Finite Group Databasebeta

← C13×#14364 #15700703

Subgroups — C13×#14364 #15700703

Order 3328.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×C22⋊Q8C211yesmaximal, characteristic
2C2×C13×#391C211yesmaximal, characteristic, complemented
3C2×C13×#388C211yesmaximal, characteristic
4C2×C13×#388C211yesmaximal, characteristic
5C2×C13×#381C211yesmaximal, characteristic
6C13×#1446C211yesmaximal, characteristic, complemented
7C13×#1445C211yesmaximal, characteristic, complemented
8C13×#1441C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1440C211yesmaximal, characteristic
11C13×#1440C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×C4⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
18C2×C13×C22⋊Q8—24no—
19C2×C13×C22⋊Q8—24no—
20C2×C13×C22⋊Q8C418yescomplemented
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C13×#391—24no—
35C13×#388—24no—
36C13×#388—24no—
37C13×#381—24no—
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
56C2×C13×#95C2211yescharacteristic
57C2×C13×#95C2211yescharacteristic
58C25×C13C2311yescharacteristic
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—41no—
64C22×Q8×C13—41no—
65C22×Q8×C13C2×C414yes—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—22no—
70C23×C4×C13—41no—
71C23×C4×C13—41no—
72C23×C4×C13C2×C414yes—
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
86C23×C4×C13C2311yescharacteristic
87C13×C22⋊Q8—232no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4C2×C414yes—
101C2×C13×C4⋊C4C2×C414yes—
102C2×C13×C4⋊C4C2×C414yes—
103C2×C13×C22⋊C4—22no—
104C2×C13×C22⋊C4—22no—
105C2×C13×C22⋊C4—22no—
106C2×C13×C22⋊C4—22no—
107C2×C13×C22⋊C4—22no—
108C2×C13×C22⋊C4—22no—
109C2×C13×C22⋊C4—22no—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—41no—
114C2×C13×C22⋊C4—41no—
115C2×C13×C22⋊C4—41no—
116C2×C13×C22⋊C4—41no—
117C2×C13×C22⋊C4C2×C414yes—
118C2×C13×C22⋊C4C2×C414yes—
119C2×C13×C22⋊C4D414yes—
120C2×C13×C22⋊C4D414yes—
121C2×C42×C13—22no—
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C2×C42×C13—41no—
126C2×C42×C13—41no—
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—41no—
141C13×#95—41no—
142C13×#95—41no—
143C13×#95—41no—
144C13×#95—41no—
145C13×#95—41no—
146C13×#95D414yes—
147#14364C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13C22×C412yes—
161C24×C13C2×D412yes—
162C24×C13C2×D412yes—
163C24×C13C2411yescharacteristic
164C2×Q8×C13—28no—
165C2×Q8×C13—28no—
166C2×Q8×C13—44no—
167C2×Q8×C13—44no—
168C2×Q8×C13—44no—
169C2×Q8×C13—44no—
170C2×Q8×C13—44no—
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—28no—
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—28no—
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×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—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13—44no—
259C22×C4×C13—44no—
260C22×C4×C13C22×C412yes—
261C22×C4×C13C22×C412yes—
262C22×C4×C13C22×C412yes—
263C22×C4×C13C22×C412yes—
264C22×C4×C13C22×C412yes—
265C22×C4×C13C22×C412yes—
266C22×C4×C13C2×D412yes—
267C22×C4×C13C2×D412yes—
268C22×C4×C13C2×D412yes—
269C22×C4×C13C2×D412yes—
270C22×C4×C13C2×D412yes—
271C22×C4×C13C2×D412yes—
272C22×C4×C13C2×D412yes—
273C22×C4×C13#4112yes—
274C22×C4×C13#4112yes—
275C22×C4×C13#4112yes—
276C13×C4⋊C4—28no—
277C13×C4⋊C4—28no—
278C13×C4⋊C4—28no—
279C13×C4⋊C4—44no—
280C13×C4⋊C4—44no—
281C13×C22⋊C4—28no—
282C13×C22⋊C4—44no—
283C13×C22⋊C4—44no—
284C13×C22⋊C4—44no—
285C13×C22⋊C4—44no—
286C13×C22⋊C4C22⋊C4116yes—
287C42×C13—44no—
288C42×C13—44no—
289C22×C22⋊Q8C2×C1311yescharacteristic
290C2×#391C2×C1311yescharacteristic, complemented
291C2×#388C2×C1311yescharacteristic
292C2×#388C2×C1311yescharacteristic
293C2×#381C2×C1311yescharacteristic
294#1446C2×C1311yescharacteristic, complemented
295#1445C2×C1311yescharacteristic, complemented
296#1441C2×C1311yescharacteristic, complemented
297#1441C2×C1311yescharacteristic, complemented
298#1440C2×C1311yescharacteristic
299#1440C2×C1311yescharacteristic
300#1436C2×C1311yescharacteristic, complemented
301#1436C2×C1311yescharacteristic, complemented
302C4⋊#95C2×C1311yescharacteristic, complemented
303C22⋊#95C2×C1311yescharacteristic
304C23×C13—22no—
305C23×C13—22no—
306C23×C13—22no—
307C23×C13—22no—
308C23×C13—22no—
309C23×C13—22no—
310C23×C13—22no—
311C23×C13—22no—
312C23×C13—22no—
313C23×C13—22no—
314C23×C13—22no—
315C23×C13—22no—
316C23×C13—22no—
317C23×C13—22no—
318C23×C13—22no—
319C23×C13—22no—
320C23×C13—22no—
321C23×C13—22no—
322C23×C13—41no—
323C23×C13—41no—
324C23×C13—41no—
325C23×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13—41no—
335C23×C13—41no—
336C23×C13—41no—
337C23×C13—41no—
338C23×C13C2×C22⋊C414yes—
339C23×C13C23×C411yescharacteristic
340C23×C13C22×D411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C2×#4111yescharacteristic
344C23×C13C2×#4111yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C13H(5,𝔽2)11yescharacteristic
349C23×C132−1+411yescharacteristic
350C23×C132−1+411yescharacteristic
351C23×C132−1+411yescharacteristic
352C23×C132−1+411yescharacteristic
353C23×C132−1+411yescharacteristic
354Q8×C13—416no—
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—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—416no—
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—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13C2×C22⋊C414yes—
452C2×C4×C13C2×C22⋊C414yes—
453C2×C4×C13C4×D414yes—
454C23×Q8C22×C1311yescharacteristic
455C24×C4C22×C1311yescharacteristic
456C2×C22⋊Q8—24no—
457C2×C22⋊Q8—24no—
458C2×C22⋊Q8C4×C1318yescomplemented
459C22×C4⋊C4C22×C1311yescharacteristic
460C22×C4⋊C4C22×C1311yescharacteristic
461C22×C4⋊C4C22×C1311yescharacteristic
462C22×C4⋊C4C22×C1311yescharacteristic
463C22×C4⋊C4C22×C1311yescharacteristic
464C22×C22⋊C4C22×C1311yescharacteristic
465C22×C22⋊C4C22×C1311yescharacteristic
466C22×C22⋊C4C22×C1311yescharacteristic
467C22×C22⋊C4C22×C1311yescharacteristic
468C22×C22⋊C4C22×C1311yescharacteristic
469C22×C22⋊C4C22×C1311yescharacteristic
470C22×C42C22×C1311yescharacteristic
471C22×C42C22×C1311yescharacteristic
472#391—24no—
473#388—24no—
474#388—24no—
475#381—24no—
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C2×#95C22×C1311yescharacteristic
481C2×#95C22×C1311yescharacteristic
482C2×#95C22×C1311yescharacteristic
483C2×#95C22×C1311yescharacteristic
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C2×#95C22×C1311yescharacteristic
492C2×#95C22×C1311yescharacteristic
493C2×#95C22×C1311yescharacteristic
494C2×#95C22×C1311yescharacteristic
495C2×#95C22×C1311yescharacteristic
496C22×C13—24no—
497C22×C13—24no—
498C22×C13—24no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13—42no—
507C22×C13—42no—
508C22×C13—42no—
509C22×C13—42no—
510C22×C13—42no—
511C22×C13C22×C22⋊C411yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C4×#4111yescharacteristic
514C22×C13#51811yescharacteristic
515C22×C13#51911yescharacteristic
516C22×C13#51911yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#53611yescharacteristic
519C22×C13#53611yescharacteristic
520C22×C13#53611yescharacteristic
521C22×C13#53611yescharacteristic
522C22×C13#53611yescharacteristic
523C22×C13#53711yescharacteristic
524C22×C13#53911yescharacteristic
525C22×C13#53911yescharacteristic
526C22×C13#54111yescharacteristic
527C22×C13#54211yescharacteristic
528C22×C13#54211yescharacteristic
529C22×C13#54211yescharacteristic
530C22×C13D4211yescharacteristic
531C22×C13D4211yescharacteristic
532C22×C13#54611yescharacteristic
533C22×C13#54611yescharacteristic
534C22×C13#54611yescharacteristic
535C22×C13#54611yescharacteristic
536C22×C13#54711yescharacteristic
537C22×C13#54711yescharacteristic
538C22×C13#54711yescharacteristic
539C22×C13#54811yescharacteristic
540C22×C13#55211yescharacteristic
541C22×C13#55611yescharacteristic
542C22×C13#56211yescharacteristic
543C22×C13#56211yescharacteristic
544C22×C13#56311yescharacteristic
545C22×C13#56311yescharacteristic
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—24no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—42no—
552C4×C13—42no—
553C4×C13—42no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—81no—
557C4×C13—81no—
558C4×C13—81no—
559C4×C13—81no—
560C25C23×C1311yescharacteristic
561C22×Q8—22no—
562C22×Q8—22no—
563C22×Q8—22no—
564C22×Q8—22no—
565C22×Q8—41no—
566C22×Q8—41no—
567C22×Q8C2×C4×C1314yes—
568C23×C4—22no—
569C23×C4—22no—
570C23×C4—22no—
571C23×C4—22no—
572C23×C4—41no—
573C23×C4—41no—
574C23×C4C2×C4×C1314yes—
575C23×C4C23×C1311yescharacteristic
576C23×C4C23×C1311yescharacteristic
577C23×C4C23×C1311yescharacteristic
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
580C23×C4C23×C1311yescharacteristic
581C23×C4C23×C1311yescharacteristic
582C23×C4C23×C1311yescharacteristic
583C23×C4C23×C1311yescharacteristic
584C23×C4C23×C1311yescharacteristic
585C23×C4C23×C1311yescharacteristic
586C23×C4C23×C1311yescharacteristic
587C23×C4C23×C1311yescharacteristic
588C23×C4C23×C1311yescharacteristic
589C22⋊Q8—232no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4C2×C4×C1314yes—
603C2×C4⋊C4C2×C4×C1314yes—
604C2×C4⋊C4C2×C4×C1314yes—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—22no—
610C2×C22⋊C4—22no—
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—41no—
616C2×C22⋊C4—41no—
617C2×C22⋊C4—41no—
618C2×C22⋊C4—41no—
619C2×C22⋊C4C2×C4×C1314yes—
620C2×C22⋊C4C2×C4×C1314yes—
621C2×C22⋊C4D4×C1314yes—
622C2×C22⋊C4D4×C1314yes—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—22no—
627C2×C42—41no—
628C2×C42—41no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—22no—
634#95—22no—
635#95—22no—
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—41no—
643#95—41no—
644#95—41no—
645#95—41no—
646#95—41no—
647#95—41no—
648#95D4×C1314yes—
649C2×C13—44no—
650C2×C13#231011yescharacteristic
651C2×C13#232311yescharacteristic
652C2×C13#233211yescharacteristic
653C2×C13D4×C22⋊C411yescharacteristic
654C2×C13#233911yescharacteristic
655C2×C13#236211yescharacteristic
656C2×C13#237811yescharacteristic
657C2×C13#267211yescharacteristic
658C2×C13#267411yescharacteristic
659C2×C13#268011yescharacteristic
660C2×C13#268111yescharacteristic
661C2×C13#268711yescharacteristic
662C2×C13#268911yescharacteristic
663C2×C13#269811yescharacteristic
664C2×C13#270011yescharacteristic
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24C22×C4×C1312yes—
678C24C2×D4×C1312yes—
679C24C2×D4×C1312yes—
680C24C24×C1311yescharacteristic
681C2×Q8—28no—
682C2×Q8—28no—
683C2×Q8—44no—
684C2×Q8—44no—
685C2×Q8—44no—
686C2×Q8—44no—
687C2×Q8—44no—
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—28no—
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—28no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—44no—
773C22×C4—44no—
774C22×C4—44no—
775C22×C4—44no—
776C22×C4—44no—
777C22×C4C22×C4×C1312yes—
778C22×C4C22×C4×C1312yes—
779C22×C4C22×C4×C1312yes—
780C22×C4C22×C4×C1312yes—
781C22×C4C22×C4×C1312yes—
782C22×C4C22×C4×C1312yes—
783C22×C4C2×D4×C1312yes—
784C22×C4C2×D4×C1312yes—
785C22×C4C2×D4×C1312yes—
786C22×C4C2×D4×C1312yes—
787C22×C4C2×D4×C1312yes—
788C22×C4C2×D4×C1312yes—
789C22×C4C2×D4×C1312yes—
790C22×C4C13×#4112yes—
791C22×C4C13×#4112yes—
792C22×C4C13×#4112yes—
793C4⋊C4—28no—
794C4⋊C4—28no—
795C4⋊C4—28no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C22⋊C4—28no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4C13×C22⋊C4116yes—
804C42—44no—
805C42—44no—
806C13#1436411yescharacteristic, direct product factor, Sylow
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23C2×C13×C22⋊C414yes—
842C23C23×C4×C1311yescharacteristic
843C23C22×D4×C1311yescharacteristic
844C23C22×D4×C1311yescharacteristic
845C23C22×D4×C1311yescharacteristic
846C23C2×C13×#4111yescharacteristic
847C23C2×C13×#4111yescharacteristic
848C23C2×C13×#4111yescharacteristic
849C23C13×H(5,𝔽2)11yescharacteristic
850C23C13×H(5,𝔽2)11yescharacteristic
851C23C13×H(5,𝔽2)11yescharacteristic
852C23C13×2−1+411yescharacteristic
853C23C13×2−1+411yescharacteristic
854C23C13×2−1+411yescharacteristic
855C23C13×2−1+411yescharacteristic
856C23C13×2−1+411yescharacteristic
857Q8—416no—
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—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—416no—
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×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4C2×C13×C22⋊C414yes—
955C2×C4C2×C13×C22⋊C414yes—
956C2×C4C4×D4×C1314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C13×C22⋊C411yescharacteristic
973C22C2×C4×D4×C1311yescharacteristic
974C22C4×C13×#4111yescharacteristic
975C22C13×#51811yescharacteristic
976C22C13×#51911yescharacteristic
977C22C13×#51911yescharacteristic
978C22C13×#52011yescharacteristic
979C22C13×#53611yescharacteristic
980C22C13×#53611yescharacteristic
981C22C13×#53611yescharacteristic
982C22C13×#53611yescharacteristic
983C22C13×#53611yescharacteristic
984C22C13×#53711yescharacteristic
985C22C13×#53911yescharacteristic
986C22C13×#53911yescharacteristic
987C22C13×#54111yescharacteristic
988C22C13×#54211yescharacteristic
989C22C13×#54211yescharacteristic
990C22C13×#54211yescharacteristic
991C22D42×C1311yescharacteristic
992C22D42×C1311yescharacteristic
993C22C13×#54611yescharacteristic
994C22C13×#54611yescharacteristic
995C22C13×#54611yescharacteristic
996C22C13×#54611yescharacteristic
997C22C13×#54711yescharacteristic
998C22C13×#54711yescharacteristic
999C22C13×#54711yescharacteristic
1000C22C13×#54811yescharacteristic
1001C22C13×#55211yescharacteristic
1002C22C13×#55611yescharacteristic
1003C22C13×#56211yescharacteristic
1004C22C13×#56211yescharacteristic
1005C22C13×#56311yescharacteristic
1006C22C13×#56311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—42no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C13×#231011yescharacteristic
1023C2C13×#232311yescharacteristic
1024C2C13×#233211yescharacteristic
1025C2D4×C13×C22⋊C411yescharacteristic
1026C2C13×#233911yescharacteristic
1027C2C13×#236211yescharacteristic
1028C2C13×#237811yescharacteristic
1029C2C13×#267211yescharacteristic
1030C2C13×#267411yescharacteristic
1031C2C13×#268011yescharacteristic
1032C2C13×#268111yescharacteristic
1033C2C13×#268711yescharacteristic
1034C2C13×#268911yescharacteristic
1035C2C13×#269811yescharacteristic
1036C2C13×#270011yescharacteristic
subgroupG/H
center, socleC24×C13C24
commutatorC23C23×C4×C13
Frattini, cosocleC24C24×C13
prime radicalC25×C13C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C13 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C13×#391C2semidirect
6. C13×#1446C2semidirect
7. C13×#1445C2semidirect
8. C13×#1441C2semidirect
9. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×C4⋊#95C2semidirect
20. C2×C13×C22⋊Q8C4semidirect
147. #14364C13direct (N × H)
290. C2×#391C2×C13semidirect
294. #1446C2×C13semidirect
295. #1445C2×C13semidirect
296. #1441C2×C13semidirect
297. #1441C2×C13semidirect
300. #1436C2×C13semidirect
301. #1436C2×C13semidirect
302. C4⋊#95C2×C13semidirect
458. C2×C22⋊Q8C4×C13semidirect
806. C13#14364direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C13×C22⋊Q82
C2×C13×#3912
C2×C13×#3882
C2×C13×#3812
C13×#14462
C13×#14452
C13×#14412
C13×#14402
C13×#14362
C13×C4⋊#952
C13×C22⋊#952
#1436413