Finite Group Databasebeta

← C13×#14788 #15701127

Subgroups — C13×#14788 #15701127

Order 3328.

1554 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#399C211yesmaximal, characteristic
2C2×C13×#398C211yesmaximal, characteristic, complemented
3C2×C13×#396C211yesmaximal, characteristic
4C2×C13×#389C211yesmaximal, characteristic, complemented
5C2×C13×#388C211yesmaximal, characteristic
6C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic
11C13×#1439C211yesmaximal, characteristic
12C13×#1437C211yesmaximal, characteristic
13C13×#1437C211yesmaximal, characteristic
14C13×#1436C211yesmaximal, characteristic, complemented
15C13×#1436C211yesmaximal, characteristic, complemented
16C22×C13×C4⋊C4C2211yescharacteristic
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×C22⋊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
34C22×C42×C13C2211yescharacteristic
35C13×#399—24no—
36C13×#398—24no—
37C13×#396—24no—
38C13×#389—24no—
39C13×#388—24no—
40C4×C13×C4⋊C4—24no—
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
57C25×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
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
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—22no—
74C2×C13×C4⋊C4—22no—
75C2×C13×C4⋊C4—22no—
76C2×C13×C4⋊C4—22no—
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—22no—
89C2×C13×C4⋊C4—22no—
90C2×C13×C4⋊C4—22no—
91C2×C13×C4⋊C4—22no—
92C2×C13×C4⋊C4—41no—
93C2×C13×C4⋊C4—41no—
94C2×C13×C4⋊C4—41no—
95C2×C13×C4⋊C4—41no—
96C2×C13×C4⋊C4—41no—
97C2×C13×C4⋊C4D414yes—
98C2×C13×C4⋊C4D414yes—
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—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—22no—
114C2×C13×C22⋊C4—22no—
115C2×C13×C22⋊C4—41no—
116C2×C13×C22⋊C4—41no—
117C2×C13×C22⋊C4—41no—
118C2×C13×C22⋊C4—41no—
119C2×C13×C22⋊C4Q814yes—
120C2×C42×C13—22no—
121C2×C42×C13—22no—
122C2×C42×C13—22no—
123C2×C42×C13—22no—
124C2×C42×C13—22no—
125C2×C42×C13—22no—
126C2×C42×C13—22no—
127C2×C42×C13—41no—
128C2×C42×C13—41no—
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—22no—
141C13×#95—22no—
142C13×#95—22no—
143C13×#95—41no—
144C13×#95D414yes—
145#14788C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
155C24×C13—21no—
156C24×C13—21no—
157C24×C13—21no—
158C24×C13—21no—
159C24×C13—21no—
160C24×C13C2×Q812yes—
161C24×C13C2411yescharacteristic
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—21no—
167C22×C4×C13—21no—
168C22×C4×C13—21no—
169C22×C4×C13—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×C13C2×D412yes—
243C22×C4×C13C2×D412yes—
244C22×C4×C13C2×D412yes—
245C22×C4×C13C2×D412yes—
246C22×C4×C13C2×D412yes—
247C22×C4×C13C2×D412yes—
248C22×C4×C13C2×D412yes—
249C22×C4×C13C2×D412yes—
250C22×C4×C13C2×D412yes—
251C22×C4×C13C2×Q812yes—
252C22×C4×C13C2×Q812yes—
253C22×C4×C13#4112yes—
254C22×C4×C13#4112yes—
255C22×C4×C13#4112yes—
256C22×C4×C13#4112yes—
257C22×C4×C13#4112yes—
258C22×C4×C13#4112yes—
259C22×C4×C13#4112yes—
260C13×C4⋊C4—28no—
261C13×C4⋊C4—28no—
262C13×C4⋊C4—28no—
263C13×C4⋊C4—44no—
264C13×C4⋊C4—44no—
265C13×C4⋊C4—44no—
266C13×C4⋊C4—44no—
267C13×C4⋊C4—44no—
268C13×C4⋊C4—44no—
269C13×C22⋊C4—28no—
270C13×C22⋊C4—44no—
271C13×C22⋊C4—44no—
272C13×C22⋊C4—44no—
273C13×C22⋊C4—44no—
274C13×C22⋊C4—44no—
275C13×C22⋊C4—44no—
276C42×C13—28no—
277C42×C13—44no—
278C42×C13—44no—
279C2×#399C2×C1311yescharacteristic
280C2×#398C2×C1311yescharacteristic, complemented
281C2×#396C2×C1311yescharacteristic
282C2×#389C2×C1311yescharacteristic, complemented
283C2×#388C2×C1311yescharacteristic
284C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
285#1444C2×C1311yescharacteristic, complemented
286#1442C2×C1311yescharacteristic, complemented
287#1441C2×C1311yescharacteristic, complemented
288#1439C2×C1311yescharacteristic
289#1439C2×C1311yescharacteristic
290#1437C2×C1311yescharacteristic
291#1437C2×C1311yescharacteristic
292#1436C2×C1311yescharacteristic, complemented
293#1436C2×C1311yescharacteristic, complemented
294C23×C13—22no—
295C23×C13—22no—
296C23×C13—22no—
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
300C23×C13—22no—
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×C13—41no—
326C23×C13—41no—
327C23×C13—41no—
328C23×C13—41no—
329C23×C13C22×D411yescharacteristic
330C23×C13C22×D411yescharacteristic
331C23×C13C22×D411yescharacteristic
332C23×C13C22×Q811yescharacteristic
333C23×C13C2×#4111yescharacteristic
334C23×C13C2×#4111yescharacteristic
335C23×C13C2×#4111yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13H(5,𝔽2)11yescharacteristic
341C23×C13H(5,𝔽2)11yescharacteristic
342C23×C132−1+411yescharacteristic
343C23×C132−1+411yescharacteristic
344C2×C4×C13—22no—
345C2×C4×C13—22no—
346C2×C4×C13—22no—
347C2×C4×C13—22no—
348C2×C4×C13—22no—
349C2×C4×C13—22no—
350C2×C4×C13—22no—
351C2×C4×C13—22no—
352C2×C4×C13—22no—
353C2×C4×C13—22no—
354C2×C4×C13—22no—
355C2×C4×C13—22no—
356C2×C4×C13—22no—
357C2×C4×C13—22no—
358C2×C4×C13—22no—
359C2×C4×C13—22no—
360C2×C4×C13—22no—
361C2×C4×C13—22no—
362C2×C4×C13—22no—
363C2×C4×C13—22no—
364C2×C4×C13—22no—
365C2×C4×C13—22no—
366C2×C4×C13—22no—
367C2×C4×C13—22no—
368C2×C4×C13—22no—
369C2×C4×C13—22no—
370C2×C4×C13—22no—
371C2×C4×C13—22no—
372C2×C4×C13—22no—
373C2×C4×C13—22no—
374C2×C4×C13—22no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—22no—
379C2×C4×C13—22no—
380C2×C4×C13—22no—
381C2×C4×C13—22no—
382C2×C4×C13—22no—
383C2×C4×C13—22no—
384C2×C4×C13—22no—
385C2×C4×C13—22no—
386C2×C4×C13—22no—
387C2×C4×C13—22no—
388C2×C4×C13—22no—
389C2×C4×C13—41no—
390C2×C4×C13—41no—
391C2×C4×C13—41no—
392C2×C4×C13—41no—
393C2×C4×C13—41no—
394C2×C4×C13—41no—
395C2×C4×C13—41no—
396C2×C4×C13—41no—
397C2×C4×C13—41no—
398C2×C4×C13—41no—
399C2×C4×C13—41no—
400C2×C4×C13—41no—
401C2×C4×C13—41no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13#12114yes—
440C2×C4×C13C22⋊Q814yes—
441C2×C4×C13#12314yes—
442C22×C4⋊C4C22×C1311yescharacteristic
443C22×C4⋊C4C22×C1311yescharacteristic
444C22×C4⋊C4C22×C1311yescharacteristic
445C22×C4⋊C4C22×C1311yescharacteristic
446C22×C4⋊C4C22×C1311yescharacteristic
447C22×C4⋊C4C22×C1311yescharacteristic
448C22×C4⋊C4C22×C1311yescharacteristic
449C22×C4⋊C4C22×C1311yescharacteristic
450C22×C4⋊C4C22×C1311yescharacteristic
451C22×C22⋊C4C22×C1311yescharacteristic
452C22×C22⋊C4C22×C1311yescharacteristic
453C22×C22⋊C4C22×C1311yescharacteristic
454C22×C22⋊C4C22×C1311yescharacteristic
455C22×C22⋊C4C22×C1311yescharacteristic
456C22×C22⋊C4C22×C1311yescharacteristic
457C22×C22⋊C4C22×C1311yescharacteristic
458C22×C42C22×C1311yescharacteristic
459C22×C42C22×C1311yescharacteristic
460C22×C42C22×C1311yescharacteristic
461#399—24no—
462#398—24no—
463#396—24no—
464#389—24no—
465#388—24no—
466C4×C4⋊C4—24no—
467C2×#95C22×C1311yescharacteristic
468C2×#95C22×C1311yescharacteristic
469C2×#95C22×C1311yescharacteristic
470C2×#95C22×C1311yescharacteristic
471C2×#95C22×C1311yescharacteristic
472C2×#95C22×C1311yescharacteristic
473C2×#95C22×C1311yescharacteristic
474C2×#95C22×C1311yescharacteristic
475C2×#95C22×C1311yescharacteristic
476C2×#95C22×C1311yescharacteristic
477C2×#95C22×C1311yescharacteristic
478C2×#95C22×C1311yescharacteristic
479C2×#95C22×C1311yescharacteristic
480C2×#95C22×C1311yescharacteristic
481C2×#95C22×C1311yescharacteristic
482C2×#95C22×C1311yescharacteristic
483C22×C13—42no—
484C22×C13—42no—
485C22×C13—42no—
486C22×C13—42no—
487C22×C13—42no—
488C22×C13—42no—
489C22×C13—42no—
490C22×C13—81no—
491C22×C13—81no—
492C22×C13—81no—
493C22×C13—81no—
494C22×C13—81no—
495C22×C13—81no—
496C22×C13—81no—
497C22×C13—81no—
498C22×C13C2×#12111yescharacteristic
499C22×C13C2×C22⋊Q811yescharacteristic
500C22×C13C2×#12311yescharacteristic
501C22×C13#52511yescharacteristic
502C22×C13#52511yescharacteristic
503C22×C13#52911yescharacteristic
504C22×C13#52911yescharacteristic
505C22×C13#52911yescharacteristic
506C22×C13#53211yescharacteristic
507C22×C13#53211yescharacteristic
508C22×C13#53211yescharacteristic
509C22×C13#53311yescharacteristic
510C22×C13#53311yescharacteristic
511C22×C13#53911yescharacteristic
512C22×C13#53911yescharacteristic
513C22×C13#54011yescharacteristic
514C22×C13#54111yescharacteristic
515C22×C13#54211yescharacteristic
516C22×C13#54211yescharacteristic
517C22×C13D4211yescharacteristic
518C22×C13D4211yescharacteristic
519C22×C13#54611yescharacteristic
520C22×C13#54711yescharacteristic
521C22×C13#54711yescharacteristic
522C22×C13#54811yescharacteristic
523C22×C13#54811yescharacteristic
524C22×C13D4×Q811yescharacteristic
525C22×C13D4×Q811yescharacteristic
526C22×C13#55011yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55211yescharacteristic
529C22×C13#55211yescharacteristic
530C22×C13#55311yescharacteristic
531C22×C13#55411yescharacteristic
532C22×C13#55411yescharacteristic
533C4×C13—24no—
534C4×C13—24no—
535C4×C13—24no—
536C4×C13—42no—
537C4×C13—42no—
538C4×C13—42no—
539C4×C13—42no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—81no—
546C4×C13—81no—
547C25C23×C1311yescharacteristic
548C23×C4C23×C1311yescharacteristic
549C23×C4C23×C1311yescharacteristic
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
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
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—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
582C2×C4⋊C4—41no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4D4×C1314yes—
588C2×C4⋊C4D4×C1314yes—
589C2×C22⋊C4—22no—
590C2×C22⋊C4—22no—
591C2×C22⋊C4—22no—
592C2×C22⋊C4—22no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—22no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—22no—
602C2×C22⋊C4—22no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—22no—
605C2×C22⋊C4—41no—
606C2×C22⋊C4—41no—
607C2×C22⋊C4—41no—
608C2×C22⋊C4—41no—
609C2×C22⋊C4Q8×C1314yes—
610C2×C42—22no—
611C2×C42—22no—
612C2×C42—22no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—41no—
618C2×C42—41no—
619#95—22no—
620#95—22no—
621#95—22no—
622#95—22no—
623#95—22no—
624#95—22no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—22no—
630#95—22no—
631#95—22no—
632#95—22no—
633#95—41no—
634#95D4×C1314yes—
635C2×C13—82no—
636C2×C13#239611yescharacteristic
637C2×C13#242311yescharacteristic
638C2×C13#242811yescharacteristic
639C2×C13#242911yescharacteristic
640C2×C13#244311yescharacteristic
641C2×C13#244911yescharacteristic
642C2×C13#245211yescharacteristic
643C2×C13#246111yescharacteristic
644C2×C13#247911yescharacteristic
645C2×C13#251911yescharacteristic
646C2×C13#252211yescharacteristic
647C2×C13#255611yescharacteristic
648C2×C13#255811yescharacteristic
649C2×C13#265411yescharacteristic
650C2×C13#285411yescharacteristic
651C24—21no—
652C24—21no—
653C24—21no—
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24C2×Q8×C1312yes—
666C24C24×C1311yescharacteristic
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×C4C2×D4×C1312yes—
748C22×C4C2×D4×C1312yes—
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×D4×C1312yes—
756C22×C4C2×Q8×C1312yes—
757C22×C4C2×Q8×C1312yes—
758C22×C4C13×#4112yes—
759C22×C4C13×#4112yes—
760C22×C4C13×#4112yes—
761C22×C4C13×#4112yes—
762C22×C4C13×#4112yes—
763C22×C4C13×#4112yes—
764C22×C4C13×#4112yes—
765C4⋊C4—28no—
766C4⋊C4—28no—
767C4⋊C4—28no—
768C4⋊C4—44no—
769C4⋊C4—44no—
770C4⋊C4—44no—
771C4⋊C4—44no—
772C4⋊C4—44no—
773C4⋊C4—44no—
774C22⋊C4—28no—
775C22⋊C4—44no—
776C22⋊C4—44no—
777C22⋊C4—44no—
778C22⋊C4—44no—
779C22⋊C4—44no—
780C22⋊C4—44no—
781C42—28no—
782C42—44no—
783C42—44no—
784C13#1478811yescharacteristic, direct product factor, Sylow
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
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—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23C22×D4×C1311yescharacteristic
821C23C22×D4×C1311yescharacteristic
822C23C22×D4×C1311yescharacteristic
823C23C22×Q8×C1311yescharacteristic
824C23C2×C13×#4111yescharacteristic
825C23C2×C13×#4111yescharacteristic
826C23C2×C13×#4111yescharacteristic
827C23C2×C13×#4111yescharacteristic
828C23C2×C13×#4111yescharacteristic
829C23C2×C13×#4111yescharacteristic
830C23C2×C13×#4111yescharacteristic
831C23C13×H(5,𝔽2)11yescharacteristic
832C23C13×H(5,𝔽2)11yescharacteristic
833C23C13×2−1+411yescharacteristic
834C23C13×2−1+411yescharacteristic
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4C13×#12114yes—
931C2×C4C13×C22⋊Q814yes—
932C2×C4C13×#12314yes—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—42no—
938C22—42no—
939C22—42no—
940C22—81no—
941C22—81no—
942C22—81no—
943C22—81no—
944C22—81no—
945C22—81no—
946C22—81no—
947C22—81no—
948C22C2×C13×#12111yescharacteristic
949C22C2×C13×C22⋊Q811yescharacteristic
950C22C2×C13×#12311yescharacteristic
951C22C13×#52511yescharacteristic
952C22C13×#52511yescharacteristic
953C22C13×#52911yescharacteristic
954C22C13×#52911yescharacteristic
955C22C13×#52911yescharacteristic
956C22C13×#53211yescharacteristic
957C22C13×#53211yescharacteristic
958C22C13×#53211yescharacteristic
959C22C13×#53311yescharacteristic
960C22C13×#53311yescharacteristic
961C22C13×#53911yescharacteristic
962C22C13×#53911yescharacteristic
963C22C13×#54011yescharacteristic
964C22C13×#54111yescharacteristic
965C22C13×#54211yescharacteristic
966C22C13×#54211yescharacteristic
967C22D42×C1311yescharacteristic
968C22D42×C1311yescharacteristic
969C22C13×#54611yescharacteristic
970C22C13×#54711yescharacteristic
971C22C13×#54711yescharacteristic
972C22C13×#54811yescharacteristic
973C22C13×#54811yescharacteristic
974C22D4×Q8×C1311yescharacteristic
975C22D4×Q8×C1311yescharacteristic
976C22C13×#55011yescharacteristic
977C22C13×#55111yescharacteristic
978C22C13×#55211yescharacteristic
979C22C13×#55211yescharacteristic
980C22C13×#55311yescharacteristic
981C22C13×#55411yescharacteristic
982C22C13×#55411yescharacteristic
983C4—24no—
984C4—24no—
985C4—24no—
986C4—42no—
987C4—42no—
988C4—42no—
989C4—42no—
990C4—42no—
991C4—42no—
992C4—42no—
993C4—42no—
994C4—42no—
995C4—81no—
996C4—81no—
997C2—82no—
998C2C13×#239611yescharacteristic
999C2C13×#242311yescharacteristic
1000C2C13×#242811yescharacteristic
1001C2C13×#242911yescharacteristic
1002C2C13×#244311yescharacteristic
1003C2C13×#244911yescharacteristic
1004C2C13×#245211yescharacteristic
1005C2C13×#246111yescharacteristic
1006C2C13×#247911yescharacteristic
1007C2C13×#251911yescharacteristic
1008C2C13×#252211yescharacteristic
1009C2C13×#255611yescharacteristic
1010C2C13×#255811yescharacteristic
1011C2C13×#265411yescharacteristic
1012C2C13×#285411yescharacteristic
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
2. C2×C13×#398C2semidirect
4. C2×C13×#389C2semidirect
6. C2×C4×C13×C4⋊C4C2semidirect
7. C13×#1444C2semidirect
8. C13×#1442C2semidirect
9. C13×#1441C2semidirect
14. C13×#1436C2semidirect
15. C13×#1436C2semidirect
145. #14788C13direct (N × H)
280. C2×#398C2×C13semidirect
282. C2×#389C2×C13semidirect
284. C2×C4×C4⋊C4C2×C13semidirect
285. #1444C2×C13semidirect
286. #1442C2×C13semidirect
287. #1441C2×C13semidirect
292. #1436C2×C13semidirect
293. #1436C2×C13semidirect
784. C13#14788direct (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×#3982
C2×C13×#3962
C2×C13×#3892
C2×C13×#3882
C2×C4×C13×C4⋊C42
C13×#14442
C13×#14422
C13×#14412
C13×#14392
C13×#14372
C13×#14362
#1478813