Finite Group Databasebeta

← C13×#17597 #15703936

Subgroups — C13×#17597 #15703936

Order 3328.

1060 conjugacy classes of subgroups.

The subgroup lattice has 1012 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C13×#3519C211yesmaximal, characteristic
2C13×#2974C211yesmaximal, characteristic, complemented
3C13×#2318C211yesmaximal, characteristic, complemented
4C13×#1521C211yesmaximal, characteristic, complemented
5C13×#1519C211yesmaximal, characteristic, complemented
6C13×#1517C211yesmaximal, characteristic, complemented
7C13×#1516C211yesmaximal, characteristic, complemented
8C13×#1514C211yesmaximal, characteristic, complemented
9C13×#1513C211yesmaximal, characteristic, complemented
10C13×#1512C211yesmaximal, characteristic, complemented
11C13×#1510C211yesmaximal, characteristic, complemented
12C13×#1507C211yesmaximal, characteristic, complemented
13C13×#1504C211yesmaximal, characteristic, complemented
14C13×#1501C211yesmaximal, characteristic, complemented
15C2×C13×#327C211yesmaximal, characteristic, complemented
16C13×#555C411yescharacteristic, complemented
17C13×#554C411yescharacteristic, complemented
18C13×#553—21no—
19C13×#553C411yescharacteristic, complemented
20C13×#553C411yescharacteristic, complemented
21C13×#550C411yescharacteristic, complemented
22C13×#546—21no—
23C13×#546—21no—
24C13×#546C411yescharacteristic, complemented
25C13×#546C411yescharacteristic, complemented
26D42×C13—21no—
27D42×C13C411yescharacteristic, complemented
28C13×#540—21no—
29C13×#538—21no—
30C13×#538—21no—
31C13×#532C2211yescharacteristic
32C13×#529C2211yescharacteristic
33C13×#525C2211yescharacteristic
34C13×#525C2211yescharacteristic
35C2×C13×#121C2211yescharacteristic
36C2×C13×#121C2211yescharacteristic
37C13×#518—21no—
38C2×C4×D4×C13C2211yescharacteristic
39C13×#436—21no—
40C13×#435—21no—
41C13×#435—21no—
42C8×D4×C13—21no—
43C13×#432C2211yescharacteristic, complemented
44C13×#431C2211yescharacteristic, complemented
45C13×#407C2211yescharacteristic, complemented
46C13×#407C2211yescharacteristic, complemented
47C2×C13×C22⋊C8C2211yescharacteristic, complemented
48C2×C13×C22⋊C8C2211yescharacteristic, complemented
49C13×#388—21no—
50C13×#387—21no—
51C13×#386—21no—
52C13×#385—21no—
53C13×#383C2211yescharacteristic, complemented
54C13×#382C2211yescharacteristic, complemented
55C13×#381C2211yescharacteristic, complemented
56C13×#380C2211yescharacteristic, complemented
57C4×C13×C22⋊C4C2211yescharacteristic, complemented
58C2×C13×#95C2211yescharacteristic, complemented
59C13×#328C2211yescharacteristic, complemented
60C13×#328C2211yescharacteristic, complemented
61C13×#328C2211yescharacteristic, complemented
62C13×#328C2211yescharacteristic, complemented
63C13×#327C2211yescharacteristic
64C13×#327C2211yescharacteristic
65C13×#327C2211yescharacteristic
66C13×#327C2211yescharacteristic
67C13×#327C2211yescharacteristic, complemented
68C13×#327C2211yescharacteristic, complemented
69C13×#327C2211yescharacteristic, complemented
70C13×#327C2211yescharacteristic, complemented
71C13×#327C2211yescharacteristic, complemented
72C13×#327C2211yescharacteristic, complemented
73C13×#327C2211yescharacteristic, complemented
74C13×#327C2211yescharacteristic, complemented
75C2×C13×#41—21no—
76C2×C13×#41C2×C411yescharacteristic
77C2×C13×#41C2×C411yescharacteristic, complemented
78C22×D4×C13—21no—
79C22×D4×C13—21no—
80C22×D4×C13—21no—
81C22×D4×C13C2×C411yescharacteristic
82C22×D4×C13C2×C411yescharacteristic, complemented
83C22×D4×C13D411yescharacteristic
84C23×C4×C13—21no—
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C2×C13×M16—21no—
88C2×C13×M16—21no—
89C22×C8×C13—21no—
90C22×C8×C13—21no—
91C13×C4⋊Q8C2×C411yescharacteristic, complemented
92C13×#127—21no—
93C13×#127C2×C411yescharacteristic, complemented
94C13×#126—21no—
95C13×#126—21no—
96C13×#126—21no—
97C13×#125—21no—
98C13×#125C2×C411yescharacteristic, complemented
99C13×#124—21no—
100C13×#124—21no—
101C13×#124—21no—
102C13×#124C2×C411yescharacteristic, complemented
103C13×#123—21no—
104C13×#123—21no—
105C13×#123—21no—
106C13×#123—21no—
107C13×#123—21no—
108C13×#123—21no—
109C13×#123—21no—
110C13×C22⋊Q8—21no—
111C13×C22⋊Q8—21no—
112C13×C22⋊Q8C2×C411yescharacteristic
113C13×C22⋊Q8C2×C411yescharacteristic, complemented
114C13×C22⋊Q8C2311yescharacteristic
115C13×#121—21no—
116C13×#121—21no—
117C13×#121—21no—
118C13×#121—21no—
119C13×#121—21no—
120C13×#121—21no—
121C13×#121—21no—
122C13×#121—21no—
123C13×#121—21no—
124C13×#121—21no—
125C13×#121—21no—
126C13×#121—21no—
127C13×#121—21no—
128C13×#121C2×C411yescharacteristic
129C13×#121C2×C411yescharacteristic
130C13×#121C2×C411yescharacteristic
131C13×#121C2×C411yescharacteristic, complemented
132C13×#121C2×C411yescharacteristic, complemented
133C13×#121C2×C411yescharacteristic, complemented
134C13×#121C2311yescharacteristic
135C13×#121C2311yescharacteristic
136C13×#121C2311yescharacteristic
137C13×#120—21no—
138C13×#120—21no—
139C13×#120—21no—
140C13×#120—21no—
141C13×#120—21no—
142C13×#120—21no—
143C4×Q8×C13C2×C411yescharacteristic, complemented
144C4×D4×C13—21no—
145C4×D4×C13—21no—
146C4×D4×C13—21no—
147C4×D4×C13—21no—
148C4×D4×C13—21no—
149C4×D4×C13—21no—
150C4×D4×C13—21no—
151C4×D4×C13—21no—
152C4×D4×C13—21no—
153C4×D4×C13—21no—
154C4×D4×C13C2×C411yescharacteristic
155C4×D4×C13C2×C411yescharacteristic
156C4×D4×C13C2×C411yescharacteristic
157C4×D4×C13C2×C411yescharacteristic
158C4×D4×C13C2×C411yescharacteristic, complemented
159C4×D4×C13C2×C411yescharacteristic, complemented
160C4×D4×C13C2×C411yescharacteristic, complemented
161C4×D4×C13D411yescharacteristic
162C4×D4×C13D411yescharacteristic
163C4×D4×C13D411yescharacteristic
164C4×D4×C13D411yescharacteristic
165C13×#117—21no—
166C13×#117—21no—
167C13×#117C2×C411yescharacteristic
168C13×#117C2×C411yescharacteristic, complemented
169C2×C13×C4⋊C4—21no—
170C2×C13×C4⋊C4—21no—
171C2×C13×C4⋊C4C2×C411yescharacteristic
172C2×C13×C4⋊C4C2×C411yescharacteristic, complemented
173C2×C13×C4⋊C4D411yescharacteristic
174C2×C13×C22⋊C4—21no—
175C2×C13×C22⋊C4—21no—
176C2×C13×C22⋊C4—21no—
177C2×C13×C22⋊C4—21no—
178C2×C13×C22⋊C4—21no—
179C2×C13×C22⋊C4—21no—
180C2×C13×C22⋊C4—21no—
181C2×C13×C22⋊C4D411yescharacteristic
182C2×C13×C22⋊C4D411yescharacteristic
183C2×C42×C13—21no—
184C2×C42×C13C2311yescharacteristic
185C13×C4⋊C8—21no—
186C13×C4⋊C8—21no—
187C13×C22⋊C8—21no—
188C13×C22⋊C8—21no—
189C13×C22⋊C8—21no—
190C13×C22⋊C8—21no—
191C13×C22⋊C8C2311yescharacteristic
192C13×C22⋊C8C2311yescharacteristic
193C13×C22⋊C8C2311yescharacteristic
194C13×C22⋊C8C2311yescharacteristic
195C13×#97—21no—
196C4×C8×C13—21no—
197C13×#95—21no—
198C13×#95—21no—
199C13×#95—21no—
200C13×#95—21no—
201C13×#95—21no—
202C13×#95C2311yescharacteristic
203C13×#95C2311yescharacteristic
204C13×#95C2311yescharacteristic
205C13×#95C2311yescharacteristic
206#17597C1311yesmaximal, characteristic, direct product factor, Sylow
207C24×C13—21no—
208C24×C13—21no—
209C24×C13C2×D411yescharacteristic
210C24×C13C2×D411yescharacteristic
211C13×#41—81no—
212C13×#41—81no—
213C13×#41—81no—
214C13×#41—81no—
215C2×Q8×C13—21no—
216C2×Q8×C13C22×C411yescharacteristic
217C2×D4×C13—21no—
218C2×D4×C13—21no—
219C2×D4×C13—21no—
220C2×D4×C13—21no—
221C2×D4×C13—21no—
222C2×D4×C13—21no—
223C2×D4×C13—21no—
224C2×D4×C13—21no—
225C2×D4×C13—21no—
226C2×D4×C13—21no—
227C2×D4×C13—21no—
228C2×D4×C13—21no—
229C2×D4×C13—21no—
230C2×D4×C13—21no—
231C2×D4×C13—21no—
232C2×D4×C13—42no—
233C2×D4×C13—44no—
234C2×D4×C13—81no—
235C2×D4×C13—81no—
236C2×D4×C13—81no—
237C2×D4×C13—81no—
238C2×D4×C13—81no—
239C2×D4×C13—81no—
240C2×D4×C13C22⋊C411yescharacteristic
241C2×D4×C13C22⋊C411yescharacteristic
242C2×D4×C13C22⋊C411yescharacteristic
243C2×D4×C13C22⋊C411yescharacteristic
244C2×D4×C13C22×C411yescharacteristic
245C2×D4×C13C22×C411yescharacteristic
246C2×D4×C13C22×C411yescharacteristic
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—21no—
256C22×C4×C13—21no—
257C22×C4×C13—21no—
258C22×C4×C13—42no—
259C22×C4×C13—81no—
260C22×C4×C13—81no—
261C22×C4×C13—81no—
262C22×C4×C13—81no—
263C22×C4×C13C22×C411yescharacteristic
264C22×C4×C13C22×C411yescharacteristic
265C22×C4×C13C22×C411yescharacteristic
266C22×C4×C13C22×C411yescharacteristic
267C22×C4×C13C2×D411yescharacteristic
268C22×C4×C13C2×D411yescharacteristic
269C22×C4×C13C2×D411yescharacteristic
270C22×C4×C13C2×D411yescharacteristic
271C22×C4×C13C2×D411yescharacteristic
272C22×C4×C13C2×D411yescharacteristic
273C22×C4×C13C2×D411yescharacteristic
274C22×C4×C13C2×D411yescharacteristic
275C22×C4×C13C2411yescharacteristic
276C13×M16—81no—
277C13×M16—81no—
278C2×C8×C13—21no—
279C2×C8×C13—21no—
280C2×C8×C13—21no—
281C2×C8×C13—21no—
282C2×C8×C13—81no—
283C2×C8×C13—81no—
284C13×C4⋊C4—21no—
285C13×C4⋊C4—21no—
286C13×C4⋊C4—21no—
287C13×C4⋊C4—21no—
288C13×C4⋊C4—21no—
289C13×C4⋊C4—21no—
290C13×C4⋊C4—21no—
291C13×C4⋊C4—21no—
292C13×C4⋊C4—21no—
293C13×C4⋊C4—81no—
294C13×C4⋊C4—81no—
295C13×C4⋊C4C22⋊C411yescharacteristic
296C13×C4⋊C4C22⋊C411yescharacteristic
297C13×C4⋊C4C22⋊C411yescharacteristic
298C13×C4⋊C4C22⋊C411yescharacteristic
299C13×C4⋊C4C22×C411yescharacteristic
300C13×C4⋊C4C22×C411yescharacteristic
301C13×C4⋊C4C22×C411yescharacteristic
302C13×C4⋊C4C22×C411yescharacteristic
303C13×C22⋊C4—21no—
304C13×C22⋊C4—21no—
305C13×C22⋊C4—21no—
306C13×C22⋊C4—21no—
307C13×C22⋊C4—21no—
308C13×C22⋊C4—21no—
309C13×C22⋊C4—21no—
310C13×C22⋊C4—21no—
311C13×C22⋊C4—21no—
312C13×C22⋊C4—21no—
313C13×C22⋊C4—21no—
314C13×C22⋊C4—21no—
315C13×C22⋊C4—21no—
316C13×C22⋊C4—21no—
317C13×C22⋊C4—21no—
318C13×C22⋊C4—21no—
319C13×C22⋊C4—21no—
320C13×C22⋊C4—21no—
321C13×C22⋊C4—21no—
322C13×C22⋊C4—42no—
323C13×C22⋊C4—81no—
324C13×C22⋊C4—81no—
325C13×C22⋊C4C22⋊C411yescharacteristic
326C13×C22⋊C4C22⋊C411yescharacteristic
327C13×C22⋊C4C22⋊C411yescharacteristic
328C13×C22⋊C4C22⋊C411yescharacteristic
329C13×C22⋊C4C22⋊C411yescharacteristic
330C13×C22⋊C4C22⋊C411yescharacteristic
331C13×C22⋊C4C22⋊C411yescharacteristic
332C13×C22⋊C4C22⋊C411yescharacteristic
333C42×C13—21no—
334C42×C13—21no—
335C42×C13—21no—
336C42×C13—81no—
337C42×C13C22×C411yescharacteristic
338C42×C13C22×C411yescharacteristic
339C42×C13C2×D411yescharacteristic
340C42×C13C2×D411yescharacteristic
341#3519C2×C1311yescharacteristic
342#2974C2×C1311yescharacteristic, complemented
343#2318C2×C1311yescharacteristic, complemented
344#1521C2×C1311yescharacteristic, complemented
345#1519C2×C1311yescharacteristic, complemented
346#1517C2×C1311yescharacteristic, complemented
347#1516C2×C1311yescharacteristic, complemented
348#1514C2×C1311yescharacteristic, complemented
349#1513C2×C1311yescharacteristic, complemented
350#1512C2×C1311yescharacteristic, complemented
351#1510C2×C1311yescharacteristic, complemented
352#1507C2×C1311yescharacteristic, complemented
353#1504C2×C1311yescharacteristic, complemented
354#1501C2×C1311yescharacteristic, complemented
355C2×#327C2×C1311yescharacteristic, complemented
356C23×C13—21no—
357C23×C13—21no—
358C23×C13—22no—
359C23×C13—21no—
360C23×C13—21no—
361C23×C13—21no—
362C23×C13—21no—
363C23×C13—21no—
364C23×C13—41no—
365C23×C13—41no—
366C23×C13—41no—
367C23×C13—42no—
368C23×C13—42no—
369C23×C13—81no—
370C23×C13—81no—
371C23×C13—81no—
372C23×C13—81no—
373C23×C13C2×C22⋊C411yescharacteristic
374C23×C13C2×C22⋊C411yescharacteristic
375C23×C13C2×C22⋊C411yescharacteristic
376C23×C13C2×C22⋊C411yescharacteristic
377C23×C13C22×D411yescharacteristic
378Q8×C13—41no—
379Q8×C13—81no—
380D4×C13—22no—
381D4×C13—22no—
382D4×C13—41no—
383D4×C13—41no—
384D4×C13—42no—
385D4×C13—41no—
386D4×C13—41no—
387D4×C13—41no—
388D4×C13—42no—
389D4×C13—41no—
390D4×C13—41no—
391D4×C13—41no—
392D4×C13—41no—
393D4×C13—41no—
394D4×C13—41no—
395D4×C13—42no—
396D4×C13—81no—
397D4×C13—81no—
398D4×C13—81no—
399D4×C13—81no—
400D4×C13—81no—
401D4×C13—81no—
402D4×C13—81no—
403D4×C13—81no—
404D4×C13—81no—
405C2×C4×C13—21no—
406C2×C4×C13—21no—
407C2×C4×C13—21no—
408C2×C4×C13—21no—
409C2×C4×C13—21no—
410C2×C4×C13—21no—
411C2×C4×C13—21no—
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—42no—
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—81no—
438C2×C4×C13—81no—
439C2×C4×C13—81no—
440C2×C4×C13—81no—
441C2×C4×C13—81no—
442C2×C4×C13—81no—
443C2×C4×C13—84no—
444C2×C4×C13C2×C22⋊C411yescharacteristic
445C2×C4×C13C2×C22⋊C411yescharacteristic
446C2×C4×C13C2×C22⋊C411yescharacteristic
447C2×C4×C13C2×C22⋊C411yescharacteristic
448C2×C4×C13C2×C22⋊C411yescharacteristic
449C2×C4×C13C2×C22⋊C411yescharacteristic
450C2×C4×C13C2×C22⋊C411yescharacteristic
451C2×C4×C13C2×C22⋊C411yescharacteristic
452C2×C4×C13C23×C411yescharacteristic
453C2×C4×C13C22×D411yescharacteristic
454C8×C13—41no—
455C8×C13—41no—
456C8×C13—41no—
457C8×C13—41no—
458#555C4×C1311yescharacteristic, complemented
459#554C4×C1311yescharacteristic, complemented
460#553—21no—
461#553C4×C1311yescharacteristic, complemented
462#553C4×C1311yescharacteristic, complemented
463#550C4×C1311yescharacteristic, complemented
464#546—21no—
465#546—21no—
466#546C4×C1311yescharacteristic, complemented
467#546C4×C1311yescharacteristic, complemented
468D42—21no—
469D42C4×C1311yescharacteristic, complemented
470#540—21no—
471#538—21no—
472#538—21no—
473#532C22×C1311yescharacteristic
474#529C22×C1311yescharacteristic
475#525C22×C1311yescharacteristic
476#525C22×C1311yescharacteristic
477C2×#121C22×C1311yescharacteristic
478C2×#121C22×C1311yescharacteristic
479#518—21no—
480C2×C4×D4C22×C1311yescharacteristic
481#436—21no—
482#435—21no—
483#435—21no—
484C8×D4—21no—
485#432C22×C1311yescharacteristic, complemented
486#431C22×C1311yescharacteristic, complemented
487#407C22×C1311yescharacteristic, complemented
488#407C22×C1311yescharacteristic, complemented
489C2×C22⋊C8C22×C1311yescharacteristic, complemented
490C2×C22⋊C8C22×C1311yescharacteristic, complemented
491#388—21no—
492#387—21no—
493#386—21no—
494#385—21no—
495#383C22×C1311yescharacteristic, complemented
496#382C22×C1311yescharacteristic, complemented
497#381C22×C1311yescharacteristic, complemented
498#380C22×C1311yescharacteristic, complemented
499C4×C22⋊C4C22×C1311yescharacteristic, complemented
500C2×#95C22×C1311yescharacteristic, complemented
501#328C22×C1311yescharacteristic, complemented
502#328C22×C1311yescharacteristic, complemented
503#328C22×C1311yescharacteristic, complemented
504#328C22×C1311yescharacteristic, complemented
505#327C22×C1311yescharacteristic
506#327C22×C1311yescharacteristic
507#327C22×C1311yescharacteristic
508#327C22×C1311yescharacteristic
509#327C22×C1311yescharacteristic, complemented
510#327C22×C1311yescharacteristic, complemented
511#327C22×C1311yescharacteristic, complemented
512#327C22×C1311yescharacteristic, complemented
513#327C22×C1311yescharacteristic, complemented
514#327C22×C1311yescharacteristic, complemented
515#327C22×C1311yescharacteristic, complemented
516#327C22×C1311yescharacteristic, complemented
517C22×C13—21no—
518C22×C13—21no—
519C22×C13—21no—
520C22×C13—21no—
521C22×C13—21no—
522C22×C13—21no—
523C22×C13—21no—
524C22×C13—21no—
525C22×C13—21no—
526C22×C13—21no—
527C22×C13—21no—
528C22×C13—21no—
529C22×C13—21no—
530C22×C13—42no—
531C22×C13—42no—
532C22×C13—41no—
533C22×C13—41no—
534C22×C13—41no—
535C22×C13—41no—
536C22×C13—41no—
537C22×C13—41no—
538C22×C13—41no—
539C22×C13—41no—
540C22×C13—41no—
541C22×C13—81no—
542C22×C13—81no—
543C22×C13—162no—
544C22×C13—162no—
545C22×C13#42112yes—
546C22×C13C22×C22⋊C411yescharacteristic
547C22×C13#57611yescharacteristic
548C22×C13#57711yescharacteristic
549C4×C13—21no—
550C4×C13—21no—
551C4×C13—21no—
552C4×C13—21no—
553C4×C13—21no—
554C4×C13—21no—
555C4×C13—21no—
556C4×C13—21no—
557C4×C13—21no—
558C4×C13—21no—
559C4×C13—41no—
560C4×C13—41no—
561C4×C13—41no—
562C4×C13—41no—
563C4×C13—41no—
564C4×C13—81no—
565C4×C13—81no—
566C4×C13—81no—
567C4×C13—81no—
568C2×#41—21no—
569C2×#41C2×C4×C1311yescharacteristic
570C2×#41C2×C4×C1311yescharacteristic, complemented
571C22×D4—21no—
572C22×D4—21no—
573C22×D4—21no—
574C22×D4C2×C4×C1311yescharacteristic
575C22×D4C2×C4×C1311yescharacteristic, complemented
576C22×D4D4×C1311yescharacteristic
577C23×C4—21no—
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
580C2×M16—21no—
581C2×M16—21no—
582C22×C8—21no—
583C22×C8—21no—
584C4⋊Q8C2×C4×C1311yescharacteristic, complemented
585#127—21no—
586#127C2×C4×C1311yescharacteristic, complemented
587#126—21no—
588#126—21no—
589#126—21no—
590#125—21no—
591#125C2×C4×C1311yescharacteristic, complemented
592#124—21no—
593#124—21no—
594#124—21no—
595#124C2×C4×C1311yescharacteristic, complemented
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603C22⋊Q8—21no—
604C22⋊Q8—21no—
605C22⋊Q8C2×C4×C1311yescharacteristic
606C22⋊Q8C2×C4×C1311yescharacteristic, complemented
607C22⋊Q8C23×C1311yescharacteristic
608#121—21no—
609#121—21no—
610#121—21no—
611#121—21no—
612#121—21no—
613#121—21no—
614#121—21no—
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121C2×C4×C1311yescharacteristic
622#121C2×C4×C1311yescharacteristic
623#121C2×C4×C1311yescharacteristic
624#121C2×C4×C1311yescharacteristic, complemented
625#121C2×C4×C1311yescharacteristic, complemented
626#121C2×C4×C1311yescharacteristic, complemented
627#121C23×C1311yescharacteristic
628#121C23×C1311yescharacteristic
629#121C23×C1311yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635#120—21no—
636C4×Q8C2×C4×C1311yescharacteristic, complemented
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4—21no—
645C4×D4—21no—
646C4×D4—21no—
647C4×D4C2×C4×C1311yescharacteristic
648C4×D4C2×C4×C1311yescharacteristic
649C4×D4C2×C4×C1311yescharacteristic
650C4×D4C2×C4×C1311yescharacteristic
651C4×D4C2×C4×C1311yescharacteristic, complemented
652C4×D4C2×C4×C1311yescharacteristic, complemented
653C4×D4C2×C4×C1311yescharacteristic, complemented
654C4×D4D4×C1311yescharacteristic
655C4×D4D4×C1311yescharacteristic
656C4×D4D4×C1311yescharacteristic
657C4×D4D4×C1311yescharacteristic
658#117—21no—
659#117—21no—
660#117C2×C4×C1311yescharacteristic
661#117C2×C4×C1311yescharacteristic, complemented
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4C2×C4×C1311yescharacteristic
665C2×C4⋊C4C2×C4×C1311yescharacteristic, complemented
666C2×C4⋊C4D4×C1311yescharacteristic
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4D4×C1311yescharacteristic
675C2×C22⋊C4D4×C1311yescharacteristic
676C2×C42—21no—
677C2×C42C23×C1311yescharacteristic
678C4⋊C8—21no—
679C4⋊C8—21no—
680C22⋊C8—21no—
681C22⋊C8—21no—
682C22⋊C8—21no—
683C22⋊C8—21no—
684C22⋊C8C23×C1311yescharacteristic
685C22⋊C8C23×C1311yescharacteristic
686C22⋊C8C23×C1311yescharacteristic
687C22⋊C8C23×C1311yescharacteristic
688#97—21no—
689C4×C8—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95C23×C1311yescharacteristic
696#95C23×C1311yescharacteristic
697#95C23×C1311yescharacteristic
698#95C23×C1311yescharacteristic
699C2×C13—21no—
700C2×C13—21no—
701C2×C13—22no—
702C2×C13—41no—
703C2×C13—41no—
704C2×C13—41no—
705C2×C13—81no—
706C2×C13—81no—
707C2×C13—81no—
708C2×C13#288311yescharacteristic
709C2×C13#289711yescharacteristic
710C2×C13C2×#42111yescharacteristic
711C24—21no—
712C24—21no—
713C24C2×D4×C1311yescharacteristic
714C24C2×D4×C1311yescharacteristic
715#41—81no—
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C22×C4×C1311yescharacteristic
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—21no—
736C2×D4—42no—
737C2×D4—44no—
738C2×D4—81no—
739C2×D4—81no—
740C2×D4—81no—
741C2×D4—81no—
742C2×D4—81no—
743C2×D4—81no—
744C2×D4C13×C22⋊C411yescharacteristic
745C2×D4C13×C22⋊C411yescharacteristic
746C2×D4C13×C22⋊C411yescharacteristic
747C2×D4C13×C22⋊C411yescharacteristic
748C2×D4C22×C4×C1311yescharacteristic
749C2×D4C22×C4×C1311yescharacteristic
750C2×D4C22×C4×C1311yescharacteristic
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—21no—
761C22×C4—21no—
762C22×C4—42no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4C22×C4×C1311yescharacteristic
768C22×C4C22×C4×C1311yescharacteristic
769C22×C4C22×C4×C1311yescharacteristic
770C22×C4C22×C4×C1311yescharacteristic
771C22×C4C2×D4×C1311yescharacteristic
772C22×C4C2×D4×C1311yescharacteristic
773C22×C4C2×D4×C1311yescharacteristic
774C22×C4C2×D4×C1311yescharacteristic
775C22×C4C2×D4×C1311yescharacteristic
776C22×C4C2×D4×C1311yescharacteristic
777C22×C4C2×D4×C1311yescharacteristic
778C22×C4C2×D4×C1311yescharacteristic
779C22×C4C24×C1311yescharacteristic
780M16—81no—
781M16—81no—
782C2×C8—21no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—81no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—81no—
798C4⋊C4—81no—
799C4⋊C4C13×C22⋊C411yescharacteristic
800C4⋊C4C13×C22⋊C411yescharacteristic
801C4⋊C4C13×C22⋊C411yescharacteristic
802C4⋊C4C13×C22⋊C411yescharacteristic
803C4⋊C4C22×C4×C1311yescharacteristic
804C4⋊C4C22×C4×C1311yescharacteristic
805C4⋊C4C22×C4×C1311yescharacteristic
806C4⋊C4C22×C4×C1311yescharacteristic
807C22⋊C4—21no—
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—42no—
827C22⋊C4—81no—
828C22⋊C4—81no—
829C22⋊C4C13×C22⋊C411yescharacteristic
830C22⋊C4C13×C22⋊C411yescharacteristic
831C22⋊C4C13×C22⋊C411yescharacteristic
832C22⋊C4C13×C22⋊C411yescharacteristic
833C22⋊C4C13×C22⋊C411yescharacteristic
834C22⋊C4C13×C22⋊C411yescharacteristic
835C22⋊C4C13×C22⋊C411yescharacteristic
836C22⋊C4C13×C22⋊C411yescharacteristic
837C42—21no—
838C42—21no—
839C42—21no—
840C42—81no—
841C42C22×C4×C1311yescharacteristic
842C42C22×C4×C1311yescharacteristic
843C42C2×D4×C1311yescharacteristic
844C42C2×D4×C1311yescharacteristic
845C13#1759711yescharacteristic, direct product factor, Sylow
846C23—22no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—21no—
853C23—21no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—81no—
860C23—81no—
861C23—81no—
862C23—81no—
863C23C2×C13×C22⋊C411yescharacteristic
864C23C2×C13×C22⋊C411yescharacteristic
865C23C2×C13×C22⋊C411yescharacteristic
866C23C2×C13×C22⋊C411yescharacteristic
867C23C22×D4×C1311yescharacteristic
868Q8—41no—
869Q8—81no—
870D4—22no—
871D4—22no—
872D4—41no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—42no—
878D4—42no—
879D4—42no—
880D4—41no—
881D4—41no—
882D4—41no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—81no—
887D4—81no—
888D4—81no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
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—42no—
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×C4—41no—
927C2×C4—81no—
928C2×C4—81no—
929C2×C4—81no—
930C2×C4—81no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—84no—
934C2×C4C2×C13×C22⋊C411yescharacteristic
935C2×C4C2×C13×C22⋊C411yescharacteristic
936C2×C4C2×C13×C22⋊C411yescharacteristic
937C2×C4C2×C13×C22⋊C411yescharacteristic
938C2×C4C2×C13×C22⋊C411yescharacteristic
939C2×C4C2×C13×C22⋊C411yescharacteristic
940C2×C4C2×C13×C22⋊C411yescharacteristic
941C2×C4C2×C13×C22⋊C411yescharacteristic
942C2×C4C23×C4×C1311yescharacteristic
943C2×C4C22×D4×C1311yescharacteristic
944C8—41no—
945C8—41no—
946C8—41no—
947C8—41no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—21no—
960C22—21no—
961C22—42no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—41no—
971C22—41no—
972C22—81no—
973C22—81no—
974C22—162no—
975C22—162no—
976C22C13×#42112yes—
977C22C22×C13×C22⋊C411yescharacteristic
978C22C13×#57611yescharacteristic
979C22C13×#57711yescharacteristic
980C4—21no—
981C4—21no—
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—21no—
987C4—21no—
988C4—21no—
989C4—21no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C4—81no—
998C4—81no—
999C2—21no—
1000C2—21no—
1001C2—22no—
1002C2—41no—
1003C2—41no—
1004C2—41no—
1005C2—81no—
1006C2—81no—
1007C2—81no—
1008C2C13×#288311yescharacteristic
1009C2C13×#289711yescharacteristic
1010C2C2×C13×#42111yescharacteristic
subgroupG/H
center, socleC22×C13C22×C22⋊C4
commutatorC2×C4C23×C4×C13
Frattini, cosocleC22×C4C24×C13
prime radicalC13×#3519C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C13 ◁ C2×C4×D4×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C13×#2974C2semidirect
3. C13×#2318C2semidirect
4. C13×#1521C2semidirect
5. C13×#1519C2semidirect
6. C13×#1517C2semidirect
7. C13×#1516C2semidirect
8. C13×#1514C2semidirect
9. C13×#1513C2semidirect
10. C13×#1512C2semidirect
11. C13×#1510C2semidirect
12. C13×#1507C2semidirect
13. C13×#1504C2semidirect
14. C13×#1501C2semidirect
15. C2×C13×#327C2semidirect
16. C13×#555C4semidirect
17. C13×#554C4semidirect
19. C13×#553C4semidirect
20. C13×#553C4semidirect
21. C13×#550C4semidirect
24. C13×#546C4semidirect
25. C13×#546C4semidirect
27. D42×C13C4semidirect
43. C13×#432C22semidirect
44. C13×#431C22semidirect
45. C13×#407C22semidirect
46. C13×#407C22semidirect
47. C2×C13×C22⋊C8C22semidirect
48. C2×C13×C22⋊C8C22semidirect
53. C13×#383C22semidirect
54. C13×#382C22semidirect
55. C13×#381C22semidirect
56. C13×#380C22semidirect
57. C4×C13×C22⋊C4C22semidirect
58. C2×C13×#95C22semidirect
59. C13×#328C22semidirect
60. C13×#328C22semidirect
61. C13×#328C22semidirect
62. C13×#328C22semidirect
67. C13×#327C22semidirect
68. C13×#327C22semidirect
69. C13×#327C22semidirect
70. C13×#327C22semidirect
71. C13×#327C22semidirect
72. C13×#327C22semidirect
73. C13×#327C22semidirect
74. C13×#327C22semidirect
77. C2×C13×#41C2×C4semidirect
82. C22×D4×C13C2×C4semidirect
91. C13×C4⋊Q8C2×C4semidirect
93. C13×#127C2×C4semidirect
98. C13×#125C2×C4semidirect
102. C13×#124C2×C4semidirect
113. C13×C22⋊Q8C2×C4semidirect
131. C13×#121C2×C4semidirect
132. C13×#121C2×C4semidirect
133. C13×#121C2×C4semidirect
143. C4×Q8×C13C2×C4semidirect
158. C4×D4×C13C2×C4semidirect
159. C4×D4×C13C2×C4semidirect
160. C4×D4×C13C2×C4semidirect
168. C13×#117C2×C4semidirect
172. C2×C13×C4⋊C4C2×C4semidirect
206. #17597C13direct (N × H)
342. #2974C2×C13semidirect
343. #2318C2×C13semidirect
344. #1521C2×C13semidirect
345. #1519C2×C13semidirect
346. #1517C2×C13semidirect
347. #1516C2×C13semidirect
348. #1514C2×C13semidirect
349. #1513C2×C13semidirect
350. #1512C2×C13semidirect
351. #1510C2×C13semidirect
352. #1507C2×C13semidirect
353. #1504C2×C13semidirect
354. #1501C2×C13semidirect
355. C2×#327C2×C13semidirect
458. #555C4×C13semidirect
459. #554C4×C13semidirect
461. #553C4×C13semidirect
462. #553C4×C13semidirect
463. #550C4×C13semidirect
466. #546C4×C13semidirect
467. #546C4×C13semidirect
469. D42C4×C13semidirect
485. #432C22×C13semidirect
486. #431C22×C13semidirect
487. #407C22×C13semidirect
488. #407C22×C13semidirect
489. C2×C22⋊C8C22×C13semidirect
490. C2×C22⋊C8C22×C13semidirect
495. #383C22×C13semidirect
496. #382C22×C13semidirect
497. #381C22×C13semidirect
498. #380C22×C13semidirect
499. C4×C22⋊C4C22×C13semidirect
500. C2×#95C22×C13semidirect
501. #328C22×C13semidirect
502. #328C22×C13semidirect
503. #328C22×C13semidirect
504. #328C22×C13semidirect
509. #327C22×C13semidirect
510. #327C22×C13semidirect
511. #327C22×C13semidirect
512. #327C22×C13semidirect
513. #327C22×C13semidirect
514. #327C22×C13semidirect
515. #327C22×C13semidirect
516. #327C22×C13semidirect
570. C2×#41C2×C4×C13semidirect
575. C22×D4C2×C4×C13semidirect
584. C4⋊Q8C2×C4×C13semidirect
586. #127C2×C4×C13semidirect
591. #125C2×C4×C13semidirect
595. #124C2×C4×C13semidirect
606. C22⋊Q8C2×C4×C13semidirect
624. #121C2×C4×C13semidirect
625. #121C2×C4×C13semidirect
626. #121C2×C4×C13semidirect
636. C4×Q8C2×C4×C13semidirect
651. C4×D4C2×C4×C13semidirect
652. C4×D4C2×C4×C13semidirect
653. C4×D4C2×C4×C13semidirect
661. #117C2×C4×C13semidirect
665. C2×C4⋊C4C2×C4×C13semidirect
845. C13#17597direct (N × H)

Maximal subgroups

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

subgroupindex
C13×#35192
C13×#29742
C13×#23182
C13×#15212
C13×#15192
C13×#15172
C13×#15162
C13×#15142
C13×#15132
C13×#15122
C13×#15102
C13×#15072
C13×#15042
C13×#15012
C2×C13×#3272
#1759713