Finite Group Databasebeta

← C13×#14008 #15700347

Subgroups — C13×#14008 #15700347

Order 3328.

1686 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#388C211yesmaximal, characteristic
2C2×C13×#387C211yesmaximal, characteristic, complemented
3C2×C13×#385C211yesmaximal, characteristic
4C2×C13×#381C211yesmaximal, characteristic
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
6C13×#1443C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×C4⋊#95C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C4×C13×#95C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C22⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C42×C13C2211yescharacteristic
28C22×C42×C13C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C13×#388—24no—
32C13×#387—24no—
33C13×#385C418yescomplemented
34C13×#381—24no—
35C4×C13×C22⋊C4—24no—
36C2×C13×#95C2211yescharacteristic
37C2×C13×#95C2211yescharacteristic
38C2×C13×#95C2211yescharacteristic
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
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—41no—
62C23×C4×C13—41no—
63C23×C4×C13C2×C414yes—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C23×C4×C13C2311yescharacteristic
69C23×C4×C13C2311yescharacteristic
70C23×C4×C13C2311yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
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—41no—
85C2×C13×C4⋊C4—41no—
86C2×C13×C4⋊C4—41no—
87C2×C13×C4⋊C4—41no—
88C2×C13×C4⋊C4C2×C414yes—
89C2×C13×C4⋊C4C2×C414yes—
90C2×C13×C22⋊C4—22no—
91C2×C13×C22⋊C4—22no—
92C2×C13×C22⋊C4—22no—
93C2×C13×C22⋊C4—22no—
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—41no—
104C2×C13×C22⋊C4—41no—
105C2×C13×C22⋊C4C2×C414yes—
106C2×C13×C22⋊C4C2×C414yes—
107C2×C13×C22⋊C4D414yes—
108C2×C42×C13—22no—
109C2×C42×C13—22no—
110C2×C42×C13—22no—
111C2×C42×C13—22no—
112C2×C42×C13—22no—
113C2×C42×C13—22no—
114C2×C42×C13—22no—
115C2×C42×C13—22no—
116C2×C42×C13—22no—
117C2×C42×C13—41no—
118C2×C42×C13—41no—
119C2×C42×C13—41no—
120C13×#95—22no—
121C13×#95—22no—
122C13×#95—22no—
123C13×#95—22no—
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—41no—
137C13×#95C2×C414yes—
138C13×#95C2×C414yes—
139C13×#95D414yes—
140#14008C1311yesmaximal, characteristic, direct product factor, Sylow
141C24×C13—21no—
142C24×C13—21no—
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×C13C22×C412yes—
154C24×C13C2×D412yes—
155C24×C13#4112yes—
156C24×C13C2411yescharacteristic
157C22×C4×C13—21no—
158C22×C4×C13—21no—
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—28no—
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—28no—
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—44no—
240C22×C4×C13—44no—
241C22×C4×C13—44no—
242C22×C4×C13—44no—
243C22×C4×C13—44no—
244C22×C4×C13C22×C412yes—
245C22×C4×C13C22×C412yes—
246C22×C4×C13C22×C412yes—
247C22×C4×C13C22×C412yes—
248C22×C4×C13C22×C412yes—
249C22×C4×C13C22×C412yes—
250C22×C4×C13C2×D412yes—
251C22×C4×C13C2×D412yes—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×D412yes—
254C22×C4×C13C2×D412yes—
255C22×C4×C13#4112yes—
256C22×C4×C13#4112yes—
257C22×C4×C13#4112yes—
258C22×C4×C13#4112yes—
259C22×C4×C13#4112yes—
260C22×C4×C13#4112yes—
261C22×C4×C13#4112yes—
262C13×C4⋊C4—28no—
263C13×C4⋊C4—44no—
264C13×C4⋊C4—44no—
265C13×C4⋊C4—44no—
266C13×C22⋊C4—28no—
267C13×C22⋊C4—28no—
268C13×C22⋊C4—28no—
269C13×C22⋊C4—28no—
270C13×C22⋊C4—44no—
271C13×C22⋊C4—44no—
272C42×C13—44no—
273C42×C13—44no—
274C42×C13—44no—
275C42×C13—44no—
276C2×#388C2×C1311yescharacteristic
277C2×#387C2×C1311yescharacteristic, complemented
278C2×#385C2×C1311yescharacteristic
279C2×#381C2×C1311yescharacteristic
280C2×C4×C22⋊C4C2×C1311yescharacteristic
281#1443C2×C1311yescharacteristic, complemented
282#1441C2×C1311yescharacteristic, complemented
283#1440C2×C1311yescharacteristic
284#1439C2×C1311yescharacteristic
285#1437C2×C1311yescharacteristic
286#1436C2×C1311yescharacteristic, complemented
287#1436C2×C1311yescharacteristic, complemented
288C4⋊#95C2×C1311yescharacteristic, complemented
289#1434C2×C1311yescharacteristic, complemented
290C4×#95C2×C1311yescharacteristic, complemented
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
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×C13—41no—
325C23×C13C4×D414yes—
326C23×C13C23×C411yescharacteristic
327C23×C13C22×D411yescharacteristic
328C23×C13C22×D411yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C13H(5,𝔽2)11yescharacteristic
339C23×C132−1+411yescharacteristic
340C23×C132−1+411yescharacteristic
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—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—416no—
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—41no—
436C2×C4×C13—41no—
437C2×C4×C13#11714yes—
438C2×C4×C13C4×D414yes—
439C2×C4×C13#12314yes—
440C24×C4C22×C1311yescharacteristic
441C22×C4⋊C4C22×C1311yescharacteristic
442C22×C4⋊C4C22×C1311yescharacteristic
443C22×C4⋊C4C22×C1311yescharacteristic
444C22×C4⋊C4C22×C1311yescharacteristic
445C22×C22⋊C4C22×C1311yescharacteristic
446C22×C22⋊C4C22×C1311yescharacteristic
447C22×C22⋊C4C22×C1311yescharacteristic
448C22×C22⋊C4C22×C1311yescharacteristic
449C22×C22⋊C4C22×C1311yescharacteristic
450C22×C22⋊C4C22×C1311yescharacteristic
451C22×C42C22×C1311yescharacteristic
452C22×C42C22×C1311yescharacteristic
453C22×C42C22×C1311yescharacteristic
454C22×C42C22×C1311yescharacteristic
455#388—24no—
456#387—24no—
457#385C4×C1318yescomplemented
458#381—24no—
459C4×C22⋊C4—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
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C22×C13—24no—
481C22×C13—24no—
482C22×C13—24no—
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13C2×#11711yescharacteristic
496C22×C13C2×C4×D411yescharacteristic
497C22×C13C2×C4×D411yescharacteristic
498C22×C13C4×#4111yescharacteristic
499C22×C13C4×#4111yescharacteristic
500C22×C13#51811yescharacteristic
501C22×C13#51911yescharacteristic
502C22×C13C2×#12311yescharacteristic
503C22×C13#52511yescharacteristic
504C22×C13#52911yescharacteristic
505C22×C13#52911yescharacteristic
506C22×C13#52911yescharacteristic
507C22×C13#52911yescharacteristic
508C22×C13#53211yescharacteristic
509C22×C13#53211yescharacteristic
510C22×C13#53911yescharacteristic
511C22×C13#53911yescharacteristic
512C22×C13#54211yescharacteristic
513C22×C13#54211yescharacteristic
514C22×C13D4211yescharacteristic
515C22×C13#54611yescharacteristic
516C22×C13#54611yescharacteristic
517C22×C13#54711yescharacteristic
518C22×C13#54711yescharacteristic
519C22×C13#54711yescharacteristic
520C22×C13#54811yescharacteristic
521C22×C13#55111yescharacteristic
522C22×C13#55111yescharacteristic
523C22×C13#55111yescharacteristic
524C22×C13#55211yescharacteristic
525C22×C13#55211yescharacteristic
526C22×C13#55211yescharacteristic
527C22×C13#55311yescharacteristic
528C22×C13#55311yescharacteristic
529C22×C13#55611yescharacteristic
530C4×C13—24no—
531C4×C13—24no—
532C4×C13—24no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—81no—
543C4×C13—81no—
544C25C23×C1311yescharacteristic
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—41no—
550C23×C4—41no—
551C23×C4C2×C4×C1314yes—
552C23×C4C23×C1311yescharacteristic
553C23×C4C23×C1311yescharacteristic
554C23×C4C23×C1311yescharacteristic
555C23×C4C23×C1311yescharacteristic
556C23×C4C23×C1311yescharacteristic
557C23×C4C23×C1311yescharacteristic
558C23×C4C23×C1311yescharacteristic
559C23×C4C23×C1311yescharacteristic
560C23×C4C23×C1311yescharacteristic
561C23×C4C23×C1311yescharacteristic
562C23×C4C23×C1311yescharacteristic
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1311yescharacteristic
565C23×C4C23×C1311yescharacteristic
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—41no—
573C2×C4⋊C4—41no—
574C2×C4⋊C4—41no—
575C2×C4⋊C4—41no—
576C2×C4⋊C4C2×C4×C1314yes—
577C2×C4⋊C4C2×C4×C1314yes—
578C2×C22⋊C4—22no—
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—41no—
592C2×C22⋊C4—41no—
593C2×C22⋊C4C2×C4×C1314yes—
594C2×C22⋊C4C2×C4×C1314yes—
595C2×C22⋊C4D4×C1314yes—
596C2×C42—22no—
597C2×C42—22no—
598C2×C42—22no—
599C2×C42—22no—
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—22no—
604C2×C42—22no—
605C2×C42—41no—
606C2×C42—41no—
607C2×C42—41no—
608#95—22no—
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—41no—
625#95C2×C4×C1314yes—
626#95C2×C4×C1314yes—
627#95D4×C1314yes—
628C2×C13—44no—
629C2×C13#229311yescharacteristic
630C2×C13C4×#12311yescharacteristic
631C2×C13#233211yescharacteristic
632C2×C13#234411yescharacteristic
633C2×C13#235311yescharacteristic
634C2×C13#235811yescharacteristic
635C2×C13#236211yescharacteristic
636C2×C13#241911yescharacteristic
637C2×C13#242211yescharacteristic
638C2×C13#246111yescharacteristic
639C2×C13#246611yescharacteristic
640C2×C13#251511yescharacteristic
641C2×C13#252711yescharacteristic
642C2×C13#255311yescharacteristic
643C2×C13#255811yescharacteristic
644C24—21no—
645C24—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24C22×C4×C1312yes—
657C24C2×D4×C1312yes—
658C24C13×#4112yes—
659C24C24×C1311yescharacteristic
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—28no—
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—28no—
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—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4C22×C4×C1312yes—
748C22×C4C22×C4×C1312yes—
749C22×C4C22×C4×C1312yes—
750C22×C4C22×C4×C1312yes—
751C22×C4C22×C4×C1312yes—
752C22×C4C22×C4×C1312yes—
753C22×C4C2×D4×C1312yes—
754C22×C4C2×D4×C1312yes—
755C22×C4C2×D4×C1312yes—
756C22×C4C2×D4×C1312yes—
757C22×C4C2×D4×C1312yes—
758C22×C4C13×#4112yes—
759C22×C4C13×#4112yes—
760C22×C4C13×#4112yes—
761C22×C4C13×#4112yes—
762C22×C4C13×#4112yes—
763C22×C4C13×#4112yes—
764C22×C4C13×#4112yes—
765C4⋊C4—28no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C4⋊C4—44no—
769C22⋊C4—28no—
770C22⋊C4—28no—
771C22⋊C4—28no—
772C22⋊C4—28no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C42—44no—
776C42—44no—
777C42—44no—
778C42—44no—
779C13#1400811yescharacteristic, direct product factor, Sylow
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23C4×D4×C1314yes—
815C23C23×C4×C1311yescharacteristic
816C23C22×D4×C1311yescharacteristic
817C23C22×D4×C1311yescharacteristic
818C23C2×C13×#4111yescharacteristic
819C23C2×C13×#4111yescharacteristic
820C23C2×C13×#4111yescharacteristic
821C23C2×C13×#4111yescharacteristic
822C23C2×C13×#4111yescharacteristic
823C23C2×C13×#4111yescharacteristic
824C23C2×C13×#4111yescharacteristic
825C23C2×C13×#4111yescharacteristic
826C23C13×H(5,𝔽2)11yescharacteristic
827C23C13×H(5,𝔽2)11yescharacteristic
828C23C13×2−1+411yescharacteristic
829C23C13×2−1+411yescharacteristic
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—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—416no—
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×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4C13×#11714yes—
927C2×C4C4×D4×C1314yes—
928C2×C4C13×#12314yes—
929C22—24no—
930C22—24no—
931C22—24no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—42no—
944C22C2×C13×#11711yescharacteristic
945C22C2×C4×D4×C1311yescharacteristic
946C22C2×C4×D4×C1311yescharacteristic
947C22C4×C13×#4111yescharacteristic
948C22C4×C13×#4111yescharacteristic
949C22C13×#51811yescharacteristic
950C22C13×#51911yescharacteristic
951C22C2×C13×#12311yescharacteristic
952C22C13×#52511yescharacteristic
953C22C13×#52911yescharacteristic
954C22C13×#52911yescharacteristic
955C22C13×#52911yescharacteristic
956C22C13×#52911yescharacteristic
957C22C13×#53211yescharacteristic
958C22C13×#53211yescharacteristic
959C22C13×#53911yescharacteristic
960C22C13×#53911yescharacteristic
961C22C13×#54211yescharacteristic
962C22C13×#54211yescharacteristic
963C22D42×C1311yescharacteristic
964C22C13×#54611yescharacteristic
965C22C13×#54611yescharacteristic
966C22C13×#54711yescharacteristic
967C22C13×#54711yescharacteristic
968C22C13×#54711yescharacteristic
969C22C13×#54811yescharacteristic
970C22C13×#55111yescharacteristic
971C22C13×#55111yescharacteristic
972C22C13×#55111yescharacteristic
973C22C13×#55211yescharacteristic
974C22C13×#55211yescharacteristic
975C22C13×#55211yescharacteristic
976C22C13×#55311yescharacteristic
977C22C13×#55311yescharacteristic
978C22C13×#55611yescharacteristic
979C4—24no—
980C4—24no—
981C4—24no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—81no—
992C4—81no—
993C2—44no—
994C2C13×#229311yescharacteristic
995C2C4×C13×#12311yescharacteristic
996C2C13×#233211yescharacteristic
997C2C13×#234411yescharacteristic
998C2C13×#235311yescharacteristic
999C2C13×#235811yescharacteristic
1000C2C13×#236211yescharacteristic
1001C2C13×#241911yescharacteristic
1002C2C13×#242211yescharacteristic
1003C2C13×#246111yescharacteristic
1004C2C13×#246611yescharacteristic
1005C2C13×#251511yescharacteristic
1006C2C13×#252711yescharacteristic
1007C2C13×#255311yescharacteristic
1008C2C13×#255811yescharacteristic
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×#387C2semidirect
6. C13×#1443C2semidirect
7. C13×#1441C2semidirect
11. C13×#1436C2semidirect
12. C13×#1436C2semidirect
13. C13×C4⋊#95C2semidirect
14. C13×#1434C2semidirect
15. C4×C13×#95C2semidirect
33. C13×#385C4semidirect
140. #14008C13direct (N × H)
277. C2×#387C2×C13semidirect
281. #1443C2×C13semidirect
282. #1441C2×C13semidirect
286. #1436C2×C13semidirect
287. #1436C2×C13semidirect
288. C4⋊#95C2×C13semidirect
289. #1434C2×C13semidirect
290. C4×#95C2×C13semidirect
457. #385C4×C13semidirect
779. C13#14008direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3882
C2×C13×#3872
C2×C13×#3852
C2×C13×#3812
C2×C4×C13×C22⋊C42
C13×#14432
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
C13×#14342
C4×C13×#952
#1400813