C4—28no—
810C22⋊C4—28no—
811C22⋊C4—28no—
812C22⋊C4—44no—
813C22⋊C4—44no—
814C42—28no—
815C42—44no—
816C42—44no—
817C42—44no—
818C13#1409911yescharacteristic, direct product factor, Sylow
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—22no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23C4×Q8×C1314yes—
854C23C23×C4×C1311yescharacteristic
855C23C22×D4×C1311yescharacteristic
856C23C22×D4×C1311yescharacteristic
857C23C22×D4×C1311yescharacteristic
858C23C22×Q8×C1311yescharacteristic
859C23C2×C13×#4111yescharacteristic
860C23C2×C13×#4111yescharacteristic
861C23C2×C13×#4111yescharacteristic
862C23C2×C13×#4111yescharacteristic
863C23C2×C13×#4111yescharacteristic
864C23C2×C13×#4111yescharacteristic
865C23C13×H(5,𝔽2)11yescharacteristic
866C23C13×H(5,𝔽2)11yescharacteristic
867C23C13×2−1+411yescharacteristic
868C23C13×2−1+411yescharacteristic
869Q8—416no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—416no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4C2×C13×C22⋊C414yes—
965C2×C4C2×C13×C22⋊C414yes—
966C2×C4C2×C13×C22⋊C414yes—
967C2×C4C4×D4×C1314yes—
968C2×C4C13×C22⋊Q814yescomplemented
969C22—24no—
970C22—24no—
971C22—24no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22C22×C13×C22⋊C411yescharacteristic
985C22C2×C4×D4×C1311yescharacteristic
986C22C2×C4×Q8×C1311yescharacteristic
987C22C4×C13×#4111yescharacteristic
988C22C4×C13×#4111yescharacteristic
989C22C13×#51811yescharacteristic
990C22C13×#51911yescharacteristic
991C22C2×C13×C22⋊Q811yescharacteristic
992C22C13×#52511yescharacteristic
993C22C13×#52511yescharacteristic
994C22C13×#52511yescharacteristic
995C22C13×#52911yescharacteristic
996C22C13×#53211yescharacteristic
997C22C13×#53211yescharacteristic
998C22C13×#53311yescharacteristic
999C22C13×#53911yescharacteristic
1000C22C13×#53911yescharacteristic
1001C22C13×#54211yescharacteristic
1002C22C13×#54211yescharacteristic
1003C22D42×C1311yescharacteristic
1004C22D42×C1311yescharacteristic
1005C22C13×#54611yescharacteristic
1006C22C13×#54611yescharacteristic
1007C22C13×#54711yescharacteristic
1008C22C13×#54811yescharacteristic
1009C22C13×#54811yescharacteristic
1010C22C13×#54811yescharacteristic
1011C22D4×Q8×C1311yescharacteristic
1012C22D4×Q8×C1311yescharacteristic
1013C22C13×#55111yescharacteristic
1014C22C13×#55111yescharacteristic
1015C22C13×#55211yescharacteristic
1016C22C13×#55411yescharacteristic
1017C22C13×#55411yescharacteristic
1018C22C13×#55611yescharacteristic
1019C4—24no—
1020C4—24no—
1021C4—24no—
1022C4—24no—
1023C4—24no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—42no—
1029C4—42no—
1030C4—42no—
1031C4—81no—
1032C4—81no—
1033C2—44no—
1034C2C13×#229711yescharacteristic
1035C2C4×C13×C22⋊Q811yescharacteristic
1036C2C13×#233211yescharacteristic
1037C2D4×C13×C22⋊C411yescharacteristic
1038C2Q8×C13×C22⋊C411yescharacteristic
1039C2C13×#236211yescharacteristic
1040C2C13×#236811yescharacteristic
1041C2C13×#244911yescharacteristic
1042C2C13×#245211yescharacteristic
1043C2C13×#246111yescharacteristic
1044C2C13×#246311yescharacteristic
1045C2C13×#246511yescharacteristic
1046C2C13×#247711yescharacteristic
1047C2C13×#255611yescharacteristic
1048C2C13×#256011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#391C2semidirect
3. C2×C13×#387C2semidirect
4. C2×C4×C13×C4⋊C4C2semidirect
6. C13×#1446C2semidirect
7. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
20. C2×C13×C22⋊Q8C4semidirect
120. C2×C13×C22⋊C4Q8semidirect
151. #14099C13direct (N × H)
284. C13×C4⋊C4C22⋊C4semidirect
296. C2×#391C2×C13semidirect
297. C2×#387C2×C13semidirect
298. C2×C4×C4⋊C4C2×C13semidirect
300. #1446C2×C13semidirect
301. #1441C2×C13semidirect
306. #1436C2×C13semidirect
307. #1436C2×C13semidirect
308. #1436C2×C13semidirect
459. C2×C4×C13C22⋊Q8semidirect
464. C2×C22⋊Q8C4×C13semidirect
628. C2×C22⋊C4Q8×C13semidirect
807. C4⋊C4C13×C22⋊C4semidirect
818. C13#14099direct (N × H)
968. 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×#3912
C2×C13×#3872
C2×C4×C13×C4⋊C42
C2×C4×C13×C22⋊C42
C13×#14462
C13×#14412
C13×#14392
C13×#14372
C13×#14362
C13×C22⋊#952
#1409913