Finite Group Databasebeta

← C13×#13987 #15700326

Subgroups — C13×#13987 #15700326

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1022 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#387C211yesmaximal, characteristic, complemented
2C2×C13×#385C211yesmaximal, characteristic
3C2×C13×#380C211yesmaximal, characteristic
4C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
5C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
6C13×#1444C211yesmaximal, characteristic, complemented
7C13×#1441C211yesmaximal, characteristic, complemented
8C13×#1439C211yesmaximal, characteristic
9C13×#1439C211yesmaximal, characteristic
10C13×#1437C211yesmaximal, characteristic
11C13×#1437C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
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×C22⋊C4C2211yescharacteristic
24C22×C13×C22⋊C4C2211yescharacteristic
25C22×C13×C22⋊C4C2211yescharacteristic
26C22×C13×C22⋊C4C2211yescharacteristic
27C22×C13×C22⋊C4C2211yescharacteristic
28C22×C13×C22⋊C4C2211yescharacteristic
29C22×C42×C13C2211yescharacteristic
30C22×C42×C13C2211yescharacteristic
31C22×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C13×#387—24no—
34C13×#385C418yescomplemented
35C13×#380—24no—
36C4×C13×C4⋊C4—24no—
37C4×C13×C22⋊C4—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
56C25×C13C2311yescharacteristic
57C23×C4×C13—22no—
58C23×C4×C13—22no—
59C23×C4×C13—22no—
60C23×C4×C13—22no—
61C23×C4×C13—41no—
62C23×C4×C13—41no—
63C23×C4×C13C2×C414yes—
64C23×C4×C13C2311yescharacteristic
65C23×C4×C13C2311yescharacteristic
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
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—41no—
91C2×C13×C4⋊C4—41no—
92C2×C13×C4⋊C4—41no—
93C2×C13×C4⋊C4—41no—
94C2×C13×C4⋊C4C2×C414yes—
95C2×C13×C4⋊C4C2×C414yes—
96C2×C13×C22⋊C4—22no—
97C2×C13×C22⋊C4—22no—
98C2×C13×C22⋊C4—22no—
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—41no—
108C2×C13×C22⋊C4—41no—
109C2×C13×C22⋊C4—41no—
110C2×C13×C22⋊C4—41no—
111C2×C13×C22⋊C4C2×C414yes—
112C2×C13×C22⋊C4C2×C414yes—
113C2×C13×C22⋊C4Q814yes—
114C2×C42×C13—22no—
115C2×C42×C13—22no—
116C2×C42×C13—22no—
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—41no—
124C2×C42×C13—41no—
125C2×C42×C13—41no—
126C13×#95—22no—
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—41no—
136C13×#95—41no—
137C13×#95—41no—
138C13×#95—41no—
139C13×#95—41no—
140C13×#95C2×C414yes—
141C13×#95C2×C414yes—
142C13×#95D414yes—
143C13×#95D414yes—
144#13987C1311yesmaximal, characteristic, direct product factor, Sylow
145C24×C13—21no—
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×C13C22×C412yes—
158C24×C13C2×Q812yes—
159C24×C13#4112yes—
160C24×C13C2411yescharacteristic
161C22×C4×C13—21no—
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—28no—
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—44no—
242C22×C4×C13—44no—
243C22×C4×C13—44no—
244C22×C4×C13—44no—
245C22×C4×C13—44no—
246C22×C4×C13C22×C412yes—
247C22×C4×C13C22×C412yes—
248C22×C4×C13C22×C412yes—
249C22×C4×C13C22×C412yes—
250C22×C4×C13C22×C412yes—
251C22×C4×C13C22×C412yes—
252C22×C4×C13C2×D412yes—
253C22×C4×C13C2×D412yes—
254C22×C4×C13C2×D412yes—
255C22×C4×C13C2×D412yes—
256C22×C4×C13C2×D412yes—
257C22×C4×C13C2×D412yes—
258C22×C4×C13C2×Q812yes—
259C22×C4×C13C2×Q812yes—
260C22×C4×C13#4112yes—
261C22×C4×C13#4112yes—
262C22×C4×C13#4112yes—
263C22×C4×C13#4112yes—
264C22×C4×C13#4112yes—
265C22×C4×C13#4112yes—
266C13×C4⋊C4—28no—
267C13×C4⋊C4—28no—
268C13×C4⋊C4—28no—
269C13×C4⋊C4—44no—
270C13×C4⋊C4—44no—
271C13×C4⋊C4—44no—
272C13×C22⋊C4—28no—
273C13×C22⋊C4—28no—
274C13×C22⋊C4—28no—
275C13×C22⋊C4—44no—
276C13×C22⋊C4—44no—
277C13×C22⋊C4—44no—
278C42×C13—28no—
279C42×C13—44no—
280C42×C13—44no—
281C42×C13—44no—
282C2×#387C2×C1311yescharacteristic, complemented
283C2×#385C2×C1311yescharacteristic
284C2×#380C2×C1311yescharacteristic
285C2×C4×C4⋊C4C2×C1311yescharacteristic, complemented
286C2×C4×C22⋊C4C2×C1311yescharacteristic
287#1444C2×C1311yescharacteristic, complemented
288#1441C2×C1311yescharacteristic, complemented
289#1439C2×C1311yescharacteristic
290#1439C2×C1311yescharacteristic
291#1437C2×C1311yescharacteristic
292#1437C2×C1311yescharacteristic
293#1436C2×C1311yescharacteristic, complemented
294#1436C2×C1311yescharacteristic, complemented
295#1436C2×C1311yescharacteristic, complemented
296#1434C2×C1311yescharacteristic, complemented
297C23×C13—22no—
298C23×C13—22no—
299C23×C13—22no—
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—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×C13—41no—
330C23×C13—41no—
331C23×C13C4×Q814yes—
332C23×C13C23×C411yescharacteristic
333C23×C13C22×D411yescharacteristic
334C23×C13C22×D411yescharacteristic
335C23×C13C22×Q811yescharacteristic
336C23×C13C2×#4111yescharacteristic
337C23×C13C2×#4111yescharacteristic
338C23×C13C2×#4111yescharacteristic
339C23×C13C2×#4111yescharacteristic
340C23×C13C2×#4111yescharacteristic
341C23×C13C2×#4111yescharacteristic
342C23×C13C2×#4111yescharacteristic
343C23×C13H(5,𝔽2)11yescharacteristic
344C23×C13H(5,𝔽2)11yescharacteristic
345C23×C13H(5,𝔽2)11yescharacteristic
346C23×C132−1+411yescharacteristic
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—22no—
390C2×C4×C13—22no—
391C2×C4×C13—22no—
392C2×C4×C13—22no—
393C2×C4×C13—22no—
394C2×C4×C13—22no—
395C2×C4×C13—416no—
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#11714yes—
443C2×C4×C13C4×D414yes—
444C2×C4×C13C4×D414yes—
445C2×C4×C13C22⋊Q814yes—
446C24×C4C22×C1311yescharacteristic
447C22×C4⋊C4C22×C1311yescharacteristic
448C22×C4⋊C4C22×C1311yescharacteristic
449C22×C4⋊C4C22×C1311yescharacteristic
450C22×C4⋊C4C22×C1311yescharacteristic
451C22×C4⋊C4C22×C1311yescharacteristic
452C22×C4⋊C4C22×C1311yescharacteristic
453C22×C22⋊C4C22×C1311yescharacteristic
454C22×C22⋊C4C22×C1311yescharacteristic
455C22×C22⋊C4C22×C1311yescharacteristic
456C22×C22⋊C4C22×C1311yescharacteristic
457C22×C22⋊C4C22×C1311yescharacteristic
458C22×C22⋊C4C22×C1311yescharacteristic
459C22×C42C22×C1311yescharacteristic
460C22×C42C22×C1311yescharacteristic
461C22×C42C22×C1311yescharacteristic
462C22×C42C22×C1311yescharacteristic
463#387—24no—
464#385C4×C1318yescomplemented
465#380—24no—
466C4×C4⋊C4—24no—
467C4×C22⋊C4—24no—
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
483C2×#95C22×C1311yescharacteristic
484C2×#95C22×C1311yescharacteristic
485C2×#95C22×C1311yescharacteristic
486C22×C13—24no—
487C22×C13—24no—
488C22×C13—24no—
489C22×C13—42no—
490C22×C13—42no—
491C22×C13—42no—
492C22×C13—42no—
493C22×C13—42no—
494C22×C13—42no—
495C22×C13—42no—
496C22×C13—42no—
497C22×C13—42no—
498C22×C13—42no—
499C22×C13—42no—
500C22×C13—42no—
501C22×C13C2×#11711yescharacteristic
502C22×C13C2×C4×D411yescharacteristic
503C22×C13C2×C4×D411yescharacteristic
504C22×C13C2×C4×Q811yescharacteristic
505C22×C13C4×#4111yescharacteristic
506C22×C13#51811yescharacteristic
507C22×C13#52011yescharacteristic
508C22×C13C2×C22⋊Q811yescharacteristic
509C22×C13#52511yescharacteristic
510C22×C13#52511yescharacteristic
511C22×C13#52511yescharacteristic
512C22×C13#52911yescharacteristic
513C22×C13#52911yescharacteristic
514C22×C13#52911yescharacteristic
515C22×C13#53311yescharacteristic
516C22×C13#53811yescharacteristic
517C22×C13#53911yescharacteristic
518C22×C13#54011yescharacteristic
519C22×C13#54211yescharacteristic
520C22×C13D4211yescharacteristic
521C22×C13#54611yescharacteristic
522C22×C13#54611yescharacteristic
523C22×C13#54611yescharacteristic
524C22×C13#54711yescharacteristic
525C22×C13D4×Q811yescharacteristic
526C22×C13#55011yescharacteristic
527C22×C13#55111yescharacteristic
528C22×C13#55211yescharacteristic
529C22×C13#55311yescharacteristic
530C22×C13#55311yescharacteristic
531C22×C13#55411yescharacteristic
532C22×C13#55411yescharacteristic
533C22×C13#55411yescharacteristic
534C22×C13#55511yescharacteristic
535C22×C13#55611yescharacteristic
536C4×C13—24no—
537C4×C13—24no—
538C4×C13—24no—
539C4×C13—24no—
540C4×C13—42no—
541C4×C13—42no—
542C4×C13—42no—
543C4×C13—42no—
544C4×C13—42no—
545C4×C13—42no—
546C4×C13—42no—
547C4×C13—42no—
548C4×C13—81no—
549C4×C13—81no—
550C25C23×C1311yescharacteristic
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—41no—
556C23×C4—41no—
557C23×C4C2×C4×C1314yes—
558C23×C4C23×C1311yescharacteristic
559C23×C4C23×C1311yescharacteristic
560C23×C4C23×C1311yescharacteristic
561C23×C4C23×C1311yescharacteristic
562C23×C4C23×C1311yescharacteristic
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
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—22no—
583C2×C4⋊C4—22no—
584C2×C4⋊C4—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4—41no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4C2×C4×C1314yes—
589C2×C4⋊C4C2×C4×C1314yes—
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—41no—
602C2×C22⋊C4—41no—
603C2×C22⋊C4—41no—
604C2×C22⋊C4—41no—
605C2×C22⋊C4C2×C4×C1314yes—
606C2×C22⋊C4C2×C4×C1314yes—
607C2×C22⋊C4Q8×C1314yes—
608C2×C42—22no—
609C2×C42—22no—
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—
619C2×C42—41no—
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—41no—
630#95—41no—
631#95—41no—
632#95—41no—
633#95—41no—
634#95C2×C4×C1314yes—
635#95C2×C4×C1314yes—
636#95D4×C1314yes—
637#95D4×C1314yes—
638C2×C13—44no—
639C2×C13#229011yescharacteristic
640C2×C13C4×C22⋊Q811yescharacteristic
641C2×C13#233511yescharacteristic
642C2×C13#234511yescharacteristic
643C2×C13#235411yescharacteristic
644C2×C13#235811yescharacteristic
645C2×C13#236011yescharacteristic
646C2×C13#244911yescharacteristic
647C2×C13#245411yescharacteristic
648C2×C13#245611yescharacteristic
649C2×C13#246511yescharacteristic
650C2×C13#246811yescharacteristic
651C2×C13#247611yescharacteristic
652C2×C13#257411yescharacteristic
653C2×C13#257711yescharacteristic
654C24—21no—
655C24—21no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24—21no—
660C24—21no—
661C24—21no—
662C24—21no—
663C24—21no—
664C24—21no—
665C24—21no—
666C24C22×C4×C1312yes—
667C24C2×Q8×C1312yes—
668C24C13×#4112yes—
669C24C24×C1311yescharacteristic
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—28no—
735C22×C4—28no—
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—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4C22×C4×C1312yes—
756C22×C4C22×C4×C1312yes—
757C22×C4C22×C4×C1312yes—
758C22×C4C22×C4×C1312yes—
759C22×C4C22×C4×C1312yes—
760C22×C4C22×C4×C1312yes—
761C22×C4C2×D4×C1312yes—
762C22×C4C2×D4×C1312yes—
763C22×C4C2×D4×C1312yes—
764C22×C4C2×D4×C1312yes—
765C22×C4C2×D4×C1312yes—
766C22×C4C2×D4×C1312yes—
767C22×C4C2×Q8×C1312yes—
768C22×C4C2×Q8×C1312yes—
769C22×C4C13×#4112yes—
770C22×C4C13×#4112yes—
771C22×C4C13×#4112yes—
772C22×C4C13×#4112yes—
773C22×C4C13×#4112yes—
774C22×C4C13×#4112yes—
775C4⋊C4—28no—
776C4⋊C4—28no—
777C4⋊C4—28no—
778C4⋊C4—44no—
779C4⋊C4—44no—
780C4⋊C4—44no—
781C22⋊C4—28no—
782C22⋊C4—28no—
783C22⋊C4—28no—
784C22⋊C4—44no—
785C22⋊C4—44no—
786C22⋊C4—44no—
787C42—28no—
788C42—44no—
789C42—44no—
790C42—44no—
791C13#1398711yescharacteristic, direct product factor, Sylow
792C23—22no—
793C23—22no—
794C23—22no—
795C23—22no—
796C23—22no—
797C23—22no—
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—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—41no—
821C23—41no—
822C23—41no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23C4×Q8×C1314yes—
827C23C23×C4×C1311yescharacteristic
828C23C22×D4×C1311yescharacteristic
829C23C22×D4×C1311yescharacteristic
830C23C22×Q8×C1311yescharacteristic
831C23C2×C13×#4111yescharacteristic
832C23C2×C13×#4111yescharacteristic
833C23C2×C13×#4111yescharacteristic
834C23C2×C13×#4111yescharacteristic
835C23C2×C13×#4111yescharacteristic
836C23C2×C13×#4111yescharacteristic
837C23C2×C13×#4111yescharacteristic
838C23C13×H(5,𝔽2)11yescharacteristic
839C23C13×H(5,𝔽2)11yescharacteristic
840C23C13×H(5,𝔽2)11yescharacteristic
841C23C13×2−1+411yescharacteristic
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—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—416no—
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×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4C13×#11714yes—
938C2×C4C4×D4×C1314yes—
939C2×C4C4×D4×C1314yes—
940C2×C4C13×C22⋊Q814yes—
941C22—24no—
942C22—24no—
943C22—24no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—42no—
953C22—42no—
954C22—42no—
955C22—42no—
956C22C2×C13×#11711yescharacteristic
957C22C2×C4×D4×C1311yescharacteristic
958C22C2×C4×D4×C1311yescharacteristic
959C22C2×C4×Q8×C1311yescharacteristic
960C22C4×C13×#4111yescharacteristic
961C22C13×#51811yescharacteristic
962C22C13×#52011yescharacteristic
963C22C2×C13×C22⋊Q811yescharacteristic
964C22C13×#52511yescharacteristic
965C22C13×#52511yescharacteristic
966C22C13×#52511yescharacteristic
967C22C13×#52911yescharacteristic
968C22C13×#52911yescharacteristic
969C22C13×#52911yescharacteristic
970C22C13×#53311yescharacteristic
971C22C13×#53811yescharacteristic
972C22C13×#53911yescharacteristic
973C22C13×#54011yescharacteristic
974C22C13×#54211yescharacteristic
975C22D42×C1311yescharacteristic
976C22C13×#54611yescharacteristic
977C22C13×#54611yescharacteristic
978C22C13×#54611yescharacteristic
979C22C13×#54711yescharacteristic
980C22D4×Q8×C1311yescharacteristic
981C22C13×#55011yescharacteristic
982C22C13×#55111yescharacteristic
983C22C13×#55211yescharacteristic
984C22C13×#55311yescharacteristic
985C22C13×#55311yescharacteristic
986C22C13×#55411yescharacteristic
987C22C13×#55411yescharacteristic
988C22C13×#55411yescharacteristic
989C22C13×#55511yescharacteristic
990C22C13×#55611yescharacteristic
991C4—24no—
992C4—24no—
993C4—24no—
994C4—24no—
995C4—42no—
996C4—42no—
997C4—42no—
998C4—42no—
999C4—42no—
1000C4—42no—
1001C4—42no—
1002C4—42no—
1003C4—81no—
1004C4—81no—
1005C2—44no—
1006C2C13×#229011yescharacteristic
1007C2C4×C13×C22⋊Q811yescharacteristic
1008C2C13×#233511yescharacteristic
1009C2C13×#234511yescharacteristic
1010C2C13×#235411yescharacteristic
1011C2C13×#235811yescharacteristic
1012C2C13×#236011yescharacteristic
1013C2C13×#244911yescharacteristic
1014C2C13×#245411yescharacteristic
1015C2C13×#245611yescharacteristic
1016C2C13×#246511yescharacteristic
1017C2C13×#246811yescharacteristic
1018C2C13×#247611yescharacteristic
1019C2C13×#257411yescharacteristic
1020C2C13×#257711yescharacteristic
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×#387C2semidirect
4. C2×C4×C13×C4⋊C4C2semidirect
6. C13×#1444C2semidirect
7. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×#1436C2semidirect
15. C13×#1434C2semidirect
34. C13×#385C4semidirect
144. #13987C13direct (N × H)
282. C2×#387C2×C13semidirect
285. C2×C4×C4⋊C4C2×C13semidirect
287. #1444C2×C13semidirect
288. #1441C2×C13semidirect
293. #1436C2×C13semidirect
294. #1436C2×C13semidirect
295. #1436C2×C13semidirect
296. #1434C2×C13semidirect
464. #385C4×C13semidirect
791. C13#13987direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3872
C2×C13×#3852
C2×C13×#3802
C2×C4×C13×C4⋊C42
C2×C4×C13×C22⋊C42
C13×#14442
C13×#14412
C13×#14392
C13×#14372
C13×#14362
C13×#14342
#1398713