Finite Group Databasebeta

← C13×#14770 #15701109

Subgroups — C13×#14770 #15701109

Order 3328.

1770 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C13×#396C211yesmaximal, characteristic
2C2×C13×#395C211yesmaximal, characteristic, complemented
3C2×C13×#393C211yesmaximal, characteristic
4C2×C13×#391C211yesmaximal, characteristic, complemented
5C2×C13×#380C211yesmaximal, characteristic
6C2×C4×C13×C22⋊C4C211yesmaximal, characteristic
7C13×#1444C211yesmaximal, characteristic, complemented
8C13×#1442C211yesmaximal, characteristic, complemented
9C13×#1441C211yesmaximal, characteristic, complemented
10C13×#1439C211yesmaximal, characteristic
11C13×#1439C211yesmaximal, characteristic
12C13×#1436C211yesmaximal, characteristic, complemented
13C13×#1436C211yesmaximal, characteristic, complemented
14C13×C4⋊#95C211yesmaximal, characteristic, complemented
15C13×C22⋊#95C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C24×C4×C13C2211yescharacteristic
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×C42×C13C2211yescharacteristic
32C22×C42×C13C2211yescharacteristic
33C13×#396—24no—
34C13×#395—24no—
35C13×#393—24no—
36C13×#391—24no—
37C13×#380—24no—
38C4×C13×C22⋊C4—24no—
39C2×C13×#95C2211yescharacteristic
40C2×C13×#95C2211yescharacteristic
41C2×C13×#95C2211yescharacteristic
42C2×C13×#95C2211yescharacteristic
43C2×C13×#95C2211yescharacteristic
44C2×C13×#95C2211yescharacteristic
45C2×C13×#95C2211yescharacteristic
46C2×C13×#95C2211yescharacteristic
47C2×C13×#95C2211yescharacteristic
48C2×C13×#95C2211yescharacteristic
49C2×C13×#95C2211yescharacteristic
50C2×C13×#95C2211yescharacteristic
51C2×C13×#95C2211yescharacteristic
52C2×C13×#95C2211yescharacteristic
53C2×C13×#95C2211yescharacteristic
54C2×C13×#95C2211yescharacteristic
55C2×C13×#95C2211yescharacteristic
56C2×C13×#95C2211yescharacteristic
57C25×C13C2311yescharacteristic
58C22×Q8×C13—22no—
59C22×Q8×C13—22no—
60C22×Q8×C13—22no—
61C22×Q8×C13—22no—
62C22×Q8×C13—22no—
63C22×Q8×C13—41no—
64C22×Q8×C13—41no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13—22no—
69C23×C4×C13—41no—
70C23×C4×C13—41no—
71C23×C4×C13Q814yescomplemented
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×C4×C13C2311yescharacteristic
75C23×C4×C13C2311yescharacteristic
76C23×C4×C13C2311yescharacteristic
77C23×C4×C13C2311yescharacteristic
78C23×C4×C13C2311yescharacteristic
79C23×C4×C13C2311yescharacteristic
80C23×C4×C13C2311yescharacteristic
81C23×C4×C13C2311yescharacteristic
82C23×C4×C13C2311yescharacteristic
83C23×C4×C13C2311yescharacteristic
84C23×C4×C13C2311yescharacteristic
85C23×C4×C13C2311yescharacteristic
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—22no—
97C2×C13×C4⋊C4—22no—
98C2×C13×C4⋊C4—22no—
99C2×C13×C4⋊C4—22no—
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×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—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⋊C4D414yes—
124C2×C13×C22⋊C4Q814yescomplemented
125C2×C42×C13—22no—
126C2×C42×C13—22no—
127C2×C42×C13—22no—
128C2×C42×C13—22no—
129C2×C42×C13—41no—
130C2×C42×C13—41no—
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—22no—
144C13×#95—22no—
145C13×#95—22no—
146C13×#95—41no—
147C13×#95D414yes—
148C13×#95D414yes—
149#14770C1311yesmaximal, characteristic, direct product factor, Sylow
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×C13—21no—
161C24×C13—21no—
162C24×C13C2×D412yes—
163C24×C13C2×Q812yes—
164C24×C13C2×Q812yes—
165C24×C13C2411yescharacteristic
166C2×Q8×C13—28no—
167C2×Q8×C13—44no—
168C2×Q8×C13—44no—
169C2×Q8×C13—44no—
170C2×Q8×C13—44no—
171C2×Q8×C13—44no—
172C2×Q8×C13—44no—
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—21no—
242C22×C4×C13—21no—
243C22×C4×C13—21no—
244C22×C4×C13—21no—
245C22×C4×C13—21no—
246C22×C4×C13—21no—
247C22×C4×C13—21no—
248C22×C4×C13—21no—
249C22×C4×C13—21no—
250C22×C4×C13—21no—
251C22×C4×C13—21no—
252C22×C4×C13—21no—
253C22×C4×C13—21no—
254C22×C4×C13—21no—
255C22×C4×C13—44no—
256C22×C4×C13—44no—
257C22×C4×C13—44no—
258C22×C4×C13—44no—
259C22×C4×C13—44no—
260C22×C4×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×C13C2×Q812yes—
271C22×C4×C13C2×Q812yes—
272C22×C4×C13#4112yes—
273C22×C4×C13#4112yes—
274C22×C4×C13#4112yes—
275C22×C4×C13#4112yes—
276C22×C4×C13#4112yes—
277C22×C4×C13#4112yes—
278C13×C4⋊C4—44no—
279C13×C4⋊C4—44no—
280C13×C4⋊C4—44no—
281C13×C4⋊C4—44no—
282C13×C4⋊C4—44no—
283C13×C4⋊C4—44no—
284C13×C4⋊C4—44no—
285C13×C22⋊C4—28no—
286C13×C22⋊C4—28no—
287C13×C22⋊C4—44no—
288C13×C22⋊C4—44no—
289C13×C22⋊C4—44no—
290C13×C22⋊C4—44no—
291C42×C13—44no—
292C42×C13—44no—
293C2×#396C2×C1311yescharacteristic
294C2×#395C2×C1311yescharacteristic, complemented
295C2×#393C2×C1311yescharacteristic
296C2×#391C2×C1311yescharacteristic, complemented
297C2×#380C2×C1311yescharacteristic
298C2×C4×C22⋊C4C2×C1311yescharacteristic
299#1444C2×C1311yescharacteristic, complemented
300#1442C2×C1311yescharacteristic, complemented
301#1441C2×C1311yescharacteristic, complemented
302#1439C2×C1311yescharacteristic
303#1439C2×C1311yescharacteristic
304#1436C2×C1311yescharacteristic, complemented
305#1436C2×C1311yescharacteristic, complemented
306C4⋊#95C2×C1311yescharacteristic, complemented
307C22⋊#95C2×C1311yescharacteristic
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—22no—
324C23×C13—22no—
325C23×C13—22no—
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×C13—41no—
340C23×C13—41no—
341C23×C13—41no—
342C23×C13C4⋊Q814yes—
343C23×C13C22×D411yescharacteristic
344C23×C13C22×D411yescharacteristic
345C23×C13C22×D411yescharacteristic
346C23×C13C22×Q811yescharacteristic
347C23×C13C22×Q811yescharacteristic
348C23×C13C2×#4111yescharacteristic
349C23×C13C2×#4111yescharacteristic
350C23×C13C2×#4111yescharacteristic
351C23×C13C2×#4111yescharacteristic
352C23×C13C2×#4111yescharacteristic
353C23×C13C2×#4111yescharacteristic
354C23×C13H(5,𝔽2)11yescharacteristic
355C23×C13H(5,𝔽2)11yescharacteristic
356C23×C13H(5,𝔽2)11yescharacteristic
357C23×C132−1+411yescharacteristic
358Q8×C13—416no—
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—22no—
400C2×C4×C13—22no—
401C2×C4×C13—416no—
402C2×C4×C13—41no—
403C2×C4×C13—41no—
404C2×C4×C13—41no—
405C2×C4×C13—41no—
406C2×C4×C13—41no—
407C2×C4×C13—41no—
408C2×C4×C13—41no—
409C2×C4×C13—41no—
410C2×C4×C13—41no—
411C2×C4×C13—41no—
412C2×C4×C13—41no—
413C2×C4×C13—41no—
414C2×C4×C13—41no—
415C2×C4×C13—41no—
416C2×C4×C13—41no—
417C2×C4×C13—41no—
418C2×C4×C13—41no—
419C2×C4×C13—41no—
420C2×C4×C13—41no—
421C2×C4×C13—41no—
422C2×C4×C13—41no—
423C2×C4×C13—41no—
424C2×C4×C13—41no—
425C2×C4×C13—41no—
426C2×C4×C13—41no—
427C2×C4×C13—41no—
428C2×C4×C13—41no—
429C2×C4×C13—41no—
430C2×C4×C13—41no—
431C2×C4×C13—41no—
432C2×C4×C13—41no—
433C2×C4×C13—41no—
434C2×C4×C13—41no—
435C2×C4×C13—41no—
436C2×C4×C13—41no—
437C2×C4×C13—41no—
438C2×C4×C13—41no—
439C2×C4×C13—41no—
440C2×C4×C13—41no—
441C2×C4×C13—41no—
442C2×C4×C13—41no—
443C2×C4×C13—41no—
444C2×C4×C13—41no—
445C2×C4×C13—41no—
446C2×C4×C13—41no—
447C2×C4×C13—41no—
448C2×C4×C13—41no—
449C2×C4×C13—41no—
450C2×C4×C13—41no—
451C2×C4×C13—41no—
452C2×C4×C13—41no—
453C2×C4×C13—41no—
454C2×C4×C13#12114yes—
455C2×C4×C13C22⋊Q814yes—
456C2×C4×C13C22⋊Q814yes—
457C2×C4×C13C22⋊Q814yes—
458C23×Q8C22×C1311yescharacteristic
459C24×C4C22×C1311yescharacteristic
460C22×C4⋊C4C22×C1311yescharacteristic
461C22×C4⋊C4C22×C1311yescharacteristic
462C22×C4⋊C4C22×C1311yescharacteristic
463C22×C4⋊C4C22×C1311yescharacteristic
464C22×C4⋊C4C22×C1311yescharacteristic
465C22×C4⋊C4C22×C1311yescharacteristic
466C22×C4⋊C4C22×C1311yescharacteristic
467C22×C22⋊C4C22×C1311yescharacteristic
468C22×C22⋊C4C22×C1311yescharacteristic
469C22×C22⋊C4C22×C1311yescharacteristic
470C22×C22⋊C4C22×C1311yescharacteristic
471C22×C22⋊C4C22×C1311yescharacteristic
472C22×C22⋊C4C22×C1311yescharacteristic
473C22×C42C22×C1311yescharacteristic
474C22×C42C22×C1311yescharacteristic
475#396—24no—
476#395—24no—
477#393—24no—
478#391—24no—
479#380—24no—
480C4×C22⋊C4—24no—
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
496C2×#95C22×C1311yescharacteristic
497C2×#95C22×C1311yescharacteristic
498C2×#95C22×C1311yescharacteristic
499C22×C13—24no—
500C22×C13—24no—
501C22×C13—24no—
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×C13—42no—
512C22×C13—42no—
513C22×C13—42no—
514C22×C13C2×#12111yescharacteristic
515C22×C13C2×C22⋊Q811yescharacteristic
516C22×C13C2×C22⋊Q811yescharacteristic
517C22×C13C2×C22⋊Q811yescharacteristic
518C22×C13#52511yescharacteristic
519C22×C13#52911yescharacteristic
520C22×C13#52911yescharacteristic
521C22×C13C2×C4⋊Q811yescharacteristic
522C22×C13#53211yescharacteristic
523C22×C13#53211yescharacteristic
524C22×C13#53311yescharacteristic
525C22×C13#53311yescharacteristic
526C22×C13#53311yescharacteristic
527C22×C13#53811yescharacteristic
528C22×C13#53811yescharacteristic
529C22×C13#54211yescharacteristic
530C22×C13#54211yescharacteristic
531C22×C13#54311yescharacteristic
532C22×C13#54411yescharacteristic
533C22×C13D4211yescharacteristic
534C22×C13D4211yescharacteristic
535C22×C13#54611yescharacteristic
536C22×C13#54611yescharacteristic
537C22×C13#54611yescharacteristic
538C22×C13#54611yescharacteristic
539C22×C13#54611yescharacteristic
540C22×C13#54711yescharacteristic
541C22×C13#54811yescharacteristic
542C22×C13D4×Q811yescharacteristic
543C22×C13#55111yescharacteristic
544C22×C13#55411yescharacteristic
545C22×C13#55411yescharacteristic
546C22×C13#55411yescharacteristic
547C22×C13#55511yescharacteristic
548C22×C13#55611yescharacteristic
549C4×C13—24no—
550C4×C13—24no—
551C4×C13—24no—
552C4×C13—24no—
553C4×C13—42no—
554C4×C13—42no—
555C4×C13—42no—
556C4×C13—42no—
557C4×C13—42no—
558C4×C13—42no—
559C4×C13—81no—
560C4×C13—81no—
561C4×C13—81no—
562C4×C13—81no—
563C25C23×C1311yescharacteristic
564C22×Q8—22no—
565C22×Q8—22no—
566C22×Q8—22no—
567C22×Q8—22no—
568C22×Q8—22no—
569C22×Q8—41no—
570C22×Q8—41no—
571C23×C4—22no—
572C23×C4—22no—
573C23×C4—22no—
574C23×C4—22no—
575C23×C4—41no—
576C23×C4—41no—
577C23×C4Q8×C1314yescomplemented
578C23×C4C23×C1311yescharacteristic
579C23×C4C23×C1311yescharacteristic
580C23×C4C23×C1311yescharacteristic
581C23×C4C23×C1311yescharacteristic
582C23×C4C23×C1311yescharacteristic
583C23×C4C23×C1311yescharacteristic
584C23×C4C23×C1311yescharacteristic
585C23×C4C23×C1311yescharacteristic
586C23×C4C23×C1311yescharacteristic
587C23×C4C23×C1311yescharacteristic
588C23×C4C23×C1311yescharacteristic
589C23×C4C23×C1311yescharacteristic
590C23×C4C23×C1311yescharacteristic
591C23×C4C23×C1311yescharacteristic
592C2×C4⋊C4—22no—
593C2×C4⋊C4—22no—
594C2×C4⋊C4—22no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4—22no—
597C2×C4⋊C4—22no—
598C2×C4⋊C4—22no—
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—22no—
604C2×C4⋊C4—22no—
605C2×C4⋊C4—22no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
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—22no—
622C2×C22⋊C4—22no—
623C2×C22⋊C4—22no—
624C2×C22⋊C4—22no—
625C2×C22⋊C4—41no—
626C2×C22⋊C4—41no—
627C2×C22⋊C4—41no—
628C2×C22⋊C4—41no—
629C2×C22⋊C4D4×C1314yes—
630C2×C22⋊C4Q8×C1314yescomplemented
631C2×C42—22no—
632C2×C42—22no—
633C2×C42—22no—
634C2×C42—22no—
635C2×C42—41no—
636C2×C42—41no—
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—22no—
647#95—22no—
648#95—22no—
649#95—22no—
650#95—22no—
651#95—22no—
652#95—41no—
653#95D4×C1314yes—
654#95D4×C1314yes—
655C2×C13—44no—
656C2×C13#239611yescharacteristic
657C2×C13#242411yescharacteristic
658C2×C13#242711yescharacteristic
659C2×C13#243711yescharacteristic
660C2×C13#243911yescharacteristic
661C2×C13#244011yescharacteristic
662C2×C13#245011yescharacteristic
663C2×C13#245211yescharacteristic
664C2×C13#246511yescharacteristic
665C2×C13#252111yescharacteristic
666C2×C13#254911yescharacteristic
667C2×C13#255511yescharacteristic
668C2×C13#257411yescharacteristic
669C2×C13#266511yescharacteristic
670C2×C13#285711yescharacteristic
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24—21no—
682C24—21no—
683C24C2×D4×C1312yes—
684C24C2×Q8×C1312yes—
685C24C2×Q8×C1312yes—
686C24C24×C1311yescharacteristic
687C2×Q8—28no—
688C2×Q8—44no—
689C2×Q8—44no—
690C2×Q8—44no—
691C2×Q8—44no—
692C2×Q8—44no—
693C2×Q8—44no—
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—28no—
747C22×C4—28no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—44no—
777C22×C4—44no—
778C22×C4—44no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C2×D4×C1312yes—
782C22×C4C2×D4×C1312yes—
783C22×C4C2×D4×C1312yes—
784C22×C4C2×D4×C1312yes—
785C22×C4C2×D4×C1312yes—
786C22×C4C2×D4×C1312yes—
787C22×C4C2×D4×C1312yes—
788C22×C4C2×D4×C1312yes—
789C22×C4C2×Q8×C1312yes—
790C22×C4C2×Q8×C1312yes—
791C22×C4C2×Q8×C1312yes—
792C22×C4C2×Q8×C1312yes—
793C22×C4C13×#4112yes—
794C22×C4C13×#4112yes—
795C22×C4C13×#4112yes—
796C22×C4C13×#4112yes—
797C22×C4C13×#4112yes—
798C22×C4C13×#4112yes—
799C4⋊C4—44no—
800C4⋊C4—44no—
801C4⋊C4—44no—
802C4⋊C4—44no—
803C4⋊C4—44no—
804C4⋊C4—44no—
805C4⋊C4—44no—
806C22⋊C4—28no—
807C22⋊C4—28no—
808C22⋊C4—44no—
809C22⋊C4—44no—
810C22⋊C4—44no—
811C22⋊C4—44no—
812C42—44no—
813C42—44no—
814C13#1477011yescharacteristic, direct product factor, Sylow
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—22no—
831C23—22no—
832C23—22no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23—41no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—41no—
848C23—41no—
849C23C13×C4⋊Q814yes—
850C23C22×D4×C1311yescharacteristic
851C23C22×D4×C1311yescharacteristic
852C23C22×D4×C1311yescharacteristic
853C23C22×Q8×C1311yescharacteristic
854C23C22×Q8×C1311yescharacteristic
855C23C2×C13×#4111yescharacteristic
856C23C2×C13×#4111yescharacteristic
857C23C2×C13×#4111yescharacteristic
858C23C2×C13×#4111yescharacteristic
859C23C2×C13×#4111yescharacteristic
860C23C2×C13×#4111yescharacteristic
861C23C13×H(5,𝔽2)11yescharacteristic
862C23C13×H(5,𝔽2)11yescharacteristic
863C23C13×H(5,𝔽2)11yescharacteristic
864C23C13×2−1+411yescharacteristic
865Q8—416no—
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—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—416no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4C13×#12114yes—
962C2×C4C13×C22⋊Q814yes—
963C2×C4C13×C22⋊Q814yes—
964C2×C4C13×C22⋊Q814yes—
965C22—24no—
966C22—24no—
967C22—24no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—42no—
979C22—42no—
980C22C2×C13×#12111yescharacteristic
981C22C2×C13×C22⋊Q811yescharacteristic
982C22C2×C13×C22⋊Q811yescharacteristic
983C22C2×C13×C22⋊Q811yescharacteristic
984C22C13×#52511yescharacteristic
985C22C13×#52911yescharacteristic
986C22C13×#52911yescharacteristic
987C22C2×C13×C4⋊Q811yescharacteristic
988C22C13×#53211yescharacteristic
989C22C13×#53211yescharacteristic
990C22C13×#53311yescharacteristic
991C22C13×#53311yescharacteristic
992C22C13×#53311yescharacteristic
993C22C13×#53811yescharacteristic
994C22C13×#53811yescharacteristic
995C22C13×#54211yescharacteristic
996C22C13×#54211yescharacteristic
997C22C13×#54311yescharacteristic
998C22C13×#54411yescharacteristic
999C22D42×C1311yescharacteristic
1000C22D42×C1311yescharacteristic
1001C22C13×#54611yescharacteristic
1002C22C13×#54611yescharacteristic
1003C22C13×#54611yescharacteristic
1004C22C13×#54611yescharacteristic
1005C22C13×#54611yescharacteristic
1006C22C13×#54711yescharacteristic
1007C22C13×#54811yescharacteristic
1008C22D4×Q8×C1311yescharacteristic
1009C22C13×#55111yescharacteristic
1010C22C13×#55411yescharacteristic
1011C22C13×#55411yescharacteristic
1012C22C13×#55411yescharacteristic
1013C22C13×#55511yescharacteristic
1014C22C13×#55611yescharacteristic
1015C4—24no—
1016C4—24no—
1017C4—24no—
1018C4—24no—
1019C4—42no—
1020C4—42no—
1021C4—42no—
1022C4—42no—
1023C4—42no—
1024C4—42no—
1025C4—81no—
1026C4—81no—
1027C4—81no—
1028C4—81no—
1029C2—44no—
1030C2C13×#239611yescharacteristic
1031C2C13×#242411yescharacteristic
1032C2C13×#242711yescharacteristic
1033C2C13×#243711yescharacteristic
1034C2C13×#243911yescharacteristic
1035C2C13×#244011yescharacteristic
1036C2C13×#245011yescharacteristic
1037C2C13×#245211yescharacteristic
1038C2C13×#246511yescharacteristic
1039C2C13×#252111yescharacteristic
1040C2C13×#254911yescharacteristic
1041C2C13×#255511yescharacteristic
1042C2C13×#257411yescharacteristic
1043C2C13×#266511yescharacteristic
1044C2C13×#285711yescharacteristic
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×#395C2semidirect
4. C2×C13×#391C2semidirect
7. C13×#1444C2semidirect
8. C13×#1442C2semidirect
9. C13×#1441C2semidirect
12. C13×#1436C2semidirect
13. C13×#1436C2semidirect
14. C13×C4⋊#95C2semidirect
71. C23×C4×C13Q8semidirect
124. C2×C13×C22⋊C4Q8semidirect
149. #14770C13direct (N × H)
294. C2×#395C2×C13semidirect
296. C2×#391C2×C13semidirect
299. #1444C2×C13semidirect
300. #1442C2×C13semidirect
301. #1441C2×C13semidirect
304. #1436C2×C13semidirect
305. #1436C2×C13semidirect
306. C4⋊#95C2×C13semidirect
577. C23×C4Q8×C13semidirect
630. C2×C22⋊C4Q8×C13semidirect
814. C13#14770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C13×#3962
C2×C13×#3952
C2×C13×#3932
C2×C13×#3912
C2×C13×#3802
C2×C4×C13×C22⋊C42
C13×#14442
C13×#14422
C13×#14412
C13×#14392
C13×#14362
C13×C4⋊#952
C13×C22⋊#952
#1477013