Finite Group Databasebeta

← C13×#14405 #15700744

Subgroups — C13×#14405 #15700744

Order 3328.

1750 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
1C2×C13×#389C211yesmaximal, characteristic, complemented
2C2×C13×#388C211yesmaximal, characteristic
3C2×C13×#388C211yesmaximal, characteristic
4C2×C13×#385C211yesmaximal, characteristic
5C2×C13×#385C211yesmaximal, characteristic
6C2×C13×#385C211yesmaximal, characteristic
7C2×C13×#384C211yesmaximal, characteristic, complemented
8C13×#1444C211yesmaximal, characteristic, complemented
9C13×#1444C211yesmaximal, characteristic, complemented
10C13×#1442C211yesmaximal, characteristic, complemented
11C13×#1441C211yesmaximal, characteristic, complemented
12C13×#1439C211yesmaximal, characteristic
13C13×#1439C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×#1434C211yesmaximal, characteristic, complemented
16C24×C4×C13C2211yescharacteristic
17C22×C13×C4⋊C4C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C22×C13×C4⋊C4C2211yescharacteristic
20C22×C13×C4⋊C4C2211yescharacteristic
21C22×C13×C4⋊C4C2211yescharacteristic
22C22×C13×C4⋊C4C2211yescharacteristic
23C22×C13×C4⋊C4C2211yescharacteristic
24C22×C13×C4⋊C4C2211yescharacteristic
25C22×C13×C4⋊C4C2211yescharacteristic
26C22×C13×C4⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C13×C22⋊C4C2211yescharacteristic
30C22×C13×C22⋊C4C2211yescharacteristic
31C22×C13×C22⋊C4C2211yescharacteristic
32C22×C13×C22⋊C4C2211yescharacteristic
33C22×C42×C13C2211yescharacteristic
34C22×C42×C13C2211yescharacteristic
35C13×#389—24no—
36C13×#388—24no—
37C13×#388C418yescomplemented
38C13×#385—24no—
39C13×#385—24no—
40C13×#385—24no—
41C13×#384—24no—
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
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—41no—
63C23×C4×C13—41no—
64C23×C4×C13—41no—
65C23×C4×C13—41no—
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
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C2×C13×C4⋊C4—22no—
81C2×C13×C4⋊C4—22no—
82C2×C13×C4⋊C4—22no—
83C2×C13×C4⋊C4—22no—
84C2×C13×C4⋊C4—22no—
85C2×C13×C4⋊C4—22no—
86C2×C13×C4⋊C4—22no—
87C2×C13×C4⋊C4—22no—
88C2×C13×C4⋊C4—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—22no—
93C2×C13×C4⋊C4—22no—
94C2×C13×C4⋊C4—22no—
95C2×C13×C4⋊C4—22no—
96C2×C13×C4⋊C4—41no—
97C2×C13×C4⋊C4—41no—
98C2×C13×C4⋊C4—41no—
99C2×C13×C4⋊C4—41no—
100C2×C13×C4⋊C4—41no—
101C2×C13×C4⋊C4—41no—
102C2×C13×C4⋊C4—41no—
103C2×C13×C4⋊C4—41no—
104C2×C13×C4⋊C4—41no—
105C2×C13×C4⋊C4—41no—
106C2×C13×C4⋊C4—41no—
107C2×C13×C4⋊C4—41no—
108C2×C13×C4⋊C4C2×C414yescomplemented
109C2×C13×C4⋊C4D414yes—
110C2×C13×C22⋊C4—22no—
111C2×C13×C22⋊C4—22no—
112C2×C13×C22⋊C4—22no—
113C2×C13×C22⋊C4—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—22no—
116C2×C13×C22⋊C4—22no—
117C2×C13×C22⋊C4—22no—
118C2×C13×C22⋊C4—22no—
119C2×C13×C22⋊C4—41no—
120C2×C13×C22⋊C4—41no—
121C2×C13×C22⋊C4—41no—
122C2×C13×C22⋊C4—41no—
123C2×C13×C22⋊C4C2×C414yes—
124C2×C13×C22⋊C4C2×C414yes—
125C2×C13×C22⋊C4C2×C414yes—
126C2×C13×C22⋊C4D414yes—
127C2×C13×C22⋊C4Q814yes—
128C2×C42×C13—22no—
129C2×C42×C13—22no—
130C2×C42×C13—22no—
131C2×C42×C13—22no—
132C2×C42×C13—41no—
133C2×C42×C13C2×C414yescomplemented
134C13×#95—22no—
135C13×#95—22no—
136C13×#95—22no—
137C13×#95—22no—
138C13×#95—22no—
139C13×#95—22no—
140C13×#95—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—22no—
144C13×#95—41no—
145C13×#95—41no—
146C13×#95—41no—
147C13×#95C2×C414yescomplemented
148C13×#95C2×C414yescomplemented
149C13×#95D414yes—
150#14405C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
161C24×C13—21no—
162C24×C13—21no—
163C24×C13C22×C412yes—
164C24×C13C2×D412yes—
165C24×C13C2×Q812yes—
166C24×C13C2411yescharacteristic
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×C13—44no—
248C22×C4×C13—44no—
249C22×C4×C13—44no—
250C22×C4×C13—44no—
251C22×C4×C13—44no—
252C22×C4×C13—44no—
253C22×C4×C13—44no—
254C22×C4×C13C22×C412yes—
255C22×C4×C13C22×C412yes—
256C22×C4×C13C22×C412yes—
257C22×C4×C13C22×C412yes—
258C22×C4×C13C22×C412yes—
259C22×C4×C13C22×C412yes—
260C22×C4×C13C2×D412yes—
261C22×C4×C13C2×D412yes—
262C22×C4×C13C2×D412yes—
263C22×C4×C13C2×D412yes—
264C22×C4×C13C2×D412yes—
265C22×C4×C13C2×D412yes—
266C22×C4×C13C2×D412yes—
267C22×C4×C13C2×D412yes—
268C22×C4×C13C2×Q812yes—
269C22×C4×C13C2×Q812yes—
270C22×C4×C13#4112yes—
271C22×C4×C13#4112yes—
272C13×C4⋊C4—28no—
273C13×C4⋊C4—44no—
274C13×C4⋊C4—44no—
275C13×C4⋊C4—44no—
276C13×C4⋊C4—44no—
277C13×C4⋊C4—44no—
278C13×C4⋊C4—44no—
279C13×C4⋊C4—44no—
280C13×C4⋊C4—44no—
281C13×C4⋊C4—44no—
282C13×C22⋊C4—28no—
283C13×C22⋊C4—28no—
284C13×C22⋊C4—44no—
285C13×C22⋊C4—44no—
286C13×C22⋊C4—44no—
287C13×C22⋊C4C4⋊C4116yescomplemented
288C42×C13—28no—
289C42×C13—44no—
290C2×#389C2×C1311yescharacteristic, complemented
291C2×#388C2×C1311yescharacteristic
292C2×#388C2×C1311yescharacteristic
293C2×#385C2×C1311yescharacteristic
294C2×#385C2×C1311yescharacteristic
295C2×#385C2×C1311yescharacteristic
296C2×#384C2×C1311yescharacteristic, complemented
297#1444C2×C1311yescharacteristic, complemented
298#1444C2×C1311yescharacteristic, complemented
299#1442C2×C1311yescharacteristic, complemented
300#1441C2×C1311yescharacteristic, complemented
301#1439C2×C1311yescharacteristic
302#1439C2×C1311yescharacteristic
303#1436C2×C1311yescharacteristic, complemented
304#1434C2×C1311yescharacteristic, complemented
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—22no—
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×C13—41no—
339C23×C13C2×C4⋊C414yes—
340C23×C13C23×C411yescharacteristic
341C23×C13C22×D411yescharacteristic
342C23×C13C22×D411yescharacteristic
343C23×C13C22×D411yescharacteristic
344C23×C13C22×Q811yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13C2×#4111yescharacteristic
347C23×C13H(5,𝔽2)11yescharacteristic
348C23×C13H(5,𝔽2)11yescharacteristic
349C23×C13H(5,𝔽2)11yescharacteristic
350C23×C13H(5,𝔽2)11yescharacteristic
351C23×C132−1+411yescharacteristic
352C23×C132−1+411yescharacteristic
353C23×C132−1+411yescharacteristic
354C23×C132−1+411yescharacteristic
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—22no—
395C2×C4×C13—22no—
396C2×C4×C13—22no—
397C2×C4×C13—416no—
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×C13C2×C4⋊C414yes—
451C2×C4×C13C2×C4⋊C414yes—
452C2×C4×C13C4×D414yes—
453C2×C4×C13C4×D414yes—
454C24×C4C22×C1311yescharacteristic
455C22×C4⋊C4C22×C1311yescharacteristic
456C22×C4⋊C4C22×C1311yescharacteristic
457C22×C4⋊C4C22×C1311yescharacteristic
458C22×C4⋊C4C22×C1311yescharacteristic
459C22×C4⋊C4C22×C1311yescharacteristic
460C22×C4⋊C4C22×C1311yescharacteristic
461C22×C4⋊C4C22×C1311yescharacteristic
462C22×C4⋊C4C22×C1311yescharacteristic
463C22×C4⋊C4C22×C1311yescharacteristic
464C22×C4⋊C4C22×C1311yescharacteristic
465C22×C22⋊C4C22×C1311yescharacteristic
466C22×C22⋊C4C22×C1311yescharacteristic
467C22×C22⋊C4C22×C1311yescharacteristic
468C22×C22⋊C4C22×C1311yescharacteristic
469C22×C22⋊C4C22×C1311yescharacteristic
470C22×C22⋊C4C22×C1311yescharacteristic
471C22×C42C22×C1311yescharacteristic
472C22×C42C22×C1311yescharacteristic
473#389—24no—
474#388—24no—
475#388C4×C1318yescomplemented
476#385—24no—
477#385—24no—
478#385—24no—
479#384—24no—
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×C4⋊C411yescharacteristic
512C22×C13C2×C4×D411yescharacteristic
513C22×C13C2×C4×D411yescharacteristic
514C22×C13#52011yescharacteristic
515C22×C13#52011yescharacteristic
516C22×C13#52011yescharacteristic
517C22×C13#52011yescharacteristic
518C22×C13#53411yescharacteristic
519C22×C13#53511yescharacteristic
520C22×C13#53511yescharacteristic
521C22×C13#53611yescharacteristic
522C22×C13#53611yescharacteristic
523C22×C13#53611yescharacteristic
524C22×C13#53911yescharacteristic
525C22×C13#53911yescharacteristic
526C22×C13#54211yescharacteristic
527C22×C13#54211yescharacteristic
528C22×C13#54411yescharacteristic
529C22×C13#54411yescharacteristic
530C22×C13D4211yescharacteristic
531C22×C13D4211yescharacteristic
532C22×C13D4211yescharacteristic
533C22×C13#54711yescharacteristic
534C22×C13#54711yescharacteristic
535C22×C13#54711yescharacteristic
536C22×C13#54811yescharacteristic
537C22×C13D4×Q811yescharacteristic
538C22×C13D4×Q811yescharacteristic
539C22×C13#55311yescharacteristic
540C22×C13#55411yescharacteristic
541C22×C13#55411yescharacteristic
542C22×C13#56011yescharacteristic
543C22×C13#56311yescharacteristic
544C22×C13#56311yescharacteristic
545C22×C13#56311yescharacteristic
546C4×C13—24no—
547C4×C13—24no—
548C4×C13—24no—
549C4×C13—24no—
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
561C23×C4—22no—
562C23×C4—22no—
563C23×C4—22no—
564C23×C4—41no—
565C23×C4—41no—
566C23×C4—41no—
567C23×C4—41no—
568C23×C4C23×C1311yescharacteristic
569C23×C4C23×C1311yescharacteristic
570C23×C4C23×C1311yescharacteristic
571C23×C4C23×C1311yescharacteristic
572C23×C4C23×C1311yescharacteristic
573C23×C4C23×C1311yescharacteristic
574C23×C4C23×C1311yescharacteristic
575C23×C4C23×C1311yescharacteristic
576C23×C4C23×C1311yescharacteristic
577C23×C4C23×C1311yescharacteristic
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
580C23×C4C23×C1311yescharacteristic
581C23×C4C23×C1311yescharacteristic
582C2×C4⋊C4—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—22no—
585C2×C4⋊C4—22no—
586C2×C4⋊C4—22no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
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—41no—
599C2×C4⋊C4—41no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4C2×C4×C1314yescomplemented
611C2×C4⋊C4D4×C1314yes—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—22no—
616C2×C22⋊C4—22no—
617C2×C22⋊C4—22no—
618C2×C22⋊C4—22no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—41no—
622C2×C22⋊C4—41no—
623C2×C22⋊C4—41no—
624C2×C22⋊C4—41no—
625C2×C22⋊C4C2×C4×C1314yes—
626C2×C22⋊C4C2×C4×C1314yes—
627C2×C22⋊C4C2×C4×C1314yes—
628C2×C22⋊C4D4×C1314yes—
629C2×C22⋊C4Q8×C1314yes—
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—41no—
635C2×C42C2×C4×C1314yescomplemented
636#95—22no—
637#95—22no—
638#95—22no—
639#95—22no—
640#95—22no—
641#95—22no—
642#95—22no—
643#95—22no—
644#95—22no—
645#95—22no—
646#95—41no—
647#95—41no—
648#95—41no—
649#95C2×C4×C1314yescomplemented
650#95C2×C4×C1314yescomplemented
651#95D4×C1314yes—
652C2×C13—44no—
653C2×C13#231711yescharacteristic
654C2×C13#232211yescharacteristic
655C2×C13#232611yescharacteristic
656C2×C13D4×C4⋊C411yescharacteristic
657C2×C13D4×C4⋊C411yescharacteristic
658C2×C13#236111yescharacteristic
659C2×C13#238311yescharacteristic
660C2×C13#266911yescharacteristic
661C2×C13#267411yescharacteristic
662C2×C13#267711yescharacteristic
663C2×C13#268011yescharacteristic
664C2×C13#271811yescharacteristic
665C2×C13#272011yescharacteristic
666C2×C13#272911yescharacteristic
667C2×C13#279011yescharacteristic
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24C22×C4×C1312yes—
681C24C2×D4×C1312yes—
682C24C2×Q8×C1312yes—
683C24C24×C1311yescharacteristic
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×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—44no—
765C22×C4—44no—
766C22×C4—44no—
767C22×C4—44no—
768C22×C4—44no—
769C22×C4—44no—
770C22×C4—44no—
771C22×C4C22×C4×C1312yes—
772C22×C4C22×C4×C1312yes—
773C22×C4C22×C4×C1312yes—
774C22×C4C22×C4×C1312yes—
775C22×C4C22×C4×C1312yes—
776C22×C4C22×C4×C1312yes—
777C22×C4C2×D4×C1312yes—
778C22×C4C2×D4×C1312yes—
779C22×C4C2×D4×C1312yes—
780C22×C4C2×D4×C1312yes—
781C22×C4C2×D4×C1312yes—
782C22×C4C2×D4×C1312yes—
783C22×C4C2×D4×C1312yes—
784C22×C4C2×D4×C1312yes—
785C22×C4C2×Q8×C1312yes—
786C22×C4C2×Q8×C1312yes—
787C22×C4C13×#4112yes—
788C22×C4C13×#4112yes—
789C4⋊C4—28no—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—44no—
793C4⋊C4—44no—
794C4⋊C4—44no—
795C4⋊C4—44no—
796C4⋊C4—44no—
797C4⋊C4—44no—
798C4⋊C4—44no—
799C22⋊C4—28no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—44no—
803C22⋊C4—44no—
804C22⋊C4C13×C4⋊C4116yescomplemented
805C42—28no—
806C42—44no—
807C13#1440511yescharacteristic, direct product factor, Sylow
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—22no—
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—
841C23—41no—
842C23C2×C13×C4⋊C414yes—
843C23C23×C4×C1311yescharacteristic
844C23C22×D4×C1311yescharacteristic
845C23C22×D4×C1311yescharacteristic
846C23C22×D4×C1311yescharacteristic
847C23C22×Q8×C1311yescharacteristic
848C23C2×C13×#4111yescharacteristic
849C23C2×C13×#4111yescharacteristic
850C23C13×H(5,𝔽2)11yescharacteristic
851C23C13×H(5,𝔽2)11yescharacteristic
852C23C13×H(5,𝔽2)11yescharacteristic
853C23C13×H(5,𝔽2)11yescharacteristic
854C23C13×2−1+411yescharacteristic
855C23C13×2−1+411yescharacteristic
856C23C13×2−1+411yescharacteristic
857C23C13×2−1+411yescharacteristic
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—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—416no—
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×C4C2×C13×C4⋊C414yes—
954C2×C4C2×C13×C4⋊C414yes—
955C2×C4C4×D4×C1314yes—
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×C4⋊C411yescharacteristic
973C22C2×C4×D4×C1311yescharacteristic
974C22C2×C4×D4×C1311yescharacteristic
975C22C13×#52011yescharacteristic
976C22C13×#52011yescharacteristic
977C22C13×#52011yescharacteristic
978C22C13×#52011yescharacteristic
979C22C13×#53411yescharacteristic
980C22C13×#53511yescharacteristic
981C22C13×#53511yescharacteristic
982C22C13×#53611yescharacteristic
983C22C13×#53611yescharacteristic
984C22C13×#53611yescharacteristic
985C22C13×#53911yescharacteristic
986C22C13×#53911yescharacteristic
987C22C13×#54211yescharacteristic
988C22C13×#54211yescharacteristic
989C22C13×#54411yescharacteristic
990C22C13×#54411yescharacteristic
991C22D42×C1311yescharacteristic
992C22D42×C1311yescharacteristic
993C22D42×C1311yescharacteristic
994C22C13×#54711yescharacteristic
995C22C13×#54711yescharacteristic
996C22C13×#54711yescharacteristic
997C22C13×#54811yescharacteristic
998C22D4×Q8×C1311yescharacteristic
999C22D4×Q8×C1311yescharacteristic
1000C22C13×#55311yescharacteristic
1001C22C13×#55411yescharacteristic
1002C22C13×#55411yescharacteristic
1003C22C13×#56011yescharacteristic
1004C22C13×#56311yescharacteristic
1005C22C13×#56311yescharacteristic
1006C22C13×#56311yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—42no—
1014C4—42no—
1015C4—42no—
1016C4—42no—
1017C4—81no—
1018C4—81no—
1019C4—81no—
1020C4—81no—
1021C2—44no—
1022C2C13×#231711yescharacteristic
1023C2C13×#232211yescharacteristic
1024C2C13×#232611yescharacteristic
1025C2D4×C13×C4⋊C411yescharacteristic
1026C2D4×C13×C4⋊C411yescharacteristic
1027C2C13×#236111yescharacteristic
1028C2C13×#238311yescharacteristic
1029C2C13×#266911yescharacteristic
1030C2C13×#267411yescharacteristic
1031C2C13×#267711yescharacteristic
1032C2C13×#268011yescharacteristic
1033C2C13×#271811yescharacteristic
1034C2C13×#272011yescharacteristic
1035C2C13×#272911yescharacteristic
1036C2C13×#279011yescharacteristic
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
1. C2×C13×#389C2semidirect
7. C2×C13×#384C2semidirect
8. C13×#1444C2semidirect
9. C13×#1444C2semidirect
10. C13×#1442C2semidirect
11. C13×#1441C2semidirect
14. C13×#1436C2semidirect
15. C13×#1434C2semidirect
37. C13×#388C4semidirect
108. C2×C13×C4⋊C4C2×C4semidirect
133. C2×C42×C13C2×C4semidirect
147. C13×#95C2×C4semidirect
148. C13×#95C2×C4semidirect
150. #14405C13direct (N × H)
287. C13×C22⋊C4C4⋊C4semidirect
290. C2×#389C2×C13semidirect
296. C2×#384C2×C13semidirect
297. #1444C2×C13semidirect
298. #1444C2×C13semidirect
299. #1442C2×C13semidirect
300. #1441C2×C13semidirect
303. #1436C2×C13semidirect
304. #1434C2×C13semidirect
475. #388C4×C13semidirect
610. C2×C4⋊C4C2×C4×C13semidirect
635. C2×C42C2×C4×C13semidirect
649. #95C2×C4×C13semidirect
650. #95C2×C4×C13semidirect
804. C22⋊C4C13×C4⋊C4semidirect
807. C13#14405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3892
C2×C13×#3882
C2×C13×#3852
C2×C13×#3842
C13×#14442
C13×#14422
C13×#14412
C13×#14392
C13×#14362
C13×#14342
#1440513