Finite Group Databasebeta

← C13×#14063 #15700402

Subgroups — C13×#14063 #15700402

Order 3328.

1962 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C13×#117C211yesmaximal, characteristic
2C2×C13×#388C211yesmaximal, characteristic
3C2×C13×#387C211yesmaximal, characteristic, complemented
4C2×C13×#385C211yesmaximal, characteristic
5C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
6C13×#1444C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1440C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1436C211yesmaximal, characteristic, complemented
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×#1434C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C13C2211yescharacteristic
17C2×C13×#117—24no—
18C2×C13×#117—24no—
19C2×C13×#117—24no—
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×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
35C22×C42×C13C2211yescharacteristic
36C13×#388—24no—
37C13×#387—24no—
38C13×#385C418yescomplemented
39C4×C13×C4⋊C4—24no—
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
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—22no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13C2×C414yes—
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
80C13×#117—232no—
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—41no—
96C2×C13×C4⋊C4C2×C414yes—
97C2×C13×C4⋊C4C2×C414yes—
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—41no—
113C2×C13×C22⋊C4—41no—
114C2×C13×C22⋊C4C2×C414yes—
115C2×C13×C22⋊C4C2×C414yes—
116C2×C13×C22⋊C4D414yes—
117C2×C42×C13—22no—
118C2×C42×C13—22no—
119C2×C42×C13—22no—
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—22no—
128C2×C42×C13D414yes—
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—41no—
143C13×#95—41no—
144C13×#95—41no—
145C13×#95C2×C414yes—
146C13×#95C2×C414yes—
147#14063C1311yesmaximal, 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×C13#4112yes—
163C24×C13C2411yescharacteristic
164C22×C4×C13—28no—
165C22×C4×C13—28no—
166C22×C4×C13—28no—
167C22×C4×C13—28no—
168C22×C4×C13—28no—
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—28no—
186C22×C4×C13—28no—
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—21no—
248C22×C4×C13—21no—
249C22×C4×C13C22×C412yes—
250C22×C4×C13C22×C412yes—
251C22×C4×C13C22×C412yes—
252C22×C4×C13C22×C412yes—
253C22×C4×C13C22×C412yes—
254C22×C4×C13C22×C412yes—
255C22×C4×C13C2×D412yes—
256C22×C4×C13C2×D412yes—
257C22×C4×C13C2×D412yes—
258C22×C4×C13C2×D412yes—
259C22×C4×C13C2×D412yes—
260C22×C4×C13C2×D412yes—
261C22×C4×C13C2×D412yes—
262C22×C4×C13C2×D412yes—
263C22×C4×C13#4112yes—
264C22×C4×C13#4112yes—
265C22×C4×C13#4112yes—
266C22×C4×C13#4112yes—
267C22×C4×C13#4112yes—
268C22×C4×C13#4112yes—
269C13×C4⋊C4—28no—
270C13×C4⋊C4—28no—
271C13×C4⋊C4—28no—
272C13×C4⋊C4—28no—
273C13×C4⋊C4—28no—
274C13×C4⋊C4—44no—
275C13×C22⋊C4—28no—
276C13×C22⋊C4—28no—
277C13×C22⋊C4—28no—
278C13×C22⋊C4—28no—
279C13×C22⋊C4—44no—
280C13×C22⋊C4—44no—
281C42×C13—28no—
282C42×C13—28no—
283C42×C13—28no—
284C42×C13—44no—
285C22×#117C2×C1311yescharacteristic
286C2×#388C2×C1311yescharacteristic
287C2×#387C2×C1311yescharacteristic, complemented
288C2×#385C2×C1311yescharacteristic
289C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
290#1444C2×C1311yescharacteristic, complemented
291#1441C2×C1311yescharacteristic, complemented
292#1440C2×C1311yescharacteristic
293#1439C2×C1311yescharacteristic
294#1437C2×C1311yescharacteristic
295#1436C2×C1311yescharacteristic, complemented
296#1436C2×C1311yescharacteristic, complemented
297#1436C2×C1311yescharacteristic, complemented
298#1434C2×C1311yescharacteristic, complemented
299C22⋊#95C2×C1311yescharacteristic
300C23×C13—22no—
301C23×C13—22no—
302C23×C13—22no—
303C23×C13—22no—
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—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×C13—41no—
330C23×C13—41no—
331C23×C13—41no—
332C23×C13—41no—
333C23×C13—41no—
334C23×C13C4×D414yes—
335C23×C13C23×C411yescharacteristic
336C23×C13C22×D411yescharacteristic
337C23×C13C22×D411yescharacteristic
338C23×C13C22×D411yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13C2×#4111yescharacteristic
344C23×C13C2×#4111yescharacteristic
345C23×C13C2×#4111yescharacteristic
346C23×C13H(5,𝔽2)11yescharacteristic
347C23×C132−1+411yescharacteristic
348C23×C132−1+411yescharacteristic
349C23×C132−1+411yescharacteristic
350C2×C4×C13—232no—
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—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—22no—
398C2×C4×C13—22no—
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#11714yescomplemented
446C2×C4×C13C4×D414yes—
447C2×C4×C13C4×D414yes—
448C2×C4×C13#12014yes—
449C24×C4C22×C1311yescharacteristic
450C2×#117—24no—
451C2×#117—24no—
452C2×#117—24no—
453C22×C4⋊C4C22×C1311yescharacteristic
454C22×C4⋊C4C22×C1311yescharacteristic
455C22×C4⋊C4C22×C1311yescharacteristic
456C22×C4⋊C4C22×C1311yescharacteristic
457C22×C4⋊C4C22×C1311yescharacteristic
458C22×C4⋊C4C22×C1311yescharacteristic
459C22×C22⋊C4C22×C1311yescharacteristic
460C22×C22⋊C4C22×C1311yescharacteristic
461C22×C22⋊C4C22×C1311yescharacteristic
462C22×C22⋊C4C22×C1311yescharacteristic
463C22×C22⋊C4C22×C1311yescharacteristic
464C22×C22⋊C4C22×C1311yescharacteristic
465C22×C42C22×C1311yescharacteristic
466C22×C42C22×C1311yescharacteristic
467C22×C42C22×C1311yescharacteristic
468C22×C42C22×C1311yescharacteristic
469#388—24no—
470#387—24no—
471#385C4×C1318yescomplemented
472C4×C4⋊C4—24no—
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
483C2×#95C22×C1311yescharacteristic
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C2×#95C22×C1311yescharacteristic
487C2×#95C22×C1311yescharacteristic
488C2×#95C22×C1311yescharacteristic
489C2×#95C22×C1311yescharacteristic
490C2×#95C22×C1311yescharacteristic
491C22×C13—24no—
492C22×C13—24no—
493C22×C13—24no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13—42no—
502C22×C13—42no—
503C22×C13—42no—
504C22×C13—42no—
505C22×C13—42no—
506C22×C13C2×#11711yescharacteristic
507C22×C13C2×C4×D411yescharacteristic
508C22×C13C2×C4×D411yescharacteristic
509C22×C13C2×C4×D411yescharacteristic
510C22×C13C4×#4111yescharacteristic
511C22×C13#51911yescharacteristic
512C22×C13#52011yescharacteristic
513C22×C13C2×#12011yescharacteristic
514C22×C13#52511yescharacteristic
515C22×C13#52511yescharacteristic
516C22×C13#52511yescharacteristic
517C22×C13#52511yescharacteristic
518C22×C13#52511yescharacteristic
519C22×C13#52911yescharacteristic
520C22×C13#52911yescharacteristic
521C22×C13#53611yescharacteristic
522C22×C13#53711yescharacteristic
523C22×C13#54111yescharacteristic
524C22×C13#54211yescharacteristic
525C22×C13#54611yescharacteristic
526C22×C13#54711yescharacteristic
527C22×C13#54711yescharacteristic
528C22×C13#54711yescharacteristic
529C22×C13#54711yescharacteristic
530C22×C13#54711yescharacteristic
531C22×C13#54811yescharacteristic
532C22×C13#55011yescharacteristic
533C22×C13#55111yescharacteristic
534C22×C13#55211yescharacteristic
535C22×C13#55211yescharacteristic
536C22×C13#55211yescharacteristic
537C22×C13#55211yescharacteristic
538C22×C13#55511yescharacteristic
539C22×C13#55611yescharacteristic
540C22×C13#55611yescharacteristic
541C4×C13—24no—
542C4×C13—24no—
543C4×C13—24no—
544C4×C13—24no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—42no—
548C4×C13—42no—
549C4×C13—42no—
550C4×C13—42no—
551C4×C13—42no—
552C4×C13—42no—
553C4×C13—81no—
554C4×C13—81no—
555C25C23×C1311yescharacteristic
556C23×C4—22no—
557C23×C4—22no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—22no—
561C23×C4—22no—
562C23×C4C2×C4×C1314yes—
563C23×C4C23×C1311yescharacteristic
564C23×C4C23×C1311yescharacteristic
565C23×C4C23×C1311yescharacteristic
566C23×C4C23×C1311yescharacteristic
567C23×C4C23×C1311yescharacteristic
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
577#117—232no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
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—41no—
593C2×C4⋊C4C2×C4×C1314yes—
594C2×C4⋊C4C2×C4×C1314yes—
595C2×C4⋊C4D4×C1314yes—
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—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—22no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—41no—
610C2×C22⋊C4—41no—
611C2×C22⋊C4C2×C4×C1314yes—
612C2×C22⋊C4C2×C4×C1314yes—
613C2×C22⋊C4D4×C1314yes—
614C2×C42—22no—
615C2×C42—22no—
616C2×C42—22no—
617C2×C42—22no—
618C2×C42—22no—
619C2×C42—22no—
620C2×C42—22no—
621C2×C42—22no—
622C2×C42—22no—
623C2×C42—22no—
624C2×C42—22no—
625C2×C42D4×C1314yes—
626#95—22no—
627#95—22no—
628#95—22no—
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—41no—
640#95—41no—
641#95—41no—
642#95C2×C4×C1314yes—
643#95C2×C4×C1314yes—
644C2×C13—44no—
645C2×C13#229011yescharacteristic
646C2×C13C4×#12011yescharacteristic
647C2×C13#232311yescharacteristic
648C2×C13#234411yescharacteristic
649C2×C13#235411yescharacteristic
650C2×C13#235911yescharacteristic
651C2×C13#236211yescharacteristic
652C2×C13#240611yescharacteristic
653C2×C13#240711yescharacteristic
654C2×C13#247411yescharacteristic
655C2×C13#247511yescharacteristic
656C2×C13#247811yescharacteristic
657C2×C13#247911yescharacteristic
658C2×C13#259911yescharacteristic
659C2×C13#260911yescharacteristic
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24—21no—
667C24—21no—
668C24—21no—
669C24—21no—
670C24—21no—
671C24—21no—
672C24C22×C4×C1312yes—
673C24C2×D4×C1312yes—
674C24C13×#4112yes—
675C24C24×C1311yescharacteristic
676C22×C4—28no—
677C22×C4—28no—
678C22×C4—28no—
679C22×C4—28no—
680C22×C4—28no—
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—28no—
698C22×C4—28no—
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×C4C22×C4×C1312yes—
762C22×C4C22×C4×C1312yes—
763C22×C4C22×C4×C1312yes—
764C22×C4C22×C4×C1312yes—
765C22×C4C22×C4×C1312yes—
766C22×C4C22×C4×C1312yes—
767C22×C4C2×D4×C1312yes—
768C22×C4C2×D4×C1312yes—
769C22×C4C2×D4×C1312yes—
770C22×C4C2×D4×C1312yes—
771C22×C4C2×D4×C1312yes—
772C22×C4C2×D4×C1312yes—
773C22×C4C2×D4×C1312yes—
774C22×C4C2×D4×C1312yes—
775C22×C4C13×#4112yes—
776C22×C4C13×#4112yes—
777C22×C4C13×#4112yes—
778C22×C4C13×#4112yes—
779C22×C4C13×#4112yes—
780C22×C4C13×#4112yes—
781C4⋊C4—28no—
782C4⋊C4—28no—
783C4⋊C4—28no—
784C4⋊C4—28no—
785C4⋊C4—28no—
786C4⋊C4—44no—
787C22⋊C4—28no—
788C22⋊C4—28no—
789C22⋊C4—28no—
790C22⋊C4—28no—
791C22⋊C4—44no—
792C22⋊C4—44no—
793C42—28no—
794C42—28no—
795C42—28no—
796C42—44no—
797C13#1406311yescharacteristic, direct product factor, Sylow
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—22no—
807C23—22no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23C4×D4×C1314yes—
833C23C23×C4×C1311yescharacteristic
834C23C22×D4×C1311yescharacteristic
835C23C22×D4×C1311yescharacteristic
836C23C22×D4×C1311yescharacteristic
837C23C2×C13×#4111yescharacteristic
838C23C2×C13×#4111yescharacteristic
839C23C2×C13×#4111yescharacteristic
840C23C2×C13×#4111yescharacteristic
841C23C2×C13×#4111yescharacteristic
842C23C2×C13×#4111yescharacteristic
843C23C2×C13×#4111yescharacteristic
844C23C13×H(5,𝔽2)11yescharacteristic
845C23C13×2−1+411yescharacteristic
846C23C13×2−1+411yescharacteristic
847C23C13×2−1+411yescharacteristic
848C2×C4—232no—
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—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—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×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×C4C13×#11714yescomplemented
944C2×C4C4×D4×C1314yes—
945C2×C4C4×D4×C1314yes—
946C2×C4C13×#12014yes—
947C22—24no—
948C22—24no—
949C22—24no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22—42no—
957C22—42no—
958C22—42no—
959C22—42no—
960C22—42no—
961C22—42no—
962C22C2×C13×#11711yescharacteristic
963C22C2×C4×D4×C1311yescharacteristic
964C22C2×C4×D4×C1311yescharacteristic
965C22C2×C4×D4×C1311yescharacteristic
966C22C4×C13×#4111yescharacteristic
967C22C13×#51911yescharacteristic
968C22C13×#52011yescharacteristic
969C22C2×C13×#12011yescharacteristic
970C22C13×#52511yescharacteristic
971C22C13×#52511yescharacteristic
972C22C13×#52511yescharacteristic
973C22C13×#52511yescharacteristic
974C22C13×#52511yescharacteristic
975C22C13×#52911yescharacteristic
976C22C13×#52911yescharacteristic
977C22C13×#53611yescharacteristic
978C22C13×#53711yescharacteristic
979C22C13×#54111yescharacteristic
980C22C13×#54211yescharacteristic
981C22C13×#54611yescharacteristic
982C22C13×#54711yescharacteristic
983C22C13×#54711yescharacteristic
984C22C13×#54711yescharacteristic
985C22C13×#54711yescharacteristic
986C22C13×#54711yescharacteristic
987C22C13×#54811yescharacteristic
988C22C13×#55011yescharacteristic
989C22C13×#55111yescharacteristic
990C22C13×#55211yescharacteristic
991C22C13×#55211yescharacteristic
992C22C13×#55211yescharacteristic
993C22C13×#55211yescharacteristic
994C22C13×#55511yescharacteristic
995C22C13×#55611yescharacteristic
996C22C13×#55611yescharacteristic
997C4—24no—
998C4—24no—
999C4—24no—
1000C4—24no—
1001C4—42no—
1002C4—42no—
1003C4—42no—
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—42no—
1008C4—42no—
1009C4—81no—
1010C4—81no—
1011C2—44no—
1012C2C13×#229011yescharacteristic
1013C2C4×C13×#12011yescharacteristic
1014C2C13×#232311yescharacteristic
1015C2C13×#234411yescharacteristic
1016C2C13×#235411yescharacteristic
1017C2C13×#235911yescharacteristic
1018C2C13×#236211yescharacteristic
1019C2C13×#240611yescharacteristic
1020C2C13×#240711yescharacteristic
1021C2C13×#247411yescharacteristic
1022C2C13×#247511yescharacteristic
1023C2C13×#247811yescharacteristic
1024C2C13×#247911yescharacteristic
1025C2C13×#259911yescharacteristic
1026C2C13×#260911yescharacteristic
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
3. C2×C13×#387C2semidirect
5. C2×C4×C13×C4⋊C4C2semidirect
6. C13×#1444C2semidirect
7. C13×#1441C2semidirect
11. C13×#1436C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1434C2semidirect
38. C13×#385C4semidirect
147. #14063C13direct (N × H)
287. C2×#387C2×C13semidirect
289. C2×C4×C4⋊C4C2×C13semidirect
290. #1444C2×C13semidirect
291. #1441C2×C13semidirect
295. #1436C2×C13semidirect
296. #1436C2×C13semidirect
297. #1436C2×C13semidirect
298. #1434C2×C13semidirect
445. C2×C4×C13#117semidirect
471. #385C4×C13semidirect
797. C13#14063direct (N × H)
943. C2×C4C13×#117semidirect

Maximal subgroups

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

subgroupindex
C22×C13×#1172
C2×C13×#3882
C2×C13×#3872
C2×C13×#3852
C2×C4×C13×C4⋊C42
C13×#14442
C13×#14412
C13×#14402
C13×#14392
C13×#14372
C13×#14362
C13×#14342
C13×C22⋊#952
#1406313