Finite Group Databasebeta

← C13×#14931 #15701270

Subgroups — C13×#14931 #15701270

Order 3328.

1614 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#126C211yesmaximal, characteristic
2C2×C13×#389C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic
4C2×C13×#387C211yesmaximal, characteristic, complemented
5C13×#1444C211yesmaximal, characteristic, complemented
6C13×#1442C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1440C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1439C211yesmaximal, characteristic
12C13×#1439C211yesmaximal, characteristic
13C13×#1437C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C2×C13×#126—24no—
17C2×C13×#126—24no—
18C2×C13×#126—24no—
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
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×C13×C22⋊C4C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C22×C42×C13C2211yescharacteristic
36C13×#389—24no—
37C13×#388—24no—
38C13×#387—24no—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C23×C4×C13C2311yescharacteristic
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C13×#126—232no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
77C2×C13×C4⋊C4—22no—
78C2×C13×C4⋊C4—22no—
79C2×C13×C4⋊C4—22no—
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—41no—
93C2×C13×C4⋊C4D414yes—
94C2×C13×C22⋊C4—22no—
95C2×C13×C22⋊C4—22no—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
99C2×C13×C22⋊C4—22no—
100C2×C13×C22⋊C4—22no—
101C2×C13×C22⋊C4—22no—
102C2×C13×C22⋊C4—22no—
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—41no—
113C2×C13×C22⋊C4—41no—
114C2×C13×C22⋊C4D414yes—
115C2×C42×C13—22no—
116C2×C42×C13—22no—
117C2×C42×C13—22no—
118C2×C42×C13—22no—
119C2×C42×C13—22no—
120C2×C42×C13—22no—
121C2×C42×C13—41no—
122C2×C42×C13—41no—
123C2×C42×C13D414yes—
124C13×#95—22no—
125C13×#95—22no—
126C13×#95—22no—
127C13×#95—22no—
128C13×#95—22no—
129C13×#95—22no—
130C13×#95—22no—
131C13×#95—22no—
132C13×#95—22no—
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—41no—
142#14931C1311yesmaximal, characteristic, direct product factor, Sylow
143C24×C13—21no—
144C24×C13—21no—
145C24×C13—21no—
146C24×C13—21no—
147C24×C13—21no—
148C24×C13—21no—
149C24×C13—21no—
150C24×C13—21no—
151C24×C13—21no—
152C24×C13—21no—
153C24×C13—21no—
154C24×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13C2×D412yes—
158C24×C13C2411yescharacteristic
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—21no—
173C22×C4×C13—21no—
174C22×C4×C13—21no—
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—21no—
238C22×C4×C13—21no—
239C22×C4×C13—21no—
240C22×C4×C13—21no—
241C22×C4×C13C2×D412yes—
242C22×C4×C13C2×D412yes—
243C22×C4×C13C2×D412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×D412yes—
249C22×C4×C13#4112yes—
250C22×C4×C13#4112yes—
251C22×C4×C13#4112yes—
252C22×C4×C13#4112yes—
253C22×C4×C13#4112yes—
254C22×C4×C13#4112yes—
255C22×C4×C13#4112yes—
256C22×C4×C13#4112yes—
257C13×C4⋊C4—28no—
258C13×C4⋊C4—28no—
259C13×C4⋊C4—28no—
260C13×C4⋊C4—28no—
261C13×C4⋊C4—28no—
262C13×C4⋊C4—44no—
263C13×C4⋊C4—44no—
264C13×C22⋊C4—28no—
265C13×C22⋊C4—28no—
266C13×C22⋊C4—28no—
267C13×C22⋊C4—28no—
268C13×C22⋊C4—44no—
269C13×C22⋊C4—44no—
270C13×C22⋊C4—44no—
271C42×C13—28no—
272C42×C13—44no—
273C42×C13—44no—
274C22×#126C2×C1311yescharacteristic
275C2×#389C2×C1311yescharacteristic, complemented
276C2×#388C2×C1311yescharacteristic
277C2×#387C2×C1311yescharacteristic, complemented
278#1444C2×C1311yescharacteristic, complemented
279#1442C2×C1311yescharacteristic, complemented
280#1442C2×C1311yescharacteristic, complemented
281#1441C2×C1311yescharacteristic, complemented
282#1440C2×C1311yescharacteristic
283#1439C2×C1311yescharacteristic
284#1439C2×C1311yescharacteristic
285#1439C2×C1311yescharacteristic
286#1437C2×C1311yescharacteristic
287#1436C2×C1311yescharacteristic, complemented
288C4×#95C2×C1311yescharacteristic, complemented
289C23×C13—22no—
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—41no—
297C23×C13—41no—
298C23×C13—41no—
299C23×C13—41no—
300C23×C13—41no—
301C23×C13—41no—
302C23×C13—41no—
303C23×C13—41no—
304C23×C13—41no—
305C23×C13—41no—
306C23×C13—41no—
307C23×C13—41no—
308C23×C13—41no—
309C23×C13—41no—
310C23×C13—41no—
311C23×C13—41no—
312C23×C13—41no—
313C23×C13—41no—
314C23×C13—41no—
315C23×C13—41no—
316C23×C13—41no—
317C23×C13—41no—
318C23×C13—41no—
319C23×C13—41no—
320C23×C13—41no—
321C23×C13—41no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13C22×D411yescharacteristic
325C23×C13C22×D411yescharacteristic
326C23×C13C22×D411yescharacteristic
327C23×C13C2×#4111yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C132−1+411yescharacteristic
337C23×C132−1+411yescharacteristic
338C23×C132−1+411yescharacteristic
339C2×C4×C13—22no—
340C2×C4×C13—22no—
341C2×C4×C13—22no—
342C2×C4×C13—22no—
343C2×C4×C13—22no—
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
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—41no—
382C2×C4×C13—41no—
383C2×C4×C13—41no—
384C2×C4×C13—41no—
385C2×C4×C13—41no—
386C2×C4×C13—41no—
387C2×C4×C13—41no—
388C2×C4×C13—41no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
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#12014yes—
436C2×C4×C13#12614yescomplemented
437C2×#126—24no—
438C2×#126—24no—
439C2×#126—24no—
440C22×C4⋊C4C22×C1311yescharacteristic
441C22×C4⋊C4C22×C1311yescharacteristic
442C22×C4⋊C4C22×C1311yescharacteristic
443C22×C4⋊C4C22×C1311yescharacteristic
444C22×C4⋊C4C22×C1311yescharacteristic
445C22×C4⋊C4C22×C1311yescharacteristic
446C22×C4⋊C4C22×C1311yescharacteristic
447C22×C22⋊C4C22×C1311yescharacteristic
448C22×C22⋊C4C22×C1311yescharacteristic
449C22×C22⋊C4C22×C1311yescharacteristic
450C22×C22⋊C4C22×C1311yescharacteristic
451C22×C22⋊C4C22×C1311yescharacteristic
452C22×C22⋊C4C22×C1311yescharacteristic
453C22×C22⋊C4C22×C1311yescharacteristic
454C22×C42C22×C1311yescharacteristic
455C22×C42C22×C1311yescharacteristic
456C22×C42C22×C1311yescharacteristic
457#389—24no—
458#388—24no—
459#387—24no—
460C2×#95C22×C1311yescharacteristic
461C2×#95C22×C1311yescharacteristic
462C2×#95C22×C1311yescharacteristic
463C2×#95C22×C1311yescharacteristic
464C2×#95C22×C1311yescharacteristic
465C2×#95C22×C1311yescharacteristic
466C2×#95C22×C1311yescharacteristic
467C2×#95C22×C1311yescharacteristic
468C2×#95C22×C1311yescharacteristic
469C2×#95C22×C1311yescharacteristic
470C2×#95C22×C1311yescharacteristic
471C2×#95C22×C1311yescharacteristic
472C2×#95C22×C1311yescharacteristic
473C2×#95C22×C1311yescharacteristic
474C2×#95C22×C1311yescharacteristic
475C2×#95C22×C1311yescharacteristic
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C22×C13—42no—
479C22×C13—42no—
480C22×C13—42no—
481C22×C13—42no—
482C22×C13—42no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—81no—
486C22×C13—81no—
487C22×C13—81no—
488C22×C13—81no—
489C22×C13—81no—
490C22×C13—81no—
491C22×C13—81no—
492C22×C13—81no—
493C22×C13C2×#12011yescharacteristic
494C22×C13#52511yescharacteristic
495C22×C13#52511yescharacteristic
496C22×C13#52511yescharacteristic
497C22×C13C2×#12611yescharacteristic
498C22×C13#52911yescharacteristic
499C22×C13#52911yescharacteristic
500C22×C13#52911yescharacteristic
501C22×C13#53211yescharacteristic
502C22×C13#53211yescharacteristic
503C22×C13#53211yescharacteristic
504C22×C13#53211yescharacteristic
505C22×C13#53211yescharacteristic
506C22×C13#53611yescharacteristic
507C22×C13#53711yescharacteristic
508C22×C13#53911yescharacteristic
509C22×C13#53911yescharacteristic
510C22×C13#54111yescharacteristic
511C22×C13#54111yescharacteristic
512C22×C13#54611yescharacteristic
513C22×C13#54611yescharacteristic
514C22×C13#54711yescharacteristic
515C22×C13#54711yescharacteristic
516C22×C13#54711yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54811yescharacteristic
519C22×C13#54811yescharacteristic
520C22×C13#55111yescharacteristic
521C22×C13#55211yescharacteristic
522C22×C13#55211yescharacteristic
523C22×C13#55211yescharacteristic
524C22×C13#55311yescharacteristic
525C22×C13#55611yescharacteristic
526C22×C13#55611yescharacteristic
527C22×C13#55611yescharacteristic
528C4×C13—24no—
529C4×C13—24no—
530C4×C13—42no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—81no—
541C4×C13—81no—
542C25C23×C1311yescharacteristic
543C23×C4C23×C1311yescharacteristic
544C23×C4C23×C1311yescharacteristic
545C23×C4C23×C1311yescharacteristic
546C23×C4C23×C1311yescharacteristic
547C23×C4C23×C1311yescharacteristic
548C23×C4C23×C1311yescharacteristic
549C23×C4C23×C1311yescharacteristic
550C23×C4C23×C1311yescharacteristic
551C23×C4C23×C1311yescharacteristic
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C23×C4C23×C1311yescharacteristic
555C23×C4C23×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557#126—232no—
558C2×C4⋊C4—22no—
559C2×C4⋊C4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
566C2×C4⋊C4—22no—
567C2×C4⋊C4—22no—
568C2×C4⋊C4—22no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—22no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—22no—
574C2×C4⋊C4—22no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4D4×C1314yes—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—22no—
582C2×C22⋊C4—22no—
583C2×C22⋊C4—22no—
584C2×C22⋊C4—22no—
585C2×C22⋊C4—22no—
586C2×C22⋊C4—22no—
587C2×C22⋊C4—22no—
588C2×C22⋊C4—22no—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4D4×C1314yes—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—22no—
606C2×C42—41no—
607C2×C42—41no—
608C2×C42D4×C1314yes—
609#95—22no—
610#95—22no—
611#95—22no—
612#95—22no—
613#95—22no—
614#95—22no—
615#95—22no—
616#95—22no—
617#95—22no—
618#95—22no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—41no—
627C2×C13—82no—
628C2×C13#238811yescharacteristic
629C2×C13#243011yescharacteristic
630C2×C13#243211yescharacteristic
631C2×C13#246611yescharacteristic
632C2×C13#246911yescharacteristic
633C2×C13#247811yescharacteristic
634C2×C13#248111yescharacteristic
635C2×C13#249611yescharacteristic
636C2×C13#251911yescharacteristic
637C2×C13#255311yescharacteristic
638C2×C13#256011yescharacteristic
639C2×C13#260111yescharacteristic
640C2×C13#260411yescharacteristic
641C2×C13#266411yescharacteristic
642C2×C13#286011yescharacteristic
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24C2×D4×C1312yes—
658C24C24×C1311yescharacteristic
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
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×C4C2×D4×C1312yes—
742C22×C4C2×D4×C1312yes—
743C22×C4C2×D4×C1312yes—
744C22×C4C2×D4×C1312yes—
745C22×C4C2×D4×C1312yes—
746C22×C4C2×D4×C1312yes—
747C22×C4C2×D4×C1312yes—
748C22×C4C2×D4×C1312yes—
749C22×C4C13×#4112yes—
750C22×C4C13×#4112yes—
751C22×C4C13×#4112yes—
752C22×C4C13×#4112yes—
753C22×C4C13×#4112yes—
754C22×C4C13×#4112yes—
755C22×C4C13×#4112yes—
756C22×C4C13×#4112yes—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—28no—
760C4⋊C4—28no—
761C4⋊C4—28no—
762C4⋊C4—44no—
763C4⋊C4—44no—
764C22⋊C4—28no—
765C22⋊C4—28no—
766C22⋊C4—28no—
767C22⋊C4—28no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C42—28no—
772C42—44no—
773C42—44no—
774C13#1493111yescharacteristic, direct product factor, Sylow
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23C22×D4×C1311yescharacteristic
811C23C22×D4×C1311yescharacteristic
812C23C22×D4×C1311yescharacteristic
813C23C2×C13×#4111yescharacteristic
814C23C2×C13×#4111yescharacteristic
815C23C2×C13×#4111yescharacteristic
816C23C2×C13×#4111yescharacteristic
817C23C2×C13×#4111yescharacteristic
818C23C2×C13×#4111yescharacteristic
819C23C2×C13×#4111yescharacteristic
820C23C2×C13×#4111yescharacteristic
821C23C13×H(5,𝔽2)11yescharacteristic
822C23C13×2−1+411yescharacteristic
823C23C13×2−1+411yescharacteristic
824C23C13×2−1+411yescharacteristic
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—22no—
828C2×C4—22no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4C13×#12014yes—
922C2×C4C13×#12614yescomplemented
923C22—42no—
924C22—42no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22C2×C13×#12011yescharacteristic
939C22C13×#52511yescharacteristic
940C22C13×#52511yescharacteristic
941C22C13×#52511yescharacteristic
942C22C2×C13×#12611yescharacteristic
943C22C13×#52911yescharacteristic
944C22C13×#52911yescharacteristic
945C22C13×#52911yescharacteristic
946C22C13×#53211yescharacteristic
947C22C13×#53211yescharacteristic
948C22C13×#53211yescharacteristic
949C22C13×#53211yescharacteristic
950C22C13×#53211yescharacteristic
951C22C13×#53611yescharacteristic
952C22C13×#53711yescharacteristic
953C22C13×#53911yescharacteristic
954C22C13×#53911yescharacteristic
955C22C13×#54111yescharacteristic
956C22C13×#54111yescharacteristic
957C22C13×#54611yescharacteristic
958C22C13×#54611yescharacteristic
959C22C13×#54711yescharacteristic
960C22C13×#54711yescharacteristic
961C22C13×#54711yescharacteristic
962C22C13×#54711yescharacteristic
963C22C13×#54811yescharacteristic
964C22C13×#54811yescharacteristic
965C22C13×#55111yescharacteristic
966C22C13×#55211yescharacteristic
967C22C13×#55211yescharacteristic
968C22C13×#55211yescharacteristic
969C22C13×#55311yescharacteristic
970C22C13×#55611yescharacteristic
971C22C13×#55611yescharacteristic
972C22C13×#55611yescharacteristic
973C4—24no—
974C4—24no—
975C4—42no—
976C4—42no—
977C4—42no—
978C4—42no—
979C4—42no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C2—82no—
988C2C13×#238811yescharacteristic
989C2C13×#243011yescharacteristic
990C2C13×#243211yescharacteristic
991C2C13×#246611yescharacteristic
992C2C13×#246911yescharacteristic
993C2C13×#247811yescharacteristic
994C2C13×#248111yescharacteristic
995C2C13×#249611yescharacteristic
996C2C13×#251911yescharacteristic
997C2C13×#255311yescharacteristic
998C2C13×#256011yescharacteristic
999C2C13×#260111yescharacteristic
1000C2C13×#260411yescharacteristic
1001C2C13×#266411yescharacteristic
1002C2C13×#286011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutator, Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#389C2semidirect
4. C2×C13×#387C2semidirect
5. C13×#1444C2semidirect
6. C13×#1442C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
14. C13×#1436C2semidirect
15. C4×C13×#95C2semidirect
142. #14931C13direct (N × H)
275. C2×#389C2×C13semidirect
277. C2×#387C2×C13semidirect
278. #1444C2×C13semidirect
279. #1442C2×C13semidirect
280. #1442C2×C13semidirect
281. #1441C2×C13semidirect
287. #1436C2×C13semidirect
288. C4×#95C2×C13semidirect
436. C2×C4×C13#126semidirect
774. C13#14931direct (N × H)
922. C2×C4C13×#126semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1262
C2×C13×#3892
C2×C13×#3882
C2×C13×#3872
C13×#14442
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C4×C13×#952
#1493113