Finite Group Databasebeta

← C13×#15499 #15701838

Subgroups — C13×#15499 #15701838

Order 3328.

1478 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic
2C2×C13×#393C211yesmaximal, characteristic
3C2×C13×#391C211yesmaximal, characteristic, complemented
4C2×C13×#391C211yesmaximal, characteristic, complemented
5C13×#1445C211yesmaximal, characteristic, complemented
6C13×#1445C211yesmaximal, characteristic, complemented
7C13×#1442C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1440C211yesmaximal, characteristic
10C13×#1439C211yesmaximal, characteristic
11C13×#1439C211yesmaximal, characteristic
12C13×#1437C211yesmaximal, characteristic
13C13×#1437C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×Q8×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C22⋊C4C2211yescharacteristic
23C22×C13×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C13×#399—24no—
32C13×#393—24no—
33C13×#391—24no—
34C13×#391—24no—
35C2×C13×#95C2211yescharacteristic
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
55C25×C13C2311yescharacteristic
56C22×Q8×C13—22no—
57C22×Q8×C13—22no—
58C22×Q8×C13—22no—
59C22×Q8×C13—22no—
60C22×Q8×C13—41no—
61C22×Q8×C13—41no—
62C22×Q8×C13D414yes—
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
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
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—41no—
89C2×C13×C4⋊C4—41no—
90C2×C13×C4⋊C4—41no—
91C2×C13×C4⋊C4—41no—
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—22no—
104C2×C13×C22⋊C4—41no—
105C2×C13×C22⋊C4—41no—
106C2×C13×C22⋊C4—41no—
107C2×C13×C22⋊C4—41no—
108C2×C13×C22⋊C4—41no—
109C2×C13×C22⋊C4—41no—
110C2×C13×C22⋊C4—41no—
111C2×C13×C22⋊C4—41no—
112C2×C13×C22⋊C4Q814yescomplemented
113C2×C42×C13—22no—
114C2×C42×C13—22no—
115C2×C42×C13—22no—
116C2×C42×C13—41no—
117C2×C42×C13—41no—
118C2×C42×C13—41no—
119C13×#95—22no—
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—41no—
132C13×#95—41no—
133C13×#95—41no—
134C13×#95—41no—
135C13×#95—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95D414yes—
139#15499C1311yesmaximal, characteristic, direct product factor, Sylow
140C24×C13—21no—
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×C13—21no—
154C24×C13C2×Q812yes—
155C24×C13C2411yescharacteristic
156C2×Q8×C13—28no—
157C2×Q8×C13—28no—
158C2×Q8×C13—44no—
159C2×Q8×C13—44no—
160C2×Q8×C13—44no—
161C2×Q8×C13—44no—
162C2×Q8×C13—44no—
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×C13—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×D412yes—
249C22×C4×C13C2×D412yes—
250C22×C4×C13C2×D412yes—
251C22×C4×C13C2×D412yes—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×Q812yes—
254C22×C4×C13C2×Q812yes—
255C22×C4×C13#4112yes—
256C22×C4×C13#4112yes—
257C22×C4×C13#4112yes—
258C22×C4×C13#4112yes—
259C22×C4×C13#4112yes—
260C22×C4×C13#4112yes—
261C13×C4⋊C4—44no—
262C13×C4⋊C4—44no—
263C13×C4⋊C4—44no—
264C13×C4⋊C4—44no—
265C13×C4⋊C4—44no—
266C13×C22⋊C4—44no—
267C13×C22⋊C4—44no—
268C13×C22⋊C4—44no—
269C13×C22⋊C4—44no—
270C13×C22⋊C4—44no—
271C13×C22⋊C4—44no—
272C13×C22⋊C4—44no—
273C42×C13—44no—
274C42×C13—44no—
275C2×#399C2×C1311yescharacteristic
276C2×#393C2×C1311yescharacteristic
277C2×#391C2×C1311yescharacteristic, complemented
278C2×#391C2×C1311yescharacteristic, complemented
279#1445C2×C1311yescharacteristic, complemented
280#1445C2×C1311yescharacteristic, complemented
281#1442C2×C1311yescharacteristic, complemented
282#1441C2×C1311yescharacteristic, complemented
283#1440C2×C1311yescharacteristic
284#1439C2×C1311yescharacteristic
285#1439C2×C1311yescharacteristic
286#1437C2×C1311yescharacteristic
287#1437C2×C1311yescharacteristic
288#1436C2×C1311yescharacteristic, complemented
289C4⋊#95C2×C1311yescharacteristic, complemented
290C23×C13—22no—
291C23×C13—22no—
292C23×C13—22no—
293C23×C13—22no—
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
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×C13—41no—
325C23×C13C22×D411yescharacteristic
326C23×C13C22×D411yescharacteristic
327C23×C13C22×Q811yescharacteristic
328C23×C13C2×#4111yescharacteristic
329C23×C13C2×#4111yescharacteristic
330C23×C13C2×#4111yescharacteristic
331C23×C13C2×#4111yescharacteristic
332C23×C13C2×#4111yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13H(5,𝔽2)11yescharacteristic
335C23×C13H(5,𝔽2)11yescharacteristic
336C23×C13H(5,𝔽2)11yescharacteristic
337C23×C13H(5,𝔽2)11yescharacteristic
338C23×C132−1+411yescharacteristic
339C23×C132−1+411yescharacteristic
340Q8×C13—416no—
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—41no—
375C2×C4×C13—41no—
376C2×C4×C13—41no—
377C2×C4×C13—41no—
378C2×C4×C13—41no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
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—41no—
436C2×C4×C13#12114yes—
437C2×C4×C13#12314yes—
438C2×C4×C13#12414yes—
439C23×Q8C22×C1311yescharacteristic
440C22×C4⋊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×C22⋊C4C22×C1311yescharacteristic
452C22×C42C22×C1311yescharacteristic
453C22×C42C22×C1311yescharacteristic
454#399—24no—
455#393—24no—
456#391—24no—
457#391—24no—
458C2×#95C22×C1311yescharacteristic
459C2×#95C22×C1311yescharacteristic
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×#12111yescharacteristic
494C22×C13C2×#12311yescharacteristic
495C22×C13C2×#12411yescharacteristic
496C22×C13#52911yescharacteristic
497C22×C13#53311yescharacteristic
498C22×C13#53311yescharacteristic
499C22×C13#53411yescharacteristic
500C22×C13#53511yescharacteristic
501C22×C13#53811yescharacteristic
502C22×C13#53911yescharacteristic
503C22×C13#54111yescharacteristic
504C22×C13#54211yescharacteristic
505C22×C13#54211yescharacteristic
506C22×C13#54211yescharacteristic
507C22×C13#54311yescharacteristic
508C22×C13#54611yescharacteristic
509C22×C13#54611yescharacteristic
510C22×C13#54711yescharacteristic
511C22×C13#54811yescharacteristic
512C22×C13D4×Q811yescharacteristic
513C22×C13D4×Q811yescharacteristic
514C22×C13#55011yescharacteristic
515C22×C13#55011yescharacteristic
516C22×C13#55111yescharacteristic
517C22×C13#55111yescharacteristic
518C22×C13#55111yescharacteristic
519C22×C13#55211yescharacteristic
520C22×C13#55411yescharacteristic
521C22×C13#55411yescharacteristic
522C22×C13#55611yescharacteristic
523C22×C13#55911yescharacteristic
524C22×C13#55911yescharacteristic
525C22×C13#55911yescharacteristic
526C22×C13#56211yescharacteristic
527C22×C13#56211yescharacteristic
528C4×C13—24no—
529C4×C13—24no—
530C4×C13—24no—
531C4×C13—42no—
532C4×C13—42no—
533C4×C13—42no—
534C4×C13—42no—
535C4×C13—42no—
536C4×C13—81no—
537C4×C13—81no—
538C4×C13—81no—
539C4×C13—81no—
540C4×C13—81no—
541C4×C13—81no—
542C25C23×C1311yescharacteristic
543C22×Q8—22no—
544C22×Q8—22no—
545C22×Q8—22no—
546C22×Q8—22no—
547C22×Q8—41no—
548C22×Q8—41no—
549C22×Q8D4×C1314yes—
550C23×C4C23×C1311yescharacteristic
551C23×C4C23×C1311yescharacteristic
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
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—41no—
576C2×C4⋊C4—41no—
577C2×C4⋊C4—41no—
578C2×C4⋊C4—41no—
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⋊C4—41no—
594C2×C22⋊C4—41no—
595C2×C22⋊C4—41no—
596C2×C22⋊C4—41no—
597C2×C22⋊C4—41no—
598C2×C22⋊C4—41no—
599C2×C22⋊C4Q8×C1314yescomplemented
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603C2×C42—41no—
604C2×C42—41no—
605C2×C42—41no—
606#95—22no—
607#95—22no—
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—41no—
619#95—41no—
620#95—41no—
621#95—41no—
622#95—41no—
623#95—41no—
624#95—41no—
625#95D4×C1314yes—
626C2×C13—82no—
627C2×C13#241211yescharacteristic
628C2×C13#242311yescharacteristic
629C2×C13#242911yescharacteristic
630C2×C13#244811yescharacteristic
631C2×C13#248811yescharacteristic
632C2×C13#249211yescharacteristic
633C2×C13#254811yescharacteristic
634C2×C13#258911yescharacteristic
635C2×C13#260711yescharacteristic
636C2×C13#269211yescharacteristic
637C2×C13#271011yescharacteristic
638C2×C13#273011yescharacteristic
639C2×C13#273211yescharacteristic
640C2×C13#275411yescharacteristic
641C2×C13#279811yescharacteristic
642C24—21no—
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—
656C24C2×Q8×C1312yes—
657C24C24×C1311yescharacteristic
658C2×Q8—28no—
659C2×Q8—28no—
660C2×Q8—44no—
661C2×Q8—44no—
662C2×Q8—44no—
663C2×Q8—44no—
664C2×Q8—44no—
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×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4C2×D4×C1312yes—
750C22×C4C2×D4×C1312yes—
751C22×C4C2×D4×C1312yes—
752C22×C4C2×D4×C1312yes—
753C22×C4C2×D4×C1312yes—
754C22×C4C2×D4×C1312yes—
755C22×C4C2×Q8×C1312yes—
756C22×C4C2×Q8×C1312yes—
757C22×C4C13×#4112yes—
758C22×C4C13×#4112yes—
759C22×C4C13×#4112yes—
760C22×C4C13×#4112yes—
761C22×C4C13×#4112yes—
762C22×C4C13×#4112yes—
763C4⋊C4—44no—
764C4⋊C4—44no—
765C4⋊C4—44no—
766C4⋊C4—44no—
767C4⋊C4—44no—
768C22⋊C4—44no—
769C22⋊C4—44no—
770C22⋊C4—44no—
771C22⋊C4—44no—
772C22⋊C4—44no—
773C22⋊C4—44no—
774C22⋊C4—44no—
775C42—44no—
776C42—44no—
777C13#1549911yescharacteristic, direct product factor, Sylow
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
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—
810C23—41no—
811C23—41no—
812C23—41no—
813C23C22×D4×C1311yescharacteristic
814C23C22×D4×C1311yescharacteristic
815C23C22×Q8×C1311yescharacteristic
816C23C2×C13×#4111yescharacteristic
817C23C2×C13×#4111yescharacteristic
818C23C2×C13×#4111yescharacteristic
819C23C2×C13×#4111yescharacteristic
820C23C2×C13×#4111yescharacteristic
821C23C2×C13×#4111yescharacteristic
822C23C13×H(5,𝔽2)11yescharacteristic
823C23C13×H(5,𝔽2)11yescharacteristic
824C23C13×H(5,𝔽2)11yescharacteristic
825C23C13×H(5,𝔽2)11yescharacteristic
826C23C13×2−1+411yescharacteristic
827C23C13×2−1+411yescharacteristic
828Q8—416no—
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—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
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×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4C13×#12114yes—
925C2×C4C13×#12314yes—
926C2×C4C13×#12414yes—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—81no—
935C22—81no—
936C22—81no—
937C22—81no—
938C22—81no—
939C22—81no—
940C22—81no—
941C22—81no—
942C22C2×C13×#12111yescharacteristic
943C22C2×C13×#12311yescharacteristic
944C22C2×C13×#12411yescharacteristic
945C22C13×#52911yescharacteristic
946C22C13×#53311yescharacteristic
947C22C13×#53311yescharacteristic
948C22C13×#53411yescharacteristic
949C22C13×#53511yescharacteristic
950C22C13×#53811yescharacteristic
951C22C13×#53911yescharacteristic
952C22C13×#54111yescharacteristic
953C22C13×#54211yescharacteristic
954C22C13×#54211yescharacteristic
955C22C13×#54211yescharacteristic
956C22C13×#54311yescharacteristic
957C22C13×#54611yescharacteristic
958C22C13×#54611yescharacteristic
959C22C13×#54711yescharacteristic
960C22C13×#54811yescharacteristic
961C22D4×Q8×C1311yescharacteristic
962C22D4×Q8×C1311yescharacteristic
963C22C13×#55011yescharacteristic
964C22C13×#55011yescharacteristic
965C22C13×#55111yescharacteristic
966C22C13×#55111yescharacteristic
967C22C13×#55111yescharacteristic
968C22C13×#55211yescharacteristic
969C22C13×#55411yescharacteristic
970C22C13×#55411yescharacteristic
971C22C13×#55611yescharacteristic
972C22C13×#55911yescharacteristic
973C22C13×#55911yescharacteristic
974C22C13×#55911yescharacteristic
975C22C13×#56211yescharacteristic
976C22C13×#56211yescharacteristic
977C4—24no—
978C4—24no—
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—81no—
987C4—81no—
988C4—81no—
989C4—81no—
990C4—81no—
991C2—82no—
992C2C13×#241211yescharacteristic
993C2C13×#242311yescharacteristic
994C2C13×#242911yescharacteristic
995C2C13×#244811yescharacteristic
996C2C13×#248811yescharacteristic
997C2C13×#249211yescharacteristic
998C2C13×#254811yescharacteristic
999C2C13×#258911yescharacteristic
1000C2C13×#260711yescharacteristic
1001C2C13×#269211yescharacteristic
1002C2C13×#271011yescharacteristic
1003C2C13×#273011yescharacteristic
1004C2C13×#273211yescharacteristic
1005C2C13×#275411yescharacteristic
1006C2C13×#279811yescharacteristic
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
3. C2×C13×#391C2semidirect
4. C2×C13×#391C2semidirect
5. C13×#1445C2semidirect
6. C13×#1445C2semidirect
7. C13×#1442C2semidirect
8. C13×#1441C2semidirect
14. C13×#1436C2semidirect
15. C13×C4⋊#95C2semidirect
112. C2×C13×C22⋊C4Q8semidirect
139. #15499C13direct (N × H)
277. C2×#391C2×C13semidirect
278. C2×#391C2×C13semidirect
279. #1445C2×C13semidirect
280. #1445C2×C13semidirect
281. #1442C2×C13semidirect
282. #1441C2×C13semidirect
288. #1436C2×C13semidirect
289. C4⋊#95C2×C13semidirect
599. C2×C22⋊C4Q8×C13semidirect
777. C13#15499direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3992
C2×C13×#3932
C2×C13×#3912
C13×#14452
C13×#14422
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×C4⋊#952
#1549913